LMFDB - Embedded newform 546.2.ch.a.305.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			305.7
Character	$\chi$	$=$	546.305
Dual form			546.2.ch.a.401.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.745885 + 1.56322i) q^{3} +1.00000i q^{4} +(1.03725 - 3.87106i) q^{5} +(1.63278 - 0.577943i) q^{6} +(-1.61433 - 2.09617i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.88731 - 2.33196i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.745885 + 1.56322i) q^{3} +1.00000i q^{4} +(1.03725 - 3.87106i) q^{5} +(1.63278 - 0.577943i) q^{6} +(-1.61433 - 2.09617i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.88731 - 2.33196i) q^{9} +(-3.47070 + 2.00381i) q^{10} +(1.57361 + 0.421648i) q^{11} +(-1.56322 - 0.745885i) q^{12} +(-2.67586 + 2.41657i) q^{13} +(-0.340714 + 2.62372i) q^{14} +(5.27765 + 4.50881i) q^{15} -1.00000 q^{16} -5.88681 q^{17} +(-0.314418 + 2.98348i) q^{18} +(1.73298 + 6.46758i) q^{19} +(3.87106 + 1.03725i) q^{20} +(4.48088 - 0.960048i) q^{21} +(-0.814562 - 1.41086i) q^{22} -5.97593 q^{23} +(0.577943 + 1.63278i) q^{24} +(-9.57911 - 5.53050i) q^{25} +(3.60089 + 0.183345i) q^{26} +(5.05309 - 1.21090i) q^{27} +(2.09617 - 1.61433i) q^{28} +(2.46222 + 1.42156i) q^{29} +(-0.543650 - 6.92008i) q^{30} +(-1.90395 - 7.10565i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.83286 + 2.14540i) q^{33} +(4.16260 + 4.16260i) q^{34} +(-9.78887 + 4.07492i) q^{35} +(2.33196 - 1.88731i) q^{36} +(-5.59196 - 5.59196i) q^{37} +(3.34787 - 5.79867i) q^{38} +(-1.78174 - 5.98543i) q^{39} +(-2.00381 - 3.47070i) q^{40} +(-2.15636 + 0.577796i) q^{41} +(-3.84732 - 2.48961i) q^{42} +(4.83953 - 2.79410i) q^{43} +(-0.421648 + 1.57361i) q^{44} +(-10.9848 + 4.88707i) q^{45} +(4.22562 + 4.22562i) q^{46} +(-2.99401 - 0.802243i) q^{47} +(0.745885 - 1.56322i) q^{48} +(-1.78788 + 6.76783i) q^{49} +(2.86280 + 10.6841i) q^{50} +(4.39089 - 9.20238i) q^{51} +(-2.41657 - 2.67586i) q^{52} +(-5.23782 - 3.02406i) q^{53} +(-4.42931 - 2.71684i) q^{54} +(3.26445 - 5.65420i) q^{55} +(-2.62372 - 0.340714i) q^{56} +(-11.4029 - 2.11504i) q^{57} +(-0.735856 - 2.74625i) q^{58} +(-2.53140 + 2.53140i) q^{59} +(-4.50881 + 5.27765i) q^{60} +(2.04412 - 3.54052i) q^{61} +(-3.67816 + 6.37075i) q^{62} +(-1.84146 + 7.72069i) q^{63} -1.00000i q^{64} +(6.57916 + 12.8650i) q^{65} +(2.81306 - 0.220998i) q^{66} +(10.2779 + 2.75396i) q^{67} -5.88681i q^{68} +(4.45736 - 9.34170i) q^{69} +(9.80318 + 4.04038i) q^{70} +(1.37770 - 5.14163i) q^{71} +(-2.98348 - 0.314418i) q^{72} +(2.06993 - 0.554635i) q^{73} +7.90822i q^{74} +(15.7903 - 10.8491i) q^{75} +(-6.46758 + 1.73298i) q^{76} +(-1.65648 - 3.97925i) q^{77} +(-2.97246 + 5.49222i) q^{78} +(0.573713 + 0.993700i) q^{79} +(-1.03725 + 3.87106i) q^{80} +(-1.87612 + 8.80228i) q^{81} +(1.93334 + 1.11622i) q^{82} +(-0.681245 - 0.681245i) q^{83} +(0.960048 + 4.48088i) q^{84} +(-6.10608 + 22.7882i) q^{85} +(-5.39779 - 1.44633i) q^{86} +(-4.05875 + 2.78867i) q^{87} +(1.41086 - 0.814562i) q^{88} +(-7.35319 + 7.35319i) q^{89} +(11.2231 + 4.31174i) q^{90} +(9.38526 + 1.70792i) q^{91} -5.97593i q^{92} +(12.5278 + 2.32370i) q^{93} +(1.54981 + 2.68436i) q^{94} +26.8339 q^{95} +(-1.63278 + 0.577943i) q^{96} +(-5.15747 - 1.38194i) q^{97} +(6.04980 - 3.52136i) q^{98} +(-1.98663 - 4.46539i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.745885	+	1.56322i	−0.430637	+	0.902525i
$3$	−0.745885	+	1.56322i	−0.430637	+	0.902525i
$4$			1.00000i			0.500000i
$5$	1.03725	−	3.87106i	0.463871	−	1.73119i	−0.196733	−	0.980457i	$-0.563033\pi$
$5$	1.03725	−	3.87106i	0.463871	−	1.73119i	0.660604	−	0.750734i	$-0.270300\pi$
$6$	1.63278	−	0.577943i	0.666581	−	0.235944i
$7$	−1.61433	−	2.09617i	−0.610159	−	0.792279i
$7$	−1.61433	−	2.09617i	−0.610159	−	0.792279i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.88731	−	2.33196i	−0.629103	−	0.777322i
$10$	−3.47070	+	2.00381i	−1.09753	+	0.633660i
$11$	1.57361	+	0.421648i	0.474462	+	0.127132i	0.488123	−	0.872775i	$-0.337682\pi$
$11$	1.57361	+	0.421648i	0.474462	+	0.127132i	−0.0136606	+	0.999907i	$0.504348\pi$
$12$	−1.56322	−	0.745885i	−0.451263	−	0.215319i
$13$	−2.67586	+	2.41657i	−0.742149	+	0.670235i
$13$	−2.67586	+	2.41657i	−0.742149	+	0.670235i
$14$	−0.340714	+	2.62372i	−0.0910597	+	0.701219i
$15$	5.27765	+	4.50881i	1.36268	+	1.16417i
$16$	−1.00000			−0.250000
$17$	−5.88681			−1.42776			−0.713881	−	0.700267i	$-0.753064\pi$
$17$	−5.88681			−1.42776			−0.713881	+	0.700267i	$0.753064\pi$
$18$	−0.314418	+	2.98348i	−0.0741091	+	0.703213i
$19$	1.73298	+	6.46758i	0.397574	+	1.48376i	0.817352	+	0.576138i	$0.195441\pi$
$19$	1.73298	+	6.46758i	0.397574	+	1.48376i	−0.419779	+	0.907627i	$0.637892\pi$
$20$	3.87106	+	1.03725i	0.865596	+	0.231936i
$21$	4.48088	−	0.960048i	0.977809	−	0.209500i
$22$	−0.814562	−	1.41086i	−0.173665	−	0.300797i
$23$	−5.97593			−1.24607			−0.623034	−	0.782195i	$-0.714100\pi$
$23$	−5.97593			−1.24607			−0.623034	+	0.782195i	$0.714100\pi$
$24$	0.577943	+	1.63278i	0.117972	+	0.333291i
$25$	−9.57911	−	5.53050i	−1.91582	−	1.10610i
$26$	3.60089	+	0.183345i	0.706192	+	0.0359568i
$27$	5.05309	−	1.21090i	0.972468	−	0.233038i
$28$	2.09617	−	1.61433i	0.396139	−	0.305080i
$29$	2.46222	+	1.42156i	0.457223	+	0.263978i	0.710876	−	0.703318i	$-0.248299\pi$
$29$	2.46222	+	1.42156i	0.457223	+	0.263978i	−0.253653	+	0.967295i	$0.581632\pi$
$30$	−0.543650	−	6.92008i	−0.0992565	−	1.26343i
$31$	−1.90395	−	7.10565i	−0.341960	−	1.27621i	−0.896124	−	0.443805i	$-0.853628\pi$
$31$	−1.90395	−	7.10565i	−0.341960	−	1.27621i	0.554163	−	0.832408i	$-0.313038\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−1.83286	+	2.14540i	−0.319061	+	0.373467i
$34$	4.16260	+	4.16260i	0.713881	+	0.713881i
$35$	−9.78887	+	4.07492i	−1.65462	+	0.688787i
$36$	2.33196	−	1.88731i	0.388661	−	0.314552i
$37$	−5.59196	−	5.59196i	−0.919312	−	0.919312i	0.0776672	−	0.996979i	$-0.475253\pi$
$37$	−5.59196	−	5.59196i	−0.919312	−	0.919312i	−0.996979	+	0.0776672i	$0.975253\pi$
$38$	3.34787	−	5.79867i	0.543096	−	0.940669i
$39$	−1.78174	−	5.98543i	−0.285307	−	0.958436i
$40$	−2.00381	−	3.47070i	−0.316830	−	0.548766i
$41$	−2.15636	+	0.577796i	−0.336767	+	0.0902365i	−0.423240	−	0.906018i	$-0.639107\pi$
$41$	−2.15636	+	0.577796i	−0.336767	+	0.0902365i	0.0864724	+	0.996254i	$0.472441\pi$
$42$	−3.84732	−	2.48961i	−0.593654	−	0.384155i
$43$	4.83953	−	2.79410i	0.738021	−	0.426097i	−0.0833284	−	0.996522i	$-0.526555\pi$
$43$	4.83953	−	2.79410i	0.738021	−	0.426097i	0.821349	+	0.570426i	$0.193222\pi$
$44$	−0.421648	+	1.57361i	−0.0635659	+	0.237231i
$45$	−10.9848	+	4.88707i	−1.63752	+	0.728521i
$46$	4.22562	+	4.22562i	0.623034	+	0.623034i
$47$	−2.99401	−	0.802243i	−0.436722	−	0.117019i	0.0337581	−	0.999430i	$-0.489252\pi$
$47$	−2.99401	−	0.802243i	−0.436722	−	0.117019i	−0.470480	+	0.882411i	$0.655919\pi$
$48$	0.745885	−	1.56322i	0.107659	−	0.225631i
$49$	−1.78788	+	6.76783i	−0.255411	+	0.966833i
$50$	2.86280	+	10.6841i	0.404861	+	1.51096i
$51$	4.39089	−	9.20238i	0.614847	−	1.28859i
$52$	−2.41657	−	2.67586i	−0.335118	−	0.371074i
$53$	−5.23782	−	3.02406i	−0.719470	−	0.415386i	0.0950876	−	0.995469i	$-0.469687\pi$
$53$	−5.23782	−	3.02406i	−0.719470	−	0.415386i	−0.814558	+	0.580083i	$0.803020\pi$
$54$	−4.42931	−	2.71684i	−0.602753	−	0.369715i
$55$	3.26445	−	5.65420i	0.440179	−	0.762412i
$56$	−2.62372	−	0.340714i	−0.350610	−	0.0455299i
$57$	−11.4029	−	2.11504i	−1.51035	−	0.280144i
$58$	−0.735856	−	2.74625i	−0.0966226	−	0.360600i
$59$	−2.53140	+	2.53140i	−0.329560	+	0.329560i	−0.852419	−	0.522859i	$-0.824865\pi$
$59$	−2.53140	+	2.53140i	−0.329560	+	0.329560i	0.522859	+	0.852419i	$0.324865\pi$
$60$	−4.50881	+	5.27765i	−0.582085	+	0.681342i
$61$	2.04412	−	3.54052i	0.261723	−	0.453317i	−0.704977	−	0.709230i	$-0.749043\pi$
$61$	2.04412	−	3.54052i	0.261723	−	0.453317i	0.966700	+	0.255913i	$0.0823761\pi$
$62$	−3.67816	+	6.37075i	−0.467126	+	0.809086i
$63$	−1.84146	+	7.72069i	−0.232002	+	0.972715i
$64$		−	1.00000i		−	0.125000i
$65$	6.57916	+	12.8650i	0.816044	+	1.59570i
$66$	2.81306	−	0.220998i	0.346264	−	0.0272029i
$67$	10.2779	+	2.75396i	1.25565	+	0.336450i	0.824516	−	0.565838i	$-0.191447\pi$
$67$	10.2779	+	2.75396i	1.25565	+	0.336450i	0.431133	+	0.902288i	$0.358114\pi$
$68$		−	5.88681i		−	0.713881i
$69$	4.45736	−	9.34170i	0.536603	−	1.12461i
$70$	9.80318	+	4.04038i	1.17170	+	0.482917i
$71$	1.37770	−	5.14163i	0.163502	−	0.610199i	−0.834724	−	0.550669i	$-0.814373\pi$
$71$	1.37770	−	5.14163i	0.163502	−	0.610199i	0.998226	−	0.0595309i	$-0.0189605\pi$
$72$	−2.98348	−	0.314418i	−0.351606	−	0.0370545i
$73$	2.06993	−	0.554635i	0.242266	−	0.0649151i	−0.135643	−	0.990758i	$-0.543310\pi$
$73$	2.06993	−	0.554635i	0.242266	−	0.0649151i	0.377909	+	0.925843i	$0.376643\pi$
$74$			7.90822i			0.919312i
$75$	15.7903	−	10.8491i	1.82331	−	1.25275i
$76$	−6.46758	+	1.73298i	−0.741882	+	0.198787i
$77$	−1.65648	−	3.97925i	−0.188774	−	0.453477i
$78$	−2.97246	+	5.49222i	−0.336564	+	0.621872i
$79$	0.573713	+	0.993700i	0.0645478	+	0.111800i	0.896493	−	0.443057i	$-0.146106\pi$
$79$	0.573713	+	0.993700i	0.0645478	+	0.111800i	−0.831946	+	0.554857i	$0.812773\pi$
$80$	−1.03725	+	3.87106i	−0.115968	+	0.432798i
