LMFDB - Embedded newform 540.2.be.a.11.47

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.47
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.47

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707517 + 1.22451i) q^{2} +(1.24536 + 1.20377i) q^{3} +(-0.998840 + 1.73272i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-0.592913 + 2.37665i) q^{6} +(-4.81853 - 0.849637i) q^{7} +(-2.82843 + 0.00284131i) q^{8} +(0.101864 + 2.99827i) q^{9} +(-1.39265 + 0.246042i) q^{10} +(3.98874 - 1.45178i) q^{11} +(-3.32972 + 0.955492i) q^{12} +(-3.21099 + 2.69434i) q^{13} +(-2.36880 - 6.50146i) q^{14} +(-1.55712 + 0.758545i) q^{15} +(-2.00464 - 3.46142i) q^{16} +(0.295964 - 0.170875i) q^{17} +(-3.59934 + 2.24606i) q^{18} +(3.65453 + 2.10994i) q^{19} +(-1.28660 - 1.53123i) q^{20} +(-4.97806 - 6.85852i) q^{21} +(4.59982 + 3.85708i) q^{22} +(0.145556 + 0.825489i) q^{23} +(-3.52584 - 3.40124i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-5.57107 - 2.02559i) q^{26} +(-3.48238 + 3.85656i) q^{27} +(6.28512 - 7.50051i) q^{28} +(-6.13042 + 7.30595i) q^{29} +(-2.03053 - 1.37002i) q^{30} +(9.68368 - 1.70749i) q^{31} +(2.82022 - 4.90371i) q^{32} +(6.71505 + 2.99354i) q^{33} +(0.418637 + 0.241513i) q^{34} +(2.44643 - 4.23734i) q^{35} +(-5.29691 - 2.81829i) q^{36} +(1.70985 + 2.96154i) q^{37} +(0.00199834 + 5.96782i) q^{38} +(-7.24222 - 0.509866i) q^{39} +(0.964709 - 2.65882i) q^{40} +(6.15853 + 7.33945i) q^{41} +(4.87626 - 10.9482i) q^{42} +(-0.233017 - 0.640210i) q^{43} +(-1.46858 + 8.36147i) q^{44} +(-2.85229 - 0.929748i) q^{45} +(-0.907835 + 0.762282i) q^{46} +(0.722780 - 4.09909i) q^{47} +(1.67026 - 6.72386i) q^{48} +(15.9185 + 5.79386i) q^{49} +(0.245109 - 1.39281i) q^{50} +(0.574277 + 0.143472i) q^{51} +(-1.46127 - 8.25495i) q^{52} -4.48618i q^{53} +(-7.18623 - 1.53562i) q^{54} +4.24473i q^{55} +(13.6313 + 2.38944i) q^{56} +(2.01133 + 7.02686i) q^{57} +(-13.2836 - 2.33766i) q^{58} +(-9.07098 - 3.30157i) q^{59} +(0.240963 - 3.45571i) q^{60} +(-0.443520 + 2.51532i) q^{61} +(8.94221 + 10.6497i) q^{62} +(2.05661 - 14.5338i) q^{63} +(7.99998 - 0.0160729i) q^{64} +(-1.43363 - 3.93886i) q^{65} +(1.08540 + 10.3406i) q^{66} +(1.14326 + 1.36248i) q^{67} +(0.000457742 + 0.683499i) q^{68} +(-0.812431 + 1.20325i) q^{69} +(6.91955 - 0.00231703i) q^{70} +(3.78738 + 6.55993i) q^{71} +(-0.296633 - 8.48009i) q^{72} +(0.0709916 - 0.122961i) q^{73} +(-2.41669 + 4.18906i) q^{74} +(-0.180234 - 1.72265i) q^{75} +(-7.30623 + 4.22478i) q^{76} +(-20.4533 + 3.60648i) q^{77} +(-4.49966 - 9.22889i) q^{78} +(-0.811925 + 0.967615i) q^{79} +(3.93830 - 0.699868i) q^{80} +(-8.97925 + 0.610829i) q^{81} +(-4.62995 + 12.7340i) q^{82} +(-5.14160 - 4.31431i) q^{83} +(16.8562 - 1.77501i) q^{84} +(0.0593442 + 0.336558i) q^{85} +(0.619079 - 0.738291i) q^{86} +(-16.4293 + 1.71894i) q^{87} +(-11.2777 + 4.11759i) q^{88} +(-3.36816 - 1.94461i) q^{89} +(-0.879560 - 4.15047i) q^{90} +(17.7614 - 10.2546i) q^{91} +(-1.57573 - 0.572324i) q^{92} +(14.1151 + 9.53050i) q^{93} +(5.53075 - 2.01512i) q^{94} +(-3.23262 + 2.71249i) q^{95} +(9.41515 - 2.71200i) q^{96} +(0.238324 - 0.0867428i) q^{97} +(4.16798 + 23.5916i) q^{98} +(4.75914 + 11.8114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.707517	+	1.22451i	0.500290	+	0.865858i
$2$	0.707517	+	1.22451i	0.500290	+	0.865858i
$3$	1.24536	+	1.20377i	0.719011	+	0.694998i
$3$	1.24536	+	1.20377i	0.719011	+	0.694998i
$4$	−0.998840	+	1.73272i	−0.499420	+	0.866360i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−0.592913	+	2.37665i	−0.242056	+	0.970262i
$7$	−4.81853	−	0.849637i	−1.82123	−	0.321133i	−0.844494	−	0.535564i	$-0.820099\pi$
$7$	−4.81853	−	0.849637i	−1.82123	−	0.321133i	−0.976739	+	0.214432i	$0.931210\pi$
$8$	−2.82843	+	0.00284131i	−0.999999	+	0.00100456i
$9$	0.101864	+	2.99827i	0.0339545	+	0.999423i
$10$	−1.39265	+	0.246042i	−0.440393	+	0.0778053i
$11$	3.98874	−	1.45178i	1.20265	−	0.437729i	0.338502	−	0.940966i	$-0.390080\pi$
$11$	3.98874	−	1.45178i	1.20265	−	0.437729i	0.864148	+	0.503237i	$0.167858\pi$
$12$	−3.32972	+	0.955492i	−0.961207	+	0.275827i
$13$	−3.21099	+	2.69434i	−0.890568	+	0.747275i	−0.968324	−	0.249697i	$-0.919669\pi$
$13$	−3.21099	+	2.69434i	−0.890568	+	0.747275i	0.0777563	+	0.996972i	$0.475224\pi$
$14$	−2.36880	−	6.50146i	−0.633090	−	1.73759i
$15$	−1.55712	+	0.758545i	−0.402046	+	0.195855i
$16$	−2.00464	−	3.46142i	−0.501160	−	0.865355i
$17$	0.295964	−	0.170875i	0.0717818	−	0.0414432i	−0.463680	−	0.886003i	$-0.653471\pi$
$17$	0.295964	−	0.170875i	0.0717818	−	0.0414432i	0.535461	+	0.844560i	$0.320138\pi$
$18$	−3.59934	+	2.24606i	−0.848372	+	0.529401i
$19$	3.65453	+	2.10994i	0.838406	+	0.484054i	0.856722	−	0.515778i	$-0.172497\pi$
$19$	3.65453	+	2.10994i	0.838406	+	0.484054i	−0.0183161	+	0.999832i	$0.505831\pi$
$20$	−1.28660	−	1.53123i	−0.287693	−	0.342393i
$21$	−4.97806	−	6.85852i	−1.08630	−	1.49665i
$22$	4.59982	+	3.85708i	0.980685	+	0.822333i
$23$	0.145556	+	0.825489i	0.0303505	+	0.172126i	0.996215	−	0.0869206i	$-0.0277026\pi$
$23$	0.145556	+	0.825489i	0.0303505	+	0.172126i	−0.965865	+	0.259047i	$0.916592\pi$
$24$	−3.52584	−	3.40124i	−0.719709	−	0.694276i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−5.57107	−	2.02559i	−1.09258	−	0.397251i
$27$	−3.48238	+	3.85656i	−0.670184	+	0.742195i
$28$	6.28512	−	7.50051i	1.18778	−	1.41746i
$29$	−6.13042	+	7.30595i	−1.13839	+	1.35668i	−0.213275	+	0.976992i	$0.568413\pi$
$29$	−6.13042	+	7.30595i	−1.13839	+	1.35668i	−0.925115	+	0.379688i	$0.876031\pi$
$30$	−2.03053	−	1.37002i	−0.370722	−	0.250130i
$31$	9.68368	−	1.70749i	1.73924	−	0.306675i	0.788126	−	0.615514i	$-0.211052\pi$
$31$	9.68368	−	1.70749i	1.73924	−	0.306675i	0.951114	+	0.308839i	$0.0999404\pi$
$32$	2.82022	−	4.90371i	0.498549	−	0.866861i
$33$	6.71505	+	2.99354i	1.16894	+	0.521108i
$34$	0.418637	+	0.241513i	0.0717957	+	0.0414192i
$35$	2.44643	−	4.23734i	0.413522	−	0.716242i
$36$	−5.29691	−	2.81829i	−0.882818	−	0.469715i
$37$	1.70985	+	2.96154i	0.281097	+	0.486874i	0.971655	−	0.236403i	$-0.0759684\pi$
$37$	1.70985	+	2.96154i	0.281097	+	0.486874i	−0.690558	+	0.723277i	$0.742635\pi$
$38$	0.00199834	+	5.96782i	0.000324173	+	0.968108i
$39$	−7.24222	−	0.509866i	−1.15968	−	0.0816439i
$40$	0.964709	−	2.65882i	0.152534	−	0.420397i
$41$	6.15853	+	7.33945i	0.961801	+	1.14623i	0.989195	+	0.146605i	$0.0468346\pi$
$41$	6.15853	+	7.33945i	0.961801	+	1.14623i	−0.0273943	+	0.999625i	$0.508721\pi$
$42$	4.87626	−	10.9482i	0.752423	−	1.68934i
$43$	−0.233017	−	0.640210i	−0.0355348	−	0.0976311i	0.920656	−	0.390374i	$-0.127654\pi$
$43$	−0.233017	−	0.640210i	−0.0355348	−	0.0976311i	−0.956191	+	0.292743i	$0.905432\pi$
$44$	−1.46858	+	8.36147i	−0.221397	+	1.26054i
$45$	−2.85229	−	0.929748i	−0.425195	−	0.138599i
$46$	−0.907835	+	0.762282i	−0.133853	+	0.112392i
$47$	0.722780	−	4.09909i	0.105428	−	0.597914i	−0.885620	−	0.464410i	$-0.846266\pi$
$47$	0.722780	−	4.09909i	0.105428	−	0.597914i	0.991048	−	0.133503i	$-0.0426226\pi$
$48$	1.67026	−	6.72386i	0.241081	−	0.970505i
$49$	15.9185	+	5.79386i	2.27407	+	0.827695i
$50$	0.245109	−	1.39281i	0.0346637	−	0.196973i
$51$	0.574277	+	0.143472i	0.0804149	+	0.0200901i
$52$	−1.46127	−	8.25495i	−0.202642	−	1.14476i
$53$		−	4.48618i		−	0.616224i	−0.951350	−	0.308112i	$-0.900303\pi$
$53$		−	4.48618i		−	0.616224i	0.951350	−	0.308112i	$-0.0996972\pi$
$54$	−7.18623	−	1.53562i	−0.977922	−	0.208971i
$55$			4.24473i			0.572359i
$56$	13.6313	+	2.38944i	1.82156	+	0.319303i
$57$	2.01133	+	7.02686i	0.266407	+	0.930731i
$58$	−13.2836	−	2.33766i	−1.74422	−	0.306950i
$59$	−9.07098	−	3.30157i	−1.18094	−	0.429828i	−0.324407	−	0.945918i	$-0.605165\pi$
$59$	−9.07098	−	3.30157i	−1.18094	−	0.429828i	−0.856534	+	0.516090i	$0.827387\pi$
$60$	0.240963	−	3.45571i	0.0311082	−	0.446130i
$61$	−0.443520	+	2.51532i	−0.0567869	+	0.322054i	−0.999947	−	0.0102840i	$-0.996726\pi$
$61$	−0.443520	+	2.51532i	−0.0567869	+	0.322054i	0.943160	+	0.332338i	$0.107838\pi$
$62$	8.94221	+	10.6497i	1.13566	+	1.35251i
$63$	2.05661	−	14.5338i	0.259108	−	1.83109i
$64$	7.99998	−	0.0160729i	0.999998	−	0.00200911i
$65$	−1.43363	−	3.93886i	−0.177820	−	0.488555i
$66$	1.08540	+	10.3406i	0.133603	+	1.27284i
$67$	1.14326	+	1.36248i	0.139671	+	0.166454i	0.831346	−	0.555756i	$-0.187571\pi$
$67$	1.14326	+	1.36248i	0.139671	+	0.166454i	−0.691674	+	0.722209i	$0.743127\pi$
$68$	0.000457742		0.683499i	5.55094e−5		0.0828864i
$69$	−0.812431	+	1.20325i	−0.0978052	+	0.144854i
$70$	6.91955	−	0.00231703i	0.827045	−	0.000276938i
$71$	3.78738	+	6.55993i	0.449479	+	0.778520i	0.998352	−	0.0573853i	$-0.0182763\pi$
$71$	3.78738	+	6.55993i	0.449479	+	0.778520i	−0.548873	+	0.835906i	$0.684943\pi$
$72$	−0.296633	−	8.48009i	−0.0349585	−	0.999389i
$73$	0.0709916	−	0.122961i	0.00830894	−	0.0143915i	−0.861841	−	0.507178i	$-0.830688\pi$
$73$	0.0709916	−	0.122961i	0.00830894	−	0.0143915i	0.870150	+	0.492787i	$0.164022\pi$
$74$	−2.41669	+	4.18906i	−0.280934	+	0.486968i
$75$	−0.180234	−	1.72265i	−0.0208117	−	0.198914i
$76$	−7.30623	+	4.22478i	−0.838082	+	0.484615i
$77$	−20.4533	+	3.60648i	−2.33088	+	0.410996i
$78$	−4.49966	−	9.22889i	−0.509486	−	1.04497i
$79$	−0.811925	+	0.967615i	−0.0913487	+	0.108865i	−0.809782	−	0.586730i	$-0.800415\pi$
