LMFDB - Embedded newform 7935.2.a.bw.1.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] 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("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,11,25,31,25,11,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.134140 q^{2} +1.00000 q^{3} -1.98201 q^{4} +1.00000 q^{5} +0.134140 q^{6} +1.40831 q^{7} -0.534145 q^{8} +1.00000 q^{9} +0.134140 q^{10} -1.28753 q^{11} -1.98201 q^{12} +3.37933 q^{13} +0.188910 q^{14} +1.00000 q^{15} +3.89236 q^{16} +0.861872 q^{17} +0.134140 q^{18} +4.53452 q^{19} -1.98201 q^{20} +1.40831 q^{21} -0.172709 q^{22} -0.534145 q^{24} +1.00000 q^{25} +0.453302 q^{26} +1.00000 q^{27} -2.79128 q^{28} +0.141924 q^{29} +0.134140 q^{30} +2.54119 q^{31} +1.59041 q^{32} -1.28753 q^{33} +0.115611 q^{34} +1.40831 q^{35} -1.98201 q^{36} +1.11109 q^{37} +0.608259 q^{38} +3.37933 q^{39} -0.534145 q^{40} -6.00377 q^{41} +0.188910 q^{42} +0.457979 q^{43} +2.55190 q^{44} +1.00000 q^{45} +9.79441 q^{47} +3.89236 q^{48} -5.01666 q^{49} +0.134140 q^{50} +0.861872 q^{51} -6.69785 q^{52} +6.86866 q^{53} +0.134140 q^{54} -1.28753 q^{55} -0.752242 q^{56} +4.53452 q^{57} +0.0190377 q^{58} -2.57337 q^{59} -1.98201 q^{60} -12.6363 q^{61} +0.340875 q^{62} +1.40831 q^{63} -7.57139 q^{64} +3.37933 q^{65} -0.172709 q^{66} +1.94132 q^{67} -1.70824 q^{68} +0.188910 q^{70} +11.7487 q^{71} -0.534145 q^{72} -13.1015 q^{73} +0.149041 q^{74} +1.00000 q^{75} -8.98745 q^{76} -1.81325 q^{77} +0.453302 q^{78} +9.02887 q^{79} +3.89236 q^{80} +1.00000 q^{81} -0.805344 q^{82} +8.77272 q^{83} -2.79128 q^{84} +0.861872 q^{85} +0.0614331 q^{86} +0.141924 q^{87} +0.687730 q^{88} +4.17368 q^{89} +0.134140 q^{90} +4.75915 q^{91} +2.54119 q^{93} +1.31382 q^{94} +4.53452 q^{95} +1.59041 q^{96} -9.81329 q^{97} -0.672933 q^{98} -1.28753 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} + 25 q^{5} + 11 q^{6} + 7 q^{7} + 33 q^{8} + 25 q^{9} + 11 q^{10} + 9 q^{11} + 31 q^{12} + 18 q^{13} + 11 q^{14} + 25 q^{15} + 39 q^{16} - 8 q^{17} + 11 q^{18} + 11 q^{19}+ \cdots + 9 q^{99}+O(q^{100}) $ 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 + 25 * q^5 + 11 * q^6 + 7 * q^7 + 33 * q^8 + 25 * q^9 + 11 * q^10 + 9 * q^11 + 31 * q^12 + 18 * q^13 + 11 * q^14 + 25 * q^15 + 39 * q^16 - 8 * q^17 + 11 * q^18 + 11 * q^19 + 31 * q^20 + 7 * q^21 + 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 - 5 * q^28 + 33 * q^29 + 11 * q^30 + 14 * q^31 + 77 * q^32 + 9 * q^33 + 13 * q^34 + 7 * q^35 + 31 * q^36 + 4 * q^37 - 23 * q^38 + 18 * q^39 + 33 * q^40 + 56 * q^41 + 11 * q^42 - 4 * q^43 - 18 * q^44 + 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 - 8 * q^51 + 49 * q^52 + 2 * q^53 + 11 * q^54 + 9 * q^55 + 33 * q^56 + 11 * q^57 + 26 * q^58 + 61 * q^59 + 31 * q^60 + 21 * q^61 + 51 * q^62 + 7 * q^63 + 71 * q^64 + 18 * q^65 + 9 * q^66 + 2 * q^67 - 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 - 47 * q^74 + 25 * q^75 - 8 * q^76 + 49 * q^77 + 35 * q^78 + 35 * q^79 + 39 * q^80 + 25 * q^81 + 35 * q^82 - 26 * q^83 - 5 * q^84 - 8 * q^85 - 33 * q^86 + 33 * q^87 + 9 * q^88 - 7 * q^89 + 11 * q^90 + 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 - 54 * q^97 + 88 * q^98 + 9 * 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 $

$2$	0.134140	0.0948510	0.0474255	−	0.998875i	$-0.484898\pi$
$2$	0.134140	0.0948510	0.0474255	+	0.998875i	$0.484898\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.98201	−0.991003
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.134140	0.0547623
$7$	1.40831	0.532292	0.266146	−	0.963933i	$-0.414250\pi$
$7$	1.40831	0.532292	0.266146	+	0.963933i	$0.414250\pi$
$8$	−0.534145	−0.188849
$9$	1.00000	0.333333
$10$	0.134140	0.0424187
$11$	−1.28753	−0.388206	−0.194103	−	0.980981i	$-0.562180\pi$
$11$	−1.28753	−0.388206	−0.194103	+	0.980981i	$0.562180\pi$
$12$	−1.98201	−0.572156
$13$	3.37933	0.937258	0.468629	−	0.883395i	$-0.344748\pi$
$13$	3.37933	0.937258	0.468629	+	0.883395i	$0.344748\pi$
$14$	0.188910	0.0504884
$15$	1.00000	0.258199
$16$	3.89236	0.973091
$17$	0.861872	0.209035	0.104517	−	0.994523i	$-0.466670\pi$
$17$	0.861872	0.209035	0.104517	+	0.994523i	$0.466670\pi$
$18$	0.134140	0.0316170
$19$	4.53452	1.04029	0.520145	−	0.854078i	$-0.325878\pi$
$19$	4.53452	1.04029	0.520145	+	0.854078i	$0.325878\pi$
$20$	−1.98201	−0.443190
$21$	1.40831	0.307319
$22$	−0.172709	−0.0368218
$23$	0	0
$23$	0	0
$24$	−0.534145	−0.109032
$25$	1.00000	0.200000
$26$	0.453302	0.0888999
$27$	1.00000	0.192450
$28$	−2.79128	−0.527503
$29$	0.141924	0.0263546	0.0131773	−	0.999913i	$-0.495805\pi$
$29$	0.141924	0.0263546	0.0131773	+	0.999913i	$0.495805\pi$
$30$	0.134140	0.0244904
$31$	2.54119	0.456412	0.228206	−	0.973613i	$-0.426714\pi$
$31$	2.54119	0.456412	0.228206	+	0.973613i	$0.426714\pi$
$32$	1.59041	0.281147
$33$	−1.28753	−0.224131
$34$	0.115611	0.0198271
$35$	1.40831	0.238048
$36$	−1.98201	−0.330334
$37$	1.11109	0.182662	0.0913312	−	0.995821i	$-0.470888\pi$
$37$	1.11109	0.182662	0.0913312	+	0.995821i	$0.470888\pi$
$38$	0.608259	0.0986726
$39$	3.37933	0.541126
$40$	−0.534145	−0.0844557
$41$	−6.00377	−0.937632	−0.468816	−	0.883296i	$-0.655319\pi$
$41$	−6.00377	−0.937632	−0.468816	+	0.883296i	$0.655319\pi$
$42$	0.188910	0.0291495
$43$	0.457979	0.0698412	0.0349206	−	0.999390i	$-0.488882\pi$
$43$	0.457979	0.0698412	0.0349206	+	0.999390i	$0.488882\pi$
$44$	2.55190	0.384714
$45$	1.00000	0.149071
$46$	0	0
$47$	9.79441	1.42866	0.714331	−	0.699808i	$-0.246731\pi$
$47$	9.79441	1.42866	0.714331	+	0.699808i	$0.246731\pi$
$48$	3.89236	0.561814
$49$	−5.01666	−0.716666
$50$	0.134140	0.0189702
$51$	0.861872	0.120686
$52$	−6.69785	−0.928825
$53$	6.86866	0.943483	0.471741	−	0.881737i	$-0.343626\pi$
$53$	6.86866	0.943483	0.471741	+	0.881737i	$0.343626\pi$
$54$	0.134140	0.0182541
$55$	−1.28753	−0.173611
$56$	−0.752242	−0.100523
$57$	4.53452	0.600612
$58$	0.0190377	0.00249977
