LMFDB - Embedded newform 546.2.bz.b.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (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:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.b.229.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0181845 - 0.0678656i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.49748 + 0.873279i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0181845 - 0.0678656i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.49748 + 0.873279i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0351298 + 0.0608466i) q^{10} +(-0.570159 + 0.152774i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.58166 - 3.24012i) q^{13} +(-2.18635 - 1.48992i) q^{14} +(-0.0496811 + 0.0496811i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.62169 + 4.54090i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-1.51323 + 5.64747i) q^{19} +(0.0496811 - 0.0496811i) q^{20} +(-1.72624 - 2.00502i) q^{21} +0.590272 q^{22} +(4.01772 - 2.31963i) q^{23} +(0.258819 + 0.965926i) q^{24} +(4.32585 + 2.49753i) q^{25} +(-2.36637 + 2.72035i) q^{26} -1.00000i q^{27} +(1.72624 + 2.00502i) q^{28} +1.18850 q^{29} +(0.0608466 - 0.0351298i) q^{30} +(8.24326 - 2.20878i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.570159 + 0.152774i) q^{33} +(3.70763 - 3.70763i) q^{34} +(0.104681 - 0.153613i) q^{35} +1.00000i q^{36} +(1.83819 - 6.86020i) q^{37} +(2.92334 - 5.06338i) q^{38} +(-2.98982 + 2.01519i) q^{39} +(-0.0608466 + 0.0351298i) q^{40} +(-3.36018 - 3.36018i) q^{41} +(1.14848 + 2.38348i) q^{42} -1.42001i q^{43} +(-0.570159 - 0.152774i) q^{44} +(0.0678656 - 0.0181845i) q^{45} +(-4.48119 + 1.20073i) q^{46} +(10.8766 + 2.91437i) q^{47} -1.00000i q^{48} +(5.47477 + 4.36198i) q^{49} +(-3.53204 - 3.53204i) q^{50} +(4.54090 - 2.62169i) q^{51} +(2.98982 - 2.01519i) q^{52} +(1.67389 - 2.89927i) q^{53} +(-0.258819 + 0.965926i) q^{54} +0.0414723i q^{55} +(-1.14848 - 2.38348i) q^{56} +(4.13423 - 4.13423i) q^{57} +(-1.14800 - 0.307607i) q^{58} +(1.13262 + 4.22701i) q^{59} +(-0.0678656 + 0.0181845i) q^{60} +(1.23581 - 0.713497i) q^{61} -8.53405 q^{62} +(0.492456 + 2.59952i) q^{63} +1.00000i q^{64} +(-0.191131 - 0.166260i) q^{65} +(-0.511191 - 0.295136i) q^{66} +(2.63245 + 9.82445i) q^{67} +(-4.54090 + 2.62169i) q^{68} -4.63927 q^{69} +(-0.140872 + 0.121285i) q^{70} +(8.04376 - 8.04376i) q^{71} +(0.258819 - 0.965926i) q^{72} +(2.94839 + 11.0035i) q^{73} +(-3.55110 + 6.15069i) q^{74} +(-2.49753 - 4.32585i) q^{75} +(-4.13423 + 4.13423i) q^{76} +(-1.55737 - 0.116359i) q^{77} +(3.40951 - 1.17271i) q^{78} +(-0.725402 - 1.25643i) q^{79} +(0.0678656 - 0.0181845i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.37601 + 4.11536i) q^{82} +(-7.15605 - 7.15605i) q^{83} +(-0.492456 - 2.59952i) q^{84} +(0.260496 + 0.260496i) q^{85} +(-0.367527 + 1.37163i) q^{86} +(-1.02927 - 0.594251i) q^{87} +(0.511191 + 0.295136i) q^{88} +(-16.1729 - 4.33350i) q^{89} -0.0702597 q^{90} +(6.77968 - 6.71088i) q^{91} +4.63927 q^{92} +(-8.24326 - 2.20878i) q^{93} +(-9.75168 - 5.63014i) q^{94} +(0.355751 + 0.205393i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-9.94645 - 9.94645i) q^{97} +(-4.15926 - 5.63033i) q^{98} +(-0.417386 - 0.417386i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.0181845	−	0.0678656i	0.00813237	−	0.0303504i	−0.961740	−	0.273962i	$-0.911666\pi$
$5$	0.0181845	−	0.0678656i	0.00813237	−	0.0303504i	0.969873	+	0.243612i	$0.0783323\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	2.49748	+	0.873279i	0.943957	+	0.330068i
$7$	2.49748	+	0.873279i	0.943957	+	0.330068i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.0351298	+	0.0608466i	−0.0111090	+	0.0192414i
$11$	−0.570159	+	0.152774i	−0.171909	+	0.0460630i	−0.343747	−	0.939062i	$-0.611696\pi$
$11$	−0.570159	+	0.152774i	−0.171909	+	0.0460630i	0.171838	+	0.985125i	$0.445030\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.58166	−	3.24012i	0.438674	−	0.898646i
$13$	1.58166	−	3.24012i	0.438674	−	0.898646i
$14$	−2.18635	−	1.48992i	−0.584328	−	0.398197i
$15$	−0.0496811	+	0.0496811i	−0.0128276	+	0.0128276i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−2.62169	+	4.54090i	−0.635852	+	1.10133i	0.350481	+	0.936570i	$0.386018\pi$
$17$	−2.62169	+	4.54090i	−0.635852	+	1.10133i	−0.986334	+	0.164759i	$0.947315\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	−1.51323	+	5.64747i	−0.347160	+	1.29562i	0.542909	+	0.839791i	$0.317323\pi$
$19$	−1.51323	+	5.64747i	−0.347160	+	1.29562i	−0.890069	+	0.455826i	$0.849344\pi$
$20$	0.0496811	−	0.0496811i	0.0111090	−	0.0111090i
$21$	−1.72624	−	2.00502i	−0.376696	−	0.437531i
$22$	0.590272			0.125846
$23$	4.01772	−	2.31963i	0.837753	−	0.483677i	−0.0187469	−	0.999824i	$-0.505968\pi$
$23$	4.01772	−	2.31963i	0.837753	−	0.483677i	0.856500	+	0.516147i	$0.172634\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	4.32585	+	2.49753i	0.865170	+	0.499506i
$26$	−2.36637	+	2.72035i	−0.464083	+	0.533504i
$27$		−	1.00000i		−	0.192450i
$28$	1.72624	+	2.00502i	0.326228	+	0.378913i
$29$	1.18850			0.220699			0.110350	−	0.993893i	$-0.464803\pi$
$29$	1.18850			0.220699			0.110350	+	0.993893i	$0.464803\pi$
$30$	0.0608466	−	0.0351298i	0.0111090	−	0.00641380i
$31$	8.24326	−	2.20878i	1.48053	−	0.396708i	0.574005	−	0.818852i	$-0.305389\pi$
$31$	8.24326	−	2.20878i	1.48053	−	0.396708i	0.906529	+	0.422144i	$0.138722\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.570159	+	0.152774i	0.0992520	+	0.0265945i
$34$	3.70763	−	3.70763i	0.635852	−	0.635852i
$35$	0.104681	−	0.153613i	0.0176943	−	0.0259653i
$36$			1.00000i			0.166667i
$37$	1.83819	−	6.86020i	0.302196	−	1.12781i	−0.633136	−	0.774040i	$-0.718233\pi$
$37$	1.83819	−	6.86020i	0.302196	−	1.12781i	0.935332	−	0.353770i	$-0.115101\pi$
$38$	2.92334	−	5.06338i	0.474229	−	0.821389i
$39$	−2.98982	+	2.01519i	−0.478754	+	0.322689i
$40$	−0.0608466	+	0.0351298i	−0.00962070	+	0.00555451i
$41$	−3.36018	−	3.36018i	−0.524772	−	0.524772i	0.394237	−	0.919009i	$-0.371009\pi$
$41$	−3.36018	−	3.36018i	−0.524772	−	0.524772i	−0.919009	+	0.394237i	$0.871009\pi$
$42$	1.14848	+	2.38348i	0.177214	+	0.367779i
$43$		−	1.42001i		−	0.216550i	−0.994121	−	0.108275i	$-0.965467\pi$
$43$		−	1.42001i		−	0.216550i	0.994121	−	0.108275i	$-0.0345327\pi$
$44$	−0.570159	−	0.152774i	−0.0859547	−	0.0230315i
$45$	0.0678656	−	0.0181845i	0.0101168	−	0.00271079i
$46$	−4.48119	+	1.20073i	−0.660715	+	0.177038i
$47$	10.8766	+	2.91437i	1.58651	+	0.425105i	0.940935	−	0.338588i	$-0.109949\pi$
$47$	10.8766	+	2.91437i	1.58651	+	0.425105i	0.645579	+	0.763693i	$0.276616\pi$
$48$		−	1.00000i		−	0.144338i
$49$	5.47477	+	4.36198i	0.782110	+	0.623141i
$50$	−3.53204	−	3.53204i	−0.499506	−	0.499506i
$51$	4.54090	−	2.62169i	0.635852	−	0.367110i
$52$	2.98982	−	2.01519i	0.414613	−	0.279457i
$53$	1.67389	−	2.89927i	0.229927	−	0.398245i	−0.727859	−	0.685726i	$-0.759485\pi$
$53$	1.67389	−	2.89927i	0.229927	−	0.398245i	0.957786	+	0.287482i	$0.0928180\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$			0.0414723i			0.00559213i
$56$	−1.14848	−	2.38348i	−0.153472	−	0.318506i
$57$	4.13423	−	4.13423i	0.547592	−	0.547592i
$58$	−1.14800	−	0.307607i	−0.150740	−	0.0403907i
$59$	1.13262	+	4.22701i	0.147455	+	0.550310i	0.999634	+	0.0270591i	$0.00861422\pi$
$59$	1.13262	+	4.22701i	0.147455	+	0.550310i	−0.852179	+	0.523251i	$0.824719\pi$
$60$	−0.0678656	+	0.0181845i	−0.00876141	+	0.00234761i
$61$	1.23581	−	0.713497i	0.158230	−	0.0913539i	−0.418794	−	0.908081i	$-0.637547\pi$
$61$	1.23581	−	0.713497i	0.158230	−	0.0913539i	0.577024	+	0.816727i	$0.304214\pi$
$62$	−8.53405			−1.08383
$63$	0.492456	+	2.59952i	0.0620436	+	0.327508i
$64$			1.00000i			0.125000i
$65$	−0.191131	−	0.166260i	−0.0237068	−	0.0206221i
$66$	−0.511191	−	0.295136i	−0.0629232	−	0.0363287i
$67$	2.63245	+	9.82445i	0.321605	+	1.20025i	0.917681	+	0.397319i	$0.130059\pi$
$67$	2.63245	+	9.82445i	0.321605	+	1.20025i	−0.596075	+	0.802929i	$0.703274\pi$
$68$	−4.54090	+	2.62169i	−0.550664	+	0.317926i
$69$	−4.63927			−0.558502
$70$	−0.140872	+	0.121285i	−0.0168374	+	0.0144963i
$71$	8.04376	−	8.04376i	0.954619	−	0.954619i	−0.0443954	−	0.999014i	$-0.514136\pi$
$71$	8.04376	−	8.04376i	0.954619	−	0.954619i	0.999014	+	0.0443954i	$0.0141361\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	2.94839	+	11.0035i	0.345083	+	1.28787i	0.892515	+	0.451017i	$0.148939\pi$
$73$	2.94839	+	11.0035i	0.345083	+	1.28787i	−0.547433	+	0.836850i	$0.684395\pi$
$74$	−3.55110	+	6.15069i	−0.412807	+	0.715003i
$75$	−2.49753	−	4.32585i	−0.288390	−	0.499506i
$76$	−4.13423	+	4.13423i	−0.474229	+	0.474229i
$77$	−1.55737	−	0.116359i	−0.177479	−	0.0132604i
$78$	3.40951	−	1.17271i	0.386051	−	0.132783i
$79$	−0.725402	−	1.25643i	−0.0816141	−	0.141360i	0.822329	−	0.569012i	$-0.192674\pi$
$79$	−0.725402	−	1.25643i	−0.0816141	−	0.141360i	−0.903943	+	0.427652i	$0.859341\pi$
$80$	0.0678656	−	0.0181845i	0.00758761	−	0.00203309i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.37601	+	4.11536i	0.262386	+	0.454466i
$83$	−7.15605	−	7.15605i	−0.785479	−	0.785479i	0.195271	−	0.980749i	$-0.437441\pi$
