LMFDB - Embedded newform 384.2.v.a.157.8

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			157.8
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.957405 + 1.04085i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-0.166750 - 1.99304i) q^{4} +(0.269342 - 0.143966i) q^{5} +(-0.941999 - 1.05482i) q^{6} +(0.809633 + 4.07030i) q^{7} +(2.23411 + 1.73458i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(-0.957405 + 1.04085i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-0.166750 - 1.99304i) q^{4} +(0.269342 - 0.143966i) q^{5} +(-0.941999 - 1.05482i) q^{6} +(0.809633 + 4.07030i) q^{7} +(2.23411 + 1.73458i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-0.108022 + 0.418179i) q^{10} +(3.25548 - 3.96681i) q^{11} +(1.99978 + 0.0294048i) q^{12} +(-0.832999 + 1.55843i) q^{13} +(-5.01173 - 3.05422i) q^{14} +(0.116873 + 0.282156i) q^{15} +(-3.94439 + 0.664677i) q^{16} +(-1.05262 + 2.54126i) q^{17} +(1.14207 - 0.834073i) q^{18} +(1.54516 + 5.09371i) q^{19} +(-0.331842 - 0.512801i) q^{20} +(-4.13006 + 0.406775i) q^{21} +(1.01205 + 7.18632i) q^{22} +(2.66734 - 1.78226i) q^{23} +(-1.94521 + 2.05333i) q^{24} +(-2.72603 + 4.07980i) q^{25} +(-0.824581 - 2.35908i) q^{26} +(0.290285 - 0.956940i) q^{27} +(7.97725 - 2.29235i) q^{28} +(-4.96675 + 4.07611i) q^{29} +(-0.405577 - 0.148490i) q^{30} +(-3.88466 + 3.88466i) q^{31} +(3.08455 - 4.74189i) q^{32} +(3.62861 + 3.62861i) q^{33} +(-1.63729 - 3.52864i) q^{34} +(0.804053 + 0.979741i) q^{35} +(-0.225276 + 1.98727i) q^{36} +(0.663712 + 0.201335i) q^{37} +(-6.78114 - 3.26846i) q^{38} +(-1.46928 - 0.981741i) q^{39} +(0.851458 + 0.145560i) q^{40} +(-4.02040 - 6.01695i) q^{41} +(3.53075 - 4.68823i) q^{42} +(-0.733450 - 7.44685i) q^{43} +(-8.44884 - 5.82682i) q^{44} +(-0.292253 + 0.0886539i) q^{45} +(-0.698657 + 4.48266i) q^{46} +(-2.51912 - 1.04345i) q^{47} +(-0.274859 - 3.99055i) q^{48} +(-9.44468 + 3.91211i) q^{49} +(-1.63655 - 6.74342i) q^{50} +(-2.42585 - 1.29664i) q^{51} +(3.24491 + 1.40033i) q^{52} +(10.1617 + 8.33951i) q^{53} +(0.718114 + 1.21832i) q^{54} +(0.305749 - 1.53710i) q^{55} +(-5.25146 + 10.4979i) q^{56} +(-5.22063 + 1.03845i) q^{57} +(0.512566 - 9.07214i) q^{58} +(0.305360 + 0.571289i) q^{59} +(0.542858 - 0.279981i) q^{60} +(7.82117 + 0.770318i) q^{61} +(-0.324166 - 7.76256i) q^{62} -4.15004i q^{63} +(1.98245 + 7.75048i) q^{64} +0.539674i q^{65} +(-7.25091 + 0.302799i) q^{66} +(13.0142 + 1.28179i) q^{67} +(5.24035 + 1.67416i) q^{68} +(1.51224 + 2.82919i) q^{69} +(-1.78957 - 0.101109i) q^{70} +(5.38424 - 1.07099i) q^{71} +(-1.85278 - 2.13710i) q^{72} +(1.26052 - 6.33704i) q^{73} +(-0.845002 + 0.498068i) q^{74} +(-3.79295 - 3.11280i) q^{75} +(9.89429 - 3.92893i) q^{76} +(18.7818 + 10.0391i) q^{77} +(2.42854 - 0.589380i) q^{78} +(10.1029 - 4.18476i) q^{79} +(-0.966697 + 0.746883i) q^{80} +(0.923880 + 0.382683i) q^{81} +(10.1119 + 1.57602i) q^{82} +(-6.59955 + 2.00195i) q^{83} +(1.49940 + 8.16353i) q^{84} +(0.0823397 + 0.836009i) q^{85} +(8.45328 + 6.36624i) q^{86} +(-3.56965 - 5.34236i) q^{87} +(14.1538 - 3.21538i) q^{88} +(-5.61758 - 3.75355i) q^{89} +(0.187529 - 0.389070i) q^{90} +(-7.01771 - 2.12880i) q^{91} +(-3.99689 - 5.01892i) q^{92} +(-3.48519 - 4.24672i) q^{93} +(3.49790 - 1.62303i) q^{94} +(1.14950 + 1.14950i) q^{95} +(4.41672 + 3.53448i) q^{96} +(-4.68172 + 4.68172i) q^{97} +(4.97045 - 13.5760i) q^{98} +(-3.96681 + 3.25548i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	−0.957405	+	1.04085i	−0.676988	+	0.735994i
$2$	−0.957405	+	1.04085i	−0.676988	+	0.735994i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	−0.166750	−	1.99304i	−0.0833749	−	0.996518i
$5$	0.269342	−	0.143966i	0.120453	−	0.0643836i	−0.410070	−	0.912054i	$-0.634496\pi$
$5$	0.269342	−	0.143966i	0.120453	−	0.0643836i	0.530523	+	0.847671i	$0.321996\pi$
$6$	−0.941999	−	1.05482i	−0.384569	−	0.430627i
$7$	0.809633	+	4.07030i	0.306013	+	1.53843i	0.761487	+	0.648180i	$0.224470\pi$
$7$	0.809633	+	4.07030i	0.306013	+	1.53843i	−0.455475	+	0.890249i	$0.650530\pi$
$8$	2.23411	+	1.73458i	0.789875	+	0.613267i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	−0.108022	+	0.418179i	−0.0341594	+	0.132240i
$11$	3.25548	−	3.96681i	0.981563	−	1.19604i	0.000966523	−	1.00000i	$-0.499692\pi$
$11$	3.25548	−	3.96681i	0.981563	−	1.19604i	0.980596	−	0.196038i	$-0.0628077\pi$
$12$	1.99978	+	0.0294048i	0.577288	+	0.00848844i
$13$	−0.832999	+	1.55843i	−0.231032	+	0.432231i	−0.970548	−	0.240908i	$-0.922555\pi$
$13$	−0.832999	+	1.55843i	−0.231032	+	0.432231i	0.739515	+	0.673140i	$0.235055\pi$
$14$	−5.01173	−	3.05422i	−1.33944	−	0.816274i
$15$	0.116873	+	0.282156i	0.0301764	+	0.0728523i
$16$	−3.94439	+	0.664677i	−0.986097	+	0.166169i
$17$	−1.05262	+	2.54126i	−0.255299	+	0.616346i	−0.998616	−	0.0525934i	$-0.983251\pi$
$17$	−1.05262	+	2.54126i	−0.255299	+	0.616346i	0.743317	+	0.668939i	$0.233251\pi$
$18$	1.14207	−	0.834073i	0.269188	−	0.196593i
$19$	1.54516	+	5.09371i	0.354484	+	1.16858i	0.935095	+	0.354396i	$0.115314\pi$
$19$	1.54516	+	5.09371i	0.354484	+	1.16858i	−0.580612	+	0.814181i	$0.697186\pi$
$20$	−0.331842	−	0.512801i	−0.0742022	−	0.114666i
$21$	−4.13006	+	0.406775i	−0.901253	+	0.0887656i
$22$	1.01205	+	7.18632i	0.215771	+	1.53213i
$23$	2.66734	−	1.78226i	0.556180	−	0.371627i	−0.245486	−	0.969400i	$-0.578947\pi$
$23$	2.66734	−	1.78226i	0.556180	−	0.371627i	0.801666	+	0.597773i	$0.203947\pi$
$24$	−1.94521	+	2.05333i	−0.397064	+	0.419134i
$25$	−2.72603	+	4.07980i	−0.545207	+	0.815959i
$26$	−0.824581	−	2.35908i	−0.161714	−	0.462654i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	7.97725	−	2.29235i	1.50756	−	0.433213i
$29$	−4.96675	+	4.07611i	−0.922302	+	0.756914i	−0.970293	−	0.241934i	$-0.922218\pi$
$29$	−4.96675	+	4.07611i	−0.922302	+	0.756914i	0.0479903	+	0.998848i	$0.484718\pi$
$30$	−0.405577	−	0.148490i	−0.0740479	−	0.0271105i
$31$	−3.88466	+	3.88466i	−0.697706	+	0.697706i	−0.963915	−	0.266209i	$-0.914229\pi$
$31$	−3.88466	+	3.88466i	−0.697706	+	0.697706i	0.266209	+	0.963915i	$0.414229\pi$
$32$	3.08455	−	4.74189i	0.545276	−	0.838256i
$33$	3.62861	+	3.62861i	0.631661	+	0.631661i
$34$	−1.63729	−	3.52864i	−0.280793	−	0.605157i
$35$	0.804053	+	0.979741i	0.135910	+	0.165606i
$36$	−0.225276	+	1.98727i	−0.0375461	+	0.331212i
$37$	0.663712	+	0.201335i	0.109114	+	0.0330993i	0.344369	−	0.938834i	$-0.388093\pi$
$37$	0.663712	+	0.201335i	0.109114	+	0.0330993i	−0.235256	+	0.971934i	$0.575593\pi$
$38$	−6.78114	−	3.26846i	−1.10005	−	0.530214i
$39$	−1.46928	−	0.981741i	−0.235273	−	0.157204i
$40$	0.851458	+	0.145560i	0.134627	+	0.0230150i
$41$	−4.02040	−	6.01695i	−0.627881	−	0.939690i	−0.999934	−	0.0114788i	$-0.996346\pi$
$41$	−4.02040	−	6.01695i	−0.627881	−	0.939690i	0.372053	−	0.928211i	$-0.378654\pi$
$42$	3.53075	−	4.68823i	0.544806	−	0.723410i
$43$	−0.733450	−	7.44685i	−0.111850	−	1.13563i	−0.873224	−	0.487320i	$-0.837975\pi$
$43$	−0.733450	−	7.44685i	−0.111850	−	1.13563i	0.761373	−	0.648314i	$-0.224525\pi$
$44$	−8.44884	−	5.82682i	−1.27371	−	0.878426i
$45$	−0.292253	+	0.0886539i	−0.0435664	+	0.0132157i
$46$	−0.698657	+	4.48266i	−0.103011	+	0.660932i
$47$	−2.51912	−	1.04345i	−0.367452	−	0.152203i	0.191314	−	0.981529i	$-0.438725\pi$
$47$	−2.51912	−	1.04345i	−0.367452	−	0.152203i	−0.558766	+	0.829325i	$0.688725\pi$
$48$	−0.274859	−	3.99055i	−0.0396725	−	0.575986i
$49$	−9.44468	+	3.91211i	−1.34924	+	0.558873i
$50$	−1.63655	−	6.74342i	−0.231443	−	0.953663i
$51$	−2.42585	−	1.29664i	−0.339686	−	0.181566i
$52$	3.24491	+	1.40033i	0.449989	+	0.194191i
$53$	10.1617	+	8.33951i	1.39582	+	1.14552i	0.970675	+	0.240395i	$0.0772771\pi$
$53$	10.1617	+	8.33951i	1.39582	+	1.14552i	0.425145	+	0.905125i	$0.360223\pi$
$54$	0.718114	+	1.21832i	0.0977230	+	0.165793i
$55$	0.305749	−	1.53710i	0.0412272	−	0.207263i
$56$	−5.25146	+	10.4979i	−0.701756	+	1.40283i
$57$	−5.22063	+	1.03845i	−0.691490	+	0.137546i
$58$	0.512566	−	9.07214i	0.0673032	−	1.19123i
$59$	0.305360	+	0.571289i	0.0397545	+	0.0743754i	0.901014	−	0.433790i	$-0.142824\pi$
$59$	0.305360	+	0.571289i	0.0397545	+	0.0743754i	−0.861260	+	0.508165i	$0.830324\pi$
$60$	0.542858	−	0.279981i	0.0700827	−	0.0361454i
$61$	7.82117	+	0.770318i	1.00140	+	0.0986291i	0.585407	−	0.810739i	$-0.300935\pi$
$61$	7.82117	+	0.770318i	1.00140	+	0.0986291i	0.415991	+	0.909369i	$0.363435\pi$
$62$	−0.324166	−	7.76256i	−0.0411691	−	0.985846i
$63$		−	4.15004i		−	0.522856i
$64$	1.98245	+	7.75048i	0.247807	+	0.968810i
$65$			0.539674i			0.0669383i
$66$	−7.25091	+	0.302799i	−0.892525	+	0.0372720i
$67$	13.0142	+	1.28179i	1.58994	+	0.156595i	0.853934	−	0.520381i	$-0.174210\pi$
$67$	13.0142	+	1.28179i	1.58994	+	0.156595i	0.736005	+	0.676976i	$0.236710\pi$
$68$	5.24035	+	1.67416i	0.635485	+	0.203022i
$69$	1.51224	+	2.82919i	0.182052	+	0.340595i
$70$	−1.78957	−	0.101109i	−0.213895	−	0.0120848i
$71$	5.38424	−	1.07099i	0.638992	−	0.127103i	0.135047	−	0.990839i	$-0.456881\pi$
$71$	5.38424	−	1.07099i	0.638992	−	0.127103i	0.503945	+	0.863736i	$0.331881\pi$
$72$	−1.85278	−	2.13710i	−0.218352	−	0.251860i
$73$	1.26052	−	6.33704i	0.147532	−	0.741695i	−0.834205	−	0.551454i	$-0.814073\pi$
$73$	1.26052	−	6.33704i	0.147532	−	0.741695i	0.981737	−	0.190241i	$-0.0609268\pi$
$74$	−0.845002	+	0.498068i	−0.0982295	+	0.0578992i
$75$	−3.79295	−	3.11280i	−0.437972	−	0.359435i
$76$	9.89429	−	3.92893i	1.13495	−	0.450680i
