LMFDB - Embedded newform 357.2.bl.a.199.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] 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("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			199.7
Character	$\chi$	$=$	357.199
Dual form			357.2.bl.a.61.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.768957 + 1.00212i) q^{2} +(0.997859 - 0.0654031i) q^{3} +(0.104680 + 0.390673i) q^{4} +(-2.22223 + 0.754346i) q^{5} +(-0.701768 + 1.05027i) q^{6} +(-1.93316 + 1.80635i) q^{7} +(-2.80599 - 1.16228i) q^{8} +(0.991445 - 0.130526i) q^{9} +(0.952852 - 2.80701i) q^{10} +(-1.75355 - 3.55585i) q^{11} +(0.130007 + 0.382990i) q^{12} +(-2.79324 + 2.79324i) q^{13} +(-0.323664 - 3.32627i) q^{14} +(-2.16814 + 0.898072i) q^{15} +(2.62190 - 1.51375i) q^{16} +(1.33935 - 3.89951i) q^{17} +(-0.631575 + 1.09392i) q^{18} +(-0.0887447 - 0.0680962i) q^{19} +(-0.527327 - 0.789200i) q^{20} +(-1.81088 + 1.92891i) q^{21} +(4.91180 + 0.977018i) q^{22} +(-0.0663552 + 1.01238i) q^{23} +(-2.87600 - 0.976271i) q^{24} +(0.402513 - 0.308859i) q^{25} +(-0.651291 - 4.94704i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-0.908054 - 0.566144i) q^{28} +(-1.75511 + 8.82356i) q^{29} +(0.767225 - 2.86332i) q^{30} +(0.565675 + 8.63053i) q^{31} +(0.293706 - 2.23092i) q^{32} +(-1.98236 - 3.43354i) q^{33} +(2.87789 + 4.34074i) q^{34} +(2.93333 - 5.47239i) q^{35} +(0.154778 + 0.373667i) q^{36} +(-4.39200 - 2.16589i) q^{37} +(0.136482 - 0.0365702i) q^{38} +(-2.60457 + 2.96994i) q^{39} +(7.11233 + 0.466167i) q^{40} +(1.46784 + 7.37932i) q^{41} +(-0.540519 - 3.29798i) q^{42} +(2.03570 - 4.91462i) q^{43} +(1.20561 - 1.05729i) q^{44} +(-2.10476 + 1.03795i) q^{45} +(-0.963511 - 0.844976i) q^{46} +(-7.58411 - 2.03215i) q^{47} +(2.51728 - 1.68199i) q^{48} +(0.474231 - 6.98392i) q^{49} +0.640867i q^{50} +(1.08144 - 3.97876i) q^{51} +(-1.38364 - 0.798843i) q^{52} +(-5.01013 - 0.659596i) q^{53} +(-0.558677 + 1.13288i) q^{54} +(6.57913 + 6.57913i) q^{55} +(7.52392 - 2.82172i) q^{56} +(-0.0930084 - 0.0621463i) q^{57} +(-7.49269 - 8.54377i) q^{58} +(2.99139 + 3.89846i) q^{59} +(-0.577814 - 0.753021i) q^{60} +(0.593979 + 0.677304i) q^{61} +(-9.08384 - 6.06963i) q^{62} +(-1.68085 + 2.04322i) q^{63} +(6.29136 + 6.29136i) q^{64} +(4.10015 - 8.31429i) q^{65} +(4.96518 + 0.653679i) q^{66} +(-4.06742 - 2.34833i) q^{67} +(1.66363 + 0.115043i) q^{68} +1.01456i q^{69} +(3.22842 + 7.14759i) q^{70} +(-10.7811 + 7.20372i) q^{71} +(-2.93369 - 0.786081i) q^{72} +(12.6383 + 11.0835i) q^{73} +(5.54775 - 2.73585i) q^{74} +(0.381451 - 0.334523i) q^{75} +(0.0173135 - 0.0417985i) q^{76} +(9.81298 + 3.70651i) q^{77} +(-0.973448 - 4.89386i) q^{78} +(10.1494 + 0.665230i) q^{79} +(-4.68458 + 5.34174i) q^{80} +(0.965926 - 0.258819i) q^{81} +(-8.52369 - 4.20342i) q^{82} +(4.35456 + 10.5128i) q^{83} +(-0.943137 - 0.505543i) q^{84} +(-0.0347577 + 9.67594i) q^{85} +(3.35969 + 5.81916i) q^{86} +(-1.17427 + 8.91946i) q^{87} +(0.787556 + 12.0158i) q^{88} +(-2.62034 + 9.77923i) q^{89} +(0.578312 - 2.90737i) q^{90} +(0.354228 - 10.4453i) q^{91} +(-0.402457 + 0.0800537i) q^{92} +(1.12893 + 8.57505i) q^{93} +(7.86832 - 6.03757i) q^{94} +(0.248580 + 0.0843814i) q^{95} +(0.147168 - 2.24535i) q^{96} +(-8.74519 - 1.73953i) q^{97} +(6.63409 + 5.84557i) q^{98} +(-2.20268 - 3.29654i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{16}\right)$	$1$

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 $

$2$	−0.768957	+	1.00212i	−0.543734	+	0.708608i	−0.981711	−	0.190378i	$-0.939029\pi$
$2$	−0.768957	+	1.00212i	−0.543734	+	0.708608i	0.437976	+	0.898986i	$0.355695\pi$
$3$	0.997859	−	0.0654031i	0.576114	−	0.0377605i
$3$	0.997859	−	0.0654031i	0.576114	−	0.0377605i
$4$	0.104680	+	0.390673i	0.0523402	+	0.195336i
$5$	−2.22223	+	0.754346i	−0.993813	+	0.337354i	−0.770533	−	0.637400i	$-0.780010\pi$
$5$	−2.22223	+	0.754346i	−0.993813	+	0.337354i	−0.223280	+	0.974754i	$0.571676\pi$
$6$	−0.701768	+	1.05027i	−0.286496	+	0.428771i
$7$	−1.93316	+	1.80635i	−0.730667	+	0.682734i
$7$	−1.93316	+	1.80635i	−0.730667	+	0.682734i
$8$	−2.80599	−	1.16228i	−0.992068	−	0.410928i
$9$	0.991445	−	0.130526i	0.330482	−	0.0435087i
$10$	0.952852	−	2.80701i	0.301318	−	0.887655i
$11$	−1.75355	−	3.55585i	−0.528715	−	1.07213i	−0.983396	−	0.181473i	$-0.941913\pi$
$11$	−1.75355	−	3.55585i	−0.528715	−	1.07213i	0.454681	−	0.890654i	$-0.349753\pi$
$12$	0.130007	+	0.382990i	0.0375299	+	0.110560i
$13$	−2.79324	+	2.79324i	−0.774704	+	0.774704i	−0.978925	−	0.204221i	$-0.934534\pi$
$13$	−2.79324	+	2.79324i	−0.774704	+	0.774704i	0.204221	+	0.978925i	$0.434534\pi$
$14$	−0.323664	−	3.32627i	−0.0865028	−	0.888983i
$15$	−2.16814	+	0.898072i	−0.559811	+	0.231881i
$16$	2.62190	−	1.51375i	0.655475	−	0.378439i
$17$	1.33935	−	3.89951i	0.324839	−	0.945769i
$17$	1.33935	−	3.89951i	0.324839	−	0.945769i
$18$	−0.631575	+	1.09392i	−0.148864	+	0.257839i
$19$	−0.0887447	−	0.0680962i	−0.0203594	−	0.0156223i	0.598532	−	0.801099i	$-0.295751\pi$
$19$	−0.0887447	−	0.0680962i	−0.0203594	−	0.0156223i	−0.618891	+	0.785477i	$0.712418\pi$
$20$	−0.527327	−	0.789200i	−0.117914	−	0.176470i
$21$	−1.81088	+	1.92891i	−0.395167	+	0.420923i
$22$	4.91180	+	0.977018i	1.04720	+	0.208301i
$23$	−0.0663552	+	1.01238i	−0.0138360	+	0.211097i	0.985343	+	0.170585i	$0.0545656\pi$
$23$	−0.0663552	+	1.01238i	−0.0138360	+	0.211097i	−0.999179	+	0.0405122i	$0.987101\pi$
$24$	−2.87600	−	0.976271i	−0.587061	−	0.199280i
$25$	0.402513	−	0.308859i	0.0805025	−	0.0617718i
$26$	−0.651291	−	4.94704i	−0.127729	−	0.970195i
$27$	0.980785	−	0.195090i	0.188752	−	0.0375451i
$28$	−0.908054	−	0.566144i	−0.171606	−	0.106991i
$29$	−1.75511	+	8.82356i	−0.325917	+	1.63849i	0.376277	+	0.926507i	$0.377204\pi$
$29$	−1.75511	+	8.82356i	−0.325917	+	1.63849i	−0.702193	+	0.711986i	$0.747796\pi$
$30$	0.767225	−	2.86332i	0.140075	−	0.522768i
$31$	0.565675	+	8.63053i	0.101598	+	1.55009i	0.679312	+	0.733849i	$0.262278\pi$
$31$	0.565675	+	8.63053i	0.101598	+	1.55009i	−0.577714	+	0.816239i	$0.696055\pi$
$32$	0.293706	−	2.23092i	0.0519205	−	0.394375i
$33$	−1.98236	−	3.43354i	−0.345084	−	0.597703i
$34$	2.87789	+	4.34074i	0.493554	+	0.744431i
$35$	2.93333	−	5.47239i	0.495823	−	0.925003i
$36$	0.154778	+	0.373667i	0.0257963	+	0.0622778i
$37$	−4.39200	−	2.16589i	−0.722040	−	0.356071i	0.0438539	−	0.999038i	$-0.486036\pi$
$37$	−4.39200	−	2.16589i	−0.722040	−	0.356071i	−0.765894	+	0.642967i	$0.777703\pi$
$38$	0.136482	−	0.0365702i	0.0221403	−	0.00593246i
$39$	−2.60457	+	2.96994i	−0.417065	+	0.475571i
$40$	7.11233	+	0.466167i	1.12456	+	0.0737074i
$41$	1.46784	+	7.37932i	0.229238	+	1.15246i	0.908282	+	0.418358i	$0.137394\pi$
$41$	1.46784	+	7.37932i	0.229238	+	1.15246i	−0.679044	+	0.734097i	$0.737606\pi$
$42$	−0.540519	−	3.29798i	−0.0834040	−	0.508889i
$43$	2.03570	−	4.91462i	0.310442	−	0.749473i	−0.689247	−	0.724527i	$-0.742058\pi$
$43$	2.03570	−	4.91462i	0.310442	−	0.749473i	0.999689	−	0.0249466i	$-0.00794156\pi$
$44$	1.20561	−	1.05729i	0.181752	−	0.159393i
$45$	−2.10476	+	1.03795i	−0.313759	+	0.154729i
$46$	−0.963511	−	0.844976i	−0.142062	−	0.124585i
$47$	−7.58411	−	2.03215i	−1.10626	−	0.296420i	−0.340946	−	0.940083i	$-0.610747\pi$
$47$	−7.58411	−	2.03215i	−1.10626	−	0.296420i	−0.765309	+	0.643663i	$0.777414\pi$
$48$	2.51728	−	1.68199i	0.363338	−	0.242775i
$49$	0.474231	−	6.98392i	0.0677473	−	0.997703i
$50$			0.640867i			0.0906322i
$51$	1.08144	−	3.97876i	0.151432	−	0.557137i
$52$	−1.38364	−	0.798843i	−0.191876	−	0.110780i
$53$	−5.01013	−	0.659596i	−0.688194	−	0.0906025i	−0.221684	−	0.975118i	$-0.571155\pi$
$53$	−5.01013	−	0.659596i	−0.688194	−	0.0906025i	−0.466510	+	0.884516i	$0.654489\pi$
$54$	−0.558677	+	1.13288i	−0.0760263	+	0.154166i
$55$	6.57913	+	6.57913i	0.887130	+	0.887130i
$56$	7.52392	−	2.82172i	1.00543	−	0.377068i
$57$	−0.0930084	−	0.0621463i	−0.0123193	−	0.00823147i
$58$	−7.49269	−	8.54377i	−0.983838	−	1.12185i
$59$	2.99139	+	3.89846i	0.389446	+	0.507536i	0.946395	−	0.323010i	$-0.104695\pi$
$59$	2.99139	+	3.89846i	0.389446	+	0.507536i	−0.556949	+	0.830547i	$0.688028\pi$
$60$	−0.577814	−	0.753021i	−0.0745954	−	0.0972146i
$61$	0.593979	+	0.677304i	0.0760513	+	0.0867198i	0.788614	−	0.614888i	$-0.210799\pi$
$61$	0.593979	+	0.677304i	0.0760513	+	0.0867198i	−0.712563	+	0.701608i	$0.752466\pi$
$62$	−9.08384	−	6.06963i	−1.15365	−	0.770843i
$63$	−1.68085	+	2.04322i	−0.211767	+	0.257422i
$64$	6.29136	+	6.29136i	0.786420	+	0.786420i
$65$	4.10015	−	8.31429i	0.508561	−	1.03126i
$66$	4.96518	+	0.653679i	0.611172	+	0.0804623i
$67$	−4.06742	−	2.34833i	−0.496915	−	0.286894i	0.230524	−	0.973067i	$-0.425956\pi$
$67$	−4.06742	−	2.34833i	−0.496915	−	0.286894i	−0.727438	+	0.686173i	$0.759289\pi$
$68$	1.66363	+	0.115043i	0.201745	+	0.0139511i
$69$			1.01456i			0.122138i
$70$	3.22842	+	7.14759i	0.385869	+	0.854300i
$71$	−10.7811	+	7.20372i	−1.27949	+	0.854925i	−0.994615	−	0.103641i	$-0.966951\pi$
$71$	−10.7811	+	7.20372i	−1.27949	+	0.854925i	−0.284870	+	0.958566i	$0.591951\pi$
$72$	−2.93369	−	0.786081i	−0.345739	−	0.0926405i
$73$	12.6383	+	11.0835i	1.47920	+	1.29722i	0.858093	+	0.513494i	$0.171649\pi$
$73$	12.6383	+	11.0835i	1.47920	+	1.29722i	0.621105	+	0.783727i	$0.286684\pi$
$74$	5.54775	−	2.73585i	0.644912	−	0.318036i
$75$	0.381451	−	0.334523i	0.0440461	−	0.0386274i
$76$	0.0173135	−	0.0417985i	0.00198599	−	0.00479461i
$77$	9.81298	+	3.70651i	1.11829	+	0.422396i