$79$	−0.811925	+	0.967615i	−0.0913487	+	0.108865i	0.718434	+	0.695595i	$0.244859\pi$
$80$	3.93830	−	0.699868i	0.440315	−	0.0782477i
$81$	−8.97925	+	0.610829i	−0.997694	+	0.0678699i
$82$	−4.62995	+	12.7340i	−0.511293	+	1.40623i
$83$	−5.14160	−	4.31431i	−0.564363	−	0.473557i	0.315407	−	0.948957i	$-0.397859\pi$
$83$	−5.14160	−	4.31431i	−0.564363	−	0.473557i	−0.879770	+	0.475399i	$0.842304\pi$
$84$	16.8562	−	1.77501i	1.83916	−	0.193670i
$85$	0.0593442	+	0.336558i	0.00643678	+	0.0365048i
$86$	0.619079	−	0.738291i	0.0667570	−	0.0796120i
$87$	−16.4293	+	1.71894i	−1.76141	+	0.184289i
$88$	−11.2777	+	4.11759i	−1.20221	+	0.438937i
$89$	−3.36816	−	1.94461i	−0.357024	−	0.206128i	0.310750	−	0.950492i	$-0.399420\pi$
$89$	−3.36816	−	1.94461i	−0.357024	−	0.206128i	−0.667775	+	0.744363i	$0.732753\pi$
$90$	−0.879560	−	4.15047i	−0.0927138	−	0.437498i
$91$	17.7614	−	10.2546i	1.86191	−	1.07497i
$92$	−1.57573	−	0.572324i	−0.164281	−	0.0596689i
$93$	14.1151	+	9.53050i	1.46367	+	0.988266i
$94$	5.53075	−	2.01512i	0.570453	−	0.207844i
$95$	−3.23262	+	2.71249i	−0.331660	+	0.278296i
$96$	9.41515	−	2.71200i	0.960930	−	0.276792i
$97$	0.238324	−	0.0867428i	0.0241981	−	0.00880740i	−0.329893	−	0.944018i	$-0.607013\pi$
$97$	0.238324	−	0.0867428i	0.0241981	−	0.00880740i	0.354091	+	0.935211i	$0.384790\pi$
$98$	4.16798	+	23.5916i	0.421030	+	2.38311i
$99$	4.75914	+	11.8114i	0.478312	+	1.18709i
$100$	1.87893	−	0.685299i	0.187893	−	0.0685299i
$101$	−5.29036	−	0.932833i	−0.526411	−	0.0928204i	−0.0958739	−	0.995393i	$-0.530565\pi$
$101$	−5.29036	−	0.932833i	−0.526411	−	0.0928204i	−0.430537	+	0.902573i	$0.641676\pi$
$102$	0.230628	+	0.804716i	0.0228356	+	0.0796787i
$103$	5.81251	−	15.9697i	0.572723	−	1.57354i	−0.227459	−	0.973788i	$-0.573042\pi$
$103$	5.81251	−	15.9697i	0.572723	−	1.57354i	0.800182	−	0.599757i	$-0.204736\pi$
$104$	9.07438	−	7.62986i	0.889816	−	0.748169i
$105$	8.14750	−	2.33209i	0.795114	−	0.227589i
$106$	5.49336	−	3.17405i	0.533563	−	0.308291i
$107$	10.4095			1.00632			0.503161	−	0.864193i	$-0.332170\pi$
$107$	10.4095			1.00632			0.503161	+	0.864193i	$0.332170\pi$
$108$	−3.20400	−	9.88607i	−0.308305	−	0.951288i
$109$	9.97152			0.955099			0.477549	−	0.878605i	$-0.341525\pi$
$109$	9.97152			0.955099			0.477549	+	0.878605i	$0.341525\pi$
$110$	−5.19770	+	3.00322i	−0.495581	+	0.286345i
$111$	−1.43564	+	5.74646i	−0.136265	+	0.545430i
$112$	6.71846	+	18.3822i	0.634835	+	1.73695i
$113$	3.28046	−	9.01299i	0.308600	−	0.847871i	−0.684331	−	0.729172i	$-0.739906\pi$
$113$	3.28046	−	9.01299i	0.308600	−	0.847871i	0.992930	−	0.118699i	$-0.0378723\pi$
$114$	−7.18140	+	7.43451i	−0.672600	+	0.696306i
$115$	−0.825489	−	0.145556i	−0.0769773	−	0.0135732i
$116$	−6.53586	−	17.9198i	−0.606839	−	1.66381i
$117$	−8.40544	−	9.35295i	−0.777083	−	0.864681i
$118$	−2.37508	−	13.4434i	−0.218644	−	1.23757i
$119$	−1.57129	+	0.571904i	−0.144040	+	0.0524263i
$120$	4.40203	−	2.14991i	0.401849	−	0.196259i
$121$	5.37587	−	4.51089i	0.488716	−	0.410081i
$122$	−3.39383	+	1.23654i	−0.307263	+	0.111951i
$123$	−1.16542	+	16.5538i	−0.105082	+	1.49260i
$124$	−6.71384	+	18.4846i	−0.602920	+	1.65997i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	19.2518	−	7.76458i	1.71509	−	0.691724i
$127$	14.4036	+	8.31590i	1.27811	+	0.737917i	0.976500	−	0.215515i	$-0.0691431\pi$
$127$	14.4036	+	8.31590i	1.27811	+	0.737917i	0.301608	+	0.953432i	$0.402476\pi$
$128$	5.67980	+	9.78467i	0.502029	+	0.864851i
$129$	0.480476	−	1.07779i	0.0423035	−	0.0948945i
$130$	3.80885	−	4.54230i	0.334058	−	0.398386i
$131$	−1.49223	−	8.46284i	−0.130377	−	0.739402i	−0.977968	−	0.208753i	$-0.933059\pi$
$131$	−1.49223	−	8.46284i	−0.130377	−	0.739402i	0.847592	−	0.530649i	$-0.178052\pi$
$132$	−11.8942	+	8.64523i	−1.03526	+	0.752471i
$133$	−15.8168	−	13.2718i	−1.37149	−	1.15081i
$134$	−0.859495	+	2.36391i	−0.0742491	+	0.204210i
$135$	−2.43294	−	4.59139i	−0.209394	−	0.395164i
$136$	−0.836626	+	0.484148i	−0.0717401	+	0.0415153i
$137$	0.465713	−	0.555016i	0.0397886	−	0.0474182i	−0.745783	−	0.666189i	$-0.767925\pi$
$137$	0.465713	−	0.555016i	0.0397886	−	0.0474182i	0.785572	+	0.618771i	$0.212369\pi$
$138$	−2.04820	−	0.143508i	−0.174354	−	0.0122162i
$139$	−14.3946	+	2.53816i	−1.22094	+	0.215284i	−0.746729	−	0.665129i	$-0.768377\pi$
$139$	−14.3946	+	2.53816i	−1.22094	+	0.215284i	−0.474208	+	0.880413i	$0.657266\pi$
$140$	4.89854	+	8.47141i	0.414002	+	0.715965i
$141$	5.83450	−	4.23480i	0.491353	−	0.356634i
$142$	−5.35305	+	9.27893i	−0.449218	+	0.778671i
$143$	−8.89620	+	15.4087i	−0.743937	+	1.28854i
$144$	10.1741	−	6.36304i	0.847839	−	0.530253i
$145$	−4.76862	−	8.25949i	−0.396012	−	0.685913i
$146$	0.200795		6.72365e-5i	0.0166179		5.56453e-6i
$147$	12.8498	+	26.3777i	1.05984	+	2.17560i
$148$	−6.83938	+	0.00458036i	−0.562194	+	0.000376504i
$149$	8.45967	+	10.0818i	0.693043	+	0.825936i	0.991720	−	0.128418i	$-0.0409898\pi$
$149$	8.45967	+	10.0818i	0.693043	+	0.825936i	−0.298677	+	0.954354i	$0.596545\pi$
$150$	1.98188	−	1.43950i	0.161820	−	0.117535i
$151$	1.35529	+	3.72362i	0.110292	+	0.303024i	0.982543	−	0.186033i	$-0.0595633\pi$
$151$	1.35529	+	3.72362i	0.110292	+	0.303024i	−0.872252	+	0.489057i	$0.837341\pi$
$152$	−10.3426	−	5.95743i	−0.838892	−	0.483211i
$153$	0.542477	+	0.869974i	0.0438567	+	0.0703332i
$154$	−18.8872	−	22.4936i	−1.52198	−	1.81259i
$155$	−1.70749	+	9.68368i	−0.137149	+	0.777812i
$156$	8.11727	−	12.0395i	0.649902	−	0.963929i
$157$	16.2303	+	5.90734i	1.29532	+	0.471457i	0.895469	−	0.445124i	$-0.146840\pi$
$157$	16.2303	+	5.90734i	1.29532	+	0.471457i	0.399849	+	0.916581i	$0.369063\pi$
$158$	−1.75930	−	0.309605i	−0.139963	−	0.0246309i
$159$	5.40034	−	5.58693i	0.428275	−	0.443072i
$160$	3.64341	+	4.32731i	0.288037	+	0.342104i
$161$		−	4.10132i		−	0.323229i
$162$	−7.10093	−	10.5630i	−0.557902	−	0.829907i
$163$			13.0910i			1.02536i	0.858578	+	0.512682i	$0.171348\pi$
$163$			13.0910i			1.02536i	−0.858578	+	0.512682i	$0.828652\pi$
$164$	−18.8686	+	3.34007i	−1.47339	+	0.260816i
$165$	−5.10969	+	5.28623i	−0.397788	+	0.411532i
$166$	1.64514	−	9.34837i	0.127688	−	0.725575i
$167$	−2.27918	−	0.829553i	−0.176368	−	0.0641928i	0.252327	−	0.967642i	$-0.418804\pi$
$167$	−2.27918	−	0.829553i	−0.176368	−	0.0641928i	−0.428695	+	0.903449i	$0.641026\pi$
$168$	14.0995	+	19.3847i	1.08780	+	1.49556i
$169$	0.793554	−	4.50047i	0.0610426	−	0.346190i
$170$	−0.370131	+	0.310788i	−0.0283877	+	0.0238363i
$171$	−5.95391	+	11.1722i	−0.455307	+	0.854358i
$172$	1.34205	+	0.235713i	0.102331	+	0.0179730i
$173$	2.30971	+	6.34587i	0.175604	+	0.482468i	0.996003	−	0.0893241i	$-0.0284707\pi$
$173$	2.30971	+	6.34587i	0.175604	+	0.482468i	−0.820399	+	0.571792i	$0.806248\pi$
$174$	−13.7289	−	18.9016i	−1.04078	−	1.43293i
$175$	3.14507	+	3.74815i	0.237745	+	0.283334i
$176$	−13.0212	−	10.8964i	−0.981510	−	0.821347i
$177$	−7.32234	−	15.0311i	−0.550381	−	1.12980i
$178$	−0.00184175	−	5.50019i	−0.000138045	−	0.412256i
$179$	−2.86311	−	4.95906i	−0.213999	−	0.370657i	0.738963	−	0.673746i	$-0.235316\pi$
$179$	−2.86311	−	4.95906i	−0.213999	−	0.370657i	−0.952962	+	0.303088i	$0.901982\pi$
$180$	4.45998	−	4.01355i	0.332427	−	0.299153i
$181$	2.30565	−	3.99350i	0.171377	−	0.296834i	−0.767524	−	0.641020i	$-0.778512\pi$
$181$	2.30565	−	3.99350i	0.171377	−	0.296834i	0.938902	+	0.344186i	$0.111845\pi$
$182$	25.1233	+	14.4938i	1.86227	+	1.07435i
$183$	−3.58022	+	2.59860i	−0.264658	+	0.192094i
$184$	−0.414040	−	2.33442i	−0.0305234	−	0.172096i
$185$	−3.36774	+	0.593823i	−0.247601	+	0.0436588i
$186$	−1.68347	+	24.0271i	−0.123438	+	1.76175i
$187$	0.932449	−	1.11125i	0.0681875	−	0.0812626i
$188$	6.38063	+	5.34671i	0.465355	+	0.389949i
$189$	20.0566	−	15.6242i	1.45890	−	1.13649i
$190$	−5.60860	−	2.03924i	−0.406890	−	0.147942i
$191$	−15.8878	−	13.3314i	−1.14960	−	0.964627i	−0.149888	−	0.988703i	$-0.547891\pi$
$191$	−15.8878	−	13.3314i	−1.14960	−	0.964627i	−0.999710	+	0.0240761i	$0.992336\pi$
$192$	9.98224	+	9.61014i	0.720406	+	0.693552i
$193$	−3.17277	−	17.9937i	−0.228381	−	1.29521i	−0.856115	−	0.516785i	$-0.827129\pi$
$193$	−3.17277	−	17.9937i	−0.228381	−	1.29521i	0.627734	−	0.778428i	$-0.283982\pi$
$194$	0.274835	+	0.230458i	0.0197320	+	0.0165459i
$195$	2.95610	−	6.63107i	0.211691	−	0.474861i
$196$	−25.9392	+	21.7952i	−1.85280	+	1.55680i
$197$	11.0851	+	6.40001i	0.789783	+	0.455982i	0.839886	−	0.542763i	$-0.182622\pi$
$197$	11.0851	+	6.40001i	0.789783	+	0.455982i	−0.0501031	+	0.998744i	$0.515955\pi$
$198$	−11.0960	+	14.1844i	−0.788560	+	1.00804i
$199$	20.0339	−	11.5666i	1.42017	−	0.819935i	0.423856	−	0.905730i	$-0.360676\pi$
$199$	20.0339	−	11.5666i	1.42017	−	0.819935i	0.996313	+	0.0857947i	$0.0273429\pi$
$200$	2.16853	+	1.81590i	0.153338	+	0.128404i
$201$	−0.216346	+	3.07301i	−0.0152598	+	0.216753i
$202$	−2.60076	−	7.13808i	−0.182989	−	0.502234i
$203$	35.7470	−	29.9953i	2.50895	−	2.10526i
$204$	−0.822207	+	0.851756i	−0.0575660	+	0.0596349i
$205$	−9.00317	+	3.27689i	−0.628809	+	0.228868i
$206$	23.6675	−	4.18139i	1.64899	−	0.291331i
$207$	−2.46021	+	0.520504i	−0.170997	+	0.0361775i
$208$	15.7631	+	5.71340i	1.09297	+	0.396153i
$209$	17.6401	+	3.11043i	1.22019	+	0.215153i
$210$	8.62015	+	8.32668i	0.594847	+	0.574596i
$211$	3.15823	−	8.67718i	0.217422	−	0.597361i	−0.782250	−	0.622964i	$-0.785928\pi$
