LMFDB - Embedded newform 230.2.j.a.219.10

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			219.10
Character	$\chi$	$=$	230.219
Dual form			230.2.j.a.209.10

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{10}{11}\right)$

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	0.587486	−	0.809234i	$-0.300118\pi$
$3$	1.59901	+	0.229903i	0.923187	+	0.132734i	0.335701	+	0.941969i	$0.391027\pi$
$4$	−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	−0.360683	−	0.932689i	$-0.617456\pi$
$7$	1.35246	−	1.17191i	0.511182	−	0.442942i	0.871865	+	0.489747i	$0.162911\pi$
$8$	−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	−0.999172	−	0.0406829i	$-0.987047\pi$
$11$	−4.81325	−	3.09329i	−1.45125	−	0.932662i	−0.452078	−	0.891979i	$-0.649317\pi$
$12$	−0.873379	+	1.35900i	−0.252123	+	0.392311i
$13$	−1.68251	−	1.45791i	−0.466646	−	0.404351i	0.389548	−	0.921006i	$-0.372631\pi$
$13$	−1.68251	−	1.45791i	−0.466646	−	0.404351i	−0.856193	+	0.516656i	$0.827177\pi$
$14$	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	0.0255153	−	0.999674i	$-0.491877\pi$
$17$	3.28912	−	1.50209i	0.797728	−	0.364310i	0.772213	+	0.635364i	$0.219150\pi$
$18$	−0.109966	−	0.374509i	−0.0259192	−	0.0882726i
$19$	−3.15305	+	6.90421i	−0.723359	+	1.58393i	0.0857782	+	0.996314i	$0.472662\pi$
$19$	−3.15305	+	6.90421i	−0.723359	+	1.58393i	−0.809137	+	0.587620i	$0.800065\pi$
$20$	−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	0.799874	−	0.600169i	$-0.204900\pi$
$29$	−0.955917	−	2.09317i	−0.177509	−	0.388691i	−0.977383	+	0.211477i	$0.932173\pi$
$30$	−0.592650	+	3.56331i	−0.108203	+	0.650568i
$31$	−1.29804	−	9.02807i	−0.233135	−	1.62149i	−0.684405	−	0.729102i	$-0.739938\pi$
$31$	−1.29804	−	9.02807i	−0.233135	−	1.62149i	0.451270	−	0.892388i	$-0.350971\pi$
$32$	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	0.805186	+	0.593023i	$0.202066\pi$
$37$	−1.17271	+	3.99387i	−0.192792	+	0.656589i	−0.997978	+	0.0635660i	$0.979753\pi$
$38$	−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	0.190331	−	0.981720i	$-0.439044\pi$
$41$	5.64246	−	1.65678i	0.881205	−	0.258745i	0.690874	+	0.722975i	$0.257226\pi$
$42$	2.62970	+	1.20094i	0.405772	+	0.185310i
$43$	−2.25812	−	0.324669i	−0.344361	−	0.0495116i	−0.0320351	−	0.999487i	$-0.510199\pi$
$43$	−2.25812	−	0.324669i	−0.344361	−	0.0495116i	−0.312325	+	0.949975i	$0.601108\pi$
$44$	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	$0.0897093\pi$
$47$			3.81331i			0.556228i	−0.960548	+	0.278114i	$0.910291\pi$
$48$	−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	−0.834472	−	0.551051i	$-0.814227\pi$
$53$	−2.96874	+	2.57243i	−0.407788	+	0.353350i	0.426684	+	0.904401i	$0.359682\pi$
$54$	−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	−0.173369	−	0.984857i	$-0.555465\pi$
$59$	6.34567	−	7.32330i	0.826136	−	0.953412i	0.999505	+	0.0314447i	$0.0100108\pi$
$60$	−3.31806	+	1.42790i	−0.428359	+	0.184341i
$61$	−0.721231	−	5.01627i	−0.0923441	−	0.642267i	−0.982452	−	0.186517i	$-0.940280\pi$
$61$	−0.721231	−	5.01627i	−0.0923441	−	0.642267i	0.890108	−	0.455750i	$-0.150629\pi$
$62$	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	0.696662	−	0.717399i	$-0.254668\pi$
$67$	−2.00796	−	3.12444i	−0.245311	−	0.381712i	−0.941973	+	0.335688i	$0.891031\pi$
$68$			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	−0.578946	−	0.815366i	$-0.696536\pi$
$71$	−0.655263	+	0.421112i	−0.0777654	+	0.0499768i	0.501180	+	0.865343i	$0.332899\pi$
$72$	0.386347	+	0.0555483i	0.0455314	+	0.00654643i
$73$	13.8519	+	6.32596i	1.62125	+	0.740398i	0.999096	−	0.0425008i	$-0.0135325\pi$
$73$	13.8519	+	6.32596i	1.62125	+	0.740398i	0.622149	+	0.782899i	$0.286260\pi$
$74$	−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	−0.997223	−	0.0744702i	$-0.976273\pi$
