LMFDB - Embedded newform 529.4.a.m.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.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:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.976043 q^{2} -6.99573 q^{3} -7.04734 q^{4} -1.89650 q^{5} -6.82813 q^{6} +11.4459 q^{7} -14.6869 q^{8} +21.9402 q^{9} -1.85107 q^{10} +24.2529 q^{11} +49.3013 q^{12} -51.2775 q^{13} +11.1717 q^{14} +13.2674 q^{15} +42.0437 q^{16} +83.4618 q^{17} +21.4146 q^{18} +150.925 q^{19} +13.3653 q^{20} -80.0727 q^{21} +23.6719 q^{22} +102.745 q^{24} -121.403 q^{25} -50.0490 q^{26} +35.3970 q^{27} -80.6634 q^{28} -252.052 q^{29} +12.9495 q^{30} +43.7775 q^{31} +158.531 q^{32} -169.667 q^{33} +81.4623 q^{34} -21.7072 q^{35} -154.620 q^{36} -35.7950 q^{37} +147.309 q^{38} +358.723 q^{39} +27.8536 q^{40} +333.709 q^{41} -78.1544 q^{42} -293.864 q^{43} -170.918 q^{44} -41.6096 q^{45} -103.530 q^{47} -294.126 q^{48} -211.990 q^{49} -118.495 q^{50} -583.876 q^{51} +361.370 q^{52} -211.734 q^{53} +34.5490 q^{54} -45.9956 q^{55} -168.105 q^{56} -1055.83 q^{57} -246.014 q^{58} -115.001 q^{59} -93.4998 q^{60} -184.073 q^{61} +42.7287 q^{62} +251.126 q^{63} -181.616 q^{64} +97.2477 q^{65} -165.602 q^{66} +545.337 q^{67} -588.184 q^{68} -21.1872 q^{70} -582.298 q^{71} -322.232 q^{72} +47.4045 q^{73} -34.9374 q^{74} +849.304 q^{75} -1063.62 q^{76} +277.597 q^{77} +350.129 q^{78} -1250.01 q^{79} -79.7359 q^{80} -840.013 q^{81} +325.714 q^{82} +759.853 q^{83} +564.299 q^{84} -158.285 q^{85} -286.824 q^{86} +1763.29 q^{87} -356.199 q^{88} -785.740 q^{89} -40.6127 q^{90} -586.919 q^{91} -306.256 q^{93} -101.050 q^{94} -286.229 q^{95} -1109.04 q^{96} +560.129 q^{97} -206.912 q^{98} +532.113 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

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 $

$2$	0.976043	0.345083	0.172542	−	0.985002i	$-0.444802\pi$
$2$	0.976043	0.345083	0.172542	+	0.985002i	$0.444802\pi$
$3$	−6.99573	−1.34633	−0.673164	−	0.739493i	$-0.735065\pi$
$3$	−6.99573	−1.34633	−0.673164	+	0.739493i	$0.735065\pi$
$4$	−7.04734	−0.880918
$5$	−1.89650	−0.169628	−0.0848140	−	0.996397i	$-0.527030\pi$
$5$	−1.89650	−0.169628	−0.0848140	+	0.996397i	$0.527030\pi$
$6$	−6.82813	−0.464595
$7$	11.4459	0.618023	0.309011	−	0.951058i	$-0.400002\pi$
$7$	11.4459	0.618023	0.309011	+	0.951058i	$0.400002\pi$
$8$	−14.6869	−0.649073
$9$	21.9402	0.812600
$10$	−1.85107	−0.0585358
$11$	24.2529	0.664775	0.332387	−	0.943143i	$-0.392146\pi$
$11$	24.2529	0.664775	0.332387	+	0.943143i	$0.392146\pi$
$12$	49.3013	1.18600
$13$	−51.2775	−1.09399	−0.546993	−	0.837137i	$-0.684227\pi$
$13$	−51.2775	−1.09399	−0.546993	+	0.837137i	$0.684227\pi$
$14$	11.1717	0.213269
$15$	13.2674	0.228375
$16$	42.0437	0.656933
$17$	83.4618	1.19073	0.595366	−	0.803454i	$-0.297007\pi$
$17$	83.4618	1.19073	0.595366	+	0.803454i	$0.297007\pi$
$18$	21.4146	0.280415
$19$	150.925	1.82234	0.911171	−	0.412029i	$-0.135180\pi$
$19$	150.925	1.82234	0.911171	+	0.412029i	$0.135180\pi$
$20$	13.3653	0.149428
$21$	−80.0727	−0.832061
$22$	23.6719	0.229403
$23$	0	0
$23$	0	0
$24$	102.745	0.873866
$25$	−121.403	−0.971226
$26$	−50.0490	−0.377516
$27$	35.3970	0.252302
$28$	−80.6634	−0.544427
$29$	−252.052	−1.61396	−0.806982	−	0.590576i	$-0.798901\pi$
$29$	−252.052	−1.61396	−0.806982	+	0.590576i	$0.798901\pi$
$30$	12.9495	0.0788084
$31$	43.7775	0.253635	0.126817	−	0.991926i	$-0.459524\pi$
$31$	43.7775	0.253635	0.126817	+	0.991926i	$0.459524\pi$
$32$	158.531	0.875770
$33$	−169.667	−0.895005
$34$	81.4623	0.410902
$35$	−21.7072	−0.104834
$36$	−154.620	−0.715833
$37$	−35.7950	−0.159045	−0.0795224	−	0.996833i	$-0.525340\pi$
$37$	−35.7950	−0.159045	−0.0795224	+	0.996833i	$0.525340\pi$
$38$	147.309	0.628860
$39$	358.723	1.47286
$40$	27.8536	0.110101
$41$	333.709	1.27113	0.635567	−	0.772045i	$-0.280766\pi$
$41$	333.709	1.27113	0.635567	+	0.772045i	$0.280766\pi$
$42$	−78.1544	−0.287131
$43$	−293.864	−1.04218	−0.521092	−	0.853501i	$-0.674475\pi$
$43$	−293.864	−1.04218	−0.521092	+	0.853501i	$0.674475\pi$
$44$	−170.918	−0.585612
$45$	−41.6096	−0.137840
$46$	0	0
$47$	−103.530	−0.321307	−0.160653	−	0.987011i	$-0.551360\pi$
$47$	−103.530	−0.321307	−0.160653	+	0.987011i	$0.551360\pi$
$48$	−294.126	−0.884448
$49$	−211.990	−0.618048
$50$	−118.495	−0.335154
$51$	−583.876	−1.60312
$52$	361.370	0.963711
$53$	−211.734	−0.548754	−0.274377	−	0.961622i	$-0.588472\pi$
$53$	−211.734	−0.548754	−0.274377	+	0.961622i	$0.588472\pi$
$54$	34.5490	0.0870653
$55$	−45.9956	−0.112765
$56$	−168.105	−0.401142
$57$	−1055.83	−2.45347
$58$	−246.014	−0.556952
$59$	−115.001	−0.253760	−0.126880	−	0.991918i	$-0.540496\pi$
$59$	−115.001	−0.253760	−0.126880	+	0.991918i	$0.540496\pi$
$60$	−93.4998	−0.201180
$61$	−184.073	−0.386363	−0.193181	−	0.981163i	$-0.561881\pi$
$61$	−184.073	−0.386363	−0.193181	+	0.981163i	$0.561881\pi$
$62$	42.7287	0.0875251
$63$	251.126	0.502205
$64$	−181.616	−0.354720
$65$	97.2477	0.185571
$66$	−165.602	−0.308851
$67$	545.337	0.994381	0.497190	−	0.867641i	$-0.334365\pi$
$67$	545.337	0.994381	0.497190	+	0.867641i	$0.334365\pi$
$68$	−588.184	−1.04894
$69$	0	0
$70$	−21.1872	−0.0361765
$71$	−582.298	−0.973324	−0.486662	−	0.873590i	$-0.661786\pi$
$71$	−582.298	−0.973324	−0.486662	+	0.873590i	$0.661786\pi$
$72$	−322.232	−0.527437
$73$	47.4045	0.0760038	0.0380019	−	0.999278i	$-0.487901\pi$
$73$	47.4045	0.0760038	0.0380019	+	0.999278i	$0.487901\pi$
$74$	−34.9374	−0.0548837
$75$	849.304	1.30759
$76$	−1063.62	−1.60533
$77$	277.597	0.410846
