LMFDB - Embedded newform 570.2.bf.a.59.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.38
Character	$\chi$	$=$	570.59
Dual form			570.2.bf.a.29.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(1.62527 - 0.598755i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.32068 - 1.80439i) q^{5} +(1.70455 - 0.307434i) q^{6} +(-0.260757 + 0.150548i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.28299 - 1.94627i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(1.62527 - 0.598755i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.32068 - 1.80439i) q^{5} +(1.70455 - 0.307434i) q^{6} +(-0.260757 + 0.150548i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.28299 - 1.94627i) q^{9} +(1.61394 - 1.54764i) q^{10} +(-1.17946 - 0.680961i) q^{11} +(1.73204 - 0.00677128i) q^{12} +(-2.32350 + 1.94965i) q^{13} +(-0.282938 + 0.102981i) q^{14} +(1.06607 - 3.72337i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.0110966 + 0.0629319i) q^{17} +(2.58627 - 1.52027i) q^{18} +(-3.34215 + 2.79822i) q^{19} +(1.85817 - 1.24387i) q^{20} +(-0.333658 + 0.400810i) q^{21} +(-1.04329 - 0.875426i) q^{22} +(-0.311004 - 0.113196i) q^{23} +(1.70690 + 0.294097i) q^{24} +(-1.51163 - 4.76602i) q^{25} +(-2.62675 + 1.51656i) q^{26} +(2.54512 - 4.53016i) q^{27} +(-0.296522 + 0.0522848i) q^{28} +(1.30430 + 7.39707i) q^{29} +(1.69643 - 3.48169i) q^{30} +(-2.02006 + 1.16628i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-2.32466 - 0.400537i) q^{33} +(-0.0218560 + 0.0600489i) q^{34} +(-0.0727285 + 0.669332i) q^{35} +(2.81097 - 1.04807i) q^{36} +3.24655 q^{37} +(-3.77728 + 2.17535i) q^{38} +(-2.60894 + 4.55990i) q^{39} +(2.04593 - 0.902307i) q^{40} +(4.00006 + 3.35645i) q^{41} +(-0.398189 + 0.336782i) q^{42} +(-1.86872 - 5.13426i) q^{43} +(-0.875426 - 1.04329i) q^{44} +(-0.496744 - 6.68979i) q^{45} +(-0.286623 - 0.165482i) q^{46} +(0.167421 + 0.949491i) q^{47} +(1.62990 + 0.586029i) q^{48} +(-3.45467 + 5.98366i) q^{49} +(-0.661051 - 4.95611i) q^{50} +(0.0196458 + 0.108925i) q^{51} +(-2.85019 + 1.03738i) q^{52} +(2.00009 - 5.49519i) q^{53} +(3.29311 - 4.01938i) q^{54} +(-2.78640 + 1.22887i) q^{55} -0.301096 q^{56} +(-3.75645 + 6.54898i) q^{57} +7.51118i q^{58} +(-1.12932 + 6.40472i) q^{59} +(2.27524 - 3.13421i) q^{60} +(2.91313 + 1.06029i) q^{61} +(-2.19190 + 0.797785i) q^{62} +(-0.302297 + 0.851203i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.449328 + 6.76734i) q^{65} +(-2.21979 - 0.798125i) q^{66} +(-1.99315 - 11.3037i) q^{67} +(-0.0319514 + 0.0553414i) q^{68} +(-0.573242 + 0.00224105i) q^{69} +(-0.187852 + 0.646534i) q^{70} +(7.92785 - 2.88550i) q^{71} +(2.95026 - 0.544028i) q^{72} +(-6.48523 + 7.72880i) q^{73} +(3.19723 + 0.563758i) q^{74} +(-5.31048 - 6.84097i) q^{75} +(-4.09764 + 1.48638i) q^{76} +0.410069 q^{77} +(-3.36113 + 4.03759i) q^{78} +(-9.29589 + 11.0784i) q^{79} +(2.17153 - 0.533326i) q^{80} +(1.42405 - 8.88662i) q^{81} +(3.35645 + 4.00006i) q^{82} +(-0.598913 - 1.03735i) q^{83} +(-0.450621 + 0.262521i) q^{84} +(0.0988985 + 0.103135i) q^{85} +(-0.948773 - 5.38076i) q^{86} +(6.54887 + 11.2413i) q^{87} +(-0.680961 - 1.17946i) q^{88} +(10.2819 - 8.62750i) q^{89} +(0.672472 - 6.67441i) q^{90} +(0.312353 - 0.858182i) q^{91} +(-0.253533 - 0.212740i) q^{92} +(-2.58482 + 3.10504i) q^{93} +0.964139i q^{94} +(0.635161 + 9.72608i) q^{95} +(1.50337 + 0.860155i) q^{96} +(-1.21710 + 6.90250i) q^{97} +(-4.44124 + 5.29286i) q^{98} +(-4.01802 + 0.740924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	1.62527	−	0.598755i	0.938348	−	0.345691i
$3$	1.62527	−	0.598755i	0.938348	−	0.345691i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	1.32068	−	1.80439i	0.590624	−	0.806947i
$5$	1.32068	−	1.80439i	0.590624	−	0.806947i
$6$	1.70455	−	0.307434i	0.695879	−	0.125509i
$7$	−0.260757	+	0.150548i	−0.0985569	+	0.0569018i	−0.548468	−	0.836171i	$-0.684789\pi$
$7$	−0.260757	+	0.150548i	−0.0985569	+	0.0569018i	0.449911	+	0.893073i	$0.351456\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	2.28299	−	1.94627i	0.760995	−	0.648757i
$10$	1.61394	−	1.54764i	0.510373	−	0.489407i
$11$	−1.17946	−	0.680961i	−0.355620	−	0.205317i	0.311538	−	0.950234i	$-0.399156\pi$
$11$	−1.17946	−	0.680961i	−0.355620	−	0.205317i	−0.667158	+	0.744916i	$0.732489\pi$
$12$	1.73204	−	0.00677128i	0.499996	−	0.00195470i
$13$	−2.32350	+	1.94965i	−0.644422	+	0.540734i	−0.905373	−	0.424618i	$-0.860409\pi$
$13$	−2.32350	+	1.94965i	−0.644422	+	0.540734i	0.260951	+	0.965352i	$0.415964\pi$
$14$	−0.282938	+	0.102981i	−0.0756183	+	0.0275228i
$15$	1.06607	−	3.72337i	0.275257	−	0.961371i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.0110966	+	0.0629319i	−0.00269132	+	0.0152632i	−0.986124	−	0.166011i	$-0.946911\pi$
$17$	−0.0110966	+	0.0629319i	−0.00269132	+	0.0152632i	0.983433	+	0.181275i	$0.0580223\pi$
$18$	2.58627	−	1.52027i	0.609589	−	0.358331i
$19$	−3.34215	+	2.79822i	−0.766743	+	0.641955i
$19$	−3.34215	+	2.79822i	−0.766743	+	0.641955i
$20$	1.85817	−	1.24387i	0.415499	−	0.278138i
$21$	−0.333658	+	0.400810i	−0.0728102	+	0.0874640i
$22$	−1.04329	−	0.875426i	−0.222431	−	0.186642i
$23$	−0.311004	−	0.113196i	−0.0648489	−	0.0236031i	0.309392	−	0.950935i	$-0.399874\pi$
$23$	−0.311004	−	0.113196i	−0.0648489	−	0.0236031i	−0.374241	+	0.927332i	$0.622097\pi$
$24$	1.70690	+	0.294097i	0.348419	+	0.0600322i
$25$	−1.51163	−	4.76602i	−0.302325	−	0.953205i
$26$	−2.62675	+	1.51656i	−0.515148	+	0.297421i
$27$	2.54512	−	4.53016i	0.489809	−	0.871830i
$28$	−0.296522	+	0.0522848i	−0.0560374	+	0.00988090i
$29$	1.30430	+	7.39707i	0.242203	+	1.37360i	0.826900	+	0.562349i	$0.190102\pi$
$29$	1.30430	+	7.39707i	0.242203	+	1.37360i	−0.584697	+	0.811252i	$0.698787\pi$
$30$	1.69643	−	3.48169i	0.309724	−	0.635666i
$31$	−2.02006	+	1.16628i	−0.362814	+	0.209471i	−0.670314	−	0.742077i	$-0.733841\pi$
$31$	−2.02006	+	1.16628i	−0.362814	+	0.209471i	0.307501	+	0.951548i	$0.400507\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	−2.32466	−	0.400537i	−0.404672	−	0.0697245i
$34$	−0.0218560	+	0.0600489i	−0.00374828	+	0.0102983i
$35$	−0.0727285	+	0.669332i	−0.0122934	+	0.113138i
$36$	2.81097	−	1.04807i	0.468495	−	0.174678i
$37$	3.24655			0.533730			0.266865	−	0.963734i	$-0.414012\pi$
$37$	3.24655			0.533730			0.266865	+	0.963734i	$0.414012\pi$
$38$	−3.77728	+	2.17535i	−0.612756	+	0.352888i
$39$	−2.60894	+	4.55990i	−0.417765	+	0.730168i
$40$	2.04593	−	0.902307i	0.323490	−	0.142667i
$41$	4.00006	+	3.35645i	0.624704	+	0.524189i	0.899278	−	0.437377i	$-0.144093\pi$
$41$	4.00006	+	3.35645i	0.624704	+	0.524189i	−0.274574	+	0.961566i	$0.588537\pi$
$42$	−0.398189	+	0.336782i	−0.0614419	+	0.0519666i
$43$	−1.86872	−	5.13426i	−0.284977	−	0.782967i	−0.996750	−	0.0805579i	$-0.974330\pi$
$43$	−1.86872	−	5.13426i	−0.284977	−	0.782967i	0.711773	−	0.702409i	$-0.247892\pi$
$44$	−0.875426	−	1.04329i	−0.131975	−	0.157282i
$45$	−0.496744	−	6.68979i	−0.0740502	−	0.997255i
$46$	−0.286623	−	0.165482i	−0.0422603	−	0.0243990i
$47$	0.167421	+	0.949491i	0.0244209	+	0.138498i	0.994580	−	0.103970i	$-0.0331545\pi$
$47$	0.167421	+	0.949491i	0.0244209	+	0.138498i	−0.970160	+	0.242467i	$0.922043\pi$
$48$	1.62990	+	0.586029i	0.235256	+	0.0845860i
$49$	−3.45467	+	5.98366i	−0.493524	+	0.854809i
$50$	−0.661051	−	4.95611i	−0.0934867	−	0.700900i
$51$	0.0196458	+	0.108925i	0.00275097	+	0.0152526i
$52$	−2.85019	+	1.03738i	−0.395250	+	0.143859i
$53$	2.00009	−	5.49519i	0.274733	−	0.754823i	−0.723205	−	0.690634i	$-0.757332\pi$
$53$	2.00009	−	5.49519i	0.274733	−	0.754823i	0.997938	−	0.0641892i	$-0.0204461\pi$
$54$	3.29311	−	4.01938i	0.448135	−	0.546969i
$55$	−2.78640	+	1.22887i	−0.375718	+	0.165701i
$56$	−0.301096			−0.0402357
$57$	−3.75645	+	6.54898i	−0.497554	+	0.867433i
$58$			7.51118i			0.986266i
$59$	−1.12932	+	6.40472i	−0.147026	+	0.833824i	0.818693	+	0.574232i	$0.194699\pi$
$59$	−1.12932	+	6.40472i	−0.147026	+	0.833824i	−0.965718	+	0.259592i	$0.916412\pi$
$60$	2.27524	−	3.13421i	0.293733	−	0.404625i
$61$	2.91313	+	1.06029i	0.372988	+	0.135757i	0.521711	−	0.853122i	$-0.325294\pi$
$61$	2.91313	+	1.06029i	0.372988	+	0.135757i	−0.148723	+	0.988879i	$0.547516\pi$
$62$	−2.19190	+	0.797785i	−0.278371	+	0.101319i
$63$	−0.302297	+	0.851203i	−0.0380858	+	0.107242i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	0.449328	+	6.76734i	0.0557323	+	0.839385i
$66$	−2.21979	−	0.798125i	−0.273238	−	0.0982424i
$67$	−1.99315	−	11.3037i	−0.243502	−	1.38097i	−0.823946	−	0.566668i	$-0.808232\pi$
$67$	−1.99315	−	11.3037i	−0.243502	−	1.38097i	0.580444	−	0.814300i	$-0.302879\pi$
$68$	−0.0319514	+	0.0553414i	−0.00387467	+	0.00671113i
$69$	−0.573242	+	0.00224105i	−0.0690102	+	0.000269791i
$70$	−0.187852	+	0.646534i	−0.0224526	+	0.0772756i
$71$	7.92785	−	2.88550i	0.940862	−	0.342446i	0.174356	−	0.984683i	$-0.444216\pi$
$71$	7.92785	−	2.88550i	0.940862	−	0.342446i	0.766506	+	0.642237i	$0.221993\pi$
$72$	2.95026	−	0.544028i	0.347691	−	0.0641144i
$73$	−6.48523	+	7.72880i	−0.759039	+	0.904587i	−0.997787	−	0.0664943i	$-0.978819\pi$
$73$	−6.48523	+	7.72880i	−0.759039	+	0.904587i	0.238748	+	0.971082i	$0.423263\pi$
$74$	3.19723	+	0.563758i	0.371671	+	0.0655355i
$75$	−5.31048	−	6.84097i	−0.613201	−	0.789927i
$76$	−4.09764	+	1.48638i	−0.470032	+	0.170499i
$77$	0.410069			0.0467317
$78$	−3.36113	+	4.03759i	−0.380573	+	0.457167i
$79$	−9.29589	+	11.0784i	−1.04587	+	1.24642i	−0.0774757	+	0.996994i	$0.524686\pi$