$78$	−0.973448	−	4.89386i	−0.110221	−	0.554120i
$79$	10.1494	+	0.665230i	1.14190	+	0.0748442i	0.624590	−	0.780953i	$-0.285266\pi$
$79$	10.1494	+	0.665230i	1.14190	+	0.0748442i	0.517312	+	0.855797i	$0.326933\pi$
$80$	−4.68458	+	5.34174i	−0.523752	+	0.597224i
$81$	0.965926	−	0.258819i	0.107325	−	0.0287577i
$82$	−8.52369	−	4.20342i	−0.941284	−	0.464190i
$83$	4.35456	+	10.5128i	0.477976	+	1.15394i	0.960557	+	0.278084i	$0.0896993\pi$
$83$	4.35456	+	10.5128i	0.477976	+	1.15394i	−0.482581	+	0.875851i	$0.660301\pi$
$84$	−0.943137	−	0.505543i	−0.102905	−	0.0551592i
$85$	−0.0347577	+	9.67594i	−0.00377000	+	1.04950i
$86$	3.35969	+	5.81916i	0.362285	+	0.627496i
$87$	−1.17427	+	8.91946i	−0.125895	+	0.956266i
$88$	0.787556	+	12.0158i	0.0839538	+	1.28089i
$89$	−2.62034	+	9.77923i	−0.277755	+	1.03660i	0.676217	+	0.736702i	$0.263618\pi$
$89$	−2.62034	+	9.77923i	−0.277755	+	1.03660i	−0.953972	+	0.299894i	$0.903049\pi$
$90$	0.578312	−	2.90737i	0.0609594	−	0.306464i
$91$	0.354228	−	10.4453i	0.0371332	−	1.09497i
$92$	−0.402457	+	0.0800537i	−0.0419590	+	0.00834617i
$93$	1.12893	+	8.57505i	0.117064	+	0.889192i
$94$	7.86832	−	6.03757i	0.811555	−	0.622728i
$95$	0.248580	+	0.0843814i	0.0255037	+	0.00865735i
$96$	0.147168	−	2.24535i	0.0150203	−	0.229166i
$97$	−8.74519	−	1.73953i	−0.887939	−	0.176622i	−0.270012	−	0.962857i	$-0.587028\pi$
$97$	−8.74519	−	1.73953i	−0.887939	−	0.176622i	−0.617928	+	0.786235i	$0.712028\pi$
$98$	6.63409	+	5.84557i	0.670144	+	0.590492i
$99$	−2.20268	−	3.29654i	−0.221377	−	0.331315i
$100$	0.162798	+	0.124919i	0.0162798	+	0.0124919i
$101$	4.59309	−	7.95547i	0.457030	−	0.791599i	−0.541772	−	0.840525i	$-0.682247\pi$
$101$	4.59309	−	7.95547i	0.457030	−	0.791599i	0.998802	+	0.0489261i	$0.0155799\pi$
$102$	3.15563	+	4.14322i	0.312454	+	0.410240i
$103$	8.82190	−	5.09333i	0.869247	−	0.501860i	0.00214937	−	0.999998i	$-0.499316\pi$
$103$	8.82190	−	5.09333i	0.869247	−	0.501860i	0.867098	+	0.498137i	$0.165983\pi$
$104$	11.0843	−	4.59128i	1.08691	−	0.450212i
$105$	2.56913	−	5.65253i	0.250722	−	0.551630i
$106$	4.51357	−	4.51357i	0.438397	−	0.438397i
$107$	−1.21106	−	3.56767i	−0.117078	−	0.344900i	0.872556	−	0.488514i	$-0.162461\pi$
$107$	−1.21106	−	3.56767i	−0.117078	−	0.344900i	−0.989634	+	0.143614i	$0.954128\pi$
$108$	0.178885	+	0.362744i	0.0172133	+	0.0349050i
$109$	3.64686	−	10.7433i	0.349306	−	1.02902i	−0.620304	−	0.784362i	$-0.712991\pi$
$109$	3.64686	−	10.7433i	0.349306	−	1.02902i	0.969609	−	0.244659i	$-0.0786761\pi$
$110$	−11.6522	+	1.53404i	−1.11099	+	0.146265i
$111$	−4.52425	−	1.87400i	−0.429423	−	0.177873i
$112$	−2.33419	+	7.66239i	−0.220561	+	0.724028i
$113$	−3.58394	+	5.36375i	−0.337149	+	0.504579i	−0.960845	−	0.277088i	$-0.910631\pi$
$113$	−3.58394	+	5.36375i	−0.337149	+	0.504579i	0.623695	+	0.781668i	$0.285631\pi$
$114$	0.133798	−	0.0454182i	0.0125313	−	0.00425380i
$115$	−0.616232	−	2.29981i	−0.0574639	−	0.214458i
$116$	−3.63085	+	0.237978i	−0.337116	+	0.0220957i
$117$	−2.40475	+	3.13393i	−0.222319	+	0.289732i
$118$	−6.20699			−0.571400
$119$	4.45469	+	9.95770i	0.408360	+	0.912821i
$120$	7.12759			0.650657
$121$	−2.87273	+	3.74381i	−0.261157	+	0.340346i
$122$	−1.13549	+	0.0744237i	−0.102802	+	0.00673801i
$123$	1.94733	+	7.26752i	0.175584	+	0.655290i
$124$	−3.31250	+	1.12444i	−0.297471	+	0.100978i
$125$	5.85750	−	8.76637i	0.523911	−	0.784088i
$126$	−0.755060	−	3.25557i	−0.0672661	−	0.290029i
$127$	−6.14766	−	2.54644i	−0.545516	−	0.225960i	0.0928674	−	0.995678i	$-0.470397\pi$
$127$	−6.14766	−	2.54644i	−0.545516	−	0.225960i	−0.638384	+	0.769718i	$0.720397\pi$
$128$	−6.68065	+	0.879525i	−0.590492	+	0.0777397i
$129$	1.70991	−	5.03724i	0.150550	−	0.443505i
$130$	5.17910	+	10.5022i	0.454237	+	0.921102i
$131$	2.46882	+	7.27291i	0.215702	+	0.635437i	0.999889	+	0.0149127i	$0.00474703\pi$
$131$	2.46882	+	7.27291i	0.215702	+	0.635437i	−0.784187	+	0.620525i	$0.786920\pi$
$132$	1.13388	−	1.13388i	0.0986914	−	0.0986914i
$133$	0.294563	−	0.0286626i	0.0255419	−	0.00248536i
$134$	5.48098	−	2.27030i	0.473485	−	0.196124i
$135$	−2.03237	+	1.17339i	−0.174918	+	0.100989i
$136$	−8.29051	+	9.38529i	−0.710905	+	0.804782i
$137$	1.17181	−	2.02964i	0.100115	−	0.173404i	−0.811617	−	0.584190i	$-0.801412\pi$
$137$	1.17181	−	2.02964i	0.100115	−	0.173404i	0.911732	+	0.410786i	$0.134746\pi$
$138$	−1.01671	−	0.780150i	−0.0865483	−	0.0664108i
$139$	9.18508	+	13.7464i	0.779068	+	1.16596i	0.982389	+	0.186846i	$0.0598264\pi$
$139$	9.18508	+	13.7464i	0.779068	+	1.16596i	−0.203321	+	0.979112i	$0.565174\pi$
$140$	2.44498	+	0.573117i	0.206638	+	0.0484373i
$141$	−7.70078	−	1.53178i	−0.648522	−	0.128999i
$142$	1.07120	−	16.3434i	0.0898932	−	1.37151i
$143$	14.8304	+	5.03424i	1.24018	+	0.420984i
$144$	2.40188	−	1.84303i	0.200157	−	0.153586i
$145$	−2.75575	−	20.9320i	−0.228852	−	1.73830i
$146$	−20.8253	+	4.14241i	−1.72351	+	0.342828i
$147$	0.0164460	−	6.99998i	0.00135644	−	0.577349i
$148$	0.386399	−	1.94256i	0.0317618	−	0.159677i
$149$	1.08096	−	4.03419i	0.0885556	−	0.330494i	−0.907408	−	0.420250i	$-0.861942\pi$
$149$	1.08096	−	4.03419i	0.0885556	−	0.330494i	0.995964	+	0.0897566i	$0.0286089\pi$
$150$	0.0419147	+	0.639494i	0.00342232	+	0.0522145i
$151$	2.02630	−	15.3913i	0.164898	−	1.25252i	−0.686159	−	0.727451i	$-0.740705\pi$
$151$	2.02630	−	15.3913i	0.164898	−	1.25252i	0.851057	−	0.525073i	$-0.175962\pi$
$152$	0.169870	+	0.294224i	0.0137783	+	0.0238647i
$153$	0.818899	−	4.04097i	0.0662041	−	0.326693i
$154$	−11.2601	+	6.98367i	−0.907368	+	0.562761i
$155$	−7.76747	−	18.7523i	−0.623898	−	1.50622i
$156$	−1.43292	−	0.706639i	−0.114726	−	0.0565764i
$157$	−17.9773	+	4.81700i	−1.43474	+	0.384438i	−0.890689	−	0.454612i	$-0.849778\pi$
$157$	−17.9773	+	4.81700i	−1.43474	+	0.384438i	−0.544053	+	0.839051i	$0.683111\pi$
$158$	−8.47112	+	9.65947i	−0.673927	+	0.768466i
$159$	−5.04254	−	0.330506i	−0.399900	−	0.0262108i
$160$	1.03020	+	5.17918i	0.0814448	+	0.409450i
$161$	−1.70044	−	2.07696i	−0.134014	−	0.163688i
$162$	−0.483386	+	1.16700i	−0.0379784	+	0.0916880i
$163$	8.47319	−	7.43079i	0.663671	−	0.582024i	−0.259814	−	0.965659i	$-0.583661\pi$
$163$	8.47319	−	7.43079i	0.663671	−	0.582024i	0.923485	+	0.383635i	$0.125328\pi$
$164$	−2.72924	+	1.34591i	−0.213118	+	0.105098i
$165$	6.99534	+	6.13475i	0.544587	+	0.477590i
$166$	−13.8836	−	3.72011i	−1.07758	−	0.288737i
$167$	1.71012	−	1.14266i	0.132333	−	0.0884220i	−0.487642	−	0.873044i	$-0.662143\pi$
$167$	1.71012	−	1.14266i	0.132333	−	0.0884220i	0.619975	+	0.784622i	$0.287143\pi$
$168$	7.32326	−	3.30776i	0.565002	−	0.255199i
$169$		−	2.60433i		−	0.200333i
$170$	−9.66976	−	7.47521i	−0.741637	−	0.573322i
$171$	−0.0968739	−	0.0559302i	−0.00740813	−	0.00427709i
$172$	2.13311	+	0.280829i	0.162648	+	0.0214130i
$173$	2.15456	−	4.36902i	0.163808	−	0.332171i	−0.799456	−	0.600724i	$-0.794879\pi$
$173$	2.15456	−	4.36902i	0.163808	−	0.332171i	0.963265	+	0.268554i	$0.0865456\pi$
$174$	−8.03544	−	8.03544i	−0.609165	−	0.609165i
$175$	−0.220216	+	1.32415i	−0.0166468	+	0.100096i
$176$	−9.98031	−	6.66863i	−0.752294	−	0.502667i
$177$	3.23996	+	3.69447i	0.243530	+	0.277693i
$178$	−7.78508	−	10.1457i	−0.583516	−	0.760453i
$179$	−14.6076	−	19.0370i	−1.09182	−	1.42289i	−0.896986	−	0.442058i	$-0.854249\pi$
$179$	−14.6076	−	19.0370i	−1.09182	−	1.42289i	−0.194838	−	0.980835i	$-0.562418\pi$
$180$	−0.625826	−	0.713618i	−0.0466464	−	0.0531900i
$181$	−12.5478	−	8.38416i	−0.932669	−	0.623189i	−0.00637033	−	0.999980i	$-0.502028\pi$
$181$	−12.5478	−	8.38416i	−0.932669	−	0.623189i	−0.926299	+	0.376790i	$0.877028\pi$
$182$	10.1951	+	8.38698i	0.755713	+	0.621684i
$183$	0.637005	+	0.637005i	0.0470888	+	0.0470888i
$184$	1.36287	−	2.76362i	0.100472	−	0.203737i
$185$	11.3939	+	1.50003i	0.837694	+	0.110284i
$186$	−9.46136	−	5.46252i	−0.693741	−	0.400531i
$187$	−16.2147	+	2.07547i	−1.18573	+	0.151774i
$188$		−	3.17563i		−	0.231606i
$189$	−1.54362	+	2.14878i	−0.112282	+	0.156301i
$190$	−0.275708	+	0.184222i	−0.0200019	+	0.0133649i
$191$	14.0065	+	3.75303i	1.01348	+	0.271560i	0.727081	−	0.686552i	$-0.240877\pi$
$191$	14.0065	+	3.75303i	1.01348	+	0.271560i	0.286394	+	0.958112i	$0.407543\pi$
$192$	6.68936	+	5.86641i	0.482763	+	0.423372i
$193$	−11.8170	+	5.82750i	−0.850606	+	0.419472i	−0.814700	−	0.579883i	$-0.803098\pi$
$193$	−11.8170	+	5.82750i	−0.850606	+	0.419472i	−0.0359060	+	0.999355i	$0.511432\pi$
$194$	8.46789	−	7.42614i	0.607959	−	0.533166i
$195$	3.54759	−	8.56465i	0.254048	−	0.613327i
$196$	2.77807	−	0.545810i	0.198433	−	0.0389864i
$197$	1.87855	+	9.44410i	0.133841	+	0.672864i	0.988199	+	0.153179i	$0.0489510\pi$
$197$	1.87855	+	9.44410i	0.133841	+	0.672864i	−0.854357	+	0.519686i	$0.826049\pi$
$198$	4.99731	+	0.327541i	0.355143	+	0.0232773i
$199$	−0.889957	+	1.01480i	−0.0630873	+	0.0719373i	−0.782523	−	0.622622i	$-0.786067\pi$
$199$	−0.889957	+	1.01480i	−0.0630873	+	0.0719373i	0.719435	+	0.694560i	$0.244401\pi$
$200$	−1.48843	+	0.398823i	−0.105248	+	0.0282010i
$201$	−4.21230	−	2.07728i	−0.297113	−	0.146520i
$202$	4.44048	+	10.7203i	0.312431	+	0.754275i
$203$	−12.5455	−	20.2277i	−0.880520	−	1.41971i
$204$	1.66760	+	0.00599030i	0.116755	+	0.000419405i
$205$	−8.82844	−	15.2913i	−0.616605	−	1.06799i
$206$	−1.67951	+	12.7572i	−0.117017	+	0.888835i
$207$	0.0663552	+	1.01238i	0.00461201	+	0.0703656i
$208$	−3.09531	+	11.5519i	−0.214621	+	0.800977i
$209$	−0.0865214	+	0.434973i	−0.00598481	+	0.0300877i