$78$	350.129	0.508261
$79$	−1250.01	−1.78022	−0.890108	−	0.455750i	$-0.849371\pi$
$79$	−1250.01	−1.78022	−0.890108	+	0.455750i	$0.849371\pi$
$80$	−79.7359	−0.111434
$81$	−840.013	−1.15228
$82$	325.714	0.438647
$83$	759.853	1.00488	0.502438	−	0.864613i	$-0.332437\pi$
$83$	759.853	1.00488	0.502438	+	0.864613i	$0.332437\pi$
$84$	564.299	0.732978
$85$	−158.285	−0.201982
$86$	−286.824	−0.359640
$87$	1763.29	2.17293
$88$	−356.199	−0.431488
$89$	−785.740	−0.935824	−0.467912	−	0.883775i	$-0.654994\pi$
$89$	−785.740	−0.935824	−0.467912	+	0.883775i	$0.654994\pi$
$90$	−40.6127	−0.0475662
$91$	−586.919	−0.676108
$92$	0	0
$93$	−306.256	−0.341476
$94$	−101.050	−0.110878
$95$	−286.229	−0.309120
$96$	−1109.04	−1.17907
$97$	560.129	0.586315	0.293157	−	0.956064i	$-0.405294\pi$
$97$	560.129	0.586315	0.293157	+	0.956064i	$0.405294\pi$
$98$	−206.912	−0.213278
$99$	532.113	0.540196
$100$	855.570	0.855570
$101$	−388.211	−0.382460	−0.191230	−	0.981545i	$-0.561248\pi$
$101$	−388.211	−0.382460	−0.191230	+	0.981545i	$0.561248\pi$
$102$	−569.888	−0.553209
$103$	−1125.58	−1.07676	−0.538380	−	0.842702i	$-0.680964\pi$
$103$	−1125.58	−1.07676	−0.538380	+	0.842702i	$0.680964\pi$
$104$	753.105	0.710077
$105$	151.858	0.141141
$106$	−206.662	−0.189366
$107$	−396.595	−0.358320	−0.179160	−	0.983820i	$-0.557338\pi$
$107$	−396.595	−0.358320	−0.179160	+	0.983820i	$0.557338\pi$
$108$	−249.455	−0.222258
$109$	1159.33	1.01875	0.509374	−	0.860545i	$-0.329877\pi$
$109$	1159.33	1.01875	0.509374	+	0.860545i	$0.329877\pi$
$110$	−44.8937	−0.0389131
$111$	250.412	0.214126
$112$	481.230	0.406000
$113$	−983.536	−0.818790	−0.409395	−	0.912357i	$-0.634260\pi$
$113$	−983.536	−0.818790	−0.409395	+	0.912357i	$0.634260\pi$
$114$	−1030.53	−0.846651
$115$	0	0
$116$	1776.30	1.42177
$117$	−1125.04	−0.888972
$118$	−112.246	−0.0875684
$119$	955.299	0.735900
$120$	−194.856	−0.148232
$121$	−742.797	−0.558074
$122$	−179.663	−0.133327
$123$	−2334.53	−1.71136
$124$	−308.515	−0.223431
$125$	467.304	0.334375
$126$	245.110	0.173303
$127$	60.3034	0.0421343	0.0210672	−	0.999778i	$-0.493294\pi$
$127$	60.3034	0.0421343	0.0210672	+	0.999778i	$0.493294\pi$
$128$	−1445.52	−0.998178
$129$	2055.79	1.40312
$130$	94.9179	0.0640373
$131$	1052.67	0.702077	0.351038	−	0.936361i	$-0.385829\pi$
$131$	1052.67	0.702077	0.351038	+	0.936361i	$0.385829\pi$
$132$	1195.70	0.788426
$133$	1727.47	1.12625
$134$	532.272	0.343144
$135$	−67.1305	−0.0427976
$136$	−1225.79	−0.772873
$137$	3098.15	1.93207	0.966033	−	0.258419i	$-0.0832015\pi$
$137$	3098.15	1.93207	0.966033	+	0.258419i	$0.0832015\pi$
$138$	0	0
$139$	511.559	0.312157	0.156079	−	0.987745i	$-0.450115\pi$
$139$	511.559	0.312157	0.156079	+	0.987745i	$0.450115\pi$
$140$	152.978	0.0923501
$141$	724.268	0.432584
$142$	−568.348	−0.335878
$143$	−1243.63	−0.727254
$144$	922.447	0.533824
$145$	478.017	0.273774
$146$	46.2688	0.0262276
$147$	1483.03	0.832095
$148$	252.259	0.140105
$149$	2445.14	1.34439	0.672195	−	0.740375i	$-0.265352\pi$
$149$	2445.14	1.34439	0.672195	+	0.740375i	$0.265352\pi$
$150$	828.957	0.451227
$151$	−10.7670	−0.00580268	−0.00290134	−	0.999996i	$-0.500924\pi$
$151$	−10.7670	−0.00580268	−0.00290134	+	0.999996i	$0.500924\pi$
$152$	−2216.61	−1.18283
$153$	1831.17	0.967589
$154$	270.947	0.141776
$155$	−83.0241	−0.0430236
$156$	−2528.04	−1.29747
$157$	1411.06	0.717293	0.358647	−	0.933473i	$-0.383238\pi$
$157$	1411.06	0.717293	0.358647	+	0.933473i	$0.383238\pi$
$158$	−1220.06	−0.614323
$159$	1481.24	0.738803
$160$	−300.655	−0.148555
$161$	0	0
$162$	−819.889	−0.397633
$163$	1287.49	0.618674	0.309337	−	0.950953i	$-0.399893\pi$
$163$	1287.49	0.618674	0.309337	+	0.950953i	$0.399893\pi$
$164$	−2351.76	−1.11977
$165$	321.773	0.151818
$166$	741.649	0.346766
$167$	−3814.73	−1.76762	−0.883810	−	0.467846i	$-0.845030\pi$
$167$	−3814.73	−1.76762	−0.883810	+	0.467846i	$0.845030\pi$
$168$	1176.02	0.540069
$169$	432.379	0.196804
$170$	−154.493	−0.0697005
$171$	3311.32	1.48083
$172$	2070.96	0.918077
$173$	−1331.42	−0.585122	−0.292561	−	0.956247i	$-0.594507\pi$
$173$	−1331.42	−0.585122	−0.292561	+	0.956247i	$0.594507\pi$
$174$	1721.05	0.749840
$175$	−1389.57	−0.600240
$176$	1019.68	0.436713
$177$	804.515	0.341645
$178$	−766.916	−0.322937
$179$	−2774.90	−1.15869	−0.579346	−	0.815082i	$-0.696692\pi$
$179$	−2774.90	−1.15869	−0.579346	+	0.815082i	$0.696692\pi$
$180$	293.237	0.121425
$181$	−1104.33	−0.453502	−0.226751	−	0.973953i	$-0.572810\pi$
$181$	−1104.33	−0.453502	−0.226751	+	0.973953i	$0.572810\pi$
$182$	−572.858	−0.233314
$183$	1287.72	0.520171
$184$	0	0
$185$	67.8852	0.0269785
$186$	−298.919	−0.117837
$187$	2024.19	0.791569
$188$	729.612	0.283045
$189$	405.152	0.155929
$190$	−279.371	−0.106672
$191$	−2290.51	−0.867725	−0.433862	−	0.900979i	$-0.642850\pi$
$191$	−2290.51	−0.867725	−0.433862	+	0.900979i	$0.642850\pi$
$192$	1270.54	0.477569
$193$	−2525.33	−0.941851	−0.470926	−	0.882173i	$-0.656080\pi$
$193$	−2525.33	−0.941851	−0.470926	+	0.882173i	$0.656080\pi$
$194$	546.710	0.202327
$195$	−680.318	−0.249839
$196$	1493.97	0.544449
$197$	−1772.11	−0.640903	−0.320451	−	0.947265i	$-0.603835\pi$
$197$	−1772.11	−0.640903	−0.320451	+	0.947265i	$0.603835\pi$
$198$	519.365	0.186413
$199$	−5093.23	−1.81432	−0.907159	−	0.420788i	$-0.861754\pi$
$199$	−5093.23	−1.81432	−0.907159	+	0.420788i	$0.861754\pi$
$200$	1783.03	0.630397
$201$	−3815.03	−1.33876
$202$	−378.910	−0.131980
$203$	−2884.98	−0.997467
$204$	4114.77	1.41221
$205$	−632.878	−0.215620
$206$	−1098.61	−0.371572
