LMFDB - Embedded newform 855.2.dl.a.523.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(127,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([0, 9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.127"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.dl (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,12,0,0,12,0,0] 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:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			523.6
Character	$\chi$	$=$	855.523
Dual form			855.2.dl.a.667.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.983828 - 1.40505i) q^{2} +(-0.322212 - 0.885271i) q^{4} +(-2.19633 + 0.419667i) q^{5} +(0.0743036 + 0.277305i) q^{7} +(1.75276 + 0.469650i) q^{8} +(-1.57116 + 3.49884i) q^{10} +(2.29500 + 3.97505i) q^{11} +(2.46682 - 0.215819i) q^{13} +(0.462730 + 0.168420i) q^{14} +(3.82765 - 3.21178i) q^{16} +(-3.94756 - 2.76411i) q^{17} +(1.73832 + 3.99728i) q^{19} +(1.07920 + 1.80913i) q^{20} +(7.84303 + 0.686176i) q^{22} +(6.88562 + 3.21082i) q^{23} +(4.64776 - 1.84346i) q^{25} +(2.12369 - 3.67833i) q^{26} +(0.221548 - 0.155130i) q^{28} +(-0.000506761 + 0.00287398i) q^{29} +(2.87440 + 1.65954i) q^{31} +(-0.430665 - 4.92252i) q^{32} +(-7.76743 + 2.82711i) q^{34} +(-0.279571 - 0.577871i) q^{35} +(-5.46158 - 5.46158i) q^{37} +(7.32659 + 1.49020i) q^{38} +(-4.04674 - 0.295934i) q^{40} +(-0.132829 - 0.158299i) q^{41} +(0.0847905 + 0.181834i) q^{43} +(2.77952 - 3.31250i) q^{44} +(11.2856 - 6.51576i) q^{46} +(2.89119 + 4.12905i) q^{47} +(5.99080 - 3.45879i) q^{49} +(1.98245 - 8.34398i) q^{50} +(-0.985897 - 2.11426i) q^{52} +(1.11603 - 2.39334i) q^{53} +(-6.70877 - 7.76740i) q^{55} +0.520945i q^{56} +(0.00353953 + 0.00353953i) q^{58} +(-0.369926 - 2.09795i) q^{59} +(-3.76621 + 1.37079i) q^{61} +(5.15965 - 2.40598i) q^{62} +(1.31435 + 0.758840i) q^{64} +(-5.32738 + 1.50925i) q^{65} +(7.42839 - 5.20141i) q^{67} +(-1.17503 + 4.38529i) q^{68} +(-1.08699 - 0.175714i) q^{70} +(-4.33266 + 11.9039i) q^{71} +(-10.7580 - 0.941200i) q^{73} +(-13.0471 + 2.30055i) q^{74} +(2.97856 - 2.82686i) q^{76} +(-0.931774 + 0.931774i) q^{77} +(-4.20092 + 3.52499i) q^{79} +(-7.05892 + 8.66048i) q^{80} +(-0.353099 + 0.0308922i) q^{82} +(-15.4419 + 4.13763i) q^{83} +(9.83016 + 4.41425i) q^{85} +(0.338905 + 0.0597581i) q^{86} +(2.15569 + 8.04514i) q^{88} +(12.1125 + 10.1636i) q^{89} +(0.243141 + 0.668024i) q^{91} +(0.623812 - 7.13020i) q^{92} +8.64596 q^{94} +(-5.49546 - 8.04984i) q^{95} +(-3.42156 + 4.88649i) q^{97} +(1.03414 - 11.8202i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.983828	−	1.40505i	0.695671	−	0.993521i	−0.303501	−	0.952831i	$-0.598155\pi$
$2$	0.983828	−	1.40505i	0.695671	−	0.993521i	0.999172	−	0.0406901i	$-0.0129556\pi$
$3$		0			0
$3$		0			0
$4$	−0.322212	−	0.885271i	−0.161106	−	0.442635i
$5$	−2.19633	+	0.419667i	−0.982230	+	0.187681i
$5$	−2.19633	+	0.419667i	−0.982230	+	0.187681i
$6$		0			0
$7$	0.0743036	+	0.277305i	0.0280841	+	0.104811i	0.978545	−	0.206032i	$-0.0660551\pi$
$7$	0.0743036	+	0.277305i	0.0280841	+	0.104811i	−0.950461	+	0.310844i	$0.899388\pi$
$8$	1.75276	+	0.469650i	0.619693	+	0.166046i
$9$		0			0
$10$	−1.57116	+	3.49884i	−0.496844	+	1.10643i
$11$	2.29500	+	3.97505i	0.691967	+	1.19852i	0.971192	+	0.238297i	$0.0765891\pi$
$11$	2.29500	+	3.97505i	0.691967	+	1.19852i	−0.279225	+	0.960226i	$0.590078\pi$
$12$		0			0
$13$	2.46682	−	0.215819i	0.684172	−	0.0598573i	0.260230	−	0.965547i	$-0.416202\pi$
$13$	2.46682	−	0.215819i	0.684172	−	0.0598573i	0.423942	+	0.905689i	$0.360646\pi$
$14$	0.462730	+	0.168420i	0.123670	+	0.0450121i
$15$		0			0
$16$	3.82765	−	3.21178i	0.956913	−	0.802946i
$17$	−3.94756	−	2.76411i	−0.957423	−	0.670395i	−0.0132738	−	0.999912i	$-0.504225\pi$
$17$	−3.94756	−	2.76411i	−0.957423	−	0.670395i	−0.944150	+	0.329517i	$0.893114\pi$
$18$		0			0
$19$	1.73832	+	3.99728i	0.398799	+	0.917038i
$19$	1.73832	+	3.99728i	0.398799	+	0.917038i
$20$	1.07920	+	1.80913i	0.241317	+	0.404533i
$21$		0			0
$22$	7.84303	+	0.686176i	1.67214	+	0.146293i
$23$	6.88562	+	3.21082i	1.43575	+	0.669501i	0.975845	−	0.218466i	$-0.0701053\pi$
$23$	6.88562	+	3.21082i	1.43575	+	0.669501i	0.459906	+	0.887968i	$0.347883\pi$
$24$		0			0
$25$	4.64776	−	1.84346i	0.929552	−	0.368691i
$26$	2.12369	−	3.67833i	0.416489	−	0.721380i
$27$		0			0
$28$	0.221548	−	0.155130i	0.0418687	−	0.0293168i
$29$	−0.000506761		0.00287398i	−9.41031e−5		0.000533685i	−0.984855	−	0.173381i	$-0.944531\pi$
$29$	−0.000506761		0.00287398i	−9.41031e−5		0.000533685i	0.984761	+	0.173915i	$0.0556418\pi$
$30$		0			0
$31$	2.87440	+	1.65954i	0.516258	+	0.298062i	0.735402	−	0.677631i	$-0.236993\pi$
$31$	2.87440	+	1.65954i	0.516258	+	0.298062i	−0.219144	+	0.975692i	$0.570327\pi$
$32$	−0.430665	−	4.92252i	−0.0761315	−	0.870187i
$33$		0			0
$34$	−7.76743	+	2.82711i	−1.33210	+	0.484846i
$35$	−0.279571	−	0.577871i	−0.0472562	−	0.0976781i
$36$		0			0
$37$	−5.46158	−	5.46158i	−0.897878	−	0.897878i	0.0973701	−	0.995248i	$-0.468957\pi$
$37$	−5.46158	−	5.46158i	−0.897878	−	0.897878i	−0.995248	+	0.0973701i	$0.968957\pi$
$38$	7.32659	+	1.49020i	1.18853	+	0.241742i
$39$		0			0
$40$	−4.04674	−	0.295934i	−0.639845	−	0.0467913i
$41$	−0.132829	−	0.158299i	−0.0207444	−	0.0247222i	0.755573	−	0.655065i	$-0.227359\pi$
$41$	−0.132829	−	0.158299i	−0.0207444	−	0.0247222i	−0.776317	+	0.630343i	$0.782914\pi$
$42$		0			0
$43$	0.0847905	+	0.181834i	0.0129304	+	0.0277294i	0.912667	−	0.408704i	$-0.134019\pi$
$43$	0.0847905	+	0.181834i	0.0129304	+	0.0277294i	−0.899737	+	0.436433i	$0.856241\pi$
$44$	2.77952	−	3.31250i	0.419028	−	0.499379i
$45$		0			0
$46$	11.2856	−	6.51576i	1.66397	−	0.960696i
$47$	2.89119	+	4.12905i	0.421724	+	0.602284i	0.972652	−	0.232269i	$-0.0746150\pi$
$47$	2.89119	+	4.12905i	0.421724	+	0.602284i	−0.550928	+	0.834553i	$0.685726\pi$
$48$		0			0
$49$	5.99080	−	3.45879i	0.855829	−	0.494113i
$50$	1.98245	−	8.34398i	0.280360	−	1.18002i
$51$		0			0
$52$	−0.985897	−	2.11426i	−0.136719	−	0.293195i
$53$	1.11603	−	2.39334i	0.153299	−	0.328751i	−0.814627	−	0.579985i	$-0.803058\pi$
$53$	1.11603	−	2.39334i	0.153299	−	0.328751i	0.967926	+	0.251234i	$0.0808363\pi$
$54$		0			0
$55$	−6.70877	−	7.76740i	−0.904610	−	1.04736i
$56$			0.520945i			0.0696142i
$57$		0			0
$58$	0.00353953	+	0.00353953i	0.000464763	+	0.000464763i
$59$	−0.369926	−	2.09795i	−0.0481602	−	0.273130i	0.951213	−	0.308536i	$-0.0998389\pi$
$59$	−0.369926	−	2.09795i	−0.0481602	−	0.273130i	−0.999373	+	0.0354053i	$0.988728\pi$
$60$		0			0
$61$	−3.76621	+	1.37079i	−0.482214	+	0.175511i	−0.571677	−	0.820479i	$-0.693707\pi$
$61$	−3.76621	+	1.37079i	−0.482214	+	0.175511i	0.0894634	+	0.995990i	$0.471485\pi$
$62$	5.15965	−	2.40598i	0.655276	−	0.305560i
$63$		0			0
$64$	1.31435	+	0.758840i	0.164294	+	0.0948550i
$65$	−5.32738	+	1.50925i	−0.660780	+	0.187199i
$66$		0			0
$67$	7.42839	−	5.20141i	0.907522	−	0.635454i	−0.0237737	−	0.999717i	$-0.507568\pi$
$67$	7.42839	−	5.20141i	0.907522	−	0.635454i	0.931296	+	0.364263i	$0.118679\pi$
$68$	−1.17503	+	4.38529i	−0.142494	+	0.531794i
$69$		0			0
$70$	−1.08699	−	0.175714i	−0.129920	−	0.0210018i
$71$	−4.33266	+	11.9039i	−0.514192	+	1.41273i	0.362639	+	0.931930i	$0.381876\pi$
$71$	−4.33266	+	11.9039i	−0.514192	+	1.41273i	−0.876830	+	0.480800i	$0.840346\pi$
$72$		0			0
$73$	−10.7580	−	0.941200i	−1.25912	−	0.110159i	−0.562017	−	0.827126i	$-0.689974\pi$
$73$	−10.7580	−	0.941200i	−1.25912	−	0.110159i	−0.697108	+	0.716967i	$0.745530\pi$
$74$	−13.0471	+	2.30055i	−1.51669	+	0.267433i
$75$		0			0
$76$	2.97856	−	2.82686i	0.341665	−	0.324263i
$77$	−0.931774	+	0.931774i	−0.106186	+	0.106186i
$78$		0			0
$79$	−4.20092	+	3.52499i	−0.472641	+	0.396592i	−0.847757	−	0.530385i	$-0.822047\pi$
$79$	−4.20092	+	3.52499i	−0.472641	+	0.396592i	0.375116	+	0.926978i	$0.377603\pi$
$80$	−7.05892	+	8.66048i	−0.789212	+	0.968271i
