LMFDB - Embedded newform 511.2.a.f.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [511,2,Mod(1,511)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("511.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(511, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 511 = 7 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	511.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.08035554329$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 9x^{8} + 50x^{7} + 4x^{6} - 194x^{5} + 123x^{4} + 224x^{3} - 231x^{2} + 11x + 27 $ x^10 - 4x^9 - 9x^8 + 50x^7 + 4x^6 - 194x^5 + 123x^4 + 224x^3 - 231x^2 + 11*x + 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.62440$ of defining polynomial
Character	$\chi$	$=$	511.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.62440 q^{2} +3.20819 q^{3} +0.638683 q^{4} -0.880948 q^{5} +5.21139 q^{6} -1.00000 q^{7} -2.21133 q^{8} +7.29249 q^{9} -1.43101 q^{10} +4.50130 q^{11} +2.04902 q^{12} -0.617862 q^{13} -1.62440 q^{14} -2.82625 q^{15} -4.86945 q^{16} -6.73844 q^{17} +11.8459 q^{18} +2.49810 q^{19} -0.562647 q^{20} -3.20819 q^{21} +7.31193 q^{22} +2.73834 q^{23} -7.09436 q^{24} -4.22393 q^{25} -1.00366 q^{26} +13.7711 q^{27} -0.638683 q^{28} -4.21227 q^{29} -4.59097 q^{30} +0.662962 q^{31} -3.48730 q^{32} +14.4410 q^{33} -10.9459 q^{34} +0.880948 q^{35} +4.65759 q^{36} -8.47222 q^{37} +4.05792 q^{38} -1.98222 q^{39} +1.94806 q^{40} +3.58769 q^{41} -5.21139 q^{42} +1.49723 q^{43} +2.87491 q^{44} -6.42430 q^{45} +4.44817 q^{46} -5.90627 q^{47} -15.6221 q^{48} +1.00000 q^{49} -6.86136 q^{50} -21.6182 q^{51} -0.394618 q^{52} -2.68808 q^{53} +22.3698 q^{54} -3.96542 q^{55} +2.21133 q^{56} +8.01438 q^{57} -6.84242 q^{58} -11.1140 q^{59} -1.80508 q^{60} -5.21745 q^{61} +1.07692 q^{62} -7.29249 q^{63} +4.07413 q^{64} +0.544305 q^{65} +23.4581 q^{66} +13.3696 q^{67} -4.30373 q^{68} +8.78513 q^{69} +1.43101 q^{70} +10.8752 q^{71} -16.1261 q^{72} +1.00000 q^{73} -13.7623 q^{74} -13.5512 q^{75} +1.59550 q^{76} -4.50130 q^{77} -3.21992 q^{78} +7.70239 q^{79} +4.28973 q^{80} +22.3029 q^{81} +5.82786 q^{82} +11.1885 q^{83} -2.04902 q^{84} +5.93622 q^{85} +2.43210 q^{86} -13.5138 q^{87} -9.95385 q^{88} +8.04790 q^{89} -10.4357 q^{90} +0.617862 q^{91} +1.74893 q^{92} +2.12691 q^{93} -9.59416 q^{94} -2.20070 q^{95} -11.1879 q^{96} -18.6092 q^{97} +1.62440 q^{98} +32.8257 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - q^{3} + 14 q^{4} + q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 39 q^{9} - 6 q^{10} + 5 q^{11} + q^{12} - q^{13} - 4 q^{14} + q^{15} + 14 q^{16} + 8 q^{17} + 26 q^{18} + 2 q^{19} - 16 q^{20}+ \cdots + 53 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 - q^3 + 14 * q^4 + q^5 + 2 * q^6 - 10 * q^7 + 6 * q^8 + 39 * q^9 - 6 * q^10 + 5 * q^11 + q^12 - q^13 - 4 * q^14 + q^15 + 14 * q^16 + 8 * q^17 + 26 * q^18 + 2 * q^19 - 16 * q^20 + q^21 - 3 * q^22 + 10 * q^23 + 9 * q^24 + 29 * q^25 + 34 * q^26 - 13 * q^27 - 14 * q^28 + 9 * q^29 - 27 * q^30 - 17 * q^31 + 36 * q^32 - 11 * q^33 + 4 * q^34 - q^35 + 68 * q^36 - 9 * q^37 + 6 * q^39 - 41 * q^40 + 39 * q^41 - 2 * q^42 - 7 * q^43 - 12 * q^44 - 8 * q^45 - 11 * q^46 - 38 * q^47 - 32 * q^48 + 10 * q^49 + 31 * q^50 + 4 * q^51 + 52 * q^52 + 9 * q^53 - 80 * q^54 + 13 * q^55 - 6 * q^56 + 20 * q^57 - 19 * q^58 + 5 * q^59 - 79 * q^60 + 10 * q^61 - 25 * q^62 - 39 * q^63 + 16 * q^64 + 55 * q^65 + 26 * q^66 - 22 * q^67 + 4 * q^68 + 4 * q^69 + 6 * q^70 + 30 * q^71 + 21 * q^72 + 10 * q^73 - 4 * q^74 - 24 * q^75 - 24 * q^76 - 5 * q^77 - 19 * q^78 - 14 * q^80 + 46 * q^81 - 6 * q^82 - 25 * q^83 - q^84 + 11 * q^85 - 28 * q^86 - 24 * q^87 - 72 * q^88 + 37 * q^89 - 64 * q^90 + q^91 + 36 * q^92 - 40 * q^93 + 29 * q^94 + 41 * q^95 - 36 * q^96 + 5 * q^97 + 4 * q^98 + 53 * 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 $

$2$	1.62440	1.14863	0.574313	−	0.818636i	$-0.305269\pi$
$2$	1.62440	1.14863	0.574313	+	0.818636i	$0.305269\pi$
$3$	3.20819	1.85225	0.926125	−	0.377217i	$-0.123119\pi$
$3$	3.20819	1.85225	0.926125	+	0.377217i	$0.123119\pi$
$4$	0.638683	0.319342
$5$	−0.880948	−0.393972	−0.196986	−	0.980406i	$-0.563115\pi$
$5$	−0.880948	−0.393972	−0.196986	+	0.980406i	$0.563115\pi$
$6$	5.21139	2.12754
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.21133	−0.781822
$9$	7.29249	2.43083
$10$	−1.43101	−0.452527
$11$	4.50130	1.35719	0.678597	−	0.734511i	$-0.262588\pi$
$11$	4.50130	1.35719	0.678597	+	0.734511i	$0.262588\pi$
$12$	2.04902	0.591501
$13$	−0.617862	−0.171364	−0.0856821	−	0.996323i	$-0.527307\pi$
$13$	−0.617862	−0.171364	−0.0856821	+	0.996323i	$0.527307\pi$
$14$	−1.62440	−0.434140
$15$	−2.82625	−0.729735
$16$	−4.86945	−1.21736
$17$	−6.73844	−1.63431	−0.817156	−	0.576417i	$-0.804450\pi$
$17$	−6.73844	−1.63431	−0.817156	+	0.576417i	$0.804450\pi$
$18$	11.8459	2.79211
$19$	2.49810	0.573104	0.286552	−	0.958065i	$-0.407491\pi$
$19$	2.49810	0.573104	0.286552	+	0.958065i	$0.407491\pi$
$20$	−0.562647	−0.125812
$21$	−3.20819	−0.700085
$22$	7.31193	1.55891
$23$	2.73834	0.570984	0.285492	−	0.958381i	$-0.407843\pi$
$23$	2.73834	0.570984	0.285492	+	0.958381i	$0.407843\pi$
$24$	−7.09436	−1.44813
$25$	−4.22393	−0.844786
$26$	−1.00366	−0.196833
$27$	13.7711	2.65025
$28$	−0.638683	−0.120700
$29$	−4.21227	−0.782198	−0.391099	−	0.920349i	$-0.627905\pi$
$29$	−4.21227	−0.782198	−0.391099	+	0.920349i	$0.627905\pi$
$30$	−4.59097	−0.838192
$31$	0.662962	0.119071	0.0595357	−	0.998226i	$-0.481038\pi$
$31$	0.662962	0.119071	0.0595357	+	0.998226i	$0.481038\pi$
$32$	−3.48730	−0.616473
$33$	14.4410	2.51386
$34$	−10.9459	−1.87721
$35$	0.880948	0.148907
$36$	4.65759	0.776265
$37$	−8.47222	−1.39282	−0.696412	−	0.717642i	$-0.745221\pi$
$37$	−8.47222	−1.39282	−0.696412	+	0.717642i	$0.745221\pi$
$38$	4.05792	0.658282
$39$	−1.98222	−0.317409
$40$	1.94806	0.308016
$41$	3.58769	0.560304	0.280152	−	0.959956i	$-0.409615\pi$
$41$	3.58769	0.560304	0.280152	+	0.959956i	$0.409615\pi$
