LMFDB - Embedded newform 475.2.b.e.324.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(324,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.324"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.2058981376.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 2x^{6} + 18x^{4} - 34x^{3} + 32x^{2} - 8x + 1 $ x^8 - 2x^7 + 2x^6 + 18x^4 - 34x^3 + 32x^2 - 8x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			324.5
Root			$0.769222 - 0.769222i$ of defining polynomial
Character	$\chi$	$=$	475.324
Dual form			475.2.b.e.324.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.816594i q^{2} -1.53844i q^{3} +1.33317 q^{4} +1.25628 q^{6} +5.03316i q^{7} +2.72185i q^{8} +0.633188 q^{9} -3.03316 q^{11} -2.05101i q^{12} +4.57160i q^{13} -4.11005 q^{14} +0.443701 q^{16} -1.07689i q^{17} +0.517058i q^{18} -1.00000 q^{19} +7.74324 q^{21} -2.47686i q^{22} -4.11005i q^{23} +4.18742 q^{24} -3.73315 q^{26} -5.58946i q^{27} +6.71008i q^{28} +1.07689 q^{29} +5.58946 q^{31} +5.80602i q^{32} +4.66635i q^{33} +0.879381 q^{34} +0.844150 q^{36} +0.0947438i q^{37} -0.816594i q^{38} +7.03316 q^{39} +10.6663 q^{41} +6.32308i q^{42} -5.03316i q^{43} -4.04373 q^{44} +3.35624 q^{46} -12.2995i q^{47} -0.682609i q^{48} -18.3327 q^{49} -1.65673 q^{51} +6.09474i q^{52} +4.09474i q^{53} +4.56432 q^{54} -13.6995 q^{56} +1.53844i q^{57} +0.879381i q^{58} +1.39997 q^{59} -5.69951 q^{61} +4.56432i q^{62} +3.18694i q^{63} -3.85376 q^{64} -3.81051 q^{66} +5.28168i q^{67} -1.43568i q^{68} -6.32308 q^{69} -5.67692 q^{71} +1.72344i q^{72} -9.07689i q^{73} -0.0773672 q^{74} -1.33317 q^{76} -15.2664i q^{77} +5.74324i q^{78} +5.39997 q^{79} -6.69951 q^{81} +8.71008i q^{82} -1.95627i q^{83} +10.3231 q^{84} +4.11005 q^{86} -1.65673i q^{87} -8.25581i q^{88} +2.18949 q^{89} -23.0096 q^{91} -5.47941i q^{92} -8.59907i q^{93} +10.0437 q^{94} +8.93225 q^{96} -2.16106i q^{97} -14.9704i q^{98} -1.92056 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 16 q^{4} - 16 q^{9} + 8 q^{11} + 16 q^{14} + 8 q^{16} - 8 q^{19} - 8 q^{21} + 48 q^{24} + 8 q^{26} - 8 q^{29} + 8 q^{31} + 8 q^{34} + 80 q^{36} + 24 q^{39} + 32 q^{41} - 48 q^{44} - 40 q^{49} - 72 q^{51}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 16 * q^4 - 16 * q^9 + 8 * q^11 + 16 * q^14 + 8 * q^16 - 8 * q^19 - 8 * q^21 + 48 * q^24 + 8 * q^26 - 8 * q^29 + 8 * q^31 + 8 * q^34 + 80 * q^36 + 24 * q^39 + 32 * q^41 - 48 * q^44 - 40 * q^49 - 72 * q^51 + 40 * q^54 - 24 * q^56 + 40 * q^61 + 8 * q^64 - 56 * q^66 - 56 * q^69 - 40 * q^71 - 64 * q^74 + 16 * q^76 + 32 * q^79 + 32 * q^81 + 88 * q^84 - 16 * q^86 - 8 * q^89 - 72 * q^91 + 96 * q^94 - 104 * q^96 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.816594i	0.577419i	0.957417	+	0.288710i	$0.0932262\pi$
$2$	0.816594i	0.577419i	−0.957417	+	0.288710i	$0.906774\pi$
$3$	− 1.53844i	− 0.888221i	−0.895972	−	0.444111i	$-0.853520\pi$
$3$	− 1.53844i	− 0.888221i	0.895972	−	0.444111i	$-0.146480\pi$
$4$	1.33317	0.666587
$5$	0	0
$5$	0	0
$6$	1.25628	0.512876
$7$	5.03316i	1.90236i	0.308644	+	0.951178i	$0.400125\pi$
$7$	5.03316i	1.90236i	−0.308644	+	0.951178i	$0.599875\pi$
$8$	2.72185i	0.962319i
$9$	0.633188	0.211063
$10$	0	0
$11$	−3.03316	−0.914532	−0.457266	−	0.889330i	$-0.651171\pi$
$11$	−3.03316	−0.914532	−0.457266	+	0.889330i	$0.651171\pi$
$12$	− 2.05101i	− 0.592077i
$13$	4.57160i	1.26793i	0.773360	+	0.633967i	$0.218575\pi$
$13$	4.57160i	1.26793i	−0.773360	+	0.633967i	$0.781425\pi$
$14$	−4.11005	−1.09846
$15$	0	0
$16$	0.443701	0.110925
$17$	− 1.07689i	− 0.261184i	−0.991436	−	0.130592i	$-0.958312\pi$
$17$	− 1.07689i	− 0.261184i	0.991436	−	0.130592i	$-0.0416878\pi$
$18$	0.517058i	0.121872i
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0	0
$21$	7.74324	1.68971
$22$	− 2.47686i	− 0.528068i
$23$	− 4.11005i	− 0.857004i	−0.903541	−	0.428502i	$-0.859041\pi$
$23$	− 4.11005i	− 0.857004i	0.903541	−	0.428502i	$-0.140959\pi$
$24$	4.18742	0.854753
$25$	0	0
$26$	−3.73315	−0.732130
$27$	− 5.58946i	− 1.07569i
$28$	6.71008i	1.26809i
$29$	1.07689	0.199973	0.0999866	−	0.994989i	$-0.468120\pi$
$29$	1.07689	0.199973	0.0999866	+	0.994989i	$0.468120\pi$
$30$	0	0
$31$	5.58946	1.00390	0.501948	−	0.864898i	$-0.332617\pi$
$31$	5.58946	1.00390	0.501948	+	0.864898i	$0.332617\pi$
$32$	5.80602i	1.02637i
$33$	4.66635i	0.812307i
$34$	0.879381	0.150813
$35$	0	0
$36$	0.844150	0.140692
$37$	0.0947438i	0.0155758i	0.999970	+	0.00778789i	$0.00247899\pi$
$37$	0.0947438i	0.0155758i	−0.999970	+	0.00778789i	$0.997521\pi$
$38$	− 0.816594i	− 0.132469i
$39$	7.03316	1.12621
$40$	0	0
$41$	10.6663	1.66580	0.832902	−	0.553421i	$-0.186678\pi$
$41$	10.6663	1.66580	0.832902	+	0.553421i	$0.186678\pi$
$42$	6.32308i	0.975673i
$43$	− 5.03316i	− 0.767550i	−0.923427	−	0.383775i	$-0.874624\pi$
$43$	− 5.03316i	− 0.767550i	0.923427	−	0.383775i	$-0.125376\pi$
$44$	−4.04373	−0.609615
$45$	0	0
$46$	3.35624	0.494851
$47$	− 12.2995i	− 1.79407i	−0.441958	−	0.897036i	$-0.645716\pi$
$47$	− 12.2995i	− 1.79407i	0.441958	−	0.897036i	$-0.354284\pi$
$48$	− 0.682609i	− 0.0985261i
$49$	−18.3327	−2.61896
$50$	0	0
$51$	−1.65673	−0.231989
$52$	6.09474i	0.845189i
$53$	4.09474i	0.562456i	0.959641	+	0.281228i	$0.0907418\pi$
$53$	4.09474i	0.562456i	−0.959641	+	0.281228i	$0.909258\pi$
$54$	4.56432	0.621125
$55$	0	0
$56$	−13.6995	−1.83067
$57$	1.53844i	0.203772i
$58$	0.879381i	0.115468i
$59$	1.39997	0.182261	0.0911304	−	0.995839i	$-0.470952\pi$
$59$	1.39997	0.182261	0.0911304	+	0.995839i	$0.470952\pi$
$60$	0	0
$61$	−5.69951	−0.729747	−0.364874	−	0.931057i	$-0.618888\pi$
$61$	−5.69951	−0.729747	−0.364874	+	0.931057i	$0.618888\pi$
$62$	4.56432i	0.579669i