$211$	3.15823	−	8.67718i	0.217422	−	0.597361i	0.999672	+	0.0256027i	$0.00815048\pi$
$212$	7.77329	+	4.48097i	0.533872	+	0.307755i
$213$	−3.18000	+	12.7286i	−0.217890	+	0.872152i
$214$	7.36487	+	12.7465i	0.503452	+	0.871331i
$215$	0.681297			0.0464641
$216$	9.83869	−	10.9179i	0.669438	−	0.742868i
$217$	−48.1119			−3.26605
$218$	7.05502	+	12.2102i	0.477826	+	0.826980i
$219$	0.236428	−	0.0676736i	0.0159763	−	0.00457296i
$220$	−7.35492	−	4.23980i	−0.495869	−	0.285847i
$221$	−0.489942	+	1.34610i	−0.0329570	+	0.0905487i
$222$	−8.05233	+	2.30777i	−0.540437	+	0.154887i
$223$	−3.90672	−	0.688860i	−0.261613	−	0.0461294i	0.0413030	−	0.999147i	$-0.486849\pi$
$223$	−3.90672	−	0.688860i	−0.261613	−	0.0461294i	−0.302916	+	0.953017i	$0.597960\pi$
$224$	−17.7557	+	21.2325i	−1.18635	+	1.41866i
$225$	1.84922	−	2.36228i	0.123281	−	0.157486i
$226$	13.3575	−	2.35989i	0.888525	−	0.156978i
$227$	−5.86521	+	2.13476i	−0.389288	+	0.141689i	−0.529246	−	0.848468i	$-0.677525\pi$
$227$	−5.86521	+	2.13476i	−0.389288	+	0.141689i	0.139959	+	0.990157i	$0.455303\pi$
$228$	−14.1846	−	3.53365i	−0.939397	−	0.234021i
$229$	1.98526	−	1.66583i	0.131190	−	0.110081i	−0.574832	−	0.818272i	$-0.694933\pi$
$229$	1.98526	−	1.66583i	0.131190	−	0.110081i	0.706022	+	0.708190i	$0.250488\pi$
$230$	−0.405813	−	1.11380i	−0.0267585	−	0.0734419i
$231$	−29.8132	−	20.1298i	−1.96157	−	1.32444i
$232$	17.3187	−	20.6817i	1.13703	−	1.35782i
$233$	4.75370	−	2.74455i	0.311425	−	0.179801i	−0.336139	−	0.941812i	$-0.609121\pi$
$233$	4.75370	−	2.74455i	0.311425	−	0.179801i	0.647564	+	0.762011i	$0.275788\pi$
$234$	5.50578	−	16.9099i	0.359924	−	1.10543i
$235$	3.60468	+	2.08116i	0.235143	+	0.135760i
$236$	14.7812	−	12.4197i	0.962171	−	0.808456i
$237$	−2.17593	+	0.227660i	−0.141342	+	0.0147881i
$238$	−1.81202	−	1.51943i	−0.117456	−	0.0984899i
$239$	−2.93726	−	16.6580i	−0.189996	−	1.07752i	−0.919367	−	0.393401i	$-0.871298\pi$
$239$	−2.93726	−	16.6580i	−0.189996	−	1.07752i	0.729371	−	0.684118i	$-0.239813\pi$
$240$	5.74710	+	3.86922i	0.370973	+	0.249757i
$241$	−2.36879	−	1.98765i	−0.152587	−	0.128036i	0.563298	−	0.826254i	$-0.309532\pi$
$241$	−2.36879	−	1.98765i	−0.152587	−	0.128036i	−0.715885	+	0.698218i	$0.753977\pi$
$242$	9.32715	+	3.39127i	0.599572	+	0.217999i
$243$	−11.9177	−	10.0483i	−0.764523	−	0.644597i
$244$	−3.91535	−	3.28090i	−0.250654	−	0.210038i
$245$	−10.8889	+	12.9769i	−0.695666	+	0.829063i
$246$	−21.0948	+	10.2850i	−1.34495	+	0.655748i
$247$	−17.4195	+	3.07153i	−1.10838	+	0.195437i
$248$	−27.3847	+	4.85703i	−1.73893	+	0.308422i
$249$	−1.20971	−	11.5622i	−0.0766623	−	0.732725i
$250$	1.22498	+	0.706697i	0.0774746	+	0.0446954i
$251$	−4.90624	+	8.49786i	−0.309679	+	0.536380i	−0.978292	−	0.207230i	$-0.933555\pi$
$251$	−4.90624	+	8.49786i	−0.309679	+	0.536380i	0.668613	+	0.743611i	$0.266888\pi$
$252$	23.1288	+	18.0805i	1.45698	+	1.13896i
$253$	1.77902	+	3.08135i	0.111846	+	0.193723i
$254$	0.00787602	+	23.5209i	0.000494186	+	1.47583i
$255$	−0.331234	+	0.490574i	−0.0207427	+	0.0307209i
$256$	−7.96285	+	13.8778i	−0.497678	+	0.867362i
$257$	−3.41053	−	4.06451i	−0.212743	−	0.253537i	0.649111	−	0.760694i	$-0.275141\pi$
$257$	−3.41053	−	4.06451i	−0.212743	−	0.253537i	−0.861854	+	0.507156i	$0.830697\pi$
$258$	1.65971	−	0.174211i	0.103329	−	0.0108459i
$259$	−5.72271	−	15.7230i	−0.355592	−	0.976981i
$260$	8.25690	+	1.45021i	0.512071	+	0.0899385i
$261$	−22.5297	−	17.6364i	−1.39455	−	1.09167i
$262$	9.30704	−	7.81485i	0.574991	−	0.482803i
$263$	−3.51612	+	19.9409i	−0.216813	+	1.22961i	0.660919	+	0.750458i	$0.270167\pi$
$263$	−3.51612	+	19.9409i	−0.216813	+	1.22961i	−0.877732	+	0.479152i	$0.840944\pi$
$264$	−19.0015	−	8.44792i	−1.16946	−	0.519933i
$265$	4.21563	+	1.53436i	0.258964	+	0.0942552i
$266$	5.06085	−	28.7578i	0.310301	−	1.76325i
$267$	−1.85372	−	6.47625i	−0.113446	−	0.396340i
$268$	−3.50273	+	0.620045i	−0.213963	+	0.0378753i
$269$		−	12.9713i		−	0.790873i	−0.918493	−	0.395437i	$-0.870593\pi$
$269$		−	12.9713i		−	0.790873i	0.918493	−	0.395437i	$-0.129407\pi$
$270$	3.90084	−	6.22763i	0.237398	−	0.379002i
$271$			3.64870i			0.221643i	0.993840	+	0.110821i	$0.0353481\pi$
$271$			3.64870i			0.221643i	−0.993840	+	0.110821i	$0.964652\pi$
$272$	−1.18477	−	0.681913i	−0.0718372	−	0.0413470i
$273$	34.4636	+	8.61006i	2.08583	+	0.521105i
$274$	1.00912	+	0.177587i	0.0609632	+	0.0107284i
$275$	−3.98874	−	1.45178i	−0.240530	−	0.0875458i
$276$	−1.27341	−	2.60957i	−0.0766502	−	0.157078i
$277$	4.05522	−	22.9983i	0.243655	−	1.38183i	−0.579942	−	0.814658i	$-0.696925\pi$
$277$	4.05522	−	22.9983i	0.243655	−	1.38183i	0.823597	−	0.567176i	$-0.191964\pi$
$278$	−13.2924	−	15.8306i	−0.797228	−	0.949453i
$279$	6.10594	+	28.8604i	0.365553	+	1.72782i
$280$	−6.90751	+	11.9920i	−0.412803	+	0.716657i
$281$	−6.98247	−	19.1842i	−0.416539	−	1.14443i	−0.953649	−	0.300920i	$-0.902706\pi$
$281$	−6.98247	−	19.1842i	−0.416539	−	1.14443i	0.537110	−	0.843512i	$-0.319516\pi$
$282$	9.31355	+	4.14820i	0.554614	+	0.247022i
$283$	16.9229	+	20.1679i	1.00596	+	1.19886i	0.979960	+	0.199195i	$0.0638328\pi$
$283$	16.9229	+	20.1679i	1.00596	+	1.19886i	0.0260009	+	0.999662i	$0.491723\pi$
$284$	−15.1495	+	0.0101457i	−0.898958	+	0.000602036i
$285$	−7.29101	−	0.513301i	−0.431882	−	0.0304053i
$286$	−25.1622	+	0.00842563i	−1.48787	+	0.000498218i
$287$	−23.4392	−	40.5979i	−1.38357	−	2.39642i
$288$	14.9899	+	7.95627i	0.883289	+	0.468828i
$289$	−8.44160	+	14.6213i	−0.496565	+	0.860076i
$290$	6.73993	−	11.6829i	0.395782	−	0.686046i
$291$	0.401219	+	0.178861i	0.0235199	+	0.0104850i
$292$	0.142148	+	0.245827i	0.00831858	+	0.0143859i
$293$	−31.2694	+	5.51365i	−1.82678	+	0.322111i	−0.978312	−	0.207136i	$-0.933586\pi$
$293$	−31.2694	+	5.51365i	−1.82678	+	0.322111i	−0.848468	+	0.529247i	$0.822475\pi$
$294$	−23.2083	+	34.3974i	−1.35353	+	2.00610i
$295$	6.20492	−	7.39473i	0.361264	−	0.430538i
$296$	−4.84459	−	8.37164i	−0.281586	−	0.486592i
$297$	−8.29141	+	20.4385i	−0.481116	+	1.18596i
$298$	−6.35994	+	17.4920i	−0.368421	+	1.01328i
$299$	−2.69153	−	2.25846i	−0.155655	−	0.130610i
$300$	3.16489	+	1.40835i	0.182725	+	0.0813113i
$301$	0.578855	+	3.28285i	0.0333647	+	0.189220i
$302$	−3.60071	+	4.29408i	−0.207198	+	0.247096i
$303$	−5.46551	−	7.53011i	−0.313985	−	0.432593i
$304$	−0.0226086	−	16.8795i	−0.00129669	−	0.968107i
$305$	−2.21194	−	1.27706i	−0.126655	−	0.0731244i
$306$	−0.681478	+	1.27979i	−0.0389575	+	0.0731606i
$307$	−22.4376	+	12.9544i	−1.28058	+	0.739345i	−0.976955	−	0.213446i	$-0.931531\pi$
$307$	−22.4376	+	12.9544i	−1.28058	+	0.739345i	−0.303628	+	0.952791i	$0.598198\pi$
$308$	14.1806	−	39.0422i	0.808015	−	2.22464i
$309$	26.4626	−	12.8912i	1.50541	−	0.733355i
$310$	−13.0658	+	4.76053i	−0.742089	+	0.270380i
$311$	−6.25959	+	5.25242i	−0.354949	+	0.297838i	−0.802774	−	0.596284i	$-0.796643\pi$
$311$	−6.25959	+	5.25242i	−0.354949	+	0.297838i	0.447825	+	0.894121i	$0.352199\pi$
$312$	20.4855	+	1.42154i	1.15976	+	0.0804789i
$313$	−0.310620	+	0.113056i	−0.0175573	+	0.00639033i	−0.350784	−	0.936456i	$-0.614085\pi$
$313$	−0.310620	+	0.113056i	−0.0175573	+	0.00639033i	0.333227	+	0.942847i	$0.391863\pi$
$314$	4.24962	+	24.0537i	0.239820	+	1.35743i
$315$	12.9539	+	6.90343i	0.729870	+	0.388964i
$316$	−0.865623	−	2.37333i	−0.0486951	−	0.133510i
$317$	0.481923	+	0.0849760i	0.0270675	+	0.00477273i	0.187166	−	0.982328i	$-0.440070\pi$
$317$	0.481923	+	0.0849760i	0.0270675	+	0.00477273i	−0.160098	+	0.987101i	$0.551181\pi$
$318$	10.6621	+	2.65991i	0.597899	+	0.149161i
$319$	−13.8460	+	38.0415i	−0.775226	+	2.12992i
$320$	−2.72105	+	7.52302i	−0.152111	+	0.420550i
$321$	12.9636	+	12.5306i	0.723556	+	0.699392i
$322$	5.02209	−	2.90175i	0.279870	−	0.161708i
$323$	1.44214			0.0802430
$324$	7.91043	−	16.1686i	0.439469	−	0.898258i
$325$	4.19165			0.232511
$326$	−16.0300	+	9.26209i	−0.887820	+	0.512979i
$327$	12.4182	+	12.0034i	0.686727	+	0.663792i
$328$	−17.4398	−	20.7416i	−0.962952	−	1.14526i
$329$	−6.96548	+	19.1375i	−0.384019	+	1.05508i
$330$	−10.0882	−	2.51675i	−0.555338	−	0.138543i
$331$	20.0469	+	3.53482i	1.10188	+	0.194291i	0.694872	−	0.719134i	$-0.255461\pi$
$331$	20.0469	+	3.53482i	1.10188	+	0.194291i	0.407008	+	0.913425i	$0.366572\pi$
$332$	12.6111	−	4.59964i	0.692125	−	0.252438i
$333$	−8.70533	+	5.42825i	−0.477049	+	0.297467i
$334$	−0.596763	−	3.37780i	−0.0326534	−	0.184825i
$335$	−1.67133	+	0.608315i	−0.0913145	+	0.0332358i
$336$	−13.7610	+	30.9800i	−0.750725	+	1.69010i
$337$	−4.81682	+	4.04179i	−0.262389	+	0.220170i	−0.764485	−	0.644641i	$-0.777007\pi$
$337$	−4.81682	+	4.04179i	−0.262389	+	0.220170i	0.502096	+	0.864812i	$0.332562\pi$
$338$	6.07231	−	2.21244i	0.330290	−	0.120341i
$339$	14.9350	−	7.27553i	0.811155	−	0.395152i
$340$	−0.642436	−	0.233340i	−0.0348410	−	0.0126547i
$341$	36.1468	−	20.8693i	1.95746	−	1.13014i
$342$	−17.8929	+	0.613895i	−0.967538	+	0.0331956i
$343$	−42.1197	−	24.3178i	−2.27425	−	1.31304i
$344$	0.660891	+	1.81012i	0.0356329	+	0.0975954i
$345$	−0.852819	−	1.17497i	−0.0459142	−	0.0632584i
$346$	−6.13641	+	7.31807i	−0.329896	+	0.393422i
$347$	−0.615165	−	3.48878i	−0.0330238	−	0.187287i	0.963834	−	0.266505i	$-0.0858689\pi$
$347$	−0.615165	−	3.48878i	−0.0330238	−	0.187287i	−0.996857	+	0.0792177i	$0.974758\pi$
$348$	13.4318	−	30.1843i	0.720020	−	1.61805i
