LMFDB - Embedded newform 855.2.dl.a.838.6

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			838.6
Character	$\chi$	$=$	855.838
Dual form			855.2.dl.a.352.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40505 - 0.983828i) q^{2} +(0.322212 - 0.885271i) q^{4} +(-1.41273 + 1.73326i) q^{5} +(-0.277305 - 0.0743036i) q^{7} +(0.469650 + 1.75276i) q^{8} +(-0.279734 + 3.82520i) q^{10} +(2.29500 - 3.97505i) q^{11} +(-0.215819 + 2.46682i) q^{13} +(-0.462730 + 0.168420i) q^{14} +(3.82765 + 3.21178i) q^{16} +(2.76411 + 3.94756i) q^{17} +(-1.73832 + 3.99728i) q^{19} +(1.07920 + 1.80913i) q^{20} +(-0.686176 - 7.84303i) q^{22} +(3.21082 + 6.88562i) q^{23} +(-1.00837 - 4.89726i) q^{25} +(2.12369 + 3.67833i) q^{26} +(-0.155130 + 0.221548i) q^{28} +(0.000506761 + 0.00287398i) q^{29} +(2.87440 - 1.65954i) q^{31} +(4.92252 + 0.430665i) q^{32} +(7.76743 + 2.82711i) q^{34} +(0.520545 - 0.375670i) q^{35} +(5.46158 + 5.46158i) q^{37} +(1.49020 + 7.32659i) q^{38} +(-3.70147 - 1.66215i) q^{40} +(-0.132829 + 0.158299i) q^{41} +(0.181834 + 0.0847905i) q^{43} +(-2.77952 - 3.31250i) q^{44} +(11.2856 + 6.51576i) q^{46} +(-4.12905 - 2.89119i) q^{47} +(-5.99080 - 3.45879i) q^{49} +(-6.23488 - 5.88884i) q^{50} +(2.11426 + 0.985897i) q^{52} +(-2.39334 + 1.11603i) q^{53} +(3.64758 + 9.59350i) q^{55} -0.520945i q^{56} +(0.00353953 + 0.00353953i) q^{58} +(0.369926 - 2.09795i) q^{59} +(-3.76621 - 1.37079i) q^{61} +(2.40598 - 5.15965i) q^{62} +(-1.31435 + 0.758840i) q^{64} +(-3.97074 - 3.85902i) q^{65} +(5.20141 - 7.42839i) q^{67} +(4.38529 - 1.17503i) q^{68} +(0.361798 - 1.03996i) q^{70} +(-4.33266 - 11.9039i) q^{71} +(-0.941200 - 10.7580i) q^{73} +(13.0471 + 2.30055i) q^{74} +(2.97856 + 2.82686i) q^{76} +(-0.931774 + 0.931774i) q^{77} +(4.20092 + 3.52499i) q^{79} +(-10.9743 + 2.09692i) q^{80} +(-0.0308922 + 0.353099i) q^{82} +(4.13763 - 15.4419i) q^{83} +(-10.7471 - 0.785925i) q^{85} +(0.338905 - 0.0597581i) q^{86} +(8.04514 + 2.15569i) q^{88} +(-12.1125 + 10.1636i) q^{89} +(0.243141 - 0.668024i) q^{91} +(7.13020 - 0.623812i) q^{92} -8.64596 q^{94} +(-4.47253 - 8.66005i) q^{95} +(-4.88649 + 3.42156i) q^{97} +(-11.8202 + 1.03414i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.40505	−	0.983828i	0.993521	−	0.695671i	0.0406901	−	0.999172i	$-0.487044\pi$
$2$	1.40505	−	0.983828i	0.993521	−	0.695671i	0.952831	+	0.303501i	$0.0981555\pi$
$3$		0			0
$3$		0			0
$4$	0.322212	−	0.885271i	0.161106	−	0.442635i
$5$	−1.41273	+	1.73326i	−0.631793	+	0.775137i
$5$	−1.41273	+	1.73326i	−0.631793	+	0.775137i
$6$		0			0
$7$	−0.277305	−	0.0743036i	−0.104811	−	0.0280841i	0.206032	−	0.978545i	$-0.433945\pi$
$7$	−0.277305	−	0.0743036i	−0.104811	−	0.0280841i	−0.310844	+	0.950461i	$0.600612\pi$
$8$	0.469650	+	1.75276i	0.166046	+	0.619693i
$9$		0			0
$10$	−0.279734	+	3.82520i	−0.0884596	+	1.20964i
$11$	2.29500	−	3.97505i	0.691967	−	1.19852i	−0.279225	−	0.960226i	$-0.590078\pi$
$11$	2.29500	−	3.97505i	0.691967	−	1.19852i	0.971192	−	0.238297i	$-0.0765891\pi$
$12$		0			0
$13$	−0.215819	+	2.46682i	−0.0598573	+	0.684172i	0.905689	+	0.423942i	$0.139354\pi$
$13$	−0.215819	+	2.46682i	−0.0598573	+	0.684172i	−0.965547	+	0.260230i	$0.916202\pi$
$14$	−0.462730	+	0.168420i	−0.123670	+	0.0450121i
$15$		0			0
$16$	3.82765	+	3.21178i	0.956913	+	0.802946i
$17$	2.76411	+	3.94756i	0.670395	+	0.957423i	0.999912	+	0.0132738i	$0.00422530\pi$
$17$	2.76411	+	3.94756i	0.670395	+	0.957423i	−0.329517	+	0.944150i	$0.606886\pi$
$18$		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
$22$	−0.686176	−	7.84303i	−0.146293	−	1.67214i
$23$	3.21082	+	6.88562i	0.669501	+	1.43575i	0.887968	+	0.459906i	$0.152117\pi$
$23$	3.21082	+	6.88562i	0.669501	+	1.43575i	−0.218466	+	0.975845i	$0.570105\pi$
$24$		0			0
$25$	−1.00837	−	4.89726i	−0.201675	−	0.979453i
$26$	2.12369	+	3.67833i	0.416489	+	0.721380i
$27$		0			0
$28$	−0.155130	+	0.221548i	−0.0293168	+	0.0418687i
$29$	0.000506761		0.00287398i	9.41031e−5		0.000533685i	0.984855	−	0.173381i	$-0.0554693\pi$
$29$	0.000506761		0.00287398i	9.41031e−5		0.000533685i	−0.984761	+	0.173915i	$0.944358\pi$
$30$		0			0
$31$	2.87440	−	1.65954i	0.516258	−	0.298062i	−0.219144	−	0.975692i	$-0.570327\pi$
$31$	2.87440	−	1.65954i	0.516258	−	0.298062i	0.735402	+	0.677631i	$0.236993\pi$
$32$	4.92252	+	0.430665i	0.870187	+	0.0761315i
$33$		0			0
$34$	7.76743	+	2.82711i	1.33210	+	0.484846i
$35$	0.520545	−	0.375670i	0.0879882	−	0.0634998i
$36$		0			0
$37$	5.46158	+	5.46158i	0.897878	+	0.897878i	0.995248	−	0.0973701i	$-0.0310431\pi$
$37$	5.46158	+	5.46158i	0.897878	+	0.897878i	−0.0973701	+	0.995248i	$0.531043\pi$
$38$	1.49020	+	7.32659i	0.241742	+	1.18853i
$39$		0			0
$40$	−3.70147	−	1.66215i	−0.585254	−	0.262809i
$41$	−0.132829	+	0.158299i	−0.0207444	+	0.0247222i	−0.776317	−	0.630343i	$-0.782914\pi$
$41$	−0.132829	+	0.158299i	−0.0207444	+	0.0247222i	0.755573	+	0.655065i	$0.227359\pi$
$42$		0			0
$43$	0.181834	+	0.0847905i	0.0277294	+	0.0129304i	0.436433	−	0.899737i	$-0.356241\pi$
$43$	0.181834	+	0.0847905i	0.0277294	+	0.0129304i	−0.408704	+	0.912667i	$0.634019\pi$
$44$	−2.77952	−	3.31250i	−0.419028	−	0.499379i
$45$		0			0
$46$	11.2856	+	6.51576i	1.66397	+	0.960696i
$47$	−4.12905	−	2.89119i	−0.602284	−	0.421724i	0.232269	−	0.972652i	$-0.425385\pi$
$47$	−4.12905	−	2.89119i	−0.602284	−	0.421724i	−0.834553	+	0.550928i	$0.814274\pi$
$48$		0			0
$49$	−5.99080	−	3.45879i	−0.855829	−	0.494113i
$50$	−6.23488	−	5.88884i	−0.881745	−	0.832808i
$51$		0			0
$52$	2.11426	+	0.985897i	0.293195	+	0.136719i
$53$	−2.39334	+	1.11603i	−0.328751	+	0.153299i	−0.579985	−	0.814627i	$-0.696942\pi$
$53$	−2.39334	+	1.11603i	−0.328751	+	0.153299i	0.251234	+	0.967926i	$0.419164\pi$
$54$		0			0
$55$	3.64758	+	9.59350i	0.491839	+	1.29359i
$56$		−	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	$-0.900161\pi$
$59$	0.369926	−	2.09795i	0.0481602	−	0.273130i	0.999373	+	0.0354053i	$0.0112722\pi$
$60$		0			0
$61$	−3.76621	−	1.37079i	−0.482214	−	0.175511i	0.0894634	−	0.995990i	$-0.471485\pi$
$61$	−3.76621	−	1.37079i	−0.482214	−	0.175511i	−0.571677	+	0.820479i	$0.693707\pi$
$62$	2.40598	−	5.15965i	0.305560	−	0.655276i
$63$		0			0
$64$	−1.31435	+	0.758840i	−0.164294	+	0.0948550i
$65$	−3.97074	−	3.85902i	−0.492510	−	0.478653i
$66$		0			0
$67$	5.20141	−	7.42839i	0.635454	−	0.907522i	−0.364263	−	0.931296i	$-0.618679\pi$
$67$	5.20141	−	7.42839i	0.635454	−	0.907522i	0.999717	+	0.0237737i	$0.00756811\pi$
$68$	4.38529	−	1.17503i	0.531794	−	0.142494i
$69$		0			0
$70$	0.361798	−	1.03996i	0.0432431	−	0.124299i
$71$	−4.33266	−	11.9039i	−0.514192	−	1.41273i	−0.876830	−	0.480800i	$-0.840346\pi$
$71$	−4.33266	−	11.9039i	−0.514192	−	1.41273i	0.362639	−	0.931930i	$-0.381876\pi$
$72$		0			0
$73$	−0.941200	−	10.7580i	−0.110159	−	1.25912i	−0.827126	−	0.562017i	$-0.810026\pi$
$73$	−0.941200	−	10.7580i	−0.110159	−	1.25912i	0.716967	−	0.697108i	$-0.245530\pi$
$74$	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	$-0.177953\pi$
$79$	4.20092	+	3.52499i	0.472641	+	0.396592i	−0.375116	+	0.926978i	$0.622397\pi$
$80$	−10.9743	+	2.09692i	−1.22696	+	0.234443i
$81$		0			0
$82$	−0.0308922	+	0.353099i	−0.00341147	+	0.0389933i
$83$	4.13763	−	15.4419i	0.454164	−	1.69496i	−0.236368	−	0.971664i	$-0.575957\pi$
$83$	4.13763	−	15.4419i	0.454164	−	1.69496i	0.690533	−	0.723301i	$-0.257376\pi$
$84$		0			0
