LMFDB - Embedded newform 230.2.j.a.219.3

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			219.3
Character	$\chi$	$=$	230.219
Dual form			230.2.j.a.209.3

$q$-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} +(0.883903 - 2.05395i) 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} +(-2.20577 + 0.366864i) 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} +(-1.88558 + 3.08107i) 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} +(1.50115 + 1.65727i) q^{20} +(2.43202 - 1.56297i) q^{21} +5.72152i q^{22} +(-4.17363 - 2.36237i) q^{23} -1.61545 q^{24} +(-3.43743 - 3.63099i) 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} +(3.61138 - 0.0795063i) 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} +(1.21161 + 3.81375i) 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} +(0.582598 - 2.15884i) 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} +(-1.19616 + 4.85481i) 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} +(-10.6079 + 7.15202i) 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} +(-2.01935 - 2.99510i) 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} +(4.48165 - 2.16716i) 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} +(4.66171 + 6.59625i) 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} +(-2.13111 + 0.677043i) 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} +(0.177960 + 8.08338i) 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} +(0.866422 + 0.105165i) q^{90} -3.98408 q^{91} +(3.88268 - 2.81510i) q^{92} +14.7344i q^{93} +(-3.20796 + 2.06163i) q^{94} +(11.3939 + 12.5789i) 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	−0.335701	−	0.941969i	$-0.608973\pi$
$3$	−1.59901	−	0.229903i	−0.923187	−	0.132734i	−0.587486	+	0.809234i	$0.699882\pi$
$4$	−0.415415	+	0.909632i	−0.207708	+	0.454816i
$5$	0.883903	−	2.05395i	0.395293	−	0.918555i
$5$	0.883903	−	2.05395i	0.395293	−	0.918555i
$6$	0.671082	+	1.46947i	0.273968	+	0.599907i
$7$	−1.35246	+	1.17191i	−0.511182	+	0.442942i	−0.871865	−	0.489747i	$-0.837089\pi$
$7$	−1.35246	+	1.17191i	−0.511182	+	0.442942i	0.360683	+	0.932689i	$0.382544\pi$
$8$	0.989821	−	0.142315i	0.349955	−	0.0503159i
$9$	−0.374509	−	0.109966i	−0.124836	−	0.0366552i
$10$	−2.20577	+	0.366864i	−0.697525	+	0.116013i
$11$	−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	0.856193	−	0.516656i	$-0.172823\pi$
$13$	1.68251	+	1.45791i	0.466646	+	0.404351i	−0.389548	+	0.921006i	$0.627369\pi$
$14$	1.71707	+	0.504178i	0.458907	+	0.134747i
$15$	−1.88558	+	3.08107i	−0.486854	+	0.795529i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−3.28912	+	1.50209i	−0.797728	+	0.364310i	−0.772213	−	0.635364i	$-0.780850\pi$
$17$	−3.28912	+	1.50209i	−0.797728	+	0.364310i	−0.0255153	+	0.999674i	$0.508123\pi$
$18$	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	$0.800065\pi$
$20$	1.50115	+	1.65727i	0.335668	+	0.370576i
$21$	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
$25$	−3.43743	−	3.63099i	−0.687487	−	0.726197i
$26$	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	$0.932173\pi$
$30$	3.61138	−	0.0795063i	0.659345	−	0.0145158i
$31$	−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
$35$	1.21161	+	3.81375i	0.204800	+	0.644641i
$36$	0.255605	−	0.294984i	0.0426008	−	0.0491640i
$37$	1.17271	−	3.99387i	0.192792	−	0.656589i	−0.805186	−	0.593023i	$-0.797934\pi$
$37$	1.17271	−	3.99387i	0.192792	−	0.656589i	0.997978	−	0.0635660i	$-0.0202473\pi$
$38$	7.51286	−	1.08019i	1.21875	−	0.175229i
$39$	−2.35518	−	2.71802i	−0.377130	−	0.435231i
$40$	0.582598	−	2.15884i	0.0921168	−	0.341342i
$41$	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	0.312325	−	0.949975i	$-0.398892\pi$
$43$	2.25812	+	0.324669i	0.344361	+	0.0495116i	0.0320351	+	0.999487i	$0.489801\pi$
$44$	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
$50$	−1.19616	+	4.85481i	−0.169163	+	0.686574i
$51$	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	$-0.640318\pi$
$53$	2.96874	−	2.57243i	0.407788	−	0.353350i	0.834472	+	0.551051i	$0.185773\pi$
$54$	−0.779443	−	5.42115i	−0.106069	−	0.737725i
$55$	−10.6079	+	7.15202i	−1.43037	+	0.964378i
$56$	−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	$0.0100108\pi$
$60$	−2.01935	−	2.99510i	−0.260696	−	0.386666i
$61$	−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
$65$	4.48165	−	2.16716i	0.555880	−	0.268803i
$66$	1.31539	−	9.14876i	0.161914	−	1.12613i
$67$	2.00796	+	3.12444i	0.245311	+	0.381712i	0.941973	−	0.335688i	$-0.108969\pi$
$67$	2.00796	+	3.12444i	0.245311	+	0.381712i	−0.696662	+	0.717399i	$0.745332\pi$
$68$		−	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	−0.622149	−	0.782899i	$-0.713740\pi$
$73$	−13.8519	−	6.32596i	−1.62125	−	0.740398i	−0.999096	+	0.0425008i	$0.986467\pi$
$74$	−3.99387	+	1.17271i	−0.464278	+	0.136324i
$75$	4.66171	+	6.59625i	0.538288	+	0.761669i
$76$	−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	$0.430819\pi$
$80$	−2.13111	+	0.677043i	−0.238265	+	0.0756957i
