LMFDB - Embedded newform 810.2.s.a.557.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.13
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.00216 + 1.99892i) q^{5} +(-0.0561590 - 0.120433i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.96745 + 1.06261i) q^{10} +(1.11291 + 1.32632i) q^{11} +(-1.22280 - 1.74633i) q^{13} +(0.0230750 - 0.130865i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(1.68152 + 6.27550i) q^{17} +(-6.47014 + 3.73554i) q^{19} +(-2.22113 - 0.258049i) q^{20} +(0.150900 + 1.72480i) q^{22} +(1.60127 + 0.746684i) q^{23} +(-2.99136 - 4.00646i) q^{25} -2.13188i q^{26} +(0.0939629 - 0.0939629i) q^{28} +(0.637912 + 3.61778i) q^{29} +(6.03428 - 2.19630i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.22206 + 6.10507i) q^{34} +(0.297017 + 0.00843582i) q^{35} +(-9.06304 + 2.42843i) q^{37} +(-7.44264 - 0.651147i) q^{38} +(-1.67143 - 1.48537i) q^{40} +(-5.12420 - 0.903535i) q^{41} +(-0.171770 + 1.96334i) q^{43} +(-0.865692 + 1.49942i) q^{44} +(0.883403 + 1.53010i) q^{46} +(-2.27592 + 1.06128i) q^{47} +(4.48816 - 5.34878i) q^{49} +(-0.152367 - 4.99768i) q^{50} +(1.22280 - 1.74633i) q^{52} +(-4.81146 - 4.81146i) q^{53} +(-3.76652 + 0.895445i) q^{55} +(0.130865 - 0.0230750i) q^{56} +(-1.55253 + 3.32940i) q^{58} +(2.47402 + 2.07595i) q^{59} +(10.3604 + 3.77087i) q^{61} +(6.20274 + 1.66202i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(4.71622 - 0.694171i) q^{65} +(7.08159 - 4.95858i) q^{67} +(-5.32193 + 3.72646i) q^{68} +(0.238464 + 0.177272i) q^{70} +(8.58515 + 4.95664i) q^{71} +(9.62186 + 2.57817i) q^{73} +(-8.81690 - 3.20909i) q^{74} +(-5.72317 - 4.80231i) q^{76} +(0.0972329 - 0.208517i) q^{77} +(-0.0585881 + 0.0103307i) q^{79} +(-0.517184 - 2.17544i) q^{80} +(-3.67925 - 3.67925i) q^{82} +(-2.58753 + 3.69538i) q^{83} +(-14.2294 - 2.92782i) q^{85} +(-1.26683 + 1.50975i) q^{86} +(-1.56917 + 0.731715i) q^{88} +(7.54680 + 13.0714i) q^{89} +(-0.141646 + 0.245338i) q^{91} +(-0.153987 + 1.76008i) q^{92} +(-2.47305 - 0.436065i) q^{94} +(-0.982942 - 16.6769i) q^{95} +(-1.11399 - 0.0974611i) q^{97} +(6.74442 - 1.80716i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−1.00216	+	1.99892i	−0.448178	+	0.893944i
$5$	−1.00216	+	1.99892i	−0.448178	+	0.893944i
$6$		0			0
$7$	−0.0561590	−	0.120433i	−0.0212261	−	0.0455196i	0.895409	−	0.445245i	$-0.146883\pi$
$7$	−0.0561590	−	0.120433i	−0.0212261	−	0.0455196i	−0.916635	+	0.399725i	$0.869106\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−1.96745	+	1.06261i	−0.622163	+	0.336025i
$11$	1.11291	+	1.32632i	0.335556	+	0.399900i	0.907267	−	0.420555i	$-0.138165\pi$
$11$	1.11291	+	1.32632i	0.335556	+	0.399900i	−0.571711	+	0.820455i	$0.693720\pi$
$12$		0			0
$13$	−1.22280	−	1.74633i	−0.339143	−	0.484346i	0.612964	−	0.790110i	$-0.289977\pi$
$13$	−1.22280	−	1.74633i	−0.339143	−	0.484346i	−0.952107	+	0.305765i	$0.901088\pi$
$14$	0.0230750	−	0.130865i	0.00616705	−	0.0349751i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	1.68152	+	6.27550i	0.407827	+	1.52203i	0.798781	+	0.601622i	$0.205479\pi$
$17$	1.68152	+	6.27550i	0.407827	+	1.52203i	−0.390953	+	0.920411i	$0.627855\pi$
$18$		0			0
$19$	−6.47014	+	3.73554i	−1.48435	+	0.856991i	−0.999842	−	0.0177955i	$-0.994335\pi$
$19$	−6.47014	+	3.73554i	−1.48435	+	0.856991i	−0.484509	+	0.874786i	$0.661002\pi$
$20$	−2.22113	−	0.258049i	−0.496659	−	0.0577015i
$21$		0			0
$22$	0.150900	+	1.72480i	0.0321720	+	0.367728i
$23$	1.60127	+	0.746684i	0.333888	+	0.155694i	0.582330	−	0.812952i	$-0.302141\pi$
$23$	1.60127	+	0.746684i	0.333888	+	0.155694i	−0.248443	+	0.968647i	$0.579919\pi$
$24$		0			0
$25$	−2.99136	−	4.00646i	−0.598272	−	0.801293i
$26$		−	2.13188i		−	0.418096i
$27$		0			0
$28$	0.0939629	−	0.0939629i	0.0177573	−	0.0177573i
$29$	0.637912	+	3.61778i	0.118457	+	0.671805i	0.984980	+	0.172667i	$0.0552386\pi$
$29$	0.637912	+	3.61778i	0.118457	+	0.671805i	−0.866523	+	0.499137i	$0.833650\pi$
$30$		0			0
$31$	6.03428	−	2.19630i	1.08379	−	0.394467i	0.262473	−	0.964939i	$-0.415462\pi$
$31$	6.03428	−	2.19630i	1.08379	−	0.394467i	0.821317	+	0.570472i	$0.193240\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$		0			0
$34$	−2.22206	+	6.10507i	−0.381081	+	1.04701i
$35$	0.297017	+	0.00843582i	0.0502050	+	0.00142591i
$36$		0			0
$37$	−9.06304	+	2.42843i	−1.48995	+	0.399232i	−0.909722	−	0.415218i	$-0.863705\pi$
$37$	−9.06304	+	2.42843i	−1.48995	+	0.399232i	−0.580233	+	0.814451i	$0.697039\pi$
$38$	−7.44264	−	0.651147i	−1.20736	−	0.105630i
$39$		0			0
$40$	−1.67143	−	1.48537i	−0.264276	−	0.234857i
$41$	−5.12420	−	0.903535i	−0.800266	−	0.141109i	−0.241464	−	0.970410i	$-0.577628\pi$
$41$	−5.12420	−	0.903535i	−0.800266	−	0.141109i	−0.558802	+	0.829301i	$0.688739\pi$
$42$		0			0
$43$	−0.171770	+	1.96334i	−0.0261947	+	0.299407i	0.971785	+	0.235869i	$0.0757938\pi$
$43$	−0.171770	+	1.96334i	−0.0261947	+	0.299407i	−0.997979	+	0.0635374i	$0.979762\pi$
$44$	−0.865692	+	1.49942i	−0.130508	+	0.226047i
$45$		0			0
$46$	0.883403	+	1.53010i	0.130251	+	0.225601i
$47$	−2.27592	+	1.06128i	−0.331977	+	0.154803i	−0.581458	−	0.813576i	$-0.697518\pi$
$47$	−2.27592	+	1.06128i	−0.331977	+	0.154803i	0.249481	+	0.968380i	$0.419740\pi$
$48$		0			0
$49$	4.48816	−	5.34878i	0.641166	−	0.764112i
$50$	−0.152367	−	4.99768i	−0.0215480	−	0.706778i
$51$		0			0
$52$	1.22280	−	1.74633i	0.169571	−	0.242173i
$53$	−4.81146	−	4.81146i	−0.660905	−	0.660905i	0.294688	−	0.955593i	$-0.404784\pi$
$53$	−4.81146	−	4.81146i	−0.660905	−	0.660905i	−0.955593	+	0.294688i	$0.904784\pi$
$54$		0			0
$55$	−3.76652	+	0.895445i	−0.507877	+	0.120742i
$56$	0.130865	−	0.0230750i	0.0174875	−	0.00308353i
$57$		0			0
$58$	−1.55253	+	3.32940i	−0.203857	+	0.437172i
$59$	2.47402	+	2.07595i	0.322090	+	0.270266i	0.789468	−	0.613792i	$-0.210357\pi$
$59$	2.47402	+	2.07595i	0.322090	+	0.270266i	−0.467378	+	0.884058i	$0.654801\pi$
$60$		0			0
$61$	10.3604	+	3.77087i	1.32651	+	0.482810i	0.905538	−	0.424264i	$-0.139467\pi$
$61$	10.3604	+	3.77087i	1.32651	+	0.482810i	0.420971	+	0.907074i	$0.361689\pi$
$62$	6.20274	+	1.66202i	0.787749	+	0.211077i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	4.71622	−	0.694171i	0.584975	−	0.0861013i
$66$		0			0
$67$	7.08159	−	4.95858i	0.865154	−	0.605787i	−0.0545012	−	0.998514i	$-0.517357\pi$
$67$	7.08159	−	4.95858i	0.865154	−	0.605787i	0.919655	+	0.392726i	$0.128468\pi$
$68$	−5.32193	+	3.72646i	−0.645379	+	0.451899i
$69$		0			0
$70$	0.238464	+	0.177272i	0.0285018	+	0.0211881i
$71$	8.58515	+	4.95664i	1.01887	+	0.588245i	0.913776	−	0.406218i	$-0.133153\pi$
$71$	8.58515	+	4.95664i	1.01887	+	0.588245i	0.105093	+	0.994462i	$0.466486\pi$
$72$		0			0
$73$	9.62186	+	2.57817i	1.12615	+	0.301752i	0.773371	−	0.633954i	$-0.218569\pi$
$73$	9.62186	+	2.57817i	1.12615	+	0.301752i	0.352782	+	0.935705i	$0.385236\pi$
$74$	−8.81690	−	3.20909i	−1.02494	−	0.373049i
$75$		0			0
$76$	−5.72317	−	4.80231i	−0.656493	−	0.550863i
$77$	0.0972329	−	0.208517i	0.0110807	−	0.0237627i
$78$		0			0
$79$	−0.0585881	+	0.0103307i	−0.00659168	+	0.00116229i	−0.176943	−	0.984221i	$-0.556621\pi$
$79$	−0.0585881	+	0.0103307i	−0.00659168	+	0.00116229i	0.170351	+	0.985383i	$0.445510\pi$
$80$	−0.517184	−	2.17544i	−0.0578229	−	0.243221i
$81$		0			0
$82$	−3.67925	−	3.67925i	−0.406306	−	0.406306i
$83$	−2.58753	+	3.69538i	−0.284019	+	0.405621i	−0.935658	−	0.352908i	$-0.885193\pi$
$83$	−2.58753	+	3.69538i	−0.284019	+	0.405621i	0.651639	+	0.758529i	$0.274082\pi$
$84$		0			0
$85$	−14.2294	−	2.92782i	−1.54339	−	0.317567i
$86$	−1.26683	+	1.50975i	−0.136606	+	0.162801i
$87$		0			0
$88$	−1.56917	+	0.731715i	−0.167274	+	0.0780011i