$210$	3.68898	+	6.92114i	0.254564	+	0.477604i
$211$	10.5715	−	2.10280i	0.727771	−	0.144763i	0.182720	−	0.983165i	$-0.441510\pi$
$211$	10.5715	−	2.10280i	0.727771	−	0.144763i	0.545052	+	0.838402i	$0.316510\pi$
$212$	−0.266776	−	2.02637i	−0.0183223	−	0.139171i
$213$	−10.2869	+	7.89342i	−0.704847	+	0.540848i
$214$	4.50651	+	1.52975i	0.308058	+	0.104572i
$215$	−0.816479	+	12.4571i	−0.0556834	+	0.849565i
$216$	−2.97883	−	0.592525i	−0.202683	−	0.0403162i
$217$	−16.6833	−	15.6624i	−1.13253	−	1.06323i
$218$	7.96184	+	11.9157i	0.539244	+	0.807035i
$219$	13.3361	+	10.2332i	0.901171	+	0.691493i
$220$	−1.88158	+	3.25899i	−0.126856	+	0.219721i
$221$	7.15113	+	14.6333i	0.481037	+	0.984345i
$222$	5.35694	−	3.09283i	0.359534	−	0.207577i
$223$	−2.18713	+	0.905939i	−0.146461	+	0.0606661i	−0.454710	−	0.890640i	$-0.650257\pi$
$223$	−2.18713	+	0.905939i	−0.146461	+	0.0606661i	0.308249	+	0.951306i	$0.400257\pi$
$224$	3.46203	+	4.84327i	0.231317	+	0.323605i
$225$	0.358755	−	0.358755i	0.0239170	−	0.0239170i
$226$	−2.61925	−	7.71605i	−0.174230	−	0.513264i
$227$	−5.51635	−	11.1861i	−0.366133	−	0.742445i	0.633374	−	0.773846i	$-0.281670\pi$
$227$	−5.51635	−	11.1861i	−0.366133	−	0.742445i	−0.999507	+	0.0314014i	$0.990003\pi$
$228$	0.0145427	−	0.0428413i	0.000963112	−	0.00283724i
$229$	−8.00543	+	1.05394i	−0.529014	+	0.0696460i	−0.390302	−	0.920687i	$-0.627629\pi$
$229$	−8.00543	+	1.05394i	−0.529014	+	0.0696460i	−0.138712	+	0.990333i	$0.544296\pi$
$230$	2.77855	+	1.15091i	0.183212	+	0.0758889i
$231$	10.0344	+	3.05677i	0.660214	+	0.201121i
$232$	15.1803	−	22.7189i	0.996635	−	1.49157i
$233$	−20.3812	+	6.91850i	−1.33522	+	0.453246i	−0.895569	−	0.444923i	$-0.853231\pi$
$233$	−20.3812	+	6.91850i	−1.33522	+	0.453246i	−0.439650	+	0.898169i	$0.644898\pi$
$234$	−1.29144	−	4.81971i	−0.0844239	−	0.315074i
$235$	18.3866	−	1.20512i	1.19941	−	0.0786134i
$236$	−1.20988	+	1.57675i	−0.0787566	+	0.102638i
$237$	10.1712			0.660692
$238$	−13.4043	−	3.19289i	−0.868872	−	0.206964i
$239$	30.1150			1.94798			0.973988	−	0.226600i	$-0.0727610\pi$
$239$	30.1150			1.94798			0.973988	+	0.226600i	$0.0727610\pi$
$240$	−4.32518	+	5.63668i	−0.279189	+	0.363846i
$241$	−19.2288	+	1.26033i	−1.23864	+	0.0811847i	−0.670601	−	0.741818i	$-0.733964\pi$
$241$	−19.2288	+	1.26033i	−1.23864	+	0.0811847i	−0.568038	+	0.823003i	$0.692297\pi$
$242$	−1.54276	−	5.75766i	−0.0991723	−	0.370116i
$243$	0.946930	−	0.321439i	0.0607456	−	0.0206204i
$244$	−0.202426	+	0.302952i	−0.0129590	+	0.0193945i
$245$	4.21444	+	15.8776i	0.269251	+	1.01438i
$246$	−8.78036	−	3.63694i	−0.559815	−	0.231883i
$247$	0.438094	−	0.0576761i	0.0278752	−	0.00366985i
$248$	8.44381	−	24.8747i	0.536183	−	1.57954i
$249$	5.03281	+	10.2055i	0.318942	+	0.646750i
$250$	4.28082	+	12.6109i	0.270743	+	0.797584i
$251$	−9.53448	+	9.53448i	−0.601811	+	0.601811i	−0.940793	−	0.338982i	$-0.889918\pi$
$251$	−9.53448	+	9.53448i	−0.601811	+	0.601811i	0.338982	+	0.940793i	$0.389918\pi$
$252$	−0.974182	−	0.442776i	−0.0613677	−	0.0278923i
$253$	3.71624	−	1.53932i	0.233638	−	0.0967761i
$254$	7.27913	−	4.20261i	0.456733	−	0.263695i
$255$	0.598154	+	9.65750i	0.0374578	+	0.604776i
$256$	−4.64158	+	8.03946i	−0.290099	+	0.502466i
$257$	9.04230	+	6.93840i	0.564043	+	0.432806i	0.851021	−	0.525132i	$-0.175984\pi$
$257$	9.04230	+	6.93840i	0.564043	+	0.432806i	−0.286978	+	0.957937i	$0.592651\pi$
$258$	3.73309	+	5.58697i	0.232412	+	0.347829i
$259$	12.4028	−	3.74644i	0.770672	−	0.232792i
$260$	3.67737	+	0.731474i	0.228061	+	0.0453641i
$261$	−0.588394	+	8.97716i	−0.0364207	+	0.555672i
$262$	−9.18678	−	3.11849i	−0.567561	−	0.192661i
$263$	8.61790	−	6.61275i	0.531402	−	0.407759i	−0.307905	−	0.951417i	$-0.599628\pi$
$263$	8.61790	−	6.61275i	0.531402	−	0.407759i	0.839307	+	0.543658i	$0.182961\pi$
$264$	1.57174	+	11.9386i	0.0967339	+	0.734767i
$265$	11.6312	−	2.31360i	0.714501	−	0.142123i
$266$	−0.197783	+	0.317229i	−0.0121268	+	0.0194506i
$267$	−1.97513	+	9.92967i	−0.120876	+	0.607686i
$268$	0.491647	−	1.83485i	0.0300321	−	0.112081i
$269$	0.731222	+	11.1563i	0.0445834	+	0.680211i	0.960402	+	0.278618i	$0.0898765\pi$
$269$	0.731222	+	11.1563i	0.0445834	+	0.680211i	−0.915818	+	0.401592i	$0.868457\pi$
$270$	0.386922	−	2.93897i	0.0235473	−	0.178860i
$271$	7.10524	+	12.3066i	0.431613	+	0.747575i	0.997012	−	0.0772419i	$-0.0246114\pi$
$271$	7.10524	+	12.3066i	0.431613	+	0.747575i	−0.565400	+	0.824817i	$0.691278\pi$
$272$	−2.39127	−	12.2516i	−0.144992	−	0.742860i
$273$	−0.329687	−	10.4461i	−0.0199536	−	0.632228i
$274$	1.13288	+	2.73500i	0.0684395	+	0.165228i
$275$	−1.80408	−	0.889674i	−0.108790	−	0.0536493i
$276$	−0.396360	+	0.106204i	−0.0238580	+	0.00639274i
$277$	−7.30054	+	8.32467i	−0.438647	+	0.500181i	−0.928349	−	0.371709i	$-0.878772\pi$
$277$	−7.30054	+	8.32467i	−0.438647	+	0.500181i	0.489703	+	0.871890i	$0.337105\pi$
$278$	−20.8386	−	1.36583i	−1.24981	−	0.0819171i
$279$	1.68735	+	8.48286i	0.101019	+	0.507855i
$280$	−14.5913	+	11.9461i	−0.872000	+	0.713919i
$281$	4.33448	−	10.4644i	0.258573	−	0.624251i	−0.740271	−	0.672308i	$-0.765303\pi$
$281$	4.33448	−	10.4644i	0.258573	−	0.624251i	0.998845	+	0.0480572i	$0.0153030\pi$
$282$	7.45660	−	6.53926i	0.444034	−	0.389407i
$283$	−0.278065	+	0.137127i	−0.0165293	+	0.00815133i	−0.450535	−	0.892759i	$-0.648767\pi$
$283$	−0.278065	+	0.137127i	−0.0165293	+	0.00815133i	0.434005	+	0.900910i	$0.357100\pi$
$284$	−3.94287	−	3.45780i	−0.233966	−	0.205183i
$285$	0.253566	+	0.0679429i	0.0150200	+	0.00402459i
$286$	−16.4489	+	10.9908i	−0.972641	+	0.649898i
$287$	−16.1672	−	11.6140i	−0.954318	−	0.685552i
$288$		−	2.25017i		−	0.132593i
$289$	−13.4123	−	10.4456i	−0.788959	−	0.614445i
$290$	23.0955	+	13.3342i	1.35621	+	0.783010i
$291$	−8.84023	−	1.16384i	−0.518224	−	0.0682254i
$292$	−3.00703	+	6.09765i	−0.175973	+	0.356838i
$293$	−10.7209	−	10.7209i	−0.626322	−	0.626322i	0.320819	−	0.947141i	$-0.396042\pi$
$293$	−10.7209	−	10.7209i	−0.626322	−	0.626322i	−0.947141	+	0.320819i	$0.896042\pi$
$294$	7.00220	+	5.39916i	0.408377	+	0.314886i
$295$	−9.58836	−	6.40674i	−0.558256	−	0.373015i
$296$	9.80653	+	11.1822i	0.569993	+	0.649953i
$297$	−2.41357	−	3.14542i	−0.140049	−	0.182516i
$298$	3.21155	+	4.18537i	0.186040	+	0.242452i
$299$	−2.64248	−	3.01318i	−0.152819	−	0.174256i
$300$	0.170619	+	0.114004i	0.00985071	+	0.00658204i
$301$	4.94216	+	13.1780i	0.284862	+	0.759564i
$302$	13.8658	+	13.8658i	0.797888	+	0.797888i
$303$	4.06295	−	8.23884i	0.233410	−	0.473309i
$304$	−0.335761	−	0.0442037i	−0.0192572	−	0.00253526i
$305$	−1.83088	−	1.05706i	−0.104836	−	0.0605271i
$306$	3.41985	+	3.92797i	0.195500	+	0.224547i
$307$			23.3959i			1.33528i	0.744486	+	0.667638i	$0.232695\pi$
$307$			23.3959i			1.33528i	−0.744486	+	0.667638i	$0.767305\pi$
$308$	−0.420805	+	4.22166i	−0.0239776	+	0.240551i
$309$	8.46989	−	5.65940i	0.481835	−	0.321952i
$310$	24.7650	+	6.63576i	1.40656	+	0.376886i
$311$	2.19811	+	1.92769i	0.124643	+	0.109309i	0.719398	−	0.694598i	$-0.244418\pi$
$311$	2.19811	+	1.92769i	0.124643	+	0.109309i	−0.594755	+	0.803907i	$0.702751\pi$
$312$	10.7603	−	5.30639i	0.609182	−	0.300415i
$313$	−9.24950	+	8.11160i	−0.522813	+	0.458495i	−0.879616	−	0.475685i	$-0.842200\pi$
$313$	−9.24950	+	8.11160i	−0.522813	+	0.458495i	0.356803	+	0.934180i	$0.383867\pi$
$314$	8.99652	−	21.7195i	0.507703	−	1.22570i
$315$	2.19394	−	5.80845i	0.123615	−	0.327269i
$316$	0.802561	+	4.03475i	0.0451476	+	0.226972i
$317$	−20.4937	−	1.34323i	−1.15104	−	0.0754432i	−0.522091	−	0.852890i	$-0.674848\pi$
$317$	−20.4937	−	1.34323i	−1.15104	−	0.0754432i	−0.628949	+	0.777447i	$0.716515\pi$
$318$	4.20870	−	4.79911i	0.236012	−	0.269121i
$319$	34.4529	−	9.23162i	1.92899	−	0.516872i
$320$	−18.7267	−	9.23500i	−1.04686	−	0.516252i
$321$	−1.44181	−	3.48083i	−0.0804738	−	0.194281i
$322$	3.38894	−	0.106957i	0.188858	−	0.00596050i
$323$	−0.384402	+	0.254856i	−0.0213887	+	0.0141806i
$324$	0.202227	+	0.350267i	0.0112348	+	0.0194593i
$325$	−0.261597	+	1.98703i	−0.0145108	+	0.110220i
$326$	0.931054	+	14.2051i	0.0515663	+	0.786749i
$327$	2.93640	−	10.9588i	0.162384	−	0.606024i
$328$	4.45809	−	22.4123i	0.246157	−	1.23751i
$329$	18.3321	−	9.77103i	1.01068	−	0.538694i
$330$	−11.5269	+	2.29284i	−0.634535	+	0.126217i
$331$	0.0974628	+	0.740303i	0.00535704	+	0.0406907i	0.993915	−	0.110153i	$-0.0351342\pi$
$331$	0.0974628	+	0.740303i	0.00535704	+	0.0406907i	−0.988558	+	0.150844i	$0.951801\pi$
$332$	−3.65124	+	2.80170i	−0.200388	+	0.153763i
$333$	−4.63713	−	1.57409i	−0.254113	−	0.0862597i
$334$	−0.169915	+	2.59241i	−0.00929736	+	0.141850i
$335$	10.8102	+	2.15028i	0.590625	+	0.117483i
$336$	−1.82805	+	7.79865i	−0.0997284	+	0.425451i
$337$	18.6667	+	27.9367i	1.01684	+	1.52181i	0.843630	+	0.536925i	$0.180414\pi$
$337$	18.6667	+	27.9367i	1.01684	+	1.52181i	0.173211	+	0.984885i	$0.444586\pi$
$338$	2.60986	+	2.00262i	0.141958	+	0.108928i
$339$	−3.22547	+	5.58667i	−0.175183	+	0.303426i
$340$	−3.78376	+	0.999302i	−0.205203	+	0.0541948i
$341$	29.6969	−	17.1455i	1.60818	−	0.928481i
$342$	0.130541	−	0.0540717i	0.00705883	−	0.00292386i
$343$	11.6986	+	14.3577i	0.631665	+	0.775241i
$344$	−11.4243	+	11.4243i	−0.615959	+	0.615959i
$345$	−0.765327	−	2.25458i	−0.0412038	−	0.121383i
$346$	2.72154	+	5.51873i	0.146311	+	0.296689i
$347$	3.21716	−	9.47745i	0.172706	−	0.508776i	−0.825767	−	0.564011i	$-0.809257\pi$
$347$	3.21716	−	9.47745i	0.172706	−	0.508776i	0.998473	+	0.0552351i	$0.0175908\pi$
