Rolling Stone’s song discards – less political than the albums?

In a post from March this year, I looked at artists discarded from Rolling Stone’s 2020 revision of its 500 Greatest Albums of All Time list (originally published in 2003) to see how many of its discarded artists might have been motivated by the discarded artists belonging to genres associated with Republican-voting poor whites. I found that whilst not all of the discarded artists belonged to genres associated to varying degrees with Republican-voting poor whites, there were about a dozen of fifty-two discarded artists (slightly fewer than one-quarter) where this association may have been the decisive factor in their being omitted.

When I first looked at the updated songs list from about two months ago, I failed to compare with the earlier issue, although Rolling Stone did say that there had been large revisions vis-à-vis the 2012 and 2004 lists. However, recently I did look at the list and attempted to note, as I did previously with the albums, which artists had been entirely excluded this year who were present  in 2004 and 2012.

Big Joe Turner	Early blues artist
B.B. King	Early black pop artist
The Penguins	Early black pop artist
The Platters	Early black pop artist
Carl Perkins	Early white rocker
The Del-Vikings	Early black pop artist
The Dells	Early black pop artist
LaVern Baker	Early soul artist
Jackie Wilson	Early soul artist
Frankie Lymon and the Teenagers	Early black pop artist
The Chantels	Early black pop artist
Archie Bell and the Drells	Early soul artist
The Coasters	Early soul artist
Ritchie Valens	Early Latino rocker
Jerry Butler and the Impressions	Early soul artist
Bobby Darin	Pop/rock
Gene Vincent and His Blue Caps	Early white rocker
Bill Haley and His Comets	Early white rocker	It is possible that like Elvis Presley his assocation with Republican-voting poor whites has affected his repuation amongst Rolling Stone and big-city Millennial critics
Dion (DiMucci)	Early white rocker	Same as for Bill Haley. Although his modern reputation is better (The Road I’m On was on David Keenan’s The Best Albums Ever...Honest), however, his history producing Christian albums and status as practicing Catholic may make Dion the more likely target
Barrett Strong	Early black pop artist
The Dixie Cups	Early black pop artist
Chubby Checker	Early black pop artist
Aaron Neville	Early black pop artist
The Spencer Davis Group	Pop/rock	This deletion also encompasses Traffic and solo Steve Winwood, neither of whom had songs on the original Rolling Stone list
Little Eva	Early black pop artist
Solomon Burke	Early soul artist
Percy Sledge	Soul/R’n’b
The Young Rascals	Pop/rock
The Lovin’ Spoonful	Pop/rock
The Troggs	Garage rock/protopunk
? and the Mysterians	Garage rock/protopunk
Love	College/hippie music	Although they had some association with hard rock and protopunk, the fact that mainman Arthur Lee was black would make them an unlikely target for Rolling Stone and big-city Millennial critics
Big Brother and the Holding Company
Janis Joplin
Eric Clapton	Hard rock Pop/rock	By genre a possible target for Rolling Stone and big-city Millennial critics, although less so for Clapton’s post-Cream work
Cream
Deep Purple	Hard rock	By genre a likely target for Rolling Stone and big-city Millennial crictics
Steppenwolf	Hard rock Heartland rock	By genre a likely target for Rolling Stone and big-city Millennial crictics
Labelle	Soul/R’n’b
The Carpenters	Pop/rock
The Five Stairsteps	Soul/R’n’b
Norman Greenbaum		By Christian faith a likely target for Rolling Stone and big-city Millennial critics
Lynyrd Skynyrd	Hard rock Heartland rock	By genre a likely target for Rolling Stone and big-city Millennial crictics
Jackson Browne	Singer/songwriter	A possible target as a standard white rocker, but political sentiments in 1980s make this less likely
The Jam	College/hippie music	This classification is not applicable outside the United States — the Jam were very much as mass-audience band in Europe
Foreigner	Hard rock Pop/rock	By genre a possible target for Rolling Stone and big-city Millennial critics, but too linked to soft rock to not exclude that they were excluded merely as an older pop band
John Cougar Mellencamp	Heartland rock	By genre a possible target for Rolling Stone and big-city Millennial critics
Salt-n-Pepa	Rap	A most surprising omission given that they were one of the first female rappers.
The Verve	College/hippie music
R. Kelly	Soul/R’n’b
Franz Ferdinand	College/hippie music

 In contrast to the albums, the song discards include many artists who might be expected to be “politically correct” from a Rolling Stone perspective, inasmuch as twenty-four of the forty-nine omitted artists (related artists counted as one) were black. However, all but five of these black artists predate the flowering of soul, funk and ultimately rap music upon which large portions of modern Rolling Stone canons have been based.

Early black pop artists, who date from a time before blacks were able to be politically active — although one could also say that with the power of Europe’s progressive working classes political conditions in the 1950s were much more favorable to advancements by black Americans than conditions since Europe’s deindustrialisation in the 1970s and 1980s — were simply not supportive of the left-wing politics with which Rolling Stone has been associated since its formation. From this fact, one could argue that Rolling Stone’s song discards are actually not that much less, or even no less, political than their album discards. Before the 1966 elections, political activism in black music was largely confined to radical forms of jazz and was not even widespread there — an example from as early as 1960 being We Insist! Max Roach’s Freedom Now Suite by drummer and composer Max Roach. Even We Insist! is not nearly so radical as bands like Public Enemy and Rage Against the Machine would become in later generations. The 1950s and 1960s Civil Rights Movement was possible because the ruling classes in the US feared they would be subject to apartheid-type sanctions otherwise. Consequently, the movement was remarkably peaceful compared to virtually any other other social movement in modern history. However, Ward Churchill demonstrated in his 2006 On the Justice of Roosting Chickens: Reflections on the Consequences of U.S. Imperial Arrogance and Criminality that this peacefulness severely limited the long-term effectiveness of the Civil Rights movement and made it extremely easy for the US ruling class to reverse the improvements in life for black Americans once threats diminished — which Churchill and others show to have occurred for most black Americans since 1980.

For these reasons, it is by no means certain that the song discards of Rolling Stone are actually less political than their earlier album discards.

Why countercultures merge into GOP orthodoxy

The 1990s Republican Revolution, whose ultra-free-market ideology has largely dictated American politics over the past three decades, was frequently justified by its supporters as a response to the supposedly ultra-liberal media of the Bush Senior Era.

When I first read the Republican Revolution’s advocates — my first experience being Peter Kreeft — I found many of their arguments absurd, but gathered that they viewed the Bush Senior Era media as excessively liberal compared to the opinions of most Americans, and government policy even in the Reagan era as similarly much more socially liberal than public opinion.

What I have come to realise in the past few years, however, is that, notwithstanding their successes in lowering taxes for the very rich to almost nothing, and eliminating public services for ordinary Americans, the “conservative counterculture” that emerged with the Republican Revolution has failed completely to achieve the social goals which it promoted during the late 1990s, like:

1. dramatically reduced immigration, especially from countries of the Tropical World and/or of Muslims
   
2. a foreign policy less supportive of and/or more hostile to strongly Islamic countries
   
3. a return of women to their traditional roles as wives and mothers
4. an end to abortion and even to all artificial birth control
5. an end to violence in entertainment, music and even video games (whether by rigid censorship or public boycotts)
6. a return to traditional religious morality in public education

Author Oliver Wiseman in his ‘Have the National Conservatives Missed Their Moment?’ argues that the nationalist/social conservatives have completely missed their moment because of their inability to challenge conservative economic orthodoxy where it opposes the interests of social conservatives as noted in the previous list. He argues that this occurs even when conservative groups try to secede from a socially liberal society that they regard as corrupt, and much more critically that the problem is that:

“[“movement conservatism” or GOP orthodoxy] removes from the political arena, and consigns to the ‘private’ sphere, the very value judgments and critical questions that most affect our humanity and our civilization”

This point reveals why countercultures on the Right move into GOP orthodoxy. Unless the existence of the private sphere (and the private sector) per se is challenged, it is impossible to challenge anything related to the hyper-capitalism that has become politically hegemonic since the 1973 energy crisis. To challenge the private sector and private sphere involves radical class struggle by the working classes. This has always been impossible in the United States due to racism, by which the ruling classes are intensely invested in tight alliances with lower-class whites and providing them with privileges — from freedom of choice in residence to fairer policing — that prevents them seeing that they have much more in common with poor people of colour than the ruling class.

The cultural interests of poorer whites in the United States — many of whom initially seceded from a Europe intolerant of their churches — has served to create what James Löwen misleadingly described as “the white ghetto”, but is much more accurately called a white cloister. This rural (sometimes exurban) white cloister is completely isolated (substantially of its own choice, as Löwen showed in Sundown Towns) from urban America, and much more still from the wider world. Since the standardisation and nationalisation of media in the late 1970s, information sources and culture available within the white cloister have become more and more uniformly hyper-capitalist, which helps explain why it is less and less able to challenge Republican orthodoxy on the economic front.