$89$	7.54680	+	13.0714i	0.799959	+	1.38557i	0.919642	+	0.392758i	$0.128479\pi$
$89$	7.54680	+	13.0714i	0.799959	+	1.38557i	−0.119682	+	0.992812i	$0.538188\pi$
$90$		0			0
$91$	−0.141646	+	0.245338i	−0.0148485	+	0.0257184i
$92$	−0.153987	+	1.76008i	−0.0160543	+	0.183501i
$93$		0			0
$94$	−2.47305	−	0.436065i	−0.255075	−	0.0449767i
$95$	−0.982942	−	16.6769i	−0.100848	−	1.71101i
$96$		0			0
$97$	−1.11399	−	0.0974611i	−0.113108	−	0.00989567i	0.0304612	−	0.999536i	$-0.490302\pi$
$97$	−1.11399	−	0.0974611i	−0.113108	−	0.00989567i	−0.143569	+	0.989640i	$0.545858\pi$
$98$	6.74442	−	1.80716i	0.681290	−	0.182551i
$99$		0			0
$100$	2.74174	−	4.18125i	0.274174	−	0.418125i
$101$	0.254823	−	0.700121i	0.0253559	−	0.0696647i	−0.926369	−	0.376617i	$-0.877087\pi$
$101$	0.254823	−	0.700121i	0.0253559	−	0.0696647i	0.951725	+	0.306953i	$0.0993094\pi$
$102$		0			0
$103$	11.6088	−	1.01564i	1.14385	−	0.100074i	0.500563	−	0.865700i	$-0.333126\pi$
$103$	11.6088	−	1.01564i	1.14385	−	0.100074i	0.643285	+	0.765626i	$0.277571\pi$
$104$	2.00331	−	0.729146i	0.196441	−	0.0714987i
$105$		0			0
$106$	−1.18158	−	6.70106i	−0.114765	−	0.650865i
$107$	12.5072	−	12.5072i	1.20912	−	1.20912i	0.237802	−	0.971314i	$-0.423573\pi$
$107$	12.5072	−	12.5072i	1.20912	−	1.20912i	0.971314	−	0.237802i	$-0.0764271\pi$
$108$		0			0
$109$			3.70273i			0.354657i	0.984152	+	0.177329i	$0.0567455\pi$
$109$			3.70273i			0.354657i	−0.984152	+	0.177329i	$0.943254\pi$
$110$	−3.59896	−	1.42688i	−0.343147	−	0.136048i
$111$		0			0
$112$	0.120433	+	0.0561590i	0.0113799	+	0.00530653i
$113$	−0.511717	−	5.84896i	−0.0481383	−	0.550224i	−0.981523	−	0.191345i	$-0.938715\pi$
$113$	−0.511717	−	5.84896i	−0.0481383	−	0.550224i	0.933384	−	0.358878i	$-0.116841\pi$
$114$		0			0
$115$	−3.09729	+	2.45251i	−0.288823	+	0.228698i
$116$	−3.18142	+	1.83680i	−0.295388	+	0.170542i
$117$		0			0
$118$	0.835883	+	3.11956i	0.0769493	+	0.287179i
$119$	0.661348	−	0.554937i	0.0606257	−	0.0508710i
$120$		0			0
$121$	1.38959	−	7.88073i	0.126326	−	0.716430i
$122$	6.32384	+	9.03138i	0.572533	+	0.817662i
$123$		0			0
$124$	4.12769	+	4.91919i	0.370678	+	0.441757i
$125$	11.0064	−	1.96439i	0.984444	−	0.175700i
$126$		0			0
$127$	−2.42152	+	9.03725i	−0.214876	+	0.801927i	0.771335	+	0.636430i	$0.219589\pi$
$127$	−2.42152	+	9.03725i	−0.214876	+	0.801927i	−0.986210	+	0.165497i	$0.947077\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$		0			0
$130$	4.26146	+	2.13648i	0.373755	+	0.187382i
$131$	1.45942	+	4.00974i	0.127511	+	0.350332i	0.986977	−	0.160859i	$-0.0514265\pi$
$131$	1.45942	+	4.00974i	0.127511	+	0.350332i	−0.859467	+	0.511191i	$0.829204\pi$
$132$		0			0
$133$	0.813240	+	0.569437i	0.0705169	+	0.0493764i
$134$	8.64503			0.746817
$135$		0			0
$136$	−6.49688			−0.557103
$137$	−13.5498	−	9.48766i	−1.15764	−	0.810585i	−0.172951	−	0.984930i	$-0.555330\pi$
$137$	−13.5498	−	9.48766i	−1.15764	−	0.810585i	−0.984685	+	0.174345i	$0.944219\pi$
$138$		0			0
$139$	2.80055	+	7.69445i	0.237540	+	0.652635i	0.999984	+	0.00558159i	$0.00177669\pi$
$139$	2.80055	+	7.69445i	0.237540	+	0.652635i	−0.762445	+	0.647053i	$0.776001\pi$
$140$	0.0936587	+	0.281990i	0.00791561	+	0.0238325i
$141$		0			0
$142$	4.18953	+	8.98448i	0.351578	+	0.753961i
$143$	0.955328	−	3.56533i	0.0798886	−	0.298148i
$144$		0			0
$145$	−7.87094	−	2.35045i	−0.653646	−	0.195194i
$146$	6.40299	+	7.63078i	0.529915	+	0.631528i
$147$		0			0
$148$	−5.38172	−	7.68590i	−0.442375	−	0.631777i
$149$	2.07416	−	11.7631i	0.169922	−	0.963674i	−0.773922	−	0.633281i	$-0.781708\pi$
$149$	2.07416	−	11.7631i	0.169922	−	0.963674i	0.943844	−	0.330393i	$-0.107181\pi$
$150$		0			0
$151$	14.1509	−	11.8741i	1.15159	−	0.966297i	0.151832	−	0.988406i	$-0.451483\pi$
$151$	14.1509	−	11.8741i	1.15159	−	0.966297i	0.999756	+	0.0221098i	$0.00703836\pi$
$152$	−1.93366	−	7.21650i	−0.156840	−	0.585335i
$153$		0			0
$154$	0.199249	−	0.115036i	0.0160559	−	0.00926989i
$155$	−1.65707	+	14.2631i	−0.133099	+	1.14564i
$156$		0			0
$157$	−1.81221	−	20.7137i	−0.144630	−	1.65313i	−0.628366	−	0.777918i	$-0.716276\pi$
$157$	−1.81221	−	20.7137i	−0.144630	−	1.65313i	0.483735	−	0.875214i	$-0.339280\pi$
$158$	−0.0539180	−	0.0251424i	−0.00428948	−	0.00200022i
$159$		0			0
$160$	0.824126	−	2.07866i	0.0651529	−	0.164332i
$161$		−	0.234779i		−	0.0185032i
$162$		0			0
$163$	5.17472	−	5.17472i	0.405315	−	0.405315i	−0.474786	−	0.880101i	$-0.657475\pi$
$163$	5.17472	−	5.17472i	0.405315	−	0.405315i	0.880101	+	0.474786i	$0.157475\pi$
$164$	−0.903535	−	5.12420i	−0.0705543	−	0.400133i
$165$		0			0
$166$	−4.23916	+	1.54293i	−0.329023	+	0.119755i
$167$	−11.4445	+	1.00127i	−0.885604	+	0.0774803i	−0.520874	−	0.853633i	$-0.674394\pi$
$167$	−11.4445	+	1.00127i	−0.885604	+	0.0774803i	−0.364729	+	0.931114i	$0.618838\pi$
$168$		0			0
$169$	2.89181	−	7.94518i	0.222447	−	0.611168i
$170$	−9.97669	−	10.5600i	−0.765177	−	0.809912i
$171$		0			0
$172$	−1.90369	+	0.510091i	−0.145155	+	0.0388941i
$173$	0.634449	+	0.0555071i	0.0482363	+	0.00422013i	0.111248	−	0.993793i	$-0.464515\pi$
$173$	0.634449	+	0.0555071i	0.0482363	+	0.00422013i	−0.0630121	+	0.998013i	$0.520071\pi$
$174$		0			0
$175$	−0.314520	+	0.585259i	−0.0237755	+	0.0442414i
$176$	−1.70508	−	0.300652i	−0.128525	−	0.0226625i
$177$		0			0
$178$	−1.31549	+	15.0362i	−0.0986005	+	1.12701i
$179$	−13.1427	+	22.7638i	−0.982329	+	1.70144i	−0.329077	+	0.944303i	$0.606738\pi$
$179$	−13.1427	+	22.7638i	−0.982329	+	1.70144i	−0.653252	+	0.757141i	$0.726596\pi$
$180$		0			0
$181$	−3.96559	−	6.86860i	−0.294760	−	0.510539i	0.680169	−	0.733055i	$-0.261906\pi$
$181$	−3.96559	−	6.86860i	−0.294760	−	0.510539i	−0.974929	+	0.222516i	$0.928573\pi$
$182$	−0.256750	+	0.119724i	−0.0190316	+	0.00887456i
$183$		0			0
$184$	−1.13568	+	1.35345i	−0.0837235	+	0.0997777i
$185$	4.22835	−	20.5500i	0.310874	−	1.51086i
$186$		0			0
$187$	−6.45193	+	9.21431i	−0.471812	+	0.673817i
$188$	−1.77569	−	1.77569i	−0.129505	−	0.129505i
$189$		0			0
$190$	8.76029	−	14.2247i	0.635538	−	1.03197i
$191$	21.4337	−	3.77933i	1.55089	−	0.273463i	0.668400	−	0.743802i	$-0.266979\pi$
$191$	21.4337	−	3.77933i	1.55089	−	0.273463i	0.882486	+	0.470339i	$0.155868\pi$
$192$		0			0
$193$	−9.18675	+	19.7010i	−0.661276	+	1.41811i	0.233838	+	0.972276i	$0.424871\pi$
$193$	−9.18675	+	19.7010i	−0.661276	+	1.41811i	−0.895114	+	0.445836i	$0.852906\pi$
$194$	−0.856622	−	0.718791i	−0.0615019	−	0.0516062i
$195$		0			0
$196$	6.56126	+	2.38810i	0.468661	+	0.170579i
$197$	−15.0328	−	4.02803i	−1.07104	−	0.286986i	−0.320122	−	0.947376i	$-0.603724\pi$
$197$	−15.0328	−	4.02803i	−1.07104	−	0.286986i	−0.750922	+	0.660391i	$0.770391\pi$
$198$		0			0
$199$	14.2759	+	8.24221i	1.01199	+	0.584275i	0.911775	−	0.410690i	$-0.134712\pi$
$199$	14.2759	+	8.24221i	1.01199	+	0.584275i	0.100219	+	0.994965i	$0.468046\pi$
$200$	4.64417	−	1.85248i	0.328392	−	0.130990i
$201$		0			0
$202$	0.610312	−	0.427345i	0.0429414	−	0.0300679i
$203$	0.399877	−	0.279997i	0.0280659	−	0.0196519i
$204$		0			0
$205$	6.94135	−	9.33739i	0.484805	−	0.652151i
$206$	10.0919	+	5.82657i	0.703137	+	0.405956i
$207$		0			0
$208$	2.05924	+	0.551771i	0.142782	+	0.0382585i
$209$	−12.1552	−	4.42413i	−0.840793	−	0.306024i
$210$		0			0
$211$	5.25939	+	4.41315i	0.362072	+	0.303814i	0.805616	−	0.592438i	$-0.201835\pi$
$211$	5.25939	+	4.41315i	0.362072	+	0.303814i	−0.443544	+	0.896252i	$0.646279\pi$
$212$	2.87568	−	6.16691i	0.197502	−	0.423545i
$213$		0			0
$214$	17.4191	−	3.07146i	1.19075	−	0.209961i
$215$	−3.75242	−	2.31093i	−0.255913	−	0.157604i
$216$		0			0
$217$	−0.603388	−	0.603388i	−0.0409606	−	0.0409606i
$218$	−2.12380	+	3.03310i	−0.143842	+	0.205427i
