LMFDB - Embedded newform 700.2.bj.a.687.54

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(127,700)] 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("700.127"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.bj (of order $20$, degree $8$, 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:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$90$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			687.54
Character	$\chi$	$=$	700.687
Dual form			700.2.bj.a.323.54

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.363714 + 1.36664i) q^{2} +(-0.602372 + 1.18222i) q^{3} +(-1.73542 + 0.994135i) q^{4} +(-2.08430 + 0.809739i) q^{5} +(-1.83477 - 0.393236i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.98983 - 2.01012i) q^{8} +(0.728560 + 1.00278i) q^{9} +(-1.86472 - 2.55398i) q^{10} +(-2.41003 + 3.31711i) q^{11} +(-0.129917 - 2.65049i) q^{12} +(-0.684643 + 4.32266i) q^{13} +(-1.22355 - 0.709177i) q^{14} +(0.298235 - 2.95187i) q^{15} +(2.02339 - 3.45049i) q^{16} +(4.81746 - 2.45462i) q^{17} +(-1.10545 + 1.36040i) q^{18} +(1.14827 - 3.53402i) q^{19} +(2.81216 - 3.47732i) q^{20} +(-0.410016 - 1.26190i) q^{21} +(-5.40987 - 2.08716i) q^{22} +(-1.18763 - 7.49840i) q^{23} +(3.57503 - 1.14157i) q^{24} +(3.68864 - 3.37549i) q^{25} +(-6.15655 + 0.636552i) q^{26} +(-5.55588 + 0.879964i) q^{27} +(0.524171 - 1.93009i) q^{28} +(-0.734772 + 0.238742i) q^{29} +(4.14263 - 0.666058i) q^{30} +(-7.18714 - 2.33524i) q^{31} +(5.45152 + 1.51026i) q^{32} +(-2.46983 - 4.84732i) q^{33} +(5.10677 + 5.69097i) q^{34} +(0.901253 - 2.04640i) q^{35} +(-2.26125 - 1.01596i) q^{36} +(0.865275 + 0.137046i) q^{37} +(5.24739 + 0.283905i) q^{38} +(-4.69794 - 3.41325i) q^{39} +(5.77508 + 2.57847i) q^{40} +(-6.17492 + 4.48634i) q^{41} +(1.57544 - 1.01932i) q^{42} +(6.75136 + 6.75136i) q^{43} +(0.884756 - 8.15249i) q^{44} +(-2.33053 - 1.50015i) q^{45} +(9.81568 - 4.35034i) q^{46} +(-3.96724 - 2.02141i) q^{47} +(2.86041 + 4.47058i) q^{48} -1.00000i q^{49} +(5.95469 + 3.81335i) q^{50} +7.17390i q^{51} +(-3.10916 - 8.18228i) q^{52} +(9.74120 + 4.96339i) q^{53} +(-3.22335 - 7.27284i) q^{54} +(2.33723 - 8.86537i) q^{55} +(2.82839 + 0.0143529i) q^{56} +(3.48631 + 3.48631i) q^{57} +(-0.593522 - 0.917337i) q^{58} +(-3.01566 + 2.19101i) q^{59} +(2.41700 + 5.41924i) q^{60} +(0.997249 + 0.724544i) q^{61} +(0.577378 - 10.6716i) q^{62} +(-1.22424 - 0.193900i) q^{63} +(-0.0811913 + 7.99959i) q^{64} +(-2.07323 - 9.56412i) q^{65} +(5.72624 - 5.13842i) q^{66} +(0.357808 + 0.702238i) q^{67} +(-5.92012 + 9.04901i) q^{68} +(9.58017 + 3.11279i) q^{69} +(3.12449 + 0.487387i) q^{70} +(-15.7194 + 5.10754i) q^{71} +(0.565998 - 3.45984i) q^{72} +(-5.58483 + 0.884550i) q^{73} +(0.127420 + 1.23237i) q^{74} +(1.76864 + 6.39409i) q^{75} +(1.52055 + 7.27457i) q^{76} +(-0.641409 - 4.04970i) q^{77} +(2.95599 - 7.66185i) q^{78} +(4.48089 + 13.7908i) q^{79} +(-1.42337 + 8.83029i) q^{80} +(1.15731 - 3.56184i) q^{81} +(-8.37713 - 6.80716i) q^{82} +(-5.68644 + 2.89739i) q^{83} +(1.96605 + 1.78232i) q^{84} +(-8.05345 + 9.01706i) q^{85} +(-6.77113 + 11.6823i) q^{86} +(0.160360 - 1.01247i) q^{87} +(11.4633 - 1.75603i) q^{88} +(1.40605 - 1.93526i) q^{89} +(1.20252 - 3.73062i) q^{90} +(-2.57247 - 3.54070i) q^{91} +(9.51547 + 11.8322i) q^{92} +(7.09011 - 7.09011i) q^{93} +(1.31960 - 6.15701i) q^{94} +(0.468287 + 8.29578i) q^{95} +(-5.06931 + 5.53517i) q^{96} +(-5.47273 + 10.7408i) q^{97} +(1.36664 - 0.363714i) q^{98} -5.08217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) $ 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$1$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	0.363714	+	1.36664i	0.257185	+	0.966362i
$2$	0.363714	+	1.36664i	0.257185	+	0.966362i
$3$	−0.602372	+	1.18222i	−0.347780	+	0.682556i	−0.996946	−	0.0780902i	$-0.975118\pi$
$3$	−0.602372	+	1.18222i	−0.347780	+	0.682556i	0.649167	+	0.760646i	$0.275118\pi$
$4$	−1.73542	+	0.994135i	−0.867712	+	0.497067i
$5$	−2.08430	+	0.809739i	−0.932129	+	0.362126i
$5$	−2.08430	+	0.809739i	−0.932129	+	0.362126i
$6$	−1.83477	−	0.393236i	−0.749040	−	0.160538i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.98983	−	2.01012i	−0.703509	−	0.710686i
$9$	0.728560	+	1.00278i	0.242853	+	0.334259i
$10$	−1.86472	−	2.55398i	−0.589675	−	0.807641i
$11$	−2.41003	+	3.31711i	−0.726650	+	1.00015i	0.272627	+	0.962120i	$0.412108\pi$
$11$	−2.41003	+	3.31711i	−0.726650	+	1.00015i	−0.999277	+	0.0380279i	$0.987892\pi$
$12$	−0.129917	−	2.65049i	−0.0375037	−	0.765132i
$13$	−0.684643	+	4.32266i	−0.189886	+	1.19889i	0.690037	+	0.723774i	$0.257594\pi$
$13$	−0.684643	+	4.32266i	−0.189886	+	1.19889i	−0.879923	+	0.475117i	$0.842406\pi$
$14$	−1.22355	−	0.709177i	−0.327007	−	0.189536i
$15$	0.298235	−	2.95187i	0.0770039	−	0.762170i
$16$	2.02339	−	3.45049i	0.505848	−	0.862623i
$17$	4.81746	−	2.45462i	1.16841	−	0.595333i	0.241417	−	0.970421i	$-0.422388\pi$
$17$	4.81746	−	2.45462i	1.16841	−	0.595333i	0.926989	+	0.375089i	$0.122388\pi$
$18$	−1.10545	+	1.36040i	−0.260557	+	0.320650i
$19$	1.14827	−	3.53402i	0.263432	−	0.810761i	−0.728618	−	0.684920i	$-0.759837\pi$
$19$	1.14827	−	3.53402i	0.263432	−	0.810761i	0.992050	−	0.125841i	$-0.0401628\pi$
$20$	2.81216	−	3.47732i	0.628818	−	0.777552i
$21$	−0.410016	−	1.26190i	−0.0894727	−	0.275369i
$22$	−5.40987	−	2.08716i	−1.15339	−	0.444984i
$23$	−1.18763	−	7.49840i	−0.247638	−	1.56353i	−0.727454	−	0.686156i	$-0.759297\pi$
$23$	−1.18763	−	7.49840i	−0.247638	−	1.56353i	0.479816	−	0.877369i	$-0.340703\pi$
$24$	3.57503	−	1.14157i	0.729749	−	0.233023i
$25$	3.68864	−	3.37549i	0.737729	−	0.675097i
$26$	−6.15655	+	0.636552i	−1.20740	+	0.124838i
$27$	−5.55588	+	0.879964i	−1.06923	+	0.169349i
$28$	0.524171	−	1.93009i	0.0990589	−	0.364753i
$29$	−0.734772	+	0.238742i	−0.136444	+	0.0443333i	−0.376443	−	0.926440i	$-0.622853\pi$
$29$	−0.734772	+	0.238742i	−0.136444	+	0.0443333i	0.239999	+	0.970773i	$0.422853\pi$
$30$	4.14263	−	0.666058i	0.756337	−	0.121605i
$31$	−7.18714	−	2.33524i	−1.29085	−	0.419422i	−0.418460	−	0.908235i	$-0.637430\pi$
$31$	−7.18714	−	2.33524i	−1.29085	−	0.419422i	−0.872389	+	0.488813i	$0.837430\pi$
$32$	5.45152	+	1.51026i	0.963702	+	0.266979i
$33$	−2.46983	−	4.84732i	−0.429943	−	0.843810i
$34$	5.10677	+	5.69097i	0.875804	+	0.975993i
$35$	0.901253	−	2.04640i	0.152340	−	0.345904i
$36$	−2.26125	−	1.01596i	−0.376876	−	0.169326i
$37$	0.865275	+	0.137046i	0.142250	+	0.0225302i	0.227154	−	0.973859i	$-0.427058\pi$
$37$	0.865275	+	0.137046i	0.142250	+	0.0225302i	−0.0849031	+	0.996389i	$0.527058\pi$
$38$	5.24739	+	0.283905i	0.851239	+	0.0460555i
$39$	−4.69794	−	3.41325i	−0.752272	−	0.546558i
$40$	5.77508	+	2.57847i	0.913120	+	0.407692i
$41$	−6.17492	+	4.48634i	−0.964360	+	0.700649i	−0.954159	−	0.299299i	$-0.903247\pi$
$41$	−6.17492	+	4.48634i	−0.964360	+	0.700649i	−0.0102011	+	0.999948i	$0.503247\pi$
$42$	1.57544	−	1.01932i	0.243095	−	0.157284i
$43$	6.75136	+	6.75136i	1.02957	+	1.02957i	0.999549	+	0.0300235i	$0.00955822\pi$
$43$	6.75136	+	6.75136i	1.02957	+	1.02957i	0.0300235	+	0.999549i	$0.490442\pi$
$44$	0.884756	−	8.15249i	0.133382	−	1.22903i
$45$	−2.33053	−	1.50015i	−0.347414	−	0.223629i
$46$	9.81568	−	4.35034i	1.44724	−	0.641423i
$47$	−3.96724	−	2.02141i	−0.578681	−	0.294853i	0.140046	−	0.990145i	$-0.455275\pi$
$47$	−3.96724	−	2.02141i	−0.578681	−	0.294853i	−0.718727	+	0.695292i	$0.755275\pi$
$48$	2.86041	+	4.47058i	0.412865	+	0.645272i
$49$		−	1.00000i		−	0.142857i
$50$	5.95469	+	3.81335i	0.842121	+	0.539289i
$51$			7.17390i			1.00455i
$52$	−3.10916	−	8.18228i	−0.431164	−	1.13468i
$53$	9.74120	+	4.96339i	1.33806	+	0.681774i	0.968868	−	0.247580i	$-0.0796352\pi$
$53$	9.74120	+	4.96339i	1.33806	+	0.681774i	0.369190	+	0.929354i	$0.379635\pi$
$54$	−3.22335	−	7.27284i	−0.438642	−	0.989708i
$55$	2.33723	−	8.86537i	0.315151	−	1.19541i
$56$	2.82839	+	0.0143529i	0.377960	+	0.00191799i
$57$	3.48631	+	3.48631i	0.461773	+	0.461773i
$58$	−0.593522	−	0.917337i	−0.0779332	−	0.120452i
$59$	−3.01566	+	2.19101i	−0.392606	+	0.285245i	−0.766522	−	0.642218i	$-0.778015\pi$
$59$	−3.01566	+	2.19101i	−0.392606	+	0.285245i	0.373917	+	0.927462i	$0.378015\pi$
$60$	2.41700	+	5.41924i	0.312033	+	0.699621i
$61$	0.997249	+	0.724544i	0.127685	+	0.0927683i	0.649795	−	0.760110i	$-0.274855\pi$
$61$	0.997249	+	0.724544i	0.127685	+	0.0927683i	−0.522110	+	0.852878i	$0.674855\pi$
$62$	0.577378	−	10.6716i	0.0733271	−	1.35530i
$63$	−1.22424	−	0.193900i	−0.154240	−	0.0244292i
$64$	−0.0811913	+	7.99959i	−0.0101489	+	0.999948i
$65$	−2.07323	−	9.56412i	−0.257152	−	1.18628i
$66$	5.72624	−	5.13842i	0.704852	−	0.632496i
$67$	0.357808	+	0.702238i	0.0437132	+	0.0857921i	0.911830	−	0.410568i	$-0.134670\pi$
$67$	0.357808	+	0.702238i	0.0437132	+	0.0857921i	−0.868117	+	0.496360i	$0.834670\pi$
$68$	−5.92012	+	9.04901i	−0.717920	+	1.09735i
$69$	9.58017	+	3.11279i	1.15332	+	0.374735i
$70$	3.12449	+	0.487387i	0.373448	+	0.0582539i
$71$	−15.7194	+	5.10754i	−1.86555	+	0.606153i	−0.872475	+	0.488659i	$0.837486\pi$
$71$	−15.7194	+	5.10754i	−1.86555	+	0.606153i	−0.993074	+	0.117494i	$0.962514\pi$
$72$	0.565998	−	3.45984i	0.0667035	−	0.407747i
$73$	−5.58483	+	0.884550i	−0.653655	+	0.103529i	−0.474449	−	0.880283i	$-0.657353\pi$
$73$	−5.58483	+	0.884550i	−0.653655	+	0.103529i	−0.179206	+	0.983812i	$0.557353\pi$
$74$	0.127420	+	1.23237i	0.0148123	+	0.143260i
$75$	1.76864	+	6.39409i	0.204225	+	0.738326i
