LMFDB - Embedded newform 864.2.bn.a.683.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			683.28
Character	$\chi$	$=$	864.683
Dual form			864.2.bn.a.611.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.484847 - 1.32850i) q^{2} +(-1.52985 - 1.28824i) q^{4} +(0.0345958 + 0.262781i) q^{5} +(0.779563 + 2.90937i) q^{7} +(-2.45318 + 1.40781i) q^{8} +(0.365879 + 0.0814479i) q^{10} +(0.904502 - 0.694049i) q^{11} +(-2.05487 + 2.67796i) q^{13} +(4.24308 + 0.374946i) q^{14} +(0.680862 + 3.94163i) q^{16} +6.62015 q^{17} +(5.15825 - 2.13662i) q^{19} +(0.285599 - 0.446582i) q^{20} +(-0.483502 - 1.53814i) q^{22} +(1.36994 + 0.367075i) q^{23} +(4.76177 - 1.27591i) q^{25} +(2.56139 + 4.02831i) q^{26} +(2.55536 - 5.45516i) q^{28} +(-5.03525 - 0.662903i) q^{29} +(2.63335 - 1.52037i) q^{31} +(5.56658 + 1.00656i) q^{32} +(3.20976 - 8.79490i) q^{34} +(-0.737557 + 0.305506i) q^{35} +(-2.21656 + 5.35125i) q^{37} +(-0.337543 - 7.88870i) q^{38} +(-0.454814 - 0.595944i) q^{40} +(-1.95155 + 7.28329i) q^{41} +(4.35237 + 5.67212i) q^{43} +(-2.27785 - 0.103430i) q^{44} +(1.15187 - 1.64200i) q^{46} +(-2.30774 - 1.33237i) q^{47} +(-1.79453 + 1.03607i) q^{49} +(0.613675 - 6.94466i) q^{50} +(6.59351 - 1.44970i) q^{52} +(4.56045 - 11.0099i) q^{53} +(0.213675 + 0.213675i) q^{55} +(-6.00824 - 6.03972i) q^{56} +(-3.32200 + 6.36794i) q^{58} +(-5.08348 + 0.669253i) q^{59} +(-1.61461 + 12.2642i) q^{61} +(-0.743041 - 4.23557i) q^{62} +(4.03616 - 6.90720i) q^{64} +(-0.774808 - 0.447335i) q^{65} +(4.48367 - 5.84323i) q^{67} +(-10.1278 - 8.52836i) q^{68} +(0.0482638 + 1.12797i) q^{70} +(-3.28684 - 3.28684i) q^{71} +(2.26326 - 2.26326i) q^{73} +(6.03447 + 5.53925i) q^{74} +(-10.6438 - 3.37638i) q^{76} +(2.72436 + 2.09048i) q^{77} +(7.66807 - 13.2815i) q^{79} +(-1.01223 + 0.315281i) q^{80} +(8.72967 + 6.12392i) q^{82} +(-1.17203 - 0.154301i) q^{83} +(0.229029 + 1.73965i) q^{85} +(9.64568 - 3.03203i) q^{86} +(-1.24182 + 2.97599i) q^{88} +(-7.53778 + 7.53778i) q^{89} +(-9.39309 - 3.89075i) q^{91} +(-1.62292 - 2.32638i) q^{92} +(-2.88896 + 2.41984i) q^{94} +(0.739916 + 1.28157i) q^{95} +(-0.177831 + 0.308013i) q^{97} +(0.506355 + 2.88638i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.484847	−	1.32850i	0.342839	−	0.939394i
$2$	0.484847	−	1.32850i	0.342839	−	0.939394i
$3$		0			0
$3$		0			0
$4$	−1.52985	−	1.28824i	−0.764923	−	0.644121i
$5$	0.0345958	+	0.262781i	0.0154717	+	0.117519i	0.997438	−	0.0715371i	$-0.0227904\pi$
$5$	0.0345958	+	0.262781i	0.0154717	+	0.117519i	−0.981966	+	0.189056i	$0.939457\pi$
$6$		0			0
$7$	0.779563	+	2.90937i	0.294647	+	1.09964i	0.941497	+	0.337021i	$0.109419\pi$
$7$	0.779563	+	2.90937i	0.294647	+	1.09964i	−0.646850	+	0.762617i	$0.723914\pi$
$8$	−2.45318	+	1.40781i	−0.867329	+	0.497735i
$9$		0			0
$10$	0.365879	+	0.0814479i	0.115701	+	0.0257561i
$11$	0.904502	−	0.694049i	0.272718	−	0.209264i	−0.463343	−	0.886179i	$-0.653350\pi$
$11$	0.904502	−	0.694049i	0.272718	−	0.209264i	0.736061	+	0.676915i	$0.236684\pi$
$12$		0			0
$13$	−2.05487	+	2.67796i	−0.569919	+	0.742734i	−0.986028	−	0.166582i	$-0.946727\pi$
$13$	−2.05487	+	2.67796i	−0.569919	+	0.742734i	0.416108	+	0.909315i	$0.363394\pi$
$14$	4.24308	+	0.374946i	1.13401	+	0.100209i
$15$		0			0
$16$	0.680862	+	3.94163i	0.170215	+	0.985407i
$17$	6.62015			1.60562			0.802812	−	0.596233i	$-0.203336\pi$
$17$	6.62015			1.60562			0.802812	+	0.596233i	$0.203336\pi$
$18$		0			0
$19$	5.15825	−	2.13662i	1.18338	−	0.490174i	0.297789	−	0.954632i	$-0.403751\pi$
$19$	5.15825	−	2.13662i	1.18338	−	0.490174i	0.885595	+	0.464458i	$0.153751\pi$
$20$	0.285599	−	0.446582i	0.0638620	−	0.0998588i
$21$		0			0
$22$	−0.483502	−	1.53814i	−0.103083	−	0.327933i
$23$	1.36994	+	0.367075i	0.285653	+	0.0765404i	0.398800	−	0.917038i	$-0.369427\pi$
$23$	1.36994	+	0.367075i	0.285653	+	0.0765404i	−0.113148	+	0.993578i	$0.536093\pi$
$24$		0			0
$25$	4.76177	−	1.27591i	0.952354	−	0.255183i
$26$	2.56139	+	4.02831i	0.502329	+	0.790017i
$27$		0			0
$28$	2.55536	−	5.45516i	0.482918	−	1.03093i
$29$	−5.03525	−	0.662903i	−0.935022	−	0.123098i	−0.352408	−	0.935847i	$-0.614637\pi$
$29$	−5.03525	−	0.662903i	−0.935022	−	0.123098i	−0.582615	+	0.812749i	$0.697970\pi$
$30$		0			0
$31$	2.63335	−	1.52037i	0.472964	−	0.273066i	−0.244515	−	0.969645i	$-0.578629\pi$
$31$	2.63335	−	1.52037i	0.472964	−	0.273066i	0.717480	+	0.696579i	$0.245296\pi$
$32$	5.56658	+	1.00656i	0.984042	+	0.177936i
$33$		0			0
$34$	3.20976	−	8.79490i	0.550470	−	1.50831i
$35$	−0.737557	+	0.305506i	−0.124670	+	0.0516400i
$36$		0			0
$37$	−2.21656	+	5.35125i	−0.364401	+	0.879741i	0.630245	+	0.776396i	$0.282954\pi$
$37$	−2.21656	+	5.35125i	−0.364401	+	0.879741i	−0.994646	+	0.103344i	$0.967046\pi$
$38$	−0.337543	−	7.88870i	−0.0547567	−	1.27972i
$39$		0			0
$40$	−0.454814	−	0.595944i	−0.0719125	−	0.0942270i
$41$	−1.95155	+	7.28329i	−0.304781	+	1.13746i	0.628353	+	0.777929i	$0.283729\pi$
$41$	−1.95155	+	7.28329i	−0.304781	+	1.13746i	−0.933134	+	0.359530i	$0.882937\pi$
$42$		0			0
$43$	4.35237	+	5.67212i	0.663731	+	0.864991i	0.996965	−	0.0778532i	$-0.0248066\pi$
$43$	4.35237	+	5.67212i	0.663731	+	0.864991i	−0.333234	+	0.942844i	$0.608140\pi$
$44$	−2.27785	−	0.103430i	−0.343399	−	0.0155926i
$45$		0			0
$46$	1.15187	−	1.64200i	0.169834	−	0.242099i
$47$	−2.30774	−	1.33237i	−0.336618	−	0.194347i	0.322157	−	0.946686i	$-0.395592\pi$
$47$	−2.30774	−	1.33237i	−0.336618	−	0.194347i	−0.658776	+	0.752339i	$0.728925\pi$
$48$		0			0
$49$	−1.79453	+	1.03607i	−0.256362	+	0.148011i
$50$	0.613675	−	6.94466i	0.0867868	−	0.982123i
$51$		0			0
$52$	6.59351	−	1.44970i	0.914355	−	0.201037i
$53$	4.56045	−	11.0099i	0.626426	−	1.51233i	−0.217608	−	0.976036i	$-0.569826\pi$
$53$	4.56045	−	11.0099i	0.626426	−	1.51233i	0.844034	−	0.536290i	$-0.180174\pi$
$54$		0			0
$55$	0.213675	+	0.213675i	0.0288119	+	0.0288119i
$56$	−6.00824	−	6.03972i	−0.802884	−	0.807092i
$57$		0			0
$58$	−3.32200	+	6.36794i	−0.436199	+	0.836152i
$59$	−5.08348	+	0.669253i	−0.661813	+	0.0871294i	−0.453948	−	0.891028i	$-0.649985\pi$
$59$	−5.08348	+	0.669253i	−0.661813	+	0.0871294i	−0.207865	+	0.978157i	$0.566652\pi$
$60$		0			0
$61$	−1.61461	+	12.2642i	−0.206730	+	1.57027i	0.502047	+	0.864840i	$0.332580\pi$
$61$	−1.61461	+	12.2642i	−0.206730	+	1.57027i	−0.708778	+	0.705432i	$0.750753\pi$
$62$	−0.743041	−	4.23557i	−0.0943663	−	0.537918i
$63$		0			0
$64$	4.03616	−	6.90720i	0.504520	−	0.863400i
$65$	−0.774808	−	0.447335i	−0.0961031	−	0.0554851i
$66$		0			0
$67$	4.48367	−	5.84323i	0.547767	−	0.713864i	−0.434643	−	0.900603i	$-0.643125\pi$
$67$	4.48367	−	5.84323i	0.547767	−	0.713864i	0.982410	+	0.186739i	$0.0597919\pi$
$68$	−10.1278	−	8.52836i	−1.22818	−	1.03422i
$69$		0			0
$70$	0.0482638	+	1.12797i	0.00576863	+	0.134818i
$71$	−3.28684	−	3.28684i	−0.390076	−	0.390076i	0.484639	−	0.874714i	$-0.338951\pi$
$71$	−3.28684	−	3.28684i	−0.390076	−	0.390076i	−0.874714	+	0.484639i	$0.838951\pi$
$72$		0			0
$73$	2.26326	−	2.26326i	0.264894	−	0.264894i	−0.562145	−	0.827039i	$-0.690024\pi$
$73$	2.26326	−	2.26326i	0.264894	−	0.264894i	0.827039	+	0.562145i	$0.190024\pi$
$74$	6.03447	+	5.53925i	0.701493	+	0.643925i
$75$		0			0
$76$	−10.6438	−	3.37638i	−1.22093	−	0.387298i
$77$	2.72436	+	2.09048i	0.310470	+	0.238232i
$78$		0			0
$79$	7.66807	−	13.2815i	0.862726	−	1.49428i	−0.00656230	−	0.999978i	$-0.502089\pi$
$79$	7.66807	−	13.2815i	0.862726	−	1.49428i	0.869288	−	0.494306i	$-0.164578\pi$
$80$	−1.01223	+	0.315281i	−0.113171	+	0.0352495i
$81$		0			0
$82$	8.72967	+	6.12392i	0.964031	+	0.676274i
$83$	−1.17203	−	0.154301i	−0.128647	−	0.0169367i	0.0659276	−	0.997824i	$-0.478999\pi$