$81$	−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	$0.409802\pi$
$83$	−4.32469	+	14.7285i	−0.474696	+	1.61667i	−0.754285	+	0.656547i	$0.772016\pi$
$84$	0.411425	+	2.86152i	0.0448901	+	0.312218i
$85$	0.177960	+	8.08338i	0.0193024	+	0.876766i
$86$	−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	$0.0415261\pi$
$90$	0.866422	+	0.105165i	0.0913289	+	0.0110854i
$91$	−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
$95$	11.3939	+	12.5789i	1.16899	+	1.29056i
$96$	0.671082	−	1.46947i	0.0684921	−	0.149977i
$97$	−3.29716	−	11.2291i	−0.334776	−	1.14014i	−0.939169	−	0.343456i	$-0.888402\pi$
$97$	−3.29716	−	11.2291i	−0.334776	−	1.14014i	0.604393	−	0.796686i	$-0.293416\pi$
$98$	3.45430	−	1.57752i	0.348937	−	0.159354i
$99$	1.46245	+	1.68776i	0.146982	+	0.169626i
$100$	4.73082	−	1.61843i	0.473082	−	0.161843i
$101$	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	$-0.454942\pi$
$103$	9.97644	−	15.5236i	0.983008	−	1.52959i	0.841927	−	0.539591i	$-0.181421\pi$
$104$	1.87287	+	1.20362i	0.183650	+	0.118025i
$105$	−1.06058	−	6.37676i	−0.103502	−	0.622308i
$106$	−3.76908	−	1.10670i	−0.366086	−	0.107492i
$107$	−0.540837	+	0.0777606i	−0.0522847	+	0.00751740i	−0.168408	−	0.985717i	$-0.553862\pi$
$107$	−0.540837	+	0.0777606i	−0.0522847	+	0.00751740i	0.116123	+	0.993235i	$0.462953\pi$
$108$	−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	$0.682441\pi$
$110$	11.7517	+	5.05727i	1.12048	+	0.482192i
$111$	−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	$-0.229359\pi$
$113$	−1.71034	−	2.66134i	−0.160895	−	0.250358i	−0.912336	+	0.409443i	$0.865723\pi$
$114$	−12.2615			−1.14839
$115$	−8.54128	+	6.48432i	−0.796479	+	0.604666i
$116$	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
$120$	−1.42790	+	3.31806i	−0.130349	+	0.302896i
$121$	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
$125$	−10.4962	+	3.85088i	−0.938811	+	0.344433i
$126$	−0.587617	−	0.377638i	−0.0523490	−	0.0336427i
$127$	−2.81661	+	4.38274i	−0.249934	+	0.388905i	−0.943439	−	0.331547i	$-0.892429\pi$
$127$	−2.81661	+	4.38274i	−0.249934	+	0.388905i	0.693505	+	0.720452i	$0.256066\pi$
$128$	−0.755750	−	0.654861i	−0.0667995	−	0.0578821i
$129$	−3.53611	−	1.03830i	−0.311337	−	0.0914169i
$130$	−4.24609	−	2.59855i	−0.372407	−	0.227908i
$131$	−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
$135$	9.07668	−	8.22166i	0.781196	−	0.707608i
$136$	−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	$0.518954\pi$
$140$	−3.97243	−	0.482168i	−0.335731	−	0.0407506i
$141$	−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
$145$	−5.14420	+	0.113252i	−0.427202	+	0.00940507i
$146$	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	$0.728785\pi$
$150$	3.02881	−	7.48788i	0.247301	−	0.611383i
$151$	−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
$155$	−19.6906	−	5.31382i	−1.58158	−	0.426817i
$156$	3.45077	−	1.01324i	0.276283	−	0.0811240i
$157$	10.2520	+	4.68192i	0.818197	+	0.373658i	0.780130	−	0.625617i	$-0.215153\pi$
$157$	10.2520	+	4.68192i	0.818197	+	0.373658i	0.0380670	+	0.999275i	$0.487880\pi$
$158$	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	$-0.247078\pi$
$163$	−2.81047	−	4.37318i	−0.220133	−	0.342534i	−0.933702	+	0.358051i	$0.883441\pi$
$164$	−0.836907	+	5.82082i	−0.0653515	+	0.454529i
$165$	18.6064	−	8.99734i	1.44851	−	0.700442i
$166$	14.7285	−	4.32469i	1.14316	−	0.335661i
$167$	2.61744	−	1.19535i	0.202544	−	0.0924986i	−0.311561	−	0.950226i	$-0.600852\pi$
$167$	2.61744	−	1.19535i	0.202544	−	0.0924986i	0.514104	+	0.857728i	$0.328124\pi$
$168$	2.18483	−	1.89317i	0.168564	−	0.146061i
$169$	−1.14473	−	7.96178i	−0.0880562	−	0.612445i
$170$	6.70396	−	4.51992i	0.514171	−	0.346662i
$171$	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	$-0.958615\pi$
$173$	−6.07296	+	9.44972i	−0.461719	+	0.718449i	0.529841	+	0.848097i	$0.322252\pi$
$174$	2.43434	−	2.80937i	0.184547	−	0.212978i
$175$	8.90420	+	0.882391i	0.673094	+	0.0667025i
$176$	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	$0.377955\pi$
$180$	−0.379953	−	0.785737i	−0.0283200	−	0.0585654i
$181$	−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
$190$	4.42198	−	16.3858i	0.320804	−	1.18875i
$191$	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	−0.991192	−	0.132436i	$-0.957720\pi$
$193$	−1.19125	+	4.05701i	−0.0857477	+	0.292030i	0.905444	+	0.424466i	$0.139538\pi$
$194$	−7.66394	+	8.84466i	−0.550239	+	0.635009i
$195$	−7.66443	+	2.43495i	−0.548861	+	0.174371i
$196$	−3.19463	−	2.05307i	−0.228188	−	0.146648i
$197$	−5.44437	−	4.71757i	−0.387895	−	0.336113i	0.438982	−	0.898496i	$-0.355339\pi$
$197$	−5.44437	−	4.71757i	−0.387895	−	0.336113i	−0.826877	+	0.562383i	$0.809885\pi$
$198$	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	$-0.327213\pi$
$200$	−3.91919	−	3.10483i	−0.277128	−	0.219545i
$201$	−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
$205$	1.58445	−	13.0538i	0.110663	−	0.911715i
$206$	−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