$79$	−9.29589	+	11.0784i	−1.04587	+	1.24642i	−0.968394	+	0.249425i	$0.919758\pi$
$80$	2.17153	−	0.533326i	0.242785	−	0.0596277i
$81$	1.42405	−	8.88662i	0.158228	−	0.987403i
$82$	3.35645	+	4.00006i	0.370657	+	0.441732i
$83$	−0.598913	−	1.03735i	−0.0657393	−	0.113864i	0.831282	−	0.555850i	$-0.187607\pi$
$83$	−0.598913	−	1.03735i	−0.0657393	−	0.113864i	−0.897022	+	0.441987i	$0.854274\pi$
$84$	−0.450621	+	0.262521i	−0.0491668	+	0.0286433i
$85$	0.0988985	+	0.103135i	0.0107271	+	0.0111866i
$86$	−0.948773	−	5.38076i	−0.102309	−	0.580222i
$87$	6.54887	+	11.2413i	0.702112	+	1.20519i
$88$	−0.680961	−	1.17946i	−0.0725907	−	0.125731i
$89$	10.2819	−	8.62750i	1.08987	−	0.914513i	0.0931717	−	0.995650i	$-0.470299\pi$
$89$	10.2819	−	8.62750i	1.08987	−	0.914513i	0.996703	+	0.0811366i	$0.0258550\pi$
$90$	0.672472	−	6.67441i	0.0708848	−	0.703545i
$91$	0.312353	−	0.858182i	0.0327435	−	0.0899619i
$92$	−0.253533	−	0.212740i	−0.0264326	−	0.0221796i
$93$	−2.58482	+	3.10504i	−0.268034	+	0.321978i
$94$			0.964139i			0.0994433i
$95$	0.635161	+	9.72608i	0.0651661	+	0.997874i
$96$	1.50337	+	0.860155i	0.153437	+	0.0877892i
$97$	−1.21710	+	6.90250i	−0.123577	+	0.700842i	0.858565	+	0.512704i	$0.171356\pi$
$97$	−1.21710	+	6.90250i	−0.123577	+	0.700842i	−0.982143	+	0.188138i	$0.939755\pi$
$98$	−4.44124	+	5.29286i	−0.448633	+	0.534660i
$99$	−4.01802	+	0.740924i	−0.403826	+	0.0744657i
$100$	0.209611	−	4.99560i	0.0209611	−	0.499560i
$101$	−8.36352	−	9.96725i	−0.832201	−	0.991779i	−0.999982	−	0.00595439i	$-0.998105\pi$
$101$	−8.36352	−	9.96725i	−0.832201	−	0.991779i	0.167781	−	0.985824i	$-0.446340\pi$
$102$	0.000432703		0.110682i	4.28440e−5		0.0109591i
$103$	7.33114	−	12.6979i	0.722359	−	1.25116i	−0.237693	−	0.971340i	$-0.576391\pi$
$103$	7.33114	−	12.6979i	0.722359	−	1.25116i	0.960052	−	0.279822i	$-0.0902753\pi$
$104$	−2.98703	+	0.526694i	−0.292902	+	0.0516466i
$105$	0.282562	+	1.13139i	0.0275753	+	0.110412i
$106$	2.92393	−	5.06440i	0.283997	−	0.491898i
$107$	−8.05254	+	4.64914i	−0.778468	+	0.449449i	−0.835887	−	0.548901i	$-0.815046\pi$
$107$	−8.05254	+	4.64914i	−0.778468	+	0.449449i	0.0574188	+	0.998350i	$0.481713\pi$
$108$	3.94104	−	3.38648i	0.379227	−	0.325864i
$109$	4.18068	+	11.4863i	0.400437	+	1.10019i	0.962069	+	0.272805i	$0.0879513\pi$
$109$	4.18068	+	11.4863i	0.400437	+	1.10019i	−0.561632	+	0.827387i	$0.689826\pi$
$110$	−2.95746	+	0.726349i	−0.281983	+	0.0692546i
$111$	5.27652	−	1.94389i	0.500825	−	0.184506i
$112$	−0.296522	−	0.0522848i	−0.0280187	−	0.00494045i
$113$		−	10.9590i		−	1.03094i	−0.856907	−	0.515470i	$-0.827617\pi$
$113$		−	10.9590i		−	1.03094i	0.856907	−	0.515470i	$-0.172383\pi$
$114$	−4.83660	+	5.79718i	−0.452989	+	0.542956i
$115$	−0.614986	+	0.411677i	−0.0573478	+	0.0383890i
$116$	−1.30430	+	7.39707i	−0.121101	+	0.686800i
$117$	−1.50997	+	8.97317i	−0.139597	+	0.829570i
$118$	−2.22434	+	6.11131i	−0.204767	+	0.562592i
$119$	−0.00658077	−	0.0180805i	−0.000603258	−	0.00165744i
$120$	2.78493	−	2.69150i	0.254228	−	0.245699i
$121$	−4.57258	−	7.91995i	−0.415690	−	0.719995i
$122$	2.68475	+	1.55004i	0.243066	+	0.140334i
$123$	8.51085	+	3.06007i	0.767397	+	0.275917i
$124$	−2.29713	+	0.405046i	−0.206288	+	0.0363742i
$125$	−10.5961	−	3.56681i	−0.947746	−	0.319026i
$126$	−0.445514	+	0.785778i	−0.0396896	+	0.0700027i
$127$	−7.76577	+	6.51626i	−0.689101	+	0.578224i	−0.918650	−	0.395073i	$-0.870719\pi$
$127$	−7.76577	+	6.51626i	−0.689101	+	0.578224i	0.229549	+	0.973297i	$0.426275\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−6.11133	−	7.22564i	−0.538072	−	0.636182i
$130$	−0.732635	+	6.74255i	−0.0642563	+	0.591361i
$131$	−9.56494	−	1.68656i	−0.835692	−	0.147355i	−0.260603	−	0.965446i	$-0.583921\pi$
$131$	−9.56494	−	1.68656i	−0.835692	−	0.147355i	−0.575089	+	0.818091i	$0.695033\pi$
$132$	−2.04748	−	1.17146i	−0.178210	−	0.101963i
$133$	0.450224	−	1.23281i	0.0390394	−	0.106898i
$134$		−	11.4781i		−	0.991556i
$135$	−4.81288	−	10.5753i	−0.414227	−	0.910174i
$136$	−0.0410759	+	0.0489523i	−0.00352223	+	0.00419763i
$137$	−8.94292	−	3.25496i	−0.764045	−	0.278090i	−0.0695416	−	0.997579i	$-0.522154\pi$
$137$	−8.94292	−	3.25496i	−0.764045	−	0.278090i	−0.694503	+	0.719489i	$0.744376\pi$
$138$	−0.564922	−	0.0973354i	−0.0480894	−	0.00828574i
$139$	−9.86691	+	8.27932i	−0.836901	+	0.702243i	−0.956864	−	0.290535i	$-0.906167\pi$
$139$	−9.86691	+	8.27932i	−0.836901	+	0.702243i	0.119964	+	0.992778i	$0.461722\pi$
$140$	−0.297267	+	0.604092i	−0.0251237	+	0.0510551i
$141$	0.840616	+	1.44293i	0.0707926	+	0.121517i
$142$	8.30847	−	1.46501i	0.697231	−	0.122941i
$143$	4.06810	−	0.717316i	0.340192	−	0.0599850i
$144$	2.99991	−	0.0234562i	0.249992	−	0.00195468i
$145$	15.0697	+	7.41567i	1.25147	+	0.615838i
$146$	−7.72880	+	6.48523i	−0.639640	+	0.536722i
$147$	−2.03201	+	11.7936i	−0.167598	+	0.972716i
$148$	3.05076	+	1.11039i	0.250771	+	0.0912732i
$149$	10.4460	−	12.4490i	0.855768	−	1.01986i	−0.143775	−	0.989610i	$-0.545924\pi$
$149$	10.4460	−	12.4490i	0.855768	−	1.01986i	0.999542	−	0.0302536i	$-0.00963149\pi$
$150$	−4.04188	−	7.65919i	−0.330018	−	0.625370i
$151$		−	12.1073i		−	0.985276i	−0.870234	−	0.492638i	$-0.836033\pi$
$151$		−	12.1073i		−	0.985276i	0.870234	−	0.492638i	$-0.163967\pi$
$152$	−4.29350	+	0.752249i	−0.348249	+	0.0610154i
$153$	0.0971493	+	0.165270i	0.00785405	+	0.0133613i
$154$	0.403840	+	0.0712078i	0.0325423	+	0.00573809i
$155$	−0.563421	+	5.18526i	−0.0452551	+	0.416490i
$156$	−4.01118	+	3.39259i	−0.321152	+	0.271625i
$157$	5.19992	+	14.2867i	0.414998	+	1.14020i	0.954499	+	0.298214i	$0.0963908\pi$
$157$	5.19992	+	14.2867i	0.414998	+	1.14020i	−0.539501	+	0.841985i	$0.681387\pi$
$158$	−11.0784	+	9.29589i	−0.881351	+	0.739542i
$159$	−0.0395975	−	10.1287i	−0.00314029	−	0.803260i
$160$	2.23116	−	0.148141i	0.176388	−	0.0117116i
$161$	0.0981380	−	0.0173044i	0.00773436	−	0.00136378i
$162$	2.94556	−	8.50433i	0.231425	−	0.668164i
$163$	1.45342	+	0.839134i	0.113841	+	0.0657260i	0.555839	−	0.831290i	$-0.312397\pi$
$163$	1.45342	+	0.839134i	0.113841	+	0.0657260i	−0.441998	+	0.897016i	$0.645730\pi$
$164$	2.61085	+	4.52213i	0.203873	+	0.353119i
$165$	−3.79285	+	3.66561i	−0.295273	+	0.285368i
$166$	−0.409681	−	1.12559i	−0.0317974	−	0.0873626i
$167$	4.56974	−	12.5552i	0.353617	−	0.971554i	−0.627581	−	0.778551i	$-0.715955\pi$
$167$	4.56974	−	12.5552i	0.353617	−	0.971554i	0.981198	−	0.193003i	$-0.0618227\pi$
$168$	−0.489362	+	0.180283i	−0.0377551	+	0.0139091i
$169$	−0.659905	+	3.74251i	−0.0507619	+	0.287885i
$170$	0.0794868	+	0.118742i	0.00609636	+	0.00910709i
$171$	−2.18400	+	12.8930i	−0.167015	+	0.985954i
$172$		−	5.46377i		−	0.416608i
$173$	9.25645	+	1.63216i	0.703755	+	0.124091i	0.514063	−	0.857753i	$-0.328140\pi$
$173$	9.25645	+	1.63216i	0.703755	+	0.124091i	0.189692	+	0.981844i	$0.439251\pi$
$174$	4.49735	+	12.2077i	0.340943	+	0.925461i
$175$	1.11168	+	1.01520i	0.0840353	+	0.0767420i
$176$	−0.465805	−	1.27979i	−0.0351113	−	0.0964676i
$177$	1.99940	+	11.0856i	0.150284	+	0.833242i
$178$	11.6238	−	6.71101i	0.871241	−	0.503011i
$179$	−9.62052	+	16.6632i	−0.719072	+	1.24547i	0.242296	+	0.970202i	$0.422099\pi$
$179$	−9.62052	+	16.6632i	−0.719072	+	1.24547i	−0.961368	+	0.275266i	$0.911234\pi$
$180$	1.82126	−	6.45624i	0.135748	−	0.481220i
$181$	15.2585	−	2.69048i	1.13415	−	0.199982i	0.425107	−	0.905143i	$-0.360237\pi$
$181$	15.2585	−	2.69048i	1.13415	−	0.199982i	0.709047	+	0.705161i	$0.249125\pi$
$182$	0.456629	−	0.790905i	0.0338476	−	0.0586258i
$183$	5.36947	−	0.0209916i	0.396922	−	0.00155174i
$184$	−0.212740	−	0.253533i	−0.0156834	−	0.0186907i
$185$	4.28765	−	5.85804i	0.315234	−	0.430692i
$186$	−3.08474	+	2.60902i	−0.226184	+	0.191303i
$187$	0.0559421	−	0.0666693i	0.00409089	−	0.00487534i
$188$	−0.167421	+	0.949491i	−0.0122104	+	0.0692488i
$189$	0.0183489	+	1.56443i	0.00133468	+	0.113796i
$190$	−1.06340	+	9.68861i	−0.0771475	+	0.702886i
$191$			4.36267i			0.315672i	0.987465	+	0.157836i	$0.0504517\pi$
$191$			4.36267i			0.315672i	−0.987465	+	0.157836i	$0.949548\pi$
$192$	1.33117	+	1.10815i	0.0960689	+	0.0799735i
$193$	−14.4475	−	12.1229i	−1.03995	−	0.872624i	−0.0479511	−	0.998850i	$-0.515269\pi$
$193$	−14.4475	−	12.1229i	−1.03995	−	0.872624i	−0.992002	+	0.126226i	$0.959714\pi$
$194$	−2.39721	+	6.58629i	−0.172110	+	0.472868i
$195$	4.78225	+	10.7297i	0.342464	+	0.768370i
$196$	−5.29286	+	4.44124i	−0.378062	+	0.317231i
$197$	−9.22534	−	15.9787i	−0.657278	−	1.13844i	−0.981318	−	0.192395i	$-0.938374\pi$
$197$	−9.22534	−	15.9787i	−0.657278	−	1.13844i	0.324040	−	0.946044i	$-0.394959\pi$
$198$	−4.08564	+	0.0319455i	−0.290354	+	0.00227027i
$199$	0.786466	+	4.46027i	0.0557511	+	0.316180i	0.999911	−	0.0133061i	$-0.00423558\pi$
$199$	0.786466	+	4.46027i	0.0557511	+	0.316180i	−0.944160	+	0.329486i	$0.893124\pi$
$200$	1.07390	−	4.88331i	0.0759365	−	0.345302i
$201$	−10.0076	−	17.1781i	−0.705878	−	1.21165i
$202$	−6.50566	−	11.2681i	−0.457737	−	0.792823i
$203$	−1.45372	−	1.73248i	−0.102031	−	0.121596i
$204$	−0.0187936	+	0.109076i	−0.00131581	+	0.00763682i
$205$	11.3391	−	2.78487i	0.791958	−	0.194504i
$206$	9.42473	−	11.2320i	0.656652	−	0.782567i
$207$	−0.930329	+	0.346874i	−0.0646624	+	0.0241094i
$208$	−3.03311			−0.210308
$209$	5.84741	−	1.02450i	0.404474	−	0.0708664i
$210$	0.0818059	+	1.16327i	0.00564514	+	0.0802731i
$211$	−10.8988	−	1.92176i	−0.750306	−	0.132299i	−0.214598	−	0.976702i	$-0.568844\pi$
