LMFDB - Embedded newform 864.2.bn.a.35.13

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)

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")

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);

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			35.13
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.886889 - 1.10156i) q^{2} +(-0.426855 + 1.95392i) q^{4} +(1.69953 + 1.30410i) q^{5} +(-0.980387 + 0.262694i) q^{7} +(2.53092 - 1.26270i) q^{8} +(-0.0707598 - 3.02872i) q^{10} +(0.561489 - 4.26493i) q^{11} +(1.48535 - 0.195551i) q^{13} +(1.15887 + 0.846971i) q^{14} +(-3.63559 - 1.66808i) q^{16} -5.39882 q^{17} +(6.75131 + 2.79649i) q^{19} +(-3.27355 + 2.76408i) q^{20} +(-5.19604 + 3.16401i) q^{22} +(0.606428 - 2.26322i) q^{23} +(-0.106358 - 0.396933i) q^{25} +(-1.53275 - 1.46277i) q^{26} +(-0.0947992 - 2.02773i) q^{28} +(2.70258 + 3.52207i) q^{29} +(8.30037 - 4.79222i) q^{31} +(1.38688 + 5.48421i) q^{32} +(4.78816 + 5.94711i) q^{34} +(-2.00877 - 0.832061i) q^{35} +(2.47820 + 5.98289i) q^{37} +(-2.90718 - 9.91713i) q^{38} +(5.94807 + 1.15456i) q^{40} +(3.87025 + 1.03703i) q^{41} +(8.39033 + 1.10461i) q^{43} +(8.09365 + 2.91761i) q^{44} +(-3.03090 + 1.33921i) q^{46} +(7.46917 + 4.31233i) q^{47} +(-5.17003 + 2.98492i) q^{49} +(-0.342916 + 0.469195i) q^{50} +(-0.251941 + 2.98573i) q^{52} +(-1.62188 - 3.91557i) q^{53} +(6.51614 - 6.51614i) q^{55} +(-2.14958 + 1.90280i) q^{56} +(1.48287 - 6.10073i) q^{58} +(1.79040 - 2.33330i) q^{59} +(0.267258 - 0.205074i) q^{61} +(-12.6404 - 4.89316i) q^{62} +(4.81116 - 6.39162i) q^{64} +(2.77942 + 1.60470i) q^{65} +(-5.23988 + 0.689843i) q^{67} +(2.30451 - 10.5489i) q^{68} +(0.864997 + 2.95072i) q^{70} +(-2.98357 + 2.98357i) q^{71} +(-1.45130 - 1.45130i) q^{73} +(4.39261 - 8.03604i) q^{74} +(-8.34593 + 11.9978i) q^{76} +(0.569895 + 4.32878i) q^{77} +(4.91023 - 8.50477i) q^{79} +(-4.00346 - 7.57610i) q^{80} +(-2.29014 - 5.18303i) q^{82} +(-1.33347 - 1.73781i) q^{83} +(-9.17546 - 7.04058i) q^{85} +(-6.22451 - 10.2221i) q^{86} +(-3.96426 - 11.5032i) q^{88} +(2.17841 + 2.17841i) q^{89} +(-1.40485 + 0.581909i) q^{91} +(4.16329 + 2.15098i) q^{92} +(-1.87405 - 12.0523i) q^{94} +(7.82717 + 13.5571i) q^{95} +(4.24778 - 7.35737i) q^{97} +(7.87330 + 3.04779i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.886889	−	1.10156i	−0.627125	−	0.778918i
$2$	−0.886889	−	1.10156i	−0.627125	−	0.778918i
$3$		0			0
$3$		0			0
$4$	−0.426855	+	1.95392i	−0.213427	+	0.976959i
$5$	1.69953	+	1.30410i	0.760053	+	0.583209i	0.914402	−	0.404807i	$-0.132661\pi$
$5$	1.69953	+	1.30410i	0.760053	+	0.583209i	−0.154349	+	0.988016i	$0.549328\pi$
$6$		0			0
$7$	−0.980387	+	0.262694i	−0.370551	+	0.0992889i	−0.439289	−	0.898346i	$-0.644770\pi$
$7$	−0.980387	+	0.262694i	−0.370551	+	0.0992889i	0.0687376	+	0.997635i	$0.478103\pi$
$8$	2.53092	−	1.26270i	0.894817	−	0.446433i
$9$		0			0
$10$	−0.0707598	−	3.02872i	−0.0223762	−	0.957764i
$11$	0.561489	−	4.26493i	0.169295	−	1.28592i	−0.670046	−	0.742320i	$-0.733726\pi$
$11$	0.561489	−	4.26493i	0.169295	−	1.28592i	0.839341	−	0.543605i	$-0.182941\pi$
$12$		0			0
$13$	1.48535	−	0.195551i	0.411963	−	0.0542360i	0.0783034	−	0.996930i	$-0.475050\pi$
$13$	1.48535	−	0.195551i	0.411963	−	0.0542360i	0.333660	+	0.942694i	$0.391716\pi$
$14$	1.15887	+	0.846971i	0.309720	+	0.226363i
$15$		0			0
$16$	−3.63559	−	1.66808i	−0.908897	−	0.417020i
$17$	−5.39882			−1.30941			−0.654703	−	0.755886i	$-0.727206\pi$
$17$	−5.39882			−1.30941			−0.654703	+	0.755886i	$0.727206\pi$
$18$		0			0
$19$	6.75131	+	2.79649i	1.54886	+	0.641558i	0.983109	−	0.183020i	$-0.0585874\pi$
$19$	6.75131	+	2.79649i	1.54886	+	0.641558i	0.565748	+	0.824578i	$0.308587\pi$
$20$	−3.27355	+	2.76408i	−0.731987	+	0.618068i
$21$		0			0
$22$	−5.19604	+	3.16401i	−1.10780	+	0.674569i
$23$	0.606428	−	2.26322i	0.126449	−	0.471914i	−0.873438	−	0.486935i	$-0.838115\pi$
$23$	0.606428	−	2.26322i	0.126449	−	0.471914i	0.999887	+	0.0150211i	$0.00478156\pi$
$24$		0			0
$25$	−0.106358	−	0.396933i	−0.0212716	−	0.0793865i
$26$	−1.53275	−	1.46277i	−0.300598	−	0.286873i
$27$		0			0
$28$	−0.0947992	−	2.02773i	−0.0179154	−	0.383204i
$29$	2.70258	+	3.52207i	0.501856	+	0.654032i	0.973749	−	0.227624i	$-0.0730957\pi$
$29$	2.70258	+	3.52207i	0.501856	+	0.654032i	−0.471893	+	0.881656i	$0.656429\pi$
$30$		0			0
$31$	8.30037	−	4.79222i	1.49079	−	0.860708i	0.490846	−	0.871246i	$-0.336688\pi$
$31$	8.30037	−	4.79222i	1.49079	−	0.860708i	0.999944	+	0.0105382i	$0.00335447\pi$
$32$	1.38688	+	5.48421i	0.245168	+	0.969481i
$33$		0			0
$34$	4.78816	+	5.94711i	0.821162	+	1.01992i
$35$	−2.00877	−	0.832061i	−0.339545	−	0.140644i
$36$		0			0
$37$	2.47820	+	5.98289i	0.407413	+	0.983582i	0.985816	+	0.167831i	$0.0536762\pi$
$37$	2.47820	+	5.98289i	0.407413	+	0.983582i	−0.578403	+	0.815751i	$0.696324\pi$
$38$	−2.90718	−	9.91713i	−0.471607	−	1.60877i
$39$		0			0
$40$	5.94807	+	1.15456i	0.940472	+	0.182553i
$41$	3.87025	+	1.03703i	0.604432	+	0.161957i	0.548040	−	0.836452i	$-0.315374\pi$
$41$	3.87025	+	1.03703i	0.604432	+	0.161957i	0.0563911	+	0.998409i	$0.482041\pi$
$42$		0			0
$43$	8.39033	+	1.10461i	1.27951	+	0.168451i	0.739472	−	0.673187i	$-0.235075\pi$
$43$	8.39033	+	1.10461i	1.27951	+	0.168451i	0.540042	+	0.841638i	$0.318408\pi$
$44$	8.09365	+	2.91761i	1.22016	+	0.439846i
$45$		0			0
$46$	−3.03090	+	1.33921i	−0.446882	+	0.197456i
$47$	7.46917	+	4.31233i	1.08949	+	0.629018i	0.933441	−	0.358732i	$-0.116791\pi$
$47$	7.46917	+	4.31233i	1.08949	+	0.629018i	0.156050	+	0.987749i	$0.450124\pi$
$48$		0			0
$49$	−5.17003	+	2.98492i	−0.738575	+	0.426417i
$50$	−0.342916	+	0.469195i	−0.0484957	+	0.0663541i
$51$		0			0
$52$	−0.251941	+	2.98573i	−0.0349379	+	0.414046i
$53$	−1.62188	−	3.91557i	−0.222783	−	0.537845i	0.772483	−	0.635035i	$-0.219014\pi$
$53$	−1.62188	−	3.91557i	−0.222783	−	0.537845i	−0.995266	+	0.0971903i	$0.969014\pi$
$54$		0			0
$55$	6.51614	−	6.51614i	0.878636	−	0.878636i
$56$	−2.14958	+	1.90280i	−0.287250	+	0.254272i
$57$		0			0
$58$	1.48287	−	6.10073i	0.194711	−	0.801065i
$59$	1.79040	−	2.33330i	0.233090	−	0.303769i	−0.662134	−	0.749386i	$-0.730349\pi$
$59$	1.79040	−	2.33330i	0.233090	−	0.303769i	0.895224	+	0.445617i	$0.147016\pi$
$60$		0			0
$61$	0.267258	−	0.205074i	0.0342188	−	0.0262570i	−0.591510	−	0.806297i	$-0.701468\pi$
$61$	0.267258	−	0.205074i	0.0342188	−	0.0262570i	0.625729	+	0.780040i	$0.284801\pi$
$62$	−12.6404	−	4.89316i	−1.60533	−	0.621432i
$63$		0			0
$64$	4.81116	−	6.39162i	0.601395	−	0.798952i
$65$	2.77942	+	1.60470i	0.344745	+	0.199038i
$66$		0			0
$67$	−5.23988	+	0.689843i	−0.640153	+	0.0842777i	−0.443613	−	0.896218i	$-0.646304\pi$
$67$	−5.23988	+	0.689843i	−0.640153	+	0.0842777i	−0.196539	+	0.980496i	$0.562970\pi$
$68$	2.30451	−	10.5489i	0.279463	−	1.27924i
$69$		0			0
$70$	0.864997	+	2.95072i	0.103387	+	0.352679i
$71$	−2.98357	+	2.98357i	−0.354085	+	0.354085i	−0.861627	−	0.507542i	$-0.830554\pi$
$71$	−2.98357	+	2.98357i	−0.354085	+	0.354085i	0.507542	+	0.861627i	$0.330554\pi$
$72$		0			0
$73$	−1.45130	−	1.45130i	−0.169862	−	0.169862i	0.617057	−	0.786919i	$-0.288325\pi$
$73$	−1.45130	−	1.45130i	−0.169862	−	0.169862i	−0.786919	+	0.617057i	$0.788325\pi$
$74$	4.39261	−	8.03604i	0.510631	−	0.934171i
$75$		0			0
$76$	−8.34593	+	11.9978i	−0.957344	+	1.37624i
$77$	0.569895	+	4.32878i	0.0649455	+	0.493310i
$78$		0			0
$79$	4.91023	−	8.50477i	0.552444	−	0.956861i	−0.445653	−	0.895206i	$-0.647029\pi$
$79$	4.91023	−	8.50477i	0.552444	−	0.956861i	0.998097	−	0.0616558i	$-0.0196381\pi$
$80$	−4.00346	−	7.57610i	−0.447600	−	0.847034i
$81$		0			0
$82$	−2.29014	−	5.18303i	−0.252903	−	0.572370i