$42$	−5.21139	−0.804135
$43$	1.49723	0.228325	0.114162	−	0.993462i	$-0.463582\pi$
$43$	1.49723	0.228325	0.114162	+	0.993462i	$0.463582\pi$
$44$	2.87491	0.433409
$45$	−6.42430	−0.957679
$46$	4.44817	0.655847
$47$	−5.90627	−0.861518	−0.430759	−	0.902467i	$-0.641754\pi$
$47$	−5.90627	−0.861518	−0.430759	+	0.902467i	$0.641754\pi$
$48$	−15.6221	−2.25486
$49$	1.00000	0.142857
$50$	−6.86136	−0.970343
$51$	−21.6182	−3.02715
$52$	−0.394618	−0.0547237
$53$	−2.68808	−0.369236	−0.184618	−	0.982810i	$-0.559105\pi$
$53$	−2.68808	−0.369236	−0.184618	+	0.982810i	$0.559105\pi$
$54$	22.3698	3.04415
$55$	−3.96542	−0.534696
$56$	2.21133	0.295501
$57$	8.01438	1.06153
$58$	−6.84242	−0.898454
$59$	−11.1140	−1.44692	−0.723460	−	0.690366i	$-0.757449\pi$
$59$	−11.1140	−1.44692	−0.723460	+	0.690366i	$0.757449\pi$
$60$	−1.80508	−0.233035
$61$	−5.21745	−0.668027	−0.334013	−	0.942568i	$-0.608403\pi$
$61$	−5.21745	−0.668027	−0.334013	+	0.942568i	$0.608403\pi$
$62$	1.07692	0.136769
$63$	−7.29249	−0.918767
$64$	4.07413	0.509266
$65$	0.544305	0.0675127
$66$	23.4581	2.88749
$67$	13.3696	1.63336	0.816681	−	0.577090i	$-0.195812\pi$
$67$	13.3696	1.63336	0.816681	+	0.577090i	$0.195812\pi$
$68$	−4.30373	−0.521904
$69$	8.78513	1.05761
$70$	1.43101	0.171039
$71$	10.8752	1.29064	0.645322	−	0.763911i	$-0.276723\pi$
$71$	10.8752	1.29064	0.645322	+	0.763911i	$0.276723\pi$
$72$	−16.1261	−1.90048
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−13.7623	−1.59983
$75$	−13.5512	−1.56475
$76$	1.59550	0.183016
$77$	−4.50130	−0.512971
$78$	−3.21992	−0.364585
$79$	7.70239	0.866586	0.433293	−	0.901253i	$-0.357351\pi$
$79$	7.70239	0.866586	0.433293	+	0.901253i	$0.357351\pi$
$80$	4.28973	0.479607
$81$	22.3029	2.47810
$82$	5.82786	0.643579
$83$	11.1885	1.22809	0.614047	−	0.789269i	$-0.289540\pi$
$83$	11.1885	1.22809	0.614047	+	0.789269i	$0.289540\pi$
$84$	−2.04902	−0.223566
$85$	5.93622	0.643873
$86$	2.43210	0.262260
$87$	−13.5138	−1.44883
$88$	−9.95385	−1.06108
$89$	8.04790	0.853076	0.426538	−	0.904470i	$-0.359733\pi$
$89$	8.04790	0.853076	0.426538	+	0.904470i	$0.359733\pi$
$90$	−10.4357	−1.10001
$91$	0.617862	0.0647696
$92$	1.74893	0.182339
$93$	2.12691	0.220550
$94$	−9.59416	−0.989562
$95$	−2.20070	−0.225787
$96$	−11.1879	−1.14186
$97$	−18.6092	−1.88948	−0.944740	−	0.327821i	$-0.893686\pi$
$97$	−18.6092	−1.88948	−0.944740	+	0.327821i	$0.893686\pi$
$98$	1.62440	0.164089
$99$	32.8257	3.29911
$100$	−2.69775	−0.269775
$101$	10.8432	1.07893	0.539467	−	0.842007i	$-0.318626\pi$
$101$	10.8432	1.07893	0.539467	+	0.842007i	$0.318626\pi$
$102$	−35.1167	−3.47707
$103$	−12.8510	−1.26624	−0.633122	−	0.774052i	$-0.718227\pi$
$103$	−12.8510	−1.26624	−0.633122	+	0.774052i	$0.718227\pi$
$104$	1.36630	0.133976
$105$	2.82625	0.275814
$106$	−4.36652	−0.424114
$107$	16.5272	1.59774	0.798872	−	0.601501i	$-0.205430\pi$
$107$	16.5272	1.59774	0.798872	+	0.601501i	$0.205430\pi$
$108$	8.79538	0.846336
$109$	12.5807	1.20501	0.602507	−	0.798114i	$-0.294169\pi$
$109$	12.5807	1.20501	0.602507	+	0.798114i	$0.294169\pi$
$110$	−6.44143	−0.614166
$111$	−27.1805	−2.57986
$112$	4.86945	0.460120
$113$	−7.85071	−0.738533	−0.369266	−	0.929324i	$-0.620391\pi$
$113$	−7.85071	−0.738533	−0.369266	+	0.929324i	$0.620391\pi$
$114$	13.0186	1.21930
$115$	−2.41234	−0.224952
$116$	−2.69031	−0.249789
$117$	−4.50575	−0.416557
$118$	−18.0536	−1.66197
$119$	6.73844	0.617712
$120$	6.24976	0.570522
$121$	9.26173	0.841975
$122$	−8.47525	−0.767313
$123$	11.5100	1.03782
$124$	0.423423	0.0380245
$125$	8.12581	0.726794
$126$	−11.8459	−1.05532
$127$	6.26305	0.555756	0.277878	−	0.960616i	$-0.410369\pi$
$127$	6.26305	0.555756	0.277878	+	0.960616i	$0.410369\pi$
$128$	13.5926	1.20143
$129$	4.80339	0.422915
$130$	0.884170	0.0775468
$131$	3.52221	0.307737	0.153868	−	0.988091i	$-0.450827\pi$
$131$	3.52221	0.307737	0.153868	+	0.988091i	$0.450827\pi$
$132$	9.22325	0.802781
$133$	−2.49810	−0.216613
$134$	21.7177	1.87612
$135$	−12.1316	−1.04413
$136$	14.9009	1.27774
$137$	−0.205413	−0.0175496	−0.00877481	−	0.999962i	$-0.502793\pi$
$137$	−0.205413	−0.0175496	−0.00877481	+	0.999962i	$0.502793\pi$
$138$	14.2706	1.21479
$139$	19.9614	1.69310	0.846551	−	0.532308i	$-0.178675\pi$
$139$	19.9614	1.69310	0.846551	+	0.532308i	$0.178675\pi$
$140$	0.562647	0.0475524
$141$	−18.9484	−1.59575
$142$	17.6656	1.48247
$143$	−2.78119	−0.232574
$144$	−35.5104	−2.95920
$145$	3.71079	0.308164
$146$	1.62440	0.134437
$147$	3.20819	0.264607
$148$	−5.41107	−0.444787
$149$	−6.38767	−0.523298	−0.261649	−	0.965163i	$-0.584266\pi$
$149$	−6.38767	−0.523298	−0.261649	+	0.965163i	$0.584266\pi$
$150$	−22.0126	−1.79732
$151$	15.5945	1.26906	0.634531	−	0.772897i	$-0.281193\pi$
$151$	15.5945	1.26906	0.634531	+	0.772897i	$0.281193\pi$
$152$	−5.52412	−0.448065
$153$	−49.1400	−3.97273
$154$	−7.31193	−0.589212
$155$	−0.584035	−0.0469108
$156$	−1.26601	−0.101362
$157$	−16.0542	−1.28126	−0.640632	−	0.767848i	$-0.721328\pi$
$157$	−16.0542	−1.28126	−0.640632	+	0.767848i	$0.721328\pi$
$158$	12.5118	0.995384
$159$	−8.62387	−0.683918
$160$	3.07213	0.242873
$161$	−2.73834	−0.215812
$162$	36.2289	2.84641
$163$	−6.75757	−0.529294	−0.264647	−	0.964345i	$-0.585255\pi$
$163$	−6.75757	−0.529294	−0.264647	+	0.964345i	$0.585255\pi$
$164$	2.29140	0.178928
$165$	−12.7218	−0.990391
$166$	18.1746	1.41062
$167$	−9.85473	−0.762582	−0.381291	−	0.924455i	$-0.624520\pi$
$167$	−9.85473	−0.762582	−0.381291	+	0.924455i	$0.624520\pi$
$168$	7.09436	0.547341
$169$	−12.6182	−0.970634
$170$	9.64280	0.739569
$171$	18.2174	1.39312
$172$	0.956253	0.0729136
$173$	10.8787	0.827094	0.413547	−	0.910483i	$-0.364290\pi$
$173$	10.8787	0.827094	0.413547	+	0.910483i	$0.364290\pi$
$174$	−21.9518	−1.66416
$175$	4.22393	0.319299
$176$	−21.9189	−1.65220
$177$	−35.6558	−2.68006
$178$	13.0730	0.979865
$179$	14.6558	1.09542	0.547712	−	0.836667i	$-0.315499\pi$
$179$	14.6558	1.09542	0.547712	+	0.836667i	$0.315499\pi$
$180$	−4.10310	−0.305827
$181$	−10.6633	−0.792600	−0.396300	−	0.918121i	$-0.629706\pi$
