LMFDB - Embedded newform 810.2.s.a.197.11

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			197.11
Character	$\chi$	$=$	810.197
Dual form			810.2.s.a.773.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 - 0.0871557i) q^{2} +(0.984808 - 0.173648i) q^{4} +(-2.20857 + 0.349587i) q^{5} +(-1.10212 + 0.771712i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 - 0.0871557i) q^{2} +(0.984808 - 0.173648i) q^{4} +(-2.20857 + 0.349587i) q^{5} +(-1.10212 + 0.771712i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.16970 + 0.540747i) q^{10} +(1.46618 + 4.02828i) q^{11} +(-0.298865 + 3.41605i) q^{13} +(-1.03067 + 0.864832i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-7.43061 - 1.99103i) q^{17} +(6.12582 + 3.53674i) q^{19} +(-2.11431 + 0.727791i) q^{20} +(1.81168 + 3.88517i) q^{22} +(-2.78440 + 3.97654i) q^{23} +(4.75558 - 1.54418i) q^{25} +3.42910i q^{26} +(-0.951369 + 0.951369i) q^{28} +(-0.00478023 - 0.00401109i) q^{29} +(0.582373 + 3.30280i) q^{31} +(0.906308 - 0.422618i) q^{32} +(-7.57586 - 1.33583i) q^{34} +(2.16433 - 2.08967i) q^{35} +(-1.24815 + 4.65816i) q^{37} +(6.41076 + 2.98938i) q^{38} +(-2.04284 + 0.909296i) q^{40} +(-0.705833 - 0.841179i) q^{41} +(3.14516 - 6.74482i) q^{43} +(2.14340 + 3.71249i) q^{44} +(-2.42723 + 4.20409i) q^{46} +(2.04873 + 2.92589i) q^{47} +(-1.77501 + 4.87681i) q^{49} +(4.60290 - 1.95278i) q^{50} +(0.298865 + 3.41605i) q^{52} +(8.13905 + 8.13905i) q^{53} +(-4.64639 - 8.38420i) q^{55} +(-0.864832 + 1.03067i) q^{56} +(-0.00511163 - 0.00357920i) q^{58} +(-8.71384 - 3.17158i) q^{59} +(1.24279 - 7.04819i) q^{61} +(0.868015 + 3.23947i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-0.534140 - 7.64906i) q^{65} +(-5.54705 - 0.485304i) q^{67} +(-7.66346 - 0.670466i) q^{68} +(1.97397 - 2.27035i) q^{70} +(2.37880 - 1.37340i) q^{71} +(-2.76825 - 10.3313i) q^{73} +(-0.837415 + 4.74922i) q^{74} +(6.64690 + 2.41927i) q^{76} +(-4.72458 - 3.30818i) q^{77} +(-3.61314 + 4.30597i) q^{79} +(-1.95581 + 1.08388i) q^{80} +(-0.776460 - 0.776460i) q^{82} +(-1.20379 - 13.7594i) q^{83} +(17.1071 + 1.79968i) q^{85} +(2.54534 - 6.99327i) q^{86} +(2.45881 + 3.51155i) q^{88} +(0.692740 - 1.19986i) q^{89} +(-2.30682 - 3.99553i) q^{91} +(-2.05158 + 4.39964i) q^{92} +(2.29594 + 2.73620i) q^{94} +(-14.7657 - 5.66964i) q^{95} +(-4.62517 - 2.15675i) q^{97} +(-1.34322 + 5.01296i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * 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} + 48 q^{92} + 60 q^{95} - 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.996195	−	0.0871557i	0.704416	−	0.0616284i
$2$	0.996195	−	0.0871557i	0.704416	−	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	−	0.173648i	0.492404	−	0.0868241i
$5$	−2.20857	+	0.349587i	−0.987703	+	0.156340i
$5$	−2.20857	+	0.349587i	−0.987703	+	0.156340i
$6$		0			0
$7$	−1.10212	+	0.771712i	−0.416562	+	0.291680i	−0.763007	−	0.646391i	$-0.776278\pi$
$7$	−1.10212	+	0.771712i	−0.416562	+	0.291680i	0.346445	+	0.938070i	$0.387389\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$		0			0
$10$	−2.16970	+	0.540747i	−0.686119	+	0.170999i
$11$	1.46618	+	4.02828i	0.442068	+	1.21457i	0.938129	+	0.346285i	$0.112557\pi$
$11$	1.46618	+	4.02828i	0.442068	+	1.21457i	−0.496061	+	0.868288i	$0.665221\pi$
$12$		0			0
$13$	−0.298865	+	3.41605i	−0.0828903	+	0.947441i	0.834907	+	0.550391i	$0.185521\pi$
$13$	−0.298865	+	3.41605i	−0.0828903	+	0.947441i	−0.917797	+	0.397050i	$0.870034\pi$
$14$	−1.03067	+	0.864832i	−0.275457	+	0.231136i
$15$		0			0
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−7.43061	−	1.99103i	−1.80219	−	0.482895i	−0.807871	−	0.589359i	$-0.799380\pi$
$17$	−7.43061	−	1.99103i	−1.80219	−	0.482895i	−0.994317	+	0.106464i	$0.966047\pi$
$18$		0			0
$19$	6.12582	+	3.53674i	1.40536	+	0.811384i	0.994936	−	0.100511i	$-0.0320477\pi$
$19$	6.12582	+	3.53674i	1.40536	+	0.811384i	0.410423	+	0.911895i	$0.365381\pi$
$20$	−2.11431	+	0.727791i	−0.472775	+	0.162739i
$21$		0			0
$22$	1.81168	+	3.88517i	0.386252	+	0.828321i
$23$	−2.78440	+	3.97654i	−0.580588	+	0.829166i	−0.996786	−	0.0801079i	$-0.974474\pi$
$23$	−2.78440	+	3.97654i	−0.580588	+	0.829166i	0.416198	+	0.909274i	$0.363362\pi$
$24$		0			0
$25$	4.75558	−	1.54418i	0.951116	−	0.308835i
$26$			3.42910i			0.672501i
$27$		0			0
$28$	−0.951369	+	0.951369i	−0.179792	+	0.179792i
$29$	−0.00478023	−	0.00401109i	−0.000887667	−	0.000744841i	0.642344	−	0.766417i	$-0.277962\pi$
$29$	−0.00478023	−	0.00401109i	−0.000887667	−	0.000744841i	−0.643231	+	0.765672i	$0.722407\pi$
$30$		0			0
$31$	0.582373	+	3.30280i	0.104597	+	0.593200i	0.991380	+	0.131015i	$0.0418235\pi$
$31$	0.582373	+	3.30280i	0.104597	+	0.593200i	−0.886783	+	0.462186i	$0.847065\pi$
$32$	0.906308	−	0.422618i	0.160214	−	0.0747091i
$33$		0			0
$34$	−7.57586	−	1.33583i	−1.29925	−	0.229093i
$35$	2.16433	−	2.08967i	0.365838	−	0.353218i
$36$		0			0
$37$	−1.24815	+	4.65816i	−0.205195	+	0.765797i	0.784196	+	0.620514i	$0.213076\pi$
$37$	−1.24815	+	4.65816i	−0.205195	+	0.765797i	−0.989390	+	0.145283i	$0.953591\pi$
$38$	6.41076	+	2.98938i	1.03996	+	0.484942i
$39$		0			0
$40$	−2.04284	+	0.909296i	−0.323001	+	0.143772i
$41$	−0.705833	−	0.841179i	−0.110233	−	0.131370i	0.708107	−	0.706105i	$-0.249549\pi$
$41$	−0.705833	−	0.841179i	−0.110233	−	0.131370i	−0.818339	+	0.574735i	$0.805105\pi$
$42$		0			0
$43$	3.14516	−	6.74482i	0.479632	−	1.02857i	−0.506443	−	0.862274i	$-0.669040\pi$
$43$	3.14516	−	6.74482i	0.479632	−	1.02857i	0.986075	−	0.166301i	$-0.0531824\pi$
$44$	2.14340	+	3.71249i	0.323130	+	0.559678i
$45$		0			0
$46$	−2.42723	+	4.20409i	−0.357876	+	0.619859i
$47$	2.04873	+	2.92589i	0.298838	+	0.426785i	0.940288	−	0.340380i	$-0.110556\pi$
$47$	2.04873	+	2.92589i	0.298838	+	0.426785i	−0.641450	+	0.767165i	$0.721667\pi$
$48$		0			0
$49$	−1.77501	+	4.87681i	−0.253573	+	0.696687i
$50$	4.60290	−	1.95278i	0.650948	−	0.276164i
$51$		0			0
$52$	0.298865	+	3.41605i	0.0414452	+	0.473720i
$53$	8.13905	+	8.13905i	1.11798	+	1.11798i	0.992037	+	0.125947i	$0.0401971\pi$
$53$	8.13905	+	8.13905i	1.11798	+	1.11798i	0.125947	+	0.992037i	$0.459803\pi$
$54$		0			0
$55$	−4.64639	−	8.38420i	−0.626519	−	1.13052i
$56$	−0.864832	+	1.03067i	−0.115568	+	0.137729i
$57$		0			0
$58$	−0.00511163	−	0.00357920i	−0.000671190	−	0.000469972i
$59$	−8.71384	−	3.17158i	−1.13444	−	0.412904i	−0.294541	−	0.955639i	$-0.595167\pi$
$59$	−8.71384	−	3.17158i	−1.13444	−	0.412904i	−0.839904	+	0.542735i	$0.817389\pi$
$60$		0			0
$61$	1.24279	−	7.04819i	0.159122	−	0.902428i	−0.795797	−	0.605563i	$-0.792948\pi$
$61$	1.24279	−	7.04819i	0.159122	−	0.902428i	0.954920	−	0.296865i	$-0.0959411\pi$
$62$	0.868015	+	3.23947i	0.110238	+	0.411414i
$63$		0			0
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−0.534140	−	7.64906i	−0.0662520	−	0.948750i
$66$		0			0
$67$	−5.54705	−	0.485304i	−0.677680	−	0.0592893i	−0.256881	−	0.966443i	$-0.582695\pi$
$67$	−5.54705	−	0.485304i	−0.677680	−	0.0592893i	−0.420799	+	0.907154i	$0.638250\pi$
$68$	−7.66346	−	0.670466i	−0.929331	−	0.0813059i
$69$		0			0
$70$	1.97397	−	2.27035i	0.235934	−	0.271359i
$71$	2.37880	−	1.37340i	0.282312	−	0.162993i	−0.352158	−	0.935941i	$-0.614552\pi$
$71$	2.37880	−	1.37340i	0.282312	−	0.162993i	0.634470	+	0.772948i	$0.281219\pi$
$72$		0			0
$73$	−2.76825	−	10.3313i	−0.323999	−	1.20918i	−0.915314	−	0.402741i	$-0.868058\pi$
$73$	−2.76825	−	10.3313i	−0.323999	−	1.20918i	0.591315	−	0.806441i	$-0.298609\pi$
$74$	−0.837415	+	4.74922i	−0.0973475	+	0.552085i
$75$		0			0
$76$	6.64690	+	2.41927i	0.762452	+	0.277510i
$77$	−4.72458	−	3.30818i	−0.538415	−	0.377002i
$78$		0			0
$79$	−3.61314	+	4.30597i	−0.406510	+	0.484459i	−0.929993	−	0.367576i	$-0.880188\pi$