$81$		0			0
$82$	−0.353099	+	0.0308922i	−0.0389933	+	0.00341147i
$83$	−15.4419	+	4.13763i	−1.69496	+	0.454164i	−0.971664	−	0.236368i	$-0.924043\pi$
$83$	−15.4419	+	4.13763i	−1.69496	+	0.454164i	−0.723301	+	0.690533i	$0.757376\pi$
$84$		0			0
$85$	9.83016	+	4.41425i	1.06623	+	0.478793i
$86$	0.338905	+	0.0597581i	0.0365451	+	0.00644388i
$87$		0			0
$88$	2.15569	+	8.04514i	0.229797	+	0.857615i
$89$	12.1125	+	10.1636i	1.28392	+	1.07734i	0.992691	+	0.120683i	$0.0385084\pi$
$89$	12.1125	+	10.1636i	1.28392	+	1.07734i	0.291228	+	0.956654i	$0.405936\pi$
$90$		0			0
$91$	0.243141	+	0.668024i	0.0254881	+	0.0700280i
$92$	0.623812	−	7.13020i	0.0650369	−	0.743375i
$93$		0			0
$94$	8.64596			0.891763
$95$	−5.49546	−	8.04984i	−0.563823	−	0.825896i
$96$		0			0
$97$	−3.42156	+	4.88649i	−0.347407	+	0.496148i	−0.954389	−	0.298567i	$-0.903491\pi$
$97$	−3.42156	+	4.88649i	−0.347407	+	0.496148i	0.606982	+	0.794716i	$0.292380\pi$
$98$	1.03414	−	11.8202i	0.104464	−	1.19402i
$99$		0			0
$100$	−3.12952	−	3.52054i	−0.312952	−	0.352054i
$101$	−8.53219	−	7.15936i	−0.848985	−	0.712383i	0.110581	−	0.993867i	$-0.464729\pi$
$101$	−8.53219	−	7.15936i	−0.848985	−	0.712383i	−0.959566	+	0.281484i	$0.909173\pi$
$102$		0			0
$103$	−0.797004	−	0.213557i	−0.0785312	−	0.0210424i	0.219340	−	0.975649i	$-0.429610\pi$
$103$	−0.797004	−	0.213557i	−0.0785312	−	0.0210424i	−0.297871	+	0.954606i	$0.596276\pi$
$104$	4.42509	+	0.780263i	0.433916	+	0.0765111i
$105$		0			0
$106$	−2.26479	−	3.92272i	−0.219975	−	0.381009i
$107$	15.0602	−	4.03536i	1.45592	−	0.390113i	0.557842	−	0.829947i	$-0.311630\pi$
$107$	15.0602	−	4.03536i	1.45592	−	0.390113i	0.898079	+	0.439835i	$0.144963\pi$
$108$		0			0
$109$	−8.88129	−	3.23252i	−0.850673	−	0.309620i	−0.120358	−	0.992731i	$-0.538404\pi$
$109$	−8.88129	−	3.23252i	−0.850673	−	0.309620i	−0.730315	+	0.683111i	$0.760627\pi$
$110$	−17.5139	+	1.78438i	−1.66988	+	0.170134i
$111$		0			0
$112$	1.17505	+	0.822780i	0.111032	+	0.0777454i
$113$	−1.30423	+	1.30423i	−0.122692	+	0.122692i	−0.765787	−	0.643095i	$-0.777650\pi$
$113$	−1.30423	+	1.30423i	−0.122692	+	0.122692i	0.643095	+	0.765787i	$0.277650\pi$
$114$		0			0
$115$	−16.4706	−	4.16236i	−1.53589	−	0.388142i
$116$	0.00270754		0.000477412i	0.000251389		4.43266e-5i
$117$		0			0
$118$	−3.31168	−	1.54426i	−0.304864	−	0.142161i
$119$	0.473183	−	1.30006i	0.0433767	−	0.119176i
$120$		0			0
$121$	−5.03401	+	8.71916i	−0.457637	+	0.792651i
$122$	−1.77927	+	6.64034i	−0.161088	+	0.601188i
$123$		0			0
$124$	0.542972	−	3.07935i	0.0487603	−	0.276534i
$125$	−9.43439	+	5.99935i	−0.843838	+	0.536598i
$126$		0			0
$127$	−0.878208	−	10.0380i	−0.0779284	−	0.890725i	−0.930062	−	0.367402i	$-0.880247\pi$
$127$	−0.878208	−	10.0380i	−0.0779284	−	0.890725i	0.852134	−	0.523324i	$-0.175308\pi$
$128$	11.3160	−	5.27675i	1.00020	−	0.466403i
$129$		0			0
$130$	−3.12065	+	8.97008i	−0.273699	+	0.786728i
$131$	−3.39696	−	19.2651i	−0.296794	−	1.68320i	−0.659820	−	0.751423i	$-0.729368\pi$
$131$	−3.39696	−	19.2651i	−0.296794	−	1.68320i	0.363026	−	0.931779i	$-0.381744\pi$
$132$		0			0
$133$	−0.979301	+	0.779058i	−0.0849162	+	0.0675529i
$134$		−	15.5546i		−	1.34371i
$135$		0			0
$136$	−5.62095	−	6.69879i	−0.481992	−	0.574416i
$137$	4.50418	−	9.65926i	0.384818	−	0.825246i	−0.614521	−	0.788901i	$-0.710651\pi$
$137$	4.50418	−	9.65926i	0.384818	−	0.825246i	0.999339	−	0.0363453i	$-0.0115716\pi$
$138$		0			0
$139$	−9.87278	+	11.7659i	−0.837399	+	0.997973i	0.162538	+	0.986702i	$0.448032\pi$
$139$	−9.87278	+	11.7659i	−0.837399	+	0.997973i	−0.999936	+	0.0112706i	$0.996412\pi$
$140$	−0.421492	+	0.433694i	−0.0356225	+	0.0366538i
$141$		0			0
$142$	12.4630	+	17.7990i	1.04587	+	1.49366i
$143$	6.51922	+	9.31042i	0.545165	+	0.778576i
$144$		0			0
$145$	−9.30989e−5	−	0.00652489i	−7.73144e−6	−	0.000541863i
$146$	−11.9064	+	14.1895i	−0.985382	+	1.17433i
$147$		0			0
$148$	−3.07519	+	6.59477i	−0.252779	+	0.542086i
$149$	−6.22102	−	7.41392i	−0.509646	−	0.607372i	0.448454	−	0.893806i	$-0.351975\pi$
$149$	−6.22102	−	7.41392i	−0.509646	−	0.607372i	−0.958100	+	0.286434i	$0.907530\pi$
$150$		0			0
$151$			3.10459i			0.252648i	0.991989	+	0.126324i	$0.0403179\pi$
$151$			3.10459i			0.252648i	−0.991989	+	0.126324i	$0.959682\pi$
$152$	1.16954	+	7.82266i	0.0948623	+	0.634502i
$153$		0			0
$154$	0.392486	+	2.22590i	0.0316274	+	0.179368i
$155$	−7.00960	−	2.43861i	−0.563024	−	0.195874i
$156$		0			0
$157$	14.6336	−	6.82378i	1.16789	−	0.544597i	0.260744	−	0.965408i	$-0.416032\pi$
$157$	14.6336	−	6.82378i	1.16789	−	0.544597i	0.907148	+	0.420811i	$0.138254\pi$
$158$	0.819812	+	9.37049i	0.0652207	+	0.745476i
$159$		0			0
$160$	3.01170	+	10.6308i	0.238096	+	0.840436i
$161$	−0.378749	+	2.14799i	−0.0298496	+	0.169285i
$162$		0			0
$163$	0.0214015	−	0.0798713i	0.00167629	−	0.00625600i	−0.965083	−	0.261946i	$-0.915636\pi$
$163$	0.0214015	−	0.0798713i	0.00167629	−	0.00625600i	0.966759	+	0.255690i	$0.0823025\pi$
$164$	−0.0973387	+	0.168596i	−0.00760088	+	0.0131651i
$165$		0			0
$166$	−9.37854	+	25.7673i	−0.727916	+	1.99993i
$167$	−7.81520	−	3.64429i	−0.604758	−	0.282003i	0.0960237	−	0.995379i	$-0.469388\pi$
$167$	−7.81520	−	3.64429i	−0.604758	−	0.282003i	−0.700782	+	0.713376i	$0.747165\pi$
$168$		0			0
$169$	−6.76389	+	1.19266i	−0.520299	+	0.0917428i
$170$	15.8734	−	9.46902i	1.21744	−	0.726240i
$171$		0			0
$172$	0.133652	−	0.133652i	0.0101908	−	0.0101908i
$173$	7.73878	+	5.41875i	0.588369	+	0.411980i	0.829495	−	0.558514i	$-0.188628\pi$
$173$	7.73878	+	5.41875i	0.588369	+	0.411980i	−0.241127	+	0.970494i	$0.577517\pi$
$174$		0			0
$175$	0.856545	+	1.15187i	0.0647487	+	0.0870733i
$176$	21.5514	+	7.84408i	1.62450	+	0.591270i
$177$		0			0
$178$	26.1969	−	7.01944i	1.96354	−	0.526130i
$179$	−3.58941	−	6.21705i	−0.268285	−	0.464684i	0.700134	−	0.714012i	$-0.253124\pi$
$179$	−3.58941	−	6.21705i	−0.268285	−	0.464684i	−0.968419	+	0.249328i	$0.919790\pi$
$180$		0			0
$181$	−1.58706	−	0.279841i	−0.117965	−	0.0208004i	0.114354	−	0.993440i	$-0.463520\pi$
$181$	−1.58706	−	0.279841i	−0.117965	−	0.0208004i	−0.232319	+	0.972640i	$0.574631\pi$
$182$	1.17782	+	0.315595i	0.0873056	+	0.0233935i
$183$		0			0
$184$	10.5609	+	8.86161i	0.778557	+	0.653287i
$185$	14.2875	+	9.70341i	1.05044	+	0.713409i
$186$		0			0
$187$	1.92784	−	22.0354i	0.140978	−	1.61139i
$188$	2.72375	−	3.88992i	0.198650	−	0.283702i
$189$		0			0
$190$	−16.7170	−	0.198243i	−1.21278	−	0.0143820i
$191$	−4.58246			−0.331575			−0.165787	−	0.986162i	$-0.553017\pi$
$191$	−4.58246			−0.331575			−0.165787	+	0.986162i	$0.553017\pi$
$192$		0			0
$193$	1.06893	−	12.2179i	0.0769431	−	0.879464i	−0.855419	−	0.517937i	$-0.826700\pi$
$193$	1.06893	−	12.2179i	0.0769431	−	0.879464i	0.932362	−	0.361526i	$-0.117744\pi$
$194$	3.49955	+	9.61494i	0.251253	+	0.690312i
$195$		0			0
$196$	−4.99228	−	4.18902i	−0.356591	−	0.299216i
$197$	−0.0436698	−	0.162978i	−0.00311135	−	0.0116117i	0.964353	−	0.264620i	$-0.0852466\pi$
$197$	−0.0436698	−	0.162978i	−0.00311135	−	0.0116117i	−0.967464	+	0.253009i	$0.918580\pi$
$198$		0			0
$199$	−4.92176	−	0.867839i	−0.348894	−	0.0615195i	−0.00354503	−	0.999994i	$-0.501128\pi$
$199$	−4.92176	−	0.867839i	−0.348894	−	0.0615195i	−0.345349	+	0.938474i	$0.612240\pi$
$200$	9.01218	−	1.04831i	0.637257	−	0.0741267i
$201$		0			0
$202$	−18.4535	+	4.94459i	−1.29838	+	0.347900i
$203$	−0.000834624	0	7.30201e-5i	−5.85791e−5	0	5.12501e-6i
$204$		0			0
$205$	0.358169	+	0.291934i	0.0250156	+	0.0203896i
$206$	−1.08417	+	0.909729i	−0.0755379	+	0.0633838i
$207$		0			0
$208$	8.74896	−	8.74896i	0.606631	−	0.606631i
$209$	−11.8999	+	16.0837i	−0.823135	+	1.11253i
$210$		0			0
$211$	−0.0936993	+	0.0165217i	−0.00645053	+	0.00113740i	−0.176873	−	0.984234i	$-0.556598\pi$
$211$	−0.0936993	+	0.0165217i	−0.00645053	+	0.00113740i	0.170422	+	0.985371i	$0.445487\pi$