$181$	−10.6633	−0.792600	−0.396300	+	0.918121i	$0.629706\pi$
$182$	1.00366	0.0743960
$183$	−16.7386	−1.23735
$184$	−6.05537	−0.446408
$185$	7.46359	0.548734
$186$	3.45495	0.253330
$187$	−30.3318	−2.21808
$188$	−3.77224	−0.275119
$189$	−13.7711	−1.00170
$190$	−3.57482	−0.259345
$191$	−20.7459	−1.50112	−0.750559	−	0.660803i	$-0.770216\pi$
$191$	−20.7459	−1.50112	−0.750559	+	0.660803i	$0.770216\pi$
$192$	13.0706	0.943288
$193$	9.84119	0.708384	0.354192	−	0.935173i	$-0.384756\pi$
$193$	9.84119	0.708384	0.354192	+	0.935173i	$0.384756\pi$
$194$	−30.2289	−2.17031
$195$	1.74623	0.125050
$196$	0.638683	0.0456202
$197$	−18.1915	−1.29609	−0.648045	−	0.761602i	$-0.724413\pi$
$197$	−18.1915	−1.29609	−0.648045	+	0.761602i	$0.724413\pi$
$198$	53.3221	3.78944
$199$	5.93354	0.420618	0.210309	−	0.977635i	$-0.432553\pi$
$199$	5.93354	0.420618	0.210309	+	0.977635i	$0.432553\pi$
$200$	9.34049	0.660472
$201$	42.8923	3.02539
$202$	17.6136	1.23929
$203$	4.21227	0.295643
$204$	−13.8072	−0.966696
$205$	−3.16057	−0.220744
$206$	−20.8752	−1.45444
$207$	19.9693	1.38796
$208$	3.00865	0.208612
$209$	11.2447	0.777813
$210$	4.59097	0.316807
$211$	6.85068	0.471620	0.235810	−	0.971799i	$-0.424226\pi$
$211$	6.85068	0.471620	0.235810	+	0.971799i	$0.424226\pi$
$212$	−1.71683	−0.117913
$213$	34.8896	2.39059
$214$	26.8468	1.83521
$215$	−1.31898	−0.0899536
$216$	−30.4524	−2.07203
$217$	−0.662962	−0.0450048
$218$	20.4361	1.38411
$219$	3.20819	0.216789
$220$	−2.53264	−0.170751
$221$	4.16343	0.280062
$222$	−44.1521	−2.96329
$223$	7.00184	0.468878	0.234439	−	0.972131i	$-0.424675\pi$
$223$	7.00184	0.468878	0.234439	+	0.972131i	$0.424675\pi$
$224$	3.48730	0.233005
$225$	−30.8030	−2.05353
$226$	−12.7527	−0.848298
$227$	−23.1349	−1.53551	−0.767757	−	0.640741i	$-0.778627\pi$
$227$	−23.1349	−1.53551	−0.767757	+	0.640741i	$0.778627\pi$
$228$	5.11865	0.338991
$229$	−22.8691	−1.51123	−0.755615	−	0.655016i	$-0.772662\pi$
$229$	−22.8691	−1.51123	−0.755615	+	0.655016i	$0.772662\pi$
$230$	−3.91861	−0.258385
$231$	−14.4410	−0.950151
$232$	9.31470	0.611540
$233$	4.47629	0.293251	0.146626	−	0.989192i	$-0.453159\pi$
$233$	4.47629	0.293251	0.146626	+	0.989192i	$0.453159\pi$
$234$	−7.31916	−0.478468
$235$	5.20312	0.339414
$236$	−7.09833	−0.462062
$237$	24.7107	1.60513
$238$	10.9459	0.709520
$239$	4.17383	0.269983	0.134991	−	0.990847i	$-0.456899\pi$
$239$	4.17383	0.269983	0.134991	+	0.990847i	$0.456899\pi$
$240$	13.7623	0.888352
$241$	−20.5892	−1.32627	−0.663134	−	0.748500i	$-0.730774\pi$
$241$	−20.5892	−1.32627	−0.663134	+	0.748500i	$0.730774\pi$
$242$	15.0448	0.967115
$243$	30.2386	1.93981
$244$	−3.33230	−0.213329
$245$	−0.880948	−0.0562817
$246$	18.6969	1.19207
$247$	−1.54348	−0.0982094
$248$	−1.46602	−0.0930927
$249$	35.8948	2.27474
$250$	13.1996	0.834815
$251$	−3.02440	−0.190898	−0.0954492	−	0.995434i	$-0.530429\pi$
$251$	−3.02440	−0.190898	−0.0954492	+	0.995434i	$0.530429\pi$
$252$	−4.65759	−0.293401
$253$	12.3261	0.774936
$254$	10.1737	0.638355
$255$	19.0445	1.19261
$256$	13.9316	0.870726
$257$	−5.19840	−0.324268	−0.162134	−	0.986769i	$-0.551838\pi$
$257$	−5.19840	−0.324268	−0.162134	+	0.986769i	$0.551838\pi$
$258$	7.80263	0.485771
$259$	8.47222	0.526438
$260$	0.347638	0.0215596
$261$	−30.7179	−1.90139
$262$	5.72148	0.353474
$263$	23.3937	1.44252	0.721258	−	0.692667i	$-0.243564\pi$
$263$	23.3937	1.44252	0.721258	+	0.692667i	$0.243564\pi$
$264$	−31.9338	−1.96539
$265$	2.36806	0.145469
$266$	−4.05792	−0.248807
$267$	25.8192	1.58011
$268$	8.53897	0.521600
$269$	5.15570	0.314348	0.157174	−	0.987571i	$-0.449762\pi$
$269$	5.15570	0.314348	0.157174	+	0.987571i	$0.449762\pi$
$270$	−19.7067	−1.19931
$271$	−24.2030	−1.47023	−0.735113	−	0.677945i	$-0.762871\pi$
$271$	−24.2030	−1.47023	−0.735113	+	0.677945i	$0.762871\pi$
$272$	32.8125	1.98955
$273$	1.98222	0.119969
$274$	−0.333673	−0.0201579
$275$	−19.0132	−1.14654
$276$	5.61092	0.337737
$277$	8.84019	0.531156	0.265578	−	0.964089i	$-0.414437\pi$
$277$	8.84019	0.531156	0.265578	+	0.964089i	$0.414437\pi$
$278$	32.4253	1.94474
$279$	4.83464	0.289442
$280$	−1.94806	−0.116419
$281$	24.5106	1.46218	0.731091	−	0.682280i	$-0.239011\pi$
$281$	24.5106	1.46218	0.731091	+	0.682280i	$0.239011\pi$
$282$	−30.7799	−1.83292
$283$	21.0649	1.25218	0.626089	−	0.779752i	$-0.284655\pi$
$283$	21.0649	1.25218	0.626089	+	0.779752i	$0.284655\pi$
$284$	6.94578	0.412156
$285$	−7.06026	−0.418214
$286$	−4.51776	−0.267141
$287$	−3.58769	−0.211775
$288$	−25.4311	−1.49854
$289$	28.4066	1.67097
$290$	6.02782	0.353966
$291$	−59.7019	−3.49979
$292$	0.638683	0.0373761
$293$	21.5098	1.25661	0.628307	−	0.777966i	$-0.283748\pi$
$293$	21.5098	1.25661	0.628307	+	0.777966i	$0.283748\pi$
$294$	5.21139	0.303935
$295$	9.79086	0.570046
$296$	18.7348	1.08894
$297$	61.9880	3.59691
$298$	−10.3761	−0.601074
$299$	−1.69192	−0.0978462
$300$	−8.65491	−0.499691
$301$	−1.49723	−0.0862987
$302$	25.3317	1.45768
$303$	34.7869	1.99846
$304$	−12.1644	−0.697675
$305$	4.59631	0.263184
$306$	−79.8231	−4.56318
$307$	−22.9024	−1.30711	−0.653554	−	0.756880i	$-0.726723\pi$
$307$	−22.9024	−1.30711	−0.653554	+	0.756880i	$0.726723\pi$
$308$	−2.87491	−0.163813
$309$	−41.2284	−2.34540
$310$	−0.948708	−0.0538830
$311$	13.0193	0.738258	0.369129	−	0.929378i	$-0.379656\pi$
$311$	13.0193	0.738258	0.369129	+	0.929378i	$0.379656\pi$
$312$	4.38334	0.248157
$313$	−17.7572	−1.00369	−0.501847	−	0.864956i	$-0.667346\pi$
$313$	−17.7572	−1.00369	−0.501847	+	0.864956i	$0.667346\pi$
$314$	−26.0785	−1.47169
$315$	6.42430	0.361969
$316$	4.91939	0.276737
$317$	33.1991	1.86465	0.932324	−	0.361624i	$-0.117778\pi$
$317$	33.1991	1.86465	0.932324	+	0.361624i	$0.117778\pi$
$318$	−14.0086	−0.785566
$319$	−18.9607	−1.06160
$320$	−3.58910	−0.200637
$321$	53.0224	2.95942
$322$	−4.44817	−0.247887
$323$	−16.8333	−0.936630
$324$	14.2445	0.791361
$325$	2.60981	0.144766
$326$	−10.9770	−0.607960
$327$	40.3613	2.23199
$328$	−7.93356	−0.438058