$207$	0	0
$208$	−2155.90	−0.718675
$209$	3660.36	1.21145
$210$	148.220	0.0487054
$211$	3756.97	1.22578	0.612892	−	0.790167i	$-0.290006\pi$
$211$	3756.97	1.22578	0.612892	+	0.790167i	$0.290006\pi$
$212$	1492.16	0.483407
$213$	4073.60	1.31041
$214$	−387.093	−0.123650
$215$	557.313	0.176784
$216$	−519.871	−0.163763
$217$	501.075	0.156752
$218$	1131.56	0.351553
$219$	−331.629	−0.102326
$220$	324.147	0.0993362
$221$	−4279.71	−1.30264
$222$	244.413	0.0738915
$223$	−5980.67	−1.79594	−0.897971	−	0.440055i	$-0.854959\pi$
$223$	−5980.67	−1.79594	−0.897971	+	0.440055i	$0.854959\pi$
$224$	1814.54	0.541246
$225$	−2663.61	−0.789218
$226$	−959.973	−0.282551
$227$	3873.22	1.13249	0.566243	−	0.824238i	$-0.308396\pi$
$227$	3873.22	1.13249	0.566243	+	0.824238i	$0.308396\pi$
$228$	7440.78	2.16130
$229$	1782.47	0.514361	0.257181	−	0.966363i	$-0.417206\pi$
$229$	1782.47	0.514361	0.257181	+	0.966363i	$0.417206\pi$
$230$	0	0
$231$	−1941.99	−0.553134
$232$	3701.86	1.04758
$233$	5942.10	1.67073	0.835365	−	0.549696i	$-0.185257\pi$
$233$	5942.10	1.67073	0.835365	+	0.549696i	$0.185257\pi$
$234$	−1098.08	−0.306769
$235$	196.345	0.0545027
$236$	810.451	0.223542
$237$	8744.72	2.39675
$238$	932.413	0.253947
$239$	460.267	0.124570	0.0622849	−	0.998058i	$-0.480161\pi$
$239$	460.267	0.124570	0.0622849	+	0.998058i	$0.480161\pi$
$240$	557.811	0.150027
$241$	−4558.20	−1.21834	−0.609170	−	0.793040i	$-0.708497\pi$
$241$	−4558.20	−1.21834	−0.609170	+	0.793040i	$0.708497\pi$
$242$	−725.002	−0.192582
$243$	4920.78	1.29905
$244$	1297.23	0.340354
$245$	402.040	0.104838
$246$	−2278.61	−0.590563
$247$	−7739.03	−1.99362
$248$	−642.954	−0.164627
$249$	−5315.72	−1.35289
$250$	456.109	0.115387
$251$	−4397.71	−1.10590	−0.552951	−	0.833214i	$-0.686498\pi$
$251$	−4397.71	−1.10590	−0.552951	+	0.833214i	$0.686498\pi$
$252$	−1769.77	−0.442401
$253$	0	0
$254$	58.8587	0.0145398
$255$	1107.32	0.271934
$256$	42.0461	0.0102652
$257$	−5011.02	−1.21626	−0.608130	−	0.793837i	$-0.708080\pi$
$257$	−5011.02	−1.21626	−0.608130	+	0.793837i	$0.708080\pi$
$258$	2006.54	0.484193
$259$	−409.707	−0.0982933
$260$	−685.338	−0.163472
$261$	−5530.08	−1.31151
$262$	1027.45	0.242275
$263$	−262.425	−0.0615278	−0.0307639	−	0.999527i	$-0.509794\pi$
$263$	−262.425	−0.0615278	−0.0307639	+	0.999527i	$0.509794\pi$
$264$	2491.87	0.580924
$265$	401.554	0.0930841
$266$	1686.09	0.388650
$267$	5496.82	1.25993
$268$	−3843.18	−0.875968
$269$	−6957.80	−1.57704	−0.788521	−	0.615007i	$-0.789153\pi$
$269$	−6957.80	−1.57704	−0.788521	+	0.615007i	$0.789153\pi$
$270$	−65.5222	−0.0147687
$271$	−2111.07	−0.473205	−0.236602	−	0.971607i	$-0.576034\pi$
$271$	−2111.07	−0.473205	−0.236602	+	0.971607i	$0.576034\pi$
$272$	3509.04	0.782232
$273$	4105.92	0.910263
$274$	3023.93	0.666724
$275$	−2944.38	−0.645647
$276$	0	0
$277$	−4005.75	−0.868888	−0.434444	−	0.900699i	$-0.643055\pi$
$277$	−4005.75	−0.868888	−0.434444	+	0.900699i	$0.643055\pi$
$278$	499.304	0.107720
$279$	960.487	0.206103
$280$	318.811	0.0680450
$281$	2775.31	0.589186	0.294593	−	0.955623i	$-0.404816\pi$
$281$	2775.31	0.589186	0.294593	+	0.955623i	$0.404816\pi$
$282$	706.917	0.149278
$283$	−3857.82	−0.810331	−0.405165	−	0.914243i	$-0.632786\pi$
$283$	−3857.82	−0.810331	−0.405165	+	0.914243i	$0.632786\pi$
$284$	4103.65	0.857418
$285$	2002.38	0.416177
$286$	−1213.83	−0.250963
$287$	3819.61	0.785590
$288$	3478.21	0.711650
$289$	2052.87	0.417845
$290$	466.565	0.0944747
$291$	−3918.51	−0.789372
$292$	−334.075	−0.0669530
$293$	−5749.21	−1.14632	−0.573161	−	0.819443i	$-0.694283\pi$
$293$	−5749.21	−1.14632	−0.573161	+	0.819443i	$0.694283\pi$
$294$	1447.50	0.287142
$295$	218.099	0.0430449
$296$	525.715	0.103232
$297$	858.481	0.167724
$298$	2386.57	0.463926
$299$	0	0
$300$	−5985.34	−1.15188
$301$	−3363.55	−0.644093
$302$	−10.5090	−0.00200241
$303$	2715.82	0.514916
$304$	6345.43	1.19716
$305$	349.095	0.0655380
$306$	1787.30	0.333899
$307$	−1182.24	−0.219785	−0.109892	−	0.993943i	$-0.535051\pi$
$307$	−1182.24	−0.219785	−0.109892	+	0.993943i	$0.535051\pi$
$308$	−1956.32	−0.361921
$309$	7874.22	1.44967
$310$	−81.0350	−0.0148467
$311$	5005.07	0.912576	0.456288	−	0.889832i	$-0.349179\pi$
$311$	5005.07	0.912576	0.456288	+	0.889832i	$0.349179\pi$
$312$	−5268.51	−0.955996
$313$	−1560.35	−0.281777	−0.140889	−	0.990025i	$-0.544996\pi$
$313$	−1560.35	−0.281777	−0.140889	+	0.990025i	$0.544996\pi$
$314$	1377.26	0.247526
$315$	−476.261	−0.0851881
$316$	8809.24	1.56822
$317$	−4410.51	−0.781448	−0.390724	−	0.920508i	$-0.627775\pi$
$317$	−4410.51	−0.781448	−0.390724	+	0.920508i	$0.627775\pi$
$318$	1445.75	0.254949
$319$	−6113.00	−1.07292
$320$	344.436	0.0601704
$321$	2774.47	0.482416
$322$	0	0
$323$	12596.4	2.16992
$324$	5919.86	1.01506
$325$	6225.25	1.06251
$326$	1256.64	0.213494
$327$	−8110.35	−1.37157
$328$	−4901.13	−0.825060
$329$	−1185.00	−0.198575
$330$	314.064	0.0523899
$331$	−7781.38	−1.29215	−0.646077	−	0.763272i	$-0.723592\pi$
$331$	−7781.38	−1.29215	−0.646077	+	0.763272i	$0.723592\pi$
$332$	−5354.94	−0.885213
$333$	−785.349	−0.129240
$334$	−3723.34	−0.609976
$335$	−1034.23	−0.168675
$336$	−3366.55	−0.546609
$337$	7538.46	1.21854	0.609268	−	0.792965i	$-0.291464\pi$
$337$	7538.46	1.21854	0.609268	+	0.792965i	$0.291464\pi$
$338$	422.020	0.0679138
$339$	6880.55	1.10236
$340$	1115.49	0.177929
$341$	1061.73	0.168610
$342$	3231.99	0.511011
$343$	−6352.39	−0.999990
$344$	4315.94	0.676453
$345$	0	0
$346$	−1299.52	−0.201916
$347$	−1634.96	−0.252937	−0.126468	−	0.991971i	$-0.540364\pi$
