LMFDB - Embedded newform 640.2.bm.a.101.49

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("640.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(640, base_ring=CyclotomicField(32)) chi = DirichletCharacter(H, H._module([0, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			101.49
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.49

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.05228 + 0.944830i) q^{2} +(-0.0933260 + 0.0498838i) q^{3} +(0.214592 + 1.98845i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-0.145337 - 0.0356854i) q^{6} +(4.13332 - 2.76180i) q^{7} +(-1.65294 + 2.29517i) q^{8} +(-1.66049 + 2.48510i) q^{9} +(-0.0628033 + 1.41282i) q^{10} +(3.77844 - 1.14618i) q^{11} +(-0.119219 - 0.174870i) q^{12} +(-0.707847 - 0.580915i) q^{13} +(6.95884 + 0.999098i) q^{14} +(-0.0977661 - 0.0404960i) q^{15} +(-3.90790 + 0.853413i) q^{16} +(2.20953 - 0.915219i) q^{17} +(-4.09530 + 1.04614i) q^{18} +(-0.0796224 - 0.808419i) q^{19} +(-1.40096 + 1.42734i) q^{20} +(-0.247977 + 0.463933i) q^{21} +(5.05893 + 2.36388i) q^{22} +(-6.53171 + 1.29924i) q^{23} +(0.0397707 - 0.296654i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.195988 - 1.28008i) q^{26} +(0.0621176 - 0.630691i) q^{27} +(6.37868 + 7.62626i) q^{28} +(-0.516420 + 1.70241i) q^{29} +(-0.0646155 - 0.134986i) q^{30} +(4.36953 + 4.36953i) q^{31} +(-4.91854 - 2.79427i) q^{32} +(-0.295451 + 0.295451i) q^{33} +(3.18978 + 1.12457i) q^{34} +(4.75705 + 1.44303i) q^{35} +(-5.29783 - 2.76852i) q^{36} +(-4.05578 - 0.399459i) q^{37} +(0.680034 - 0.925914i) q^{38} +(0.0950388 + 0.0189044i) q^{39} +(-2.82280 + 0.178298i) q^{40} +(0.967253 + 4.86271i) q^{41} +(-0.699280 + 0.253892i) q^{42} +(-1.77551 - 0.949030i) q^{43} +(3.08995 + 7.26730i) q^{44} +(-2.97441 + 0.292954i) q^{45} +(-8.10076 - 4.80419i) q^{46} +(0.705146 + 1.70237i) q^{47} +(0.322137 - 0.274587i) q^{48} +(6.77803 - 16.3636i) q^{49} +(-1.13197 + 0.847735i) q^{50} +(-0.160552 + 0.195634i) q^{51} +(1.00322 - 1.53218i) q^{52} +(-3.24511 - 10.6977i) q^{53} +(0.661261 - 0.604974i) q^{54} +(3.28303 + 2.19365i) q^{55} +(-0.493349 + 14.0517i) q^{56} +(0.0477579 + 0.0714747i) q^{57} +(-2.15191 + 1.30348i) q^{58} +(-8.52214 + 6.99394i) q^{59} +(0.0595447 - 0.203094i) q^{60} +(-5.41722 - 10.1349i) q^{61} +(0.469511 + 8.72643i) q^{62} +14.8576i q^{63} +(-2.53558 - 7.58755i) q^{64} -0.915702i q^{65} +(-0.590049 + 0.0317466i) q^{66} +(-0.660208 - 1.23516i) q^{67} +(2.29402 + 4.19716i) q^{68} +(0.544768 - 0.447079i) q^{69} +(3.64233 + 6.01308i) q^{70} +(1.74577 + 2.61272i) q^{71} +(-2.95902 - 7.91882i) q^{72} +(5.33283 + 3.56328i) q^{73} +(-3.89040 - 4.25237i) q^{74} +(-0.0307183 - 0.101265i) q^{75} +(1.59042 - 0.331806i) q^{76} +(12.4520 - 15.1728i) q^{77} +(0.0821461 + 0.109688i) q^{78} +(0.902295 - 2.17833i) q^{79} +(-3.13884 - 2.47945i) q^{80} +(-3.40563 - 8.22192i) q^{81} +(-3.57661 + 6.03083i) q^{82} +(7.68377 - 0.756786i) q^{83} +(-0.975723 - 0.393535i) q^{84} +(2.10919 + 1.12738i) q^{85} +(-0.971665 - 2.67620i) q^{86} +(-0.0367272 - 0.184640i) q^{87} +(-3.61487 + 10.5667i) q^{88} +(-0.982917 - 0.195514i) q^{89} +(-3.40671 - 2.50204i) q^{90} +(-4.53013 - 0.446179i) q^{91} +(-3.98513 - 12.7092i) q^{92} +(-0.625759 - 0.189822i) q^{93} +(-0.866442 + 2.45762i) q^{94} +(0.574405 - 0.574405i) q^{95} +(0.598417 + 0.0154227i) q^{96} +(-11.3708 - 11.3708i) q^{97} +(22.5932 - 10.8150i) q^{98} +(-3.42570 + 11.2930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	1.05228	+	0.944830i	0.744075	+	0.668096i
$2$	1.05228	+	0.944830i	0.744075	+	0.668096i
$3$	−0.0933260	+	0.0498838i	−0.0538818	+	0.0288004i	−0.498118	−	0.867109i	$-0.665975\pi$
$3$	−0.0933260	+	0.0498838i	−0.0538818	+	0.0288004i	0.444236	+	0.895910i	$0.353475\pi$
$4$	0.214592	+	1.98845i	0.107296	+	0.994227i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	−0.145337	−	0.0356854i	−0.0593335	−	0.0145685i
$7$	4.13332	−	2.76180i	1.56225	−	1.04386i	0.590737	−	0.806864i	$-0.298837\pi$
$7$	4.13332	−	2.76180i	1.56225	−	1.04386i	0.971510	−	0.236997i	$-0.0761631\pi$
$8$	−1.65294	+	2.29517i	−0.584403	+	0.811464i
$9$	−1.66049	+	2.48510i	−0.553496	+	0.828366i
$10$	−0.0628033	+	1.41282i	−0.0198602	+	0.446772i
$11$	3.77844	−	1.14618i	1.13924	−	0.345586i	0.336367	−	0.941731i	$-0.390802\pi$
$11$	3.77844	−	1.14618i	1.13924	−	0.345586i	0.802876	+	0.596146i	$0.203302\pi$
$12$	−0.119219	−	0.174870i	−0.0344155	−	0.0504806i
$13$	−0.707847	−	0.580915i	−0.196321	−	0.161117i	0.531097	−	0.847311i	$-0.321780\pi$
$13$	−0.707847	−	0.580915i	−0.196321	−	0.161117i	−0.727418	+	0.686194i	$0.759280\pi$
$14$	6.95884	+	0.999098i	1.85983	+	0.267020i
$15$	−0.0977661	−	0.0404960i	−0.0252431	−	0.0104560i
$16$	−3.90790	+	0.853413i	−0.976975	+	0.213353i
$17$	2.20953	−	0.915219i	0.535891	−	0.221973i	−0.0982903	−	0.995158i	$-0.531337\pi$
$17$	2.20953	−	0.915219i	0.535891	−	0.221973i	0.634181	+	0.773185i	$0.281337\pi$
$18$	−4.09530	+	1.04614i	−0.965271	+	0.246578i
$19$	−0.0796224	−	0.808419i	−0.0182666	−	0.185464i	0.981722	−	0.190323i	$-0.0609534\pi$
$19$	−0.0796224	−	0.808419i	−0.0182666	−	0.185464i	−0.999988	+	0.00485861i	$0.998453\pi$
$20$	−1.40096	+	1.42734i	−0.313264	+	0.319164i
$21$	−0.247977	+	0.463933i	−0.0541131	+	0.101238i
$22$	5.05893	+	2.36388i	1.07857	+	0.503982i
$23$	−6.53171	+	1.29924i	−1.36196	+	0.270910i	−0.821378	−	0.570384i	$-0.806794\pi$
$23$	−6.53171	+	1.29924i	−1.36196	+	0.270910i	−0.540578	+	0.841294i	$0.681794\pi$
$24$	0.0397707	−	0.296654i	0.00811816	−	0.0605542i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−0.195988	−	1.28008i	−0.0384365	−	0.251045i
$27$	0.0621176	−	0.630691i	0.0119545	−	0.121377i
$28$	6.37868	+	7.62626i	1.20546	+	1.44123i
$29$	−0.516420	+	1.70241i	−0.0958968	+	0.316129i	−0.991744	−	0.128233i	$-0.959070\pi$
$29$	−0.516420	+	1.70241i	−0.0958968	+	0.316129i	0.895847	+	0.444362i	$0.146570\pi$
$30$	−0.0646155	−	0.134986i	−0.0117971	−	0.0246449i
$31$	4.36953	+	4.36953i	0.784790	+	0.784790i	0.980635	−	0.195845i	$-0.0627449\pi$
$31$	4.36953	+	4.36953i	0.784790	+	0.784790i	−0.195845	+	0.980635i	$0.562745\pi$
$32$	−4.91854	−	2.79427i	−0.869483	−	0.493962i
$33$	−0.295451	+	0.295451i	−0.0514314	+	0.0514314i
$34$	3.18978	+	1.12457i	0.547043	+	0.192862i
$35$	4.75705	+	1.44303i	0.804088	+	0.243917i
$36$	−5.29783	−	2.76852i	−0.882972	−	0.461421i
$37$	−4.05578	−	0.399459i	−0.666766	−	0.0656707i	−0.241029	−	0.970518i	$-0.577485\pi$
$37$	−4.05578	−	0.399459i	−0.666766	−	0.0656707i	−0.425737	+	0.904847i	$0.639985\pi$
$38$	0.680034	−	0.925914i	0.110316	−	0.150203i
$39$	0.0950388	+	0.0189044i	0.0152184	+	0.00302712i
$40$	−2.82280	+	0.178298i	−0.446324	+	0.0281914i
$41$	0.967253	+	4.86271i	0.151059	+	0.759427i	0.979829	+	0.199837i	$0.0640414\pi$
$41$	0.967253	+	4.86271i	0.151059	+	0.759427i	−0.828770	+	0.559590i	$0.810959\pi$
$42$	−0.699280	+	0.253892i	−0.107901	+	0.0391763i
$43$	−1.77551	−	0.949030i	−0.270763	−	0.144726i	0.330428	−	0.943831i	$-0.392807\pi$
$43$	−1.77551	−	0.949030i	−0.270763	−	0.144726i	−0.601191	+	0.799105i	$0.705307\pi$
$44$	3.08995	+	7.26730i	0.465827	+	1.09559i
$45$	−2.97441	+	0.292954i	−0.443399	+	0.0436710i
$46$	−8.10076	−	4.80419i	−1.19439	−	0.708340i
$47$	0.705146	+	1.70237i	0.102856	+	0.248317i	0.966927	−	0.255054i	$-0.0820931\pi$
$47$	0.705146	+	1.70237i	0.102856	+	0.248317i	−0.864071	+	0.503370i	$0.832093\pi$
$48$	0.322137	−	0.274587i	0.0464965	−	0.0396332i
$49$	6.77803	−	16.3636i	0.968290	−	2.33766i
$50$	−1.13197	+	0.847735i	−0.160084	+	0.119888i
$51$	−0.160552	+	0.195634i	−0.0224818	+	0.0273942i
$52$	1.00322	−	1.53218i	0.139122	−	0.212475i
$53$	−3.24511	−	10.6977i	−0.445751	−	1.46944i	−0.835998	−	0.548733i	$-0.815111\pi$
$53$	−3.24511	−	10.6977i	−0.445751	−	1.46944i	0.390247	−	0.920710i	$-0.372389\pi$
$54$	0.661261	−	0.604974i	0.0899862	−	0.0823265i
$55$	3.28303	+	2.19365i	0.442683	+	0.295791i
$56$	−0.493349	+	14.0517i	−0.0659265	+	1.87774i
$57$	0.0477579	+	0.0714747i	0.00632568	+	0.00946705i
$58$	−2.15191	+	1.30348i	−0.282559	+	0.171156i
$59$	−8.52214	+	6.99394i	−1.10949	+	0.910533i	−0.996544	−	0.0830680i	$-0.973528\pi$
$59$	−8.52214	+	6.99394i	−1.10949	+	0.910533i	−0.112944	+	0.993601i	$0.536028\pi$
$60$	0.0595447	−	0.203094i	0.00768719	−	0.0262193i
$61$	−5.41722	−	10.1349i	−0.693605	−	1.29764i	−0.944143	−	0.329536i	$-0.893108\pi$
$61$	−5.41722	−	10.1349i	−0.693605	−	1.29764i	0.250538	−	0.968107i	$-0.419392\pi$
$62$	0.469511	+	8.72643i	0.0596280	+	1.10826i
$63$			14.8576i			1.87189i
$64$	−2.53558	−	7.58755i	−0.316947	−	0.948443i
$65$		−	0.915702i		−	0.113579i
$66$	−0.590049	+	0.0317466i	−0.0726300	+	0.00390774i
$67$	−0.660208	−	1.23516i	−0.0806572	−	0.150899i	0.838359	−	0.545118i	$-0.183515\pi$
$67$	−0.660208	−	1.23516i	−0.0806572	−	0.150899i	−0.919017	+	0.394219i	$0.871015\pi$
$68$	2.29402	+	4.19716i	0.278191	+	0.508980i
$69$	0.544768	−	0.447079i	0.0655823	−	0.0538220i
$70$	3.64233	+	6.01308i	0.435342	+	0.718700i
$71$	1.74577	+	2.61272i	0.207184	+	0.310073i	0.920480	−	0.390790i	$-0.127798\pi$
$71$	1.74577	+	2.61272i	0.207184	+	0.310073i	−0.713296	+	0.700863i	$0.752798\pi$
$72$	−2.95902	−	7.91882i	−0.348724	−	0.933242i
$73$	5.33283	+	3.56328i	0.624160	+	0.417051i	0.827032	−	0.562155i	$-0.190027\pi$
$73$	5.33283	+	3.56328i	0.624160	+	0.417051i	−0.202872	+	0.979205i	$0.565027\pi$
$74$	−3.89040	−	4.25237i	−0.452250	−	0.494327i
$75$	−0.0307183	−	0.101265i	−0.00354704	−	0.0116930i
