LMFDB - Embedded newform 7935.2.a.bi.1.4

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)

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")

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);

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 = [8,0,8,8,8,0,6] 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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 12x^{6} - 2x^{5} + 44x^{4} + 12x^{3} - 50x^{2} - 8x + 16 $ x^8 - 12x^6 - 2x^5 + 44x^4 + 12x^3 - 50x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.798063$ of defining polynomial
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)

$f(q)$	$=$	\(q-0.798063 q^{2} +1.00000 q^{3} -1.36310 q^{4} +1.00000 q^{5} -0.798063 q^{6} -0.435759 q^{7} +2.68396 q^{8} +1.00000 q^{9} -0.798063 q^{10} -4.14141 q^{11} -1.36310 q^{12} +1.76513 q^{13} +0.347763 q^{14} +1.00000 q^{15} +0.584222 q^{16} +7.75235 q^{17} -0.798063 q^{18} +0.0329352 q^{19} -1.36310 q^{20} -0.435759 q^{21} +3.30511 q^{22} +2.68396 q^{24} +1.00000 q^{25} -1.40868 q^{26} +1.00000 q^{27} +0.593981 q^{28} +2.78230 q^{29} -0.798063 q^{30} -0.294148 q^{31} -5.83417 q^{32} -4.14141 q^{33} -6.18686 q^{34} -0.435759 q^{35} -1.36310 q^{36} +7.72698 q^{37} -0.0262843 q^{38} +1.76513 q^{39} +2.68396 q^{40} +4.59797 q^{41} +0.347763 q^{42} +1.89891 q^{43} +5.64514 q^{44} +1.00000 q^{45} -11.5033 q^{47} +0.584222 q^{48} -6.81011 q^{49} -0.798063 q^{50} +7.75235 q^{51} -2.40604 q^{52} +2.47441 q^{53} -0.798063 q^{54} -4.14141 q^{55} -1.16956 q^{56} +0.0329352 q^{57} -2.22045 q^{58} +3.68016 q^{59} -1.36310 q^{60} +1.63180 q^{61} +0.234748 q^{62} -0.435759 q^{63} +3.48759 q^{64} +1.76513 q^{65} +3.30511 q^{66} -2.79862 q^{67} -10.5672 q^{68} +0.347763 q^{70} +0.419274 q^{71} +2.68396 q^{72} +3.62570 q^{73} -6.16662 q^{74} +1.00000 q^{75} -0.0448938 q^{76} +1.80466 q^{77} -1.40868 q^{78} -8.13319 q^{79} +0.584222 q^{80} +1.00000 q^{81} -3.66947 q^{82} +14.3722 q^{83} +0.593981 q^{84} +7.75235 q^{85} -1.51545 q^{86} +2.78230 q^{87} -11.1154 q^{88} -11.8324 q^{89} -0.798063 q^{90} -0.769170 q^{91} -0.294148 q^{93} +9.18036 q^{94} +0.0329352 q^{95} -5.83417 q^{96} +14.7339 q^{97} +5.43490 q^{98} -4.14141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27}+ \cdots + 12 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * 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 $

$2$	−0.798063	−0.564316	−0.282158	−	0.959368i	$-0.591050\pi$
$2$	−0.798063	−0.564316	−0.282158	+	0.959368i	$0.591050\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.36310	−0.681548
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.798063	−0.325808
$7$	−0.435759	−0.164701	−0.0823506	−	0.996603i	$-0.526243\pi$
$7$	−0.435759	−0.164701	−0.0823506	+	0.996603i	$0.526243\pi$
$8$	2.68396	0.948924
$9$	1.00000	0.333333
$10$	−0.798063	−0.252370
$11$	−4.14141	−1.24868	−0.624341	−	0.781152i	$-0.714633\pi$
$11$	−4.14141	−1.24868	−0.624341	+	0.781152i	$0.714633\pi$
$12$	−1.36310	−0.393492
$13$	1.76513	0.489558	0.244779	−	0.969579i	$-0.421285\pi$
$13$	1.76513	0.489558	0.244779	+	0.969579i	$0.421285\pi$
$14$	0.347763	0.0929435
$15$	1.00000	0.258199
$16$	0.584222	0.146056
$17$	7.75235	1.88022	0.940111	−	0.340869i	$-0.110721\pi$
$17$	7.75235	1.88022	0.940111	+	0.340869i	$0.110721\pi$
$18$	−0.798063	−0.188105
$19$	0.0329352	0.00755584	0.00377792	−	0.999993i	$-0.498797\pi$
$19$	0.0329352	0.00755584	0.00377792	+	0.999993i	$0.498797\pi$
$20$	−1.36310	−0.304798
$21$	−0.435759	−0.0950903
$22$	3.30511	0.704651
$23$	0	0
$23$	0	0
$24$	2.68396	0.547861
$25$	1.00000	0.200000
$26$	−1.40868	−0.276265
$27$	1.00000	0.192450
$28$	0.593981	0.112252
$29$	2.78230	0.516661	0.258330	−	0.966057i	$-0.416828\pi$
$29$	2.78230	0.516661	0.258330	+	0.966057i	$0.416828\pi$
$30$	−0.798063	−0.145706
$31$	−0.294148	−0.0528305	−0.0264152	−	0.999651i	$-0.508409\pi$
$31$	−0.294148	−0.0528305	−0.0264152	+	0.999651i	$0.508409\pi$
$32$	−5.83417	−1.03135
$33$	−4.14141	−0.720927
$34$	−6.18686	−1.06104
$35$	−0.435759	−0.0736567
$36$	−1.36310	−0.227183
$37$	7.72698	1.27031	0.635154	−	0.772385i	$-0.280937\pi$
$37$	7.72698	1.27031	0.635154	+	0.772385i	$0.280937\pi$
$38$	−0.0262843	−0.00426388
$39$	1.76513	0.282647
$40$	2.68396	0.424372
$41$	4.59797	0.718082	0.359041	−	0.933322i	$-0.383104\pi$
$41$	4.59797	0.718082	0.359041	+	0.933322i	$0.383104\pi$
$42$	0.347763	0.0536610
$43$	1.89891	0.289581	0.144790	−	0.989462i	$-0.453749\pi$
$43$	1.89891	0.289581	0.144790	+	0.989462i	$0.453749\pi$
$44$	5.64514	0.851037
$45$	1.00000	0.149071
$46$	0	0
$47$	−11.5033	−1.67793	−0.838965	−	0.544185i	$-0.816839\pi$
$47$	−11.5033	−1.67793	−0.838965	+	0.544185i	$0.816839\pi$
$48$	0.584222	0.0843252
$49$	−6.81011	−0.972873
$50$	−0.798063	−0.112863
$51$	7.75235	1.08555
$52$	−2.40604	−0.333657
$53$	2.47441	0.339886	0.169943	−	0.985454i	$-0.445642\pi$
$53$	2.47441	0.339886	0.169943	+	0.985454i	$0.445642\pi$
$54$	−0.798063	−0.108603
$55$	−4.14141	−0.558428
$56$	−1.16956	−0.156289
$57$	0.0329352	0.00436237
$58$	−2.22045	−0.291560
$59$	3.68016	0.479117	0.239558	−	0.970882i	$-0.422997\pi$
$59$	3.68016	0.479117	0.239558	+	0.970882i	$0.422997\pi$
$60$	−1.36310	−0.175975
$61$	1.63180	0.208931	0.104465	−	0.994529i	$-0.466687\pi$
$61$	1.63180	0.208931	0.104465	+	0.994529i	$0.466687\pi$
$62$	0.234748	0.0298131
$63$	−0.435759	−0.0549004
$64$	3.48759	0.435948
$65$	1.76513	0.218937
$66$	3.30511	0.406830
$67$	−2.79862	−0.341906	−0.170953	−	0.985279i	$-0.554685\pi$
$67$	−2.79862	−0.341906	−0.170953	+	0.985279i	$0.554685\pi$
$68$	−10.5672	−1.28146
$69$	0	0
$70$	0.347763	0.0415656
$71$	0.419274	0.0497587	0.0248793	−	0.999690i	$-0.492080\pi$
$71$	0.419274	0.0497587	0.0248793	+	0.999690i	$0.492080\pi$