$76$	1.52055	+	7.27457i	0.174419	+	0.834450i
$77$	−0.641409	−	4.04970i	−0.0730954	−	0.461506i
$78$	2.95599	−	7.66185i	0.334700	−	0.867533i
$79$	4.48089	+	13.7908i	0.504140	+	1.55158i	0.802212	+	0.597040i	$0.203657\pi$
$79$	4.48089	+	13.7908i	0.504140	+	1.55158i	−0.298072	+	0.954543i	$0.596343\pi$
$80$	−1.42337	+	8.83029i	−0.159137	+	0.987256i
$81$	1.15731	−	3.56184i	0.128590	−	0.395760i
$82$	−8.37713	−	6.80716i	−0.925099	−	0.751725i
$83$	−5.68644	+	2.89739i	−0.624168	+	0.318029i	−0.737315	−	0.675549i	$-0.763907\pi$
$83$	−5.68644	+	2.89739i	−0.624168	+	0.318029i	0.113147	+	0.993578i	$0.463907\pi$
$84$	1.96605	+	1.78232i	0.214513	+	0.194467i
$85$	−8.05345	+	9.01706i	−0.873520	+	0.978038i
$86$	−6.77113	+	11.6823i	−0.730150	+	1.25973i
$87$	0.160360	−	1.01247i	0.0171924	−	0.108549i
$88$	11.4633	−	1.75603i	1.22200	−	0.187194i
$89$	1.40605	−	1.93526i	0.149041	−	0.205137i	−0.727968	−	0.685611i	$-0.759535\pi$
$89$	1.40605	−	1.93526i	0.149041	−	0.205137i	0.877009	+	0.480474i	$0.159535\pi$
$90$	1.20252	−	3.73062i	0.126757	−	0.393242i
$91$	−2.57247	−	3.54070i	−0.269668	−	0.371166i
$92$	9.51547	+	11.8322i	0.992056	+	1.23360i
$93$	7.09011	−	7.09011i	0.735210	−	0.735210i
$94$	1.31960	−	6.15701i	0.136107	−	0.635047i
$95$	0.468287	+	8.29578i	0.0480452	+	0.851129i
$96$	−5.06931	+	5.53517i	−0.517384	+	0.564931i
$97$	−5.47273	+	10.7408i	−0.555672	+	1.09057i	0.426833	+	0.904330i	$0.359629\pi$
$97$	−5.47273	+	10.7408i	−0.555672	+	1.09057i	−0.982505	+	0.186237i	$0.940371\pi$
$98$	1.36664	−	0.363714i	0.138052	−	0.0367407i
$99$	−5.08217			−0.510777
$100$	−3.04567	+	9.52491i	−0.304567	+	0.952491i
$101$	−19.6491			−1.95516			−0.977578	−	0.210572i	$-0.932467\pi$
$101$	−19.6491			−1.95516			−0.977578	+	0.210572i	$0.932467\pi$
$102$	−9.80416	+	2.60925i	−0.970757	+	0.258354i
$103$	6.30856	−	12.3812i	0.621601	−	1.21996i	−0.338674	−	0.940904i	$-0.609978\pi$
$103$	6.30856	−	12.3812i	0.621601	−	1.21996i	0.960275	−	0.279057i	$-0.0900218\pi$
$104$	10.0514	−	7.22513i	0.985621	−	0.708482i
$105$	1.87641	+	2.29817i	0.183118	+	0.224279i
$106$	−3.24017	+	15.1180i	−0.314713	+	1.46839i
$107$	8.04406	−	8.04406i	0.777649	−	0.777649i	−0.201782	−	0.979430i	$-0.564673\pi$
$107$	8.04406	−	8.04406i	0.777649	−	0.777649i	0.979430	+	0.201782i	$0.0646732\pi$
$108$	8.76700	−	7.05040i	0.843605	−	0.678425i
$109$	−9.39425	−	12.9301i	−0.899806	−	1.23848i	−0.970530	−	0.240980i	$-0.922531\pi$
$109$	−9.39425	−	12.9301i	−0.899806	−	1.23848i	0.0707245	−	0.997496i	$-0.477469\pi$
$110$	12.9659	−	0.0303082i	1.23625	−	0.00288978i
$111$	−0.683237	+	0.940394i	−0.0648499	+	0.0892583i
$112$	1.00911	+	3.87062i	0.0953520	+	0.365739i
$113$	2.32215	−	14.6615i	0.218450	−	1.37924i	−0.597850	−	0.801608i	$-0.703978\pi$
$113$	2.32215	−	14.6615i	0.218450	−	1.37924i	0.816299	−	0.577629i	$-0.196022\pi$
$114$	−3.49652	+	6.03256i	−0.327479	+	0.565001i
$115$	8.54714	+	14.6673i	0.797024	+	1.36773i
$116$	1.03780	−	1.14478i	0.0963572	−	0.106290i
$117$	−4.83347	+	2.46277i	−0.446854	+	0.227684i
$118$	−4.09116	−	3.32443i	−0.376622	−	0.306039i
$119$	−1.67078	+	5.14214i	−0.153160	+	0.471379i
$120$	−6.52706	+	5.27422i	−0.595837	+	0.481469i
$121$	−1.79584	−	5.52704i	−0.163259	−	0.502458i
$122$	−0.627479	+	1.62641i	−0.0568093	+	0.147248i
$123$	−1.58425	−	10.0026i	−0.142847	−	0.901901i
$124$	14.7943	−	3.09235i	1.32857	−	0.277701i
$125$	−4.95499	+	10.0224i	−0.443188	+	0.896429i
$126$	−0.180281	−	1.74362i	−0.0160607	−	0.155334i
$127$	0.0584558	−	0.00925849i	0.00518711	−	0.000821558i	−0.153840	−	0.988096i	$-0.549164\pi$
$127$	0.0584558	−	0.00925849i	0.00518711	−	0.000821558i	0.159027	+	0.987274i	$0.449164\pi$
$128$	−10.9621	+	2.79860i	−0.968923	+	0.247364i
$129$	−12.0484	+	3.91477i	−1.06081	+	0.344677i
$130$	12.3167	−	6.31197i	1.08024	−	0.553596i
$131$	−11.3737	−	3.69555i	−0.993727	−	0.322882i	−0.233371	−	0.972388i	$-0.574976\pi$
$131$	−11.3737	−	3.69555i	−0.993727	−	0.322882i	−0.760356	+	0.649506i	$0.774976\pi$
$132$	9.10510	+	5.95681i	0.792497	+	0.518474i
$133$	1.68698	+	3.31088i	0.146280	+	0.287090i
$134$	−0.829569	+	0.744410i	−0.0716638	+	0.0643072i
$135$	10.8676	−	6.33293i	0.935333	−	0.545051i
$136$	−14.5200	−	4.79943i	−1.24508	−	0.411548i
$137$	13.8648	+	2.19597i	1.18455	+	0.187615i	0.717464	−	0.696596i	$-0.245303\pi$
$137$	13.8648	+	2.19597i	1.18455	+	0.187615i	0.467089	+	0.884210i	$0.345303\pi$
$138$	−0.769622	+	14.2248i	−0.0655146	+	1.21090i
$139$	12.7893	+	9.29195i	1.08477	+	0.788133i	0.978509	−	0.206205i	$-0.0661113\pi$
$139$	12.7893	+	9.29195i	1.08477	+	0.788133i	0.106263	+	0.994338i	$0.466111\pi$
$140$	0.470339	+	4.44733i	0.0397509	+	0.375868i
$141$	4.77950	−	3.47251i	0.402507	−	0.292438i
$142$	−12.6975	−	19.6251i	−1.06555	−	1.64690i
$143$	−12.6888	−	12.6888i	−1.06109	−	1.06109i
$144$	4.93423	−	0.484878i	0.411186	−	0.0404065i
$145$	1.33817	−	1.09258i	0.111129	−	0.0907342i
$146$	−3.24015	−	7.31074i	−0.268156	−	0.605041i
$147$	1.18222	+	0.602372i	0.0975080	+	0.0496828i
$148$	−1.63786	+	0.622367i	−0.134631	+	0.0511583i
$149$		−	3.93006i		−	0.321963i	−0.986957	−	0.160982i	$-0.948534\pi$
$149$		−	3.93006i		−	0.321963i	0.986957	−	0.160982i	$-0.0514660\pi$
$150$	−8.09516	+	4.74272i	−0.660967	+	0.387241i
$151$			22.5795i			1.83750i	0.394844	+	0.918748i	$0.370799\pi$
$151$			22.5795i			1.83750i	−0.394844	+	0.918748i	$0.629201\pi$
$152$	−9.38869	+	4.72392i	−0.761523	+	0.383160i
$153$	5.97124	+	3.04250i	0.482747	+	0.245972i
$154$	5.30120	−	2.34951i	0.427183	−	0.189329i
$155$	16.8711	−	0.952354i	1.35512	−	0.0764949i
$156$	11.5461	+	1.25306i	0.924431	+	0.100325i
$157$	1.17060	+	1.17060i	0.0934244	+	0.0934244i	0.752274	−	0.658850i	$-0.228957\pi$
$157$	1.17060	+	1.17060i	0.0934244	+	0.0934244i	−0.658850	+	0.752274i	$0.728957\pi$
$158$	−17.2173	+	11.1397i	−1.36973	+	0.886225i
$159$	−11.7357	+	8.52646i	−0.930698	+	0.676192i
$160$	−12.5855	+	1.26647i	−0.994975	+	0.100123i
$161$	6.14195	+	4.46239i	0.484054	+	0.351686i
$162$	5.28869	+	0.286140i	0.415519	+	0.0224813i
$163$	−0.0969543	−	0.0153561i	−0.00759405	−	0.00120278i	0.152636	−	0.988282i	$-0.451224\pi$
$163$	−0.0969543	−	0.0153561i	−0.00759405	−	0.00120278i	−0.160230	+	0.987080i	$0.551224\pi$
$164$	6.25607	−	13.9244i	0.488517	−	1.08731i
$165$	9.07295	+	8.10337i	0.706328	+	0.630846i
$166$	−6.02793	−	6.71751i	−0.467858	−	0.521380i
$167$	−2.83115	−	5.55644i	−0.219081	−	0.429970i	0.755141	−	0.655562i	$-0.227568\pi$
$167$	−2.83115	−	5.55644i	−0.219081	−	0.429970i	−0.974222	+	0.225592i	$0.927568\pi$
$168$	−1.72071	+	3.33514i	−0.132756	+	0.257312i
$169$	−5.85294	−	1.90174i	−0.450227	−	0.146287i
$170$	−15.2523	−	7.72656i	−1.16979	−	0.592600i
$171$	4.38042	−	1.42329i	0.334979	−	0.108841i
$172$	−18.4282	−	5.00471i	−1.40514	−	0.381606i
$173$	−6.22679	+	0.986226i	−0.473414	+	0.0749814i	−0.388582	−	0.921414i	$-0.627035\pi$
$173$	−6.22679	+	0.986226i	−0.473414	+	0.0749814i	−0.0848313	+	0.996395i	$0.527035\pi$
$174$	1.44202	−	0.149096i	0.109319	−	0.0113030i
$175$	−0.221436	+	4.99509i	−0.0167390	+	0.377594i
$176$	6.56925	+	15.0276i	0.495176	+	1.13275i
$177$	−0.773705	−	4.88498i	−0.0581552	−	0.367178i
$178$	3.15620	+	1.21768i	0.236567	+	0.0912691i
$179$	−1.19833	−	3.68809i	−0.0895675	−	0.275661i	0.896232	−	0.443585i	$-0.146294\pi$
$179$	−1.19833	−	3.68809i	−0.0895675	−	0.275661i	−0.985800	+	0.167924i	$0.946294\pi$
$180$	5.53580	+	0.286533i	0.412614	+	0.0213569i
$181$	0.281545	−	0.866507i	0.0209271	−	0.0644070i	−0.940048	−	0.341043i	$-0.889220\pi$
$181$	0.281545	−	0.866507i	0.0209271	−	0.0644070i	0.960975	+	0.276636i	$0.0892197\pi$
$182$	3.90323	−	4.80345i	0.289326	−	0.356055i
$183$	−1.45729	+	0.742524i	−0.107726	+	0.0548890i
$184$	−12.7095	+	17.3078i	−0.936960	+	1.27595i
$185$	−1.91447	+	0.415002i	−0.140754	+	0.0305115i
$186$	12.2684	+	7.11087i	0.899564	+	0.521394i
$187$	−3.46795	+	21.8958i	−0.253602	+	1.60118i
$188$	8.89439	−	0.435968i	0.648690	−	0.0317962i
$189$	3.30637	−	4.55083i	0.240503	−	0.331024i
$190$	−11.1670	+	3.65727i	−0.810143	+	0.265327i
$191$	−4.83104	−	6.64936i	−0.349562	−	0.481131i	0.597642	−	0.801763i	$-0.296105\pi$
$191$	−4.83104	−	6.64936i	−0.349562	−	0.481131i	−0.947204	+	0.320633i	$0.896105\pi$
$192$	−9.40838	−	4.91471i	−0.678991	−	0.354689i
$193$	−11.6001	+	11.6001i	−0.834997	+	0.834997i	−0.988195	−	0.153199i	$-0.951043\pi$
$193$	−11.6001	+	11.6001i	−0.834997	+	0.834997i	0.153199	+	0.988195i	$0.451043\pi$
$194$	−16.6694	−	3.57267i	−1.19679	−	0.256503i
$195$	12.5558	+	3.31015i	0.899137	+	0.237045i
$196$	0.994135	+	1.73542i	0.0710096	+	0.123959i
$197$	−3.11450	+	6.11254i	−0.221899	+	0.435501i	−0.974939	−	0.222474i	$-0.928587\pi$
$197$	−3.11450	+	6.11254i	−0.221899	+	0.435501i	0.753040	+	0.657975i	$0.228587\pi$
$198$	−1.84846	−	6.94551i	−0.131364	−	0.493596i
$199$	13.3116			0.943634			0.471817	−	0.881696i	$-0.343598\pi$
$199$	13.3116			0.943634			0.471817	+	0.881696i	$0.343598\pi$
$200$	−14.1249	−	0.698003i	−0.998781	−	0.0493563i
$201$	−1.04574			−0.0737605
$202$	−7.14665	−	26.8533i	−0.502837	−	1.88939i
$203$	0.350746	−	0.688378i	0.0246176	−	0.0483147i
$204$	−7.13183	−	12.4498i	−0.499328	−	0.871658i
$205$	9.23764	−	14.3510i	0.645185	−	1.00232i
$206$	19.2153	+	4.11831i	1.33879	+	0.286936i
$207$	6.65396	−	6.65396i	0.462482	−	0.462482i
$208$	13.5300	+	11.1088i	0.938137	+	0.770256i
$209$	8.95539	+	12.3260i	0.619458	+	0.852610i
$210$	−2.45831	+	3.40025i	−0.169639	+	0.234640i
$211$	−1.75628	+	2.41732i	−0.120908	+	0.166415i	−0.865180	−	0.501461i	$-0.832796\pi$