$76$	1.59042	−	0.331806i	0.182434	−	0.0380607i
$77$	12.4520	−	15.1728i	1.41904	−	1.72910i
$78$	0.0821461	+	0.109688i	0.00930121	+	0.0124197i
$79$	0.902295	−	2.17833i	0.101516	−	0.245082i	−0.864959	−	0.501843i	$-0.832655\pi$
$79$	0.902295	−	2.17833i	0.101516	−	0.245082i	0.966475	+	0.256762i	$0.0826555\pi$
$80$	−3.13884	−	2.47945i	−0.350933	−	0.277211i
$81$	−3.40563	−	8.22192i	−0.378403	−	0.913547i
$82$	−3.57661	+	6.03083i	−0.394971	+	0.665993i
$83$	7.68377	−	0.756786i	0.843404	−	0.0830680i	0.332920	−	0.942955i	$-0.391966\pi$
$83$	7.68377	−	0.756786i	0.843404	−	0.0830680i	0.510484	+	0.859887i	$0.329466\pi$
$84$	−0.975723	−	0.393535i	−0.106460	−	0.0429382i
$85$	2.10919	+	1.12738i	0.228774	+	0.122282i
$86$	−0.971665	−	2.67620i	−0.104777	−	0.288582i
$87$	−0.0367272	−	0.184640i	−0.00393757	−	0.0197955i
$88$	−3.61487	+	10.5667i	−0.385346	+	1.12642i
$89$	−0.982917	−	0.195514i	−0.104189	−	0.0207245i	0.142720	−	0.989763i	$-0.454415\pi$
$89$	−0.982917	−	0.195514i	−0.104189	−	0.0207245i	−0.246909	+	0.969039i	$0.579415\pi$
$90$	−3.40671	−	2.50204i	−0.359099	−	0.263738i
$91$	−4.53013	−	0.446179i	−0.474886	−	0.0467722i
$92$	−3.98513	−	12.7092i	−0.415479	−	1.32503i
$93$	−0.625759	−	0.189822i	−0.0648882	−	0.0196836i
$94$	−0.866442	+	2.45762i	−0.0893666	+	0.253484i
$95$	0.574405	−	0.574405i	0.0589327	−	0.0589327i
$96$	0.598417	+	0.0154227i	0.0610756	+	0.00157407i
$97$	−11.3708	−	11.3708i	−1.15453	−	1.15453i	−0.985633	−	0.168900i	$-0.945978\pi$
$97$	−11.3708	−	11.3708i	−1.15453	−	1.15453i	−0.168900	−	0.985633i	$-0.554022\pi$
$98$	22.5932	−	10.8150i	2.28226	−	1.09248i
$99$	−3.42570	+	11.2930i	−0.344296	+	1.13499i
$100$	−1.99211	−	0.177459i	−0.199211	−	0.0177459i
$101$	−0.180701	+	1.83469i	−0.0179804	+	0.182558i	−0.999980	−	0.00632492i	$-0.997987\pi$
$101$	−0.180701	+	1.83469i	−0.0179804	+	0.182558i	0.982000	+	0.188883i	$0.0604867\pi$
$102$	−0.353787	+	0.0541669i	−0.0350301	+	0.00536333i
$103$	3.24290	−	16.3031i	0.319532	−	1.60640i	−0.403095	−	0.915158i	$-0.632066\pi$
$103$	3.24290	−	16.3031i	0.319532	−	1.60640i	0.722627	−	0.691238i	$-0.242934\pi$
$104$	2.50333	−	0.664409i	0.245471	−	0.0651507i
$105$	−0.515940	+	0.102627i	−0.0503506	+	0.0100154i
$106$	6.69274	−	14.3231i	0.650056	−	1.39118i
$107$	8.31494	−	15.5562i	0.803835	−	1.50387i	−0.0589283	−	0.998262i	$-0.518768\pi$
$107$	8.31494	−	15.5562i	0.803835	−	1.50387i	0.862764	−	0.505608i	$-0.168732\pi$
$108$	1.26743	−	0.0118232i	0.121958	−	0.00113769i
$109$	−0.583579	−	5.92518i	−0.0558968	−	0.567529i	−0.981820	−	0.189817i	$-0.939211\pi$
$109$	−0.583579	−	5.92518i	−0.0558968	−	0.567529i	0.925923	−	0.377713i	$-0.123289\pi$
$110$	1.38204	+	5.41024i	0.131773	+	0.515846i
$111$	0.398436	−	0.165038i	0.0378179	−	0.0156647i
$112$	−13.7956	+	14.3203i	−1.30357	+	1.35314i
$113$	17.0137	+	7.04729i	1.60051	+	0.662953i	0.991488	−	0.130200i	$-0.0415620\pi$
$113$	17.0137	+	7.04729i	1.60051	+	0.662953i	0.609022	+	0.793153i	$0.291562\pi$
$114$	−0.0172767	+	0.120335i	−0.00161811	+	0.0112704i
$115$	−5.14800	−	4.22485i	−0.480053	−	0.393970i
$116$	−3.49598	−	0.661554i	−0.324594	−	0.0614238i
$117$	2.61900	−	0.794466i	0.242127	−	0.0734484i
$118$	−15.5758	−	0.692382i	−1.43387	−	0.0637389i
$119$	6.60506	−	9.88518i	0.605485	−	0.906173i
$120$	0.254547	−	0.157452i	0.0232368	−	0.0143733i
$121$	3.81673	−	2.55026i	0.346976	−	0.231842i
$122$	3.87533	−	15.7831i	0.350856	−	1.42894i
$123$	−0.332840	−	0.405567i	−0.0300112	−	0.0365687i
$124$	−7.75094	+	9.62627i	−0.696055	+	0.864464i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−14.0379	+	15.6344i	−1.25060	+	1.39282i
$127$	15.7441			1.39706			0.698530	−	0.715581i	$-0.253838\pi$
$127$	15.7441			1.39706			0.698530	+	0.715581i	$0.253838\pi$
$128$	4.50080	−	10.3799i	0.397818	−	0.917464i
$129$	0.213043			0.0187574
$130$	0.865183	−	0.963576i	0.0758815	−	0.0845112i
$131$	−14.2849	+	7.63545i	−1.24808	+	0.667112i	−0.957139	−	0.289629i	$-0.906468\pi$
$131$	−14.2849	+	7.63545i	−1.24808	+	0.667112i	−0.290940	+	0.956741i	$0.593968\pi$
$132$	−0.650893	−	0.524090i	−0.0566529	−	0.0456161i
$133$	−2.56179	−	3.12156i	−0.222136	−	0.270673i
$134$	0.472294	−	1.92352i	0.0408000	−	0.166167i
$135$	0.526938	−	0.352088i	0.0453516	−	0.0303029i
$136$	−1.55165	+	6.58405i	−0.133053	+	0.564578i
$137$	−10.9504	+	16.3884i	−0.935554	+	1.40016i	−0.0191868	+	0.999816i	$0.506108\pi$
$137$	−10.9504	+	16.3884i	−0.935554	+	1.40016i	−0.916367	+	0.400339i	$0.868892\pi$
$138$	0.995663	+	0.0442597i	0.0847565	+	0.00376764i
$139$	−18.6892	+	5.66932i	−1.58520	+	0.480866i	−0.955258	−	0.295775i	$-0.904422\pi$
$139$	−18.6892	+	5.66932i	−1.58520	+	0.480866i	−0.629944	+	0.776641i	$0.716922\pi$
$140$	−1.84858	+	9.76883i	−0.156234	+	0.825617i
$141$	−0.150729	−	0.123700i	−0.0126937	−	0.0104175i
$142$	−0.631542	+	4.39877i	−0.0529979	+	0.369137i
$143$	−3.34039	−	1.38364i	−0.279338	−	0.115705i
$144$	4.36821	−	11.1286i	0.364018	−	0.927383i
$145$	−1.64359	+	0.680799i	−0.136493	+	0.0565373i
$146$	2.24494	+	8.78819i	0.185793	+	0.727316i
$147$	0.183712	+	1.86526i	0.0151523	+	0.153844i
$148$	−0.0760316	−	8.15045i	−0.00624976	−	0.669963i
$149$	6.32288	−	11.8293i	0.517990	−	0.969091i	−0.477891	−	0.878419i	$-0.658598\pi$
$149$	6.32288	−	11.8293i	0.517990	−	0.969091i	0.995881	−	0.0906721i	$-0.0289015\pi$
$150$	0.0633536	−	0.135582i	0.00517280	−	0.0110703i
$151$	−5.58271	+	1.11047i	−0.454314	+	0.0903687i	−0.416943	−	0.908933i	$-0.636898\pi$
$151$	−5.58271	+	1.11047i	−0.454314	+	0.0903687i	−0.0373715	+	0.999301i	$0.511898\pi$
$152$	1.98707	+	1.15352i	0.161173	+	0.0935630i
$153$	−1.39450	+	7.01062i	−0.112739	+	0.566775i
$154$	27.4387	−	4.20104i	2.21108	−	0.338529i
$155$	−0.605691	+	6.14969i	−0.0486503	+	0.493955i
$156$	−0.0171959	+	0.193037i	−0.00137678	+	0.0154553i
$157$	−0.690357	+	2.27580i	−0.0550965	+	0.181629i	−0.980170	−	0.198160i	$-0.936503\pi$
$157$	−0.690357	+	2.27580i	−0.0550965	+	0.181629i	0.925073	+	0.379789i	$0.124003\pi$
$158$	3.00762	−	1.43970i	0.239274	−	0.114537i
$159$	0.836495	+	0.836495i	0.0663384	+	0.0663384i
$160$	−0.960289	−	5.57475i	−0.0759175	−	0.440723i
$161$	−23.4094	+	23.4094i	−1.84492	+	1.84492i
$162$	4.18464	−	11.8695i	0.328776	−	0.932557i
$163$	12.8124	+	3.88661i	1.00355	+	0.304423i	0.748952	−	0.662624i	$-0.230557\pi$
$163$	12.8124	+	3.88661i	1.00355	+	0.304423i	0.254596	+	0.967047i	$0.418057\pi$
$164$	−9.46171	+	2.96684i	−0.738835	+	0.231671i
$165$	−0.415819	−	0.0409546i	−0.0323715	−	0.00318831i
$166$	8.80053	+	6.46351i	0.683053	+	0.501666i
$167$	13.6853	+	2.72218i	1.05900	+	0.210648i	0.693717	−	0.720248i	$-0.255972\pi$
$167$	13.6853	+	2.72218i	1.05900	+	0.210648i	0.365284	+	0.930896i	$0.380972\pi$
$168$	−0.654912	−	1.33600i	−0.0505275	−	0.103075i
$169$	−2.37259	−	11.9278i	−0.182507	−	0.917524i
$170$	1.15427	+	3.17915i	0.0885286	+	0.243830i
$171$	2.14121	+	1.14450i	0.163743	+	0.0875223i
$172$	1.50609	−	3.73418i	0.114838	−	0.284728i
$173$	−19.5050	+	1.92108i	−1.48294	+	0.146057i	−0.806847	−	0.590761i	$-0.798828\pi$
$173$	−19.5050	+	1.92108i	−1.48294	+	0.146057i	−0.676092	+	0.736817i	$0.736328\pi$
$174$	0.135806	−	0.228994i	0.0102954	−	0.0173600i
$175$	1.90236	+	4.59270i	0.143805	+	0.347175i
$176$	−13.7876	+	7.70372i	−1.03928	+	0.580690i
$177$	0.446453	−	1.07783i	0.0335575	−	0.0810149i
$178$	−0.849578	−	1.13443i	−0.0636785	−	0.0850288i
$179$	−8.63842	+	10.5259i	−0.645666	+	0.786746i	−0.988267	−	0.152735i	$-0.951192\pi$
$179$	−8.63842	+	10.5259i	−0.645666	+	0.786746i	0.342601	+	0.939481i	$0.388692\pi$
$180$	−1.22081	−	5.85161i	−0.0909938	−	0.436153i
$181$	−0.816363	−	2.69119i	−0.0606798	−	0.200034i	0.921359	−	0.388712i	$-0.127080\pi$
$181$	−0.816363	−	2.69119i	−0.0606798	−	0.200034i	−0.982039	+	0.188678i	$0.939580\pi$
$182$	−4.34540	−	4.74971i	−0.322103	−	0.352072i
$183$	1.01114	+	0.675619i	0.0747453	+	0.0499432i
$184$	7.81456	−	17.1389i	0.576097	−	1.26350i
$185$	−2.26417	−	3.38857i	−0.166465	−	0.249133i
$186$	−0.479125	−	0.790982i	−0.0351311	−	0.0579976i
$187$	7.29959	−	5.99062i	0.533799	−	0.438078i
$188$	−3.23377	+	1.76747i	−0.235847	+	0.128906i
$189$	−1.48509	−	2.77840i	−0.108024	−	0.202099i
$190$	1.14715	−	0.0617205i	0.0832230	−	0.00447768i
$191$		−	24.1938i		−	1.75060i	−0.483580	−	0.875300i	$-0.660664\pi$
$191$		−	24.1938i		−	1.75060i	0.483580	−	0.875300i	$-0.339336\pi$
$192$	0.615131	+	0.581631i	0.0443932	+	0.0419756i
$193$			8.35327i			0.601281i	0.953737	+	0.300641i	$0.0972005\pi$
$193$			8.35327i			0.601281i	−0.953737	+	0.300641i	$0.902799\pi$
$194$	−1.22181	−	22.7088i	−0.0877209	−	1.63040i
$195$	0.0456787	+	0.0854588i	0.00327112	+	0.00611983i
$196$	33.9928	+	9.96630i	2.42806	+	0.711878i
$197$	9.42066	−	7.73133i	0.671194	−	0.550835i	−0.235892	−	0.971779i	$-0.575801\pi$
$197$	9.42066	−	7.73133i	0.671194	−	0.550835i	0.907086	+	0.420944i	$0.138301\pi$
$198$	−14.2748	+	8.64672i	−1.01446	+	0.614496i
$199$	4.80253	+	7.18749i	0.340442	+	0.509508i	0.961702	−	0.274097i	$-0.0883788\pi$
$199$	4.80253	+	7.18749i	0.340442	+	0.509508i	−0.621260	+	0.783605i	$0.713379\pi$
$200$	−1.92859	−	2.06894i	−0.136372	−	0.146296i
$201$	0.123229	+	0.0823390i	0.00869191	+	0.00580775i
$202$	−1.92361	+	1.75987i	−0.135345	+	0.123824i
$203$	2.56718	+	8.46285i	0.180180	+	0.593975i
$204$	−0.423462	−	0.277270i	−0.0296483	−	0.0194128i
$205$	−3.14531	+	3.83257i	−0.219678	+	0.267678i
$206$	18.8161	−	14.0915i	1.31098	−	0.981802i
$207$	7.61711	−	18.3893i	0.529425	−	1.27815i
$208$	3.26196	+	1.66607i	0.226176	+	0.115521i