$77$	18.7818	+	10.0391i	2.14039	+	1.14406i
$78$	2.42854	−	0.589380i	0.274978	−	0.0667341i
$79$	10.1029	−	4.18476i	1.13667	−	0.470823i	0.266625	−	0.963800i	$-0.414092\pi$
$79$	10.1029	−	4.18476i	1.13667	−	0.470823i	0.870042	+	0.492978i	$0.164092\pi$
$80$	−0.966697	+	0.746883i	−0.108080	+	0.0835041i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	10.1119	+	1.57602i	1.11667	+	0.174042i
$83$	−6.59955	+	2.00195i	−0.724395	+	0.219743i	−0.630886	−	0.775876i	$-0.717308\pi$
$83$	−6.59955	+	2.00195i	−0.724395	+	0.219743i	−0.0935091	+	0.995618i	$0.529808\pi$
$84$	1.49940	+	8.16353i	0.163598	+	0.890714i
$85$	0.0823397	+	0.836009i	0.00893099	+	0.0906779i
$86$	8.45328	+	6.36624i	0.911541	+	0.686489i
$87$	−3.56965	−	5.34236i	−0.382707	−	0.572761i
$88$	14.1538	−	3.21538i	1.50880	−	0.342761i
$89$	−5.61758	−	3.75355i	−0.595463	−	0.397875i	0.221000	−	0.975274i	$-0.429068\pi$
$89$	−5.61758	−	3.75355i	−0.595463	−	0.397875i	−0.816462	+	0.577398i	$0.804068\pi$
$90$	0.187529	−	0.389070i	0.0197673	−	0.0410115i
$91$	−7.01771	−	2.12880i	−0.735656	−	0.223159i
$92$	−3.99689	−	5.01892i	−0.416705	−	0.523259i
$93$	−3.48519	−	4.24672i	−0.361398	−	0.440364i
$94$	3.49790	−	1.62303i	0.360781	−	0.167402i
$95$	1.14950	+	1.14950i	0.117936	+	0.117936i
$96$	4.41672	+	3.53448i	0.450780	+	0.360737i
$97$	−4.68172	+	4.68172i	−0.475356	+	0.475356i	−0.903643	−	0.428287i	$-0.859117\pi$
$97$	−4.68172	+	4.68172i	−0.475356	+	0.475356i	0.428287	+	0.903643i	$0.359117\pi$
$98$	4.97045	−	13.5760i	0.502091	−	1.37138i
$99$	−3.96681	+	3.25548i	−0.398679	+	0.327188i
$100$	8.58575	+	4.75278i	0.858575	+	0.475278i
$101$	−0.692908	+	2.28421i	−0.0689469	+	0.227288i	−0.984642	−	0.174587i	$-0.944141\pi$
$101$	−0.692908	+	2.28421i	−0.0689469	+	0.227288i	0.915695	+	0.401874i	$0.131641\pi$
$102$	3.67213	−	1.28354i	0.363595	−	0.127089i
$103$	−4.84243	+	7.24721i	−0.477139	+	0.714088i	−0.989476	−	0.144696i	$-0.953780\pi$
$103$	−4.84243	+	7.24721i	−0.477139	+	0.714088i	0.512338	+	0.858784i	$0.328780\pi$
$104$	−4.56424	+	2.03680i	−0.447560	+	0.199724i
$105$	−1.05383	+	0.704150i	−0.102844	+	0.0687180i
$106$	−18.4091	+	2.59257i	−1.78805	+	0.251813i
$107$	19.3610	−	1.90689i	1.87170	−	0.184346i	0.902512	−	0.430665i	$-0.141721\pi$
$107$	19.3610	−	1.90689i	1.87170	−	0.184346i	0.969189	+	0.246318i	$0.0792209\pi$
$108$	−1.95562	−	0.418978i	−0.188180	−	0.0403162i
$109$	−2.38964	−	7.87758i	−0.228886	−	0.754536i	−0.993877	−	0.110494i	$-0.964757\pi$
$109$	−2.38964	−	7.87758i	−0.228886	−	0.754536i	0.764991	−	0.644041i	$-0.222743\pi$
$110$	1.30717	+	1.78987i	0.124634	+	0.170658i
$111$	−0.265421	+	0.640782i	−0.0251926	+	0.0608203i
$112$	−5.89894	−	15.5167i	−0.557398	−	1.46619i
$113$	−6.68651	−	16.1427i	−0.629014	−	1.51857i	−0.840849	−	0.541269i	$-0.817944\pi$
$113$	−6.68651	−	16.1427i	−0.629014	−	1.51857i	0.211835	−	0.977305i	$-0.432056\pi$
$114$	3.91739	−	6.42813i	0.366897	−	0.602049i
$115$	0.461841	−	0.864045i	0.0430669	−	0.0805726i
$116$	8.95204	+	9.21923i	0.831176	+	0.855984i
$117$	1.12103	−	1.36598i	0.103639	−	0.126285i
$118$	−0.886981	−	0.229120i	−0.0816532	−	0.0210922i
$119$	−11.1959	−	2.22701i	−1.02633	−	0.204149i
$120$	−0.228316	+	0.833091i	−0.0208423	+	0.0760505i
$121$	−2.99145	−	15.0391i	−0.271950	−	1.36719i
$122$	−8.28982	+	7.40318i	−0.750525	+	0.670253i
$123$	6.38205	−	3.41128i	0.575450	−	0.307584i
$124$	8.39004	+	7.09451i	0.753448	+	0.637105i
$125$	−0.296555	+	3.01098i	−0.0265247	+	0.269310i
$126$	4.31958	+	3.97327i	0.384819	+	0.353967i
$127$	20.0215			1.77662			0.888312	−	0.459241i	$-0.151879\pi$
$127$	20.0215			1.77662			0.888312	+	0.459241i	$0.151879\pi$
$128$	−9.96512	−	5.35691i	−0.880800	−	0.473488i
$129$	7.48288			0.658831
$130$	−0.561721	−	0.516687i	−0.0492662	−	0.0453164i
$131$	1.65214	−	16.7744i	0.144348	−	1.46559i	−0.601179	−	0.799115i	$-0.705302\pi$
$131$	1.65214	−	16.7744i	0.144348	−	1.46559i	0.745527	−	0.666476i	$-0.232198\pi$
$132$	6.62689	−	7.83703i	0.576797	−	0.682126i
$133$	−19.4819	+	10.4133i	−1.68930	+	0.902947i
$134$	−13.7940	+	12.3187i	−1.19162	+	1.06417i
$135$	−0.0595812	−	0.299535i	−0.00512793	−	0.0257799i
$136$	−6.75969	+	3.85158i	−0.579639	+	0.330270i
$137$	−4.35107	−	0.865481i	−0.371737	−	0.0739430i	0.00568673	−	0.999984i	$-0.498190\pi$
$137$	−4.35107	−	0.865481i	−0.371737	−	0.0739430i	−0.377423	+	0.926041i	$0.623190\pi$
$138$	−4.39260	−	1.13467i	−0.373923	−	0.0965895i
$139$	9.96647	−	12.1442i	0.845345	−	1.03006i	−0.153775	−	0.988106i	$-0.549143\pi$
$139$	9.96647	−	12.1442i	0.845345	−	1.03006i	0.999120	−	0.0419496i	$-0.0133569\pi$
$140$	1.81858	−	1.76588i	0.153698	−	0.149244i
$141$	1.28535	−	2.40471i	0.108246	−	0.202514i
$142$	−4.04016	+	6.62958i	−0.339042	+	0.556342i
$143$	3.47019	+	8.37778i	0.290192	+	0.700586i
$144$	3.99827	+	0.117607i	0.333189	+	0.00980054i
$145$	−0.750931	+	1.81291i	−0.0623615	+	0.150554i
$146$	5.38910	+	7.37913i	0.446005	+	0.610701i
$147$	−2.96754	−	9.78265i	−0.244758	−	0.806860i
$148$	0.290594	−	1.35638i	0.0238867	−	0.111493i
$149$	8.09619	−	0.797405i	0.663266	−	0.0653260i	0.239218	−	0.970966i	$-0.423109\pi$
$149$	8.09619	−	0.797405i	0.663266	−	0.0653260i	0.424048	+	0.905640i	$0.360609\pi$
$150$	6.87136	−	0.967699i	0.561044	−	0.0790123i
$151$	−5.67404	+	3.79127i	−0.461747	+	0.308530i	−0.764597	−	0.644509i	$-0.777062\pi$
$151$	−5.67404	+	3.79127i	−0.461747	+	0.308530i	0.302850	+	0.953038i	$0.402062\pi$
$152$	−5.38340	+	14.0601i	−0.436652	+	1.14042i
$153$	1.52817	−	2.28707i	0.123545	−	0.184899i
$154$	−28.4311	+	9.93764i	−2.29104	+	0.800798i
$155$	−0.487041	+	1.60556i	−0.0391201	+	0.128962i
$156$	−1.71164	+	3.09203i	−0.137041	+	0.247561i
$157$	−6.79256	+	5.57451i	−0.542106	+	0.444895i	−0.865167	−	0.501483i	$-0.832788\pi$
$157$	−6.79256	+	5.57451i	−0.542106	+	0.444895i	0.323062	+	0.946378i	$0.395288\pi$
$158$	−5.31686	+	14.5222i	−0.422987	+	1.15532i
$159$	−9.29538	+	9.29538i	−0.737172	+	0.737172i
$160$	0.148125	−	1.72126i	0.0117103	−	0.136078i
$161$	9.41391	+	9.41391i	0.741920	+	0.741920i
$162$	−1.28284	+	0.595240i	−0.100790	+	0.0467664i
$163$	−3.96709	−	4.83391i	−0.310726	−	0.378621i	0.594108	−	0.804385i	$-0.297505\pi$
$163$	−3.96709	−	4.83391i	−0.310726	−	0.378621i	−0.904834	+	0.425764i	$0.860005\pi$
$164$	−11.3216	+	9.01613i	−0.884069	+	0.704041i
$165$	1.49973	+	0.454939i	0.116754	+	0.0354170i
$166$	4.23471	−	8.78584i	0.328677	−	0.681914i
$167$	1.82560	+	1.21983i	0.141269	+	0.0943932i	0.624197	−	0.781267i	$-0.285426\pi$
$167$	1.82560	+	1.21983i	0.141269	+	0.0943932i	−0.482927	+	0.875661i	$0.660426\pi$
$168$	−9.93257	−	6.25514i	−0.766314	−	0.482595i
$169$	5.48759	+	8.21276i	0.422122	+	0.631751i
$170$	−0.948994	−	0.714696i	−0.0727845	−	0.0548146i
$171$	−0.521736	−	5.29728i	−0.0398982	−	0.405093i
$172$	−14.7195	+	2.70355i	−1.12235	+	0.206144i
$173$	17.4011	−	5.27858i	1.32298	−	0.401323i	0.451730	−	0.892155i	$-0.350807\pi$
$173$	17.4011	−	5.27858i	1.32298	−	0.401323i	0.871255	+	0.490832i	$0.163307\pi$
$174$	8.97822	+	1.39932i	0.680637	+	0.106082i
$175$	−18.8131	−	7.79263i	−1.42214	−	0.589068i
$176$	−10.2042	+	17.8105i	−0.769172	+	1.34252i
$177$	−0.598468	+	0.247894i	−0.0449836	+	0.0186328i
$178$	9.28520	−	2.25341i	0.695955	−	0.168900i
$179$	2.97488	+	1.59011i	0.222353	+	0.118850i	0.578813	−	0.815461i	$-0.303516\pi$
$179$	2.97488	+	1.59011i	0.222353	+	0.118850i	−0.356460	+	0.934311i	$0.616016\pi$
$180$	0.225423	+	0.567687i	0.0168021	+	0.0423129i
$181$	−15.9289	−	13.0725i	−1.18399	−	0.971671i	−0.184048	−	0.982917i	$-0.558920\pi$
$181$	−15.9289	−	13.0725i	−1.18399	−	0.971671i	−0.999937	+	0.0112457i	$0.996420\pi$
$182$	8.93456	−	5.26628i	0.662274	−	0.390363i
$183$	−1.53322	+	7.70801i	−0.113339	+	0.569792i
$184$	9.05061	+	0.644965i	0.667220	+	0.0475474i
$185$	0.207751	−	0.0413242i	0.0152741	−	0.00303821i
$186$	7.75695	+	0.438259i	0.568767	+	0.0321347i
$187$	6.65389	+	12.4486i	0.486581	+	0.910329i
$188$	−1.65958	+	5.19470i	−0.121037	+	0.378862i
$189$	4.13006	+	0.406775i	0.300418	+	0.0295885i
$190$	−2.29699	+	0.0959227i	−0.166641	+	0.00695897i
$191$		−	12.8623i		−	0.930684i	−0.885131	−	0.465342i	$-0.845931\pi$
$191$		−	12.8623i		−	0.930684i	0.885131	−	0.465342i	$-0.154069\pi$
$192$	−7.90747	+	1.21323i	−0.570672	+	0.0875571i
$193$		−	11.2195i		−	0.807599i	−0.914847	−	0.403800i	$-0.867689\pi$
$193$		−	11.2195i		−	0.807599i	0.914847	−	0.403800i	$-0.132311\pi$
$194$	−0.390678	−	9.35528i	−0.0280490	−	0.671670i
$195$	−0.537075	−	0.0528973i	−0.0384608	−	0.00378806i
$196$	9.37188	+	18.1712i	0.669420	+	1.29795i
$197$	0.932517	+	1.74462i	0.0664391	+	0.124299i	0.912948	−	0.408075i	$-0.133800\pi$
$197$	0.932517	+	1.74462i	0.0664391	+	0.124299i	−0.846509	+	0.532374i	$0.821300\pi$
$198$	0.409372	−	7.24567i	0.0290928	−	0.514928i
$199$	−23.7130	+	4.71680i	−1.68097	+	0.334365i	−0.941033	−	0.338314i	$-0.890143\pi$
$199$	−23.7130	+	4.71680i	−1.68097	+	0.334365i	−0.739934	+	0.672679i	$0.765143\pi$
$200$	−13.1670	+	4.38617i	−0.931046	+	0.310149i
$201$	−2.55123	+	12.8259i	−0.179950	+	0.904670i
$202$	−1.71413	−	2.90813i	−0.120606	−	0.204615i
$203$	−20.6122	−	16.9160i	−1.44669	−	1.18727i
$204$	−2.17974	+	5.05101i	−0.152613	+	0.353642i
$205$	−1.94910	−	1.04181i	−0.136131	−	0.0727635i
$206$	−2.90711	−	11.9788i	−0.202548	−	0.834600i
$207$	−2.96379	+	1.22764i	−0.205998	+	0.0853272i
$208$	2.24982	−	6.70074i	0.155997	−	0.464613i
$209$	25.2360	+	10.4531i	1.74561	+	0.723055i
$210$	0.276031	−	1.77104i	0.0190479	−	0.122214i
