LMFDB - Embedded newform 7935.2.a.bw.1.14

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 = [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			1.14
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)

$f(q)$	$=$	\(q+0.940321 q^{2} +1.00000 q^{3} -1.11580 q^{4} +1.00000 q^{5} +0.940321 q^{6} +0.900767 q^{7} -2.92985 q^{8} +1.00000 q^{9} +0.940321 q^{10} +4.51292 q^{11} -1.11580 q^{12} -6.09945 q^{13} +0.847010 q^{14} +1.00000 q^{15} -0.523404 q^{16} -1.27051 q^{17} +0.940321 q^{18} +1.58545 q^{19} -1.11580 q^{20} +0.900767 q^{21} +4.24360 q^{22} -2.92985 q^{24} +1.00000 q^{25} -5.73544 q^{26} +1.00000 q^{27} -1.00507 q^{28} +3.74391 q^{29} +0.940321 q^{30} +3.96180 q^{31} +5.36753 q^{32} +4.51292 q^{33} -1.19469 q^{34} +0.900767 q^{35} -1.11580 q^{36} +6.50667 q^{37} +1.49083 q^{38} -6.09945 q^{39} -2.92985 q^{40} -6.80395 q^{41} +0.847010 q^{42} -8.12528 q^{43} -5.03551 q^{44} +1.00000 q^{45} -4.16466 q^{47} -0.523404 q^{48} -6.18862 q^{49} +0.940321 q^{50} -1.27051 q^{51} +6.80575 q^{52} +10.9791 q^{53} +0.940321 q^{54} +4.51292 q^{55} -2.63911 q^{56} +1.58545 q^{57} +3.52047 q^{58} +12.4963 q^{59} -1.11580 q^{60} +8.78067 q^{61} +3.72536 q^{62} +0.900767 q^{63} +6.09401 q^{64} -6.09945 q^{65} +4.24360 q^{66} +2.29868 q^{67} +1.41763 q^{68} +0.847010 q^{70} +2.63284 q^{71} -2.92985 q^{72} +16.9959 q^{73} +6.11836 q^{74} +1.00000 q^{75} -1.76904 q^{76} +4.06509 q^{77} -5.73544 q^{78} +1.89618 q^{79} -0.523404 q^{80} +1.00000 q^{81} -6.39790 q^{82} +1.85661 q^{83} -1.00507 q^{84} -1.27051 q^{85} -7.64037 q^{86} +3.74391 q^{87} -13.2222 q^{88} -7.87622 q^{89} +0.940321 q^{90} -5.49418 q^{91} +3.96180 q^{93} -3.91612 q^{94} +1.58545 q^{95} +5.36753 q^{96} +7.91711 q^{97} -5.81929 q^{98} +4.51292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.940321	0.664907	0.332454	−	0.943120i	$-0.392124\pi$
$2$	0.940321	0.664907	0.332454	+	0.943120i	$0.392124\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.11580	−0.557898
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.940321	0.383884
$7$	0.900767	0.340458	0.170229	−	0.985405i	$-0.445549\pi$
$7$	0.900767	0.340458	0.170229	+	0.985405i	$0.445549\pi$
$8$	−2.92985	−1.03586
$9$	1.00000	0.333333
$10$	0.940321	0.297356
$11$	4.51292	1.36070	0.680349	−	0.732888i	$-0.261828\pi$
$11$	4.51292	1.36070	0.680349	+	0.732888i	$0.261828\pi$
$12$	−1.11580	−0.322103
$13$	−6.09945	−1.69168	−0.845841	−	0.533435i	$-0.820901\pi$
$13$	−6.09945	−1.69168	−0.845841	+	0.533435i	$0.820901\pi$
$14$	0.847010	0.226373
$15$	1.00000	0.258199
$16$	−0.523404	−0.130851
$17$	−1.27051	−0.308144	−0.154072	−	0.988060i	$-0.549239\pi$
$17$	−1.27051	−0.308144	−0.154072	+	0.988060i	$0.549239\pi$
$18$	0.940321	0.221636
$19$	1.58545	0.363728	0.181864	−	0.983324i	$-0.441787\pi$
$19$	1.58545	0.363728	0.181864	+	0.983324i	$0.441787\pi$
$20$	−1.11580	−0.249500
$21$	0.900767	0.196564
$22$	4.24360	0.904738
$23$	0	0
$23$	0	0
$24$	−2.92985	−0.598053
$25$	1.00000	0.200000
$26$	−5.73544	−1.12481
$27$	1.00000	0.192450
$28$	−1.00507	−0.189941
$29$	3.74391	0.695226	0.347613	−	0.937638i	$-0.386992\pi$
$29$	3.74391	0.695226	0.347613	+	0.937638i	$0.386992\pi$
$30$	0.940321	0.171678
$31$	3.96180	0.711560	0.355780	−	0.934570i	$-0.384215\pi$
$31$	3.96180	0.711560	0.355780	+	0.934570i	$0.384215\pi$
$32$	5.36753	0.948854
$33$	4.51292	0.785599
$34$	−1.19469	−0.204887
$35$	0.900767	0.152257
$36$	−1.11580	−0.185966
$37$	6.50667	1.06969	0.534845	−	0.844950i	$-0.320370\pi$
$37$	6.50667	1.06969	0.534845	+	0.844950i	$0.320370\pi$
$38$	1.49083	0.241845
$39$	−6.09945	−0.976693
$40$	−2.92985	−0.463250
$41$	−6.80395	−1.06260	−0.531299	−	0.847184i	$-0.678296\pi$
$41$	−6.80395	−1.06260	−0.531299	+	0.847184i	$0.678296\pi$
$42$	0.847010	0.130696
$43$	−8.12528	−1.23909	−0.619547	−	0.784960i	$-0.712684\pi$
$43$	−8.12528	−1.23909	−0.619547	+	0.784960i	$0.712684\pi$
$44$	−5.03551	−0.759131
$45$	1.00000	0.149071
$46$	0	0
$47$	−4.16466	−0.607478	−0.303739	−	0.952755i	$-0.598235\pi$
$47$	−4.16466	−0.607478	−0.303739	+	0.952755i	$0.598235\pi$
$48$	−0.523404	−0.0755468
$49$	−6.18862	−0.884088
$50$	0.940321	0.132981
$51$	−1.27051	−0.177907
$52$	6.80575	0.943787
$53$	10.9791	1.50809	0.754045	−	0.656822i	$-0.228100\pi$
$53$	10.9791	1.50809	0.754045	+	0.656822i	$0.228100\pi$
$54$	0.940321	0.127961
$55$	4.51292	0.608522
$56$	−2.63911	−0.352666
$57$	1.58545	0.209998
$58$	3.52047	0.462261
$59$	12.4963	1.62688	0.813440	−	0.581649i	$-0.197592\pi$
$59$	12.4963	1.62688	0.813440	+	0.581649i	$0.197592\pi$
$60$	−1.11580	−0.144049
$61$	8.78067	1.12425	0.562125	−	0.827053i	$-0.309984\pi$
$61$	8.78067	1.12425	0.562125	+	0.827053i	$0.309984\pi$
$62$	3.72536	0.473121
$63$	0.900767	0.113486
$64$	6.09401	0.761751
$65$	−6.09945	−0.756543
$66$	4.24360	0.522350
$67$	2.29868	0.280828	0.140414	−	0.990093i	$-0.455157\pi$
$67$	2.29868	0.280828	0.140414	+	0.990093i	$0.455157\pi$
$68$	1.41763	0.171913
$69$	0	0
$70$	0.847010	0.101237
$71$	2.63284	0.312461	0.156230	−	0.987721i	$-0.450066\pi$
$71$	2.63284	0.312461	0.156230	+	0.987721i	$0.450066\pi$
$72$	−2.92985	−0.345286
$73$	16.9959	1.98922	0.994612	−	0.103670i	$-0.0330586\pi$
$73$	16.9959	1.98922	0.994612	+	0.103670i	$0.0330586\pi$
$74$	6.11836	0.711245
$75$	1.00000	0.115470
$76$	−1.76904	−0.202923
$77$	4.06509	0.463260
$78$	−5.73544	−0.649410
$79$	1.89618	0.213337	0.106669	−	0.994295i	$-0.465982\pi$
$79$	1.89618	0.213337	0.106669	+	0.994295i	$0.465982\pi$
$80$	−0.523404	−0.0585183
$81$	1.00000	0.111111