$210$	−4.79108	+	4.33976i	−0.330616	+	0.299472i
$211$	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
$215$	2.66282	−	4.35110i	0.181602	−	0.296743i
$216$	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
$220$	−2.09902	−	12.6203i	−0.141516	−	0.850864i
$221$	−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	$-0.608349\pi$
$223$	8.23813	−	7.13838i	0.551666	−	0.478022i	0.885519	+	0.464604i	$0.153803\pi$
$224$	−0.743411	−	1.62784i	−0.0496712	−	0.108765i
$225$	0.888065	+	1.73784i	0.0592043	+	0.115856i
$226$	−1.31418	+	2.87766i	−0.0874181	+	0.191419i
$227$	0.0964927	+	0.0138736i	0.00640444	+	0.000920820i	0.145516	−	0.989356i	$-0.453516\pi$
$227$	0.0964927	+	0.0138736i	0.00640444	+	0.000920820i	−0.139112	+	0.990277i	$0.544425\pi$
$228$	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	$0.622040\pi$
$230$	10.0727	+	3.67970i	0.664176	+	0.242632i
$231$	−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	$-0.528686\pi$
$233$	−6.97486	−	1.00283i	−0.456938	−	0.0656978i	−0.366941	+	0.930244i	$0.619595\pi$
$234$	−0.360980	+	0.790436i	−0.0235980	+	0.0516724i
$235$	−7.83235	−	3.37059i	−0.510926	−	0.219873i
$236$	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	$0.759109\pi$
$240$	3.56331	−	0.592650i	0.230011	−	0.0382554i
$241$	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
$245$	7.24273	+	4.43245i	0.462721	+	0.283179i
$246$	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
$250$	8.91425	+	6.74804i	0.563787	+	0.426784i
$251$	−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
$255$	1.57383	−	12.9663i	0.0985572	−	0.811982i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−17.2578	−	7.88135i	−1.07651	−	0.491625i	−0.203373	−	0.979101i	$-0.565190\pi$
$257$	−17.2578	−	7.88135i	−1.07651	−	0.491625i	−0.873136	+	0.487476i	$0.837918\pi$
$258$	1.03830	+	3.53611i	0.0646415	+	0.220149i
$259$	3.09444	+	6.77587i	0.192279	+	0.421032i
$260$	0.109569	+	4.97692i	0.00679520	+	0.308655i
$261$	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	$-0.0578588\pi$
$263$	15.3183	+	13.2734i	0.944566	+	0.818471i	−0.0389594	+	0.999241i	$0.512404\pi$
$264$	7.77557	+	4.99705i	0.478553	+	0.307547i
$265$	−2.65956	−	8.37142i	−0.163376	−	0.514252i
$266$	−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	$0.957056\pi$
$270$	−11.8237	−	3.19083i	−0.719569	−	0.194188i
$271$	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	$0.253306\pi$
$277$			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
$280$	1.74203	+	3.60250i	0.104106	+	0.215290i
$281$	−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	−0.522272	−	0.852779i	$-0.674916\pi$
$283$	4.16358	−	3.60776i	0.247499	−	0.214459i	0.769771	+	0.638320i	$0.220370\pi$
$284$	−0.110851	−	0.770985i	−0.00657779	−	0.0457495i
$285$	−15.3271	−	22.7332i	−0.907897	−	1.34660i
$286$	−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
$290$	2.87644	+	4.26635i	0.168910	+	0.250529i
$291$	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	$-0.623516\pi$
$293$	1.25658	−	0.573859i	0.0734099	−	0.0335252i	0.451782	+	0.892129i	$0.350789\pi$
$294$	−5.88612	+	1.72832i	−0.343286	+	0.100798i
$295$	−9.43274	−	19.5068i	−0.549195	−	1.13573i
$296$	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
$305$	−10.9407	−	2.95252i	−0.626461	−	0.169061i
$306$	−0.924236	−	1.06662i	−0.0528350	−	0.0609749i
$307$	−4.89410	+	0.703666i	−0.279321	+	0.0401603i	−0.280552	−	0.959839i	$-0.590517\pi$
$307$	−4.89410	+	0.703666i	−0.279321	+	0.0401603i	0.00123044	+	0.999999i	$0.499608\pi$
$308$	−2.88467	+	9.82427i	−0.164369	+	0.559790i
$309$	−19.5213	+	22.5288i	−1.11053	+	1.28162i
$310$	6.17525	+	19.4376i	0.350731	+	1.10398i
$311$	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	$0.289709\pi$
$313$	−5.82901	+	19.8518i	−0.329475	+	1.12209i	−0.943105	+	0.332495i	$0.892109\pi$
$314$	−1.60396	−	11.1558i	−0.0905165	−	0.629556i
$315$	−0.0343776	−	1.56152i	−0.00193696	−	0.0879815i
$316$	−4.40683	−	9.64962i	−0.247904	−	0.542833i
$317$	3.90010	+	13.2825i	0.219051	+	0.746020i	0.993545	+	0.113439i	$0.0361865\pi$
$317$	3.90010	+	13.2825i	0.219051	+	0.746020i	−0.774494	+	0.632582i	$0.781995\pi$
$318$	5.77236	+	2.63615i	0.323698	+	0.147828i
$319$	−1.87370	+	13.0319i	−0.104907	+	0.729644i
$320$	0.269433	−	2.21978i	0.0150618	−	0.124089i
$321$	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
$325$	−0.489890	−	11.1206i	−0.0271742	−	0.616862i
$326$	−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
$330$	−17.6284	−	10.7884i	−0.970413	−	0.593880i
$331$	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
$335$	8.19229	−	1.36254i	0.447593	−	0.0744438i
$336$	−2.77385	−	0.814475i	−0.151326	−	0.0444332i
$337$	−20.1545	+	2.89779i	−1.09789	+	0.157852i	−0.667368	−	0.744728i	$-0.732579\pi$
$337$	−20.1545	+	2.89779i	−1.09789	+	0.157852i	−0.430520	+	0.902581i	$0.641670\pi$
$338$	−6.07899	+	5.26747i	−0.330653	+	0.286513i
$339$	2.12300	+	4.64871i	0.115305	+	0.252483i
$340$	−7.42683	−	3.19608i	−0.402777	−	0.173332i