$348$	−3.60751	+	0.474938i	−0.193383	+	0.0254593i
$349$	−3.75751	−	1.55641i	−0.201135	−	0.0833129i	0.279842	−	0.960046i	$-0.409718\pi$
$349$	−3.75751	−	1.55641i	−0.201135	−	0.0833129i	−0.480977	+	0.876733i	$0.659718\pi$
$350$	−1.15763	−	1.23890i	−0.0618777	−	0.0662219i
$351$	−2.19463	+	3.28450i	−0.117141	+	0.175314i
$352$	−8.44784	+	2.86766i	−0.450272	+	0.152847i
$353$	0.931332	+	3.47578i	0.0495698	+	0.184997i	0.986272	−	0.165131i	$-0.0528047\pi$
$353$	0.931332	+	3.47578i	0.0495698	+	0.184997i	−0.936702	+	0.350128i	$0.886138\pi$
$354$	−6.19370	+	0.405957i	−0.329192	+	0.0215764i
$355$	18.5241	−	24.1411i	0.983156	−	1.28127i
$356$	−4.09478			−0.217023
$357$	5.09641	+	9.64503i	0.269731	+	0.510469i
$358$	30.3101			1.60194
$359$	1.34096	−	1.74757i	0.0707732	−	0.0922334i	−0.756625	−	0.653849i	$-0.773153\pi$
$359$	1.34096	−	1.74757i	0.0707732	−	0.0922334i	0.827398	+	0.561615i	$0.189820\pi$
$360$	7.11233	−	0.466167i	0.374853	−	0.0245691i
$361$	−4.91432	−	18.3405i	−0.258649	−	0.965290i
$362$	18.0507	−	6.12737i	0.948721	−	0.322048i
$363$	−2.62172	+	3.92368i	−0.137605	+	0.205940i
$364$	4.11778	−	0.955033i	0.215830	−	0.0500574i
$365$	−36.4460	−	15.0964i	−1.90767	−	0.790182i
$366$	−1.12819	+	0.148529i	−0.0589713	+	0.00776372i
$367$	9.31610	−	27.4443i	0.486296	−	1.43258i	−0.376209	−	0.926535i	$-0.622772\pi$
$367$	9.31610	−	27.4443i	0.486296	−	1.43258i	0.862505	−	0.506048i	$-0.168894\pi$
$368$	1.35853	+	2.75482i	0.0708180	+	0.143605i
$369$	2.41847	+	7.12459i	0.125901	+	0.370892i
$370$	−10.2646	+	10.2646i	−0.533632	+	0.533632i
$371$	10.8769	−	7.77492i	0.564698	−	0.403654i
$372$	−3.23186	+	1.33868i	−0.167564	+	0.0694074i
$373$	−22.6460	+	13.0747i	−1.17256	+	0.676980i	−0.954283	−	0.298906i	$-0.903378\pi$
$373$	−22.6460	+	13.0747i	−1.17256	+	0.676980i	−0.218282	+	0.975886i	$0.570045\pi$
$374$	10.3885	−	17.8450i	0.537176	−	0.922745i
$375$	5.27161	−	9.13070i	0.272225	−	0.471507i
$376$	18.9190	+	14.5171i	0.975673	+	0.748660i
$377$	−19.7438	−	29.5487i	−1.01686	−	1.52184i
$378$	−0.966368	−	3.19921i	−0.0497046	−	0.164550i
$379$	23.9602	+	4.76597i	1.23075	+	0.244812i	0.767287	−	0.641304i	$-0.221606\pi$
$379$	23.9602	+	4.76597i	1.23075	+	0.244812i	0.463464	+	0.886116i	$0.346606\pi$
$380$	−0.00694409	+	0.105946i	−0.000356224	+	0.00543493i
$381$	−6.30104	−	2.13891i	−0.322812	−	0.109580i
$382$	−14.5314	+	11.1503i	−0.743491	+	0.570501i
$383$	2.03774	+	15.4782i	0.104124	+	0.790898i	0.961228	+	0.275755i	$0.0889278\pi$
$383$	2.03774	+	15.4782i	0.104124	+	0.790898i	−0.857104	+	0.515143i	$0.827739\pi$
$384$	−6.60883	+	1.31458i	−0.337255	+	0.0670842i
$385$	−24.6027	−	0.834343i	−1.25387	−	0.0425220i
$386$	3.24688	−	16.3232i	0.165262	−	0.830828i
$387$	1.37680	−	5.13829i	0.0699867	−	0.261194i
$388$	−0.235865	−	3.59860i	−0.0119742	−	0.182691i
$389$	−1.83719	+	13.9549i	−0.0931494	+	0.707540i	0.879606	+	0.475704i	$0.157807\pi$
$389$	−1.83719	+	13.9549i	−0.0931494	+	0.707540i	−0.972755	+	0.231836i	$0.925527\pi$
$390$	5.85489	+	10.1410i	0.296474	+	0.513508i
$391$	3.85893	+	1.61469i	0.195154	+	0.0816582i
$392$	−9.44796	+	19.0456i	−0.477194	+	0.961950i
$393$	2.93921	+	7.09587i	0.148263	+	0.357939i
$394$	−10.9087	−	5.37957i	−0.549571	−	0.271019i
$395$	−23.0562	+	6.17790i	−1.16009	+	0.310844i
$396$	1.05729	−	1.20561i	0.0531309	−	0.0605841i
$397$	5.55390	+	0.364022i	0.278742	+	0.0182697i	0.204133	−	0.978943i	$-0.434562\pi$
$397$	5.55390	+	0.364022i	0.278742	+	0.0182697i	0.0746090	+	0.997213i	$0.476229\pi$
$398$	−0.332618	−	1.67218i	−0.0166726	−	0.0838190i
$399$	0.292058	−	0.0478666i	0.0146212	−	0.00239633i
$400$	0.587811	−	1.41910i	0.0293906	−	0.0709551i
$401$	−9.03446	+	7.92301i	−0.451160	+	0.395656i	−0.854548	−	0.519373i	$-0.826166\pi$
$401$	−9.03446	+	7.92301i	−0.451160	+	0.395656i	0.403388	+	0.915029i	$0.367832\pi$
$402$	5.32076	−	2.62391i	0.265376	−	0.130869i
$403$	−25.6872	−	22.5270i	−1.27957	−	1.12215i
$404$	3.58879	+	0.961614i	0.178549	+	0.0478421i
$405$	−1.95127	+	1.30380i	−0.0969595	+	0.0647863i
$406$	29.9176	+	2.98212i	1.48479	+	0.148000i
$407$			19.4153i			0.962379i
$408$	−7.65893	+	9.90742i	−0.379174	+	0.490491i
$409$	−23.3064	−	13.4560i	−1.15243	−	0.665355i	−0.202951	−	0.979189i	$-0.565053\pi$
$409$	−23.3064	−	13.4560i	−1.15243	−	0.665355i	−0.949478	+	0.313834i	$0.898387\pi$
$410$	22.1125	+	2.91116i	1.09206	+	0.143772i
$411$	1.03656	−	2.10193i	0.0511296	−	0.103681i
$412$	2.91330	+	2.91330i	0.143528	+	0.143528i
$413$	−12.8248	−	2.13287i	−0.631068	−	0.104951i
$414$	−1.06556	−	0.711984i	−0.0523694	−	0.0349921i
$415$	−17.6072	−	20.0771i	−0.864303	−	0.985548i
$416$	5.41110	+	7.05188i	0.265301	+	0.345747i
$417$	10.0645	+	13.1163i	0.492859	+	0.642307i
$418$	−0.369365	−	0.421180i	−0.0180662	−	0.0206006i
$419$	21.6434	+	14.4617i	1.05735	+	0.706498i	0.957479	−	0.288502i	$-0.0931573\pi$
$419$	21.6434	+	14.4617i	1.05735	+	0.706498i	0.0998700	+	0.995000i	$0.468157\pi$
$420$	2.47722	+	0.411981i	0.120876	+	0.0201026i
$421$	−26.2524	−	26.2524i	−1.27946	−	1.27946i	−0.940968	−	0.338497i	$-0.890082\pi$
$421$	−26.2524	−	26.2524i	−1.27946	−	1.27946i	−0.338497	−	0.940968i	$-0.609918\pi$
$422$	−6.02175	+	12.2109i	−0.293134	+	0.594417i
$423$	−7.78447	−	1.02485i	−0.378494	−	0.0498297i
$424$	13.2918	+	7.67400i	0.645505	+	0.372682i
$425$	−0.665294	−	1.98327i	−0.0322715	−	0.0962027i
$426$		−	16.3784i		−	0.793538i
$427$	−2.37170	−	0.236406i	−0.114775	−	0.0114405i
$428$	1.26702	−	0.846594i	0.0612436	−	0.0409217i
$429$	15.1279	+	4.05351i	0.730381	+	0.195705i
$430$	−11.8557	−	10.3972i	−0.571732	−	0.501395i
$431$	−35.4736	+	17.4937i	−1.70870	+	0.842640i	−0.719783	+	0.694199i	$0.755759\pi$
$431$	−35.4736	+	17.4937i	−1.70870	+	0.842640i	−0.988921	+	0.148441i	$0.952575\pi$
$432$	2.27620	−	1.99618i	0.109514	−	0.0960410i
$433$	5.05109	−	12.1944i	0.242740	−	0.586026i	−0.754813	−	0.655940i	$-0.772272\pi$
$433$	5.05109	−	12.1944i	0.242740	−	0.586026i	0.997553	+	0.0699140i	$0.0222725\pi$
$434$	28.5244	−	4.67498i	1.36921	−	0.224406i
$435$	−4.11886	−	20.7069i	−0.197484	−	0.992820i
$436$	4.57886	+	0.300115i	0.219288	+	0.0143729i
$437$	0.0748283	−	0.0853253i	0.00357952	−	0.00408166i
$438$	−20.5098	+	5.49558i	−0.979995	+	0.262589i
$439$	34.0875	+	16.8101i	1.62691	+	0.802301i	0.999726	+	0.0234278i	$0.00745797\pi$
$439$	34.0875	+	16.8101i	1.62691	+	0.802301i	0.627181	+	0.778874i	$0.284209\pi$
$440$	−10.8142	−	26.1078i	−0.515547	−	1.24464i
$441$	−0.441410	−	6.98607i	−0.0210195	−	0.332670i
$442$	−20.1633	−	4.08609i	−0.959072	−	0.194355i
$443$	14.0068	+	24.2605i	0.665483	+	1.15265i	0.979154	+	0.203119i	$0.0651077\pi$
$443$	14.0068	+	24.2605i	0.665483	+	1.15265i	−0.313671	+	0.949532i	$0.601559\pi$
$444$	0.258522	−	1.96367i	0.0122689	−	0.0931917i
$445$	−1.55393	−	23.7084i	−0.0736633	−	1.12388i
$446$	0.773945	−	2.88840i	0.0366473	−	0.136770i
$447$	0.814795	−	4.09625i	0.0385385	−	0.193746i
$448$	−23.5266	−	0.797848i	−1.11153	−	0.0376948i
$449$	−31.9372	+	6.35271i	−1.50721	+	0.299803i	−0.878464	−	0.477808i	$-0.841431\pi$
$449$	−31.9372	+	6.35271i	−1.50721	+	0.299803i	−0.628746	+	0.777611i	$0.716431\pi$
$450$	0.0836499	+	0.635384i	0.00394329	+	0.0299523i
$451$	23.6658	−	18.1594i	1.11438	−	0.855093i
$452$	−2.47064	−	0.838669i	−0.116209	−	0.0394477i
$453$	1.01532	−	15.4908i	0.0477041	−	0.727823i
$454$	15.4516	+	3.07352i	0.725182	+	0.144248i
$455$	7.09221	+	23.4792i	0.332488	+	1.10072i
$456$	0.188750	+	0.282484i	0.00883901	+	0.0132285i
$457$	19.6746	+	15.0968i	0.920338	+	0.706200i	0.956063	−	0.293161i	$-0.0947073\pi$
$457$	19.6746	+	15.0968i	0.920338	+	0.706200i	−0.0357249	+	0.999362i	$0.511374\pi$
$458$	5.09966	−	8.83286i	0.238291	−	0.412733i
$459$	0.552854	−	4.08587i	0.0258050	−	0.190712i
$460$	0.833965	−	0.481490i	0.0388838	−	0.0224496i
$461$	24.5799	−	10.1813i	1.14480	−	0.474191i	0.272013	−	0.962294i	$-0.412311\pi$
$461$	24.5799	−	10.1813i	1.14480	−	0.474191i	0.872786	+	0.488102i	$0.162311\pi$
$462$	−10.7793	+	7.70517i	−0.501497	+	0.358477i
$463$	6.85803	−	6.85803i	0.318720	−	0.318720i	−0.529556	−	0.848275i	$-0.677641\pi$
$463$	6.85803	−	6.85803i	0.318720	−	0.318720i	0.848275	+	0.529556i	$0.177641\pi$
$464$	8.75497	+	25.7913i	0.406439	+	1.19733i
$465$	−8.97730	−	18.2042i	−0.416312	−	0.844198i
$466$	8.73909	−	25.7445i	0.404831	−	1.19259i
$467$	6.46318	−	0.850894i	0.299080	−	0.0393747i	0.0205073	−	0.999790i	$-0.493472\pi$
$467$	6.46318	−	0.850894i	0.299080	−	0.0393747i	0.278573	+	0.960415i	$0.410139\pi$
$468$	−1.47607	−	0.611408i	−0.0682314	−	0.0282624i
$469$	12.1049	−	2.80747i	0.558951	−	0.129637i
$470$	−12.9308	+	19.3523i	−0.596454	+	0.892656i
$471$	−17.6237	+	5.98245i	−0.812059	+	0.275657i
$472$	−3.86273	−	14.4159i	−0.177796	−	0.663545i
$473$	−21.0454	+	1.37939i	−0.967666	+	0.0634242i
$474$	−7.82123	+	10.1928i	−0.359241	+	0.468172i
$475$	−0.0567530			−0.00260401
$476$	−3.42388	+	2.78270i	−0.156933	+	0.127545i
$477$	−5.05336			−0.231378
$478$	−23.1571	+	30.1789i	−1.05918	+	1.38035i
$479$	−21.2403	+	1.39216i	−0.970495	+	0.0636096i	−0.542397	−	0.840122i	$-0.682483\pi$
$479$	−21.2403	+	1.39216i	−0.970495	+	0.0636096i	−0.428098	+	0.903732i	$0.640816\pi$
$480$	1.36673	+	5.10072i	0.0623825	+	0.232815i
$481$	18.3177	−	6.21803i	0.835216	−	0.283518i
$482$	13.5231	−	20.2388i	0.615962	−	0.921853i
$483$	−1.83264	−	1.96130i	−0.0833880	−	0.0892424i
$484$	−1.76332	−	0.730392i	−0.0801510	−	0.0331996i