$83$	−1.33347	−	1.73781i	−0.146367	−	0.190750i	0.714416	−	0.699721i	$-0.246692\pi$
$83$	−1.33347	−	1.73781i	−0.146367	−	0.190750i	−0.860783	+	0.508972i	$0.830026\pi$
$84$		0			0
$85$	−9.17546	−	7.04058i	−0.995218	−	0.763658i
$86$	−6.22451	−	10.2221i	−0.671206	−	1.10228i
$87$		0			0
$88$	−3.96426	−	11.5032i	−0.422591	−	1.22625i
$89$	2.17841	+	2.17841i	0.230911	+	0.230911i	0.813073	−	0.582162i	$-0.197793\pi$
$89$	2.17841	+	2.17841i	0.230911	+	0.230911i	−0.582162	+	0.813073i	$0.697793\pi$
$90$		0			0
$91$	−1.40485	+	0.581909i	−0.147268	+	0.0610006i
$92$	4.16329	+	2.15098i	0.434053	+	0.224255i
$93$		0			0
$94$	−1.87405	−	12.0523i	−0.193294	−	1.24310i
$95$	7.82717	+	13.5571i	0.803051	+	1.39093i
$96$		0			0
$97$	4.24778	−	7.35737i	0.431297	−	0.747028i	−0.565689	−	0.824619i	$-0.691390\pi$
$97$	4.24778	−	7.35737i	0.431297	−	0.747028i	0.996985	+	0.0775912i	$0.0247229\pi$
$98$	7.87330	+	3.04779i	0.795323	+	0.307873i
$99$		0			0
$100$	0.820973	−	0.0383817i	0.0820973	−	0.00383817i
$101$	1.31379	−	9.97923i	0.130727	−	0.992971i	−0.792812	−	0.609466i	$-0.791384\pi$
$101$	1.31379	−	9.97923i	0.130727	−	0.992971i	0.923539	−	0.383505i	$-0.125283\pi$
$102$		0			0
$103$	−4.33702	+	16.1860i	−0.427339	+	1.59485i	0.331423	+	0.943482i	$0.392471\pi$
$103$	−4.33702	+	16.1860i	−0.427339	+	1.59485i	−0.758762	+	0.651368i	$0.774195\pi$
$104$	3.51240	−	2.37049i	0.344419	−	0.232445i
$105$		0			0
$106$	−2.87479	+	5.25927i	−0.279225	+	0.510826i
$107$	−8.79307	+	3.64221i	−0.850058	+	0.352106i	−0.764811	−	0.644254i	$-0.777168\pi$
$107$	−8.79307	+	3.64221i	−0.850058	+	0.352106i	−0.0852469	+	0.996360i	$0.527168\pi$
$108$		0			0
$109$	2.67483	−	6.45762i	0.256203	−	0.618528i	−0.742479	−	0.669870i	$-0.766350\pi$
$109$	2.67483	−	6.45762i	0.256203	−	0.618528i	0.998681	+	0.0513420i	$0.0163499\pi$
$110$	−12.9570	−	1.39880i	−1.23540	−	0.133371i
$111$		0			0
$112$	4.00248	+	0.680316i	0.378199	+	0.0642838i
$113$	3.88868	+	6.73539i	0.365816	+	0.633612i	0.988907	−	0.148537i	$-0.0474565\pi$
$113$	3.88868	+	6.73539i	0.365816	+	0.633612i	−0.623091	+	0.782150i	$0.714123\pi$
$114$		0			0
$115$	3.98209	−	3.05557i	0.371332	−	0.284933i
$116$	−8.03545	+	3.77721i	−0.746072	+	0.350705i
$117$		0			0
$118$	−4.15814	+	0.0971466i	−0.382788	+	0.00894307i
$119$	5.29293	−	1.41824i	0.485202	−	0.130010i
$120$		0			0
$121$	−7.24917	−	1.94241i	−0.659016	−	0.176583i
$122$	−0.462928	−	0.112522i	−0.0419116	−	0.0101872i
$123$		0			0
$124$	5.82055	+	18.2638i	0.522701	+	1.64014i
$125$	4.43582	−	10.7090i	0.396752	−	0.957844i
$126$		0			0
$127$		−	16.4140i		−	1.45650i	−0.685309	−	0.728252i	$-0.740333\pi$
$127$		−	16.4140i		−	1.45650i	0.685309	−	0.728252i	$-0.259667\pi$
$128$	−11.3077	+	0.368890i	−0.999468	+	0.0326056i
$129$		0			0
$130$	−0.697371	−	4.48488i	−0.0611635	−	0.393350i
$131$	−2.28810	−	17.3799i	−0.199912	−	1.51849i	−0.737540	−	0.675303i	$-0.764013\pi$
$131$	−2.28810	−	17.3799i	−0.199912	−	1.51849i	0.537628	−	0.843182i	$-0.319321\pi$
$132$		0			0
$133$	−7.35352	−	0.968109i	−0.637631	−	0.0839457i
$134$	5.40709	+	5.16021i	0.467101	+	0.445774i
$135$		0			0
$136$	−13.6640	+	6.81711i	−1.17168	+	0.584562i
$137$	5.42840	+	20.2591i	0.463780	+	1.73085i	0.660904	+	0.750470i	$0.270173\pi$
$137$	5.42840	+	20.2591i	0.463780	+	1.73085i	−0.197125	+	0.980378i	$0.563160\pi$
$138$		0			0
$139$	−1.63763	+	2.13421i	−0.138902	+	0.181021i	−0.857625	−	0.514276i	$-0.828061\pi$
$139$	−1.63763	+	2.13421i	−0.138902	+	0.181021i	0.718722	+	0.695297i	$0.244727\pi$
$140$	2.48323	−	3.56981i	0.209872	−	0.301704i
$141$		0			0
$142$	5.93267	+	0.640476i	0.497859	+	0.0537476i
$143$		−	6.44473i		−	0.538935i
$144$		0			0
$145$			9.51028i			0.789786i
$146$	−0.311547	+	2.88583i	−0.0257838	+	0.238833i
$147$		0			0
$148$	−12.7479	+	2.28836i	−1.04787	+	0.188102i
$149$	−10.2620	+	13.3737i	−0.840695	+	1.09561i	0.153514	+	0.988146i	$0.450941\pi$
$149$	−10.2620	+	13.3737i	−0.840695	+	1.09561i	−0.994209	+	0.107468i	$0.965726\pi$
$150$		0			0
$151$	3.08432	+	11.5109i	0.250999	+	0.936740i	0.970273	+	0.242014i	$0.0778078\pi$
$151$	3.08432	+	11.5109i	0.250999	+	0.936740i	−0.719274	+	0.694726i	$0.755525\pi$
$152$	20.6182	−	1.44721i	1.67236	−	0.117385i
$153$		0			0
$154$	4.26296	−	4.46692i	0.343519	−	0.359955i
$155$	20.3562	+	2.67995i	1.63505	+	0.215259i
$156$		0			0
$157$	−1.93241	−	14.6781i	−0.154223	−	1.17144i	−0.877046	−	0.480407i	$-0.840489\pi$
$157$	−1.93241	−	14.6781i	−0.154223	−	1.17144i	0.722823	−	0.691033i	$-0.242844\pi$
$158$	−13.7233	+	2.13389i	−1.09177	+	0.169763i
$159$		0			0
$160$	−4.79488	+	11.1292i	−0.379069	+	0.879841i
$161$			2.37813i			0.187423i
$162$		0			0
$163$	1.16595	−	2.81484i	0.0913240	−	0.220476i	−0.871617	−	0.490187i	$-0.836928\pi$
$163$	1.16595	−	2.81484i	0.0913240	−	0.220476i	0.962941	+	0.269712i	$0.0869284\pi$
$164$	−3.67831	+	7.11949i	−0.287228	+	0.555939i
$165$		0			0
$166$	−0.731658	+	3.01014i	−0.0567877	+	0.233632i
$167$	−3.51362	−	0.941472i	−0.271892	−	0.0728533i	0.120297	−	0.992738i	$-0.461615\pi$
$167$	−3.51362	−	0.941472i	−0.271892	−	0.0728533i	−0.392189	+	0.919885i	$0.628282\pi$
$168$		0			0
$169$	−10.3890	+	2.78372i	−0.799154	+	0.214133i
$170$	0.382020	+	16.3515i	0.0292996	+	1.25410i
$171$		0			0
$172$	−5.73977	+	15.9225i	−0.437653	+	1.21408i
$173$	−15.0058	+	11.5144i	−1.14087	+	0.875420i	−0.993519	−	0.113664i	$-0.963741\pi$
$173$	−15.0058	+	11.5144i	−1.14087	+	0.875420i	−0.147351	+	0.989084i	$0.547075\pi$
$174$		0			0
$175$	0.208544	+	0.361208i	0.0157644	+	0.0273048i
$176$	−9.15558	+	14.5689i	−0.690128	+	1.09817i
$177$		0			0
$178$	0.467633	−	4.33164i	0.0350506	−	0.324670i
$179$	2.08061	−	5.02303i	0.155512	−	0.375439i	−0.826852	−	0.562420i	$-0.809870\pi$
$179$	2.08061	−	5.02303i	0.155512	−	0.375439i	0.982363	+	0.186981i	$0.0598704\pi$
$180$		0			0
$181$	−1.19920	+	0.496727i	−0.0891362	+	0.0369214i	−0.426806	−	0.904343i	$-0.640361\pi$
$181$	−1.19920	+	0.496727i	−0.0891362	+	0.0369214i	0.337670	+	0.941265i	$0.390361\pi$
$182$	1.88695	+	1.03144i	0.139870	+	0.0764551i
$183$		0			0
$184$	−1.32295	−	6.49377i	−0.0975293	−	0.478727i
$185$	−3.59050	+	13.3999i	−0.263978	+	0.985181i
$186$		0			0
$187$	−3.03138	+	23.0256i	−0.221676	+	1.68380i
$188$	−11.6142	+	12.7534i	−0.847052	+	0.930138i
$189$		0			0
$190$	7.99204	−	20.6457i	0.579804	−	1.49780i
$191$	9.67208	−	16.7525i	0.699847	−	1.21217i	−0.268672	−	0.963232i	$-0.586585\pi$
$191$	9.67208	−	16.7525i	0.699847	−	1.21217i	0.968519	−	0.248939i	$-0.0800819\pi$
$192$		0			0
$193$	7.28617	+	12.6200i	0.524470	+	0.908408i	0.999594	+	0.0284897i	$0.00906978\pi$
$193$	7.28617	+	12.6200i	0.524470	+	0.908408i	−0.475124	+	0.879919i	$0.657597\pi$
$194$	−11.8719	+	1.84600i	−0.852351	+	0.132535i
$195$		0			0
$196$	−3.62543	−	11.3759i	−0.258959	−	0.812567i
$197$	9.24225	−	3.82826i	0.658483	−	0.272753i	−0.0283171	−	0.999599i	$-0.509015\pi$
$197$	9.24225	−	3.82826i	0.658483	−	0.272753i	0.686800	+	0.726846i	$0.259015\pi$
$198$		0			0
$199$	−18.4609	−	18.4609i	−1.30866	−	1.30866i	−0.922383	−	0.386276i	$-0.873761\pi$
$199$	−18.4609	−	18.4609i	−1.30866	−	1.30866i	−0.386276	−	0.922383i	$-0.626239\pi$
$200$	−0.770392	−	0.870308i	−0.0544749	−	0.0615401i
$201$		0			0
$202$	−12.1579	+	7.40326i	−0.855426	+	0.520892i
$203$	−3.57480	−	2.74304i	−0.250902	−	0.192524i
$204$		0			0
$205$	5.22522	+	6.80964i	0.364945	+	0.475606i
$206$	21.6762	−	9.57769i	1.51025	−	0.667309i
$207$		0			0
$208$	−5.72633	−	1.76675i	−0.397050	−	0.122502i
$209$	15.7176	−	27.2237i	1.08721	−	1.88310i
$210$		0			0
$211$	1.00560	+	7.63830i	0.0692285	+	0.525842i	0.990562	+	0.137068i	$0.0437680\pi$
