LMFDB - Embedded newform 931.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,6,Mod(1,931)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("931.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	931.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$149.317336246$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{177}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 44 $ x^2 - x - 44
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$7.15207$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.1521 q^{2} -16.4562 q^{3} +71.0645 q^{4} +99.7603 q^{5} +167.064 q^{6} -396.585 q^{8} +27.8066 q^{9} +O(q^{10})$	\(q-10.1521 q^{2} -16.4562 q^{3} +71.0645 q^{4} +99.7603 q^{5} +167.064 q^{6} -396.585 q^{8} +27.8066 q^{9} -1012.77 q^{10} -438.977 q^{11} -1169.45 q^{12} +477.590 q^{13} -1641.68 q^{15} +1752.10 q^{16} -1671.39 q^{17} -282.294 q^{18} +361.000 q^{19} +7089.42 q^{20} +4456.52 q^{22} +459.514 q^{23} +6526.29 q^{24} +6827.12 q^{25} -4848.53 q^{26} +3541.27 q^{27} -2696.78 q^{29} +16666.4 q^{30} +2314.43 q^{31} -5096.67 q^{32} +7223.89 q^{33} +16968.0 q^{34} +1976.06 q^{36} +3022.51 q^{37} -3664.90 q^{38} -7859.32 q^{39} -39563.5 q^{40} -5483.05 q^{41} +5101.80 q^{43} -31195.7 q^{44} +2773.99 q^{45} -4665.02 q^{46} -5803.63 q^{47} -28832.8 q^{48} -69309.4 q^{50} +27504.7 q^{51} +33939.7 q^{52} -23207.5 q^{53} -35951.2 q^{54} -43792.5 q^{55} -5940.69 q^{57} +27377.9 q^{58} +32849.5 q^{59} -116665. q^{60} +46911.5 q^{61} -23496.2 q^{62} -4325.31 q^{64} +47644.5 q^{65} -73337.4 q^{66} -3565.12 q^{67} -118776. q^{68} -7561.86 q^{69} +2346.44 q^{71} -11027.7 q^{72} -57370.0 q^{73} -30684.7 q^{74} -112349. q^{75} +25654.3 q^{76} +79788.3 q^{78} -29715.8 q^{79} +174790. q^{80} -65032.8 q^{81} +55664.3 q^{82} -60526.0 q^{83} -166738. q^{85} -51793.8 q^{86} +44378.8 q^{87} +174092. q^{88} -19134.9 q^{89} -28161.8 q^{90} +32655.1 q^{92} -38086.7 q^{93} +58918.9 q^{94} +36013.5 q^{95} +83871.9 q^{96} +43189.4 q^{97} -12206.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 7 q^{2} + 7 q^{3} + 49 q^{4} + 133 q^{5} + 241 q^{6} - 567 q^{8} + 335 q^{9}+O(q^{10}) $ 2 * q - 7 * q^2 + 7 * q^3 + 49 * q^4 + 133 * q^5 + 241 * q^6 - 567 * q^8 + 335 * q^9	\( 2 q - 7 q^{2} + 7 q^{3} + 49 q^{4} + 133 q^{5} + 241 q^{6} - 567 q^{8} + 335 q^{9} - 908 q^{10} - 705 q^{11} - 1687 q^{12} + 1341 q^{13} - 862 q^{15} + 1921 q^{16} - 2784 q^{17} + 686 q^{18} + 722 q^{19} + 6356 q^{20} + 3618 q^{22} - 2713 q^{23} + 2529 q^{24} + 4807 q^{25} - 2127 q^{26} + 5047 q^{27} - 7775 q^{29} + 19124 q^{30} - 7132 q^{31} + 889 q^{32} + 984 q^{33} + 13461 q^{34} - 4802 q^{36} - 6248 q^{37} - 2527 q^{38} + 12393 q^{39} - 45228 q^{40} + 4174 q^{41} + 25357 q^{43} - 25326 q^{44} + 12985 q^{45} - 14665 q^{46} - 11727 q^{47} - 24871 q^{48} - 75677 q^{50} + 1407 q^{51} + 14889 q^{52} - 29133 q^{53} - 31205 q^{54} - 52635 q^{55} + 2527 q^{57} + 11371 q^{58} + 64515 q^{59} - 133868 q^{60} + 40939 q^{61} - 53272 q^{62} + 9137 q^{64} + 76344 q^{65} - 93006 q^{66} + 19039 q^{67} - 94227 q^{68} - 81977 q^{69} - 70236 q^{71} - 63378 q^{72} - 67058 q^{73} - 59906 q^{74} - 159733 q^{75} + 17689 q^{76} + 143625 q^{78} - 32850 q^{79} + 180404 q^{80} - 104362 q^{81} + 86104 q^{82} - 71534 q^{83} - 203721 q^{85} + 12052 q^{86} - 74737 q^{87} + 219426 q^{88} + 87268 q^{89} + 4024 q^{90} + 102655 q^{92} - 259664 q^{93} + 40248 q^{94} + 48013 q^{95} + 224273 q^{96} + 62458 q^{97} - 93927 q^{99}+O(q^{100}) \) 2 * q - 7 * q^2 + 7 * q^3 + 49 * q^4 + 133 * q^5 + 241 * q^6 - 567 * q^8 + 335 * q^9 - 908 * q^10 - 705 * q^11 - 1687 * q^12 + 1341 * q^13 - 862 * q^15 + 1921 * q^16 - 2784 * q^17 + 686 * q^18 + 722 * q^19 + 6356 * q^20 + 3618 * q^22 - 2713 * q^23 + 2529 * q^24 + 4807 * q^25 - 2127 * q^26 + 5047 * q^27 - 7775 * q^29 + 19124 * q^30 - 7132 * q^31 + 889 * q^32 + 984 * q^33 + 13461 * q^34 - 4802 * q^36 - 6248 * q^37 - 2527 * q^38 + 12393 * q^39 - 45228 * q^40 + 4174 * q^41 + 25357 * q^43 - 25326 * q^44 + 12985 * q^45 - 14665 * q^46 - 11727 * q^47 - 24871 * q^48 - 75677 * q^50 + 1407 * q^51 + 14889 * q^52 - 29133 * q^53 - 31205 * q^54 - 52635 * q^55 + 2527 * q^57 + 11371 * q^58 + 64515 * q^59 - 133868 * q^60 + 40939 * q^61 - 53272 * q^62 + 9137 * q^64 + 76344 * q^65 - 93006 * q^66 + 19039 * q^67 - 94227 * q^68 - 81977 * q^69 - 70236 * q^71 - 63378 * q^72 - 67058 * q^73 - 59906 * q^74 - 159733 * q^75 + 17689 * q^76 + 143625 * q^78 - 32850 * q^79 + 180404 * q^80 - 104362 * q^81 + 86104 * q^82 - 71534 * q^83 - 203721 * q^85 + 12052 * q^86 - 74737 * q^87 + 219426 * q^88 + 87268 * q^89 + 4024 * q^90 + 102655 * q^92 - 259664 * q^93 + 40248 * q^94 + 48013 * q^95 + 224273 * q^96 + 62458 * q^97 - 93927 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−10.1521	−1.79465	−0.897324	−	0.441372i	$-0.854492\pi$
$2$	−10.1521	−1.79465	−0.897324	+	0.441372i	$0.854492\pi$
$3$	−16.4562	−1.05567	−0.527833	−	0.849348i	$-0.676995\pi$
$3$	−16.4562	−1.05567	−0.527833	+	0.849348i	$0.676995\pi$
$4$	71.0645	2.22076
$5$	99.7603	1.78457	0.892284	−	0.451475i	$-0.149102\pi$
$5$	99.7603	1.78457	0.892284	+	0.451475i	$0.149102\pi$
$6$	167.064	1.89455
$7$	0	0
$7$	0	0
$8$	−396.585	−2.19084
$9$	27.8066	0.114430
$10$	−1012.77	−3.20267
$11$	−438.977	−1.09386	−0.546928	−	0.837180i	$-0.684203\pi$
$11$	−438.977	−1.09386	−0.546928	+	0.837180i	$0.684203\pi$
$12$	−1169.45	−2.34439
$13$	477.590	0.783785	0.391892	−	0.920011i	$-0.371821\pi$
$13$	477.590	0.783785	0.391892	+	0.920011i	$0.371821\pi$
$14$	0	0
$15$	−1641.68	−1.88391
$16$	1752.10	1.71103
$17$	−1671.39	−1.40267	−0.701334	−	0.712833i	$-0.747412\pi$
$17$	−1671.39	−1.40267	−0.701334	+	0.712833i	$0.747412\pi$
$18$	−282.294	−0.205362
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	7089.42	3.96310
$21$	0	0
$22$	4456.52	1.96309
$23$	459.514	0.181125	0.0905627	−	0.995891i	$-0.471133\pi$
$23$	459.514	0.181125	0.0905627	+	0.995891i	$0.471133\pi$
$24$	6526.29	2.31280
$25$	6827.12	2.18468
$26$	−4848.53	−1.40662
$27$	3541.27	0.934866
$28$	0	0
$29$	−2696.78	−0.595457	−0.297729	−	0.954651i	$-0.596229\pi$
$29$	−2696.78	−0.595457	−0.297729	+	0.954651i	$0.596229\pi$