$212$	−2.47836	−	0.216828i	−0.170214	−	0.0148918i
$213$		0			0
$214$	9.14671	−	25.1304i	0.625257	−	1.71788i
$215$	−0.262538	−	0.363784i	−0.0179049	−	0.0248098i
$216$		0			0
$217$	−0.246619	+	0.920396i	−0.0167416	+	0.0624805i
$218$	−13.2795	+	9.29842i	−0.899402	+	0.629768i
$219$		0			0
$220$	−4.71461	+	8.44183i	−0.317859	+	0.569148i
$221$	−10.3344	−	5.96660i	−0.695170	−	0.401357i
$222$		0			0
$223$	0.622900	−	0.290463i	0.0417125	−	0.0194508i	−0.401650	−	0.915793i	$-0.631563\pi$
$223$	0.622900	−	0.290463i	0.0417125	−	0.0194508i	0.443363	+	0.896342i	$0.353785\pi$
$224$	1.33304	−	0.485187i	0.0890675	−	0.0324179i
$225$		0			0
$226$	0.549375	+	3.11566i	0.0365439	+	0.207250i
$227$	−3.13234	−	3.13234i	−0.207901	−	0.207901i	0.595474	−	0.803375i	$-0.296964\pi$
$227$	−3.13234	−	3.13234i	−0.207901	−	0.207901i	−0.803375	+	0.595474i	$0.796964\pi$
$228$		0			0
$229$		−	1.64132i		−	0.108462i	−0.998528	−	0.0542308i	$-0.982729\pi$
$229$		−	1.64132i		−	0.108462i	0.998528	−	0.0542308i	$-0.0172707\pi$
$230$	−22.0525	+	19.0470i	−1.45410	+	1.25592i
$231$		0			0
$232$	−0.00223799	+	0.00479939i	−0.000146932	+	0.000315096i
$233$	−4.08407	−	8.75832i	−0.267556	−	0.573776i	0.725925	−	0.687774i	$-0.241412\pi$
$233$	−4.08407	−	8.75832i	−0.267556	−	0.573776i	−0.993481	+	0.113998i	$0.963634\pi$
$234$		0			0
$235$	−8.08285	−	7.85543i	−0.527267	−	0.512432i
$236$	−1.73806	+	1.00347i	−0.113138	+	0.0653204i
$237$		0			0
$238$	−1.36112	−	1.94388i	−0.0882284	−	0.126003i
$239$	5.41584	−	3.12684i	0.350321	−	0.202258i	−0.314505	−	0.949256i	$-0.601839\pi$
$239$	5.41584	−	3.12684i	0.350321	−	0.202258i	0.664827	+	0.746998i	$0.268505\pi$
$240$		0			0
$241$	−8.06290	+	9.60899i	−0.519377	+	0.618970i	−0.960433	−	0.278510i	$-0.910159\pi$
$241$	−8.06290	+	9.60899i	−0.519377	+	0.618970i	0.441056	+	0.897479i	$0.354604\pi$
$242$	7.29827	+	15.6512i	0.469151	+	1.00610i
$243$		0			0
$244$	2.42704	+	2.89243i	0.155375	+	0.185169i
$245$	−11.7063	+	10.1108i	−0.747885	+	0.645955i
$246$		0			0
$247$	5.15081	+	9.48539i	0.327739	+	0.603541i
$248$	4.25873	+	4.25873i	0.270430	+	0.270430i
$249$		0			0
$250$	−0.852420	+	19.1581i	−0.0539118	+	1.21167i
$251$	8.58890	−	3.12610i	0.542127	−	0.197318i	−0.0564182	−	0.998407i	$-0.517968\pi$
$251$	8.58890	−	3.12610i	0.542127	−	0.197318i	0.598545	+	0.801089i	$0.295746\pi$
$252$		0			0
$253$	3.03931	+	34.7395i	0.191080	+	2.18405i
$254$	−14.9679	−	8.64170i	−0.939167	−	0.542228i
$255$		0			0
$256$	3.19183	−	18.1018i	0.199489	−	1.13136i
$257$	24.3625	−	17.0588i	1.51969	−	1.06410i	0.545576	−	0.838062i	$-0.316311\pi$
$257$	24.3625	−	17.0588i	1.51969	−	1.06410i	0.974118	−	0.226040i	$-0.0725779\pi$
$258$		0			0
$259$	1.10871	−	1.92034i	0.0688918	−	0.119324i
$260$	3.05264	+	4.22988i	0.189317	+	0.262326i
$261$		0			0
$262$	−30.4105	−	14.1807i	−1.87877	−	0.876084i
$263$	15.7124	+	1.37466i	0.968867	+	0.0847649i	0.560590	−	0.828093i	$-0.310574\pi$
$263$	15.7124	+	1.37466i	0.968867	+	0.0847649i	0.408277	+	0.912858i	$0.366130\pi$
$264$		0			0
$265$	−1.44678	+	5.72494i	−0.0888748	+	0.351680i
$266$	0.131154	+	2.14243i	0.00804154	+	0.131361i
$267$		0			0
$268$	−6.99818	−	4.90018i	−0.427482	−	0.299326i
$269$	8.63004	−	7.24147i	0.526183	−	0.441520i	−0.340598	−	0.940209i	$-0.610629\pi$
$269$	8.63004	−	7.24147i	0.526183	−	0.441520i	0.866781	+	0.498689i	$0.166185\pi$
$270$		0			0
$271$	−19.5383	−	7.11134i	−1.18686	−	0.431983i	−0.328243	−	0.944593i	$-0.606456\pi$
$271$	−19.5383	−	7.11134i	−1.18686	−	0.431983i	−0.858621	+	0.512610i	$0.828679\pi$
$272$	−23.9876	+	2.09864i	−1.45446	+	0.127249i
$273$		0			0
$274$	−9.14041	−	15.8317i	−0.552192	−	0.956425i
$275$	17.9944	+	14.2444i	1.08510	+	0.858967i
$276$		0			0
$277$	7.37493	+	1.97611i	0.443116	+	0.118733i	0.473477	−	0.880806i	$-0.342999\pi$
$277$	7.37493	+	1.97611i	0.443116	+	0.118733i	−0.0303603	+	0.999539i	$0.509665\pi$
$278$	6.81861	+	25.4474i	0.408953	+	1.52623i
$279$		0			0
$280$	−0.218623	−	1.14417i	−0.0130652	−	0.0683772i
$281$	1.88216	+	5.17119i	0.112280	+	0.308488i	0.983087	−	0.183137i	$-0.0586253\pi$
$281$	1.88216	+	5.17119i	0.112280	+	0.308488i	−0.870807	+	0.491625i	$0.836403\pi$
$282$		0			0
$283$	6.62055	−	9.45513i	0.393551	−	0.562049i	−0.572663	−	0.819791i	$-0.694090\pi$
$283$	6.62055	−	9.45513i	0.393551	−	0.562049i	0.966214	+	0.257742i	$0.0829785\pi$
$284$	11.9342			0.708164
$285$		0			0
$286$	19.4954			1.15279
$287$	0.0340275	−	0.0485963i	0.00200858	−	0.00286855i
$288$		0			0
$289$	2.12857	+	5.84820i	0.125210	+	0.344012i
$290$	−0.00925940	−	0.00628856i	−0.000543731	−	0.000369277i
$291$		0			0
$292$	2.63313	+	9.82698i	0.154092	+	0.575080i
$293$	−23.4584	−	6.28567i	−1.37046	−	0.367213i	−0.502811	−	0.864397i	$-0.667701\pi$
$293$	−23.4584	−	6.28567i	−1.37046	−	0.367213i	−0.867645	+	0.497184i	$0.834367\pi$
$294$		0			0
$295$	1.69292	+	4.45256i	0.0985657	+	0.259238i
$296$	−7.00780	−	12.1379i	−0.407320	−	0.705499i
$297$		0			0
$298$	−16.5374	+	1.44683i	−0.957983	+	0.0838127i
$299$	17.6785	+	6.43445i	1.02237	+	0.372114i
$300$		0			0
$301$	−0.0441232	+	0.0370237i	−0.00254322	+	0.00213401i
$302$	4.36211	+	3.05438i	0.251011	+	0.175760i
$303$		0			0
$304$	19.4921	+	9.71707i	1.11795	+	0.557312i
$305$	7.69658	−	4.59126i	0.440705	−	0.262895i
$306$		0			0
$307$	4.54580	+	0.397706i	0.259442	+	0.0226983i	0.216135	−	0.976364i	$-0.430655\pi$
$307$	4.54580	+	0.397706i	0.259442	+	0.0226983i	0.0433075	+	0.999062i	$0.486210\pi$
$308$	1.12510	+	0.524644i	0.0641086	+	0.0298943i
$309$		0			0
$310$	−10.3226	+	7.44968i	−0.586284	+	0.423113i
$311$	2.78134	−	4.81742i	0.157715	−	0.273171i	−0.776329	−	0.630328i	$-0.782921\pi$
$311$	2.78134	−	4.81742i	0.157715	−	0.273171i	0.934044	+	0.357157i	$0.116254\pi$
$312$		0			0
$313$	8.29578	−	5.80877i	0.468905	−	0.328331i	−0.315129	−	0.949049i	$-0.602048\pi$
$313$	8.29578	−	5.80877i	0.468905	−	0.328331i	0.784034	+	0.620718i	$0.213159\pi$
$314$	4.80922	−	27.2744i	0.271400	−	1.53919i
$315$		0			0
$316$	4.47416	+	2.58316i	0.251691	+	0.145314i
$317$	−2.24516	−	25.6623i	−0.126101	−	1.44134i	−0.750829	−	0.660497i	$-0.770346\pi$
$317$	−2.24516	−	25.6623i	−0.126101	−	1.44134i	0.624728	−	0.780843i	$-0.285210\pi$
$318$		0			0
$319$	−0.0125872	+	0.00458138i	−0.000704750	+	0.000256508i
$320$	−3.20521	−	1.11508i	−0.179177	−	0.0623347i
$321$		0			0
$322$	2.64541	+	2.64541i	0.147423	+	0.147423i
$323$	4.18678	−	20.5844i	0.232959	−	1.14535i
$324$		0			0
$325$	11.0673	−	5.55054i	0.613905	−	0.307888i
$326$	−0.0911679	−	0.108650i	−0.00504933	−	0.00601755i
$327$		0			0
$328$	−0.158472	−	0.339844i	−0.00875013	−	0.0187647i
$329$	−0.930180	+	1.10855i	−0.0512825	+	0.0611161i
$330$		0			0
$331$	−11.0824	+	6.39845i	−0.609146	+	0.351690i	−0.772631	−	0.634855i	$-0.781060\pi$
$331$	−11.0824	+	6.39845i	−0.609146	+	0.351690i	0.163485	+	0.986546i	$0.447726\pi$
$332$	8.63849	+	12.3370i	0.474098	+	0.677083i
$333$		0			0
$334$	−12.8092	+	7.39540i	−0.700889	+	0.404658i
$335$	−14.1324	+	14.5415i	−0.772133	+	0.794486i
$336$		0			0
$337$	8.64171	+	18.5322i	0.470744	+	1.00951i	0.988110	+	0.153749i	$0.0491347\pi$
$337$	8.64171	+	18.5322i	0.470744	+	1.00951i	−0.517366	+	0.855764i	$0.673087\pi$
$338$	−4.97876	+	10.6770i	−0.270809	+	0.580751i
$339$		0			0
$340$	0.740409	−	10.1247i	0.0401543	−	0.549088i
$341$			15.2345i			0.824996i
$342$		0			0
$343$	2.82529	+	2.82529i	0.152551	+	0.152551i
$344$	0.0632189	+	0.358532i	0.00340854	+	0.0193308i
$345$		0			0
$346$	15.2272	−	5.54227i	0.818622	−	0.297954i
$347$	−16.0127	+	7.46684i	−0.859606	+	0.400841i	−0.801875	−	0.597491i	$-0.796164\pi$
$347$	−16.0127	+	7.46684i	−0.859606	+	0.400841i	−0.0577308	+	0.998332i	$0.518386\pi$
$348$		0			0
$349$	−10.6670	−	6.15858i	−0.570990	−	0.329661i	0.186555	−	0.982445i	$-0.440268\pi$
$349$	−10.6670	−	6.15858i	−0.570990	−	0.329661i	−0.757545	+	0.652783i	$0.773601\pi$
$350$	2.46113	−	0.0702464i	0.131553	−	0.00375483i