$81$	−1.87612	+	8.80228i	−0.208458	+	0.978031i
$82$	1.93334	+	1.11622i	0.213502	+	0.123265i
$83$	−0.681245	−	0.681245i	−0.0747764	−	0.0747764i	0.668729	−	0.743506i	$-0.266838\pi$
$83$	−0.681245	−	0.681245i	−0.0747764	−	0.0747764i	−0.743506	+	0.668729i	$0.766838\pi$
$84$	0.960048	+	4.48088i	0.104750	+	0.488904i
$85$	−6.10608	+	22.7882i	−0.662298	+	2.47173i
$86$	−5.39779	−	1.44633i	−0.582059	−	0.155962i
$87$	−4.05875	+	2.78867i	−0.435144	+	0.298977i
$88$	1.41086	−	0.814562i	0.150399	−	0.0868326i
$89$	−7.35319	+	7.35319i	−0.779436	+	0.779436i	−0.979735	−	0.200299i	$-0.935809\pi$
$89$	−7.35319	+	7.35319i	−0.779436	+	0.779436i	0.200299	+	0.979735i	$0.435809\pi$
$90$	11.2231	+	4.31174i	1.18302	+	0.454497i
$91$	9.38526	+	1.70792i	0.983842	+	0.179039i
$92$		−	5.97593i		−	0.623034i
$93$	12.5278	+	2.32370i	1.29907	+	0.240957i
$94$	1.54981	+	2.68436i	0.159851	+	0.276870i
$95$	26.8339			2.75310
$96$	−1.63278	+	0.577943i	−0.166645	+	0.0589860i
$97$	−5.15747	−	1.38194i	−0.523662	−	0.140315i	−0.0127021	−	0.999919i	$-0.504043\pi$
$97$	−5.15747	−	1.38194i	−0.523662	−	0.140315i	−0.510960	+	0.859605i	$0.670710\pi$
$98$	6.04980	−	3.52136i	0.611122	−	0.355711i
$99$	−1.98663	−	4.46539i	−0.199664	−	0.448789i
$100$	5.53050	−	9.57911i	0.553050	−	0.957911i
$101$	−1.12814	−	1.95400i	−0.112254	−	0.194430i	0.804425	−	0.594055i	$-0.202474\pi$
$101$	−1.12814	−	1.95400i	−0.112254	−	0.194430i	−0.916679	+	0.399625i	$0.869140\pi$
$102$	−9.61189	+	3.40224i	−0.951719	+	0.336872i
$103$	1.04826	−	0.605216i	0.103289	−	0.0596337i	−0.447466	−	0.894301i	$-0.647673\pi$
$103$	1.04826	−	0.605216i	0.103289	−	0.0596337i	0.550754	+	0.834667i	$0.314340\pi$
$104$	−0.183345	+	3.60089i	−0.0179784	+	0.353096i
$105$	0.931382	−	18.3416i	0.0908936	−	1.78995i
$106$	1.56537	+	5.84203i	0.152042	+	0.567428i
$107$			2.17128i			0.209905i	0.994477	+	0.104953i	$0.0334691\pi$
$107$			2.17128i			0.209905i	−0.994477	+	0.104953i	$0.966531\pi$
$108$	1.21090	+	5.05309i	0.116519	+	0.486234i
$109$	−4.69427	−	17.5193i	−0.449630	−	1.67804i	−0.703414	−	0.710781i	$-0.748342\pi$
$109$	−4.69427	−	17.5193i	−0.449630	−	1.67804i	0.253784	−	0.967261i	$-0.418325\pi$
$110$	−6.30644	+	1.68981i	−0.601296	+	0.161117i
$111$	12.9124	−	4.57050i	1.22559	−	0.433812i
$112$	1.61433	+	2.09617i	0.152540	+	0.198070i
$113$	11.9494	−	6.89900i	1.12411	−	0.649004i	0.181661	−	0.983361i	$-0.441853\pi$
$113$	11.9494	−	6.89900i	1.12411	−	0.649004i	0.942446	+	0.334358i	$0.108519\pi$
$114$	6.56748	+	9.55860i	0.615101	+	0.895245i
$115$	−6.19852	+	23.1332i	−0.578015	+	2.15718i
$116$	−1.42156	+	2.46222i	−0.131989	+	0.228611i
$117$	10.6855	+	1.67919i	0.987877	+	0.155241i
$118$	3.57993			0.329560
$119$	9.50326	+	12.3398i	0.871162	+	1.13119i
$120$	6.92008	−	0.543650i	0.631714	−	0.0496282i
$121$	−7.22781	−	4.17298i	−0.657073	−	0.379362i
$122$	−3.94893	+	1.05811i	−0.357520	+	0.0957971i
$123$	0.705178	−	3.80184i	0.0635838	−	0.342800i
$124$	7.10565	−	1.90395i	0.638106	−	0.170980i
$125$	−17.1758	+	17.1758i	−1.53625	+	1.53625i
$126$	6.76146	−	4.15724i	0.602359	−	0.370357i
$127$	−12.5477	−	7.24444i	−1.11343	−	0.642840i	−0.173716	−	0.984796i	$-0.555577\pi$
$127$	−12.5477	−	7.24444i	−1.11343	−	0.642840i	−0.939716	+	0.341956i	$0.888911\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.758063	+	9.64932i	0.0667437	+	0.849575i
$130$	4.44475	−	13.7491i	0.389830	−	1.20587i
$131$	−5.52239	+	3.18836i	−0.482494	+	0.278568i	−0.721455	−	0.692461i	$-0.756526\pi$
$131$	−5.52239	+	3.18836i	−0.482494	+	0.278568i	0.238961	+	0.971029i	$0.423193\pi$
$132$	−2.14540	−	1.83286i	−0.186733	−	0.159530i
$133$	10.7596	−	14.0734i	0.932972	−	1.22032i
$134$	−5.32025	−	9.21494i	−0.459600	−	0.796050i
$135$	0.553830	−	20.8168i	0.0476661	−	1.79163i
$136$	−4.16260	+	4.16260i	−0.356940	+	0.356940i
$137$	11.3200	−	11.3200i	0.967133	−	0.967133i	−0.0323438	−	0.999477i	$-0.510297\pi$
$137$	11.3200	−	11.3200i	0.967133	−	0.967133i	0.999477	+	0.0323438i	$0.0102972\pi$
$138$	−9.75741	+	3.45375i	−0.830606	+	0.294002i
$139$	0.531967	+	0.921393i	0.0451208	+	0.0781516i	0.887704	−	0.460415i	$-0.152299\pi$
$139$	0.531967	+	0.921393i	0.0451208	+	0.0781516i	−0.842583	+	0.538567i	$0.818966\pi$
$140$	−4.07492	−	9.78887i	−0.344394	−	0.827311i
$141$	3.48727	−	4.08192i	0.293681	−	0.343759i
$142$	−4.60986	+	2.66150i	−0.386851	+	0.223349i
$143$	−5.22970	+	2.67447i	−0.437330	+	0.223651i
$144$	1.88731	+	2.33196i	0.157276	+	0.194330i
$145$	8.05689	−	8.05689i	0.669089	−	0.669089i
$146$	−1.85584	−	1.07147i	−0.153591	−	0.0886757i
$147$	−9.24605	−	7.84287i	−0.762601	−	0.646869i
$148$	5.59196	−	5.59196i	0.459656	−	0.459656i
$149$	6.39255	−	1.71288i	0.523698	−	0.140324i	0.0127215	−	0.999919i	$-0.495951\pi$
$149$	6.39255	−	1.71288i	0.523698	−	0.140324i	0.510977	+	0.859595i	$0.329284\pi$
$150$	−18.8369	−	3.49394i	−1.53803	−	0.285279i
$151$	18.3450	−	4.91552i	1.49289	−	0.400019i	0.582180	−	0.813060i	$-0.302200\pi$
$151$	18.3450	−	4.91552i	1.49289	−	0.400019i	0.910713	+	0.413041i	$0.135533\pi$
$152$	5.79867	+	3.34787i	0.470335	+	0.271548i
$153$	11.1102	+	13.7278i	0.898210	+	1.10983i
$154$	−1.64244	+	3.98506i	−0.132352	+	0.321125i
$155$	−29.4813			−2.36799
$156$	5.98543	−	1.78174i	0.479218	−	0.142654i
$157$	−4.35942	+	7.55074i	−0.347920	+	0.602614i	−0.985880	−	0.167455i	$-0.946445\pi$
$157$	−4.35942	+	7.55074i	−0.347920	+	0.602614i	0.637960	+	0.770069i	$0.279778\pi$
$158$	0.296976	−	1.10833i	0.0236261	−	0.0881739i
$159$	8.63408	−	5.93226i	0.684727	−	0.470459i
$160$	3.47070	−	2.00381i	0.274383	−	0.158415i
$161$	9.64713	+	12.5266i	0.760300	+	0.987233i
$162$	7.55077	−	4.89754i	0.593245	−	0.384787i
$163$	−6.48055	+	1.73646i	−0.507596	+	0.136010i	−0.503523	−	0.863982i	$-0.667963\pi$
$163$	−6.48055	+	1.73646i	−0.507596	+	0.136010i	−0.00407280	+	0.999992i	$0.501296\pi$
$164$	−0.577796	−	2.15636i	−0.0451183	−	0.168384i
$165$	6.40385	+	9.32044i	0.498539	+	0.725596i
$166$			0.963426i			0.0747764i
$167$	−1.29865	−	4.84662i	−0.100492	−	0.375043i	0.897302	−	0.441416i	$-0.145524\pi$
$167$	−1.29865	−	4.84662i	−0.100492	−	0.375043i	−0.997795	+	0.0663734i	$0.978857\pi$
$168$	2.48961	−	3.84732i	0.192077	−	0.296827i
$169$	1.32041	−	12.9328i	0.101570	−	0.994828i
$170$	20.4314	−	11.7960i	1.56701	−	0.904715i
$171$	11.8115	−	16.2476i	0.903248	−	1.24248i
$172$	2.79410	+	4.83953i	0.213048	+	0.369010i
$173$	−0.813892	+	1.40970i	−0.0618791	+	0.107178i	−0.895305	−	0.445453i	$-0.853043\pi$
$173$	−0.813892	+	1.40970i	−0.0618791	+	0.107178i	0.833426	+	0.552631i	$0.186376\pi$
$174$	4.84186	+	0.898084i	0.367060	+	0.0680836i
$175$	3.87096	+	29.0075i	0.292617	+	2.19276i
$176$	−1.57361	−	0.421648i	−0.118616	−	0.0317829i
$177$	−2.06900	−	5.84526i	−0.155515	−	0.439357i
$178$	10.3990			0.779436
$179$	−7.90152	−	13.6858i	−0.590587	−	1.02293i	−0.994153	−	0.107977i	$-0.965563\pi$
$179$	−7.90152	−	13.6858i	−0.590587	−	1.02293i	0.403566	−	0.914951i	$-0.367771\pi$
$180$	−4.88707	−	10.9848i	−0.364261	−	0.818758i
$181$		−	6.41426i		−	0.476768i	−0.971171	−	0.238384i	$-0.923382\pi$
$181$		−	6.41426i		−	0.476768i	0.971171	−	0.238384i	$-0.0766177\pi$
$182$	−5.42870	−	7.84406i	−0.402402	−	0.581440i
$183$	4.00993	+	5.83622i	0.296422	+	0.431426i
$184$	−4.22562	+	4.22562i	−0.311517	+	0.311517i
$185$	−27.4471	+	15.8466i	−2.01795	+	1.16506i
$186$	−7.21540	−	10.5016i	−0.529059	−	0.770016i
$187$	−9.26357	−	2.48217i	−0.677419	−	0.181514i
$188$	0.802243	−	2.99401i	0.0585096	−	0.218361i
$189$	−10.6956	−	8.63735i	−0.777991	−	0.628275i
$190$	−18.9745	−	18.9745i	−1.37655	−	1.37655i
$191$	18.0922	+	10.4455i	1.30911	+	0.755813i	0.981947	−	0.189157i	$-0.0605754\pi$
$191$	18.0922	+	10.4455i	1.30911	+	0.755813i	0.327159	+	0.944969i	$0.393909\pi$
$192$	1.56322	+	0.745885i	0.112816	+	0.0538296i
$193$	0.827812	−	3.08944i	0.0595872	−	0.222383i	−0.929711	−	0.368290i	$-0.879943\pi$
$193$	0.827812	−	3.08944i	0.0595872	−	0.222383i	0.989298	+	0.145907i	$0.0466101\pi$
$194$	2.66970	+	4.62406i	0.191674	+	0.331988i
$195$	−25.0181	+	0.688864i	−1.79158	+	0.0493306i
$196$	−6.76783	−	1.78788i	−0.483416	−	0.127706i
$197$	17.4647	−	4.67965i	1.24431	−	0.333411i	0.424173	−	0.905581i	$-0.360565\pi$
$197$	17.4647	−	4.67965i	1.24431	−	0.333411i	0.820135	+	0.572170i	$0.193898\pi$
$198$	−1.75275	+	4.56227i	−0.124563	+	0.324226i
$199$		−	1.70055i		−	0.120549i	−0.998182	−	0.0602744i	$-0.980802\pi$
$199$		−	1.70055i		−	0.120549i	0.998182	−	0.0602744i	$-0.0191976\pi$
$200$	−10.6841	+	2.86280i	−0.755480	+	0.202430i
$201$	−11.9712	+	14.0125i	−0.844384	+	0.988367i
$202$	−0.583969	+	2.17940i	−0.0410879	+	0.153342i
$203$	−0.994993	−	7.45611i	−0.0698348	−	0.523316i
$204$	9.20238	+	4.39089i	0.644295	+	0.307424i
$205$			8.94673i			0.624867i
$206$	−1.16919	−	0.313283i	−0.0814612	−	0.0218275i
$207$	11.2784	+	13.9357i	0.783906	+	0.968596i
$208$	2.67586	−	2.41657i	0.185537	−	0.167559i
$209$			10.9082i			0.754535i
$210$	−13.6280	+	12.3109i	−0.940424	+	0.849531i
$211$	−3.14641	+	5.44974i	−0.216608	+	0.375176i	−0.953769	−	0.300541i	$-0.902833\pi$
$211$	−3.14641	+	5.44974i	−0.216608	+	0.375176i	0.737161	+	0.675717i	$0.236166\pi$
$212$	3.02406	−	5.23782i	0.207693	−	0.359735i