$30$	16666.4	3.38095
$31$	2314.43	0.432553	0.216277	−	0.976332i	$-0.430609\pi$
$31$	2314.43	0.432553	0.216277	+	0.976332i	$0.430609\pi$
$32$	−5096.67	−0.879856
$33$	7223.89	1.15475
$34$	16968.0	2.51730
$35$	0	0
$36$	1976.06	0.254123
$37$	3022.51	0.362964	0.181482	−	0.983394i	$-0.441911\pi$
$37$	3022.51	0.362964	0.181482	+	0.983394i	$0.441911\pi$
$38$	−3664.90	−0.411721
$39$	−7859.32	−0.827415
$40$	−39563.5	−3.90971
$41$	−5483.05	−0.509404	−0.254702	−	0.967020i	$-0.581977\pi$
$41$	−5483.05	−0.509404	−0.254702	+	0.967020i	$0.581977\pi$
$42$	0	0
$43$	5101.80	0.420777	0.210388	−	0.977618i	$-0.432527\pi$
$43$	5101.80	0.420777	0.210388	+	0.977618i	$0.432527\pi$
$44$	−31195.7	−2.42920
$45$	2773.99	0.204209
$46$	−4665.02	−0.325057
$47$	−5803.63	−0.383226	−0.191613	−	0.981471i	$-0.561372\pi$
$47$	−5803.63	−0.383226	−0.191613	+	0.981471i	$0.561372\pi$
$48$	−28832.8	−1.80628
$49$	0	0
$50$	−69309.4	−3.92073
$51$	27504.7	1.48075
$52$	33939.7	1.74060
$53$	−23207.5	−1.13485	−0.567426	−	0.823424i	$-0.692061\pi$
$53$	−23207.5	−1.13485	−0.567426	+	0.823424i	$0.692061\pi$
$54$	−35951.2	−1.67776
$55$	−43792.5	−1.95206
$56$	0	0
$57$	−5940.69	−0.242186
$58$	27377.9	1.06864
$59$	32849.5	1.22857	0.614284	−	0.789085i	$-0.289445\pi$
$59$	32849.5	1.22857	0.614284	+	0.789085i	$0.289445\pi$
$60$	−116665.	−4.18371
$61$	46911.5	1.61419	0.807095	−	0.590422i	$-0.201039\pi$
$61$	46911.5	1.61419	0.807095	+	0.590422i	$0.201039\pi$
$62$	−23496.2	−0.776281
$63$	0	0
$64$	−4325.31	−0.131998
$65$	47644.5	1.39872
$66$	−73337.4	−2.07236
$67$	−3565.12	−0.0970257	−0.0485128	−	0.998823i	$-0.515448\pi$
$67$	−3565.12	−0.0970257	−0.0485128	+	0.998823i	$0.515448\pi$
$68$	−118776.	−3.11499
$69$	−7561.86	−0.191208
$70$	0	0
$71$	2346.44	0.0552413	0.0276207	−	0.999618i	$-0.491207\pi$
$71$	2346.44	0.0552413	0.0276207	+	0.999618i	$0.491207\pi$
$72$	−11027.7	−0.250699
$73$	−57370.0	−1.26002	−0.630010	−	0.776587i	$-0.716949\pi$
$73$	−57370.0	−1.26002	−0.630010	+	0.776587i	$0.716949\pi$
$74$	−30684.7	−0.651393
$75$	−112349.	−2.30629
$76$	25654.3	0.509478
$77$	0	0
$78$	79788.3	1.48492
$79$	−29715.8	−0.535698	−0.267849	−	0.963461i	$-0.586313\pi$
$79$	−29715.8	−0.535698	−0.267849	+	0.963461i	$0.586313\pi$
$80$	174790.	3.05345
$81$	−65032.8	−1.10134
$82$	55664.3	0.914202
$83$	−60526.0	−0.964377	−0.482188	−	0.876068i	$-0.660158\pi$
$83$	−60526.0	−0.964377	−0.482188	+	0.876068i	$0.660158\pi$
$84$	0	0
$85$	−166738.	−2.50315
$86$	−51793.8	−0.755147
$87$	44378.8	0.628604
$88$	174092.	2.39647
$89$	−19134.9	−0.256066	−0.128033	−	0.991770i	$-0.540866\pi$
$89$	−19134.9	−0.256066	−0.128033	+	0.991770i	$0.540866\pi$
$90$	−28161.8	−0.366483
$91$	0	0
$92$	32655.1	0.402237
$93$	−38086.7	−0.456631
$94$	58918.9	0.687756
$95$	36013.5	0.409408
$96$	83871.9	0.928834
$97$	43189.4	0.466067	0.233033	−	0.972469i	$-0.425135\pi$
$97$	43189.4	0.466067	0.233033	+	0.972469i	$0.425135\pi$
$98$	0	0
$99$	−12206.4	−0.125170
$100$	485166.	4.85166
$101$	55330.5	0.539711	0.269855	−	0.962901i	$-0.413024\pi$
$101$	55330.5	0.539711	0.269855	+	0.962901i	$0.413024\pi$
$102$	−279229.	−2.65742
$103$	205641.	1.90993	0.954964	−	0.296722i	$-0.0958933\pi$
$103$	205641.	1.90993	0.954964	+	0.296722i	$0.0958933\pi$
$104$	−189405.	−1.71715
$105$	0	0
$106$	235604.	2.03666
$107$	181889.	1.53585	0.767923	−	0.640543i	$-0.221291\pi$
$107$	181889.	1.53585	0.767923	+	0.640543i	$0.221291\pi$
$108$	251658.	2.07612
$109$	24288.8	0.195813	0.0979063	−	0.995196i	$-0.468785\pi$
$109$	24288.8	0.195813	0.0979063	+	0.995196i	$0.468785\pi$
$110$	444584.	3.50326
$111$	−49739.0	−0.383169
$112$	0	0
$113$	−229667.	−1.69201	−0.846006	−	0.533174i	$-0.820999\pi$
$113$	−229667.	−1.69201	−0.846006	+	0.533174i	$0.820999\pi$
$114$	60310.3	0.434639
$115$	45841.3	0.323231
$116$	−191645.	−1.32237
$117$	13280.1	0.0896888
$118$	−333491.	−2.20485
$119$	0	0
$120$	651064.	4.12735
$121$	31649.7	0.196520
$122$	−476248.	−2.89690
$123$	90230.2	0.537761
$124$	164474.	0.960599
$125$	369325.	2.11414
$126$	0	0
$127$	8086.69	0.0444899	0.0222450	−	0.999753i	$-0.492919\pi$
$127$	8086.69	0.0444899	0.0222450	+	0.999753i	$0.492919\pi$
$128$	207004.	1.11675
$129$	−83956.2	−0.444200
$130$	−483691.	−2.51021
$131$	−118712.	−0.604390	−0.302195	−	0.953246i	$-0.597719\pi$
$131$	−118712.	−0.604390	−0.302195	+	0.953246i	$0.597719\pi$
$132$	513362.	2.56442
$133$	0	0
$134$	36193.3	0.174127
$135$	353278.	1.66833
$136$	662847.	3.07303
$137$	65348.7	0.297465	0.148732	−	0.988877i	$-0.452481\pi$
$137$	65348.7	0.297465	0.148732	+	0.988877i	$0.452481\pi$
$138$	76768.5	0.343151
$139$	28437.6	0.124841	0.0624203	−	0.998050i	$-0.480118\pi$
$139$	28437.6	0.124841	0.0624203	+	0.998050i	$0.480118\pi$
$140$	0	0
$141$	95505.7	0.404559
$142$	−23821.3	−0.0991388
$143$	−209651.	−0.857347
$144$	48719.8	0.195794
$145$	−269032.	−1.06263
$146$	582424.	2.26130
$147$	0	0
$148$	214793.	0.806057
$149$	115852.	0.427502	0.213751	−	0.976888i	$-0.431432\pi$
$149$	115852.	0.427502	0.213751	+	0.976888i	$0.431432\pi$
$150$	1.14057e6	4.13898
$151$	35980.9	0.128419	0.0642096	−	0.997936i	$-0.479547\pi$
$151$	35980.9	0.128419	0.0642096	+	0.997936i	$0.479547\pi$
$152$	−143167.	−0.502614
$153$	−46475.6	−0.160508
$154$	0	0
$155$	230888.	0.771920
$156$	−558518.	−1.83749
$157$	−566234.	−1.83336	−0.916678	−	0.399627i	$-0.869140\pi$
$157$	−566234.	−1.83336	−0.916678	+	0.399627i	$0.869140\pi$
$158$	301677.	0.961390
$159$	381908.	1.19802
$160$	−508446.	−1.57016
$161$	0	0
$162$	660217.	1.97651
$163$	−307841.	−0.907523	−0.453761	−	0.891123i	$-0.649918\pi$
$163$	−307841.	−0.907523	−0.453761	+	0.891123i	$0.649918\pi$
$164$	−389650.	−1.13127
$165$	720658.	2.06072
$166$	614464.	1.73072
$167$	−126991.	−0.352357	−0.176179	−	0.984358i	$-0.556374\pi$
$167$	−126991.	−0.352357	−0.176179	+	0.984358i	$0.556374\pi$
$168$	0	0
$169$	−143201.	−0.385681
$170$	1.69274e6	4.49228
$171$	10038.2	0.0262521
$172$	362556.	0.934446
$173$	582515.	1.47976	0.739881	−	0.672738i	$-0.234882\pi$
$173$	582515.	1.47976	0.739881	+	0.672738i	$0.234882\pi$
$174$	−450536.	−1.12812
$175$	0	0
$176$	−769130.	−1.87162
$177$	−540579.	−1.29696
$178$	194259.	0.459548