$59$	−2.57337	−0.335024	−0.167512	−	0.985870i	$-0.553573\pi$
$59$	−2.57337	−0.335024	−0.167512	+	0.985870i	$0.553573\pi$
$60$	−1.98201	−0.255876
$61$	−12.6363	−1.61792	−0.808959	−	0.587866i	$-0.799968\pi$
$61$	−12.6363	−1.61792	−0.808959	+	0.587866i	$0.799968\pi$
$62$	0.340875	0.0432911
$63$	1.40831	0.177431
$64$	−7.57139	−0.946424
$65$	3.37933	0.419154
$66$	−0.172709	−0.0212590
$67$	1.94132	0.237171	0.118585	−	0.992944i	$-0.462164\pi$
$67$	1.94132	0.237171	0.118585	+	0.992944i	$0.462164\pi$
$68$	−1.70824	−0.207154
$69$	0	0
$70$	0.188910	0.0225791
$71$	11.7487	1.39431	0.697155	−	0.716920i	$-0.254449\pi$
$71$	11.7487	1.39431	0.697155	+	0.716920i	$0.254449\pi$
$72$	−0.534145	−0.0629496
$73$	−13.1015	−1.53342	−0.766710	−	0.641993i	$-0.778108\pi$
$73$	−13.1015	−1.53342	−0.766710	+	0.641993i	$0.778108\pi$
$74$	0.149041	0.0173257
$75$	1.00000	0.115470
$76$	−8.98745	−1.03093
$77$	−1.81325	−0.206639
$78$	0.453302	0.0513264
$79$	9.02887	1.01583	0.507914	−	0.861408i	$-0.330417\pi$
$79$	9.02887	1.01583	0.507914	+	0.861408i	$0.330417\pi$
$80$	3.89236	0.435179
$81$	1.00000	0.111111
$82$	−0.805344	−0.0889354
$83$	8.77272	0.962931	0.481465	−	0.876465i	$-0.340105\pi$
$83$	8.77272	0.962931	0.481465	+	0.876465i	$0.340105\pi$
$84$	−2.79128	−0.304554
$85$	0.861872	0.0934831
$86$	0.0614331	0.00662451
$87$	0.141924	0.0152159
$88$	0.687730	0.0733122
$89$	4.17368	0.442409	0.221205	−	0.975227i	$-0.429001\pi$
$89$	4.17368	0.442409	0.221205	+	0.975227i	$0.429001\pi$
$90$	0.134140	0.0141396
$91$	4.75915	0.498894
$92$	0	0
$93$	2.54119	0.263510
$94$	1.31382	0.135510
$95$	4.53452	0.465232
$96$	1.59041	0.162321
$97$	−9.81329	−0.996388	−0.498194	−	0.867066i	$-0.666003\pi$
$97$	−9.81329	−0.996388	−0.498194	+	0.867066i	$0.666003\pi$
$98$	−0.672933	−0.0679765
$99$	−1.28753	−0.129402
$100$	−1.98201	−0.198201
$101$	11.7058	1.16477	0.582385	−	0.812913i	$-0.302120\pi$
$101$	11.7058	1.16477	0.582385	+	0.812913i	$0.302120\pi$
$102$	0.115611	0.0114472
$103$	1.60861	0.158501	0.0792507	−	0.996855i	$-0.474747\pi$
$103$	1.60861	0.158501	0.0792507	+	0.996855i	$0.474747\pi$
$104$	−1.80505	−0.177000
$105$	1.40831	0.137437
$106$	0.921359	0.0894903
$107$	−11.4559	−1.10748	−0.553742	−	0.832688i	$-0.686801\pi$
$107$	−11.4559	−1.10748	−0.553742	+	0.832688i	$0.686801\pi$
$108$	−1.98201	−0.190719
$109$	−13.3491	−1.27861	−0.639305	−	0.768953i	$-0.720778\pi$
$109$	−13.3491	−1.27861	−0.639305	+	0.768953i	$0.720778\pi$
$110$	−0.172709	−0.0164672
$111$	1.11109	0.105460
$112$	5.48166	0.517968
$113$	0.688799	0.0647968	0.0323984	−	0.999475i	$-0.489685\pi$
$113$	0.688799	0.0647968	0.0323984	+	0.999475i	$0.489685\pi$
$114$	0.608259	0.0569686
$115$	0	0
$116$	−0.281295	−0.0261175
$117$	3.37933	0.312419
$118$	−0.345190	−0.0317773
$119$	1.21378	0.111267
$120$	−0.534145	−0.0487605
$121$	−9.34226	−0.849296
$122$	−1.69503	−0.153461
$123$	−6.00377	−0.541342
$124$	−5.03666	−0.452306
$125$	1.00000	0.0894427
$126$	0.188910	0.0168295
$127$	11.7849	1.04574	0.522871	−	0.852412i	$-0.324861\pi$
$127$	11.7849	1.04574	0.522871	+	0.852412i	$0.324861\pi$
$128$	−4.19644	−0.370917
$129$	0.457979	0.0403228
$130$	0.453302	0.0397572
$131$	−3.01470	−0.263396	−0.131698	−	0.991290i	$-0.542043\pi$
$131$	−3.01470	−0.263396	−0.131698	+	0.991290i	$0.542043\pi$
$132$	2.55190	0.222114
$133$	6.38602	0.553738
$134$	0.260409	0.0224959
$135$	1.00000	0.0860663
$136$	−0.460364	−0.0394759
$137$	−13.3619	−1.14158	−0.570792	−	0.821095i	$-0.693364\pi$
$137$	−13.3619	−1.14158	−0.570792	+	0.821095i	$0.693364\pi$
$138$	0	0
$139$	21.1795	1.79642	0.898211	−	0.439564i	$-0.144867\pi$
$139$	21.1795	1.79642	0.898211	+	0.439564i	$0.144867\pi$
$140$	−2.79128	−0.235906
$141$	9.79441	0.824838
$142$	1.57596	0.132252
$143$	−4.35100	−0.363849
$144$	3.89236	0.324364
$145$	0.141924	0.0117862
$146$	−1.75744	−0.145447
$147$	−5.01666	−0.413767
$148$	−2.20219	−0.181019
$149$	18.8009	1.54023	0.770116	−	0.637903i	$-0.220198\pi$
$149$	18.8009	1.54023	0.770116	+	0.637903i	$0.220198\pi$
$150$	0.134140	0.0109525
$151$	8.46485	0.688860	0.344430	−	0.938812i	$-0.388072\pi$
$151$	8.46485	0.688860	0.344430	+	0.938812i	$0.388072\pi$
$152$	−2.42209	−0.196457
$153$	0.861872	0.0696782
$154$	−0.243229	−0.0195999
$155$	2.54119	0.204114
$156$	−6.69785	−0.536258
$157$	10.9352	0.872725	0.436363	−	0.899771i	$-0.356266\pi$
$157$	10.9352	0.872725	0.436363	+	0.899771i	$0.356266\pi$
$158$	1.21113	0.0963523
$159$	6.86866	0.544720
$160$	1.59041	0.125733
$161$	0	0
$162$	0.134140	0.0105390
$163$	−0.692478	−0.0542391	−0.0271196	−	0.999632i	$-0.508633\pi$
$163$	−0.692478	−0.0542391	−0.0271196	+	0.999632i	$0.508633\pi$
$164$	11.8995	0.929196
$165$	−1.28753	−0.100234
$166$	1.17677	0.0913350
$167$	10.1707	0.787029	0.393515	−	0.919318i	$-0.371259\pi$
$167$	10.1707	0.787029	0.393515	+	0.919318i	$0.371259\pi$
$168$	−0.752242	−0.0580368
$169$	−1.58013	−0.121548
$170$	0.115611	0.00886697
$171$	4.53452	0.346763
$172$	−0.907717	−0.0692128
$173$	−4.95681	−0.376860	−0.188430	−	0.982087i	$-0.560340\pi$
$173$	−4.95681	−0.376860	−0.188430	+	0.982087i	$0.560340\pi$
$174$	0.0190377	0.00144324
$175$	1.40831	0.106458
$176$	−5.01155	−0.377760
$177$	−2.57337	−0.193426
$178$	0.559856	0.0419630
$179$	3.66827	0.274179	0.137090	−	0.990559i	$-0.456225\pi$
$179$	3.66827	0.274179	0.137090	+	0.990559i	$0.456225\pi$
$180$	−1.98201	−0.147730
$181$	−11.2547	−0.836553	−0.418277	−	0.908320i	$-0.637366\pi$
$181$	−11.2547	−0.836553	−0.418277	+	0.908320i	$0.637366\pi$
$182$	0.638391	0.0473207
$183$	−12.6363	−0.934105
$184$	0	0
$185$	1.11109	0.0816891
$186$	0.340875	0.0249942
$187$	−1.10969	−0.0811485
$188$	−19.4126	−1.41581
$189$	1.40831	0.102440
$190$	0.608259	0.0441277
$191$	−14.6343	−1.05890	−0.529450	−	0.848341i	$-0.677602\pi$
$191$	−14.6343	−1.05890	−0.529450	+	0.848341i	$0.677602\pi$
$192$	−7.57139	−0.546418
$193$	16.6634	1.19945	0.599727	−	0.800204i	$-0.295276\pi$
