LMFDB - Embedded newform 666.2.bs.b.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			89.3
Character	$\chi$	$=$	666.89
Dual form			666.2.bs.b.449.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.38993 - 1.67345i) q^{5} +(0.280864 - 1.59286i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.38993 - 1.67345i) q^{5} +(0.280864 - 1.59286i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.45878 + 2.52669i) q^{10} +(-2.53723 - 4.39461i) q^{11} +(4.83452 - 0.422966i) q^{13} +(0.418622 + 1.56232i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-4.75587 - 0.416085i) q^{17} +(0.560982 - 1.20303i) q^{19} +(0.254283 - 2.90646i) q^{20} +(4.15675 + 2.91059i) q^{22} +(-5.76869 + 1.54571i) q^{23} +(1.20124 - 3.30038i) q^{25} +(-4.20281 + 2.42650i) q^{26} +(-1.03966 - 1.23902i) q^{28} +(1.55703 + 0.417205i) q^{29} +(-1.10262 - 1.10262i) q^{31} +(0.573576 + 0.819152i) q^{32} +(4.48613 - 1.63282i) q^{34} +(-1.99432 - 4.27683i) q^{35} +(-5.89410 + 1.50320i) q^{37} +1.32740i q^{38} +(0.997867 + 2.74162i) q^{40} +(-0.186381 - 0.156392i) q^{41} +(0.254623 - 0.254623i) q^{43} +(-4.99736 - 0.881170i) q^{44} +(4.57496 - 3.83885i) q^{46} +(-2.26327 - 1.30670i) q^{47} +(4.11954 + 1.49939i) q^{49} +(0.306108 + 3.49883i) q^{50} +(2.78356 - 3.97534i) q^{52} +(12.6205 - 2.22534i) q^{53} +(-13.4179 - 6.25689i) q^{55} +(1.46589 + 0.683555i) q^{56} +(-1.58747 + 0.279913i) q^{58} +(6.27933 - 8.96781i) q^{59} +(0.440625 + 5.03637i) q^{61} +(1.46530 + 0.533325i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(10.8464 - 9.10118i) q^{65} +(13.0588 + 2.30261i) q^{67} +(-3.37576 + 3.37576i) q^{68} +(3.61493 + 3.03329i) q^{70} +(-1.51488 - 4.16210i) q^{71} -15.9658i q^{73} +(4.70659 - 3.85331i) q^{74} +(-0.560982 - 1.20303i) q^{76} +(-7.71259 + 2.80715i) q^{77} +(-3.56565 - 5.09227i) q^{79} +(-2.06303 - 2.06303i) q^{80} +(0.235013 + 0.0629715i) q^{82} +(8.64132 + 10.2983i) q^{83} +(-12.0625 + 6.96429i) q^{85} +(-0.123158 + 0.338375i) q^{86} +(4.90155 - 1.31337i) q^{88} +(13.6677 + 9.57024i) q^{89} +(0.684118 - 7.81950i) q^{91} +(-2.52395 + 5.41264i) q^{92} +(2.60346 + 0.227773i) q^{94} +(-0.672499 - 3.81393i) q^{95} +(1.29315 + 4.82610i) q^{97} +(-4.36724 + 0.382084i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{13}{36}\right)$

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 $

$2$	−0.906308	+	0.422618i	−0.640856	+	0.298836i
$2$	−0.906308	+	0.422618i	−0.640856	+	0.298836i
$3$		0			0
$3$		0			0
$4$	0.642788	−	0.766044i	0.321394	−	0.383022i
$5$	2.38993	−	1.67345i	1.06881	−	0.748388i	0.0996995	−	0.995018i	$-0.468212\pi$
$5$	2.38993	−	1.67345i	1.06881	−	0.748388i	0.969110	+	0.246629i	$0.0793230\pi$
$6$		0			0
$7$	0.280864	−	1.59286i	0.106156	−	0.602043i	−0.884596	−	0.466359i	$-0.845566\pi$
$7$	0.280864	−	1.59286i	0.106156	−	0.602043i	0.990752	−	0.135684i	$-0.0433233\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−1.45878	+	2.52669i	−0.461308	+	0.799009i
$11$	−2.53723	−	4.39461i	−0.765003	−	1.32502i	−0.940245	−	0.340498i	$-0.889404\pi$
$11$	−2.53723	−	4.39461i	−0.765003	−	1.32502i	0.175242	−	0.984525i	$-0.443929\pi$
$12$		0			0
$13$	4.83452	−	0.422966i	1.34086	−	0.117310i	0.605963	−	0.795493i	$-0.292788\pi$
$13$	4.83452	−	0.422966i	1.34086	−	0.117310i	0.734893	+	0.678183i	$0.237232\pi$
$14$	0.418622	+	1.56232i	0.111881	+	0.417547i
$15$		0			0
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	−4.75587	−	0.416085i	−1.15347	−	0.100915i	−0.505670	−	0.862727i	$-0.668755\pi$
$17$	−4.75587	−	0.416085i	−1.15347	−	0.100915i	−0.647799	+	0.761812i	$0.724310\pi$
$18$		0			0
$19$	0.560982	−	1.20303i	0.128698	−	0.275994i	−0.831391	−	0.555688i	$-0.812455\pi$
$19$	0.560982	−	1.20303i	0.128698	−	0.275994i	0.960089	+	0.279694i	$0.0902329\pi$
$20$	0.254283	−	2.90646i	0.0568593	−	0.649905i
$21$		0			0
$22$	4.15675	+	2.91059i	0.886222	+	0.620539i
$23$	−5.76869	+	1.54571i	−1.20285	+	0.322304i	−0.803955	−	0.594691i	$-0.797275\pi$
$23$	−5.76869	+	1.54571i	−1.20285	+	0.322304i	−0.398900	+	0.916995i	$0.630608\pi$
$24$		0			0
$25$	1.20124	−	3.30038i	0.240248	−	0.660077i
$26$	−4.20281	+	2.42650i	−0.824240	+	0.475875i
$27$		0			0
$28$	−1.03966	−	1.23902i	−0.196478	−	0.234153i
$29$	1.55703	+	0.417205i	0.289133	+	0.0774729i	0.400470	−	0.916310i	$-0.368847\pi$
$29$	1.55703	+	0.417205i	0.289133	+	0.0774729i	−0.111337	+	0.993783i	$0.535513\pi$
$30$		0			0
$31$	−1.10262	−	1.10262i	−0.198036	−	0.198036i	0.601122	−	0.799158i	$-0.294721\pi$
$31$	−1.10262	−	1.10262i	−0.198036	−	0.198036i	−0.799158	+	0.601122i	$0.794721\pi$
$32$	0.573576	+	0.819152i	0.101395	+	0.144807i
$33$		0			0
$34$	4.48613	−	1.63282i	0.769365	−	0.280026i
$35$	−1.99432	−	4.27683i	−0.337101	−	0.722916i
$36$		0			0
$37$	−5.89410	+	1.50320i	−0.968984	+	0.247124i
$37$	−5.89410	+	1.50320i	−0.968984	+	0.247124i
$38$			1.32740i			0.215332i
$39$		0			0
$40$	0.997867	+	2.74162i	0.157777	+	0.433488i
$41$	−0.186381	−	0.156392i	−0.0291078	−	0.0244244i	0.628118	−	0.778118i	$-0.283826\pi$
$41$	−0.186381	−	0.156392i	−0.0291078	−	0.0244244i	−0.657226	+	0.753694i	$0.728270\pi$
$42$		0			0
$43$	0.254623	−	0.254623i	0.0388296	−	0.0388296i	−0.687425	−	0.726255i	$-0.741259\pi$
$43$	0.254623	−	0.254623i	0.0388296	−	0.0388296i	0.726255	+	0.687425i	$0.241259\pi$
$44$	−4.99736	−	0.881170i	−0.753381	−	0.132841i
$45$		0			0
$46$	4.57496	−	3.83885i	0.674541	−	0.566007i
$47$	−2.26327	−	1.30670i	−0.330132	−	0.190602i	0.325768	−	0.945450i	$-0.394377\pi$
$47$	−2.26327	−	1.30670i	−0.330132	−	0.190602i	−0.655900	+	0.754848i	$0.727711\pi$
$48$		0			0
$49$	4.11954	+	1.49939i	0.588506	+	0.214199i
$50$	0.306108	+	3.49883i	0.0432902	+	0.494809i
$51$		0			0
$52$	2.78356	−	3.97534i	0.386011	−	0.551280i
$53$	12.6205	−	2.22534i	1.73356	−	0.305674i	0.784353	−	0.620315i	$-0.212995\pi$
$53$	12.6205	−	2.22534i	1.73356	−	0.305674i	0.949211	+	0.314641i	$0.101884\pi$
$54$		0			0
$55$	−13.4179	−	6.25689i	−1.80927	−	0.843679i
$56$	1.46589	+	0.683555i	0.195888	+	0.0913439i
$57$		0			0
$58$	−1.58747	+	0.279913i	−0.208444	+	0.0367544i
$59$	6.27933	−	8.96781i	0.817499	−	1.16751i	−0.165916	−	0.986140i	$-0.553058\pi$
$59$	6.27933	−	8.96781i	0.817499	−	1.16751i	0.983415	−	0.181370i	$-0.0580531\pi$
$60$		0			0
$61$	0.440625	+	5.03637i	0.0564163	+	0.644841i	0.970784	+	0.239956i	$0.0771329\pi$
$61$	0.440625	+	5.03637i	0.0564163	+	0.644841i	−0.914368	+	0.404885i	$0.867312\pi$
$62$	1.46530	+	0.533325i	0.186093	+	0.0677323i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	10.8464	−	9.10118i	1.34533	−	1.12886i
$66$		0			0
$67$	13.0588	+	2.30261i	1.59538	+	0.281309i	0.899525	−	0.436870i	$-0.143913\pi$
$67$	13.0588	+	2.30261i	1.59538	+	0.281309i	0.695858	+	0.718179i	$0.255024\pi$
$68$	−3.37576	+	3.37576i	−0.409371	+	0.409371i
$69$		0			0
$70$	3.61493	+	3.03329i	0.432067	+	0.362547i
$71$	−1.51488	−	4.16210i	−0.179783	−	0.493951i	0.816765	−	0.576971i	$-0.195765\pi$
$71$	−1.51488	−	4.16210i	−0.179783	−	0.493951i	−0.996548	+	0.0830206i	$0.973543\pi$
$72$		0			0
$73$		−	15.9658i		−	1.86865i	−0.356420	−	0.934326i	$-0.616003\pi$
$73$		−	15.9658i		−	1.86865i	0.356420	−	0.934326i	$-0.383997\pi$
$74$	4.70659	−	3.85331i	0.547130	−	0.447938i
$75$		0			0
$76$	−0.560982	−	1.20303i	−0.0643491	−	0.137997i
$77$	−7.71259	+	2.80715i	−0.878932	+	0.319905i
$78$		0			0
$79$	−3.56565	−	5.09227i	−0.401167	−	0.572925i	0.566847	−	0.823823i	$-0.308163\pi$
$79$	−3.56565	−	5.09227i	−0.401167	−	0.572925i	−0.968014	+	0.250898i	$0.919274\pi$
$80$	−2.06303	−	2.06303i	−0.230654	−	0.230654i
$81$		0			0
$82$	0.235013	+	0.0629715i	0.0259528	+	0.00695404i
$83$	8.64132	+	10.2983i	0.948509	+	1.13039i	0.991342	+	0.131306i	$0.0419171\pi$