$179$	−233819.	−0.545440	−0.272720	−	0.962093i	$-0.587923\pi$
$179$	−233819.	−0.545440	−0.272720	+	0.962093i	$0.587923\pi$
$180$	197132.	0.453500
$181$	−318180.	−0.721899	−0.360950	−	0.932585i	$-0.617547\pi$
$181$	−318180.	−0.721899	−0.360950	+	0.932585i	$0.617547\pi$
$182$	0	0
$183$	−771985.	−1.70404
$184$	−182237.	−0.396818
$185$	301527.	0.647734
$186$	386659.	0.819493
$187$	733700.	1.53432
$188$	−412432.	−0.851055
$189$	0	0
$190$	−365611.	−0.734743
$191$	−182032.	−0.361047	−0.180523	−	0.983571i	$-0.557779\pi$
$191$	−182032.	−0.361047	−0.180523	+	0.983571i	$0.557779\pi$
$192$	71178.2	0.139346
$193$	286026.	0.552729	0.276365	−	0.961053i	$-0.410870\pi$
$193$	286026.	0.552729	0.276365	+	0.961053i	$0.410870\pi$
$194$	−438462.	−0.836426
$195$	−784048.	−1.47658
$196$	0	0
$197$	−465880.	−0.855281	−0.427640	−	0.903949i	$-0.640655\pi$
$197$	−465880.	−0.855281	−0.427640	+	0.903949i	$0.640655\pi$
$198$	123921.	0.224637
$199$	−1.06447e6	−1.90547	−0.952736	−	0.303798i	$-0.901745\pi$
$199$	−1.06447e6	−1.90547	−0.952736	+	0.303798i	$0.901745\pi$
$200$	−2.70754e6	−4.78629
$201$	58668.3	0.102427
$202$	−561719.	−0.968591
$203$	0	0
$204$	1.95461e6	3.28839
$205$	−546991.	−0.909067
$206$	−2.08768e6	−3.42765
$207$	12777.5	0.0207263
$208$	836784.	1.34108
$209$	−158471.	−0.250948
$210$	0	0
$211$	1.00586e6	1.55536	0.777679	−	0.628662i	$-0.216397\pi$
$211$	1.00586e6	1.55536	0.777679	+	0.628662i	$0.216397\pi$
$212$	−1.64923e6	−2.52024
$213$	−38613.5	−0.0583164
$214$	−1.84655e6	−2.75630
$215$	508957.	0.750905
$216$	−1.40441e6	−2.04814
$217$	0	0
$218$	−246582.	−0.351415
$219$	944092.	1.33016
$220$	−3.11209e6	−4.33506
$221$	−798238.	−1.09939
$222$	504954.	0.687653
$223$	377403.	0.508210	0.254105	−	0.967177i	$-0.418219\pi$
$223$	377403.	0.508210	0.254105	+	0.967177i	$0.418219\pi$
$224$	0	0
$225$	189839.	0.249994
$226$	2.33160e6	3.03657
$227$	1.28433e6	1.65429	0.827145	−	0.561989i	$-0.189964\pi$
$227$	1.28433e6	1.65429	0.827145	+	0.561989i	$0.189964\pi$
$228$	−422172.	−0.537839
$229$	−299103.	−0.376905	−0.188452	−	0.982082i	$-0.560347\pi$
$229$	−299103.	−0.376905	−0.188452	+	0.982082i	$0.560347\pi$
$230$	−465384.	−0.580085
$231$	0	0
$232$	1.06950e6	1.30455
$233$	564942.	0.681732	0.340866	−	0.940112i	$-0.389280\pi$
$233$	564942.	0.681732	0.340866	+	0.940112i	$0.389280\pi$
$234$	−134821.	−0.160960
$235$	−578972.	−0.683893
$236$	2.33443e6	2.72836
$237$	489010.	0.565518
$238$	0	0
$239$	−1.03635e6	−1.17358	−0.586789	−	0.809740i	$-0.699608\pi$
$239$	−1.03635e6	−1.17358	−0.586789	+	0.809740i	$0.699608\pi$
$240$	−2.87637e6	−3.22342
$241$	−821274.	−0.910847	−0.455423	−	0.890275i	$-0.650512\pi$
$241$	−821274.	−0.910847	−0.455423	+	0.890275i	$0.650512\pi$
$242$	−321310.	−0.352684
$243$	209665.	0.227777
$244$	3.33374e6	3.58473
$245$	0	0
$246$	−916023.	−0.965092
$247$	172410.	0.179813
$248$	−917868.	−0.947656
$249$	996028.	1.01806
$250$	−3.74941e6	−3.79414
$251$	−1.23062e6	−1.23293	−0.616467	−	0.787380i	$-0.711437\pi$
$251$	−1.23062e6	−1.23293	−0.616467	+	0.787380i	$0.711437\pi$
$252$	0	0
$253$	−201716.	−0.198125
$254$	−82096.7	−0.0798438
$255$	2.74388e6	2.64249
$256$	−1.96311e6	−1.87217
$257$	1.05206e6	0.993592	0.496796	−	0.867867i	$-0.334510\pi$
$257$	1.05206e6	0.993592	0.496796	+	0.867867i	$0.334510\pi$
$258$	852329.	0.797183
$259$	0	0
$260$	3.38583e6	3.10622
$261$	−74988.2	−0.0681384
$262$	1.20517e6	1.08467
$263$	1.88157e6	1.67738	0.838688	−	0.544612i	$-0.183323\pi$
$263$	1.88157e6	1.67738	0.838688	+	0.544612i	$0.183323\pi$
$264$	−2.86489e6	−2.52987
$265$	−2.31519e6	−2.02522
$266$	0	0
$267$	314888.	0.270320
$268$	−253353.	−0.215471
$269$	1.05389e6	0.888002	0.444001	−	0.896026i	$-0.353559\pi$
$269$	1.05389e6	0.888002	0.444001	+	0.896026i	$0.353559\pi$
$270$	−3.58650e6	−2.99407
$271$	−688686.	−0.569637	−0.284818	−	0.958581i	$-0.591933\pi$
$271$	−688686.	−0.569637	−0.284818	+	0.958581i	$0.591933\pi$
$272$	−2.92843e6	−2.40001
$273$	0	0
$274$	−663425.	−0.533845
$275$	−2.99695e6	−2.38972
$276$	−537380.	−0.424628
$277$	−522720.	−0.409326	−0.204663	−	0.978832i	$-0.565610\pi$
$277$	−522720.	−0.409326	−0.204663	+	0.978832i	$0.565610\pi$
$278$	−288701.	−0.224045
$279$	64356.3	0.0494972
$280$	0	0
$281$	−2.00251e6	−1.51290	−0.756448	−	0.654053i	$-0.773067\pi$
$281$	−2.00251e6	−1.51290	−0.756448	+	0.654053i	$0.773067\pi$
$282$	−969581.	−0.726041
$283$	2.25219e6	1.67163	0.835813	−	0.549014i	$-0.184997\pi$
$283$	2.25219e6	1.67163	0.835813	+	0.549014i	$0.184997\pi$
$284$	166749.	0.122678
$285$	−592645.	−0.432198
$286$	2.12839e6	1.53864
$287$	0	0
$288$	−141721.	−0.100682
$289$	1.37368e6	0.967476
$290$	2.73123e6	1.90705
$291$	−710734.	−0.492011
$292$	−4.07697e6	−2.79821
$293$	−1.76627e6	−1.20195	−0.600976	−	0.799267i	$-0.705221\pi$
$293$	−1.76627e6	−1.20195	−0.600976	+	0.799267i	$0.705221\pi$
$294$	0	0
$295$	3.27708e6	2.19246
$296$	−1.19868e6	−0.795197
$297$	−1.55453e6	−1.02261
$298$	−1.17614e6	−0.767216
$299$	219459.	0.141963
$300$	−7.98399e6	−5.12173
$301$	0	0
$302$	−365281.	−0.230467
$303$	−910530.	−0.569754
$304$	632507.	0.392537
$305$	4.67990e6	2.88063
$306$	471823.	0.288055
$307$	1.71867e6	1.04075	0.520376	−	0.853937i	$-0.325792\pi$
$307$	1.71867e6	1.04075	0.520376	+	0.853937i	$0.325792\pi$
$308$	0	0
$309$	−3.38407e6	−2.01625
$310$	−2.34399e6	−1.38533
$311$	−1.58149e6	−0.927182	−0.463591	−	0.886049i	$-0.653439\pi$
$311$	−1.58149e6	−0.927182	−0.463591	+	0.886049i	$0.653439\pi$
$312$	3.11689e6	1.81274
$313$	−54617.0	−0.0315114	−0.0157557	−	0.999876i	$-0.505015\pi$
$313$	−54617.0	−0.0315114	−0.0157557	+	0.999876i	$0.505015\pi$
$314$	5.74844e6	3.29023
$315$	0	0
$316$	−2.11174e6	−1.18966
$317$	−1.03467e6	−0.578303	−0.289151	−	0.957283i	$-0.593373\pi$
$317$	−1.03467e6	−0.578303	−0.289151	+	0.957283i	$0.593373\pi$
$318$	−3.87715e6	−2.15003
$319$	1.18382e6	0.651344
$320$	−431495.	−0.235559
$321$	−2.99321e6	−1.62134
$322$	0	0
$323$	−603371.	−0.321794
$324$	−4.62152e6	−2.44581
$325$	3.26057e6	1.71232
$326$	3.12522e6	1.62868
$327$	−399702.	−0.206713
$328$	2.17450e6	1.11603
$329$	0	0
$330$	−7.31617e6	−3.69827
$331$	2.03987e6	1.02337	0.511685	−	0.859173i	$-0.329021\pi$