$79$	−3.61314	+	4.30597i	−0.406510	+	0.484459i	0.523484	+	0.852036i	$0.324632\pi$
$80$	−1.95581	+	1.08388i	−0.218667	+	0.121182i
$81$		0			0
$82$	−0.776460	−	0.776460i	−0.0857457	−	0.0857457i
$83$	−1.20379	−	13.7594i	−0.132133	−	1.51029i	−0.715806	−	0.698300i	$-0.753940\pi$
$83$	−1.20379	−	13.7594i	−0.132133	−	1.51029i	0.583672	−	0.811989i	$-0.301615\pi$
$84$		0			0
$85$	17.1071	+	1.79968i	1.85552	+	0.195202i
$86$	2.54534	−	6.99327i	0.274471	−	0.754104i
$87$		0			0
$88$	2.45881	+	3.51155i	0.262110	+	0.374332i
$89$	0.692740	−	1.19986i	0.0734303	−	0.127185i	−0.826972	−	0.562243i	$-0.809939\pi$
$89$	0.692740	−	1.19986i	0.0734303	−	0.127185i	0.900403	+	0.435058i	$0.143272\pi$
$90$		0			0
$91$	−2.30682	−	3.99553i	−0.241820	−	0.418845i
$92$	−2.05158	+	4.39964i	−0.213892	+	0.458694i
$93$		0			0
$94$	2.29594	+	2.73620i	0.236808	+	0.282217i
$95$	−14.7657	−	5.66964i	−1.51493	−	0.581693i
$96$		0			0
$97$	−4.62517	−	2.15675i	−0.469615	−	0.218985i	0.173381	−	0.984855i	$-0.444531\pi$
$97$	−4.62517	−	2.15675i	−0.469615	−	0.218985i	−0.642995	+	0.765870i	$0.722309\pi$
$98$	−1.34322	+	5.01296i	−0.135685	+	0.506385i
$99$		0			0
$100$	4.41519	−	2.34651i	0.441519	−	0.234651i
$101$	14.0387	+	2.47539i	1.39690	+	0.246311i	0.820868	−	0.571118i	$-0.193490\pi$
$101$	14.0387	+	2.47539i	1.39690	+	0.246311i	0.576030	+	0.817428i	$0.304601\pi$
$102$		0			0
$103$	1.83486	−	0.855607i	0.180794	−	0.0843055i	−0.330114	−	0.943941i	$-0.607087\pi$
$103$	1.83486	−	0.855607i	0.180794	−	0.0843055i	0.510908	+	0.859636i	$0.329309\pi$
$104$	0.595456	+	3.37700i	0.0583893	+	0.331142i
$105$		0			0
$106$	8.81744	+	7.39871i	0.856426	+	0.718626i
$107$	6.58564	−	6.58564i	0.636658	−	0.636658i	−0.313071	−	0.949730i	$-0.601358\pi$
$107$	6.58564	−	6.58564i	0.636658	−	0.636658i	0.949730	+	0.313071i	$0.101358\pi$
$108$		0			0
$109$			0.997902i			0.0955817i	0.998857	+	0.0477908i	$0.0152181\pi$
$109$			0.997902i			0.0955817i	−0.998857	+	0.0477908i	$0.984782\pi$
$110$	−5.35944	−	7.94733i	−0.511002	−	0.757748i
$111$		0			0
$112$	−0.771712	+	1.10212i	−0.0729200	+	0.104140i
$113$	4.69253	+	10.0632i	0.441436	+	0.946662i	0.993603	+	0.112929i	$0.0360231\pi$
$113$	4.69253	+	10.0632i	0.441436	+	0.946662i	−0.552167	+	0.833733i	$0.686199\pi$
$114$		0			0
$115$	4.75941	−	9.75587i	0.443817	−	0.909739i
$116$	−0.00540413	−	0.00312007i	−0.000501761	−	0.000289692i
$117$		0			0
$118$	−8.95710	−	2.40005i	−0.824568	−	0.220942i
$119$	9.72592	−	3.53994i	0.891573	−	0.324506i
$120$		0			0
$121$	−5.65090	+	4.74167i	−0.513719	+	0.431061i
$122$	0.623767	−	7.12968i	0.0564732	−	0.645491i
$123$		0			0
$124$	1.14705	+	3.15149i	0.103008	+	0.283013i
$125$	−9.96321	+	5.07291i	−0.891137	+	0.453735i
$126$		0			0
$127$	10.7439	−	2.87882i	0.953368	−	0.255454i	0.251577	−	0.967837i	$-0.419051\pi$
$127$	10.7439	−	2.87882i	0.953368	−	0.255454i	0.701791	+	0.712383i	$0.252384\pi$
$128$	0.819152	−	0.573576i	0.0724035	−	0.0506975i
$129$		0			0
$130$	−1.19877	−	7.57340i	−0.105139	−	0.664231i
$131$	7.17885	−	1.26582i	0.627219	−	0.110596i	0.149001	−	0.988837i	$-0.452394\pi$
$131$	7.17885	−	1.26582i	0.627219	−	0.110596i	0.478218	+	0.878241i	$0.341283\pi$
$132$		0			0
$133$	−9.48073	+	0.829456i	−0.822084	+	0.0719230i
$134$	−5.56824			−0.481023
$135$		0			0
$136$	−7.69273			−0.659646
$137$	−11.8699	+	1.03848i	−1.01411	+	0.0887234i	−0.582078	−	0.813133i	$-0.697760\pi$
$137$	−11.8699	+	1.03848i	−1.01411	+	0.0887234i	−0.432035	+	0.901857i	$0.642204\pi$
$138$		0			0
$139$	−6.01894	+	1.06130i	−0.510520	+	0.0900184i	−0.422974	−	0.906142i	$-0.639014\pi$
$139$	−6.01894	+	1.06130i	−0.510520	+	0.0900184i	−0.0875463	+	0.996160i	$0.527903\pi$
$140$	1.76858	−	2.43375i	0.149472	−	0.205690i
$141$		0			0
$142$	2.25005	−	1.57550i	0.188820	−	0.132213i
$143$	−14.1990	+	3.80461i	−1.18738	+	0.318157i
$144$		0			0
$145$	0.0119597	+	0.00718767i	0.000993200	+	0.000596904i
$146$	−3.65814	−	10.0507i	−0.302750	−	0.831799i
$147$		0			0
$148$	−0.420307	+	4.80413i	−0.0345490	+	0.394897i
$149$	1.65154	−	1.38581i	0.135299	−	0.113530i	−0.572627	−	0.819816i	$-0.694075\pi$
$149$	1.65154	−	1.38581i	0.135299	−	0.113530i	0.707926	+	0.706287i	$0.249631\pi$
$150$		0			0
$151$	14.2033	−	5.16957i	1.15585	−	0.420693i	0.308234	−	0.951311i	$-0.400262\pi$
$151$	14.2033	−	5.16957i	1.15585	−	0.420693i	0.847612	+	0.530617i	$0.178040\pi$
$152$	6.83246	+	1.83075i	0.554186	+	0.148494i
$153$		0			0
$154$	−4.99492	−	2.88382i	−0.402502	−	0.232385i
$155$	−2.44083	−	7.09088i	−0.196052	−	0.569553i
$156$		0			0
$157$	−0.631683	−	1.35465i	−0.0504138	−	0.108113i	0.879487	−	0.475922i	$-0.157886\pi$
$157$	−0.631683	−	1.35465i	−0.0504138	−	0.108113i	−0.929901	+	0.367810i	$0.880108\pi$
$158$	−3.22410	+	4.60449i	−0.256495	+	0.366314i
$159$		0			0
$160$	−1.85390	+	1.25022i	−0.146564	+	0.0988383i
$161$		−	6.53138i		−	0.514745i
$162$		0			0
$163$	−11.5642	+	11.5642i	−0.905779	+	0.905779i	−0.995928	−	0.0901493i	$-0.971266\pi$
$163$	−11.5642	+	11.5642i	−0.905779	+	0.905779i	0.0901493	+	0.995928i	$0.471266\pi$
$164$	−0.841179	−	0.705833i	−0.0656850	−	0.0551163i
$165$		0			0
$166$	−2.39842	−	13.6021i	−0.186153	−	1.05573i
$167$	−7.74478	+	3.61145i	−0.599309	+	0.279462i	−0.698505	−	0.715606i	$-0.746151\pi$
$167$	−7.74478	+	3.61145i	−0.599309	+	0.279462i	0.0991955	+	0.995068i	$0.468373\pi$
$168$		0			0
$169$	1.22245	+	0.215550i	0.0940343	+	0.0165808i
$170$	17.1988	+	0.301850i	1.31909	+	0.0231509i
$171$		0			0
$172$	1.92615	−	7.18850i	0.146868	−	0.548118i
$173$	18.7601	+	8.74798i	1.42630	+	0.665097i	0.973954	−	0.226744i	$-0.0728080\pi$
$173$	18.7601	+	8.74798i	1.42630	+	0.665097i	0.452350	+	0.891840i	$0.350586\pi$
$174$		0			0
$175$	−4.04955	+	5.37180i	−0.306118	+	0.406070i
$176$	2.75551	+	3.28389i	0.207704	+	0.247532i
$177$		0			0
$178$	0.585529	−	1.25567i	0.0438873	−	0.0941166i
$179$	7.96252	+	13.7915i	0.595147	+	1.03082i	0.993526	+	0.113604i	$0.0362394\pi$
$179$	7.96252	+	13.7915i	0.595147	+	1.03082i	−0.398379	+	0.917221i	$0.630427\pi$
$180$		0			0
$181$	−3.45571	+	5.98546i	−0.256861	+	0.444896i	−0.965399	−	0.260776i	$-0.916022\pi$
$181$	−3.45571	+	5.98546i	−0.256861	+	0.444896i	0.708538	+	0.705672i	$0.249355\pi$
$182$	−2.64628	−	3.77927i	−0.196155	−	0.280138i
$183$		0			0
$184$	−1.66032	+	4.56170i	−0.122401	+	0.336293i
$185$	1.12820	−	10.7242i	0.0829467	−	0.788460i
$186$		0			0
$187$	−2.87416	−	32.8518i	−0.210179	−	2.40236i
$188$	2.52568	+	2.52568i	0.184204	+	0.184204i
$189$		0			0
$190$	−15.2037	−	4.36115i	−1.10299	−	0.316391i
$191$	17.4482	−	20.7940i	1.26251	−	1.50460i	0.486798	−	0.873515i	$-0.338165\pi$
$191$	17.4482	−	20.7940i	1.26251	−	1.50460i	0.775712	−	0.631087i	$-0.217391\pi$
$192$		0			0
$193$	14.5121	+	10.1615i	1.04461	+	0.731441i	0.964161	−	0.265318i	$-0.0854769\pi$
$193$	14.5121	+	10.1615i	1.04461	+	0.731441i	0.0804452	+	0.996759i	$0.474366\pi$
$194$	−4.79554	−	1.74543i	−0.344300	−	0.125315i
$195$		0			0
$196$	−0.901198	+	5.11095i	−0.0643713	+	0.365068i
$197$	−2.27387	−	8.48620i	−0.162006	−	0.604616i	−0.998403	−	0.0564917i	$-0.982009\pi$
$197$	−2.27387	−	8.48620i	−0.162006	−	0.604616i	0.836397	−	0.548125i	$-0.184658\pi$
$198$		0			0
$199$	−10.6250	+	6.13434i	−0.753186	+	0.434852i	−0.826844	−	0.562431i	$-0.809866\pi$
$199$	−10.6250	+	6.13434i	−0.753186	+	0.434852i	0.0736580	+	0.997284i	$0.476533\pi$
$200$	4.19387	−	2.72239i	0.296552	−	0.192502i
$201$		0			0
$202$	14.2010	+	1.24242i	0.999177	+	0.0874167i
$203$	0.00836379		0.000731737i	0.000587023		5.13579e-5i
$204$		0			0
$205$	1.85295	+	1.61105i	0.129415	+	0.112521i
$206$	1.75330	−	1.01227i	0.122158	−	0.0705282i
$207$		0			0
$208$	0.887515	+	3.31225i	0.0615381	+	0.229663i
$209$	−5.26548	+	29.8620i	−0.364221	+	2.06560i
$210$		0			0