$347$	−1634.96	−0.252937	−0.126468	+	0.991971i	$0.540364\pi$
$348$	−12426.5	−1.91417
$349$	−2149.95	−0.329754	−0.164877	−	0.986314i	$-0.552723\pi$
$349$	−2149.95	−0.329754	−0.164877	+	0.986314i	$0.552723\pi$
$350$	−1356.28	−0.207133
$351$	−1815.07	−0.276015
$352$	3844.84	0.582190
$353$	1333.51	0.201064	0.100532	−	0.994934i	$-0.467946\pi$
$353$	1333.51	0.201064	0.100532	+	0.994934i	$0.467946\pi$
$354$	785.242	0.117896
$355$	1104.33	0.165103
$356$	5537.38	0.824383
$357$	−6683.01	−0.990763
$358$	−2708.42	−0.399845
$359$	−1935.35	−0.284523	−0.142261	−	0.989829i	$-0.545437\pi$
$359$	−1935.35	−0.284523	−0.142261	+	0.989829i	$0.545437\pi$
$360$	611.113	0.0894681
$361$	15919.2	2.32093
$362$	−1077.87	−0.156496
$363$	5196.40	0.751351
$364$	4136.22	0.595595
$365$	−89.9026	−0.0128924
$366$	1256.87	0.179502
$367$	−419.985	−0.0597359	−0.0298679	−	0.999554i	$-0.509509\pi$
$367$	−419.985	−0.0597359	−0.0298679	+	0.999554i	$0.509509\pi$
$368$	0	0
$369$	7321.63	1.03292
$370$	66.2588	0.00930982
$371$	−2423.50	−0.339142
$372$	2158.29	0.300812
$373$	−216.563	−0.0300623	−0.0150311	−	0.999887i	$-0.504785\pi$
$373$	−216.563	−0.0300623	−0.0150311	+	0.999887i	$0.504785\pi$
$374$	1975.70	0.273157
$375$	−3269.13	−0.450179
$376$	1520.53	0.208552
$377$	12924.6	1.76565
$378$	395.446	0.0538084
$379$	3612.85	0.489656	0.244828	−	0.969567i	$-0.421269\pi$
$379$	3612.85	0.489656	0.244828	+	0.969567i	$0.421269\pi$
$380$	2017.15	0.272309
$381$	−421.866	−0.0567266
$382$	−2235.64	−0.299437
$383$	5389.88	0.719086	0.359543	−	0.933128i	$-0.382933\pi$
$383$	5389.88	0.719086	0.359543	+	0.933128i	$0.382933\pi$
$384$	10112.4	1.34387
$385$	−526.463	−0.0696910
$386$	−2464.83	−0.325017
$387$	−6447.44	−0.846878
$388$	−3947.42	−0.516495
$389$	−10855.6	−1.41491	−0.707453	−	0.706760i	$-0.750156\pi$
$389$	−10855.6	−1.41491	−0.707453	+	0.706760i	$0.750156\pi$
$390$	−664.020	−0.0862153
$391$	0	0
$392$	3113.47	0.401158
$393$	−7364.18	−0.945226
$394$	−1729.66	−0.221165
$395$	2370.64	0.301975
$396$	−3749.98	−0.475868
$397$	−6124.16	−0.774213	−0.387107	−	0.922035i	$-0.626525\pi$
$397$	−6124.16	−0.774213	−0.387107	+	0.922035i	$0.626525\pi$
$398$	−4971.21	−0.626091
$399$	−12084.9	−1.51630
$400$	−5104.25	−0.638031
$401$	3825.29	0.476373	0.238187	−	0.971219i	$-0.423447\pi$
$401$	3825.29	0.476373	0.238187	+	0.971219i	$0.423447\pi$
$402$	−3723.63	−0.461985
$403$	−2244.80	−0.277473
$404$	2735.85	0.336915
$405$	1593.08	0.195459
$406$	−2815.86	−0.344209
$407$	−868.132	−0.105729
$408$	8575.30	1.04054
$409$	11735.5	1.41878	0.709391	−	0.704815i	$-0.248970\pi$
$409$	11735.5	1.41878	0.709391	+	0.704815i	$0.248970\pi$
$410$	−617.716	−0.0744069
$411$	−21673.8	−2.60119
$412$	7932.32	0.948537
$413$	−1316.29	−0.156830
$414$	0	0
$415$	−1441.06	−0.170455
$416$	−8129.08	−0.958080
$417$	−3578.73	−0.420266
$418$	3572.67	0.418050
$419$	−4616.94	−0.538311	−0.269156	−	0.963097i	$-0.586745\pi$
$419$	−4616.94	−0.538311	−0.269156	+	0.963097i	$0.586745\pi$
$420$	−1070.19	−0.124334
$421$	890.986	0.103145	0.0515724	−	0.998669i	$-0.483577\pi$
$421$	890.986	0.103145	0.0515724	+	0.998669i	$0.483577\pi$
$422$	3666.96	0.422998
$423$	−2271.47	−0.261094
$424$	3109.71	0.356181
$425$	−10132.5	−1.15647
$426$	3976.00	0.452202
$427$	−2106.89	−0.238781
$428$	2794.94	0.315650
$429$	8700.08	0.979123
$430$	543.962	0.0610050
$431$	−777.663	−0.0869112	−0.0434556	−	0.999055i	$-0.513837\pi$
$431$	−777.663	−0.0869112	−0.0434556	+	0.999055i	$0.513837\pi$
$432$	1488.22	0.165746
$433$	8919.78	0.989970	0.494985	−	0.868901i	$-0.335173\pi$
$433$	8919.78	0.989970	0.494985	+	0.868901i	$0.335173\pi$
$434$	489.071	0.0540925
$435$	−3344.08	−0.368589
$436$	−8170.19	−0.897434
$437$	0	0
$438$	−323.684	−0.0353110
$439$	−6510.99	−0.707864	−0.353932	−	0.935271i	$-0.615156\pi$
$439$	−6510.99	−0.707864	−0.353932	+	0.935271i	$0.615156\pi$
$440$	675.531	0.0731924
$441$	−4651.11	−0.502226
$442$	−4177.18	−0.449521
$443$	11735.9	1.25867	0.629333	−	0.777136i	$-0.283328\pi$
$443$	11735.9	1.25867	0.629333	+	0.777136i	$0.283328\pi$
$444$	−1764.74	−0.188628
$445$	1490.16	0.158742
$446$	−5837.39	−0.619749
$447$	−17105.6	−1.80999
$448$	−2078.77	−0.219225
$449$	−11103.7	−1.16708	−0.583539	−	0.812085i	$-0.698333\pi$
$449$	−11103.7	−1.16708	−0.583539	+	0.812085i	$0.698333\pi$
$450$	−2599.80	−0.272346
$451$	8093.40	0.845019
$452$	6931.31	0.721286
$453$	75.3229	0.00781231
$454$	3780.43	0.390802
$455$	1113.09	0.114687
$456$	15506.8	1.59248
$457$	4696.48	0.480727	0.240364	−	0.970683i	$-0.422733\pi$
$457$	4696.48	0.480727	0.240364	+	0.970683i	$0.422733\pi$
$458$	1739.76	0.177497
$459$	2954.30	0.300425
$460$	0	0
$461$	−3603.63	−0.364074	−0.182037	−	0.983292i	$-0.558269\pi$
$461$	−3603.63	−0.364074	−0.182037	+	0.983292i	$0.558269\pi$
$462$	−1895.47	−0.190877
$463$	−4059.96	−0.407522	−0.203761	−	0.979021i	$-0.565316\pi$
$463$	−4059.96	−0.407522	−0.203761	+	0.979021i	$0.565316\pi$
$464$	−10597.2	−1.06027
$465$	580.814	0.0579238
$466$	5799.74	0.576541
$467$	−13178.8	−1.30587	−0.652936	−	0.757413i	$-0.726463\pi$
$467$	−13178.8	−1.30587	−0.652936	+	0.757413i	$0.726463\pi$
$468$	7928.52	0.783111
$469$	6241.90	0.614550
$470$	191.641	0.0188080
$471$	−9871.41	−0.965712
$472$	1689.00	0.164709
$473$	−7127.06	−0.692817
$474$	8535.23	0.827080
$475$	−18322.7	−1.76991
$476$	−6732.32	−0.648267
$477$	−4645.49	−0.445917
$478$	449.240	0.0429870
$479$	−18975.1	−1.81001	−0.905003	−	0.425406i	$-0.860131\pi$
$479$	−18975.1	−1.81001	−0.905003	+	0.425406i	$0.860131\pi$
$480$	2103.30	0.200004