$193$	16.6634	1.19945	0.599727	+	0.800204i	$0.295276\pi$
$194$	−1.31635	−0.0945085
$195$	3.37933	0.241999
$196$	9.94305	0.710218
$197$	−0.330824	−0.0235702	−0.0117851	−	0.999931i	$-0.503751\pi$
$197$	−0.330824	−0.0235702	−0.0117851	+	0.999931i	$0.503751\pi$
$198$	−0.172709	−0.0122739
$199$	−0.859901	−0.0609568	−0.0304784	−	0.999535i	$-0.509703\pi$
$199$	−0.859901	−0.0609568	−0.0304784	+	0.999535i	$0.509703\pi$
$200$	−0.534145	−0.0377697
$201$	1.94132	0.136930
$202$	1.57021	0.110480
$203$	0.199873	0.0140284
$204$	−1.70824	−0.119600
$205$	−6.00377	−0.419322
$206$	0.215779	0.0150340
$207$	0	0
$208$	13.1536	0.912037
$209$	−5.83835	−0.403847
$210$	0.188910	0.0130361
$211$	−9.90476	−0.681872	−0.340936	−	0.940087i	$-0.610744\pi$
$211$	−9.90476	−0.681872	−0.340936	+	0.940087i	$0.610744\pi$
$212$	−13.6137	−0.934995
$213$	11.7487	0.805005
$214$	−1.53669	−0.105046
$215$	0.457979	0.0312339
$216$	−0.534145	−0.0363440
$217$	3.57879	0.242944
$218$	−1.79064	−0.121278
$219$	−13.1015	−0.885321
$220$	2.55190	0.172049
$221$	2.91255	0.195919
$222$	0.149041	0.0100030
$223$	16.2314	1.08694	0.543468	−	0.839430i	$-0.317111\pi$
$223$	16.2314	1.08694	0.543468	+	0.839430i	$0.317111\pi$
$224$	2.23979	0.149652
$225$	1.00000	0.0666667
$226$	0.0923953	0.00614604
$227$	−4.16741	−0.276601	−0.138300	−	0.990390i	$-0.544164\pi$
$227$	−4.16741	−0.276601	−0.138300	+	0.990390i	$0.544164\pi$
$228$	−8.98745	−0.595208
$229$	16.8228	1.11168	0.555842	−	0.831288i	$-0.312396\pi$
$229$	16.8228	1.11168	0.555842	+	0.831288i	$0.312396\pi$
$230$	0	0
$231$	−1.81325	−0.119303
$232$	−0.0758081	−0.00497704
$233$	15.1068	0.989678	0.494839	−	0.868985i	$-0.335227\pi$
$233$	15.1068	0.989678	0.494839	+	0.868985i	$0.335227\pi$
$234$	0.453302	0.0296333
$235$	9.79441	0.638917
$236$	5.10043	0.332010
$237$	9.02887	0.586488
$238$	0.162817	0.0105538
$239$	12.3303	0.797580	0.398790	−	0.917042i	$-0.369430\pi$
$239$	12.3303	0.797580	0.398790	+	0.917042i	$0.369430\pi$
$240$	3.89236	0.251251
$241$	−12.9679	−0.835336	−0.417668	−	0.908600i	$-0.637153\pi$
$241$	−12.9679	−0.835336	−0.417668	+	0.908600i	$0.637153\pi$
$242$	−1.25317	−0.0805566
$243$	1.00000	0.0641500
$244$	25.0453	1.60336
$245$	−5.01666	−0.320503
$246$	−0.805344	−0.0513469
$247$	15.3236	0.975020
$248$	−1.35737	−0.0861928
$249$	8.77272	0.555948
$250$	0.134140	0.00848374
$251$	−5.73804	−0.362182	−0.181091	−	0.983466i	$-0.557963\pi$
$251$	−5.73804	−0.362182	−0.181091	+	0.983466i	$0.557963\pi$
$252$	−2.79128	−0.175834
$253$	0	0
$254$	1.58082	0.0991897
$255$	0.861872	0.0539725
$256$	14.5799	0.911242
$257$	14.3494	0.895091	0.447546	−	0.894261i	$-0.352298\pi$
$257$	14.3494	0.895091	0.447546	+	0.894261i	$0.352298\pi$
$258$	0.0614331	0.00382466
$259$	1.56476	0.0972297
$260$	−6.69785	−0.415383
$261$	0.141924	0.00878488
$262$	−0.404391	−0.0249833
$263$	26.1373	1.61170	0.805848	−	0.592122i	$-0.201710\pi$
$263$	26.1373	1.61170	0.805848	+	0.592122i	$0.201710\pi$
$264$	0.687730	0.0423268
$265$	6.86866	0.421938
$266$	0.856618	0.0525226
$267$	4.17368	0.255425
$268$	−3.84772	−0.235037
$269$	22.9787	1.40104	0.700519	−	0.713633i	$-0.252952\pi$
$269$	22.9787	1.40104	0.700519	+	0.713633i	$0.252952\pi$
$270$	0.134140	0.00816348
$271$	−0.852912	−0.0518107	−0.0259054	−	0.999664i	$-0.508247\pi$
$271$	−0.852912	−0.0518107	−0.0259054	+	0.999664i	$0.508247\pi$
$272$	3.35472	0.203410
$273$	4.75915	0.288037
$274$	−1.79236	−0.108280
$275$	−1.28753	−0.0776412
$276$	0	0
$277$	25.8752	1.55469	0.777346	−	0.629074i	$-0.216566\pi$
$277$	25.8752	1.55469	0.777346	+	0.629074i	$0.216566\pi$
$278$	2.84101	0.170393
$279$	2.54119	0.152137
$280$	−0.752242	−0.0449551
$281$	−13.8201	−0.824438	−0.412219	−	0.911085i	$-0.635246\pi$
$281$	−13.8201	−0.824438	−0.412219	+	0.911085i	$0.635246\pi$
$282$	1.31382	0.0782367
$283$	−24.8397	−1.47657	−0.738285	−	0.674489i	$-0.764364\pi$
$283$	−24.8397	−1.47657	−0.738285	+	0.674489i	$0.764364\pi$
$284$	−23.2859	−1.38177
$285$	4.53452	0.268602
$286$	−0.583642	−0.0345115
$287$	−8.45518	−0.499094
$288$	1.59041	0.0937158
$289$	−16.2572	−0.956305
$290$	0.0190377	0.00111793
$291$	−9.81329	−0.575265
$292$	25.9674	1.51962
$293$	29.1869	1.70511	0.852557	−	0.522634i	$-0.175051\pi$
$293$	29.1869	1.70511	0.852557	+	0.522634i	$0.175051\pi$
$294$	−0.672933	−0.0392462
$295$	−2.57337	−0.149827
$296$	−0.593484	−0.0344956
$297$	−1.28753	−0.0747103
$298$	2.52195	0.146093
$299$	0	0
$300$	−1.98201	−0.114431
$301$	0.644977	0.0371759
$302$	1.13547	0.0653391
$303$	11.7058	0.672480
$304$	17.6500	1.01230
$305$	−12.6363	−0.723554
$306$	0.115611	0.00660905
$307$	−6.60542	−0.376991	−0.188496	−	0.982074i	$-0.560361\pi$
$307$	−6.60542	−0.376991	−0.188496	+	0.982074i	$0.560361\pi$
$308$	3.59387	0.204780
$309$	1.60861	0.0915109
$310$	0.340875	0.0193604
$311$	10.4145	0.590551	0.295275	−	0.955412i	$-0.404589\pi$
$311$	10.4145	0.590551	0.295275	+	0.955412i	$0.404589\pi$
$312$	−1.80505	−0.102191
$313$	−11.7947	−0.666673	−0.333337	−	0.942808i	$-0.608175\pi$
$313$	−11.7947	−0.666673	−0.333337	+	0.942808i	$0.608175\pi$
$314$	1.46685	0.0827789
$315$	1.40831	0.0793494
$316$	−17.8953	−1.00669
$317$	6.78166	0.380896	0.190448	−	0.981697i	$-0.439006\pi$
$317$	6.78166	0.380896	0.190448	+	0.981697i	$0.439006\pi$
$318$	0.921359	0.0516673
$319$	−0.182732	−0.0102310
$320$	−7.57139	−0.423254
$321$	−11.4559	−0.639406
$322$	0	0
$323$	3.90817	0.217457
$324$	−1.98201	−0.110111
$325$	3.37933	0.187452
$326$	−0.0928888	−0.00514464
$327$	−13.3491	−0.738206
$328$	3.20689	0.177071
$329$	13.7936	0.760464
$330$	−0.172709	−0.00950734
$331$	−2.93591	−0.161372	−0.0806861	−	0.996740i	$-0.525711\pi$
$331$	−2.93591	−0.161372	−0.0806861	+	0.996740i	$0.525711\pi$
$332$	−17.3876	−0.954268
$333$	1.11109	0.0608875
$334$	1.36429	0.0746505
$335$	1.94132	0.106066
$336$	5.48166	0.299049
$337$	0.496772	0.0270609	0.0135304	−	0.999908i	$-0.495693\pi$