$351$		0			0
$352$	18.5789	−	13.0091i	0.990258	−	0.693386i
$353$	1.47805	−	5.51616i	0.0786687	−	0.293596i	−0.915371	−	0.402610i	$-0.868103\pi$
$353$	1.47805	−	5.51616i	0.0786687	−	0.293596i	0.994040	+	0.109015i	$0.0347696\pi$
$354$		0			0
$355$	4.52030	−	27.9631i	0.239913	−	1.48413i
$356$	5.09473	−	13.9976i	0.270020	−	0.741874i
$357$		0			0
$358$	−12.2666	−	1.07319i	−0.648312	−	0.0567199i
$359$	−25.5870	+	4.51167i	−1.35043	+	0.238117i	−0.801621	−	0.597832i	$-0.796029\pi$
$359$	−25.5870	+	4.51167i	−1.35043	+	0.238117i	−0.548807	+	0.835949i	$0.684918\pi$
$360$		0			0
$361$	−12.9565	+	13.8971i	−0.681919	+	0.731428i
$362$	−1.95458	+	1.95458i	−0.102731	+	0.102731i
$363$		0			0
$364$	0.513040	−	0.430491i	0.0268906	−	0.0225639i
$365$	24.0231	−	2.44757i	1.25742	−	0.128112i
$366$		0			0
$367$	−0.0825751	+	0.00722438i	−0.00431038	+	0.000377110i	−0.0893107	−	0.996004i	$-0.528466\pi$
$367$	−0.0825751	+	0.00722438i	−0.00431038	+	0.000377110i	0.0850003	+	0.996381i	$0.472911\pi$
$368$	36.6682	−	9.82521i	1.91146	−	0.512175i
$369$		0			0
$370$	27.6902	−	10.5282i	1.43955	−	0.547334i
$371$	0.746612	+	0.131648i	0.0387621	+	0.00683481i
$372$		0			0
$373$	0.678465	+	2.53207i	0.0351296	+	0.131105i	0.981264	−	0.192670i	$-0.0617146\pi$
$373$	0.678465	+	2.53207i	0.0351296	+	0.131105i	−0.946134	+	0.323775i	$0.895048\pi$
$374$	−29.0641	−	24.3877i	−1.50287	−	1.26106i
$375$		0			0
$376$	3.12835	+	8.59507i	0.161332	+	0.443257i
$377$	−0.000629827		0.00719896i	−3.24377e−5		0.000370765i
$378$		0			0
$379$	29.0243			1.49088			0.745440	−	0.666573i	$-0.232239\pi$
$379$	29.0243			1.49088			0.745440	+	0.666573i	$0.232239\pi$
$380$	−5.35558	+	7.45873i	−0.274736	+	0.382625i
$381$		0			0
$382$	−4.50835	+	6.43858i	−0.230667	+	0.329427i
$383$	−1.84015	+	21.0330i	−0.0940271	+	1.07473i	0.791819	+	0.610756i	$0.209134\pi$
$383$	−1.84015	+	21.0330i	−0.0940271	+	1.07473i	−0.885846	+	0.463979i	$0.846421\pi$
$384$		0			0
$385$	1.65545	−	2.43752i	0.0843697	−	0.124228i
$386$	−16.1151	−	13.5222i	−0.820239	−	0.688262i
$387$		0			0
$388$	5.42834	+	1.45452i	0.275582	+	0.0738420i
$389$	4.17947	+	0.736954i	0.211908	+	0.0373650i	0.278594	−	0.960409i	$-0.410132\pi$
$389$	4.17947	+	0.736954i	0.211908	+	0.0373650i	−0.0666864	+	0.997774i	$0.521243\pi$
$390$		0			0
$391$	−18.3063	−	31.7075i	−0.925791	−	1.60352i
$392$	12.1248	−	3.24884i	0.612397	−	0.164091i
$393$		0			0
$394$	−0.271956	−	0.0989839i	−0.0137009	−	0.00498674i
$395$	7.74730	−	9.50504i	0.389809	−	0.478251i
$396$		0			0
$397$	−16.9218	−	11.8488i	−0.849282	−	0.594674i	0.0658493	−	0.997830i	$-0.479024\pi$
$397$	−16.9218	−	11.8488i	−0.849282	−	0.594674i	−0.915131	+	0.403156i	$0.867913\pi$
$398$	−6.06152	+	6.06152i	−0.303837	+	0.303837i
$399$		0			0
$400$	11.8692	−	21.9837i	0.593462	−	1.09918i
$401$	−17.8894	+	3.15438i	−0.893354	+	0.157522i	−0.601436	−	0.798921i	$-0.705404\pi$
$401$	−17.8894	+	3.15438i	−0.893354	+	0.157522i	−0.291918	+	0.956443i	$0.594293\pi$
$402$		0			0
$403$	7.44878	+	3.47342i	0.371050	+	0.173024i
$404$	−3.58880	+	9.86014i	−0.178549	+	0.490560i
$405$		0			0
$406$	−0.000718529		0.00124453i	−3.56600e−5		6.17649e-5i
$407$	9.17575	−	34.2444i	0.454825	−	1.69743i
$408$		0			0
$409$	2.14098	−	12.1421i	0.105865	−	0.600388i	−0.885007	−	0.465578i	$-0.845846\pi$
$409$	2.14098	−	12.1421i	0.105865	−	0.600388i	0.990871	−	0.134810i	$-0.0430425\pi$
$410$	0.762560	−	0.216034i	0.0376601	−	0.0106691i
$411$		0			0
$412$	0.0677491	+	0.774375i	0.00333776	+	0.0381507i
$413$	0.554286	−	0.258468i	0.0272746	−	0.0127184i
$414$		0			0
$415$	32.1791	−	15.5681i	1.57961	−	0.764206i
$416$	−2.12474	−	12.0500i	−0.104174	−	0.590800i
$417$		0			0
$418$	10.8909	+	32.5436i	0.532691	+	1.59176i
$419$		−	30.7781i		−	1.50361i	−0.659386	−	0.751805i	$-0.729184\pi$
$419$		−	30.7781i		−	1.50361i	0.659386	−	0.751805i	$-0.270816\pi$
$420$		0			0
$421$	10.7205	+	12.7761i	0.522483	+	0.622671i	0.961166	−	0.275971i	$-0.0889994\pi$
$421$	10.7205	+	12.7761i	0.522483	+	0.622671i	−0.438683	+	0.898642i	$0.644555\pi$
$422$	−0.0689701	+	0.147907i	−0.00335741	+	0.00720000i
$423$		0			0
$424$	3.08017	−	3.67081i	0.149586	−	0.178270i
$425$	−23.4428	−	5.56977i	−1.13714	−	0.270174i
$426$		0			0
$427$	−0.659969	−	0.942534i	−0.0319382	−	0.0456124i
$428$	−8.42495	−	12.0321i	−0.407235	−	0.581593i
$429$		0			0
$430$	−0.769427	+	0.0109784i	−0.0371050	+	0.000529424i
$431$	−9.97761	+	11.8908i	−0.480604	+	0.572762i	−0.950802	−	0.309799i	$-0.899738\pi$
$431$	−9.97761	+	11.8908i	−0.480604	+	0.572762i	0.470198	+	0.882561i	$0.344183\pi$
$432$		0			0
$433$	−5.44902	+	11.6855i	−0.261863	+	0.561568i	−0.992648	−	0.121041i	$-0.961377\pi$
$433$	−5.44902	+	11.6855i	−0.261863	+	0.561568i	0.730784	+	0.682608i	$0.239155\pi$
$434$	1.05057	+	1.25202i	0.0504291	+	0.0600990i
$435$		0			0
$436$			8.90391i			0.426420i
$437$	−0.865085	+	33.1052i	−0.0413826	+	1.58363i
$438$		0			0
$439$	−5.84172	−	33.1300i	−0.278810	−	1.58121i	−0.726593	−	0.687068i	$-0.758898\pi$
$439$	−5.84172	−	33.1300i	−0.278810	−	1.58121i	0.447783	−	0.894142i	$-0.352214\pi$
$440$	−8.11089	−	16.7651i	−0.386672	−	0.799247i
$441$		0			0
$442$	−18.5507	+	8.65033i	−0.882366	+	0.411454i
$443$	1.46104	+	16.6998i	0.0694162	+	0.793431i	0.948503	+	0.316769i	$0.102598\pi$
$443$	1.46104	+	16.6998i	0.0694162	+	0.793431i	−0.879087	+	0.476662i	$0.841846\pi$
$444$		0			0
$445$	−30.8683	−	17.2394i	−1.46330	−	0.817225i
$446$	0.204711	−	1.16097i	0.00969333	−	0.0549736i
$447$		0			0
$448$	−0.112769	+	0.420860i	−0.00532784	+	0.0198838i
$449$	8.68158	−	15.0369i	0.409709	−	0.709637i	−0.585148	−	0.810927i	$-0.698964\pi$
$449$	8.68158	−	15.0369i	0.409709	−	0.709637i	0.994857	+	0.101290i	$0.0322969\pi$
$450$		0			0
$451$	0.324406	−	0.891298i	0.0152757	−	0.0419696i
$452$	1.57484	+	0.734361i	0.0740743	+	0.0345414i
$453$		0			0
$454$	−7.48278	+	1.31942i	−0.351184	+	0.0619233i
$455$	−0.814366	−	1.36517i	−0.0381781	−	0.0640000i
$456$		0			0
$457$	−4.18473	+	4.18473i	−0.195753	+	0.195753i	−0.798177	−	0.602423i	$-0.794202\pi$
$457$	−4.18473	+	4.18473i	−0.195753	+	0.195753i	0.602423	+	0.798177i	$0.294202\pi$
$458$	−2.30614	−	1.61478i	−0.107759	−	0.0754535i
$459$		0			0
$460$	1.62221	+	15.9221i	0.0756358	+	0.742371i
$461$	−13.1750	−	4.79530i	−0.613620	−	0.223339i	0.0164665	−	0.999864i	$-0.494758\pi$
$461$	−13.1750	−	4.79530i	−0.613620	−	0.223339i	−0.630086	+	0.776525i	$0.716981\pi$
$462$		0			0
$463$	13.9101	−	3.72721i	0.646459	−	0.173218i	0.0793316	−	0.996848i	$-0.474721\pi$
$463$	13.9101	−	3.72721i	0.646459	−	0.173218i	0.567127	+	0.823630i	$0.308055\pi$
$464$	0.00729090	+	0.0126282i	0.000338472	+	0.000586250i
$465$		0			0
$466$	−16.3239	−	2.87835i	−0.756190	−	0.133337i
$467$	8.43685	+	2.26065i	0.390411	+	0.104610i	0.448684	−	0.893690i	$-0.351893\pi$
$467$	8.43685	+	2.26065i	0.390411	+	0.104610i	−0.0582734	+	0.998301i	$0.518560\pi$
$468$		0			0
$469$	1.99433	+	1.67345i	0.0920898	+	0.0772725i
$470$	−18.9894	+	3.62842i	−0.875916	+	0.167367i
$471$		0			0
$472$	0.336914	−	3.85094i	0.0155077	−	0.177254i
$473$	−0.528204	+	0.754354i	−0.0242869	+	0.0346852i
$474$		0			0
$475$	15.4481	+	15.3739i	0.708808	+	0.705401i
$476$	−1.30337			−0.0597399
$477$		0			0
$478$	0.934886	−	10.6858i	0.0427607	−	0.488757i
$479$	−6.83164	−	18.7698i	−0.312145	−	0.857613i	−0.992223	−	0.124473i	$-0.960276\pi$
$479$	−6.83164	−	18.7698i	−0.312145	−	0.857613i	0.680078	−	0.733140i	$-0.261946\pi$
$480$		0			0
$481$	−14.6514	−	12.2940i	−0.668048	−	0.560558i
$482$	5.56862	+	20.7824i	0.253644	+	0.946611i
$483$		0			0
$484$	9.34084	+	1.64704i	0.424584	+	0.0748656i
$485$	5.46419	−	12.1683i	0.248116	−	0.552533i
$486$		0			0
$487$	12.8690	−	3.44824i	0.583150	−	0.156254i	0.0448291	−	0.998995i	$-0.485726\pi$
$487$	12.8690	−	3.44824i	0.583150	−	0.156254i	0.538320	+	0.842740i	$0.319059\pi$
$488$	−7.24504	+	0.633859i	−0.327968	+	0.0286935i