$83$	8.64132	+	10.2983i	0.948509	+	1.13039i	−0.0428333	+	0.999082i	$0.513638\pi$
$84$		0			0
$85$	−12.0625	+	6.96429i	−1.30836	+	0.755383i
$86$	−0.123158	+	0.338375i	−0.0132805	+	0.0364879i
$87$		0			0
$88$	4.90155	−	1.31337i	0.522507	−	0.140005i
$89$	13.6677	+	9.57024i	1.44878	+	1.01444i	0.992186	+	0.124766i	$0.0398182\pi$
$89$	13.6677	+	9.57024i	1.44878	+	1.01444i	0.456590	+	0.889677i	$0.349071\pi$
$90$		0			0
$91$	0.684118	−	7.81950i	0.0717150	−	0.819706i
$92$	−2.52395	+	5.41264i	−0.263140	+	0.564306i
$93$		0			0
$94$	2.60346	+	0.227773i	0.268526	+	0.0234930i
$95$	−0.672499	−	3.81393i	−0.0689970	−	0.391301i
$96$		0			0
$97$	1.29315	+	4.82610i	0.131300	+	0.490017i	0.999986	−	0.00534628i	$-0.00170178\pi$
$97$	1.29315	+	4.82610i	0.131300	+	0.490017i	−0.868686	+	0.495363i	$0.835035\pi$
$98$	−4.36724	+	0.382084i	−0.441158	+	0.0385963i
$99$		0			0
$100$	−1.75610	−	3.04165i	−0.175610	−	0.304165i
$101$	−1.63005	+	2.82333i	−0.162196	+	0.280932i	−0.935656	−	0.352913i	$-0.885191\pi$
$101$	−1.63005	+	2.82333i	−0.162196	+	0.280932i	0.773460	+	0.633845i	$0.218524\pi$
$102$		0			0
$103$	1.01731	−	3.79666i	0.100239	−	0.374096i	−0.897523	−	0.440968i	$-0.854635\pi$
$103$	1.01731	−	3.79666i	0.100239	−	0.374096i	0.997762	+	0.0668718i	$0.0213019\pi$
$104$	−0.842713	+	4.77926i	−0.0826348	+	0.468645i
$105$		0			0
$106$	−10.4976	+	7.35051i	−1.01962	+	0.713945i
$107$	0.106549	−	0.126981i	0.0103005	−	0.0122757i	−0.760870	−	0.648905i	$-0.775227\pi$
$107$	0.106549	−	0.126981i	0.0103005	−	0.0122757i	0.771170	+	0.636629i	$0.219672\pi$
$108$		0			0
$109$	0.0178250	−	0.00831196i	0.00170733	−	0.000796141i	−0.421764	−	0.906705i	$-0.638589\pi$
$109$	0.0178250	−	0.00831196i	0.00170733	−	0.000796141i	0.423472	+	0.905909i	$0.360811\pi$
$110$	14.8051			1.41161
$111$		0			0
$112$	−1.61743			−0.152833
$113$	−15.8680	+	7.39935i	−1.49273	+	0.696072i	−0.986110	−	0.166096i	$-0.946884\pi$
$113$	−15.8680	+	7.39935i	−1.49273	+	0.696072i	−0.506622	+	0.862168i	$0.669106\pi$
$114$		0			0
$115$	−11.2001	+	13.3477i	−1.04441	+	1.24468i
$116$	1.32044	−	0.924579i	0.122599	−	0.0858450i
$117$		0			0
$118$	−1.90104	+	10.7814i	−0.175005	+	0.992504i
$119$	−1.99852	+	7.45856i	−0.183204	+	0.683725i
$120$		0			0
$121$	−7.37504	+	12.7739i	−0.670458	+	1.16127i
$122$	−2.52780	−	4.37828i	−0.228857	−	0.396391i
$123$		0			0
$124$	−1.55340	+	0.135905i	−0.139500	+	0.0122047i
$125$	1.12347	+	4.19286i	0.100487	+	0.375021i
$126$		0			0
$127$	2.17878	+	12.3565i	0.193336	+	1.09646i	0.914769	+	0.403978i	$0.132373\pi$
$127$	2.17878	+	12.3565i	0.193336	+	1.09646i	−0.721433	+	0.692484i	$0.756516\pi$
$128$	0.996195	+	0.0871557i	0.0880520	+	0.00770355i
$129$		0			0
$130$	−5.98382	+	12.8323i	−0.524816	+	1.12547i
$131$	1.79344	−	20.4991i	0.156694	−	1.79102i	−0.358082	−	0.933690i	$-0.616569\pi$
$131$	1.79344	−	20.4991i	0.156694	−	1.79102i	0.514775	−	0.857325i	$-0.327875\pi$
$132$		0			0
$133$	−1.75870	−	1.23145i	−0.152498	−	0.106780i
$134$	−12.8084	+	3.43200i	−1.10648	+	0.296480i
$135$		0			0
$136$	1.63282	−	4.48613i	0.140013	−	0.384683i
$137$	−0.571818	+	0.330139i	−0.0488537	+	0.0282057i	−0.524228	−	0.851578i	$-0.675646\pi$
$137$	−0.571818	+	0.330139i	−0.0488537	+	0.0282057i	0.475374	+	0.879784i	$0.342313\pi$
$138$		0			0
$139$	−4.13165	−	4.92391i	−0.350442	−	0.417641i	0.561812	−	0.827265i	$-0.310104\pi$
$139$	−4.13165	−	4.92391i	−0.350442	−	0.417641i	−0.912254	+	0.409624i	$0.865660\pi$
$140$	−4.55816	−	1.22136i	−0.385235	−	0.103223i
$141$		0			0
$142$	3.13193	+	3.13193i	0.262826	+	0.262826i
$143$	−14.1251	−	20.1727i	−1.18120	−	1.68692i
$144$		0			0
$145$	4.41936	−	1.60852i	0.367008	−	0.133580i
$146$	6.74743	+	14.4699i	0.558421	+	1.19754i
$147$		0			0
$148$	−2.63714	+	5.48138i	−0.216771	+	0.450566i
$149$			6.73879i			0.552063i	0.961149	+	0.276032i	$0.0890194\pi$
$149$			6.73879i			0.552063i	−0.961149	+	0.276032i	$0.910981\pi$
$150$		0			0
$151$	0.880682	+	2.41965i	0.0716689	+	0.196909i	0.970355	−	0.241683i	$-0.0776995\pi$
$151$	0.880682	+	2.41965i	0.0716689	+	0.196909i	−0.898686	+	0.438592i	$0.855477\pi$
$152$	1.01684	+	0.853234i	0.0824770	+	0.0692064i
$153$		0			0
$154$	5.80363	−	5.80363i	0.467670	−	0.467670i
$155$	−4.48036	−	0.790008i	−0.359871	−	0.0634549i
$156$		0			0
$157$	9.26922	−	7.77780i	0.739764	−	0.620736i	−0.193010	−	0.981197i	$-0.561825\pi$
$157$	9.26922	−	7.77780i	0.739764	−	0.620736i	0.932774	+	0.360461i	$0.117381\pi$
$158$	5.38366	+	3.10826i	0.428301	+	0.247280i
$159$		0			0
$160$	2.74162	+	0.997867i	0.216744	+	0.0788883i
$161$	0.841888	+	9.62283i	0.0663501	+	0.758385i
$162$		0			0
$163$	−13.4511	+	19.2101i	−1.05357	+	1.50465i	−0.202724	+	0.979236i	$0.564979\pi$
$163$	−13.4511	+	19.2101i	−1.05357	+	1.50465i	−0.850845	+	0.525417i	$0.823909\pi$
$164$	−0.239607	+	0.0422492i	−0.0187102	+	0.00329911i
$165$		0			0
$166$	−12.1840	−	5.68147i	−0.945659	−	0.440968i
$167$	13.7772	+	6.42441i	1.06611	+	0.497135i	0.874845	−	0.484403i	$-0.160963\pi$
$167$	13.7772	+	6.42441i	1.06611	+	0.497135i	0.191265	+	0.981538i	$0.438741\pi$
$168$		0			0
$169$	10.3912	−	1.83225i	0.799325	−	0.140943i
$170$	7.98911	−	11.4096i	0.612736	−	0.875078i
$171$		0			0
$172$	−0.0313840	−	0.358721i	−0.00239301	−	0.0273522i
$173$	17.3913	+	6.32993i	1.32224	+	0.481256i	0.904175	−	0.427162i	$-0.140487\pi$
$173$	17.3913	+	6.32993i	1.32224	+	0.481256i	0.418064	+	0.908418i	$0.362709\pi$
$174$		0			0
$175$	−4.91965	−	2.84036i	−0.371891	−	0.214711i
$176$	−3.88726	+	3.26180i	−0.293013	+	0.245867i
$177$		0			0
$178$	−16.4317	−	2.89736i	−1.23161	−	0.217166i
$179$	−8.68256	+	8.68256i	−0.648965	+	0.648965i	−0.952743	−	0.303778i	$-0.901752\pi$
$179$	−8.68256	+	8.68256i	−0.648965	+	0.648965i	0.303778	+	0.952743i	$0.401752\pi$
$180$		0			0
$181$	−11.8357	−	9.93129i	−0.879737	−	0.738187i	0.0863880	−	0.996262i	$-0.472468\pi$
$181$	−11.8357	−	9.93129i	−0.879737	−	0.738187i	−0.966125	+	0.258075i	$0.916912\pi$
$182$	2.68464	+	7.37600i	0.198999	+	0.546745i
$183$		0			0
$184$		−	5.97218i		−	0.440275i
$185$	−11.5710	+	13.4560i	−0.850714	+	0.989305i
$186$		0			0
$187$	10.2382	+	21.9559i	0.748691	+	1.60557i
$188$	−2.45579	+	0.893836i	−0.179107	+	0.0651897i
$189$		0			0
$190$	2.22133	+	3.17239i	0.161152	+	0.230149i
$191$	14.8998	+	14.8998i	1.07811	+	1.07811i	0.996679	+	0.0814356i	$0.0259505\pi$
$191$	14.8998	+	14.8998i	1.07811	+	1.07811i	0.0814356	+	0.996679i	$0.474050\pi$
$192$		0			0
$193$	14.2467	+	3.81739i	1.02550	+	0.274782i	0.732092	−	0.681206i	$-0.238544\pi$
$193$	14.2467	+	3.81739i	1.02550	+	0.274782i	0.293407	+	0.955988i	$0.405211\pi$
$194$	−3.21159	−	3.82743i	−0.230579	−	0.274793i
$195$		0			0
$196$	3.79659	−	2.19196i	0.271185	−	0.156569i
$197$	−2.88975	+	7.93952i	−0.205886	+	0.565667i	−0.999061	−	0.0433266i	$-0.986204\pi$
$197$	−2.88975	+	7.93952i	−0.205886	+	0.565667i	0.793175	+	0.608994i	$0.208427\pi$
$198$		0			0
$199$	−15.8166	+	4.23806i	−1.12121	+	0.300428i	−0.771374	−	0.636382i	$-0.780430\pi$
$199$	−15.8166	+	4.23806i	−1.12121	+	0.300428i	−0.349839	+	0.936810i	$0.613764\pi$
$200$	2.87702	+	2.01451i	0.203436	+	0.142448i
$201$		0			0
$202$	0.284137	−	3.24770i	0.0199918	−	0.228507i
$203$	1.10186	−	2.36295i	0.0773354	−	0.165846i
$204$		0			0
$205$	−0.707152	−	0.0618678i	−0.0493897	−	0.00432104i
$206$	0.682540	+	3.87088i	0.0475548	+	0.269697i
$207$		0			0
$208$	−1.25605	−	4.68763i	−0.0870912	−	0.325029i
$209$	−6.71018	+	0.587065i	−0.464153	+	0.0406081i
$210$		0			0
$211$	0.695345	+	1.20437i	0.0478695	+	0.0829124i	0.888967	−	0.457971i	$-0.151423\pi$
$211$	0.695345	+	1.20437i	0.0478695	+	0.0829124i	−0.841098	+	0.540883i	$0.818090\pi$