$211$	−1.75628	+	2.41732i	−0.120908	+	0.166415i	0.744273	+	0.667876i	$0.232796\pi$
$212$	−21.8394	+	1.07048i	−1.49994	+	0.0735209i
$213$	3.43068	−	21.6604i	0.235066	−	1.48415i
$214$	13.9191	+	8.06762i	0.951490	+	0.551491i
$215$	−19.5387	−	8.60504i	−1.33253	−	0.586859i
$216$	12.8241	+	9.41702i	0.872567	+	0.640747i
$217$	6.73334	−	3.43081i	0.457089	−	0.232899i
$218$	14.2540	−	17.5414i	0.965400	−	1.18806i
$219$	2.31841	−	7.13534i	0.156664	−	0.482161i
$220$	4.75729	+	17.7087i	0.320737	+	1.19392i
$221$	7.31226	+	22.5048i	0.491876	+	1.51384i
$222$	−1.53369	−	0.591705i	−0.102934	−	0.0397127i
$223$	−0.655580	−	4.13917i	−0.0439009	−	0.277179i	0.955966	−	0.293476i	$-0.0948122\pi$
$223$	−0.655580	−	4.13917i	−0.0439009	−	0.277179i	−0.999867	+	0.0162971i	$0.994812\pi$
$224$	−4.92273	+	2.78689i	−0.328913	+	0.186207i
$225$	6.07225	+	1.23964i	0.404817	+	0.0826428i
$226$	20.8816	−	2.15904i	1.38902	−	0.143617i
$227$	−11.6111	+	1.83902i	−0.770656	+	0.122060i	−0.529367	−	0.848393i	$-0.677570\pi$
$227$	−11.6111	+	1.83902i	−0.770656	+	0.122060i	−0.241290	+	0.970453i	$0.577570\pi$
$228$	−9.51609	−	2.58437i	−0.630219	−	0.171154i
$229$	10.6878	−	3.47267i	0.706268	−	0.229480i	0.0662085	−	0.997806i	$-0.478910\pi$
$229$	10.6878	−	3.47267i	0.706268	−	0.229480i	0.640059	+	0.768325i	$0.278910\pi$
$230$	−16.9362	+	17.0156i	−1.11674	+	1.12197i
$231$	5.17401	+	1.68114i	0.340425	+	0.110611i
$232$	1.94197	+	1.00193i	0.127496	+	0.0657798i
$233$	−0.0892520	−	0.175167i	−0.00584709	−	0.0114756i	0.888065	−	0.459719i	$-0.152050\pi$
$233$	−0.0892520	−	0.175167i	−0.00584709	−	0.0114756i	−0.893912	+	0.448243i	$0.852050\pi$
$234$	−5.12373	−	5.70988i	−0.334949	−	0.373266i
$235$	9.90574	+	1.00080i	0.646179	+	0.0652850i
$236$	3.05529	−	6.80030i	0.198883	−	0.442662i
$237$	−19.0029	−	3.00977i	−1.23437	−	0.195505i
$238$	−7.63515	−	0.413093i	−0.494914	−	0.0267768i
$239$	5.81869	+	4.22753i	0.376380	+	0.273456i	0.759852	−	0.650097i	$-0.225272\pi$
$239$	5.81869	+	4.22753i	0.376380	+	0.273456i	−0.383472	+	0.923553i	$0.625272\pi$
$240$	−9.58196	−	7.00185i	−0.618513	−	0.451968i
$241$	−1.43959	+	1.04593i	−0.0927324	+	0.0673740i	−0.633185	−	0.774000i	$-0.718253\pi$
$241$	−1.43959	+	1.04593i	−0.0927324	+	0.0673740i	0.540453	+	0.841374i	$0.318253\pi$
$242$	6.90031	−	4.46454i	0.443569	−	0.286991i
$243$	−8.41895	−	8.41895i	−0.540076	−	0.540076i
$244$	−2.45094	−	0.265991i	−0.156906	−	0.0170283i
$245$	0.809739	+	2.08430i	0.0517324	+	0.133161i
$246$	13.0937	−	5.80318i	0.834825	−	0.369997i
$247$	14.4902	+	7.38314i	0.921992	+	0.469778i
$248$	9.60703	+	19.0938i	0.610047	+	1.21246i
$249$		−	8.46794i		−	0.536634i
$250$	−15.4992	−	3.12642i	−0.980256	−	0.197732i
$251$			21.6717i			1.36791i	0.729525	+	0.683954i	$0.239741\pi$
$251$			21.6717i			1.36791i	−0.729525	+	0.683954i	$0.760259\pi$
$252$	2.31734	−	0.880559i	0.145979	−	0.0554700i
$253$	27.7353	+	14.1318i	1.74370	+	0.888461i
$254$	0.0339143	+	0.0765207i	0.00212797	+	0.00480134i
$255$	−5.80899	−	14.9526i	−0.363773	−	0.936368i
$256$	−7.81177	−	13.9634i	−0.488235	−	0.872712i
$257$	1.28847	+	1.28847i	0.0803724	+	0.0803724i	0.746150	−	0.665778i	$-0.231900\pi$
$257$	1.28847	+	1.28847i	0.0803724	+	0.0803724i	−0.665778	+	0.746150i	$0.731900\pi$
$258$	−9.73228	−	15.0420i	−0.605906	−	0.936477i
$259$	−0.708748	+	0.514936i	−0.0440395	+	0.0319965i
$260$	13.1060	+	14.5367i	0.812797	+	0.901531i
$261$	−0.774730	−	0.562874i	−0.0479546	−	0.0348410i
$262$	0.913707	−	16.8879i	0.0564490	−	1.04334i
$263$	−13.5544	−	2.14680i	−0.835798	−	0.132377i	−0.276157	−	0.961113i	$-0.589061\pi$
$263$	−13.5544	−	2.14680i	−0.835798	−	0.132377i	−0.559641	+	0.828735i	$0.689061\pi$
$264$	−4.82918	+	14.6100i	−0.297215	+	0.899183i
$265$	−24.3227	−	2.45738i	−1.49413	−	0.150956i
$266$	−3.91122	+	3.50971i	−0.239812	+	0.215194i
$267$	1.44094	+	2.82800i	0.0881840	+	0.173071i
$268$	−1.31907	−	0.862972i	−0.0805749	−	0.0527144i
$269$	−15.8231	−	5.14125i	−0.964753	−	0.313467i	−0.216057	−	0.976381i	$-0.569320\pi$
$269$	−15.8231	−	5.14125i	−0.964753	−	0.313467i	−0.748696	+	0.662913i	$0.769320\pi$
$270$	12.6075	+	12.5487i	0.767271	+	0.763692i
$271$	−9.16408	+	2.97759i	−0.556678	+	0.180876i	−0.573826	−	0.818977i	$-0.694541\pi$
$271$	−9.16408	+	2.97759i	−0.556678	+	0.180876i	0.0171477	+	0.999853i	$0.494541\pi$
$272$	1.27798	−	21.5893i	0.0774886	−	1.30904i
$273$	5.73548	−	0.908410i	0.347127	−	0.0549795i
$274$	2.04173	+	19.7470i	0.123345	+	1.19296i
$275$	2.30715	+	20.3707i	0.139126	+	1.22840i
$276$	−19.7202	+	4.12198i	−1.18702	+	0.248114i
$277$	1.18442	+	7.47812i	0.0711648	+	0.449317i	0.997381	+	0.0723245i	$0.0230417\pi$
$277$	1.18442	+	7.47812i	0.0711648	+	0.449317i	−0.926216	+	0.376992i	$0.876958\pi$
$278$	−8.04714	+	20.8580i	−0.482635	+	1.25098i
$279$	−2.89453	−	8.90846i	−0.173291	−	0.533336i
$280$	−5.90685	+	2.26034i	−0.353002	+	0.135081i
$281$	4.78352	−	14.7222i	0.285361	−	0.878251i	−0.700929	−	0.713231i	$-0.747231\pi$
$281$	4.78352	−	14.7222i	0.285361	−	0.878251i	0.986290	−	0.165020i	$-0.0527688\pi$
$282$	6.48406	+	5.26887i	0.386120	+	0.313757i
$283$	9.99663	−	5.09354i	0.594238	−	0.302779i	−0.130886	−	0.991397i	$-0.541782\pi$
$283$	9.99663	−	5.09354i	0.594238	−	0.302779i	0.725124	+	0.688618i	$0.241782\pi$
$284$	22.2022	−	24.4909i	1.31746	−	1.45327i
$285$	−10.0895	−	4.44353i	−0.597653	−	0.263212i
$286$	12.7259	−	21.9561i	0.752499	−	1.29829i
$287$	1.19400	−	7.53865i	0.0704799	−	0.444992i
$288$	2.45731	+	6.56697i	0.144798	+	0.386963i
$289$	7.19044	−	9.89679i	0.422967	−	0.582164i
$290$	1.97988	+	1.43141i	0.116263	+	0.0840553i
$291$	−9.40144	−	12.9400i	−0.551122	−	0.758554i
$292$	8.81269	−	7.08714i	0.515723	−	0.414744i
$293$	−5.83381	+	5.83381i	−0.340815	+	0.340815i	−0.856674	−	0.515859i	$-0.827473\pi$
$293$	−5.83381	+	5.83381i	−0.340815	+	0.340815i	0.515859	+	0.856674i	$0.327473\pi$
$294$	−0.393236	+	1.83477i	−0.0229340	+	0.107006i
$295$	4.51141	−	7.00862i	0.262664	−	0.408058i
$296$	−1.44627	−	2.01201i	−0.0840626	−	0.116946i
$297$	10.4709	−	20.5502i	0.607581	−	1.19244i
$298$	5.37099	−	1.42942i	0.311133	−	0.0828040i
$299$	33.2262			1.92152
$300$	−9.42592	−	9.33820i	−0.544206	−	0.539141i
$301$	−9.54786			−0.550330
$302$	−30.8581	+	8.21250i	−1.77569	+	0.472576i
$303$	11.8361	−	23.2296i	0.679964	−	1.33450i
$304$	−9.87071	−	11.1128i	−0.566124	−	0.637364i
$305$	−2.66526	−	0.702658i	−0.152612	−	0.0402341i
$306$	−1.98618	+	9.26716i	−0.113543	+	0.529768i
$307$	11.3533	−	11.3533i	0.647969	−	0.647969i	−0.304533	−	0.952502i	$-0.598500\pi$
$307$	11.3533	−	11.3533i	0.647969	−	0.647969i	0.952502	+	0.304533i	$0.0985003\pi$
$308$	5.13906	+	6.39030i	0.292825	+	0.364121i
$309$	10.8373	+	14.9162i	0.616511	+	0.848555i
$310$	7.43780	+	22.7104i	0.422438	+	1.28986i
$311$	6.68637	−	9.20300i	0.379149	−	0.521854i	−0.576210	−	0.817302i	$-0.695469\pi$
$311$	6.68637	−	9.20300i	0.379149	−	0.521854i	0.955359	+	0.295448i	$0.0954688\pi$
$312$	2.48702	+	16.2352i	0.140800	+	0.919137i
$313$	−3.80898	+	24.0489i	−0.215296	+	1.35933i	0.609001	+	0.793169i	$0.291570\pi$
$313$	−3.80898	+	24.0489i	−0.215296	+	1.35933i	−0.824297	+	0.566157i	$0.808430\pi$
$314$	−1.17403	+	2.02556i	−0.0662544	+	0.114309i
$315$	2.70870	−	0.587167i	0.152618	−	0.0330831i
$316$	−21.4861	−	19.4782i	−1.20869	−	1.09574i
$317$	−23.9091	+	12.1823i	−1.34287	+	0.684227i	−0.969874	−	0.243605i	$-0.921670\pi$
$317$	−23.9091	+	12.1823i	−1.34287	+	0.684227i	−0.372997	+	0.927832i	$0.621670\pi$
$318$	−15.9210	−	12.9373i	−0.892808	−	0.725485i
$319$	0.978885	−	3.01270i	0.0548070	−	0.168679i
$320$	−6.30835	−	16.7393i	−0.352648	−	0.935756i
$321$	4.66435	+	14.3554i	0.260338	+	0.801239i
$322$	−3.86458	+	10.0169i	−0.215364	+	0.558219i
$323$	−3.14292	−	19.8436i	−0.174877	−	1.10413i
$324$	1.53252	+	7.33183i	0.0851401	+	0.407324i
$325$	12.0657	+	18.2558i	0.669284	+	1.01265i
$326$	−0.0142774	−	0.138087i	−0.000790753	−	0.00764794i
$327$	20.9450	−	3.31737i	1.15826	−	0.183451i
$328$	21.3051	+	3.48531i	1.17638	+	0.192444i
$329$	4.23461	−	1.37591i	0.233462	−	0.0758563i
$330$	−7.77445	+	15.3468i	−0.427969	+	0.844813i
$331$	5.85400	+	1.90208i	0.321765	+	0.104548i	0.465446	−	0.885076i	$-0.345894\pi$
$331$	5.85400	+	1.90208i	0.321765	+	0.104548i	−0.143681	+	0.989624i	$0.545894\pi$
$332$	6.98799	−	10.6813i	0.383516	−	0.586211i
$333$	0.492978	+	0.967524i	0.0270150	+	0.0530200i
$334$	6.56394	−	5.89013i	0.359163	−	0.322293i
$335$	−1.31441	−	1.17395i	−0.0718140	−	0.0641396i
$336$	−5.18379	−	1.13856i	−0.282799	−	0.0621136i
$337$	10.2307	+	1.62038i	0.557300	+	0.0882677i	0.428730	−	0.903433i	$-0.358961\pi$
$337$	10.2307	+	1.62038i	0.557300	+	0.0882677i	0.128570	+	0.991700i	$0.458961\pi$
$338$	0.470196	−	8.69057i	0.0255753	−	0.472705i
$339$	15.9343	+	11.5770i	0.865434	+	0.628775i
$340$	5.01198	−	23.6546i	0.271813	−	1.28285i
$341$	25.0675	−	18.2126i	1.35748	−	0.986267i
$342$	3.53834	+	5.46880i	0.191332	+	0.295719i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	0.137040	−	27.0051i	0.00738868	−	1.45602i
$345$	−22.4885	+	1.26945i	−1.21074	+	0.0683449i
$346$	−3.61259	−	8.15109i	−0.194214	−	0.438205i
$347$	12.5432	+	6.39106i	0.673352	+	0.343090i	0.757009	−	0.653405i	$-0.226660\pi$
$347$	12.5432	+	6.39106i	0.673352	+	0.343090i	−0.0836569	+	0.996495i	$0.526660\pi$
$348$	0.728243	+	1.91649i	0.0390379	+	0.102735i
$349$			19.2253i			1.02911i	0.857459	+	0.514553i	$0.172042\pi$