$82$	−6.39790	−0.706530
$83$	1.85661	0.203789	0.101895	−	0.994795i	$-0.467510\pi$
$83$	1.85661	0.203789	0.101895	+	0.994795i	$0.467510\pi$
$84$	−1.00507	−0.109662
$85$	−1.27051	−0.137806
$86$	−7.64037	−0.823882
$87$	3.74391	0.401389
$88$	−13.2222	−1.40949
$89$	−7.87622	−0.834878	−0.417439	−	0.908705i	$-0.637072\pi$
$89$	−7.87622	−0.834878	−0.417439	+	0.908705i	$0.637072\pi$
$90$	0.940321	0.0991185
$91$	−5.49418	−0.575947
$92$	0	0
$93$	3.96180	0.410819
$94$	−3.91612	−0.403917
$95$	1.58545	0.162664
$96$	5.36753	0.547821
$97$	7.91711	0.803861	0.401930	−	0.915670i	$-0.368339\pi$
$97$	7.91711	0.803861	0.401930	+	0.915670i	$0.368339\pi$
$98$	−5.81929	−0.587837
$99$	4.51292	0.453566
$100$	−1.11580	−0.111580
$101$	−6.35098	−0.631947	−0.315973	−	0.948768i	$-0.602331\pi$
$101$	−6.35098	−0.631947	−0.315973	+	0.948768i	$0.602331\pi$
$102$	−1.19469	−0.118291
$103$	−13.8741	−1.36706	−0.683529	−	0.729924i	$-0.739556\pi$
$103$	−13.8741	−1.36706	−0.683529	+	0.729924i	$0.739556\pi$
$104$	17.8705	1.75234
$105$	0.900767	0.0879059
$106$	10.3238	1.00274
$107$	9.02378	0.872362	0.436181	−	0.899859i	$-0.356331\pi$
$107$	9.02378	0.872362	0.436181	+	0.899859i	$0.356331\pi$
$108$	−1.11580	−0.107368
$109$	−2.82629	−0.270710	−0.135355	−	0.990797i	$-0.543217\pi$
$109$	−2.82629	−0.270710	−0.135355	+	0.990797i	$0.543217\pi$
$110$	4.24360	0.404611
$111$	6.50667	0.617586
$112$	−0.471465	−0.0445492
$113$	−12.0708	−1.13552	−0.567761	−	0.823193i	$-0.692190\pi$
$113$	−12.0708	−1.13552	−0.567761	+	0.823193i	$0.692190\pi$
$114$	1.49083	0.139629
$115$	0	0
$116$	−4.17744	−0.387866
$117$	−6.09945	−0.563894
$118$	11.7505	1.08172
$119$	−1.14443	−0.104910
$120$	−2.92985	−0.267457
$121$	9.36648	0.851498
$122$	8.25664	0.747521
$123$	−6.80395	−0.613492
$124$	−4.42056	−0.396978
$125$	1.00000	0.0894427
$126$	0.847010	0.0754576
$127$	17.1749	1.52403	0.762013	−	0.647562i	$-0.224211\pi$
$127$	17.1749	1.52403	0.762013	+	0.647562i	$0.224211\pi$
$128$	−5.00474	−0.442361
$129$	−8.12528	−0.715391
$130$	−5.73544	−0.503031
$131$	10.9640	0.957932	0.478966	−	0.877834i	$-0.341012\pi$
$131$	10.9640	0.957932	0.478966	+	0.877834i	$0.341012\pi$
$132$	−5.03551	−0.438285
$133$	1.42812	0.123834
$134$	2.16149	0.186725
$135$	1.00000	0.0860663
$136$	3.72240	0.319193
$137$	−20.8050	−1.77749	−0.888744	−	0.458405i	$-0.848421\pi$
$137$	−20.8050	−1.77749	−0.888744	+	0.458405i	$0.848421\pi$
$138$	0	0
$139$	5.01420	0.425299	0.212649	−	0.977129i	$-0.431791\pi$
$139$	5.01420	0.425299	0.212649	+	0.977129i	$0.431791\pi$
$140$	−1.00507	−0.0849442
$141$	−4.16466	−0.350728
$142$	2.47571	0.207757
$143$	−27.5263	−2.30187
$144$	−0.523404	−0.0436170
$145$	3.74391	0.310915
$146$	15.9816	1.32265
$147$	−6.18862	−0.510429
$148$	−7.26012	−0.596779
$149$	17.6816	1.44854	0.724268	−	0.689519i	$-0.242178\pi$
$149$	17.6816	1.44854	0.724268	+	0.689519i	$0.242178\pi$
$150$	0.940321	0.0767769
$151$	16.3307	1.32898	0.664488	−	0.747299i	$-0.268650\pi$
$151$	16.3307	1.32898	0.664488	+	0.747299i	$0.268650\pi$
$152$	−4.64514	−0.376770
$153$	−1.27051	−0.102715
$154$	3.82249	0.308025
$155$	3.96180	0.318219
$156$	6.80575	0.544896
$157$	14.6183	1.16667	0.583333	−	0.812233i	$-0.301748\pi$
$157$	14.6183	1.16667	0.583333	+	0.812233i	$0.301748\pi$
$158$	1.78302	0.141850
$159$	10.9791	0.870697
$160$	5.36753	0.424340
$161$	0	0
$162$	0.940321	0.0738786
$163$	0.827944	0.0648496	0.0324248	−	0.999474i	$-0.489677\pi$
$163$	0.827944	0.0648496	0.0324248	+	0.999474i	$0.489677\pi$
$164$	7.59183	0.592822
$165$	4.51292	0.351331
$166$	1.74581	0.135501
$167$	13.5622	1.04947	0.524737	−	0.851264i	$-0.324164\pi$
$167$	13.5622	1.04947	0.524737	+	0.851264i	$0.324164\pi$
$168$	−2.63911	−0.203612
$169$	24.2033	1.86179
$170$	−1.19469	−0.0916282
$171$	1.58545	0.121243
$172$	9.06616	0.691288
$173$	−2.78577	−0.211798	−0.105899	−	0.994377i	$-0.533772\pi$
$173$	−2.78577	−0.211798	−0.105899	+	0.994377i	$0.533772\pi$
$174$	3.52047	0.266886
$175$	0.900767	0.0680916
$176$	−2.36208	−0.178048
$177$	12.4963	0.939280
$178$	−7.40617	−0.555116
$179$	3.73006	0.278798	0.139399	−	0.990236i	$-0.455483\pi$
$179$	3.73006	0.278798	0.139399	+	0.990236i	$0.455483\pi$
$180$	−1.11580	−0.0831666
$181$	−13.8263	−1.02770	−0.513850	−	0.857880i	$-0.671781\pi$
$181$	−13.8263	−1.02770	−0.513850	+	0.857880i	$0.671781\pi$
$182$	−5.16629	−0.382951
$183$	8.78067	0.649086
$184$	0	0
$185$	6.50667	0.478380
$186$	3.72536	0.273157
$187$	−5.73371	−0.419290
$188$	4.64692	0.338911
$189$	0.900767	0.0655212
$190$	1.49083	0.108156
$191$	0.0561299	0.00406142	0.00203071	−	0.999998i	$-0.499354\pi$
$191$	0.0561299	0.00406142	0.00203071	+	0.999998i	$0.499354\pi$
$192$	6.09401	0.439797
$193$	−15.3652	−1.10601	−0.553004	−	0.833178i	$-0.686519\pi$
$193$	−15.3652	−1.10601	−0.553004	+	0.833178i	$0.686519\pi$
$194$	7.44462	0.534493
$195$	−6.09945	−0.436791
$196$	6.90524	0.493232
$197$	11.4603	0.816510	0.408255	−	0.912868i	$-0.366137\pi$
$197$	11.4603	0.816510	0.408255	+	0.912868i	$0.366137\pi$
$198$	4.24360	0.301579
$199$	−9.94742	−0.705154	−0.352577	−	0.935783i	$-0.614695\pi$
$199$	−9.94742	−0.705154	−0.352577	+	0.935783i	$0.614695\pi$
$200$	−2.92985	−0.207172
$201$	2.29868	0.162136
$202$	−5.97196	−0.420186
$203$	3.37239	0.236695
$204$	1.41763	0.0992539
$205$	−6.80395	−0.475209
$206$	−13.0461	−0.908966
$207$	0	0
$208$	3.19247	0.221358
$209$	7.15503	0.494924
$210$	0.847010	0.0584492
$211$	17.7720	1.22347	0.611736	−	0.791062i	$-0.290471\pi$
$211$	17.7720	1.22347	0.611736	+	0.791062i	$0.290471\pi$