$337$	0.496772	0.0270609	0.0135304	+	0.999908i	$0.495693\pi$
$338$	−0.211958	−0.0115290
$339$	0.688799	0.0374105
$340$	−1.70824	−0.0926421
$341$	−3.27187	−0.177182
$342$	0.608259	0.0328909
$343$	−16.9232	−0.913767
$344$	−0.244627	−0.0131894
$345$	0	0
$346$	−0.664905	−0.0357455
$347$	−1.64036	−0.0880591	−0.0440295	−	0.999030i	$-0.514020\pi$
$347$	−1.64036	−0.0880591	−0.0440295	+	0.999030i	$0.514020\pi$
$348$	−0.281295	−0.0150790
$349$	3.83098	0.205068	0.102534	−	0.994730i	$-0.467305\pi$
$349$	3.83098	0.205068	0.102534	+	0.994730i	$0.467305\pi$
$350$	0.188910	0.0100977
$351$	3.37933	0.180375
$352$	−2.04771	−0.109143
$353$	24.6561	1.31231	0.656156	−	0.754625i	$-0.272181\pi$
$353$	24.6561	1.31231	0.656156	+	0.754625i	$0.272181\pi$
$354$	−0.345190	−0.0183467
$355$	11.7487	0.623554
$356$	−8.27226	−0.438429
$357$	1.21378	0.0642402
$358$	0.492060	0.0260062
$359$	−0.343744	−0.0181421	−0.00907105	−	0.999959i	$-0.502887\pi$
$359$	−0.343744	−0.0181421	−0.00907105	+	0.999959i	$0.502887\pi$
$360$	−0.534145	−0.0281519
$361$	1.56186	0.0822033
$362$	−1.50970	−0.0793479
$363$	−9.34226	−0.490341
$364$	−9.43267	−0.494406
$365$	−13.1015	−0.685766
$366$	−1.69503	−0.0886008
$367$	37.1658	1.94004	0.970018	−	0.243032i	$-0.0781420\pi$
$367$	37.1658	1.94004	0.970018	+	0.243032i	$0.0781420\pi$
$368$	0	0
$369$	−6.00377	−0.312544
$370$	0.149041	0.00774830
$371$	9.67321	0.502208
$372$	−5.03666	−0.261139
$373$	−16.6661	−0.862938	−0.431469	−	0.902128i	$-0.642005\pi$
$373$	−16.6661	−0.862938	−0.431469	+	0.902128i	$0.642005\pi$
$374$	−0.148853	−0.00769702
$375$	1.00000	0.0516398
$376$	−5.23163	−0.269801
$377$	0.479609	0.0247011
$378$	0.188910	0.00971650
$379$	−24.2487	−1.24557	−0.622787	−	0.782391i	$-0.714000\pi$
$379$	−24.2487	−1.24557	−0.622787	+	0.782391i	$0.714000\pi$
$380$	−8.98745	−0.461046
$381$	11.7849	0.603759
$382$	−1.96304	−0.100438
$383$	−33.1413	−1.69344	−0.846719	−	0.532040i	$-0.821426\pi$
$383$	−33.1413	−1.69344	−0.846719	+	0.532040i	$0.821426\pi$
$384$	−4.19644	−0.214149
$385$	−1.81325	−0.0924117
$386$	2.23522	0.113770
$387$	0.457979	0.0232804
$388$	19.4500	0.987424
$389$	−23.9454	−1.21408	−0.607039	−	0.794672i	$-0.707643\pi$
$389$	−23.9454	−1.21408	−0.607039	+	0.794672i	$0.707643\pi$
$390$	0.453302	0.0229538
$391$	0	0
$392$	2.67962	0.135341
$393$	−3.01470	−0.152071
$394$	−0.0443766	−0.00223566
$395$	9.02887	0.454292
$396$	2.55190	0.128238
$397$	28.0776	1.40918	0.704588	−	0.709617i	$-0.251132\pi$
$397$	28.0776	1.40918	0.704588	+	0.709617i	$0.251132\pi$
$398$	−0.115347	−0.00578181
$399$	6.38602	0.319701
$400$	3.89236	0.194618
$401$	32.0970	1.60285	0.801425	−	0.598096i	$-0.204076\pi$
$401$	32.0970	1.60285	0.801425	+	0.598096i	$0.204076\pi$
$402$	0.260409	0.0129880
$403$	8.58753	0.427775
$404$	−23.2010	−1.15429
$405$	1.00000	0.0496904
$406$	0.0268109	0.00133060
$407$	−1.43057	−0.0709106
$408$	−0.460364	−0.0227914
$409$	21.2017	1.04835	0.524177	−	0.851609i	$-0.324373\pi$
$409$	21.2017	1.04835	0.524177	+	0.851609i	$0.324373\pi$
$410$	−0.805344	−0.0397731
$411$	−13.3619	−0.659094
$412$	−3.18828	−0.157075
$413$	−3.62410	−0.178330
$414$	0	0
$415$	8.77272	0.430636
$416$	5.37452	0.263508
$417$	21.1795	1.03717
$418$	−0.783154	−0.0383053
$419$	−11.6106	−0.567216	−0.283608	−	0.958940i	$-0.591531\pi$
$419$	−11.6106	−0.567216	−0.283608	+	0.958940i	$0.591531\pi$
$420$	−2.79128	−0.136201
$421$	−31.6491	−1.54248	−0.771241	−	0.636543i	$-0.780364\pi$
$421$	−31.6491	−1.54248	−0.771241	+	0.636543i	$0.780364\pi$
$422$	−1.32862	−0.0646762
$423$	9.79441	0.476220
$424$	−3.66886	−0.178176
$425$	0.861872	0.0418069
$426$	1.57596	0.0763556
$427$	−17.7959	−0.861204
$428$	22.7057	1.09752
$429$	−4.35100	−0.210068
$430$	0.0614331	0.00296257
$431$	−39.1490	−1.88574	−0.942870	−	0.333160i	$-0.891885\pi$
$431$	−39.1490	−1.88574	−0.942870	+	0.333160i	$0.891885\pi$
$432$	3.89236	0.187271
$433$	17.4268	0.837480	0.418740	−	0.908106i	$-0.362472\pi$
$433$	17.4268	0.837480	0.418740	+	0.908106i	$0.362472\pi$
$434$	0.480058	0.0230435
$435$	0.141924	0.00680474
$436$	26.4580	1.26711
$437$	0	0
$438$	−1.75744	−0.0839736
$439$	−18.9444	−0.904168	−0.452084	−	0.891975i	$-0.649319\pi$
$439$	−18.9444	−0.904168	−0.452084	+	0.891975i	$0.649319\pi$
$440$	0.687730	0.0327862
$441$	−5.01666	−0.238889
$442$	0.390688	0.0185831
$443$	38.0054	1.80569	0.902846	−	0.429963i	$-0.141474\pi$
$443$	38.0054	1.80569	0.902846	+	0.429963i	$0.141474\pi$
$444$	−2.20219	−0.104511
$445$	4.17368	0.197851
$446$	2.17728	0.103097
$447$	18.8009	0.889254
$448$	−10.6629	−0.503773
$449$	12.4939	0.589622	0.294811	−	0.955556i	$-0.404743\pi$
$449$	12.4939	0.589622	0.294811	+	0.955556i	$0.404743\pi$
$450$	0.134140	0.00632340
$451$	7.73006	0.363994
$452$	−1.36520	−0.0642138
$453$	8.46485	0.397713
$454$	−0.559015	−0.0262359
$455$	4.75915	0.223112
$456$	−2.42209	−0.113425
$457$	−11.2994	−0.528566	−0.264283	−	0.964445i	$-0.585135\pi$
$457$	−11.2994	−0.528566	−0.264283	+	0.964445i	$0.585135\pi$
$458$	2.25661	0.105444
$459$	0.861872	0.0402287
$460$	0	0
$461$	−28.8897	−1.34553	−0.672764	−	0.739857i	$-0.734893\pi$
$461$	−28.8897	−1.34553	−0.672764	+	0.739857i	$0.734893\pi$
$462$	−0.243229	−0.0113160
$463$	−40.4788	−1.88121	−0.940605	−	0.339503i	$-0.889741\pi$
$463$	−40.4788	−1.88121	−0.940605	+	0.339503i	$0.889741\pi$
$464$	0.552420	0.0256455
$465$	2.54119	0.117845
$466$	2.02642	0.0938720
$467$	25.5647	1.18299	0.591496	−	0.806308i	$-0.298538\pi$
$467$	25.5647	1.18299	0.591496	+	0.806308i	$0.298538\pi$
$468$	−6.69785	−0.309608
$469$	2.73399	0.126244
$470$	1.31382	0.0606019
$471$	10.9352	0.503868
$472$	1.37455	0.0632688
$473$	−0.589664	−0.0271128
$474$	1.21113	0.0556290
$475$	4.53452	0.208058
$476$	−2.40573	−0.110266
$477$	6.86866	0.314494
$478$	1.65398	0.0756513
$479$	−3.38669	−0.154742	−0.0773709	−	0.997002i	$-0.524653\pi$
$479$	−3.38669	−0.154742	−0.0773709	+	0.997002i	$0.524653\pi$
$480$	1.59041	0.0725920