$85$	−10.7471	−	0.785925i	−1.16569	−	0.0852455i
$86$	0.338905	−	0.0597581i	0.0365451	−	0.00644388i
$87$		0			0
$88$	8.04514	+	2.15569i	0.857615	+	0.229797i
$89$	−12.1125	+	10.1636i	−1.28392	+	1.07734i	−0.291228	+	0.956654i	$0.594064\pi$
$89$	−12.1125	+	10.1636i	−1.28392	+	1.07734i	−0.992691	+	0.120683i	$0.961492\pi$
$90$		0			0
$91$	0.243141	−	0.668024i	0.0254881	−	0.0700280i
$92$	7.13020	−	0.623812i	0.743375	−	0.0650369i
$93$		0			0
$94$	−8.64596			−0.891763
$95$	−4.47253	−	8.66005i	−0.458872	−	0.888502i
$96$		0			0
$97$	−4.88649	+	3.42156i	−0.496148	+	0.347407i	−0.794716	−	0.606982i	$-0.792380\pi$
$97$	−4.88649	+	3.42156i	−0.496148	+	0.347407i	0.298567	+	0.954389i	$0.403491\pi$
$98$	−11.8202	+	1.03414i	−1.19402	+	0.104464i
$99$		0			0
$100$	−4.66031	−	0.685274i	−0.466031	−	0.0685274i
$101$	−8.53219	+	7.15936i	−0.848985	+	0.712383i	−0.959566	−	0.281484i	$-0.909173\pi$
$101$	−8.53219	+	7.15936i	−0.848985	+	0.712383i	0.110581	+	0.993867i	$0.464729\pi$
$102$		0			0
$103$	−0.213557	−	0.797004i	−0.0210424	−	0.0785312i	0.954606	−	0.297871i	$-0.0962764\pi$
$103$	−0.213557	−	0.797004i	−0.0210424	−	0.0785312i	−0.975649	+	0.219340i	$0.929610\pi$
$104$	−4.42509	+	0.780263i	−0.433916	+	0.0765111i
$105$		0			0
$106$	−2.26479	+	3.92272i	−0.219975	+	0.381009i
$107$	4.03536	−	15.0602i	0.390113	−	1.45592i	−0.439835	−	0.898079i	$-0.644963\pi$
$107$	4.03536	−	15.0602i	0.390113	−	1.45592i	0.829947	−	0.557842i	$-0.188370\pi$
$108$		0			0
$109$	8.88129	−	3.23252i	0.850673	−	0.309620i	0.120358	−	0.992731i	$-0.461596\pi$
$109$	8.88129	−	3.23252i	0.850673	−	0.309620i	0.730315	+	0.683111i	$0.239373\pi$
$110$	14.5634	+	9.89078i	1.38856	+	0.943049i
$111$		0			0
$112$	−0.822780	−	1.17505i	−0.0777454	−	0.111032i
$113$	1.30423	−	1.30423i	0.122692	−	0.122692i	−0.643095	−	0.765787i	$-0.722350\pi$
$113$	1.30423	−	1.30423i	0.122692	−	0.122692i	0.765787	+	0.643095i	$0.222350\pi$
$114$		0			0
$115$	−16.4706	−	4.16236i	−1.53589	−	0.388142i
$116$	0.00270754		0.000477412i	0.000251389		4.43266e-5i
$117$		0			0
$118$	−1.54426	−	3.31168i	−0.142161	−	0.304864i
$119$	−0.473183	−	1.30006i	−0.0433767	−	0.119176i
$120$		0			0
$121$	−5.03401	−	8.71916i	−0.457637	−	0.792651i
$122$	−6.64034	+	1.77927i	−0.601188	+	0.161088i
$123$		0			0
$124$	−0.542972	−	3.07935i	−0.0487603	−	0.276534i
$125$	9.91279	+	5.17075i	0.886627	+	0.462486i
$126$		0			0
$127$	10.0380	+	0.878208i	0.890725	+	0.0779284i	0.523324	−	0.852134i	$-0.324692\pi$
$127$	10.0380	+	0.878208i	0.890725	+	0.0779284i	0.367402	+	0.930062i	$0.380247\pi$
$128$	−5.27675	+	11.3160i	−0.466403	+	1.00020i
$129$		0			0
$130$	−9.37570	−	1.51560i	−0.822304	−	0.132927i
$131$	−3.39696	+	19.2651i	−0.296794	+	1.68320i	0.363026	+	0.931779i	$0.381744\pi$
$131$	−3.39696	+	19.2651i	−0.296794	+	1.68320i	−0.659820	+	0.751423i	$0.729368\pi$
$132$		0			0
$133$	0.779058	−	0.979301i	0.0675529	−	0.0849162i
$134$		−	15.5546i		−	1.34371i
$135$		0			0
$136$	−5.62095	+	6.69879i	−0.481992	+	0.574416i
$137$	9.65926	−	4.50418i	0.825246	−	0.384818i	0.0363453	−	0.999339i	$-0.488428\pi$
$137$	9.65926	−	4.50418i	0.825246	−	0.384818i	0.788901	+	0.614521i	$0.210651\pi$
$138$		0			0
$139$	9.87278	+	11.7659i	0.837399	+	0.997973i	0.999936	+	0.0112706i	$0.00358761\pi$
$139$	9.87278	+	11.7659i	0.837399	+	0.997973i	−0.162538	+	0.986702i	$0.551968\pi$
$140$	−0.164844	−	0.581869i	−0.0139318	−	0.0491769i
$141$		0			0
$142$	−17.7990	−	12.4630i	−1.49366	−	1.04587i
$143$	9.31042	+	6.51922i	0.778576	+	0.545165i
$144$		0			0
$145$	−0.00569727	−	0.00318182i	−0.000473133	−	0.000264236i
$146$	−11.9064	−	14.1895i	−0.985382	−	1.17433i
$147$		0			0
$148$	6.59477	−	3.07519i	0.542086	−	0.252779i
$149$	6.22102	−	7.41392i	0.509646	−	0.607372i	−0.448454	−	0.893806i	$-0.648025\pi$
$149$	6.22102	−	7.41392i	0.509646	−	0.607372i	0.958100	+	0.286434i	$0.0924698\pi$
$150$		0			0
$151$		−	3.10459i		−	0.252648i	−0.991989	−	0.126324i	$-0.959682\pi$
$151$		−	3.10459i		−	0.252648i	0.991989	−	0.126324i	$-0.0403179\pi$
$152$	−7.82266	−	1.16954i	−0.634502	−	0.0948623i
$153$		0			0
$154$	−0.392486	+	2.22590i	−0.0316274	+	0.179368i
$155$	−1.18435	+	7.32657i	−0.0951296	+	0.588484i
$156$		0			0
$157$	6.82378	−	14.6336i	0.544597	−	1.16789i	−0.420811	−	0.907148i	$-0.638254\pi$
$157$	6.82378	−	14.6336i	0.544597	−	1.16789i	0.965408	−	0.260744i	$-0.0839678\pi$
$158$	9.37049	+	0.819812i	0.745476	+	0.0652207i
$159$		0			0
$160$	−7.70066	+	7.92359i	−0.608791	+	0.626415i
$161$	−0.378749	−	2.14799i	−0.0298496	−	0.169285i
$162$		0			0
$163$	−0.0798713	+	0.0214015i	−0.00625600	+	0.00167629i	−0.261946	−	0.965083i	$-0.584364\pi$
$163$	−0.0798713	+	0.0214015i	−0.00625600	+	0.00167629i	0.255690	+	0.966759i	$0.417697\pi$
$164$	0.0973387	+	0.168596i	0.00760088	+	0.0131651i
$165$		0			0
$166$	−9.37854	−	25.7673i	−0.727916	−	1.99993i
$167$	3.64429	+	7.81520i	0.282003	+	0.604758i	0.995379	−	0.0960237i	$-0.0306125\pi$
$167$	3.64429	+	7.81520i	0.282003	+	0.604758i	−0.713376	+	0.700782i	$0.752835\pi$
$168$		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
$173$	5.41875	+	7.73878i	0.411980	+	0.588369i	0.970494	−	0.241127i	$-0.0775170\pi$
$173$	5.41875	+	7.73878i	0.411980	+	0.588369i	−0.558514	+	0.829495i	$0.688628\pi$
$174$		0			0
$175$	−0.0842574	+	1.43296i	−0.00636926	+	0.108322i
$176$	21.5514	−	7.84408i	1.62450	−	0.591270i
$177$		0			0
$178$	−7.01944	+	26.1969i	−0.526130	+	1.96354i
$179$	3.58941	−	6.21705i	0.268285	−	0.464684i	−0.700134	−	0.714012i	$-0.746876\pi$
$179$	3.58941	−	6.21705i	0.268285	−	0.464684i	0.968419	+	0.249328i	$0.0802096\pi$
$180$		0			0
$181$	−1.58706	+	0.279841i	−0.117965	+	0.0208004i	−0.232319	−	0.972640i	$-0.574631\pi$
$181$	−1.58706	+	0.279841i	−0.117965	+	0.0208004i	0.114354	+	0.993440i	$0.463520\pi$
$182$	−0.315595	−	1.17782i	−0.0233935	−	0.0873056i
$183$		0			0
$184$	−10.5609	+	8.86161i	−0.778557	+	0.653287i
$185$	−17.1821	+	1.75058i	−1.26325	+	0.128705i
$186$		0			0
$187$	22.0354	−	1.92784i	1.61139	−	0.140978i
$188$	−3.88992	+	2.72375i	−0.283702	+	0.198650i
$189$		0			0
$190$	−14.8041	−	7.76762i	−1.07400	−	0.563522i
$191$	−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
$193$	−12.2179	+	1.06893i	−0.879464	+	0.0769431i	−0.517937	−	0.855419i	$-0.673300\pi$
$193$	−12.2179	+	1.06893i	−0.879464	+	0.0769431i	−0.361526	+	0.932362i	$0.617744\pi$
$194$	−3.49955	+	9.61494i	−0.251253	+	0.690312i
$195$		0			0
$196$	−4.99228	+	4.18902i	−0.356591	+	0.299216i
$197$	0.162978	+	0.0436698i	0.0116117	+	0.00311135i	0.264620	−	0.964353i	$-0.414753\pi$
$197$	0.162978	+	0.0436698i	0.0116117	+	0.00311135i	−0.253009	+	0.967464i	$0.581420\pi$
$198$		0			0
$199$	4.92176	−	0.867839i	0.348894	−	0.0615195i	0.00354503	−	0.999994i	$-0.498872\pi$
$199$	4.92176	−	0.867839i	0.348894	−	0.0615195i	0.345349	+	0.938474i	$0.387760\pi$
$200$	8.11013	−	4.06743i	0.573473	−	0.287611i
$201$		0			0
$202$	−4.94459	+	18.4535i	−0.347900	+	1.29838i
$203$	7.30201e−5	0	0.000834624i	5.12501e−6	0	5.85791e-5i
$204$		0			0
$205$	−0.0867220	−	0.453862i	−0.00605693	−	0.0316991i
$206$	−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	0.170422	−	0.985371i	$-0.445487\pi$
$211$	−0.0936993	−	0.0165217i	−0.00645053	−	0.00113740i	−0.176873	+	0.984234i	$0.556598\pi$
$212$	0.216828	+	2.47836i	0.0148918	+	0.170214i
$213$		0			0
$214$	−9.14671	−	25.1304i	−0.625257	−	1.71788i