$83$	−7.15605	−	7.15605i	−0.785479	−	0.785479i	−0.980749	+	0.195271i	$0.937441\pi$
$84$	−0.492456	−	2.59952i	−0.0537314	−	0.283631i
$85$	0.260496	+	0.260496i	0.0282548	+	0.0282548i
$86$	−0.367527	+	1.37163i	−0.0396314	+	0.147906i
$87$	−1.02927	−	0.594251i	−0.110350	−	0.0637104i
$88$	0.511191	+	0.295136i	0.0544931	+	0.0314616i
$89$	−16.1729	−	4.33350i	−1.71432	−	0.459350i	−0.737842	−	0.674973i	$-0.764155\pi$
$89$	−16.1729	−	4.33350i	−1.71432	−	0.459350i	−0.976477	+	0.215623i	$0.930822\pi$
$90$	−0.0702597			−0.00740602
$91$	6.77968	−	6.71088i	0.710704	−	0.703491i
$92$	4.63927			0.483677
$93$	−8.24326	−	2.20878i	−0.854787	−	0.229039i
$94$	−9.75168	−	5.63014i	−1.00581	−	0.580704i
$95$	0.355751	+	0.205393i	0.0364993	+	0.0210729i
$96$	−0.258819	+	0.965926i	−0.0264156	+	0.0985844i
$97$	−9.94645	−	9.94645i	−1.00991	−	1.00991i	−0.999950	−	0.00995900i	$-0.996830\pi$
$97$	−9.94645	−	9.94645i	−1.00991	−	1.00991i	−0.00995900	−	0.999950i	$-0.503170\pi$
$98$	−4.15926	−	5.63033i	−0.420148	−	0.568749i
$99$	−0.417386	−	0.417386i	−0.0419488	−	0.0419488i
$100$	2.49753	+	4.32585i	0.249753	+	0.432585i
$101$	−6.12795	+	10.6139i	−0.609754	+	1.05613i	0.381527	+	0.924358i	$0.375398\pi$
$101$	−6.12795	+	10.6139i	−0.609754	+	1.05613i	−0.991281	+	0.131767i	$0.957935\pi$
$102$	−5.06471	+	1.35709i	−0.501481	+	0.134371i
$103$	4.16441	+	7.21297i	0.410331	+	0.710715i	0.994926	−	0.100611i	$-0.0320797\pi$
$103$	4.16441	+	7.21297i	0.410331	+	0.710715i	−0.584594	+	0.811326i	$0.698746\pi$
$104$	−3.40951	+	1.17271i	−0.334330	+	0.114993i
$105$	−0.167463	+	0.0806918i	−0.0163427	+	0.00787472i
$106$	−2.36724	+	2.36724i	−0.229927	+	0.229927i
$107$	7.58623	+	13.1397i	0.733389	+	1.27027i	0.955427	+	0.295229i	$0.0953958\pi$
$107$	7.58623	+	13.1397i	0.733389	+	1.27027i	−0.222038	+	0.975038i	$0.571271\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−3.56404	−	13.3012i	−0.341373	−	1.27402i	−0.896793	−	0.442451i	$-0.854109\pi$
$109$	−3.56404	−	13.3012i	−0.341373	−	1.27402i	0.555420	−	0.831570i	$-0.312558\pi$
$110$	0.0107338	−	0.0400592i	0.00102343	−	0.00381949i
$111$	−5.02202	+	5.02202i	−0.476669	+	0.476669i
$112$	0.492456	+	2.59952i	0.0465327	+	0.245631i
$113$	15.7720			1.48371			0.741854	−	0.670562i	$-0.233947\pi$
$113$	15.7720			1.48371			0.741854	+	0.670562i	$0.233947\pi$
$114$	−5.06338	+	2.92334i	−0.474229	+	0.273796i
$115$	−0.0843629	−	0.314847i	−0.00786688	−	0.0293596i
$116$	1.02927	+	0.594251i	0.0955655	+	0.0551748i
$117$	3.59685	−	0.250300i	0.332529	−	0.0231403i
$118$		−	4.37612i		−	0.402855i
$119$	−10.5131	+	9.05131i	−0.963731	+	0.829732i
$120$	0.0702597			0.00641380
$121$	−9.22454	+	5.32579i	−0.838594	+	0.484163i
$122$	−1.37837	+	0.369333i	−0.124792	+	0.0334378i
$123$	1.22991	+	4.59009i	0.110897	+	0.413874i
$124$	8.24326	+	2.20878i	0.740267	+	0.198354i
$125$	0.496566	−	0.496566i	0.0444142	−	0.0444142i
$126$	0.197128	−	2.63840i	0.0175616	−	0.235047i
$127$			1.11448i			0.0988944i	0.998777	+	0.0494472i	$0.0157459\pi$
$127$			1.11448i			0.0988944i	−0.998777	+	0.0494472i	$0.984254\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−0.710007	+	1.22977i	−0.0625126	+	0.108275i
$130$	0.141587	+	0.210063i	0.0124180	+	0.0184238i
$131$	−12.8146	+	7.39849i	−1.11961	+	0.646409i	−0.941302	−	0.337565i	$-0.890397\pi$
$131$	−12.8146	+	7.39849i	−1.11961	+	0.646409i	−0.178312	+	0.983974i	$0.557063\pi$
$132$	0.417386	+	0.417386i	0.0363287	+	0.0363287i
$133$	−8.71108	+	12.7829i	−0.755346	+	1.10842i
$134$		−	10.1710i		−	0.878642i
$135$	−0.0678656	−	0.0181845i	−0.00584094	−	0.00156508i
$136$	5.06471	−	1.35709i	0.434295	−	0.116369i
$137$	−4.24908	+	1.13854i	−0.363024	+	0.0972719i	−0.435720	−	0.900082i	$-0.643506\pi$
$137$	−4.24908	+	1.13854i	−0.363024	+	0.0972719i	0.0726965	+	0.997354i	$0.476840\pi$
$138$	4.48119	+	1.20073i	0.381464	+	0.102213i
$139$		−	1.27208i		−	0.107896i	−0.998544	−	0.0539482i	$-0.982819\pi$
$139$		−	1.27208i		−	0.107896i	0.998544	−	0.0539482i	$-0.0171806\pi$
$140$	0.167463	−	0.0806918i	0.0141532	−	0.00681971i
$141$	−7.96222	−	7.96222i	−0.670540	−	0.670540i
$142$	−9.85155	+	5.68780i	−0.826724	+	0.477309i
$143$	−0.406794	+	2.08902i	−0.0340178	+	0.174692i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.0216123	−	0.0806584i	0.00179481	−	0.00669831i
$146$		−	11.3917i		−	0.942784i
$147$	−2.56030	−	6.51497i	−0.211170	−	0.537346i
$148$	5.02202	−	5.02202i	0.412807	−	0.412807i
$149$	−16.4280	−	4.40187i	−1.34583	−	0.360615i	−0.487239	−	0.873269i	$-0.661996\pi$
$149$	−16.4280	−	4.40187i	−1.34583	−	0.360615i	−0.858596	+	0.512653i	$0.828663\pi$
$150$	1.29282	+	4.82486i	0.105558	+	0.393948i
$151$	−2.30519	+	0.617674i	−0.187594	+	0.0502656i	−0.351393	−	0.936228i	$-0.614292\pi$
$151$	−2.30519	+	0.617674i	−0.187594	+	0.0502656i	0.163799	+	0.986494i	$0.447625\pi$
$152$	5.06338	−	2.92334i	0.410694	−	0.237114i
$153$	−5.24337			−0.423902
$154$	1.47419	+	0.515472i	0.118794	+	0.0415379i
$155$		−	0.599600i		−	0.0481610i
$156$	−3.59685	+	0.250300i	−0.287979	+	0.0200401i
$157$	−9.18889	−	5.30521i	−0.733353	−	0.423402i	0.0862943	−	0.996270i	$-0.472497\pi$
$157$	−9.18889	−	5.30521i	−0.733353	−	0.423402i	−0.819648	+	0.572868i	$0.805831\pi$
$158$	0.375496	+	1.40137i	0.0298728	+	0.111487i
$159$	−2.89927	+	1.67389i	−0.229927	+	0.132748i
$160$	−0.0702597			−0.00555451
$161$	12.0598	−	2.28463i	0.950449	−	0.180054i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	3.38916	−	12.6485i	0.265459	−	0.990708i	−0.696509	−	0.717548i	$-0.745264\pi$
$163$	3.38916	−	12.6485i	0.265459	−	0.990708i	0.961969	−	0.273160i	$-0.0880688\pi$
$164$	−1.22991	−	4.59009i	−0.0960399	−	0.358426i
$165$	0.0207362	−	0.0359161i	0.00161431	−	0.00279606i
$166$	5.06009	+	8.76434i	0.392739	+	0.680244i
$167$	1.45904	−	1.45904i	0.112904	−	0.112904i	−0.648398	−	0.761302i	$-0.724561\pi$
$167$	1.45904	−	1.45904i	0.112904	−	0.112904i	0.761302	+	0.648398i	$0.224561\pi$
$168$	−0.197128	+	2.63840i	−0.0152088	+	0.203557i
$169$	−7.99670	−	10.2495i	−0.615131	−	0.788425i
$170$	−0.184199	−	0.319042i	−0.0141274	−	0.0244694i
$171$	−5.64747	+	1.51323i	−0.431872	+	0.115720i
$172$	0.710007	−	1.22977i	0.0541375	−	0.0937689i
$173$	−2.65968	−	4.60670i	−0.202212	−	0.350241i	0.747029	−	0.664791i	$-0.231480\pi$
$173$	−2.65968	−	4.60670i	−0.202212	−	0.350241i	−0.949241	+	0.314550i	$0.898146\pi$
$174$	0.840397	+	0.840397i	0.0637104	+	0.0637104i
$175$	8.62267	+	10.0152i	0.651812	+	0.757078i
$176$	−0.417386	−	0.417386i	−0.0314616	−	0.0314616i
$177$	1.13262	−	4.22701i	0.0851332	−	0.317722i
$178$	14.5002	+	8.37168i	1.08683	+	0.627484i
$179$	7.35012	+	4.24360i	0.549374	+	0.317181i	0.748869	−	0.662718i	$-0.230597\pi$
$179$	7.35012	+	4.24360i	0.549374	+	0.317181i	−0.199495	+	0.979899i	$0.563930\pi$
$180$	0.0678656	+	0.0181845i	0.00505840	+	0.00135540i
$181$	−9.72851			−0.723115			−0.361557	−	0.932350i	$-0.617755\pi$
$181$	−9.72851			−0.723115			−0.361557	+	0.932350i	$0.617755\pi$
$182$	−8.28557	+	4.72750i	−0.614168	+	0.350426i
$183$	−1.42699			−0.105486
$184$	−4.48119	−	1.20073i	−0.330357	−	0.0885190i
$185$	−0.432145	−	0.249499i	−0.0317720	−	0.0183436i
$186$	7.39071	+	4.26703i	0.541913	+	0.312874i
$187$	0.801050	−	2.98956i	0.0585786	−	0.218618i
$188$	7.96222	+	7.96222i	0.580704	+	0.580704i
$189$	0.873279	−	2.49748i	0.0635217	−	0.181665i
$190$	−0.290470	−	0.290470i	−0.0210729	−	0.0210729i
$191$	5.04013	+	8.72977i	0.364691	+	0.631664i	0.988727	−	0.149732i	$-0.0478412\pi$
$191$	5.04013	+	8.72977i	0.364691	+	0.631664i	−0.624035	+	0.781396i	$0.714508\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−14.1731	+	3.79768i	−1.02020	+	0.273363i	−0.729887	−	0.683567i	$-0.760428\pi$
$193$	−14.1731	+	3.79768i	−1.02020	+	0.273363i	−0.290317	+	0.956930i	$0.593761\pi$
$194$	7.03321	+	12.1819i	0.504955	+	0.874607i
$195$	0.0823939	+	0.239551i	0.00590035	+	0.0171546i
$196$	2.56030	+	6.51497i	0.182878	+	0.465355i
$197$	10.6286	−	10.6286i	0.757254	−	0.757254i	−0.218567	−	0.975822i	$-0.570138\pi$
$197$	10.6286	−	10.6286i	0.757254	−	0.757254i	0.975822	+	0.218567i	$0.0701383\pi$
$198$	0.295136	+	0.511191i	0.0209744	+	0.0363287i
$199$	−8.78580	+	15.2175i	−0.622809	+	1.07874i	0.366151	+	0.930555i	$0.380675\pi$
$199$	−8.78580	+	15.2175i	−0.622809	+	1.07874i	−0.988960	+	0.148181i	$0.952658\pi$
$200$	−1.29282	−	4.82486i	−0.0914160	−	0.341169i
$201$	2.63245	−	9.82445i	0.185679	−	0.692963i
$202$	8.66623	−	8.66623i	0.609754	−	0.609754i
$203$	2.96825	+	1.03789i	0.208331	+	0.0728458i
$204$	5.24337			0.367110
$205$	−0.289144	+	0.166937i	−0.0201947	+	0.0116594i
$206$	−2.15566	−	8.04502i	−0.150192	−	0.560523i
$207$	4.01772	+	2.31963i	0.279251	+	0.161226i
$208$	3.59685	−	0.250300i	0.249397	−	0.0173552i
$209$		−	3.45114i		−	0.238720i
$210$	0.182641	−	0.0345998i	0.0126034	−	0.00238761i
$211$	−6.01060			−0.413787			−0.206893	−	0.978364i	$-0.566335\pi$
$211$	−6.01060			−0.413787			−0.206893	+	0.978364i	$0.566335\pi$
$212$	2.89927	−	1.67389i	0.199122	−	0.114963i
$213$	−10.9880	+	2.94422i	−0.752884	+	0.201735i
$214$	−3.92692	−	14.6555i	−0.268439	−	1.00183i
