LMFDB - Embedded newform 950.2.bb.c.143.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(143,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([27, 34]))

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

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

chi := DirichletCharacter("950.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.bb (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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.6
Character	$\chi$	$=$	950.143
Dual form			950.2.bb.c.857.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(0.181419 - 2.07363i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-1.59456 - 1.33799i) q^{6} +(-1.21655 - 4.54023i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.31260 - 0.231446i) q^{9} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(0.181419 - 2.07363i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-1.59456 - 1.33799i) q^{6} +(-1.21655 - 4.54023i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.31260 - 0.231446i) q^{9} +(-2.68929 - 4.65799i) q^{11} +(-2.01062 + 0.538744i) q^{12} +(2.58102 - 0.225810i) q^{13} +(-4.41693 - 1.60763i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(6.05395 + 4.23902i) q^{17} +(-0.942464 + 0.942464i) q^{18} +(0.918889 + 4.26094i) q^{19} +(-9.63546 + 1.69899i) q^{21} +(-5.35812 - 0.468775i) q^{22} +(0.739436 + 0.344805i) q^{23} +(-0.711932 + 1.95602i) q^{24} +(1.29544 - 2.24377i) q^{26} +(0.898170 - 3.35202i) q^{27} +(-3.85034 + 2.69604i) q^{28} +(-1.60619 + 9.10916i) q^{29} +(0.614073 + 0.354535i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(-10.1468 + 4.73155i) q^{33} +(6.94481 - 2.52770i) q^{34} +(0.231446 + 1.31260i) q^{36} +(-1.28938 - 1.28938i) q^{37} +(4.01741 + 1.69127i) q^{38} -5.39304i q^{39} +(-6.73200 - 8.02289i) q^{41} +(-4.13494 + 8.86741i) q^{42} +(2.29552 + 4.92275i) q^{43} +(-3.45729 + 4.12024i) q^{44} +(0.706570 - 0.407939i) q^{46} +(-2.93842 - 4.19649i) q^{47} +(1.19393 + 1.70510i) q^{48} +(-13.0716 + 7.54687i) q^{49} +(9.88845 - 11.7846i) q^{51} +(-1.09495 - 2.34813i) q^{52} +(1.07982 - 2.31569i) q^{53} +(-2.23064 - 2.65838i) q^{54} +4.70040i q^{56} +(9.00232 - 1.13242i) q^{57} +(6.54051 + 6.54051i) q^{58} +(-1.60593 - 9.10767i) q^{59} +(8.94905 - 3.25719i) q^{61} +(0.642636 - 0.299666i) q^{62} +(0.546022 + 6.24106i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.94413 + 11.0257i) q^{66} +(-0.0267485 + 0.0187295i) q^{67} +(1.91280 - 7.13868i) q^{68} +(0.849144 - 1.47076i) q^{69} +(-1.39776 + 3.84033i) q^{71} +(1.20797 + 0.563285i) q^{72} +(9.16903 + 0.802186i) q^{73} +(-1.79576 + 0.316641i) q^{74} +(3.68970 - 2.32080i) q^{76} +(-17.8767 + 17.8767i) q^{77} +(-4.41772 - 3.09332i) q^{78} +(1.40718 - 1.18076i) q^{79} +(-10.5453 - 3.83817i) q^{81} +(-10.4333 + 0.912794i) q^{82} +(-3.28521 + 0.880269i) q^{83} +(4.89205 + 8.47328i) q^{84} +(5.34914 + 0.943197i) q^{86} +(18.5976 + 4.98321i) q^{87} +(1.39208 + 5.19532i) q^{88} +(1.52577 + 1.28028i) q^{89} +(-4.16518 - 11.4437i) q^{91} +(0.0711084 - 0.812773i) q^{92} +(0.846579 - 1.20904i) q^{93} -5.12297 q^{94} +2.08155 q^{96} +(4.19754 - 5.99470i) q^{97} +(-1.31551 + 15.0363i) q^{98} +(2.45188 + 6.73649i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 24 q^{6}+O(q^{10}) $ 72 * q + 24 * q^6	$ 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) $ 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$3$	0.181419	−	2.07363i	0.104742	−	1.19721i	−0.743918	−	0.668271i	$-0.767035\pi$
$3$	0.181419	−	2.07363i	0.104742	−	1.19721i	0.848660	−	0.528939i	$-0.177410\pi$
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$		0			0
$5$		0			0
$6$	−1.59456	−	1.33799i	−0.650976	−	0.546234i
$7$	−1.21655	−	4.54023i	−0.459814	−	1.71605i	−0.673537	−	0.739153i	$-0.735226\pi$
$7$	−1.21655	−	4.54023i	−0.459814	−	1.71605i	0.213724	−	0.976894i	$-0.431441\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	−1.31260	−	0.231446i	−0.437532	−	0.0771487i
$10$		0			0
$11$	−2.68929	−	4.65799i	−0.810853	−	1.40444i	−0.912268	−	0.409594i	$-0.865670\pi$
$11$	−2.68929	−	4.65799i	−0.810853	−	1.40444i	0.101415	−	0.994844i	$-0.467663\pi$
$12$	−2.01062	+	0.538744i	−0.580416	+	0.155522i
$13$	2.58102	−	0.225810i	0.715846	−	0.0626284i	0.276587	−	0.960989i	$-0.410797\pi$
$13$	2.58102	−	0.225810i	0.715846	−	0.0626284i	0.439259	+	0.898360i	$0.355241\pi$
$14$	−4.41693	−	1.60763i	−1.18047	−	0.429657i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	6.05395	+	4.23902i	1.46830	+	1.02811i	0.988581	+	0.150691i	$0.0481498\pi$
$17$	6.05395	+	4.23902i	1.46830	+	1.02811i	0.479718	+	0.877423i	$0.340739\pi$
$18$	−0.942464	+	0.942464i	−0.222141	+	0.222141i
$19$	0.918889	+	4.26094i	0.210808	+	0.977528i
$19$	0.918889	+	4.26094i	0.210808	+	0.977528i
$20$		0			0
$21$	−9.63546	+	1.69899i	−2.10263	+	0.370750i
$22$	−5.35812	−	0.468775i	−1.14236	−	0.0999432i
$23$	0.739436	+	0.344805i	0.154183	+	0.0718967i	0.498178	−	0.867075i	$-0.334003\pi$
$23$	0.739436	+	0.344805i	0.154183	+	0.0718967i	−0.343995	+	0.938971i	$0.611780\pi$
$24$	−0.711932	+	1.95602i	−0.145322	+	0.399270i
$25$		0			0
$26$	1.29544	−	2.24377i	0.254057	−	0.440039i
$27$	0.898170	−	3.35202i	0.172853	−	0.645096i
$28$	−3.85034	+	2.69604i	−0.727646	+	0.509503i
$29$	−1.60619	+	9.10916i	−0.298262	+	1.69153i	0.355378	+	0.934723i	$0.384352\pi$
$29$	−1.60619	+	9.10916i	−0.298262	+	1.69153i	−0.653640	+	0.756806i	$0.726759\pi$
$30$		0			0
$31$	0.614073	+	0.354535i	0.110291	+	0.0636764i	0.554131	−	0.832430i	$-0.313051\pi$
$31$	0.614073	+	0.354535i	0.110291	+	0.0636764i	−0.443840	+	0.896106i	$0.646384\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$	−10.1468	+	4.73155i	−1.76634	+	0.823657i
$34$	6.94481	−	2.52770i	1.19102	−	0.433497i
$35$		0			0
$36$	0.231446	+	1.31260i	0.0385744	+	0.218766i
$37$	−1.28938	−	1.28938i	−0.211973	−	0.211973i	0.593132	−	0.805105i	$-0.297891\pi$
$37$	−1.28938	−	1.28938i	−0.211973	−	0.211973i	−0.805105	+	0.593132i	$0.797891\pi$
$38$	4.01741	+	1.69127i	0.651711	+	0.274360i
$39$		−	5.39304i		−	0.863578i
$40$		0			0
$41$	−6.73200	−	8.02289i	−1.05136	−	1.25296i	−0.966526	−	0.256569i	$-0.917408\pi$
$41$	−6.73200	−	8.02289i	−1.05136	−	1.25296i	−0.0848360	−	0.996395i	$-0.527037\pi$
$42$	−4.13494	+	8.86741i	−0.638035	+	1.36827i
$43$	2.29552	+	4.92275i	0.350063	+	0.750713i	0.999957	−	0.00931258i	$-0.00296433\pi$
$43$	2.29552	+	4.92275i	0.350063	+	0.750713i	−0.649894	+	0.760025i	$0.725187\pi$
$44$	−3.45729	+	4.12024i	−0.521206	+	0.621149i
$45$		0			0
$46$	0.706570	−	0.407939i	0.104178	−	0.0601473i
$47$	−2.93842	−	4.19649i	−0.428612	−	0.612122i	0.545521	−	0.838097i	$-0.316332\pi$
$47$	−2.93842	−	4.19649i	−0.428612	−	0.612122i	−0.974133	+	0.225976i	$0.927443\pi$
$48$	1.19393	+	1.70510i	0.172329	+	0.246111i
$49$	−13.0716	+	7.54687i	−1.86736	+	1.07812i
$50$		0			0
$51$	9.88845	−	11.7846i	1.38466	−	1.65017i
$52$	−1.09495	−	2.34813i	−0.151843	−	0.325628i
$53$	1.07982	−	2.31569i	0.148325	−	0.318084i	−0.818081	−	0.575102i	$-0.804962\pi$
$53$	1.07982	−	2.31569i	0.148325	−	0.318084i	0.966407	+	0.257018i	$0.0827400\pi$
$54$	−2.23064	−	2.65838i	−0.303552	−	0.361759i
$55$		0			0
$56$			4.70040i			0.628117i
$57$	9.00232	−	1.13242i	1.19239	−	0.149992i
$58$	6.54051	+	6.54051i	0.858811	+	0.858811i
$59$	−1.60593	−	9.10767i	−0.209074	−	1.18572i	−0.890899	−	0.454202i	$-0.849925\pi$
$59$	−1.60593	−	9.10767i	−0.209074	−	1.18572i	0.681825	−	0.731515i	$-0.261187\pi$
$60$		0			0
$61$	8.94905	−	3.25719i	1.14581	−	0.417040i	0.301801	−	0.953371i	$-0.402412\pi$
$61$	8.94905	−	3.25719i	1.14581	−	0.417040i	0.844008	+	0.536331i	$0.180190\pi$
$62$	0.642636	−	0.299666i	0.0816149	−	0.0380576i
$63$	0.546022	+	6.24106i	0.0687923	+	0.786300i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$		0			0
$66$	−1.94413	+	11.0257i	−0.239306	+	1.35717i
$67$	−0.0267485	+	0.0187295i	−0.00326785	+	0.00228817i	−0.575209	−	0.818006i	$-0.695079\pi$
$67$	−0.0267485	+	0.0187295i	−0.00326785	+	0.00228817i	0.571941	+	0.820295i	$0.306190\pi$
$68$	1.91280	−	7.13868i	0.231962	−	0.865692i
$69$	0.849144	−	1.47076i	0.102225	−	0.177059i
$70$		0			0
$71$	−1.39776	+	3.84033i	−0.165884	+	0.455763i	−0.994585	−	0.103929i	$-0.966858\pi$
$71$	−1.39776	+	3.84033i	−0.165884	+	0.455763i	0.828701	+	0.559692i	$0.189081\pi$
$72$	1.20797	+	0.563285i	0.142360	+	0.0663837i
$73$	9.16903	+	0.802186i	1.07315	+	0.0938888i	0.610010	−	0.792394i	$-0.291166\pi$
$73$	9.16903	+	0.802186i	1.07315	+	0.0938888i	0.463144	+	0.886283i	$0.346721\pi$
