LMFDB - Embedded newform 1890.2.l.i.1801.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1890,2,Mod(361,1890)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1890, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 4]))

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

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

chi := DirichletCharacter("1890.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1890.l (of order $3$, degree $2$, 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:	$15.0917259820$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 2 x^{14} - 4 x^{13} + 5 x^{12} + 2 x^{11} - 35 x^{10} + 81 x^{9} - 66 x^{8} + \cdots + 6561 $ x^16 - x^15 + 2x^14 - 4x^13 + 5x^12 + 2x^11 - 35x^10 + 81x^9 - 66x^8 + 243x^7 - 315x^6 + 54x^5 + 405x^4 - 972x^3 + 1458x^2 - 2187x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.8
Root			$-1.03843 - 1.38624i$ of defining polynomial
Character	$\chi$	$=$	1890.1801
Dual form			1890.2.l.i.361.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.63512 + 0.236999i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.63512 + 0.236999i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} -1.64324 q^{11} +(-2.49250 - 4.31714i) q^{13} +(-1.11231 - 2.40058i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.52620 - 6.10755i) q^{17} +(-3.51153 + 6.08215i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.821620 + 1.42309i) q^{22} -7.45235 q^{23} +1.00000 q^{25} +(-2.49250 + 4.31714i) q^{26} +(-1.52280 + 2.16358i) q^{28} +(2.86866 - 4.96867i) q^{29} +(-1.82162 + 3.15514i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.52620 + 6.10755i) q^{34} +(2.63512 + 0.236999i) q^{35} +(-2.87466 + 4.97906i) q^{37} +7.02306 q^{38} +1.00000 q^{40} +(-4.30588 - 7.45800i) q^{41} +(2.96195 - 5.13024i) q^{43} +(0.821620 - 1.42309i) q^{44} +(3.72617 + 6.45392i) q^{46} +(0.820581 + 1.42129i) q^{47} +(6.88766 + 1.24904i) q^{49} +(-0.500000 - 0.866025i) q^{50} +4.98501 q^{52} +(-6.46391 - 11.1958i) q^{53} -1.64324 q^{55} +(2.63512 + 0.236999i) q^{56} -5.73732 q^{58} +(0.391083 - 0.677376i) q^{59} +(-2.38034 - 4.12287i) q^{61} +3.64324 q^{62} +1.00000 q^{64} +(-2.49250 - 4.31714i) q^{65} +(4.97772 - 8.62167i) q^{67} +7.05240 q^{68} +(-1.11231 - 2.40058i) q^{70} +7.26549 q^{71} +(-0.392899 - 0.680521i) q^{73} +5.74933 q^{74} +(-3.51153 - 6.08215i) q^{76} +(-4.33013 - 0.389446i) q^{77} +(-2.93134 - 5.07722i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.30588 + 7.45800i) q^{82} +(-3.28544 + 5.69055i) q^{83} +(-3.52620 - 6.10755i) q^{85} -5.92389 q^{86} -1.64324 q^{88} +(-4.63848 + 8.03409i) q^{89} +(-5.54488 - 11.9669i) q^{91} +(3.72617 - 6.45392i) q^{92} +(0.820581 - 1.42129i) q^{94} +(-3.51153 + 6.08215i) q^{95} +(2.99028 - 5.17932i) q^{97} +(-2.36213 - 6.58941i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8}+O(q^{10}) $ 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8	$ 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8} - 8 q^{10} + 2 q^{11} + 2 q^{13} - 8 q^{14} - 8 q^{16} - 11 q^{17} - 2 q^{19} - 8 q^{20} - q^{22} + 22 q^{23} + 16 q^{25} + 2 q^{26} + 4 q^{28} - 17 q^{29} - 15 q^{31} - 8 q^{32} - 11 q^{34} + 4 q^{35} - 2 q^{37} + 4 q^{38} + 16 q^{40} - 7 q^{41} - 13 q^{43} - q^{44} - 11 q^{46} + 5 q^{47} + 10 q^{49} - 8 q^{50} - 4 q^{52} - 18 q^{53} + 2 q^{55} + 4 q^{56} + 34 q^{58} - q^{59} - 27 q^{61} + 30 q^{62} + 16 q^{64} + 2 q^{65} - 10 q^{67} + 22 q^{68} - 8 q^{70} + 38 q^{71} - 8 q^{73} + 4 q^{74} - 2 q^{76} + 19 q^{77} - 25 q^{79} - 8 q^{80} - 7 q^{82} - 2 q^{83} - 11 q^{85} + 26 q^{86} + 2 q^{88} + 6 q^{89} + 14 q^{91} - 11 q^{92} + 5 q^{94} - 2 q^{95} + 26 q^{97} - 14 q^{98}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8 - 8 * q^10 + 2 * q^11 + 2 * q^13 - 8 * q^14 - 8 * q^16 - 11 * q^17 - 2 * q^19 - 8 * q^20 - q^22 + 22 * q^23 + 16 * q^25 + 2 * q^26 + 4 * q^28 - 17 * q^29 - 15 * q^31 - 8 * q^32 - 11 * q^34 + 4 * q^35 - 2 * q^37 + 4 * q^38 + 16 * q^40 - 7 * q^41 - 13 * q^43 - q^44 - 11 * q^46 + 5 * q^47 + 10 * q^49 - 8 * q^50 - 4 * q^52 - 18 * q^53 + 2 * q^55 + 4 * q^56 + 34 * q^58 - q^59 - 27 * q^61 + 30 * q^62 + 16 * q^64 + 2 * q^65 - 10 * q^67 + 22 * q^68 - 8 * q^70 + 38 * q^71 - 8 * q^73 + 4 * q^74 - 2 * q^76 + 19 * q^77 - 25 * q^79 - 8 * q^80 - 7 * q^82 - 2 * q^83 - 11 * q^85 + 26 * q^86 + 2 * q^88 + 6 * q^89 + 14 * q^91 - 11 * q^92 + 5 * q^94 - 2 * q^95 + 26 * q^97 - 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times$.

$n$	$757$	$1081$	$1541$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	2.63512	+	0.236999i	0.995980	+	0.0895771i
$7$	2.63512	+	0.236999i	0.995980	+	0.0895771i
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.64324			−0.495456			−0.247728	−	0.968830i	$-0.579684\pi$
$11$	−1.64324			−0.495456			−0.247728	+	0.968830i	$0.579684\pi$
$12$		0			0
$13$	−2.49250	−	4.31714i	−0.691296	−	1.19736i	−0.971413	−	0.237395i	$-0.923707\pi$
$13$	−2.49250	−	4.31714i	−0.691296	−	1.19736i	0.280117	−	0.959966i	$-0.409627\pi$
$14$	−1.11231	−	2.40058i	−0.297278	−	0.641581i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.52620	−	6.10755i	−0.855229	−	1.48130i	−0.876433	−	0.481524i	$-0.840083\pi$
$17$	−3.52620	−	6.10755i	−0.855229	−	1.48130i	0.0212039	−	0.999775i	$-0.493250\pi$
$18$		0			0
$19$	−3.51153	+	6.08215i	−0.805601	+	1.39534i	0.110284	+	0.993900i	$0.464824\pi$
$19$	−3.51153	+	6.08215i	−0.805601	+	1.39534i	−0.915885	+	0.401441i	$0.868509\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	0.821620	+	1.42309i	0.175170	+	0.303403i
$23$	−7.45235			−1.55392			−0.776961	−	0.629549i	$-0.783240\pi$
$23$	−7.45235			−1.55392			−0.776961	+	0.629549i	$0.783240\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$	−2.49250	+	4.31714i	−0.488820	+	0.846662i
$27$		0			0
$28$	−1.52280	+	2.16358i	−0.287783	+	0.408878i
$29$	2.86866	−	4.96867i	0.532697	−	0.922658i	−0.466574	−	0.884482i	$-0.654512\pi$
$29$	2.86866	−	4.96867i	0.532697	−	0.922658i	0.999271	−	0.0381762i	$-0.0121548\pi$
$30$		0			0
$31$	−1.82162	+	3.15514i	−0.327173	+	0.566680i	−0.981950	−	0.189142i	$-0.939429\pi$
$31$	−1.82162	+	3.15514i	−0.327173	+	0.566680i	0.654777	+	0.755822i	$0.272763\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−3.52620	+	6.10755i	−0.604738	+	1.04744i
$35$	2.63512	+	0.236999i	0.445416	+	0.0400601i
$36$		0			0
$37$	−2.87466	+	4.97906i	−0.472592	+	0.818553i	−0.999508	−	0.0313643i	$-0.990015\pi$
$37$	−2.87466	+	4.97906i	−0.472592	+	0.818553i	0.526916	+	0.849917i	$0.323348\pi$
$38$	7.02306			1.13929
$39$		0			0
$40$	1.00000			0.158114
$41$	−4.30588	−	7.45800i	−0.672465	−	1.16474i	−0.977203	−	0.212307i	$-0.931902\pi$
$41$	−4.30588	−	7.45800i	−0.672465	−	1.16474i	0.304738	−	0.952436i	$-0.401431\pi$
$42$		0			0
$43$	2.96195	−	5.13024i	0.451692	−	0.782354i	−0.546799	−	0.837264i	$-0.684154\pi$
$43$	2.96195	−	5.13024i	0.451692	−	0.782354i	0.998491	+	0.0549098i	$0.0174871\pi$
$44$	0.821620	−	1.42309i	0.123864	−	0.214539i
$45$		0			0
$46$	3.72617	+	6.45392i	0.549394	+	0.951579i
$47$	0.820581	+	1.42129i	0.119694	+	0.207316i	0.919646	−	0.392747i	$-0.128475\pi$
$47$	0.820581	+	1.42129i	0.119694	+	0.207316i	−0.799952	+	0.600064i	$0.795142\pi$
$48$		0			0
$49$	6.88766	+	1.24904i	0.983952	+	0.178434i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	4.98501			0.691296
$53$	−6.46391	−	11.1958i	−0.887886	−	1.53786i	−0.842370	−	0.538900i	$-0.818840\pi$
$53$	−6.46391	−	11.1958i	−0.887886	−	1.53786i	−0.0455161	−	0.998964i	$-0.514493\pi$