$211$	−6.43443	−	2.34194i	−0.442965	−	0.161226i	0.110902	−	0.993831i	$-0.464626\pi$
$211$	−6.43443	−	2.34194i	−0.442965	−	0.161226i	−0.553867	+	0.832605i	$0.686848\pi$
$212$	9.42873	+	6.60207i	0.647568	+	0.453432i
$213$		0			0
$214$	5.98661	−	7.13456i	0.409236	−	0.487708i
$215$	−4.58841	+	15.9959i	−0.312927	+	1.09091i
$216$		0			0
$217$	−3.19066	−	3.19066i	−0.216596	−	0.216596i
$218$	0.0869729	+	0.994105i	0.00589055	+	0.0673293i
$219$		0			0
$220$	−6.03170	−	7.44998i	−0.406657	−	0.502278i
$221$	9.02219	−	24.7883i	0.606898	−	1.66744i
$222$		0			0
$223$	0.0323543	+	0.0462067i	0.00216660	+	0.00309423i	0.820234	−	0.572028i	$-0.193843\pi$
$223$	0.0323543	+	0.0462067i	0.00216660	+	0.00309423i	−0.818067	+	0.575123i	$0.804954\pi$
$224$	−0.672720	+	1.16518i	−0.0449480	+	0.0778522i
$225$		0			0
$226$	5.55173	+	9.61588i	0.369296	+	0.639639i
$227$	3.14003	−	6.73382i	0.208411	−	0.446939i	−0.774120	−	0.633039i	$-0.781807\pi$
$227$	3.14003	−	6.73382i	0.208411	−	0.446939i	0.982531	+	0.186100i	$0.0595849\pi$
$228$		0			0
$229$	−7.90847	−	9.42495i	−0.522606	−	0.622818i	0.438589	−	0.898688i	$-0.355479\pi$
$229$	−7.90847	−	9.42495i	−0.522606	−	0.622818i	−0.961195	+	0.275870i	$0.911034\pi$
$230$	3.89102	−	10.1336i	0.256566	−	0.668187i
$231$		0			0
$232$	−0.00565550	−	0.00263720i	−0.000371301	−	0.000173141i
$233$	3.38830	−	12.6453i	0.221975	−	0.828421i	−0.761619	−	0.648025i	$-0.775595\pi$
$233$	3.38830	−	12.6453i	0.221975	−	0.828421i	0.983594	−	0.180396i	$-0.0577380\pi$
$234$		0			0
$235$	−5.54762	−	5.74582i	−0.361887	−	0.374816i
$236$	−9.13219	−	1.61025i	−0.594455	−	0.104818i
$237$		0			0
$238$	9.38038	−	4.37414i	0.608040	−	0.283534i
$239$	−0.00469859	−	0.0266470i	−0.000303927	−	0.00172365i	0.984655	−	0.174510i	$-0.0558341\pi$
$239$	−0.00469859	−	0.0266470i	−0.000303927	−	0.00172365i	−0.984959	+	0.172786i	$0.944723\pi$
$240$		0			0
$241$	5.56632	+	4.67069i	0.358558	+	0.300866i	0.804216	−	0.594338i	$-0.202586\pi$
$241$	5.56632	+	4.67069i	0.358558	+	0.300866i	−0.445658	+	0.895203i	$0.647030\pi$
$242$	−5.21614	+	5.21614i	−0.335306	+	0.335306i
$243$		0			0
$244$		−	7.15692i		−	0.458175i
$245$	2.21538	−	11.3913i	0.141535	−	0.727764i
$246$		0			0
$247$	−13.9125	+	19.8691i	−0.885230	+	1.26424i
$248$	1.41736	+	3.03953i	0.0900022	+	0.193010i
$249$		0			0
$250$	−9.48316	+	5.92196i	−0.599768	+	0.374538i
$251$	−9.23875	−	5.33400i	−0.583145	−	0.336679i	0.179237	−	0.983806i	$-0.442637\pi$
$251$	−9.23875	−	5.33400i	−0.583145	−	0.336679i	−0.762382	+	0.647127i	$0.775970\pi$
$252$		0			0
$253$	−20.1011	−	5.38606i	−1.26374	−	0.338619i
$254$	10.4521	−	3.80426i	0.655824	−	0.238701i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−0.545692	+	6.23728i	−0.0340393	+	0.389071i	0.959996	+	0.280013i	$0.0903389\pi$
$257$	−0.545692	+	6.23728i	−0.0340393	+	0.389071i	−0.994035	+	0.109058i	$0.965217\pi$
$258$		0			0
$259$	−2.21915	−	6.09706i	−0.137891	−	0.378853i
$260$	−1.85427	−	7.44010i	−0.114997	−	0.461416i
$261$		0			0
$262$	7.04121	−	1.88669i	0.435007	−	0.116560i
$263$	−1.84417	+	1.29130i	−0.113716	+	0.0796249i	−0.629051	−	0.777364i	$-0.716556\pi$
$263$	−1.84417	+	1.29130i	−0.113716	+	0.0796249i	0.515335	+	0.856989i	$0.327668\pi$
$264$		0			0
$265$	−20.8210	−	15.1304i	−1.27902	−	0.929451i
$266$	−9.37236	+	1.65260i	−0.574656	+	0.101327i
$267$		0			0
$268$	−5.54705	+	0.485304i	−0.338840	+	0.0296447i
$269$	20.0830			1.22448			0.612240	−	0.790672i	$-0.290269\pi$
$269$	20.0830			1.22448			0.612240	+	0.790672i	$0.290269\pi$
$270$		0			0
$271$	22.3527			1.35783			0.678914	−	0.734218i	$-0.262451\pi$
$271$	22.3527			1.35783			0.678914	+	0.734218i	$0.262451\pi$
$272$	−7.66346	+	0.670466i	−0.464666	+	0.0406530i
$273$		0			0
$274$	−11.7342	+	2.06906i	−0.708890	+	0.124996i
$275$	13.1929	+	16.8928i	0.795561	+	1.01867i
$276$		0			0
$277$	−4.15972	+	2.91267i	−0.249933	+	0.175005i	−0.691829	−	0.722061i	$-0.743195\pi$
$277$	−4.15972	+	2.91267i	−0.249933	+	0.175005i	0.441896	+	0.897066i	$0.354306\pi$
$278$	−5.90354	+	1.58185i	−0.354071	+	0.0948729i
$279$		0			0
$280$	1.54974	−	2.57863i	0.0926144	−	0.154103i
$281$	5.51412	+	15.1499i	0.328945	+	0.903769i	0.988379	+	0.152007i	$0.0485736\pi$
$281$	5.51412	+	15.1499i	0.328945	+	0.903769i	−0.659435	+	0.751762i	$0.729204\pi$
$282$		0			0
$283$	1.35460	−	15.4831i	0.0805226	−	0.920377i	−0.843272	−	0.537488i	$-0.819373\pi$
$283$	1.35460	−	15.4831i	0.0805226	−	0.920377i	0.923794	−	0.382890i	$-0.125071\pi$
$284$	2.10417	−	1.76561i	0.124860	−	0.104770i
$285$		0			0
$286$	−13.8134	+	5.02765i	−0.816801	+	0.297291i
$287$	1.42706	+	0.382380i	0.0842367	+	0.0225712i
$288$		0			0
$289$	36.5273	+	21.0891i	2.14867	+	1.24053i
$290$	0.0125406	+	0.00611796i	0.000736412	+	0.000359259i
$291$		0			0
$292$	−4.52020	−	9.69360i	−0.264525	−	0.567275i
$293$	−18.4183	+	26.3041i	−1.07601	+	1.53670i	−0.254017	+	0.967200i	$0.581752\pi$
$293$	−18.4183	+	26.3041i	−1.07601	+	1.53670i	−0.821991	+	0.569500i	$0.807137\pi$
$294$		0			0
$295$	20.3539	+	3.95841i	1.18505	+	0.230468i
$296$			4.82248i			0.280301i
$297$		0			0
$298$	1.52447	−	1.52447i	0.0883104	−	0.0883104i
$299$	−12.7519	−	10.7001i	−0.737461	−	0.618803i
$300$		0			0
$301$	1.73872	+	9.86075i	0.100218	+	0.568364i
$302$	13.6987	−	6.38779i	0.788269	−	0.367576i
$303$		0			0
$304$	6.96602	+	1.22830i	0.399529	+	0.0704477i
$305$	−0.280826	+	16.0009i	−0.0160800	+	0.916209i
$306$		0			0
$307$	−0.658671	+	2.45819i	−0.0375923	+	0.140296i	−0.982171	−	0.187987i	$-0.939804\pi$
$307$	−0.658671	+	2.45819i	−0.0375923	+	0.140296i	0.944579	+	0.328284i	$0.106470\pi$
$308$	−5.22726	−	2.43751i	−0.297851	−	0.138890i
$309$		0			0
$310$	−3.04955	−	6.85117i	−0.173203	−	0.389120i
$311$	10.8671	+	12.9510i	0.616219	+	0.734382i	0.980415	−	0.196941i	$-0.0631006\pi$
$311$	10.8671	+	12.9510i	0.616219	+	0.734382i	−0.364196	+	0.931322i	$0.618656\pi$
$312$		0			0
$313$	−10.5221	+	22.5647i	−0.594743	+	1.27543i	0.346610	+	0.938009i	$0.387333\pi$
$313$	−10.5221	+	22.5647i	−0.594743	+	1.27543i	−0.941354	+	0.337422i	$0.890445\pi$
$314$	−0.747344	−	1.29444i	−0.0421751	−	0.0730494i
$315$		0			0
$316$	−2.81052	+	4.86797i	−0.158104	+	0.273845i
$317$	14.7708	+	21.0949i	0.829611	+	1.18481i	0.980551	+	0.196264i	$0.0628811\pi$
$317$	14.7708	+	21.0949i	0.829611	+	1.18481i	−0.150940	+	0.988543i	$0.548230\pi$
$318$		0			0
$319$	0.00914915	−	0.0251371i	0.000512254	−	0.00140741i
$320$	−1.73789	+	1.40704i	−0.0971508	+	0.0786558i
$321$		0			0
$322$	−0.569248	−	6.50653i	−0.0317229	−	0.362595i
$323$	−38.4768	−	38.4768i	−2.14091	−	2.14091i
$324$		0			0
$325$	3.85370	+	16.7068i	0.213765	+	0.926725i
$326$	−10.5123	+	12.5281i	−0.582223	+	0.693867i
$327$		0			0
$328$	−0.899495	−	0.629833i	−0.0496663	−	0.0347767i
$329$	−4.51589	−	1.64365i	−0.248969	−	0.0906173i
$330$		0			0
$331$	0.572221	−	3.24523i	0.0314521	−	0.178374i	−0.965035	−	0.262121i	$-0.915578\pi$
$331$	0.572221	−	3.24523i	0.0314521	−	0.178374i	0.996487	+	0.0837477i	$0.0266890\pi$
$332$	−3.57479	−	13.3413i	−0.196192	−	0.732200i
$333$		0			0
$334$	−7.40055	+	4.27271i	−0.404940	+	0.233792i
$335$	12.4207	−	0.867349i	0.678616	−	0.0473883i
$336$		0			0
$337$	23.2238	+	2.03182i	1.26508	+	0.110680i	0.699872	−	0.714269i	$-0.253241\pi$
$337$	23.2238	+	2.03182i	1.26508	+	0.110680i	0.565208	+	0.824949i	$0.308796\pi$
$338$	1.23658	+	0.108187i	0.0672611	+	0.00588459i
$339$		0			0
$340$	17.1597	−	1.19827i	0.930615	−	0.0649856i
$341$	−12.4508	+	7.18844i	−0.674246	+	0.389276i
$342$		0			0
$343$	−4.24479	−	15.8418i	−0.229197	−	0.855376i
$344$	1.29230	−	7.32902i	0.0696764	−	0.395154i
$345$		0			0
$346$	19.4512	+	7.07964i	1.04570	+	0.380604i
$347$	−4.06509	−	2.84641i	−0.218226	−	0.152803i	0.459352	−	0.888254i	$-0.348082\pi$
$347$	−4.06509	−	2.84641i	−0.218226	−	0.152803i	−0.677578	+	0.735451i	$0.736970\pi$