$63$	3.18694i	0.401516i
$64$	−3.85376	−0.481720
$65$	0	0
$66$	−3.81051	−0.469042
$67$	5.28168i	0.645260i	0.946525	+	0.322630i	$0.104567\pi$
$67$	5.28168i	0.645260i	−0.946525	+	0.322630i	$0.895433\pi$
$68$	− 1.43568i	− 0.174102i
$69$	−6.32308	−0.761210
$70$	0	0
$71$	−5.67692	−0.673726	−0.336863	−	0.941554i	$-0.609366\pi$
$71$	−5.67692	−0.673726	−0.336863	+	0.941554i	$0.609366\pi$
$72$	1.72344i	0.203110i
$73$	− 9.07689i	− 1.06237i	−0.847256	−	0.531185i	$-0.821747\pi$
$73$	− 9.07689i	− 1.06237i	0.847256	−	0.531185i	$-0.178253\pi$
$74$	−0.0773672	−0.00899375
$75$	0	0
$76$	−1.33317	−0.152926
$77$	− 15.2664i	− 1.73977i
$78$	5.74324i	0.650294i
$79$	5.39997	0.607544	0.303772	−	0.952745i	$-0.401754\pi$
$79$	5.39997	0.607544	0.303772	+	0.952745i	$0.401754\pi$
$80$	0	0
$81$	−6.69951	−0.744390
$82$	8.71008i	0.961867i
$83$	− 1.95627i	− 0.214729i	−0.994220	−	0.107364i	$-0.965759\pi$
$83$	− 1.95627i	− 0.214729i	0.994220	−	0.107364i	$-0.0342411\pi$
$84$	10.3231	1.12634
$85$	0	0
$86$	4.11005	0.443198
$87$	− 1.65673i	− 0.177621i
$88$	− 8.25581i	− 0.880072i
$89$	2.18949	0.232085	0.116043	−	0.993244i	$-0.462979\pi$
$89$	2.18949	0.232085	0.116043	+	0.993244i	$0.462979\pi$
$90$	0	0
$91$	−23.0096	−2.41206
$92$	− 5.47941i	− 0.571268i
$93$	− 8.59907i	− 0.891682i
$94$	10.0437	1.03593
$95$	0	0
$96$	8.93225	0.911644
$97$	− 2.16106i	− 0.219423i	−0.993963	−	0.109711i	$-0.965007\pi$
$97$	− 2.16106i	− 0.219423i	0.993963	−	0.109711i	$-0.0349926\pi$
$98$	− 14.9704i	− 1.51224i
$99$	−1.92056	−0.193024
$100$	0	0
$101$	12.5869	1.25244	0.626222	−	0.779645i	$-0.284600\pi$
$101$	12.5869	1.25244	0.626222	+	0.779645i	$0.284600\pi$
$102$	− 1.35288i	− 0.133955i
$103$	6.20479i	0.611376i	0.952132	+	0.305688i	$0.0988865\pi$
$103$	6.20479i	0.611376i	−0.952132	+	0.305688i	$0.901113\pi$
$104$	−12.4432	−1.22016
$105$	0	0
$106$	−3.34374	−0.324773
$107$	− 12.5481i	− 1.21307i	−0.795058	−	0.606533i	$-0.792560\pi$
$107$	− 12.5481i	− 1.21307i	0.795058	−	0.606533i	$-0.207440\pi$
$108$	− 7.45172i	− 0.717042i
$109$	15.8096	1.51428	0.757140	−	0.653252i	$-0.226596\pi$
$109$	15.8096	1.51428	0.757140	+	0.653252i	$0.226596\pi$
$110$	0	0
$111$	0.145758	0.0138347
$112$	2.23322i	0.211019i
$113$	5.49472i	0.516899i	0.966025	+	0.258450i	$0.0832116\pi$
$113$	5.49472i	0.516899i	−0.966025	+	0.258450i	$0.916788\pi$
$114$	−1.25628	−0.117662
$115$	0	0
$116$	1.43568	0.133300
$117$	2.89469i	0.267614i
$118$	1.14321i	0.105241i
$119$	5.42015	0.496865
$120$	0	0
$121$	−1.79994	−0.163631
$122$	− 4.65418i	− 0.421370i
$123$	− 16.4096i	− 1.47960i
$124$	7.45172	0.669184
$125$	0	0
$126$	−2.60243	−0.231843
$127$	− 8.61533i	− 0.764487i	−0.924062	−	0.382244i	$-0.875152\pi$
$127$	− 8.61533i	− 0.764487i	0.924062	−	0.382244i	$-0.124848\pi$
$128$	8.46509i	0.748215i
$129$	−7.74324	−0.681754
$130$	0	0
$131$	−2.15378	−0.188176	−0.0940882	−	0.995564i	$-0.529994\pi$
$131$	−2.15378	−0.188176	−0.0940882	+	0.995564i	$0.529994\pi$
$132$	6.22105i	0.541473i
$133$	− 5.03316i	− 0.436430i
$134$	−4.31299	−0.372586
$135$	0	0
$136$	2.93113	0.251342
$137$	2.18949i	0.187061i	0.995616	+	0.0935303i	$0.0298152\pi$
$137$	2.18949i	0.187061i	−0.995616	+	0.0935303i	$0.970185\pi$
$138$	− 5.16339i	− 0.439537i
$139$	−22.5196	−1.91009	−0.955045	−	0.296460i	$-0.904194\pi$
$139$	−22.5196	−1.91009	−0.955045	+	0.296460i	$0.904194\pi$
$140$	0	0
$141$	−18.9222	−1.59353
$142$	− 4.63574i	− 0.389022i
$143$	− 13.8664i	− 1.15957i
$144$	0.280946	0.0234122
$145$	0	0
$146$	7.41213	0.613433
$147$	28.2038i	2.32621i
$148$	0.126310i	0.0103826i
$149$	−9.78697	−0.801780	−0.400890	−	0.916126i	$-0.631299\pi$
$149$	−9.78697	−0.801780	−0.400890	+	0.916126i	$0.631299\pi$
$150$	0	0
$151$	5.87683	0.478250	0.239125	−	0.970989i	$-0.423139\pi$
$151$	5.87683	0.478250	0.239125	+	0.970989i	$0.423139\pi$
$152$	− 2.72185i	− 0.220771i
$153$	− 0.681874i	− 0.0551262i
$154$	12.4664	1.00457
$155$	0	0
$156$	9.37643	0.750715
$157$	10.1895i	0.813210i	0.913604	+	0.406605i	$0.133287\pi$
$157$	10.1895i	0.813210i	−0.913604	+	0.406605i	$0.866713\pi$
$158$	4.40959i	0.350808i
$159$	6.29954	0.499586
$160$	0	0
$161$	20.6865	1.63033
$162$	− 5.47078i	− 0.429825i
$163$	10.3659i	0.811916i	0.913892	+	0.405958i	$0.133062\pi$
$163$	10.3659i	0.811916i	−0.913892	+	0.405958i	$0.866938\pi$
$164$	14.2201	1.11040
$165$	0	0
$166$	1.59748	0.123988
$167$	− 15.6048i	− 1.20753i	−0.797161	−	0.603766i	$-0.793666\pi$
$167$	− 15.6048i	− 1.20753i	0.797161	−	0.603766i	$-0.206334\pi$
$168$	21.0759i	1.62604i
$169$	−7.89956	−0.607659
$170$	0	0
$171$	−0.633188	−0.0484211
$172$	− 6.71008i	− 0.511639i
$173$	− 0.571604i	− 0.0434583i	−0.999764	−	0.0217291i	$-0.993083\pi$
$173$	− 0.571604i	− 0.0434583i	0.999764	−	0.0217291i	$-0.00691714\pi$
$174$	1.35288	0.102562
$175$	0	0
$176$	−1.34582	−0.101445
$177$	− 2.15378i	− 0.161888i
$178$	1.78792i	0.134010i
$179$	−24.8864	−1.86010	−0.930050	−	0.367433i	$-0.880237\pi$
$179$	−24.8864	−1.86010	−0.930050	+	0.367433i	$0.880237\pi$
$180$	0	0
$181$	6.95372	0.516866	0.258433	−	0.966029i	$-0.416794\pi$
$181$	6.95372	0.516866	0.258433	+	0.966029i	$0.416794\pi$
$182$	− 18.7895i	− 1.39277i
$183$	8.76838i	0.648177i
$184$	11.1869	0.824712
$185$	0	0
$186$	7.02195	0.514875
$187$	3.26638i	0.238861i
$188$	− 16.3974i	− 1.19590i
$189$	28.1326	2.04635
$190$	0	0
$191$	−3.91254	−0.283102	−0.141551	−	0.989931i	$-0.545209\pi$
$191$	−3.91254	−0.283102	−0.141551	+	0.989931i	$0.545209\pi$
$192$	5.92880i	0.427874i
$193$	9.20734i	0.662759i	0.943498	+	0.331379i	$0.107514\pi$
$193$	9.20734i	0.662759i	−0.943498	+	0.331379i	$0.892486\pi$
$194$	1.76471	0.126699
$195$	0	0
$196$	−24.4407	−1.74576