$79$	−6.94694	+	8.01719i	−0.781591	+	0.902005i	0.215632	+	0.976475i	$0.430819\pi$
$80$	−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	−0.279588	−	0.960120i	$-0.590198\pi$
$83$	4.32469	−	14.7285i	0.474696	−	1.61667i	0.754285	−	0.656547i	$-0.227984\pi$
$84$	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	−0.987990	−	0.154520i	$-0.950617\pi$
$89$	0.0331388	−	0.230486i	0.00351271	−	0.0244314i	0.991502	+	0.130088i	$0.0415261\pi$
$90$	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	0.939169	+	0.343456i	$0.111598\pi$
$97$	3.29716	+	11.2291i	0.334776	+	1.14014i	−0.604393	+	0.796686i	$0.706584\pi$
$98$	−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	0.440017	−	0.897989i	$-0.354972\pi$
$101$	3.26313	+	0.958141i	0.324694	+	0.0953386i	−0.115324	+	0.993328i	$0.536791\pi$
$102$	4.41454	+	3.82522i	0.437104	+	0.378753i
$103$	−9.97644	+	15.5236i	−0.983008	+	1.52959i	−0.141081	+	0.989998i	$0.545058\pi$
$103$	−9.97644	+	15.5236i	−0.983008	+	1.52959i	−0.841927	+	0.539591i	$0.818579\pi$
$104$	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	−0.116123	−	0.993235i	$-0.537047\pi$
$107$	0.540837	−	0.0777606i	0.0522847	−	0.00751740i	0.168408	+	0.985717i	$0.446138\pi$
$108$	4.13916	−	3.58660i	0.398291	−	0.345121i
$109$	4.67529	+	10.2375i	0.447811	+	0.980570i	0.990098	+	0.140377i	$0.0448313\pi$
$109$	4.67529	+	10.2375i	0.447811	+	0.980570i	−0.542287	+	0.840193i	$0.682441\pi$
$110$	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	0.912336	−	0.409443i	$-0.134277\pi$
$113$	1.71034	+	2.66134i	0.160895	+	0.250358i	−0.751440	+	0.659801i	$0.770641\pi$
$114$	−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	−0.693505	−	0.720452i	$-0.743934\pi$
$127$	2.81661	−	4.38274i	0.249934	−	0.388905i	0.943439	+	0.331547i	$0.107571\pi$
$128$	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	−0.990696	−	0.136093i	$-0.956545\pi$
$131$	−11.2671	−	13.0030i	−0.984413	−	1.13607i	0.00628251	−	0.999980i	$-0.498000\pi$
$132$	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	$0.00262322\pi$
$137$			0.192917i			0.0164820i	−0.999966	+	0.00824100i	$0.997377\pi$
$138$	−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	0.411089	−	0.911595i	$-0.365149\pi$
$149$	−3.01935	−	1.94042i	−0.247355	−	0.158965i	−0.658444	+	0.752630i	$0.728785\pi$
$150$	−5.55300	+	5.86568i	−0.453401	+	0.478931i
$151$	−0.744802	+	0.859547i	−0.0606111	+	0.0699489i	−0.785245	−	0.619185i	$-0.787463\pi$
$151$	−0.744802	+	0.859547i	−0.0606111	+	0.0699489i	0.724634	+	0.689134i	$0.242009\pi$
$152$	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	−0.0380670	−	0.999275i	$-0.512120\pi$
$157$	−10.2520	−	4.68192i	−0.818197	−	0.373658i	−0.780130	+	0.625617i	$0.784847\pi$
$158$	−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	0.933702	−	0.358051i	$-0.116559\pi$
$163$	2.81047	+	4.37318i	0.220133	+	0.342534i	−0.713569	+	0.700585i	$0.752922\pi$
$164$	−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	−0.514104	−	0.857728i	$-0.671876\pi$
$167$	−2.61744	+	1.19535i	−0.202544	+	0.0924986i	0.311561	+	0.950226i	$0.399148\pi$
$168$	−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	−0.529841	−	0.848097i	$-0.677748\pi$
$173$	6.07296	−	9.44972i	0.461719	−	0.718449i	0.991560	+	0.129648i	$0.0413848\pi$
$174$	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	−0.186682	−	0.982420i	$-0.559773\pi$
$179$	2.50736	−	0.736226i	0.187409	−	0.0550281i	0.374090	+	0.927392i	$0.377955\pi$
$180$	0.842636	−	0.227399i	0.0628064	−	0.0169493i
$181$	−3.65316	+	25.4083i	−0.271537	+	1.88858i	0.160981	+	0.986958i	$0.448534\pi$
$181$	−3.65316	+	25.4083i	−0.271537	+	1.88858i	−0.432518	+	0.901625i	$0.642375\pi$
$182$	−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	0.949819	−	0.312800i	$-0.101267\pi$
$191$	6.97965	+	8.05494i	0.505030	+	0.582835i	−0.444789	+	0.895635i	$0.646722\pi$