$72$	2.68396	0.316308
$73$	3.62570	0.424357	0.212178	−	0.977231i	$-0.431944\pi$
$73$	3.62570	0.424357	0.212178	+	0.977231i	$0.431944\pi$
$74$	−6.16662	−0.716855
$75$	1.00000	0.115470
$76$	−0.0448938	−0.00514967
$77$	1.80466	0.205660
$78$	−1.40868	−0.159502
$79$	−8.13319	−0.915055	−0.457527	−	0.889196i	$-0.651265\pi$
$79$	−8.13319	−0.915055	−0.457527	+	0.889196i	$0.651265\pi$
$80$	0.584222	0.0653181
$81$	1.00000	0.111111
$82$	−3.66947	−0.405225
$83$	14.3722	1.57756	0.788779	−	0.614677i	$-0.210714\pi$
$83$	14.3722	1.57756	0.788779	+	0.614677i	$0.210714\pi$
$84$	0.593981	0.0648086
$85$	7.75235	0.840861
$86$	−1.51545	−0.163415
$87$	2.78230	0.298294
$88$	−11.1154	−1.18490
$89$	−11.8324	−1.25423	−0.627114	−	0.778928i	$-0.715764\pi$
$89$	−11.8324	−1.25423	−0.627114	+	0.778928i	$0.715764\pi$
$90$	−0.798063	−0.0841232
$91$	−0.769170	−0.0806309
$92$	0	0
$93$	−0.294148	−0.0305017
$94$	9.18036	0.946882
$95$	0.0329352	0.00337908
$96$	−5.83417	−0.595447
$97$	14.7339	1.49600	0.747999	−	0.663699i	$-0.231015\pi$
$97$	14.7339	1.49600	0.747999	+	0.663699i	$0.231015\pi$
$98$	5.43490	0.549008
$99$	−4.14141	−0.416228
$100$	−1.36310	−0.136310
$101$	−7.64346	−0.760552	−0.380276	−	0.924873i	$-0.624171\pi$
$101$	−7.64346	−0.760552	−0.380276	+	0.924873i	$0.624171\pi$
$102$	−6.18686	−0.612591
$103$	4.13785	0.407715	0.203857	−	0.979001i	$-0.434652\pi$
$103$	4.13785	0.407715	0.203857	+	0.979001i	$0.434652\pi$
$104$	4.73753	0.464553
$105$	−0.435759	−0.0425257
$106$	−1.97473	−0.191803
$107$	−5.80764	−0.561445	−0.280723	−	0.959789i	$-0.590574\pi$
$107$	−5.80764	−0.561445	−0.280723	+	0.959789i	$0.590574\pi$
$108$	−1.36310	−0.131164
$109$	−18.8964	−1.80994	−0.904972	−	0.425470i	$-0.860109\pi$
$109$	−18.8964	−1.80994	−0.904972	+	0.425470i	$0.860109\pi$
$110$	3.30511	0.315130
$111$	7.72698	0.733413
$112$	−0.254580	−0.0240555
$113$	14.5948	1.37296	0.686482	−	0.727147i	$-0.259154\pi$
$113$	14.5948	1.37296	0.686482	+	0.727147i	$0.259154\pi$
$114$	−0.0262843	−0.00246175
$115$	0	0
$116$	−3.79255	−0.352129
$117$	1.76513	0.163186
$118$	−2.93700	−0.270373
$119$	−3.37815	−0.309675
$120$	2.68396	0.245011
$121$	6.15129	0.559209
$122$	−1.30228	−0.117903
$123$	4.59797	0.414585
$124$	0.400951	0.0360065
$125$	1.00000	0.0894427
$126$	0.347763	0.0309812
$127$	−9.86931	−0.875760	−0.437880	−	0.899033i	$-0.644270\pi$
$127$	−9.86931	−0.875760	−0.437880	+	0.899033i	$0.644270\pi$
$128$	8.88502	0.785333
$129$	1.89891	0.167190
$130$	−1.40868	−0.123550
$131$	−22.8252	−1.99424	−0.997121	−	0.0758227i	$-0.975842\pi$
$131$	−22.8252	−1.99424	−0.997121	+	0.0758227i	$0.975842\pi$
$132$	5.64514	0.491347
$133$	−0.0143518	−0.00124446
$134$	2.23347	0.192943
$135$	1.00000	0.0860663
$136$	20.8070	1.78419
$137$	5.55454	0.474556	0.237278	−	0.971442i	$-0.423745\pi$
$137$	5.55454	0.474556	0.237278	+	0.971442i	$0.423745\pi$
$138$	0	0
$139$	2.66403	0.225960	0.112980	−	0.993597i	$-0.463960\pi$
$139$	2.66403	0.225960	0.112980	+	0.993597i	$0.463960\pi$
$140$	0.593981	0.0502005
$141$	−11.5033	−0.968753
$142$	−0.334607	−0.0280796
$143$	−7.31012	−0.611303
$144$	0.584222	0.0486852
$145$	2.78230	0.231058
$146$	−2.89354	−0.239471
$147$	−6.81011	−0.561689
$148$	−10.5326	−0.865776
$149$	−1.23678	−0.101321	−0.0506605	−	0.998716i	$-0.516133\pi$
$149$	−1.23678	−0.101321	−0.0506605	+	0.998716i	$0.516133\pi$
$150$	−0.798063	−0.0651615
$151$	11.9114	0.969336	0.484668	−	0.874698i	$-0.338940\pi$
$151$	11.9114	0.969336	0.484668	+	0.874698i	$0.338940\pi$
$152$	0.0883967	0.00716992
$153$	7.75235	0.626741
$154$	−1.44023	−0.116057
$155$	−0.294148	−0.0236265
$156$	−2.40604	−0.192637
$157$	16.3259	1.30295	0.651475	−	0.758670i	$-0.274151\pi$
$157$	16.3259	1.30295	0.651475	+	0.758670i	$0.274151\pi$
$158$	6.49079	0.516380
$159$	2.47441	0.196233
$160$	−5.83417	−0.461232
$161$	0	0
$162$	−0.798063	−0.0627017
$163$	24.4859	1.91788	0.958941	−	0.283605i	$-0.0915305\pi$
$163$	24.4859	1.91788	0.958941	+	0.283605i	$0.0915305\pi$
$164$	−6.26747	−0.489407
$165$	−4.14141	−0.322409
$166$	−11.4699	−0.890240
$167$	21.4305	1.65834	0.829172	−	0.558994i	$-0.188812\pi$
$167$	21.4305	1.65834	0.829172	+	0.558994i	$0.188812\pi$
$168$	−1.16956	−0.0902335
$169$	−9.88432	−0.760333
$170$	−6.18686	−0.474511
$171$	0.0329352	0.00251861
$172$	−2.58839	−0.197363
$173$	3.02583	0.230049	0.115025	−	0.993363i	$-0.463305\pi$
$173$	3.02583	0.230049	0.115025	+	0.993363i	$0.463305\pi$
$174$	−2.22045	−0.168332
$175$	−0.435759	−0.0329403
$176$	−2.41951	−0.182377
$177$	3.68016	0.276618
$178$	9.44297	0.707780
$179$	−5.76047	−0.430558	−0.215279	−	0.976553i	$-0.569066\pi$
$179$	−5.76047	−0.430558	−0.215279	+	0.976553i	$0.569066\pi$
$180$	−1.36310	−0.101599
$181$	1.37306	0.102058	0.0510292	−	0.998697i	$-0.483750\pi$
$181$	1.37306	0.102058	0.0510292	+	0.998697i	$0.483750\pi$
$182$	0.613846	0.0455013
$183$	1.63180	0.120626
$184$	0	0
$185$	7.72698	0.568099
$186$	0.234748	0.0172126
$187$	−32.1057	−2.34780
$188$	15.6801	1.14359
$189$	−0.435759	−0.0316968
$190$	−0.0262843	−0.00190687
$191$	−16.7735	−1.21369	−0.606843	−	0.794822i	$-0.707564\pi$
$191$	−16.7735	−1.21369	−0.606843	+	0.794822i	$0.707564\pi$
$192$	3.48759	0.251695
$193$	6.17605	0.444562	0.222281	−	0.974983i	$-0.428650\pi$
$193$	6.17605	0.444562	0.222281	+	0.974983i	$0.428650\pi$
$194$	−11.7586	−0.844215
$195$	1.76513	0.126403
$196$	9.28284	0.663060
$197$	12.5645	0.895183	0.447591	−	0.894238i	$-0.352282\pi$
$197$	12.5645	0.895183	0.447591	+	0.894238i	$0.352282\pi$
$198$	3.30511	0.234884
$199$	22.4562	1.59188	0.795940	−	0.605375i	$-0.206977\pi$
$199$	22.4562	1.59188	0.795940	+	0.605375i	$0.206977\pi$
$200$	2.68396	0.189785
$201$	−2.79862	−0.197399
$202$	6.09996	0.429191
$203$	−1.21241	−0.0850947