$213$	7.00990	+	5.98871i	0.480310	+	0.410340i
$214$	1.53533	−	1.53533i	0.104953	−	0.104953i
$215$	−5.79635	−	21.6323i	−0.395308	−	1.47531i
$216$	2.71684	−	4.42931i	0.184857	−	0.301376i
$217$	−11.8211	+	15.4619i	−0.802466	+	1.04962i
$218$	−9.06864	+	15.7073i	−0.614206	+	1.06384i
$219$	−0.676911	+	3.64944i	−0.0457414	+	0.246606i
$220$	5.65420	+	3.26445i	0.381206	+	0.220089i
$221$	15.7523	−	14.2259i	1.05961	−	0.956936i
$222$	−12.3623	−	5.89863i	−0.829702	−	0.395890i
$223$	1.55730	+	5.81191i	0.104284	+	0.389194i	0.998263	−	0.0589152i	$-0.0187642\pi$
$223$	1.55730	+	5.81191i	0.104284	+	0.389194i	−0.893979	+	0.448109i	$0.852098\pi$
$224$	0.340714	−	2.62372i	0.0227649	−	0.175305i
$225$	5.18182	+	32.7759i	0.345454	+	2.18506i
$226$	−13.3278	−	3.57119i	−0.886555	−	0.237552i
$227$	11.3976	+	11.3976i	0.756488	+	0.756488i	0.975681	−	0.219194i	$-0.0703427\pi$
$227$	11.3976	+	11.3976i	0.756488	+	0.756488i	−0.219194	+	0.975681i	$0.570343\pi$
$228$	2.11504	−	11.4029i	0.140072	−	0.755173i
$229$	−4.49023	+	16.7578i	−0.296723	+	1.10739i	0.643116	+	0.765769i	$0.277641\pi$
$229$	−4.49023	+	16.7578i	−0.296723	+	1.10739i	−0.939839	+	0.341617i	$0.889025\pi$
$230$	20.7407	−	11.9746i	1.36760	−	0.789584i
$231$	7.45598	+	0.378613i	0.490567	+	0.0249109i
$232$	2.74625	−	0.735856i	0.180300	−	0.0483113i
$233$	6.51018	+	11.2760i	0.426496	+	0.738712i	0.996559	−	0.0828886i	$-0.0264146\pi$
$233$	6.51018	+	11.2760i	0.426496	+	0.738712i	−0.570063	+	0.821601i	$0.693081\pi$
$234$	−6.36844	−	8.74317i	−0.416318	−	0.571559i
$235$	−6.21106	+	10.7579i	−0.405165	+	0.701767i
$236$	−2.53140	−	2.53140i	−0.164780	−	0.164780i
$237$	−1.98130	+	0.155653i	−0.128699	+	0.0101108i
$238$	2.00572	−	15.4454i	0.130012	−	1.00117i
$239$	15.1157	+	15.1157i	0.977756	+	0.977756i	0.999758	−	0.0220017i	$-0.00700392\pi$
$239$	15.1157	+	15.1157i	0.977756	+	0.977756i	−0.0220017	+	0.999758i	$0.507004\pi$
$240$	−5.27765	−	4.50881i	−0.340671	−	0.291043i
$241$	2.86892	+	2.86892i	0.184803	+	0.184803i	0.793445	−	0.608642i	$-0.208285\pi$
$241$	2.86892	+	2.86892i	0.184803	+	0.184803i	−0.608642	+	0.793445i	$0.708285\pi$
$242$	2.16009	+	8.06157i	0.138856	+	0.518217i
$243$	−12.3605	−	9.49828i	−0.792928	−	0.609315i
$244$	3.54052	+	2.04412i	0.226658	+	0.130861i
$245$	24.3442	+	13.9409i	1.55529	+	0.890652i
$246$	−3.18694	+	2.18967i	−0.203192	+	0.139608i
$247$	−20.2666	−	13.1184i	−1.28953	−	0.834707i
$248$	−6.37075	−	3.67816i	−0.404543	−	0.233563i
$249$	1.57307	−	0.556805i	0.0996890	−	0.0352861i
$250$	24.2902			1.53625
$251$	−0.388071	−	0.672159i	−0.0244948	−	0.0424263i	0.853518	−	0.521063i	$-0.174464\pi$
$251$	−0.388071	−	0.672159i	−0.0244948	−	0.0424263i	−0.878013	+	0.478637i	$0.841131\pi$
$252$	−7.72069	−	1.84146i	−0.486358	−	0.116001i
$253$	−9.40381	−	2.51974i	−0.591212	−	0.158415i
$254$	3.75000	+	13.9952i	0.235296	+	0.878136i
$255$	−31.0685	−	26.5425i	−1.94559	−	1.66216i
$256$	1.00000			0.0625000
$257$	7.87093			0.490975			0.245488	−	0.969400i	$-0.421052\pi$
$257$	7.87093			0.490975			0.245488	+	0.969400i	$0.421052\pi$
$258$	6.28707	−	7.35913i	0.391416	−	0.458160i
$259$	−2.69444	+	20.7490i	−0.167425	+	1.28928i
$260$	−12.8650	+	6.57916i	−0.797852	+	0.408022i
$261$	−1.33194	−	8.42474i	−0.0824449	−	0.521479i
$262$	6.15943	+	1.65041i	0.380531	+	0.101963i
$263$	−4.63532	+	2.67620i	−0.285826	+	0.165022i	−0.636058	−	0.771641i	$-0.719436\pi$
$263$	−4.63532	+	2.67620i	−0.285826	+	0.165022i	0.350232	+	0.936663i	$0.386103\pi$
$264$	0.220998	+	2.81306i	0.0136015	+	0.173132i
$265$	−17.1392	+	17.1392i	−1.05285	+	1.05285i
$266$	−17.5596	+	2.34327i	−1.07665	+	0.143675i
$267$	−6.01001	−	16.9793i	−0.367807	−	1.03912i
$268$	−2.75396	+	10.2779i	−0.168225	+	0.627825i
$269$		−	20.9401i		−	1.27674i	−0.769731	−	0.638369i	$-0.779610\pi$
$269$		−	20.9401i		−	1.27674i	0.769731	−	0.638369i	$-0.220390\pi$
$270$	−15.1113	+	14.3281i	−0.919647	+	0.871981i
$271$	−5.61422	−	5.61422i	−0.341040	−	0.341040i	0.515718	−	0.856758i	$-0.327525\pi$
$271$	−5.61422	−	5.61422i	−0.341040	−	0.341040i	−0.856758	+	0.515718i	$0.827525\pi$
$272$	5.88681			0.356940
$273$	−9.67018	+	13.3973i	−0.585266	+	0.810842i
$274$	−16.0089			−0.967133
$275$	−12.7419	−	12.7419i	−0.768365	−	0.768365i
$276$	9.34170	+	4.45736i	0.562304	+	0.268302i
$277$			1.13058i			0.0679298i	0.999423	+	0.0339649i	$0.0108134\pi$
$277$			1.13058i			0.0679298i	−0.999423	+	0.0339649i	$0.989187\pi$
$278$	0.275366	−	1.02768i	0.0165154	−	0.0616362i
$279$	−12.9768	+	17.8505i	−0.776899	+	1.06868i
$280$	−4.04038	+	9.80318i	−0.241459	+	0.585852i
$281$	0.557025	−	0.557025i	0.0332293	−	0.0332293i	−0.690297	−	0.723526i	$-0.742520\pi$
$281$	0.557025	−	0.557025i	0.0332293	−	0.0332293i	0.723526	+	0.690297i	$0.242520\pi$
$282$	−5.35222	+	0.420478i	−0.318720	+	0.0250391i
$283$	−3.02685	+	1.74756i	−0.179928	+	0.103881i	−0.587259	−	0.809399i	$-0.699793\pi$
$283$	−3.02685	+	1.74756i	−0.179928	+	0.103881i	0.407331	+	0.913281i	$0.366460\pi$
$284$	5.14163	+	1.37770i	0.305100	+	0.0817512i
$285$	−20.0150	+	41.9473i	−1.18559	+	2.48475i
$286$	5.58910	+	1.80682i	0.330490	+	0.106840i
$287$	4.69224	+	3.58736i	0.276974	+	0.211755i
$288$	0.314418	−	2.98348i	0.0185273	−	0.175803i
$289$	17.6546			1.03850
$290$	−11.3942			−0.669089
$291$	6.00716	−	7.03149i	0.352146	−	0.412193i
$292$	0.554635	+	2.06993i	0.0324575	+	0.121133i
$293$	−32.7508	−	8.77554i	−1.91332	−	0.512673i	−0.992423	−	0.122867i	$-0.960791\pi$
$293$	−32.7508	−	8.77554i	−1.91332	−	0.512673i	−0.920897	−	0.389806i	$-0.872542\pi$
$294$	0.992197	+	12.0837i	0.0578661	+	0.704735i
$295$	7.17351	+	12.4249i	0.417658	+	0.723404i
$296$	−7.90822			−0.459656
$297$	8.46219	+	0.225136i	0.491026	+	0.0130637i
$298$	−5.73140	−	3.30903i	−0.332011	−	0.191687i
$299$	15.9907	−	14.4412i	0.924768	−	0.835159i
$300$	10.8491	+	15.7903i	0.626375	+	0.911654i
$301$	−13.6695	−	5.63388i	−0.787898	−	0.324731i
$302$	−16.4477	−	9.49606i	−0.946456	−	0.546437i
$303$	3.89599	−	0.306074i	0.223819	−	0.0175835i
$304$	−1.73298	−	6.46758i	−0.0993934	−	0.370941i
$305$	−11.5853	−	11.5853i	−0.663372	−	0.663372i
$306$	1.85092	−	17.5632i	0.105810	−	1.00402i
$307$	1.07278	+	1.07278i	0.0612269	+	0.0612269i	0.737057	−	0.675830i	$-0.236215\pi$
$307$	1.07278	+	1.07278i	0.0612269	+	0.0612269i	−0.675830	+	0.737057i	$0.736215\pi$
$308$	3.97925	−	1.65648i	0.226739	−	0.0943869i
$309$	0.164200	+	2.09009i	0.00934102	+	0.118901i
$310$	20.8464	+	20.8464i	1.18400	+	1.18400i
$311$	13.8659	−	24.0165i	0.786264	−	1.36185i	−0.141977	−	0.989870i	$-0.545346\pi$
$311$	13.8659	−	24.0165i	0.786264	−	1.36185i	0.928241	−	0.371979i	$-0.121321\pi$
$312$	−5.49222	−	2.97246i	−0.310936	−	0.168282i
$313$	−13.5852	−	23.5302i	−0.767880	−	1.33001i	−0.938711	−	0.344706i	$-0.887979\pi$
$313$	−13.5852	−	23.5302i	−0.767880	−	1.33001i	0.170831	−	0.985300i	$-0.445355\pi$
$314$	8.42175	−	2.25660i	0.475267	−	0.127347i
$315$	27.9772	+	15.1367i	1.57634	+	0.852855i
$316$	−0.993700	+	0.573713i	−0.0559000	+	0.0322739i
$317$	3.68425	−	13.7498i	0.206928	−	0.772266i	−0.781925	−	0.623372i	$-0.785762\pi$
$317$	3.68425	−	13.7498i	0.206928	−	0.772266i	0.988853	−	0.148894i	$-0.0475712\pi$
$318$	−10.3000	−	1.91047i	−0.577593	−	0.107134i
$319$	3.27518	+	3.27518i	0.183375	+	0.183375i
$320$	−3.87106	−	1.03725i	−0.216399	−	0.0579839i
$321$	−3.39419	−	1.61953i	−0.189445	−	0.0903931i
$322$	2.03609	−	15.6792i	0.113467	−	0.873767i
$323$	−10.2017	−	38.0734i	−0.567640	−	2.11846i
$324$	−8.80228	−	1.87612i	−0.489016	−	0.104229i
$325$	38.9971	−	8.34974i	2.16317	−	0.463160i
$326$	5.81030	+	3.35458i	0.321803	+	0.185793i
$327$	30.8879	+	5.72918i	1.70810	+	0.316825i
$328$	−1.11622	+	1.93334i	−0.0616327	+	0.106751i
$329$	3.15168	+	7.57105i	0.173758	+	0.417406i
$330$	2.06234	−	11.1188i	0.113528	−	0.612067i
$331$	4.03171	+	15.0466i	0.221603	+	0.827033i	0.983737	+	0.179614i	$0.0574850\pi$
$331$	4.03171	+	15.0466i	0.221603	+	0.827033i	−0.762134	+	0.647419i	$0.775848\pi$
$332$	0.681245	−	0.681245i	0.0373882	−	0.0373882i
$333$	−2.48649	+	23.5940i	−0.136259	+	1.29294i
$334$	−2.50880	+	4.34536i	−0.137275	+	0.237768i
$335$	21.3215	−	36.9300i	1.16492	−	2.01770i
$336$	−4.48088	+	0.960048i	−0.244452	+	0.0523749i
$337$		−	34.7050i		−	1.89050i	−0.326347	−	0.945250i	$-0.605818\pi$
$337$		−	34.7050i		−	1.89050i	0.326347	−	0.945250i	$-0.394182\pi$
$338$	−10.0785	+	8.21118i	−0.548199	+	0.446629i
$339$	1.87176	+	23.8254i	0.101660	+	1.29402i
$340$	−22.7882	−	6.10608i	−1.23586	−	0.331149i
$341$		−	11.9843i		−	0.648989i
$342$	−19.8408	+	3.13679i	−1.07287	+	0.169618i
$343$	17.0728	−	7.17780i	0.921842	−	0.387565i
$344$	1.44633	−	5.39779i	0.0779811	−	0.291029i
$345$	−31.5389	−	26.9444i	−1.69800	−	1.45064i
$346$	1.57232	−	0.421302i	0.0845284	−	0.0226493i
$347$		−	5.43458i		−	0.291744i	−0.989303	−	0.145872i	$-0.953401\pi$
$347$		−	5.43458i		−	0.291744i	0.989303	−	0.145872i	$-0.0465987\pi$
$348$	−2.78867	−	4.05875i	−0.149488	−	0.217572i
$349$	28.2484	−	7.56913i	1.51210	−	0.405166i	0.594969	−	0.803749i	$-0.297164\pi$
$349$	28.2484	−	7.56913i	1.51210	−	0.405166i	0.917133	+	0.398582i	$0.130498\pi$
$350$	17.7742	−	23.2486i	0.950073	−	1.24269i
$351$	−10.5951	+	15.4513i	−0.565525	+	0.824731i
