LMFDB - Embedded newform 384.2.v.a.349.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			349.31
Character	$\chi$	$=$	384.349
Dual form			384.2.v.a.373.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40251 + 0.181550i) q^{2} +(0.995185 + 0.0980171i) q^{3} +(1.93408 + 0.509252i) q^{4} +(1.31642 + 2.46285i) q^{5} +(1.37796 + 0.318146i) q^{6} +(-0.901722 - 4.53326i) q^{7} +(2.62011 + 1.06536i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(1.40251 + 0.181550i) q^{2} +(0.995185 + 0.0980171i) q^{3} +(1.93408 + 0.509252i) q^{4} +(1.31642 + 2.46285i) q^{5} +(1.37796 + 0.318146i) q^{6} +(-0.901722 - 4.53326i) q^{7} +(2.62011 + 1.06536i) q^{8} +(0.980785 + 0.195090i) q^{9} +(1.39917 + 3.69317i) q^{10} +(-3.61553 - 2.96719i) q^{11} +(1.87485 + 0.696373i) q^{12} +(-0.706057 - 0.377395i) q^{13} +(-0.441661 - 6.52166i) q^{14} +(1.06868 + 2.58002i) q^{15} +(3.48132 + 1.96987i) q^{16} +(-2.89337 + 6.98522i) q^{17} +(1.34014 + 0.451678i) q^{18} +(-0.380664 + 0.115473i) q^{19} +(1.29185 + 5.43374i) q^{20} +(-0.453042 - 4.59982i) q^{21} +(-4.53213 - 4.81791i) q^{22} +(-5.16718 + 3.45260i) q^{23} +(2.50307 + 1.31705i) q^{24} +(-1.55482 + 2.32695i) q^{25} +(-0.921737 - 0.657486i) q^{26} +(0.956940 + 0.290285i) q^{27} +(0.564573 - 9.22689i) q^{28} +(0.0117413 + 0.0143068i) q^{29} +(1.03043 + 3.81253i) q^{30} +(-0.0486579 + 0.0486579i) q^{31} +(4.52497 + 3.39480i) q^{32} +(-3.30728 - 3.30728i) q^{33} +(-5.32615 + 9.27156i) q^{34} +(9.97770 - 8.18849i) q^{35} +(1.79757 + 0.876787i) q^{36} +(1.34080 - 4.42004i) q^{37} +(-0.554850 + 0.0928429i) q^{38} +(-0.665666 - 0.444784i) q^{39} +(0.825339 + 7.85542i) q^{40} +(-3.57602 - 5.35189i) q^{41} +(0.199700 - 6.53355i) q^{42} +(-3.24361 + 0.319468i) q^{43} +(-5.48167 - 7.57999i) q^{44} +(0.810648 + 2.67235i) q^{45} +(-7.87385 + 3.90421i) q^{46} +(9.89282 + 4.09774i) q^{47} +(3.27148 + 2.30161i) q^{48} +(-13.2702 + 5.49670i) q^{49} +(-2.60311 + 2.98130i) q^{50} +(-3.56411 + 6.66798i) q^{51} +(-1.17338 - 1.08947i) q^{52} +(9.12159 - 11.1147i) q^{53} +(1.28942 + 0.580860i) q^{54} +(2.54818 - 12.8106i) q^{55} +(2.46696 - 12.8383i) q^{56} +(-0.390149 + 0.0776055i) q^{57} +(0.0138699 + 0.0221970i) q^{58} +(-4.37579 + 2.33891i) q^{59} +(0.753030 + 5.53420i) q^{60} +(0.556994 - 5.65526i) q^{61} +(-0.0770772 + 0.0594095i) q^{62} -4.62207i q^{63} +(5.73000 + 5.58275i) q^{64} -2.23572i q^{65} +(-4.03807 - 5.23894i) q^{66} +(0.0180106 - 0.182865i) q^{67} +(-9.15325 + 12.0365i) q^{68} +(-5.48071 + 2.92950i) q^{69} +(15.4805 - 9.67300i) q^{70} +(0.279494 - 0.0555948i) q^{71} +(2.36193 + 1.55605i) q^{72} +(-2.11289 + 10.6222i) q^{73} +(2.68295 - 5.95573i) q^{74} +(-1.77541 + 2.16335i) q^{75} +(-0.795039 + 0.0294802i) q^{76} +(-10.1908 + 19.0657i) q^{77} +(-0.852854 - 0.744666i) q^{78} +(0.948679 - 0.392956i) q^{79} +(-0.268605 + 11.1672i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-4.04377 - 8.15532i) q^{82} +(0.874437 + 2.88263i) q^{83} +(1.46625 - 9.12712i) q^{84} +(-21.0124 + 2.06954i) q^{85} +(-4.60721 - 0.140821i) q^{86} +(0.0102824 + 0.0153887i) q^{87} +(-6.31196 - 11.6262i) q^{88} +(10.5720 + 7.06396i) q^{89} +(0.651778 + 3.89517i) q^{90} +(-1.07416 + 3.54105i) q^{91} +(-11.7520 + 4.04620i) q^{92} +(-0.0531929 + 0.0436543i) q^{93} +(13.1308 + 7.54317i) q^{94} +(-0.785507 - 0.785507i) q^{95} +(4.17043 + 3.82198i) q^{96} +(-4.10574 + 4.10574i) q^{97} +(-19.6095 + 5.29998i) q^{98} +(-2.96719 - 3.61553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	1.40251	+	0.181550i	0.991726	+	0.128375i
$2$	1.40251	+	0.181550i	0.991726	+	0.128375i
$3$	0.995185	+	0.0980171i	0.574570	+	0.0565902i
$3$	0.995185	+	0.0980171i	0.574570	+	0.0565902i
$4$	1.93408	+	0.509252i	0.967040	+	0.254626i
$5$	1.31642	+	2.46285i	0.588721	+	1.10142i	0.983203	+	0.182516i	$0.0584243\pi$
$5$	1.31642	+	2.46285i	0.588721	+	1.10142i	−0.394481	+	0.918904i	$0.629076\pi$
$6$	1.37796	+	0.318146i	0.562551	+	0.129883i
$7$	−0.901722	−	4.53326i	−0.340819	−	1.71341i	−0.647897	−	0.761728i	$-0.724351\pi$
$7$	−0.901722	−	4.53326i	−0.340819	−	1.71341i	0.307079	−	0.951684i	$-0.400649\pi$
$8$	2.62011	+	1.06536i	0.926350	+	0.376663i
$9$	0.980785	+	0.195090i	0.326928	+	0.0650301i
$10$	1.39917	+	3.69317i	0.442455	+	1.16788i
$11$	−3.61553	−	2.96719i	−1.09012	−	0.894641i	−0.0952176	−	0.995456i	$-0.530355\pi$
$11$	−3.61553	−	2.96719i	−1.09012	−	0.894641i	−0.994905	+	0.100816i	$0.967855\pi$
$12$	1.87485	+	0.696373i	0.541223	+	0.201026i
$13$	−0.706057	−	0.377395i	−0.195825	−	0.104671i	0.370570	−	0.928805i	$-0.379162\pi$
$13$	−0.706057	−	0.377395i	−0.195825	−	0.104671i	−0.566395	+	0.824134i	$0.691662\pi$
$14$	−0.441661	−	6.52166i	−0.118039	−	1.74299i
$15$	1.06868	+	2.58002i	0.275932	+	0.666159i
$16$	3.48132	+	1.96987i	0.870331	+	0.492467i
$17$	−2.89337	+	6.98522i	−0.701746	+	1.69416i	0.0179169	+	0.999839i	$0.494297\pi$
$17$	−2.89337	+	6.98522i	−0.701746	+	1.69416i	−0.719662	+	0.694324i	$0.755703\pi$
$18$	1.34014	+	0.451678i	0.315875	+	0.106462i
$19$	−0.380664	+	0.115473i	−0.0873303	+	0.0264914i	−0.333647	−	0.942698i	$-0.608280\pi$
$19$	−0.380664	+	0.115473i	−0.0873303	+	0.0264914i	0.246317	+	0.969189i	$0.420780\pi$
$20$	1.29185	+	5.43374i	0.288866	+	1.21502i
$21$	−0.453042	−	4.59982i	−0.0988620	−	1.00376i
$22$	−4.53213	−	4.81791i	−0.966253	−	1.02718i
$23$	−5.16718	+	3.45260i	−1.07743	+	0.719917i	−0.961904	−	0.273387i	$-0.911856\pi$
$23$	−5.16718	+	3.45260i	−1.07743	+	0.719917i	−0.115528	+	0.993304i	$0.536856\pi$
$24$	2.50307	+	1.31705i	0.510938	+	0.268842i
$25$	−1.55482	+	2.32695i	−0.310964	+	0.465390i
$26$	−0.921737	−	0.657486i	−0.180768	−	0.128944i
$27$	0.956940	+	0.290285i	0.184163	+	0.0558653i
$28$	0.564573	−	9.22689i	0.106694	−	1.74372i
$29$	0.0117413	+	0.0143068i	0.00218030	+	0.00265670i	0.774099	−	0.633064i	$-0.218203\pi$
$29$	0.0117413	+	0.0143068i	0.00218030	+	0.00265670i	−0.771919	+	0.635721i	$0.780703\pi$
$30$	1.03043	+	3.81253i	0.188131	+	0.696070i
$31$	−0.0486579	+	0.0486579i	−0.00873922	+	0.00873922i	−0.711463	−	0.702724i	$-0.751967\pi$
$31$	−0.0486579	+	0.0486579i	−0.00873922	+	0.00873922i	0.702724	+	0.711463i	$0.251967\pi$
$32$	4.52497	+	3.39480i	0.799909	+	0.600121i
$33$	−3.30728	−	3.30728i	−0.575724	−	0.575724i
$34$	−5.32615	+	9.27156i	−0.913428	+	1.59006i
$35$	9.97770	−	8.18849i	1.68654	−	1.38411i
$36$	1.79757	+	0.876787i	0.299594	+	0.146131i
$37$	1.34080	−	4.42004i	0.220427	−	0.726649i	−0.775072	−	0.631873i	$-0.782286\pi$
$37$	1.34080	−	4.42004i	0.220427	−	0.726649i	0.995499	−	0.0947763i	$-0.0302136\pi$
$38$	−0.554850	+	0.0928429i	−0.0900085	+	0.0150611i
$39$	−0.665666	−	0.444784i	−0.106592	−	0.0712224i
$40$	0.825339	+	7.85542i	0.130498	+	1.24205i
$41$	−3.57602	−	5.35189i	−0.558481	−	0.835825i	0.439572	−	0.898207i	$-0.355130\pi$
$41$	−3.57602	−	5.35189i	−0.558481	−	0.835825i	−0.998052	+	0.0623823i	$0.980130\pi$
$42$	0.199700	−	6.53355i	0.0308144	−	1.00815i
$43$	−3.24361	+	0.319468i	−0.494646	+	0.0487184i	−0.342265	−	0.939603i	$-0.611194\pi$
$43$	−3.24361	+	0.319468i	−0.494646	+	0.0487184i	−0.152381	+	0.988322i	$0.548694\pi$
$44$	−5.48167	−	7.57999i	−0.826393	−	1.14273i
$45$	0.810648	+	2.67235i	0.120844	+	0.398370i
$46$	−7.87385	+	3.90421i	−1.16094	+	0.575644i
$47$	9.89282	+	4.09774i	1.44302	+	0.597717i	0.960527	−	0.278186i	$-0.0897331\pi$
$47$	9.89282	+	4.09774i	1.44302	+	0.597717i	0.482488	+	0.875902i	$0.339733\pi$
$48$	3.27148	+	2.30161i	0.472197	+	0.332209i
$49$	−13.2702	+	5.49670i	−1.89574	+	0.785242i
$50$	−2.60311	+	2.98130i	−0.368135	+	0.421619i
$51$	−3.56411	+	6.66798i	−0.499075	+	0.933704i
$52$	−1.17338	−	1.08947i	−0.162719	−	0.151083i
$53$	9.12159	−	11.1147i	1.25295	−	1.52672i	0.504706	−	0.863291i	$-0.331601\pi$
$53$	9.12159	−	11.1147i	1.25295	−	1.52672i	0.748240	−	0.663428i	$-0.230899\pi$
$54$	1.28942	+	0.580860i	0.175468	+	0.0790451i
$55$	2.54818	−	12.8106i	0.343597	−	1.72738i
$56$	2.46696	−	12.8383i	0.329662	−	1.71559i
$57$	−0.390149	+	0.0776055i	−0.0516765	+	0.0102791i
$58$	0.0138699	+	0.0221970i	0.00182120	+	0.00291461i
$59$	−4.37579	+	2.33891i	−0.569679	+	0.304500i	−0.730973	−	0.682407i	$-0.760933\pi$
$59$	−4.37579	+	2.33891i	−0.569679	+	0.304500i	0.161294	+	0.986906i	$0.448433\pi$
$60$	0.753030	+	5.53420i	0.0972157	+	0.714462i
$61$	0.556994	−	5.65526i	0.0713158	−	0.724081i	−0.891337	−	0.453342i	$-0.850232\pi$
$61$	0.556994	−	5.65526i	0.0713158	−	0.724081i	0.962653	−	0.270740i	$-0.0872683\pi$
$62$	−0.0770772	+	0.0594095i	−0.00978881	+	0.00754501i
$63$		−	4.62207i		−	0.582327i
$64$	5.73000	+	5.58275i	0.716249	+	0.697844i
$65$		−	2.23572i		−	0.277308i
$66$	−4.03807	−	5.23894i	−0.497052	−	0.644869i
$67$	0.0180106	−	0.182865i	0.00220034	−	0.0223405i	−0.994022	−	0.109181i	$-0.965177\pi$
$67$	0.0180106	−	0.182865i	0.00220034	−	0.0223405i	0.996222	+	0.0868407i	$0.0276771\pi$
$68$	−9.15325	+	12.0365i	−1.10999	+	1.45964i
$69$	−5.48071	+	2.92950i	−0.659800	+	0.352671i
$70$	15.4805	−	9.67300i	1.85027	−	1.15614i
$71$	0.279494	−	0.0555948i	0.0331698	−	0.00659789i	−0.178478	−	0.983944i	$-0.557117\pi$
$71$	0.279494	−	0.0555948i	0.0331698	−	0.00659789i	0.211647	+	0.977346i	$0.432117\pi$
$72$	2.36193	+	1.55605i	0.278356	+	0.183383i
$73$	−2.11289	+	10.6222i	−0.247295	+	1.24324i	0.634989	+	0.772521i	$0.281005\pi$
$73$	−2.11289	+	10.6222i	−0.247295	+	1.24324i	−0.882284	+	0.470717i	$0.843995\pi$
$74$	2.68295	−	5.95573i	0.311887	−	0.692339i
$75$	−1.77541	+	2.16335i	−0.205007	+	0.249802i
