LMFDB - Embedded newform 585.2.cw.a.71.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(71,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("585.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.cw (of order $12$, degree $4$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.3
Character	$\chi$	$=$	585.71
Dual form			585.2.cw.a.206.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.59774 + 0.428113i) q^{2} +(0.637436 - 0.368024i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.07084 + 3.99644i) q^{7} +(1.47835 - 1.47835i) q^{8} +O(q^{10})$	\(q+(-1.59774 + 0.428113i) q^{2} +(0.637436 - 0.368024i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.07084 + 3.99644i) q^{7} +(1.47835 - 1.47835i) q^{8} +(1.43249 + 0.827050i) q^{10} +(-1.35793 - 5.06786i) q^{11} +(-0.741149 - 3.52855i) q^{13} -6.84371i q^{14} +(-2.46516 + 4.26979i) q^{16} +(2.05707 + 3.56295i) q^{17} +(2.19440 + 0.587987i) q^{19} +(-0.710968 - 0.190503i) q^{20} +(4.33923 + 7.51576i) q^{22} +(-0.647596 + 1.12167i) q^{23} +1.00000i q^{25} +(2.69478 + 5.32041i) q^{26} +(0.788192 + 2.94157i) q^{28} +(-3.29188 - 1.90057i) q^{29} +(3.95022 - 3.95022i) q^{31} +(1.02851 - 3.83845i) q^{32} +(-4.81201 - 4.81201i) q^{34} +(3.58311 - 2.06871i) q^{35} +(9.14858 - 2.45136i) q^{37} -3.75779 q^{38} -2.09070 q^{40} +(1.89876 - 0.508772i) q^{41} +(11.0208 - 6.36286i) q^{43} +(-2.73069 - 2.73069i) q^{44} +(0.554488 - 2.06938i) q^{46} +(6.64428 - 6.64428i) q^{47} +(-8.76266 - 5.05912i) q^{49} +(-0.428113 - 1.59774i) q^{50} +(-1.77103 - 1.97647i) q^{52} +9.94699i q^{53} +(-2.62332 + 4.54372i) q^{55} +(4.32506 + 7.49122i) q^{56} +(6.07322 + 1.62731i) q^{58} +(4.55554 + 1.22065i) q^{59} +(-1.36172 - 2.35857i) q^{61} +(-4.62028 + 8.00256i) q^{62} -3.28751i q^{64} +(-1.97099 + 3.01914i) q^{65} +(2.92991 + 10.9346i) q^{67} +(2.62250 + 1.51410i) q^{68} +(-4.83923 + 4.83923i) q^{70} +(3.72068 - 13.8858i) q^{71} +(4.66372 + 4.66372i) q^{73} +(-13.5676 + 7.83325i) q^{74} +(1.61518 - 0.432786i) q^{76} +21.7075 q^{77} +2.21562 q^{79} +(4.76233 - 1.27606i) q^{80} +(-2.81592 + 1.62577i) q^{82} +(1.87062 + 1.87062i) q^{83} +(1.06482 - 3.97396i) q^{85} +(-14.8843 + 14.8843i) q^{86} +(-9.49956 - 5.48458i) q^{88} +(-1.91392 - 7.14286i) q^{89} +(14.8953 + 0.816571i) q^{91} +0.953324i q^{92} +(-7.77133 + 13.4603i) q^{94} +(-1.13590 - 1.96744i) q^{95} +(-11.6120 - 3.11142i) q^{97} +(16.1663 + 4.33175i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 24 q^{4} - 8 q^{7}+O(q^{10}) $ 40 * q - 24 * q^4 - 8 * q^7	$ 40 q - 24 q^{4} - 8 q^{7} - 4 q^{13} + 32 q^{16} + 20 q^{19} - 36 q^{22} - 4 q^{28} - 4 q^{31} - 24 q^{34} + 72 q^{37} - 48 q^{43} - 120 q^{46} + 60 q^{49} + 140 q^{52} + 8 q^{55} + 156 q^{58} - 8 q^{67} - 4 q^{73} - 16 q^{76} - 176 q^{79} - 204 q^{82} - 4 q^{85} + 72 q^{88} + 76 q^{91} - 72 q^{94} + 80 q^{97}+O(q^{100}) $ 40 * q - 24 * q^4 - 8 * q^7 - 4 * q^13 + 32 * q^16 + 20 * q^19 - 36 * q^22 - 4 * q^28 - 4 * q^31 - 24 * q^34 + 72 * q^37 - 48 * q^43 - 120 * q^46 + 60 * q^49 + 140 * q^52 + 8 * q^55 + 156 * q^58 - 8 * q^67 - 4 * q^73 - 16 * q^76 - 176 * q^79 - 204 * q^82 - 4 * q^85 + 72 * q^88 + 76 * q^91 - 72 * q^94 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	−1.59774	+	0.428113i	−1.12977	+	0.302721i	−0.774832	−	0.632168i	$-0.782165\pi$
$2$	−1.59774	+	0.428113i	−1.12977	+	0.302721i	−0.354940	+	0.934889i	$0.615499\pi$
$3$		0			0
$3$		0			0
$4$	0.637436	−	0.368024i	0.318718	−	0.184012i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$	−1.07084	+	3.99644i	−0.404741	+	1.51051i	0.399793	+	0.916605i	$0.369082\pi$
$7$	−1.07084	+	3.99644i	−0.404741	+	1.51051i	−0.804534	+	0.593907i	$0.797585\pi$
$8$	1.47835	−	1.47835i	0.522676	−	0.522676i
$9$		0			0
$10$	1.43249	+	0.827050i	0.452994	+	0.261536i
$11$	−1.35793	−	5.06786i	−0.409431	−	1.52802i	−0.795735	−	0.605645i	$-0.792915\pi$
$11$	−1.35793	−	5.06786i	−0.409431	−	1.52802i	0.386304	−	0.922371i	$-0.373751\pi$
$12$		0			0
$13$	−0.741149	−	3.52855i	−0.205558	−	0.978645i
$13$	−0.741149	−	3.52855i	−0.205558	−	0.978645i
$14$		−	6.84371i		−	1.82906i
$15$		0			0
$16$	−2.46516	+	4.26979i	−0.616291	+	1.06745i
$17$	2.05707	+	3.56295i	0.498913	+	0.864143i	0.999999	−	0.00125462i	$-0.000399357\pi$
$17$	2.05707	+	3.56295i	0.498913	+	0.864143i	−0.501086	+	0.865397i	$0.667066\pi$
$18$		0			0
$19$	2.19440	+	0.587987i	0.503429	+	0.134893i	0.501591	−	0.865105i	$-0.332748\pi$
$19$	2.19440	+	0.587987i	0.503429	+	0.134893i	0.00183798	+	0.999998i	$0.499415\pi$
$20$	−0.710968	−	0.190503i	−0.158977	−	0.0425978i
$21$		0			0
$22$	4.33923	+	7.51576i	0.925126	+	1.60237i
$23$	−0.647596	+	1.12167i	−0.135033	+	0.233884i	−0.925610	−	0.378478i	$-0.876447\pi$
$23$	−0.647596	+	1.12167i	−0.135033	+	0.233884i	0.790577	+	0.612363i	$0.209781\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$	2.69478	+	5.32041i	0.528490	+	1.04342i
$27$		0			0
$28$	0.788192	+	2.94157i	0.148954	+	0.555905i
$29$	−3.29188	−	1.90057i	−0.611287	−	0.352927i	0.162182	−	0.986761i	$-0.448147\pi$
$29$	−3.29188	−	1.90057i	−0.611287	−	0.352927i	−0.773469	+	0.633834i	$0.781480\pi$
$30$		0			0
$31$	3.95022	−	3.95022i	0.709480	−	0.709480i	−0.256946	−	0.966426i	$-0.582716\pi$
$31$	3.95022	−	3.95022i	0.709480	−	0.709480i	0.966426	+	0.256946i	$0.0827161\pi$
$32$	1.02851	−	3.83845i	0.181816	−	0.678548i
$33$		0			0
$34$	−4.81201	−	4.81201i	−0.825252	−	0.825252i
$35$	3.58311	−	2.06871i	0.605656	−	0.349676i
$36$		0			0
$37$	9.14858	−	2.45136i	1.50402	−	0.403000i	0.589575	−	0.807714i	$-0.299295\pi$
$37$	9.14858	−	2.45136i	1.50402	−	0.403000i	0.914444	+	0.404714i	$0.132629\pi$
$38$	−3.75779			−0.609595
$39$		0			0
$40$	−2.09070			−0.330569
$41$	1.89876	−	0.508772i	0.296537	−	0.0794569i	−0.107483	−	0.994207i	$-0.534279\pi$
$41$	1.89876	−	0.508772i	0.296537	−	0.0794569i	0.404020	+	0.914750i	$0.367613\pi$
$42$		0			0
$43$	11.0208	−	6.36286i	1.68066	−	0.970327i	0.719431	−	0.694564i	$-0.244403\pi$
$43$	11.0208	−	6.36286i	1.68066	−	0.970327i	0.961225	−	0.275764i	$-0.0889307\pi$
$44$	−2.73069	−	2.73069i	−0.411666	−	0.411666i
$45$		0			0
$46$	0.554488	−	2.06938i	0.0817549	−	0.305113i
$47$	6.64428	−	6.64428i	0.969169	−	0.969169i	−0.0303702	−	0.999539i	$-0.509669\pi$
$47$	6.64428	−	6.64428i	0.969169	−	0.969169i	0.999539	+	0.0303702i	$0.00966861\pi$
$48$		0			0
$49$	−8.76266	−	5.05912i	−1.25181	−	0.722732i
$50$	−0.428113	−	1.59774i	−0.0605443	−	0.225954i
$51$		0			0
$52$	−1.77103	−	1.97647i	−0.245597	−	0.274087i
$53$			9.94699i			1.36632i	0.730267	+	0.683162i	$0.239396\pi$
$53$			9.94699i			1.36632i	−0.730267	+	0.683162i	$0.760604\pi$
$54$		0			0
$55$	−2.62332	+	4.54372i	−0.353728	+	0.612675i
$56$	4.32506	+	7.49122i	0.577960	+	1.00106i
$57$		0			0
$58$	6.07322	+	1.62731i	0.797453	+	0.213677i
$59$	4.55554	+	1.22065i	0.593081	+	0.158916i	0.542861	−	0.839823i	$-0.317341\pi$
$59$	4.55554	+	1.22065i	0.593081	+	0.158916i	0.0502202	+	0.998738i	$0.484008\pi$
$60$		0			0
$61$	−1.36172	−	2.35857i	−0.174350	−	0.301984i	0.765586	−	0.643334i	$-0.222449\pi$
$61$	−1.36172	−	2.35857i	−0.174350	−	0.301984i	−0.939936	+	0.341350i	$0.889116\pi$
$62$	−4.62028	+	8.00256i	−0.586776	+	1.01633i
$63$		0			0
$64$		−	3.28751i		−	0.410939i
$65$	−1.97099	+	3.01914i	−0.244472	+	0.374478i
$66$		0			0
$67$	2.92991	+	10.9346i	0.357945	+	1.33587i	0.876737	+	0.480969i	$0.159715\pi$
$67$	2.92991	+	10.9346i	0.357945	+	1.33587i	−0.518792	+	0.854900i	$0.673618\pi$
$68$	2.62250	+	1.51410i	0.318025	+	0.183612i
$69$		0			0
$70$	−4.83923	+	4.83923i	−0.578399	+	0.578399i