$204$	−10.5672	−0.739852
$205$	4.59797	0.321136
$206$	−3.30226	−0.230080
$207$	0	0
$208$	1.03123	0.0715027
$209$	−0.136398	−0.00943485
$210$	0.347763	0.0239979
$211$	22.3938	1.54165	0.770826	−	0.637046i	$-0.219844\pi$
$211$	22.3938	1.54165	0.770826	+	0.637046i	$0.219844\pi$
$212$	−3.37286	−0.231649
$213$	0.419274	0.0287282
$214$	4.63486	0.316832
$215$	1.89891	0.129504
$216$	2.68396	0.182620
$217$	0.128177	0.00870125
$218$	15.0805	1.02138
$219$	3.62570	0.245002
$220$	5.64514	0.380595
$221$	13.6839	0.920478
$222$	−6.16662	−0.413876
$223$	−22.0428	−1.47609	−0.738047	−	0.674750i	$-0.764252\pi$
$223$	−22.0428	−1.47609	−0.738047	+	0.674750i	$0.764252\pi$
$224$	2.54229	0.169864
$225$	1.00000	0.0666667
$226$	−11.6476	−0.774785
$227$	8.93036	0.592729	0.296365	−	0.955075i	$-0.404226\pi$
$227$	8.93036	0.592729	0.296365	+	0.955075i	$0.404226\pi$
$228$	−0.0448938	−0.00297316
$229$	15.9670	1.05513	0.527565	−	0.849515i	$-0.323105\pi$
$229$	15.9670	1.05513	0.527565	+	0.849515i	$0.323105\pi$
$230$	0	0
$231$	1.80466	0.118738
$232$	7.46760	0.490272
$233$	10.5728	0.692648	0.346324	−	0.938115i	$-0.387430\pi$
$233$	10.5728	0.692648	0.346324	+	0.938115i	$0.387430\pi$
$234$	−1.40868	−0.0920885
$235$	−11.5033	−0.750393
$236$	−5.01642	−0.326541
$237$	−8.13319	−0.528307
$238$	2.69598	0.174754
$239$	1.81371	0.117319	0.0586594	−	0.998278i	$-0.481317\pi$
$239$	1.81371	0.117319	0.0586594	+	0.998278i	$0.481317\pi$
$240$	0.584222	0.0377114
$241$	−22.4236	−1.44443	−0.722216	−	0.691668i	$-0.756876\pi$
$241$	−22.4236	−1.44443	−0.722216	+	0.691668i	$0.756876\pi$
$242$	−4.90912	−0.315570
$243$	1.00000	0.0641500
$244$	−2.22430	−0.142396
$245$	−6.81011	−0.435082
$246$	−3.66947	−0.233957
$247$	0.0581348	0.00369903
$248$	−0.789481	−0.0501321
$249$	14.3722	0.910803
$250$	−0.798063	−0.0504739
$251$	7.77122	0.490515	0.245258	−	0.969458i	$-0.421127\pi$
$251$	7.77122	0.490515	0.245258	+	0.969458i	$0.421127\pi$
$252$	0.593981	0.0374173
$253$	0	0
$254$	7.87633	0.494205
$255$	7.75235	0.485471
$256$	−14.0660	−0.879124
$257$	−3.89401	−0.242901	−0.121451	−	0.992597i	$-0.538755\pi$
$257$	−3.89401	−0.242901	−0.121451	+	0.992597i	$0.538755\pi$
$258$	−1.51545	−0.0943477
$259$	−3.36710	−0.209221
$260$	−2.40604	−0.149216
$261$	2.78230	0.172220
$262$	18.2159	1.12538
$263$	−9.00577	−0.555320	−0.277660	−	0.960679i	$-0.589559\pi$
$263$	−9.00577	−0.555320	−0.277660	+	0.960679i	$0.589559\pi$
$264$	−11.1154	−0.684105
$265$	2.47441	0.152002
$266$	0.0114536	0.000702267 0
$267$	−11.8324	−0.724129
$268$	3.81478	0.233025
$269$	20.2302	1.23346	0.616728	−	0.787176i	$-0.288458\pi$
$269$	20.2302	1.23346	0.616728	+	0.787176i	$0.288458\pi$
$270$	−0.798063	−0.0485685
$271$	−16.4807	−1.00113	−0.500567	−	0.865698i	$-0.666875\pi$
$271$	−16.4807	−1.00113	−0.500567	+	0.865698i	$0.666875\pi$
$272$	4.52910	0.274617
$273$	−0.769170	−0.0465523
$274$	−4.43287	−0.267800
$275$	−4.14141	−0.249737
$276$	0	0
$277$	21.1630	1.27156	0.635780	−	0.771871i	$-0.280679\pi$
$277$	21.1630	1.27156	0.635780	+	0.771871i	$0.280679\pi$
$278$	−2.12606	−0.127513
$279$	−0.294148	−0.0176102
$280$	−1.16956	−0.0698945
$281$	28.5724	1.70448	0.852242	−	0.523147i	$-0.175242\pi$
$281$	28.5724	1.70448	0.852242	+	0.523147i	$0.175242\pi$
$282$	9.18036	0.546683
$283$	12.8180	0.761951	0.380976	−	0.924585i	$-0.375588\pi$
$283$	12.8180	0.761951	0.380976	+	0.924585i	$0.375588\pi$
$284$	−0.571511	−0.0339129
$285$	0.0329352	0.00195091
$286$	5.83393	0.344968
$287$	−2.00360	−0.118269
$288$	−5.83417	−0.343782
$289$	43.0990	2.53523
$290$	−2.22045	−0.130389
$291$	14.7339	0.863715
$292$	−4.94218	−0.289219
$293$	19.9992	1.16837	0.584184	−	0.811621i	$-0.301415\pi$
$293$	19.9992	1.16837	0.584184	+	0.811621i	$0.301415\pi$
$294$	5.43490	0.316970
$295$	3.68016	0.214267
$296$	20.7389	1.20543
$297$	−4.14141	−0.240309
$298$	0.987028	0.0571770
$299$	0	0
$300$	−1.36310	−0.0786984
$301$	−0.827466	−0.0476943
$302$	−9.50605	−0.547011
$303$	−7.64346	−0.439105
$304$	0.0192415	0.00110357
$305$	1.63180	0.0934366
$306$	−6.18686	−0.353679
$307$	−20.7190	−1.18250	−0.591248	−	0.806490i	$-0.701365\pi$
$307$	−20.7190	−1.18250	−0.591248	+	0.806490i	$0.701365\pi$
$308$	−2.45992	−0.140167
$309$	4.13785	0.235394
$310$	0.234748	0.0133328
$311$	−29.7519	−1.68708	−0.843539	−	0.537068i	$-0.819532\pi$
$311$	−29.7519	−1.68708	−0.843539	+	0.537068i	$0.819532\pi$
$312$	4.73753	0.268210
$313$	10.0923	0.570453	0.285226	−	0.958460i	$-0.407931\pi$
$313$	10.0923	0.570453	0.285226	+	0.958460i	$0.407931\pi$
$314$	−13.0291	−0.735275
$315$	−0.435759	−0.0245522
$316$	11.0863	0.623654
$317$	−21.6756	−1.21742	−0.608712	−	0.793391i	$-0.708314\pi$
$317$	−21.6756	−1.21742	−0.608712	+	0.793391i	$0.708314\pi$
$318$	−1.97473	−0.110738
$319$	−11.5227	−0.645145
$320$	3.48759	0.194962
$321$	−5.80764	−0.324151
$322$	0	0
$323$	0.255325	0.0142067
$324$	−1.36310	−0.0757276
$325$	1.76513	0.0979117
$326$	−19.5413	−1.08229
$327$	−18.8964	−1.04497
$328$	12.3408	0.681405
$329$	5.01267	0.276357
$330$	3.30511	0.181940
$331$	−18.8531	−1.03626	−0.518130	−	0.855302i	$-0.673372\pi$
$331$	−18.8531	−1.03626	−0.518130	+	0.855302i	$0.673372\pi$
$332$	−19.5907	−1.07518
$333$	7.72698	0.423436
$334$	−17.1029	−0.935829
$335$	−2.79862	−0.152905
$336$	−0.254580	−0.0138885
$337$	14.4054	0.784712	0.392356	−	0.919813i	$-0.371660\pi$
$337$	14.4054	0.784712	0.392356	+	0.919813i	$0.371660\pi$
$338$	7.88831	0.429068
$339$	14.5948	0.792681
$340$	−10.5672	−0.573087
$341$	1.21819	0.0659685
$342$	−0.0262843	−0.00142129
$343$	6.01788	0.324935
$344$	5.09660	0.274790
$345$	0	0
$346$	−2.41480	−0.129820
$347$	3.99715	0.214578	0.107289	−	0.994228i	$-0.465783\pi$
$347$	3.99715	0.214578	0.107289	+	0.994228i	$0.465783\pi$
$348$	−3.79255	−0.203302