$76$	−0.795039	+	0.0294802i	−0.0911973	+	0.00338161i
$77$	−10.1908	+	19.0657i	−1.16135	+	2.17274i
$78$	−0.852854	−	0.744666i	−0.0965667	−	0.0843169i
$79$	0.948679	−	0.392956i	0.106735	−	0.0442110i	−0.328677	−	0.944442i	$-0.606603\pi$
$79$	0.948679	−	0.392956i	0.106735	−	0.0442110i	0.435412	+	0.900231i	$0.356603\pi$
$80$	−0.268605	+	11.1672i	−0.0300309	+	1.24853i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	−4.04377	−	8.15532i	−0.446560	−	0.900604i
$83$	0.874437	+	2.88263i	0.0959820	+	0.316410i	0.991763	−	0.128085i	$-0.0408831\pi$
$83$	0.874437	+	2.88263i	0.0959820	+	0.316410i	−0.895781	+	0.444495i	$0.853383\pi$
$84$	1.46625	−	9.12712i	0.159981	−	0.995851i
$85$	−21.0124	+	2.06954i	−2.27912	+	0.224474i
$86$	−4.60721	−	0.140821i	−0.496808	−	0.0151851i
$87$	0.0102824	+	0.0153887i	0.00110239	+	0.00164984i
$88$	−6.31196	−	11.6262i	−0.672857	−	1.23936i
$89$	10.5720	+	7.06396i	1.12063	+	0.748778i	0.970789	−	0.239933i	$-0.0771255\pi$
$89$	10.5720	+	7.06396i	1.12063	+	0.748778i	0.149836	+	0.988711i	$0.452126\pi$
$90$	0.651778	+	3.89517i	0.0687035	+	0.410587i
$91$	−1.07416	+	3.54105i	−0.112603	+	0.371203i
$92$	−11.7520	+	4.04620i	−1.22523	+	0.421846i
$93$	−0.0531929	+	0.0436543i	−0.00551585	+	0.00452674i
$94$	13.1308	+	7.54317i	1.35434	+	0.778019i
$95$	−0.785507	−	0.785507i	−0.0805914	−	0.0805914i
$96$	4.17043	+	3.82198i	0.425643	+	0.390079i
$97$	−4.10574	+	4.10574i	−0.416874	+	0.416874i	−0.884125	−	0.467251i	$-0.845245\pi$
$97$	−4.10574	+	4.10574i	−0.416874	+	0.416874i	0.467251	+	0.884125i	$0.345245\pi$
$98$	−19.6095	+	5.29998i	−1.98086	+	0.535378i
$99$	−2.96719	−	3.61553i	−0.298214	−	0.363374i
$100$	−4.19215	+	3.70871i	−0.419215	+	0.370871i
$101$	2.95961	+	0.897788i	0.294492	+	0.0893332i	0.434074	−	0.900877i	$-0.357076\pi$
$101$	2.95961	+	0.897788i	0.294492	+	0.0893332i	−0.139582	+	0.990211i	$0.544576\pi$
$102$	−6.20928	+	8.70486i	−0.614810	+	0.861909i
$103$	10.0012	−	14.9679i	0.985448	−	1.47483i	0.108584	−	0.994087i	$-0.465368\pi$
$103$	10.0012	−	14.9679i	0.985448	−	1.47483i	0.876864	−	0.480739i	$-0.159632\pi$
$104$	−1.44789	−	1.74103i	−0.141977	−	0.170722i
$105$	10.7323	−	7.17107i	1.04736	−	0.699825i
$106$	14.8110	−	13.9325i	1.43857	−	1.35324i
$107$	−0.801320	−	8.13594i	−0.0774665	−	0.786531i	−0.952919	−	0.303226i	$-0.901936\pi$
$107$	−0.801320	−	8.13594i	−0.0774665	−	0.786531i	0.875452	−	0.483305i	$-0.160564\pi$
$108$	1.70297	+	1.04876i	0.163868	+	0.100917i
$109$	1.40763	−	0.427001i	0.134827	−	0.0408992i	−0.222150	−	0.975012i	$-0.571308\pi$
$109$	1.40763	−	0.427001i	0.134827	−	0.0408992i	0.356977	+	0.934113i	$0.383808\pi$
$110$	5.89962	−	17.5044i	0.562506	−	1.66898i
$111$	1.76759	−	4.26733i	0.167772	−	0.405037i
$112$	5.79075	−	17.5580i	0.547174	−	1.65908i
$113$	−2.06493	−	4.98518i	−0.194252	−	0.468966i	0.796502	−	0.604636i	$-0.206681\pi$
$113$	−2.06493	−	4.98518i	−0.194252	−	0.468966i	−0.990754	+	0.135670i	$0.956681\pi$
$114$	−0.561278	+	0.0380110i	−0.0525685	+	0.00356006i
$115$	−15.3054	−	8.18092i	−1.42724	−	0.762875i
$116$	0.0154228	+	0.0336497i	0.00143197	+	0.00312429i
$117$	−0.618864	−	0.507889i	−0.0572140	−	0.0469543i
$118$	−6.56173	+	2.48592i	−0.604056	+	0.228848i
$119$	34.2748	+	6.81769i	3.14197	+	0.624976i
$120$	0.0513990	+	7.89849i	0.00469206	+	0.721030i
$121$	2.12185	+	10.6673i	0.192895	+	0.969751i
$122$	1.80790	−	7.83044i	0.163680	−	0.708935i
$123$	−3.03422	−	5.67663i	−0.273587	−	0.511845i
$124$	−0.118887	+	0.0693291i	−0.0106764	+	0.00622594i
$125$	6.11802	+	0.602573i	0.547213	+	0.0538957i
$126$	0.839138	−	6.48251i	0.0747564	−	0.577508i
$127$	−7.55347			−0.670262			−0.335131	−	0.942171i	$-0.608781\pi$
$127$	−7.55347			−0.670262			−0.335131	+	0.942171i	$0.608781\pi$
$128$	7.02284	+	8.87016i	0.620737	+	0.784019i
$129$	−3.25931			−0.286966
$130$	0.405896	−	3.13563i	0.0355994	−	0.275013i
$131$	−16.9256	−	1.66703i	−1.47880	−	0.145649i	−0.673794	−	0.738919i	$-0.735336\pi$
$131$	−16.9256	−	1.66703i	−1.47880	−	0.145649i	−0.805003	+	0.593271i	$0.797836\pi$
$132$	−4.71230	−	8.08079i	−0.410153	−	0.703342i
$133$	0.866723	+	1.62152i	0.0751544	+	0.140604i
$134$	0.0584591	−	0.253200i	0.00505010	−	0.0218731i
$135$	0.544809	+	2.73894i	0.0468897	+	0.235730i
$136$	−15.0228	+	15.2196i	−1.28819	+	1.30507i
$137$	17.7065	+	3.52203i	1.51276	+	0.300908i	0.880575	−	0.473907i	$-0.157157\pi$
$137$	17.7065	+	3.52203i	1.51276	+	0.300908i	0.632189	+	0.774814i	$0.282157\pi$
$138$	−8.21862	+	3.11364i	−0.699615	+	0.265050i
$139$	12.1259	+	9.95146i	1.02850	+	0.844072i	0.987898	−	0.155103i	$-0.0495710\pi$
$139$	12.1259	+	9.95146i	1.02850	+	0.844072i	0.0406064	+	0.999175i	$0.487071\pi$
$140$	23.4677	−	10.7560i	1.98338	−	0.909049i
$141$	9.44353	+	5.04767i	0.795289	+	0.425091i
$142$	0.402087	−	0.0272302i	0.0337424	−	0.00228511i
$143$	1.43297	+	3.45949i	0.119831	+	0.289297i
$144$	3.03013	+	2.61119i	0.252511	+	0.217599i
$145$	−0.0197790	+	0.0477507i	−0.00164255	+	0.00396548i
$146$	−4.89182	+	14.5142i	−0.404850	+	1.20120i
$147$	−13.7451	+	4.16952i	−1.13367	+	0.343896i
$148$	4.84413	−	7.86589i	0.398185	−	0.646572i
$149$	−0.719131	−	7.30146i	−0.0589135	−	0.598159i	−0.978637	−	0.205593i	$-0.934088\pi$
$149$	−0.719131	−	7.30146i	−0.0589135	−	0.598159i	0.919724	−	0.392566i	$-0.128412\pi$
$150$	−2.88279	+	2.71179i	−0.235379	+	0.221417i
$151$	−9.66853	+	6.46031i	−0.786814	+	0.525732i	−0.882855	−	0.469645i	$-0.844382\pi$
$151$	−9.66853	+	6.46031i	−0.786814	+	0.525732i	0.0960414	+	0.995377i	$0.469382\pi$
$152$	−1.12040	−	0.102993i	−0.0908768	−	0.00835385i
$153$	−4.20052	+	6.28653i	−0.339592	+	0.508236i
$154$	−17.7541	+	24.8897i	−1.43067	+	2.00567i
$155$	−0.183892	−	0.0557829i	−0.0147705	−	0.00448059i
$156$	−1.06094	−	1.19924i	−0.0849435	−	0.0960160i
$157$	−2.69606	−	3.28516i	−0.215169	−	0.262184i	0.654229	−	0.756296i	$-0.272993\pi$
$157$	−2.69606	−	3.28516i	−0.215169	−	0.262184i	−0.869398	+	0.494112i	$0.835493\pi$
$158$	1.40187	−	0.378892i	0.111527	−	0.0301430i
$159$	10.1671	−	10.1671i	0.806303	−	0.806303i
$160$	−2.40412	+	15.6133i	−0.190062	+	1.23434i
$161$	20.3109	+	20.3109i	1.60072	+	1.60072i
$162$	1.22628	+	0.704449i	0.0963453	+	0.0553467i
$163$	8.77852	−	7.20435i	0.687587	−	0.564288i	−0.224405	−	0.974496i	$-0.572044\pi$
$163$	8.77852	−	7.20435i	0.687587	−	0.564288i	0.911992	+	0.410208i	$0.134544\pi$
$164$	−4.19084	−	12.1721i	−0.327250	−	0.950480i
$165$	3.79157	−	12.4991i	0.295173	−	0.973055i
$166$	0.703066	+	4.20168i	0.0545685	+	0.326114i
$167$	−6.35210	−	4.24434i	−0.491540	−	0.328437i	0.284975	−	0.958535i	$-0.408015\pi$
$167$	−6.35210	−	4.24434i	−0.491540	−	0.328437i	−0.776515	+	0.630098i	$0.783015\pi$
$168$	3.71346	−	12.5347i	0.286500	−	0.967073i
$169$	−6.86632	−	10.2762i	−0.528179	−	0.790475i
$170$	−29.8459	−	0.912250i	−2.28908	−	0.0699664i
$171$	−0.395877	+	0.0389905i	−0.0302735	+	0.00298168i
$172$	−6.43609	−	1.03394i	−0.490748	−	0.0788373i
$173$	−3.94567	−	13.0071i	−0.299984	−	0.988914i	−0.969289	−	0.245926i	$-0.920908\pi$
$173$	−3.94567	−	13.0071i	−0.299984	−	0.988914i	0.669305	−	0.742988i	$-0.266592\pi$
$174$	0.0116274	+	0.0234496i	0.000881469	+	0.00177771i
$175$	11.9507	+	4.95014i	0.903387	+	0.374195i
$176$	−6.74185	−	17.4519i	−0.508186	−	1.31548i
$177$	−4.58397	+	1.89874i	−0.344552	+	0.142718i
$178$	13.5448	+	11.8266i	1.01523	+	0.886443i
$179$	−7.22298	+	13.5132i	−0.539871	+	1.01003i	0.453077	+	0.891471i	$0.350326\pi$
$179$	−7.22298	+	13.5132i	−0.539871	+	1.01003i	−0.992947	+	0.118555i	$0.962174\pi$
$180$	0.206958	+	5.58136i	0.0154257	+	0.416010i
$181$	−6.50731	+	7.92919i	−0.483685	+	0.589372i	−0.956479	−	0.291801i	$-0.905745\pi$
$181$	−6.50731	+	7.92919i	−0.483685	+	0.589372i	0.472794	+	0.881173i	$0.343245\pi$
$182$	−2.14941	+	4.77135i	−0.159325	+	0.353676i
$183$	1.10862	−	5.57343i	0.0819519	−	0.412000i
$184$	−17.2169	+	3.54127i	−1.26925	+	0.261066i
$185$	12.6510	−	2.51643i	0.930116	−	0.185012i
$186$	−0.0825292	+	0.0515685i	−0.00605133	+	0.00378119i
$187$	31.1875	−	16.6701i	2.28066	−	1.21904i
$188$	17.0467	+	12.9633i	1.24326	+	0.945445i
$189$	0.453042	−	4.59982i	0.0329540	−	0.334587i
$190$	−0.959074	−	1.24429i	−0.0695786	−	0.0902705i
$191$			24.2291i			1.75316i	0.481259	+	0.876578i	$0.340180\pi$
$191$			24.2291i			1.75316i	−0.481259	+	0.876578i	$0.659820\pi$
$192$	5.15520	+	6.11751i	0.372044	+	0.441493i
$193$			17.1801i			1.23665i	0.785921	+	0.618327i	$0.212189\pi$
$193$			17.1801i			1.23665i	−0.785921	+	0.618327i	$0.787811\pi$
$194$	−6.50374	+	5.01295i	−0.466941	+	0.359909i
$195$	0.219139	−	2.22496i	0.0156929	−	0.159333i
$196$	−28.4648	+	3.87317i	−2.03320	+	0.276655i
$197$	−10.5582	+	5.64346i	−0.752239	+	0.402080i	−0.802497	−	0.596656i	$-0.796496\pi$
$197$	−10.5582	+	5.64346i	−0.752239	+	0.402080i	0.0502583	+	0.998736i	$0.483996\pi$
$198$	−3.50512	−	5.60951i	−0.249098	−	0.398651i
$199$	23.7143	−	4.71707i	1.68106	−	0.334384i	0.739998	−	0.672609i	$-0.234826\pi$
$199$	23.7143	−	4.71707i	1.68106	−	0.334384i	0.941065	+	0.338225i	$0.109826\pi$
$200$	−6.55285	+	4.44043i	−0.463357	+	0.313986i
$201$	0.0358477	−	0.180219i	0.00252850	−	0.0127116i
$202$	3.98789	+	1.79648i	0.280587	+	0.126400i
$203$	0.0542689	−	0.0661269i	0.00380893	−	0.00464120i
$204$	−10.2890	+	11.0814i	−0.720371	+	0.775851i
$205$	8.47336	−	15.8525i	0.591805	−	1.10719i
$206$	16.7442	−	19.1769i	1.16663	−	1.33612i
$207$	−5.74146	+	2.37819i	−0.399059	+	0.165296i
$208$	−1.71459	−	2.70468i	−0.118886	−	0.187536i
$209$	1.71893	+	0.712005i	0.118901	+	0.0492504i