$211$	6.96738	−	2.11353i	0.479654	−	0.145502i	−0.0411933	−	0.999151i	$-0.513116\pi$
$211$	6.96738	−	2.11353i	0.479654	−	0.145502i	0.520848	+	0.853650i	$0.325616\pi$
$212$	14.9265	−	21.6433i	1.02516	−	1.48647i
$213$	0.538087	+	5.46329i	0.0368691	+	0.374339i
$214$	−16.5516	+	21.9777i	−1.13144	+	1.50236i
$215$	−1.26964	−	1.90015i	−0.0865889	−	0.129589i
$216$	2.30842	−	1.63438i	0.157068	−	0.111206i
$217$	−18.9569	−	12.6666i	−1.28688	−	0.859864i
$218$	10.4873	+	5.05478i	0.710287	+	0.342353i
$219$	6.18298	+	1.87559i	0.417807	+	0.126740i
$220$	−3.11449	−	0.353057i	−0.209979	−	0.0238031i
$221$	−3.08354	−	3.75731i	−0.207422	−	0.252744i
$222$	−0.412845	−	0.889752i	−0.0277083	−	0.0597163i
$223$	14.4399	+	14.4399i	0.966969	+	0.966969i	0.999472	−	0.0325024i	$-0.0103477\pi$
$223$	14.4399	+	14.4399i	0.966969	+	0.966969i	−0.0325024	+	0.999472i	$0.510348\pi$
$224$	21.7983	+	8.71584i	1.45646	+	0.582352i
$225$	3.46958	−	3.46958i	0.231305	−	0.231305i
$226$	23.2038	+	8.49540i	1.54350	+	0.565106i
$227$	−14.6124	+	11.9921i	−0.969856	+	0.795941i	−0.978967	−	0.204018i	$-0.934600\pi$
$227$	−14.6124	+	11.9921i	−0.969856	+	0.795941i	0.00911068	+	0.999958i	$0.497100\pi$
$228$	2.94021	+	10.2317i	0.194720	+	0.677614i
$229$	2.29455	−	7.56413i	0.151628	−	0.499852i	−0.847913	−	0.530136i	$-0.822141\pi$
$229$	2.29455	−	7.56413i	0.151628	−	0.499852i	0.999541	+	0.0302836i	$0.00964103\pi$
$230$	0.457174	+	1.30795i	0.0301452	+	0.0862437i
$231$	−11.8317	+	17.7074i	−0.778469	+	1.16506i
$232$	−18.1666	+	0.491217i	−1.19269	+	0.0322500i
$233$	−20.5340	+	13.7204i	−1.34523	+	0.898851i	−0.999224	−	0.0393824i	$-0.987461\pi$
$233$	−20.5340	+	13.7204i	−1.34523	+	0.898851i	−0.346002	+	0.938234i	$0.612461\pi$
$234$	0.348503	+	2.47462i	0.0227823	+	0.161771i
$235$	−0.828726	+	0.0816224i	−0.0540601	+	0.00532446i
$236$	1.08768	−	0.703856i	0.0708020	−	0.0458171i
$237$	3.17435	+	10.4644i	0.206196	+	0.679739i
$238$	13.0370	−	9.52116i	0.845065	−	0.617165i
$239$	−2.48587	+	6.00141i	−0.160797	+	0.388199i	−0.983659	−	0.180043i	$-0.942376\pi$
$239$	−2.48587	+	6.00141i	−0.160797	+	0.388199i	0.822861	+	0.568242i	$0.192376\pi$
$240$	−0.648534	−	1.03525i	−0.0418627	−	0.0668251i
$241$	−2.69180	−	6.49859i	−0.173394	−	0.418611i	0.813161	−	0.582039i	$-0.197745\pi$
$241$	−2.69180	−	6.49859i	−0.173394	−	0.418611i	−0.986555	+	0.163428i	$0.947745\pi$
$242$	18.5175	+	11.2848i	1.19035	+	0.725415i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	0.231093	−	15.7163i	0.0147942	−	1.00614i
$245$	−1.98063	+	2.41341i	−0.126538	+	0.154187i
$246$	−2.55957	+	9.90875i	−0.163192	+	0.631759i
$247$	−9.22531	−	1.83503i	−0.586993	−	0.116760i
$248$	−15.4170	+	1.94048i	−0.978981	+	0.123221i
$249$	−1.34544	−	6.76400i	−0.0852640	−	0.428651i
$250$	−2.85006	−	3.19140i	−0.180254	−	0.201842i
$251$	−3.82059	+	2.04215i	−0.241153	+	0.128899i	−0.587547	−	0.809190i	$-0.699906\pi$
$251$	−3.82059	+	2.04215i	−0.241153	+	0.128899i	0.346394	+	0.938089i	$0.387406\pi$
$252$	−8.27118	+	0.692019i	−0.521036	+	0.0435931i
$253$	1.61358	−	16.3830i	0.101445	−	1.02999i
$254$	−19.1687	+	20.8395i	−1.20275	+	1.30758i
$255$	−0.840054			−0.0526062
$256$	15.1164	−	5.24349i	0.944776	−	0.327718i
$257$	−17.5268			−1.09329			−0.546645	−	0.837365i	$-0.684095\pi$
$257$	−17.5268			−1.09329			−0.546645	+	0.837365i	$0.684095\pi$
$258$	−7.16415	+	7.78858i	−0.446020	+	0.484896i
$259$	−0.282130	+	2.86452i	−0.0175307	+	0.177992i
$260$	1.07559	−	0.0899906i	0.0667053	−	0.00558098i
$261$	5.66653	−	3.02882i	0.350749	−	0.187479i
$262$	15.8780	+	17.7796i	0.980944	+	1.09843i
$263$	−1.57280	−	7.90701i	−0.0969831	−	0.487567i	−0.998496	−	0.0548157i	$-0.982543\pi$
$263$	−1.57280	−	7.90701i	−0.0969831	−	0.487567i	0.901513	−	0.432751i	$-0.142457\pi$
$264$	1.81258	+	14.4008i	0.111556	+	0.886310i
$265$	3.93758	+	0.783234i	0.241884	+	0.0481137i
$266$	7.81337	−	30.2475i	0.479069	−	1.85460i
$267$	4.28609	−	5.22262i	0.262305	−	0.319619i
$268$	0.384532	−	26.1515i	0.0234890	−	1.59746i
$269$	4.33918	−	8.11803i	0.264564	−	0.494965i	−0.714203	−	0.699938i	$-0.753211\pi$
$269$	4.33918	−	8.11803i	0.264564	−	0.494965i	0.978768	+	0.204973i	$0.0657107\pi$
$270$	0.368815	+	0.224761i	0.0224454	+	0.0136785i
$271$	4.31548	+	10.4185i	0.262147	+	0.632878i	0.999071	−	0.0430971i	$-0.0137225\pi$
$271$	4.31548	+	10.4185i	0.262147	+	0.632878i	−0.736924	+	0.675976i	$0.763722\pi$
$272$	2.46284	−	10.7234i	0.149332	−	0.650200i
$273$	2.80640	−	6.77526i	0.169851	−	0.410057i
$274$	5.06657	−	3.70020i	0.306083	−	0.223538i
$275$	7.30924	+	24.0953i	0.440764	+	1.45300i
$276$	5.38652	−	3.48571i	0.324230	−	0.209815i
$277$	−2.45544	+	0.241840i	−0.147533	+	0.0145307i	−0.171514	−	0.985182i	$-0.554866\pi$
$277$	−2.45544	+	0.241840i	−0.147533	+	0.0145307i	0.0239810	+	0.999712i	$0.492366\pi$
$278$	3.09835	+	22.0005i	0.185827	+	1.31950i
$279$	4.56788	−	3.05216i	0.273472	−	0.182728i
$280$	0.0968974	+	3.58354i	0.00579073	+	0.214158i
$281$	9.65012	−	14.4424i	0.575678	−	0.861563i	−0.423335	−	0.905973i	$-0.639141\pi$
$281$	9.65012	−	14.4424i	0.575678	−	0.861563i	0.999013	+	0.0444100i	$0.0141408\pi$
$282$	1.27236	+	3.64014i	0.0757677	+	0.216767i
$283$	5.96469	−	19.6629i	0.354564	−	1.16884i	−0.580470	−	0.814282i	$-0.697131\pi$
$283$	5.96469	−	19.6629i	0.354564	−	1.16884i	0.935034	−	0.354558i	$-0.115369\pi$
$284$	−3.03235	−	10.5524i	−0.179937	−	0.626170i
$285$	−1.25663	+	1.03129i	−0.0744365	+	0.0610884i
$286$	−12.0424	−	4.40898i	−0.712083	−	0.260708i
$287$	21.2358	−	21.2358i	1.25351	−	1.25351i
$288$	−3.95038	+	4.04901i	−0.232778	+	0.238590i
$289$	6.67084	+	6.67084i	0.392402	+	0.392402i
$290$	−1.16803	−	2.51730i	−0.0685888	−	0.147821i
$291$	−4.20028	−	5.11806i	−0.246225	−	0.300026i
$292$	−12.8401	−	1.45555i	−0.751413	−	0.0851798i
$293$	−23.7460	−	7.20327i	−1.38726	−	0.420819i	−0.493645	−	0.869663i	$-0.664336\pi$
$293$	−23.7460	−	7.20327i	−1.38726	−	0.420819i	−0.893610	+	0.448844i	$0.851836\pi$
$294$	13.0234	+	6.27720i	0.759542	+	0.366094i
$295$	0.164492	+	0.109910i	0.00957711	+	0.00639922i
$296$	1.13357	+	1.60107i	0.0658875	+	0.0930601i
$297$	−2.85098	−	4.26680i	−0.165431	−	0.247585i
$298$	−6.92135	+	9.19038i	−0.400943	+	0.532385i
$299$	0.555639	+	5.64150i	0.0321334	+	0.326256i
$300$	−5.57144	+	8.07855i	−0.321667	+	0.466415i
$301$	29.7171	−	9.01458i	1.71286	−	0.519591i
$302$	1.48620	−	9.53563i	0.0855212	−	0.548714i
$303$	−2.20530	−	0.913463i	−0.126691	−	0.0524771i
$304$	−9.48038	−	19.0645i	−0.543737	−	1.09343i
$305$	2.21747	−	0.918505i	0.126972	−	0.0525934i
$306$	0.917425	+	3.78026i	0.0524457	+	0.216103i
$307$	29.4634	+	15.7485i	1.68156	+	0.898815i	0.983077	+	0.183192i	$0.0586431\pi$
$307$	29.4634	+	15.7485i	1.68156	+	0.898815i	0.698487	+	0.715623i	$0.253857\pi$
$308$	16.8764	−	39.1069i	0.961624	−	2.22832i
$309$	−6.73767	−	5.52946i	−0.383293	−	0.314560i
$310$	−1.20486	−	2.04411i	−0.0684312	−	0.116098i
$311$	−4.76846	+	23.9727i	−0.270395	+	1.35937i	0.571889	+	0.820331i	$0.306211\pi$
$311$	−4.76846	+	23.9727i	−0.270395	+	1.35937i	−0.842283	+	0.539035i	$0.818789\pi$
$312$	−1.57961	−	4.74190i	−0.0894281	−	0.268457i
$313$	26.4178	−	5.25483i	1.49322	−	0.297020i	0.620101	−	0.784522i	$-0.287092\pi$
$313$	26.4178	−	5.25483i	1.49322	−	0.297020i	0.873122	+	0.487502i	$0.162092\pi$
$314$	0.700989	−	12.4071i	0.0395591	−	0.700175i
$315$	−0.597465	−	1.11778i	−0.0336633	−	0.0629797i
$316$	−10.0250	−	19.4377i	−0.563953	−	1.09345i
$317$	14.6871	+	1.44655i	0.824910	+	0.0812465i	0.501657	−	0.865066i	$-0.332724\pi$
$317$	14.6871	+	1.44655i	0.824910	+	0.0812465i	0.323252	+	0.946313i	$0.395224\pi$
$318$	−0.775677	−	18.5746i	−0.0434978	−	1.04161i
$319$			32.9718i			1.84607i
$320$	1.64976	+	1.80212i	0.0922245	+	0.100742i
$321$			19.4547i			1.08586i
$322$	−18.8114	+	0.785569i	−1.04832	+	0.0437780i
$323$	−14.5709	−	1.43511i	−0.810746	−	0.0798516i
$324$	0.608645	−	1.90514i	0.0338136	−	0.105841i
$325$	−4.08730	−	7.64680i	−0.226723	−	0.424168i
$326$	8.82950	+	0.498857i	0.489021	+	0.0276291i
$327$	8.07388	−	1.60599i	0.446486	−	0.0888117i
$328$	1.45490	−	20.4162i	0.0803335	−	1.12730i
$329$	2.20761	−	11.0984i	0.121709	−	0.611874i
$330$	−1.90938	+	1.12544i	−0.105108	+	0.0619535i
$331$	0.790947	+	0.649114i	0.0434744	+	0.0356785i	0.655880	−	0.754866i	$-0.272298\pi$
$331$	0.790947	+	0.649114i	0.0434744	+	0.0356785i	−0.612405	+	0.790544i	$0.709798\pi$
$332$	5.09044	+	12.8193i	0.279374	+	0.703552i
$333$	−0.611681	−	0.326950i	−0.0335199	−	0.0179168i
$334$	−3.01751	+	0.732314i	−0.165111	+	0.0400704i
$335$	3.68980	−	1.52837i	0.201595	−	0.0835036i
$336$	16.0202	−	4.34964i	0.873973	−	0.237292i
$337$	−13.0263	−	5.39567i	−0.709588	−	0.293921i	−0.00145365	−	0.999999i	$-0.500463\pi$
$337$	−13.0263	−	5.39567i	−0.709588	−	0.293921i	−0.708134	+	0.706078i	$0.750463\pi$
$338$	−13.8021	−	2.15117i	−0.750737	−	0.117008i
$339$	16.7203	−	5.07206i	0.908124	−	0.275476i
$340$	1.65247	−	0.303510i	0.0896175	−	0.0164602i
$341$	2.76329	+	28.0561i	0.149640	+	1.51932i
$342$	6.01320	+	4.52859i	0.325157	+	0.244878i
$343$	−7.43072	−	11.1209i	−0.401221	−	0.600470i
$344$	11.2786	−	17.9093i	0.608099	−	0.965603i
$345$	0.814616	+	0.544309i	0.0438574	+	0.0293046i
$346$	−11.1657	+	23.1658i	−0.600273	+	1.24540i
$347$	−2.99113	−	0.907349i	−0.160572	−	0.0487090i	0.208975	−	0.977921i	$-0.432987\pi$
$347$	−2.99113	−	0.907349i	−0.160572	−	0.0487090i	−0.369547	+	0.929212i	$0.620487\pi$