An easily-read planetary insolation table

Although of relatively marginal relevance to the actual climate of Earth today — and mainly in the field of glacial/interglacial cycles where small change have large effects — the relationship between planetary insolation and obliquity has been interesting to me ever since I read Darren M. Williams’ and David Pollard’s ‘Extraordinary Climates of Earth-Like Planets: Three-Dimensional Climate Simulations at Extreme Obliquity’. The article was originally published in 2003 by the International Journal of Astrobiology, but I first read it over a decade later and it was very interesting. Before reading ‘Extraordinary Climates of Earth-Like Planets’, I had circa 2000 read World-Building (Science Fiction Writing Series) by Stephen L. Gillett and Ben Bova, but, although I did find it somewhat interesting, I did not do any research related to it (although at the time I may not have had the resources to do so).

It was only when I read Alice Nadeau’s 2019 ‘Generalizations for Insolation and Albedo To Adapt an Energy Balance Model to Other Planets’ — originally published with Richard McGehee in 2015 in a much shorter form as ‘A Simple Formula for a Planet's Mean Annual Insolation by Latitude’ —that the subject attracted really serious attention. Basic studies of the topic usually simply note that equatorial insolation equals polar insolation at 54˚obliquity, and that beyond 54˚ the poles receive more insolation than the equator. Actually, though, when equatorial insulation equals polar insolation, as discussed explicitly by Anthony R. Dobrovolskis in ‘On a Planet’s Annual Mean Insolation’, the insolation has a “W” shape with peaks at the equator and the poles, and a shallow trough in the mid-latitudes. This “W” shape was noted by Nadeau, who mentioned that conventional approximations for Earthlike obliquities do not capture the shape well.

The graph below will provide an illustration of insolation at these obliquities:

Annual relative planetary insolation for obliquities 135˚ or 45˚ (green), arcsine(π/4) (orange), 126.103˚ or 53.897˚ (red dotted), 122.3747˚ or 57.6253˚ (red continuous line), and 114.645˚ or 65.355˚ (purple)

Originally when planning this post I intended to graph all the columns in the table below, but on Excel this proved impossible, because I could not find a way to graph the obliquity column (x-axis) by actual size (I may not have tried that hard to be frank). So I have provided a lengthy table with obliquities over 0.25 degrees from 0˚to 180˚, plus several other important obliquities where there is:

• a transition between above- and below-average insolation at the equator or at the poles
• these correspond to transitions between two and one latitude with average insolation
• a transition between “W” shape and single insolation maximum
• these occur at 45˚ and 135˚ which are the boundaries of the obliquities where the poles are the least insulated part of the planet
• these also occur at approximately 65.355˚ and 114.645˚ between which the equator is the least insulated part of the planet, and outside which the equator is an insolation maximum

The columns in the table below show:

1. obliquity in degrees
2. the latitude of minimum annual insolation (Dobrovolskis’ “cold front”)
3. the latitude or latitudes at which annual planetary insolation equals that for the planet as a whole
4. the latitude, if any, of equal insolation to the equator
5. the latitude, if any, of equal insolation to the poles
6. the maximum percentage insolation for each obliquity
7. the minimum percentage insolation for each obliquity
8. the insolation of the secondary peak, if it exists, as a percentage of total planetary insolation
9. the percentage above minimum planetary insolation of the secondary peak
10. the percentage of the planet’s total surface receiving an insolation above the planetary average