$210$	16.3540	−	8.10907i	1.12854	−	0.559579i
$211$	−0.0459642	−	0.151524i	−0.00316430	−	0.0104313i	0.955344	−	0.295496i	$-0.0954849\pi$
$211$	−0.0459642	−	0.151524i	−0.00316430	−	0.0104313i	−0.958508	+	0.285065i	$0.907985\pi$
$212$	23.3020	−	16.8515i	1.60039	−	1.15737i
$213$	0.283597	−	0.0279319i	0.0194318	−	0.00191386i
$214$	0.353220	−	11.5562i	0.0241456	−	0.789968i
$215$	−5.05676	−	7.56798i	−0.344868	−	0.516132i
$216$	2.19803	+	1.78007i	0.149557	+	0.121118i
$217$	0.264455	+	0.176703i	0.0179524	+	0.0119954i
$218$	2.05174	−	0.343318i	0.138962	−	0.0232524i
$219$	−3.14388	+	10.3640i	−0.212444	+	0.700333i
$220$	11.4522	−	23.4790i	0.772107	−	1.58295i
$221$	4.67907	−	3.84002i	0.314749	−	0.258307i
$222$	3.25379	−	5.66408i	0.218380	−	0.380148i
$223$	1.92628	+	1.92628i	0.128993	+	0.128993i	0.768656	−	0.639662i	$-0.220926\pi$
$223$	1.92628	+	1.92628i	0.128993	+	0.128993i	−0.639662	+	0.768656i	$0.720926\pi$
$224$	11.3093	−	23.5740i	0.755631	−	1.57511i
$225$	−1.97891	+	1.97891i	−0.131927	+	0.131927i
$226$	−1.99103	−	7.36665i	−0.132441	−	0.490023i
$227$	2.60100	+	3.16933i	0.172635	+	0.210356i	0.852139	−	0.523316i	$-0.175305\pi$
$227$	2.60100	+	3.16933i	0.172635	+	0.210356i	−0.679504	+	0.733671i	$0.737805\pi$
$228$	−0.794100	−	0.0485893i	−0.0525906	−	0.00321790i
$229$	22.8400	+	6.92842i	1.50931	+	0.457843i	0.933147	−	0.359494i	$-0.117051\pi$
$229$	22.8400	+	6.92842i	1.50931	+	0.457843i	0.576159	+	0.817337i	$0.304551\pi$
$230$	−19.9808	−	14.2525i	−1.31749	−	0.939785i
$231$	−12.0105	+	17.9750i	−0.790235	+	1.18267i
$232$	0.0155215	+	0.0499941i	0.00101904	+	0.00328227i
$233$	−11.9125	+	7.95968i	−0.780414	+	0.521456i	−0.880798	−	0.473493i	$-0.842993\pi$
$233$	−11.9125	+	7.95968i	−0.780414	+	0.521456i	0.100383	+	0.994949i	$0.467993\pi$
$234$	−0.775757	−	0.824675i	−0.0507128	−	0.0539107i
$235$	2.93099	+	29.7589i	0.191197	+	1.94126i
$236$	−9.65422	+	2.29525i	−0.628436	+	0.149408i
$237$	0.982627	−	0.298077i	0.0638285	−	0.0193622i
$238$	46.8331	+	15.7845i	3.03574	+	1.02316i
$239$	−2.05271	+	4.95569i	−0.132779	+	0.320557i	−0.976260	−	0.216602i	$-0.930503\pi$
$239$	−2.05271	+	4.95569i	−0.132779	+	0.320557i	0.843481	+	0.537159i	$0.180503\pi$
$240$	−1.36188	+	11.0871i	−0.0879093	+	0.715667i
$241$	−3.86666	−	9.33494i	−0.249073	−	0.601316i	0.749052	−	0.662511i	$-0.230509\pi$
$241$	−3.86666	−	9.33494i	−0.249073	−	0.601316i	−0.998126	+	0.0611943i	$0.980509\pi$
$242$	1.03928	+	15.3462i	0.0668073	+	0.986490i
$243$	0.881921	+	0.471397i	0.0565753	+	0.0302401i
$244$	3.95722	−	10.6541i	0.253335	−	0.682056i
$245$	−31.0067	−	25.4466i	−1.98095	−	1.62572i
$246$	−3.22494	−	8.51241i	−0.205615	−	0.542731i
$247$	0.312350	+	0.0621302i	0.0198743	+	0.00395325i
$248$	−0.179328	+	0.0756509i	−0.0113873	+	0.00480384i
$249$	0.587679	+	2.95446i	0.0372427	+	0.187231i
$250$	8.47120	+	1.95584i	0.535766	+	0.123698i
$251$	6.80178	+	12.7252i	0.429325	+	0.803210i	0.999837	−	0.0180794i	$-0.00575516\pi$
$251$	6.80178	+	12.7252i	0.429325	+	0.803210i	−0.570512	+	0.821289i	$0.693255\pi$
$252$	2.35380	−	8.93946i	0.148276	−	0.563133i
$253$	28.9266	+	2.84902i	1.81860	+	0.179116i
$254$	−10.5938	−	1.37133i	−0.664716	−	0.0860451i
$255$	−21.1141			−1.32222
$256$	8.23923	+	13.7155i	0.514952	+	0.857219i
$257$	−7.54149			−0.470425			−0.235212	−	0.971944i	$-0.575579\pi$
$257$	−7.54149			−0.470425			−0.235212	+	0.971944i	$0.575579\pi$
$258$	−4.57122	−	0.591728i	−0.284592	−	0.0368394i
$259$	−21.2462	−	2.09257i	−1.32018	−	0.130026i
$260$	1.13855	−	4.32407i	0.0706098	−	0.268167i
$261$	0.00872454	+	0.0163225i	0.000540035	+	0.00101034i
$262$	−23.4357	−	5.41087i	−1.44786	−	0.334285i
$263$	−2.56464	−	12.8933i	−0.158143	−	0.795037i	−0.975687	−	0.219171i	$-0.929665\pi$
$263$	−2.56464	−	12.8933i	−0.158143	−	0.795037i	0.817544	−	0.575866i	$-0.195335\pi$
$264$	−5.14200	−	12.1889i	−0.316468	−	0.750176i
$265$	39.3817	+	7.83350i	2.41920	+	0.481208i
$266$	0.921201	+	2.43156i	0.0564825	+	0.149089i
$267$	9.82866	+	8.06617i	0.601504	+	0.493642i
$268$	0.127958	−	0.344503i	0.00781629	−	0.0210438i
$269$	−12.1131	−	6.47460i	−0.738550	−	0.394763i	0.0588081	−	0.998269i	$-0.481270\pi$
$269$	−12.1131	−	6.47460i	−0.738550	−	0.394763i	−0.797359	+	0.603506i	$0.793770\pi$
$270$	0.266846	+	3.94030i	0.0162397	+	0.239799i
$271$	3.34468	+	8.07476i	0.203175	+	0.490507i	0.992320	−	0.123700i	$-0.0394761\pi$
$271$	3.34468	+	8.07476i	0.203175	+	0.490507i	−0.789145	+	0.614207i	$0.789476\pi$
$272$	−23.8327	+	18.6182i	−1.44507	+	1.12890i
$273$	−1.41608	+	3.41871i	−0.0857048	+	0.206910i
$274$	24.1941	+	8.15430i	1.46162	+	0.492619i
$275$	12.5260	−	3.79972i	0.755345	−	0.229131i
$276$	−12.0920	+	2.87482i	−0.727852	+	0.173044i
$277$	1.40250	+	14.2398i	0.0842679	+	0.855587i	0.940680	+	0.339294i	$0.110188\pi$
$277$	1.40250	+	14.2398i	0.0842679	+	0.855587i	−0.856412	+	0.516292i	$0.827312\pi$
$278$	15.2000	+	16.1585i	0.911636	+	0.969122i
$279$	−0.0572157	+	0.0382303i	−0.00342541	+	0.00228879i
$280$	34.8664	−	10.8249i	2.08367	−	0.646910i
$281$	1.70791	−	2.55606i	0.101885	−	0.152482i	−0.777024	−	0.629471i	$-0.783272\pi$
$281$	1.70791	−	2.55606i	0.101885	−	0.152482i	0.878909	+	0.476989i	$0.158272\pi$
$282$	12.3283	+	8.79390i	0.734137	+	0.523669i
$283$	−18.4065	−	5.58354i	−1.09415	−	0.331907i	−0.308906	−	0.951092i	$-0.599963\pi$
$283$	−18.4065	−	5.58354i	−1.09415	−	0.331907i	−0.785245	+	0.619185i	$0.787463\pi$
$284$	0.568875	+	0.0348082i	0.0337565	+	0.00206549i
$285$	−0.704732	−	0.858718i	−0.0417447	−	0.0508661i
$286$	1.38168	+	5.11213i	0.0817006	+	0.302286i
$287$	−21.0370	+	21.0370i	−1.24177	+	1.24177i
$288$	3.77573	+	4.21235i	0.222487	+	0.248215i
$289$	−28.4008	−	28.4008i	−1.67064	−	1.67064i
$290$	−0.0364094	+	0.0633800i	−0.00213803	+	0.00372180i
$291$	−4.48840	+	3.68353i	−0.263115	+	0.215933i
$292$	−9.49590	+	19.4682i	−0.555705	+	1.13929i
$293$	7.29155	−	24.0370i	0.425977	−	1.40426i	−0.437204	−	0.899363i	$-0.644031\pi$
$293$	7.29155	−	24.0370i	0.425977	−	1.40426i	0.863181	−	0.504895i	$-0.168469\pi$
$294$	−20.0346	+	3.35238i	−1.16844	+	0.195515i
$295$	−11.5208	−	7.69793i	−0.670765	−	0.448191i
$296$	8.22201	−	10.1526i	0.477895	−	0.590105i
$297$	−2.59852	−	3.88895i	−0.150781	−	0.225660i
$298$	0.316991	−	10.3709i	0.0183628	−	0.600773i
$299$	4.95132	−	0.487663i	0.286342	−	0.0282023i
$300$	−4.53548	+	3.27995i	−0.261856	+	0.189368i
$301$	4.37307	+	14.4161i	0.252059	+	0.830929i
$302$	−14.7331	+	7.30533i	−0.847795	+	0.420375i
$303$	2.85736	+	1.18356i	0.164151	+	0.0679936i
$304$	−1.55268	−	0.347859i	−0.0890524	−	0.0199511i
$305$	14.6613	−	6.07291i	0.839503	−	0.347734i
$306$	−7.03260	+	8.05432i	−0.402027	+	0.460435i
$307$	14.2405	−	26.6420i	0.812746	−	1.52054i	−0.0405871	−	0.999176i	$-0.512923\pi$
$307$	14.2405	−	26.6420i	0.812746	−	1.52054i	0.853333	−	0.521365i	$-0.174577\pi$
$308$	−29.4191	+	31.6849i	−1.67631	+	1.80541i
$309$	11.4201	−	13.9155i	0.649670	−	0.791625i
$310$	−0.247783	−	0.111622i	−0.0140731	−	0.00633969i
$311$	−4.40912	+	22.1662i	−0.250018	+	1.25693i	0.627967	+	0.778240i	$0.283887\pi$
$311$	−4.40912	+	22.1662i	−0.250018	+	1.25693i	−0.877985	+	0.478687i	$0.841113\pi$
$312$	−1.27026	−	1.87456i	−0.0719145	−	0.106126i
$313$	−7.11136	+	1.41454i	−0.401958	+	0.0799544i	−0.391929	−	0.919995i	$-0.628192\pi$
$313$	−7.11136	+	1.41454i	−0.401958	+	0.0799544i	−0.0100284	+	0.999950i	$0.503192\pi$
$314$	−3.18484	−	5.09695i	−0.179731	−	0.287637i
$315$	11.3835	−	6.08460i	0.641386	−	0.342828i
$316$	2.03493	−	0.276890i	0.114474	−	0.0155763i
$317$	0.536090	−	5.44301i	0.0301098	−	0.305710i	−0.968321	−	0.249709i	$-0.919665\pi$
$317$	0.536090	−	5.44301i	0.0301098	−	0.305710i	0.998431	−	0.0560010i	$-0.0178350\pi$
$318$	16.1053	−	12.4136i	0.903141	−	0.696122i
$319$		−	0.0865650i		−	0.00484671i
$320$	−6.20641	+	21.4614i	−0.346949	+	1.19973i
$321$		−	8.17531i		−	0.456301i
$322$	24.7988	+	32.1737i	1.38198	+	1.79297i
$323$	0.294797	−	2.99313i	0.0164030	−	0.166542i
$324$	1.59197	+	1.21063i	0.0884430	+	0.0672571i
$325$	1.97597	−	1.05618i	0.109607	−	0.0585862i
$326$	13.6199	−	8.51044i	0.754338	−	0.471350i
$327$	1.44271	−	0.286972i	0.0797819	−	0.0158696i
$328$	−3.66786	−	17.8323i	−0.202524	−	0.984626i
$329$	9.65555	−	48.5417i	0.532328	−	2.67619i
$330$	7.58694	−	16.8418i	0.417647	−	0.927111i
$331$	−15.0028	+	18.2809i	−0.824626	+	1.00481i	0.175168	+	0.984538i	$0.443953\pi$
$331$	−15.0028	+	18.2809i	−0.824626	+	1.00481i	−0.999795	+	0.0202714i	$0.993547\pi$
$332$	0.223243	+	6.02055i	0.0122520	+	0.330421i
$333$	2.17735	−	4.07353i	0.119318	−	0.223228i
$334$	−8.13833	−	7.10595i	−0.445310	−	0.388821i
$335$	0.474078	−	0.196369i	0.0259016	−	0.0107288i
$336$	7.48385	−	16.9059i	0.408277	−	0.922292i
$337$	23.2548	+	9.63245i	1.26677	+	0.524713i	0.911981	−	0.410233i	$-0.134553\pi$
$337$	23.2548	+	9.63245i	1.26677	+	0.524713i	0.354789	+	0.934946i	$0.384553\pi$
$338$	−7.76446	−	15.6590i	−0.422331	−	0.851740i
$339$	−1.56635	−	5.16357i	−0.0850725	−	0.280447i
$340$	−41.6936	−	6.69797i	−2.26116	−	0.363249i
$341$	0.320301	−	0.0315469i	0.0173453	−	0.00170836i
$342$	−0.562301	−	0.0171869i	−0.0304058	−	0.000929362i
$343$	18.9088	+	28.2990i	1.02098	+	1.52800i
$344$	−8.83899	−	2.61859i	−0.476566	−	0.141185i
$345$	−14.4299	−	9.64172i	−0.776877	−	0.519093i
$346$	−3.17240	−	18.9590i	−0.170550	−	1.01924i
$347$	2.43562	−	8.02916i	0.130751	−	0.431028i	−0.866981	−	0.498341i	$-0.833943\pi$
$347$	2.43562	−	8.02916i	0.130751	−	0.431028i	0.997732	+	0.0673133i	$0.0214427\pi$
