LMFDB - Embedded newform 230.2.j.a.209.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(9,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			209.10
Character	$\chi$	$=$	230.209
Dual form			230.2.j.a.219.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.540641 - 0.841254i) q^{2} +(1.59901 - 0.229903i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.85404 - 1.25002i) q^{5} +(0.671082 - 1.46947i) q^{6} +(1.35246 + 1.17191i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-0.374509 + 0.109966i) q^{9} +(-0.0492162 - 2.23553i) q^{10} +(-4.81325 + 3.09329i) q^{11} +(-0.873379 - 1.35900i) q^{12} +(-1.68251 + 1.45791i) q^{13} +(1.71707 - 0.504178i) q^{14} +(2.67723 - 2.42504i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(3.28912 + 1.50209i) q^{17} +(-0.109966 + 0.374509i) q^{18} +(-3.15305 - 6.90421i) q^{19} +(-1.90725 - 1.16721i) q^{20} +(2.43202 + 1.56297i) q^{21} +5.72152i q^{22} +(4.17363 - 2.36237i) q^{23} -1.61545 q^{24} +(1.87490 - 4.63516i) q^{25} +(0.316833 + 2.20363i) q^{26} +(-4.98196 + 2.27518i) q^{27} +(0.504178 - 1.71707i) q^{28} +(-0.955917 + 2.09317i) q^{29} +(-0.592650 - 3.56331i) q^{30} +(-1.29804 + 9.02807i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-6.98527 + 6.05277i) q^{33} +(3.04187 - 1.95489i) q^{34} +(3.97243 + 0.482168i) q^{35} +(0.255605 + 0.294984i) q^{36} +(-1.17271 - 3.99387i) q^{37} +(-7.51286 - 1.08019i) q^{38} +(-2.35518 + 2.71802i) q^{39} +(-2.01306 + 0.973440i) q^{40} +(5.64246 + 1.65678i) q^{41} +(2.62970 - 1.20094i) q^{42} +(-2.25812 + 0.324669i) q^{43} +(4.81325 + 3.09329i) q^{44} +(-0.556894 + 0.672024i) q^{45} +(0.269079 - 4.78828i) q^{46} -3.81331i q^{47} +(-0.873379 + 1.35900i) q^{48} +(-0.540436 - 3.75881i) q^{49} +(-2.88570 - 4.08323i) q^{50} +(5.60466 + 1.64568i) q^{51} +(2.02510 + 0.924833i) q^{52} +(-2.96874 - 2.57243i) q^{53} +(-0.779443 + 5.42115i) q^{54} +(-5.05727 + 11.7517i) q^{55} +(-1.17191 - 1.35246i) q^{56} +(-6.62904 - 10.3150i) q^{57} +(1.24408 + 1.93582i) q^{58} +(6.34567 + 7.32330i) q^{59} +(-3.31806 - 1.42790i) q^{60} +(-0.721231 + 5.01627i) q^{61} +(6.89313 + 5.97293i) q^{62} +(-0.635379 - 0.290168i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-1.29703 + 4.80619i) q^{65} +(1.31539 + 9.14876i) q^{66} +(-2.00796 + 3.12444i) q^{67} -3.61588i q^{68} +(6.13055 - 4.73698i) q^{69} +(2.55328 - 3.08114i) q^{70} +(-0.655263 - 0.421112i) q^{71} +(0.386347 - 0.0555483i) q^{72} +(13.8519 - 6.32596i) q^{73} +(-3.99387 - 1.17271i) q^{74} +(1.93234 - 7.84271i) q^{75} +(-4.97047 + 5.73623i) q^{76} +(-10.1348 - 1.45716i) q^{77} +(1.01324 + 3.45077i) q^{78} +(-6.94694 - 8.01719i) q^{79} +(-0.269433 + 2.21978i) q^{80} +(-6.45804 + 4.15033i) q^{81} +(4.44432 - 3.85102i) q^{82} +(4.32469 + 14.7285i) q^{83} +(0.411425 - 2.86152i) q^{84} +(7.97578 - 1.32653i) q^{85} +(-0.947705 + 2.07518i) q^{86} +(-1.04729 + 3.56676i) q^{87} +(5.20448 - 2.37681i) q^{88} +(0.0331388 + 0.230486i) q^{89} +(0.264263 + 0.831812i) q^{90} -3.98408 q^{91} +(-3.88268 - 2.81510i) q^{92} +14.7344i q^{93} +(-3.20796 - 2.06163i) q^{94} +(-14.4763 - 8.85928i) q^{95} +(0.671082 + 1.46947i) q^{96} +(3.29716 - 11.2291i) q^{97} +(-3.45430 - 1.57752i) q^{98} +(1.46245 - 1.68776i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{1}{11}\right)$

Coefficient data

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

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

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

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	1.59901	−	0.229903i	0.923187	−	0.132734i	0.335701	−	0.941969i	$-0.391027\pi$
$3$	1.59901	−	0.229903i	0.923187	−	0.132734i	0.587486	+	0.809234i	$0.300118\pi$
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	1.85404	−	1.25002i	0.829150	−	0.559026i
$5$	1.85404	−	1.25002i	0.829150	−	0.559026i
$6$	0.671082	−	1.46947i	0.273968	−	0.599907i
$7$	1.35246	+	1.17191i	0.511182	+	0.442942i	0.871865	−	0.489747i	$-0.162911\pi$
$7$	1.35246	+	1.17191i	0.511182	+	0.442942i	−0.360683	+	0.932689i	$0.617456\pi$
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	−0.374509	+	0.109966i	−0.124836	+	0.0366552i
$10$	−0.0492162	−	2.23553i	−0.0155635	−	0.706935i
$11$	−4.81325	+	3.09329i	−1.45125	+	0.932662i	−0.452078	+	0.891979i	$0.649317\pi$
$11$	−4.81325	+	3.09329i	−1.45125	+	0.932662i	−0.999172	+	0.0406829i	$0.987047\pi$
$12$	−0.873379	−	1.35900i	−0.252123	−	0.392311i
$13$	−1.68251	+	1.45791i	−0.466646	+	0.404351i	−0.856193	−	0.516656i	$-0.827177\pi$
$13$	−1.68251	+	1.45791i	−0.466646	+	0.404351i	0.389548	+	0.921006i	$0.372631\pi$
$14$	1.71707	−	0.504178i	0.458907	−	0.134747i
$15$	2.67723	−	2.42504i	0.691259	−	0.626142i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	3.28912	+	1.50209i	0.797728	+	0.364310i	0.772213	−	0.635364i	$-0.219150\pi$
$17$	3.28912	+	1.50209i	0.797728	+	0.364310i	0.0255153	+	0.999674i	$0.491877\pi$
$18$	−0.109966	+	0.374509i	−0.0259192	+	0.0882726i
$19$	−3.15305	−	6.90421i	−0.723359	−	1.58393i	−0.809137	−	0.587620i	$-0.800065\pi$
$19$	−3.15305	−	6.90421i	−0.723359	−	1.58393i	0.0857782	−	0.996314i	$-0.472662\pi$
$20$	−1.90725	−	1.16721i	−0.426475	−	0.260997i
$21$	2.43202	+	1.56297i	0.530711	+	0.341067i
$22$			5.72152i			1.21983i
$23$	4.17363	−	2.36237i	0.870262	−	0.492589i
$23$	4.17363	−	2.36237i	0.870262	−	0.492589i
$24$	−1.61545			−0.329752
$25$	1.87490	−	4.63516i	0.374980	−	0.927033i
$26$	0.316833	+	2.20363i	0.0621362	+	0.432166i
$27$	−4.98196	+	2.27518i	−0.958778	+	0.437859i
$28$	0.504178	−	1.71707i	0.0952807	−	0.324496i
$29$	−0.955917	+	2.09317i	−0.177509	+	0.388691i	−0.977383	−	0.211477i	$-0.932173\pi$
$29$	−0.955917	+	2.09317i	−0.177509	+	0.388691i	0.799874	+	0.600169i	$0.204900\pi$
$30$	−0.592650	−	3.56331i	−0.108203	−	0.650568i
$31$	−1.29804	+	9.02807i	−0.233135	+	1.62149i	0.451270	+	0.892388i	$0.350971\pi$
$31$	−1.29804	+	9.02807i	−0.233135	+	1.62149i	−0.684405	+	0.729102i	$0.739938\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	−6.98527	+	6.05277i	−1.21598	+	1.05365i
$34$	3.04187	−	1.95489i	0.521676	−	0.335261i
$35$	3.97243	+	0.482168i	0.671463	+	0.0815012i
$36$	0.255605	+	0.294984i	0.0426008	+	0.0491640i
$37$	−1.17271	−	3.99387i	−0.192792	−	0.656589i	−0.997978	−	0.0635660i	$-0.979753\pi$
$37$	−1.17271	−	3.99387i	−0.192792	−	0.656589i	0.805186	−	0.593023i	$-0.202066\pi$
$38$	−7.51286	−	1.08019i	−1.21875	−	0.175229i
$39$	−2.35518	+	2.71802i	−0.377130	+	0.435231i
$40$	−2.01306	+	0.973440i	−0.318293	+	0.153914i
$41$	5.64246	+	1.65678i	0.881205	+	0.258745i	0.690874	−	0.722975i	$-0.257226\pi$
$41$	5.64246	+	1.65678i	0.881205	+	0.258745i	0.190331	+	0.981720i	$0.439044\pi$
$42$	2.62970	−	1.20094i	0.405772	−	0.185310i
$43$	−2.25812	+	0.324669i	−0.344361	+	0.0495116i	−0.312325	−	0.949975i	$-0.601108\pi$
$43$	−2.25812	+	0.324669i	−0.344361	+	0.0495116i	−0.0320351	+	0.999487i	$0.510199\pi$
$44$	4.81325	+	3.09329i	0.725625	+	0.466331i
$45$	−0.556894	+	0.672024i	−0.0830168	+	0.100179i
$46$	0.269079	−	4.78828i	0.0396735	−	0.705993i
$47$		−	3.81331i		−	0.556228i	−0.960548	−	0.278114i	$-0.910291\pi$
$47$		−	3.81331i		−	0.556228i	0.960548	−	0.278114i	$-0.0897093\pi$
$48$	−0.873379	+	1.35900i	−0.126061	+	0.196155i
$49$	−0.540436	−	3.75881i	−0.0772051	−	0.536973i
$50$	−2.88570	−	4.08323i	−0.408100	−	0.577455i
$51$	5.60466	+	1.64568i	0.784809	+	0.230441i
$52$	2.02510	+	0.924833i	0.280831	+	0.128251i
$53$	−2.96874	−	2.57243i	−0.407788	−	0.353350i	0.426684	−	0.904401i	$-0.359682\pi$
$53$	−2.96874	−	2.57243i	−0.407788	−	0.353350i	−0.834472	+	0.551051i	$0.814227\pi$
$54$	−0.779443	+	5.42115i	−0.106069	+	0.737725i
$55$	−5.05727	+	11.7517i	−0.681922	+	1.58460i
$56$	−1.17191	−	1.35246i	−0.156604	−	0.180730i
$57$	−6.62904	−	10.3150i	−0.878038	−	1.36625i
$58$	1.24408	+	1.93582i	0.163355	+	0.254186i
$59$	6.34567	+	7.32330i	0.826136	+	0.953412i	0.999505	−	0.0314447i	$-0.0100108\pi$
$59$	6.34567	+	7.32330i	0.826136	+	0.953412i	−0.173369	+	0.984857i	$0.555465\pi$
$60$	−3.31806	−	1.42790i	−0.428359	−	0.184341i
$61$	−0.721231	+	5.01627i	−0.0923441	+	0.642267i	0.890108	+	0.455750i	$0.150629\pi$
$61$	−0.721231	+	5.01627i	−0.0923441	+	0.642267i	−0.982452	+	0.186517i	$0.940280\pi$
$62$	6.89313	+	5.97293i	0.875428	+	0.758562i
$63$	−0.635379	−	0.290168i	−0.0800502	−	0.0365577i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−1.29703	+	4.80619i	−0.160877	+	0.596134i
$66$	1.31539	+	9.14876i	0.161914	+	1.12613i
$67$	−2.00796	+	3.12444i	−0.245311	+	0.381712i	−0.941973	−	0.335688i	$-0.891031\pi$
$67$	−2.00796	+	3.12444i	−0.245311	+	0.381712i	0.696662	+	0.717399i	$0.254668\pi$
$68$		−	3.61588i		−	0.438489i
$69$	6.13055	−	4.73698i	0.738031	−	0.570266i
$70$	2.55328	−	3.08114i	0.305176	−	0.368267i
$71$	−0.655263	−	0.421112i	−0.0777654	−	0.0499768i	0.501180	−	0.865343i	$-0.332899\pi$
$71$	−0.655263	−	0.421112i	−0.0777654	−	0.0499768i	−0.578946	+	0.815366i	$0.696536\pi$
$72$	0.386347	−	0.0555483i	0.0455314	−	0.00654643i
$73$	13.8519	−	6.32596i	1.62125	−	0.740398i	0.622149	−	0.782899i	$-0.286260\pi$
$73$	13.8519	−	6.32596i	1.62125	−	0.740398i	0.999096	+	0.0425008i	$0.0135325\pi$
$74$	−3.99387	−	1.17271i	−0.464278	−	0.136324i
$75$	1.93234	−	7.84271i	0.223128	−	0.905598i
$76$	−4.97047	+	5.73623i	−0.570152	+	0.657990i