Obliquity (˚)	Latitude of minimum insolation (˚)	Latitude(s) of average insolation (˚)			Equal to equator	Equal to poles	Maximum percentage	Minimum percentage	Secondary peak	% of surface above mean
0	90.000	38.24						127.32%	0.00%				61.90%
0.25	90.000	38.24													127.30%	0.56%				61.90%
0.5	90.000	38.24													127.32%	1.11%				61.90%
0.75	90.000	38.24													127.32%	1.67%				61.90%
1	90.000	38.24													127.31%	2.22%				61.90%
1.25	90.000	38.24													127.31%	2.78%				61.90%
1.5	90.000	38.23													127.30%	3.33%				61.88%
1.75	90.000	38.23													127.29%	3.89%				61.88%
2	90.000	38.23													127.28%	4.44%				61.88%
2.25	90.000	38.23													127.27%	5.00%				61.88%
2.5	90.000	38.23													127.26%	5.55%				61.88%
2.75	90.000	38.23													127.25%	6.11%				61.88%
3	90.000	38.22													127.24%	6.66%				61.87%
3.25	90.000	38.22													127.22%	7.22%				61.87%
3.5	90.000	38.21													127.21%	7.77%				61.85%
3.75	90.000	38.21													127.19%	8.33%				61.85%
4	90.000	38.21													127.17%	8.88%				61.85%
4.25	90.000	38.20													127.15%	9.44%				61.84%
4.5	90.000	38.20													127.13%	9.99%				61.84%
4.75	90.000	38.19													127.11%	10.54%				61.83%
5	90.000	38.19													127.08%	11.10%				61.83%
5.25	90.000	38.18													127.06%	11.65%				61.81%
5.5	90.000	38.18													127.03%	12.20%				61.81%
5.75	90.000	38.17													127.00%	12.76%				61.80%
6	90.000	38.16													126.98%	13.31%				61.79%
6.25	90.000	38.16													126.95%	13.86%				61.79%
6.5	90.000	38.15													126.92%	14.41%				61.77%
6.75	90.000	38.15													126.88%	14.97%				61.77%
7	90.000	38.14													126.85%	15.52%				61.76%
7.25	90.000	38.13													126.82%	16.07%				61.74%
7.5	90.000	38.12													126.78%	16.62%				61.73%
7.75	90.000	38.12													126.74%	17.17%				61.73%
8	90.000	38.11													126.71%	17.72%				61.72%
8.25	90.000	38.10													126.67%	18.27%				61.70%
8.5	90.000	38.09													126.63%	18.82%				61.69%
8.75	90.000	38.08													126.58%	19.37%				61.68%
9	90.000	38.07													126.54%	19.92%				61.66%
9.25	90.000	38.06													126.50%	20.47%				61.65%
9.5	90.000	38.05													126.45%	21.01%				61.63%
9.75	90.000	38.04													126.41%	21.56%				61.62%
10	90.000	38.03													126.36%	22.11%				61.61%
10.25	90.000	38.02													126.31%	22.66%				61.59%
10.5	90.000	38.01													126.26%	23.20%				61.58%
10.75	90.000	37.99													126.21%	23.75%				61.55%
11	90.000	37.98													126.16%	24.29%				61.54%
11.25	90.000	37.97													126.10%	24.84%				61.52%
11.5	90.000	37.96													126.05%	25.38%				61.51%
11.75	90.000	37.95													125.99%	25.93%				61.50%
12	90.000	37.93													125.94%	26.47%				61.47%
12.25	90.000	37.92													125.88%	27.02%				61.46%
12.5	90.000	37.91													125.82%	27.56%				61.44%
12.75	90.000	37.89													125.76%	28.10%				61.41%
13	90.000	37.88													125.70%	28.64%				61.40%
13.25	90.000	37.86													125.63%	29.18%				61.37%
13.5	90.000	37.85													125.57%	29.72%				61.36%
13.75	90.000	37.84													125.51%	30.26%				61.35%
14	90.000	37.82													125.44%	30.80%				61.32%
14.25	90.000	37.80													125.37%	31.34%				61.29%
14.5	90.000	37.78													125.30%	31.88%				61.26%
14.75	90.000	37.77													125.23%	32.42%				61.25%
15	90.000	37.75													125.16%	32.95%				61.22%
15.25	90.000	37.74													125.09%	33.49%				61.21%
15.5	90.000	37.72													125.02%	34.03%				61.18%
15.75	90.000	37.70													124.95%	34.56%				61.15%
16	90.000	37.68						124.87%	35.10%				61.13%
16.25	90.000	37.67						124.79%	35.63%				61.11%
16.5	90.000	37.65						124.72%	36.16%				61.08%
16.75	90.000	37.63						124.64%	36.69%				61.06%
17	90.000	37.61						124.56%	37.23%				61.03%
17.25	90.000	37.59						124.48%	37.76%				61.00%
17.5	90.000	37.58						124.39%	38.29%				60.99%
17.75	90.000	37.55						124.31%	38.82%				60.95%
18	90.000	37.53						124.23%	39.35%				60.92%
18.25	90.000	37.51						124.14%	39.87%				60.89%
18.5	90.000	37.49						124.06%	40.40%				60.86%
18.75	90.000	37.47						123.96%	40.93%				60.83%
19	90.000	37.46						123.88%	41.45%				60.82%
19.25	90.000	37.43						123.79%	41.98%				60.78%
19.5	90.000	37.40						123.70%	42.50%				60.74%
19.75	90.000	37.38						123.61%	43.02%				60.71%
20	90.000	37.35						123.51%	43.55%				60.67%
20.25	90.000	37.32						123.42%	44.07%				60.63%
20.5	90.000	37.30						123.33%	44.59%				60.60%
20.75	90.000	37.28						123.23%	45.11%				60.57%
21	90.000	37.25						123.13%	45.63%				60.53%
21.25	90.000	37.23						123.03%	46.15%				60.50%
21.5	90.000	37.20						122.93%	46.66%				60.46%
21.75	90.000	37.18						122.83%	47.18%				60.43%
22	90.000	37.15						122.73%	47.70%				60.39%
22.25	90.000	37.12						122.63%	48.21%				60.35%
22.5	90.000	37.09						122.53%	48.72%				60.31%
22.75	90.000	37.07						122.42%	49.24%				60.28%
23	90.000	37.04						122.32%	49.75%				60.24%
23.25	90.000	37.01						122.21%	50.26%				60.20%
23.5	90.000	36.98						122.10%	50.77%				60.15%
23.75	90.000	36.95						121.99%	51.28%				60.11%
24	90.000	36.92						121.88%	51.79%				60.07%
24.25	90.000	36.89						121.77%	52.29%				60.03%
24.5	90.000	36.86						121.66%	52.80%				59.99%
24.75	90.000	36.83						121.55%	53.31%				59.94%
25	90.000	36.80						121.43%	53.81%				59.90%
25.25	90.000	36.77						121.32%	54.31%				59.86%
25.5	90.000	36.73						121.20%	54.81%				59.80%
25.75	90.000	36.70						121.08%	55.32%				59.76%
26	90.000	36.66						120.97%	55.82%				59.71%
26.25	90.000	36.63						120.85%	56.31%				59.66%
26.5	90.000	36.60						120.73%	56.80%				59.62%
26.75	90.000	36.56						120.61%	57.31%				59.57%
27	90.000	36.53						120.49%	57.80%				59.52%
27.25	90.000	36.49						120.36%	58.30%				59.47%
27.5	90.000	36.45						120.24%	58.79%				59.41%
27.75	90.000	36.41						120.11%	59.28%				59.36%
28	90.000	36.38						119.99%	59.77%				59.31%
28.25	90.000	36.34						119.86%	60.26%				59.26%
28.5	90.000	36.30						119.73%	60.75%				59.20%
28.75	90.000	36.26						119.61%	61.24%				59.15%
29	90.000	36.22						119.48%	61.73%				59.09%
29.25	90.000	36.18						119.35%	62.21%				59.03%
29.5	90.000	36.14						119.21%	62.70%				58.98%
29.75	90.000	36.09						119.08%	63.18%				58.91%
30	90.000	36.05						118.95%	63.66%				58.85%
30.25	90.000	36.01						118.81%	64.14%				58.79%
30.5	90.000	35.96						118.68%	64.62%				58.72%
30.75	90.000	35.92						118.54%	65.10%				58.67%
31	90.000	35.88						118.41%	65.58%				58.61%
31.25	90.000	35.83						118.27%	66.05%				58.54%
31.5	90.000	35.78						118.13%	66.53%				58.47%
31.75	90.000	35.73						117.99%	67.00%				58.40%
32	90.000	35.69						117.85%	67.47%				58.34%
32.25	90.000	35.64						117.71%	67.94%				58.27%
32.5	90.000	35.59						117.57%	68.41%				58.20%
32.75	90.000	35.54						117.42%	68.88%				58.13%
33	90.000	35.49						117.28%	69.35%				58.06%
33.25	90.000	35.44						117.13%	69.81%				57.99%
33.5	90.000	35.38						116.99%	70.27%				57.90%
33.75	90.000	35.33						116.84%	70.74%				57.83%
34	90.000	35.28						116.69%	71.20%				57.76%
34.25	90.000	35.22						116.55%	71.66%				57.67%
34.5	90.000	35.16						116.40%	72.12%				57.59%
34.75	90.000	35.11						116.25%	72.57%				57.51%
35	90.000	35.05						116.10%	73.03%				57.43%
35.25	90.000	34.99						115.95%	73.48%				57.34%
35.5	90.000	34.93						115.79%	73.94%				57.26%
35.75	90.000	34.87						115.64%	74.39%				57.17%
36	90.000	34.81						115.49%	74.84%				57.09%
36.25	90.000	34.74						115.33%	75.29%				56.99%
36.5	90.000	34.67						115.18%	75.74%				56.88%
36.75	90.000	34.61						115.02%	76.18%				56.80%
37	90.000	34.55						114.86%	76.63%				56.71%
37.25	90.000	34.48						114.71%	77.07%				56.61%
37.5	90.000	34.42						114.55%	77.51%				56.53%
37.75	90.000	34.34						114.39%	77.95%				56.41%
38	90.000	34.27						114.23%	78.39%				56.31%
38.25	90.000	34.20						114.07%	78.83%				56.21%
38.5	90.000	34.12						113.91%	79.26%				56.09%
38.75	90.000	34.05						113.74%	79.70%				55.99%
39	90.000	33.97						113.58%	80.13%				55.88%