$197$	− 3.84622i	− 0.274032i	−0.990569	−	0.137016i	$-0.956249\pi$
$197$	− 3.84622i	− 0.274032i	0.990569	−	0.137016i	$-0.0437512\pi$
$198$	− 1.56832i	− 0.111456i
$199$	18.2864	1.29629	0.648145	−	0.761517i	$-0.275545\pi$
$199$	18.2864	1.29629	0.648145	+	0.761517i	$0.275545\pi$
$200$	0	0
$201$	8.12557	0.573134
$202$	10.2784i	0.723185i
$203$	5.42015i	0.380420i
$204$	−2.20871	−0.154641
$205$	0	0
$206$	−5.06680	−0.353020
$207$	− 2.60243i	− 0.180882i
$208$	2.02842i	0.140646i
$209$	3.03316	0.209808
$210$	0	0
$211$	−19.2970	−1.32846	−0.664230	−	0.747529i	$-0.731240\pi$
$211$	−19.2970	−1.32846	−0.664230	+	0.747529i	$0.731240\pi$
$212$	5.45901i	0.374926i
$213$	8.73362i	0.598418i
$214$	10.2467	0.700448
$215$	0	0
$216$	15.2137	1.03516
$217$	28.1326i	1.90977i
$218$	12.9100i	0.874375i
$219$	−13.9643	−0.943619
$220$	0	0
$221$	4.92311	0.331164
$222$	0.119025i	0.00798844i
$223$	− 0.615334i	− 0.0412058i	−0.999788	−	0.0206029i	$-0.993441\pi$
$223$	− 0.615334i	− 0.0412058i	0.999788	−	0.0206029i	$-0.00655857\pi$
$224$	−29.2226	−1.95252
$225$	0	0
$226$	−4.48695	−0.298468
$227$	17.4712i	1.15960i	0.814758	+	0.579801i	$0.196870\pi$
$227$	17.4712i	1.15960i	−0.814758	+	0.579801i	$0.803130\pi$
$228$	2.05101i	0.135832i
$229$	−9.69951	−0.640962	−0.320481	−	0.947255i	$-0.603844\pi$
$229$	−9.69951	−0.640962	−0.320481	+	0.947255i	$0.603844\pi$
$230$	0	0
$231$	−23.4865	−1.54530
$232$	2.93113i	0.192438i
$233$	8.15378i	0.534172i	0.963673	+	0.267086i	$0.0860607\pi$
$233$	8.15378i	0.534172i	−0.963673	+	0.267086i	$0.913939\pi$
$234$	−2.36378	−0.154525
$235$	0	0
$236$	1.86641	0.121493
$237$	− 8.30756i	− 0.539634i
$238$	4.42607i	0.286899i
$239$	−24.5991	−1.59118	−0.795591	−	0.605834i	$-0.792839\pi$
$239$	−24.5991	−1.59118	−0.795591	+	0.605834i	$0.792839\pi$
$240$	0	0
$241$	25.7738	1.66024	0.830120	−	0.557585i	$-0.188272\pi$
$241$	25.7738	1.66024	0.830120	+	0.557585i	$0.188272\pi$
$242$	− 1.46982i	− 0.0944838i
$243$	− 6.46156i	− 0.414509i
$244$	−7.59844	−0.486440
$245$	0	0
$246$	13.4000	0.854351
$247$	− 4.57160i	− 0.290884i
$248$	15.2137i	0.966069i
$249$	−3.00961	−0.190727
$250$	0	0
$251$	12.5991	0.795246	0.397623	−	0.917549i	$-0.369835\pi$
$251$	12.5991	0.795246	0.397623	+	0.917549i	$0.369835\pi$
$252$	4.24874i	0.267646i
$253$	12.4664i	0.783758i
$254$	7.03523	0.441430
$255$	0	0
$256$	−14.6201	−0.913754
$257$	0.182203i	0.0113655i	0.999984	+	0.00568275i	$0.00180888\pi$
$257$	0.182203i	0.0113655i	−0.999984	+	0.00568275i	$0.998191\pi$
$258$	− 6.32308i	− 0.393658i
$259$	−0.476860	−0.0296307
$260$	0	0
$261$	0.681874	0.0422069
$262$	− 1.75876i	− 0.108657i
$263$	− 7.37643i	− 0.454850i	−0.973796	−	0.227425i	$-0.926969\pi$
$263$	− 7.37643i	− 0.454850i	0.973796	−	0.227425i	$-0.0730306\pi$
$264$	−12.7011	−0.781699
$265$	0	0
$266$	4.11005	0.252003
$267$	− 3.36841i	− 0.206143i
$268$	7.04140i	0.430122i
$269$	−4.70206	−0.286689	−0.143345	−	0.989673i	$-0.545786\pi$
$269$	−4.70206	−0.286689	−0.143345	+	0.989673i	$0.545786\pi$
$270$	0	0
$271$	9.92056	0.602631	0.301316	−	0.953524i	$-0.402574\pi$
$271$	9.92056	0.602631	0.301316	+	0.953524i	$0.402574\pi$
$272$	− 0.477817i	− 0.0289719i
$273$	35.3990i	2.14245i
$274$	−1.78792	−0.108012
$275$	0	0
$276$	−8.42977	−0.507412
$277$	− 22.6297i	− 1.35969i	−0.733358	−	0.679843i	$-0.762048\pi$
$277$	− 22.6297i	− 1.35969i	0.733358	−	0.679843i	$-0.237952\pi$
$278$	− 18.3894i	− 1.10292i
$279$	3.53918	0.211885
$280$	0	0
$281$	−3.95386	−0.235868	−0.117934	−	0.993021i	$-0.537627\pi$
$281$	−3.95386	−0.235868	−0.117934	+	0.993021i	$0.537627\pi$
$282$	− 15.4517i	− 0.920137i
$283$	13.0638i	0.776561i	0.921541	+	0.388280i	$0.126931\pi$
$283$	13.0638i	0.776561i	−0.921541	+	0.388280i	$0.873069\pi$
$284$	−7.56832	−0.449097
$285$	0	0
$286$	11.3232	0.669556
$287$	53.6854i	3.16895i
$288$	3.67631i	0.216628i
$289$	15.8403	0.931783
$290$	0	0
$291$	−3.32468	−0.194896
$292$	− 12.1011i	− 0.708162i
$293$	9.69463i	0.566366i	0.959066	+	0.283183i	$0.0913904\pi$
$293$	9.69463i	0.566366i	−0.959066	+	0.283183i	$0.908610\pi$
$294$	−23.0311	−1.34320
$295$	0	0
$296$	−0.257878	−0.0149889
$297$	16.9537i	0.983755i
$298$	− 7.99198i	− 0.462963i
$299$	18.7895	1.08663
$300$	0	0
$301$	25.3327	1.46015
$302$	4.79899i	0.276151i
$303$	− 19.3643i	− 1.11245i
$304$	−0.443701	−0.0254480
$305$	0	0
$306$	0.556814	0.0318309
$307$	− 28.5481i	− 1.62932i	−0.579936	−	0.814662i	$-0.696923\pi$
$307$	− 28.5481i	− 1.62932i	0.579936	−	0.814662i	$-0.303077\pi$
$308$	− 20.3527i	− 1.15970i
$309$	9.54573	0.543038
$310$	0	0
$311$	25.4070	1.44070	0.720350	−	0.693610i	$-0.243981\pi$
$311$	25.4070	1.44070	0.720350	+	0.693610i	$0.243981\pi$
$312$	19.1432i	1.08377i
$313$	− 16.7999i	− 0.949589i	−0.880097	−	0.474794i	$-0.842522\pi$
$313$	− 16.7999i	− 0.949589i	0.880097	−	0.474794i	$-0.157478\pi$
$314$	−8.32068	−0.469563
$315$	0	0
$316$	7.19910	0.404981
$317$	− 31.7505i	− 1.78329i	−0.452738	−	0.891643i	$-0.649553\pi$
$317$	− 31.7505i	− 1.78329i	0.452738	−	0.891643i	$-0.350447\pi$
$318$	5.14416i	0.288470i
$319$	−3.26638	−0.182882
$320$	0	0
$321$	−19.3045	−1.07747
$322$	16.8925i	0.941382i
$323$	1.07689i	0.0599197i
$324$	−8.93161	−0.496201
$325$	0	0
$326$	−8.46470	−0.468816
$327$	− 24.3221i	− 1.34502i
$328$	29.0322i	1.60304i
$329$	61.9055	3.41296
$330$	0	0
$331$	−9.96429	−0.547687	−0.273843	−	0.961774i	$-0.588295\pi$
$331$	−9.96429	−0.547687	−0.273843	+	0.961774i	$0.588295\pi$
$332$	− 2.60805i	− 0.143135i
$333$	0.0599906i	0.00328747i
$334$	12.7428	0.697253
$335$	0	0
$336$	3.43568	0.187432
$337$	23.1918i	1.26334i	0.775238	+	0.631669i	$0.217630\pi$
$337$	23.1918i	1.26334i	−0.775238	+	0.631669i	$0.782370\pi$
$338$	− 6.45074i	− 0.350874i
$339$	8.45331	0.459121