$77$	−10.1348	−	1.45716i	−1.15497	−	0.166059i
$78$	1.01324	+	3.45077i	0.114727	+	0.390723i
$79$	−6.94694	−	8.01719i	−0.781591	−	0.902005i	0.215632	−	0.976475i	$-0.430819\pi$
$79$	−6.94694	−	8.01719i	−0.781591	−	0.902005i	−0.997223	+	0.0744702i	$0.976273\pi$
$80$	−0.269433	+	2.21978i	−0.0301236	+	0.248179i
$81$	−6.45804	+	4.15033i	−0.717560	+	0.461148i
$82$	4.44432	−	3.85102i	0.490793	−	0.425274i
$83$	4.32469	+	14.7285i	0.474696	+	1.61667i	0.754285	+	0.656547i	$0.227984\pi$
$83$	4.32469	+	14.7285i	0.474696	+	1.61667i	−0.279588	+	0.960120i	$0.590198\pi$
$84$	0.411425	−	2.86152i	0.0448901	−	0.312218i
$85$	7.97578	−	1.32653i	0.865095	−	0.143883i
$86$	−0.947705	+	2.07518i	−0.102194	+	0.223773i
$87$	−1.04729	+	3.56676i	−0.112282	+	0.382396i
$88$	5.20448	−	2.37681i	0.554799	−	0.253368i
$89$	0.0331388	+	0.230486i	0.00351271	+	0.0244314i	0.991502	−	0.130088i	$-0.0415261\pi$
$89$	0.0331388	+	0.230486i	0.00351271	+	0.0244314i	−0.987990	+	0.154520i	$0.950617\pi$
$90$	0.264263	+	0.831812i	0.0278558	+	0.0876807i
$91$	−3.98408			−0.417645
$92$	−3.88268	−	2.81510i	−0.404797	−	0.293495i
$93$			14.7344i			1.52788i
$94$	−3.20796	−	2.06163i	−0.330876	−	0.212641i
$95$	−14.4763	−	8.85928i	−1.48523	−	0.908943i
$96$	0.671082	+	1.46947i	0.0684921	+	0.149977i
$97$	3.29716	−	11.2291i	0.334776	−	1.14014i	−0.604393	−	0.796686i	$-0.706584\pi$
$97$	3.29716	−	11.2291i	0.334776	−	1.14014i	0.939169	−	0.343456i	$-0.111598\pi$
$98$	−3.45430	−	1.57752i	−0.348937	−	0.159354i
$99$	1.46245	−	1.68776i	0.146982	−	0.169626i
$100$	−4.99516	+	0.220048i	−0.499516	+	0.0220048i
$101$	3.26313	−	0.958141i	0.324694	−	0.0953386i	−0.115324	−	0.993328i	$-0.536791\pi$
$101$	3.26313	−	0.958141i	0.324694	−	0.0953386i	0.440017	+	0.897989i	$0.354972\pi$
$102$	4.41454	−	3.82522i	0.437104	−	0.378753i
$103$	−9.97644	−	15.5236i	−0.983008	−	1.52959i	−0.841927	−	0.539591i	$-0.818579\pi$
$103$	−9.97644	−	15.5236i	−0.983008	−	1.52959i	−0.141081	−	0.989998i	$-0.545058\pi$
$104$	1.87287	−	1.20362i	0.183650	−	0.118025i
$105$	6.46279	−	0.142281i	0.630704	−	0.0138853i
$106$	−3.76908	+	1.10670i	−0.366086	+	0.107492i
$107$	0.540837	+	0.0777606i	0.0522847	+	0.00751740i	0.168408	−	0.985717i	$-0.446138\pi$
$107$	0.540837	+	0.0777606i	0.0522847	+	0.00751740i	−0.116123	+	0.993235i	$0.537047\pi$
$108$	4.13916	+	3.58660i	0.398291	+	0.345121i
$109$	4.67529	−	10.2375i	0.447811	−	0.980570i	−0.542287	−	0.840193i	$-0.682441\pi$
$109$	4.67529	−	10.2375i	0.447811	−	0.980570i	0.990098	−	0.140377i	$-0.0448313\pi$
$110$	7.15202	+	10.6079i	0.681918	+	1.01142i
$111$	−2.79337	−	6.11662i	−0.265135	−	0.580564i
$112$	−1.77135	+	0.254681i	−0.167377	+	0.0240651i
$113$	1.71034	−	2.66134i	0.160895	−	0.250358i	−0.751440	−	0.659801i	$-0.770641\pi$
$113$	1.71034	−	2.66134i	0.160895	−	0.250358i	0.912336	+	0.409443i	$0.134277\pi$
$114$	−12.2615			−1.14839
$115$	4.78505	−	9.59705i	0.446208	−	0.894929i
$116$	2.30111			0.213653
$117$	0.469797	−	0.731018i	0.0434327	−	0.0675826i
$118$	9.59148	−	1.37905i	0.882967	−	0.126952i
$119$	2.68808	+	5.88608i	0.246416	+	0.539576i
$120$	−2.99510	+	2.01935i	−0.273414	+	0.184340i
$121$	9.02938	−	19.7716i	0.820853	−	1.79742i
$122$	3.83003	+	3.31874i	0.346754	+	0.300464i
$123$	9.40324	+	1.35198i	0.847862	+	0.121904i
$124$	8.75145	−	2.56966i	0.785903	−	0.230762i
$125$	−2.31792	−	10.9374i	−0.207321	−	0.978273i
$126$	−0.587617	+	0.377638i	−0.0523490	+	0.0336427i
$127$	2.81661	+	4.38274i	0.249934	+	0.388905i	0.943439	−	0.331547i	$-0.107571\pi$
$127$	2.81661	+	4.38274i	0.249934	+	0.388905i	−0.693505	+	0.720452i	$0.743934\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	−3.53611	+	1.03830i	−0.311337	+	0.0914169i
$130$	3.34200	+	3.68955i	0.293112	+	0.323595i
$131$	−11.2671	+	13.0030i	−0.984413	+	1.13607i	0.00628251	+	0.999980i	$0.498000\pi$
$131$	−11.2671	+	13.0030i	−0.984413	+	1.13607i	−0.990696	+	0.136093i	$0.956545\pi$
$132$	8.40758	+	3.83961i	0.731786	+	0.334195i
$133$	3.82677	−	13.0328i	0.331823	−	1.13008i
$134$	1.54287	+	3.37840i	0.133283	+	0.291850i
$135$	−6.39270	+	10.4458i	−0.550196	+	0.899033i
$136$	−3.04187	−	1.95489i	−0.260838	−	0.167630i
$137$		−	0.192917i		−	0.0164820i	−0.999966	−	0.00824100i	$-0.997377\pi$
$137$		−	0.192917i		−	0.0164820i	0.999966	−	0.00824100i	$-0.00262322\pi$
$138$	−0.670578	−	7.71835i	−0.0570834	−	0.657030i
$139$	−1.40321			−0.119018			−0.0595092	−	0.998228i	$-0.518954\pi$
$139$	−1.40321			−0.119018			−0.0595092	+	0.998228i	$0.518954\pi$
$140$	−1.21161	−	3.81375i	−0.102400	−	0.322320i
$141$	−0.876689	−	6.09751i	−0.0738306	−	0.513503i
$142$	−0.708524	+	0.323572i	−0.0594580	+	0.0271536i
$143$	3.58864	−	12.2218i	0.300097	−	1.02204i
$144$	0.162145	−	0.355047i	0.0135120	−	0.0295873i
$145$	0.844195	+	5.07572i	0.0701066	+	0.421516i
$146$	2.16718	−	15.0731i	0.179357	−	1.24746i
$147$	−1.72832	−	5.88612i	−0.142550	−	0.485479i
$148$	−3.14579	+	2.72585i	−0.258583	+	0.224063i
$149$	−3.01935	+	1.94042i	−0.247355	+	0.158965i	−0.658444	−	0.752630i	$-0.728785\pi$
$149$	−3.01935	+	1.94042i	−0.247355	+	0.158965i	0.411089	+	0.911595i	$0.365149\pi$
$150$	−5.55300	−	5.86568i	−0.453401	−	0.478931i
$151$	−0.744802	−	0.859547i	−0.0606111	−	0.0699489i	0.724634	−	0.689134i	$-0.242009\pi$
$151$	−0.744802	−	0.859547i	−0.0606111	−	0.0699489i	−0.785245	+	0.619185i	$0.787463\pi$
$152$	2.13838	+	7.28266i	0.173446	+	0.590702i
$153$	−1.39698	−	0.200856i	−0.112939	−	0.0162382i
$154$	−6.70513	+	7.73814i	−0.540315	+	0.623557i
$155$	8.87866	+	18.3610i	0.713151	+	1.47479i
$156$	3.45077	+	1.01324i	0.276283	+	0.0811240i
$157$	−10.2520	+	4.68192i	−0.818197	+	0.373658i	−0.780130	−	0.625617i	$-0.784847\pi$
$157$	−10.2520	+	4.68192i	−0.818197	+	0.373658i	−0.0380670	+	0.999275i	$0.512120\pi$
$158$	−10.5003	+	1.50971i	−0.835358	+	0.120106i
$159$	−5.33844	−	3.43081i	−0.423366	−	0.272081i
$160$	1.72173	+	1.42676i	0.136115	+	0.112796i
$161$	8.41317	+	1.69612i	0.663051	+	0.133673i
$162$			7.67669i			0.603138i
$163$	2.81047	−	4.37318i	0.220133	−	0.342534i	−0.713569	−	0.700585i	$-0.752922\pi$
$163$	2.81047	−	4.37318i	0.220133	−	0.342534i	0.933702	+	0.358051i	$0.116559\pi$
$164$	−0.836907	−	5.82082i	−0.0653515	−	0.454529i
$165$	−5.38486	+	19.9538i	−0.419211	+	1.55340i
$166$	14.7285	+	4.32469i	1.14316	+	0.335661i
$167$	−2.61744	−	1.19535i	−0.202544	−	0.0924986i	0.311561	−	0.950226i	$-0.399148\pi$
$167$	−2.61744	−	1.19535i	−0.202544	−	0.0924986i	−0.514104	+	0.857728i	$0.671876\pi$
$168$	−2.18483	−	1.89317i	−0.168564	−	0.146061i
$169$	−1.14473	+	7.96178i	−0.0880562	+	0.612445i
$170$	3.19608	−	7.42683i	0.245128	−	0.569612i
$171$	1.94007	+	2.23896i	0.148361	+	0.171218i
$172$	1.23339	+	1.91919i	0.0940449	+	0.146337i
$173$	6.07296	+	9.44972i	0.461719	+	0.718449i	0.991560	−	0.129648i	$-0.0413848\pi$
$173$	6.07296	+	9.44972i	0.461719	+	0.718449i	−0.529841	+	0.848097i	$0.677748\pi$
$174$	2.43434	+	2.80937i	0.184547	+	0.212978i
$175$	7.96774	−	4.07166i	0.602305	−	0.307788i
$176$	0.814257	−	5.66329i	0.0613770	−	0.426886i
$177$	11.8304	+	10.2511i	0.889229	+	0.770522i
$178$	0.211813	+	0.0967318i	0.0158761	+	0.00725036i
$179$	2.50736	+	0.736226i	0.187409	+	0.0550281i	0.374090	−	0.927392i	$-0.377955\pi$
$179$	2.50736	+	0.736226i	0.187409	+	0.0550281i	−0.186682	+	0.982420i	$0.559773\pi$
$180$	0.842636	+	0.227399i	0.0628064	+	0.0169493i
$181$	−3.65316	−	25.4083i	−0.271537	−	1.88858i	−0.432518	−	0.901625i	$-0.642375\pi$
$181$	−3.65316	−	25.4083i	−0.271537	−	1.88858i	0.160981	−	0.986958i	$-0.448534\pi$
$182$	−2.15395	+	3.35162i	−0.159662	+	0.248439i
$183$			8.18687i			0.605191i
$184$	−4.46735	+	1.74436i	−0.329337	+	0.128596i
$185$	−7.16666	−	5.93888i	−0.526903	−	0.436635i
$186$	12.3954	+	7.96601i	0.908871	+	0.584096i
$187$	−20.4777	+	2.94425i	−1.49748	+	0.215305i
$188$	−3.46871	+	1.58411i	−0.252981	+	0.115533i
$189$	−9.40422	−	2.76133i	−0.684057	−	0.200857i
$190$	−15.2794	+	7.38852i	−1.10848	+	0.536019i
$191$	6.97965	−	8.05494i	0.505030	−	0.582835i	−0.444789	−	0.895635i	$-0.646722\pi$
$191$	6.97965	−	8.05494i	0.505030	−	0.582835i	0.949819	+	0.312800i	$0.101267\pi$
$192$	1.59901	+	0.229903i	0.115398	+	0.0165918i
$193$	1.19125	+	4.05701i	0.0857477	+	0.292030i	0.991192	−	0.132436i	$-0.0422800\pi$
$193$	1.19125	+	4.05701i	0.0857477	+	0.292030i	−0.905444	+	0.424466i	$0.860462\pi$
$194$	−7.66394	−	8.84466i	−0.550239	−	0.635009i
$195$	−0.969005	+	7.98332i	−0.0693919	+	0.571698i
$196$	−3.19463	+	2.05307i	−0.228188	+	0.146648i
$197$	5.44437	−	4.71757i	0.387895	−	0.336113i	−0.438982	−	0.898496i	$-0.644661\pi$
$197$	5.44437	−	4.71757i	0.387895	−	0.336113i	0.826877	+	0.562383i	$0.190115\pi$
$198$	−0.629171	−	2.14276i	−0.0447133	−	0.152279i
$199$	−3.10785	+	21.6156i	−0.220310	+	1.53229i	0.516558	+	0.856252i	$0.327213\pi$
$199$	−3.10785	+	21.6156i	−0.220310	+	1.53229i	−0.736868	+	0.676037i	$0.763696\pi$
$200$	−2.51547	+	4.32116i	−0.177870	+	0.305552i
$201$	−2.49242	+	5.45764i	−0.175802	+	0.384953i
$202$	0.958141	−	3.26313i	0.0674146	−	0.229593i
$203$	−3.74585	+	1.71067i	−0.262907	+	0.120066i
$204$	−0.831299	−	5.78181i	−0.0582026	−	0.404808i
$205$	12.5323	−	3.98147i	0.875296	−	0.278078i
$206$	−18.4530			−1.28568
$207$	−1.30328	+	1.34369i	−0.0905843	+	0.0933927i
$208$		−	2.22629i		−	0.154365i
$209$	36.5331	+	23.4784i	2.52705	+	1.62404i