$209$	−1.22744	−	2.96330i	−0.0849039	−	0.204976i
$210$	−0.639879	−	0.379483i	−0.0441559	−	0.0261868i
$211$	−13.9997	+	1.37885i	−0.963778	+	0.0949238i	−0.567649	−	0.823271i	$-0.692147\pi$
$211$	−13.9997	+	1.37885i	−0.963778	+	0.0949238i	−0.396129	+	0.918195i	$0.629647\pi$
$212$	20.5755	−	8.74840i	1.41313	−	0.600843i
$213$	−0.293258	−	0.156750i	−0.0200937	−	0.0107403i
$214$	23.4476	−	8.51325i	1.60284	−	0.581954i
$215$	−0.392762	−	1.97455i	−0.0267861	−	0.134663i
$216$	1.34486	+	1.18506i	0.0915064	+	0.0806334i
$217$	30.1284	+	5.99291i	2.04525	+	0.406825i
$218$	4.98420	−	6.78634i	0.337573	−	0.459629i
$219$	−0.675442	−	0.0665252i	−0.0456421	−	0.00449536i
$220$	−3.65746	+	6.99889i	−0.246586	+	0.471865i
$221$	−2.09568	−	0.635717i	−0.140970	−	0.0427629i
$222$	0.575199	+	0.202788i	0.0386049	+	0.0136103i
$223$	−2.41635	+	2.41635i	−0.161811	+	0.161811i	−0.783368	−	0.621558i	$-0.786500\pi$
$223$	−2.41635	+	2.41635i	−0.161811	+	0.161811i	0.621558	+	0.783368i	$0.286500\pi$
$224$	−28.0471	+	2.03439i	−1.87398	+	0.135928i
$225$	−2.11340	−	2.11340i	−0.140893	−	0.140893i
$226$	11.2447	+	23.4907i	0.747984	+	1.56258i
$227$	−6.01853	+	19.8404i	−0.399464	+	1.31686i	0.494680	+	0.869075i	$0.335285\pi$
$227$	−6.01853	+	19.8404i	−0.399464	+	1.31686i	−0.894144	+	0.447780i	$0.852215\pi$
$228$	−0.131876	+	0.110302i	−0.00873368	+	0.00730494i
$229$	−0.846414	+	8.59379i	−0.0559326	+	0.567893i	0.925851	+	0.377889i	$0.123350\pi$
$229$	−0.846414	+	8.59379i	−0.0559326	+	0.567893i	−0.981783	+	0.190004i	$0.939150\pi$
$230$	−1.42537	−	9.30972i	−0.0939864	−	0.613865i
$231$	−0.405218	+	2.03717i	−0.0266614	+	0.134036i
$232$	−3.05370	−	3.99925i	−0.200485	−	0.262564i
$233$	−11.8111	+	2.34937i	−0.773770	+	0.153912i	−0.566156	−	0.824298i	$-0.691570\pi$
$233$	−11.8111	+	2.34937i	−0.773770	+	0.153912i	−0.207614	+	0.978211i	$0.566570\pi$
$234$	3.50656	+	1.63851i	0.229231	+	0.107113i
$235$	−0.868613	+	1.62506i	−0.0566620	+	0.106007i
$236$	−15.7359	−	15.4450i	−1.02432	−	1.00539i
$237$	0.0244559	+	0.248305i	0.00158858	+	0.0161291i
$238$	16.2902	−	4.16132i	1.05594	−	0.269739i
$239$	5.52854	−	2.29000i	0.357611	−	0.148127i	−0.196642	−	0.980475i	$-0.563004\pi$
$239$	5.52854	−	2.29000i	0.357611	−	0.148127i	0.554254	+	0.832348i	$0.313004\pi$
$240$	0.416620	+	0.0748196i	0.0268927	+	0.00482958i
$241$	−2.12398	−	0.879781i	−0.136817	−	0.0566717i	0.313224	−	0.949679i	$-0.398591\pi$
$241$	−2.12398	−	0.879781i	−0.136817	−	0.0566717i	−0.450042	+	0.893008i	$0.648591\pi$
$242$	6.42584	+	0.922574i	0.413069	+	0.0593053i
$243$	2.19764	+	1.80356i	0.140979	+	0.115698i
$244$	18.9903	−	12.9468i	1.21573	−	0.828832i
$245$	16.9492	−	5.14148i	1.08284	−	0.328477i
$246$	0.0329503	−	0.741248i	0.00210084	−	0.0472602i
$247$	−0.413263	+	0.618491i	−0.0262953	+	0.0393537i
$248$	−17.2514	+	2.80622i	−1.09546	+	0.178195i
$249$	−0.679345	+	0.453923i	−0.0430517	+	0.0287662i
$250$	−1.37342	−	0.337224i	−0.0868627	−	0.0213279i
$251$	13.6696	+	16.6564i	0.862816	+	1.05134i	0.998165	+	0.0605463i	$0.0192843\pi$
$251$	13.6696	+	16.6564i	0.862816	+	1.05134i	−0.135349	+	0.990798i	$0.543216\pi$
$252$	−29.5437	+	3.18833i	−1.86108	+	0.200846i
$253$	−23.1905	+	12.3956i	−1.45798	+	0.779305i
$254$	16.5672	+	14.8755i	1.03952	+	0.933369i
$255$	−0.253080			−0.0158485
$256$	14.5434	−	6.67011i	0.908961	−	0.416882i
$257$	17.3442			1.08190			0.540950	−	0.841055i	$-0.318065\pi$
$257$	17.3442			1.08190			0.540950	+	0.841055i	$0.318065\pi$
$258$	0.224181	+	0.201289i	0.0139569	+	0.0125317i
$259$	−17.8671	+	9.55014i	−1.11020	+	0.593417i
$260$	1.82083	−	0.196502i	0.112923	−	0.0121866i
$261$	−3.37314	−	4.11019i	−0.208792	−	0.254414i
$262$	−22.2459	−	5.46218i	−1.37436	−	0.337455i
$263$	−18.8400	+	12.5885i	−1.16172	+	0.776239i	−0.978381	−	0.206810i	$-0.933692\pi$
$263$	−18.8400	+	12.5885i	−1.16172	+	0.776239i	−0.183343	+	0.983049i	$0.558692\pi$
$264$	−0.189747	−	1.16647i	−0.0116781	−	0.0717914i
$265$	6.21076	−	9.29506i	0.381524	−	0.570991i
$266$	0.253611	−	5.70521i	0.0155499	−	0.349809i
$267$	0.101485	−	0.0307851i	0.00621077	−	0.00188402i
$268$	2.31439	−	1.57785i	0.141374	−	0.0963824i
$269$	1.41222	+	1.15898i	0.0861046	+	0.0706642i	0.676461	−	0.736479i	$-0.263513\pi$
$269$	1.41222	+	1.15898i	0.0861046	+	0.0706642i	−0.590356	+	0.807143i	$0.701013\pi$
$270$	0.887150	+	0.127370i	0.0539903	+	0.00775152i
$271$	10.5867	+	4.38516i	0.643097	+	0.266379i	0.680306	−	0.732928i	$-0.261847\pi$
$271$	10.5867	+	4.38516i	0.643097	+	0.266379i	−0.0372095	+	0.999307i	$0.511847\pi$
$272$	−7.85358	+	5.46223i	−0.476193	+	0.331196i
$273$	0.445036	−	0.184340i	0.0269348	−	0.0111568i
$274$	−27.0071	+	6.89896i	−1.63156	+	0.416781i
$275$	0.387017	+	3.92945i	0.0233380	+	0.236955i
$276$	1.00590	+	0.987306i	0.0605480	+	0.0594288i
$277$	−0.304710	+	0.570072i	−0.0183082	+	0.0342523i	−0.890909	−	0.454182i	$-0.849932\pi$
$277$	−0.304710	+	0.570072i	−0.0183082	+	0.0342523i	0.872601	+	0.488434i	$0.162432\pi$
$278$	−25.0229	−	11.6924i	−1.50077	−	0.701266i
$279$	−18.1142	+	3.60315i	−1.08447	+	0.215715i
$280$	−11.1751	+	8.53296i	−0.667841	+	0.509942i
$281$	−5.85930	+	29.4567i	−0.349536	+	1.75724i	0.261085	+	0.965316i	$0.415920\pi$
$281$	−5.85930	+	29.4567i	−0.349536	+	1.75724i	−0.610621	+	0.791923i	$0.709080\pi$
$282$	−0.0417338	−	0.272581i	−0.00248521	−	0.0162320i
$283$	2.03395	−	20.6511i	0.120906	−	1.22758i	−0.722909	−	0.690943i	$-0.757195\pi$
$283$	2.03395	−	20.6511i	0.120906	−	1.22758i	0.843815	−	0.536635i	$-0.180305\pi$
$284$	−4.82065	+	4.03204i	−0.286053	+	0.239258i
$285$	−0.0249534	+	0.0822604i	−0.00147811	+	0.00487269i
$286$	−2.20773	−	4.61208i	−0.130546	−	0.272718i
$287$	17.4278	+	17.4278i	1.02873	+	1.02873i
$288$	15.1112	−	7.58320i	0.890437	−	0.446844i
$289$	−7.97640	+	7.97640i	−0.469200	+	0.469200i
$290$	−2.37276	−	0.836525i	−0.139333	−	0.0491224i
$291$	1.62841	+	0.493974i	0.0954594	+	0.0289573i
$292$	−5.94104	+	11.3687i	−0.347673	+	0.665305i
$293$	−3.67387	−	0.361845i	−0.214630	−	0.0211392i	−0.00986939	−	0.999951i	$-0.503142\pi$
$293$	−3.67387	−	0.361845i	−0.214630	−	0.0211392i	−0.204761	+	0.978812i	$0.565642\pi$
$294$	−1.56904	+	2.13636i	−0.0915083	+	0.124595i
$295$	−10.8128	−	2.15079i	−0.629544	−	0.125224i
$296$	7.62078	−	8.64840i	0.442949	−	0.502678i
$297$	−0.488176	−	2.45423i	−0.0283268	−	0.142409i
$298$	17.8301	−	6.47368i	1.03287	−	0.375010i
$299$	5.37820	+	2.87471i	0.311029	+	0.166249i
$300$	0.194768	−	0.0828125i	0.0112449	−	0.00478118i
$301$	−9.95978	+	0.980953i	−0.574072	+	0.0565412i
$302$	−6.92379	−	4.10618i	−0.398419	−	0.236284i
$303$	−0.0746570	−	0.180238i	−0.00428893	−	0.0103544i
$304$	1.00107	+	3.09127i	0.0574154	+	0.177297i
$305$	4.39774	−	10.6171i	0.251814	−	0.607933i
$306$	−8.09125	+	6.05958i	−0.462546	+	0.346403i
$307$	−5.63184	+	6.86241i	−0.321426	+	0.391659i	−0.908507	−	0.417870i	$-0.862777\pi$
$307$	−5.63184	+	6.86241i	−0.321426	+	0.391659i	0.587081	+	0.809528i	$0.300277\pi$
$308$	32.8425	+	21.5043i	1.87138	+	1.22532i
$309$	0.510616	+	1.68327i	0.0290479	+	0.0957582i
$310$	−6.44777	+	5.89892i	−0.366209	+	0.335036i
$311$	17.5393	+	11.7194i	0.994560	+	0.664544i	0.942537	−	0.334102i	$-0.108433\pi$
$311$	17.5393	+	11.7194i	0.994560	+	0.664544i	0.0520235	+	0.998646i	$0.483433\pi$
$312$	−0.200482	+	0.186882i	−0.0113501	+	0.0105801i
$313$	−9.29305	−	13.9080i	−0.525274	−	0.786128i	0.470058	−	0.882635i	$-0.344233\pi$
$313$	−9.29305	−	13.9080i	−0.525274	−	0.786128i	−0.995332	+	0.0965073i	$0.969233\pi$
$314$	−2.87670	+	1.74251i	−0.162341	+	0.0983358i
$315$	−11.4851	+	9.42558i	−0.647112	+	0.531071i
$316$	4.52514	+	1.32672i	0.254559	+	0.0746338i
$317$	−4.55077	−	8.51390i	−0.255597	−	0.478188i	0.721094	−	0.692837i	$-0.243639\pi$
$317$	−4.55077	−	8.51390i	−0.255597	−	0.478188i	−0.976691	+	0.214649i	$0.931139\pi$
$318$	0.0898825	+	1.67057i	0.00504036	+	0.0936812i
$319$			7.02436i			0.393289i
$320$	4.25670	−	6.77352i	0.237957	−	0.378651i
$321$			1.86657i			0.104182i
$322$	−46.7512	+	2.51537i	−2.60534	+	0.140176i
$323$	−0.915809	−	1.71336i	−0.0509570	−	0.0953338i
$324$	15.6181	−	8.53630i	0.867672	−	0.474239i
$325$	0.707847	−	0.580915i	0.0392643	−	0.0322234i
$326$	9.81011	+	16.1954i	0.543332	+	0.896980i
$327$	0.350034	+	0.523862i	0.0193569	+	0.0289697i
$328$	−12.7595	−	5.81776i	−0.704527	−	0.321232i
$329$	7.61620	+	5.08898i	0.419895	+	0.280565i
$330$	−0.398864	−	0.435974i	−0.0219567	−	0.0239996i
$331$	0.159572	+	0.526038i	0.00877086	+	0.0289136i	0.961217	−	0.275795i	$-0.0889410\pi$
$331$	0.159572	+	0.526038i	0.00877086	+	0.0289136i	−0.952446	+	0.304708i	$0.901441\pi$
$332$	3.15371	+	15.1164i	0.173082	+	0.829622i
$333$	7.72727	−	9.41571i	0.423452	−	0.515978i
$334$	11.8288	+	15.7948i	0.647243	+	0.864253i
$335$	0.535962	−	1.29393i	0.0292827	−	0.0706947i
$336$	0.573144	−	2.02463i	0.0312676	−	0.110453i
$337$	10.0890	+	24.3569i	0.549581	+	1.32681i	0.917791	+	0.397063i	$0.129971\pi$
$337$	10.0890	+	24.3569i	0.549581	+	1.32681i	−0.368211	+	0.929742i	$0.620029\pi$
$338$	8.77312	−	14.7931i	0.477195	−	0.804639i
$339$	−1.93936	+	0.191010i	−0.105332	+	0.0103743i
$340$	−1.78914	+	4.43595i	−0.0970296	+	0.240573i
$341$	21.5182	+	11.5017i	1.16528	+	0.622854i
$342$	1.17180	+	3.22742i	0.0633636	+	0.174519i
$343$	−10.3885	−	52.2265i	−0.560926	−	2.81996i
$344$	5.11300	−	2.50640i	0.275674	−	0.135136i
$345$	0.691194	+	0.137487i	0.0372126	+	0.00740205i
$346$	−22.3399	−	16.4074i	−1.20100	−	0.882068i