$341$	−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
$345$	15.1483	−	8.40482i	0.815559	−	0.452500i
$346$	11.2329			0.603884
$347$	−11.0868	−	17.2515i	−0.595173	−	0.926108i	−0.999932	−	0.0116840i	$-0.996281\pi$
$347$	−11.0868	−	17.2515i	−0.595173	−	0.926108i	0.404759	−	0.914424i	$-0.367356\pi$
$348$	−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	$-0.0510722\pi$
$350$	−4.07166	−	7.96774i	−0.217639	−	0.425894i
$351$	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	$-0.437327\pi$
$353$	12.3929	−	1.78184i	0.659610	−	0.0948376i	0.463988	+	0.885842i	$0.346418\pi$
$354$	15.0198	+	4.41021i	0.798294	+	0.234400i
$355$	0.285755	+	1.71810i	0.0151663	+	0.0911873i
$356$	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	$0.677729\pi$
$360$	−0.455586	+	0.744438i	−0.0240115	+	0.0392353i
$361$	−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
$365$	−25.2370	+	22.8597i	−1.32096	+	1.19653i
$366$	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
$370$	−1.12151	+	9.23978i	−0.0583046	+	0.480353i
$371$	−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	$0.0188600\pi$
$373$	3.67883	+	12.5289i	0.190482	+	0.648724i	−0.807763	+	0.589508i	$0.799322\pi$
$374$	−8.59424	−	18.8187i	−0.444397	−	0.973094i
$375$	17.6689	−	3.74448i	0.912416	−	0.193364i
$376$	−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	$0.410985\pi$
$380$	−16.1753	+	5.13883i	−0.829777	+	0.263617i
$381$	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	$-0.856015\pi$
$383$	−32.0813	+	4.61260i	−1.63928	+	0.235693i	−0.739855	+	0.672767i	$0.765106\pi$
$384$	1.05790	+	1.22088i	0.0539855	+	0.0623026i
$385$	5.96523	−	22.1044i	0.304016	−	1.12654i
$386$	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
$395$	10.3265	+	21.3551i	0.519583	+	1.07449i
$396$	−2.14276	+	0.629171i	−0.107678	+	0.0316170i
$397$	23.0457	−	10.5246i	1.15663	−	0.528216i	0.257666	−	0.966234i	$-0.417047\pi$
$397$	23.0457	−	10.5246i	1.15663	−	0.528216i	0.898966	+	0.438018i	$0.144319\pi$
$398$	−16.5040	+	14.3008i	−0.827269	+	0.716833i
$399$	3.12276	+	21.7193i	0.156334	+	1.08732i
$400$	−0.493076	+	4.97563i	−0.0246538	+	0.248781i
$401$	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
$405$	−14.2329	+	9.59602i	−0.707237	+	0.476830i
$406$	−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	$0.682908\pi$
$410$	−11.8382	+	5.72448i	−0.584645	+	0.282712i
$411$	−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	$0.279675\pi$
$420$	6.24109	+	1.68426i	0.304534	+	0.0821835i
$421$	−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
$425$	16.7602	+	6.77940i	0.812988	+	0.328849i
$426$	−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
$430$	−5.10000	+	0.112279i	−0.245944	+	0.00541458i
$431$	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	$0.0206095\pi$
$433$	35.3808	+	16.1579i	1.70029	+	0.776497i	0.702387	+	0.711796i	$0.252118\pi$
$434$	2.32293	−	16.1563i	0.111504	−	0.775527i
$435$	8.25165	+	1.00157i	0.395636	+	0.0480218i
$436$	−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	$0.416610\pi$
$440$	−9.48210	+	8.58888i	−0.452041	+	0.409459i
$441$	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	$-0.550174\pi$
$443$	10.2419	−	4.67732i	0.486607	−	0.222226i	0.643583	+	0.765376i	$0.277447\pi$
$444$	−4.40347	−	5.08187i	−0.208979	−	0.241175i
$445$	−0.444115	−	0.271792i	−0.0210531	−	0.0128842i
$446$	−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	$0.766703\pi$
$450$	0.981837	−	1.68663i	0.0462842	−	0.0795086i
$451$	−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
$455$	−3.52154	+	8.18310i	−0.165092	+	0.383630i
$456$	5.09359	−	11.1534i	0.238529	−	0.522306i
$457$	−36.2905	−	5.21779i	−1.69760	−	0.244078i	−0.775587	−	0.631240i	$-0.782546\pi$
$457$	−36.2905	−	5.21779i	−1.69760	−	0.244078i	−0.922012	+	0.387162i	$0.873455\pi$
$458$	6.12092	+	9.52434i	0.286012	+	0.445043i
$459$	−19.8038			−0.924361
$460$	−2.35017	−	10.4631i	−0.109577	−	0.487845i
$461$	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	$-0.0951405\pi$
$463$	38.5088	+	5.53673i	1.78966	+	0.257314i	0.833992	+	0.551776i	$0.186050\pi$
$464$	−0.955917	+	2.09317i	−0.0443773	+	0.0971728i
$465$	30.2637	+	13.0238i	1.40345	+	0.603962i
$466$	2.92726	+	6.40980i	0.135603	+	0.296928i
$467$	−2.38069	+	2.06288i	−0.110165	+	0.0954587i	−0.708202	−	0.706010i	$-0.750493\pi$
$467$	−2.38069	+	2.06288i	−0.110165	+	0.0954587i	0.598036	+	0.801469i	$0.295948\pi$
$468$	0.860118	−	0.123666i	0.0397590	−	0.00571648i
$469$	−6.37726	−	1.87253i	−0.294475	−	0.0864656i
$470$	1.39896	+	8.41127i	0.0645294	+	0.387983i
$471$	−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
$475$	35.9075	−	12.2841i	1.64755	−	0.563633i
$476$	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	$-0.00716256\pi$
$480$	−2.42504	−	2.67723i	−0.110687	−	0.122198i
$481$	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
$485$	−25.9784	−	3.15322i	−1.17962	−	0.143180i
$486$	−0.573438	+	3.98835i	−0.0260117	+	0.180915i