$54$		0			0
$55$	−1.64324			−0.221575
$56$	2.63512	+	0.236999i	0.352132	+	0.0316703i
$57$		0			0
$58$	−5.73732			−0.753347
$59$	0.391083	−	0.677376i	0.0509147	−	0.0881869i	−0.839445	−	0.543445i	$-0.817120\pi$
$59$	0.391083	−	0.677376i	0.0509147	−	0.0881869i	0.890360	+	0.455258i	$0.150453\pi$
$60$		0			0
$61$	−2.38034	−	4.12287i	−0.304772	−	0.527880i	0.672439	−	0.740153i	$-0.265247\pi$
$61$	−2.38034	−	4.12287i	−0.304772	−	0.527880i	−0.977210	+	0.212273i	$0.931913\pi$
$62$	3.64324			0.462692
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.49250	−	4.31714i	−0.309157	−	0.535476i
$66$		0			0
$67$	4.97772	−	8.62167i	0.608126	−	1.05330i	−0.383423	−	0.923573i	$-0.625255\pi$
$67$	4.97772	−	8.62167i	0.608126	−	1.05330i	0.991549	−	0.129732i	$-0.0414117\pi$
$68$	7.05240			0.855229
$69$		0			0
$70$	−1.11231	−	2.40058i	−0.132947	−	0.286924i
$71$	7.26549			0.862255			0.431127	−	0.902291i	$-0.358116\pi$
$71$	7.26549			0.862255			0.431127	+	0.902291i	$0.358116\pi$
$72$		0			0
$73$	−0.392899	−	0.680521i	−0.0459854	−	0.0796490i	0.842117	−	0.539296i	$-0.181309\pi$
$73$	−0.392899	−	0.680521i	−0.0459854	−	0.0796490i	−0.888102	+	0.459647i	$0.847976\pi$
$74$	5.74933			0.668346
$75$		0			0
$76$	−3.51153	−	6.08215i	−0.402800	−	0.697671i
$77$	−4.33013	−	0.389446i	−0.493464	−	0.0443815i
$78$		0			0
$79$	−2.93134	−	5.07722i	−0.329801	−	0.571232i	0.652671	−	0.757641i	$-0.273648\pi$
$79$	−2.93134	−	5.07722i	−0.329801	−	0.571232i	−0.982472	+	0.186409i	$0.940315\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$		0			0
$82$	−4.30588	+	7.45800i	−0.475504	+	0.823598i
$83$	−3.28544	+	5.69055i	−0.360624	+	0.624619i	−0.988064	−	0.154046i	$-0.950770\pi$
$83$	−3.28544	+	5.69055i	−0.360624	+	0.624619i	0.627440	+	0.778665i	$0.284103\pi$
$84$		0			0
$85$	−3.52620	−	6.10755i	−0.382470	−	0.662457i
$86$	−5.92389			−0.638790
$87$		0			0
$88$	−1.64324			−0.175170
$89$	−4.63848	+	8.03409i	−0.491678	+	0.851612i	−0.999954	−	0.00958252i	$-0.996950\pi$
$89$	−4.63848	+	8.03409i	−0.491678	+	0.851612i	0.508276	+	0.861194i	$0.330283\pi$
$90$		0			0
$91$	−5.54488	−	11.9669i	−0.581261	−	1.25447i
$92$	3.72617	−	6.45392i	0.388481	−	0.672868i
$93$		0			0
$94$	0.820581	−	1.42129i	0.0846365	−	0.146595i
$95$	−3.51153	+	6.08215i	−0.360276	+	0.624016i
$96$		0			0
$97$	2.99028	−	5.17932i	0.303617	−	0.525880i	−0.673335	−	0.739337i	$-0.735139\pi$
$97$	2.99028	−	5.17932i	0.303617	−	0.525880i	0.976953	+	0.213457i	$0.0684723\pi$
$98$	−2.36213	−	6.58941i	−0.238611	−	0.665631i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	4.67998			0.465676			0.232838	−	0.972516i	$-0.425199\pi$
$101$	4.67998			0.465676			0.232838	+	0.972516i	$0.425199\pi$
$102$		0			0
$103$	5.59496			0.551287			0.275644	−	0.961260i	$-0.411109\pi$
$103$	5.59496			0.551287			0.275644	+	0.961260i	$0.411109\pi$
$104$	−2.49250	−	4.31714i	−0.244410	−	0.423331i
$105$		0			0
$106$	−6.46391	+	11.1958i	−0.627830	+	1.08743i
$107$	−3.83855	+	6.64856i	−0.371086	+	0.642740i	−0.989733	−	0.142929i	$-0.954348\pi$
$107$	−3.83855	+	6.64856i	−0.371086	+	0.642740i	0.618647	+	0.785669i	$0.287681\pi$
$108$		0			0
$109$	9.68250	+	16.7706i	0.927415	+	1.60633i	0.787630	+	0.616149i	$0.211308\pi$
$109$	9.68250	+	16.7706i	0.927415	+	1.60633i	0.139786	+	0.990182i	$0.455359\pi$
$110$	0.821620	+	1.42309i	0.0783384	+	0.135686i
$111$		0			0
$112$	−1.11231	−	2.40058i	−0.105103	−	0.226833i
$113$	0.830795	+	1.43898i	0.0781546	+	0.135368i	0.902454	−	0.430787i	$-0.141764\pi$
$113$	0.830795	+	1.43898i	0.0781546	+	0.135368i	−0.824299	+	0.566154i	$0.808431\pi$
$114$		0			0
$115$	−7.45235			−0.694935
$116$	2.86866	+	4.96867i	0.266349	+	0.461329i
$117$		0			0
$118$	−0.782167			−0.0720043
$119$	−7.84446	−	16.9298i	−0.719100	−	1.55195i
$120$		0			0
$121$	−8.29976			−0.754524
$122$	−2.38034	+	4.12287i	−0.215506	+	0.373268i
$123$		0			0
$124$	−1.82162	−	3.15514i	−0.163586	−	0.283340i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−16.4680			−1.46130			−0.730649	−	0.682754i	$-0.760782\pi$
$127$	−16.4680			−1.46130			−0.730649	+	0.682754i	$0.760782\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−2.49250	+	4.31714i	−0.218607	+	0.378639i
$131$	−13.6762			−1.19489			−0.597445	−	0.801910i	$-0.703818\pi$
$131$	−13.6762			−1.19489			−0.597445	+	0.801910i	$0.703818\pi$
$132$		0			0
$133$	−10.6948	+	15.1949i	−0.927353	+	1.31757i
$134$	−9.95545			−0.860020
$135$		0			0
$136$	−3.52620	−	6.10755i	−0.302369	−	0.523719i
$137$	−0.843533			−0.0720679			−0.0360340	−	0.999351i	$-0.511472\pi$
$137$	−0.843533			−0.0720679			−0.0360340	+	0.999351i	$0.511472\pi$
$138$		0			0
$139$	2.92189	+	5.06087i	0.247832	+	0.429257i	0.962924	−	0.269773i	$-0.0869486\pi$
$139$	2.92189	+	5.06087i	0.247832	+	0.429257i	−0.715092	+	0.699030i	$0.753615\pi$
$140$	−1.52280	+	2.16358i	−0.128700	+	0.182856i
$141$		0			0
$142$	−3.63274	−	6.29210i	−0.304853	−	0.528021i
$143$	4.09579	+	7.09411i	0.342507	+	0.593239i
$144$		0			0
$145$	2.86866	−	4.96867i	0.238229	−	0.412625i
$146$	−0.392899	+	0.680521i	−0.0325166	+	0.0563203i
$147$		0			0
$148$	−2.87466	−	4.97906i	−0.236296	−	0.409276i
$149$	13.6621			1.11924			0.559622	−	0.828748i	$-0.310947\pi$
$149$	13.6621			1.11924			0.559622	+	0.828748i	$0.310947\pi$
$150$		0			0
$151$	−0.578439			−0.0470727			−0.0235363	−	0.999723i	$-0.507493\pi$
$151$	−0.578439			−0.0470727			−0.0235363	+	0.999723i	$0.507493\pi$
$152$	−3.51153	+	6.08215i	−0.284823	+	0.493328i
$153$		0			0
$154$	1.82779	+	3.94472i	0.147288	+	0.317875i
$155$	−1.82162	+	3.15514i	−0.146316	+	0.253427i
$156$		0			0
$157$	1.64913	−	2.85638i	0.131615	−	0.227964i	−0.792684	−	0.609632i	$-0.791317\pi$
$157$	1.64913	−	2.85638i	0.131615	−	0.227964i	0.924299	+	0.381669i	$0.124650\pi$
$158$	−2.93134	+	5.07722i	−0.233205	+	0.403922i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−19.6378	−	1.76620i	−1.54768	−	0.139196i
$162$		0			0
$163$	11.5863	−	20.0681i	0.907510	−	1.57185i	0.0899989	−	0.995942i	$-0.471314\pi$
$163$	11.5863	−	20.0681i	0.907510	−	1.57185i	0.817512	−	0.575912i	$-0.195353\pi$
$164$	8.61175			0.672465
$165$		0			0
$166$	6.57089			0.510000
$167$	6.21246	+	10.7603i	0.480734	+	0.832656i	0.999756	−	0.0221051i	$-0.00703684\pi$
$167$	6.21246	+	10.7603i	0.480734	+	0.832656i	−0.519021	+	0.854761i	$0.673704\pi$
$168$		0			0
$169$	−5.92516	+	10.2627i	−0.455782	+	0.789437i
$170$	−3.52620	+	6.10755i	−0.270447	+	0.468428i
$171$		0			0
$172$	2.96195	+	5.13024i	0.225846	+	0.391177i
$173$	−6.32646	−	10.9577i	−0.480992	−	0.833102i	0.518771	−	0.854914i	$-0.326390\pi$
$173$	−6.32646	−	10.9577i	−0.480992	−	0.833102i	−0.999762	+	0.0218117i	$0.993057\pi$
$174$		0			0
$175$	2.63512	+	0.236999i	0.199196	+	0.0179154i
$176$	0.821620	+	1.42309i	0.0619320	+	0.107269i
$177$		0			0
$178$	9.27697			0.695338
$179$	−4.33144	−	7.50227i	−0.323747	−	0.560746i	0.657511	−	0.753445i	$-0.271609\pi$
$179$	−4.33144	−	7.50227i	−0.323747	−	0.560746i	−0.981258	+	0.192699i	$0.938276\pi$
$180$		0			0
$181$	−10.4358			−0.775688			−0.387844	−	0.921725i	$-0.626780\pi$
$181$	−10.4358			−0.775688			−0.387844	+	0.921725i	$0.626780\pi$
$182$	−7.59119	+	10.7855i	−0.562697	+	0.799471i
$183$		0			0
$184$	−7.45235			−0.549394
$185$	−2.87466	+	4.97906i	−0.211349	+	0.366068i
$186$		0			0
$187$	5.79439	+	10.0362i	0.423728	+	0.733918i
$188$	−1.64116			−0.119694
$189$		0			0
$190$	7.02306			0.509507
$191$	−8.96784	−	15.5328i	−0.648890	−	1.12391i	−0.983388	−	0.181515i	$-0.941900\pi$