$347$	30.3828	+	2.99244i	1.63103	+	0.160643i	0.871693	−	0.490052i	$-0.163022\pi$
$347$	30.3828	+	2.99244i	1.63103	+	0.160643i	0.759340	+	0.650694i	$0.225522\pi$
$348$	0.359267	−	0.112653i	0.0192587	−	0.00603881i
$349$	−25.4772	−	7.72842i	−1.36376	−	0.413693i	−0.478215	−	0.878243i	$-0.658716\pi$
$349$	−25.4772	−	7.72842i	−1.36376	−	0.413693i	−0.885547	+	0.464550i	$0.846216\pi$
$350$	−2.33750	+	6.63022i	−0.124945	+	0.354400i
$351$	−0.410348	+	0.410348i	−0.0219027	+	0.0219027i
$352$	−21.7872	−	4.92047i	−1.16126	−	0.262262i
$353$	2.40237	+	2.40237i	0.127865	+	0.127865i	0.768143	−	0.640278i	$-0.221181\pi$
$353$	2.40237	+	2.40237i	0.127865	+	0.127865i	−0.640278	+	0.768143i	$0.721181\pi$
$354$	1.48816	−	0.712361i	0.0790950	−	0.0378616i
$355$	−0.912160	+	3.00699i	−0.0484124	+	0.159594i
$356$	0.177845	−	1.99644i	0.00942577	−	0.105811i
$357$	−0.123314	+	1.25203i	−0.00652648	+	0.0662644i
$358$	−19.0353	+	2.91442i	−1.00605	+	0.154032i
$359$	−4.02552	+	20.2376i	−0.212459	+	1.06810i	0.716406	+	0.697683i	$0.245786\pi$
$359$	−4.02552	+	20.2376i	−0.212459	+	1.06810i	−0.928865	+	0.370418i	$0.879214\pi$
$360$	4.24414	−	7.31100i	0.223686	−	0.385324i
$361$	17.9877	−	3.57798i	0.946722	−	0.188315i
$362$	1.68367	−	3.60321i	0.0884918	−	0.189381i
$363$	−0.228984	+	0.428399i	−0.0120185	+	0.0224851i
$364$	−0.0849240	−	9.10370i	−0.00445122	−	0.477163i
$365$	0.628656	+	6.38285i	0.0329054	+	0.334094i
$366$	0.425654	+	1.66629i	0.0222493	+	0.0870985i
$367$	−22.8273	+	9.45538i	−1.19158	+	0.493567i	−0.888268	−	0.459326i	$-0.848091\pi$
$367$	−22.8273	+	9.45538i	−1.19158	+	0.493567i	−0.303308	+	0.952893i	$0.598091\pi$
$368$	24.4165	−	10.6515i	1.27280	−	0.555250i
$369$	−13.6904	−	5.67076i	−0.712695	−	0.295208i
$370$	0.819080	−	5.70499i	0.0425819	−	0.296588i
$371$	−42.9580	−	35.2547i	−2.23027	−	1.83033i
$372$	0.243169	−	1.28503i	0.0126077	−	0.0666255i
$373$	2.65271	−	0.804690i	0.137352	−	0.0416653i	−0.220860	−	0.975305i	$-0.570886\pi$
$373$	2.65271	−	0.804690i	0.137352	−	0.0416653i	0.358212	+	0.933640i	$0.383386\pi$
$374$	13.3413	+	0.593056i	0.689865	+	0.0306662i
$375$	0.0587911	−	0.0879871i	0.00303596	−	0.00454364i
$376$	−5.07280	−	1.19549i	−0.261609	−	0.0616529i
$377$	1.35450	−	0.905049i	0.0697604	−	0.0466124i
$378$	1.06239	−	4.32682i	0.0546434	−	0.222547i
$379$	5.68419	+	6.92620i	0.291977	+	0.355775i	0.898253	−	0.439480i	$-0.144837\pi$
$379$	5.68419	+	6.92620i	0.291977	+	0.355775i	−0.606275	+	0.795255i	$0.707337\pi$
$380$	1.26544	+	1.01891i	0.0649157	+	0.0522692i
$381$	−1.46933	+	0.785373i	−0.0752761	+	0.0402359i
$382$	22.8590	−	25.4587i	1.16957	−	1.30258i
$383$	24.1220			1.23258			0.616288	−	0.787521i	$-0.288636\pi$
$383$	24.1220			1.23258			0.616288	+	0.787521i	$0.288636\pi$
$384$	0.0977482	+	1.19323i	0.00498819	+	0.0608920i
$385$	19.6282			1.00035
$386$	−7.89242	+	8.78999i	−0.401714	+	0.447399i
$387$	5.30665	−	2.83646i	0.269752	−	0.144186i
$388$	20.1703	−	25.0505i	1.02399	−	1.27175i
$389$	−4.03141	−	4.91229i	−0.204401	−	0.249063i	0.660713	−	0.750638i	$-0.270254\pi$
$389$	−4.03141	−	4.91229i	−0.204401	−	0.249063i	−0.865114	+	0.501576i	$0.832754\pi$
$390$	−0.0326772	+	0.133085i	−0.00165468	+	0.00673904i
$391$	−13.2430	+	8.84866i	−0.669725	+	0.447496i
$392$	26.3535	+	42.6048i	1.33105	+	2.15187i
$393$	0.952269	−	1.42517i	0.0480356	−	0.0718904i
$394$	17.2180	+	0.765382i	0.867429	+	0.0385594i
$395$	2.25628	−	0.684436i	0.113526	−	0.0344377i
$396$	−23.1908	−	4.38845i	−1.16538	−	0.220528i
$397$	−18.7954	−	15.4250i	−0.943312	−	0.774156i	0.0309623	−	0.999521i	$-0.490143\pi$
$397$	−18.7954	−	15.4250i	−0.943312	−	0.774156i	−0.974275	+	0.225364i	$0.927643\pi$
$398$	−1.73735	+	12.1008i	−0.0870854	+	0.606560i
$399$	0.394797	+	0.163530i	0.0197646	+	0.00818675i
$400$	−0.0746216	−	3.99930i	−0.00373108	−	0.199965i
$401$	2.73279	−	1.13196i	0.136469	−	0.0565273i	−0.313404	−	0.949620i	$-0.601469\pi$
$401$	2.73279	−	1.13196i	0.136469	−	0.0565273i	0.449873	+	0.893093i	$0.351469\pi$
$402$	0.0518753	+	0.203074i	0.00258730	+	0.0101284i
$403$	−0.554633	−	5.63128i	−0.0276282	−	0.280514i
$404$	−3.68697	+	0.0343939i	−0.183433	+	0.00171116i
$405$	4.19512	−	7.84852i	0.208457	−	0.389996i
$406$	−5.29456	+	11.3308i	−0.262765	+	0.562340i
$407$	−15.7824	+	3.13931i	−0.782303	+	0.155610i
$408$	−0.183628	−	0.691865i	−0.00909096	−	0.0342524i
$409$	−6.34855	+	31.9163i	−0.313916	+	1.57816i	0.425530	+	0.904944i	$0.360088\pi$
$409$	−6.34855	+	31.9163i	−0.313916	+	1.57816i	−0.739446	+	0.673216i	$0.764912\pi$
$410$	−6.93087	+	1.06116i	−0.342291	+	0.0524069i
$411$	0.204440	−	2.07571i	0.0100843	−	0.102387i
$412$	33.1139	+	2.94982i	1.63141	+	0.145327i
$413$	−15.9089	+	52.4446i	−0.782825	+	2.58063i
$414$	25.3901	−	12.1539i	1.24786	−	0.597330i
$415$	5.45954	+	5.45954i	0.267998	+	0.267998i
$416$	1.85834	+	4.83517i	0.0911127	+	0.237064i
$417$	1.46139	−	1.46139i	0.0715644	−	0.0715644i
$418$	1.50821	−	4.27795i	0.0737688	−	0.209242i
$419$	0.688981	+	0.209000i	0.0336589	+	0.0102103i	0.307069	−	0.951687i	$-0.400652\pi$
$419$	0.688981	+	0.209000i	0.0336589	+	0.0102103i	−0.273410	+	0.961897i	$0.588152\pi$
$420$	−0.314786	−	1.00390i	−0.0153600	−	0.0489853i
$421$	−18.0637	−	1.77911i	−0.880368	−	0.0867087i	−0.352277	−	0.935896i	$-0.614592\pi$
$421$	−18.0637	−	1.77911i	−0.880368	−	0.0867087i	−0.528092	+	0.849187i	$0.677092\pi$
$422$	−16.0344	−	11.7764i	−0.780541	−	0.573265i
$423$	−5.40145	−	1.07442i	−0.262628	−	0.0522399i
$424$	29.9170	+	10.2346i	1.45290	+	0.497036i
$425$	0.466575	+	2.34563i	0.0226322	+	0.113780i
$426$	−0.160488	−	0.442023i	−0.00777567	−	0.0214161i
$427$	−50.3817	−	26.9296i	−2.43814	−	1.30321i
$428$	32.7170	+	13.1956i	1.58144	+	0.637835i
$429$	0.380766	−	0.0375022i	0.0183836	−	0.00181062i
$430$	1.45232	−	2.44887i	0.0700369	−	0.118095i
$431$	7.03021	+	16.9724i	0.338633	+	0.817533i	0.997847	+	0.0655780i	$0.0208891\pi$
$431$	7.03021	+	16.9724i	0.338633	+	0.817533i	−0.659214	+	0.751955i	$0.729111\pi$
$432$	0.295490	+	2.51769i	0.0142168	+	0.121132i
$433$	−4.83790	+	11.6797i	−0.232495	+	0.561292i	−0.996470	−	0.0839542i	$-0.973245\pi$
$433$	−4.83790	+	11.6797i	−0.232495	+	0.561292i	0.763975	+	0.645246i	$0.223245\pi$
$434$	26.0413	+	34.7724i	1.25002	+	1.66913i
$435$	0.119429	−	0.145525i	0.00572619	−	0.00697738i
$436$	11.6567	−	2.43192i	0.558256	−	0.116468i
$437$	1.57040	+	5.17692i	0.0751224	+	0.247645i
$438$	−0.647900	−	0.708181i	−0.0309578	−	0.0338382i
$439$	17.5784	+	11.7455i	0.838969	+	0.560581i	0.899167	−	0.437605i	$-0.144173\pi$
$439$	17.5784	+	11.7455i	0.838969	+	0.560581i	−0.0601978	+	0.998186i	$0.519173\pi$
$440$	−10.4614	+	3.90912i	−0.498729	+	0.186360i
$441$	29.4103	+	44.0157i	1.40049	+	2.09598i
$442$	−1.60460	−	2.64901i	−0.0763229	−	0.126001i
$443$	12.6085	−	10.3475i	0.599049	−	0.491627i	−0.285309	−	0.958435i	$-0.592096\pi$
$443$	12.6085	−	10.3475i	0.599049	−	0.491627i	0.884358	+	0.466809i	$0.154596\pi$
$444$	0.413671	+	0.756856i	0.0196320	+	0.0359188i
$445$	−0.472422	−	0.883839i	−0.0223949	−	0.0418980i
$446$	−4.82572	+	0.259640i	−0.228505	+	0.0122943i
$447$			1.41939i			0.0671347i
$448$	−31.4356	−	24.3590i	−1.48519	−	1.15085i
$449$		−	17.1169i		−	0.807798i	−0.914804	−	0.403899i	$-0.867655\pi$
$449$		−	17.1169i		−	0.807798i	0.914804	−	0.403899i	$-0.132345\pi$
$450$	−0.227088	−	4.22070i	−0.0107050	−	0.198966i
$451$	9.22823	+	17.2648i	0.434541	+	0.812968i
$452$	−10.3622	+	35.3432i	−0.487397	+	1.66240i
$453$	0.465617	−	0.382122i	0.0218766	−	0.0179537i
$454$	−25.0790	+	15.1912i	−1.17702	+	0.712960i
$455$	−2.52898	−	3.78489i	−0.118560	−	0.177438i
$456$	−0.242987	−	0.00853114i	−0.0113789	−	0.000399507i
$457$	−6.60608	−	4.41404i	−0.309019	−	0.206480i	0.391384	−	0.920228i	$-0.371996\pi$
$457$	−6.60608	−	4.41404i	−0.309019	−	0.206480i	−0.700403	+	0.713747i	$0.746996\pi$
$458$	−9.01033	+	8.24336i	−0.421025	+	0.385187i
$459$	−0.439969	−	1.45038i	−0.0205360	−	0.0676981i
$460$	7.29621	−	11.1432i	0.340188	−	0.519554i
$461$	−10.6327	+	12.9560i	−0.495214	+	0.603420i	−0.959307	−	0.282367i	$-0.908881\pi$
$461$	−10.6327	+	12.9560i	−0.495214	+	0.603420i	0.464093	+	0.885787i	$0.346381\pi$
$462$	−2.35118	+	1.76081i	−0.109387	+	0.0819205i
$463$	3.92309	−	9.47119i	0.182322	−	0.440163i	−0.806123	−	0.591749i	$-0.798438\pi$
$463$	3.92309	−	9.47119i	0.182322	−	0.440163i	0.988444	+	0.151585i	$0.0484378\pi$
$464$	0.565260	−	7.09356i	0.0262415	−	0.329310i
$465$	−0.250243	−	0.604140i	−0.0116047	−	0.0280163i
$466$	−14.6483	−	8.68727i	−0.678571	−	0.402430i
$467$	8.59399	−	0.846434i	0.397682	−	0.0391683i	0.102800	−	0.994702i	$-0.467220\pi$
$467$	8.59399	−	0.846434i	0.397682	−	0.0391683i	0.294882	+	0.955534i	$0.404720\pi$
$468$	2.14178	+	5.03728i	0.0990037	+	0.232848i
$469$	−6.14011	−	3.28196i	−0.283524	−	0.151547i
$470$	−2.44943	+	0.889329i	−0.112984	+	0.0410217i
$471$	−0.0490974	−	0.246829i	−0.00226229	−	0.0113733i
$472$	−1.96567	−	31.1203i	−0.0904772	−	1.43243i
$473$	−7.79642	−	1.55080i	−0.358480	−	0.0713061i
$474$	−0.208871	+	0.284393i	−0.00959378	+	0.0130626i
$475$	0.808419	+	0.0796224i	0.0370928	+	0.00365332i
$476$	21.0736	+	11.0126i	0.965908	+	0.504761i
$477$	31.9733	+	9.69900i	1.46396	+	0.444087i
$478$	7.98123	+	2.81381i	0.365053	+	0.128701i
$479$	−2.90821	+	2.90821i	−0.132879	+	0.132879i	−0.770418	−	0.637539i	$-0.779953\pi$
$479$	−2.90821	+	2.90821i	−0.132879	+	0.132879i	0.637539	+	0.770418i	$0.279953\pi$
$480$	0.367710	+	0.472366i	0.0167836	+	0.0215605i
$481$	2.63882	+	2.63882i	0.120320	+	0.120320i