$349$			19.2253i			1.02911i	−0.857459	+	0.514553i	$0.827958\pi$
$350$	−6.90705	+	1.51416i	−0.369197	+	0.0809354i
$351$		−	24.6186i		−	1.31405i
$352$	−18.1480	+	14.4436i	−0.967293	+	0.769844i
$353$	6.76424	+	3.44655i	0.360024	+	0.183441i	0.624641	−	0.780912i	$-0.285245\pi$
$353$	6.76424	+	3.44655i	0.360024	+	0.183441i	−0.264617	+	0.964354i	$0.585245\pi$
$354$	6.39461	−	2.83411i	0.339870	−	0.150631i
$355$	28.6282	−	23.3743i	1.51943	−	1.24058i
$356$	−0.516180	+	4.75629i	−0.0273575	+	0.252083i
$357$	−5.07272	−	5.07272i	−0.268477	−	0.268477i
$358$	4.60445	−	2.97910i	0.243353	−	0.157450i
$359$	−14.9907	+	10.8914i	−0.791177	+	0.574824i	−0.908313	−	0.418292i	$-0.862629\pi$
$359$	−14.9907	+	10.8914i	−0.791177	+	0.574824i	0.117135	+	0.993116i	$0.462629\pi$
$360$	1.62186	+	7.66968i	0.0854796	+	0.404227i
$361$	4.20053	+	3.05186i	0.221081	+	0.160624i
$362$	1.28661	+	0.0696108i	0.0676226	+	0.00365866i
$363$	7.61595	+	1.20625i	0.399734	+	0.0633116i
$364$	7.98426	+	3.58723i	0.418489	+	0.188022i
$365$	10.9242	−	6.36593i	0.571800	−	0.333208i
$366$	−1.54480	−	1.72152i	−0.0807481	−	0.0899854i
$367$	15.4140	+	30.2516i	0.804603	+	1.57912i	0.815200	+	0.579179i	$0.196627\pi$
$367$	15.4140	+	30.2516i	0.804603	+	1.57912i	−0.0105967	+	0.999944i	$0.503373\pi$
$368$	−28.2762	−	11.0743i	−1.47400	−	0.577288i
$369$	−8.99759	−	2.92350i	−0.468396	−	0.152191i
$370$	−1.26348	−	2.46545i	−0.0656851	−	0.128173i
$371$	−10.3977	+	3.37842i	−0.539823	+	0.175399i
$372$	−5.25582	+	19.3529i	−0.272502	+	1.00340i
$373$	−4.83086	+	0.765133i	−0.250133	+	0.0396171i	−0.280242	−	0.959930i	$-0.590415\pi$
$373$	−4.83086	+	0.765133i	−0.250133	+	0.0396171i	0.0301090	+	0.999547i	$0.490415\pi$
$374$	−31.1850	+	3.22436i	−1.61254	+	0.166728i
$375$	−8.86392	−	11.8951i	−0.457731	−	0.614260i
$376$	3.83083	+	11.9969i	0.197560	+	0.618692i
$377$	−0.528944	−	3.33962i	−0.0272420	−	0.171999i
$378$	7.42193	+	2.86342i	0.381743	+	0.147279i
$379$	2.70083	+	8.31229i	0.138732	+	0.426973i	0.996152	−	0.0876442i	$-0.0279339\pi$
$379$	2.70083	+	8.31229i	0.138732	+	0.426973i	−0.857420	+	0.514618i	$0.827934\pi$
$380$	−9.05980	−	13.9312i	−0.464758	−	0.714653i
$381$	−0.0242666	+	0.0746848i	−0.00124321	+	0.00382622i
$382$	7.33018	−	9.02077i	0.375045	−	0.461543i
$383$	0.0868228	−	0.0442384i	0.00443644	−	0.00226048i	−0.451771	−	0.892134i	$-0.649208\pi$
$383$	0.0868228	−	0.0442384i	0.00443644	−	0.00226048i	0.456207	+	0.889874i	$0.349208\pi$
$384$	3.29470	−	14.6454i	0.168132	−	0.747372i
$385$	4.61609	+	7.92143i	0.235258	+	0.403713i
$386$	−20.0724	−	11.6341i	−1.02166	−	0.592161i
$387$	−1.85134	+	11.6889i	−0.0941087	+	0.594179i
$388$	−1.18033	−	24.0805i	−0.0599223	−	1.22250i
$389$	−21.0636	+	28.9915i	−1.06797	+	1.46993i	−0.195848	+	0.980634i	$0.562746\pi$
$389$	−21.0636	+	28.9915i	−1.06797	+	1.46993i	−0.872118	+	0.489295i	$0.837254\pi$
$390$	0.0429247	+	18.3632i	0.00217358	+	0.929857i
$391$	−24.1271	−	33.2081i	−1.22016	−	1.67941i
$392$	−2.01012	+	1.98983i	−0.101527	+	0.100501i
$393$	11.2202	−	11.2202i	0.565983	−	0.565983i
$394$	−9.48645	−	2.03318i	−0.477920	−	0.102430i
$395$	−20.5065	−	25.1158i	−1.03179	−	1.26371i
$396$	8.81972	−	5.05236i	0.443208	−	0.253891i
$397$	12.9858	−	25.4861i	0.651739	−	1.27911i	−0.294504	−	0.955650i	$-0.595154\pi$
$397$	12.9858	−	25.4861i	0.651739	−	1.27911i	0.946242	−	0.323459i	$-0.104846\pi$
$398$	4.84162	+	18.1922i	0.242688	+	0.911892i
$399$	−4.93039			−0.246828
$400$	−4.18351	−	19.5576i	−0.209175	−	0.977878i
$401$	13.5837			0.678336			0.339168	−	0.940726i	$-0.389855\pi$
$401$	13.5837			0.678336			0.339168	+	0.940726i	$0.389855\pi$
$402$	−0.380349	−	1.42915i	−0.0189701	−	0.0712793i
$403$	15.0151	−	29.4688i	0.747955	−	1.46794i
$404$	34.0995	−	19.5338i	1.69651	−	0.971845i
$405$	0.471973	+	8.36108i	0.0234525	+	0.415465i
$406$	1.06834	+	0.228972i	0.0530207	+	0.0113637i
$407$	−2.53993	+	2.53993i	−0.125900	+	0.125900i
$408$	14.4204	−	14.2748i	0.713918	−	0.706709i
$409$	1.95042	+	2.68453i	0.0964423	+	0.132741i	0.854511	−	0.519433i	$-0.173857\pi$
$409$	1.95042	+	2.68453i	0.0964423	+	0.132741i	−0.758069	+	0.652175i	$0.773857\pi$
$410$	22.9725	+	7.40490i	1.13453	+	0.365702i
$411$	−10.9479	+	15.0685i	−0.540021	+	0.743275i
$412$	1.36060	+	27.7583i	0.0670320	+	1.36755i
$413$	0.583119	−	3.68167i	0.0286934	−	0.181163i
$414$	11.5137	+	6.67345i	0.565869	+	0.327982i
$415$	9.50614	−	10.6436i	0.466638	−	0.522472i
$416$	−10.2607	+	22.5311i	−0.503072	+	1.10468i
$417$	−18.6891	+	9.52255i	−0.915207	+	0.466321i
$418$	−13.5881	+	16.7220i	−0.664615	+	0.817899i
$419$	−3.23145	+	9.94537i	−0.157866	+	0.485863i	−0.998440	−	0.0558344i	$-0.982218\pi$
$419$	−3.23145	+	9.94537i	−0.157866	+	0.485863i	0.840574	+	0.541697i	$0.182218\pi$
$420$	−5.54105	−	2.12291i	−0.270376	−	0.103587i
$421$	−9.97453	−	30.6985i	−0.486129	−	1.49615i	−0.830339	−	0.557259i	$-0.811853\pi$
$421$	−9.97453	−	30.6985i	−0.486129	−	1.49615i	0.344210	−	0.938893i	$-0.388147\pi$
$422$	−3.94240	−	1.52100i	−0.191913	−	0.0740411i
$423$	−0.863348	−	5.45097i	−0.0419774	−	0.265035i
$424$	−9.40627	−	29.4573i	−0.456809	−	1.43057i
$425$	9.48437	−	25.3155i	0.460060	−	1.22798i
$426$	30.8499	−	3.18970i	1.49468	−	0.154542i
$427$	−1.21749	+	0.192832i	−0.0589185	+	0.00933178i
$428$	−5.96297	+	21.9567i	−0.288231	+	1.06132i
$429$	22.6443	−	7.35758i	1.09328	−	0.355227i
$430$	4.65350	−	29.8322i	0.224412	−	1.43864i
$431$	16.4560	+	5.34687i	0.792656	+	0.257549i	0.677235	−	0.735767i	$-0.263178\pi$
$431$	16.4560	+	5.34687i	0.792656	+	0.257549i	0.115421	+	0.993317i	$0.463178\pi$
$432$	−8.20541	+	20.9510i	−0.394783	+	1.00801i
$433$	−2.26425	−	4.44384i	−0.108813	−	0.213557i	0.830179	−	0.557497i	$-0.188238\pi$
$433$	−2.26425	−	4.44384i	−0.108813	−	0.213557i	−0.938992	+	0.343940i	$0.888238\pi$
$434$	7.13770	+	7.95424i	0.342621	+	0.381816i
$435$	0.485601	+	2.24015i	0.0232828	+	0.107407i
$436$	29.1572	+	13.1000i	1.39638	+	0.627377i
$437$	−27.8633	−	4.41311i	−1.33288	−	0.211108i
$438$	10.5947	+	0.573216i	0.506234	+	0.0273893i
$439$	10.4855	+	7.61816i	0.500445	+	0.363595i	0.809187	−	0.587551i	$-0.199908\pi$
$439$	10.4855	+	7.61816i	0.500445	+	0.363595i	−0.308742	+	0.951146i	$0.599908\pi$
$440$	−22.4712	+	12.9424i	−1.07127	+	0.617006i
$441$	1.00278	−	0.728560i	0.0477513	−	0.0346933i
$442$	−28.0965	+	18.1786i	−1.33641	+	0.864666i
$443$	−6.56766	−	6.56766i	−0.312039	−	0.312039i	0.533660	−	0.845699i	$-0.320816\pi$
$443$	−6.56766	−	6.56766i	−0.312039	−	0.312039i	−0.845699	+	0.533660i	$0.820816\pi$
$444$	0.250826	−	2.31121i	0.0119037	−	0.109685i
$445$	−1.36357	+	5.17219i	−0.0646396	+	0.245185i
$446$	5.41832	−	2.40142i	0.256565	−	0.113710i
$447$	4.64620	+	2.36736i	0.219758	+	0.111972i
$448$	−5.59915	−	5.71397i	−0.264535	−	0.269960i
$449$		−	4.28013i		−	0.201992i	−0.994887	−	0.100996i	$-0.967797\pi$
$449$		−	4.28013i		−	0.201992i	0.994887	−	0.100996i	$-0.0322029\pi$
$450$	0.514417	+	8.74948i	0.0242499	+	0.412454i
$451$		−	31.2951i		−	1.47363i
$452$	10.5456	+	27.7524i	0.496022	+	1.30536i
$453$	−26.6940	−	13.6013i	−1.25419	−	0.639044i
$454$	−6.73641	−	15.1994i	−0.316155	−	0.713341i
$455$	8.22885	+	5.29686i	0.385774	+	0.248321i
$456$	0.0707654	−	13.9451i	0.00331389	−	0.653038i
$457$	−8.26094	−	8.26094i	−0.386431	−	0.386431i	0.486982	−	0.873412i	$-0.338098\pi$
$457$	−8.26094	−	8.26094i	−0.386431	−	0.386431i	−0.873412	+	0.486982i	$0.838098\pi$
$458$	8.63319	+	13.3433i	0.403402	+	0.623492i
$459$	−24.6053	+	17.8768i	−1.14847	+	0.834416i
$460$	−29.4142	−	16.9569i	−1.37144	−	0.790622i
$461$	8.34853	+	6.06556i	0.388830	+	0.282501i	0.764976	−	0.644059i	$-0.222751\pi$
$461$	8.34853	+	6.06556i	0.388830	+	0.282501i	−0.376146	+	0.926560i	$0.622751\pi$
$462$	−0.415653	+	7.68248i	−0.0193379	+	0.357421i
$463$	11.4380	+	1.81160i	0.531570	+	0.0841924i	0.416449	−	0.909159i	$-0.363274\pi$
$463$	11.4380	+	1.81160i	0.531570	+	0.0841924i	0.115121	+	0.993351i	$0.463274\pi$
$464$	−0.662955	+	3.01839i	−0.0307769	+	0.140125i
$465$	−9.03680	+	20.5191i	−0.419072	+	0.951550i
$466$	0.206928	−	0.185686i	0.00958576	−	0.00860175i
$467$	12.0613	+	23.6716i	0.558130	+	1.09539i	0.981861	+	0.189604i	$0.0607204\pi$
$467$	12.0613	+	23.6716i	0.558130	+	1.09539i	−0.423731	+	0.905788i	$0.639280\pi$
$468$	5.93978	−	9.07908i	0.274567	−	0.419680i
$469$	−0.749566	−	0.243549i	−0.0346118	−	0.0112460i
$470$	2.23512	+	13.9016i	0.103098	+	0.641233i
$471$	−2.08905	+	0.678774i	−0.0962584	+	0.0312763i
$472$	10.4048	+	1.70213i	0.478921	+	0.0783469i
$473$	−38.6660	+	6.12409i	−1.77786	+	0.281586i
$474$	−2.79836	−	27.0649i	−0.128533	−	1.24313i
$475$	−7.69347	−	16.9117i	−0.353001	−	0.775964i
$476$	−2.21246	−	10.5848i	−0.101408	−	0.485152i
$477$	2.11988	+	13.3844i	0.0970625	+	0.612829i
$478$	−3.66118	+	9.48969i	−0.167458	+	0.434048i
$479$	2.28283	+	7.02583i	0.104305	+	0.321018i	0.989567	−	0.144075i	$-0.0460207\pi$
$479$	2.28283	+	7.02583i	0.104305	+	0.321018i	−0.885262	+	0.465093i	$0.846021\pi$
$480$	6.08394	−	15.6418i	0.277692	−	0.713947i
$481$	−1.18481	+	3.64647i	−0.0540226	+	0.166265i
$482$	−1.95301	−	1.58699i	−0.0889571	−	0.0722855i
$483$	−8.97528	+	4.57313i	−0.408389	+	0.208085i
$484$	8.61117	+	7.80644i	0.391417	+	0.354838i
$485$	2.70955	−	26.8187i	0.123034	−	1.21777i
$486$	8.44361	−	14.5678i	0.383010	−	0.660808i
$487$	2.72568	−	17.2093i	0.123512	−	0.779826i	−0.845711	−	0.533641i	$-0.820823\pi$
$487$	2.72568	−	17.2093i	0.123512	−	0.779826i	0.969223	−	0.246184i	$-0.0791768\pi$
$488$	−0.527929	−	3.44631i	−0.0238982	−	0.156007i