$71$	3.72068	−	13.8858i	0.441563	−	1.64794i	−0.283291	−	0.959034i	$-0.591426\pi$
$71$	3.72068	−	13.8858i	0.441563	−	1.64794i	0.724854	−	0.688902i	$-0.241907\pi$
$72$		0			0
$73$	4.66372	+	4.66372i	0.545847	+	0.545847i	0.925237	−	0.379390i	$-0.123866\pi$
$73$	4.66372	+	4.66372i	0.545847	+	0.545847i	−0.379390	+	0.925237i	$0.623866\pi$
$74$	−13.5676	+	7.83325i	−1.57720	+	0.910597i
$75$		0			0
$76$	1.61518	−	0.432786i	0.185274	−	0.0496440i
$77$	21.7075			2.47380
$78$		0			0
$79$	2.21562			0.249277			0.124638	−	0.992202i	$-0.460223\pi$
$79$	2.21562			0.249277			0.124638	+	0.992202i	$0.460223\pi$
$80$	4.76233	−	1.27606i	0.532445	−	0.142668i
$81$		0			0
$82$	−2.81592	+	1.62577i	−0.310966	+	0.179536i
$83$	1.87062	+	1.87062i	0.205328	+	0.205328i	0.802278	−	0.596951i	$-0.203621\pi$
$83$	1.87062	+	1.87062i	0.205328	+	0.205328i	−0.596951	+	0.802278i	$0.703621\pi$
$84$		0			0
$85$	1.06482	−	3.97396i	0.115496	−	0.431036i
$86$	−14.8843	+	14.8843i	−1.60502	+	1.60502i
$87$		0			0
$88$	−9.49956	−	5.48458i	−1.01266	−	0.584658i
$89$	−1.91392	−	7.14286i	−0.202876	−	0.757142i	−0.990087	−	0.140458i	$-0.955142\pi$
$89$	−1.91392	−	7.14286i	−0.202876	−	0.757142i	0.787211	−	0.616684i	$-0.211524\pi$
$90$		0			0
$91$	14.8953	+	0.816571i	1.56145	+	0.0855999i
$92$			0.953324i			0.0993909i
$93$		0			0
$94$	−7.77133	+	13.4603i	−0.801551	+	1.38833i
$95$	−1.13590	−	1.96744i	−0.116541	−	0.201855i
$96$		0			0
$97$	−11.6120	−	3.11142i	−1.17902	−	0.315917i	−0.384481	−	0.923133i	$-0.625620\pi$
$97$	−11.6120	−	3.11142i	−1.17902	−	0.315917i	−0.794537	+	0.607216i	$0.792286\pi$
$98$	16.1663	+	4.33175i	1.63304	+	0.437573i
$99$		0			0
$100$	0.368024	+	0.637436i	0.0368024	+	0.0637436i
$101$	2.16281	−	3.74609i	0.215207	−	0.372750i	−0.738129	−	0.674659i	$-0.764291\pi$
$101$	2.16281	−	3.74609i	0.215207	−	0.372750i	0.953337	+	0.301909i	$0.0976240\pi$
$102$		0			0
$103$		−	13.3990i		−	1.32024i	−0.751161	−	0.660119i	$-0.770506\pi$
$103$		−	13.3990i		−	1.32024i	0.751161	−	0.660119i	$-0.229494\pi$
$104$	−6.31212	−	4.12076i	−0.618954	−	0.404074i
$105$		0			0
$106$	−4.25843	−	15.8927i	−0.413615	−	1.54363i
$107$	−0.251377	−	0.145132i	−0.0243015	−	0.0140305i	0.487800	−	0.872955i	$-0.337800\pi$
$107$	−0.251377	−	0.145132i	−0.0243015	−	0.0140305i	−0.512102	+	0.858925i	$0.671133\pi$
$108$		0			0
$109$	4.70875	−	4.70875i	0.451016	−	0.451016i	−0.444675	−	0.895692i	$-0.646681\pi$
$109$	4.70875	−	4.70875i	0.451016	−	0.451016i	0.895692	+	0.444675i	$0.146681\pi$
$110$	2.24615	−	8.38274i	0.214162	−	0.799263i
$111$		0			0
$112$	−14.4242	−	14.4242i	−1.36295	−	1.36295i
$113$	−11.1308	+	6.42637i	−1.04710	+	0.604542i	−0.921836	−	0.387581i	$-0.873311\pi$
$113$	−11.1308	+	6.42637i	−1.04710	+	0.604542i	−0.125263	+	0.992124i	$0.539977\pi$
$114$		0			0
$115$	1.25106	−	0.335221i	0.116662	−	0.0312595i
$116$	−2.79782			−0.259771
$117$		0			0
$118$	−7.80114			−0.718154
$119$	−16.4419	+	4.40560i	−1.50723	+	0.403861i
$120$		0			0
$121$	−14.3129	+	8.26357i	−1.30118	+	0.751234i
$122$	3.18541	+	3.18541i	0.288393	+	0.288393i
$123$		0			0
$124$	1.06424	−	3.97179i	0.0955713	−	0.356677i
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	−1.99150	−	1.14979i	−0.176717	−	0.102028i	0.409032	−	0.912520i	$-0.365866\pi$
$127$	−1.99150	−	1.14979i	−0.176717	−	0.102028i	−0.585749	+	0.810492i	$0.699200\pi$
$128$	3.46444	+	12.9295i	0.306216	+	1.14281i
$129$		0			0
$130$	1.85660	−	5.66760i	0.162835	−	0.497081i
$131$			22.6535i			1.97925i	0.143687	+	0.989623i	$0.454104\pi$
$131$			22.6535i			1.97925i	−0.143687	+	0.989623i	$0.545896\pi$
$132$		0			0
$133$	−4.69971	+	8.14013i	−0.407516	+	0.705839i
$134$	−9.36245	−	16.2162i	−0.808793	−	1.40087i
$135$		0			0
$136$	8.30837	+	2.22622i	0.712436	+	0.190897i
$137$	−6.67984	−	1.78986i	−0.570697	−	0.152918i	−0.0380809	−	0.999275i	$-0.512124\pi$
$137$	−6.67984	−	1.78986i	−0.570697	−	0.152918i	−0.532616	+	0.846357i	$0.678791\pi$
$138$		0			0
$139$	−3.22191	−	5.58051i	−0.273279	−	0.473332i	0.696421	−	0.717634i	$-0.254775\pi$
$139$	−3.22191	−	5.58051i	−0.273279	−	0.473332i	−0.969699	+	0.244301i	$0.921441\pi$
$140$	1.52267	−	2.63734i	0.128689	−	0.222896i
$141$		0			0
$142$			23.7787i			1.99546i
$143$	−16.8758	+	8.54756i	−1.41122	+	0.714783i
$144$		0			0
$145$	0.983806	+	3.67162i	0.0817007	+	0.304911i
$146$	−9.44800	−	5.45480i	−0.781922	−	0.451443i
$147$		0			0
$148$	4.92948	−	4.92948i	0.405201	−	0.405201i
$149$	4.32010	−	16.1228i	0.353916	−	1.32083i	−0.527927	−	0.849290i	$-0.677030\pi$
$149$	4.32010	−	16.1228i	0.353916	−	1.32083i	0.881843	−	0.471543i	$-0.156303\pi$
$150$		0			0
$151$	−0.942270	−	0.942270i	−0.0766808	−	0.0766808i	0.667726	−	0.744407i	$-0.267268\pi$
$151$	−0.942270	−	0.942270i	−0.0766808	−	0.0766808i	−0.744407	+	0.667726i	$0.767268\pi$
$152$	4.11334	−	2.37484i	0.333636	−	0.192625i
$153$		0			0
$154$	−34.6829	+	9.29326i	−2.79483	+	0.748873i
$155$	−5.58645			−0.448715
$156$		0			0
$157$	2.43419			0.194269			0.0971347	−	0.995271i	$-0.469032\pi$
$157$	2.43419			0.194269			0.0971347	+	0.995271i	$0.469032\pi$
$158$	−3.53998	+	0.948534i	−0.281626	+	0.0754613i
$159$		0			0
$160$	−3.44146	+	1.98693i	−0.272071	+	0.157080i
$161$	−3.78921	−	3.78921i	−0.298632	−	0.298632i
$162$		0			0
$163$	2.44589	−	9.12819i	0.191577	−	0.714975i	−0.801549	−	0.597929i	$-0.795991\pi$
$163$	2.44589	−	9.12819i	0.191577	−	0.714975i	0.993126	−	0.117047i	$-0.0373427\pi$
$164$	1.02310	−	1.02310i	0.0798907	−	0.0798907i
$165$		0			0
$166$	−3.78960	−	2.18793i	−0.294130	−	0.169816i
$167$	−2.46644	−	9.20489i	−0.190859	−	0.712296i	−0.993300	−	0.115564i	$-0.963132\pi$
$167$	−2.46644	−	9.20489i	−0.190859	−	0.712296i	0.802441	−	0.596732i	$-0.203534\pi$
$168$		0			0
$169$	−11.9014	+	5.23037i	−0.915492	+	0.402336i
$170$			6.80520i			0.521935i
$171$		0			0
$172$	4.68337	−	8.11184i	0.357104	−	0.618522i
$173$	2.34441	+	4.06063i	0.178242	+	0.308724i	0.941278	−	0.337631i	$-0.109626\pi$
$173$	2.34441	+	4.06063i	0.178242	+	0.308724i	−0.763036	+	0.646356i	$0.776292\pi$
$174$		0			0
$175$	−3.99644	−	1.07084i	−0.302103	−	0.0809481i
$176$	24.9862	+	6.69503i	1.88341	+	0.504657i
$177$		0			0
$178$	6.11590	+	10.5931i	0.458406	+	0.793983i
$179$	7.24675	−	12.5517i	0.541648	−	0.938161i	−0.457162	−	0.889383i	$-0.651134\pi$
$179$	7.24675	−	12.5517i	0.541648	−	0.938161i	0.998810	−	0.0487777i	$-0.0155326\pi$
$180$		0			0
$181$			16.0245i			1.19109i	0.803320	+	0.595547i	$0.203065\pi$
$181$			16.0245i			1.19109i	−0.803320	+	0.595547i	$0.796935\pi$
$182$	−24.1484	+	5.07221i	−1.79000	+	0.375977i
$183$		0			0
$184$	0.700847	+	2.61560i	0.0516671	+	0.192824i
$185$	−8.20240	−	4.73566i	−0.603052	−	0.348172i
$186$		0			0
$187$	15.2632	−	15.2632i	1.11615	−	1.11615i
$188$	1.79005	−	6.68056i	0.130553	−	0.487230i
$189$		0			0
$190$	2.65716	+	2.65716i	0.192771	+	0.192771i
$191$	−8.21436	+	4.74256i	−0.594370	+	0.343160i	−0.766824	−	0.641858i	$-0.778164\pi$
$191$	−8.21436	+	4.74256i	−0.594370	+	0.343160i	0.172454	+	0.985018i	$0.444831\pi$
$192$		0			0
$193$	−11.4296	+	3.06256i	−0.822723	+	0.220448i	−0.645537	−	0.763729i	$-0.723366\pi$
$193$	−11.4296	+	3.06256i	−0.822723	+	0.220448i	−0.177187	+	0.984177i	$0.556700\pi$
$194$	19.8850			1.42766
$195$		0			0
$196$	−7.44751			−0.531965
$197$	−16.5438	+	4.43290i	−1.17870	+	0.315831i	−0.794410	−	0.607382i	$-0.792220\pi$
$197$	−16.5438	+	4.43290i	−1.17870	+	0.315831i	−0.384288	+	0.923213i	$0.625553\pi$
$198$		0			0
$199$	20.4801	−	11.8242i	1.45179	−	0.838194i	0.453211	−	0.891403i	$-0.350278\pi$
$199$	20.4801	−	11.8242i	1.45179	−	0.838194i	0.998583	+	0.0532089i	$0.0169449\pi$
$200$	1.47835	+	1.47835i	0.104535	+	0.104535i