$352$	0.814562	+	1.41086i	0.0434163	+	0.0751993i
$353$	−8.91150	+	33.2582i	−0.474311	+	1.77015i	0.149692	+	0.988733i	$0.452172\pi$
$353$	−8.91150	+	33.2582i	−0.474311	+	1.77015i	−0.624003	+	0.781422i	$0.714495\pi$
$354$	−2.67022	+	5.59622i	−0.141921	+	0.297436i
$355$	−18.4746	−	10.6663i	−0.980528	−	0.566108i
$356$	−7.35319	−	7.35319i	−0.389718	−	0.389718i
$357$	−26.3781	+	5.65162i	−1.39608	+	0.299115i
$358$	−4.09013	+	15.2646i	−0.216170	+	0.806757i
$359$	−29.8962	−	8.01066i	−1.57786	−	0.422787i	−0.639598	−	0.768710i	$-0.720899\pi$
$359$	−29.8962	−	8.01066i	−1.57786	−	0.422787i	−0.938263	+	0.345923i	$0.887566\pi$
$360$	−4.31174	+	11.2231i	−0.227249	+	0.591509i
$361$	−22.3719	+	12.9164i	−1.17747	+	0.679812i
$362$	−4.53557	+	4.53557i	−0.238384	+	0.238384i
$363$	11.9144	−	8.18609i	0.625343	−	0.429658i
$364$	−1.70792	+	9.38526i	−0.0895193	+	0.491921i
$365$		−	8.58810i		−	0.449522i
$366$	1.29139	−	6.96228i	0.0675019	−	0.363924i
$367$	−7.58574	−	13.1389i	−0.395972	−	0.685844i	0.597252	−	0.802053i	$-0.296259\pi$
$367$	−7.58574	−	13.1389i	−0.395972	−	0.685844i	−0.993225	+	0.116209i	$0.962926\pi$
$368$	5.97593			0.311517
$369$	5.41713	+	3.93808i	0.282004	+	0.205008i
$370$	30.6132	+	8.20279i	1.59151	+	0.426443i
$371$	2.11662	+	15.8612i	0.109890	+	0.823472i
$372$	−2.32370	+	12.5278i	−0.120478	+	0.649537i
$373$	11.7793	−	20.4023i	0.609909	−	1.05639i	−0.381346	−	0.924432i	$-0.624539\pi$
$373$	11.7793	−	20.4023i	0.609909	−	1.05639i	0.991255	−	0.131961i	$-0.0421272\pi$
$374$	4.79517	+	8.30549i	0.247953	+	0.429466i
$375$	−14.0383	−	39.6606i	−0.724936	−	2.04807i
$376$	−2.68436	+	1.54981i	−0.138435	+	0.0799256i
$377$	−10.0239	+	2.14622i	−0.516255	+	0.110536i
$378$	1.45541	+	13.6705i	0.0748582	+	0.703133i
$379$	−5.19815	−	19.3998i	−0.267011	−	0.996499i	−0.961008	−	0.276521i	$-0.910818\pi$
$379$	−5.19815	−	19.3998i	−0.267011	−	0.996499i	0.693997	−	0.719978i	$-0.255848\pi$
$380$			26.8339i			1.37655i
$381$	20.6838	−	14.2113i	1.05966	−	0.728070i
$382$	−5.40701	−	20.1792i	−0.276647	−	1.03246i
$383$	−13.4463	+	3.60292i	−0.687073	+	0.184101i	−0.585433	−	0.810720i	$-0.699076\pi$
$383$	−13.4463	+	3.60292i	−0.687073	+	0.184101i	−0.101640	+	0.994821i	$0.532409\pi$
$384$	−0.577943	−	1.63278i	−0.0294930	−	0.0833226i
$385$	−17.1221	+	2.28489i	−0.872622	+	0.116449i
$386$	−2.76991	+	1.59921i	−0.140985	+	0.0813977i
$387$	−15.6494	−	6.01227i	−0.795505	−	0.305621i
$388$	1.38194	−	5.15747i	0.0701574	−	0.261831i
$389$	−11.2945	+	19.5627i	−0.572656	+	0.991870i	0.423636	+	0.905833i	$0.360754\pi$
$389$	−11.2945	+	19.5627i	−0.572656	+	0.991870i	−0.996292	+	0.0860370i	$0.972580\pi$
$390$	18.1776	+	17.2034i	0.920456	+	0.871126i
$391$	35.1792			1.77909
$392$	3.52136	+	6.04980i	0.177855	+	0.305561i
$393$	−0.865027	−	11.0109i	−0.0436349	−	0.555424i
$394$	−15.6584	−	9.04039i	−0.788860	−	0.455448i
$395$	4.44176	−	1.19017i	0.223489	−	0.0598837i
$396$	4.46539	−	1.98663i	0.224394	−	0.0998318i
$397$	−31.4639	+	8.43072i	−1.57913	+	0.423126i	−0.938656	−	0.344856i	$-0.887928\pi$
$397$	−31.4639	+	8.43072i	−1.57913	+	0.423126i	−0.640471	+	0.767982i	$0.721261\pi$
$398$	−1.20247	+	1.20247i	−0.0602744	+	0.0602744i
$399$	13.9745	+	27.3167i	0.699599	+	1.36755i
$400$	9.57911	+	5.53050i	0.478955	+	0.276525i
$401$	6.96710	−	6.96710i	0.347921	−	0.347921i	−0.511414	−	0.859334i	$-0.670878\pi$
$401$	6.96710	−	6.96710i	0.347921	−	0.347921i	0.859334	+	0.511414i	$0.170878\pi$
$402$	18.3733	−	1.44343i	0.916376	−	0.0719916i
$403$	22.2660	+	14.4127i	1.10915	+	0.717946i
$404$	1.95400	−	1.12814i	0.0972150	−	0.0561271i
$405$	32.1282	+	16.3927i	1.59646	+	0.814561i
$406$	−4.56870	+	5.97583i	−0.226741	+	0.296576i
$407$	−6.44174	−	11.1574i	−0.319305	−	0.553053i
$408$	−3.40224	−	9.61189i	−0.168436	−	0.475859i
$409$	10.5643	−	10.5643i	0.522371	−	0.522371i	−0.395916	−	0.918287i	$-0.629573\pi$
$409$	10.5643	−	10.5643i	0.522371	−	0.522371i	0.918287	+	0.395916i	$0.129573\pi$
$410$	6.32630	−	6.32630i	0.312433	−	0.312433i
$411$	9.25222	+	26.1391i	0.456379	+	1.28935i
$412$	0.605216	+	1.04826i	0.0298169	+	0.0516443i
$413$	9.39275	+	1.21973i	0.462187	+	0.0600192i
$414$	1.87894	−	17.8291i	0.0923450	−	0.876251i
$415$	−3.34376	+	1.93052i	−0.164139	+	0.0947656i
$416$	−3.60089	−	0.183345i	−0.176548	−	0.00898921i
$417$	−1.83713	+	0.144327i	−0.0899645	+	0.00706772i
$418$	7.71325	−	7.71325i	0.377267	−	0.377267i
$419$	5.80464	+	3.35131i	0.283575	+	0.163722i	0.635041	−	0.772478i	$-0.280983\pi$
$419$	5.80464	+	3.35131i	0.283575	+	0.163722i	−0.351466	+	0.936201i	$0.614317\pi$
$420$	18.3416	+	0.931382i	0.894977	+	0.0454468i
$421$	5.14250	−	5.14250i	0.250630	−	0.250630i	−0.570599	−	0.821229i	$-0.693289\pi$
$421$	5.14250	−	5.14250i	0.250630	−	0.250630i	0.821229	+	0.570599i	$0.193289\pi$
$422$	6.07840	−	1.62870i	0.295892	−	0.0792840i
$423$	3.77983	+	8.49601i	0.183781	+	0.413090i
$424$	−5.84203	+	1.56537i	−0.283714	+	0.0760209i
$425$	56.3904	+	32.5570i	2.73534	+	1.57925i
$426$	−0.722088	−	9.19140i	−0.0349853	−	0.445325i
$427$	−10.7214	+	1.43074i	−0.518846	+	0.0692382i
$428$	−2.17128			−0.104953
$429$	−0.280028	−	10.1700i	−0.0135199	−	0.491013i
$430$	−11.1977	+	19.3950i	−0.540001	+	0.935309i
$431$	−3.47149	+	12.9558i	−0.167216	+	0.624058i	0.830531	+	0.556972i	$0.188037\pi$
$431$	−3.47149	+	12.9558i	−0.167216	+	0.624058i	−0.997747	+	0.0670861i	$0.978630\pi$
$432$	−5.05309	+	1.21090i	−0.243117	+	0.0582596i
$433$	−19.8711	+	11.4726i	−0.954946	+	0.551338i	−0.894614	−	0.446840i	$-0.852549\pi$
$433$	−19.8711	+	11.4726i	−0.954946	+	0.551338i	−0.0603318	+	0.998178i	$0.519216\pi$
$434$	19.2920	−	2.57445i	0.926043	−	0.123577i
$435$	6.58518	+	18.6042i	0.315735	+	0.892004i
$436$	17.5193	−	4.69427i	0.839021	−	0.224815i
$437$	−10.3562	−	38.6498i	−0.495404	−	1.84887i
$438$	3.05919	−	2.10190i	0.146174	−	0.100433i
$439$			29.2721i			1.39708i	0.715570	+	0.698541i	$0.246167\pi$
$439$			29.2721i			1.39708i	−0.715570	+	0.698541i	$0.753833\pi$
$440$	−1.68981	−	6.30644i	−0.0805583	−	0.300648i
$441$	19.1566	−	8.60372i	0.912220	−	0.409701i
$442$	−21.1977	−	1.07932i	−1.00827	−	0.0513378i
$443$	1.83898	−	1.06174i	0.0873727	−	0.0504447i	−0.455677	−	0.890145i	$-0.650603\pi$
$443$	1.83898	−	1.06174i	0.0873727	−	0.0504447i	0.543050	+	0.839701i	$0.317269\pi$
$444$	4.57050	+	12.9124i	0.216906	+	0.612796i
$445$	20.8376	+	36.0917i	0.987795	+	1.71091i
$446$	3.00847	−	5.21081i	0.142455	−	0.246739i
$447$	−2.09050	+	11.2706i	−0.0988774	+	0.533080i
$448$	−2.09617	+	1.61433i	−0.0990348	+	0.0762699i
$449$	0.156551	+	0.0419478i	0.00738811	+	0.00197964i	0.262511	−	0.964929i	$-0.415449\pi$
$449$	0.156551	+	0.0419478i	0.00738811	+	0.00197964i	−0.255123	+	0.966909i	$0.582116\pi$
$450$	19.5120	−	26.8402i	0.919803	−	1.26526i
$451$	−3.63691			−0.171255
$452$	6.89900	+	11.9494i	0.324502	+	0.562054i
$453$	−5.99921	+	32.3436i	−0.281867	+	1.51964i
$454$		−	16.1187i		−	0.756488i
$455$	16.3463	−	34.5594i	0.766326	−	1.62017i
$456$	−9.55860	+	6.56748i	−0.447622	+	0.307550i
$457$	−1.06817	+	1.06817i	−0.0499671	+	0.0499671i	−0.731649	−	0.681682i	$-0.761249\pi$
$457$	−1.06817	+	1.06817i	−0.0499671	+	0.0499671i	0.681682	+	0.731649i	$0.261249\pi$
$458$	15.0246	−	8.67447i	0.702054	−	0.405331i
$459$	−29.7466	+	7.12835i	−1.38845	+	0.332723i
$460$	−23.1332	−	6.19852i	−1.07859	−	0.289008i
$461$	3.45441	−	12.8920i	0.160888	−	0.600442i	−0.837641	−	0.546221i	$-0.816066\pi$
$461$	3.45441	−	12.8920i	0.160888	−	0.600442i	0.998529	−	0.0542207i	$-0.0172674\pi$
$462$	−5.00445	−	5.53989i	−0.232828	−	0.257739i
$463$	7.79325	+	7.79325i	0.362183	+	0.362183i	0.864616	−	0.502433i	$-0.167562\pi$
$463$	7.79325	+	7.79325i	0.362183	+	0.362183i	−0.502433	+	0.864616i	$0.667562\pi$
$464$	−2.46222	−	1.42156i	−0.114306	−	0.0659944i
$465$	21.9897	−	46.0857i	1.01975	−	2.13717i
$466$	3.36992	−	12.5767i	0.156108	−	0.582604i
$467$	−4.07972	−	7.06628i	−0.188787	−	0.326988i	0.756059	−	0.654503i	$-0.227122\pi$
$467$	−4.07972	−	7.06628i	−0.188787	−	0.326988i	−0.944846	+	0.327515i	$0.893789\pi$
$468$	−1.67919	+	10.6855i	−0.0776205	+	0.493938i
$469$	−10.8192	−	25.9901i	−0.499584	−	1.20011i
$470$	11.9989	−	3.21508i	0.553466	−	0.148301i
$471$	−8.55183	−	12.4467i	−0.394048	−	0.573514i
$472$			3.57993i			0.164780i
$473$	8.79367	−	2.35626i	0.404333	−	0.108341i
$474$	1.51105	+	1.29092i	0.0694049	+	0.0592941i
$475$	19.1685	−	71.5379i	0.879513	−	3.28239i
$476$	−12.3398	+	9.50326i	−0.565593	+	0.435581i
$477$	2.83340	+	17.9217i	0.129732	+	0.820580i
$478$		−	21.3769i		−	0.977756i
$479$	−1.35591	−	0.363316i	−0.0619533	−	0.0166003i	0.227709	−	0.973729i	$-0.426876\pi$
$479$	−1.35591	−	0.363316i	−0.0619533	−	0.0166003i	−0.289663	+	0.957129i	$0.593543\pi$
$480$	0.543650	+	6.92008i	0.0248141	+	0.315857i
$481$	28.4766	+	1.44993i	1.29842	+	0.0661111i
$482$		−	4.05726i		−	0.184803i
$483$	−26.7775	+	5.73718i	−1.21842	+	0.261051i
$484$	4.17298	−	7.22781i	0.189681	−	0.328537i
$485$	−10.6992	+	18.5315i	−0.485824	+	0.841471i
$486$	2.02392	+	15.4565i	0.0918067	+	0.701122i
$487$	−24.9806	+	24.9806i	−1.13198	+	1.13198i	−0.142130	+	0.989848i	$0.545395\pi$
$487$	−24.9806	+	24.9806i	−1.13198	+	1.13198i	−0.989848	+	0.142130i	$0.954605\pi$