$74$	−1.79576	+	0.316641i	−0.208753	+	0.0368088i
$75$		0			0
$76$	3.68970	−	2.32080i	0.423237	−	0.266214i
$77$	−17.8767	+	17.8767i	−2.03724	+	2.03724i
$78$	−4.41772	−	3.09332i	−0.500208	−	0.350250i
$79$	1.40718	−	1.18076i	0.158320	−	0.132846i	−0.560187	−	0.828366i	$-0.689271\pi$
$79$	1.40718	−	1.18076i	0.158320	−	0.132846i	0.718506	+	0.695520i	$0.244826\pi$
$80$		0			0
$81$	−10.5453	−	3.83817i	−1.17170	−	0.426463i
$82$	−10.4333	+	0.912794i	−1.15216	+	0.100801i
$83$	−3.28521	+	0.880269i	−0.360598	+	0.0966220i	−0.434569	−	0.900638i	$-0.643099\pi$
$83$	−3.28521	+	0.880269i	−0.360598	+	0.0966220i	0.0739710	+	0.997260i	$0.476433\pi$
$84$	4.89205	+	8.47328i	0.533767	+	0.924511i
$85$		0			0
$86$	5.34914	+	0.943197i	0.576812	+	0.101708i
$87$	18.5976	+	4.98321i	1.99387	+	0.534257i
$88$	1.39208	+	5.19532i	0.148396	+	0.553823i
$89$	1.52577	+	1.28028i	0.161732	+	0.135709i	0.720062	−	0.693910i	$-0.244113\pi$
$89$	1.52577	+	1.28028i	0.161732	+	0.135709i	−0.558330	+	0.829619i	$0.688558\pi$
$90$		0			0
$91$	−4.16518	−	11.4437i	−0.436629	−	1.19963i
$92$	0.0711084	−	0.812773i	0.00741356	−	0.0847374i
$93$	0.846579	−	1.20904i	0.0877861	−	0.125372i
$94$	−5.12297			−0.528394
$95$		0			0
$96$	2.08155			0.212447
$97$	4.19754	−	5.99470i	0.426195	−	0.608670i	−0.547422	−	0.836857i	$-0.684391\pi$
$97$	4.19754	−	5.99470i	0.426195	−	0.608670i	0.973617	+	0.228187i	$0.0732797\pi$
$98$	−1.31551	+	15.0363i	−0.132886	+	1.51890i
$99$	2.45188	+	6.73649i	0.246424	+	0.677043i
$100$		0			0
$101$	9.75068	+	8.18179i	0.970229	+	0.814119i	0.982587	−	0.185805i	$-0.0594893\pi$
$101$	9.75068	+	8.18179i	0.970229	+	0.814119i	−0.0123578	+	0.999924i	$0.503934\pi$
$102$	−3.98160	−	14.8595i	−0.394237	−	1.47131i
$103$	−5.63632	−	1.51025i	−0.555364	−	0.148809i	−0.0297881	−	0.999556i	$-0.509483\pi$
$103$	−5.63632	−	1.51025i	−0.555364	−	0.148809i	−0.525575	+	0.850747i	$0.676150\pi$
$104$	−2.55152	−	0.449901i	−0.250197	−	0.0441165i
$105$		0			0
$106$	−1.27754	−	2.21276i	−0.124086	−	0.214923i
$107$	−4.73347	+	1.26833i	−0.457602	+	0.122614i	−0.480254	−	0.877129i	$-0.659456\pi$
$107$	−4.73347	+	1.26833i	−0.457602	+	0.122614i	0.0226522	+	0.999743i	$0.492789\pi$
$108$	−3.45706	+	0.302453i	−0.332656	+	0.0291036i
$109$	15.3341	+	5.58116i	1.46874	+	0.534578i	0.947758	−	0.318989i	$-0.103343\pi$
$109$	15.3341	+	5.58116i	1.46874	+	0.534578i	0.520983	+	0.853567i	$0.325566\pi$
$110$		0			0
$111$	−2.90762	+	2.43978i	−0.275979	+	0.231574i
$112$	3.85034	+	2.69604i	0.363823	+	0.254752i
$113$	2.92238	−	2.92238i	0.274915	−	0.274915i	−0.556160	−	0.831075i	$-0.687726\pi$
$113$	2.92238	−	2.92238i	0.274915	−	0.274915i	0.831075	+	0.556160i	$0.187726\pi$
$114$	4.23589	−	8.02379i	0.396728	−	0.751497i
$115$		0			0
$116$	9.10916	−	1.60619i	0.845764	−	0.149131i
$117$	−3.44010	−	0.300970i	−0.318037	−	0.0278247i
$118$	−8.38169	−	3.90844i	−0.771597	−	0.359801i
$119$	11.8812	−	32.6433i	1.08915	−	2.99241i
$120$		0			0
$121$	−8.96461	+	15.5272i	−0.814965	+	1.41156i
$122$	2.46483	−	9.19888i	0.223156	−	0.832828i
$123$	−17.8578	+	12.5042i	−1.61018	+	1.12746i
$124$	0.123129	−	0.698298i	0.0110573	−	0.0627090i
$125$		0			0
$126$	5.42556	+	3.13245i	0.483348	+	0.279061i
$127$	−0.269926	−	3.08526i	−0.0239520	−	0.273773i	−0.998721	−	0.0505574i	$-0.983900\pi$
$127$	−0.269926	−	3.08526i	−0.0239520	−	0.273773i	0.974769	−	0.223215i	$-0.0716554\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$	10.6244	−	3.86697i	0.935427	−	0.340467i
$130$		0			0
$131$	0.104715	+	0.593867i	0.00914896	+	0.0518864i	0.989040	−	0.147645i	$-0.0471692\pi$
$131$	0.104715	+	0.593867i	0.00914896	+	0.0518864i	−0.979891	+	0.199531i	$0.936058\pi$
$132$	7.91662	+	7.91662i	0.689054	+	0.689054i
$133$	18.2278	−	9.35563i	1.58055	−	0.811236i
$134$			0.0326539i			0.00282087i
$135$		0			0
$136$	−4.75053	−	5.66146i	−0.407354	−	0.485466i
$137$	4.96171	−	10.6404i	0.423908	−	0.909073i	−0.572132	−	0.820162i	$-0.693883\pi$
$137$	4.96171	−	10.6404i	0.423908	−	0.909073i	0.996040	−	0.0889115i	$-0.0283388\pi$
$138$	−0.717728	−	1.53917i	−0.0610970	−	0.131023i
$139$	−0.912240	+	1.08717i	−0.0773752	+	0.0922122i	−0.803343	−	0.595516i	$-0.796948\pi$
$139$	−0.912240	+	1.08717i	−0.0773752	+	0.0922122i	0.725968	+	0.687728i	$0.241392\pi$
$140$		0			0
$141$	−9.23505	+	5.33186i	−0.777732	+	0.449024i
$142$	2.34409	+	3.34770i	0.196711	+	0.280933i
$143$	−7.99294	−	11.4151i	−0.668404	−	0.954579i
$144$	1.15428	−	0.666423i	0.0961898	−	0.0555352i
$145$		0			0
$146$	5.91625	−	7.05072i	0.489633	−	0.583521i
$147$	13.2780	+	28.4747i	1.09515	+	2.34855i
$148$	−0.770629	+	1.65262i	−0.0633453	+	0.135844i
$149$	−0.886956	−	1.05703i	−0.0726623	−	0.0865955i	0.728489	−	0.685058i	$-0.240223\pi$
$149$	−0.886956	−	1.05703i	−0.0726623	−	0.0865955i	−0.801151	+	0.598462i	$0.795779\pi$
$150$		0			0
$151$			12.3491i			1.00496i	0.864589	+	0.502480i	$0.167579\pi$
$151$			12.3491i			1.00496i	−0.864589	+	0.502480i	$0.832421\pi$
$152$	0.215235	−	4.35358i	0.0174578	−	0.353122i
$153$	−6.96529	−	6.96529i	−0.563110	−	0.563110i
$154$	4.39009	+	24.8974i	0.353763	+	2.00629i
$155$		0			0
$156$	−5.06780	+	1.84453i	−0.405749	+	0.147680i
$157$	14.6326	−	6.82331i	1.16781	−	0.544560i	0.260688	−	0.965423i	$-0.416051\pi$
$157$	14.6326	−	6.82331i	1.16781	−	0.544560i	0.907124	+	0.420863i	$0.138273\pi$
$158$	−0.160100	−	1.82995i	−0.0127369	−	0.145583i
$159$	−4.60597	−	2.65926i	−0.365278	−	0.210893i
$160$		0			0
$161$	0.665932	−	3.77669i	0.0524828	−	0.297645i
$162$	−9.19257	+	6.43671i	−0.722237	+	0.505716i
$163$	1.29935	−	4.84925i	0.101773	−	0.379822i	−0.896186	−	0.443679i	$-0.853673\pi$
$163$	1.29935	−	4.84925i	0.101773	−	0.379822i	0.997959	+	0.0638561i	$0.0203399\pi$
$164$	−5.23657	+	9.07000i	−0.408907	+	0.708248i
$165$		0			0
$166$	−1.16324	+	3.19599i	−0.0902852	+	0.248057i
$167$	7.22061	+	3.36702i	0.558747	+	0.260548i	0.681412	−	0.731900i	$-0.261366\pi$
$167$	7.22061	+	3.36702i	0.558747	+	0.260548i	−0.122665	+	0.992448i	$0.539144\pi$
$168$	9.74687	+	0.852741i	0.751988	+	0.0657904i
$169$	−6.19183	+	1.09179i	−0.476294	+	0.0839836i
$170$		0			0
$171$	−0.219952	−	5.80557i	−0.0168201	−	0.443963i
$172$	3.84076	−	3.84076i	0.292855	−	0.292855i
$173$	−4.47064	−	3.13037i	−0.339896	−	0.237998i	0.391148	−	0.920328i	$-0.372078\pi$
$173$	−4.47064	−	3.13037i	−0.339896	−	0.237998i	−0.731044	+	0.682330i	$0.760967\pi$
$174$	14.7492	−	12.3760i	1.11813	−	0.938223i
$175$		0			0
$176$	5.05422	+	1.83959i	0.380976	+	0.138664i
$177$	−19.1773	+	1.67779i	−1.44145	+	0.126111i
$178$	1.92389	−	0.515505i	0.144202	−	0.0386387i
$179$	7.66932	+	13.2837i	0.573232	+	0.992867i	0.996231	+	0.0867367i	$0.0276439\pi$
$179$	7.66932	+	13.2837i	0.573232	+	0.992867i	−0.422999	+	0.906130i	$0.639023\pi$
$180$		0			0
$181$	−24.6791	−	4.35159i	−1.83438	−	0.323451i	−0.853956	−	0.520345i	$-0.825803\pi$
$181$	−24.6791	−	4.35159i	−1.83438	−	0.323451i	−0.980425	+	0.196894i	$0.936915\pi$
$182$	−11.7632	−	3.15194i	−0.871946	−	0.233637i
$183$	−5.13067	−	19.1479i	−0.379270	−	1.41546i
$184$	−0.624998	−	0.524436i	−0.0460755	−	0.0386619i
$185$		0			0
$186$	−0.504810	−	1.38695i	−0.0370144	−	0.101696i
$187$	3.46449	−	39.5992i	0.253348	−	2.89578i
$188$	−2.93842	+	4.19649i	−0.214306	+	0.306061i
$189$	−16.3116			−1.18650
$190$		0			0
$191$	−11.0633			−0.800511			−0.400256	−	0.916403i	$-0.631079\pi$
$191$	−11.0633			−0.800511			−0.400256	+	0.916403i	$0.631079\pi$
$192$	1.19393	−	1.70510i	0.0861643	−	0.123055i
$193$	2.03681	−	23.2808i	0.146613	−	1.67579i	−0.465523	−	0.885036i	$-0.654134\pi$
$193$	2.03681	−	23.2808i	0.146613	−	1.67579i	0.612135	−	0.790753i	$-0.290311\pi$
$194$	−2.50297	−	6.87684i	−0.179702	−	0.493728i
$195$		0			0
$196$	11.5625	+	9.70206i	0.825891	+	0.693004i
$197$	1.40077	+	5.22773i	0.0998004	+	0.372460i	0.997703	−	0.0677330i	$-0.0215766\pi$
$197$	1.40077	+	5.22773i	0.0998004	+	0.372460i	−0.897903	+	0.440193i	$0.854910\pi$
$198$	6.92456	+	1.85543i	0.492107	+	0.131860i
$199$	−9.55427	−	1.68468i	−0.677284	−	0.119424i	−0.175583	−	0.984465i	$-0.556181\pi$
$199$	−9.55427	−	1.68468i	−0.677284	−	0.119424i	−0.501701	+	0.865041i	$0.667292\pi$
$200$		0			0
$201$	0.0339854	+	0.0588644i	0.00239714	+	0.00415197i
$202$	12.2949	−	3.29441i	0.865065	−	0.231794i
$203$	43.3117	−	3.78929i	3.03989	−	0.265956i
$204$	−14.4560	−	5.26154i	−1.01212	−	0.368381i
$205$		0			0
$206$	−4.46999	+	3.75076i	−0.311439	+	0.261328i
$207$	−0.890777	−	0.623729i	−0.0619133	−	0.0433522i
$208$	−1.83203	+	1.83203i	−0.127028	+	0.127028i