39.25	90.000	33.90						113.42%	80.56%				55.77%
39.5	90.000	33.81						113.25%	80.99%				55.64%
39.75	90.000	33.74						113.09%	81.42%				55.54%
40	90.000	33.66						112.92%	81.84%				55.43%
40.25	90.000	33.57						112.76%	82.27%				55.30%
40.5	90.000	33.49						112.59%	82.69%				55.18%
40.75	90.000	33.40						112.42%	83.11%				55.05%
41	90.000	33.30						112.25%	83.53%				54.90%
41.25	90.000	33.21						112.09%	83.95%				54.77%
41.5	90.000	33.12						111.92%	84.37%				54.64%
41.75	90.000	33.03						111.75%	84.78%				54.51%
42	90.000	32.93						111.58%	85.20%				54.36%
42.25	90.000	32.83						111.40%	85.61%				54.21%
42.5	90.000	32.73						111.23%	86.02%				54.07%
42.75	90.000	32.62						111.06%	86.43%				53.91%
43	90.000	32.51						110.89%	86.83%				53.74%
43.25	90.000	32.40						110.71%	87.24%				53.58%
43.5	90.000	32.30						110.54%	87.64%				53.44%
43.75	90.000	32.18						110.36%	88.05%				53.26%
44	90.000	32.07						110.19%	88.45%				53.10%
44.25	90.000	31.94						110.01%	88.85%				52.90%
44.5	90.000	31.82						109.83%	89.24%				52.73%
44.75	90.000	31.70						109.66%	89.64%				52.55%
45	90.000	31.56				90.00	109.48%	90.03%	90.03%	0.00%	52.34%
45.125	82.458	31.50							79.35	109.390%	90.226%	90.228%	0.002%	52.25%
45.25	79.372	31.43							75.01	109.301%	90.417%	90.424%	0.008%	52.15%
45.5	75.076	31.30							69.02	109.122%	90.787%	90.814%	0.030%	51.95%
45.75	71.848	31.15							64.56	108.943%	91.143%	91.202%	0.065%	51.73%
46	69.183	31.01							60.92	108.763%	91.485%	91.589%	0.114%	51.52%
46.25	66.881	30.86							57.81	108.583%	91.813%	91.974%	0.175%	51.29%
46.5	64.841	30.70							55.09	108.402%	92.129%	92.358%	0.249%	51.05%
46.75	63.001	30.54							52.68	108.22%	92.43%	92.74%	0.34%	50.81%
47	61.321	30.38							50.50	108.04%	92.72%	93.12%	0.43%	50.57%
47.25	59.772	30.21							48.53	107.86%	93.00%	93.50%	0.54%	50.32%
47.5	58.334	30.04							46.74	107.67%	93.27%	93.87%	0.64%	50.06%
47.75	56.990	29.86							45.11	107.49%	93.52%	94.25%	0.78%	49.79%
48	55.729	29.67							43.62	107.31%	93.77%	94.62%	0.91%	49.50%
48.25	54.540	29.48							42.28	107.12%	94.00%	94.99%	1.05%	49.21%
48.5	53.416	29.28							41.10	106.94%	94.22%	95.36%	1.21%	48.91%
48.75	52.349	29.07							40.02	106.75%	94.44%	95.73%	1.37%	48.59%
49	51.335	28.86							38.97	106.57%	94.64%	96.09%	1.53%	48.27%
49.25	50.368	28.63							37.92	106.38%	94.84%	96.46%	1.71%	47.92%
49.5	49.444	28.40							36.86	106.20%	95.02%	96.82%	1.89%	47.56%
49.75	48.560	28.16							35.78	106.01%	95.20%	97.18%	2.08%	47.19%
50	47.712	27.91							34.69	105.82%	95.36%	97.54%	2.29%	46.81%
50.25	46.898	27.65							33.56	105.64%	95.52%	97.89%	2.48%	46.41%
50.5	46.116	27.37							32.41	105.45%	95.67%	98.25%	2.70%	45.97%
50.75	45.363	27.10							31.20	105.26%	95.82%	98.60%	2.90%	45.55%
51	44.638	26.80							29.97	105.07%	95.95%	98.95%	3.13%	45.09%
51.25	43.938	26.49							28.66	104.88%	96.08%	99.30%	3.35%	44.60%
51.5	43.262	26.17							27.30	104.70%	96.20%	99.64%	3.58%	44.10%
51.75	42.610	25.83							25.86	104.51%	96.31%	99.99%	3.82%	43.57%
51.7575	42.590	25.81	90.00		25.81	104.50%	96.32%	100.00%	3.82%	43.54%
51.875	42.291	25.65	82.59			25.11	104.41%	96.36%	100.16%	3.94%	44.12%
52	41.978	25.47	79.34			24.33	104.32%	96.41%	100.33%	4.07%	44.73%
52.25	41.368	25.10	74.93			22.70	104.13%	96.51%	100.67%	4.31%	45.86%
52.5	40.776	24.70	71.65			20.93	103.94%	96.60%	101.01%	4.57%	46.87%
52.75	40.203	24.29	68.97			18.99	103.75%	96.68%	101.35%	4.83%	47.80%
53	39.648	23.85	66.67			16.81	103.56%	96.76%	101.69%	5.10%	48.61%
53.25	39.110	23.39	64.64			14.30	103.37%	96.83%	102.02%	5.36%	49.34%
53.5	38.588	22.90	62.83			11.21	103.17%	96.90%	102.35%	5.62%	49.95%
53.75	38.082	22.38	61.20			6.82	102.98%	96.96%	102.68%	5.90%	50.44%
53.8225	37.938	22.22	60.75			4.85	102.93%	96.97%	102.77%	5.98%	50.57%
53.8962	37.793	22.06	60.31	90.00	0.00	102.87%	96.99%	102.87%	6.06%	50.69%
53.9375	37.712	21.98	60.09	85.47		102.93%	97.00%	102.84%	6.02%	50.75%
54	37.590	21.82	59.71	82.35			103.01%	97.01%	102.79%	5.96%	50.82%
54.25	37.114	21.24	58.33	75.94			103.33%	97.06%	102.60%	5.71%	51.12%
54.5	36.652	20.61	57.06	71.71			103.66%	97.10%	102.41%	5.47%	51.28%
54.75	36.204	19.94	55.90	68.34			103.98%	97.13%	102.22%	5.24%	51.30%
55	35.770	19.21	54.80	65.43			104.30%	97.16%	102.02%	5.00%	51.19%
55.25	35.350	18.43	53.77	62.94			104.62%	97.19%	101.83%	4.77%	50.95%
55.5	34.944	17.59	52.82	60.66			104.93%	97.21%	101.64%	4.56%	50.55%
55.75	34.552	16.64	51.92	58.60			105.24%	97.22%	101.45%	4.35%	49.92%
56	34.177	15.65	51.08	56.66			105.56%	97.23%	101.25%	4.13%	49.17%
56.25	33.820	14.51	50.29	54.88			105.87%	97.24%	101.06%	3.93%	48.13%
56.5	33.492	13.24	49.55	53.20			106.17%	97.24%	100.87%	3.73%	46.81%
56.75	33.153	11.78	48.85	51.62			106.48%	97.24%	100.68%	3.54%	45.12%
57	32.791	10.04	48.18	50.12			106.78%	97.23%	100.48%	3.34%	42.91%
57.25	32.411	7.85	47.56	48.69			107.08%	97.22%	100.29%	3.16%	39.86%
57.5	32.016	4.57	46.96	47.34			107.38%	97.20%	100.10%	2.98%	34.88%
57.5625	31.915	3.24	46.82	47.00			107.46%	97.20%	100.05%	2.93%	32.73%
57.6	31.854	2.06	46.73	46.81			107.50%	97.20%	100.02%	2.90%	30.78%
57.6253	31.813	0.00	46.68	46.68			107.53%	97.19%	100.00%	2.89%	27.25%
57.6875	31.710		46.54	46.36			107.61%	97.19%	99.95%	2.84%	27.41%
57.75	31.606			46.40		46.04		107.68%	97.18%	99.90%	2.80%	27.58%
58	31.183			45.87		44.79		107.98%	97.16%	99.71%	2.62%	28.22%
58.25	30.745			45.36		43.59		108.27%	97.13%	99.52%	2.46%	28.85%
58.5	30.293			44.88		42.44		108.56%	97.09%	99.32%	2.30%	29.44%
58.75	29.827			44.43		41.33		108.85%	97.05%	99.13%	2.14%	30.00%
59	29.346			43.99		40.25		109.14%	97.01%	98.94%	1.99%	30.55%
59.25	28.850			43.58		39.21		109.42%	96.96%	98.74%	1.84%	31.06%
59.5	28.337			43.18		38.20		109.71%	96.90%	98.55%	1.70%	31.57%
59.75	27.080			42.81		37.22		109.99%	96.84%	98.36%	1.57%	32.04%
60	27.261			42.45		36.27		110.27%	96.78%	98.16%	1.43%	32.51%
60.25	26.696			42.11		35.34		110.54%	96.71%	97.97%	1.30%	32.94%
60.5	26.110			41.78		34.43		110.82%	96.63%	97.78%	1.19%	33.37%
60.75	25.504			41.47		33.54		111.09%	96.55%	97.59%	1.08%	33.78%
61	24.875			41.17		32.67		111.36%	96.46%	97.39%	0.96%	34.17%
61.25	24.221			40.88		31.81		111.63%	96.37%	97.20%	0.86%	34.55%
61.5	23.541			40.61		30.96		111.89%	96.27%	97.01%	0.77%	34.91%
61.75	22.831			40.34		30.13		112.16%	96.17%	96.82%	0.68%	35.27%
62	22.090			40.09		29.28		112.42%	96.06%	96.62%	0.58%	35.60%
62.25	21.314			39.85		28.45		112.680%	95.951%	96.432%	0.501%	35.92%
62.5	20.498			39.61		27.57		112.937%	95.832%	96.239%	0.425%	36.24%
62.75	19.638			39.39		26.60		113.193%	95.707%	96.048%	0.356%	36.54%
63	18.728			39.17		25.51		113.446%	95.578%	95.857%	0.292%	36.84%
63.25	17.966			38.96		24.31		113.698%	95.442%	95.666%	0.235%	37.12%
63.5	16.721			38.75		23.00		113.947%	95.301%	95.475%	0.183%	37.41%
63.75	15.600			38.56		21.55		114.193%	95.154%	95.285%	0.138%	37.67%
64	14.377			38.38		19.94		114.438%	95.001%	95.094%	0.098%	37.91%
64.25	13.022			38.20		18.13		114.680%	94.824%	94.904%	0.084%	38.16%
64.5	11.490			38.02		16.06		114.921%	94.677%	94.715%	0.040%	38.41%
64.75	9.695			37.85		13.60		115.159%	94.506%	94.525%	0.020%	38.64%
65	7.449			37.69		10.49		115.395%	94.330%	94.336%	0.006%	38.86%
65.25	4.063			37.53		5.74		115.628%	94.147%	94.148%	0.001%	39.08%
65.3	2.942			37.50		4.16		115.675%	94.1098%	94.1100%	0.0002%	39.12%
65.35496	0.000			37.47		0.00		115.726%	94.070%	94.070%	0.000%	39.17%
65.5	0.000			37.37				115.86%	93.96%				39.30%
65.75	0.000			37.23										116.09%	93.77%				39.50%
66	0.000			37.08										116.32%	93.58%				39.71%
66.25	0.000			36.96										116.54%	93.40%				39.87%
66.5	0.000			36.81										116.76%	93.21%				40.08%
66.75	0.000			36.68										116.98%	93.02%				40.27%
67	0.000			36.56										117.20%	92.84%				40.43%
67.25	0.000			36.42										117.42%	92.65%				40.63%
67.5	0.000			36.30										117.63%	92.47%				40.80%
67.75	0.000			36.19										117.84%	92.28%				40.95%
68	0.000			36.08										118.05%	92.10%				41.11%
68.25	0.000			35.96										118.26%	91.92%				41.28%
68.5	0.000			35.86										118.46%	91.73%				41.42%
68.75	0.000			35.76										118.67%	91.55%				41.56%