$219$		0			0
$220$	−2.12967	−	3.23311i	−0.143582	−	0.217976i
$221$	8.90297	−	10.6101i	0.598879	−	0.713716i
$222$		0			0
$223$	−3.62799	+	1.69176i	−0.242948	+	0.113289i	−0.540279	−	0.841486i	$-0.681681\pi$
$223$	−3.62799	+	1.69176i	−0.242948	+	0.113289i	0.297331	+	0.954775i	$0.403904\pi$
$224$	0.0664418	+	0.115081i	0.00443933	+	0.00768915i
$225$		0			0
$226$	2.93565	−	5.08469i	0.195276	−	0.338229i
$227$	−0.271143	+	3.09917i	−0.0179964	+	0.205699i	0.981873	+	0.189540i	$0.0606996\pi$
$227$	−0.271143	+	3.09917i	−0.0179964	+	0.205699i	−0.999869	+	0.0161597i	$0.994856\pi$
$228$		0			0
$229$	20.8959	+	3.68452i	1.38084	+	0.243480i	0.814248	−	0.580517i	$-0.197150\pi$
$229$	20.8959	+	3.68452i	1.38084	+	0.243480i	0.566594	+	0.823997i	$0.308261\pi$
$230$	−3.94385	+	0.232452i	−0.260050	+	0.0153274i
$231$		0			0
$232$	−3.65961	−	0.320174i	−0.240265	−	0.0210205i
$233$	6.03367	−	1.61672i	0.395279	−	0.105915i	−0.0557038	−	0.998447i	$-0.517740\pi$
$233$	6.03367	−	1.61672i	0.395279	−	0.105915i	0.450983	+	0.892533i	$0.351074\pi$
$234$		0			0
$235$	0.159418	−	5.61295i	0.0103993	−	0.366148i
$236$	−1.10459	+	3.03484i	−0.0719027	+	0.197551i
$237$		0			0
$238$	0.860043	−	0.0752441i	0.0557483	−	0.00487735i
$239$	−6.08130	+	2.21341i	−0.393366	+	0.143174i	−0.531128	−	0.847292i	$-0.678232\pi$
$239$	−6.08130	+	2.21341i	−0.393366	+	0.143174i	0.137761	+	0.990465i	$0.456009\pi$
$240$		0			0
$241$	3.98845	+	22.6196i	0.256919	+	1.45706i	0.791099	+	0.611688i	$0.209509\pi$
$241$	3.98845	+	22.6196i	0.256919	+	1.45706i	−0.534180	+	0.845371i	$0.679380\pi$
$242$	5.65849	−	5.65849i	0.363741	−	0.363741i
$243$		0			0
$244$			11.0253i			0.705821i
$245$	6.19395	+	14.3318i	0.395717	+	0.915625i
$246$		0			0
$247$	14.4352	+	6.73122i	0.918487	+	0.428297i
$248$	0.559675	+	6.39712i	0.0355394	+	0.406217i
$249$		0			0
$250$	10.1427	+	4.70389i	0.641478	+	0.297500i
$251$	−16.6741	+	9.62680i	−1.05246	+	0.607638i	−0.923337	−	0.383990i	$-0.874550\pi$
$251$	−16.6741	+	9.62680i	−1.05246	+	0.607638i	−0.129123	+	0.991629i	$0.541216\pi$
$252$		0			0
$253$	0.791733	+	2.95479i	0.0497758	+	0.185766i
$254$	−7.16715	+	6.01395i	−0.449707	+	0.377349i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−12.7102	−	18.1520i	−0.792839	−	1.13229i	−0.988441	−	0.151608i	$-0.951555\pi$
$257$	−12.7102	−	18.1520i	−0.792839	−	1.13229i	0.195602	−	0.980683i	$-0.437334\pi$
$258$		0			0
$259$	0.801437	+	0.955115i	0.0497988	+	0.0593480i
$260$	2.26535	+	4.19437i	0.140491	+	0.260124i
$261$		0			0
$262$	−1.10440	+	4.12168i	−0.0682300	+	0.254638i
$263$	6.20076	+	13.2976i	0.382355	+	0.819963i	0.999453	+	0.0330768i	$0.0105306\pi$
$263$	6.20076	+	13.2976i	0.382355	+	0.819963i	−0.617098	+	0.786887i	$0.711692\pi$
$264$		0			0
$265$	14.4396	−	4.79589i	0.887016	−	0.294609i
$266$	0.339552	+	0.932911i	0.0208193	+	0.0572004i
$267$		0			0
$268$	7.08159	+	4.95858i	0.432577	+	0.302894i
$269$	−4.01941			−0.245068			−0.122534	−	0.992464i	$-0.539102\pi$
$269$	−4.01941			−0.245068			−0.122534	+	0.992464i	$0.539102\pi$
$270$		0			0
$271$	−6.78465			−0.412138			−0.206069	−	0.978537i	$-0.566067\pi$
$271$	−6.78465			−0.412138			−0.206069	+	0.978537i	$0.566067\pi$
$272$	−5.32193	−	3.72646i	−0.322689	−	0.225950i
$273$		0			0
$274$	−5.65743	−	15.5437i	−0.341778	−	0.939027i
$275$	1.98472	−	8.42634i	0.119683	−	0.508128i
$276$		0			0
$277$	−11.2808	−	24.1917i	−0.677795	−	1.45354i	−0.880378	−	0.474272i	$-0.842711\pi$
$277$	−11.2808	−	24.1917i	−0.677795	−	1.45354i	0.202583	−	0.979265i	$-0.435066\pi$
$278$	−2.11928	+	7.90926i	−0.127106	+	0.474366i
$279$		0			0
$280$	−0.0850220	+	0.284713i	−0.00508104	+	0.0170149i
$281$	−3.60661	−	4.29819i	−0.215152	−	0.256408i	0.647664	−	0.761926i	$-0.275746\pi$
$281$	−3.60661	−	4.29819i	−0.215152	−	0.256408i	−0.862816	+	0.505518i	$0.831302\pi$
$282$		0			0
$283$	−4.89607	−	6.99232i	−0.291041	−	0.415650i	0.646830	−	0.762635i	$-0.276095\pi$
$283$	−4.89607	−	6.99232i	−0.291041	−	0.415650i	−0.937871	+	0.346985i	$0.887206\pi$
$284$	−1.72142	+	9.76267i	−0.102148	+	0.579308i
$285$		0			0
$286$	2.82755	−	2.37260i	0.167197	−	0.140295i
$287$	0.178954	+	0.667867i	0.0105633	+	0.0394230i
$288$		0			0
$289$	−21.8320	+	12.6047i	−1.28424	+	0.741454i
$290$	−5.09934	−	6.43996i	−0.299443	−	0.378168i
$291$		0			0
$292$	0.868183	+	9.92337i	0.0508066	+	0.580722i
$293$	7.67044	+	3.57679i	0.448112	+	0.208958i	0.633556	−	0.773697i	$-0.281595\pi$
$293$	7.67044	+	3.57679i	0.448112	+	0.208958i	−0.185444	+	0.982655i	$0.559372\pi$
$294$		0			0
$295$	−6.62901	+	2.86494i	−0.385956	+	0.166803i
$296$		−	9.38275i		−	0.545361i
$297$		0			0
$298$	8.44611	−	8.44611i	0.489270	−	0.489270i
$299$	−0.654066	−	3.70939i	−0.0378256	−	0.214520i
$300$		0			0
$301$	0.246099	−	0.0895725i	0.0141849	−	0.00516288i
$302$	18.4024	−	1.61001i	1.05894	−	0.0926454i
$303$		0			0
$304$	2.55526	−	7.02051i	0.146554	−	0.402654i
$305$	−17.9204	+	16.9305i	−1.02612	+	0.969440i
$306$		0			0
$307$	−4.44445	+	1.19089i	−0.253658	+	0.0679676i	−0.383407	−	0.923579i	$-0.625249\pi$
$307$	−4.44445	+	1.19089i	−0.253658	+	0.0679676i	0.129749	+	0.991547i	$0.458583\pi$
$308$	0.229197	+	0.0200522i	0.0130597	+	0.00114258i
$309$		0			0
$310$	−9.53837	+	10.7332i	−0.541743	+	0.609604i
$311$	33.2169	+	5.85703i	1.88355	+	0.332122i	0.992547	−	0.121865i	$-0.0388876\pi$
$311$	33.2169	+	5.85703i	1.88355	+	0.332122i	0.891008	+	0.453987i	$0.149999\pi$
$312$		0			0
$313$	−0.777418	+	8.88593i	−0.0439423	+	0.502262i	0.942050	+	0.335472i	$0.108896\pi$
$313$	−0.777418	+	8.88593i	−0.0439423	+	0.502262i	−0.985992	+	0.166790i	$0.946660\pi$
$314$	10.3964	−	18.0071i	0.586703	−	1.01620i
$315$		0			0
$316$	−0.0297460	−	0.0515215i	−0.00167334	−	0.00289831i
$317$	23.0835	−	10.7640i	1.29650	−	0.604566i	0.352899	−	0.935661i	$-0.385196\pi$
$317$	23.0835	−	10.7640i	1.29650	−	0.604566i	0.943597	+	0.331095i	$0.107418\pi$
$318$		0			0
$319$	−4.08839	+	4.87235i	−0.228906	+	0.272799i
$320$	1.86735	−	1.23004i	0.104388	−	0.0687612i
$321$		0			0
$322$	0.134664	−	0.192320i	0.00750453	−	0.0107176i
$323$	−34.3220	−	34.3220i	−1.90973	−	1.90973i
$324$		0			0
$325$	−3.33880	+	10.1230i	−0.185203	+	0.561523i
$326$	7.20698	−	1.27078i	0.399158	−	0.0703822i
$327$		0			0
$328$	2.19899	−	4.71575i	0.121419	−	0.260384i
$329$	0.255627	+	0.214496i	0.0140932	+	0.0118256i
$330$		0			0
$331$	−13.6054	−	4.95196i	−0.747820	−	0.272184i	−0.0601321	−	0.998190i	$-0.519152\pi$
$331$	−13.6054	−	4.95196i	−0.747820	−	0.272184i	−0.687688	+	0.726006i	$0.741374\pi$
$332$	−4.35751	−	1.16759i	−0.239149	−	0.0640799i
$333$		0			0
$334$	−9.94911	−	5.74412i	−0.544391	−	0.314304i
$335$	2.81494	+	19.1248i	0.153797	+	1.04490i
$336$		0			0
$337$	−11.6046	+	8.12563i	−0.632143	+	0.442631i	−0.845230	−	0.534402i	$-0.820537\pi$
$337$	−11.6046	+	8.12563i	−0.632143	+	0.442631i	0.213088	+	0.977033i	$0.431648\pi$
$338$	6.92600	−	4.84964i	0.376725	−	0.263786i
$339$		0			0
$340$	−2.11548	−	14.3726i	−0.114728	−	0.779464i
$341$	9.62862	+	5.55909i	0.521419	+	0.301042i
$342$		0			0
$343$	−1.79471	−	0.480892i	−0.0969054	−	0.0259657i
$344$	−1.85199	−	0.674068i	−0.0998524	−	0.0363433i
$345$		0			0
$346$	0.487873	+	0.409374i	0.0262282	+	0.0220081i
$347$	−12.6714	+	27.1740i	−0.680238	+	1.45877i	0.197829	+	0.980237i	$0.436611\pi$
$347$	−12.6714	+	27.1740i	−0.680238	+	1.45877i	−0.878067	+	0.478538i	$0.841167\pi$
$348$		0			0
$349$	−13.2211	+	2.33123i	−0.707708	+	0.124788i	−0.515905	−	0.856646i	$-0.672544\pi$
$349$	−13.2211	+	2.33123i	−0.707708	+	0.124788i	−0.191802	+	0.981434i	$0.561433\pi$
$350$	−0.593331	+	0.299015i	−0.0317149	+	0.0159830i
$351$		0			0
$352$	−1.22427	−	1.22427i	−0.0652540	−	0.0652540i