$348$	0.0120503	+	0.0349993i	0.000645961	+	0.00187616i
$349$	−5.73422	+	4.70595i	−0.306946	+	0.251904i	−0.775237	−	0.631670i	$-0.782370\pi$
$349$	−5.73422	+	4.70595i	−0.306946	+	0.251904i	0.468292	+	0.883574i	$0.344870\pi$
$350$	15.8623	+	9.11227i	0.847875	+	0.487072i
$351$	−0.566102	−	0.566102i	−0.0302163	−	0.0302163i
$352$	−6.28714	−	25.7004i	−0.335106	−	1.36984i
$353$	8.43885	−	8.43885i	0.449155	−	0.449155i	−0.445919	−	0.895074i	$-0.647123\pi$
$353$	8.43885	−	8.43885i	0.449155	−	0.449155i	0.895074	+	0.445919i	$0.147123\pi$
$354$	−6.77379	+	1.83079i	−0.360023	+	0.0973054i
$355$	0.504853	+	0.615165i	0.0267948	+	0.0326496i
$356$	16.8497	+	19.0460i	0.893030	+	1.00944i
$357$	33.4415	+	10.1444i	1.76991	+	0.536897i
$358$	−12.5836	+	17.6411i	−0.665066	+	0.932363i
$359$	10.2627	−	15.3592i	0.541642	−	0.810625i	−0.455170	−	0.890405i	$-0.650422\pi$
$359$	10.2627	−	15.3592i	0.541642	−	0.810625i	0.996813	+	0.0797793i	$0.0254215\pi$
$360$	−0.723036	+	7.86549i	−0.0381073	+	0.414548i
$361$	−15.6664	+	10.4679i	−0.824545	+	0.550943i
$362$	−10.5661	+	9.93937i	−0.555343	+	0.522402i
$363$	1.06606	+	10.8239i	0.0559535	+	0.568106i
$364$	−3.88081	+	6.30164i	−0.203410	+	0.330296i
$365$	−28.9424	+	8.77959i	−1.51492	+	0.459545i
$366$	2.56672	−	7.61553i	0.134164	−	0.398070i
$367$	−3.70150	+	8.93622i	−0.193217	+	0.466467i	−0.990563	−	0.137055i	$-0.956236\pi$
$367$	−3.70150	+	8.93622i	−0.193217	+	0.466467i	0.797347	+	0.603522i	$0.206236\pi$
$368$	−24.7898	+	1.84095i	−1.29226	+	0.0959661i
$369$	−2.46321	−	5.94670i	−0.128229	−	0.309573i
$370$	18.2000	−	1.23254i	0.946171	−	0.0640768i
$371$	−58.6109	−	31.3282i	−3.04293	−	1.62648i
$372$	−0.125110	+	0.0573423i	−0.00648667	+	0.00297306i
$373$	−9.56415	−	7.84910i	−0.495213	−	0.406411i	0.353361	−	0.935487i	$-0.385039\pi$
$373$	−9.56415	−	7.84910i	−0.495213	−	0.406411i	−0.848574	+	0.529076i	$0.822539\pi$
$374$	46.7673	−	17.7179i	2.41828	−	0.916169i
$375$	6.02950	+	1.19934i	0.311362	+	0.0619338i
$376$	21.5547	+	21.2760i	1.11160	+	1.09723i
$377$	−0.00289069	−	0.0145325i	−0.000148878	−	0.000748461i
$378$	1.47049	−	6.36905i	0.0756341	−	0.327588i
$379$	−14.5871	−	27.2905i	−0.749288	−	1.40182i	−0.909911	−	0.414803i	$-0.863851\pi$
$379$	−14.5871	−	27.2905i	−0.749288	−	1.40182i	0.160624	−	0.987016i	$-0.448649\pi$
$380$	−1.11921	−	1.91925i	−0.0574144	−	0.0984557i
$381$	−7.51710	−	0.740370i	−0.385113	−	0.0379303i
$382$	−4.39880	+	33.9816i	−0.225062	+	1.73865i
$383$	−18.6327			−0.952087			−0.476043	−	0.879422i	$-0.657929\pi$
$383$	−18.6327			−0.952087			−0.476043	+	0.879422i	$0.657929\pi$
$384$	6.11959	+	9.51581i	0.312289	+	0.485602i
$385$	−60.3714			−3.07681
$386$	−3.11906	+	24.0954i	−0.158756	+	1.22642i
$387$	−3.24361	−	0.319468i	−0.164882	−	0.0162395i
$388$	−10.0317	+	5.84996i	−0.509281	+	0.296987i
$389$	−2.15202	−	4.02614i	−0.109112	−	0.204133i	0.821439	−	0.570296i	$-0.193171\pi$
$389$	−2.15202	−	4.02614i	−0.109112	−	0.204133i	−0.930551	+	0.366162i	$0.880671\pi$
$390$	0.711287	−	3.08075i	0.0360174	−	0.156000i
$391$	−9.16658	−	46.0835i	−0.463574	−	2.33054i
$392$	−40.6254	+	0.264368i	−2.05189	+	0.0133526i
$393$	−16.6807	−	3.31800i	−0.841430	−	0.167371i
$394$	−15.8325	+	5.99818i	−0.797631	+	0.302184i
$395$	2.21665	+	1.81916i	0.111532	+	0.0915318i
$396$	−3.89756	−	8.50376i	−0.195860	−	0.427330i
$397$	−7.72728	−	4.13032i	−0.387821	−	0.207295i	0.265950	−	0.963987i	$-0.414314\pi$
$397$	−7.72728	−	4.13032i	−0.387821	−	0.207295i	−0.653772	+	0.756692i	$0.726814\pi$
$398$	34.1160	−	2.31041i	1.71008	−	0.115810i
$399$	0.703612	+	1.69867i	0.0352247	+	0.0850399i
$400$	−9.99661	+	5.03808i	−0.499831	+	0.251904i
$401$	−5.82728	+	14.0683i	−0.291000	+	0.702537i	−0.999996	−	0.00267538i	$-0.999148\pi$
$401$	−5.82728	+	14.0683i	−0.291000	+	0.702537i	0.708996	+	0.705212i	$0.249148\pi$
$402$	0.0829956	−	0.246251i	0.00413944	−	0.0122819i
$403$	0.0527186	−	0.0159920i	0.00262610	−	0.000796618i
$404$	5.26692	+	3.24358i	0.262039	+	0.161374i
$405$	0.273722	+	2.77915i	0.0136014	+	0.138097i
$406$	0.0881182	−	0.0828912i	0.00437323	−	0.00411382i
$407$	−17.9628	+	12.0023i	−0.890382	+	0.594934i
$408$	−16.4422	+	13.6738i	−0.814010	+	0.676954i
$409$	10.0435	−	15.0311i	0.496617	−	0.743240i	−0.495493	−	0.868612i	$-0.665013\pi$
$409$	10.0435	−	15.0311i	0.496617	−	0.743240i	0.992110	+	0.125372i	$0.0400125\pi$
$410$	14.7620	−	20.6950i	0.729045	−	1.02206i
$411$	17.2760	+	5.24061i	0.852161	+	0.258500i
$412$	26.9655	−	23.8559i	1.32850	−	1.17529i
$413$	14.5486	+	17.7276i	0.715891	+	0.872316i
$414$	−8.48423	+	2.29308i	−0.416977	+	0.112699i
$415$	−5.94837	+	5.94837i	−0.291994	+	0.291994i
$416$	−1.91370	−	4.10462i	−0.0938271	−	0.201246i
$417$	11.0921	+	11.0921i	0.543182	+	0.543182i
$418$	2.28156	+	1.31067i	0.111595	+	0.0641068i
$419$	−25.7773	+	21.1549i	−1.25931	+	1.03349i	−0.261642	+	0.965165i	$0.584264\pi$
$419$	−25.7773	+	21.1549i	−1.25931	+	1.03349i	−0.997663	+	0.0683205i	$0.978236\pi$
$420$	24.4089	−	8.40399i	1.19103	−	0.410073i
$421$	−4.70789	+	15.5198i	−0.229448	+	0.756390i	0.764311	+	0.644847i	$0.223079\pi$
$421$	−4.70789	+	15.5198i	−0.229448	+	0.756390i	−0.993760	+	0.111542i	$0.964421\pi$
$422$	−0.0369562	−	0.220858i	−0.00179900	−	0.0107512i
$423$	8.90330	+	5.94899i	0.432893	+	0.289250i
$424$	35.7408	−	19.4039i	1.73573	−	0.942338i
$425$	−11.7556	−	17.5935i	−0.570229	−	0.853409i
$426$	0.402820	+	0.0123123i	0.0195167	+	0.000596533i
$427$	−26.1390	+	2.57447i	−1.26496	+	0.124587i
$428$	2.59343	−	16.1436i	0.125358	−	0.780332i
$429$	1.08698	+	3.58328i	0.0524798	+	0.173003i
$430$	−5.71820	−	11.5322i	−0.275756	−	0.556134i
$431$	−29.0805	−	12.0455i	−1.40076	−	0.580213i	−0.450810	−	0.892620i	$-0.648865\pi$
$431$	−29.0805	−	12.0455i	−1.40076	−	0.580213i	−0.949948	+	0.312407i	$0.898865\pi$
$432$	2.75960	+	2.89562i	0.132771	+	0.139316i
$433$	32.6042	−	13.5051i	1.56686	−	0.649013i	0.580593	−	0.814194i	$-0.302821\pi$
$433$	32.6042	−	13.5051i	1.56686	−	0.649013i	0.986263	+	0.165181i	$0.0528208\pi$
$434$	0.338821	+	0.295840i	0.0162639	+	0.0142008i
$435$	−0.0243641	+	0.0455821i	−0.00116817	+	0.00218549i
$436$	2.93992	−	0.109013i	0.140797	−	0.00522076i
$437$	1.56828	−	1.91095i	0.0750209	−	0.0914132i
$438$	−6.29091	+	13.9648i	−0.300591	+	0.667265i
$439$	3.10324	−	15.6011i	0.148110	−	0.744598i	−0.833322	−	0.552787i	$-0.813564\pi$
$439$	3.10324	−	15.6011i	0.148110	−	0.744598i	0.981432	−	0.191810i	$-0.0614358\pi$
$440$	20.3245	−	30.8504i	0.968931	−	1.47074i
$441$	−14.0876	+	2.80219i	−0.670837	+	0.133438i
$442$	7.25961	−	4.53618i	0.345305	−	0.215764i
$443$	0.0457434	−	0.0244504i	0.00217334	−	0.00116167i	−0.470310	−	0.882501i	$-0.655858\pi$
$443$	0.0457434	−	0.0244504i	0.00217334	−	0.00116167i	0.472483	+	0.881340i	$0.343358\pi$
$444$	5.59180	−	7.35321i	0.265375	−	0.348968i
$445$	−3.48032	+	35.3363i	−0.164983	+	1.67510i
$446$	2.35192	+	3.05135i	0.111367	+	0.144486i
$447$		−	7.33679i		−	0.347018i
$448$	20.1412	−	31.0097i	0.951584	−	1.46507i
$449$			6.36898i			0.300571i	0.988643	+	0.150285i	$0.0480193\pi$
$449$			6.36898i			0.300571i	−0.988643	+	0.150285i	$0.951981\pi$
$450$	−3.13471	+	2.41617i	−0.147772	+	0.113899i
$451$	−2.95087	+	29.9606i	−0.138951	+	1.41079i
$452$	−1.45502	−	10.6933i	−0.0684384	−	0.502970i
$453$	−10.2552	+	5.48152i	−0.481831	+	0.257544i
$454$	3.07254	+	4.91723i	0.144202	+	0.230777i
$455$	−10.1351	+	2.01600i	−0.475142	+	0.0945116i
$456$	−1.10491	−	0.212316i	−0.0517423	−	0.00994261i
$457$	2.64907	−	13.3178i	0.123918	−	0.622979i	−0.868048	−	0.496479i	$-0.834626\pi$
$457$	2.64907	−	13.3178i	0.123918	−	0.622979i	0.991967	−	0.126499i	$-0.0403742\pi$
$458$	30.7754	+	13.8638i	1.43804	+	0.647813i
$459$	−4.79648	+	5.84453i	−0.223881	+	0.272799i
$460$	−25.4358	−	23.6169i	−1.18595	−	1.10114i
$461$	−17.7995	+	33.3006i	−0.829007	+	1.55096i	0.00551203	+	0.999985i	$0.498245\pi$
$461$	−17.7995	+	33.3006i	−0.829007	+	1.55096i	−0.834519	+	0.550979i	$0.814255\pi$
$462$	−20.1083	+	23.0297i	−0.935522	+	1.07144i
$463$	−20.2054	+	8.36934i	−0.939024	+	0.388956i	−0.799095	−	0.601205i	$-0.794687\pi$
$463$	−20.2054	+	8.36934i	−0.939024	+	0.388956i	−0.139929	+	0.990162i	$0.544687\pi$
$464$	0.0126927	+	0.0729352i	0.000589242	+	0.00338593i
$465$	−0.177538	−	0.0735388i	−0.00823315	−	0.00341028i
$466$	−18.1525	+	9.00083i	−0.840899	+	0.416956i
$467$	−6.63488	−	21.8723i	−0.307026	−	1.01213i	−0.965691	−	0.259692i	$-0.916379\pi$
$467$	−6.63488	−	21.8723i	−0.307026	−	1.01213i	0.658666	−	0.752436i	$-0.271121\pi$
$468$	−0.938289	−	1.29746i	−0.0433724	−	0.0599749i
$469$	−0.845213	+	0.0832463i	−0.0390283	+	0.00384395i
$470$	−1.29197	+	42.2693i	−0.0595944	+	1.94974i
$471$	−2.36108	−	3.53360i	−0.108793	−	0.162820i
$472$	−13.9569	+	1.46639i	−0.642417	+	0.0674963i
$473$	12.6753	+	8.46936i	0.582811	+	0.389422i
$474$	1.43226	−	0.239660i	0.0657860	−	0.0110079i
$475$	0.323163	−	1.06533i	0.0148277	−	0.0488805i
$476$	62.8183	+	30.6405i	2.87927	+	1.40440i
$477$	11.1147	−	9.12159i	0.508906	−	0.417649i
$478$	−3.77866	+	6.57775i	−0.172832	+	0.300859i
$479$	13.9838	+	13.9838i	0.638938	+	0.638938i	0.950294	−	0.311355i	$-0.100783\pi$
$479$	13.9838	+	13.9838i	0.638938	+	0.638938i	−0.311355	+	0.950294i	$0.600783\pi$
$480$	−3.92292	+	15.3025i	−0.179056	+	0.698459i
$481$	−2.61478	+	2.61478i	−0.119224	+	0.119224i
$482$	−3.72828	−	13.7944i	−0.169818	−	0.628316i
$483$	18.2223	+	22.2039i	0.829143	+	1.01031i
$484$	−1.32850	+	21.7119i	−0.0603864	+	0.986903i