$485$	20.7460	−	2.73127i	0.942029	−	0.124021i
$486$	−0.406026	+	1.19611i	−0.0184177	+	0.0542568i
$487$	8.15091	+	16.5284i	0.369353	+	0.748973i	0.999625	−	0.0274012i	$-0.00872316\pi$
$487$	8.15091	+	16.5284i	0.369353	+	0.748973i	−0.630272	+	0.776375i	$0.717056\pi$
$488$	−0.879485	−	2.59088i	−0.0398124	−	0.117284i
$489$	7.96905	−	7.96905i	0.360373	−	0.360373i
$490$	−19.1521	−	7.98581i	−0.865202	−	0.360762i
$491$	8.37447	−	3.46882i	0.377934	−	0.156546i	−0.185626	−	0.982620i	$-0.559431\pi$
$491$	8.37447	−	3.46882i	0.377934	−	0.156546i	0.563560	+	0.826075i	$0.309431\pi$
$492$	−2.63537	+	1.52153i	−0.118812	+	0.0685960i
$493$	32.0568	+	18.6619i	1.44377	+	0.840488i
$494$	−0.279076	+	0.483375i	−0.0125562	+	0.0217481i
$495$	7.38160	+	5.66410i	0.331778	+	0.254582i
$496$	14.5476	+	21.7721i	0.653209	+	0.977596i
$497$	7.82927	−	33.4004i	0.351191	−	1.49821i
$498$	−14.0972	−	2.80411i	−0.631712	−	0.125655i
$499$	−1.19692	+	18.2615i	−0.0535814	+	0.817495i	0.883510	+	0.468412i	$0.155174\pi$
$499$	−1.19692	+	18.2615i	−0.0535814	+	0.817495i	−0.937092	+	0.349083i	$0.886493\pi$
$500$	4.03795	+	1.37070i	0.180582	+	0.0612995i
$501$	1.63172	−	1.25206i	0.0729000	−	0.0559381i
$502$	−2.22313	−	16.8863i	−0.0992231	−	0.753674i
$503$	−3.63688	+	0.723420i	−0.162160	+	0.0322557i	−0.275503	−	0.961300i	$-0.588844\pi$
$503$	−3.63688	+	0.723420i	−0.162160	+	0.0322557i	0.113342	+	0.993556i	$0.463844\pi$
$504$	7.09124	−	3.77964i	0.315869	−	0.168359i
$505$	−4.20574	+	21.1437i	−0.187153	+	0.940882i
$506$	−1.31504	+	4.90780i	−0.0584607	+	0.218178i
$507$	−0.170331	−	2.59875i	−0.00756468	−	0.115415i
$508$	0.351286	−	2.66828i	0.0155858	−	0.118386i
$509$	6.97344	+	12.0783i	0.309092	+	0.535363i	0.978164	−	0.207834i	$-0.0666415\pi$
$509$	6.97344	+	12.0783i	0.309092	+	0.535363i	−0.669072	+	0.743198i	$0.733308\pi$
$510$	−10.1380	−	6.82677i	−0.448916	−	0.302295i
$511$	−44.4524	+	1.40295i	−1.96646	+	0.0620628i
$512$	−9.64463	−	23.2842i	−0.426236	−	1.02903i
$513$	−0.100324	−	0.0494745i	−0.00442943	−	0.00218435i
$514$	−13.9063	+	3.72617i	−0.613379	+	0.164355i
$515$	−15.7622	+	17.9733i	−0.694565	+	0.791999i
$516$	2.14691	+	0.140716i	0.0945123	+	0.00619466i
$517$	6.07307	+	30.5314i	0.267093	+	1.34277i
$518$	−5.78281	+	15.3100i	−0.254082	+	0.672682i
$519$	1.86420	−	4.50058i	0.0818294	−	0.197554i
$520$	−21.1685	+	18.5643i	−0.928301	+	0.814098i
$521$	−5.57157	+	2.74759i	−0.244095	+	0.120374i	−0.560222	−	0.828343i	$-0.689284\pi$
$521$	−5.57157	+	2.74759i	−0.244095	+	0.120374i	0.316127	+	0.948717i	$0.397617\pi$
$522$	−8.54377	−	7.49269i	−0.373951	−	0.327946i
$523$	1.02998	+	0.275981i	0.0450377	+	0.0120678i	0.281268	−	0.959629i	$-0.409245\pi$
$523$	1.02998	+	0.275981i	0.0450377	+	0.0120678i	−0.236230	+	0.971697i	$0.575912\pi$
$524$	−2.58289	+	1.72583i	−0.112834	+	0.0753933i
$525$	−0.133141	+	1.33572i	−0.00581076	+	0.0582956i
$526$			13.7211i			0.598269i
$527$	34.4124	+	9.35340i	1.49903	+	0.407441i
$528$	−10.3951	−	6.00161i	−0.452388	−	0.261186i
$529$	21.7827	+	2.86775i	0.947074	+	0.124685i
$530$	−6.62541	+	13.4350i	−0.287789	+	0.583579i
$531$	3.47465	+	3.47465i	0.150787	+	0.150787i
$532$	0.0420327	+	0.112077i	0.00182235	+	0.00485917i
$533$	−24.7122	−	16.5122i	−1.07040	−	0.715221i
$534$	−8.43197	−	9.61482i	−0.364887	−	0.416074i
$535$	5.38253	+	7.01464i	0.232707	+	0.303269i
$536$	8.68374	+	11.3169i	0.375080	+	0.488814i
$537$	−15.8214	−	18.0409i	−0.682745	−	0.778521i
$538$	−11.7423	−	7.84593i	−0.506245	−	0.338262i
$539$	−25.6653	+	10.5603i	−1.10548	+	0.454866i
$540$	−0.671159	−	0.671159i	−0.0288821	−	0.0288821i
$541$	14.3766	−	29.1528i	0.618098	−	1.25338i	−0.332544	−	0.943088i	$-0.607907\pi$
$541$	14.3766	−	29.1528i	0.618098	−	1.25338i	0.950642	−	0.310291i	$-0.100426\pi$
$542$	−17.7964	−	2.34294i	−0.764421	−	0.100638i
$543$	−13.0693	−	7.54554i	−0.560856	−	0.323810i
$544$	−8.30612	−	4.13329i	−0.356122	−	0.177213i
$545$			26.6251i			1.14049i
$546$	10.7218	+	7.70223i	0.458852	+	0.329625i
$547$	4.61428	−	3.08316i	0.197292	−	0.131826i	−0.453000	−	0.891510i	$-0.649646\pi$
$547$	4.61428	−	3.08316i	0.197292	−	0.131826i	0.650293	+	0.759684i	$0.274646\pi$
$548$	0.915589	+	0.245331i	0.0391120	+	0.0104800i
$549$	0.677304	+	0.593979i	0.0289066	+	0.0253504i
$550$	2.27882	−	1.12379i	0.0971693	−	0.0479186i
$551$	0.756608	−	0.663528i	0.0322326	−	0.0282672i
$552$	1.17920	−	2.84684i	0.0501901	−	0.121170i
$553$	−20.8222	+	17.0474i	−0.885448	+	0.724930i
$554$	−2.72855	−	13.7174i	−0.115925	−	0.582794i
$555$	11.4676	+	0.751625i	0.486772	+	0.0319047i
$556$	−4.40886	+	5.02734i	−0.186977	+	0.213207i
$557$	12.0580	−	3.23092i	0.510912	−	0.136898i	0.00585232	−	0.999983i	$-0.498137\pi$
$557$	12.0580	−	3.23092i	0.510912	−	0.136898i	0.505060	+	0.863084i	$0.331470\pi$
$558$	−9.79837	−	4.83202i	−0.414798	−	0.204556i
$559$	8.04150	+	19.4139i	0.340119	+	0.821121i
$560$	−0.592975	−	18.7884i	−0.0250578	−	0.793955i
$561$	−16.0442	+	3.13152i	−0.677386	+	0.132213i
$562$	7.15355	+	12.3903i	0.301754	+	0.522654i
$563$	0.0772263	−	0.586592i	0.00325470	−	0.0247219i	−0.989740	−	0.142877i	$-0.954365\pi$
$563$	0.0772263	−	0.586592i	0.00325470	−	0.0247219i	0.992995	+	0.118155i	$0.0376980\pi$
$564$	−0.207696	−	3.16883i	−0.00874558	−	0.133432i
$565$	3.91823	−	14.6230i	0.164841	−	0.615196i
$566$	0.0764022	−	0.384100i	0.00321143	−	0.0161449i
$567$	−1.39977	+	2.24514i	−0.0587850	+	0.0942868i
$568$	38.6245	−	7.68289i	1.62065	−	0.322367i
$569$	1.86326	+	14.1529i	0.0781120	+	0.593320i	0.985077	+	0.172114i	$0.0550597\pi$
$569$	1.86326	+	14.1529i	0.0781120	+	0.593320i	−0.906965	+	0.421206i	$0.861607\pi$
$570$	−0.263069	+	0.201860i	−0.0110187	+	0.00845497i
$571$	−31.6912	−	10.7577i	−1.32624	−	0.450196i	−0.433653	−	0.901080i	$-0.642776\pi$
$571$	−31.6912	−	10.7577i	−1.32624	−	0.450196i	−0.892583	+	0.450884i	$0.851109\pi$
$572$	−0.414288	+	6.32081i	−0.0173222	+	0.264286i
$573$	14.2220	+	2.82893i	0.594132	+	0.118180i
$574$	24.0705	−	7.27084i	1.00468	−	0.303479i
$575$	0.285975	+	0.427992i	0.0119260	+	0.0178485i
$576$	7.05872	+	5.41635i	0.294113	+	0.225681i
$577$	9.45131	−	16.3701i	0.393463	−	0.681498i	−0.599441	−	0.800419i	$-0.704610\pi$
$577$	9.45131	−	16.3701i	0.393463	−	0.681498i	0.992904	+	0.118921i	$0.0379436\pi$
$578$	20.7812	−	5.40860i	0.864386	−	0.224968i
$579$	−11.4106	+	6.58789i	−0.474207	+	0.273783i
$580$	7.88907	−	3.26776i	0.327576	−	0.135686i
$581$	−27.4079	−	12.4572i	−1.13707	−	0.516811i
$582$	7.96407	−	7.96407i	0.330121	−	0.330121i
$583$	6.44009	+	18.9719i	0.266721	+	0.785735i
$584$	−22.5808	−	45.7893i	−0.934400	−	1.89478i
$585$	2.97984	−	8.77833i	0.123201	−	0.362939i
$586$	18.9876	−	2.49976i	0.784369	−	0.103264i
$587$	−5.28769	−	2.19023i	−0.218246	−	0.0904005i	0.270882	−	0.962613i	$-0.412685\pi$
$587$	−5.28769	−	2.19023i	−0.218246	−	0.0904005i	−0.489128	+	0.872212i	$0.662685\pi$
$588$	2.73642	−	0.726336i	0.112848	−	0.0299536i
$589$	0.537506	−	0.804434i	0.0221475	−	0.0331461i
$590$	13.7934	−	4.68222i	0.567865	−	0.192764i
$591$	2.49220	+	9.30102i	0.102515	+	0.382593i
$592$	−14.7940	+	0.969650i	−0.608030	+	0.0398524i
$593$	−7.02415	+	9.15405i	−0.288447	+	0.375912i	−0.914991	−	0.403475i	$-0.867802\pi$
$593$	−7.02415	+	9.15405i	−0.288447	+	0.375912i	0.626544	+	0.779386i	$0.284469\pi$
$594$	5.00803			0.205482
$595$	−17.4109	−	18.7679i	−0.713777	−	0.769411i
$596$	1.68920			0.0691924
$597$	−0.821680	+	1.07083i	−0.0336291	+	0.0438263i
$598$	5.05153	−	0.331095i	0.206572	−	0.0135395i
$599$	5.76167	+	21.5028i	0.235415	+	0.878582i	0.977961	+	0.208787i	$0.0669515\pi$
$599$	5.76167	+	21.5028i	0.235415	+	0.878582i	−0.742546	+	0.669795i	$0.766382\pi$
$600$	−1.45916	+	0.495317i	−0.0595698	+	0.0202212i
$601$	−24.8720	+	37.2236i	−1.01455	+	1.51838i	−0.168202	+	0.985753i	$0.553796\pi$
$601$	−24.8720	+	37.2236i	−1.01455	+	1.51838i	−0.846349	+	0.532629i	$0.821204\pi$
$602$	−17.0062	−	5.18061i	−0.693123	−	0.211146i
$603$	−4.33914	−	1.79733i	−0.176703	−	0.0731930i
$604$	6.22506	−	0.819545i	0.253294	−	0.0333468i
$605$	3.55974	−	10.4866i	0.144724	−	0.426343i
$606$	5.13211	+	10.4069i	0.208478	+	0.422751i
$607$	−11.3902	−	33.5545i	−0.462315	−	1.36194i	−0.889154	−	0.457609i	$-0.848706\pi$
$607$	−11.3902	−	33.5545i	−0.462315	−	1.36194i	0.426838	−	0.904328i	$-0.359627\pi$
$608$	−0.177982	+	0.177982i	−0.00721814	+	0.00721814i
$609$	−13.8416	−	19.3639i	−0.560889	−	0.784664i
$610$	2.46717	−	1.02194i	0.0998929	−	0.0413770i
$611$	26.8605	−	15.5079i	1.08666	−	0.627383i
$612$	1.66442	−	0.103089i	0.0672801	−	0.00416711i
$613$	−9.53616	+	16.5171i	−0.385162	+	0.667120i	−0.991792	−	0.127865i	$-0.959188\pi$
$613$	−9.53616	+	16.5171i	−0.385162	+	0.667120i	0.606630	+	0.794984i	$0.292521\pi$
$614$	−23.4456	−	17.9904i	−0.946188	−	0.726035i
$615$	−9.80963	−	14.6812i	−0.395563	−	0.592001i
$616$	−23.2271	−	21.8059i	−0.935848	−	0.878584i
$617$	−19.4061	−	3.86012i	−0.781261	−	0.155402i	−0.211682	−	0.977339i	$-0.567894\pi$
$617$	−19.4061	−	3.86012i	−0.781261	−	0.155402i	−0.569580	+	0.821936i	$0.692894\pi$
$618$	−0.841559	+	12.8397i	−0.0338525	+	0.516489i
$619$	−1.15322	−	0.391464i	−0.0463516	−	0.0157343i	0.298167	−	0.954514i	$-0.403625\pi$
$619$	−1.15322	−	0.391464i	−0.0463516	−	0.0157343i	−0.344519	+	0.938779i	$0.611958\pi$
$620$	6.51292	−	4.99754i	0.261565	−	0.200706i
$621$	0.132426	+	1.00588i	0.00531408	+	0.0403645i
$622$	−3.62203	+	0.720466i	−0.145230	+	0.0288881i
$623$	−12.5991	−	23.6381i	−0.504774	−	0.947040i