$212$	−12.2504	−0.841362
$213$	2.63284	0.180399
$214$	8.48525	0.580039
$215$	−8.12528	−0.554140
$216$	−2.92985	−0.199351
$217$	3.56866	0.242256
$218$	−2.65762	−0.179997
$219$	16.9959	1.14848
$220$	−5.03551	−0.339494
$221$	7.74940	0.521281
$222$	6.11836	0.410637
$223$	4.42153	0.296088	0.148044	−	0.988981i	$-0.452702\pi$
$223$	4.42153	0.296088	0.148044	+	0.988981i	$0.452702\pi$
$224$	4.83489	0.323045
$225$	1.00000	0.0666667
$226$	−11.3504	−0.755017
$227$	−4.58802	−0.304518	−0.152259	−	0.988341i	$-0.548655\pi$
$227$	−4.58802	−0.304518	−0.152259	+	0.988341i	$0.548655\pi$
$228$	−1.76904	−0.117158
$229$	21.0759	1.39273	0.696366	−	0.717687i	$-0.254799\pi$
$229$	21.0759	1.39273	0.696366	+	0.717687i	$0.254799\pi$
$230$	0	0
$231$	4.06509	0.267463
$232$	−10.9691	−0.720156
$233$	9.07587	0.594580	0.297290	−	0.954787i	$-0.403917\pi$
$233$	9.07587	0.594580	0.297290	+	0.954787i	$0.403917\pi$
$234$	−5.73544	−0.374937
$235$	−4.16466	−0.271673
$236$	−13.9433	−0.907634
$237$	1.89618	0.123170
$238$	−1.07613	−0.0697554
$239$	−3.81330	−0.246662	−0.123331	−	0.992366i	$-0.539358\pi$
$239$	−3.81330	−0.246662	−0.123331	+	0.992366i	$0.539358\pi$
$240$	−0.523404	−0.0337856
$241$	22.0471	1.42018	0.710088	−	0.704113i	$-0.248655\pi$
$241$	22.0471	1.42018	0.710088	+	0.704113i	$0.248655\pi$
$242$	8.80749	0.566167
$243$	1.00000	0.0641500
$244$	−9.79744	−0.627217
$245$	−6.18862	−0.395376
$246$	−6.39790	−0.407915
$247$	−9.67039	−0.615312
$248$	−11.6075	−0.737075
$249$	1.85661	0.117658
$250$	0.940321	0.0594711
$251$	18.1889	1.14808	0.574038	−	0.818829i	$-0.305376\pi$
$251$	18.1889	1.14808	0.574038	+	0.818829i	$0.305376\pi$
$252$	−1.00507	−0.0633137
$253$	0	0
$254$	16.1499	1.01334
$255$	−1.27051	−0.0795623
$256$	−16.8941	−1.05588
$257$	8.45524	0.527423	0.263712	−	0.964602i	$-0.415053\pi$
$257$	8.45524	0.527423	0.263712	+	0.964602i	$0.415053\pi$
$258$	−7.64037	−0.475669
$259$	5.86100	0.364185
$260$	6.80575	0.422074
$261$	3.74391	0.231742
$262$	10.3097	0.636936
$263$	−13.6747	−0.843219	−0.421609	−	0.906778i	$-0.638535\pi$
$263$	−13.6747	−0.843219	−0.421609	+	0.906778i	$0.638535\pi$
$264$	−13.2222	−0.813769
$265$	10.9791	0.674439
$266$	1.34289	0.0823381
$267$	−7.87622	−0.482017
$268$	−2.56486	−0.156673
$269$	−28.9955	−1.76789	−0.883943	−	0.467595i	$-0.845120\pi$
$269$	−28.9955	−1.76789	−0.883943	+	0.467595i	$0.845120\pi$
$270$	0.940321	0.0572261
$271$	−8.89950	−0.540606	−0.270303	−	0.962775i	$-0.587124\pi$
$271$	−8.89950	−0.540606	−0.270303	+	0.962775i	$0.587124\pi$
$272$	0.664989	0.0403209
$273$	−5.49418	−0.332523
$274$	−19.5633	−1.18186
$275$	4.51292	0.272140
$276$	0	0
$277$	−19.9351	−1.19778	−0.598892	−	0.800830i	$-0.704392\pi$
$277$	−19.9351	−1.19778	−0.598892	+	0.800830i	$0.704392\pi$
$278$	4.71495	0.282784
$279$	3.96180	0.237187
$280$	−2.63911	−0.157717
$281$	−15.8844	−0.947585	−0.473793	−	0.880636i	$-0.657115\pi$
$281$	−15.8844	−0.947585	−0.473793	+	0.880636i	$0.657115\pi$
$282$	−3.91612	−0.233201
$283$	2.37591	0.141233	0.0706165	−	0.997504i	$-0.477503\pi$
$283$	2.37591	0.141233	0.0706165	+	0.997504i	$0.477503\pi$
$284$	−2.93772	−0.174321
$285$	1.58545	0.0939141
$286$	−25.8836	−1.53053
$287$	−6.12878	−0.361770
$288$	5.36753	0.316285
$289$	−15.3858	−0.905048
$290$	3.52047	0.206729
$291$	7.91711	0.464109
$292$	−18.9640	−1.10978
$293$	−27.5667	−1.61046	−0.805231	−	0.592962i	$-0.797959\pi$
$293$	−27.5667	−1.61046	−0.805231	+	0.592962i	$0.797959\pi$
$294$	−5.81929	−0.339388
$295$	12.4963	0.727563
$296$	−19.0636	−1.10805
$297$	4.51292	0.261866
$298$	16.6264	0.963142
$299$	0	0
$300$	−1.11580	−0.0644206
$301$	−7.31899	−0.421859
$302$	15.3561	0.883645
$303$	−6.35098	−0.364854
$304$	−0.829832	−0.0475941
$305$	8.78067	0.502780
$306$	−1.19469	−0.0682956
$307$	−23.5739	−1.34543	−0.672717	−	0.739900i	$-0.734873\pi$
$307$	−23.5739	−1.34543	−0.672717	+	0.739900i	$0.734873\pi$
$308$	−4.53582	−0.258452
$309$	−13.8741	−0.789271
$310$	3.72536	0.211586
$311$	8.25013	0.467822	0.233911	−	0.972258i	$-0.424848\pi$
$311$	8.25013	0.467822	0.233911	+	0.972258i	$0.424848\pi$
$312$	17.8705	1.01172
$313$	−5.04722	−0.285286	−0.142643	−	0.989774i	$-0.545560\pi$
$313$	−5.04722	−0.285286	−0.142643	+	0.989774i	$0.545560\pi$
$314$	13.7459	0.775725
$315$	0.900767	0.0507525
$316$	−2.11576	−0.119021
$317$	−13.4338	−0.754517	−0.377259	−	0.926108i	$-0.623133\pi$
$317$	−13.4338	−0.754517	−0.377259	+	0.926108i	$0.623133\pi$
$318$	10.3238	0.578932
$319$	16.8960	0.945993
$320$	6.09401	0.340665
$321$	9.02378	0.503658
$322$	0	0
$323$	−2.01433	−0.112080
$324$	−1.11580	−0.0619887
$325$	−6.09945	−0.338337
$326$	0.778533	0.0431189
$327$	−2.82629	−0.156294
$328$	19.9346	1.10070
$329$	−3.75139	−0.206821
$330$	4.24360	0.233602
$331$	31.4909	1.73090	0.865448	−	0.500999i	$-0.167034\pi$
$331$	31.4909	1.73090	0.865448	+	0.500999i	$0.167034\pi$
$332$	−2.07160	−0.113694
$333$	6.50667	0.356563
$334$	12.7528	0.697803
$335$	2.29868	0.125590
$336$	−0.471465	−0.0257205
$337$	−0.698321	−0.0380400	−0.0190200	−	0.999819i	$-0.506055\pi$
$337$	−0.698321	−0.0380400	−0.0190200	+	0.999819i	$0.506055\pi$
$338$	22.7588	1.23792
$339$	−12.0708	−0.655594
$340$	1.41763	0.0768817
$341$	17.8793	0.968218
$342$	1.49083	0.0806151
$343$	−11.8799	−0.641453
$344$	23.8058	1.28352
$345$	0	0
$346$	−2.61952	−0.140826
$347$	0.0482511	0.00259026	0.00129513	−	0.999999i	$-0.499588\pi$
$347$	0.0482511	0.00259026	0.00129513	+	0.999999i	$0.499588\pi$
$348$	−4.17744	−0.223934
$349$	20.1329	1.07769	0.538846	−	0.842404i	$-0.318861\pi$