$348$		0			0
$349$	−18.4096	+	21.9397i	−0.985443	+	1.17440i	−0.000768814		1.00000i	$0.500245\pi$
$349$	−18.4096	+	21.9397i	−0.985443	+	1.17440i	−0.984674	+	0.174405i	$0.944200\pi$
$350$	−3.56596	+	5.70430i	−0.190609	+	0.304908i
$351$		0			0
$352$	3.03123	+	3.03123i	0.161565	+	0.161565i
$353$	−1.14797	−	13.1214i	−0.0611003	−	0.698380i	−0.963540	−	0.267564i	$-0.913781\pi$
$353$	−1.14797	−	13.1214i	−0.0611003	−	0.698380i	0.902440	−	0.430816i	$-0.141774\pi$
$354$		0			0
$355$	−4.77363	+	3.86485i	−0.253358	+	0.205125i
$356$	0.473862	−	1.30193i	0.0251146	−	0.0690019i
$357$		0			0
$358$	9.13423	+	13.0450i	0.482759	+	0.689451i
$359$	−2.89200	+	5.00910i	−0.152634	+	0.264370i	−0.932195	−	0.361956i	$-0.882109\pi$
$359$	−2.89200	+	5.00910i	−0.152634	+	0.264370i	0.779561	+	0.626326i	$0.215442\pi$
$360$		0			0
$361$	15.5171	+	26.8764i	0.816690	+	1.41455i
$362$	−2.92089	+	6.26387i	−0.153519	+	0.329222i
$363$		0			0
$364$	−2.96559	−	3.53425i	−0.155439	−	0.185245i
$365$	9.72555	+	21.8496i	0.509059	+	1.14366i
$366$		0			0
$367$	−9.77555	−	4.55841i	−0.510280	−	0.237947i	0.150386	−	0.988627i	$-0.451948\pi$
$367$	−9.77555	−	4.55841i	−0.510280	−	0.237947i	−0.660666	+	0.750680i	$0.729726\pi$
$368$	−1.25643	+	4.68905i	−0.0654958	+	0.244434i
$369$		0			0
$370$	0.189226	−	10.7817i	0.00983740	−	0.560516i
$371$	−15.2512	−	2.68920i	−0.791803	−	0.139616i
$372$		0			0
$373$	3.38202	−	1.57706i	0.175114	−	0.0816572i	−0.333084	−	0.942897i	$-0.608089\pi$
$373$	3.38202	−	1.57706i	0.175114	−	0.0816572i	0.508199	+	0.861240i	$0.330312\pi$
$374$	−5.72644	−	32.4763i	−0.296107	−	1.67931i
$375$		0			0
$376$	2.73620	+	2.29594i	0.141109	+	0.118404i
$377$	0.0151307	−	0.0151307i	0.000779272	−	0.000779272i
$378$		0			0
$379$		−	20.3733i		−	1.04651i	−0.852177	−	0.523253i	$-0.824718\pi$
$379$		−	20.3733i		−	1.04651i	0.852177	−	0.523253i	$-0.175282\pi$
$380$	−15.5259	−	3.01947i	−0.796462	−	0.154896i
$381$		0			0
$382$	15.5695	−	22.2356i	0.796606	−	1.13767i
$383$	5.74785	+	12.3263i	0.293701	+	0.629845i	0.996685	−	0.0813617i	$-0.0259269\pi$
$383$	5.74785	+	12.3263i	0.293701	+	0.629845i	−0.702983	+	0.711206i	$0.748149\pi$
$384$		0			0
$385$	11.5911	+	5.65471i	0.590735	+	0.288191i
$386$	15.3425	+	8.85802i	0.780915	+	0.450861i
$387$		0			0
$388$	−4.92942	−	1.32083i	−0.250253	−	0.0670551i
$389$	6.23872	−	2.27071i	0.316316	−	0.115129i	−0.178983	−	0.983852i	$-0.557281\pi$
$389$	6.23872	−	2.27071i	0.316316	−	0.115129i	0.495299	+	0.868723i	$0.335059\pi$
$390$		0			0
$391$	28.6072	−	24.0043i	1.44673	−	1.21395i
$392$	−0.452320	+	5.17004i	−0.0228456	+	0.261127i
$393$		0			0
$394$	−3.00484	−	8.25572i	−0.151382	−	0.415917i
$395$	6.47456	−	10.7731i	0.325771	−	0.542056i
$396$		0			0
$397$	−28.2089	+	7.55855i	−1.41576	+	0.379353i	−0.883979	−	0.467527i	$-0.845145\pi$
$397$	−28.2089	+	7.55855i	−1.41576	+	0.379353i	−0.531785	+	0.846879i	$0.678479\pi$
$398$	−10.0499	+	7.03703i	−0.503757	+	0.352734i
$399$		0			0
$400$	3.94064	−	3.07755i	0.197032	−	0.153878i
$401$	13.2541	−	2.33705i	0.661876	−	0.116707i	0.167388	−	0.985891i	$-0.446467\pi$
$401$	13.2541	−	2.33705i	0.661876	−	0.116707i	0.494488	+	0.869184i	$0.335356\pi$
$402$		0			0
$403$	−11.4566	+	1.00232i	−0.570692	+	0.0499291i
$404$	14.2552			0.709224
$405$		0			0
$406$	0.00839574			0.000416674
$407$	−20.5944	+	1.80178i	−1.02083	+	0.0893107i
$408$		0			0
$409$	−8.85097	+	1.56066i	−0.437652	+	0.0771699i	−0.388133	−	0.921603i	$-0.626880\pi$
$409$	−8.85097	+	1.56066i	−0.437652	+	0.0771699i	−0.0495190	+	0.998773i	$0.515769\pi$
$410$	1.98631	+	1.44343i	0.0980968	+	0.0712858i
$411$		0			0
$412$	1.65841	−	1.16123i	0.0817038	−	0.0572096i
$413$	12.0512	−	3.22912i	0.593002	−	0.158894i
$414$		0			0
$415$	7.46876	+	29.9678i	0.366627	+	1.47106i
$416$	1.17282	+	3.22230i	0.0575022	+	0.157986i
$417$		0			0
$418$	−2.64280	+	30.2073i	−0.129263	+	1.47749i
$419$	9.47636	−	7.95161i	0.462950	−	0.388461i	−0.381265	−	0.924466i	$-0.624511\pi$
$419$	9.47636	−	7.95161i	0.462950	−	0.388461i	0.844215	+	0.536004i	$0.180067\pi$
$420$		0			0
$421$	−18.9688	+	6.90407i	−0.924481	+	0.336484i	−0.760020	−	0.649900i	$-0.774811\pi$
$421$	−18.9688	+	6.90407i	−0.924481	+	0.336484i	−0.164461	+	0.986384i	$0.552589\pi$
$422$	−6.61406	−	1.77223i	−0.321967	−	0.0862709i
$423$		0			0
$424$	9.96826	+	5.75518i	0.484101	+	0.279496i
$425$	−38.4113	+	2.00569i	−1.86322	+	0.0972904i
$426$		0			0
$427$	4.06948	+	8.72702i	0.196936	+	0.422330i
$428$	5.34201	−	7.62918i	0.258216	−	0.368770i
$429$		0			0
$430$	−3.17681	+	16.3350i	−0.153200	+	0.787741i
$431$			8.26858i			0.398283i	0.979971	+	0.199142i	$0.0638154\pi$
$431$			8.26858i			0.398283i	−0.979971	+	0.199142i	$0.936185\pi$
$432$		0			0
$433$	24.6631	−	24.6631i	1.18523	−	1.18523i	0.206865	−	0.978369i	$-0.433674\pi$
$433$	24.6631	−	24.6631i	1.18523	−	1.18523i	0.978369	−	0.206865i	$-0.0663262\pi$
$434$	−3.45660	−	2.90043i	−0.165922	−	0.139225i
$435$		0			0
$436$	0.173284	+	0.982742i	0.00829879	+	0.0470648i
$437$	−31.1208	+	14.5118i	−1.48871	+	0.694196i
$438$		0			0
$439$	2.32992	+	0.410828i	0.111201	+	0.0196077i	0.228972	−	0.973433i	$-0.426464\pi$
$439$	2.32992	+	0.410828i	0.111201	+	0.0196077i	−0.117771	+	0.993041i	$0.537575\pi$
$440$	−6.65806	−	6.89594i	−0.317410	−	0.328751i
$441$		0			0
$442$	6.82742	−	25.4803i	0.324747	−	1.21197i
$443$	−3.14927	−	1.46853i	−0.149626	−	0.0697719i	0.346363	−	0.938101i	$-0.387417\pi$
$443$	−3.14927	−	1.46853i	−0.149626	−	0.0697719i	−0.495989	+	0.868329i	$0.665194\pi$
$444$		0			0
$445$	−1.11051	+	2.89215i	−0.0526432	+	0.137101i
$446$	0.0362583	+	0.0432110i	0.00171688	+	0.00204610i
$447$		0			0
$448$	−0.568607	+	1.21938i	−0.0268642	+	0.0576104i
$449$	2.75309	+	4.76849i	0.129926	+	0.225039i	0.923648	−	0.383242i	$-0.125193\pi$
$449$	2.75309	+	4.76849i	0.129926	+	0.225039i	−0.793721	+	0.608281i	$0.791859\pi$
$450$		0			0
$451$	2.35363	−	4.07661i	0.110828	−	0.191960i
$452$	6.36868	+	9.09542i	0.299558	+	0.427813i
$453$		0			0
$454$	2.54119	−	6.98187i	0.119264	−	0.327675i
$455$	6.49156	+	8.01798i	0.304329	+	0.375889i
$456$		0			0
$457$	0.879530	+	10.0531i	0.0411427	+	0.470263i	0.988619	+	0.150438i	$0.0480685\pi$
$457$	0.879530	+	10.0531i	0.0411427	+	0.470263i	−0.947477	+	0.319825i	$0.896376\pi$
$458$	−8.69981	−	8.69981i	−0.406516	−	0.406516i
$459$		0			0
$460$	2.99301	−	10.4341i	0.139550	−	0.486493i
$461$	−7.75567	+	9.24285i	−0.361218	+	0.430482i	−0.915793	−	0.401651i	$-0.868436\pi$
$461$	−7.75567	+	9.24285i	−0.361218	+	0.430482i	0.554575	+	0.832134i	$0.312881\pi$
$462$		0			0
$463$	−8.32374	−	5.82835i	−0.386837	−	0.270866i	0.363939	−	0.931423i	$-0.381432\pi$
$463$	−8.32374	−	5.82835i	−0.386837	−	0.270866i	−0.750776	+	0.660556i	$0.770320\pi$
$464$	−0.00586382	−	0.00213426i	−0.000272221	−	9.90804e-5i
$465$		0			0
$466$	2.27329	−	12.8925i	0.105308	−	0.597233i
$467$	−5.28342	−	19.7180i	−0.244487	−	0.912440i	−0.973640	−	0.228089i	$-0.926752\pi$
$467$	−5.28342	−	19.7180i	−0.244487	−	0.912440i	0.729153	−	0.684351i	$-0.239914\pi$
$468$		0			0
$469$	6.48803	−	3.74587i	0.299589	−	0.172968i
$470$	−6.02729	−	5.24045i	−0.278018	−	0.241724i
$471$		0			0
$472$	−9.23778	−	0.808201i	−0.425203	−	0.0372005i
$473$	31.7814	+	2.78051i	1.46131	+	0.127848i
$474$		0			0
$475$	34.5932	+	7.35991i	1.58724	+	0.337696i
$476$	8.96345	−	5.17505i	0.410839	−	0.237198i
$477$		0			0
$478$	−0.00700316	−	0.0261361i	−0.000320317	−	0.00119544i
$479$	−7.22274	+	40.9622i	−0.330015	+	1.87161i	0.141774	+	0.989899i	$0.454719\pi$
$479$	−7.22274	+	40.9622i	−0.330015	+	1.87161i	−0.471789	+	0.881711i	$0.656392\pi$
$480$		0			0
$481$	−15.5395	−	5.65590i	−0.708538	−	0.257887i
$482$	5.95221	+	4.16778i	0.271116	+	0.189837i
$483$		0			0
$484$	−4.74167	+	5.65090i	−0.215531	+	0.256859i