$348$	−10.0523	+	8.00529i	−0.538859	+	0.429128i
$349$	−7.72285	−	9.41032i	−0.413395	−	0.503723i	0.524132	−	0.851637i	$-0.324390\pi$
$349$	−7.72285	−	9.41032i	−0.413395	−	0.503723i	−0.937526	+	0.347914i	$0.886890\pi$
$350$	26.1227	−	12.1209i	1.39632	−	0.647892i
$351$	1.24952	+	1.24952i	0.0666944	+	0.0666944i
$352$	−8.76852	−	27.6729i	−0.467363	−	1.47497i
$353$	9.26175	−	9.26175i	0.492953	−	0.492953i	−0.416282	−	0.909235i	$-0.636667\pi$
$353$	9.26175	−	9.26175i	0.492953	−	0.492953i	0.909235	+	0.416282i	$0.136667\pi$
$354$	0.314956	−	0.860252i	0.0167397	−	0.0457219i
$355$	1.29601	−	1.06361i	0.0687853	−	0.0564506i
$356$	−6.54423	+	11.8219i	−0.346843	+	0.626562i
$357$	3.31368	−	10.9237i	0.175378	−	0.578145i
$358$	−4.50324	+	1.57404i	−0.238003	+	0.0831904i
$359$	11.4822	−	17.1843i	0.606005	−	0.906951i	−0.393921	−	0.919144i	$-0.628882\pi$
$359$	11.4822	−	17.1843i	0.606005	−	0.906951i	0.999926	+	0.0121939i	$0.00388154\pi$
$360$	−0.806701	−	0.308874i	−0.0425168	−	0.0162791i
$361$	−7.76042	+	5.18535i	−0.408443	+	0.272913i
$362$	28.8570	−	4.06395i	1.51669	−	0.213596i
$363$	15.2599	−	1.50296i	0.800935	−	0.0788852i
$364$	−3.07257	+	14.3415i	−0.161046	+	0.751700i
$365$	−0.572810	−	1.88830i	−0.0299822	−	0.0988382i
$366$	−6.55499	−	8.97554i	−0.342635	−	0.469159i
$367$	−12.5492	+	30.2964i	−0.655061	+	1.58146i	0.150279	+	0.988644i	$0.451983\pi$
$367$	−12.5492	+	30.2964i	−0.655061	+	1.58146i	−0.805340	+	0.592814i	$0.798017\pi$
$368$	−9.33642	+	8.80286i	−0.486694	+	0.458881i
$369$	2.76930	+	6.68568i	0.144164	+	0.348043i
$370$	−0.155889	+	0.255802i	−0.00810430	+	0.0132985i
$371$	−25.7171	+	48.1132i	−1.33516	+	2.49791i
$372$	−7.88271	+	7.65426i	−0.408700	+	0.396855i
$373$	−10.6208	+	12.9414i	−0.549922	+	0.670082i	−0.971591	−	0.236668i	$-0.923945\pi$
$373$	−10.6208	+	12.9414i	−0.549922	+	0.670082i	0.421668	+	0.906750i	$0.361445\pi$
$374$	−19.3276	−	4.99259i	−0.999406	−	0.258161i
$375$	−2.96741	−	0.590255i	−0.153236	−	0.0304806i
$376$	−3.81803	−	6.70081i	−0.196900	−	0.345568i
$377$	−2.21504	−	11.1357i	−0.114080	−	0.573520i
$378$	−4.37753	+	3.90933i	−0.225156	+	0.201074i
$379$	−23.8731	+	12.7604i	−1.22628	+	0.655459i	−0.951972	−	0.306184i	$-0.900948\pi$
$379$	−23.8731	+	12.7604i	−1.22628	+	0.655459i	−0.274304	+	0.961643i	$0.588448\pi$
$380$	2.09931	−	2.48267i	0.107692	−	0.127358i
$381$	−1.96245	+	19.9251i	−0.100540	+	1.02079i
$382$	13.3878	+	12.3144i	0.684978	+	0.630062i
$383$	22.4843			1.14890			0.574448	−	0.818541i	$-0.305217\pi$
$383$	22.4843			1.14890			0.574448	+	0.818541i	$0.305217\pi$
$384$	6.30786	−	9.39206i	0.321897	−	0.479287i
$385$	6.50402			0.331476
$386$	11.6779	+	10.7416i	0.594388	+	0.546735i
$387$	−0.733450	+	7.44685i	−0.0372834	+	0.378544i
$388$	10.1115	+	8.55016i	0.513334	+	0.434068i
$389$	5.89556	−	3.15124i	0.298917	−	0.159774i	−0.315120	−	0.949052i	$-0.602045\pi$
$389$	5.89556	−	3.15124i	0.298917	−	0.159774i	0.614037	+	0.789277i	$0.289545\pi$
$390$	0.569257	−	0.508372i	0.0288255	−	0.0257424i
$391$	1.72148	+	8.65446i	0.0870590	+	0.437675i
$392$	−27.8863	−	7.64249i	−1.40847	−	0.386004i
$393$	16.5317	+	3.28837i	0.833916	+	0.165876i
$394$	−2.70868	−	0.699692i	−0.136462	−	0.0352500i
$395$	2.11867	−	2.58161i	0.106602	−	0.129895i
$396$	7.14975	+	7.36314i	0.359288	+	0.370012i
$397$	13.5458	−	25.3424i	0.679844	−	1.27190i	−0.271104	−	0.962550i	$-0.587389\pi$
$397$	13.5458	−	25.3424i	0.679844	−	1.27190i	0.950948	−	0.309349i	$-0.100111\pi$
$398$	17.7934	−	29.1976i	0.891904	−	1.46354i
$399$	−8.45359	−	20.4088i	−0.423209	−	1.02172i
$400$	8.04079	−	17.9042i	0.402039	−	0.895212i
$401$	−1.91805	+	4.63057i	−0.0957826	+	0.231240i	−0.964508	−	0.264055i	$-0.914940\pi$
$401$	−1.91805	+	4.63057i	−0.0957826	+	0.231240i	0.868725	+	0.495295i	$0.164940\pi$
$402$	−10.9073	−	14.9351i	−0.544008	−	0.744893i
$403$	−2.81806	−	9.28990i	−0.140378	−	0.462763i
$404$	4.66806	+	1.00010i	0.232245	+	0.0497568i
$405$	0.303933	−	0.0299347i	0.0151025	−	0.00148747i
$406$	37.3413	−	5.25881i	1.85322	−	0.260990i
$407$	2.95936	−	1.97738i	0.146690	−	0.0980150i
$408$	−3.17046	−	7.10466i	−0.156961	−	0.351733i
$409$	6.19417	−	9.27024i	0.306282	−	0.458384i	−0.646117	−	0.763239i	$-0.723608\pi$
$409$	6.19417	−	9.27024i	0.306282	−	0.458384i	0.952399	+	0.304855i	$0.0986080\pi$
$410$	2.95045	−	1.03129i	0.145712	−	0.0509316i
$411$	1.28779	−	4.24528i	0.0635221	−	0.209404i
$412$	15.2514	+	8.44267i	0.751384	+	0.415940i
$413$	−2.07809	+	1.70544i	−0.102256	+	0.0839193i
$414$	1.55976	−	4.26023i	0.0766578	−	0.209379i
$415$	−1.48932	+	1.48932i	−0.0731079	+	0.0731079i
$416$	4.82049	+	8.75705i	0.236344	+	0.429350i
$417$	11.1088	+	11.1088i	0.544001	+	0.544001i
$418$	−35.0412	+	16.2591i	−1.71392	+	0.795259i
$419$	5.19843	+	6.33431i	0.253960	+	0.309451i	0.884347	−	0.466830i	$-0.154604\pi$
$419$	5.19843	+	6.33431i	0.253960	+	0.309451i	−0.630387	+	0.776281i	$0.717104\pi$
$420$	1.57912	+	1.98291i	0.0770533	+	0.0967563i
$421$	33.8904	+	10.2805i	1.65172	+	0.501043i	0.972502	−	0.232896i	$-0.0748203\pi$
$421$	33.8904	+	10.2805i	1.65172	+	0.501043i	0.679215	+	0.733939i	$0.262320\pi$
$422$	−4.47073	+	9.27553i	−0.217632	+	0.451526i
$423$	2.26715	+	1.51486i	0.110233	+	0.0736550i
$424$	8.23680	+	36.2577i	0.400014	+	1.76083i
$425$	−7.49833	−	11.2220i	−0.363722	−	0.544349i
$426$	−6.20165	−	4.67052i	−0.300471	−	0.226287i
$427$	3.19685	+	32.4582i	0.154707	+	1.57076i
$428$	−7.02896	−	38.2693i	−0.339758	−	1.84981i
$429$	−8.67758	+	2.63232i	−0.418958	+	0.127089i
$430$	3.19334	+	0.497706i	0.153997	+	0.0240015i
$431$	−18.4877	−	7.65787i	−0.890522	−	0.368866i	−0.109954	−	0.993937i	$-0.535070\pi$
$431$	−18.4877	−	7.65787i	−0.890522	−	0.368866i	−0.780569	+	0.625070i	$0.785070\pi$
$432$	−0.508939	+	3.96749i	−0.0244864	+	0.190886i
$433$	2.80126	−	1.16032i	0.134620	−	0.0557615i	−0.314356	−	0.949305i	$-0.601789\pi$
$433$	2.80126	−	1.16032i	0.134620	−	0.0557615i	0.448976	+	0.893544i	$0.351789\pi$
$434$	31.3335	−	7.60427i	1.50406	−	0.365017i
$435$	−1.73057	−	0.925012i	−0.0829747	−	0.0443509i
$436$	−15.3018	+	6.07622i	−0.732825	+	0.290998i
$437$	13.1998	+	10.8328i	0.631432	+	0.518203i
$438$	−7.87182	+	4.63987i	−0.376130	+	0.221702i
$439$	7.42940	−	37.3501i	0.354586	−	1.78262i	−0.231979	−	0.972721i	$-0.574520\pi$
$439$	7.42940	−	37.3501i	0.354586	−	1.78262i	0.586564	−	0.809903i	$-0.300480\pi$
$440$	3.34931	−	2.90371i	0.159672	−	0.138429i
$441$	10.0264	−	1.99438i	0.477448	−	0.0949704i
$442$	6.86301	+	0.387752i	0.326440	+	0.0184435i
$443$	−13.8673	−	25.9439i	−0.658857	−	1.23263i	−0.960252	−	0.279135i	$-0.909952\pi$
$443$	−13.8673	−	25.9439i	−0.658857	−	1.23263i	0.301395	−	0.953499i	$-0.402548\pi$
$444$	1.32136	+	0.422143i	0.0627090	+	0.0200340i
$445$	−2.05343	−	0.202245i	−0.0973420	−	0.00958735i
$446$	−28.8547	+	1.20498i	−1.36631	+	0.0570573i
$447$			8.13536i			0.384789i
$448$	−29.9417	+	14.3442i	−1.41461	+	0.677701i
$449$			15.1569i			0.715298i	0.933856	+	0.357649i	$0.116422\pi$
$449$			15.1569i			0.715298i	−0.933856	+	0.357649i	$0.883578\pi$
$450$	0.289528	+	6.93312i	0.0136485	+	0.326830i
$451$	−36.9564	−	3.63989i	−1.74021	−	0.171396i
$452$	−31.0580	+	16.0183i	−1.46084	+	0.753435i
$453$	−3.21687	−	6.01833i	−0.151142	−	0.282766i
$454$	1.50799	−	26.6906i	0.0707733	−	1.25265i
$455$	−2.19664	+	0.436938i	−0.102980	+	0.0204840i
$456$	−13.4647	−	6.73561i	−0.630543	−	0.315424i
$457$	−0.509073	+	2.55928i	−0.0238134	+	0.119718i	−0.990864	−	0.134867i	$-0.956939\pi$
$457$	−0.509073	+	2.55928i	−0.0238134	+	0.119718i	0.967050	+	0.254586i	$0.0819391\pi$
$458$	5.67633	+	9.63024i	0.265238	+	0.449991i
$459$	2.12627	+	1.74499i	0.0992459	+	0.0814490i
$460$	−1.79908	−	0.776388i	−0.0838827	−	0.0361993i
$461$	−13.7399	−	7.34412i	−0.639930	−	0.342050i	0.119313	−	0.992857i	$-0.461931\pi$
$461$	−13.7399	−	7.34412i	−0.639930	−	0.342050i	−0.759243	+	0.650807i	$0.774431\pi$
$462$	−7.10306	−	29.2682i	−0.330464	−	1.36168i
$463$	8.25311	−	3.41855i	0.383554	−	0.158873i	−0.182571	−	0.983193i	$-0.558442\pi$
$463$	8.25311	−	3.41855i	0.383554	−	0.158873i	0.566125	+	0.824319i	$0.308442\pi$
$464$	16.8815	−	19.3790i	0.783704	−	0.899649i
$465$	−1.55009	−	0.642069i	−0.0718837	−	0.0297752i
$466$	5.37846	−	34.5088i	0.249152	−	1.59859i
$467$	−17.5271	+	5.31677i	−0.811055	+	0.246031i	−0.668458	−	0.743750i	$-0.733045\pi$
$467$	−17.5271	+	5.31677i	−0.811055	+	0.246031i	−0.142597	+	0.989781i	$0.545545\pi$
$468$	−2.90937	−	2.00647i	−0.134486	−	0.0927493i
$469$	5.31947	+	54.0095i	0.245630	+	2.49393i
$470$	0.708470	−	0.940728i	0.0326793	−	0.0433925i
$471$	−4.88188	−	7.30625i	−0.224945	−	0.336654i
$472$	−0.308740	+	1.80599i	−0.0142109	+	0.0831275i
$473$	−31.9279	−	21.3336i	−1.46805	−	0.980919i
$474$	−13.9311	−	6.71468i	−0.639876	−	0.308415i
$475$	−24.9934	−	7.58168i	−1.14678	−	0.347871i
$476$	−2.57159	+	22.6852i	−0.117869	+	1.03978i
$477$	−8.33951	−	10.1617i	−0.381840	−	0.465274i
$478$	−3.86661	−	8.33321i	−0.176854	−	0.381152i
$479$	1.46342	+	1.46342i	0.0668653	+	0.0668653i	0.739749	−	0.672883i	$-0.234944\pi$
$479$	1.46342	+	1.46342i	0.0668653	+	0.0668653i	−0.672883	+	0.739749i	$0.734944\pi$
$480$	1.69845	+	0.316125i	0.0775234	+	0.0144291i
$481$	−0.866639	+	0.866639i	−0.0395153	+	0.0395153i
$482$	9.34122	+	3.42001i	0.425481	+	0.155777i
$483$	−10.2913	+	8.44586i	−0.468271	+	0.384300i
$484$	−29.4746	+	8.46984i	−1.33975	+	0.384993i
$485$	−0.586973	+	1.93499i	−0.0266531	+	0.0878633i