$485$	−15.5167	−	4.70694i	−0.704577	−	0.213731i
$486$	1.15132	+	0.821252i	0.0522251	+	0.0372528i
$487$	−3.15265	+	4.71827i	−0.142860	+	0.213805i	−0.895999	−	0.444057i	$-0.853539\pi$
$487$	−3.15265	+	4.71827i	−0.142860	+	0.213805i	0.753139	+	0.657862i	$0.228539\pi$
$488$	7.48430	−	14.2240i	0.338798	−	0.643891i
$489$	9.44240	−	6.30921i	0.427000	−	0.285312i
$490$	−38.8675	−	41.3184i	−1.75585	−	1.86657i
$491$	−2.87299	−	29.1700i	−0.129656	−	1.31642i	−0.811253	−	0.584695i	$-0.801214\pi$
$491$	−2.87299	−	29.1700i	−0.129656	−	1.31642i	0.681597	−	0.731728i	$-0.261286\pi$
$492$	−2.97759	−	12.5242i	−0.134240	−	0.564636i
$493$	−0.133908	+	0.0406204i	−0.00603089	+	0.00182945i
$494$	0.426794	+	0.143845i	0.0192024	+	0.00647191i
$495$	4.99844	−	12.0673i	0.224663	−	0.542385i
$496$	−0.265244	+	0.0735443i	−0.0119098	+	0.00330224i
$497$	−0.504051	−	1.21689i	−0.0226098	−	0.0545849i
$498$	0.287844	+	4.25036i	0.0128986	+	0.190463i
$499$	10.7708	+	5.75709i	0.482165	+	0.257723i	0.694525	−	0.719469i	$-0.255615\pi$
$499$	10.7708	+	5.75709i	0.482165	+	0.257723i	−0.212360	+	0.977192i	$0.568115\pi$
$500$	11.5259	+	4.28104i	0.515453	+	0.191454i
$501$	−5.90549	−	4.84651i	−0.263838	−	0.216526i
$502$	7.22931	+	19.0822i	0.322660	+	0.851679i
$503$	14.6702	+	2.91809i	0.654112	+	0.130111i	0.510980	−	0.859593i	$-0.329283\pi$
$503$	14.6702	+	2.91809i	0.654112	+	0.130111i	0.143132	+	0.989704i	$0.454283\pi$
$504$	4.92419	−	12.1104i	0.219341	−	0.539438i
$505$	1.68498	+	8.47094i	0.0749804	+	0.376952i
$506$	40.0527	+	9.24741i	1.78056	+	0.411098i
$507$	−5.82602	−	10.8997i	−0.258743	−	0.484073i
$508$	−14.6090	−	3.84662i	−0.648170	−	0.170666i
$509$	27.2532	+	2.68420i	1.20798	+	0.118975i	0.681889	−	0.731456i	$-0.261159\pi$
$509$	27.2532	+	2.68420i	1.20798	+	0.118975i	0.526087	+	0.850431i	$0.323659\pi$
$510$	−29.6128	−	3.83327i	−1.31128	−	0.169740i
$511$	50.0586			2.21446
$512$	9.06557	+	20.7320i	0.400645	+	0.916233i
$513$	−0.397793			−0.0175630
$514$	−10.5770	−	1.36916i	−0.466532	−	0.0603910i
$515$	50.0294	+	4.92746i	2.20456	+	0.217130i
$516$	−6.30376	−	1.65981i	−0.277507	−	0.0730691i
$517$	−23.6090	−	44.1693i	−1.03832	−	1.94256i
$518$	−29.4182	−	6.79210i	−1.29256	−	0.298428i
$519$	−2.65175	−	13.3312i	−0.116399	−	0.585177i
$520$	2.38186	−	5.85785i	0.104452	−	0.256884i
$521$	−18.9108	−	3.76159i	−0.828496	−	0.164798i	−0.237413	−	0.971409i	$-0.576299\pi$
$521$	−18.9108	−	3.76159i	−0.828496	−	0.164798i	−0.591083	+	0.806611i	$0.701299\pi$
$522$	0.00927292	+	0.0244764i	0.000405865	+	0.00107130i
$523$	2.74903	+	2.25607i	0.120206	+	0.0986509i	0.692576	−	0.721345i	$-0.256476\pi$
$523$	2.74903	+	2.25607i	0.120206	+	0.0986509i	−0.572370	+	0.819996i	$0.693976\pi$
$524$	−31.8865	−	11.8436i	−1.39297	−	0.517389i
$525$	11.4079	+	6.09767i	0.497883	+	0.266124i
$526$	−1.25616	−	18.5487i	−0.0547710	−	0.808761i
$527$	−0.199101	−	0.480672i	−0.00867296	−	0.0209384i
$528$	−4.99881	−	18.0286i	−0.217545	−	0.784596i
$529$	5.97760	−	14.4312i	0.259896	−	0.627443i
$530$	53.8111	+	18.1363i	2.33740	+	0.787791i
$531$	−4.74801	+	1.44029i	−0.206046	+	0.0625034i
$532$	0.850546	+	3.57754i	0.0368758	+	0.155106i
$533$	0.505095	+	5.12832i	0.0218781	+	0.222132i
$534$	12.3204	+	13.0973i	0.533156	+	0.566776i
$535$	18.9827	−	12.6839i	0.820695	−	0.548371i
$536$	0.242007	−	0.459938i	0.0104531	−	0.0198663i
$537$	−8.51272	+	12.7402i	−0.367351	+	0.549780i
$538$	−15.8133	−	11.2798i	−0.681762	−	0.486309i
$539$	64.2885	+	19.5017i	2.76910	+	0.839998i
$540$	−0.341108	+	5.57477i	−0.0146789	+	0.239900i
$541$	−10.7298	−	13.0744i	−0.461312	−	0.562111i	0.489450	−	0.872031i	$-0.337197\pi$
$541$	−10.7298	−	13.0744i	−0.461312	−	0.562111i	−0.950762	+	0.309921i	$0.899697\pi$
$542$	3.22497	+	11.9322i	0.138524	+	0.512531i
$543$	−7.25318	+	7.25318i	−0.311264	+	0.311264i
$544$	−36.8058	+	21.7855i	−1.57804	+	0.934044i
$545$	2.90468	+	2.90468i	0.124423	+	0.124423i
$546$	−2.60673	+	4.53769i	−0.111558	+	0.194195i
$547$	19.1052	−	15.6792i	0.816878	−	0.670395i	−0.130168	−	0.991492i	$-0.541552\pi$
$547$	19.1052	−	15.6792i	0.816878	−	0.670395i	0.947046	+	0.321097i	$0.104052\pi$
$548$	32.4521	+	15.8289i	1.38628	+	0.676179i
$549$	1.64958	−	5.43793i	0.0704022	−	0.232085i
$550$	18.2577	−	3.05505i	0.778510	−	0.130268i
$551$	−0.00612152	−	0.00409027i	−0.000260785	−	0.000174251i
$552$	−17.4811	+	1.83667i	−0.744044	+	0.0781739i
$553$	−2.63681	−	3.94627i	−0.112129	−	0.167813i
$554$	−0.618218	+	20.2261i	−0.0262655	+	0.859325i
$555$	12.8367	−	1.26430i	0.544887	−	0.0536667i
$556$	18.3846	+	25.4221i	0.779682	+	1.07814i
$557$	−1.18544	−	3.90789i	−0.0502289	−	0.165582i	0.928238	−	0.371987i	$-0.121324\pi$
$557$	−1.18544	−	3.90789i	−0.0502289	−	0.165582i	−0.978467	+	0.206405i	$0.933824\pi$
$558$	−0.0871864	+	0.0432309i	−0.00369089	+	0.00183011i
$559$	2.41074	+	0.998562i	0.101964	+	0.0422347i
$560$	50.8659	−	8.85201i	2.14947	−	0.374066i
$561$	32.6713	−	13.5329i	1.37938	−	0.571359i
$562$	2.85941	−	3.27484i	0.120617	−	0.138141i
$563$	11.2670	−	21.0791i	0.474849	−	0.888379i	−0.524469	−	0.851430i	$-0.675736\pi$
$563$	11.2670	−	21.0791i	0.474849	−	0.888379i	0.999317	−	0.0369494i	$-0.0117640\pi$
$564$	15.6940	+	14.5717i	0.660837	+	0.613581i
$565$	9.55943	−	11.6482i	0.402168	−	0.490043i
$566$	−24.8016	−	11.1727i	−1.04249	−	0.469623i
$567$	0.901722	−	4.53326i	0.0378688	−	0.190379i
$568$	0.791534	+	0.152098i	0.0332120	+	0.00638190i
$569$	8.67602	−	1.72577i	0.363718	−	0.0723479i	−0.00984847	−	0.999952i	$-0.503135\pi$
$569$	8.67602	−	1.72577i	0.363718	−	0.0723479i	0.373566	+	0.927604i	$0.378135\pi$
$570$	−0.832494	−	1.33231i	−0.0348693	−	0.0558042i
$571$	−0.695506	+	0.371756i	−0.0291060	+	0.0155575i	−0.485886	−	0.874022i	$-0.661503\pi$
$571$	−0.695506	+	0.371756i	−0.0291060	+	0.0155575i	0.456780	+	0.889580i	$0.349003\pi$
$572$	1.00972	+	7.42066i	0.0422184	+	0.310274i
$573$	−2.37487	+	24.1124i	−0.0992115	+	1.00731i
$574$	−33.3238	+	25.6853i	−1.39091	+	1.07208i
$575$		−	17.3919i		−	0.725294i
$576$	4.53075	+	6.59335i	0.188781	+	0.274723i
$577$			6.81875i			0.283868i	0.989876	+	0.141934i	$0.0453321\pi$
$577$			6.81875i			0.283868i	−0.989876	+	0.141934i	$0.954668\pi$
$578$	−34.6763	−	44.9887i	−1.44234	−	1.87128i
$579$	−1.68395	+	17.0974i	−0.0699825	+	0.710545i
$580$	−0.0625713	+	0.0822811i	−0.00259813	+	0.00341654i
$581$	12.2792	−	6.56339i	0.509428	−	0.272295i
$582$	−6.96378	+	4.35133i	−0.288658	+	0.180368i
$583$	−65.9587	+	13.1200i	−2.73173	+	0.543375i
$584$	−16.8526	+	25.5804i	−0.697364	+	1.05853i
$585$	0.436168	−	2.19277i	0.0180333	−	0.0906597i
$586$	14.5904	−	32.3884i	0.602724	−	1.33795i
$587$	−6.54472	+	7.97477i	−0.270130	+	0.329154i	−0.890353	−	0.455272i	$-0.849542\pi$
$587$	−6.54472	+	7.97477i	−0.270130	+	0.329154i	0.620223	+	0.784426i	$0.287042\pi$
$588$	−28.7074	+	1.06447i	−1.18387	+	0.0438982i
$589$	0.0129036	−	0.0241410i	0.000531685	−	0.000994713i
$590$	−14.7604	−	12.8880i	−0.607678	−	0.530592i
$591$	−11.0605	+	4.58140i	−0.454968	+	0.188454i
$592$	13.3747	−	12.7464i	0.549695	−	0.523873i
$593$	35.5390	+	14.7207i	1.45941	+	0.604509i	0.964417	−	0.264386i	$-0.0851694\pi$
$593$	35.5390	+	14.7207i	1.45941	+	0.604509i	0.494996	+	0.868895i	$0.335169\pi$
$594$	−2.93841	−	5.92606i	−0.120564	−	0.243149i
$595$	28.3292	+	93.3887i	1.16138	+	3.82856i
$596$	2.32743	−	14.4878i	0.0953353	−	0.593445i
$597$	24.0625	−	2.36995i	0.984812	−	0.0969955i
$598$	7.03282	+	0.214960i	0.287593	+	0.00879039i
$599$	−4.21137	−	6.30276i	−0.172072	−	0.257524i	0.735403	−	0.677630i	$-0.236993\pi$
$599$	−4.21137	−	6.30276i	−0.172072	−	0.257524i	−0.907475	+	0.420106i	$0.861993\pi$
$600$	−6.95654	+	3.77675i	−0.283999	+	0.154185i
$601$	−1.69317	−	1.13134i	−0.0690659	−	0.0461484i	0.520558	−	0.853826i	$-0.325724\pi$
$601$	−1.69317	−	1.13134i	−0.0690659	−	0.0461484i	−0.589624	+	0.807678i	$0.700724\pi$
$602$	3.51604	+	21.0126i	0.143303	+	0.856412i
$603$	0.0533396	−	0.175837i	0.00217216	−	0.00716064i
$604$	−21.9896	+	7.57102i	−0.894745	+	0.308060i
$605$	−23.4786	+	19.2684i	−0.954541	+	0.783372i
$606$	3.79261	+	2.17871i	0.154064	+	0.0885039i
$607$	6.45589	+	6.45589i	0.262036	+	0.262036i	0.825881	−	0.563845i	$-0.190678\pi$
$607$	6.45589	+	6.45589i	0.262036	+	0.262036i	−0.563845	+	0.825881i	$0.690678\pi$
$608$	−2.11450	−	0.769766i	−0.0857543	−	0.0312181i
$609$	0.0604892	−	0.0604892i	0.00245115	−	0.00245115i
$610$	21.6652	−	5.85556i	0.877197	−	0.237085i
$611$	−5.43843	−	6.62674i	−0.220015	−	0.268089i
$612$	−11.3256	+	10.0195i	−0.457809	+	0.405015i
$613$	23.1515	+	7.02292i	0.935079	+	0.283653i	0.720819	−	0.693124i	$-0.243766\pi$
$613$	23.1515	+	7.02292i	0.935079	+	0.283653i	0.214260	+	0.976777i	$0.431266\pi$
$614$	24.8093	−	34.7804i	1.00122	−	1.40362i
$615$	9.98638	−	14.9457i	0.402690	−	0.602668i
$616$	−47.0131	+	39.0974i	−1.89421	+	1.57528i
$617$	−10.5034	+	7.01813i	−0.422850	+	0.282539i	−0.748734	−	0.662870i	$-0.769338\pi$
$617$	−10.5034	+	7.01813i	−0.422850	+	0.282539i	0.325884	+	0.945410i	$0.394338\pi$
$618$	18.5433	−	17.4433i	0.745919	−	0.701673i
$619$	0.243489	+	2.47218i	0.00978663	+	0.0993654i	0.998837	−	0.0482122i	$-0.0153524\pi$
$619$	0.243489	+	2.47218i	0.00978663	+	0.0993654i	−0.989050	+	0.147578i	$0.952852\pi$
$620$	−0.327253	−	0.201536i	−0.0131428	−	0.00809387i
$621$	−5.94692	+	1.80398i	−0.238642	+	0.0723912i
$622$	−10.2081	+	30.2878i	−0.409308	+	1.21443i
$623$	22.4898	−	54.2952i	0.901035	−	2.17529i
$624$	−1.44123	−	2.85971i	−0.0576955	−	0.114480i