$489$		0			0
$490$	2.68925	+	26.3952i	0.121488	+	1.19241i
$491$	18.9123	−	15.8693i	0.853501	−	0.716172i	−0.107057	−	0.994253i	$-0.534143\pi$
$491$	18.9123	−	15.8693i	0.853501	−	0.716172i	0.960558	+	0.278081i	$0.0896983\pi$
$492$		0			0
$493$	0.00994447	−	0.00994447i	0.000447876	−	0.000447876i
$494$	18.3950	+	2.09483i	0.827629	+	0.0942507i
$495$		0			0
$496$	16.3323	−	2.87982i	0.733341	−	0.129308i
$497$	−3.62294	−	0.316966i	−0.162511	−	0.0142179i
$498$		0			0
$499$	6.45641	−	17.7388i	0.289028	−	0.794099i	−0.707175	−	0.707039i	$-0.750031\pi$
$499$	6.45641	−	17.7388i	0.289028	−	0.794099i	0.996203	−	0.0870601i	$-0.0277472\pi$
$500$	8.35093	+	6.41893i	0.373465	+	0.287063i
$501$		0			0
$502$	4.05766	−	15.1434i	0.181102	−	0.675883i
$503$	11.7261	−	8.21072i	0.522842	−	0.366098i	−0.282162	−	0.959367i	$-0.591052\pi$
$503$	11.7261	−	8.21072i	0.522842	−	0.366098i	0.805005	+	0.593269i	$0.202163\pi$
$504$		0			0
$505$	21.7441	+	12.1437i	0.967599	+	0.540386i
$506$	51.8009	+	29.9073i	2.30283	+	1.32954i
$507$		0			0
$508$	−8.60335	+	4.01181i	−0.381712	+	0.177995i
$509$	−32.7191	+	11.9088i	−1.45025	+	0.527847i	−0.942661	−	0.333752i	$-0.891685\pi$
$509$	−32.7191	+	11.9088i	−1.45025	+	0.527847i	−0.507588	+	0.861600i	$0.669463\pi$
$510$		0			0
$511$	−0.538357	−	3.05317i	−0.0238155	−	0.135064i
$512$	−4.63603	−	4.63603i	−0.204886	−	0.204886i
$513$		0			0
$514$		−	51.0136i		−	2.25011i
$515$	1.84011	+	0.134566i	0.0810849	+	0.00592967i
$516$		0			0
$517$	−9.77791	+	20.9688i	−0.430032	+	0.922206i
$518$	−1.60740	−	3.44707i	−0.0706250	−	0.151456i
$519$		0			0
$520$	−10.0464	+	0.143345i	−0.440565	+	0.00628609i
$521$	−3.47559	+	2.00663i	−0.152268	+	0.0879121i	−0.574198	−	0.818716i	$-0.694686\pi$
$521$	−3.47559	+	2.00663i	−0.152268	+	0.0879121i	0.421930	+	0.906628i	$0.361353\pi$
$522$		0			0
$523$	18.5171	+	26.4451i	0.809695	+	1.15636i	0.985119	+	0.171872i	$0.0549815\pi$
$523$	18.5171	+	26.4451i	0.809695	+	1.15636i	−0.175424	+	0.984493i	$0.556130\pi$
$524$	−15.9603	+	9.21469i	−0.697230	+	0.402546i
$525$		0			0
$526$	17.3897	−	20.7243i	0.758228	−	0.903621i
$527$	−6.75973	−	14.4963i	−0.294458	−	0.631468i
$528$		0			0
$529$	22.3183	+	26.5979i	0.970360	+	1.15643i
$530$	6.62046	+	7.66515i	0.287574	+	0.332953i
$531$		0			0
$532$	1.00522	+	0.615925i	0.0435818	+	0.0267037i
$533$	−0.361829	−	0.361829i	−0.0156725	−	0.0156725i
$534$		0			0
$535$	−31.3836	+	15.1832i	−1.35683	+	0.656428i
$536$	15.4630	−	5.62808i	0.667900	−	0.243096i
$537$		0			0
$538$	−1.68416	−	19.2500i	−0.0726092	−	0.829927i
$539$	27.4977	+	15.8758i	1.18441	+	0.683820i
$540$		0			0
$541$	−2.75071	+	15.6000i	−0.118262	+	0.670698i	0.866821	+	0.498620i	$0.166160\pi$
$541$	−2.75071	+	15.6000i	−0.118262	+	0.670698i	−0.985083	+	0.172079i	$0.944952\pi$
$542$	−29.2141	+	20.4559i	−1.25485	+	0.878657i
$543$		0			0
$544$	−11.9063	+	20.6223i	−0.510479	+	0.884176i
$545$	20.8629	+	3.37252i	0.893666	+	0.144463i
$546$		0			0
$547$	−38.1131	−	17.7724i	−1.62960	−	0.759893i	−0.629740	−	0.776806i	$-0.716838\pi$
$547$	−38.1131	−	17.7724i	−1.62960	−	0.759893i	−0.999857	+	0.0169130i	$0.994616\pi$
$548$	−10.0024	−	0.875093i	−0.427280	−	0.0373821i
$549$		0			0
$550$	37.7174	−	11.2691i	1.60828	−	0.480516i
$551$	−0.0123690	+	0.00297025i	−0.000526938	+	0.000126537i
$552$		0			0
$553$	−1.28964	−	0.903017i	−0.0548411	−	0.0384002i
$554$	10.0322	−	8.41800i	0.426227	−	0.357647i
$555$		0			0
$556$	13.5972	+	4.94896i	0.576648	+	0.209883i
$557$	−19.2126	+	1.68089i	−0.814066	+	0.0712215i	−0.486582	−	0.873635i	$-0.661756\pi$
$557$	−19.2126	+	1.68089i	−0.814066	+	0.0712215i	−0.327484	+	0.944857i	$0.606201\pi$
$558$		0			0
$559$	0.248406	+	0.430251i	0.0105064	+	0.0181977i
$560$	−2.92610	−	1.31397i	−0.123650	−	0.0555253i
$561$		0			0
$562$	9.11752	+	2.44303i	0.384599	+	0.103053i
$563$	−4.96746	−	18.5388i	−0.209354	−	0.781318i	−0.988078	−	0.153952i	$-0.950800\pi$
$563$	−4.96746	−	18.5388i	−0.209354	−	0.781318i	0.778725	−	0.627366i	$-0.215867\pi$
$564$		0			0
$565$	2.31719	−	3.41188i	0.0974849	−	0.143539i
$566$	−6.77146	−	18.6044i	−0.284626	−	0.782002i
$567$		0			0
$568$	−13.1848	+	18.8298i	−0.553220	+	0.790080i
$569$	32.0305			1.34279			0.671393	−	0.741101i	$-0.265696\pi$
$569$	32.0305			1.34279			0.671393	+	0.741101i	$0.265696\pi$
$570$		0			0
$571$	24.9840			1.04555			0.522774	−	0.852471i	$-0.324897\pi$
$571$	24.9840			1.04555			0.522774	+	0.852471i	$0.324897\pi$
$572$	6.14167	−	8.77121i	0.256796	−	0.366743i
$573$		0			0
$574$	−0.0348031	−	0.0956208i	−0.00145265	−	0.00399114i
$575$	37.9217	+	2.22978i	1.58144	+	0.0929881i
$576$		0			0
$577$	−0.896843	−	3.34706i	−0.0373361	−	0.139340i	0.944742	−	0.327815i	$-0.106312\pi$
$577$	−0.896843	−	3.34706i	−0.0373361	−	0.139340i	−0.982078	+	0.188475i	$0.939646\pi$
$578$	10.3112	+	2.76287i	0.428888	+	0.114920i
$579$		0			0
$580$	−0.00574630	+	0.00218482i	−0.000238602	+	9.07196e-5i
$581$	−2.29477	−	3.97466i	−0.0952032	−	0.164897i
$582$		0			0
$583$	12.0750	−	1.05642i	0.500094	−	0.0437525i
$584$	−18.4141	−	6.70217i	−0.761980	−	0.277338i
$585$		0			0
$586$	−31.9107	+	26.7763i	−1.31822	+	1.10612i
$587$	−25.8643	−	18.1103i	−1.06753	−	0.747494i	−0.0986764	−	0.995120i	$-0.531461\pi$
$587$	−25.8643	−	18.1103i	−1.06753	−	0.747494i	−0.968856	+	0.247625i	$0.920350\pi$
$588$		0			0
$589$	−1.63699	+	14.3746i	−0.0674508	+	0.592295i
$590$	7.92162	+	2.00191i	0.326128	+	0.0824173i
$591$		0			0
$592$	−38.4464	−	3.36363i	−1.58014	−	0.138244i
$593$	8.33375	+	3.88609i	0.342226	+	0.159583i	0.586131	−	0.810217i	$-0.300651\pi$
$593$	8.33375	+	3.88609i	0.342226	+	0.159583i	−0.243904	+	0.969799i	$0.578428\pi$
$594$		0			0
$595$	−0.493677	+	3.05395i	−0.0202388	+	0.125200i
$596$	−4.55884	+	7.89615i	−0.186737	+	0.323439i
$597$		0			0
$598$	26.4333	−	18.5088i	1.08094	−	0.756882i
$599$	−7.60255	+	43.1162i	−0.310632	+	1.76168i	0.285102	+	0.958497i	$0.407973\pi$
$599$	−7.60255	+	43.1162i	−0.310632	+	1.76168i	−0.595734	+	0.803182i	$0.703139\pi$
$600$		0			0
$601$	26.5782	+	15.3449i	1.08415	+	0.625932i	0.932012	−	0.362428i	$-0.118052\pi$
$601$	26.5782	+	15.3449i	1.08415	+	0.625932i	0.152134	+	0.988360i	$0.451385\pi$
$602$	0.00861066	+	0.0984203i	0.000350944	+	0.00401131i
$603$		0			0
$604$	2.74840	−	1.00034i	0.111831	−	0.0407031i
$605$	7.39723	−	21.2628i	0.300740	−	0.864456i
$606$		0			0
$607$	7.95200	+	7.95200i	0.322762	+	0.322762i	0.849826	−	0.527064i	$-0.176707\pi$
$607$	7.95200	+	7.95200i	0.322762	+	0.322762i	−0.527064	+	0.849826i	$0.676707\pi$
$608$	18.9280	−	10.2784i	0.767634	−	0.416845i
$609$		0			0
$610$	1.12115	−	15.3311i	0.0453940	−	0.620738i
$611$	8.02317	+	9.56164i	0.324583	+	0.386822i
$612$		0			0
$613$	−16.8269	−	36.0854i	−0.679632	−	1.45748i	−0.878644	−	0.477478i	$-0.841551\pi$
$613$	−16.8269	−	36.0854i	−0.679632	−	1.45748i	0.199012	−	0.979997i	$-0.436227\pi$
$614$	5.03108	−	5.99580i	0.203038	−	0.241971i
$615$		0			0
$616$	−2.07078	+	1.19557i	−0.0834342	+	0.0481708i
$617$	14.9718	+	21.3819i	0.602740	+	0.860803i	0.998339	−	0.0576212i	$-0.0183516\pi$
$617$	14.9718	+	21.3819i	0.602740	+	0.860803i	−0.395598	+	0.918424i	$0.629463\pi$
$618$		0			0
$619$	−14.8409	+	8.56837i	−0.596504	+	0.344392i	−0.767665	−	0.640851i	$-0.778582\pi$
$619$	−14.8409	+	8.56837i	−0.596504	+	0.344392i	0.171161	+	0.985243i	$0.445248\pi$
$620$	0.0997514	+	6.99114i	0.00400611	+	0.280771i
$621$		0			0
$622$	−4.03237	−	8.64743i	−0.161683	−	0.346731i
$623$	−1.91841	+	4.11404i	−0.0768594	+	0.164825i
$624$		0			0
$625$	18.2033	−	17.1359i	0.728134	−	0.685435i
$626$		−	17.3708i		−	0.694277i
$627$		0			0
$628$	−10.7560	−	10.7560i	−0.429213	−	0.429213i
$629$	6.46350	+	36.6563i	0.257716	+	1.46158i
$630$		0			0
$631$	20.1799	−	7.34487i	0.803348	−	0.292395i	0.0924747	−	0.995715i	$-0.470522\pi$
$631$	20.1799	−	7.34487i	0.803348	−	0.292395i	0.710873	+	0.703320i	$0.248300\pi$