$209$	17.3763	−	15.7391i	1.20194	−	1.08870i
$210$		0			0
$211$	17.8518	−	3.14776i	1.22897	−	0.216701i	0.478788	−	0.877931i	$-0.341076\pi$
$211$	17.8518	−	3.14776i	1.22897	−	0.216701i	0.750183	+	0.661230i	$0.229965\pi$
$212$	−2.54536	−	0.222690i	−0.174816	−	0.0152944i
$213$	7.70983	+	3.59515i	0.528269	+	0.246336i
$214$	−1.67605	+	4.60492i	−0.114573	+	0.314786i
$215$		0			0
$216$	−1.73513	+	3.00534i	−0.118061	+	0.204487i
$217$	0.862621	−	3.21935i	0.0585585	−	0.218543i
$218$	13.3671	−	9.35974i	0.905334	−	0.633922i
$219$	3.32687	−	18.8676i	0.224809	−	1.27496i
$220$		0			0
$221$	16.5826	+	9.57396i	1.11546	+	0.644014i
$222$	0.330811	+	3.78118i	0.0222026	+	0.253776i
$223$	−5.98874	+	2.79260i	−0.401036	+	0.187006i	−0.612663	−	0.790344i	$-0.709902\pi$
$223$	−5.98874	+	2.79260i	−0.401036	+	0.187006i	0.211627	+	0.977351i	$0.432124\pi$
$224$	4.41693	−	1.60763i	0.295118	−	0.107414i
$225$		0			0
$226$	−0.717666	−	4.07009i	−0.0477384	−	0.270738i
$227$	−1.19619	−	1.19619i	−0.0793940	−	0.0793940i	0.666295	−	0.745689i	$-0.267879\pi$
$227$	−1.19619	−	1.19619i	−0.0793940	−	0.0793940i	−0.745689	+	0.666295i	$0.767879\pi$
$228$	−4.14310	−	8.07210i	−0.274383	−	0.534588i
$229$		−	13.1722i		−	0.870442i	−0.900324	−	0.435221i	$-0.856670\pi$
$229$		−	13.1722i		−	0.870442i	0.900324	−	0.435221i	$-0.143330\pi$
$230$		0			0
$231$	33.8265	+	40.3128i	2.22562	+	2.65239i
$232$	3.90908	−	8.38306i	0.256644	−	0.550375i
$233$	−4.76631	−	10.2214i	−0.312251	−	0.669625i	0.686071	−	0.727535i	$-0.259334\pi$
$233$	−4.76631	−	10.2214i	−0.312251	−	0.669625i	−0.998322	+	0.0579103i	$0.981556\pi$
$234$	−2.21970	+	2.64534i	−0.145106	+	0.172931i
$235$		0			0
$236$	−8.00915	+	4.62408i	−0.521351	+	0.301002i
$237$	−2.19317	−	3.13217i	−0.142462	−	0.203457i
$238$	−19.9251	−	28.4560i	−1.29155	−	1.84453i
$239$	−18.1671	+	10.4888i	−1.17513	+	0.678462i	−0.954883	−	0.296982i	$-0.904020\pi$
$239$	−18.1671	+	10.4888i	−1.17513	+	0.678462i	−0.220248	+	0.975444i	$0.570687\pi$
$240$		0			0
$241$	7.72373	−	9.20478i	0.497529	−	0.592932i	−0.457587	−	0.889165i	$-0.651286\pi$
$241$	7.72373	−	9.20478i	0.497529	−	0.592932i	0.955116	+	0.296233i	$0.0957305\pi$
$242$	7.57722	+	16.2494i	0.487082	+	1.04455i
$243$	−5.47226	+	11.7353i	−0.351046	+	0.752820i
$244$	−6.12151	−	7.29534i	−0.391890	−	0.467036i
$245$		0			0
$246$			21.8003i			1.38994i
$247$	3.33383	+	10.7901i	0.212127	+	0.686557i
$248$	−0.501388	−	0.501388i	−0.0318382	−	0.0318382i
$249$	1.22935	+	6.97200i	0.0779069	+	0.441832i
$250$		0			0
$251$	13.3775	−	4.86903i	0.844383	−	0.307330i	0.116635	−	0.993175i	$-0.462789\pi$
$251$	13.3775	−	4.86903i	0.844383	−	0.307330i	0.727748	+	0.685845i	$0.240567\pi$
$252$	5.67793	−	2.64766i	0.357676	−	0.166787i
$253$	−0.382463	−	4.37157i	−0.0240452	−	0.274838i
$254$	−2.68212	−	1.54852i	−0.168291	−	0.0971631i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−17.4372	+	12.2097i	−1.08771	+	0.761620i	−0.972774	−	0.231754i	$-0.925554\pi$
$257$	−17.4372	+	12.2097i	−1.08771	+	0.761620i	−0.114931	+	0.993373i	$0.536665\pi$
$258$	2.92627	−	10.9210i	0.182182	−	0.679912i
$259$	−4.28550	+	7.42270i	−0.266288	+	0.461224i
$260$		0			0
$261$	4.21656	−	11.5849i	0.260998	−	0.717087i
$262$	0.546529	+	0.254851i	0.0337647	+	0.0157447i
$263$	0.150532	+	0.0131698i	0.00928220	+	0.000812088i	0.0917959	−	0.995778i	$-0.470739\pi$
$263$	0.150532	+	0.0131698i	0.00928220	+	0.000812088i	−0.0825137	+	0.996590i	$0.526295\pi$
$264$	11.0257	−	1.94413i	0.678585	−	0.119653i
$265$		0			0
$266$	2.79135	−	20.2975i	0.171149	−	1.24452i
$267$	2.93162	−	2.93162i	0.179412	−	0.179412i
$268$	0.0267485	+	0.0187295i	0.00163393	+	0.00114409i
$269$	−14.1041	+	11.8348i	−0.859944	+	0.721578i	−0.961956	−	0.273205i	$-0.911916\pi$
$269$	−14.1041	+	11.8348i	−0.859944	+	0.721578i	0.102012	+	0.994783i	$0.467472\pi$
$270$		0			0
$271$	14.1876	+	5.16386i	0.861834	+	0.313682i	0.734856	−	0.678223i	$-0.237250\pi$
$271$	14.1876	+	5.16386i	0.861834	+	0.313682i	0.126979	+	0.991905i	$0.459472\pi$
$272$	−7.36239	+	0.644125i	−0.446410	+	0.0390558i
$273$	−24.4857	+	6.56092i	−1.48194	+	0.397085i
$274$	−5.87021	−	10.1675i	−0.354632	−	0.614241i
$275$		0			0
$276$	−1.67249	−	0.294905i	−0.100672	−	0.0177512i
$277$	−1.45739	−	0.390507i	−0.0875662	−	0.0234633i	0.214770	−	0.976665i	$-0.431100\pi$
$277$	−1.45739	−	0.390507i	−0.0875662	−	0.0234633i	−0.302336	+	0.953201i	$0.597767\pi$
$278$	0.367314	+	1.37084i	0.0220301	+	0.0822173i
$279$	−0.723974	−	0.607486i	−0.0433432	−	0.0363693i
$280$		0			0
$281$	3.98917	+	10.9602i	0.237974	+	0.653829i	0.999980	+	0.00625902i	$0.00199232\pi$
$281$	3.98917	+	10.9602i	0.237974	+	0.653829i	−0.762006	+	0.647570i	$0.775785\pi$
$282$	−0.929404	+	10.6231i	−0.0553452	+	0.632599i
$283$	−13.2335	+	18.8994i	−0.786651	+	1.12345i	0.202890	+	0.979202i	$0.434967\pi$
$283$	−13.2335	+	18.8994i	−0.786651	+	1.12345i	−0.989541	+	0.144253i	$0.953922\pi$
$284$	4.08679			0.242506
$285$		0			0
$286$	−13.9353			−0.824010
$287$	−28.2360	+	40.3251i	−1.66672	+	2.38032i
$288$	0.116165	−	1.32777i	0.00684509	−	0.0782398i
$289$	12.8667	+	35.3509i	0.756863	+	2.07946i
$290$		0			0
$291$	−11.6693	−	9.79168i	−0.684065	−	0.573999i
$292$	−2.38219	−	8.89044i	−0.139407	−	0.520273i
$293$	−8.64105	−	2.31536i	−0.504816	−	0.135265i	−0.00258159	−	0.999997i	$-0.500822\pi$
$293$	−8.64105	−	2.31536i	−0.504816	−	0.135265i	−0.502234	+	0.864732i	$0.667488\pi$
$294$	30.9410	+	5.45574i	1.80452	+	0.318185i
$295$		0			0
$296$	0.911731	+	1.57917i	0.0529933	+	0.0917871i
$297$	−18.0291	+	4.83089i	−1.04616	+	0.280317i
$298$	−1.37461	+	0.120263i	−0.0796289	+	0.00696663i
$299$	1.98636	+	0.722976i	0.114874	+	0.0418108i
$300$		0			0
$301$	19.5578	−	16.4110i	1.12729	−	0.945913i
$302$	10.1158	+	7.08318i	0.582100	+	0.407591i
$303$	18.7349	−	18.7349i	1.07629	−	1.07629i
$304$	−3.44279	−	2.67342i	−0.197458	−	0.153331i
$305$		0			0
$306$	−9.70075	+	1.71050i	−0.554555	+	0.0977830i
$307$	2.81298	+	0.246104i	0.160545	+	0.0140459i	0.167145	−	0.985932i	$-0.446545\pi$
$307$	2.81298	+	0.246104i	0.160545	+	0.0140459i	−0.00659970	+	0.999978i	$0.502101\pi$
$308$	22.9128	+	10.6844i	1.30558	+	0.608802i
$309$	−4.15423	+	11.4137i	−0.236326	+	0.649300i
$310$		0			0
$311$	−11.0092	+	19.0685i	−0.624275	+	1.08128i	0.364405	+	0.931240i	$0.381272\pi$
$311$	−11.0092	+	19.0685i	−0.624275	+	1.08128i	−0.988681	+	0.150036i	$0.952061\pi$
$312$	−1.39582	+	5.20928i	−0.0790228	+	0.294917i
$313$	13.0047	−	9.10602i	0.735072	−	0.514703i	−0.145066	−	0.989422i	$-0.546339\pi$
$313$	13.0047	−	9.10602i	0.735072	−	0.514703i	0.880137	+	0.474719i	$0.157450\pi$
$314$	2.80361	−	15.9001i	0.158217	−	0.897292i
$315$		0			0
$316$	−1.59084	−	0.918470i	−0.0894915	−	0.0516680i
$317$	−0.102364	−	1.17003i	−0.00574936	−	0.0657154i	0.992778	−	0.119966i	$-0.0382786\pi$
$317$	−0.102364	−	1.17003i	−0.00574936	−	0.0657154i	−0.998527	+	0.0542506i	$0.982723\pi$
$318$	−4.82022	+	2.24770i	−0.270304	+	0.126045i
$319$	46.7499	−	17.0156i	2.61749	−	0.952690i
$320$		0			0
$321$	1.77130	+	10.0456i	0.0988645	+	0.560688i
$322$	−2.71172	−	2.71172i	−0.151118	−	0.151118i
$323$	−12.4993	+	29.6907i	−0.695481	+	1.65204i
$324$			11.2221i			0.623448i
$325$		0			0
$326$	−3.22699	−	3.84578i	−0.178727	−	0.212998i
$327$	14.3551	−	30.7847i	0.793841	−	1.70240i
$328$	4.42614	+	9.49188i	0.244393	+	0.524102i
$329$	−15.4783	+	18.4464i	−0.853348	+	1.01698i
$330$		0			0
$331$	14.9625	−	8.63860i	0.822413	−	0.474820i	−0.0288348	−	0.999584i	$-0.509180\pi$
$331$	14.9625	−	8.63860i	0.822413	−	0.474820i	0.851248	+	0.524764i	$0.175846\pi$
$332$	1.95079	+	2.78602i	0.107063	+	0.152902i
$333$	1.39402	+	1.99086i	0.0763916	+	0.109099i
$334$	6.89967	−	3.98353i	0.377533	−	0.217969i
$335$		0			0
$336$	6.28910	−	7.49506i	0.343099	−	0.408889i
$337$	−1.77754	−	3.81194i	−0.0968287	−	0.207650i	0.851927	−	0.523661i	$-0.175434\pi$
$337$	−1.77754	−	3.81194i	−0.0968287	−	0.207650i	−0.948755	+	0.316011i	$0.897656\pi$
$338$	−2.65715	+	5.69827i	−0.144530	+	0.309945i
$339$	−5.52976	−	6.59011i	−0.300335	−	0.357926i
$340$		0			0
$341$		−	3.81380i		−	0.206529i
$342$	−4.88181	−	3.14977i	−0.263978	−	0.170320i
$343$	26.9010	+	26.9010i	1.45252	+	1.45252i
$344$	−0.943197	−	5.34914i	−0.0508538	−	0.288406i
$345$		0			0
$346$	−5.12850	+	1.86662i	−0.275710	+	0.100350i
$347$	25.3728	−	11.8315i	1.36208	−	0.635149i	0.402199	−	0.915552i	$-0.368246\pi$
$347$	25.3728	−	11.8315i	1.36208	−	0.635149i	0.959882	+	0.280403i	$0.0904681\pi$
$348$	−1.67807	−	19.1804i	−0.0899539	−	1.02818i