$212$	6.40761	−	11.0983i	0.440077	−	0.762235i
$213$		0			0
$214$	−0.0429022	+	0.160113i	−0.00293274	+	0.0109451i
$215$	0.182433	−	1.03463i	0.0124418	−	0.0705610i
$216$		0			0
$217$	−2.06600	+	1.44663i	−0.140249	+	0.0982035i
$218$	−0.0126422	+	0.0150664i	−0.000856237	+	0.00102042i
$219$		0			0
$220$	−13.4179	+	6.25689i	−0.904637	+	0.421839i
$221$	−23.1684			−1.55847
$222$		0			0
$223$	−10.0208			−0.671040			−0.335520	−	0.942033i	$-0.608912\pi$
$223$	−10.0208			−0.671040			−0.335520	+	0.942033i	$0.608912\pi$
$224$	1.46589	−	0.683555i	0.0979438	−	0.0456720i
$225$		0			0
$226$	11.2541	−	13.4122i	0.748615	−	0.892164i
$227$	16.8305	−	11.7848i	1.11708	−	0.782186i	0.138972	−	0.990296i	$-0.455620\pi$
$227$	16.8305	−	11.7848i	1.11708	−	0.782186i	0.978105	+	0.208110i	$0.0667312\pi$
$228$		0			0
$229$	3.24979	−	18.4305i	0.214752	−	1.21792i	−0.666583	−	0.745431i	$-0.732244\pi$
$229$	3.24979	−	18.4305i	0.214752	−	1.21792i	0.881336	−	0.472491i	$-0.156645\pi$
$230$	4.50973	−	16.8305i	0.297363	−	1.10977i
$231$		0			0
$232$	−0.805977	+	1.39599i	−0.0529150	+	0.0916515i
$233$	−2.49054	−	4.31374i	−0.163161	−	0.282603i	0.772840	−	0.634601i	$-0.218836\pi$
$233$	−2.49054	−	4.31374i	−0.163161	−	0.282603i	−0.936001	+	0.351998i	$0.885502\pi$
$234$		0			0
$235$	−7.59576	+	0.664543i	−0.495493	+	0.0433500i
$236$	−2.83347	−	10.5746i	−0.184443	−	0.688351i
$237$		0			0
$238$	−1.34085	−	7.60436i	−0.0869147	−	0.492918i
$239$	−2.59537	−	0.227066i	−0.167881	−	0.0146877i	0.00290540	−	0.999996i	$-0.499075\pi$
$239$	−2.59537	−	0.227066i	−0.167881	−	0.0146877i	−0.170786	+	0.985308i	$0.554631\pi$
$240$		0			0
$241$	2.75647	−	5.91126i	0.177560	−	0.380778i	−0.797305	−	0.603577i	$-0.793742\pi$
$241$	2.75647	−	5.91126i	0.177560	−	0.380778i	0.974864	+	0.222799i	$0.0715194\pi$
$242$	1.28555	−	14.6940i	0.0826386	−	0.944563i
$243$		0			0
$244$	4.14131	+	2.89978i	0.265120	+	0.185639i
$245$	12.3546	−	3.31040i	0.789304	−	0.211493i
$246$		0			0
$247$	2.20324	−	6.05335i	0.140189	−	0.385166i
$248$	1.35043	−	0.779669i	0.0857522	−	0.0495090i
$249$		0			0
$250$	−2.79019	−	3.32522i	−0.176467	−	0.210306i
$251$	−12.0566	−	3.23057i	−0.761008	−	0.203911i	−0.142613	−	0.989779i	$-0.545550\pi$
$251$	−12.0566	−	3.23057i	−0.761008	−	0.203911i	−0.618395	+	0.785867i	$0.712217\pi$
$252$		0			0
$253$	21.4293	+	21.4293i	1.34725	+	1.34725i
$254$	−7.19673	−	10.2780i	−0.451563	−	0.644899i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	8.51391	+	18.2581i	0.531083	+	1.13891i	0.970605	+	0.240679i	$0.0773703\pi$
$257$	8.51391	+	18.2581i	0.531083	+	1.13891i	−0.439521	+	0.898232i	$0.644852\pi$
$258$		0			0
$259$	0.738938	+	9.81065i	0.0459154	+	0.609604i
$260$		−	14.1589i		−	0.878099i
$261$		0			0
$262$	7.03789	+	19.3364i	0.434802	+	1.19461i
$263$	−2.54147	−	2.13255i	−0.156714	−	0.131499i	0.561059	−	0.827776i	$-0.310394\pi$
$263$	−2.54147	−	2.13255i	−0.156714	−	0.131499i	−0.717773	+	0.696277i	$0.754838\pi$
$264$		0			0
$265$	26.4382	−	26.4382i	1.62409	−	1.62409i
$266$	2.11435	+	0.372818i	0.129639	+	0.0228589i
$267$		0			0
$268$	10.1579	−	8.52351i	0.620494	−	0.520656i
$269$	−6.38782	−	3.68801i	−0.389472	−	0.224862i	0.292459	−	0.956278i	$-0.405526\pi$
$269$	−6.38782	−	3.68801i	−0.389472	−	0.224862i	−0.681931	+	0.731416i	$0.738860\pi$
$270$		0			0
$271$	−11.6576	−	4.24302i	−0.708148	−	0.257745i	−0.0372624	−	0.999306i	$-0.511864\pi$
$271$	−11.6576	−	4.24302i	−0.708148	−	0.257745i	−0.670886	+	0.741561i	$0.734086\pi$
$272$	0.416085	+	4.75587i	0.0252289	+	0.288367i
$273$		0			0
$274$	0.378720	−	0.540868i	0.0228793	−	0.0326751i
$275$	−17.5517	+	3.09484i	−1.05841	+	0.186626i
$276$		0			0
$277$	18.4132	+	8.58623i	1.10634	+	0.515897i	0.887939	−	0.459961i	$-0.152137\pi$
$277$	18.4132	+	8.58623i	1.10634	+	0.515897i	0.218405	+	0.975858i	$0.429915\pi$
$278$	5.82548	+	2.71647i	0.349389	+	0.162923i
$279$		0			0
$280$	4.64727	−	0.819438i	0.277727	−	0.0489708i
$281$	12.3074	−	17.5767i	0.734195	−	1.04854i	−0.262308	−	0.964984i	$-0.584484\pi$
$281$	12.3074	−	17.5767i	0.734195	−	1.04854i	0.996503	−	0.0835555i	$-0.0266276\pi$
$282$		0			0
$283$	2.57451	+	29.4268i	0.153039	+	1.74924i	0.553428	+	0.832897i	$0.313319\pi$
$283$	2.57451	+	29.4268i	0.153039	+	1.74924i	−0.400390	+	0.916345i	$0.631125\pi$
$284$	−4.16210	−	1.51488i	−0.246975	−	0.0898916i
$285$		0			0
$286$	21.3270	+	12.3131i	1.26109	+	0.728091i
$287$	−0.301458	+	0.252954i	−0.0177945	+	0.0149314i
$288$		0			0
$289$	5.70348	+	1.00568i	0.335499	+	0.0591574i
$290$	−3.32551	+	3.32551i	−0.195281	+	0.195281i
$291$		0			0
$292$	−12.2305	−	10.2626i	−0.715735	−	0.600573i
$293$	1.49449	+	4.10609i	0.0873092	+	0.239880i	0.975661	−	0.219283i	$-0.0703717\pi$
$293$	1.49449	+	4.10609i	0.0873092	+	0.239880i	−0.888352	+	0.459163i	$0.848149\pi$
$294$		0			0
$295$		−	31.9406i		−	1.85965i
$296$	0.0735290	−	6.08232i	0.00427379	−	0.353528i
$297$		0			0
$298$	−2.84794	−	6.10742i	−0.164976	−	0.353793i
$299$	−27.2351	+	9.91275i	−1.57504	+	0.573269i
$300$		0			0
$301$	−0.334063	−	0.477092i	−0.0192551	−	0.0274991i
$302$	−1.82076	−	1.82076i	−0.104773	−	0.104773i
$303$		0			0
$304$	−1.28217	−	0.343556i	−0.0735373	−	0.0197043i
$305$	9.48116	+	11.2992i	0.542890	+	0.646991i
$306$		0			0
$307$	−8.34340	+	4.81706i	−0.476183	+	0.274924i	−0.718824	−	0.695192i	$-0.755319\pi$
$307$	−8.34340	+	4.81706i	−0.476183	+	0.274924i	0.242642	+	0.970116i	$0.421986\pi$
$308$	−2.80715	+	7.71259i	−0.159952	+	0.439466i
$309$		0			0
$310$	4.39445	−	1.17749i	0.249588	−	0.0668769i
$311$	−0.417620	−	0.292421i	−0.0236811	−	0.0165817i	0.561676	−	0.827357i	$-0.310157\pi$
$311$	−0.417620	−	0.292421i	−0.0236811	−	0.0165817i	−0.585357	+	0.810776i	$0.699046\pi$
$312$		0			0
$313$	−0.445690	+	5.09426i	−0.0251919	+	0.287945i	0.973140	+	0.230213i	$0.0739423\pi$
$313$	−0.445690	+	5.09426i	−0.0251919	+	0.287945i	−0.998332	+	0.0577316i	$0.981613\pi$
$314$	−5.11372	+	10.9664i	−0.288584	+	0.618871i
$315$		0			0
$316$	−6.19286	−	0.541805i	−0.348376	−	0.0304789i
$317$	2.39710	+	13.5947i	0.134635	+	0.763552i	0.975113	+	0.221707i	$0.0711629\pi$
$317$	2.39710	+	13.5947i	0.134635	+	0.763552i	−0.840478	+	0.541845i	$0.817726\pi$
$318$		0			0
$319$	−2.11709	−	7.90107i	−0.118534	−	0.442375i
$320$	−2.90646	+	0.254283i	−0.162476	+	0.0142148i
$321$		0			0
$322$	−4.82979	−	8.36545i	−0.269154	−	0.466188i
$323$	−3.16852	+	5.48804i	−0.176301	+	0.305363i
$324$		0			0
$325$	4.41148	−	16.4639i	0.244705	−	0.913251i
$326$	4.07226	−	23.0949i	0.225542	−	1.27911i
$327$		0			0
$328$	0.199302	−	0.139553i	0.0110046	−	0.00770553i
$329$	−2.71706	+	3.23807i	−0.149796	+	0.178520i
$330$		0			0
$331$	18.1600	−	8.46816i	0.998165	−	0.465452i	0.146315	−	0.989238i	$-0.453259\pi$
$331$	18.1600	−	8.46816i	0.998165	−	0.465452i	0.851850	+	0.523786i	$0.175481\pi$
$332$	13.4435			0.737809
$333$		0			0
$334$	−15.2014			−0.831786
$335$	35.0629	−	16.3501i	1.91569	−	0.893300i
$336$		0			0
$337$	−3.90675	+	4.65588i	−0.212814	+	0.253622i	−0.861882	−	0.507108i	$-0.830714\pi$
$337$	−3.90675	+	4.65588i	−0.212814	+	0.253622i	0.649068	+	0.760730i	$0.275159\pi$
$338$	−8.64330	+	6.05211i	−0.470134	+	0.329191i
$339$		0			0
$340$	−2.41867	+	13.7170i	−0.131171	+	0.743907i
$341$	−2.04798	+	7.64317i	−0.110904	+	0.413901i
$342$		0			0
$343$	9.20634	−	15.9459i	0.497096	−	0.860995i
$344$	0.180045	+	0.311848i	0.00970740	+	0.0168137i
$345$		0			0
$346$	−18.4371	+	1.61303i	−0.991182	+	0.0867172i
$347$	−7.39699	−	27.6059i	−0.397091	−	1.48196i	−0.818189	−	0.574949i	$-0.805022\pi$
$347$	−7.39699	−	27.6059i	−0.397091	−	1.48196i	0.421098	−	0.907015i	$-0.361645\pi$
$348$		0			0