$349$	−31.1307	−1.66639	−0.833193	−	0.552982i	$-0.813490\pi$
$349$	−31.1307	−1.66639	−0.833193	+	0.552982i	$0.813490\pi$
$350$	0.347763	0.0185887
$351$	1.76513	0.0942155
$352$	24.1617	1.28782
$353$	2.10222	0.111890	0.0559451	−	0.998434i	$-0.482183\pi$
$353$	2.10222	0.111890	0.0559451	+	0.998434i	$0.482183\pi$
$354$	−2.93700	−0.156100
$355$	0.419274	0.0222528
$356$	16.1286	0.854816
$357$	−3.37815	−0.178791
$358$	4.59722	0.242970
$359$	17.3869	0.917644	0.458822	−	0.888528i	$-0.348272\pi$
$359$	17.3869	0.917644	0.458822	+	0.888528i	$0.348272\pi$
$360$	2.68396	0.141457
$361$	−18.9989	−0.999943
$362$	−1.09578	−0.0575931
$363$	6.15129	0.322859
$364$	1.04845	0.0549538
$365$	3.62570	0.189778
$366$	−1.30228	−0.0680712
$367$	−15.8777	−0.828810	−0.414405	−	0.910092i	$-0.636010\pi$
$367$	−15.8777	−0.828810	−0.414405	+	0.910092i	$0.636010\pi$
$368$	0	0
$369$	4.59797	0.239361
$370$	−6.16662	−0.320587
$371$	−1.07825	−0.0559797
$372$	0.400951	0.0207884
$373$	−18.2919	−0.947119	−0.473560	−	0.880762i	$-0.657031\pi$
$373$	−18.2919	−0.947119	−0.473560	+	0.880762i	$0.657031\pi$
$374$	25.6224	1.32490
$375$	1.00000	0.0516398
$376$	−30.8744	−1.59223
$377$	4.91112	0.252936
$378$	0.347763	0.0178870
$379$	17.6859	0.908466	0.454233	−	0.890883i	$-0.349913\pi$
$379$	17.6859	0.908466	0.454233	+	0.890883i	$0.349913\pi$
$380$	−0.0448938	−0.00230300
$381$	−9.86931	−0.505620
$382$	13.3863	0.684902
$383$	24.8288	1.26869	0.634345	−	0.773050i	$-0.281270\pi$
$383$	24.8288	1.26869	0.634345	+	0.773050i	$0.281270\pi$
$384$	8.88502	0.453412
$385$	1.80466	0.0919738
$386$	−4.92887	−0.250873
$387$	1.89891	0.0965269
$388$	−20.0837	−1.01959
$389$	36.5420	1.85275	0.926376	−	0.376600i	$-0.122907\pi$
$389$	36.5420	1.85275	0.926376	+	0.376600i	$0.122907\pi$
$390$	−1.40868	−0.0713314
$391$	0	0
$392$	−18.2781	−0.923183
$393$	−22.8252	−1.15138
$394$	−10.0273	−0.505166
$395$	−8.13319	−0.409225
$396$	5.64514	0.283679
$397$	0.133574	0.00670388	0.00335194	−	0.999994i	$-0.498933\pi$
$397$	0.133574	0.00670388	0.00335194	+	0.999994i	$0.498933\pi$
$398$	−17.9215	−0.898323
$399$	−0.0143518	−0.000718488 0
$400$	0.584222	0.0292111
$401$	−10.9066	−0.544647	−0.272324	−	0.962206i	$-0.587792\pi$
$401$	−10.9066	−0.544647	−0.272324	+	0.962206i	$0.587792\pi$
$402$	2.23347	0.111395
$403$	−0.519208	−0.0258636
$404$	10.4188	0.518353
$405$	1.00000	0.0496904
$406$	0.967582	0.0480203
$407$	−32.0006	−1.58621
$408$	20.8070	1.03010
$409$	30.6038	1.51326	0.756630	−	0.653843i	$-0.226845\pi$
$409$	30.6038	1.51326	0.756630	+	0.653843i	$0.226845\pi$
$410$	−3.66947	−0.181222
$411$	5.55454	0.273985
$412$	−5.64029	−0.277877
$413$	−1.60366	−0.0789111
$414$	0	0
$415$	14.3722	0.705505
$416$	−10.2981	−0.504904
$417$	2.66403	0.130458
$418$	0.108854	0.00532423
$419$	36.4844	1.78238	0.891191	−	0.453629i	$-0.149871\pi$
$419$	36.4844	1.78238	0.891191	+	0.453629i	$0.149871\pi$
$420$	0.593981	0.0289833
$421$	−23.4902	−1.14484	−0.572421	−	0.819960i	$-0.693996\pi$
$421$	−23.4902	−1.14484	−0.572421	+	0.819960i	$0.693996\pi$
$422$	−17.8716	−0.869978
$423$	−11.5033	−0.559310
$424$	6.64122	0.322526
$425$	7.75235	0.376044
$426$	−0.334607	−0.0162118
$427$	−0.711071	−0.0344112
$428$	7.91637	0.382652
$429$	−7.31012	−0.352936
$430$	−1.51545	−0.0730814
$431$	14.6664	0.706455	0.353227	−	0.935537i	$-0.385084\pi$
$431$	14.6664	0.706455	0.353227	+	0.935537i	$0.385084\pi$
$432$	0.584222	0.0281084
$433$	−26.4024	−1.26882	−0.634409	−	0.772997i	$-0.718757\pi$
$433$	−26.4024	−1.26882	−0.634409	+	0.772997i	$0.718757\pi$
$434$	−0.102294	−0.00491025
$435$	2.78230	0.133401
$436$	25.7576	1.23356
$437$	0	0
$438$	−2.89354	−0.138259
$439$	−8.76922	−0.418532	−0.209266	−	0.977859i	$-0.567107\pi$
$439$	−8.76922	−0.418532	−0.209266	+	0.977859i	$0.567107\pi$
$440$	−11.1154	−0.529905
$441$	−6.81011	−0.324291
$442$	−10.9206	−0.519440
$443$	10.8705	0.516474	0.258237	−	0.966082i	$-0.416858\pi$
$443$	10.8705	0.516474	0.258237	+	0.966082i	$0.416858\pi$
$444$	−10.5326	−0.499856
$445$	−11.8324	−0.560908
$446$	17.5915	0.832982
$447$	−1.23678	−0.0584977
$448$	−1.51975	−0.0718013
$449$	−32.5934	−1.53818	−0.769088	−	0.639143i	$-0.779289\pi$
$449$	−32.5934	−1.53818	−0.769088	+	0.639143i	$0.779289\pi$
$450$	−0.798063	−0.0376210
$451$	−19.0421	−0.896657
$452$	−19.8941	−0.935741
$453$	11.9114	0.559646
$454$	−7.12699	−0.334486
$455$	−0.769170	−0.0360592
$456$	0.0883967	0.00413955
$457$	−19.8706	−0.929508	−0.464754	−	0.885440i	$-0.653857\pi$
$457$	−19.8706	−0.929508	−0.464754	+	0.885440i	$0.653857\pi$
$458$	−12.7427	−0.595426
$459$	7.75235	0.361849
$460$	0	0
$461$	11.4542	0.533474	0.266737	−	0.963769i	$-0.414054\pi$
$461$	11.4542	0.533474	0.266737	+	0.963769i	$0.414054\pi$
$462$	−1.44023	−0.0670055
$463$	−2.29042	−0.106445	−0.0532225	−	0.998583i	$-0.516949\pi$
$463$	−2.29042	−0.106445	−0.0532225	+	0.998583i	$0.516949\pi$
$464$	1.62548	0.0754612
$465$	−0.294148	−0.0136408
$466$	−8.43777	−0.390872
$467$	−16.2901	−0.753817	−0.376908	−	0.926251i	$-0.623013\pi$
$467$	−16.2901	−0.753817	−0.376908	+	0.926251i	$0.623013\pi$
$468$	−2.40604	−0.111219
$469$	1.21952	0.0563123
$470$	9.18036	0.423458
$471$	16.3259	0.752258
$472$	9.87742	0.454645
$473$	−7.86416	−0.361595
$474$	6.49079	0.298132
$475$	0.0329352	0.00151117
$476$	4.60475	0.211058
$477$	2.47441	0.113295
$478$	−1.44745	−0.0662048
$479$	17.3811	0.794162	0.397081	−	0.917784i	$-0.370023\pi$
$479$	17.3811	0.794162	0.397081	+	0.917784i	$0.370023\pi$
$480$	−5.83417	−0.266292
$481$	13.6391	0.621890
$482$	17.8954	0.815115
$483$	0	0
$484$	−8.38480	−0.381127
$485$	14.7339	0.669031
$486$	−0.798063	−0.0362009
$487$	12.6674	0.574012	0.287006	−	0.957929i	$-0.407340\pi$
$487$	12.6674	0.574012	0.287006	+	0.957929i	$0.407340\pi$