$215$	−0.0963701	−	0.0258223i	−0.00657239	−	0.00176107i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	22.5162	+	1.68230i	1.52850	+	0.114202i
$218$			13.7704i			0.932648i
$219$	2.94839	−	11.0035i	0.199234	−	0.743550i
$220$	−0.0207362	+	0.0359161i	−0.00139803	+	0.00242146i
$221$	10.5664	+	15.6767i	0.710774	+	1.05453i
$222$	6.15069	−	3.55110i	0.412807	−	0.238334i
$223$	−5.71584	−	5.71584i	−0.382761	−	0.382761i	0.489335	−	0.872096i	$-0.337240\pi$
$223$	−5.71584	−	5.71584i	−0.382761	−	0.382761i	−0.872096	+	0.489335i	$0.837240\pi$
$224$	0.197128	−	2.63840i	0.0131712	−	0.176285i
$225$			4.99506i			0.333004i
$226$	−15.2346	−	4.08210i	−1.01339	−	0.271537i
$227$	19.1314	−	5.12624i	1.26980	−	0.340241i	0.439843	−	0.898075i	$-0.355034\pi$
$227$	19.1314	−	5.12624i	1.26980	−	0.340241i	0.829952	+	0.557834i	$0.188368\pi$
$228$	5.64747	−	1.51323i	0.374013	−	0.100216i
$229$	−7.26771	−	1.94738i	−0.480264	−	0.128686i	0.0105617	−	0.999944i	$-0.496638\pi$
$229$	−7.26771	−	1.94738i	−0.480264	−	0.128686i	−0.490825	+	0.871258i	$0.663305\pi$
$230$			0.325953i			0.0214927i
$231$	1.29054	+	0.879457i	0.0849116	+	0.0578640i
$232$	−0.840397	−	0.840397i	−0.0551748	−	0.0551748i
$233$	15.7322	−	9.08297i	1.03065	−	0.595045i	0.113478	−	0.993541i	$-0.463801\pi$
$233$	15.7322	−	9.08297i	1.03065	−	0.595045i	0.917170	+	0.398496i	$0.130468\pi$
$234$	−3.53908	−	0.689162i	−0.231357	−	0.0450520i
$235$	0.395572	−	0.685150i	0.0258042	−	0.0446943i
$236$	−1.13262	+	4.22701i	−0.0737275	+	0.275155i
$237$			1.45080i			0.0942398i
$238$	12.4975	−	6.02191i	0.810092	−	0.390343i
$239$	6.20443	−	6.20443i	0.401331	−	0.401331i	−0.477371	−	0.878702i	$-0.658410\pi$
$239$	6.20443	−	6.20443i	0.401331	−	0.401331i	0.878702	+	0.477371i	$0.158410\pi$
$240$	−0.0678656	−	0.0181845i	−0.00438071	−	0.00117381i
$241$	−5.47280	−	20.4248i	−0.352534	−	1.31568i	−0.883559	−	0.468319i	$-0.844860\pi$
$241$	−5.47280	−	20.4248i	−0.352534	−	1.31568i	0.531025	−	0.847356i	$-0.321807\pi$
$242$	10.2886	−	2.75683i	0.661379	−	0.177216i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.42699			0.0913539
$245$	0.395585	−	0.292228i	0.0252730	−	0.0186698i
$246$		−	4.75201i		−	0.302977i
$247$	15.9050	+	13.8354i	1.01201	+	0.880327i
$248$	−7.39071	−	4.26703i	−0.469310	−	0.270956i
$249$	2.61930	+	9.77535i	0.165991	+	0.619487i
$250$	−0.608166	+	0.351125i	−0.0384638	+	0.0222071i
$251$	5.53902			0.349620			0.174810	−	0.984602i	$-0.444069\pi$
$251$	5.53902			0.349620			0.174810	+	0.984602i	$0.444069\pi$
$252$	−0.873279	+	2.49748i	−0.0550114	+	0.157326i
$253$	−1.93636	+	1.93636i	−0.121738	+	0.121738i
$254$	0.288449	−	1.07651i	0.0180989	−	0.0675461i
$255$	−0.0953483	−	0.355845i	−0.00597094	−	0.0222839i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.6413	+	27.0915i	0.975678	+	1.68992i	0.677679	+	0.735358i	$0.262986\pi$
$257$	15.6413	+	27.0915i	0.975678	+	1.68992i	0.297999	+	0.954566i	$0.403681\pi$
$258$	1.00410	−	1.00410i	0.0625126	−	0.0625126i
$259$	10.5817	−	15.5279i	0.657515	−	0.964860i
$260$	−0.0823939	−	0.239551i	−0.00510985	−	0.0148563i
$261$	0.594251	+	1.02927i	0.0367832	+	0.0637104i
$262$	14.2928	−	3.82974i	0.883012	−	0.236602i
$263$	1.49241	−	2.58493i	0.0920261	−	0.159394i	−0.816337	−	0.577575i	$-0.803999\pi$
$263$	1.49241	−	2.58493i	0.0920261	−	0.159394i	0.908364	+	0.418181i	$0.137332\pi$
$264$	−0.295136	−	0.511191i	−0.0181644	−	0.0314616i
$265$	−0.166322	−	0.166322i	−0.0102170	−	0.0102170i
$266$	11.7227	−	10.0928i	0.718766	−	0.618828i
$267$	11.8393	+	11.8393i	0.724556	+	0.724556i
$268$	−2.63245	+	9.82445i	−0.160803	+	0.600124i
$269$	−11.6753	−	6.74072i	−0.711853	−	0.410989i	0.0998935	−	0.994998i	$-0.468150\pi$
$269$	−11.6753	−	6.74072i	−0.711853	−	0.410989i	−0.811747	+	0.584009i	$0.801483\pi$
$270$	0.0608466	+	0.0351298i	0.00370301	+	0.00213793i
$271$	−26.5854	−	7.12354i	−1.61495	−	0.432724i	−0.665437	−	0.746454i	$-0.731755\pi$
$271$	−26.5854	−	7.12354i	−1.61495	−	0.432724i	−0.949512	+	0.313730i	$0.898421\pi$
$272$	−5.24337			−0.317926
$273$	−9.22682	+	2.42195i	−0.558432	+	0.146583i
$274$	4.39897			0.265752
$275$	−2.84798	−	0.763114i	−0.171740	−	0.0460175i
$276$	−4.01772	−	2.31963i	−0.241838	−	0.139625i
$277$	−10.0663	−	5.81177i	−0.604824	−	0.349195i	0.166113	−	0.986107i	$-0.446878\pi$
$277$	−10.0663	−	5.81177i	−0.604824	−	0.349195i	−0.770937	+	0.636911i	$0.780212\pi$
$278$	−0.329238	+	1.22873i	−0.0197464	+	0.0736946i
$279$	6.03449	+	6.03449i	0.361275	+	0.361275i
$280$	−0.182641	+	0.0345998i	−0.0109149	+	0.00206773i
$281$	1.44518	+	1.44518i	0.0862125	+	0.0862125i	0.748898	−	0.662685i	$-0.230583\pi$
$281$	1.44518	+	1.44518i	0.0862125	+	0.0862125i	−0.662685	+	0.748898i	$0.730583\pi$
$282$	5.63014	+	9.75168i	0.335270	+	0.580704i
$283$	2.74605	−	4.75630i	0.163236	−	0.282733i	−0.772792	−	0.634660i	$-0.781140\pi$
$283$	2.74605	−	4.75630i	0.163236	−	0.282733i	0.936027	+	0.351927i	$0.114474\pi$
$284$	10.9880	−	2.94422i	0.652017	−	0.174707i
$285$	−0.205393	−	0.355751i	−0.0121664	−	0.0210729i
$286$	0.933610	−	1.91255i	0.0552055	−	0.113091i
$287$	−5.45759	−	11.3263i	−0.322151	−	0.668573i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	−5.24649	−	9.08718i	−0.308617	−	0.534540i
$290$	−0.0417518	+	0.0723163i	−0.00245175	+	0.00424656i
$291$	3.64065	+	13.5871i	0.213419	+	0.796490i
$292$	−2.94839	+	11.0035i	−0.172541	+	0.643933i
$293$	−8.23159	+	8.23159i	−0.480895	+	0.480895i	−0.905417	−	0.424523i	$-0.860442\pi$
$293$	−8.23159	+	8.23159i	−0.480895	+	0.480895i	0.424523	+	0.905417i	$0.360442\pi$
$294$	0.786857	+	6.95563i	0.0458904	+	0.405661i
$295$	0.307465			0.0179013
$296$	−6.15069	+	3.55110i	−0.357502	+	0.206404i
$297$	0.152774	+	0.570159i	0.00886483	+	0.0330840i
$298$	14.7289	+	8.50376i	0.853225	+	0.492610i
$299$	−1.16121	−	16.6868i	−0.0671545	−	0.965020i
$300$		−	4.99506i		−	0.288390i
$301$	1.24007	−	3.54645i	0.0714763	−	0.204414i
$302$	2.38651			0.137328
$303$	10.6139	−	6.12795i	0.609754	−	0.352042i
$304$	−5.64747	+	1.51323i	−0.323904	+	0.0867899i
$305$	−0.0259492	−	0.0968438i	−0.00148585	−	0.00554526i
$306$	5.06471	+	1.35709i	0.289530	+	0.0775794i
$307$	−5.96544	+	5.96544i	−0.340466	+	0.340466i	−0.856542	−	0.516077i	$-0.827392\pi$
$307$	−5.96544	+	5.96544i	−0.340466	+	0.340466i	0.516077	+	0.856542i	$0.327392\pi$
$308$	−1.29054	−	0.879457i	−0.0735356	−	0.0501117i
$309$		−	8.32882i		−	0.473810i
$310$	−0.155188	+	0.579169i	−0.00881408	+	0.0328946i
$311$	−12.8433	+	22.2452i	−0.728277	+	1.26141i	0.229334	+	0.973348i	$0.426345\pi$
$311$	−12.8433	+	22.2452i	−0.728277	+	1.26141i	−0.957611	+	0.288065i	$0.906988\pi$
$312$	3.53908	+	0.689162i	0.200361	+	0.0390161i
$313$	13.7032	−	7.91154i	0.774550	−	0.447187i	−0.0599453	−	0.998202i	$-0.519093\pi$
$313$	13.7032	−	7.91154i	0.774550	−	0.447187i	0.834495	+	0.551015i	$0.185759\pi$
$314$	7.50270	+	7.50270i	0.423402	+	0.423402i
$315$	0.185373	+	0.0138502i	0.0104446	+	0.000780368i
$316$		−	1.45080i		−	0.0816141i
$317$	25.0866	+	6.72192i	1.40900	+	0.377541i	0.881569	−	0.472056i	$-0.156488\pi$
$317$	25.0866	+	6.72192i	1.40900	+	0.377541i	0.527433	+	0.849597i	$0.323155\pi$
$318$	3.23371	−	0.866470i	0.181337	−	0.0485892i
$319$	−0.677635	+	0.181572i	−0.0379403	+	0.0101661i
$320$	0.0678656	+	0.0181845i	0.00379380	+	0.00101655i
$321$		−	15.1725i		−	0.846844i
$322$	−12.2402	−	0.914530i	−0.682121	−	0.0509648i
$323$	−21.6773	−	21.6773i	−1.20616	−	1.20616i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	14.9343	−	10.0660i	0.828407	−	0.558362i
$326$	−6.54735	+	11.3403i	−0.362624	+	0.628084i
$327$	−3.56404	+	13.3012i	−0.197092	+	0.735556i
$328$			4.75201i			0.262386i
$329$	24.6190	+	16.7769i	1.35729	+	0.924939i
$330$	−0.0293254	+	0.0293254i	−0.00161431	+	0.00161431i
$331$	−16.1387	−	4.32435i	−0.887063	−	0.237688i	−0.213611	−	0.976919i	$-0.568522\pi$
$331$	−16.1387	−	4.32435i	−0.887063	−	0.237688i	−0.673452	+	0.739231i	$0.735189\pi$
$332$	−2.61930	−	9.77535i	−0.143753	−	0.536492i
$333$	6.86020	−	1.83819i	0.375937	−	0.100732i
$334$	−1.78695	+	1.03170i	−0.0977776	+	0.0564519i
$335$	0.714612			0.0390434
$336$	0.873279	−	2.49748i	0.0476413	−	0.136248i
$337$			30.1043i			1.63989i	0.572444	+	0.819944i	$0.305996\pi$
$337$			30.1043i			1.63989i	−0.572444	+	0.819944i	$0.694004\pi$
$338$	5.07145	+	11.9700i	0.275851	+	0.651081i
$339$	−13.6590	−	7.88601i	−0.741854	−	0.428309i
$340$	0.0953483	+	0.355845i	0.00517099	+	0.0192984i
$341$	−4.36253	+	2.51871i	−0.236244	+	0.136396i
$342$	5.84669			0.316153
$343$	9.86387	+	15.6749i	0.532599	+	0.846368i
$344$	−1.00410	+	1.00410i	−0.0541375	+	0.0541375i
$345$	−0.0843629	+	0.314847i	−0.00454195	+	0.0169508i
$346$	1.37675	+	5.13811i	0.0740147	+	0.276226i
$347$	3.73740	−	6.47337i	0.200634	−	0.347509i	−0.748099	−	0.663588i	$-0.769033\pi$
$347$	3.73740	−	6.47337i	0.200634	−	0.347509i	0.948733	+	0.316079i	$0.102366\pi$
$348$	−0.594251	−	1.02927i	−0.0318552	−	0.0551748i
$349$	10.4092	−	10.4092i	0.557194	−	0.557194i	−0.371314	−	0.928507i	$-0.621093\pi$
$349$	10.4092	−	10.4092i	0.557194	−	0.557194i	0.928507	+	0.371314i	$0.121093\pi$
$350$	−5.73673	−	11.9057i	−0.306641	−	0.636384i
$351$	−3.24012	−	1.58166i	−0.172945	−	0.0844228i