$210$	3.37436	−	5.51377i	0.232853	−	0.380486i
$211$	4.60785	+	10.0898i	0.317217	+	0.694609i	0.999329	−	0.0366394i	$-0.0116653\pi$
$211$	4.60785	+	10.0898i	0.317217	+	0.694609i	−0.682111	+	0.731248i	$0.738938\pi$
$212$	−1.10670	+	3.76908i	−0.0760087	+	0.258862i
$213$	−1.14459	−	0.522715i	−0.0784257	−	0.0358158i
$214$	0.357815	−	0.412940i	0.0244597	−	0.0282280i
$215$	−3.78080	+	3.42465i	−0.257848	+	0.233559i
$216$	5.25504	−	1.54302i	0.357560	−	0.104989i
$217$	−12.3357	+	10.6889i	−0.837400	+	0.725611i
$218$	−6.08464	−	9.46789i	−0.412104	−	0.641246i
$219$	20.6950	−	13.2999i	1.39844	−	0.898721i
$220$	12.7906	−	0.281591i	0.862343	−	0.0189849i
$221$	−7.72389	+	2.26794i	−0.519565	+	0.152558i
$222$	−6.65584	−	0.956965i	−0.446711	−	0.0642273i
$223$	−8.23813	−	7.13838i	−0.551666	−	0.478022i	0.333852	−	0.942625i	$-0.391651\pi$
$223$	−8.23813	−	7.13838i	−0.551666	−	0.478022i	−0.885519	+	0.464604i	$0.846197\pi$
$224$	−0.743411	+	1.62784i	−0.0496712	+	0.108765i
$225$	−0.192457	+	1.94208i	−0.0128305	+	0.129472i
$226$	−1.31418	−	2.87766i	−0.0874181	−	0.191419i
$227$	−0.0964927	+	0.0138736i	−0.00640444	+	0.000920820i	−0.145516	−	0.989356i	$-0.546484\pi$
$227$	−0.0964927	+	0.0138736i	−0.00640444	+	0.000920820i	0.139112	+	0.990277i	$0.455575\pi$
$228$	−6.62904	+	10.3150i	−0.439019	+	0.683127i
$229$	−11.3216			−0.748153			−0.374076	−	0.927398i	$-0.622040\pi$
$229$	−11.3216			−0.748153			−0.374076	+	0.927398i	$0.622040\pi$
$230$	−5.48656	−	9.21399i	−0.361773	−	0.607553i
$231$	−16.5406			−1.08829
$232$	1.24408	−	1.93582i	0.0816776	−	0.127093i
$233$	6.97486	−	1.00283i	0.456938	−	0.0656978i	0.0899973	−	0.995942i	$-0.471314\pi$
$233$	6.97486	−	1.00283i	0.456938	−	0.0656978i	0.366941	+	0.930244i	$0.380405\pi$
$234$	−0.360980	−	0.790436i	−0.0235980	−	0.0516724i
$235$	−4.76671	−	7.07001i	−0.310946	−	0.461197i
$236$	4.02542	−	8.81444i	0.262032	−	0.573771i
$237$	−12.9514	−	11.2224i	−0.841282	−	0.728975i
$238$	6.40497	+	0.920896i	0.415173	+	0.0596928i
$239$	−14.9570	+	4.39177i	−0.967487	+	0.284080i	−0.727050	−	0.686585i	$-0.759109\pi$
$239$	−14.9570	+	4.39177i	−0.967487	+	0.284080i	−0.240437	+	0.970665i	$0.577291\pi$
$240$	0.0795063	+	3.61138i	0.00513211	+	0.233114i
$241$	3.55666	−	2.28573i	0.229105	−	0.147237i	−0.421053	−	0.907036i	$-0.638339\pi$
$241$	3.55666	−	2.28573i	0.229105	−	0.147237i	0.650158	+	0.759799i	$0.274703\pi$
$242$	−11.7513	−	18.2853i	−0.755400	−	1.17543i
$243$	3.04519	−	2.63867i	0.195349	−	0.169271i
$244$	4.86257	−	1.42778i	0.311294	−	0.0914042i
$245$	−5.70058	−	6.29342i	−0.364197	−	0.402072i
$246$	6.22114	−	7.17957i	0.396645	−	0.457753i
$247$	15.3707	+	7.01958i	0.978017	+	0.446645i
$248$	2.56966	−	8.75145i	0.163173	−	0.555718i
$249$	10.3013	+	22.5568i	0.652821	+	1.42948i
$250$	−10.4543	−	3.96326i	−0.661188	−	0.250659i
$251$	−12.4550	−	8.00432i	−0.786151	−	0.505228i	0.0849190	−	0.996388i	$-0.472937\pi$
$251$	−12.4550	−	8.00432i	−0.786151	−	0.505228i	−0.871070	+	0.491160i	$0.836573\pi$
$252$			0.698501i			0.0440014i
$253$	−12.7812	+	24.2809i	−0.803549	+	1.52653i
$254$	5.20977			0.326890
$255$	12.4484	−	3.95479i	0.779547	−	0.247659i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	17.2578	−	7.88135i	1.07651	−	0.491625i	0.203373	−	0.979101i	$-0.434810\pi$
$257$	17.2578	−	7.88135i	1.07651	−	0.491625i	0.873136	+	0.487476i	$0.162082\pi$
$258$	−1.03830	+	3.53611i	−0.0646415	+	0.220149i
$259$	3.09444	−	6.77587i	0.192279	−	0.421032i
$260$	4.91067	−	0.816744i	0.304547	−	0.0506523i
$261$	0.127823	−	0.889027i	0.00791203	−	0.0550294i
$262$	4.84732	+	16.5084i	0.299468	+	1.01989i
$263$	−15.3183	+	13.2734i	−0.944566	+	0.818471i	−0.983525	−	0.180770i	$-0.942141\pi$
$263$	−15.3183	+	13.2734i	−0.944566	+	0.818471i	0.0389594	+	0.999241i	$0.487596\pi$
$264$	7.77557	−	4.99705i	0.478553	−	0.307547i
$265$	−8.71973	−	1.05839i	−0.535649	−	0.0650163i
$266$	−8.89496	−	10.2653i	−0.545385	−	0.629408i
$267$	0.105979	+	0.360930i	0.00648578	+	0.0220885i
$268$	3.67623	+	0.528562i	0.224561	+	0.0322871i
$269$	−11.7557	+	13.5668i	−0.716756	+	0.827180i	−0.990913	−	0.134505i	$-0.957056\pi$
$269$	−11.7557	+	13.5668i	−0.716756	+	0.827180i	0.274157	+	0.961685i	$0.411601\pi$
$270$	5.33143	+	11.0253i	0.324460	+	0.670980i
$271$	18.5238	+	5.43907i	1.12524	+	0.330400i	0.790834	−	0.612030i	$-0.209647\pi$
$271$	18.5238	+	5.43907i	1.12524	+	0.330400i	0.334404	+	0.942430i	$0.391465\pi$
$272$	−3.28912	+	1.50209i	−0.199432	+	0.0910775i
$273$	−6.37057	+	0.915950i	−0.385564	+	0.0554358i
$274$	−0.162292	−	0.104299i	−0.00980442	−	0.00630092i
$275$	5.31354	+	28.1098i	0.320418	+	1.69509i
$276$	−6.85563	−	3.60873i	−0.412661	−	0.217220i
$277$			23.7804i			1.42882i	0.699725	+	0.714412i	$0.253306\pi$
$277$			23.7804i			1.42882i	−0.699725	+	0.714412i	$0.746694\pi$
$278$	−0.758631	+	1.18045i	−0.0454996	+	0.0707988i
$279$	−0.506651	−	3.52383i	−0.0303324	−	0.210966i
$280$	−3.86337	−	1.04260i	−0.230881	−	0.0623070i
$281$	−3.49475	−	1.02615i	−0.208479	−	0.0612150i	0.175825	−	0.984421i	$-0.443741\pi$
$281$	−3.49475	−	1.02615i	−0.208479	−	0.0612150i	−0.384305	+	0.923206i	$0.625559\pi$
$282$	−5.60352	−	2.55904i	−0.333685	−	0.152389i
$283$	−4.16358	−	3.60776i	−0.247499	−	0.214459i	0.522272	−	0.852779i	$-0.325084\pi$
$283$	−4.16358	−	3.60776i	−0.247499	−	0.214459i	−0.769771	+	0.638320i	$0.779630\pi$
$284$	−0.110851	+	0.770985i	−0.00657779	+	0.0457495i
$285$	−25.1844	−	10.8379i	−1.49180	−	0.641984i
$286$	−8.34145	−	9.62654i	−0.493240	−	0.569229i
$287$	5.68961	+	8.85321i	0.335847	+	0.522588i
$288$	−0.211023	−	0.328358i	−0.0124346	−	0.0193487i
$289$	−2.57062	−	2.96665i	−0.151213	−	0.174509i
$290$	4.72637	+	2.03396i	0.277542	+	0.119438i
$291$	2.69059	−	18.7134i	0.157725	−	1.09700i
$292$	−11.5086	−	9.97226i	−0.673490	−	0.583582i
$293$	−1.25658	−	0.573859i	−0.0734099	−	0.0335252i	0.378372	−	0.925654i	$-0.376484\pi$
$293$	−1.25658	−	0.573859i	−0.0734099	−	0.0335252i	−0.451782	+	0.892129i	$0.649211\pi$
$294$	−5.88612	−	1.72832i	−0.343286	−	0.100798i
$295$	20.9194	+	5.64544i	1.21797	+	0.328690i
$296$	0.592383	+	4.12011i	0.0344316	+	0.239477i
$297$	16.9416	−	26.3617i	0.983052	−	1.52966i
$298$			3.58911i			0.207911i
$299$	−3.57807	+	10.0595i	−0.206925	+	0.581756i
$300$	−7.93670	+	1.50026i	−0.458226	+	0.0866174i
$301$	−3.43451	−	2.20722i	−0.197962	−	0.127222i
$302$	−1.12577	+	0.161861i	−0.0647806	+	0.00931405i
$303$	4.99749	−	2.28228i	0.287098	−	0.131113i
$304$	7.28266	+	2.13838i	0.417689	+	0.122645i
$305$	4.93325	+	10.2019i	0.282477	+	0.584159i
$306$	−0.924236	+	1.06662i	−0.0528350	+	0.0609749i
$307$	4.89410	+	0.703666i	0.279321	+	0.0401603i	0.280552	−	0.959839i	$-0.409483\pi$
$307$	4.89410	+	0.703666i	0.279321	+	0.0401603i	−0.00123044	+	0.999999i	$0.500392\pi$
$308$	2.88467	+	9.82427i	0.164369	+	0.559790i
$309$	−19.5213	−	22.5288i	−1.11053	−	1.28162i
$310$	20.2464	+	2.45748i	1.14992	+	0.139575i
$311$	5.54880	−	3.56600i	0.314643	−	0.202209i	−0.373781	−	0.927517i	$-0.621939\pi$
$311$	5.54880	−	3.56600i	0.314643	−	0.202209i	0.688425	+	0.725308i	$0.258303\pi$
$312$	2.71802	−	2.35518i	0.153878	−	0.133336i
$313$	5.82901	+	19.8518i	0.329475	+	1.12209i	0.943105	+	0.332495i	$0.107891\pi$
$313$	5.82901	+	19.8518i	0.329475	+	1.12209i	−0.613630	+	0.789594i	$0.710291\pi$
$314$	−1.60396	+	11.1558i	−0.0905165	+	0.629556i
$315$	−1.54073	+	0.256255i	−0.0868104	+	0.0144383i
$316$	−4.40683	+	9.64962i	−0.247904	+	0.542833i
$317$	−3.90010	+	13.2825i	−0.219051	+	0.746020i	0.774494	+	0.632582i	$0.218005\pi$
$317$	−3.90010	+	13.2825i	−0.219051	+	0.746020i	−0.993545	+	0.113439i	$0.963813\pi$
$318$	−5.77236	+	2.63615i	−0.323698	+	0.147828i
$319$	−1.87370	−	13.0319i	−0.104907	−	0.729644i
$320$	2.13111	−	0.677043i	0.119132	−	0.0378479i
$321$	0.882680			0.0492664
$322$	5.97537	−	6.16062i	0.332994	−	0.343318i
$323$		−	27.4449i		−	1.52708i
$324$	6.45804	+	4.15033i	0.358780	+	0.230574i
$325$	3.60309	+	10.5322i	0.199864	+	0.584219i
$326$	−2.15950	−	4.72864i	−0.119604	−	0.261895i
$327$	5.12220	−	17.4446i	0.283258	−	0.964690i
$328$	−5.34925	−	2.44292i	−0.295363	−	0.134888i
$329$	4.46887	−	5.15735i	0.246377	−	0.284334i
$330$	13.8749	+	15.3179i	0.763789	+	0.843220i
$331$	25.0123	−	7.34426i	1.37480	−	0.403677i	0.490843	−	0.871248i	$-0.336689\pi$
$331$	25.0123	−	7.34426i	1.37480	−	0.403677i	0.883955	+	0.467571i	$0.154871\pi$
$332$	11.6010	−	10.0523i	0.636688	−	0.551693i
$333$	0.878378	+	1.36678i	0.0481348	+	0.0748992i
$334$	−2.42069	+	1.55568i	−0.132454	+	0.0851230i
$335$	0.182791	+	8.30282i	0.00998691	+	0.453631i
$336$	−2.77385	+	0.814475i	−0.151326	+	0.0444332i
$337$	20.1545	+	2.89779i	1.09789	+	0.157852i	0.667368	−	0.744728i	$-0.267421\pi$
$337$	20.1545	+	2.89779i	1.09789	+	0.157852i	0.430520	+	0.902581i	$0.358330\pi$
$338$	6.07899	+	5.26747i	0.330653	+	0.286513i
$339$	2.12300	−	4.64871i	0.115305	−	0.252483i
$340$	−4.51992	−	6.70396i	−0.245127	−	0.363573i
$341$	−21.6786	−	47.4696i	−1.17396	−	2.57062i
$342$	2.93241	−	0.421618i	0.158567	−	0.0227985i
$343$	10.4467	−	16.2553i	0.564067	−	0.877705i
$344$	2.28134			0.123002
$345$	5.44494	−	16.4458i	0.293146	−	0.885415i
$346$	11.2329			0.603884
$347$	11.0868	−	17.2515i	0.595173	−	0.926108i	−0.404759	−	0.914424i	$-0.632644\pi$
$347$	11.0868	−	17.2515i	0.595173	−	0.926108i	0.999932	−	0.0116840i	$-0.00371921\pi$