$488$	−1.05811	−	3.94893i	−0.0478985	−	0.178760i
$489$	2.11928	−	11.4257i	0.0958372	−	0.516689i
$490$	−7.35625	−	27.0717i	−0.332321	−	1.22297i
$491$	−14.6438	+	25.3639i	−0.660867	+	1.14466i	0.319521	+	0.947579i	$0.396478\pi$
$491$	−14.6438	+	25.3639i	−0.660867	+	1.14466i	−0.980388	+	0.197076i	$0.936855\pi$
$492$	3.80184	+	0.705178i	0.171400	+	0.0317919i
$493$	−14.4946	−	8.36848i	−0.652805	−	0.376897i
$494$	5.05448	+	23.6068i	0.227412	+	1.06212i
$495$	−19.3464	+	3.05864i	−0.869558	+	0.137476i
$496$	1.90395	+	7.10565i	0.0854900	+	0.319053i
$497$	−13.0018	+	5.41240i	−0.583211	+	0.242779i
$498$	−1.50605	−	0.718605i	−0.0674876	−	0.0322015i
$499$	21.8644	+	5.85855i	0.978785	+	0.262265i	0.712533	−	0.701639i	$-0.247548\pi$
$499$	21.8644	+	5.85855i	0.978785	+	0.262265i	0.266252	+	0.963903i	$0.414215\pi$
$500$	−17.1758	−	17.1758i	−0.768123	−	0.768123i
$501$	8.54498	+	1.58495i	0.381762	+	0.0708104i
$502$	−0.200880	+	0.749696i	−0.00896573	+	0.0334606i
$503$	−14.3824	+	8.30369i	−0.641280	+	0.370243i	−0.785107	−	0.619360i	$-0.787392\pi$
$503$	−14.3824	+	8.30369i	−0.641280	+	0.370243i	0.143827	+	0.989603i	$0.454059\pi$
$504$	4.15724	+	6.76146i	0.185178	+	0.301179i
$505$	−8.73421	+	2.34032i	−0.388667	+	0.104143i
$506$	4.86777	+	8.43123i	0.216399	+	0.374814i
$507$	19.2319	+	11.7104i	0.854118	+	0.520079i
$508$	7.24444	−	12.5477i	0.321420	−	0.556716i
$509$	−15.8260	−	15.8260i	−0.701475	−	0.701475i	0.263252	−	0.964727i	$-0.415205\pi$
$509$	−15.8260	−	15.8260i	−0.701475	−	0.701475i	−0.964727	+	0.263252i	$0.915205\pi$
$510$	3.20037	+	40.7372i	0.141715	+	1.80387i
$511$	−4.50415	−	3.44356i	−0.199252	−	0.152334i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	16.5885	+	30.5828i	0.732401	+	1.35026i
$514$	−5.56559	−	5.56559i	−0.245488	−	0.245488i
$515$	−1.25552	−	4.68566i	−0.0553247	−	0.206475i
$516$	−9.64932	+	0.758063i	−0.424788	+	0.0333719i
$517$	−4.37315	−	2.52484i	−0.192331	−	0.111042i
$518$	16.5770	−	12.7665i	0.728351	−	0.560927i
$519$	−1.59660	−	2.32377i	−0.0700832	−	0.102002i
$520$	13.7491	+	4.44475i	0.602937	+	0.194915i
$521$	−2.07162	−	1.19605i	−0.0907594	−	0.0524000i	0.453933	−	0.891036i	$-0.350020\pi$
$521$	−2.07162	−	1.19605i	−0.0907594	−	0.0524000i	−0.544693	+	0.838636i	$0.683354\pi$
$522$	−5.01537	+	6.89902i	−0.219517	+	0.301962i
$523$	−2.75163			−0.120320			−0.0601602	−	0.998189i	$-0.519161\pi$
$523$	−2.75163			−0.120320			−0.0601602	+	0.998189i	$0.519161\pi$
$524$	−3.18836	−	5.52239i	−0.139284	−	0.241247i
$525$	−48.2324	−	15.5851i	−2.10503	−	0.680191i
$526$	5.17003	+	1.38530i	0.225424	+	0.0604021i
$527$	11.2082	+	41.8296i	0.488237	+	1.82213i
$528$	1.83286	−	2.14540i	0.0797652	−	0.0933666i
$529$	12.7118			0.552686
$530$	24.2385			1.05285
$531$	10.6807	+	1.12560i	0.463501	+	0.0488467i
$532$	14.0734	+	10.7596i	0.610161	+	0.466486i
$533$	4.37383	−	6.75709i	0.189452	−	0.292682i
$534$	−7.75644	+	16.2559i	−0.335654	+	0.703461i
$535$	8.40516	+	2.25215i	0.363387	+	0.0973691i
$536$	9.21494	−	5.32025i	0.398025	−	0.229800i
$537$	27.2876	−	2.14375i	1.17755	−	0.0925096i
$538$	−14.8069	+	14.8069i	−0.638369	+	0.638369i
$539$	−5.66707	+	9.89609i	−0.244098	+	0.426255i
$540$	20.8168	+	0.553830i	0.895814	+	0.0238330i
$541$	2.92973	−	10.9339i	0.125959	−	0.470085i	−0.873913	−	0.486082i	$-0.838426\pi$
$541$	2.92973	−	10.9339i	0.125959	−	0.470085i	0.999872	+	0.0159971i	$0.00509224\pi$
$542$			7.93971i			0.341040i
$543$	10.0269	+	4.78430i	0.430295	+	0.205314i
$544$	−4.16260	−	4.16260i	−0.178470	−	0.178470i
$545$	−72.6873			−3.11358
$546$	16.3112	−	2.63548i	0.698054	−	0.112788i
$547$	−3.12274			−0.133519			−0.0667593	−	0.997769i	$-0.521266\pi$
$547$	−3.12274			−0.133519			−0.0667593	+	0.997769i	$0.521266\pi$
$548$	11.3200	+	11.3200i	0.483566	+	0.483566i
$549$	−12.1142	+	1.91524i	−0.517023	+	0.0817405i
$550$			18.0198i			0.768365i
$551$	−4.92709	+	18.3882i	−0.209901	+	0.783362i
$552$	−3.45375	−	9.75741i	−0.147001	−	0.415303i
$553$	1.15680	−	2.80676i	0.0491923	−	0.119356i
$554$	0.799438	−	0.799438i	0.0339649	−	0.0339649i
$555$	−4.29930	−	54.7255i	−0.182495	−	2.32297i
$556$	−0.921393	+	0.531967i	−0.0390758	+	0.0225604i
$557$	4.77392	+	1.27917i	0.202277	+	0.0542001i	0.358535	−	0.933516i	$-0.383276\pi$
$557$	4.77392	+	1.27917i	0.202277	+	0.0542001i	−0.156258	+	0.987716i	$0.549943\pi$
$558$	21.7982	−	3.44626i	0.922791	−	0.145892i
$559$	−6.19774	+	19.1717i	−0.262136	+	0.810875i
$560$	9.78887	−	4.07492i	0.413655	−	0.172197i
$561$	10.7897	−	12.6296i	0.455543	−	0.533221i
$562$	−0.787752			−0.0332293
$563$	39.9101			1.68201			0.841006	−	0.541026i	$-0.181964\pi$
$563$	39.9101			1.68201			0.841006	+	0.541026i	$0.181964\pi$
$564$	4.08192	+	3.48727i	0.171880	+	0.146841i
$565$	−14.3120	−	53.4129i	−0.602108	−	2.24710i
$566$	3.37602	+	0.904601i	0.141905	+	0.0380232i
$567$	21.4798	−	10.2771i	0.902066	−	0.431598i
$568$	−2.66150	−	4.60986i	−0.111674	−	0.193425i
$569$	−4.84910			−0.203285			−0.101642	−	0.994821i	$-0.532410\pi$
$569$	−4.84910			−0.203285			−0.101642	+	0.994821i	$0.532410\pi$
$570$	43.8140	−	15.5085i	1.83517	−	0.649579i
$571$	−28.5983	−	16.5112i	−1.19680	−	0.690973i	−0.236960	−	0.971519i	$-0.576151\pi$
$571$	−28.5983	−	16.5112i	−1.19680	−	0.690973i	−0.959841	+	0.280546i	$0.909484\pi$
$572$	−2.67447	−	5.22970i	−0.111825	−	0.218665i
$573$	−29.8234	+	20.4909i	−1.24589	+	0.856020i
$574$	−0.781271	−	5.85456i	−0.0326096	−	0.244365i
$575$	57.2441	+	33.0499i	2.38724	+	1.37828i
$576$	−2.33196	+	1.88731i	−0.0971652	+	0.0786379i
$577$	5.90704	+	22.0454i	0.245913	+	0.917761i	0.972922	+	0.231133i	$0.0742433\pi$
$577$	5.90704	+	22.0454i	0.245913	+	0.917761i	−0.727009	+	0.686628i	$0.759090\pi$
$578$	−12.4837	−	12.4837i	−0.519251	−	0.519251i
$579$	4.21202	+	3.59842i	0.175045	+	0.149545i
$580$	8.05689	+	8.05689i	0.334544	+	0.334544i
$581$	−0.328253	+	2.52776i	−0.0136182	+	0.104869i
$582$	−9.21972	+	0.724313i	−0.382170	+	0.0300237i
$583$	−6.96722	−	6.96722i	−0.288553	−	0.288553i
$584$	1.07147	−	1.85584i	0.0443378	−	0.0767954i
$585$	17.5838	−	39.6226i	0.727000	−	1.63819i
$586$	16.9530	+	29.3635i	0.700324	+	1.21300i
$587$	−21.3929	+	5.73221i	−0.882979	+	0.236593i	−0.671692	−	0.740831i	$-0.734432\pi$
$587$	−21.3929	+	5.73221i	−0.882979	+	0.236593i	−0.211287	+	0.977424i	$0.567765\pi$
$588$	7.84287	−	9.24605i	0.323434	−	0.381301i
$589$	42.6569	−	24.6279i	1.75765	−	1.01478i
$590$	3.71328	−	13.8581i	0.152873	−	0.570531i
$591$	−5.71134	+	30.7916i	−0.234933	+	1.26660i
$592$	5.59196	+	5.59196i	0.229828	+	0.229828i
$593$	37.7046	+	10.1029i	1.54834	+	0.414877i	0.928951	−	0.370204i	$-0.120712\pi$
$593$	37.7046	+	10.1029i	1.54834	+	0.414877i	0.619393	+	0.785081i	$0.287379\pi$
$594$	−5.82447	−	6.14286i	−0.238981	−	0.252045i
$595$	57.6253	−	23.9883i	2.36241	−	0.983424i
$596$	1.71288	+	6.39255i	0.0701622	+	0.261849i
$597$	2.65833	+	1.26841i	0.108798	+	0.0519127i
$598$	−21.5187	−	1.09566i	−0.879963	−	0.0448047i
$599$	1.25903	+	0.726901i	0.0514426	+	0.0297004i	0.525501	−	0.850793i	$-0.323878\pi$
$599$	1.25903	+	0.726901i	0.0514426	+	0.0297004i	−0.474058	+	0.880494i	$0.657211\pi$
$600$	3.49394	−	18.8369i	0.142639	−	0.769014i
$601$	−10.9581	+	18.9800i	−0.446992	+	0.774212i	−0.998189	−	0.0601629i	$-0.980838\pi$
$601$	−10.9581	+	18.9800i	−0.446992	+	0.774212i	0.551197	+	0.834375i	$0.314171\pi$
$602$	5.68205	+	13.6496i	0.231583	+	0.556314i
$603$	−12.9755	−	29.1654i	−0.528403	−	1.18771i
$604$	4.91552	+	18.3450i	0.200010	+	0.746446i
$605$	−23.6509	+	23.6509i	−0.961545	+	0.961545i
$606$	−2.97131	−	2.53846i	−0.120701	−	0.103118i
$607$	20.5289	−	35.5572i	0.833244	−	1.44322i	−0.0622085	−	0.998063i	$-0.519814\pi$
$607$	20.5289	−	35.5572i	0.833244	−	1.44322i	0.895452	−	0.445157i	$-0.146852\pi$
$608$	−3.34787	+	5.79867i	−0.135774	+	0.235167i
$609$	12.3977	+	4.00601i	0.502380	+	0.162332i
$610$			16.3841i			0.663372i
$611$	9.95022	−	5.08854i	0.402543	−	0.205860i
$612$	−13.7278	+	11.1102i	−0.554915	+	0.449105i
$613$	−18.0909	−	4.84743i	−0.730683	−	0.195786i	−0.125750	−	0.992062i	$-0.540134\pi$
$613$	−18.0909	−	4.84743i	−0.730683	−	0.195786i	−0.604934	+	0.796276i	$0.706800\pi$
$614$		−	1.51714i		−	0.0612269i
$615$	−13.9857	−	6.67324i	−0.563958	−	0.269091i
$616$	−3.98506	−	1.64244i	−0.160563	−	0.0661758i
$617$	6.25626	−	23.3487i	0.251868	−	0.939983i	−0.717939	−	0.696106i	$-0.754914\pi$
$617$	6.25626	−	23.3487i	0.251868	−	0.939983i	0.969806	−	0.243877i	$-0.0784192\pi$
$618$	1.36181	−	1.59402i	0.0547800	−	0.0641210i
$619$	10.2088	−	2.73543i	0.410326	−	0.109946i	−0.0477508	−	0.998859i	$-0.515205\pi$
$619$	10.2088	−	2.73543i	0.410326	−	0.109946i	0.458076	+	0.888913i	$0.348539\pi$
$620$		−	29.4813i		−	1.18400i
$621$	−30.1969	+	7.23627i	−1.21176	+	0.290382i
$622$	−26.7869	+	7.17753i	−1.07406	+	0.287793i
$623$	27.2840	+	3.54308i	1.09311	+	0.141951i
$624$	1.78174	+	5.98543i	0.0713268	+	0.239609i
$625$	21.0204	+	36.4084i	0.840815	+	1.45633i
$626$	−7.03220	+	26.2445i	−0.281063	+	1.04894i
$627$	−17.0519	−	8.13625i	−0.680987	−	0.324931i
$628$	−7.55074	−	4.35942i	−0.301307	−	0.173960i
$629$	32.9188	+	32.9188i	1.31256	+	1.31256i
$630$	−9.07963	−	30.4861i	−0.361741	−	1.21460i
$631$	−11.3344	+	42.3005i	−0.451214	+	1.68395i	0.247771	+	0.968819i	$0.420302\pi$