$329$	5.90627	0.325623
$330$	−20.6653	−1.13759
$331$	−22.5879	−1.24154	−0.620772	−	0.783991i	$-0.713181\pi$
$331$	−22.5879	−1.24154	−0.620772	+	0.783991i	$0.713181\pi$
$332$	7.14589	0.392182
$333$	−61.7835	−3.38572
$334$	−16.0081	−0.875922
$335$	−11.7780	−0.643499
$336$	15.6221	0.852257
$337$	−27.1088	−1.47671	−0.738354	−	0.674413i	$-0.764397\pi$
$337$	−27.1088	−1.47671	−0.738354	+	0.674413i	$0.764397\pi$
$338$	−20.4971	−1.11490
$339$	−25.1866	−1.36795
$340$	3.79136	0.205616
$341$	2.98419	0.161603
$342$	29.5923	1.60017
$343$	−1.00000	−0.0539949
$344$	−3.31085	−0.178509
$345$	−7.73924	−0.416667
$346$	17.6714	0.950021
$347$	12.0004	0.644214	0.322107	−	0.946703i	$-0.395609\pi$
$347$	12.0004	0.644214	0.322107	+	0.946703i	$0.395609\pi$
$348$	−8.63101	−0.462671
$349$	29.5953	1.58420	0.792099	−	0.610393i	$-0.208988\pi$
$349$	29.5953	1.58420	0.792099	+	0.610393i	$0.208988\pi$
$350$	6.86136	0.366755
$351$	−8.50865	−0.454158
$352$	−15.6974	−0.836673
$353$	16.1778	0.861057	0.430529	−	0.902577i	$-0.358327\pi$
$353$	16.1778	0.861057	0.430529	+	0.902577i	$0.358327\pi$
$354$	−57.9194	−3.07838
$355$	−9.58045	−0.508477
$356$	5.14006	0.272423
$357$	21.6182	1.14416
$358$	23.8069	1.25823
$359$	−33.8537	−1.78673	−0.893365	−	0.449332i	$-0.851662\pi$
$359$	−33.8537	−1.78673	−0.893365	+	0.449332i	$0.851662\pi$
$360$	14.2062	0.748734
$361$	−12.7595	−0.671552
$362$	−17.3216	−0.910401
$363$	29.7134	1.55955
$364$	0.394618	0.0206836
$365$	−0.880948	−0.0461109
$366$	−27.1902	−1.42125
$367$	2.59216	0.135310	0.0676548	−	0.997709i	$-0.478448\pi$
$367$	2.59216	0.135310	0.0676548	+	0.997709i	$0.478448\pi$
$368$	−13.3342	−0.695095
$369$	26.1632	1.36200
$370$	12.1239	0.630290
$371$	2.68808	0.139558
$372$	1.35842	0.0704308
$373$	−30.7810	−1.59378	−0.796890	−	0.604125i	$-0.793523\pi$
$373$	−30.7810	−1.59378	−0.796890	+	0.604125i	$0.793523\pi$
$374$	−49.2710	−2.54774
$375$	26.0691	1.34620
$376$	13.0607	0.673554
$377$	2.60260	0.134041
$378$	−22.3698	−1.15058
$379$	14.2840	0.733721	0.366861	−	0.930276i	$-0.380433\pi$
$379$	14.2840	0.733721	0.366861	+	0.930276i	$0.380433\pi$
$380$	−1.40555	−0.0721031
$381$	20.0931	1.02940
$382$	−33.6996	−1.72422
$383$	−36.6876	−1.87465	−0.937323	−	0.348461i	$-0.886704\pi$
$383$	−36.6876	−1.87465	−0.937323	+	0.348461i	$0.886704\pi$
$384$	43.6077	2.22535
$385$	3.96542	0.202096
$386$	15.9861	0.813669
$387$	10.9185	0.555019
$388$	−11.8854	−0.603390
$389$	32.8493	1.66553	0.832763	−	0.553630i	$-0.186758\pi$
$389$	32.8493	1.66553	0.832763	+	0.553630i	$0.186758\pi$
$390$	2.83659	0.143636
$391$	−18.4522	−0.933166
$392$	−2.21133	−0.111689
$393$	11.2999	0.570005
$394$	−29.5503	−1.48872
$395$	−6.78540	−0.341411
$396$	20.9652	1.05354
$397$	−18.4025	−0.923593	−0.461796	−	0.886986i	$-0.652795\pi$
$397$	−18.4025	−0.923593	−0.461796	+	0.886986i	$0.652795\pi$
$398$	9.63846	0.483132
$399$	−8.01438	−0.401221
$400$	20.5682	1.02841
$401$	0.867103	0.0433011	0.0216505	−	0.999766i	$-0.493108\pi$
$401$	0.867103	0.0433011	0.0216505	+	0.999766i	$0.493108\pi$
$402$	69.6744	3.47504
$403$	−0.409619	−0.0204046
$404$	6.92534	0.344549
$405$	−19.6477	−0.976302
$406$	6.84242	0.339584
$407$	−38.1360	−1.89033
$408$	47.8049	2.36669
$409$	−18.3204	−0.905885	−0.452942	−	0.891540i	$-0.649626\pi$
$409$	−18.3204	−0.905885	−0.452942	+	0.891540i	$0.649626\pi$
$410$	−5.13404	−0.253552
$411$	−0.659004	−0.0325063
$412$	−8.20771	−0.404365
$413$	11.1140	0.546884
$414$	32.4382	1.59425
$415$	−9.85647	−0.483835
$416$	2.15467	0.105641
$417$	64.0399	3.13605
$418$	18.2659	0.893416
$419$	34.6358	1.69207	0.846035	−	0.533127i	$-0.178983\pi$
$419$	34.6358	1.69207	0.846035	+	0.533127i	$0.178983\pi$
$420$	1.80508	0.0880788
$421$	−22.1175	−1.07794	−0.538970	−	0.842325i	$-0.681186\pi$
$421$	−22.1175	−1.07794	−0.538970	+	0.842325i	$0.681186\pi$
$422$	11.1283	0.541715
$423$	−43.0714	−2.09420
$424$	5.94422	0.288677
$425$	28.4627	1.38064
$426$	56.6747	2.74590
$427$	5.21745	0.252490
$428$	10.5556	0.510226
$429$	−8.92257	−0.430786
$430$	−2.14255	−0.103323
$431$	5.54252	0.266974	0.133487	−	0.991051i	$-0.457383\pi$
$431$	5.54252	0.266974	0.133487	+	0.991051i	$0.457383\pi$
$432$	−67.0578	−3.22632
$433$	−20.3386	−0.977409	−0.488704	−	0.872449i	$-0.662530\pi$
$433$	−20.3386	−0.977409	−0.488704	+	0.872449i	$0.662530\pi$
$434$	−1.07692	−0.0516937
$435$	11.9049	0.570797
$436$	8.03509	0.384811
$437$	6.84066	0.327233
$438$	5.21139	0.249010
$439$	1.88008	0.0897312	0.0448656	−	0.998993i	$-0.485714\pi$
$439$	1.88008	0.0897312	0.0448656	+	0.998993i	$0.485714\pi$
$440$	8.76883	0.418037
$441$	7.29249	0.347261
$442$	6.76308	0.321687
$443$	24.1949	1.14953	0.574767	−	0.818317i	$-0.305093\pi$
$443$	24.1949	1.14953	0.574767	+	0.818317i	$0.305093\pi$
$444$	−17.3597	−0.823856
$445$	−7.08978	−0.336088
$446$	11.3738	0.538565
$447$	−20.4929	−0.969279
$448$	−4.07413	−0.192485
$449$	4.03626	0.190483	0.0952414	−	0.995454i	$-0.469638\pi$
$449$	4.03626	0.190483	0.0952414	+	0.995454i	$0.469638\pi$
$450$	−50.0364	−2.35874
$451$	16.1493	0.760441
$452$	−5.01412	−0.235844
$453$	50.0301	2.35062
$454$	−37.5803	−1.76373
$455$	−0.544305	−0.0255174
$456$	−17.7224	−0.829928
$457$	−7.11969	−0.333045	−0.166522	−	0.986038i	$-0.553254\pi$
$457$	−7.11969	−0.333045	−0.166522	+	0.986038i	$0.553254\pi$
$458$	−37.1485	−1.73584
$459$	−92.7958	−4.33134
$460$	−1.54072	−0.0718365
$461$	−7.96449	−0.370943	−0.185472	−	0.982650i	$-0.559381\pi$
$461$	−7.96449	−0.370943	−0.185472	+	0.982650i	$0.559381\pi$
$462$	−23.4581	−1.09137
$463$	−8.83566	−0.410628	−0.205314	−	0.978696i	$-0.565822\pi$
$463$	−8.83566	−0.410628	−0.205314	+	0.978696i	$0.565822\pi$
$464$	20.5114	0.952219
$465$	−1.87370	−0.0868906
$466$	7.27130	0.336836
$467$	−10.9742	−0.507824	−0.253912	−	0.967227i	$-0.581717\pi$
$467$	−10.9742	−0.507824	−0.253912	+	0.967227i	$0.581717\pi$
$468$	−2.87775	−0.133024
$469$	−13.3696	−0.617352
$470$	8.45196	0.389860
$471$	−51.5049	−2.37322
$472$	24.5767	1.13123
$473$	6.73947	0.309881
$474$	40.1402	1.84370