$211$	1.00560	+	7.63830i	0.0692285	+	0.525842i	−0.921333	+	0.388774i	$0.872899\pi$
$212$	8.34301	−	1.49764i	0.573000	−	0.102859i
$213$		0			0
$214$	11.8106	+	6.45583i	0.807355	+	0.441312i
$215$	12.8191	+	12.8191i	0.874256	+	0.874256i
$216$		0			0
$217$	−6.87868	+	6.87868i	−0.466956	+	0.466956i
$218$	−9.48572	+	2.78071i	−0.642454	+	0.188334i
$219$		0			0
$220$	9.95056	+	15.5135i	0.670866	+	1.04592i
$221$	−8.01916	+	1.05574i	−0.539427	+	0.0710169i
$222$		0			0
$223$	15.0037	+	8.66241i	1.00472	+	0.580078i	0.909643	−	0.415392i	$-0.136355\pi$
$223$	15.0037	+	8.66241i	1.00472	+	0.580078i	0.0950816	+	0.995469i	$0.469689\pi$
$224$	−2.80035	−	5.01232i	−0.187106	−	0.334900i
$225$		0			0
$226$	3.97059	−	10.2571i	0.264120	−	0.682295i
$227$	−20.3919	+	15.6473i	−1.35346	+	1.03855i	−0.359010	+	0.933334i	$0.616886\pi$
$227$	−20.3919	+	15.6473i	−1.35346	+	1.03855i	−0.994450	+	0.105213i	$0.966448\pi$
$228$		0			0
$229$	−1.90619	+	2.48419i	−0.125964	+	0.164160i	−0.852078	−	0.523415i	$-0.824658\pi$
$229$	−1.90619	+	2.48419i	−0.125964	+	0.164160i	0.726114	+	0.687575i	$0.241325\pi$
$230$	−6.89756	−	1.67655i	−0.454812	−	0.110549i
$231$		0			0
$232$	11.2874	+	5.50154i	0.741051	+	0.361194i
$233$	−20.9855	+	20.9855i	−1.37481	+	1.37481i	−0.521645	+	0.853163i	$0.674681\pi$
$233$	−20.9855	+	20.9855i	−1.37481	+	1.37481i	−0.853163	+	0.521645i	$0.825319\pi$
$234$		0			0
$235$	7.07039	+	17.0694i	0.461222	+	1.11349i
$236$	3.79483	+	4.49427i	0.247022	+	0.292552i
$237$		0			0
$238$	−6.25651	−	4.57265i	−0.405550	−	0.296401i
$239$	3.78438	−	2.18491i	0.244791	−	0.141330i	−0.372586	−	0.927998i	$-0.621529\pi$
$239$	3.78438	−	2.18491i	0.244791	−	0.141330i	0.617377	+	0.786667i	$0.288195\pi$
$240$		0			0
$241$	6.71220	+	3.87529i	0.432371	+	0.249629i	0.700356	−	0.713794i	$-0.253025\pi$
$241$	6.71220	+	3.87529i	0.432371	+	0.249629i	−0.267985	+	0.963423i	$0.586358\pi$
$242$	4.28954	+	9.70808i	0.275742	+	0.624059i
$243$		0			0
$244$	0.286617	+	0.609736i	0.0183488	+	0.0390344i
$245$	−12.6792	−	1.66925i	−0.810046	−	0.106645i
$246$		0			0
$247$	10.5749	+	2.83355i	0.672868	+	0.180294i
$248$	14.9565	−	22.6097i	0.949736	−	1.43571i
$249$		0			0
$250$	−15.7307	+	4.61141i	−0.994895	+	0.291651i
$251$	2.35690	+	5.69006i	0.148766	+	0.359153i	0.980642	−	0.195808i	$-0.0627330\pi$
$251$	2.35690	+	5.69006i	0.148766	+	0.359153i	−0.831876	+	0.554961i	$0.812733\pi$
$252$		0			0
$253$	−9.31197	−	3.85714i	−0.585438	−	0.242497i
$254$	−18.0809	+	14.5574i	−1.13450	+	0.913411i
$255$		0			0
$256$	10.4350	+	12.1289i	0.652189	+	0.758056i
$257$	−13.5420	+	7.81847i	−0.844726	+	0.487703i	−0.858868	−	0.512197i	$-0.828832\pi$
$257$	−13.5420	+	7.81847i	−0.844726	+	0.487703i	0.0141420	+	0.999900i	$0.495498\pi$
$258$		0			0
$259$	−4.00126	−	5.21454i	−0.248626	−	0.324016i
$260$	−4.32186	+	4.74578i	−0.268030	+	0.294321i
$261$		0			0
$262$	−17.1156	+	17.9345i	−1.05741	+	1.10800i
$263$	−1.32028	−	4.92734i	−0.0814117	−	0.303833i	0.913199	−	0.407514i	$-0.133604\pi$
$263$	−1.32028	−	4.92734i	−0.0814117	−	0.303833i	−0.994611	+	0.103682i	$0.966938\pi$
$264$		0			0
$265$	2.34984	−	8.76972i	0.144349	−	0.538719i
$266$	5.45533	+	8.95892i	0.334488	+	0.549307i
$267$		0			0
$268$	0.888771	−	10.5327i	0.0542903	−	0.643390i
$269$	−1.56831	−	0.649614i	−0.0956214	−	0.0396077i	0.334360	−	0.942445i	$-0.391480\pi$
$269$	−1.56831	−	0.649614i	−0.0956214	−	0.0396077i	−0.429981	+	0.902838i	$0.641480\pi$
$270$		0			0
$271$	−1.58685			−0.0963942			−0.0481971	−	0.998838i	$-0.515348\pi$
$271$	−1.58685			−0.0963942			−0.0481971	+	0.998838i	$0.515348\pi$
$272$	19.6279	+	9.00566i	1.19012	+	0.546048i
$273$		0			0
$274$	17.5021	−	23.9472i	1.05734	−	1.44671i
$275$	−1.75261	+	0.230735i	−0.105686	+	0.0139139i
$276$		0			0
$277$	1.70800	−	12.9736i	0.102624	−	0.779506i	−0.860310	−	0.509770i	$-0.829730\pi$
$277$	1.70800	−	12.9736i	0.102624	−	0.779506i	0.962934	−	0.269736i	$-0.0869363\pi$
$278$	3.80335	−	0.0888576i	0.228110	−	0.00532932i
$279$		0			0
$280$	−6.13470	+	0.430601i	−0.366619	+	0.0257334i
$281$	−2.60992	+	0.699325i	−0.155695	+	0.0417182i	−0.335824	−	0.941925i	$-0.609015\pi$
$281$	−2.60992	+	0.699325i	−0.155695	+	0.0417182i	0.180130	+	0.983643i	$0.442348\pi$
$282$		0			0
$283$	−4.77941	−	3.66737i	−0.284106	−	0.218002i	0.456870	−	0.889533i	$-0.348970\pi$
$283$	−4.77941	−	3.66737i	−0.284106	−	0.218002i	−0.740977	+	0.671531i	$0.765637\pi$
$284$	−4.55610	−	7.10321i	−0.270355	−	0.421498i
$285$		0			0
$286$	−7.09924	+	5.71576i	−0.419787	+	0.337980i
$287$	−4.06676			−0.240053
$288$		0			0
$289$	12.1473			0.714545
$290$	10.4761	−	8.43457i	0.615179	−	0.495295i
$291$		0			0
$292$	3.45522	−	2.21623i	0.202201	−	0.129695i
$293$	−6.94632	−	5.33010i	−0.405808	−	0.311388i	0.385611	−	0.922662i	$-0.373991\pi$
$293$	−6.94632	−	5.33010i	−0.405808	−	0.311388i	−0.791419	+	0.611274i	$0.790657\pi$
$294$		0			0
$295$	6.08568	−	1.63065i	0.354322	−	0.0949403i
$296$	13.8268	+	12.0130i	0.803664	+	0.698243i
$297$		0			0
$298$	23.8331	−	0.556812i	1.38062	−	0.0322553i
$299$	0.458186	−	3.48027i	0.0264976	−	0.201269i
$300$		0			0
$301$	−8.51594	+	1.12115i	−0.490851	+	0.0646217i
$302$	9.94440	−	13.6064i	0.572236	−	0.782961i
$303$		0			0
$304$	−19.8802	−	21.4286i	−1.14021	−	1.22901i
$305$	0.721648			0.0413214
$306$		0			0
$307$	−25.8866	−	10.7226i	−1.47742	−	0.611969i	−0.508886	−	0.860834i	$-0.669942\pi$
$307$	−25.8866	−	10.7226i	−1.47742	−	0.611969i	−0.968538	+	0.248865i	$0.919942\pi$
$308$	−8.70134	−	0.734234i	−0.495805	−	0.0418369i
$309$		0			0
$310$	−15.1016	−	24.8004i	−0.857714	−	1.40857i
$311$	−0.221754	+	0.827596i	−0.0125745	+	0.0469287i	−0.971928	−	0.235278i	$-0.924400\pi$
$311$	−0.221754	+	0.827596i	−0.0125745	+	0.0469287i	0.959354	+	0.282207i	$0.0910665\pi$
$312$		0			0
$313$	−4.71691	−	17.6037i	−0.266615	−	0.995022i	−0.961254	−	0.275663i	$-0.911102\pi$
$313$	−4.71691	−	17.6037i	−0.266615	−	0.995022i	0.694639	−	0.719359i	$-0.255564\pi$
$314$	−14.4549	+	15.1465i	−0.815739	+	0.854767i
$315$		0			0
$316$	14.5217	+	13.2245i	0.816908	+	0.743936i
$317$	7.31614	+	9.53458i	0.410915	+	0.535515i	0.952261	−	0.305285i	$-0.0987517\pi$
$317$	7.31614	+	9.53458i	0.410915	+	0.535515i	−0.541346	+	0.840800i	$0.682085\pi$
$318$		0			0
$319$	16.5389	−	9.54871i	0.925998	−	0.534625i
$320$	16.5120	−	4.58853i	0.923048	−	0.256507i
$321$		0			0
$322$	2.61965	−	2.10914i	0.145987	−	0.117538i
$323$	−36.4491	−	15.0977i	−2.02808	−	0.840060i
$324$		0			0
$325$	−0.235599	−	0.568787i	−0.0130687	−	0.0315506i
$326$	−4.13478	+	1.21210i	−0.229004	+	0.0671319i
$327$		0			0
$328$	11.1048	−	2.26233i	0.613159	−	0.124916i
$329$	−8.45550	−	2.26564i	−0.466167	−	0.124909i
$330$		0			0
$331$	−16.0077	−	2.10746i	−0.879864	−	0.115836i	−0.322960	−	0.946413i	$-0.604678\pi$
$331$	−16.0077	−	2.10746i	−0.879864	−	0.115836i	−0.556905	+	0.830576i	$0.688011\pi$
$332$	3.96474	−	1.86370i	0.217593	−	0.102284i
$333$		0			0
$334$	2.07911	+	4.70544i	0.113764	+	0.257470i
$335$	−9.80494	−	5.66089i	−0.535701	−	0.309287i
$336$		0			0
$337$	11.5406	−	6.66299i	0.628658	−	0.362956i	−0.151574	−	0.988446i	$-0.548434\pi$
$337$	11.5406	−	6.66299i	0.628658	−	0.362956i	0.780232	+	0.625490i	$0.215101\pi$
$338$	12.2803	+	8.97522i	0.667961	+	0.488188i
$339$		0			0
$340$	17.6733	−	14.9228i	0.958469	−	0.809302i
$341$	−15.7779	−	38.0913i	−0.854422	−	2.06276i
$342$		0			0
$343$	9.30836	−	9.30836i	0.502604	−	0.502604i
$344$	22.6301	−	7.79882i	1.22013	−	0.420484i
$345$		0			0
$346$	25.9922	+	6.31778i	1.39735	+	0.339646i
$347$	3.32426	−	4.33225i	0.178455	−	0.232568i	−0.695557	−	0.718471i	$-0.744842\pi$
$347$	3.32426	−	4.33225i	0.178455	−	0.232568i	0.874013	+	0.485903i	$0.161509\pi$
$348$		0			0