$348$	3.67950	−	0.529032i	0.197242	−	0.0283591i
$349$	8.62051	+	18.8763i	0.461445	+	1.01042i	0.987156	+	0.159761i	$0.0510722\pi$
$349$	8.62051	+	18.8763i	0.461445	+	1.01042i	−0.525711	+	0.850663i	$0.676201\pi$
$350$	0.882391	−	8.90420i	0.0471658	−	0.475949i
$351$	5.06521	−	11.0913i	0.270361	−	0.592008i
$352$	−4.32404	−	3.74680i	−0.230472	−	0.199705i
$353$	−12.3929	−	1.78184i	−0.659610	−	0.0948376i	−0.195622	−	0.980679i	$-0.562673\pi$
$353$	−12.3929	−	1.78184i	−0.659610	−	0.0948376i	−0.463988	+	0.885842i	$0.653582\pi$
$354$	15.0198	−	4.41021i	0.798294	−	0.234400i
$355$	−1.74128	+	0.0383351i	−0.0924176	+	0.00203462i
$356$	0.195891	−	0.125891i	0.0103822	−	0.00667223i
$357$	5.65149	+	8.79389i	0.299108	+	0.465422i
$358$	1.97493	−	1.71129i	0.104378	−	0.0904444i
$359$	−9.79469	+	2.87598i	−0.516944	+	0.151788i	−0.529790	−	0.848129i	$-0.677729\pi$
$359$	−9.79469	+	2.87598i	−0.516944	+	0.151788i	0.0128458	+	0.999917i	$0.495911\pi$
$360$	0.646864	−	0.585930i	0.0340927	−	0.0308812i
$361$	−25.2841	+	29.1794i	−1.33074	+	1.53576i
$362$	−23.3499	−	10.6635i	−1.22724	−	0.560462i
$363$	9.89251	−	33.6908i	0.519222	−	1.76831i
$364$	1.65505	+	3.62404i	0.0867479	+	0.189952i
$365$	17.7744	−	29.0438i	0.930354	−	1.52022i
$366$	6.88723	+	4.42615i	0.360001	+	0.231359i
$367$		−	6.54858i		−	0.341833i	−0.985286	−	0.170917i	$-0.945327\pi$
$367$		−	6.54858i		−	0.341833i	0.985286	−	0.170917i	$-0.0546729\pi$
$368$	−0.947783	+	4.70125i	−0.0494066	+	0.245069i
$369$	−2.29534			−0.119491
$370$	−8.87069	+	2.81818i	−0.461165	+	0.146510i
$371$	−1.00044	−	6.95821i	−0.0519402	−	0.361252i
$372$	13.4029	−	6.12088i	0.694906	−	0.317353i
$373$	−3.67883	+	12.5289i	−0.190482	+	0.648724i	0.807763	+	0.589508i	$0.200678\pi$
$373$	−3.67883	+	12.5289i	−0.190482	+	0.648724i	−0.998245	+	0.0592159i	$0.981140\pi$
$374$	−8.59424	+	18.8187i	−0.444397	+	0.973094i
$375$	−6.22091	−	16.9561i	−0.321246	−	0.875611i
$376$	−0.542690	+	3.77449i	−0.0279871	+	0.194655i
$377$	−1.44330	−	4.91542i	−0.0743336	−	0.253157i
$378$	−7.40728	+	6.41845i	−0.380990	+	0.330129i
$379$	24.6264	−	15.8264i	1.26497	−	0.812949i	0.276017	−	0.961153i	$-0.410985\pi$
$379$	24.6264	−	15.8264i	1.26497	−	0.812949i	0.988957	+	0.148203i	$0.0473490\pi$
$380$	−2.04503	+	16.8484i	−0.104908	+	0.864302i
$381$	5.51139	+	6.36048i	0.282357	+	0.325857i
$382$	−3.00277	−	10.2265i	−0.153635	−	0.523232i
$383$	32.0813	+	4.61260i	1.63928	+	0.235693i	0.899426	−	0.437074i	$-0.143985\pi$
$383$	32.0813	+	4.61260i	1.63928	+	0.235693i	0.739855	+	0.672767i	$0.234894\pi$
$384$	1.05790	−	1.22088i	0.0539855	−	0.0623026i
$385$	−20.6118	+	9.96707i	−1.05047	+	0.507969i
$386$	4.05701	+	1.19125i	0.206496	+	0.0606328i
$387$	0.809985	−	0.369908i	0.0411738	−	0.0188035i
$388$	−11.5840	+	1.66553i	−0.588090	+	0.0845546i
$389$	−12.2417	−	7.86729i	−0.620681	−	0.398888i	0.192168	−	0.981362i	$-0.438448\pi$
$389$	−12.2417	−	7.86729i	−0.620681	−	0.398888i	−0.812849	+	0.582474i	$0.802085\pi$
$390$	6.19212	+	5.13129i	0.313550	+	0.259833i
$391$	17.2760	−	1.50096i	0.873687	−	0.0759068i
$392$			3.79747i			0.191801i
$393$	−15.0268	+	23.3822i	−0.758002	+	1.17947i
$394$	−1.02523	−	7.13061i	−0.0516502	−	0.359235i
$395$	−22.9015	−	6.18035i	−1.15230	−	0.310967i
$396$	−2.14276	−	0.629171i	−0.107678	−	0.0316170i
$397$	−23.0457	−	10.5246i	−1.15663	−	0.528216i	−0.257666	−	0.966234i	$-0.582953\pi$
$397$	−23.0457	−	10.5246i	−1.15663	−	0.528216i	−0.898966	+	0.438018i	$0.855681\pi$
$398$	16.5040	+	14.3008i	0.827269	+	0.716833i
$399$	3.12276	−	21.7193i	0.156334	−	1.08732i
$400$	2.27523	+	4.45234i	0.113761	+	0.222617i
$401$	24.3576	+	28.1102i	1.21636	+	1.40376i	0.888404	+	0.459063i	$0.151815\pi$
$401$	24.3576	+	28.1102i	1.21636	+	1.40376i	0.327957	+	0.944693i	$0.393640\pi$
$402$	3.24376	+	5.04738i	0.161784	+	0.251741i
$403$	−10.9781	−	17.0823i	−0.546859	−	0.850929i
$404$	−2.22711	−	2.57022i	−0.110803	−	0.127873i
$405$	−6.78545	+	15.7676i	−0.337172	+	0.783496i
$406$	−0.586050	+	4.07607i	−0.0290852	+	0.202292i
$407$	17.9987	+	15.5960i	0.892164	+	0.773064i
$408$	−5.31340	−	2.42655i	−0.263053	−	0.120132i
$409$	−29.4168	−	8.63754i	−1.45456	−	0.427099i	−0.543517	−	0.839398i	$-0.682908\pi$
$409$	−29.4168	−	8.63754i	−1.45456	−	0.427099i	−0.911048	+	0.412300i	$0.864726\pi$
$410$	3.42607	−	12.6954i	0.169201	−	0.626982i
$411$	−0.0443521	−	0.308476i	−0.00218773	−	0.0152160i
$412$	−9.97644	+	15.5236i	−0.491504	+	0.764795i
$413$			17.3411i			0.853298i
$414$	0.425774	+	1.82284i	0.0209256	+	0.0895878i
$415$	26.4291	+	21.9013i	1.29735	+	1.07509i
$416$	−1.87287	−	1.20362i	−0.0918250	−	0.0590124i
$417$	−2.24374	+	0.322601i	−0.109876	+	0.0157978i
$418$	39.5026	−	18.0402i	1.93213	−	0.882376i
$419$	15.5341	+	4.56121i	0.758889	+	0.222830i	0.638211	−	0.769862i	$-0.279675\pi$
$419$	15.5341	+	4.56121i	0.758889	+	0.222830i	0.120678	+	0.992692i	$0.461493\pi$
$420$	−2.81417	−	5.81966i	−0.137317	−	0.283970i
$421$	−11.6105	+	13.3992i	−0.565861	+	0.653039i	−0.964504	−	0.264067i	$-0.914936\pi$
$421$	−11.6105	+	13.3992i	−0.565861	+	0.653039i	0.398643	+	0.917106i	$0.369481\pi$
$422$	10.9793	+	1.57858i	0.534462	+	0.0768440i
$423$	0.419333	+	1.42812i	0.0203887	+	0.0694375i
$424$	2.57243	+	2.96874i	0.124928	+	0.144175i
$425$	13.1292	−	12.4293i	0.636859	−	0.602911i
$426$	−1.05855	+	0.680286i	−0.0512867	+	0.0329600i
$427$	−6.85407	+	5.93909i	−0.331692	+	0.287413i
$428$	−0.153938	−	0.524265i	−0.00744088	−	0.0253413i
$429$	2.92844	−	20.3677i	0.141386	−	0.983364i
$430$	0.836942	+	5.03211i	0.0403610	+	0.242670i
$431$	2.83606	−	6.21010i	0.136608	−	0.299130i	−0.828948	−	0.559326i	$-0.811060\pi$
$431$	2.83606	−	6.21010i	0.136608	−	0.299130i	0.965556	+	0.260196i	$0.0837872\pi$
$432$	1.54302	−	5.25504i	0.0742385	−	0.252833i
$433$	−35.3808	+	16.1579i	−1.70029	+	0.776497i	−0.702387	+	0.711796i	$0.747882\pi$
$433$	−35.3808	+	16.1579i	−1.70029	+	0.776497i	−0.997905	+	0.0647013i	$0.979391\pi$
$434$	2.32293	+	16.1563i	0.111504	+	0.775527i
$435$	2.51680	+	7.92203i	0.120671	+	0.379832i
$436$	−11.2545			−0.538993
$437$	−29.4700	−	21.3669i	−1.40974	−	1.02212i
$438$		−	24.6002i		−	1.17544i
$439$	−10.7280	−	6.89444i	−0.512018	−	0.329054i	0.258990	−	0.965880i	$-0.416610\pi$
$439$	−10.7280	−	6.89444i	−0.512018	−	0.329054i	−0.771007	+	0.636826i	$0.780247\pi$
$440$	6.67824	−	10.9124i	0.318372	−	0.520228i
$441$	0.615739	+	1.34828i	0.0293209	+	0.0642038i
$442$	−2.26794	+	7.72389i	−0.107875	+	0.367388i
$443$	−10.2419	−	4.67732i	−0.486607	−	0.222226i	0.156976	−	0.987602i	$-0.449826\pi$
$443$	−10.2419	−	4.67732i	−0.486607	−	0.222226i	−0.643583	+	0.765376i	$0.722553\pi$
$444$	−4.40347	+	5.08187i	−0.208979	+	0.241175i
$445$	0.349552	+	0.385905i	0.0165704	+	0.0182936i
$446$	−10.4591	+	3.07106i	−0.495251	+	0.145419i
$447$	−4.38185	+	3.79690i	−0.207255	+	0.179587i
$448$	0.967510	+	1.50548i	0.0457106	+	0.0711270i
$449$	−9.39510	+	6.03787i	−0.443382	+	0.284945i	−0.743222	−	0.669045i	$-0.766703\pi$
$449$	−9.39510	+	6.03787i	−0.443382	+	0.284945i	0.299839	+	0.953990i	$0.403067\pi$
$450$	1.52974	+	1.21188i	0.0721124	+	0.0571284i
$451$	−32.2835	+	9.47929i	−1.52017	+	0.446362i
$452$	−3.13134	−	0.450219i	−0.147286	−	0.0211765i
$453$	−1.38856	−	1.20319i	−0.0652400	−	0.0565308i
$454$	−0.0404967	+	0.0886754i	−0.00190060	+	0.00416174i
$455$	−7.38662	+	4.98018i	−0.346290	+	0.233474i
$456$	5.09359	+	11.1534i	0.238529	+	0.522306i
$457$	36.2905	−	5.21779i	1.69760	−	0.244078i	0.775587	−	0.631240i	$-0.217454\pi$
$457$	36.2905	−	5.21779i	1.69760	−	0.244078i	0.922012	+	0.387162i	$0.126545\pi$
$458$	−6.12092	+	9.52434i	−0.286012	+	0.445043i
$459$	−19.8038			−0.924361
$460$	−10.7176	−	0.365872i	−0.499709	−	0.0170589i
$461$	33.6731			1.56831			0.784157	−	0.620563i	$-0.213096\pi$
$461$	33.6731			1.56831			0.784157	+	0.620563i	$0.213096\pi$
$462$	−8.94254	+	13.9149i	−0.416045	+	0.647378i
$463$	−38.5088	+	5.53673i	−1.78966	+	0.257314i	−0.955663	−	0.294462i	$-0.904859\pi$
$463$	−38.5088	+	5.53673i	−1.78966	+	0.257314i	−0.833992	+	0.551776i	$0.813950\pi$
$464$	−0.955917	−	2.09317i	−0.0443773	−	0.0971728i
$465$	18.4183	+	27.3181i	0.854127	+	1.26685i
$466$	2.92726	−	6.40980i	0.135603	−	0.296928i
$467$	2.38069	+	2.06288i	0.110165	+	0.0954587i	0.708202	−	0.706010i	$-0.249507\pi$
$467$	2.38069	+	2.06288i	0.110165	+	0.0954587i	−0.598036	+	0.801469i	$0.704052\pi$
$468$	−0.860118	−	0.123666i	−0.0397590	−	0.00571648i
$469$	−6.37726	+	1.87253i	−0.294475	+	0.0864656i
$470$	−8.52475	+	0.187676i	−0.393217	+	0.00865687i
$471$	−15.3166	+	9.84339i	−0.705752	+	0.453559i
$472$	−5.23887	−	8.15184i	−0.241139	−	0.375219i
$473$	9.86462	−	8.54774i	0.453576	−	0.393025i
$474$	−16.4430	+	4.82809i	−0.755250	+	0.221761i
$475$	−37.9138	+	1.67019i	−1.73960	+	0.0766336i
$476$	4.23750	−	4.89033i	0.194225	−	0.224148i
$477$	1.39470	+	0.636937i	0.0638588	+	0.0291633i
$478$	−4.39177	+	14.9570i	−0.200875	+	0.684116i
$479$	7.92399	+	17.3511i	0.362056	+	0.792793i	0.999747	+	0.0225000i	$0.00716256\pi$
$479$	7.92399	+	17.3511i	0.362056	+	0.792793i	−0.637691	+	0.770293i	$0.720110\pi$
$480$	3.08107	+	1.88558i	0.140631	+	0.0860644i
$481$	7.79579	+	5.01005i	0.355457	+	0.228439i
$482$		−	4.22781i		−	0.192572i
$483$	13.8427	+	0.777893i	0.629863	+	0.0353954i
$484$	−21.7358			−0.987992