$352$	0.295136	+	0.511191i	0.0157308	+	0.0272466i
$353$	−28.0655	+	7.52013i	−1.49378	+	0.400256i	−0.911010	−	0.412384i	$-0.864696\pi$
$353$	−28.0655	+	7.52013i	−1.49378	+	0.400256i	−0.582766	+	0.812640i	$0.698030\pi$
$354$	−2.18806	+	3.78983i	−0.116294	+	0.201427i
$355$	−0.399623	−	0.692167i	−0.0212098	−	0.0367364i
$356$	−11.8393	−	11.8393i	−0.627484	−	0.627484i
$357$	13.6302	−	2.58213i	0.721389	−	0.136661i
$358$	−6.00135	−	6.00135i	−0.317181	−	0.317181i
$359$	−2.83096	+	10.5653i	−0.149413	+	0.557615i	0.850107	+	0.526611i	$0.176537\pi$
$359$	−2.83096	+	10.5653i	−0.149413	+	0.557615i	−0.999519	+	0.0310047i	$0.990129\pi$
$360$	−0.0608466	−	0.0351298i	−0.00320690	−	0.00185150i
$361$	−13.1495	−	7.59187i	−0.692079	−	0.399572i
$362$	9.39702	+	2.51792i	0.493897	+	0.132339i
$363$	10.6516			0.559063
$364$	9.22682	−	2.42195i	0.483617	−	0.126945i
$365$	0.800377			0.0418936
$366$	1.37837	+	0.369333i	0.0720485	+	0.0193053i
$367$	10.3835	+	5.99489i	0.542012	+	0.312931i	0.745894	−	0.666065i	$-0.232023\pi$
$367$	10.3835	+	5.99489i	0.542012	+	0.312931i	−0.203882	+	0.978995i	$0.565356\pi$
$368$	4.01772	+	2.31963i	0.209438	+	0.120919i
$369$	1.22991	−	4.59009i	0.0640266	−	0.238951i
$370$	0.352845	+	0.352845i	0.0183436	+	0.0183436i
$371$	6.71237	−	5.77907i	0.348489	−	0.300034i
$372$	−6.03449	−	6.03449i	−0.312874	−	0.312874i
$373$	−13.5947	−	23.5466i	−0.703905	−	1.21920i	−0.967085	−	0.254452i	$-0.918105\pi$
$373$	−13.5947	−	23.5466i	−0.703905	−	1.21920i	0.263180	−	0.964747i	$-0.415229\pi$
$374$	−1.54751	+	2.68036i	−0.0800198	+	0.138598i
$375$	−0.678321	+	0.181756i	−0.0350284	+	0.00938582i
$376$	−5.63014	−	9.75168i	−0.290352	−	0.502905i
$377$	1.87980	−	3.85088i	0.0968149	−	0.198331i
$378$	−1.48992	+	2.18635i	−0.0766330	+	0.112454i
$379$	−24.9859	+	24.9859i	−1.28344	+	1.28344i	−0.344738	+	0.938699i	$0.612032\pi$
$379$	−24.9859	+	24.9859i	−1.28344	+	1.28344i	−0.938699	+	0.344738i	$0.887968\pi$
$380$	0.205393	+	0.355751i	0.0105364	+	0.0182497i
$381$	0.557241	−	0.965171i	0.0285483	−	0.0494472i
$382$	−2.60896	−	9.73679i	−0.133486	−	0.498178i
$383$	3.62658	−	13.5346i	0.185310	−	0.691585i	−0.809254	−	0.587459i	$-0.800129\pi$
$383$	3.62658	−	13.5346i	0.185310	−	0.691585i	0.994564	−	0.104127i	$-0.0332048\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−0.0362169	+	0.103576i	−0.00184578	+	0.00527873i
$386$	14.6731			0.746842
$387$	1.22977	−	0.710007i	0.0625126	−	0.0360917i
$388$	−3.64065	−	13.5871i	−0.184826	−	0.689781i
$389$	10.7754	+	6.22116i	0.546333	+	0.315425i	0.747642	−	0.664102i	$-0.231186\pi$
$389$	10.7754	+	6.22116i	0.546333	+	0.315425i	−0.201309	+	0.979528i	$0.564519\pi$
$390$	−0.0175860	−	0.252714i	−0.000890502	−	0.0127967i
$391$			24.3254i			1.23019i
$392$	−0.786857	−	6.95563i	−0.0397423	−	0.351313i
$393$	14.7970			0.746409
$394$	−13.0173	+	7.51554i	−0.655802	+	0.378627i
$395$	−0.0984597	+	0.0263822i	−0.00495404	+	0.00132743i
$396$	−0.152774	−	0.570159i	−0.00767717	−	0.0286516i
$397$	−4.23964	−	1.13601i	−0.212781	−	0.0570146i	0.150854	−	0.988556i	$-0.451798\pi$
$397$	−4.23964	−	1.13601i	−0.212781	−	0.0570146i	−0.363635	+	0.931542i	$0.618464\pi$
$398$	12.4250	−	12.4250i	0.622809	−	0.622809i
$399$	13.9355	−	6.71481i	0.697647	−	0.336161i
$400$			4.99506i			0.249753i
$401$	−2.15598	+	8.04624i	−0.107665	+	0.401810i	−0.998634	−	0.0522537i	$-0.983360\pi$
$401$	−2.15598	+	8.04624i	−0.107665	+	0.401810i	0.890969	+	0.454064i	$0.150026\pi$
$402$	−5.08551	+	8.80836i	−0.253642	+	0.439321i
$403$	5.88135	−	30.2027i	0.292971	−	1.50450i
$404$	−10.6139	+	6.12795i	−0.528063	+	0.304877i
$405$	0.0496811	+	0.0496811i	0.00246867	+	0.00246867i
$406$	−2.59849	−	1.77077i	−0.128961	−	0.0878817i
$407$			4.19224i			0.207801i
$408$	−5.06471	−	1.35709i	−0.250741	−	0.0671857i
$409$	14.5347	−	3.89457i	0.718696	−	0.192574i	0.119106	−	0.992882i	$-0.461997\pi$
$409$	14.5347	−	3.89457i	0.718696	−	0.192574i	0.599590	+	0.800307i	$0.295330\pi$
$410$	0.322498	−	0.0864131i	0.0159270	−	0.00426764i
$411$	4.24908	+	1.13854i	0.209592	+	0.0561599i
$412$			8.32882i			0.410331i
$413$	−0.862658	+	11.5460i	−0.0424486	+	0.568139i
$414$	−3.28046	−	3.28046i	−0.161226	−	0.161226i
$415$	−0.615779	+	0.355520i	−0.0302274	+	0.0174518i
$416$	−3.53908	−	0.689162i	−0.173517	−	0.0337890i
$417$	−0.636040	+	1.10165i	−0.0311470	+	0.0539482i
$418$	−0.893220	+	3.33354i	−0.0436888	+	0.163049i
$419$		−	4.79365i		−	0.234185i	−0.993121	−	0.117093i	$-0.962643\pi$
$419$		−	4.79365i		−	0.234185i	0.993121	−	0.117093i	$-0.0373574\pi$
$420$	−0.185373	−	0.0138502i	−0.00904527	−	0.000675819i
$421$	21.0099	−	21.0099i	1.02396	−	1.02396i	0.0242554	−	0.999706i	$-0.492279\pi$
$421$	21.0099	−	21.0099i	1.02396	−	1.02396i	0.999706	−	0.0242554i	$-0.00772149\pi$
$422$	5.80579	+	1.55566i	0.282621	+	0.0757282i
$423$	2.91437	+	10.8766i	0.141702	+	0.528838i
$424$	−3.23371	+	0.866470i	−0.157043	+	0.0420795i
$425$	−22.6821	+	13.0955i	−1.10024	+	0.635225i
$426$	11.3756			0.551149
$427$	3.70949	−	0.702732i	0.179515	−	0.0340076i
$428$			15.1725i			0.733389i
$429$	1.39680	−	1.60575i	0.0674383	−	0.0775261i
$430$	0.0864031	+	0.0498848i	0.00416673	+	0.00240566i
$431$	−9.09240	−	33.9333i	−0.437965	−	1.63451i	−0.733869	−	0.679291i	$-0.762287\pi$
$431$	−9.09240	−	33.9333i	−0.437965	−	1.63451i	0.295904	−	0.955218i	$-0.404379\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−36.0673			−1.73328			−0.866642	−	0.498930i	$-0.833727\pi$
$433$	−36.0673			−1.73328			−0.866642	+	0.498930i	$0.833727\pi$
$434$	−21.3136	−	7.45261i	−1.02309	−	0.357737i
$435$	−0.0590460	+	0.0590460i	−0.00283104	+	0.00283104i
$436$	3.56404	−	13.3012i	0.170686	−	0.637010i
$437$	7.02029	+	26.2001i	0.335826	+	1.25332i
$438$	−5.69585	+	9.86550i	−0.272158	+	0.471392i
$439$	8.40046	+	14.5500i	0.400932	+	0.694435i	0.993839	−	0.110837i	$-0.0353530\pi$
$439$	8.40046	+	14.5500i	0.400932	+	0.694435i	−0.592907	+	0.805271i	$0.702020\pi$
$440$	0.0293254	−	0.0293254i	0.00139803	−	0.00139803i
$441$	−1.04021	+	6.92228i	−0.0495336	+	0.329632i
$442$	−6.14893	−	17.8773i	−0.292475	−	0.850338i
$443$	−18.9484	−	32.8195i	−0.900264	−	1.55930i	−0.827152	−	0.561979i	$-0.810040\pi$
$443$	−18.9484	−	32.8195i	−0.900264	−	1.55930i	−0.0731121	−	0.997324i	$-0.523293\pi$
$444$	−6.86020	+	1.83819i	−0.325571	+	0.0872365i
$445$	−0.588192	+	1.01878i	−0.0278830	+	0.0482947i
$446$	4.04171	+	7.00045i	0.191381	+	0.331481i
$447$	12.0261	+	12.0261i	0.568817	+	0.568817i
$448$	−0.873279	+	2.49748i	−0.0412585	+	0.117995i
$449$	−4.53580	−	4.53580i	−0.214057	−	0.214057i	0.591931	−	0.805989i	$-0.298366\pi$
$449$	−4.53580	−	4.53580i	−0.214057	−	0.214057i	−0.805989	+	0.591931i	$0.798366\pi$
$450$	1.29282	−	4.82486i	0.0609440	−	0.227446i
$451$	2.42918	+	1.40249i	0.114386	+	0.0660407i
$452$	13.6590	+	7.88601i	0.642464	+	0.370927i
$453$	2.30519	+	0.617674i	0.108307	+	0.0290209i
$454$	−19.8063			−0.929555
$455$	−0.332153	−	0.582142i	−0.0155716	−	0.0272912i
$456$	−5.84669			−0.273796
$457$	−1.94632	−	0.521515i	−0.0910450	−	0.0243954i	0.213009	−	0.977050i	$-0.431674\pi$
$457$	−1.94632	−	0.521515i	−0.0910450	−	0.0243954i	−0.304054	+	0.952655i	$0.598340\pi$
$458$	6.51605	+	3.76204i	0.304475	+	0.175789i
$459$	4.54090	+	2.62169i	0.211951	+	0.122370i
$460$	0.0843629	−	0.314847i	0.00393344	−	0.0146798i
$461$	5.28080	+	5.28080i	0.245951	+	0.245951i	0.819307	−	0.573355i	$-0.194359\pi$
$461$	5.28080	+	5.28080i	0.245951	+	0.245951i	−0.573355	+	0.819307i	$0.694359\pi$
$462$	−1.01895	−	1.18351i	−0.0474059	−	0.0550617i
$463$	−8.46725	−	8.46725i	−0.393506	−	0.393506i	0.482429	−	0.875935i	$-0.339755\pi$
$463$	−8.46725	−	8.46725i	−0.393506	−	0.393506i	−0.875935	+	0.482429i	$0.839755\pi$
$464$	0.594251	+	1.02927i	0.0275874	+	0.0477828i
$465$	−0.299800	+	0.519269i	−0.0139029	+	0.0240805i
$466$	−17.5469	+	4.70169i	−0.812847	+	0.217802i
$467$	−11.5419	−	19.9911i	−0.534095	−	0.925079i	−0.999207	−	0.0398273i	$-0.987319\pi$
$467$	−11.5419	−	19.9911i	−0.534095	−	0.925079i	0.465112	−	0.885252i	$-0.346014\pi$
$468$	3.24012	+	1.58166i	0.149774	+	0.0731123i
$469$	−2.00500	+	26.8352i	−0.0925821	+	1.23913i
$470$	−0.559423	+	0.559423i	−0.0258042	+	0.0258042i
$471$	5.30521	+	9.18889i	0.244451	+	0.423402i
$472$	2.18806	−	3.78983i	0.100714	−	0.174441i
$473$	0.216941	+	0.809634i	0.00997495	+	0.0372270i
$474$	0.375496	−	1.40137i	0.0172471	−	0.0643670i
$475$	−20.6508	+	20.6508i	−0.947521	+	0.947521i
$476$	−13.6302	+	2.58213i	−0.624741	+	0.118352i
$477$	3.34778			0.153284
$478$	−7.59885	+	4.38720i	−0.347563	+	0.200666i
$479$	−0.871788	−	3.25356i	−0.0398330	−	0.148659i	0.943145	−	0.332381i	$-0.107852\pi$
$479$	−0.871788	−	3.25356i	−0.0398330	−	0.148659i	−0.982978	+	0.183722i	$0.941185\pi$
$480$	0.0608466	+	0.0351298i	0.00277726	+	0.00160345i
$481$	−19.3205	−	16.8064i	−0.880938	−	0.766308i
$482$			21.1453i			0.963141i
$483$	−11.5865	−	4.05137i	−0.527202	−	0.184344i
$484$	−10.6516			−0.484163
$485$	−0.855894	+	0.494151i	−0.0388641	+	0.0224382i
$486$	−0.965926	+	0.258819i	−0.0438153	+	0.0117403i
$487$	−6.03507	−	22.5232i	−0.273475	−	1.02062i	−0.956856	−	0.290561i	$-0.906158\pi$
$487$	−6.03507	−	22.5232i	−0.273475	−	1.02062i	0.683381	−	0.730062i	$-0.260509\pi$