$331$	2.03987e6	1.02337	0.511685	+	0.859173i	$0.329021\pi$
$332$	−4.30125e6	−2.14165
$333$	84045.7	0.0415341
$334$	1.28923e6	0.632358
$335$	−355657.	−0.173149
$336$	0	0
$337$	1.22774e6	0.588887	0.294444	−	0.955669i	$-0.404866\pi$
$337$	1.22774e6	0.588887	0.294444	+	0.955669i	$0.404866\pi$
$338$	1.45378e6	0.692162
$339$	3.77945e6	1.78620
$340$	−1.18492e7	−5.55892
$341$	−1.01598e6	−0.473150
$342$	−101908.	−0.0471134
$343$	0	0
$344$	−2.02330e6	−0.921857
$345$	−754374.	−0.341223
$346$	−5.91373e6	−2.65565
$347$	3.93267e6	1.75333	0.876665	−	0.481101i	$-0.159763\pi$
$347$	3.93267e6	1.75333	0.876665	+	0.481101i	$0.159763\pi$
$348$	3.15375e6	1.39598
$349$	3.46176e6	1.52136	0.760682	−	0.649125i	$-0.224865\pi$
$349$	3.46176e6	1.52136	0.760682	+	0.649125i	$0.224865\pi$
$350$	0	0
$351$	1.69127e6	0.732734
$352$	2.23732e6	0.962436
$353$	3.91227e6	1.67106	0.835531	−	0.549443i	$-0.185160\pi$
$353$	3.91227e6	1.67106	0.835531	+	0.549443i	$0.185160\pi$
$354$	5.48799e6	2.32758
$355$	234082.	0.0985819
$356$	−1.35981e6	−0.568662
$357$	0	0
$358$	2.37375e6	0.978874
$359$	−949856.	−0.388975	−0.194487	−	0.980905i	$-0.562304\pi$
$359$	−949856.	−0.388975	−0.194487	+	0.980905i	$0.562304\pi$
$360$	−1.10012e6	−0.447389
$361$	130321.	0.0526316
$362$	3.23018e6	1.29556
$363$	−520834.	−0.207459
$364$	0	0
$365$	−5.72325e6	−2.24859
$366$	7.83724e6	3.05816
$367$	−3.72584e6	−1.44397	−0.721986	−	0.691908i	$-0.756770\pi$
$367$	−3.72584e6	−1.44397	−0.721986	+	0.691908i	$0.756770\pi$
$368$	805113.	0.309911
$369$	−152465.	−0.0582914
$370$	−3.06112e6	−1.16245
$371$	0	0
$372$	−2.70661e6	−1.01407
$373$	−4.15376e6	−1.54586	−0.772929	−	0.634493i	$-0.781209\pi$
$373$	−4.15376e6	−1.54586	−0.772929	+	0.634493i	$0.781209\pi$
$374$	−7.44857e6	−2.75356
$375$	−6.07769e6	−2.23183
$376$	2.30163e6	0.839589
$377$	−1.28796e6	−0.466710
$378$	0	0
$379$	2.29264e6	0.819857	0.409928	−	0.912118i	$-0.365554\pi$
$379$	2.29264e6	0.819857	0.409928	+	0.912118i	$0.365554\pi$
$380$	2.55928e6	0.909198
$381$	−133076.	−0.0469665
$382$	1.84800e6	0.647952
$383$	−3.09365e6	−1.07764	−0.538821	−	0.842420i	$-0.681130\pi$
$383$	−3.09365e6	−1.07764	−0.538821	+	0.842420i	$0.681130\pi$
$384$	−3.40651e6	−1.17891
$385$	0	0
$386$	−2.90376e6	−0.991955
$387$	141864.	0.0481497
$388$	3.06923e6	1.03502
$389$	−4.53732e6	−1.52029	−0.760144	−	0.649755i	$-0.774871\pi$
$389$	−4.53732e6	−1.52029	−0.760144	+	0.649755i	$0.774871\pi$
$390$	7.95971e6	2.64994
$391$	−768026.	−0.254059
$392$	0	0
$393$	1.95355e6	0.638034
$394$	4.72965e6	1.53493
$395$	−2.96446e6	−0.955989
$396$	−867445.	−0.277974
$397$	404604.	0.128841	0.0644205	−	0.997923i	$-0.479480\pi$
$397$	404604.	0.128841	0.0644205	+	0.997923i	$0.479480\pi$
$398$	1.08066e7	3.41965
$399$	0	0
$400$	1.19618e7	3.73806
$401$	−5.08752e6	−1.57996	−0.789978	−	0.613135i	$-0.789908\pi$
$401$	−5.08752e6	−1.57996	−0.789978	+	0.613135i	$0.789908\pi$
$402$	−595604.	−0.183820
$403$	1.10535e6	0.339029
$404$	3.93203e6	1.19857
$405$	−6.48769e6	−1.96541
$406$	0	0
$407$	−1.32681e6	−0.397030
$408$	−1.09079e7	−3.24409
$409$	−367772.	−0.108710	−0.0543551	−	0.998522i	$-0.517310\pi$
$409$	−367772.	−0.108710	−0.0543551	+	0.998522i	$0.517310\pi$
$410$	5.55309e6	1.63146
$411$	−1.07539e6	−0.314024
$412$	1.46138e7	4.24150
$413$	0	0
$414$	−129718.	−0.0371964
$415$	−6.03809e6	−1.72099
$416$	−2.43412e6	−0.689618
$417$	−467975.	−0.131790
$418$	1.60880e6	0.450363
$419$	4.12612e6	1.14817	0.574086	−	0.818795i	$-0.305357\pi$
$419$	4.12612e6	1.14817	0.574086	+	0.818795i	$0.305357\pi$
$420$	0	0
$421$	−2.05918e6	−0.566224	−0.283112	−	0.959087i	$-0.591367\pi$
$421$	−2.05918e6	−0.566224	−0.283112	+	0.959087i	$0.591367\pi$
$422$	−1.02115e7	−2.79132
$423$	−161379.	−0.0438527
$424$	9.20376e6	2.48628
$425$	−1.14108e7	−3.06438
$426$	392007.	0.104657
$427$	0	0
$428$	1.29259e7	3.41075
$429$	3.45006e6	0.905072
$430$	−5.16696e6	−1.34761
$431$	−3.23089e6	−0.837777	−0.418889	−	0.908038i	$-0.637580\pi$
$431$	−3.23089e6	−0.837777	−0.418889	+	0.908038i	$0.637580\pi$
$432$	6.20464e6	1.59958
$433$	4.46477e6	1.14440	0.572202	−	0.820113i	$-0.306089\pi$
$433$	4.46477e6	1.14440	0.572202	+	0.820113i	$0.306089\pi$
$434$	0	0
$435$	4.42724e6	1.12179
$436$	1.72607e6	0.434854
$437$	165885.	0.0415530
$438$	−9.58449e6	−2.38717
$439$	−3.96204e6	−0.981201	−0.490601	−	0.871385i	$-0.663223\pi$
$439$	−3.96204e6	−0.981201	−0.490601	+	0.871385i	$0.663223\pi$
$440$	1.73674e7	4.27666
$441$	0	0
$442$	8.10376e6	1.97302
$443$	5.87689e6	1.42278	0.711391	−	0.702797i	$-0.248066\pi$
$443$	5.87689e6	1.42278	0.711391	+	0.702797i	$0.248066\pi$
$444$	−3.53468e6	−0.850927
$445$	−1.90890e6	−0.456966
$446$	−3.83142e6	−0.912059
$447$	−1.90649e6	−0.451299
$448$	0	0
$449$	−2.62215e6	−0.613820	−0.306910	−	0.951739i	$-0.599295\pi$
$449$	−2.62215e6	−0.613820	−0.306910	+	0.951739i	$0.599295\pi$
$450$	−1.92726e6	−0.448651
$451$	2.40693e6	0.557215
$452$	−1.63212e7	−3.75756
$453$	−592109.	−0.135568
$454$	−1.30386e7	−2.96887
$455$	0	0
$456$	2.35599e6	0.530593
$457$	5.12578e6	1.14807	0.574037	−	0.818830i	$-0.305377\pi$
$457$	5.12578e6	1.14807	0.574037	+	0.818830i	$0.305377\pi$
$458$	3.03651e6	0.676411
$459$	−5.91883e6	−1.31131
$460$	3.25769e6	0.717819
$461$	−2.65571e6	−0.582008	−0.291004	−	0.956722i	$-0.593989\pi$
$461$	−2.65571e6	−0.582008	−0.291004	+	0.956722i	$0.593989\pi$
$462$	0	0
$463$	−2.94632e6	−0.638744	−0.319372	−	0.947629i	$-0.603472\pi$
$463$	−2.94632e6	−0.638744	−0.319372	+	0.947629i	$0.603472\pi$
$464$	−4.72502e6	−1.01885
$465$	−3.79954e6	−0.814890
$466$	−5.73533e6	−1.22347
$467$	−1.82563e6	−0.387364	−0.193682	−	0.981064i	$-0.562043\pi$
$467$	−1.82563e6	−0.387364	−0.193682	+	0.981064i	$0.562043\pi$
$468$	943747.	0.199178
$469$	0	0
$470$	5.87776e6	1.22735
$471$	9.31806e6	1.93541
$472$	−1.30276e7	−2.69160
$473$	−2.23957e6	−0.460269
$474$	−4.96446e6	−1.01491
$475$	2.46459e6	0.501200
$476$	0	0
$477$	−645322.	−0.129862
$478$	1.05211e7	2.10616
$479$	−5.92850e6	−1.18061	−0.590304	−	0.807181i	$-0.700992\pi$
$479$	−5.92850e6	−1.18061	−0.590304	+	0.807181i	$0.700992\pi$
$480$	8.36709e6	1.65757
$481$	1.44352e6	0.284486
$482$	8.33763e6	1.63465
$483$	0	0
$484$	2.24917e6	0.436424