$349$	20.1329	1.07769	0.538846	+	0.842404i	$0.318861\pi$
$350$	0.847010	0.0452746
$351$	−6.09945	−0.325564
$352$	24.2233	1.29110
$353$	18.0732	0.961941	0.480970	−	0.876737i	$-0.340284\pi$
$353$	18.0732	0.961941	0.480970	+	0.876737i	$0.340284\pi$
$354$	11.7505	0.624534
$355$	2.63284	0.139737
$356$	8.78826	0.465777
$357$	−1.14443	−0.0605698
$358$	3.50745	0.185375
$359$	25.6829	1.35549	0.677746	−	0.735296i	$-0.262957\pi$
$359$	25.6829	1.35549	0.677746	+	0.735296i	$0.262957\pi$
$360$	−2.92985	−0.154417
$361$	−16.4863	−0.867702
$362$	−13.0012	−0.683325
$363$	9.36648	0.491613
$364$	6.13039	0.321320
$365$	16.9959	0.889608
$366$	8.25664	0.431582
$367$	11.0459	0.576593	0.288296	−	0.957541i	$-0.406911\pi$
$367$	11.0459	0.576593	0.288296	+	0.957541i	$0.406911\pi$
$368$	0	0
$369$	−6.80395	−0.354200
$370$	6.11836	0.318078
$371$	9.88958	0.513442
$372$	−4.42056	−0.229195
$373$	22.4932	1.16465	0.582327	−	0.812955i	$-0.302142\pi$
$373$	22.4932	1.16465	0.582327	+	0.812955i	$0.302142\pi$
$374$	−5.39152	−0.278789
$375$	1.00000	0.0516398
$376$	12.2018	0.629261
$377$	−22.8358	−1.17610
$378$	0.847010	0.0435655
$379$	31.4499	1.61547	0.807736	−	0.589544i	$-0.200693\pi$
$379$	31.4499	1.61547	0.807736	+	0.589544i	$0.200693\pi$
$380$	−1.76904	−0.0907500
$381$	17.1749	0.879896
$382$	0.0527801	0.00270047
$383$	−6.92241	−0.353719	−0.176859	−	0.984236i	$-0.556594\pi$
$383$	−6.92241	−0.353719	−0.176859	+	0.984236i	$0.556594\pi$
$384$	−5.00474	−0.255397
$385$	4.06509	0.207176
$386$	−14.4482	−0.735393
$387$	−8.12528	−0.413031
$388$	−8.83389	−0.448473
$389$	1.27636	0.0647141	0.0323571	−	0.999476i	$-0.489699\pi$
$389$	1.27636	0.0647141	0.0323571	+	0.999476i	$0.489699\pi$
$390$	−5.73544	−0.290425
$391$	0	0
$392$	18.1317	0.915790
$393$	10.9640	0.553062
$394$	10.7763	0.542904
$395$	1.89618	0.0954074
$396$	−5.03551	−0.253044
$397$	24.2092	1.21503	0.607513	−	0.794310i	$-0.292167\pi$
$397$	24.2092	1.21503	0.607513	+	0.794310i	$0.292167\pi$
$398$	−9.35377	−0.468862
$399$	1.42812	0.0714956
$400$	−0.523404	−0.0261702
$401$	−29.1390	−1.45513	−0.727566	−	0.686038i	$-0.759348\pi$
$401$	−29.1390	−1.45513	−0.727566	+	0.686038i	$0.759348\pi$
$402$	2.16149	0.107805
$403$	−24.1648	−1.20373
$404$	7.08641	0.352562
$405$	1.00000	0.0496904
$406$	3.17113	0.157380
$407$	29.3641	1.45553
$408$	3.72240	0.184286
$409$	20.1242	0.995078	0.497539	−	0.867442i	$-0.334237\pi$
$409$	20.1242	0.995078	0.497539	+	0.867442i	$0.334237\pi$
$410$	−6.39790	−0.315970
$411$	−20.8050	−1.02623
$412$	15.4807	0.762679
$413$	11.2563	0.553884
$414$	0	0
$415$	1.85661	0.0911374
$416$	−32.7390	−1.60516
$417$	5.01420	0.245546
$418$	6.72802	0.329078
$419$	35.6028	1.73931	0.869655	−	0.493660i	$-0.164341\pi$
$419$	35.6028	1.73931	0.869655	+	0.493660i	$0.164341\pi$
$420$	−1.00507	−0.0490425
$421$	9.23595	0.450132	0.225066	−	0.974343i	$-0.427740\pi$
$421$	9.23595	0.450132	0.225066	+	0.974343i	$0.427740\pi$
$422$	16.7113	0.813496
$423$	−4.16466	−0.202493
$424$	−32.1670	−1.56217
$425$	−1.27051	−0.0616287
$426$	2.47571	0.119949
$427$	7.90934	0.382760
$428$	−10.0687	−0.486689
$429$	−27.5263	−1.32898
$430$	−7.64037	−0.368451
$431$	−13.0545	−0.628815	−0.314407	−	0.949288i	$-0.601806\pi$
$431$	−13.0545	−0.628815	−0.314407	+	0.949288i	$0.601806\pi$
$432$	−0.523404	−0.0251823
$433$	−25.9145	−1.24537	−0.622687	−	0.782471i	$-0.713959\pi$
$433$	−25.9145	−1.24537	−0.622687	+	0.782471i	$0.713959\pi$
$434$	3.35568	0.161078
$435$	3.74391	0.179507
$436$	3.15357	0.151028
$437$	0	0
$438$	15.9816	0.763632
$439$	−4.50428	−0.214977	−0.107489	−	0.994206i	$-0.534281\pi$
$439$	−4.50428	−0.214977	−0.107489	+	0.994206i	$0.534281\pi$
$440$	−13.2222	−0.630343
$441$	−6.18862	−0.294696
$442$	7.28692	0.346604
$443$	14.6140	0.694334	0.347167	−	0.937803i	$-0.387144\pi$
$443$	14.6140	0.694334	0.347167	+	0.937803i	$0.387144\pi$
$444$	−7.26012	−0.344550
$445$	−7.87622	−0.373369
$446$	4.15766	0.196871
$447$	17.6816	0.836313
$448$	5.48928	0.259344
$449$	−11.2963	−0.533107	−0.266553	−	0.963820i	$-0.585885\pi$
$449$	−11.2963	−0.533107	−0.266553	+	0.963820i	$0.585885\pi$
$450$	0.940321	0.0443271
$451$	−30.7057	−1.44588
$452$	13.4685	0.633506
$453$	16.3307	0.767284
$454$	−4.31421	−0.202476
$455$	−5.49418	−0.257571
$456$	−4.64514	−0.217528
$457$	−35.0417	−1.63918	−0.819592	−	0.572948i	$-0.805800\pi$
$457$	−35.0417	−1.63918	−0.819592	+	0.572948i	$0.805800\pi$
$458$	19.8181	0.926038
$459$	−1.27051	−0.0593023
$460$	0	0
$461$	24.5923	1.14538	0.572688	−	0.819773i	$-0.305901\pi$
$461$	24.5923	1.14538	0.572688	+	0.819773i	$0.305901\pi$
$462$	3.82249	0.177838
$463$	−40.3524	−1.87534	−0.937668	−	0.347531i	$-0.887020\pi$
$463$	−40.3524	−1.87534	−0.937668	+	0.347531i	$0.887020\pi$
$464$	−1.95957	−0.0909710
$465$	3.96180	0.183724
$466$	8.53423	0.395341
$467$	30.1423	1.39482	0.697410	−	0.716672i	$-0.254336\pi$
$467$	30.1423	1.39482	0.697410	+	0.716672i	$0.254336\pi$
$468$	6.80575	0.314596
$469$	2.07057	0.0956101
$470$	−3.91612	−0.180637
$471$	14.6183	0.673575
$472$	−36.6123	−1.68522
$473$	−36.6688	−1.68603
$474$	1.78302	0.0818969
$475$	1.58545	0.0727456
$476$	1.27695	0.0585291
$477$	10.9791	0.502697
$478$	−3.58573	−0.164007
$479$	11.4493	0.523134	0.261567	−	0.965185i	$-0.415761\pi$
$479$	11.4493	0.523134	0.261567	+	0.965185i	$0.415761\pi$
$480$	5.36753	0.244993
$481$	−39.6871	−1.80958
$482$	20.7313	0.944285
$483$	0	0
$484$	−10.4511	−0.475049
$485$	7.91711	0.359498
$486$	0.940321	0.0426538
$487$	−7.02770	−0.318456	−0.159228	−	0.987242i	$-0.550900\pi$