$631$	−11.3344	+	42.3005i	−0.451214	+	1.68395i	−0.698985	+	0.715136i	$0.746365\pi$
$632$	1.10833	+	0.296976i	0.0440869	+	0.0118131i
$633$	−6.17229	−	8.98342i	−0.245326	−	0.357059i
$634$	−12.3277	+	7.11742i	−0.489597	+	0.282669i
$635$	−41.0588	+	41.0588i	−1.62937	+	1.62937i
$636$	5.93226	+	8.63408i	0.235230	+	0.342363i
$637$	−11.5708	−	22.4303i	−0.458452	−	0.888719i
$638$		−	4.63181i		−	0.183375i
$639$	−14.5902	+	6.49112i	−0.577181	+	0.256785i
$640$	2.00381	+	3.47070i	0.0792075	+	0.137191i
$641$	−37.2486			−1.47123			−0.735615	−	0.677399i	$-0.763107\pi$
$641$	−37.2486			−1.47123			−0.735615	+	0.677399i	$0.763107\pi$
$642$	1.25487	+	3.54523i	0.0495260	+	0.139919i
$643$	4.46902	+	1.19747i	0.176241	+	0.0472236i	0.345860	−	0.938286i	$-0.387587\pi$
$643$	4.46902	+	1.19747i	0.176241	+	0.0472236i	−0.169619	+	0.985510i	$0.554254\pi$
$644$	−12.5266	+	9.64713i	−0.493617	+	0.380150i
$645$	38.1394	+	7.07423i	1.50174	+	0.278547i
$646$	−19.7083	+	34.1357i	−0.775411	+	1.34305i
$647$	13.0140	+	22.5410i	0.511635	+	0.886177i	0.999909	+	0.0134870i	$0.00429317\pi$
$647$	13.0140	+	22.5410i	0.511635	+	0.886177i	−0.488274	+	0.872690i	$0.662373\pi$
$648$	4.89754	+	7.55077i	0.192393	+	0.296622i
$649$	−5.05080	+	2.91608i	−0.198261	+	0.114466i
$650$	−33.4793	−	21.6710i	−1.31317	−	0.850006i
$651$	−15.3532	−	30.0117i	−0.601738	−	1.17625i
$652$	−1.73646	−	6.48055i	−0.0680049	−	0.253798i
$653$			18.5565i			0.726172i	0.931756	+	0.363086i	$0.118277\pi$
$653$			18.5565i			0.726172i	−0.931756	+	0.363086i	$0.881723\pi$
$654$	−17.7899	−	25.8922i	−0.695639	−	1.01246i
$655$	6.61423	+	24.6846i	0.258439	+	0.964509i
$656$	2.15636	−	0.577796i	0.0841918	−	0.0225591i
$657$	−5.19998	−	3.78023i	−0.202871	−	0.147481i
$658$	3.12496	−	7.58212i	0.121824	−	0.295582i
$659$	−5.91854	+	3.41707i	−0.230554	+	0.133110i	−0.610827	−	0.791764i	$-0.709163\pi$
$659$	−5.91854	+	3.41707i	−0.230554	+	0.133110i	0.380274	+	0.924874i	$0.375830\pi$
$660$	−9.32044	+	6.40385i	−0.362798	+	0.249269i
$661$	−8.15436	+	30.4325i	−0.317168	+	1.18369i	0.604786	+	0.796388i	$0.293259\pi$
$661$	−8.15436	+	30.4325i	−0.317168	+	1.18369i	−0.921954	+	0.387299i	$0.873408\pi$
$662$	7.78867	−	13.4904i	0.302715	−	0.524318i
$663$	10.4888	+	35.2351i	0.407351	+	1.36842i
$664$	−0.963426			−0.0373882
$665$	−43.3188	−	56.2486i	−1.67983	−	2.18123i
$666$	18.4417	−	14.9253i	0.714601	−	0.578342i
$667$	−14.7141	−	8.49517i	−0.569731	−	0.328934i
$668$	4.84662	−	1.29865i	0.187522	−	0.0502462i
$669$	−10.2469	−	1.90062i	−0.396166	−	0.0734823i
$670$	−41.1900	+	11.0368i	−1.59131	+	0.426390i
$671$	4.70951	−	4.70951i	0.181808	−	0.181808i
$672$	3.84732	+	2.48961i	0.148414	+	0.0960386i
$673$	26.3309	+	15.2022i	1.01498	+	0.586001i	0.912647	−	0.408749i	$-0.134035\pi$
$673$	26.3309	+	15.2022i	1.01498	+	0.586001i	0.102336	+	0.994750i	$0.467368\pi$
$674$	−24.5401	+	24.5401i	−0.945250	+	0.945250i
$675$	−55.1010	−	16.3468i	−2.12084	−	0.629187i
$676$	12.9328	+	1.32041i	0.497414	+	0.0507849i
$677$	2.15766	−	1.24573i	0.0829257	−	0.0478772i	−0.457964	−	0.888971i	$-0.651421\pi$
$677$	2.15766	−	1.24573i	0.0829257	−	0.0478772i	0.540889	+	0.841094i	$0.318088\pi$
$678$	15.5236	−	18.1707i	0.596180	−	0.697840i
$679$	5.42908	+	13.0419i	0.208349	+	0.500501i
$680$	11.7960	+	20.4314i	0.452358	+	0.783507i
$681$	−26.3183	+	9.31568i	−1.00852	+	0.356978i
$682$	−8.47421	+	8.47421i	−0.324494	+	0.324494i
$683$	32.4099	−	32.4099i	1.24013	−	1.24013i	0.280183	−	0.959946i	$-0.409605\pi$
$683$	32.4099	−	32.4099i	1.24013	−	1.24013i	0.959946	−	0.280183i	$-0.0903953\pi$
$684$	16.2476	+	11.8115i	0.621242	+	0.451624i
$685$	−32.0788	−	55.5621i	−1.22567	−	2.12292i
$686$	−17.1477	−	6.99679i	−0.654704	−	0.267139i
$687$	−22.8469	−	19.5186i	−0.871663	−	0.744681i
$688$	−4.83953	+	2.79410i	−0.184505	+	0.106524i
$689$	21.3235	−	4.56560i	0.812360	−	0.173936i
$690$	3.24882	+	41.3539i	0.123680	+	1.57432i
$691$	26.8524	−	26.8524i	1.02151	−	1.02151i	0.0217482	−	0.999763i	$-0.493077\pi$
$691$	26.8524	−	26.8524i	1.02151	−	1.02151i	0.999763	−	0.0217482i	$-0.00692322\pi$
$692$	−1.40970	−	0.813892i	−0.0535889	−	0.0309395i
$693$	−6.15316	+	11.3729i	−0.233739	+	0.432022i
$694$	−3.84283	+	3.84283i	−0.145872	+	0.145872i
$695$	4.11855	−	1.10356i	0.156226	−	0.0418605i
$696$	−0.898084	+	4.84186i	−0.0340418	+	0.183530i
$697$	12.6941	−	3.40137i	0.480823	−	0.128836i
$698$	−25.3268	−	14.6224i	−0.958634	−	0.553468i
$699$	−22.4826	+	1.76626i	−0.850371	+	0.0668063i
$700$	−29.0075	+	3.87096i	−1.09638	+	0.146308i
$701$	−32.7280			−1.23612			−0.618059	−	0.786132i	$-0.712081\pi$
$701$	−32.7280			−1.23612			−0.618059	+	0.786132i	$0.712081\pi$
$702$	18.4176	−	3.43386i	0.695128	−	0.129603i
$703$	26.4757	−	45.8572i	0.998549	−	1.72954i
$704$	0.421648	−	1.57361i	0.0158915	−	0.0593078i
$705$	−12.1842	−	17.7334i	−0.458883	−	0.667879i
$706$	29.8185	−	17.2157i	1.12223	−	0.647921i
$707$	−2.27472	+	5.51918i	−0.0855498	+	0.207570i
$708$	5.84526	−	2.06900i	0.219678	−	0.0777577i
$709$	16.5669	−	4.43907i	0.622181	−	0.166713i	0.0660620	−	0.997816i	$-0.478956\pi$
$709$	16.5669	−	4.43907i	0.622181	−	0.166713i	0.556119	+	0.831103i	$0.312290\pi$
$710$	5.52128	+	20.6057i	0.207210	+	0.773318i
$711$	1.23450	−	3.21330i	0.0462973	−	0.120508i
$712$			10.3990i			0.389718i
$713$	11.3779	+	42.4629i	0.426106	+	1.59025i
$714$	22.6484	+	14.6558i	0.847597	+	0.548481i
$715$	4.92855	+	23.0186i	0.184317	+	0.860847i
$716$	13.6858	−	7.90152i	0.511464	−	0.295294i
$717$	−34.9038	+	12.3546i	−1.30351	+	0.461392i
$718$	15.4754	+	26.8042i	0.577537	+	1.00032i
$719$	8.79359	−	15.2310i	0.327946	−	0.568019i	−0.654158	−	0.756358i	$-0.726977\pi$
$719$	8.79359	−	15.2310i	0.327946	−	0.568019i	0.982104	+	0.188339i	$0.0603104\pi$
$720$	10.9848	−	4.88707i	0.409379	−	0.182130i
$721$	−2.96088	−	1.22033i	−0.110269	−	0.0454473i
$722$	24.9526	+	6.68603i	0.928640	+	0.248828i
$723$	−6.62463	+	2.34487i	−0.246373	+	0.0872065i
$724$	6.41426			0.238384
$725$	−15.7239	−	27.2346i	−0.583972	−	1.01147i
$726$	−14.2132	−	2.63631i	−0.527501	−	0.0978426i
$727$			33.1927i			1.23105i	0.788117	+	0.615525i	$0.211056\pi$
$727$			33.1927i			1.23105i	−0.788117	+	0.615525i	$0.788944\pi$
$728$	7.84406	−	5.42870i	0.290720	−	0.201201i
$729$	24.0674	−	12.2376i	0.891386	−	0.453244i
$730$	−6.07271	+	6.07271i	−0.224761	+	0.224761i
$731$	−28.4894	+	16.4484i	−1.05372	+	0.608364i
$732$	−5.83622	+	4.00993i	−0.215713	+	0.148211i
$733$	4.47930	+	1.20022i	0.165447	+	0.0443313i	0.340591	−	0.940211i	$-0.389373\pi$
$733$	4.47930	+	1.20022i	0.165447	+	0.0443313i	−0.175145	+	0.984543i	$0.556039\pi$
$734$	−3.92667	+	14.6545i	−0.144936	+	0.540908i
$735$	−39.9507	+	27.6570i	−1.47360	+	1.02014i
$736$	−4.22562	−	4.22562i	−0.155759	−	0.155759i
$737$	15.0123	+	8.66735i	0.552985	+	0.319266i
$738$	−1.04584	−	6.61513i	−0.0384979	−	0.243506i
$739$	9.25219	−	34.5297i	0.340347	−	1.27019i	−0.557607	−	0.830105i	$-0.688280\pi$
$739$	9.25219	−	34.5297i	0.340347	−	1.27019i	0.897954	−	0.440089i	$-0.145053\pi$
$740$	−15.8466	−	27.4471i	−0.582531	−	1.00897i
$741$	35.6235	−	21.8962i	1.30866	−	0.804378i
$742$	9.71888	−	12.7122i	0.356791	−	0.466681i
$743$	−47.0180	+	12.5984i	−1.72492	+	0.462191i	−0.979003	−	0.203846i	$-0.934656\pi$
$743$	−47.0180	+	12.5984i	−1.72492	+	0.462191i	−0.745919	+	0.666037i	$0.767989\pi$
$744$	10.5016	−	7.21540i	0.385008	−	0.264529i
$745$		−	26.5226i		−	0.971714i
$746$	−22.7558	+	6.09741i	−0.833151	+	0.223242i
$747$	−0.302919	+	2.87436i	−0.0110832	+	0.105167i
$748$	2.48217	−	9.26357i	0.0907569	−	0.338710i
$749$	4.55138	−	3.50516i	0.166304	−	0.128076i
$750$	−18.1177	+	37.9709i	−0.661564	+	1.38650i
$751$		−	1.81013i		−	0.0660525i	−0.999454	−	0.0330263i	$-0.989486\pi$
$751$		−	1.81013i		−	0.0660525i	0.999454	−	0.0330263i	$-0.0105145\pi$
$752$	2.99401	+	0.802243i	0.109180	+	0.0292548i
$753$	1.34019	−	0.105287i	0.0488392	−	0.00383687i
$754$	8.60554	+	5.57032i	0.313395	+	0.202859i
$755$		−	76.1131i		−	2.77004i
$756$	8.63735	−	10.6956i	0.314137	−	0.388996i
$757$	−10.5511	+	18.2751i	−0.383488	+	0.664221i	−0.991558	−	0.129663i	$-0.958611\pi$
$757$	−10.5511	+	18.2751i	−0.383488	+	0.664221i	0.608070	+	0.793883i	$0.291944\pi$
$758$	−10.0421	+	17.3934i	−0.364744	+	0.631755i
$759$	10.9531	−	12.8208i	0.397571	−	0.465365i
$760$	18.9745	−	18.9745i	0.688276	−	0.688276i
$761$	−4.55899	−	17.0144i	−0.165263	−	0.616771i	−0.998006	−	0.0631115i	$-0.979898\pi$
$761$	−4.55899	−	17.0144i	−0.165263	−	0.616771i	0.832743	−	0.553659i	$-0.186769\pi$
$762$	−24.6746	−	4.57673i	−0.893867	−	0.165797i
$763$	−29.1453	+	38.1219i	−1.05513	+	1.38010i
$764$	−10.4455	+	18.0922i	−0.377906	+	0.654553i
$765$	64.6654	−	28.7693i	2.33798	−	1.04015i
$766$	12.0556	+	6.96031i	0.435587	+	0.251486i
$767$	0.656362	−	12.8909i	0.0236998	−	0.465465i
$768$	−0.745885	+	1.56322i	−0.0269148	+	0.0564078i
$769$	−10.5719	−	39.4550i	−0.381234	−	1.42279i	−0.844018	−	0.536314i	$-0.819816\pi$
$769$	−10.5719	−	39.4550i	−0.381234	−	1.42279i	0.462784	−	0.886471i	$-0.346850\pi$
$770$	13.7228	+	10.4915i	0.494535	+	0.378087i
$771$	−5.87081	+	12.3040i	−0.211432	+	0.443118i
$772$	3.08944	+	0.827812i	0.111191	+	0.0297936i