$489$	0.0765568	−	0.105371i	0.00346202	−	0.00476506i
$490$	−2.55398	+	1.86472i	−0.115377	+	0.0842392i
$491$	20.4046	+	28.0845i	0.920847	+	1.26744i	0.963324	+	0.268339i	$0.0864748\pi$
$491$	20.4046	+	28.0845i	0.920847	+	1.26744i	−0.0424778	+	0.999097i	$0.513525\pi$
$492$	12.6933	+	15.7837i	0.572256	+	0.711586i
$493$	−2.95372	+	2.95372i	−0.133029	+	0.133029i
$494$	−4.81981	+	22.4883i	−0.216854	+	1.01180i
$495$	10.5928	−	4.11523i	0.476110	−	0.184966i
$496$	−22.6001	+	20.0740i	−1.01478	+	0.901351i
$497$	7.50371	−	14.7269i	0.336587	−	0.660590i
$498$	11.5726	−	3.07991i	0.518583	−	0.138014i
$499$	2.30450			0.103164			0.0515818	−	0.998669i	$-0.483574\pi$
$499$	2.30450			0.103164			0.0515818	+	0.998669i	$0.483574\pi$
$500$	−1.36458	−	22.3190i	−0.0610261	−	0.998136i
$501$	8.27435			0.369671
$502$	−29.6175	+	7.88232i	−1.32189	+	0.351805i
$503$	−4.61222	+	9.05200i	−0.205649	+	0.403609i	−0.970677	−	0.240389i	$-0.922725\pi$
$503$	−4.61222	+	9.05200i	−0.205649	+	0.403609i	0.765028	+	0.643997i	$0.222725\pi$
$504$	2.04626	+	2.84670i	0.0911476	+	0.126802i
$505$	40.9547	−	15.9106i	1.82246	−	0.708014i
$506$	−9.22545	+	43.0442i	−0.410121	+	1.91355i
$507$	5.77393	−	5.77393i	0.256429	−	0.256429i
$508$	−0.0922414	+	0.0741804i	−0.00409255	+	0.00329122i
$509$	−11.0220	−	15.1704i	−0.488540	−	0.672417i	0.491578	−	0.870834i	$-0.336420\pi$
$509$	−11.0220	−	15.1704i	−0.488540	−	0.672417i	−0.980118	+	0.198416i	$0.936420\pi$
$510$	18.3220	−	13.3773i	0.811314	−	0.592356i
$511$	3.32360	−	4.57454i	0.147027	−	0.202366i
$512$	16.2417	−	15.7546i	0.717789	−	0.696261i
$513$	−3.26985	+	20.6450i	−0.144368	+	0.911501i
$514$	−1.29224	+	2.22951i	−0.0569983	+	0.0983394i
$515$	−3.12337	+	30.9146i	−0.137632	+	1.36226i
$516$	17.0173	−	18.7716i	0.749146	−	0.826372i
$517$	16.2664	−	8.28814i	0.715395	−	0.364512i
$518$	−0.961515	−	0.781316i	−0.0422465	−	0.0343291i
$519$	2.58490	−	7.95552i	0.113465	−	0.349208i
$520$	−15.0997	+	23.1984i	−0.662166	+	1.01732i
$521$	−8.43296	−	25.9540i	−0.369455	−	1.13707i	−0.947144	−	0.320808i	$-0.896045\pi$
$521$	−8.43296	−	25.9540i	−0.369455	−	1.13707i	0.577689	−	0.816257i	$-0.303955\pi$
$522$	0.487468	−	1.26350i	0.0213359	−	0.0553021i
$523$	3.68398	+	23.2597i	0.161089	+	1.01708i	0.927254	+	0.374433i	$0.122163\pi$
$523$	3.68398	+	23.2597i	0.161089	+	1.01708i	−0.766165	+	0.642644i	$0.777837\pi$
$524$	23.4121	−	4.89367i	1.02276	−	0.213781i
$525$	−5.77192	−	3.27069i	−0.251907	−	0.142745i
$526$	−1.99601	−	19.3048i	−0.0870300	−	0.841729i
$527$	−40.3559	+	6.39175i	−1.75793	+	0.278429i
$528$	−21.7231	−	1.28590i	−0.945376	−	0.0559614i
$529$	−32.9413	+	10.7033i	−1.43223	+	0.465360i
$530$	−5.48815	−	34.1342i	−0.238390	−	1.48269i
$531$	−4.39418	−	1.42775i	−0.190691	−	0.0619593i
$532$	−6.21909	−	4.06870i	−0.269632	−	0.176401i
$533$	−15.1653	−	29.7636i	−0.656883	−	1.28921i
$534$	−3.34078	+	2.99783i	−0.144570	+	0.129729i
$535$	−10.2527	+	23.2799i	−0.443262	+	1.00648i
$536$	0.699610	−	2.11657i	0.0302185	−	0.0914219i
$537$	5.08198	+	0.804906i	0.219304	+	0.0347343i
$538$	1.27115	−	23.4945i	0.0548031	−	1.01292i
$539$	3.31711	+	2.41003i	0.142878	+	0.103807i
$540$	−12.5641	+	21.7942i	−0.540673	+	0.937871i
$541$	−4.74013	+	3.44391i	−0.203794	+	0.148065i	−0.685001	−	0.728542i	$-0.740198\pi$
$541$	−4.74013	+	3.44391i	−0.203794	+	0.148065i	0.481207	+	0.876607i	$0.340198\pi$
$542$	−7.40241	−	11.4410i	−0.317961	−	0.491435i
$543$	0.854809	+	0.854809i	0.0366834	+	0.0366834i
$544$	29.9696	−	6.10579i	1.28494	−	0.261784i
$545$	30.0504	+	19.3433i	1.28722	+	0.828576i
$546$	3.32755	+	7.50794i	0.142406	+	0.321310i
$547$	−6.42880	−	3.27564i	−0.274876	−	0.140056i	0.311119	−	0.950371i	$-0.399296\pi$
$547$	−6.42880	−	3.27564i	−0.274876	−	0.140056i	−0.585995	+	0.810315i	$0.699296\pi$
$548$	−26.2445	+	9.97257i	−1.12111	+	0.426007i
$549$			1.52789i			0.0652088i
$550$	−27.0003	+	10.5621i	−1.15130	+	0.450372i
$551$			2.87084i			0.122302i
$552$	−12.8058	−	25.4512i	−0.545050	−	1.08328i
$553$	−12.9200	−	6.58308i	−0.549415	−	0.279941i
$554$	−9.78913	+	4.33858i	−0.415900	+	0.184328i
$555$	0.662598	−	2.51331i	0.0281257	−	0.106684i
$556$	−31.4323	−	3.41121i	−1.33303	−	0.144668i
$557$	27.9763	+	27.9763i	1.18540	+	1.18540i	0.978326	+	0.207070i	$0.0663926\pi$
$557$	27.9763	+	27.9763i	1.18540	+	1.18540i	0.207070	+	0.978326i	$0.433607\pi$
$558$	11.1219	−	7.19593i	0.470828	−	0.304628i
$559$	−33.8061	+	24.5616i	−1.42985	+	1.03884i
$560$	−5.23749	−	7.25043i	−0.221324	−	0.306387i
$561$	−23.7967	−	17.2893i	−1.00470	−	0.729954i
$562$	21.8598	+	1.18270i	0.922099	+	0.0498893i
$563$	−44.2487	−	7.00830i	−1.86486	−	0.295365i	−0.880838	−	0.473418i	$-0.843020\pi$
$563$	−44.2487	−	7.00830i	−1.86486	−	0.295365i	−0.984021	+	0.178054i	$0.943020\pi$
$564$	−4.84232	+	10.7778i	−0.203898	+	0.453825i
$565$	7.03192	+	32.4393i	0.295835	+	1.36473i
$566$	10.5970	+	11.8092i	0.445424	+	0.496379i
$567$	1.70026	+	3.33695i	0.0714041	+	0.140139i
$568$	41.5456	+	21.4348i	1.74322	+	0.899384i
$569$	30.7013	+	9.97546i	1.28707	+	0.418193i	0.871064	−	0.491170i	$-0.163431\pi$
$569$	30.7013	+	9.97546i	1.28707	+	0.418193i	0.416002	+	0.909363i	$0.363431\pi$
$570$	2.40301	−	15.4050i	0.100651	−	0.645243i
$571$	−4.88166	+	1.58615i	−0.204291	+	0.0663782i	−0.409375	−	0.912366i	$-0.634253\pi$
$571$	−4.88166	+	1.58615i	−0.204291	+	0.0663782i	0.205084	+	0.978744i	$0.434253\pi$
$572$	34.6347	+	9.40604i	1.44815	+	0.393286i
$573$	10.7711	−	1.70597i	0.449969	−	0.0712681i
$574$	10.7369	−	1.11014i	0.448150	−	0.0463362i
$575$	−29.6915	−	23.6501i	−1.23822	−	0.986278i
$576$	−8.08095	+	5.74676i	−0.336706	+	0.239448i
$577$	1.12416	+	7.09766i	0.0467994	+	0.295480i	0.999976	−	0.00693470i	$-0.00220740\pi$
$577$	1.12416	+	7.09766i	0.0467994	+	0.295480i	−0.953177	+	0.302414i	$0.902207\pi$
$578$	16.1406	+	6.22716i	0.671362	+	0.259016i
$579$	−6.72634	−	20.7016i	−0.279537	−	0.860327i
$580$	−1.23611	+	3.22642i	−0.0513269	+	0.133970i
$581$	1.97216	−	6.06968i	0.0818189	−	0.251813i
$582$	14.2649	−	17.5549i	0.591298	−	0.727672i
$583$	−39.9407	+	20.3508i	−1.65417	+	0.842844i
$584$	12.8909	+	9.46610i	0.533429	+	0.391710i
$585$	8.08021	−	9.04702i	0.334075	−	0.374048i
$586$	−10.0946	−	5.85090i	−0.417003	−	0.241698i
$587$	−2.86887	+	18.1133i	−0.118411	+	0.747617i	0.855013	+	0.518607i	$0.173549\pi$
$587$	−2.86887	+	18.1133i	−0.118411	+	0.747617i	−0.973424	+	0.229011i	$0.926451\pi$
$588$	−2.65049	+	0.129917i	−0.109305	+	0.00535768i
$589$	−16.5056	+	22.7180i	−0.680102	+	0.936080i
$590$	11.2191	+	3.61635i	0.461885	+	0.148883i
$591$	−5.35029	−	7.36405i	−0.220082	−	0.302917i
$592$	2.22367	−	2.70833i	0.0913922	−	0.111312i
$593$	16.3957	−	16.3957i	0.673290	−	0.673290i	−0.285183	−	0.958473i	$-0.592054\pi$
$593$	16.3957	−	16.3957i	0.673290	−	0.673290i	0.958473	+	0.285183i	$0.0920544\pi$
$594$	31.8932	+	6.83551i	1.30859	+	0.280465i
$595$	−0.681375	−	12.0707i	−0.0279336	−	0.494850i
$596$	3.90701	+	6.82032i	0.160037	+	0.279371i
$597$	−8.01853	+	15.7373i	−0.328177	+	0.644083i
$598$	12.0848	+	45.4083i	0.494186	+	1.85688i
$599$	0.0159088			0.000650018			0.000325009	−	1.00000i	$-0.499897\pi$
$599$	0.0159088			0.000650018			0.000325009		1.00000i	$0.499897\pi$
$600$	9.33364	−	16.2783i	0.381044	−	0.664559i
$601$	−27.6404			−1.12748			−0.563738	−	0.825954i	$-0.690637\pi$
$601$	−27.6404			−1.12748			−0.563738	+	0.825954i	$0.690637\pi$
$602$	−3.47269	−	13.0485i	−0.141536	−	0.531818i
$603$	−0.443503	+	0.870424i	−0.0180609	+	0.0354464i
$604$	−22.4471	−	39.1851i	−0.913359	−	1.59442i
$605$	8.21854	+	10.0659i	0.334131	+	0.409235i
$606$	36.0515	+	7.72673i	1.46449	+	0.313877i
$607$	11.2492	−	11.2492i	0.456592	−	0.456592i	−0.440943	−	0.897535i	$-0.645356\pi$
$607$	11.2492	−	11.2492i	0.456592	−	0.456592i	0.897535	+	0.440943i	$0.145356\pi$
$608$	11.5971	−	17.5316i	0.470326	−	0.711001i
$609$	0.602536	+	0.829320i	0.0244160	+	0.0336057i
$610$	−0.00911179	−	3.89803i	−0.000368925	−	0.157826i
$611$	11.4540	−	15.7651i	0.463379	−	0.637787i
$612$	−13.3873	+	0.656192i	−0.541149	+	0.0265250i
$613$	1.59598	−	10.0766i	0.0644610	−	0.406991i	−0.934267	−	0.356574i	$-0.883945\pi$
$613$	1.59598	−	10.0766i	0.0644610	−	0.406991i	0.998728	−	0.0504172i	$-0.0160551\pi$
$614$	19.6453	+	11.3866i	0.792821	+	0.459525i
$615$	11.4015	+	19.5656i	0.459754	+	0.788960i
$616$	−6.86410	+	9.34751i	−0.276563	+	0.376622i
$617$	7.07786	−	3.60635i	0.284944	−	0.145186i	−0.305677	−	0.952135i	$-0.598883\pi$
$617$	7.07786	−	3.60635i	0.284944	−	0.145186i	0.590621	+	0.806949i	$0.298883\pi$
$618$	−16.4435	+	20.2359i	−0.661454	+	0.814009i
$619$	3.00021	−	9.23370i	0.120589	−	0.371134i	−0.872483	−	0.488645i	$-0.837492\pi$
$619$	3.00021	−	9.23370i	0.120589	−	0.371134i	0.993072	+	0.117511i	$0.0374915\pi$
$620$	−28.3318	+	18.4249i	−1.13783	+	0.739962i
$621$	13.1967	+	40.6151i	0.529564	+	1.62983i
$622$	15.0091	+	5.79062i	0.601812	+	0.232183i
$623$	0.374208	+	2.36266i	0.0149923	+	0.0946579i
$624$	−21.2832	+	9.30384i	−0.852008	+	0.372452i
$625$	2.21219	−	24.9019i	0.0884877	−	0.996077i
$626$	−34.2517	+	3.54143i	−1.36897	+	0.141544i
$627$	−19.9666	+	3.16240i	−0.797389	+	0.126294i
$628$	−3.19523	−	0.867756i	−0.127504	−	0.0346272i
$629$	4.50483	−	1.46371i	0.179619	−	0.0583618i
$630$	1.78764	+	3.48826i	0.0712213	+	0.138976i
$631$	−20.6435	−	6.70747i	−0.821803	−	0.267020i	−0.132214	−	0.991221i	$-0.542209\pi$
$631$	−20.6435	−	6.70747i	−0.821803	−	0.267020i	−0.689589	+	0.724201i	$0.742209\pi$