$353$	−4.84736	+	6.92274i	−0.257999	+	0.368460i	−0.927166	−	0.374652i	$-0.877762\pi$
$353$	−4.84736	+	6.92274i	−0.257999	+	0.368460i	0.669167	+	0.743112i	$0.266651\pi$
$354$		0			0
$355$	−18.5116	+	12.1937i	−0.982493	+	0.647174i
$356$	−9.70198	+	11.5624i	−0.514204	+	0.612804i
$357$		0			0
$358$	−23.8226	+	11.1087i	−1.25906	+	0.587111i
$359$	8.69033	+	15.0521i	0.458658	+	0.794420i	0.998890	−	0.0470966i	$-0.0149969\pi$
$359$	8.69033	+	15.0521i	0.458658	+	0.794420i	−0.540232	+	0.841516i	$0.681664\pi$
$360$		0			0
$361$	18.4084	−	31.8844i	0.968865	−	1.67812i
$362$	0.691248	−	7.90100i	0.0363312	−	0.415267i
$363$		0			0
$364$	−0.278988	−	0.0491931i	−0.0146230	−	0.00257842i
$365$	−14.7962	+	16.6496i	−0.774467	+	0.871480i
$366$		0			0
$367$	−7.50848	−	0.656907i	−0.391940	−	0.0342903i	−0.110517	−	0.993874i	$-0.535251\pi$
$367$	−7.50848	−	0.656907i	−0.391940	−	0.0342903i	−0.281423	+	0.959584i	$0.590806\pi$
$368$	−1.70660	+	0.457283i	−0.0889628	+	0.0238375i
$369$		0			0
$370$	15.2506	−	14.4083i	0.792843	−	0.749050i
$371$	−0.309254	+	0.849668i	−0.0160557	+	0.0441126i
$372$		0			0
$373$	−36.1757	+	3.16497i	−1.87311	+	0.163876i	−0.966258	−	0.257576i	$-0.917076\pi$
$373$	−36.1757	+	3.16497i	−1.87311	+	0.163876i	−0.906851	+	0.421452i	$0.861521\pi$
$374$	−10.5702	+	3.84725i	−0.546573	+	0.198936i
$375$		0			0
$376$	−0.436065	−	2.47305i	−0.0224883	−	0.127538i
$377$	5.53782	−	5.53782i	0.285212	−	0.285212i
$378$		0			0
$379$			23.0474i			1.18387i	0.805987	+	0.591933i	$0.201635\pi$
$379$			23.0474i			1.18387i	−0.805987	+	0.591933i	$0.798365\pi$
$380$	15.3350	−	6.62749i	0.786667	−	0.339983i
$381$		0			0
$382$	19.7252	+	9.19800i	1.00923	+	0.470611i
$383$	1.11115	+	12.7005i	0.0567770	+	0.648964i	0.970256	+	0.242079i	$0.0778294\pi$
$383$	1.11115	+	12.7005i	0.0567770	+	0.648964i	−0.913479	+	0.406885i	$0.866615\pi$
$384$		0			0
$385$	0.319366	+	0.403327i	0.0162764	+	0.0205555i
$386$	−18.8254	+	10.8688i	−0.958187	+	0.553210i
$387$		0			0
$388$	−0.289422	−	1.08014i	−0.0146932	−	0.0548357i
$389$	20.3897	−	17.1090i	1.03380	−	0.867462i	0.0425023	−	0.999096i	$-0.486467\pi$
$389$	20.3897	−	17.1090i	1.03380	−	0.867462i	0.991298	+	0.131635i	$0.0420226\pi$
$390$		0			0
$391$	−1.99326	+	11.3043i	−0.100803	+	0.571684i
$392$	4.00491	+	5.71960i	0.202278	+	0.288883i
$393$		0			0
$394$	−10.0038	−	11.9220i	−0.503983	−	0.600624i
$395$	0.0380643	−	0.127466i	0.00191522	−	0.00641350i
$396$		0			0
$397$	4.55032	−	16.9820i	0.228374	−	0.852303i	−0.752651	−	0.658420i	$-0.771225\pi$
$397$	4.55032	−	16.9820i	0.228374	−	0.852303i	0.981025	−	0.193883i	$-0.0621083\pi$
$398$	6.96662	+	14.9400i	0.349205	+	0.748873i
$399$		0			0
$400$	4.86682	+	1.14632i	0.243341	+	0.0573159i
$401$	−7.41342	−	20.3682i	−0.370209	−	1.01714i	−0.975281	−	0.220969i	$-0.929078\pi$
$401$	−7.41342	−	20.3682i	−0.370209	−	1.01714i	0.605072	−	0.796171i	$-0.293144\pi$
$402$		0			0
$403$	−11.2142	−	7.85225i	−0.558618	−	0.391148i
$404$	0.745053			0.0370678
$405$		0			0
$406$	0.488160			0.0242270
$407$	−13.3072	−	9.31784i	−0.659616	−	0.461868i
$408$		0			0
$409$	−5.64316	−	15.5044i	−0.279036	−	0.766645i	−0.997473	−	0.0710528i	$-0.977364\pi$
$409$	−5.64316	−	15.5044i	−0.279036	−	0.766645i	0.718436	−	0.695593i	$-0.244858\pi$
$410$	11.0417	−	3.66734i	0.545312	−	0.181117i
$411$		0			0
$412$	4.92483	+	10.5613i	0.242629	+	0.520319i
$413$	0.111075	−	0.414538i	0.00546565	−	0.0203981i
$414$		0			0
$415$	−4.79365	−	8.87562i	−0.235311	−	0.435687i
$416$	1.37035	+	1.63312i	0.0671868	+	0.0800701i
$417$		0			0
$418$	−7.41938	−	10.5960i	−0.362894	−	0.518266i
$419$	−5.57280	+	31.6049i	−0.272249	+	1.54400i	0.475317	+	0.879815i	$0.342333\pi$
$419$	−5.57280	+	31.6049i	−0.272249	+	1.54400i	−0.747566	+	0.664188i	$0.768778\pi$
$420$		0			0
$421$	−5.92328	+	4.97023i	−0.288683	+	0.242234i	−0.775615	−	0.631206i	$-0.782560\pi$
$421$	−5.92328	+	4.97023i	−0.288683	+	0.242234i	0.486932	+	0.873440i	$0.338116\pi$
$422$	1.77696	+	6.63171i	0.0865011	+	0.322826i
$423$		0			0
$424$	5.89281	−	3.40222i	0.286180	−	0.165226i
$425$	20.1126	−	25.5092i	0.975602	−	1.23738i
$426$		0			0
$427$	−0.127690	−	1.45950i	−0.00617935	−	0.0706303i
$428$	16.0306	+	7.47521i	0.774870	+	0.361328i
$429$		0			0
$430$	−1.74831	−	4.04531i	−0.0843109	−	0.195082i
$431$		−	6.41912i		−	0.309198i	−0.987977	−	0.154599i	$-0.950591\pi$
$431$		−	6.41912i		−	0.309198i	0.987977	−	0.154599i	$-0.0494086\pi$
$432$		0			0
$433$	2.53748	−	2.53748i	0.121943	−	0.121943i	−0.643501	−	0.765445i	$-0.722519\pi$
$433$	2.53748	−	2.53748i	0.121943	−	0.121943i	0.765445	+	0.643501i	$0.222519\pi$
$434$	−0.148177	−	0.840355i	−0.00711274	−	0.0403383i
$435$		0			0
$436$	−3.47943	+	1.26641i	−0.166634	+	0.0606499i
$437$	−13.1497	+	1.15045i	−0.629035	+	0.0550334i
$438$		0			0
$439$	9.19122	−	25.2527i	0.438673	−	1.20524i	−0.501683	−	0.865052i	$-0.667285\pi$
$439$	9.19122	−	25.2527i	0.438673	−	1.20524i	0.940356	−	0.340193i	$-0.110492\pi$
$440$	0.109913	−	3.86993i	0.00523990	−	0.184492i
$441$		0			0
$442$	13.3786	−	3.58479i	0.636356	−	0.170511i
$443$	−37.4867	−	3.27966i	−1.78105	−	0.155821i	−0.851459	−	0.524421i	$-0.824282\pi$
$443$	−37.4867	−	3.27966i	−1.78105	−	0.155821i	−0.929588	+	0.368600i	$0.879837\pi$
$444$		0			0
$445$	−33.6919	+	1.98581i	−1.59715	+	0.0941365i
$446$	−3.94223	−	0.695122i	−0.186670	−	0.0329150i
$447$		0			0
$448$	−0.0115816	+	0.132378i	−0.000547178	+	0.00625427i
$449$	−0.652865	+	1.13080i	−0.0308106	+	0.0533656i	−0.881020	−	0.473080i	$-0.843142\pi$
$449$	−0.652865	+	1.13080i	−0.0308106	+	0.0533656i	0.850209	+	0.526445i	$0.176476\pi$
$450$		0			0
$451$	−4.50442	−	7.80188i	−0.212105	−	0.367376i
$452$	5.32120	−	2.48132i	0.250288	−	0.116711i
$453$		0			0
$454$	−1.99972	+	2.38317i	−0.0938515	+	0.111848i
$455$	−0.348460	−	0.529006i	−0.0163360	−	0.0248002i
$456$		0			0
$457$	−13.1500	+	18.7802i	−0.615132	+	0.878500i	−0.998992	−	0.0448915i	$-0.985706\pi$
$457$	−13.1500	+	18.7802i	−0.615132	+	0.878500i	0.383860	+	0.923391i	$0.374595\pi$
$458$	15.0036	+	15.0036i	0.701072	+	0.701072i
$459$		0			0
$460$	−3.36394	−	2.07169i	−0.156845	−	0.0965929i
$461$	6.72312	−	1.18547i	0.313127	−	0.0552127i	−0.0148763	−	0.999889i	$-0.504735\pi$
$461$	6.72312	−	1.18547i	0.313127	−	0.0552127i	0.328003	+	0.944677i	$0.393624\pi$
$462$		0			0
$463$	11.1119	−	23.8295i	0.516414	−	1.10745i	−0.459275	−	0.888294i	$-0.651891\pi$
$463$	11.1119	−	23.8295i	0.516414	−	1.10745i	0.975689	−	0.219159i	$-0.0703313\pi$
$464$	−2.81413	−	2.36134i	−0.130643	−	0.109622i
$465$		0			0
$466$	5.86981	+	2.13643i	0.271914	+	0.0989684i
$467$	−19.0757	−	5.11132i	−0.882719	−	0.236524i	−0.211139	−	0.977456i	$-0.567717\pi$
$467$	−19.0757	−	5.11132i	−0.882719	−	0.236524i	−0.671580	+	0.740932i	$0.734384\pi$
$468$		0			0
$469$	−0.994875	−	0.574391i	−0.0459391	−	0.0265229i
$470$	3.35004	−	4.50642i	0.154526	−	0.207866i
$471$		0			0
$472$	−2.64554	+	1.85243i	−0.121771	+	0.0852648i
$473$	−2.79518	+	1.95721i	−0.128523	+	0.0899925i
$474$		0			0
$475$	34.3208	+	14.7480i	1.57475	+	0.676686i
$476$	0.747665	+	0.431664i	0.0342692	+	0.0197853i
$477$		0			0
$478$	−6.25107	−	1.67497i	−0.285917	−	0.0766113i
$479$	10.6103	+	3.86184i	0.484798	+	0.176452i	0.572844	−	0.819664i	$-0.305840\pi$
$479$	10.6103	+	3.86184i	0.484798	+	0.176452i	−0.0880461	+	0.996116i	$0.528062\pi$
$480$		0			0
$481$	15.3231	+	12.8576i	0.698674	+	0.586257i
$482$	−9.70694	+	20.8166i	−0.442139	+	0.948170i
$483$		0			0
$484$	7.88073	−	1.38959i	0.358215	−	0.0631630i
$485$	1.31121	−	2.12910i	0.0595388	−	0.0966773i
$486$		0			0
$487$	12.9399	+	12.9399i	0.586362	+	0.586362i	0.936644	−	0.350282i	$-0.113914\pi$