$83$	−1.17203	−	0.154301i	−0.128647	−	0.0169367i	−0.194575	+	0.980888i	$0.562333\pi$
$84$		0			0
$85$	0.229029	+	1.73965i	0.0248417	+	0.188692i
$86$	9.64568	−	3.03203i	1.04012	−	0.326953i
$87$		0			0
$88$	−1.24182	+	2.97599i	−0.132378	+	0.317242i
$89$	−7.53778	+	7.53778i	−0.799003	+	0.799003i	−0.982938	−	0.183935i	$-0.941116\pi$
$89$	−7.53778	+	7.53778i	−0.799003	+	0.799003i	0.183935	+	0.982938i	$0.441116\pi$
$90$		0			0
$91$	−9.39309	−	3.89075i	−0.984663	−	0.407861i
$92$	−1.62292	−	2.32638i	−0.169201	−	0.242542i
$93$		0			0
$94$	−2.88896	+	2.41984i	−0.297974	+	0.249588i
$95$	0.739916	+	1.28157i	0.0759138	+	0.131487i
$96$		0			0
$97$	−0.177831	+	0.308013i	−0.0180560	+	0.0312740i	−0.874912	−	0.484282i	$-0.839081\pi$
$97$	−0.177831	+	0.308013i	−0.0180560	+	0.0312740i	0.856856	+	0.515555i	$0.172414\pi$
$98$	0.506355	+	2.88638i	0.0511496	+	0.291569i
$99$		0			0
$100$	−8.92847	−	4.18237i	−0.892847	−	0.418237i
$101$	−6.60978	+	5.07186i	−0.657698	+	0.504669i	−0.882850	−	0.469654i	$-0.844379\pi$
$101$	−6.60978	+	5.07186i	−0.657698	+	0.504669i	0.225153	+	0.974323i	$0.427712\pi$
$102$		0			0
$103$	−0.263483	−	0.0706001i	−0.0259618	−	0.00695644i	0.245815	−	0.969317i	$-0.420944\pi$
$103$	−0.263483	−	0.0706001i	−0.0259618	−	0.00695644i	−0.271777	+	0.962360i	$0.587611\pi$
$104$	1.27091	−	9.46239i	0.124623	−	0.927863i
$105$		0			0
$106$	−12.4156	−	11.3967i	−1.20591	−	1.10694i
$107$	−6.64771	−	2.75357i	−0.642659	−	0.266198i	0.0374621	−	0.999298i	$-0.488073\pi$
$107$	−6.64771	−	2.75357i	−0.642659	−	0.266198i	−0.680121	+	0.733100i	$0.738073\pi$
$108$		0			0
$109$	1.54546	+	3.73107i	0.148028	+	0.357372i	0.980449	−	0.196772i	$-0.0630459\pi$
$109$	1.54546	+	3.73107i	0.148028	+	0.357372i	−0.832421	+	0.554144i	$0.813046\pi$
$110$	0.387467	−	0.180268i	0.0369436	−	0.0171879i
$111$		0			0
$112$	−10.9369	+	5.05363i	−1.03344	+	0.477523i
$113$	8.65034	+	14.9828i	0.813756	+	1.40947i	0.910218	+	0.414129i	$0.135914\pi$
$113$	8.65034	+	14.9828i	0.813756	+	1.40947i	−0.0964624	+	0.995337i	$0.530753\pi$
$114$		0			0
$115$	−0.0490661	+	0.372694i	−0.00457543	+	0.0347539i
$116$	6.84918	+	7.50076i	0.635930	+	0.696428i
$117$		0			0
$118$	−1.57561	+	7.07792i	−0.145046	+	0.651575i
$119$	5.16083	+	19.2605i	0.473092	+	1.76560i
$120$		0			0
$121$	−2.51059	+	9.36965i	−0.228235	+	0.851786i
$122$	15.5102	+	8.09129i	1.40423	+	0.732551i
$123$		0			0
$124$	−5.98723	−	1.06647i	−0.537669	−	0.0957718i
$125$	1.00717	+	2.43153i	0.0900841	+	0.217482i
$126$		0			0
$127$			0.469475i			0.0416592i	0.999783	+	0.0208296i	$0.00663074\pi$
$127$			0.469475i			0.0416592i	−0.999783	+	0.0208296i	$0.993369\pi$
$128$	−7.21933	−	8.71099i	−0.638104	−	0.769950i
$129$		0			0
$130$	−0.969950	+	0.812446i	−0.0850703	+	0.0712562i
$131$	−7.31034	−	5.60942i	−0.638707	−	0.490097i	0.237909	−	0.971287i	$-0.423538\pi$
$131$	−7.31034	−	5.60942i	−0.638707	−	0.490097i	−0.876616	+	0.481190i	$0.840205\pi$
$132$		0			0
$133$	10.2374	+	13.3416i	0.887695	+	1.15687i
$134$	−5.58886	−	8.78964i	−0.482804	−	0.759309i
$135$		0			0
$136$	−16.2404	+	9.31990i	−1.39260	+	0.799175i
$137$	20.4598	−	5.48217i	1.74799	−	0.468374i	0.763798	−	0.645455i	$-0.223332\pi$
$137$	20.4598	−	5.48217i	1.74799	−	0.468374i	0.984196	+	0.177081i	$0.0566655\pi$
$138$		0			0
$139$	6.59649	−	0.868444i	0.559507	−	0.0736605i	0.154531	−	0.987988i	$-0.450613\pi$
$139$	6.59649	−	0.868444i	0.559507	−	0.0736605i	0.404976	+	0.914327i	$0.367280\pi$
$140$	1.52192	+	0.482775i	0.128625	+	0.0408019i
$141$		0			0
$142$	−5.96019	+	2.77296i	−0.500168	+	0.232702i
$143$			3.84841i			0.321820i
$144$		0			0
$145$		−	1.34610i		−	0.111788i
$146$	−1.90941	−	4.10408i	−0.158024	−	0.339656i
$147$		0			0
$148$	10.2847	−	5.33113i	0.845398	−	0.438216i
$149$	−4.02528	+	0.529938i	−0.329764	+	0.0434142i	−0.293590	−	0.955931i	$-0.594850\pi$
$149$	−4.02528	+	0.529938i	−0.329764	+	0.0434142i	−0.0361734	+	0.999346i	$0.511517\pi$
$150$		0			0
$151$	−18.3805	+	4.92505i	−1.49579	+	0.400795i	−0.911687	−	0.410886i	$-0.865219\pi$
$151$	−18.3805	+	4.92505i	−1.49579	+	0.400795i	−0.584101	+	0.811681i	$0.698553\pi$
$152$	−9.64617	+	12.5033i	−0.782407	+	1.01415i
$153$		0			0
$154$	4.09811	−	2.60576i	0.330235	−	0.209979i
$155$	0.490627	+	0.639397i	0.0394081	+	0.0513576i
$156$		0			0
$157$	−16.3433	−	12.5406i	−1.30434	−	1.00085i	−0.998815	−	0.0486661i	$-0.984503\pi$
$157$	−16.3433	−	12.5406i	−1.30434	−	1.00085i	−0.305520	−	0.952186i	$-0.598830\pi$
$158$	−13.9267	−	16.6266i	−1.10795	−	1.32274i
$159$		0			0
$160$	−0.0719242	+	1.49761i	−0.00568611	+	0.118397i
$161$			4.27182i			0.336667i
$162$		0			0
$163$	−7.29151	−	17.6033i	−0.571115	−	1.37879i	−0.900607	−	0.434635i	$-0.856877\pi$
$163$	−7.29151	−	17.6033i	−0.571115	−	1.37879i	0.329492	−	0.944159i	$-0.393123\pi$
$164$	12.3682	−	8.62824i	0.965795	−	0.673752i
$165$		0			0
$166$	−0.773246	+	1.48224i	−0.0600155	+	0.115044i
$167$	0.626404	−	2.33777i	0.0484726	−	0.180902i	−0.937445	−	0.348133i	$-0.886816\pi$
$167$	0.626404	−	2.33777i	0.0484726	−	0.180902i	0.985918	+	0.167231i	$0.0534825\pi$
$168$		0			0
$169$	0.415664	+	1.55128i	0.0319742	+	0.119329i
$170$	2.42218	+	0.539198i	0.185772	+	0.0413546i
$171$		0			0
$172$	0.648607	−	14.2844i	0.0494559	−	1.08917i
$173$	−2.78766	+	21.1744i	−0.211942	+	1.60986i	0.472865	+	0.881135i	$0.343220\pi$
$173$	−2.78766	+	21.1744i	−0.211942	+	1.60986i	−0.684807	+	0.728725i	$0.740113\pi$
$174$		0			0
$175$	7.42420	+	12.8591i	0.561217	+	0.972057i
$176$	3.35152	+	3.09266i	0.252631	+	0.233118i
$177$		0			0
$178$	6.35930	+	13.6686i	0.476650	+	1.02451i
$179$	−0.878974	−	2.12203i	−0.0656976	−	0.158608i	0.887621	−	0.460575i	$-0.152357\pi$
$179$	−0.878974	−	2.12203i	−0.0656976	−	0.158608i	−0.953318	+	0.301967i	$0.902357\pi$
$180$		0			0
$181$	−10.5272	−	4.36050i	−0.782478	−	0.324113i	−0.0445631	−	0.999007i	$-0.514190\pi$
$181$	−10.5272	−	4.36050i	−0.782478	−	0.324113i	−0.737915	+	0.674893i	$0.764190\pi$
$182$	−9.72308	+	10.5923i	−0.720723	+	0.785157i
$183$		0			0
$184$	−3.87748	+	1.02811i	−0.285852	+	0.0757936i
$185$	−1.48289	−	0.397340i	−0.109024	−	0.0292130i
$186$		0			0
$187$	5.98794	−	4.59471i	0.437882	−	0.335999i
$188$	1.81407	+	5.01126i	0.132304	+	0.365483i
$189$		0			0
$190$	2.06132	−	0.361615i	0.149544	−	0.0262343i
$191$	4.80107	−	8.31569i	0.347393	−	0.601703i	−0.638392	−	0.769711i	$-0.720400\pi$
$191$	4.80107	−	8.31569i	0.347393	−	0.601703i	0.985786	+	0.168009i	$0.0537336\pi$
$192$		0			0
$193$	−13.3346	−	23.0963i	−0.959848	−	1.66251i	−0.722861	−	0.690993i	$-0.757173\pi$
$193$	−13.3346	−	23.0963i	−0.959848	−	1.66251i	−0.236987	−	0.971513i	$-0.576160\pi$
$194$	0.322975	+	0.385589i	0.0231883	+	0.0276836i
$195$		0			0
$196$	4.08008	+	0.726759i	0.291434	+	0.0519114i
$197$	1.38480	+	0.573602i	0.0986628	+	0.0408675i	0.431469	−	0.902128i	$-0.357995\pi$
$197$	1.38480	+	0.573602i	0.0986628	+	0.0408675i	−0.332806	+	0.942995i	$0.607995\pi$
$198$		0			0
$199$	6.42238	−	6.42238i	0.455271	−	0.455271i	−0.441829	−	0.897099i	$-0.645670\pi$
$199$	6.42238	−	6.42238i	0.455271	−	0.455271i	0.897099	+	0.441829i	$0.145670\pi$
$200$	−9.88523	+	9.83370i	−0.698991	+	0.695347i
$201$		0			0
$202$	3.53326	+	11.2402i	0.248599	+	0.790857i
$203$	−1.99666	−	15.1662i	−0.140138	−	1.06446i
$204$		0			0
$205$	−1.98142	−	0.260859i	−0.138389	−	0.0182192i
$206$	−0.221542	+	0.315808i	−0.0154355	+	0.0220034i
$207$		0			0
$208$	−11.9546	−	6.27622i	−0.828904	−	0.435178i
$209$	3.18273	−	5.51266i	0.220154	−	0.381319i
$210$		0			0
$211$	8.22670	+	6.31257i	0.566349	+	0.434575i	0.851837	−	0.523807i	$-0.175489\pi$
$211$	8.22670	+	6.31257i	0.566349	+	0.434575i	−0.285487	+	0.958382i	$0.592155\pi$
$212$	−21.1602	+	10.9685i	−1.45329	+	0.753319i