$192$	1.59901	−	0.229903i	0.115398	−	0.0165918i
$193$	1.19125	−	4.05701i	0.0857477	−	0.292030i	−0.905444	−	0.424466i	$-0.860462\pi$
$193$	1.19125	−	4.05701i	0.0857477	−	0.292030i	0.991192	+	0.132436i	$0.0422800\pi$
$194$	−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	0.826877	−	0.562383i	$-0.190115\pi$
$197$	5.44437	+	4.71757i	0.387895	+	0.336113i	−0.438982	+	0.898496i	$0.644661\pi$
$198$	−0.629171	+	2.14276i	−0.0447133	+	0.152279i
$199$	−3.10785	−	21.6156i	−0.220310	−	1.53229i	−0.736868	−	0.676037i	$-0.763696\pi$
$199$	−3.10785	−	21.6156i	−0.220310	−	1.53229i	0.516558	−	0.856252i	$-0.327213\pi$
$200$	−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	−0.682111	−	0.731248i	$-0.738938\pi$
$211$	4.60785	−	10.0898i	0.317217	−	0.694609i	0.999329	+	0.0366394i	$0.0116653\pi$
$212$	−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	−0.885519	−	0.464604i	$-0.846197\pi$
$223$	−8.23813	+	7.13838i	−0.551666	+	0.478022i	0.333852	+	0.942625i	$0.391651\pi$
$224$	−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	0.139112	−	0.990277i	$-0.455575\pi$
$227$	−0.0964927	−	0.0138736i	−0.00640444	−	0.000920820i	−0.145516	+	0.989356i	$0.546484\pi$
$228$	−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	0.366941	−	0.930244i	$-0.380405\pi$
$233$	6.97486	+	1.00283i	0.456938	+	0.0656978i	0.0899973	+	0.995942i	$0.471314\pi$
$234$	−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	−0.240437	−	0.970665i	$-0.577291\pi$
$239$	−14.9570	−	4.39177i	−0.967487	−	0.284080i	−0.727050	+	0.686585i	$0.759109\pi$
$240$	0.0795063	−	3.61138i	0.00513211	−	0.233114i
$241$	3.55666	+	2.28573i	0.229105	+	0.147237i	0.650158	−	0.759799i	$-0.274703\pi$
$241$	3.55666	+	2.28573i	0.229105	+	0.147237i	−0.421053	+	0.907036i	$0.638339\pi$
$242$	−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	−0.871070	−	0.491160i	$-0.836573\pi$
$251$	−12.4550	+	8.00432i	−0.786151	+	0.505228i	0.0849190	+	0.996388i	$0.472937\pi$
$252$		−	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	0.873136	−	0.487476i	$-0.162082\pi$
$257$	17.2578	+	7.88135i	1.07651	+	0.491625i	0.203373	+	0.979101i	$0.434810\pi$
$258$	−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	0.0389594	−	0.999241i	$-0.487596\pi$
$263$	−15.3183	−	13.2734i	−0.944566	−	0.818471i	−0.983525	+	0.180770i	$0.942141\pi$
$264$	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	0.274157	−	0.961685i	$-0.411601\pi$
$269$	−11.7557	−	13.5668i	−0.716756	−	0.827180i	−0.990913	+	0.134505i	$0.957056\pi$
$270$	5.33143	−	11.0253i	0.324460	−	0.670980i
$271$	18.5238	−	5.43907i	1.12524	−	0.330400i	0.334404	−	0.942430i	$-0.391465\pi$
$271$	18.5238	−	5.43907i	1.12524	−	0.330400i	0.790834	+	0.612030i	$0.209647\pi$
$272$	−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	$-0.746694\pi$
$277$		−	23.7804i		−	1.42882i	0.699725	−	0.714412i	$-0.253306\pi$
$278$	−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	−0.384305	−	0.923206i	$-0.625559\pi$
$281$	−3.49475	+	1.02615i	−0.208479	+	0.0612150i	0.175825	+	0.984421i	$0.443741\pi$
$282$	−5.60352	+	2.55904i	−0.333685	+	0.152389i
$283$	−4.16358	+	3.60776i	−0.247499	+	0.214459i	−0.769771	−	0.638320i	$-0.779630\pi$
$283$	−4.16358	+	3.60776i	−0.247499	+	0.214459i	0.522272	+	0.852779i	$0.325084\pi$
$284$	−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	−0.451782	−	0.892129i	$-0.649211\pi$
$293$	−1.25658	+	0.573859i	−0.0734099	+	0.0335252i	0.378372	+	0.925654i	$0.376484\pi$
$294$	−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	−0.00123044	−	0.999999i	$-0.500392\pi$
$307$	4.89410	−	0.703666i	0.279321	−	0.0401603i	0.280552	+	0.959839i	$0.409483\pi$
$308$	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	0.688425	−	0.725308i	$-0.258303\pi$
$311$	5.54880	+	3.56600i	0.314643	+	0.202209i	−0.373781	+	0.927517i	$0.621939\pi$