$349$	−26.2821	+	20.1669i	−1.40685	+	1.07951i	−0.421902	+	0.906642i	$0.638637\pi$
$349$	−26.2821	+	20.1669i	−1.40685	+	1.07951i	−0.984945	+	0.172870i	$0.944696\pi$
$350$	0.212936	−	0.550074i	0.0113819	−	0.0294027i
$351$		0			0
$352$	24.1685	−	2.83563i	1.28818	−	0.151140i
$353$	−29.4504	−	17.0032i	−1.56748	−	0.904988i	−0.996461	−	0.0840537i	$-0.973213\pi$
$353$	−29.4504	−	17.0032i	−1.56748	−	0.904988i	−0.571023	−	0.820934i	$-0.693453\pi$
$354$		0			0
$355$	−8.96153	+	1.17981i	−0.475629	+	0.0626177i
$356$	−5.18629	+	3.32656i	−0.274873	+	0.176308i
$357$		0			0
$358$	−7.37842	+	2.16296i	−0.389962	+	0.114316i
$359$	13.1660	−	13.1660i	0.694877	−	0.694877i	−0.268424	−	0.963301i	$-0.586503\pi$
$359$	13.1660	−	13.1660i	0.694877	−	0.694877i	0.963301	+	0.268424i	$0.0865027\pi$
$360$		0			0
$361$	24.3249	+	24.3249i	1.28026	+	1.28026i
$362$	1.61073	+	0.880450i	0.0846583	+	0.0462754i
$363$		0			0
$364$	−0.537334	−	2.99335i	−0.0281639	−	0.156894i
$365$	−0.573894	−	4.35916i	−0.0300390	−	0.228169i
$366$		0			0
$367$	−0.868465	+	1.50423i	−0.0453335	+	0.0785199i	−0.887802	−	0.460226i	$-0.847768\pi$
$367$	−0.868465	+	1.50423i	−0.0453335	+	0.0785199i	0.842468	+	0.538746i	$0.181102\pi$
$368$	−5.97995	+	7.21657i	−0.311726	+	0.376189i
$369$		0			0
$370$	17.9451	−	7.92910i	0.932923	−	0.412214i
$371$	2.61867	+	3.41271i	0.135954	+	0.177179i
$372$		0			0
$373$	−24.9233	−	19.1243i	−1.29048	−	0.990220i	−0.999438	−	0.0335095i	$-0.989332\pi$
$373$	−24.9233	−	19.1243i	−1.29048	−	0.990220i	−0.291041	−	0.956710i	$-0.594002\pi$
$374$	28.0525	−	17.0819i	1.45056	−	0.883285i
$375$		0			0
$376$	24.3491	+	1.48283i	1.25571	+	0.0764710i
$377$	4.70303	+	4.70303i	0.242218	+	0.242218i
$378$		0			0
$379$	−24.9141	+	10.3198i	−1.27975	+	0.530091i	−0.915915	−	0.401372i	$-0.868534\pi$
$379$	−24.9141	+	10.3198i	−1.27975	+	0.530091i	−0.363837	+	0.931462i	$0.618534\pi$
$380$	−29.8305	+	9.50676i	−1.53027	+	0.487686i
$381$		0			0
$382$	−27.0319	+	4.20330i	−1.38307	+	0.215059i
$383$	5.45733	+	9.45238i	0.278857	+	0.482994i	0.971101	−	0.238669i	$-0.0767112\pi$
$383$	5.45733	+	9.45238i	0.278857	+	0.482994i	−0.692244	+	0.721663i	$0.743378\pi$
$384$		0			0
$385$	−4.67659	+	8.10009i	−0.238341	+	0.412819i
$386$	7.43964	−	19.2187i	0.378668	−	0.978205i
$387$		0			0
$388$	12.5625	+	11.4403i	0.637765	+	0.580795i
$389$	−0.404985	+	3.07617i	−0.0205336	+	0.155968i	−0.998640	−	0.0521379i	$-0.983396\pi$
$389$	−0.404985	+	3.07617i	−0.0205336	+	0.155968i	0.978106	+	0.208106i	$0.0667298\pi$
$390$		0			0
$391$	−3.27399	+	12.2187i	−0.165573	+	0.617927i
$392$	−9.31589	+	14.0828i	−0.470523	+	0.711289i
$393$		0			0
$394$	−12.4139	−	6.78562i	−0.625403	−	0.341854i
$395$	19.4361	−	8.05070i	0.977937	−	0.405075i
$396$		0			0
$397$	−9.05217	+	21.8539i	−0.454316	+	1.09681i	0.516349	+	0.856378i	$0.327291\pi$
$397$	−9.05217	+	21.8539i	−0.454316	+	1.09681i	−0.970665	+	0.240437i	$0.922709\pi$
$398$	−3.96296	+	36.7085i	−0.198645	+	1.84003i
$399$		0			0
$400$	−0.275442	+	1.62050i	−0.0137721	+	0.0810249i
$401$	7.88970	+	13.6654i	0.393993	+	0.682416i	0.992972	−	0.118349i	$-0.0377601\pi$
$401$	7.88970	+	13.6654i	0.393993	+	0.682416i	−0.598979	+	0.800765i	$0.704427\pi$
$402$		0			0
$403$	11.3919	−	8.74129i	0.567469	−	0.435435i
$404$	18.9378	+	6.82673i	0.942191	+	0.339642i
$405$		0			0
$406$	0.148837	+	6.37062i	0.00738663	+	0.316168i
$407$	26.9081	−	7.21001i	1.33379	−	0.357387i
$408$		0			0
$409$	25.6939	+	6.88466i	1.27048	+	0.340425i	0.830215	−	0.557443i	$-0.188217\pi$
$409$	25.6939	+	6.88466i	1.27048	+	0.340425i	0.440266	+	0.897867i	$0.354884\pi$
$410$	2.86701	−	11.7953i	0.141592	−	0.582527i
$411$		0			0
$412$	−29.7748	−	15.3832i	−1.46690	−	0.757878i
$413$	−1.14234	+	2.75786i	−0.0562110	+	0.135705i
$414$		0			0
$415$		−	4.69243i		−	0.230342i
$416$	3.13245	+	7.87479i	0.153581	+	0.386093i
$417$		0			0
$418$	−43.9282	+	6.83056i	−2.14860	+	0.334094i
$419$	2.32281	+	17.6435i	0.113477	+	0.861942i	0.949614	+	0.313421i	$0.101475\pi$
$419$	2.32281	+	17.6435i	0.113477	+	0.861942i	−0.836137	+	0.548520i	$0.815191\pi$
$420$		0			0
$421$	10.3511	+	1.36274i	0.504480	+	0.0664160i	0.378471	−	0.925613i	$-0.376450\pi$
$421$	10.3511	+	1.36274i	0.504480	+	0.0664160i	0.126009	+	0.992029i	$0.459783\pi$
$422$	7.52217	−	7.88206i	0.366173	−	0.383692i
$423$		0			0
$424$	−9.04907	−	7.86206i	−0.439462	−	0.381815i
$425$	0.574207	+	2.14297i	0.0278531	+	0.103949i
$426$		0			0
$427$	−0.208144	+	0.271259i	−0.0100728	+	0.0131271i
$428$	−3.36321	−	18.7356i	−0.162567	−	0.905621i
$429$		0			0
$430$	2.75185	−	25.4901i	0.132706	−	1.22924i
$431$		−	33.1788i		−	1.59817i	−0.601220	−	0.799084i	$-0.705318\pi$
$431$		−	33.1788i		−	1.59817i	0.601220	−	0.799084i	$-0.294682\pi$
$432$		0			0
$433$			12.9633i			0.622976i	0.950250	+	0.311488i	$0.100827\pi$
$433$			12.9633i			0.622976i	−0.950250	+	0.311488i	$0.899173\pi$
$434$	13.6779	+	1.47663i	0.656560	+	0.0708805i
$435$		0			0
$436$	11.4759	+	7.98287i	0.549596	+	0.382310i
$437$	10.4232	−	13.5838i	0.498611	−	0.649803i
$438$		0			0
$439$	−3.27390	−	12.2184i	−0.156255	−	0.583151i	−0.998995	−	0.0448299i	$-0.985725\pi$
$439$	−3.27390	−	12.2184i	−0.156255	−	0.583151i	0.842740	−	0.538321i	$-0.180941\pi$
$440$	8.26391	−	24.7198i	0.393966	−	1.17847i
$441$		0			0
$442$	8.27507	+	7.89724i	0.393605	+	0.375633i
$443$	−8.49813	−	1.11880i	−0.403759	−	0.0531558i	−0.0740876	−	0.997252i	$-0.523604\pi$
$443$	−8.49813	−	1.11880i	−0.403759	−	0.0531558i	−0.329671	+	0.944096i	$0.606938\pi$
$444$		0			0
$445$	0.861417	+	6.54312i	0.0408351	+	0.310173i
$446$	−3.76451	−	24.2101i	−0.178255	−	1.14638i
$447$		0			0
$448$	−3.03776	+	7.53012i	−0.143521	+	0.355765i
$449$			14.4515i			0.682010i	0.940061	+	0.341005i	$0.110767\pi$
$449$			14.4515i			0.682010i	−0.940061	+	0.341005i	$0.889233\pi$
$450$		0			0
$451$	6.59596	−	15.9241i	0.310592	−	0.749835i
$452$	−14.8203	+	4.72313i	−0.697089	+	0.222157i
$453$		0			0
$454$	35.3218	+	8.58547i	1.65773	+	0.402936i
$455$	−3.14645	−	0.843089i	−0.147508	−	0.0395246i
$456$		0			0
$457$	−40.5132	+	10.8555i	−1.89513	+	0.507797i	−0.897335	+	0.441349i	$0.854500\pi$
$457$	−40.5132	+	10.8555i	−1.89513	+	0.507797i	−0.997790	+	0.0664480i	$0.978833\pi$
$458$	4.42706	−	0.103429i	0.206863	−	0.00483293i
$459$		0			0
$460$	4.27055	+	9.08497i	0.199116	+	0.423589i
$461$	29.5975	−	22.7110i	1.37850	−	1.05776i	0.387787	−	0.921749i	$-0.373239\pi$
$461$	29.5975	−	22.7110i	1.37850	−	1.05776i	0.990708	−	0.136008i	$-0.0434272\pi$
$462$		0			0
$463$	−3.54843	−	6.14606i	−0.164910	−	0.285632i	0.771714	−	0.635970i	$-0.219400\pi$
$463$	−3.54843	−	6.14606i	−0.164910	−	0.285632i	−0.936623	+	0.350339i	$0.886067\pi$
$464$	−3.95038	−	17.3129i	−0.183392	−	0.803732i
$465$		0			0
$466$	41.7286	+	4.50491i	1.93304	+	0.208686i
$467$	4.76497	−	11.5037i	0.220497	−	0.532326i	−0.774461	−	0.632622i	$-0.781979\pi$
$467$	4.76497	−	11.5037i	0.220497	−	0.532326i	0.994958	+	0.100296i	$0.0319789\pi$
$468$		0			0
$469$	4.95589	−	2.05280i	0.228842	−	0.0947893i
$470$	12.5323	−	22.9271i	0.578072	−	1.05755i
$471$		0			0
$472$	1.58511	−	8.16614i	0.0729605	−	0.375877i
$473$	9.42215	−	35.1640i	0.433231	−	1.61684i
$474$		0			0
$475$	0.391962	−	2.97725i	0.0179844	−	0.136605i
$476$	0.511804	+	10.9473i	0.0234585	+	0.501770i
$477$		0			0
$478$	−5.76314	−	2.23094i	−0.263600	−	0.102041i
$479$	17.9620	−	31.1111i	0.820706	−	1.42150i	−0.0844520	−	0.996428i	$-0.526914\pi$
$479$	17.9620	−	31.1111i	0.820706	−	1.42150i	0.905158	−	0.425076i	$-0.139753\pi$
$480$		0			0
$481$	4.85096	+	8.40210i	0.221185	+	0.383103i
$482$	−1.68412	−	10.8308i	−0.0767098	−	0.493330i
$483$		0			0
$484$	6.88966	−	13.3352i	0.313166	−	0.606144i