$213$		0			0
$214$	−6.88126	+	7.49645i	−0.470393	+	0.512447i
$215$	−1.33995	+	1.33995i	−0.0913840	+	0.0913840i
$216$		0			0
$217$	6.47618	+	6.47618i	0.439632	+	0.439632i
$218$	5.70605	−	0.244152i	0.386463	−	0.0165360i
$219$		0			0
$220$	−0.0516247	−	0.602155i	−0.00348054	−	0.0405973i
$221$	−13.6036	+	17.7285i	−0.915076	+	1.19255i
$222$		0			0
$223$	18.1004	+	10.4503i	1.21209	+	0.699802i	0.963215	−	0.268733i	$-0.0866050\pi$
$223$	18.1004	+	10.4503i	1.21209	+	0.699802i	0.248878	+	0.968535i	$0.419938\pi$
$224$	1.41105	+	16.9799i	0.0942799	+	1.13452i
$225$		0			0
$226$	24.0988	−	4.22763i	1.60303	−	0.281218i
$227$	1.35199	−	10.2694i	0.0897349	−	0.681604i	−0.886162	−	0.463375i	$-0.846638\pi$
$227$	1.35199	−	10.2694i	0.0897349	−	0.681604i	0.975897	−	0.218230i	$-0.0700282\pi$
$228$		0			0
$229$	7.89688	−	1.03964i	0.521840	−	0.0687016i	0.134995	−	0.990846i	$-0.456898\pi$
$229$	7.89688	−	1.03964i	0.521840	−	0.0687016i	0.386845	+	0.922145i	$0.373565\pi$
$230$	0.471336	+	0.245884i	0.0310790	+	0.0162131i
$231$		0			0
$232$	13.2856	−	5.46244i	0.872242	−	0.358627i
$233$	−1.21008	−	1.21008i	−0.0792748	−	0.0792748i	0.666358	−	0.745632i	$-0.267852\pi$
$233$	−1.21008	−	1.21008i	−0.0792748	−	0.0792748i	−0.745632	+	0.666358i	$0.767852\pi$
$234$		0			0
$235$	0.270284	−	0.652524i	0.0176314	−	0.0425660i
$236$	8.63911	+	5.52491i	0.562358	+	0.359641i
$237$		0			0
$238$	28.0898	+	2.48220i	1.82079	+	0.160897i
$239$	−15.6470	+	9.03378i	−1.01212	+	0.584347i	−0.911811	−	0.410610i	$-0.865316\pi$
$239$	−15.6470	+	9.03378i	−1.01212	+	0.584347i	−0.100307	+	0.994957i	$0.531983\pi$
$240$		0			0
$241$	−12.1405	−	7.00930i	−0.782036	−	0.451509i	0.0551154	−	0.998480i	$-0.482447\pi$
$241$	−12.1405	−	7.00930i	−0.782036	−	0.451509i	−0.837151	+	0.546971i	$0.815781\pi$
$242$	11.2304	+	7.87817i	0.721915	+	0.506428i
$243$		0			0
$244$	18.2694	−	16.6824i	1.16958	−	1.06798i
$245$	−0.334344	−	0.435725i	−0.0213604	−	0.0278375i
$246$		0			0
$247$	−4.87777	+	18.2041i	−0.310365	+	1.15830i
$248$	−4.31970	+	7.43699i	−0.274301	+	0.472249i
$249$		0			0
$250$	3.71862	−	0.159113i	0.235186	−	0.0100632i
$251$	10.1807	−	24.5783i	0.642597	−	1.55137i	−0.180567	−	0.983563i	$-0.557793\pi$
$251$	10.1807	−	24.5783i	0.642597	−	1.55137i	0.823164	−	0.567804i	$-0.192207\pi$
$252$		0			0
$253$	1.49388	−	0.618787i	0.0939196	−	0.0389028i
$254$	0.623699	+	0.227623i	0.0391344	+	0.0142824i
$255$		0			0
$256$	−15.0729	+	5.36741i	−0.942053	+	0.335463i
$257$	−15.6830	+	9.05459i	−0.978279	+	0.564810i	−0.901750	−	0.432258i	$-0.857717\pi$
$257$	−15.6830	+	9.05459i	−0.978279	+	0.564810i	−0.0765289	+	0.997067i	$0.524384\pi$
$258$		0			0
$259$	−17.2967	−	2.27716i	−1.07477	−	0.141496i
$260$	0.609060	+	1.68250i	0.0377723	+	0.104344i
$261$		0			0
$262$	−10.9965	+	6.99210i	−0.679368	+	0.431974i
$263$	13.7483	−	3.68384i	0.847755	−	0.227155i	0.191310	−	0.981530i	$-0.438726\pi$
$263$	13.7483	−	3.68384i	0.847755	−	0.227155i	0.656444	+	0.754374i	$0.272060\pi$
$264$		0			0
$265$	3.05096	+	0.817503i	0.187419	+	0.0502188i
$266$	22.6880	−	7.13177i	1.39109	−	0.437277i
$267$		0			0
$268$	−14.3868	+	3.16319i	−0.878815	+	0.193223i
$269$	9.33715	−	3.86758i	0.569296	−	0.235810i	−0.0794191	−	0.996841i	$-0.525307\pi$
$269$	9.33715	−	3.86758i	0.569296	−	0.235810i	0.648715	+	0.761031i	$0.275307\pi$
$270$		0			0
$271$	−1.06895			−0.0649338			−0.0324669	−	0.999473i	$-0.510336\pi$
$271$	−1.06895			−0.0649338			−0.0324669	+	0.999473i	$0.510336\pi$
$272$	4.50741	+	26.0942i	0.273302	+	1.58219i
$273$		0			0
$274$	2.63676	−	29.8389i	0.159292	−	1.80263i
$275$	3.42149	−	4.45897i	0.206323	−	0.268886i
$276$		0			0
$277$	−13.4899	+	10.3512i	−0.810530	+	0.621941i	−0.928608	−	0.371063i	$-0.878993\pi$
$277$	−13.4899	+	10.3512i	−0.810530	+	0.621941i	0.118078	+	0.993004i	$0.462327\pi$
$278$	2.04456	−	9.18453i	0.122624	−	0.550851i
$279$		0			0
$280$	1.37926	−	1.78780i	0.0824268	−	0.106841i
$281$	4.45151	+	16.6133i	0.265555	+	0.991064i	0.961910	+	0.273367i	$0.0881373\pi$
$281$	4.45151	+	16.6133i	0.265555	+	0.991064i	−0.696355	+	0.717698i	$0.745196\pi$
$282$		0			0
$283$	0.845916	+	6.42537i	0.0502845	+	0.381949i	0.998020	+	0.0628925i	$0.0200325\pi$
$283$	0.845916	+	6.42537i	0.0502845	+	0.381949i	−0.947736	+	0.319056i	$0.896634\pi$
$284$	0.794113	+	9.26260i	0.0471219	+	0.549634i
$285$		0			0
$286$	5.11263	+	1.86589i	0.302316	+	0.110332i
$287$	−22.7111			−1.34060
$288$		0			0
$289$	26.8264			1.57803
$290$	−1.78830	−	0.652653i	−0.105013	−	0.0383251i
$291$		0			0
$292$	−6.37806	+	0.546812i	−0.373248	+	0.0319998i
$293$	−3.47402	−	26.3878i	−0.202954	−	1.54159i	−0.725045	−	0.688701i	$-0.758181\pi$
$293$	−3.47402	−	26.3878i	−0.202954	−	1.54159i	0.522091	−	0.852890i	$-0.325152\pi$
$294$		0			0
$295$	−0.351734	−	1.31269i	−0.0204787	−	0.0764277i
$296$	−2.09591	−	16.2481i	−0.121823	−	0.944400i
$297$		0			0
$298$	−1.24762	+	5.60454i	−0.0722727	+	0.324662i
$299$	−3.79807	+	2.91436i	−0.219648	+	0.168542i
$300$		0			0
$301$	−13.1094	+	17.0844i	−0.755611	+	0.984731i
$302$	−2.36880	+	26.8065i	−0.136309	+	1.54254i
$303$		0			0
$304$	11.9338	+	18.8772i	0.684451	+	1.08268i
$305$	−3.27866			−0.187736
$306$		0			0
$307$	−5.20812	+	2.15728i	−0.297243	+	0.123122i	−0.526321	−	0.850286i	$-0.676429\pi$
$307$	−5.20812	+	2.15728i	−0.297243	+	0.123122i	0.229078	+	0.973408i	$0.426429\pi$
$308$	−1.47482	−	6.70775i	−0.0840354	−	0.382209i
$309$		0			0
$310$	1.08732	−	0.341790i	0.0617556	−	0.0194124i
$311$	19.6599	+	5.26787i	1.11481	+	0.298713i	0.768783	−	0.639510i	$-0.220863\pi$
$311$	19.6599	+	5.26787i	1.11481	+	0.298713i	0.346030	+	0.938223i	$0.387529\pi$
$312$		0			0
$313$	−1.25379	+	0.335953i	−0.0708686	+	0.0189892i	−0.294079	−	0.955781i	$-0.595013\pi$
$313$	−1.25379	+	0.335953i	−0.0708686	+	0.0189892i	0.223211	+	0.974770i	$0.428346\pi$
$314$	−24.5843	+	15.6318i	−1.38737	+	0.882155i
$315$		0			0
$316$	−28.8408	+	10.4403i	−1.62242	+	0.587313i
$317$	−23.3733	−	3.07716i	−1.31278	−	0.172830i	−0.558565	−	0.829461i	$-0.688648\pi$
$317$	−23.3733	−	3.07716i	−1.31278	−	0.172830i	−0.754212	+	0.656631i	$0.771981\pi$
$318$		0			0
$319$	−5.01448	+	2.89511i	−0.280757	+	0.162095i
$320$	1.95471	+	0.821666i	0.109272	+	0.0459325i
$321$		0			0
$322$	5.67514	+	2.07118i	0.316263	+	0.115422i
$323$	34.1484	−	14.1447i	1.90007	−	0.787035i
$324$		0			0
$325$	−6.36799	+	15.3737i	−0.353233	+	0.852779i
$326$	−26.9213	+	1.15191i	−1.49103	+	0.0637985i
$327$		0			0
$328$	−5.46596	−	20.6146i	−0.301807	−	1.13825i
$329$	2.07734	−	7.75273i	0.114527	−	0.427422i
$330$		0			0
$331$	−22.0420	−	28.7257i	−1.21154	−	1.57891i	−0.684333	−	0.729170i	$-0.739906\pi$
$331$	−22.0420	−	28.7257i	−1.21154	−	1.57891i	−0.527206	−	0.849738i	$-0.676760\pi$
$332$	1.59425	+	1.74592i	0.0874960	+	0.0958197i
$333$		0			0
$334$	−2.80203	−	1.96564i	−0.153320	−	0.107555i
$335$	1.69060	+	0.976071i	0.0923676	+	0.0533285i
$336$		0			0
$337$	−0.235650	+	0.136053i	−0.0128367	+	0.00741126i	−0.506405	−	0.862296i	$-0.669026\pi$
$337$	−0.235650	+	0.136053i	−0.0128367	+	0.00741126i	0.493568	+	0.869707i	$0.335692\pi$
$338$	2.26241	+	0.199922i	0.123059	+	0.0108743i
$339$		0			0
$340$	1.89071	−	2.95644i	0.102538	−	0.160336i
$341$	1.32667	−	3.20285i	0.0718429	−	0.173444i
$342$		0			0
$343$	10.4954	+	10.4954i	0.566697	+	0.566697i
$344$	−18.6624	−	7.78742i	−1.00621	−	0.419870i
$345$		0			0
$346$	26.7787	+	13.9698i	1.43963	+	0.751019i
$347$	−20.9301	+	2.75551i	−1.12359	+	0.147923i	−0.669343	−	0.742953i	$-0.733424\pi$
$347$	−20.9301	+	2.75551i	−1.12359	+	0.147923i	−0.454246	+	0.890877i	$0.650091\pi$
$348$		0			0
$349$	3.12296	−	23.7212i	0.167168	−	1.26977i	−0.677918	−	0.735137i	$-0.737118\pi$