$632$	−9.01871	+	4.20549i	−0.358745	+	0.167286i
$633$		0			0
$634$	−38.2657	−	22.0927i	−1.51973	−	0.877415i
$635$	6.14144	+	21.6782i	0.243715	+	0.860272i
$636$		0			0
$637$	14.0317	−	9.82513i	0.555958	−	0.389286i
$638$	−0.00594660	+	0.0221930i	−0.000235428	+	0.000878629i
$639$		0			0
$640$	−22.6393	+	16.3385i	−0.894896	+	0.645834i
$641$	−12.0700	+	33.1619i	−0.476735	+	1.30982i	0.435515	+	0.900182i	$0.356566\pi$
$641$	−12.0700	+	33.1619i	−0.476735	+	1.30982i	−0.912249	+	0.409636i	$0.865656\pi$
$642$		0			0
$643$	18.7728	+	1.64241i	0.740327	+	0.0647702i	0.451079	−	0.892484i	$-0.351039\pi$
$643$	18.7728	+	1.64241i	0.740327	+	0.0647702i	0.289248	+	0.957254i	$0.406595\pi$
$644$	2.02359	−	0.356814i	0.0797407	−	0.0140604i
$645$		0			0
$646$	−24.8031	−	26.1341i	−0.975864	−	1.02823i
$647$	17.6606	−	17.6606i	0.694309	−	0.694309i	−0.268868	−	0.963177i	$-0.586650\pi$
$647$	17.6606	−	17.6606i	0.694309	−	0.694309i	0.963177	+	0.268868i	$0.0866496\pi$
$648$		0			0
$649$	7.49049	−	6.28527i	0.294027	−	0.246718i
$650$	3.08954	−	21.0109i	0.121182	−	0.824116i
$651$		0			0
$652$	−0.0776036	+	0.00678943i	−0.00303919	+	0.000265895i
$653$	−5.40330	+	1.44781i	−0.211447	+	0.0566572i	−0.362988	−	0.931794i	$-0.618243\pi$
$653$	−5.40330	+	1.44781i	−0.211447	+	0.0566572i	0.151540	+	0.988451i	$0.451577\pi$
$654$		0			0
$655$	15.5458	+	40.8871i	0.607424	+	1.59759i
$656$	−1.01685	−	0.179297i	−0.0397012	−	0.00700039i
$657$		0			0
$658$	0.642427	+	2.39757i	0.0250444	+	0.0934669i
$659$	5.03828	+	4.22762i	0.196264	+	0.164685i	0.735623	−	0.677391i	$-0.236889\pi$
$659$	5.03828	+	4.22762i	0.196264	+	0.164685i	−0.539360	+	0.842075i	$0.681334\pi$
$660$		0			0
$661$	−13.4502	−	36.9540i	−0.523150	−	1.43734i	−0.866995	−	0.498317i	$-0.833951\pi$
$661$	−13.4502	−	36.9540i	−0.523150	−	1.43734i	0.343844	−	0.939027i	$-0.388271\pi$
$662$	−1.91306	+	21.8664i	−0.0743531	+	0.849860i
$663$		0			0
$664$	−29.0091			−1.12577
$665$	1.82393	−	2.12205i	0.0707289	−	0.0822896i
$666$		0			0
$667$	−0.0127172	+	0.0181620i	−0.000492411	+	0.000703236i
$668$	−0.708028	+	8.09280i	−0.0273944	+	0.313120i
$669$		0			0
$670$	6.52773	+	34.1630i	0.252188	+	1.31983i
$671$	−14.0924	−	11.8249i	−0.544031	−	0.456496i
$672$		0			0
$673$	9.39609	+	2.51767i	0.362193	+	0.0970492i	0.435326	−	0.900273i	$-0.356633\pi$
$673$	9.39609	+	2.51767i	0.362193	+	0.0970492i	−0.0731333	+	0.997322i	$0.523300\pi$
$674$	34.5406	+	6.09045i	1.33046	+	0.234595i
$675$		0			0
$676$	3.23523	+	5.60359i	0.124432	+	0.215523i
$677$	−39.3476	+	10.5432i	−1.51225	+	0.405207i	−0.917182	−	0.398468i	$-0.869542\pi$
$677$	−39.3476	+	10.5432i	−1.51225	+	0.405207i	−0.595069	+	0.803675i	$0.702875\pi$
$678$		0			0
$679$	−1.60928	−	0.585731i	−0.0617586	−	0.0224783i
$680$	15.1567	+	12.3538i	0.581234	+	0.473748i
$681$		0			0
$682$	21.4053	+	14.9881i	0.819651	+	0.573926i
$683$	−11.3169	+	11.3169i	−0.433030	+	0.433030i	−0.889658	−	0.456628i	$-0.849057\pi$
$683$	−11.3169	+	11.3169i	−0.433030	+	0.433030i	0.456628	+	0.889658i	$0.349057\pi$
$684$		0			0
$685$	−5.83903	+	23.1052i	−0.223098	+	0.882804i
$686$	6.74927	−	1.19008i	0.257688	−	0.0454374i
$687$		0			0
$688$	0.908559	+	0.423668i	0.0346385	+	0.0161522i
$689$	2.23652	−	6.14480i	0.0852048	−	0.234098i
$690$		0			0
$691$	1.45852	−	2.52622i	0.0554846	−	0.0961021i	−0.836949	−	0.547281i	$-0.815663\pi$
$691$	1.45852	−	2.52622i	0.0554846	−	0.0961021i	0.892434	+	0.451179i	$0.148996\pi$
$692$	2.30353	−	8.59691i	0.0875672	−	0.326805i
$693$		0			0
$694$	−5.26243	+	29.8447i	−0.199759	+	1.13289i
$695$	16.7462	−	29.9852i	0.635218	−	1.13740i
$696$		0			0
$697$	0.0867931	+	0.992050i	0.00328752	+	0.0375766i
$698$	−19.1476	+	8.92866i	−0.724747	+	0.337955i
$699$		0			0
$700$	0.743729	−	1.12942i	0.0281103	−	0.0426881i
$701$	7.75792	+	43.9973i	0.293012	+	1.66176i	0.675173	+	0.737660i	$0.264069\pi$
$701$	7.75792	+	43.9973i	0.293012	+	1.66176i	−0.382160	+	0.924096i	$0.624820\pi$
$702$		0			0
$703$	12.3375	−	31.3254i	0.465316	−	1.18146i
$704$			6.96614i			0.262546i
$705$		0			0
$706$	−6.29634	−	7.50369i	−0.236966	−	0.282405i
$707$	1.35135	−	2.89799i	0.0508229	−	0.108990i
$708$		0			0
$709$	−27.4318	+	32.6919i	−1.03022	+	1.22777i	−0.0568877	+	0.998381i	$0.518118\pi$
$709$	−27.4318	+	32.6919i	−1.03022	+	1.22777i	−0.973334	+	0.229390i	$0.926327\pi$
$710$	−34.8425	−	33.8622i	−1.30761	−	1.27082i
$711$		0			0
$712$	16.4569	+	23.5029i	0.616749	+	0.880808i
$713$	14.4636	+	20.6561i	0.541665	+	0.773577i
$714$		0			0
$715$	−18.2257	−	17.7129i	−0.681601	−	0.662424i
$716$	−4.34722	+	5.18081i	−0.162463	+	0.193616i
$717$		0			0
$718$	−18.8340	+	40.3897i	−0.702880	+	1.50733i
$719$	11.9438	+	14.2341i	0.445429	+	0.530841i	0.941307	−	0.337550i	$-0.109598\pi$
$719$	11.9438	+	14.2341i	0.445429	+	0.530841i	−0.495879	+	0.868392i	$0.665154\pi$
$720$		0			0
$721$		−	0.236881i		−	0.00882192i
$722$	6.77927	+	31.8769i	0.252298	+	1.18633i
$723$		0			0
$724$	0.263635	+	1.49515i	0.00979790	+	0.0555667i
$725$	0.00294276	+	0.0142918i	0.000109291	+	0.000530783i
$726$		0			0
$727$	16.0098	−	7.46550i	0.593771	−	0.276880i	−0.102414	−	0.994742i	$-0.532657\pi$
$727$	16.0098	−	7.46550i	0.593771	−	0.276880i	0.696186	+	0.717862i	$0.254879\pi$
$728$	0.112430	+	1.28508i	0.00416692	+	0.0476281i
$729$		0			0
$730$	20.1956	−	36.1616i	0.747472	−	1.33840i
$731$	0.167893	−	0.952169i	0.00620975	−	0.0352173i
$732$		0			0
$733$	−10.6117	+	39.6034i	−0.391952	+	1.46279i	0.434957	+	0.900451i	$0.356764\pi$
$733$	−10.6117	+	39.6034i	−0.391952	+	1.46279i	−0.826909	+	0.562335i	$0.809903\pi$
$734$	−0.0710890	+	0.123130i	−0.00262394	+	0.00454480i
$735$		0			0
$736$	12.8399	−	35.2774i	0.473286	−	1.30034i
$737$	37.7240	+	17.5910i	1.38958	+	0.647973i
$738$		0			0
$739$	13.0374	−	2.29884i	0.479587	−	0.0845642i	0.0713718	−	0.997450i	$-0.477262\pi$
$739$	13.0374	−	2.29884i	0.479587	−	0.0845642i	0.408215	+	0.912886i	$0.366151\pi$
$740$	3.98654	−	15.7749i	0.146548	−	0.579895i
$741$		0			0
$742$	0.919509	−	0.919509i	0.0337562	−	0.0337562i
$743$	−0.404372	−	0.283145i	−0.0148350	−	0.0103876i	0.566135	−	0.824312i	$-0.308438\pi$
$743$	−0.404372	−	0.283145i	−0.0148350	−	0.0103876i	−0.580970	+	0.813925i	$0.697327\pi$
$744$		0			0
$745$	16.7748	+	13.6727i	0.614581	+	0.500929i
$746$	4.22518	+	1.53784i	0.154695	+	0.0563043i
$747$		0			0
$748$	−20.1284	+	5.39340i	−0.735969	+	0.197202i
$749$	2.23805	+	3.87642i	0.0817765	+	0.141641i
$750$		0			0
$751$	−41.0072	−	7.23068i	−1.49637	−	0.263851i	−0.635275	−	0.772286i	$-0.719113\pi$
$751$	−41.0072	−	7.23068i	−1.49637	−	0.263851i	−0.861100	+	0.508435i	$0.830224\pi$
$752$	24.3281	+	6.51869i	0.887154	+	0.237712i
$753$		0			0
$754$	0.00949526	+	0.00796747i	0.000345797	+	0.000290158i
$755$	−1.30289	−	6.81871i	−0.0474171	−	0.248158i
$756$		0			0
$757$	−3.70042	+	42.2960i	−0.134494	+	1.53728i	0.566472	+	0.824081i	$0.308308\pi$
$757$	−3.70042	+	42.2960i	−0.134494	+	1.53728i	−0.700966	+	0.713195i	$0.747248\pi$
$758$	28.5549	−	40.7807i	1.03716	−	1.48122i
$759$		0			0
$760$	−5.85161	−	16.6904i	−0.212260	−	0.605423i
$761$	24.7086			0.895686			0.447843	−	0.894112i	$-0.352192\pi$
$761$	24.7086			0.895686			0.447843	+	0.894112i	$0.352192\pi$
$762$		0			0
$763$	0.236483	−	2.70301i	0.00856126	−	0.0978557i
$764$	1.47652	+	4.05671i	0.0534187	+	0.146767i
$765$		0			0
$766$	27.7420	+	23.2783i	1.00236	+	0.841080i
$767$	−1.36532	−	5.09543i	−0.0492987	−	0.183985i
$768$		0			0
$769$	28.5485	+	5.03387i	1.02948	+	0.181526i	0.662782	−	0.748812i	$-0.269376\pi$
$769$	28.5485	+	5.03387i	1.02948	+	0.181526i	0.366703	+	0.930338i	$0.380487\pi$
$770$	−1.79616	−	4.72410i	−0.0647292	−	0.170245i
$771$		0			0
$772$	−11.1606	+	2.99047i	−0.401678	+	0.107629i
$773$	−32.1932	+	2.81654i	−1.15791	+	0.101304i	−0.649880	−	0.760037i	$-0.725181\pi$
$773$	−32.1932	+	2.81654i	−1.15791	+	0.101304i	−0.508028	+	0.861341i	$0.669625\pi$
$774$		0			0