$632$	18.8050	−	36.4484i	0.748021	−	1.44984i
$633$	−1.79987	−	3.53244i	−0.0715384	−	0.140402i
$634$	−25.3450	−	28.2444i	−1.00658	−	1.12173i
$635$	−0.114343	+	0.0666315i	−0.00453755	+	0.00264419i
$636$	11.8899	−	26.4638i	0.471465	−	1.04936i
$637$	4.32266	+	0.684643i	0.171270	+	0.0271265i
$638$	4.47331	+	0.242025i	0.177100	+	0.00958184i
$639$	−16.5742	−	12.0419i	−0.655667	−	0.476370i
$640$	20.5822	−	14.7096i	0.813584	−	0.581448i
$641$	−9.98367	+	7.25356i	−0.394331	+	0.286498i	−0.767228	−	0.641374i	$-0.778365\pi$
$641$	−9.98367	+	7.25356i	−0.394331	+	0.286498i	0.372897	+	0.927873i	$0.378365\pi$
$642$	−17.9222	+	11.5957i	−0.707332	+	0.457648i
$643$	31.8513	+	31.8513i	1.25609	+	1.25609i	0.952942	+	0.303153i	$0.0980392\pi$
$643$	31.8513	+	31.8513i	1.25609	+	1.25609i	0.303153	+	0.952942i	$0.401961\pi$
$644$	−15.0951	−	1.63821i	−0.594831	−	0.0645545i
$645$	21.9427	−	17.9157i	0.863991	−	0.705429i
$646$	25.9760	−	11.5126i	1.02201	−	0.452959i
$647$	37.3689	+	19.0404i	1.46912	+	0.748556i	0.991512	−	0.130015i	$-0.0415027\pi$
$647$	37.3689	+	19.0404i	1.46912	+	0.748556i	0.477611	+	0.878571i	$0.341503\pi$
$648$	−9.46259	+	4.76110i	−0.371726	+	0.187034i
$649$		−	15.2837i		−	0.599937i
$650$	−20.5606	+	23.1294i	−0.806455	+	0.907208i
$651$			10.0269i			0.392986i
$652$	0.183523	−	0.0697364i	0.00718731	−	0.00273109i
$653$	23.9489	+	12.2026i	0.937194	+	0.477524i	0.854732	−	0.519070i	$-0.173722\pi$
$653$	23.9489	+	12.2026i	0.937194	+	0.477524i	0.0824620	+	0.996594i	$0.473722\pi$
$654$	12.1517	+	27.4178i	0.475168	+	1.07212i
$655$	26.6987	−	1.50711i	1.04321	−	0.0588877i
$656$	2.98579	+	30.3841i	0.116576	+	1.18630i
$657$	−4.95589	−	4.95589i	−0.193348	−	0.193348i
$658$	3.42056	+	5.28676i	0.133347	+	0.206099i
$659$	−22.1650	+	16.1038i	−0.863424	+	0.627314i	−0.928814	−	0.370546i	$-0.879171\pi$
$659$	−22.1650	+	16.1038i	−0.863424	+	0.627314i	0.0653904	+	0.997860i	$0.479171\pi$
$660$	−23.8013	−	5.04304i	−0.926463	−	0.196300i
$661$	32.3034	+	23.4698i	1.25646	+	0.912868i	0.998578	−	0.0533096i	$-0.0169770\pi$
$661$	32.3034	+	23.4698i	1.25646	+	0.912868i	0.257877	+	0.966178i	$0.416977\pi$
$662$	−0.470280	+	8.69214i	−0.0182780	+	0.337830i
$663$	−31.0104	−	4.91156i	−1.20434	−	0.190749i
$664$	17.1391	+	5.66515i	0.665127	+	0.219851i
$665$	−6.19713	−	5.53488i	−0.240314	−	0.214633i
$666$	−1.14296	+	1.02563i	−0.0442887	+	0.0397422i
$667$	2.66282	+	5.22608i	0.103105	+	0.202355i
$668$	10.4371	+	6.82824i	0.403823	+	0.264193i
$669$	5.28832	+	1.71828i	0.204458	+	0.0664325i
$670$	1.12630	−	2.22331i	0.0435126	−	0.0858940i
$671$	−4.80679	+	1.56182i	−0.185564	+	0.0602934i
$672$	−0.329413	−	7.49850i	−0.0127074	−	0.289261i
$673$	23.2323	−	3.67964i	0.895540	−	0.141840i	0.308335	−	0.951278i	$-0.400228\pi$
$673$	23.2323	−	3.67964i	0.895540	−	0.141840i	0.587205	+	0.809438i	$0.300228\pi$
$674$	1.50656	+	14.5710i	0.0580306	+	0.561255i
$675$	−17.5233	+	21.9997i	−0.674474	+	0.846767i
$676$	12.0479	−	2.51830i	0.463382	−	0.0968575i
$677$	−6.52387	−	41.1901i	−0.250733	−	1.58306i	−0.716133	−	0.697964i	$-0.754089\pi$
$677$	−6.52387	−	41.1901i	−0.250733	−	1.58306i	0.465400	−	0.885101i	$-0.345911\pi$
$678$	−10.0260	+	25.9873i	−0.385048	+	0.998034i
$679$	−3.72512	−	11.4647i	−0.142957	−	0.439976i
$680$	34.1504	−	1.75395i	1.30961	−	0.0672607i
$681$	4.82008	−	14.8347i	0.184706	−	0.568466i
$682$	34.0075	+	27.6341i	1.30221	+	1.05816i
$683$	−17.9615	+	9.15184i	−0.687278	+	0.350186i	−0.762506	−	0.646981i	$-0.776031\pi$
$683$	−17.9615	+	9.15184i	−0.687278	+	0.350186i	0.0752284	+	0.997166i	$0.476031\pi$
$684$	−6.18695	+	6.82473i	−0.236564	+	0.260950i
$685$	−30.6767	+	6.64982i	−1.17210	+	0.254077i
$686$	−0.709177	+	1.22355i	−0.0270765	+	0.0467152i
$687$	−2.33255	+	14.7272i	−0.0889924	+	0.561876i
$688$	36.9562	−	9.63485i	1.40894	−	0.367325i
$689$	−28.1243	+	38.7098i	−1.07145	+	1.47473i
$690$	−9.91428	−	30.2721i	−0.377430	−	1.15244i
$691$	−2.39802	−	3.30059i	−0.0912249	−	0.125560i	0.760965	−	0.648793i	$-0.224726\pi$
$691$	−2.39802	−	3.30059i	−0.0912249	−	0.125560i	−0.852190	+	0.523233i	$0.824726\pi$
$692$	9.82567	−	7.90179i	0.373516	−	0.300381i
$693$	3.59364	−	3.59364i	0.136511	−	0.136511i
$694$	−4.17217	+	19.4665i	−0.158373	+	0.738939i
$695$	−34.1808	−	9.01127i	−1.29655	−	0.341817i
$696$	−2.35429	+	1.69230i	−0.0892391	+	0.0641466i
$697$	−18.7352	+	36.7699i	−0.709646	+	1.39276i
$698$	−26.2741	+	6.99251i	−0.994489	+	0.264670i
$699$	0.260849			0.00986621
$700$	−4.58151	−	8.88874i	−0.173165	−	0.335963i
$701$	−43.8387			−1.65576			−0.827882	−	0.560902i	$-0.810455\pi$
$701$	−43.8387			−1.65576			−0.827882	+	0.560902i	$0.810455\pi$
$702$	33.6449	−	8.95415i	1.26984	−	0.337953i
$703$	1.47790	−	2.90054i	0.0557400	−	0.109396i
$704$	−26.3399	−	19.5485i	−0.992722	−	0.736763i
$705$	−7.15011	+	11.1079i	−0.269289	+	0.418349i
$706$	−2.24995	+	10.4979i	−0.0846781	+	0.395092i
$707$	13.8940	−	13.8940i	0.522538	−	0.522538i
$708$	6.19903	+	7.70834i	0.232974	+	0.289697i
$709$	−12.1303	−	16.6959i	−0.455563	−	0.627028i	0.518019	−	0.855369i	$-0.326670\pi$
$709$	−12.1303	−	16.6959i	−0.455563	−	0.627028i	−0.973581	+	0.228341i	$0.926670\pi$
$710$	42.3568	+	30.6230i	1.58962	+	1.14926i
$711$	−10.5645	+	14.5407i	−0.396198	+	0.545320i
$712$	−6.68789	+	1.02450i	−0.250639	+	0.0383946i
$713$	−8.97493	+	56.6655i	−0.336114	+	2.12214i
$714$	5.08757	−	8.77761i	0.190398	−	0.328494i
$715$	36.7218	+	16.1726i	1.37332	+	0.604823i
$716$	5.74607	+	5.20909i	0.214741	+	0.194673i
$717$	−8.50289	+	4.33244i	−0.317546	+	0.161798i
$718$	−20.3369	−	16.5255i	−0.758967	−	0.616728i
$719$	0.469324	−	1.44443i	0.0175028	−	0.0538682i	−0.941924	−	0.335827i	$-0.890984\pi$
$719$	0.469324	−	1.44443i	0.0175028	−	0.0538682i	0.959426	+	0.281959i	$0.0909842\pi$
$720$	−9.89181	+	5.00608i	−0.368646	+	0.186565i
$721$	4.29404	+	13.2157i	0.159918	+	0.492178i
$722$	−2.64301	+	6.85063i	−0.0983628	+	0.254954i
$723$	−0.369345	−	2.33196i	−0.0137361	−	0.0867264i
$724$	0.372825	+	1.78365i	0.0138559	+	0.0662889i
$725$	−1.90444	+	3.36085i	−0.0707292	+	0.124819i
$726$	1.12152	+	10.8470i	0.0416235	+	0.402570i
$727$	11.6582	−	1.84647i	0.432377	−	0.0684819i	0.0635477	−	0.997979i	$-0.479759\pi$
$727$	11.6582	−	1.84647i	0.432377	−	0.0684819i	0.368830	+	0.929497i	$0.379759\pi$
$728$	−1.99848	+	12.2164i	−0.0740686	+	0.452768i
$729$	25.7099	−	8.35366i	0.952220	−	0.309395i
$730$	12.6732	+	12.6141i	0.469058	+	0.466870i
$731$	49.0965	+	15.9524i	1.81590	+	0.590021i
$732$	1.79084	−	2.73733i	0.0661914	−	0.101175i
$733$	−4.09235	−	8.03168i	−0.151154	−	0.296657i	0.802996	−	0.595984i	$-0.203238\pi$
$733$	−4.09235	−	8.03168i	−0.151154	−	0.296657i	−0.954151	+	0.299327i	$0.903238\pi$
$734$	−35.7369	+	32.0684i	−1.31907	+	1.18366i
$735$	−2.95187	−	0.298235i	−0.108881	−	0.0110006i
$736$	4.85016	−	42.6714i	0.178779	−	1.57289i
$737$	−3.19173	−	0.505521i	−0.117569	−	0.0186211i
$738$	0.722821	−	13.3598i	0.0266074	−	0.491782i
$739$	10.2537	+	7.44972i	0.377187	+	0.274042i	0.760185	−	0.649707i	$-0.225108\pi$
$739$	10.2537	+	7.44972i	0.377187	+	0.274042i	−0.382998	+	0.923749i	$0.625108\pi$
$740$	2.90985	−	2.62344i	0.106968	−	0.0964397i
$741$	−17.4570	+	12.6833i	−0.641300	+	0.465932i
$742$	−8.39890	−	12.9812i	−0.308333	−	0.476554i
$743$	37.8805	+	37.8805i	1.38970	+	1.38970i	0.825938	+	0.563761i	$0.190646\pi$
$743$	37.8805	+	37.8805i	1.38970	+	1.38970i	0.563761	+	0.825938i	$0.309354\pi$
$744$	−28.3601	−	0.143916i	−1.03973	−	0.00527620i
$745$	3.18232	+	8.19144i	0.116591	+	0.300111i
$746$	−2.80272	−	6.32377i	−0.102615	−	0.231530i
$747$	−7.04834	−	3.59131i	−0.257885	−	0.131399i
$748$	−15.7490	−	41.4461i	−0.575840	−	1.51542i
$749$			11.3760i			0.415671i
$750$	13.0324	−	16.4402i	0.475876	−	0.600312i
$751$		−	8.39524i		−	0.306347i	−0.988199	−	0.153173i	$-0.951051\pi$
$751$		−	8.39524i		−	0.306347i	0.988199	−	0.153173i	$-0.0489493\pi$
$752$	−15.0021	+	9.59881i	−0.547071	+	0.350033i
$753$	−25.6208	−	13.0544i	−0.933674	−	0.475731i
$754$	4.37169	−	1.93755i	0.159207	−	0.0705613i
$755$	−18.2835	−	47.0626i	−0.665406	−	1.71278i
$756$	−1.21382	+	11.1846i	−0.0441461	+	0.406780i
$757$	−27.2474	−	27.2474i	−0.990323	−	0.990323i	0.00963062	−	0.999954i	$-0.496934\pi$
$757$	−27.2474	−	27.2474i	−0.990323	−	0.990323i	−0.999954	+	0.00963062i	$0.996934\pi$
$758$	−10.3776	+	6.71436i	−0.376931	+	0.243877i
$759$	−33.4139	+	24.2766i	−1.21285	+	0.881186i
$760$	15.7437	−	17.4485i	0.571085	−	0.632923i
$761$	16.8471	+	12.2402i	0.610708	+	0.443705i	0.849664	−	0.527325i	$-0.176805\pi$
$761$	16.8471	+	12.2402i	0.610708	+	0.443705i	−0.238956	+	0.971030i	$0.576805\pi$
$762$	−0.110893	−	0.00599979i	−0.00401725	−	0.000217350i
$763$	15.7857	+	2.50021i	0.571480	+	0.0905135i
$764$	14.9943	+	6.73675i	0.542473	+	0.243727i
$765$	−14.9095	−	1.50634i	−0.539055	−	0.0544620i
$766$	0.0920368	+	0.102566i	0.00332542	+	0.00370584i
$767$	−7.40633	−	14.5357i	−0.267427	−	0.524855i
$768$	21.2134	−	0.824084i	0.765473	−	0.0297366i
$769$	45.6149	+	14.8212i	1.64492	+	0.534465i	0.977629	−	0.210336i	$-0.0674558\pi$
$769$	45.6149	+	14.8212i	1.64492	+	0.534465i	0.667286	+	0.744801i	$0.267456\pi$
$770$	−9.14682	+	9.18969i	−0.329629	+	0.331173i
$771$	−2.29939	+	0.747117i	−0.0828105	+	0.0269068i
$772$	8.59906	−	31.6633i	0.309487	−	1.13959i
$773$	15.0600	−	2.38527i	0.541671	−	0.0857923i	0.120397	−	0.992726i	$-0.461583\pi$
$773$	15.0600	−	2.38527i	0.541671	−	0.0857923i	0.421274	+	0.906933i	$0.361583\pi$