$624$	−2.33316	+	11.7296i	−0.0934010	+	0.469558i
$625$	−7.06042	+	26.3498i	−0.282417	+	1.05399i
$626$	−1.01636	−	15.5066i	−0.0406218	−	0.619769i
$627$	−0.0578876	+	0.439700i	−0.00231181	+	0.0175599i
$628$	−3.76374	−	6.51898i	−0.150189	−	0.260136i
$629$	−14.3283	+	14.2257i	−0.571307	+	0.567217i
$630$	4.13374	+	6.66505i	0.164692	+	0.265542i
$631$	2.88055	+	6.95425i	0.114673	+	0.276844i	0.970787	−	0.239942i	$-0.0771283\pi$
$631$	2.88055	+	6.95425i	0.114673	+	0.276844i	−0.856115	+	0.516786i	$0.827128\pi$
$632$	−27.7061	−	13.6631i	−1.10209	−	0.543490i
$633$	10.4113	−	2.78971i	0.413813	−	0.110881i
$634$	17.1048	−	19.5043i	0.679320	−	0.774616i
$635$	15.5824	+	1.02133i	0.618370	+	0.0405301i
$636$	−0.398736	−	2.00458i	−0.0158109	−	0.0794868i
$637$	18.1831	+	20.8324i	0.720440	+	0.825408i
$638$	−17.2415	+	41.6248i	−0.682599	+	1.64794i
$639$	−9.74862	+	8.54931i	−0.385650	+	0.338206i
$640$	14.1825	−	6.99403i	0.560613	−	0.276463i
$641$	27.2953	+	23.9373i	1.07810	+	0.945467i	0.998679	−	0.0513739i	$-0.0163600\pi$
$641$	27.2953	+	23.9373i	1.07810	+	0.945467i	0.0794195	+	0.996841i	$0.474693\pi$
$642$	4.59691	+	1.23174i	0.181425	+	0.0486128i
$643$	36.6422	−	24.4835i	1.44503	−	0.965536i	0.447570	−	0.894249i	$-0.352289\pi$
$643$	36.6422	−	24.4835i	1.44503	−	0.965536i	0.997456	−	0.0712867i	$-0.0227105\pi$
$644$	0.633410	−	0.881733i	0.0249599	−	0.0347452i
$645$			12.4838i			0.491549i
$646$	0.0401905	−	0.581191i	0.00158127	−	0.0228667i
$647$	−1.78066	−	1.02806i	−0.0700048	−	0.0404173i	0.464589	−	0.885526i	$-0.346202\pi$
$647$	−1.78066	−	1.02806i	−0.0700048	−	0.0404173i	−0.534594	+	0.845109i	$0.679535\pi$
$648$	−3.01120	−	0.396432i	−0.118291	−	0.0155733i
$649$	8.61677	−	17.4731i	0.338238	−	0.685878i
$650$	−1.79009	−	1.79009i	−0.0702131	−	0.0702131i
$651$	−17.6719	−	14.5377i	−0.692617	−	0.569779i
$652$	3.78998	+	2.53238i	0.148427	+	0.0991758i
$653$	0.120450	+	0.137347i	0.00471358	+	0.00537480i	0.754192	−	0.656654i	$-0.228029\pi$
$653$	0.120450	+	0.137347i	0.00471358	+	0.00537480i	−0.749478	+	0.662029i	$0.769696\pi$
$654$	8.72412	+	11.3695i	0.341140	+	0.444582i
$655$	−10.9726	−	14.2998i	−0.428735	−	0.558738i
$656$	15.0190	+	17.1259i	0.586393	+	0.668653i
$657$	13.9768	+	9.33902i	0.545288	+	0.364350i
$658$	−4.30479	+	25.8845i	−0.167818	+	1.00908i
$659$	−22.2419	−	22.2419i	−0.866423	−	0.866423i	0.125652	−	0.992074i	$-0.459898\pi$
$659$	−22.2419	−	22.2419i	−0.866423	−	0.866423i	−0.992074	+	0.125652i	$0.959898\pi$
$660$	−1.66440	+	3.37508i	−0.0647868	+	0.131375i
$661$	16.4308	+	2.16316i	0.639085	+	0.0841371i	0.443103	−	0.896471i	$-0.353877\pi$
$661$	16.4308	+	2.16316i	0.639085	+	0.0841371i	0.195981	+	0.980608i	$0.437211\pi$
$662$	−0.816820	−	0.471591i	−0.0317466	−	0.0183289i
$663$	8.09289	+	14.1343i	0.314302	+	0.548931i
$664$		−	34.5602i		−	1.34120i
$665$	−0.632967	+	0.285898i	−0.0245454	+	0.0110866i
$666$	5.14318	−	3.43657i	0.199294	−	0.133164i
$667$	−8.81638	−	2.36234i	−0.341371	−	0.0914702i
$668$	0.625423	+	0.548482i	0.0241984	+	0.0212214i
$669$	−2.12320	+	1.04704i	−0.0820875	+	0.0404811i
$670$	−10.4674	+	9.17969i	−0.404392	+	0.354642i
$671$	1.36682	−	3.29978i	0.0527653	−	0.127387i
$672$	3.77139	+	4.60647i	0.145484	+	0.177699i
$673$	6.06211	+	30.4763i	0.233677	+	1.17477i	0.902278	+	0.431154i	$0.141893\pi$
$673$	6.06211	+	30.4763i	0.233677	+	1.17477i	−0.668601	+	0.743621i	$0.733107\pi$
$674$	−42.3499	−	2.77576i	−1.63126	−	0.106918i
$675$	0.334523	−	0.381451i	0.0128758	−	0.0146820i
$676$	1.01744	−	0.272622i	0.0391323	−	0.0104855i
$677$	−2.04254	−	1.00727i	−0.0785012	−	0.0387125i	0.402614	−	0.915370i	$-0.368102\pi$
$677$	−2.04254	−	1.00727i	−0.0785012	−	0.0387125i	−0.481116	+	0.876657i	$0.659768\pi$
$678$	−3.11829	−	7.52822i	−0.119757	−	0.289120i
$679$	20.0481	−	12.4340i	0.769374	−	0.477175i
$680$	11.3437	−	27.1102i	0.435010	−	1.03963i
$681$	−6.23614	−	10.8013i	−0.238970	−	0.413907i
$682$	−5.65370	+	42.9441i	−0.216491	+	1.64441i
$683$	−2.67780	−	40.8553i	−0.102463	−	1.56329i	−0.671519	−	0.740987i	$-0.734358\pi$
$683$	−2.67780	−	40.8553i	−0.102463	−	1.56329i	0.569056	−	0.822299i	$-0.307309\pi$
$684$	0.0117096	−	0.0437007i	0.000447727	−	0.00167094i
$685$	−1.07299	+	5.39428i	−0.0409968	+	0.206105i
$686$	−23.3839	+	0.683022i	−0.892801	+	0.0260779i
$687$	−7.91936	+	1.57526i	−0.302143	+	0.0600999i
$688$	−2.10212	−	15.9672i	−0.0801427	−	0.608744i
$689$	15.8369	−	12.1521i	0.603337	−	0.462957i
$690$	2.84787	+	0.966723i	0.108417	+	0.0368025i
$691$	−2.00181	+	30.5418i	−0.0761526	+	1.16186i	0.773244	+	0.634109i	$0.218633\pi$
$691$	−2.00181	+	30.5418i	−0.0761526	+	1.16186i	−0.849397	+	0.527755i	$0.823034\pi$
$692$	1.93240	+	0.384378i	0.0734588	+	0.0146119i
$693$	10.2128	+	2.39395i	0.387953	+	0.0909386i
$694$	7.02372	+	10.5117i	0.266617	+	0.399020i
$695$	−30.7810	−	23.6191i	−1.16759	−	0.895922i
$696$	13.6619	−	23.6631i	0.517853	−	0.896947i
$697$	30.7416	+	4.15961i	1.16442	+	0.157556i
$698$	4.44908	−	2.56868i	0.168400	−	0.0972260i
$699$	−19.8851	+	8.23668i	−0.752124	+	0.311540i
$700$	−0.540362	+	0.0525801i	−0.0204238	+	0.00198734i
$701$	14.0877	−	14.0877i	0.532086	−	0.532086i	−0.389107	−	0.921193i	$-0.627216\pi$
$701$	14.0877	−	14.0877i	0.532086	−	0.532086i	0.921193	+	0.389107i	$0.127216\pi$
$702$	−1.60390	−	4.72493i	−0.0605352	−	0.178331i
$703$	0.242277	+	0.491290i	0.00913767	+	0.0185294i
$704$	11.3389	−	33.4033i	0.427351	−	1.25893i
$705$	18.2684	−	2.40508i	0.688028	−	0.0905806i
$706$	−4.19931	−	1.73941i	−0.158043	−	0.0654637i
$707$	5.49114	+	23.6759i	0.206515	+	0.890425i
$708$	−1.10417	+	1.65250i	−0.0414971	+	0.0621048i
$709$	29.1603	−	9.89858i	1.09514	−	0.371749i	0.285321	−	0.958432i	$-0.407900\pi$
$709$	29.1603	−	9.89858i	1.09514	−	0.371749i	0.809817	+	0.586683i	$0.199566\pi$
$710$	9.94811	+	37.1268i	0.373346	+	1.39335i
$711$	10.1494	−	0.665230i	0.380634	−	0.0249481i
$712$	18.7189	−	24.3949i	0.701519	−	0.914237i
$713$	−8.77495			−0.328625
$714$	−13.5844	−	2.30937i	−0.508385	−	0.0864261i
$715$	−36.7541			−1.37453
$716$	5.90811	−	7.69960i	0.220796	−	0.287747i
$717$	30.0505	−	1.96961i	1.12226	−	0.0735566i
$718$	0.720144	+	2.68762i	0.0268756	+	0.100301i
$719$	33.7248	−	11.4480i	1.25772	−	0.426939i	0.388540	−	0.921432i	$-0.372980\pi$
$719$	33.7248	−	11.4480i	1.25772	−	0.426939i	0.869182	+	0.494493i	$0.164646\pi$
$720$	−3.94726	+	5.90750i	−0.147106	+	0.220159i
$721$	−7.85385	+	25.7816i	−0.292493	+	0.960158i
$722$	22.1584	+	9.17829i	0.824649	+	0.341581i
$723$	−19.1052	+	2.51525i	−0.710532	+	0.0935433i
$724$	1.96195	−	5.77973i	0.0729154	−	0.214802i
$725$	2.01878	+	4.09368i	0.0749755	+	0.152035i
$726$	−1.91602	−	5.64443i	−0.0711103	−	0.209484i
$727$	−8.62599	+	8.62599i	−0.319920	+	0.319920i	−0.848736	−	0.528816i	$-0.822636\pi$
$727$	−8.62599	+	8.62599i	−0.319920	+	0.319920i	0.528816	+	0.848736i	$0.322636\pi$
$728$	−13.1344	+	28.8978i	−0.486792	+	1.07102i
$729$	0.923880	−	0.382683i	0.0342178	−	0.0141735i
$730$	43.1538	−	24.9149i	1.59719	−	0.922141i
$731$	−16.4381	−	14.5206i	−0.607985	−	0.537065i
$732$	−0.182179	+	0.315542i	−0.00673351	+	0.0116628i
$733$	−17.1166	−	13.1340i	−0.632215	−	0.485115i	0.242244	−	0.970215i	$-0.422117\pi$
$733$	−17.1166	−	13.1340i	−0.632215	−	0.485115i	−0.874459	+	0.485100i	$0.838783\pi$
$734$	20.3390	+	30.4394i	0.750724	+	1.12354i
$735$	5.24386	+	15.5680i	0.193423	+	0.574234i
$736$	2.23906	+	0.445377i	0.0825330	+	0.0164168i
$737$	−1.21786	+	18.5810i	−0.0448606	+	0.684441i
$738$	−8.99943	−	3.05489i	−0.331273	−	0.112452i
$739$	23.8937	−	18.3343i	0.878946	−	0.674439i	−0.0673542	−	0.997729i	$-0.521456\pi$
$739$	23.8937	−	18.3343i	0.878946	−	0.674439i	0.946300	+	0.323291i	$0.104789\pi$
$740$	0.606694	+	4.60830i	0.0223025	+	0.169404i
$741$	0.433384	−	0.0862054i	0.0159207	−	0.00316683i
$742$	−0.572395	+	16.8785i	−0.0210133	+	0.619630i
$743$	−5.01447	+	25.2095i	−0.183963	+	0.924845i	0.772949	+	0.634468i	$0.218781\pi$
$743$	−5.01447	+	25.2095i	−0.183963	+	0.924845i	−0.956912	+	0.290377i	$0.906219\pi$
$744$	6.79885	−	25.3737i	0.249258	−	0.930244i
$745$	0.641037	+	9.78033i	0.0234858	+	0.358324i
$746$	4.31134	−	32.7479i	0.157850	−	1.19899i
$747$	5.68951	+	9.85453i	0.208168	+	0.360558i
$748$	−2.50819	−	6.11736i	−0.0917084	−	0.223673i
$749$	8.78563	+	4.70930i	0.321020	+	0.172074i
$750$	5.09645	+	12.3039i	0.186096	+	0.449276i
$751$	−6.44068	−	3.17619i	−0.235024	−	0.115901i	0.320964	−	0.947091i	$-0.395993\pi$
$751$	−6.44068	−	3.17619i	−0.235024	−	0.115901i	−0.555988	+	0.831191i	$0.687660\pi$
$752$	−22.9609	+	6.15237i	−0.837300	+	0.224354i
$753$	−8.89049	+	10.1377i	−0.323987	+	0.369437i
$754$	44.7936	+	2.93593i	1.63129	+	0.106920i
$755$	7.10744	+	35.7315i	0.258666	+	1.30040i
$756$	−1.00106	−	0.378114i	−0.0364080	−	0.0137519i
$757$	−7.35364	+	17.7533i	−0.267273	+	0.645253i	−0.999353	−	0.0359651i	$-0.988549\pi$
$757$	−7.35364	+	17.7533i	−0.267273	+	0.645253i	0.732080	+	0.681218i	$0.238549\pi$
$758$	−23.2004	+	20.3462i	−0.842677	+	0.739008i
$759$	3.60761	−	1.77908i	0.130948	−	0.0645764i
$760$	−0.599438	−	0.525693i	−0.0217439	−	0.0190689i
$761$	23.8025	+	6.37786i	0.862840	+	0.231197i	0.662989	−	0.748629i	$-0.269288\pi$
$761$	23.8025	+	6.37786i	0.862840	+	0.231197i	0.199851	+	0.979826i	$0.435954\pi$
$762$	6.98868	−	4.66969i	0.253173	−	0.169165i
$763$	12.3561	+	27.3560i	0.447322	+	0.990354i
$764$			5.86483i			0.212182i
$765$	1.22850	+	9.59770i	0.0444166	+	0.347006i