$340$	0	0
$341$	−16.9537	−0.918095
$342$	− 0.517058i	− 0.0279593i
$343$	− 57.0393i	− 3.07983i
$344$	13.6995	0.738628
$345$	0	0
$346$	0.466769	0.0250936
$347$	21.1352i	1.13460i	0.823512	+	0.567298i	$0.192011\pi$
$347$	21.1352i	1.13460i	−0.823512	+	0.567298i	$0.807989\pi$
$348$	− 2.20871i	− 0.118400i
$349$	5.04628	0.270121	0.135061	−	0.990837i	$-0.456877\pi$
$349$	5.04628	0.270121	0.135061	+	0.990837i	$0.456877\pi$
$350$	0	0
$351$	25.5528	1.36391
$352$	− 17.6106i	− 0.938648i
$353$	− 12.5634i	− 0.668680i	−0.942452	−	0.334340i	$-0.891487\pi$
$353$	− 12.5634i	− 0.668680i	0.942452	−	0.334340i	$-0.108513\pi$
$354$	1.75876	0.0934772
$355$	0	0
$356$	2.91897	0.154705
$357$	− 8.33861i	− 0.441326i
$358$	− 20.3221i	− 1.07406i
$359$	17.6534	0.931709	0.465855	−	0.884861i	$-0.345747\pi$
$359$	17.6534	0.931709	0.465855	+	0.884861i	$0.345747\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	5.67837i	0.298448i
$363$	2.76911i	0.145341i
$364$	−30.6758	−1.60785
$365$	0	0
$366$	−7.16021	−0.374270
$367$	4.43409i	0.231457i	0.993281	+	0.115729i	$0.0369203\pi$
$367$	4.43409i	0.231457i	−0.993281	+	0.115729i	$0.963080\pi$
$368$	− 1.82363i	− 0.0950634i
$369$	6.75381	0.351589
$370$	0	0
$371$	−20.6095	−1.06999
$372$	− 11.4641i	− 0.594384i
$373$	20.8735i	1.08079i	0.841411	+	0.540396i	$0.181725\pi$
$373$	20.8735i	1.08079i	−0.841411	+	0.540396i	$0.818275\pi$
$374$	−2.66730	−0.137923
$375$	0	0
$376$	33.4775	1.72647
$377$	4.92311i	0.253553i
$378$	22.9729i	1.18160i
$379$	6.79994	0.349290	0.174645	−	0.984632i	$-0.444122\pi$
$379$	6.79994	0.349290	0.174645	+	0.984632i	$0.444122\pi$
$380$	0	0
$381$	−13.2542	−0.679034
$382$	− 3.19496i	− 0.163468i
$383$	10.9078i	0.557363i	0.960384	+	0.278681i	$0.0898974\pi$
$383$	10.9078i	0.557363i	−0.960384	+	0.278681i	$0.910103\pi$
$384$	13.0231	0.664581
$385$	0	0
$386$	−7.51866	−0.382690
$387$	− 3.18694i	− 0.162001i
$388$	− 2.88107i	− 0.146264i
$389$	−20.9326	−1.06132	−0.530662	−	0.847584i	$-0.678057\pi$
$389$	−20.9326	−1.06132	−0.530662	+	0.847584i	$0.678057\pi$
$390$	0	0
$391$	−4.42607	−0.223836
$392$	− 49.8989i	− 2.52027i
$393$	3.31347i	0.167142i
$394$	3.14080	0.158231
$395$	0	0
$396$	−2.56044	−0.128667
$397$	13.1221i	0.658578i	0.944229	+	0.329289i	$0.106809\pi$
$397$	13.1221i	0.658578i	−0.944229	+	0.329289i	$0.893191\pi$
$398$	14.9326i	0.748503i
$399$	−7.74324	−0.387647
$400$	0	0
$401$	−11.5528	−0.576919	−0.288459	−	0.957492i	$-0.593143\pi$
$401$	−11.5528	−0.576919	−0.288459	+	0.957492i	$0.593143\pi$
$402$	6.63530i	0.330939i
$403$	25.5528i	1.27288i
$404$	16.7805	0.834863
$405$	0	0
$406$	−4.42607	−0.219662
$407$	− 0.287373i	− 0.0142445i
$408$	− 4.50938i	− 0.223248i
$409$	18.9433	0.936686	0.468343	−	0.883547i	$-0.344851\pi$
$409$	18.9433	0.936686	0.468343	+	0.883547i	$0.344851\pi$
$410$	0	0
$411$	3.36841	0.166151
$412$	8.27207i	0.407536i
$413$	7.04628i	0.346725i
$414$	2.12513	0.104445
$415$	0	0
$416$	−26.5428	−1.30137
$417$	34.6452i	1.69658i
$418$	2.47686i	0.121147i
$419$	−27.2664	−1.33205	−0.666025	−	0.745930i	$-0.732006\pi$
$419$	−27.2664	−1.33205	−0.666025	+	0.745930i	$0.732006\pi$
$420$	0	0
$421$	6.66635	0.324898	0.162449	−	0.986717i	$-0.448061\pi$
$421$	6.66635	0.324898	0.162449	+	0.986717i	$0.448061\pi$
$422$	− 15.7578i	− 0.767078i
$423$	− 7.78792i	− 0.378662i
$424$	−11.1453	−0.541263
$425$	0	0
$426$	−7.13183	−0.345538
$427$	− 28.6865i	− 1.38824i
$428$	− 16.7287i	− 0.808614i
$429$	−21.3327	−1.02995
$430$	0	0
$431$	−32.4548	−1.56329	−0.781646	−	0.623723i	$-0.785619\pi$
$431$	−32.4548	−1.56329	−0.781646	+	0.623723i	$0.785619\pi$
$432$	− 2.48005i	− 0.119321i
$433$	− 33.8168i	− 1.62513i	−0.582868	−	0.812567i	$-0.698070\pi$
$433$	− 33.8168i	− 1.62513i	0.582868	−	0.812567i	$-0.301930\pi$
$434$	−22.9729	−1.10274
$435$	0	0
$436$	21.0769	1.00940
$437$	4.11005i	0.196610i
$438$	− 11.4032i	− 0.544864i
$439$	27.8453	1.32898	0.664491	−	0.747296i	$-0.268648\pi$
$439$	27.8453	1.32898	0.664491	+	0.747296i	$0.268648\pi$
$440$	0	0
$441$	−11.6080	−0.552764
$442$	4.02018i	0.191221i
$443$	− 22.7754i	− 1.08209i	−0.840992	−	0.541047i	$-0.818028\pi$
$443$	− 22.7754i	− 1.08209i	0.840992	−	0.541047i	$-0.181972\pi$
$444$	0.194321	0.00922206
$445$	0	0
$446$	0.502478	0.0237930
$447$	15.0567i	0.712158i
$448$	− 19.3966i	− 0.916404i
$449$	−24.8507	−1.17278	−0.586389	−	0.810029i	$-0.699451\pi$
$449$	−24.8507	−1.17278	−0.586389	+	0.810029i	$0.699451\pi$
$450$	0	0
$451$	−32.3527	−1.52343
$452$	7.32541i	0.344558i
$453$	− 9.04118i	− 0.424792i
$454$	−14.2669	−0.669577
$455$	0	0
$456$	−4.18742	−0.196094
$457$	− 7.33270i	− 0.343009i	−0.985183	−	0.171505i	$-0.945137\pi$
$457$	− 7.33270i	− 0.343009i	0.985183	−	0.171505i	$-0.0548628\pi$
$458$	− 7.92056i	− 0.370104i
$459$	−6.01923	−0.280953
$460$	0	0
$461$	10.3076	0.480071	0.240035	−	0.970764i	$-0.422841\pi$
$461$	10.3076	0.480071	0.240035	+	0.970764i	$0.422841\pi$
$462$	− 19.1789i	− 0.892284i
$463$	− 7.80249i	− 0.362613i	−0.983427	−	0.181306i	$-0.941967\pi$
$463$	− 7.80249i	− 0.362613i	0.983427	−	0.181306i	$-0.0580325\pi$
$464$	0.477817	0.0221821
$465$	0	0
$466$	−6.65833	−0.308441
$467$	− 7.37643i	− 0.341340i	−0.985328	−	0.170670i	$-0.945407\pi$
$467$	− 7.37643i	− 0.341340i	0.985328	−	0.170670i	$-0.0545932\pi$
$468$	3.85912i	0.178388i
$469$	−26.5835	−1.22751
$470$	0	0
$471$	15.6760	0.722310
$472$	3.81051i	0.175393i
$473$	15.2664i	0.701949i
$474$	6.78390	0.311595
$475$	0	0
$476$	7.22601	0.331204
$477$	2.59274i	0.118714i
$478$	− 20.0875i	− 0.918779i
$479$	16.1458	0.737719	0.368859	−	0.929485i	$-0.379748\pi$
$479$	16.1458	0.737719	0.368859	+	0.929485i	$0.379748\pi$
$480$	0	0
$481$	−0.433131	−0.0197491