$201$		0			0
$202$	−1.85185	+	6.91119i	−0.130296	+	0.486270i
$203$	11.1206	−	11.1206i	0.780513	−	0.780513i
$204$		0			0
$205$	−1.70239	−	0.982873i	−0.118900	−	0.0686468i
$206$	5.73626	+	21.4080i	0.399664	+	1.49157i
$207$		0			0
$208$	16.8932	+	5.53392i	1.17134	+	0.383708i
$209$		−	11.9193i		−	0.824477i
$210$		0			0
$211$	−9.04720	+	15.6702i	−0.622835	+	1.07878i	0.366120	+	0.930568i	$0.380686\pi$
$211$	−9.04720	+	15.6702i	−0.622835	+	1.07878i	−0.988955	+	0.148215i	$0.952647\pi$
$212$	3.66073	+	6.34057i	0.251420	+	0.435472i
$213$		0			0
$214$	0.463767	+	0.124266i	0.0317025	+	0.00849465i
$215$	−12.2921	−	3.29366i	−0.838315	−	0.224626i
$216$		0			0
$217$	11.5568	+	20.0169i	0.784524	+	1.35883i
$218$	−5.50747	+	9.53922i	−0.373013	+	0.646078i
$219$		0			0
$220$			3.86177i			0.260361i
$221$	11.0475	−	9.89917i	0.743134	−	0.665890i
$222$		0			0
$223$	−3.14711	−	11.7452i	−0.210746	−	0.786514i	−0.987621	−	0.156859i	$-0.949863\pi$
$223$	−3.14711	−	11.7452i	−0.210746	−	0.786514i	0.776875	−	0.629655i	$-0.216804\pi$
$224$	14.2388	+	8.22075i	0.951367	+	0.549272i
$225$		0			0
$226$	15.0329	−	15.0329i	0.999974	−	0.999974i
$227$	−2.43208	+	9.07665i	−0.161423	+	0.602438i	0.837047	+	0.547132i	$0.184280\pi$
$227$	−2.43208	+	9.07665i	−0.161423	+	0.602438i	−0.998469	+	0.0553067i	$0.982386\pi$
$228$		0			0
$229$	−4.78915	−	4.78915i	−0.316476	−	0.316476i	0.530936	−	0.847412i	$-0.321840\pi$
$229$	−4.78915	−	4.78915i	−0.316476	−	0.316476i	−0.847412	+	0.530936i	$0.821840\pi$
$230$	−1.85535	+	1.07119i	−0.122338	+	0.0706321i
$231$		0			0
$232$	−7.67626	+	2.05685i	−0.503971	+	0.135039i
$233$	24.1853			1.58443			0.792217	−	0.610240i	$-0.208927\pi$
$233$	24.1853			1.58443			0.792217	+	0.610240i	$0.208927\pi$
$234$		0			0
$235$	−9.39644			−0.612956
$236$	3.35310	−	0.898460i	0.218268	−	0.0584848i
$237$		0			0
$238$	24.3838	−	14.0780i	1.58057	−	0.912541i
$239$	3.65280	+	3.65280i	0.236280	+	0.236280i	0.815308	−	0.579028i	$-0.196568\pi$
$239$	3.65280	+	3.65280i	0.236280	+	0.236280i	−0.579028	+	0.815308i	$0.696568\pi$
$240$		0			0
$241$	1.60991	−	6.00827i	0.103704	−	0.387027i	−0.894491	−	0.447085i	$-0.852462\pi$
$241$	1.60991	−	6.00827i	0.103704	−	0.387027i	0.998195	+	0.0600585i	$0.0191287\pi$
$242$	19.3306	−	19.3306i	1.24262	−	1.24262i
$243$		0			0
$244$	−1.73602	−	1.00229i	−0.111137	−	0.0641651i
$245$	2.61879	+	9.77347i	0.167309	+	0.624404i
$246$		0			0
$247$	0.448369	−	8.17883i	0.0285290	−	0.520407i
$248$		−	11.6796i		−	0.741657i
$249$		0			0
$250$	−0.827050	+	1.43249i	−0.0523072	+	0.0905988i
$251$	−5.84012	−	10.1154i	−0.368625	−	0.638477i	0.620726	−	0.784028i	$-0.286838\pi$
$251$	−5.84012	−	10.1154i	−0.368625	−	0.638477i	−0.989351	+	0.145550i	$0.953505\pi$
$252$		0			0
$253$	6.56385	+	1.75878i	0.412666	+	0.110573i
$254$	3.67414	+	0.984483i	0.230536	+	0.0617719i
$255$		0			0
$256$	−7.78303	−	13.4806i	−0.486439	−	0.842538i
$257$	−6.57188	+	11.3828i	−0.409942	+	0.710041i	−0.994883	−	0.101035i	$-0.967785\pi$
$257$	−6.57188	+	11.3828i	−0.409942	+	0.710041i	0.584940	+	0.811076i	$0.301118\pi$
$258$		0			0
$259$			39.1868i			2.43495i
$260$	−0.145268	+	2.64988i	−0.00900915	+	0.164339i
$261$		0			0
$262$	−9.69825	−	36.1944i	−0.599160	−	2.23610i
$263$	−11.4962	−	6.63734i	−0.708886	−	0.409276i	0.101762	−	0.994809i	$-0.467552\pi$
$263$	−11.4962	−	6.63734i	−0.708886	−	0.409276i	−0.810649	+	0.585533i	$0.800885\pi$
$264$		0			0
$265$	7.03358	−	7.03358i	0.432070	−	0.432070i
$266$	4.02401	−	15.0178i	0.246728	−	0.920800i
$267$		0			0
$268$	5.89181	+	5.89181i	0.359900	+	0.359900i
$269$	−2.39287	+	1.38152i	−0.145896	+	0.0842331i	−0.571171	−	0.820831i	$-0.693511\pi$
$269$	−2.39287	+	1.38152i	−0.145896	+	0.0842331i	0.425275	+	0.905064i	$0.360177\pi$
$270$		0			0
$271$	16.3643	−	4.38480i	0.994060	−	0.266358i	0.275105	−	0.961414i	$-0.411287\pi$
$271$	16.3643	−	4.38480i	0.994060	−	0.266358i	0.718955	+	0.695057i	$0.244621\pi$
$272$	−20.2841			−1.22990
$273$		0			0
$274$	11.4389			0.691049
$275$	5.06786	−	1.35793i	0.305603	−	0.0818862i
$276$		0			0
$277$	25.8030	−	14.8974i	1.55035	−	0.895097i	0.552241	−	0.833685i	$-0.313773\pi$
$277$	25.8030	−	14.8974i	1.55035	−	0.895097i	0.998113	−	0.0614120i	$-0.0195603\pi$
$278$	7.53685	+	7.53685i	0.452030	+	0.452030i
$279$		0			0
$280$	2.23882	−	8.35537i	0.133795	−	0.499329i
$281$	−2.39701	+	2.39701i	−0.142993	+	0.142993i	−0.774980	−	0.631986i	$-0.782240\pi$
$281$	−2.39701	+	2.39701i	−0.142993	+	0.142993i	0.631986	+	0.774980i	$0.282240\pi$
$282$		0			0
$283$	6.44627	+	3.72175i	0.383191	+	0.221235i	0.679206	−	0.733948i	$-0.262324\pi$
$283$	6.44627	+	3.72175i	0.383191	+	0.221235i	−0.296015	+	0.955183i	$0.595658\pi$
$284$	−2.73860	−	10.2206i	−0.162506	−	0.606480i
$285$		0			0
$286$	23.3038	−	20.8815i	1.37798	−	1.23475i
$287$			8.13311i			0.480083i
$288$		0			0
$289$	0.0369152	−	0.0639390i	0.00217148	−	0.00376112i
$290$	−3.14373	−	5.44510i	−0.184606	−	0.319747i
$291$		0			0
$292$	4.68918	+	1.25646i	0.274414	+	0.0735289i
$293$	4.57609	+	1.22616i	0.267338	+	0.0716330i	0.389998	−	0.920816i	$-0.372476\pi$
$293$	4.57609	+	1.22616i	0.267338	+	0.0716330i	−0.122660	+	0.992449i	$0.539142\pi$
$294$		0			0
$295$	−2.35812	−	4.08439i	−0.137295	−	0.237802i
$296$	9.90085	−	17.1488i	0.575475	−	0.996753i
$297$		0			0
$298$			27.6095i			1.59938i
$299$	4.43784	+	1.45376i	0.256647	+	0.0840728i
$300$		0			0
$301$	13.6273	+	50.8576i	0.785462	+	2.93138i
$302$	1.90890	+	1.10210i	0.109845	+	0.0634189i
$303$		0			0
$304$	−7.92013	+	7.92013i	−0.454250	+	0.454250i
$305$	−0.704878	+	2.63064i	−0.0403612	+	0.150630i
$306$		0			0
$307$	−20.9183	−	20.9183i	−1.19387	−	1.19387i	−0.975971	−	0.217899i	$-0.930080\pi$
$307$	−20.9183	−	20.9183i	−1.19387	−	1.19387i	−0.217899	−	0.975971i	$-0.569920\pi$
$308$	13.8372	−	7.98889i	0.788445	−	0.455209i
$309$		0			0
$310$	8.92569	−	2.39163i	0.506945	−	0.135836i
$311$	15.2872			0.866860			0.433430	−	0.901187i	$-0.357303\pi$
$311$	15.2872			0.866860			0.433430	+	0.901187i	$0.357303\pi$
$312$		0			0
$313$	−24.5240			−1.38618			−0.693089	−	0.720852i	$-0.743751\pi$
$313$	−24.5240			−1.38618			−0.693089	+	0.720852i	$0.743751\pi$
$314$	−3.88920	+	1.04211i	−0.219480	+	0.0588095i
$315$		0			0
$316$	1.41232	−	0.815401i	0.0794489	−	0.0458699i
$317$	13.3264	+	13.3264i	0.748488	+	0.748488i	0.974195	−	0.225707i	$-0.0724693\pi$
$317$	13.3264	+	13.3264i	0.748488	+	0.748488i	−0.225707	+	0.974195i	$0.572469\pi$
$318$		0			0
$319$	−5.16167	+	19.2636i	−0.288998	+	1.07856i
$320$	−2.32462	+	2.32462i	−0.129950	+	0.129950i
$321$		0			0
$322$	7.67638	+	4.43196i	0.427788	+	0.246984i
$323$	2.41906	+	9.02806i	0.134600	+	0.502334i
$324$		0			0
$325$	3.52855	−	0.741149i	0.195729	−	0.0411115i
$326$			15.6316i			0.865753i
$327$		0			0
$328$	2.05490	−	3.55918i	0.113463	−	0.196523i
$329$	19.4385	+	33.6685i	1.07168	+	1.85620i
$330$		0			0
$331$	10.2535	+	2.74741i	0.563582	+	0.151011i	0.529351	−	0.848403i	$-0.322435\pi$
$331$	10.2535	+	2.74741i	0.563582	+	0.151011i	0.0342304	+	0.999414i	$0.489102\pi$
$332$	1.88084	+	0.503969i	0.103224	+	0.0276589i
$333$		0			0
$334$	7.88146	+	13.6511i	0.431254	+	0.746954i
$335$	5.66015	−	9.80366i	0.309247	−	0.535631i
$336$		0			0
$337$			22.6276i			1.23261i	0.787509	+	0.616303i	$0.211370\pi$
$337$			22.6276i			1.23261i	−0.787509	+	0.616303i	$0.788630\pi$
$338$	16.7761	−	13.4519i	0.912501	−	0.731687i
$339$		0			0
$340$	−0.783757	−	2.92502i	−0.0425052	−	0.158632i
$341$	−25.3833	−	14.6550i	−1.37458	−	0.793615i
$342$		0			0
$343$	9.12273	−	9.12273i	0.492581	−	0.492581i
$344$	6.88607	−	25.6992i	0.371272	−	1.38561i