$487$	12.9399	+	12.9399i	0.586362	+	0.586362i	−0.350282	+	0.936644i	$0.613914\pi$
$488$	−6.32384	+	9.03138i	−0.286267	+	0.408831i
$489$		0			0
$490$	−3.14660	+	15.2926i	−0.142149	+	0.690850i
$491$	8.10756	−	9.66222i	0.365889	−	0.436050i	−0.551419	−	0.834229i	$-0.685913\pi$
$491$	8.10756	−	9.66222i	0.365889	−	0.436050i	0.917308	+	0.398179i	$0.130358\pi$
$492$		0			0
$493$	−21.6307	+	10.0866i	−0.974199	+	0.454276i
$494$	7.96371	+	13.7936i	0.358304	+	0.620601i
$495$		0			0
$496$	−3.21078	+	5.56123i	−0.144168	+	0.249706i
$497$	0.114811	−	1.31230i	0.00514999	−	0.0588647i
$498$		0			0
$499$	9.91345	+	1.74801i	0.443787	+	0.0782516i	0.391076	−	0.920358i	$-0.372103\pi$
$499$	9.91345	+	1.74801i	0.443787	+	0.0782516i	0.0527105	+	0.998610i	$0.483214\pi$
$500$	5.61034	+	9.67079i	0.250902	+	0.432491i
$501$		0			0
$502$	−19.1803	−	1.67806i	−0.856060	−	0.0748956i
$503$	12.8017	−	3.43021i	0.570800	−	0.152946i	0.0381368	−	0.999273i	$-0.487858\pi$
$503$	12.8017	−	3.43021i	0.570800	−	0.152946i	0.532664	+	0.846327i	$0.321191\pi$
$504$		0			0
$505$	1.14411	+	1.21100i	0.0509124	+	0.0538889i
$506$	−1.04625	+	2.87454i	−0.0465113	+	0.127789i
$507$		0			0
$508$	−9.32045	+	0.815434i	−0.413528	+	0.0361790i
$509$	−11.2582	+	4.09765i	−0.499011	+	0.181625i	−0.579249	−	0.815151i	$-0.696654\pi$
$509$	−11.2582	+	4.09765i	−0.499011	+	0.181625i	0.0802381	+	0.996776i	$0.474432\pi$
$510$		0			0
$511$	−0.229857	−	1.30358i	−0.0101683	−	0.0576670i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$		−	22.1595i		−	0.977414i
$515$	−9.60366	+	24.2229i	−0.423188	+	1.06739i
$516$		0			0
$517$	−3.94049	−	1.83748i	−0.173303	−	0.0808123i
$518$	0.108667	+	1.24207i	0.00477455	+	0.0545734i
$519$		0			0
$520$	−0.550129	+	4.73518i	−0.0241248	+	0.207651i
$521$	−21.4889	+	12.4066i	−0.941447	+	0.543545i	−0.890414	−	0.455152i	$-0.849585\pi$
$521$	−21.4889	+	12.4066i	−0.941447	+	0.543545i	−0.0510334	+	0.998697i	$0.516251\pi$
$522$		0			0
$523$	9.08976	+	33.9235i	0.397468	+	1.48337i	0.817536	+	0.575877i	$0.195339\pi$
$523$	9.08976	+	33.9235i	0.397468	+	1.48337i	−0.420069	+	0.907492i	$0.637994\pi$
$524$	−3.26877	+	2.74282i	−0.142797	+	0.119821i
$525$		0			0
$526$	−2.54781	+	14.4493i	−0.111090	+	0.630021i
$527$	23.9296	+	34.1751i	1.04239	+	1.48869i
$528$		0			0
$529$	−12.7776	−	15.2277i	−0.555547	−	0.662076i
$530$	14.5790	+	4.35364i	0.633272	+	0.189110i
$531$		0			0
$532$	−0.256951	+	0.958955i	−0.0111402	+	0.0415760i
$533$	4.68798	+	10.0534i	0.203059	+	0.435462i
$534$		0			0
$535$	12.4667	+	37.5351i	0.538983	+	1.62278i
$536$	2.95677	+	8.12367i	0.127713	+	0.350889i
$537$		0			0
$538$	−3.29251	−	2.30544i	−0.141950	−	0.0993946i
$539$	12.0891			0.520715
$540$		0			0
$541$	−11.7514			−0.505234			−0.252617	−	0.967566i	$-0.581291\pi$
$541$	−11.7514			−0.505234			−0.252617	+	0.967566i	$0.581291\pi$
$542$	−5.55766	−	3.89151i	−0.238722	−	0.167155i
$543$		0			0
$544$	−2.22206	−	6.10507i	−0.0952702	−	0.261753i
$545$	−7.40146	−	3.71072i	−0.317044	−	0.158950i
$546$		0			0
$547$	−13.2418	−	28.3971i	−0.566179	−	1.21417i	−0.956023	−	0.293293i	$-0.905249\pi$
$547$	−13.2418	−	28.3971i	−0.566179	−	1.21417i	0.389844	−	0.920881i	$-0.372529\pi$
$548$	4.28118	−	15.9776i	0.182883	−	0.682529i
$549$		0			0
$550$	6.45894	−	5.76407i	0.275410	−	0.245781i
$551$	−17.6417	−	21.0246i	−0.751563	−	0.895678i
$552$		0			0
$553$	0.00453441	+	0.00647581i	0.000192823	+	0.000275379i
$554$	4.63511	−	26.2870i	0.196927	−	1.11683i
$555$		0			0
$556$	−6.27258	+	5.26332i	−0.266016	+	0.223214i
$557$	3.20099	+	11.9463i	0.135630	+	0.506180i	0.999995	+	0.00331318i	$0.00105462\pi$
$557$	3.20099	+	11.9463i	0.135630	+	0.506180i	−0.864364	+	0.502867i	$0.832279\pi$
$558$		0			0
$559$	3.63869	−	2.10080i	0.153900	−	0.0888543i
$560$	−0.232951	+	0.184457i	−0.00984396	+	0.00779472i
$561$		0			0
$562$	−0.489021	−	5.58953i	−0.0206281	−	0.235780i
$563$	−0.864232	−	0.402998i	−0.0364230	−	0.0169843i	0.404321	−	0.914617i	$-0.367508\pi$
$563$	−0.864232	−	0.402998i	−0.0364230	−	0.0169843i	−0.440744	+	0.897633i	$0.645286\pi$
$564$		0			0
$565$	12.2044	+	4.83869i	0.513444	+	0.203565i
$566$		−	8.53604i		−	0.358797i
$567$		0			0
$568$	−7.00974	+	7.00974i	−0.294122	+	0.294122i
$569$	−4.78100	−	27.1144i	−0.200430	−	1.13669i	−0.904471	−	0.426535i	$-0.859734\pi$
$569$	−4.78100	−	27.1144i	−0.200430	−	1.13669i	0.704041	−	0.710159i	$-0.251377\pi$
$570$		0			0
$571$	38.4108	−	13.9804i	1.60744	−	0.585061i	0.626511	−	0.779413i	$-0.284482\pi$
$571$	38.4108	−	13.9804i	1.60744	−	0.585061i	0.980932	+	0.194351i	$0.0622602\pi$
$572$	3.67706	−	0.321701i	0.153746	−	0.0134510i
$573$		0			0
$574$	−0.236482	+	0.649729i	−0.00987057	+	0.0271192i
$575$	−1.79841	−	8.64903i	−0.0749990	−	0.360689i
$576$		0			0
$577$	7.60211	−	2.03698i	0.316480	−	0.0848006i	−0.0970823	−	0.995276i	$-0.530951\pi$
$577$	7.60211	−	2.03698i	0.316480	−	0.0848006i	0.413562	+	0.910476i	$0.364284\pi$
$578$	−25.1135	−	2.19715i	−1.04458	−	0.0913892i
$579$		0			0
$580$	−0.483321	−	8.20017i	−0.0200688	−	0.340493i
$581$	0.590361	+	0.104097i	0.0244923	+	0.00431865i
$582$		0			0
$583$	1.02679	−	11.7363i	0.0425253	−	0.486067i
$584$	−4.98064	+	8.62672i	−0.206100	+	0.356976i
$585$		0			0
$586$	4.23170	+	7.32952i	0.174810	+	0.302780i
$587$	6.89440	−	3.21491i	0.284562	−	0.132694i	−0.275097	−	0.961417i	$-0.588710\pi$
$587$	6.89440	−	3.21491i	0.284562	−	0.132694i	0.559659	+	0.828723i	$0.310932\pi$
$588$		0			0
$589$	−30.8383	+	36.7516i	−1.27067	+	1.51432i
$590$	−7.07343	−	1.45542i	−0.291209	−	0.0599189i
$591$		0			0
$592$	5.38172	−	7.68590i	0.221188	−	0.315889i
$593$	−8.52962	−	8.52962i	−0.350270	−	0.350270i	0.509940	−	0.860210i	$-0.329668\pi$
$593$	−8.52962	−	8.52962i	−0.350270	−	0.350270i	−0.860210	+	0.509940i	$0.829668\pi$
$594$		0			0
$595$	0.446500	+	1.87812i	0.0183047	+	0.0769953i
$596$	11.7631	−	2.07416i	0.481837	−	0.0849609i
$597$		0			0
$598$	1.59184	−	3.41371i	0.0650952	−	0.139597i
$599$	−11.1483	−	9.35457i	−0.455509	−	0.382217i	0.385967	−	0.922513i	$-0.373868\pi$
$599$	−11.1483	−	9.35457i	−0.455509	−	0.382217i	−0.841475	+	0.540296i	$0.818312\pi$
$600$		0			0
$601$	8.43673	+	3.07072i	0.344141	+	0.125257i	0.508308	−	0.861175i	$-0.330271\pi$
$601$	8.43673	+	3.07072i	0.344141	+	0.125257i	−0.164167	+	0.986433i	$0.552493\pi$
$602$	0.252969	+	0.0677828i	0.0103102	+	0.00276262i
$603$		0			0
$604$	15.9979	+	9.23637i	0.650944	+	0.375823i
$605$	14.3604	+	10.6754i	0.583832	+	0.434017i
$606$		0			0
$607$	12.8402	−	8.99079i	0.521167	−	0.364925i	−0.283197	−	0.959062i	$-0.591395\pi$
$607$	12.8402	−	8.99079i	0.521167	−	0.364925i	0.804364	+	0.594137i	$0.202506\pi$
$608$	6.11994	−	4.28523i	0.248196	−	0.173789i
$609$		0			0
$610$	−24.3905	+	3.58999i	−0.987542	+	0.145354i
$611$	4.63633	+	2.67679i	0.187566	+	0.108291i
$612$		0			0
$613$	32.7054	+	8.76339i	1.32096	+	0.353950i	0.849337	−	0.527851i	$-0.177002\pi$
$613$	32.7054	+	8.76339i	1.32096	+	0.353950i	0.471622	+	0.881801i	$0.343669\pi$
$614$	−4.32375	−	1.57372i	−0.174492	−	0.0635100i
$615$		0			0
$616$	0.176246	+	0.147888i	0.00710115	+	0.00595857i
$617$	−12.0846	+	25.9156i	−0.486509	+	1.04332i	0.497869	+	0.867252i	$0.334116\pi$
$617$	−12.0846	+	25.9156i	−0.486509	+	1.04332i	−0.984378	+	0.176069i	$0.943662\pi$
$618$		0			0
$619$	−5.39482	+	0.951252i	−0.216836	+	0.0382341i	−0.281011	−	0.959705i	$-0.590670\pi$
$619$	−5.39482	+	0.951252i	−0.216836	+	0.0382341i	0.0641746	+	0.997939i	$0.479559\pi$
$620$	−13.9697	+	3.32112i	−0.561036	+	0.133380i
$621$		0			0
$622$	23.8502	+	23.8502i	0.956306	+	0.956306i
$623$	1.15042	−	1.64297i	0.0460905	−	0.0658241i
$624$		0			0
$625$	−7.10351	+	23.9696i	−0.284140	+	0.958783i