$349$	−5.25989	−	29.8303i	−0.281555	−	1.59678i	−0.717336	−	0.696727i	$-0.754639\pi$
$349$	−5.25989	−	29.8303i	−0.281555	−	1.59678i	0.435781	−	0.900053i	$-0.356472\pi$
$350$	5.65911	+	0.495108i	0.302492	+	0.0264646i
$351$		0			0
$352$	2.14456	−	4.59902i	0.114305	−	0.245128i
$353$	−0.356290	+	4.07241i	−0.0189634	+	0.216752i	0.980800	+	0.195015i	$0.0624754\pi$
$353$	−0.356290	+	4.07241i	−0.0189634	+	0.216752i	−0.999764	+	0.0217378i	$0.993080\pi$
$354$		0			0
$355$	−10.5855	−	7.41206i	−0.561821	−	0.393391i
$356$	16.1167	−	4.31845i	0.854182	−	0.228877i
$357$		0			0
$358$	4.19966	−	11.5385i	0.221959	−	0.609828i
$359$	−6.33070	+	3.65503i	−0.334121	+	0.192905i	−0.657669	−	0.753307i	$-0.728458\pi$
$359$	−6.33070	+	3.65503i	−0.334121	+	0.192905i	0.323548	+	0.946212i	$0.395124\pi$
$360$		0			0
$361$	11.0804	+	13.2051i	0.583178	+	0.695005i
$362$	14.9239	+	3.99884i	0.784382	+	0.210175i
$363$		0			0
$364$	−5.55034	−	5.55034i	−0.290917	−	0.290917i
$365$	−26.7179	−	38.1571i	−1.39848	−	1.99723i
$366$		0			0
$367$	32.6491	−	11.8833i	1.70427	−	0.620303i	0.707969	−	0.706244i	$-0.249612\pi$
$367$	32.6491	−	11.8833i	1.70427	−	0.620303i	0.996300	+	0.0859407i	$0.0273896\pi$
$368$	2.52395	+	5.41264i	0.131570	+	0.282153i
$369$		0			0
$370$	4.80011	−	17.0854i	0.249546	−	0.888227i
$371$		−	20.7277i		−	1.07613i
$372$		0			0
$373$	−2.93048	−	8.05144i	−0.151735	−	0.416888i	0.840415	−	0.541943i	$-0.182311\pi$
$373$	−2.93048	−	8.05144i	−0.151735	−	0.416888i	−0.992150	+	0.125056i	$0.960089\pi$
$374$	−18.5579	−	15.5719i	−0.959607	−	0.805206i
$375$		0			0
$376$	1.84795	−	1.84795i	0.0953010	−	0.0953010i
$377$	7.70396	+	1.35842i	0.396774	+	0.0699619i
$378$		0			0
$379$	−16.1668	+	13.5656i	−0.830433	+	0.696816i	−0.955390	−	0.295346i	$-0.904565\pi$
$379$	−16.1668	+	13.5656i	−0.830433	+	0.696816i	0.124957	+	0.992162i	$0.460121\pi$
$380$	−3.35392	−	1.93638i	−0.172052	−	0.0993344i
$381$		0			0
$382$	−19.8008	−	7.20689i	−1.01310	−	0.368737i
$383$	1.68291	+	19.2357i	0.0859925	+	0.982898i	0.909530	+	0.415637i	$0.136441\pi$
$383$	1.68291	+	19.2357i	0.0859925	+	0.982898i	−0.823538	+	0.567261i	$0.808003\pi$
$384$		0			0
$385$	−13.7349	+	19.6155i	−0.699997	+	0.999700i
$386$	−14.5252	+	2.56118i	−0.739312	+	0.130361i
$387$		0			0
$388$	4.52823	+	2.11155i	0.229886	+	0.107198i
$389$	3.15735	+	1.47230i	0.160084	+	0.0746483i	0.501009	−	0.865442i	$-0.332962\pi$
$389$	3.15735	+	1.47230i	0.160084	+	0.0746483i	−0.340925	+	0.940091i	$0.610740\pi$
$390$		0			0
$391$	28.0783	−	4.95096i	1.41998	−	0.250381i
$392$	−2.51451	+	3.59110i	−0.127002	+	0.181378i
$393$		0			0
$394$	−0.736384	−	8.41691i	−0.0370985	−	0.424038i
$395$	−17.0433	−	6.20325i	−0.857542	−	0.312120i
$396$		0			0
$397$	22.7382	+	13.1279i	1.14120	+	0.658872i	0.946727	−	0.322036i	$-0.104367\pi$
$397$	22.7382	+	13.1279i	1.14120	+	0.658872i	0.194472	+	0.980908i	$0.437701\pi$
$398$	12.5437	−	10.5254i	0.628757	−	0.527590i
$399$		0			0
$400$	−3.45884	−	0.609886i	−0.172942	−	0.0304943i
$401$	19.6576	−	19.6576i	0.981656	−	0.981656i	−0.0181788	−	0.999835i	$-0.505787\pi$
$401$	19.6576	−	19.6576i	0.981656	−	0.981656i	0.999835	+	0.0181788i	$0.00578680\pi$
$402$		0			0
$403$	−5.79701	−	4.86427i	−0.288769	−	0.242306i
$404$	1.11502	+	3.06350i	0.0554744	+	0.152415i
$405$		0			0
$406$			2.60722i			0.129394i
$407$	21.5606	+	22.0883i	1.06872	+	1.09488i
$408$		0			0
$409$	−8.72572	−	18.7124i	−0.431459	−	0.925267i	−0.995065	−	0.0992232i	$-0.968364\pi$
$409$	−8.72572	−	18.7124i	−0.431459	−	0.925267i	0.563606	−	0.826044i	$-0.309414\pi$
$410$	0.667044	−	0.242784i	0.0329430	−	0.0119903i
$411$		0			0
$412$	−2.25450	−	3.21975i	−0.111071	−	0.158626i
$413$	−12.5208	−	12.5208i	−0.616109	−	0.616109i
$414$		0			0
$415$	37.8859	+	10.1515i	1.85974	+	0.498317i
$416$	3.11944	+	3.71761i	0.152943	+	0.182271i
$417$		0			0
$418$	5.83339	−	3.36791i	0.285320	−	0.164730i
$419$	−7.63490	+	20.9767i	−0.372989	+	1.02478i	0.601210	+	0.799091i	$0.294686\pi$
$419$	−7.63490	+	20.9767i	−0.372989	+	1.02478i	−0.974199	+	0.225689i	$0.927537\pi$
$420$		0			0
$421$	−23.7537	+	6.36477i	−1.15768	+	0.310200i	−0.786040	−	0.618176i	$-0.787872\pi$
$421$	−23.7537	+	6.36477i	−1.15768	+	0.310200i	−0.371643	+	0.928376i	$0.621205\pi$
$422$	−1.13919	−	0.797667i	−0.0554547	−	0.0388298i
$423$		0			0
$424$	−1.11692	+	12.7665i	−0.0542424	+	0.619994i
$425$	−7.08619	+	15.1964i	−0.343731	+	0.737133i
$426$		0			0
$427$	8.14597	+	0.712680i	0.394211	+	0.0344890i
$428$	−0.0287842	−	0.163243i	−0.00139134	−	0.00789066i
$429$		0			0
$430$	0.271912	+	1.01479i	0.0131128	+	0.0489376i
$431$	−10.7814	+	0.943252i	−0.519323	+	0.0454349i	−0.343804	−	0.939041i	$-0.611716\pi$
$431$	−10.7814	+	0.943252i	−0.519323	+	0.0454349i	−0.175518	+	0.984476i	$0.556160\pi$
$432$		0			0
$433$	−10.5953	−	18.3517i	−0.509180	−	0.881926i	−0.999943	−	0.0106328i	$-0.996615\pi$
$433$	−10.5953	−	18.3517i	−0.509180	−	0.881926i	0.490763	−	0.871293i	$-0.336718\pi$
$434$	1.26106	−	2.18422i	0.0605328	−	0.104846i
$435$		0			0
$436$	0.00509039	−	0.0189976i	0.000243786	−	0.000909820i
$437$	−1.37659	+	7.80702i	−0.0658512	+	0.373460i
$438$		0			0
$439$	12.3985	−	8.68152i	0.591748	−	0.414347i	−0.238980	−	0.971024i	$-0.576813\pi$
$439$	12.3985	−	8.68152i	0.591748	−	0.414347i	0.830728	+	0.556678i	$0.187924\pi$
$440$	9.51651	−	11.3413i	0.453682	−	0.540677i
$441$		0			0
$442$	20.9977	−	9.79138i	0.998758	−	0.465728i
$443$	−23.2295			−1.10367			−0.551834	−	0.833954i	$-0.686072\pi$
$443$	−23.2295			−1.10367			−0.551834	+	0.833954i	$0.686072\pi$
$444$		0			0
$445$	48.6802			2.30766
$446$	9.08190	−	4.23496i	0.430040	−	0.200531i
$447$		0			0
$448$	−1.03966	+	1.23902i	−0.0491195	+	0.0585383i
$449$	−7.51318	+	5.26079i	−0.354569	+	0.248272i	−0.737267	−	0.675602i	$-0.763884\pi$
$449$	−7.51318	+	5.26079i	−0.354569	+	0.248272i	0.382698	+	0.923874i	$0.374995\pi$
$450$		0			0
$451$	−0.214391	+	1.21587i	−0.0100953	+	0.0572533i
$452$	−4.53149	+	16.9118i	−0.213144	+	0.795462i
$453$		0			0
$454$	−10.2731	+	17.7935i	−0.482141	+	0.835092i
$455$	−11.4505	−	19.8329i	−0.536809	−	0.929781i
$456$		0			0
$457$	−39.0925	+	3.42015i	−1.82867	+	0.159988i	−0.948934	−	0.315476i	$-0.897836\pi$
$457$	−39.0925	+	3.42015i	−1.82867	+	0.159988i	−0.879735	+	0.475464i	$0.842280\pi$
$458$	4.84375	+	18.0771i	0.226334	+	0.844688i
$459$		0			0
$460$	3.02569	+	17.1595i	0.141073	+	0.800067i
$461$	32.1580	+	2.81346i	1.49775	+	0.131036i	0.806350	−	0.591439i	$-0.201440\pi$
$461$	32.1580	+	2.81346i	1.49775	+	0.131036i	0.691397	+	0.722475i	$0.256995\pi$
$462$		0			0
$463$	−16.9439	+	36.3364i	−0.787452	+	1.68870i	−0.0643770	+	0.997926i	$0.520506\pi$
$463$	−16.9439	+	36.3364i	−0.787452	+	1.68870i	−0.723075	+	0.690770i	$0.757272\pi$
$464$	0.140491	−	1.60582i	0.00652214	−	0.0745483i
$465$		0			0
$466$	4.08026	+	2.85703i	0.189014	+	0.132349i
$467$	15.0218	−	4.02509i	0.695127	−	0.186259i	0.106080	−	0.994358i	$-0.466170\pi$
$467$	15.0218	−	4.02509i	0.695127	−	0.186259i	0.589047	+	0.808099i	$0.299503\pi$
$468$		0			0
$469$	7.33547	−	20.1540i	0.338720	−	0.930627i
$470$	6.60325	−	3.81239i	0.304585	−	0.175852i
$471$		0			0
$472$	7.03703	+	8.38641i	0.323906	+	0.386016i
$473$	−1.76500	−	0.472931i	−0.0811549	−	0.0217454i
$474$		0			0
$475$	−3.29659	−	3.29659i	−0.151258	−	0.151258i
$476$	4.42897	+	6.32522i	0.203001	+	0.289916i
$477$		0			0
$478$	2.44817	−	0.891061i	0.111977	−	0.0407562i
$479$	0.990182	+	2.12345i	0.0452426	+	0.0970230i	0.927630	−	0.373501i	$-0.121843\pi$
$479$	0.990182	+	2.12345i	0.0452426	+	0.0970230i	−0.882387	+	0.470524i	$0.844065\pi$
$480$		0			0
$481$	−27.8594	+	9.76024i	−1.27028	+	0.445029i
$482$			6.52235i			0.297085i
$483$		0			0