$215$	−0.403846	+	0.195379i	−0.0275421	+	0.0133247i
$216$		0			0
$217$	−0.920396	+	0.246619i	−0.0624805	+	0.0167416i
$218$	9.29842	−	13.2795i	0.629768	−	0.899402i
$219$		0			0
$220$	9.66814	−	0.137948i	0.651826	−	0.00930042i
$221$	−10.3344	+	5.96660i	−0.695170	+	0.401357i
$222$		0			0
$223$	−0.290463	+	0.622900i	−0.0194508	+	0.0417125i	−0.915793	−	0.401650i	$-0.868437\pi$
$223$	−0.290463	+	0.622900i	−0.0194508	+	0.0417125i	0.896342	+	0.443363i	$0.146215\pi$
$224$	−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	0.803375	−	0.595474i	$-0.203036\pi$
$227$	3.13234	+	3.13234i	0.207901	+	0.207901i	−0.595474	+	0.803375i	$0.703036\pi$
$228$		0			0
$229$		−	1.64132i		−	0.108462i	−0.998528	−	0.0542308i	$-0.982729\pi$
$229$		−	1.64132i		−	0.108462i	0.998528	−	0.0542308i	$-0.0172707\pi$
$230$	−27.2371	+	10.3559i	−1.79596	+	0.682847i
$231$		0			0
$232$	−0.00479939	+	0.00223799i	−0.000315096	+	0.000146932i
$233$	−8.75832	−	4.08407i	−0.573776	−	0.267556i	0.113998	−	0.993481i	$-0.463634\pi$
$233$	−8.75832	−	4.08407i	−0.573776	−	0.267556i	−0.687774	+	0.725925i	$0.741412\pi$
$234$		0			0
$235$	10.8444	−	3.07223i	0.707413	−	0.200410i
$236$	−1.73806	−	1.00347i	−0.113138	−	0.0653204i
$237$		0			0
$238$	−1.94388	−	1.36112i	−0.126003	−	0.0882284i
$239$	−5.41584	−	3.12684i	−0.350321	−	0.202258i	0.314505	−	0.949256i	$-0.398161\pi$
$239$	−5.41584	−	3.12684i	−0.350321	−	0.202258i	−0.664827	+	0.746998i	$0.731495\pi$
$240$		0			0
$241$	−8.06290	−	9.60899i	−0.519377	−	0.618970i	0.441056	−	0.897479i	$-0.354604\pi$
$241$	−8.06290	−	9.60899i	−0.519377	−	0.618970i	−0.960433	+	0.278510i	$0.910159\pi$
$242$	−15.6512	−	7.29827i	−1.00610	−	0.469151i
$243$		0			0
$244$	−2.42704	+	2.89243i	−0.155375	+	0.185169i
$245$	14.4584	−	5.49726i	0.923712	−	0.351207i
$246$		0			0
$247$	−9.48539	−	5.15081i	−0.603541	−	0.327739i
$248$	4.25873	+	4.25873i	0.270430	+	0.270430i
$249$		0			0
$250$	19.0151	−	2.48730i	1.20262	−	0.157311i
$251$	8.58890	+	3.12610i	0.542127	+	0.197318i	0.598545	−	0.801089i	$-0.295746\pi$
$251$	8.58890	+	3.12610i	0.542127	+	0.197318i	−0.0564182	+	0.998407i	$0.517968\pi$
$252$		0			0
$253$	34.7395	+	3.03931i	2.18405	+	0.191080i
$254$	14.9679	−	8.64170i	0.939167	−	0.542228i
$255$		0			0
$256$	3.19183	+	18.1018i	0.199489	+	1.13136i
$257$	17.0588	−	24.3625i	1.06410	−	1.51969i	0.226040	−	0.974118i	$-0.427422\pi$
$257$	17.0588	−	24.3625i	1.06410	−	1.51969i	0.838062	−	0.545576i	$-0.183689\pi$
$258$		0			0
$259$	−1.10871	−	1.92034i	−0.0688918	−	0.119324i
$260$	−4.69570	+	2.27176i	−0.291215	+	0.140888i
$261$		0			0
$262$	14.1807	+	30.4105i	0.876084	+	1.87877i
$263$	1.37466	+	15.7124i	0.0847649	+	0.968867i	0.912858	+	0.408277i	$0.133870\pi$
$263$	1.37466	+	15.7124i	0.0847649	+	0.968867i	−0.828093	+	0.560590i	$0.810574\pi$
$264$		0			0
$265$	1.44678	−	5.72494i	0.0888748	−	0.351680i
$266$	0.131154	−	2.14243i	0.00804154	−	0.131361i
$267$		0			0
$268$	−4.90018	−	6.99818i	−0.299326	−	0.427482i
$269$	−8.63004	−	7.24147i	−0.526183	−	0.441520i	0.340598	−	0.940209i	$-0.389371\pi$
$269$	−8.63004	−	7.24147i	−0.526183	−	0.441520i	−0.866781	+	0.498689i	$0.833815\pi$
$270$		0			0
$271$	−19.5383	+	7.11134i	−1.18686	+	0.431983i	−0.858621	−	0.512610i	$-0.828679\pi$
$271$	−19.5383	+	7.11134i	−1.18686	+	0.431983i	−0.328243	+	0.944593i	$0.606456\pi$
$272$	−2.09864	+	23.9876i	−0.127249	+	1.45446i
$273$		0			0
$274$	9.14041	−	15.8317i	0.552192	−	0.956425i
$275$	−21.7811	−	7.23086i	−1.31345	−	0.436037i
$276$		0			0
$277$	−1.97611	−	7.37493i	−0.118733	−	0.443116i	0.880806	−	0.473477i	$-0.157001\pi$
$277$	−1.97611	−	7.37493i	−0.118733	−	0.443116i	−0.999539	+	0.0303603i	$0.990335\pi$
$278$	25.4474	+	6.81861i	1.52623	+	0.408953i
$279$		0			0
$280$	0.902933	+	0.735956i	0.0539606	+	0.0439818i
$281$	1.88216	−	5.17119i	0.112280	−	0.308488i	−0.870807	−	0.491625i	$-0.836403\pi$
$281$	1.88216	−	5.17119i	0.112280	−	0.308488i	0.983087	+	0.183137i	$0.0586253\pi$
$282$		0			0
$283$	−9.45513	+	6.62055i	−0.562049	+	0.393551i	−0.819791	−	0.572663i	$-0.805910\pi$
$283$	−9.45513	+	6.62055i	−0.562049	+	0.393551i	0.257742	+	0.966214i	$0.417022\pi$
$284$	−11.9342			−0.708164
$285$		0			0
$286$	19.4954			1.15279
$287$	0.0485963	−	0.0340275i	0.00286855	−	0.00200858i
$288$		0			0
$289$	−2.12857	+	5.84820i	−0.125210	+	0.344012i
$290$	−0.0111353	+	0.00113451i	−0.000653889	+	6.66209e-5i
$291$		0			0
$292$	−9.82698	−	2.63313i	−0.575080	−	0.154092i
$293$	−6.28567	−	23.4584i	−0.367213	−	1.37046i	−0.864397	−	0.502811i	$-0.832299\pi$
$293$	−6.28567	−	23.4584i	−0.367213	−	1.37046i	0.497184	−	0.867645i	$-0.334367\pi$
$294$		0			0
$295$	3.11369	+	3.60502i	0.181286	+	0.209893i
$296$	−7.00780	+	12.1379i	−0.407320	+	0.705499i
$297$		0			0
$298$	1.44683	−	16.5374i	0.0838127	−	0.957983i
$299$	−17.6785	+	6.43445i	−1.02237	+	0.372114i
$300$		0			0
$301$	−0.0441232	−	0.0370237i	−0.00254322	−	0.00213401i
$302$	−3.05438	−	4.36211i	−0.175760	−	0.251011i
$303$		0			0
$304$	−19.4921	+	9.71707i	−1.11795	+	0.557312i
$305$	7.69658	−	4.59126i	0.440705	−	0.262895i
$306$		0			0
$307$	−0.397706	−	4.54580i	−0.0226983	−	0.259442i	−0.999062	−	0.0433075i	$-0.986210\pi$
$307$	−0.397706	−	4.54580i	−0.0226983	−	0.259442i	0.976364	−	0.216135i	$-0.0693451\pi$
$308$	0.524644	+	1.12510i	0.0298943	+	0.0641086i
$309$		0			0
$310$	5.54400	+	11.4594i	0.314878	+	0.650850i
$311$	2.78134	+	4.81742i	0.157715	+	0.273171i	0.934044	−	0.357157i	$-0.116254\pi$
$311$	2.78134	+	4.81742i	0.157715	+	0.273171i	−0.776329	+	0.630328i	$0.782921\pi$
$312$		0			0
$313$	−5.80877	+	8.29578i	−0.328331	+	0.468905i	−0.949049	−	0.315129i	$-0.897952\pi$
$313$	−5.80877	+	8.29578i	−0.328331	+	0.468905i	0.620718	+	0.784034i	$0.286841\pi$
$314$	−4.80922	−	27.2744i	−0.271400	−	1.53919i
$315$		0			0
$316$	4.47416	−	2.58316i	0.251691	−	0.145314i
$317$	25.6623	+	2.24516i	1.44134	+	0.126101i	0.780843	−	0.624728i	$-0.214790\pi$
$317$	25.6623	+	2.24516i	1.44134	+	0.126101i	0.660497	+	0.750829i	$0.270346\pi$
$318$		0			0
$319$	0.0125872	+	0.00458138i	0.000704750	+	0.000256508i
$320$	0.541558	−	3.35015i	0.0302740	−	0.187279i
$321$		0			0
$322$	−2.64541	−	2.64541i	−0.147423	−	0.147423i
$323$	−20.5844	+	4.18678i	−1.14535	+	0.232959i
$324$		0			0
$325$	12.2983	−	1.43055i	0.682186	−	0.0793528i
$326$	−0.0911679	+	0.108650i	−0.00504933	+	0.00601755i
$327$		0			0
$328$	−0.339844	−	0.158472i	−0.0187647	−	0.00875013i
$329$	0.930180	+	1.10855i	0.0512825	+	0.0611161i
$330$		0			0
$331$	−11.0824	−	6.39845i	−0.609146	−	0.351690i	0.163485	−	0.986546i	$-0.447726\pi$
$331$	−11.0824	−	6.39845i	−0.609146	−	0.351690i	−0.772631	+	0.634855i	$0.781060\pi$
$332$	−12.3370	−	8.63849i	−0.677083	−	0.474098i
$333$		0			0
$334$	12.8092	+	7.39540i	0.700889	+	0.404658i
$335$	5.52712	+	19.5097i	0.301979	+	1.06593i
$336$		0			0
$337$	−18.5322	−	8.64171i	−1.00951	−	0.470744i	−0.153749	−	0.988110i	$-0.549135\pi$
$337$	−18.5322	−	8.64171i	−1.00951	−	0.470744i	−0.855764	+	0.517366i	$0.826913\pi$
$338$	10.6770	−	4.97876i	0.580751	−	0.270809i
$339$		0			0
$340$	−4.15860	+	9.26085i	−0.225532	+	0.502240i
$341$		−	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
$347$	−7.46684	+	16.0127i	−0.400841	+	0.859606i	0.597491	+	0.801875i	$0.296164\pi$
$347$	−7.46684	+	16.0127i	−0.400841	+	0.859606i	−0.998332	+	0.0577308i	$0.981614\pi$
$348$		0			0
$349$	10.6670	−	6.15858i	0.570990	−	0.329661i	−0.186555	−	0.982445i	$-0.559732\pi$