$626$	−5.73358	+	6.83302i	−0.229160	+	0.273102i
$627$		0			0
$628$	18.8447	−	8.78742i	0.751985	−	0.350656i
$629$	−30.4793	−	52.7917i	−1.21529	−	2.10494i
$630$		0			0
$631$	−19.5963	+	33.9418i	−0.780117	+	1.35120i	0.151756	+	0.988418i	$0.451507\pi$
$631$	−19.5963	+	33.9418i	−0.780117	+	1.35120i	−0.931873	+	0.362784i	$0.881826\pi$
$632$	0.00518506	−	0.0592655i	0.000206251	−	0.00235746i
$633$		0			0
$634$	25.0828	+	4.42278i	0.996167	+	0.175651i
$635$	−15.6380	−	13.8972i	−0.620575	−	0.551493i
$636$		0			0
$637$	−14.8289	−	1.29736i	−0.587541	−	0.0514032i
$638$	−6.14367	+	1.64619i	−0.243230	+	0.0651734i
$639$		0			0
$640$	2.23517	+	0.0634828i	0.0883527	+	0.00250938i
$641$	10.9964	−	30.2123i	0.434330	−	1.19331i	−0.508799	−	0.860886i	$-0.669910\pi$
$641$	10.9964	−	30.2123i	0.434330	−	1.19331i	0.943129	−	0.332427i	$-0.107868\pi$
$642$		0			0
$643$	27.0846	−	2.36960i	1.06811	−	0.0934477i	0.460483	−	0.887668i	$-0.347676\pi$
$643$	27.0846	−	2.36960i	1.06811	−	0.0934477i	0.607629	+	0.794221i	$0.292121\pi$
$644$	0.220621	−	0.0802993i	0.00869367	−	0.00316424i
$645$		0			0
$646$	−8.42864	−	47.8012i	−0.331621	−	1.88071i
$647$	−1.16772	+	1.16772i	−0.0459080	+	0.0459080i	−0.729688	−	0.683780i	$-0.760335\pi$
$647$	−1.16772	+	1.16772i	−0.0459080	+	0.0459080i	0.683780	+	0.729688i	$0.260335\pi$
$648$		0			0
$649$			5.59169i			0.219493i
$650$	−8.54130	+	6.37723i	−0.335017	+	0.250135i
$651$		0			0
$652$	6.63250	+	3.09279i	0.259749	+	0.121123i
$653$	2.74605	+	31.3876i	0.107461	+	1.22829i	0.838097	+	0.545522i	$0.183668\pi$
$653$	2.74605	+	31.3876i	0.107461	+	1.22829i	−0.730635	+	0.682768i	$0.760776\pi$
$654$		0			0
$655$	−9.47771	−	1.10111i	−0.370325	−	0.0430240i
$656$	4.50615	−	2.60163i	0.175936	−	0.101576i
$657$		0			0
$658$	0.0863672	+	0.322327i	0.00336694	+	0.0125656i
$659$	17.4560	−	14.6474i	0.679991	−	0.570580i	−0.236013	−	0.971750i	$-0.575841\pi$
$659$	17.4560	−	14.6474i	0.679991	−	0.570580i	0.916004	+	0.401170i	$0.131396\pi$
$660$		0			0
$661$	−4.88442	+	27.7009i	−0.189982	+	1.07744i	0.729403	+	0.684084i	$0.239798\pi$
$661$	−4.88442	+	27.7009i	−0.189982	+	1.07744i	−0.919385	+	0.393358i	$0.871313\pi$
$662$	−8.30456	−	11.8601i	−0.322766	−	0.460958i
$663$		0			0
$664$	−2.89976	−	3.45580i	−0.112532	−	0.134111i
$665$	−1.95325	+	1.05494i	−0.0757439	+	0.0409087i
$666$		0			0
$667$	−1.67987	+	6.26936i	−0.0650448	+	0.242751i
$668$	−4.85514	−	10.4119i	−0.187851	−	0.402848i
$669$		0			0
$670$	−8.66368	+	17.2807i	−0.334707	+	0.667612i
$671$	6.52882	+	17.9378i	0.252042	+	0.692481i
$672$		0			0
$673$	1.45722	+	1.02036i	0.0561718	+	0.0393319i	0.601325	−	0.799004i	$-0.294640\pi$
$673$	1.45722	+	1.02036i	0.0561718	+	0.0393319i	−0.545153	+	0.838336i	$0.683529\pi$
$674$	−14.1666			−0.545677
$675$		0			0
$676$	8.45509			0.325196
$677$	11.7364	+	8.21791i	0.451066	+	0.315840i	0.776941	−	0.629573i	$-0.216770\pi$
$677$	11.7364	+	8.21791i	0.451066	+	0.315840i	−0.325875	+	0.945413i	$0.605659\pi$
$678$		0			0
$679$	0.0508228	+	0.139634i	0.00195040	+	0.00535868i
$680$	6.51089	−	12.9867i	0.249681	−	0.498019i
$681$		0			0
$682$	4.69874	+	10.0765i	0.179924	+	0.385849i
$683$	2.94318	−	10.9841i	0.112618	−	0.420295i	−0.886480	−	0.462767i	$-0.846857\pi$
$683$	2.94318	−	10.9841i	0.112618	−	0.420295i	0.999098	+	0.0424719i	$0.0135233\pi$
$684$		0			0
$685$	32.5441	−	17.5768i	1.24345	−	0.671575i
$686$	−1.19432	−	1.42333i	−0.0455992	−	0.0543430i
$687$		0			0
$688$	−1.13043	−	1.61442i	−0.0430972	−	0.0615491i
$689$	−2.51898	+	14.2859i	−0.0959656	+	0.544248i
$690$		0			0
$691$	−15.5250	+	13.0270i	−0.590598	+	0.495571i	−0.888408	−	0.459055i	$-0.848188\pi$
$691$	−15.5250	+	13.0270i	−0.590598	+	0.495571i	0.297810	+	0.954625i	$0.403744\pi$
$692$	0.164835	+	0.615172i	0.00626608	+	0.0233853i
$693$		0			0
$694$	−25.9662	+	14.9916i	−0.985662	+	0.569072i
$695$	−18.1872	−	2.11297i	−0.689879	−	0.0801496i
$696$		0			0
$697$	−2.94629	−	33.6763i	−0.111599	−	1.27558i
$698$	−12.1672	−	5.67366i	−0.460536	−	0.214751i
$699$		0			0
$700$	−0.657536	−	0.0953819i	−0.0248525	−	0.00360510i
$701$			27.0751i			1.02261i	0.859398	+	0.511307i	$0.170839\pi$
$701$			27.0751i			1.02261i	−0.859398	+	0.511307i	$0.829161\pi$
$702$		0			0
$703$	49.5676	−	49.5676i	1.86948	−	1.86948i
$704$	−0.300652	−	1.70508i	−0.0113312	−	0.0642627i
$705$		0			0
$706$	−7.94144	+	2.89045i	−0.298880	+	0.108783i
$707$	−0.0986286	+	0.00862889i	−0.00370931	+	0.000324523i
$708$		0			0
$709$	8.49166	−	23.3306i	0.318911	−	0.876201i	−0.671863	−	0.740675i	$-0.734506\pi$
$709$	8.49166	−	23.3306i	0.318911	−	0.876201i	0.990774	−	0.135525i	$-0.0432721\pi$
$710$	−22.1578	−	0.629322i	−0.831568	−	0.0236180i
$711$		0			0
$712$	−14.5793	+	3.90651i	−0.546382	+	0.146403i
$713$	11.3025	+	0.988837i	0.423280	+	0.0370322i
$714$		0			0
$715$	6.16943	+	5.48265i	0.230724	+	0.205039i
$716$	−25.8860	−	4.56440i	−0.967405	−	0.170580i
$717$		0			0
$718$	−1.51483	+	17.3145i	−0.0565328	+	0.646173i
$719$	17.2231	−	29.8313i	0.642314	−	1.11252i	−0.342601	−	0.939481i	$-0.611308\pi$
$719$	17.2231	−	29.8313i	0.642314	−	1.11252i	0.984915	−	0.173039i	$-0.0553586\pi$
$720$		0			0
$721$	−0.774256	−	1.34105i	−0.0288348	−	0.0499433i
$722$	33.3674	−	15.5595i	1.24181	−	0.579064i
$723$		0			0
$724$	5.09806	−	6.07563i	0.189468	−	0.225799i
$725$	12.5863	−	13.3779i	0.467443	−	0.496841i
$726$		0			0
$727$	26.9538	−	38.4941i	0.999662	−	1.42767i	0.0980196	−	0.995184i	$-0.468749\pi$
$727$	26.9538	−	38.4941i	0.999662	−	1.42767i	0.901643	−	0.432481i	$-0.142362\pi$
$728$	−0.200318	−	0.200318i	−0.00742427	−	0.00742427i
$729$		0			0
$730$	−21.6701	+	5.15182i	−0.802047	+	0.190677i
$731$	−12.6098	+	2.22345i	−0.466390	+	0.0822371i
$732$		0			0
$733$	12.0280	−	25.7941i	0.444264	−	0.952728i	−0.548887	−	0.835896i	$-0.684948\pi$
$733$	12.0280	−	25.7941i	0.444264	−	0.952728i	0.993152	−	0.116832i	$-0.0372738\pi$
$734$	−5.77380	−	4.84480i	−0.213115	−	0.178825i
$735$		0			0
$736$	−1.66025	−	0.604283i	−0.0611978	−	0.0222742i
$737$	14.4579	+	3.87397i	0.532562	+	0.142700i
$738$		0			0
$739$	0.741384	+	0.428038i	0.0272723	+	0.0157457i	0.513574	−	0.858045i	$-0.328321\pi$
$739$	0.741384	+	0.428038i	0.0272723	+	0.0157457i	−0.486302	+	0.873791i	$0.661654\pi$
$740$	20.7568	−	3.05516i	0.763036	−	0.112310i
$741$		0			0
$742$	−0.740676	+	0.518627i	−0.0271911	+	0.0190394i
$743$	36.3851	−	25.4771i	1.33484	−	0.934664i	0.334867	−	0.942265i	$-0.391309\pi$
$743$	36.3851	−	25.4771i	1.33484	−	0.934664i	0.999971	+	0.00760174i	$0.00241973\pi$
$744$		0			0
$745$	21.4349	+	15.9346i	0.785315	+	0.583798i
$746$	−31.4488	−	18.1570i	−1.15142	−	0.664774i
$747$		0			0
$748$	−10.8653	−	2.91135i	−0.397275	−	0.106450i
$749$	−2.20868	−	0.803893i	−0.0807033	−	0.0293736i
$750$		0			0
$751$	−19.3873	−	16.2679i	−0.707452	−	0.593623i	0.216431	−	0.976298i	$-0.430558\pi$
$751$	−19.3873	−	16.2679i	−0.707452	−	0.593623i	−0.923883	+	0.382675i	$0.875003\pi$
$752$	1.06128	−	2.27592i	0.0387008	−	0.0829942i
$753$		0			0
$754$	7.71267	−	1.35995i	0.280879	−	0.0495266i
$755$	9.55381	+	40.1863i	0.347699	+	1.46253i
$756$		0			0
$757$	−4.67113	−	4.67113i	−0.169775	−	0.169775i	0.617105	−	0.786881i	$-0.288305\pi$
$757$	−4.67113	−	4.67113i	−0.169775	−	0.169775i	−0.786881	+	0.617105i	$0.788305\pi$
$758$	−13.2195	+	18.8793i	−0.480152	+	0.685729i
$759$		0			0
$760$	16.3630	+	3.36684i	0.593550	+	0.122128i
$761$	−11.3003	+	13.4672i	−0.409636	+	0.488186i	−0.930933	−	0.365190i	$-0.881004\pi$
$761$	−11.3003	+	13.4672i	−0.409636	+	0.488186i	0.521297	+	0.853376i	$0.325449\pi$
$762$		0			0
$763$	0.445933	−	0.207942i	0.0161438	−	0.00752800i
$764$	10.8822	+	18.8485i	0.393703	+	0.681913i
$765$		0			0