$481$	1835.48	0.173993
$482$	−4449.00	−0.420429
$483$	0	0
$484$	5234.74	0.491617
$485$	−1062.29	−0.0994554
$486$	4802.90	0.448279
$487$	1641.31	0.152720	0.0763600	−	0.997080i	$-0.475670\pi$
$487$	1641.31	0.152720	0.0763600	+	0.997080i	$0.475670\pi$
$488$	2703.45	0.250778
$489$	−9006.91	−0.832938
$490$	392.408	0.0361779
$491$	−2822.20	−0.259398	−0.129699	−	0.991553i	$-0.541401\pi$
$491$	−2822.20	−0.259398	−0.129699	+	0.991553i	$0.541401\pi$
$492$	16452.3	1.50757
$493$	−21036.7	−1.92180
$494$	−7553.63	−0.687963
$495$	−1009.15	−0.0916324
$496$	1840.57	0.166621
$497$	−6664.95	−0.601537
$498$	−5188.37	−0.466861
$499$	−8976.11	−0.805262	−0.402631	−	0.915362i	$-0.631904\pi$
$499$	−8976.11	−0.805262	−0.402631	+	0.915362i	$0.631904\pi$
$500$	−3293.25	−0.294557
$501$	26686.8	2.37980
$502$	−4292.36	−0.381628
$503$	4506.75	0.399495	0.199747	−	0.979847i	$-0.435988\pi$
$503$	4506.75	0.399495	0.199747	+	0.979847i	$0.435988\pi$
$504$	−3688.25	−0.325968
$505$	736.242	0.0648759
$506$	0	0
$507$	−3024.80	−0.264963
$508$	−424.978	−0.0371169
$509$	3033.74	0.264181	0.132091	−	0.991238i	$-0.457831\pi$
$509$	3033.74	0.264181	0.132091	+	0.991238i	$0.457831\pi$
$510$	1080.79	0.0938398
$511$	542.589	0.0469720
$512$	11605.2	1.00172
$513$	5342.29	0.459781
$514$	−4890.97	−0.419711
$515$	2134.65	0.182649
$516$	−14487.9	−1.23603
$517$	−2510.91	−0.213597
$518$	−399.892	−0.0339194
$519$	9314.25	0.787766
$520$	−1428.26	−0.120449
$521$	−225.173	−0.0189348	−0.00946739	−	0.999955i	$-0.503014\pi$
$521$	−225.173	−0.0189348	−0.00946739	+	0.999955i	$0.503014\pi$
$522$	−5397.59	−0.452579
$523$	13965.4	1.16762	0.583809	−	0.811891i	$-0.301562\pi$
$523$	13965.4	1.16762	0.583809	+	0.811891i	$0.301562\pi$
$524$	−7418.51	−0.618472
$525$	9721.09	0.808120
$526$	−256.138	−0.0212322
$527$	3653.75	0.302011
$528$	−7133.42	−0.587959
$529$	0	0
$530$	391.934	0.0321218
$531$	−2523.14	−0.206205
$532$	−12174.1	−0.992132
$533$	−17111.7	−1.39060
$534$	5365.14	0.434779
$535$	752.141	0.0607811
$536$	−8009.28	−0.645426
$537$	19412.5	1.55998
$538$	−6791.11	−0.544211
$539$	−5141.38	−0.410863
$540$	473.091	0.0377011
$541$	14464.1	1.14946	0.574731	−	0.818343i	$-0.305107\pi$
$541$	14464.1	1.14946	0.574731	+	0.818343i	$0.305107\pi$
$542$	−2060.50	−0.163295
$543$	7725.57	0.610563
$544$	13231.3	1.04281
$545$	−2198.67	−0.172808
$546$	4007.56	0.314117
$547$	3435.63	0.268550	0.134275	−	0.990944i	$-0.457129\pi$
$547$	3435.63	0.268550	0.134275	+	0.990944i	$0.457129\pi$
$548$	−21833.7	−1.70199
$549$	−4038.60	−0.313958
$550$	−2873.84	−0.222802
$551$	−38040.9	−2.94119
$552$	0	0
$553$	−14307.5	−1.10021
$554$	−3909.78	−0.299839
$555$	−474.906	−0.0363219
$556$	−3605.13	−0.274985
$557$	−16149.5	−1.22851	−0.614253	−	0.789109i	$-0.710542\pi$
$557$	−16149.5	−1.22851	−0.614253	+	0.789109i	$0.710542\pi$
$558$	937.477	0.0711229
$559$	15068.6	1.14013
$560$	−912.653	−0.0688689
$561$	−14160.7	−1.06571
$562$	2708.82	0.203318
$563$	−15799.5	−1.18272	−0.591360	−	0.806408i	$-0.701409\pi$
$563$	−15799.5	−1.18272	−0.591360	+	0.806408i	$0.701409\pi$
$564$	−5104.17	−0.381071
$565$	1865.27	0.138890
$566$	−3765.40	−0.279632
$567$	−9614.74	−0.712136
$568$	8552.12	0.631759
$569$	−18975.0	−1.39802	−0.699010	−	0.715112i	$-0.746376\pi$
$569$	−18975.0	−1.39802	−0.699010	+	0.715112i	$0.746376\pi$
$570$	1954.41	0.143616
$571$	21023.1	1.54079	0.770395	−	0.637567i	$-0.220059\pi$
$571$	21023.1	1.54079	0.770395	+	0.637567i	$0.220059\pi$
$572$	8764.26	0.640651
$573$	16023.8	1.16824
$574$	3728.10	0.271094
$575$	0	0
$576$	−3984.70	−0.288245
$577$	4123.92	0.297541	0.148770	−	0.988872i	$-0.452468\pi$
$577$	4123.92	0.297541	0.148770	+	0.988872i	$0.452468\pi$
$578$	2003.69	0.144191
$579$	17666.5	1.26804
$580$	−3368.75	−0.241172
$581$	8697.23	0.621036
$582$	−3824.64	−0.272399
$583$	−5135.17	−0.364798
$584$	−696.222	−0.0493320
$585$	2133.63	0.150795
$586$	−5611.47	−0.395577
$587$	−1377.37	−0.0968488	−0.0484244	−	0.998827i	$-0.515420\pi$
$587$	−1377.37	−0.0968488	−0.0484244	+	0.998827i	$0.515420\pi$
$588$	−10451.4	−0.733007
$589$	6607.11	0.462209
$590$	212.874	0.0148541
$591$	12397.2	0.862865
$592$	−1504.95	−0.104482
$593$	−11421.1	−0.790908	−0.395454	−	0.918486i	$-0.629413\pi$
$593$	−11421.1	−0.790908	−0.395454	+	0.918486i	$0.629413\pi$
$594$	837.914	0.0578788
$595$	−1811.72	−0.124829
$596$	−17231.8	−1.18430
$597$	35630.8	2.44267
$598$	0	0
$599$	6209.30	0.423548	0.211774	−	0.977319i	$-0.432076\pi$
$599$	6209.30	0.423548	0.211774	+	0.977319i	$0.432076\pi$
$600$	−12473.6	−0.848721
$601$	5467.09	0.371060	0.185530	−	0.982639i	$-0.440600\pi$
$601$	5467.09	0.371060	0.185530	+	0.982639i	$0.440600\pi$
$602$	−3282.97	−0.222266
$603$	11964.8	0.808034
$604$	75.8786	0.00511168
$605$	1408.71	0.0946651
$606$	2650.75	0.177689
$607$	20600.7	1.37752	0.688762	−	0.724988i	$-0.258154\pi$
$607$	20600.7	1.37752	0.688762	+	0.724988i	$0.258154\pi$
$608$	23926.3	1.59595
$609$	20182.5	1.34292
$610$	340.731	0.0226161
$611$	5308.76	0.351505
$612$	−12904.9	−0.852366
$613$	10396.7	0.685025	0.342513	−	0.939513i	$-0.388722\pi$
$613$	10396.7	0.685025	0.342513	+	0.939513i	$0.388722\pi$
$614$	−1153.92	−0.0758440
$615$	4427.44	0.290296
$616$	−4077.03	−0.266669
$617$	−15241.2	−0.994472	−0.497236	−	0.867615i	$-0.665652\pi$
$617$	−15241.2	−0.994472	−0.497236	+	0.867615i	$0.665652\pi$
$618$	7685.58	0.500258
$619$	12683.1	0.823549	0.411775	−	0.911286i	$-0.364909\pi$
$619$	12683.1	0.823549	0.411775	+	0.911286i	$0.364909\pi$
$620$	585.099	0.0379002
$621$	0	0