$488$	−1.37837	−	0.369333i	−0.0623959	−	0.0167189i
$489$	−9.25935	+	9.25935i	−0.418722	+	0.418722i
$490$	−0.457740	+	0.179886i	−0.0206786	+	0.00812640i
$491$			4.42542i			0.199716i	0.995002	+	0.0998581i	$0.0318389\pi$
$491$			4.42542i			0.199716i	−0.995002	+	0.0998581i	$0.968161\pi$
$492$	−1.22991	+	4.59009i	−0.0554487	+	0.206937i
$493$	−3.11588	+	5.39686i	−0.140332	+	0.243062i
$494$	−11.7822	−	17.4805i	−0.530106	−	0.786486i
$495$	−0.0359161	+	0.0207362i	−0.00161431	+	0.000932021i
$496$	6.03449	+	6.03449i	0.270956	+	0.270956i
$497$	27.1135	−	13.0646i	1.21621	−	0.586030i
$498$		−	10.1202i		−	0.453496i
$499$	13.3700	+	3.58248i	0.598523	+	0.160374i	0.545346	−	0.838211i	$-0.316398\pi$
$499$	13.3700	+	3.58248i	0.598523	+	0.160374i	0.0531777	+	0.998585i	$0.483065\pi$
$500$	0.678321	−	0.181756i	0.0303354	−	0.00812836i
$501$	−1.99308	+	0.534045i	−0.0890444	+	0.0238594i
$502$	−5.35028	−	1.43360i	−0.238795	−	0.0639849i
$503$		−	6.61704i		−	0.295039i	−0.989059	−	0.147520i	$-0.952871\pi$
$503$		−	6.61704i		−	0.295039i	0.989059	−	0.147520i	$-0.0471290\pi$
$504$	1.48992	−	2.18635i	0.0663662	−	0.0973880i
$505$	0.608887	+	0.608887i	0.0270951	+	0.0270951i
$506$	2.37155	−	1.36921i	0.105428	−	0.0608690i
$507$	1.80059	+	12.8747i	0.0799669	+	0.571785i
$508$	−0.557241	+	0.965171i	−0.0247236	+	0.0428225i
$509$	0.323500	−	1.20732i	0.0143389	−	0.0535134i	−0.958386	−	0.285476i	$-0.907848\pi$
$509$	0.323500	−	1.20732i	0.0143389	−	0.0535134i	0.972725	+	0.231963i	$0.0745148\pi$
$510$			0.368398i			0.0163129i
$511$	−2.24563	+	30.0558i	−0.0993407	+	1.32959i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	5.64747	+	1.51323i	0.249342	+	0.0668109i
$514$	−8.09654	−	30.2167i	−0.357123	−	1.33280i
$515$	0.565240	−	0.151456i	0.0249075	−	0.00667394i
$516$	−1.22977	+	0.710007i	−0.0541375	+	0.0312563i
$517$	−6.64663			−0.292318
$518$	−14.2401	+	12.2601i	−0.625672	+	0.538678i
$519$			5.31936i			0.233494i
$520$	0.0175860	+	0.252714i	0.000771198	+	0.0110822i
$521$	−31.1749	−	17.9988i	−1.36580	−	0.788544i	−0.375410	−	0.926859i	$-0.622498\pi$
$521$	−31.1749	−	17.9988i	−1.36580	−	0.788544i	−0.990388	+	0.138315i	$0.955831\pi$
$522$	−0.307607	−	1.14800i	−0.0134636	−	0.0502468i
$523$	−6.00348	+	3.46611i	−0.262514	+	0.151562i	−0.625481	−	0.780240i	$-0.715097\pi$
$523$	−6.00348	+	3.46611i	−0.262514	+	0.151562i	0.362967	+	0.931802i	$0.381764\pi$
$524$	−14.7970			−0.646409
$525$	−2.45985	−	12.9848i	−0.107357	−	0.566701i
$526$	−2.11059	+	2.11059i	−0.0920261	+	0.0920261i
$527$	−11.5814	+	43.2225i	−0.504495	+	1.88280i
$528$	0.152774	+	0.570159i	0.00664862	+	0.0248130i
$529$	−0.738609	+	1.27931i	−0.0321134	+	0.0556221i
$530$	0.117607	+	0.203701i	0.00510852	+	0.00884822i
$531$	−3.09439	+	3.09439i	−0.134285	+	0.134285i
$532$	−13.9355	+	6.71481i	−0.604180	+	0.291124i
$533$	−16.2020	+	5.57271i	−0.701788	+	0.241381i
$534$	−8.37168	−	14.5002i	−0.362278	−	0.627484i
$535$	1.02969	−	0.275904i	0.0445173	−	0.0119284i
$536$	5.08551	−	8.80836i	0.219661	−	0.380463i
$537$	−4.24360	−	7.35012i	−0.183125	−	0.317181i
$538$	9.53281	+	9.53281i	0.410989	+	0.410989i
$539$	−3.78789	−	1.65063i	−0.163156	−	0.0710975i
$540$	−0.0496811	−	0.0496811i	−0.00213793	−	0.00213793i
$541$	−0.112404	+	0.419496i	−0.00483261	+	0.0180355i	−0.968300	−	0.249790i	$-0.919638\pi$
$541$	−0.112404	+	0.419496i	−0.00483261	+	0.0180355i	0.963467	+	0.267826i	$0.0863051\pi$
$542$	23.8358	+	13.7616i	1.02384	+	0.591112i
$543$	8.42514	+	4.86426i	0.361557	+	0.208745i
$544$	5.06471	+	1.35709i	0.217148	+	0.0581845i
$545$	−0.967502			−0.0414432
$546$	9.53927	+	0.0486498i	0.408243	+	0.00208202i
$547$	3.43477			0.146860			0.0734300	−	0.997300i	$-0.476605\pi$
$547$	3.43477			0.146860			0.0734300	+	0.997300i	$0.476605\pi$
$548$	−4.24908	−	1.13854i	−0.181512	−	0.0486359i
$549$	1.23581	+	0.713497i	0.0527432	+	0.0304513i
$550$	2.55343	+	1.47422i	0.108879	+	0.0628611i
$551$	−1.79848	+	6.71202i	−0.0766178	+	0.285942i
$552$	3.28046	+	3.28046i	0.139625	+	0.139625i
$553$	−0.714457	−	3.77139i	−0.0303818	−	0.160376i
$554$	8.21908	+	8.21908i	0.349195	+	0.349195i
$555$	0.249499	+	0.432145i	0.0105907	+	0.0183436i
$556$	0.636040	−	1.10165i	0.0269741	−	0.0467205i
$557$	−32.5308	+	8.71661i	−1.37837	+	0.369334i	−0.870531	−	0.492114i	$-0.836224\pi$
$557$	−32.5308	+	8.71661i	−1.37837	+	0.369334i	−0.507844	+	0.861449i	$0.669557\pi$
$558$	−4.26703	−	7.39071i	−0.180638	−	0.312874i
$559$	−4.60101	−	2.24598i	−0.194602	−	0.0949948i
$560$	0.185373	+	0.0138502i	0.00783343	+	0.000585276i
$561$	−2.18851	+	2.18851i	−0.0923989	+	0.0923989i
$562$	−1.02190	−	1.76998i	−0.0431063	−	0.0746622i
$563$	−12.6735	+	21.9511i	−0.534123	+	0.925128i	0.465082	+	0.885267i	$0.346025\pi$
$563$	−12.6735	+	21.9511i	−0.534123	+	0.925128i	−0.999205	+	0.0398606i	$0.987309\pi$
$564$	−2.91437	−	10.8766i	−0.122717	−	0.457987i
$565$	0.286807	−	1.07038i	0.0120661	−	0.0450312i
$566$	−3.88350	+	3.88350i	−0.163236	+	0.163236i
$567$	−2.00502	+	1.72624i	−0.0842029	+	0.0724952i
$568$	−11.3756			−0.477309
$569$	2.81740	−	1.62663i	0.118112	−	0.0681918i	−0.439780	−	0.898105i	$-0.644944\pi$
$569$	2.81740	−	1.62663i	0.118112	−	0.0681918i	0.557892	+	0.829914i	$0.311610\pi$
$570$	0.106319	+	0.396789i	0.00445322	+	0.0166197i
$571$	−0.769493	−	0.444267i	−0.0322023	−	0.0185920i	0.483812	−	0.875172i	$-0.339252\pi$
$571$	−0.769493	−	0.444267i	−0.0322023	−	0.0185920i	−0.516015	+	0.856580i	$0.672585\pi$
$572$	−1.39680	+	1.60575i	−0.0584033	+	0.0671396i
$573$		−	10.0803i		−	0.421109i
$574$	2.34016	+	12.3529i	0.0976763	+	0.515601i
$575$	23.1734			0.966399
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	37.6000	−	10.0749i	1.56531	−	0.419424i	0.630970	−	0.775807i	$-0.282657\pi$
$577$	37.6000	−	10.0749i	1.56531	−	0.419424i	0.934340	+	0.356384i	$0.115990\pi$
$578$	2.71578	+	10.1354i	0.112962	+	0.421578i
$579$	14.1731	+	3.79768i	0.589016	+	0.157826i
$580$	0.0590460	−	0.0590460i	0.00245175	−	0.00245175i
$581$	−11.6228	−	24.1213i	−0.482196	−	1.00072i
$582$		−	14.0664i		−	0.583071i
$583$	−0.511453	+	1.90877i	−0.0211822	+	0.0790532i
$584$	5.69585	−	9.86550i	0.235696	−	0.408237i
$585$	0.0484203	−	0.248654i	0.00200193	−	0.0102806i
$586$	10.0816	−	5.82062i	0.416467	−	0.240447i
$587$	22.5880	+	22.5880i	0.932306	+	0.932306i	0.997850	−	0.0655441i	$-0.0208783\pi$
$587$	22.5880	+	22.5880i	0.932306	+	0.932306i	−0.0655441	+	0.997850i	$0.520878\pi$
$588$	1.04021	−	6.92228i	0.0428973	−	0.285470i
$589$			49.8959i			2.05593i
$590$	−0.296988	−	0.0795778i	−0.0122268	−	0.00327616i
$591$	−14.5189	+	3.89033i	−0.597228	+	0.160027i
$592$	6.86020	−	1.83819i	0.281953	−	0.0755490i
$593$	−4.71486	−	1.26334i	−0.193616	−	0.0518793i	0.160708	−	0.987002i	$-0.448622\pi$
$593$	−4.71486	−	1.26334i	−0.193616	−	0.0518793i	−0.354324	+	0.935123i	$0.615289\pi$
$594$		−	0.590272i		−	0.0242192i
$595$	0.423098	+	0.878070i	0.0173453	+	0.0359973i
$596$	−12.0261	−	12.0261i	−0.492610	−	0.492610i
$597$	15.2175	−	8.78580i	0.622809	−	0.359579i
$598$	−3.19721	+	16.4187i	−0.130744	+	0.671411i
$599$	1.94346	−	3.36617i	0.0794076	−	0.137538i	−0.823587	−	0.567190i	$-0.808030\pi$
$599$	1.94346	−	3.36617i	0.0794076	−	0.137538i	0.902995	+	0.429652i	$0.141364\pi$
$600$	−1.29282	+	4.82486i	−0.0527791	+	0.196974i
$601$		−	26.7332i		−	1.09047i	−0.838283	−	0.545236i	$-0.816440\pi$
$601$		−	26.7332i		−	1.09047i	0.838283	−	0.545236i	$-0.183560\pi$
$602$	−2.11570	+	3.10465i	−0.0862296	+	0.126536i
$603$	−7.19200	+	7.19200i	−0.292881	+	0.292881i
$604$	−2.30519	−	0.617674i	−0.0937969	−	0.0251328i
$605$	0.193694	+	0.722876i	0.00787478	+	0.0293891i
$606$	−11.8383	+	3.17206i	−0.480898	+	0.128856i
$607$	30.2365	−	17.4570i	1.22726	−	0.708560i	0.260805	−	0.965391i	$-0.416012\pi$
$607$	30.2365	−	17.4570i	1.22726	−	0.708560i	0.966456	+	0.256832i	$0.0826786\pi$
$608$	5.84669			0.237114
$609$	−2.05164	−	2.38297i	−0.0831365	−	0.0965627i
$610$			0.100260i			0.00405941i
$611$	26.6460	−	30.6319i	1.07798	−	1.23923i
$612$	−4.54090	−	2.62169i	−0.183555	−	0.105975i
$613$	−8.15350	−	30.4293i	−0.329317	−	1.22903i	−0.909901	−	0.414826i	$-0.863842\pi$
$613$	−8.15350	−	30.4293i	−0.329317	−	1.22903i	0.580584	−	0.814200i	$-0.302824\pi$
$614$	7.30614	−	4.21820i	0.294852	−	0.170233i
$615$	0.333875			0.0134631
$616$	1.01895	+	1.18351i	0.0410547	+	0.0476849i
$617$	8.40580	−	8.40580i	0.338405	−	0.338405i	−0.517362	−	0.855767i	$-0.673086\pi$
$617$	8.40580	−	8.40580i	0.338405	−	0.338405i	0.855767	+	0.517362i	$0.173086\pi$
$618$	−2.15566	+	8.04502i	−0.0867132	+	0.323618i
$619$	−10.5569	−	39.3989i	−0.424318	−	1.58358i	−0.765408	−	0.643545i	$-0.777463\pi$
$619$	−10.5569	−	39.3989i	−0.424318	−	1.58358i	0.341091	−	0.940030i	$-0.389204\pi$
$620$	0.299800	−	0.519269i	0.0120403	−	0.0208543i
$621$	−2.31963	−	4.01772i	−0.0930837	−	0.161226i
$622$	18.1632	−	18.1632i	0.728277	−	0.728277i
$623$	−36.6069	−	24.9462i	−1.46663	−	0.999449i
$624$	−3.24012	−	1.58166i	−0.129708	−	0.0633171i
$625$	12.4630	+	21.5865i	0.498520	+	0.863461i
$626$	−15.2839	+	4.09531i	−0.610868	+	0.163682i
$627$	−1.72557	+	2.98877i	−0.0689126	+	0.119360i