$484$	5.04482	+	13.8605i	0.229310	+	0.630025i
$485$	11.1668	+	9.37003i	0.507057	+	0.425471i
$486$		0			0
$487$	−9.50218	+	9.50218i	−0.430585	+	0.430585i	−0.888827	−	0.458243i	$-0.848479\pi$
$487$	−9.50218	+	9.50218i	−0.430585	+	0.430585i	0.458243	+	0.888827i	$0.348479\pi$
$488$	−4.97880	−	0.877897i	−0.225380	−	0.0397405i
$489$		0			0
$490$	−9.79800	+	8.22150i	−0.442629	+	0.371410i
$491$	−33.6867	−	19.4490i	−1.52026	−	0.877723i	−0.999715	−	0.0238901i	$-0.992395\pi$
$491$	−33.6867	−	19.4490i	−1.52026	−	0.877723i	−0.520547	−	0.853833i	$-0.674272\pi$
$492$		0			0
$493$	−7.23144	−	2.63203i	−0.325688	−	0.118541i
$494$	0.561444	+	6.41733i	0.0252606	+	0.288729i
$495$		0			0
$496$	−0.894399	+	1.27733i	−0.0401597	+	0.0573540i
$497$	−7.05511	+	1.24401i	−0.316465	+	0.0558013i
$498$		0			0
$499$	36.1168	+	16.8415i	1.61681	+	0.753931i	0.999463	−	0.0327603i	$-0.0104298\pi$
$499$	36.1168	+	16.8415i	1.61681	+	0.753931i	0.617347	+	0.786691i	$0.288208\pi$
$500$	3.93407	+	1.83449i	0.175937	+	0.0820408i
$501$		0			0
$502$	12.2923	−	2.16747i	0.548633	−	0.0967388i
$503$	7.90819	−	11.2941i	0.352609	−	0.503577i	−0.603191	−	0.797597i	$-0.706104\pi$
$503$	7.90819	−	11.2941i	0.352609	−	0.503577i	0.955799	+	0.294020i	$0.0949931\pi$
$504$		0			0
$505$	0.828989	+	9.47538i	0.0368895	+	0.421649i
$506$	−28.4779	−	10.3651i	−1.26600	−	0.460786i
$507$		0			0
$508$	10.8661	+	6.27356i	0.482106	+	0.278344i
$509$	−20.8088	+	17.4607i	−0.922336	+	0.773932i	−0.974426	−	0.224711i	$-0.927856\pi$
$509$	−20.8088	+	17.4607i	−0.922336	+	0.773932i	0.0520897	+	0.998642i	$0.483412\pi$
$510$		0			0
$511$	−25.4312	−	4.48420i	−1.12501	−	0.198370i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−15.4324	−	12.9494i	−0.680696	−	0.571172i
$515$	−3.92221	−	10.7762i	−0.172833	−	0.474855i
$516$		0			0
$517$			13.2616i			0.583244i
$518$	−4.81587	−	8.57918i	−0.211597	−	0.376947i
$519$		0			0
$520$	5.98382	+	12.8323i	0.262408	+	0.562736i
$521$	−24.7678	+	9.01472i	−1.08509	+	0.394942i	−0.821802	−	0.569774i	$-0.807031\pi$
$521$	−24.7678	+	9.01472i	−1.08509	+	0.394942i	−0.263293	+	0.964716i	$0.584809\pi$
$522$		0			0
$523$	−19.2707	−	27.5214i	−0.842649	−	1.20343i	−0.977158	−	0.212515i	$-0.931835\pi$
$523$	−19.2707	−	27.5214i	−0.842649	−	1.20343i	0.134509	−	0.990912i	$-0.457054\pi$
$524$	−14.5504	−	14.5504i	−0.635638	−	0.635638i
$525$		0			0
$526$	3.20461	+	0.858672i	0.139728	+	0.0374399i
$527$	4.78513	+	5.70270i	0.208444	+	0.248413i
$528$		0			0
$529$	10.9699	−	6.33349i	0.476953	−	0.275369i
$530$	−12.7879	+	35.1344i	−0.555470	+	1.52614i
$531$		0			0
$532$	−2.07381	+	0.555677i	−0.0899113	+	0.0240916i
$533$	−0.967213	−	0.677250i	−0.0418946	−	0.0293349i
$534$		0			0
$535$	0.0421503	−	0.481780i	0.00182231	−	0.0208292i
$536$	−5.60401	+	12.0178i	−0.242056	+	0.519092i
$537$		0			0
$538$	7.34795	+	0.642862i	0.316793	+	0.0277158i
$539$	−3.86298	−	21.9080i	−0.166390	−	0.943646i
$540$		0			0
$541$	0.715820	+	2.67148i	0.0307755	+	0.114856i	0.979605	−	0.200933i	$-0.0643975\pi$
$541$	0.715820	+	2.67148i	0.0307755	+	0.114856i	−0.948829	+	0.315789i	$0.897731\pi$
$542$	12.3585	−	1.08123i	0.530845	−	0.0464429i
$543$		0			0
$544$	−2.38702	−	4.13444i	−0.102343	−	0.177263i
$545$	0.0286910	−	0.0496943i	0.00122899	−	0.00212867i
$546$		0			0
$547$	−11.6111	+	43.3333i	−0.496456	+	1.85280i	0.0252634	+	0.999681i	$0.491958\pi$
$547$	−11.6111	+	43.3333i	−0.496456	+	1.85280i	−0.521719	+	0.853117i	$0.674709\pi$
$548$	−0.114656	+	0.650247i	−0.00489787	+	0.0277772i
$549$		0			0
$550$	14.5993	−	10.2225i	0.622517	−	0.435891i
$551$	1.37537	−	1.63911i	0.0585929	−	0.0698283i
$552$		0			0
$553$	−9.11272	+	4.24933i	−0.387512	+	0.180700i
$554$	−20.3168			−0.863176
$555$		0			0
$556$	−6.42771			−0.272596
$557$	29.1315	−	13.5843i	1.23434	−	0.575584i	0.307685	−	0.951488i	$-0.400446\pi$
$557$	29.1315	−	13.5843i	1.23434	−	0.575584i	0.926658	+	0.375905i	$0.122668\pi$
$558$		0			0
$559$	1.12328	−	1.33868i	0.0475098	−	0.0566200i
$560$	−3.86554	+	2.70668i	−0.163349	+	0.114378i
$561$		0			0
$562$	−3.72601	+	21.1312i	−0.157172	+	0.891368i
$563$	3.24461	−	12.1090i	0.136744	−	0.510336i	−0.863241	−	0.504793i	$-0.831569\pi$
$563$	3.24461	−	12.1090i	0.136744	−	0.510336i	0.999985	−	0.00554292i	$-0.00176438\pi$
$564$		0			0
$565$	−25.5409	+	44.2381i	−1.07451	+	1.86111i
$566$	−14.7696	−	25.5817i	−0.620813	−	1.07528i
$567$		0			0
$568$	4.41236	−	0.386032i	0.185139	−	0.0161975i
$569$	8.67086	+	32.3601i	0.363501	+	1.35661i	0.869441	+	0.494037i	$0.164479\pi$
$569$	8.67086	+	32.3601i	0.363501	+	1.35661i	−0.505940	+	0.862569i	$0.668854\pi$
$570$		0			0
$571$	−5.58341	−	31.6651i	−0.233658	−	1.32514i	−0.845421	−	0.534101i	$-0.820650\pi$
$571$	−5.58341	−	31.6651i	−0.233658	−	1.32514i	0.611762	−	0.791042i	$-0.290461\pi$
$572$	−24.5326	−	2.14632i	−1.02576	−	0.0897422i
$573$		0			0
$574$	0.166311	−	0.356656i	0.00694170	−	0.0148865i
$575$	−1.82813	+	20.8957i	−0.0762384	+	0.871409i
$576$		0			0
$577$	27.8775	+	19.5200i	1.16056	+	0.812630i	0.985121	−	0.171861i	$-0.0549780\pi$
$577$	27.8775	+	19.5200i	1.16056	+	0.812630i	0.175435	+	0.984491i	$0.443867\pi$
$578$	−5.59412	+	1.49894i	−0.232685	+	0.0623477i
$579$		0			0
$580$	1.60852	−	4.41936i	0.0667900	−	0.183504i
$581$	18.8308	−	10.8720i	0.781233	−	0.451045i
$582$		0			0
$583$	−41.8006	−	49.8161i	−1.73121	−	2.06317i
$584$	15.4217	+	4.13225i	0.638157	+	0.170994i
$585$		0			0
$586$	−3.08978	−	3.08978i	−0.127638	−	0.127638i
$587$	18.7461	+	26.7722i	0.773733	+	1.10500i	0.991640	+	0.129035i	$0.0411881\pi$
$587$	18.7461	+	26.7722i	0.773733	+	1.10500i	−0.217907	+	0.975969i	$0.569923\pi$
$588$		0			0
$589$	−1.94503	+	0.707934i	−0.0801437	+	0.0291699i
$590$	13.4987	+	28.9480i	0.555731	+	1.19177i
$591$		0			0
$592$	2.50386	+	5.54353i	0.102908	+	0.227838i
$593$		−	20.3583i		−	0.836015i	−0.908443	−	0.418008i	$-0.862728\pi$
$593$		−	20.3583i		−	0.836015i	0.908443	−	0.418008i	$-0.137272\pi$
$594$		0			0
$595$	7.70520	+	21.1699i	0.315882	+	0.867880i
$596$	5.16221	+	4.33161i	0.211452	+	0.177430i
$597$		0			0
$598$	20.4940	−	20.4940i	0.838064	−	0.838064i
$599$	30.3286	+	5.34774i	1.23919	+	0.218503i	0.754569	−	0.656221i	$-0.227846\pi$
$599$	30.3286	+	5.34774i	1.23919	+	0.218503i	0.484622	+	0.874724i	$0.338957\pi$
$600$		0			0
$601$	−30.1913	+	25.3335i	−1.23153	+	1.03338i	−0.233391	+	0.972383i	$0.574982\pi$
$601$	−30.1913	+	25.3335i	−1.23153	+	1.03338i	−0.998138	+	0.0609928i	$0.980573\pi$
$602$	0.504392	+	0.291211i	0.0205575	+	0.0118689i
$603$		0			0
$604$	2.41965	+	0.880682i	0.0984543	+	0.0358344i
$605$	3.75069	+	42.8706i	0.152487	+	1.74294i
$606$		0			0
$607$	−19.4246	+	27.7412i	−0.788421	+	1.12598i	0.200812	+	0.979630i	$0.435642\pi$
$607$	−19.4246	+	27.7412i	−0.788421	+	1.12598i	−0.989233	+	0.146351i	$0.953247\pi$
$608$	1.30723	−	0.230500i	0.0530152	−	0.00934801i
$609$		0			0
$610$	−13.3681	−	6.23365i	−0.541259	−	0.252393i
$611$	−11.4945	−	5.35999i	−0.465019	−	0.216842i
$612$		0			0
$613$	−38.2246	+	6.74002i	−1.54388	+	0.272227i	−0.879766	−	0.475407i	$-0.842301\pi$
$613$	−38.2246	+	6.74002i	−1.54388	+	0.272227i	−0.664111	+	0.747634i	$0.731190\pi$
$614$	5.52591	−	7.89181i	0.223007	−	0.318488i
$615$		0			0
$616$	−0.715337	−	8.17634i	−0.0288217	−	0.329434i
$617$	34.4461	+	12.5374i	1.38675	+	0.504735i	0.924217	−	0.381868i	$-0.124719\pi$
$617$	34.4461	+	12.5374i	1.38675	+	0.504735i	0.462532	+	0.886603i	$0.346941\pi$
$618$		0			0
$619$	5.88562	+	3.39806i	0.236563	+	0.136580i	0.613596	−	0.789620i	$-0.289722\pi$
$619$	5.88562	+	3.39806i	0.236563	+	0.136580i	−0.377033	+	0.926200i	$0.623056\pi$
$620$	−3.48510	+	2.92434i	−0.139965	+	0.117444i