$485$	−7.92354	−	24.9407i	−0.359790	−	1.13250i
$486$	−0.573438	−	3.98835i	−0.0260117	−	0.180915i
$487$	−24.4449	+	11.1636i	−1.10770	+	0.505871i	−0.883387	−	0.468645i	$-0.844742\pi$
$487$	−24.4449	+	11.1636i	−1.10770	+	0.505871i	−0.224317	+	0.974516i	$0.572015\pi$
$488$	1.42778	−	4.86257i	0.0646325	−	0.220118i
$489$	3.48856	−	7.63888i	0.157758	−	0.345442i
$490$	−8.37633	+	1.39315i	−0.378404	+	0.0629362i
$491$	−3.88274	+	27.0050i	−0.175225	+	1.21872i	0.692405	+	0.721509i	$0.256551\pi$
$491$	−3.88274	+	27.0050i	−0.175225	+	1.21872i	−0.867630	+	0.497210i	$0.834358\pi$
$492$	−2.67644	−	9.11512i	−0.120663	−	0.410941i
$493$	−6.28824	+	5.44879i	−0.283208	+	0.245401i
$494$	14.2153	−	9.13562i	0.639577	−	0.411031i
$495$	0.601704	−	4.95725i	0.0270446	−	0.222812i
$496$	−5.97293	−	6.89313i	−0.268192	−	0.309510i
$497$	−0.392711	−	1.33745i	−0.0176155	−	0.0599928i
$498$	24.5453	+	3.52908i	1.09990	+	0.158142i
$499$	−1.73494	+	2.00222i	−0.0776664	+	0.0896318i	−0.793253	−	0.608892i	$-0.791614\pi$
$499$	−1.73494	+	2.00222i	−0.0776664	+	0.0896318i	0.715586	+	0.698524i	$0.246160\pi$
$500$	−8.98613	+	6.65202i	−0.401872	+	0.297487i
$501$	−4.46012	−	1.30961i	−0.199264	−	0.0585091i
$502$	−13.4673	+	6.15032i	−0.601076	+	0.274502i
$503$	28.9325	−	4.15987i	1.29004	−	0.185479i	0.537070	−	0.843538i	$-0.319531\pi$
$503$	28.9325	−	4.15987i	1.29004	−	0.185479i	0.752967	+	0.658058i	$0.228622\pi$
$504$	0.587617	+	0.377638i	0.0261745	+	0.0168213i
$505$	4.85226	−	5.85541i	0.215923	−	0.260562i
$506$	13.5164	+	23.8795i	0.600876	+	1.06157i
$507$			12.9941i			0.577089i
$508$	2.81661	−	4.38274i	0.124967	−	0.194452i
$509$	0.971607	+	6.75767i	0.0430657	+	0.299529i	0.999959	+	0.00908787i	$0.00289280\pi$
$509$	0.971607	+	6.75767i	0.0430657	+	0.299529i	−0.956893	+	0.290441i	$0.906198\pi$
$510$	3.40311	−	12.6103i	0.150692	−	0.558396i
$511$	26.1477	+	7.67765i	1.15671	+	0.339639i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	31.4167	+	27.2227i	1.38708	+	1.20191i
$514$	2.70003	−	18.7791i	0.119093	−	0.828312i
$515$	−37.9015	−	16.3106i	−1.67014	−	0.718733i
$516$	2.41342	+	2.78524i	0.106245	+	0.122613i
$517$	11.7957	+	18.3544i	0.518773	+	0.807226i
$518$	−4.02724	−	6.26652i	−0.176947	−	0.275335i
$519$	11.8832	+	13.7140i	0.521616	+	0.601977i
$520$	1.96782	−	4.57268i	0.0862946	−	0.200525i
$521$	3.37781	−	23.4932i	0.147985	−	1.02926i	−0.771528	−	0.636196i	$-0.780507\pi$
$521$	3.37781	−	23.4932i	0.147985	−	1.02926i	0.919512	−	0.393061i	$-0.128584\pi$
$522$	−0.678791	−	0.588176i	−0.0297099	−	0.0257438i
$523$	−0.268516	−	0.122627i	−0.0117414	−	0.00536211i	0.409536	−	0.912294i	$-0.365691\pi$
$523$	−0.268516	−	0.122627i	−0.0117414	−	0.00536211i	−0.421277	+	0.906932i	$0.638418\pi$
$524$	16.5084	+	4.84732i	0.721175	+	0.211756i
$525$	11.8044	−	8.34242i	0.515186	−	0.364093i
$526$	2.88458	+	20.0627i	0.125774	+	0.874775i
$527$	−17.8304	+	27.7446i	−0.776703	+	1.20857i
$528$		−	9.24284i		−	0.402243i
$529$	11.8384	−	19.7194i	0.514712	−	0.857363i
$530$	−5.60462	+	6.76330i	−0.243449	+	0.293779i
$531$	−3.18182	−	2.04483i	−0.138079	−	0.0887382i
$532$	−13.4447	+	1.93306i	−0.582903	+	0.0838088i
$533$	−11.9090	+	5.43864i	−0.515834	+	0.235574i
$534$	0.360930	+	0.105979i	0.0156190	+	0.00458614i
$535$	1.09993	−	0.531886i	0.0475543	−	0.0229954i
$536$	2.43217	−	2.80688i	0.105054	−	0.121239i
$537$	4.17854	+	0.600783i	0.180317	+	0.0259257i
$538$	5.05749	+	17.2242i	0.218044	+	0.742590i
$539$	14.2283	+	16.4204i	0.612858	+	0.707276i
$540$	12.1575	+	1.47566i	0.523175	+	0.0635022i
$541$	−10.7351	+	6.89903i	−0.461538	+	0.296613i	−0.750671	−	0.660676i	$-0.770270\pi$
$541$	−10.7351	+	6.89903i	−0.461538	+	0.296613i	0.289132	+	0.957289i	$0.406633\pi$
$542$	14.5903	−	12.6426i	0.626708	−	0.543046i
$543$	−11.6829	−	39.7882i	−0.501360	−	1.70747i
$544$	−0.514593	+	3.57907i	−0.0220630	+	0.153451i
$545$	−4.12887	−	24.8248i	−0.176861	−	1.06338i
$546$	−2.67364	+	5.85446i	−0.114421	+	0.250548i
$547$	−6.00299	+	20.4443i	−0.256669	+	0.874135i	0.725831	+	0.687873i	$0.241456\pi$
$547$	−6.00299	+	20.4443i	−0.256669	+	0.874135i	−0.982500	+	0.186262i	$0.940363\pi$
$548$	−0.175483	+	0.0801406i	−0.00749628	+	0.00342344i
$549$	−0.281510	−	1.95795i	−0.0120146	−	0.0835632i
$550$	26.5202	+	10.7273i	1.13082	+	0.457413i
$551$	17.4657			0.744064
$552$	−6.74229	+	3.81630i	−0.286971	+	0.162432i
$553$		−	18.9842i		−	0.807288i
$554$	20.0053	+	12.8566i	0.849944	+	0.546226i
$555$	−12.8249	−	7.84867i	−0.544387	−	0.333158i
$556$	0.582913	+	1.27640i	0.0247210	+	0.0541315i
$557$	−5.53158	+	18.8388i	−0.234381	+	0.798227i	0.755355	+	0.655316i	$0.227464\pi$
$557$	−5.53158	+	18.8388i	−0.234381	+	0.798227i	−0.989736	+	0.142911i	$0.954354\pi$
$558$	−3.23835	−	1.47891i	−0.137090	−	0.0626071i
$559$	3.32599	−	3.83839i	0.140674	−	0.162347i
$560$	−2.96578	+	2.68641i	−0.125327	+	0.113521i
$561$	−32.0672	+	9.41577i	−1.35388	+	0.397534i
$562$	−2.75265	+	2.38519i	−0.116114	+	0.100613i
$563$	−19.7813	−	30.7803i	−0.833684	−	1.29724i	−0.952567	−	0.304329i	$-0.901568\pi$
$563$	−19.7813	−	30.7803i	−0.833684	−	1.29724i	0.118884	−	0.992908i	$-0.462068\pi$
$564$	−5.18230	+	3.33046i	−0.218214	+	0.140238i
$565$	−0.155697	−	7.07218i	−0.00655024	−	0.297529i
$566$	−5.28604	+	1.55212i	−0.222189	+	0.0652405i
$567$	−13.5981	−	1.95511i	−0.571066	−	0.0821069i
$568$	0.588663	+	0.510080i	0.0246998	+	0.0214025i
$569$	−2.23346	+	4.89059i	−0.0936314	+	0.205024i	−0.950653	−	0.310257i	$-0.899585\pi$
$569$	−2.23346	+	4.89059i	−0.0936314	+	0.205024i	0.857021	+	0.515281i	$0.172312\pi$
$570$	−22.7332	+	15.3271i	−0.952188	+	0.641980i
$571$	3.43096	+	7.51275i	0.143581	+	0.314399i	0.967736	−	0.251965i	$-0.0810769\pi$
$571$	3.43096	+	7.51275i	0.143581	+	0.314399i	−0.824155	+	0.566364i	$0.808350\pi$
$572$	−12.6081	+	1.81277i	−0.527171	+	0.0757957i
$573$	9.30866	−	14.4846i	0.388875	−	0.605101i
$574$	10.5238			0.439256
$575$	−3.12486	−	23.7747i	−0.130316	−	0.991473i
$576$	−0.390320			−0.0162633
$577$	2.54963	−	3.96730i	0.106143	−	0.165161i	−0.784119	−	0.620610i	$-0.786885\pi$
$577$	2.54963	−	3.96730i	0.106143	−	0.165161i	0.890262	+	0.455449i	$0.150521\pi$
$578$	−3.88549	+	0.558649i	−0.161615	+	0.0232367i
$579$	2.83753	+	6.21332i	0.117924	+	0.258217i
$580$	4.26635	−	2.87644i	0.177150	−	0.119438i
$581$	−11.4116	+	24.9879i	−0.473433	+	1.03667i
$582$	−14.2881	−	12.3807i	−0.592261	−	0.513197i
$583$	22.2465	+	3.19857i	0.921357	+	0.132471i
$584$	−14.6112	+	4.29024i	−0.604616	+	0.177531i
$585$	−0.0427670	−	1.94259i	−0.00176820	−	0.0803162i
$586$	−1.16212	+	0.746847i	−0.0480066	+	0.0308520i
$587$	0.633296	+	0.985428i	0.0261389	+	0.0406730i	0.854077	−	0.520146i	$-0.174123\pi$
$587$	0.633296	+	0.985428i	0.0261389	+	0.0406730i	−0.827938	+	0.560819i	$0.810486\pi$
$588$	−4.63624	+	4.01732i	−0.191195	+	0.165672i
$589$	66.4245	−	19.5040i	2.73697	−	0.803648i
$590$	16.0591	−	14.5463i	0.661143	−	0.598864i
$591$	7.62100	−	8.79511i	0.313486	−	0.361782i
$592$	3.78633	+	1.72916i	0.155617	+	0.0710679i
$593$	10.8835	−	37.0657i	0.446931	−	1.52211i	−0.360851	−	0.932624i	$-0.617514\pi$
$593$	10.8835	−	37.0657i	0.446931	−	1.52211i	0.807781	−	0.589482i	$-0.200668\pi$
$594$	−13.0175	−	28.5044i	−0.534115	−	1.16955i
$595$	12.3415	+	7.55285i	0.505953	+	0.309636i
$596$	3.01935	+	1.94042i	0.123677	+	0.0794826i
$597$			35.2780i			1.44383i
$598$	6.52813	+	8.44864i	0.266955	+	0.345490i
$599$	−27.8085			−1.13622			−0.568112	−	0.822951i	$-0.692326\pi$
$599$	−27.8085			−1.13622			−0.568112	+	0.822951i	$0.692326\pi$
$600$	−3.02881	+	7.48788i	−0.123651	+	0.305691i
$601$	5.79738	+	40.3217i	0.236480	+	1.64476i	0.669095	+	0.743177i	$0.266682\pi$
$601$	5.79738	+	40.3217i	0.236480	+	1.64476i	−0.432615	+	0.901579i	$0.642409\pi$
$602$	−3.71367	+	1.69598i	−0.151358	+	0.0691228i
$603$	0.408416	−	1.39094i	0.0166320	−	0.0566434i
$604$	−0.472470	+	1.03456i	−0.0192245	+	0.0420958i
$605$	−7.97408	−	47.9442i	−0.324193	−	1.94921i
$606$	0.781873	−	5.43805i	0.0317614	−	0.220906i
$607$	−12.9794	−	44.2036i	−0.526816	−	1.79417i	−0.603797	−	0.797138i	$-0.706346\pi$
$607$	−12.9794	−	44.2036i	−0.526816	−	1.79417i	0.0769809	−	0.997033i	$-0.475472\pi$
$608$	5.73623	−	4.97047i	0.232635	−	0.201579i
$609$	−5.59636	+	3.59656i	−0.226776	+	0.145740i
$610$	11.2495	+	1.36545i	0.455479	+	0.0552854i
$611$	5.55945	+	6.41595i	0.224911	+	0.259561i
$612$	0.397622	+	1.35418i	0.0160729	+	0.0547394i
$613$	22.8521	+	3.28564i	0.922989	+	0.132706i	0.587395	−	0.809301i	$-0.300154\pi$
$613$	22.8521	+	3.28564i	0.922989	+	0.132706i	0.335595	+	0.942007i	$0.391063\pi$
$614$	3.23791	−	3.73675i	0.130672	−	0.150803i
$615$	19.1240	−	9.24762i	0.771152	−	0.372900i
$616$	9.82427	+	2.88467i	0.395831	+	0.116226i
$617$	33.8682	−	15.4671i	1.36348	−	0.622681i	0.406720	−	0.913553i	$-0.366673\pi$
$617$	33.8682	−	15.4671i	1.36348	−	0.622681i	0.956762	+	0.290872i	$0.0939452\pi$
$618$	−29.5065	+	4.24239i	−1.18692	+	0.170654i
$619$	−2.37072	−	1.52357i	−0.0952873	−	0.0612375i	0.492129	−	0.870522i	$-0.336219\pi$
$619$	−2.37072	−	1.52357i	−0.0952873	−	0.0612375i	−0.587417	+	0.809285i	$0.699855\pi$
$620$	13.0134	−	15.7037i	0.522630	−	0.630677i
$621$	−15.4180	+	21.2650i	−0.618703	+	0.853336i
$622$		−	6.59587i		−	0.264470i
$623$	−0.225290	+	0.350559i	−0.00902607	+	0.0140448i
$624$	−0.511829	−	3.55985i	−0.0204896	−	0.142508i