$628$	−5.30521	−	9.18889i	−0.211701	−	0.366677i
$629$	26.3323	+	26.3323i	1.04994	+	1.04994i
$630$	−0.175472	−	0.0613563i	−0.00699096	−	0.00244449i
$631$	25.8977	+	25.8977i	1.03097	+	1.03097i	0.999505	+	0.0314652i	$0.0100174\pi$
$631$	25.8977	+	25.8977i	1.03097	+	1.03097i	0.0314652	+	0.999505i	$0.489983\pi$
$632$	−0.375496	+	1.40137i	−0.0149364	+	0.0557435i
$633$	5.20533	+	3.00530i	0.206893	+	0.119450i
$634$	−22.4920	−	12.9858i	−0.893271	−	0.515730i
$635$	0.0756351	+	0.0202664i	0.00300149	+	0.000804246i
$636$	−3.34778			−0.132748
$637$	22.7926	−	10.8397i	0.903074	−	0.429485i
$638$	0.701539			0.0277742
$639$	10.9880	+	2.94422i	0.434678	+	0.116472i
$640$	−0.0608466	−	0.0351298i	−0.00240517	−	0.00138863i
$641$	1.79927	+	1.03881i	0.0710669	+	0.0410305i	0.535112	−	0.844781i	$-0.320269\pi$
$641$	1.79927	+	1.03881i	0.0710669	+	0.0410305i	−0.464046	+	0.885811i	$0.653603\pi$
$642$	−3.92692	+	14.6555i	−0.154983	+	0.578405i
$643$	13.7775	+	13.7775i	0.543333	+	0.543333i	0.924504	−	0.381172i	$-0.124479\pi$
$643$	13.7775	+	13.7775i	0.543333	+	0.543333i	−0.381172	+	0.924504i	$0.624479\pi$
$644$	11.5865	+	4.05137i	0.456570	+	0.159646i
$645$	0.0705478	+	0.0705478i	0.00277782	+	0.00277782i
$646$	15.3282	+	26.5492i	0.603079	+	1.04456i
$647$	17.9006	−	31.0047i	0.703743	−	1.21892i	−0.263400	−	0.964687i	$-0.584844\pi$
$647$	17.9006	−	31.0047i	0.703743	−	1.21892i	0.967143	−	0.254232i	$-0.0818228\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	−1.29155	−	2.23703i	−0.0506979	−	0.0878113i
$650$	−17.0307	+	5.85774i	−0.668000	+	0.229759i
$651$	−18.6585	−	12.7150i	−0.731283	−	0.498341i
$652$	9.25935	−	9.25935i	0.362624	−	0.362624i
$653$	10.5379	+	18.2522i	0.412380	+	0.714263i	0.995149	−	0.0983745i	$-0.0313643\pi$
$653$	10.5379	+	18.2522i	0.412380	+	0.714263i	−0.582770	+	0.812637i	$0.698031\pi$
$654$	6.88519	−	11.9255i	0.269232	−	0.466324i
$655$	0.269076	+	1.00421i	0.0105137	+	0.0392376i
$656$	1.22991	−	4.59009i	0.0480199	−	0.179213i
$657$	−8.05515	+	8.05515i	−0.314261	+	0.314261i
$658$	−19.4379	−	22.5771i	−0.757769	−	0.880146i
$659$	−4.53126			−0.176513			−0.0882564	−	0.996098i	$-0.528129\pi$
$659$	−4.53126			−0.176513			−0.0882564	+	0.996098i	$0.528129\pi$
$660$	0.0359161	−	0.0207362i	0.00139803	−	0.000807154i
$661$	8.69164	+	32.4376i	0.338066	+	1.26168i	0.900507	+	0.434841i	$0.143196\pi$
$661$	8.69164	+	32.4376i	0.338066	+	1.26168i	−0.562441	+	0.826837i	$0.690138\pi$
$662$	14.4696	+	8.35400i	0.562375	+	0.324688i
$663$	−1.31242	−	18.8596i	−0.0509701	−	0.732448i
$664$			10.1202i			0.392739i
$665$	0.709115	+	0.823634i	0.0274983	+	0.0319392i
$666$	−7.10221			−0.275205
$667$	4.77507	−	2.75689i	0.184891	−	0.106747i
$668$	1.99308	−	0.534045i	0.0771147	−	0.0206628i
$669$	2.09214	+	7.80799i	0.0808870	+	0.301874i
$670$	−0.690263	−	0.184955i	−0.0266672	−	0.00714545i
$671$	−0.595606	+	0.595606i	−0.0229931	+	0.0229931i
$672$	−1.48992	+	2.18635i	−0.0574748	+	0.0843405i
$673$			39.9747i			1.54091i	0.637494	+	0.770455i	$0.279971\pi$
$673$			39.9747i			1.54091i	−0.637494	+	0.770455i	$0.720029\pi$
$674$	7.79158	−	29.0786i	0.300120	−	1.12006i
$675$	2.49753	−	4.32585i	0.0961300	−	0.166502i
$676$	−1.80059	−	12.8747i	−0.0692533	−	0.495181i
$677$	7.07724	−	4.08604i	0.272000	−	0.157039i	−0.357796	−	0.933800i	$-0.616472\pi$
$677$	7.07724	−	4.08604i	0.272000	−	0.157039i	0.629796	+	0.776760i	$0.283138\pi$
$678$	11.1525	+	11.1525i	0.428309	+	0.428309i
$679$	−16.1550	−	33.5271i	−0.619972	−	1.28665i
$680$		−	0.368398i		−	0.0141274i
$681$	−19.1314	−	5.12624i	−0.733117	−	0.196438i
$682$	4.86577	−	1.30378i	0.186320	−	0.0499243i
$683$	−27.7411	+	7.43319i	−1.06148	+	0.284423i	−0.746989	−	0.664837i	$-0.768501\pi$
$683$	−27.7411	+	7.43319i	−1.06148	+	0.284423i	−0.314493	+	0.949260i	$0.601835\pi$
$684$	−5.64747	−	1.51323i	−0.215936	−	0.0578599i
$685$			0.309070i			0.0118090i
$686$	−5.47079	−	17.6938i	−0.208876	−	0.675552i
$687$	5.32033	+	5.32033i	0.202983	+	0.202983i
$688$	1.22977	−	0.710007i	0.0468845	−	0.0270688i
$689$	−6.74643	−	10.0093i	−0.257018	−	0.381322i
$690$	0.162977	−	0.282284i	0.00620441	−	0.0107464i
$691$	−2.54094	+	9.48291i	−0.0966619	+	0.360747i	−0.997266	−	0.0738930i	$-0.976458\pi$
$691$	−2.54094	+	9.48291i	−0.0966619	+	0.360747i	0.900604	+	0.434640i	$0.143124\pi$
$692$		−	5.31936i		−	0.202212i
$693$	−0.677916	−	1.40690i	−0.0257519	−	0.0534439i
$694$	−5.28549	+	5.28549i	−0.200634	+	0.200634i
$695$	−0.0863304	−	0.0231322i	−0.00327470	−	0.000877453i
$696$	0.307607	+	1.14800i	0.0116598	+	0.0435150i
$697$	24.0676	−	6.44888i	0.911624	−	0.244269i
$698$	−12.7487	+	7.36044i	−0.482544	+	0.278597i
$699$	−18.1659			−0.687099
$700$	2.45985	+	12.9848i	0.0929736	+	0.490777i
$701$		−	9.70243i		−	0.366456i	−0.983070	−	0.183228i	$-0.941345\pi$
$701$		−	9.70243i		−	0.366456i	0.983070	−	0.183228i	$-0.0586546\pi$
$702$	2.72035	+	2.36637i	0.102673	+	0.0893129i
$703$	35.9612	+	20.7622i	1.35630	+	0.783061i
$704$	−0.152774	−	0.570159i	−0.00575788	−	0.0214887i
$705$	−0.685150	+	0.395572i	−0.0258042	+	0.0148981i
$706$	29.0556			1.09352
$707$	−24.5733	+	21.1566i	−0.924175	+	0.795676i
$708$	3.09439	−	3.09439i	0.116294	−	0.116294i
$709$	9.10115	−	33.9660i	0.341801	−	1.27562i	−0.554504	−	0.832181i	$-0.687092\pi$
$709$	9.10115	−	33.9660i	0.341801	−	1.27562i	0.896305	−	0.443438i	$-0.146241\pi$
$710$	0.206860	+	0.772012i	0.00776331	+	0.0289731i
$711$	0.725402	−	1.25643i	0.0272047	−	0.0471199i
$712$	8.37168	+	14.5002i	0.313742	+	0.543417i
$713$	27.9956	−	27.9956i	1.04844	−	1.04844i
$714$	−13.8341	−	1.03362i	−0.517728	−	0.0386822i
$715$	0.134375	+	0.0655951i	0.00502535	+	0.00245312i
$716$	4.24360	+	7.35012i	0.158591	+	0.274687i
$717$	−8.47541	+	2.27098i	−0.316520	+	0.0848113i
$718$	5.46900	−	9.47259i	0.204101	−	0.353514i
$719$	−24.6843	−	42.7544i	−0.920568	−	1.59447i	−0.798539	−	0.601943i	$-0.794393\pi$
$719$	−24.6843	−	42.7544i	−0.920568	−	1.59447i	−0.122029	−	0.992527i	$-0.538940\pi$
$720$	0.0496811	+	0.0496811i	0.00185150	+	0.00185150i
$721$	4.10158	+	21.6509i	0.152751	+	0.806322i
$722$	10.7365	+	10.7365i	0.399572	+	0.399572i
$723$	−5.47280	+	20.4248i	−0.203536	+	0.759606i
$724$	−8.42514	−	4.86426i	−0.313118	−	0.180779i
$725$	5.14128	+	2.96832i	0.190942	+	0.110241i
$726$	−10.2886	−	2.75683i	−0.381847	−	0.102316i
$727$	16.0560			0.595483			0.297742	−	0.954647i	$-0.403767\pi$
$727$	16.0560			0.595483			0.297742	+	0.954647i	$0.403767\pi$
$728$	−9.53927	−	0.0486498i	−0.353549	−	0.00180308i
$729$	−1.00000			−0.0370370
$730$	−0.773105	−	0.207153i	−0.0286139	−	0.00766707i
$731$	6.44813	+	3.72283i	0.238493	+	0.137694i
$732$	−1.23581	−	0.713497i	−0.0456769	−	0.0263716i
$733$	−9.31447	+	34.7621i	−0.344038	+	1.28397i	0.549694	+	0.835366i	$0.314744\pi$
$733$	−9.31447	+	34.7621i	−0.344038	+	1.28397i	−0.893732	+	0.448601i	$0.851922\pi$
$734$	−8.47806	−	8.47806i	−0.312931	−	0.312931i
$735$	−0.488700	+	0.0552843i	−0.0180260	+	0.00203919i
$736$	−3.28046	−	3.28046i	−0.120919	−	0.120919i
$737$	−3.00184	−	5.19933i	−0.110574	−	0.191520i
$738$	−2.37601	+	4.11536i	−0.0874620	+	0.151489i
$739$	33.4060	−	8.95110i	1.22886	−	0.329272i	0.414723	−	0.909948i	$-0.363878\pi$
$739$	33.4060	−	8.95110i	1.22886	−	0.329272i	0.814135	+	0.580676i	$0.197212\pi$
$740$	−0.249499	−	0.432145i	−0.00917178	−	0.0158860i
$741$	−6.85644	−	19.9343i	−0.251878	−	0.732306i
$742$	−7.97939	+	3.84486i	−0.292932	+	0.141149i
$743$	−8.70489	+	8.70489i	−0.319352	+	0.319352i	−0.848518	−	0.529166i	$-0.822505\pi$
$743$	−8.70489	+	8.70489i	−0.319352	+	0.319352i	0.529166	+	0.848518i	$0.322505\pi$
$744$	4.26703	+	7.39071i	0.156437	+	0.270956i
$745$	−0.597471	+	1.03485i	−0.0218897	+	0.0379140i
$746$	7.03711	+	26.2629i	0.257647	+	0.961552i
$747$	2.61930	−	9.77535i	0.0958350	−	0.357661i
$748$	2.18851	−	2.18851i	0.0800198	−	0.0800198i
$749$	7.47177	+	39.4411i	0.273013	+	1.44115i
$750$	0.702250			0.0256425
$751$	9.92632	−	5.73096i	0.362216	−	0.209126i	−0.307836	−	0.951439i	$-0.599605\pi$
$751$	9.92632	−	5.73096i	0.362216	−	0.209126i	0.670053	+	0.742314i	$0.266272\pi$
$752$	2.91437	+	10.8766i	0.106276	+	0.396628i
$753$	−4.79693	−	2.76951i	−0.174810	−	0.100927i
$754$	−2.81243	+	3.23314i	−0.102423	+	0.117744i
$755$			0.167675i			0.00610233i
$756$	2.00502	−	1.72624i	0.0729218	−	0.0627827i
$757$	−13.7286			−0.498976			−0.249488	−	0.968378i	$-0.580262\pi$
$757$	−13.7286			−0.498976			−0.249488	+	0.968378i	$0.580262\pi$
$758$	30.6013	−	17.6677i	1.11149	−	0.641719i
$759$	2.64512	−	0.708758i	0.0960118	−	0.0257263i
$760$	−0.106319	−	0.396789i	−0.00385661	−	0.0143930i
$761$	9.69095	+	2.59668i	0.351297	+	0.0941297i	0.430152	−	0.902756i	$-0.358460\pi$
$761$	9.69095	+	2.59668i	0.351297	+	0.0941297i	−0.0788554	+	0.996886i	$0.525127\pi$
$762$	−0.788058	+	0.788058i	−0.0285483	+	0.0285483i
$763$	2.71453	−	36.3317i	0.0982726	−	1.31530i
$764$			10.0803i			0.364691i
$765$	−0.0953483	+	0.355845i	−0.00344733	+	0.0128656i
$766$	−7.00602	+	12.1348i	−0.253138	+	0.438448i
$767$	15.4874	+	3.01586i	0.559219	+	0.108896i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	13.7331	+	13.7331i	0.495230	+	0.495230i	0.909949	−	0.414719i	$-0.136120\pi$