$486$	−0.466633	−	1.33501i	−0.0211669	−	0.0605573i
$487$	−3.87338	+	5.79692i	−0.175519	+	0.262683i	−0.908790	−	0.417253i	$-0.862993\pi$
$487$	−3.87338	+	5.79692i	−0.175519	+	0.262683i	0.733271	+	0.679937i	$0.237993\pi$
$488$	16.1371	+	15.2874i	0.730494	+	0.692030i
$489$	5.19948	−	3.47418i	0.235128	−	0.157108i
$490$	−0.615735	−	4.37216i	−0.0278160	−	0.197514i
$491$	−14.8984	+	1.46737i	−0.672357	+	0.0662214i	−0.428434	−	0.903573i	$-0.640934\pi$
$491$	−14.8984	+	1.46737i	−0.672357	+	0.0662214i	−0.243923	+	0.969795i	$0.578434\pi$
$492$	−7.86300	−	12.1508i	−0.354492	−	0.547801i
$493$	−5.13032	−	16.9124i	−0.231058	−	0.761696i
$494$	10.7424	−	7.84533i	0.483322	−	0.352978i
$495$	−0.599748	+	1.44792i	−0.0269567	+	0.0650792i
$496$	12.7406	−	17.9047i	0.572069	−	0.803943i
$497$	8.71852	+	21.0484i	0.391079	+	0.944149i
$498$	8.32846	+	5.07548i	0.373207	+	0.227438i
$499$	16.4485	−	30.7731i	0.736338	−	1.37759i	−0.182599	−	0.983188i	$-0.558451\pi$
$499$	16.4485	−	30.7731i	0.736338	−	1.37759i	0.918937	−	0.394404i	$-0.129049\pi$
$500$	6.05044	+	0.0889656i	0.270584	+	0.00397866i
$501$	−1.39290	+	1.69725i	−0.0622300	+	0.0758275i
$502$	1.53228	−	5.93183i	0.0683888	−	0.264750i
$503$	−11.7317	−	2.33357i	−0.523089	−	0.104049i	−0.0735187	−	0.997294i	$-0.523423\pi$
$503$	−11.7317	−	2.33357i	−0.523089	−	0.104049i	−0.449570	+	0.893245i	$0.648423\pi$
$504$	7.19859	−	9.27163i	0.320651	−	0.412991i
$505$	0.142220	+	0.714988i	0.00632871	+	0.0318166i
$506$	15.5074	+	17.3646i	0.689388	+	0.771952i
$507$	−8.71109	+	4.65618i	−0.386873	+	0.206788i
$508$	−3.33859	−	39.9036i	−0.148126	−	1.77044i
$509$	−1.88666	+	19.1556i	−0.0836248	+	0.849057i	0.858281	+	0.513180i	$0.171533\pi$
$509$	−1.88666	+	19.1556i	−0.0836248	+	0.849057i	−0.941906	+	0.335877i	$0.890967\pi$
$510$	0.804272	−	0.874372i	0.0356138	−	0.0387179i
$511$	26.8142			1.18619
$512$	−9.01483	+	20.7541i	−0.398403	+	0.917211i
$513$	5.32291			0.235012
$514$	16.7802	−	18.2428i	0.740144	−	0.804655i
$515$	−0.260915	+	2.64912i	−0.0114973	+	0.116734i
$516$	−1.24777	−	14.9136i	−0.0549300	−	0.656537i
$517$	−12.3401	+	6.59593i	−0.542718	+	0.290089i
$518$	−2.71143	−	3.03616i	−0.119133	−	0.133401i
$519$	3.54755	+	17.8347i	0.155720	+	0.782859i
$520$	−0.936109	+	1.20569i	−0.0410511	+	0.0528729i
$521$	−2.27988	−	0.453496i	−0.0998833	−	0.0198680i	0.144896	−	0.989447i	$-0.453715\pi$
$521$	−2.27988	−	0.453496i	−0.0998833	−	0.0198680i	−0.244779	+	0.969579i	$0.578715\pi$
$522$	−2.27260	+	8.79783i	−0.0994692	+	0.385071i
$523$	10.3742	−	12.6411i	0.453634	−	0.552755i	−0.495098	−	0.868837i	$-0.664868\pi$
$523$	10.3742	−	12.6411i	0.453634	−	0.552755i	0.948732	+	0.316083i	$0.102368\pi$
$524$	−33.7076	−	0.495636i	−1.47252	−	0.0216520i
$525$	9.59911	−	17.9587i	0.418940	−	0.783781i
$526$	9.73584	+	5.93316i	0.424503	+	0.258698i
$527$	−5.78284	−	13.9610i	−0.251905	−	0.608151i
$528$	−16.7245	−	11.9008i	−0.727842	−	0.517916i
$529$	−4.86345	+	11.7414i	−0.211454	+	0.510496i
$530$	−4.58509	+	3.34857i	−0.199164	+	0.145453i
$531$	−0.188040	−	0.619884i	−0.00816023	−	0.0269007i
$532$	24.0027	+	37.0917i	1.04065	+	1.60813i
$533$	12.7260	−	1.25340i	0.551224	−	0.0542909i
$534$	1.33245	+	9.46136i	0.0576608	+	0.409433i
$535$	4.94020	−	3.30094i	0.213584	−	0.142712i
$536$	26.8518	+	25.4379i	1.15982	+	1.09875i
$537$	−1.87404	+	2.80470i	−0.0808708	+	0.121032i
$538$	4.29533	+	12.2887i	0.185185	+	0.529803i
$539$	−15.2283	+	50.2010i	−0.655930	+	2.16231i
$540$	−0.587049	+	0.168695i	−0.0252626	+	0.00725947i
$541$	−12.1930	+	10.0065i	−0.524217	+	0.430214i	−0.858920	−	0.512110i	$-0.828864\pi$
$541$	−12.1930	+	10.0065i	−0.524217	+	0.430214i	0.334703	+	0.942324i	$0.391364\pi$
$542$	−14.9758	−	5.48294i	−0.643265	−	0.235512i
$543$	14.5709	−	14.5709i	0.625295	−	0.625295i
$544$	8.80351	+	12.8301i	0.377447	+	0.550084i
$545$	−1.77773	−	1.77773i	−0.0761497	−	0.0761497i
$546$	4.36518	+	9.40772i	0.186813	+	0.402613i
$547$	25.8884	+	31.5451i	1.10691	+	1.34877i	0.931276	+	0.364314i	$0.118696\pi$
$547$	25.8884	+	31.5451i	1.10691	+	1.34877i	0.175631	+	0.984456i	$0.443804\pi$
$548$	−0.999395	+	8.81615i	−0.0426920	+	0.376607i
$549$	−7.52061	−	2.28135i	−0.320972	−	0.0973657i
$550$	−32.0776	−	15.4612i	−1.36779	−	0.659266i
$551$	−28.4369	−	19.0009i	−1.21145	−	0.809467i
$552$	−1.52897	+	8.94381i	−0.0650775	+	0.380674i
$553$	25.2129	+	37.7338i	1.07216	+	1.60460i
$554$	2.09913	−	2.78729i	0.0891836	−	0.118421i
$555$	0.0207621	+	0.210801i	0.000881301	+	0.00894800i
$556$	−25.8657	−	17.8385i	−1.09695	−	0.756521i
$557$	−4.34038	+	1.31664i	−0.183908	+	0.0557878i	−0.380895	−	0.924618i	$-0.624384\pi$
$557$	−4.34038	+	1.31664i	−0.183908	+	0.0557878i	0.196988	+	0.980406i	$0.436884\pi$
$558$	−1.19646	+	7.67664i	−0.0506503	+	0.324978i
$559$	12.2164	+	5.06018i	0.516697	+	0.214023i
$560$	−3.82271	−	3.33005i	−0.161539	−	0.140720i
$561$	−13.0408	+	5.40168i	−0.550584	+	0.228059i
$562$	5.79337	+	23.8716i	0.244378	+	1.00696i
$563$	26.8118	+	14.3312i	1.12998	+	0.603988i	0.926950	−	0.375184i	$-0.122421\pi$
$563$	26.8118	+	14.3312i	1.12998	+	0.603988i	0.203032	+	0.979172i	$0.434921\pi$
$564$	−5.00702	−	2.16076i	−0.210833	−	0.0909843i
$565$	−4.12495	−	3.38526i	−0.173538	−	0.142419i
$566$	14.7556	+	25.0338i	0.620224	+	1.05225i
$567$	−0.809633	+	4.07030i	−0.0340014	+	0.170937i
$568$	13.8867	+	6.94670i	0.582673	+	0.291477i
$569$	29.0123	−	5.77091i	1.21626	−	0.241929i	0.455069	−	0.890456i	$-0.349615\pi$
$569$	29.0123	−	5.77091i	1.21626	−	0.241929i	0.761191	+	0.648527i	$0.224615\pi$
$570$	0.129684	−	2.29533i	0.00543185	−	0.0961409i
$571$	11.6319	+	21.7617i	0.486779	+	0.910700i	0.998665	+	0.0516465i	$0.0164469\pi$
$571$	11.6319	+	21.7617i	0.486779	+	0.910700i	−0.511886	+	0.859053i	$0.671053\pi$
$572$	16.1186	−	8.31321i	0.673952	−	0.347593i
$573$	12.8004	+	1.26073i	0.534743	+	0.0526676i
$574$	1.77207	+	42.4345i	0.0739649	+	1.77118i
$575$			15.7407i			0.656434i
$576$	−0.432317	−	7.98831i	−0.0180132	−	0.332846i
$577$			24.7070i			1.02857i	0.857621	+	0.514283i	$0.171942\pi$
$577$			24.7070i			1.02857i	−0.857621	+	0.514283i	$0.828058\pi$
$578$	−13.3301	+	0.556666i	−0.554457	+	0.0231542i
$579$	11.1655	+	1.09971i	0.464022	+	0.0457022i
$580$	3.73841	+	1.19433i	0.155229	+	0.0495919i
$581$	−13.4918	−	25.2413i	−0.559733	−	1.04719i
$582$	9.34852	+	0.528181i	0.387509	+	0.0218938i
$583$	66.1625	−	13.1605i	2.74017	−	0.545054i
$584$	13.8082	−	11.9712i	0.571389	−	0.495370i
$585$	0.105285	−	0.529304i	0.00435301	−	0.0218840i
$586$	30.2321	−	17.8196i	1.24888	−	0.736123i
$587$	−3.36131	−	2.75856i	−0.138736	−	0.113858i	0.562466	−	0.826821i	$-0.309853\pi$
$587$	−3.36131	−	2.75856i	−0.138736	−	0.113858i	−0.701202	+	0.712963i	$0.747353\pi$
$588$	−19.0024	+	7.54566i	−0.783644	+	0.311178i
$589$	−25.7898	−	13.7849i	−1.06265	−	0.567997i
$590$	−0.271886	+	0.0659837i	−0.0111934	+	0.00271650i
$591$	−1.82762	+	0.757024i	−0.0751781	+	0.0311398i
$592$	−2.75176	−	0.352989i	−0.113097	−	0.0145078i
$593$	−17.3292	−	7.17799i	−0.711625	−	0.294765i	−0.00264794	−	0.999996i	$-0.500843\pi$
$593$	−17.3292	−	7.17799i	−0.711625	−	0.294765i	−0.708977	+	0.705232i	$0.750843\pi$
$594$	7.17066	+	1.11760i	0.294216	+	0.0458557i
$595$	−3.33614	+	1.01201i	−0.136768	+	0.0414882i
$596$	−2.93930	−	16.0030i	−0.120398	−	0.655510i
$597$	−2.36981	−	24.0611i	−0.0969900	−	0.984756i
$598$	−6.40394	−	4.82286i	−0.261877	−	0.197222i
$599$	−12.9972	−	19.4516i	−0.531050	−	0.794772i	0.464835	−	0.885397i	$-0.346113\pi$
$599$	−12.9972	−	19.4516i	−0.531050	−	0.794772i	−0.995885	+	0.0906252i	$0.971113\pi$
$600$	−3.07446	−	13.5335i	−0.125514	−	0.552503i
$601$	21.6546	+	14.4691i	0.883308	+	0.590207i	0.912368	−	0.409370i	$-0.134252\pi$
$601$	21.6546	+	14.4691i	0.883308	+	0.590207i	−0.0290606	+	0.999578i	$0.509252\pi$
$602$	−19.0684	+	39.5617i	−0.777171	+	1.61241i
$603$	−12.5141	−	3.79611i	−0.509613	−	0.154589i
$604$	8.50229	+	10.6764i	0.345953	+	0.434416i
$605$	−2.97084	−	3.61998i	−0.120782	−	0.147173i
$606$	3.06214	−	1.42083i	0.124391	−	0.0577174i
$607$	−21.8130	−	21.8130i	−0.885362	−	0.885362i	0.108711	−	0.994073i	$-0.465328\pi$
$607$	−21.8130	−	21.8130i	−0.885362	−	0.885362i	−0.994073	+	0.108711i	$0.965328\pi$
$608$	28.9199	+	8.38480i	1.17286	+	0.340049i
$609$	18.8549	−	18.8549i	0.764040	−	0.764040i
$610$	−1.16699	+	3.18744i	−0.0472499	+	0.129056i
$611$	3.72458	−	3.05668i	0.150680	−	0.123660i
$612$	−4.81304	−	2.66433i	−0.194556	−	0.107699i
$613$	−1.34406	+	4.43076i	−0.0542860	+	0.178957i	−0.979891	−	0.199534i	$-0.936057\pi$
$613$	−1.34406	+	4.43076i	−0.0542860	+	0.178957i	0.925605	+	0.378491i	$0.123557\pi$
$614$	−44.6003	+	15.5893i	−1.79992	+	0.629135i
$615$	1.22784	−	1.83760i	0.0495114	−	0.0740990i
$616$	24.5470	+	55.0070i	0.989025	+	2.21630i
$617$	−18.7119	+	12.5029i	−0.753312	+	0.503347i	−0.871953	−	0.489590i	$-0.837146\pi$
$617$	−18.7119	+	12.5029i	−0.753312	+	0.503347i	0.118640	+	0.992937i	$0.462146\pi$
$618$	12.2060	−	1.71899i	0.490999	−	0.0691477i
$619$	−8.88703	+	0.875296i	−0.357200	+	0.0351811i	−0.275026	−	0.961437i	$-0.588686\pi$
$619$	−8.88703	+	0.875296i	−0.357200	+	0.0351811i	−0.0821742	+	0.996618i	$0.526186\pi$
$620$	3.28115	+	0.702964i	0.131774	+	0.0282317i
$621$	−0.931230	−	3.06985i	−0.0373690	−	0.123189i
$622$	−20.3867	−	27.9148i	−0.817432	−	1.11928i
$623$	10.7299	−	25.9042i	0.429884	−	1.03783i
$624$	6.44795	+	2.89577i	0.258125	+	0.115924i
$625$	−9.03502	−	21.8125i	−0.361401	−	0.872498i