$621$		0			0
$622$	0.502075	+	0.0885293i	0.0201314	+	0.00354970i
$623$	19.0828	−	19.0828i	0.764536	−	0.764536i
$624$		0			0
$625$	23.1540	+	19.4286i	0.926162	+	0.777142i
$626$	−1.74900	−	4.80533i	−0.0699039	−	0.192059i
$627$		0			0
$628$		−	12.1001i		−	0.482847i
$629$	28.6570	−	4.69656i	1.14263	−	0.187264i
$630$		0			0
$631$	−4.22611	−	9.06291i	−0.168239	−	0.360789i	0.804054	−	0.594556i	$-0.202672\pi$
$631$	−4.22611	−	9.06291i	−0.168239	−	0.360789i	−0.972293	+	0.233768i	$0.924895\pi$
$632$	5.84162	−	2.12617i	0.232367	−	0.0845747i
$633$		0			0
$634$	−7.91787	−	11.3079i	−0.314459	−	0.449093i
$635$	25.8851	+	25.8851i	1.02722	+	1.02722i
$636$		0			0
$637$	20.5502	+	5.50641i	0.814229	+	0.218172i
$638$	5.25787	+	6.26608i	0.208161	+	0.248077i
$639$		0			0
$640$	2.52669	−	1.45878i	0.0998761	−	0.0576635i
$641$	5.22942	−	14.3677i	0.206550	−	0.567491i	−0.792555	−	0.609801i	$-0.791249\pi$
$641$	5.22942	−	14.3677i	0.206550	−	0.567491i	0.999105	+	0.0423099i	$0.0134717\pi$
$642$		0			0
$643$	5.99376	−	1.60602i	0.236371	−	0.0633353i	−0.138689	−	0.990336i	$-0.544289\pi$
$643$	5.99376	−	1.60602i	0.236371	−	0.0633353i	0.375060	+	0.927001i	$0.377622\pi$
$644$	7.91267	+	5.54051i	0.311803	+	0.218327i
$645$		0			0
$646$	0.552310	−	6.31293i	0.0217303	−	0.248379i
$647$	−13.3571	+	28.6445i	−0.525123	+	1.12613i	0.447616	+	0.894226i	$0.352273\pi$
$647$	−13.3571	+	28.6445i	−0.525123	+	1.12613i	−0.972739	+	0.231904i	$0.925505\pi$
$648$		0			0
$649$	−55.3421	−	4.84180i	−2.17237	−	0.190057i
$650$	2.95977	+	16.7857i	0.116092	+	0.658389i
$651$		0			0
$652$	6.06962	+	22.6521i	0.237705	+	0.887126i
$653$	−39.2711	+	3.43578i	−1.53680	+	0.134452i	−0.823868	−	0.566782i	$-0.808188\pi$
$653$	−39.2711	+	3.43578i	−1.53680	+	0.134452i	−0.712931	+	0.701234i	$0.752633\pi$
$654$		0			0
$655$	−30.0180	−	51.9927i	−1.17290	−	2.03152i
$656$	−0.121652	+	0.210707i	−0.00474970	+	0.00822672i
$657$		0			0
$658$	1.09403	−	4.08296i	0.0426496	−	0.159170i
$659$	0.299343	−	1.69766i	0.0116608	−	0.0661314i	−0.978422	−	0.206616i	$-0.933755\pi$
$659$	0.299343	−	1.69766i	0.0116608	−	0.0661314i	0.990083	+	0.140485i	$0.0448660\pi$
$660$		0			0
$661$	21.9741	−	15.3864i	0.854694	−	0.598463i	−0.0619899	−	0.998077i	$-0.519745\pi$
$661$	21.9741	−	15.3864i	0.854694	−	0.598463i	0.916684	+	0.399614i	$0.130856\pi$
$662$	−12.8798	+	15.3495i	−0.500587	+	0.596576i
$663$		0			0
$664$	−12.1840	+	5.68147i	−0.472829	+	0.220484i
$665$	−6.26393			−0.242905
$666$		0			0
$667$	−9.62689			−0.372755
$668$	13.7772	−	6.42441i	0.533055	−	0.248568i
$669$		0			0
$670$	−24.8679	+	29.6364i	−0.960731	+	1.14495i
$671$	21.0149	−	14.7148i	0.811271	−	0.568058i
$672$		0			0
$673$	4.11101	−	23.3147i	0.158468	−	0.898715i	−0.797079	−	0.603875i	$-0.793622\pi$
$673$	4.11101	−	23.3147i	0.158468	−	0.898715i	0.955547	−	0.294840i	$-0.0952664\pi$
$674$	1.57306	−	5.87072i	0.0605918	−	0.226132i
$675$		0			0
$676$	5.27576	−	9.13789i	0.202914	−	0.351457i
$677$	−8.65196	−	14.9856i	−0.332522	−	0.575945i	0.650484	−	0.759520i	$-0.274566\pi$
$677$	−8.65196	−	14.9856i	−0.332522	−	0.575945i	−0.983006	+	0.183575i	$0.941233\pi$
$678$		0			0
$679$	8.05049	−	0.704327i	0.308950	−	0.0270296i
$680$	−3.60498	−	13.4540i	−0.138245	−	0.515936i
$681$		0			0
$682$	−1.37404	−	7.79258i	−0.0526148	−	0.298393i
$683$	−31.0545	−	2.71692i	−1.18827	−	0.103960i	−0.524176	−	0.851610i	$-0.675627\pi$
$683$	−31.0545	−	2.71692i	−1.18827	−	0.103960i	−0.664093	+	0.747650i	$0.731182\pi$
$684$		0			0
$685$	−0.814135	+	1.74592i	−0.0311065	+	0.0667081i
$686$	−1.60477	+	18.3426i	−0.0612705	+	0.700325i
$687$		0			0
$688$	−0.294969	−	0.206540i	−0.0112456	−	0.00787425i
$689$	60.0730	−	16.0965i	2.28860	−	0.613229i
$690$		0			0
$691$	−2.38710	+	6.55851i	−0.0908097	+	0.249498i	−0.976780	−	0.214244i	$-0.931271\pi$
$691$	−2.38710	+	6.55851i	−0.0908097	+	0.249498i	0.885970	+	0.463742i	$0.153493\pi$
$692$	16.0279	−	9.25374i	0.609291	−	0.351774i
$693$		0			0
$694$	18.3707	+	21.8934i	0.697343	+	0.831061i
$695$	−18.1143	−	4.85370i	−0.687113	−	0.184111i
$696$		0			0
$697$	0.821333	+	0.821333i	0.0311102	+	0.0311102i
$698$	17.3739	+	24.8125i	0.657612	+	0.939167i
$699$		0			0
$700$	−5.33814	+	1.94292i	−0.201763	+	0.0734356i
$701$	−2.00158	−	4.29239i	−0.0755985	−	0.162121i	0.864876	−	0.501985i	$-0.167397\pi$
$701$	−2.00158	−	4.29239i	−0.0755985	−	0.162121i	−0.940475	+	0.339864i	$0.889619\pi$
$702$		0			0
$703$	−1.49809	+	7.93404i	−0.0565017	+	0.299238i
$704$			5.07445i			0.191251i
$705$		0			0
$706$	−1.39817	−	3.84143i	−0.0526207	−	0.144574i
$707$	4.03935	+	3.38941i	0.151915	+	0.127472i
$708$		0			0
$709$	14.3233	−	14.3233i	0.537922	−	0.537922i	−0.384996	−	0.922918i	$-0.625797\pi$
$709$	14.3233	−	14.3233i	0.537922	−	0.537922i	0.922918	+	0.384996i	$0.125797\pi$
$710$	12.7262	+	2.24397i	0.477606	+	0.0842148i
$711$		0			0
$712$	−12.7816	+	10.7250i	−0.479011	+	0.401938i
$713$	8.06499	+	4.65633i	0.302036	+	0.174381i
$714$		0			0
$715$	−67.5158	−	24.5737i	−2.52495	−	0.919006i
$716$	1.07019	+	12.2323i	0.0399947	+	0.457141i
$717$		0			0
$718$	4.19288	−	5.98805i	0.156477	−	0.223472i
$719$	11.3636	−	2.00370i	0.423789	−	0.0747255i	0.0423136	−	0.999104i	$-0.486527\pi$
$719$	11.3636	−	2.00370i	0.423789	−	0.0747255i	0.381476	+	0.924379i	$0.375416\pi$
$720$		0			0
$721$	−5.76181	−	2.68678i	−0.214581	−	0.100061i
$722$	−15.6229	−	7.28510i	−0.581426	−	0.271123i
$723$		0			0
$724$	−15.2156	+	2.68292i	−0.565484	+	0.0997101i
$725$	3.24730	−	4.63763i	0.120602	−	0.172237i
$726$		0			0
$727$	1.01577	+	11.6104i	0.0376730	+	0.430604i	0.991487	+	0.130206i	$0.0415640\pi$
$727$	1.01577	+	11.6104i	0.0376730	+	0.430604i	−0.953814	+	0.300398i	$0.902880\pi$
$728$	7.37600	+	2.68464i	0.273373	+	0.0994995i
$729$		0			0
$730$	40.3405	+	23.2906i	1.49307	+	0.862024i
$731$	−1.31690	+	1.10501i	−0.0487072	+	0.0408702i
$732$		0			0
$733$	3.56789	+	0.629115i	0.131783	+	0.0232369i	0.239151	−	0.970982i	$-0.423131\pi$
$733$	3.56789	+	0.629115i	0.131783	+	0.0232369i	−0.107368	+	0.994219i	$0.534242\pi$
$734$	−24.5680	+	24.5680i	−0.906823	+	0.906823i
$735$		0			0
$736$	−4.57496	−	3.83885i	−0.168635	−	0.141502i
$737$	−23.0140	−	63.2304i	−0.847731	−	2.32912i
$738$		0			0
$739$		−	38.7706i		−	1.42620i	−0.701062	−	0.713101i	$-0.747290\pi$
$739$		−	38.7706i		−	1.42620i	0.701062	−	0.713101i	$-0.252710\pi$
$740$	2.87022	+	17.5132i	0.105511	+	0.643799i
$741$		0			0
$742$	8.75991	+	18.7857i	0.321587	+	0.689644i
$743$	47.3898	−	17.2485i	1.73856	−	0.632785i	0.739382	−	0.673286i	$-0.235118\pi$
$743$	47.3898	−	17.2485i	1.73856	−	0.632785i	0.999179	+	0.0405015i	$0.0128955\pi$
$744$		0			0
$745$	11.2770	+	16.1052i	0.413158	+	0.590050i
$746$	6.05860	+	6.05860i	0.221821	+	0.221821i
$747$		0			0
$748$	23.4002	+	6.27006i	0.855595	+	0.229256i
$749$	−0.172336	−	0.205382i	−0.00629702	−	0.00750450i
$750$		0			0
$751$	26.4974	−	15.2983i	0.966904	−	0.558242i	0.0686129	−	0.997643i	$-0.478143\pi$
$751$	26.4974	−	15.2983i	0.966904	−	0.558242i	0.898291	+	0.439401i	$0.144809\pi$
$752$	−0.893836	+	2.45579i	−0.0325949	+	0.0895536i
$753$		0			0
$754$	−7.55625	+	2.02469i	−0.275182	+	0.0737349i
$755$	6.15393	+	4.30903i	0.223965	+	0.156822i
$756$		0			0
$757$	0.678303	−	7.75304i	0.0246534	−	0.281789i	−0.973854	−	0.227174i	$-0.927051\pi$
$757$	0.678303	−	7.75304i	0.0246534	−	0.281789i	0.998507	−	0.0546150i	$-0.0173931\pi$
$758$	8.91905	−	19.1270i	0.323955	−	0.694723i
$759$		0			0
$760$	3.85803	+	0.337534i	0.139946	+	0.0122436i
$761$	2.71535	+	15.3995i	0.0984315	+	0.558233i	0.993642	+	0.112589i	$0.0359143\pi$
$761$	2.71535	+	15.3995i	0.0984315	+	0.558233i	−0.895210	+	0.445644i	$0.852975\pi$