$625$	11.9247	+	28.7889i	0.476989	+	1.15155i
$626$	−10.2306	+	0.692837i	−0.408896	+	0.0276913i
$627$	1.64087	+	0.877061i	0.0655299	+	0.0350264i
$628$	−3.54142	−	7.72674i	−0.141318	−	0.308330i
$629$	26.9955	+	22.1546i	1.07638	+	0.883362i
$630$	17.0701	−	6.46705i	0.680090	−	0.257653i
$631$	−28.2963	−	5.62848i	−1.12646	−	0.224066i	−0.403514	−	0.914974i	$-0.632211\pi$
$631$	−28.2963	−	5.62848i	−1.12646	−	0.224066i	−0.722943	+	0.690907i	$0.757211\pi$
$632$	2.90429	−	0.0188995i	0.115526	−	0.000751781i
$633$	−0.0308909	−	0.155299i	−0.00122780	−	0.00617259i
$634$	1.74005	−	7.53657i	0.0691063	−	0.299315i
$635$	−9.94355	−	18.6031i	−0.394598	−	0.738241i
$636$	24.8416	−	14.4863i	0.985033	−	0.574421i
$637$	11.4439	+	1.12713i	0.453426	+	0.0446585i
$638$	0.0157159	−	0.121408i	0.000622198	−	0.00480660i
$639$	0.284969			0.0112732
$640$	−12.6009	+	28.9731i	−0.498093	+	1.14526i
$641$	−34.7149			−1.37115			−0.685577	−	0.728000i	$-0.740450\pi$
$641$	−34.7149			−1.37115			−0.685577	+	0.728000i	$0.740450\pi$
$642$	1.48423	−	11.4660i	0.0585778	−	0.452525i
$643$	32.5776	+	3.20862i	1.28474	+	0.126535i	0.717232	−	0.696835i	$-0.245409\pi$
$643$	32.5776	+	3.20862i	1.28474	+	0.126535i	0.567504	+	0.823370i	$0.307909\pi$
$644$	28.9395	+	49.6263i	1.14038	+	1.95555i
$645$	−4.29062	−	8.02719i	−0.168943	−	0.316070i
$646$	0.956859	−	4.14438i	0.0376471	−	0.163058i
$647$	−0.605791	−	3.04552i	−0.0238161	−	0.119732i	0.967048	−	0.254592i	$-0.0819413\pi$
$647$	−0.605791	−	3.04552i	−0.0238161	−	0.119732i	−0.990865	+	0.134861i	$0.956941\pi$
$648$	2.01297	+	1.98694i	0.0790770	+	0.0780545i
$649$	22.7608	+	4.52740i	0.893438	+	0.177716i
$650$	2.96307	−	1.12256i	0.116221	−	0.0440306i
$651$	0.245862	+	0.201773i	0.00963608	+	0.00790813i
$652$	20.6472	−	9.46330i	0.808607	−	0.370611i
$653$	29.6366	+	15.8411i	1.15977	+	0.619910i	0.935051	−	0.354514i	$-0.115354\pi$
$653$	29.6366	+	15.8411i	1.15977	+	0.619910i	0.224719	+	0.974424i	$0.427854\pi$
$654$	2.07551	−	0.140558i	0.0811590	−	0.00549627i
$655$	−18.1756	−	43.8797i	−0.710179	−	1.71452i
$656$	−1.90676	−	25.6760i	−0.0744464	−	1.00248i
$657$	−4.14459	+	10.0059i	−0.161696	+	0.390368i
$658$	22.3548	−	66.3274i	0.871480	−	2.58571i
$659$	−29.6022	+	8.97972i	−1.15314	+	0.349800i	−0.808248	−	0.588843i	$-0.799584\pi$
$659$	−29.6022	+	8.97972i	−1.15314	+	0.349800i	−0.344890	+	0.938643i	$0.612084\pi$
$660$	13.6984	−	22.2434i	0.533209	−	0.865824i
$661$	−2.80196	−	28.4488i	−0.108984	−	1.10653i	−0.881710	−	0.471791i	$-0.843608\pi$
$661$	−2.80196	−	28.4488i	−0.108984	−	1.10653i	0.772726	−	0.634739i	$-0.218892\pi$
$662$	−24.3604	+	22.9154i	−0.946796	+	0.890634i
$663$	5.03293	−	3.36290i	0.195463	−	0.130604i
$664$	−0.779931	+	8.48442i	−0.0302672	+	0.329260i
$665$	−2.85260	+	4.26922i	−0.110619	+	0.165553i
$666$	3.79330	−	5.31787i	0.146988	−	0.206063i
$667$	−0.110065	−	0.0333878i	−0.00426172	−	0.00129278i
$668$	−10.1240	−	11.4437i	−0.391710	−	0.442770i
$669$	1.72820	+	2.10582i	0.0668160	+	0.0814156i
$670$	0.700550	−	0.189342i	0.0270646	−	0.00731490i
$671$	−18.7940	+	18.7940i	−0.725536	+	0.725536i
$672$	13.5655	−	22.3520i	0.523299	−	0.862248i
$673$	−22.5278	−	22.5278i	−0.868384	−	0.868384i	0.123909	−	0.992294i	$-0.460457\pi$
$673$	−22.5278	−	22.5278i	−0.868384	−	0.868384i	−0.992294	+	0.123909i	$0.960457\pi$
$674$	30.8664	+	17.7315i	1.18893	+	0.682994i
$675$	−2.16335	+	1.77541i	−0.0832672	+	0.0683357i
$676$	−8.04684	−	23.3716i	−0.309494	−	0.898909i
$677$	−6.40453	+	21.1129i	−0.246146	+	0.811435i	0.743604	+	0.668621i	$0.233115\pi$
$677$	−6.40453	+	21.1129i	−0.246146	+	0.811435i	−0.989750	+	0.142814i	$0.954385\pi$
$678$	−1.25938	−	7.52634i	−0.0483662	−	0.289047i
$679$	22.3146	+	14.9101i	0.856356	+	0.572199i
$680$	−57.2598	−	16.9635i	−2.19581	−	0.650519i
$681$	2.27783	+	3.40901i	0.0872866	+	0.130634i
$682$	0.454954	+	0.0139058i	0.0174211	+	0.000532481i
$683$	44.3139	−	4.36454i	1.69563	−	0.167005i	0.796483	−	0.604661i	$-0.206691\pi$
$683$	44.3139	−	4.36454i	1.69563	−	0.167005i	0.899142	+	0.437656i	$0.144191\pi$
$684$	−0.785514	−	0.126191i	−0.0300349	−	0.00482502i
$685$	14.6349	+	48.2448i	0.559171	+	1.84334i
$686$	21.3821	+	43.1226i	0.816373	+	1.64643i
$687$	22.0509	+	9.13377i	0.841293	+	0.348475i
$688$	−11.9214	−	5.27732i	−0.454498	−	0.201196i
$689$	−10.6350	+	4.40516i	−0.405161	+	0.167823i
$690$	−18.4876	−	16.1424i	−0.703811	−	0.614530i
$691$	22.4222	−	41.9490i	0.852981	−	1.59581i	0.0508190	−	0.998708i	$-0.483817\pi$
$691$	22.4222	−	41.9490i	0.852981	−	1.59581i	0.802162	−	0.597107i	$-0.203683\pi$
$692$	−1.00733	−	27.1662i	−0.0382928	−	1.03270i
$693$	−13.7146	+	16.7112i	−0.520973	+	0.634807i
$694$	4.87368	−	10.8188i	0.185002	−	0.410676i
$695$	−8.54619	+	42.9646i	−0.324175	+	1.62974i
$696$	0.0105465	+	0.0512747i	0.000399764	+	0.00194356i
$697$	47.7309	−	9.49426i	1.80794	−	0.359621i
$698$	−8.89667	+	5.55910i	−0.336744	+	0.210415i
$699$	−12.6353	+	6.75373i	−0.477912	+	0.255449i
$700$	20.5927	+	15.6599i	0.778331	+	0.591888i
$701$	2.89073	−	29.3501i	0.109181	−	1.10854i	−0.771956	−	0.635676i	$-0.780721\pi$
$701$	2.89073	−	29.3501i	0.109181	−	1.10854i	0.881137	−	0.472861i	$-0.156779\pi$
$702$	−0.691189	−	0.896741i	−0.0260873	−	0.0338453i
$703$			1.83738i			0.0692979i
$704$	−4.15188	−	37.1866i	−0.156480	−	1.40152i
$705$			29.9029i			1.12621i
$706$	13.3677	−	10.3035i	0.503099	−	0.387778i
$707$	1.40116	−	14.2262i	0.0526961	−	0.535033i
$708$	−9.83270	+	1.33792i	−0.369536	+	0.0502822i
$709$	−11.4977	+	6.14564i	−0.431805	+	0.230804i	−0.672955	−	0.739683i	$-0.734975\pi$
$709$	−11.4977	+	6.14564i	−0.431805	+	0.230804i	0.241150	+	0.970488i	$0.422475\pi$
$710$	0.596379	+	0.954433i	0.0223817	+	0.0358192i
$711$	1.00711	−	0.200327i	0.0377697	−	0.00751285i
$712$	20.1740	+	29.7714i	0.756054	+	1.11573i
$713$	0.0834280	−	0.419421i	0.00312440	−	0.0157074i
$714$	45.0604	+	20.2989i	1.68634	+	0.759668i
$715$	−6.63381	+	8.08332i	−0.248091	+	0.302299i
$716$	−20.8515	+	22.4574i	−0.779255	+	0.839271i
$717$	−2.52857	+	4.73063i	−0.0944313	+	0.176669i
$718$	17.1820	−	19.6782i	0.641225	−	0.734384i
$719$	−3.75251	+	1.55434i	−0.139945	+	0.0579672i	−0.451557	−	0.892242i	$-0.649131\pi$
$719$	−3.75251	+	1.55434i	−0.139945	+	0.0579672i	0.311612	+	0.950210i	$0.399131\pi$
$720$	−2.44205	+	10.9002i	−0.0910098	+	0.406226i
$721$	−76.8715	−	31.8412i	−2.86284	−	1.18583i
$722$	−23.8727	+	11.8372i	−0.888450	+	0.440533i
$723$	−2.93306	−	9.66899i	−0.109082	−	0.359594i
$724$	−16.6236	+	12.0218i	−0.617812	+	0.446787i
$725$	−0.0515466	+	0.00507690i	−0.00191439	+	0.000188551i
$726$	−0.469916	+	15.3741i	−0.0174402	+	0.570588i
$727$	3.25148	+	4.86618i	0.120591	+	0.180477i	0.886854	−	0.462050i	$-0.152886\pi$
$727$	3.25148	+	4.86618i	0.120591	+	0.180477i	−0.766263	+	0.642527i	$0.777886\pi$
$728$	−6.58694	+	8.13357i	−0.244128	+	0.301450i
$729$	0.831470	+	0.555570i	0.0307952	+	0.0205767i
$730$	−42.1860	+	7.05897i	−1.56137	+	0.261264i
$731$	7.15342	−	23.5817i	0.264579	−	0.872200i
$732$	4.98245	−	10.2149i	0.184157	−	0.377553i
$733$	24.6006	−	20.1892i	0.908644	−	0.745705i	−0.0589379	−	0.998262i	$-0.518771\pi$
$733$	24.6006	−	20.1892i	0.908644	−	0.745705i	0.967582	+	0.252557i	$0.0812714\pi$
$734$	−6.81377	+	11.8611i	−0.251501	+	0.437803i
$735$	−28.3632	−	28.3632i	−1.04619	−	1.04619i
$736$	−35.1022	−	1.91864i	−1.29388	−	0.0707219i
$737$	−0.607711	+	0.607711i	−0.0223853	+	0.0223853i
$738$	−2.37505	−	8.78752i	−0.0874268	−	0.323473i
$739$	17.3269	+	21.1129i	0.637380	+	0.776649i	0.987083	−	0.160211i	$-0.0512176\pi$
$739$	17.3269	+	21.1129i	0.637380	+	0.776649i	−0.349703	+	0.936861i	$0.613718\pi$
$740$	25.7494	+	1.57555i	0.946568	+	0.0579184i
$741$	0.304756	+	0.0924466i	0.0111955	+	0.00339611i
$742$	−76.5149	−	54.5790i	−2.80895	−	2.00366i
$743$	−22.4769	+	33.6391i	−0.824599	+	1.23410i	0.145008	+	0.989431i	$0.453679\pi$
$743$	−22.4769	+	33.6391i	−0.824599	+	1.23410i	−0.969607	+	0.244669i	$0.921321\pi$
$744$	−0.185879	+	0.0577094i	−0.00681467	+	0.00211573i
$745$	17.0357	−	11.3829i	0.624141	−	0.417038i
$746$	−11.9888	−	12.7448i	−0.438942	−	0.466621i
$747$	0.295261	+	2.99784i	0.0108030	+	0.109685i
$748$	68.8084	−	16.3589i	2.51588	−	0.598141i
$749$	−36.1598	+	10.9689i	−1.32125	+	0.400797i
$750$	8.23871	+	2.77675i	0.300835	+	0.101393i
$751$	0.506157	−	1.22197i	0.0184699	−	0.0445904i	−0.914376	−	0.404867i	$-0.867318\pi$
$751$	0.506157	−	1.22197i	0.0184699	−	0.0445904i	0.932845	+	0.360277i	$0.117318\pi$
$752$	26.3681	+	33.7531i	0.961545	+	1.23085i
$753$	5.52174	+	13.3307i	0.201223	+	0.485796i
$754$	−0.00141585	−	0.0209068i	−5.15624e−5	−	0.000761380i
$755$	−28.6386	−	15.3077i	−1.04227	−	0.557103i
$756$	3.21869	−	8.66570i	0.117063	−	0.315168i
$757$	−11.0376	−	9.05834i	−0.401169	−	0.329231i	0.412079	−	0.911148i	$-0.364803\pi$
$757$	−11.0376	−	9.05834i	−0.401169	−	0.329231i	−0.813248	+	0.581917i	$0.802303\pi$
$758$	−15.5040	−	40.9235i	−0.563129	−	1.48641i
$759$	28.5081	+	5.67061i	1.03478	+	0.205830i
$760$	−1.22127	−	2.89497i	−0.0443000	−	0.105012i
$761$	9.97684	+	50.1569i	0.361660	+	1.81819i	0.548917	+	0.835877i	$0.315040\pi$
$761$	9.97684	+	50.1569i	0.361660	+	1.81819i	−0.187257	+	0.982311i	$0.559960\pi$
$762$	−10.4084	−	2.40311i	−0.377057	−	0.0870554i
$763$	−3.20500	−	5.99613i	−0.116029	−	0.217074i
$764$	−12.3387	+	46.8610i	−0.446400	+	1.69537i
$765$	−21.0124	−	2.06954i	−0.759706	−	0.0748245i
$766$	−26.1326	−	3.38277i	−0.944209	−	0.122224i
$767$	3.97225			0.143430