$488$	4.37969	0.198259
$489$	24.4859	1.10729
$490$	5.43490	0.245524
$491$	−16.3388	−0.737359	−0.368680	−	0.929557i	$-0.620190\pi$
$491$	−16.3388	−0.737359	−0.368680	+	0.929557i	$0.620190\pi$
$492$	−6.26747	−0.282559
$493$	21.5694	0.971437
$494$	−0.0463952	−0.00208742
$495$	−4.14141	−0.186143
$496$	−0.171848	−0.00771619
$497$	−0.182702	−0.00819532
$498$	−11.4699	−0.513981
$499$	16.3731	0.732961	0.366480	−	0.930426i	$-0.380563\pi$
$499$	16.3731	0.732961	0.366480	+	0.930426i	$0.380563\pi$
$500$	−1.36310	−0.0609595
$501$	21.4305	0.957445
$502$	−6.20192	−0.276805
$503$	27.6656	1.23355	0.616774	−	0.787140i	$-0.288439\pi$
$503$	27.6656	1.23355	0.616774	+	0.787140i	$0.288439\pi$
$504$	−1.16956	−0.0520963
$505$	−7.64346	−0.340129
$506$	0	0
$507$	−9.88432	−0.438978
$508$	13.4528	0.596872
$509$	11.6775	0.517595	0.258797	−	0.965932i	$-0.416674\pi$
$509$	11.6775	0.517595	0.258797	+	0.965932i	$0.416674\pi$
$510$	−6.18686	−0.273959
$511$	−1.57993	−0.0698921
$512$	−6.54451	−0.289229
$513$	0.0329352	0.00145412
$514$	3.10766	0.137073
$515$	4.13785	0.182336
$516$	−2.58839	−0.113948
$517$	47.6399	2.09520
$518$	2.68716	0.118067
$519$	3.02583	0.132819
$520$	4.73753	0.207755
$521$	30.3093	1.32787	0.663936	−	0.747789i	$-0.268885\pi$
$521$	30.3093	1.32787	0.663936	+	0.747789i	$0.268885\pi$
$522$	−2.22045	−0.0971866
$523$	10.2243	0.447078	0.223539	−	0.974695i	$-0.428239\pi$
$523$	10.2243	0.447078	0.223539	+	0.974695i	$0.428239\pi$
$524$	31.1129	1.35917
$525$	−0.435759	−0.0190181
$526$	7.18717	0.313375
$527$	−2.28034	−0.0993330
$528$	−2.41951	−0.105295
$529$	0	0
$530$	−1.97473	−0.0857770
$531$	3.68016	0.159706
$532$	0.0195629	0.000848157 0
$533$	8.11600	0.351543
$534$	9.44297	0.408637
$535$	−5.80764	−0.251086
$536$	−7.51138	−0.324442
$537$	−5.76047	−0.248583
$538$	−16.1450	−0.696059
$539$	28.2035	1.21481
$540$	−1.36310	−0.0586583
$541$	11.2883	0.485323	0.242661	−	0.970111i	$-0.421980\pi$
$541$	11.2883	0.485323	0.242661	+	0.970111i	$0.421980\pi$
$542$	13.1527	0.564955
$543$	1.37306	0.0589234
$544$	−45.2285	−1.93916
$545$	−18.8964	−0.809432
$546$	0.613846	0.0262702
$547$	−36.2734	−1.55094	−0.775470	−	0.631384i	$-0.782487\pi$
$547$	−36.2734	−1.55094	−0.775470	+	0.631384i	$0.782487\pi$
$548$	−7.57137	−0.323433
$549$	1.63180	0.0696436
$550$	3.30511	0.140930
$551$	0.0916356	0.00390381
$552$	0	0
$553$	3.54411	0.150711
$554$	−16.8894	−0.717561
$555$	7.72698	0.327992
$556$	−3.63133	−0.154003
$557$	1.94642	0.0824726	0.0412363	−	0.999149i	$-0.486870\pi$
$557$	1.94642	0.0824726	0.0412363	+	0.999149i	$0.486870\pi$
$558$	0.234748	0.00993769
$559$	3.35182	0.141767
$560$	−0.254580	−0.0107580
$561$	−32.1057	−1.35550
$562$	−22.8025	−0.961867
$563$	38.7808	1.63441	0.817207	−	0.576344i	$-0.195521\pi$
$563$	38.7808	1.63441	0.817207	+	0.576344i	$0.195521\pi$
$564$	15.6801	0.660252
$565$	14.5948	0.614008
$566$	−10.2296	−0.429981
$567$	−0.435759	−0.0183001
$568$	1.12532	0.0472172
$569$	26.6958	1.11915	0.559574	−	0.828780i	$-0.310965\pi$
$569$	26.6958	1.11915	0.559574	+	0.828780i	$0.310965\pi$
$570$	−0.0262843	−0.00110093
$571$	−8.81258	−0.368795	−0.184397	−	0.982852i	$-0.559033\pi$
$571$	−8.81258	−0.368795	−0.184397	+	0.982852i	$0.559033\pi$
$572$	9.96440	0.416632
$573$	−16.7735	−0.700722
$574$	1.59900	0.0667411
$575$	0	0
$576$	3.48759	0.145316
$577$	32.6831	1.36062	0.680308	−	0.732926i	$-0.261846\pi$
$577$	32.6831	1.36062	0.680308	+	0.732926i	$0.261846\pi$
$578$	−34.3957	−1.43067
$579$	6.17605	0.256668
$580$	−3.79255	−0.157477
$581$	−6.26283	−0.259826
$582$	−11.7586	−0.487408
$583$	−10.2476	−0.424410
$584$	9.73125	0.402682
$585$	1.76513	0.0729790
$586$	−15.9606	−0.659328
$587$	−24.1319	−0.996031	−0.498016	−	0.867168i	$-0.665938\pi$
$587$	−24.1319	−0.996031	−0.498016	+	0.867168i	$0.665938\pi$
$588$	9.28284	0.382818
$589$	−0.00968780	−0.000399179 0
$590$	−2.93700	−0.120914
$591$	12.5645	0.516834
$592$	4.51428	0.185536
$593$	45.9118	1.88537	0.942686	−	0.333682i	$-0.108291\pi$
$593$	45.9118	1.88537	0.942686	+	0.333682i	$0.108291\pi$
$594$	3.30511	0.135610
$595$	−3.37815	−0.138491
$596$	1.68585	0.0690551
$597$	22.4562	0.919073
$598$	0	0
$599$	11.4319	0.467094	0.233547	−	0.972346i	$-0.424967\pi$
$599$	11.4319	0.467094	0.233547	+	0.972346i	$0.424967\pi$
$600$	2.68396	0.109572
$601$	−13.3903	−0.546200	−0.273100	−	0.961986i	$-0.588049\pi$
$601$	−13.3903	−0.546200	−0.273100	+	0.961986i	$0.588049\pi$
$602$	0.660370	0.0269147
$603$	−2.79862	−0.113969
$604$	−16.2364	−0.660649
$605$	6.15129	0.250086
$606$	6.09996	0.247794
$607$	39.2626	1.59362	0.796810	−	0.604230i	$-0.206519\pi$
$607$	39.2626	1.59362	0.796810	+	0.604230i	$0.206519\pi$
$608$	−0.192149	−0.00779268
$609$	−1.21241	−0.0491295
$610$	−1.30228	−0.0527277
$611$	−20.3048	−0.821445
$612$	−10.5672	−0.427154
$613$	32.2155	1.30117	0.650586	−	0.759433i	$-0.274523\pi$
$613$	32.2155	1.30117	0.650586	+	0.759433i	$0.274523\pi$
$614$	16.5351	0.667301
$615$	4.59797	0.185408
$616$	4.84363	0.195155
$617$	41.9880	1.69037	0.845186	−	0.534472i	$-0.179489\pi$
$617$	41.9880	1.69037	0.845186	+	0.534472i	$0.179489\pi$
$618$	−3.30226	−0.132837
$619$	27.5104	1.10574	0.552869	−	0.833268i	$-0.313533\pi$
$619$	27.5104	1.10574	0.552869	+	0.833268i	$0.313533\pi$
$620$	0.400951	0.0161026
$621$	0	0
$622$	23.7439	0.952044
$623$	5.15605	0.206573
$624$	1.03123	0.0412821
$625$	1.00000	0.0400000
$626$	−8.05432	−0.321915
$627$	−0.136398	−0.00544721
$628$	−22.2538	−0.888022
$629$	59.9023	2.38846
$630$	0.347763	0.0138552
$631$	−42.7335	−1.70119	−0.850597	−	0.525817i	$-0.823759\pi$
$631$	−42.7335	−1.70119	−0.850597	+	0.525817i	$0.823759\pi$
$632$	−21.8292	−0.868317
$633$	22.3938	0.890073
$634$	17.2985	0.687012
$635$	−9.86931	−0.391652
$636$	−3.37286	−0.133743