69	0.000			35.66										118.87%	91.37%				41.70%
69.25	0.000			35.56										119.07%	91.19%				41.84%
69.5	0.000			35.46										119.26%	91.01%				41.99%
69.75	0.000			35.37										119.45%	90.83%				42.11%
70	0.000			35.28										119.65%	90.65%				42.24%
70.25	0.000			35.18										119.83%	90.47%				42.39%
70.5	0.000			35.10										120.02%	90.30%				42.50%
70.75	0.000			35.02										120.21%	90.12%				42.61%
71	0.000			34.94										120.39%	89.94%				42.73%
71.25	0.000			34.85										120.57%	89.77%				42.86%
71.5	0.000			34.76										120.74%	89.59%				42.99%
71.75	0.000			34.70										120.92%	89.42%				43.07%
72	0.000			34.62										121.09%	89.25%				43.19%
72.25	0.000			34.55										121.26%	89.08%				43.29%
72.5	0.000			34.48										121.43%	88.91%				43.39%
72.75	0.000			34.40										121.60%	88.74%				43.50%
73	0.000		34.34						121.76%				88.57%				43.59%
73.25	0.000		34.27						121.92%				88.40%				43.69%
73.5	0.000		34.21						122.08%				88.23%				43.78%
73.75	0.000		34.15						122.24%				88.07%				43.86%
74	0.000		34.08						122.39%				87.90%				43.97%
74.25	0.000		34.03						122.54%				87.74%				44.04%
74.5	0.000		33.96						122.69%				87.57%				44.14%
74.75	0.000		33.91						122.84%				87.41%				44.21%
75	0.000		33.85						122.99%				87.25%				44.30%
75.25	0.000		33.80						123.13%				87.09%				44.37%
75.5	0.000		33.74						123.27%				86.93%				44.46%
75.75	0.000		33.69						123.41%				86.77%				44.53%
76	0.000		33.64						123.54%				86.62%				44.60%
76.25	0.000		33.59						123.68%				86.46%				44.68%
76.5	0.000		33.55						123.81%				86.31%				44.73%
76.75	0.000		33.50						123.93%				86.16%				44.81%
77	0.000		33.46						124.06%				86.01%				44.86%
77.25	0.000		33.41						124.18%				85.86%				44.94%
77.5	0.000		33.37						124.31%				85.71%				45.00%
77.75	0.000		33.33						124.42%				85.56%				45.05%
78	0.000		33.29						124.54%				85.42%				45.11%
78.25	0.000		33.25						124.66%				85.27%				45.17%
78.5	0.000		33.21						124.77%				85.13%				45.23%
78.75	0.000		33.17						124.88%				84.99%				45.29%
79	0.000		33.13						124.98%				84.85%				45.35%
79.25	0.000		33.10						125.09%				84.71%				45.39%
79.5	0.000		33.07						125.19%				84.58%				45.43%
79.75	0.000		33.03						125.29%				84.44%				45.49%
80	0.000		33.00						125.39%				84.31%				45.54%
80.25	0.000		32.96						125.48%				84.18%				45.59%
80.5	0.000		32.93						125.58%				84.05%				45.64%
80.75	0.000		32.90						125.67%				83.92%				45.68%
81	0.000		32.87						125.76%				83.80%				45.73%
81.25	0.000		32.84						125.84%				83.67%				45.77%
81.5	0.000		32.82				125.93%	83.55%				45.80%
81.75	0.000		32.79				126.01%	83.43%				45.84%
82	0.000		32.77				126.08%	83.31%				45.87%
82.25	0.000		32.74				126.16%	83.20%				45.92%
82.5	0.000		32.72				126.23%	83.09%				45.95%
82.75	0.000		32.69				126.31%	82.97%				45.99%
83	0.000		32.67				126.37%	82.87%				46.02%
83.25	0.000		32.65				126.44%	82.76%				46.05%
83.5	0.000		32.63				126.51%	82.65%				46.08%
83.75	0.000		32.61				126.57%	82.55%				46.11%
84	0.000		32.59				126.63%	82.45%				46.14%
84.25	0.000		32.57				126.68%	82.36%				46.17%
84.5	0.000		32.56				126.74%	82.26%				46.18%
84.75	0.000		32.54				126.79%	82.17%				46.21%
85	0.000		32.53				126.84%	82.08%				46.23%
85.25	0.000		32.51				126.89%	82.00%				46.26%
85.5	0.000		32.50				126.93%	81.91%				46.27%
85.75	0.000		32.49				126.97%	81.83%				46.28%
86	0.000		32.47				127.01%	81.76%				46.31%
86.25	0.000		32.46				127.05%	81.68%				46.33%
86.5	0.000		32.45				127.09%	81.61%				46.34%
86.75	0.000		32.44				127.12%	81.55%				46.36%
87	0.000		32.43				127.15%	81.48%				46.37%
87.25	0.000		32.42				127.18%	81.42%				46.39%
87.5	0.000		32.41				127.20%	81.37%				46.40%
87.75	0.000		32.40				127.22%	81.31%				46.42%
88	0.000		32.40				127.25%	81.27%				46.42%
88.25	0.000		32.39				127.26%	81.22%				46.43%
88.5	0.000		32.39				127.28%	81.18%				46.43%
88.75	0.000		32.39				127.29%	81.15%				46.43%
89	0.000		32.38				127.30%	81.12%				46.45%
89.25	0.000		32.38				127.31%	81.09%				46.45%
89.5	0.000		32.38				127.32%	81.07%				46.45%
89.75	0.000		32.37				127.32%	81.06%				46.46%
90	0.000		32.37				127.32%	81.06%				46.46%
90.25	0.000		32.37				127.32%	81.06%				46.46%
90.5	0.000		32.38				127.32%	81.07%				46.45%
90.75	0.000		32.38				127.31%	81.09%				46.45%
91	0.000		32.38				127.30%	81.12%				46.45%
91.25	0.000		32.39				127.29%	81.15%				46.43%
91.5	0.000		32.39				127.28%	81.18%				46.43%
91.75	0.000		32.39				127.26%	81.22%				46.43%
92	0.000		32.40				127.25%	81.27%				46.42%
92.25	0.000		32.40				127.22%	81.31%				46.42%
92.5	0.000		32.41				127.20%	81.37%				46.40%
92.75	0.000		32.42				127.18%	81.42%				46.39%
93	0.000		32.43				127.15%	81.48%				46.37%
93.25	0.000		32.44				127.12%	81.55%				46.36%
93.5	0.000		32.45				127.09%	81.61%				46.34%
93.75	0.000		32.46				127.05%	81.68%				46.33%
94	0.000		32.47				127.01%	81.76%				46.31%
94.25	0.000		32.49				126.97%	81.83%				46.28%
94.5	0.000		32.50				126.93%	81.91%				46.27%
94.75	0.000		32.51				126.89%	82.00%				46.26%
95	0.000		32.53				126.84%	82.08%				46.23%
95.25	0.000		32.54				126.79%	82.17%				46.21%
95.5	0.000		32.56				126.74%	82.26%				46.18%
95.75	0.000		32.57				126.68%	82.36%				46.17%
96	0.000		32.59				126.63%	82.45%				46.14%
96.25	0.000		32.61				126.57%	82.55%				46.11%
96.5	0.000		32.63				126.51%	82.65%				46.08%
96.75	0.000		32.65				126.44%	82.76%				46.05%
97	0.000		32.67				126.37%	82.87%				46.02%
97.25	0.000		32.69				126.31%	82.97%				45.99%
97.5	0.000		32.72				126.23%	83.09%				45.95%
97.75	0.000		32.74				126.16%	83.20%				45.92%
98	0.000		32.77				126.08%	83.31%				45.87%
98.25	0.000		32.79				126.01%	83.43%				45.84%
98.5	0.000		32.82				125.93%	83.55%				45.80%
98.75	0.000		32.84				125.84%	83.67%				45.77%
99	0.000		32.87				125.76%	83.80%				45.73%
99.25	0.000		32.90				125.67%	83.92%				45.68%
99.5	0.000		32.93				125.58%	84.05%				45.64%
99.75	0.000		32.96				125.48%	84.18%				45.59%
100	0.000		33.00				125.39%	84.31%				45.54%
100.25	0.000		33.03				125.29%	84.44%				45.49%
100.5	0.000		33.07				125.19%	84.58%				45.43%
100.75	0.000		33.10				125.09%	84.71%				45.39%
101	0.000		33.13				124.98%	84.85%				45.35%
101.25	0.000		33.17				124.88%	84.99%				45.29%
101.5	0.000		33.21				124.77%	85.13%				45.23%
101.75	0.000		33.25				124.66%	85.27%				45.17%
102	0.000		33.29				124.54%	85.42%				45.11%
102.25	0.000		33.33				124.42%	85.56%				45.05%
102.5	0.000		33.37				124.31%	85.71%				45.00%
102.75	0.000		33.41				124.18%	85.86%				44.94%
103	0.000		33.46				124.06%	86.01%				44.86%
103.25	0.000		33.50				123.93%	86.16%				44.81%
103.5	0.000		33.55				123.81%	86.31%				44.73%
103.75	0.000		33.59				123.68%	86.46%				44.68%
104	0.000		33.64				123.54%	86.62%				44.60%
104.25	0.000		33.69				123.41%	86.77%				44.53%
104.5	0.000		33.74				123.27%	86.93%				44.46%
104.75	0.000		33.80				123.13%	87.09%				44.37%
105	0.000		33.85				122.99%	87.25%				44.30%
105.25	0.000		33.91				122.84%	87.41%				44.21%
105.5	0.000		33.96				122.69%	87.57%				44.14%
105.75	0.000		34.03				122.54%	87.74%				44.04%
106	0.000		34.08				122.39%	87.90%				43.97%
106.25	0.000		34.15				122.24%	88.07%				43.86%
106.5	0.000		34.21				122.08%	88.23%				43.78%
106.75	0.000		34.27				121.92%	88.40%				43.69%
107	0.000		34.34				121.76%	88.57%				43.59%
107.25	0.000		34.40				121.60%	88.74%				43.50%
107.5	0.000		34.48				121.43%	88.91%				43.39%
107.75	0.000		34.55				121.26%	89.08%				43.29%
108	0.000		34.62				121.09%	89.25%				43.19%
108.25	0.000		34.70				120.92%	89.42%				43.07%
108.5	0.000		34.76				120.74%	89.59%				42.99%
108.75	0.000		34.85				120.57%	89.77%				42.86%
109	0.000		34.94				120.39%	89.94%				42.73%
109.25	0.000		35.02				120.21%	90.12%				42.61%
109.5	0.000		35.10				120.02%	90.30%				42.50%
109.75	0.000		35.18				119.83%	90.47%				42.39%
110	0.000		35.28				119.65%	90.65%				42.24%
110.25	0.000		35.37				119.45%	90.83%				42.11%
110.5	0.000		35.46				119.26%	91.01%				41.99%
110.75	0.000		35.56				119.07%	91.19%				41.84%
111	0.000		35.66				118.87%	91.37%				41.70%