$475$	−10.5518	−0.484150
$476$	4.30373	0.197261
$477$	−19.6028	−0.897550
$478$	6.77998	0.310109
$479$	15.1286	0.691244	0.345622	−	0.938374i	$-0.387668\pi$
$479$	15.1286	0.691244	0.345622	+	0.938374i	$0.387668\pi$
$480$	9.85597	0.449861
$481$	5.23466	0.238680
$482$	−33.4452	−1.52339
$483$	−8.78513	−0.399737
$484$	5.91531	0.268878
$485$	16.3938	0.744402
$486$	49.1197	2.22811
$487$	−20.6579	−0.936099	−0.468049	−	0.883702i	$-0.655043\pi$
$487$	−20.6579	−0.936099	−0.468049	+	0.883702i	$0.655043\pi$
$488$	11.5375	0.522278
$489$	−21.6796	−0.980384
$490$	−1.43101	−0.0646466
$491$	17.3728	0.784023	0.392012	−	0.919960i	$-0.371779\pi$
$491$	17.3728	0.784023	0.392012	+	0.919960i	$0.371779\pi$
$492$	7.35125	0.331420
$493$	28.3841	1.27836
$494$	−2.50724	−0.112806
$495$	−28.9177	−1.29976
$496$	−3.22826	−0.144953
$497$	−10.8752	−0.487817
$498$	58.3075	2.61282
$499$	−24.8042	−1.11039	−0.555195	−	0.831720i	$-0.687357\pi$
$499$	−24.8042	−1.11039	−0.555195	+	0.831720i	$0.687357\pi$
$500$	5.18982	0.232096
$501$	−31.6159	−1.41249
$502$	−4.91284	−0.219271
$503$	−31.3716	−1.39879	−0.699396	−	0.714734i	$-0.746548\pi$
$503$	−31.3716	−1.39879	−0.699396	+	0.714734i	$0.746548\pi$
$504$	16.1261	0.718312
$505$	−9.55226	−0.425070
$506$	20.0226	0.890112
$507$	−40.4817	−1.79786
$508$	4.00010	0.177476
$509$	−15.0918	−0.668933	−0.334466	−	0.942408i	$-0.608556\pi$
$509$	−15.0918	−0.668933	−0.334466	+	0.942408i	$0.608556\pi$
$510$	30.9360	1.36987
$511$	−1.00000	−0.0442374
$512$	−4.55467	−0.201290
$513$	34.4016	1.51887
$514$	−8.44430	−0.372462
$515$	11.3210	0.498865
$516$	3.06784	0.135054
$517$	−26.5859	−1.16925
$518$	13.7623	0.604680
$519$	34.9010	1.53198
$520$	−1.20364	−0.0527829
$521$	−8.83021	−0.386858	−0.193429	−	0.981114i	$-0.561961\pi$
$521$	−8.83021	−0.386858	−0.193429	+	0.981114i	$0.561961\pi$
$522$	−49.8982	−2.18399
$523$	5.17012	0.226074	0.113037	−	0.993591i	$-0.463942\pi$
$523$	5.17012	0.226074	0.113037	+	0.993591i	$0.463942\pi$
$524$	2.24957	0.0982731
$525$	13.5512	0.591422
$526$	38.0007	1.65691
$527$	−4.46733	−0.194600
$528$	−70.3199	−3.06028
$529$	−15.5015	−0.673977
$530$	3.84668	0.167089
$531$	−81.0487	−3.51721
$532$	−1.59550	−0.0691735
$533$	−2.21670	−0.0960160
$534$	41.9408	1.81495
$535$	−14.5596	−0.629466
$536$	−29.5646	−1.27700
$537$	47.0185	2.02900
$538$	8.37493	0.361069
$539$	4.50130	0.193885
$540$	−7.74828	−0.333433
$541$	7.90173	0.339722	0.169861	−	0.985468i	$-0.445668\pi$
$541$	7.90173	0.339722	0.169861	+	0.985468i	$0.445668\pi$
$542$	−39.3154	−1.68874
$543$	−34.2100	−1.46809
$544$	23.4989	1.00751
$545$	−11.0830	−0.474742
$546$	3.21992	0.137800
$547$	8.08897	0.345859	0.172930	−	0.984934i	$-0.444677\pi$
$547$	8.08897	0.345859	0.172930	+	0.984934i	$0.444677\pi$
$548$	−0.131194	−0.00560433
$549$	−38.0482	−1.62386
$550$	−30.8851	−1.31694
$551$	−10.5227	−0.448281
$552$	−19.4268	−0.826859
$553$	−7.70239	−0.327539
$554$	14.3600	0.610099
$555$	23.9446	1.01639
$556$	12.7490	0.540678
$557$	−30.5737	−1.29545	−0.647724	−	0.761875i	$-0.724279\pi$
$557$	−30.5737	−1.29545	−0.647724	+	0.761875i	$0.724279\pi$
$558$	7.85340	0.332461
$559$	−0.925080	−0.0391267
$560$	−4.28973	−0.181274
$561$	−97.3101	−4.10843
$562$	39.8151	1.67950
$563$	−2.04178	−0.0860508	−0.0430254	−	0.999074i	$-0.513700\pi$
$563$	−2.04178	−0.0860508	−0.0430254	+	0.999074i	$0.513700\pi$
$564$	−12.1021	−0.509589
$565$	6.91607	0.290961
$566$	34.2179	1.43828
$567$	−22.3029	−0.936634
$568$	−24.0485	−1.00905
$569$	6.48920	0.272041	0.136021	−	0.990706i	$-0.456569\pi$
$569$	6.48920	0.272041	0.136021	+	0.990706i	$0.456569\pi$
$570$	−11.4687	−0.480371
$571$	−29.7786	−1.24620	−0.623098	−	0.782144i	$-0.714126\pi$
$571$	−29.7786	−1.24620	−0.623098	+	0.782144i	$0.714126\pi$
$572$	−1.77630	−0.0742707
$573$	−66.5567	−2.78045
$574$	−5.82786	−0.243250
$575$	−11.5666	−0.482359
$576$	29.7105	1.23794
$577$	24.1885	1.00698	0.503490	−	0.864001i	$-0.332049\pi$
$577$	24.1885	1.00698	0.503490	+	0.864001i	$0.332049\pi$
$578$	46.1437	1.91932
$579$	31.5724	1.31210
$580$	2.37002	0.0984097
$581$	−11.1885	−0.464176
$582$	−96.9799	−4.01995
$583$	−12.0999	−0.501125
$584$	−2.21133	−0.0915053
$585$	3.96934	0.164112
$586$	34.9405	1.44338
$587$	14.7506	0.608824	0.304412	−	0.952540i	$-0.401540\pi$
$587$	14.7506	0.608824	0.304412	+	0.952540i	$0.401540\pi$
$588$	2.04902	0.0845001
$589$	1.65615	0.0682403
$590$	15.9043	0.654770
$591$	−58.3617	−2.40068
$592$	41.2550	1.69557
$593$	3.56494	0.146395	0.0731973	−	0.997317i	$-0.476680\pi$
$593$	3.56494	0.146395	0.0731973	+	0.997317i	$0.476680\pi$
$594$	100.693	4.13150
$595$	−5.93622	−0.243361
$596$	−4.07970	−0.167111
$597$	19.0359	0.779089
$598$	−2.74836	−0.112389
$599$	11.5677	0.472642	0.236321	−	0.971675i	$-0.424058\pi$
$599$	11.5677	0.472642	0.236321	+	0.971675i	$0.424058\pi$
$600$	29.9661	1.22336
$601$	33.1217	1.35106	0.675532	−	0.737331i	$-0.263914\pi$
$601$	33.1217	1.35106	0.675532	+	0.737331i	$0.263914\pi$
$602$	−2.43210	−0.0991249
$603$	97.4979	3.97042
$604$	9.95995	0.405265
$605$	−8.15910	−0.331715
$606$	56.5079	2.29548
$607$	2.48973	0.101055	0.0505276	−	0.998723i	$-0.483910\pi$
$607$	2.48973	0.101055	0.0505276	+	0.998723i	$0.483910\pi$
$608$	−8.71161	−0.353303
$609$	13.5138	0.547605
$610$	7.46625	0.302300
$611$	3.64926	0.147633
$612$	−31.3849	−1.26866
$613$	21.2847	0.859680	0.429840	−	0.902905i	$-0.358570\pi$
$613$	21.2847	0.859680	0.429840	+	0.902905i	$0.358570\pi$
$614$	−37.2027	−1.50138
$615$	−10.1397	−0.408873
$616$	9.95385	0.401052
$617$	32.9482	1.32645	0.663223	−	0.748422i	$-0.269188\pi$
$617$	32.9482	1.32645	0.663223	+	0.748422i	$0.269188\pi$
$618$	−66.9715	−2.69399
$619$	−35.3623	−1.42133	−0.710665	−	0.703531i	$-0.751606\pi$
$619$	−35.3623	−1.42133	−0.710665	+	0.703531i	$0.751606\pi$
$620$	−0.373014	−0.0149806
$621$	37.7100	1.51325
$622$	21.1486	0.847982
$623$	−8.04790	−0.322432
$624$	9.65232	0.386402
$625$	13.9612	0.558449
$626$	−28.8448	−1.15287
$627$	36.0752	1.44070
$628$	−10.2535	−0.409161