$482$	−1.40378	−	2.93258i	−0.0639404	−	0.133575i
$483$	1.01696	−	3.35246i	0.0462732	−	0.152542i
$484$	5.89011	+	7.04213i	0.267732	+	0.320097i
$485$	1.57619	−	16.0034i	0.0715712	−	0.726675i
$486$	0.608482	+	3.97425i	0.0276013	+	0.180276i
$487$	−1.57195	+	7.90270i	−0.0712316	+	0.358106i	−0.999919	−	0.0127589i	$-0.995939\pi$
$487$	−1.57195	+	7.90270i	−0.0712316	+	0.358106i	0.928687	+	0.370865i	$0.120939\pi$
$488$	32.2157	+	4.31897i	1.45833	+	0.195511i
$489$	−1.38961	+	0.276411i	−0.0628405	+	0.0124998i
$490$	22.6931	+	10.6038i	1.02517	+	0.479031i
$491$	10.3132	−	19.2946i	0.465427	−	0.870753i	−0.534250	−	0.845327i	$-0.679406\pi$
$491$	10.3132	−	19.2946i	0.465427	−	0.870753i	0.999677	−	0.0254261i	$-0.00809425\pi$
$492$	0.735026	−	0.748869i	0.0331375	−	0.0337616i
$493$	0.417029	+	4.23417i	0.0187821	+	0.190697i
$494$	−1.01924	+	0.260364i	−0.0458577	+	0.0117143i
$495$	−10.9029	+	4.51611i	−0.490047	+	0.202984i
$496$	−20.8047	−	13.3467i	−0.934158	−	0.599283i
$497$	14.4316	+	5.97777i	0.647346	+	0.268140i
$498$	−1.14374	−	0.164210i	−0.0512523	−	0.00735842i
$499$	−2.30555	−	1.89211i	−0.103210	−	0.0847027i	0.581373	−	0.813637i	$-0.302516\pi$
$499$	−2.30555	−	1.89211i	−0.103210	−	0.0847027i	−0.684583	+	0.728935i	$0.740016\pi$
$500$	−1.12660	−	1.65250i	−0.0503833	−	0.0739021i
$501$	−1.41299	+	0.428625i	−0.0631277	+	0.0191496i
$502$	−1.35325	+	30.4427i	−0.0603986	+	1.35872i
$503$	19.0434	−	28.5004i	0.849101	−	1.27077i	−0.111759	−	0.993735i	$-0.535648\pi$
$503$	19.0434	−	28.5004i	0.849101	−	1.27077i	0.960860	−	0.277034i	$-0.0893516\pi$
$504$	−34.1007	−	24.5588i	−1.51897	−	1.09394i
$505$	−1.53287	+	1.02423i	−0.0682117	+	0.0455776i
$506$	−36.1147	−	8.86746i	−1.60549	−	0.394207i
$507$	0.816429	+	0.994821i	0.0362589	+	0.0441816i
$508$	3.37855	+	31.3063i	0.149899	+	1.38899i
$509$	8.02855	−	4.29135i	0.355859	−	0.190211i	−0.283773	−	0.958891i	$-0.591586\pi$
$509$	8.02855	−	4.29135i	0.355859	−	0.190211i	0.639633	+	0.768681i	$0.279086\pi$
$510$	−0.266312	−	0.239118i	−0.0117925	−	0.0105883i
$511$	31.8833			1.41044
$512$	21.6058	+	6.72218i	0.954852	+	0.297081i
$513$	−0.514809			−0.0227294
$514$	18.2509	+	16.3873i	0.805015	+	0.722812i
$515$	14.6598	−	7.83581i	0.645987	−	0.345287i
$516$	0.0457173	+	0.423625i	0.00201259	+	0.0186491i
$517$	4.61558	+	5.62410i	0.202993	+	0.247348i
$518$	−27.8244	−	6.83190i	−1.22253	−	0.300176i
$519$	1.72449	−	1.15227i	0.0756969	−	0.0505791i
$520$	2.10169	+	1.51360i	0.0921651	+	0.0663758i
$521$	−2.81411	+	4.21162i	−0.123289	+	0.184514i	−0.887980	−	0.459883i	$-0.847892\pi$
$521$	−2.81411	+	4.21162i	−0.123289	+	0.184514i	0.764691	+	0.644397i	$0.222892\pi$
$522$	0.333933	−	7.51212i	0.0146158	−	0.328797i
$523$	−1.53826	+	0.466625i	−0.0672632	+	0.0204041i	−0.323737	−	0.946147i	$-0.604939\pi$
$523$	−1.53826	+	0.466625i	−0.0672632	+	0.0204041i	0.256474	+	0.966551i	$0.417439\pi$
$524$	−18.2482	−	26.7664i	−0.797175	−	1.16930i
$525$	−0.406641	−	0.333721i	−0.0177473	−	0.0145648i
$526$	−31.7190	−	4.55397i	−1.38301	−	0.198563i
$527$	13.6537	+	5.65554i	0.594764	+	0.246359i
$528$	0.902452	−	1.40674i	0.0392742	−	0.0612203i
$529$	19.7260	−	8.17079i	0.857654	−	0.355252i
$530$	15.3177	−	3.91290i	0.665359	−	0.169966i
$531$	−3.22970	−	32.7917i	−0.140157	−	1.42304i
$532$	5.65733	−	5.76387i	0.245276	−	0.249896i
$533$	2.14015	−	4.00394i	0.0927003	−	0.173430i
$534$	0.135877	+	0.0634913i	0.00587998	+	0.00274754i
$535$	17.3000	−	3.44119i	0.747945	−	0.148775i
$536$	3.92619	+	0.526362i	0.169585	+	0.0227354i
$537$	0.281115	−	1.41326i	0.0121310	−	0.0609868i
$538$	0.391015	+	2.55388i	0.0168578	+	0.110106i
$539$	6.85478	−	69.5978i	0.295256	−	2.99779i
$540$	0.813188	+	0.972236i	0.0349941	+	0.0418384i
$541$	12.1774	−	40.1435i	0.523547	−	1.72590i	−0.151809	−	0.988410i	$-0.548510\pi$
$541$	12.1774	−	40.1435i	0.523547	−	1.72590i	0.675355	−	0.737492i	$-0.263990\pi$
$542$	6.99696	+	14.6171i	0.300545	+	0.627856i
$543$	0.210435	+	0.210435i	0.00903061	+	0.00903061i
$544$	−13.4251	−	1.67250i	−0.575595	−	0.0717076i
$545$	4.21001	−	4.21001i	0.180337	−	0.180337i
$546$	0.642473	+	0.226506i	0.0274953	+	0.00969355i
$547$	−44.1646	−	13.3972i	−1.88834	−	0.572822i	−0.991434	−	0.130605i	$-0.958308\pi$
$547$	−44.1646	−	13.3972i	−1.88834	−	0.572822i	−0.896908	−	0.442217i	$-0.854192\pi$
$548$	−34.9374	−	18.2575i	−1.49245	−	0.779922i
$549$	34.1815	+	3.36658i	1.45883	+	0.143682i
$550$	−3.30541	+	4.50055i	−0.140943	+	0.191904i
$551$	1.41738	+	0.281934i	0.0603824	+	0.0120108i
$552$	0.125653	+	1.98933i	0.00534815	+	0.0846714i
$553$	−2.28664	−	11.4957i	−0.0972377	−	0.488847i
$554$	−0.859261	+	0.311977i	−0.0365065	+	0.0132546i
$555$	0.380341	+	0.203297i	0.0161446	+	0.00862946i
$556$	−15.2838	−	35.9461i	−0.648175	−	1.52446i
$557$	16.7652	−	1.65123i	0.710366	−	0.0699649i	0.263621	−	0.964626i	$-0.415083\pi$
$557$	16.7652	−	1.65123i	0.710366	−	0.0699649i	0.446745	+	0.894661i	$0.352583\pi$
$558$	−22.4656	−	13.3234i	−0.951047	−	0.564023i
$559$	0.705484	+	1.70319i	0.0298388	+	0.0720372i
$560$	−19.8216	−	1.57951i	−0.837614	−	0.0667464i
$561$	−0.382407	+	0.923212i	−0.0161452	+	0.0389780i
$562$	−33.9972	+	25.4607i	−1.43409	+	1.07399i
$563$	−19.2249	+	23.4256i	−0.810231	+	0.987270i	0.189754	+	0.981832i	$0.439231\pi$
$563$	−19.2249	+	23.4256i	−0.810231	+	0.987270i	−0.999985	+	0.00543799i	$0.998269\pi$
$564$	0.213627	−	0.326264i	0.00899533	−	0.0137382i
$565$	5.34572	+	17.6225i	0.224896	+	0.741384i
$566$	21.6520	−	19.8090i	0.910103	−	0.832634i
$567$	−36.7838	−	24.5782i	−1.54478	−	1.03219i
$568$	−8.88228	−	0.311852i	−0.372692	−	0.0130850i
$569$	0.274426	+	0.410707i	0.0115045	+	0.0172177i	0.837177	−	0.546932i	$-0.184204\pi$
$569$	0.274426	+	0.410707i	0.0115045	+	0.0172177i	−0.825673	+	0.564149i	$0.809204\pi$
$570$	−0.103980	+	0.0629843i	−0.00435525	+	0.00263812i
$571$	21.7519	−	17.8513i	0.910290	−	0.747055i	−0.0576241	−	0.998338i	$-0.518352\pi$
$571$	21.7519	−	17.8513i	0.910290	−	0.747055i	0.967914	+	0.251283i	$0.0808525\pi$
$572$	2.03447	−	6.93913i	0.0850656	−	0.290140i
$573$	1.20688	+	2.25791i	0.0504180	+	0.0943255i
$574$	1.87264	+	34.8052i	0.0781623	+	1.45274i
$575$		−	6.65968i		−	0.277728i
$576$	23.0661	+	6.29788i	0.961087	+	0.262412i
$577$		−	16.0625i		−	0.668691i	−0.942450	−	0.334346i	$-0.891485\pi$
$577$		−	16.0625i		−	0.668691i	0.942450	−	0.334346i	$-0.108515\pi$
$578$	−15.9298	+	0.857074i	−0.662591	+	0.0356496i
$579$	−0.416693	−	0.779577i	−0.0173172	−	0.0323981i
$580$	−1.70644	−	3.12212i	−0.0708560	−	0.129639i
$581$	29.6694	−	24.3490i	1.23089	−	1.01017i
$582$	1.24683	+	2.05838i	0.0516827	+	0.0853224i
$583$	−24.5229	−	36.7012i	−1.01564	−	1.52001i
$584$	−16.9932	+	6.34984i	−0.703182	+	0.262758i
$585$	2.27561	+	1.52051i	0.0940848	+	0.0628655i
$586$	−3.52407	−	3.85195i	−0.145578	−	0.159123i
$587$	6.75355	+	22.2635i	0.278749	+	0.918912i	0.978800	+	0.204819i	$0.0656606\pi$
$587$	6.75355	+	22.2635i	0.278749	+	0.918912i	−0.700051	+	0.714093i	$0.746839\pi$
$588$	−3.66957	+	0.765575i	−0.151330	+	0.0315718i
$589$	3.18450	−	3.88032i	0.131215	−	0.159886i
$590$	−9.34595	−	12.4795i	−0.384767	−	0.513772i
$591$	−0.493524	+	1.19147i	−0.0203009	+	0.0490106i
$592$	16.1905	−	1.90021i	0.665425	−	0.0780981i
$593$	−8.71885	−	21.0492i	−0.358040	−	0.864385i	−0.995576	−	0.0939644i	$-0.970046\pi$
$593$	−8.71885	−	21.0492i	−0.358040	−	0.864385i	0.637535	−	0.770421i	$-0.279954\pi$
$594$	1.80513	−	3.04378i	0.0740653	−	0.124888i
$595$	11.8316	−	1.16531i	0.485046	−	0.0477729i
$596$	24.8788	+	10.0343i	1.01908	+	0.411020i
$597$	−0.806740	−	0.431212i	−0.0330177	−	0.0176483i
$598$	2.94327	+	8.10649i	0.120359	+	0.331499i
$599$	−1.18775	−	5.97122i	−0.0485302	−	0.243978i	0.948904	−	0.315564i	$-0.102194\pi$
$599$	−1.18775	−	5.97122i	−0.0485302	−	0.243978i	−0.997434	+	0.0715866i	$0.977194\pi$
$600$	0.283195	+	0.0968808i	0.0115614	+	0.00395514i
$601$	−1.75312	−	0.348718i	−0.0715115	−	0.0142245i	0.159205	−	0.987246i	$-0.449107\pi$
$601$	−1.75312	−	0.348718i	−0.0715115	−	0.0142245i	−0.230716	+	0.973021i	$0.574107\pi$
$602$	−11.4073	−	8.37806i	−0.464928	−	0.341464i
$603$	4.16577	+	0.410292i	0.169643	+	0.0167084i
$604$	−3.40612	−	10.8627i	−0.138593	−	0.441995i
$605$	4.39269	+	1.33251i	0.178588	+	0.0541741i
$606$	0.0917341	−	0.260199i	0.00372644	−	0.0105699i
$607$	18.0909	−	18.0909i	0.734285	−	0.734285i	−0.237180	−	0.971466i	$-0.576223\pi$
$607$	18.0909	−	18.0909i	0.734285	−	0.734285i	0.971466	+	0.237180i	$0.0762232\pi$
$608$	−1.86732	+	4.19873i	−0.0757297	+	0.170281i
$609$	−0.661743	−	0.661743i	−0.0268152	−	0.0268152i
$610$	14.6590	−	7.01705i	0.593526	−	0.284112i
$611$	0.489799	−	1.61465i	0.0198151	−	0.0653218i
$612$	−14.2395	−	1.26847i	−0.575600	−	0.0512750i
$613$	−4.08508	+	41.4765i	−0.164995	+	1.67522i	0.454906	+	0.890539i	$0.349673\pi$
$613$	−4.08508	+	41.4765i	−0.164995	+	1.67522i	−0.619901	+	0.784680i	$0.712827\pi$
$614$	−12.4101	+	1.90006i	−0.500830	+	0.0766802i
$615$	0.102356	−	0.514578i	0.00412739	−	0.0207498i
$616$	14.2417	+	53.6591i	0.573814	+	2.16199i
$617$	−23.9944	+	4.77279i	−0.965979	+	0.192145i	−0.652784	−	0.757544i	$-0.726399\pi$
$617$	−23.9944	+	4.77279i	−0.965979	+	0.192145i	−0.313195	+	0.949689i	$0.601399\pi$
$618$	−1.05310	+	2.25372i	−0.0423618	+	0.0906581i
$619$	−13.5208	+	25.2957i	−0.543447	+	1.01672i	0.448940	+	0.893562i	$0.351802\pi$
$619$	−13.5208	+	25.2957i	−0.543447	+	1.01672i	−0.992387	+	0.123157i	$0.960698\pi$
$620$	−12.3583	+	0.115285i	−0.496323	+	0.00462996i