$211$	−10.8988	−	1.92176i	−0.750306	−	0.132299i	−0.535708	+	0.844403i	$0.679955\pi$
$212$	3.75893	−	4.47972i	0.258165	−	0.307669i
$213$	11.1572	−	9.43654i	0.764476	−	0.646581i
$214$	−8.73752	+	3.18020i	−0.597284	+	0.217394i
$215$	−11.7322	−	3.40881i	−0.800127	−	0.232479i
$216$	4.46922	−	2.65067i	0.304092	−	0.180355i
$217$	0.351163	−	0.608233i	0.0238385	−	0.0412895i
$218$	2.12259	+	12.0378i	0.143760	+	0.815303i
$219$	−5.91258	+	16.4444i	−0.399535	+	1.11121i
$220$	−3.03866	+	0.201756i	−0.204866	+	0.0136024i
$221$	−0.0969120	−	0.167857i	−0.00651901	−	0.0112913i
$222$	5.53391	−	0.998099i	0.371411	−	0.0669881i
$223$	−11.4237	+	4.15790i	−0.764990	+	0.278433i	−0.694899	−	0.719107i	$-0.744551\pi$
$223$	−11.4237	+	4.15790i	−0.764990	+	0.278433i	−0.0700905	+	0.997541i	$0.522329\pi$
$224$	−0.282938	−	0.102981i	−0.0189046	−	0.00688071i
$225$	−12.7270	−	7.93873i	−0.848467	−	0.529248i
$226$	1.90302	−	10.7926i	0.126587	−	0.717910i
$227$		−	24.7503i		−	1.64274i	−0.570399	−	0.821368i	$-0.693211\pi$
$227$		−	24.7503i		−	1.64274i	0.570399	−	0.821368i	$-0.306789\pi$
$228$	−5.76979	+	4.86924i	−0.382114	+	0.322474i
$229$	5.31192			0.351021			0.175511	−	0.984478i	$-0.443842\pi$
$229$	5.31192			0.351021			0.175511	+	0.984478i	$0.443842\pi$
$230$	−0.677130	+	0.298631i	−0.0446486	+	0.0196911i
$231$	0.666472	−	0.245531i	0.0438507	−	0.0161548i
$232$	−2.56897	+	7.05820i	−0.168661	+	0.463394i
$233$	13.5006	−	4.91382i	0.884455	−	0.321915i	0.140449	−	0.990088i	$-0.455145\pi$
$233$	13.5006	−	4.91382i	0.884455	−	0.321915i	0.744006	+	0.668173i	$0.232923\pi$
$234$	−3.04520	+	8.57465i	−0.199071	+	0.560542i
$235$	1.93436	+	0.951879i	0.126184	+	0.0620937i
$236$	−3.25176	+	5.63222i	−0.211672	+	0.366626i
$237$	−8.47506	+	23.5713i	−0.550514	+	1.53112i
$238$	−0.00334114	−	0.0189486i	−0.000216574	−	0.00122825i
$239$	8.88918	+	5.13217i	0.574993	+	0.331973i	0.759141	−	0.650926i	$-0.225619\pi$
$239$	8.88918	+	5.13217i	0.574993	+	0.331973i	−0.184148	+	0.982899i	$0.558953\pi$
$240$	3.20999	−	2.16701i	0.207204	−	0.139880i
$241$	−3.59890	−	4.28901i	−0.231826	−	0.276279i	0.637573	−	0.770390i	$-0.279938\pi$
$241$	−3.59890	−	4.28901i	−0.231826	−	0.276279i	−0.869399	+	0.494110i	$0.835494\pi$
$242$	−3.12783	−	8.59365i	−0.201065	−	0.552421i
$243$	−3.00645	−	15.2958i	−0.192864	−	0.981226i
$244$	2.37480	+	1.99270i	0.152031	+	0.127569i
$245$	6.23435	+	14.1360i	0.398298	+	0.903119i
$246$	7.85017	+	4.49147i	0.500509	+	0.286366i
$247$	2.30996	−	13.0177i	0.146979	−	0.828294i
$248$	−2.33257			−0.148118
$249$	−1.59451	−	1.32737i	−0.101048	−	0.0841184i
$250$	−9.81577	−	5.35262i	−0.620804	−	0.338530i
$251$	1.76923	−	4.86093i	0.111673	−	0.306819i	−0.871249	−	0.490841i	$-0.836690\pi$
$251$	1.76923	−	4.86093i	0.111673	−	0.306819i	0.982922	+	0.184022i	$0.0589118\pi$
$252$	−0.575195	+	0.696478i	−0.0362339	+	0.0438740i
$253$	0.289735	+	0.345292i	0.0182155	+	0.0217083i
$254$	−8.77933	+	5.06875i	−0.550864	+	0.318041i
$255$	0.222489	+	0.108406i	0.0139328	+	0.00678867i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	28.2371	−	4.97896i	1.76138	−	0.310579i	0.802981	−	0.596005i	$-0.203246\pi$
$257$	28.2371	−	4.97896i	1.76138	−	0.310579i	0.958401	+	0.285425i	$0.0921349\pi$
$258$	−4.76376	−	8.17709i	−0.296579	−	0.509083i
$259$	−0.846561	+	0.488762i	−0.0526028	+	0.0303702i
$260$	−1.89234	+	6.51290i	−0.117358	+	0.403913i
$261$	17.3744	+	14.3489i	1.07545	+	0.888173i
$262$	−9.12676	−	3.32187i	−0.563853	−	0.205226i
$263$	−1.57055	−	1.31785i	−0.0968442	−	0.0812619i	0.593080	−	0.805143i	$-0.297912\pi$
$263$	−1.57055	−	1.31785i	−0.0968442	−	0.0812619i	−0.689924	+	0.723882i	$0.742356\pi$
$264$	−1.81295	−	1.50921i	−0.111579	−	0.0928853i
$265$	−7.27399	−	10.8663i	−0.446838	−	0.667512i
$266$	0.657459	−	1.13590i	0.0403114	−	0.0696465i
$267$	11.5450	−	20.1783i	0.706543	−	1.23489i
$268$	1.99315	−	11.3037i	0.121751	−	0.690484i
$269$	12.2049	+	10.2411i	0.744144	+	0.624411i	0.933947	−	0.357411i	$-0.116340\pi$
$269$	12.2049	+	10.2411i	0.744144	+	0.624411i	−0.189803	+	0.981822i	$0.560785\pi$
$270$	−2.90339	−	11.2503i	−0.176695	−	0.684674i
$271$	16.9517	−	6.16992i	1.02974	−	0.374796i	0.228761	−	0.973483i	$-0.426533\pi$
$271$	16.9517	−	6.16992i	1.02974	−	0.374796i	0.800983	+	0.598687i	$0.204310\pi$
$272$	−0.0489523	+	0.0410759i	−0.00296817	+	0.00249059i
$273$	−0.00618392	−	1.58180i	−0.000374268	−	0.0957347i
$274$	−8.24184	−	4.75843i	−0.497908	−	0.287467i
$275$	−1.46257	+	6.65069i	−0.0881965	+	0.401052i
$276$	−0.539438	−	0.193954i	−0.0324703	−	0.0116747i
$277$	0.895389	+	0.516953i	0.0537987	+	0.0310607i	0.526658	−	0.850077i	$-0.323445\pi$
$277$	0.895389	+	0.516953i	0.0537987	+	0.0310607i	−0.472859	+	0.881138i	$0.656778\pi$
$278$	−11.1547	+	6.44017i	−0.669015	+	0.386256i
$279$	−2.34187	+	6.59420i	−0.140204	+	0.394784i
$280$	−0.397651	+	0.543294i	−0.0237642	+	0.0324680i
$281$	14.7019	+	5.35105i	0.877042	+	0.319217i	0.741015	−	0.671488i	$-0.234345\pi$
$281$	14.7019	+	5.35105i	0.877042	+	0.319217i	0.136027	+	0.990705i	$0.456567\pi$
$282$	0.577283	+	1.56698i	0.0343767	+	0.0933125i
$283$	7.62181	+	1.34393i	0.453070	+	0.0798884i	0.395526	−	0.918455i	$-0.370562\pi$
$283$	7.62181	+	1.34393i	0.453070	+	0.0798884i	0.0575432	+	0.998343i	$0.481673\pi$
$284$	8.43664			0.500622
$285$	6.85584	+	15.4272i	0.406105	+	0.913826i
$286$	4.13086			0.244263
$287$	−1.54835	−	0.273016i	−0.0913961	−	0.0161156i
$288$	2.95841	+	0.497829i	0.174326	+	0.0293348i
$289$	15.9709	+	5.81295i	0.939467	+	0.341938i
$290$	13.5531	+	9.91984i	0.795864	+	0.582513i
$291$	2.15480	+	11.9471i	0.126316	+	0.700354i
$292$	−8.73753	+	5.04461i	−0.511325	+	0.295214i
$293$	26.7166	+	15.4248i	1.56080	+	0.901128i	0.997176	+	0.0750949i	$0.0239260\pi$
$293$	26.7166	+	15.4248i	1.56080	+	0.901128i	0.563622	+	0.826033i	$0.309407\pi$
$294$	−4.04907	+	11.2615i	−0.236147	+	0.656786i
$295$	10.0651	+	10.4963i	0.586014	+	0.611118i
$296$	2.81160	+	1.62328i	0.163421	+	0.0943510i
$297$	−6.08673	+	3.61001i	−0.353188	+	0.209474i
$298$	12.4490	−	10.4460i	0.721153	−	0.605119i
$299$	0.943311	−	0.343337i	0.0545531	−	0.0198557i
$300$	−2.65047	−	8.24470i	−0.153025	−	0.476008i
$301$	1.26023	+	1.05746i	0.0726387	+	0.0609511i
$302$	2.10241	−	11.9233i	0.120980	−	0.686111i
$303$	−19.5609	−	11.1918i	−1.12374	−	0.642949i
$304$	−4.35890	−	0.00473766i	−0.250000	−	0.000271724i
$305$	5.76048	−	3.85611i	0.329844	−	0.220800i
$306$	0.0669746	+	0.179629i	0.00382868	+	0.0102687i
$307$	−5.35862	−	4.49641i	−0.305832	−	0.256624i	0.476935	−	0.878939i	$-0.341748\pi$
$307$	−5.35862	−	4.49641i	−0.305832	−	0.256624i	−0.782767	+	0.622315i	$0.786192\pi$
$308$	0.385339	+	0.140252i	0.0219567	+	0.00799160i
$309$	4.31213	−	25.0270i	0.245308	−	1.42374i
$310$	−1.45527	+	5.00864i	−0.0826539	+	0.284472i
$311$	8.39956	−	4.84949i	0.476295	−	0.274989i	−0.242576	−	0.970132i	$-0.577992\pi$
$311$	8.39956	−	4.84949i	0.476295	−	0.274989i	0.718871	+	0.695143i	$0.244659\pi$
$312$	−4.53936	+	2.64452i	−0.256991	+	0.149716i
$313$	19.4845	−	3.43564i	1.10133	−	0.194194i	0.406700	−	0.913562i	$-0.366680\pi$
$313$	19.4845	−	3.43564i	1.10133	−	0.194194i	0.694629	+	0.719368i	$0.255568\pi$
$314$	2.64007	+	14.9726i	0.148988	+	0.844950i
$315$	1.13666	+	1.66962i	0.0640438	+	0.0940727i
$316$	−12.5243	+	7.23092i	−0.704548	+	0.406771i
$317$	−7.42447	−	8.84814i	−0.417000	−	0.496961i	0.516125	−	0.856513i	$-0.327374\pi$
$317$	−7.42447	−	8.84814i	−0.417000	−	0.496961i	−0.933125	+	0.359552i	$0.882929\pi$
$318$	1.71984	−	9.98172i	0.0964437	−	0.559747i
$319$	3.49874	−	9.61271i	0.195892	−	0.538209i
$320$	2.22298	+	0.241546i	0.124269	+	0.0135028i
$321$	−10.3038	+	12.3776i	−0.575104	+	0.690849i
$322$	0.0996520			0.00555339
$323$	−0.139011	−	0.241379i	−0.00773475	−	0.0134307i
$324$	4.37757	−	7.86364i	0.243198	−	0.436869i
$325$	12.8043	+	8.12671i	0.710256	+	0.450789i
$326$	1.28563	+	1.07877i	0.0712043	+	0.0597475i
$327$	13.6722	+	16.1652i	0.756076	+	0.893935i
$328$	1.78593	+	4.90679i	0.0986113	+	0.270932i
$329$	−0.186600	−	0.222382i	−0.0102876	−	0.0122603i
$330$	−4.37176	+	2.95130i	−0.240657	+	0.162464i
$331$	−19.1300	−	11.0447i	−1.05148	−	0.607072i	−0.128416	−	0.991720i	$-0.540989\pi$
$331$	−19.1300	−	11.0447i	−1.05148	−	0.607072i	−0.923063	+	0.384648i	$0.874323\pi$
$332$	−0.208000	−	1.17963i	−0.0114155	−	0.0647405i
$333$	7.41183	−	6.31868i	0.406166	−	0.346261i
$334$	6.68051	−	11.5710i	0.365541	−	0.633136i
$335$	−23.0286	−	11.3321i	−1.25819	−	0.619141i
$336$	−0.513233	+	0.0925671i	−0.0279992	+	0.00504995i
$337$	3.75445	−	1.36651i	0.204518	−	0.0744385i	−0.237730	−	0.971331i	$-0.576403\pi$
$337$	3.75445	−	1.36651i	0.204518	−	0.0744385i	0.442248	+	0.896893i	$0.354181\pi$
$338$	−1.29976	+	3.57106i	−0.0706976	+	0.194240i
$339$	−6.56178	−	17.8114i	−0.356387	−	0.967381i
$340$	0.0576599	+	0.130741i	0.00312705	+	0.00709041i
$341$	3.17677			0.172032
$342$	−4.38967	+	12.3179i	−0.237366	+	0.666076i
$343$		−	4.18805i		−	0.226133i
$344$	0.948773	−	5.38076i	0.0511544	−	0.290111i
$345$	−0.753023	+	1.03731i	−0.0405414	+	0.0558469i
$346$	8.83241	+	3.21473i	0.474833	+	0.172825i
$347$	13.1531	−	4.78733i	0.706095	−	0.256997i	0.0360839	−	0.999349i	$-0.488512\pi$
$347$	13.1531	−	4.78733i	0.706095	−	0.256997i	0.670011	+	0.742351i	$0.266289\pi$
$348$	2.30919	+	12.8032i	0.123786	+	0.686322i
$349$	3.44103	+	5.96003i	0.184194	+	0.319033i	0.943305	−	0.331928i	$-0.107699\pi$
$349$	3.44103	+	5.96003i	0.184194	+	0.319033i	−0.759111	+	0.650962i	$0.774366\pi$