$349$	−9.41288	−	7.89835i	−0.503860	−	0.422789i	0.355102	−	0.934827i	$-0.384446\pi$
$349$	−9.41288	−	7.89835i	−0.503860	−	0.422789i	−0.858962	+	0.512039i	$0.828890\pi$
$350$	−2.36445	+	6.50305i	−0.126385	+	0.347602i
$351$	0.790997	−	21.7661i	0.0422203	−	1.16179i
$352$	4.13001	−	23.6540i	0.220130	−	1.26076i
$353$	−6.31403	+	7.52477i	−0.336062	+	0.400503i	−0.907438	−	0.420185i	$-0.861965\pi$
$353$	−6.31403	+	7.52477i	−0.336062	+	0.400503i	0.571376	+	0.820688i	$0.306410\pi$
$354$	13.2250	−	19.6010i	0.702899	−	1.04178i
$355$	−7.45968	+	1.31534i	−0.395919	+	0.0698111i
$356$	6.73372	−	3.89373i	0.356886	−	0.206367i
$357$	−2.64527	−	1.17925i	−0.140003	−	0.0624125i
$358$	4.04670	−	7.01452i	0.213875	−	0.370729i
$359$	15.6457	−	27.0992i	0.825750	−	1.43024i	−0.0755956	−	0.997139i	$-0.524086\pi$
$359$	15.6457	−	27.0992i	0.825750	−	1.43024i	0.901345	−	0.433102i	$-0.142581\pi$
$360$	8.07014	+	2.62162i	0.425334	+	0.138171i
$361$	−0.596290	−	1.03280i	−0.0313837	−	0.0543581i
$362$	6.52136	−	0.00218369i	0.342755	−	0.000114772i
$363$	12.1250	+	0.853624i	0.636398	+	0.0448036i
$364$	0.0274701	+	41.0183i	0.00143983	+	2.14994i
$365$	0.0912651	+	0.108765i	0.00477703	+	0.00569304i
$366$	−5.71507	−	2.54546i	−0.298732	−	0.133053i
$367$	−1.49925	−	4.11917i	−0.0782604	−	0.215019i	0.894392	−	0.447284i	$-0.147609\pi$
$367$	−1.49925	−	4.11917i	−0.0782604	−	0.215019i	−0.972653	+	0.232265i	$0.925386\pi$
$368$	2.56558	−	2.15864i	0.133740	−	0.112527i
$369$	−21.3783	+	19.2126i	−1.11291	+	1.00017i
$370$	−3.10987	−	3.70368i	−0.161675	−	0.192545i
$371$	−3.81162	+	21.6168i	−0.197890	+	1.12229i
$372$	−30.6124	+	14.9382i	−1.58718	+	0.774507i
$373$	22.4501	+	8.17115i	1.16242	+	0.423086i	0.849961	−	0.526845i	$-0.176625\pi$
$373$	22.4501	+	8.17115i	1.16242	+	0.423086i	0.312459	+	0.949931i	$0.398847\pi$
$374$	2.02046	+	0.355564i	0.104475	+	0.0183858i
$375$	1.68040	+	0.419815i	0.0867756	+	0.0216792i
$376$	−2.03268	+	11.5960i	−0.104828	+	0.598019i
$377$		−	39.9767i		−	2.05891i
$378$	33.3223	+	13.5051i	1.71392	+	0.694628i
$379$		−	21.0859i		−	1.08311i	−0.840665	−	0.541555i	$-0.817836\pi$
$379$		−	21.0859i		−	1.08311i	0.840665	−	0.541555i	$-0.182164\pi$
$380$	−1.47112	−	8.31057i	−0.0754667	−	0.426323i
$381$	7.92722	+	27.6949i	0.406124	+	1.41885i
$382$	5.08356	−	28.8869i	0.260098	−	1.47798i
$383$	7.89751	+	2.87446i	0.403544	+	0.146878i	0.535815	−	0.844336i	$-0.320005\pi$
$383$	7.89751	+	2.87446i	0.403544	+	0.146878i	−0.132271	+	0.991214i	$0.542227\pi$
$384$	−4.70509	+	19.0227i	−0.240106	+	0.970747i
$385$	3.60648	−	20.4533i	0.183803	−	1.04240i
$386$	19.7886	−	16.6159i	1.00721	−	0.845727i
$387$	1.89579	−	0.763863i	0.0963683	−	0.0388294i
$388$	−0.0877464	+	0.499591i	−0.00445465	+	0.0253629i
$389$	−7.24995	−	19.9191i	−0.367587	−	1.00994i	−0.976276	−	0.216528i	$-0.930527\pi$
$389$	−7.24995	−	19.9191i	−0.367587	−	1.00994i	0.608689	−	0.793409i	$-0.291696\pi$
$390$	10.2113	−	1.07183i	0.517069	−	0.0542741i
$391$	0.184135	+	0.219443i	0.00931209	+	0.0110977i
$392$	−45.0408	−	16.3423i	−2.27490	−	0.825410i
$393$	8.32897	−	12.3356i	0.420141	−	0.622250i
$394$	0.00606147	+	18.1019i	0.000305373	+	0.911963i
$395$	−0.631566	−	1.09390i	−0.0317775	−	0.0550403i
$396$	−25.2195	−	3.55147i	−1.26733	−	0.178468i
$397$	−11.9390	+	20.6790i	−0.599203	+	1.03785i	0.393736	+	0.919224i	$0.371182\pi$
$397$	−11.9390	+	20.6790i	−0.599203	+	1.03785i	−0.992939	+	0.118627i	$0.962151\pi$
$398$	28.3378	+	16.3482i	1.42044	+	0.819459i
$399$	−3.72135	−	35.5681i	−0.186301	−	1.78063i
$400$	−0.689316	+	3.94016i	−0.0344658	+	0.197008i
$401$	15.6733	−	2.76363i	0.782688	−	0.138009i	0.231995	−	0.972717i	$-0.425475\pi$
$401$	15.6733	−	2.76363i	0.782688	−	0.138009i	0.550693	+	0.834708i	$0.314364\pi$
$402$	−3.91599	+	1.90929i	−0.195312	+	0.0952266i
$403$	−26.4936	+	31.5738i	−1.31974	+	1.57281i
$404$	6.90056	−	8.23496i	0.343316	−	0.409705i
$405$	2.49709	−	8.64665i	0.124081	−	0.429655i
$406$	62.0211	+	22.5503i	3.07805	+	1.11915i
$407$	11.1196	+	9.33049i	0.551180	+	0.462495i
$408$	−1.62471	−	0.404168i	−0.0804350	−	0.0200093i
$409$	3.21241	+	18.2185i	0.158844	+	0.900847i	0.955187	+	0.296002i	$0.0956536\pi$
$409$	3.21241	+	18.2185i	0.158844	+	0.900847i	−0.796344	+	0.604844i	$0.793235\pi$
$410$	−10.3825	−	8.70600i	−0.512753	−	0.429959i
$411$	1.24810	−	0.130584i	0.0615640	−	0.00644121i
$412$	21.8653	+	26.0227i	1.07723	+	1.28204i
$413$	40.9037	+	23.6157i	2.01274	+	1.16206i
$414$	−2.37800	−	2.64429i	−0.116872	−	0.129960i
$415$	5.81266	−	3.35594i	0.285332	−	0.164737i
$416$	4.15655	+	23.3444i	0.203792	+	1.14455i
$417$	−20.9819	−	14.1669i	−1.02749	−	0.693757i
$418$	8.67194	+	23.8012i	0.424158	+	1.16415i
$419$	−5.00868	+	4.20278i	−0.244690	+	0.205319i	−0.756882	−	0.653552i	$-0.773278\pi$
$419$	−5.00868	+	4.20278i	−0.244690	+	0.205319i	0.512192	+	0.858871i	$0.328834\pi$
$420$	−4.09719	+	16.4467i	−0.199922	+	0.802518i
$421$	1.80540	−	0.657111i	0.0879897	−	0.0320256i	−0.297650	−	0.954675i	$-0.596203\pi$
$421$	1.80540	−	0.657111i	0.0879897	−	0.0320256i	0.385640	+	0.922649i	$0.373981\pi$
$422$	12.8598	−	2.27197i	0.626004	−	0.110598i
$423$	12.3638	+	1.74954i	0.601149	+	0.0850656i
$424$	0.0127466	+	12.6888i	0.000619032	+	0.616224i
$425$	−0.336558	−	0.0593442i	−0.0163254	−	0.00287862i
$426$	−17.8362	+	5.11179i	−0.864168	+	0.247667i
$427$	4.27422	−	11.7433i	0.206844	−	0.568300i
$428$	−10.3974	+	18.0367i	−0.502577	+	0.871837i
$429$	−29.6275	+	8.48040i	−1.43043	+	0.409438i
$430$	0.482029	+	0.834254i	0.0232455	+	0.0402313i
$431$	−25.6608			−1.23604			−0.618018	−	0.786164i	$-0.712064\pi$
$431$	−25.6608			−1.23604			−0.618018	+	0.786164i	$0.712064\pi$
$432$	20.3301	+	4.32297i	0.978131	+	0.207989i
$433$	11.1869			0.537607			0.268804	−	0.963195i	$-0.413372\pi$
$433$	11.1869			0.537607			0.268804	+	0.963195i	$0.413372\pi$
$434$	−34.0399	−	58.9134i	−1.63397	−	2.82793i
$435$	4.00388	−	16.0264i	0.191971	−	0.768407i
$436$	−9.95995	+	17.2779i	−0.476995	+	0.827459i
$437$	−1.20980	+	3.32389i	−0.0578724	+	0.159003i
$438$	0.250143	+	0.241627i	0.0119523	+	0.0115454i
$439$	−3.20948	−	0.565917i	−0.153180	−	0.0270098i	0.0965322	−	0.995330i	$-0.469225\pi$
$439$	−3.20948	−	0.565917i	−0.153180	−	0.0270098i	−0.249712	+	0.968320i	$0.580336\pi$
$440$	−0.0120606	−	12.0059i	−0.000574966	−	0.572359i
$441$	−15.7500	+	48.3182i	−0.750002	+	2.30086i
$442$	−1.99496	+	0.352454i	−0.0948904	+	0.0167645i
$443$	4.14433	−	1.50841i	0.196903	−	0.0716669i	−0.241686	−	0.970354i	$-0.577700\pi$
$443$	4.14433	−	1.50841i	0.196903	−	0.0716669i	0.438589	+	0.898688i	$0.355478\pi$
$444$	−8.52304	−	8.22736i	−0.404485	−	0.390453i
$445$	2.97931	−	2.49994i	0.141233	−	0.118509i
$446$	−1.92055	−	5.27119i	−0.0909409	−	0.249598i
$447$	−1.60087	+	22.7391i	−0.0757187	+	1.07552i
$448$	−38.5618	−	6.71963i	−1.82187	−	0.317473i
$449$	−6.48399	+	3.74353i	−0.305998	+	0.176668i	−0.645134	−	0.764069i	$-0.723199\pi$
$449$	−6.48399	+	3.74353i	−0.305998	+	0.176668i	0.339136	+	0.940737i	$0.389865\pi$
$450$	4.20099	+	0.593027i	0.198037	+	0.0279556i
$451$	35.2200	+	20.3343i	1.65845	+	0.957505i
$452$	12.3403	+	14.6866i	0.580440	+	0.690802i
$453$	−2.79456	+	6.26871i	−0.131300	+	0.294530i
$454$	−6.76377	−	5.67162i	−0.317440	−	0.266182i
$455$	3.56138	+	20.1976i	0.166960	+	0.946877i
$456$	−5.70885	−	19.8693i	−0.267342	−	0.930463i
$457$	26.8546	+	22.5336i	1.25620	+	1.05408i	0.996076	+	0.0885052i	$0.0282090\pi$
$457$	26.8546	+	22.5336i	1.25620	+	1.05408i	0.260127	+	0.965574i	$0.416235\pi$
$458$	3.44443	+	1.25236i	0.160948	+	0.0585191i
$459$	−0.371669	+	1.73645i	−0.0173480	+	0.0810507i
$460$	1.07674	−	1.28495i	0.0502032	−	0.0599113i
$461$	6.47980	−	7.72233i	0.301795	−	0.359665i	−0.593740	−	0.804657i	$-0.702349\pi$
$461$	6.47980	−	7.72233i	0.301795	−	0.359665i	0.895534	+	0.444992i	$0.146794\pi$
$462$	3.55573	−	50.7487i	0.165427	−	2.36104i
$463$	3.25602	−	0.574124i	0.151320	−	0.0266818i	−0.0974749	−	0.995238i	$-0.531077\pi$
$463$	3.25602	−	0.574124i	0.151320	−	0.0266818i	0.248795	+	0.968556i	$0.419965\pi$
$464$	37.5782	+	6.57417i	1.74452	+	0.305198i
$465$	−13.7834	+	10.0043i	−0.639190	+	0.463937i
$466$	6.72404	+	3.87912i	0.311485	+	0.179697i
$467$	−9.51439	+	16.4794i	−0.440273	+	0.762576i	−0.997710	−	0.0676440i	$-0.978452\pi$
$467$	−9.51439	+	16.4794i	−0.440273	+	0.762576i	0.557436	+	0.830220i	$0.311785\pi$
$468$	24.6017	−	5.22217i	1.13722	−	0.241395i
$469$	−4.35121	−	7.53651i	−0.200920	−	0.348004i
$470$	0.00197108	+	5.88642i	9.09190e−5	+	0.271520i
$471$	13.1015	+	26.8944i	0.603686	+	1.23923i
$472$	25.6660	+	9.31247i	1.18137	+	0.428641i
$473$	−1.85889	−	2.21534i	−0.0854719	−	0.101861i
$474$	−1.81828	−	2.50337i	−0.0835163	−	0.114984i
$475$	−1.44329	−	3.96539i	−0.0662225	−	0.181945i
$476$	0.578520	−	3.29385i	0.0265164	−	0.150973i
$477$	13.4508	−	0.456979i	0.615869	−	0.0209236i
$478$	18.3197	−	15.3826i	0.837926	−	0.703582i
$479$	0.562418	−	3.18963i	0.0256975	−	0.145738i	−0.969259	−	0.246041i	$-0.920870\pi$
$479$	0.562418	−	3.18963i	0.0256975	−	0.145738i	0.994957	+	0.100303i	$0.0319813\pi$
$480$	−0.671727	+	9.77491i	−0.0306600	+	0.446161i
$481$	−13.4697	−	4.90257i	−0.614165	−	0.223538i
$482$	0.757936	−	4.30690i	0.0345230	−	0.196174i
$483$	4.93705	−	5.10763i	0.224644	−	0.232405i
$484$	2.44648	+	13.8205i	0.111204	+	0.628207i
$485$			0.253619i			0.0115162i
$486$	3.87219	−	21.7027i	0.175646	−	0.984453i