$349$	3.12296	−	23.7212i	0.167168	−	1.26977i	0.845086	−	0.534630i	$-0.179549\pi$
$350$	20.6830	−	3.62839i	1.10555	−	0.193946i
$351$		0			0
$352$	5.73359	−	2.95305i	0.305601	−	0.157398i
$353$	11.5807	+	6.68611i	0.616378	+	0.355866i	0.775457	−	0.631400i	$-0.217519\pi$
$353$	11.5807	+	6.68611i	0.616378	+	0.355866i	−0.159080	+	0.987266i	$0.550853\pi$
$354$		0			0
$355$	0.750007	−	0.977429i	0.0398063	−	0.0518765i
$356$	21.2421	−	1.82116i	1.12583	−	0.0965212i
$357$		0			0
$358$	−3.24529	+	0.138860i	−0.171519	+	0.00733899i
$359$	−9.45820	−	9.45820i	−0.499185	−	0.499185i	0.411999	−	0.911184i	$-0.364831\pi$
$359$	−9.45820	−	9.45820i	−0.499185	−	0.499185i	−0.911184	+	0.411999i	$0.864831\pi$
$360$		0			0
$361$	8.60742	−	8.60742i	0.453022	−	0.453022i
$362$	−10.8970	+	11.8712i	−0.572734	+	0.623937i
$363$		0			0
$364$	9.35776	+	18.0528i	0.490480	+	0.946225i
$365$	0.673040	+	0.516442i	0.0352285	+	0.0270318i
$366$		0			0
$367$	17.9630	−	31.1128i	0.937661	−	1.62408i	0.167841	−	0.985814i	$-0.446320\pi$
$367$	17.9630	−	31.1128i	0.937661	−	1.62408i	0.769819	−	0.638262i	$-0.220346\pi$
$368$	−0.514131	+	5.64973i	−0.0268009	+	0.294512i
$369$		0			0
$370$	−1.24684	+	1.77738i	−0.0648203	+	0.0924015i
$371$	35.5870	+	4.68512i	1.84759	+	0.243239i
$372$		0			0
$373$	−4.50258	−	34.2005i	−0.233135	−	1.77083i	−0.562663	−	0.826687i	$-0.690223\pi$
$373$	−4.50258	−	34.2005i	−0.233135	−	1.77083i	0.329528	−	0.944146i	$-0.393110\pi$
$374$	−3.20086	−	10.1827i	−0.165512	−	0.526537i
$375$		0			0
$376$	7.53702	+	0.0196978i	0.388692	+	0.00101584i
$377$	12.1220	−	12.1220i	0.624316	−	0.624316i
$378$		0			0
$379$	−27.9266	−	11.5676i	−1.43449	−	0.594187i	−0.476038	−	0.879425i	$-0.657927\pi$
$379$	−27.9266	−	11.5676i	−1.43449	−	0.594187i	−0.958457	+	0.285238i	$0.907927\pi$
$380$	0.519018	−	2.91380i	0.0266251	−	0.149475i
$381$		0			0
$382$	−8.71965	−	10.4101i	−0.446136	−	0.532626i
$383$	−13.9736	−	24.2030i	−0.714017	−	1.23671i	−0.963337	−	0.268293i	$-0.913541\pi$
$383$	−13.9736	−	24.2030i	−0.714017	−	1.23671i	0.249320	−	0.968421i	$-0.419793\pi$
$384$		0			0
$385$	−0.455086	+	0.788232i	−0.0231933	+	0.0401720i
$386$	−37.1488	+	6.51696i	−1.89082	+	0.331705i
$387$		0			0
$388$	0.668850	−	0.242122i	0.0339557	−	0.0122919i
$389$	18.0693	−	13.8651i	0.916151	−	0.702987i	−0.0389586	−	0.999241i	$-0.512404\pi$
$389$	18.0693	−	13.8651i	0.916151	−	0.702987i	0.955109	+	0.296254i	$0.0957374\pi$
$390$		0			0
$391$	9.06922	+	2.43009i	0.458650	+	0.122895i
$392$	2.94372	−	5.06803i	0.148680	−	0.255974i
$393$		0			0
$394$	1.43345	−	1.56160i	0.0722161	−	0.0786723i
$395$	3.75541	+	1.55554i	0.188955	+	0.0782677i
$396$		0			0
$397$	4.54017	+	10.9609i	0.227864	+	0.550113i	0.995917	−	0.0902734i	$-0.0287741\pi$
$397$	4.54017	+	10.9609i	0.227864	+	0.550113i	−0.768053	+	0.640387i	$0.778774\pi$
$398$	−5.41829	−	11.6460i	−0.271594	−	0.583763i
$399$		0			0
$400$	8.27128	+	17.9004i	0.413564	+	0.895021i
$401$	−11.6633	−	20.2014i	−0.582437	−	1.00881i	−0.995190	−	0.0979670i	$-0.968766\pi$
$401$	−11.6633	−	20.2014i	−0.582437	−	1.00881i	0.412753	−	0.910843i	$-0.364567\pi$
$402$		0			0
$403$	−1.33972	+	10.1762i	−0.0667363	+	0.506912i
$404$	16.6457	+	0.755828i	0.828156	+	0.0376039i
$405$		0			0
$406$	−21.1164	−	4.70070i	−1.04799	−	0.233292i
$407$	1.70915	+	6.37862i	0.0847193	+	0.316177i
$408$		0			0
$409$	−0.194109	+	0.724424i	−0.00959807	+	0.0358205i	−0.970559	−	0.240864i	$-0.922569\pi$
$409$	−0.194109	+	0.724424i	−0.00959807	+	0.0358205i	0.960961	+	0.276685i	$0.0892358\pi$
$410$	−1.30724	+	2.50585i	−0.0645600	+	0.123755i
$411$		0			0
$412$	0.312139	+	0.447438i	0.0153780	+	0.0220437i
$413$	−5.91000	−	14.2680i	−0.290812	−	0.702083i
$414$		0			0
$415$		−	0.313326i		−	0.0153806i
$416$	−14.1342	+	12.8388i	−0.692984	+	0.629472i
$417$		0			0
$418$	−5.78045	−	6.90107i	−0.282731	−	0.337542i
$419$	−0.850799	−	0.652841i	−0.0415642	−	0.0318934i	0.587770	−	0.809028i	$-0.300006\pi$
$419$	−0.850799	−	0.652841i	−0.0415642	−	0.0318934i	−0.629335	+	0.777134i	$0.716673\pi$
$420$		0			0
$421$	11.9771	+	15.6089i	0.583729	+	0.760731i	0.988091	−	0.153868i	$-0.0491732\pi$
$421$	11.9771	+	15.6089i	0.583729	+	0.760731i	−0.404362	+	0.914599i	$0.632507\pi$
$422$	12.3750	−	7.86858i	0.602404	−	0.383036i
$423$		0			0
$424$	4.31222	+	33.4295i	0.209420	+	1.62348i
$425$	31.5237	−	8.44674i	1.52912	−	0.409727i
$426$		0			0
$427$	−36.9398	+	4.86322i	−1.78764	+	0.235348i
$428$	6.62271	+	12.7764i	0.320121	+	0.617571i
$429$		0			0
$430$	1.13046	+	2.42980i	0.0545156	+	0.117176i
$431$			1.14937i			0.0553631i	0.999617	+	0.0276815i	$0.00881243\pi$
$431$			1.14937i			0.0553631i	−0.999617	+	0.0276815i	$0.991188\pi$
$432$		0			0
$433$		−	13.4381i		−	0.645792i	−0.946434	−	0.322896i	$-0.895344\pi$
$433$		−	13.4381i		−	0.645792i	0.946434	−	0.322896i	$-0.104656\pi$
$434$	11.7436	−	5.46367i	0.563710	−	0.262265i
$435$		0			0
$436$	2.44221	−	7.69889i	0.116960	−	0.368710i
$437$	7.85080	−	1.03358i	0.375555	−	0.0494427i
$438$		0			0
$439$	18.5478	−	4.96986i	0.885237	−	0.237199i	0.212572	−	0.977145i	$-0.431816\pi$
$439$	18.5478	−	4.96986i	0.885237	−	0.237199i	0.672665	+	0.739947i	$0.265149\pi$
$440$	−0.824995	−	0.223369i	−0.0393301	−	0.0106487i
$441$		0			0
$442$	16.9568	+	26.6680i	0.806551	+	1.26847i
$443$	−15.7477	−	20.5228i	−0.748196	−	0.975068i	−0.999973	−	0.00728264i	$-0.997682\pi$
$443$	−15.7477	−	20.5228i	−0.748196	−	0.975068i	0.251778	−	0.967785i	$-0.418985\pi$
$444$		0			0
$445$	−2.24156	−	1.72001i	−0.106260	−	0.0815363i
$446$	22.6591	−	18.9797i	1.07294	−	0.898713i
$447$		0			0
$448$	23.2420	+	6.35808i	1.09808	+	0.300391i
$449$		−	28.8086i		−	1.35956i	−0.733414	−	0.679782i	$-0.762074\pi$
$449$		−	28.8086i		−	1.35956i	0.733414	−	0.679782i	$-0.237926\pi$
$450$		0			0
$451$	3.28978	+	7.94222i	0.154909	+	0.373985i
$452$	6.06782	−	34.0652i	0.285406	−	1.60229i
$453$		0			0
$454$	−12.9874	−	6.77522i	−0.609531	−	0.317977i
$455$	0.697453	−	2.60293i	0.0326971	−	0.122027i
$456$		0			0
$457$	2.55106	+	9.52070i	0.119334	+	0.445360i	0.999575	−	0.0291677i	$-0.00928569\pi$
$457$	2.55106	+	9.52070i	0.119334	+	0.445360i	−0.880241	+	0.474527i	$0.842619\pi$
$458$	2.44761	−	10.9951i	0.114369	−	0.513767i
$459$		0			0
$460$	0.555183	−	0.506955i	0.0258856	−	0.0236369i
$461$	−2.43585	+	18.5021i	−0.113449	+	0.861730i	0.836202	+	0.548421i	$0.184771\pi$
$461$	−2.43585	+	18.5021i	−0.113449	+	0.861730i	−0.949651	+	0.313309i	$0.898562\pi$
$462$		0			0
$463$	−12.7222	−	22.0354i	−0.591249	−	1.02407i	−0.994065	−	0.108792i	$-0.965302\pi$
$463$	−12.7222	−	22.0354i	−0.591249	−	1.02407i	0.402816	−	0.915281i	$-0.368032\pi$
$464$	−0.815392	−	20.2984i	−0.0378536	−	0.942331i
$465$		0			0
$466$	−2.19429	+	1.02089i	−0.101649	+	0.0472918i
$467$	−0.653601	−	1.57793i	−0.0302451	−	0.0730181i	0.908035	−	0.418894i	$-0.137582\pi$
$467$	−0.653601	−	1.57793i	−0.0302451	−	0.0730181i	−0.938280	+	0.345875i	$0.887582\pi$
$468$		0			0
$469$	20.4954	+	8.48948i	0.946390	+	0.392008i
$470$	−0.735835	−	0.675448i	−0.0339415	−	0.0311561i
$471$		0			0
$472$	11.5285	−	8.79836i	0.530643	−	0.404977i
$473$	7.87347	+	2.10969i	0.362022	+	0.0970036i
$474$		0			0
$475$	21.8363	−	16.7556i	1.00192	−	0.768799i
$476$	16.9169	−	36.1140i	0.775384	−	1.65528i
$477$		0			0
$478$	4.41503	+	25.1671i	0.201939	+	1.15111i
$479$	−3.28151	+	5.68375i	−0.149936	+	0.259697i	−0.931204	−	0.364499i	$-0.881240\pi$
$479$	−3.28151	+	5.68375i	−0.149936	+	0.259697i	0.781267	+	0.624196i	$0.214574\pi$
$480$		0			0
$481$	−9.77571	−	16.9320i	−0.445734	−	0.772034i
$482$	−15.1982	+	12.7302i	−0.692257	+	0.579846i
$483$		0			0
$484$	15.9112	−	11.0999i	0.723236	−	0.504540i
$485$	−0.0870921	−	0.0360747i	−0.00395465	−	0.00163807i