$349$	10.6670	−	6.15858i	0.570990	−	0.329661i	0.757545	+	0.652783i	$0.226399\pi$
$350$	1.29140	+	2.09628i	0.0690283	+	0.112051i
$351$		0			0
$352$	13.0091	−	18.5789i	0.693386	−	0.990258i
$353$	−5.51616	+	1.47805i	−0.293596	+	0.0786687i	−0.402610	−	0.915371i	$-0.631897\pi$
$353$	−5.51616	+	1.47805i	−0.293596	+	0.0786687i	0.109015	+	0.994040i	$0.465230\pi$
$354$		0			0
$355$	26.7534	+	9.30737i	1.41992	+	0.493984i
$356$	5.09473	+	13.9976i	0.270020	+	0.741874i
$357$		0			0
$358$	−1.07319	−	12.2666i	−0.0567199	−	0.648312i
$359$	25.5870	+	4.51167i	1.35043	+	0.238117i	0.801621	−	0.597832i	$-0.203971\pi$
$359$	25.5870	+	4.51167i	1.35043	+	0.238117i	0.548807	+	0.835949i	$0.315082\pi$
$360$		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
$365$	19.9760	+	13.5668i	1.04559	+	0.710118i
$366$		0			0
$367$	−0.00722438	+	0.0825751i	−0.000377110	+	0.00431038i	−0.996381	−	0.0850003i	$-0.972911\pi$
$367$	−0.00722438	+	0.0825751i	−0.000377110	+	0.00431038i	0.996004	+	0.0893107i	$0.0284664\pi$
$368$	−9.82521	+	36.6682i	−0.512175	+	1.91146i
$369$		0			0
$370$	−22.4194	+	19.3639i	−1.16553	+	1.00668i
$371$	0.746612	−	0.131648i	0.0387621	−	0.00683481i
$372$		0			0
$373$	2.53207	+	0.678465i	0.131105	+	0.0351296i	0.323775	−	0.946134i	$-0.395048\pi$
$373$	2.53207	+	0.678465i	0.131105	+	0.0351296i	−0.192670	+	0.981264i	$0.561715\pi$
$374$	29.0641	−	24.3877i	1.50287	−	1.26106i
$375$		0			0
$376$	3.12835	−	8.59507i	0.161332	−	0.443257i
$377$	−0.00719896		0.000629827i	−0.000370765		3.24377e-5i
$378$		0			0
$379$	−29.0243			−1.49088			−0.745440	−	0.666573i	$-0.767761\pi$
$379$	−29.0243			−1.49088			−0.745440	+	0.666573i	$0.767761\pi$
$380$	−9.10760	+	1.16903i	−0.467210	+	0.0599698i
$381$		0			0
$382$	−6.43858	+	4.50835i	−0.329427	+	0.230667i
$383$	21.0330	−	1.84015i	1.07473	−	0.0940271i	0.463979	−	0.885846i	$-0.346421\pi$
$383$	21.0330	−	1.84015i	1.07473	−	0.0940271i	0.610756	+	0.791819i	$0.290866\pi$
$384$		0			0
$385$	−0.298658	−	2.93135i	−0.0152210	−	0.149396i
$386$	−16.1151	+	13.5222i	−0.820239	+	0.688262i
$387$		0			0
$388$	1.45452	+	5.42834i	0.0738420	+	0.275582i
$389$	−4.17947	+	0.736954i	−0.211908	+	0.0373650i	−0.278594	−	0.960409i	$-0.589868\pi$
$389$	−4.17947	+	0.736954i	−0.211908	+	0.0373650i	0.0666864	+	0.997774i	$0.478757\pi$
$390$		0			0
$391$	−18.3063	+	31.7075i	−0.925791	+	1.60352i
$392$	3.24884	−	12.1248i	0.164091	−	0.612397i
$393$		0			0
$394$	0.271956	−	0.0989839i	0.0137009	−	0.00498674i
$395$	−12.0445	+	2.30141i	−0.606025	+	0.115797i
$396$		0			0
$397$	11.8488	+	16.9218i	0.594674	+	0.849282i	0.997830	−	0.0658493i	$-0.0209757\pi$
$397$	11.8488	+	16.9218i	0.594674	+	0.849282i	−0.403156	+	0.915131i	$0.632087\pi$
$398$	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	−0.291918	−	0.956443i	$-0.594293\pi$
$401$	−17.8894	−	3.15438i	−0.893354	−	0.157522i	−0.601436	+	0.798921i	$0.705404\pi$
$402$		0			0
$403$	3.47342	+	7.44878i	0.173024	+	0.371050i
$404$	3.58880	+	9.86014i	0.178549	+	0.490560i
$405$		0			0
$406$	−0.000718529	−	0.00124453i	−3.56600e−5	−	6.17649e-5i
$407$	34.2444	−	9.17575i	1.69743	−	0.454825i
$408$		0			0
$409$	−2.14098	−	12.1421i	−0.105865	−	0.600388i	−0.990871	−	0.134810i	$-0.956958\pi$
$409$	−2.14098	−	12.1421i	−0.105865	−	0.600388i	0.885007	−	0.465578i	$-0.154154\pi$
$410$	−0.568370	−	0.552379i	−0.0280698	−	0.0272801i
$411$		0			0
$412$	−0.774375	−	0.0677491i	−0.0381507	−	0.00333776i
$413$	−0.258468	+	0.554286i	−0.0127184	+	0.0272746i
$414$		0			0
$415$	20.9194	+	28.9868i	1.02689	+	1.42291i
$416$	−2.12474	+	12.0500i	−0.104174	+	0.590800i
$417$		0			0
$418$	32.5436	+	10.8909i	1.59176	+	0.532691i
$419$		−	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	−0.438683	−	0.898642i	$-0.644555\pi$
$421$	10.7205	−	12.7761i	0.522483	−	0.622671i	0.961166	+	0.275971i	$0.0889994\pi$
$422$	−0.147907	+	0.0689701i	−0.00720000	+	0.00335741i
$423$		0			0
$424$	−3.08017	−	3.67081i	−0.149586	−	0.178270i
$425$	16.5450	−	17.5172i	0.802549	−	0.849708i
$426$		0			0
$427$	0.942534	+	0.659969i	0.0456124	+	0.0319382i
$428$	−12.0321	−	8.42495i	−0.581593	−	0.407235i
$429$		0			0
$430$	−0.375206	+	0.671832i	−0.0180940	+	0.0323986i
$431$	−9.97761	−	11.8908i	−0.480604	−	0.572762i	0.470198	−	0.882561i	$-0.344183\pi$
$431$	−9.97761	−	11.8908i	−0.480604	−	0.572762i	−0.950802	+	0.309799i	$0.899738\pi$
$432$		0			0
$433$	11.6855	−	5.44902i	0.561568	−	0.261863i	−0.121041	−	0.992648i	$-0.538623\pi$
$433$	11.6855	−	5.44902i	0.561568	−	0.261863i	0.682608	+	0.730784i	$0.260845\pi$
$434$	−1.05057	+	1.25202i	−0.0504291	+	0.0600990i
$435$		0			0
$436$		−	8.90391i		−	0.426420i
$437$	−33.1052	+	0.865085i	−1.58363	+	0.0413826i
$438$		0			0
$439$	5.84172	−	33.1300i	0.278810	−	1.58121i	−0.447783	−	0.894142i	$-0.647786\pi$
$439$	5.84172	−	33.1300i	0.278810	−	1.58121i	0.726593	−	0.687068i	$-0.241102\pi$
$440$	−15.1020	+	10.8989i	−0.719960	+	0.519585i
$441$		0			0
$442$	−8.65033	+	18.5507i	−0.411454	+	0.882366i
$443$	16.6998	+	1.46104i	0.793431	+	0.0694162i	0.476662	−	0.879087i	$-0.341846\pi$
$443$	16.6998	+	1.46104i	0.793431	+	0.0694162i	0.316769	+	0.948503i	$0.397402\pi$
$444$		0			0
$445$	−0.504418	−	35.3525i	−0.0239117	−	1.67587i
$446$	0.204711	+	1.16097i	0.00969333	+	0.0549736i
$447$		0			0
$448$	0.420860	−	0.112769i	0.0198838	−	0.00532784i
$449$	−8.68158	−	15.0369i	−0.409709	−	0.709637i	0.585148	−	0.810927i	$-0.301036\pi$
$449$	−8.68158	−	15.0369i	−0.409709	−	0.709637i	−0.994857	+	0.101290i	$0.967703\pi$
$450$		0			0
$451$	0.324406	+	0.891298i	0.0152757	+	0.0419696i
$452$	−0.734361	−	1.57484i	−0.0345414	−	0.0740743i
$453$		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	$0.294202\pi$
$458$	−1.61478	−	2.30614i	−0.0754535	−	0.107759i
$459$		0			0
$460$	−8.99184	+	13.2398i	−0.419247	+	0.617307i
$461$	−13.1750	+	4.79530i	−0.613620	+	0.223339i	−0.630086	−	0.776525i	$-0.716981\pi$
$461$	−13.1750	+	4.79530i	−0.613620	+	0.223339i	0.0164665	+	0.999864i	$0.494758\pi$
$462$		0			0
$463$	−3.72721	+	13.9101i	−0.173218	+	0.646459i	0.823630	+	0.567127i	$0.191945\pi$
$463$	−3.72721	+	13.9101i	−0.173218	+	0.646459i	−0.996848	+	0.0793316i	$0.974721\pi$
$464$	−0.00729090	+	0.0126282i	−0.000338472	+	0.000586250i
$465$		0			0
$466$	−16.3239	+	2.87835i	−0.756190	+	0.133337i
$467$	−2.26065	−	8.43685i	−0.104610	−	0.390411i	0.893690	−	0.448684i	$-0.148107\pi$
$467$	−2.26065	−	8.43685i	−0.104610	−	0.390411i	−0.998301	+	0.0582734i	$0.981440\pi$
$468$		0			0
$469$	−1.99433	+	1.67345i	−0.0920898	+	0.0772725i
$470$	12.2144	−	14.9857i	0.563410	−	0.691238i
$471$		0			0
$472$	3.85094	−	0.336914i	0.177254	−	0.0155077i
$473$	0.754354	−	0.528204i	0.0346852	−	0.0242869i
$474$		0			0
$475$	21.3286	+	4.48228i	0.978623	+	0.205661i
$476$	−1.30337			−0.0597399
$477$		0			0
$478$	−10.6858	+	0.934886i	−0.488757	+	0.0427607i
$479$	6.83164	−	18.7698i	0.312145	−	0.857613i	−0.680078	−	0.733140i	$-0.738054\pi$
$479$	6.83164	−	18.7698i	0.312145	−	0.857613i	0.992223	−	0.124473i	$-0.0397239\pi$
$480$		0			0
$481$	−14.6514	+	12.2940i	−0.668048	+	0.560558i
$482$	−20.7824	−	5.56862i	−0.946611	−	0.253644i
$483$		0			0
$484$	−9.34084	+	1.64704i	−0.424584	+	0.0748656i
$485$	0.972859	−	13.3033i	0.0441753	−	0.604072i
$486$		0			0
$487$	3.44824	−	12.8690i	0.156254	−	0.583150i	−0.842740	−	0.538320i	$-0.819059\pi$