$482$	21.0468i	0.958654i
$483$	− 31.8251i	− 1.44809i
$484$	−2.39964	−0.109074
$485$	0	0
$486$	5.27647	0.239345
$487$	− 8.40566i	− 0.380897i	−0.981697	−	0.190448i	$-0.939006\pi$
$487$	− 8.40566i	− 0.380897i	0.981697	−	0.190448i	$-0.0609942\pi$
$488$	− 15.5132i	− 0.702250i
$489$	15.9473	0.721162
$490$	0	0
$491$	−36.0855	−1.62852	−0.814259	−	0.580502i	$-0.802856\pi$
$491$	−36.0855	−1.62852	−0.814259	+	0.580502i	$0.802856\pi$
$492$	− 21.8768i	− 0.986284i
$493$	− 1.15969i	− 0.0522298i
$494$	3.73315	0.167962
$495$	0	0
$496$	2.48005	0.111357
$497$	− 28.5728i	− 1.28167i
$498$	− 2.45763i	− 0.110129i
$499$	3.30035	0.147744	0.0738720	−	0.997268i	$-0.476464\pi$
$499$	3.30035	0.147744	0.0738720	+	0.997268i	$0.476464\pi$
$500$	0	0
$501$	−24.0071	−1.07256
$502$	10.2883i	0.459191i
$503$	− 3.53530i	− 0.157631i	−0.996889	−	0.0788157i	$-0.974886\pi$
$503$	− 3.53530i	− 0.157631i	0.996889	−	0.0788157i	$-0.0251139\pi$
$504$	−8.67437	−0.386387
$505$	0	0
$506$	−10.1800	−0.452557
$507$	12.1530i	0.539736i
$508$	− 11.4857i	− 0.509597i
$509$	−22.4096	−0.993287	−0.496644	−	0.867955i	$-0.665434\pi$
$509$	−22.4096	−0.993287	−0.496644	+	0.867955i	$0.665434\pi$
$510$	0	0
$511$	45.6854	2.02100
$512$	4.99151i	0.220596i
$513$	5.58946i	0.246781i
$514$	−0.148786	−0.00656266
$515$	0	0
$516$	−10.3231	−0.454448
$517$	37.3065i	1.64074i
$518$	− 0.389401i	− 0.0171093i
$519$	−0.879381	−0.0386006
$520$	0	0
$521$	34.4402	1.50885	0.754426	−	0.656385i	$-0.227915\pi$
$521$	34.4402	1.50885	0.754426	+	0.656385i	$0.227915\pi$
$522$	0.556814i	0.0243711i
$523$	30.4451i	1.33127i	0.746277	+	0.665635i	$0.231839\pi$
$523$	30.4451i	1.33127i	−0.746277	+	0.665635i	$0.768161\pi$
$524$	−2.87136	−0.125436
$525$	0	0
$526$	6.02355	0.262639
$527$	− 6.01923i	− 0.262202i
$528$	2.07046i	0.0901053i
$529$	6.10750	0.265543
$530$	0	0
$531$	0.886445	0.0384685
$532$	− 6.71008i	− 0.290919i
$533$	48.7623i	2.11213i
$534$	2.75062	0.119031
$535$	0	0
$536$	−14.3759	−0.620946
$537$	38.2864i	1.65218i
$538$	− 3.83967i	− 0.165540i
$539$	55.6060	2.39512
$540$	0	0
$541$	−12.2794	−0.527931	−0.263965	−	0.964532i	$-0.585030\pi$
$541$	−12.2794	−0.527931	−0.263965	+	0.964532i	$0.585030\pi$
$542$	8.10107i	0.347971i
$543$	− 10.6979i	− 0.459091i
$544$	6.25244	0.268071
$545$	0	0
$546$	−28.9066	−1.23709
$547$	0.250928i	0.0107289i	0.999986	+	0.00536446i	$0.00170757\pi$
$547$	0.250928i	0.0107289i	−0.999986	+	0.00536446i	$0.998292\pi$
$548$	2.91897i	0.124692i
$549$	−3.60886	−0.154022
$550$	0	0
$551$	−1.07689	−0.0458770
$552$	− 17.2105i	− 0.732527i
$553$	27.1789i	1.15577i
$554$	18.4793	0.785109
$555$	0	0
$556$	−30.0226	−1.27324
$557$	1.67596i	0.0710128i	0.999369	+	0.0355064i	$0.0113044\pi$
$557$	1.67596i	0.0710128i	−0.999369	+	0.0355064i	$0.988696\pi$
$558$	2.89007i	0.122347i
$559$	23.0096	0.973203
$560$	0	0
$561$	5.02514	0.212162
$562$	− 3.22870i	− 0.136195i
$563$	− 20.6605i	− 0.870737i	−0.900252	−	0.435368i	$-0.856618\pi$
$563$	− 20.6605i	− 0.870737i	0.900252	−	0.435368i	$-0.143382\pi$
$564$	−25.2265	−1.06223
$565$	0	0
$566$	−10.6678	−0.448401
$567$	− 33.7197i	− 1.41609i
$568$	− 15.4517i	− 0.648340i
$569$	−40.9673	−1.71744	−0.858720	−	0.512445i	$-0.828740\pi$
$569$	−40.9673	−1.71744	−0.858720	+	0.512445i	$0.828740\pi$
$570$	0	0
$571$	24.2070	1.01303	0.506515	−	0.862231i	$-0.330933\pi$
$571$	24.2070	1.01303	0.506515	+	0.862231i	$0.330933\pi$
$572$	− 18.4863i	− 0.772952i
$573$	6.01923i	0.251457i
$574$	−43.8392	−1.82981
$575$	0	0
$576$	−2.44016	−0.101673
$577$	40.2864i	1.67715i	0.544790	+	0.838573i	$0.316609\pi$
$577$	40.2864i	1.67715i	−0.544790	+	0.838573i	$0.683391\pi$
$578$	12.9351i	0.538029i
$579$	14.1650	0.588677
$580$	0	0
$581$	9.84622	0.408490
$582$	− 2.71491i	− 0.112537i
$583$	− 12.4200i	− 0.514384i
$584$	24.7059	1.02234
$585$	0	0
$586$	−7.91658	−0.327031
$587$	− 34.7754i	− 1.43534i	−0.696385	−	0.717668i	$-0.745210\pi$
$587$	− 34.7754i	− 1.43534i	0.696385	−	0.717668i	$-0.254790\pi$
$588$	37.6006i	1.55062i
$589$	−5.58946	−0.230310
$590$	0	0
$591$	−5.91720	−0.243401
$592$	0.0420379i	0.00172775i
$593$	35.0864i	1.44082i	0.693546	+	0.720412i	$0.256047\pi$
$593$	35.0864i	1.44082i	−0.693546	+	0.720412i	$0.743953\pi$
$594$	−13.8443	−0.568039
$595$	0	0
$596$	−13.0477	−0.534456
$597$	− 28.1326i	− 1.15139i
$598$	15.3434i	0.627439i
$599$	−30.8201	−1.25928	−0.629638	−	0.776889i	$-0.716797\pi$
$599$	−30.8201	−1.25928	−0.629638	+	0.776889i	$0.716797\pi$
$600$	0	0
$601$	−7.10654	−0.289882	−0.144941	−	0.989440i	$-0.546299\pi$
$601$	−7.10654	−0.289882	−0.144941	+	0.989440i	$0.546299\pi$
$602$	20.6865i	0.843120i
$603$	3.34430i	0.136190i
$604$	7.83484	0.318795
$605$	0	0
$606$	15.8127	0.642349
$607$	2.01531i	0.0817987i	0.999163	+	0.0408994i	$0.0130223\pi$
$607$	2.01531i	0.0817987i	−0.999163	+	0.0408994i	$0.986978\pi$
$608$	− 5.80602i	− 0.235465i
$609$	8.33861	0.337897
$610$	0	0
$611$	56.2286	2.27477
$612$	− 0.909056i	− 0.0367464i
$613$	11.6096i	0.468909i	0.972127	+	0.234455i	$0.0753304\pi$
$613$	11.6096i	0.468909i	−0.972127	+	0.234455i	$0.924670\pi$
$614$	23.3122	0.940803
$615$	0	0
$616$	41.5528	1.67421
$617$	12.4307i	0.500442i	0.968189	+	0.250221i	$0.0805033\pi$
$617$	12.4307i	0.500442i	−0.968189	+	0.250221i	$0.919497\pi$
$618$	7.79499i	0.313560i
$619$	−3.85424	−0.154915	−0.0774575	−	0.996996i	$-0.524680\pi$
$619$	−3.85424	−0.154915	−0.0774575	+	0.996996i	$0.524680\pi$
$620$	0	0
$621$	−22.9729	−0.921873
$622$	20.7472i	0.831888i
$623$	11.0200i	0.441509i
$624$	3.12062	0.124925
$625$	0	0
$626$	13.7187	0.548311
$627$	− 4.66635i	− 0.186356i
$628$	13.5844i	0.542075i
$629$	0.102029	0.00406814
$630$	0	0
$631$	−16.8794	−0.671958	−0.335979	−	0.941870i	$-0.609067\pi$