$191$	−8.96784	−	15.5328i	−0.648890	−	1.12391i	0.334498	−	0.942396i	$-0.391433\pi$
$192$		0			0
$193$	−2.08058	+	3.60367i	−0.149763	+	0.259398i	−0.931140	−	0.364662i	$-0.881185\pi$
$193$	−2.08058	+	3.60367i	−0.149763	+	0.259398i	0.781377	+	0.624060i	$0.214518\pi$
$194$	−5.98057			−0.429380
$195$		0			0
$196$	−4.52553	+	5.34037i	−0.323252	+	0.381455i
$197$	7.80338			0.555967			0.277984	−	0.960586i	$-0.410334\pi$
$197$	7.80338			0.555967			0.277984	+	0.960586i	$0.410334\pi$
$198$		0			0
$199$	−12.2477	−	21.2136i	−0.868214	−	1.50379i	−0.863821	−	0.503800i	$-0.831935\pi$
$199$	−12.2477	−	21.2136i	−0.868214	−	1.50379i	−0.00439303	−	0.999990i	$-0.501398\pi$
$200$	1.00000			0.0707107
$201$		0			0
$202$	−2.33999	−	4.05298i	−0.164641	−	0.285167i
$203$	8.73682	−	12.4131i	0.613205	−	0.871232i
$204$		0			0
$205$	−4.30588	−	7.45800i	−0.300735	−	0.520889i
$206$	−2.79748	−	4.84537i	−0.194910	−	0.337593i
$207$		0			0
$208$	−2.49250	+	4.31714i	−0.172824	+	0.299340i
$209$	5.77029	−	9.99444i	0.399139	−	0.691330i
$210$		0			0
$211$	5.31753	+	9.21023i	0.366074	+	0.634059i	0.988948	−	0.148264i	$-0.0473684\pi$
$211$	5.31753	+	9.21023i	0.366074	+	0.634059i	−0.622874	+	0.782322i	$0.714035\pi$
$212$	12.9278			0.887886
$213$		0			0
$214$	7.67709			0.524795
$215$	2.96195	−	5.13024i	0.202003	−	0.349879i
$216$		0			0
$217$	−5.54794	+	7.88243i	−0.376619	+	0.535094i
$218$	9.68250	−	16.7706i	0.655782	−	1.13585i
$219$		0			0
$220$	0.821620	−	1.42309i	0.0553936	−	0.0959446i
$221$	−17.5781	+	30.4462i	−1.18243	+	2.04803i
$222$		0			0
$223$	12.8215	−	22.2074i	0.858589	−	1.48712i	−0.0146860	−	0.999892i	$-0.504675\pi$
$223$	12.8215	−	22.2074i	0.858589	−	1.48712i	0.873275	−	0.487228i	$-0.161992\pi$
$224$	−1.52280	+	2.16358i	−0.101747	+	0.144560i
$225$		0			0
$226$	0.830795	−	1.43898i	0.0552636	−	0.0957194i
$227$	18.9946			1.26072			0.630358	−	0.776305i	$-0.282908\pi$
$227$	18.9946			1.26072			0.630358	+	0.776305i	$0.282908\pi$
$228$		0			0
$229$	4.48895			0.296638			0.148319	−	0.988940i	$-0.452614\pi$
$229$	4.48895			0.296638			0.148319	+	0.988940i	$0.452614\pi$
$230$	3.72617	+	6.45392i	0.245697	+	0.425559i
$231$		0			0
$232$	2.86866	−	4.96867i	0.188337	−	0.326209i
$233$	−2.86866	+	4.96867i	−0.187932	+	0.325508i	−0.944561	−	0.328337i	$-0.893512\pi$
$233$	−2.86866	+	4.96867i	−0.187932	+	0.325508i	0.756628	+	0.653845i	$0.226845\pi$
$234$		0			0
$235$	0.820581	+	1.42129i	0.0535288	+	0.0927147i
$236$	0.391083	+	0.677376i	0.0254574	+	0.0440934i
$237$		0			0
$238$	−10.7394	+	15.2584i	−0.696133	+	0.989056i
$239$	13.7619	+	23.8363i	0.890183	+	1.54184i	0.839656	+	0.543119i	$0.182757\pi$
$239$	13.7619	+	23.8363i	0.890183	+	1.54184i	0.0505270	+	0.998723i	$0.483910\pi$
$240$		0			0
$241$	−20.1967			−1.30098			−0.650492	−	0.759513i	$-0.725437\pi$
$241$	−20.1967			−1.30098			−0.650492	+	0.759513i	$0.725437\pi$
$242$	4.14988	+	7.18780i	0.266764	+	0.462049i
$243$		0			0
$244$	4.76069			0.304772
$245$	6.88766	+	1.24904i	0.440037	+	0.0797981i
$246$		0			0
$247$	35.0100			2.22764
$248$	−1.82162	+	3.15514i	−0.115673	+	0.200352i
$249$		0			0
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−24.3941			−1.53974			−0.769871	−	0.638200i	$-0.779679\pi$
$251$	−24.3941			−1.53974			−0.769871	+	0.638200i	$0.779679\pi$
$252$		0			0
$253$	12.2460			0.769900
$254$	8.23399	+	14.2617i	0.516647	+	0.894858i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.71485			0.481239			0.240620	−	0.970620i	$-0.422649\pi$
$257$	7.71485			0.481239			0.240620	+	0.970620i	$0.422649\pi$
$258$		0			0
$259$	−8.75510	+	12.4391i	−0.544015	+	0.772929i
$260$	4.98501			0.309157
$261$		0			0
$262$	6.83808	+	11.8439i	0.422458	+	0.731718i
$263$	12.9732			0.799959			0.399979	−	0.916524i	$-0.369017\pi$
$263$	12.9732			0.799959			0.399979	+	0.916524i	$0.369017\pi$
$264$		0			0
$265$	−6.46391	−	11.1958i	−0.397075	−	0.687753i
$266$	18.5066	+	1.66446i	1.13471	+	0.102054i
$267$		0			0
$268$	4.97772	+	8.62167i	0.304063	+	0.526652i
$269$	−10.5195	−	18.2203i	−0.641384	−	1.11091i	−0.985124	−	0.171844i	$-0.945027\pi$
$269$	−10.5195	−	18.2203i	−0.641384	−	1.11091i	0.343741	−	0.939065i	$-0.388306\pi$
$270$		0			0
$271$	−7.04460	+	12.2016i	−0.427929	+	0.741195i	−0.996689	−	0.0813089i	$-0.974090\pi$
$271$	−7.04460	+	12.2016i	−0.427929	+	0.741195i	0.568760	+	0.822503i	$0.307423\pi$
$272$	−3.52620	+	6.10755i	−0.213807	+	0.370325i
$273$		0			0
$274$	0.421767	+	0.730521i	0.0254799	+	0.0441324i
$275$	−1.64324			−0.0990911
$276$		0			0
$277$	6.78303			0.407553			0.203776	−	0.979017i	$-0.434678\pi$
$277$	6.78303			0.407553			0.203776	+	0.979017i	$0.434678\pi$
$278$	2.92189	−	5.06087i	0.175244	−	0.303531i
$279$		0			0
$280$	2.63512	+	0.236999i	0.157478	+	0.0141634i
$281$	−5.76128	+	9.97883i	−0.343689	+	0.595287i	−0.985115	−	0.171898i	$-0.945010\pi$
$281$	−5.76128	+	9.97883i	−0.343689	+	0.595287i	0.641426	+	0.767185i	$0.278343\pi$
$282$		0			0
$283$	−2.46998	+	4.27813i	−0.146825	+	0.254308i	−0.930052	−	0.367427i	$-0.880239\pi$
$283$	−2.46998	+	4.27813i	−0.146825	+	0.254308i	0.783227	+	0.621735i	$0.213572\pi$
$284$	−3.63274	+	6.29210i	−0.215564	+	0.373367i
$285$		0			0
$286$	4.09579	−	7.09411i	0.242189	−	0.419483i
$287$	−9.57894	−	20.6732i	−0.565427	−	1.22030i
$288$		0			0
$289$	−16.3682	+	28.3505i	−0.962832	+	1.66767i
$290$	−5.73732			−0.336907
$291$		0			0
$292$	0.785798			0.0459854
$293$	−1.17274	−	2.03124i	−0.0685121	−	0.118667i	0.829734	−	0.558158i	$-0.188492\pi$
$293$	−1.17274	−	2.03124i	−0.0685121	−	0.118667i	−0.898247	+	0.439492i	$0.855159\pi$
$294$		0			0
$295$	0.391083	−	0.677376i	0.0227698	−	0.0394384i
$296$	−2.87466	+	4.97906i	−0.167086	+	0.289402i
$297$		0			0
$298$	−6.83105	−	11.8317i	−0.395712	−	0.685394i
$299$	18.5750	+	32.1729i	1.07422	+	1.86061i
$300$		0			0
$301$	9.02093	−	12.8168i	0.519958	−	0.738748i
$302$	0.289219	+	0.500943i	0.0166427	+	0.0288260i
$303$		0			0
$304$	7.02306			0.402800
$305$	−2.38034	−	4.12287i	−0.136298	−	0.236075i
$306$		0			0
$307$	4.00934			0.228825			0.114412	−	0.993433i	$-0.463501\pi$
$307$	4.00934			0.228825			0.114412	+	0.993433i	$0.463501\pi$
$308$	2.50233	−	3.55528i	0.142584	−	0.202581i
$309$		0			0
$310$	3.64324			0.206922
$311$	−8.97252	+	15.5409i	−0.508785	+	0.881242i	0.491163	+	0.871068i	$0.336572\pi$
$311$	−8.97252	+	15.5409i	−0.508785	+	0.881242i	−0.999948	+	0.0101740i	$0.996761\pi$
$312$		0			0
$313$	3.17015	+	5.49087i	0.179188	+	0.310362i	0.941603	−	0.336726i	$-0.109320\pi$
$313$	3.17015	+	5.49087i	0.179188	+	0.310362i	−0.762415	+	0.647089i	$0.775986\pi$
$314$	−3.29826			−0.186132
$315$		0			0
$316$	5.86267			0.329801
$317$	5.45724	+	9.45221i	0.306509	+	0.530889i	0.977596	−	0.210489i	$-0.0675057\pi$
$317$	5.45724	+	9.45221i	0.306509	+	0.530889i	−0.671087	+	0.741378i	$0.734172\pi$
$318$		0			0
$319$	−4.71390	+	8.16472i	−0.263928	+	0.457136i
$320$	1.00000			0.0559017
$321$		0			0
$322$	8.28933	+	17.8899i	0.461946	+	0.996967i
$323$	49.5294			2.75589
$324$		0			0
$325$	−2.49250	−	4.31714i	−0.138259	−	0.239472i
$326$	−23.1726			−1.28341
$327$		0			0
$328$	−4.30588	−	7.45800i	−0.237752	−	0.411799i
$329$	1.82548	+	3.93974i	0.100642	+	0.217205i
$330$		0			0
$331$	−13.1462	−	22.7699i	−0.722580	−	1.25154i	−0.959962	−	0.280129i	$-0.909623\pi$
$331$	−13.1462	−	22.7699i	−0.722580	−	1.25154i	0.237383	−	0.971416i	$-0.423710\pi$
$332$	−3.28544	−	5.69055i	−0.180312	−	0.312310i
$333$		0			0
$334$	6.21246	−	10.7603i	0.339930	−	0.588777i
$335$	4.97772	−	8.62167i	0.271962	−	0.471052i
$336$		0			0