111.25	0.000		35.76				118.67%	91.55%				41.56%
111.5	0.000		35.86				118.46%	91.73%				41.42%
111.75	0.000		35.96				118.26%	91.92%				41.28%
112	0.000		36.08				118.05%	92.10%				41.11%
112.25	0.000		36.19				117.84%	92.28%				40.95%
112.5	0.000		36.30				117.63%	92.47%				40.80%
112.75	0.000		36.42				117.42%	92.65%				40.63%
113	0.000		36.56				117.20%	92.84%				40.43%
113.25	0.000		36.68				116.98%	93.02%				40.27%
113.5	0.000		36.81				116.76%	93.21%				40.08%
113.75	0.000		36.96				116.54%	93.40%				39.87%
114	0.000		37.08				116.32%	93.58%				39.71%
114.25	0.000		37.23				116.09%	93.77%				39.50%
114.5	0.000		37.37				115.86%	93.96%				39.30%
114.645	0.000		37.47	0.00		115.726%	94.070%	94.070%	0.000%	39.17%
114.7	2.942		37.50	4.16			115.675%	94.1098%	94.1100%	0.0002%	39.12%
114.75	4.063		37.53	5.74			115.628%	94.147%	94.148%	0.001%	39.08%
115	7.449		37.69	10.49			115.395%	94.330%	94.336%	0.006%	38.86%
115.25	9.695		37.85	13.60			115.159%	94.506%	94.525%	0.020%	38.64%
115.5	11.490		38.02	16.06			114.921%	94.677%	94.715%	0.040%	38.41%
115.75	13.022		38.20	18.13			114.680%	94.824%	94.904%	0.084%	38.16%
116	14.377		38.38	19.94			114.438%	95.001%	95.094%	0.098%	37.91%
116.25	15.600		38.56	21.55			114.193%	95.154%	95.285%	0.138%	37.67%
116.5	16.721		38.75	23.00			113.947%	95.301%	95.475%	0.183%	37.41%
116.75	17.966		38.96	24.31			113.698%	95.442%	95.666%	0.235%	37.12%
117	18.728		39.17	25.51			113.446%	95.578%	95.857%	0.292%	36.84%
117.25	19.638		39.39	26.60			113.193%	95.707%	96.048%	0.356%	36.54%
117.5	20.498		39.61	27.57			112.937%	95.832%	96.239%	0.425%	36.24%
117.75	21.314		39.85	28.45			112.680%	95.951%	96.432%	0.501%	35.92%
118	22.090		40.09	29.29			112.42%	96.06%	96.62%	0.58%	35.60%
118.25	22.831		40.34	30.13			112.16%	96.17%	96.82%	0.68%	35.27%
118.5	23.541		40.61	30.96			111.89%	96.27%	97.01%	0.77%	34.91%
118.75	24.221		40.88	31.81			111.63%	96.37%	97.20%	0.86%	34.55%
119	24.875		41.17	32.67			111.36%	96.46%	97.39%	0.96%	34.17%
119.25	25.504		41.47	33.54			111.09%	96.55%	97.59%	1.08%	33.78%
119.5	26.110		41.78	34.43			110.82%	96.63%	97.78%	1.19%	33.37%
119.75	26.696		42.11	35.34			110.54%	96.71%	97.97%	1.30%	32.94%
120	27.261		42.45	36.27			110.27%	96.78%	98.16%	1.43%	32.51%
120.25	27.080		42.81	37.22			109.99%	96.84%	98.36%	1.57%	32.04%
120.5	28.337		43.18	38.20			109.71%	96.90%	98.55%	1.70%	31.57%
120.75	28.850		43.58	39.21			109.42%	96.96%	98.74%	1.84%	31.06%
121	29.346		43.99	40.25			109.14%	97.01%	98.94%	1.99%	30.55%
121.25	29.827		44.43	41.33			108.85%	97.05%	99.13%	2.14%	30.00%
121.5	30.293		44.88	42.44			108.56%	97.09%	99.32%	2.30%	29.44%
121.75	30.745		45.36	43.59			108.27%	97.13%	99.52%	2.46%	28.85%
122	31.183		45.87	44.79			107.98%	97.16%	99.71%	2.62%	28.22%
122.25	31.606		46.40	46.04			107.68%	97.18%	99.90%	2.80%	27.58%
122.3125	31.710		46.54	46.36			107.61%	97.19%	99.95%	2.84%	27.41%
122.3747	31.813	0.00	46.68	46.68			107.53%	97.19%	100.00%	2.89%	27.25%
122.4	31.854	2.06	46.73	46.81			107.50%	97.20%	100.02%	2.90%	30.78%
122.4375	31.915	3.24	46.82	47.00			107.46%	97.20%	100.05%	2.93%	32.73%
122.5	32.016	4.57	46.96	47.34			107.38%	97.20%	100.10%	2.98%	34.88%
122.75	32.411	7.85	47.56	48.69			107.08%	97.22%	100.29%	3.16%	39.86%
123	32.791	10.04	48.18	50.12			106.78%	97.23%	100.48%	3.34%	42.91%
123.25	33.153	11.78	48.85	51.62			106.48%	97.24%	100.68%	3.54%	45.12%
123.5	33.492	13.24	49.55	53.20			106.17%	97.24%	100.87%	3.73%	46.81%
123.75	33.820	14.51	50.29	54.88			105.87%	97.24%	101.06%	3.93%	48.13%
124	34.177	15.65	51.08	56.66			105.56%	97.23%	101.25%	4.13%	49.17%
124.25	34.552	16.64	51.92	58.60			105.24%	97.22%	101.45%	4.35%	49.92%
124.5	34.944	17.59	52.82	60.66			104.93%	97.21%	101.64%	4.56%	50.55%
124.75	35.350	18.43	53.77	62.94			104.62%	97.19%	101.83%	4.77%	50.95%
125	35.770	19.21	54.80	65.43			104.30%	97.16%	102.02%	5.00%	51.19%
125.25	36.204	19.94	55.90	68.34			103.98%	97.13%	102.22%	5.24%	51.30%
125.5	36.652	20.61	57.06	71.71			103.66%	97.10%	102.41%	5.47%	51.28%
125.75	37.114	21.24	58.33	75.94			103.33%	97.06%	102.60%	5.71%	51.12%
126	37.590	21.82	59.71	82.35			103.01%	97.01%	102.79%	5.96%	50.82%
126.0625	37.712	21.98	60.09	85.47			102.93%	97.00%	102.84%	6.02%	50.75%
126.1038	37.793	22.06	60.31	90.00	0.00	102.87%	96.99%	102.87%	6.06%	50.69%
126.1775	37.938	22.22	60.75		4.85	102.93%	96.97%	102.77%	5.98%	50.57%
126.25	38.082	22.38	61.20			6.82	102.98%	96.96%	102.68%	5.90%	50.44%
126.5	38.588	22.90	62.83			11.21	103.17%	96.90%	102.35%	5.62%	49.95%
126.75	39.110	23.39	64.64			14.30	103.37%	96.83%	102.02%	5.36%	49.34%
127	39.648	23.85	66.67			16.81	103.56%	96.76%	101.69%	5.10%	48.61%
127.25	40.203	24.29	68.97			18.99	103.75%	96.68%	101.35%	4.83%	47.80%
127.5	40.776	24.70	71.65			20.93	103.94%	96.60%	101.01%	4.57%	46.87%
127.75	41.368	25.10	74.93			22.70	104.13%	96.51%	100.67%	4.31%	45.86%
128	41.978	25.47	79.34			24.33	104.32%	96.41%	100.33%	4.07%	44.73%
128.125	42.291	25.65	82.59			25.11	104.41%	96.36%	100.16%	3.94%	44.12%
128.2425	42.590	25.81	90.00			25.81	104.50%	96.32%	100.00%	3.82%	43.54%
128.25	42.610	25.83				25.86	104.51%	96.31%	99.99%	3.82%	43.57%
128.5	43.262	26.17							27.30	104.70%	96.20%	99.64%	3.58%	44.10%
128.75	43.938	26.49							28.66	104.88%	96.08%	99.30%	3.35%	44.60%
129	44.638	26.80							29.97	105.07%	95.95%	98.95%	3.13%	45.09%
129.25	45.363	27.10							31.20	105.26%	95.82%	98.60%	2.90%	45.55%
129.5	46.116	27.38							32.41	105.45%	95.67%	98.25%	2.70%	45.99%
129.75	46.898	27.65							33.56	105.64%	95.52%	97.89%	2.48%	46.41%
130	47.712	27.91							34.69	105.82%	95.36%	97.54%	2.29%	46.81%
130.25	48.560	28.16							35.78	106.01%	95.20%	97.18%	2.08%	47.19%
130.5	49.444	28.40							36.86	106.20%	95.02%	96.82%	1.89%	47.56%
130.75	50.368	28.63							37.92	106.38%	94.84%	96.46%	1.71%	47.92%
131	51.335	28.86							38.97	106.57%	94.64%	96.09%	1.53%	48.27%
131.25	52.349	29.07							40.02	106.75%	94.44%	95.73%	1.37%	48.59%
131.5	53.416	29.28							41.10	106.94%	94.22%	95.36%	1.21%	48.91%
131.75	54.540	29.48							42.28	107.12%	94.00%	94.99%	1.05%	49.21%
132	55.729	29.67							43.62	107.31%	93.77%	94.62%	0.91%	49.50%
132.25	56.990	29.86							45.11	107.49%	93.52%	94.25%	0.78%	49.79%
132.5	58.334	30.04							46.74	107.67%	93.27%	93.87%	0.64%	50.06%
132.75	59.772	30.21							48.53	107.86%	93.00%	93.50%	0.54%	50.32%
133	61.321	30.38							50.50	108.04%	92.72%	93.12%	0.43%	50.57%
133.25	63.001	30.54							52.68	108.22%	92.43%	92.74%	0.34%	50.81%
133.5	64.841	30.70							55.09	108.402%	92.129%	92.358%	0.249%	51.05%
133.75	66.881	30.86							57.81	108.583%	91.813%	91.974%	0.175%	51.29%
134	69.183	31.01							60.92	108.763%	91.485%	91.589%	0.114%	51.52%
134.25	71.848	31.15							64.56	108.943%	91.143%	91.202%	0.065%	51.73%
134.5	75.076	31.30							69.02	109.122%	90.787%	90.814%	0.030%	51.95%
134.75	79.372	31.43							75.01	109.301%	90.417%	90.424%	0.008%	52.15%
134.875	82.458	31.50							79.35	109.390%	90.226%	90.228%	0.002%	52.25%
135	90.000	31.56							90.00	109.48%	90.03%	90.03%	0.00%	52.34%
135.25	90.000	31.70						109.66%	89.64%				52.55%
135.5	90.000	31.82													109.83%	89.24%				52.73%
135.75	90.000	31.94													110.01%	88.85%				52.90%
136	90.000	32.07													110.19%	88.45%				53.10%
136.25	90.000	32.18													110.36%	88.05%				53.26%
136.5	90.000	32.30													110.54%	87.64%				53.44%
136.75	90.000	32.40													110.71%	87.24%				53.58%
137	90.000	32.51													110.89%	86.83%				53.74%
137.25	90.000	32.62													111.06%	86.43%				53.91%
137.5	90.000	32.73													111.23%	86.02%				54.07%
137.75	90.000	32.83													111.40%	85.61%				54.21%
138	90.000	32.93													111.58%	85.20%				54.36%
138.25	90.000	33.03													111.75%	84.78%				54.51%
138.5	90.000	33.12													111.92%	84.37%				54.64%
138.75	90.000	33.21													112.09%	83.95%				54.77%
139	90.000	33.30													112.25%	83.53%				54.90%
139.25	90.000	33.40													112.42%	83.11%				55.05%
139.5	90.000	33.49													112.59%	82.69%				55.18%
139.75	90.000	33.57													112.76%	82.27%				55.30%
140	90.000	33.66													112.92%	81.84%				55.43%
140.25	90.000	33.74													113.09%	81.42%				55.54%