$485$	16.8139	−	6.96456i	0.763482	−	0.316244i
$486$		0			0
$487$	1.72336	+	1.72336i	0.0780927	+	0.0780927i	0.745074	−	0.666982i	$-0.232414\pi$
$487$	1.72336	+	1.72336i	0.0780927	+	0.0780927i	−0.666982	+	0.745074i	$0.732414\pi$
$488$	0.417461	−	0.856494i	0.0188976	−	0.0387717i
$489$		0			0
$490$	9.40630	+	15.4473i	0.424933	+	0.697840i
$491$	−5.69994	−	4.37372i	−0.257235	−	0.197383i	0.472091	−	0.881550i	$-0.343499\pi$
$491$	−5.69994	−	4.37372i	−0.257235	−	0.197383i	−0.729326	+	0.684167i	$0.760166\pi$
$492$		0			0
$493$	−14.5907	−	19.0150i	−0.657134	−	0.856394i
$494$	−6.25749	−	14.1619i	−0.281538	−	0.637176i
$495$		0			0
$496$	−38.1705	+	3.57687i	−1.71391	+	0.160606i
$497$	2.14129	−	3.70882i	0.0960499	−	0.166363i
$498$		0			0
$499$	4.62069	+	35.0976i	0.206850	+	1.57118i	0.708245	+	0.705966i	$0.249487\pi$
$499$	4.62069	+	35.0976i	0.206850	+	1.57118i	−0.501395	+	0.865218i	$0.667180\pi$
$500$	19.0311	+	13.2384i	0.851096	+	0.592041i
$501$		0			0
$502$	4.17761	−	7.64271i	0.186456	−	0.341111i
$503$	−14.0204	−	14.0204i	−0.625137	−	0.625137i	0.321704	−	0.946840i	$-0.395745\pi$
$503$	−14.0204	−	14.0204i	−0.625137	−	0.625137i	−0.946840	+	0.321704i	$0.895745\pi$
$504$		0			0
$505$	15.2467	−	15.2467i	0.678469	−	0.678469i
$506$	4.00982	+	13.6785i	0.178258	+	0.608084i
$507$		0			0
$508$	32.0716	+	7.00639i	1.42295	+	0.310858i
$509$	30.9407	−	4.07342i	1.37142	−	0.180551i	0.591438	−	0.806351i	$-0.298561\pi$
$509$	30.9407	−	4.07342i	1.37142	−	0.180551i	0.779984	+	0.625800i	$0.215227\pi$
$510$		0			0
$511$	1.80408	+	1.04159i	0.0798079	+	0.0460771i
$512$	4.10596	−	22.2518i	0.181460	−	0.983398i
$513$		0			0
$514$	20.6227	+	7.98315i	0.909629	+	0.352122i
$515$	−28.4789	+	21.8527i	−1.25493	+	0.962943i
$516$		0			0
$517$	22.5856	−	29.4342i	0.993315	−	1.29451i
$518$	−2.19544	+	9.03234i	−0.0964622	+	0.396858i
$519$		0			0
$520$	9.06076	+	0.551788i	0.397341	+	0.0241975i
$521$	−6.89274	+	6.89274i	−0.301977	+	0.301977i	−0.841787	−	0.539810i	$-0.818496\pi$
$521$	−6.89274	+	6.89274i	−0.301977	+	0.301977i	0.539810	+	0.841787i	$0.318496\pi$
$522$		0			0
$523$	−0.948159	−	2.28906i	−0.0414601	−	0.100094i	0.901793	−	0.432168i	$-0.142251\pi$
$523$	−0.948159	−	2.28906i	−0.0414601	−	0.100094i	−0.943253	+	0.332075i	$0.892251\pi$
$524$	34.9355	+	2.94792i	1.52617	+	0.128780i
$525$		0			0
$526$	−4.25680	+	5.82436i	−0.185605	+	0.253954i
$527$	−44.8122	+	25.8723i	−1.95205	+	1.12702i
$528$		0			0
$529$	15.1642	+	8.75504i	0.659312	+	0.380654i
$530$	−11.7444	+	5.18929i	−0.510144	+	0.225408i
$531$		0			0
$532$	5.03049	−	13.9549i	0.218099	−	0.605023i
$533$	5.95148	+	0.783528i	0.257787	+	0.0339384i
$534$		0			0
$535$	−19.6939	−	5.27696i	−0.851440	−	0.228143i
$536$	−12.3907	+	8.36235i	−0.535195	+	0.361199i
$537$		0			0
$538$	0.675328	+	2.30371i	0.0291154	+	0.0993202i
$539$	9.82755	+	23.7258i	0.423303	+	1.02194i
$540$		0			0
$541$	−33.1384	−	13.7264i	−1.42473	−	0.590142i	−0.468685	−	0.883365i	$-0.655272\pi$
$541$	−33.1384	−	13.7264i	−1.42473	−	0.590142i	−0.956044	+	0.293223i	$0.905272\pi$
$542$	1.40736	+	1.74800i	0.0604512	+	0.0750832i
$543$		0			0
$544$	−7.48752	−	29.6083i	−0.321025	−	1.26944i
$545$	12.9673	−	7.48668i	0.555459	−	0.320694i
$546$		0			0
$547$	−13.7601	−	17.9325i	−0.588340	−	0.766740i	0.400407	−	0.916338i	$-0.368869\pi$
$547$	−13.7601	−	17.9325i	−0.588340	−	0.766740i	−0.988747	+	0.149598i	$0.952202\pi$
$548$	−41.9017	+	1.95897i	−1.78995	+	0.0836828i
$549$		0			0
$550$	1.80854	+	1.72596i	0.0771163	+	0.0735953i
$551$	8.39654	+	31.3363i	0.357705	+	1.33497i
$552$		0			0
$553$	−2.57977	+	9.62785i	−0.109703	+	0.409418i
$554$	−15.8059	+	9.62465i	−0.671530	+	0.408912i
$555$		0			0
$556$	−3.47103	−	4.11080i	−0.147205	−	0.174337i
$557$	27.8912	+	11.5529i	1.18179	+	0.489513i	0.885073	−	0.465453i	$-0.154108\pi$
$557$	27.8912	+	11.5529i	1.18179	+	0.489513i	0.296716	+	0.954966i	$0.404108\pi$
$558$		0			0
$559$	12.6786			0.536249
$560$	5.91513	+	6.37583i	0.249960	+	0.269428i
$561$		0			0
$562$	3.08505	+	2.25475i	0.130135	+	0.0951108i
$563$	−22.8162	+	3.00381i	−0.961588	+	0.126595i	−0.594945	−	0.803766i	$-0.702826\pi$
$563$	−22.8162	+	3.00381i	−0.961588	+	0.126595i	−0.366643	+	0.930362i	$0.619493\pi$
$564$		0			0
$565$	−2.17466	+	16.5182i	−0.0914888	+	0.694926i
$566$	0.198990	+	8.51734i	0.00836419	+	0.358011i
$567$		0			0
$568$	−3.78383	+	11.3186i	−0.158766	+	0.474917i
$569$	−32.3753	+	8.67494i	−1.35724	+	0.363673i	−0.862804	−	0.505539i	$-0.831294\pi$
$569$	−32.3753	+	8.67494i	−1.35724	+	0.363673i	−0.494441	+	0.869211i	$0.664627\pi$
$570$		0			0
$571$	1.71995	+	1.31976i	0.0719776	+	0.0552303i	0.644124	−	0.764921i	$-0.277222\pi$
$571$	1.71995	+	1.31976i	0.0719776	+	0.0552303i	−0.572146	+	0.820152i	$0.693889\pi$
$572$	12.5925	+	2.75097i	0.526518	+	0.115024i
$573$		0			0
$574$	3.60677	+	4.47977i	0.150544	+	0.186982i
$575$	−0.962844			−0.0401534
$576$		0			0
$577$	26.0027			1.08251			0.541254	−	0.840859i	$-0.317950\pi$
$577$	26.0027			1.08251			0.541254	+	0.840859i	$0.317950\pi$
$578$	−10.7733	−	13.3809i	−0.448110	−	0.556572i
$579$		0			0
$580$	−18.5823	−	4.05951i	−0.771589	−	0.168562i
$581$	1.76383	+	1.35343i	0.0731759	+	0.0561498i
$582$		0			0
$583$	−17.6103	+	4.71867i	−0.729344	+	0.195427i
$584$	−5.50569	−	1.84057i	−0.227827	−	0.0761633i
$585$		0			0
$586$	0.289210	+	12.3790i	0.0119471	+	0.511371i
$587$	−0.394924	+	2.99975i	−0.0163003	+	0.123813i	−0.997660	−	0.0683651i	$-0.978222\pi$
$587$	−0.394924	+	2.99975i	−0.0163003	+	0.123813i	0.981360	+	0.192178i	$0.0615551\pi$
$588$		0			0
$589$	69.4398	−	9.14192i	2.86122	−	0.376686i
$590$	−7.19358	−	5.25751i	−0.296155	−	0.216448i
$591$		0			0
$592$	0.970237	−	25.8852i	0.0398765	−	1.06387i
$593$	11.5374			0.473783			0.236891	−	0.971536i	$-0.423871\pi$
$593$	11.5374			0.473783			0.236891	+	0.971536i	$0.423871\pi$
$594$		0			0
$595$	10.8450	+	4.49215i	0.444602	+	0.184160i
$596$	−21.7507	−	25.7597i	−0.890943	−	1.05516i
$597$		0			0
$598$	−4.24007	+	2.58189i	−0.173390	+	0.105582i
$599$	−11.1639	+	41.6644i	−0.456146	+	1.70236i	0.228551	+	0.973532i	$0.426601\pi$
$599$	−11.1639	+	41.6644i	−0.456146	+	1.70236i	−0.684697	+	0.728828i	$0.740065\pi$
$600$		0			0
$601$	−8.54420	−	31.8874i	−0.348525	−	1.30071i	−0.888440	−	0.458994i	$-0.848210\pi$
$601$	−8.54420	−	31.8874i	−0.348525	−	1.30071i	0.539914	−	0.841720i	$-0.318457\pi$
$602$	8.78770	+	8.38646i	0.358160	+	0.341807i
$603$		0			0
$604$	−23.8078	+	1.11305i	−0.968726	+	0.0452894i
$605$	−9.78710	−	12.7548i	−0.397902	−	0.518556i
$606$		0			0
$607$	−18.3285	+	10.5819i	−0.743929	+	0.429508i	−0.823496	−	0.567322i	$-0.807980\pi$
$607$	−18.3285	+	10.5819i	−0.743929	+	0.429508i	0.0795670	+	0.996830i	$0.474646\pi$
$608$	−5.97324	+	40.9040i	−0.242247	+	1.65888i
$609$		0			0
$610$	−0.640022	−	0.794936i	−0.0259137	−	0.0321860i
$611$	11.9376	+	4.94473i	0.482945	+	0.200042i
$612$		0			0
$613$	−7.04864	−	17.0169i	−0.284692	−	0.687307i	0.715241	−	0.698878i	$-0.246317\pi$
$613$	−7.04864	−	17.0169i	−0.284692	−	0.687307i	−0.999933	+	0.0115710i	$0.996317\pi$
$614$	11.1470	+	38.0252i	0.449856	+	1.53457i
$615$		0			0
$616$	6.90833	+	10.2362i	0.278344	+	0.412429i
$617$	14.1277	+	3.78551i	0.568760	+	0.152399i	0.531728	−	0.846915i	$-0.321543\pi$
$617$	14.1277	+	3.78551i	0.568760	+	0.152399i	0.0370322	+	0.999314i	$0.488210\pi$
$618$		0			0
$619$	35.0162	+	4.60997i	1.40742	+	0.185290i	0.795655	−	0.605750i	$-0.207127\pi$
$619$	35.0162	+	4.60997i	1.40742	+	0.185290i	0.611765	+	0.791040i	$0.290460\pi$
$620$	−13.9256	+	38.6305i	−0.559264	+	1.55144i
$621$		0			0
$622$	1.10831	−	0.489712i	0.0444394	−	0.0196356i
$623$	−2.70793	−	1.56343i	−0.108491	−	0.0626374i