$769$	13.7331	+	13.7331i	0.495230	+	0.495230i	−0.414719	+	0.909949i	$0.636120\pi$
$770$	0.0617903	−	0.0906732i	0.00222677	−	0.00326764i
$771$		−	31.2826i		−	1.12662i
$772$	−14.1731	−	3.79768i	−0.510102	−	0.136682i
$773$	27.0864	−	7.25778i	0.974230	−	0.261044i	0.263617	−	0.964627i	$-0.415085\pi$
$773$	27.0864	−	7.25778i	0.974230	−	0.261044i	0.710613	+	0.703583i	$0.248418\pi$
$774$	−1.37163	+	0.367527i	−0.0493021	+	0.0132105i
$775$	41.1756	+	11.0330i	1.47907	+	0.396316i
$776$			14.0664i			0.504955i
$777$	−16.9280	+	8.15675i	−0.607288	+	0.292622i
$778$	−8.79805	−	8.79805i	−0.315425	−	0.315425i
$779$	24.0612	−	13.8918i	0.862083	−	0.497724i
$780$	−0.0484203	+	0.248654i	−0.00173373	+	0.00890325i
$781$	−3.35735	+	5.81510i	−0.120135	+	0.208081i
$782$	6.29588	−	23.4965i	0.225140	−	0.840234i
$783$		−	1.18850i		−	0.0424736i
$784$	−1.04021	+	6.92228i	−0.0371502	+	0.247224i
$785$	−0.527137	+	0.527137i	−0.0188143	+	0.0188143i
$786$	−14.2928	−	3.82974i	−0.509807	−	0.136602i
$787$	−11.6002	−	43.2926i	−0.413503	−	1.54321i	−0.787815	−	0.615912i	$-0.788788\pi$
$787$	−11.6002	−	43.2926i	−0.413503	−	1.54321i	0.374312	−	0.927303i	$-0.377879\pi$
$788$	14.5189	−	3.89033i	0.517214	−	0.138587i
$789$	−2.58493	+	1.49241i	−0.0920261	+	0.0531313i
$790$	0.101933			0.00362661
$791$	39.3903	+	13.7734i	1.40056	+	0.489725i
$792$			0.590272i			0.0209744i
$793$	−0.357177	−	5.13268i	−0.0126837	−	0.182267i
$794$	3.80115	+	2.19460i	0.134898	+	0.0778833i
$795$	0.0608779	+	0.227199i	0.00215912	+	0.00805793i
$796$	−15.2175	+	8.78580i	−0.539368	+	0.311404i
$797$	37.7602			1.33753			0.668767	−	0.743472i	$-0.266822\pi$
$797$	37.7602			1.33753			0.668767	+	0.743472i	$0.266822\pi$
$798$	−15.1986	+	2.87924i	−0.538023	+	0.101924i
$799$	−41.7489	+	41.7489i	−1.47697	+	1.47697i
$800$	1.29282	−	4.82486i	0.0457080	−	0.170585i
$801$	−4.33350	−	16.1729i	−0.153117	−	0.571440i
$802$	4.16504	−	7.21406i	0.147073	−	0.254737i
$803$	−3.36210	−	5.82333i	−0.118646	−	0.205501i
$804$	7.19200	−	7.19200i	0.253642	−	0.253642i
$805$	0.0642546	−	0.859994i	0.00226468	−	0.0303108i
$806$	−13.4980	+	27.6513i	−0.475446	+	0.973976i
$807$	6.74072	+	11.6753i	0.237284	+	0.410989i
$808$	11.8383	−	3.17206i	0.416470	−	0.111593i
$809$	−1.46973	+	2.54565i	−0.0516730	+	0.0895002i	−0.890705	−	0.454582i	$-0.849789\pi$
$809$	−1.46973	+	2.54565i	−0.0516730	+	0.0895002i	0.839032	+	0.544082i	$0.183122\pi$
$810$	−0.0351298	−	0.0608466i	−0.00123434	−	0.00213793i
$811$	30.0979	+	30.0979i	1.05688	+	1.05688i	0.998282	+	0.0585995i	$0.0186635\pi$
$811$	30.0979	+	30.0979i	1.05688	+	1.05688i	0.0585995	+	0.998282i	$0.481337\pi$
$812$	2.05164	+	2.38297i	0.0719983	+	0.0836258i
$813$	19.4619	+	19.4619i	0.682558	+	0.682558i
$814$	1.08503	−	4.04939i	0.0380303	−	0.141931i
$815$	−0.796769	−	0.460015i	−0.0279096	−	0.0161136i
$816$	4.54090	+	2.62169i	0.158963	+	0.0917774i
$817$	8.01948	+	2.14881i	0.280566	+	0.0751774i
$818$	−15.0475			−0.526122
$819$	9.20163	+	2.51594i	0.321531	+	0.0879139i
$820$	−0.333875			−0.0116594
$821$	9.83448	+	2.63514i	0.343226	+	0.0919670i	0.426314	−	0.904575i	$-0.359812\pi$
$821$	9.83448	+	2.63514i	0.343226	+	0.0919670i	−0.0830886	+	0.996542i	$0.526478\pi$
$822$	−3.80962	−	2.19949i	−0.132876	−	0.0767159i
$823$	−17.6881	−	10.2122i	−0.616567	−	0.355975i	0.158964	−	0.987284i	$-0.449185\pi$
$823$	−17.6881	−	10.2122i	−0.616567	−	0.355975i	−0.775531	+	0.631309i	$0.782518\pi$
$824$	2.15566	−	8.04502i	0.0750959	−	0.280262i
$825$	2.08487	+	2.08487i	0.0725858	+	0.0725858i
$826$	3.82158	−	10.9293i	0.132970	−	0.380278i
$827$	−34.3549	−	34.3549i	−1.19464	−	1.19464i	−0.975750	−	0.218887i	$-0.929757\pi$
$827$	−34.3549	−	34.3549i	−1.19464	−	1.19464i	−0.218887	−	0.975750i	$-0.570243\pi$
$828$	2.31963	+	4.01772i	0.0806128	+	0.139625i
$829$	−4.28007	+	7.41330i	−0.148653	+	0.257474i	−0.930730	−	0.365707i	$-0.880827\pi$
$829$	−4.28007	+	7.41330i	−0.148653	+	0.257474i	0.782077	+	0.623182i	$0.214160\pi$
$830$	0.686813	−	0.184031i	0.0238396	−	0.00638780i
$831$	5.81177	+	10.0663i	0.201608	+	0.349195i
$832$	3.24012	+	1.58166i	0.112331	+	0.0548342i
$833$	−34.1604	+	13.4246i	−1.18359	+	0.465134i
$834$	0.899496	−	0.899496i	0.0311470	−	0.0311470i
$835$	−0.0724866	−	0.125550i	−0.00250850	−	0.00434485i
$836$	1.72557	−	2.98877i	0.0596800	−	0.103369i
$837$	−2.20878	−	8.24326i	−0.0763465	−	0.284929i
$838$	−1.24069	+	4.63031i	−0.0428589	+	0.159951i
$839$	−12.3099	+	12.3099i	−0.424985	+	0.424985i	−0.886916	−	0.461931i	$-0.847157\pi$
$839$	−12.3099	+	12.3099i	−0.424985	+	0.424985i	0.461931	+	0.886916i	$0.347157\pi$
$840$	0.175472	+	0.0613563i	0.00605435	+	0.00211699i
$841$	−27.5875			−0.951292
$842$	−25.7318	+	14.8563i	−0.886776	+	0.511981i
$843$	−0.528974	−	1.97416i	−0.0182188	−	0.0679937i
$844$	−5.20533	−	3.00530i	−0.179175	−	0.103447i
$845$	−0.841007	+	0.356318i	−0.0289315	+	0.0122577i
$846$		−	11.2603i		−	0.387136i
$847$	−27.6890	+	5.24544i	−0.951404	+	0.180235i
$848$	3.34778			0.114963
$849$	−4.75630	+	2.74605i	−0.163236	+	0.0942442i
$850$	25.2986	−	6.77873i	0.867733	−	0.232508i
$851$	−8.52783	−	31.8263i	−0.292330	−	1.09099i
$852$	−10.9880	−	2.94422i	−0.376442	−	0.100867i
$853$	18.1195	−	18.1195i	0.620399	−	0.620399i	−0.325234	−	0.945633i	$-0.605443\pi$
$853$	18.1195	−	18.1195i	0.620399	−	0.620399i	0.945633	+	0.325234i	$0.105443\pi$
$854$	−3.76498	−	0.281301i	−0.128835	−	0.00962591i
$855$			0.410786i			0.0140486i
$856$	3.92692	−	14.6555i	0.134219	−	0.500914i
$857$	1.54899	−	2.68293i	0.0529124	−	0.0916470i	−0.838356	−	0.545123i	$-0.816483\pi$
$857$	1.54899	−	2.68293i	0.0529124	−	0.0916470i	0.891268	+	0.453476i	$0.149816\pi$
$858$	−1.76481	+	1.18951i	−0.0602495	+	0.0406093i
$859$	15.8368	−	9.14337i	0.540344	−	0.311968i	−0.204874	−	0.978788i	$-0.565679\pi$
$859$	15.8368	−	9.14337i	0.540344	−	0.311968i	0.745218	+	0.666821i	$0.232345\pi$
$860$	−0.0705478	−	0.0705478i	−0.00240566	−	0.00240566i
$861$	−0.936756	+	12.5377i	−0.0319245	+	0.427283i
$862$			35.1303i			1.19654i
$863$	−48.2735	−	12.9349i	−1.64325	−	0.440307i	−0.685538	−	0.728037i	$-0.740433\pi$
$863$	−48.2735	−	12.9349i	−1.64325	−	0.440307i	−0.957712	+	0.287729i	$0.907100\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	−0.361002	+	0.0967301i	−0.0122744	+	0.00328892i
$866$	34.8384	+	9.33491i	1.18386	+	0.317213i
$867$			10.4930i			0.356360i
$868$	18.6585	+	12.7150i	0.633310	+	0.431576i
$869$	0.605544	+	0.605544i	0.0205417	+	0.0205417i
$870$	0.0723163	−	0.0417518i	0.00245175	−	0.00141552i
$871$	35.9960	+	7.00949i	1.21968	+	0.237507i
$872$	−6.88519	+	11.9255i	−0.233162	+	0.403848i
$873$	3.64065	−	13.5871i	0.123217	−	0.459854i
$874$		−	27.1243i		−	0.917494i
$875$	1.67380	−	0.806520i	0.0565848	−	0.0272654i
$876$	8.05515	−	8.05515i	0.272158	−	0.272158i
$877$	−35.2863	−	9.45492i	−1.19153	−	0.319270i	−0.392041	−	0.919948i	$-0.628231\pi$
$877$	−35.2863	−	9.45492i	−1.19153	−	0.319270i	−0.799491	+	0.600678i	$0.794898\pi$
$878$	−4.34840	−	16.2284i	−0.146751	−	0.547683i
$879$	11.2446	−	3.01297i	0.379270	−	0.101625i
$880$	−0.0359161	+	0.0207362i	−0.00121073	+	0.000699016i
$881$	46.7253			1.57422			0.787108	−	0.616815i	$-0.211577\pi$
$881$	46.7253			1.57422			0.787108	+	0.616815i	$0.211577\pi$
$882$	2.79638	−	6.41718i	0.0941590	−	0.216078i
$883$			21.3471i			0.718387i	0.933263	+	0.359194i	$0.116948\pi$
$883$			21.3471i			0.718387i	−0.933263	+	0.359194i	$0.883052\pi$
$884$	1.31242	+	18.8596i	0.0441414	+	0.634318i
$885$	−0.266272	−	0.153732i	−0.00895065	−	0.00516766i
$886$	9.80839	+	36.6054i	0.329519	+	1.22978i
$887$	12.3821	−	7.14880i	0.415750	−	0.240033i	−0.277508	−	0.960723i	$-0.589508\pi$
$887$	12.3821	−	7.14880i	0.415750	−	0.240033i	0.693257	+	0.720690i	$0.256175\pi$
$888$	7.10221			0.238334
$889$	−0.973254	+	2.78339i	−0.0326419	+	0.0933520i
$890$	0.831829	−	0.831829i	0.0278830	−	0.0278830i
$891$	0.152774	−	0.570159i	0.00511811	−	0.0191011i
$892$	−2.09214	−	7.80799i	−0.0700502	−	0.261431i
$893$	−32.9176	+	57.0150i	−1.10155	+	1.90794i
$894$	−8.50376	−	14.7289i	−0.284408	−	0.492610i
$895$	0.421653	−	0.421653i	0.0140943	−	0.0140943i
$896$	1.48992	−	2.18635i	0.0497746	−	0.0730410i
$897$	−7.33774	+	15.0318i	−0.245000	+	0.501896i
$898$	3.20729	+	5.55519i	0.107029	+	0.185379i
$899$	9.79713	−	2.62513i	0.326753	−	0.0875531i
$900$	−2.49753	+	4.32585i	−0.0832511	+	0.144195i
$901$	8.77684	+	15.2019i	0.292399	+	0.506450i
$902$	−1.98342	−	1.98342i	−0.0660407	−	0.0660407i
$903$	−2.84716	+	2.45128i	−0.0947474	+	0.0815735i
$904$	−11.1525	−	11.1525i	−0.370927	−	0.370927i
$905$	−0.176909	+	0.660232i	−0.00588064	+	0.0219468i
$906$	−2.06678	−	1.19326i	−0.0686641	−	0.0396432i
$907$	−37.7829	−	21.8140i	−1.25456	−	0.724321i	−0.282550	−	0.959253i	$-0.591180\pi$
$907$	−37.7829	−	21.8140i	−1.25456	−	0.724321i	−0.972012	+	0.234931i	$0.924513\pi$
$908$	19.1314	+	5.12624i	0.634898	+	0.170120i
$909$	−12.2559			−0.406503
$910$	0.170166	+	0.648273i	0.00564093	+	0.0214900i
$911$	−23.6785			−0.784503			−0.392251	−	0.919858i	$-0.628304\pi$
$911$	−23.6785			−0.784503			−0.392251	+	0.919858i	$0.628304\pi$
$912$	5.64747	+	1.51323i	0.187006	+	0.0501082i