$485$	10.9690	+	3.14644i	0.498076	+	0.142872i
$486$		0			0
$487$	21.5643	+	21.5643i	0.977171	+	0.977171i	0.999745	−	0.0225745i	$-0.00718628\pi$
$487$	21.5643	+	21.5643i	0.977171	+	0.977171i	−0.0225745	+	0.999745i	$0.507186\pi$
$488$	−0.623767	−	7.12968i	−0.0282366	−	0.322746i
$489$		0			0
$490$	1.21413	−	11.5410i	0.0548487	−	0.521371i
$491$	−2.06551	+	5.67493i	−0.0932150	+	0.256106i	−0.977534	−	0.210777i	$-0.932401\pi$
$491$	−2.06551	+	5.67493i	−0.0932150	+	0.256106i	0.884319	+	0.466883i	$0.154623\pi$
$492$		0			0
$493$	0.0275339	+	0.0393224i	0.00124006	+	0.00177099i
$494$	−12.1278	+	21.0060i	−0.545657	+	0.945105i
$495$		0			0
$496$	1.67688	+	2.90443i	0.0752939	+	0.130413i
$497$	−1.56185	+	3.34940i	−0.0700586	+	0.150241i
$498$		0			0
$499$	−9.82974	−	11.7146i	−0.440040	−	0.524419i	0.499751	−	0.866169i	$-0.333425\pi$
$499$	−9.82974	−	11.7146i	−0.440040	−	0.524419i	−0.939791	+	0.341750i	$0.888980\pi$
$500$	−8.93094	+	6.72594i	−0.399404	+	0.300793i
$501$		0			0
$502$	−9.66849	−	4.50849i	−0.431526	−	0.201224i
$503$	4.09733	−	15.2915i	0.182691	−	0.681813i	−0.812422	−	0.583070i	$-0.801851\pi$
$503$	4.09733	−	15.2915i	0.182691	−	0.681813i	0.995113	−	0.0987425i	$-0.0314820\pi$
$504$		0			0
$505$	−31.8707	−	0.559351i	−1.41823	−	0.0248908i
$506$	−20.4940	−	3.61364i	−0.911069	−	0.160646i
$507$		0			0
$508$	10.0808	−	4.70075i	0.447263	−	0.208562i
$509$	−5.47407	−	31.0450i	−0.242634	−	1.37604i	−0.825924	−	0.563781i	$-0.809346\pi$
$509$	−5.47407	−	31.0450i	−0.242634	−	1.37604i	0.583291	−	0.812264i	$-0.301765\pi$
$510$		0			0
$511$	11.0237	+	9.24998i	0.487660	+	0.409195i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			6.26111i			0.276166i
$515$	−3.75330	+	2.53111i	−0.165390	+	0.111534i
$516$		0			0
$517$	−8.78251	+	12.5427i	−0.386254	+	0.551628i
$518$	−2.74210	−	5.88045i	−0.120481	−	0.258372i
$519$		0			0
$520$	−2.49566	−	7.25018i	−0.109442	−	0.317942i
$521$	18.5639	+	10.7179i	0.813300	+	0.469559i	0.848100	−	0.529835i	$-0.177746\pi$
$521$	18.5639	+	10.7179i	0.813300	+	0.469559i	−0.0348007	+	0.999394i	$0.511080\pi$
$522$		0			0
$523$	33.9851	+	9.10628i	1.48606	+	0.398190i	0.908406	−	0.418089i	$-0.137300\pi$
$523$	33.9851	+	9.10628i	1.48606	+	0.398190i	0.577658	+	0.816279i	$0.303967\pi$
$524$	6.84998	−	2.49319i	0.299243	−	0.108915i
$525$		0			0
$526$	−1.72460	+	1.44711i	−0.0751963	+	0.0630972i
$527$	2.24858	−	25.7013i	0.0979495	−	1.11957i
$528$		0			0
$529$	−0.193512	−	0.531670i	−0.00841357	−	0.0231161i
$530$	−22.0604	−	13.2581i	−0.958245	−	0.575896i
$531$		0			0
$532$	−9.19266	+	2.46317i	−0.398553	+	0.106792i
$533$	3.08445	−	2.15976i	0.133603	−	0.0935495i
$534$		0			0
$535$	−12.2426	+	16.8471i	−0.529294	+	0.728364i
$536$	−5.48365	+	0.966915i	−0.236857	+	0.0417644i
$537$		0			0
$538$	20.0065	−	1.75035i	0.862543	−	0.0754628i
$539$	−22.2477			−0.958274
$540$		0			0
$541$	−1.73780			−0.0747137			−0.0373569	−	0.999302i	$-0.511894\pi$
$541$	−1.73780			−0.0747137			−0.0373569	+	0.999302i	$0.511894\pi$
$542$	22.2676	−	1.94816i	0.956476	−	0.0836808i
$543$		0			0
$544$	−7.57586	+	1.33583i	−0.324812	+	0.0572732i
$545$	−0.348854	−	2.20394i	−0.0149432	−	0.0944063i
$546$		0			0
$547$	−24.3181	+	17.0277i	−1.03977	+	0.728052i	−0.963138	−	0.269008i	$-0.913304\pi$
$547$	−24.3181	+	17.0277i	−1.03977	+	0.728052i	−0.0766277	+	0.997060i	$0.524415\pi$
$548$	−11.5092	+	3.08389i	−0.491650	+	0.131737i
$549$		0			0
$550$	14.6150	+	15.6787i	0.623185	+	0.668540i
$551$	−0.0150966	−	0.0414777i	−0.000643138	−	0.00176701i
$552$		0			0
$553$	0.659139	−	7.53399i	0.0280294	−	0.320378i
$554$	−3.89003	+	3.26413i	−0.165272	+	0.138679i
$555$		0			0
$556$	−5.74321	+	2.09036i	−0.243566	+	0.0886508i
$557$	30.6627	+	8.21606i	1.29922	+	0.348125i	0.841156	−	0.540793i	$-0.181876\pi$
$557$	30.6627	+	8.21606i	1.29922	+	0.348125i	0.458066	+	0.888918i	$0.348542\pi$
$558$		0			0
$559$	22.1006	+	12.7598i	0.934757	+	0.539682i
$560$	1.31910	−	2.70389i	0.0557419	−	0.114260i
$561$		0			0
$562$	6.81354	+	14.6117i	0.287412	+	0.616357i
$563$	−12.2805	+	17.5384i	−0.517561	+	0.739154i	−0.989823	−	0.142305i	$-0.954549\pi$
$563$	−12.2805	+	17.5384i	−0.517561	+	0.739154i	0.472262	+	0.881458i	$0.343438\pi$
$564$		0			0
$565$	−13.8817	−	20.5848i	−0.584009	−	0.866007i
$566$		−	15.5423i		−	0.653291i
$567$		0			0
$568$	1.94228	−	1.94228i	0.0814964	−	0.0814964i
$569$	26.5911	+	22.3126i	1.11476	+	0.935393i	0.998328	−	0.0578062i	$-0.0184105\pi$
$569$	26.5911	+	22.3126i	1.11476	+	0.935393i	0.116430	+	0.993199i	$0.462855\pi$
$570$		0			0
$571$	−3.94694	−	22.3842i	−0.165174	−	0.936750i	−0.948885	−	0.315623i	$-0.897786\pi$
$571$	−3.94694	−	22.3842i	−0.165174	−	0.936750i	0.783710	−	0.621127i	$-0.213325\pi$
$572$	−13.3226	+	6.21244i	−0.557046	+	0.259755i
$573$		0			0
$574$	1.45496	+	0.256548i	0.0607287	+	0.0107081i
$575$	−7.10097	+	23.2104i	−0.296131	+	0.967939i
$576$		0			0
$577$	5.75013	−	21.4598i	0.239381	−	0.893383i	−0.736744	−	0.676172i	$-0.763638\pi$
$577$	5.75013	−	21.4598i	0.239381	−	0.893383i	0.976125	−	0.217210i	$-0.0696958\pi$
$578$	38.2264	+	17.8253i	1.59001	+	0.741433i
$579$		0			0
$580$	0.0130261	+	0.00500169i	0.000540881	+	0.000207684i
$581$	11.9450	+	14.2355i	0.495562	+	0.590588i
$582$		0			0
$583$	−20.8531	+	44.7197i	−0.863648	+	1.85210i
$584$	−5.34785	−	9.26275i	−0.221296	−	0.383295i
$585$		0			0
$586$	−16.0557	+	27.8092i	−0.663253	+	1.14879i
$587$	−4.24785	−	6.06656i	−0.175327	−	0.250394i	0.721864	−	0.692034i	$-0.243285\pi$
$587$	−4.24785	−	6.06656i	−0.175327	−	0.250394i	−0.897192	+	0.441641i	$0.854397\pi$
$588$		0			0
$589$	−8.11364	+	22.2921i	−0.334317	+	0.918528i
$590$	20.6214	+	2.16939i	0.848970	+	0.0893124i
$591$		0			0
$592$	0.420307	+	4.80413i	0.0172745	+	0.197449i
$593$	10.8659	+	10.8659i	0.446208	+	0.446208i	0.894092	−	0.447884i	$-0.147822\pi$
$593$	10.8659	+	10.8659i	0.446208	+	0.446208i	−0.447884	+	0.894092i	$0.647822\pi$
$594$		0			0
$595$	−20.2429	+	11.2183i	−0.829877	+	0.459905i
$596$	1.38581	−	1.65154i	0.0567648	−	0.0676497i
$597$		0			0
$598$	−13.6359	−	9.54799i	−0.557615	−	0.390446i
$599$	37.1726	+	13.5297i	1.51883	+	0.552809i	0.960856	−	0.277049i	$-0.0893566\pi$
$599$	37.1726	+	13.5297i	1.51883	+	0.552809i	0.557974	+	0.829858i	$0.311579\pi$
$600$		0			0
$601$	−1.53626	+	8.71259i	−0.0626655	+	0.355394i	0.937311	+	0.348495i	$0.113307\pi$
$601$	−1.53626	+	8.71259i	−0.0626655	+	0.355394i	−0.999976	+	0.00689897i	$0.997804\pi$
$602$	2.59152	+	9.67169i	0.105623	+	0.394189i
$603$		0			0
$604$	13.0898	−	7.55740i	0.532616	−	0.307506i
$605$	10.8228	−	12.4478i	0.440009	−	0.506075i
$606$		0			0
$607$	−19.5481	−	1.71024i	−0.793433	−	0.0694164i	−0.316770	−	0.948502i	$-0.602598\pi$
$607$	−19.5481	−	1.71024i	−0.793433	−	0.0694164i	−0.476663	+	0.879086i	$0.658154\pi$
$608$	7.04657	+	0.616495i	0.285776	+	0.0250022i
$609$		0			0
$610$	1.11481	+	15.9645i	0.0451374	+	0.646383i
$611$	−10.6073	+	6.12411i	−0.429124	+	0.247755i
$612$		0			0
$613$	−10.4403	−	38.9638i	−0.421680	−	1.57373i	−0.771067	−	0.636754i	$-0.780277\pi$
$613$	−10.4403	−	38.9638i	−0.421680	−	1.57373i	0.349387	−	0.936979i	$-0.386390\pi$
$614$	−0.441919	+	2.50625i	−0.0178344	+	0.101144i
$615$		0			0
$616$	−5.41981	−	1.97265i	−0.218370	−	0.0794803i
$617$	−3.15147	−	2.20668i	−0.126873	−	0.0888377i	0.508417	−	0.861111i	$-0.330231\pi$
$617$	−3.15147	−	2.20668i	−0.126873	−	0.0888377i	−0.635291	+	0.772273i	$0.719120\pi$
$618$		0			0
$619$	31.5228	−	37.5674i	1.26701	−	1.50996i	0.503786	−	0.863828i	$-0.331940\pi$
$619$	31.5228	−	37.5674i	1.26701	−	1.50996i	0.763223	−	0.646135i	$-0.223616\pi$
$620$	−3.63506	−	6.55931i	−0.145988	−	0.263428i
$621$		0			0
$622$	11.9545	+	11.9545i	0.479334	+	0.479334i
$623$	0.162465	+	1.85699i	0.00650903	+	0.0743986i