$775$	16.4188	+	2.41430i	0.589781	+	0.0867241i
$776$	−8.29211	+	6.95791i	−0.297669	+	0.249774i
$777$		0			0
$778$	5.14734	−	5.14734i	0.184541	−	0.184541i
$779$	0.401867	−	0.806130i	0.0143984	−	0.0288826i
$780$		0			0
$781$	−57.2619	+	10.0968i	−2.04899	+	0.361293i
$782$	−62.5609	−	5.47337i	−2.23717	−	0.195727i
$783$		0			0
$784$	11.8218	−	32.4802i	0.422208	−	1.16001i
$785$	−29.2767	+	21.1285i	−1.04493	+	0.754110i
$786$		0			0
$787$	−4.81711	+	17.9777i	−0.171711	+	0.640836i	0.825377	+	0.564582i	$0.190963\pi$
$787$	−4.81711	+	17.9777i	−0.171711	+	0.640836i	−0.997088	+	0.0762539i	$0.975704\pi$
$788$	−0.130209	+	0.0911732i	−0.00463850	+	0.00324791i
$789$		0			0
$790$	−5.73306	−	20.2367i	−0.203973	−	0.719989i
$791$	−0.458580	−	0.264761i	−0.0163052	−	0.00941383i
$792$		0			0
$793$	−8.99471	+	4.19430i	−0.319411	+	0.148944i
$794$	−33.2963	+	12.1189i	−1.18164	+	0.430082i
$795$		0			0
$796$	0.817579	+	4.63672i	0.0289783	+	0.164344i
$797$	−17.8040	−	17.8040i	−0.630650	−	0.630650i	0.317581	−	0.948231i	$-0.397129\pi$
$797$	−17.8040	−	17.8040i	−0.630650	−	0.630650i	−0.948231	+	0.317581i	$0.897129\pi$
$798$		0			0
$799$		−	24.2912i		−	0.859362i
$800$	−11.0761	−	22.0848i	−0.391598	−	0.780815i
$801$		0			0
$802$	−13.1680	+	28.2389i	−0.464979	+	0.997150i
$803$	−20.9482	−	44.9235i	−0.739245	−	1.58532i
$804$		0			0
$805$	−0.0695813	−	4.87665i	−0.00245242	−	0.171879i
$806$	12.2087	−	7.04867i	0.430032	−	0.248279i
$807$		0			0
$808$	−11.5925	−	16.5558i	−0.407822	−	0.582430i
$809$	9.34965	−	5.39802i	0.328716	−	0.189784i	−0.326555	−	0.945178i	$-0.605888\pi$
$809$	9.34965	−	5.39802i	0.328716	−	0.189784i	0.655271	+	0.755394i	$0.272554\pi$
$810$		0			0
$811$	−29.9351	+	35.6753i	−1.05116	+	1.25273i	−0.0845686	+	0.996418i	$0.526951\pi$
$811$	−29.9351	+	35.6753i	−1.05116	+	1.25273i	−0.966595	+	0.256310i	$0.917493\pi$
$812$	0.000333569	0	0.000715340i	1.17060e−5	0	2.51035e-5i
$813$		0			0
$814$	−39.0877	−	46.5829i	−1.37002	−	1.63273i
$815$	−0.0134854	+	0.184405i	−0.000472373	+	0.00645944i
$816$		0			0
$817$	−0.579447	+	0.655017i	−0.0202723	+	0.0229161i
$818$	−14.9539	−	14.9539i	−0.522852	−	0.522852i
$819$		0			0
$820$	0.143034	−	0.411142i	0.00499497	−	0.0143577i
$821$	−42.5776	+	15.4970i	−1.48597	+	0.540848i	−0.952384	−	0.304900i	$-0.901377\pi$
$821$	−42.5776	+	15.4970i	−1.48597	+	0.540848i	−0.533583	+	0.845748i	$0.679155\pi$
$822$		0			0
$823$	−4.79043	−	54.7548i	−0.166984	−	1.90863i	−0.369296	−	0.929312i	$-0.620401\pi$
$823$	−4.79043	−	54.7548i	−0.166984	−	1.90863i	0.202312	−	0.979321i	$-0.435154\pi$
$824$	−1.29666	−	0.748626i	−0.0451712	−	0.0260796i
$825$		0			0
$826$	0.182161	−	1.03309i	0.00633820	−	0.0359457i
$827$	5.78980	−	4.05406i	0.201331	−	0.140973i	−0.468563	−	0.883430i	$-0.655228\pi$
$827$	5.78980	−	4.05406i	0.201331	−	0.140973i	0.669894	+	0.742456i	$0.266339\pi$
$828$		0			0
$829$	3.92941	−	6.80594i	0.136474	−	0.236380i	−0.789685	−	0.613512i	$-0.789756\pi$
$829$	3.92941	−	6.80594i	0.136474	−	0.236380i	0.926160	+	0.377132i	$0.123090\pi$
$830$	9.78472	−	60.5295i	0.339632	−	2.10101i
$831$		0			0
$832$	3.40603	+	1.58826i	0.118083	+	0.0550630i
$833$	−33.2095	−	2.90546i	−1.15064	−	0.100668i
$834$		0			0
$835$	18.6942	+	4.72429i	0.646938	+	0.163491i
$836$	18.0727	+	5.35231i	0.625057	+	0.185113i
$837$		0			0
$838$	−43.2448	−	30.2804i	−1.49387	−	1.04602i
$839$	−13.3579	+	11.2087i	−0.461168	+	0.386966i	−0.843560	−	0.537034i	$-0.819545\pi$
$839$	−13.3579	+	11.2087i	−0.461168	+	0.386966i	0.382393	+	0.924000i	$0.375100\pi$
$840$		0			0
$841$	27.2511	+	9.91858i	0.939692	+	0.342020i
$842$	28.4982	−	2.49327i	0.982113	−	0.0859238i
$843$		0			0
$844$	0.0448173	+	0.0776258i	0.00154267	+	0.00267199i
$845$	14.3552	−	5.45805i	0.493835	−	0.187763i
$846$		0			0
$847$	−2.79191	−	0.748091i	−0.0959313	−	0.0257047i
$848$	−3.41511	−	12.7453i	−0.117275	−	0.437677i
$849$		0			0
$850$	−30.8895	+	27.4587i	−1.05950	+	0.941824i
$851$	−20.0702	−	55.1425i	−0.687998	−	1.89026i
$852$		0			0
$853$	−28.1590	+	40.2152i	−0.964146	+	1.37694i	−0.0382064	+	0.999270i	$0.512164\pi$
$853$	−28.1590	+	40.2152i	−0.964146	+	1.37694i	−0.925939	+	0.377673i	$0.876724\pi$
$854$	−1.97360			−0.0675354
$855$		0			0
$856$	28.2920			0.967001
$857$	−0.0631803	+	0.0902309i	−0.00215820	+	0.00308223i	−0.820230	−	0.572034i	$-0.806154\pi$
$857$	−0.0631803	+	0.0902309i	−0.00215820	+	0.00308223i	0.818071	+	0.575117i	$0.195043\pi$
$858$		0			0
$859$	13.8823	+	38.1414i	0.473659	+	1.30137i	0.914792	+	0.403926i	$0.132355\pi$
$859$	13.8823	+	38.1414i	0.473659	+	1.30137i	−0.441132	+	0.897442i	$0.645423\pi$
$860$	−0.237454	+	0.349633i	−0.00809713	+	0.0119224i
$861$		0			0
$862$	6.89101	+	25.7176i	0.234709	+	0.875945i
$863$	−17.8927	−	4.79433i	−0.609074	−	0.163201i	−0.0589178	−	0.998263i	$-0.518765\pi$
$863$	−17.8927	−	4.79433i	−0.609074	−	0.163201i	−0.550156	+	0.835062i	$0.685432\pi$
$864$		0			0
$865$	−19.2710	−	8.65368i	−0.655234	−	0.294234i
$866$	11.0578	+	19.1526i	0.375759	+	0.650833i
$867$		0			0
$868$	0.894263	−	0.0782379i	0.0303533	−	0.00265557i
$869$	−23.6531	−	8.60903i	−0.802377	−	0.292041i
$870$		0			0
$871$	17.2019	−	14.4341i	0.582865	−	0.489082i
$872$	−14.0486	−	9.83693i	−0.475745	−	0.333121i
$873$		0			0
$874$	45.6634	+	33.7853i	1.54459	+	1.14280i
$875$	−2.36466	−	2.17043i	−0.0799401	−	0.0733740i
$876$		0			0
$877$	30.8351	+	2.69772i	1.04123	+	0.0910956i	0.594921	−	0.803784i	$-0.297183\pi$
$877$	30.8351	+	2.69772i	1.04123	+	0.0910956i	0.446307	+	0.894880i	$0.352739\pi$
$878$	−52.2966	−	24.3863i	−1.76493	−	0.822998i
$879$		0			0
$880$	−50.6260	−	8.18380i	−1.70660	−	0.275876i
$881$	−0.542908	+	0.940344i	−0.0182910	+	0.0316810i	−0.875026	−	0.484076i	$-0.839156\pi$
$881$	−0.542908	+	0.940344i	−0.0182910	+	0.0316810i	0.856735	+	0.515757i	$0.172489\pi$
$882$		0			0
$883$	−22.0280	+	15.4242i	−0.741302	+	0.519065i	−0.882151	−	0.470966i	$-0.843905\pi$
$883$	−22.0280	+	15.4242i	−0.741302	+	0.519065i	0.140850	+	0.990031i	$0.455017\pi$
$884$	−1.95217	+	11.0713i	−0.0656585	+	0.372368i
$885$		0			0
$886$	24.9015	+	14.3769i	0.836582	+	0.483001i
$887$	2.05570	+	23.4968i	0.0690238	+	0.788946i	0.949277	+	0.314441i	$0.101817\pi$
$887$	2.05570	+	23.4968i	0.0690238	+	0.788946i	−0.880253	+	0.474504i	$0.842627\pi$
$888$		0			0
$889$	2.71832	−	0.989389i	0.0911696	−	0.0331830i
$890$	−54.5913	+	26.4110i	−1.82991	+	0.885299i
$891$		0			0
$892$	−0.457845	−	0.457845i	−0.0153298	−	0.0153298i
$893$	−11.4791	+	18.7345i	−0.384134	+	0.626927i
$894$		0			0
$895$	10.4926	+	12.1484i	0.350730	+	0.406075i
$896$	2.30409	+	2.74591i	0.0769743	+	0.0917344i
$897$		0			0
$898$	−12.5865	−	26.9918i	−0.420017	−	0.900729i
$899$	−0.00622611	+	0.00741999i	−0.000207652	+	0.000247471i
$900$		0			0
$901$	−11.0211	+	6.36302i	−0.367165	+	0.211983i
$902$	−0.933160	−	1.33269i	−0.0310708	−	0.0443737i
$903$		0			0
$904$	−2.89854	+	1.67347i	−0.0964040	+	0.0556589i
$905$	3.60315	−	0.0514107i	0.119773	−	0.00170895i
$906$		0			0
$907$	−2.75446	−	5.90696i	−0.0914603	−	0.196137i	0.855256	−	0.518205i	$-0.173400\pi$
$907$	−2.75446	−	5.90696i	−0.0914603	−	0.196137i	−0.946716	+	0.322068i	$0.895622\pi$
$908$	−1.76369	+	3.78225i	−0.0585301	+	0.125518i
$909$		0			0
$910$	−2.71932	−	0.198862i	−0.0901447	−	0.00659220i
$911$			27.6418i			0.915812i	0.889001	+	0.457906i	$0.151400\pi$
$911$			27.6418i			0.915812i	−0.889001	+	0.457906i	$0.848600\pi$
$912$		0			0
$913$	−51.8863	−	51.8863i	−1.71719	−	1.71719i
$914$	1.76271	+	9.99681i	0.0583052	+	0.330665i
$915$		0			0
$916$	−1.45301	+	0.528854i	−0.0480089	+	0.0174738i
$917$	5.08991	−	2.37346i	0.168084	−	0.0783787i
$918$		0			0
$919$	23.3008	+	13.4527i	0.768623	+	0.443764i	0.832383	−	0.554201i	$-0.186976\pi$
$919$	23.3008	+	13.4527i	0.768623	+	0.443764i	−0.0637605	+	0.997965i	$0.520309\pi$
$920$	−26.9141	−	15.0310i	−0.887331	−	0.495558i
$921$		0			0