$487$	24.4449	+	11.1636i	1.10770	+	0.505871i	0.883387	−	0.468645i	$-0.155258\pi$
$487$	24.4449	+	11.1636i	1.10770	+	0.505871i	0.224317	+	0.974516i	$0.427985\pi$
$488$	−1.42778	−	4.86257i	−0.0646325	−	0.220118i
$489$	3.48856	+	7.63888i	0.157758	+	0.345442i
$490$	−0.186897	−	8.48934i	−0.00844314	−	0.383509i
$491$	−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
$495$	4.75923	−	1.51199i	0.213912	−	0.0679588i
$496$	−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	$0.791614\pi$
$500$	0.857404	−	11.1474i	0.0383443	−	0.498528i
$501$	−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	$-0.680469\pi$
$503$	−28.9325	−	4.15987i	−1.29004	−	0.185479i	−0.752967	+	0.658058i	$0.771378\pi$
$504$	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	$-0.00289280\pi$
$510$	−11.7588	+	5.68612i	−0.520690	+	0.251786i
$511$	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
$515$	−23.0666	−	34.2125i	−1.01644	−	1.50758i
$516$	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
$520$	4.12761	−	2.78290i	0.181008	−	0.122038i
$521$	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	−0.409536	−	0.912294i	$-0.634309\pi$
$523$	0.268516	−	0.122627i	0.0117414	−	0.00536211i	0.421277	+	0.906932i	$0.361582\pi$
$524$	16.5084	−	4.84732i	0.721175	−	0.211756i
$525$	−14.0350	−	3.45805i	−0.612538	−	0.150922i
$526$	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
$535$	−0.318331	+	1.17959i	−0.0137626	+	0.0509979i
$536$	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
$540$	3.70809	+	11.6718i	0.159571	+	0.502276i
$541$	−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
$545$	25.1597	−	0.553903i	1.07772	−	0.0237266i
$546$	−2.67364	−	5.85446i	−0.114421	−	0.250548i
$547$	6.00299	+	20.4443i	0.256669	+	0.874135i	0.982500	+	0.186262i	$0.0596374\pi$
$547$	6.00299	+	20.4443i	0.256669	+	0.874135i	−0.725831	+	0.687873i	$0.758544\pi$
$548$	0.175483	+	0.0801406i	0.00749628	+	0.00342344i
$549$	−0.281510	+	1.95795i	−0.0120146	+	0.0835632i
$550$	20.7748	−	19.6673i	0.885839	−	0.838618i
$551$	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
$555$	10.0942	+	11.1439i	0.428474	+	0.473034i
$556$	0.582913	−	1.27640i	0.0247210	−	0.0541315i
$557$	5.53158	+	18.8388i	0.234381	+	0.798227i	0.989736	+	0.142911i	$0.0456463\pi$
$557$	5.53158	+	18.8388i	0.234381	+	0.798227i	−0.755355	+	0.655316i	$0.772536\pi$
$558$	3.23835	−	1.47891i	0.137090	−	0.0626071i
$559$	3.32599	+	3.83839i	0.140674	+	0.162347i
$560$	2.08880	−	3.41315i	0.0882680	−	0.144232i
$561$	−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	$-0.537932\pi$
$563$	19.7813	−	30.7803i	0.833684	−	1.29724i	0.952567	−	0.304329i	$-0.0984321\pi$
$564$	−5.18230	−	3.33046i	−0.218214	−	0.140238i
$565$	−6.97803	+	1.16059i	−0.293568	+	0.0488263i
$566$	−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	$0.899585\pi$
$570$	−10.8379	+	25.1844i	−0.453951	+	1.05486i
$571$	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
$575$	5.76882	+	23.2749i	0.240577	+	0.970630i
$576$	−0.390320			−0.0162633
$577$	−2.54963	−	3.96730i	−0.106143	−	0.165161i	0.784119	−	0.620610i	$-0.213115\pi$
$577$	−2.54963	−	3.96730i	−0.106143	−	0.165161i	−0.890262	+	0.455449i	$0.849479\pi$
$578$	3.88549	+	0.558649i	0.161615	+	0.0232367i
$579$	2.83753	−	6.21332i	0.117924	−	0.258217i
$580$	2.03396	−	4.72637i	0.0844556	−	0.196252i
$581$	−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
$585$	−1.91673	+	0.318791i	−0.0792470	+	0.0131804i
$586$	−1.16212	−	0.746847i	−0.0480066	−	0.0308520i
$587$	−0.633296	+	0.985428i	−0.0261389	+	0.0406730i	−0.854077	−	0.520146i	$-0.825877\pi$
$587$	−0.633296	+	0.985428i	−0.0261389	+	0.0406730i	0.827938	+	0.560819i	$0.189514\pi$
$588$	4.63624	+	4.01732i	0.191195	+	0.165672i
$589$	66.4245	+	19.5040i	2.73697	+	0.803648i
$590$	−11.3104	+	18.4815i	−0.465643	+	0.760871i
$591$	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	$-0.799332\pi$
$593$	−10.8835	−	37.0657i	−0.446931	−	1.52211i	0.360851	−	0.932624i	$-0.382486\pi$
$594$	−13.0175	+	28.5044i	−0.534115	+	1.16955i
$595$	−9.71372	−	10.7239i	−0.398224	−	0.439637i
$596$	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	$0.692326\pi$
$600$	5.55300	+	5.86568i	0.226700	+	0.239465i
$601$	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
$605$	48.5910	−	1.06975i	1.97550	−	0.0434917i
$606$	0.781873	+	5.43805i	0.0317614	+	0.220906i
$607$	12.9794	−	44.2036i	0.526816	−	1.79417i	−0.0769809	−	0.997033i	$-0.524528\pi$
$607$	12.9794	−	44.2036i	0.526816	−	1.79417i	0.603797	−	0.797138i	$-0.293654\pi$
$608$	−5.73623	−	4.97047i	−0.232635	−	0.201579i
$609$	−5.59636	−	3.59656i	−0.226776	−	0.145740i
$610$	3.43115	+	10.8001i	0.138923	+	0.437285i
$611$	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	$-0.699846\pi$
$613$	−22.8521	+	3.28564i	−0.922989	+	0.132706i	−0.335595	+	0.942007i	$0.608937\pi$
$614$	3.23791	+	3.73675i	0.130672	+	0.150803i
$615$	−5.53464	+	20.5088i	−0.223178	+	0.826995i
$616$	9.82427	−	2.88467i	0.395831	−	0.116226i