$350$	0.918506	+	1.19282i	0.0490962	+	0.0637589i
$351$	2.91862	+	15.4879i	0.155785	+	0.826683i
$352$	−0.236495	−	1.34123i	−0.0126052	−	0.0714879i
$353$	7.96374	−	13.7936i	0.423867	−	0.734159i	−0.572447	−	0.819942i	$-0.694006\pi$
$353$	7.96374	−	13.7936i	0.423867	−	0.734159i	0.996314	+	0.0857827i	$0.0273391\pi$
$354$	0.0440372	+	11.2643i	0.00234055	+	0.598693i
$355$	5.26356	−	18.1157i	0.279361	−	0.961482i
$356$	12.6126	−	4.59060i	0.668465	−	0.243301i
$357$	−0.0215213	−	0.0254454i	−0.00113903	−	0.00134671i
$358$	−12.3679	+	14.7395i	−0.653664	+	0.779007i
$359$	−21.1878	−	3.73598i	−1.11825	−	0.197177i	−0.416176	−	0.909284i	$-0.636630\pi$
$359$	−21.1878	−	3.73598i	−1.11825	−	0.197177i	−0.702071	+	0.712107i	$0.747741\pi$
$360$	2.91470	−	6.04190i	0.153618	−	0.318436i
$361$	3.33998	−	18.7041i	0.175789	−	0.984428i
$362$	15.4939			0.814340
$363$	−12.1738	−	10.1342i	−0.638958	−	0.531906i
$364$	0.587031	−	0.699596i	0.0307688	−	0.0366688i
$365$	5.38085	+	21.9091i	0.281647	+	1.14678i
$366$	5.29154	+	0.911726i	0.276593	+	0.0476567i
$367$	1.43718	+	1.71277i	0.0750202	+	0.0894056i	0.802249	−	0.596989i	$-0.203637\pi$
$367$	1.43718	+	1.71277i	0.0750202	+	0.0894056i	−0.727229	+	0.686395i	$0.759192\pi$
$368$	−0.165482	−	0.286623i	−0.00862634	−	0.0149413i
$369$	15.6646	−	0.122481i	0.815468	−	0.00637613i
$370$	5.23975	−	5.02450i	0.272401	−	0.261211i
$371$	0.305754	+	1.73402i	0.0158740	+	0.0900258i
$372$	−3.49093	+	2.03373i	−0.180996	+	0.105444i
$373$	8.49126	+	14.7073i	0.439661	+	0.761515i	0.997663	−	0.0683245i	$-0.0217653\pi$
$373$	8.49126	+	14.7073i	0.439661	+	0.761515i	−0.558002	+	0.829839i	$0.688432\pi$
$374$	0.0666693	−	0.0559421i	0.00344738	−	0.00289270i
$375$	−19.3572	+	0.547453i	−0.999600	+	0.0282704i
$376$	−0.329755	+	0.905994i	−0.0170058	+	0.0467231i
$377$	−17.4522	−	14.6441i	−0.898834	−	0.754212i
$378$	−0.253591	+	1.54385i	−0.0130433	+	0.0794072i
$379$		−	31.6333i		−	1.62489i	−0.583037	−	0.812446i	$-0.698136\pi$
$379$		−	31.6333i		−	1.62489i	0.583037	−	0.812446i	$-0.301864\pi$
$380$	−2.72966	+	9.35676i	−0.140029	+	0.479992i
$381$	−8.71981	+	15.2404i	−0.446730	+	0.780792i
$382$	−0.757570	+	4.29639i	−0.0387607	+	0.219823i
$383$	3.91617	−	4.66711i	0.200107	−	0.238478i	−0.656654	−	0.754192i	$-0.728029\pi$
$383$	3.91617	−	4.66711i	0.200107	−	0.238478i	0.856761	+	0.515714i	$0.172473\pi$
$384$	1.11852	+	1.32247i	0.0570792	+	0.0674868i
$385$	0.541569	−	0.739924i	0.0276009	−	0.0377100i
$386$	−12.1229	−	14.4475i	−0.617038	−	0.735358i
$387$	−14.2589	−	8.08441i	−0.724822	−	0.410954i
$388$	−3.50449	+	6.06995i	−0.177914	+	0.308155i
$389$	−16.3942	+	2.89073i	−0.831217	+	0.146566i	−0.573036	−	0.819530i	$-0.694234\pi$
$389$	−16.3942	+	2.89073i	−0.831217	+	0.146566i	−0.258182	+	0.966096i	$0.583123\pi$
$390$	2.84641	+	11.3971i	0.144134	+	0.577116i
$391$	0.0105748	−	0.0183160i	0.000534788	−	0.000926280i
$392$	−5.98366	+	3.45467i	−0.302221	+	0.174487i
$393$	−16.5554	+	2.98595i	−0.835110	+	0.150621i
$394$	−6.31050	−	17.3380i	−0.317918	−	0.873474i
$395$	7.71288	+	31.4044i	0.388077	+	1.58013i
$396$	−4.02912	−	0.678004i	−0.202471	−	0.0340710i
$397$	31.3959	+	5.53594i	1.57571	+	0.277841i	0.892043	−	0.451951i	$-0.149272\pi$
$397$	31.3959	+	5.53594i	1.57571	+	0.277841i	0.683670	+	0.729791i	$0.260383\pi$
$398$			4.52908i			0.227022i
$399$	−0.00641620	−	2.27322i	−0.000321212	−	0.113803i
$400$	1.90557	−	4.62264i	0.0952784	−	0.231132i
$401$	−6.36197	+	36.0805i	−0.317702	+	1.80177i	0.238953	+	0.971031i	$0.423196\pi$
$401$	−6.36197	+	36.0805i	−0.317702	+	1.80177i	−0.556655	+	0.830744i	$0.687915\pi$
$402$	−6.87256	−	18.6550i	−0.342772	−	0.930425i
$403$	2.41977	−	6.64826i	0.120537	−	0.331174i
$404$	−4.45013	−	12.2266i	−0.221402	−	0.608298i
$405$	−14.1542	−	14.3059i	−0.703328	−	0.710865i
$406$	−1.13079	−	1.95859i	−0.0561204	−	0.0972033i
$407$	−3.82918	−	2.21078i	−0.189805	−	0.109584i
$408$	−0.0374488	+	0.104155i	−0.00185399	+	0.00515644i
$409$	16.0690	−	2.83340i	0.794562	−	0.140103i	0.238389	−	0.971170i	$-0.423381\pi$
$409$	16.0690	−	2.83340i	0.794562	−	0.140103i	0.556172	+	0.831067i	$0.312269\pi$
$410$	11.6504	−	0.773548i	0.575374	−	0.0382028i
$411$	−16.4836	+	0.0644413i	−0.813074	+	0.00317865i
$412$	11.2320	−	9.42473i	0.553359	−	0.464323i
$413$	−0.669739	−	1.84009i	−0.0329557	−	0.0905451i
$414$	−0.976430	+	0.180054i	−0.0479889	+	0.00884916i
$415$	−2.66275	−	0.289330i	−0.130709	−	0.0142026i
$416$	−2.98703	−	0.526694i	−0.146451	−	0.0258233i
$417$	−11.0791	+	19.3640i	−0.542545	+	0.948258i
$418$	5.93648	+	0.00645233i	0.290362	+	0.000315594i
$419$			16.2266i			0.792723i	0.918095	+	0.396361i	$0.129727\pi$
$419$			16.2266i			0.792723i	−0.918095	+	0.396361i	$0.870273\pi$
$420$	−0.121436	+	1.15980i	−0.00592548	+	0.0565925i
$421$	−2.31467	+	2.75851i	−0.112810	+	0.134442i	−0.819494	−	0.573087i	$-0.805746\pi$
$421$	−2.31467	+	2.75851i	−0.112810	+	0.134442i	0.706684	+	0.707529i	$0.250190\pi$
$422$	−10.3995	−	3.78512i	−0.506241	−	0.184257i
$423$	2.23019	+	1.84183i	0.108435	+	0.0895528i
$424$	4.47972	−	3.75893i	0.217555	−	0.182550i
$425$	0.316709	−	0.0422430i	0.0153626	−	0.00204909i
$426$	12.6263	−	7.35576i	0.611746	−	0.356388i
$427$	−0.919244	+	0.162087i	−0.0444853	+	0.00784396i
$428$	−9.15701	+	1.61463i	−0.442621	+	0.0780460i
$429$	6.18225	−	3.60162i	0.298482	−	0.173888i
$430$	−10.9620	−	5.39429i	−0.528634	−	0.260136i
$431$	−0.498544	+	0.418328i	−0.0240140	+	0.0201502i	−0.654716	−	0.755875i	$-0.727212\pi$
$431$	−0.498544	+	0.418328i	−0.0240140	+	0.0201502i	0.630702	+	0.776025i	$0.282767\pi$
$432$	4.86161	−	1.83433i	0.233904	−	0.0882543i
$433$	−2.08615	−	0.759297i	−0.100254	−	0.0364895i	0.291406	−	0.956599i	$-0.405877\pi$
$433$	−2.08615	−	0.759297i	−0.100254	−	0.0364895i	−0.391660	+	0.920110i	$0.628099\pi$
$434$	0.451447	−	0.538014i	0.0216702	−	0.0258255i
$435$	28.9325	+	3.02936i	1.38721	+	0.145247i
$436$			12.2235i			0.585400i
$437$	1.35617	−	0.491938i	0.0648745	−	0.0235326i
$438$	−8.67830	+	15.1679i	−0.414665	+	0.724750i
$439$	1.63843	+	0.288899i	0.0781980	+	0.0137884i	0.212610	−	0.977137i	$-0.431804\pi$
$439$	1.63843	+	0.288899i	0.0781980	+	0.0137884i	−0.134412	+	0.990925i	$0.542915\pi$
$440$	−3.02753	−	0.328966i	−0.144332	−	0.0156829i
$441$	3.75888	+	20.3844i	0.178994	+	0.970683i
$442$	−0.0662917	−	0.182135i	−0.00315318	−	0.00866328i
$443$	−26.1390	+	21.9332i	−1.24190	+	1.04208i	−0.244529	+	0.969642i	$0.578633\pi$
$443$	−26.1390	+	21.9332i	−1.24190	+	1.04208i	−0.997373	+	0.0724371i	$0.976922\pi$
$444$	5.62315	−	0.0219833i	0.266863	−	0.00104328i
$445$	−1.98835	−	29.9466i	−0.0942568	−	1.41960i
$446$	−11.9722	+	2.11102i	−0.566900	+	0.0999597i
$447$	9.52358	−	26.4876i	0.450450	−	1.25282i
$448$	−0.260757	−	0.150548i	−0.0123196	−	0.00711273i
$449$	−19.7245	−	34.1638i	−0.930855	−	1.61229i	−0.781863	−	0.623450i	$-0.785730\pi$
$449$	−19.7245	−	34.1638i	−0.930855	−	1.61229i	−0.148992	−	0.988838i	$-0.547603\pi$
$450$	−11.1551	−	10.0281i	−0.525857	−	0.472731i
$451$	−2.43229	−	6.68267i	−0.114532	−	0.314675i
$452$	3.74821	−	10.2981i	0.176301	−	0.484384i
$453$	−7.24928	−	19.6775i	−0.340601	−	0.924532i
$454$	4.29785	−	24.3743i	0.201708	−	1.14394i
$455$	−1.13598	−	1.69699i	−0.0532554	−	0.0795559i
$456$	−6.52767	+	3.79336i	−0.305686	+	0.177640i
$457$		−	20.8281i		−	0.974295i	−0.873320	−	0.487148i	$-0.838037\pi$
$457$		−	20.8281i		−	0.974295i	0.873320	−	0.487148i	$-0.161963\pi$
$458$	5.23122	+	0.922404i	0.244439	+	0.0431011i
$459$	0.256850	+	0.210439i	0.0119887	+	0.00982244i
$460$	−0.718700	+	0.176512i	−0.0335095	+	0.00822991i
$461$	−3.47801	−	9.55575i	−0.161987	−	0.445056i	0.831971	−	0.554820i	$-0.187213\pi$
$461$	−3.47801	−	9.55575i	−0.161987	−	0.445056i	−0.993958	+	0.109764i	$0.964991\pi$
$462$	0.698983	−	0.126069i	0.0325196	−	0.00586527i
$463$	−21.1384	+	12.2042i	−0.982383	+	0.567179i	−0.902989	−	0.429664i	$-0.858632\pi$
$463$	−21.1384	+	12.2042i	−0.982383	+	0.567179i	−0.0793943	+	0.996843i	$0.525299\pi$
$464$	−3.75559	+	6.50487i	−0.174349	+	0.301981i
$465$	2.18899	+	8.76478i	0.101512	+	0.406457i
$466$	14.1488	−	2.49481i	0.655430	−	0.115570i
$467$	−4.56140	+	7.90057i	−0.211076	+	0.365595i	−0.952052	−	0.305937i	$-0.901030\pi$
$467$	−4.56140	+	7.90057i	−0.211076	+	0.365595i	0.740975	+	0.671532i	$0.234364\pi$
$468$	−4.48791	+	7.91558i	−0.207454	+	0.365898i
$469$	2.22148	+	2.64746i	0.102578	+	0.122248i
$470$	1.73968	+	1.27332i	0.0802454	+	0.0587337i
$471$	17.0055	+	20.1061i	0.783570	+	0.926442i
$472$	−4.18038	+	4.98199i	−0.192418	+	0.229315i
$473$	−1.29215	+	7.32817i	−0.0594133	+	0.336950i
$474$	−12.4394	+	21.7416i	−0.571362	+	0.998623i
$475$	18.3885	+	11.6989i	0.843720	+	0.536783i
$476$		−	0.0192409i		−	0.000881904i
$477$	−6.12897	−	16.4382i	−0.280626	−	0.752652i
$478$	7.86294	+	6.59779i	0.359643	+	0.301776i
$479$	10.5719	−	29.0461i	0.483043	−	1.32715i	−0.423829	−	0.905742i	$-0.639314\pi$
$479$	10.5719	−	29.0461i	0.483043	−	1.32715i	0.906872	−	0.421407i	$-0.138464\pi$
$480$	3.53752	−	1.57668i	0.161465	−	0.0719654i
$481$	−7.54336	+	6.32963i	−0.343948	+	0.288606i
$482$	−2.79945	−	4.84879i	−0.127511	−	0.220856i
$483$	0.149139	−	0.0868849i	0.00678608	−	0.00395340i
$484$	−1.58804	−	9.00623i	−0.0721837	−	0.409374i
$485$	10.8474	+	11.3121i	0.492555	+	0.513655i
$486$	−0.304689	−	15.5855i	−0.0138210	−	0.706972i
$487$	19.2347	+	33.3156i	0.871609	+	1.50967i	0.860331	+	0.509735i	$0.170257\pi$
$487$	19.2347	+	33.3156i	0.871609	+	1.50967i	0.0112782	+	0.999936i	$0.496410\pi$