$621$	0.413683	+	4.20020i	0.0166005	+	0.168548i
$622$	7.38344	+	28.9037i	0.296049	+	1.15893i
$623$	−4.60268	+	1.90649i	−0.184403	+	0.0763820i
$624$	−0.387535	+	0.00723089i	−0.0155138	+	0.000289467i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	3.36182	−	23.4155i	0.134365	−	0.935872i
$627$	0.262373	+	0.215324i	0.0104782	+	0.00859921i
$628$	−4.67347	−	0.884374i	−0.186492	−	0.0352904i
$629$	−9.32698	+	2.82931i	−0.371891	+	0.112812i
$630$	−20.9911	−	0.933109i	−0.836307	−	0.0371759i
$631$	24.1911	−	36.2046i	0.963034	−	1.44128i	0.0667670	−	0.997769i	$-0.478732\pi$
$631$	24.1911	−	36.2046i	0.963034	−	1.44128i	0.896267	−	0.443514i	$-0.146268\pi$
$632$	3.50820	+	5.67157i	0.139549	+	0.225603i
$633$	1.23775	−	0.827039i	0.0491962	−	0.0328719i
$634$	3.25549	−	13.2587i	0.129292	−	0.526571i
$635$	9.98793	+	12.1703i	0.396359	+	0.482965i
$636$	−1.48383	+	1.84284i	−0.0588376	+	0.0730733i
$637$	−14.3037	+	7.64547i	−0.566732	+	0.302925i
$638$	−6.63683	+	7.39161i	−0.262755	+	0.292636i
$639$	−9.39170			−0.371530
$640$	10.8791	−	3.10579i	0.430033	−	0.122767i
$641$	−16.9826			−0.670772			−0.335386	−	0.942081i	$-0.608867\pi$
$641$	−16.9826			−0.670772			−0.335386	+	0.942081i	$0.608867\pi$
$642$	−1.76360	+	1.96416i	−0.0696036	+	0.0775193i
$643$	−2.13872	+	1.14317i	−0.0843428	+	0.0450821i	−0.513029	−	0.858371i	$-0.671477\pi$
$643$	−2.13872	+	1.14317i	−0.0843428	+	0.0450821i	0.428686	+	0.903453i	$0.358977\pi$
$644$	−51.5720	−	41.5251i	−2.03222	−	1.63632i
$645$	0.135153	+	0.164684i	0.00532164	+	0.00648443i
$646$	0.655144	−	2.66822i	0.0257763	−	0.104980i
$647$	25.8480	−	17.2711i	1.01619	−	0.678996i	0.0683222	−	0.997663i	$-0.478235\pi$
$647$	25.8480	−	17.2711i	1.01619	−	0.678996i	0.947866	+	0.318668i	$0.103235\pi$
$648$	24.5000	+	5.77385i	0.962450	+	0.226818i
$649$	−24.1841	+	36.1941i	−0.949309	+	1.42074i
$650$	1.29372	+	0.0575091i	0.0507439	+	0.00225569i
$651$	−3.11071	+	0.943624i	−0.121918	+	0.0369835i
$652$	−4.97890	+	26.3110i	−0.194989	+	1.03042i
$653$	13.0898	+	10.7426i	0.512245	+	0.420389i	0.854682	−	0.519152i	$-0.173752\pi$
$653$	13.0898	+	10.7426i	0.512245	+	0.420389i	−0.342437	+	0.939541i	$0.611252\pi$
$654$	−0.126627	+	0.881973i	−0.00495151	+	0.0344879i
$655$	−14.9645	−	6.19851i	−0.584713	−	0.242196i
$656$	−7.92983	−	18.1775i	−0.309608	−	0.709713i
$657$	−17.7102	+	7.33581i	−0.690941	+	0.286197i
$658$	3.20616	+	12.5511i	0.124989	+	0.489291i
$659$	1.81557	+	18.4338i	0.0707246	+	0.718079i	0.963524	+	0.267623i	$0.0862383\pi$
$659$	1.81557	+	18.4338i	0.0707246	+	0.718079i	−0.892799	+	0.450455i	$0.851262\pi$
$660$	−0.00779515	−	0.835626i	−0.000303426	−	0.0325267i
$661$	17.9235	−	33.5325i	0.697144	−	1.30426i	−0.245153	−	0.969484i	$-0.578838\pi$
$661$	17.9235	−	33.5325i	0.697144	−	1.30426i	0.942296	−	0.334780i	$-0.108662\pi$
$662$	−0.329102	+	0.704308i	−0.0127909	+	0.0273737i
$663$	0.227293	−	0.0452114i	0.00882733	−	0.00175587i
$664$	−10.9639	+	18.8865i	−0.425481	+	0.732937i
$665$	0.787810	−	3.96059i	0.0305500	−	0.153585i
$666$	17.0275	−	2.60702i	0.659803	−	0.101020i
$667$	1.16127	−	11.7906i	0.0449647	−	0.456534i
$668$	−2.47617	+	27.7968i	−0.0958057	+	1.07549i
$669$	0.104972	−	0.346045i	0.00405844	−	0.0133789i
$670$	1.78652	−	0.855181i	0.0690194	−	0.0330385i
$671$	−32.0851	−	32.0851i	−1.23863	−	1.23863i
$672$	2.51604	−	1.58896i	0.0970584	−	0.0612954i
$673$	5.28203	−	5.28203i	0.203607	−	0.203607i	−0.597936	−	0.801544i	$-0.704012\pi$
$673$	5.28203	−	5.28203i	0.203607	−	0.203607i	0.801544	+	0.597936i	$0.204012\pi$
$674$	−12.3967	+	35.1627i	−0.477504	+	1.35442i
$675$	0.606454	+	0.183966i	0.0233424	+	0.00708084i
$676$	23.2088	−	7.27740i	0.892645	−	0.279900i
$677$	−32.2666	−	3.17798i	−1.24011	−	0.122140i	−0.543386	−	0.839483i	$-0.682858\pi$
$677$	−32.2666	−	3.17798i	−1.24011	−	0.122140i	−0.696720	+	0.717343i	$0.745358\pi$
$678$	−2.22123	−	1.63137i	−0.0853057	−	0.0626524i
$679$	−78.4032	−	15.5954i	−3.00884	−	0.598495i
$680$	−6.07390	+	2.97744i	−0.232923	+	0.114180i
$681$	−0.428031	−	2.15186i	−0.0164022	−	0.0824593i
$682$	11.7761	+	32.4342i	0.450929	+	1.24197i
$683$	18.4577	+	9.86586i	0.706266	+	0.377507i	0.785090	−	0.619382i	$-0.212617\pi$
$683$	18.4577	+	9.86586i	0.706266	+	0.377507i	−0.0788244	+	0.996889i	$0.525117\pi$
$684$	−1.81630	+	4.50331i	−0.0694481	+	0.172188i
$685$	−19.6152	+	1.93193i	−0.749460	+	0.0738154i
$686$	38.4135	−	64.7723i	1.46664	−	2.47302i
$687$	−0.349698	−	0.844246i	−0.0133418	−	0.0322100i
$688$	7.74843	+	2.19347i	0.295406	+	0.0836253i
$689$	−3.91741	+	9.45747i	−0.149242	+	0.360301i
$690$	0.597429	+	0.797736i	0.0227437	+	0.0303693i
$691$	6.75463	−	8.23055i	0.256958	−	0.313105i	−0.628513	−	0.777799i	$-0.716336\pi$
$691$	6.75463	−	8.23055i	0.256958	−	0.313105i	0.885471	+	0.464695i	$0.153836\pi$
$692$	−8.00560	−	38.3726i	−0.304327	−	1.45871i
$693$	17.0295	+	56.1387i	0.646897	+	2.13253i
$694$	29.1439	+	31.8555i	1.10629	+	1.20922i
$695$	−16.2388	−	10.8504i	−0.615972	−	0.411579i
$696$	0.484487	+	0.220904i	0.0183644	+	0.00837334i
$697$	6.58762	+	9.85907i	0.249524	+	0.373439i
$698$	−19.5071	−	32.2041i	−0.738355	−	1.21894i
$699$	0.985086	−	0.808439i	0.0372594	−	0.0305780i
$700$	−8.72414	+	4.76831i	−0.329741	+	0.180225i
$701$	4.61349	+	8.63124i	0.174249	+	0.325997i	0.953852	−	0.300277i	$-0.0970790\pi$
$701$	4.61349	+	8.63124i	0.174249	+	0.325997i	−0.779603	+	0.626274i	$0.784579\pi$
$702$	−0.819510	+	0.0440924i	−0.0309304	+	0.00166416i
$703$			3.31058i			0.124861i
$704$	−18.2772	−	25.7629i	−0.688848	−	0.970975i
$705$		−	0.194990i		−	0.00734375i
$706$	0.258138	+	4.79781i	0.00971515	+	0.180568i
$707$	4.32013	+	8.08240i	0.162475	+	0.303970i
$708$	2.23903	+	0.656457i	0.0841478	+	0.0246712i
$709$	10.1233	−	8.30800i	0.380190	−	0.312014i	−0.424817	−	0.905279i	$-0.639662\pi$
$709$	10.1233	−	8.30800i	0.380190	−	0.312014i	0.805007	+	0.593266i	$0.202162\pi$
$710$	−3.80094	+	2.30236i	−0.142647	+	0.0864061i
$711$	3.91512	+	5.85939i	0.146828	+	0.219744i
$712$	2.07344	−	1.93279i	0.0777055	−	0.0724342i
$713$	−34.2175	−	22.8634i	−1.28146	−	0.856242i
$714$	−1.31272	+	1.20098i	−0.0491272	+	0.0449454i
$715$	−1.04956	−	3.45993i	−0.0392512	−	0.129394i
$716$	−22.7841	−	14.9183i	−0.851482	−	0.557524i
$717$	−0.401723	+	0.489500i	−0.0150026	+	0.0182807i
$718$	−23.3571	+	17.4923i	−0.871680	+	0.652805i
$719$	−9.11906	+	22.0154i	−0.340083	+	0.821034i	0.657623	+	0.753347i	$0.271562\pi$
$719$	−9.11906	+	22.0154i	−0.340083	+	0.821034i	−0.997707	+	0.0676870i	$0.978438\pi$
$720$	11.3737	−	3.68324i	0.423872	−	0.137266i
$721$	−31.6220	−	76.3423i	−1.17767	−	2.84314i
$722$	22.3087	+	13.2303i	0.830245	+	0.492381i
$723$	0.242109	−	0.0238457i	0.00900414	−	0.000886830i
$724$	5.17612	−	2.20081i	0.192369	−	0.0817924i
$725$	−1.56895	−	0.838621i	−0.0582693	−	0.0311456i
$726$	−0.645719	+	0.234445i	−0.0239649	+	0.00870107i
$727$	−5.60201	−	28.1632i	−0.207767	−	1.04452i	−0.934056	−	0.357126i	$-0.883757\pi$
$727$	−5.60201	−	28.1632i	−0.207767	−	1.04452i	0.726289	−	0.687389i	$-0.241243\pi$
$728$	8.51208	−	9.65989i	0.315479	−	0.358019i
$729$	25.8900	+	5.14983i	0.958888	+	0.190735i
$730$	−5.36919	+	7.31053i	−0.198723	+	0.270575i
$731$	−4.79162	−	0.471934i	−0.177225	−	0.0174551i
$732$	−1.12646	+	2.15558i	−0.0416350	+	0.0796725i
$733$	35.7429	+	10.8425i	1.32020	+	0.400477i	0.870264	−	0.492586i	$-0.163948\pi$
$733$	35.7429	+	10.8425i	1.32020	+	0.400477i	0.449932	+	0.893063i	$0.351448\pi$
$734$	−32.9545	−	11.6182i	−1.21637	−	0.428836i
$735$	−1.32532	+	1.32532i	−0.0488853	+	0.0488853i
$736$	35.7569	+	11.8610i	1.31802	+	0.437203i
$737$	−3.91027	−	3.91027i	−0.144037	−	0.144037i
$738$	−9.04827	−	18.9023i	−0.333071	−	0.695805i
$739$	0.166058	−	0.547419i	0.00610853	−	0.0201371i	−0.953833	−	0.300337i	$-0.902901\pi$
$739$	0.166058	−	0.547419i	0.00610853	−	0.0201371i	0.959942	+	0.280200i	$0.0904008\pi$
$740$	6.25215	−	5.22936i	0.229834	−	0.192235i
$741$	0.00771546	−	0.0783364i	0.000283435	−	0.00287776i
$742$	−11.8942	−	77.6858i	−0.436649	−	2.85194i
$743$	−3.90527	+	19.6331i	−0.143271	+	0.720270i	0.840638	+	0.541597i	$0.182180\pi$
$743$	−3.90527	+	19.6331i	−0.143271	+	0.720270i	−0.983909	+	0.178672i	$0.942820\pi$
$744$	1.47001	−	1.12246i	0.0538933	−	0.0411512i
$745$	13.1553	−	2.61676i	0.481974	−	0.0958706i
$746$	3.55169	+	1.65960i	0.130037	+	0.0607622i
$747$	−10.8781	+	20.3516i	−0.398010	+	0.744625i
$748$	13.4785	+	13.2294i	0.492823	+	0.483714i
$749$	−8.59463	−	87.2627i	−0.314041	−	3.18851i
$750$	0.144998	−	0.0370396i	0.00529457	−	0.00135250i
$751$	−28.1756	+	11.6707i	−1.02814	+	0.425870i	−0.832041	−	0.554714i	$-0.812828\pi$
$751$	−28.1756	+	11.6707i	−1.02814	+	0.425870i	−0.196100	+	0.980584i	$0.562828\pi$
$752$	−4.20847	−	6.05093i	−0.153467	−	0.220655i
$753$	−2.10661	−	0.872587i	−0.0767692	−	0.0317989i
$754$	2.28043	+	0.327408i	0.0830485	+	0.0119235i
$755$	−4.40004	−	3.61102i	−0.160134	−	0.131418i
$756$	5.20604	−	3.54925i	0.189342	−	0.129085i
$757$	40.5915	−	12.3133i	1.47532	−	0.447534i	0.552747	−	0.833349i	$-0.313580\pi$
$757$	40.5915	−	12.3133i	1.47532	−	0.447534i	0.922576	+	0.385815i	$0.126080\pi$
$758$	−0.562720	+	12.6589i	−0.0204389	+	0.459792i
$759$	1.54594	−	2.31366i	0.0561141	−	0.0839807i
$760$	0.368898	+	2.26781i	0.0133813	+	0.0822622i
$761$	−39.6291	+	26.4793i	−1.43655	+	0.959874i	−0.438421	+	0.898770i	$0.644462\pi$
$761$	−39.6291	+	26.4793i	−1.43655	+	0.959874i	−0.998131	+	0.0611039i	$0.980538\pi$
$762$	−2.28819	−	0.561834i	−0.0828925	−	0.0203531i