$337$	−8.15482	−	14.1246i	−0.444221	−	0.769414i	0.553776	−	0.832665i	$-0.313186\pi$
$337$	−8.15482	−	14.1246i	−0.444221	−	0.769414i	−0.997998	+	0.0632518i	$0.979853\pi$
$338$	11.8503			0.644572
$339$		0			0
$340$	7.05240			0.382470
$341$	2.99336	−	5.18465i	0.162100	−	0.280765i
$342$		0			0
$343$	17.8538	+	4.92373i	0.964013	+	0.265856i
$344$	2.96195	−	5.13024i	0.159697	−	0.276604i
$345$		0			0
$346$	−6.32646	+	10.9577i	−0.340112	+	0.589092i
$347$	3.85402	−	6.67535i	0.206894	−	0.358352i	−0.743840	−	0.668357i	$-0.766998\pi$
$347$	3.85402	−	6.67535i	0.206894	−	0.358352i	0.950735	+	0.310006i	$0.100331\pi$
$348$		0			0
$349$	16.9427	−	29.3456i	0.906923	−	1.57084i	0.0886077	−	0.996067i	$-0.471758\pi$
$349$	16.9427	−	29.3456i	0.906923	−	1.57084i	0.818315	−	0.574770i	$-0.194908\pi$
$350$	−1.11231	−	2.40058i	−0.0594555	−	0.128316i
$351$		0			0
$352$	0.821620	−	1.42309i	0.0437925	−	0.0758509i
$353$	−11.9883			−0.638075			−0.319038	−	0.947742i	$-0.603360\pi$
$353$	−11.9883			−0.638075			−0.319038	+	0.947742i	$0.603360\pi$
$354$		0			0
$355$	7.26549			0.385612
$356$	−4.63848	−	8.03409i	−0.245839	−	0.425806i
$357$		0			0
$358$	−4.33144	+	7.50227i	−0.228924	+	0.396507i
$359$	6.92259	−	11.9903i	0.365360	−	0.632823i	−0.623474	−	0.781844i	$-0.714279\pi$
$359$	6.92259	−	11.9903i	0.365360	−	0.632823i	0.988834	+	0.149022i	$0.0476125\pi$
$360$		0			0
$361$	−15.1617	−	26.2608i	−0.797985	−	1.38215i
$362$	5.21791	+	9.03768i	0.274247	+	0.475010i
$363$		0			0
$364$	13.1361	+	1.18144i	0.688517	+	0.0619243i
$365$	−0.392899	−	0.680521i	−0.0205653	−	0.0356201i
$366$		0			0
$367$	−17.2848			−0.902258			−0.451129	−	0.892459i	$-0.648979\pi$
$367$	−17.2848			−0.902258			−0.451129	+	0.892459i	$0.648979\pi$
$368$	3.72617	+	6.45392i	0.194240	+	0.336434i
$369$		0			0
$370$	5.74933			0.298893
$371$	−14.3797	−	31.0342i	−0.746559	−	1.61122i
$372$		0			0
$373$	−15.5426			−0.804765			−0.402383	−	0.915472i	$-0.631818\pi$
$373$	−15.5426			−0.804765			−0.402383	+	0.915472i	$0.631818\pi$
$374$	5.79439	−	10.0362i	0.299621	−	0.518959i
$375$		0			0
$376$	0.820581	+	1.42129i	0.0423183	+	0.0732974i
$377$	−28.6006			−1.47301
$378$		0			0
$379$	21.7020			1.11476			0.557379	−	0.830259i	$-0.311807\pi$
$379$	21.7020			1.11476			0.557379	+	0.830259i	$0.311807\pi$
$380$	−3.51153	−	6.08215i	−0.180138	−	0.312008i
$381$		0			0
$382$	−8.96784	+	15.5328i	−0.458835	+	0.794725i
$383$	25.4155			1.29867			0.649334	−	0.760503i	$-0.275048\pi$
$383$	25.4155			1.29867			0.649334	+	0.760503i	$0.275048\pi$
$384$		0			0
$385$	−4.33013	−	0.389446i	−0.220684	−	0.0198480i
$386$	4.16116			0.211797
$387$		0			0
$388$	2.99028	+	5.17932i	0.151809	+	0.262940i
$389$	10.3954			0.527068			0.263534	−	0.964650i	$-0.415112\pi$
$389$	10.3954			0.527068			0.263534	+	0.964650i	$0.415112\pi$
$390$		0			0
$391$	26.2785	+	45.5156i	1.32896	+	2.30182i
$392$	6.88766	+	1.24904i	0.347880	+	0.0630859i
$393$		0			0
$394$	−3.90169	−	6.75792i	−0.196564	−	0.340459i
$395$	−2.93134	−	5.07722i	−0.147492	−	0.255463i
$396$		0			0
$397$	1.36768	−	2.36890i	0.0686421	−	0.118892i	−0.829662	−	0.558266i	$-0.811467\pi$
$397$	1.36768	−	2.36890i	0.0686421	−	0.118892i	0.898304	+	0.439375i	$0.144800\pi$
$398$	−12.2477	+	21.2136i	−0.613920	+	1.06334i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	0.0354191			0.00176874			0.000884372	−	1.00000i	$-0.499718\pi$
$401$	0.0354191			0.00176874			0.000884372		1.00000i	$0.499718\pi$
$402$		0			0
$403$	18.1616			0.904693
$404$	−2.33999	+	4.05298i	−0.116419	+	0.201644i
$405$		0			0
$406$	−15.1185	−	1.35974i	−0.750319	−	0.0674827i
$407$	4.72376	−	8.18180i	0.234148	−	0.405557i
$408$		0			0
$409$	−8.17292	+	14.1559i	−0.404125	+	0.699965i	−0.994219	−	0.107369i	$-0.965757\pi$
$409$	−8.17292	+	14.1559i	−0.404125	+	0.699965i	0.590094	+	0.807334i	$0.299091\pi$
$410$	−4.30588	+	7.45800i	−0.212652	+	0.368324i
$411$		0			0
$412$	−2.79748	+	4.84537i	−0.137822	+	0.238714i
$413$	1.19109	−	1.69228i	0.0586096	−	0.0832716i
$414$		0			0
$415$	−3.28544	+	5.69055i	−0.161276	+	0.279338i
$416$	4.98501			0.244410
$417$		0			0
$418$	−11.5406			−0.564468
$419$	4.00800	+	6.94206i	0.195804	+	0.339142i	0.947164	−	0.320751i	$-0.103935\pi$
$419$	4.00800	+	6.94206i	0.195804	+	0.339142i	−0.751360	+	0.659892i	$0.770602\pi$
$420$		0			0
$421$	16.7469	−	29.0066i	0.816196	−	1.41369i	−0.0922696	−	0.995734i	$-0.529412\pi$
$421$	16.7469	−	29.0066i	0.816196	−	1.41369i	0.908466	−	0.417959i	$-0.137255\pi$
$422$	5.31753	−	9.21023i	0.258853	−	0.448347i
$423$		0			0
$424$	−6.46391	−	11.1958i	−0.313915	−	0.543717i
$425$	−3.52620	−	6.10755i	−0.171046	−	0.296260i
$426$		0			0
$427$	−5.29536	−	11.4284i	−0.256260	−	0.553058i
$428$	−3.83855	−	6.64856i	−0.185543	−	0.321370i
$429$		0			0
$430$	−5.92389			−0.285675
$431$	12.2779	+	21.2660i	0.591406	+	1.02434i	0.994043	+	0.108985i	$0.0347602\pi$
$431$	12.2779	+	21.2660i	0.591406	+	1.02434i	−0.402638	+	0.915360i	$0.631906\pi$
$432$		0			0
$433$	25.8917			1.24428			0.622138	−	0.782907i	$-0.286264\pi$
$433$	25.8917			1.24428			0.622138	+	0.782907i	$0.286264\pi$
$434$	9.60036	+	0.863443i	0.460832	+	0.0414466i
$435$		0			0
$436$	−19.3650			−0.927415
$437$	26.1692	−	45.3263i	1.25184	−	2.16825i
$438$		0			0
$439$	6.01813	+	10.4237i	0.287230	+	0.497497i	0.973147	−	0.230182i	$-0.0739323\pi$
$439$	6.01813	+	10.4237i	0.287230	+	0.497497i	−0.685918	+	0.727679i	$0.740599\pi$
$440$	−1.64324			−0.0783384
$441$		0			0
$442$	35.1563			1.67221
$443$	1.00770	+	1.74539i	0.0478773	+	0.0829259i	0.888971	−	0.457964i	$-0.151421\pi$
$443$	1.00770	+	1.74539i	0.0478773	+	0.0829259i	−0.841094	+	0.540890i	$0.818088\pi$
$444$		0			0
$445$	−4.63848	+	8.03409i	−0.219885	+	0.380852i
$446$	−25.6429			−1.21423
$447$		0			0
$448$	2.63512	+	0.236999i	0.124497	+	0.0111971i
$449$	0.742369			0.0350346			0.0175173	−	0.999847i	$-0.494424\pi$
$449$	0.742369			0.0350346			0.0175173	+	0.999847i	$0.494424\pi$
$450$		0			0
$451$	7.07559	+	12.2553i	0.333177	+	0.577079i
$452$	−1.66159			−0.0781546
$453$		0			0
$454$	−9.49730	−	16.4498i	−0.445730	−	0.772027i
$455$	−5.54488	−	11.9669i	−0.259948	−	0.561017i
$456$		0			0
$457$	5.61374	+	9.72328i	0.262600	+	0.454836i	0.966932	−	0.255035i	$-0.0820869\pi$
$457$	5.61374	+	9.72328i	0.262600	+	0.454836i	−0.704332	+	0.709870i	$0.748754\pi$
$458$	−2.24447	−	3.88754i	−0.104877	−	0.181653i
$459$		0			0
$460$	3.72617	−	6.45392i	0.173734	−	0.300916i
$461$	−9.12633	+	15.8073i	−0.425056	+	0.736218i	−0.996426	−	0.0844747i	$-0.973079\pi$
$461$	−9.12633	+	15.8073i	−0.425056	+	0.736218i	0.571370	+	0.820693i	$0.306412\pi$
$462$		0			0
$463$	14.5347	+	25.1748i	0.675484	+	1.16997i	0.976327	+	0.216299i	$0.0693985\pi$
$463$	14.5347	+	25.1748i	0.675484	+	1.16997i	−0.300843	+	0.953674i	$0.597268\pi$
$464$	−5.73732			−0.266349
$465$		0			0
$466$	5.73732			0.265776
$467$	3.65873	−	6.33711i	0.169306	−	0.293246i	−0.768870	−	0.639405i	$-0.779181\pi$
$467$	3.65873	−	6.33711i	0.169306	−	0.293246i	0.938176	+	0.346159i	$0.112514\pi$
$468$		0			0
$469$	15.1602	−	21.5394i	0.700033	−	0.994596i
$470$	0.820581	−	1.42129i	0.0378506	−	0.0655592i
$471$		0			0
$472$	0.391083	−	0.677376i	0.0180011	−	0.0311788i
$473$	−4.86719	+	8.43022i	−0.223794	+	0.387622i
$474$		0			0
$475$	−3.51153	+	6.08215i	−0.161120	+	0.279068i
$476$	18.5839	+	1.67141i	0.851791	+	0.0766089i
$477$		0			0
$478$	13.7619	−	23.8363i	0.629454	−	1.09025i
$479$	−6.17671			−0.282221			−0.141110	−	0.989994i	$-0.545067\pi$
$479$	−6.17671			−0.282221			−0.141110	+	0.989994i	$0.545067\pi$