$349$	10.3196	+	5.95804i	0.552397	+	0.318927i	0.750088	−	0.661338i	$-0.230011\pi$
$349$	10.3196	+	5.95804i	0.552397	+	0.318927i	−0.197691	+	0.980264i	$0.563344\pi$
$350$		0			0
$351$	1.56128	−	8.85444i	0.0833348	−	0.472615i
$352$	4.40588	−	3.08503i	0.234834	−	0.164433i
$353$	0.286410	−	1.06889i	0.0152440	−	0.0568915i	−0.957885	−	0.287153i	$-0.907291\pi$
$353$	0.286410	−	1.06889i	0.0152440	−	0.0568915i	0.973129	+	0.230261i	$0.0739580\pi$
$354$	−9.62526	+	16.6714i	−0.511577	+	0.886077i
$355$		0			0
$356$	0.681221	−	1.87164i	0.0361046	−	0.0991967i
$357$	−65.5347	−	30.5593i	−3.46846	−	1.61737i
$358$	15.2803	+	1.33685i	0.807587	+	0.0706547i
$359$	−26.3798	+	4.65148i	−1.39227	+	0.245496i	−0.818965	−	0.573843i	$-0.805452\pi$
$359$	−26.3798	+	4.65148i	−1.39227	+	0.245496i	−0.573310	+	0.819339i	$0.694341\pi$
$360$		0			0
$361$	−17.3113	+	7.83067i	−0.911120	+	0.412141i
$362$	−17.7199	+	17.7199i	−0.931340	+	0.931340i
$363$	30.5712	+	21.4062i	1.60457	+	1.12353i
$364$	−9.32901	+	7.82797i	−0.488973	+	0.410297i
$365$		0			0
$366$	−18.6279	−	6.78000i	−0.973696	−	0.354396i
$367$	30.8002	−	2.69467i	1.60776	−	0.140661i	0.752403	−	0.658703i	$-0.228895\pi$
$367$	30.8002	−	2.69467i	1.60776	−	0.140661i	0.855355	+	0.518042i	$0.173339\pi$
$368$	−0.788077	+	0.211165i	−0.0410813	+	0.0110077i
$369$	6.97953	+	12.0889i	0.363340	+	0.629323i
$370$		0			0
$371$	−11.8274	−	2.08549i	−0.614049	−	0.108273i
$372$	−1.42567	−	0.382008i	−0.0739177	−	0.0198062i
$373$	−8.67757	−	32.3851i	−0.449308	−	1.67684i	−0.704306	−	0.709897i	$-0.748742\pi$
$373$	−8.67757	−	32.3851i	−0.449308	−	1.67684i	0.254998	−	0.966942i	$-0.417925\pi$
$374$	−30.4507	−	25.5511i	−1.57457	−	1.32122i
$375$		0			0
$376$	1.75216	+	4.81402i	0.0903608	+	0.248264i
$377$	−2.08867	+	23.8736i	−0.107572	+	1.22955i
$378$	−9.35596	+	13.3617i	−0.481219	+	0.687251i
$379$	5.29491			0.271981			0.135991	−	0.990710i	$-0.456578\pi$
$379$	5.29491			0.271981			0.135991	+	0.990710i	$0.456578\pi$
$380$		0			0
$381$	−6.44666			−0.330272
$382$	−6.34564	+	9.06252i	−0.324671	+	0.463679i
$383$	−1.81030	+	20.6918i	−0.0925019	+	1.05730i	0.798102	+	0.602522i	$0.205837\pi$
$383$	−1.81030	+	20.6918i	−0.0925019	+	1.05730i	−0.890604	+	0.454779i	$0.849718\pi$
$384$	−0.711932	−	1.95602i	−0.0363306	−	0.0998175i
$385$		0			0
$386$	−17.9023	−	15.0218i	−0.911201	−	0.764588i
$387$	−1.87374	−	6.99287i	−0.0952473	−	0.355468i
$388$	−7.06882	−	1.89408i	−0.358865	−	0.0961576i
$389$	11.3558	+	2.00234i	0.575763	+	0.101523i	0.453945	−	0.891030i	$-0.350016\pi$
$389$	11.3558	+	2.00234i	0.575763	+	0.101523i	0.121819	+	0.992552i	$0.461127\pi$
$390$		0			0
$391$	3.01487	+	5.22191i	0.152469	+	0.264084i
$392$	14.5794	−	3.90654i	0.736372	−	0.197310i
$393$	1.25046	−	0.109401i	0.0630771	−	0.00551853i
$394$	5.08575	+	1.85106i	0.256216	+	0.0932551i
$395$		0			0
$396$	5.49164	−	4.60803i	0.275965	−	0.231562i
$397$	27.2937	+	19.1113i	1.36983	+	0.959166i	0.999542	+	0.0302496i	$0.00963021\pi$
$397$	27.2937	+	19.1113i	1.36983	+	0.959166i	0.370289	+	0.928917i	$0.379259\pi$
$398$	−6.86011	+	6.86011i	−0.343866	+	0.343866i
$399$	−16.0932	−	39.4950i	−0.805669	−	1.97722i
$400$		0			0
$401$	7.17694	−	1.26549i	0.358399	−	0.0631955i	0.00845058	−	0.999964i	$-0.497310\pi$
$401$	7.17694	−	1.26549i	0.358399	−	0.0631955i	0.349949	+	0.936769i	$0.386199\pi$
$402$	0.0677121	+	0.00592404i	0.00337717	+	0.000295464i
$403$	1.66499	+	0.776399i	0.0829392	+	0.0386752i
$404$	4.35344	−	11.9610i	0.216592	−	0.595081i
$405$		0			0
$406$	21.7386	−	37.6523i	1.07887	−	1.86865i
$407$	−2.53841	+	9.47347i	−0.125824	+	0.469582i
$408$	−12.6016	+	8.82373i	−0.623872	+	0.436840i
$409$	0.504543	−	2.86141i	0.0249481	−	0.141487i	−0.969789	−	0.243943i	$-0.921559\pi$
$409$	0.504543	−	2.86141i	0.0249481	−	0.141487i	0.994738	+	0.102456i	$0.0326700\pi$
$410$		0			0
$411$	−21.1641	−	12.2191i	−1.04395	−	0.602725i
$412$	0.508567	+	5.81295i	0.0250553	+	0.286383i
$413$	−39.3972	+	18.3712i	−1.93861	+	0.903990i
$414$	−1.02186	+	0.371926i	−0.0502216	+	0.0182792i
$415$		0			0
$416$	0.449901	+	2.55152i	0.0220582	+	0.125098i
$417$	2.08888	+	2.08888i	0.102293	+	0.102293i
$418$	−2.92610	−	23.2614i	−0.143120	−	1.13775i
$419$		−	3.06291i		−	0.149633i	−0.997197	−	0.0748166i	$-0.976163\pi$
$419$		−	3.06291i		−	0.149633i	0.997197	−	0.0748166i	$-0.0238371\pi$
$420$		0			0
$421$	−4.96695	−	5.91938i	−0.242074	−	0.288493i	0.631304	−	0.775536i	$-0.282520\pi$
$421$	−4.96695	−	5.91938i	−0.242074	−	0.288493i	−0.873378	+	0.487043i	$0.838076\pi$
$422$	7.66090	−	16.4289i	0.372927	−	0.799744i
$423$	2.88569	+	6.18839i	0.140307	+	0.300890i
$424$	−1.64237	+	1.95730i	−0.0797607	+	0.0950551i
$425$		0			0
$426$	7.36715	−	4.25343i	0.356940	−	0.206079i
$427$	−25.6754	−	36.6683i	−1.24252	−	1.77450i
$428$	2.81078	+	4.01421i	0.135864	+	0.194034i
$429$	−25.1208	+	14.5035i	−1.21284	+	0.700234i
$430$		0			0
$431$	−15.4255	+	18.3834i	−0.743022	+	0.885499i	−0.996649	−	0.0818029i	$-0.973932\pi$
$431$	−15.4255	+	18.3834i	−0.743022	+	0.885499i	0.253626	+	0.967302i	$0.418377\pi$
$432$	1.46660	+	3.14513i	0.0705617	+	0.151320i
$433$	−15.2859	+	32.7807i	−0.734593	+	1.57534i	0.0810009	+	0.996714i	$0.474188\pi$
$433$	−15.2859	+	32.7807i	−0.734593	+	1.57534i	−0.815594	+	0.578625i	$0.803589\pi$
$434$	−2.14235	−	2.55316i	−0.102836	−	0.122556i
$435$		0			0
$436$		−	16.3182i		−	0.781501i
$437$	−0.789733	+	3.46753i	−0.0377781	+	0.165875i
$438$	−13.5472	−	13.5472i	−0.647312	−	0.647312i
$439$	0.952715	+	5.40312i	0.0454706	+	0.257877i	0.999066	−	0.0432151i	$-0.0137601\pi$
$439$	0.952715	+	5.40312i	0.0454706	+	0.257877i	−0.953595	+	0.301092i	$0.902649\pi$
$440$		0			0
$441$	18.9044	−	6.88063i	0.900208	−	0.327649i
$442$	17.3539	−	8.09226i	0.825441	−	0.384909i
$443$	−1.70371	−	19.4735i	−0.0809457	−	0.925214i	−0.922742	−	0.385418i	$-0.874057\pi$
$443$	−1.70371	−	19.4735i	−0.0809457	−	0.925214i	0.841796	−	0.539796i	$-0.181498\pi$
$444$	3.28711	+	1.89781i	0.155999	+	0.0900662i
$445$		0			0
$446$	−1.14744	+	6.50746i	−0.0543329	+	0.308137i
$447$	−2.35280	+	1.64745i	−0.111284	+	0.0779218i
$448$	1.21655	−	4.54023i	0.0574767	−	0.214506i
$449$	6.03729	−	10.4569i	0.284918	−	0.493492i	−0.687672	−	0.726022i	$-0.741367\pi$
$449$	6.03729	−	10.4569i	0.284918	−	0.493492i	0.972589	+	0.232530i	$0.0747004\pi$
$450$		0			0
$451$	−19.2662	+	52.9335i	−0.907211	+	2.49254i
$452$	−3.74566	−	1.74663i	−0.176181	−	0.0821545i
$453$	25.6075	+	2.24037i	1.20315	+	0.105262i
$454$	−1.66597	+	0.293755i	−0.0781878	+	0.0137866i
$455$		0			0
$456$	−8.98866	−	1.23614i	−0.420933	−	0.0578875i
$457$	20.2869	−	20.2869i	0.948981	−	0.948981i	−0.0497789	−	0.998760i	$-0.515852\pi$
$457$	20.2869	−	20.2869i	0.948981	−	0.948981i	0.998760	+	0.0497789i	$0.0158517\pi$
$458$	−10.7900	−	7.55525i	−0.504184	−	0.353034i
$459$	19.6468	−	16.4856i	0.917032	−	0.769481i
$460$		0			0
$461$	33.7441	+	12.2818i	1.57162	+	0.572022i	0.973360	−	0.229282i	$-0.0736378\pi$
$461$	33.7441	+	12.2818i	1.57162	+	0.572022i	0.598258	+	0.801304i	$0.295860\pi$
$462$	52.4244	−	4.58654i	2.43901	−	0.213385i
$463$	29.1592	−	7.81317i	1.35514	−	0.363109i	0.493111	−	0.869966i	$-0.335860\pi$
$463$	29.1592	−	7.81317i	1.35514	−	0.363109i	0.862030	+	0.506857i	$0.169193\pi$
$464$	−4.62484	−	8.01046i	−0.214703	−	0.371876i
$465$		0			0
$466$	−11.1067	−	1.95841i	−0.514508	−	0.0907216i
$467$	−16.0697	−	4.30586i	−0.743617	−	0.199252i	−0.132932	−	0.991125i	$-0.542439\pi$
$467$	−16.0697	−	4.30586i	−0.743617	−	0.199252i	−0.610685	+	0.791874i	$0.709106\pi$
$468$	0.893764	+	3.33557i	0.0413143	+	0.154187i
$469$	0.117577	+	0.0986591i	0.00542922	+	0.00455566i
$470$		0			0
$471$	−11.4944	−	31.5805i	−0.529633	−	1.45515i
$472$	−0.806031	+	9.21297i	−0.0371006	+	0.424062i
$473$	16.7568	−	23.9312i	0.770480	−	1.10036i
$474$	−3.82368			−0.175627
$475$		0			0
$476$	−34.7383			−1.59223
$477$	−1.95333	+	2.78964i	−0.0894368	+	0.127729i
$478$	−1.82831	+	20.8977i	−0.0836251	+	0.955839i
$479$	1.57743	+	4.33395i	0.0720745	+	0.198023i	0.970499	−	0.241105i	$-0.0775097\pi$
$479$	1.57743	+	4.33395i	0.0720745	+	0.198023i	−0.898425	+	0.439128i	$0.855288\pi$
$480$		0			0
$481$	−3.61908	−	3.03677i	−0.165016	−	0.138465i
$482$	−3.10997	−	11.6066i	−0.141655	−	0.528664i
$483$	−7.71063	−	2.06606i	−0.350846	−	0.0940088i
$484$	17.6568	+	3.11338i	0.802584	+	0.141517i
$485$		0			0
$486$	6.47424	+	11.2137i	0.293677	+	0.508664i
$487$	−19.6433	+	5.26341i	−0.890124	+	0.238508i	−0.674770	−	0.738028i	$-0.735757\pi$