$622$	4885.16	0.314915
$623$	−8993.54	−0.578360
$624$	15082.1	0.967573
$625$	14289.2	0.914507
$626$	−1522.97	−0.0972366
$627$	−25606.9	−1.63101
$628$	−9944.24	−0.631876
$629$	−2987.51	−0.189380
$630$	−464.851	−0.0293970
$631$	18851.6	1.18933	0.594667	−	0.803972i	$-0.297284\pi$
$631$	18851.6	1.18933	0.594667	+	0.803972i	$0.297284\pi$
$632$	18358.7	1.15549
$633$	−26282.7	−1.65031
$634$	−4304.85	−0.269665
$635$	−114.365	−0.00714716
$636$	−10438.8	−0.650824
$637$	10870.3	0.676135
$638$	−5966.55	−0.370248
$639$	−12775.7	−0.790923
$640$	2741.42	0.169319
$641$	−8024.02	−0.494430	−0.247215	−	0.968961i	$-0.579515\pi$
$641$	−8024.02	−0.494430	−0.247215	+	0.968961i	$0.579515\pi$
$642$	2708.00	0.166474
$643$	16814.4	1.03125	0.515627	−	0.856813i	$-0.327559\pi$
$643$	16814.4	1.03125	0.515627	+	0.856813i	$0.327559\pi$
$644$	0	0
$645$	−3898.81	−0.238009
$646$	12294.7	0.748804
$647$	−21369.7	−1.29850	−0.649251	−	0.760574i	$-0.724918\pi$
$647$	−21369.7	−1.29850	−0.649251	+	0.760574i	$0.724918\pi$
$648$	12337.1	0.747915
$649$	−2789.11	−0.168693
$650$	6076.11	0.366654
$651$	−3505.38	−0.211040
$652$	−9073.36	−0.545000
$653$	7739.68	0.463824	0.231912	−	0.972737i	$-0.425502\pi$
$653$	7739.68	0.463824	0.231912	+	0.972737i	$0.425502\pi$
$654$	−7916.05	−0.473306
$655$	−1996.39	−0.119092
$656$	14030.4	0.835051
$657$	1040.06	0.0617606
$658$	−1156.61	−0.0685249
$659$	8062.59	0.476592	0.238296	−	0.971193i	$-0.423411\pi$
$659$	8062.59	0.476592	0.238296	+	0.971193i	$0.423411\pi$
$660$	−2267.64	−0.133739
$661$	13292.5	0.782175	0.391088	−	0.920353i	$-0.372099\pi$
$661$	13292.5	0.782175	0.391088	+	0.920353i	$0.372099\pi$
$662$	−7594.96	−0.445901
$663$	29939.7	1.75379
$664$	−11159.8	−0.652238
$665$	−3276.16	−0.191043
$666$	−766.534	−0.0445985
$667$	0	0
$668$	26883.7	1.55713
$669$	41839.1	2.41793
$670$	−1009.45	−0.0582069
$671$	−4464.31	−0.256844
$672$	−12694.0	−0.728694
$673$	−9422.80	−0.539706	−0.269853	−	0.962902i	$-0.586975\pi$
$673$	−9422.80	−0.539706	−0.269853	+	0.962902i	$0.586975\pi$
$674$	7357.86	0.420496
$675$	−4297.32	−0.245043
$676$	−3047.12	−0.173368
$677$	2837.83	0.161103	0.0805515	−	0.996750i	$-0.474332\pi$
$677$	2837.83	0.161103	0.0805515	+	0.996750i	$0.474332\pi$
$678$	6715.71	0.380406
$679$	6411.21	0.362356
$680$	2324.71	0.131101
$681$	−27096.0	−1.52470
$682$	1036.30	0.0581845
$683$	2482.80	0.139095	0.0695473	−	0.997579i	$-0.477845\pi$
$683$	2482.80	0.139095	0.0695473	+	0.997579i	$0.477845\pi$
$684$	−23336.0	−1.30449
$685$	−5875.64	−0.327733
$686$	−6200.20	−0.345080
$687$	−12469.7	−0.692499
$688$	−12355.1	−0.684645
$689$	10857.2	0.600329
$690$	0	0
$691$	−20470.8	−1.12699	−0.563493	−	0.826121i	$-0.690543\pi$
$691$	−20470.8	−1.12699	−0.563493	+	0.826121i	$0.690543\pi$
$692$	9382.97	0.515444
$693$	6090.54	0.333853
$694$	−1595.79	−0.0872842
$695$	−970.172	−0.0529507
$696$	−25897.2	−1.41039
$697$	27851.9	1.51358
$698$	−2098.44	−0.113793
$699$	−41569.3	−2.24935
$700$	9792.81	0.528762
$701$	23934.1	1.28956	0.644779	−	0.764369i	$-0.276950\pi$
$701$	23934.1	1.28956	0.644779	+	0.764369i	$0.276950\pi$
$702$	−1771.59	−0.0952482
$703$	−5402.34	−0.289834
$704$	−4404.73	−0.235809
$705$	−1373.57	−0.0733785
$706$	1301.56	0.0693837
$707$	−4443.44	−0.236369
$708$	−5669.69	−0.300961
$709$	−6356.35	−0.336697	−0.168348	−	0.985728i	$-0.553843\pi$
$709$	−6356.35	−0.336697	−0.168348	+	0.985728i	$0.553843\pi$
$710$	1077.87	0.0569743
$711$	−27425.4	−1.44660
$712$	11540.1	0.607418
$713$	0	0
$714$	−6522.90	−0.341896
$715$	2358.54	0.123363
$716$	19555.7	1.02071
$717$	−3219.90	−0.167712
$718$	−1888.98	−0.0981841
$719$	11750.5	0.609485	0.304743	−	0.952435i	$-0.401430\pi$
$719$	11750.5	0.609485	0.304743	+	0.952435i	$0.401430\pi$
$720$	−1749.42	−0.0905515
$721$	−12883.3	−0.665462
$722$	15537.9	0.800914
$723$	31888.0	1.64028
$724$	7782.56	0.399498
$725$	30600.0	1.56752
$726$	5071.91	0.259279
$727$	−4275.35	−0.218107	−0.109054	−	0.994036i	$-0.534782\pi$
$727$	−4275.35	−0.218107	−0.109054	+	0.994036i	$0.534782\pi$
$728$	8619.99	0.438844
$729$	−11744.1	−0.596662
$730$	−87.7488	−0.00444894
$731$	−24526.4	−1.24096
$732$	−9075.04	−0.458228
$733$	26942.9	1.35765	0.678826	−	0.734299i	$-0.262489\pi$
$733$	26942.9	1.35765	0.678826	+	0.734299i	$0.262489\pi$
$734$	−409.924	−0.0206138
$735$	−2812.56	−0.141147
$736$	0	0
$737$	13226.0	0.661040
$738$	7146.23	0.356445
$739$	2467.16	0.122809	0.0614046	−	0.998113i	$-0.480442\pi$
$739$	2467.16	0.122809	0.0614046	+	0.998113i	$0.480442\pi$
$740$	−478.410	−0.0237658
$741$	54140.2	2.68406
$742$	−2365.44	−0.117032
$743$	−4429.40	−0.218707	−0.109353	−	0.994003i	$-0.534878\pi$
$743$	−4429.40	−0.218707	−0.109353	+	0.994003i	$0.534878\pi$
$744$	4497.93	0.221643
$745$	−4637.21	−0.228046
$746$	−211.375	−0.0103740
$747$	16671.3	0.816562
$748$	−14265.2	−0.697307
$749$	−4539.40	−0.221450
$750$	−3190.81	−0.155349
$751$	−28222.9	−1.37133	−0.685664	−	0.727918i	$-0.740488\pi$
$751$	−28222.9	−1.37133	−0.685664	+	0.727918i	$0.740488\pi$
$752$	−4352.79	−0.211077
$753$	30765.2	1.48891
$754$	12615.0	0.609297
$755$	20.4196	0.000984297 0
$756$	−2855.25	−0.137360
$757$	40706.7	1.95444	0.977218	−	0.212236i	$-0.0680746\pi$
$757$	40706.7	1.95444	0.977218	+	0.212236i	$0.0680746\pi$
$758$	3526.30	0.168972
$759$	0	0
$760$	4203.80	0.200642
$761$	−20094.0	−0.957173	−0.478586	−	0.878040i	$-0.658851\pi$
$761$	−20094.0	−0.957173	−0.478586	+	0.878040i	$0.658851\pi$
$762$	−411.759	−0.0195754
$763$	13269.6	0.629610
$764$	16142.0	0.764394
$765$	−3472.81	−0.164130