$485$	4.30859e6	0.831727
$486$	−2.12853e6	−0.408780
$487$	−3.61261e6	−0.690237	−0.345118	−	0.938559i	$-0.612161\pi$
$487$	−3.61261e6	−0.690237	−0.345118	+	0.938559i	$0.612161\pi$
$488$	−1.86044e7	−3.53644
$489$	5.06589e6	0.958041
$490$	0	0
$491$	−4.32852e6	−0.810281	−0.405140	−	0.914255i	$-0.632777\pi$
$491$	−4.32852e6	−0.810281	−0.405140	+	0.914255i	$0.632777\pi$
$492$	6.41216e6	1.19424
$493$	4.50736e6	0.835228
$494$	−1.75032e6	−0.322700
$495$	−1.21772e6	−0.223375
$496$	4.05510e6	0.740112
$497$	0	0
$498$	−1.01117e7	−1.82706
$499$	−4.93615e6	−0.887435	−0.443718	−	0.896167i	$-0.646341\pi$
$499$	−4.93615e6	−0.887435	−0.443718	+	0.896167i	$0.646341\pi$
$500$	2.62459e7	4.69501
$501$	2.08980e6	0.371972
$502$	1.24933e7	2.21268
$503$	−1.03023e6	−0.181557	−0.0907786	−	0.995871i	$-0.528936\pi$
$503$	−1.03023e6	−0.181557	−0.0907786	+	0.995871i	$0.528936\pi$
$504$	0	0
$505$	5.51979e6	0.963150
$506$	2.04784e6	0.355565
$507$	2.35654e6	0.407151
$508$	574677.	0.0988017
$509$	−4.99120e6	−0.853907	−0.426954	−	0.904274i	$-0.640413\pi$
$509$	−4.99120e6	−0.853907	−0.426954	+	0.904274i	$0.640413\pi$
$510$	−2.78560e7	−4.74235
$511$	0	0
$512$	1.33055e7	2.24314
$513$	1.27840e6	0.214473
$514$	−1.06806e7	−1.78315
$515$	2.05148e7	3.40839
$516$	−5.96630e6	−0.986463
$517$	2.54766e6	0.419194
$518$	0	0
$519$	−9.58598e6	−1.56213
$520$	−1.88951e7	−3.06437
$521$	−9.78050e6	−1.57858	−0.789291	−	0.614020i	$-0.789551\pi$
$521$	−9.78050e6	−1.57858	−0.789291	+	0.614020i	$0.789551\pi$
$522$	761286.	0.122284
$523$	6.73157e6	1.07612	0.538062	−	0.842905i	$-0.319157\pi$
$523$	6.73157e6	1.07612	0.538062	+	0.842905i	$0.319157\pi$
$524$	−8.43622e6	−1.34221
$525$	0	0
$526$	−1.91018e7	−3.01030
$527$	−3.86830e6	−0.606728
$528$	1.26570e7	1.97581
$529$	−6.22519e6	−0.967194
$530$	2.35040e7	3.63456
$531$	913433.	0.140586
$532$	0	0
$533$	−2.61865e6	−0.399264
$534$	−3.19676e6	−0.485129
$535$	1.81453e7	2.74082
$536$	1.41387e6	0.212568
$537$	3.84777e6	0.575803
$538$	−1.06991e7	−1.59365
$539$	0	0
$540$	2.51055e7	3.70497
$541$	−6.68215e6	−0.981574	−0.490787	−	0.871280i	$-0.663291\pi$
$541$	−6.68215e6	−0.981574	−0.490787	+	0.871280i	$0.663291\pi$
$542$	6.99159e6	1.02230
$543$	5.23603e6	0.762084
$544$	8.51851e6	1.23415
$545$	2.42306e6	0.349441
$546$	0	0
$547$	−235187.	−0.0336081	−0.0168041	−	0.999859i	$-0.505349\pi$
$547$	−235187.	−0.0336081	−0.0168041	+	0.999859i	$0.505349\pi$
$548$	4.64397e6	0.660600
$549$	1.30445e6	0.184712
$550$	3.04252e7	4.28872
$551$	−973538.	−0.136607
$552$	2.99892e6	0.418907
$553$	0	0
$554$	5.30668e6	0.734597
$555$	−4.96198e6	−0.683790
$556$	2.02090e6	0.277242
$557$	−4.80203e6	−0.655824	−0.327912	−	0.944708i	$-0.606345\pi$
$557$	−4.80203e6	−0.655824	−0.327912	+	0.944708i	$0.606345\pi$
$558$	−653350.	−0.0888301
$559$	2.43657e6	0.329799
$560$	0	0
$561$	−1.20739e7	−1.61972
$562$	2.03296e7	2.71512
$563$	8.37831e6	1.11400	0.557000	−	0.830512i	$-0.311952\pi$
$563$	8.37831e6	1.11400	0.557000	+	0.830512i	$0.311952\pi$
$564$	6.78706e6	0.898430
$565$	−2.29117e7	−3.01951
$566$	−2.28644e7	−2.99998
$567$	0	0
$568$	−930565.	−0.121025
$569$	−8.38130e6	−1.08525	−0.542626	−	0.839974i	$-0.682570\pi$
$569$	−8.38130e6	−1.08525	−0.542626	+	0.839974i	$0.682570\pi$
$570$	6.01657e6	0.775643
$571$	3.97400e6	0.510079	0.255040	−	0.966931i	$-0.417912\pi$
$571$	3.97400e6	0.510079	0.255040	+	0.966931i	$0.417912\pi$
$572$	−1.48987e7	−1.90397
$573$	2.99555e6	0.381145
$574$	0	0
$575$	3.13716e6	0.395701
$576$	−120272.	−0.0151046
$577$	−1.40884e7	−1.76166	−0.880830	−	0.473432i	$-0.843015\pi$
$577$	−1.40884e7	−1.76166	−0.880830	+	0.473432i	$0.843015\pi$
$578$	−1.39457e7	−1.73628
$579$	−4.70690e6	−0.583497
$580$	−1.91186e7	−2.35986
$581$	0	0
$582$	7.21542e6	0.882986
$583$	1.01876e7	1.24136
$584$	2.27521e7	2.76051
$585$	1.32483e6	0.160056
$586$	1.79313e7	2.15708
$587$	−3.14647e6	−0.376901	−0.188451	−	0.982083i	$-0.560347\pi$
$587$	−3.14647e6	−0.376901	−0.188451	+	0.982083i	$0.560347\pi$
$588$	0	0
$589$	835508.	0.0992345
$590$	−3.32691e7	−3.93470
$591$	7.66662e6	0.902891
$592$	5.29573e6	0.621043
$593$	4.29402e6	0.501450	0.250725	−	0.968058i	$-0.419331\pi$
$593$	4.29402e6	0.501450	0.250725	+	0.968058i	$0.419331\pi$
$594$	1.57817e7	1.83522
$595$	0	0
$596$	8.23297e6	0.949382
$597$	1.75172e7	2.01154
$598$	−2.22797e6	−0.254774
$599$	−6.82650e6	−0.777376	−0.388688	−	0.921370i	$-0.627072\pi$
$599$	−6.82650e6	−0.777376	−0.388688	+	0.921370i	$0.627072\pi$
$600$	4.45558e7	5.05273
$601$	−1.82575e6	−0.206184	−0.103092	−	0.994672i	$-0.532874\pi$
$601$	−1.82575e6	−0.206184	−0.103092	+	0.994672i	$0.532874\pi$
$602$	0	0
$603$	−99133.7	−0.0111027
$604$	2.55697e6	0.285189
$605$	3.15738e6	0.350703
$606$	9.24376e6	1.02251
$607$	2.44884e6	0.269767	0.134883	−	0.990861i	$-0.456934\pi$
$607$	2.44884e6	0.269767	0.134883	+	0.990861i	$0.456934\pi$
$608$	−1.83990e6	−0.201853
$609$	0	0
$610$	−4.75107e7	−5.16972
$611$	−2.77176e6	−0.300367
$612$	−3.30276e6	−0.356450
$613$	−6.05994e6	−0.651354	−0.325677	−	0.945481i	$-0.605592\pi$
$613$	−6.05994e6	−0.651354	−0.325677	+	0.945481i	$0.605592\pi$
$614$	−1.74481e7	−1.86778
$615$	9.00140e6	0.959670
$616$	0	0
$617$	9.33155e6	0.986827	0.493414	−	0.869795i	$-0.335749\pi$
$617$	9.33155e6	0.986827	0.493414	+	0.869795i	$0.335749\pi$
$618$	3.43553e7	3.61845
$619$	9.73252e6	1.02094	0.510468	−	0.859897i	$-0.329472\pi$
$619$	9.73252e6	1.02094	0.510468	+	0.859897i	$0.329472\pi$
$620$	1.64079e7	1.71425
$621$	1.62726e6	0.169328
$622$	1.60554e7	1.66397
$623$	0	0
$624$	−1.37703e7	−1.41573
$625$	1.55092e7	1.58815
$626$	554475.	0.0565518
$627$	2.60783e6	0.264917
$628$	−4.02391e7	−4.07145
$629$	−5.05178e6	−0.509118
$630$	0	0
$631$	8.09784e6	0.809647	0.404824	−	0.914395i	$-0.367333\pi$
$631$	8.09784e6	0.809647	0.404824	+	0.914395i	$0.367333\pi$
$632$	1.17849e7	1.17363
$633$	−1.65526e7	−1.64194
$634$	1.05041e7	1.03785
$635$	806731.	0.0793953
$636$	2.71401e7	2.66053
$637$	0	0
$638$	−1.20183e7	−1.16893
$639$	65246.6	0.00632129
$640$	2.06508e7	1.99291
$641$	−1.54883e7	−1.48887	−0.744436	−	0.667694i	$-0.767282\pi$
$641$	−1.54883e7	−1.48887	−0.744436	+	0.667694i	$0.767282\pi$
$642$	3.03872e7	2.90973