$487$	−19.6433	+	5.26341i	−0.890124	+	0.238508i	−0.215354	+	0.976536i	$0.569091\pi$
$488$	−9.48715	+	0.830018i	−0.429463	+	0.0375731i
$489$	−9.81981	−	3.57412i	−0.444067	−	0.161627i
$490$		0			0
$491$	2.28352	−	1.91610i	0.103054	−	0.0864724i	−0.589805	−	0.807546i	$-0.700795\pi$
$491$	2.28352	−	1.91610i	0.103054	−	0.0864724i	0.692859	+	0.721073i	$0.256351\pi$
$492$	17.8578	+	12.5042i	0.805091	+	0.563731i
$493$	−48.3377	+	48.3377i	−2.17702	+	2.17702i
$494$	10.7509	+	3.45802i	0.483707	+	0.155584i
$495$		0			0
$496$	−0.698298	+	0.123129i	−0.0313545	+	0.00552865i
$497$	19.1364	+	1.67422i	0.858386	+	0.0750991i
$498$	6.41625	+	2.99195i	0.287519	+	0.134072i
$499$	−7.22085	+	19.8391i	−0.323250	+	0.888121i	0.666525	+	0.745482i	$0.267781\pi$
$499$	−7.22085	+	19.8391i	−0.323250	+	0.888121i	−0.989775	+	0.142638i	$0.954441\pi$
$500$		0			0
$501$	8.29191	−	14.3620i	0.370455	−	0.641647i
$502$	3.68457	−	13.7510i	0.164450	−	0.613737i
$503$	−27.9746	+	19.5880i	−1.24733	+	0.873387i	−0.995535	−	0.0943951i	$-0.969908\pi$
$503$	−27.9746	+	19.5880i	−1.24733	+	0.873387i	−0.251791	+	0.967782i	$0.581019\pi$
$504$	1.08789	−	6.16972i	0.0484584	−	0.274821i
$505$		0			0
$506$	−3.80035	−	2.19413i	−0.168946	−	0.0975412i
$507$	1.14064	+	13.0376i	0.0506578	+	0.579021i
$508$	−2.80688	+	1.30887i	−0.124535	+	0.0580717i
$509$	−10.1155	+	3.68175i	−0.448363	+	0.163191i	−0.556326	−	0.830964i	$-0.687789\pi$
$509$	−10.1155	+	3.68175i	−0.448363	+	0.163191i	0.107963	+	0.994155i	$0.465567\pi$
$510$		0			0
$511$	−7.51249	−	42.6055i	−0.332333	−	1.88475i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	15.1081	+	0.746921i	0.667038	+	0.0329774i
$514$			21.2870i			0.938927i
$515$		0			0
$516$	−7.26752	−	8.66109i	−0.319935	−	0.381283i
$517$	−11.6450	+	24.9727i	−0.512146	+	1.09830i
$518$	3.62226	+	7.76796i	0.159153	+	0.341305i
$519$	−7.30229	+	8.70253i	−0.320535	+	0.381999i
$520$		0			0
$521$	−6.32910	+	3.65411i	−0.277283	+	0.160089i	−0.632193	−	0.774811i	$-0.717845\pi$
$521$	−6.32910	+	3.65411i	−0.277283	+	0.160089i	0.354910	+	0.934901i	$0.384512\pi$
$522$	−7.07128	−	10.0988i	−0.309501	−	0.442014i
$523$	−2.74368	−	3.91839i	−0.119973	−	0.171339i	0.754673	−	0.656101i	$-0.227795\pi$
$523$	−2.74368	−	3.91839i	−0.119973	−	0.171339i	−0.874646	+	0.484761i	$0.838906\pi$
$524$	0.522237	−	0.301514i	0.0228140	−	0.0131717i
$525$		0			0
$526$	0.0971297	−	0.115755i	0.00423506	−	0.00504715i
$527$	2.21468	+	4.74941i	0.0964732	+	0.206887i
$528$	4.73155	−	10.1468i	0.205914	−	0.441584i
$529$	−14.3562	−	17.1091i	−0.624184	−	0.743874i
$530$		0			0
$531$			12.3264i			0.534919i
$532$	−15.0257	−	13.9287i	−0.651447	−	0.603887i
$533$	−19.1871	−	19.1871i	−0.831084	−	0.831084i
$534$	−0.719935	−	4.08295i	−0.0311546	−	0.176687i
$535$		0			0
$536$	0.0306846	−	0.0111683i	0.00132537	−	0.000482397i
$537$	28.9367	−	13.4934i	1.24871	−	0.582284i
$538$	1.60468	+	18.3416i	0.0691826	+	0.790761i
$539$	70.3065	+	40.5915i	3.02832	+	1.74840i
$540$		0			0
$541$	4.69194	−	26.6093i	0.201722	−	1.14402i	−0.700793	−	0.713365i	$-0.747170\pi$
$541$	4.69194	−	26.6093i	0.201722	−	1.14402i	0.902515	−	0.430658i	$-0.141718\pi$
$542$	12.3676	−	8.65992i	0.531236	−	0.371975i
$543$	−13.5008	+	50.3858i	−0.579376	+	2.16226i
$544$	−3.69525	+	6.40037i	−0.158433	+	0.274414i
$545$		0			0
$546$	−8.67002	+	23.8207i	−0.371042	+	1.01943i
$547$	−28.5879	−	13.3308i	−1.22233	−	0.569982i	−0.299098	−	0.954223i	$-0.596686\pi$
$547$	−28.5879	−	13.3308i	−1.22233	−	0.569982i	−0.923233	+	0.384240i	$0.874463\pi$
$548$	−11.6957	−	1.02324i	−0.499617	−	0.0437108i
$549$	−12.5004	+	2.20415i	−0.533502	+	0.0940709i
$550$		0			0
$551$	−40.2895	+	1.52642i	−1.71639	+	0.0650277i
$552$	−1.20087	+	1.20087i	−0.0511125	+	0.0511125i
$553$	−7.07284	−	4.95246i	−0.300768	−	0.210600i
$554$	−1.15581	+	0.969840i	−0.0491057	+	0.0412046i
$555$		0			0
$556$	1.33361	+	0.485393i	0.0565575	+	0.0205852i
$557$	11.7008	−	1.02369i	0.495781	−	0.0433752i	0.163476	−	0.986547i	$-0.447729\pi$
$557$	11.7008	−	1.02369i	0.495781	−	0.0433752i	0.332305	+	0.943172i	$0.392174\pi$
$558$	−0.912878	+	0.244605i	−0.0386452	+	0.0103550i
$559$	7.03638	+	12.1874i	0.297607	+	0.515471i
$560$		0			0
$561$	−81.4856	−	14.3681i	−3.44032	−	0.606622i
$562$	11.2661	+	3.01875i	0.475233	+	0.127338i
$563$	9.46184	+	35.3121i	0.398769	+	1.48823i	0.815265	+	0.579089i	$0.196591\pi$
$563$	9.46184	+	35.3121i	0.398769	+	1.48823i	−0.416496	+	0.909138i	$0.636742\pi$
$564$	8.16888	+	6.85451i	0.343972	+	0.288627i
$565$		0			0
$566$	7.89107	+	21.6805i	0.331686	+	0.911301i
$567$	−4.59730	+	52.5474i	−0.193069	+	2.20678i
$568$	2.34409	−	3.34770i	0.0983557	−	0.140466i
$569$	−37.2842			−1.56304			−0.781518	−	0.623883i	$-0.785554\pi$
$569$	−37.2842			−1.56304			−0.781518	+	0.623883i	$0.785554\pi$
$570$		0			0
$571$	36.7103			1.53628			0.768139	−	0.640283i	$-0.221183\pi$
$571$	36.7103			1.53628			0.768139	+	0.640283i	$0.221183\pi$
$572$	−7.99294	+	11.4151i	−0.334202	+	0.477290i
$573$	−2.00709	+	22.9411i	−0.0838474	+	0.958380i
$574$	16.8369	+	46.2591i	0.702760	+	1.93082i
$575$		0			0
$576$	−1.02102	−	0.856736i	−0.0425424	−	0.0356973i
$577$	−6.19002	−	23.1015i	−0.257694	−	0.961727i	−0.966572	−	0.256396i	$-0.917465\pi$
$577$	−6.19002	−	23.1015i	−0.257694	−	0.961727i	0.708878	−	0.705331i	$-0.249202\pi$
$578$	36.3378	+	9.73667i	1.51145	+	0.404992i
$579$	−47.9062	−	8.44716i	−1.99091	−	0.351052i
$580$		0			0
$581$	7.99325	+	13.8447i	0.331616	+	0.574376i
$582$	−14.7141	+	3.94263i	−0.609919	+	0.163427i
$583$	−13.6904	+	1.19776i	−0.566999	+	0.0496060i
$584$	−8.64898	−	3.14797i	−0.357897	−	0.130264i
$585$		0			0
$586$	−6.85294	+	5.75030i	−0.283092	+	0.237543i
$587$	15.7230	+	11.0093i	0.648956	+	0.454404i	0.851136	−	0.524945i	$-0.175914\pi$
$587$	15.7230	+	11.0093i	0.648956	+	0.454404i	−0.202181	+	0.979348i	$0.564803\pi$
$588$	22.2161	−	22.2161i	0.916177	−	0.916177i
$589$	−0.946390	+	2.94231i	−0.0389953	+	0.121236i
$590$		0			0
$591$	11.0945	−	1.95626i	0.456366	−	0.0804697i
$592$	1.81652	+	0.158925i	0.0746587	+	0.00653179i
$593$	−25.3600	−	11.8255i	−1.04141	−	0.485617i	−0.174800	−	0.984604i	$-0.555928\pi$
$593$	−25.3600	−	11.8255i	−1.04141	−	0.485617i	−0.866609	+	0.498987i	$0.833706\pi$
$594$	−6.38385	+	17.5395i	−0.261932	+	0.719654i
$595$		0			0
$596$	−0.689929	+	1.19499i	−0.0282606	+	0.0489488i
$597$	−5.22672	+	19.5064i	−0.213915	+	0.798343i
$598$	1.73156	−	1.21245i	0.0708086	−	0.0495807i
$599$	1.40483	−	7.96719i	0.0573998	−	0.325531i	−0.942564	−	0.334025i	$-0.891593\pi$
$599$	1.40483	−	7.96719i	0.0573998	−	0.325531i	0.999964	+	0.00849471i	$0.00270398\pi$
$600$		0			0
$601$	27.7499	+	16.0214i	1.13194	+	0.653527i	0.944423	−	0.328734i	$-0.106622\pi$
$601$	27.7499	+	16.0214i	1.13194	+	0.653527i	0.187520	+	0.982261i	$0.439955\pi$
$602$	−2.22517	−	25.4338i	−0.0906911	−	1.03660i
$603$	0.0394449	−	0.0183935i	0.00160632	−	0.000749039i
$604$	11.6044	−	4.22366i	0.472176	−	0.171858i
$605$		0			0
$606$	−4.60085	−	26.0927i	−0.186897	−	1.05994i
$607$	4.89399	+	4.89399i	0.198641	+	0.198641i	0.799417	−	0.600776i	$-0.205142\pi$
$607$	4.89399	+	4.89399i	0.198641	+	0.198641i	−0.600776	+	0.799417i	$0.705142\pi$
$608$	−4.16464	+	1.28676i	−0.168899	+	0.0521849i
$609$		−	90.4999i		−	3.66724i
$610$		0			0
$611$	−8.53172	−	10.1677i	−0.345157	−	0.411342i
$612$	−4.16296	+	8.92750i	−0.168278	+	0.360873i
$613$	5.96736	+	12.7970i	0.241019	+	0.516868i	0.989190	−	0.146639i	$-0.0468454\pi$
$613$	5.96736	+	12.7970i	0.241019	+	0.516868i	−0.748171	+	0.663506i	$0.769068\pi$
$614$	1.81506	−	2.16310i	0.0732497	−	0.0872956i
$615$		0			0
$616$	21.8944	−	12.6408i	0.882152	−	0.509310i
$617$	11.2452	+	16.0599i	0.452717	+	0.646546i	0.979023	−	0.203748i	$-0.0653125\pi$
$617$	11.2452	+	16.0599i	0.452717	+	0.646546i	−0.526307	+	0.850295i	$0.676424\pi$
$618$	6.96675	+	9.94955i	0.280244	+	0.400229i
$619$	9.10749	−	5.25821i	0.366061	−	0.211345i	−0.305675	−	0.952136i	$-0.598882\pi$
$619$	9.10749	−	5.25821i	0.366061	−	0.211345i	0.671736	+	0.740790i	$0.265549\pi$
$620$		0			0
$621$	1.81993	−	2.16891i	0.0730313	−	0.0870353i
$622$	9.30539	+	19.9555i	0.373112	+	0.800141i
$623$	3.95657	−	8.48490i	0.158517	−	0.339940i
$624$	3.46658	+	4.13131i	0.138774	+	0.165385i
$625$		0			0
$626$		−	15.8759i		−	0.634527i
$627$	−29.4847	−	38.8873i	−1.17750	−	1.55301i
$628$	−11.4165	−	11.4165i	−0.455567	−	0.455567i
$629$	−2.34014	−	13.2716i	−0.0933074	−	0.529173i
$630$		0			0
$631$	20.9133	−	7.61182i	0.832545	−	0.303022i	0.109642	−	0.993971i	$-0.465030\pi$