$762$		0			0
$763$	−0.00823335	−	0.0307273i	−0.000298067	−	0.00111240i
$764$	20.9914	−	1.83651i	0.759441	−	0.0664425i
$765$		0			0
$766$	−9.65459	−	16.7222i	−0.348835	−	0.604199i
$767$	26.5645	−	46.0110i	0.959188	−	1.66136i
$768$		0			0
$769$	5.31036	−	19.8185i	0.191496	−	0.714675i	−0.801650	−	0.597794i	$-0.796044\pi$
$769$	5.31036	−	19.8185i	0.191496	−	0.714675i	0.993146	−	0.116880i	$-0.0372894\pi$
$770$	4.15820	−	23.5823i	0.149851	−	0.849848i
$771$		0			0
$772$	12.0819	−	8.45983i	0.434837	−	0.304476i
$773$	−6.55707	+	7.81442i	−0.235842	+	0.281065i	−0.870964	−	0.491346i	$-0.836505\pi$
$773$	−6.55707	+	7.81442i	−0.235842	+	0.281065i	0.635123	+	0.772411i	$0.280949\pi$
$774$		0			0
$775$	−4.96357	+	2.31455i	−0.178297	+	0.0831412i
$776$	−4.99635			−0.179359
$777$		0			0
$778$	−3.48375			−0.124898
$779$	−0.292701	+	0.136489i	−0.0104871	+	0.00489022i
$780$		0			0
$781$	−14.4472	+	17.2175i	−0.516961	+	0.616091i
$782$	−23.3552	+	16.3535i	−0.835181	+	0.584800i
$783$		0			0
$784$	0.761260	−	4.31732i	0.0271879	−	0.154190i
$785$	9.13705	−	34.0999i	0.326115	−	1.21708i
$786$		0			0
$787$	−3.19833	+	5.53966i	−0.114008	+	0.197468i	−0.917383	−	0.398006i	$-0.869702\pi$
$787$	−3.19833	+	5.53966i	−0.114008	+	0.197468i	0.803375	+	0.595474i	$0.203036\pi$
$788$	4.22453	+	7.31710i	0.150493	+	0.260661i
$789$		0			0
$790$	18.0681	−	1.58075i	0.642834	−	0.0562407i
$791$	7.32937	+	27.3536i	0.260602	+	0.972581i
$792$		0			0
$793$	4.26043	+	24.1621i	0.151292	+	0.858020i
$794$	−26.1560	−	2.28835i	−0.928240	−	0.0812105i
$795$		0			0
$796$	−6.92021	+	14.8404i	−0.245280	+	0.526005i
$797$	1.52293	−	17.4071i	0.0539448	−	0.616592i	−0.920317	−	0.391173i	$-0.872069\pi$
$797$	1.52293	−	17.4071i	0.0539448	−	0.616592i	0.974262	−	0.225419i	$-0.0723751\pi$
$798$		0			0
$799$	10.2201	+	7.15622i	0.361563	+	0.253169i
$800$	3.39252	−	0.909023i	0.119944	−	0.0321388i
$801$		0			0
$802$	−9.50820	+	26.1236i	−0.335746	+	0.922455i
$803$	−70.1633	+	40.5088i	−2.47601	+	1.42952i
$804$		0			0
$805$	18.1154	+	21.5890i	0.638482	+	0.760913i
$806$	7.30960	+	1.95860i	0.257470	+	0.0689888i
$807$		0			0
$808$	−2.30524	−	2.30524i	−0.0810982	−	0.0810982i
$809$	−18.7884	−	26.8327i	−0.660566	−	0.943386i	−0.999996	−	0.00275476i	$-0.999123\pi$
$809$	−18.7884	−	26.8327i	−0.660566	−	0.943386i	0.339430	−	0.940631i	$-0.389766\pi$
$810$		0			0
$811$	−33.8955	+	12.3369i	−1.19023	+	0.433209i	−0.859805	−	0.510623i	$-0.829415\pi$
$811$	−33.8955	+	12.3369i	−1.19023	+	0.433209i	−0.330427	+	0.943832i	$0.607193\pi$
$812$	−1.10186	−	2.36295i	−0.0386677	−	0.0829231i
$813$		0			0
$814$	−28.8755	−	10.9069i	−1.01208	−	0.382286i
$815$			68.4205i			2.39667i
$816$		0			0
$817$	−0.163480	−	0.449157i	−0.00571944	−	0.0157140i
$818$	15.8164	+	13.2715i	0.553006	+	0.464028i
$819$		0			0
$820$	−0.501942	+	0.501942i	−0.0175286	+	0.0175286i
$821$	−30.3066	−	5.34388i	−1.05771	−	0.186503i	−0.382369	−	0.924010i	$-0.624892\pi$
$821$	−30.3066	−	5.34388i	−1.05771	−	0.186503i	−0.675339	+	0.737507i	$0.736003\pi$
$822$		0			0
$823$	16.1425	−	13.5452i	0.562692	−	0.472155i	−0.316520	−	0.948586i	$-0.602514\pi$
$823$	16.1425	−	13.5452i	0.562692	−	0.472155i	0.879212	+	0.476431i	$0.158070\pi$
$824$	3.40399	+	1.96530i	0.118584	+	0.0684644i
$825$		0			0
$826$	16.6392	+	6.05618i	0.578953	+	0.210722i
$827$	0.647818	+	7.40459i	0.0225268	+	0.257483i	0.999104	+	0.0423165i	$0.0134738\pi$
$827$	0.647818	+	7.40459i	0.0225268	+	0.257483i	−0.976577	+	0.215166i	$0.930971\pi$
$828$		0			0
$829$	−20.2748	+	28.9554i	−0.704173	+	1.00566i	0.294575	+	0.955628i	$0.404822\pi$
$829$	−20.2748	+	28.9554i	−0.704173	+	1.00566i	−0.998747	+	0.0500345i	$0.984067\pi$
$830$	−38.6265	+	6.81089i	−1.34074	+	0.236409i
$831$		0			0
$832$	−4.39830	−	2.05096i	−0.152484	−	0.0711043i
$833$	−18.9681	−	8.84499i	−0.657207	−	0.306461i
$834$		0			0
$835$	43.6774	−	7.70151i	1.51152	−	0.266522i
$836$	−3.86350	+	5.51766i	−0.133622	+	0.190832i
$837$		0			0
$838$	−1.94557	−	22.2380i	−0.0672088	−	0.768200i
$839$	−30.8169	−	11.2164i	−1.06392	−	0.387235i	−0.250019	−	0.968241i	$-0.580437\pi$
$839$	−30.8169	−	11.2164i	−1.06392	−	0.387235i	−0.813899	+	0.581006i	$0.802659\pi$
$840$		0			0
$841$	−22.8645	−	13.2008i	−0.788430	−	0.455200i
$842$	18.8383	−	15.8072i	0.649209	−	0.544751i
$843$		0			0
$844$	1.36956	+	0.241491i	0.0471423	+	0.00831246i
$845$	21.7681	−	21.7681i	0.748846	−	0.748846i
$846$		0			0
$847$	18.2757	+	15.3351i	0.627960	+	0.526921i
$848$	−4.38306	−	12.0424i	−0.150515	−	0.413537i
$849$		0			0
$850$		−	16.7674i		−	0.575116i
$851$	31.6777	−	17.7821i	1.08590	−	0.609561i
$852$		0			0
$853$	−13.9738	−	29.9670i	−0.478455	−	1.02605i	−0.986355	−	0.164634i	$-0.947356\pi$
$853$	−13.9738	−	29.9670i	−0.478455	−	1.02605i	0.507900	−	0.861416i	$-0.330422\pi$
$854$	−7.68395	+	2.79673i	−0.262939	+	0.0957021i
$855$		0			0
$856$	0.0950768	+	0.135784i	0.00324966	+	0.00464100i
$857$	−18.7581	−	18.7581i	−0.640764	−	0.640764i	0.309979	−	0.950743i	$-0.399678\pi$
$857$	−18.7581	−	18.7581i	−0.640764	−	0.640764i	−0.950743	+	0.309979i	$0.899678\pi$
$858$		0			0
$859$	26.7333	+	7.16316i	0.912128	+	0.244404i	0.684217	−	0.729278i	$-0.260144\pi$
$859$	26.7333	+	7.16316i	0.912128	+	0.244404i	0.227910	+	0.973682i	$0.426811\pi$
$860$	−0.675305	−	0.804798i	−0.0230277	−	0.0274434i
$861$		0			0
$862$	9.37265	−	5.41130i	0.319234	−	0.184310i
$863$	6.32608	−	17.3808i	0.215342	−	0.591648i	−0.784243	−	0.620454i	$-0.786948\pi$
$863$	6.32608	−	17.3808i	0.215342	−	0.591648i	0.999585	+	0.0288062i	$0.00917057\pi$
$864$		0			0
$865$	52.1569	−	13.9754i	1.77339	−	0.475178i
$866$	17.3584	+	12.1545i	0.589863	+	0.413026i
$867$		0			0
$868$	−0.219817	+	2.51252i	−0.00746108	+	0.0852805i
$869$	−13.3317	+	28.5899i	−0.452246	+	0.969845i
$870$		0			0
$871$	64.1069	+	5.60862i	2.17218	+	0.190041i
$872$	0.00341527	+	0.0193690i	0.000115656	+	0.000655916i
$873$		0			0
$874$	−2.05178	−	7.65734i	−0.0694024	−	0.259013i
$875$	6.99417	−	0.611911i	0.236446	−	0.0206864i
$876$		0			0
$877$	−15.6296	−	27.0713i	−0.527775	−	0.914133i	−0.999476	−	0.0323746i	$-0.989693\pi$
$877$	−15.6296	−	27.0713i	−0.527775	−	0.914133i	0.471701	−	0.881759i	$-0.343640\pi$
$878$	−7.56789	+	13.1080i	−0.255404	+	0.442372i
$879$		0			0
$880$	−3.83183	+	14.3006i	−0.129171	+	0.482073i
$881$	1.46714	−	8.32058i	0.0494293	−	0.280327i	−0.950068	−	0.312044i	$-0.898986\pi$
$881$	1.46714	−	8.32058i	0.0494293	−	0.280327i	0.999497	+	0.0317167i	$0.0100974\pi$
$882$		0			0
$883$	2.96247	−	2.07434i	0.0996950	−	0.0698072i	−0.522666	−	0.852538i	$-0.675062\pi$
$883$	2.96247	−	2.07434i	0.0996950	−	0.0698072i	0.622361	+	0.782730i	$0.286174\pi$
$884$	−14.8923	+	17.7480i	−0.500884	+	0.596930i
$885$		0			0
$886$	21.0531	−	9.81722i	0.707293	−	0.329816i
$887$	10.4178			0.349794			0.174897	−	0.984587i	$-0.444041\pi$
$887$	10.4178			0.349794			0.174897	+	0.984587i	$0.444041\pi$
$888$		0			0
$889$	20.2941			0.680641
$890$	−44.1193	+	20.5731i	−1.47888	+	0.689613i
$891$		0			0
$892$	−6.44122	+	7.67635i	−0.215668	+	0.257023i
$893$	−2.84166	+	1.98975i	−0.0950924	+	0.0665844i
$894$		0			0
$895$	−6.22091	+	35.2805i	−0.207942	+	1.17930i
$896$	0.418622	−	1.56232i	0.0139852	−	0.0521933i
$897$		0			0
$898$	4.58595	−	7.94310i	0.153035	−	0.265065i
$899$	−1.25679	−	2.17683i	−0.0419163	−	0.0726012i
$900$		0			0
$901$	−60.9476	+	5.33222i	−2.03046	+	0.177642i
$902$	−0.319546	−	1.19256i	−0.0106397	−	0.0397080i
$903$		0			0
$904$	−3.04029	−	17.2424i	−0.101119	−	0.573472i
$905$	−44.9059	−	3.92875i	−1.49272	−	0.130596i
$906$		0			0
$907$	−10.3702	+	22.2390i	−0.344338	+	0.738435i	−0.999860	−	0.0167413i	$-0.994671\pi$