$643$	−1.43966e7	−1.37320	−0.686600	−	0.727036i	$-0.740897\pi$
$643$	−1.43966e7	−1.37320	−0.686600	+	0.727036i	$0.740897\pi$
$644$	0	0
$645$	−8.37550e6	−0.792704
$646$	6.12546e6	0.577507
$647$	6.47992e6	0.608568	0.304284	−	0.952581i	$-0.401583\pi$
$647$	6.47992e6	0.608568	0.304284	+	0.952581i	$0.401583\pi$
$648$	2.57910e7	2.41286
$649$	−1.44202e7	−1.34388
$650$	−3.31015e7	−3.07301
$651$	0	0
$652$	−2.18766e7	−2.01539
$653$	−7.89619e6	−0.724660	−0.362330	−	0.932050i	$-0.618019\pi$
$653$	−7.89619e6	−0.724660	−0.362330	+	0.932050i	$0.618019\pi$
$654$	4.05780e6	0.370977
$655$	−1.18428e7	−1.07857
$656$	−9.60683e6	−0.871607
$657$	−1.59526e6	−0.144185
$658$	0	0
$659$	−1.08756e7	−0.975530	−0.487765	−	0.872975i	$-0.662188\pi$
$659$	−1.08756e7	−0.975530	−0.487765	+	0.872975i	$0.662188\pi$
$660$	5.12132e7	4.57638
$661$	8.09950e6	0.721032	0.360516	−	0.932753i	$-0.382601\pi$
$661$	8.09950e6	0.721032	0.360516	+	0.932753i	$0.382601\pi$
$662$	−2.07089e7	−1.83659
$663$	1.31360e7	1.16059
$664$	2.40037e7	2.11280
$665$	0	0
$666$	−853238.	−0.0745391
$667$	−1.23921e6	−0.107852
$668$	−9.02458e6	−0.782503
$669$	−6.21062e6	−0.536500
$670$	3.61066e6	0.310741
$671$	−2.05930e7	−1.76569
$672$	0	0
$673$	6.23497e6	0.530636	0.265318	−	0.964161i	$-0.414523\pi$
$673$	6.23497e6	0.530636	0.265318	+	0.964161i	$0.414523\pi$
$674$	−1.24641e7	−1.05685
$675$	2.41767e7	2.04238
$676$	−1.01765e7	−0.856507
$677$	−1.16588e7	−0.977649	−0.488824	−	0.872382i	$-0.662574\pi$
$677$	−1.16588e7	−0.977649	−0.488824	+	0.872382i	$0.662574\pi$
$678$	−3.83693e7	−3.20560
$679$	0	0
$680$	6.61259e7	5.48402
$681$	−2.11352e7	−1.74638
$682$	1.03143e7	0.849139
$683$	−1.22340e6	−0.100350	−0.0501748	−	0.998740i	$-0.515978\pi$
$683$	−1.22340e6	−0.100350	−0.0501748	+	0.998740i	$0.515978\pi$
$684$	713358.	0.0582998
$685$	6.51921e6	0.530846
$686$	0	0
$687$	4.92209e6	0.397885
$688$	8.93884e6	0.719962
$689$	−1.10837e7	−0.889480
$690$	7.65845e6	0.612376
$691$	5.82015e6	0.463702	0.231851	−	0.972751i	$-0.425522\pi$
$691$	5.82015e6	0.463702	0.231851	+	0.972751i	$0.425522\pi$
$692$	4.13961e7	3.28620
$693$	0	0
$694$	−3.99247e7	−3.14661
$695$	2.83695e6	0.222787
$696$	−1.76000e7	−1.37717
$697$	9.16430e6	0.714525
$698$	−3.51440e7	−2.73031
$699$	−9.29680e6	−0.719682
$700$	0	0
$701$	9.44191e6	0.725713	0.362856	−	0.931845i	$-0.381802\pi$
$701$	9.44191e6	0.725713	0.362856	+	0.931845i	$0.381802\pi$
$702$	−1.71699e7	−1.31500
$703$	1.09113e6	0.0832696
$704$	1.89871e6	0.144387
$705$	9.52768e6	0.721962
$706$	−3.97177e7	−2.99897
$707$	0	0
$708$	−3.84159e7	−2.88024
$709$	7.88964e6	0.589443	0.294721	−	0.955583i	$-0.404773\pi$
$709$	7.88964e6	0.589443	0.294721	+	0.955583i	$0.404773\pi$
$710$	−2.37642e6	−0.176920
$711$	−826296.	−0.0613002
$712$	7.58862e6	0.561000
$713$	1.06351e6	0.0783464
$714$	0	0
$715$	−2.09149e7	−1.52999
$716$	−1.66162e7	−1.21129
$717$	1.70544e7	1.23891
$718$	9.64300e6	0.698073
$719$	−1.89500e7	−1.36706	−0.683530	−	0.729922i	$-0.739556\pi$
$719$	−1.89500e7	−1.36706	−0.683530	+	0.729922i	$0.739556\pi$
$720$	4.86030e6	0.349408
$721$	0	0
$722$	−1.32303e6	−0.0944552
$723$	1.35150e7	0.961550
$724$	−2.26113e7	−1.60317
$725$	−1.84113e7	−1.30088
$726$	5.28754e6	0.372316
$727$	−6.46947e6	−0.453976	−0.226988	−	0.973898i	$-0.572888\pi$
$727$	−6.46947e6	−0.453976	−0.226988	+	0.973898i	$0.572888\pi$
$728$	0	0
$729$	1.23527e7	0.860879
$730$	5.81028e7	4.03543
$731$	−8.52707e6	−0.590210
$732$	−5.48607e7	−3.78428
$733$	−6.39936e6	−0.439923	−0.219962	−	0.975509i	$-0.570593\pi$
$733$	−6.39936e6	−0.439923	−0.219962	+	0.975509i	$0.570593\pi$
$734$	3.78249e7	2.59142
$735$	0	0
$736$	−2.34199e6	−0.159364
$737$	1.56500e6	0.106132
$738$	1.54783e6	0.104613
$739$	−1.28565e7	−0.865987	−0.432993	−	0.901397i	$-0.642543\pi$
$739$	−1.28565e7	−0.865987	−0.432993	+	0.901397i	$0.642543\pi$
$740$	2.14278e7	1.43846
$741$	−2.83721e6	−0.189822
$742$	0	0
$743$	−2.19966e7	−1.46179	−0.730893	−	0.682492i	$-0.760896\pi$
$743$	−2.19966e7	−1.46179	−0.730893	+	0.682492i	$0.760896\pi$
$744$	1.51046e7	1.00041
$745$	1.15574e7	0.762906
$746$	4.21693e7	2.77427
$747$	−1.68302e6	−0.110354
$748$	5.21400e7	3.40735
$749$	0	0
$750$	6.17011e7	4.00534
$751$	4.73982e6	0.306663	0.153332	−	0.988175i	$-0.451000\pi$
$751$	4.73982e6	0.306663	0.153332	+	0.988175i	$0.451000\pi$
$752$	−1.01685e7	−0.655712
$753$	2.02514e7	1.30157
$754$	1.30754e7	0.837581
$755$	3.58947e6	0.229173
$756$	0	0
$757$	−8.15849e6	−0.517452	−0.258726	−	0.965951i	$-0.583303\pi$
$757$	−8.15849e6	−0.517452	−0.258726	+	0.965951i	$0.583303\pi$
$758$	−2.32750e7	−1.47135
$759$	3.31948e6	0.209154
$760$	−1.42824e7	−0.896949
$761$	2.40805e7	1.50731	0.753657	−	0.657268i	$-0.228288\pi$
$761$	2.40805e7	1.50731	0.753657	+	0.657268i	$0.228288\pi$
$762$	1.35100e6	0.0842884
$763$	0	0
$764$	−1.29360e7	−0.801800
$765$	−4.63642e6	−0.286437
$766$	3.14069e7	1.93399
$767$	1.56886e7	0.962933
$768$	3.23054e7	1.97639
$769$	3.57395e6	0.217938	0.108969	−	0.994045i	$-0.465245\pi$
$769$	3.57395e6	0.217938	0.108969	+	0.994045i	$0.465245\pi$
$770$	0	0
$771$	−1.73129e7	−1.04890
$772$	2.03263e7	1.22748
$773$	−1.38262e7	−0.832251	−0.416126	−	0.909307i	$-0.636612\pi$
$773$	−1.38262e7	−0.832251	−0.416126	+	0.909307i	$0.636612\pi$
$774$	−1.44021e6	−0.0864117
$775$	1.58009e7	0.944990
$776$	−1.71283e7	−1.02108
$777$	0	0
$778$	4.60632e7	2.72838
$779$	−1.97938e6	−0.116865
$780$	−5.57180e7	−3.27913
$781$	−1.03003e6	−0.0604260
$782$	7.79705e6	0.455946
$783$	−9.55002e6	−0.556672
$784$	0	0
$785$	−5.64877e7	−3.27175
$786$	−1.98326e7	−1.14505
$787$	−2.52043e7	−1.45057	−0.725283	−	0.688451i	$-0.758291\pi$
$787$	−2.52043e7	−1.45057	−0.725283	+	0.688451i	$0.758291\pi$
$788$	−3.31075e7	−1.89938
$789$	−3.09635e7	−1.77075
$790$	3.00954e7	1.71567
$791$	0	0
$792$	4.84090e6	0.274229
$793$	2.24045e7	1.26518
$794$	−4.10757e6	−0.231224
$795$	3.80993e7	2.13796
$796$	−7.56464e7	−4.23161
$797$	−3.37562e7	−1.88238	−0.941190	−	0.337877i	$-0.890291\pi$
$797$	−3.37562e7	−1.88238	−0.941190	+	0.337877i	$0.890291\pi$
$798$	0	0
$799$	9.70011e6	0.537539
$800$	−3.47956e7	−1.92220
$801$	−532076.	−0.0293017
$802$	5.16488e7	2.83547
$803$	2.51841e7	1.37828