$345$		0			0
$346$	−5.48416	−	5.48416i	−0.294830	−	0.294830i
$347$	10.4795	−	6.05032i	0.562567	−	0.324798i	−0.191608	−	0.981471i	$-0.561370\pi$
$347$	10.4795	−	6.05032i	0.562567	−	0.324798i	0.754175	+	0.656674i	$0.228037\pi$
$348$		0			0
$349$	14.4836	−	3.88087i	0.775289	−	0.207738i	0.150582	−	0.988597i	$-0.451885\pi$
$349$	14.4836	−	3.88087i	0.775289	−	0.207738i	0.624707	+	0.780859i	$0.285218\pi$
$350$	6.84371			0.365812
$351$		0			0
$352$	−20.8493			−1.11127
$353$	1.43209	−	0.383729i	0.0762227	−	0.0204238i	−0.220506	−	0.975386i	$-0.570771\pi$
$353$	1.43209	−	0.383729i	0.0762227	−	0.0204238i	0.296729	+	0.954962i	$0.404104\pi$
$354$		0			0
$355$	−12.4496	+	7.18780i	−0.660758	+	0.381489i
$356$	−3.84875	−	3.84875i	−0.203983	−	0.203983i
$357$		0			0
$358$	−6.20485	+	23.1568i	−0.327937	+	1.22388i
$359$	−5.51307	+	5.51307i	−0.290968	+	0.290968i	−0.837463	−	0.546494i	$-0.815962\pi$
$359$	−5.51307	+	5.51307i	−0.290968	+	0.290968i	0.546494	+	0.837463i	$0.315962\pi$
$360$		0			0
$361$	−11.9848	−	6.91945i	−0.630781	−	0.364182i
$362$	−6.86031	−	25.6030i	−0.360570	−	1.34566i
$363$		0			0
$364$	9.79533	−	4.96132i	0.513415	−	0.260044i
$365$		−	6.59549i		−	0.345224i
$366$		0			0
$367$	6.92106	−	11.9876i	0.361276	−	0.625749i	−0.626895	−	0.779104i	$-0.715674\pi$
$367$	6.92106	−	11.9876i	0.361276	−	0.625749i	0.988171	+	0.153355i	$0.0490078\pi$
$368$	−3.19286	−	5.53020i	−0.166440	−	0.288282i
$369$		0			0
$370$	15.1327	+	4.05479i	0.786710	+	0.210798i
$371$	−39.7525	−	10.6517i	−2.06385	−	0.553007i
$372$		0			0
$373$	6.28298	+	10.8824i	0.325320	+	0.563472i	0.981577	−	0.191066i	$-0.0611945\pi$
$373$	6.28298	+	10.8824i	0.325320	+	0.563472i	−0.656257	+	0.754538i	$0.727861\pi$
$374$	−17.8522	+	30.9209i	−0.923115	+	1.59888i
$375$		0			0
$376$		−	19.6452i		−	1.01312i
$377$	−4.26649	+	13.0242i	−0.219735	+	0.670780i
$378$		0			0
$379$	−0.0547530	−	0.204341i	−0.00281247	−	0.0104963i	0.964505	−	0.264063i	$-0.0850628\pi$
$379$	−0.0547530	−	0.204341i	−0.00281247	−	0.0104963i	−0.967318	+	0.253567i	$0.918396\pi$
$380$	−1.44813	−	0.836079i	−0.0742875	−	0.0428899i
$381$		0			0
$382$	11.0940	−	11.0940i	0.567621	−	0.567621i
$383$	2.73178	−	10.1951i	0.139587	−	0.520948i	−0.860349	−	0.509705i	$-0.829755\pi$
$383$	2.73178	−	10.1951i	0.139587	−	0.520948i	0.999937	−	0.0112427i	$-0.00357874\pi$
$384$		0			0
$385$	−15.3495	−	15.3495i	−0.782285	−	0.782285i
$386$	16.9504	−	9.78635i	0.862755	−	0.498112i
$387$		0			0
$388$	−8.54698	+	2.29016i	−0.433907	+	0.116265i
$389$	19.6503			0.996311			0.498155	−	0.867088i	$-0.334011\pi$
$389$	19.6503			0.996311			0.498155	+	0.867088i	$0.334011\pi$
$390$		0			0
$391$	−5.32861			−0.269479
$392$	−20.4334	+	5.47512i	−1.03204	+	0.276535i
$393$		0			0
$394$	24.5349	−	14.1652i	1.23605	−	0.713634i
$395$	−1.56668	−	1.56668i	−0.0788282	−	0.0788282i
$396$		0			0
$397$	3.16997	−	11.8305i	0.159096	−	0.593756i	−0.839623	−	0.543169i	$-0.817224\pi$
$397$	3.16997	−	11.8305i	0.159096	−	0.593756i	0.998720	−	0.0505866i	$-0.0161091\pi$
$398$	−27.6597	+	27.6597i	−1.38646	+	1.38646i
$399$		0			0
$400$	−4.26979	−	2.46516i	−0.213490	−	0.123258i
$401$	6.82125	+	25.4572i	0.340637	+	1.27127i	0.897627	+	0.440755i	$0.145289\pi$
$401$	6.82125	+	25.4572i	0.340637	+	1.27127i	−0.556991	+	0.830519i	$0.688044\pi$
$402$		0			0
$403$	−16.8663	−	11.0109i	−0.840169	−	0.548490i
$404$		−	3.18386i		−	0.158403i
$405$		0			0
$406$	−13.0069	+	22.5287i	−0.645523	+	1.11808i
$407$	−24.8462	−	43.0350i	−1.23158	−	2.13316i
$408$		0			0
$409$	14.3442	+	3.84351i	0.709274	+	0.190050i	0.595381	−	0.803443i	$-0.297001\pi$
$409$	14.3442	+	3.84351i	0.709274	+	0.190050i	0.113893	+	0.993493i	$0.463668\pi$
$410$	3.14075	+	0.841560i	0.155110	+	0.0415617i
$411$		0			0
$412$	−4.93114	−	8.54098i	−0.242940	−	0.420784i
$413$	−9.75655	+	16.8988i	−0.480088	+	0.831537i
$414$		0			0
$415$		−	2.64546i		−	0.129861i
$416$	−14.3064	−	0.784289i	−0.701431	−	0.0384529i
$417$		0			0
$418$	5.10281	+	19.0440i	0.249587	+	0.931471i
$419$	−14.1443	−	8.16623i	−0.690995	−	0.398946i	0.112990	−	0.993596i	$-0.463957\pi$
$419$	−14.1443	−	8.16623i	−0.690995	−	0.398946i	−0.803985	+	0.594650i	$0.797291\pi$
$420$		0			0
$421$	−19.9020	+	19.9020i	−0.969964	+	0.969964i	−0.999562	−	0.0295975i	$-0.990577\pi$
$421$	−19.9020	+	19.9020i	−0.969964	+	0.969964i	0.0295975	+	0.999562i	$0.490577\pi$
$422$	7.74645	−	28.9101i	0.377091	−	1.40732i
$423$		0			0
$424$	14.7051	+	14.7051i	0.714145	+	0.714145i
$425$	−3.56295	+	2.05707i	−0.172829	+	0.0997826i
$426$		0			0
$427$	10.8841	−	2.91638i	0.526717	−	0.141133i
$428$	−0.213649			−0.0103271
$429$		0			0
$430$	21.0496			1.01510
$431$	11.3153	−	3.03192i	0.545037	−	0.146042i	0.0242139	−	0.999707i	$-0.492292\pi$
$431$	11.3153	−	3.03192i	0.545037	−	0.146042i	0.520823	+	0.853665i	$0.325625\pi$
$432$		0			0
$433$	−29.9523	+	17.2930i	−1.43942	+	0.831048i	−0.997809	−	0.0661593i	$-0.978925\pi$
$433$	−29.9523	+	17.2930i	−1.43942	+	0.831048i	−0.441609	+	0.897208i	$0.645592\pi$
$434$	−27.0341	−	27.0341i	−1.29768	−	1.29768i
$435$		0			0
$436$	1.26859	−	4.73446i	0.0607546	−	0.226739i
$437$	−2.08061	+	2.08061i	−0.0995291	+	0.0995291i
$438$		0			0
$439$	23.8729	+	13.7830i	1.13939	+	0.657829i	0.946280	−	0.323348i	$-0.104808\pi$
$439$	23.8729	+	13.7830i	1.13939	+	0.657829i	0.193113	+	0.981177i	$0.438142\pi$
$440$	2.83903	+	10.5954i	0.135345	+	0.505115i
$441$		0			0
$442$	−13.4130	+	20.5458i	−0.637992	+	0.977266i
$443$			5.03590i			0.239263i	0.992818	+	0.119631i	$0.0381713\pi$
$443$			5.03590i			0.239263i	−0.992818	+	0.119631i	$0.961829\pi$
$444$		0			0
$445$	−3.69742	+	6.40412i	−0.175274	+	0.303584i
$446$	10.0565	+	17.4184i	0.476189	+	0.824784i
$447$		0			0
$448$	13.1383	+	3.52041i	0.620728	+	0.166324i
$449$	22.5403	+	6.03965i	1.06374	+	0.285029i	0.747920	−	0.663789i	$-0.231053\pi$
$449$	22.5403	+	6.03965i	1.06374	+	0.285029i	0.315823	+	0.948818i	$0.397720\pi$
$450$		0			0
$451$	−5.15677	−	8.93179i	−0.242823	−	0.420582i
$452$	−4.73012	+	8.19280i	−0.222486	+	0.385357i
$453$		0			0
$454$		−	15.5433i		−	0.729484i
$455$	−9.95517	−	11.1100i	−0.466706	−	0.520844i
$456$		0			0
$457$	−4.11569	−	15.3599i	−0.192524	−	0.718508i	−0.992894	−	0.119002i	$-0.962030\pi$
$457$	−4.11569	−	15.3599i	−0.192524	−	0.718508i	0.800370	−	0.599506i	$-0.204636\pi$
$458$	9.70210	+	5.60151i	0.453350	+	0.261742i
$459$		0			0
$460$	0.674102	−	0.674102i	0.0314302	−	0.0314302i
$461$	6.80355	−	25.3912i	0.316873	−	1.18259i	−0.605360	−	0.795952i	$-0.706971\pi$
$461$	6.80355	−	25.3912i	0.316873	−	1.18259i	0.922233	−	0.386634i	$-0.126362\pi$
$462$		0			0
$463$	−14.7236	−	14.7236i	−0.684262	−	0.684262i	0.276696	−	0.960958i	$-0.410761\pi$
$463$	−14.7236	−	14.7236i	−0.684262	−	0.684262i	−0.960958	+	0.276696i	$0.910761\pi$
$464$	16.2301	−	9.37043i	0.753461	−	0.435011i
$465$		0			0
$466$	−38.6418	+	10.3540i	−1.79005	+	0.479642i
$467$	−5.89065			−0.272587			−0.136293	−	0.990669i	$-0.543519\pi$
$467$	−5.89065			−0.272587			−0.136293	+	0.990669i	$0.543519\pi$
$468$		0			0
$469$	−46.8368			−2.16272
$470$	15.0130	−	4.02273i	0.692500	−	0.185555i
$471$		0			0
$472$	8.53925	−	4.93014i	0.393051	−	0.226928i
$473$	−47.2115	−	47.2115i	−2.17079	−	2.17079i
$474$		0			0
$475$	−0.587987	+	2.19440i	−0.0269787	+	0.100686i
$476$	−8.85931	+	8.85931i	−0.406066	+	0.406066i
$477$		0			0
$478$	−7.40002	−	4.27240i	−0.338469	−	0.195415i
$479$	5.30113	+	19.7841i	0.242215	+	0.903958i	0.974763	+	0.223242i	$0.0716642\pi$
$479$	5.30113	+	19.7841i	0.242215	+	0.903958i	−0.732548	+	0.680715i	$0.761669\pi$
$480$		0			0