$486$		0			0
$487$	−24.6314	+	24.6314i	−1.11616	+	1.11616i	−0.123856	+	0.992300i	$0.539526\pi$
$487$	−24.6314	+	24.6314i	−1.11616	+	1.11616i	−0.992300	+	0.123856i	$0.960474\pi$
$488$	−13.3047	−	32.3594i	−0.602276	−	1.46484i
$489$		0			0
$490$	−0.740969	+	0.232917i	−0.0334735	+	0.0105221i
$491$	3.63549	+	27.6143i	0.164067	+	1.24622i	0.853201	+	0.521582i	$0.174658\pi$
$491$	3.63549	+	27.6143i	0.164067	+	1.24622i	−0.689134	+	0.724634i	$0.742009\pi$
$492$		0			0
$493$	−33.3341	−	4.38852i	−1.50129	−	0.197649i
$494$	21.8192	+	15.3063i	0.981694	+	0.688665i
$495$		0			0
$496$	7.78567	+	9.34454i	0.349587	+	0.419582i
$497$	7.00032	−	12.1249i	0.314007	−	0.543877i
$498$		0			0
$499$	18.6348	+	14.2990i	0.834207	+	0.640110i	0.934941	−	0.354804i	$-0.115452\pi$
$499$	18.6348	+	14.2990i	0.834207	+	0.640110i	−0.100734	+	0.994913i	$0.532119\pi$
$500$	1.59158	−	5.01734i	0.0711775	−	0.224382i
$501$		0			0
$502$	−27.7163	−	25.4417i	−1.23704	−	1.13552i
$503$	−20.8337	+	20.8337i	−0.928930	+	0.928930i	−0.997637	−	0.0687068i	$-0.978113\pi$
$503$	−20.8337	+	20.8337i	−0.928930	+	0.928930i	0.0687068	+	0.997637i	$0.478113\pi$
$504$		0			0
$505$	−1.56146	−	1.56146i	−0.0694840	−	0.0694840i
$506$	−0.0977558	−	2.28465i	−0.00434578	−	0.101565i
$507$		0			0
$508$	0.604797	−	0.718224i	0.0268335	−	0.0318661i
$509$	8.00983	−	10.4386i	0.355030	−	0.462684i	−0.581360	−	0.813647i	$-0.697479\pi$
$509$	8.00983	−	10.4386i	0.355030	−	0.462684i	0.936389	+	0.350963i	$0.114146\pi$
$510$		0			0
$511$	8.34900	+	4.82030i	0.369338	+	0.213237i
$512$	−0.177406	+	22.6267i	−0.00784031	+	0.999969i
$513$		0			0
$514$	4.42520	+	25.2250i	0.195187	+	1.11263i
$515$	0.00943696	−	0.0716808i	0.000415842	−	0.00315863i
$516$		0			0
$517$	−3.01209	+	0.396549i	−0.132471	+	0.0174402i
$518$	−11.4115	+	21.8747i	−0.501392	+	0.961119i
$519$		0			0
$520$	2.53050	+	0.00661340i	0.110970	+	0.000290017i
$521$	11.1752	+	11.1752i	0.489592	+	0.489592i	0.908178	−	0.418585i	$-0.137474\pi$
$521$	11.1752	+	11.1752i	0.489592	+	0.489592i	−0.418585	+	0.908178i	$0.637474\pi$
$522$		0			0
$523$	4.41161	−	10.6506i	0.192906	−	0.465717i	−0.797600	−	0.603187i	$-0.793897\pi$
$523$	4.41161	−	10.6506i	0.192906	−	0.465717i	0.990506	+	0.137470i	$0.0438971\pi$
$524$	3.95740	+	17.9990i	0.172880	+	0.786292i
$525$		0			0
$526$	1.77181	−	20.0507i	0.0772548	−	0.874254i
$527$	17.4332	−	10.0651i	0.759403	−	0.438441i
$528$		0			0
$529$	−18.1766	−	10.4943i	−0.790286	−	0.456272i
$530$	2.56531	−	3.65685i	0.111430	−	0.158844i
$531$		0			0
$532$	1.52562	−	33.5989i	0.0661438	−	1.45670i
$533$	−15.4942	−	20.1924i	−0.671128	−	0.874631i
$534$		0			0
$535$	0.493604	−	1.84215i	0.0213404	−	0.0796433i
$536$	−2.77309	+	20.6466i	−0.119779	+	0.891798i
$537$		0			0
$538$	−0.610999	−	14.2796i	−0.0263420	−	0.615639i
$539$	−0.904073	+	2.18263i	−0.0389412	+	0.0940123i
$540$		0			0
$541$	−4.88193	+	2.02216i	−0.209891	+	0.0869396i	−0.485152	−	0.874430i	$-0.661236\pi$
$541$	−4.88193	+	2.02216i	−0.209891	+	0.0869396i	0.275261	+	0.961369i	$0.411236\pi$
$542$	−0.518275	+	1.42010i	−0.0222618	+	0.0609985i
$543$		0			0
$544$	36.8516	+	6.66357i	1.58000	+	0.285698i
$545$	−0.926988	+	0.535197i	−0.0397078	+	0.0229253i
$546$		0			0
$547$	−2.53143	−	0.333269i	−0.108236	−	0.0142495i	0.0762136	−	0.997092i	$-0.475717\pi$
$547$	−2.53143	−	0.333269i	−0.108236	−	0.0142495i	−0.184450	+	0.982842i	$0.559050\pi$
$548$	−38.3627	−	17.9702i	−1.63877	−	0.767651i
$549$		0			0
$550$	−4.26486	−	6.70738i	−0.181854	−	0.286004i
$551$	−27.3895	+	7.33899i	−1.16683	+	0.312651i
$552$		0			0
$553$	44.6185	+	11.9555i	1.89737	+	0.508399i
$554$	7.21103	+	22.9401i	0.306367	+	0.974632i
$555$		0			0
$556$	−11.2104	−	7.16929i	−0.475426	−	0.304046i
$557$	−19.4433	+	8.05366i	−0.823838	+	0.341245i	−0.754460	−	0.656346i	$-0.772101\pi$
$557$	−19.4433	+	8.05366i	−0.823838	+	0.341245i	−0.0693774	+	0.997590i	$0.522101\pi$
$558$		0			0
$559$	−24.1333			−1.02073
$560$	−1.70637	−	2.69917i	−0.0721071	−	0.114061i
$561$		0			0
$562$	24.2291	+	2.14104i	1.02204	+	0.0903144i
$563$	−11.2281	+	14.6327i	−0.473206	+	0.616694i	−0.967583	−	0.252554i	$-0.918730\pi$
$563$	−11.2281	+	14.6327i	−0.473206	+	0.616694i	0.494377	+	0.869248i	$0.335396\pi$
$564$		0			0
$565$	−3.63794	+	2.79149i	−0.153049	+	0.117439i
$566$	8.94627	+	1.99152i	0.376040	+	0.0837098i
$567$		0			0
$568$	12.6904	+	3.43596i	0.532478	+	0.144170i
$569$	−0.0592096	−	0.220973i	−0.00248220	−	0.00926368i	0.964674	−	0.263448i	$-0.0848597\pi$
$569$	−0.0592096	−	0.220973i	−0.00248220	−	0.00926368i	−0.967156	+	0.254184i	$0.918193\pi$
$570$		0			0
$571$	2.55267	+	19.3894i	0.106826	+	0.811422i	0.958046	+	0.286614i	$0.0925297\pi$
$571$	2.55267	+	19.3894i	0.106826	+	0.811422i	−0.851220	+	0.524808i	$0.824137\pi$
$572$	4.95768	−	5.88747i	0.207291	−	0.246168i
$573$		0			0
$574$	−11.0114	+	30.1718i	−0.459608	+	1.25935i
$575$	6.99170			0.291574
$576$		0			0
$577$	14.9051			0.620507			0.310254	−	0.950654i	$-0.399586\pi$
$577$	14.9051			0.620507			0.310254	+	0.950654i	$0.399586\pi$
$578$	13.0067	−	35.6390i	0.541008	−	1.48239i
$579$		0			0
$580$	−1.73410	+	2.05933i	−0.0720048	+	0.0855090i
$581$	−0.464755	−	3.53016i	−0.0192813	−	0.146456i
$582$		0			0
$583$	−3.51647	−	13.1237i	−0.145637	−	0.543526i
$584$	−2.36594	+	8.73840i	−0.0979034	+	0.361598i
$585$		0			0
$586$	−36.7407	−	8.17879i	−1.51774	−	0.337863i
$587$	−21.3266	+	16.3645i	−0.880243	+	0.675434i	−0.946617	−	0.322360i	$-0.895524\pi$
$587$	−21.3266	+	16.3645i	−0.880243	+	0.675434i	0.0663737	+	0.997795i	$0.478857\pi$
$588$		0			0
$589$	10.3351	−	13.4689i	0.425849	−	0.554977i
$590$	−1.91445	−	0.169173i	−0.0788167	−	0.00696476i
$591$		0			0
$592$	−22.6018	−	5.09340i	−0.928929	−	0.209337i
$593$	−11.8751			−0.487652			−0.243826	−	0.969819i	$-0.578403\pi$
$593$	−11.8751			−0.487652			−0.243826	+	0.969819i	$0.578403\pi$
$594$		0			0
$595$	−4.88274	+	2.02250i	−0.200173	+	0.0829143i
$596$	6.84075	+	4.37481i	0.280208	+	0.179199i
$597$		0			0
$598$	2.03026	+	6.45877i	0.0830234	+	0.264119i
$599$	40.3284	+	10.8060i	1.64777	+	0.441520i	0.958988	−	0.283445i	$-0.0914774\pi$
$599$	40.3284	+	10.8060i	1.64777	+	0.441520i	0.688786	+	0.724965i	$0.258144\pi$
$600$		0			0
$601$	−8.99022	+	2.40892i	−0.366719	+	0.0982620i	−0.437472	−	0.899232i	$-0.644126\pi$
$601$	−8.99022	+	2.40892i	−0.366719	+	0.0982620i	0.0707537	+	0.997494i	$0.477460\pi$
$602$	16.3407	+	25.6992i	0.665998	+	1.04742i
$603$		0			0
$604$	34.4641	+	16.1440i	1.40232	+	0.656891i
$605$	−2.54902	−	0.335585i	−0.103632	−	0.0136435i
$606$		0			0
$607$	35.1470	−	20.2921i	1.42657	−	0.823632i	0.429724	−	0.902960i	$-0.358611\pi$
$607$	35.1470	−	20.2921i	1.42657	−	0.823632i	0.996849	+	0.0793280i	$0.0252774\pi$
$608$	30.8645	−	6.70158i	1.25172	−	0.271785i
$609$		0			0
$610$	−1.58965	+	4.35572i	−0.0643630	+	0.176358i
$611$	8.31016	−	3.44218i	0.336193	−	0.139256i
$612$		0			0
$613$	11.7152	−	28.2829i	0.473171	−	1.14234i	−0.489583	−	0.871957i	$-0.662851\pi$
$613$	11.7152	−	28.2829i	0.473171	−	1.14234i	0.962754	−	0.270379i	$-0.0871489\pi$
$614$	0.340806	+	7.96496i	0.0137538	+	0.321440i
$615$		0			0
$616$	−9.62633	−	1.29293i	−0.387856	−	0.0520938i
$617$	5.17000	−	19.2947i	0.208136	−	0.776776i	−0.780334	−	0.625363i	$-0.784951\pi$
$617$	5.17000	−	19.2947i	0.208136	−	0.776776i	0.988471	−	0.151413i	$-0.0483823\pi$
$618$		0			0
$619$	−6.37543	−	8.30863i	−0.256250	−	0.333952i	0.647458	−	0.762101i	$-0.275832\pi$
$619$	−6.37543	−	8.30863i	−0.256250	−	0.333952i	−0.903708	+	0.428150i	$0.859166\pi$
$620$	0.0731150	−	1.61023i	0.00293637	−	0.0646682i
$621$		0			0
$622$	16.5304	−	23.5642i	0.662811	−	0.944839i
$623$	−27.8064	−	16.0540i	−1.11404	−	0.643191i