$624$		0			0
$625$	20.2310	−	14.6869i	0.809242	−	0.587476i
$626$	−8.51540	+	23.3959i	−0.340344	+	0.935087i
$627$		0			0
$628$	−0.857318	−	1.22438i	−0.0342107	−	0.0488580i
$629$	18.5490	−	32.1279i	0.739598	−	1.28102i
$630$		0			0
$631$	−21.7434	−	37.6606i	−0.865590	−	1.49925i	−0.866460	−	0.499246i	$-0.833610\pi$
$631$	−21.7434	−	37.6606i	−0.865590	−	1.49925i	0.000870334	−	1.00000i	$-0.499723\pi$
$632$	−2.37556	+	5.09440i	−0.0944945	+	0.202644i
$633$		0			0
$634$	16.5531	+	19.7273i	0.657409	+	0.783470i
$635$	−22.7223	+	10.1140i	−0.901707	+	0.401363i
$636$		0			0
$637$	−16.1289	−	7.52104i	−0.639051	−	0.297994i
$638$	0.00692349	−	0.0258388i	0.000274104	−	0.00102297i
$639$		0			0
$640$	−1.60864	+	1.55315i	−0.0635871	+	0.0613936i
$641$	−31.6672	−	5.58379i	−1.25078	−	0.220546i	−0.491250	−	0.871018i	$-0.663460\pi$
$641$	−31.6672	−	5.58379i	−1.25078	−	0.220546i	−0.759530	+	0.650472i	$0.774571\pi$
$642$		0			0
$643$	−15.3924	+	7.17758i	−0.607016	+	0.283056i	−0.701724	−	0.712449i	$-0.747586\pi$
$643$	−15.3924	+	7.17758i	−0.607016	+	0.283056i	0.0947082	+	0.995505i	$0.469808\pi$
$644$	−1.13416	−	6.43216i	−0.0446923	−	0.253462i
$645$		0			0
$646$	−41.6839	−	34.9769i	−1.64003	−	1.37615i
$647$	21.6407	−	21.6407i	0.850784	−	0.850784i	−0.139446	−	0.990230i	$-0.544532\pi$
$647$	21.6407	−	21.6407i	0.850784	−	0.850784i	0.990230	+	0.139446i	$0.0445320\pi$
$648$		0			0
$649$		−	39.7519i		−	1.56040i
$650$	5.29513	+	16.3073i	0.207692	+	0.639626i
$651$		0			0
$652$	−9.38042	+	13.3966i	−0.367366	+	0.524652i
$653$	−8.25358	−	17.6999i	−0.322988	−	0.692649i	0.676034	−	0.736870i	$-0.263697\pi$
$653$	−8.25358	−	17.6999i	−0.322988	−	0.692649i	−0.999022	+	0.0442212i	$0.985919\pi$
$654$		0			0
$655$	−15.4125	+	5.30530i	−0.602216	+	0.207295i
$656$	−0.950966	−	0.549040i	−0.0371290	−	0.0214364i
$657$		0			0
$658$	−4.64196	−	1.24381i	−0.180962	−	0.0484887i
$659$	−3.03288	+	1.10388i	−0.118144	+	0.0430009i	−0.400416	−	0.916334i	$-0.631134\pi$
$659$	−3.03288	+	1.10388i	−0.118144	+	0.0430009i	0.282272	+	0.959335i	$0.408912\pi$
$660$		0			0
$661$	−13.9565	+	11.7109i	−0.542844	+	0.455500i	−0.872509	−	0.488598i	$-0.837509\pi$
$661$	−13.9565	+	11.7109i	−0.542844	+	0.455500i	0.329665	+	0.944098i	$0.393064\pi$
$662$	0.287203	−	3.28275i	0.0111625	−	0.127588i
$663$		0			0
$664$	−4.72396	−	12.9790i	−0.183325	−	0.503682i
$665$	20.6489	−	5.14626i	0.800730	−	0.199563i
$666$		0			0
$667$	0.0292604	−	0.00784029i	0.00113297	−	0.000303577i
$668$	−7.00000	+	4.90145i	−0.270838	+	0.189643i
$669$		0			0
$670$	12.2979	−	1.94659i	0.475108	−	0.0752032i
$671$	30.2142	−	5.32759i	1.16641	−	0.205669i
$672$		0			0
$673$	−47.1598	+	4.12595i	−1.81788	+	0.159044i	−0.944610	−	0.328196i	$-0.893559\pi$
$673$	−47.1598	+	4.12595i	−1.81788	+	0.159044i	−0.873268	+	0.487239i	$0.838004\pi$
$674$	23.3125			0.897963
$675$		0			0
$676$	1.24130			0.0477425
$677$	9.89706	−	0.865881i	0.380375	−	0.0332785i	0.104635	−	0.994511i	$-0.466633\pi$
$677$	9.89706	−	0.865881i	0.380375	−	0.0332785i	0.275740	+	0.961232i	$0.411077\pi$
$678$		0			0
$679$	6.76188	−	1.19230i	0.259497	−	0.0457563i
$680$	16.9900	−	2.68928i	0.651535	−	0.103129i
$681$		0			0
$682$	−11.7769	+	8.24624i	−0.450959	+	0.315765i
$683$	17.7729	−	4.76224i	0.680062	−	0.182222i	0.0977790	−	0.995208i	$-0.468826\pi$
$683$	17.7729	−	4.76224i	0.680062	−	0.182222i	0.582283	+	0.812986i	$0.302160\pi$
$684$		0			0
$685$	25.8525	−	6.44312i	0.987772	−	0.246179i
$686$	−5.60934	−	15.4115i	−0.214166	−	0.588416i
$687$		0			0
$688$	0.648620	−	7.41376i	0.0247284	−	0.282647i
$689$	−30.2359	+	25.3709i	−1.15189	+	0.966554i
$690$		0			0
$691$	7.98078	−	2.90477i	0.303603	−	0.110503i	−0.185726	−	0.982602i	$-0.559464\pi$
$691$	7.98078	−	2.90477i	0.303603	−	0.110503i	0.489329	+	0.872099i	$0.337242\pi$
$692$	19.9942	+	5.35742i	0.760064	+	0.203659i
$693$		0			0
$694$	−4.29770	−	2.48128i	−0.163139	−	0.0941881i
$695$	12.9222	−	4.44810i	0.490169	−	0.168726i
$696$		0			0
$697$	3.56996	+	7.65580i	0.135222	+	0.289984i
$698$	−16.4274	+	23.4607i	−0.621785	+	0.888001i
$699$		0			0
$700$	−3.05523	+	5.99339i	−0.115477	+	0.226529i
$701$		−	21.8864i		−	0.826637i	−0.910586	−	0.413319i	$-0.864370\pi$
$701$		−	21.8864i		−	0.826637i	0.910586	−	0.413319i	$-0.135630\pi$
$702$		0			0
$703$	−24.1207	+	24.1207i	−0.909728	+	0.909728i
$704$	3.28389	+	2.75551i	0.123766	+	0.103852i
$705$		0			0
$706$	−2.28721	−	12.9714i	−0.0860801	−	0.488185i
$707$	−17.3826	+	8.10562i	−0.653739	+	0.304843i
$708$		0			0
$709$	−2.29997	−	0.405546i	−0.0863770	−	0.0152306i	0.130293	−	0.991476i	$-0.458408\pi$
$709$	−2.29997	−	0.405546i	−0.0863770	−	0.0152306i	−0.216670	+	0.976245i	$0.569519\pi$
$710$	−4.41862	+	4.26620i	−0.165828	+	0.160107i
$711$		0			0
$712$	0.358589	−	1.33827i	0.0134387	−	0.0501538i
$713$	−14.7553	−	6.88050i	−0.552590	−	0.257677i
$714$		0			0
$715$	30.0294	−	13.3665i	1.12304	−	0.499880i
$716$	10.2364	+	12.1993i	0.382553	+	0.455909i
$717$		0			0
$718$	−2.44443	+	5.24209i	−0.0912252	+	0.195633i
$719$	−20.7200	−	35.8882i	−0.772727	−	1.33840i	−0.936063	−	0.351832i	$-0.885559\pi$
$719$	−20.7200	−	35.8882i	−0.772727	−	1.33840i	0.163336	−	0.986570i	$-0.447774\pi$
$720$		0			0
$721$	−1.36195	+	2.35896i	−0.0507216	+	0.0878524i
$722$	17.8005	+	25.4217i	0.662466	+	0.946099i
$723$		0			0
$724$	−2.36384	+	6.49461i	−0.0878516	+	0.241370i
$725$	−0.0289266	−	0.0116935i	−0.00107431	−	0.000434287i
$726$		0			0
$727$	0.853202	+	9.75214i	0.0316435	+	0.361687i	0.995464	+	0.0951358i	$0.0303285\pi$
$727$	0.853202	+	9.75214i	0.0316435	+	0.361687i	−0.963821	+	0.266551i	$0.914116\pi$
$728$	−3.26234	−	3.26234i	−0.120910	−	0.120910i
$729$		0			0
$730$	11.5929	+	20.9188i	0.429071	+	0.774239i
$731$	−36.7996	+	43.8560i	−1.36108	+	1.62207i
$732$		0			0
$733$	29.1774	+	20.4302i	1.07769	+	0.754608i	0.970855	−	0.239669i	$-0.0770389\pi$
$733$	29.1774	+	20.4302i	1.07769	+	0.754608i	0.106837	+	0.994277i	$0.465928\pi$
$734$	−10.1356	−	3.68907i	−0.374114	−	0.136166i
$735$		0			0
$736$	−0.842968	+	4.78071i	−0.0310722	+	0.176219i
$737$	−6.17801	−	23.0566i	−0.227570	−	0.849302i
$738$		0			0
$739$	43.5295	−	25.1318i	1.60126	−	0.924487i	0.610023	−	0.792384i	$-0.291160\pi$
$739$	43.5295	−	25.1318i	1.60126	−	0.924487i	0.991236	−	0.132104i	$-0.0421732\pi$
$740$	−0.751184	−	10.7572i	−0.0276141	−	0.395443i
$741$		0			0
$742$	−15.4276	−	1.34974i	−0.566363	−	0.0495504i
$743$	−13.4718	−	1.17863i	−0.494232	−	0.0432397i	−0.162684	−	0.986678i	$-0.552015\pi$
$743$	−13.4718	−	1.17863i	−0.494232	−	0.0432397i	−0.331548	+	0.943439i	$0.607571\pi$
$744$		0			0
$745$	−3.16308	+	3.63801i	−0.115886	+	0.133286i
$746$	3.23170	−	1.86582i	0.118321	−	0.0683127i
$747$		0			0
$748$	−8.53515	−	31.8536i	−0.312076	−	1.16468i
$749$	−2.17594	+	12.3404i	−0.0795072	+	0.450908i
$750$		0			0
$751$	−40.9996	−	14.9226i	−1.49610	−	0.544535i	−0.541051	−	0.840990i	$-0.681973\pi$
$751$	−40.9996	−	14.9226i	−1.49610	−	0.544535i	−0.955047	+	0.296455i	$0.904195\pi$
$752$	2.92589	+	2.04873i	0.106696	+	0.0747095i
$753$		0			0
$754$	0.0137544	−	0.0163919i	0.000500906	−	0.000596957i
$755$	−29.5617	+	16.3826i	−1.07586	+	0.596225i
$756$		0			0
$757$	17.7448	+	17.7448i	0.644944	+	0.644944i	0.951767	−	0.306823i	$-0.0992658\pi$
$757$	17.7448	+	17.7448i	0.644944	+	0.644944i	−0.306823	+	0.951767i	$0.599266\pi$
$758$	−1.77565	−	20.2958i	−0.0644945	−	0.737176i
$759$		0			0
$760$	−15.7300	−	1.65481i	−0.570587	−	0.0600262i
$761$	12.4805	−	34.2900i	0.452419	−	1.24301i	−0.478597	−	0.878035i	$-0.658854\pi$
$761$	12.4805	−	34.2900i	0.452419	−	1.24301i	0.931016	−	0.364977i	$-0.118923\pi$
$762$		0			0
$763$	−0.770093	−	1.09981i	−0.0278792	−	0.0398157i
$764$	13.5723	−	23.5079i	0.491029	−	0.850488i
$765$		0			0