$487$	−7.02770	−0.318456	−0.159228	+	0.987242i	$0.550900\pi$
$488$	−25.7260	−1.16456
$489$	0.827944	0.0374409
$490$	−5.81929	−0.262889
$491$	−42.2142	−1.90510	−0.952549	−	0.304384i	$-0.901549\pi$
$491$	−42.2142	−1.90510	−0.952549	+	0.304384i	$0.901549\pi$
$492$	7.59183	0.342266
$493$	−4.75667	−0.214229
$494$	−9.09327	−0.409125
$495$	4.51292	0.202841
$496$	−2.07362	−0.0931082
$497$	2.37158	0.106380
$498$	1.74581	0.0782315
$499$	10.8302	0.484828	0.242414	−	0.970173i	$-0.422061\pi$
$499$	10.8302	0.484828	0.242414	+	0.970173i	$0.422061\pi$
$500$	−1.11580	−0.0499000
$501$	13.5622	0.605914
$502$	17.1034	0.763364
$503$	15.5135	0.691712	0.345856	−	0.938288i	$-0.387589\pi$
$503$	15.5135	0.691712	0.345856	+	0.938288i	$0.387589\pi$
$504$	−2.63911	−0.117555
$505$	−6.35098	−0.282615
$506$	0	0
$507$	24.2033	1.07490
$508$	−19.1637	−0.850251
$509$	25.9348	1.14954	0.574770	−	0.818315i	$-0.305091\pi$
$509$	25.9348	1.14954	0.574770	+	0.818315i	$0.305091\pi$
$510$	−1.19469	−0.0529016
$511$	15.3094	0.677247
$512$	−5.87637	−0.259701
$513$	1.58545	0.0699995
$514$	7.95064	0.350688
$515$	−13.8741	−0.611367
$516$	9.06616	0.399116
$517$	−18.7948	−0.826594
$518$	5.51122	0.242149
$519$	−2.78577	−0.122282
$520$	17.8705	0.783671
$521$	−14.9243	−0.653843	−0.326922	−	0.945051i	$-0.606011\pi$
$521$	−14.9243	−0.653843	−0.326922	+	0.945051i	$0.606011\pi$
$522$	3.52047	0.154087
$523$	21.2952	0.931173	0.465587	−	0.885002i	$-0.345843\pi$
$523$	21.2952	0.931173	0.465587	+	0.885002i	$0.345843\pi$
$524$	−12.2336	−0.534429
$525$	0.900767	0.0393127
$526$	−12.8586	−0.560662
$527$	−5.03350	−0.219263
$528$	−2.36208	−0.102796
$529$	0	0
$530$	10.3238	0.448439
$531$	12.4963	0.542293
$532$	−1.59350	−0.0690868
$533$	41.5004	1.79758
$534$	−7.40617	−0.320496
$535$	9.02378	0.390132
$536$	−6.73477	−0.290898
$537$	3.73006	0.160964
$538$	−27.2650	−1.17548
$539$	−27.9288	−1.20298
$540$	−1.11580	−0.0480163
$541$	−40.6751	−1.74876	−0.874379	−	0.485244i	$-0.838731\pi$
$541$	−40.6751	−1.74876	−0.874379	+	0.485244i	$0.838731\pi$
$542$	−8.36838	−0.359453
$543$	−13.8263	−0.593343
$544$	−6.81949	−0.292383
$545$	−2.82629	−0.121065
$546$	−5.16629	−0.221097
$547$	−7.12983	−0.304850	−0.152425	−	0.988315i	$-0.548708\pi$
$547$	−7.12983	−0.304850	−0.152425	+	0.988315i	$0.548708\pi$
$548$	23.2141	0.991657
$549$	8.78067	0.374750
$550$	4.24360	0.180948
$551$	5.93579	0.252873
$552$	0	0
$553$	1.70802	0.0726324
$554$	−18.7454	−0.796415
$555$	6.50667	0.276193
$556$	−5.59482	−0.237273
$557$	−6.68273	−0.283156	−0.141578	−	0.989927i	$-0.545218\pi$
$557$	−6.68273	−0.283156	−0.141578	+	0.989927i	$0.545218\pi$
$558$	3.72536	0.157707
$559$	49.5597	2.09615
$560$	−0.471465	−0.0199230
$561$	−5.73371	−0.242077
$562$	−14.9365	−0.630056
$563$	16.7057	0.704060	0.352030	−	0.935989i	$-0.385491\pi$
$563$	16.7057	0.704060	0.352030	+	0.935989i	$0.385491\pi$
$564$	4.64692	0.195670
$565$	−12.0708	−0.507821
$566$	2.23412	0.0939069
$567$	0.900767	0.0378287
$568$	−7.71382	−0.323665
$569$	−2.82864	−0.118583	−0.0592913	−	0.998241i	$-0.518884\pi$
$569$	−2.82864	−0.118583	−0.0592913	+	0.998241i	$0.518884\pi$
$570$	1.49083	0.0624442
$571$	−25.7150	−1.07614	−0.538070	−	0.842900i	$-0.680847\pi$
$571$	−25.7150	−1.07614	−0.538070	+	0.842900i	$0.680847\pi$
$572$	30.7138	1.28421
$573$	0.0561299	0.00234486
$574$	−5.76302	−0.240544
$575$	0	0
$576$	6.09401	0.253917
$577$	−28.5476	−1.18845	−0.594225	−	0.804299i	$-0.702541\pi$
$577$	−28.5476	−1.18845	−0.594225	+	0.804299i	$0.702541\pi$
$578$	−14.4676	−0.601773
$579$	−15.3652	−0.638555
$580$	−4.17744	−0.173459
$581$	1.67237	0.0693817
$582$	7.44462	0.308590
$583$	49.5477	2.05206
$584$	−49.7955	−2.06055
$585$	−6.09945	−0.252181
$586$	−25.9215	−1.07081
$587$	37.9216	1.56519	0.782596	−	0.622529i	$-0.213895\pi$
$587$	37.9216	1.56519	0.782596	+	0.622529i	$0.213895\pi$
$588$	6.90524	0.284767
$589$	6.28124	0.258814
$590$	11.7505	0.483762
$591$	11.4603	0.471412
$592$	−3.40562	−0.139970
$593$	−24.9412	−1.02421	−0.512106	−	0.858922i	$-0.671135\pi$
$593$	−24.9412	−1.02421	−0.512106	+	0.858922i	$0.671135\pi$
$594$	4.24360	0.174117
$595$	−1.14443	−0.0469171
$596$	−19.7291	−0.808136
$597$	−9.94742	−0.407121
$598$	0	0
$599$	10.9837	0.448783	0.224391	−	0.974499i	$-0.427961\pi$
$599$	10.9837	0.448783	0.224391	+	0.974499i	$0.427961\pi$
$600$	−2.92985	−0.119611
$601$	2.38656	0.0973496	0.0486748	−	0.998815i	$-0.484500\pi$
$601$	2.38656	0.0973496	0.0486748	+	0.998815i	$0.484500\pi$
$602$	−6.88219	−0.280497
$603$	2.29868	0.0936093
$604$	−18.2218	−0.741433
$605$	9.36648	0.380801
$606$	−5.97196	−0.242594
$607$	39.5841	1.60667	0.803335	−	0.595528i	$-0.203057\pi$
$607$	39.5841	1.60667	0.803335	+	0.595528i	$0.203057\pi$
$608$	8.50997	0.345125
$609$	3.37239	0.136656
$610$	8.25664	0.334302
$611$	25.4021	1.02766
$612$	1.41763	0.0573043
$613$	−22.1806	−0.895867	−0.447934	−	0.894067i	$-0.647840\pi$
$613$	−22.1806	−0.895867	−0.447934	+	0.894067i	$0.647840\pi$
$614$	−22.1670	−0.894589
$615$	−6.80395	−0.274362
$616$	−11.9101	−0.479872
$617$	−20.3895	−0.820849	−0.410424	−	0.911895i	$-0.634619\pi$
$617$	−20.3895	−0.820849	−0.410424	+	0.911895i	$0.634619\pi$
$618$	−13.0461	−0.524792
$619$	−39.6478	−1.59358	−0.796789	−	0.604258i	$-0.793470\pi$
$619$	−39.6478	−1.59358	−0.796789	+	0.604258i	$0.793470\pi$
$620$	−4.42056	−0.177534
$621$	0	0
$622$	7.75777	0.311058
$623$	−7.09464	−0.284241
$624$	3.19247	0.127801
$625$	1.00000	0.0400000
$626$	−4.74601	−0.189689
$627$	7.15503	0.285744
$628$	−16.3110	−0.650881