$626$	−19.8230	+	32.5281i	−0.792288	+	1.30008i
$627$	−12.8763	+	24.0899i	−0.514230	+	0.962058i
$628$	12.2429	+	12.6083i	0.488544	+	0.503125i
$629$	−1.21028	+	1.47473i	−0.0482572	+	0.0588015i
$630$	1.73546	+	0.448294i	0.0691424	+	0.0178605i
$631$	−15.2077	−	3.02501i	−0.605411	−	0.120424i	−0.117139	−	0.993116i	$-0.537372\pi$
$631$	−15.2077	−	3.02501i	−0.605411	−	0.120424i	−0.488271	+	0.872692i	$0.662372\pi$
$632$	29.8298	+	8.17513i	1.18657	+	0.325189i
$633$	1.42043	+	7.14099i	0.0564571	+	0.283829i
$634$	−15.5672	+	13.9022i	−0.618251	+	0.552126i
$635$	5.39263	−	2.88242i	0.214000	−	0.114385i
$636$	20.0760	+	16.9760i	0.796067	+	0.673143i
$637$	1.77065	−	17.9777i	0.0701556	−	0.712301i
$638$	−34.3188	−	31.5674i	−1.35869	−	1.24977i
$639$	−5.48973			−0.217170
$640$	−3.45523	−	0.00819887i	−0.136580	−	0.000324089i
$641$	−46.8801			−1.85165			−0.925825	−	0.377951i	$-0.876629\pi$
$641$	−46.8801			−1.85165			−0.925825	+	0.377951i	$0.876629\pi$
$642$	−20.2495	−	18.6260i	−0.799184	−	0.735111i
$643$	3.56727	−	36.2191i	0.140680	−	1.42834i	−0.622734	−	0.782433i	$-0.713978\pi$
$643$	3.56727	−	36.2191i	0.140680	−	1.42834i	0.763414	−	0.645910i	$-0.223522\pi$
$644$	17.1925	−	20.3320i	0.677480	−	0.801195i
$645$	2.01545	−	1.07728i	0.0793583	−	0.0424179i
$646$	15.4440	−	13.7922i	0.607636	−	0.542646i
$647$	7.92384	+	39.8358i	0.311518	+	1.56611i	0.746323	+	0.665584i	$0.231817\pi$
$647$	7.92384	+	39.8358i	0.311518	+	1.56611i	−0.434805	+	0.900525i	$0.643183\pi$
$648$	1.40025	+	2.45750i	0.0550070	+	0.0965397i
$649$	3.26028	+	0.648511i	0.127977	+	0.0254563i
$650$	11.8724	+	3.06681i	0.465674	+	0.120290i
$651$	14.4637	−	17.6241i	0.566877	−	0.690742i
$652$	−8.97265	+	8.71260i	−0.351396	+	0.341212i
$653$	0.158997	−	0.297463i	0.00622204	−	0.0116406i	−0.878791	−	0.477207i	$-0.841649\pi$
$653$	0.158997	−	0.297463i	0.00622204	−	0.0116406i	0.885013	+	0.465566i	$0.154149\pi$
$654$	−6.05837	+	9.94130i	−0.236901	+	0.388736i
$655$	−1.96996	−	4.75591i	−0.0769728	−	0.185829i
$656$	19.8574	+	21.0609i	0.775299	+	0.822291i
$657$	−2.47259	+	5.96936i	−0.0964650	+	0.232887i
$658$	9.43822	+	12.9235i	0.367940	+	0.503809i
$659$	−11.2464	−	37.0746i	−0.438099	−	1.44422i	−0.846976	−	0.531631i	$-0.821579\pi$
$659$	−11.2464	−	37.0746i	−0.438099	−	1.44422i	0.408877	−	0.912590i	$-0.365921\pi$
$660$	0.656630	−	3.06489i	0.0255593	−	0.119301i
$661$	6.74909	−	0.664728i	0.262509	−	0.0258549i	0.0340938	−	0.999419i	$-0.489146\pi$
$661$	6.74909	−	0.664728i	0.262509	−	0.0258549i	0.228416	+	0.973564i	$0.426646\pi$
$662$	−1.43289	+	0.201795i	−0.0556908	+	0.00784298i
$663$	4.04146	−	2.70041i	0.156957	−	0.104875i
$664$	−18.2166	−	6.97489i	−0.706943	−	0.270678i
$665$	−3.74813	+	5.60947i	−0.145346	+	0.217526i
$666$	0.925934	−	0.323646i	0.0358792	−	0.0125410i
$667$	−5.98334	+	19.7244i	−0.231676	+	0.763733i
$668$	2.12674	−	3.84190i	0.0822862	−	0.148648i
$669$	−15.7858	+	12.9550i	−0.610313	+	0.500871i
$670$	−1.94183	+	5.30381i	−0.0750195	+	0.204904i
$671$	28.5173	−	28.5173i	1.10090	−	1.10090i
$672$	−10.8105	+	20.8390i	−0.417023	+	0.803883i
$673$	30.6782	+	30.6782i	1.18256	+	1.18256i	0.979079	+	0.203481i	$0.0652254\pi$
$673$	30.6782	+	30.6782i	1.18256	+	1.18256i	0.203481	+	0.979079i	$0.434775\pi$
$674$	18.0875	−	8.39262i	0.696706	−	0.323272i
$675$	3.11280	+	3.79295i	0.119812	+	0.145991i
$676$	15.4533	−	12.3064i	0.594357	−	0.473325i
$677$	−4.45901	−	1.35263i	−0.171374	−	0.0519856i	0.203432	−	0.979089i	$-0.434790\pi$
$677$	−4.45901	−	1.35263i	−0.171374	−	0.0519856i	−0.374805	+	0.927103i	$0.622290\pi$
$678$	−10.7289	+	22.2594i	−0.412040	+	0.854868i
$679$	−22.8465	−	15.2655i	−0.876767	−	0.585837i
$680$	−1.26617	+	2.01056i	−0.0485554	+	0.0771013i
$681$	−10.5020	−	15.7174i	−0.402439	−	0.602293i
$682$	−31.8479	−	23.9849i	−1.21952	−	0.918430i
$683$	0.108529	+	1.10191i	0.00415273	+	0.0421634i	0.997038	−	0.0769135i	$-0.0245065\pi$
$683$	0.108529	+	1.10191i	0.00415273	+	0.0421634i	−0.992885	+	0.119077i	$0.962007\pi$
$684$	−10.4707	+	1.92316i	−0.400356	+	0.0735339i
$685$	−1.29652	+	0.393296i	−0.0495376	+	0.0150271i
$686$	18.6894	+	2.91288i	0.713564	+	0.111214i
$687$	7.30280	+	3.02492i	0.278619	+	0.115408i
$688$	7.84276	+	28.8858i	0.299003	+	1.10126i
$689$	−21.4613	+	8.88955i	−0.817609	+	0.338665i
$690$	−1.34646	+	0.326771i	−0.0512590	+	0.0124400i
$691$	17.5661	+	9.38928i	0.668246	+	0.357185i	0.770379	−	0.637586i	$-0.220067\pi$
$691$	17.5661	+	9.38928i	0.668246	+	0.357185i	−0.102133	+	0.994771i	$0.532567\pi$
$692$	−13.4220	−	33.8009i	−0.510230	−	1.28492i
$693$	−16.4624	−	13.5104i	−0.625356	−	0.513216i
$694$	3.80814	−	2.24462i	0.144555	−	0.0852048i
$695$	0.936035	−	4.70576i	0.0355058	−	0.178500i
$696$	1.29179	−	18.1273i	0.0489650	−	0.687112i
$697$	19.5226	−	3.88329i	0.739471	−	0.147090i
$698$	17.1887	+	0.971140i	0.650600	+	0.0367582i
$699$	−11.6416	−	21.7799i	−0.440327	−	0.823793i
$700$	−12.3939	+	38.7946i	−0.468446	+	1.46630i
$701$	−8.48453	−	0.835653i	−0.320456	−	0.0315622i	−0.0634897	−	0.997982i	$-0.520223\pi$
$701$	−8.48453	−	0.835653i	−0.320456	−	0.0315622i	−0.256967	+	0.966420i	$0.582723\pi$
$702$	−2.49686	+	0.104269i	−0.0942380	+	0.00393540i
$703$			3.69185i			0.139241i
$704$	37.1985	+	17.3675i	1.40197	+	0.654561i
$705$		−	0.832736i		−	0.0313626i
$706$	0.772871	+	18.5074i	0.0290874	+	0.696534i
$707$	−9.85843	−	0.970970i	−0.370764	−	0.0365171i
$708$	0.593856	+	1.15143i	0.0223185	+	0.0432735i
$709$	−16.5731	−	31.0060i	−0.622414	−	1.16446i	−0.973624	−	0.228159i	$-0.926730\pi$
$709$	−16.5731	−	31.0060i	−0.622414	−	1.16446i	0.351210	−	0.936297i	$-0.385770\pi$
$710$	−0.133748	+	2.36727i	−0.00501947	+	0.0888419i
$711$	−10.7252	+	2.13337i	−0.402226	+	0.0800078i
$712$	−6.03943	−	18.1300i	−0.226337	−	0.679450i
$713$	−3.43824	+	17.2852i	−0.128763	+	0.647337i
$714$	8.19746	+	13.9075i	0.306782	+	0.520474i
$715$	2.14078	+	1.75690i	0.0800608	+	0.0657042i
$716$	2.67308	−	6.19420i	0.0998977	−	0.231488i
$717$	−5.72886	−	3.06214i	−0.213948	−	0.114358i
$718$	6.89321	+	28.4035i	0.257252	+	1.06001i
$719$	−19.3738	+	8.02488i	−0.722519	+	0.299277i	−0.713474	−	0.700682i	$-0.752879\pi$
$719$	−19.3738	+	8.02488i	−0.722519	+	0.299277i	−0.00904547	+	0.999959i	$0.502879\pi$
$720$	1.09383	−	0.543939i	0.0407647	−	0.0202714i
$721$	−33.4189	−	13.8426i	−1.24458	−	0.515524i
$722$	2.03268	−	13.0419i	0.0756487	−	0.485370i
$723$	6.73114	−	2.04187i	0.250334	−	0.0759379i
$724$	−23.3978	+	33.9267i	−0.869574	+	1.26088i
$725$	−3.09016	−	31.3749i	−0.114766	−	1.16524i
$726$	−13.0455	+	17.3222i	−0.484164	+	0.642887i
$727$	−16.4790	−	24.6626i	−0.611173	−	0.914685i	0.388805	−	0.921320i	$-0.372888\pi$
$727$	−16.4790	−	24.6626i	−0.611173	−	0.914685i	−0.999978	+	0.00663517i	$0.997888\pi$
$728$	−11.9857	−	16.9287i	−0.444220	−	0.627421i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	2.51385	+	1.21166i	0.0930419	+	0.0448455i
$731$	19.6964	+	5.97484i	0.728498	+	0.220987i
$732$	15.6180	+	1.77045i	0.577258	+	0.0654377i
$733$	−5.36735	−	6.54014i	−0.198248	−	0.241565i	0.664392	−	0.747384i	$-0.268690\pi$
$733$	−5.36735	−	6.54014i	−0.198248	−	0.241565i	−0.862640	+	0.505819i	$0.831190\pi$
$734$	−19.5194	−	42.0677i	−0.720475	−	1.55275i
$735$	−2.20765	−	2.20765i	−0.0814304	−	0.0814304i
$736$	−0.223749	−	18.1457i	−0.00824751	−	0.668861i
$737$	47.4521	−	47.4521i	1.74792	−	1.74792i
$738$	−9.61015	−	3.51847i	−0.353755	−	0.129517i
$739$	−8.69822	+	7.13845i	−0.319969	+	0.262592i	−0.780643	−	0.624978i	$-0.785108\pi$
$739$	−8.69822	+	7.13845i	−0.319969	+	0.262592i	0.460673	+	0.887570i	$0.347608\pi$
$740$	−0.117003	−	0.407164i	−0.00430112	−	0.0149676i
$741$	2.73043	−	9.00103i	0.100305	−	0.330661i
$742$	−25.4571	−	72.8315i	−0.934561	−	2.67373i
$743$	−22.9946	+	34.4139i	−0.843591	+	1.26252i	0.119361	+	0.992851i	$0.461915\pi$
$743$	−22.9946	+	34.4139i	−0.843591	+	1.26252i	−0.962952	+	0.269672i	$0.913085\pi$
$744$	−0.420005	−	15.5330i	−0.0153981	−	0.569466i
$745$	2.06584	−	1.38035i	0.0756866	−	0.0505721i
$746$	−3.30176	−	23.4449i	−0.120886	−	0.858377i
$747$	6.86331	−	0.675977i	0.251115	−	0.0247327i
$748$	23.7009	−	15.3372i	0.866591	−	0.560785i
$749$	23.4370	+	77.2613i	0.856368	+	2.82307i
$750$	3.45538	−	2.52353i	0.126173	−	0.0921461i
$751$	−8.91529	+	21.5234i	−0.325324	+	0.785401i	0.673604	+	0.739093i	$0.264746\pi$
$751$	−8.91529	+	21.5234i	−0.325324	+	0.785401i	−0.998927	+	0.0463079i	$0.985254\pi$
$752$	10.6300	+	2.44139i	0.387635	+	0.0890282i
$753$	−1.65783	−	4.00235i	−0.0604147	−	0.145854i
$754$	13.7114	+	8.35589i	0.499338	+	0.304303i
$755$	−0.982441	+	1.83802i	−0.0357547	+	0.0668923i
$756$	0.122031	−	8.29919i	0.00443823	−	0.301838i
$757$	−26.3974	+	32.1653i	−0.959429	+	1.16907i	0.0261163	+	0.999659i	$0.491686\pi$
$757$	−26.3974	+	32.1653i	−0.959429	+	1.16907i	−0.985546	+	0.169409i	$0.945814\pi$
$758$	9.57448	−	37.0652i	0.347761	−	1.34627i
$759$	16.1459	+	3.21162i	0.586059	+	0.116574i
$760$	0.574201	+	4.56199i	0.0208284	+	0.165481i
$761$	−0.352270	−	1.77098i	−0.0127698	−	0.0641980i	0.973875	−	0.227085i	$-0.0729195\pi$
$761$	−0.352270	−	1.77098i	−0.0127698	−	0.0641980i	−0.986645	+	0.162887i	$0.947919\pi$
$762$	−18.8603	−	21.1190i	−0.683235	−	0.765062i
$763$	30.1294	−	16.1045i	1.09076	−	0.583022i
$764$	−25.6350	+	2.14479i	−0.927443	+	0.0775957i
$765$	0.0823397	−	0.836009i	0.00297700	−	0.0302260i
$766$	−21.5266	+	23.4029i	−0.777788	+	0.845581i
$767$	−1.14468			−0.0413320