$488$	1.99270	+	2.37480i	0.0902052	+	0.107502i
$489$	2.86463	+	0.493573i	0.129543	+	0.0223201i
$490$	3.68493	+	15.0039i	0.166468	+	0.677806i
$491$	−9.08306	+	10.8248i	−0.409913	+	0.488515i	−0.931016	−	0.364979i	$-0.881076\pi$
$491$	−9.08306	+	10.8248i	−0.409913	+	0.488515i	0.521103	+	0.853494i	$0.325521\pi$
$492$	6.95097	+	5.78640i	0.313374	+	0.260871i
$493$	−0.479985			−0.0216174
$494$	4.53536	−	12.4188i	0.204055	−	0.558747i
$495$	−3.96959	+	8.22859i	−0.178420	+	0.369848i
$496$	−2.29713	−	0.405046i	−0.103144	−	0.0181871i
$497$	−1.63283	+	1.94594i	−0.0732426	+	0.0872872i
$498$	−1.33979	−	1.58408i	−0.0600375	−	0.0709845i
$499$	2.10380	−	0.765722i	0.0941792	−	0.0342784i	−0.294501	−	0.955651i	$-0.595153\pi$
$499$	2.10380	−	0.765722i	0.0941792	−	0.0342784i	0.388680	+	0.921373i	$0.372931\pi$
$500$	−8.73718	−	6.97580i	−0.390738	−	0.311967i
$501$	−0.0904711	−	23.1418i	−0.00404195	−	1.03390i
$502$	2.58645	−	4.47986i	0.115439	−	0.199946i
$503$	6.16336	+	34.9542i	0.274811	+	1.55853i	0.739562	+	0.673088i	$0.235033\pi$
$503$	6.16336	+	34.9542i	0.274811	+	1.55853i	−0.464751	+	0.885441i	$0.653856\pi$
$504$	−0.687398	+	0.586015i	−0.0306192	+	0.0261032i
$505$	−29.0303	+	1.92751i	−1.29183	+	0.0857731i
$506$	0.225373	+	0.390358i	0.0100191	+	0.0173535i
$507$	1.16832	+	6.47769i	0.0518870	+	0.287685i
$508$	−9.52613	+	3.46723i	−0.422654	+	0.153833i
$509$	−33.7020	−	12.2665i	−1.49382	−	0.543704i	−0.539364	−	0.842073i	$-0.681335\pi$
$509$	−33.7020	−	12.2665i	−1.49382	−	0.543704i	−0.954451	+	0.298368i	$0.903558\pi$
$510$	0.200285	+	0.145394i	0.00886875	+	0.00643817i
$511$	0.527513	−	2.99168i	0.0233358	−	0.132344i
$512$			1.00000i			0.0441942i
$513$	4.17018	+	22.2623i	0.184118	+	0.982904i
$514$	28.6727			1.26470
$515$	−13.2299	−	29.9980i	−0.582978	−	1.32187i
$516$	−3.27146	−	8.88008i	−0.144018	−	0.390924i
$517$	0.449100	−	1.23389i	0.0197514	−	0.0542665i
$518$	−0.918573	+	0.334333i	−0.0403598	+	0.0146898i
$519$	16.0215	−	2.88965i	0.703265	−	0.126841i
$520$	−2.99454	+	6.08535i	−0.131319	+	0.266860i
$521$	−7.48895	+	12.9712i	−0.328097	+	0.568280i	−0.982134	−	0.188182i	$-0.939741\pi$
$521$	−7.48895	+	12.9712i	−0.328097	+	0.568280i	0.654037	+	0.756462i	$0.273074\pi$
$522$	14.6188	+	17.1479i	0.639848	+	0.750544i
$523$	4.94711	+	28.0565i	0.216322	+	1.22682i	0.878598	+	0.477563i	$0.158480\pi$
$523$	4.94711	+	28.0565i	0.216322	+	1.22682i	−0.662276	+	0.749260i	$0.730409\pi$
$524$	−8.41127	−	4.85625i	−0.367448	−	0.212146i
$525$	2.41464	+	0.984348i	0.105383	+	0.0429605i
$526$	−1.31785	−	1.57055i	−0.0574609	−	0.0684792i
$527$	−0.0509806	−	0.140068i	−0.00222075	−	0.00610146i
$528$	−1.52334	−	1.80109i	−0.0662947	−	0.0783826i
$529$	−17.5351	−	14.7137i	−0.762396	−	0.639726i
$530$	−5.27657	−	11.9643i	−0.229200	−	0.519698i
$531$	9.88710	+	16.8199i	0.429063	+	0.729920i
$532$	0.844717	−	1.00448i	0.0366231	−	0.0435496i
$533$	−15.8380			−0.686020
$534$	14.8735	−	17.8670i	0.643641	−	0.773180i
$535$	−2.24596	+	20.6699i	−0.0971012	+	0.893638i
$536$	3.92574	−	10.7859i	0.169566	−	0.465879i
$537$	−5.65873	+	32.8425i	−0.244192	+	1.41726i
$538$	10.2411	+	12.2049i	0.441525	+	0.526189i
$539$	8.14928	−	4.70499i	0.351014	−	0.202658i
$540$	−0.905677	−	11.5836i	−0.0389741	−	0.498479i
$541$	1.87963	+	10.6599i	0.0808118	+	0.458306i	0.998182	+	0.0602715i	$0.0191966\pi$
$541$	1.87963	+	10.6599i	0.0808118	+	0.458306i	−0.917370	+	0.398035i	$0.869692\pi$
$542$	17.7656	−	3.13255i	0.763097	−	0.134555i
$543$	23.1882	−	13.5088i	0.995099	−	0.579720i
$544$	−0.0553414	+	0.0319514i	−0.00237274	+	0.00136990i
$545$	26.2471	+	7.62616i	1.12430	+	0.326669i
$546$	0.268586	−	1.55884i	0.0114944	−	0.0667122i
$547$	−42.1511	−	15.3418i	−1.80225	−	0.655966i	−0.998105	−	0.0615348i	$-0.980400\pi$
$547$	−42.1511	−	15.3418i	−1.80225	−	0.655966i	−0.804147	−	0.594431i	$-0.797377\pi$
$548$	−7.29033	−	6.11732i	−0.311428	−	0.261319i
$549$	8.71425	−	3.24911i	0.371915	−	0.138669i
$550$	−2.59523	+	6.29568i	−0.110661	+	0.268448i
$551$	−25.0578	−	21.0724i	−1.06750	−	0.897715i
$552$	−0.497563	−	0.284680i	−0.0211777	−	0.0121168i
$553$	0.756135	−	4.28825i	0.0321541	−	0.182355i
$554$	0.792018	+	0.664582i	0.0336496	+	0.0282354i
$555$	3.46104	−	12.0881i	0.146913	−	0.513112i
$556$	−12.1036	+	4.40534i	−0.513305	+	0.186828i
$557$	−28.6909	+	24.0745i	−1.21567	+	1.02007i	−0.216631	+	0.976253i	$0.569507\pi$
$557$	−28.6909	+	24.0745i	−1.21567	+	1.02007i	−0.999040	+	0.0438157i	$0.986049\pi$
$558$	−3.45136	+	6.08736i	−0.146108	+	0.257698i
$559$	14.3520	+	8.28610i	0.607023	+	0.350465i
$560$	−0.485951	+	0.465989i	−0.0205352	+	0.0196916i
$561$	0.0510024	−	0.141851i	0.00215332	−	0.00598895i
$562$	13.5493	+	7.82272i	0.571545	+	0.329981i
$563$	−33.9867	+	19.6222i	−1.43237	+	0.826978i	−0.997301	−	0.0734196i	$-0.976609\pi$
$563$	−33.9867	+	19.6222i	−1.43237	+	0.826978i	−0.435067	+	0.900398i	$0.643275\pi$
$564$	0.296409	+	1.64342i	0.0124811	+	0.0692005i
$565$	−19.7744	−	14.4734i	−0.831914	−	0.608899i
$566$	7.27265	+	2.64703i	0.305692	+	0.111263i
$567$	0.966534	+	2.53164i	0.0405906	+	0.106319i
$568$	8.30847	+	1.46501i	0.348615	+	0.0614703i
$569$	19.4653			0.816026			0.408013	−	0.912976i	$-0.366222\pi$
$569$	19.4653			0.816026			0.408013	+	0.912976i	$0.366222\pi$
$570$	4.07278	+	16.3833i	0.170590	+	0.686221i
$571$	−33.7349			−1.41176			−0.705880	−	0.708332i	$-0.749448\pi$
$571$	−33.7349			−1.41176			−0.705880	+	0.708332i	$0.749448\pi$
$572$	4.06810	+	0.717316i	0.170096	+	0.0299925i
$573$	2.61217	+	7.09051i	0.109125	+	0.296210i
$574$	−1.47742	−	0.537736i	−0.0616662	−	0.0224447i
$575$	−0.0693737	+	1.65336i	−0.00289308	+	0.0689501i
$576$	2.82701	+	1.00399i	0.117792	+	0.0418328i
$577$	−39.1212	+	22.5866i	−1.62864	+	0.940294i	−0.644137	+	0.764910i	$0.722783\pi$
$577$	−39.1212	+	22.5866i	−1.62864	+	0.940294i	−0.984500	+	0.175384i	$0.943883\pi$
$578$	14.7189	+	8.49796i	0.612225	+	0.353468i
$579$	−30.7396	−	11.0524i	−1.27750	−	0.459323i
$580$	11.6246	+	12.1226i	0.482686	+	0.503364i
$581$	0.312342	+	0.180331i	0.0129581	+	0.00748137i
$582$	0.0474597	+	12.1398i	0.00196727	+	0.503212i
$583$	−6.10103	+	5.11937i	−0.252679	+	0.212023i
$584$	−9.48077	+	3.45072i	−0.392317	+	0.142792i
$585$	14.1969	+	14.5752i	0.586969	+	0.602611i
$586$	23.6322	+	19.8298i	0.976237	+	0.819160i
$587$	−1.74499	+	9.89633i	−0.0720234	+	0.408465i	0.927386	+	0.374106i	$0.122050\pi$
$587$	−1.74499	+	9.89633i	−0.0720234	+	0.408465i	−0.999410	+	0.0343596i	$0.989061\pi$
$588$	−5.94310	+	10.3873i	−0.245089	+	0.428366i
$589$	3.48785	−	9.55047i	0.143714	−	0.393520i
$590$	8.08955	+	12.0846i	0.333041	+	0.497516i
$591$	−24.5610	−	20.4460i	−1.01030	−	0.841037i
$592$	2.48700	+	2.08684i	0.102215	+	0.0857688i
$593$	8.78941	+	3.19908i	0.360938	+	0.131371i	0.516122	−	0.856515i	$-0.327375\pi$
$593$	8.78941	+	3.19908i	0.360938	+	0.131371i	−0.155184	+	0.987886i	$0.549597\pi$
$594$	−6.62113	+	2.49822i	−0.271668	+	0.102503i
$595$	−0.0413153	−	0.0120042i	−0.00169376	−	0.000492126i
$596$	14.0738	−	8.12553i	0.576486	−	0.332834i
$597$	3.94882	+	6.77823i	0.161615	+	0.277414i
$598$	0.988599	−	0.174317i	0.0404268	−	0.00712834i
$599$	−0.282246	−	1.60070i	−0.0115323	−	0.0654028i	0.978499	−	0.206254i	$-0.0661273\pi$
$599$	−0.282246	−	1.60070i	−0.0115323	−	0.0654028i	−0.990031	+	0.140851i	$0.955016\pi$
$600$	−1.17852	−	8.57969i	−0.0481131	−	0.350264i
$601$	−27.3240	+	15.7755i	−1.11457	+	0.643497i	−0.940009	−	0.341149i	$-0.889184\pi$
$601$	−27.3240	+	15.7755i	−1.11457	+	0.643497i	−0.174561	+	0.984646i	$0.555851\pi$
$602$	1.05746	+	1.26023i	0.0430989	+	0.0513633i
$603$	−26.5504	−	21.9270i	−1.08122	−	0.892937i
$604$	4.14093	−	11.3771i	0.168492	−	0.462928i
$605$	−20.3296	−	2.20898i	−0.826514	−	0.0898077i
$606$	−17.3203	−	14.4184i	−0.703589	−	0.585709i
$607$	35.4233			1.43779			0.718895	−	0.695119i	$-0.244648\pi$
$607$	35.4233			1.43779			0.718895	+	0.695119i	$0.244648\pi$
$608$	−4.29185	−	0.761580i	−0.174058	−	0.0308862i
$609$	−3.40001	−	1.94532i	−0.137775	−	0.0788281i
$610$	6.34257	−	2.79723i	0.256803	−	0.113257i
$611$	−2.24017	−	1.87973i	−0.0906277	−	0.0760457i
$612$	0.0347649	+	0.188530i	0.00140529	+	0.00762086i
$613$	3.55306	+	9.76196i	0.143507	+	0.394282i	0.990534	−	0.137268i	$-0.0438321\pi$
$613$	3.55306	+	9.76196i	0.143507	+	0.394282i	−0.847027	+	0.531550i	$0.821610\pi$
$614$	−4.49641	−	5.35862i	−0.181460	−	0.216256i
$615$	16.7616	−	11.3155i	0.675894	−	0.456285i
$616$	0.355131	+	0.205035i	0.0143086	+	0.00826108i
$617$	−4.72712	−	26.8088i	−0.190307	−	1.07928i	−0.918946	−	0.394384i	$-0.870958\pi$
$617$	−4.72712	−	26.8088i	−0.190307	−	1.07928i	0.728639	−	0.684898i	$-0.240153\pi$
$618$	8.59252	−	23.8980i	0.345642	−	0.961320i
$619$	−20.8777	+	36.1613i	−0.839146	+	1.45344i	0.0514634	+	0.998675i	$0.483611\pi$
$619$	−20.8777	+	36.1613i	−0.839146	+	1.45344i	−0.890610	+	0.454769i	$0.849722\pi$
$620$	−2.30291	+	4.67985i	−0.0924869	+	0.187947i
$621$	−1.30434	+	1.12080i	−0.0523414	+	0.0449762i
$622$	9.11406	−	3.31725i	0.365440	−	0.133009i
$623$	−1.38221	+	3.79760i	−0.0553771	+	0.152147i
$624$	−4.92961	+	1.81609i	−0.197343	+	0.0727017i
$625$	−20.4300	+	14.4089i	−0.817199	+	0.576356i
$626$	19.7851			0.790771
$627$	8.89017	−	5.16625i	0.355039	−	0.206320i
$628$			15.2035i			0.606687i
$629$	−0.0360257	+	0.204312i	−0.00143644	+	0.00814645i
$630$	0.829468	+	1.84164i	0.0330468	+	0.0733726i
$631$	39.1946	+	14.2657i	1.56031	+	0.567907i	0.970808	−	0.239858i	$-0.0771010\pi$