$629$	−8.26678	−0.329618
$630$	0.847010	0.0337457
$631$	23.4803	0.934737	0.467369	−	0.884063i	$-0.345202\pi$
$631$	23.4803	0.934737	0.467369	+	0.884063i	$0.345202\pi$
$632$	−5.55553	−0.220987
$633$	17.7720	0.706372
$634$	−12.6321	−0.501684
$635$	17.1749	0.681565
$636$	−12.2504	−0.485760
$637$	37.7472	1.49560
$638$	15.8876	0.628997
$639$	2.63284	0.104154
$640$	−5.00474	−0.197830
$641$	10.2947	0.406616	0.203308	−	0.979115i	$-0.434831\pi$
$641$	10.2947	0.406616	0.203308	+	0.979115i	$0.434831\pi$
$642$	8.48525	0.334886
$643$	−0.936695	−0.0369397	−0.0184698	−	0.999829i	$-0.505879\pi$
$643$	−0.936695	−0.0369397	−0.0184698	+	0.999829i	$0.505879\pi$
$644$	0	0
$645$	−8.12528	−0.319933
$646$	−1.89412	−0.0745231
$647$	−16.1377	−0.634438	−0.317219	−	0.948352i	$-0.602749\pi$
$647$	−16.1377	−0.634438	−0.317219	+	0.948352i	$0.602749\pi$
$648$	−2.92985	−0.115095
$649$	56.3949	2.21369
$650$	−5.73544	−0.224962
$651$	3.56866	0.139867
$652$	−0.923817	−0.0361795
$653$	15.3731	0.601597	0.300798	−	0.953688i	$-0.402747\pi$
$653$	15.3731	0.601597	0.300798	+	0.953688i	$0.402747\pi$
$654$	−2.65762	−0.103921
$655$	10.9640	0.428400
$656$	3.56121	0.139042
$657$	16.9959	0.663074
$658$	−3.52751	−0.137517
$659$	−7.37808	−0.287409	−0.143705	−	0.989621i	$-0.545902\pi$
$659$	−7.37808	−0.287409	−0.143705	+	0.989621i	$0.545902\pi$
$660$	−5.03551	−0.196007
$661$	−40.2012	−1.56365	−0.781823	−	0.623501i	$-0.785710\pi$
$661$	−40.2012	−1.56365	−0.781823	+	0.623501i	$0.785710\pi$
$662$	29.6115	1.15089
$663$	7.74940	0.300962
$664$	−5.43958	−0.211097
$665$	1.42812	0.0553803
$666$	6.11836	0.237082
$667$	0	0
$668$	−15.1327	−0.585500
$669$	4.42153	0.170946
$670$	2.16149	0.0835058
$671$	39.6265	1.52976
$672$	4.83489	0.186510
$673$	40.2647	1.55209	0.776045	−	0.630677i	$-0.217223\pi$
$673$	40.2647	1.55209	0.776045	+	0.630677i	$0.217223\pi$
$674$	−0.656646	−0.0252930
$675$	1.00000	0.0384900
$676$	−27.0059	−1.03869
$677$	8.89475	0.341853	0.170927	−	0.985284i	$-0.445324\pi$
$677$	8.89475	0.341853	0.170927	+	0.985284i	$0.445324\pi$
$678$	−11.3504	−0.435909
$679$	7.13147	0.273681
$680$	3.72240	0.142747
$681$	−4.58802	−0.175813
$682$	16.8123	0.643775
$683$	18.8086	0.719692	0.359846	−	0.933012i	$-0.382829\pi$
$683$	18.8086	0.719692	0.359846	+	0.933012i	$0.382829\pi$
$684$	−1.76904	−0.0676411
$685$	−20.8050	−0.794916
$686$	−11.1709	−0.426507
$687$	21.0759	0.804094
$688$	4.25280	0.162137
$689$	−66.9662	−2.55121
$690$	0	0
$691$	28.9522	1.10139	0.550697	−	0.834705i	$-0.314362\pi$
$691$	28.9522	1.10139	0.550697	+	0.834705i	$0.314362\pi$
$692$	3.10835	0.118162
$693$	4.06509	0.154420
$694$	0.0453715	0.00172228
$695$	5.01420	0.190199
$696$	−10.9691	−0.415782
$697$	8.64448	0.327433
$698$	18.9314	0.716565
$699$	9.07587	0.343281
$700$	−1.00507	−0.0379882
$701$	−25.9224	−0.979074	−0.489537	−	0.871983i	$-0.662834\pi$
$701$	−25.9224	−0.979074	−0.489537	+	0.871983i	$0.662834\pi$
$702$	−5.73544	−0.216470
$703$	10.3160	0.389076
$704$	27.5018	1.03651
$705$	−4.16466	−0.156850
$706$	16.9946	0.639601
$707$	−5.72076	−0.215151
$708$	−13.9433	−0.524023
$709$	17.3151	0.650283	0.325142	−	0.945665i	$-0.394588\pi$
$709$	17.3151	0.650283	0.325142	+	0.945665i	$0.394588\pi$
$710$	2.47571	0.0929119
$711$	1.89618	0.0711124
$712$	23.0761	0.864814
$713$	0	0
$714$	−1.07613	−0.0402733
$715$	−27.5263	−1.02943
$716$	−4.16199	−0.155541
$717$	−3.81330	−0.142410
$718$	24.1502	0.901276
$719$	−32.8202	−1.22399	−0.611993	−	0.790863i	$-0.709632\pi$
$719$	−32.8202	−1.22399	−0.611993	+	0.790863i	$0.709632\pi$
$720$	−0.523404	−0.0195061
$721$	−12.4973	−0.465426
$722$	−15.5024	−0.576941
$723$	22.0471	0.819939
$724$	15.4273	0.573353
$725$	3.74391	0.139045
$726$	8.80749	0.326877
$727$	26.0789	0.967212	0.483606	−	0.875286i	$-0.339327\pi$
$727$	26.0789	0.967212	0.483606	+	0.875286i	$0.339327\pi$
$728$	16.0971	0.596599
$729$	1.00000	0.0370370
$730$	15.9816	0.591507
$731$	10.3232	0.381819
$732$	−9.79744	−0.362124
$733$	18.0171	0.665477	0.332738	−	0.943019i	$-0.392027\pi$
$733$	18.0171	0.665477	0.332738	+	0.943019i	$0.392027\pi$
$734$	10.3867	0.383381
$735$	−6.18862	−0.228271
$736$	0	0
$737$	10.3737	0.382122
$738$	−6.39790	−0.235510
$739$	−9.55183	−0.351370	−0.175685	−	0.984446i	$-0.556214\pi$
$739$	−9.55183	−0.351370	−0.175685	+	0.984446i	$0.556214\pi$
$740$	−7.26012	−0.266887
$741$	−9.67039	−0.355251
$742$	9.29938	0.341391
$743$	−38.1371	−1.39911	−0.699557	−	0.714577i	$-0.746619\pi$
$743$	−38.1371	−1.39911	−0.699557	+	0.714577i	$0.746619\pi$
$744$	−11.6075	−0.425550
$745$	17.6816	0.647805
$746$	21.1508	0.774386
$747$	1.85661	0.0679298
$748$	6.39765	0.233921
$749$	8.12832	0.297002
$750$	0.940321	0.0343357
$751$	−52.9770	−1.93316	−0.966580	−	0.256367i	$-0.917475\pi$
$751$	−52.9770	−1.93316	−0.966580	+	0.256367i	$0.917475\pi$
$752$	2.17980	0.0794891
$753$	18.1889	0.662842
$754$	−21.4729	−0.781999
$755$	16.3307	0.594336
$756$	−1.00507	−0.0365542
$757$	−15.1249	−0.549722	−0.274861	−	0.961484i	$-0.588632\pi$
$757$	−15.1249	−0.549722	−0.274861	+	0.961484i	$0.588632\pi$
$758$	29.5730	1.07414
$759$	0	0
$760$	−4.64514	−0.168497
$761$	24.7091	0.895704	0.447852	−	0.894108i	$-0.352189\pi$
$761$	24.7091	0.895704	0.447852	+	0.894108i	$0.352189\pi$
$762$	16.1499	0.585049
$763$	−2.54583	−0.0921653
$764$	−0.0626296	−0.00226586
$765$	−1.27051	−0.0459353
$766$	−6.50928	−0.235190
$767$	−76.2205	−2.75216
$768$	−16.8941	−0.609612
$769$	−33.1942	−1.19701	−0.598507	−	0.801117i	$-0.704239\pi$
$769$	−33.1942	−1.19701	−0.598507	+	0.801117i	$0.704239\pi$