$637$	−12.0207	−0.476278
$638$	9.19581	0.364066
$639$	0.419274	0.0165862
$640$	8.88502	0.351211
$641$	−0.388556	−0.0153470	−0.00767352	−	0.999971i	$-0.502443\pi$
$641$	−0.388556	−0.0153470	−0.00767352	+	0.999971i	$0.502443\pi$
$642$	4.63486	0.182923
$643$	44.3007	1.74705	0.873525	−	0.486778i	$-0.161828\pi$
$643$	44.3007	1.74705	0.873525	+	0.486778i	$0.161828\pi$
$644$	0	0
$645$	1.89891	0.0747694
$646$	−0.203765	−0.00801704
$647$	−5.05019	−0.198543	−0.0992717	−	0.995060i	$-0.531651\pi$
$647$	−5.05019	−0.198543	−0.0992717	+	0.995060i	$0.531651\pi$
$648$	2.68396	0.105436
$649$	−15.2411	−0.598265
$650$	−1.40868	−0.0552531
$651$	0.128177	0.00502367
$652$	−33.3766	−1.30713
$653$	−22.5591	−0.882806	−0.441403	−	0.897309i	$-0.645519\pi$
$653$	−22.5591	−0.882806	−0.441403	+	0.897309i	$0.645519\pi$
$654$	15.0805	0.589694
$655$	−22.8252	−0.891852
$656$	2.68624	0.104880
$657$	3.62570	0.141452
$658$	−4.00042	−0.155953
$659$	−25.3177	−0.986236	−0.493118	−	0.869962i	$-0.664143\pi$
$659$	−25.3177	−0.986236	−0.493118	+	0.869962i	$0.664143\pi$
$660$	5.64514	0.219737
$661$	−12.4677	−0.484938	−0.242469	−	0.970159i	$-0.577957\pi$
$661$	−12.4677	−0.484938	−0.242469	+	0.970159i	$0.577957\pi$
$662$	15.0460	0.584778
$663$	13.6839	0.531438
$664$	38.5745	1.49698
$665$	−0.0143518	−0.000556538 0
$666$	−6.16662	−0.238952
$667$	0	0
$668$	−29.2119	−1.13024
$669$	−22.0428	−0.852223
$670$	2.23347	0.0862866
$671$	−6.75796	−0.260888
$672$	2.54229	0.0980710
$673$	4.86176	0.187407	0.0937036	−	0.995600i	$-0.470129\pi$
$673$	4.86176	0.187407	0.0937036	+	0.995600i	$0.470129\pi$
$674$	−11.4964	−0.442825
$675$	1.00000	0.0384900
$676$	13.4733	0.518203
$677$	13.8248	0.531329	0.265665	−	0.964065i	$-0.414409\pi$
$677$	13.8248	0.531329	0.265665	+	0.964065i	$0.414409\pi$
$678$	−11.6476	−0.447322
$679$	−6.42042	−0.246393
$680$	20.8070	0.797913
$681$	8.93036	0.342212
$682$	−0.972189	−0.0372271
$683$	−34.4929	−1.31983	−0.659916	−	0.751339i	$-0.729408\pi$
$683$	−34.4929	−1.31983	−0.659916	+	0.751339i	$0.729408\pi$
$684$	−0.0448938	−0.00171656
$685$	5.55454	0.212228
$686$	−4.80264	−0.183366
$687$	15.9670	0.609180
$688$	1.10938	0.0422949
$689$	4.36765	0.166394
$690$	0	0
$691$	35.2516	1.34103	0.670517	−	0.741894i	$-0.266072\pi$
$691$	35.2516	1.34103	0.670517	+	0.741894i	$0.266072\pi$
$692$	−4.12449	−0.156790
$693$	1.80466	0.0685532
$694$	−3.18998	−0.121090
$695$	2.66403	0.101052
$696$	7.46760	0.283058
$697$	35.6451	1.35015
$698$	24.8442	0.940368
$699$	10.5728	0.399901
$700$	0.593981	0.0224504
$701$	6.15056	0.232303	0.116152	−	0.993231i	$-0.462944\pi$
$701$	6.15056	0.232303	0.116152	+	0.993231i	$0.462944\pi$
$702$	−1.40868	−0.0531673
$703$	0.254489	0.00959825
$704$	−14.4435	−0.544361
$705$	−11.5033	−0.433240
$706$	−1.67771	−0.0631413
$707$	3.33070	0.125264
$708$	−5.01642	−0.188529
$709$	−3.15128	−0.118349	−0.0591744	−	0.998248i	$-0.518847\pi$
$709$	−3.15128	−0.118349	−0.0591744	+	0.998248i	$0.518847\pi$
$710$	−0.334607	−0.0125576
$711$	−8.13319	−0.305018
$712$	−31.7576	−1.19017
$713$	0	0
$714$	2.69598	0.100894
$715$	−7.31012	−0.273383
$716$	7.85207	0.293446
$717$	1.81371	0.0677341
$718$	−13.8758	−0.517841
$719$	−37.4680	−1.39732	−0.698661	−	0.715453i	$-0.746220\pi$
$719$	−37.4680	−1.39732	−0.698661	+	0.715453i	$0.746220\pi$
$720$	0.584222	0.0217727
$721$	−1.80310	−0.0671511
$722$	15.1623	0.564283
$723$	−22.4236	−0.833943
$724$	−1.87161	−0.0695577
$725$	2.78230	0.103332
$726$	−4.90912	−0.182194
$727$	−5.64033	−0.209188	−0.104594	−	0.994515i	$-0.533354\pi$
$727$	−5.64033	−0.209188	−0.104594	+	0.994515i	$0.533354\pi$
$728$	−2.06442	−0.0765126
$729$	1.00000	0.0370370
$730$	−2.89354	−0.107095
$731$	14.7210	0.544476
$732$	−2.22430	−0.0822125
$733$	−38.0852	−1.40671	−0.703355	−	0.710839i	$-0.748315\pi$
$733$	−38.0852	−1.40671	−0.703355	+	0.710839i	$0.748315\pi$
$734$	12.6714	0.467711
$735$	−6.81011	−0.251195
$736$	0	0
$737$	11.5902	0.426932
$738$	−3.66947	−0.135075
$739$	14.7309	0.541884	0.270942	−	0.962596i	$-0.412665\pi$
$739$	14.7309	0.541884	0.270942	+	0.962596i	$0.412665\pi$
$740$	−10.5326	−0.387187
$741$	0.0581348	0.00213563
$742$	0.860508	0.0315902
$743$	−35.6893	−1.30931	−0.654657	−	0.755926i	$-0.727187\pi$
$743$	−35.6893	−1.30931	−0.654657	+	0.755926i	$0.727187\pi$
$744$	−0.789481	−0.0289438
$745$	−1.23678	−0.0453121
$746$	14.5981	0.534474
$747$	14.3722	0.525853
$748$	43.7631	1.60014
$749$	2.53073	0.0924708
$750$	−0.798063	−0.0291411
$751$	2.53770	0.0926020	0.0463010	−	0.998928i	$-0.485257\pi$
$751$	2.53770	0.0926020	0.0463010	+	0.998928i	$0.485257\pi$
$752$	−6.72049	−0.245071
$753$	7.77122	0.283199
$754$	−3.91938	−0.142735
$755$	11.9114	0.433500
$756$	0.593981	0.0216029
$757$	14.5108	0.527405	0.263703	−	0.964604i	$-0.415056\pi$
$757$	14.5108	0.527405	0.263703	+	0.964604i	$0.415056\pi$
$758$	−14.1145	−0.512661
$759$	0	0
$760$	0.0883967	0.00320649
$761$	−13.0355	−0.472535	−0.236268	−	0.971688i	$-0.575924\pi$
$761$	−13.0355	−0.472535	−0.236268	+	0.971688i	$0.575924\pi$
$762$	7.87633	0.285329
$763$	8.23426	0.298100
$764$	22.8639	0.827185
$765$	7.75235	0.280287
$766$	−19.8149	−0.715941
$767$	6.49596	0.234556
$768$	−14.0660	−0.507562
$769$	−29.6026	−1.06750	−0.533748	−	0.845643i	$-0.679217\pi$
$769$	−29.6026	−1.06750	−0.533748	+	0.845643i	$0.679217\pi$
$770$	−1.44023	−0.0519022
$771$	−3.89401	−0.140239
$772$	−8.41855	−0.302990
$773$	7.63028	0.274442	0.137221	−	0.990540i	$-0.456183\pi$
$773$	7.63028	0.274442	0.137221	+	0.990540i	$0.456183\pi$
$774$	−1.51545	−0.0544717
$775$	−0.294148	−0.0105661
$776$	39.5452	1.41959
$777$	−3.36710	−0.120794
$778$	−29.1628	−1.04554
$779$	0.151435	0.00542572
$780$	−2.40604	−0.0861500
$781$	−1.73639	−0.0621328
$782$	0	0