$481$	−15.4302	−	30.4645i	−0.703557	−	1.38906i
$482$			10.2889i			0.468645i
$483$		0			0
$484$	−6.08238	+	10.5350i	−0.276472	+	0.478864i
$485$	6.01081	+	10.4110i	0.272937	+	0.472740i
$486$		0			0
$487$	−16.2243	−	4.34729i	−0.735193	−	0.196994i	−0.128252	−	0.991742i	$-0.540937\pi$
$487$	−16.2243	−	4.34729i	−0.735193	−	0.196994i	−0.606941	+	0.794747i	$0.707603\pi$
$488$	−5.49989	−	1.47369i	−0.248968	−	0.0667109i
$489$		0			0
$490$	−8.36829	−	14.4943i	−0.378041	−	0.654786i
$491$	14.5488	−	25.1992i	0.656577	−	1.13723i	−0.324918	−	0.945742i	$-0.605337\pi$
$491$	14.5488	−	25.1992i	0.656577	−	1.13723i	0.981496	−	0.191483i	$-0.0613298\pi$
$492$		0			0
$493$		−	15.6384i		−	0.704319i
$494$	2.78508	+	13.2596i	0.125307	+	0.596577i
$495$		0			0
$496$	7.12867	+	26.6046i	0.320087	+	1.19458i
$497$	51.5094	+	29.7389i	2.31051	+	1.33397i
$498$		0			0
$499$	3.00053	−	3.00053i	0.134322	−	0.134322i	−0.636749	−	0.771071i	$-0.719721\pi$
$499$	3.00053	−	3.00053i	0.134322	−	0.134322i	0.771071	+	0.636749i	$0.219721\pi$
$500$	0.190503	−	0.710968i	0.00851956	−	0.0317954i
$501$		0			0
$502$	13.6615	+	13.6615i	0.609743	+	0.609743i
$503$	5.95857	−	3.44018i	0.265680	−	0.153390i	−0.361243	−	0.932472i	$-0.617648\pi$
$503$	5.95857	−	3.44018i	0.265680	−	0.153390i	0.626923	+	0.779082i	$0.284314\pi$
$504$		0			0
$505$	−4.17822	+	1.11955i	−0.185928	+	0.0498193i
$506$	−11.2403			−0.499691
$507$		0			0
$508$	−1.69261			−0.0750973
$509$	−8.07544	+	2.16381i	−0.357937	+	0.0959090i	−0.433306	−	0.901247i	$-0.642653\pi$
$509$	−8.07544	+	2.16381i	−0.357937	+	0.0959090i	0.0753690	+	0.997156i	$0.475987\pi$
$510$		0			0
$511$	−23.6324	+	13.6442i	−1.04544	+	0.603582i
$512$	−0.723595	−	0.723595i	−0.0319787	−	0.0319787i
$513$		0			0
$514$	5.62701	−	21.0003i	0.248197	−	0.926282i
$515$	−9.47449	+	9.47449i	−0.417496	+	0.417496i
$516$		0			0
$517$	−42.6947	−	24.6498i	−1.87771	−	1.08410i
$518$	−16.7764	−	62.6102i	−0.737111	−	2.75094i
$519$		0			0
$520$	1.54952	+	7.37716i	0.0679511	+	0.323510i
$521$			15.7170i			0.688573i	0.938865	+	0.344287i	$0.111879\pi$
$521$			15.7170i			0.688573i	−0.938865	+	0.344287i	$0.888121\pi$
$522$		0			0
$523$	−12.7516	+	22.0864i	−0.557589	+	0.965772i	0.440109	+	0.897945i	$0.354940\pi$
$523$	−12.7516	+	22.0864i	−0.557589	+	0.965772i	−0.997697	+	0.0678271i	$0.978393\pi$
$524$	8.33703	+	14.4402i	0.364205	+	0.630822i
$525$		0			0
$526$	21.2095	+	5.68306i	0.924776	+	0.247793i
$527$	22.2003	+	5.94856i	0.967061	+	0.259123i
$528$		0			0
$529$	10.6612	+	18.4658i	0.463532	+	0.802861i
$530$	−8.22666	+	14.2490i	−0.357343	+	0.618937i
$531$		0			0
$532$			6.91842i			0.299951i
$533$	−3.20250	−	6.32282i	−0.138716	−	0.273872i
$534$		0			0
$535$	0.0751260	+	0.280374i	0.00324798	+	0.0121216i
$536$	20.4966	+	11.8337i	0.885316	+	0.511138i
$537$		0			0
$538$	3.23173	−	3.23173i	0.139330	−	0.139330i
$539$	−13.7398	+	51.2778i	−0.591817	+	2.20869i
$540$		0			0
$541$	16.8129	+	16.8129i	0.722842	+	0.722842i	0.969183	−	0.246341i	$-0.0792283\pi$
$541$	16.8129	+	16.8129i	0.722842	+	0.722842i	−0.246341	+	0.969183i	$0.579228\pi$
$542$	−24.2687	+	14.0115i	−1.04243	+	0.601846i
$543$		0			0
$544$	15.7919	−	4.23143i	0.677073	−	0.181421i
$545$	−6.65918			−0.285248
$546$		0			0
$547$	14.5401			0.621690			0.310845	−	0.950461i	$-0.399388\pi$
$547$	14.5401			0.621690			0.310845	+	0.950461i	$0.399388\pi$
$548$	−4.91668	+	1.31742i	−0.210030	+	0.0562774i
$549$		0			0
$550$	−7.51576	+	4.33923i	−0.320473	+	0.185025i
$551$	−6.10618	−	6.10618i	−0.260132	−	0.260132i
$552$		0			0
$553$	−2.37258	+	8.85459i	−0.100892	+	0.376535i
$554$	−34.8487	+	34.8487i	−1.48058	+	1.48058i
$555$		0			0
$556$	−4.10752	−	2.37148i	−0.174198	−	0.100573i
$557$	8.21593	+	30.6622i	0.348120	+	1.29920i	0.888925	+	0.458053i	$0.151453\pi$
$557$	8.21593	+	30.6622i	0.348120	+	1.29920i	−0.540805	+	0.841148i	$0.681880\pi$
$558$		0			0
$559$	−30.6198	−	34.1717i	−1.29508	−	1.44531i
$560$			20.3988i			0.862008i
$561$		0			0
$562$	2.80360	−	4.85598i	0.118263	−	0.204837i
$563$	12.2594	+	21.2339i	0.516672	+	0.894903i	0.999813	+	0.0193597i	$0.00616276\pi$
$563$	12.2594	+	21.2339i	0.516672	+	0.894903i	−0.483140	+	0.875543i	$0.660504\pi$
$564$		0			0
$565$	12.4148	+	3.32654i	0.522295	+	0.139948i
$566$	−11.8928	−	3.18666i	−0.499891	−	0.133945i
$567$		0			0
$568$	−15.0276	−	26.0285i	−0.630542	−	1.09213i
$569$	−7.14531	+	12.3760i	−0.299547	+	0.518831i	−0.976032	−	0.217626i	$-0.930169\pi$
$569$	−7.14531	+	12.3760i	−0.299547	+	0.518831i	0.676485	+	0.736456i	$0.263502\pi$
$570$		0			0
$571$		−	37.3591i		−	1.56343i	−0.623636	−	0.781715i	$-0.714345\pi$
$571$		−	37.3591i		−	1.56343i	0.623636	−	0.781715i	$-0.285655\pi$
$572$	−7.61153	+	11.6592i	−0.318254	+	0.487496i
$573$		0			0
$574$	−3.48189	−	12.9946i	−0.145331	−	0.542384i
$575$	−1.12167	−	0.647596i	−0.0467769	−	0.0270066i
$576$		0			0
$577$	−9.25987	+	9.25987i	−0.385494	+	0.385494i	−0.873077	−	0.487583i	$-0.837879\pi$
$577$	−9.25987	+	9.25987i	−0.385494	+	0.385494i	0.487583	+	0.873077i	$0.337879\pi$
$578$	−0.0316077	+	0.117962i	−0.00131471	+	0.00490656i
$579$		0			0
$580$	1.97836	+	1.97836i	0.0821468	+	0.0821468i
$581$	−9.47898	+	5.47269i	−0.393254	+	0.227045i
$582$		0			0
$583$	50.4099	−	13.5073i	2.08777	−	0.559415i
$584$	13.7892			0.570602
$585$		0			0
$586$	−7.83632			−0.323716
$587$	21.1431	−	5.66527i	0.872668	−	0.233831i	0.205427	−	0.978673i	$-0.434142\pi$
$587$	21.1431	−	5.66527i	0.872668	−	0.233831i	0.667241	+	0.744842i	$0.267475\pi$
$588$		0			0
$589$	10.9910	−	6.34567i	0.452877	−	0.261469i
$590$	5.51624	+	5.51624i	0.227100	+	0.227100i
$591$		0			0
$592$	−12.0860	+	45.1055i	−0.496731	+	1.85383i
$593$	−7.96501	+	7.96501i	−0.327084	+	0.327084i	−0.851476	−	0.524393i	$-0.824292\pi$
$593$	−7.96501	+	7.96501i	−0.327084	+	0.327084i	0.524393	+	0.851476i	$0.324292\pi$
$594$		0			0
$595$	14.7414	+	8.51097i	0.604340	+	0.348916i
$596$	−3.17980	−	11.8672i	−0.130250	−	0.486098i
$597$		0			0
$598$	−7.71288	−	0.422825i	−0.315403	−	0.0172906i
$599$			2.08260i			0.0850926i	0.999094	+	0.0425463i	$0.0135470\pi$
$599$			2.08260i			0.0850926i	−0.999094	+	0.0425463i	$0.986453\pi$
$600$		0			0
$601$	14.0978	−	24.4180i	0.575060	−	0.996033i	−0.420975	−	0.907072i	$-0.638312\pi$
$601$	14.0978	−	24.4180i	0.575060	−	0.996033i	0.996035	−	0.0889605i	$-0.0283545\pi$
$602$	−43.5456	−	75.4231i	−1.77479	−	3.07402i
$603$		0			0
$604$	−0.947415	−	0.253859i	−0.0385498	−	0.0103294i
$605$	15.9640	+	4.27754i	0.649029	+	0.173907i
$606$		0			0
$607$	15.6540	+	27.1134i	0.635374	+	1.10050i	0.986436	+	0.164148i	$0.0524875\pi$
$607$	15.6540	+	27.1134i	0.635374	+	1.10050i	−0.351061	+	0.936352i	$0.614179\pi$
$608$	4.51391	−	7.81832i	0.183063	−	0.317075i
$609$		0			0
$610$		−	4.50484i		−	0.182396i
$611$	−28.3691	−	18.5203i	−1.14769	−	0.749252i
$612$		0			0
$613$	−12.0358	−	44.9183i	−0.486122	−	1.81423i	−0.574955	−	0.818185i	$-0.694981\pi$
$613$	−12.0358	−	44.9183i	−0.486122	−	1.81423i	0.0888337	−	0.996046i	$-0.471686\pi$
$614$	42.3774	+	24.4666i	1.71021	+	0.987391i
$615$		0			0
$616$	32.0913	−	32.0913i	1.29300	−	1.29300i
$617$	−8.22581	+	30.6991i	−0.331159	+	1.23590i	0.576815	+	0.816874i	$0.304295\pi$
$617$	−8.22581	+	30.6991i	−0.331159	+	1.23590i	−0.907974	+	0.419026i	$0.862371\pi$
$618$		0			0
$619$	−21.4733	−	21.4733i	−0.863085	−	0.863085i	0.128610	−	0.991695i	$-0.458948\pi$
$619$	−21.4733	−	21.4733i	−0.863085	−	0.863085i	−0.991695	+	0.128610i	$0.958948\pi$
$620$	−3.56101	+	2.05595i	−0.143014	+	0.0825689i
$621$		0			0
$622$	−24.4250	+	6.54466i	−0.979354	+	0.262417i
$623$	30.5955			1.22578