$766$	6.80029	+	11.7784i	0.245704	+	0.425572i
$767$	13.4385	−	28.8190i	0.485237	−	1.04059i
$768$		0			0
$769$	−11.5933	−	13.8163i	−0.418063	−	0.498228i	0.515376	−	0.856964i	$-0.327652\pi$
$769$	−11.5933	−	13.8163i	−0.418063	−	0.498228i	−0.933439	+	0.358736i	$0.883208\pi$
$770$	12.0398	+	4.62296i	0.433884	+	0.166600i
$771$		0			0
$772$	16.0562	+	7.48712i	0.577875	+	0.269467i
$773$	7.27975	−	27.1684i	0.261834	−	0.977179i	−0.702325	−	0.711856i	$-0.747855\pi$
$773$	7.27975	−	27.1684i	0.261834	−	0.977179i	0.964160	−	0.265323i	$-0.0854785\pi$
$774$		0			0
$775$	7.86962	+	14.8074i	0.282685	+	0.531899i
$776$	−5.02578	−	0.886180i	−0.180415	−	0.0318120i
$777$		0			0
$778$	6.01707	−	2.80581i	0.215723	−	0.100593i
$779$	−1.34877	−	7.64926i	−0.0483247	−	0.274063i
$780$		0			0
$781$	9.02019	+	7.56884i	0.322768	+	0.270834i
$782$	26.4062	−	26.4062i	0.944286	−	0.944286i
$783$		0			0
$784$			5.18979i			0.185350i
$785$	1.86868	+	2.77101i	0.0666962	+	0.0989015i
$786$		0			0
$787$	21.8945	−	31.2685i	0.780453	−	1.11460i	−0.210127	−	0.977674i	$-0.567388\pi$
$787$	21.8945	−	31.2685i	0.780453	−	1.11460i	0.990581	−	0.136929i	$-0.0437232\pi$
$788$	−3.71294	−	7.96242i	−0.132268	−	0.283649i
$789$		0			0
$790$	5.51098	−	11.2964i	0.196072	−	0.401910i
$791$	−12.9376	−	7.46952i	−0.460007	−	0.265585i
$792$		0			0
$793$	23.7055	+	6.35187i	0.841808	+	0.225562i
$794$	−27.4428	+	9.98836i	−0.973908	+	0.354473i
$795$		0			0
$796$	−9.39836	+	7.88616i	−0.333116	+	0.279518i
$797$	2.84657	−	32.5365i	0.100831	−	1.15250i	−0.762197	−	0.647345i	$-0.775879\pi$
$797$	2.84657	−	32.5365i	0.100831	−	1.15250i	0.863028	−	0.505156i	$-0.168565\pi$
$798$		0			0
$799$	−9.39779	−	25.8202i	−0.332470	−	0.913453i
$800$	3.65742	−	3.40929i	0.129309	−	0.120537i
$801$		0			0
$802$	12.9999	−	3.48332i	0.459044	−	0.123000i
$803$	37.5585	−	26.2987i	1.32541	−	0.928062i
$804$		0			0
$805$	2.28329	+	14.4250i	0.0804753	+	0.508415i
$806$	−11.3256	+	1.99701i	−0.398928	+	0.0703417i
$807$		0			0
$808$	14.2010	−	1.24242i	0.499589	−	0.0437083i
$809$	−18.8465			−0.662608			−0.331304	−	0.943524i	$-0.607488\pi$
$809$	−18.8465			−0.662608			−0.331304	+	0.943524i	$0.607488\pi$
$810$		0			0
$811$	23.8763			0.838409			0.419205	−	0.907892i	$-0.362309\pi$
$811$	23.8763			0.838409			0.419205	+	0.907892i	$0.362309\pi$
$812$	0.00836379		0.000731737i	0.000293512		2.56789e-5i
$813$		0			0
$814$	−20.3590	+	3.58984i	−0.713582	+	0.125824i
$815$	21.4977	−	29.5831i	0.753031	−	1.03625i
$816$		0			0
$817$	43.1214	−	30.1939i	1.50863	−	1.05635i
$818$	−8.68127	+	2.32614i	−0.303533	+	0.0813315i
$819$		0			0
$820$	2.10455	+	1.26482i	0.0734942	+	0.0441693i
$821$	−7.71011	−	21.1833i	−0.269085	−	0.739304i	−0.998475	−	0.0552062i	$-0.982418\pi$
$821$	−7.71011	−	21.1833i	−0.269085	−	0.739304i	0.729390	−	0.684098i	$-0.239804\pi$
$822$		0			0
$823$	4.54252	−	51.9212i	0.158342	−	1.80986i	−0.337370	−	0.941372i	$-0.609537\pi$
$823$	4.54252	−	51.9212i	0.158342	−	1.80986i	0.495712	−	0.868487i	$-0.334907\pi$
$824$	1.55089	−	1.30135i	0.0540277	−	0.0453346i
$825$		0			0
$826$	11.7239	−	4.26716i	0.407928	−	0.148474i
$827$	−19.7756	−	5.29886i	−0.687665	−	0.184259i	−0.101966	−	0.994788i	$-0.532513\pi$
$827$	−19.7756	−	5.29886i	−0.687665	−	0.184259i	−0.585699	+	0.810529i	$0.699180\pi$
$828$		0			0
$829$	8.17054	+	4.71726i	0.283775	+	0.163837i	0.635131	−	0.772404i	$-0.280946\pi$
$829$	8.17054	+	4.71726i	0.283775	+	0.163837i	−0.351356	+	0.936242i	$0.614279\pi$
$830$	10.0522	+	29.2028i	0.348917	+	1.01364i
$831$		0			0
$832$	1.44920	+	3.10782i	0.0502419	+	0.107744i
$833$	22.8993	−	32.7036i	0.793413	−	1.13311i
$834$		0			0
$835$	15.8424	−	10.6836i	0.548248	−	0.369722i
$836$			30.3227i			1.04873i
$837$		0			0
$838$	8.74727	−	8.74727i	0.302169	−	0.302169i
$839$	−34.6389	−	29.0655i	−1.19587	−	1.00345i	−0.999738	−	0.0228742i	$-0.992718\pi$
$839$	−34.6389	−	29.0655i	−1.19587	−	1.00345i	−0.196129	−	0.980578i	$-0.562837\pi$
$840$		0			0
$841$	−5.03579	−	28.5594i	−0.173648	−	0.984806i
$842$	−18.2949	+	8.53103i	−0.630482	+	0.293999i
$843$		0			0
$844$	−6.74335	−	1.18903i	−0.232116	−	0.0409283i
$845$	−2.77521	−	0.0487068i	−0.0954703	−	0.00167556i
$846$		0			0
$847$	2.56876	−	9.58676i	0.0882638	−	0.329405i
$848$	10.4319	+	4.86449i	0.358234	+	0.167047i
$849$		0			0
$850$	−38.0904	+	5.34583i	−1.30649	+	0.183360i
$851$	−15.0480	−	17.9335i	−0.515839	−	0.614753i
$852$		0			0
$853$	18.5338	−	39.7458i	0.634584	−	1.36087i	−0.281375	−	0.959598i	$-0.590791\pi$
$853$	18.5338	−	39.7458i	0.634584	−	1.36087i	0.915959	−	0.401272i	$-0.131432\pi$
$854$	4.81460	+	8.33913i	0.164752	+	0.285359i
$855$		0			0
$856$	4.65675	−	8.06573i	0.159165	−	0.275681i
$857$	−1.31729	−	1.88128i	−0.0449977	−	0.0642633i	0.796023	−	0.605267i	$-0.206934\pi$
$857$	−1.31729	−	1.88128i	−0.0449977	−	0.0642633i	−0.841020	+	0.541003i	$0.818045\pi$
$858$		0			0
$859$	−1.23367	+	3.38949i	−0.0420924	+	0.115648i	−0.958958	−	0.283548i	$-0.908488\pi$
$859$	−1.23367	+	3.38949i	−0.0420924	+	0.115648i	0.916866	+	0.399196i	$0.130711\pi$
$860$	−1.74104	+	16.5497i	−0.0593689	+	0.564339i
$861$		0			0
$862$	0.720654	+	8.23711i	0.0245456	+	0.280557i
$863$	−11.9419	−	11.9419i	−0.406507	−	0.406507i	0.474012	−	0.880518i	$-0.342805\pi$
$863$	−11.9419	−	11.9419i	−0.406507	−	0.406507i	−0.880518	+	0.474012i	$0.842805\pi$
$864$		0			0
$865$	−44.4912	−	12.7623i	−1.51275	−	0.433930i
$866$	22.4198	−	26.7188i	0.761854	−	0.907942i
$867$		0			0
$868$	−3.69623	−	2.58813i	−0.125458	−	0.0878469i
$869$	−22.6432	−	8.24143i	−0.768116	−	0.279571i
$870$		0			0
$871$	3.31564	−	18.8039i	0.112346	−	0.637148i
$872$	0.258276	+	0.963899i	0.00874633	+	0.0326417i
$873$		0			0
$874$	−29.7375	+	17.1690i	−1.00589	+	0.580749i
$875$	7.06582	−	13.2797i	0.238868	−	0.448935i
$876$		0			0
$877$	44.3005	+	3.87579i	1.49592	+	0.130876i	0.805528	−	0.592558i	$-0.201882\pi$
$877$	44.3005	+	3.87579i	1.49592	+	0.130876i	0.690394	+	0.723434i	$0.257437\pi$
$878$	2.35686	+	0.206198i	0.0795401	+	0.00695886i
$879$		0			0
$880$	−7.23374	−	6.28941i	−0.243849	−	0.212016i
$881$	−20.0596	+	11.5814i	−0.675825	+	0.390188i	−0.798280	−	0.602286i	$-0.794257\pi$
$881$	−20.0596	+	11.5814i	−0.675825	+	0.390188i	0.122455	+	0.992474i	$0.460923\pi$
$882$		0			0
$883$	5.68779	+	21.2271i	0.191409	+	0.714350i	0.993167	+	0.116701i	$0.0372318\pi$
$883$	5.68779	+	21.2271i	0.191409	+	0.714350i	−0.801758	+	0.597649i	$0.796102\pi$
$884$	4.58069	−	25.9784i	0.154065	−	0.873747i
$885$		0			0
$886$	−3.26528	−	1.18846i	−0.109699	−	0.0399272i
$887$	29.4217	+	20.6013i	0.987883	+	0.691723i	0.951511	−	0.307615i	$-0.0995309\pi$
$887$	29.4217	+	20.6013i	0.987883	+	0.691723i	0.0363722	+	0.999338i	$0.488420\pi$
$888$		0			0
$889$	−9.61945	+	11.4640i	−0.322626	+	0.384491i
$890$	−0.854217	+	2.97793i	−0.0286334	+	0.0998206i
$891$		0			0
$892$	0.0398865	+	0.0398865i	0.00133550	+	0.00133550i
$893$	2.20203	+	25.1693i	0.0736880	+	0.842258i
$894$		0			0
$895$	−22.4071	−	27.6759i	−0.748988	−	0.925103i
$896$	−0.460167	+	1.26430i	−0.0153731	+	0.0422373i
$897$		0			0
$898$	3.15822	+	4.51040i	0.105391	+	0.150514i
$899$	0.0104640	−	0.0181241i	0.000348992	−	0.000604472i
$900$		0			0
$901$	−44.2730	−	76.6832i	−1.47495	−	2.55469i
$902$	1.98938	−	4.26623i	0.0662390	−	0.142050i
$903$		0			0
$904$	7.13717	+	8.50575i	0.237379	+	0.282897i
$905$	5.53974	−	14.4274i	0.184147	−	0.479583i
$906$		0			0
$907$	−23.5226	−	10.9688i	−0.781055	−	0.364212i	−0.00915710	−	0.999958i	$-0.502915\pi$
$907$	−23.5226	−	10.9688i	−0.781055	−	0.364212i	−0.771898	+	0.635746i	$0.780693\pi$
$908$	1.92301	−	7.17678i	0.0638174	−	0.238170i
$909$		0			0
$910$	7.16567	+	7.42169i	0.237540	+	0.246027i
$911$	13.9071	+	2.45220i	0.460763	+	0.0812449i	0.399211	−	0.916859i	$-0.369284\pi$