$922$	−19.6995	+	13.7938i	−0.648770	+	0.454274i
$923$	−8.11879	+	30.2997i	−0.267233	+	0.997328i
$924$		0			0
$925$	−35.4523	−	15.3159i	−1.16566	−	0.503585i
$926$	8.44826	−	23.2114i	0.277627	−	0.762774i
$927$		0			0
$928$	0.0143655	+	0.00125682i	0.000471570	+	4.12570e-5i
$929$	49.9574	−	8.80883i	1.63905	−	0.289008i	0.723232	−	0.690605i	$-0.242656\pi$
$929$	49.9574	−	8.80883i	1.63905	−	0.289008i	0.915817	+	0.401597i	$0.131545\pi$
$930$		0			0
$931$	24.2397	+	17.9344i	0.794424	+	0.587776i
$932$	−6.43755	+	6.43755i	−0.210869	+	0.210869i
$933$		0			0
$934$	11.4767	−	9.63011i	0.375530	−	0.315107i
$935$	5.01331	+	49.2060i	0.163953	+	1.60921i
$936$		0			0
$937$	8.98755	−	0.786309i	0.293610	−	0.0256876i	0.0606010	−	0.998162i	$-0.480698\pi$
$937$	8.98755	−	0.786309i	0.293610	−	0.0256876i	0.233009	+	0.972474i	$0.425143\pi$
$938$	4.31336	−	1.15576i	0.140836	−	0.0377369i
$939$		0			0
$940$	−4.34980	+	9.68663i	−0.141875	+	0.315943i
$941$	1.15162	+	0.203063i	0.0375419	+	0.00661965i	0.192388	−	0.981319i	$-0.438377\pi$
$941$	1.15162	+	0.203063i	0.0375419	+	0.00661965i	−0.154846	+	0.987939i	$0.549488\pi$
$942$		0			0
$943$	−0.406339	−	1.51648i	−0.0132322	−	0.0493833i
$944$	−8.15412	−	6.84212i	−0.265394	−	0.222692i
$945$		0			0
$946$	0.540244	+	1.48431i	0.0175648	+	0.0482590i
$947$	−0.504745	+	5.76927i	−0.0164020	+	0.187476i	0.983574	+	0.180507i	$0.0577739\pi$
$947$	−0.504745	+	5.76927i	−0.0164020	+	0.187476i	−0.999976	+	0.00696893i	$0.997782\pi$
$948$		0			0
$949$	−26.7411			−0.868051
$950$	36.7993	−	6.58017i	1.19393	−	0.213489i
$951$		0			0
$952$	1.43995	−	2.05646i	0.0466690	−	0.0666503i
$953$	0.183503	−	2.09745i	0.00594425	−	0.0679431i	−0.992643	−	0.121077i	$-0.961365\pi$
$953$	0.183503	−	2.09745i	0.00594425	−	0.0679431i	0.998587	+	0.0531335i	$0.0169209\pi$
$954$		0			0
$955$	10.0646	−	1.92310i	0.325683	−	0.0622302i
$956$	−4.51315	−	3.78698i	−0.145966	−	0.122480i
$957$		0			0
$958$	−33.0936	−	8.86741i	−1.06921	−	0.286493i
$959$	3.01324	+	0.531315i	0.0973025	+	0.0171571i
$960$		0			0
$961$	−9.99187	−	17.3064i	−0.322319	−	0.558272i
$962$	−31.6882	+	8.49082i	−1.02167	+	0.273755i
$963$		0			0
$964$	11.1045	+	4.04172i	0.357653	+	0.130175i
$965$	2.77972	+	27.2832i	0.0894824	+	0.878276i
$966$		0			0
$967$	−35.0900	−	24.5703i	−1.12842	−	0.790127i	−0.148379	−	0.988931i	$-0.547405\pi$
$967$	−35.0900	−	24.5703i	−1.12842	−	0.790127i	−0.980039	+	0.198804i	$0.936294\pi$
$968$	−12.9184	+	12.9184i	−0.415212	+	0.415212i
$969$		0			0
$970$	−11.7212	−	19.6490i	−0.376347	−	0.630890i
$971$	−29.4711	+	5.19655i	−0.945772	+	0.166765i	−0.625205	−	0.780461i	$-0.714985\pi$
$971$	−29.4711	+	5.19655i	−0.945772	+	0.166765i	−0.320567	+	0.947226i	$0.603874\pi$
$972$		0			0
$973$	−3.99633	−	1.86352i	−0.128117	−	0.0597417i
$974$	7.81592	−	21.4741i	0.250438	−	0.688073i
$975$		0			0
$976$	−10.0131	+	17.3431i	−0.320511	+	0.555141i
$977$	4.89371	−	18.2636i	0.156564	−	0.584303i	−0.842403	−	0.538848i	$-0.818860\pi$
$977$	4.89371	−	18.2636i	0.156564	−	0.584303i	0.998966	−	0.0454549i	$-0.0144737\pi$
$978$		0			0
$979$	−12.6026	+	71.4730i	−0.402782	+	2.28429i
$980$	12.7227	+	7.10539i	0.406412	+	0.226973i
$981$		0			0
$982$	−3.69075	−	42.1854i	−0.117777	−	1.34619i
$983$	46.3328	−	21.6053i	1.47779	−	0.689103i	0.494168	−	0.869367i	$-0.335473\pi$
$983$	46.3328	−	21.6053i	1.47779	−	0.689103i	0.983618	+	0.180264i	$0.0576951\pi$
$984$		0			0
$985$	0.164310	+	0.339627i	0.00523535	+	0.0108214i
$986$	−0.00418885	−	0.0237561i	−0.000133400	−	0.000756549i
$987$		0			0
$988$	6.73748	−	7.61618i	0.214348	−	0.242303i
$989$			1.52428i			0.0484694i
$990$		0			0
$991$	35.3727	+	42.1556i	1.12365	+	1.33912i	0.934003	+	0.357264i	$0.116290\pi$
$991$	35.3727	+	42.1556i	1.12365	+	1.33912i	0.189648	+	0.981852i	$0.439265\pi$
$992$	6.93120	−	14.8640i	0.220066	−	0.471933i
$993$		0			0
$994$	−4.00970	+	4.77857i	−0.127180	+	0.151567i
$995$	11.1740	−	0.159434i	0.354240	−	0.00505439i
$996$		0			0
$997$	−8.15440	−	11.6457i	−0.258252	−	0.368823i	0.668998	−	0.743264i	$-0.266723\pi$
$997$	−8.15440	−	11.6457i	−0.258252	−	0.368823i	−0.927251	+	0.374441i	$0.877834\pi$
$998$	−18.5720	−	26.5235i	−0.587886	−	0.839588i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.dl.a.523.6		96
3.2	odd	2		95.2.r.a.48.3	yes	96
5.2	odd	4	inner	855.2.dl.a.352.6		96
15.2	even	4		95.2.r.a.67.3	yes	96
15.8	even	4		475.2.bb.b.257.6		96
15.14	odd	2		475.2.bb.b.143.6		96
19.2	odd	18	inner	855.2.dl.a.838.6		96
57.2	even	18		95.2.r.a.78.3	yes	96
95.2	even	36	inner	855.2.dl.a.667.6		96
285.2	odd	36		95.2.r.a.2.3	✓	96
285.59	even	18		475.2.bb.b.268.6		96
285.173	odd	36		475.2.bb.b.382.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.3	✓	96	285.2	odd	36
95.2.r.a.48.3	yes	96	3.2	odd	2
95.2.r.a.67.3	yes	96	15.2	even	4
95.2.r.a.78.3	yes	96	57.2	even	18
475.2.bb.b.143.6		96	15.14	odd	2
475.2.bb.b.257.6		96	15.8	even	4
475.2.bb.b.268.6		96	285.59	even	18
475.2.bb.b.382.6		96	285.173	odd	36
855.2.dl.a.352.6		96	5.2	odd	4	inner
855.2.dl.a.523.6		96	1.1	even	1	trivial
855.2.dl.a.667.6		96	95.2	even	36	inner
855.2.dl.a.838.6		96	19.2	odd	18	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.dl (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.983828 - 1.40505i) q^{2} +(-0.322212 - 0.885271i) q^{4} +(-2.19633 + 0.419667i) q^{5} +(0.0743036 + 0.277305i) q^{7} +(1.75276 + 0.469650i) q^{8} +(-1.57116 + 3.49884i) q^{10} +(2.29500 + 3.97505i) q^{11} +(2.46682 - 0.215819i) q^{13} +(0.462730 + 0.168420i) q^{14} +(3.82765 - 3.21178i) q^{16} +(-3.94756 - 2.76411i) q^{17} +(1.73832 + 3.99728i) q^{19} +(1.07920 + 1.80913i) q^{20} +(7.84303 + 0.686176i) q^{22} +(6.88562 + 3.21082i) q^{23} +(4.64776 - 1.84346i) q^{25} +(2.12369 - 3.67833i) q^{26} +(0.221548 - 0.155130i) q^{28} +(-0.000506761 + 0.00287398i) q^{29} +(2.87440 + 1.65954i) q^{31} +(-0.430665 - 4.92252i) q^{32} +(-7.76743 + 2.82711i) q^{34} +(-0.279571 - 0.577871i) q^{35} +(-5.46158 - 5.46158i) q^{37} +(7.32659 + 1.49020i) q^{38} +(-4.04674 - 0.295934i) q^{40} +(-0.132829 - 0.158299i) q^{41} +(0.0847905 + 0.181834i) q^{43} +(2.77952 - 3.31250i) q^{44} +(11.2856 - 6.51576i) q^{46} +(2.89119 + 4.12905i) q^{47} +(5.99080 - 3.45879i) q^{49} +(1.98245 - 8.34398i) q^{50} +(-0.985897 - 2.11426i) q^{52} +(1.11603 - 2.39334i) q^{53} +(-6.70877 - 7.76740i) q^{55} +0.520945i q^{56} +(0.00353953 + 0.00353953i) q^{58} +(-0.369926 - 2.09795i) q^{59} +(-3.76621 + 1.37079i) q^{61} +(5.15965 - 2.40598i) q^{62} +(1.31435 + 0.758840i) q^{64} +(-5.32738 + 1.50925i) q^{65} +(7.42839 - 5.20141i) q^{67} +(-1.17503 + 4.38529i) q^{68} +(-1.08699 - 0.175714i) q^{70} +(-4.33266 + 11.9039i) q^{71} +(-10.7580 - 0.941200i) q^{73} +(-13.0471 + 2.30055i) q^{74} +(2.97856 - 2.82686i) q^{76} +(-0.931774 + 0.931774i) q^{77} +(-4.20092 + 3.52499i) q^{79} +(-7.05892 + 8.66048i) q^{80} +(-0.353099 + 0.0308922i) q^{82} +(-15.4419 + 4.13763i) q^{83} +(9.83016 + 4.41425i) q^{85} +(0.338905 + 0.0597581i) q^{86} +(2.15569 + 8.04514i) q^{88} +(12.1125 + 10.1636i) q^{89} +(0.243141 + 0.668024i) q^{91} +(0.623812 - 7.13020i) q^{92} +8.64596 q^{94} +(-5.49546 - 8.04984i) q^{95} +(-3.42156 + 4.88649i) q^{97} +(1.03414 - 11.8202i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^5 + 18 * q^8 - 12 * q^10 + 12 * q^11 - 12 * q^13 + 12 * q^16 + 30 * q^17 + 84 * q^20 - 24 * q^22 + 12 * q^25 + 48 * q^26 - 36 * q^31 - 18 * q^32 + 30 * q^35 - 54 * q^38 + 54 * q^40 - 12 * q^41 + 48 * q^43 - 36 * q^46 + 24 * q^47 - 126 * q^50 + 30 * q^53 + 18 * q^55 + 120 * q^58 - 48 * q^61 - 60 * q^62 - 72 * q^65 + 108 * q^67 - 18 * q^68 + 36 * q^70 + 24 * q^71 + 6 * q^73 + 60 * q^76 - 168 * q^77 + 60 * q^80 + 60 * q^82 - 36 * q^85 + 180 * q^86 - 198 * q^88 - 24 * q^91 + 72 * q^92 + 24 * q^95 - 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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