$312$	2.71802	+	2.35518i	0.153878	+	0.133336i
$313$	5.82901	−	19.8518i	0.329475	−	1.12209i	−0.613630	−	0.789594i	$-0.710291\pi$
$313$	5.82901	−	19.8518i	0.329475	−	1.12209i	0.943105	−	0.332495i	$-0.107891\pi$
$314$	−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	−0.993545	−	0.113439i	$-0.963813\pi$
$317$	−3.90010	−	13.2825i	−0.219051	−	0.746020i	0.774494	−	0.632582i	$-0.218005\pi$
$318$	−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	0.883955	−	0.467571i	$-0.154871\pi$
$331$	25.0123	+	7.34426i	1.37480	+	0.403677i	0.490843	+	0.871248i	$0.336689\pi$
$332$	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	0.430520	−	0.902581i	$-0.358330\pi$
$337$	20.1545	−	2.89779i	1.09789	−	0.157852i	0.667368	+	0.744728i	$0.267421\pi$
$338$	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	0.999932	+	0.0116840i	$0.00371921\pi$
$347$	11.0868	+	17.2515i	0.595173	+	0.926108i	−0.404759	+	0.914424i	$0.632644\pi$
$348$	3.67950	+	0.529032i	0.197242	+	0.0283591i
$349$	8.62051	−	18.8763i	0.461445	−	1.01042i	−0.525711	−	0.850663i	$-0.676201\pi$
$349$	8.62051	−	18.8763i	0.461445	−	1.01042i	0.987156	−	0.159761i	$-0.0510722\pi$
$350$	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	−0.463988	−	0.885842i	$-0.653582\pi$
$353$	−12.3929	+	1.78184i	−0.659610	+	0.0948376i	−0.195622	+	0.980679i	$0.562673\pi$
$354$	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	0.0128458	−	0.999917i	$-0.495911\pi$
$359$	−9.79469	−	2.87598i	−0.516944	−	0.151788i	−0.529790	+	0.848129i	$0.677729\pi$
$360$	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	$0.0546729\pi$
$367$			6.54858i			0.341833i	−0.985286	+	0.170917i	$0.945327\pi$
$368$	−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	−0.998245	−	0.0592159i	$-0.981140\pi$
$373$	−3.67883	−	12.5289i	−0.190482	−	0.648724i	0.807763	−	0.589508i	$-0.200678\pi$
$374$	−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	0.988957	−	0.148203i	$-0.0473490\pi$
$379$	24.6264	+	15.8264i	1.26497	+	0.812949i	0.276017	+	0.961153i	$0.410985\pi$
$380$	−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	0.739855	−	0.672767i	$-0.234894\pi$
$383$	32.0813	−	4.61260i	1.63928	−	0.235693i	0.899426	+	0.437074i	$0.143985\pi$
$384$	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	−0.812849	−	0.582474i	$-0.802085\pi$
$389$	−12.2417	+	7.86729i	−0.620681	+	0.398888i	0.192168	+	0.981362i	$0.438448\pi$
$390$	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	−0.898966	−	0.438018i	$-0.855681\pi$
$397$	−23.0457	+	10.5246i	−1.15663	+	0.528216i	−0.257666	+	0.966234i	$0.582953\pi$
$398$	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	0.327957	−	0.944693i	$-0.393640\pi$
$401$	24.3576	−	28.1102i	1.21636	−	1.40376i	0.888404	−	0.459063i	$-0.151815\pi$
$402$	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	−0.911048	−	0.412300i	$-0.864726\pi$
$409$	−29.4168	+	8.63754i	−1.45456	+	0.427099i	−0.543517	+	0.839398i	$0.682908\pi$
$410$	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	0.120678	−	0.992692i	$-0.461493\pi$
$419$	15.5341	−	4.56121i	0.758889	−	0.222830i	0.638211	+	0.769862i	$0.279675\pi$
$420$	−2.81417	+	5.81966i	−0.137317	+	0.283970i
$421$	−11.6105	−	13.3992i	−0.565861	−	0.653039i	0.398643	−	0.917106i	$-0.369481\pi$
$421$	−11.6105	−	13.3992i	−0.565861	−	0.653039i	−0.964504	+	0.264067i	$0.914936\pi$
$422$	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	0.965556	−	0.260196i	$-0.0837872\pi$
$431$	2.83606	+	6.21010i	0.136608	+	0.299130i	−0.828948	+	0.559326i	$0.811060\pi$
$432$	1.54302	+	5.25504i	0.0742385	+	0.252833i
$433$	−35.3808	−	16.1579i	−1.70029	−	0.776497i	−0.997905	−	0.0647013i	$-0.979391\pi$
$433$	−35.3808	−	16.1579i	−1.70029	−	0.776497i	−0.702387	−	0.711796i	$-0.747882\pi$
$434$	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	−0.771007	−	0.636826i	$-0.780247\pi$