$768$	6.85520	+	14.4570i	0.247366	+	0.521674i
$769$	−38.7005			−1.39558			−0.697789	−	0.716304i	$-0.745833\pi$
$769$	−38.7005			−1.39558			−0.697789	+	0.716304i	$0.745833\pi$
$770$	−84.6716	−	10.9604i	−3.05135	−	0.394987i
$771$	−7.50517	−	0.739195i	−0.270292	−	0.0266215i
$772$	−8.74903	+	33.2278i	−0.314885	+	1.19589i
$773$	−2.39304	−	4.47706i	−0.0860716	−	0.161029i	0.835203	−	0.549942i	$-0.185350\pi$
$773$	−2.39304	−	4.47706i	−0.0860716	−	0.161029i	−0.921274	+	0.388914i	$0.872850\pi$
$774$	−4.49121	−	1.03694i	−0.161433	−	0.0372719i
$775$	−0.0375703	−	0.188879i	−0.00134957	−	0.00678473i
$776$	−15.1316	+	6.38339i	−0.543193	+	0.229150i
$777$	−20.9388	−	4.16499i	−0.751175	−	0.149418i
$778$	−2.28728	−	6.03741i	−0.0820030	−	0.216452i
$779$	1.97926	+	1.62434i	0.0709144	+	0.0581980i
$780$	1.55690	−	4.19165i	0.0557459	−	0.150085i
$781$	−1.17548	−	0.628306i	−0.0420619	−	0.0224826i
$782$	−4.48977	−	66.2969i	−0.160554	−	2.37077i
$783$	0.00708265	+	0.0170990i	0.000253113	+	0.000611069i
$784$	−57.0256	−	7.00477i	−2.03663	−	0.250170i
$785$	4.54171	−	10.9647i	0.162101	−	0.391345i
$786$	−22.7925	−	7.68192i	−0.812982	−	0.274005i
$787$	−1.54799	+	0.469578i	−0.0551799	+	0.0167386i	−0.317754	−	0.948173i	$-0.602929\pi$
$787$	−1.54799	+	0.469578i	−0.0551799	+	0.0167386i	0.262574	+	0.964912i	$0.415429\pi$
$788$	−23.2943	+	5.53812i	−0.829825	+	0.197288i
$789$	−1.28853	−	13.0826i	−0.0458728	−	0.465754i
$790$	2.77861	+	2.95383i	0.0988586	+	0.105092i
$791$	−20.7371	+	13.8561i	−0.737327	+	0.492666i
$792$	−3.92251	−	12.6342i	−0.139380	−	0.448938i
$793$	−2.52754	+	3.78273i	−0.0897555	+	0.134329i
$794$	−10.0877	−	7.19571i	−0.358001	−	0.255366i
$795$	38.4242	+	11.6559i	1.36277	+	0.413391i
$796$	48.2675	+	2.95338i	1.71080	+	0.104680i
$797$	−30.7341	−	37.4497i	−1.08866	−	1.32654i	−0.941345	−	0.337445i	$-0.890437\pi$
$797$	−30.7341	−	37.4497i	−1.08866	−	1.32654i	−0.147314	−	0.989090i	$-0.547063\pi$
$798$	0.678431	+	2.51015i	0.0240162	+	0.0888582i
$799$	−57.2472	+	57.2472i	−2.02526	+	2.02526i
$800$	−14.9350	+	5.25108i	−0.528033	+	0.185654i
$801$	8.99071	+	8.99071i	0.317671	+	0.317671i
$802$	−10.7269	+	18.6730i	−0.378781	+	0.659367i
$803$	39.1574	−	32.1356i	1.38183	−	1.13404i
$804$	0.161109	−	0.330302i	0.00568188	−	0.0116488i
$805$	−23.2850	+	76.7604i	−0.820689	+	2.70545i
$806$	0.0768418	−	0.0128579i	0.00270664	−	0.000452901i
$807$	−11.4202	−	7.63072i	−0.402009	−	0.268614i
$808$	6.79804	+	5.50537i	0.239154	+	0.193678i
$809$	0.838992	+	1.25564i	0.0294974	+	0.0441460i	0.845925	−	0.533301i	$-0.179049\pi$
$809$	0.838992	+	1.25564i	0.0294974	+	0.0441460i	−0.816428	+	0.577447i	$0.804049\pi$
$810$	−0.120656	+	3.94749i	−0.00423943	+	0.138700i
$811$	0.604327	−	0.0595211i	0.0212208	−	0.00209007i	−0.0874012	−	0.996173i	$-0.527856\pi$
$811$	0.604327	−	0.0595211i	0.0212208	−	0.00209007i	0.108622	+	0.994083i	$0.465356\pi$
$812$	0.138636	−	0.100258i	0.00486516	−	0.00351837i
$813$	2.53710	+	8.36371i	0.0889801	+	0.293328i
$814$	−27.3720	+	13.5723i	−0.959390	+	0.475709i
$815$	29.2995	+	12.1362i	1.02632	+	0.425114i
$816$	−25.5429	+	16.1926i	−0.894179	+	0.566853i
$817$	1.19784	−	0.496160i	0.0419070	−	0.0173584i
$818$	16.8150	−	19.2579i	0.587921	−	0.673337i
$819$	−1.74435	+	3.26345i	−0.0609525	+	0.114034i
$820$	24.4611	−	26.3450i	0.854219	−	0.920007i
$821$	−17.3017	+	21.0822i	−0.603835	+	0.735775i	−0.981773	−	0.190056i	$-0.939133\pi$
$821$	−17.3017	+	21.0822i	−0.603835	+	0.735775i	0.377938	+	0.925831i	$0.376633\pi$
$822$	23.2783	+	10.4865i	0.811925	+	0.365758i
$823$	10.4372	−	52.4711i	0.363816	−	1.82903i	−0.172497	−	0.985010i	$-0.555184\pi$
$823$	10.4372	−	52.4711i	0.363816	−	1.82903i	0.536314	−	0.844019i	$-0.319816\pi$
$824$	42.1505	−	28.5626i	1.46838	−	0.995024i
$825$	12.8381	−	2.55366i	0.446965	−	0.0889070i
$826$	17.1862	+	27.5044i	0.597984	+	0.957001i
$827$	3.62506	−	1.93764i	0.126056	−	0.0673782i	−0.407163	−	0.913355i	$-0.633482\pi$
$827$	3.62506	−	1.93764i	0.126056	−	0.0673782i	0.533219	+	0.845977i	$0.320982\pi$
$828$	−12.3155	+	1.67576i	−0.427995	+	0.0582366i
$829$	3.10309	−	31.5062i	0.107775	−	1.09426i	−0.777403	−	0.629003i	$-0.783463\pi$
$829$	3.10309	−	31.5062i	0.107775	−	1.09426i	0.885177	−	0.465254i	$-0.154037\pi$
$830$	−9.42259	+	7.26273i	−0.327063	+	0.252093i
$831$			14.3087i			0.496363i
$832$	−1.93880	−	6.10422i	−0.0672157	−	0.211626i
$833$		−	108.599i		−	3.76274i
$834$	13.5430	+	17.5706i	0.468956	+	0.608419i
$835$	2.09113	−	21.2316i	0.0723665	−	0.734750i
$836$	2.96196	+	2.25244i	0.102442	+	0.0779024i
$837$	−0.0606874	+	0.0324381i	−0.00209766	+	0.00112122i
$838$	−39.9937	+	24.9901i	−1.38156	+	0.863270i
$839$	−6.87839	+	1.36820i	−0.237469	+	0.0472354i	−0.312390	−	0.949954i	$-0.601129\pi$
$839$	−6.87839	+	1.36820i	−0.237469	+	0.0472354i	0.0749212	+	0.997189i	$0.476129\pi$
$840$	35.7596	−	7.35525i	1.23382	−	0.253780i
$841$	5.65755	−	28.4424i	0.195088	−	0.980774i
$842$	−9.42049	+	20.9120i	−0.324652	+	0.720676i
$843$	1.95022	−	2.37635i	0.0671692	−	0.0818459i
$844$	−0.0117346	−	0.316466i	−0.000403921	−	0.0108932i
$845$	16.2697	−	30.4385i	0.559695	−	1.04712i
$846$	11.4069	+	9.95993i	0.392179	+	0.342429i
$847$	46.4441	−	19.2378i	1.59584	−	0.661018i
$848$	53.6497	−	20.7255i	1.84234	−	0.711716i
$849$	−17.7706	−	7.36081i	−0.609884	−	0.252622i
$850$	−13.2932	−	26.8093i	−0.455955	−	0.919551i
$851$	8.33244	+	27.4684i	0.285632	+	0.941604i
$852$	0.562724	+	0.0904001i	0.0192786	+	0.00309706i
$853$	15.2594	−	1.50292i	0.522473	−	0.0514591i	0.166657	−	0.986015i	$-0.446703\pi$
$853$	15.2594	−	1.50292i	0.522473	−	0.0514591i	0.355816	+	0.934556i	$0.384203\pi$
$854$	−37.1277	−	1.13482i	−1.27048	−	0.0388327i
$855$	−0.617169	−	0.923659i	−0.0211067	−	0.0315885i
$856$	6.56819	−	22.1708i	0.224496	−	0.757782i
$857$	6.78739	+	4.53519i	0.231853	+	0.154919i	0.666070	−	0.745889i	$-0.267975\pi$
$857$	6.78739	+	4.53519i	0.231853	+	0.154919i	−0.434218	+	0.900808i	$0.642975\pi$
$858$	0.873953	+	5.22294i	0.0298363	+	0.178308i
$859$	1.22162	−	4.02715i	0.0416812	−	0.137405i	−0.933630	−	0.358238i	$-0.883378\pi$
$859$	1.22162	−	4.02715i	0.0416812	−	0.137405i	0.975312	+	0.220833i	$0.0708777\pi$
$860$	−5.92617	−	17.2122i	−0.202081	−	0.586933i
$861$	−22.9976	+	18.8737i	−0.783757	+	0.643213i
$862$	−38.5989	−	22.1736i	−1.31468	−	0.755235i
$863$	12.9084	+	12.9084i	0.439407	+	0.439407i	0.891812	−	0.452406i	$-0.149434\pi$
$863$	12.9084	+	12.9084i	0.439407	+	0.439407i	−0.452406	+	0.891812i	$0.649434\pi$
$864$	3.34467	+	4.56215i	0.113788	+	0.155207i
$865$	26.8405	−	26.8405i	0.912603	−	0.912603i
$866$	48.1796	−	13.0218i	1.63721	−	0.442497i
$867$	−25.4803	−	31.0478i	−0.865356	−	1.05444i
$868$	0.421490	+	0.476432i	0.0143063	+	0.0161712i
$869$	−4.59595	−	1.39417i	−0.155907	−	0.0472938i
$870$	−0.0424464	+	0.0595061i	−0.00143907	+	0.00201744i
$871$	−0.0817287	+	0.122316i	−0.00276927	+	0.00414451i
$872$	4.14307	+	0.380852i	0.140302	+	0.0128973i
$873$	−4.82784	+	3.22586i	−0.163397	+	0.109179i
$874$	2.54646	−	2.39541i	0.0861353	−	0.0810260i
$875$	−2.78514	−	28.2780i	−0.0941548	−	0.955969i
$876$	−11.3584	+	18.4437i	−0.383764	+	0.623156i
$877$	−17.0228	+	5.16380i	−0.574818	+	0.174369i	−0.564292	−	0.825575i	$-0.690851\pi$
$877$	−17.0228	+	5.16380i	−0.574818	+	0.174369i	−0.0105265	+	0.999945i	$0.503351\pi$
$878$	7.18471	−	21.3173i	0.242472	−	0.719423i
$879$	9.61248	−	23.2066i	0.324221	−	0.782739i
$880$	34.1062	−	39.5782i	1.14972	−	1.33418i
$881$	−7.84617	−	18.9423i	−0.264344	−	0.638184i	0.734854	−	0.678226i	$-0.237251\pi$
$881$	−7.84617	−	18.9423i	−0.264344	−	0.638184i	−0.999198	+	0.0400421i	$0.987251\pi$
$882$	−20.2667	+	1.37251i	−0.682416	+	0.0462147i
$883$	−7.84880	−	4.19527i	−0.264133	−	0.141182i	0.334015	−	0.942568i	$-0.391596\pi$
$883$	−7.84880	−	4.19527i	−0.264133	−	0.141182i	−0.598148	+	0.801386i	$0.704096\pi$
$884$	11.0052	−	5.04407i	0.370146	−	0.169650i
$885$	−10.7108	−	8.79009i	−0.360038	−	0.295476i
$886$	0.0685947	−	0.0259872i	0.00230448	−	0.000873057i
$887$	−17.9236	−	3.56522i	−0.601815	−	0.119708i	−0.115226	−	0.993339i	$-0.536759\pi$
$887$	−17.9236	−	3.56522i	−0.601815	−	0.119708i	−0.486589	+	0.873631i	$0.661759\pi$
$888$	9.17754	−	9.29777i	0.307978	−	0.312013i
$889$	6.81113	+	34.2419i	0.228438	+	1.14844i
$890$	−11.2965	+	48.9277i	−0.378660	+	1.64006i
$891$	−2.20482	−	4.12493i	−0.0738642	−	0.138190i
$892$	2.74462	+	4.70655i	0.0918967	+	0.157587i
$893$	−4.23902	−	0.417507i	−0.141853	−	0.0139713i
$894$	1.33200	−	10.2899i	0.0445486	−	0.344147i
$895$	−42.7896			−1.43030
$896$	33.8781	−	39.8348i	1.13179	−	1.33079i
$897$	4.97528			0.166120
$898$	−1.15629	+	8.93257i	−0.0385859	+	0.298084i
$899$	−0.00126744		0.000124832i	−4.22716e−5		4.16339e-6i
$900$	−4.83513	+	2.81960i	−0.161171	+	0.0939867i
$901$	51.2463	+	95.8752i	1.70726	+	3.19406i
$902$	−9.57798	+	41.4844i	−0.318912	+	1.38128i
$903$	2.93899	+	14.7753i	0.0978034	+	0.491691i
$904$	−0.0993142	−	15.2616i	−0.00330314	−	0.507594i
$905$	−28.0948	−	5.58840i	−0.933902	−	0.185765i
$906$	−15.3782	+	5.82606i	−0.510907	+	0.193558i
$907$	−3.22598	−	2.64749i	−0.107117	−	0.0879086i	0.579310	−	0.815107i	$-0.303322\pi$
$907$	−3.22598	−	2.64749i	−0.107117	−	0.0879086i	−0.686427	+	0.727198i	$0.740822\pi$
$908$	3.41655	+	7.45430i	0.113382	+	0.247380i
$909$	2.72759	+	1.45793i	0.0904685	+	0.0483564i
$910$	−14.5806	+	0.987433i	−0.483343	+	0.0327331i
$911$	−4.90590	−	11.8439i	−0.162540	−	0.392406i	0.821536	−	0.570157i	$-0.193118\pi$