$617$	−33.8682	−	15.4671i	−1.36348	−	0.622681i	−0.406720	−	0.913553i	$-0.633327\pi$
$617$	−33.8682	−	15.4671i	−1.36348	−	0.622681i	−0.956762	+	0.290872i	$0.906055\pi$
$618$	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
$625$	−1.36812	+	24.9625i	−0.0547246	+	0.998501i
$626$	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
$630$	−1.29505	+	0.873140i	−0.0515959	+	0.0347867i
$631$	−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
$635$	6.51231	+	9.65910i	0.258433	+	0.383310i
$636$	−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
$640$	−2.01306	+	0.973440i	−0.0795732	+	0.0384786i
$641$	−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	$-0.903749\pi$
$643$		−	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	$-0.802356\pi$
$647$	−44.7080	−	6.42803i	−1.75765	−	0.252712i	−0.944306	+	0.329069i	$0.893265\pi$
$648$	−6.98296	−	3.18901i	−0.274317	−	0.125276i
$649$	−53.1964	+	15.6199i	−2.08814	+	0.613134i
$650$	−9.09043	+	6.42440i	−0.356556	+	0.251986i
$651$	−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	$-0.976669\pi$
$653$	−3.03397	+	10.3328i	−0.118729	+	0.404352i	0.878586	+	0.477583i	$0.158487\pi$
$654$	−11.9061	+	13.7403i	−0.465564	+	0.537290i
$655$	−36.6665	+	11.6488i	−1.43268	+	0.455156i
$656$	−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	$-0.247744\pi$
$660$	0.454897	+	20.6626i	0.0177068	+	0.804291i
$661$	−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
$665$	−30.1512	−	3.65971i	−1.16921	−	0.141917i
$666$	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
$670$	−5.57533	−	6.15515i	−0.215394	−	0.237794i
$671$	−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	$-0.652865\pi$
$673$	−2.44556	+	1.11685i	−0.0942695	+	0.0430514i	0.367722	+	0.929936i	$0.380138\pi$
$674$	13.3341	+	15.3884i	0.513612	+	0.592740i
$675$	−8.86398	−	25.9102i	−0.341175	−	0.997284i
$676$	7.71783	+	2.26616i	0.296840	+	0.0871599i
$677$	1.34462	+	1.16512i	0.0516779	+	0.0447791i	0.680317	−	0.732918i	$-0.261842\pi$
$677$	1.34462	+	1.16512i	0.0516779	+	0.0447791i	−0.628639	+	0.777697i	$0.716388\pi$
$678$	2.76297	−	4.29926i	0.106111	−	0.165112i
$679$	17.6188	+	11.3229i	0.676148	+	0.434534i
$680$	1.32653	+	7.97578i	0.0508702	+	0.305857i
$681$	−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	$-0.658708\pi$
$683$	8.44314	−	7.31602i	0.323068	−	0.279940i	0.801261	+	0.598315i	$0.204163\pi$
$684$	1.23070	+	2.69485i	0.0470568	+	0.103040i
$685$	−0.396242	−	0.170520i	−0.0151396	−	0.00651522i
$686$	−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
$690$	−15.2604	−	8.19961i	−0.580953	−	0.312154i
$691$	−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
$695$	−1.24030	+	2.88212i	−0.0470472	+	0.109325i
$696$	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
$700$	−4.50159	+	7.73298i	−0.170144	+	0.292279i
$701$	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
$705$	11.7491	+	7.19028i	0.442496	+	0.270802i
$706$	−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	$0.0330935\pi$
$710$	1.29087	−	1.16927i	0.0484454	−	0.0438818i
$711$	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
$715$	−28.2749	−	3.43197i	−1.05742	−	0.128348i
$716$	−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	$0.806490\pi$
$720$	0.872570	−	0.0192100i	0.0325187	−	0.000715916i
$721$	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
$725$	−4.31436	+	10.6660i	−0.160231	+	0.396127i
$726$	−22.9942	+	26.5367i	−0.853395	+	0.984871i
$727$	3.40755	−	11.6050i	0.126379	−	0.430407i	−0.871858	−	0.489758i	$-0.837085\pi$
$727$	3.40755	−	11.6050i	0.126379	−	0.430407i	0.998237	+	0.0593512i	$0.0189032\pi$
$728$	−3.94352	+	0.566993i	−0.146157	+	0.0210142i
$729$	19.3441	+	22.3243i	0.716450	+	0.826827i
$730$	32.8749	+	8.87183i	1.21675	+	0.328361i
$731$	−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	$-0.322298\pi$
$733$	21.6326	+	3.11030i	0.799019	+	0.114882i	0.269302	+	0.963056i	$0.413207\pi$
$734$	−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	$-0.108514\pi$
$740$	8.37933	−	4.05193i	0.308030	−	0.148952i
$741$	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	$0.562204\pi$
$743$	−32.5133	+	28.1729i	−1.19280	+	1.03356i	−0.998616	+	0.0525972i	$0.983250\pi$
$744$	2.09692	+	14.5844i	0.0768769	+	0.534690i
$745$	−6.65433	+	4.48645i	−0.243796	+	0.164371i
$746$	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
$750$	−12.7026	−	12.8396i	−0.463832	−	0.468835i
$751$	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
$755$	1.10714	+	2.28954i	0.0402928	+	0.0833250i
$756$	1.39486	−	9.70148i	0.0507306	−	0.352839i
$757$	−25.8293	−	40.1912i	−0.938783	−	1.46077i	−0.886814	−	0.462126i	$-0.847087\pi$
$757$	−25.8293	−	40.1912i	−0.938783	−	1.46077i	−0.0519685	−	0.998649i	$-0.516550\pi$
$758$		−	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
$765$	0.822248	−	3.04687i	0.0297284	−	0.110160i
$766$	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	$0.141403\pi$
$770$	−21.8204	+	6.93226i	−0.786354	+	0.249821i
$771$	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	$-0.752881\pi$