$631$	20.9133	−	7.61182i	0.832545	−	0.303022i	0.722903	+	0.690949i	$0.242807\pi$
$632$	−1.66483	+	0.776324i	−0.0662235	+	0.0308805i
$633$	−3.28862	−	37.5891i	−0.130711	−	1.49403i
$634$	−1.01715	−	0.587250i	−0.0403960	−	0.0233227i
$635$		0			0
$636$	−0.923551	+	5.23772i	−0.0366212	+	0.207689i
$637$	−32.0338	+	22.4303i	−1.26922	+	0.888721i
$638$	12.8763	−	48.0550i	0.509778	−	1.90252i
$639$	2.72353	−	4.71729i	0.107741	−	0.186613i
$640$		0			0
$641$	11.4634	−	31.4954i	0.452777	−	1.24400i	−0.477984	−	0.878368i	$-0.658632\pi$
$641$	11.4634	−	31.4954i	0.452777	−	1.24400i	0.930761	−	0.365627i	$-0.119145\pi$
$642$	9.24482	+	4.31093i	0.364864	+	0.170139i
$643$	30.7343	+	2.68891i	1.21204	+	0.106040i	0.675196	−	0.737639i	$-0.264059\pi$
$643$	30.7343	+	2.68891i	1.21204	+	0.106040i	0.536848	+	0.843679i	$0.319615\pi$
$644$	−3.77669	+	0.665932i	−0.148822	+	0.0262414i
$645$		0			0
$646$	17.1519	+	27.2688i	0.674833	+	1.07287i
$647$	−11.9925	+	11.9925i	−0.471472	+	0.471472i	−0.902391	−	0.430919i	$-0.858190\pi$
$647$	−11.9925	+	11.9925i	−0.471472	+	0.471472i	0.430919	+	0.902391i	$0.358190\pi$
$648$	9.19257	+	6.43671i	0.361118	+	0.252858i
$649$	−38.1047	+	31.9736i	−1.49574	+	1.25507i
$650$		0			0
$651$	−6.51923	−	2.37281i	−0.255509	−	0.0929976i
$652$	−5.00121	+	0.437549i	−0.195862	+	0.0171357i
$653$	35.6537	−	9.55338i	1.39524	−	0.373853i	0.518605	−	0.855014i	$-0.326451\pi$
$653$	35.6537	−	9.55338i	1.39524	−	0.373853i	0.876632	+	0.481161i	$0.159785\pi$
$654$	−16.9836	−	29.4164i	−0.664111	−	1.15027i
$655$		0			0
$656$	10.3140	+	1.81864i	0.402695	+	0.0710060i
$657$	−11.8496	−	3.17508i	−0.462296	−	0.123872i
$658$	6.23237	+	23.2595i	0.242963	+	0.906750i
$659$	22.1129	+	18.5550i	0.861398	+	0.722798i	0.962269	−	0.272101i	$-0.0877185\pi$
$659$	22.1129	+	18.5550i	0.861398	+	0.722798i	−0.100871	+	0.994900i	$0.532163\pi$
$660$		0			0
$661$	14.9090	+	40.9622i	0.579893	+	1.59324i	0.788360	+	0.615215i	$0.210931\pi$
$661$	14.9090	+	40.9622i	0.579893	+	1.59324i	−0.208466	+	0.978030i	$0.566847\pi$
$662$	1.50581	−	17.2115i	0.0585249	−	0.668942i
$663$	22.8612	−	32.6492i	0.887856	−	1.26799i
$664$	3.40110			0.131988
$665$		0			0
$666$	2.43039			0.0941758
$667$	−4.32855	+	6.18182i	−0.167602	+	0.239361i
$668$	0.694375	−	7.93674i	0.0268662	−	0.307082i
$669$	4.70434	+	12.9251i	0.181880	+	0.499711i
$670$		0			0
$671$	−39.2386	−	32.9251i	−1.51479	−	1.27106i
$672$	−2.53231	−	9.45072i	−0.0976861	−	0.364569i
$673$	6.04317	+	1.61926i	0.232947	+	0.0624180i	0.373404	−	0.927669i	$-0.378190\pi$
$673$	6.04317	+	1.61926i	0.232947	+	0.0624180i	−0.140457	+	0.990087i	$0.544857\pi$
$674$	−4.14211	−	0.730367i	−0.159548	−	0.0281327i
$675$		0			0
$676$	3.14367	+	5.44500i	0.120911	+	0.209423i
$677$	−30.9375	+	8.28968i	−1.18903	+	0.318598i	−0.798501	−	0.601994i	$-0.794373\pi$
$677$	−30.9375	+	8.28968i	−1.18903	+	0.318598i	−0.390525	+	0.920592i	$0.627706\pi$
$678$	−8.57004	+	0.749782i	−0.329131	+	0.0287952i
$679$	−32.3239	−	11.7649i	−1.24048	−	0.451497i
$680$		0			0
$681$	−2.69747	+	2.26344i	−0.103367	+	0.0867354i
$682$	−3.12408	−	2.18750i	−0.119627	−	0.0837639i
$683$	−17.3530	+	17.3530i	−0.663993	+	0.663993i	−0.956319	−	0.292326i	$-0.905571\pi$
$683$	−17.3530	+	17.3530i	−0.663993	+	0.663993i	0.292326	+	0.956319i	$0.405571\pi$
$684$	−5.38023	+	2.19231i	−0.205718	+	0.0838251i
$685$		0			0
$686$	37.4658	−	6.60623i	1.43045	−	0.252227i
$687$	−27.3142	−	2.38968i	−1.04210	−	0.0911721i
$688$	−4.92275	−	2.29552i	−0.187678	−	0.0875158i
$689$	2.26414	−	6.22067i	0.0862568	−	0.236989i
$690$		0			0
$691$	11.8822	−	20.5806i	0.452021	−	0.782924i	−0.546490	−	0.837465i	$-0.684037\pi$
$691$	11.8822	−	20.5806i	0.452021	−	0.782924i	0.998511	+	0.0545419i	$0.0173698\pi$
$692$	−1.41254	+	5.27167i	−0.0536967	+	0.200399i
$693$	27.6024	−	19.3274i	1.04853	−	0.734188i
$694$	4.86141	−	27.5704i	0.184537	−	1.04656i
$695$		0			0
$696$	−16.6742	−	9.62683i	−0.632032	−	0.364904i
$697$	−6.74601	−	77.1072i	−0.255523	−	2.92065i
$698$	10.7996	−	5.03596i	0.408773	−	0.190614i
$699$	−22.0600	+	8.02919i	−0.834387	+	0.303692i
$700$		0			0
$701$	0.276291	+	1.56692i	0.0104354	+	0.0591819i	0.989581	−	0.143979i	$-0.0459897\pi$
$701$	0.276291	+	1.56692i	0.0104354	+	0.0591819i	−0.979145	+	0.203161i	$0.934879\pi$
$702$	−6.35762	−	6.35762i	−0.239953	−	0.239953i
$703$	4.30919	−	6.67879i	0.162524	−	0.251895i
$704$		−	5.37859i		−	0.202713i
$705$		0			0
$706$	−0.711310	−	0.847706i	−0.0267705	−	0.0319038i
$707$	25.2850	−	54.2239i	0.950942	−	2.03930i
$708$	8.13562	+	17.4469i	0.305755	+	0.655694i
$709$	−15.0796	+	17.9711i	−0.566325	+	0.674920i	−0.970872	−	0.239597i	$-0.922985\pi$
$709$	−15.0796	+	17.9711i	−0.566325	+	0.674920i	0.404547	+	0.914517i	$0.367429\pi$
$710$		0			0
$711$	−2.12034	+	1.22418i	−0.0795189	+	0.0459103i
$712$	−1.14242	−	1.63155i	−0.0428142	−	0.0611450i
$713$	0.331822	+	0.473891i	0.0124268	+	0.0177474i
$714$	−62.6219	+	36.1548i	−2.34356	+	1.35306i
$715$		0			0
$716$	9.85949	−	11.7501i	0.368466	−	0.439121i
$717$	18.4540	+	39.5746i	0.689175	+	1.47794i
$718$	−11.3206	+	24.2771i	−0.422481	+	0.906013i
$719$	28.5047	+	33.9706i	1.06305	+	1.26689i	0.962304	+	0.271975i	$0.0876769\pi$
$719$	28.5047	+	33.9706i	1.06305	+	1.26689i	0.100741	+	0.994913i	$0.467879\pi$
$720$		0			0
$721$			27.4275i			1.02145i
$722$	−3.51483	+	18.6721i	−0.130809	+	0.694902i
$723$	−17.6861	−	17.6861i	−0.657752	−	0.657752i
$724$	4.35159	+	24.6791i	0.161725	+	0.917191i
$725$		0			0
$726$	35.0698	−	12.7644i	1.30156	−	0.473731i
$727$	−16.9126	+	7.88649i	−0.627255	+	0.292494i	−0.710135	−	0.704066i	$-0.751366\pi$
$727$	−16.9126	+	7.88649i	−0.627255	+	0.292494i	0.0828797	+	0.996560i	$0.473588\pi$
$728$	1.06140	+	12.1318i	0.0393380	+	0.449635i
$729$	−5.81389	−	3.35665i	−0.215329	−	0.124320i
$730$		0			0
$731$	−6.97071	+	39.5328i	−0.257821	+	1.46217i
$732$	−16.2384	+	11.3702i	−0.600187	+	0.420256i
$733$	−6.58562	+	24.5779i	−0.243245	+	0.907804i	0.731012	+	0.682365i	$0.239048\pi$
$733$	−6.58562	+	24.5779i	−0.243245	+	0.907804i	−0.974257	+	0.225439i	$0.927618\pi$
$734$	15.4589	−	26.7757i	0.570600	−	0.988308i
$735$		0			0
$736$	−0.279046	+	0.766674i	−0.0102858	+	0.0282600i
$737$	0.159177	+	0.0742253i	0.00586335	+	0.00273412i
$738$	13.9059	+	1.21661i	0.511885	+	0.0447841i
$739$	49.5919	−	8.74440i	1.82427	−	0.321668i	0.846666	−	0.532125i	$-0.178606\pi$
$739$	49.5919	−	8.74440i	1.82427	−	0.321668i	0.977603	+	0.210457i	$0.0674952\pi$
$740$		0			0
$741$	22.9794	−	4.95561i	0.844171	−	0.182049i
$742$	−8.49227	+	8.49227i	−0.311761	+	0.311761i
$743$	14.3956	+	10.0799i	0.528125	+	0.369797i	0.807020	−	0.590525i	$-0.201079\pi$
$743$	14.3956	+	10.0799i	0.528125	+	0.369797i	−0.278895	+	0.960322i	$0.589968\pi$
$744$	−1.13065	+	0.948732i	−0.0414518	+	0.0347822i
$745$		0			0
$746$	−31.5056	−	11.4671i	−1.15350	−	0.419840i
$747$	4.51589	−	0.395089i	0.165228	−	0.0144555i
$748$	−38.3960	+	10.2882i	−1.40390	+	0.376173i
$749$	11.5170	+	19.9481i	0.420823	+	0.728887i
$750$		0			0
$751$	25.8984	+	4.56659i	0.945047	+	0.166637i	0.624878	−	0.780723i	$-0.285149\pi$
$751$	25.8984	+	4.56659i	0.945047	+	0.166637i	0.320170	+	0.947360i	$0.396260\pi$
$752$	4.94841	+	1.32592i	0.180450	+	0.0483514i
$753$	−7.66961	−	28.6234i	−0.279496	−	1.04309i
$754$	18.3581	+	15.4043i	0.668563	+	0.560991i
$755$		0			0
$756$	5.57890	+	15.3279i	0.202903	+	0.557471i
$757$	−1.78315	+	20.3816i	−0.0648099	+	0.740780i	0.892373	+	0.451298i	$0.149039\pi$
$757$	−1.78315	+	20.3816i	−0.0648099	+	0.740780i	−0.957183	+	0.289482i	$0.906517\pi$
$758$	3.03703	−	4.33733i	0.110310	−	0.157539i
$759$	−9.13440			−0.331558
$760$		0			0
$761$	−36.1259			−1.30956			−0.654782	−	0.755818i	$-0.727240\pi$
$761$	−36.1259			−1.30956			−0.654782	+	0.755818i	$0.727240\pi$
$762$	−3.69765	+	5.28079i	−0.133952	+	0.191303i
$763$	6.68503	−	76.4102i	0.242014	−	2.76624i
$764$	3.78387	+	10.3961i	0.136896	+	0.376117i
$765$		0			0
$766$	15.9114	+	13.3512i	0.574902	+	0.482400i
$767$	−6.20153	−	23.1444i	−0.223924	−	0.835697i
$768$	−2.01062	−	0.538744i	−0.0725521	−	0.0194403i
$769$	9.17590	+	1.61796i	0.330891	+	0.0583451i	0.336626	−	0.941638i	$-0.390714\pi$
$769$	9.17590	+	1.61796i	0.330891	+	0.0583451i	−0.00573451	+	0.999984i	$0.501825\pi$
$770$		0			0
$771$	22.1549	+	38.3734i	0.797890	+	1.38199i
$772$	−22.5734	+	6.04853i	−0.812436	+	0.217691i
$773$	14.9183	−	1.30518i	0.536575	−	0.0469442i	0.184352	−	0.982860i	$-0.440981\pi$
$773$	14.9183	−	1.30518i	0.536575	−	0.0469442i	0.352223	+	0.935916i	$0.385426\pi$