$768$	3.73657	+	15.5576i	0.134832	+	0.561385i
$769$	27.1477			0.978970			0.489485	−	0.872012i	$-0.337185\pi$
$769$	27.1477			0.978970			0.489485	+	0.872012i	$0.337185\pi$
$770$	−6.22698	+	6.76973i	−0.224405	+	0.243964i
$771$	1.71792	−	17.4424i	0.0618695	−	0.628171i
$772$	−22.3609	+	1.87085i	−0.804787	+	0.0673335i
$773$	−43.2409	+	23.1127i	−1.55527	+	0.831307i	−1.00000		0.000366471i	$-0.999883\pi$
$773$	−43.2409	+	23.1127i	−1.55527	+	0.831307i	−0.555265	+	0.831673i	$0.687383\pi$
$774$	−7.04886	−	7.89306i	−0.253366	−	0.283710i
$775$	−5.25891	−	26.4383i	−0.188906	−	0.949693i
$776$	−18.5803	+	2.33863i	−0.666993	+	0.0839518i
$777$	−2.82307	−	0.561543i	−0.101277	−	0.0201453i
$778$	−2.36446	+	9.15343i	−0.0847701	+	0.328167i
$779$	24.4364	−	29.7759i	0.875526	−	1.06683i
$780$	−0.0158690	+	1.07923i	−0.000568202	+	0.0386427i
$781$	13.2798	−	24.8448i	0.475190	−	0.889019i
$782$	−10.6562	−	6.49402i	−0.381064	−	0.232226i
$783$	2.45882	+	5.93612i	0.0878710	+	0.212139i
$784$	34.6532	−	21.7086i	1.23761	−	0.775306i
$785$	−1.02698	+	2.47935i	−0.0366545	+	0.0884917i
$786$	−19.2503	+	14.0588i	−0.686635	+	0.501461i
$787$	−3.05588	−	10.0739i	−0.108930	−	0.359096i	0.885480	−	0.464677i	$-0.153830\pi$
$787$	−3.05588	−	10.0739i	−0.108930	−	0.359096i	−0.994411	+	0.105582i	$0.966330\pi$
$788$	3.32159	−	2.14945i	0.118327	−	0.0765711i
$789$	8.02309	−	0.790206i	0.285630	−	0.0281321i
$790$	0.658647	+	4.67687i	0.0234336	+	0.166396i
$791$	60.2919	−	40.2857i	2.14373	−	1.43240i
$792$	−14.5092	+	0.392321i	−0.515560	+	0.0139405i
$793$	−7.71552	+	11.5471i	−0.273986	+	0.410049i
$794$	13.4089	+	38.3622i	0.475864	+	1.36142i
$795$	−1.16541	+	3.84185i	−0.0413329	+	0.136256i
$796$	13.3549	+	46.4743i	0.473352	+	1.64724i
$797$	−1.49502	+	1.22693i	−0.0529563	+	0.0434601i	−0.660499	−	0.750827i	$-0.729655\pi$
$797$	−1.49502	+	1.22693i	−0.0529563	+	0.0434601i	0.607543	+	0.794287i	$0.292155\pi$
$798$	29.3361	+	10.7405i	1.03848	+	0.380211i
$799$	5.30337	−	5.30337i	0.187620	−	0.187620i
$800$	10.9374	+	25.5109i	0.386695	+	0.901946i
$801$	4.77736	+	4.77736i	0.168800	+	0.168800i
$802$	−2.98340	−	6.42974i	−0.105347	−	0.227042i
$803$	−21.0343	−	25.6303i	−0.742283	−	0.904474i
$804$	25.9879	+	2.94598i	0.916523	+	0.103897i
$805$	3.89084	+	1.18027i	0.137134	+	0.0415992i
$806$	12.3674	+	5.96101i	0.435625	+	0.209968i
$807$	7.65363	+	5.11399i	0.269421	+	0.180021i
$808$	−5.51018	+	3.90126i	−0.193848	+	0.137246i
$809$	6.78609	+	10.1561i	0.238586	+	0.357069i	0.931369	−	0.364077i	$-0.118615\pi$
$809$	6.78609	+	10.1561i	0.238586	+	0.357069i	−0.692783	+	0.721146i	$0.743615\pi$
$810$	−0.259829	+	0.345009i	−0.00912946	+	0.0121224i
$811$	−2.14102	−	21.7381i	−0.0751813	−	0.763328i	−0.956680	−	0.291142i	$-0.905965\pi$
$811$	−2.14102	−	21.7381i	−0.0751813	−	0.763328i	0.881499	−	0.472187i	$-0.156535\pi$
$812$	−30.2771	+	43.9017i	−1.06252	+	1.54065i
$813$	−10.7913	+	3.27351i	−0.378468	+	0.114807i
$814$	−0.775143	+	4.97341i	−0.0271688	+	0.174318i
$815$	−1.76442	−	0.730847i	−0.0618049	−	0.0256004i
$816$	10.4303	+	3.50205i	0.365135	+	0.122596i
$817$	36.7988	−	15.2425i	1.28743	−	0.533269i
$818$	3.71862	+	15.3226i	0.130018	+	0.535742i
$819$	6.46756	+	3.45698i	0.225995	+	0.120797i
$820$	−1.75136	+	4.05835i	−0.0611602	+	0.141724i
$821$	−26.6669	−	21.8850i	−0.930682	−	0.763791i	0.0412269	−	0.999150i	$-0.486873\pi$
$821$	−26.6669	−	21.8850i	−0.930682	−	0.763791i	−0.971908	+	0.235359i	$0.924373\pi$
$822$	3.18578	+	5.40486i	0.111117	+	0.188516i
$823$	4.92422	−	24.7557i	0.171647	−	0.862930i	−0.794959	−	0.606663i	$-0.792508\pi$
$823$	4.92422	−	24.7557i	0.171647	−	0.862930i	0.966606	−	0.256266i	$-0.0824924\pi$
$824$	−23.3894	+	7.79143i	−0.814807	+	0.271427i
$825$	−24.6957	+	4.91229i	−0.859795	+	0.171024i
$826$	0.214457	−	3.79578i	0.00746192	−	0.132072i
$827$	18.0557	+	33.7798i	0.627858	+	1.17464i	0.971835	+	0.235662i	$0.0757259\pi$
$827$	18.0557	+	33.7798i	0.627858	+	1.17464i	−0.343977	+	0.938978i	$0.611774\pi$
$828$	2.94095	+	5.70224i	0.102205	+	0.198167i
$829$	−16.1868	−	1.59426i	−0.562192	−	0.0553711i	−0.187070	−	0.982347i	$-0.559899\pi$
$829$	−16.1868	−	1.59426i	−0.562192	−	0.0553711i	−0.375122	+	0.926975i	$0.622399\pi$
$830$	−0.124280	−	2.97605i	−0.00431383	−	0.103300i
$831$		−	2.46732i		−	0.0855904i
$832$	−13.7300	−	3.36662i	−0.476001	−	0.116717i
$833$		−	28.1193i		−	0.974278i
$834$	−22.1983	+	0.927004i	−0.768664	+	0.0320995i
$835$	0.667325	+	0.0657258i	0.0230937	+	0.00227453i
$836$	16.6253	−	52.0393i	0.574998	−	1.79982i
$837$	2.58973	+	4.84505i	0.0895142	+	0.167469i
$838$	−11.5701	−	0.653697i	−0.399682	−	0.0225816i
$839$	42.4391	−	8.44167i	1.46516	−	0.291439i	0.602865	−	0.797843i	$-0.294026\pi$
$839$	42.4391	−	8.44167i	1.46516	−	0.291439i	0.862296	+	0.506405i	$0.169026\pi$
$840$	−3.57578	−	0.254818i	−0.123376	−	0.00879204i
$841$	2.39635	−	12.0472i	0.0826326	−	0.415422i
$842$	−43.1474	+	25.4323i	−1.48696	+	0.876454i
$843$	13.4270	+	11.0193i	0.462451	+	0.379523i
$844$	−5.37416	−	13.5338i	−0.184986	−	0.465853i
$845$	2.66040	+	1.42201i	0.0915204	+	0.0489187i
$846$	−3.74733	+	0.909433i	−0.128836	+	0.0312670i
$847$	58.7915	−	24.3522i	2.02010	−	0.836753i
$848$	−45.6249	−	26.1400i	−1.56677	−	0.897652i
$849$	18.9836	+	7.86327i	0.651516	+	0.269867i
$850$	18.8594	+	2.93939i	0.646873	+	0.100820i
$851$	2.12918	−	0.645880i	0.0729874	−	0.0221405i
$852$	10.7988	−	1.98343i	0.369961	−	0.0679512i
$853$	0.489695	+	4.97195i	0.0167668	+	0.170236i	0.999921	−	0.0125398i	$-0.00399163\pi$
$853$	0.489695	+	4.97195i	0.0167668	+	0.170236i	−0.983155	+	0.182776i	$0.941492\pi$
$854$	−36.8449	−	27.7482i	−1.26081	−	0.949524i
$855$	−0.903154	−	1.35167i	−0.0308872	−	0.0462260i
$856$	46.5622	+	29.3231i	1.59146	+	1.00224i
$857$	−6.75464	−	4.51331i	−0.230734	−	0.154172i	0.434829	−	0.900513i	$-0.356809\pi$
$857$	−6.75464	−	4.51331i	−0.230734	−	0.154172i	−0.665564	+	0.746341i	$0.731809\pi$
$858$	5.56811	−	11.5523i	0.190092	−	0.394388i
$859$	−32.7025	−	9.92020i	−1.11580	−	0.338473i	−0.322050	−	0.946723i	$-0.604372\pi$
$859$	−32.7025	−	9.92020i	−1.11580	−	0.338473i	−0.793746	+	0.608250i	$0.791872\pi$
$860$	−3.57536	+	2.84729i	−0.121919	+	0.0970919i
$861$	19.0520	+	23.2150i	0.649291	+	0.791164i
$862$	25.6710	−	11.9113i	0.874356	−	0.405701i
$863$	−8.95261	−	8.95261i	−0.304750	−	0.304750i	0.538119	−	0.842869i	$-0.319135\pi$
$863$	−8.95261	−	8.95261i	−0.304750	−	0.304750i	−0.842869	+	0.538119i	$0.819135\pi$
$864$	−3.64231	−	4.32823i	−0.123914	−	0.147249i
$865$	3.92692	−	3.92692i	0.133519	−	0.133519i
$866$	−1.47422	+	4.02660i	−0.0500960	+	0.136829i
$867$	−7.29257	+	5.98486i	−0.247669	+	0.203257i
$868$	−22.0839	+	39.8939i	−0.749577	+	1.35409i
$869$	16.2896	−	53.6997i	0.552588	−	1.82164i
$870$	2.61966	−	0.915663i	0.0888149	−	0.0310439i
$871$	−12.8384	+	19.2140i	−0.435013	+	0.651043i
$872$	8.32561	−	21.7444i	0.281941	−	0.736357i
$873$	5.50512	−	3.67840i	0.186320	−	0.124495i
$874$	−23.9129	+	3.36767i	−0.808866	+	0.113913i
$875$	−12.4957	+	1.23072i	−0.422431	+	0.0416058i
$876$	2.70710	−	12.6356i	0.0914644	−	0.426919i
$877$	−2.81349	−	9.27484i	−0.0950049	−	0.313189i	0.896538	−	0.442966i	$-0.146074\pi$
$877$	−2.81349	−	9.27484i	−0.0950049	−	0.313189i	−0.991543	+	0.129777i	$0.958574\pi$
$878$	31.7630	+	43.4921i	1.07195	+	1.46779i
$879$	9.49610	−	22.9256i	0.320295	−	0.773261i
$880$	−0.184315	+	6.26616i	−0.00621326	+	0.211232i
$881$	−1.74624	−	4.21580i	−0.0588323	−	0.142034i	0.891730	−	0.452568i	$-0.149492\pi$
$881$	−1.74624	−	4.21580i	−0.0588323	−	0.142034i	−0.950562	+	0.310534i	$0.899492\pi$
$882$	−7.52349	+	12.3455i	−0.253329	+	0.415693i
$883$	−4.05186	+	7.58049i	−0.136356	+	0.255104i	−0.940827	−	0.338888i	$-0.889949\pi$
$883$	−4.05186	+	7.58049i	−0.136356	+	0.255104i	0.804471	+	0.593992i	$0.202449\pi$
$884$	−6.97427	+	6.77214i	−0.234570	+	0.227772i
$885$	−0.125504	+	0.152927i	−0.00421877	+	0.00514059i
$886$	40.2805	+	10.4050i	1.35325	+	0.349564i
$887$	47.1557	+	9.37986i	1.58333	+	0.314945i	0.906831	−	0.421494i	$-0.138494\pi$
$887$	47.1557	+	9.37986i	1.58333	+	0.314945i	0.676504	+	0.736439i	$0.263494\pi$
$888$	−1.70447	+	0.971181i	−0.0571982	+	0.0325907i
$889$	16.2101	+	81.4936i	0.543669	+	2.73321i
$890$	2.17647	−	1.94369i	0.0729556	−	0.0651526i
$891$	4.52570	−	2.41904i	0.151617	−	0.0810408i
$892$	26.3715	−	31.1872i	0.882981	−	1.04422i
$893$	1.42261	−	14.4440i	0.0476057	−	0.483349i
$894$	−8.46772	−	7.78884i	−0.283203	−	0.260498i
$895$	1.03018			0.0344351
$896$	13.7361	−	44.8981i	0.458892	−	1.49994i
$897$	−5.66880			−0.189276
$898$	−15.7761	−	14.5113i	−0.526455	−	0.484248i
$899$	3.45985	−	35.1284i	0.115392	−	1.17160i
$900$	−7.49355	−	6.33645i	−0.249785	−	0.211215i
$901$	−31.8893	+	17.0452i	−1.06239	+	0.567858i
$902$	39.1709	−	34.9813i	1.30425	−	1.16475i
$903$	6.05839	+	30.4576i	0.201610	+	1.01356i
$904$	13.0624	−	47.6627i	0.434449	−	1.58524i
$905$	−6.17231	−	1.22775i	−0.205175	−	0.0408117i
$906$	9.34404	+	2.41370i	0.310435	+	0.0801898i
$907$	−14.2245	+	17.3327i	−0.472318	+	0.575521i	−0.953612	−	0.301038i	$-0.902667\pi$
$907$	−14.2245	+	17.3327i	−0.472318	+	0.575521i	0.481294	+	0.876559i	$0.340167\pi$
$908$	26.3372	+	27.1233i	0.874031	+	0.900118i
$909$	1.12522	−	2.10514i	0.0373212	−	0.0698231i
$910$	1.64828	−	2.70470i	0.0546400	−	0.0896600i
$911$	−16.6765	−	40.2606i	−0.552517	−	1.33389i	−0.915583	−	0.402130i	$-0.868270\pi$
$911$	−16.6765	−	40.2606i	−0.552517	−	1.33389i	0.363066	−	0.931763i	$-0.381730\pi$