$907$	−10.3702	+	22.2390i	−0.344338	+	0.738435i	0.655522	+	0.755176i	$0.272449\pi$
$908$	1.79072	−	20.4680i	0.0594271	−	0.679255i
$909$		0			0
$910$	18.7595	+	13.1355i	0.621870	+	0.435438i
$911$	12.4230	−	3.32872i	0.411591	−	0.110285i	−0.0470811	−	0.998891i	$-0.514992\pi$
$911$	12.4230	−	3.32872i	0.411591	−	0.110285i	0.458672	+	0.888606i	$0.348325\pi$
$912$		0			0
$913$	23.3321	−	64.1044i	0.772180	−	2.12155i
$914$	33.9844	−	19.6209i	1.12410	−	0.649002i
$915$		0			0
$916$	−12.0296	−	14.3364i	−0.397471	−	0.473687i
$917$	−32.1484	−	8.61415i	−1.06163	−	0.284464i
$918$		0			0
$919$	16.5035	+	16.5035i	0.544399	+	0.544399i	0.924815	−	0.380416i	$-0.124219\pi$
$919$	16.5035	+	16.5035i	0.544399	+	0.544399i	−0.380416	+	0.924815i	$0.624219\pi$
$920$	−9.99414	−	14.2731i	−0.329497	−	0.470570i
$921$		0			0
$922$	−30.3341	+	11.0407i	−0.998999	+	0.363606i
$923$	−9.08416	−	19.4810i	−0.299009	−	0.641226i
$924$		0			0
$925$	−2.11911	+	21.2585i	−0.0696760	+	0.698975i
$926$		−	40.0928i		−	1.31753i
$927$		0			0
$928$	0.551321	+	1.51474i	0.0180980	+	0.0497238i
$929$	−6.41025	−	5.37884i	−0.210314	−	0.176474i	0.531546	−	0.847030i	$-0.321611\pi$
$929$	−6.41025	−	5.37884i	−0.210314	−	0.176474i	−0.741859	+	0.670556i	$0.766056\pi$
$930$		0			0
$931$	4.11480	−	4.11480i	0.134857	−	0.134857i
$932$	−4.90541	−	0.864955i	−0.160682	−	0.0283326i
$933$		0			0
$934$	−11.9133	+	9.99646i	−0.389816	+	0.327094i
$935$	61.2106	+	35.3400i	2.00180	+	1.15574i
$936$		0			0
$937$	−11.0517	−	4.02248i	−0.361043	−	0.131409i	0.155128	−	0.987894i	$-0.450421\pi$
$937$	−11.0517	−	4.02248i	−0.361043	−	0.131409i	−0.516171	+	0.856486i	$0.672643\pi$
$938$	1.86927	+	21.3659i	0.0610339	+	0.697620i
$939$		0			0
$940$	−4.37339	+	6.24585i	−0.142644	+	0.203717i
$941$	−32.9406	+	5.80831i	−1.07383	+	0.189345i	−0.682486	−	0.730898i	$-0.739101\pi$
$941$	−32.9406	+	5.80831i	−1.07383	+	0.189345i	−0.391345	+	0.920244i	$0.627990\pi$
$942$		0			0
$943$	1.31691	+	0.614086i	0.0428846	+	0.0199974i
$944$	−9.92196	−	4.62669i	−0.322932	−	0.150586i
$945$		0			0
$946$	1.79950	−	0.317301i	0.0585069	−	0.0103163i
$947$	−6.14612	+	8.77758i	−0.199722	+	0.285233i	−0.906503	−	0.422200i	$-0.861258\pi$
$947$	−6.14612	+	8.77758i	−0.199722	+	0.285233i	0.706780	+	0.707433i	$0.250147\pi$
$948$		0			0
$949$	−6.75298	−	77.1869i	−0.219211	−	2.50559i
$950$	4.38092	+	1.59452i	0.142136	+	0.0517332i
$951$		0			0
$952$	−6.68716	−	3.86084i	−0.216732	−	0.125130i
$953$	9.49893	−	7.97054i	0.307700	−	0.258191i	−0.475840	−	0.879532i	$-0.657856\pi$
$953$	9.49893	−	7.97054i	0.307700	−	0.258191i	0.783541	+	0.621340i	$0.213412\pi$
$954$		0			0
$955$	60.5437	+	10.6755i	1.95915	+	0.345450i
$956$	−1.84222	+	1.84222i	−0.0595815	+	0.0595815i
$957$		0			0
$958$	−1.79482	−	1.50603i	−0.0579880	−	0.0486577i
$959$	0.365262	+	1.00355i	0.0117949	+	0.0324063i
$960$		0			0
$961$		−	28.5685i		−	0.921563i
$962$	21.1243	−	20.6197i	0.681075	−	0.664804i
$963$		0			0
$964$	−2.75647	−	5.91126i	−0.0887798	−	0.190389i
$965$	40.4368	−	14.7178i	1.30171	−	0.473782i
$966$		0			0
$967$	22.4703	+	32.0910i	0.722597	+	1.03198i	0.997511	+	0.0705068i	$0.0224616\pi$
$967$	22.4703	+	32.0910i	0.722597	+	1.03198i	−0.274914	+	0.961469i	$0.588649\pi$
$968$	−10.4299	−	10.4299i	−0.335229	−	0.335229i
$969$		0			0
$970$	−14.0805	−	3.77285i	−0.452097	−	0.121139i
$971$	23.9856	+	28.5850i	0.769735	+	0.917335i	0.998421	−	0.0561653i	$-0.0178874\pi$
$971$	23.9856	+	28.5850i	0.769735	+	0.917335i	−0.228686	+	0.973500i	$0.573443\pi$
$972$		0			0
$973$	−9.00352	+	5.19818i	−0.288640	+	0.166646i
$974$	4.59610	−	12.6277i	0.147269	−	0.404617i
$975$		0			0
$976$	4.88334	−	1.30849i	0.156312	−	0.0418836i
$977$	−9.88131	−	6.91897i	−0.316131	−	0.221357i	0.404731	−	0.914436i	$-0.367365\pi$
$977$	−9.88131	−	6.91897i	−0.316131	−	0.221357i	−0.720862	+	0.693078i	$0.756254\pi$
$978$		0			0
$979$	7.37933	−	84.3461i	0.235844	−	2.69571i
$980$	5.40545	−	11.5920i	0.172671	−	0.370294i
$981$		0			0
$982$	38.7501	+	3.39019i	1.23656	+	0.108185i
$983$	−8.96115	−	50.8212i	−0.285816	−	1.62094i	−0.702355	−	0.711827i	$-0.747868\pi$
$983$	−8.96115	−	50.8212i	−0.285816	−	1.62094i	0.416539	−	0.909118i	$-0.363243\pi$
$984$		0			0
$985$	6.38007	+	23.8107i	0.203286	+	0.758673i
$986$	7.66625	−	0.670710i	0.244143	−	0.0213598i
$987$		0			0
$988$	−3.22092	−	5.57880i	−0.102471	−	0.177485i
$989$	−1.07526	+	1.86241i	−0.0341914	+	0.0592213i
$990$		0			0
$991$	−2.51908	+	9.40135i	−0.0800213	+	0.298644i	−0.994325	−	0.106386i	$-0.966072\pi$
$991$	−2.51908	+	9.40135i	−0.0800213	+	0.298644i	0.914304	+	0.405030i	$0.132739\pi$
$992$	0.270776	−	1.53565i	0.00859715	−	0.0487569i
$993$		0			0
$994$	5.86836	−	4.10907i	0.186133	−	0.130332i
$995$	−30.7085	+	36.5970i	−0.973526	+	1.16020i
$996$		0			0
$997$	−43.3199	+	20.2004i	−1.37196	+	0.639753i	−0.962175	−	0.272431i	$-0.912172\pi$
$997$	−43.3199	+	20.2004i	−1.37196	+	0.639753i	−0.409780	+	0.912184i	$0.634395\pi$
$998$	−39.8505			−1.26144
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.89.3	✓	96
3.2	odd	2	inner	666.2.bs.b.89.6	yes	96
37.5	odd	36	inner	666.2.bs.b.449.6	yes	96
111.5	even	36	inner	666.2.bs.b.449.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.89.3	✓	96	1.1	even	1	trivial
666.2.bs.b.89.6	yes	96	3.2	odd	2	inner
666.2.bs.b.449.3	yes	96	111.5	even	36	inner
666.2.bs.b.449.6	yes	96	37.5	odd	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.38993 - 1.67345i) q^{5} +(0.280864 - 1.59286i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(-0.906308 + 0.422618i) q^{2} +(0.642788 - 0.766044i) q^{4} +(2.38993 - 1.67345i) q^{5} +(0.280864 - 1.59286i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.45878 + 2.52669i) q^{10} +(-2.53723 - 4.39461i) q^{11} +(4.83452 - 0.422966i) q^{13} +(0.418622 + 1.56232i) q^{14} +(-0.173648 - 0.984808i) q^{16} +(-4.75587 - 0.416085i) q^{17} +(0.560982 - 1.20303i) q^{19} +(0.254283 - 2.90646i) q^{20} +(4.15675 + 2.91059i) q^{22} +(-5.76869 + 1.54571i) q^{23} +(1.20124 - 3.30038i) q^{25} +(-4.20281 + 2.42650i) q^{26} +(-1.03966 - 1.23902i) q^{28} +(1.55703 + 0.417205i) q^{29} +(-1.10262 - 1.10262i) q^{31} +(0.573576 + 0.819152i) q^{32} +(4.48613 - 1.63282i) q^{34} +(-1.99432 - 4.27683i) q^{35} +(-5.89410 + 1.50320i) q^{37} +1.32740i q^{38} +(0.997867 + 2.74162i) q^{40} +(-0.186381 - 0.156392i) q^{41} +(0.254623 - 0.254623i) q^{43} +(-4.99736 - 0.881170i) q^{44} +(4.57496 - 3.83885i) q^{46} +(-2.26327 - 1.30670i) q^{47} +(4.11954 + 1.49939i) q^{49} +(0.306108 + 3.49883i) q^{50} +(2.78356 - 3.97534i) q^{52} +(12.6205 - 2.22534i) q^{53} +(-13.4179 - 6.25689i) q^{55} +(1.46589 + 0.683555i) q^{56} +(-1.58747 + 0.279913i) q^{58} +(6.27933 - 8.96781i) q^{59} +(0.440625 + 5.03637i) q^{61} +(1.46530 + 0.533325i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(10.8464 - 9.10118i) q^{65} +(13.0588 + 2.30261i) q^{67} +(-3.37576 + 3.37576i) q^{68} +(3.61493 + 3.03329i) q^{70} +(-1.51488 - 4.16210i) q^{71} -15.9658i q^{73} +(4.70659 - 3.85331i) q^{74} +(-0.560982 - 1.20303i) q^{76} +(-7.71259 + 2.80715i) q^{77} +(-3.56565 - 5.09227i) q^{79} +(-2.06303 - 2.06303i) q^{80} +(0.235013 + 0.0629715i) q^{82} +(8.64132 + 10.2983i) q^{83} +(-12.0625 + 6.96429i) q^{85} +(-0.123158 + 0.338375i) q^{86} +(4.90155 - 1.31337i) q^{88} +(13.6677 + 9.57024i) q^{89} +(0.684118 - 7.81950i) q^{91} +(-2.52395 + 5.41264i) q^{92} +(2.60346 + 0.227773i) q^{94} +(-0.672499 - 3.81393i) q^{95} +(1.29315 + 4.82610i) q^{97} +(-4.36724 + 0.382084i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

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Database

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