$481$	3.75475	0.171202
$482$	−1.73951	−0.0792325
$483$	0	0
$484$	18.5164	0.841655
$485$	−9.81329	−0.445598
$486$	0.134140	0.00608470
$487$	−15.8311	−0.717374	−0.358687	−	0.933458i	$-0.616775\pi$
$487$	−15.8311	−0.717374	−0.358687	+	0.933458i	$0.616775\pi$
$488$	6.74963	0.305542
$489$	−0.692478	−0.0313150
$490$	−0.672933	−0.0304000
$491$	−42.9674	−1.93909	−0.969545	−	0.244912i	$-0.921241\pi$
$491$	−42.9674	−1.93909	−0.969545	+	0.244912i	$0.921241\pi$
$492$	11.8995	0.536472
$493$	0.122320	0.00550903
$494$	2.05551	0.0924816
$495$	−1.28753	−0.0578703
$496$	9.89125	0.444130
$497$	16.5458	0.742180
$498$	1.17677	0.0527323
$499$	6.76943	0.303041	0.151521	−	0.988454i	$-0.451583\pi$
$499$	6.76943	0.303041	0.151521	+	0.988454i	$0.451583\pi$
$500$	−1.98201	−0.0886380
$501$	10.1707	0.454391
$502$	−0.769699	−0.0343533
$503$	−0.984445	−0.0438942	−0.0219471	−	0.999759i	$-0.506987\pi$
$503$	−0.984445	−0.0438942	−0.0219471	+	0.999759i	$0.506987\pi$
$504$	−0.752242	−0.0335075
$505$	11.7058	0.520901
$506$	0	0
$507$	−1.58013	−0.0701759
$508$	−23.3578	−1.03633
$509$	44.4901	1.97199	0.985995	−	0.166775i	$-0.0533354\pi$
$509$	44.4901	1.97199	0.985995	+	0.166775i	$0.0533354\pi$
$510$	0.115611	0.00511935
$511$	−18.4511	−0.816227
$512$	10.3486	0.457349
$513$	4.53452	0.200204
$514$	1.92482	0.0849003
$515$	1.60861	0.0708840
$516$	−0.907717	−0.0399600
$517$	−12.6106	−0.554615
$518$	0.209897	0.00922234
$519$	−4.95681	−0.217580
$520$	−1.80505	−0.0791568
$521$	−11.9964	−0.525574	−0.262787	−	0.964854i	$-0.584642\pi$
$521$	−11.9964	−0.525574	−0.262787	+	0.964854i	$0.584642\pi$
$522$	0.0190377	0.000833255 0
$523$	32.0276	1.40047	0.700234	−	0.713913i	$-0.253079\pi$
$523$	32.0276	1.40047	0.700234	+	0.713913i	$0.253079\pi$
$524$	5.97515	0.261026
$525$	1.40831	0.0614638
$526$	3.50605	0.152871
$527$	2.19018	0.0954059
$528$	−5.01155	−0.218100
$529$	0	0
$530$	0.921359	0.0400213
$531$	−2.57337	−0.111675
$532$	−12.6571	−0.548756
$533$	−20.2887	−0.878803
$534$	0.559856	0.0242273
$535$	−11.4559	−0.495282
$536$	−1.03695	−0.0447894
$537$	3.66827	0.158297
$538$	3.08236	0.132890
$539$	6.45912	0.278214
$540$	−1.98201	−0.0852920
$541$	37.0420	1.59256	0.796281	−	0.604928i	$-0.206798\pi$
$541$	37.0420	1.59256	0.796281	+	0.604928i	$0.206798\pi$
$542$	−0.114409	−0.00491430
$543$	−11.2547	−0.482984
$544$	1.37073	0.0587695
$545$	−13.3491	−0.571812
$546$	0.638391	0.0273206
$547$	25.1082	1.07355	0.536775	−	0.843725i	$-0.319642\pi$
$547$	25.1082	1.07355	0.536775	+	0.843725i	$0.319642\pi$
$548$	26.4834	1.13131
$549$	−12.6363	−0.539306
$550$	−0.172709	−0.00736435
$551$	0.643558	0.0274165
$552$	0	0
$553$	12.7155	0.540717
$554$	3.47089	0.147464
$555$	1.11109	0.0471632
$556$	−41.9779	−1.78026
$557$	23.0692	0.977474	0.488737	−	0.872431i	$-0.337458\pi$
$557$	23.0692	0.977474	0.488737	+	0.872431i	$0.337458\pi$
$558$	0.340875	0.0144304
$559$	1.54766	0.0654592
$560$	5.48166	0.231642
$561$	−1.10969	−0.0468511
$562$	−1.85382	−0.0781988
$563$	−4.58369	−0.193180	−0.0965898	−	0.995324i	$-0.530794\pi$
$563$	−4.58369	−0.193180	−0.0965898	+	0.995324i	$0.530794\pi$
$564$	−19.4126	−0.817417
$565$	0.688799	0.0289780
$566$	−3.33199	−0.140054
$567$	1.40831	0.0591435
$568$	−6.27549	−0.263314
$569$	−6.41641	−0.268990	−0.134495	−	0.990914i	$-0.542941\pi$
$569$	−6.41641	−0.268990	−0.134495	+	0.990914i	$0.542941\pi$
$570$	0.608259	0.0254772
$571$	−7.89001	−0.330187	−0.165093	−	0.986278i	$-0.552793\pi$
$571$	−7.89001	−0.330187	−0.165093	+	0.986278i	$0.552793\pi$
$572$	8.62372	0.360576
$573$	−14.6343	−0.611356
$574$	−1.13418	−0.0473396
$575$	0	0
$576$	−7.57139	−0.315475
$577$	16.4756	0.685887	0.342943	−	0.939356i	$-0.388576\pi$
$577$	16.4756	0.685887	0.342943	+	0.939356i	$0.388576\pi$
$578$	−2.18073	−0.0907065
$579$	16.6634	0.692505
$580$	−0.281295	−0.0116801
$581$	12.3547	0.512560
$582$	−1.31635	−0.0545645
$583$	−8.84363	−0.366266
$584$	6.99813	0.289585
$585$	3.37933	0.139718
$586$	3.91511	0.161732
$587$	1.41824	0.0585369	0.0292684	−	0.999572i	$-0.490682\pi$
$587$	1.41824	0.0585369	0.0292684	+	0.999572i	$0.490682\pi$
$588$	9.94305	0.410044
$589$	11.5231	0.474801
$590$	−0.345190	−0.0142113
$591$	−0.330824	−0.0136083
$592$	4.32477	0.177747
$593$	−4.81969	−0.197921	−0.0989605	−	0.995091i	$-0.531552\pi$
$593$	−4.81969	−0.197921	−0.0989605	+	0.995091i	$0.531552\pi$
$594$	−0.172709	−0.00708635
$595$	1.21378	0.0497603
$596$	−37.2636	−1.52638
$597$	−0.859901	−0.0351934
$598$	0	0
$599$	32.5707	1.33080	0.665400	−	0.746487i	$-0.268261\pi$
$599$	32.5707	1.33080	0.665400	+	0.746487i	$0.268261\pi$
$600$	−0.534145	−0.0218064
$601$	−26.5112	−1.08141	−0.540707	−	0.841211i	$-0.681843\pi$
$601$	−26.5112	−1.08141	−0.540707	+	0.841211i	$0.681843\pi$
$602$	0.0865170	0.00352617
$603$	1.94132	0.0790569
$604$	−16.7774	−0.682662
$605$	−9.34226	−0.379817
$606$	1.57021	0.0637855
$607$	−23.1138	−0.938162	−0.469081	−	0.883155i	$-0.655415\pi$
$607$	−23.1138	−0.938162	−0.469081	+	0.883155i	$0.655415\pi$
$608$	7.21174	0.292475
$609$	0.199873	0.00809928
$610$	−1.69503	−0.0686299
$611$	33.0985	1.33902
$612$	−1.70824	−0.0690513
$613$	6.96631	0.281367	0.140683	−	0.990055i	$-0.455070\pi$
$613$	6.96631	0.281367	0.140683	+	0.990055i	$0.455070\pi$
$614$	−0.886049	−0.0357580
$615$	−6.00377	−0.242096
$616$	0.968538	0.0390235
$617$	1.10971	0.0446752	0.0223376	−	0.999750i	$-0.492889\pi$
$617$	1.10971	0.0446752	0.0223376	+	0.999750i	$0.492889\pi$
$618$	0.215779	0.00867990
$619$	20.4682	0.822688	0.411344	−	0.911480i	$-0.365059\pi$
$619$	20.4682	0.822688	0.411344	+	0.911480i	$0.365059\pi$
$620$	−5.03666	−0.202277
$621$	0	0
$622$	1.39699	0.0560144
$623$	5.87784	0.235491
$624$	13.1536	0.526565
$625$	1.00000	0.0400000
$626$	−1.58213	−0.0632346
$627$	−5.83835	−0.233161
$628$	−21.6737	−0.864874
$629$	0.957619	0.0381828
$630$	0.188910	0.00752637
$631$	41.8153	1.66464	0.832320	−	0.554296i	$-0.187012\pi$