$624$		0			0
$625$	19.7250	−	11.3882i	0.789000	−	0.455529i
$626$	−15.2081	+	20.8085i	−0.607840	+	0.831675i
$627$		0			0
$628$	29.5047	+	2.48965i	1.17736	+	0.0993480i
$629$	−13.3793	−	32.3006i	−0.533469	−	1.28791i
$630$		0			0
$631$	−18.2865	+	18.2865i	−0.727975	+	0.727975i	−0.970216	−	0.242241i	$-0.922117\pi$
$631$	−18.2865	+	18.2865i	−0.727975	+	0.727975i	0.242241	+	0.970216i	$0.422117\pi$
$632$	1.68842	−	27.7251i	0.0671618	−	1.10285i
$633$		0			0
$634$	4.01427	−	16.5153i	0.159427	−	0.655905i
$635$	21.4054	−	27.8960i	0.849447	−	1.10702i
$636$		0			0
$637$	−7.09562	+	5.44466i	−0.281139	+	0.215725i
$638$	−25.1866	−	9.74984i	−0.997146	−	0.386000i
$639$		0			0
$640$	−19.6988	−	14.1194i	−0.778665	−	0.558117i
$641$	26.6775	+	15.4023i	1.05370	+	0.608352i	0.923682	−	0.383160i	$-0.125164\pi$
$641$	26.6775	+	15.4023i	1.05370	+	0.608352i	0.130015	+	0.991512i	$0.458497\pi$
$642$		0			0
$643$	−14.3097	+	1.88391i	−0.564319	+	0.0742941i	−0.407288	−	0.913300i	$-0.633526\pi$
$643$	−14.3097	+	1.88391i	−0.564319	+	0.0742941i	−0.157031	+	0.987594i	$0.550192\pi$
$644$	−4.64668	−	1.01512i	−0.183105	−	0.0400013i
$645$		0			0
$646$	15.6953	+	53.5408i	0.617525	+	2.10653i
$647$	−24.9147	+	24.9147i	−0.979498	+	0.979498i	−0.999794	−	0.0202960i	$-0.993539\pi$
$647$	−24.9147	+	24.9147i	−0.979498	+	0.979498i	0.0202960	+	0.999794i	$0.493539\pi$
$648$		0			0
$649$	−8.94605	−	8.94605i	−0.351163	−	0.351163i
$650$	−0.417601	+	0.763978i	−0.0163797	+	0.0299657i
$651$		0			0
$652$	5.00228	+	3.47969i	0.195905	+	0.136275i
$653$	−0.0340762	−	0.258835i	−0.00133351	−	0.0101290i	0.990765	−	0.135589i	$-0.0432927\pi$
$653$	−0.0340762	−	0.258835i	−0.00133351	−	0.0101290i	−0.992099	+	0.125460i	$0.959959\pi$
$654$		0			0
$655$	18.7763	−	32.5215i	0.733651	−	1.27072i
$656$	−12.3408	−	10.2261i	−0.481827	−	0.399262i
$657$		0			0
$658$	5.00335	+	11.3236i	0.195051	+	0.441439i
$659$	−5.80030	−	7.55910i	−0.225948	−	0.294461i	0.666598	−	0.745417i	$-0.267750\pi$
$659$	−5.80030	−	7.55910i	−0.225948	−	0.294461i	−0.892546	+	0.450956i	$0.851083\pi$
$660$		0			0
$661$	−5.86632	−	4.50139i	−0.228173	−	0.175084i	0.488347	−	0.872649i	$-0.337600\pi$
$661$	−5.86632	−	4.50139i	−0.228173	−	0.175084i	−0.716521	+	0.697566i	$0.754267\pi$
$662$	11.8756	+	19.5025i	0.461558	+	0.757986i
$663$		0			0
$664$	−5.56925	−	2.71449i	−0.216129	−	0.105343i
$665$	−11.2350	−	11.2350i	−0.435675	−	0.435675i
$666$		0			0
$667$	9.61014	−	3.98065i	0.372106	−	0.154131i
$668$	3.33937	−	6.46346i	0.129204	−	0.250079i
$669$		0			0
$670$	2.46011	+	15.8213i	0.0950424	+	0.611230i
$671$	−0.724564	−	1.25498i	−0.0279715	−	0.0484480i
$672$		0			0
$673$	−2.66322	+	4.61284i	−0.102660	+	0.177812i	−0.912780	−	0.408452i	$-0.866069\pi$
$673$	−2.66322	+	4.61284i	−0.102660	+	0.177812i	0.810120	+	0.586264i	$0.199402\pi$
$674$	−17.5749	−	6.80333i	−0.676961	−	0.262054i
$675$		0			0
$676$	−1.00457	−	21.4875i	−0.0386374	−	0.826442i
$677$	−2.55792	+	19.4294i	−0.0983090	+	0.746731i	0.869301	+	0.494283i	$0.164569\pi$
$677$	−2.55792	+	19.4294i	−0.0983090	+	0.746731i	−0.967610	+	0.252448i	$0.918764\pi$
$678$		0			0
$679$	−2.23173	+	8.32893i	−0.0856460	+	0.319635i
$680$	−32.1126	−	6.23328i	−1.23146	−	0.239036i
$681$		0			0
$682$	−27.9664	+	51.1630i	−1.07089	+	1.95913i
$683$	−19.9067	+	8.24564i	−0.761710	+	0.315510i	−0.729509	−	0.683971i	$-0.760251\pi$
$683$	−19.9067	+	8.24564i	−0.761710	+	0.315510i	−0.0322004	+	0.999481i	$0.510251\pi$
$684$		0			0
$685$	−17.1940	+	41.5100i	−0.656950	+	1.58602i
$686$	−18.5092	−	1.99820i	−0.706683	−	0.0762917i
$687$		0			0
$688$	−28.6612	−	18.0116i	−1.09270	−	0.686687i
$689$	−3.17476	−	5.49885i	−0.120949	−	0.209489i
$690$		0			0
$691$	22.8987	−	17.5708i	0.871106	−	0.668423i	−0.0732626	−	0.997313i	$-0.523341\pi$
$691$	22.8987	−	17.5708i	0.871106	−	0.668423i	0.944368	+	0.328890i	$0.106674\pi$
$692$	−16.0928	−	34.2351i	−0.611757	−	1.30142i
$693$		0			0
$694$	−7.72047	+	0.180373i	−0.293065	+	0.00684687i
$695$	−5.56642	+	1.49152i	−0.211146	+	0.0565765i
$696$		0			0
$697$	−20.8948	−	5.59874i	−0.791447	−	0.212067i
$698$	45.5243	+	11.0653i	1.72312	+	0.418830i
$699$		0			0
$700$	−0.794789	+	0.253293i	−0.0300402	+	0.00957359i
$701$	−17.0186	+	41.0865i	−0.642784	+	1.55182i	0.180125	+	0.983644i	$0.442350\pi$
$701$	−17.0186	+	41.0865i	−0.642784	+	1.55182i	−0.822909	+	0.568174i	$0.807650\pi$
$702$		0			0
$703$			47.3226i			1.78481i
$704$	−24.5584	−	24.1081i	−0.925579	−	0.908607i
$705$		0			0
$706$	7.38925	+	47.5212i	0.278098	+	1.78848i
$707$	1.33346	+	10.1286i	0.0501499	+	0.380926i
$708$		0			0
$709$	−12.8554	−	1.69244i	−0.482794	−	0.0635610i	−0.114799	−	0.993389i	$-0.536622\pi$
$709$	−12.8554	−	1.69244i	−0.482794	−	0.0635610i	−0.367995	+	0.929828i	$0.619956\pi$
$710$	9.24751	+	8.82528i	0.347053	+	0.331207i
$711$		0			0
$712$	8.26406	+	2.76270i	0.309709	+	0.103537i
$713$	−5.81227	−	21.6917i	−0.217671	−	0.812360i
$714$		0			0
$715$	8.40454	−	10.9530i	0.314312	−	0.409619i
$716$	8.92647	+	6.20944i	0.333598	+	0.232058i
$717$		0			0
$718$	−26.1800	−	2.82632i	−0.977028	−	0.105477i
$719$			18.1643i			0.677416i	0.940892	+	0.338708i	$0.109990\pi$
$719$			18.1643i			0.677416i	−0.940892	+	0.338708i	$0.890010\pi$
$720$		0			0
$721$		−	17.0078i		−	0.633404i
$722$	5.22176	−	48.3687i	0.194334	−	1.80010i
$723$		0			0
$724$	−0.458677	−	2.55518i	−0.0170466	−	0.0949624i
$725$	1.11058	−	1.44734i	0.0412461	−	0.0537529i
$726$		0			0
$727$	10.6602	+	39.7845i	0.395366	+	1.47552i	0.821157	+	0.570703i	$0.193329\pi$
$727$	10.6602	+	39.7845i	0.395366	+	1.47552i	−0.425791	+	0.904822i	$0.640004\pi$
$728$	−2.82080	+	3.24668i	−0.104546	+	0.120330i
$729$		0			0
$730$	−4.29288	+	4.49827i	−0.158887	+	0.166488i
$731$	−45.2979	−	5.96358i	−1.67540	−	0.220571i
$732$		0			0
$733$	3.65188	+	27.7388i	0.134885	+	1.02456i	0.916285	+	0.400526i	$0.131173\pi$
$733$	3.65188	+	27.7388i	0.134885	+	1.02456i	−0.781400	+	0.624030i	$0.785494\pi$
$734$	2.42722	−	0.377418i	0.0895904	−	0.0139307i
$735$		0			0
$736$	13.2530	+	0.186961i	0.488512	+	0.00689146i
$737$			22.7350i			0.837456i
$738$		0			0
$739$	−10.8083	+	26.0935i	−0.397590	+	0.959866i	0.590646	+	0.806931i	$0.298873\pi$
$739$	−10.8083	+	26.0935i	−0.397590	+	0.959866i	−0.988236	+	0.152936i	$0.951127\pi$
$740$	−24.6497	−	12.7354i	−0.906141	−	0.468161i
$741$		0			0
$742$	1.43683	−	5.91131i	0.0527477	−	0.217011i
$743$	20.2082	+	5.41476i	0.741366	+	0.198648i	0.609685	−	0.792644i	$-0.291296\pi$
$743$	20.2082	+	5.41476i	0.741366	+	0.198648i	0.131681	+	0.991292i	$0.457963\pi$
$744$		0			0
$745$	−34.8811	+	9.34636i	−1.27794	+	0.342424i
$746$	1.03768	+	44.4156i	0.0379922	+	1.62617i
$747$		0			0
$748$	−43.6962	−	15.7517i	−1.59769	−	0.575937i
$749$	7.66382	−	5.88066i	0.280030	−	0.214875i
$750$		0			0
$751$	−5.34187	−	9.25238i	−0.194927	−	0.337624i	0.751949	−	0.659221i	$-0.229114\pi$
$751$	−5.34187	−	9.25238i	−0.194927	−	0.337624i	−0.946877	+	0.321597i	$0.895780\pi$
$752$	−19.9615	−	28.1370i	−0.727922	−	1.02605i
$753$		0			0
$754$	1.00959	−	9.35172i	0.0367670	−	0.340570i
$755$	−9.76935	+	23.5853i	−0.355543	+	0.858356i
$756$		0			0
$757$	8.88251	−	3.67926i	0.322840	−	0.133725i	−0.215377	−	0.976531i	$-0.569098\pi$
$757$	8.88251	−	3.67926i	0.322840	−	0.133725i	0.538217	+	0.842806i	$0.319098\pi$
$758$	33.4639	+	18.2918i	1.21546	+	0.664389i
$759$		0			0
$760$	36.9285	+	24.4285i	1.33954	+	0.886115i
$761$	−3.39875	+	12.6843i	−0.123204	+	0.459805i	−0.999769	−	0.0214785i	$-0.993163\pi$
$761$	−3.39875	+	12.6843i	−0.123204	+	0.459805i	0.876565	+	0.481284i	$0.159829\pi$
$762$		0			0
$763$	−0.925995	+	7.03363i	−0.0335233	+	0.254634i