$439$	−10.7280	+	6.89444i	−0.512018	+	0.329054i	0.258990	+	0.965880i	$0.416610\pi$
$440$	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	−0.643583	−	0.765376i	$-0.722553\pi$
$443$	−10.2419	+	4.67732i	−0.486607	+	0.222226i	0.156976	+	0.987602i	$0.449826\pi$
$444$	−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	0.299839	−	0.953990i	$-0.403067\pi$
$449$	−9.39510	−	6.03787i	−0.443382	−	0.284945i	−0.743222	+	0.669045i	$0.766703\pi$
$450$	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	0.922012	−	0.387162i	$-0.126545\pi$
$457$	36.2905	+	5.21779i	1.69760	+	0.244078i	0.775587	+	0.631240i	$0.217454\pi$
$458$	−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	−0.833992	−	0.551776i	$-0.813950\pi$
$463$	−38.5088	−	5.53673i	−1.78966	−	0.257314i	−0.955663	+	0.294462i	$0.904859\pi$
$464$	−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	−0.598036	−	0.801469i	$-0.704052\pi$
$467$	2.38069	−	2.06288i	0.110165	−	0.0954587i	0.708202	+	0.706010i	$0.249507\pi$
$468$	−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	−0.637691	−	0.770293i	$-0.720110\pi$
$479$	7.92399	−	17.3511i	0.362056	−	0.792793i	0.999747	−	0.0225000i	$-0.00716256\pi$
$480$	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	−0.224317	−	0.974516i	$-0.572015\pi$
$487$	−24.4449	−	11.1636i	−1.10770	−	0.505871i	−0.883387	+	0.468645i	$0.844742\pi$
$488$	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	−0.867630	−	0.497210i	$-0.834358\pi$
$491$	−3.88274	−	27.0050i	−0.175225	−	1.21872i	0.692405	−	0.721509i	$-0.256551\pi$
$492$	−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	0.715586	−	0.698524i	$-0.246160\pi$
$499$	−1.73494	−	2.00222i	−0.0776664	−	0.0896318i	−0.793253	+	0.608892i	$0.791614\pi$
$500$	−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	0.752967	−	0.658058i	$-0.228622\pi$
$503$	28.9325	+	4.15987i	1.29004	+	0.185479i	0.537070	+	0.843538i	$0.319531\pi$
$504$	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	−0.956893	−	0.290441i	$-0.906198\pi$
$509$	0.971607	−	6.75767i	0.0430657	−	0.299529i	0.999959	−	0.00908787i	$-0.00289280\pi$
$510$	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	0.919512	+	0.393061i	$0.128584\pi$
$521$	3.37781	+	23.4932i	0.147985	+	1.02926i	−0.771528	+	0.636196i	$0.780507\pi$
$522$	−0.678791	+	0.588176i	−0.0297099	+	0.0257438i
$523$	−0.268516	+	0.122627i	−0.0117414	+	0.00536211i	−0.421277	−	0.906932i	$-0.638418\pi$
$523$	−0.268516	+	0.122627i	−0.0117414	+	0.00536211i	0.409536	+	0.912294i	$0.365691\pi$
$524$	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	0.289132	−	0.957289i	$-0.406633\pi$
$541$	−10.7351	−	6.89903i	−0.461538	−	0.296613i	−0.750671	+	0.660676i	$0.770270\pi$
$542$	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	−0.982500	−	0.186262i	$-0.940363\pi$
$547$	−6.00299	−	20.4443i	−0.256669	−	0.874135i	0.725831	−	0.687873i	$-0.241456\pi$
$548$	−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	−0.989736	−	0.142911i	$-0.954354\pi$
$557$	−5.53158	−	18.8388i	−0.234381	−	0.798227i	0.755355	−	0.655316i	$-0.227464\pi$
$558$	−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	0.118884	+	0.992908i	$0.462068\pi$
$563$	−19.7813	+	30.7803i	−0.833684	+	1.29724i	−0.952567	+	0.304329i	$0.901568\pi$
$564$	−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	0.857021	−	0.515281i	$-0.172312\pi$
$569$	−2.23346	−	4.89059i	−0.0936314	−	0.205024i	−0.950653	+	0.310257i	$0.899585\pi$
$570$	−22.7332	−	15.3271i	−0.952188	−	0.641980i
$571$	3.43096	−	7.51275i	0.143581	−	0.314399i	−0.824155	−	0.566364i	$-0.808350\pi$
$571$	3.43096	−	7.51275i	0.143581	−	0.314399i	0.967736	+	0.251965i	$0.0810769\pi$
$572$	−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	0.890262	−	0.455449i	$-0.150521\pi$