$766$	−17.0780	−	9.85997i	−0.617052	−	0.356255i
$767$	−19.2450	−	2.53365i	−0.694896	−	0.0914848i
$768$	−4.10584	+	8.32582i	−0.148157	+	0.300432i
$769$	−0.907247	−	0.907247i	−0.0327162	−	0.0327162i	0.690559	−	0.723276i	$-0.257364\pi$
$769$	−0.907247	−	0.907247i	−0.0327162	−	0.0327162i	−0.723276	+	0.690559i	$0.757364\pi$
$770$	19.7545	−	24.0134i	0.711904	−	0.865383i
$771$	9.47673	+	6.33215i	0.341296	+	0.228047i
$772$	−3.51365	−	4.00655i	−0.126459	−	0.144199i
$773$	11.4315	+	14.8978i	0.411162	+	0.535837i	0.952327	−	0.305080i	$-0.0986830\pi$
$773$	11.4315	+	14.8978i	0.411162	+	0.535837i	−0.541165	+	0.840917i	$0.682016\pi$
$774$	4.09050	+	5.33085i	0.147030	+	0.191613i
$775$	2.89331	+	3.29918i	0.103931	+	0.118510i
$776$	22.5171	+	15.0455i	0.808317	+	0.540100i
$777$	12.1312	−	4.54960i	0.435205	−	0.163216i
$778$	−12.5718	−	12.5718i	−0.450720	−	0.450720i
$779$	0.372241	−	0.754830i	0.0133369	−	0.0270446i
$780$	3.71734	+	0.489397i	0.133102	+	0.0175232i
$781$	44.5206	+	25.7040i	1.59307	+	0.919760i
$782$	−4.58546	+	2.62550i	−0.163976	+	0.0938877i
$783$			8.99642i			0.321506i
$784$	−9.32855	−	19.0290i	−0.333162	−	0.679607i
$785$	36.3160	−	24.2656i	1.29617	−	0.866076i
$786$	−9.37106	−	2.51097i	−0.334255	−	0.0895633i
$787$	8.57314	+	7.51844i	0.305599	+	0.268003i	0.798385	−	0.602147i	$-0.205688\pi$
$787$	8.57314	+	7.51844i	0.305599	+	0.268003i	−0.492786	+	0.870151i	$0.664021\pi$
$788$	−3.49290	+	1.72251i	−0.124430	+	0.0613619i
$789$	8.16695	−	7.16223i	0.290751	−	0.254982i
$790$	11.5382	−	27.8557i	0.410512	−	0.991063i
$791$	−2.76044	−	16.8428i	−0.0981501	−	0.598863i
$792$	2.34919	+	11.8102i	0.0834750	+	0.419657i
$793$	−3.55099	−	0.232744i	−0.126099	−	0.00826499i
$794$	−4.63550	+	5.28578i	−0.164508	+	0.187585i
$795$	11.4550	−	3.06936i	0.406268	−	0.108859i
$796$	−0.489616	−	0.241452i	−0.0173540	−	0.00855803i
$797$	6.59333	+	15.9177i	0.233548	+	0.563834i	0.996590	−	0.0825146i	$-0.0262951\pi$
$797$	6.59333	+	15.9177i	0.233548	+	0.563834i	−0.763042	+	0.646349i	$0.776295\pi$
$798$	−0.176612	+	0.329486i	−0.00625198	+	0.0116637i
$799$	−18.0821	+	26.8525i	−0.639700	+	0.949974i
$800$	−0.570819	−	0.988688i	−0.0201815	−	0.0349554i
$801$	−1.32147	+	10.0376i	−0.0466920	+	0.354661i
$802$	−0.992728	−	15.1461i	−0.0350544	−	0.534827i
$803$	17.2493	−	64.3751i	0.608713	−	2.27175i
$804$	0.370590	−	1.86308i	0.0130697	−	0.0657058i
$805$	5.34553	+	3.33278i	0.188405	+	0.117465i
$806$	42.3272	−	8.41940i	1.49091	−	0.296561i
$807$	1.45931	+	11.0846i	0.0513702	+	0.390196i
$808$	−22.1347	+	16.9845i	−0.778695	+	0.597514i
$809$	14.5873	+	4.95171i	0.512861	+	0.174093i	0.565859	−	0.824502i	$-0.308544\pi$
$809$	14.5873	+	4.95171i	0.512861	+	0.174093i	−0.0529984	+	0.998595i	$0.516878\pi$
$810$	0.193876	−	2.95798i	0.00681212	−	0.103933i
$811$	−41.9513	−	8.34464i	−1.47311	−	0.293020i	−0.607733	−	0.794141i	$-0.707921\pi$
$811$	−41.9513	−	8.34464i	−1.47311	−	0.293020i	−0.865377	+	0.501121i	$0.832921\pi$
$812$	6.58915	−	7.01862i	0.231234	−	0.246305i
$813$	7.89492	+	11.8156i	0.276887	+	0.414391i
$814$	−19.4565	−	14.9295i	−0.681950	−	0.523278i
$815$	−13.2240	+	22.9046i	−0.463217	+	0.802315i
$816$	−3.18744	−	12.0689i	−0.111583	−	0.422497i
$817$	−0.515325	+	0.297523i	−0.0180290	+	0.0104090i
$818$	31.4062	−	13.0089i	1.09809	−	0.454844i
$819$	−1.01219	−	10.4022i	−0.0353688	−	0.363482i
$820$	5.04973	−	5.04973i	0.176344	−	0.176344i
$821$	7.70609	+	22.7014i	0.268945	+	0.792285i	0.994558	+	0.104183i	$0.0332227\pi$
$821$	7.70609	+	22.7014i	0.268945	+	0.792285i	−0.725614	+	0.688102i	$0.758444\pi$
$822$	1.30933	+	2.65505i	0.0456680	+	0.0926056i
$823$	−8.96708	+	26.4162i	−0.312573	+	0.920810i	0.671182	+	0.741293i	$0.265787\pi$
$823$	−8.96708	+	26.4162i	−0.312573	+	0.920810i	−0.983755	+	0.179517i	$0.942546\pi$
$824$	−30.6740	+	4.03832i	−1.06858	+	0.140681i
$825$	−1.85840	−	0.769776i	−0.0647013	−	0.0268002i
$826$	11.9991	−	11.2120i	0.417503	−	0.390114i
$827$	18.4165	−	27.5623i	0.640406	−	0.958435i	−0.359276	−	0.933231i	$-0.616976\pi$
$827$	18.4165	−	27.5623i	0.640406	−	0.958435i	0.999682	−	0.0252042i	$-0.00802360\pi$
$828$	−0.388565	+	0.131900i	−0.0135036	+	0.00458384i
$829$	−3.55327	−	13.2610i	−0.123410	−	0.460572i	0.876368	−	0.481642i	$-0.159959\pi$
$829$	−3.55327	−	13.2610i	−0.123410	−	0.460572i	−0.999778	+	0.0210697i	$0.993293\pi$
$830$	33.6589	−	2.20612i	1.16832	−	0.0765757i
$831$	−6.74045	+	8.78432i	−0.233824	+	0.304725i
$832$	−35.1465			−1.21849
$833$	−26.5987	−	11.2031i	−0.921589	−	0.388166i
$834$	−20.8833			−0.723128
$835$	−2.93831	+	3.82929i	−0.101685	+	0.132518i
$836$	−0.178989	+	0.0117316i	−0.00619046	+	0.000405744i
$837$	2.23854	+	8.35434i	0.0773752	+	0.288768i
$838$	−31.1352	+	10.5690i	−1.07555	+	0.365099i
$839$	8.43751	−	12.6276i	0.291295	−	0.435954i	−0.656741	−	0.754116i	$-0.728066\pi$
$839$	8.43751	−	12.6276i	0.291295	−	0.435954i	0.948036	+	0.318162i	$0.103066\pi$
$840$	−13.7788	+	12.8749i	−0.475413	+	0.444226i
$841$	−47.9822	−	19.8749i	−1.65456	−	0.685341i
$842$	46.4951	−	6.12120i	1.60233	−	0.210950i
$843$	3.64080	−	10.7254i	0.125396	−	0.369404i
$844$	1.92813	+	3.90987i	0.0663691	+	0.134583i
$845$	1.96457	+	5.78743i	0.0675831	+	0.199093i
$846$	7.01294	−	7.01294i	0.241110	−	0.241110i
$847$	−1.20917	−	12.4265i	−0.0415475	−	0.426981i
$848$	−14.1345	+	5.85471i	−0.485382	+	0.201052i
$849$	−0.268501	+	0.155019i	−0.00921494	+	0.00532025i
$850$	2.49906	+	0.858341i	0.0857172	+	0.0294409i
$851$	2.48415	−	4.30267i	0.0851555	−	0.147494i
$852$	−4.16058	−	3.19252i	−0.142539	−	0.109374i
$853$	−2.54917	−	3.81510i	−0.0872818	−	0.130626i	0.785260	−	0.619167i	$-0.212530\pi$
$853$	−2.54917	−	3.81510i	−0.0872818	−	0.130626i	−0.872541	+	0.488540i	$0.837530\pi$
$854$	2.06064	−	2.19495i	0.0705138	−	0.0751098i
$855$	0.257467	+	0.0512134i	0.00880518	+	0.00175146i
$856$	−0.748406	+	11.4185i	−0.0255800	+	0.390275i
$857$	43.2647	+	14.6864i	1.47789	+	0.501677i	0.939952	−	0.341305i	$-0.110869\pi$
$857$	43.2647	+	14.6864i	1.47789	+	0.501677i	0.537941	+	0.842983i	$0.319202\pi$
$858$	−15.6948	+	12.0430i	−0.535812	+	0.411143i
$859$	5.16782	+	39.2535i	0.176324	+	1.33931i	0.819273	+	0.573404i	$0.194377\pi$
$859$	5.16782	+	39.2535i	0.176324	+	1.33931i	−0.642949	+	0.765909i	$0.722289\pi$
$860$	−4.95210	+	0.985034i	−0.168865	+	0.0335894i
$861$	−16.8921	−	10.5317i	−0.575683	−	0.358921i
$862$	9.74687	−	49.0008i	0.331980	−	1.66897i
$863$	10.2558	−	38.2751i	0.349111	−	1.30290i	−0.538624	−	0.842546i	$-0.681056\pi$
$863$	10.2558	−	38.2751i	0.349111	−	1.30290i	0.887735	−	0.460355i	$-0.152278\pi$
$864$	−0.147168	−	2.24535i	−0.00500677	−	0.0763885i
$865$	−1.49219	+	11.3343i	−0.0507358	+	0.385377i
$866$	8.33624	+	14.4388i	0.283277	+	0.490650i
$867$	−14.0668	−	9.54600i	−0.477732	−	0.324199i
$868$	4.37246	−	8.15724i	0.148411	−	0.276875i
$869$	−15.4321	−	37.2564i	−0.523498	−	1.26384i
$870$	23.9181	+	11.7951i	0.810900	+	0.399892i
$871$	17.9207	−	4.80184i	0.607219	−	0.162704i
$872$	−22.7198	+	25.9069i	−0.769389	+	0.877320i
$873$	−8.89742	−	0.583168i	−0.301132	−	0.0197372i
$874$	0.0279668	+	0.140599i	0.000945991	+	0.00475582i
$875$	4.51160	+	27.5275i	0.152520	+	0.930599i
$876$	−2.60178	+	6.28126i	−0.0879061	+	0.212224i
$877$	−19.0302	+	16.6890i	−0.642603	+	0.563547i	−0.917406	−	0.397953i	$-0.869721\pi$
$877$	−19.0302	+	16.6890i	−0.642603	+	0.563547i	0.274803	+	0.961501i	$0.411387\pi$
$878$	−43.0576	+	21.2336i	−1.45312	+	0.716601i
$879$	−11.3991	−	9.99677i	−0.384483	−	0.337183i
$880$	27.2090	+	7.29063i	0.917216	+	0.245767i
$881$	−38.7483	+	25.8908i	−1.30546	+	0.872282i	−0.996881	−	0.0789158i	$-0.974854\pi$
$881$	−38.7483	+	25.8908i	−1.30546	+	0.872282i	−0.308581	+	0.951198i	$0.599854\pi$
$882$	7.34033	+	4.92964i	0.247162	+	0.165989i
$883$			31.9956i			1.07674i	0.842709	+	0.538369i	$0.180959\pi$
$883$			31.9956i			1.07674i	−0.842709	+	0.538369i	$0.819041\pi$
$884$	−4.96826	+	4.32558i	−0.167101	+	0.145485i
$885$	−9.98686	−	5.76591i	−0.335704	−	0.193819i
$886$	−35.0826	−	4.61872i	−1.17862	−	0.155169i
$887$	−9.42120	+	19.1043i	−0.316333	+	0.641460i	−0.995730	−	0.0923109i	$-0.970575\pi$
$887$	−9.42120	+	19.1043i	−0.316333	+	0.641460i	0.679397	+	0.733771i	$0.262241\pi$
$888$	10.5169	+	10.5169i	0.352924	+	0.352924i
$889$	16.4842	−	6.18211i	0.552861	−	0.207341i
$890$	24.9536	+	16.6735i	0.836447	+	0.558896i
$891$	−2.61412	−	2.98083i	−0.0875763	−	0.0998616i
$892$	−0.582875	−	0.759617i	−0.0195161	−	0.0254339i
$893$	0.534667	+	0.696792i	0.0178920	+	0.0233173i
$894$	3.47841	+	3.96637i	0.116335	+	0.132655i
$895$	46.8220	+	31.2855i	1.56509	+	1.04576i
$896$	11.3261	−	13.7678i	0.378377	−	0.459951i
$897$	−2.83390	−	2.83390i	−0.0946211	−	0.0946211i
$898$	18.1921	−	36.8900i	0.607079	−	1.23103i
$899$	−77.1448	−	10.1563i	−2.57292	−	0.338732i
$900$	0.177710	+	0.102601i	0.00592368	+	0.00342004i
$901$	−9.28239	+	18.6536i	−0.309241	+	0.621442i
$902$			37.6798i			1.25460i
$903$	5.79346	+	12.8265i	0.192794	+	0.426839i
$904$	16.2907	−	10.8851i	0.541821	−	0.362033i
$905$	34.2086	+	9.16618i	1.13713	+	0.304694i
$906$	14.7430	+	12.9293i	0.489803	+	0.429546i
$907$	−43.1808	+	21.2944i	−1.43379	+	0.707069i	−0.982665	−	0.185390i	$-0.940645\pi$
$907$	−43.1808	+	21.2944i	−1.43379	+	0.707069i	−0.451129	+	0.892459i	$0.648978\pi$
$908$	3.79263	−	3.32605i	0.125863	−	0.110379i
$909$	3.51540	−	8.48693i	0.116599	−	0.281494i
$910$	−28.9826	−	10.9472i	−0.960765	−	0.362895i