$766$	5260.76	0.248145
$767$	5896.96	0.277610
$768$	−294.143	−0.0138203
$769$	19329.4	0.906421	0.453210	−	0.891404i	$-0.350279\pi$
$769$	19329.4	0.906421	0.453210	+	0.891404i	$0.350279\pi$
$770$	−513.851	−0.0240492
$771$	35055.7	1.63749
$772$	17796.9	0.829693
$773$	30502.2	1.41926	0.709629	−	0.704575i	$-0.248863\pi$
$773$	30502.2	1.41926	0.709629	+	0.704575i	$0.248863\pi$
$774$	−6292.98	−0.292243
$775$	−5314.74	−0.246337
$776$	−8226.54	−0.380561
$777$	2866.20	0.132335
$778$	−10595.5	−0.488260
$779$	50364.9	2.31644
$780$	4794.43	0.220088
$781$	−14122.4	−0.647042
$782$	0	0
$783$	−8921.91	−0.407207
$784$	−8912.87	−0.406016
$785$	−2676.08	−0.121673
$786$	−7187.76	−0.326182
$787$	1690.36	0.0765629	0.0382814	−	0.999267i	$-0.487812\pi$
$787$	1690.36	0.0765629	0.0382814	+	0.999267i	$0.487812\pi$
$788$	12488.7	0.564582
$789$	1835.85	0.0828367
$790$	2313.85	0.104206
$791$	−11257.5	−0.506031
$792$	−7815.07	−0.350627
$793$	9438.80	0.422675
$794$	−5977.44	−0.267168
$795$	−2809.16	−0.125322
$796$	35893.7	1.59826
$797$	18197.7	0.808778	0.404389	−	0.914587i	$-0.367484\pi$
$797$	18197.7	0.808778	0.404389	+	0.914587i	$0.367484\pi$
$798$	−11795.4	−0.523250
$799$	−8640.81	−0.382591
$800$	−19246.2	−0.850571
$801$	−17239.3	−0.760450
$802$	3733.65	0.164389
$803$	1149.70	0.0505254
$804$	26885.8	1.17934
$805$	0	0
$806$	−2191.02	−0.0957512
$807$	48674.9	2.12322
$808$	5701.59	0.248244
$809$	−11740.4	−0.510225	−0.255112	−	0.966911i	$-0.582112\pi$
$809$	−11740.4	−0.510225	−0.255112	+	0.966911i	$0.582112\pi$
$810$	1554.92	0.0674497
$811$	16603.3	0.718891	0.359446	−	0.933166i	$-0.382966\pi$
$811$	16603.3	0.718891	0.359446	+	0.933166i	$0.382966\pi$
$812$	20331.4	0.878686
$813$	14768.5	0.637089
$814$	−847.334	−0.0364853
$815$	−2441.72	−0.104944
$816$	−24548.3	−1.05314
$817$	−44351.4	−1.89921
$818$	11454.3	0.489598
$819$	−12877.1	−0.549405
$820$	4460.11	0.189944
$821$	−41823.8	−1.77790	−0.888952	−	0.457999i	$-0.848566\pi$
$821$	−41823.8	−1.77790	−0.888952	+	0.457999i	$0.848566\pi$
$822$	−21154.6	−0.897629
$823$	6012.68	0.254665	0.127332	−	0.991860i	$-0.459359\pi$
$823$	6012.68	0.254665	0.127332	+	0.991860i	$0.459359\pi$
$824$	16531.2	0.698896
$825$	20598.1	0.869253
$826$	−1284.76	−0.0541193
$827$	−33118.9	−1.39257	−0.696286	−	0.717764i	$-0.745166\pi$
$827$	−33118.9	−1.39257	−0.696286	+	0.717764i	$0.745166\pi$
$828$	0	0
$829$	2680.69	0.112309	0.0561545	−	0.998422i	$-0.482116\pi$
$829$	2680.69	0.112309	0.0561545	+	0.998422i	$0.482116\pi$
$830$	−1406.54	−0.0588212
$831$	28023.1	1.16981
$832$	9312.83	0.388058
$833$	−17693.1	−0.735930
$834$	−3492.99	−0.145027
$835$	7234.63	0.299838
$836$	−25795.8	−1.06718
$837$	1549.59	0.0639926
$838$	−4506.33	−0.185762
$839$	10649.8	0.438225	0.219113	−	0.975700i	$-0.429684\pi$
$839$	10649.8	0.438225	0.219113	+	0.975700i	$0.429684\pi$
$840$	−2230.31	−0.0916108
$841$	39141.4	1.60488
$842$	869.641	0.0355936
$843$	−19415.3	−0.793237
$844$	−26476.6	−1.07981
$845$	−820.006	−0.0333835
$846$	−2217.05	−0.0900991
$847$	−8502.01	−0.344903
$848$	−8902.10	−0.360495
$849$	26988.3	1.09097
$850$	−9889.79	−0.399079
$851$	0	0
$852$	−28708.0	−1.15437
$853$	13056.9	0.524104	0.262052	−	0.965054i	$-0.415601\pi$
$853$	13056.9	0.524104	0.262052	+	0.965054i	$0.415601\pi$
$854$	−2056.41	−0.0823994
$855$	−6279.91	−0.251191
$856$	5824.73	0.232576
$857$	16103.1	0.641857	0.320928	−	0.947103i	$-0.396005\pi$
$857$	16103.1	0.641857	0.320928	+	0.947103i	$0.396005\pi$
$858$	8491.65	0.337879
$859$	19332.2	0.767875	0.383937	−	0.923359i	$-0.374568\pi$
$859$	19332.2	0.767875	0.383937	+	0.923359i	$0.374568\pi$
$860$	−3927.58	−0.155732
$861$	−26720.9	−1.05766
$862$	−759.033	−0.0299916
$863$	34748.6	1.37063	0.685316	−	0.728246i	$-0.259664\pi$
$863$	34748.6	1.37063	0.685316	+	0.728246i	$0.259664\pi$
$864$	5611.54	0.220959
$865$	2525.04	0.0992531
$866$	8706.09	0.341622
$867$	−14361.3	−0.562556
$868$	−3531.25	−0.138086
$869$	−30316.4	−1.18344
$870$	−3263.96	−0.127194
$871$	−27963.5	−1.08784
$872$	−17026.9	−0.661243
$873$	12289.3	0.476439
$874$	0	0
$875$	5348.73	0.206652
$876$	2337.10	0.0901408
$877$	−10501.6	−0.404350	−0.202175	−	0.979349i	$-0.564801\pi$
$877$	−10501.6	−0.404350	−0.202175	+	0.979349i	$0.564801\pi$
$878$	−6355.00	−0.244272
$879$	40219.9	1.54333
$880$	−1933.83	−0.0740787
$881$	−42462.2	−1.62382	−0.811912	−	0.583780i	$-0.801573\pi$
$881$	−42462.2	−1.62382	−0.811912	+	0.583780i	$0.801573\pi$
$882$	−4539.68	−0.173310
$883$	−8273.87	−0.315332	−0.157666	−	0.987493i	$-0.550397\pi$
$883$	−8273.87	−0.315332	−0.157666	+	0.987493i	$0.550397\pi$
$884$	30160.6	1.14752
$885$	−1525.76	−0.0579525
$886$	11454.7	0.434344
$887$	−7538.67	−0.285371	−0.142685	−	0.989768i	$-0.545574\pi$
$887$	−7538.67	−0.285371	−0.142685	+	0.989768i	$0.545574\pi$
$888$	−3677.76	−0.138984
$889$	690.229	0.0260400
$890$	1454.46	0.0547792
$891$	−20372.8	−0.766008
$892$	42147.8	1.58208
$893$	−15625.2	−0.585531
$894$	−16695.8	−0.624597
$895$	5262.60	0.196547
$896$	−16545.3	−0.616897
$897$	0	0
$898$	−10837.7	−0.402739
$899$	−11034.2	−0.409357
$900$	18771.4	0.695236
$901$	−17671.7	−0.653419
$902$	7899.51	0.291602
$903$	23530.5	0.867160
$904$	14445.0	0.531455
$905$	2094.35	0.0769267
$906$	73.5184	0.00269590
$907$	−31302.8	−1.14597	−0.572983	−	0.819567i	$-0.694214\pi$
$907$	−31302.8	−1.14597	−0.572983	+	0.819567i	$0.694214\pi$
$908$	−27295.9	−0.997628
$909$	−8517.42	−0.310787
$910$	1086.43	0.0395765
$911$	−45518.9	−1.65544	−0.827722	−	0.561138i	$-0.810364\pi$
$911$	−45518.9	−1.65544	−0.827722	+	0.561138i	$0.810364\pi$