140.5	90.000	33.81													113.25%	80.99%				55.64%
140.75	90.000	33.90													113.42%	80.56%				55.77%
141	90.000	33.97													113.58%	80.13%				55.88%
141.25	90.000	34.05													113.74%	79.70%				55.99%
141.5	90.000	34.12													113.91%	79.26%				56.09%
141.75	90.000	34.20													114.07%	78.83%				56.21%
142	90.000	34.27													114.23%	78.39%				56.31%
142.25	90.000	34.34													114.39%	77.95%				56.41%
142.5	90.000	34.42													114.55%	77.51%				56.53%
142.75	90.000	34.48													114.71%	77.07%				56.61%
143	90.000	34.55													114.86%	76.63%				56.71%
143.25	90.000	34.61													115.02%	76.18%				56.80%
143.5	90.000	34.67													115.18%	75.74%				56.88%
143.75	90.000	34.74													115.33%	75.29%				56.99%
144	90.000	34.81													115.49%	74.84%				57.09%
144.25	90.000	34.87													115.64%	74.39%				57.17%
144.5	90.000	34.93													115.79%	73.94%				57.26%
144.75	90.000	34.99													115.95%	73.48%				57.34%
145	90.000	35.05													116.10%	73.03%				57.43%
145.25	90.000	35.11													116.25%	72.57%				57.51%
145.5	90.000	35.16													116.40%	72.12%				57.59%
145.75	90.000	35.22													116.55%	71.66%				57.67%
146	90.000	35.28													116.69%	71.20%				57.76%
146.25	90.000	35.33													116.84%	70.74%				57.83%
146.5	90.000	35.38													116.99%	70.27%				57.90%
146.75	90.000	35.44													117.13%	69.81%				57.99%
147	90.000	35.49													117.28%	69.35%				58.06%
147.25	90.000	35.54													117.42%	68.88%				58.13%
147.5	90.000	35.59													117.57%	68.41%				58.20%
147.75	90.000	35.64													117.71%	67.94%				58.27%
148	90.000	35.69													117.85%	67.47%				58.34%
148.25	90.000	35.73													117.99%	67.00%				58.40%
148.5	90.000	35.78													118.13%	66.53%				58.47%
148.75	90.000	35.83													118.27%	66.05%				58.54%
149	90.000	35.88													118.41%	65.58%				58.61%
149.25	90.000	35.92													118.54%	65.10%				58.67%
149.5	90.000	35.96													118.68%	64.62%				58.72%
149.75	90.000	36.01													118.81%	64.14%				58.79%
150	90.000	36.05													118.95%	63.66%				58.85%
150.25	90.000	36.09													119.08%	63.18%				58.91%
150.5	90.000	36.14													119.21%	62.70%				58.98%
150.75	90.000	36.18													119.35%	62.21%				59.03%
151	90.000	36.22													119.48%	61.73%				59.09%
151.25	90.000	36.26						119.61%	61.24%				59.15%
151.5	90.000	36.30						119.73%	60.75%				59.20%
151.75	90.000	36.34						119.86%	60.26%				59.26%
152	90.000	36.38						119.99%	59.77%				59.31%
152.25	90.000	36.41						120.11%	59.28%				59.36%
152.5	90.000	36.45						120.24%	58.79%				59.41%
152.75	90.000	36.49						120.36%	58.30%				59.47%
153	90.000	36.53						120.49%	57.80%				59.52%
153.25	90.000	36.56						120.61%	57.31%				59.57%
153.5	90.000	36.60						120.73%	56.80%				59.62%
153.75	90.000	36.63						120.85%	56.31%				59.66%
154	90.000	36.66						120.97%	55.82%				59.71%
154.25	90.000	36.70						121.08%	55.32%				59.76%
154.5	90.000	36.73						121.20%	54.81%				59.80%
154.75	90.000	36.77						121.32%	54.31%				59.86%
155	90.000	36.80						121.43%	53.81%				59.90%
155.25	90.000	36.83						121.55%	53.31%				59.94%
155.5	90.000	36.86						121.66%	52.80%				59.99%
155.75	90.000	36.89						121.77%	52.29%				60.03%
156	90.000	36.92						121.88%	51.79%				60.07%
156.25	90.000	36.95						121.99%	51.28%				60.11%
156.5	90.000	36.98						122.10%	50.77%				60.15%
156.75	90.000	37.01						122.21%	50.26%				60.20%
157	90.000	37.04						122.32%	49.75%				60.24%
157.25	90.000	37.07						122.42%	49.24%				60.28%
157.5	90.000	37.09						122.53%	48.72%				60.31%
157.75	90.000	37.12						122.63%	48.21%				60.35%
158	90.000	37.15						122.73%	47.70%				60.39%
158.25	90.000	37.18						122.83%	47.18%				60.43%
158.5	90.000	37.20						122.93%	46.66%				60.46%
158.75	90.000	37.23						123.03%	46.15%				60.50%
159	90.000	37.25						123.13%	45.63%				60.53%
159.25	90.000	37.28						123.23%	45.11%				60.57%
159.5	90.000	37.30						123.33%	44.59%				60.60%
159.75	90.000	37.32						123.42%	44.07%				60.63%
160	90.000	37.35						123.51%	43.55%				60.67%
160.25	90.000	37.38						123.61%	43.02%				60.71%
160.5	90.000	37.40						123.70%	42.50%				60.74%
160.75	90.000	37.43						123.79%	41.98%				60.78%
161	90.000	37.46						123.88%	41.45%				60.82%
161.25	90.000	37.47						123.96%	40.93%				60.83%
161.5	90.000	37.49						124.06%	40.40%				60.86%
161.75	90.000	37.51						124.14%	39.87%				60.89%
162	90.000	37.53						124.23%	39.35%				60.92%
162.25	90.000	37.55						124.31%	38.82%				60.95%
162.5	90.000	37.58						124.39%	38.29%				60.99%
162.75	90.000	37.59						124.48%	37.76%				61.00%
163	90.000	37.61						124.56%	37.23%				61.03%
163.25	90.000	37.63						124.64%	36.69%				61.06%
163.5	90.000	37.65						124.72%	36.16%				61.08%
163.75	90.000	37.67						124.79%	35.63%				61.11%
164	90.000	37.68						124.87%	35.10%				61.13%
164.25	90.000	37.70						124.95%	34.56%				61.15%
164.5	90.000	37.72						125.02%	34.03%				61.18%
164.75	90.000	37.74						125.09%	33.49%				61.21%
165	90.000	37.75						125.16%	32.95%				61.22%
165.25	90.000	37.77						125.23%	32.42%				61.25%
165.5	90.000	37.78						125.30%	31.88%				61.26%
165.75	90.000	37.80						125.37%	31.34%				61.29%
166	90.000	37.82						125.44%	30.80%				61.32%
166.25	90.000	37.84						125.51%	30.26%				61.35%
166.5	90.000	37.85						125.57%	29.72%				61.36%
166.75	90.000	37.86						125.63%	29.18%				61.37%
167	90.000	37.88						125.70%	28.64%				61.40%
167.25	90.000	37.89						125.76%	28.10%				61.41%
167.5	90.000	37.91						125.82%	27.56%				61.44%
167.75	90.000	37.92						125.88%	27.02%				61.46%
168	90.000	37.93						125.94%	26.47%				61.47%
168.25	90.000	37.95						125.99%	25.93%				61.50%
168.5	90.000	37.96						126.05%	25.38%				61.51%
168.75	90.000	37.97						126.10%	24.84%				61.52%
169	90.000	37.98						126.16%	24.29%				61.54%
169.25	90.000	37.99						126.21%	23.75%				61.55%
169.5	90.000	38.01						126.26%	23.20%				61.58%
169.75	90.000	38.02						126.31%	22.66%				61.59%
170	90.000	38.03						126.36%	22.11%				61.61%
170.25	90.000	38.04						126.41%	21.56%				61.62%
170.5	90.000	38.05						126.45%	21.01%				61.63%
170.75	90.000	38.06						126.50%	20.47%				61.65%
171	90.000	38.07						126.54%	19.92%				61.66%
171.25	90.000	38.08						126.58%	19.37%				61.68%
171.5	90.000	38.09						126.63%	18.82%				61.69%
171.75	90.000	38.10						126.67%	18.27%				61.70%
172	90.000	38.11						126.71%	17.72%				61.72%
172.25	90.000	38.12						126.74%	17.17%				61.73%
172.5	90.000	38.12						126.78%	16.62%				61.73%
172.75	90.000	38.13						126.82%	16.07%				61.74%
173	90.000	38.14						126.85%	15.52%				61.76%
173.25	90.000	38.15						126.88%	14.97%				61.77%
173.5	90.000	38.15						126.92%	14.41%				61.77%
173.75	90.000	38.16						126.95%	13.86%				61.79%
174	90.000	38.16						126.98%	13.31%				61.79%
174.25	90.000	38.17						127.00%	12.76%				61.80%
174.5	90.000	38.18						127.03%	12.20%				61.81%
174.75	90.000	38.18						127.06%	11.65%				61.81%
175	90.000	38.19						127.08%	11.10%				61.83%
175.25	90.000	38.19						127.11%	10.54%				61.83%
175.5	90.000	38.20						127.13%	9.99%				61.84%
175.75	90.000	38.20						127.15%	9.44%				61.84%
176	90.000	38.21						127.17%	8.88%				61.85%
176.25	90.000	38.21						127.19%	8.33%				61.85%
176.5	90.000	38.21						127.21%	7.77%				61.85%
176.75	90.000	38.22						127.22%	7.22%				61.87%
177	90.000	38.22						127.24%	6.66%				61.87%
177.25	90.000	38.23						127.25%	6.11%				61.88%
177.5	90.000	38.23						127.26%	5.55%				61.88%
177.75	90.000	38.23						127.27%	5.00%				61.88%
178	90.000	38.23						127.28%	4.44%				61.88%
178.25	90.000	38.23						127.29%	3.89%				61.88%
178.5	90.000	38.23						127.30%	3.33%				61.88%
178.75	90.000	38.24						127.31%	2.78%				61.90%
179	90.000	38.24						127.31%	2.22%				61.90%
179.25	90.000	38.24						127.32%	1.67%				61.90%
179.5	90.000	38.24						127.32%	1.11%				61.90%
179.75	90.000	38.24						127.30%	0.56%				61.90%
180	90.000	38.24						127.32%	0.00%				61.90%