$764$	28.6045	+	26.0494i	1.03487	+	0.942433i
$765$		0			0
$766$	5.57228	−	14.3948i	0.201335	−	0.520104i
$767$	2.20310	−	3.81588i	0.0795494	−	0.137784i
$768$		0			0
$769$	−10.0871	−	17.4713i	−0.363750	−	0.630033i	0.624825	−	0.780765i	$-0.285170\pi$
$769$	−10.0871	−	17.4713i	−0.363750	−	0.630033i	−0.988575	+	0.150732i	$0.951837\pi$
$770$	13.0703	−	2.03235i	0.471022	−	0.0732409i
$771$		0			0
$772$	−27.7686	+	8.84966i	−0.999414	+	0.318506i
$773$	29.7330	−	12.3158i	1.06942	−	0.442969i	0.222635	−	0.974902i	$-0.428534\pi$
$773$	29.7330	−	12.3158i	1.06942	−	0.442969i	0.846786	+	0.531933i	$0.178534\pi$
$774$		0			0
$775$	−2.78500	−	2.78500i	−0.100040	−	0.100040i
$776$	1.46063	−	23.9846i	0.0524336	−	0.860998i
$777$		0			0
$778$	3.74775	−	2.28211i	0.134363	−	0.0818174i
$779$	23.2292	+	17.8244i	0.832274	+	0.638626i
$780$		0			0
$781$	11.0495	+	14.4000i	0.395382	+	0.515272i
$782$	16.3633	−	7.23015i	0.585150	−	0.258550i
$783$		0			0
$784$	23.7752	−	2.22792i	0.849113	−	0.0795685i
$785$	15.8575	−	27.4659i	0.565977	−	0.980300i
$786$		0			0
$787$	−2.70462	−	20.5437i	−0.0964095	−	0.732303i	−0.969560	−	0.244853i	$-0.921260\pi$
$787$	−2.70462	−	20.5437i	−0.0964095	−	0.732303i	0.873151	−	0.487450i	$-0.162073\pi$
$788$	3.53501	+	19.6927i	0.125930	+	0.701524i
$789$		0			0
$790$	−26.1060	−	14.2699i	−0.928809	−	0.507700i
$791$	−5.58176	−	5.58176i	−0.198464	−	0.198464i
$792$		0			0
$793$	0.356870	−	0.356870i	0.0126728	−	0.0126728i
$794$	32.1016	−	9.41049i	1.13924	−	0.333966i
$795$		0			0
$796$	43.9512	−	28.1910i	1.55781	−	0.999203i
$797$	−25.3840	+	3.34187i	−0.899148	+	0.118375i	−0.565909	−	0.824467i	$-0.691475\pi$
$797$	−25.3840	+	3.34187i	−0.899148	+	0.118375i	−0.333239	+	0.942843i	$0.608141\pi$
$798$		0			0
$799$	−40.3247	−	23.2815i	−1.42659	−	0.823640i
$800$	2.02936	−	1.13379i	0.0717486	−	0.0400854i
$801$		0			0
$802$	8.05588	−	20.8106i	0.284463	−	0.734849i
$803$	−7.00458	+	5.37480i	−0.247186	+	0.189673i
$804$		0			0
$805$	−3.10131	+	4.04171i	−0.109307	+	0.142452i
$806$	−19.7323	−	4.79624i	−0.695042	−	0.168940i
$807$		0			0
$808$	−9.27571	−	26.9156i	−0.326318	−	0.946888i
$809$	−10.6460	+	10.6460i	−0.374293	+	0.374293i	−0.869038	−	0.494745i	$-0.835261\pi$
$809$	−10.6460	+	10.6460i	−0.374293	+	0.374293i	0.494745	+	0.869038i	$0.335261\pi$
$810$		0			0
$811$	−4.07895	−	9.84747i	−0.143231	−	0.345791i	0.835942	−	0.548818i	$-0.184922\pi$
$811$	−4.07895	−	9.84747i	−0.143231	−	0.345791i	−0.979173	+	0.203027i	$0.934922\pi$
$812$	6.88560	−	5.81398i	0.241637	−	0.204031i
$813$		0			0
$814$	−31.8067	−	23.2463i	−1.11483	−	0.814784i
$815$	5.65239	−	3.26341i	0.197994	−	0.114312i
$816$		0			0
$817$	53.5567	+	30.9210i	1.87371	+	1.08179i
$818$	−15.2038	−	34.4092i	−0.531588	−	1.20309i
$819$		0			0
$820$	−15.5359	+	7.30292i	−0.542537	+	0.255029i
$821$	31.0074	+	4.08220i	1.08217	+	0.142470i	0.650457	−	0.759543i	$-0.274577\pi$
$821$	31.0074	+	4.08220i	1.08217	+	0.142470i	0.431709	+	0.902013i	$0.357911\pi$
$822$		0			0
$823$	5.03815	+	1.34997i	0.175619	+	0.0470569i	0.345557	−	0.938398i	$-0.387690\pi$
$823$	5.03815	+	1.34997i	0.175619	+	0.0470569i	−0.169938	+	0.985455i	$0.554357\pi$
$824$	9.46142	+	46.4418i	0.329604	+	1.61788i
$825$		0			0
$826$	4.05107	−	1.18756i	0.140955	−	0.0413205i
$827$	7.61758	+	18.3905i	0.264889	+	0.639499i	0.999228	−	0.0392837i	$-0.0125076\pi$
$827$	7.61758	+	18.3905i	0.264889	+	0.639499i	−0.734339	+	0.678783i	$0.762508\pi$
$828$		0			0
$829$	39.0063	+	16.1569i	1.35475	+	0.561154i	0.937609	−	0.347690i	$-0.113034\pi$
$829$	39.0063	+	16.1569i	1.35475	+	0.561154i	0.417136	+	0.908844i	$0.363034\pi$
$830$	−5.16898	+	4.16167i	−0.179418	+	0.144454i
$831$		0			0
$832$	5.89639	−	10.4346i	0.204421	−	0.361756i
$833$	27.9121	−	16.1150i	0.967095	−	0.558353i
$834$		0			0
$835$	−4.74374	−	6.18216i	−0.164164	−	0.213942i
$836$	46.4837	+	42.3315i	1.60767	+	1.46406i
$837$		0			0
$838$	17.3752	−	18.2065i	0.600218	−	0.628935i
$839$	5.11950	+	19.1062i	0.176745	+	0.659620i	0.996248	+	0.0865457i	$0.0275829\pi$
$839$	5.11950	+	19.1062i	0.176745	+	0.659620i	−0.819503	+	0.573075i	$0.805750\pi$
$840$		0			0
$841$	2.40471	−	8.97450i	0.0829210	−	0.309465i
$842$	−7.67910	−	12.6109i	−0.264639	−	0.434600i
$843$		0			0
$844$	−15.3539	−	1.29558i	−0.528502	−	0.0445959i
$845$	−21.2867	−	8.81722i	−0.732283	−	0.303322i
$846$		0			0
$847$	7.61725			0.261732
$848$	−0.634982	+	16.9408i	−0.0218054	+	0.581751i
$849$		0			0
$850$	1.85134	−	2.53310i	0.0635006	−	0.0868845i
$851$	15.0434	−	1.98051i	0.515683	−	0.0678909i
$852$		0			0
$853$	4.95062	−	37.6037i	0.169506	−	1.28753i	−0.669258	−	0.743030i	$-0.733388\pi$
$853$	4.95062	−	37.6037i	0.169506	−	1.28753i	0.838764	−	0.544496i	$-0.183279\pi$
$854$	0.483408	−	0.0112938i	0.0165419	−	0.000386467i
$855$		0			0
$856$	−17.6556	+	20.3212i	−0.603455	+	0.694564i
$857$	27.0897	−	7.25866i	0.925366	−	0.247951i	0.235488	−	0.971877i	$-0.424331\pi$
$857$	27.0897	−	7.25866i	0.925366	−	0.247951i	0.689878	+	0.723926i	$0.257664\pi$
$858$		0			0
$859$	−26.3697	−	20.2342i	−0.899722	−	0.690381i	0.0515707	−	0.998669i	$-0.483577\pi$
$859$	−26.3697	−	20.2342i	−0.899722	−	0.690381i	−0.951293	+	0.308288i	$0.900244\pi$
$860$	−30.5194	+	19.5756i	−1.04070	+	0.667522i
$861$		0			0
$862$	−36.5484	+	29.4259i	−1.24484	+	1.00225i
$863$	33.6814			1.14653			0.573264	−	0.819371i	$-0.305677\pi$
$863$	33.6814			1.14653			0.573264	+	0.819371i	$0.305677\pi$
$864$		0			0
$865$	−40.5186			−1.37767
$866$	14.2798	−	11.4970i	0.485247	−	0.390684i
$867$		0			0
$868$	−10.5042	−	16.3766i	−0.356535	−	0.555858i
$869$	−33.5152	−	25.7171i	−1.13693	−	0.872394i
$870$		0			0
$871$	−7.64817	+	2.04932i	−0.259148	+	0.0694386i
$872$	−1.38426	−	19.7213i	−0.0468769	−	0.667847i
$873$		0			0
$874$	−24.2076	+	0.565562i	−0.818835	+	0.0191304i
$875$	−1.53563	+	11.6642i	−0.0519137	+	0.394323i
$876$		0			0
$877$	31.7025	−	4.17372i	1.07052	−	0.140936i	0.425390	−	0.905010i	$-0.360137\pi$
$877$	31.7025	−	4.17372i	1.07052	−	0.140936i	0.645129	+	0.764074i	$0.276804\pi$
$878$	−10.5556	+	14.4427i	−0.356236	+	0.487419i
$879$		0			0
$880$	−34.5595	+	12.8206i	−1.16500	+	0.432182i
$881$	1.81478			0.0611416			0.0305708	−	0.999533i	$-0.490267\pi$
$881$	1.81478			0.0611416			0.0305708	+	0.999533i	$0.490267\pi$
$882$		0			0
$883$	−40.2761	−	16.6829i	−1.35540	−	0.561425i	−0.417610	−	0.908627i	$-0.637132\pi$
$883$	−40.2761	−	16.6829i	−1.35540	−	0.561425i	−0.937791	+	0.347201i	$0.887132\pi$
$884$	1.36018	−	16.1194i	0.0457480	−	0.542155i
$885$		0			0
$886$	6.30448	+	10.3534i	0.211803	+	0.347830i
$887$	3.06187	−	11.4271i	0.102808	−	0.383683i	−0.895280	−	0.445505i	$-0.853024\pi$
$887$	3.06187	−	11.4271i	0.102808	−	0.383683i	0.998087	+	0.0618215i	$0.0196910\pi$
$888$		0			0
$889$	4.31185	+	16.0920i	0.144615	+	0.539710i
$890$	6.44363	−	6.75192i	0.215991	−	0.226325i
$891$		0			0
$892$	−23.3301	+	25.6185i	−0.781148	+	0.857770i
$893$	38.3673	+	50.0013i	1.28391	+	1.67323i
$894$		0			0
$895$	10.0866	−	5.82348i	0.337156	−	0.194657i
$896$	10.9890	−	3.33212i	0.367117	−	0.111318i
$897$		0			0
$898$	15.9192	−	12.8169i	0.531230	−	0.427706i
$899$	39.3109	+	16.2831i	1.31109	+	0.543073i
$900$		0			0
$901$	8.75625	+	21.1395i	0.291713	+	0.704258i
$902$	−23.3912	+	6.85705i	−0.778840	+	0.228315i
$903$		0			0
$904$	18.3468	+	12.1365i	0.610204	+	0.403655i
$905$	−2.68586	−	0.719675i	−0.0892811	−	0.0239228i
$906$		0			0
$907$	6.90261	+	0.908745i	0.229197	+	0.0301744i	0.244250	−	0.969712i	$-0.421458\pi$
$907$	6.90261	+	0.908745i	0.229197	+	0.0301744i	−0.0150527	+	0.999887i	$0.504792\pi$
$908$	−21.8691	−	46.5233i	−0.725752	−	1.54393i
$909$		0			0
$910$	1.86184	+	4.21372i	0.0617195	+	0.139683i