$766$	−6.37450	+	11.0410i	−0.230320	+	0.398926i
$767$	0.600079	−	6.85893i	0.0216676	−	0.247662i
$768$		0			0
$769$	39.0115	+	6.87878i	1.40679	+	0.248055i	0.824930	−	0.565234i	$-0.191214\pi$
$769$	39.0115	+	6.87878i	1.40679	+	0.248055i	0.581859	+	0.813289i	$0.302325\pi$
$770$	0.0302698	+	0.513567i	0.00109085	+	0.0185077i
$771$		0			0
$772$	−21.6550	−	1.89456i	−0.779380	−	0.0681869i
$773$	27.3064	−	7.31673i	0.982143	−	0.263164i	0.268196	−	0.963364i	$-0.413573\pi$
$773$	27.3064	−	7.31673i	0.982143	−	0.263164i	0.713947	+	0.700200i	$0.246906\pi$
$774$		0			0
$775$	−26.8501	−	17.6062i	−0.964485	−	0.632434i
$776$	0.382461	−	1.05080i	0.0137295	−	0.0377216i
$777$		0			0
$778$	26.5156	−	2.31982i	0.950631	−	0.0831695i
$779$	36.5295	−	13.2956i	1.30880	−	0.476366i
$780$		0			0
$781$	2.98044	+	16.9029i	0.106649	+	0.604835i
$782$	−8.11668	+	8.11668i	−0.290252	+	0.290252i
$783$		0			0
$784$			6.98234i			0.249369i
$785$	43.2211	+	17.1359i	1.54263	+	0.611607i
$786$		0			0
$787$	23.1473	+	10.7937i	0.825111	+	0.384755i	0.788849	−	0.614587i	$-0.210677\pi$
$787$	23.1473	+	10.7937i	0.825111	+	0.384755i	0.0362616	+	0.999342i	$0.488455\pi$
$788$	−1.35642	−	15.5039i	−0.0483203	−	0.552304i
$789$		0			0
$790$	0.104292	−	0.0825811i	0.00371054	−	0.00293810i
$791$	−0.675673	+	0.390100i	−0.0240242	+	0.0138704i
$792$		0			0
$793$	−6.08343	−	22.7037i	−0.216029	−	0.806231i
$794$	13.4679	−	11.3009i	0.477958	−	0.401054i
$795$		0			0
$796$	−2.86249	+	16.2340i	−0.101458	+	0.575399i
$797$	−0.652471	−	0.931825i	−0.0231117	−	0.0330069i	0.807430	−	0.589963i	$-0.200858\pi$
$797$	−0.652471	−	0.931825i	−0.0231117	−	0.0330069i	−0.830542	+	0.556957i	$0.811969\pi$
$798$		0			0
$799$	−10.4870	−	12.4980i	−0.371005	−	0.442147i
$800$	3.32917	+	3.73050i	0.117704	+	0.131893i
$801$		0			0
$802$	5.61001	−	20.9368i	0.198096	−	0.739305i
$803$	7.28882	+	15.6309i	0.257217	+	0.551603i
$804$		0			0
$805$	0.469305	+	0.235286i	0.0165408	+	0.00829274i
$806$	−4.68225	−	12.8644i	−0.164925	−	0.453128i
$807$		0			0
$808$	0.610312	+	0.427345i	0.0214707	+	0.0150339i
$809$	48.5182			1.70581			0.852905	−	0.522066i	$-0.174839\pi$
$809$	48.5182			1.70581			0.852905	+	0.522066i	$0.174839\pi$
$810$		0			0
$811$	−40.9981			−1.43964			−0.719820	−	0.694161i	$-0.755776\pi$
$811$	−40.9981			−1.43964			−0.719820	+	0.694161i	$0.755776\pi$
$812$	0.399877	+	0.279997i	0.0140329	+	0.00982597i
$813$		0			0
$814$	−5.55617	−	15.2654i	−0.194744	−	0.535054i
$815$	5.15797	+	15.5297i	0.180676	+	0.543983i
$816$		0			0
$817$	−6.22276	−	13.3447i	−0.217707	−	0.466874i
$818$	4.27038	−	15.9373i	0.149310	−	0.557234i
$819$		0			0
$820$	11.1484	+	3.32916i	0.389317	+	0.116259i
$821$	−15.7202	−	18.7346i	−0.548638	−	0.653842i	0.418463	−	0.908234i	$-0.362569\pi$
$821$	−15.7202	−	18.7346i	−0.548638	−	0.653842i	−0.967101	+	0.254392i	$0.918125\pi$
$822$		0			0
$823$	−25.5543	−	36.4953i	−0.890767	−	1.27215i	−0.961543	−	0.274654i	$-0.911437\pi$
$823$	−25.5543	−	36.4953i	−0.890767	−	1.27215i	0.0707764	−	0.997492i	$-0.477452\pi$
$824$	−2.02355	+	11.4761i	−0.0704936	+	0.399789i
$825$		0			0
$826$	0.328757	−	0.275860i	0.0114389	−	0.00959839i
$827$	−1.77575	−	6.62719i	−0.0617489	−	0.230450i	0.928154	−	0.372196i	$-0.121395\pi$
$827$	−1.77575	−	6.62719i	−0.0617489	−	0.230450i	−0.989903	+	0.141746i	$0.954728\pi$
$828$		0			0
$829$	25.2777	−	14.5941i	0.877930	−	0.506873i	0.00795467	−	0.999968i	$-0.497468\pi$
$829$	25.2777	−	14.5941i	0.877930	−	0.506873i	0.869975	+	0.493095i	$0.164135\pi$
$830$	1.16412	−	10.0200i	0.0404071	−	0.347800i
$831$		0			0
$832$	0.185806	+	2.12377i	0.00644165	+	0.0736284i
$833$	41.1132	+	19.1714i	1.42449	+	0.664250i
$834$		0			0
$835$	9.46776	−	23.8801i	0.327645	−	0.826405i
$836$		−	12.9353i		−	0.447377i
$837$		0			0
$838$	−22.6928	+	22.6928i	−0.783911	+	0.783911i
$839$	−4.57756	−	25.9606i	−0.158035	−	0.896260i	−0.955959	−	0.293502i	$-0.905179\pi$
$839$	−4.57756	−	25.9606i	−0.158035	−	0.896260i	0.797924	−	0.602759i	$-0.205932\pi$
$840$		0			0
$841$	14.5697	−	5.30293i	0.502403	−	0.182860i
$842$	−7.70287	+	0.673914i	−0.265459	+	0.0232246i
$843$		0			0
$844$	−2.34819	+	6.45160i	−0.0808280	+	0.222073i
$845$	12.9837	+	13.7428i	0.446654	+	0.472767i
$846$		0			0
$847$	−1.02714	+	0.275222i	−0.0352930	+	0.00945673i
$848$	6.77854	+	0.593046i	0.232776	+	0.0203653i
$849$		0			0
$850$	31.1067	−	9.35985i	1.06695	−	0.321040i
$851$	−16.3256	−	2.87865i	−0.559636	−	0.0986789i
$852$		0			0
$853$	−1.31023	+	14.9760i	−0.0448613	+	0.512767i	0.940207	+	0.340604i	$0.110631\pi$
$853$	−1.31023	+	14.9760i	−0.0448613	+	0.512767i	−0.985068	+	0.172164i	$0.944924\pi$
$854$	0.732539	−	1.26880i	0.0250670	−	0.0434173i
$855$		0			0
$856$	8.84392	+	15.3181i	0.302279	+	0.523563i
$857$	−33.1034	+	15.4364i	−1.13079	+	0.527297i	−0.895692	−	0.444674i	$-0.853319\pi$
$857$	−33.1034	+	15.4364i	−1.13079	+	0.527297i	−0.235100	+	0.971971i	$0.575542\pi$
$858$		0			0
$859$	−21.6541	+	25.8064i	−0.738829	+	0.880503i	−0.996314	−	0.0857798i	$-0.972662\pi$
$859$	−21.6541	+	25.8064i	−0.738829	+	0.880503i	0.257485	+	0.966282i	$0.417106\pi$
$860$	0.888162	−	4.31651i	0.0302861	−	0.147192i
$861$		0			0
$862$	3.68185	−	5.25823i	0.125404	−	0.179096i
$863$	−22.9912	−	22.9912i	−0.782630	−	0.782630i	0.197644	−	0.980274i	$-0.436671\pi$
$863$	−22.9912	−	22.9912i	−0.782630	−	0.782630i	−0.980274	+	0.197644i	$0.936671\pi$
$864$		0			0
$865$	−0.746772	+	1.21259i	−0.0253910	+	0.0412292i
$866$	3.53402	−	0.623143i	0.120091	−	0.0211752i
$867$		0			0
$868$	0.360628	−	0.773370i	0.0122405	−	0.0262499i
$869$	−0.0789052	−	0.0662093i	−0.00267667	−	0.00224600i
$870$		0			0
$871$	−17.3187	−	6.30349i	−0.586821	−	0.213586i
$872$	−3.57656	−	0.958337i	−0.121118	−	0.0324534i
$873$		0			0
$874$	−11.4315	−	6.59996i	−0.386675	−	0.223247i
$875$	−0.854688	−	1.21522i	−0.0288937	−	0.0410820i
$876$		0			0
$877$	−13.1012	+	9.17353i	−0.442395	+	0.309768i	−0.773466	−	0.633838i	$-0.781479\pi$
$877$	−13.1012	+	9.17353i	−0.442395	+	0.309768i	0.331071	+	0.943606i	$0.392590\pi$
$878$	22.0134	−	15.4139i	0.742915	−	0.520194i
$879$		0			0
$880$	2.30974	−	3.10702i	0.0778613	−	0.104738i
$881$	−17.3126	−	9.99544i	−0.583277	−	0.336755i	0.179158	−	0.983820i	$-0.442663\pi$
$881$	−17.3126	−	9.99544i	−0.583277	−	0.336755i	−0.762435	+	0.647065i	$0.775996\pi$
$882$		0			0
$883$	43.1918	+	11.5732i	1.45352	+	0.389469i	0.897246	−	0.441530i	$-0.145564\pi$
$883$	43.1918	+	11.5732i	1.45352	+	0.389469i	0.556273	+	0.831000i	$0.312231\pi$
$884$	13.0153	+	4.73717i	0.437751	+	0.159328i
$885$		0			0
$886$	−28.8262	−	24.1880i	−0.968434	−	0.812613i
$887$	17.9788	−	38.5556i	0.603668	−	1.29457i	−0.332529	−	0.943093i	$-0.607902\pi$
$887$	17.9788	−	38.5556i	0.603668	−	1.29457i	0.936197	−	0.351476i	$-0.114320\pi$
$888$		0			0
$889$	1.22438	−	0.215891i	0.0410643	−	0.00724075i
$890$	−28.7378	−	17.6982i	−0.963292	−	0.593244i
$891$		0			0
$892$	−2.83058	−	2.83058i	−0.0947749	−	0.0947749i
$893$	10.7611	−	15.3684i	0.360105	−	0.514284i
$894$		0			0
$895$	−32.3319	−	49.0840i	−1.08074	−	1.64070i
$896$	−0.0854160	+	0.101795i	−0.00285355	+	0.00340072i
$897$		0			0
$898$	−1.18339	+	0.551826i	−0.0394904	+	0.0184147i
$899$	11.7951	+	20.4297i	0.393388	+	0.681368i
$900$		0			0
$901$	22.1038	−	38.2849i	0.736384	−	1.27545i
$902$	0.785171	−	8.97455i	0.0261434	−	0.298820i
$903$		0			0
$904$	5.78210	+	1.01954i	0.192310	+	0.0339094i
$905$	17.7039	−	1.04348i	0.588498	−	0.0346863i
$906$		0			0
$907$	50.1405	+	4.38673i	1.66489	+	0.145659i	0.880319	−	0.474382i	$-0.157328\pi$
$907$	50.1405	+	4.38673i	1.66489	+	0.145659i	0.784570	+	0.620041i	$0.212884\pi$
$908$	−3.00501	+	0.805189i	−0.0997246	+	0.0267211i