$631$	−16.8794	−0.671958	−0.335979	+	0.941870i	$0.609067\pi$
$632$	14.6979i	0.584652i
$633$	29.6873i	1.17997i
$634$	25.9273	1.02970
$635$	0	0
$636$	8.39838	0.333017
$637$	− 83.8098i	− 3.32067i
$638$	− 2.66730i	− 0.105600i
$639$	−3.59456	−0.142199
$640$	0	0
$641$	43.4855	1.71757	0.858787	−	0.512332i	$-0.171218\pi$
$641$	43.4855	1.71757	0.858787	+	0.512332i	$0.171218\pi$
$642$	− 15.7639i	− 0.622153i
$643$	− 11.0689i	− 0.436514i	−0.975891	−	0.218257i	$-0.929963\pi$
$643$	− 11.0689i	− 0.436514i	0.975891	−	0.218257i	$-0.0700370\pi$
$644$	27.5787	1.08675
$645$	0	0
$646$	−0.879381	−0.0345988
$647$	5.61766i	0.220853i	0.993884	+	0.110427i	$0.0352217\pi$
$647$	5.61766i	0.220853i	−0.993884	+	0.110427i	$0.964778\pi$
$648$	− 18.2351i	− 0.716341i
$649$	−4.24634	−0.166683
$650$	0	0
$651$	43.2805	1.69630
$652$	13.8195i	0.541213i
$653$	− 44.5211i	− 1.74224i	−0.491066	−	0.871122i	$-0.663393\pi$
$653$	− 44.5211i	− 1.74224i	0.491066	−	0.871122i	$-0.336607\pi$
$654$	19.8613	0.776639
$655$	0	0
$656$	4.73267	0.184780
$657$	− 5.74738i	− 0.224227i
$658$	50.5517i	1.97071i
$659$	6.89154	0.268456	0.134228	−	0.990950i	$-0.457144\pi$
$659$	6.89154	0.268456	0.134228	+	0.990950i	$0.457144\pi$
$660$	0	0
$661$	−44.3989	−1.72692	−0.863458	−	0.504421i	$-0.831706\pi$
$661$	−44.3989	−1.72692	−0.863458	+	0.504421i	$0.831706\pi$
$662$	− 8.13678i	− 0.316245i
$663$	− 7.57393i	− 0.294147i
$664$	5.32468	0.206637
$665$	0	0
$666$	−0.0489880	−0.00189825
$667$	− 4.42607i	− 0.171378i
$668$	− 20.8039i	− 0.804926i
$669$	−0.946657	−0.0365999
$670$	0	0
$671$	17.2875	0.667377
$672$	44.9574i	1.73427i
$673$	− 38.6214i	− 1.48875i	−0.667763	−	0.744374i	$-0.732748\pi$
$673$	− 38.6214i	− 1.48875i	0.667763	−	0.744374i	$-0.267252\pi$
$674$	−18.9383	−0.729476
$675$	0	0
$676$	−10.5315	−0.405057
$677$	43.3917i	1.66768i	0.552006	+	0.833840i	$0.313862\pi$
$677$	43.3917i	1.66768i	−0.552006	+	0.833840i	$0.686138\pi$
$678$	6.90293i	0.265105i
$679$	10.8770	0.417420
$680$	0	0
$681$	26.8784	1.02998
$682$	− 13.8443i	− 0.530126i
$683$	34.7123i	1.32823i	0.747631	+	0.664114i	$0.231191\pi$
$683$	34.7123i	1.32823i	−0.747631	+	0.664114i	$0.768809\pi$
$684$	−0.844150	−0.0322769
$685$	0	0
$686$	46.5779	1.77835
$687$	14.9222i	0.569316i
$688$	− 2.23322i	− 0.0851406i
$689$	−18.7195	−0.713158
$690$	0	0
$691$	2.94570	0.112060	0.0560299	−	0.998429i	$-0.482156\pi$
$691$	2.94570	0.112060	0.0560299	+	0.998429i	$0.482156\pi$
$692$	− 0.762048i	− 0.0289687i
$693$	− 9.66649i	− 0.367200i
$694$	−17.2589	−0.655138
$695$	0	0
$696$	4.50938	0.170928
$697$	− 11.4865i	− 0.435081i
$698$	4.12076i	0.155973i
$699$	12.5441	0.474463
$700$	0	0
$701$	18.5920	0.702210	0.351105	−	0.936336i	$-0.385806\pi$
$701$	18.5920	0.702210	0.351105	+	0.936336i	$0.385806\pi$
$702$	20.8663i	0.787546i
$703$	− 0.0947438i	− 0.00357333i
$704$	11.6891	0.440549
$705$	0	0
$706$	10.2592	0.386109
$707$	63.3519i	2.38259i
$708$	− 2.87136i	− 0.107912i
$709$	−39.8443	−1.49638	−0.748192	−	0.663482i	$-0.769078\pi$
$709$	−39.8443	−1.49638	−0.748192	+	0.663482i	$0.769078\pi$
$710$	0	0
$711$	3.41920	0.128230
$712$	5.95946i	0.223340i
$713$	− 22.9729i	− 0.860344i
$714$	6.80926	0.254830
$715$	0	0
$716$	−33.1780	−1.23992
$717$	37.8443i	1.41332i
$718$	14.4156i	0.537987i
$719$	−21.2321	−0.791824	−0.395912	−	0.918288i	$-0.629572\pi$
$719$	−21.2321	−0.791824	−0.395912	+	0.918288i	$0.629572\pi$
$720$	0	0
$721$	−31.2297	−1.16306
$722$	0.816594i	0.0303905i
$723$	− 39.6516i	− 1.47466i
$724$	9.27052	0.344536
$725$	0	0
$726$	−2.26124	−0.0839225
$727$	− 49.1658i	− 1.82346i	−0.410792	−	0.911729i	$-0.634748\pi$
$727$	− 49.1658i	− 1.82346i	0.410792	−	0.911729i	$-0.365252\pi$
$728$	− 62.6287i	− 2.32118i
$729$	−30.0393	−1.11257
$730$	0	0
$731$	−5.42015	−0.200472
$732$	11.6898i	0.432066i
$733$	− 1.60498i	− 0.0592815i	−0.999561	−	0.0296407i	$-0.990564\pi$
$733$	− 1.60498i	− 0.0592815i	0.999561	−	0.0296407i	$-0.00943632\pi$
$734$	−3.62085	−0.133648
$735$	0	0
$736$	23.8630	0.879603
$737$	− 16.0202i	− 0.590111i
$738$	5.51512i	0.203014i
$739$	−8.13264	−0.299164	−0.149582	−	0.988749i	$-0.547793\pi$
$739$	−8.13264	−0.299164	−0.149582	+	0.988749i	$0.547793\pi$
$740$	0	0
$741$	−7.03316	−0.258370
$742$	− 16.8296i	− 0.617834i
$743$	42.9261i	1.57481i	0.616439	+	0.787403i	$0.288575\pi$
$743$	42.9261i	1.57481i	−0.616439	+	0.787403i	$0.711425\pi$
$744$	23.4054	0.858083
$745$	0	0
$746$	−17.0452	−0.624070
$747$	− 1.23869i	− 0.0453212i
$748$	4.35465i	0.159222i
$749$	63.1564	2.30768
$750$	0	0
$751$	4.05685	0.148037	0.0740183	−	0.997257i	$-0.476418\pi$
$751$	4.05685	0.148037	0.0740183	+	0.997257i	$0.476418\pi$
$752$	− 5.45731i	− 0.199008i
$753$	− 19.3830i	− 0.706355i
$754$	−4.02018	−0.146406
$755$	0	0
$756$	37.5057	1.36407
$757$	22.6151i	0.821960i	0.911644	+	0.410980i	$0.134813\pi$
$757$	22.6151i	0.821960i	−0.911644	+	0.410980i	$0.865187\pi$
$758$	5.55279i	0.201687i
$759$	19.1789	0.696151
$760$	0	0
$761$	−41.3609	−1.49933	−0.749666	−	0.661817i	$-0.769786\pi$
$761$	−41.3609	−1.49933	−0.749666	+	0.661817i	$0.769786\pi$
$762$	− 10.8233i	− 0.392087i
$763$	79.5720i	2.88070i
$764$	−5.21610	−0.188712
$765$	0	0
$766$	−8.90725	−0.321832
$767$	6.40011i	0.231095i
$768$	22.4922i	0.811616i
$769$	−17.9196	−0.646197	−0.323099	−	0.946365i	$-0.604725\pi$
$769$	−17.9196	−0.646197	−0.323099	+	0.946365i	$0.604725\pi$
$770$	0	0
$771$	0.280309	0.0100951
$772$	12.2750i	0.441787i
$773$	21.9043i	0.787843i	0.919144	+	0.393921i	$0.128882\pi$
$773$	21.9043i	0.787843i	−0.919144	+	0.393921i	$0.871118\pi$
$774$	2.60243	0.0935426
$775$	0	0
$776$	5.88209	0.211155
$777$	0.733623i	0.0263186i
$778$	− 17.0934i	− 0.612829i
$779$	−10.6663	−0.382162