$577$	2.54963	+	3.96730i	0.106143	+	0.165161i	−0.784119	+	0.620610i	$0.786885\pi$
$578$	−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	−0.827938	−	0.560819i	$-0.810486\pi$
$587$	0.633296	−	0.985428i	0.0261389	−	0.0406730i	0.854077	+	0.520146i	$0.174123\pi$
$588$	−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	0.807781	+	0.589482i	$0.200668\pi$
$593$	10.8835	+	37.0657i	0.446931	+	1.52211i	−0.360851	+	0.932624i	$0.617514\pi$
$594$	−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	−0.432615	−	0.901579i	$-0.642409\pi$
$601$	5.79738	−	40.3217i	0.236480	−	1.64476i	0.669095	−	0.743177i	$-0.266682\pi$
$602$	−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	0.0769809	+	0.997033i	$0.475472\pi$
$607$	−12.9794	+	44.2036i	−0.526816	+	1.79417i	−0.603797	+	0.797138i	$0.706346\pi$
$608$	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	0.335595	−	0.942007i	$-0.391063\pi$
$613$	22.8521	−	3.28564i	0.922989	−	0.132706i	0.587395	+	0.809301i	$0.300154\pi$
$614$	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	0.956762	−	0.290872i	$-0.0939452\pi$
$617$	33.8682	+	15.4671i	1.36348	+	0.622681i	0.406720	+	0.913553i	$0.366673\pi$
$618$	−29.5065	−	4.24239i	−1.18692	−	0.170654i
$619$	−2.37072	+	1.52357i	−0.0952873	+	0.0612375i	−0.587417	−	0.809285i	$-0.699855\pi$
$619$	−2.37072	+	1.52357i	−0.0952873	+	0.0612375i	0.492129	+	0.870522i	$0.336219\pi$
$620$	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	−0.813596	−	0.581431i	$-0.802493\pi$
$631$	−3.07204	+	3.54533i	−0.122296	+	0.141137i	0.691300	+	0.722568i	$0.257038\pi$
$632$	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	−0.994675	−	0.103060i	$-0.967137\pi$
$641$	−0.284982	+	1.98209i	−0.0112561	+	0.0782880i	0.983419	+	0.181348i	$0.0580459\pi$
$642$	0.477213	+	0.742557i	0.0188341	+	0.0293064i
$643$			15.1027i			0.595591i	0.954630	+	0.297796i	$0.0962514\pi$
$643$			15.1027i			0.595591i	−0.954630	+	0.297796i	$0.903749\pi$
$644$	−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	0.944306	−	0.329069i	$-0.106735\pi$
$647$	44.7080	+	6.42803i	1.75765	+	0.252712i	0.813345	+	0.581781i	$0.197644\pi$
$648$	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	−0.878586	−	0.477583i	$-0.841513\pi$
$653$	3.03397	−	10.3328i	0.118729	−	0.404352i	0.997315	+	0.0732310i	$0.0233310\pi$
$654$	−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	−0.881054	−	0.473016i	$-0.843165\pi$
$659$	−4.33719	−	30.1658i	−0.168953	−	1.17509i	0.712101	−	0.702077i	$-0.247744\pi$
$660$	20.3875	+	3.39086i	0.793584	+	0.131989i
$661$	−12.6470	−	27.6932i	−0.491913	−	1.07714i	−0.979014	−	0.203794i	$-0.934673\pi$
$661$	−12.6470	−	27.6932i	−0.491913	−	1.07714i	0.487101	−	0.873346i	$-0.338054\pi$
$662$	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	−0.367722	−	0.929936i	$-0.619862\pi$
$673$	2.44556	−	1.11685i	0.0942695	−	0.0430514i	0.461992	+	0.886884i	$0.347135\pi$
$674$	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	0.628639	−	0.777697i	$-0.283612\pi$
$677$	−1.34462	−	1.16512i	−0.0516779	−	0.0447791i	−0.680317	+	0.732918i	$0.738158\pi$
$678$	−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	−0.801261	−	0.598315i	$-0.795837\pi$
$683$	−8.44314	+	7.31602i	−0.323068	+	0.279940i	0.478193	+	0.878255i	$0.341292\pi$
$684$	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	0.592631	−	0.805474i	$-0.298089\pi$
$701$	2.81002	+	1.80589i	0.106133	+	0.0682076i	−0.486498	+	0.873682i	$0.661726\pi$
$702$	−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	−0.729756	−	0.683708i	$-0.760366\pi$
$709$	7.05203	−	15.4418i	0.264845	−	0.579929i	0.994600	+	0.103779i	$0.0330935\pi$
$710$	−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	0.969192	−	0.246308i	$-0.0792174\pi$
$719$	3.97812	+	8.71088i	0.148359	+	0.324861i	−0.820833	+	0.571169i	$0.806490\pi$