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	39.1829	−	10.4990i	1.56607	−	0.419626i
$627$		0			0
$628$	1.55164	−	0.895839i	0.0619172	−	0.0357479i
$629$	27.5534	+	27.5534i	1.09862	+	1.09862i
$630$		0			0
$631$	−1.86108	+	6.94563i	−0.0740883	+	0.276501i	−0.993025	−	0.117904i	$-0.962383\pi$
$631$	−1.86108	+	6.94563i	−0.0740883	+	0.276501i	0.918937	+	0.394405i	$0.129049\pi$
$632$	3.27546	−	3.27546i	0.130291	−	0.130291i
$633$		0			0
$634$	−26.9974	−	15.5869i	−1.07220	−	0.619037i
$635$	0.595177	+	2.22123i	0.0236189	+	0.0881469i
$636$		0			0
$637$	−11.3570	+	34.6691i	−0.449979	+	1.37364i
$638$		−	32.9880i		−	1.30601i
$639$		0			0
$640$	6.69279	−	11.5922i	0.264556	−	0.458224i
$641$	4.46307	+	7.73027i	0.176281	+	0.305327i	0.940604	−	0.339506i	$-0.110260\pi$
$641$	4.46307	+	7.73027i	0.176281	+	0.305327i	−0.764323	+	0.644834i	$0.776927\pi$
$642$		0			0
$643$	−28.6675	−	7.68142i	−1.13053	−	0.302926i	−0.355395	−	0.934716i	$-0.615654\pi$
$643$	−28.6675	−	7.68142i	−1.13053	−	0.302926i	−0.775139	+	0.631791i	$0.782320\pi$
$644$	−3.80990	−	1.02086i	−0.150131	−	0.0402275i
$645$		0			0
$646$	−7.73005	−	13.3888i	−0.304135	−	0.526777i
$647$	−9.62938	+	16.6786i	−0.378570	+	0.655703i	−0.990854	−	0.134935i	$-0.956917\pi$
$647$	−9.62938	+	16.6786i	−0.378570	+	0.655703i	0.612284	+	0.790638i	$0.290251\pi$
$648$		0			0
$649$		−	24.7444i		−	0.971303i
$650$	−5.32041	+	2.69478i	−0.208684	+	0.105698i
$651$		0			0
$652$	−1.80029	−	6.71879i	−0.0705049	−	0.263128i
$653$	−11.3645	−	6.56128i	−0.444726	−	0.256763i	0.260874	−	0.965373i	$-0.415989\pi$
$653$	−11.3645	−	6.56128i	−0.444726	−	0.256763i	−0.705600	+	0.708610i	$0.749323\pi$
$654$		0			0
$655$	16.0185	−	16.0185i	0.625893	−	0.625893i
$656$	−2.50842	+	9.36153i	−0.0979372	+	0.365506i
$657$		0			0
$658$	−45.4715	−	45.4715i	−1.77267	−	1.77267i
$659$	21.1474	−	12.2094i	0.823785	−	0.475612i	−0.0279350	−	0.999610i	$-0.508893\pi$
$659$	21.1474	−	12.2094i	0.823785	−	0.475612i	0.851720	+	0.523997i	$0.175560\pi$
$660$		0			0
$661$	−24.3078	+	6.51327i	−0.945466	+	0.253337i	−0.698437	−	0.715671i	$-0.746121\pi$
$661$	−24.3078	+	6.51327i	−0.945466	+	0.253337i	−0.247029	+	0.969008i	$0.579454\pi$
$662$	−17.5586			−0.682433
$663$		0			0
$664$	5.53087			0.214640
$665$	9.07914	−	2.43275i	0.352074	−	0.0943379i
$666$		0			0
$667$	4.26362	−	2.46160i	0.165088	−	0.0953136i
$668$	−4.95982	−	4.95982i	−0.191901	−	0.191901i
$669$		0			0
$670$	−4.84636	+	18.0869i	−0.187231	+	0.698757i
$671$	−10.1038	+	10.1038i	−0.390052	+	0.390052i
$672$		0			0
$673$	−4.54380	−	2.62336i	−0.175151	−	0.101123i	0.409862	−	0.912148i	$-0.365577\pi$
$673$	−4.54380	−	2.62336i	−0.175151	−	0.101123i	−0.585012	+	0.811024i	$0.698910\pi$
$674$	−9.68718	−	36.1531i	−0.373136	−	1.39256i
$675$		0			0
$676$	−5.66148	+	7.71402i	−0.217749	+	0.296693i
$677$			1.76098i			0.0676799i	0.999427	+	0.0338399i	$0.0107736\pi$
$677$			1.76098i			0.0676799i	−0.999427	+	0.0338399i	$0.989226\pi$
$678$		0			0
$679$	24.8692	−	43.0748i	0.954393	−	1.65306i
$680$	−4.30073	−	7.44908i	−0.164925	−	0.285659i
$681$		0			0
$682$	46.8298	+	12.5480i	1.79321	+	0.480488i
$683$	27.7031	+	7.42302i	1.06003	+	0.284034i	0.746391	−	0.665508i	$-0.231785\pi$
$683$	27.7031	+	7.42302i	1.06003	+	0.284034i	0.313639	+	0.949542i	$0.398452\pi$
$684$		0			0
$685$	3.45774	+	5.98898i	0.132113	+	0.228827i
$686$	−10.6702	+	18.4813i	−0.407389	+	0.705619i
$687$		0			0
$688$			62.7420i			2.39202i
$689$	35.0985	−	7.37220i	1.33715	−	0.280858i
$690$		0			0
$691$	8.25298	+	30.8005i	0.313958	+	1.17171i	0.924956	+	0.380075i	$0.124102\pi$
$691$	8.25298	+	30.8005i	0.313958	+	1.17171i	−0.610998	+	0.791632i	$0.709232\pi$
$692$	2.98882	+	1.72560i	0.113618	+	0.0655973i
$693$		0			0
$694$	−14.1532	+	14.1532i	−0.537248	+	0.537248i
$695$	−1.66778	+	6.22425i	−0.0632626	+	0.236099i
$696$		0			0
$697$	5.71862	+	5.71862i	0.216608	+	0.216608i
$698$	−21.4796	+	12.4012i	−0.813013	+	0.469393i
$699$		0			0
$700$	−2.94157	+	0.788192i	−0.111181	+	0.0297908i
$701$	−23.0986			−0.872421			−0.436211	−	0.899845i	$-0.643680\pi$
$701$	−23.0986			−0.872421			−0.436211	+	0.899845i	$0.643680\pi$
$702$		0			0
$703$	21.5170			0.811528
$704$	−16.6606	+	4.46420i	−0.627921	+	0.168251i
$705$		0			0
$706$	−2.12383	+	1.22620i	−0.0799315	+	0.0461485i
$707$	12.6550	+	12.6550i	0.475940	+	0.475940i
$708$		0			0
$709$	4.86877	−	18.1705i	0.182850	−	0.682407i	−0.812230	−	0.583337i	$-0.801747\pi$
$709$	4.86877	−	18.1705i	0.182850	−	0.682407i	0.995081	−	0.0990696i	$-0.0315867\pi$
$710$	16.8141	−	16.8141i	0.631021	−	0.631021i
$711$		0			0
$712$	−13.3891	−	7.73021i	−0.501778	−	0.289702i
$713$	1.87269	+	6.98899i	0.0701330	+	0.261740i
$714$		0			0
$715$	17.9770	+	5.88894i	0.672302	+	0.220234i
$716$		−	10.6679i		−	0.398678i
$717$		0			0
$718$	6.44822	−	11.1686i	0.240645	−	0.416810i
$719$	−7.71367	−	13.3605i	−0.287671	−	0.498261i	0.685582	−	0.727995i	$-0.259548\pi$
$719$	−7.71367	−	13.3605i	−0.287671	−	0.498261i	−0.973253	+	0.229734i	$0.926214\pi$
$720$		0			0
$721$	53.5481	+	14.3482i	1.99424	+	0.534354i
$722$	22.1109	+	5.92461i	0.822884	+	0.220491i
$723$		0			0
$724$	5.89741	+	10.2146i	0.219176	+	0.379623i
$725$	1.90057	−	3.29188i	0.0705853	−	0.122257i
$726$		0			0
$727$			10.4554i			0.387769i	0.981024	+	0.193885i	$0.0621088\pi$
$727$			10.4554i			0.387769i	−0.981024	+	0.193885i	$0.937891\pi$
$728$	23.2277	−	20.8133i	0.860875	−	0.771393i
$729$		0			0
$730$	2.82361	+	10.5379i	0.104507	+	0.390024i
$731$	45.3412	+	26.1777i	1.67700	+	0.968218i
$732$		0			0
$733$	−27.4480	+	27.4480i	−1.01382	+	1.01382i	−0.0139129	+	0.999903i	$0.504429\pi$
$733$	−27.4480	+	27.4480i	−1.01382	+	1.01382i	−0.999903	+	0.0139129i	$0.995571\pi$
$734$	−5.92598	+	22.1161i	−0.218732	+	0.816319i
$735$		0			0
$736$	3.63941	+	3.63941i	0.134150	+	0.134150i
$737$	51.4362	−	29.6967i	1.89468	−	1.09389i
$738$		0			0
$739$	28.6134	−	7.66694i	1.05256	−	0.282033i	0.309252	−	0.950980i	$-0.399922\pi$
$739$	28.6134	−	7.66694i	1.05256	−	0.282033i	0.743310	+	0.668947i	$0.233255\pi$
$740$	−6.97134			−0.256271
$741$		0			0
$742$	68.0743			2.49909
$743$	−25.2630	+	6.76921i	−0.926811	+	0.248338i	−0.690494	−	0.723338i	$-0.742607\pi$
$743$	−25.2630	+	6.76921i	−0.926811	+	0.248338i	−0.236317	+	0.971676i	$0.575940\pi$
$744$		0			0
$745$	−14.4553	+	8.34579i	−0.529602	+	0.305766i
$746$	−14.6975	−	14.6975i	−0.538113	−	0.538113i
$747$		0			0
$748$	4.11209	−	15.3465i	0.150353	−	0.561124i
$749$	0.849198	−	0.849198i	0.0310290	−	0.0310290i
$750$		0			0
$751$	−1.04739	−	0.604708i	−0.0382196	−	0.0220661i	0.480768	−	0.876848i	$-0.340358\pi$
$751$	−1.04739	−	0.604708i	−0.0382196	−	0.0220661i	−0.518988	+	0.854781i	$0.673691\pi$
$752$	11.9904	+	44.7490i	0.437247	+	1.63183i
$753$		0			0
$754$	1.24091	−	22.6358i	0.0451912	−	0.824346i
$755$			1.33257i			0.0484972i
$756$		0			0
$757$	−16.9100	+	29.2890i	−0.614605	+	1.06453i	0.375848	+	0.926681i	$0.377351\pi$
$757$	−16.9100	+	29.2890i	−0.614605	+	1.06453i	−0.990454	+	0.137847i	$0.955982\pi$
$758$	0.174962	+	0.303043i	0.00635490	+	0.0110070i
$759$		0			0
$760$	−4.58783	−	1.22931i	−0.166418	−	0.0445916i
$761$	−26.7925	−	7.17903i	−0.971227	−	0.260240i	−0.261881	−	0.965100i	$-0.584343\pi$
$761$	−26.7925	−	7.17903i	−0.971227	−	0.260240i	−0.709346	+	0.704860i	$0.751010\pi$
$762$		0			0
$763$	13.7759	+	23.8606i	0.498721	+	0.863810i
$764$	−3.49075	+	6.04616i	−0.126291	+	0.218742i
$765$		0			0
$766$			17.4587i			0.630808i
$767$	0.930810	−	16.9792i	0.0336096	−	0.613082i
$768$		0			0
$769$	−0.369770	−	1.38000i	−0.0133343	−	0.0497641i	0.958938	−	0.283615i	$-0.0915338\pi$