$629$	57.0895	2.27631
$630$	10.4357	0.415766
$631$	1.03726	0.0412927	0.0206463	−	0.999787i	$-0.493428\pi$
$631$	1.03726	0.0412927	0.0206463	+	0.999787i	$0.493428\pi$
$632$	−17.0325	−0.677516
$633$	21.9783	0.873559
$634$	53.9287	2.14178
$635$	−5.51742	−0.218952
$636$	−5.50792	−0.218403
$637$	−0.617862	−0.0244806
$638$	−30.7998	−1.21938
$639$	79.3069	3.13733
$640$	−11.9744	−0.473329
$641$	−9.66180	−0.381618	−0.190809	−	0.981627i	$-0.561111\pi$
$641$	−9.66180	−0.381618	−0.190809	+	0.981627i	$0.561111\pi$
$642$	86.1297	3.39927
$643$	22.2556	0.877677	0.438838	−	0.898566i	$-0.355390\pi$
$643$	22.2556	0.877677	0.438838	+	0.898566i	$0.355390\pi$
$644$	−1.74893	−0.0689177
$645$	−4.23153	−0.166617
$646$	−27.3441	−1.07584
$647$	23.6169	0.928476	0.464238	−	0.885711i	$-0.346328\pi$
$647$	23.6169	0.928476	0.464238	+	0.885711i	$0.346328\pi$
$648$	−49.3190	−1.93743
$649$	−50.0275	−1.96375
$650$	4.23938	0.166282
$651$	−2.12691	−0.0833601
$652$	−4.31595	−0.169026
$653$	6.39245	0.250156	0.125078	−	0.992147i	$-0.460082\pi$
$653$	6.39245	0.250156	0.125078	+	0.992147i	$0.460082\pi$
$654$	65.5630	2.56372
$655$	−3.10288	−0.121240
$656$	−17.4701	−0.682093
$657$	7.29249	0.284507
$658$	9.59416	0.374019
$659$	−30.2307	−1.17762	−0.588810	−	0.808272i	$-0.700403\pi$
$659$	−30.2307	−1.17762	−0.588810	+	0.808272i	$0.700403\pi$
$660$	−8.12521	−0.316273
$661$	28.6336	1.11372	0.556859	−	0.830607i	$-0.312006\pi$
$661$	28.6336	1.11372	0.556859	+	0.830607i	$0.312006\pi$
$662$	−36.6919	−1.42607
$663$	13.3571	0.518746
$664$	−24.7414	−0.960151
$665$	2.20070	0.0853394
$666$	−100.361	−3.88892
$667$	−11.5346	−0.446623
$668$	−6.29405	−0.243524
$669$	22.4632	0.868479
$670$	−19.1321	−0.739139
$671$	−23.4853	−0.906642
$672$	11.1879	0.431583
$673$	−2.52011	−0.0971430	−0.0485715	−	0.998820i	$-0.515467\pi$
$673$	−2.52011	−0.0971430	−0.0485715	+	0.998820i	$0.515467\pi$
$674$	−44.0355	−1.69619
$675$	−58.1682	−2.23890
$676$	−8.05906	−0.309964
$677$	37.9771	1.45958	0.729789	−	0.683673i	$-0.239618\pi$
$677$	37.9771	1.45958	0.729789	+	0.683673i	$0.239618\pi$
$678$	−40.9131	−1.57126
$679$	18.6092	0.714156
$680$	−13.1269	−0.503394
$681$	−74.2210	−2.84416
$682$	4.84753	0.185622
$683$	−20.7916	−0.795568	−0.397784	−	0.917479i	$-0.630221\pi$
$683$	−20.7916	−0.795568	−0.397784	+	0.917479i	$0.630221\pi$
$684$	11.6351	0.444880
$685$	0.180958	0.00691406
$686$	−1.62440	−0.0620200
$687$	−73.3683	−2.79917
$688$	−7.29067	−0.277954
$689$	1.66086	0.0632739
$690$	−12.5716	−0.478594
$691$	−39.5238	−1.50356	−0.751778	−	0.659416i	$-0.770804\pi$
$691$	−39.5238	−1.50356	−0.751778	+	0.659416i	$0.770804\pi$
$692$	6.94806	0.264126
$693$	−32.8257	−1.24694
$694$	19.4934	0.739961
$695$	−17.5849	−0.667035
$696$	29.8833	1.13272
$697$	−24.1755	−0.915711
$698$	48.0746	1.81965
$699$	14.3608	0.543175
$700$	2.69775	0.101966
$701$	21.2131	0.801207	0.400603	−	0.916252i	$-0.368800\pi$
$701$	21.2131	0.801207	0.400603	+	0.916252i	$0.368800\pi$
$702$	−13.8215	−0.521658
$703$	−21.1645	−0.798233
$704$	18.3389	0.691173
$705$	16.6926	0.628680
$706$	26.2793	0.989033
$707$	−10.8432	−0.407799
$708$	−22.7728	−0.855854
$709$	4.60680	0.173012	0.0865060	−	0.996251i	$-0.472430\pi$
$709$	4.60680	0.173012	0.0865060	+	0.996251i	$0.472430\pi$
$710$	−15.5625	−0.584050
$711$	56.1696	2.10652
$712$	−17.7965	−0.666953
$713$	1.81542	0.0679879
$714$	35.1167	1.31421
$715$	2.45008	0.0916278
$716$	9.36040	0.349815
$717$	13.3904	0.500075
$718$	−54.9920	−2.05228
$719$	31.1662	1.16230	0.581152	−	0.813795i	$-0.302602\pi$
$719$	31.1662	1.16230	0.581152	+	0.813795i	$0.302602\pi$
$720$	31.2828	1.16584
$721$	12.8510	0.478595
$722$	−20.7266	−0.771362
$723$	−66.0542	−2.45658
$724$	−6.81050	−0.253110
$725$	17.7923	0.660790
$726$	48.2665	1.79134
$727$	−8.59039	−0.318600	−0.159300	−	0.987230i	$-0.550924\pi$
$727$	−8.59039	−0.318600	−0.159300	+	0.987230i	$0.550924\pi$
$728$	−1.36630	−0.0506383
$729$	30.1025	1.11491
$730$	−1.43101	−0.0529642
$731$	−10.0890	−0.373154
$732$	−10.6907	−0.395138
$733$	−13.5761	−0.501444	−0.250722	−	0.968059i	$-0.580668\pi$
$733$	−13.5761	−0.501444	−0.250722	+	0.968059i	$0.580668\pi$
$734$	4.21071	0.155420
$735$	−2.82625	−0.104248
$736$	−9.54941	−0.351996
$737$	60.1808	2.21679
$738$	42.4996	1.56443
$739$	−6.40748	−0.235703	−0.117851	−	0.993031i	$-0.537601\pi$
$739$	−6.40748	−0.235703	−0.117851	+	0.993031i	$0.537601\pi$
$740$	4.76687	0.175234
$741$	−4.95179	−0.181908
$742$	4.36652	0.160300
$743$	25.6333	0.940394	0.470197	−	0.882562i	$-0.344183\pi$
$743$	25.6333	0.940394	0.470197	+	0.882562i	$0.344183\pi$
$744$	−4.70329	−0.172431
$745$	5.62721	0.206165
$746$	−50.0007	−1.83066
$747$	81.5918	2.98529
$748$	−19.3724	−0.708325
$749$	−16.5272	−0.603890
$750$	42.3468	1.54629
$751$	−41.9192	−1.52965	−0.764826	−	0.644236i	$-0.777175\pi$
$751$	−41.9192	−1.52965	−0.764826	+	0.644236i	$0.777175\pi$
$752$	28.7603	1.04878
$753$	−9.70285	−0.353592
$754$	4.22767	0.153963
$755$	−13.7379	−0.499975
$756$	−8.79538	−0.319885
$757$	41.3346	1.50233	0.751166	−	0.660114i	$-0.229492\pi$
$757$	41.3346	1.50233	0.751166	+	0.660114i	$0.229492\pi$
$758$	23.2030	0.842771
$759$	39.5445	1.43538
$760$	4.86646	0.176525
$761$	−20.1311	−0.729753	−0.364877	−	0.931056i	$-0.618889\pi$
$761$	−20.1311	−0.729753	−0.364877	+	0.931056i	$0.618889\pi$
$762$	32.6392	1.18239
$763$	−12.5807	−0.455452
$764$	−13.2500	−0.479370
$765$	43.2898	1.56515
$766$	−59.5954	−2.15327
$767$	6.86692	0.247950
$768$	44.6953	1.61280
$769$	17.3899	0.627095	0.313547	−	0.949573i	$-0.398483\pi$
$769$	17.3899	0.627095	0.313547	+	0.949573i	$0.398483\pi$
$770$	6.44143	0.232133
$771$	−16.6775	−0.600624
$772$	6.28541	0.226217
$773$	−20.6756	−0.743648	−0.371824	−	0.928303i	$-0.621268\pi$
$773$	−20.6756	−0.743648	−0.371824	+	0.928303i	$0.621268\pi$
$774$	17.7360	0.637509
$775$	−2.80030	−0.100590
$776$	41.1510	1.47724
$777$	27.1805	0.975095
$778$	53.3605	1.91307
$779$	8.96242	0.321112
$780$	1.11529	0.0399338
$781$	48.9524	1.75165