$487$	3.44824	−	12.8690i	0.156254	−	0.583150i	0.998995	−	0.0448291i	$-0.0142743\pi$
$488$	0.633859	−	7.24504i	0.0286935	−	0.327968i
$489$		0			0
$490$	14.9064	−	21.9485i	0.673403	−	0.991532i
$491$	18.9123	+	15.8693i	0.853501	+	0.716172i	0.960558	−	0.278081i	$-0.0896983\pi$
$491$	18.9123	+	15.8693i	0.853501	+	0.716172i	−0.107057	+	0.994253i	$0.534143\pi$
$492$		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
$497$	0.316966	+	3.62294i	0.0142179	+	0.162511i
$498$		0			0
$499$	−6.45641	−	17.7388i	−0.289028	−	0.794099i	−0.996203	−	0.0870601i	$-0.972253\pi$
$499$	−6.45641	−	17.7388i	−0.289028	−	0.794099i	0.707175	−	0.707039i	$-0.249969\pi$
$500$	7.77154	−	7.10942i	0.347554	−	0.317943i
$501$		0			0
$502$	15.1434	−	4.05766i	0.675883	−	0.181102i
$503$	−8.21072	+	11.7261i	−0.366098	+	0.522842i	−0.959367	−	0.282162i	$-0.908948\pi$
$503$	−8.21072	+	11.7261i	−0.366098	+	0.522842i	0.593269	+	0.805005i	$0.297837\pi$
$504$		0			0
$505$	−0.355319	−	24.9028i	−0.0158115	−	1.10816i
$506$	51.8009	−	29.9073i	2.30283	−	1.32954i
$507$		0			0
$508$	4.01181	−	8.60335i	0.177995	−	0.381712i
$509$	32.7191	+	11.9088i	1.45025	+	0.527847i	0.942661	−	0.333752i	$-0.108315\pi$
$509$	32.7191	+	11.9088i	1.45025	+	0.527847i	0.507588	+	0.861600i	$0.330537\pi$
$510$		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
$515$	1.68311	+	0.755805i	0.0741668	+	0.0333047i
$516$		0			0
$517$	−20.9688	+	9.77791i	−0.922206	+	0.430032i
$518$	−3.44707	−	1.60740i	−0.151456	−	0.0706250i
$519$		0			0
$520$	4.89907	−	8.77213i	0.214839	−	0.384684i
$521$	−3.47559	−	2.00663i	−0.152268	−	0.0879121i	0.421930	−	0.906628i	$-0.361353\pi$
$521$	−3.47559	−	2.00663i	−0.152268	−	0.0879121i	−0.574198	+	0.818716i	$0.694686\pi$
$522$		0			0
$523$	26.4451	+	18.5171i	1.15636	+	0.809695i	0.984493	−	0.175424i	$-0.0561296\pi$
$523$	26.4451	+	18.5171i	1.15636	+	0.809695i	0.171872	+	0.985119i	$0.445019\pi$
$524$	15.9603	+	9.21469i	0.697230	+	0.402546i
$525$		0			0
$526$	17.3897	+	20.7243i	0.758228	+	0.903621i
$527$	14.4963	+	6.75973i	0.631468	+	0.294458i
$528$		0			0
$529$	−22.3183	+	26.5979i	−0.970360	+	1.15643i
$530$	−3.59956	−	9.46722i	−0.156355	−	0.411230i
$531$		0			0
$532$	−0.615925	−	1.00522i	−0.0267037	−	0.0435818i
$533$	−0.361829	−	0.361829i	−0.0156725	−	0.0156725i
$534$		0			0
$535$	20.4023	+	28.2703i	0.882067	+	1.22223i
$536$	15.4630	+	5.62808i	0.667900	+	0.243096i
$537$		0			0
$538$	−19.2500	−	1.68416i	−0.829927	−	0.0726092i
$539$	−27.4977	+	15.8758i	−1.18441	+	0.683820i
$540$		0			0
$541$	−2.75071	−	15.6000i	−0.118262	−	0.670698i	−0.985083	−	0.172079i	$-0.944952\pi$
$541$	−2.75071	−	15.6000i	−0.118262	−	0.670698i	0.866821	−	0.498620i	$-0.166160\pi$
$542$	−20.4559	+	29.2141i	−0.878657	+	1.25485i
$543$		0			0
$544$	11.9063	+	20.6223i	0.510479	+	0.884176i
$545$	−6.94408	+	19.9603i	−0.297452	+	0.855004i
$546$		0			0
$547$	17.7724	+	38.1131i	0.759893	+	1.62960i	0.776806	+	0.629740i	$0.216838\pi$
$547$	17.7724	+	38.1131i	0.759893	+	1.62960i	−0.0169130	+	0.999857i	$0.505384\pi$
$548$	−0.875093	−	10.0024i	−0.0373821	−	0.427280i
$549$		0			0
$550$	−37.7174	+	11.2691i	−1.60828	+	0.480516i
$551$	−0.0123690	−	0.00297025i	−0.000526938	−	0.000126537i
$552$		0			0
$553$	−0.903017	−	1.28964i	−0.0384002	−	0.0548411i
$554$	−10.0322	−	8.41800i	−0.426227	−	0.357647i
$555$		0			0
$556$	13.5972	−	4.94896i	0.576648	−	0.209883i
$557$	−1.68089	+	19.2126i	−0.0712215	+	0.814066i	0.873635	+	0.486582i	$0.161756\pi$
$557$	−1.68089	+	19.2126i	−0.0712215	+	0.814066i	−0.944857	+	0.327484i	$0.893799\pi$
$558$		0			0
$559$	−0.248406	+	0.430251i	−0.0105064	+	0.0181977i
$560$	3.19904	+	0.233943i	0.135184	+	0.00988589i
$561$		0			0
$562$	−2.44303	−	9.11752i	−0.103053	−	0.384599i
$563$	−18.5388	−	4.96746i	−0.781318	−	0.209354i	−0.153952	−	0.988078i	$-0.549200\pi$
$563$	−18.5388	−	4.96746i	−0.781318	−	0.209354i	−0.627366	+	0.778725i	$0.715867\pi$
$564$		0			0
$565$	0.418042	+	4.10311i	0.0175871	+	0.172619i
$566$	−6.77146	+	18.6044i	−0.284626	+	0.782002i
$567$		0			0
$568$	18.8298	−	13.1848i	0.790080	−	0.553220i
$569$	−32.0305			−1.34279			−0.671393	−	0.741101i	$-0.734304\pi$
$569$	−32.0305			−1.34279			−0.671393	+	0.741101i	$0.734304\pi$
$570$		0			0
$571$	24.9840			1.04555			0.522774	−	0.852471i	$-0.324897\pi$
$571$	24.9840			1.04555			0.522774	+	0.852471i	$0.324897\pi$
$572$	8.77121	−	6.14167i	0.366743	−	0.256796i
$573$		0			0
$574$	0.0348031	−	0.0956208i	0.00145265	−	0.00399114i
$575$	30.4830	−	22.6675i	1.27123	−	0.945299i
$576$		0			0
$577$	3.34706	+	0.896843i	0.139340	+	0.0373361i	0.327815	−	0.944742i	$-0.393688\pi$
$577$	3.34706	+	0.896843i	0.139340	+	0.0373361i	−0.188475	+	0.982078i	$0.560354\pi$
$578$	2.76287	+	10.3112i	0.114920	+	0.428888i
$579$		0			0
$580$	−0.00465250	+	0.00401841i	−0.000193185	+	0.000166855i
$581$	−2.29477	+	3.97466i	−0.0952032	+	0.164897i
$582$		0			0
$583$	−1.05642	+	12.0750i	−0.0437525	+	0.500094i
$584$	18.4141	−	6.70217i	0.761980	−	0.277338i
$585$		0			0
$586$	−31.9107	−	26.7763i	−1.31822	−	1.10612i
$587$	18.1103	+	25.8643i	0.747494	+	1.06753i	0.995120	+	0.0986764i	$0.0314609\pi$
$587$	18.1103	+	25.8643i	0.747494	+	1.06753i	−0.247625	+	0.968856i	$0.579650\pi$
$588$		0			0
$589$	1.63699	+	14.3746i	0.0674508	+	0.592295i
$590$	7.92162	+	2.00191i	0.326128	+	0.0824173i
$591$		0			0
$592$	3.36363	+	38.4464i	0.138244	+	1.58014i
$593$	3.88609	+	8.33375i	0.159583	+	0.342226i	0.969799	−	0.243904i	$-0.0784283\pi$
$593$	3.88609	+	8.33375i	0.159583	+	0.342226i	−0.810217	+	0.586131i	$0.800651\pi$
$594$		0			0
$595$	2.92182	+	1.01649i	0.119783	+	0.0416720i
$596$	−4.55884	−	7.89615i	−0.186737	−	0.323439i
$597$		0			0
$598$	−18.5088	+	26.4333i	−0.756882	+	1.08094i
$599$	7.60255	+	43.1162i	0.310632	+	1.76168i	0.595734	+	0.803182i	$0.296861\pi$
$599$	7.60255	+	43.1162i	0.310632	+	1.76168i	−0.285102	+	0.958497i	$0.592027\pi$
$600$		0			0
$601$	26.5782	−	15.3449i	1.08415	−	0.625932i	0.152134	−	0.988360i	$-0.451385\pi$
$601$	26.5782	−	15.3449i	1.08415	−	0.625932i	0.932012	+	0.362428i	$0.118052\pi$
$602$	−0.0984203	−	0.00861066i	−0.00401131	−	0.000350944i
$603$		0			0
$604$	−2.74840	−	1.00034i	−0.111831	−	0.0407031i
$605$	22.2243	+	3.59260i	0.903546	+	0.146060i
$606$		0			0
$607$	−7.95200	−	7.95200i	−0.322762	−	0.322762i	0.527064	−	0.849826i	$-0.323293\pi$
$607$	−7.95200	−	7.95200i	−0.322762	−	0.322762i	−0.849826	+	0.527064i	$0.823293\pi$
$608$	−10.2784	+	18.9280i	−0.416845	+	0.767634i
$609$		0			0
$610$	6.29708	−	14.0231i	0.254961	−	0.567777i
$611$	8.02317	−	9.56164i	0.324583	−	0.386822i
$612$		0			0
$613$	−36.0854	−	16.8269i	−1.45748	−	0.679632i	−0.477478	−	0.878644i	$-0.658449\pi$
$613$	−36.0854	−	16.8269i	−1.45748	−	0.679632i	−0.979997	+	0.199012i	$0.936227\pi$
$614$	−5.03108	−	5.99580i	−0.203038	−	0.241971i
$615$		0			0
$616$	−2.07078	−	1.19557i	−0.0834342	−	0.0481708i
$617$	−21.3819	−	14.9718i	−0.860803	−	0.602740i	0.0576212	−	0.998339i	$-0.481648\pi$
$617$	−21.3819	−	14.9718i	−0.860803	−	0.602740i	−0.918424	+	0.395598i	$0.870537\pi$
$618$		0			0
$619$	14.8409	+	8.56837i	0.596504	+	0.344392i	0.767665	−	0.640851i	$-0.221418\pi$
$619$	14.8409	+	8.56837i	0.596504	+	0.344392i	−0.171161	+	0.985243i	$0.554752\pi$
$620$	6.10438	+	3.40918i	0.245158	+	0.136916i
$621$		0			0
$622$	8.64743	+	4.03237i	0.346731	+	0.161683i
$623$	4.11404	−	1.91841i	0.164825	−	0.0768594i
$624$		0			0