$720$	−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	−0.998237	−	0.0593512i	$-0.981097\pi$
$727$	−3.40755	+	11.6050i	−0.126379	+	0.430407i	0.871858	+	0.489758i	$0.162915\pi$
$728$	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	−0.269302	−	0.963056i	$-0.586793\pi$
$733$	−21.6326	−	3.11030i	−0.799019	−	0.114882i	−0.529717	+	0.848174i	$0.677702\pi$
$734$	−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	−0.810081	−	0.586318i	$-0.800577\pi$
$739$	3.59844	−	25.0277i	0.132371	−	0.920659i	0.942452	−	0.334342i	$-0.108514\pi$
$740$	−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	0.194180	−	0.980966i	$-0.437796\pi$
$743$	32.5133	−	28.1729i	1.19280	−	1.03356i	0.998616	−	0.0525972i	$-0.0167499\pi$
$744$	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	0.990558	+	0.137095i	$0.0437765\pi$
$751$	2.15806	+	15.0096i	0.0787487	+	0.547709i	−0.911809	+	0.410614i	$0.865314\pi$
$752$	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	0.886814	+	0.462126i	$0.152913\pi$
$757$	25.8293	+	40.1912i	0.938783	+	1.46077i	0.0519685	+	0.998649i	$0.483450\pi$
$758$			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	−0.263377	−	0.964693i	$-0.584836\pi$
$761$	13.9235	−	8.94812i	0.504728	−	0.324369i	0.768105	+	0.640324i	$0.221200\pi$
$762$	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	−0.553890	−	0.832590i	$-0.686857\pi$
$769$	9.67951	−	11.1707i	0.349052	−	0.402827i	0.902942	+	0.429762i	$0.141403\pi$
$770$	−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	0.713477	+	0.700678i	$0.247119\pi$
$773$	−7.38315	+	25.1447i	−0.265553	+	0.904392i	−0.979031	+	0.203713i	$0.934699\pi$
$774$	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	0.986995	−	0.160748i	$-0.0513906\pi$
$787$	1.95744	+	6.66642i	0.0697751	+	0.237632i	−0.917220	+	0.398380i	$0.869572\pi$
$788$	−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	−0.578534	−	0.815658i	$-0.696375\pi$
$797$	−25.5164	+	3.66870i	−0.903837	+	0.129952i	−0.325302	+	0.945610i	$0.605466\pi$
$798$	−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	−0.757281	−	0.653089i	$-0.773473\pi$
$809$	6.60456	−	14.4620i	0.232204	−	0.508456i	0.989485	+	0.144633i	$0.0462001\pi$
$810$	9.59602	−	14.2329i	0.337170	−	0.500092i
$811$	10.2065	+	22.3491i	0.358398	+	0.784783i	0.999845	+	0.0176149i	$0.00560730\pi$
$811$	10.2065	+	22.3491i	0.358398	+	0.784783i	−0.641447	+	0.767168i	$0.721665\pi$
$812$	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	0.930218	−	0.367008i	$-0.119618\pi$
$821$	12.4515	+	14.3698i	0.434561	+	0.501511i	−0.495656	+	0.868519i	$0.665072\pi$
$822$	−0.283485	+	0.129463i	−0.00988767	+	0.00451555i
$823$	−5.17918	−	17.6387i	−0.180535	−	0.614846i	−0.999178	−	0.0405427i	$-0.987091\pi$
$823$	−5.17918	−	17.6387i	−0.180535	−	0.614846i	0.818643	−	0.574303i	$-0.194727\pi$
$824$	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	$0.360064\pi$
$827$			52.0462i			1.80982i	−0.425598	+	0.904912i	$0.639936\pi$
$828$	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	0.154673	−	0.987966i	$-0.450568\pi$
$839$	−19.6896	−	12.6537i	−0.679759	−	0.436855i	−0.834432	+	0.551111i	$0.814204\pi$
$840$	−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	0.881791	−	0.471641i	$-0.156338\pi$
$853$	2.52524	+	3.92934i	0.0864624	+	0.134538i	−0.795328	+	0.606179i	$0.792702\pi$
$854$	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	−0.613662	−	0.789569i	$-0.710304\pi$
$857$	−12.2604	+	5.59914i	−0.418808	+	0.191263i	0.194854	+	0.980832i	$0.437577\pi$
$858$	−15.5512	+	13.4752i	−0.530909	+	0.460036i
$859$	1.06688	+	7.42035i	0.0364016	+	0.253179i	0.999894	−	0.0145567i	$-0.00463370\pi$
$859$	1.06688	+	7.42035i	0.0364016	+	0.253179i	−0.963492	+	0.267736i	$0.913725\pi$
$860$	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	−0.345020	−	0.938595i	$-0.612128\pi$