$909$		0			0
$910$	0.0179842	−	0.633205i	0.000596169	−	0.0209905i
$911$	−20.5086	+	56.3468i	−0.679479	+	1.86685i	−0.231405	+	0.972857i	$0.574332\pi$
$911$	−20.5086	+	56.3468i	−0.679479	+	1.86685i	−0.448074	+	0.893997i	$0.647890\pi$
$912$		0			0
$913$	−7.78094	+	0.680744i	−0.257512	+	0.0225294i
$914$	−21.5437	+	7.84128i	−0.712604	+	0.259367i
$915$		0			0
$916$	3.68452	+	20.8959i	0.121740	+	0.690421i
$917$	0.400947	−	0.400947i	0.0132404	−	0.0132404i
$918$		0			0
$919$		−	39.5860i		−	1.30582i	−0.757435	−	0.652911i	$-0.773548\pi$
$919$		−	39.5860i		−	1.30582i	0.757435	−	0.652911i	$-0.226452\pi$
$920$	−1.56731	−	3.62650i	−0.0516727	−	0.119562i
$921$		0			0
$922$	6.18721	+	2.88515i	0.203765	+	0.0950172i
$923$	−1.84194	−	21.0535i	−0.0606283	−	0.692984i
$924$		0			0
$925$	36.8403	+	29.0464i	1.21130	+	0.955040i
$926$	22.7704	−	13.1465i	0.748282	−	0.432021i
$927$		0			0
$928$	−0.950795	−	3.54842i	−0.0312114	−	0.116482i
$929$	4.14920	−	3.48160i	0.136131	−	0.114227i	−0.572180	−	0.820128i	$-0.693902\pi$
$929$	4.14920	−	3.48160i	0.136131	−	0.114227i	0.708311	+	0.705901i	$0.249458\pi$
$930$		0			0
$931$	−9.05846	+	51.3731i	−0.296879	+	1.68368i
$932$	3.58286	+	5.11685i	0.117360	+	0.167608i
$933$		0			0
$934$	−12.6942	−	15.1283i	−0.415366	−	0.495014i
$935$	−11.9528	−	22.1311i	−0.390899	−	0.723764i
$936$		0			0
$937$	−4.27069	+	15.9384i	−0.139517	+	0.520686i	0.860421	+	0.509584i	$0.170201\pi$
$937$	−4.27069	+	15.9384i	−0.139517	+	0.520686i	−0.999938	+	0.0111023i	$0.996466\pi$
$938$	−0.485497	−	1.04115i	−0.0158520	−	0.0339948i
$939$		0			0
$940$	5.32897	−	1.76994i	0.173812	−	0.0577290i
$941$	−11.8457	−	32.5459i	−0.386160	−	1.06097i	−0.968715	−	0.248174i	$-0.920169\pi$
$941$	−11.8457	−	32.5459i	−0.386160	−	1.06097i	0.582556	−	0.812791i	$-0.302053\pi$
$942$		0			0
$943$	−7.53057	−	5.27296i	−0.245229	−	0.171711i
$944$	−3.22960			−0.105115
$945$		0			0
$946$	−3.41229			−0.110943
$947$	−14.2591	−	9.98434i	−0.463359	−	0.324448i	0.318478	−	0.947930i	$-0.396828\pi$
$947$	−14.2591	−	9.98434i	−0.463359	−	0.324448i	−0.781837	+	0.623483i	$0.785717\pi$
$948$		0			0
$949$	−7.26323	−	19.9556i	−0.235774	−	0.647785i
$950$	19.6548	+	31.7665i	0.637687	+	1.03064i
$951$		0			0
$952$	0.364858	+	0.782442i	0.0118251	+	0.0253591i
$953$	−1.24639	+	4.65159i	−0.0403746	+	0.150680i	−0.983170	−	0.182691i	$-0.941519\pi$
$953$	−1.24639	+	4.65159i	−0.0403746	+	0.150680i	0.942796	+	0.333371i	$0.108186\pi$
$954$		0			0
$955$	−13.9253	+	46.6317i	−0.450613	+	1.50897i
$956$	−4.15985	−	4.95752i	−0.134539	−	0.160338i
$957$		0			0
$958$	6.47641	+	9.24927i	0.209243	+	0.298830i
$959$	−0.381689	+	2.16466i	−0.0123254	+	0.0699007i
$960$		0			0
$961$	7.84148	−	6.57978i	0.252951	−	0.212251i
$962$	5.17713	+	19.3213i	0.166917	+	0.622944i
$963$		0			0
$964$	−19.8914	+	11.4843i	−0.640658	+	0.369884i
$965$	−30.1742	−	38.1071i	−0.971343	−	1.22671i
$966$		0			0
$967$	−1.49543	−	17.0929i	−0.0480898	−	0.549669i	−0.981578	−	0.191061i	$-0.938807\pi$
$967$	−1.49543	−	17.0929i	−0.0480898	−	0.549669i	0.933488	−	0.358608i	$-0.116749\pi$
$968$	7.25255	+	3.38192i	0.233106	+	0.108699i
$969$		0			0
$970$	2.29528	−	0.991977i	0.0736969	−	0.0318505i
$971$		−	22.5738i		−	0.724428i	−0.932095	−	0.362214i	$-0.882021\pi$
$971$		−	22.5738i		−	0.724428i	0.932095	−	0.362214i	$-0.117979\pi$
$972$		0			0
$973$	0.769393	−	0.769393i	0.0246656	−	0.0246656i
$974$	3.17772	+	18.0217i	0.101821	+	0.577454i
$975$		0			0
$976$	−10.3604	+	3.77087i	−0.331627	+	0.120702i
$977$	−1.95617	+	0.171143i	−0.0625834	+	0.00547534i	−0.118404	−	0.992965i	$-0.537778\pi$
$977$	−1.95617	+	0.171143i	−0.0625834	+	0.00547534i	0.0558210	+	0.998441i	$0.482222\pi$
$978$		0			0
$979$	−8.93796	+	24.5568i	−0.285658	+	0.784840i
$980$	−11.3490	+	10.7222i	−0.362532	+	0.342507i
$981$		0			0
$982$	12.1833	−	3.26452i	0.388786	−	0.104175i
$983$	28.8706	+	2.52585i	0.920828	+	0.0805620i	0.537703	−	0.843134i	$-0.319292\pi$
$983$	28.8706	+	2.52585i	0.920828	+	0.0805620i	0.383125	+	0.923696i	$0.374848\pi$
$984$		0			0
$985$	23.1170	−	26.0127i	0.736568	−	0.828833i
$986$	−23.5043	−	4.14444i	−0.748529	−	0.131986i
$987$		0			0
$988$	−1.38817	+	15.8668i	−0.0441635	+	0.504791i
$989$	−1.74105	+	3.01558i	−0.0553621	+	0.0958899i
$990$		0			0
$991$	−5.78192	−	10.0146i	−0.183669	−	0.318124i	0.759458	−	0.650556i	$-0.225464\pi$
$991$	−5.78192	−	10.0146i	−0.183669	−	0.318124i	−0.943127	+	0.332432i	$0.892131\pi$
$992$	−5.81990	+	2.71386i	−0.184782	+	0.0861653i
$993$		0			0
$994$	0.846752	−	1.00912i	0.0268573	−	0.0320073i
$995$	−30.7823	+	20.2765i	−0.975863	+	0.642807i
$996$		0			0
$997$	−24.6092	+	35.1456i	−0.779381	+	1.11307i	0.211374	+	0.977405i	$0.432206\pi$
$997$	−24.6092	+	35.1456i	−0.779381	+	1.11307i	−0.990755	+	0.135666i	$0.956683\pi$
$998$	7.11801	+	7.11801i	0.225317	+	0.225317i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.13		216
3.2	odd	2		270.2.r.a.257.2	yes	216
5.3	odd	4	inner	810.2.s.a.233.11		216
15.8	even	4		270.2.r.a.203.7	yes	216
27.2	odd	18	inner	810.2.s.a.737.11		216
27.25	even	9		270.2.r.a.137.7	yes	216
135.83	even	36	inner	810.2.s.a.413.13		216
135.133	odd	36		270.2.r.a.83.2	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.2	✓	216	135.133	odd	36
270.2.r.a.137.7	yes	216	27.25	even	9
270.2.r.a.203.7	yes	216	15.8	even	4
270.2.r.a.257.2	yes	216	3.2	odd	2
810.2.s.a.233.11		216	5.3	odd	4	inner
810.2.s.a.413.13		216	135.83	even	36	inner
810.2.s.a.557.13		216	1.1	even	1	trivial
810.2.s.a.737.11		216	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.00216 + 1.99892i) q^{5} +(-0.0561590 - 0.120433i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.96745 + 1.06261i) q^{10} +(1.11291 + 1.32632i) q^{11} +(-1.22280 - 1.74633i) q^{13} +(0.0230750 - 0.130865i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(1.68152 + 6.27550i) q^{17} +(-6.47014 + 3.73554i) q^{19} +(-2.22113 - 0.258049i) q^{20} +(0.150900 + 1.72480i) q^{22} +(1.60127 + 0.746684i) q^{23} +(-2.99136 - 4.00646i) q^{25} -2.13188i q^{26} +(0.0939629 - 0.0939629i) q^{28} +(0.637912 + 3.61778i) q^{29} +(6.03428 - 2.19630i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(-2.22206 + 6.10507i) q^{34} +(0.297017 + 0.00843582i) q^{35} +(-9.06304 + 2.42843i) q^{37} +(-7.44264 - 0.651147i) q^{38} +(-1.67143 - 1.48537i) q^{40} +(-5.12420 - 0.903535i) q^{41} +(-0.171770 + 1.96334i) q^{43} +(-0.865692 + 1.49942i) q^{44} +(0.883403 + 1.53010i) q^{46} +(-2.27592 + 1.06128i) q^{47} +(4.48816 - 5.34878i) q^{49} +(-0.152367 - 4.99768i) q^{50} +(1.22280 - 1.74633i) q^{52} +(-4.81146 - 4.81146i) q^{53} +(-3.76652 + 0.895445i) q^{55} +(0.130865 - 0.0230750i) q^{56} +(-1.55253 + 3.32940i) q^{58} +(2.47402 + 2.07595i) q^{59} +(10.3604 + 3.77087i) q^{61} +(6.20274 + 1.66202i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(4.71622 - 0.694171i) q^{65} +(7.08159 - 4.95858i) q^{67} +(-5.32193 + 3.72646i) q^{68} +(0.238464 + 0.177272i) q^{70} +(8.58515 + 4.95664i) q^{71} +(9.62186 + 2.57817i) q^{73} +(-8.81690 - 3.20909i) q^{74} +(-5.72317 - 4.80231i) q^{76} +(0.0972329 - 0.208517i) q^{77} +(-0.0585881 + 0.0103307i) q^{79} +(-0.517184 - 2.17544i) q^{80} +(-3.67925 - 3.67925i) q^{82} +(-2.58753 + 3.69538i) q^{83} +(-14.2294 - 2.92782i) q^{85} +(-1.26683 + 1.50975i) q^{86} +(-1.56917 + 0.731715i) q^{88} +(7.54680 + 13.0714i) q^{89} +(-0.141646 + 0.245338i) q^{91} +(-0.153987 + 1.76008i) q^{92} +(-2.47305 - 0.436065i) q^{94} +(-0.982942 - 16.6769i) q^{95} +(-1.11399 - 0.0974611i) q^{97} +(6.74442 - 1.80716i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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