$782$	−29.9737	−1.07186
$783$	−58.0076	−2.07302
$784$	−4.86945	−0.173909
$785$	14.1429	0.504782
$786$	18.3556	0.654723
$787$	12.3077	0.438722	0.219361	−	0.975644i	$-0.429603\pi$
$787$	12.3077	0.438722	0.219361	+	0.975644i	$0.429603\pi$
$788$	−11.6186	−0.413895
$789$	75.0514	2.67190
$790$	−11.0222	−0.392153
$791$	7.85071	0.279139
$792$	−72.5883	−2.57931
$793$	3.22367	0.114476
$794$	−29.8930	−1.06086
$795$	7.59719	0.269444
$796$	3.78965	0.134321
$797$	−31.4262	−1.11317	−0.556587	−	0.830789i	$-0.687890\pi$
$797$	−31.4262	−1.11317	−0.556587	+	0.830789i	$0.687890\pi$
$798$	−13.0186	−0.460853
$799$	39.7991	1.40799
$800$	14.7301	0.520787
$801$	58.6892	2.07368
$802$	1.40852	0.0497367
$803$	4.50130	0.158848
$804$	27.3946	0.966134
$805$	2.41234	0.0850238
$806$	−0.665386	−0.0234372
$807$	16.5405	0.582252
$808$	−23.9777	−0.843534
$809$	15.0651	0.529661	0.264830	−	0.964295i	$-0.414684\pi$
$809$	15.0651	0.529661	0.264830	+	0.964295i	$0.414684\pi$
$810$	−31.9158	−1.12141
$811$	47.6685	1.67387	0.836934	−	0.547304i	$-0.184346\pi$
$811$	47.6685	1.67387	0.836934	+	0.547304i	$0.184346\pi$
$812$	2.69031	0.0944112
$813$	−77.6477	−2.72322
$814$	−61.9482	−2.17128
$815$	5.95307	0.208527
$816$	105.269	3.68514
$817$	3.74022	0.130854
$818$	−29.7597	−1.04052
$819$	4.50575	0.157444
$820$	−2.01861	−0.0704928
$821$	−28.6778	−1.00086	−0.500430	−	0.865777i	$-0.666825\pi$
$821$	−28.6778	−1.00086	−0.500430	+	0.865777i	$0.666825\pi$
$822$	−1.07049	−0.0373376
$823$	24.2730	0.846102	0.423051	−	0.906106i	$-0.360959\pi$
$823$	24.2730	0.846102	0.423051	+	0.906106i	$0.360959\pi$
$824$	28.4177	0.989977
$825$	−60.9979	−2.12368
$826$	18.0536	0.628165
$827$	−49.1492	−1.70909	−0.854543	−	0.519381i	$-0.826162\pi$
$827$	−49.1492	−1.70909	−0.854543	+	0.519381i	$0.826162\pi$
$828$	12.7541	0.443235
$829$	−13.0152	−0.452037	−0.226018	−	0.974123i	$-0.572571\pi$
$829$	−13.0152	−0.452037	−0.226018	+	0.974123i	$0.572571\pi$
$830$	−16.0109	−0.555745
$831$	28.3610	0.983833
$832$	−2.51725	−0.0872700
$833$	−6.73844	−0.233473
$834$	104.027	3.60215
$835$	8.68151	0.300436
$836$	7.18181	0.248388
$837$	9.12973	0.315569
$838$	56.2625	1.94356
$839$	42.3855	1.46331	0.731655	−	0.681675i	$-0.238748\pi$
$839$	42.3855	1.46331	0.731655	+	0.681675i	$0.238748\pi$
$840$	−6.24976	−0.215637
$841$	−11.2568	−0.388166
$842$	−35.9277	−1.23815
$843$	78.6348	2.70833
$844$	4.37542	0.150608
$845$	11.1160	0.382403
$846$	−69.9653	−2.40546
$847$	−9.26173	−0.318237
$848$	13.0895	0.449494
$849$	67.5802	2.31935
$850$	46.2349	1.58584
$851$	−23.1998	−0.795280
$852$	22.2834	0.763416
$853$	−2.19471	−0.0751455	−0.0375727	−	0.999294i	$-0.511963\pi$
$853$	−2.19471	−0.0751455	−0.0375727	+	0.999294i	$0.511963\pi$
$854$	8.47525	0.290017
$855$	−16.0486	−0.548849
$856$	−36.5470	−1.24915
$857$	−39.9409	−1.36435	−0.682177	−	0.731187i	$-0.738967\pi$
$857$	−39.9409	−1.36435	−0.682177	+	0.731187i	$0.738967\pi$
$858$	−14.4939	−0.494812
$859$	−28.1417	−0.960184	−0.480092	−	0.877218i	$-0.659397\pi$
$859$	−28.1417	−0.960184	−0.480092	+	0.877218i	$0.659397\pi$
$860$	−0.842410	−0.0287259
$861$	−11.5100	−0.392260
$862$	9.00329	0.306653
$863$	36.5123	1.24289	0.621446	−	0.783457i	$-0.286546\pi$
$863$	36.5123	1.24289	0.621446	+	0.783457i	$0.286546\pi$
$864$	−48.0239	−1.63381
$865$	−9.58359	−0.325852
$866$	−33.0380	−1.12268
$867$	91.1337	3.09506
$868$	−0.423423	−0.0143719
$869$	34.6708	1.17613
$870$	19.3384	0.655633
$871$	−8.26060	−0.279900
$872$	−27.8200	−0.942106
$873$	−135.707	−4.59300
$874$	11.1120	0.375868
$875$	−8.12581	−0.274702
$876$	2.04902	0.0692299
$877$	−52.9376	−1.78757	−0.893787	−	0.448491i	$-0.851962\pi$
$877$	−52.9376	−1.78757	−0.893787	+	0.448491i	$0.851962\pi$
$878$	3.05400	0.103068
$879$	69.0074	2.32756
$880$	19.3094	0.650919
$881$	−14.8074	−0.498875	−0.249437	−	0.968391i	$-0.580246\pi$
$881$	−14.8074	−0.498875	−0.249437	+	0.968391i	$0.580246\pi$
$882$	11.8459	0.398873
$883$	−13.7091	−0.461347	−0.230674	−	0.973031i	$-0.574093\pi$
$883$	−13.7091	−0.461347	−0.230674	+	0.973031i	$0.574093\pi$
$884$	2.65911	0.0894356
$885$	31.4109	1.05587
$886$	39.3023	1.32039
$887$	16.4683	0.552951	0.276475	−	0.961021i	$-0.410834\pi$
$887$	16.4683	0.552951	0.276475	+	0.961021i	$0.410834\pi$
$888$	60.1049	2.01699
$889$	−6.26305	−0.210056
$890$	−11.5167	−0.386039
$891$	100.392	3.36326
$892$	4.47196	0.149732
$893$	−14.7545	−0.493739
$894$	−33.2887	−1.11334
$895$	−12.9110	−0.431566
$896$	−13.5926	−0.454097
$897$	−5.42800	−0.181236
$898$	6.55650	0.218793
$899$	−2.79257	−0.0931375
$900$	−19.6733	−0.655778
$901$	18.1135	0.603447
$902$	26.2330	0.873462
$903$	−4.80339	−0.159847
$904$	17.3605	0.577401
$905$	9.39385	0.312262
$906$	81.2691	2.69998
$907$	12.0473	0.400025	0.200012	−	0.979793i	$-0.435902\pi$
$907$	12.0473	0.400025	0.200012	+	0.979793i	$0.435902\pi$
$908$	−14.7759	−0.490354
$909$	79.0736	2.62270
$910$	−0.884170	−0.0293100
$911$	−44.1292	−1.46207	−0.731033	−	0.682342i	$-0.760962\pi$
$911$	−44.1292	−1.46207	−0.731033	+	0.682342i	$0.760962\pi$
$912$	−39.0256	−1.29227
$913$	50.3627	1.66676
$914$	−11.5652	−0.382544
$915$	14.7458	0.487482
$916$	−14.6061	−0.482599
$917$	−3.52221	−0.116314
$918$	−150.738	−4.97509
$919$	−20.2317	−0.667381	−0.333691	−	0.942683i	$-0.608294\pi$
$919$	−20.2317	−0.667381	−0.333691	+	0.942683i	$0.608294\pi$
$920$	5.33447	0.175872
$921$	−73.4752	−2.42109
$922$	−12.9375	−0.426075
$923$	−6.71935	−0.221170
$924$	−9.22325	−0.303423
$925$	35.7861	1.17664
$926$	−14.3527	−0.471658
$927$	−93.7156	−3.07802
$928$	14.6894	0.482204
$929$	7.48985	0.245734	0.122867	−	0.992423i	$-0.460791\pi$
$929$	7.48985	0.245734	0.122867	+	0.992423i	$0.460791\pi$
$930$	−3.04364	−0.0998048
$931$	2.49810	0.0818719
$932$	2.85893	0.0936474
$933$	41.7684	1.36744
$934$	−17.8265	−0.583300
$935$	26.7207	0.873861
$936$	9.96369	0.325673
$937$	−47.9671	−1.56702	−0.783508	−	0.621381i	$-0.786572\pi$
$937$	−47.9671	−1.56702	−0.783508	+	0.621381i	$0.786572\pi$
$938$	−21.7177	−0.709107