$625$	−22.9664	+	9.87654i	−0.918655	+	0.395062i
$626$			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	0.710873	−	0.703320i	$-0.248300\pi$
$631$	20.1799	+	7.34487i	0.803348	+	0.292395i	0.0924747	+	0.995715i	$0.470522\pi$
$632$	−4.20549	+	9.01871i	−0.167286	+	0.358745i
$633$		0			0
$634$	38.2657	−	22.0927i	1.51973	−	0.877415i
$635$	−15.7031	+	16.1577i	−0.623159	+	0.641200i
$636$		0			0
$637$	9.82513	−	14.0317i	0.389286	−	0.555958i
$638$	0.0221930	−	0.00594660i	0.000878629	−	0.000235428i
$639$		0			0
$640$	−12.1590	−	25.1325i	−0.480625	−	0.993449i
$641$	−12.0700	−	33.1619i	−0.476735	−	1.30982i	−0.912249	−	0.409636i	$-0.865656\pi$
$641$	−12.0700	−	33.1619i	−0.476735	−	1.30982i	0.435515	−	0.900182i	$-0.356566\pi$
$642$		0			0
$643$	1.64241	+	18.7728i	0.0647702	+	0.740327i	0.957254	+	0.289248i	$0.0934052\pi$
$643$	1.64241	+	18.7728i	0.0647702	+	0.740327i	−0.892484	+	0.451079i	$0.851039\pi$
$644$	−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
$650$	15.8723	−	14.1094i	0.622562	−	0.553416i
$651$		0			0
$652$	−0.00678943	+	0.0776036i	−0.000265895	+	0.00303919i
$653$	1.44781	−	5.40330i	0.0566572	−	0.211447i	−0.931794	−	0.362988i	$-0.881757\pi$
$653$	1.44781	−	5.40330i	0.0566572	−	0.211447i	0.988451	+	0.151540i	$0.0484233\pi$
$654$		0			0
$655$	−28.5925	−	33.1043i	−1.11720	−	1.29349i
$656$	−1.01685	+	0.179297i	−0.0397012	+	0.00700039i
$657$		0			0
$658$	2.39757	+	0.642427i	0.0934669	+	0.0250444i
$659$	−5.03828	+	4.22762i	−0.196264	+	0.164685i	−0.735623	−	0.677391i	$-0.763111\pi$
$659$	−5.03828	+	4.22762i	−0.196264	+	0.164685i	0.539360	+	0.842075i	$0.318666\pi$
$660$		0			0
$661$	−13.4502	+	36.9540i	−0.523150	+	1.43734i	0.343844	+	0.939027i	$0.388271\pi$
$661$	−13.4502	+	36.9540i	−0.523150	+	1.43734i	−0.866995	+	0.498317i	$0.833951\pi$
$662$	−21.8664	+	1.91306i	−0.849860	+	0.0743531i
$663$		0			0
$664$	29.0091			1.12577
$665$	0.596781	+	2.73380i	0.0231422	+	0.106012i
$666$		0			0
$667$	−0.0181620	+	0.0127172i	−0.000703236	+	0.000492411i
$668$	8.09280	−	0.708028i	0.313120	−	0.0273944i
$669$		0			0
$670$	26.9601	+	21.9744i	1.04156	+	0.848947i
$671$	−14.0924	+	11.8249i	−0.544031	+	0.456496i
$672$		0			0
$673$	2.51767	+	9.39609i	0.0970492	+	0.362193i	0.997322	−	0.0731333i	$-0.0232998\pi$
$673$	2.51767	+	9.39609i	0.0970492	+	0.362193i	−0.900273	+	0.435326i	$0.856633\pi$
$674$	−34.5406	+	6.09045i	−1.33046	+	0.234595i
$675$		0			0
$676$	3.23523	−	5.60359i	0.124432	−	0.215523i
$677$	−10.5432	+	39.3476i	−0.405207	+	1.51225i	0.398468	+	0.917182i	$0.369542\pi$
$677$	−10.5432	+	39.3476i	−0.405207	+	1.51225i	−0.803675	+	0.595069i	$0.797125\pi$
$678$		0			0
$679$	1.60928	−	0.585731i	0.0617586	−	0.0224783i
$680$	−3.66983	−	19.2062i	−0.140732	−	0.736522i
$681$		0			0
$682$	−14.9881	−	21.4053i	−0.573926	−	0.819651i
$683$	11.3169	−	11.3169i	0.433030	−	0.433030i	−0.456628	−	0.889658i	$-0.650943\pi$
$683$	11.3169	−	11.3169i	0.433030	−	0.433030i	0.889658	+	0.456628i	$0.150943\pi$
$684$		0			0
$685$	−5.83903	+	23.1052i	−0.223098	+	0.882804i
$686$	6.74927	+	1.19008i	0.257688	+	0.0454374i
$687$		0			0
$688$	0.423668	+	0.908559i	0.0161522	+	0.0346385i
$689$	−2.23652	−	6.14480i	−0.0852048	−	0.234098i
$690$		0			0
$691$	1.45852	+	2.52622i	0.0554846	+	0.0961021i	0.892434	−	0.451179i	$-0.148996\pi$
$691$	1.45852	+	2.52622i	0.0554846	+	0.0961021i	−0.836949	+	0.547281i	$0.815663\pi$
$692$	8.59691	−	2.30353i	0.326805	−	0.0875672i
$693$		0			0
$694$	5.26243	+	29.8447i	0.199759	+	1.13289i
$695$	−34.3410	+	0.489986i	−1.30263	+	0.0185862i
$696$		0			0
$697$	−0.992050	−	0.0867931i	−0.0375766	−	0.00328752i
$698$	8.92866	−	19.1476i	0.337955	−	0.724747i
$699$		0			0
$700$	1.24141	+	0.536308i	0.0469209	+	0.0202705i
$701$	7.75792	−	43.9973i	0.293012	−	1.66176i	−0.382160	−	0.924096i	$-0.624820\pi$
$701$	7.75792	−	43.9973i	0.293012	−	1.66176i	0.675173	−	0.737660i	$-0.264069\pi$
$702$		0			0
$703$	−31.3254	+	12.3375i	−1.18146	+	0.465316i
$704$			6.96614i			0.262546i
$705$		0			0
$706$	−6.29634	+	7.50369i	−0.236966	+	0.282405i
$707$	2.89799	−	1.35135i	0.108990	−	0.0508229i
$708$		0			0
$709$	27.4318	+	32.6919i	1.03022	+	1.22777i	0.973334	+	0.229390i	$0.0736733\pi$
$709$	27.4318	+	32.6919i	1.03022	+	1.22777i	0.0568877	+	0.998381i	$0.481882\pi$
$710$	46.7467	−	13.2434i	1.75437	−	0.497015i
$711$		0			0
$712$	−23.5029	−	16.4569i	−0.880808	−	0.616749i
$713$	20.6561	+	14.4636i	0.773577	+	0.541665i
$714$		0			0
$715$	−24.4526	+	6.92744i	−0.914477	+	0.259072i
$716$	−4.34722	−	5.18081i	−0.162463	−	0.193616i
$717$		0			0
$718$	40.3897	−	18.8340i	1.50733	−	0.702880i
$719$	−11.9438	+	14.2341i	−0.445429	+	0.530841i	−0.941307	−	0.337550i	$-0.890402\pi$
$719$	−11.9438	+	14.2341i	−0.445429	+	0.530841i	0.495879	+	0.868392i	$0.334846\pi$
$720$		0			0
$721$			0.236881i			0.00882192i
$722$	−31.8769	−	6.77927i	−1.18633	−	0.252298i
$723$		0			0
$724$	−0.263635	+	1.49515i	−0.00979790	+	0.0555667i
$725$	0.0135636	−	0.00537979i	0.000503741	−	0.000199800i
$726$		0			0
$727$	7.46550	−	16.0098i	0.276880	−	0.593771i	−0.717862	−	0.696186i	$-0.754879\pi$
$727$	7.46550	−	16.0098i	0.276880	−	0.593771i	0.994742	+	0.102414i	$0.0326568\pi$
$728$	1.28508	+	0.112430i	0.0476281	+	0.00416692i
$729$		0			0
$730$	41.4147	−	0.590915i	1.53283	−	0.0218708i
$731$	0.167893	+	0.952169i	0.00620975	+	0.0352173i
$732$		0			0
$733$	39.6034	−	10.6117i	1.46279	−	0.391952i	0.562335	−	0.826909i	$-0.309903\pi$
$733$	39.6034	−	10.6117i	1.46279	−	0.391952i	0.900451	+	0.434957i	$0.143236\pi$
$734$	0.0710890	+	0.123130i	0.00262394	+	0.00454480i
$735$		0			0
$736$	12.8399	+	35.2774i	0.473286	+	1.30034i
$737$	−17.5910	−	37.7240i	−0.647973	−	1.38958i
$738$		0			0
$739$	−13.0374	−	2.29884i	−0.479587	−	0.0845642i	−0.0713718	−	0.997450i	$-0.522738\pi$
$739$	−13.0374	−	2.29884i	−0.479587	−	0.0845642i	−0.408215	+	0.912886i	$0.633849\pi$
$740$	−3.98654	+	15.7749i	−0.146548	+	0.579895i
$741$		0			0
$742$	0.919509	−	0.919509i	0.0337562	−	0.0337562i
$743$	−0.283145	−	0.404372i	−0.0103876	−	0.0148350i	0.813925	−	0.580970i	$-0.197327\pi$
$743$	−0.283145	−	0.404372i	−0.0103876	−	0.0148350i	−0.824312	+	0.566135i	$0.808438\pi$
$744$		0			0
$745$	4.06161	+	21.2565i	0.148806	+	0.778779i
$746$	4.22518	−	1.53784i	0.154695	−	0.0563043i
$747$		0			0
$748$	5.39340	−	20.1284i	0.197202	−	0.735969i
$749$	−2.23805	+	3.87642i	−0.0817765	+	0.141641i
$750$		0			0
$751$	−41.0072	+	7.23068i	−1.49637	+	0.263851i	−0.861100	−	0.508435i	$-0.830224\pi$
$751$	−41.0072	+	7.23068i	−1.49637	+	0.263851i	−0.635275	+	0.772286i	$0.719113\pi$
$752$	−6.51869	−	24.3281i	−0.237712	−	0.887154i
$753$		0			0
$754$	−0.00949526	+	0.00796747i	−0.000345797	+	0.000290158i
$755$	5.38106	+	4.38595i	0.195837	+	0.159621i
$756$		0			0
$757$	−42.2960	+	3.70042i	−1.53728	+	0.134494i	−0.824081	−	0.566472i	$-0.808308\pi$
$757$	−42.2960	+	3.70042i	−1.53728	+	0.134494i	−0.713195	+	0.700966i	$0.752752\pi$
$758$	−40.7807	+	28.5549i	−1.48122	+	1.03716i
$759$		0			0
$760$	13.0784	−	11.9065i	0.474405	−	0.431893i
$761$	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
$763$	−2.70301	+	0.236483i	−0.0978557	+	0.00856126i
$764$	−1.47652	+	4.05671i	−0.0534187	+	0.146767i
$765$		0			0
$766$	27.7420	−	23.2783i	1.00236	−	0.841080i
$767$	5.09543	+	1.36532i	0.183985	+	0.0492987i
$768$		0			0
$769$	−28.5485	+	5.03387i	−1.02948	+	0.181526i	−0.662782	−	0.748812i	$-0.730624\pi$