$763$	−18.7763	−	22.8789i	−0.679746	−	0.828273i
$764$	48.1082	−	5.19179i	1.74049	−	0.187833i
$765$	−6.30394	+	3.36953i	−0.227920	+	0.121826i
$766$	25.3831	+	22.7912i	0.917129	+	0.823479i
$767$	10.0953			0.364519
$768$	−1.02454	+	1.34797i	−0.0369701	+	0.0486408i
$769$	−3.60433			−0.129976			−0.0649878	−	0.997886i	$-0.520701\pi$
$769$	−3.60433			−0.129976			−0.0649878	+	0.997886i	$0.520701\pi$
$770$	20.6544	+	18.5453i	0.744332	+	0.668327i
$771$	−1.61866	+	0.865193i	−0.0582947	+	0.0311592i
$772$	−16.6101	+	1.79255i	−0.597810	+	0.0645151i
$773$	−7.27999	−	8.87069i	−0.261843	−	0.319057i	0.625449	−	0.780265i	$-0.284916\pi$
$773$	−7.27999	−	8.87069i	−0.261843	−	0.319057i	−0.887292	+	0.461209i	$0.847416\pi$
$774$	8.26407	+	2.02913i	0.297046	+	0.0729354i
$775$	−5.13802	+	3.43311i	−0.184563	+	0.123321i
$776$	44.8933	−	7.30265i	1.61157	−	0.262150i
$777$	1.19106	−	1.78255i	0.0427292	−	0.0639487i
$778$	0.399099	−	8.97811i	0.0143084	−	0.321881i
$779$	3.85409	−	1.16913i	0.138087	−	0.0418883i
$780$	−0.160129	+	0.109169i	−0.00573352	+	0.00390887i
$781$	9.59092	+	7.87106i	0.343190	+	0.281649i
$782$	−22.2958	−	3.20106i	−0.797296	−	0.114470i
$783$	1.04161	+	0.431451i	0.0372243	+	0.0154188i
$784$	−12.5229	+	69.7318i	−0.447248	+	2.49042i
$785$	−2.19718	+	0.910101i	−0.0784206	+	0.0324829i
$786$	2.34860	−	0.599949i	0.0837718	−	0.0213995i
$787$	4.48651	+	45.5523i	0.159927	+	1.62376i	0.655498	+	0.755197i	$0.272459\pi$
$787$	4.48651	+	45.5523i	0.159927	+	1.62376i	−0.495571	+	0.868568i	$0.665041\pi$
$788$	17.3950	+	17.0735i	0.619671	+	0.608217i
$789$	1.13030	−	2.11464i	0.0402398	−	0.0752833i
$790$	3.02092	+	1.41159i	0.107480	+	0.0502219i
$791$	89.7860	−	17.8596i	3.19242	−	0.635013i
$792$	−20.2569	−	26.5292i	−0.719797	−	0.942675i
$793$	−2.05296	+	10.3209i	−0.0729027	+	0.366507i
$794$	−5.20405	−	33.9898i	−0.184685	−	1.20625i
$795$	−0.115953	+	1.17729i	−0.00411242	+	0.0417541i
$796$	−13.2614	+	11.0920i	−0.470039	+	0.393145i
$797$	−8.34236	+	27.5011i	−0.295501	+	0.974138i	0.675960	+	0.736939i	$0.263729\pi$
$797$	−8.34236	+	27.5011i	−0.295501	+	0.974138i	−0.971461	+	0.237199i	$0.923771\pi$
$798$	0.260929	+	0.545096i	0.00923679	+	0.0192962i
$799$	3.11609	+	3.11609i	0.110239	+	0.110239i
$800$	3.70014	−	4.27890i	0.130820	−	0.151282i
$801$	2.11800	−	2.11800i	0.0748357	−	0.0748357i
$802$	3.94517	+	1.39088i	0.139309	+	0.0491138i
$803$	24.2339	+	7.35128i	0.855197	+	0.259421i
$804$	−0.137283	+	0.262705i	−0.00484161	+	0.00926488i
$805$	−32.9465	−	3.24495i	−1.16121	−	0.114369i
$806$	4.73697	−	6.44972i	0.166853	−	0.227182i
$807$	−0.189611	−	0.0377160i	−0.00667463	−	0.00132767i
$808$	−3.91222	−	3.44736i	−0.137632	−	0.121278i
$809$	−10.8932	−	54.7639i	−0.382985	−	1.92540i	−0.378983	−	0.925404i	$-0.623726\pi$
$809$	−10.8932	−	54.7639i	−0.382985	−	1.92540i	−0.00400208	−	0.999992i	$-0.501274\pi$
$810$	11.8300	−	4.29517i	0.415663	−	0.150917i
$811$	−38.7348	−	20.7042i	−1.36016	−	0.727021i	−0.379956	−	0.925005i	$-0.624061\pi$
$811$	−38.7348	−	20.7042i	−1.36016	−	0.727021i	−0.980205	+	0.197983i	$0.936561\pi$
$812$	−16.2771	+	6.92077i	−0.571214	+	0.242872i
$813$	−1.20676	+	0.118856i	−0.0423230	+	0.00416845i
$814$	−19.5736	−	11.6082i	−0.686055	−	0.406868i
$815$	5.12374	+	12.3698i	0.179477	+	0.433295i
$816$	0.460467	−	0.901535i	0.0161196	−	0.0315600i
$817$	−0.625844	+	1.51092i	−0.0218955	+	0.0528605i
$818$	−36.8360	+	27.5866i	−1.28794	+	0.964544i
$819$	8.63102	−	10.5169i	0.301592	−	0.367491i
$820$	−8.29584	−	5.43186i	−0.289703	−	0.189689i
$821$	12.4728	+	41.1172i	0.435303	+	1.43500i	0.850840	+	0.525425i	$0.176094\pi$
$821$	12.4728	+	41.1172i	0.435303	+	1.43500i	−0.415537	+	0.909576i	$0.636406\pi$
$822$	2.17632	−	1.99107i	0.0759079	−	0.0694465i
$823$	21.0653	+	14.0754i	0.734291	+	0.490638i	0.865620	−	0.500701i	$-0.166924\pi$
$823$	21.0653	+	14.0754i	0.734291	+	0.490638i	−0.131329	+	0.991339i	$0.541924\pi$
$824$	32.0581	+	34.3911i	1.11680	+	1.19807i
$825$	−0.232134	−	0.347414i	−0.00808189	−	0.0120954i
$826$	−66.2919	+	40.1553i	−2.30659	+	1.39718i
$827$	33.7591	−	27.7054i	1.17392	−	0.963410i	0.174146	−	0.984720i	$-0.444284\pi$
$827$	33.7591	−	27.7054i	1.17392	−	0.963410i	0.999773	+	0.0213097i	$0.00678360\pi$
$828$	38.2009	+	11.2001i	1.32757	+	0.389229i
$829$	23.8844	+	44.6846i	0.829540	+	1.55196i	0.833864	+	0.551970i	$0.186124\pi$
$829$	23.8844	+	44.6846i	0.829540	+	1.55196i	−0.00432417	+	0.999991i	$0.501376\pi$
$830$	0.586634	+	10.9033i	0.0203624	+	0.378459i
$831$		−	0.0684026i		−	0.00237286i
$832$	−2.61292	+	6.84378i	−0.0905866	+	0.237265i
$833$		−	42.3593i		−	1.46766i
$834$	2.91855	−	0.157028i	0.101061	−	0.00543742i
$835$	6.57760	+	12.3058i	0.227627	+	0.425861i
$836$	5.62900	−	3.07661i	0.194683	−	0.106407i
$837$	3.02724	−	2.48439i	0.104637	−	0.0858732i
$838$	0.527532	+	0.870897i	0.0182233	+	0.0300846i
$839$	12.4580	+	18.6447i	0.430097	+	0.643685i	0.981703	−	0.190420i	$-0.0609849\pi$
$839$	12.4580	+	18.6447i	0.430097	+	0.643685i	−0.551606	+	0.834105i	$0.685985\pi$
$840$	0.617272	−	1.35380i	0.0212979	−	0.0467107i
$841$	21.4811	+	14.3532i	0.740728	+	0.494939i
$842$	−17.3271	−	18.9392i	−0.597131	−	0.652688i
$843$	−0.922586	−	3.04136i	−0.0317756	−	0.104750i
$844$	−5.74600	−	27.5418i	−0.197785	−	0.948029i
$845$	7.71517	−	9.40096i	0.265410	−	0.323403i
$846$	−4.66871	−	6.23404i	−0.160514	−	0.214331i
$847$	8.73248	−	21.0821i	0.300052	−	0.724388i
$848$	21.8111	+	39.0361i	0.748998	+	1.34051i
$849$	0.840333	+	2.02874i	0.0288401	+	0.0696263i
$850$	−1.72525	+	2.90910i	−0.0591757	+	0.0997812i
$851$	27.0102	−	2.66027i	0.925897	−	0.0911929i
$852$	0.248758	−	0.616767i	0.00852233	−	0.0211301i
$853$	16.1489	+	8.63179i	0.552929	+	0.295547i	0.724100	−	0.689695i	$-0.242255\pi$
$853$	16.1489	+	8.63179i	0.552929	+	0.295547i	−0.171171	+	0.985241i	$0.554755\pi$
$854$	−27.5718	−	75.9396i	−0.943489	−	2.59860i
$855$	0.473659	+	2.38125i	0.0161988	+	0.0814369i
$856$	21.9599	+	44.7975i	0.750573	+	1.53115i
$857$	21.9921	+	4.37451i	0.751237	+	0.149430i	0.555835	−	0.831293i	$-0.312399\pi$
$857$	21.9921	+	4.37451i	0.751237	+	0.149430i	0.195402	+	0.980723i	$0.437399\pi$
$858$	0.436106	+	0.320297i	0.0148884	+	0.0109347i
$859$	28.9715	+	2.85345i	0.988496	+	0.0973584i	0.579323	−	0.815098i	$-0.303317\pi$
$859$	28.9715	+	2.85345i	0.988496	+	0.0973584i	0.409173	+	0.912457i	$0.365817\pi$
$860$	3.84201	−	1.20471i	0.131012	−	0.0410803i
$861$	−2.49583	−	0.757101i	−0.0850576	−	0.0258019i
$862$	−8.63830	+	24.5021i	−0.294222	+	0.834546i
$863$	−7.08934	+	7.08934i	−0.241324	+	0.241324i	−0.817398	−	0.576074i	$-0.804584\pi$
$863$	−7.08934	+	7.08934i	−0.241324	+	0.241324i	0.576074	+	0.817398i	$0.304584\pi$
$864$	−2.06785	+	2.92851i	−0.0703497	+	0.0996298i
$865$	−13.8589	−	13.8589i	−0.471215	−	0.471215i
$866$	−16.1262	+	7.71936i	−0.547990	+	0.262315i
$867$	0.346512	−	1.14230i	0.0117682	−	0.0387945i
$868$	−5.45131	+	61.1949i	−0.185029	+	2.07709i
$869$	0.912512	−	9.26489i	0.0309549	−	0.314290i
$870$	0.263169	−	0.0402928i	0.00892228	−	0.00136606i
$871$	−0.250198	+	1.25783i	−0.00847763	+	0.0426199i
$872$	14.5639	+	8.45456i	0.493196	+	0.286307i
$873$	47.1388	−	9.37649i	1.59541	−	0.317346i
$874$	−3.23880	+	6.93133i	−0.109554	+	0.234456i
$875$	−2.34336	+	4.38412i	−0.0792200	+	0.148210i
$876$	−0.0126622	−	1.35736i	−0.000427815	−	0.0458610i
$877$	−3.63145	−	36.8708i	−0.122625	−	1.24504i	−0.837756	−	0.546046i	$-0.816133\pi$
$877$	−3.63145	−	36.8708i	−0.122625	−	1.24504i	0.715130	−	0.698991i	$-0.246367\pi$
$878$	7.39989	+	28.9681i	0.249734	+	0.977627i
$879$	0.360918	−	0.149497i	0.0121735	−	0.00504241i
$880$	−14.7018	−	5.77078i	−0.495598	−	0.194533i
$881$	−18.7405	−	7.76259i	−0.631385	−	0.261528i	0.0439565	−	0.999033i	$-0.486004\pi$
$881$	−18.7405	−	7.76259i	−0.631385	−	0.261528i	−0.675341	+	0.737505i	$0.736004\pi$
$882$	−10.6394	+	74.1046i	−0.358247	+	2.49523i
$883$	32.9574	+	27.0475i	1.10911	+	0.910220i	0.996514	−	0.0834218i	$-0.0265849\pi$
$883$	32.9574	+	27.0475i	1.10911	+	0.910220i	0.112591	+	0.993641i	$0.464085\pi$
$884$	0.814378	−	4.30358i	0.0273905	−	0.144745i
$885$	1.11640	−	0.338657i	0.0375275	−	0.0113838i
$886$	23.0444	+	1.02438i	0.774191	+	0.0344147i
$887$	−28.8339	+	43.1529i	−0.968147	+	1.44893i	−0.0760425	+	0.997105i	$0.524228\pi$
$887$	−28.8339	+	43.1529i	−0.968147	+	1.44893i	−0.892104	+	0.451830i	$0.850772\pi$
$888$	−0.279802	+	1.18727i	−0.00938955	+	0.0398423i
$889$	65.0752	−	43.4819i	2.18255	−	1.45834i
$890$	0.337957	−	1.37640i	0.0113283	−	0.0461372i
$891$	−22.2918	−	27.1626i	−0.746802	−	0.909981i
$892$	−5.32333	−	4.28627i	−0.178238	−	0.143515i
$893$	1.32009	−	0.705601i	0.0441750	−	0.0236120i
$894$	−1.34108	+	1.49359i	−0.0448524	+	0.0499533i
$895$	−13.6168			−0.455160
$896$	−10.0640	−	55.3338i	−0.336214	−	1.84857i
$897$	−0.645327			−0.0215469
$898$	16.1726	−	18.0118i	0.539686	−	0.601062i
$899$	−9.69523	+	5.18221i	−0.323354	+	0.172836i
$900$	3.74888	−	4.65592i	0.124963	−	0.155197i
$901$	−16.9609	−	20.6670i	−0.565051	−	0.688516i
$902$	−6.60162	+	26.8866i	−0.219810	+	0.895224i
$903$	0.880573	−	0.588380i	0.0293036	−	0.0195801i
$904$	−44.2972	+	27.4004i	−1.47330	+	0.911325i
$905$	1.56242	−	2.33833i	0.0519366	−	0.0777287i
$906$	0.851001	+	0.0378291i	0.0282726	+	0.00125679i
$907$	31.9832	−	9.70201i	1.06199	−	0.322150i	0.289498	−	0.957179i	$-0.406512\pi$
$907$	31.9832	−	9.70201i	1.06199	−	0.322150i	0.772489	+	0.635029i	$0.219012\pi$
$908$	−40.7433	−	7.70997i	−1.35211	−	0.255864i