$911$	−4.90590	−	11.8439i	−0.162540	−	0.392406i	−0.984075	+	0.177751i	$0.943118\pi$
$912$	−1.51111	−	0.498373i	−0.0500378	−	0.0165028i
$913$	5.39176	−	13.0169i	0.178441	−	0.430795i
$914$	6.13319	−	18.1974i	0.202868	−	0.601916i
$915$	15.1859	−	4.60661i	0.502032	−	0.152290i
$916$	40.6460	+	25.0314i	1.34298	+	0.827061i
$917$	7.70512	+	78.2314i	0.254445	+	2.58343i
$918$	−7.78820	+	7.32622i	−0.257049	+	0.241801i
$919$	−24.0382	+	16.0618i	−0.792948	+	0.529831i	−0.884816	−	0.465940i	$-0.845716\pi$
$919$	−24.0382	+	16.0618i	−0.792948	+	0.529831i	0.0918683	+	0.995771i	$0.470716\pi$
$920$	−31.3863	−	37.7408i	−1.03478	−	1.24428i
$921$	16.7833	−	25.1179i	0.553028	−	0.827664i
$922$	−31.0098	+	43.4730i	−1.02125	+	1.43171i
$923$	−0.218320	−	0.0662266i	−0.00718608	−	0.00217987i
$924$	−32.3831	+	28.6487i	−1.06533	+	0.942474i
$925$	8.20050	+	9.99233i	0.269631	+	0.328546i
$926$	−29.8577	+	8.06981i	−0.981186	+	0.265191i
$927$	12.7291	−	12.7291i	0.418079	−	0.418079i
$928$	0.00456022	+	0.104597i	0.000149697	+	0.00343356i
$929$	17.3164	+	17.3164i	0.568133	+	0.568133i	0.931605	−	0.363472i	$-0.118409\pi$
$929$	17.3164	+	17.3164i	0.568133	+	0.568133i	−0.363472	+	0.931605i	$0.618409\pi$
$930$	−0.235649	−	0.135371i	−0.00772723	−	0.00443900i
$931$	4.41677	−	3.62475i	0.144754	−	0.118796i
$932$	−27.0932	+	9.32818i	−0.887468	+	0.305555i
$933$	−6.56055	+	21.6273i	−0.214783	+	0.708044i
$934$	−5.33458	−	31.8807i	−0.174553	−	1.04317i
$935$	82.1118	+	54.8653i	2.68534	+	1.79429i
$936$	−1.08041	−	1.99004i	−0.0353142	−	0.0650466i
$937$	13.1025	+	19.6093i	0.428041	+	0.640608i	0.981319	−	0.192388i	$-0.0616233\pi$
$937$	13.1025	+	19.6093i	0.428041	+	0.640608i	−0.553278	+	0.832997i	$0.686623\pi$
$938$	−1.20054	−	0.0366947i	−0.0391989	−	0.00119813i
$939$	−7.21576	+	0.710691i	−0.235478	+	0.0231925i
$940$	−9.48601	+	59.0487i	−0.309399	+	1.92595i
$941$	8.37990	+	27.6248i	0.273177	+	0.900544i	0.980976	+	0.194130i	$0.0621883\pi$
$941$	8.37990	+	27.6248i	0.273177	+	0.900544i	−0.707799	+	0.706414i	$0.750312\pi$
$942$	−2.66991	−	5.38457i	−0.0869905	−	0.175439i
$943$	36.9559	+	15.3076i	1.20345	+	0.498485i
$944$	−19.8409	−	0.477235i	−0.645766	−	0.0155327i
$945$	11.9251	−	4.93952i	0.387922	−	0.160683i
$946$	16.2396	+	14.1796i	0.527996	+	0.461018i
$947$	2.08024	−	3.89185i	0.0675986	−	0.126468i	−0.845852	−	0.533417i	$-0.820907\pi$
$947$	2.08024	−	3.89185i	0.0675986	−	0.126468i	0.913451	+	0.406949i	$0.133407\pi$
$948$	2.05227	−	0.0760986i	0.0666548	−	0.00247157i
$949$	5.50060	−	6.70250i	0.178557	−	0.217572i
$950$	0.646650	−	1.43546i	0.0209801	−	0.0465725i
$951$	1.06702	−	5.36426i	0.0346004	−	0.173948i
$952$	82.5406	+	54.3783i	2.67516	+	1.76241i
$953$	−52.9036	+	10.5232i	−1.71372	+	0.340879i	−0.951782	−	0.306776i	$-0.900750\pi$
$953$	−52.9036	+	10.5232i	−1.71372	+	0.340879i	−0.761934	+	0.647655i	$0.775750\pi$
$954$	17.2445	−	10.7753i	0.558311	−	0.348862i
$955$	−59.6727	+	31.8957i	−1.93096	+	1.03212i
$956$	−6.49381	+	8.53935i	−0.210025	+	0.276182i
$957$	0.00848485	−	0.0861481i	0.000274276	−	0.00278477i
$958$	17.0737	+	22.1513i	0.551628	+	0.715675i
$959$		−	83.4439i		−	2.69454i
$960$	−8.28010	+	20.7497i	−0.267239	+	0.669694i
$961$			30.9953i			0.999847i
$962$	−4.14198	+	3.19255i	−0.133543	+	0.102932i
$963$	0.801320	−	8.13594i	0.0258222	−	0.262177i
$964$	−2.72458	−	20.0236i	−0.0877529	−	0.644917i
$965$	−42.3121	+	22.6163i	−1.36208	+	0.728045i
$966$	21.5258	+	34.4495i	0.692583	+	1.10839i
$967$	−20.1643	+	4.01094i	−0.648441	+	0.128983i	−0.508343	−	0.861155i	$-0.669742\pi$
$967$	−20.1643	+	4.01094i	−0.648441	+	0.128983i	−0.140098	+	0.990138i	$0.544742\pi$
$968$	−5.80503	+	30.2100i	−0.186581	+	0.970985i
$969$	0.586755	−	2.94982i	0.0188493	−	0.0947618i
$970$	−20.9078	−	9.41859i	−0.671309	−	0.302413i
$971$	−22.2475	+	27.1086i	−0.713956	+	0.869958i	−0.995992	−	0.0894461i	$-0.971490\pi$
$971$	−22.2475	+	27.1086i	−0.713956	+	0.869958i	0.282036	+	0.959404i	$0.408990\pi$
$972$	1.46565	+	1.36084i	0.0470106	+	0.0436489i
$973$	34.1784	−	63.9433i	1.09571	−	2.04993i
$974$	−5.27823	+	6.04506i	−0.169125	+	0.193696i
$975$	2.06998	−	0.857414i	0.0662924	−	0.0274592i
$976$	13.0792	−	18.5906i	0.418655	−	0.595070i
$977$	9.17933	+	3.80220i	0.293673	+	0.121643i	0.524656	−	0.851315i	$-0.324194\pi$
$977$	9.17933	+	3.80220i	0.293673	+	0.121643i	−0.230983	+	0.972958i	$0.574194\pi$
$978$	14.3885	−	7.13448i	0.460094	−	0.228135i
$979$	−17.2631	−	56.9089i	−0.551732	−	1.81882i
$980$	−47.0107	−	65.0059i	−1.50170	−	2.07654i
$981$	1.46389	−	0.144180i	0.0467384	−	0.00460333i
$982$	1.26641	−	41.4328i	0.0404127	−	1.32217i
$983$	8.04822	+	12.0450i	0.256698	+	0.384176i	0.937326	−	0.348453i	$-0.113293\pi$
$983$	8.04822	+	12.0450i	0.256698	+	0.384176i	−0.680628	+	0.732629i	$0.738293\pi$
$984$	−1.90233	−	18.1060i	−0.0606439	−	0.577198i
$985$	−27.7980	−	18.5740i	−0.885718	−	0.591818i
$986$	−0.195182	+	0.0326597i	−0.00621585	+	0.00104010i
$987$	14.3670	−	47.3616i	0.457306	−	1.50754i
$988$	0.572469	+	0.279229i	0.0182127	+	0.00888347i
$989$	15.6573	−	12.8496i	0.497875	−	0.408595i
$990$	9.20119	−	16.0171i	0.292433	−	0.509056i
$991$	−3.07576	−	3.07576i	−0.0977049	−	0.0977049i	0.656565	−	0.754270i	$-0.272009\pi$
$991$	−3.07576	−	3.07576i	−0.0977049	−	0.0977049i	−0.754270	+	0.656565i	$0.772009\pi$
$992$	−0.385360	+	0.0549917i	−0.0122352	+	0.00174599i
$993$	−16.7224	+	16.7224i	−0.530668	+	0.530668i
$994$	−0.486012	−	1.79821i	−0.0154154	−	0.0570358i
$995$	42.8355	+	52.1952i	1.35798	+	1.65470i
$996$	−0.367949	+	6.01344i	−0.0116589	+	0.190543i
$997$	−5.24099	−	1.58984i	−0.165984	−	0.0503507i	0.206199	−	0.978510i	$-0.433891\pi$
$997$	−5.24099	−	1.58984i	−0.165984	−	0.0503507i	−0.372183	+	0.928159i	$0.621391\pi$
$998$	14.0609	+	10.0298i	0.445090	+	0.317488i
$999$	2.56614	−	3.84050i	0.0811890	−	0.121508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.349.31	✓	512
128.117	even	32	inner	384.2.v.a.373.31	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.349.31	✓	512	1.1	even	1	trivial
384.2.v.a.373.31	yes	512	128.117	even	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40251 + 0.181550i) q^{2} +(0.995185 + 0.0980171i) q^{3} +(1.93408 + 0.509252i) q^{4} +(1.31642 + 2.46285i) q^{5} +(1.37796 + 0.318146i) q^{6} +(-0.901722 - 4.53326i) q^{7} +(2.62011 + 1.06536i) q^{8} +(0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.40251 + 0.181550i) q^{2} +(0.995185 + 0.0980171i) q^{3} +(1.93408 + 0.509252i) q^{4} +(1.31642 + 2.46285i) q^{5} +(1.37796 + 0.318146i) q^{6} +(-0.901722 - 4.53326i) q^{7} +(2.62011 + 1.06536i) q^{8} +(0.980785 + 0.195090i) q^{9} +(1.39917 + 3.69317i) q^{10} +(-3.61553 - 2.96719i) q^{11} +(1.87485 + 0.696373i) q^{12} +(-0.706057 - 0.377395i) q^{13} +(-0.441661 - 6.52166i) q^{14} +(1.06868 + 2.58002i) q^{15} +(3.48132 + 1.96987i) q^{16} +(-2.89337 + 6.98522i) q^{17} +(1.34014 + 0.451678i) q^{18} +(-0.380664 + 0.115473i) q^{19} +(1.29185 + 5.43374i) q^{20} +(-0.453042 - 4.59982i) q^{21} +(-4.53213 - 4.81791i) q^{22} +(-5.16718 + 3.45260i) q^{23} +(2.50307 + 1.31705i) q^{24} +(-1.55482 + 2.32695i) q^{25} +(-0.921737 - 0.657486i) q^{26} +(0.956940 + 0.290285i) q^{27} +(0.564573 - 9.22689i) q^{28} +(0.0117413 + 0.0143068i) q^{29} +(1.03043 + 3.81253i) q^{30} +(-0.0486579 + 0.0486579i) q^{31} +(4.52497 + 3.39480i) q^{32} +(-3.30728 - 3.30728i) q^{33} +(-5.32615 + 9.27156i) q^{34} +(9.97770 - 8.18849i) q^{35} +(1.79757 + 0.876787i) q^{36} +(1.34080 - 4.42004i) q^{37} +(-0.554850 + 0.0928429i) q^{38} +(-0.665666 - 0.444784i) q^{39} +(0.825339 + 7.85542i) q^{40} +(-3.57602 - 5.35189i) q^{41} +(0.199700 - 6.53355i) q^{42} +(-3.24361 + 0.319468i) q^{43} +(-5.48167 - 7.57999i) q^{44} +(0.810648 + 2.67235i) q^{45} +(-7.87385 + 3.90421i) q^{46} +(9.89282 + 4.09774i) q^{47} +(3.27148 + 2.30161i) q^{48} +(-13.2702 + 5.49670i) q^{49} +(-2.60311 + 2.98130i) q^{50} +(-3.56411 + 6.66798i) q^{51} +(-1.17338 - 1.08947i) q^{52} +(9.12159 - 11.1147i) q^{53} +(1.28942 + 0.580860i) q^{54} +(2.54818 - 12.8106i) q^{55} +(2.46696 - 12.8383i) q^{56} +(-0.390149 + 0.0776055i) q^{57} +(0.0138699 + 0.0221970i) q^{58} +(-4.37579 + 2.33891i) q^{59} +(0.753030 + 5.53420i) q^{60} +(0.556994 - 5.65526i) q^{61} +(-0.0770772 + 0.0594095i) q^{62} -4.62207i q^{63} +(5.73000 + 5.58275i) q^{64} -2.23572i q^{65} +(-4.03807 - 5.23894i) q^{66} +(0.0180106 - 0.182865i) q^{67} +(-9.15325 + 12.0365i) q^{68} +(-5.48071 + 2.92950i) q^{69} +(15.4805 - 9.67300i) q^{70} +(0.279494 - 0.0555948i) q^{71} +(2.36193 + 1.55605i) q^{72} +(-2.11289 + 10.6222i) q^{73} +(2.68295 - 5.95573i) q^{74} +(-1.77541 + 2.16335i) q^{75} +(-0.795039 + 0.0294802i) q^{76} +(-10.1908 + 19.0657i) q^{77} +(-0.852854 - 0.744666i) q^{78} +(0.948679 - 0.392956i) q^{79} +(-0.268605 + 11.1672i) q^{80} +(0.923880 + 0.382683i) q^{81} +(-4.04377 - 8.15532i) q^{82} +(0.874437 + 2.88263i) q^{83} +(1.46625 - 9.12712i) q^{84} +(-21.0124 + 2.06954i) q^{85} +(-4.60721 - 0.140821i) q^{86} +(0.0102824 + 0.0153887i) q^{87} +(-6.31196 - 11.6262i) q^{88} +(10.5720 + 7.06396i) q^{89} +(0.651778 + 3.89517i) q^{90} +(-1.07416 + 3.54105i) q^{91} +(-11.7520 + 4.04620i) q^{92} +(-0.0531929 + 0.0436543i) q^{93} +(13.1308 + 7.54317i) q^{94} +(-0.785507 - 0.785507i) q^{95} +(4.17043 + 3.82198i) q^{96} +(-4.10574 + 4.10574i) q^{97} +(-19.6095 + 5.29998i) q^{98} +(-2.96719 - 3.61553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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