$774$	−6.80296	−	2.47607i	−0.244527	−	0.0890006i
$775$		0			0
$776$	−5.60605	+	4.70404i	−0.201246	+	0.168865i
$777$	14.6145	+	10.2331i	0.524291	+	0.367112i
$778$	8.15366	−	8.15366i	0.292323	−	0.292323i
$779$	27.9991	−	36.0568i	1.00317	−	1.29187i
$780$		0			0
$781$	21.6472	−	3.81699i	0.774598	−	0.136583i
$782$	6.00680	+	0.525527i	0.214803	+	0.0187928i
$783$	29.0914	+	13.5656i	1.03964	+	0.484793i
$784$	5.16236	−	14.1835i	0.184370	−	0.506552i
$785$		0			0
$786$	0.627616	−	1.08706i	0.0223863	−	0.0387742i
$787$	−5.36528	+	20.0235i	−0.191251	+	0.713760i	0.801954	+	0.597386i	$0.203794\pi$
$787$	−5.36528	+	20.0235i	−0.191251	+	0.713760i	−0.993205	+	0.116374i	$0.962873\pi$
$788$	4.43337	−	3.10428i	0.157932	−	0.110585i
$789$	0.0546187	−	0.309758i	0.00194448	−	0.0110277i
$790$		0			0
$791$	−16.8235	−	9.71307i	−0.598176	−	0.345357i
$792$	−0.624804	−	7.14155i	−0.0222015	−	0.253764i
$793$	22.3622	−	10.4277i	0.794104	−	0.370297i
$794$	31.3100	−	11.3959i	1.11115	−	0.404426i
$795$		0			0
$796$	1.68468	+	9.55427i	0.0597118	+	0.338642i
$797$	15.0589	+	15.0589i	0.533414	+	0.533414i	0.921587	−	0.388172i	$-0.126893\pi$
$797$	15.0589	+	15.0589i	0.533414	+	0.533414i	−0.388172	+	0.921587i	$0.626893\pi$
$798$	−41.5831	−	9.47059i	−1.47203	−	0.335255i
$799$		−	37.8614i		−	1.33944i
$800$		0			0
$801$	−1.70641	−	2.03362i	−0.0602930	−	0.0718545i
$802$	3.07990	−	6.60486i	0.108755	−	0.233226i
$803$	−20.9216	−	44.8666i	−0.738309	−	1.58331i
$804$	0.0436907	−	0.0520686i	0.00154085	−	0.00183632i
$805$		0			0
$806$	1.59099	−	0.918558i	0.0560402	−	0.0323548i
$807$	21.9821	+	31.3938i	0.773808	+	1.10511i
$808$	−7.30083	−	10.4267i	−0.256842	−	0.366809i
$809$	14.6163	−	8.43875i	0.513883	−	0.296691i	−0.220545	−	0.975377i	$-0.570784\pi$
$809$	14.6163	−	8.43875i	0.513883	−	0.296691i	0.734428	+	0.678686i	$0.237450\pi$
$810$		0			0
$811$	−1.32164	+	1.57507i	−0.0464091	+	0.0553082i	−0.788750	−	0.614715i	$-0.789271\pi$
$811$	−1.32164	+	1.57507i	−0.0464091	+	0.0553082i	0.742341	+	0.670023i	$0.233716\pi$
$812$	−18.3742	−	39.4037i	−0.644810	−	1.38280i
$813$	13.2818	−	28.4829i	0.465814	−	0.998940i
$814$	6.30424	+	7.51310i	0.220964	+	0.263334i
$815$		0			0
$816$			15.3837i			0.538537i
$817$	−18.8662	+	14.3045i	−0.660046	+	0.500452i
$818$	−2.05453	−	2.05453i	−0.0718351	−	0.0718351i
$819$	2.81859	+	15.9850i	0.0984894	+	0.558561i
$820$		0			0
$821$	16.6758	−	6.06951i	0.581990	−	0.211827i	−0.0342125	−	0.999415i	$-0.510892\pi$
$821$	16.6758	−	6.06951i	0.581990	−	0.211827i	0.616203	+	0.787587i	$0.288670\pi$
$822$	−22.1486	+	10.3280i	−0.772520	+	0.360232i
$823$	4.51203	+	51.5727i	0.157279	+	1.79771i	0.508129	+	0.861281i	$0.330337\pi$
$823$	4.51203	+	51.5727i	0.157279	+	1.79771i	−0.350850	+	0.936432i	$0.614107\pi$
$824$	5.05339	+	2.91758i	0.176043	+	0.101639i
$825$		0			0
$826$	−7.54850	+	42.8096i	−0.262646	+	1.48954i
$827$	6.13859	−	4.29828i	0.213460	−	0.149466i	−0.461957	−	0.886902i	$-0.652853\pi$
$827$	6.13859	−	4.29828i	0.213460	−	0.149466i	0.675417	+	0.737436i	$0.263964\pi$
$828$	−0.281450	+	1.05038i	−0.00978105	+	0.0365034i
$829$	13.7629	−	23.8381i	0.478006	−	0.827931i	−0.521676	−	0.853144i	$-0.674693\pi$
$829$	13.7629	−	23.8381i	0.478006	−	0.827931i	0.999682	+	0.0252124i	$0.00802622\pi$
$830$		0			0
$831$	−1.07416	+	2.95124i	−0.0372624	+	0.102377i
$832$	2.34813	+	1.09495i	0.0814069	+	0.0379607i
$833$	−111.126	−	9.72225i	−3.85028	−	0.336856i
$834$	2.90924	−	0.512978i	0.100739	−	0.0177630i
$835$		0			0
$836$	−20.7330	−	10.9453i	−0.717065	−	0.378550i
$837$	1.73995	−	1.73995i	0.0601415	−	0.0601415i
$838$	−2.50899	−	1.75682i	−0.0866717	−	0.0606882i
$839$	12.6998	−	10.6564i	0.438444	−	0.367899i	−0.396682	−	0.917956i	$-0.629839\pi$
$839$	12.6998	−	10.6564i	0.438444	−	0.367899i	0.835127	+	0.550057i	$0.185394\pi$
$840$		0			0
$841$	−53.1458	−	19.3435i	−1.83261	−	0.667017i
$842$	−7.69779	+	0.673470i	−0.265284	+	0.0232093i
$843$	23.4510	−	6.28368i	0.807696	−	0.216421i
$844$	−9.06362	−	15.6986i	−0.311983	−	0.540370i
$845$		0			0
$846$	6.72440	+	1.18569i	0.231190	+	0.0407650i
$847$	81.4029	+	21.8118i	2.79704	+	0.749464i
$848$	0.661303	+	2.46802i	0.0227092	+	0.0847520i
$849$	36.7896	+	30.8701i	1.26261	+	1.05946i
$850$		0			0
$851$	−0.508831	−	1.39800i	−0.0174425	−	0.0479229i
$852$	0.741421	−	8.47448i	0.0254007	−	0.290331i
$853$	11.0672	−	15.8055i	0.378932	−	0.541171i	−0.583705	−	0.811966i	$-0.698398\pi$
$853$	11.0672	−	15.8055i	0.378932	−	0.541171i	0.962637	+	0.270795i	$0.0872864\pi$
$854$	−44.7637			−1.53178
$855$		0			0
$856$	4.90045			0.167494
$857$	32.6268	−	46.5959i	1.11451	−	1.59169i	0.363237	−	0.931697i	$-0.381672\pi$
$857$	32.6268	−	46.5959i	1.11451	−	1.59169i	0.751275	−	0.659990i	$-0.229439\pi$
$858$	−2.52812	+	28.8966i	−0.0863087	+	0.986513i
$859$	2.68377	+	7.37359i	0.0915689	+	0.251584i	0.977019	−	0.213150i	$-0.0683723\pi$
$859$	2.68377	+	7.37359i	0.0915689	+	0.251584i	−0.885451	+	0.464734i	$0.846150\pi$
$860$		0			0
$861$	78.4968	+	65.8666i	2.67516	+	2.24473i
$862$	6.21111	+	23.1802i	0.211551	+	0.789520i
$863$	−23.4234	−	6.27629i	−0.797343	−	0.213647i	−0.162926	−	0.986638i	$-0.552093\pi$
$863$	−23.4234	−	6.27629i	−0.797343	−	0.213647i	−0.634417	+	0.772991i	$0.718760\pi$
$864$	3.41754	+	0.602605i	0.116267	+	0.0205010i
$865$		0			0
$866$	18.0847	+	31.3237i	0.614545	+	1.06442i
$867$	75.6388	−	20.2674i	2.56883	−	0.688316i
$868$	−3.32023	+	0.290482i	−0.112696	+	0.00985962i
$869$	−9.28430	−	3.37921i	−0.314948	−	0.114632i
$870$		0			0
$871$	−0.0648092	+	0.0543813i	−0.00219597	+	0.00184264i
$872$	−13.3671	−	9.35974i	−0.452667	−	0.316961i
$873$	−6.89712	+	6.89712i	−0.233432	+	0.233432i
$874$	2.38746	+	2.63581i	0.0807572	+	0.0891575i
$875$		0			0
$876$	−18.8676	+	3.32687i	−0.637478	+	0.112405i
$877$	−16.5226	−	1.44554i	−0.557927	−	0.0488123i	−0.195295	−	0.980745i	$-0.562566\pi$
$877$	−16.5226	−	1.44554i	−0.557927	−	0.0488123i	−0.362632	+	0.931932i	$0.618122\pi$
$878$	4.97243	+	2.31868i	0.167811	+	0.0782517i
$879$	−6.36885	+	17.4983i	−0.214816	+	0.590202i
$880$		0			0
$881$	24.3096	−	42.1055i	0.819013	−	1.41857i	−0.0873979	−	0.996173i	$-0.527855\pi$
$881$	24.3096	−	42.1055i	0.819013	−	1.41857i	0.906410	−	0.422398i	$-0.138812\pi$
$882$	5.20682	−	19.4321i	0.175323	−	0.654313i
$883$	16.7765	−	11.7470i	0.564574	−	0.395319i	−0.256156	−	0.966636i	$-0.582456\pi$
$883$	16.7765	−	11.7470i	0.564574	−	0.395319i	0.820730	+	0.571316i	$0.193567\pi$
$884$	3.32500	−	18.8570i	0.111832	−	0.634230i
$885$		0			0
$886$	−16.9290	−	9.77394i	−0.568740	−	0.328362i
$887$	−0.590341	−	6.74763i	−0.0198217	−	0.226563i	−0.999644	−	0.0266911i	$-0.991503\pi$
$887$	−0.590341	−	6.74763i	−0.0198217	−	0.226563i	0.979822	−	0.199872i	$-0.0640526\pi$
$888$	3.44001	−	1.60410i	0.115439	−	0.0538301i
$889$	−13.6794	+	4.97891i	−0.458794	+	0.166987i
$890$		0			0
$891$	10.4812	+	59.4419i	0.351134	+	1.99138i
$892$	4.67245	+	4.67245i	0.156445	+	0.156445i
$893$	15.1809	−	16.3765i	0.508011	−	0.548020i
$894$			2.87224i			0.0960622i
$895$		0			0
$896$	−3.02136	−	3.60071i	−0.100936	−	0.120291i
$897$	1.85955	−	3.98781i	0.0620884	−	0.133149i
$898$	−5.10294	−	10.9433i	−0.170287	−	0.365182i
$899$	−4.21584	+	5.02424i	−0.140606	+	0.167568i
$900$		0			0
$901$	16.3534	−	9.44167i	0.544812	−	0.314547i
$902$	32.3100	+	46.1434i	1.07580	+	1.53641i
$903$	−30.4821	−	43.5329i	−1.01438	−	1.44869i
$904$	−3.57917	+	2.06644i	−0.119042	+	0.0687287i
$905$		0			0
$906$	16.5231	−	19.6914i	0.548943	−	0.654204i
$907$	17.8918	+	38.3690i	0.594086	+	1.27402i	0.941722	+	0.336392i	$0.109207\pi$
$907$	17.8918	+	38.3690i	0.594086	+	1.27402i	−0.347636	+	0.937630i	$0.613015\pi$
$908$	−0.714931	+	1.53317i	−0.0237258	+	0.0508802i
$909$	−10.9051	−	12.9961i	−0.361698	−	0.431055i
$910$		0			0
$911$			30.9004i			1.02377i	0.859053	+	0.511887i	$0.171053\pi$
$911$			30.9004i			1.02377i	−0.859053	+	0.511887i	$0.828947\pi$
$912$	−6.16827	+	6.65406i	−0.204252	+	0.220338i
$913$	12.9352	+	12.9352i	0.428092	+	0.428092i
$914$	−4.98197	−	28.2542i	−0.164789	−	0.934564i
$915$		0			0
$916$	−12.3778	+	4.50515i	−0.408974	+	0.148854i
$917$	2.56890	−	1.19790i	0.0848326	−	0.0395581i
$918$	−2.23528	−	25.5494i	−0.0737754	−	0.843257i
$919$	1.17628	+	0.679126i	0.0388019	+	0.0224023i	0.519275	−	0.854607i	$-0.326202\pi$
$919$	1.17628	+	0.679126i	0.0388019	+	0.0224023i	−0.480474	+	0.877009i	$0.659535\pi$
$920$		0			0
$921$	1.02066	−	5.78843i	0.0336317	−	0.190735i
$922$	29.4155	−	20.5969i	0.968747	−	0.678324i
$923$	−2.74047	+	10.2276i	−0.0902038	+	0.336645i