$631$	39.1946	+	14.2657i	1.56031	+	0.567907i	0.589504	+	0.807765i	$0.299323\pi$
$632$	−13.5897	+	4.94624i	−0.540569	+	0.196751i
$633$	−18.8642	+	3.40235i	−0.749783	+	0.135231i
$634$	−5.77521	−	10.0030i	−0.229363	−	0.397268i
$635$	1.50178	+	22.6183i	0.0595962	+	0.897581i
$636$	3.42702	−	9.53143i	0.135890	−	0.377946i
$637$	−3.63911	−	20.6384i	−0.144187	−	0.817724i
$638$	5.11482	−	8.85913i	0.202498	−	0.350736i
$639$	12.4832	−	22.0173i	0.493827	−	0.870991i
$640$	2.14727	+	0.623893i	0.0848782	+	0.0246615i
$641$	5.88345	−	2.14140i	0.232382	−	0.0845803i	−0.223204	−	0.974772i	$-0.571652\pi$
$641$	5.88345	−	2.14140i	0.232382	−	0.0845803i	0.455587	+	0.890191i	$0.349430\pi$
$642$	−12.2966	+	10.4003i	−0.485310	+	0.410467i
$643$	21.6550	−	25.8074i	0.853988	−	1.01774i	−0.145609	−	0.989342i	$-0.546514\pi$
$643$	21.6550	−	25.8074i	0.853988	−	1.01774i	0.999597	−	0.0284009i	$-0.00904151\pi$
$644$	0.0981380	+	0.0173044i	0.00386718	+	0.000681888i
$645$	−21.1089	+	1.48447i	−0.831164	+	0.0584509i
$646$	−0.0949837	−	0.261851i	−0.00373708	−	0.0103024i
$647$	8.85339			0.348063			0.174031	−	0.984740i	$-0.444321\pi$
$647$	8.85339			0.348063			0.174031	+	0.984740i	$0.444321\pi$
$648$	5.67657	−	6.98402i	0.222997	−	0.274358i
$649$	5.69336	−	6.78508i	0.223484	−	0.266338i
$650$	11.1986	+	10.2267i	0.439245	+	0.401124i
$651$	0.206552	−	1.19880i	0.00809541	−	0.0469847i
$652$	1.07877	+	1.28563i	0.0422479	+	0.0503491i
$653$	0.213128	+	0.369148i	0.00834034	+	0.0144459i	0.870165	−	0.492760i	$-0.164012\pi$
$653$	0.213128	+	0.369148i	0.00834034	+	0.0144459i	−0.861825	+	0.507206i	$0.830678\pi$
$654$	10.6575	+	18.2937i	0.416740	+	0.715342i
$655$	−15.6754	+	15.0315i	−0.612488	+	0.587328i
$656$	0.906739	+	5.14237i	0.0354022	+	0.200776i
$657$	0.236655	+	30.2668i	0.00923279	+	1.18082i
$658$	−0.145149	−	0.251406i	−0.00565851	−	0.00980082i
$659$	3.04626	−	2.55612i	0.118665	−	0.0995721i	−0.581524	−	0.813529i	$-0.697543\pi$
$659$	3.04626	−	2.55612i	0.118665	−	0.0995721i	0.700189	+	0.713957i	$0.253099\pi$
$660$	−4.81783	+	2.14732i	−0.187534	+	0.0835843i
$661$	−8.53117	+	23.4392i	−0.331824	+	0.911679i	0.655813	+	0.754923i	$0.272326\pi$
$661$	−8.53117	+	23.4392i	−0.331824	+	0.911679i	−0.987637	+	0.156756i	$0.949896\pi$
$662$	−16.9215	−	14.1988i	−0.657672	−	0.551852i
$663$	−0.258013	−	0.214785i	−0.0100204	−	0.00834157i
$664$		−	1.19783i		−	0.0464847i
$665$	−1.62986	−	2.44052i	−0.0632035	−	0.0946393i
$666$	8.39646	−	4.93563i	0.325356	−	0.191252i
$667$	0.431677	−	2.44816i	0.0167146	−	0.0947932i
$668$	8.58829	−	10.2351i	0.332291	−	0.396009i
$669$	−16.0771	+	13.5977i	−0.621575	+	0.525718i
$670$	−20.7109	−	15.1588i	−0.800133	−	0.585637i
$671$	−2.71390	−	3.23430i	−0.104769	−	0.124859i
$672$	−0.521510	+	0.00203881i	−0.0201177	+	7.86486e-5i
$673$	23.7354	−	41.1110i	0.914933	−	1.58471i	0.107935	−	0.994158i	$-0.465576\pi$
$673$	23.7354	−	41.1110i	0.914933	−	1.58471i	0.806999	−	0.590553i	$-0.201090\pi$
$674$	3.93471	−	0.693795i	0.151559	−	0.0267240i
$675$	−25.4381	−	5.28220i	−0.979114	−	0.203312i
$676$	−1.90012	+	3.29111i	−0.0730816	+	0.126581i
$677$	−16.7209	+	9.65384i	−0.642638	+	0.371027i	−0.785630	−	0.618697i	$-0.787661\pi$
$677$	−16.7209	+	9.65384i	−0.642638	+	0.371027i	0.142992	+	0.989724i	$0.454328\pi$
$678$	−3.36918	−	18.6802i	−0.129393	−	0.717410i
$679$	−0.721791	−	1.98311i	−0.0276998	−	0.0761046i
$680$	0.0340810	+	0.138767i	0.00130695	+	0.00532147i
$681$	−14.8194	−	40.2259i	−0.567879	−	1.54146i
$682$	3.12851	+	0.551641i	0.119797	+	0.0211234i
$683$		−	23.7348i		−	0.908186i	−0.890954	−	0.454093i	$-0.849963\pi$
$683$		−	23.7348i		−	0.908186i	0.890954	−	0.454093i	$-0.150037\pi$
$684$	−6.46196	+	11.3685i	−0.247079	+	0.434686i
$685$	−17.6839	+	11.8377i	−0.675667	+	0.452297i
$686$	0.727247	−	4.12442i	0.0277664	−	0.157471i
$687$	8.63328	−	3.18053i	0.329380	−	0.121345i
$688$	1.86872	−	5.13426i	0.0712442	−	0.195742i
$689$	6.06649	+	16.6675i	0.231115	+	0.634982i
$690$	−0.921710	+	0.890790i	−0.0350889	+	0.0339118i
$691$	−6.88252	−	11.9209i	−0.261823	−	0.453491i	0.704903	−	0.709304i	$-0.250990\pi$
$691$	−6.88252	−	11.9209i	−0.261823	−	0.453491i	−0.966726	+	0.255812i	$0.917657\pi$
$692$	8.13999	+	4.69963i	0.309436	+	0.178653i
$693$	0.936183	−	0.798107i	0.0355626	−	0.0303176i
$694$	13.7846	−	2.43059i	0.523255	−	0.0922640i
$695$	1.90811	+	28.7380i	0.0723786	+	1.09010i
$696$	0.0508603	+	13.0096i	0.00192785	+	0.493129i
$697$	−0.255615	+	0.214486i	−0.00968209	+	0.00812424i
$698$	2.35380	+	6.46702i	0.0890927	+	0.244780i
$699$	18.9999	−	16.0698i	0.718644	−	0.607817i
$700$	0.697421	+	1.33420i	0.0263600	+	0.0504278i
$701$	37.8763	+	6.67861i	1.43057	+	0.252248i	0.834642	−	0.550793i	$-0.185674\pi$
$701$	37.8763	+	6.67861i	1.43057	+	0.252248i	0.595925	+	0.803040i	$0.296786\pi$
$702$	0.184839	+	15.7594i	0.00697628	+	0.594801i
$703$	−10.8505	+	9.08456i	−0.409234	+	0.342630i
$704$		−	1.36192i		−	0.0513294i
$705$	3.71379	+	0.388850i	0.139869	+	0.0146450i
$706$	10.2380	−	12.2012i	0.385312	−	0.459196i
$707$	3.68140	+	1.33992i	0.138453	+	0.0503928i
$708$	−1.91267	+	11.1009i	−0.0718824	+	0.417196i
$709$	−16.6759	+	13.9928i	−0.626277	+	0.525509i	−0.899770	−	0.436365i	$-0.856266\pi$
$709$	−16.6759	+	13.9928i	−0.626277	+	0.525509i	0.273492	+	0.961874i	$0.411821\pi$
$710$	8.32936	−	16.9265i	0.312595	−	0.635240i
$711$	0.339220	+	43.3842i	0.0127217	+	1.62703i
$712$	13.2181	−	2.33071i	0.495369	−	0.0873470i
$713$	0.760267	−	0.134056i	0.0284722	−	0.00502042i
$714$	−0.0167758	−	0.0287959i	−0.000627818	−	0.00107766i
$715$	4.07833	−	8.28777i	0.152521	−	0.309945i
$716$	−14.7395	+	12.3679i	−0.550841	+	0.462210i
$717$	17.5202	+	3.01871i	0.654304	+	0.112736i
$718$	−20.2171	−	7.35844i	−0.754497	−	0.274614i
$719$	−21.3466	+	25.4399i	−0.796094	+	0.948748i	−0.999540	−	0.0303382i	$-0.990342\pi$
$719$	−21.3466	+	25.4399i	−0.796094	+	0.948748i	0.203446	+	0.979086i	$0.434786\pi$
$720$	3.91958	−	5.44397i	0.146074	−	0.202885i
$721$			4.41476i			0.164414i
$722$	6.53718	−	17.8400i	0.243289	−	0.663936i
$723$	−8.41724	−	4.81592i	−0.313041	−	0.179106i
$724$	15.2585	+	2.69048i	0.567077	+	0.0999910i
$725$	33.2830	−	17.3979i	1.23610	−	0.646144i
$726$	−10.2290	−	12.0942i	−0.379636	−	0.448857i
$727$	−11.6972	−	32.1379i	−0.433827	−	1.19193i	−0.943445	−	0.331529i	$-0.892436\pi$
$727$	−11.6972	−	32.1379i	−0.433827	−	1.19193i	0.509618	−	0.860401i	$-0.329787\pi$
$728$	0.699596	−	0.587031i	0.0259288	−	0.0217568i
$729$	−14.0447	−	23.0596i	−0.520174	−	0.854060i
$730$	1.49463	+	22.5106i	0.0553187	+	0.833156i
$731$	0.343845	−	0.0606292i	0.0127176	−	0.00224245i
$732$	5.05283	+	1.81674i	0.186758	+	0.0671487i
$733$	−43.0329	−	24.8451i	−1.58946	−	0.917673i	−0.993396	−	0.114734i	$-0.963398\pi$
$733$	−43.0329	−	24.8451i	−1.58946	−	0.917673i	−0.596061	−	0.802939i	$-0.703268\pi$
$734$	1.11793	+	1.93631i	0.0412635	+	0.0714705i
$735$	18.5965	+	19.2420i	0.685942	+	0.709752i
$736$	−0.113196	−	0.311004i	−0.00417247	−	0.0114638i
$737$	−5.34655	+	14.6895i	−0.196943	+	0.541096i
$738$	15.4479	+	2.59951i	0.568646	+	0.0956894i
$739$	3.87529	−	21.9779i	0.142555	−	0.808469i	−0.826743	−	0.562580i	$-0.809809\pi$
$739$	3.87529	−	21.9779i	0.142555	−	0.808469i	0.969298	−	0.245889i	$-0.0790800\pi$
$740$	6.03264	−	4.03830i	0.221764	−	0.148451i
$741$	−4.04009	−	22.5403i	−0.148416	−	0.828038i
$742$			1.76077i			0.0646399i
$743$	29.8429	+	5.26211i	1.09483	+	0.193048i	0.691765	−	0.722123i	$-0.256834\pi$
$743$	29.8429	+	5.26211i	1.09483	+	0.193048i	0.403065	+	0.915171i	$0.367945\pi$
$744$	−3.79104	+	1.39664i	−0.138986	+	0.0512031i
$745$	−8.66711	−	35.2897i	−0.317539	−	1.29292i
$746$	5.80836	+	15.9583i	0.212659	+	0.584277i
$747$	−3.38627	−	1.20260i	−0.123897	−	0.0440009i
$748$	0.0753706	−	0.0435153i	0.00275582	−	0.00159108i
$749$	1.39984	−	2.42459i	0.0511489	−	0.0885925i
$750$	−19.1582	−	2.82220i	−0.699557	−	0.103052i
$751$	19.0123	−	3.35237i	0.693767	−	0.122330i	0.184364	−	0.982858i	$-0.440977\pi$
$751$	19.0123	−	3.35237i	0.693767	−	0.122330i	0.509403	+	0.860528i	$0.329866\pi$
$752$	−0.482069	+	0.834969i	−0.0175793	+	0.0304482i
$753$	−0.0350271	−	8.95965i	−0.00127646	−	0.326508i
$754$	−14.6441	−	17.4522i	−0.533308	−	0.635572i
$755$	−21.8462	−	15.9898i	−0.795065	−	0.581928i
$756$	−0.517826	+	1.47636i	−0.0188331	+	0.0536948i
$757$	−18.8437	+	22.4570i	−0.684886	+	0.816215i	−0.990727	−	0.135868i	$-0.956618\pi$
$757$	−18.8437	+	22.4570i	−0.684886	+	0.816215i	0.305841	+	0.952082i	$0.401062\pi$
$758$	5.49306	−	31.1527i	0.199517	−	1.13152i
$759$	0.677641	+	0.387712i	0.0245968	+	0.0140731i
$760$	−4.31297	+	8.74061i	−0.156448	+	0.317055i
$761$			5.20717i			0.188760i	0.995536	+	0.0943799i	$0.0300868\pi$
$761$			5.20717i			0.188760i	−0.995536	+	0.0943799i	$0.969913\pi$
$762$	−11.2338	+	13.4947i	−0.406958	+	0.488862i
$763$	−2.81939	−	2.36575i	−0.102069	−	0.0856458i
$764$	−1.49212	+	4.09957i	−0.0539831	+	0.148317i
$765$	0.426513	+	0.0429728i	0.0154206	+	0.00155369i
$766$	4.66711	−	3.91617i	0.168629	−	0.141497i
$767$	−9.86295	−	17.0831i	−0.356131	−	0.616836i
$768$	0.871883	+	1.49660i	0.0314614	+	0.0540040i
$769$	1.80555	+	10.2398i	0.0651097	+	0.369256i	0.999901	+	0.0140585i	$0.00447511\pi$
$769$	1.80555	+	10.2398i	0.0651097	+	0.369256i	−0.934791	+	0.355197i	$0.884414\pi$
$770$	0.661828	−	0.634640i	0.0238506	−	0.0228709i
$771$	42.9117	−	24.9992i	1.54543	−	0.900326i
$772$	−9.42993	−	16.3331i	−0.339390	−	0.587842i