$804$	4.16923e6	0.227466
$805$	0	0
$806$	−1.12216e7	−0.608437
$807$	−1.73430e7	−0.937433
$808$	−2.19433e7	−1.18242
$809$	−2.10318e7	−1.12981	−0.564906	−	0.825155i	$-0.691088\pi$
$809$	−2.10318e7	−1.12981	−0.564906	+	0.825155i	$0.691088\pi$
$810$	6.58635e7	3.52722
$811$	2.27692e7	1.21561	0.607807	−	0.794085i	$-0.292050\pi$
$811$	2.27692e7	1.21561	0.607807	+	0.794085i	$0.292050\pi$
$812$	0	0
$813$	1.13332e7	0.601346
$814$	1.34699e7	0.712530
$815$	−3.07103e7	−1.61954
$816$	4.81908e7	2.53361
$817$	1.84175e6	0.0965328
$818$	3.73365e6	0.195097
$819$	0	0
$820$	−3.88716e7	−2.01882
$821$	−2.30273e7	−1.19230	−0.596149	−	0.802874i	$-0.703303\pi$
$821$	−2.30273e7	−1.19230	−0.596149	+	0.802874i	$0.703303\pi$
$822$	1.09175e7	0.563562
$823$	−1.70408e7	−0.876979	−0.438490	−	0.898736i	$-0.644486\pi$
$823$	−1.70408e7	−0.876979	−0.438490	+	0.898736i	$0.644486\pi$
$824$	−8.15542e7	−4.18435
$825$	4.93184e7	2.52275
$826$	0	0
$827$	3.62225e6	0.184168	0.0920840	−	0.995751i	$-0.470647\pi$
$827$	3.62225e6	0.184168	0.0920840	+	0.995751i	$0.470647\pi$
$828$	908028.	0.0460281
$829$	−1.36980e7	−0.692261	−0.346131	−	0.938186i	$-0.612505\pi$
$829$	−1.36980e7	−0.692261	−0.346131	+	0.938186i	$0.612505\pi$
$830$	6.12991e7	3.08858
$831$	8.60198e6	0.432112
$832$	−2.06573e6	−0.103458
$833$	0	0
$834$	4.75091e6	0.236517
$835$	−1.26687e7	−0.628805
$836$	−1.12616e7	−0.557296
$837$	8.19600e6	0.404379
$838$	−4.18887e7	−2.06057
$839$	8.15272e6	0.399850	0.199925	−	0.979811i	$-0.435930\pi$
$839$	8.15272e6	0.399850	0.199925	+	0.979811i	$0.435930\pi$
$840$	0	0
$841$	−1.32385e7	−0.645431
$842$	2.09049e7	1.01617
$843$	3.29537e7	1.59711
$844$	7.14807e7	3.45408
$845$	−1.42858e7	−0.688274
$846$	1.63833e6	0.0787002
$847$	0	0
$848$	−4.06618e7	−1.94177
$849$	−3.70625e7	−1.76468
$850$	1.15843e8	5.49948
$851$	1.38889e6	0.0657420
$852$	−2.74405e6	−0.129507
$853$	3.76514e7	1.77178	0.885888	−	0.463899i	$-0.153550\pi$
$853$	3.76514e7	1.77178	0.885888	+	0.463899i	$0.153550\pi$
$854$	0	0
$855$	1.00141e6	0.0468487
$856$	−7.21345e7	−3.36480
$857$	−1.18679e7	−0.551980	−0.275990	−	0.961160i	$-0.589006\pi$
$857$	−1.18679e7	−0.551980	−0.275990	+	0.961160i	$0.589006\pi$
$858$	−3.50252e7	−1.62429
$859$	8.63985e6	0.399506	0.199753	−	0.979846i	$-0.435986\pi$
$859$	8.63985e6	0.399506	0.199753	+	0.979846i	$0.435986\pi$
$860$	3.61687e7	1.66758
$861$	0	0
$862$	3.28002e7	1.50352
$863$	−1.39409e7	−0.637181	−0.318591	−	0.947892i	$-0.603210\pi$
$863$	−1.39409e7	−0.637181	−0.318591	+	0.947892i	$0.603210\pi$
$864$	−1.80487e7	−0.822547
$865$	5.81119e7	2.64073
$866$	−4.53267e7	−2.05380
$867$	−2.26055e7	−1.02133
$868$	0	0
$869$	1.30446e7	0.585976
$870$	−4.49456e7	−2.01321
$871$	−1.70266e6	−0.0760473
$872$	−9.63260e6	−0.428995
$873$	1.20095e6	0.0533322
$874$	−1.68407e6	−0.0745731
$875$	0	0
$876$	6.70914e7	2.95397
$877$	2.92561e7	1.28445	0.642224	−	0.766517i	$-0.278012\pi$
$877$	2.92561e7	1.28445	0.642224	+	0.766517i	$0.278012\pi$
$878$	4.02229e7	1.76091
$879$	2.90661e7	1.26886
$880$	−7.67286e7	−3.34003
$881$	1.44235e7	0.626081	0.313041	−	0.949740i	$-0.398652\pi$
$881$	1.44235e7	0.626081	0.313041	+	0.949740i	$0.398652\pi$
$882$	0	0
$883$	−4.94360e6	−0.213374	−0.106687	−	0.994293i	$-0.534024\pi$
$883$	−4.94360e6	−0.213374	−0.106687	+	0.994293i	$0.534024\pi$
$884$	−5.67263e7	−2.44149
$885$	−5.39283e7	−2.31451
$886$	−5.96626e7	−2.55339
$887$	1.32368e7	0.564903	0.282452	−	0.959282i	$-0.408852\pi$
$887$	1.32368e7	0.564903	0.282452	+	0.959282i	$0.408852\pi$
$888$	1.97258e7	0.839463
$889$	0	0
$890$	1.93793e7	0.820094
$891$	2.85479e7	1.20470
$892$	2.68200e7	1.12862
$893$	−2.09511e6	−0.0879181
$894$	1.93548e7	0.809924
$895$	−2.33259e7	−0.973375
$896$	0	0
$897$	−3.61147e6	−0.149866
$898$	2.66202e7	1.10159
$899$	−6.24150e6	−0.257567
$900$	1.34908e7	0.555177
$901$	3.87888e7	1.59182
$902$	−2.44353e7	−1.00001
$903$	0	0
$904$	9.10827e7	3.70693
$905$	−3.17417e7	−1.28828
$906$	6.01113e6	0.243297
$907$	7.51989e6	0.303524	0.151762	−	0.988417i	$-0.451505\pi$
$907$	7.51989e6	0.303524	0.151762	+	0.988417i	$0.451505\pi$
$908$	9.12701e7	3.67379
$909$	1.53855e6	0.0617593
$910$	0	0
$911$	4.53248e7	1.80942	0.904710	−	0.426027i	$-0.140087\pi$
$911$	4.53248e7	1.80942	0.904710	+	0.426027i	$0.140087\pi$
$912$	−1.04087e7	−0.414388
$913$	2.65695e7	1.05489
$914$	−5.20373e7	−2.06039
$915$	−7.70134e7	−3.04098
$916$	−2.12556e7	−0.837016
$917$	0	0
$918$	6.00883e7	2.35333
$919$	1.47088e7	0.574497	0.287249	−	0.957856i	$-0.407259\pi$
$919$	1.47088e7	0.574497	0.287249	+	0.957856i	$0.407259\pi$
$920$	−1.81800e7	−0.708148
$921$	−2.82828e7	−1.09869
$922$	2.69610e7	1.04450
$923$	1.12064e6	0.0432973
$924$	0	0
$925$	2.06351e7	0.792960
$926$	2.99112e7	1.14632
$927$	5.71818e6	0.218554
$928$	1.37446e7	0.523917
$929$	1.35395e7	0.514711	0.257356	−	0.966317i	$-0.417149\pi$
$929$	1.35395e7	0.514711	0.257356	+	0.966317i	$0.417149\pi$
$930$	3.85732e7	1.46244
$931$	0	0
$932$	4.01473e7	1.51397
$933$	2.60253e7	0.978795
$934$	1.85339e7	0.695183
$935$	7.31942e7	2.73809
$936$	−5.26671e6	−0.196494
$937$	1.21203e7	0.450988	0.225494	−	0.974245i	$-0.427600\pi$
$937$	1.21203e7	0.450988	0.225494	+	0.974245i	$0.427600\pi$
$938$	0	0
$939$	898788.	0.0332655
$940$	−4.11444e7	−1.51877
$941$	−2.61927e7	−0.964288	−0.482144	−	0.876092i	$-0.660142\pi$
$941$	−2.61927e7	−0.964288	−0.482144	+	0.876092i	$0.660142\pi$
$942$	−9.45976e7	−3.47338
$943$	−2.51954e6	−0.0922661
$944$	5.75555e7	2.10212
$945$	0	0
$946$	2.27363e7	0.826021
$947$	−3.47875e7	−1.26051	−0.630257	−	0.776386i	$-0.717051\pi$
$947$	−3.47875e7	−1.26051	−0.630257	+	0.776386i	$0.717051\pi$
$948$	3.47512e7	1.25588
$949$	−2.73993e7	−0.987585
$950$	−2.50207e7	−0.899478
$951$	1.70268e7	0.610494
$952$	0	0
$953$	1.16268e7	0.414695	0.207347	−	0.978267i	$-0.433517\pi$
$953$	1.16268e7	0.414695	0.207347	+	0.978267i	$0.433517\pi$
$954$	6.55136e6	0.233056
$955$	−1.81595e7	−0.644312
$956$	−7.36477e7	−2.60624
$957$	−1.94812e7	−0.687602
$958$	6.01865e7	2.11878
$959$	0	0
$960$	7.10077e6	0.248672
$961$	−2.32726e7	−0.812898
$962$	−1.46547e7	−0.510552
$963$	5.05772e6	0.175747
$964$	−5.83634e7	−2.02278
$965$	2.85341e7	0.986383
$966$	0	0