$769$	−0.369770	−	1.38000i	−0.0133343	−	0.0497641i	−0.972272	+	0.233851i	$0.924867\pi$
$770$	31.0959	+	17.9532i	1.12062	+	0.646989i
$771$		0			0
$772$	−6.15857	+	6.15857i	−0.221652	+	0.221652i
$773$	−9.03253	+	33.7099i	−0.324878	+	1.21246i	0.589557	+	0.807726i	$0.299302\pi$
$773$	−9.03253	+	33.7099i	−0.324878	+	1.21246i	−0.914435	+	0.404733i	$0.867364\pi$
$774$		0			0
$775$	3.95022	+	3.95022i	0.141896	+	0.141896i
$776$	−21.7664	+	12.5668i	−0.781367	+	0.451122i
$777$		0			0
$778$	−31.3961	+	8.41255i	−1.12560	+	0.301605i
$779$	4.46579			0.160004
$780$		0			0
$781$	−75.4235			−2.69886
$782$	8.51372	−	2.28124i	0.304450	−	0.0815771i
$783$		0			0
$784$	43.2028	−	24.9431i	1.54296	−	0.890826i
$785$	−1.72123	−	1.72123i	−0.0614334	−	0.0614334i
$786$		0			0
$787$	−12.7444	+	47.5627i	−0.454288	+	1.69543i	0.235884	+	0.971781i	$0.424201\pi$
$787$	−12.7444	+	47.5627i	−0.454288	+	1.69543i	−0.690172	+	0.723645i	$0.742465\pi$
$788$	−8.91421	+	8.91421i	−0.317556	+	0.317556i
$789$		0			0
$790$	3.17386	+	1.83243i	0.112921	+	0.0651949i
$791$	−13.7633	−	51.3652i	−0.489366	−	1.82634i
$792$		0			0
$793$	−7.31310	+	6.55296i	−0.259696	+	0.232702i
$794$			20.2591i			0.718970i
$795$		0			0
$796$	8.70316	−	15.0743i	0.308475	−	0.534295i
$797$	−24.6703	−	42.7302i	−0.873866	−	1.51358i	−0.857966	−	0.513706i	$-0.828272\pi$
$797$	−24.6703	−	42.7302i	−0.873866	−	1.51358i	−0.0158996	−	0.999874i	$-0.505061\pi$
$798$		0			0
$799$	37.3410	+	10.0055i	1.32103	+	0.353969i
$800$	3.83845	+	1.02851i	0.135710	+	0.0363633i
$801$		0			0
$802$	−21.7971	−	37.7537i	−0.769684	−	1.33313i
$803$	17.3021	−	29.9681i	0.610577	−	1.05755i
$804$		0			0
$805$			5.35876i			0.188871i
$806$	31.6618	+	10.3718i	1.11524	+	0.365332i
$807$		0			0
$808$	−2.34065	−	8.73542i	−0.0823437	−	0.307311i
$809$	−39.9550	−	23.0680i	−1.40474	−	0.811029i	−0.409869	−	0.912144i	$-0.634426\pi$
$809$	−39.9550	−	23.0680i	−1.40474	−	0.811029i	−0.994875	+	0.101115i	$0.967759\pi$
$810$		0			0
$811$	−29.6219	+	29.6219i	−1.04017	+	1.04017i	−0.0410063	+	0.999159i	$0.513056\pi$
$811$	−29.6219	+	29.6219i	−1.04017	+	1.04017i	−0.999159	+	0.0410063i	$0.986944\pi$
$812$	2.99602	−	11.1813i	0.105140	−	0.392387i
$813$		0			0
$814$	58.1216	+	58.1216i	2.03716	+	2.03716i
$815$	−8.18411	+	4.72510i	−0.286677	+	0.165513i
$816$		0			0
$817$	27.9253	−	7.48256i	0.976982	−	0.261781i
$818$	−24.5637			−0.858850
$819$		0			0
$820$	−1.44688			−0.0505273
$821$	18.2435	−	4.88833i	0.636702	−	0.170604i	0.0739928	−	0.997259i	$-0.476426\pi$
$821$	18.2435	−	4.88833i	0.636702	−	0.170604i	0.562709	+	0.826655i	$0.309759\pi$
$822$		0			0
$823$	−6.59188	+	3.80582i	−0.229779	+	0.132663i	−0.610470	−	0.792039i	$-0.709019\pi$
$823$	−6.59188	+	3.80582i	−0.229779	+	0.132663i	0.380691	+	0.924702i	$0.375686\pi$
$824$	−19.8084	−	19.8084i	−0.690057	−	0.690057i
$825$		0			0
$826$	8.35380	−	31.1768i	0.290666	−	1.08478i
$827$	34.7183	−	34.7183i	1.20727	−	1.20727i	0.235367	−	0.971907i	$-0.424371\pi$
$827$	34.7183	−	34.7183i	1.20727	−	1.20727i	0.971907	−	0.235367i	$-0.0756291\pi$
$828$		0			0
$829$	−34.7503	−	20.0631i	−1.20693	−	0.696821i	−0.244842	−	0.969563i	$-0.578736\pi$
$829$	−34.7503	−	20.0631i	−1.20693	−	0.696821i	−0.962087	+	0.272742i	$0.912069\pi$
$830$	1.13255	+	4.22675i	0.0393116	+	0.146713i
$831$		0			0
$832$	−11.6002	+	2.43653i	−0.402163	+	0.0844716i
$833$		−	41.6279i		−	1.44232i
$834$		0			0
$835$	−4.76480	+	8.25288i	−0.164893	+	0.285603i
$836$	−4.38660	−	7.59781i	−0.151714	−	0.262776i
$837$		0			0
$838$	26.0950	+	6.99213i	0.901436	+	0.241539i
$839$	−50.8437	−	13.6235i	−1.75532	−	0.470336i	−0.769570	−	0.638563i	$-0.779529\pi$
$839$	−50.8437	−	13.6235i	−1.75532	−	0.470336i	−0.985748	+	0.168227i	$0.946196\pi$
$840$		0			0
$841$	−7.27568	−	12.6019i	−0.250886	−	0.434547i
$842$	23.2779	−	40.3185i	0.802209	−	1.38947i
$843$		0			0
$844$			13.3184i			0.458437i
$845$	12.1140	+	4.71713i	0.416734	+	0.162274i
$846$		0			0
$847$	−17.6980	−	66.0498i	−0.608110	−	2.26950i
$848$	−42.4716	−	24.5210i	−1.45848	−	0.842053i
$849$		0			0
$850$	4.81201	−	4.81201i	0.165050	−	0.165050i
$851$	−3.17498	+	11.8492i	−0.108837	+	0.406185i
$852$		0			0
$853$	32.4352	+	32.4352i	1.11056	+	1.11056i	0.993074	+	0.117487i	$0.0374837\pi$
$853$	32.4352	+	32.4352i	1.11056	+	1.11056i	0.117487	+	0.993074i	$0.462516\pi$
$854$	−16.1414	+	9.31922i	−0.552346	+	0.318897i
$855$		0			0
$856$	−0.586179	+	0.157066i	−0.0200352	+	0.00536841i
$857$	23.5952			0.805995			0.402998	−	0.915201i	$-0.367968\pi$
$857$	23.5952			0.805995			0.402998	+	0.915201i	$0.367968\pi$
$858$		0			0
$859$	16.5309			0.564027			0.282013	−	0.959410i	$-0.408998\pi$
$859$	16.5309			0.564027			0.282013	+	0.959410i	$0.408998\pi$
$860$	−9.04758	+	2.42429i	−0.308520	+	0.0826677i
$861$		0			0
$862$	−16.7808	+	9.68842i	−0.571557	+	0.329989i
$863$	6.22093	+	6.22093i	0.211763	+	0.211763i	0.805016	−	0.593253i	$-0.202157\pi$
$863$	6.22093	+	6.22093i	0.211763	+	0.211763i	−0.593253	+	0.805016i	$0.702157\pi$
$864$		0			0
$865$	1.21356	−	4.52905i	0.0412621	−	0.153992i
$866$	40.4527	−	40.4527i	1.37464	−	1.37464i
$867$		0			0
$868$	14.7334	+	8.50632i	0.500084	+	0.288723i
$869$	−3.00865	−	11.2284i	−0.102062	−	0.380899i
$870$		0			0
$871$	36.4117	−	18.4425i	1.23376	−	0.624900i
$872$		−	13.9224i		−	0.471471i
$873$		0			0
$874$	2.43353	−	4.21500i	0.0823155	−	0.142575i
$875$	2.06871	+	3.58311i	0.0699352	+	0.121131i
$876$		0			0
$877$	−1.68900	−	0.452567i	−0.0570336	−	0.0152821i	0.230189	−	0.973146i	$-0.426065\pi$
$877$	−1.68900	−	0.452567i	−0.0570336	−	0.0152821i	−0.287223	+	0.957864i	$0.592732\pi$
$878$	−44.0434	−	11.8014i	−1.48639	−	0.398278i
$879$		0			0
$880$	−12.9338	−	22.4020i	−0.435999	−	0.755172i
$881$	−19.1433	+	33.1572i	−0.644955	+	1.11710i	0.339356	+	0.940658i	$0.389791\pi$
$881$	−19.1433	+	33.1572i	−0.644955	+	1.11710i	−0.984312	+	0.176438i	$0.943543\pi$
$882$		0			0
$883$		−	3.61695i		−	0.121720i	−0.998146	−	0.0608601i	$-0.980616\pi$
$883$		−	3.61695i		−	0.121720i	0.998146	−	0.0608601i	$-0.0193843\pi$
$884$	3.39893	−	10.3758i	0.114318	−	0.348977i
$885$		0			0
$886$	−2.15593	−	8.04605i	−0.0724299	−	0.270312i
$887$	−13.8194	−	7.97865i	−0.464011	−	0.267897i	0.249718	−	0.968319i	$-0.419662\pi$
$887$	−13.8194	−	7.97865i	−0.464011	−	0.267897i	−0.713729	+	0.700422i	$0.752995\pi$
$888$		0			0
$889$	6.72767	−	6.72767i	0.225639	−	0.225639i
$890$	3.16582	−	11.8150i	0.106119	−	0.396040i
$891$		0			0
$892$	−6.32858	−	6.32858i	−0.211896	−	0.211896i
$893$	18.4869	−	10.6734i	0.618642	−	0.357173i
$894$		0			0
$895$	−13.9996	+	3.75119i	−0.467957	+	0.125389i
$896$	−55.3817			−1.85017
$897$		0			0
$898$	−38.5991			−1.28807
$899$	−20.5113	+	5.49599i	−0.684091	+	0.183302i
$900$		0			0
$901$	−35.4406	+	20.4617i	−1.18070	+	0.681677i
$902$	12.0630	+	12.0630i	0.401653	+	0.401653i
$903$		0			0
$904$	−6.95480	+	25.9557i	−0.231313	+	0.863273i
$905$	11.3311	−	11.3311i	0.376657	−	0.376657i
$906$		0			0
$907$	16.8532	+	9.73022i	0.559602	+	0.323087i	0.752986	−	0.658037i	$-0.228613\pi$
$907$	16.8532	+	9.73022i	0.559602	+	0.323087i	−0.193383	+	0.981123i	$0.561946\pi$
$908$	1.79013	+	6.68085i	0.0594075	+	0.221712i
$909$		0			0
$910$	20.6621	+	13.4889i	0.684941	+	0.447153i
$911$		−	15.3382i		−	0.508176i	−0.967181	−	0.254088i	$-0.918225\pi$
$911$		−	15.3382i		−	0.508176i	0.967181	−	0.254088i	$-0.0817752\pi$
$912$		0			0
$913$	6.93988	−	12.0202i	0.229676	−	0.397811i
$914$	13.1516	+	22.7792i	0.435015	+	0.753469i
$915$		0			0
$916$	−4.81530	−	1.29026i	−0.159102	−	0.0426312i
$917$	−90.5334	−	24.2584i	−2.98968	−	0.801081i
$918$		0			0