$631$	41.8153	1.66464	0.832320	+	0.554296i	$0.187012\pi$
$632$	−4.82273	−0.191838
$633$	−9.90476	−0.393679
$634$	0.909690	0.0361284
$635$	11.7849	0.467670
$636$	−13.6137	−0.539819
$637$	−16.9529	−0.671700
$638$	−0.0245116	−0.000970424 0
$639$	11.7487	0.464770
$640$	−4.19644	−0.165879
$641$	−3.61951	−0.142962	−0.0714811	−	0.997442i	$-0.522773\pi$
$641$	−3.61951	−0.142962	−0.0714811	+	0.997442i	$0.522773\pi$
$642$	−1.53669	−0.0606483
$643$	−15.3747	−0.606319	−0.303159	−	0.952940i	$-0.598041\pi$
$643$	−15.3747	−0.606319	−0.303159	+	0.952940i	$0.598041\pi$
$644$	0	0
$645$	0.457979	0.0180329
$646$	0.524241	0.0206260
$647$	−24.7287	−0.972184	−0.486092	−	0.873908i	$-0.661578\pi$
$647$	−24.7287	−0.972184	−0.486092	+	0.873908i	$0.661578\pi$
$648$	−0.534145	−0.0209832
$649$	3.31330	0.130058
$650$	0.453302	0.0177800
$651$	3.57879	0.140264
$652$	1.37250	0.0537511
$653$	17.0730	0.668117	0.334058	−	0.942552i	$-0.391582\pi$
$653$	17.0730	0.668117	0.334058	+	0.942552i	$0.391582\pi$
$654$	−1.79064	−0.0700196
$655$	−3.01470	−0.117794
$656$	−23.3689	−0.912401
$657$	−13.1015	−0.511140
$658$	1.85027	0.0721308
$659$	35.7517	1.39269	0.696344	−	0.717708i	$-0.254809\pi$
$659$	35.7517	1.39269	0.696344	+	0.717708i	$0.254809\pi$
$660$	2.55190	0.0993326
$661$	33.2447	1.29307	0.646535	−	0.762884i	$-0.276217\pi$
$661$	33.2447	1.29307	0.646535	+	0.762884i	$0.276217\pi$
$662$	−0.393822	−0.0153063
$663$	2.91255	0.113114
$664$	−4.68590	−0.181848
$665$	6.38602	0.247639
$666$	0.149041	0.00577524
$667$	0	0
$668$	−20.1583	−0.779948
$669$	16.2314	0.627543
$670$	0.260409	0.0100605
$671$	16.2697	0.628085
$672$	2.23979	0.0864019
$673$	30.4717	1.17460	0.587300	−	0.809370i	$-0.300191\pi$
$673$	30.4717	1.17460	0.587300	+	0.809370i	$0.300191\pi$
$674$	0.0666368	0.00256675
$675$	1.00000	0.0384900
$676$	3.13182	0.120455
$677$	7.32746	0.281617	0.140809	−	0.990037i	$-0.455030\pi$
$677$	7.32746	0.281617	0.140809	+	0.990037i	$0.455030\pi$
$678$	0.0923953	0.00354842
$679$	−13.8202	−0.530369
$680$	−0.460364	−0.0176542
$681$	−4.16741	−0.159696
$682$	−0.438888	−0.0168059
$683$	−40.1671	−1.53695	−0.768475	−	0.639879i	$-0.778984\pi$
$683$	−40.1671	−1.53695	−0.768475	+	0.639879i	$0.778984\pi$
$684$	−8.98745	−0.343644
$685$	−13.3619	−0.510532
$686$	−2.27007	−0.0866717
$687$	16.8228	0.641831
$688$	1.78262	0.0679618
$689$	23.2115	0.884287
$690$	0	0
$691$	−7.48468	−0.284731	−0.142365	−	0.989814i	$-0.545471\pi$
$691$	−7.48468	−0.284731	−0.142365	+	0.989814i	$0.545471\pi$
$692$	9.82444	0.373469
$693$	−1.81325	−0.0688796
$694$	−0.220037	−0.00835250
$695$	21.1795	0.803385
$696$	−0.0758081	−0.00287350
$697$	−5.17448	−0.195997
$698$	0.513886	0.0194509
$699$	15.1068	0.571391
$700$	−2.79128	−0.105501
$701$	−0.806050	−0.0304441	−0.0152220	−	0.999884i	$-0.504846\pi$
$701$	−0.806050	−0.0304441	−0.0152220	+	0.999884i	$0.504846\pi$
$702$	0.453302	0.0171088
$703$	5.03827	0.190022
$704$	9.74842	0.367407
$705$	9.79441	0.368879
$706$	3.30736	0.124474
$707$	16.4854	0.619998
$708$	5.10043	0.191686
$709$	−12.4518	−0.467639	−0.233819	−	0.972280i	$-0.575122\pi$
$709$	−12.4518	−0.467639	−0.233819	+	0.972280i	$0.575122\pi$
$710$	1.57596	0.0591448
$711$	9.02887	0.338609
$712$	−2.22935	−0.0835484
$713$	0	0
$714$	0.162817	0.00609325
$715$	−4.35100	−0.162718
$716$	−7.27053	−0.271712
$717$	12.3303	0.460483
$718$	−0.0461096	−0.00172080
$719$	−51.2299	−1.91055	−0.955276	−	0.295714i	$-0.904442\pi$
$719$	−51.2299	−1.91055	−0.955276	+	0.295714i	$0.904442\pi$
$720$	3.89236	0.145060
$721$	2.26543	0.0843690
$722$	0.209508	0.00779707
$723$	−12.9679	−0.482282
$724$	22.3068	0.829027
$725$	0.141924	0.00527093
$726$	−1.25317	−0.0465094
$727$	25.6236	0.950325	0.475163	−	0.879898i	$-0.342389\pi$
$727$	25.6236	0.950325	0.475163	+	0.879898i	$0.342389\pi$
$728$	−2.54208	−0.0942156
$729$	1.00000	0.0370370
$730$	−1.75744	−0.0650457
$731$	0.394719	0.0145992
$732$	25.0453	0.925701
$733$	−19.7238	−0.728515	−0.364257	−	0.931298i	$-0.618677\pi$
$733$	−19.7238	−0.728515	−0.364257	+	0.931298i	$0.618677\pi$
$734$	4.98540	0.184014
$735$	−5.01666	−0.185042
$736$	0	0
$737$	−2.49952	−0.0920711
$738$	−0.805344	−0.0296451
$739$	−12.4989	−0.459778	−0.229889	−	0.973217i	$-0.573836\pi$
$739$	−12.4989	−0.459778	−0.229889	+	0.973217i	$0.573836\pi$
$740$	−2.20219	−0.0809542
$741$	15.3236	0.562928
$742$	1.29756	0.0476350
$743$	−16.0706	−0.589574	−0.294787	−	0.955563i	$-0.595249\pi$
$743$	−16.0706	−0.589574	−0.294787	+	0.955563i	$0.595249\pi$
$744$	−1.35737	−0.0497634
$745$	18.8009	0.688813
$746$	−2.23559	−0.0818506
$747$	8.77272	0.320977
$748$	2.19941	0.0804184
$749$	−16.1335	−0.589504
$750$	0.134140	0.00489809
$751$	−22.9626	−0.837918	−0.418959	−	0.908005i	$-0.637605\pi$
$751$	−22.9626	−0.837918	−0.418959	+	0.908005i	$0.637605\pi$
$752$	38.1234	1.39022
$753$	−5.73804	−0.209106
$754$	0.0643345	0.00234292
$755$	8.46485	0.308067
$756$	−2.79128	−0.101518
$757$	35.5853	1.29337	0.646685	−	0.762757i	$-0.276155\pi$
$757$	35.5853	1.29337	0.646685	+	0.762757i	$0.276155\pi$
$758$	−3.25272	−0.118144
$759$	0	0
$760$	−2.42209	−0.0878584
$761$	36.1897	1.31188	0.655938	−	0.754815i	$-0.272273\pi$
$761$	36.1897	1.31188	0.655938	+	0.754815i	$0.272273\pi$
$762$	1.58082	0.0572672
$763$	−18.7997	−0.680594
$764$	29.0053	1.04937
$765$	0.861872	0.0311610
$766$	−4.44556	−0.160624
$767$	−8.69625	−0.314003
$768$	14.5799	0.526106
$769$	13.5259	0.487757	0.243879	−	0.969806i	$-0.421580\pi$
$769$	13.5259	0.487757	0.243879	+	0.969806i	$0.421580\pi$
$770$	−0.243229	−0.00876535
$771$	14.3494	0.516781
$772$	−33.0269	−1.18866
$773$	−43.3601	−1.55955	−0.779777	−	0.626057i	$-0.784668\pi$
$773$	−43.3601	−1.55955	−0.779777	+	0.626057i	$0.784668\pi$
$774$	0.0614331	0.00220817
$775$	2.54119	0.0912824
$776$	5.24172	0.188167
$777$	1.56476	0.0561356
$778$	−3.21202	−0.115157
$779$	−27.2242	−0.975409
$780$	−6.69785	−0.239822
$781$	−15.1268	−0.541280