$967$	−2.70316e7	−0.929622	−0.464811	−	0.885410i	$-0.653878\pi$
$967$	−2.70316e7	−0.929622	−0.464811	+	0.885410i	$0.653878\pi$
$968$	−1.25518e7	−0.430544
$969$	9.92919e6	0.339707
$970$	−4.37411e7	−1.49266
$971$	5.13472e6	0.174771	0.0873854	−	0.996175i	$-0.472149\pi$
$971$	5.13472e6	0.174771	0.0873854	+	0.996175i	$0.472149\pi$
$972$	1.48997e7	0.505840
$973$	0	0
$974$	3.66754e7	1.23873
$975$	−5.36565e7	−1.80764
$976$	8.21934e7	2.76193
$977$	−5.11922e6	−0.171580	−0.0857902	−	0.996313i	$-0.527341\pi$
$977$	−5.11922e6	−0.171580	−0.0857902	+	0.996313i	$0.527341\pi$
$978$	−5.14293e7	−1.71935
$979$	8.39978e6	0.280099
$980$	0	0
$981$	675390.	0.0224069
$982$	4.39434e7	1.45417
$983$	−3.30087e7	−1.08954	−0.544771	−	0.838585i	$-0.683384\pi$
$983$	−3.30087e7	−1.08954	−0.544771	+	0.838585i	$0.683384\pi$
$984$	−3.57840e7	−1.17815
$985$	−4.64764e7	−1.52631
$986$	−4.57590e7	−1.49894
$987$	0	0
$988$	1.22522e7	0.399321
$989$	2.34435e6	0.0762134
$990$	1.23624e7	0.400879
$991$	−3.54462e7	−1.14653	−0.573265	−	0.819370i	$-0.694324\pi$
$991$	−3.54462e7	−1.14653	−0.573265	+	0.819370i	$0.694324\pi$
$992$	−1.17959e7	−0.380585
$993$	−3.35685e7	−1.08034
$994$	0	0
$995$	−1.06192e8	−3.40044
$996$	7.07822e7	2.26087
$997$	−4.51197e7	−1.43757	−0.718784	−	0.695233i	$-0.755301\pi$
$997$	−4.51197e7	−1.43757	−0.718784	+	0.695233i	$0.755301\pi$
$998$	5.01121e7	1.59264
$999$	1.07035e7	0.339322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.6.a.c.1.1		2
7.6	odd	2		19.6.a.c.1.1	✓	2
21.20	even	2		171.6.a.f.1.2		2
28.27	even	2		304.6.a.g.1.1		2
35.34	odd	2		475.6.a.d.1.2		2
133.132	even	2		361.6.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.6.a.c.1.1	✓	2	7.6	odd	2
171.6.a.f.1.2		2	21.20	even	2
304.6.a.g.1.1		2	28.27	even	2
361.6.a.d.1.2		2	133.132	even	2
475.6.a.d.1.2		2	35.34	odd	2
931.6.a.c.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-10.1521 q^{2} -16.4562 q^{3} +71.0645 q^{4} +99.7603 q^{5} +167.064 q^{6} -396.585 q^{8} +27.8066 q^{9} +O(q^{10})\)	\(q-10.1521 q^{2} -16.4562 q^{3} +71.0645 q^{4} +99.7603 q^{5} +167.064 q^{6} -396.585 q^{8} +27.8066 q^{9} -1012.77 q^{10} -438.977 q^{11} -1169.45 q^{12} +477.590 q^{13} -1641.68 q^{15} +1752.10 q^{16} -1671.39 q^{17} -282.294 q^{18} +361.000 q^{19} +7089.42 q^{20} +4456.52 q^{22} +459.514 q^{23} +6526.29 q^{24} +6827.12 q^{25} -4848.53 q^{26} +3541.27 q^{27} -2696.78 q^{29} +16666.4 q^{30} +2314.43 q^{31} -5096.67 q^{32} +7223.89 q^{33} +16968.0 q^{34} +1976.06 q^{36} +3022.51 q^{37} -3664.90 q^{38} -7859.32 q^{39} -39563.5 q^{40} -5483.05 q^{41} +5101.80 q^{43} -31195.7 q^{44} +2773.99 q^{45} -4665.02 q^{46} -5803.63 q^{47} -28832.8 q^{48} -69309.4 q^{50} +27504.7 q^{51} +33939.7 q^{52} -23207.5 q^{53} -35951.2 q^{54} -43792.5 q^{55} -5940.69 q^{57} +27377.9 q^{58} +32849.5 q^{59} -116665. q^{60} +46911.5 q^{61} -23496.2 q^{62} -4325.31 q^{64} +47644.5 q^{65} -73337.4 q^{66} -3565.12 q^{67} -118776. q^{68} -7561.86 q^{69} +2346.44 q^{71} -11027.7 q^{72} -57370.0 q^{73} -30684.7 q^{74} -112349. q^{75} +25654.3 q^{76} +79788.3 q^{78} -29715.8 q^{79} +174790. q^{80} -65032.8 q^{81} +55664.3 q^{82} -60526.0 q^{83} -166738. q^{85} -51793.8 q^{86} +44378.8 q^{87} +174092. q^{88} -19134.9 q^{89} -28161.8 q^{90} +32655.1 q^{92} -38086.7 q^{93} +58918.9 q^{94} +36013.5 q^{95} +83871.9 q^{96} +43189.4 q^{97} -12206.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 7 q^{2} + 7 q^{3} + 49 q^{4} + 133 q^{5} + 241 q^{6} - 567 q^{8} + 335 q^{9}+O(q^{10}) \) 2 * q - 7 * q^2 + 7 * q^3 + 49 * q^4 + 133 * q^5 + 241 * q^6 - 567 * q^8 + 335 * q^9	\( 2 q - 7 q^{2} + 7 q^{3} + 49 q^{4} + 133 q^{5} + 241 q^{6} - 567 q^{8} + 335 q^{9} - 908 q^{10} - 705 q^{11} - 1687 q^{12} + 1341 q^{13} - 862 q^{15} + 1921 q^{16} - 2784 q^{17} + 686 q^{18} + 722 q^{19} + 6356 q^{20} + 3618 q^{22} - 2713 q^{23} + 2529 q^{24} + 4807 q^{25} - 2127 q^{26} + 5047 q^{27} - 7775 q^{29} + 19124 q^{30} - 7132 q^{31} + 889 q^{32} + 984 q^{33} + 13461 q^{34} - 4802 q^{36} - 6248 q^{37} - 2527 q^{38} + 12393 q^{39} - 45228 q^{40} + 4174 q^{41} + 25357 q^{43} - 25326 q^{44} + 12985 q^{45} - 14665 q^{46} - 11727 q^{47} - 24871 q^{48} - 75677 q^{50} + 1407 q^{51} + 14889 q^{52} - 29133 q^{53} - 31205 q^{54} - 52635 q^{55} + 2527 q^{57} + 11371 q^{58} + 64515 q^{59} - 133868 q^{60} + 40939 q^{61} - 53272 q^{62} + 9137 q^{64} + 76344 q^{65} - 93006 q^{66} + 19039 q^{67} - 94227 q^{68} - 81977 q^{69} - 70236 q^{71} - 63378 q^{72} - 67058 q^{73} - 59906 q^{74} - 159733 q^{75} + 17689 q^{76} + 143625 q^{78} - 32850 q^{79} + 180404 q^{80} - 104362 q^{81} + 86104 q^{82} - 71534 q^{83} - 203721 q^{85} + 12052 q^{86} - 74737 q^{87} + 219426 q^{88} + 87268 q^{89} + 4024 q^{90} + 102655 q^{92} - 259664 q^{93} + 40248 q^{94} + 48013 q^{95} + 224273 q^{96} + 62458 q^{97} - 93927 q^{99}+O(q^{100}) \) 2 * q - 7 * q^2 + 7 * q^3 + 49 * q^4 + 133 * q^5 + 241 * q^6 - 567 * q^8 + 335 * q^9 - 908 * q^10 - 705 * q^11 - 1687 * q^12 + 1341 * q^13 - 862 * q^15 + 1921 * q^16 - 2784 * q^17 + 686 * q^18 + 722 * q^19 + 6356 * q^20 + 3618 * q^22 - 2713 * q^23 + 2529 * q^24 + 4807 * q^25 - 2127 * q^26 + 5047 * q^27 - 7775 * q^29 + 19124 * q^30 - 7132 * q^31 + 889 * q^32 + 984 * q^33 + 13461 * q^34 - 4802 * q^36 - 6248 * q^37 - 2527 * q^38 + 12393 * q^39 - 45228 * q^40 + 4174 * q^41 + 25357 * q^43 - 25326 * q^44 + 12985 * q^45 - 14665 * q^46 - 11727 * q^47 - 24871 * q^48 - 75677 * q^50 + 1407 * q^51 + 14889 * q^52 - 29133 * q^53 - 31205 * q^54 - 52635 * q^55 + 2527 * q^57 + 11371 * q^58 + 64515 * q^59 - 133868 * q^60 + 40939 * q^61 - 53272 * q^62 + 9137 * q^64 + 76344 * q^65 - 93006 * q^66 + 19039 * q^67 - 94227 * q^68 - 81977 * q^69 - 70236 * q^71 - 63378 * q^72 - 67058 * q^73 - 59906 * q^74 - 159733 * q^75 + 17689 * q^76 + 143625 * q^78 - 32850 * q^79 + 180404 * q^80 - 104362 * q^81 + 86104 * q^82 - 71534 * q^83 - 203721 * q^85 + 12052 * q^86 - 74737 * q^87 + 219426 * q^88 + 87268 * q^89 + 4024 * q^90 + 102655 * q^92 - 259664 * q^93 + 40248 * q^94 + 48013 * q^95 + 224273 * q^96 + 62458 * q^97 - 93927 * q^99

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