$487$			3.81047i			0.172669i	0.996266	+	0.0863345i	$0.0275154\pi$
$487$			3.81047i			0.172669i	−0.996266	+	0.0863345i	$0.972485\pi$
$488$	1.24732	−	7.11567i	0.0564633	−	0.322111i
$489$	−15.7586	+	16.3030i	−0.712627	+	0.737249i
$490$	−23.5944	−	4.15218i	−1.06589	−	0.187576i
$491$	9.42612	+	3.43083i	0.425395	+	0.154831i	0.545841	−	0.837889i	$-0.316210\pi$
$491$	9.42612	+	3.43083i	0.425395	+	0.154831i	−0.120446	+	0.992720i	$0.538432\pi$
$492$	−27.5190	−	18.5539i	−1.24065	−	0.836474i
$493$	−0.565980	+	3.20983i	−0.0254904	+	0.144563i
$494$	−16.0857	−	19.1572i	−0.723731	−	0.861923i
$495$	−12.7268	+	0.432383i	−0.572029	+	0.0194342i
$496$	−25.3226	−	30.0964i	−1.13702	−	1.35137i
$497$	−12.6760	−	34.8271i	−0.568598	−	1.56221i
$498$	13.3021	−	9.66175i	0.596082	−	0.432953i
$499$	10.5537	+	12.5774i	0.472447	+	0.563041i	0.948663	−	0.316288i	$-0.102436\pi$
$499$	10.5537	+	12.5774i	0.472447	+	0.563041i	−0.476216	+	0.879328i	$0.657992\pi$
$500$	0.00133941	+	2.00000i	5.99001e−5	+	0.0894427i
$501$	−1.83981	−	3.77671i	−0.0821968	−	0.168731i
$502$	−13.8770	+	0.00464673i	−0.619359	+	0.000207394i
$503$	−0.734881	−	1.27285i	−0.0327667	−	0.0567536i	0.849177	−	0.528108i	$-0.177099\pi$
$503$	−0.734881	−	1.27285i	−0.0327667	−	0.0567536i	−0.881944	+	0.471355i	$0.843765\pi$
$504$	−5.77567	+	41.1136i	−0.257269	+	1.83135i
$505$	2.68599	−	4.65227i	0.119525	−	0.207023i
$506$	−2.51445	+	4.35852i	−0.111781	+	0.193760i
$507$	6.40581	−	4.64946i	0.284492	−	0.206490i
$508$	−28.7960	+	16.6511i	−1.27761	+	0.738772i
$509$	19.9765	−	3.52239i	0.885442	−	0.156127i	0.287609	−	0.957748i	$-0.407140\pi$
$509$	19.9765	−	3.52239i	0.885442	−	0.156127i	0.597833	+	0.801621i	$0.296029\pi$
$510$	−0.835065	−	0.0585092i	−0.0369773	−	0.00259083i
$511$	−0.446547	+	0.532175i	−0.0197541	+	0.0235420i
$512$	−22.6273	+	0.0681914i	−0.999995	+	0.00301366i
$513$	−20.8636	+	6.74628i	−0.921149	+	0.297856i
$514$	2.56402	−	7.05193i	0.113094	−	0.311047i
$515$	13.0186	+	10.9239i	0.573670	+	0.481366i
$516$	1.38760	+	1.90907i	0.0610856	+	0.0840423i
$517$	−3.06800	−	17.3995i	−0.134931	−	0.765230i
$518$	15.2041	−	18.1318i	0.668028	−	0.796666i
$519$	−4.76256	+	10.6833i	−0.209053	+	0.468944i
$520$	4.06610	+	11.1367i	0.178310	+	0.488376i
$521$	−0.500010	−	0.288681i	−0.0219059	−	0.0126473i	0.489007	−	0.872280i	$-0.337359\pi$
$521$	−0.500010	−	0.288681i	−0.0219059	−	0.0126473i	−0.510913	+	0.859632i	$0.670693\pi$
$522$	5.65584	−	40.0658i	0.247549	−	1.75363i
$523$	−0.721015	+	0.416278i	−0.0315278	+	0.0182026i	−0.515681	−	0.856781i	$-0.672461\pi$
$523$	−0.721015	+	0.416278i	−0.0315278	+	0.0182026i	0.484153	+	0.874983i	$0.339128\pi$
$524$	16.1542	+	5.86741i	0.705701	+	0.256319i
$525$	−0.595161	+	8.45376i	−0.0259750	+	0.368953i
$526$	−26.9055	+	9.80301i	−1.17314	+	0.427432i
$527$	2.57425	−	2.16005i	0.112136	−	0.0940934i
$528$	−3.09935	−	29.2446i	−0.134882	−	1.27271i
$529$	20.9527	−	7.62615i	0.910986	−	0.331572i
$530$	1.10379	+	6.24766i	0.0479455	+	0.271381i
$531$	8.97499	−	27.5336i	0.389481	−	1.19486i
$532$	38.7948	−	14.1496i	1.68197	−	0.613462i
$533$	−39.5499	−	6.97372i	−1.71310	−	0.302065i
$534$	6.61868	−	6.85195i	0.286418	−	0.296513i
$535$	−3.56025	+	9.78170i	−0.153923	+	0.422900i
$536$	−3.23749	−	3.85043i	−0.139838	−	0.166313i
$537$	2.40396	−	9.62237i	0.103738	−	0.415236i
$538$	15.8834	−	9.17740i	0.684784	−	0.395666i
$539$	71.9062			3.09722
$540$	10.3857	+	0.370461i	0.446929	+	0.0159421i
$541$	0.684258			0.0294186			0.0147093	−	0.999892i	$-0.495318\pi$
$541$	0.684258			0.0294186			0.0147093	+	0.999892i	$0.495318\pi$
$542$	−4.46786	+	2.58152i	−0.191911	+	0.110886i
$543$	7.67863	−	2.19789i	0.329522	−	0.0943203i
$544$	−0.00323672	−	1.93323i	−0.000138773	−	0.0828863i
$545$	−3.41046	+	9.37017i	−0.146088	+	0.401374i
$546$	13.8405	+	48.2928i	0.592320	+	2.06674i
$547$	2.80558	+	0.494699i	0.119958	+	0.0211518i	0.233305	−	0.972404i	$-0.425046\pi$
$547$	2.80558	+	0.494699i	0.119958	+	0.0211518i	−0.113347	+	0.993555i	$0.536157\pi$
$548$	0.496514	+	1.36132i	0.0212100	+	0.0581528i
$549$	−7.58680	−	1.07357i	−0.323797	−	0.0458189i
$550$	−1.04438	−	5.91140i	−0.0445326	−	0.252063i
$551$	−37.8189	+	13.7650i	−1.61114	+	0.586407i
$552$	2.29448	−	3.40562i	0.0976597	−	0.144953i
$553$	4.73441	−	3.97264i	0.201328	−	0.168934i
$554$	31.0307	−	11.3060i	1.31837	−	0.480347i
$555$	−4.90889	−	3.31447i	−0.208371	−	0.140691i
$556$	9.98001	−	27.4771i	0.423247	−	1.16529i
$557$	−16.7235	+	9.65534i	−0.708599	+	0.409110i	−0.810542	−	0.585680i	$-0.800827\pi$
$557$	−16.7235	+	9.65534i	−0.708599	+	0.409110i	0.101943	+	0.994790i	$0.467494\pi$
$558$	−31.0197	+	27.8960i	−1.31317	+	1.18093i
$559$	2.47316	+	1.42788i	0.104603	+	0.0603928i
$560$	−19.5714	+	0.0262142i	−0.827044	+	0.00110775i
$561$	2.49893	−	0.261454i	0.105505	−	0.0110386i
$562$	18.5510	−	22.1232i	0.782526	−	0.933212i
$563$	3.08191	+	17.4784i	0.129887	+	0.736626i	0.978285	+	0.207266i	$0.0664566\pi$
$563$	3.08191	+	17.4784i	0.129887	+	0.736626i	−0.848398	+	0.529360i	$0.822432\pi$
$564$	1.50999	+	14.3394i	0.0635821	+	0.603799i
$565$	7.34746	+	6.16525i	0.309110	+	0.259374i
$566$	−12.7225	+	34.9913i	−0.534768	+	1.47080i
$567$	43.7858	+	4.68580i	1.83883	+	0.196785i
$568$	−10.7310	−	18.5435i	−0.450261	−	0.778068i
$569$	12.0208	−	14.3259i	0.503940	−	0.600572i	−0.452766	−	0.891629i	$-0.649563\pi$
$569$	12.0208	−	14.3259i	0.503940	−	0.600572i	0.956706	+	0.291057i	$0.0940071\pi$
$570$	−4.52997	−	9.29107i	−0.189740	−	0.389160i
$571$	16.1788	−	2.85276i	0.677063	−	0.119384i	0.175466	−	0.984486i	$-0.443857\pi$
$571$	16.1788	−	2.85276i	0.677063	−	0.119384i	0.501598	+	0.865101i	$0.332746\pi$
$572$	−17.8130	−	30.8054i	−0.744800	−	1.28804i
$573$	−3.73806	−	35.7277i	−0.156160	−	1.49255i
$574$	33.1288	−	57.4252i	1.38277	−	2.39688i
$575$	0.419112	−	0.725923i	0.0174782	−	0.0302731i
$576$	0.863098	+	23.9845i	0.0359624	+	0.999353i
$577$	11.4843	+	19.8915i	0.478099	+	0.828092i	0.999685	−	0.0251068i	$-0.00799258\pi$
$577$	11.4843	+	19.8915i	0.478099	+	0.828092i	−0.521585	+	0.853199i	$0.674659\pi$
$578$	−23.8765	+	0.00799508i	−0.993130	+	0.000332552i
$579$	17.7090	−	26.2280i	0.735962	−	1.09000i
$580$	19.0745	−	0.0127742i	0.792024	−	0.000530422i
$581$	21.1093	+	25.1571i	0.875763	+	1.04369i
$582$	0.0648518	+	0.617843i	0.00268819	+	0.0256104i
$583$	−6.51295	−	17.8942i	−0.269739	−	0.741102i
$584$	−0.200445	+	0.347988i	−0.00829448	+	0.0143998i
$585$	11.6637	−	4.69963i	0.482236	−	0.194306i
$586$	−28.8752	−	34.3887i	−1.19282	−	1.42058i
$587$	4.45884	−	25.2874i	0.184036	−	1.04372i	−0.743151	−	0.669123i	$-0.766670\pi$
$587$	4.45884	−	25.2874i	0.184036	−	1.04372i	0.927187	−	0.374598i	$-0.122219\pi$
$588$	−58.5402	−	4.08194i	−2.41416	−	0.168336i
$589$	38.9920	+	14.1919i	1.60664	+	0.584768i
$590$	13.4450	+	2.36607i	0.553522	+	0.0974097i
$591$	6.10088	+	21.3143i	0.250957	+	0.876754i
$592$	6.82351	−	11.8553i	0.280445	−	0.487250i
$593$			40.4426i			1.66078i	0.557184	+	0.830389i	$0.311882\pi$
$593$			40.4426i			1.66078i	−0.557184	+	0.830389i	$0.688118\pi$
$594$	−30.8934	+	4.30765i	−1.26757	+	0.176745i
$595$		−	1.67213i		−	0.0685508i
$596$	−25.9189	+	4.58809i	−1.06168	+	0.187936i
$597$	38.8731	+	9.71168i	1.59097	+	0.397473i
$598$	0.861201	−	4.89369i	0.0352171	−	0.200118i
$599$	32.5226	+	11.8373i	1.32884	+	0.483658i	0.906280	−	0.422678i	$-0.138910\pi$
$599$	32.5226	+	11.8373i	1.32884	+	0.483658i	0.422558	+	0.906336i	$0.361132\pi$
$600$	0.514674	+	4.87187i	0.0210115	+	0.198893i
$601$	−4.51409	+	25.6007i	−0.184134	+	1.04427i	0.742930	+	0.669369i	$0.233436\pi$
$601$	−4.51409	+	25.6007i	−0.184134	+	1.04427i	−0.927064	+	0.374904i	$0.877676\pi$
$602$	−3.61033	+	3.03149i	−0.147146	+	0.123554i
$603$	−3.96863	+	3.56658i	−0.161615	+	0.145242i
$604$	−7.80570	−	1.37097i	−0.317609	−	0.0557838i
$605$	2.40020	+	6.59449i	0.0975819	+	0.268104i
$606$	5.35374	−	12.0202i	0.217481	−	0.488289i
$607$	−26.4194	−	31.4854i	−1.07233	−	1.27795i	−0.958696	−	0.284431i	$-0.908195\pi$
$607$	−26.4194	−	31.4854i	−1.07233	−	1.27795i	−0.113634	−	0.993523i	$-0.536249\pi$
$608$	20.6531	−	11.9702i	0.837594	−	0.485457i
$609$	80.6255	+	5.67619i	3.26711	+	0.230011i
$610$	−0.00120951	−	3.61208i	−4.89717e−5	−	0.146249i
$611$	8.72350	+	15.1095i	0.352915	+	0.611266i
$612$	−2.04927	+	0.0709961i	−0.0828368	+	0.00286985i
$613$	15.4590	−	26.7758i	0.624383	−	1.08146i	−0.364277	−	0.931291i	$-0.618684\pi$
$613$	15.4590	−	26.7758i	0.624383	−	1.08146i	0.988660	−	0.150173i	$-0.0479829\pi$
$614$	−31.7377	−	18.3096i	−1.28083	−	0.738916i
$615$	−15.1568	−	6.75685i	−0.611183	−	0.272463i
$616$	57.8405	−	10.2588i	2.33046	−	0.413337i
$617$	30.7668	−	5.42502i	1.23862	−	0.218403i	0.484298	−	0.874903i	$-0.339075\pi$
$617$	30.7668	−	5.42502i	1.23862	−	0.218403i	0.754326	+	0.656500i	$0.227964\pi$
$618$	34.5081	+	23.2829i	1.38812	+	0.936577i
$619$	−11.8866	+	14.1659i	−0.477762	+	0.569374i	−0.950061	−	0.312064i	$-0.898980\pi$
$619$	−11.8866	+	14.1659i	−0.477762	+	0.569374i	0.472299	+	0.881438i	$0.343424\pi$
$620$	−15.0736	−	12.6311i	−0.605370	−	0.507275i
$621$	−3.69043	−	2.31332i	−0.148092	−	0.0928304i
$622$	−10.8604	−	3.94874i	−0.435462	−	0.158330i
$623$	14.5774	+	12.2319i	0.584030	+	0.490060i
$624$	12.7532	+	26.0905i	0.510535	+	1.04445i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−0.358207	−	0.300367i	−0.0143168	−	0.0120051i