$480$		0			0
$481$	28.6604			1.30680
$482$	10.0984	+	17.4909i	0.459967	+	0.796687i
$483$		0			0
$484$	4.14988	−	7.18780i	0.188631	−	0.326718i
$485$	2.99028	−	5.17932i	0.135782	−	0.235181i
$486$		0			0
$487$	3.11014	+	5.38693i	0.140934	+	0.244105i	0.927849	−	0.372957i	$-0.121656\pi$
$487$	3.11014	+	5.38693i	0.140934	+	0.244105i	−0.786915	+	0.617062i	$0.788323\pi$
$488$	−2.38034	−	4.12287i	−0.107753	−	0.186634i
$489$		0			0
$490$	−2.36213	−	6.58941i	−0.106710	−	0.297679i
$491$	3.94447	+	6.83202i	0.178011	+	0.308325i	0.941199	−	0.337852i	$-0.109700\pi$
$491$	3.94447	+	6.83202i	0.178011	+	0.308325i	−0.763188	+	0.646177i	$0.776367\pi$
$492$		0			0
$493$	−40.4619			−1.82231
$494$	−17.5050	−	30.3196i	−0.787588	−	1.36414i
$495$		0			0
$496$	3.64324			0.163586
$497$	19.1454	+	1.72191i	0.858789	+	0.0772383i
$498$		0			0
$499$	8.68946			0.388994			0.194497	−	0.980903i	$-0.437693\pi$
$499$	8.68946			0.388994			0.194497	+	0.980903i	$0.437693\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$		0			0
$502$	12.1970	+	21.1259i	0.544381	+	0.942895i
$503$	−23.0236			−1.02657			−0.513285	−	0.858218i	$-0.671572\pi$
$503$	−23.0236			−1.02657			−0.513285	+	0.858218i	$0.671572\pi$
$504$		0			0
$505$	4.67998			0.208257
$506$	−6.12300	−	10.6054i	−0.272201	−	0.471465i
$507$		0			0
$508$	8.23399	−	14.2617i	0.365324	−	0.632760i
$509$	−16.5940			−0.735514			−0.367757	−	0.929922i	$-0.619874\pi$
$509$	−16.5940			−0.735514			−0.367757	+	0.929922i	$0.619874\pi$
$510$		0			0
$511$	−0.874052	−	1.88637i	−0.0386658	−	0.0834480i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.85742	−	6.68125i	−0.170144	−	0.294698i
$515$	5.59496			0.246543
$516$		0			0
$517$	−1.34841	−	2.33552i	−0.0593031	−	0.102716i
$518$	15.1501	+	1.36258i	0.665659	+	0.0598685i
$519$		0			0
$520$	−2.49250	−	4.31714i	−0.109304	−	0.189319i
$521$	0.696803	+	1.20690i	0.0305275	+	0.0528751i	0.880886	−	0.473329i	$-0.156948\pi$
$521$	0.696803	+	1.20690i	0.0305275	+	0.0528751i	−0.850358	+	0.526205i	$0.823615\pi$
$522$		0			0
$523$	−7.36346	+	12.7539i	−0.321982	+	0.557689i	−0.980897	−	0.194529i	$-0.937682\pi$
$523$	−7.36346	+	12.7539i	−0.321982	+	0.557689i	0.658915	+	0.752217i	$0.271016\pi$
$524$	6.83808	−	11.8439i	0.298723	−	0.517403i
$525$		0			0
$526$	−6.48658	−	11.2351i	−0.282828	−	0.489873i
$527$	25.6936			1.11923
$528$		0			0
$529$	32.5375			1.41467
$530$	−6.46391	+	11.1958i	−0.280774	+	0.486315i
$531$		0			0
$532$	−7.81183	−	16.8594i	−0.338686	−	0.730948i
$533$	−21.4648	+	37.1782i	−0.929745	+	1.61037i
$534$		0			0
$535$	−3.83855	+	6.64856i	−0.165955	+	0.287442i
$536$	4.97772	−	8.62167i	0.215005	−	0.372399i
$537$		0			0
$538$	−10.5195	+	18.2203i	−0.453527	+	0.785531i
$539$	−11.3181	−	2.05247i	−0.487505	−	0.0884061i
$540$		0			0
$541$	12.5237	−	21.6917i	0.538437	−	0.932601i	−0.460551	−	0.887633i	$-0.652348\pi$
$541$	12.5237	−	21.6917i	0.538437	−	0.932601i	0.998988	−	0.0449675i	$-0.0143184\pi$
$542$	14.0892			0.605183
$543$		0			0
$544$	7.05240			0.302369
$545$	9.68250	+	16.7706i	0.414753	+	0.718373i
$546$		0			0
$547$	5.32171	−	9.21747i	0.227540	−	0.394110i	−0.729539	−	0.683940i	$-0.760265\pi$
$547$	5.32171	−	9.21747i	0.227540	−	0.394110i	0.957078	+	0.289829i	$0.0935985\pi$
$548$	0.421767	−	0.730521i	0.0180170	−	0.0312063i
$549$		0			0
$550$	0.821620	+	1.42309i	0.0350340	+	0.0606807i
$551$	20.1468	+	34.8953i	0.858282	+	1.48659i
$552$		0			0
$553$	−6.52111	−	14.0738i	−0.277306	−	0.598478i
$554$	−3.39152	−	5.87428i	−0.144092	−	0.249574i
$555$		0			0
$556$	−5.84379			−0.247832
$557$	21.3732	+	37.0195i	0.905613	+	1.56857i	0.820092	+	0.572232i	$0.193922\pi$
$557$	21.3732	+	37.0195i	0.905613	+	1.56857i	0.0855219	+	0.996336i	$0.472744\pi$
$558$		0			0
$559$	−29.5306			−1.24901
$560$	−1.11231	−	2.40058i	−0.0470037	−	0.101443i
$561$		0			0
$562$	11.5226			0.486050
$563$	−6.57437	+	11.3872i	−0.277077	+	0.479911i	−0.970657	−	0.240468i	$-0.922699\pi$
$563$	−6.57437	+	11.3872i	−0.277077	+	0.479911i	0.693580	+	0.720379i	$0.256032\pi$
$564$		0			0
$565$	0.830795	+	1.43898i	0.0349518	+	0.0605383i
$566$	4.93996			0.207642
$567$		0			0
$568$	7.26549			0.304853
$569$	−1.17495	−	2.03507i	−0.0492563	−	0.0853144i	0.840346	−	0.542050i	$-0.182352\pi$
$569$	−1.17495	−	2.03507i	−0.0492563	−	0.0853144i	−0.889602	+	0.456736i	$0.849018\pi$
$570$		0			0
$571$	7.30646	−	12.6552i	0.305766	−	0.529602i	−0.671666	−	0.740854i	$-0.734421\pi$
$571$	7.30646	−	12.6552i	0.305766	−	0.529602i	0.977432	+	0.211252i	$0.0677541\pi$
$572$	−8.19157			−0.342507
$573$		0			0
$574$	−13.1140	+	18.6322i	−0.547368	+	0.777693i
$575$	−7.45235			−0.310784
$576$		0			0
$577$	4.53371	+	7.85261i	0.188741	+	0.326909i	0.944831	−	0.327559i	$-0.106226\pi$
$577$	4.53371	+	7.85261i	0.188741	+	0.326909i	−0.756090	+	0.654468i	$0.772893\pi$
$578$	32.7363			1.36165
$579$		0			0
$580$	2.86866	+	4.96867i	0.119115	+	0.206313i
$581$	−10.0062	+	14.2166i	−0.415126	+	0.589805i
$582$		0			0
$583$	10.6218	+	18.3974i	0.439908	+	0.761943i
$584$	−0.392899	−	0.680521i	−0.0162583	−	0.0281602i
$585$		0			0
$586$	−1.17274	+	2.03124i	−0.0484454	+	0.0839099i
$587$	19.8453	−	34.3730i	0.819103	−	1.41873i	−0.0872417	−	0.996187i	$-0.527805\pi$
$587$	19.8453	−	34.3730i	0.819103	−	1.41873i	0.906344	−	0.422540i	$-0.138861\pi$
$588$		0			0
$589$	−12.7934	−	22.1587i	−0.527141	−	0.913035i
$590$	−0.782167			−0.0322013
$591$		0			0
$592$	5.74933			0.236296
$593$	−17.8017	+	30.8334i	−0.731028	+	1.26618i	0.225416	+	0.974263i	$0.427626\pi$
$593$	−17.8017	+	30.8334i	−0.731028	+	1.26618i	−0.956444	+	0.291915i	$0.905708\pi$
$594$		0			0
$595$	−7.84446	−	16.9298i	−0.321591	−	0.694055i
$596$	−6.83105	+	11.8317i	−0.279811	+	0.484646i
$597$		0			0
$598$	18.5750	−	32.1729i	0.759589	−	1.31565i
$599$	1.11211	−	1.92624i	0.0454398	−	0.0787040i	−0.842411	−	0.538836i	$-0.818864\pi$
$599$	1.11211	−	1.92624i	0.0454398	−	0.0787040i	0.887851	+	0.460132i	$0.152198\pi$
$600$		0			0
$601$	2.28720	−	3.96154i	0.0932967	−	0.161595i	−0.815600	−	0.578616i	$-0.803593\pi$
$601$	2.28720	−	3.96154i	0.0932967	−	0.161595i	0.908896	+	0.417022i	$0.136926\pi$
$602$	−15.6101	−	1.40395i	−0.636222	−	0.0572209i
$603$		0			0
$604$	0.289219	−	0.500943i	0.0117682	−	0.0203831i
$605$	−8.29976			−0.337433
$606$		0			0
$607$	30.2757			1.22885			0.614427	−	0.788974i	$-0.289387\pi$
$607$	30.2757			1.22885			0.614427	+	0.788974i	$0.289387\pi$
$608$	−3.51153	−	6.08215i	−0.142411	−	0.246664i
$609$		0			0
$610$	−2.38034	+	4.12287i	−0.0963773	+	0.166930i
$611$	4.09061	−	7.08514i	0.165488	−	0.286634i
$612$		0			0
$613$	−2.43790	−	4.22257i	−0.0984660	−	0.170548i	0.812584	−	0.582844i	$-0.198060\pi$
$613$	−2.43790	−	4.22257i	−0.0984660	−	0.170548i	−0.911050	+	0.412296i	$0.864727\pi$
$614$	−2.00467	−	3.47219i	−0.0809018	−	0.140126i
$615$		0			0
$616$	−4.33013	−	0.389446i	−0.174466	−	0.0156912i
$617$	−12.4725	−	21.6030i	−0.502125	−	0.869705i	−0.999997	−	0.00245498i	$-0.999219\pi$
$617$	−12.4725	−	21.6030i	−0.502125	−	0.869705i	0.497872	−	0.867250i	$-0.334115\pi$
$618$		0			0
$619$	37.0943			1.49094			0.745472	−	0.666537i	$-0.232224\pi$
$619$	37.0943			1.49094			0.745472	+	0.666537i	$0.232224\pi$
$620$	−1.82162	−	3.15514i	−0.0731580	−	0.126713i
$621$		0			0
$622$	17.9450			0.719531
$623$	−14.1270	+	20.0714i	−0.565987	+	0.804145i
$624$		0			0
$625$	1.00000			0.0400000
$626$	3.17015	−	5.49087i	0.126705	−	0.219459i
$627$		0			0
$628$	1.64913	+	2.85638i	0.0658075	+	0.113982i
$629$	40.5465			1.61670