$624$		0			0
$625$	20.7423	−	11.9756i	0.829693	−	0.479023i
$626$	−0.161583	+	1.82855i	−0.00645816	+	0.0730837i
$627$		0			0
$628$	8.84732	+	40.2394i	0.353047	+	1.60572i
$629$	−14.6740	+	35.4261i	−0.585090	+	1.41253i
$630$		0			0
$631$	22.7060	+	22.7060i	0.903913	+	0.903913i	0.995772	−	0.0918593i	$-0.0292810\pi$
$631$	22.7060	+	22.7060i	0.903913	+	0.903913i	−0.0918593	+	0.995772i	$0.529281\pi$
$632$	−0.113365	+	43.3770i	−0.00450940	+	1.72545i
$633$		0			0
$634$	−15.4205	+	29.5596i	−0.612427	+	1.17396i
$635$	−0.123369	+	0.0162418i	−0.00489575	+	0.000644538i
$636$		0			0
$637$	0.912970	−	6.93470i	0.0361732	−	0.274763i
$638$	1.41491	+	8.06545i	0.0560169	+	0.319314i
$639$		0			0
$640$	2.03932	−	2.19846i	0.0806114	−	0.0869019i
$641$	−27.5561	−	15.9095i	−1.08840	−	0.628389i	−0.155251	−	0.987875i	$-0.549619\pi$
$641$	−27.5561	−	15.9095i	−1.08840	−	0.628389i	−0.933150	+	0.359486i	$0.882952\pi$
$642$		0			0
$643$	21.8644	−	28.4942i	0.862247	−	1.12370i	−0.128996	−	0.991645i	$-0.541175\pi$
$643$	21.8644	−	28.4942i	0.862247	−	1.12370i	0.991242	−	0.132056i	$-0.0421580\pi$
$644$	5.50314	−	6.53523i	0.216854	−	0.257524i
$645$		0			0
$646$	−2.23459	−	52.2244i	−0.0879186	−	2.05474i
$647$	24.1345	+	24.1345i	0.948824	+	0.948824i	0.998753	−	0.0499284i	$-0.0158993\pi$
$647$	24.1345	+	24.1345i	0.948824	+	0.948824i	−0.0499284	+	0.998753i	$0.515899\pi$
$648$		0			0
$649$	−4.13353	+	4.13353i	−0.162255	+	0.162255i
$650$	17.3365	+	15.9138i	0.679994	+	0.624190i
$651$		0			0
$652$	−11.5224	+	36.3235i	−0.451251	+	1.42254i
$653$	2.66142	+	2.04218i	0.104150	+	0.0799168i	0.659523	−	0.751684i	$-0.270758\pi$
$653$	2.66142	+	2.04218i	0.104150	+	0.0799168i	−0.555374	+	0.831601i	$0.687425\pi$
$654$		0			0
$655$	1.22114	−	2.11508i	0.0477140	−	0.0826430i
$656$	−30.0367	−	2.73337i	−1.17274	−	0.106720i
$657$		0			0
$658$	−9.29235	−	6.51864i	−0.362253	−	0.254123i
$659$	31.3084	+	4.12183i	1.21960	+	0.160564i	0.712718	−	0.701451i	$-0.247464\pi$
$659$	31.3084	+	4.12183i	1.21960	+	0.160564i	0.506884	+	0.862014i	$0.330797\pi$
$660$		0			0
$661$	0.0570210	+	0.433117i	0.00221786	+	0.0168463i	0.992518	−	0.122098i	$-0.0389623\pi$
$661$	0.0570210	+	0.433117i	0.00221786	+	0.0168463i	−0.990300	+	0.138945i	$0.955629\pi$
$662$	−48.8492	+	15.3553i	−1.89858	+	0.596802i
$663$		0			0
$664$	3.09243	−	1.27147i	0.120009	−	0.0493425i
$665$	−3.15176	+	3.15176i	−0.122220	+	0.122220i
$666$		0			0
$667$	−6.65466	−	2.75645i	−0.257670	−	0.106730i
$668$	−3.96992	+	2.76947i	−0.153601	+	0.107154i
$669$		0			0
$670$	2.11640	−	1.77273i	0.0817636	−	0.0684865i
$671$	7.05155	+	12.2136i	0.272222	+	0.471502i
$672$		0			0
$673$	−4.03557	+	6.98981i	−0.155560	+	0.269438i	−0.933263	−	0.359194i	$-0.883051\pi$
$673$	−4.03557	+	6.98981i	−0.155560	+	0.269438i	0.777703	+	0.628632i	$0.216385\pi$
$674$	0.0664923	+	0.379027i	0.00256119	+	0.0145996i
$675$		0			0
$676$	1.36252	−	2.90870i	0.0524047	−	0.111873i
$677$	−16.1027	+	12.3561i	−0.618878	+	0.474882i	−0.869985	−	0.493077i	$-0.835872\pi$
$677$	−16.1027	+	12.3561i	−0.618878	+	0.474882i	0.251107	+	0.967959i	$0.419205\pi$
$678$		0			0
$679$	−1.03475	−	0.277261i	−0.0397102	−	0.0106403i
$680$	−3.01094	−	3.94524i	−0.115464	−	0.151293i
$681$		0			0
$682$	−3.61177	−	3.31537i	−0.138302	−	0.126952i
$683$	−2.59322	−	1.07415i	−0.0992269	−	0.0411011i	0.332518	−	0.943097i	$-0.392102\pi$
$683$	−2.59322	−	1.07415i	−0.0992269	−	0.0411011i	−0.431745	+	0.901996i	$0.642102\pi$
$684$		0			0
$685$	2.14843	+	5.18677i	0.0820874	+	0.198176i
$686$	19.0318	−	8.85449i	0.726637	−	0.338066i
$687$		0			0
$688$	−19.3940	+	21.0174i	−0.739391	+	0.801280i
$689$	20.1130	+	34.8367i	0.766243	+	1.32717i
$690$		0			0
$691$	−2.01546	+	15.3089i	−0.0766717	+	0.582380i	0.909383	+	0.415959i	$0.136554\pi$
$691$	−2.01546	+	15.3089i	−0.0766717	+	0.582380i	−0.986055	+	0.166420i	$0.946779\pi$
$692$	31.5425	−	28.8024i	1.19906	−	1.09490i
$693$		0			0
$694$	−6.48722	+	29.1418i	−0.246251	+	1.10621i
$695$	0.456421	+	1.70339i	0.0173130	+	0.0646132i
$696$		0			0
$697$	−12.9196	+	48.2165i	−0.489363	+	1.82633i
$698$	−29.9996	−	15.6500i	−1.13550	−	0.592362i
$699$		0			0
$700$	5.20775	−	29.2366i	0.196834	−	1.10504i
$701$	3.78858	+	9.14644i	0.143093	+	0.345456i	0.979136	−	0.203208i	$-0.0651366\pi$
$701$	3.78858	+	9.14644i	0.143093	+	0.345456i	−0.836043	+	0.548664i	$0.815137\pi$
$702$		0			0
$703$			32.3391i			1.21969i
$704$	−1.14322	−	9.04887i	−0.0430868	−	0.341042i
$705$		0			0
$706$	14.4974	−	12.1432i	0.545616	−	0.457017i
$707$	−19.9087	−	15.2764i	−0.748742	−	0.574530i
$708$		0			0
$709$	2.79341	+	3.64044i	0.104909	+	0.136720i	0.842857	−	0.538138i	$-0.180872\pi$
$709$	2.79341	+	3.64044i	0.104909	+	0.136720i	−0.737948	+	0.674857i	$0.764205\pi$
$710$	−0.934879	−	1.47029i	−0.0350854	−	0.0551790i
$711$		0			0
$712$	7.87977	−	29.1033i	0.295307	−	1.09069i
$713$	4.16563	−	1.11618i	0.156004	−	0.0418012i
$714$		0			0
$715$	−1.01129	+	0.133139i	−0.0378200	+	0.00497910i
$716$	−1.38899	+	4.37871i	−0.0519092	+	0.163640i
$717$		0			0
$718$	−17.1510	+	7.97948i	−0.640071	+	0.297792i
$719$			51.3863i			1.91639i	0.286124	+	0.958193i	$0.407633\pi$
$719$			51.3863i			1.91639i	−0.286124	+	0.958193i	$0.592367\pi$
$720$		0			0
$721$		−	0.821607i		−	0.0305983i
$722$	−7.26171	−	15.6083i	−0.270253	−	0.580880i
$723$		0			0
$724$	10.4876	+	20.2324i	0.389768	+	0.751933i
$725$	−24.8225	+	3.26795i	−0.921885	+	0.121368i
$726$		0			0
$727$	−20.4427	+	5.47760i	−0.758177	+	0.203153i	−0.617142	−	0.786852i	$-0.711710\pi$
$727$	−20.4427	+	5.47760i	−0.758177	+	0.203153i	−0.141035	+	0.990005i	$0.545043\pi$
$728$	28.5203	−	3.67897i	1.05703	−	0.136352i
$729$		0			0
$730$	1.01242	−	0.643741i	0.0374712	−	0.0238259i
$731$	28.8134	+	37.5503i	1.06570	+	1.38885i
$732$		0			0
$733$	7.07162	+	5.42625i	0.261196	+	0.200423i	0.731055	−	0.682319i	$-0.239028\pi$
$733$	7.07162	+	5.42625i	0.261196	+	0.200423i	−0.469858	+	0.882742i	$0.655695\pi$
$734$	−32.6242	−	38.9489i	−1.20418	−	1.43763i
$735$		0			0
$736$	7.25641	+	3.42228i	0.267475	+	0.126147i
$737$		−	8.39710i		−	0.309311i
$738$		0			0
$739$	6.91091	+	16.6844i	0.254222	+	0.613746i	0.998536	−	0.0540833i	$-0.0172236\pi$
$739$	6.91091	+	16.6844i	0.254222	+	0.613746i	−0.744315	+	0.667829i	$0.767224\pi$
$740$	1.75673	+	2.51819i	0.0645786	+	0.0925706i
$741$		0			0
$742$	23.4785	−	45.0059i	0.861921	−	1.65222i
$743$	−1.20425	+	4.49432i	−0.0441796	+	0.164880i	−0.984491	−	0.175434i	$-0.943867\pi$
$743$	−1.20425	+	4.49432i	−0.0441796	+	0.164880i	0.940312	+	0.340315i	$0.110534\pi$
$744$		0			0
$745$	−0.278515	−	1.03943i	−0.0102040	−	0.0380819i
$746$	−47.6185	−	10.6003i	−1.74344	−	0.388105i
$747$		0			0
$748$	−15.0797	−	0.684721i	−0.551370	−	0.0250359i
$749$	2.82885	−	21.4872i	0.103364	−	0.785127i
$750$		0			0
$751$	12.6948	+	21.9881i	0.463241	+	0.802357i	0.999120	−	0.0419377i	$-0.0133531\pi$
$751$	12.6948	+	21.9881i	0.463241	+	0.802357i	−0.535879	+	0.844295i	$0.680020\pi$
$752$	3.68047	−	10.0034i	0.134213	−	0.364787i
$753$		0			0
$754$	−10.2268	−	21.9815i	−0.372440	−	0.800519i
$755$	−1.93010	−	4.65967i	−0.0702435	−	0.169583i
$756$		0			0
$757$	−5.75348	−	2.38317i	−0.209114	−	0.0866178i	0.275668	−	0.961253i	$-0.411101\pi$
$757$	−5.75348	−	2.38317i	−0.209114	−	0.0866178i	−0.484782	+	0.874635i	$0.661101\pi$
$758$	−28.9077	+	31.4921i	−1.04998	+	1.14385i
$759$		0			0
$760$	−3.61935	−	2.10227i	−0.131288	−	0.0762572i
$761$	8.21213	+	2.20043i	0.297689	+	0.0797657i	0.404572	−	0.914506i	$-0.367420\pi$
$761$	8.21213	+	2.20043i	0.297689	+	0.0797657i	−0.106883	+	0.994272i	$0.534087\pi$
$762$		0			0
$763$	−9.65028	+	7.40492i	−0.349363	+	0.268076i
$764$	−18.0575	+	6.53680i	−0.653299	+	0.236493i