$770$	3.82249	0.137753
$771$	8.45524	0.304508
$772$	17.1444	0.617041
$773$	−53.2984	−1.91701	−0.958505	−	0.285075i	$-0.907982\pi$
$773$	−53.2984	−1.91701	−0.958505	+	0.285075i	$0.907982\pi$
$774$	−7.64037	−0.274627
$775$	3.96180	0.142312
$776$	−23.1959	−0.832686
$777$	5.86100	0.210262
$778$	1.20019	0.0430289
$779$	−10.7873	−0.386497
$780$	6.80575	0.243685
$781$	11.8818	0.425164
$782$	0	0
$783$	3.74391	0.133796
$784$	3.23914	0.115684
$785$	14.6183	0.521749
$786$	10.3097	0.367735
$787$	10.2904	0.366812	0.183406	−	0.983037i	$-0.441288\pi$
$787$	10.2904	0.366812	0.183406	+	0.983037i	$0.441288\pi$
$788$	−12.7873	−0.455530
$789$	−13.6747	−0.486832
$790$	1.78302	0.0634370
$791$	−10.8730	−0.386598
$792$	−13.2222	−0.469830
$793$	−53.5572	−1.90187
$794$	22.7644	0.807879
$795$	10.9791	0.389387
$796$	11.0993	0.393404
$797$	−2.58303	−0.0914956	−0.0457478	−	0.998953i	$-0.514567\pi$
$797$	−2.58303	−0.0914956	−0.0457478	+	0.998953i	$0.514567\pi$
$798$	1.34289	0.0475380
$799$	5.29124	0.187191
$800$	5.36753	0.189771
$801$	−7.87622	−0.278293
$802$	−27.4000	−0.967527
$803$	76.7013	2.70673
$804$	−2.56486	−0.0904555
$805$	0	0
$806$	−22.7226	−0.800371
$807$	−28.9955	−1.02069
$808$	18.6074	0.654607
$809$	−22.6860	−0.797596	−0.398798	−	0.917039i	$-0.630573\pi$
$809$	−22.6860	−0.797596	−0.398798	+	0.917039i	$0.630573\pi$
$810$	0.940321	0.0330395
$811$	32.5759	1.14390	0.571948	−	0.820290i	$-0.306188\pi$
$811$	32.5759	1.14390	0.571948	+	0.820290i	$0.306188\pi$
$812$	−3.76290	−0.132052
$813$	−8.89950	−0.312119
$814$	27.6117	0.967789
$815$	0.827944	0.0290016
$816$	0.664989	0.0232793
$817$	−12.8823	−0.450693
$818$	18.9232	0.661634
$819$	−5.49418	−0.191982
$820$	7.59183	0.265118
$821$	15.1522	0.528814	0.264407	−	0.964411i	$-0.414824\pi$
$821$	15.1522	0.528814	0.264407	+	0.964411i	$0.414824\pi$
$822$	−19.5633	−0.682350
$823$	−33.0458	−1.15190	−0.575952	−	0.817484i	$-0.695368\pi$
$823$	−33.0458	−1.15190	−0.575952	+	0.817484i	$0.695368\pi$
$824$	40.6491	1.41608
$825$	4.51292	0.157120
$826$	10.5845	0.368282
$827$	−37.7559	−1.31290	−0.656451	−	0.754369i	$-0.727943\pi$
$827$	−37.7559	−1.31290	−0.656451	+	0.754369i	$0.727943\pi$
$828$	0	0
$829$	22.1388	0.768913	0.384456	−	0.923143i	$-0.374389\pi$
$829$	22.1388	0.768913	0.384456	+	0.923143i	$0.374389\pi$
$830$	1.74581	0.0605979
$831$	−19.9351	−0.691540
$832$	−37.1701	−1.28864
$833$	7.86269	0.272426
$834$	4.71495	0.163265
$835$	13.5622	0.469339
$836$	−7.98356	−0.276117
$837$	3.96180	0.136940
$838$	33.4780	1.15648
$839$	13.2454	0.457282	0.228641	−	0.973511i	$-0.426572\pi$
$839$	13.2454	0.457282	0.228641	+	0.973511i	$0.426572\pi$
$840$	−2.63911	−0.0910580
$841$	−14.9832	−0.516661
$842$	8.68475	0.299296
$843$	−15.8844	−0.547089
$844$	−19.8299	−0.682573
$845$	24.2033	0.832618
$846$	−3.91612	−0.134639
$847$	8.43701	0.289899
$848$	−5.74648	−0.197335
$849$	2.37591	0.0815409
$850$	−1.19469	−0.0409774
$851$	0	0
$852$	−2.93772	−0.100644
$853$	−1.64644	−0.0563730	−0.0281865	−	0.999603i	$-0.508973\pi$
$853$	−1.64644	−0.0563730	−0.0281865	+	0.999603i	$0.508973\pi$
$854$	7.43731	0.254500
$855$	1.58545	0.0542213
$856$	−26.4383	−0.903643
$857$	6.64062	0.226839	0.113420	−	0.993547i	$-0.463820\pi$
$857$	6.64062	0.226839	0.113420	+	0.993547i	$0.463820\pi$
$858$	−25.8836	−0.883651
$859$	−16.5104	−0.563326	−0.281663	−	0.959513i	$-0.590886\pi$
$859$	−16.5104	−0.563326	−0.281663	+	0.959513i	$0.590886\pi$
$860$	9.06616	0.309154
$861$	−6.12878	−0.208868
$862$	−12.2754	−0.418103
$863$	−45.9851	−1.56535	−0.782676	−	0.622430i	$-0.786146\pi$
$863$	−45.9851	−1.56535	−0.782676	+	0.622430i	$0.786146\pi$
$864$	5.36753	0.182607
$865$	−2.78577	−0.0947190
$866$	−24.3680	−0.828058
$867$	−15.3858	−0.522529
$868$	−3.98190	−0.135154
$869$	8.55733	0.290288
$870$	3.52047	0.119355
$871$	−14.0207	−0.475072
$872$	8.28061	0.280417
$873$	7.91711	0.267954
$874$	0	0
$875$	0.900767	0.0304515
$876$	−18.9640	−0.640734
$877$	−52.7762	−1.78213	−0.891063	−	0.453879i	$-0.850040\pi$
$877$	−52.7762	−1.78213	−0.891063	+	0.453879i	$0.850040\pi$
$878$	−4.23546	−0.142940
$879$	−27.5667	−0.929800
$880$	−2.36208	−0.0796257
$881$	5.29724	0.178469	0.0892343	−	0.996011i	$-0.471558\pi$
$881$	5.29724	0.178469	0.0892343	+	0.996011i	$0.471558\pi$
$882$	−5.81929	−0.195946
$883$	−1.61448	−0.0543315	−0.0271657	−	0.999631i	$-0.508648\pi$
$883$	−1.61448	−0.0543315	−0.0271657	+	0.999631i	$0.508648\pi$
$884$	−8.64676	−0.290822
$885$	12.4963	0.420059
$886$	13.7419	0.461668
$887$	−31.8760	−1.07029	−0.535146	−	0.844760i	$-0.679743\pi$
$887$	−31.8760	−1.07029	−0.535146	+	0.844760i	$0.679743\pi$
$888$	−19.0636	−0.639731
$889$	15.4706	0.518867
$890$	−7.40617	−0.248255
$891$	4.51292	0.151189
$892$	−4.93353	−0.165187
$893$	−6.60288	−0.220957
$894$	16.6264	0.556070
$895$	3.73006	0.124682
$896$	−4.50810	−0.150605
$897$	0	0
$898$	−10.6222	−0.354467
$899$	14.8326	0.494695
$900$	−1.11580	−0.0371932
$901$	−13.9490	−0.464708
$902$	−28.8732	−0.961373
$903$	−7.31899	−0.243561
$904$	35.3655	1.17624
$905$	−13.8263	−0.459602
$906$	15.3561	0.510173
$907$	38.5836	1.28115	0.640574	−	0.767896i	$-0.278696\pi$
$907$	38.5836	1.28115	0.640574	+	0.767896i	$0.278696\pi$
$908$	5.11930	0.169890
$909$	−6.35098	−0.210649
$910$	−5.16629	−0.171261
$911$	−37.4135	−1.23957	−0.619783	−	0.784774i	$-0.712779\pi$
$911$	−37.4135	−1.23957	−0.619783	+	0.784774i	$0.712779\pi$
$912$	−0.829832	−0.0274785
$913$	8.37874	0.277296
$914$	−32.9505	−1.08991
$915$	8.78067	0.290280