$774$	−16.6479	+	1.72130i	−0.598395	+	0.0618707i
$775$	−34.3934	+	15.6462i	−1.23545	+	0.562029i
$776$	32.4802	−	10.3715i	1.16597	−	0.372316i
$777$	−0.181838	−	1.14808i	−0.00652340	−	0.0411872i
$778$	−47.2822	−	18.2418i	−1.69515	−	0.653999i
$779$	8.76434	+	26.9739i	0.314015	+	0.966439i
$780$	−25.0803	+	6.73762i	−0.898019	+	0.241245i
$781$	20.9418	−	64.4523i	0.749358	−	2.30629i
$782$	36.6082	−	45.0514i	1.30911	−	1.61103i
$783$	3.87222	−	1.97299i	0.138382	−	0.0705090i
$784$	−3.45049	−	2.02339i	−0.123232	−	0.0722640i
$785$	−3.38778	−	1.49201i	−0.120915	−	0.0532521i
$786$	19.4149	+	11.2530i	0.692507	+	0.401382i
$787$	0.835112	−	5.27269i	0.0297685	−	0.187951i	−0.968323	−	0.249700i	$-0.919668\pi$
$787$	0.835112	−	5.27269i	0.0297685	−	0.187951i	0.998092	+	0.0617492i	$0.0196679\pi$
$788$	−0.671720	−	13.7041i	−0.0239290	−	0.488188i
$789$	10.7028	−	14.7311i	0.381028	−	0.524440i
$790$	26.8658	−	37.1600i	0.955843	−	1.32209i
$791$	8.72523	+	12.0093i	0.310234	+	0.427000i
$792$	10.1126	+	10.2158i	0.359337	+	0.363002i
$793$	−3.81472	+	3.81472i	−0.135465	+	0.135465i
$794$	39.5535	+	8.47730i	1.40370	+	0.300848i
$795$	17.5565	−	27.2745i	0.622664	−	0.967329i
$796$	−23.1013	+	13.2335i	−0.818803	+	0.469050i
$797$	−2.38285	+	4.67660i	−0.0844048	+	0.165654i	−0.929351	−	0.369198i	$-0.879632\pi$
$797$	−2.38285	+	4.67660i	−0.0844048	+	0.165654i	0.844946	+	0.534852i	$0.179632\pi$
$798$	−1.79325	−	6.73808i	−0.0634805	−	0.238525i
$799$	−24.0738			−0.851670
$800$	25.2066	−	12.8307i	0.891188	−	0.453635i
$801$	2.96502			0.104764
$802$	4.94057	+	18.5640i	0.174458	+	0.655518i
$803$	10.5254	−	20.6573i	0.371434	−	0.728981i
$804$	1.81479	−	1.03960i	0.0640028	−	0.0366639i
$805$	−16.4151	−	4.32760i	−0.578555	−	0.152528i
$806$	45.7345	+	9.80205i	1.61093	+	0.345263i
$807$	15.6095	−	15.6095i	0.549481	−	0.549481i
$808$	39.0982	+	39.4971i	1.37547	+	1.38950i
$809$	−9.15277	−	12.5977i	−0.321794	−	0.442912i	0.617220	−	0.786791i	$-0.288259\pi$
$809$	−9.15277	−	12.5977i	−0.321794	−	0.442912i	−0.939014	+	0.343879i	$0.888259\pi$
$810$	−11.2549	+	3.68606i	−0.395458	+	0.129515i
$811$	−21.1889	+	29.1641i	−0.744044	+	1.02409i	0.254332	+	0.967117i	$0.418144\pi$
$811$	−21.1889	+	29.1641i	−0.744044	+	1.02409i	−0.998376	+	0.0569716i	$0.981856\pi$
$812$	0.0756473	+	1.54332i	0.00265470	+	0.0541598i
$813$	2.00001	−	12.6276i	0.0701436	−	0.442869i
$814$	−4.39499	−	2.54737i	−0.154044	−	0.0892853i
$815$	0.214517	−	0.0465010i	0.00751419	−	0.00162886i
$816$	24.7535	+	14.5156i	0.866545	+	0.508148i
$817$	31.6119	−	16.1071i	1.10596	−	0.563515i
$818$	−2.95939	+	3.64193i	−0.103473	+	0.127337i
$819$	1.67633	−	5.15922i	0.0585758	−	0.180278i
$820$	−1.76442	+	34.0885i	−0.0616162	+	1.19042i
$821$	−11.3343	−	34.8835i	−0.395571	−	1.21744i	−0.928516	−	0.371293i	$-0.878915\pi$
$821$	−11.3343	−	34.8835i	−0.395571	−	1.21744i	0.532945	−	0.846150i	$-0.321085\pi$
$822$	−24.5752	−	9.48125i	−0.857158	−	0.330697i
$823$	8.75540	+	55.2794i	0.305194	+	1.92692i	0.370024	+	0.929022i	$0.379349\pi$
$823$	8.75540	+	55.2794i	0.305194	+	1.92692i	−0.0648302	+	0.997896i	$0.520651\pi$
$824$	−37.4408	+	11.9555i	−1.30431	+	0.416491i
$825$	−25.4724	−	9.54316i	−0.886835	−	0.332250i
$826$	5.24361	−	0.542160i	0.182449	−	0.0188642i
$827$	14.1782	−	2.24561i	0.493025	−	0.0780875i	0.0950289	−	0.995475i	$-0.469706\pi$
$827$	14.1782	−	2.24561i	0.493025	−	0.0780875i	0.397996	+	0.917387i	$0.369706\pi$
$828$	−4.93251	+	18.1624i	−0.171417	+	0.631186i
$829$	7.08550	−	2.30222i	0.246090	−	0.0799593i	−0.183375	−	0.983043i	$-0.558702\pi$
$829$	7.08550	−	2.30222i	0.246090	−	0.0799593i	0.429465	+	0.903084i	$0.358702\pi$
$830$	18.0035	+	9.12028i	0.624910	+	0.316570i
$831$	−9.55426	−	3.10437i	−0.331434	−	0.107689i
$832$	−34.5239	−	5.82782i	−1.19690	−	0.202043i
$833$	−2.45462	−	4.81746i	−0.0850475	−	0.166915i
$834$	−19.8114	−	22.0778i	−0.686012	−	0.764491i
$835$	10.4002	+	9.28882i	0.359915	+	0.321453i
$836$	−27.7952	−	12.4880i	−0.961315	−	0.431908i
$837$	41.9858	+	6.64990i	1.45124	+	0.229854i
$838$	−14.7671	−	0.798960i	−0.510121	−	0.0275996i
$839$	−38.7893	−	28.1821i	−1.33916	−	0.972953i	−0.999475	−	0.0324127i	$-0.989681\pi$
$839$	−38.7893	−	28.1821i	−1.33916	−	0.972953i	−0.339681	−	0.940541i	$-0.610319\pi$
$840$	0.885893	−	8.34477i	0.0305662	−	0.287922i
$841$	−22.9786	+	16.6949i	−0.792366	+	0.575687i
$842$	38.3259	−	24.7971i	1.32080	−	0.854564i
$843$	14.5234	+	14.5234i	0.500213	+	0.500213i
$844$	0.644758	−	5.94106i	0.0221935	−	0.204500i
$845$	13.7392	−	0.775562i	0.472644	−	0.0266802i
$846$	7.13551	−	3.16248i	0.245324	−	0.108728i
$847$	5.17806	+	2.63835i	0.177920	+	0.0906549i
$848$	36.8364	−	23.5690i	1.26497	−	0.809364i
$849$			14.8864i			0.510901i
$850$	38.0468	+	3.75414i	1.30500	+	0.128766i
$851$		−	6.65094i		−	0.227991i
$852$	15.5797	+	41.0006i	0.533752	+	1.40466i
$853$	−1.36670	−	0.696370i	−0.0467950	−	0.0238432i	0.430436	−	0.902621i	$-0.358360\pi$
$853$	−1.36670	−	0.696370i	−0.0467950	−	0.0238432i	−0.477231	+	0.878778i	$0.658360\pi$
$854$	−0.706351	−	1.59374i	−0.0241708	−	0.0545367i
$855$	−7.97764	+	6.51356i	−0.272830	+	0.222759i
$856$	−32.1758	−	0.163279i	−1.09975	−	0.00558076i
$857$	28.5845	+	28.5845i	0.976430	+	0.976430i	0.999729	−	0.0232990i	$-0.00741698\pi$
$857$	28.5845	+	28.5845i	0.976430	+	0.976430i	−0.0232990	+	0.999729i	$0.507417\pi$
$858$	18.2912	+	28.2706i	0.624452	+	0.965142i
$859$	−2.02040	+	1.46791i	−0.0689352	+	0.0500844i	−0.621719	−	0.783240i	$-0.713565\pi$
$859$	−2.02040	+	1.46791i	−0.0689352	+	0.0500844i	0.552784	+	0.833325i	$0.313565\pi$
$860$	42.4625	−	4.49073i	1.44796	−	0.153133i
$861$	8.19312	+	5.95265i	0.279221	+	0.202866i
$862$	−1.32199	+	24.4341i	−0.0450271	+	0.832230i
$863$	−2.70874	−	0.429022i	−0.0922065	−	0.0146041i	0.110161	−	0.993914i	$-0.464863\pi$
$863$	−2.70874	−	0.429022i	−0.0922065	−	0.0146041i	−0.202367	+	0.979310i	$0.564863\pi$
$864$	−31.6170	−	3.59368i	−1.07563	−	0.122260i
$865$	12.1799	−	7.09767i	0.414130	−	0.241328i
$866$	5.24960	−	4.71071i	0.178389	−	0.160076i
$867$	7.36888	+	14.4622i	0.250260	+	0.491164i
$868$	−8.27452	+	12.6478i	−0.280855	+	0.429293i
$869$	−56.5446	−	18.3725i	−1.91815	−	0.623243i
$870$	−2.88487	+	1.47842i	−0.0978063	+	0.0501231i
$871$	−3.28051	+	1.06590i	−0.111156	+	0.0361167i
$872$	−7.29813	+	44.6122i	−0.247146	+	1.51076i
$873$	−14.7579	+	2.33742i	−0.499478	+	0.0791096i
$874$	−4.10312	−	39.6842i	−0.138790	−	1.34234i
$875$	−3.58318	−	10.5906i	−0.121134	−	0.358028i
$876$	3.07006	+	14.6876i	0.103728	+	0.496250i
$877$	4.88749	+	30.8584i	0.165039	+	1.04201i	0.921614	+	0.388108i	$0.126871\pi$
$877$	4.88749	+	30.8584i	0.165039	+	1.04201i	−0.756575	+	0.653907i	$0.773129\pi$
$878$	−6.59758	+	17.1008i	−0.222657	+	0.577123i
$879$	−3.38273	−	10.4110i	−0.114097	−	0.351154i
$880$	−25.8607	−	26.0027i	−0.871765	−	0.876551i
$881$	−14.7365	+	45.3543i	−0.496485	+	1.52802i	0.318144	+	0.948042i	$0.396941\pi$
$881$	−14.7365	+	45.3543i	−0.496485	+	1.52802i	−0.814629	+	0.579982i	$0.803059\pi$
$882$	1.36040	+	1.10545i	0.0458072	+	0.0372224i
$883$	−41.0109	+	20.8961i	−1.38013	+	0.703209i	−0.977259	−	0.212050i	$-0.931986\pi$
$883$	−41.0109	+	20.8961i	−1.38013	+	0.703209i	−0.402866	+	0.915259i	$0.631986\pi$
$884$	−35.0627	−	31.7860i	−1.17929	−	1.06908i
$885$	5.56820	+	9.55528i	0.187173	+	0.321197i
$886$	6.58690	−	11.3644i	0.221291	−	0.381795i
$887$	−2.44501	+	15.4372i	−0.0820955	+	0.518331i	0.912032	+	0.410118i	$0.134513\pi$
$887$	−2.44501	+	15.4372i	−0.0820955	+	0.518331i	−0.994128	+	0.108212i	$0.965487\pi$
$888$	3.24983	−	0.497831i	0.109057	−	0.0167061i
$889$	−0.0347878	+	0.0478812i	−0.00116674	+	0.00160589i
$890$	−7.56449	+	0.0176823i	−0.253562	+	0.000592712i
$891$	9.02588	+	12.4231i	0.302378	+	0.416188i
$892$	5.25260	+	6.53148i	0.175870	+	0.218690i
$893$	−11.6992	+	11.6992i	−0.391498	+	0.391498i
$894$	−1.54544	+	7.21074i	−0.0516873	+	0.241163i
$895$	5.48408	+	6.71676i	0.183312	+	0.224516i
$896$	5.77247	−	9.73029i	0.192845	−	0.325066i
$897$	−20.0145	+	39.2807i	−0.668265	+	1.31154i
$898$	5.84941	−	1.55674i	0.195197	−	0.0519492i
$899$	5.83843			0.194723
$900$	−11.7703	+	3.88533i	−0.392344	+	0.129511i
$901$	59.1111			1.96928
$902$	42.7692	−	11.3825i	1.42406	−	0.378995i
$903$	5.75137	−	11.2877i	0.191393	−	0.375631i
$904$	−34.0921	+	24.5060i	−1.13389	+	0.815057i
$905$	0.114819	+	2.03404i	0.00381672	+	0.0676139i
$906$	8.87909	−	41.4281i	0.294988	−	1.37636i
$907$	−8.88866	+	8.88866i	−0.295143	+	0.295143i	−0.839108	−	0.543965i	$-0.816922\pi$
$907$	−8.88866	+	8.88866i	−0.295143	+	0.295143i	0.543965	+	0.839108i	$0.316922\pi$
$908$	18.3220	−	14.7345i	0.608036	−	0.488981i
$909$	−14.3155	−	19.7036i	−0.474816	−	0.653528i
$910$	−4.24597	+	13.1724i	−0.140753	+	0.436662i
$911$	17.2476	−	23.7392i	0.571438	−	0.786516i	−0.421287	−	0.906928i	$-0.638421\pi$
$911$	17.2476	−	23.7392i	0.571438	−	0.786516i	0.992724	+	0.120411i	$0.0384213\pi$
$912$	19.0837	−	4.97531i	0.631923	−	0.164749i
$913$	4.09350	−	25.8453i	0.135475	−	0.855356i
$914$	8.28513	−	14.2944i	0.274048	−	0.472816i
$915$	2.43618	−	2.72767i	0.0805375	−	0.0901739i
$916$	−15.0955	+	16.6516i	−0.498770	+	0.550186i
$917$	10.6556	−	5.42929i	0.351878	−	0.179291i
$918$	−33.3804	−	27.1246i	−1.10172	−	0.895244i
$919$	6.75696	−	20.7958i	0.222892	−	0.685990i	−0.775607	−	0.631216i	$-0.782556\pi$
$919$	6.75696	−	20.7958i	0.222892	−	0.685990i	0.998499	−	0.0547739i	$-0.0174438\pi$
$920$	12.4757	−	46.3661i	0.411313	−	1.52865i