$911$	13.9071	+	2.45220i	0.460763	+	0.0812449i	0.0615515	+	0.998104i	$0.480395\pi$
$912$		0			0
$913$	53.6617	−	25.0229i	1.77594	−	0.828136i
$914$	1.75237	+	9.93817i	0.0579631	+	0.328725i
$915$		0			0
$916$	−9.42495	−	7.90847i	−0.311409	−	0.261303i
$917$	−6.93510	+	6.93510i	−0.229017	+	0.229017i
$918$		0			0
$919$			27.7976i			0.916959i	0.888705	+	0.458479i	$0.151606\pi$
$919$			27.7976i			0.916959i	−0.888705	+	0.458479i	$0.848394\pi$
$920$	2.07223	−	10.6553i	0.0683194	−	0.351294i
$921$		0			0
$922$	−6.92059	+	9.88363i	−0.227917	+	0.325500i
$923$	3.98066	+	8.53656i	0.131025	+	0.280984i
$924$		0			0
$925$	1.25735	+	24.0796i	0.0413413	+	0.791733i
$926$	−8.80004	−	5.08071i	−0.289187	−	0.166962i
$927$		0			0
$928$	−0.00602752	−	0.00161507i	−0.000197863	−	5.30172e-5i
$929$	−30.6608	+	11.1596i	−1.00595	+	0.366135i	−0.791875	−	0.610683i	$-0.790895\pi$
$929$	−30.6608	+	11.1596i	−1.00595	+	0.366135i	−0.214072	+	0.976818i	$0.568673\pi$
$930$		0			0
$931$	−28.1214	+	23.5967i	−0.921643	+	0.773350i
$932$	1.14099	−	13.0416i	0.0373743	−	0.427190i
$933$		0			0
$934$	−6.98185	−	19.1825i	−0.228453	−	0.627670i
$935$	17.8323	+	71.5508i	0.583180	+	2.33996i
$936$		0			0
$937$	−40.8389	+	10.9427i	−1.33415	+	0.357484i	−0.854260	−	0.519846i	$-0.825989\pi$
$937$	−40.8389	+	10.9427i	−1.33415	+	0.357484i	−0.479888	+	0.877330i	$0.659323\pi$
$938$	6.13687	−	4.29708i	0.200376	−	0.140305i
$939$		0			0
$940$	−6.46109	−	4.69520i	−0.210737	−	0.153140i
$941$	−55.9278	+	9.86158i	−1.82319	+	0.321478i	−0.977298	−	0.211869i	$-0.932045\pi$
$941$	−55.9278	+	9.86158i	−1.82319	+	0.321478i	−0.845896	+	0.533348i	$0.820934\pi$
$942$		0			0
$943$	5.31031	−	0.464592i	0.172927	−	0.0151292i
$944$	−9.27307			−0.301813
$945$		0			0
$946$	31.9028			1.03725
$947$	44.2394	−	3.87045i	1.43759	−	0.125773i	0.658450	−	0.752625i	$-0.271212\pi$
$947$	44.2394	−	3.87045i	1.43759	−	0.125773i	0.779138	+	0.626852i	$0.215657\pi$
$948$		0			0
$949$	36.1194	−	6.36882i	1.17248	−	0.206741i
$950$	35.1030	+	4.31691i	1.13889	+	0.140059i
$951$		0			0
$952$	8.47831	−	5.93658i	0.274784	−	0.192406i
$953$	9.05327	−	2.42582i	0.293264	−	0.0785799i	−0.109187	−	0.994021i	$-0.534825\pi$
$953$	9.05327	−	2.42582i	0.293264	−	0.0785799i	0.402452	+	0.915441i	$0.368158\pi$
$954$		0			0
$955$	−31.2664	+	52.0247i	−1.01176	+	1.68348i
$956$	−0.00925442	−	0.0254263i	−0.000299309	−	0.000822346i
$957$		0			0
$958$	−3.62516	+	41.4358i	−0.117124	+	1.33873i
$959$	12.2806	−	10.3047i	0.396562	−	0.332755i
$960$		0			0
$961$	18.5611	−	6.75570i	0.598747	−	0.217926i
$962$	−15.9733	−	4.28003i	−0.514999	−	0.137994i
$963$		0			0
$964$	6.29281	+	3.63315i	0.202678	+	0.117016i
$965$	−35.6034	−	17.3692i	−1.14611	−	0.559133i
$966$		0			0
$967$	10.2031	+	21.8807i	0.328111	+	0.703636i	0.999291	−	0.0376584i	$-0.0119899\pi$
$967$	10.2031	+	21.8807i	0.328111	+	0.703636i	−0.671180	+	0.741295i	$0.734212\pi$
$968$	−4.23112	+	6.04266i	−0.135993	+	0.194219i
$969$		0			0
$970$	11.2015	+	2.17846i	0.359658	+	0.0699460i
$971$			42.1000i			1.35105i	0.737336	+	0.675526i	$0.236083\pi$
$971$			42.1000i			1.35105i	−0.737336	+	0.675526i	$0.763917\pi$
$972$		0			0
$973$	5.81457	−	5.81457i	0.186407	−	0.186407i
$974$	23.3617	+	19.6028i	0.748556	+	0.628113i
$975$		0			0
$976$	−1.24279	−	7.04819i	−0.0397806	−	0.225607i
$977$	−14.8310	+	6.91579i	−0.474484	+	0.221256i	−0.645124	−	0.764078i	$-0.723194\pi$
$977$	−14.8310	+	6.91579i	−0.474484	+	0.221256i	0.170640	+	0.985333i	$0.445417\pi$
$978$		0			0
$979$	5.84906	+	1.03135i	0.186937	+	0.0329620i
$980$	0.203639	−	11.6029i	0.00650501	−	0.370642i
$981$		0			0
$982$	−1.56304	+	5.83336i	−0.0498787	+	0.186150i
$983$	−5.97463	−	2.78601i	−0.190561	−	0.0888601i	0.324996	−	0.945715i	$-0.394637\pi$
$983$	−5.97463	−	2.78601i	−0.190561	−	0.0888601i	−0.515557	+	0.856855i	$0.672415\pi$
$984$		0			0
$985$	7.98867	+	17.9475i	0.254540	+	0.571854i
$986$	0.0308562	+	0.0367730i	0.000982663	+	0.00117109i
$987$		0			0
$988$	−10.2509	+	21.9831i	−0.326124	+	0.699375i
$989$	18.0636	+	31.2872i	0.574391	+	0.994874i
$990$		0			0
$991$	−27.5644	+	47.7429i	−0.875612	+	1.51660i	−0.0195020	+	0.999810i	$0.506208\pi$
$991$	−27.5644	+	47.7429i	−0.875612	+	1.51660i	−0.856110	+	0.516794i	$0.827125\pi$
$992$	1.92363	+	2.74723i	0.0610754	+	0.0872247i
$993$		0			0
$994$	−1.26399	+	3.47278i	−0.0400913	+	0.110150i
$995$	21.3216	−	17.2625i	0.675939	−	0.547258i
$996$		0			0
$997$	2.30128	+	26.3037i	0.0728822	+	0.833047i	0.941379	+	0.337352i	$0.109531\pi$
$997$	2.30128	+	26.3037i	0.0728822	+	0.833047i	−0.868497	+	0.495695i	$0.834913\pi$
$998$	−10.8133	−	10.8133i	−0.342290	−	0.342290i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.197.11		216
3.2	odd	2		270.2.r.a.227.1	yes	216
5.3	odd	4	inner	810.2.s.a.683.7		216
15.8	even	4		270.2.r.a.173.14	yes	216
27.5	odd	18	inner	810.2.s.a.287.7		216
27.22	even	9		270.2.r.a.167.14	yes	216
135.103	odd	36		270.2.r.a.113.1	✓	216
135.113	even	36	inner	810.2.s.a.773.11		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.1	✓	216	135.103	odd	36
270.2.r.a.167.14	yes	216	27.22	even	9
270.2.r.a.173.14	yes	216	15.8	even	4
270.2.r.a.227.1	yes	216	3.2	odd	2
810.2.s.a.197.11		216	1.1	even	1	trivial
810.2.s.a.287.7		216	27.5	odd	18	inner
810.2.s.a.683.7		216	5.3	odd	4	inner
810.2.s.a.773.11		216	135.113	even	36	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)

\(f(q)\)	\(=\)	\(q+(0.996195 - 0.0871557i) q^{2} +(0.984808 - 0.173648i) q^{4} +(-2.20857 + 0.349587i) q^{5} +(-1.10212 + 0.771712i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 - 0.0871557i) q^{2} +(0.984808 - 0.173648i) q^{4} +(-2.20857 + 0.349587i) q^{5} +(-1.10212 + 0.771712i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.16970 + 0.540747i) q^{10} +(1.46618 + 4.02828i) q^{11} +(-0.298865 + 3.41605i) q^{13} +(-1.03067 + 0.864832i) q^{14} +(0.939693 - 0.342020i) q^{16} +(-7.43061 - 1.99103i) q^{17} +(6.12582 + 3.53674i) q^{19} +(-2.11431 + 0.727791i) q^{20} +(1.81168 + 3.88517i) q^{22} +(-2.78440 + 3.97654i) q^{23} +(4.75558 - 1.54418i) q^{25} +3.42910i q^{26} +(-0.951369 + 0.951369i) q^{28} +(-0.00478023 - 0.00401109i) q^{29} +(0.582373 + 3.30280i) q^{31} +(0.906308 - 0.422618i) q^{32} +(-7.57586 - 1.33583i) q^{34} +(2.16433 - 2.08967i) q^{35} +(-1.24815 + 4.65816i) q^{37} +(6.41076 + 2.98938i) q^{38} +(-2.04284 + 0.909296i) q^{40} +(-0.705833 - 0.841179i) q^{41} +(3.14516 - 6.74482i) q^{43} +(2.14340 + 3.71249i) q^{44} +(-2.42723 + 4.20409i) q^{46} +(2.04873 + 2.92589i) q^{47} +(-1.77501 + 4.87681i) q^{49} +(4.60290 - 1.95278i) q^{50} +(0.298865 + 3.41605i) q^{52} +(8.13905 + 8.13905i) q^{53} +(-4.64639 - 8.38420i) q^{55} +(-0.864832 + 1.03067i) q^{56} +(-0.00511163 - 0.00357920i) q^{58} +(-8.71384 - 3.17158i) q^{59} +(1.24279 - 7.04819i) q^{61} +(0.868015 + 3.23947i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-0.534140 - 7.64906i) q^{65} +(-5.54705 - 0.485304i) q^{67} +(-7.66346 - 0.670466i) q^{68} +(1.97397 - 2.27035i) q^{70} +(2.37880 - 1.37340i) q^{71} +(-2.76825 - 10.3313i) q^{73} +(-0.837415 + 4.74922i) q^{74} +(6.64690 + 2.41927i) q^{76} +(-4.72458 - 3.30818i) q^{77} +(-3.61314 + 4.30597i) q^{79} +(-1.95581 + 1.08388i) q^{80} +(-0.776460 - 0.776460i) q^{82} +(-1.20379 - 13.7594i) q^{83} +(17.1071 + 1.79968i) q^{85} +(2.54534 - 6.99327i) q^{86} +(2.45881 + 3.51155i) q^{88} +(0.692740 - 1.19986i) q^{89} +(-2.30682 - 3.99553i) q^{91} +(-2.05158 + 4.39964i) q^{92} +(2.29594 + 2.73620i) q^{94} +(-14.7657 - 5.66964i) q^{95} +(-4.62517 - 2.15675i) q^{97} +(-1.34322 + 5.01296i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 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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