$924$	26.3123	−	45.5743i	0.865612	−	1.49928i
$925$		0			0
$926$	10.3248	−	28.3672i	0.339295	−	0.932205i
$927$	7.04868	+	3.28685i	0.231509	+	0.107954i
$928$	−9.21448	−	0.806163i	−0.302480	−	0.0264636i
$929$	13.0888	−	2.30791i	0.429429	−	0.0757200i	0.0452441	−	0.998976i	$-0.485593\pi$
$929$	13.0888	−	2.30791i	0.429429	−	0.0757200i	0.384185	+	0.923256i	$0.374482\pi$
$930$		0			0
$931$	−44.1681	−	48.7624i	−1.44755	−	1.59812i
$932$	−7.97478	+	7.97478i	−0.261223	+	0.261223i
$933$	37.5437	+	26.2884i	1.22913	+	0.860643i
$934$	−12.7444	+	10.6938i	−0.417008	+	0.349911i
$935$		0			0
$936$	3.24498	+	1.18108i	0.106066	+	0.0386047i
$937$	39.2893	−	3.43737i	1.28353	−	0.112294i	0.575103	−	0.818081i	$-0.304962\pi$
$937$	39.2893	−	3.43737i	1.28353	−	0.112294i	0.708424	+	0.705787i	$0.249407\pi$
$938$	0.148256	−	0.0397252i	0.00484074	−	0.00129707i
$939$	−16.5232	−	28.6190i	−0.539214	−	0.933946i
$940$		0			0
$941$	−33.9728	−	5.99032i	−1.10748	−	0.195279i	−0.410143	−	0.912021i	$-0.634521\pi$
$941$	−33.9728	−	5.99032i	−1.10748	−	0.195279i	−0.697338	+	0.716742i	$0.745632\pi$
$942$	−32.4622	−	8.69821i	−1.05767	−	0.283403i
$943$	−2.21155	−	8.25363i	−0.0720181	−	0.268775i
$944$	7.08451	+	5.94461i	0.230581	+	0.193480i
$945$		0			0
$946$	−9.99200	−	27.4528i	−0.324868	−	0.892567i
$947$	−0.940417	+	10.7490i	−0.0305594	+	0.349296i	0.965486	+	0.260454i	$0.0838722\pi$
$947$	−0.940417	+	10.7490i	−0.0305594	+	0.349296i	−0.996046	+	0.0888421i	$0.971683\pi$
$948$	−2.19317	+	3.13217i	−0.0712309	+	0.101728i
$949$	23.8466			0.774093
$950$		0			0
$951$	−2.44478			−0.0792774
$952$	−19.9251	+	28.4560i	−0.645776	+	0.922263i
$953$	0.567093	−	6.48191i	0.0183700	−	0.209970i	−0.981462	−	0.191655i	$-0.938614\pi$
$953$	0.567093	−	6.48191i	0.0183700	−	0.209970i	0.999832	−	0.0183144i	$-0.00582997\pi$
$954$	1.16476	+	3.20015i	0.0377104	+	0.103609i
$955$		0			0
$956$	16.0697	+	13.4841i	0.519732	+	0.436107i
$957$	−26.8027	−	100.029i	−0.866407	−	3.23348i
$958$	4.45494	+	1.19370i	0.143932	+	0.0385666i
$959$	−54.3462	−	9.58271i	−1.75493	−	0.309442i
$960$		0			0
$961$	−15.2486	−	26.4114i	−0.491891	−	0.851980i
$962$	−4.56339	+	1.22276i	−0.147130	+	0.0394233i
$963$	6.50669	−	0.569262i	0.209675	−	0.0183442i
$964$	−11.2913	−	4.10971i	−0.363670	−	0.132365i
$965$		0			0
$966$	−6.11505	+	5.13114i	−0.196748	+	0.165092i
$967$	−26.8639	−	18.8103i	−0.863886	−	0.604900i	0.0554110	−	0.998464i	$-0.482353\pi$
$967$	−26.8639	−	18.8103i	−0.863886	−	0.604900i	−0.919297	+	0.393564i	$0.871242\pi$
$968$	12.6779	−	12.6779i	0.407482	−	0.407482i
$969$	59.2999	+	31.3054i	1.90499	+	1.00567i
$970$		0			0
$971$	22.2554	−	3.92422i	0.714209	−	0.125934i	0.195275	−	0.980749i	$-0.437440\pi$
$971$	22.2554	−	3.92422i	0.714209	−	0.125934i	0.518934	+	0.854814i	$0.326329\pi$
$972$	12.8992	+	1.12853i	0.413742	+	0.0361977i
$973$	6.04577	+	2.81919i	0.193819	+	0.0903791i
$974$	−6.95541	+	19.1098i	−0.222866	+	0.612319i
$975$		0			0
$976$	−4.76169	+	8.24749i	−0.152418	+	0.263996i
$977$	2.05941	−	7.68581i	0.0658863	−	0.245891i	−0.925126	−	0.379659i	$-0.876041\pi$
$977$	2.05941	−	7.68581i	0.0658863	−	0.245891i	0.991013	+	0.133769i	$0.0427079\pi$
$978$	−8.56016	+	5.99389i	−0.273724	+	0.191663i
$979$	1.86027	−	10.5501i	0.0594543	−	0.337182i
$980$		0			0
$981$	−18.8358	−	10.8748i	−0.601379	−	0.347207i
$982$	−0.259804	−	2.96958i	−0.00829069	−	0.0947631i
$983$	−9.74600	+	4.54464i	−0.310849	+	0.144951i	−0.571782	−	0.820406i	$-0.693748\pi$
$983$	−9.74600	+	4.54464i	−0.310849	+	0.144951i	0.260933	+	0.965357i	$0.415970\pi$
$984$	20.4856	−	7.45615i	0.653058	−	0.237694i
$985$		0			0
$986$	11.8706	+	67.3213i	0.378036	+	2.14395i
$987$	35.4428	+	35.4428i	1.12816	+	1.12816i
$988$	8.99913	−	6.82321i	0.286300	−	0.217075i
$989$			4.43156i			0.140916i
$990$		0			0
$991$	10.4936	+	12.5057i	0.333339	+	0.397258i	0.906514	−	0.422175i	$-0.138733\pi$
$991$	10.4936	+	12.5057i	0.333339	+	0.397258i	−0.573176	+	0.819432i	$0.694289\pi$
$992$	−0.299666	+	0.642636i	−0.00951441	+	0.0204037i
$993$	−15.1988	−	32.5939i	−0.482318	−	1.03433i
$994$	12.3476	−	14.7154i	0.391644	−	0.466743i
$995$		0			0
$996$	6.13107	−	3.53977i	0.194270	−	0.112162i
$997$	−25.2710	−	36.0907i	−0.800340	−	1.14300i	−0.987022	−	0.160584i	$-0.948662\pi$
$997$	−25.2710	−	36.0907i	−0.800340	−	1.14300i	0.186682	−	0.982420i	$-0.440227\pi$
$998$	12.1095	+	17.2942i	0.383321	+	0.547439i
$999$	−5.48012	+	3.16395i	−0.173383	+	0.100103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.bb.c.143.6	yes	72
5.2	odd	4	inner	950.2.bb.c.257.4	yes	72
5.3	odd	4	inner	950.2.bb.c.257.3	yes	72
5.4	even	2	inner	950.2.bb.c.143.1	✓	72
19.2	odd	18	inner	950.2.bb.c.743.4	yes	72
95.2	even	36	inner	950.2.bb.c.857.6	yes	72
95.59	odd	18	inner	950.2.bb.c.743.3	yes	72
95.78	even	36	inner	950.2.bb.c.857.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.bb.c.143.1	✓	72	5.4	even	2	inner
950.2.bb.c.143.6	yes	72	1.1	even	1	trivial
950.2.bb.c.257.3	yes	72	5.3	odd	4	inner
950.2.bb.c.257.4	yes	72	5.2	odd	4	inner
950.2.bb.c.743.3	yes	72	95.59	odd	18	inner
950.2.bb.c.743.4	yes	72	19.2	odd	18	inner
950.2.bb.c.857.1	yes	72	95.78	even	36	inner
950.2.bb.c.857.6	yes	72	95.2	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.181419 - 2.07363i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-1.59456 - 1.33799i) q^{6} +(-1.21655 - 4.54023i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.31260 - 0.231446i) q^{9} +O(q^{10})\)	\(q+(0.573576 - 0.819152i) q^{2} +(0.181419 - 2.07363i) q^{3} +(-0.342020 - 0.939693i) q^{4} +(-1.59456 - 1.33799i) q^{6} +(-1.21655 - 4.54023i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.31260 - 0.231446i) q^{9} +(-2.68929 - 4.65799i) q^{11} +(-2.01062 + 0.538744i) q^{12} +(2.58102 - 0.225810i) q^{13} +(-4.41693 - 1.60763i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(6.05395 + 4.23902i) q^{17} +(-0.942464 + 0.942464i) q^{18} +(0.918889 + 4.26094i) q^{19} +(-9.63546 + 1.69899i) q^{21} +(-5.35812 - 0.468775i) q^{22} +(0.739436 + 0.344805i) q^{23} +(-0.711932 + 1.95602i) q^{24} +(1.29544 - 2.24377i) q^{26} +(0.898170 - 3.35202i) q^{27} +(-3.85034 + 2.69604i) q^{28} +(-1.60619 + 9.10916i) q^{29} +(0.614073 + 0.354535i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(-10.1468 + 4.73155i) q^{33} +(6.94481 - 2.52770i) q^{34} +(0.231446 + 1.31260i) q^{36} +(-1.28938 - 1.28938i) q^{37} +(4.01741 + 1.69127i) q^{38} -5.39304i q^{39} +(-6.73200 - 8.02289i) q^{41} +(-4.13494 + 8.86741i) q^{42} +(2.29552 + 4.92275i) q^{43} +(-3.45729 + 4.12024i) q^{44} +(0.706570 - 0.407939i) q^{46} +(-2.93842 - 4.19649i) q^{47} +(1.19393 + 1.70510i) q^{48} +(-13.0716 + 7.54687i) q^{49} +(9.88845 - 11.7846i) q^{51} +(-1.09495 - 2.34813i) q^{52} +(1.07982 - 2.31569i) q^{53} +(-2.23064 - 2.65838i) q^{54} +4.70040i q^{56} +(9.00232 - 1.13242i) q^{57} +(6.54051 + 6.54051i) q^{58} +(-1.60593 - 9.10767i) q^{59} +(8.94905 - 3.25719i) q^{61} +(0.642636 - 0.299666i) q^{62} +(0.546022 + 6.24106i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-1.94413 + 11.0257i) q^{66} +(-0.0267485 + 0.0187295i) q^{67} +(1.91280 - 7.13868i) q^{68} +(0.849144 - 1.47076i) q^{69} +(-1.39776 + 3.84033i) q^{71} +(1.20797 + 0.563285i) q^{72} +(9.16903 + 0.802186i) q^{73} +(-1.79576 + 0.316641i) q^{74} +(3.68970 - 2.32080i) q^{76} +(-17.8767 + 17.8767i) q^{77} +(-4.41772 - 3.09332i) q^{78} +(1.40718 - 1.18076i) q^{79} +(-10.5453 - 3.83817i) q^{81} +(-10.4333 + 0.912794i) q^{82} +(-3.28521 + 0.880269i) q^{83} +(4.89205 + 8.47328i) q^{84} +(5.34914 + 0.943197i) q^{86} +(18.5976 + 4.98321i) q^{87} +(1.39208 + 5.19532i) q^{88} +(1.52577 + 1.28028i) q^{89} +(-4.16518 - 11.4437i) q^{91} +(0.0711084 - 0.812773i) q^{92} +(0.846579 - 1.20904i) q^{93} -5.12297 q^{94} +2.08155 q^{96} +(4.19754 - 5.99470i) q^{97} +(-1.31551 + 15.0363i) q^{98} +(2.45188 + 6.73649i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 24 q^{6}+O(q^{10}) \) 72 * q + 24 * q^6	\( 72 q + 24 q^{6} + 24 q^{21} + 12 q^{26} + 36 q^{31} - 24 q^{36} + 48 q^{41} - 36 q^{46} + 156 q^{51} + 168 q^{61} - 36 q^{66} - 84 q^{71} - 48 q^{76} - 60 q^{81} - 60 q^{86} - 264 q^{91} + 24 q^{96}+O(q^{100}) \) 72 * q + 24 * q^6 + 24 * q^21 + 12 * q^26 + 36 * q^31 - 24 * q^36 + 48 * q^41 - 36 * q^46 + 156 * q^51 + 168 * q^61 - 36 * q^66 - 84 * q^71 - 48 * q^76 - 60 * q^81 - 60 * q^86 - 264 * q^91 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Database

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