$773$	7.38315	−	25.1447i	0.265553	−	0.904392i	0.979031	−	0.203713i	$-0.0653010\pi$
$774$	0.126725	+	0.881390i	0.00455502	+	0.0316809i
$775$	−28.3189	+	35.7466i	−1.01724	+	1.28405i
$776$	−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
$780$	0.969005	−	7.98332i	0.0346959	−	0.285849i
$781$	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
$785$	18.6782	−	16.9187i	0.666654	−	0.603855i
$786$	11.5462	−	25.2827i	0.411840	−	0.901804i
$787$	−1.95744	−	6.66642i	−0.0697751	−	0.237632i	0.917220	−	0.398380i	$-0.130428\pi$
$787$	−1.95744	−	6.66642i	−0.0697751	−	0.237632i	−0.986995	+	0.160748i	$0.948609\pi$
$788$	6.55293	−	2.99262i	0.233438	−	0.106608i
$789$	−21.4425	−	24.7459i	−0.763372	−	0.880979i
$790$	12.3821	−	20.2326i	0.440536	−	0.719845i
$791$	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
$795$	2.32805	+	13.9974i	0.0825675	+	0.496437i
$796$	20.9533	+	6.15244i	0.742670	+	0.218068i
$797$	25.5164	−	3.66870i	0.903837	−	0.129952i	0.325302	−	0.945610i	$-0.394534\pi$
$797$	25.5164	−	3.66870i	0.903837	−	0.129952i	0.578534	+	0.815658i	$0.303625\pi$
$798$	16.5831	−	14.3694i	0.587037	−	0.508670i
$799$	5.72793	+	12.5424i	0.202640	+	0.443719i
$800$	4.45234	−	2.27523i	0.157414	−	0.0804414i
$801$	−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
$805$	3.95268	−	18.7794i	0.139314	−	0.661889i
$806$	−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	$0.0462001\pi$
$810$	15.7676	+	6.78545i	0.554015	+	0.238416i
$811$	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
$815$	−11.4665	+	1.90711i	−0.401653	+	0.0668031i
$816$	−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
$820$	11.2159	+	6.86400i	0.391677	+	0.239701i
$821$	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	$0.0129087\pi$
$823$	5.17918	+	17.6387i	0.180535	+	0.614846i	−0.818643	+	0.574303i	$0.805273\pi$
$824$	7.66565	−	16.7854i	0.267045	−	0.584748i
$825$	−2.03387	−	46.1694i	−0.0708102	−	1.60741i
$826$	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	$0.595775\pi$
$830$	4.13589	−	34.0743i	0.143559	−	1.18274i
$831$	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
$835$	−0.141618	−	6.43267i	−0.00490090	−	0.222612i
$836$	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	$0.814204\pi$
$840$	−1.95730	−	6.16092i	−0.0675332	−	0.212572i
$841$	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
$845$	−17.3649	−	4.68622i	−0.597372	−	0.161211i
$846$	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	$-0.207298\pi$
$853$	−2.52524	−	3.92934i	−0.0864624	−	0.134538i	−0.881791	+	0.471641i	$0.843662\pi$
$854$	1.29069	−	8.97693i	0.0441664	−	0.307184i
$855$	−2.88388	−	5.96383i	−0.0986267	−	0.203959i
$856$	−0.524265	+	0.153938i	−0.0179190	+	0.00526150i
$857$	12.2604	−	5.59914i	0.418808	−	0.191263i	−0.194854	−	0.980832i	$-0.562423\pi$
$857$	12.2604	−	5.59914i	0.418808	−	0.191263i	0.613662	+	0.789569i	$0.289696\pi$
$858$	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	$0.913725\pi$
$860$	2.85173	+	4.22969i	0.0972430	+	0.144231i
$861$	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	$0.387872\pi$
$863$	−19.1561	+	29.8075i	−0.652083	+	1.01466i	−0.997103	+	0.0760652i	$0.975764\pi$
$864$	−3.58660	+	4.13916i	−0.122019	+	0.140817i
$865$	14.0414	+	20.8262i	0.477420	+	0.708112i
$866$	−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
$870$	−3.61860	−	7.48322i	−0.122682	−	0.253705i
$871$	−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	$-0.488916\pi$
$877$	−6.31801	−	0.908393i	−0.213344	−	0.0306743i	−0.248158	+	0.968720i	$0.579825\pi$
$878$	11.5999	+	5.29752i	0.391479	+	0.178783i
$879$	−2.14121	+	0.628715i	−0.0722211	+	0.0212060i
$880$	12.3518	+	3.33335i	0.416380	+	0.112367i
$881$	−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	$0.193093\pi$
$883$	−5.28319	+	17.9929i	−0.177794	+	0.605509i	−0.999373	+	0.0354147i	$0.988725\pi$
$884$	5.27161	−	6.08376i	0.177303	−	0.204619i
$885$	10.5984	+	33.3601i	0.356260	+	1.12139i
$886$	−9.47200	−	6.08728i	−0.318218	−	0.204506i
$887$	37.0965	+	32.1443i	1.24558	+	1.07930i	0.993762	+	0.111525i	$0.0355736\pi$
$887$	37.0965	+	32.1443i	1.24558	+	1.07930i	0.251817	+	0.967775i	$0.418972\pi$
$888$	−1.89445	+	6.45190i	−0.0635736	+	0.216512i
$889$	−1.32683	−	9.22831i	−0.0445005	−	0.309508i
$890$	0.0114603	+	0.520555i	0.000384149	+	0.0174491i
$891$	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
$895$	0.704086	−	5.80074i	0.0235350	−	0.193897i
$896$	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
$900$	−1.94971	+	0.0858891i	−0.0649902	+	0.00286297i
$901$	−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
$905$	48.9583	+	29.9619i	1.62743	+	0.995966i
$906$	−1.76290	−	0.517633i	−0.0585684	−	0.0171972i
$907$	−15.3449	−	13.2964i	−0.509519	−	0.441501i	0.361772	−	0.932266i	$-0.382172\pi$
$907$	−15.3449	−	13.2964i	−0.509519	−	0.441501i	−0.871292	+	0.490765i	$0.836717\pi$
$908$	−0.0527043	+	0.0820095i	−0.00174905	+	0.00272158i
$909$	−1.11671	−	0.717665i	−0.0370389	−	0.0238034i