$782$	0	0
$783$	0.141924	0.00507195
$784$	−19.5267	−0.697381
$785$	10.9352	0.390295
$786$	−0.404391	−0.0144241
$787$	−47.0308	−1.67647	−0.838234	−	0.545311i	$-0.816412\pi$
$787$	−47.0308	−1.67647	−0.838234	+	0.545311i	$0.816412\pi$
$788$	0.655695	0.0233582
$789$	26.1373	0.930513
$790$	1.21113	0.0430901
$791$	0.970044	0.0344908
$792$	0.687730	0.0244374
$793$	−42.7024	−1.51641
$794$	3.76632	0.133662
$795$	6.86866	0.243606
$796$	1.70433	0.0604084
$797$	−52.1974	−1.84893	−0.924464	−	0.381269i	$-0.875487\pi$
$797$	−52.1974	−1.84893	−0.924464	+	0.381269i	$0.875487\pi$
$798$	0.856618	0.0303239
$799$	8.44152	0.298640
$800$	1.59041	0.0562295
$801$	4.17368	0.147470
$802$	4.30548	0.152032
$803$	16.8687	0.595283
$804$	−3.84772	−0.135699
$805$	0	0
$806$	1.15193	0.0405750
$807$	22.9787	0.808890
$808$	−6.25259	−0.219965
$809$	46.5559	1.63682	0.818409	−	0.574636i	$-0.194856\pi$
$809$	46.5559	1.63682	0.818409	+	0.574636i	$0.194856\pi$
$810$	0.134140	0.00471319
$811$	−19.6910	−0.691445	−0.345722	−	0.938337i	$-0.612366\pi$
$811$	−19.6910	−0.691445	−0.345722	+	0.938337i	$0.612366\pi$
$812$	−0.396150	−0.0139022
$813$	−0.852912	−0.0299129
$814$	−0.191896	−0.00672595
$815$	−0.692478	−0.0242565
$816$	3.35472	0.117439
$817$	2.07671	0.0726551
$818$	2.84398	0.0994376
$819$	4.75915	0.166298
$820$	11.8995	0.415549
$821$	42.8422	1.49520	0.747601	−	0.664148i	$-0.231205\pi$
$821$	42.8422	1.49520	0.747601	+	0.664148i	$0.231205\pi$
$822$	−1.79236	−0.0625157
$823$	−30.7325	−1.07127	−0.535634	−	0.844451i	$-0.679927\pi$
$823$	−30.7325	−1.07127	−0.535634	+	0.844451i	$0.679927\pi$
$824$	−0.859233	−0.0299328
$825$	−1.28753	−0.0448262
$826$	−0.486135	−0.0169148
$827$	−9.86962	−0.343200	−0.171600	−	0.985167i	$-0.554894\pi$
$827$	−9.86962	−0.343200	−0.171600	+	0.985167i	$0.554894\pi$
$828$	0	0
$829$	23.7648	0.825387	0.412693	−	0.910870i	$-0.364588\pi$
$829$	23.7648	0.825387	0.412693	+	0.910870i	$0.364588\pi$
$830$	1.17677	0.0408463
$831$	25.8752	0.897601
$832$	−25.5862	−0.887043
$833$	−4.32372	−0.149808
$834$	2.84101	0.0983762
$835$	10.1707	0.351970
$836$	11.5716	0.400214
$837$	2.54119	0.0878365
$838$	−1.55744	−0.0538010
$839$	20.4028	0.704384	0.352192	−	0.935928i	$-0.385436\pi$
$839$	20.4028	0.704384	0.352192	+	0.935928i	$0.385436\pi$
$840$	−0.752242	−0.0259548
$841$	−28.9799	−0.999305
$842$	−4.24540	−0.146306
$843$	−13.8201	−0.475989
$844$	19.6313	0.675737
$845$	−1.58013	−0.0543580
$846$	1.31382	0.0451700
$847$	−13.1568	−0.452073
$848$	26.7353	0.918095
$849$	−24.8397	−0.852498
$850$	0.115611	0.00396543
$851$	0	0
$852$	−23.2859	−0.797763
$853$	−11.0469	−0.378240	−0.189120	−	0.981954i	$-0.560563\pi$
$853$	−11.0469	−0.378240	−0.189120	+	0.981954i	$0.560563\pi$
$854$	−2.38714	−0.0816861
$855$	4.53452	0.155077
$856$	6.11911	0.209147
$857$	20.3681	0.695761	0.347881	−	0.937539i	$-0.386901\pi$
$857$	20.3681	0.695761	0.347881	+	0.937539i	$0.386901\pi$
$858$	−0.583642	−0.0199252
$859$	−45.2088	−1.54251	−0.771253	−	0.636529i	$-0.780369\pi$
$859$	−45.2088	−1.54251	−0.771253	+	0.636529i	$0.780369\pi$
$860$	−0.907717	−0.0309529
$861$	−8.45518	−0.288152
$862$	−5.25143	−0.178864
$863$	24.0949	0.820200	0.410100	−	0.912040i	$-0.365494\pi$
$863$	24.0949	0.820200	0.410100	+	0.912040i	$0.365494\pi$
$864$	1.59041	0.0541068
$865$	−4.95681	−0.168537
$866$	2.33763	0.0794358
$867$	−16.2572	−0.552123
$868$	−7.09319	−0.240759
$869$	−11.6250	−0.394350
$870$	0.0190377	0.000645437 0
$871$	6.56038	0.222290
$872$	7.13035	0.241464
$873$	−9.81329	−0.332129
$874$	0	0
$875$	1.40831	0.0476096
$876$	25.9674	0.877356
$877$	−19.1614	−0.647035	−0.323518	−	0.946222i	$-0.604866\pi$
$877$	−19.1614	−0.647035	−0.323518	+	0.946222i	$0.604866\pi$
$878$	−2.54120	−0.0857612
$879$	29.1869	0.984448
$880$	−5.01155	−0.168939
$881$	17.7454	0.597857	0.298928	−	0.954276i	$-0.403371\pi$
$881$	17.7454	0.597857	0.298928	+	0.954276i	$0.403371\pi$
$882$	−0.672933	−0.0226588
$883$	−45.7868	−1.54085	−0.770424	−	0.637532i	$-0.779955\pi$
$883$	−45.7868	−1.54085	−0.770424	+	0.637532i	$0.779955\pi$
$884$	−5.77269	−0.194157
$885$	−2.57337	−0.0865027
$886$	5.09804	0.171272
$887$	39.6672	1.33189	0.665947	−	0.745999i	$-0.268028\pi$
$887$	39.6672	1.33189	0.665947	+	0.745999i	$0.268028\pi$
$888$	−0.593484	−0.0199160
$889$	16.5968	0.556640
$890$	0.559856	0.0187664
$891$	−1.28753	−0.0431340
$892$	−32.1708	−1.07716
$893$	44.4129	1.48622
$894$	2.52195	0.0843467
$895$	3.66827	0.122617
$896$	−5.90990	−0.197436
$897$	0	0
$898$	1.67592	0.0559262
$899$	0.360657	0.0120286
$900$	−1.98201	−0.0660669
$901$	5.91990	0.197221
$902$	1.03691	0.0345253
$903$	0.644977	0.0214635
$904$	−0.367919	−0.0122368
$905$	−11.2547	−0.374118
$906$	1.13547	0.0377235
$907$	−10.0618	−0.334098	−0.167049	−	0.985949i	$-0.553424\pi$
$907$	−10.0618	−0.334098	−0.167049	+	0.985949i	$0.553424\pi$
$908$	8.25984	0.274112
$909$	11.7058	0.388257
$910$	0.638391	0.0211624
$911$	−35.4259	−1.17371	−0.586856	−	0.809691i	$-0.699635\pi$
$911$	−35.4259	−1.17371	−0.586856	+	0.809691i	$0.699635\pi$
$912$	17.6500	0.584450
$913$	−11.2952	−0.373816
$914$	−1.51570	−0.0501350
$915$	−12.6363	−0.417744
$916$	−33.3429	−1.10168
$917$	−4.24564	−0.140203
$918$	0.115611	0.00381574
$919$	44.2150	1.45852	0.729259	−	0.684238i	$-0.239865\pi$
$919$	44.2150	1.45852	0.729259	+	0.684238i	$0.239865\pi$
$920$	0	0
$921$	−6.60542	−0.217656
$922$	−3.87526	−0.127625
$923$	39.7026	1.30683
$924$	3.59387	0.118230
$925$	1.11109	0.0365325
$926$	−5.42981	−0.178435
$927$	1.60861	0.0528338
$928$	0.225718	0.00740954
$929$	−11.1729	−0.366569	−0.183285	−	0.983060i	$-0.558673\pi$
$929$	−11.1729	−0.366569	−0.183285	+	0.983060i	$0.558673\pi$
$930$	0.340875	0.0111777
$931$	−22.7481	−0.745540
$932$	−29.9417	−0.980775
$933$	10.4145	0.340955
$934$	3.42923	0.112208
$935$	−1.10969	−0.0362907
$936$	−1.80505	−0.0590000
$937$	20.0999	0.656635	0.328318	−	0.944567i	$-0.393518\pi$