$769$	−28.5485	+	5.03387i	−1.02948	+	0.181526i	−0.366703	+	0.930338i	$0.619513\pi$
$770$	−3.30358	−	3.82487i	−0.119053	−	0.137839i
$771$		0			0
$772$	−2.99047	+	11.1606i	−0.107629	+	0.401678i
$773$	2.81654	−	32.1932i	0.101304	−	1.15791i	−0.760037	−	0.649880i	$-0.774819\pi$
$773$	2.81654	−	32.1932i	0.101304	−	1.15791i	0.861341	−	0.508028i	$-0.169625\pi$
$774$		0			0
$775$	−11.0257	−	12.4033i	−0.396053	−	0.445539i
$776$	−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
$782$	5.47337	+	62.5609i	0.195727	+	2.23717i
$783$		0			0
$784$	−11.8218	−	32.4802i	−0.422208	−	1.16001i
$785$	15.7237	+	32.5008i	0.561204	+	1.16000i
$786$		0			0
$787$	−17.9777	+	4.81711i	−0.640836	+	0.171711i	−0.564582	−	0.825377i	$-0.690963\pi$
$787$	−17.9777	+	4.81711i	−0.640836	+	0.171711i	−0.0762539	+	0.997088i	$0.524296\pi$
$788$	0.0911732	−	0.130209i	0.00324791	−	0.00463850i
$789$		0			0
$790$	−14.6589	+	15.0833i	−0.521542	+	0.536640i
$791$	−0.458580	+	0.264761i	−0.0163052	+	0.00941383i
$792$		0			0
$793$	4.19430	−	8.99471i	0.148944	−	0.319411i
$794$	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	0.948231	−	0.317581i	$-0.102871\pi$
$797$	17.8040	+	17.8040i	0.630650	+	0.630650i	−0.317581	+	0.948231i	$0.602871\pi$
$798$		0			0
$799$		−	24.2912i		−	0.859362i
$800$	−2.85466	−	24.5412i	−0.100928	−	0.867661i
$801$		0			0
$802$	−28.2389	+	13.1680i	−0.997150	+	0.464979i
$803$	−44.9235	−	20.9482i	−1.58532	−	0.739245i
$804$		0			0
$805$	4.25810	+	2.37807i	0.150078	+	0.0838159i
$806$	12.2087	+	7.04867i	0.430032	+	0.248279i
$807$		0			0
$808$	−16.5558	−	11.5925i	−0.582430	−	0.407822i
$809$	−9.34965	−	5.39802i	−0.328716	−	0.189784i	0.326555	−	0.945178i	$-0.394112\pi$
$809$	−9.34965	−	5.39802i	−0.328716	−	0.189784i	−0.655271	+	0.755394i	$0.727446\pi$
$810$		0			0
$811$	−29.9351	−	35.6753i	−1.05116	−	1.25273i	−0.966595	−	0.256310i	$-0.917493\pi$
$811$	−29.9351	−	35.6753i	−1.05116	−	1.25273i	−0.0845686	−	0.996418i	$-0.526951\pi$
$812$	−0.000715340	0	0.000333569i	−2.51035e−5	0	1.17060e-5i
$813$		0			0
$814$	39.0877	−	46.5829i	1.37002	−	1.63273i
$815$	0.0757425	−	0.168672i	0.00265314	−	0.00590833i
$816$		0			0
$817$	−0.655017	+	0.579447i	−0.0229161	+	0.0202723i
$818$	−14.9539	−	14.9539i	−0.522852	−	0.522852i
$819$		0			0
$820$	−0.429733	−	0.0694673i	−0.0150069	−	0.00242590i
$821$	−42.5776	−	15.4970i	−1.48597	−	0.540848i	−0.533583	−	0.845748i	$-0.679155\pi$
$821$	−42.5776	−	15.4970i	−1.48597	−	0.540848i	−0.952384	+	0.304900i	$0.901377\pi$
$822$		0			0
$823$	−54.7548	−	4.79043i	−1.90863	−	0.166984i	−0.929312	−	0.369296i	$-0.879599\pi$
$823$	−54.7548	−	4.79043i	−1.90863	−	0.166984i	−0.979321	+	0.202312i	$0.935154\pi$
$824$	1.29666	−	0.748626i	0.0451712	−	0.0260796i
$825$		0			0
$826$	0.182161	+	1.03309i	0.00633820	+	0.0359457i
$827$	4.05406	−	5.78980i	0.140973	−	0.201331i	−0.742456	−	0.669894i	$-0.766339\pi$
$827$	4.05406	−	5.78980i	0.140973	−	0.201331i	0.883430	+	0.468563i	$0.155228\pi$
$828$		0			0
$829$	−3.92941	−	6.80594i	−0.136474	−	0.236380i	0.789685	−	0.613512i	$-0.210244\pi$
$829$	−3.92941	−	6.80594i	−0.136474	−	0.236380i	−0.926160	+	0.377132i	$0.876910\pi$
$830$	57.9108	+	20.1469i	2.01011	+	0.699309i
$831$		0			0
$832$	−1.58826	−	3.40603i	−0.0550630	−	0.118083i
$833$	−2.90546	−	33.2095i	−0.100668	−	1.15064i
$834$		0			0
$835$	−18.6942	−	4.72429i	−0.646938	−	0.163491i
$836$	18.0727	−	5.35231i	0.625057	−	0.185113i
$837$		0			0
$838$	−30.2804	−	43.2448i	−1.04602	−	1.49387i
$839$	13.3579	+	11.2087i	0.461168	+	0.386966i	0.843560	−	0.537034i	$-0.180455\pi$
$839$	13.3579	+	11.2087i	0.461168	+	0.386966i	−0.382393	+	0.924000i	$0.624900\pi$
$840$		0			0
$841$	27.2511	−	9.91858i	0.939692	−	0.342020i
$842$	2.49327	−	28.4982i	0.0859238	−	0.982113i
$843$		0			0
$844$	−0.0448173	+	0.0776258i	−0.00154267	+	0.00267199i
$845$	−11.6228	+	10.0387i	−0.399835	+	0.345341i
$846$		0			0
$847$	0.748091	+	2.79191i	0.0257047	+	0.0959313i
$848$	−12.7453	−	3.41511i	−0.437677	−	0.117275i
$849$		0			0
$850$	6.01265	−	40.8899i	0.206232	−	1.40251i
$851$	−20.0702	+	55.1425i	−0.687998	+	1.89026i
$852$		0			0
$853$	40.2152	−	28.1590i	1.37694	−	0.964146i	0.377673	−	0.925939i	$-0.376724\pi$
$853$	40.2152	−	28.1590i	1.37694	−	0.964146i	0.999270	−	0.0382064i	$-0.0121644\pi$
$854$	1.97360			0.0675354
$855$		0			0
$856$	28.2920			0.967001
$857$	−0.0902309	+	0.0631803i	−0.00308223	+	0.00215820i	−0.575117	−	0.818071i	$-0.695043\pi$
$857$	−0.0902309	+	0.0631803i	−0.00308223	+	0.00215820i	0.572034	+	0.820230i	$0.306154\pi$
$858$		0			0
$859$	−13.8823	+	38.1414i	−0.473659	+	1.30137i	0.441132	+	0.897442i	$0.354577\pi$
$859$	−13.8823	+	38.1414i	−0.473659	+	1.30137i	−0.914792	+	0.403926i	$0.867645\pi$
$860$	0.0428389	+	0.420467i	0.00146079	+	0.0143378i
$861$		0			0
$862$	−25.7176	−	6.89101i	−0.875945	−	0.234709i
$863$	−4.79433	−	17.8927i	−0.163201	−	0.609074i	−0.998263	−	0.0589178i	$-0.981235\pi$
$863$	−4.79433	−	17.8927i	−0.163201	−	0.609074i	0.835062	−	0.550156i	$-0.185432\pi$
$864$		0			0
$865$	−21.0686	−	1.54073i	−0.716352	−	0.0523862i
$866$	11.0578	−	19.1526i	0.375759	−	0.650833i
$867$		0			0
$868$	−0.0782379	+	0.894263i	−0.00265557	+	0.0303533i
$869$	23.6531	−	8.60903i	0.802377	−	0.292041i
$870$		0			0
$871$	17.2019	+	14.4341i	0.582865	+	0.489082i
$872$	9.83693	+	14.0486i	0.333121	+	0.475745i
$873$		0			0
$874$	−45.6634	+	33.7853i	−1.54459	+	1.14280i
$875$	−2.36466	−	2.17043i	−0.0799401	−	0.0733740i
$876$		0			0
$877$	−2.69772	−	30.8351i	−0.0910956	−	1.04123i	−0.894880	−	0.446307i	$-0.852739\pi$
$877$	−2.69772	−	30.8351i	−0.0910956	−	1.04123i	0.803784	−	0.594921i	$-0.202817\pi$
$878$	−24.3863	−	52.2966i	−0.822998	−	1.76493i
$879$		0			0
$880$	−16.8506	+	48.4358i	−0.568033	+	1.63277i
$881$	−0.542908	−	0.940344i	−0.0182910	−	0.0316810i	0.856735	−	0.515757i	$-0.172489\pi$
$881$	−0.542908	−	0.940344i	−0.0182910	−	0.0316810i	−0.875026	+	0.484076i	$0.839156\pi$
$882$		0			0
$883$	15.4242	−	22.0280i	0.519065	−	0.741302i	−0.470966	−	0.882151i	$-0.656095\pi$
$883$	15.4242	−	22.0280i	0.519065	−	0.741302i	0.990031	+	0.140850i	$0.0449834\pi$
$884$	1.95217	+	11.0713i	0.0656585	+	0.372368i
$885$		0			0
$886$	24.9015	−	14.3769i	0.836582	−	0.483001i
$887$	−23.4968	−	2.05570i	−0.788946	−	0.0690238i	−0.314441	−	0.949277i	$-0.601817\pi$
$887$	−23.4968	−	2.05570i	−0.788946	−	0.0690238i	−0.474504	+	0.880253i	$0.657373\pi$
$888$		0			0
$889$	−2.71832	−	0.989389i	−0.0911696	−	0.0331830i
$890$	−35.4895	−	49.1758i	−1.18961	−	1.64838i
$891$		0			0
$892$	0.457845	+	0.457845i	0.0153298	+	0.0153298i
$893$	18.7345	−	11.4791i	0.626927	−	0.384134i
$894$		0			0
$895$	5.70487	+	15.0044i	0.190693	+	0.501542i
$896$	2.30409	−	2.74591i	0.0769743	−	0.0917344i
$897$		0			0
$898$	−26.9918	−	12.5865i	−0.900729	−	0.420017i
$899$	0.00622611	+	0.00741999i	0.000207652	+	0.000247471i
$900$		0			0
$901$	−11.0211	−	6.36302i	−0.367165	−	0.211983i
$902$	1.33269	+	0.933160i	0.0443737	+	0.0310708i
$903$		0			0
$904$	2.89854	+	1.67347i	0.0964040	+	0.0556589i
$905$	1.75705	−	3.14613i	0.0584064	−	0.104581i
$906$		0			0
$907$	5.90696	+	2.75446i	0.196137	+	0.0914603i	0.518205	−	0.855256i	$-0.326600\pi$
$907$	5.90696	+	2.75446i	0.196137	+	0.0914603i	−0.322068	+	0.946716i	$0.604378\pi$
$908$	3.78225	−	1.76369i	0.125518	−	0.0585301i
$909$		0			0
$910$	2.48731	+	1.11693i	0.0824537	+	0.0370260i