$919$	12.1330	+	21.0150i	0.400232	+	0.693222i	0.993754	−	0.111596i	$-0.0355963\pi$
$919$	12.1330	+	21.0150i	0.400232	+	0.693222i	−0.593522	+	0.804818i	$0.702263\pi$
$920$	1.35393	−	2.34508i	0.0446378	−	0.0773150i
$921$		0			0
$922$			43.4812i			1.43198i
$923$	−51.7542	−	2.83720i	−1.70351	−	0.0933876i
$924$		0			0
$925$	2.45136	+	9.14858i	0.0806001	+	0.300804i
$926$	29.8277	+	17.2210i	0.980200	+	0.565919i
$927$		0			0
$928$	−10.6810	+	10.6810i	−0.350620	+	0.350620i
$929$	−14.4986	+	54.1094i	−0.475683	+	1.77527i	0.143098	+	0.989708i	$0.454293\pi$
$929$	−14.4986	+	54.1094i	−0.475683	+	1.77527i	−0.618781	+	0.785563i	$0.712373\pi$
$930$		0			0
$931$	−16.2540	−	16.2540i	−0.532705	−	0.532705i
$932$	15.4166	−	8.90078i	0.504987	−	0.291555i
$933$		0			0
$934$	9.41172	−	2.52186i	0.307961	−	0.0825179i
$935$	−21.5854			−0.705918
$936$		0			0
$937$	53.5441			1.74921			0.874605	−	0.484837i	$-0.161121\pi$
$937$	53.5441			1.74921			0.874605	+	0.484837i	$0.161121\pi$
$938$	74.8330	−	20.0514i	2.44338	−	0.654703i
$939$		0			0
$940$	−5.98963	+	3.45811i	−0.195360	+	0.112791i
$941$	−12.8048	−	12.8048i	−0.417426	−	0.417426i	0.466890	−	0.884316i	$-0.345375\pi$
$941$	−12.8048	−	12.8048i	−0.417426	−	0.417426i	−0.884316	+	0.466890i	$0.845375\pi$
$942$		0			0
$943$	−0.658958	+	2.45927i	−0.0214586	+	0.0800847i
$944$	−16.4421	+	16.4421i	−0.535145	+	0.535145i
$945$		0			0
$946$	95.6435	+	55.2198i	3.10964	+	1.79535i
$947$	11.2602	+	42.0237i	0.365907	+	1.36559i	0.866186	+	0.499721i	$0.166564\pi$
$947$	11.2602	+	42.0237i	0.365907	+	1.36559i	−0.500279	+	0.865864i	$0.666769\pi$
$948$		0			0
$949$	12.9997	−	19.9127i	0.421987	−	0.646393i
$950$		−	3.75779i		−	0.121919i
$951$		0			0
$952$	−17.7939	+	30.8200i	−0.576704	+	0.998881i
$953$	−7.37765	−	12.7785i	−0.238986	−	0.413935i	0.721438	−	0.692479i	$-0.243482\pi$
$953$	−7.37765	−	12.7785i	−0.238986	−	0.413935i	−0.960423	+	0.278544i	$0.910148\pi$
$954$		0			0
$955$	9.16193	+	2.45493i	0.296473	+	0.0794397i
$956$	3.67274	+	0.984108i	0.118785	+	0.0318283i
$957$		0			0
$958$	−16.9396	−	29.3403i	−0.547295	−	0.947942i
$959$	14.3061	−	24.7789i	0.461969	−	0.800153i
$960$		0			0
$961$		−	0.208469i		−	0.00672482i
$962$	37.6957	+	42.0684i	1.21536	+	1.35634i
$963$		0			0
$964$	−1.18497	−	4.42238i	−0.0381654	−	0.142435i
$965$	10.2475	+	5.91642i	0.329880	+	0.190456i
$966$		0			0
$967$	7.33868	−	7.33868i	0.235996	−	0.235996i	−0.579194	−	0.815190i	$-0.696633\pi$
$967$	7.33868	−	7.33868i	0.235996	−	0.235996i	0.815190	+	0.579194i	$0.196633\pi$
$968$	−8.94307	+	33.3760i	−0.287441	+	1.07274i
$969$		0			0
$970$	−14.0608	−	14.0608i	−0.451465	−	0.451465i
$971$	16.1557	−	9.32751i	0.518461	−	0.299334i	−0.217843	−	0.975984i	$-0.569902\pi$
$971$	16.1557	−	9.32751i	0.518461	−	0.299334i	0.736305	+	0.676650i	$0.236569\pi$
$972$		0			0
$973$	25.7523	−	6.90031i	0.825582	−	0.221214i
$974$	27.7833			0.890234
$975$		0			0
$976$	13.4275			0.429803
$977$	25.2431	−	6.76388i	0.807600	−	0.216396i	0.168682	−	0.985671i	$-0.446049\pi$
$977$	25.2431	−	6.76388i	0.807600	−	0.216396i	0.638918	+	0.769275i	$0.279382\pi$
$978$		0			0
$979$	−33.6000	+	19.3990i	−1.07386	+	0.619995i
$980$	5.26619	+	5.26619i	0.168222	+	0.168222i
$981$		0			0
$982$	−12.4570	+	46.4903i	−0.397520	+	1.48356i
$983$	−9.08894	+	9.08894i	−0.289892	+	0.289892i	−0.837038	−	0.547145i	$-0.815714\pi$
$983$	−9.08894	+	9.08894i	−0.289892	+	0.289892i	0.547145	+	0.837038i	$0.315714\pi$
$984$		0			0
$985$	14.8328	+	8.56371i	0.472612	+	0.272862i
$986$	6.69500	+	24.9861i	0.213212	+	0.795719i
$987$		0			0
$988$	−2.72420	−	5.37849i	−0.0866683	−	0.171113i
$989$			16.4823i			0.524106i
$990$		0			0
$991$	3.02952	−	5.24728i	0.0962358	−	0.166685i	−0.813888	−	0.581022i	$-0.802653\pi$
$991$	3.02952	−	5.24728i	0.0962358	−	0.166685i	0.910124	+	0.414337i	$0.135986\pi$
$992$	−11.0999	−	19.2255i	−0.352421	−	0.610411i
$993$		0			0
$994$	−95.0301	−	25.4632i	−3.01417	−	0.807645i
$995$	−22.8426	−	6.12065i	−0.724158	−	0.194038i
$996$		0			0
$997$	−12.5104	−	21.6686i	−0.396208	−	0.686252i	0.597047	−	0.802206i	$-0.296341\pi$
$997$	−12.5104	−	21.6686i	−0.396208	−	0.686252i	−0.993255	+	0.115955i	$0.963007\pi$
$998$	−3.50950	+	6.07863i	−0.111091	+	0.192416i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.cw.a.71.3	✓	40
3.2	odd	2	inner	585.2.cw.a.71.8	yes	40
13.11	odd	12	inner	585.2.cw.a.206.8	yes	40
39.11	even	12	inner	585.2.cw.a.206.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.cw.a.71.3	✓	40	1.1	even	1	trivial
585.2.cw.a.71.8	yes	40	3.2	odd	2	inner
585.2.cw.a.206.3	yes	40	39.11	even	12	inner
585.2.cw.a.206.8	yes	40	13.11	odd	12	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.cw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.59774 + 0.428113i) q^{2} +(0.637436 - 0.368024i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.07084 + 3.99644i) q^{7} +(1.47835 - 1.47835i) q^{8} +O(q^{10})\)	\(q+(-1.59774 + 0.428113i) q^{2} +(0.637436 - 0.368024i) q^{4} +(-0.707107 - 0.707107i) q^{5} +(-1.07084 + 3.99644i) q^{7} +(1.47835 - 1.47835i) q^{8} +(1.43249 + 0.827050i) q^{10} +(-1.35793 - 5.06786i) q^{11} +(-0.741149 - 3.52855i) q^{13} -6.84371i q^{14} +(-2.46516 + 4.26979i) q^{16} +(2.05707 + 3.56295i) q^{17} +(2.19440 + 0.587987i) q^{19} +(-0.710968 - 0.190503i) q^{20} +(4.33923 + 7.51576i) q^{22} +(-0.647596 + 1.12167i) q^{23} +1.00000i q^{25} +(2.69478 + 5.32041i) q^{26} +(0.788192 + 2.94157i) q^{28} +(-3.29188 - 1.90057i) q^{29} +(3.95022 - 3.95022i) q^{31} +(1.02851 - 3.83845i) q^{32} +(-4.81201 - 4.81201i) q^{34} +(3.58311 - 2.06871i) q^{35} +(9.14858 - 2.45136i) q^{37} -3.75779 q^{38} -2.09070 q^{40} +(1.89876 - 0.508772i) q^{41} +(11.0208 - 6.36286i) q^{43} +(-2.73069 - 2.73069i) q^{44} +(0.554488 - 2.06938i) q^{46} +(6.64428 - 6.64428i) q^{47} +(-8.76266 - 5.05912i) q^{49} +(-0.428113 - 1.59774i) q^{50} +(-1.77103 - 1.97647i) q^{52} +9.94699i q^{53} +(-2.62332 + 4.54372i) q^{55} +(4.32506 + 7.49122i) q^{56} +(6.07322 + 1.62731i) q^{58} +(4.55554 + 1.22065i) q^{59} +(-1.36172 - 2.35857i) q^{61} +(-4.62028 + 8.00256i) q^{62} -3.28751i q^{64} +(-1.97099 + 3.01914i) q^{65} +(2.92991 + 10.9346i) q^{67} +(2.62250 + 1.51410i) q^{68} +(-4.83923 + 4.83923i) q^{70} +(3.72068 - 13.8858i) q^{71} +(4.66372 + 4.66372i) q^{73} +(-13.5676 + 7.83325i) q^{74} +(1.61518 - 0.432786i) q^{76} +21.7075 q^{77} +2.21562 q^{79} +(4.76233 - 1.27606i) q^{80} +(-2.81592 + 1.62577i) q^{82} +(1.87062 + 1.87062i) q^{83} +(1.06482 - 3.97396i) q^{85} +(-14.8843 + 14.8843i) q^{86} +(-9.49956 - 5.48458i) q^{88} +(-1.91392 - 7.14286i) q^{89} +(14.8953 + 0.816571i) q^{91} +0.953324i q^{92} +(-7.77133 + 13.4603i) q^{94} +(-1.13590 - 1.96744i) q^{95} +(-11.6120 - 3.11142i) q^{97} +(16.1663 + 4.33175i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 24 q^{4} - 8 q^{7}+O(q^{10}) \) 40 * q - 24 * q^4 - 8 * q^7	\( 40 q - 24 q^{4} - 8 q^{7} - 4 q^{13} + 32 q^{16} + 20 q^{19} - 36 q^{22} - 4 q^{28} - 4 q^{31} - 24 q^{34} + 72 q^{37} - 48 q^{43} - 120 q^{46} + 60 q^{49} + 140 q^{52} + 8 q^{55} + 156 q^{58} - 8 q^{67} - 4 q^{73} - 16 q^{76} - 176 q^{79} - 204 q^{82} - 4 q^{85} + 72 q^{88} + 76 q^{91} - 72 q^{94} + 80 q^{97}+O(q^{100}) \) 40 * q - 24 * q^4 - 8 * q^7 - 4 * q^13 + 32 * q^16 + 20 * q^19 - 36 * q^22 - 4 * q^28 - 4 * q^31 - 24 * q^34 + 72 * q^37 - 48 * q^43 - 120 * q^46 + 60 * q^49 + 140 * q^52 + 8 * q^55 + 156 * q^58 - 8 * q^67 - 4 * q^73 - 16 * q^76 - 176 * q^79 - 204 * q^82 - 4 * q^85 + 72 * q^88 + 76 * q^91 - 72 * q^94 + 80 * q^97

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