$627$	18.2241	+	25.1083i	0.727802	+	1.00273i
$628$	−26.4472	+	22.2221i	−1.05536	+	0.886757i
$629$	1.01211	+	0.584339i	0.0403553	+	0.0232991i
$630$	0.711798	+	20.7465i	0.0283587	+	0.826559i
$631$	−36.3571	+	20.9908i	−1.44735	+	0.835630i	−0.998323	−	0.0578859i	$-0.981564\pi$
$631$	−36.3571	+	20.9908i	−1.44735	+	0.835630i	−0.449031	+	0.893516i	$0.648231\pi$
$632$	2.29372	−	2.73913i	0.0912393	−	0.108957i
$633$	14.3785	−	7.00445i	0.571494	−	0.278402i
$634$	0.236915	+	0.650240i	0.00940908	+	0.0258243i
$635$	−12.7407	+	10.6907i	−0.505599	+	0.424248i
$636$	4.28651	+	14.9377i	0.169971	+	0.592319i
$637$	−66.7247	+	24.2858i	−2.64373	+	0.962239i
$638$	−56.3784	+	9.96051i	−2.23204	+	0.394340i
$639$	−19.2826	+	12.0238i	−0.762810	+	0.475654i
$640$	−11.1372	+	1.99072i	−0.440236	+	0.0786899i
$641$	19.6448	+	3.46390i	0.775922	+	0.136816i	0.547567	−	0.836762i	$-0.315554\pi$
$641$	19.6448	+	3.46390i	0.775922	+	0.136816i	0.228355	+	0.973578i	$0.426665\pi$
$642$	−6.17191	+	24.7396i	−0.243586	+	0.976396i
$643$	14.2006	−	39.0159i	0.560017	−	1.53864i	−0.259595	−	0.965717i	$-0.583589\pi$
$643$	14.2006	−	39.0159i	0.560017	−	1.53864i	0.819613	−	0.572918i	$-0.194189\pi$
$644$	7.10643	+	4.09656i	0.280033	+	0.161427i
$645$	0.848463	+	0.820127i	0.0334082	+	0.0322925i
$646$	1.02034	+	1.76592i	0.0401448	+	0.0694791i
$647$	33.7400			1.32646			0.663228	−	0.748418i	$-0.269186\pi$
$647$	33.7400			1.32646			0.663228	+	0.748418i	$0.269186\pi$
$648$	25.3954	−	1.75320i	0.997625	−	0.0688721i
$649$	−40.9749			−1.60841
$650$	2.96566	+	5.13270i	0.116323	+	0.201321i
$651$	−59.9168	−	57.9157i	−2.34832	−	2.26990i
$652$	−22.6830	−	13.0758i	−0.888335	−	0.512087i
$653$	−8.87123	+	24.3735i	−0.347158	+	0.953809i	0.636103	+	0.771605i	$0.280546\pi$
$653$	−8.87123	+	24.3735i	−0.347158	+	0.953809i	−0.983261	+	0.182205i	$0.941677\pi$
$654$	−5.91224	+	23.6988i	−0.231187	+	0.926696i
$655$	8.46284	+	1.49223i	0.330671	+	0.0583062i
$656$	13.0593	−	36.0302i	0.509880	−	1.40674i
$657$	0.375902	+	0.200327i	0.0146653	+	0.00781549i
$658$	−28.3622	+	5.01081i	−1.10567	+	0.195342i
$659$	−25.0168	+	9.10537i	−0.974516	+	0.354695i	−0.779706	−	0.626146i	$-0.784631\pi$
$659$	−25.0168	+	9.10537i	−0.974516	+	0.354695i	−0.194810	+	0.980841i	$0.562409\pi$
$660$	−4.05580	−	14.1338i	−0.157872	−	0.550156i
$661$	0.251454	−	0.210995i	0.00978041	−	0.00820674i	−0.637884	−	0.770132i	$-0.720190\pi$
$661$	0.251454	−	0.210995i	0.00978041	−	0.00820674i	0.647665	+	0.761925i	$0.275746\pi$
$662$	9.85514	+	27.0486i	0.383031	+	1.05127i
$663$	−2.23056	+	1.08661i	−0.0866277	+	0.0422005i
$664$	14.5549	+	12.1881i	0.564839	+	0.472990i
$665$	17.8811	−	10.3237i	0.693399	−	0.400334i
$666$	−12.8061	−	6.81916i	−0.496227	−	0.264237i
$667$	−6.92330	−	3.99717i	−0.268071	−	0.154771i
$668$	3.71392	−	3.12059i	0.143696	−	0.120739i
$669$	−4.03605	−	5.56068i	−0.156043	−	0.214988i
$670$	−1.92738	−	1.61616i	−0.0744612	−	0.0624379i
$671$	1.88262	+	10.6769i	0.0726777	+	0.412176i
$672$	−47.6714	+	5.06838i	−1.83896	+	0.195517i
$673$	−29.3779	−	24.6510i	−1.13243	−	0.950225i	−0.133269	−	0.991080i	$-0.542547\pi$
$673$	−29.3779	−	24.6510i	−1.13243	−	0.950225i	−0.999165	+	0.0408553i	$0.986992\pi$
$674$	−8.35718	−	3.03860i	−0.321907	−	0.117042i
$675$	5.14660	−	0.715866i	0.198093	−	0.0275537i
$676$	7.00542	+	5.87026i	0.269439	+	0.225779i
$677$	−17.2004	+	20.4986i	−0.661064	+	0.787825i	−0.987538	−	0.157381i	$-0.949695\pi$
$677$	−17.2004	+	20.4986i	−0.661064	+	0.787825i	0.326474	+	0.945206i	$0.394139\pi$
$678$	19.4757	+	13.1404i	0.747959	+	0.504655i
$679$	−1.22207	+	0.215484i	−0.0468988	+	0.00826952i
$680$	−0.168807	−	0.951760i	−0.00647345	−	0.0364983i
$681$	−9.87409	−	4.40182i	−0.378376	−	0.168678i
$682$	51.1291	+	29.4966i	1.95783	+	1.12948i
$683$	−4.27114	+	7.39783i	−0.163431	+	0.283070i	−0.936097	−	0.351742i	$-0.885589\pi$
$683$	−4.27114	+	7.39783i	−0.163431	+	0.283070i	0.772666	+	0.634813i	$0.218923\pi$
$684$	−13.4113	−	21.4757i	−0.512793	−	0.821143i
$685$	0.362261	+	0.627454i	0.0138413	+	0.0239738i
$686$	−0.0230315	−	68.7812i	−0.000879348	−	2.62608i
$687$	4.47765	+	0.315235i	0.170833	+	0.0120270i
$688$	−1.74892	+	2.08996i	−0.0666770	+	0.0796790i
$689$	12.0873	+	14.4051i	0.460489	+	0.548789i
$690$	0.835379	−	1.87560i	0.0318023	−	0.0714027i
$691$	−3.93765	−	10.8186i	−0.149795	−	0.411559i	0.841987	−	0.539498i	$-0.181386\pi$
$691$	−3.93765	−	10.8186i	−0.149795	−	0.411559i	−0.991782	+	0.127939i	$0.959164\pi$
$692$	−13.3026	−	2.33643i	−0.505691	−	0.0888178i
$693$	−12.8966	−	60.9573i	−0.489903	−	2.31558i
$694$	3.83679	−	3.22164i	0.145643	−	0.122292i
$695$	2.53816	−	14.3946i	0.0962780	−	0.546020i
$696$	46.4642	−	4.90856i	1.76122	−	0.186059i
$697$	3.07683	+	1.11987i	0.116543	+	0.0424183i
$698$	3.01182	−	17.1144i	0.113999	−	0.647788i
$699$	9.22389	+	2.30441i	0.348880	+	0.0871607i
$700$	−9.63592	+	1.70573i	−0.364204	+	0.0644704i
$701$			22.3369i			0.843652i	0.906677	+	0.421826i	$0.138611\pi$
$701$			22.3369i			0.843652i	−0.906677	+	0.421826i	$0.861389\pi$
$702$	27.2124	−	14.4313i	1.02706	−	0.544673i
$703$			14.4307i			0.544264i
$704$	31.8865	−	11.6783i	1.20177	−	0.440144i
$705$	1.98389	+	6.93102i	0.0747177	+	0.261037i
$706$	−13.6814	−	2.40768i	−0.514907	−	0.0906143i
$707$	24.6992	+	8.98977i	0.928909	+	0.338095i
$708$	33.3585	+	2.32605i	1.25369	+	0.0874183i
$709$	2.49989	−	14.1776i	0.0938852	−	0.532450i	−0.901198	−	0.433408i	$-0.857311\pi$
$709$	2.49989	−	14.1776i	0.0938852	−	0.532450i	0.995083	−	0.0990420i	$-0.0315778\pi$
$710$	−6.88849	−	8.20381i	−0.258521	−	0.307883i
$711$	−2.98388	−	2.33581i	−0.111904	−	0.0875996i
$712$	9.53212	+	5.49061i	0.357231	+	0.205769i
$713$	2.81904	+	7.74524i	0.105574	+	0.290061i
$714$	−0.427574	−	4.07350i	−0.0160016	−	0.152447i
$715$	−11.4367	−	13.6298i	−0.427709	−	0.509724i
$716$	11.4524	−	0.00766975i	0.427998	−	0.000286632i
$717$	16.3945	−	24.2811i	0.612265	−	0.906795i
$718$	44.2528	−	0.0148181i	1.65150	−	0.000553008i
$719$	−18.6228	−	32.2556i	−0.694512	−	1.20293i	−0.970345	−	0.241724i	$-0.922287\pi$
$719$	−18.6228	−	32.2556i	−0.694512	−	1.20293i	0.275833	−	0.961206i	$-0.411046\pi$
$720$	2.49956	+	11.7368i	0.0931532	+	0.437404i
$721$	−41.5762	+	72.0121i	−1.54838	+	2.68187i
$722$	0.842792	−	1.46089i	0.0313655	−	0.0543686i
$723$	−0.557327	−	5.32683i	−0.0207272	−	0.198107i
$724$	4.61664	+	7.98391i	0.171576	+	0.296720i
$725$	9.39234	−	1.65612i	0.348823	−	0.0615069i
$726$	7.53338	+	15.4511i	0.279590	+	0.573445i
$727$	19.7835	−	23.5771i	0.733729	−	0.874425i	−0.262158	−	0.965025i	$-0.584434\pi$
$727$	19.7835	−	23.5771i	0.733729	−	0.874425i	0.995887	+	0.0906004i	$0.0288786\pi$
$728$	−50.2078	+	29.0548i	−1.86082	+	1.07684i
$729$	−2.74609	−	26.8600i	−0.101707	−	0.994814i
$730$	−0.0686126	+	0.188708i	−0.00253947	+	0.00698440i
$731$	−0.178361	−	0.149662i	−0.00659690	−	0.00553546i
$732$	−0.926575	−	8.79910i	−0.0342472	−	0.325224i
$733$	8.34751	+	47.3411i	0.308322	+	1.74858i	0.607440	+	0.794366i	$0.292197\pi$
$733$	8.34751	+	47.3411i	0.308322	+	1.74858i	−0.299117	+	0.954216i	$0.596692\pi$
$734$	3.98321	−	4.75023i	0.147023	−	0.175334i
$735$	−29.1819	+	3.05319i	−1.07639	+	0.112619i
$736$	4.45846	+	1.61430i	0.164341	+	0.0595038i
$737$	6.53818	+	3.77482i	0.240837	+	0.139047i
$738$	−38.6515	−	12.5847i	−1.42278	−	0.463250i
$739$	−13.1975	+	7.61958i	−0.485478	+	0.280291i	−0.722697	−	0.691165i	$-0.757098\pi$
$739$	−13.1975	+	7.61958i	−0.485478	+	0.280291i	0.237219	+	0.971456i	$0.423764\pi$
$740$	2.33490	−	6.42849i	0.0858327	−	0.236316i
$741$	−25.3911	−	17.1440i	−0.932765	−	0.629800i
$742$	−29.1667	+	10.6269i	−1.07074	+	0.390125i
$743$	−29.1653	+	24.4726i	−1.06997	+	0.897812i	−0.995050	−	0.0993771i	$-0.968315\pi$
$743$	−29.1653	+	24.4726i	−1.06997	+	0.897812i	−0.0749212	+	0.997189i	$0.523871\pi$
$744$	−39.9507	−	26.9162i	−1.46466	−	0.986796i
$745$	−12.3672	+	4.50130i	−0.453099	+	0.164915i
$746$	5.87815	+	33.2715i	0.215214	+	1.21816i
$747$	12.4117	−	15.8554i	0.454121	−	0.580117i
$748$	0.994118	+	2.72563i	0.0363485	+	0.0996591i
$749$	−50.1583	−	8.84427i	−1.83275	−	0.323163i
$750$	0.674846	+	2.35469i	0.0246419	+	0.0859813i
$751$	12.1293	−	33.3249i	0.442603	−	1.21604i	−0.495171	−	0.868795i	$-0.664895\pi$
$751$	12.1293	−	33.3249i	0.442603	−	1.21604i	0.937774	−	0.347246i	$-0.112883\pi$
$752$	−15.6376	+	5.71535i	−0.570244	+	0.208417i
$753$	−16.3396	+	4.67693i	−0.595446	+	0.170437i
$754$	48.9518	−	28.2842i	1.78272	−	1.03005i
$755$	−3.96259			−0.144213
$756$	7.03900	+	50.3586i	0.256006	+	1.83152i
$757$	41.1263			1.49476			0.747380	−	0.664397i	$-0.231311\pi$
$757$	41.1263			1.49476			0.747380	+	0.664397i	$0.231311\pi$
$758$	25.8199	−	14.9186i	0.937819	−	0.541869i
$759$	−1.49372	+	5.97893i	−0.0542185	+	0.217021i
$760$	9.13551	−	7.68126i	0.331380	−	0.278629i
$761$	−12.6875	+	34.8587i	−0.459923	+	1.26363i	0.465620	+	0.884985i	$0.345831\pi$
$761$	−12.6875	+	34.8587i	−0.459923	+	1.26363i	−0.925543	+	0.378643i	$0.876391\pi$
$762$	−28.3040	+	29.3016i	−1.02535	+	1.06148i
$763$	−48.0481	−	8.47217i	−1.73946	−	0.306713i
$764$	38.9689	−	14.2131i	1.40985	−	0.514212i
$765$	−1.00305	+	0.212213i	−0.0362652	+	0.00767258i
$766$	2.06782	+	11.7043i	0.0747135	+	0.422893i
$767$	38.0224	−	13.8390i	1.37291	−	0.499698i