$913$	5.17334	+	2.98683i	0.171213	+	0.0988497i
$914$	1.74502	+	1.00749i	0.0577202	+	0.0333248i
$915$	−0.0259492	+	0.0968438i	−0.000857854	+	0.00320156i
$916$	−5.32033	−	5.32033i	−0.175789	−	0.175789i
$917$	−38.4650	+	7.28687i	−1.27023	+	0.240634i
$918$	−3.70763	−	3.70763i	−0.122370	−	0.122370i
$919$	7.69879	+	13.3347i	0.253960	+	0.439871i	0.964612	−	0.263672i	$-0.0849337\pi$
$919$	7.69879	+	13.3347i	0.253960	+	0.439871i	−0.710653	+	0.703543i	$0.751600\pi$
$920$	−0.162977	+	0.282284i	−0.00537318	+	0.00930662i
$921$	8.14894	−	2.18350i	0.268517	−	0.0719488i
$922$	−3.73409	−	6.46763i	−0.122976	−	0.213000i
$923$	−13.3402	−	38.7852i	−0.439099	−	1.27663i
$924$	0.677916	+	1.40690i	0.0223018	+	0.0462837i
$925$	25.0853	−	25.0853i	0.824800	−	0.824800i
$926$	5.98725	+	10.3702i	0.196753	+	0.340786i
$927$	−4.16441	+	7.21297i	−0.136777	+	0.236905i
$928$	−0.307607	−	1.14800i	−0.0100977	−	0.0376851i
$929$	0.426517	−	1.59178i	0.0139936	−	0.0522248i	−0.958576	−	0.284837i	$-0.908061\pi$
$929$	0.426517	−	1.59178i	0.0139936	−	0.0522248i	0.972570	+	0.232612i	$0.0747272\pi$
$930$	0.423981	−	0.423981i	0.0139029	−	0.0139029i
$931$	−32.9188	+	24.3179i	−1.07887	+	0.796986i
$932$	18.1659			0.595045
$933$	22.2452	−	12.8433i	0.728277	−	0.420471i
$934$	5.97452	+	22.2972i	0.195492	+	0.729587i
$935$	−0.188321	−	0.108727i	−0.00615877	−	0.00355577i
$936$	−2.72035	−	2.36637i	−0.0889174	−	0.0773472i
$937$			17.0996i			0.558618i	0.960201	+	0.279309i	$0.0901054\pi$
$937$			17.0996i			0.558618i	−0.960201	+	0.279309i	$0.909895\pi$
$938$	8.88214	−	25.4019i	0.290012	−	0.829401i
$939$	−15.8231			−0.516367
$940$	0.685150	−	0.395572i	0.0223471	−	0.0129021i
$941$	−19.3263	+	5.17847i	−0.630020	+	0.168813i	−0.559679	−	0.828710i	$-0.689076\pi$
$941$	−19.3263	+	5.17847i	−0.630020	+	0.168813i	−0.0703413	+	0.997523i	$0.522409\pi$
$942$	−2.74618	−	10.2489i	−0.0894753	−	0.333926i
$943$	−21.2946	−	5.70588i	−0.693449	−	0.185809i
$944$	−3.09439	+	3.09439i	−0.100714	+	0.100714i
$945$	−0.153613	−	0.104681i	−0.00499702	−	0.00340527i
$946$		−	0.838195i		−	0.0272521i
$947$	−8.54207	+	31.8794i	−0.277580	+	1.03594i	0.676513	+	0.736431i	$0.263490\pi$
$947$	−8.54207	+	31.8794i	−0.277580	+	1.03594i	−0.954093	+	0.299511i	$0.903176\pi$
$948$	−0.725402	+	1.25643i	−0.0235600	+	0.0408070i
$949$	40.3161	+	7.85073i	1.30872	+	0.254846i
$950$	25.2919	−	14.6023i	0.820578	−	0.473761i
$951$	−18.3646	−	18.3646i	−0.595514	−	0.595514i
$952$	13.8341	+	1.03362i	0.448366	+	0.0334997i
$953$		−	56.5734i		−	1.83259i	−0.400501	−	0.916296i	$-0.631164\pi$
$953$		−	56.5734i		−	1.83259i	0.400501	−	0.916296i	$-0.368836\pi$
$954$	−3.23371	−	0.866470i	−0.104695	−	0.0280530i
$955$	0.684103	−	0.183305i	0.0221371	−	0.00593161i
$956$	8.47541	−	2.27098i	0.274114	−	0.0734487i
$957$	0.677635	+	0.181572i	0.0219048	+	0.00586938i
$958$			3.36833i			0.108826i
$959$	−11.6062	−	0.867162i	−0.374785	−	0.0280021i
$960$	−0.0496811	−	0.0496811i	−0.00160345	−	0.00160345i
$961$	36.2259	−	20.9150i	1.16858	−	0.674679i
$962$	14.3123	+	21.2343i	0.461448	+	0.684621i
$963$	−7.58623	+	13.1397i	−0.244463	+	0.423422i
$964$	5.47280	−	20.4248i	0.176267	−	0.657838i
$965$			1.03093i			0.0331867i
$966$	10.1431	+	6.91212i	0.326348	+	0.222394i
$967$	−3.56848	+	3.56848i	−0.114755	+	0.114755i	−0.762152	−	0.647398i	$-0.775857\pi$
$967$	−3.56848	+	3.56848i	−0.114755	+	0.114755i	0.647398	+	0.762152i	$0.275857\pi$
$968$	10.2886	+	2.75683i	0.330689	+	0.0886079i
$969$	7.93445	+	29.6118i	0.254891	+	0.951267i
$970$	0.954626	−	0.255791i	0.0306512	−	0.00821296i
$971$	42.2212	−	24.3764i	1.35494	−	0.782276i	0.366005	−	0.930613i	$-0.380725\pi$
$971$	42.2212	−	24.3764i	1.35494	−	0.782276i	0.988937	+	0.148337i	$0.0473920\pi$
$972$	1.00000			0.0320750
$973$	1.11088	−	3.17699i	0.0356132	−	0.101850i
$974$			23.3177i			0.747148i
$975$	−17.9665	+	1.25027i	−0.575389	+	0.0400406i
$976$	1.23581	+	0.713497i	0.0395574	+	0.0228385i
$977$	15.4193	+	57.5455i	0.493306	+	1.84104i	0.539319	+	0.842102i	$0.318682\pi$
$977$	15.4193	+	57.5455i	0.493306	+	1.84104i	−0.0460131	+	0.998941i	$0.514652\pi$
$978$	11.3403	−	6.54735i	0.362624	−	0.209361i
$979$	9.88315			0.315867
$980$	0.488700	−	0.0552843i	0.0156110	−	0.00176599i
$981$	9.73713	−	9.73713i	0.310883	−	0.310883i
$982$	1.14538	−	4.27462i	0.0365506	−	0.136409i
$983$	0.381817	+	1.42496i	0.0121781	+	0.0454492i	0.971748	−	0.236023i	$-0.0758440\pi$
$983$	0.381817	+	1.42496i	0.0121781	+	0.0454492i	−0.959569	+	0.281472i	$0.909177\pi$
$984$	2.37601	−	4.11536i	0.0757443	−	0.131193i
$985$	−0.528039	−	0.914590i	−0.0168247	−	0.0291413i
$986$	4.40652	−	4.40652i	0.140332	−	0.140332i
$987$	−12.9322	−	26.8387i	−0.411637	−	0.854284i
$988$	6.85644	+	19.9343i	0.218132	+	0.634196i
$989$	−3.29391	−	5.70522i	−0.104740	−	0.181415i
$990$	0.0400592	−	0.0107338i	0.00127316	−	0.000341143i
$991$	−28.0655	+	48.6108i	−0.891529	+	1.54417i	−0.0534871	+	0.998569i	$0.517034\pi$
$991$	−28.0655	+	48.6108i	−0.891529	+	1.54417i	−0.838042	+	0.545605i	$0.816300\pi$
$992$	−4.26703	−	7.39071i	−0.135478	−	0.234655i
$993$	11.8143	+	11.8143i	0.374917	+	0.374917i
$994$	−29.5710	+	5.60198i	−0.937937	+	0.177684i
$995$	0.872976	+	0.872976i	0.0276752	+	0.0276752i
$996$	−2.61930	+	9.77535i	−0.0829956	+	0.309744i
$997$	−23.0111	−	13.2855i	−0.728770	−	0.420756i	0.0892019	−	0.996014i	$-0.471568\pi$
$997$	−23.0111	−	13.2855i	−0.728770	−	0.420756i	−0.817972	+	0.575258i	$0.804902\pi$
$998$	−11.9872	−	6.92082i	−0.379449	−	0.219075i
$999$	−6.86020	−	1.83819i	−0.217047	−	0.0581576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.b.31.3	yes	40
7.5	odd	6		546.2.bz.a.187.8	yes	40
13.8	odd	4		546.2.bz.a.73.8	✓	40
91.47	even	12	inner	546.2.bz.b.229.3	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.8	✓	40	13.8	odd	4
546.2.bz.a.187.8	yes	40	7.5	odd	6
546.2.bz.b.31.3	yes	40	1.1	even	1	trivial
546.2.bz.b.229.3	yes	40	91.47	even	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.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0181845 - 0.0678656i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.49748 + 0.873279i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.0181845 - 0.0678656i) q^{5} +(0.707107 + 0.707107i) q^{6} +(2.49748 + 0.873279i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.0351298 + 0.0608466i) q^{10} +(-0.570159 + 0.152774i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.58166 - 3.24012i) q^{13} +(-2.18635 - 1.48992i) q^{14} +(-0.0496811 + 0.0496811i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-2.62169 + 4.54090i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(-1.51323 + 5.64747i) q^{19} +(0.0496811 - 0.0496811i) q^{20} +(-1.72624 - 2.00502i) q^{21} +0.590272 q^{22} +(4.01772 - 2.31963i) q^{23} +(0.258819 + 0.965926i) q^{24} +(4.32585 + 2.49753i) q^{25} +(-2.36637 + 2.72035i) q^{26} -1.00000i q^{27} +(1.72624 + 2.00502i) q^{28} +1.18850 q^{29} +(0.0608466 - 0.0351298i) q^{30} +(8.24326 - 2.20878i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.570159 + 0.152774i) q^{33} +(3.70763 - 3.70763i) q^{34} +(0.104681 - 0.153613i) q^{35} +1.00000i q^{36} +(1.83819 - 6.86020i) q^{37} +(2.92334 - 5.06338i) q^{38} +(-2.98982 + 2.01519i) q^{39} +(-0.0608466 + 0.0351298i) q^{40} +(-3.36018 - 3.36018i) q^{41} +(1.14848 + 2.38348i) q^{42} -1.42001i q^{43} +(-0.570159 - 0.152774i) q^{44} +(0.0678656 - 0.0181845i) q^{45} +(-4.48119 + 1.20073i) q^{46} +(10.8766 + 2.91437i) q^{47} -1.00000i q^{48} +(5.47477 + 4.36198i) q^{49} +(-3.53204 - 3.53204i) q^{50} +(4.54090 - 2.62169i) q^{51} +(2.98982 - 2.01519i) q^{52} +(1.67389 - 2.89927i) q^{53} +(-0.258819 + 0.965926i) q^{54} +0.0414723i q^{55} +(-1.14848 - 2.38348i) q^{56} +(4.13423 - 4.13423i) q^{57} +(-1.14800 - 0.307607i) q^{58} +(1.13262 + 4.22701i) q^{59} +(-0.0678656 + 0.0181845i) q^{60} +(1.23581 - 0.713497i) q^{61} -8.53405 q^{62} +(0.492456 + 2.59952i) q^{63} +1.00000i q^{64} +(-0.191131 - 0.166260i) q^{65} +(-0.511191 - 0.295136i) q^{66} +(2.63245 + 9.82445i) q^{67} +(-4.54090 + 2.62169i) q^{68} -4.63927 q^{69} +(-0.140872 + 0.121285i) q^{70} +(8.04376 - 8.04376i) q^{71} +(0.258819 - 0.965926i) q^{72} +(2.94839 + 11.0035i) q^{73} +(-3.55110 + 6.15069i) q^{74} +(-2.49753 - 4.32585i) q^{75} +(-4.13423 + 4.13423i) q^{76} +(-1.55737 - 0.116359i) q^{77} +(3.40951 - 1.17271i) q^{78} +(-0.725402 - 1.25643i) q^{79} +(0.0678656 - 0.0181845i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.37601 + 4.11536i) q^{82} +(-7.15605 - 7.15605i) q^{83} +(-0.492456 - 2.59952i) q^{84} +(0.260496 + 0.260496i) q^{85} +(-0.367527 + 1.37163i) q^{86} +(-1.02927 - 0.594251i) q^{87} +(0.511191 + 0.295136i) q^{88} +(-16.1729 - 4.33350i) q^{89} -0.0702597 q^{90} +(6.77968 - 6.71088i) q^{91} +4.63927 q^{92} +(-8.24326 - 2.20878i) q^{93} +(-9.75168 - 5.63014i) q^{94} +(0.355751 + 0.205393i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-9.94645 - 9.94645i) q^{97} +(-4.15926 - 5.63033i) q^{98} +(-0.417386 - 0.417386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Introduction

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