$630$		0			0
$631$	−21.4560			−0.854152			−0.427076	−	0.904216i	$-0.640456\pi$
$631$	−21.4560			−0.854152			−0.427076	+	0.904216i	$0.640456\pi$
$632$	−2.93134	−	5.07722i	−0.116602	−	0.201961i
$633$		0			0
$634$	5.45724	−	9.45221i	0.216735	−	0.375395i
$635$	−16.4680			−0.653512
$636$		0			0
$637$	−11.7753	−	32.8483i	−0.466553	−	1.30150i
$638$	9.42780			0.373250
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	42.7642			1.68908			0.844542	−	0.535490i	$-0.179873\pi$
$641$	42.7642			1.68908			0.844542	+	0.535490i	$0.179873\pi$
$642$		0			0
$643$	−9.01808	−	15.6198i	−0.355638	−	0.615983i	0.631589	−	0.775304i	$-0.282403\pi$
$643$	−9.01808	−	15.6198i	−0.355638	−	0.615983i	−0.987227	+	0.159320i	$0.949070\pi$
$644$	11.3485	−	16.1237i	0.447192	−	0.635364i
$645$		0			0
$646$	−24.7647	−	42.8937i	−0.974355	−	1.68763i
$647$	−13.8584	−	24.0035i	−0.544831	−	0.943676i	−0.998618	−	0.0525650i	$-0.983260\pi$
$647$	−13.8584	−	24.0035i	−0.544831	−	0.943676i	0.453786	−	0.891111i	$-0.350073\pi$
$648$		0			0
$649$	−0.642644	+	1.11309i	−0.0252260	+	0.0436927i
$650$	−2.49250	+	4.31714i	−0.0977641	+	0.169332i
$651$		0			0
$652$	11.5863	+	20.0681i	0.453755	+	0.785927i
$653$	11.6085			0.454276			0.227138	−	0.973863i	$-0.427063\pi$
$653$	11.6085			0.454276			0.227138	+	0.973863i	$0.427063\pi$
$654$		0			0
$655$	−13.6762			−0.534371
$656$	−4.30588	+	7.45800i	−0.168116	+	0.291186i
$657$		0			0
$658$	2.49917	−	3.55078i	0.0974278	−	0.138424i
$659$	2.05194	−	3.55407i	0.0799324	−	0.138447i	−0.823288	−	0.567624i	$-0.807863\pi$
$659$	2.05194	−	3.55407i	0.0799324	−	0.138447i	0.903221	+	0.429177i	$0.141196\pi$
$660$		0			0
$661$	−8.05561	+	13.9527i	−0.313327	+	0.542698i	−0.979080	−	0.203474i	$-0.934777\pi$
$661$	−8.05561	+	13.9527i	−0.313327	+	0.542698i	0.665753	+	0.746172i	$0.268110\pi$
$662$	−13.1462	+	22.7699i	−0.510941	+	0.884976i
$663$		0			0
$664$	−3.28544	+	5.69055i	−0.127500	+	0.220836i
$665$	−10.6948	+	15.1949i	−0.414725	+	0.589234i
$666$		0			0
$667$	−21.3783	+	37.0282i	−0.827770	+	1.43374i
$668$	−12.4249			−0.480734
$669$		0			0
$670$	−9.95545			−0.384613
$671$	3.91148	+	6.77488i	0.151001	+	0.261541i
$672$		0			0
$673$	18.0611	−	31.2827i	0.696203	−	1.20586i	−0.273571	−	0.961852i	$-0.588205\pi$
$673$	18.0611	−	31.2827i	0.696203	−	1.20586i	0.969774	−	0.244007i	$-0.0784619\pi$
$674$	−8.15482	+	14.1246i	−0.314112	+	0.544058i
$675$		0			0
$676$	−5.92516	−	10.2627i	−0.227891	−	0.394718i
$677$	0.0268412	+	0.0464903i	0.00103159	+	0.00178677i	0.866541	−	0.499106i	$-0.166338\pi$
$677$	0.0268412	+	0.0464903i	0.00103159	+	0.00178677i	−0.865509	+	0.500893i	$0.833005\pi$
$678$		0			0
$679$	9.10723	−	12.9394i	0.349503	−	0.496569i
$680$	−3.52620	−	6.10755i	−0.135224	−	0.234214i
$681$		0			0
$682$	−5.98672			−0.229243
$683$	7.74990	+	13.4232i	0.296542	+	0.513625i	0.975342	−	0.220697i	$-0.0708333\pi$
$683$	7.74990	+	13.4232i	0.296542	+	0.513625i	−0.678801	+	0.734323i	$0.737500\pi$
$684$		0			0
$685$	−0.843533			−0.0322298
$686$	−4.66281	−	17.9237i	−0.178027	−	0.684329i
$687$		0			0
$688$	−5.92389			−0.225846
$689$	−32.2226	+	55.8112i	−1.22758	+	2.12624i
$690$		0			0
$691$	−16.3801	−	28.3712i	−0.623129	−	1.07929i	−0.988899	−	0.148586i	$-0.952528\pi$
$691$	−16.3801	−	28.3712i	−0.623129	−	1.07929i	0.365770	−	0.930705i	$-0.380806\pi$
$692$	12.6529			0.480992
$693$		0			0
$694$	−7.70803			−0.292593
$695$	2.92189	+	5.06087i	0.110834	+	0.191970i
$696$		0			0
$697$	−30.3667	+	52.5967i	−1.15022	+	1.99224i
$698$	−33.8854			−1.28258
$699$		0			0
$700$	−1.52280	+	2.16358i	−0.0575566	+	0.0817755i
$701$	20.2343			0.764237			0.382119	−	0.924113i	$-0.375195\pi$
$701$	20.2343			0.764237			0.382119	+	0.924113i	$0.375195\pi$
$702$		0			0
$703$	−20.1889	−	34.9683i	−0.761440	−	1.31885i
$704$	−1.64324			−0.0619320
$705$		0			0
$706$	5.99417	+	10.3822i	0.225594	+	0.390740i
$707$	12.3323	+	1.10915i	0.463804	+	0.0417139i
$708$		0			0
$709$	12.7836	+	22.1418i	0.480097	+	0.831553i	0.999739	−	0.0228313i	$-0.00726807\pi$
$709$	12.7836	+	22.1418i	0.480097	+	0.831553i	−0.519642	+	0.854384i	$0.673935\pi$
$710$	−3.63274	−	6.29210i	−0.136334	−	0.236138i
$711$		0			0
$712$	−4.63848	+	8.03409i	−0.173835	+	0.301090i
$713$	13.5754	−	23.5132i	0.508401	−	0.880576i
$714$		0			0
$715$	4.09579	+	7.09411i	0.153174	+	0.265305i
$716$	8.66287			0.323747
$717$		0			0
$718$	−13.8452			−0.516697
$719$	−10.0236	+	17.3614i	−0.373818	+	0.647472i	−0.990149	−	0.140015i	$-0.955285\pi$
$719$	−10.0236	+	17.3614i	−0.373818	+	0.647472i	0.616331	+	0.787487i	$0.288618\pi$
$720$		0			0
$721$	14.7434	+	1.32600i	0.549071	+	0.0493827i
$722$	−15.1617	+	26.2608i	−0.564260	+	0.977328i
$723$		0			0
$724$	5.21791	−	9.03768i	0.193922	−	0.335883i
$725$	2.86866	−	4.96867i	0.106539	−	0.184532i
$726$		0			0
$727$	5.67928	−	9.83680i	0.210633	−	0.364827i	−0.741280	−	0.671196i	$-0.765781\pi$
$727$	5.67928	−	9.83680i	0.210633	−	0.364827i	0.951913	+	0.306369i	$0.0991142\pi$
$728$	−5.54488	−	11.9669i	−0.205507	−	0.443523i
$729$		0			0
$730$	−0.392899	+	0.680521i	−0.0145418	+	0.0251872i
$731$	−41.7776			−1.54520
$732$		0			0
$733$	−33.3366			−1.23131			−0.615657	−	0.788014i	$-0.711109\pi$
$733$	−33.3366			−1.23131			−0.615657	+	0.788014i	$0.711109\pi$
$734$	8.64239	+	14.9691i	0.318997	+	0.552518i
$735$		0			0
$736$	3.72617	−	6.45392i	0.137349	−	0.237895i
$737$	−8.17960	+	14.1675i	−0.301299	+	0.521866i
$738$		0			0
$739$	20.5958	+	35.6730i	0.757630	+	1.31225i	0.944056	+	0.329784i	$0.106976\pi$
$739$	20.5958	+	35.6730i	0.757630	+	1.31225i	−0.186427	+	0.982469i	$0.559691\pi$
$740$	−2.87466	−	4.97906i	−0.105675	−	0.183034i
$741$		0			0
$742$	−19.6865	+	27.9703i	−0.722715	+	1.02682i
$743$	12.2773	+	21.2649i	0.450410	+	0.780133i	0.998411	−	0.0563442i	$-0.0179444\pi$
$743$	12.2773	+	21.2649i	0.450410	+	0.780133i	−0.548001	+	0.836478i	$0.684611\pi$
$744$		0			0
$745$	13.6621			0.500541
$746$	7.77130	+	13.4603i	0.284528	+	0.492816i
$747$		0			0
$748$	−11.5888			−0.423728
$749$	−11.6907	+	16.6100i	−0.427169	+	0.606916i
$750$		0			0
$751$	−12.3239			−0.449706			−0.224853	−	0.974393i	$-0.572190\pi$
$751$	−12.3239			−0.449706			−0.224853	+	0.974393i	$0.572190\pi$
$752$	0.820581	−	1.42129i	0.0299235	−	0.0518291i
$753$		0			0
$754$	14.3003	+	24.7689i	0.520786	+	0.902028i
$755$	−0.578439			−0.0210515
$756$		0			0
$757$	−16.4874			−0.599245			−0.299622	−	0.954058i	$-0.596861\pi$
$757$	−16.4874			−0.599245			−0.299622	+	0.954058i	$0.596861\pi$
$758$	−10.8510	−	18.7945i	−0.394126	−	0.682646i
$759$		0			0
$760$	−3.51153	+	6.08215i	−0.127377	+	0.220623i
$761$	−40.0477			−1.45173			−0.725864	−	0.687838i	$-0.758560\pi$
$761$	−40.0477			−1.45173			−0.725864	+	0.687838i	$0.758560\pi$
$762$		0			0
$763$	21.5399	+	46.4872i	0.779797	+	1.68295i
$764$	17.9357			0.648890
$765$		0			0
$766$	−12.7077	−	22.0104i	−0.459149	−	0.795269i
$767$	−3.89911			−0.140789
$768$		0			0
$769$	−3.91652	−	6.78361i	−0.141233	−	0.244623i	0.786728	−	0.617300i	$-0.211773\pi$
$769$	−3.91652	−	6.78361i	−0.141233	−	0.244623i	−0.927961	+	0.372677i	$0.878440\pi$
$770$	1.82779	+	3.94472i	0.0658691	+	0.142158i
$771$		0			0
$772$	−2.08058	−	3.60367i	−0.0748817	−	0.129699i
$773$	−16.2391	−	28.1269i	−0.584079	−	1.01165i	−0.994990	−	0.0999786i	$-0.968123\pi$
$773$	−16.2391	−	28.1269i	−0.584079	−	1.01165i	0.410911	−	0.911676i	$-0.365211\pi$
$774$		0			0
$775$	−1.82162	+	3.15514i	−0.0654345	+	0.113336i
$776$	2.99028	−	5.17932i	0.107345	−	0.185927i
$777$		0			0
$778$	−5.19770	−	9.00269i	−0.186347	−	0.322762i