Converting Insolation by Obliquity To Insolation By Latitude:

The table above is of insolation with latitude by obliquity.

However, one can use the table above to see how insolation varies with obliquity for a constant latitude thus:

1. Add 90˚ to the absolute value of the required latitude
2. Add 90˚ to all the latitudinal values in the above table.
• if one desires obliquity to be less than 90˚, then subtract the resulting obliquity from 180˚
• I generally prefer to quote retrograde obliquities because in out solar system high obliquities are always retrograde, and theoretical astronomy suggests that high obliquities are much more likely to be retrograde owing to the instability of high direct obliquities
3. “Equal to Equator” becomes “Equal to 90˚ obliquity”
4. “Equal to Poles” becomes “Equal to 180˚ or 0˚ obliquity”

For example, at 37.75˚ (approximately the latitude of Melbourne):

1. we see the table for 127.75˚ and by adding 90˚, we see that:
1. the lowest insolation will be for an obliquity of 131.368˚ (or 48.642˚)
2. planetary average insolation will occur at 115.10˚ and 164.93˚ (or 64.90˚ and 15.07˚)
• insolation will be above average below 15.07˚, between 64.90˚ and 115.10˚, and above 164.93˚
3. no value will equal the insolation at 90˚ obliquity (90˚ give the maximum possible insolation)
4. an insolation equal to that at 180˚ or 0˚ obliquity will occur at 112.70˚ (or 67.30˚) obliquity