$910$	8.78795	−	1.46161i	0.291318	−	0.0484520i
$911$	−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
$915$	16.8154	+	7.23639i	0.555901	+	0.239228i
$916$	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	$0.660697\pi$
$920$	−7.53153	+	7.63387i	−0.248307	+	0.251681i
$921$	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
$925$	−18.5328	+	9.47059i	−0.609355	+	0.311391i
$926$	−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	$0.290560\pi$
$930$	−5.40551	−	32.5006i	−0.177254	−	1.06574i
$931$	−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
$935$	24.1477	−	39.4578i	0.789713	−	1.29041i
$936$	−0.569050	−	0.656718i	−0.0186000	−	0.0214655i
$937$	6.19564	−	2.82945i	0.202403	−	0.0924342i	−0.311635	−	0.950202i	$-0.600877\pi$
$937$	6.19564	−	2.82945i	0.202403	−	0.0924342i	0.514037	+	0.857768i	$0.328149\pi$
$938$	1.87253	+	6.37726i	0.0611404	+	0.208225i
$939$	13.8846	−	30.4030i	0.453107	−	0.992166i
$940$	6.31967	−	5.72436i	0.206125	−	0.186708i
$941$	−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
$945$	−2.64078	+	21.7566i	−0.0859046	+	0.707741i
$946$	−1.85760	+	12.9199i	−0.0603958	+	0.420062i
$947$	21.6964	+	9.90842i	0.705039	+	0.321980i	0.735471	−	0.677557i	$-0.236961\pi$
$947$	21.6964	+	9.90842i	0.705039	+	0.321980i	−0.0304322	+	0.999537i	$0.509688\pi$
$948$	4.82809	+	16.4430i	0.156809	+	0.534042i
$949$	−14.0834	−	30.8383i	−0.457167	−	1.00106i
$950$	−29.7471	−	23.5660i	−0.965123	−	0.764582i
$951$	−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	$0.0384943\pi$
$953$	38.6928	+	33.5275i	1.25338	+	1.08606i	0.260686	+	0.965424i	$0.416051\pi$
$954$	1.28986	+	0.828940i	0.0417606	+	0.0268379i
$955$	22.7138	−	7.21607i	0.735001	−	0.233507i
$956$	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
$960$	−0.941158	+	3.48750i	−0.0303757	+	0.112558i
$961$	−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
$970$	11.3923	+	23.5592i	0.365785	+	0.756439i
$971$	−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
$975$	−1.77333	+	17.8946i	−0.0567919	+	0.573087i
$976$	−3.31874	+	3.83003i	−0.106230	+	0.122596i
$977$	−4.18672	+	6.51466i	−0.133945	+	0.208422i	−0.901746	−	0.432265i	$-0.857714\pi$
$977$	−4.18672	+	6.51466i	−0.133945	+	0.208422i	0.767801	+	0.640688i	$0.221351\pi$
$978$	4.54018	−	7.06466i	0.145179	−	0.225903i
$979$	−0.872464	+	1.00688i	−0.0278841	+	0.0321799i
$980$	−7.04064	+	4.74691i	−0.224905	+	0.151634i
$981$	−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	$-0.672554\pi$
$983$	−6.47106	+	2.95523i	−0.206395	+	0.0942573i	0.309536	+	0.950888i	$0.399826\pi$
$984$	−9.11512	+	2.67644i	−0.290579	+	0.0853218i
$985$	−14.5020	+	7.01259i	−0.462071	+	0.223440i
$986$	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
$995$	−47.1444	−	12.7227i	−1.49458	−	0.403337i
$996$	16.2390	+	18.7409i	0.514554	+	0.593827i
$997$	14.6103	−	2.10065i	0.462714	−	0.0665282i	0.0929842	−	0.995668i	$-0.470359\pi$
$997$	14.6103	−	2.10065i	0.462714	−	0.0665282i	0.369730	+	0.929139i	$0.379450\pi$
$998$	−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.219.3	yes	120
5.4	even	2	inner	230.2.j.a.219.10	yes	120
23.2	even	11	inner	230.2.j.a.209.10	yes	120
115.94	even	22	inner	230.2.j.a.209.3	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.209.3	✓	120	115.94	even	22	inner
230.2.j.a.209.10	yes	120	23.2	even	11	inner
230.2.j.a.219.3	yes	120	1.1	even	1	trivial
230.2.j.a.219.10	yes	120	5.4	even	2	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} +(0.883903 - 2.05395i) 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} +(-2.20577 + 0.366864i) 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} +(-1.88558 + 3.08107i) 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} +(1.50115 + 1.65727i) q^{20} +(2.43202 - 1.56297i) q^{21} +5.72152i q^{22} +(-4.17363 - 2.36237i) q^{23} -1.61545 q^{24} +(-3.43743 - 3.63099i) 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} +(3.61138 - 0.0795063i) 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} +(1.21161 + 3.81375i) 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} +(0.582598 - 2.15884i) 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} +(-1.19616 + 4.85481i) 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} +(-10.6079 + 7.15202i) 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} +(-2.01935 - 2.99510i) 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} +(4.48165 - 2.16716i) 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} +(4.66171 + 6.59625i) 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} +(-2.13111 + 0.677043i) 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} +(0.177960 + 8.08338i) 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} +(0.866422 + 0.105165i) q^{90} -3.98408 q^{91} +(3.88268 - 2.81510i) q^{92} +14.7344i q^{93} +(-3.20796 + 2.06163i) q^{94} +(11.3939 + 12.5789i) 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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