$921$	6.58323	+	20.2611i	0.216925	+	0.667626i
$922$	−5.25297	+	13.6156i	−0.172997	+	0.448405i
$923$	−11.3160	−	71.4465i	−0.372471	−	2.35169i
$924$	−10.6504	+	2.22618i	−0.350372	+	0.0732358i
$925$	3.65429	−	2.41521i	0.120152	−	0.0794116i
$926$	1.68435	+	16.2906i	0.0553513	+	0.535342i
$927$	17.0118	−	2.69440i	0.558740	−	0.0884958i
$928$	−4.36619	+	0.191809i	−0.143327	+	0.00629644i
$929$	−12.2112	+	3.96767i	−0.400637	+	0.130175i	−0.502403	−	0.864633i	$-0.667551\pi$
$929$	−12.2112	+	3.96767i	−0.400637	+	0.130175i	0.101766	+	0.994808i	$0.467551\pi$
$930$	−31.3291	−	4.88699i	−1.02732	−	0.160251i
$931$	−3.53402	−	1.14827i	−0.115823	−	0.0376332i
$932$	0.329029	+	0.215260i	0.0107777	+	0.00705108i
$933$	6.85230	+	13.4484i	0.224334	+	0.440281i
$934$	−27.9638	+	25.0932i	−0.915003	+	0.821074i
$935$	−10.5016	−	48.4456i	−0.343439	−	1.58434i
$936$	14.5682	+	4.81537i	0.476178	+	0.157395i
$937$	−33.6277	−	5.32610i	−1.09857	−	0.173996i	−0.419273	−	0.907860i	$-0.637715\pi$
$937$	−33.6277	−	5.32610i	−1.09857	−	0.173996i	−0.679296	+	0.733864i	$0.737715\pi$
$938$	0.0602163	−	1.11297i	0.00196613	−	0.0363398i
$939$	−26.1368	−	18.9895i	−0.852941	−	0.619698i
$940$	−18.1856	+	8.11083i	−0.593148	+	0.264546i
$941$	20.9813	−	15.2438i	0.683972	−	0.496935i	−0.190701	−	0.981648i	$-0.561076\pi$
$941$	20.9813	−	15.2438i	0.683972	−	0.496935i	0.874673	+	0.484713i	$0.161076\pi$
$942$	−1.68746	−	2.60811i	−0.0549804	−	0.0849768i
$943$	40.9739	+	40.9739i	1.33429	+	1.33429i
$944$	1.45818	+	14.8388i	0.0474597	+	0.482961i
$945$	−3.20649	+	12.1626i	−0.104307	+	0.395649i
$946$	−22.4328	−	50.6152i	−0.729354	−	1.64564i
$947$	14.7764	+	7.52895i	0.480169	+	0.244658i	0.677283	−	0.735722i	$-0.263157\pi$
$947$	14.7764	+	7.52895i	0.480169	+	0.244658i	−0.197115	+	0.980380i	$0.563157\pi$
$948$	35.9702	−	13.6682i	1.16826	−	0.443924i
$949$		−	24.7469i		−	0.803320i
$950$	20.3141	−	16.6653i	0.659076	−	0.540693i
$951$		−	35.6042i		−	1.15455i
$952$	13.6609	−	6.87348i	0.442752	−	0.222771i
$953$	−20.0136	−	10.1974i	−0.648303	−	0.330327i	0.0987295	−	0.995114i	$-0.468522\pi$
$953$	−20.0136	−	10.1974i	−0.648303	−	0.330327i	−0.747033	+	0.664787i	$0.768522\pi$
$954$	−17.5206	+	7.76520i	−0.567251	+	0.251408i
$955$	15.4536	+	9.94740i	0.500067	+	0.321890i
$956$	−14.3006	−	1.55199i	−0.462515	−	0.0501949i
$957$	2.97202	+	2.97202i	0.0960719	+	0.0960719i
$958$	−8.77150	+	5.67520i	−0.283394	+	0.183358i
$959$	−11.3567	+	8.25113i	−0.366727	+	0.266443i
$960$	23.5896	+	2.62542i	0.761350	+	0.0847351i
$961$	21.1221	+	15.3461i	0.681359	+	0.495036i
$962$	−5.41435	−	0.292938i	−0.174566	−	0.00944471i
$963$	13.9270	+	2.20582i	0.448790	+	0.0710814i
$964$	1.45851	−	3.24627i	0.0469756	−	0.104555i
$965$	14.7851	−	33.5713i	0.475950	−	1.08070i
$966$	−9.51427	−	10.6027i	−0.306117	−	0.341136i
$967$	−24.5008	−	48.0856i	−0.787893	−	1.54633i	−0.836790	−	0.547524i	$-0.815571\pi$
$967$	−24.5008	−	48.0856i	−0.787893	−	1.54633i	0.0488971	−	0.998804i	$-0.484429\pi$
$968$	−7.53661	+	14.6077i	−0.242236	+	0.469510i
$969$	25.3527	+	8.23761i	0.814448	+	0.264630i
$970$	37.6370	−	6.05134i	1.20845	−	0.194297i
$971$	30.9985	−	10.0720i	0.994790	−	0.323227i	0.234008	−	0.972235i	$-0.424816\pi$
$971$	30.9985	−	10.0720i	0.994790	−	0.323227i	0.760782	+	0.649008i	$0.224816\pi$
$972$	22.9800	+	6.24088i	0.737085	+	0.200176i
$973$	−15.6138	+	2.47298i	−0.500555	+	0.0792801i
$974$	24.5103	−	2.53422i	0.785360	−	0.0812017i
$975$	−28.8504	+	3.26755i	−0.923952	+	0.104645i
$976$	4.51786	−	1.97496i	0.144613	−	0.0632170i
$977$	−8.28468	−	52.3074i	−0.265051	−	1.67346i	−0.657319	−	0.753612i	$-0.728310\pi$
$977$	−8.28468	−	52.3074i	−0.265051	−	1.67346i	0.392269	−	0.919851i	$-0.371690\pi$
$978$	0.171850	+	0.0663007i	0.00549515	+	0.00212006i
$979$	3.03086	+	9.32803i	0.0968667	+	0.298125i
$980$	−3.47732	−	2.81216i	−0.111079	−	0.0898312i
$981$	6.12170	−	18.8407i	0.195451	−	0.601536i
$982$	−30.9601	+	38.1005i	−0.987975	+	1.21584i
$983$	16.2320	−	8.27064i	0.517722	−	0.263792i	−0.175548	−	0.984471i	$-0.556170\pi$
$983$	16.2320	−	8.27064i	0.517722	−	0.263792i	0.693269	+	0.720679i	$0.256170\pi$
$984$	−16.9540	+	23.0879i	−0.540474	+	0.736016i
$985$	1.54199	−	15.2623i	0.0491319	−	0.486298i
$986$	−5.11098	−	2.96237i	−0.162767	−	0.0943409i
$987$	−0.924182	+	5.83506i	−0.0294170	+	0.185732i
$988$	−32.4865	+	1.59236i	−1.03353	+	0.0506598i
$989$	42.6063	−	58.6425i	1.35480	−	1.86472i
$990$	9.47680	+	12.9798i	0.301193	+	0.412525i
$991$	−25.0664	−	34.5009i	−0.796259	−	1.09596i	−0.993300	−	0.115561i	$-0.963133\pi$
$991$	−25.0664	−	34.5009i	−0.796259	−	1.09596i	0.197041	−	0.980395i	$-0.436867\pi$
$992$	−35.6540	−	23.5851i	−1.13202	−	0.748828i
$993$	−5.77497	+	5.77497i	−0.183263	+	0.183263i
$994$	22.8556	+	4.89852i	0.724935	+	0.155372i
$995$	−27.7454	+	10.7789i	−0.879589	+	0.341715i
$996$	8.41827	+	14.6955i	0.266743	+	0.465643i
$997$	9.34870	−	18.3479i	0.296076	−	0.581083i	−0.694267	−	0.719717i	$-0.744271\pi$
$997$	9.34870	−	18.3479i	0.296076	−	0.581083i	0.990344	+	0.138635i	$0.0442714\pi$
$998$	0.838180	+	3.14943i	0.0265321	+	0.0996935i
$999$	−4.92796			−0.155914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.bj.a.687.54	yes	720
4.3	odd	2	inner	700.2.bj.a.687.48	yes	720
25.23	odd	20	inner	700.2.bj.a.323.48	✓	720
100.23	even	20	inner	700.2.bj.a.323.54	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.2.bj.a.323.48	✓	720	25.23	odd	20	inner
700.2.bj.a.323.54	yes	720	100.23	even	20	inner
700.2.bj.a.687.48	yes	720	4.3	odd	2	inner
700.2.bj.a.687.54	yes	720	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.363714 + 1.36664i) q^{2} +(-0.602372 + 1.18222i) q^{3} +(-1.73542 + 0.994135i) q^{4} +(-2.08430 + 0.809739i) q^{5} +(-1.83477 - 0.393236i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.98983 - 2.01012i) q^{8} +(0.728560 + 1.00278i) q^{9} +(-1.86472 - 2.55398i) q^{10} +(-2.41003 + 3.31711i) q^{11} +(-0.129917 - 2.65049i) q^{12} +(-0.684643 + 4.32266i) q^{13} +(-1.22355 - 0.709177i) q^{14} +(0.298235 - 2.95187i) q^{15} +(2.02339 - 3.45049i) q^{16} +(4.81746 - 2.45462i) q^{17} +(-1.10545 + 1.36040i) q^{18} +(1.14827 - 3.53402i) q^{19} +(2.81216 - 3.47732i) q^{20} +(-0.410016 - 1.26190i) q^{21} +(-5.40987 - 2.08716i) q^{22} +(-1.18763 - 7.49840i) q^{23} +(3.57503 - 1.14157i) q^{24} +(3.68864 - 3.37549i) q^{25} +(-6.15655 + 0.636552i) q^{26} +(-5.55588 + 0.879964i) q^{27} +(0.524171 - 1.93009i) q^{28} +(-0.734772 + 0.238742i) q^{29} +(4.14263 - 0.666058i) q^{30} +(-7.18714 - 2.33524i) q^{31} +(5.45152 + 1.51026i) q^{32} +(-2.46983 - 4.84732i) q^{33} +(5.10677 + 5.69097i) q^{34} +(0.901253 - 2.04640i) q^{35} +(-2.26125 - 1.01596i) q^{36} +(0.865275 + 0.137046i) q^{37} +(5.24739 + 0.283905i) q^{38} +(-4.69794 - 3.41325i) q^{39} +(5.77508 + 2.57847i) q^{40} +(-6.17492 + 4.48634i) q^{41} +(1.57544 - 1.01932i) q^{42} +(6.75136 + 6.75136i) q^{43} +(0.884756 - 8.15249i) q^{44} +(-2.33053 - 1.50015i) q^{45} +(9.81568 - 4.35034i) q^{46} +(-3.96724 - 2.02141i) q^{47} +(2.86041 + 4.47058i) q^{48} -1.00000i q^{49} +(5.95469 + 3.81335i) q^{50} +7.17390i q^{51} +(-3.10916 - 8.18228i) q^{52} +(9.74120 + 4.96339i) q^{53} +(-3.22335 - 7.27284i) q^{54} +(2.33723 - 8.86537i) q^{55} +(2.82839 + 0.0143529i) q^{56} +(3.48631 + 3.48631i) q^{57} +(-0.593522 - 0.917337i) q^{58} +(-3.01566 + 2.19101i) q^{59} +(2.41700 + 5.41924i) q^{60} +(0.997249 + 0.724544i) q^{61} +(0.577378 - 10.6716i) q^{62} +(-1.22424 - 0.193900i) q^{63} +(-0.0811913 + 7.99959i) q^{64} +(-2.07323 - 9.56412i) q^{65} +(5.72624 - 5.13842i) q^{66} +(0.357808 + 0.702238i) q^{67} +(-5.92012 + 9.04901i) q^{68} +(9.58017 + 3.11279i) q^{69} +(3.12449 + 0.487387i) q^{70} +(-15.7194 + 5.10754i) q^{71} +(0.565998 - 3.45984i) q^{72} +(-5.58483 + 0.884550i) q^{73} +(0.127420 + 1.23237i) q^{74} +(1.76864 + 6.39409i) q^{75} +(1.52055 + 7.27457i) q^{76} +(-0.641409 - 4.04970i) q^{77} +(2.95599 - 7.66185i) q^{78} +(4.48089 + 13.7908i) q^{79} +(-1.42337 + 8.83029i) q^{80} +(1.15731 - 3.56184i) q^{81} +(-8.37713 - 6.80716i) q^{82} +(-5.68644 + 2.89739i) q^{83} +(1.96605 + 1.78232i) q^{84} +(-8.05345 + 9.01706i) q^{85} +(-6.77113 + 11.6823i) q^{86} +(0.160360 - 1.01247i) q^{87} +(11.4633 - 1.75603i) q^{88} +(1.40605 - 1.93526i) q^{89} +(1.20252 - 3.73062i) q^{90} +(-2.57247 - 3.54070i) q^{91} +(9.51547 + 11.8322i) q^{92} +(7.09011 - 7.09011i) q^{93} +(1.31960 - 6.15701i) q^{94} +(0.468287 + 8.29578i) q^{95} +(-5.06931 + 5.53517i) q^{96} +(-5.47273 + 10.7408i) q^{97} +(1.36664 - 0.363714i) q^{98} -5.08217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q + 16 q^{10} + 16 q^{12} + 4 q^{13} + 20 q^{17} - 28 q^{18} - 20 q^{20} - 4 q^{22} + 20 q^{25} + 4 q^{30} - 20 q^{37} - 64 q^{40} - 80 q^{42} - 140 q^{44} - 20 q^{45} - 236 q^{48} - 40 q^{50} - 16 q^{52}+ \cdots - 20 q^{97}+O(q^{100}) \) 720 * q + 16 * q^10 + 16 * q^12 + 4 * q^13 + 20 * q^17 - 28 * q^18 - 20 * q^20 - 4 * q^22 + 20 * q^25 + 4 * q^30 - 20 * q^37 - 64 * q^40 - 80 * q^42 - 140 * q^44 - 20 * q^45 - 236 * q^48 - 40 * q^50 - 16 * q^52 + 44 * q^53 - 260 * q^54 + 16 * q^57 - 136 * q^58 - 140 * q^60 - 140 * q^62 - 4 * q^65 - 80 * q^68 - 80 * q^72 - 52 * q^73 + 76 * q^78 + 20 * q^80 + 180 * q^81 + 24 * q^82 - 80 * q^85 + 160 * q^88 - 260 * q^89 + 16 * q^90 + 256 * q^92 - 112 * q^93 + 320 * q^94 - 40 * q^96 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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