$779$	60.4809			2.16695
$780$		0			0
$781$	−11.9389			−0.427209
$782$	26.2785	−	45.5156i	0.939716	−	1.62764i
$783$		0			0
$784$	−2.36213	−	6.58941i	−0.0843619	−	0.235336i
$785$	1.64913	−	2.85638i	0.0588600	−	0.101949i
$786$		0			0
$787$	−8.78696	+	15.2195i	−0.313221	+	0.542515i	−0.979058	−	0.203583i	$-0.934741\pi$
$787$	−8.78696	+	15.2195i	−0.313221	+	0.542515i	0.665837	+	0.746098i	$0.268075\pi$
$788$	−3.90169	+	6.75792i	−0.138992	+	0.240741i
$789$		0			0
$790$	−2.93134	+	5.07722i	−0.104292	+	0.180640i
$791$	1.84820	+	3.98877i	0.0657145	+	0.141824i
$792$		0			0
$793$	−11.8660	+	20.5526i	−0.421375	+	0.729843i
$794$	−2.73537			−0.0970745
$795$		0			0
$796$	24.4953			0.868214
$797$	−27.9349	−	48.3847i	−0.989506	−	1.71388i	−0.619884	−	0.784694i	$-0.712820\pi$
$797$	−27.9349	−	48.3847i	−0.989506	−	1.71388i	−0.369623	−	0.929182i	$-0.620513\pi$
$798$		0			0
$799$	5.78707	−	10.0235i	0.204732	−	0.354606i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$		0			0
$802$	−0.0177095	−	0.0306738i	−0.000625345	−	0.00108313i
$803$	0.645628	+	1.11826i	0.0227837	+	0.0394625i
$804$		0			0
$805$	−19.6378	−	1.76620i	−0.692141	−	0.0622503i
$806$	−9.08079	−	15.7284i	−0.319857	−	0.554009i
$807$		0			0
$808$	4.67998			0.164641
$809$	−17.3337	−	30.0228i	−0.609420	−	1.05555i	−0.991336	−	0.131349i	$-0.958069\pi$
$809$	−17.3337	−	30.0228i	−0.609420	−	1.05555i	0.381917	−	0.924197i	$-0.375264\pi$
$810$		0			0
$811$	32.8549			1.15369			0.576845	−	0.816854i	$-0.304284\pi$
$811$	32.8549			1.15369			0.576845	+	0.816854i	$0.304284\pi$
$812$	6.38169	+	13.7729i	0.223953	+	0.483333i
$813$		0			0
$814$	−9.44753			−0.331136
$815$	11.5863	−	20.0681i	0.405851	−	0.702955i
$816$		0			0
$817$	20.8019	+	36.0300i	0.727767	+	1.26053i
$818$	16.3458			0.571519
$819$		0			0
$820$	8.61175			0.300735
$821$	−6.81852	−	11.8100i	−0.237968	−	0.412173i	0.722163	−	0.691723i	$-0.243148\pi$
$821$	−6.81852	−	11.8100i	−0.237968	−	0.412173i	−0.960131	+	0.279550i	$0.909815\pi$
$822$		0			0
$823$	1.04275	−	1.80609i	0.0363478	−	0.0629563i	−0.847279	−	0.531148i	$-0.821761\pi$
$823$	1.04275	−	1.80609i	0.0363478	−	0.0629563i	0.883627	+	0.468191i	$0.155094\pi$
$824$	5.59496			0.194910
$825$		0			0
$826$	−2.06110	−	0.185373i	−0.0717148	−	0.00644993i
$827$	4.20031			0.146059			0.0730295	−	0.997330i	$-0.476733\pi$
$827$	4.20031			0.146059			0.0730295	+	0.997330i	$0.476733\pi$
$828$		0			0
$829$	13.2645	+	22.9747i	0.460694	+	0.797945i	0.998996	−	0.0448071i	$-0.0142673\pi$
$829$	13.2645	+	22.9747i	0.460694	+	0.797945i	−0.538302	+	0.842752i	$0.680934\pi$
$830$	6.57089			0.228079
$831$		0			0
$832$	−2.49250	−	4.31714i	−0.0864121	−	0.149670i
$833$	−16.6587	−	46.4711i	−0.577190	−	1.61013i
$834$		0			0
$835$	6.21246	+	10.7603i	0.214991	+	0.372375i
$836$	5.77029	+	9.99444i	0.199570	+	0.345665i
$837$		0			0
$838$	4.00800	−	6.94206i	0.138454	−	0.239810i
$839$	−2.18181	+	3.77901i	−0.0753244	+	0.130466i	−0.901227	−	0.433347i	$-0.857333\pi$
$839$	−2.18181	+	3.77901i	−0.0753244	+	0.130466i	0.825903	+	0.563812i	$0.190666\pi$
$840$		0			0
$841$	−1.95844	−	3.39211i	−0.0675323	−	0.116969i
$842$	−33.4939			−1.15428
$843$		0			0
$844$	−10.6351			−0.366074
$845$	−5.92516	+	10.2627i	−0.203832	+	0.353047i
$846$		0			0
$847$	−21.8708	−	1.96703i	−0.751490	−	0.0675880i
$848$	−6.46391	+	11.1958i	−0.221971	+	0.384466i
$849$		0			0
$850$	−3.52620	+	6.10755i	−0.120948	+	0.209487i
$851$	21.4230	−	37.1057i	0.734371	−	1.27197i
$852$		0			0
$853$	−13.9693	+	24.1956i	−0.478300	+	0.828440i	−0.999690	−	0.0248783i	$-0.992080\pi$
$853$	−13.9693	+	24.1956i	−0.478300	+	0.828440i	0.521390	+	0.853318i	$0.325414\pi$
$854$	−7.24959	+	10.3001i	−0.248076	+	0.352463i
$855$		0			0
$856$	−3.83855	+	6.64856i	−0.131199	+	0.227243i
$857$	4.53888			0.155045			0.0775225	−	0.996991i	$-0.475299\pi$
$857$	4.53888			0.155045			0.0775225	+	0.996991i	$0.475299\pi$
$858$		0			0
$859$	−14.6827			−0.500968			−0.250484	−	0.968121i	$-0.580590\pi$
$859$	−14.6827			−0.500968			−0.250484	+	0.968121i	$0.580590\pi$
$860$	2.96195	+	5.13024i	0.101001	+	0.174940i
$861$		0			0
$862$	12.2779	−	21.2660i	0.418187	−	0.724321i
$863$	−14.6627	+	25.3966i	−0.499125	+	0.864510i	−0.999999	−	0.00100981i	$-0.999679\pi$
$863$	−14.6627	+	25.3966i	−0.499125	+	0.864510i	0.500874	+	0.865520i	$0.333012\pi$
$864$		0			0
$865$	−6.32646	−	10.9577i	−0.215106	−	0.372574i
$866$	−12.9459	−	22.4229i	−0.439918	−	0.761961i
$867$		0			0
$868$	−4.05242	−	8.74588i	−0.137548	−	0.296854i
$869$	4.81689	+	8.34310i	0.163402	+	0.283020i
$870$		0			0
$871$	−49.6280			−1.68158
$872$	9.68250	+	16.7706i	0.327891	+	0.567924i
$873$		0			0
$874$	−52.3383			−1.77037
$875$	2.63512	+	0.236999i	0.0890831	+	0.00801202i
$876$		0			0
$877$	35.5683			1.20106			0.600529	−	0.799603i	$-0.294957\pi$
$877$	35.5683			1.20106			0.600529	+	0.799603i	$0.294957\pi$
$878$	6.01813	−	10.4237i	0.203102	−	0.351783i
$879$		0			0
$880$	0.821620	+	1.42309i	0.0276968	+	0.0479723i
$881$	−5.92938			−0.199766			−0.0998829	−	0.994999i	$-0.531847\pi$
$881$	−5.92938			−0.199766			−0.0998829	+	0.994999i	$0.531847\pi$
$882$		0			0
$883$	11.3953			0.383483			0.191742	−	0.981445i	$-0.438586\pi$
$883$	11.3953			0.383483			0.191742	+	0.981445i	$0.438586\pi$
$884$	−17.5781	−	30.4462i	−0.591217	−	1.02402i
$885$		0			0
$886$	1.00770	−	1.74539i	0.0338543	−	0.0586374i
$887$	−7.84921			−0.263551			−0.131775	−	0.991280i	$-0.542068\pi$
$887$	−7.84921			−0.263551			−0.131775	+	0.991280i	$0.542068\pi$
$888$		0			0
$889$	−43.3950	−	3.90289i	−1.45542	−	0.130899i
$890$	9.27697			0.310965
$891$		0			0
$892$	12.8215	+	22.2074i	0.429295	+	0.743560i
$893$	−11.5260			−0.385703
$894$		0			0
$895$	−4.33144	−	7.50227i	−0.144784	−	0.250773i
$896$	−1.11231	−	2.40058i	−0.0371597	−	0.0801976i
$897$		0			0
$898$	−0.371185	−	0.642911i	−0.0123866	−	0.0214542i
$899$	10.4512	+	18.1021i	0.348568	+	0.603737i
$900$		0			0
$901$	−45.5860	+	78.9573i	−1.51869	+	2.63045i
$902$	7.07559	−	12.2553i	0.235591	−	0.408056i
$903$		0			0
$904$	0.830795	+	1.43898i	0.0276318	+	0.0478597i
$905$	−10.4358			−0.346898
$906$		0			0
$907$	19.7902			0.657121			0.328561	−	0.944483i	$-0.393436\pi$
$907$	19.7902			0.657121			0.328561	+	0.944483i	$0.393436\pi$
$908$	−9.49730	+	16.4498i	−0.315179	+	0.545906i
$909$		0			0
$910$	−7.59119	+	10.7855i	−0.251646	+	0.357534i
$911$	0.911882	−	1.57943i	0.0302120	−	0.0523287i	−0.850524	−	0.525936i	$-0.823715\pi$
$911$	0.911882	−	1.57943i	0.0302120	−	0.0523287i	0.880736	+	0.473607i	$0.157048\pi$
$912$		0			0
$913$	5.39877	−	9.35095i	0.178673	−	0.309471i
$914$	5.61374	−	9.72328i	0.185686	−	0.321617i
$915$		0			0
$916$	−2.24447	+	3.88754i	−0.0741595	+	0.128448i
$917$	−36.0382	−	3.24123i	−1.19009	−	0.107035i
$918$		0			0
$919$	16.5671	−	28.6951i	0.546499	−	0.946564i	−0.452012	−	0.892012i	$-0.649294\pi$
$919$	16.5671	−	28.6951i	0.546499	−	0.946564i	0.998511	−	0.0545518i	$-0.0173730\pi$
$920$	−7.45235			−0.245697
$921$		0			0
$922$	18.2527			0.601119
$923$	−18.1093	−	31.3662i	−0.596074	−	1.03243i
$924$		0			0
$925$	−2.87466	+	4.97906i	−0.0945183	+	0.163711i
$926$	14.5347	−	25.1748i	0.477639	−	0.827295i
$927$		0			0
$928$	2.86866	+	4.96867i	0.0941684	+	0.163104i
$929$	−0.739757	−	1.28130i	−0.0242706	−	0.0420380i	0.853635	−	0.520872i	$-0.174393\pi$
$929$	−0.739757	−	1.28130i	−0.0242706	−	0.0420380i	−0.877906	+	0.478834i	$0.841060\pi$
$930$		0			0
$931$	−31.7831	+	37.5058i	−1.04165	+	1.22920i
$932$	−2.86866	−	4.96867i	−0.0939662	−	0.162754i