$863$	19.1561	−	29.8075i	0.652083	−	1.01466i	0.997103	−	0.0760652i	$-0.0242357\pi$
$864$	−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	0.248158	−	0.968720i	$-0.420175\pi$
$877$	6.31801	+	0.908393i	0.213344	+	0.0306743i	−0.0348139	+	0.999394i	$0.511084\pi$
$878$	−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	0.205659	−	0.978624i	$-0.434066\pi$
$881$	−23.5159	−	27.1388i	−0.792272	−	0.914330i	−0.997931	+	0.0642934i	$0.979521\pi$
$882$	1.46714	−	0.210943i	0.0494011	−	0.00710281i
$883$	5.28319	−	17.9929i	0.177794	−	0.605509i	−0.821579	−	0.570094i	$-0.806907\pi$
$883$	5.28319	−	17.9929i	0.177794	−	0.605509i	0.999373	−	0.0354147i	$-0.0112752\pi$
$884$	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	−0.993762	−	0.111525i	$-0.964426\pi$
$887$	−37.0965	−	32.1443i	−1.24558	−	1.07930i	−0.251817	−	0.967775i	$-0.581028\pi$
$888$	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	0.871292	−	0.490765i	$-0.163283\pi$
$907$	15.3449	+	13.2964i	0.509519	+	0.441501i	−0.361772	+	0.932266i	$0.617828\pi$
$908$	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	−0.255881	−	0.966708i	$-0.582365\pi$
$911$	−29.9951	−	8.80737i	−0.993783	−	0.291801i	−0.737903	+	0.674907i	$0.764184\pi$
$912$	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	0.942213	−	0.335016i	$-0.108742\pi$
$929$	47.3569	+	13.9052i	1.55373	+	0.456216i	0.611516	+	0.791232i	$0.290560\pi$
$930$	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	−0.514037	−	0.857768i	$-0.671851\pi$
$937$	−6.19564	+	2.82945i	−0.202403	+	0.0924342i	0.311635	+	0.950202i	$0.399123\pi$
$938$	−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	−0.771000	−	0.636835i	$-0.780243\pi$
$941$	−15.7059	+	10.0936i	−0.511999	+	0.329042i	0.259001	+	0.965877i	$0.416607\pi$
$942$		−	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	0.0304322	−	0.999537i	$-0.490312\pi$
$947$	−21.6964	−	9.90842i	−0.705039	−	0.321980i	−0.735471	+	0.677557i	$0.763039\pi$
$948$	−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	−0.992696	−	0.120639i	$-0.961506\pi$
$953$	−38.6928	−	33.5275i	−1.25338	−	1.08606i	−0.260686	−	0.965424i	$-0.583949\pi$
$954$	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	$0.177114\pi$
$967$			32.8474i			1.05630i	−0.849151	+	0.528151i	$0.822886\pi$
$968$	−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	−0.878880	−	0.477042i	$-0.841709\pi$
$971$	−42.3892	+	12.4466i	−1.36033	+	0.399430i	−0.481453	+	0.876472i	$0.659891\pi$
$972$	−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	−0.767801	−	0.640688i	$-0.778649\pi$
$977$	4.18672	−	6.51466i	0.133945	−	0.208422i	0.901746	+	0.432265i	$0.142286\pi$
$978$	−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	−0.309536	−	0.950888i	$-0.600174\pi$
$983$	6.47106	−	2.95523i	0.206395	−	0.0942573i	0.515930	+	0.856631i	$0.327446\pi$
$984$	−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	−0.907642	−	0.419745i	$-0.862120\pi$
$991$	−28.4227	+	18.2662i	−0.902877	+	0.580244i	0.00476532	+	0.999989i	$0.498483\pi$
$992$	−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	−0.369730	−	0.929139i	$-0.620550\pi$
$997$	−14.6103	+	2.10065i	−0.462714	+	0.0665282i	−0.0929842	+	0.995668i	$0.529641\pi$
$998$	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.219.10	yes	120
5.4	even	2	inner	230.2.j.a.219.3	yes	120
23.2	even	11	inner	230.2.j.a.209.3	✓	120
115.94	even	22	inner	230.2.j.a.209.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.3	✓	120	23.2	even	11	inner
230.2.j.a.209.10	yes	120	115.94	even	22	inner
230.2.j.a.219.3	yes	120	5.4	even	2	inner
230.2.j.a.219.10	yes	120	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
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

Fields

Representations

Groups

Database

Properties

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