History of Petersson norms of level one cusp forms

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2026-09-18 10:18 zeta3 clarify Petersson norm prose and PARI program current reviewed
2026-09-18 10:15 zeta3 with codex-cli Petersson norms for level one cusp forms with weights up to 40, sorted by a_2 and checked against PARI
2026-09-18 09:43 zeta3 with codex Petersson norms for level one cusp forms with weights up to 40, sorted by a_2 and checked against PARI
2026-09-18 09:33 zeta3 claim Petersson norms draft

What changed between 2026-09-18 09:33 and 2026-09-18 09:43

from line 115 (141 lines, 138 more than before) @@ -115,3 +115,141 @@
   - - k   - - i-Numbers: []+Numbers:+- params:+    k: '12'+    i: '1'+  number: '0.00000103536205680432092234781681223'+  comment: $a_2=-24.00000000000000$, the root of HREF{Hecke_polynomials_of_level_one_cusp_forms#12,2}[$\chi_{12,2}$].+- params:+    k: '16'+    i: '1'+  number: '0.00000216906134759063332432422387084'+  comment: $a_2=216.0000000000000$, the root of HREF{Hecke_polynomials_of_level_one_cusp_forms#16,2}[$\chi_{16,2}$].+- params:+    k: '18'+    i: '1'+  number: '0.00000459473619763924661011587324802'+  comment: $a_2=-528.0000000000000$, the root of HREF{Hecke_polynomials_of_level_one_cusp_forms#18,2}[$\chi_{18,2}$].+- params:+    k: '20'+    i: '1'+  number: '0.00000826554153165970316423006276026'+  comment: $a_2=456.0000000000000$, the root of HREF{Hecke_polynomials_of_level_one_cusp_forms#20,2}[$\chi_{20,2}$].+- params:+    k: '22'+    i: '1'+  number: '0.0000200998183274306452315831330634'+  comment: $a_2=-288.0000000000000$, the root of HREF{Hecke_polynomials_of_level_one_cusp_forms#22,2}[$\chi_{22,2}$].+- params:+    k: '24'+    i: '1'+  number: '0.000107836545077234026820943374035'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#24,2}[$\chi_{24,2}$]+    in increasing order, with $a_2\approx -4016.351171716245$.+- params:+    k: '24'+    i: '2'+  number: '0.000128992800758160472019099313271'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#24,2}[$\chi_{24,2}$]+    in increasing order, with $a_2\approx 5096.351171716245$.+- params:+    k: '26'+    i: '1'+  number: '0.000205334716815372379243519562956'+  comment: $a_2=-48.00000000000000$, the root of HREF{Hecke_polynomials_of_level_one_cusp_forms#26,2}[$\chi_{26,2}$].+- params:+    k: '28'+    i: '1'+  number: '0.00236428002656855536683619961491'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#28,2}[$\chi_{28,2}$]+    in increasing order, with $a_2\approx -18713.59859471915$.+- params:+    k: '28'+    i: '2'+  number: '0.00131542730871571614006541980065'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#28,2}[$\chi_{28,2}$]+    in increasing order, with $a_2\approx 10433.59859471915$.+- params:+    k: '30'+    i: '1'+  number: '0.00675086417656698477174246013613'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#30,2}[$\chi_{30,2}$]+    in increasing order, with $a_2\approx -17433.90502875288$.+- params:+    k: '30'+    i: '2'+  number: '0.0100997800473221939384580046955'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#30,2}[$\chi_{30,2}$]+    in increasing order, with $a_2\approx 26073.90502875288$.+- params:+    k: '32'+    i: '1'+  number: '0.0320925558714875814394415038967'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#32,2}[$\chi_{32,2}$]+    in increasing order, with $a_2\approx -31347.87172677239$.+- params:+    k: '32'+    i: '2'+  number: '0.0729994924629061249311411160214'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#32,2}[$\chi_{32,2}$]+    in increasing order, with $a_2\approx 71307.87172677239$.+- params:+    k: '34'+    i: '1'+  number: '0.623070453157424716952166922143'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#34,2}[$\chi_{34,2}$]+    in increasing order, with $a_2\approx -171359.4371321172$.+- params:+    k: '34'+    i: '2'+  number: '0.180637193843065066573942997006'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#34,2}[$\chi_{34,2}$]+    in increasing order, with $a_2\approx 49679.43713211717$.+- params:+    k: '36'+    i: '1'+  number: '2.67742333549761657636239939753'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#36,2}[$\chi_{36,2}$]+    in increasing order, with $a_2\approx -165109.1678324939$.+- params:+    k: '36'+    i: '2'+  number: '2.42584430383642443883211696130'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#36,2}[$\chi_{36,2}$]+    in increasing order, with $a_2\approx -26808.00761087159$.+- params:+    k: '36'+    i: '3'+  number: '4.55969950662225591954959544292'+  comment: $a_2$ is the third root of HREF{Hecke_polynomials_of_level_one_cusp_forms#36,2}[$\chi_{36,2}$]+    in increasing order, with $a_2\approx 331573.1754433655$.+- params:+    k: '38'+    i: '1'+  number: '21.2742918225116448063549453159'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#38,2}[$\chi_{38,2}$]+    in increasing order, with $a_2\approx -480411.7539742225$.+- params:+    k: '38'+    i: '2'+  number: '12.6655885373653394405955792016'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#38,2}[$\chi_{38,2}$]+    in increasing order, with $a_2\approx 286011.7539742225$.+- params:+    k: '40'+    i: '1'+  number: '171.581094673690839287635257177'+  comment: $a_2$ is the first root of HREF{Hecke_polynomials_of_level_one_cusp_forms#40,2}[$\chi_{40,2}$]+    in increasing order, with $a_2\approx -799151.7631007462$.+- params:+    k: '40'+    i: '2'+  number: '190.225804606637761285194728054'+  comment: $a_2$ is the second root of HREF{Hecke_polynomials_of_level_one_cusp_forms#40,2}[$\chi_{40,2}$]+    in increasing order, with $a_2\approx 241487.7444577613$.+- params:+    k: '40'+    i: '3'+  number: '326.590585884552929043398261462'+  comment: $a_2$ is the third root of HREF{Hecke_polynomials_of_level_one_cusp_forms#40,2}[$\chi_{40,2}$]+    in increasing order, with $a_2\approx 1106520.018642985$. 

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