$625$	−17.9695	−	17.3809i	−0.718780	−	0.695238i
$626$	19.8518	+	5.82901i	0.793437	+	0.232974i
$627$	63.8145	+	29.1431i	2.54851	+	1.16386i
$628$	8.51766	+	7.38059i	0.339892	+	0.294518i
$629$	2.14198	−	14.8978i	0.0854065	−	0.594015i
$630$	−0.617407	+	1.43469i	−0.0245981	+	0.0571593i
$631$	−3.07204	−	3.54533i	−0.122296	−	0.141137i	0.691300	−	0.722568i	$-0.257038\pi$
$631$	−3.07204	−	3.54533i	−0.122296	−	0.141137i	−0.813596	+	0.581431i	$0.802493\pi$
$632$	5.73526	+	8.92424i	0.228136	+	0.354987i
$633$	9.68765	+	15.0743i	0.385049	+	0.599149i
$634$	9.06541	+	10.4620i	0.360033	+	0.415501i
$635$	10.7006	+	4.60493i	0.424641	+	0.182741i
$636$	−0.903104	+	6.28123i	−0.0358104	+	0.249067i
$637$	6.38929	+	5.53635i	0.253153	+	0.219358i
$638$	−11.9761	−	5.46930i	−0.474138	−	0.216532i
$639$	0.291710	+	0.0856537i	0.0115399	+	0.00338841i
$640$	0.582598	−	2.15884i	0.0230292	−	0.0853355i
$641$	−0.284982	−	1.98209i	−0.0112561	−	0.0782880i	0.983419	−	0.181348i	$-0.0580459\pi$
$641$	−0.284982	−	1.98209i	−0.0112561	−	0.0782880i	−0.994675	+	0.103060i	$0.967137\pi$
$642$	0.477213	−	0.742557i	0.0188341	−	0.0293064i
$643$		−	15.1027i		−	0.595591i	−0.954630	−	0.297796i	$-0.903749\pi$
$643$		−	15.1027i		−	0.595591i	0.954630	−	0.297796i	$-0.0962514\pi$
$644$	−1.95212	−	8.35748i	−0.0769241	−	0.329331i
$645$	−5.25819	+	6.34525i	−0.207041	+	0.249844i
$646$	−23.0881	−	14.8378i	−0.908390	−	0.583787i
$647$	44.7080	−	6.42803i	1.75765	−	0.252712i	0.813345	−	0.581781i	$-0.197644\pi$
$647$	44.7080	−	6.42803i	1.75765	−	0.252712i	0.944306	+	0.329069i	$0.106735\pi$
$648$	6.98296	−	3.18901i	0.274317	−	0.125276i
$649$	−53.1964	−	15.6199i	−2.08814	−	0.613134i
$650$	10.8082	+	2.66300i	0.423932	+	0.104452i
$651$	−17.2674	+	19.9277i	−0.676764	+	0.781027i
$652$	−5.14550	−	0.739811i	−0.201513	−	0.0289732i
$653$	3.03397	+	10.3328i	0.118729	+	0.404352i	0.997315	−	0.0732310i	$-0.0233310\pi$
$653$	3.03397	+	10.3328i	0.118729	+	0.404352i	−0.878586	+	0.477583i	$0.841513\pi$
$654$	−11.9061	−	13.7403i	−0.465564	−	0.537290i
$655$	−4.63570	+	38.1921i	−0.181132	+	1.49229i
$656$	−4.94714	+	3.17933i	−0.193153	+	0.124132i
$657$	−4.49203	+	3.89237i	−0.175251	+	0.151856i
$658$	−1.92259	−	6.54773i	−0.0749502	−	0.255257i
$659$	−4.33719	+	30.1658i	−0.168953	+	1.17509i	0.712101	+	0.702077i	$0.247744\pi$
$659$	−4.33719	+	30.1658i	−0.168953	+	1.17509i	−0.881054	+	0.473016i	$0.843165\pi$
$660$	20.3875	−	3.39086i	0.793584	−	0.131989i
$661$	−12.6470	+	27.6932i	−0.491913	+	1.07714i	0.487101	+	0.873346i	$0.338054\pi$
$661$	−12.6470	+	27.6932i	−0.491913	+	1.07714i	−0.979014	+	0.203794i	$0.934673\pi$
$662$	7.34426	−	25.0123i	0.285443	−	0.972129i
$663$	−11.8292	+	5.40219i	−0.459406	+	0.209804i
$664$	−2.18458	−	15.1941i	−0.0847782	−	0.589645i
$665$	−9.19626	−	28.9468i	−0.356616	−	1.12251i
$666$	1.62470			0.0629558
$667$	0.955199	+	10.9943i	0.0369854	+	0.425702i
$668$			2.87747i			0.111333i
$669$	−14.8140	−	9.52036i	−0.572741	−	0.368078i
$670$	7.08360	+	4.33507i	0.273663	+	0.167478i
$671$	−12.0453	−	26.3755i	−0.465004	−	1.01822i
$672$	−0.814475	+	2.77385i	−0.0314190	+	0.107003i
$673$	2.44556	+	1.11685i	0.0942695	+	0.0430514i	0.461992	−	0.886884i	$-0.347135\pi$
$673$	2.44556	+	1.11685i	0.0942695	+	0.0430514i	−0.367722	+	0.929936i	$0.619862\pi$
$674$	13.3341	−	15.3884i	0.513612	−	0.592740i
$675$	1.20518	+	27.3579i	0.0463874	+	1.05301i
$676$	7.71783	−	2.26616i	0.296840	−	0.0871599i
$677$	−1.34462	+	1.16512i	−0.0516779	+	0.0447791i	−0.680317	−	0.732918i	$-0.738158\pi$
$677$	−1.34462	+	1.16512i	−0.0516779	+	0.0447791i	0.628639	+	0.777697i	$0.283612\pi$
$678$	−2.76297	−	4.29926i	−0.106111	−	0.165112i
$679$	17.6188	−	11.3229i	0.676148	−	0.434534i
$680$	−8.08338	+	0.177960i	−0.309984	+	0.00682444i
$681$	−0.151103	+	0.0443678i	−0.00579028	+	0.00170018i
$682$	−51.6543	−	7.42677i	−1.97795	−	0.284386i
$683$	−8.44314	−	7.31602i	−0.323068	−	0.279940i	0.478193	−	0.878255i	$-0.341292\pi$
$683$	−8.44314	−	7.31602i	−0.323068	−	0.279940i	−0.801261	+	0.598315i	$0.795837\pi$
$684$	1.23070	−	2.69485i	0.0470568	−	0.103040i
$685$	−0.241150	−	0.357675i	−0.00921387	−	0.0136661i
$686$	−8.02696	−	17.5766i	−0.306471	−	0.671077i
$687$	−18.1033	+	2.60287i	−0.690685	+	0.0993055i
$688$	1.23339	−	1.91919i	0.0470225	−	0.0731684i
$689$	8.74530			0.333170
$690$	−10.8914	−	13.4719i	−0.414627	−	0.512865i
$691$	−12.7801			−0.486178			−0.243089	−	0.970004i	$-0.578161\pi$
$691$	−12.7801			−0.486178			−0.243089	+	0.970004i	$0.578161\pi$
$692$	6.07296	−	9.44972i	0.230859	−	0.359224i
$693$	3.95581	−	0.568760i	0.150269	−	0.0216054i
$694$	−8.51886	−	18.6537i	−0.323371	−	0.708085i
$695$	−2.60160	+	1.75404i	−0.0986841	+	0.0665344i
$696$	1.54424	−	3.38141i	0.0585341	−	0.128172i
$697$	16.0701	+	13.9248i	0.608698	+	0.527440i
$698$	20.5403	+	2.95325i	0.777463	+	0.111782i
$699$	10.9223	−	3.20708i	0.413119	−	0.121303i
$700$	−7.01363	−	5.55629i	−0.265090	−	0.210008i
$701$	2.81002	−	1.80589i	0.106133	−	0.0682076i	−0.486498	−	0.873682i	$-0.661726\pi$
$701$	2.81002	−	1.80589i	0.106133	−	0.0682076i	0.592631	+	0.805474i	$0.298089\pi$
$702$	−6.59210	−	10.2575i	−0.248803	−	0.387145i
$703$	−23.8769	+	20.6895i	−0.900536	+	0.780319i
$704$	−5.48976	+	1.61194i	−0.206903	+	0.0607522i
$705$	−9.24742	−	10.2091i	−0.348278	−	0.384498i
$706$	−8.19911	+	9.46228i	−0.308578	+	0.356117i
$707$	5.53611	+	2.52826i	0.208207	+	0.0950850i
$708$	4.41021	−	15.0198i	0.165746	−	0.564479i
$709$	7.05203	+	15.4418i	0.264845	+	0.579929i	0.994600	−	0.103779i	$-0.0330935\pi$
$709$	7.05203	+	15.4418i	0.264845	+	0.579929i	−0.729756	+	0.683708i	$0.760366\pi$
$710$	−0.909158	+	1.48558i	−0.0341201	+	0.0557530i
$711$	3.48331	+	2.23858i	0.130634	+	0.0839535i
$712$		−	0.232856i		−	0.00872664i
$713$	15.9101	+	40.7463i	0.595840	+	1.52596i
$714$	10.4533			0.391205
$715$	−8.62400	−	27.1455i	−0.322519	−	1.01518i
$716$	−0.371898	−	2.58661i	−0.0138985	−	0.0966662i
$717$	−22.9067	+	10.4611i	−0.855465	+	0.390678i
$718$	−2.87598	+	9.79469i	−0.107331	+	0.365534i
$719$	3.97812	−	8.71088i	0.148359	−	0.324861i	−0.820833	−	0.571169i	$-0.806490\pi$
$719$	3.97812	−	8.71088i	0.148359	−	0.324861i	0.969192	+	0.246308i	$0.0792174\pi$
$720$	−0.143194	−	0.860954i	−0.00533653	−	0.0320859i
$721$	4.69963	−	32.6866i	0.175023	−	1.21731i
$722$	10.8776	+	37.0459i	0.404824	+	1.37870i
$723$	5.16164	−	4.47258i	0.191963	−	0.166337i
$724$	−21.5946	+	13.8780i	−0.802557	+	0.515772i
$725$	7.90992	+	8.35531i	0.293767	+	0.310308i
$726$	−22.9942	−	26.5367i	−0.853395	−	0.984871i
$727$	−3.40755	−	11.6050i	−0.126379	−	0.430407i	0.871858	−	0.489758i	$-0.162915\pi$
$727$	−3.40755	−	11.6050i	−0.126379	−	0.430407i	−0.998237	+	0.0593512i	$0.981097\pi$
$728$	3.94352	+	0.566993i	0.146157	+	0.0210142i
$729$	19.3441	−	22.3243i	0.716450	−	0.826827i
$730$	−14.8236	−	30.6550i	−0.548646	−	1.13459i
$731$	−7.91491	−	2.32403i	−0.292744	−	0.0859573i
$732$	7.44703	−	3.40095i	0.275250	−	0.125703i
$733$	−21.6326	+	3.11030i	−0.799019	+	0.114882i	−0.529717	−	0.848174i	$-0.677702\pi$
$733$	−21.6326	+	3.11030i	−0.799019	+	0.114882i	−0.269302	+	0.963056i	$0.586793\pi$
$734$	−5.50902	−	3.54043i	−0.203342	−	0.130680i
$735$	−10.5621	−	8.75265i	−0.389591	−	0.322846i
$736$	3.44253	+	3.33901i	0.126893	+	0.123078i
$737$		−	21.2499i		−	0.782751i
$738$	−1.24096	+	1.93096i	−0.0456802	+	0.0710798i
$739$	3.59844	+	25.0277i	0.132371	+	0.920659i	0.942452	+	0.334342i	$0.108514\pi$
$739$	3.59844	+	25.0277i	0.132371	+	0.920659i	−0.810081	+	0.586318i	$0.800577\pi$
$740$	−2.42505	+	8.98612i	−0.0891467	+	0.330336i
$741$	26.1918	+	7.69059i	0.962178	+	0.282521i
$742$	−6.39450	−	2.92027i	−0.234749	−	0.107206i
$743$	32.5133	+	28.1729i	1.19280	+	1.03356i	0.998616	+	0.0525972i	$0.0167499\pi$
$743$	32.5133	+	28.1729i	1.19280	+	1.03356i	0.194180	+	0.980966i	$0.437796\pi$
$744$	2.09692	−	14.5844i	0.0768769	−	0.534690i
$745$	−3.17242	+	7.37185i	−0.116228	+	0.270084i
$746$	8.55108	+	9.86848i	0.313077	+	0.361311i
$747$	−3.23927	−	5.04040i	−0.118519	−	0.184419i
$748$	11.1849	+	17.4041i	0.408962	+	0.636357i
$749$	0.640332	+	0.738982i	0.0233972	+	0.0270018i
$750$	−17.6277	−	3.93381i	−0.643672	−	0.143643i
$751$	2.15806	−	15.0096i	0.0787487	−	0.547709i	−0.911809	−	0.410614i	$-0.865314\pi$
$751$	2.15806	−	15.0096i	0.0787487	−	0.547709i	0.990558	−	0.137095i	$-0.0437765\pi$
$752$	2.88191	+	2.49719i	0.105092	+	0.0910630i
$753$	−21.7558	−	9.93554i	−0.792826	−	0.362071i
$754$	−4.91542	−	1.44330i	−0.179009	−	0.0525618i
$755$	−2.45534	−	0.662614i	−0.0893590	−	0.0241150i
$756$	1.39486	+	9.70148i	0.0507306	+	0.352839i
$757$	25.8293	−	40.1912i	0.938783	−	1.46077i	0.0519685	−	0.998649i	$-0.483450\pi$
$757$	25.8293	−	40.1912i	0.938783	−	1.46077i	0.886814	−	0.462126i	$-0.152913\pi$
$758$		−	29.2735i		−	1.06326i
$759$	−14.8550	+	41.7638i	−0.539203	+	1.51593i
$760$	13.0681	+	10.8293i	0.474030	+	0.392820i
$761$	13.9235	+	8.94812i	0.504728	+	0.324369i	0.768105	−	0.640324i	$-0.221200\pi$
$761$	13.9235	+	8.94812i	0.504728	+	0.324369i	−0.263377	+	0.964693i	$0.584836\pi$
$762$	8.33046	−	1.19774i	0.301781	−	0.0433895i
$763$	18.3206	−	8.36672i	0.663249	−	0.302896i
$764$	−10.2265	−	3.00277i	−0.369981	−	0.108636i
$765$	−2.84113	+	1.37386i	−0.102721	+	0.0496721i
$766$	21.2249	−	24.4948i	0.766885	−	0.885033i