$768$	−26.6223	+	7.69744i	−0.960651	+	0.277757i
$769$	−38.0400	+	31.9193i	−1.37176	+	1.15104i	−0.399606	+	0.916687i	$0.630853\pi$
$769$	−38.0400	+	31.9193i	−1.37176	+	1.15104i	−0.972151	+	0.234354i	$0.924703\pi$
$770$	27.5969	−	10.0549i	0.994524	−	0.362354i
$771$	0.645395	−	9.16730i	0.0232433	−	0.330152i
$772$	34.3471	+	12.4753i	1.23618	+	0.448995i
$773$	2.33158	−	1.34614i	0.0838609	−	0.0484171i	−0.457483	−	0.889218i	$-0.651249\pi$
$773$	2.33158	−	1.34614i	0.0838609	−	0.0484171i	0.541344	+	0.840801i	$0.317916\pi$
$774$	2.27666	+	1.78096i	0.0818328	+	0.0640153i
$775$	−8.51569	−	4.91653i	−0.305892	−	0.176607i
$776$	−0.673835	+	0.246023i	−0.0241893	+	0.00883170i
$777$	11.8001	−	26.4697i	0.423326	−	0.949596i
$778$	19.2616	−	22.9707i	0.690562	−	0.823539i
$779$	7.02070	+	39.8164i	0.251543	+	1.42657i
$780$	8.53712	+	11.7455i	0.305678	+	0.420556i
$781$	24.6304	+	20.6674i	0.881347	+	0.739538i
$782$	−0.138432	+	0.380734i	−0.00495030	+	0.0136150i
$783$	−6.82738	−	49.0844i	−0.243991	−	1.75413i
$784$	−11.8559	−	66.7152i	−0.423423	−	2.38269i
$785$	−11.1022	+	13.2311i	−0.396253	+	0.472237i
$786$	20.9980	+	1.47123i	0.748972	+	0.0524770i
$787$	−42.0935	+	7.42222i	−1.50047	+	0.264574i	−0.862725	−	0.505673i	$-0.831244\pi$
$787$	−42.0935	+	7.42222i	−1.50047	+	0.264574i	−0.637746	+	0.770247i	$0.720133\pi$
$788$	−22.1617	+	12.8149i	−0.789478	+	0.456510i
$789$	−28.3832	+	20.6011i	−1.01047	+	0.733418i
$790$	0.892651	−	1.54731i	0.0317591	−	0.0550509i
$791$	−23.4648	+	40.6422i	−0.834311	+	1.44507i
$792$	−13.4944	−	33.3942i	−0.479504	−	1.18661i
$793$	−5.35300	−	9.27167i	−0.190091	−	0.329246i
$794$	−33.7687	+	0.0113075i	−1.19841	+	0.000401289i
$795$	3.40297	+	6.98550i	0.120691	+	0.247750i
$796$	0.0309848	+	46.2664i	0.00109823	+	1.63987i
$797$	−17.2811	−	20.5949i	−0.612129	−	0.729507i	0.367567	−	0.929997i	$-0.380191\pi$
$797$	−17.2811	−	20.5949i	−0.612129	−	0.729507i	−0.979696	+	0.200490i	$0.935747\pi$
$798$	40.9205	−	29.7218i	1.44857	−	1.05214i
$799$	−0.486514	−	1.33669i	−0.0172116	−	0.0472886i
$800$	−5.31246	+	1.94366i	−0.187824	+	0.0687186i
$801$	5.48737	−	10.2967i	0.193887	−	0.363818i
$802$	14.4732	+	17.2368i	0.511067	+	0.608652i
$803$	0.104654	−	0.593524i	0.00369317	−	0.0209450i
$804$	−5.10857	−	3.44431i	−0.180165	−	0.121471i
$805$	3.85398	+	1.40273i	0.135835	+	0.0494398i
$806$	−57.4071	−	10.1026i	−2.02208	−	0.355849i
$807$	15.6145	−	16.1540i	0.549656	−	0.568647i
$808$	14.9660	+	2.62342i	0.526504	+	0.0922915i
$809$		−	50.2707i		−	1.76742i	−0.468031	−	0.883712i	$-0.655037\pi$
$809$		−	50.2707i		−	1.76742i	0.468031	−	0.883712i	$-0.344963\pi$
$810$	12.3546	−	3.05994i	0.434097	−	0.107515i
$811$		−	9.68875i		−	0.340218i	−0.985425	−	0.170109i	$-0.945588\pi$
$811$		−	9.68875i		−	0.340218i	0.985425	−	0.170109i	$-0.0544120\pi$
$812$	16.2679	+	91.9000i	0.570892	+	3.22506i
$813$	−4.39220	+	4.54396i	−0.154041	+	0.159364i
$814$	−3.55792	+	20.2176i	−0.124705	+	0.708625i
$815$	−12.3015	−	4.47738i	−0.430903	−	0.156836i
$816$	−0.654602	−	2.27542i	−0.0229156	−	0.0796558i
$817$	0.499238	−	2.83132i	0.0174661	−	0.0990553i
$818$	−20.0359	+	16.8235i	−0.700538	+	0.588221i
$819$	32.5552	+	52.2091i	1.13757	+	1.82433i
$820$	3.31480	−	18.8731i	0.115758	−	0.659076i
$821$	5.96698	+	16.3941i	0.208249	+	0.572159i	0.999211	−	0.0397053i	$-0.0126419\pi$
$821$	5.96698	+	16.3941i	0.208249	+	0.572159i	−0.790962	+	0.611865i	$0.790420\pi$
$822$	1.04295	+	1.43591i	0.0363770	+	0.0500832i
$823$	−9.41765	−	11.2235i	−0.328279	−	0.391227i	0.576509	−	0.817091i	$-0.304415\pi$
$823$	−9.41765	−	11.2235i	−0.328279	−	0.391227i	−0.904787	+	0.425864i	$0.859970\pi$
$824$	−16.3949	+	45.1857i	−0.571142	+	1.57412i
$825$	−3.21982	−	6.60953i	−0.112100	−	0.230114i
$826$	0.0223666	+	66.7954i	0.000778233	+	2.32411i
$827$	−1.27601	−	2.21012i	−0.0443713	−	0.0768534i	0.842987	−	0.537934i	$-0.180795\pi$
$827$	−1.27601	−	2.21012i	−0.0443713	−	0.0768534i	−0.887358	+	0.461081i	$0.847462\pi$
$828$	1.55547	−	4.78276i	0.0540564	−	0.166212i
$829$	0.668152	−	1.15727i	0.0232059	−	0.0401938i	−0.854189	−	0.519962i	$-0.825946\pi$
$829$	0.668152	−	1.15727i	0.0232059	−	0.0401938i	0.877395	+	0.479768i	$0.159279\pi$
$830$	8.22193	+	4.74326i	0.285387	+	0.164641i
$831$	32.7349	−	23.7597i	1.13556	−	0.824215i
$832$	−25.6445	+	21.6063i	−0.889064	+	0.749063i
$833$	5.70133	−	1.00530i	0.197539	−	0.0348315i
$834$	2.50245	−	35.7159i	0.0866527	−	1.23674i
$835$	1.55905	−	1.85800i	0.0539532	−	0.0642989i
$836$	−23.0092	+	27.4586i	−0.795789	+	0.949675i
$837$	−27.1372	+	43.2918i	−0.937998	+	1.49638i
$838$	−8.69006	−	3.15963i	−0.300193	−	0.109148i
$839$	−34.2297	−	28.7222i	−1.18174	−	0.991599i	−0.999966	−	0.00825892i	$-0.997371\pi$
$839$	−34.2297	−	28.7222i	−1.18174	−	0.991599i	−0.181776	−	0.983340i	$-0.558184\pi$
$840$	−23.0380	+	6.61929i	−0.794885	+	0.228387i
$841$	−10.7590	−	61.0176i	−0.371002	−	2.10405i
$842$	2.08199	+	1.74581i	0.0717500	+	0.0601645i
$843$	14.3977	−	32.2966i	0.495882	−	1.11235i
$844$	11.8805	+	14.1394i	0.408945	+	0.486700i
$845$	3.95765	+	2.28495i	0.136147	+	0.0786046i
$846$	6.60527	+	16.3774i	0.227094	+	0.563067i
$847$	−29.7364	+	17.1683i	−1.02176	+	0.589911i
$848$	−15.5285	+	8.99317i	−0.533253	+	0.308827i
$849$	−3.20242	+	45.4877i	−0.109907	+	1.56113i
$850$	−0.165453	−	0.454105i	−0.00567498	−	0.0155757i
$851$	−2.19584	+	1.84253i	−0.0752725	+	0.0631611i
$852$	−18.8789	−	18.2239i	−0.646779	−	0.624341i
$853$	29.6346	−	10.7861i	1.01467	−	0.369310i	0.219445	−	0.975625i	$-0.429575\pi$
$853$	29.6346	−	10.7861i	1.01467	−	0.369310i	0.795224	+	0.606315i	$0.207353\pi$
$854$	17.4039	−	3.07479i	0.595549	−	0.105217i
$855$	−8.46206	−	9.41596i	−0.289396	−	0.322019i
$856$	−29.4424	+	0.0295766i	−1.00632	+	0.00101091i
$857$	5.60466	+	0.988252i	0.191451	+	0.0337581i	0.268552	−	0.963265i	$-0.413455\pi$
$857$	5.60466	+	0.988252i	0.191451	+	0.0337581i	−0.0771001	+	0.997023i	$0.524566\pi$
$858$	−31.3463	−	30.2791i	−1.07014	−	1.03371i
$859$	12.2613	−	33.6876i	0.418350	−	1.14941i	−0.534289	−	0.845302i	$-0.679421\pi$
$859$	12.2613	−	33.6876i	0.418350	−	1.14941i	0.952639	−	0.304104i	$-0.0983571\pi$
$860$	−0.680507	+	1.18050i	−0.0232051	+	0.0402546i
$861$	19.6803	−	78.7746i	0.670702	−	2.68463i
$862$	−18.1554	−	31.4218i	−0.618376	−	1.07023i
$863$	14.6761			0.499580			0.249790	−	0.968300i	$-0.419638\pi$
$863$	14.6761			0.499580			0.249790	+	0.968300i	$0.419638\pi$
$864$	9.09036	+	27.9529i	0.309260	+	0.950977i
$865$	−6.75314			−0.229614
$866$	7.91491	+	13.6984i	0.268960	+	0.465492i
$867$	−28.1136	+	8.04706i	−0.954787	+	0.273292i
$868$	48.0560	−	83.3644i	1.63113	−	2.82957i
$869$	−1.83379	+	5.03830i	−0.0622071	+	0.170913i
$870$	22.4573	−	6.43617i	0.761373	−	0.218206i
$871$	−7.34197	−	1.29459i	−0.248773	−	0.0438654i
$872$	−28.2037	+	0.0283322i	−0.955098	+	0.000959450i
$873$	0.284355	+	0.705724i	0.00962396	+	0.0238851i
$874$	−4.92608	+	0.870301i	−0.166627	+	0.0294384i
$875$	−4.59779	+	1.67346i	−0.155434	+	0.0565732i
$876$	−0.118894	+	0.477258i	−0.00401705	+	0.0161250i
$877$	18.0681	−	15.1610i	0.610118	−	0.511950i	−0.284562	−	0.958658i	$-0.591848\pi$
$877$	18.0681	−	15.1610i	0.610118	−	0.511950i	0.894680	+	0.446708i	$0.147404\pi$
$878$	−1.57779	−	4.33043i	−0.0532478	−	0.146145i
$879$	−45.5790	−	30.7748i	−1.53734	−	1.03801i
$880$	14.6928	−	8.50914i	0.495294	−	0.286843i
$881$	−29.1055	+	16.8041i	−0.980589	+	0.566143i	−0.902448	−	0.430799i	$-0.858232\pi$
$881$	−29.1055	+	16.8041i	−0.980589	+	0.566143i	−0.0781409	+	0.996942i	$0.524898\pi$
$882$	−70.3094	+	14.8999i	−2.36744	+	0.501704i
$883$	40.2245	+	23.2236i	1.35366	+	0.781536i	0.988760	−	0.149510i	$-0.0477697\pi$
$883$	40.2245	+	23.2236i	1.35366	+	0.781536i	0.364900	+	0.931047i	$0.381103\pi$
$884$	−1.84305	−	2.19347i	−0.0619884	−	0.0737745i
$885$	16.6290	−	1.73983i	0.558976	−	0.0584836i
$886$	4.77925	+	4.00754i	0.160562	+	0.134636i
$887$	−6.00206	−	34.0394i	−0.201529	−	1.14293i	−0.902808	−	0.430043i	$-0.858498\pi$
$887$	−6.00206	−	34.0394i	−0.201529	−	1.14293i	0.701279	−	0.712887i	$-0.252613\pi$
$888$	4.04427	−	16.2575i	0.135717	−	0.545567i
$889$	−62.3385	−	52.3082i	−2.09077	−	1.75436i
$890$	5.16911	+	1.87944i	0.173269	+	0.0629991i
$891$	−34.9291	+	15.4723i	−1.17017	+	0.518343i
$892$	5.09578	−	6.08119i	0.170619	−	0.203613i
$893$	11.2903	−	13.4552i	0.377814	−	0.450261i
$894$	−28.9768	+	14.1280i	−0.969130	+	0.472511i
$895$	5.63923	−	0.994349i	0.188499	−	0.0332374i
$896$	−19.0549	−	51.9735i	−0.636579	−	1.73631i
$897$	−0.633260	−	6.05259i	−0.0211439	−	0.202090i
$898$	−9.17151	−	5.29108i	−0.306057	−	0.176566i
$899$	−46.8901	+	81.2161i	−1.56387	+	2.70871i
$900$	2.24611	+	5.56372i	0.0748702	+	0.185457i
$901$	−0.766575	−	1.32775i	−0.0255383	−	0.0442337i
$902$	0.0192587	+	57.5141i	0.000641245	+	1.91501i
$903$	−3.23092	+	4.78516i	−0.107518	+	0.159240i
$904$	−9.25293	+	25.5019i	−0.307748	+	0.848180i
$905$	2.96408	+	3.53246i	0.0985295	+	0.117423i
$906$	−9.65329	+	1.01326i	−0.320709	+	0.0336632i
$907$	8.27478	+	22.7348i	0.274759	+	0.754895i	0.997935	+	0.0642311i	$0.0204595\pi$
$907$	8.27478	+	22.7348i	0.274759	+	0.754895i	−0.723176	+	0.690664i	$0.757318\pi$
$908$	2.15946	−	12.2951i	0.0716642	−	0.408026i
$909$	2.25799	−	15.9570i	0.0748928	−	0.529259i
$910$	−22.2124	+	18.6511i	−0.736332	+	0.618277i