$783$	2.78230	0.0994314
$784$	−3.97862	−0.142094
$785$	16.3259	0.582697
$786$	18.2159	0.649740
$787$	−41.6700	−1.48538	−0.742688	−	0.669637i	$-0.766450\pi$
$787$	−41.6700	−1.48538	−0.742688	+	0.669637i	$0.766450\pi$
$788$	−17.1266	−0.610110
$789$	−9.00577	−0.320614
$790$	6.49079	0.230932
$791$	−6.35981	−0.226129
$792$	−11.1154	−0.394968
$793$	2.88034	0.102284
$794$	−0.106600	−0.00378311
$795$	2.47441	0.0877583
$796$	−30.6100	−1.08494
$797$	1.17201	0.0415149	0.0207574	−	0.999785i	$-0.493392\pi$
$797$	1.17201	0.0415149	0.0207574	+	0.999785i	$0.493392\pi$
$798$	0.0114536	0.000405454 0
$799$	−89.1777	−3.15488
$800$	−5.83417	−0.206269
$801$	−11.8324	−0.418076
$802$	8.70412	0.307353
$803$	−15.0155	−0.529887
$804$	3.81478	0.134537
$805$	0	0
$806$	0.414361	0.0145952
$807$	20.2302	0.712136
$808$	−20.5147	−0.721706
$809$	12.7810	0.449356	0.224678	−	0.974433i	$-0.427867\pi$
$809$	12.7810	0.449356	0.224678	+	0.974433i	$0.427867\pi$
$810$	−0.798063	−0.0280411
$811$	−10.9206	−0.383475	−0.191738	−	0.981446i	$-0.561412\pi$
$811$	−10.9206	−0.383475	−0.191738	+	0.981446i	$0.561412\pi$
$812$	1.65264	0.0579961
$813$	−16.4807	−0.578005
$814$	25.5385	0.895124
$815$	24.4859	0.857703
$816$	4.52910	0.158550
$817$	0.0625409	0.00218803
$818$	−24.4237	−0.853956
$819$	−0.769170	−0.0268770
$820$	−6.26747	−0.218870
$821$	15.2276	0.531447	0.265723	−	0.964049i	$-0.414389\pi$
$821$	15.2276	0.531447	0.265723	+	0.964049i	$0.414389\pi$
$822$	−4.43287	−0.154614
$823$	−8.64508	−0.301349	−0.150674	−	0.988583i	$-0.548144\pi$
$823$	−8.64508	−0.301349	−0.150674	+	0.988583i	$0.548144\pi$
$824$	11.1058	0.386890
$825$	−4.14141	−0.144185
$826$	1.27982	0.0445308
$827$	33.1850	1.15395	0.576977	−	0.816760i	$-0.304232\pi$
$827$	33.1850	1.15395	0.576977	+	0.816760i	$0.304232\pi$
$828$	0	0
$829$	12.4212	0.431405	0.215702	−	0.976459i	$-0.430796\pi$
$829$	12.4212	0.431405	0.215702	+	0.976459i	$0.430796\pi$
$830$	−11.4699	−0.398128
$831$	21.1630	0.734135
$832$	6.15604	0.213422
$833$	−52.7944	−1.82922
$834$	−2.12606	−0.0736195
$835$	21.4305	0.741634
$836$	0.185924	0.00643030
$837$	−0.294148	−0.0101672
$838$	−29.1169	−1.00583
$839$	21.2806	0.734686	0.367343	−	0.930085i	$-0.380267\pi$
$839$	21.2806	0.734686	0.367343	+	0.930085i	$0.380267\pi$
$840$	−1.16956	−0.0403536
$841$	−21.2588	−0.733062
$842$	18.7467	0.646053
$843$	28.5724	0.984085
$844$	−30.5249	−1.05071
$845$	−9.88432	−0.340031
$846$	9.18036	0.315627
$847$	−2.68048	−0.0921024
$848$	1.44561	0.0496423
$849$	12.8180	0.439913
$850$	−6.18686	−0.212208
$851$	0	0
$852$	−0.571511	−0.0195796
$853$	−19.9771	−0.684004	−0.342002	−	0.939699i	$-0.611105\pi$
$853$	−19.9771	−0.684004	−0.342002	+	0.939699i	$0.611105\pi$
$854$	0.567479	0.0194187
$855$	0.0329352	0.00112636
$856$	−15.5875	−0.532769
$857$	−16.9170	−0.577873	−0.288936	−	0.957348i	$-0.593302\pi$
$857$	−16.9170	−0.577873	−0.288936	+	0.957348i	$0.593302\pi$
$858$	5.83393	0.199167
$859$	8.46825	0.288933	0.144466	−	0.989510i	$-0.453853\pi$
$859$	8.46825	0.288933	0.144466	+	0.989510i	$0.453853\pi$
$860$	−2.58839	−0.0882635
$861$	−2.00360	−0.0682827
$862$	−11.7047	−0.398663
$863$	37.3603	1.27176	0.635879	−	0.771789i	$-0.280638\pi$
$863$	37.3603	1.27176	0.635879	+	0.771789i	$0.280638\pi$
$864$	−5.83417	−0.198482
$865$	3.02583	0.102881
$866$	21.0708	0.716014
$867$	43.0990	1.46372
$868$	−0.174718	−0.00593032
$869$	33.6829	1.14261
$870$	−2.22045	−0.0752804
$871$	−4.93992	−0.167383
$872$	−50.7172	−1.71750
$873$	14.7339	0.498666
$874$	0	0
$875$	−0.435759	−0.0147313
$876$	−4.94218	−0.166981
$877$	−4.54697	−0.153540	−0.0767701	−	0.997049i	$-0.524461\pi$
$877$	−4.54697	−0.153540	−0.0767701	+	0.997049i	$0.524461\pi$
$878$	6.99838	0.236184
$879$	19.9992	0.674558
$880$	−2.41951	−0.0815615
$881$	42.8081	1.44224	0.721121	−	0.692809i	$-0.243627\pi$
$881$	42.8081	1.44224	0.721121	+	0.692809i	$0.243627\pi$
$882$	5.43490	0.183003
$883$	18.3344	0.617003	0.308501	−	0.951224i	$-0.400173\pi$
$883$	18.3344	0.617003	0.308501	+	0.951224i	$0.400173\pi$
$884$	−18.6525	−0.627350
$885$	3.68016	0.123707
$886$	−8.67536	−0.291454
$887$	−25.2764	−0.848699	−0.424350	−	0.905498i	$-0.639497\pi$
$887$	−25.2764	−0.848699	−0.424350	+	0.905498i	$0.639497\pi$
$888$	20.7389	0.695953
$889$	4.30064	0.144239
$890$	9.44297	0.316529
$891$	−4.14141	−0.138743
$892$	30.0464	1.00603
$893$	−0.378863	−0.0126782
$894$	0.987028	0.0330112
$895$	−5.76047	−0.192551
$896$	−3.87173	−0.129345
$897$	0	0
$898$	26.0116	0.868017
$899$	−0.818408	−0.0272954
$900$	−1.36310	−0.0454365
$901$	19.1825	0.639062
$902$	15.1968	0.505997
$903$	−0.827466	−0.0275363
$904$	39.1719	1.30284
$905$	1.37306	0.0456419
$906$	−9.50605	−0.315817
$907$	24.6138	0.817288	0.408644	−	0.912694i	$-0.366002\pi$
$907$	24.6138	0.817288	0.408644	+	0.912694i	$0.366002\pi$
$908$	−12.1729	−0.403973
$909$	−7.64346	−0.253517
$910$	0.613846	0.0203488
$911$	24.1205	0.799147	0.399574	−	0.916701i	$-0.369158\pi$
$911$	24.1205	0.799147	0.399574	+	0.916701i	$0.369158\pi$
$912$	0.0192415	0.000637148 0
$913$	−59.5214	−1.96987
$914$	15.8580	0.524536
$915$	1.63180	0.0539457
$916$	−21.7646	−0.719122
$917$	9.94626	0.328454
$918$	−6.18686	−0.204197
$919$	−14.6891	−0.484548	−0.242274	−	0.970208i	$-0.577893\pi$
$919$	−14.6891	−0.484548	−0.242274	+	0.970208i	$0.577893\pi$
$920$	0	0
$921$	−20.7190	−0.682715
$922$	−9.14115	−0.301048
$923$	0.740072	0.0243598
$924$	−2.45992	−0.0809254
$925$	7.72698	0.254062
$926$	1.82790	0.0600686
$927$	4.13785	0.135905
$928$	−16.2324	−0.532856
$929$	45.5423	1.49419	0.747097	−	0.664715i	$-0.231447\pi$
$929$	45.5423	1.49419	0.747097	+	0.664715i	$0.231447\pi$
$930$	0.234748	0.00769770
$931$	−0.224292	−0.00735088
$932$	−14.4118	−0.472073
$933$	−29.7519	−0.974035