$911$	−4.22132	−	2.43718i	−0.139859	−	0.0807474i	0.428438	−	0.903571i	$-0.359064\pi$
$911$	−4.22132	−	2.43718i	−0.139859	−	0.0807474i	−0.568297	+	0.822824i	$0.692397\pi$
$912$		0			0
$913$	−8.16037	+	4.71139i	−0.270069	+	0.155924i
$914$	47.8886	+	34.9999i	1.58401	+	1.15770i
$915$		0			0
$916$	−4.04024	−	4.78492i	−0.133493	−	0.158098i
$917$	6.80881	+	16.4379i	0.224847	+	0.542828i
$918$		0			0
$919$	23.9876	−	23.9876i	0.791278	−	0.791278i	−0.190424	−	0.981702i	$-0.560986\pi$
$919$	23.9876	−	23.9876i	0.791278	−	0.791278i	0.981702	+	0.190424i	$0.0609862\pi$
$920$	6.22010	−	12.7616i	0.205071	−	0.420738i
$921$		0			0
$922$	−51.2672	−	12.4612i	−1.68840	−	0.410389i
$923$	−3.84822	+	5.01510i	−0.126666	+	0.165074i
$924$		0			0
$925$	2.11123	−	1.62000i	0.0694169	−	0.0532654i
$926$	−3.62317	+	9.35967i	−0.119065	+	0.307578i
$927$		0			0
$928$	−15.5676	+	19.7062i	−0.511032	+	0.646888i
$929$	−0.758151	−	0.437718i	−0.0248741	−	0.0143611i	0.487511	−	0.873117i	$-0.337905\pi$
$929$	−0.758151	−	0.437718i	−0.0248741	−	0.0143611i	−0.512385	+	0.858756i	$0.671238\pi$
$930$		0			0
$931$	−43.2518	+	5.69420i	−1.41752	+	0.186620i
$932$	−32.0462	−	49.9618i	−1.04971	−	1.63655i
$933$		0			0
$934$	−16.8979	+	4.95359i	−0.552918	+	0.162086i
$935$	−35.1795	+	35.1795i	−1.15049	+	1.15049i
$936$		0			0
$937$	24.9448	+	24.9448i	0.814909	+	0.814909i	0.985365	−	0.170456i	$-0.0545240\pi$
$937$	24.9448	+	24.9448i	0.814909	+	0.814909i	−0.170456	+	0.985365i	$0.554524\pi$
$938$	−6.65659	−	3.63859i	−0.217345	−	0.118804i
$939$		0			0
$940$	−36.3703	+	6.52879i	−1.18627	+	0.212946i
$941$	−6.27508	−	47.6639i	−0.204562	−	1.55380i	−0.718227	−	0.695809i	$-0.755046\pi$
$941$	−6.27508	−	47.6639i	−0.204562	−	1.55380i	0.513665	−	0.857991i	$-0.328287\pi$
$942$		0			0
$943$	4.69405	−	8.13034i	0.152859	−	0.264760i
$944$	−10.4013	+	5.49638i	−0.338533	+	0.178892i
$945$		0			0
$946$	−47.0915	+	20.8075i	−1.53108	+	0.676510i
$947$	4.50923	+	5.87654i	0.146530	+	0.190962i	0.860852	−	0.508856i	$-0.169931\pi$
$947$	4.50923	+	5.87654i	0.146530	+	0.190962i	−0.714322	+	0.699817i	$0.753265\pi$
$948$		0			0
$949$	−2.43950	−	1.87189i	−0.0791894	−	0.0607642i
$950$	−3.62723	+	2.20872i	−0.117683	+	0.0716603i
$951$		0			0
$952$	11.6052	−	10.2729i	0.376127	−	0.332945i
$953$	−20.7163	−	20.7163i	−0.671065	−	0.671065i	0.286896	−	0.957962i	$-0.407377\pi$
$953$	−20.7163	−	20.7163i	−0.671065	−	0.671065i	−0.957962	+	0.286896i	$0.907377\pi$
$954$		0			0
$955$	38.2849	−	15.8581i	1.23887	−	0.513157i
$956$	2.65376	+	8.32702i	0.0858288	+	0.269315i
$957$		0			0
$958$	−50.2010	+	7.80594i	−1.62192	+	0.252198i
$959$	−10.6439	−	18.4357i	−0.343708	−	0.595320i
$960$		0			0
$961$	30.4308	−	52.7076i	0.981637	−	1.70025i
$962$	4.95313	−	12.7953i	0.159695	−	0.412538i
$963$		0			0
$964$	−10.4371	+	11.4609i	−0.336157	+	0.369131i
$965$	−4.07464	+	30.9499i	−0.131167	+	0.996314i
$966$		0			0
$967$	4.54228	−	16.9520i	0.146070	−	0.545140i	−0.853635	−	0.520871i	$-0.825607\pi$
$967$	4.54228	−	16.9520i	0.146070	−	0.545140i	0.999705	−	0.0242696i	$-0.00772602\pi$
$968$	−20.7998	+	4.23746i	−0.668531	+	0.136197i
$969$		0			0
$970$	−22.5840	−	12.3447i	−0.725127	−	0.396365i
$971$	28.6212	−	11.8553i	0.918497	−	0.380454i	0.127194	−	0.991878i	$-0.459403\pi$
$971$	28.6212	−	11.8553i	0.918497	−	0.380454i	0.791303	+	0.611424i	$0.209403\pi$
$972$		0			0
$973$	1.04487	−	2.52254i	0.0334971	−	0.0808691i
$974$	0.369949	−	3.42680i	0.0118539	−	0.109802i
$975$		0			0
$976$	−1.31372	+	0.299758i	−0.0420511	+	0.00959502i
$977$	−2.69148	−	4.66178i	−0.0861081	−	0.149144i	0.819755	−	0.572715i	$-0.194110\pi$
$977$	−2.69148	−	4.66178i	−0.0861081	−	0.149144i	−0.905863	+	0.423571i	$0.860776\pi$
$978$		0			0
$979$	10.5139	−	8.06760i	0.336026	−	0.257842i
$980$	8.67378	−	24.0616i	0.277074	−	0.768621i
$981$		0			0
$982$	0.237317	+	10.1578i	0.00757308	+	0.324149i
$983$	−34.5510	+	9.25791i	−1.10200	+	0.295281i	−0.763581	−	0.645712i	$-0.776561\pi$
$983$	−34.5510	+	9.25791i	−1.10200	+	0.295281i	−0.338424	+	0.940994i	$0.609894\pi$
$984$		0			0
$985$	20.6999	+	5.54652i	0.659554	+	0.176727i
$986$	−8.00576	+	32.9368i	−0.254955	+	1.04892i
$987$		0			0
$988$	−10.0505	+	19.4531i	−0.319749	+	0.618884i
$989$	7.58810	−	18.3193i	0.241288	−	0.582520i
$990$		0			0
$991$			24.3967i			0.774986i	0.921873	+	0.387493i	$0.126659\pi$
$991$			24.3967i			0.774986i	−0.921873	+	0.387493i	$0.873341\pi$
$992$	37.7932	+	38.8747i	1.19993	+	1.23427i
$993$		0			0
$994$	−5.98456	+	0.930562i	−0.189819	+	0.0295156i
$995$	−7.30009	−	55.4497i	−0.231428	−	1.75787i
$996$		0			0
$997$	38.2846	+	5.04027i	1.21249	+	0.159627i	0.709524	−	0.704682i	$-0.248910\pi$
$997$	38.2846	+	5.04027i	1.21249	+	0.159627i	0.502962	+	0.864308i	$0.332243\pi$
$998$	34.5640	−	36.2176i	1.09410	−	1.14645i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.35.13		368
3.2	odd	2		288.2.bf.a.227.34	yes	368
9.4	even	3		288.2.bf.a.131.45	yes	368
9.5	odd	6	inner	864.2.bn.a.611.2		368
32.11	odd	8	inner	864.2.bn.a.683.2		368
96.11	even	8		288.2.bf.a.11.45	✓	368
288.139	odd	24		288.2.bf.a.203.34	yes	368
288.203	even	24	inner	864.2.bn.a.395.13		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.45	✓	368	96.11	even	8
288.2.bf.a.131.45	yes	368	9.4	even	3
288.2.bf.a.203.34	yes	368	288.139	odd	24
288.2.bf.a.227.34	yes	368	3.2	odd	2
864.2.bn.a.35.13		368	1.1	even	1	trivial
864.2.bn.a.395.13		368	288.203	even	24	inner
864.2.bn.a.611.2		368	9.5	odd	6	inner
864.2.bn.a.683.2		368	32.11	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.886889 - 1.10156i) q^{2} +(-0.426855 + 1.95392i) q^{4} +(1.69953 + 1.30410i) q^{5} +(-0.980387 + 0.262694i) q^{7} +(2.53092 - 1.26270i) q^{8} +(-0.0707598 - 3.02872i) q^{10} +(0.561489 - 4.26493i) q^{11} +(1.48535 - 0.195551i) q^{13} +(1.15887 + 0.846971i) q^{14} +(-3.63559 - 1.66808i) q^{16} -5.39882 q^{17} +(6.75131 + 2.79649i) q^{19} +(-3.27355 + 2.76408i) q^{20} +(-5.19604 + 3.16401i) q^{22} +(0.606428 - 2.26322i) q^{23} +(-0.106358 - 0.396933i) q^{25} +(-1.53275 - 1.46277i) q^{26} +(-0.0947992 - 2.02773i) q^{28} +(2.70258 + 3.52207i) q^{29} +(8.30037 - 4.79222i) q^{31} +(1.38688 + 5.48421i) q^{32} +(4.78816 + 5.94711i) q^{34} +(-2.00877 - 0.832061i) q^{35} +(2.47820 + 5.98289i) q^{37} +(-2.90718 - 9.91713i) q^{38} +(5.94807 + 1.15456i) q^{40} +(3.87025 + 1.03703i) q^{41} +(8.39033 + 1.10461i) q^{43} +(8.09365 + 2.91761i) q^{44} +(-3.03090 + 1.33921i) q^{46} +(7.46917 + 4.31233i) q^{47} +(-5.17003 + 2.98492i) q^{49} +(-0.342916 + 0.469195i) q^{50} +(-0.251941 + 2.98573i) q^{52} +(-1.62188 - 3.91557i) q^{53} +(6.51614 - 6.51614i) q^{55} +(-2.14958 + 1.90280i) q^{56} +(1.48287 - 6.10073i) q^{58} +(1.79040 - 2.33330i) q^{59} +(0.267258 - 0.205074i) q^{61} +(-12.6404 - 4.89316i) q^{62} +(4.81116 - 6.39162i) q^{64} +(2.77942 + 1.60470i) q^{65} +(-5.23988 + 0.689843i) q^{67} +(2.30451 - 10.5489i) q^{68} +(0.864997 + 2.95072i) q^{70} +(-2.98357 + 2.98357i) q^{71} +(-1.45130 - 1.45130i) q^{73} +(4.39261 - 8.03604i) q^{74} +(-8.34593 + 11.9978i) q^{76} +(0.569895 + 4.32878i) q^{77} +(4.91023 - 8.50477i) q^{79} +(-4.00346 - 7.57610i) q^{80} +(-2.29014 - 5.18303i) q^{82} +(-1.33347 - 1.73781i) q^{83} +(-9.17546 - 7.04058i) q^{85} +(-6.22451 - 10.2221i) q^{86} +(-3.96426 - 11.5032i) q^{88} +(2.17841 + 2.17841i) q^{89} +(-1.40485 + 0.581909i) q^{91} +(4.16329 + 2.15098i) q^{92} +(-1.87405 - 12.0523i) q^{94} +(7.82717 + 13.5571i) q^{95} +(4.24778 - 7.35737i) q^{97} +(7.87330 + 3.04779i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 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

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