$912$	−44390.9	−1.61177
$913$	18428.6	0.668016
$914$	4583.97	0.165891
$915$	−2442.17	−0.0882357
$916$	−12561.7	−0.453110
$917$	12048.8	0.433899
$918$	2883.52	0.103672
$919$	7630.92	0.273907	0.136954	−	0.990577i	$-0.456269\pi$
$919$	7630.92	0.273907	0.136954	+	0.990577i	$0.456269\pi$
$920$	0	0
$921$	8270.62	0.295902
$922$	−3517.30	−0.125636
$923$	29858.8	1.06480
$924$	13685.9	0.487265
$925$	4345.63	0.154468
$926$	−3962.70	−0.140629
$927$	−24695.4	−0.874975
$928$	−39958.2	−1.41346
$929$	41303.0	1.45867	0.729337	−	0.684155i	$-0.239829\pi$
$929$	41303.0	1.45867	0.729337	+	0.684155i	$0.239829\pi$
$930$	566.899	0.0199885
$931$	−31994.6	−1.12629
$932$	−41876.0	−1.47177
$933$	−35014.1	−1.22863
$934$	−12863.1	−0.450635
$935$	−3838.88	−0.134272
$936$	16523.3	0.577008
$937$	−34295.5	−1.19571	−0.597857	−	0.801603i	$-0.703981\pi$
$937$	−34295.5	−1.19571	−0.597857	+	0.801603i	$0.703981\pi$
$938$	6092.36	0.212071
$939$	10915.8	0.379365
$940$	−1383.71	−0.0480123
$941$	−42263.9	−1.46415	−0.732074	−	0.681225i	$-0.761448\pi$
$941$	−42263.9	−1.46415	−0.732074	+	0.681225i	$0.761448\pi$
$942$	−9634.92	−0.333251
$943$	0	0
$944$	−4835.07	−0.166703
$945$	−768.371	−0.0264499
$946$	−6956.32	−0.239080
$947$	−1172.46	−0.0402320	−0.0201160	−	0.999798i	$-0.506404\pi$
$947$	−1172.46	−0.0402320	−0.0201160	+	0.999798i	$0.506404\pi$
$948$	−61627.0	−2.11134
$949$	−2430.78	−0.0831470
$950$	−17883.8	−0.610765
$951$	30854.7	1.05209
$952$	−14030.3	−0.477653
$953$	17286.8	0.587590	0.293795	−	0.955868i	$-0.405082\pi$
$953$	17286.8	0.587590	0.293795	+	0.955868i	$0.405082\pi$
$954$	−4534.20	−0.153879
$955$	4343.95	0.147191
$956$	−3243.66	−0.109736
$957$	42764.9	1.44451
$958$	−18520.5	−0.624603
$959$	35461.3	1.19406
$960$	−2409.58	−0.0810091
$961$	−27874.5	−0.935669
$962$	1791.50	0.0600420
$963$	−8701.36	−0.291171
$964$	32123.2	1.07326
$965$	4789.29	0.159764
$966$	0	0
$967$	−25025.4	−0.832225	−0.416113	−	0.909313i	$-0.636608\pi$
$967$	−25025.4	−0.832225	−0.416113	+	0.909313i	$0.636608\pi$
$968$	10909.3	0.362231
$969$	−88121.3	−2.92143
$970$	−1036.84	−0.0343204
$971$	−32767.0	−1.08295	−0.541474	−	0.840718i	$-0.682133\pi$
$971$	−32767.0	−1.08295	−0.541474	+	0.840718i	$0.682133\pi$
$972$	−34678.4	−1.14435
$973$	5855.28	0.192920
$974$	1601.99	0.0527011
$975$	−43550.2	−1.43048
$976$	−7739.12	−0.253815
$977$	20295.0	0.664581	0.332291	−	0.943177i	$-0.392179\pi$
$977$	20295.0	0.664581	0.332291	+	0.943177i	$0.392179\pi$
$978$	−8791.13	−0.287433
$979$	−19056.5	−0.622112
$980$	−2833.31	−0.0923539
$981$	25435.9	0.827835
$982$	−2754.59	−0.0895138
$983$	40144.1	1.30254	0.651270	−	0.758846i	$-0.274236\pi$
$983$	40144.1	1.30254	0.651270	+	0.758846i	$0.274236\pi$
$984$	34287.0	1.11080
$985$	3360.81	0.108715
$986$	−20532.8	−0.663181
$987$	8289.93	0.267347
$988$	54539.6	1.75621
$989$	0	0
$990$	−984.976	−0.0316208
$991$	−39720.6	−1.27323	−0.636613	−	0.771184i	$-0.719665\pi$
$991$	−39720.6	−1.27323	−0.636613	+	0.771184i	$0.719665\pi$
$992$	6940.11	0.222126
$993$	54436.4	1.73966
$994$	−6505.27	−0.207580
$995$	9659.30	0.307759
$996$	37461.7	1.19179
$997$	30487.0	0.968439	0.484220	−	0.874947i	$-0.339104\pi$
$997$	30487.0	0.968439	0.484220	+	0.874947i	$0.339104\pi$
$998$	−8761.07	−0.277882
$999$	−1267.04	−0.0401274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.15		25
23.17	odd	22		23.4.c.a.13.3	✓	50
23.19	odd	22		23.4.c.a.16.3	yes	50
23.22	odd	2		529.4.a.n.1.15		25
69.17	even	22		207.4.i.a.82.3		50
69.65	even	22		207.4.i.a.154.3		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.13.3	✓	50	23.17	odd	22
23.4.c.a.16.3	yes	50	23.19	odd	22
207.4.i.a.82.3		50	69.17	even	22
207.4.i.a.154.3		50	69.65	even	22
529.4.a.m.1.15		25	1.1	even	1	trivial
529.4.a.n.1.15		25	23.22	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q+0.976043 q^{2} -6.99573 q^{3} -7.04734 q^{4} -1.89650 q^{5} -6.82813 q^{6} +11.4459 q^{7} -14.6869 q^{8} +21.9402 q^{9} -1.85107 q^{10} +24.2529 q^{11} +49.3013 q^{12} -51.2775 q^{13} +11.1717 q^{14} +13.2674 q^{15} +42.0437 q^{16} +83.4618 q^{17} +21.4146 q^{18} +150.925 q^{19} +13.3653 q^{20} -80.0727 q^{21} +23.6719 q^{22} +102.745 q^{24} -121.403 q^{25} -50.0490 q^{26} +35.3970 q^{27} -80.6634 q^{28} -252.052 q^{29} +12.9495 q^{30} +43.7775 q^{31} +158.531 q^{32} -169.667 q^{33} +81.4623 q^{34} -21.7072 q^{35} -154.620 q^{36} -35.7950 q^{37} +147.309 q^{38} +358.723 q^{39} +27.8536 q^{40} +333.709 q^{41} -78.1544 q^{42} -293.864 q^{43} -170.918 q^{44} -41.6096 q^{45} -103.530 q^{47} -294.126 q^{48} -211.990 q^{49} -118.495 q^{50} -583.876 q^{51} +361.370 q^{52} -211.734 q^{53} +34.5490 q^{54} -45.9956 q^{55} -168.105 q^{56} -1055.83 q^{57} -246.014 q^{58} -115.001 q^{59} -93.4998 q^{60} -184.073 q^{61} +42.7287 q^{62} +251.126 q^{63} -181.616 q^{64} +97.2477 q^{65} -165.602 q^{66} +545.337 q^{67} -588.184 q^{68} -21.1872 q^{70} -582.298 q^{71} -322.232 q^{72} +47.4045 q^{73} -34.9374 q^{74} +849.304 q^{75} -1063.62 q^{76} +277.597 q^{77} +350.129 q^{78} -1250.01 q^{79} -79.7359 q^{80} -840.013 q^{81} +325.714 q^{82} +759.853 q^{83} +564.299 q^{84} -158.285 q^{85} -286.824 q^{86} +1763.29 q^{87} -356.199 q^{88} -785.740 q^{89} -40.6127 q^{90} -586.919 q^{91} -306.256 q^{93} -101.050 q^{94} -286.229 q^{95} -1109.04 q^{96} +560.129 q^{97} -206.912 q^{98} +532.113 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

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Database

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