$765$		0			0
$766$	−38.9288	+	6.82924i	−1.40655	+	0.246750i
$767$	8.65368	−	14.9886i	0.312466	−	0.541208i
$768$		0			0
$769$	−6.57551	−	11.3891i	−0.237119	−	0.410702i	0.722767	−	0.691091i	$-0.242870\pi$
$769$	−6.57551	−	11.3891i	−0.237119	−	0.410702i	−0.959886	+	0.280389i	$0.909537\pi$
$770$	0.826522	+	0.986756i	0.0297858	+	0.0355602i
$771$		0			0
$772$	−9.35365	+	52.5120i	−0.336645	+	1.88995i
$773$	29.2765	+	12.1267i	1.05300	+	0.436168i	0.840963	−	0.541093i	$-0.181989\pi$
$773$	29.2765	+	12.1267i	1.05300	+	0.436168i	0.212040	+	0.977261i	$0.431989\pi$
$774$		0			0
$775$	10.5996	−	10.5996i	0.380748	−	0.380748i
$776$	0.00262905	−	1.00596i	9.43775e−5	−	0.0361119i
$777$		0			0
$778$	−9.65895	−	30.7276i	−0.346290	−	1.10164i
$779$	5.49501	+	41.7388i	0.196879	+	1.49545i
$780$		0			0
$781$	−5.25418	−	0.691726i	−0.188009	−	0.0247519i
$782$	7.62557	−	10.8703i	0.272690	−	0.388720i
$783$		0			0
$784$	−5.30565	−	6.36796i	−0.189487	−	0.227427i
$785$	2.73003	−	4.72855i	0.0974390	−	0.168769i
$786$		0			0
$787$	−4.75669	−	3.64994i	−0.169558	−	0.130106i	0.520497	−	0.853864i	$-0.325747\pi$
$787$	−4.75669	−	3.64994i	−0.169558	−	0.130106i	−0.690054	+	0.723757i	$0.742413\pi$
$788$	−1.37959	−	2.66148i	−0.0491459	−	0.0948113i
$789$		0			0
$790$	3.88734	−	4.23487i	0.138305	−	0.150670i
$791$	−36.8471	+	36.8471i	−1.31013	+	1.31013i
$792$		0			0
$793$	−29.5253	−	29.5253i	−1.04847	−	1.04847i
$794$	16.7629	−	0.717255i	0.594894	−	0.0254544i
$795$		0			0
$796$	−18.0988	+	1.55167i	−0.641497	+	0.0549976i
$797$	25.3211	−	32.9991i	0.896919	−	1.16889i	−0.0880434	−	0.996117i	$-0.528061\pi$
$797$	25.3211	−	32.9991i	0.896919	−	1.16889i	0.984962	−	0.172771i	$-0.0552719\pi$
$798$		0			0
$799$	−15.2776	−	8.82052i	−0.540482	−	0.312048i
$800$	27.7911	−	2.30947i	0.982563	−	0.0816522i
$801$		0			0
$802$	−32.4926	+	5.70013i	−1.14735	+	0.201279i
$803$	0.476310	−	3.61793i	0.0168086	−	0.127674i
$804$		0			0
$805$	−1.12255	+	0.147787i	−0.0395648	+	0.00520881i
$806$	12.8696	+	6.71372i	0.453311	+	0.236481i
$807$		0			0
$808$	9.07476	−	21.7475i	0.319249	−	0.765073i
$809$	−27.0808	−	27.0808i	−0.952111	−	0.952111i	0.0467934	−	0.998905i	$-0.485100\pi$
$809$	−27.0808	−	27.0808i	−0.952111	−	0.952111i	−0.998905	+	0.0467934i	$0.985100\pi$
$810$		0			0
$811$	−20.6708	+	49.9036i	−0.725848	+	1.75235i	−0.0698911	+	0.997555i	$0.522265\pi$
$811$	−20.6708	+	49.9036i	−0.725848	+	1.75235i	−0.655957	+	0.754798i	$0.727735\pi$
$812$	−16.4831	+	25.7741i	−0.578444	+	0.904494i
$813$		0			0
$814$	9.30270	+	0.822048i	0.326060	+	0.0288128i
$815$	4.37355	−	2.52507i	0.153199	−	0.0884493i
$816$		0			0
$817$	34.5698	+	19.9589i	1.20944	+	0.698273i
$818$	0.868288	+	0.609109i	0.0303590	+	0.0212970i
$819$		0			0
$820$	2.69522	+	2.95163i	0.0941213	+	0.103075i
$821$	−10.6012	−	13.8157i	−0.369984	−	0.482172i	0.570843	−	0.821059i	$-0.306616\pi$
$821$	−10.6012	−	13.8157i	−0.369984	−	0.482172i	−0.940827	+	0.338887i	$0.889950\pi$
$822$		0			0
$823$	−9.82579	+	36.6703i	−0.342505	+	1.27825i	0.552994	+	0.833185i	$0.313485\pi$
$823$	−9.82579	+	36.6703i	−0.342505	+	1.27825i	−0.895499	+	0.445063i	$0.853181\pi$
$824$	0.745762	−	0.197739i	0.0259799	−	0.00688856i
$825$		0			0
$826$	−21.8206	+	0.933661i	−0.759234	+	0.0324862i
$827$	8.01205	−	19.3428i	0.278606	−	0.672615i	−0.721191	−	0.692736i	$-0.756405\pi$
$827$	8.01205	−	19.3428i	0.278606	−	0.672615i	0.999798	+	0.0201210i	$0.00640515\pi$
$828$		0			0
$829$	−19.1561	+	7.93471i	−0.665318	+	0.275584i	−0.689675	−	0.724119i	$-0.742246\pi$
$829$	−19.1561	+	7.93471i	−0.665318	+	0.275584i	0.0243563	+	0.999703i	$0.492246\pi$
$830$	−0.416255	−	0.151915i	−0.0144484	−	0.00527305i
$831$		0			0
$832$	10.2034	+	25.0021i	0.353741	+	0.866792i
$833$	−11.8801	+	6.85897i	−0.411621	+	0.237649i
$834$		0			0
$835$	0.635993	+	0.0837301i	0.0220094	+	0.00289760i
$836$	−11.9707	+	4.33339i	−0.414017	+	0.149873i
$837$		0			0
$838$	−1.27981	+	0.813762i	−0.0442103	+	0.0281109i
$839$	−4.59959	+	1.23246i	−0.158795	+	0.0425491i	−0.337341	−	0.941383i	$-0.609527\pi$
$839$	−4.59959	+	1.23246i	−0.158795	+	0.0425491i	0.178546	+	0.983932i	$0.442861\pi$
$840$		0			0
$841$	−3.09755	−	0.829987i	−0.106812	−	0.0286202i
$842$	26.5435	−	8.34373i	0.914751	−	0.287544i
$843$		0			0
$844$	−4.45347	−	20.2553i	−0.153295	−	0.697214i
$845$	−0.393266	+	0.162896i	−0.0135288	+	0.00560380i
$846$		0			0
$847$	−29.2169			−1.00391
$848$	46.5019	+	10.4794i	1.59688	+	0.359863i
$849$		0			0
$850$	4.06263	−	45.9747i	0.139347	−	1.57692i
$851$	−5.00087	+	6.51726i	−0.171428	+	0.223409i
$852$		0			0
$853$	21.4402	−	16.4516i	0.734098	−	0.563293i	−0.172642	−	0.984985i	$-0.555230\pi$
$853$	21.4402	−	16.4516i	0.734098	−	0.563293i	0.906739	+	0.421692i	$0.138564\pi$
$854$	−11.4494	+	51.4326i	−0.391789	+	1.75999i
$855$		0			0
$856$	20.1845	−	2.60369i	0.689893	−	0.0889925i
$857$	4.43416	+	16.5485i	0.151468	+	0.565286i	0.999382	+	0.0351522i	$0.0111916\pi$
$857$	4.43416	+	16.5485i	0.151468	+	0.565286i	−0.847914	+	0.530134i	$0.822142\pi$
$858$		0			0
$859$	−2.95798	−	22.4681i	−0.100925	−	0.766600i	−0.964817	−	0.262923i	$-0.915313\pi$
$859$	−2.95798	−	22.4681i	−0.100925	−	0.766600i	0.863892	−	0.503677i	$-0.168020\pi$
$860$	3.77611	−	0.323738i	0.128764	−	0.0110394i
$861$		0			0
$862$	1.52694	+	0.557267i	0.0520078	+	0.0189806i
$863$	37.9392			1.29147			0.645733	−	0.763564i	$-0.276552\pi$
$863$	37.9392			1.29147			0.645733	+	0.763564i	$0.276552\pi$
$864$		0			0
$865$	−5.66067			−0.192469
$866$	−17.8525	−	6.51541i	−0.606653	−	0.221402i
$867$		0			0
$868$	−1.56467	−	18.2504i	−0.0531084	−	0.619460i
$869$	−2.28222	−	17.3352i	−0.0774189	−	0.588055i
$870$		0			0
$871$	6.43458	+	24.0142i	0.218028	+	0.813690i
$872$	−9.04391	−	6.97727i	−0.306266	−	0.236280i
$873$		0			0
$874$	2.43333	−	10.9310i	0.0823085	−	0.369745i
$875$	−6.28905	+	4.82576i	−0.212609	+	0.163140i
$876$		0			0
$877$	8.94330	−	11.6551i	0.301994	−	0.393566i	−0.617564	−	0.786521i	$-0.711880\pi$
$877$	8.94330	−	11.6551i	0.301994	−	0.393566i	0.919558	+	0.392955i	$0.128547\pi$
$878$	2.39035	−	27.0504i	0.0806705	−	0.912907i
$879$		0			0
$880$	−0.696744	+	0.987710i	−0.0234872	+	0.0332957i
$881$	−39.5715			−1.33320			−0.666598	−	0.745417i	$-0.732250\pi$
$881$	−39.5715			−1.33320			−0.666598	+	0.745417i	$0.732250\pi$
$882$		0			0
$883$	−7.71952	+	3.19753i	−0.259782	+	0.107605i	−0.508774	−	0.860900i	$-0.669901\pi$
$883$	−7.71952	+	3.19753i	−0.259782	+	0.107605i	0.248991	+	0.968506i	$0.419901\pi$
$884$	43.6500	−	9.59722i	1.46811	−	0.322790i
$885$		0			0
$886$	−34.8999	+	10.9705i	−1.17248	+	0.368560i
$887$	−6.06787	−	1.62588i	−0.203739	−	0.0545918i	0.155506	−	0.987835i	$-0.450299\pi$
$887$	−6.06787	−	1.62588i	−0.203739	−	0.0545918i	−0.359245	+	0.933243i	$0.616966\pi$
$888$		0			0
$889$	−1.36588	+	0.365985i	−0.0458100	+	0.0122748i
$890$	−3.37186	+	2.14398i	−0.113025	+	0.0718664i
$891$		0			0
$892$	−14.2283	−	39.3050i	−0.476400	−	1.31603i
$893$	−14.7507	−	1.94196i	−0.493613	−	0.0649853i
$894$		0			0
$895$	0.527220	−	0.304391i	0.0176230	−	0.0101747i
$896$	19.7156	−	27.7945i	0.658651	−	0.928547i
$897$		0			0
$898$	−38.2724	−	13.9678i	−1.27717	−	0.466111i
$899$	−14.2675	+	5.90977i	−0.475846	+	0.197102i
$900$		0			0
$901$	30.1909	−	72.8872i	1.00580	−	2.42823i
$902$	12.1463	−	0.519718i	0.404428	−	0.0173047i
$903$		0			0
$904$	−42.3138	−	24.5775i	−1.40733	−	0.817436i
$905$	0.781660	−	2.91719i	0.0259832	−	0.0969708i
$906$		0			0
$907$	13.0875	+	17.0560i	0.434565	+	0.566336i	0.958380	−	0.285496i	$-0.0921584\pi$
$907$	13.0875	+	17.0560i	0.434565	+	0.566336i	−0.523815	+	0.851832i	$0.675492\pi$
$908$	−15.2978	+	13.9689i	−0.507676	+	0.463575i
$909$		0			0