$767$	−21.3534	−	3.07015i	−0.771026	−	0.110857i
$768$	−0.455125	−	1.55001i	−0.0164229	−	0.0559313i
$769$	9.67951	+	11.1707i	0.349052	+	0.402827i	0.902942	−	0.429762i	$-0.141403\pi$
$769$	9.67951	+	11.1707i	0.349052	+	0.402827i	−0.553890	+	0.832590i	$0.686857\pi$
$770$	−2.75873	+	22.7283i	−0.0994178	+	0.819072i
$771$	25.7833	−	16.5699i	0.928564	−	0.596752i
$772$	3.19552	−	2.76894i	0.115009	−	0.0996562i
$773$	−7.38315	−	25.1447i	−0.265553	−	0.904392i	−0.979031	−	0.203713i	$-0.934699\pi$
$773$	−7.38315	−	25.1447i	−0.265553	−	0.904392i	0.713477	−	0.700678i	$-0.247119\pi$
$774$	0.126725	−	0.881390i	0.00455502	−	0.0316809i
$775$	39.4129	+	22.9434i	1.41575	+	0.824150i
$776$	−4.86167	+	10.6456i	−0.174524	+	0.382154i
$777$	3.39024	−	11.5461i	0.121624	−	0.414213i
$778$	−13.2368	+	6.04503i	−0.474561	+	0.216725i
$779$	−6.35222	−	44.1807i	−0.227592	−	1.58294i
$780$	7.66443	−	2.43495i	0.274430	−	0.0871854i
$781$	4.45657			0.159469
$782$	8.07745	−	15.3450i	0.288849	−	0.548737i
$783$		−	12.6030i		−	0.450393i
$784$	3.19463	+	2.05307i	0.114094	+	0.0733238i
$785$	−13.1551	+	21.4956i	−0.469524	+	0.767212i
$786$	11.5462	+	25.2827i	0.411840	+	0.901804i
$787$	1.95744	−	6.66642i	0.0697751	−	0.237632i	−0.917220	−	0.398380i	$-0.869572\pi$
$787$	1.95744	−	6.66642i	0.0697751	−	0.237632i	0.986995	+	0.160748i	$0.0513906\pi$
$788$	−6.55293	−	2.99262i	−0.233438	−	0.106608i
$789$	−21.4425	+	24.7459i	−0.763372	+	0.880979i
$790$	−17.5807	+	15.9246i	−0.625495	+	0.566573i
$791$	5.43203	−	1.59499i	0.193141	−	0.0567112i
$792$	−1.68776	+	1.46245i	−0.0599718	+	0.0519659i
$793$	−6.09977	−	9.49143i	−0.216609	−	0.337051i
$794$	−21.3134	+	13.6973i	−0.756383	+	0.486098i
$795$	−14.1862	+	0.312317i	−0.503134	+	0.0110767i
$796$	20.9533	−	6.15244i	0.742670	−	0.218068i
$797$	−25.5164	−	3.66870i	−0.903837	−	0.129952i	−0.325302	−	0.945610i	$-0.605466\pi$
$797$	−25.5164	−	3.66870i	−0.903837	−	0.129952i	−0.578534	+	0.815658i	$0.696375\pi$
$798$	−16.5831	−	14.3694i	−0.587037	−	0.508670i
$799$	5.72793	−	12.5424i	0.202640	−	0.443719i
$800$	4.97563	+	0.493076i	0.175915	+	0.0174329i
$801$	−0.0377563	−	0.0826748i	−0.00133405	−	0.00292117i
$802$	36.8165	−	5.29341i	1.30004	−	0.186917i
$803$	−47.1048	+	73.2965i	−1.66229	+	2.58658i
$804$	5.99984			0.211598
$805$	17.7185	−	7.37197i	0.624495	−	0.259828i
$806$	−20.3058			−0.715240
$807$	−15.6784	+	24.3960i	−0.551905	+	0.858781i
$808$	−3.36627	+	0.483997i	−0.118425	+	0.0170270i
$809$	6.60456	+	14.4620i	0.232204	+	0.508456i	0.989485	−	0.144633i	$-0.0462001\pi$
$809$	6.60456	+	14.4620i	0.232204	+	0.508456i	−0.757281	+	0.653089i	$0.773473\pi$
$810$	9.59602	+	14.2329i	0.337170	+	0.500092i
$811$	10.2065	−	22.3491i	0.358398	−	0.784783i	−0.641447	−	0.767168i	$-0.721665\pi$
$811$	10.2065	−	22.3491i	0.358398	−	0.784783i	0.999845	−	0.0176149i	$-0.00560730\pi$
$812$	3.11217	+	2.69671i	0.109216	+	0.0946359i
$813$	30.8701	+	4.43845i	1.08266	+	0.155663i
$814$	22.8510	−	6.70967i	0.800928	−	0.235174i
$815$	−0.255846	−	11.6212i	−0.00896189	−	0.407072i
$816$	−4.91399	+	3.15803i	−0.172024	+	0.110553i
$817$	9.36155	+	14.5669i	0.327519	+	0.509630i
$818$	−23.1703	+	20.0771i	−0.810129	+	0.701981i
$819$	1.49207	−	0.438112i	0.0521372	−	0.0153089i
$820$	−8.82779	−	9.74585i	−0.308280	−	0.340340i
$821$	12.4515	−	14.3698i	0.434561	−	0.501511i	−0.495656	−	0.868519i	$-0.665072\pi$
$821$	12.4515	−	14.3698i	0.434561	−	0.501511i	0.930218	+	0.367008i	$0.119618\pi$
$822$	−0.283485	−	0.129463i	−0.00988767	−	0.00451555i
$823$	−5.17918	+	17.6387i	−0.180535	+	0.614846i	0.818643	+	0.574303i	$0.194727\pi$
$823$	−5.17918	+	17.6387i	−0.180535	+	0.614846i	−0.999178	+	0.0405427i	$0.987091\pi$
$824$	7.66565	+	16.7854i	0.267045	+	0.584748i
$825$	14.9589	+	43.7262i	0.520802	+	1.52235i
$826$	14.5882	+	9.37528i	0.507589	+	0.326208i
$827$		−	52.0462i		−	1.80982i	−0.425598	−	0.904912i	$-0.639936\pi$
$827$		−	52.0462i		−	1.80982i	0.425598	−	0.904912i	$-0.360064\pi$
$828$	1.76366	+	0.627319i	0.0612915	+	0.0218008i
$829$	−17.0662			−0.592733			−0.296367	−	0.955074i	$-0.595775\pi$
$829$	−17.0662			−0.592733			−0.296367	+	0.955074i	$0.595775\pi$
$830$	32.7132	−	10.3928i	1.13549	−	0.360741i
$831$	5.46717	+	38.0250i	0.189654	+	1.31907i
$832$	−2.02510	+	0.924833i	−0.0702077	+	0.0320628i
$833$	3.86852	−	13.1750i	0.134036	−	0.456485i
$834$	−0.941667	+	2.06196i	−0.0326073	+	0.0714000i
$835$	−6.34704	+	1.05564i	−0.219648	+	0.0365320i
$836$	6.18031	−	42.9850i	0.213750	−	1.48667i
$837$	−14.0737	−	47.9308i	−0.486460	−	1.65673i
$838$	12.2355	−	10.6021i	0.422668	−	0.366244i
$839$	−19.6896	+	12.6537i	−0.679759	+	0.436855i	−0.834432	−	0.551111i	$-0.814204\pi$
$839$	−19.6896	+	12.6537i	−0.679759	+	0.436855i	0.154673	+	0.987966i	$0.450568\pi$
$840$	−6.41726	−	0.778918i	−0.221417	−	0.0268752i
$841$	15.5234	+	17.9150i	0.535289	+	0.617757i
$842$	4.99504	+	17.0116i	0.172141	+	0.586257i
$843$	−5.82404	−	0.837371i	−0.200591	−	0.0288406i
$844$	7.26382	−	8.38289i	0.250031	−	0.288551i
$845$	7.83001	+	16.1924i	0.269361	+	0.557034i
$846$	1.42812	+	0.419333i	0.0490997	+	0.0144170i
$847$	35.3825	−	16.1586i	1.21576	−	0.555218i
$848$	3.88822	−	0.559042i	0.133522	−	0.0191976i
$849$	−7.48703	−	4.81162i	−0.256954	−	0.165134i
$850$	−3.35804	−	17.7648i	−0.115180	−	0.609327i
$851$	−14.3295	−	13.8986i	−0.491208	−	0.476437i
$852$			1.25830i			0.0431085i
$853$	2.52524	−	3.92934i	0.0864624	−	0.134538i	−0.795328	−	0.606179i	$-0.792702\pi$
$853$	2.52524	−	3.92934i	0.0864624	−	0.134538i	0.881791	+	0.471641i	$0.156338\pi$
$854$	1.29069	+	8.97693i	0.0441664	+	0.307184i
$855$	6.39571	+	1.72599i	0.218729	+	0.0590275i
$856$	−0.524265	−	0.153938i	−0.0179190	−	0.00526150i
$857$	−12.2604	−	5.59914i	−0.418808	−	0.191263i	0.194854	−	0.980832i	$-0.437577\pi$
$857$	−12.2604	−	5.59914i	−0.418808	−	0.191263i	−0.613662	+	0.789569i	$0.710304\pi$
$858$	−15.5512	−	13.4752i	−0.530909	−	0.460036i
$859$	1.06688	−	7.42035i	0.0364016	−	0.253179i	−0.963492	−	0.267736i	$-0.913725\pi$
$859$	1.06688	−	7.42035i	0.0364016	−	0.253179i	0.999894	+	0.0145567i	$0.00463370\pi$
$860$	4.68577	+	2.01649i	0.159783	+	0.0687616i
$861$	11.1331	+	12.8483i	0.379415	+	0.437869i
$862$	−3.69098	−	5.74328i	−0.125715	−	0.195617i
$863$	19.1561	+	29.8075i	0.652083	+	1.01466i	0.997103	+	0.0760652i	$0.0242357\pi$
$863$	19.1561	+	29.8075i	0.652083	+	1.01466i	−0.345020	+	0.938595i	$0.612128\pi$
$864$	−3.58660	−	4.13916i	−0.122019	−	0.140817i
$865$	23.0718	+	9.92879i	0.784466	+	0.337589i
$866$	−5.53543	+	38.4998i	−0.188102	+	1.30828i
$867$	−4.79248	−	4.15271i	−0.162761	−	0.141033i
$868$	14.8474	+	6.78059i	0.503954	+	0.230148i
$869$	58.2368	+	17.0999i	1.97555	+	0.580074i
$870$	8.02512	+	2.16571i	0.272077	+	0.0734245i
$871$	−1.17673	−	8.18434i	−0.0398720	−	0.277316i
$872$	−6.08464	+	9.46789i	−0.206052	+	0.320623i
$873$			4.56797i			0.154602i
$874$	−33.9077	+	13.2399i	−1.14694	+	0.447846i
$875$	9.68283	−	17.5088i	0.327339	−	0.591907i
$876$	−20.6950	−	13.2999i	−0.699219	−	0.449361i
$877$	6.31801	−	0.908393i	0.213344	−	0.0306743i	−0.0348139	−	0.999394i	$-0.511084\pi$
$877$	6.31801	−	0.908393i	0.213344	−	0.0306743i	0.248158	+	0.968720i	$0.420175\pi$
$878$	−11.5999	+	5.29752i	−0.391479	+	0.178783i
$879$	−2.14121	−	0.628715i	−0.0722211	−	0.0212060i
$880$	−5.56956	−	11.5178i	−0.187750	−	0.388264i
$881$	−23.5159	+	27.1388i	−0.792272	+	0.914330i	−0.997931	−	0.0642934i	$-0.979521\pi$
$881$	−23.5159	+	27.1388i	−0.792272	+	0.914330i	0.205659	+	0.978624i	$0.434066\pi$
$882$	1.46714	+	0.210943i	0.0494011	+	0.00710281i
$883$	5.28319	+	17.9929i	0.177794	+	0.605509i	0.999373	+	0.0354147i	$0.0112752\pi$
$883$	5.28319	+	17.9929i	0.177794	+	0.605509i	−0.821579	+	0.570094i	$0.806907\pi$
$884$	5.27161	+	6.08376i	0.177303	+	0.204619i
$885$	34.7481	+	4.21768i	1.16805	+	0.141776i
$886$	−9.47200	+	6.08728i	−0.318218	+	0.204506i
$887$	−37.0965	+	32.1443i	−1.24558	+	1.07930i	−0.251817	+	0.967775i	$0.581028\pi$
$887$	−37.0965	+	32.1443i	−1.24558	+	1.07930i	−0.993762	+	0.111525i	$0.964426\pi$
$888$	1.89445	+	6.45190i	0.0635736	+	0.216512i
$889$	−1.32683	+	9.22831i	−0.0445005	+	0.309508i
$890$	0.513626	−	0.0854264i	0.0172168	−	0.00286350i
$891$	18.2460	−	39.9532i	0.611264	−	1.33848i
$892$	−3.07106	+	10.4591i	−0.102827	+	0.350195i
$893$	−26.3279	+	12.0235i	−0.881029	+	0.402352i
$894$	0.825145	+	5.73901i	0.0275970	+	0.191941i
$895$	5.56903	−	1.76926i	0.186152	−	0.0591397i
$896$	1.78956			0.0597851
$897$	−3.40866	+	16.9078i	−0.113812	+	0.564536i
$898$			11.1680i			0.372680i
$899$	−17.6564	−	11.3471i	−0.588875	−	0.378447i
$900$	1.84653	−	0.631706i	0.0615511	−	0.0210569i
$901$	−5.90051	−	12.9203i	−0.196575	−	0.430438i
$902$	−9.47929	+	32.2835i	−0.315626	+	1.07492i
$903$	−5.99925	−	2.73977i	−0.199643	−	0.0911737i
$904$	−2.07168	+	2.39084i	−0.0689030	+	0.0795183i
$905$	−38.5340	−	42.5414i	−1.28091	−	1.41412i
$906$	−1.76290	+	0.517633i	−0.0585684	+	0.0171972i
$907$	15.3449	−	13.2964i	0.509519	−	0.441501i	−0.361772	−	0.932266i	$-0.617828\pi$
$907$	15.3449	−	13.2964i	0.509519	−	0.441501i	0.871292	+	0.490765i	$0.163283\pi$
$908$	0.0527043	+	0.0820095i	0.00174905	+	0.00272158i
$909$	−1.11671	+	0.717665i	−0.0370389	+	0.0238034i
$910$	0.196081	+	8.90651i	0.00650002	+	0.295248i
$911$	−29.9951	+	8.80737i	−0.993783	+	0.291801i	−0.737903	−	0.674907i	$-0.764184\pi$