$911$	−5.06552	+	28.7280i	−0.167828	+	0.951802i	0.778272	+	0.627928i	$0.216097\pi$
$911$	−5.06552	+	28.7280i	−0.167828	+	0.951802i	−0.946100	+	0.323874i	$0.895015\pi$
$912$	20.2909	−	21.0484i	0.671900	−	0.696981i
$913$	−26.7719	−	9.74418i	−0.886021	−	0.322485i
$914$	−8.59258	+	48.8266i	−0.284217	+	1.61504i
$915$	−1.21738	−	4.25308i	−0.0402452	−	0.140603i
$916$	0.903462	+	5.10380i	0.0298512	+	0.168634i
$917$			42.0463i			1.38849i
$918$	−2.38926	+	0.773458i	−0.0788574	+	0.0255279i
$919$		−	18.9546i		−	0.625254i	−0.949876	−	0.312627i	$-0.898791\pi$
$919$		−	18.9546i		−	0.625254i	0.949876	−	0.312627i	$-0.101209\pi$
$920$	2.33525	+	0.409349i	0.0769909	+	0.0134958i
$921$	−43.5371	−	10.8769i	−1.43460	−	0.358406i
$922$	14.0406	+	2.47089i	0.462403	+	0.0813746i
$923$	−29.8359	−	10.8594i	−0.982060	−	0.357441i
$924$	64.6580	−	31.5516i	2.12709	−	1.03797i
$925$	0.593823	−	3.36774i	0.0195248	−	0.110731i
$926$	3.00671	+	3.58082i	0.0988066	+	0.117673i
$927$	48.4737	+	15.8007i	1.59208	+	0.518964i
$928$	18.5371	+	50.6662i	0.608510	+	1.66320i
$929$	−7.52291	−	20.6690i	−0.246819	−	0.678128i	−0.999798	−	0.0200846i	$-0.993606\pi$
$929$	−7.52291	−	20.6690i	−0.246819	−	0.678128i	0.752980	−	0.658044i	$-0.228616\pi$
$930$	−22.0023	−	9.79969i	−0.721484	−	0.321345i
$931$	45.9499	+	54.7609i	1.50595	+	1.79472i
$932$	0.00735214	+	10.9782i	0.000240827	+	0.359602i
$933$	−14.1182	−	0.993947i	−0.462209	−	0.0325404i
$934$	−26.9107	+	0.00901112i	−0.880547	+	0.000294853i
$935$	0.725317	+	1.25629i	0.0237204	+	0.0410849i
$936$	23.8007	+	26.4302i	0.777951	+	0.863900i
$937$	24.5895	−	42.5902i	0.803303	−	1.39136i	−0.114128	−	0.993466i	$-0.536407\pi$
$937$	24.5895	−	42.5902i	0.803303	−	1.39136i	0.917431	−	0.397896i	$-0.130259\pi$
$938$	6.14997	−	10.6603i	0.200804	−	0.348071i
$939$	−0.522929	−	0.233119i	−0.0170651	−	0.00760756i
$940$	−7.20657	+	4.16715i	−0.235052	+	0.135917i
$941$	−15.5396	+	2.74006i	−0.506578	+	0.0893234i	−0.421096	−	0.907016i	$-0.638354\pi$
$941$	−15.5396	+	2.74006i	−0.506578	+	0.0893234i	−0.0854825	+	0.996340i	$0.527243\pi$
$942$	−23.6628	+	35.0711i	−0.770976	+	1.14268i
$943$	−5.16223	+	6.15210i	−0.168105	+	0.200340i
$944$	6.75593	+	38.0169i	0.219887	+	1.23735i
$945$	7.82217	+	24.1908i	0.254455	+	0.786928i
$946$	1.39751	−	3.84362i	0.0454368	−	0.124967i
$947$	12.0941	+	10.1482i	0.393006	+	0.329771i	0.817783	−	0.575527i	$-0.195203\pi$
$947$	12.0941	+	10.1482i	0.393006	+	0.329771i	−0.424777	+	0.905298i	$0.639647\pi$
$948$	1.77894	−	3.99768i	0.0577772	−	0.129838i
$949$	0.103346	+	0.586102i	0.00335474	+	0.0190257i
$950$	3.83451	−	4.57290i	0.124408	−	0.148364i
$951$	0.497878	+	0.685951i	0.0161448	+	0.0222435i
$952$	4.44266	−	1.62205i	0.143987	−	0.0525710i
$953$	−9.75977	−	5.63480i	−0.316150	−	0.182529i	0.333525	−	0.942741i	$-0.391762\pi$
$953$	−9.75977	−	5.63480i	−0.316150	−	0.182529i	−0.649675	+	0.760212i	$0.725095\pi$
$954$	10.0762	+	16.1473i	0.326230	+	0.522787i
$955$	17.9614	−	10.3700i	0.581216	−	0.335565i
$956$	31.7976	+	11.5493i	1.02841	+	0.373530i
$957$	−63.0367	+	30.7081i	−2.03769	+	0.992653i
$958$	4.30365	−	1.56803i	0.139044	−	0.0506608i
$959$	−2.71562	+	2.27867i	−0.0876918	+	0.0735822i
$960$	−12.4447	+	6.09338i	−0.401651	+	0.196663i
$961$	61.7276	−	22.4670i	1.99121	−	0.724743i
$962$	−3.52680	−	19.9624i	−0.113709	−	0.643613i
$963$	1.06035	+	31.2104i	0.0341692	+	1.00574i
$964$	5.81009	−	2.11911i	0.187130	−	0.0682518i
$965$	17.9937	+	3.17277i	0.579237	+	0.102135i
$966$	9.74738	+	2.43172i	0.313617	+	0.0782394i
$967$	2.61687	−	7.18979i	0.0841529	−	0.231208i	−0.890478	−	0.455026i	$-0.849630\pi$
$967$	2.61687	−	7.18979i	0.0841529	−	0.231208i	0.974631	+	0.223818i	$0.0718521\pi$
$968$	−15.1924	+	12.7740i	−0.488304	+	0.410572i
$969$	1.79599	+	1.73601i	0.0576956	+	0.0557688i
$970$	−0.310559	+	0.179440i	−0.00997143	+	0.00576146i
$971$	−6.10264			−0.195843			−0.0979215	−	0.995194i	$-0.531219\pi$
$971$	−6.10264			−0.195843			−0.0979215	+	0.995194i	$0.531219\pi$
$972$	29.3147	−	10.6135i	0.940271	−	0.340428i
$973$	71.5175			2.29275
$974$	−4.66595	+	2.69597i	−0.149507	+	0.0863845i
$975$	5.22013	+	5.04579i	0.167178	+	0.161595i
$976$	9.59569	−	3.50711i	0.307151	−	0.112260i
$977$	−3.26550	+	8.97189i	−0.104473	+	0.287036i	−0.980905	−	0.194490i	$-0.937695\pi$
$977$	−3.26550	+	8.97189i	−0.104473	+	0.287036i	0.876432	+	0.481526i	$0.159917\pi$
$978$	−31.1126	−	7.76181i	−0.994872	−	0.248195i
$979$	−16.2579	−	2.86670i	−0.519604	−	0.0916202i
$980$	−11.6090	−	31.8292i	−0.370837	−	1.01675i
$981$	1.01574	+	29.8973i	0.0324299	+	0.954548i
$982$	2.46806	+	13.9697i	0.0787591	+	0.445792i
$983$	53.0190	−	19.2973i	1.69104	−	0.615489i	0.696286	−	0.717765i	$-0.254835\pi$
$983$	53.0190	−	19.2973i	1.69104	−	0.615489i	0.994756	+	0.102276i	$0.0326124\pi$
$984$	3.24926	−	46.8244i	0.103583	−	1.49271i
$985$	−9.80538	+	8.22769i	−0.312425	+	0.262156i
$986$	−4.33090	+	1.57796i	−0.137924	+	0.0502526i
$987$	−31.7117	+	15.4483i	−1.00940	+	0.491725i
$988$	12.0772	−	33.2512i	0.384227	−	1.05786i
$989$	0.494570	−	0.285540i	0.0157264	−	0.00907964i
$990$	−9.53391	−	15.2782i	−0.303008	−	0.485573i
$991$	9.90675	+	5.71966i	0.314698	+	0.181691i	0.649027	−	0.760765i	$-0.275176\pi$
$991$	9.90675	+	5.71966i	0.314698	+	0.181691i	−0.334329	+	0.942457i	$0.608510\pi$
$992$	18.9371	−	52.3015i	0.601252	−	1.66057i
$993$	20.7106	+	28.5341i	0.657232	+	0.905502i
$994$	33.6776	−	40.1627i	1.06819	−	1.27388i
$995$	4.01704	+	22.7818i	0.127349	+	0.722230i
$996$	21.2424	+	9.45270i	0.673090	+	0.299520i
$997$	43.5472	+	36.5404i	1.37915	+	1.15725i	0.969525	+	0.244994i	$0.0787860\pi$
$997$	43.5472	+	36.5404i	1.37915	+	1.15725i	0.409628	+	0.912253i	$0.365658\pi$
$998$	−7.93420	+	21.8218i	−0.251153	+	0.690756i
$999$	−17.3757	−	3.71908i	−0.549742	−	0.117667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.47	yes	432
4.3	odd	2	inner	540.2.be.a.11.8	✓	432
27.5	odd	18	inner	540.2.be.a.491.8	yes	432
108.59	even	18	inner	540.2.be.a.491.47	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.8	✓	432	4.3	odd	2	inner
540.2.be.a.11.47	yes	432	1.1	even	1	trivial
540.2.be.a.491.8	yes	432	27.5	odd	18	inner
540.2.be.a.491.47	yes	432	108.59	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707517 + 1.22451i) q^{2} +(1.24536 + 1.20377i) q^{3} +(-0.998840 + 1.73272i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-0.592913 + 2.37665i) q^{6} +(-4.81853 - 0.849637i) q^{7} +(-2.82843 + 0.00284131i) q^{8} +(0.101864 + 2.99827i) q^{9} +(-1.39265 + 0.246042i) q^{10} +(3.98874 - 1.45178i) q^{11} +(-3.32972 + 0.955492i) q^{12} +(-3.21099 + 2.69434i) q^{13} +(-2.36880 - 6.50146i) q^{14} +(-1.55712 + 0.758545i) q^{15} +(-2.00464 - 3.46142i) q^{16} +(0.295964 - 0.170875i) q^{17} +(-3.59934 + 2.24606i) q^{18} +(3.65453 + 2.10994i) q^{19} +(-1.28660 - 1.53123i) q^{20} +(-4.97806 - 6.85852i) q^{21} +(4.59982 + 3.85708i) q^{22} +(0.145556 + 0.825489i) q^{23} +(-3.52584 - 3.40124i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-5.57107 - 2.02559i) q^{26} +(-3.48238 + 3.85656i) q^{27} +(6.28512 - 7.50051i) q^{28} +(-6.13042 + 7.30595i) q^{29} +(-2.03053 - 1.37002i) q^{30} +(9.68368 - 1.70749i) q^{31} +(2.82022 - 4.90371i) q^{32} +(6.71505 + 2.99354i) q^{33} +(0.418637 + 0.241513i) q^{34} +(2.44643 - 4.23734i) q^{35} +(-5.29691 - 2.81829i) q^{36} +(1.70985 + 2.96154i) q^{37} +(0.00199834 + 5.96782i) q^{38} +(-7.24222 - 0.509866i) q^{39} +(0.964709 - 2.65882i) q^{40} +(6.15853 + 7.33945i) q^{41} +(4.87626 - 10.9482i) q^{42} +(-0.233017 - 0.640210i) q^{43} +(-1.46858 + 8.36147i) q^{44} +(-2.85229 - 0.929748i) q^{45} +(-0.907835 + 0.762282i) q^{46} +(0.722780 - 4.09909i) q^{47} +(1.67026 - 6.72386i) q^{48} +(15.9185 + 5.79386i) q^{49} +(0.245109 - 1.39281i) q^{50} +(0.574277 + 0.143472i) q^{51} +(-1.46127 - 8.25495i) q^{52} -4.48618i q^{53} +(-7.18623 - 1.53562i) q^{54} +4.24473i q^{55} +(13.6313 + 2.38944i) q^{56} +(2.01133 + 7.02686i) q^{57} +(-13.2836 - 2.33766i) q^{58} +(-9.07098 - 3.30157i) q^{59} +(0.240963 - 3.45571i) q^{60} +(-0.443520 + 2.51532i) q^{61} +(8.94221 + 10.6497i) q^{62} +(2.05661 - 14.5338i) q^{63} +(7.99998 - 0.0160729i) q^{64} +(-1.43363 - 3.93886i) q^{65} +(1.08540 + 10.3406i) q^{66} +(1.14326 + 1.36248i) q^{67} +(0.000457742 + 0.683499i) q^{68} +(-0.812431 + 1.20325i) q^{69} +(6.91955 - 0.00231703i) q^{70} +(3.78738 + 6.55993i) q^{71} +(-0.296633 - 8.48009i) q^{72} +(0.0709916 - 0.122961i) q^{73} +(-2.41669 + 4.18906i) q^{74} +(-0.180234 - 1.72265i) q^{75} +(-7.30623 + 4.22478i) q^{76} +(-20.4533 + 3.60648i) q^{77} +(-4.49966 - 9.22889i) q^{78} +(-0.811925 + 0.967615i) q^{79} +(3.93830 - 0.699868i) q^{80} +(-8.97925 + 0.610829i) q^{81} +(-4.62995 + 12.7340i) q^{82} +(-5.14160 - 4.31431i) q^{83} +(16.8562 - 1.77501i) q^{84} +(0.0593442 + 0.336558i) q^{85} +(0.619079 - 0.738291i) q^{86} +(-16.4293 + 1.71894i) q^{87} +(-11.2777 + 4.11759i) q^{88} +(-3.36816 - 1.94461i) q^{89} +(-0.879560 - 4.15047i) q^{90} +(17.7614 - 10.2546i) q^{91} +(-1.57573 - 0.572324i) q^{92} +(14.1151 + 9.53050i) q^{93} +(5.53075 - 2.01512i) q^{94} +(-3.23262 + 2.71249i) q^{95} +(9.41515 - 2.71200i) q^{96} +(0.238324 - 0.0867428i) q^{97} +(4.16798 + 23.5916i) q^{98} +(4.75914 + 11.8114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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