$780$	0	0
$781$	17.2190	0.616144
$782$	− 3.61430i	− 0.129247i
$783$	− 6.01923i	− 0.215110i
$784$	−8.13423	−0.290508
$785$	0	0
$786$	−2.70576	−0.0965112
$787$	− 31.6354i	− 1.12768i	−0.825884	−	0.563840i	$-0.809324\pi$
$787$	− 31.6354i	− 1.12768i	0.825884	−	0.563840i	$-0.190676\pi$
$788$	− 5.12768i	− 0.182666i
$789$	−11.3482	−0.404007
$790$	0	0
$791$	−27.6558	−0.983326
$792$	− 5.22748i	− 0.185750i
$793$	− 26.0559i	− 0.925272i
$794$	−10.7154	−0.380275
$795$	0	0
$796$	24.3790	0.864090
$797$	− 15.4486i	− 0.547217i	−0.961841	−	0.273608i	$-0.911783\pi$
$797$	− 15.4486i	− 0.547217i	0.961841	−	0.273608i	$-0.0882172\pi$
$798$	− 6.32308i	− 0.223835i
$799$	−13.2452	−0.468583
$800$	0	0
$801$	1.38636	0.0489845
$802$	− 9.43394i	− 0.333124i
$803$	27.5317i	0.971571i
$804$	10.8328	0.382044
$805$	0	0
$806$	−20.8663	−0.734983
$807$	7.23385i	0.254644i
$808$	34.2597i	1.20525i
$809$	32.9326	1.15785	0.578924	−	0.815382i	$-0.303473\pi$
$809$	32.9326	1.15785	0.578924	+	0.815382i	$0.303473\pi$
$810$	0	0
$811$	−25.5895	−0.898567	−0.449284	−	0.893389i	$-0.648321\pi$
$811$	−25.5895	−0.898567	−0.449284	+	0.893389i	$0.648321\pi$
$812$	7.22601i	0.253583i
$813$	− 15.2622i	− 0.535270i
$814$	0.234667	0.00822508
$815$	0	0
$816$	−0.735094	−0.0257334
$817$	5.03316i	0.176088i
$818$	15.4690i	0.540860i
$819$	−14.5694	−0.509097
$820$	0	0
$821$	17.8674	0.623575	0.311788	−	0.950152i	$-0.399072\pi$
$821$	17.8674	0.623575	0.311788	+	0.950152i	$0.399072\pi$
$822$	2.75062i	0.0959389i
$823$	18.4533i	0.643242i	0.946868	+	0.321621i	$0.104228\pi$
$823$	18.4533i	0.643242i	−0.946868	+	0.321621i	$0.895772\pi$
$824$	−16.8885	−0.588339
$825$	0	0
$826$	−5.75395	−0.200206
$827$	47.5460i	1.65334i	0.562690	+	0.826668i	$0.309767\pi$
$827$	47.5460i	1.65334i	−0.562690	+	0.826668i	$0.690233\pi$
$828$	− 3.46950i	− 0.120573i
$829$	−19.0308	−0.660965	−0.330483	−	0.943812i	$-0.607212\pi$
$829$	−19.0308	−0.660965	−0.330483	+	0.943812i	$0.607212\pi$
$830$	0	0
$831$	−34.8145	−1.20770
$832$	− 17.6179i	− 0.610790i
$833$	19.7423i	0.684029i
$834$	−28.2911	−0.979640
$835$	0	0
$836$	4.04373	0.139855
$837$	− 31.2420i	− 1.07988i
$838$	− 22.2656i	− 0.769151i
$839$	−3.04022	−0.104960	−0.0524801	−	0.998622i	$-0.516713\pi$
$839$	−3.04022	−0.104960	−0.0524801	+	0.998622i	$0.516713\pi$
$840$	0	0
$841$	−27.8403	−0.960011
$842$	5.44370i	0.187602i
$843$	6.08280i	0.209503i
$844$	−25.7262	−0.885534
$845$	0	0
$846$	6.35957	0.218647
$847$	− 9.05940i	− 0.311285i
$848$	1.81684i	0.0623906i
$849$	20.0979	0.689758
$850$	0	0
$851$	0.389401	0.0133485
$852$	11.6434i	0.398898i
$853$	18.2201i	0.623844i	0.950108	+	0.311922i	$0.100973\pi$
$853$	18.2201i	0.623844i	−0.950108	+	0.311922i	$0.899027\pi$
$854$	23.4253	0.801596
$855$	0	0
$856$	34.1539	1.16736
$857$	19.3611i	0.661363i	0.943742	+	0.330682i	$0.107279\pi$
$857$	19.3611i	0.661363i	−0.943742	+	0.330682i	$0.892721\pi$
$858$	− 17.4202i	− 0.594714i
$859$	−3.44129	−0.117415	−0.0587077	−	0.998275i	$-0.518698\pi$
$859$	−3.44129	−0.117415	−0.0587077	+	0.998275i	$0.518698\pi$
$860$	0	0
$861$	82.5921	2.81473
$862$	− 26.5024i	− 0.902674i
$863$	26.5471i	0.903674i	0.892101	+	0.451837i	$0.149231\pi$
$863$	26.5471i	0.903674i	−0.892101	+	0.451837i	$0.850769\pi$
$864$	32.4525	1.10406
$865$	0	0
$866$	27.6146	0.938383
$867$	− 24.3694i	− 0.827630i
$868$	37.5057i	1.27303i
$869$	−16.3790	−0.555619
$870$	0	0
$871$	−24.1458	−0.818148
$872$	43.0312i	1.45722i
$873$	− 1.36836i	− 0.0463120i
$874$	−3.35624	−0.113527
$875$	0	0
$876$	−18.6168	−0.629004
$877$	20.5495i	0.693908i	0.937882	+	0.346954i	$0.112784\pi$
$877$	20.5495i	0.693908i	−0.937882	+	0.346954i	$0.887216\pi$
$878$	22.7383i	0.767380i
$879$	14.9146	0.503059
$880$	0	0
$881$	−31.1911	−1.05085	−0.525427	−	0.850839i	$-0.676094\pi$
$881$	−31.1911	−1.05085	−0.525427	+	0.850839i	$0.676094\pi$
$882$	− 9.47906i	− 0.319177i
$883$	− 14.1861i	− 0.477401i	−0.971093	−	0.238701i	$-0.923279\pi$
$883$	− 14.1861i	− 0.477401i	0.971093	−	0.238701i	$-0.0767214\pi$
$884$	6.56336	0.220750
$885$	0	0
$886$	18.5983	0.624822
$887$	46.6046i	1.56483i	0.622757	+	0.782415i	$0.286012\pi$
$887$	46.6046i	1.56483i	−0.622757	+	0.782415i	$0.713988\pi$
$888$	0.396732i	0.0133134i
$889$	43.3623	1.45433
$890$	0	0
$891$	20.3207	0.680768
$892$	− 0.820347i	− 0.0274672i
$893$	12.2995i	0.411588i
$894$	−12.2952	−0.411214
$895$	0	0
$896$	−42.6061	−1.42337
$897$	− 28.9066i	− 0.965164i
$898$	− 20.2930i	− 0.677185i
$899$	6.01923	0.200752
$900$	0	0
$901$	4.40959	0.146905
$902$	− 26.4191i	− 0.879658i
$903$	− 38.9729i	− 1.29694i
$904$	−14.9558	−0.497422
$905$	0	0
$906$	7.38297	0.245283
$907$	− 0.754028i	− 0.0250371i	−0.999922	−	0.0125185i	$-0.996015\pi$
$907$	− 0.754028i	− 0.0250371i	0.999922	−	0.0125185i	$-0.00398488\pi$
$908$	23.2921i	0.772976i
$909$	7.96988	0.264344
$910$	0	0
$911$	−53.1413	−1.76065	−0.880325	−	0.474371i	$-0.842675\pi$
$911$	−53.1413	−1.76065	−0.880325	+	0.474371i	$0.842675\pi$
$912$	0.682609i	0.0226034i
$913$	5.93368i	0.196376i
$914$	5.98784	0.198060
$915$	0	0
$916$	−12.9311	−0.427257
$917$	− 10.8403i	− 0.357979i
$918$	− 4.91527i	− 0.162228i
$919$	−37.4202	−1.23438	−0.617189	−	0.786815i	$-0.711728\pi$
$919$	−37.4202	−1.23438	−0.617189	+	0.786815i	$0.711728\pi$
$920$	0	0
$921$	−43.9196	−1.44720
$922$	8.41709i	0.277202i
$923$	− 25.9526i	− 0.854241i
$924$	−31.3116	−1.03007
$925$	0	0
$926$	6.37147	0.209379
$927$	3.92880i	0.129039i
$928$	6.25244i	0.205247i
$929$	19.1981	0.629871	0.314935	−	0.949113i	$-0.398017\pi$
$929$	19.1981	0.629871	0.314935	+	0.949113i	$0.398017\pi$
$930$	0	0
$931$	18.3327	0.600830
$932$	10.8704i	0.356072i
$933$	− 39.0873i	− 1.27966i
$934$	6.02355	0.197096