$912$	19.9020	−	7.56608i	0.659020	−	0.250538i
$913$	−13.5433	+	32.6965i	−0.448219	+	1.08210i
$914$	−2.17645	−	2.98014i	−0.0719906	−	0.0985744i
$915$	0.696732	+	2.29682i	0.0230333	+	0.0759305i
$916$	−15.4582	−	3.31181i	−0.510754	−	0.109425i
$917$	69.6147	−	6.85645i	2.29888	−	0.226420i
$918$	−3.85198	+	0.542477i	−0.127134	+	0.0179044i
$919$	3.94408	−	2.63535i	0.130103	−	0.0869322i	−0.488816	−	0.872387i	$-0.662571\pi$
$919$	3.94408	−	2.63535i	0.130103	−	0.0869322i	0.618919	+	0.785455i	$0.287571\pi$
$920$	2.53056	−	1.12926i	0.0834300	−	0.0372308i
$921$	−18.5606	+	27.7779i	−0.611592	+	0.915313i
$922$	20.7988	−	7.26989i	0.684971	−	0.239421i
$923$	−2.81600	+	9.28311i	−0.0926898	+	0.305557i
$924$	37.2644	+	20.6283i	1.22591	+	0.678622i
$925$	−2.63071	+	2.15897i	−0.0864971	+	0.0709863i
$926$	−4.34336	+	11.8632i	−0.142732	+	0.389849i
$927$	6.16324	−	6.16324i	0.202427	−	0.202427i
$928$	4.00829	+	36.1248i	0.131579	+	1.18585i
$929$	8.70267	+	8.70267i	0.285525	+	0.285525i	0.835308	−	0.549782i	$-0.185289\pi$
$929$	8.70267	+	8.70267i	0.285525	+	0.285525i	−0.549782	+	0.835308i	$0.685289\pi$
$930$	2.15236	−	0.998697i	0.0705788	−	0.0327486i
$931$	−34.5207	−	42.0636i	−1.13137	−	1.37858i
$932$	30.7692	+	38.6371i	1.00788	+	1.26560i
$933$	−23.3899	−	7.09524i	−0.765750	−	0.232288i
$934$	11.2465	−	23.3334i	0.367997	−	0.763492i
$935$	3.58434	+	2.39498i	0.117220	+	0.0783242i
$936$	4.87389	−	1.10722i	0.159308	−	0.0361906i
$937$	3.67563	+	5.50097i	0.120078	+	0.179709i	0.886639	−	0.462462i	$-0.153034\pi$
$937$	3.67563	+	5.50097i	0.120078	+	0.179709i	−0.766561	+	0.642171i	$0.778034\pi$
$938$	−61.3089	−	46.1722i	−2.00181	−	1.50758i
$939$	2.64013	+	26.8057i	0.0861573	+	0.874770i
$940$	0.300866	+	1.63807i	0.00981318	+	0.0534280i
$941$	−35.0220	+	10.6238i	−1.14169	+	0.346326i	−0.803823	−	0.594869i	$-0.797204\pi$
$941$	−35.0220	+	10.6238i	−1.14169	+	0.346326i	−0.337863	+	0.941195i	$0.609704\pi$
$942$	12.2787	+	1.91372i	0.400061	+	0.0623525i
$943$	−21.4476	−	8.88388i	−0.698429	−	0.289299i
$944$	−1.58418	−	2.05042i	−0.0515607	−	0.0667354i
$945$	1.17096	−	0.485027i	0.0380913	−	0.0157779i
$946$	52.7731	−	12.8074i	1.71580	−	0.416405i
$947$	13.5063	+	7.21925i	0.438894	+	0.234594i	0.676017	−	0.736886i	$-0.263704\pi$
$947$	13.5063	+	7.21925i	0.438894	+	0.234594i	−0.237123	+	0.971480i	$0.576204\pi$
$948$	20.3267	−	8.07155i	0.660180	−	0.262152i
$949$	8.82584	+	7.24318i	0.286499	+	0.235124i
$950$	31.8203	−	18.7558i	1.03239	−	0.608517i
$951$	−2.87917	+	14.4746i	−0.0933636	+	0.469371i
$952$	−21.1499	−	24.3956i	−0.685473	−	0.790666i
$953$	12.2070	−	2.42812i	0.395423	−	0.0786544i	0.00662593	−	0.999978i	$-0.497891\pi$
$953$	12.2070	−	2.42812i	0.395423	−	0.0786544i	0.388797	+	0.921324i	$0.372891\pi$
$954$	18.5612	+	1.04868i	0.600940	+	0.0339524i
$955$	−1.85174	−	3.46435i	−0.0599208	−	0.112104i
$956$	12.3756	+	3.95369i	0.400254	+	0.127871i
$957$	−32.8130	−	3.23180i	−1.06070	−	0.104469i
$958$	−2.92429	+	0.122119i	−0.0944795	+	0.00394548i
$959$		−	18.4109i		−	0.594518i
$960$	−1.95515	+	1.46518i	−0.0631021	+	0.0472885i
$961$			0.818803i			0.0264130i
$962$	−0.0723189	−	1.73177i	−0.00233166	−	0.0558344i
$963$	−19.3610	−	1.90689i	−0.623900	−	0.0614488i
$964$	−12.5031	+	6.44850i	−0.402696	+	0.207692i
$965$	−1.61523	−	3.02188i	−0.0519961	−	0.0972779i
$966$	1.06206	−	18.7978i	0.0341711	−	0.604811i
$967$	−18.9615	+	3.77168i	−0.609761	+	0.121289i	−0.490306	−	0.871551i	$-0.663115\pi$
$967$	−18.9615	+	3.77168i	−0.609761	+	0.121289i	−0.119455	+	0.992840i	$0.538115\pi$
$968$	19.4032	−	38.7878i	0.623644	−	1.24669i
$969$	2.85640	−	14.3601i	0.0917606	−	0.461312i
$970$	−1.45207	−	2.46352i	−0.0466231	−	0.0790989i
$971$	−12.2524	−	10.0553i	−0.393199	−	0.322690i	0.416934	−	0.908937i	$-0.363105\pi$
$971$	−12.2524	−	10.0553i	−0.393199	−	0.322690i	−0.810132	+	0.586247i	$0.800605\pi$
$972$	1.83631	+	0.792451i	0.0588996	+	0.0254179i
$973$	57.4996	+	30.7342i	1.84335	+	0.985293i
$974$	−2.32535	−	9.58161i	−0.0745089	−	0.307015i
$975$	8.01061	−	3.31810i	0.256545	−	0.106264i
$976$	−31.3618	+	2.16012i	−1.00387	+	0.0691438i
$977$	−5.41229	−	2.24185i	−0.173155	−	0.0717230i	0.294422	−	0.955675i	$-0.404873\pi$
$977$	−5.41229	−	2.24185i	−0.173155	−	0.0717230i	−0.467577	+	0.883952i	$0.654873\pi$
$978$	−1.36190	+	8.73809i	−0.0435487	+	0.279413i
$979$	−33.1775	+	10.0643i	−1.06036	+	0.321656i
$980$	5.14028	+	3.54504i	0.164200	+	0.113242i
$981$	0.806882	+	8.19241i	0.0257618	+	0.261564i
$982$	12.7365	−	16.9119i	0.406439	−	0.539682i
$983$	31.6172	+	47.3184i	1.00843	+	1.50922i	0.853361	+	0.521321i	$0.174560\pi$
$983$	31.6172	+	47.3184i	1.00843	+	1.50922i	0.155070	+	0.987903i	$0.450440\pi$
$984$	20.1753	+	3.44903i	0.643165	+	0.109951i
$985$	0.502331	+	0.335647i	0.0160056	+	0.0106946i
$986$	22.5151	+	10.8521i	0.717028	+	0.345602i
$987$	10.8286	+	3.28481i	0.344677	+	0.104557i
$988$	−2.11896	+	18.6924i	−0.0674131	+	0.594684i
$989$	−15.2286	−	18.5561i	−0.484241	−	0.590050i
$990$	−0.932870	−	2.01050i	−0.0296486	−	0.0638978i
$991$	−42.7714	−	42.7714i	−1.35868	−	1.35868i	−0.875548	−	0.483131i	$-0.839499\pi$
$991$	−42.7714	−	42.7714i	−1.35868	−	1.35868i	−0.483131	−	0.875548i	$-0.660501\pi$
$992$	6.43823	+	30.4031i	0.204414	+	0.965299i
$993$	−0.723514	+	0.723514i	−0.0229600	+	0.0229600i
$994$	−30.2554	−	11.0771i	−0.959644	−	0.351345i
$995$	−5.70783	+	4.68429i	−0.180950	+	0.148502i
$996$	−13.2565	+	3.80941i	−0.420050	+	0.120706i
$997$	1.82253	−	6.00806i	0.0577200	−	0.190277i	−0.923339	−	0.383985i	$-0.874551\pi$
$997$	1.82253	−	6.00806i	0.0577200	−	0.190277i	0.981059	+	0.193708i	$0.0620514\pi$
$998$	16.2823	+	46.5828i	0.515408	+	1.47455i
$999$	0.385331	−	0.576689i	0.0121913	−	0.0182456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.8	✓	512
128.53	even	32	inner	384.2.v.a.181.8	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.8	✓	512	1.1	even	1	trivial
384.2.v.a.181.8	yes	512	128.53	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)

\(f(q)\)	\(=\)	\(q+(-0.957405 + 1.04085i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-0.166750 - 1.99304i) q^{4} +(0.269342 - 0.143966i) q^{5} +(-0.941999 - 1.05482i) q^{6} +(0.809633 + 4.07030i) q^{7} +(2.23411 + 1.73458i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(-0.957405 + 1.04085i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(-0.166750 - 1.99304i) q^{4} +(0.269342 - 0.143966i) q^{5} +(-0.941999 - 1.05482i) q^{6} +(0.809633 + 4.07030i) q^{7} +(2.23411 + 1.73458i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(-0.108022 + 0.418179i) q^{10} +(3.25548 - 3.96681i) q^{11} +(1.99978 + 0.0294048i) q^{12} +(-0.832999 + 1.55843i) q^{13} +(-5.01173 - 3.05422i) q^{14} +(0.116873 + 0.282156i) q^{15} +(-3.94439 + 0.664677i) q^{16} +(-1.05262 + 2.54126i) q^{17} +(1.14207 - 0.834073i) q^{18} +(1.54516 + 5.09371i) q^{19} +(-0.331842 - 0.512801i) q^{20} +(-4.13006 + 0.406775i) q^{21} +(1.01205 + 7.18632i) q^{22} +(2.66734 - 1.78226i) q^{23} +(-1.94521 + 2.05333i) q^{24} +(-2.72603 + 4.07980i) q^{25} +(-0.824581 - 2.35908i) q^{26} +(0.290285 - 0.956940i) q^{27} +(7.97725 - 2.29235i) q^{28} +(-4.96675 + 4.07611i) q^{29} +(-0.405577 - 0.148490i) q^{30} +(-3.88466 + 3.88466i) q^{31} +(3.08455 - 4.74189i) q^{32} +(3.62861 + 3.62861i) q^{33} +(-1.63729 - 3.52864i) q^{34} +(0.804053 + 0.979741i) q^{35} +(-0.225276 + 1.98727i) q^{36} +(0.663712 + 0.201335i) q^{37} +(-6.78114 - 3.26846i) q^{38} +(-1.46928 - 0.981741i) q^{39} +(0.851458 + 0.145560i) q^{40} +(-4.02040 - 6.01695i) q^{41} +(3.53075 - 4.68823i) q^{42} +(-0.733450 - 7.44685i) q^{43} +(-8.44884 - 5.82682i) q^{44} +(-0.292253 + 0.0886539i) q^{45} +(-0.698657 + 4.48266i) q^{46} +(-2.51912 - 1.04345i) q^{47} +(-0.274859 - 3.99055i) q^{48} +(-9.44468 + 3.91211i) q^{49} +(-1.63655 - 6.74342i) q^{50} +(-2.42585 - 1.29664i) q^{51} +(3.24491 + 1.40033i) q^{52} +(10.1617 + 8.33951i) q^{53} +(0.718114 + 1.21832i) q^{54} +(0.305749 - 1.53710i) q^{55} +(-5.25146 + 10.4979i) q^{56} +(-5.22063 + 1.03845i) q^{57} +(0.512566 - 9.07214i) q^{58} +(0.305360 + 0.571289i) q^{59} +(0.542858 - 0.279981i) q^{60} +(7.82117 + 0.770318i) q^{61} +(-0.324166 - 7.76256i) q^{62} -4.15004i q^{63} +(1.98245 + 7.75048i) q^{64} +0.539674i q^{65} +(-7.25091 + 0.302799i) q^{66} +(13.0142 + 1.28179i) q^{67} +(5.24035 + 1.67416i) q^{68} +(1.51224 + 2.82919i) q^{69} +(-1.78957 - 0.101109i) q^{70} +(5.38424 - 1.07099i) q^{71} +(-1.85278 - 2.13710i) q^{72} +(1.26052 - 6.33704i) q^{73} +(-0.845002 + 0.498068i) q^{74} +(-3.79295 - 3.11280i) q^{75} +(9.89429 - 3.92893i) q^{76} +(18.7818 + 10.0391i) q^{77} +(2.42854 - 0.589380i) q^{78} +(10.1029 - 4.18476i) q^{79} +(-0.966697 + 0.746883i) q^{80} +(0.923880 + 0.382683i) q^{81} +(10.1119 + 1.57602i) q^{82} +(-6.59955 + 2.00195i) q^{83} +(1.49940 + 8.16353i) q^{84} +(0.0823397 + 0.836009i) q^{85} +(8.45328 + 6.36624i) q^{86} +(-3.56965 - 5.34236i) q^{87} +(14.1538 - 3.21538i) q^{88} +(-5.61758 - 3.75355i) q^{89} +(0.187529 - 0.389070i) q^{90} +(-7.01771 - 2.12880i) q^{91} +(-3.99689 - 5.01892i) q^{92} +(-3.48519 - 4.24672i) q^{93} +(3.49790 - 1.62303i) q^{94} +(1.14950 + 1.14950i) q^{95} +(4.41672 + 3.53448i) q^{96} +(-4.68172 + 4.68172i) q^{97} +(4.97045 - 13.5760i) q^{98} +(-3.96681 + 3.25548i) 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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