$773$	−12.1616	−	14.4936i	−0.437421	−	0.521298i	0.501627	−	0.865084i	$-0.332735\pi$
$773$	−12.1616	−	14.4936i	−0.437421	−	0.521298i	−0.939048	+	0.343786i	$0.888290\pi$
$774$	−12.6385	−	10.4376i	−0.454280	−	0.375173i
$775$	8.61212	+	7.86468i	0.309356	+	0.282508i
$776$	−4.50529	+	5.36919i	−0.161730	+	0.192743i
$777$	−1.08324	+	1.30125i	−0.0388610	+	0.0466822i
$778$	−16.6471			−0.596826
$779$	−22.7609	−	0.0247387i	−0.815492	−	0.000886355i
$780$	0.824076	+	11.7182i	0.0295067	+	0.419580i
$781$	−11.3155	−	1.99522i	−0.404900	−	0.0713947i
$782$	0.0135946	−	0.0162015i	0.000486143	−	0.000579363i
$783$	36.8295	+	12.9177i	1.31618	+	0.461642i
$784$	−6.49266	+	2.36313i	−0.231881	+	0.0843976i
$785$	32.6461	+	9.48538i	1.16519	+	0.338548i
$786$	−16.8224	+	0.0657660i	−0.600035	+	0.00234579i
$787$	−3.81152	+	6.60175i	−0.135866	+	0.235327i	−0.925928	−	0.377700i	$-0.876715\pi$
$787$	−3.81152	+	6.60175i	−0.135866	+	0.235327i	0.790062	+	0.613027i	$0.210048\pi$
$788$	−3.20393	−	18.1704i	−0.114135	−	0.647292i
$789$	−3.34163	−	1.20148i	−0.118965	−	0.0427738i
$790$	2.14239	+	32.2666i	0.0762229	+	1.14799i
$791$	1.64986	+	2.85765i	0.0586624	+	0.101606i
$792$	−3.85017	−	1.36735i	−0.136810	−	0.0485867i
$793$	−8.83584	+	3.21598i	−0.313770	+	0.114203i
$794$	29.9576	+	10.9037i	1.06315	+	0.386957i
$795$	−18.3284	−	13.3053i	−0.650042	−	0.471891i
$796$	−0.786466	+	4.46027i	−0.0278755	+	0.158090i
$797$		−	9.62716i		−	0.341011i	−0.985357	−	0.170506i	$-0.945460\pi$
$797$		−	9.62716i		−	0.341011i	0.985357	−	0.170506i	$-0.0545401\pi$
$798$	0.388421	−	2.23980i	0.0137500	−	0.0792879i
$799$	−0.0616111			−0.00217964
$800$	2.67933	−	4.22151i	0.0947286	−	0.149253i
$801$	6.68186	−	39.7078i	0.236092	−	1.40300i
$802$	−12.5306	+	34.4276i	−0.442472	+	1.21568i
$803$	12.9121	−	4.69961i	0.455657	−	0.165846i
$804$	−3.52875	−	19.5650i	−0.124449	−	0.690003i
$805$	0.0983848	−	0.199933i	0.00346761	−	0.00704670i
$806$	3.53747	−	6.12707i	0.124602	−	0.215817i
$807$	25.9681	+	9.33680i	0.914120	+	0.328671i
$808$	−2.25939	−	12.8137i	−0.0794852	−	0.450783i
$809$	31.5002	+	18.1866i	1.10749	+	0.639409i	0.938178	−	0.346154i	$-0.112513\pi$
$809$	31.5002	+	18.1866i	1.10749	+	0.639409i	0.169310	+	0.985563i	$0.445846\pi$
$810$	−11.4550	−	16.5464i	−0.402487	−	0.581381i
$811$	34.8980	+	41.5898i	1.22543	+	1.46042i	0.844278	+	0.535905i	$0.180030\pi$
$811$	34.8980	+	41.5898i	1.22543	+	1.46042i	0.381156	+	0.924511i	$0.375526\pi$
$812$	−0.773508	−	2.12520i	−0.0271448	−	0.0745798i
$813$	23.8568	−	20.1777i	0.836695	−	0.707663i
$814$	−3.38710	−	2.84212i	−0.118718	−	0.0996162i
$815$	3.43362	−	1.51431i	0.120275	−	0.0530441i
$816$	−0.0549662	+	0.0960697i	−0.00192420	+	0.00336311i
$817$	20.6123	+	11.9304i	0.721133	+	0.417392i
$818$	16.3169			0.570507
$819$	−0.957159	−	2.56714i	−0.0334458	−	0.0897031i
$820$	11.6078	+	1.26128i	0.405360	+	0.0440458i
$821$	8.44787	−	23.2103i	0.294833	−	0.810046i	−0.700510	−	0.713643i	$-0.747044\pi$
$821$	8.44787	−	23.2103i	0.294833	−	0.810046i	0.995342	−	0.0964030i	$-0.0307338\pi$
$822$	−16.2443	−	2.79888i	−0.566586	−	0.0976220i
$823$	9.78343	+	11.6594i	0.341029	+	0.406422i	0.909114	−	0.416547i	$-0.136760\pi$
$823$	9.78343	+	11.6594i	0.341029	+	0.406422i	−0.568085	+	0.822970i	$0.692316\pi$
$824$	12.6979	−	7.33114i	0.442352	−	0.255392i
$825$	1.60506	+	11.6849i	0.0558809	+	0.406815i
$826$	−0.340035	−	1.92844i	−0.0118313	−	0.0670989i
$827$	41.6855	−	7.35028i	1.44955	−	0.255594i	0.607209	−	0.794542i	$-0.292289\pi$
$827$	41.6855	−	7.35028i	1.44955	−	0.255594i	0.842339	+	0.538948i	$0.181178\pi$
$828$	−0.992861	+	0.00776316i	−0.0345043	+	0.000269788i
$829$	34.0137	−	19.6378i	1.18135	−	0.682050i	0.225021	−	0.974354i	$-0.427755\pi$
$829$	34.0137	−	19.6378i	1.18135	−	0.682050i	0.956326	+	0.292304i	$0.0944218\pi$
$830$	−2.57205	−	0.747316i	−0.0892773	−	0.0259397i
$831$	1.76478	+	0.304069i	0.0612194	+	0.0105480i
$832$	−2.85019	−	1.03738i	−0.0988126	−	0.0359648i
$833$	−0.338228	−	0.283807i	−0.0117189	−	0.00983334i
$834$	−14.2733	+	17.1459i	−0.494244	+	0.593715i
$835$	−16.6194	−	24.8270i	−0.575137	−	0.859173i
$836$	5.84517	+	1.03721i	0.202159	+	0.0358727i
$837$	0.142147	+	12.1195i	0.00491333	+	0.418913i
$838$	−2.81772	+	15.9801i	−0.0973367	+	0.552024i
$839$	−28.5137	−	23.9258i	−0.984403	−	0.826012i	0.000345029	−	1.00000i	$-0.499890\pi$
$839$	−28.5137	−	23.9258i	−0.984403	−	0.826012i	−0.984748	+	0.173988i	$0.944335\pi$
$840$	−0.320989	+	1.12109i	−0.0110752	+	0.0386814i
$841$	−25.7643	+	9.37744i	−0.888425	+	0.323360i
$842$	−2.75851	+	2.31467i	−0.0950647	+	0.0797688i
$843$	27.0985	−	0.105940i	0.933321	−	0.00364875i
$844$	−9.58426	−	5.53348i	−0.329904	−	0.190470i
$845$	5.88141	+	6.13337i	0.202327	+	0.210994i
$846$	1.87648	+	2.20111i	0.0645146	+	0.0756759i
$847$	2.38467	+	1.37679i	0.0819381	+	0.0473070i
$848$	5.06440	−	2.92393i	0.173912	−	0.100408i
$849$	13.1922	−	2.37935i	0.452754	−	0.0816590i
$850$	0.319233	+	0.0133947i	0.0109496	+	0.000459435i
$851$	−1.00969	−	0.367498i	−0.0346118	−	0.0125977i
$852$	13.7118	−	5.05148i	0.469758	−	0.173061i
$853$	−24.8551	−	4.38262i	−0.851021	−	0.150058i	−0.268908	−	0.963166i	$-0.586663\pi$
$853$	−24.8551	−	4.38262i	−0.851021	−	0.150058i	−0.582113	+	0.813108i	$0.697774\pi$
$854$	−0.933424			−0.0319411
$855$	20.3797	+	20.9683i	0.696970	+	0.717101i
$856$	−9.29827			−0.317808
$857$	−17.2684	−	3.04489i	−0.589879	−	0.104012i	−0.129262	−	0.991611i	$-0.541261\pi$
$857$	−17.2684	−	3.04489i	−0.589879	−	0.104012i	−0.460617	+	0.887599i	$0.652372\pi$
$858$	6.71375	−	2.47337i	0.229204	−	0.0844395i
$859$	15.2743	+	5.55938i	0.521151	+	0.189684i	0.589183	−	0.808000i	$-0.299450\pi$
$859$	15.2743	+	5.55938i	0.521151	+	0.189684i	−0.0680318	+	0.997683i	$0.521672\pi$
$860$	−9.85875	−	7.21587i	−0.336181	−	0.246059i
$861$	−2.67995	+	0.483358i	−0.0913324	+	0.0164728i
$862$	−0.563612	+	0.325402i	−0.0191967	+	0.0110832i
$863$	19.6081	+	11.3208i	0.667469	+	0.385363i	0.795117	−	0.606456i	$-0.207409\pi$
$863$	19.6081	+	11.3208i	0.667469	+	0.385363i	−0.127648	+	0.991820i	$0.540743\pi$
$864$	5.10628	−	0.962255i	0.173719	−	0.0327366i
$865$	15.1698	−	14.5467i	0.515790	−	0.494602i
$866$	−1.92261	−	1.11002i	−0.0653329	−	0.0377200i
$867$	29.4376	−	0.115084i	0.999752	−	0.00390846i
$868$	0.538014	−	0.451447i	0.0182614	−	0.0153231i
$869$	18.5081	−	6.73639i	0.627844	−	0.228517i
$870$	27.9669	+	8.00742i	0.948167	+	0.271477i
$871$	26.6693	+	22.3782i	0.903655	+	0.758257i
$872$	−2.12259	+	12.0378i	−0.0718799	+	0.407651i
$873$	10.6555	+	18.1271i	0.360635	+	0.613510i
$874$	1.42099	−	0.248967i	0.0480658	−	0.00842144i
$875$	3.29999	−	0.665155i	0.111560	−	0.0224863i
$876$	−11.1803	+	13.4305i	−0.377748	+	0.453774i
$877$	0.184200	+	0.154562i	0.00621998	+	0.00521918i	0.645892	−	0.763429i	$-0.276485\pi$
$877$	0.184200	+	0.154562i	0.00621998	+	0.00521918i	−0.639672	+	0.768648i	$0.720930\pi$
$878$	1.56337	+	0.569021i	0.0527612	+	0.0192035i
$879$	52.6572	+	9.07278i	1.77608	+	0.306017i
$880$	−2.92441	−	0.849694i	−0.0985818	−	0.0286432i
$881$	−38.9467	+	22.4859i	−1.31215	+	0.757568i	−0.982451	−	0.186519i	$-0.940279\pi$
$881$	−38.9467	+	22.4859i	−1.31215	+	0.757568i	−0.329695	+	0.944087i	$0.606946\pi$
$882$	0.162067	+	20.7274i	0.00545708	+	0.697928i
$883$	−1.92621	+	0.339643i	−0.0648221	+	0.0114299i	−0.205965	−	0.978559i	$-0.566033\pi$
$883$	−1.92621	+	0.339643i	−0.0648221	+	0.0114299i	0.141143	+	0.989989i	$0.454922\pi$
$884$	−0.0336572	−	0.190879i	−0.00113201	−	0.00641997i
$885$	22.6432	+	11.0328i	0.761144	+	0.370862i
$886$	−29.5506	+	17.0610i	−0.992770	+	0.573176i
$887$	19.0223	+	22.6699i	0.638706	+	0.761180i	0.984165	−	0.177253i	$-0.0567212\pi$
$887$	19.0223	+	22.6699i	0.638706	+	0.761180i	−0.345459	+	0.938434i	$0.612277\pi$
$888$	5.54154	+	0.954801i	0.185962	+	0.0320410i
$889$	1.04397	−	2.86828i	0.0350136	−	0.0961991i
$890$	3.24203	−	29.8369i	0.108673	−	1.00014i
$891$	−7.73105	+	9.51169i	−0.259000	+	0.318653i
$892$	−12.1569			−0.407043
$893$	−3.21643	−	2.70487i	−0.107634	−	0.0905149i
$894$	13.9784	−	24.4314i	0.467508	−	0.817109i
$895$	17.3613	+	39.3659i	0.580325	+	1.31586i
$896$	−0.230653	−	0.193541i	−0.00770558	−	0.00646575i
$897$	1.32756	−	1.12283i	0.0443258	−	0.0374901i
$898$	−13.4923	−	37.0699i	−0.450245	−	1.23704i
$899$	−11.2618	−	13.4213i	−0.375604	−	0.447627i
$900$	−9.24427	−	11.8129i	−0.308142	−	0.393762i
$901$	0.323629	+	0.186847i	0.0107816	+	0.00622479i
$902$	−1.23491	−	7.00351i	−0.0411179	−	0.233191i
$903$	2.68138	+	0.964087i	0.0892307	+	0.0320828i
$904$	5.47952	−	9.49081i	0.182246	−	0.315660i
$905$	15.2968	−	31.0855i	0.508484	−	1.03332i
$906$	−3.72218	−	20.6374i	−0.123661	−	0.685632i
$907$	50.0874	−	18.2303i	1.66313	−	0.605328i	0.672276	−	0.740300i	$-0.265317\pi$
$907$	50.0874	−	18.2303i	1.66313	−	0.605328i	0.990849	+	0.134972i	$0.0430945\pi$
$908$	8.46510	−	23.2577i	0.280924	−	0.771833i
$909$	−38.4928	−	6.47741i	−1.27672	−	0.214842i
$910$	−0.824039	−	1.86846i	−0.0273166	−	0.0619390i
$911$	33.9996			1.12646			0.563229	−	0.826301i	$-0.309559\pi$
$911$	33.9996			1.12646			0.563229	+	0.826301i	$0.309559\pi$
$912$	−7.08721	+	2.60221i	−0.234681	+	0.0861678i
$913$			1.63135i			0.0539897i
$914$	3.61675	−	20.5116i	0.119632	−	0.678464i
$915$	7.05345	−	9.71632i	0.233180	−	0.321212i
$916$	4.99157	+	1.81678i	0.164926	+	0.0600282i
$917$	2.74803	−	1.00020i	0.0907480	−	0.0330296i
$918$	0.216405	+	0.251843i	0.00714243	+	0.00831206i