$773$	2.23708	+	2.23708i	0.0804623	+	0.0804623i	0.746193	−	0.665730i	$-0.231880\pi$
$773$	2.23708	+	2.23708i	0.0804623	+	0.0804623i	−0.665730	+	0.746193i	$0.731880\pi$
$774$	6.81451	+	15.3171i	0.244942	+	0.550563i
$775$	−21.0596	+	78.5956i	−0.756484	+	2.82324i
$776$	−4.62406	+	2.66970i	−0.165994	+	0.0958368i
$777$	−30.4254	−	19.6884i	−1.09151	−	0.706316i
$778$	21.8194	−	5.84649i	0.782263	−	0.209607i
$779$	−7.47388	−	12.9451i	−0.267780	−	0.463808i
$780$	−0.688864	−	25.0181i	−0.0246653	−	0.895791i
$781$	4.33592	−	7.51004i	0.155152	−	0.268730i
$782$	−24.8754	−	24.8754i	−0.889544	−	0.889544i
$783$	14.1632	+	4.20178i	0.506151	+	0.150159i
$784$	1.78788	−	6.76783i	0.0638528	−	0.241708i
$785$	24.7076	+	24.7076i	0.881851	+	0.881851i
$786$	−7.17419	+	8.39752i	−0.255895	+	0.299530i
$787$	−20.1583	−	20.1583i	−0.718568	−	0.718568i	0.249744	−	0.968312i	$-0.419653\pi$
$787$	−20.1583	−	20.1583i	−0.718568	−	0.718568i	−0.968312	+	0.249744i	$0.919653\pi$
$788$	4.67965	+	17.4647i	0.166706	+	0.622154i
$789$	−0.726076	−	9.24216i	−0.0258490	−	0.329030i
$790$	−3.98237	−	2.29922i	−0.141686	−	0.0818027i
$791$	−33.7518	−	13.9108i	−1.20008	−	0.494611i
$792$	−4.56227	−	1.75275i	−0.162113	−	0.0622813i
$793$	3.08613	+	14.4137i	0.109592	+	0.511844i
$794$	28.2097	+	16.2869i	1.00113	+	0.578001i
$795$	−14.0085	−	39.5763i	−0.496829	−	1.40363i
$796$	1.70055			0.0602744
$797$	−15.4393	−	26.7417i	−0.546888	−	0.947238i	−0.998485	−	0.0550164i	$-0.982479\pi$
$797$	−15.4393	−	26.7417i	−0.546888	−	0.947238i	0.451597	−	0.892222i	$-0.350854\pi$
$798$	9.43439	−	29.1973i	0.333974	−	1.03357i
$799$	17.6252	+	4.72265i	0.623534	+	0.167075i
$800$	−2.86280	−	10.6841i	−0.101215	−	0.377740i
$801$	31.0251	+	3.26963i	1.09622	+	0.115527i
$802$	−9.85297			−0.347921
$803$	3.49112			0.123199
$804$	−14.0125	−	11.9712i	−0.494184	−	0.422192i
$805$	58.4977	−	24.3515i	2.06177	−	0.858276i
$806$	−5.55314	−	25.9357i	−0.195601	−	0.913547i
$807$	32.7339	+	15.6189i	1.15229	+	0.549810i
$808$	−2.17940	−	0.583969i	−0.0766711	−	0.0205440i
$809$	7.63148	−	4.40603i	0.268308	−	0.154908i	−0.359810	−	0.933025i	$-0.617159\pi$
$809$	7.63148	−	4.40603i	0.268308	−	0.154908i	0.628119	+	0.778118i	$0.283825\pi$
$810$	−11.1266	−	34.3095i	−0.390951	−	1.20551i
$811$	−3.82355	+	3.82355i	−0.134263	+	0.134263i	−0.771044	−	0.636781i	$-0.780265\pi$
$811$	−3.82355	+	3.82355i	−0.134263	+	0.134263i	0.636781	+	0.771044i	$0.280265\pi$
$812$	7.45611	−	0.994993i	0.261658	−	0.0349174i
$813$	12.9638	−	4.58870i	0.454661	−	0.160933i
$814$	−3.33449	+	12.4445i	−0.116874	+	0.436179i
$815$			26.8877i			0.941837i
$816$	−4.39089	+	9.20238i	−0.153712	+	0.322148i
$817$	26.4579	+	26.4579i	0.925645	+	0.925645i
$818$	−14.9402			−0.522371
$819$	−13.7301	−	25.1095i	−0.479768	−	0.877395i
$820$	−8.94673			−0.312433
$821$	−9.09759	−	9.09759i	−0.317508	−	0.317508i	0.530301	−	0.847809i	$-0.322079\pi$
$821$	−9.09759	−	9.09759i	−0.317508	−	0.317508i	−0.847809	+	0.530301i	$0.822079\pi$
$822$	11.9408	−	25.0254i	0.416483	−	0.872862i
$823$			45.9195i			1.60065i	0.599564	+	0.800327i	$0.295341\pi$
$823$			45.9195i			1.60065i	−0.599564	+	0.800327i	$0.704659\pi$
$824$	0.313283	−	1.16919i	0.0109137	−	0.0407306i
$825$	29.4224	−	10.4144i	1.02435	−	0.362582i
$826$	−5.77920	−	7.50416i	−0.201084	−	0.261103i
$827$	−22.5384	+	22.5384i	−0.783739	+	0.783739i	−0.980460	−	0.196721i	$-0.936971\pi$
$827$	−22.5384	+	22.5384i	−0.783739	+	0.783739i	0.196721	+	0.980460i	$0.436971\pi$
$828$	−13.9357	+	11.2784i	−0.484298	+	0.391953i
$829$	−9.43184	+	5.44548i	−0.327581	+	0.189129i	−0.654767	−	0.755831i	$-0.727233\pi$
$829$	−9.43184	+	5.44548i	−0.327581	+	0.189129i	0.327185	+	0.944960i	$0.393900\pi$
$830$	3.72948	+	0.999312i	0.129452	+	0.0346866i
$831$	−1.76734	−	0.843280i	−0.0613083	−	0.0292531i
$832$	2.41657	+	2.67586i	0.0837794	+	0.0927686i
$833$	10.5249	−	39.8409i	0.364666	−	1.38041i
$834$	1.40110	+	1.19699i	0.0485161	+	0.0414484i
$835$	−20.1086			−0.695887
$836$	−10.9082			−0.377267
$837$	−18.2251	−	33.6000i	−0.629951	−	1.16139i
$838$	−1.73477	−	6.47424i	−0.0599265	−	0.223649i
$839$	17.6633	+	4.73287i	0.609805	+	0.163397i	0.550489	−	0.834843i	$-0.314441\pi$
$839$	17.6633	+	4.73287i	0.609805	+	0.163397i	0.0593160	+	0.998239i	$0.481108\pi$
$840$	−12.3109	−	13.6280i	−0.424765	−	0.470212i
$841$	−10.4583	−	18.1143i	−0.360631	−	0.624632i
$842$	−7.27259			−0.250630
$843$	0.455275	+	1.28623i	0.0156805	+	0.0443001i
$844$	−5.44974	−	3.14641i	−0.187588	−	0.108304i
$845$	−48.6940	−	18.5259i	−1.67512	−	0.637309i
$846$	3.33485	−	8.68033i	0.114654	−	0.298436i
$847$	2.92079	+	21.8873i	0.100359	+	0.752056i
$848$	5.23782	+	3.02406i	0.179867	+	0.103847i
$849$	−0.474126	−	6.03511i	−0.0162720	−	0.207125i
$850$	−16.8528	−	62.8953i	−0.578045	−	2.15729i
$851$	33.4172	+	33.4172i	1.14553	+	1.14553i
$852$	−5.98871	+	7.00990i	−0.205170	+	0.240155i
$853$	4.22516	+	4.22516i	0.144667	+	0.144667i	0.775731	−	0.631064i	$-0.217381\pi$
$853$	4.22516	+	4.22516i	0.144667	+	0.144667i	−0.631064	+	0.775731i	$0.717381\pi$
$854$	8.59287	+	6.56950i	0.294042	+	0.224804i
$855$	−50.6440	−	62.5758i	−1.73199	−	2.14005i
$856$	1.53533	+	1.53533i	0.0524764	+	0.0524764i
$857$	16.8572	−	29.1975i	0.575831	−	0.997369i	−0.420119	−	0.907469i	$-0.638012\pi$
$857$	16.8572	−	29.1975i	0.575831	−	0.997369i	0.995951	−	0.0899004i	$-0.0286549\pi$
$858$	−6.99328	+	7.38930i	−0.238747	+	0.252267i
$859$	3.62423	+	6.27736i	0.123657	+	0.214181i	0.921207	−	0.389072i	$-0.127204\pi$
$859$	3.62423	+	6.27736i	0.123657	+	0.214181i	−0.797550	+	0.603253i	$0.793871\pi$
$860$	21.6323	−	5.79635i	0.737655	−	0.197654i
$861$	−9.10770	+	4.65925i	−0.310390	+	0.158787i
$862$	11.6158	−	6.70640i	0.395637	−	0.228421i
$863$	−10.0036	+	37.3338i	−0.340525	+	1.27086i	0.557229	+	0.830359i	$0.311864\pi$
$863$	−10.0036	+	37.3338i	−0.340525	+	1.27086i	−0.897754	+	0.440497i	$0.854802\pi$
$864$	4.42931	+	2.71684i	0.150688	+	0.0924287i
$865$	4.61284	+	4.61284i	0.156841	+	0.156841i
$866$	22.1634	+	5.93866i	0.753142	+	0.201804i
$867$	−13.1683	+	27.5979i	−0.447218	+	0.937275i
$868$	−15.4619	−	11.8211i	−0.524810	−	0.401233i
$869$	0.483810	+	1.80561i	0.0164121	+	0.0612510i
$870$	8.49874	−	17.8116i	0.288134	−	0.603869i
$871$	−34.1574	+	17.4681i	−1.15738	+	0.591884i
$872$	−15.7073	−	9.06864i	−0.531918	−	0.307103i
$873$	6.51112	+	14.6352i	0.220368	+	0.495326i
$874$	−20.0066	+	34.6525i	−0.676734	+	1.17214i
$875$	63.7307	+	8.27601i	2.15449	+	0.279780i
$876$	−3.64944	−	0.676911i	−0.123303	−	0.0228707i
$877$	8.32938	+	31.0857i	0.281263	+	1.04969i	0.951527	+	0.307565i	$0.0995143\pi$
$877$	8.32938	+	31.0857i	0.281263	+	1.04969i	−0.670264	+	0.742123i	$0.733819\pi$
$878$	20.6985	−	20.6985i	0.698541	−	0.698541i
$879$	38.1464	−	44.6511i	1.28665	−	1.50604i
$880$	−3.26445	+	5.65420i	−0.110045	+	0.190603i
$881$	−18.1685	+	31.4688i	−0.612113	+	1.06021i	0.378770	+	0.925491i	$0.376347\pi$
$881$	−18.1685	+	31.4688i	−0.612113	+	1.06021i	−0.990884	+	0.134721i	$0.956986\pi$
$882$	−19.6295	−	7.46202i	−0.660960	−	0.251259i
$883$		−	15.1642i		−	0.510316i	−0.966899	−	0.255158i	$-0.917872\pi$
$883$		−	15.1642i		−	0.510316i	0.966899	−	0.255158i	$-0.0821276\pi$
$884$	14.2259	+	15.7523i	0.478468	+	0.529806i
$885$	−24.7734	+	1.94623i	−0.832749	+	0.0654219i
$886$	−2.05112	−	0.549596i	−0.0689087	−	0.0184640i
$887$		−	11.0080i		−	0.369613i	−0.982775	−	0.184806i	$-0.940834\pi$
$887$		−	11.0080i		−	0.369613i	0.982775	−	0.184806i	$-0.0591658\pi$
$888$	5.89863	−	12.3623i	0.197945	−	0.414851i
$889$	5.07059	+	37.9971i	0.170062	+	1.27438i
$890$	10.7863	−	40.2551i	0.361558	−	1.34935i
$891$	−6.66376	+	13.0603i	−0.223244	+	0.437537i
$892$	−5.81191	+	1.55730i	−0.194597	+	0.0521421i
$893$		−	20.7543i		−	0.694516i
$894$	9.44771	−	6.49129i	0.315979	−	0.217101i
$895$	−61.1746	+	16.3917i	−2.04484	+	0.547913i
$896$	2.62372	+	0.340714i	0.0876524	+	0.0113825i
$897$	10.6476	+	35.7685i	0.355512	+	1.19428i
$898$	−0.0810369	−	0.140360i	−0.00270423	−	0.00468387i
$899$	5.41318	−	20.2023i	0.180540	−	0.673783i
$900$	−32.7759	+	5.18182i	−1.09253	+	0.172727i
$901$	30.8341	+	17.8021i	1.02723	+	0.593072i
$902$	2.57168	+	2.57168i	0.0856277	+	0.0856277i
$903$	19.0029	−	17.1662i	0.632376	−	0.571256i
$904$	3.57119	−	13.3278i	0.118776	−	0.443278i
$905$	−24.8300	−	6.65318i	−0.825377	−	0.221159i
$906$	27.1125	−	18.6283i	0.900752	−	0.618884i
$907$	−25.4464	+	14.6915i	−0.844935	+	0.487823i	−0.858939	−	0.512079i	$-0.828876\pi$
$907$	−25.4464	+	14.6915i	−0.844935	+	0.487823i	0.0140037	+	0.999902i	$0.495542\pi$
$908$	−11.3976	+	11.3976i	−0.378244	+	0.378244i
$909$	−2.42750	+	6.31859i	−0.0805152	+	0.209574i
$910$	−35.9957	+	12.8786i	−1.19325	+	0.426921i
$911$		−	6.02200i		−	0.199518i	−0.995012	−	0.0997589i	$-0.968193\pi$
$911$		−	6.02200i		−	0.199518i	0.995012	−	0.0997589i	$-0.0318071\pi$
$912$	11.4029	+	2.11504i	0.377586	+	0.0700360i
$913$	−0.784771	−	1.35926i	−0.0259721	−	0.0449850i
$914$	1.51063			0.0499671
$915$	26.7517	−	9.46906i	0.884383	−	0.313038i
$916$	−16.7578	−	4.49023i	−0.553693	−	0.148362i
$917$	15.5983	+	6.42883i	0.515101	+	0.212299i
$918$	26.0745	+	15.9935i	0.860587	+	0.527864i
$919$	18.0470	−	31.2584i	0.595317	−	1.03112i	−0.398185	−	0.917305i	$-0.630360\pi$