$910$	−3.11984	−	2.18859i	−0.103422	−	0.0725511i
$911$	−41.5522	−	23.9902i	−1.37668	−	0.794829i	−0.384926	−	0.922948i	$-0.625773\pi$
$911$	−41.5522	−	23.9902i	−1.37668	−	0.794829i	−0.991759	+	0.128118i	$0.959106\pi$
$912$		0			0
$913$	−1.16720	+	0.673882i	−0.0386286	+	0.0223022i
$914$	13.8852	+	1.22698i	0.459280	+	0.0405850i
$915$		0			0
$916$	−13.4203	−	8.58260i	−0.443420	−	0.283577i
$917$	10.6210	−	25.6414i	0.350736	−	0.846753i
$918$		0			0
$919$	−19.6503	−	19.6503i	−0.648203	−	0.648203i	0.304356	−	0.952558i	$-0.401559\pi$
$919$	−19.6503	−	19.6503i	−0.648203	−	0.648203i	−0.952558	+	0.304356i	$0.901559\pi$
$920$	−0.404313	−	0.983359i	−0.0133298	−	0.0324204i
$921$		0			0
$922$	23.3991	+	12.2067i	0.770609	+	0.402008i
$923$	15.5561	−	2.04799i	0.512034	−	0.0674106i
$924$		0			0
$925$	−3.72703	+	28.3096i	−0.122544	+	0.930814i
$926$	−35.4425	+	6.21763i	−1.16471	+	0.204324i
$927$		0			0
$928$	−27.3619	−	8.75838i	−0.898198	−	0.287508i
$929$	−12.4296	−	7.17623i	−0.407802	−	0.235445i	0.282043	−	0.959402i	$-0.408988\pi$
$929$	−12.4296	−	7.17623i	−0.407802	−	0.235445i	−0.689845	+	0.723957i	$0.742321\pi$
$930$		0			0
$931$	−7.04296	+	9.17857i	−0.230824	+	0.300815i
$932$	0.292360	+	3.41011i	0.00957655	+	0.111702i
$933$		0			0
$934$	−2.41319	+	0.103256i	−0.0789619	+	0.00337864i
$935$	1.41456	+	1.41456i	0.0462611	+	0.0462611i
$936$		0			0
$937$	18.7763	−	18.7763i	0.613394	−	0.613394i	−0.330435	−	0.943829i	$-0.607195\pi$
$937$	18.7763	−	18.7763i	0.613394	−	0.613394i	0.943829	+	0.330435i	$0.107195\pi$
$938$	21.2154	−	23.1121i	0.692709	−	0.754638i
$939$		0			0
$940$	−1.25410	+	0.650070i	−0.0409043	+	0.0212030i
$941$	3.06173	+	2.34935i	0.0998096	+	0.0765866i	0.657461	−	0.753489i	$-0.271631\pi$
$941$	3.06173	+	2.34935i	0.0998096	+	0.0765866i	−0.557651	+	0.830075i	$0.688297\pi$
$942$		0			0
$943$	−5.34702	+	9.26131i	−0.174123	+	0.301590i
$944$	−6.09910	−	19.5815i	−0.198509	−	0.637325i
$945$		0			0
$946$	6.62016	−	9.43706i	0.215240	−	0.306825i
$947$	−21.4607	−	2.82535i	−0.697378	−	0.0918116i	−0.226502	−	0.974011i	$-0.572729\pi$
$947$	−21.4607	−	2.82535i	−0.697378	−	0.0918116i	−0.470876	+	0.882199i	$0.656062\pi$
$948$		0			0
$949$	1.41021	+	10.7116i	0.0457774	+	0.347714i
$950$	−11.6726	−	37.1335i	−0.378709	−	1.20477i
$951$		0			0
$952$	−39.7755	−	39.9839i	−1.28913	−	1.29589i
$953$	−33.7540	+	33.7540i	−1.09340	+	1.09340i	−0.0982373	+	0.995163i	$0.531320\pi$
$953$	−33.7540	+	33.7540i	−1.09340	+	1.09340i	−0.995163	+	0.0982373i	$0.968680\pi$
$954$		0			0
$955$	2.35130	+	0.973941i	0.0760864	+	0.0315160i
$956$	35.5752	+	6.33679i	1.15058	+	0.204946i
$957$		0			0
$958$	5.95985	+	7.11526i	0.192554	+	0.229883i
$959$	31.8993	+	55.2513i	1.03008	+	1.78416i
$960$		0			0
$961$	−10.8770	+	18.8395i	−0.350870	+	0.607724i
$962$	−27.2340	+	4.77763i	−0.878059	+	0.154037i
$963$		0			0
$964$	9.54337	+	26.3630i	0.307371	+	0.849096i
$965$	5.60794	−	4.30312i	0.180526	−	0.138522i
$966$		0			0
$967$	−50.2128	−	13.4545i	−1.61474	−	0.432667i	−0.665286	−	0.746588i	$-0.731691\pi$
$967$	−50.2128	−	13.4545i	−1.61474	−	0.432667i	−0.949449	+	0.313921i	$0.898357\pi$
$968$	−7.03173	−	26.5198i	−0.226008	−	0.852380i
$969$		0			0
$970$	−0.0901518	+	0.0982115i	−0.00289460	+	0.00315338i
$971$	22.5790	+	9.35251i	0.724593	+	0.300136i	0.714328	−	0.699811i	$-0.246732\pi$
$971$	22.5790	+	9.35251i	0.724593	+	0.300136i	0.0102652	+	0.999947i	$0.496732\pi$
$972$		0			0
$973$	7.66900	+	18.5146i	0.245857	+	0.593551i
$974$	20.7805	+	44.6654i	0.665849	+	1.43117i
$975$		0			0
$976$	−49.4403	+	1.98603i	−1.58255	+	0.0635712i
$977$	−18.3789	−	31.8332i	−0.587994	−	1.01844i	−0.994495	−	0.104785i	$-0.966584\pi$
$977$	−18.3789	−	31.8332i	−0.587994	−	1.01844i	0.406501	−	0.913650i	$-0.366749\pi$
$978$		0			0
$979$	−1.58635	+	12.0495i	−0.0507000	+	0.385105i
$980$	−0.0498252	+	1.09731i	−0.00159161	+	0.0350522i
$981$		0			0
$982$	38.4484	+	8.55895i	1.22694	+	0.273127i
$983$	−9.93099	−	37.0629i	−0.316749	−	1.18212i	−0.922350	−	0.386356i	$-0.873734\pi$
$983$	−9.93099	−	37.0629i	−0.316749	−	1.18212i	0.605601	−	0.795769i	$-0.292933\pi$
$984$		0			0
$985$	−0.102824	+	0.383743i	−0.00327623	+	0.0122271i
$986$	−21.9921	+	42.1568i	−0.700372	+	1.34254i
$987$		0			0
$988$	30.9135	−	21.5657i	0.983491	−	0.686097i
$989$	3.88040	+	9.36813i	0.123390	+	0.297889i
$990$		0			0
$991$		−	7.63952i		−	0.242677i	−0.992611	−	0.121339i	$-0.961281\pi$
$991$		−	7.63952i		−	0.242677i	0.992611	−	0.121339i	$-0.0387187\pi$
$992$	16.1891	−	5.81263i	0.514005	−	0.184551i
$993$		0			0
$994$	−12.7139	−	15.1787i	−0.403261	−	0.481439i
$995$	1.90987	+	1.46549i	0.0605468	+	0.0464592i
$996$		0			0
$997$	32.1606	+	41.9125i	1.01854	+	1.32738i	0.943922	+	0.330169i	$0.107106\pi$
$997$	32.1606	+	41.9125i	1.01854	+	1.32738i	0.0746143	+	0.997212i	$0.476227\pi$
$998$	28.0312	−	17.8236i	0.887314	−	0.564195i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.683.28		368
3.2	odd	2		288.2.bf.a.11.19	✓	368
9.4	even	3		288.2.bf.a.203.35	yes	368
9.5	odd	6	inner	864.2.bn.a.395.12		368
32.3	odd	8	inner	864.2.bn.a.35.12		368
96.35	even	8		288.2.bf.a.227.35	yes	368
288.67	odd	24		288.2.bf.a.131.19	yes	368
288.131	even	24	inner	864.2.bn.a.611.28		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.19	✓	368	3.2	odd	2
288.2.bf.a.131.19	yes	368	288.67	odd	24
288.2.bf.a.203.35	yes	368	9.4	even	3
288.2.bf.a.227.35	yes	368	96.35	even	8
864.2.bn.a.35.12		368	32.3	odd	8	inner
864.2.bn.a.395.12		368	9.5	odd	6	inner
864.2.bn.a.611.28		368	288.131	even	24	inner
864.2.bn.a.683.28		368	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.484847 - 1.32850i) q^{2} +(-1.52985 - 1.28824i) q^{4} +(0.0345958 + 0.262781i) q^{5} +(0.779563 + 2.90937i) q^{7} +(-2.45318 + 1.40781i) q^{8} +(0.365879 + 0.0814479i) q^{10} +(0.904502 - 0.694049i) q^{11} +(-2.05487 + 2.67796i) q^{13} +(4.24308 + 0.374946i) q^{14} +(0.680862 + 3.94163i) q^{16} +6.62015 q^{17} +(5.15825 - 2.13662i) q^{19} +(0.285599 - 0.446582i) q^{20} +(-0.483502 - 1.53814i) q^{22} +(1.36994 + 0.367075i) q^{23} +(4.76177 - 1.27591i) q^{25} +(2.56139 + 4.02831i) q^{26} +(2.55536 - 5.45516i) q^{28} +(-5.03525 - 0.662903i) q^{29} +(2.63335 - 1.52037i) q^{31} +(5.56658 + 1.00656i) q^{32} +(3.20976 - 8.79490i) q^{34} +(-0.737557 + 0.305506i) q^{35} +(-2.21656 + 5.35125i) q^{37} +(-0.337543 - 7.88870i) q^{38} +(-0.454814 - 0.595944i) q^{40} +(-1.95155 + 7.28329i) q^{41} +(4.35237 + 5.67212i) q^{43} +(-2.27785 - 0.103430i) q^{44} +(1.15187 - 1.64200i) q^{46} +(-2.30774 - 1.33237i) q^{47} +(-1.79453 + 1.03607i) q^{49} +(0.613675 - 6.94466i) q^{50} +(6.59351 - 1.44970i) q^{52} +(4.56045 - 11.0099i) q^{53} +(0.213675 + 0.213675i) q^{55} +(-6.00824 - 6.03972i) q^{56} +(-3.32200 + 6.36794i) q^{58} +(-5.08348 + 0.669253i) q^{59} +(-1.61461 + 12.2642i) q^{61} +(-0.743041 - 4.23557i) q^{62} +(4.03616 - 6.90720i) q^{64} +(-0.774808 - 0.447335i) q^{65} +(4.48367 - 5.84323i) q^{67} +(-10.1278 - 8.52836i) q^{68} +(0.0482638 + 1.12797i) q^{70} +(-3.28684 - 3.28684i) q^{71} +(2.26326 - 2.26326i) q^{73} +(6.03447 + 5.53925i) q^{74} +(-10.6438 - 3.37638i) q^{76} +(2.72436 + 2.09048i) q^{77} +(7.66807 - 13.2815i) q^{79} +(-1.01223 + 0.315281i) q^{80} +(8.72967 + 6.12392i) q^{82} +(-1.17203 - 0.154301i) q^{83} +(0.229029 + 1.73965i) q^{85} +(9.64568 - 3.03203i) q^{86} +(-1.24182 + 2.97599i) q^{88} +(-7.53778 + 7.53778i) q^{89} +(-9.39309 - 3.89075i) q^{91} +(-1.62292 - 2.32638i) q^{92} +(-2.88896 + 2.41984i) q^{94} +(0.739916 + 1.28157i) q^{95} +(-0.177831 + 0.308013i) q^{97} +(0.506355 + 2.88638i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

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