$933$		0			0
$934$	−7.31746			−0.239435
$935$	5.79439	+	10.0362i	0.189497	+	0.328218i
$936$		0			0
$937$	−31.9616			−1.04414			−0.522070	−	0.852902i	$-0.674840\pi$
$937$	−31.9616			−1.04414			−0.522070	+	0.852902i	$0.674840\pi$
$938$	−26.2338	−	2.35943i	−0.856562	−	0.0770381i
$939$		0			0
$940$	−1.64116			−0.0535288
$941$	−9.39061	+	16.2650i	−0.306125	+	0.530224i	−0.977511	−	0.210884i	$-0.932366\pi$
$941$	−9.39061	+	16.2650i	−0.306125	+	0.530224i	0.671386	+	0.741108i	$0.265699\pi$
$942$		0			0
$943$	32.0889	+	55.5796i	1.04496	+	1.80992i
$944$	−0.782167			−0.0254574
$945$		0			0
$946$	9.73438			0.316492
$947$	−6.41697	−	11.1145i	−0.208523	−	0.361173i	0.742726	−	0.669595i	$-0.233532\pi$
$947$	−6.41697	−	11.1145i	−0.208523	−	0.361173i	−0.951250	+	0.308422i	$0.900199\pi$
$948$		0			0
$949$	−1.95861	+	3.39240i	−0.0635790	+	0.110122i
$950$	7.02306			0.227858
$951$		0			0
$952$	−7.84446	−	16.9298i	−0.254240	−	0.548698i
$953$	34.9964			1.13364			0.566822	−	0.823841i	$-0.308173\pi$
$953$	34.9964			1.13364			0.566822	+	0.823841i	$0.308173\pi$
$954$		0			0
$955$	−8.96784	−	15.5328i	−0.290193	−	0.502628i
$956$	−27.5238			−0.890183
$957$		0			0
$958$	3.08835	+	5.34918i	0.0997802	+	0.172824i
$959$	−2.22281	−	0.199916i	−0.0717782	−	0.00645563i
$960$		0			0
$961$	8.86340	+	15.3519i	0.285916	+	0.495221i
$962$	−14.3302	−	24.8207i	−0.462025	−	0.800251i
$963$		0			0
$964$	10.0984	−	17.4909i	0.325246	−	0.563343i
$965$	−2.08058	+	3.60367i	−0.0669762	+	0.116006i
$966$		0			0
$967$	−13.2132	−	22.8860i	−0.424908	−	0.735963i	0.571503	−	0.820600i	$-0.306360\pi$
$967$	−13.2132	−	22.8860i	−0.424908	−	0.735963i	−0.996412	+	0.0846367i	$0.973027\pi$
$968$	−8.29976			−0.266764
$969$		0			0
$970$	−5.98057			−0.192024
$971$	16.2985	−	28.2298i	0.523043	−	0.905938i	−0.476597	−	0.879122i	$-0.658130\pi$
$971$	16.2985	−	28.2298i	0.523043	−	0.905938i	0.999640	−	0.0268157i	$-0.00853673\pi$
$972$		0			0
$973$	6.50011	+	14.0285i	0.208384	+	0.449732i
$974$	3.11014	−	5.38693i	0.0996554	−	0.172608i
$975$		0			0
$976$	−2.38034	+	4.12287i	−0.0761929	+	0.131970i
$977$	20.4822	−	35.4762i	0.655284	−	1.13499i	−0.326538	−	0.945184i	$-0.605882\pi$
$977$	20.4822	−	35.4762i	0.655284	−	1.13499i	0.981823	−	0.189801i	$-0.0607844\pi$
$978$		0			0
$979$	7.62215	−	13.2019i	0.243605	−	0.421936i
$980$	−4.52553	+	5.34037i	−0.144563	+	0.170592i
$981$		0			0
$982$	3.94447	−	6.83202i	0.125873	−	0.218019i
$983$	−15.3520			−0.489652			−0.244826	−	0.969567i	$-0.578731\pi$
$983$	−15.3520			−0.489652			−0.244826	+	0.969567i	$0.578731\pi$
$984$		0			0
$985$	7.80338			0.248636
$986$	20.2309	+	35.0410i	0.644284	+	1.11593i
$987$		0			0
$988$	−17.5050	+	30.3196i	−0.556909	+	0.964594i
$989$	−22.0734	+	38.2323i	−0.701895	+	1.21572i
$990$		0			0
$991$	−4.62129	−	8.00431i	−0.146800	−	0.254265i	0.783243	−	0.621716i	$-0.213564\pi$
$991$	−4.62129	−	8.00431i	−0.146800	−	0.254265i	−0.930043	+	0.367450i	$0.880231\pi$
$992$	−1.82162	−	3.15514i	−0.0578365	−	0.100176i
$993$		0			0
$994$	−8.08148	−	17.4414i	−0.256329	−	0.553206i
$995$	−12.2477	−	21.2136i	−0.388277	−	0.672515i
$996$		0			0
$997$	−10.7325			−0.339902			−0.169951	−	0.985453i	$-0.554361\pi$
$997$	−10.7325			−0.339902			−0.169951	+	0.985453i	$0.554361\pi$
$998$	−4.34473	−	7.52530i	−0.137530	−	0.238209i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1890.2.l.i.1801.8		16
3.2	odd	2		630.2.l.i.331.2	yes	16
7.4	even	3		1890.2.i.i.991.2		16
9.4	even	3		1890.2.i.i.1171.2		16
9.5	odd	6		630.2.i.i.121.5	✓	16
21.11	odd	6		630.2.i.i.151.5	yes	16
63.4	even	3	inner	1890.2.l.i.361.8		16
63.32	odd	6		630.2.l.i.571.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.i.i.121.5	✓	16	9.5	odd	6
630.2.i.i.151.5	yes	16	21.11	odd	6
630.2.l.i.331.2	yes	16	3.2	odd	2
630.2.l.i.571.2	yes	16	63.32	odd	6
1890.2.i.i.991.2		16	7.4	even	3
1890.2.i.i.1171.2		16	9.4	even	3
1890.2.l.i.361.8		16	63.4	even	3	inner
1890.2.l.i.1801.8		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.63512 + 0.236999i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(2.63512 + 0.236999i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{10} -1.64324 q^{11} +(-2.49250 - 4.31714i) q^{13} +(-1.11231 - 2.40058i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.52620 - 6.10755i) q^{17} +(-3.51153 + 6.08215i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.821620 + 1.42309i) q^{22} -7.45235 q^{23} +1.00000 q^{25} +(-2.49250 + 4.31714i) q^{26} +(-1.52280 + 2.16358i) q^{28} +(2.86866 - 4.96867i) q^{29} +(-1.82162 + 3.15514i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.52620 + 6.10755i) q^{34} +(2.63512 + 0.236999i) q^{35} +(-2.87466 + 4.97906i) q^{37} +7.02306 q^{38} +1.00000 q^{40} +(-4.30588 - 7.45800i) q^{41} +(2.96195 - 5.13024i) q^{43} +(0.821620 - 1.42309i) q^{44} +(3.72617 + 6.45392i) q^{46} +(0.820581 + 1.42129i) q^{47} +(6.88766 + 1.24904i) q^{49} +(-0.500000 - 0.866025i) q^{50} +4.98501 q^{52} +(-6.46391 - 11.1958i) q^{53} -1.64324 q^{55} +(2.63512 + 0.236999i) q^{56} -5.73732 q^{58} +(0.391083 - 0.677376i) q^{59} +(-2.38034 - 4.12287i) q^{61} +3.64324 q^{62} +1.00000 q^{64} +(-2.49250 - 4.31714i) q^{65} +(4.97772 - 8.62167i) q^{67} +7.05240 q^{68} +(-1.11231 - 2.40058i) q^{70} +7.26549 q^{71} +(-0.392899 - 0.680521i) q^{73} +5.74933 q^{74} +(-3.51153 - 6.08215i) q^{76} +(-4.33013 - 0.389446i) q^{77} +(-2.93134 - 5.07722i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.30588 + 7.45800i) q^{82} +(-3.28544 + 5.69055i) q^{83} +(-3.52620 - 6.10755i) q^{85} -5.92389 q^{86} -1.64324 q^{88} +(-4.63848 + 8.03409i) q^{89} +(-5.54488 - 11.9669i) q^{91} +(3.72617 - 6.45392i) q^{92} +(0.820581 - 1.42129i) q^{94} +(-3.51153 + 6.08215i) q^{95} +(2.99028 - 5.17932i) q^{97} +(-2.36213 - 6.58941i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8}+O(q^{10}) \) 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8	\( 16 q - 8 q^{2} - 8 q^{4} + 16 q^{5} + 4 q^{7} + 16 q^{8} - 8 q^{10} + 2 q^{11} + 2 q^{13} - 8 q^{14} - 8 q^{16} - 11 q^{17} - 2 q^{19} - 8 q^{20} - q^{22} + 22 q^{23} + 16 q^{25} + 2 q^{26} + 4 q^{28} - 17 q^{29} - 15 q^{31} - 8 q^{32} - 11 q^{34} + 4 q^{35} - 2 q^{37} + 4 q^{38} + 16 q^{40} - 7 q^{41} - 13 q^{43} - q^{44} - 11 q^{46} + 5 q^{47} + 10 q^{49} - 8 q^{50} - 4 q^{52} - 18 q^{53} + 2 q^{55} + 4 q^{56} + 34 q^{58} - q^{59} - 27 q^{61} + 30 q^{62} + 16 q^{64} + 2 q^{65} - 10 q^{67} + 22 q^{68} - 8 q^{70} + 38 q^{71} - 8 q^{73} + 4 q^{74} - 2 q^{76} + 19 q^{77} - 25 q^{79} - 8 q^{80} - 7 q^{82} - 2 q^{83} - 11 q^{85} + 26 q^{86} + 2 q^{88} + 6 q^{89} + 14 q^{91} - 11 q^{92} + 5 q^{94} - 2 q^{95} + 26 q^{97} - 14 q^{98}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^4 + 16 * q^5 + 4 * q^7 + 16 * q^8 - 8 * q^10 + 2 * q^11 + 2 * q^13 - 8 * q^14 - 8 * q^16 - 11 * q^17 - 2 * q^19 - 8 * q^20 - q^22 + 22 * q^23 + 16 * q^25 + 2 * q^26 + 4 * q^28 - 17 * q^29 - 15 * q^31 - 8 * q^32 - 11 * q^34 + 4 * q^35 - 2 * q^37 + 4 * q^38 + 16 * q^40 - 7 * q^41 - 13 * q^43 - q^44 - 11 * q^46 + 5 * q^47 + 10 * q^49 - 8 * q^50 - 4 * q^52 - 18 * q^53 + 2 * q^55 + 4 * q^56 + 34 * q^58 - q^59 - 27 * q^61 + 30 * q^62 + 16 * q^64 + 2 * q^65 - 10 * q^67 + 22 * q^68 - 8 * q^70 + 38 * q^71 - 8 * q^73 + 4 * q^74 - 2 * q^76 + 19 * q^77 - 25 * q^79 - 8 * q^80 - 7 * q^82 - 2 * q^83 - 11 * q^85 + 26 * q^86 + 2 * q^88 + 6 * q^89 + 14 * q^91 - 11 * q^92 + 5 * q^94 - 2 * q^95 + 26 * q^97 - 14 * q^98

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