$939$	−56.9683	−1.85909
$940$	3.32315	0.108389
$941$	−46.6694	−1.52138	−0.760689	−	0.649116i	$-0.775139\pi$
$941$	−46.6694	−1.52138	−0.760689	+	0.649116i	$0.775139\pi$
$942$	−83.6647	−2.72594
$943$	9.82434	0.319925
$944$	54.1191	1.76143
$945$	12.1316	0.394642
$946$	10.9476	0.355937
$947$	−35.1680	−1.14281	−0.571403	−	0.820670i	$-0.693601\pi$
$947$	−35.1680	−1.14281	−0.571403	+	0.820670i	$0.693601\pi$
$948$	15.7823	0.512586
$949$	−0.617862	−0.0200567
$950$	−17.1404	−0.556107
$951$	106.509	3.45379
$952$	−14.9009	−0.482941
$953$	−18.1085	−0.586591	−0.293296	−	0.956022i	$-0.594752\pi$
$953$	−18.1085	−0.586591	−0.293296	+	0.956022i	$0.594752\pi$
$954$	−31.8428	−1.03095
$955$	18.2760	0.591399
$956$	2.66576	0.0862167
$957$	−60.8295	−1.96634
$958$	24.5750	0.793981
$959$	0.205413	0.00663313
$960$	−11.5145	−0.371629
$961$	−30.5605	−0.985822
$962$	8.50320	0.274154
$963$	120.524	3.88384
$964$	−13.1500	−0.423533
$965$	−8.66958	−0.279084
$966$	−14.2706	−0.459148
$967$	−16.6255	−0.534641	−0.267320	−	0.963608i	$-0.586138\pi$
$967$	−16.6255	−0.534641	−0.267320	+	0.963608i	$0.586138\pi$
$968$	−20.4807	−0.658275
$969$	−54.0044	−1.73487
$970$	26.6301	0.855040
$971$	27.6146	0.886193	0.443097	−	0.896474i	$-0.353880\pi$
$971$	27.6146	0.886193	0.443097	+	0.896474i	$0.353880\pi$
$972$	19.3129	0.619462
$973$	−19.9614	−0.639932
$974$	−33.5567	−1.07523
$975$	8.37276	0.268143
$976$	25.4061	0.813231
$977$	−41.1140	−1.31535	−0.657676	−	0.753301i	$-0.728460\pi$
$977$	−41.1140	−1.31535	−0.657676	+	0.753301i	$0.728460\pi$
$978$	−35.2163	−1.12609
$979$	36.2260	1.15779
$980$	−0.562647	−0.0179731
$981$	91.7446	2.92918
$982$	28.2204	0.900549
$983$	−16.3109	−0.520238	−0.260119	−	0.965577i	$-0.583762\pi$
$983$	−16.3109	−0.520238	−0.260119	+	0.965577i	$0.583762\pi$
$984$	−25.4524	−0.811392
$985$	16.0258	0.510623
$986$	46.1072	1.46835
$987$	18.9484	0.603136
$988$	−0.985797	−0.0313624
$989$	4.09992	0.130370
$990$	−46.9740	−1.49293
$991$	24.4159	0.775596	0.387798	−	0.921744i	$-0.373236\pi$
$991$	24.4159	0.775596	0.387798	+	0.921744i	$0.373236\pi$
$992$	−2.31194	−0.0734043
$993$	−72.4663	−2.29965
$994$	−17.6656	−0.560320
$995$	−5.22714	−0.165712
$996$	22.9254	0.726419
$997$	20.9978	0.665008	0.332504	−	0.943102i	$-0.392106\pi$
$997$	20.9978	0.665008	0.332504	+	0.943102i	$0.392106\pi$
$998$	−40.2921	−1.27542
$999$	−116.672	−3.69134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	511.2.a.f.1.7	✓	10
3.2	odd	2		4599.2.a.q.1.4		10
4.3	odd	2		8176.2.a.t.1.1		10
7.6	odd	2		3577.2.a.i.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
511.2.a.f.1.7	✓	10	1.1	even	1	trivial
3577.2.a.i.1.7		10	7.6	odd	2
4599.2.a.q.1.4		10	3.2	odd	2
8176.2.a.t.1.1		10	4.3	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:	\( N \)	\(=\)	\( 511 = 7 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	511.a (trivial)

\(f(q)\)	\(=\)	\(q+1.62440 q^{2} +3.20819 q^{3} +0.638683 q^{4} -0.880948 q^{5} +5.21139 q^{6} -1.00000 q^{7} -2.21133 q^{8} +7.29249 q^{9} -1.43101 q^{10} +4.50130 q^{11} +2.04902 q^{12} -0.617862 q^{13} -1.62440 q^{14} -2.82625 q^{15} -4.86945 q^{16} -6.73844 q^{17} +11.8459 q^{18} +2.49810 q^{19} -0.562647 q^{20} -3.20819 q^{21} +7.31193 q^{22} +2.73834 q^{23} -7.09436 q^{24} -4.22393 q^{25} -1.00366 q^{26} +13.7711 q^{27} -0.638683 q^{28} -4.21227 q^{29} -4.59097 q^{30} +0.662962 q^{31} -3.48730 q^{32} +14.4410 q^{33} -10.9459 q^{34} +0.880948 q^{35} +4.65759 q^{36} -8.47222 q^{37} +4.05792 q^{38} -1.98222 q^{39} +1.94806 q^{40} +3.58769 q^{41} -5.21139 q^{42} +1.49723 q^{43} +2.87491 q^{44} -6.42430 q^{45} +4.44817 q^{46} -5.90627 q^{47} -15.6221 q^{48} +1.00000 q^{49} -6.86136 q^{50} -21.6182 q^{51} -0.394618 q^{52} -2.68808 q^{53} +22.3698 q^{54} -3.96542 q^{55} +2.21133 q^{56} +8.01438 q^{57} -6.84242 q^{58} -11.1140 q^{59} -1.80508 q^{60} -5.21745 q^{61} +1.07692 q^{62} -7.29249 q^{63} +4.07413 q^{64} +0.544305 q^{65} +23.4581 q^{66} +13.3696 q^{67} -4.30373 q^{68} +8.78513 q^{69} +1.43101 q^{70} +10.8752 q^{71} -16.1261 q^{72} +1.00000 q^{73} -13.7623 q^{74} -13.5512 q^{75} +1.59550 q^{76} -4.50130 q^{77} -3.21992 q^{78} +7.70239 q^{79} +4.28973 q^{80} +22.3029 q^{81} +5.82786 q^{82} +11.1885 q^{83} -2.04902 q^{84} +5.93622 q^{85} +2.43210 q^{86} -13.5138 q^{87} -9.95385 q^{88} +8.04790 q^{89} -10.4357 q^{90} +0.617862 q^{91} +1.74893 q^{92} +2.12691 q^{93} -9.59416 q^{94} -2.20070 q^{95} -11.1879 q^{96} -18.6092 q^{97} +1.62440 q^{98} +32.8257 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - q^{3} + 14 q^{4} + q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 39 q^{9} - 6 q^{10} + 5 q^{11} + q^{12} - q^{13} - 4 q^{14} + q^{15} + 14 q^{16} + 8 q^{17} + 26 q^{18} + 2 q^{19} - 16 q^{20}+ \cdots + 53 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - q^3 + 14 * q^4 + q^5 + 2 * q^6 - 10 * q^7 + 6 * q^8 + 39 * q^9 - 6 * q^10 + 5 * q^11 + q^12 - q^13 - 4 * q^14 + q^15 + 14 * q^16 + 8 * q^17 + 26 * q^18 + 2 * q^19 - 16 * q^20 + q^21 - 3 * q^22 + 10 * q^23 + 9 * q^24 + 29 * q^25 + 34 * q^26 - 13 * q^27 - 14 * q^28 + 9 * q^29 - 27 * q^30 - 17 * q^31 + 36 * q^32 - 11 * q^33 + 4 * q^34 - q^35 + 68 * q^36 - 9 * q^37 + 6 * q^39 - 41 * q^40 + 39 * q^41 - 2 * q^42 - 7 * q^43 - 12 * q^44 - 8 * q^45 - 11 * q^46 - 38 * q^47 - 32 * q^48 + 10 * q^49 + 31 * q^50 + 4 * q^51 + 52 * q^52 + 9 * q^53 - 80 * q^54 + 13 * q^55 - 6 * q^56 + 20 * q^57 - 19 * q^58 + 5 * q^59 - 79 * q^60 + 10 * q^61 - 25 * q^62 - 39 * q^63 + 16 * q^64 + 55 * q^65 + 26 * q^66 - 22 * q^67 + 4 * q^68 + 4 * q^69 + 6 * q^70 + 30 * q^71 + 21 * q^72 + 10 * q^73 - 4 * q^74 - 24 * q^75 - 24 * q^76 - 5 * q^77 - 19 * q^78 - 14 * q^80 + 46 * q^81 - 6 * q^82 - 25 * q^83 - q^84 + 11 * q^85 - 28 * q^86 - 24 * q^87 - 72 * q^88 + 37 * q^89 - 64 * q^90 + q^91 + 36 * q^92 - 40 * q^93 + 29 * q^94 + 41 * q^95 - 36 * q^96 + 5 * q^97 + 4 * q^98 + 53 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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