$937$	20.0999	0.656635	0.328318	+	0.944567i	$0.393518\pi$
$938$	0.366736	0.0119744
$939$	−11.7947	−0.384904
$940$	−19.4126	−0.633169
$941$	−24.9926	−0.814737	−0.407368	−	0.913264i	$-0.633553\pi$
$941$	−24.9926	−0.814737	−0.407368	+	0.913264i	$0.633553\pi$
$942$	1.46685	0.0477924
$943$	0	0
$944$	−10.0165	−0.326008
$945$	1.40831	0.0458124
$946$	−0.0790973	−0.00257167
$947$	−20.1426	−0.654547	−0.327273	−	0.944930i	$-0.606130\pi$
$947$	−20.1426	−0.654547	−0.327273	+	0.944930i	$0.606130\pi$
$948$	−17.8953	−0.581212
$949$	−44.2745	−1.43721
$950$	0.608259	0.0197345
$951$	6.78166	0.219911
$952$	−0.648336	−0.0210127
$953$	−41.4384	−1.34232	−0.671161	−	0.741312i	$-0.734204\pi$
$953$	−41.4384	−1.34232	−0.671161	+	0.741312i	$0.734204\pi$
$954$	0.921359	0.0298301
$955$	−14.6343	−0.473555
$956$	−24.4387	−0.790404
$957$	−0.182732	−0.00590689
$958$	−0.454289	−0.0146774
$959$	−18.8177	−0.607656
$960$	−7.57139	−0.244366
$961$	−24.5423	−0.791688
$962$	0.503660	0.0162387
$963$	−11.4559	−0.369161
$964$	25.7025	0.827821
$965$	16.6634	0.536412
$966$	0	0
$967$	−5.04617	−0.162274	−0.0811370	−	0.996703i	$-0.525855\pi$
$967$	−5.04617	−0.162274	−0.0811370	+	0.996703i	$0.525855\pi$
$968$	4.99012	0.160388
$969$	3.90817	0.125549
$970$	−1.31635	−0.0422655
$971$	−52.5547	−1.68656	−0.843280	−	0.537475i	$-0.819378\pi$
$971$	−52.5547	−1.68656	−0.843280	+	0.537475i	$0.819378\pi$
$972$	−1.98201	−0.0635729
$973$	29.8273	0.956221
$974$	−2.12357	−0.0680437
$975$	3.37933	0.108225
$976$	−49.1852	−1.57438
$977$	45.0569	1.44150	0.720749	−	0.693196i	$-0.243798\pi$
$977$	45.0569	1.44150	0.720749	+	0.693196i	$0.243798\pi$
$978$	−0.0928888	−0.00297026
$979$	−5.37375	−0.171746
$980$	9.94305	0.317619
$981$	−13.3491	−0.426204
$982$	−5.76363	−0.183925
$983$	22.7903	0.726897	0.363449	−	0.931614i	$-0.381599\pi$
$983$	22.7903	0.726897	0.363449	+	0.931614i	$0.381599\pi$
$984$	3.20689	0.102232
$985$	−0.330824	−0.0105409
$986$	0.0164080	0.000522538 0
$987$	13.7936	0.439054
$988$	−30.3716	−0.966248
$989$	0	0
$990$	−0.172709	−0.00548906
$991$	4.96243	0.157637	0.0788183	−	0.996889i	$-0.474885\pi$
$991$	4.96243	0.157637	0.0788183	+	0.996889i	$0.474885\pi$
$992$	4.04154	0.128319
$993$	−2.93591	−0.0931683
$994$	2.21945	0.0703965
$995$	−0.859901	−0.0272607
$996$	−17.3876	−0.550947
$997$	5.19258	0.164451	0.0822253	−	0.996614i	$-0.473797\pi$
$997$	5.19258	0.164451	0.0822253	+	0.996614i	$0.473797\pi$
$998$	0.908049	0.0287438
$999$	1.11109	0.0351534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bw.1.12		25
23.5	odd	22		345.2.m.c.301.3	yes	50
23.14	odd	22		345.2.m.c.196.3	✓	50
23.22	odd	2		7935.2.a.bv.1.12		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.196.3	✓	50	23.14	odd	22
345.2.m.c.301.3	yes	50	23.5	odd	22
7935.2.a.bv.1.12		25	23.22	odd	2
7935.2.a.bw.1.12		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.134140 q^{2} +1.00000 q^{3} -1.98201 q^{4} +1.00000 q^{5} +0.134140 q^{6} +1.40831 q^{7} -0.534145 q^{8} +1.00000 q^{9} +0.134140 q^{10} -1.28753 q^{11} -1.98201 q^{12} +3.37933 q^{13} +0.188910 q^{14} +1.00000 q^{15} +3.89236 q^{16} +0.861872 q^{17} +0.134140 q^{18} +4.53452 q^{19} -1.98201 q^{20} +1.40831 q^{21} -0.172709 q^{22} -0.534145 q^{24} +1.00000 q^{25} +0.453302 q^{26} +1.00000 q^{27} -2.79128 q^{28} +0.141924 q^{29} +0.134140 q^{30} +2.54119 q^{31} +1.59041 q^{32} -1.28753 q^{33} +0.115611 q^{34} +1.40831 q^{35} -1.98201 q^{36} +1.11109 q^{37} +0.608259 q^{38} +3.37933 q^{39} -0.534145 q^{40} -6.00377 q^{41} +0.188910 q^{42} +0.457979 q^{43} +2.55190 q^{44} +1.00000 q^{45} +9.79441 q^{47} +3.89236 q^{48} -5.01666 q^{49} +0.134140 q^{50} +0.861872 q^{51} -6.69785 q^{52} +6.86866 q^{53} +0.134140 q^{54} -1.28753 q^{55} -0.752242 q^{56} +4.53452 q^{57} +0.0190377 q^{58} -2.57337 q^{59} -1.98201 q^{60} -12.6363 q^{61} +0.340875 q^{62} +1.40831 q^{63} -7.57139 q^{64} +3.37933 q^{65} -0.172709 q^{66} +1.94132 q^{67} -1.70824 q^{68} +0.188910 q^{70} +11.7487 q^{71} -0.534145 q^{72} -13.1015 q^{73} +0.149041 q^{74} +1.00000 q^{75} -8.98745 q^{76} -1.81325 q^{77} +0.453302 q^{78} +9.02887 q^{79} +3.89236 q^{80} +1.00000 q^{81} -0.805344 q^{82} +8.77272 q^{83} -2.79128 q^{84} +0.861872 q^{85} +0.0614331 q^{86} +0.141924 q^{87} +0.687730 q^{88} +4.17368 q^{89} +0.134140 q^{90} +4.75915 q^{91} +2.54119 q^{93} +1.31382 q^{94} +4.53452 q^{95} +1.59041 q^{96} -9.81329 q^{97} -0.672933 q^{98} -1.28753 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} + 25 q^{5} + 11 q^{6} + 7 q^{7} + 33 q^{8} + 25 q^{9} + 11 q^{10} + 9 q^{11} + 31 q^{12} + 18 q^{13} + 11 q^{14} + 25 q^{15} + 39 q^{16} - 8 q^{17} + 11 q^{18} + 11 q^{19}+ \cdots + 9 q^{99}+O(q^{100}) \) 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 + 25 * q^5 + 11 * q^6 + 7 * q^7 + 33 * q^8 + 25 * q^9 + 11 * q^10 + 9 * q^11 + 31 * q^12 + 18 * q^13 + 11 * q^14 + 25 * q^15 + 39 * q^16 - 8 * q^17 + 11 * q^18 + 11 * q^19 + 31 * q^20 + 7 * q^21 + 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 - 5 * q^28 + 33 * q^29 + 11 * q^30 + 14 * q^31 + 77 * q^32 + 9 * q^33 + 13 * q^34 + 7 * q^35 + 31 * q^36 + 4 * q^37 - 23 * q^38 + 18 * q^39 + 33 * q^40 + 56 * q^41 + 11 * q^42 - 4 * q^43 - 18 * q^44 + 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 - 8 * q^51 + 49 * q^52 + 2 * q^53 + 11 * q^54 + 9 * q^55 + 33 * q^56 + 11 * q^57 + 26 * q^58 + 61 * q^59 + 31 * q^60 + 21 * q^61 + 51 * q^62 + 7 * q^63 + 71 * q^64 + 18 * q^65 + 9 * q^66 + 2 * q^67 - 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 - 47 * q^74 + 25 * q^75 - 8 * q^76 + 49 * q^77 + 35 * q^78 + 35 * q^79 + 39 * q^80 + 25 * q^81 + 35 * q^82 - 26 * q^83 - 5 * q^84 - 8 * q^85 - 33 * q^86 + 33 * q^87 + 9 * q^88 - 7 * q^89 + 11 * q^90 + 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 - 54 * q^97 + 88 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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