$916$	−23.5164	−0.777003
$917$	9.87604	0.326135
$918$	−1.19469	−0.0394305
$919$	11.9517	0.394250	0.197125	−	0.980378i	$-0.436839\pi$
$919$	11.9517	0.394250	0.197125	+	0.980378i	$0.436839\pi$
$920$	0	0
$921$	−23.5739	−0.776787
$922$	23.1246	0.761569
$923$	−16.0589	−0.528584
$924$	−4.53582	−0.149217
$925$	6.50667	0.213938
$926$	−37.9442	−1.24692
$927$	−13.8741	−0.455686
$928$	20.0955	0.659668
$929$	11.9971	0.393613	0.196806	−	0.980442i	$-0.436943\pi$
$929$	11.9971	0.393613	0.196806	+	0.980442i	$0.436943\pi$
$930$	3.72536	0.122159
$931$	−9.81176	−0.321568
$932$	−10.1268	−0.331715
$933$	8.25013	0.270097
$934$	28.3435	0.927426
$935$	−5.73371	−0.187512
$936$	17.8705	0.584114
$937$	−10.0805	−0.329316	−0.164658	−	0.986351i	$-0.552652\pi$
$937$	−10.0805	−0.329316	−0.164658	+	0.986351i	$0.552652\pi$
$938$	1.94700	0.0635719
$939$	−5.04722	−0.164710
$940$	4.64692	0.151566
$941$	−1.51673	−0.0494441	−0.0247220	−	0.999694i	$-0.507870\pi$
$941$	−1.51673	−0.0494441	−0.0247220	+	0.999694i	$0.507870\pi$
$942$	13.7459	0.447865
$943$	0	0
$944$	−6.54061	−0.212879
$945$	0.900767	0.0293020
$946$	−34.4804	−1.12105
$947$	−39.5098	−1.28389	−0.641947	−	0.766749i	$-0.721873\pi$
$947$	−39.5098	−1.28389	−0.641947	+	0.766749i	$0.721873\pi$
$948$	−2.11576	−0.0687166
$949$	−103.666	−3.36513
$950$	1.49083	0.0483691
$951$	−13.4338	−0.435621
$952$	3.35301	0.108672
$953$	6.03918	0.195628	0.0978142	−	0.995205i	$-0.468815\pi$
$953$	6.03918	0.195628	0.0978142	+	0.995205i	$0.468815\pi$
$954$	10.3238	0.334247
$955$	0.0561299	0.00181632
$956$	4.25487	0.137612
$957$	16.8960	0.546169
$958$	10.7661	0.347836
$959$	−18.7404	−0.605160
$960$	6.09401	0.196683
$961$	−15.3042	−0.493683
$962$	−37.3186	−1.20320
$963$	9.02378	0.290787
$964$	−24.6000	−0.792314
$965$	−15.3652	−0.494622
$966$	0	0
$967$	−34.1074	−1.09682	−0.548410	−	0.836210i	$-0.684767\pi$
$967$	−34.1074	−1.09682	−0.548410	+	0.836210i	$0.684767\pi$
$968$	−27.4424	−0.882031
$969$	−2.01433	−0.0647096
$970$	7.44462	0.239032
$971$	−20.2923	−0.651211	−0.325606	−	0.945506i	$-0.605568\pi$
$971$	−20.2923	−0.651211	−0.325606	+	0.945506i	$0.605568\pi$
$972$	−1.11580	−0.0357892
$973$	4.51662	0.144796
$974$	−6.60830	−0.211743
$975$	−6.09945	−0.195339
$976$	−4.59583	−0.147109
$977$	29.2983	0.937334	0.468667	−	0.883375i	$-0.344734\pi$
$977$	29.2983	0.937334	0.468667	+	0.883375i	$0.344734\pi$
$978$	0.778533	0.0248947
$979$	−35.5448	−1.13602
$980$	6.90524	0.220580
$981$	−2.82629	−0.0902366
$982$	−39.6949	−1.26671
$983$	−30.8443	−0.983780	−0.491890	−	0.870657i	$-0.663694\pi$
$983$	−30.8443	−0.983780	−0.491890	+	0.870657i	$0.663694\pi$
$984$	19.9346	0.635490
$985$	11.4603	0.365155
$986$	−4.47279	−0.142443
$987$	−3.75139	−0.119408
$988$	10.7902	0.343282
$989$	0	0
$990$	4.24360	0.134870
$991$	40.2423	1.27834	0.639170	−	0.769065i	$-0.279278\pi$
$991$	40.2423	1.27834	0.639170	+	0.769065i	$0.279278\pi$
$992$	21.2651	0.675167
$993$	31.4909	0.999333
$994$	2.23004	0.0707326
$995$	−9.94742	−0.315354
$996$	−2.07160	−0.0656411
$997$	−2.43066	−0.0769797	−0.0384898	−	0.999259i	$-0.512255\pi$
$997$	−2.43066	−0.0769797	−0.0384898	+	0.999259i	$0.512255\pi$
$998$	10.1839	0.322366
$999$	6.50667	0.205862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bw.1.14		25
23.17	odd	22		345.2.m.c.151.3	yes	50
23.19	odd	22		345.2.m.c.16.3	✓	50
23.22	odd	2		7935.2.a.bv.1.14		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.16.3	✓	50	23.19	odd	22
345.2.m.c.151.3	yes	50	23.17	odd	22
7935.2.a.bv.1.14		25	23.22	odd	2
7935.2.a.bw.1.14		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)

\(f(q)\)	\(=\)	\(q+0.940321 q^{2} +1.00000 q^{3} -1.11580 q^{4} +1.00000 q^{5} +0.940321 q^{6} +0.900767 q^{7} -2.92985 q^{8} +1.00000 q^{9} +0.940321 q^{10} +4.51292 q^{11} -1.11580 q^{12} -6.09945 q^{13} +0.847010 q^{14} +1.00000 q^{15} -0.523404 q^{16} -1.27051 q^{17} +0.940321 q^{18} +1.58545 q^{19} -1.11580 q^{20} +0.900767 q^{21} +4.24360 q^{22} -2.92985 q^{24} +1.00000 q^{25} -5.73544 q^{26} +1.00000 q^{27} -1.00507 q^{28} +3.74391 q^{29} +0.940321 q^{30} +3.96180 q^{31} +5.36753 q^{32} +4.51292 q^{33} -1.19469 q^{34} +0.900767 q^{35} -1.11580 q^{36} +6.50667 q^{37} +1.49083 q^{38} -6.09945 q^{39} -2.92985 q^{40} -6.80395 q^{41} +0.847010 q^{42} -8.12528 q^{43} -5.03551 q^{44} +1.00000 q^{45} -4.16466 q^{47} -0.523404 q^{48} -6.18862 q^{49} +0.940321 q^{50} -1.27051 q^{51} +6.80575 q^{52} +10.9791 q^{53} +0.940321 q^{54} +4.51292 q^{55} -2.63911 q^{56} +1.58545 q^{57} +3.52047 q^{58} +12.4963 q^{59} -1.11580 q^{60} +8.78067 q^{61} +3.72536 q^{62} +0.900767 q^{63} +6.09401 q^{64} -6.09945 q^{65} +4.24360 q^{66} +2.29868 q^{67} +1.41763 q^{68} +0.847010 q^{70} +2.63284 q^{71} -2.92985 q^{72} +16.9959 q^{73} +6.11836 q^{74} +1.00000 q^{75} -1.76904 q^{76} +4.06509 q^{77} -5.73544 q^{78} +1.89618 q^{79} -0.523404 q^{80} +1.00000 q^{81} -6.39790 q^{82} +1.85661 q^{83} -1.00507 q^{84} -1.27051 q^{85} -7.64037 q^{86} +3.74391 q^{87} -13.2222 q^{88} -7.87622 q^{89} +0.940321 q^{90} -5.49418 q^{91} +3.96180 q^{93} -3.91612 q^{94} +1.58545 q^{95} +5.36753 q^{96} +7.91711 q^{97} -5.81929 q^{98} +4.51292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} + 25 q^{5} + 11 q^{6} + 7 q^{7} + 33 q^{8} + 25 q^{9} + 11 q^{10} + 9 q^{11} + 31 q^{12} + 18 q^{13} + 11 q^{14} + 25 q^{15} + 39 q^{16} - 8 q^{17} + 11 q^{18} + 11 q^{19}+ \cdots + 9 q^{99}+O(q^{100}) \) 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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