$919$	29.6548	+	51.3636i	0.978221	+	1.69433i	0.668866	+	0.743383i	$0.266780\pi$
$919$	29.6548	+	51.3636i	0.978221	+	1.69433i	0.309355	+	0.950947i	$0.399887\pi$
$920$	−0.738432	+	0.0490293i	−0.0243454	+	0.00161645i
$921$	−11.4014	−	4.09937i	−0.375690	−	0.135079i
$922$	−1.76583	−	10.0145i	−0.0581546	−	0.329811i
$923$	−12.7946	+	22.1609i	−0.421140	+	0.729436i
$924$	0.710256	−	0.00277669i	0.0233657	−	9.13465e-5i
$925$	−4.90758	−	15.4732i	−0.161360	−	0.508754i
$926$	−22.9365	+	8.34819i	−0.753739	+	0.274339i
$927$	−7.97670	−	43.2575i	−0.261989	−	1.42076i
$928$	−4.82809	+	5.75390i	−0.158490	+	0.188881i
$929$	−13.9625	−	2.46197i	−0.458095	−	0.0807746i	−0.0601614	−	0.998189i	$-0.519162\pi$
$929$	−13.9625	−	2.46197i	−0.458095	−	0.0807746i	−0.397934	+	0.917414i	$0.630273\pi$
$930$	0.633743	+	9.01174i	0.0207813	+	0.295506i
$931$	−5.19754	−	29.6652i	−0.170343	−	0.972239i
$932$	14.3671			0.470609
$933$	10.7479	−	12.9110i	0.351870	−	0.422687i
$934$	−5.86402	+	6.98847i	−0.191877	+	0.228670i
$935$	−0.0464157	−	0.188990i	−0.00151796	−	0.00618063i
$936$	−5.79426	+	7.01601i	−0.189391	+	0.229325i
$937$	12.0682	+	14.3824i	0.394252	+	0.469852i	0.926258	−	0.376889i	$-0.123006\pi$
$937$	12.0682	+	14.3824i	0.394252	+	0.469852i	−0.532006	+	0.846740i	$0.678562\pi$
$938$	1.72801	+	2.99299i	0.0564214	+	0.0977247i
$939$	29.6104	−	17.2503i	0.966299	−	0.562941i
$940$	1.49214	+	1.55606i	0.0486683	+	0.0507532i
$941$	1.44831	+	8.21380i	0.0472137	+	0.267762i	0.999272	−	0.0381549i	$-0.0121480\pi$
$941$	1.44831	+	8.21380i	0.0472137	+	0.267762i	−0.952058	+	0.305917i	$0.901037\pi$
$942$	13.2557	+	22.7537i	0.431894	+	0.741354i
$943$	−0.864097	−	1.49666i	−0.0281389	−	0.0487380i
$944$	−4.98199	+	4.18038i	−0.162150	+	0.136060i
$945$	2.84708	+	2.03300i	0.0926155	+	0.0661336i
$946$	−2.54505	+	6.99246i	−0.0827466	+	0.227344i
$947$	4.56951	+	3.83427i	0.148489	+	0.124597i	0.714006	−	0.700140i	$-0.246879\pi$
$947$	4.56951	+	3.83427i	0.148489	+	0.124597i	−0.565517	+	0.824737i	$0.691323\pi$
$948$	−16.0258	+	19.2512i	−0.520495	+	0.625249i
$949$		−	30.6017i		−	0.993375i
$950$	16.0776	+	14.7143i	0.521626	+	0.477395i
$951$	−17.3646	−	9.93515i	−0.563086	−	0.322169i
$952$	0.00334114	−	0.0189486i	0.000108287	−	0.000614126i
$953$	36.0155	−	42.9217i	1.16666	−	1.39037i	0.261548	−	0.965190i	$-0.415767\pi$
$953$	36.0155	−	42.9217i	1.16666	−	1.39037i	0.905110	−	0.425178i	$-0.139789\pi$
$954$	−3.18140	−	17.2527i	−0.103002	−	0.558577i
$955$	7.87195	+	5.76168i	0.254730	+	0.186444i
$956$	6.59779	+	7.86294i	0.213388	+	0.254306i
$957$	−0.0692677	−	17.7181i	−0.00223911	−	0.572745i
$958$	15.4551	−	26.7690i	0.499332	−	0.864868i
$959$	2.82196	−	0.497587i	0.0911257	−	0.0160679i
$960$	3.75757	−	0.938445i	0.121275	−	0.0302882i
$961$	−12.7796	+	22.1349i	−0.412244	+	0.714028i
$962$	−8.52789	+	4.92358i	−0.274950	+	0.158743i
$963$	−9.33535	+	26.2863i	−0.300827	+	0.847066i
$964$	−1.91494	−	5.26125i	−0.0616760	−	0.169453i
$965$	−40.9548	+	10.0585i	−1.31838	+	0.323793i
$966$	0.161961	−	0.0596671i	0.00521101	−	0.00191976i
$967$	−38.1057	−	6.71906i	−1.22540	−	0.216070i	−0.476749	−	0.879039i	$-0.658185\pi$
$967$	−38.1057	−	6.71906i	−1.22540	−	0.216070i	−0.748647	+	0.662969i	$0.769296\pi$
$968$		−	9.14517i		−	0.293937i
$969$	−0.370456	−	0.309072i	−0.0119008	−	0.00992882i
$970$	8.71827	+	13.0239i	0.279927	+	0.418171i
$971$	3.65699	−	20.7398i	0.117358	−	0.665573i	−0.868197	−	0.496220i	$-0.834721\pi$
$971$	3.65699	−	20.7398i	0.117358	−	0.665573i	0.985555	−	0.169353i	$-0.0541679\pi$
$972$	2.40633	−	15.4016i	0.0771831	−	0.494007i
$973$	1.32643	−	3.64434i	0.0425234	−	0.116832i
$974$	13.1573	+	36.1495i	0.421588	+	1.15830i
$975$	25.6763	+	5.54142i	0.822301	+	0.177467i
$976$	1.55004	+	2.68475i	0.0496157	+	0.0859369i
$977$	−20.0256	−	11.5618i	−0.640677	−	0.369895i	0.144198	−	0.989549i	$-0.453940\pi$
$977$	−20.0256	−	11.5618i	−0.640677	−	0.369895i	−0.784875	+	0.619654i	$0.787273\pi$
$978$	2.73541	+	0.983513i	0.0874687	+	0.0314493i
$979$	−18.0020	+	3.17424i	−0.575347	+	0.101449i
$980$	1.02356	+	15.4158i	0.0326963	+	0.492440i
$981$	31.9000	+	18.0864i	1.01849	+	0.577454i
$982$	−10.8248	+	9.08306i	−0.345432	+	0.289852i
$983$	−2.67476	−	7.34884i	−0.0853116	−	0.234392i	0.889700	−	0.456546i	$-0.150913\pi$
$983$	−2.67476	−	7.34884i	−0.0853116	−	0.234392i	−0.975012	+	0.222154i	$0.928691\pi$
$984$	5.84058	+	6.90552i	0.186191	+	0.220140i
$985$	−41.0155	−	4.45668i	−1.30686	−	0.142002i
$986$	−0.472693	−	0.0833485i	−0.0150536	−	0.00265436i
$987$	−0.436427	−	0.249702i	−0.0138916	−	0.00794809i
$988$	6.62295	−	11.4425i	0.210704	−	0.364036i
$989$			1.80831i			0.0575009i
$990$	−5.33817	+	7.41427i	−0.169658	+	0.235641i
$991$	37.1967	−	44.3294i	1.18159	−	1.40817i	0.288986	−	0.957333i	$-0.406682\pi$
$991$	37.1967	−	44.3294i	1.18159	−	1.40817i	0.892607	−	0.450835i	$-0.148874\pi$
$992$	−2.19190	−	0.797785i	−0.0695928	−	0.0253297i
$993$	−37.7044	−	6.49643i	−1.19651	−	0.206158i
$994$	−1.94594	+	1.63283i	−0.0617213	+	0.0517904i
$995$	9.08672	+	4.47148i	0.288068	+	0.141756i
$996$	−1.04436	−	1.79267i	−0.0330920	−	0.0568029i
$997$	−26.6216	+	4.69411i	−0.843115	+	0.148664i	−0.578492	−	0.815688i	$-0.696359\pi$
$997$	−26.6216	+	4.69411i	−0.843115	+	0.148664i	−0.264623	+	0.964352i	$0.585247\pi$
$998$	2.20481	−	0.388767i	0.0697920	−	0.0123062i
$999$	8.26287	−	14.7074i	0.261426	−	0.465322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.59.38	yes	240
3.2	odd	2	inner	570.2.bf.a.59.9	yes	240
5.4	even	2	inner	570.2.bf.a.59.3	yes	240
15.14	odd	2	inner	570.2.bf.a.59.32	yes	240
19.10	odd	18	inner	570.2.bf.a.29.32	yes	240
57.29	even	18	inner	570.2.bf.a.29.3	✓	240
95.29	odd	18	inner	570.2.bf.a.29.9	yes	240
285.29	even	18	inner	570.2.bf.a.29.38	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.3	✓	240	57.29	even	18	inner
570.2.bf.a.29.9	yes	240	95.29	odd	18	inner
570.2.bf.a.29.32	yes	240	19.10	odd	18	inner
570.2.bf.a.29.38	yes	240	285.29	even	18	inner
570.2.bf.a.59.3	yes	240	5.4	even	2	inner
570.2.bf.a.59.9	yes	240	3.2	odd	2	inner
570.2.bf.a.59.32	yes	240	15.14	odd	2	inner
570.2.bf.a.59.38	yes	240	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(1.62527 - 0.598755i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.32068 - 1.80439i) q^{5} +(1.70455 - 0.307434i) q^{6} +(-0.260757 + 0.150548i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.28299 - 1.94627i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(1.62527 - 0.598755i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.32068 - 1.80439i) q^{5} +(1.70455 - 0.307434i) q^{6} +(-0.260757 + 0.150548i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.28299 - 1.94627i) q^{9} +(1.61394 - 1.54764i) q^{10} +(-1.17946 - 0.680961i) q^{11} +(1.73204 - 0.00677128i) q^{12} +(-2.32350 + 1.94965i) q^{13} +(-0.282938 + 0.102981i) q^{14} +(1.06607 - 3.72337i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.0110966 + 0.0629319i) q^{17} +(2.58627 - 1.52027i) q^{18} +(-3.34215 + 2.79822i) q^{19} +(1.85817 - 1.24387i) q^{20} +(-0.333658 + 0.400810i) q^{21} +(-1.04329 - 0.875426i) q^{22} +(-0.311004 - 0.113196i) q^{23} +(1.70690 + 0.294097i) q^{24} +(-1.51163 - 4.76602i) q^{25} +(-2.62675 + 1.51656i) q^{26} +(2.54512 - 4.53016i) q^{27} +(-0.296522 + 0.0522848i) q^{28} +(1.30430 + 7.39707i) q^{29} +(1.69643 - 3.48169i) q^{30} +(-2.02006 + 1.16628i) q^{31} +(0.642788 + 0.766044i) q^{32} +(-2.32466 - 0.400537i) q^{33} +(-0.0218560 + 0.0600489i) q^{34} +(-0.0727285 + 0.669332i) q^{35} +(2.81097 - 1.04807i) q^{36} +3.24655 q^{37} +(-3.77728 + 2.17535i) q^{38} +(-2.60894 + 4.55990i) q^{39} +(2.04593 - 0.902307i) q^{40} +(4.00006 + 3.35645i) q^{41} +(-0.398189 + 0.336782i) q^{42} +(-1.86872 - 5.13426i) q^{43} +(-0.875426 - 1.04329i) q^{44} +(-0.496744 - 6.68979i) q^{45} +(-0.286623 - 0.165482i) q^{46} +(0.167421 + 0.949491i) q^{47} +(1.62990 + 0.586029i) q^{48} +(-3.45467 + 5.98366i) q^{49} +(-0.661051 - 4.95611i) q^{50} +(0.0196458 + 0.108925i) q^{51} +(-2.85019 + 1.03738i) q^{52} +(2.00009 - 5.49519i) q^{53} +(3.29311 - 4.01938i) q^{54} +(-2.78640 + 1.22887i) q^{55} -0.301096 q^{56} +(-3.75645 + 6.54898i) q^{57} +7.51118i q^{58} +(-1.12932 + 6.40472i) q^{59} +(2.27524 - 3.13421i) q^{60} +(2.91313 + 1.06029i) q^{61} +(-2.19190 + 0.797785i) q^{62} +(-0.302297 + 0.851203i) q^{63} +(0.500000 + 0.866025i) q^{64} +(0.449328 + 6.76734i) q^{65} +(-2.21979 - 0.798125i) q^{66} +(-1.99315 - 11.3037i) q^{67} +(-0.0319514 + 0.0553414i) q^{68} +(-0.573242 + 0.00224105i) q^{69} +(-0.187852 + 0.646534i) q^{70} +(7.92785 - 2.88550i) q^{71} +(2.95026 - 0.544028i) q^{72} +(-6.48523 + 7.72880i) q^{73} +(3.19723 + 0.563758i) q^{74} +(-5.31048 - 6.84097i) q^{75} +(-4.09764 + 1.48638i) q^{76} +0.410069 q^{77} +(-3.36113 + 4.03759i) q^{78} +(-9.29589 + 11.0784i) q^{79} +(2.17153 - 0.533326i) q^{80} +(1.42405 - 8.88662i) q^{81} +(3.35645 + 4.00006i) q^{82} +(-0.598913 - 1.03735i) q^{83} +(-0.450621 + 0.262521i) q^{84} +(0.0988985 + 0.103135i) q^{85} +(-0.948773 - 5.38076i) q^{86} +(6.54887 + 11.2413i) q^{87} +(-0.680961 - 1.17946i) q^{88} +(10.2819 - 8.62750i) q^{89} +(0.672472 - 6.67441i) q^{90} +(0.312353 - 0.858182i) q^{91} +(-0.253533 - 0.212740i) q^{92} +(-2.58482 + 3.10504i) q^{93} +0.964139i q^{94} +(0.635161 + 9.72608i) q^{95} +(1.50337 + 0.860155i) q^{96} +(-1.21710 + 6.90250i) q^{97} +(-4.44124 + 5.29286i) q^{98} +(-4.01802 + 0.740924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more