$935$	0	0
$936$	−7.87890	−0.257530
$937$	− 20.0095i	− 0.653681i	−0.945080	−	0.326840i	$-0.894016\pi$
$937$	− 20.0095i	− 0.653681i	0.945080	−	0.326840i	$-0.105984\pi$
$938$	− 21.7080i	− 0.708790i
$939$	−25.8458	−0.843445
$940$	0	0
$941$	15.3327	0.499832	0.249916	−	0.968268i	$-0.419597\pi$
$941$	15.3327	0.499832	0.249916	+	0.968268i	$0.419597\pi$
$942$	12.8009i	0.417076i
$943$	− 43.8392i	− 1.42760i
$944$	0.621168	0.0202173
$945$	0	0
$946$	−12.4664	−0.405319
$947$	− 29.8217i	− 0.969076i	−0.874770	−	0.484538i	$-0.838988\pi$
$947$	− 29.8217i	− 0.969076i	0.874770	−	0.484538i	$-0.161012\pi$
$948$	− 11.0754i	− 0.359713i
$949$	41.4959	1.34702
$950$	0	0
$951$	−48.8464	−1.58395
$952$	14.7529i	0.478143i
$953$	− 31.4938i	− 1.02018i	−0.860120	−	0.510091i	$-0.829612\pi$
$953$	− 31.4938i	− 1.02018i	0.860120	−	0.510091i	$-0.170388\pi$
$954$	−2.11722	−0.0685475
$955$	0	0
$956$	−32.7948	−1.06066
$957$	5.02514i	0.162440i
$958$	13.1845i	0.425973i
$959$	−11.0200	−0.355856
$960$	0	0
$961$	0.242050	0.00780806
$962$	− 0.353692i	− 0.0114035i
$963$	− 7.94528i	− 0.256033i
$964$	34.3610	1.10669
$965$	0	0
$966$	25.9882	0.836156
$967$	1.16143i	0.0373490i	0.999826	+	0.0186745i	$0.00594462\pi$
$967$	1.16143i	0.0373490i	−0.999826	+	0.0186745i	$0.994055\pi$
$968$	− 4.89917i	− 0.157465i
$969$	1.65673	0.0532220
$970$	0	0
$971$	18.4557	0.592272	0.296136	−	0.955146i	$-0.404302\pi$
$971$	18.4557	0.592272	0.296136	+	0.955146i	$0.404302\pi$
$972$	− 8.61438i	− 0.276306i
$973$	− 113.345i	− 3.63367i
$974$	6.86401	0.219937
$975$	0	0
$976$	−2.52888	−0.0809474
$977$	5.62735i	0.180035i	0.995940	+	0.0900175i	$0.0286923\pi$
$977$	5.62735i	0.180035i	−0.995940	+	0.0900175i	$0.971308\pi$
$978$	13.0225i	0.416413i
$979$	−6.64107	−0.212249
$980$	0	0
$981$	10.0104	0.319608
$982$	− 29.4672i	− 0.940338i
$983$	25.1228i	0.801293i	0.916233	+	0.400647i	$0.131214\pi$
$983$	25.1228i	0.801293i	−0.916233	+	0.400647i	$0.868786\pi$
$984$	44.6644	1.42385
$985$	0	0
$986$	0.946996	0.0301585
$987$	− 95.2382i	− 3.03147i
$988$	− 6.09474i	− 0.193900i
$989$	−20.6865	−0.657793
$990$	0	0
$991$	−41.8749	−1.33020	−0.665100	−	0.746754i	$-0.731611\pi$
$991$	−41.8749	−1.33020	−0.665100	+	0.746754i	$0.731611\pi$
$992$	32.4525i	1.03037i
$993$	15.3295i	0.486467i
$994$	23.3324	0.740059
$995$	0	0
$996$	−4.01234	−0.127136
$997$	− 37.0346i	− 1.17290i	−0.809986	−	0.586449i	$-0.800525\pi$
$997$	− 37.0346i	− 1.17290i	0.809986	−	0.586449i	$-0.199475\pi$
$998$	2.69505i	0.0853102i
$999$	0.529566	0.0167547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.b.e.324.5		8
5.2	odd	4		475.2.a.i.1.2		4
5.3	odd	4		95.2.a.b.1.3	✓	4
5.4	even	2	inner	475.2.b.e.324.4		8
15.2	even	4		4275.2.a.bo.1.3		4
15.8	even	4		855.2.a.m.1.2		4
20.3	even	4		1520.2.a.t.1.2		4
20.7	even	4		7600.2.a.cf.1.3		4
35.13	even	4		4655.2.a.y.1.3		4
40.3	even	4		6080.2.a.ch.1.3		4
40.13	odd	4		6080.2.a.cc.1.2		4
95.18	even	4		1805.2.a.p.1.2		4
95.37	even	4		9025.2.a.bf.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.a.b.1.3	✓	4	5.3	odd	4
475.2.a.i.1.2		4	5.2	odd	4
475.2.b.e.324.4		8	5.4	even	2	inner
475.2.b.e.324.5		8	1.1	even	1	trivial
855.2.a.m.1.2		4	15.8	even	4
1520.2.a.t.1.2		4	20.3	even	4
1805.2.a.p.1.2		4	95.18	even	4
4275.2.a.bo.1.3		4	15.2	even	4
4655.2.a.y.1.3		4	35.13	even	4
6080.2.a.cc.1.2		4	40.13	odd	4
6080.2.a.ch.1.3		4	40.3	even	4
7600.2.a.cf.1.3		4	20.7	even	4
9025.2.a.bf.1.3		4	95.37	even	4

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+0.816594i q^{2} -1.53844i q^{3} +1.33317 q^{4} +1.25628 q^{6} +5.03316i q^{7} +2.72185i q^{8} +0.633188 q^{9} -3.03316 q^{11} -2.05101i q^{12} +4.57160i q^{13} -4.11005 q^{14} +0.443701 q^{16} -1.07689i q^{17} +0.517058i q^{18} -1.00000 q^{19} +7.74324 q^{21} -2.47686i q^{22} -4.11005i q^{23} +4.18742 q^{24} -3.73315 q^{26} -5.58946i q^{27} +6.71008i q^{28} +1.07689 q^{29} +5.58946 q^{31} +5.80602i q^{32} +4.66635i q^{33} +0.879381 q^{34} +0.844150 q^{36} +0.0947438i q^{37} -0.816594i q^{38} +7.03316 q^{39} +10.6663 q^{41} +6.32308i q^{42} -5.03316i q^{43} -4.04373 q^{44} +3.35624 q^{46} -12.2995i q^{47} -0.682609i q^{48} -18.3327 q^{49} -1.65673 q^{51} +6.09474i q^{52} +4.09474i q^{53} +4.56432 q^{54} -13.6995 q^{56} +1.53844i q^{57} +0.879381i q^{58} +1.39997 q^{59} -5.69951 q^{61} +4.56432i q^{62} +3.18694i q^{63} -3.85376 q^{64} -3.81051 q^{66} +5.28168i q^{67} -1.43568i q^{68} -6.32308 q^{69} -5.67692 q^{71} +1.72344i q^{72} -9.07689i q^{73} -0.0773672 q^{74} -1.33317 q^{76} -15.2664i q^{77} +5.74324i q^{78} +5.39997 q^{79} -6.69951 q^{81} +8.71008i q^{82} -1.95627i q^{83} +10.3231 q^{84} +4.11005 q^{86} -1.65673i q^{87} -8.25581i q^{88} +2.18949 q^{89} -23.0096 q^{91} -5.47941i q^{92} -8.59907i q^{93} +10.0437 q^{94} +8.93225 q^{96} -2.16106i q^{97} -14.9704i q^{98} -1.92056 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 16 q^{4} - 16 q^{9} + 8 q^{11} + 16 q^{14} + 8 q^{16} - 8 q^{19} - 8 q^{21} + 48 q^{24} + 8 q^{26} - 8 q^{29} + 8 q^{31} + 8 q^{34} + 80 q^{36} + 24 q^{39} + 32 q^{41} - 48 q^{44} - 40 q^{49} - 72 q^{51}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 16 * q^4 - 16 * q^9 + 8 * q^11 + 16 * q^14 + 8 * q^16 - 8 * q^19 - 8 * q^21 + 48 * q^24 + 8 * q^26 - 8 * q^29 + 8 * q^31 + 8 * q^34 + 80 * q^36 + 24 * q^39 + 32 * q^41 - 48 * q^44 - 40 * q^49 - 72 * q^51 + 40 * q^54 - 24 * q^56 + 40 * q^61 + 8 * q^64 - 56 * q^66 - 56 * q^69 - 40 * q^71 - 64 * q^74 + 16 * q^76 + 32 * q^79 + 32 * q^81 + 88 * q^84 - 16 * q^86 - 8 * q^89 - 72 * q^91 + 96 * q^94 - 104 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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