$909$	−4.25932	−	3.49554i	−0.141273	−	0.115940i
$910$	0.914876	−	6.37222i	0.0303279	−	0.211237i
$911$	−29.1323	−	12.0670i	−0.965197	−	0.399798i	−0.156275	−	0.987714i	$-0.549949\pi$
$911$	−29.1323	−	12.0670i	−0.965197	−	0.399798i	−0.808922	+	0.587916i	$0.799949\pi$
$912$	−0.247630	−	0.238559i	−0.00819986	−	0.00789947i
$913$	28.1653	−	11.6664i	0.932135	−	0.386103i
$914$	−2.78094	−	10.8864i	−0.0919852	−	0.360091i
$915$	0.119197	+	1.21023i	0.00394053	+	0.0400089i
$916$	−17.2700	+	0.161103i	−0.570616	+	0.00532300i
$917$	−37.9566	+	71.0117i	−1.25344	+	2.34501i
$918$	0.907395	−	1.94191i	0.0299485	−	0.0640925i
$919$	−35.2793	+	7.01749i	−1.16376	+	0.231486i	−0.738926	−	0.673787i	$-0.764667\pi$
$919$	−35.2793	+	7.01749i	−1.16376	+	0.231486i	−0.424832	+	0.905272i	$0.639667\pi$
$920$	18.2061	−	4.83209i	0.600237	−	0.159309i
$921$	0.183274	−	0.921379i	0.00603907	−	0.0303605i
$922$	−23.4298	+	3.58724i	−0.771619	+	0.118140i
$923$	0.282035	−	2.86355i	0.00928329	−	0.0942549i
$924$	−4.13778	−	0.368597i	−0.136123	−	0.0121260i
$925$	1.18303	−	3.89992i	0.0388977	−	0.128228i
$926$	13.0769	−	6.25970i	0.429732	−	0.205706i
$927$	35.1301	+	35.1301i	1.15382	+	1.15382i
$928$	7.29703	−	6.93035i	0.239537	−	0.227500i
$929$	−9.33548	+	9.33548i	−0.306287	+	0.306287i	−0.843467	−	0.537180i	$-0.819489\pi$
$929$	−9.33548	+	9.33548i	−0.306287	+	0.306287i	0.537180	+	0.843467i	$0.319489\pi$
$930$	0.307484	−	0.872162i	0.0100828	−	0.0285993i
$931$	−13.7683	−	4.17658i	−0.451239	−	0.136882i
$932$	−7.20618	−	22.9816i	−0.236046	−	0.752789i
$933$	−2.22148	−	0.218796i	−0.0727278	−	0.00716307i
$934$	9.84303	+	7.22917i	0.322074	+	0.236546i
$935$	9.26163	+	1.84225i	0.302888	+	0.0602481i
$936$	−2.50562	+	7.32425i	−0.0818989	+	0.239401i
$937$	4.70475	+	23.6524i	0.153698	+	0.772690i	0.978335	+	0.207028i	$0.0663791\pi$
$937$	4.70475	+	23.6524i	0.153698	+	0.772690i	−0.824638	+	0.565662i	$0.808621\pi$
$938$	−3.36023	−	9.25491i	−0.109715	−	0.302183i
$939$	1.56107	+	0.834408i	0.0509435	+	0.0272299i
$940$	−3.41776	−	1.37847i	−0.111475	−	0.0449608i
$941$	−13.4872	+	1.32837i	−0.439669	+	0.0433036i	−0.315430	−	0.948949i	$-0.602149\pi$
$941$	−13.4872	+	1.32837i	−0.439669	+	0.0433036i	−0.124238	+	0.992252i	$0.539649\pi$
$942$	0.181547	−	0.306122i	0.00591513	−	0.00997401i
$943$	−12.6356	−	30.5051i	−0.411473	−	0.993383i
$944$	27.3350	−	34.6045i	0.889677	−	1.12628i
$945$	1.20560	−	2.91059i	0.0392183	−	0.0946814i
$946$	−6.73878	−	8.99818i	−0.219097	−	0.292556i
$947$	21.7270	−	26.4744i	0.706033	−	0.860304i	−0.289256	−	0.957252i	$-0.593408\pi$
$947$	21.7270	−	26.4744i	0.706033	−	0.860304i	0.995289	+	0.0969480i	$0.0309080\pi$
$948$	−0.488495	+	0.101914i	−0.0158656	+	0.00331000i
$949$	−1.70486	−	5.62018i	−0.0553422	−	0.182439i
$950$	0.775455	+	0.847604i	0.0251591	+	0.0274999i
$951$	0.849411	+	0.567558i	0.0275440	+	0.0184043i
$952$	11.7703	+	31.4993i	0.381479	+	1.02090i
$953$	20.5433	+	30.7452i	0.665463	+	0.995935i	0.998592	+	0.0530539i	$0.0168955\pi$
$953$	20.5433	+	30.7452i	0.665463	+	0.995935i	−0.333129	+	0.942881i	$0.608104\pi$
$954$	24.4810	+	40.4154i	0.792602	+	1.30850i
$955$	18.7020	−	15.3484i	0.605184	−	0.496662i
$956$	5.73993	+	10.5018i	0.185643	+	0.339653i
$957$	−0.350402	−	0.655556i	−0.0113269	−	0.0211911i
$958$	−5.80801	+	0.312490i	−0.187648	+	0.0100961i
$959$			97.9812i			3.16398i
$960$	−0.0593720	+	0.844485i	−0.00191622	+	0.0272556i
$961$			7.18550i			0.231790i
$962$	0.283544	+	5.27002i	0.00914184	+	0.169912i
$963$	24.8517	+	46.4943i	0.800835	+	1.49826i
$964$	1.29361	−	4.41223i	0.0416645	−	0.142108i
$965$	−6.45716	+	5.29926i	−0.207863	+	0.170589i
$966$	4.23763	−	2.56688i	0.136343	−	0.0825880i
$967$	−12.2437	−	18.3240i	−0.393731	−	0.589260i	0.580653	−	0.814151i	$-0.302797\pi$
$967$	−12.2437	−	18.3240i	−0.393731	−	0.589260i	−0.974384	+	0.224891i	$0.927797\pi$
$968$	−0.455561	+	12.9755i	−0.0146423	+	0.417047i
$969$	0.170938	+	0.114217i	0.00549131	+	0.00366918i
$970$	16.7791	−	15.3508i	0.538743	−	0.492884i
$971$	1.73423	+	5.71698i	0.0556540	+	0.183467i	0.980360	−	0.197215i	$-0.0631896\pi$
$971$	1.73423	+	5.71698i	0.0556540	+	0.183467i	−0.924706	+	0.380681i	$0.875690\pi$
$972$	−3.11470	+	4.75694i	−0.0999040	+	0.152579i
$973$	−61.5911	+	75.0490i	−1.97452	+	2.40596i
$974$	−9.12084	+	6.83064i	−0.292251	+	0.218868i
$975$	−0.0370823	+	0.0895246i	−0.00118758	+	0.00286708i
$976$	29.8192	+	34.9831i	0.954491	+	1.11978i
$977$	6.10601	+	14.7412i	0.195349	+	0.471613i	0.990954	−	0.134202i	$-0.0428471\pi$
$977$	6.10601	+	14.7412i	0.195349	+	0.471613i	−0.795605	+	0.605815i	$0.792847\pi$
$978$	−1.72343	−	1.02209i	−0.0551091	−	0.0326827i
$979$	−3.93799	+	0.387858i	−0.125859	+	0.0123960i
$980$	13.8608	+	32.5993i	0.442765	+	1.04135i
$981$	15.6937	+	8.38845i	0.501061	+	0.267823i
$982$	29.0825	−	10.5591i	0.928059	−	0.336956i
$983$	3.85648	+	19.3878i	0.123003	+	0.618376i	0.992277	+	0.124045i	$0.0395868\pi$
$983$	3.85648	+	19.3878i	0.123003	+	0.618376i	−0.869274	+	0.494331i	$0.835413\pi$
$984$	1.48101	−	0.0935457i	0.0472128	−	0.00298213i
$985$	11.9528	+	2.37756i	0.380848	+	0.0757554i
$986$	−3.56174	+	4.84956i	−0.113429	+	0.154441i
$987$	−0.964648	−	0.0950095i	−0.0307051	−	0.00302419i
$988$	−1.31852	−	0.689030i	−0.0419478	−	0.0219210i
$989$	12.8301	+	3.89198i	0.407975	+	0.123758i
$990$	−15.7398	−	5.54913i	−0.500245	−	0.176363i
$991$	−9.00677	+	9.00677i	−0.286110	+	0.286110i	−0.835540	−	0.549430i	$-0.814845\pi$
$991$	−9.00677	+	9.00677i	−0.286110	+	0.286110i	0.549430	+	0.835540i	$0.314845\pi$
$992$	−9.28205	−	33.7013i	−0.294705	−	1.07002i
$993$	−0.0411330	−	0.0411330i	−0.00130531	−	0.00130531i
$994$	9.53814	+	19.9257i	0.302531	+	0.632005i
$995$	−2.50932	+	8.27210i	−0.0795506	+	0.262243i
$996$	−1.04839	−	1.25344i	−0.0332194	−	0.0397167i
$997$	−1.43877	+	14.6081i	−0.0455664	+	0.462644i	0.945144	+	0.326654i	$0.105921\pi$
$997$	−1.43877	+	14.6081i	−0.0455664	+	0.462644i	−0.990710	+	0.135989i	$0.956579\pi$
$998$	−0.638358	−	4.16939i	−0.0202069	−	0.131980i
$999$	−0.503871	+	2.53313i	−0.0159418	+	0.0801446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.49	✓	1024
128.109	even	32	inner	640.2.bm.a.621.49	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.49	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.49	yes	1024	128.109	even	32	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.05228 + 0.944830i) q^{2} +(-0.0933260 + 0.0498838i) q^{3} +(0.214592 + 1.98845i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-0.145337 - 0.0356854i) q^{6} +(4.13332 - 2.76180i) q^{7} +(-1.65294 + 2.29517i) q^{8} +(-1.66049 + 2.48510i) q^{9} +(-0.0628033 + 1.41282i) q^{10} +(3.77844 - 1.14618i) q^{11} +(-0.119219 - 0.174870i) q^{12} +(-0.707847 - 0.580915i) q^{13} +(6.95884 + 0.999098i) q^{14} +(-0.0977661 - 0.0404960i) q^{15} +(-3.90790 + 0.853413i) q^{16} +(2.20953 - 0.915219i) q^{17} +(-4.09530 + 1.04614i) q^{18} +(-0.0796224 - 0.808419i) q^{19} +(-1.40096 + 1.42734i) q^{20} +(-0.247977 + 0.463933i) q^{21} +(5.05893 + 2.36388i) q^{22} +(-6.53171 + 1.29924i) q^{23} +(0.0397707 - 0.296654i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.195988 - 1.28008i) q^{26} +(0.0621176 - 0.630691i) q^{27} +(6.37868 + 7.62626i) q^{28} +(-0.516420 + 1.70241i) q^{29} +(-0.0646155 - 0.134986i) q^{30} +(4.36953 + 4.36953i) q^{31} +(-4.91854 - 2.79427i) q^{32} +(-0.295451 + 0.295451i) q^{33} +(3.18978 + 1.12457i) q^{34} +(4.75705 + 1.44303i) q^{35} +(-5.29783 - 2.76852i) q^{36} +(-4.05578 - 0.399459i) q^{37} +(0.680034 - 0.925914i) q^{38} +(0.0950388 + 0.0189044i) q^{39} +(-2.82280 + 0.178298i) q^{40} +(0.967253 + 4.86271i) q^{41} +(-0.699280 + 0.253892i) q^{42} +(-1.77551 - 0.949030i) q^{43} +(3.08995 + 7.26730i) q^{44} +(-2.97441 + 0.292954i) q^{45} +(-8.10076 - 4.80419i) q^{46} +(0.705146 + 1.70237i) q^{47} +(0.322137 - 0.274587i) q^{48} +(6.77803 - 16.3636i) q^{49} +(-1.13197 + 0.847735i) q^{50} +(-0.160552 + 0.195634i) q^{51} +(1.00322 - 1.53218i) q^{52} +(-3.24511 - 10.6977i) q^{53} +(0.661261 - 0.604974i) q^{54} +(3.28303 + 2.19365i) q^{55} +(-0.493349 + 14.0517i) q^{56} +(0.0477579 + 0.0714747i) q^{57} +(-2.15191 + 1.30348i) q^{58} +(-8.52214 + 6.99394i) q^{59} +(0.0595447 - 0.203094i) q^{60} +(-5.41722 - 10.1349i) q^{61} +(0.469511 + 8.72643i) q^{62} +14.8576i q^{63} +(-2.53558 - 7.58755i) q^{64} -0.915702i q^{65} +(-0.590049 + 0.0317466i) q^{66} +(-0.660208 - 1.23516i) q^{67} +(2.29402 + 4.19716i) q^{68} +(0.544768 - 0.447079i) q^{69} +(3.64233 + 6.01308i) q^{70} +(1.74577 + 2.61272i) q^{71} +(-2.95902 - 7.91882i) q^{72} +(5.33283 + 3.56328i) q^{73} +(-3.89040 - 4.25237i) q^{74} +(-0.0307183 - 0.101265i) q^{75} +(1.59042 - 0.331806i) q^{76} +(12.4520 - 15.1728i) q^{77} +(0.0821461 + 0.109688i) q^{78} +(0.902295 - 2.17833i) q^{79} +(-3.13884 - 2.47945i) q^{80} +(-3.40563 - 8.22192i) q^{81} +(-3.57661 + 6.03083i) q^{82} +(7.68377 - 0.756786i) q^{83} +(-0.975723 - 0.393535i) q^{84} +(2.10919 + 1.12738i) q^{85} +(-0.971665 - 2.67620i) q^{86} +(-0.0367272 - 0.184640i) q^{87} +(-3.61487 + 10.5667i) q^{88} +(-0.982917 - 0.195514i) q^{89} +(-3.40671 - 2.50204i) q^{90} +(-4.53013 - 0.446179i) q^{91} +(-3.98513 - 12.7092i) q^{92} +(-0.625759 - 0.189822i) q^{93} +(-0.866442 + 2.45762i) q^{94} +(0.574405 - 0.574405i) q^{95} +(0.598417 + 0.0154227i) q^{96} +(-11.3708 - 11.3708i) q^{97} +(22.5932 - 10.8150i) q^{98} +(-3.42570 + 11.2930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more