$911$	−29.9951	+	8.80737i	−0.993783	+	0.291801i	−0.255881	+	0.966708i	$0.582365\pi$
$912$	12.1366	+	1.74499i	0.401885	+	0.0577823i
$913$	−66.3754	−	57.5146i	−2.19671	−	1.90346i
$914$	15.2307	−	33.3505i	0.503785	−	1.10314i
$915$	10.2337	+	15.1787i	0.338317	+	0.501794i
$916$	4.70316	+	10.2985i	0.155397	+	0.340272i
$917$	−30.4767	+	4.38189i	−1.00643	+	0.144703i
$918$	−10.7067	+	16.6600i	−0.353375	+	0.549862i
$919$	−29.3249			−0.967341			−0.483670	−	0.875250i	$-0.660697\pi$
$919$	−29.3249			−0.967341			−0.483670	+	0.875250i	$0.660697\pi$
$920$	−6.10214	+	8.81838i	−0.201182	+	0.290733i
$921$	7.98748			0.263197
$922$	18.2051	−	28.3276i	0.599552	−	0.932921i
$923$	1.71643	−	0.246786i	0.0564971	−	0.00812305i
$924$	6.87123	+	15.0459i	0.226047	+	0.494973i
$925$	−20.7110	−	2.05242i	−0.680972	−	0.0674832i
$926$	−16.1616	+	35.3890i	−0.531104	+	1.16296i
$927$	5.44333	+	4.71667i	0.178782	+	0.154916i
$928$	−2.27769	−	0.327483i	−0.0747689	−	0.0107501i
$929$	47.3569	−	13.9052i	1.55373	−	0.456216i	0.611516	−	0.791232i	$-0.290560\pi$
$929$	47.3569	−	13.9052i	1.55373	−	0.456216i	0.942213	+	0.335016i	$0.108742\pi$
$930$	32.9391	−	0.725170i	1.08012	−	0.0237793i
$931$	−24.2476	+	15.5830i	−0.794684	+	0.510712i
$932$	−3.80967	−	5.92796i	−0.124790	−	0.194177i
$933$	8.05274	−	6.97774i	0.263635	−	0.228441i
$934$	3.02250	−	0.887487i	0.0988993	−	0.0290395i
$935$	−34.2861	+	31.0563i	−1.12127	+	1.01565i
$936$	−0.569050	+	0.656718i	−0.0186000	+	0.0214655i
$937$	−6.19564	−	2.82945i	−0.202403	−	0.0924342i	0.311635	−	0.950202i	$-0.399123\pi$
$937$	−6.19564	−	2.82945i	−0.202403	−	0.0924342i	−0.514037	+	0.857768i	$0.671851\pi$
$938$	−1.87253	+	6.37726i	−0.0611404	+	0.208225i
$939$	13.8846	+	30.4030i	0.453107	+	0.992166i
$940$	−4.45094	+	7.27294i	−0.145174	+	0.237217i
$941$	−15.7059	−	10.0936i	−0.511999	−	0.329042i	0.259001	−	0.965877i	$-0.416607\pi$
$941$	−15.7059	−	10.0936i	−0.511999	−	0.329042i	−0.771000	+	0.636835i	$0.780243\pi$
$942$			18.2069i			0.593213i
$943$	27.4635	−	6.41484i	0.894334	−	0.208896i
$944$	−9.69011			−0.315386
$945$	−20.8875	+	6.63586i	−0.679470	+	0.215865i
$946$	−1.85760	−	12.9199i	−0.0603958	−	0.420062i
$947$	−21.6964	+	9.90842i	−0.705039	+	0.321980i	−0.735471	−	0.677557i	$-0.763039\pi$
$947$	−21.6964	+	9.90842i	−0.705039	+	0.321980i	0.0304322	+	0.999537i	$0.490312\pi$
$948$	−4.82809	+	16.4430i	−0.156809	+	0.534042i
$949$	−14.0834	+	30.8383i	−0.457167	+	1.00106i
$950$	−19.0927	+	32.7981i	−0.619449	+	1.06411i
$951$	−3.18260	+	22.1355i	−0.103203	+	0.717792i
$952$	−1.82304	−	6.20872i	−0.0590852	−	0.201226i
$953$	−38.6928	+	33.5275i	−1.25338	+	1.08606i	−0.260686	+	0.965424i	$0.583949\pi$
$953$	−38.6928	+	33.5275i	−1.25338	+	1.08606i	−0.992696	+	0.120639i	$0.961506\pi$
$954$	1.28986	−	0.828940i	0.0417606	−	0.0268379i
$955$	2.87168	−	23.6589i	0.0929253	−	0.765582i
$956$	10.2082	+	11.7809i	0.330158	+	0.381023i
$957$	−5.99212	−	20.4073i	−0.193698	−	0.659674i
$958$	18.8807	+	2.71464i	0.610008	+	0.0877059i
$959$	0.226082	−	0.260913i	0.00730057	−	0.00842531i
$960$	3.25200	−	1.57254i	0.104958	−	0.0507536i
$961$	−50.0769	−	14.7039i	−1.61538	−	0.474320i
$962$	8.42945	−	3.84960i	0.271776	−	0.124116i
$963$	−0.211099	+	0.0303515i	−0.00680258	+	0.000978063i
$964$	−3.55666	−	2.28573i	−0.114552	−	0.0736184i
$965$	7.27996	+	6.03276i	0.234350	+	0.194201i
$966$	8.13832	−	11.2246i	0.261846	−	0.361147i
$967$		−	32.8474i		−	1.05630i	−0.849151	−	0.528151i	$-0.822886\pi$
$967$		−	32.8474i		−	1.05630i	0.849151	−	0.528151i	$-0.177114\pi$
$968$	−11.7513	+	18.2853i	−0.377700	+	0.587713i
$969$	−6.30965	−	43.8846i	−0.202695	−	1.40978i
$970$	−25.2652	−	6.81824i	−0.811217	−	0.218920i
$971$	−42.3892	−	12.4466i	−1.36033	−	0.399430i	−0.481453	−	0.876472i	$-0.659891\pi$
$971$	−42.3892	−	12.4466i	−1.36033	−	0.399430i	−0.878880	+	0.477042i	$0.841709\pi$
$972$	−3.66524	−	1.67386i	−0.117563	−	0.0536890i
$973$	−1.89778	−	1.64444i	−0.0608401	−	0.0527182i
$974$	−3.82448	+	26.5999i	−0.122544	+	0.852314i
$975$	8.18274	+	16.0126i	0.262058	+	0.512815i
$976$	−3.31874	−	3.83003i	−0.106230	−	0.122596i
$977$	4.18672	+	6.51466i	0.133945	+	0.208422i	0.901746	−	0.432265i	$-0.142286\pi$
$977$	4.18672	+	6.51466i	0.133945	+	0.208422i	−0.767801	+	0.640688i	$0.778649\pi$
$978$	−4.54018	−	7.06466i	−0.145179	−	0.225903i
$979$	−0.872464	−	1.00688i	−0.0278841	−	0.0321799i
$980$	−3.35659	+	7.79981i	−0.107222	+	0.249156i
$981$	−0.625168	+	4.34814i	−0.0199601	+	0.138825i
$982$	20.6189	+	17.8664i	0.657976	+	0.570139i
$983$	6.47106	+	2.95523i	0.206395	+	0.0942573i	0.515930	−	0.856631i	$-0.327446\pi$
$983$	6.47106	+	2.95523i	0.206395	+	0.0942573i	−0.309536	+	0.950888i	$0.600174\pi$
$984$	−9.11512	−	2.67644i	−0.290579	−	0.0853218i
$985$	4.19700	−	15.5521i	0.133727	−	0.495532i
$986$	1.18414	+	8.23585i	0.0377106	+	0.262283i
$987$	5.96007	−	9.27405i	0.189711	−	0.295196i
$988$		−	16.8978i		−	0.537589i
$989$	−8.65758	+	6.68958i	−0.275295	+	0.212716i
$990$	−3.84500	−	3.18628i	−0.122202	−	0.101267i
$991$	−28.4227	−	18.2662i	−0.902877	−	0.580244i	0.00476532	−	0.999989i	$-0.498483\pi$
$991$	−28.4227	−	18.2662i	−0.902877	−	0.580244i	−0.907642	+	0.419745i	$0.862120\pi$
$992$	−9.02807	+	1.29804i	−0.286642	+	0.0412128i
$993$	38.3063	−	17.4939i	1.21561	−	0.555152i
$994$	−1.33745	−	0.392711i	−0.0424213	−	0.0124560i
$995$	21.2579	+	43.9610i	0.673920	+	1.39366i
$996$	16.2390	−	18.7409i	0.514554	−	0.593827i
$997$	−14.6103	−	2.10065i	−0.462714	−	0.0665282i	−0.0929842	−	0.995668i	$-0.529641\pi$
$997$	−14.6103	−	2.10065i	−0.462714	−	0.0665282i	−0.369730	+	0.929139i	$0.620550\pi$
$998$	0.746400	+	2.54200i	0.0236269	+	0.0804657i
$999$	14.9292	+	17.2292i	0.472338	+	0.545107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.209.10	yes	120
5.4	even	2	inner	230.2.j.a.209.3	✓	120
23.12	even	11	inner	230.2.j.a.219.3	yes	120
115.104	even	22	inner	230.2.j.a.219.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.3	✓	120	5.4	even	2	inner
230.2.j.a.209.10	yes	120	1.1	even	1	trivial
230.2.j.a.219.3	yes	120	23.12	even	11	inner
230.2.j.a.219.10	yes	120	115.104	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(1.59901 - 0.229903i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.85404 - 1.25002i) q^{5} +(0.671082 - 1.46947i) q^{6} +(1.35246 + 1.17191i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-0.374509 + 0.109966i) q^{9} +(-0.0492162 - 2.23553i) q^{10} +(-4.81325 + 3.09329i) q^{11} +(-0.873379 - 1.35900i) q^{12} +(-1.68251 + 1.45791i) q^{13} +(1.71707 - 0.504178i) q^{14} +(2.67723 - 2.42504i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(3.28912 + 1.50209i) q^{17} +(-0.109966 + 0.374509i) q^{18} +(-3.15305 - 6.90421i) q^{19} +(-1.90725 - 1.16721i) q^{20} +(2.43202 + 1.56297i) q^{21} +5.72152i q^{22} +(4.17363 - 2.36237i) q^{23} -1.61545 q^{24} +(1.87490 - 4.63516i) q^{25} +(0.316833 + 2.20363i) q^{26} +(-4.98196 + 2.27518i) q^{27} +(0.504178 - 1.71707i) q^{28} +(-0.955917 + 2.09317i) q^{29} +(-0.592650 - 3.56331i) q^{30} +(-1.29804 + 9.02807i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-6.98527 + 6.05277i) q^{33} +(3.04187 - 1.95489i) q^{34} +(3.97243 + 0.482168i) q^{35} +(0.255605 + 0.294984i) q^{36} +(-1.17271 - 3.99387i) q^{37} +(-7.51286 - 1.08019i) q^{38} +(-2.35518 + 2.71802i) q^{39} +(-2.01306 + 0.973440i) q^{40} +(5.64246 + 1.65678i) q^{41} +(2.62970 - 1.20094i) q^{42} +(-2.25812 + 0.324669i) q^{43} +(4.81325 + 3.09329i) q^{44} +(-0.556894 + 0.672024i) q^{45} +(0.269079 - 4.78828i) q^{46} -3.81331i q^{47} +(-0.873379 + 1.35900i) q^{48} +(-0.540436 - 3.75881i) q^{49} +(-2.88570 - 4.08323i) q^{50} +(5.60466 + 1.64568i) q^{51} +(2.02510 + 0.924833i) q^{52} +(-2.96874 - 2.57243i) q^{53} +(-0.779443 + 5.42115i) q^{54} +(-5.05727 + 11.7517i) q^{55} +(-1.17191 - 1.35246i) q^{56} +(-6.62904 - 10.3150i) q^{57} +(1.24408 + 1.93582i) q^{58} +(6.34567 + 7.32330i) q^{59} +(-3.31806 - 1.42790i) q^{60} +(-0.721231 + 5.01627i) q^{61} +(6.89313 + 5.97293i) q^{62} +(-0.635379 - 0.290168i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-1.29703 + 4.80619i) q^{65} +(1.31539 + 9.14876i) q^{66} +(-2.00796 + 3.12444i) q^{67} -3.61588i q^{68} +(6.13055 - 4.73698i) q^{69} +(2.55328 - 3.08114i) q^{70} +(-0.655263 - 0.421112i) q^{71} +(0.386347 - 0.0555483i) q^{72} +(13.8519 - 6.32596i) q^{73} +(-3.99387 - 1.17271i) q^{74} +(1.93234 - 7.84271i) q^{75} +(-4.97047 + 5.73623i) q^{76} +(-10.1348 - 1.45716i) q^{77} +(1.01324 + 3.45077i) q^{78} +(-6.94694 - 8.01719i) q^{79} +(-0.269433 + 2.21978i) q^{80} +(-6.45804 + 4.15033i) q^{81} +(4.44432 - 3.85102i) q^{82} +(4.32469 + 14.7285i) q^{83} +(0.411425 - 2.86152i) q^{84} +(7.97578 - 1.32653i) q^{85} +(-0.947705 + 2.07518i) q^{86} +(-1.04729 + 3.56676i) q^{87} +(5.20448 - 2.37681i) q^{88} +(0.0331388 + 0.230486i) q^{89} +(0.264263 + 0.831812i) q^{90} -3.98408 q^{91} +(-3.88268 - 2.81510i) q^{92} +14.7344i q^{93} +(-3.20796 - 2.06163i) q^{94} +(-14.4763 - 8.85928i) q^{95} +(0.671082 + 1.46947i) q^{96} +(3.29716 - 11.2291i) q^{97} +(-3.45430 - 1.57752i) q^{98} +(1.46245 - 1.68776i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41}+ \cdots + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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