$911$	7.56144	+	38.0139i	0.250522	+	1.25946i	0.877179	+	0.480163i	$0.159422\pi$
$911$	7.56144	+	38.0139i	0.250522	+	1.25946i	−0.626658	+	0.779295i	$0.715578\pi$
$912$	−0.337933	−	0.0221493i	−0.0111901	−	0.000733437i
$913$	29.7461	−	33.9190i	0.984453	−	1.12255i
$914$	−30.2578	+	8.10755i	−1.00084	+	0.268174i
$915$	−1.89610	−	0.935051i	−0.0626830	−	0.0309118i
$916$	−1.24976	−	3.01718i	−0.0412931	−	0.0996903i
$917$	−17.9100	−	9.60018i	−0.591441	−	0.317026i
$918$	3.66943	+	3.69589i	0.121109	+	0.121982i
$919$	3.03287	+	5.25308i	0.100045	+	0.173283i	0.911703	−	0.410850i	$-0.134768\pi$
$919$	3.03287	+	5.25308i	0.100045	+	0.173283i	−0.811658	+	0.584133i	$0.801435\pi$
$920$	−0.943880	+	7.16948i	−0.0311188	+	0.236371i
$921$	1.53017	+	23.3458i	0.0504207	+	0.769271i
$922$	−8.69792	+	32.4611i	−0.286451	+	1.06905i
$923$	9.99255	−	50.2359i	0.328909	−	1.65354i
$924$	−0.143794	+	4.24014i	−0.00473049	+	0.139490i
$925$	−2.43679	+	0.484707i	−0.0801211	+	0.0159371i
$926$	1.59907	+	12.1461i	0.0525486	+	0.399146i
$927$	8.08161	−	6.20124i	0.265435	−	0.203675i
$928$	19.1692	+	6.50706i	0.629259	+	0.213605i
$929$	2.59869	−	39.6484i	0.0852604	−	1.30082i	−0.714131	−	0.700012i	$-0.753178\pi$
$929$	2.59869	−	39.6484i	0.0852604	−	1.30082i	0.799392	−	0.600810i	$-0.205155\pi$
$930$	25.1460	+	5.00184i	0.824569	+	0.164017i
$931$	−0.517664	+	0.587493i	−0.0169658	+	0.0192543i
$932$	−4.83638	−	7.23816i	−0.158421	−	0.237094i
$933$	2.31948	+	1.77980i	0.0759362	+	0.0582679i
$934$	−4.11721	+	7.13121i	−0.134719	+	0.233340i
$935$	34.4671	−	16.8436i	1.12719	−	0.550846i
$936$	10.3902	−	5.99879i	0.339615	−	0.196077i
$937$	−2.55471	+	1.05819i	−0.0834586	+	0.0345697i	−0.424022	−	0.905652i	$-0.639382\pi$
$937$	−2.55471	+	1.05819i	−0.0834586	+	0.0345697i	0.340564	+	0.940221i	$0.389382\pi$
$938$	−6.49469	+	14.2894i	−0.212059	+	0.466566i
$939$	−8.69918	+	8.69918i	−0.283887	+	0.283887i
$940$	2.39552	+	7.05698i	0.0781334	+	0.230173i
$941$	3.71553	+	7.53436i	0.121123	+	0.245613i	0.948987	−	0.315316i	$-0.102111\pi$
$941$	3.71553	+	7.53436i	0.121123	+	0.245613i	−0.827864	+	0.560929i	$0.810444\pi$
$942$	7.55673	−	22.2614i	0.246212	−	0.725316i
$943$	−7.56811	+	0.996360i	−0.246451	+	0.0324460i
$944$	13.7444	+	5.69314i	0.447344	+	0.185296i
$945$	1.80935	−	5.93951i	0.0588582	−	0.193212i
$946$	14.8006	−	22.1507i	0.481211	−	0.720182i
$947$	−14.3110	+	4.85793i	−0.465045	+	0.157861i	−0.544120	−	0.839007i	$-0.683137\pi$
$947$	−14.3110	+	4.85793i	−0.465045	+	0.157861i	0.0790755	+	0.996869i	$0.474803\pi$
$948$	1.06473	+	3.97362i	0.0345807	+	0.129057i
$949$	−66.2604	+	4.34294i	−2.15090	+	0.140978i
$950$	0.0436406	−	0.0568735i	0.00141589	−	0.00184522i
$951$	−20.5377			−0.665979
$952$	−0.926179	−	33.1188i	−0.0300176	−	1.07339i
$953$	31.5463			1.02189			0.510943	−	0.859615i	$-0.329296\pi$
$953$	31.5463			1.02189			0.510943	+	0.859615i	$0.329296\pi$
$954$	3.88582	−	5.06409i	0.125808	−	0.163956i
$955$	−33.9568	+	2.22565i	−1.09882	+	0.0720202i
$956$	3.15245	+	11.7651i	0.101957	+	0.380510i
$957$	33.7753	−	11.4652i	1.09180	−	0.370617i
$958$	14.9378	−	22.3559i	0.482617	−	0.722288i
$959$	1.40092	+	6.04031i	0.0452382	+	0.195052i
$960$	−19.2906	−	7.99044i	−0.622602	−	0.257890i
$961$	−43.4312	+	5.71783i	−1.40101	+	0.184446i
$962$	−7.85430	+	23.1380i	−0.253233	+	0.746000i
$963$	−1.66638	−	3.37908i	−0.0536982	−	0.108889i
$964$	−2.50526	−	7.38025i	−0.0806889	−	0.237702i
$965$	21.8642	−	21.8642i	0.703832	−	0.703832i
$966$	3.37469	−	0.328376i	0.108579	−	0.0105653i
$967$	−27.0401	+	11.2004i	−0.869552	+	0.360180i	−0.772436	−	0.635093i	$-0.780962\pi$
$967$	−27.0401	+	11.2004i	−0.869552	+	0.360180i	−0.0971162	+	0.995273i	$0.530962\pi$
$968$	12.4122	−	7.16619i	0.398943	−	0.230330i
$969$	−0.366910	+	0.279452i	−0.0117869	+	0.00897728i
$970$	−13.2157	+	22.8903i	−0.424332	+	0.734964i
$971$	−29.2089	−	22.4128i	−0.937358	−	0.719260i	0.0225003	−	0.999747i	$-0.492837\pi$
$971$	−29.2089	−	22.4128i	−0.937358	−	0.719260i	−0.959858	+	0.280487i	$0.909504\pi$
$972$	0.224703	+	0.336291i	0.00720734	+	0.0107865i
$973$	−42.5871	−	9.98267i	−1.36528	−	0.320030i
$974$	−22.8312	−	4.54141i	−0.731559	−	0.145516i
$975$	−0.131079	+	1.99988i	−0.00419790	+	0.0640475i
$976$	2.58263	+	0.876683i	0.0826678	+	0.0280619i
$977$	28.1810	−	21.6240i	0.901590	−	0.691815i	−0.0501426	−	0.998742i	$-0.515968\pi$
$977$	28.1810	−	21.6240i	0.901590	−	0.691815i	0.951733	+	0.306927i	$0.0993009\pi$
$978$	1.85812	+	14.1138i	0.0594161	+	0.451310i
$979$	39.3683	−	7.83085i	1.25822	−	0.250275i
$980$	−5.76178	+	3.30854i	−0.184053	+	0.105687i
$981$	2.21338	−	11.1274i	0.0706677	−	0.355270i
$982$	−2.96342	+	11.0596i	−0.0945664	+	0.352927i
$983$	−1.03171	−	15.7409i	−0.0329066	−	0.502058i	−0.982221	−	0.187729i	$-0.939887\pi$
$983$	−1.03171	−	15.7409i	−0.0329066	−	0.502058i	0.949314	−	0.314329i	$-0.101779\pi$
$984$	2.98271	−	22.6559i	0.0950853	−	0.722245i
$985$	−11.2987	−	19.5699i	−0.360006	−	0.623549i
$986$	−43.3518	+	17.7747i	−1.38060	+	0.566063i
$987$	17.6538	−	10.9491i	0.561926	−	0.348513i
$988$	0.0683923	+	0.165114i	0.00217585	+	0.00525296i
$989$	4.84041	+	2.38703i	0.153916	+	0.0759030i
$990$	−11.3523	+	3.04183i	−0.360798	+	0.0966756i
$991$	24.7634	−	28.2373i	0.786636	−	0.896987i	−0.210103	−	0.977679i	$-0.567380\pi$
$991$	24.7634	−	28.2373i	0.786636	−	0.896987i	0.996739	+	0.0806927i	$0.0257132\pi$
$992$	19.4202	+	1.27287i	0.616591	+	0.0404135i
$993$	0.145672	+	0.732344i	0.00462277	+	0.0232402i
$994$	27.4510	+	33.5294i	0.870692	+	1.06349i
$995$	1.21218	−	2.92646i	0.0384287	−	0.0927750i
$996$	−3.46019	+	3.03450i	−0.109640	+	0.0961519i
$997$	21.8597	−	10.7800i	0.692302	−	0.341406i	−0.0618683	−	0.998084i	$-0.519706\pi$
$997$	21.8597	−	10.7800i	0.692302	−	0.341406i	0.754171	+	0.656679i	$0.228039\pi$
$998$	−17.3799	−	15.2417i	−0.550150	−	0.482468i
$999$	−4.73015	−	1.26744i	−0.149655	−	0.0401000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.199.7	yes	384
7.5	odd	6	inner	357.2.bl.a.250.18	yes	384
17.10	odd	16	inner	357.2.bl.a.10.18	✓	384
119.61	even	48	inner	357.2.bl.a.61.7	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.18	✓	384	17.10	odd	16	inner
357.2.bl.a.61.7	yes	384	119.61	even	48	inner
357.2.bl.a.199.7	yes	384	1.1	even	1	trivial
357.2.bl.a.250.18	yes	384	7.5	odd	6	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.768957 + 1.00212i) q^{2} +(0.997859 - 0.0654031i) q^{3} +(0.104680 + 0.390673i) q^{4} +(-2.22223 + 0.754346i) q^{5} +(-0.701768 + 1.05027i) q^{6} +(-1.93316 + 1.80635i) q^{7} +(-2.80599 - 1.16228i) q^{8} +(0.991445 - 0.130526i) q^{9} +(0.952852 - 2.80701i) q^{10} +(-1.75355 - 3.55585i) q^{11} +(0.130007 + 0.382990i) q^{12} +(-2.79324 + 2.79324i) q^{13} +(-0.323664 - 3.32627i) q^{14} +(-2.16814 + 0.898072i) q^{15} +(2.62190 - 1.51375i) q^{16} +(1.33935 - 3.89951i) q^{17} +(-0.631575 + 1.09392i) q^{18} +(-0.0887447 - 0.0680962i) q^{19} +(-0.527327 - 0.789200i) q^{20} +(-1.81088 + 1.92891i) q^{21} +(4.91180 + 0.977018i) q^{22} +(-0.0663552 + 1.01238i) q^{23} +(-2.87600 - 0.976271i) q^{24} +(0.402513 - 0.308859i) q^{25} +(-0.651291 - 4.94704i) q^{26} +(0.980785 - 0.195090i) q^{27} +(-0.908054 - 0.566144i) q^{28} +(-1.75511 + 8.82356i) q^{29} +(0.767225 - 2.86332i) q^{30} +(0.565675 + 8.63053i) q^{31} +(0.293706 - 2.23092i) q^{32} +(-1.98236 - 3.43354i) q^{33} +(2.87789 + 4.34074i) q^{34} +(2.93333 - 5.47239i) q^{35} +(0.154778 + 0.373667i) q^{36} +(-4.39200 - 2.16589i) q^{37} +(0.136482 - 0.0365702i) q^{38} +(-2.60457 + 2.96994i) q^{39} +(7.11233 + 0.466167i) q^{40} +(1.46784 + 7.37932i) q^{41} +(-0.540519 - 3.29798i) q^{42} +(2.03570 - 4.91462i) q^{43} +(1.20561 - 1.05729i) q^{44} +(-2.10476 + 1.03795i) q^{45} +(-0.963511 - 0.844976i) q^{46} +(-7.58411 - 2.03215i) q^{47} +(2.51728 - 1.68199i) q^{48} +(0.474231 - 6.98392i) q^{49} +0.640867i q^{50} +(1.08144 - 3.97876i) q^{51} +(-1.38364 - 0.798843i) q^{52} +(-5.01013 - 0.659596i) q^{53} +(-0.558677 + 1.13288i) q^{54} +(6.57913 + 6.57913i) q^{55} +(7.52392 - 2.82172i) q^{56} +(-0.0930084 - 0.0621463i) q^{57} +(-7.49269 - 8.54377i) q^{58} +(2.99139 + 3.89846i) q^{59} +(-0.577814 - 0.753021i) q^{60} +(0.593979 + 0.677304i) q^{61} +(-9.08384 - 6.06963i) q^{62} +(-1.68085 + 2.04322i) q^{63} +(6.29136 + 6.29136i) q^{64} +(4.10015 - 8.31429i) q^{65} +(4.96518 + 0.653679i) q^{66} +(-4.06742 - 2.34833i) q^{67} +(1.66363 + 0.115043i) q^{68} +1.01456i q^{69} +(3.22842 + 7.14759i) q^{70} +(-10.7811 + 7.20372i) q^{71} +(-2.93369 - 0.786081i) q^{72} +(12.6383 + 11.0835i) q^{73} +(5.54775 - 2.73585i) q^{74} +(0.381451 - 0.334523i) q^{75} +(0.0173135 - 0.0417985i) q^{76} +(9.81298 + 3.70651i) q^{77} +(-0.973448 - 4.89386i) q^{78} +(10.1494 + 0.665230i) q^{79} +(-4.68458 + 5.34174i) q^{80} +(0.965926 - 0.258819i) q^{81} +(-8.52369 - 4.20342i) q^{82} +(4.35456 + 10.5128i) q^{83} +(-0.943137 - 0.505543i) q^{84} +(-0.0347577 + 9.67594i) q^{85} +(3.35969 + 5.81916i) q^{86} +(-1.17427 + 8.91946i) q^{87} +(0.787556 + 12.0158i) q^{88} +(-2.62034 + 9.77923i) q^{89} +(0.578312 - 2.90737i) q^{90} +(0.354228 - 10.4453i) q^{91} +(-0.402457 + 0.0800537i) q^{92} +(1.12893 + 8.57505i) q^{93} +(7.86832 - 6.03757i) q^{94} +(0.248580 + 0.0843814i) q^{95} +(0.147168 - 2.24535i) q^{96} +(-8.74519 - 1.73953i) q^{97} +(6.63409 + 5.84557i) q^{98} +(-2.20268 - 3.29654i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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