$919$	18.0470	−	31.2584i	0.595317	−	1.03112i	0.993502	−	0.113814i	$-0.0363067\pi$
$920$	11.9746	+	20.7407i	0.394792	+	0.683800i
$921$	−2.47716	+	0.876821i	−0.0816254	+	0.0288922i
$922$	−11.5587	+	6.67341i	−0.380665	+	0.219777i
$923$	8.73858	+	17.0876i	0.287634	+	0.562444i
$924$	−0.378613	+	7.45598i	−0.0124555	+	0.245284i
$925$	22.6396	+	84.4923i	0.744387	+	2.77809i
$926$		−	11.0213i		−	0.362183i
$927$	−3.38974	−	1.30229i	−0.111334	−	0.0427727i
$928$	0.735856	+	2.74625i	0.0241556	+	0.0901501i
$929$	−7.08984	+	1.89972i	−0.232610	+	0.0623277i	−0.373241	−	0.927734i	$-0.621754\pi$
$929$	−7.08984	+	1.89972i	−0.232610	+	0.0623277i	0.140631	+	0.990062i	$0.455087\pi$
$930$	−48.1366	+	17.0385i	−1.57846	+	0.558714i
$931$	−46.8698	+	0.165282i	−1.53610	+	0.00541689i
$932$	−11.2760	+	6.51018i	−0.369356	+	0.213248i
$933$	27.2006	+	39.5890i	0.890509	+	1.29609i
$934$	−2.11182	+	7.88141i	−0.0691008	+	0.257888i
$935$	−19.2172	+	33.2852i	−0.628471	+	1.08854i
$936$	8.74317	−	6.36844i	0.285779	−	0.208159i
$937$	−7.95486			−0.259874			−0.129937	−	0.991522i	$-0.541478\pi$
$937$	−7.95486			−0.259874			−0.129937	+	0.991522i	$0.541478\pi$
$938$	−10.7275	+	26.0281i	−0.350264	+	0.849848i
$939$	46.9159	−	3.68577i	1.53104	−	0.120281i
$940$	−10.7579	−	6.21106i	−0.350883	−	0.202583i
$941$	27.5390	−	7.37906i	0.897746	−	0.240550i	0.219698	−	0.975568i	$-0.429493\pi$
$941$	27.5390	−	7.37906i	0.897746	−	0.240550i	0.678048	+	0.735018i	$0.262826\pi$
$942$	−2.75410	+	14.8482i	−0.0897333	+	0.483781i
$943$	12.8863	−	3.45287i	0.419635	−	0.112441i
$944$	2.53140	−	2.53140i	0.0823899	−	0.0823899i
$945$	−44.5297	+	32.4443i	−1.44855	+	1.05541i
$946$	−7.88419	−	4.55194i	−0.256337	−	0.147996i
$947$	−14.1421	+	14.1421i	−0.459558	+	0.459558i	−0.898510	−	0.438953i	$-0.855350\pi$
$947$	−14.1421	+	14.1421i	−0.459558	+	0.459558i	0.438953	+	0.898510i	$0.355350\pi$
$948$	−0.155653	−	1.98130i	−0.00505538	−	0.0643495i
$949$	−4.19851	+	6.48624i	−0.136289	+	0.210552i
$950$	−64.1392	+	37.0308i	−2.08095	+	1.20144i
$951$	18.7459	+	16.0151i	0.607878	+	0.519324i
$952$	15.4454	+	2.00572i	0.500587	+	0.0650058i
$953$	11.8957	+	20.6039i	0.385339	+	0.667426i	0.991816	−	0.127675i	$-0.0407513\pi$
$953$	11.8957	+	20.6039i	0.385339	+	0.667426i	−0.606478	+	0.795101i	$0.707418\pi$
$954$	10.6691	−	14.6761i	0.345424	−	0.475156i
$955$	59.2014	−	59.2014i	1.91571	−	1.91571i
$956$	−15.1157	+	15.1157i	−0.488878	+	0.488878i
$957$	−7.56274	+	2.67692i	−0.244469	+	0.0865325i
$958$	0.701873	+	1.21568i	0.0226765	+	0.0392768i
$959$	−42.0029	−	5.45446i	−1.35634	−	0.176134i
$960$	4.50881	−	5.27765i	0.145521	−	0.170335i
$961$	−20.0184	+	11.5577i	−0.645756	+	0.372828i
$962$	−19.1107	−	21.1613i	−0.616155	−	0.682266i
$963$	5.06335	−	4.09788i	0.163164	−	0.132052i
$964$	−2.86892	+	2.86892i	−0.0924017	+	0.0924017i
$965$	−11.1008	−	6.40903i	−0.357346	−	0.206314i
$966$	22.9913	+	14.8777i	0.739734	+	0.478683i
$967$	−27.0050	+	27.0050i	−0.868423	+	0.868423i	−0.992298	−	0.123875i	$-0.960468\pi$
$967$	−27.0050	+	27.0050i	−0.868423	+	0.868423i	0.123875	+	0.992298i	$0.460468\pi$
$968$	−8.06157	+	2.16009i	−0.259109	+	0.0694280i
$969$	67.1265	+	12.4508i	2.15641	+	0.399979i
$970$	20.6692	−	5.53829i	0.663647	−	0.177824i
$971$	5.25022	+	3.03121i	0.168487	+	0.0972763i	0.581872	−	0.813280i	$-0.302320\pi$
$971$	5.25022	+	3.03121i	0.168487	+	0.0972763i	−0.413385	+	0.910556i	$0.635654\pi$
$972$	9.49828	−	12.3605i	0.304657	−	0.396464i
$973$	1.07263	−	2.60253i	0.0343869	−	0.0834332i
$974$	35.3279			1.13198
$975$	−16.0349	+	67.1890i	−0.513528	+	2.15177i
$976$	−2.04412	+	3.54052i	−0.0654306	+	0.113329i
$977$	−0.872705	+	3.25698i	−0.0279203	+	0.104200i	−0.978480	−	0.206342i	$-0.933844\pi$
$977$	−0.872705	+	3.25698i	−0.0279203	+	0.104200i	0.950560	+	0.310542i	$0.100511\pi$
$978$	−9.57776	+	6.58065i	−0.306263	+	0.210426i
$979$	−14.6715	+	8.47062i	−0.468904	+	0.270722i
$980$	−13.9409	+	24.3442i	−0.445326	+	0.777647i
$981$	−31.9948	+	44.0112i	−1.02151	+	1.40517i
$982$	28.2897	−	7.58021i	0.902761	−	0.241894i
$983$	5.35913	+	20.0005i	0.170930	+	0.637918i	0.997209	+	0.0746577i	$0.0237864\pi$
$983$	5.35913	+	20.0005i	0.170930	+	0.637918i	−0.826280	+	0.563260i	$0.809547\pi$
$984$	−2.18967	−	3.18694i	−0.0698041	−	0.101596i
$985$		−	72.4609i		−	2.30880i
$986$	4.33184	+	16.1667i	0.137954	+	0.514851i
$987$	−14.1860	−	0.720363i	−0.451546	−	0.0229294i
$988$	13.1184	−	20.2666i	0.417353	−	0.644765i
$989$	−28.9207	+	16.6974i	−0.919624	+	0.530945i
$990$	15.8428	+	11.5172i	0.503517	+	0.366041i
$991$	−23.6841	−	41.0220i	−0.752349	−	1.30311i	−0.946681	−	0.322171i	$-0.895587\pi$
$991$	−23.6841	−	41.0220i	−0.752349	−	1.30311i	0.194332	−	0.980936i	$-0.437746\pi$
$992$	3.67816	−	6.37075i	0.116782	−	0.202272i
$993$	−26.5283	−	4.92055i	−0.841849	−	0.156149i
$994$	13.0208	+	5.36652i	0.412995	+	0.170216i
$995$	−6.58293	−	1.76389i	−0.208693	−	0.0559191i
$996$	0.556805	+	1.57307i	0.0176430	+	0.0498445i
$997$	−15.8214			−0.501070			−0.250535	−	0.968108i	$-0.580606\pi$
$997$	−15.8214			−0.501070			−0.250535	+	0.968108i	$0.580606\pi$
$998$	−11.3178	−	19.6031i	−0.358260	−	0.620525i
$999$	−35.0280	−	21.4853i	−1.10824	−	0.679766i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.305.7	yes	152
3.2	odd	2	inner	546.2.ch.a.305.38	yes	152
7.2	even	3		546.2.bw.a.149.6	yes	152
13.11	odd	12		546.2.bw.a.11.25	yes	152
21.2	odd	6		546.2.bw.a.149.25	yes	152
39.11	even	12		546.2.bw.a.11.6	✓	152
91.37	odd	12	inner	546.2.ch.a.401.38	yes	152
273.128	even	12	inner	546.2.ch.a.401.7	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.6	✓	152	39.11	even	12
546.2.bw.a.11.25	yes	152	13.11	odd	12
546.2.bw.a.149.6	yes	152	7.2	even	3
546.2.bw.a.149.25	yes	152	21.2	odd	6
546.2.ch.a.305.7	yes	152	1.1	even	1	trivial
546.2.ch.a.305.38	yes	152	3.2	odd	2	inner
546.2.ch.a.401.7	yes	152	273.128	even	12	inner
546.2.ch.a.401.38	yes	152	91.37	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.745885 + 1.56322i) q^{3} +1.00000i q^{4} +(1.03725 - 3.87106i) q^{5} +(1.63278 - 0.577943i) q^{6} +(-1.61433 - 2.09617i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.88731 - 2.33196i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.745885 + 1.56322i) q^{3} +1.00000i q^{4} +(1.03725 - 3.87106i) q^{5} +(1.63278 - 0.577943i) q^{6} +(-1.61433 - 2.09617i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.88731 - 2.33196i) q^{9} +(-3.47070 + 2.00381i) q^{10} +(1.57361 + 0.421648i) q^{11} +(-1.56322 - 0.745885i) q^{12} +(-2.67586 + 2.41657i) q^{13} +(-0.340714 + 2.62372i) q^{14} +(5.27765 + 4.50881i) q^{15} -1.00000 q^{16} -5.88681 q^{17} +(-0.314418 + 2.98348i) q^{18} +(1.73298 + 6.46758i) q^{19} +(3.87106 + 1.03725i) q^{20} +(4.48088 - 0.960048i) q^{21} +(-0.814562 - 1.41086i) q^{22} -5.97593 q^{23} +(0.577943 + 1.63278i) q^{24} +(-9.57911 - 5.53050i) q^{25} +(3.60089 + 0.183345i) q^{26} +(5.05309 - 1.21090i) q^{27} +(2.09617 - 1.61433i) q^{28} +(2.46222 + 1.42156i) q^{29} +(-0.543650 - 6.92008i) q^{30} +(-1.90395 - 7.10565i) q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.83286 + 2.14540i) q^{33} +(4.16260 + 4.16260i) q^{34} +(-9.78887 + 4.07492i) q^{35} +(2.33196 - 1.88731i) q^{36} +(-5.59196 - 5.59196i) q^{37} +(3.34787 - 5.79867i) q^{38} +(-1.78174 - 5.98543i) q^{39} +(-2.00381 - 3.47070i) q^{40} +(-2.15636 + 0.577796i) q^{41} +(-3.84732 - 2.48961i) q^{42} +(4.83953 - 2.79410i) q^{43} +(-0.421648 + 1.57361i) q^{44} +(-10.9848 + 4.88707i) q^{45} +(4.22562 + 4.22562i) q^{46} +(-2.99401 - 0.802243i) q^{47} +(0.745885 - 1.56322i) q^{48} +(-1.78788 + 6.76783i) q^{49} +(2.86280 + 10.6841i) q^{50} +(4.39089 - 9.20238i) q^{51} +(-2.41657 - 2.67586i) q^{52} +(-5.23782 - 3.02406i) q^{53} +(-4.42931 - 2.71684i) q^{54} +(3.26445 - 5.65420i) q^{55} +(-2.62372 - 0.340714i) q^{56} +(-11.4029 - 2.11504i) q^{57} +(-0.735856 - 2.74625i) q^{58} +(-2.53140 + 2.53140i) q^{59} +(-4.50881 + 5.27765i) q^{60} +(2.04412 - 3.54052i) q^{61} +(-3.67816 + 6.37075i) q^{62} +(-1.84146 + 7.72069i) q^{63} -1.00000i q^{64} +(6.57916 + 12.8650i) q^{65} +(2.81306 - 0.220998i) q^{66} +(10.2779 + 2.75396i) q^{67} -5.88681i q^{68} +(4.45736 - 9.34170i) q^{69} +(9.80318 + 4.04038i) q^{70} +(1.37770 - 5.14163i) q^{71} +(-2.98348 - 0.314418i) q^{72} +(2.06993 - 0.554635i) q^{73} +7.90822i q^{74} +(15.7903 - 10.8491i) q^{75} +(-6.46758 + 1.73298i) q^{76} +(-1.65648 - 3.97925i) q^{77} +(-2.97246 + 5.49222i) q^{78} +(0.573713 + 0.993700i) q^{79} +(-1.03725 + 3.87106i) q^{80} +(-1.87612 + 8.80228i) q^{81} +(1.93334 + 1.11622i) q^{82} +(-0.681245 - 0.681245i) q^{83} +(0.960048 + 4.48088i) q^{84} +(-6.10608 + 22.7882i) q^{85} +(-5.39779 - 1.44633i) q^{86} +(-4.05875 + 2.78867i) q^{87} +(1.41086 - 0.814562i) q^{88} +(-7.35319 + 7.35319i) q^{89} +(11.2231 + 4.31174i) q^{90} +(9.38526 + 1.70792i) q^{91} -5.97593i q^{92} +(12.5278 + 2.32370i) q^{93} +(1.54981 + 2.68436i) q^{94} +26.8339 q^{95} +(-1.63278 + 0.577943i) q^{96} +(-5.15747 - 1.38194i) q^{97} +(6.04980 - 3.52136i) q^{98} +(-1.98663 - 4.46539i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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