$934$	13.0005	0.425390
$935$	−32.1057	−1.04997
$936$	4.73753	0.154851
$937$	−19.5261	−0.637889	−0.318945	−	0.947773i	$-0.603328\pi$
$937$	−19.5261	−0.637889	−0.318945	+	0.947773i	$0.603328\pi$
$938$	−0.973255	−0.0317779
$939$	10.0923	0.329351
$940$	15.6801	0.511429
$941$	21.6317	0.705172	0.352586	−	0.935779i	$-0.385302\pi$
$941$	21.6317	0.705172	0.352586	+	0.935779i	$0.385302\pi$
$942$	−13.0291	−0.424511
$943$	0	0
$944$	2.15003	0.0699777
$945$	−0.435759	−0.0141752
$946$	6.27609	0.204053
$947$	0.315793	0.0102619	0.00513095	−	0.999987i	$-0.498367\pi$
$947$	0.315793	0.0102619	0.00513095	+	0.999987i	$0.498367\pi$
$948$	11.0863	0.360067
$949$	6.39983	0.207747
$950$	−0.0262843	−0.000852776 0
$951$	−21.6756	−0.702880
$952$	−9.06684	−0.293858
$953$	7.54727	0.244480	0.122240	−	0.992501i	$-0.460992\pi$
$953$	7.54727	0.244480	0.122240	+	0.992501i	$0.460992\pi$
$954$	−1.97473	−0.0639344
$955$	−16.7735	−0.542777
$956$	−2.47225	−0.0799584
$957$	−11.5227	−0.372475
$958$	−13.8712	−0.448158
$959$	−2.42044	−0.0781600
$960$	3.48759	0.112561
$961$	−30.9135	−0.997209
$962$	−10.8849	−0.350942
$963$	−5.80764	−0.187148
$964$	30.5655	0.984450
$965$	6.17605	0.198814
$966$	0	0
$967$	−16.4316	−0.528404	−0.264202	−	0.964467i	$-0.585109\pi$
$967$	−16.4316	−0.528404	−0.264202	+	0.964467i	$0.585109\pi$
$968$	16.5098	0.530646
$969$	0.255325	0.00820222
$970$	−11.7586	−0.377545
$971$	7.52999	0.241649	0.120825	−	0.992674i	$-0.461446\pi$
$971$	7.52999	0.241649	0.120825	+	0.992674i	$0.461446\pi$
$972$	−1.36310	−0.0437213
$973$	−1.16087	−0.0372159
$974$	−10.1093	−0.323924
$975$	1.76513	0.0565293
$976$	0.953335	0.0305155
$977$	−4.88019	−0.156131	−0.0780655	−	0.996948i	$-0.524874\pi$
$977$	−4.88019	−0.156131	−0.0780655	+	0.996948i	$0.524874\pi$
$978$	−19.5413	−0.624861
$979$	49.0027	1.56613
$980$	9.28284	0.296529
$981$	−18.8964	−0.603315
$982$	13.0394	0.416103
$983$	−25.8720	−0.825190	−0.412595	−	0.910915i	$-0.635377\pi$
$983$	−25.8720	−0.825190	−0.412595	+	0.910915i	$0.635377\pi$
$984$	12.3408	0.393409
$985$	12.5645	0.400338
$986$	−17.2137	−0.548197
$987$	5.01267	0.159555
$988$	−0.0792433	−0.00252106
$989$	0	0
$990$	3.30511	0.105043
$991$	48.0783	1.52726	0.763628	−	0.645656i	$-0.223416\pi$
$991$	48.0783	1.52726	0.763628	+	0.645656i	$0.223416\pi$
$992$	1.71611	0.0544865
$993$	−18.8531	−0.598286
$994$	0.145808	0.00462475
$995$	22.4562	0.711911
$996$	−19.5907	−0.620756
$997$	−19.3684	−0.613403	−0.306701	−	0.951806i	$-0.599225\pi$
$997$	−19.3684	−0.613403	−0.306701	+	0.951806i	$0.599225\pi$
$998$	−13.0668	−0.413621
$999$	7.72698	0.244471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bi.1.4	yes	8
23.22	odd	2		7935.2.a.bh.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bh.1.4	✓	8	23.22	odd	2
7935.2.a.bi.1.4	yes	8	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)

\(f(q)\)	\(=\)	\(q-0.798063 q^{2} +1.00000 q^{3} -1.36310 q^{4} +1.00000 q^{5} -0.798063 q^{6} -0.435759 q^{7} +2.68396 q^{8} +1.00000 q^{9} -0.798063 q^{10} -4.14141 q^{11} -1.36310 q^{12} +1.76513 q^{13} +0.347763 q^{14} +1.00000 q^{15} +0.584222 q^{16} +7.75235 q^{17} -0.798063 q^{18} +0.0329352 q^{19} -1.36310 q^{20} -0.435759 q^{21} +3.30511 q^{22} +2.68396 q^{24} +1.00000 q^{25} -1.40868 q^{26} +1.00000 q^{27} +0.593981 q^{28} +2.78230 q^{29} -0.798063 q^{30} -0.294148 q^{31} -5.83417 q^{32} -4.14141 q^{33} -6.18686 q^{34} -0.435759 q^{35} -1.36310 q^{36} +7.72698 q^{37} -0.0262843 q^{38} +1.76513 q^{39} +2.68396 q^{40} +4.59797 q^{41} +0.347763 q^{42} +1.89891 q^{43} +5.64514 q^{44} +1.00000 q^{45} -11.5033 q^{47} +0.584222 q^{48} -6.81011 q^{49} -0.798063 q^{50} +7.75235 q^{51} -2.40604 q^{52} +2.47441 q^{53} -0.798063 q^{54} -4.14141 q^{55} -1.16956 q^{56} +0.0329352 q^{57} -2.22045 q^{58} +3.68016 q^{59} -1.36310 q^{60} +1.63180 q^{61} +0.234748 q^{62} -0.435759 q^{63} +3.48759 q^{64} +1.76513 q^{65} +3.30511 q^{66} -2.79862 q^{67} -10.5672 q^{68} +0.347763 q^{70} +0.419274 q^{71} +2.68396 q^{72} +3.62570 q^{73} -6.16662 q^{74} +1.00000 q^{75} -0.0448938 q^{76} +1.80466 q^{77} -1.40868 q^{78} -8.13319 q^{79} +0.584222 q^{80} +1.00000 q^{81} -3.66947 q^{82} +14.3722 q^{83} +0.593981 q^{84} +7.75235 q^{85} -1.51545 q^{86} +2.78230 q^{87} -11.1154 q^{88} -11.8324 q^{89} -0.798063 q^{90} -0.769170 q^{91} -0.294148 q^{93} +9.18036 q^{94} +0.0329352 q^{95} -5.83417 q^{96} +14.7339 q^{97} +5.43490 q^{98} -4.14141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 8 q^{4} + 8 q^{5} + 6 q^{7} + 6 q^{8} + 8 q^{9} + 12 q^{11} + 8 q^{12} + 4 q^{13} + 8 q^{15} + 20 q^{17} + 4 q^{19} + 8 q^{20} + 6 q^{21} + 14 q^{22} + 6 q^{24} + 8 q^{25} - 22 q^{26} + 8 q^{27}+ \cdots + 12 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 8 * q^4 + 8 * q^5 + 6 * q^7 + 6 * q^8 + 8 * q^9 + 12 * q^11 + 8 * q^12 + 4 * q^13 + 8 * q^15 + 20 * q^17 + 4 * q^19 + 8 * q^20 + 6 * q^21 + 14 * q^22 + 6 * q^24 + 8 * q^25 - 22 * q^26 + 8 * q^27 - 8 * q^28 + 2 * q^31 + 12 * q^32 + 12 * q^33 + 8 * q^34 + 6 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^38 + 4 * q^39 + 6 * q^40 + 28 * q^41 + 4 * q^43 + 54 * q^44 + 8 * q^45 - 12 * q^47 + 14 * q^49 + 20 * q^51 - 22 * q^52 + 6 * q^53 + 12 * q^55 - 24 * q^56 + 4 * q^57 + 32 * q^58 + 2 * q^59 + 8 * q^60 + 32 * q^61 - 24 * q^62 + 6 * q^63 - 8 * q^64 + 4 * q^65 + 14 * q^66 + 32 * q^67 + 34 * q^68 + 2 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 + 8 * q^75 + 24 * q^76 - 30 * q^77 - 22 * q^78 - 36 * q^79 + 8 * q^81 + 16 * q^82 + 10 * q^83 - 8 * q^84 + 20 * q^85 + 50 * q^86 + 6 * q^88 + 42 * q^89 + 4 * q^91 + 2 * q^93 - 40 * q^94 + 4 * q^95 + 12 * q^96 + 16 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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