$911$		−	27.6418i		−	0.915812i	−0.889001	−	0.457906i	$-0.848600\pi$
$911$		−	27.6418i		−	0.915812i	0.889001	−	0.457906i	$-0.151400\pi$
$912$		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
$917$	2.37346	−	5.08991i	0.0783787	−	0.168084i
$918$		0			0
$919$	−23.3008	+	13.4527i	−0.768623	+	0.443764i	−0.832383	−	0.554201i	$-0.813024\pi$
$919$	−23.3008	+	13.4527i	−0.768623	+	0.443764i	0.0637605	+	0.997965i	$0.479691\pi$
$920$	−0.439802	−	30.8238i	−0.0144998	−	1.01623i
$921$		0			0
$922$	−13.7938	+	19.6995i	−0.454274	+	0.648770i
$923$	30.2997	−	8.11879i	0.997328	−	0.267233i
$924$		0			0
$925$	21.2395	−	32.2541i	0.698350	−	1.06051i
$926$	8.44826	+	23.2114i	0.277627	+	0.762774i
$927$		0			0
$928$	0.00125682	+	0.0143655i	4.12570e−5	+	0.000471570i
$929$	−49.9574	−	8.80883i	−1.63905	−	0.289008i	−0.723232	−	0.690605i	$-0.757344\pi$
$929$	−49.9574	−	8.80883i	−1.63905	−	0.289008i	−0.915817	+	0.401597i	$0.868455\pi$
$930$		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
$935$	−27.7886	+	40.9165i	−0.908785	+	1.33811i
$936$		0			0
$937$	0.786309	−	8.98755i	0.0256876	−	0.293610i	−0.972474	−	0.233009i	$-0.925143\pi$
$937$	0.786309	−	8.98755i	0.0256876	−	0.293610i	0.998162	−	0.0606010i	$-0.0193017\pi$
$938$	−1.15576	+	4.31336i	−0.0377369	+	0.140836i
$939$		0			0
$940$	0.774450	−	10.5902i	0.0252598	−	0.345413i
$941$	1.15162	−	0.203063i	0.0375419	−	0.00661965i	−0.154846	−	0.987939i	$-0.549488\pi$
$941$	1.15162	−	0.203063i	0.0375419	−	0.00661965i	0.192388	+	0.981319i	$0.438377\pi$
$942$		0			0
$943$	−1.51648	−	0.406339i	−0.0493833	−	0.0132322i
$944$	8.15412	−	6.84212i	0.265394	−	0.222692i
$945$		0			0
$946$	0.540244	−	1.48431i	0.0175648	−	0.0482590i
$947$	−5.76927	+	0.504745i	−0.187476	+	0.0164020i	−0.180507	−	0.983574i	$-0.557774\pi$
$947$	−5.76927	+	0.504745i	−0.187476	+	0.0164020i	−0.00696893	+	0.999976i	$0.502218\pi$
$948$		0			0
$949$	26.7411			0.868051
$950$	34.3776	−	14.6858i	1.11536	−	0.476471i
$951$		0			0
$952$	2.05646	−	1.43995i	0.0666503	−	0.0466690i
$953$	−2.09745	+	0.183503i	−0.0679431	+	0.00594425i	−0.121077	−	0.992643i	$-0.538635\pi$
$953$	−2.09745	+	0.183503i	−0.0679431	+	0.00594425i	0.0531335	+	0.998587i	$0.483079\pi$
$954$		0			0
$955$	6.47378	−	7.94258i	0.209487	−	0.257016i
$956$	−4.51315	+	3.78698i	−0.145966	+	0.122480i
$957$		0			0
$958$	−8.86741	−	33.0936i	−0.286493	−	1.06921i
$959$	−3.01324	+	0.531315i	−0.0973025	+	0.0171571i
$960$		0			0
$961$	−9.99187	+	17.3064i	−0.322319	+	0.558272i
$962$	−8.49082	+	31.6882i	−0.273755	+	1.02167i
$963$		0			0
$964$	−11.1045	+	4.04172i	−0.357653	+	0.130175i
$965$	15.4079	−	22.6869i	0.495998	−	0.730317i
$966$		0			0
$967$	24.5703	+	35.0900i	0.790127	+	1.12842i	0.988931	+	0.148379i	$0.0474055\pi$
$967$	24.5703	+	35.0900i	0.790127	+	1.12842i	−0.198804	+	0.980039i	$0.563706\pi$
$968$	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	−0.320567	−	0.947226i	$-0.603874\pi$
$971$	−29.4711	−	5.19655i	−0.945772	−	0.166765i	−0.625205	+	0.780461i	$0.714985\pi$
$972$		0			0
$973$	−1.86352	−	3.99633i	−0.0597417	−	0.128117i
$974$	−7.81592	−	21.4741i	−0.250438	−	0.688073i
$975$		0			0
$976$	−10.0131	−	17.3431i	−0.320511	−	0.555141i
$977$	18.2636	−	4.89371i	0.584303	−	0.156564i	0.0454549	−	0.998966i	$-0.485526\pi$
$977$	18.2636	−	4.89371i	0.584303	−	0.156564i	0.538848	+	0.842403i	$0.318860\pi$
$978$		0			0
$979$	12.6026	+	71.4730i	0.402782	+	2.28429i
$980$	−0.207901	−	14.5709i	−0.00664115	−	0.465449i
$981$		0			0
$982$	42.1854	+	3.69075i	1.34619	+	0.117777i
$983$	−21.6053	+	46.3328i	−0.689103	+	1.47779i	0.180264	+	0.983618i	$0.442305\pi$
$983$	−21.6053	+	46.3328i	−0.689103	+	1.47779i	−0.869367	+	0.494168i	$0.835473\pi$
$984$		0			0
$985$	−0.305935	+	0.220789i	−0.00974792	+	0.00703493i
$986$	−0.00418885	+	0.0237561i	−0.000133400	+	0.000756549i
$987$		0			0
$988$	−7.61618	+	6.73748i	−0.242303	+	0.214348i
$989$			1.52428i			0.0484694i
$990$		0			0
$991$	35.3727	−	42.1556i	1.12365	−	1.33912i	0.189648	−	0.981852i	$-0.439265\pi$
$991$	35.3727	−	42.1556i	1.12365	−	1.33912i	0.934003	−	0.357264i	$-0.116290\pi$
$992$	14.8640	−	6.93120i	0.471933	−	0.220066i
$993$		0			0
$994$	4.00970	+	4.77857i	0.127180	+	0.151567i
$995$	−5.44894	+	9.75671i	−0.172743	+	0.309308i
$996$		0			0
$997$	11.6457	+	8.15440i	0.368823	+	0.258252i	0.743264	−	0.668998i	$-0.233277\pi$
$997$	11.6457	+	8.15440i	0.368823	+	0.258252i	−0.374441	+	0.927251i	$0.622166\pi$
$998$	−26.5235	−	18.5720i	−0.839588	−	0.587886i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.3	✓	96	15.2	even	4
95.2.r.a.48.3	yes	96	57.29	even	18
95.2.r.a.67.3	yes	96	285.257	odd	36
95.2.r.a.78.3	yes	96	3.2	odd	2
475.2.bb.b.143.6		96	285.29	even	18
475.2.bb.b.257.6		96	285.143	odd	36
475.2.bb.b.268.6		96	15.14	odd	2
475.2.bb.b.382.6		96	15.8	even	4
855.2.dl.a.352.6		96	95.67	even	36	inner
855.2.dl.a.523.6		96	19.10	odd	18	inner
855.2.dl.a.667.6		96	5.2	odd	4	inner
855.2.dl.a.838.6		96	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.40505 - 0.983828i) q^{2} +(0.322212 - 0.885271i) q^{4} +(-1.41273 + 1.73326i) q^{5} +(-0.277305 - 0.0743036i) q^{7} +(0.469650 + 1.75276i) q^{8} +(-0.279734 + 3.82520i) q^{10} +(2.29500 - 3.97505i) q^{11} +(-0.215819 + 2.46682i) q^{13} +(-0.462730 + 0.168420i) q^{14} +(3.82765 + 3.21178i) q^{16} +(2.76411 + 3.94756i) q^{17} +(-1.73832 + 3.99728i) q^{19} +(1.07920 + 1.80913i) q^{20} +(-0.686176 - 7.84303i) q^{22} +(3.21082 + 6.88562i) q^{23} +(-1.00837 - 4.89726i) q^{25} +(2.12369 + 3.67833i) q^{26} +(-0.155130 + 0.221548i) q^{28} +(0.000506761 + 0.00287398i) q^{29} +(2.87440 - 1.65954i) q^{31} +(4.92252 + 0.430665i) q^{32} +(7.76743 + 2.82711i) q^{34} +(0.520545 - 0.375670i) q^{35} +(5.46158 + 5.46158i) q^{37} +(1.49020 + 7.32659i) q^{38} +(-3.70147 - 1.66215i) q^{40} +(-0.132829 + 0.158299i) q^{41} +(0.181834 + 0.0847905i) q^{43} +(-2.77952 - 3.31250i) q^{44} +(11.2856 + 6.51576i) q^{46} +(-4.12905 - 2.89119i) q^{47} +(-5.99080 - 3.45879i) q^{49} +(-6.23488 - 5.88884i) q^{50} +(2.11426 + 0.985897i) q^{52} +(-2.39334 + 1.11603i) q^{53} +(3.64758 + 9.59350i) q^{55} -0.520945i q^{56} +(0.00353953 + 0.00353953i) q^{58} +(0.369926 - 2.09795i) q^{59} +(-3.76621 - 1.37079i) q^{61} +(2.40598 - 5.15965i) q^{62} +(-1.31435 + 0.758840i) q^{64} +(-3.97074 - 3.85902i) q^{65} +(5.20141 - 7.42839i) q^{67} +(4.38529 - 1.17503i) q^{68} +(0.361798 - 1.03996i) q^{70} +(-4.33266 - 11.9039i) q^{71} +(-0.941200 - 10.7580i) q^{73} +(13.0471 + 2.30055i) q^{74} +(2.97856 + 2.82686i) q^{76} +(-0.931774 + 0.931774i) q^{77} +(4.20092 + 3.52499i) q^{79} +(-10.9743 + 2.09692i) q^{80} +(-0.0308922 + 0.353099i) q^{82} +(4.13763 - 15.4419i) q^{83} +(-10.7471 - 0.785925i) q^{85} +(0.338905 - 0.0597581i) q^{86} +(8.04514 + 2.15569i) q^{88} +(-12.1125 + 10.1636i) q^{89} +(0.243141 - 0.668024i) q^{91} +(7.13020 - 0.623812i) q^{92} -8.64596 q^{94} +(-4.47253 - 8.66005i) q^{95} +(-4.88649 + 3.42156i) q^{97} +(-11.8202 + 1.03414i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{5} + 18 q^{8} - 12 q^{10} + 12 q^{11} - 12 q^{13} + 12 q^{16} + 30 q^{17} + 84 q^{20} - 24 q^{22} + 12 q^{25} + 48 q^{26} - 36 q^{31} - 18 q^{32} + 30 q^{35} - 54 q^{38} + 54 q^{40}+ \cdots + 90 q^{98}+O(q^{100}) \) 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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