LMFDB - Embedded newform 570.2.v.c.83.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(83,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("570.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.v (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			83.9
Character	$\chi$	$=$	570.83
Dual form			570.2.v.c.467.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.396548 - 1.68605i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.12625 + 0.692155i) q^{5} +(1.73123 + 0.0533452i) q^{6} +(-3.45963 + 3.45963i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.68550 + 1.33719i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.396548 - 1.68605i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.12625 + 0.692155i) q^{5} +(1.73123 + 0.0533452i) q^{6} +(-3.45963 + 3.45963i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.68550 + 1.33719i) q^{9} +(-1.21888 + 1.87465i) q^{10} -3.72347i q^{11} +(-0.499603 + 1.65843i) q^{12} +(-5.36924 + 1.43868i) q^{13} +(-2.44633 - 4.23716i) q^{14} +(0.323848 - 3.85942i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.844879 + 3.15313i) q^{17} +(-0.596572 - 2.94009i) q^{18} +(-1.79416 - 3.97253i) q^{19} +(-1.49531 - 1.66255i) q^{20} +(7.20499 + 4.46118i) q^{21} +(3.59660 + 0.963705i) q^{22} +(0.0790051 + 0.294851i) q^{23} +(-1.47262 - 0.911813i) q^{24} +(4.04184 + 2.94338i) q^{25} -5.55864i q^{26} +(3.31950 + 3.99761i) q^{27} +(4.72594 - 1.26631i) q^{28} +(-2.67316 + 4.63005i) q^{29} +(3.64410 + 1.31170i) q^{30} -9.34472 q^{31} +(-0.965926 + 0.258819i) q^{32} +(-6.27794 + 1.47653i) q^{33} +(-2.82702 - 1.63218i) q^{34} +(-9.75062 + 4.96142i) q^{35} +(2.99431 + 0.184705i) q^{36} +(-0.548978 + 0.548978i) q^{37} +(4.30153 - 0.704863i) q^{38} +(4.55484 + 8.48227i) q^{39} +(1.99291 - 1.01405i) q^{40} +(-5.45339 + 3.14852i) q^{41} +(-6.17396 + 5.80485i) q^{42} +(-0.0182401 + 0.0680730i) q^{43} +(-1.86174 + 3.22462i) q^{44} +(-6.63558 + 0.984421i) q^{45} -0.305252 q^{46} +(5.23390 - 1.40242i) q^{47} +(1.26188 - 1.18644i) q^{48} -16.9380i q^{49} +(-3.88920 + 3.14232i) q^{50} +(5.65136 + 0.174138i) q^{51} +(5.36924 + 1.43868i) q^{52} +(0.254873 + 0.951199i) q^{53} +(-4.72055 + 2.17173i) q^{54} +(2.57722 - 7.91701i) q^{55} +4.89265i q^{56} +(-5.98639 + 4.60034i) q^{57} +(-3.78042 - 3.78042i) q^{58} +(1.56772 + 2.71537i) q^{59} +(-2.21017 + 3.18043i) q^{60} +(-1.34339 + 2.32681i) q^{61} +(2.41859 - 9.02631i) q^{62} +(4.66463 - 13.9170i) q^{63} -1.00000i q^{64} +(-12.4121 - 0.657354i) q^{65} +(0.198629 - 6.44618i) q^{66} +(2.21885 + 8.28088i) q^{67} +(2.30825 - 2.30825i) q^{68} +(0.465803 - 0.250129i) q^{69} +(-2.26872 - 10.7025i) q^{70} +(-4.14476 + 2.39298i) q^{71} +(-0.953396 + 2.84447i) q^{72} +(-1.61314 + 6.02031i) q^{73} +(-0.388186 - 0.672358i) q^{74} +(3.35990 - 7.98192i) q^{75} +(-0.432473 + 4.33739i) q^{76} +(12.8818 + 12.8818i) q^{77} +(-9.37213 + 2.20427i) q^{78} +(-1.14768 + 0.662611i) q^{79} +(0.463699 + 2.18746i) q^{80} +(5.42382 - 7.18207i) q^{81} +(-1.62979 - 6.08247i) q^{82} +(9.89021 - 9.89021i) q^{83} +(-4.00912 - 7.46599i) q^{84} +(-3.97888 + 6.11954i) q^{85} +(-0.0610325 - 0.0352372i) q^{86} +(8.86651 + 2.67104i) q^{87} +(-2.63289 - 2.63289i) q^{88} +(7.15944 - 12.4005i) q^{89} +(0.766536 - 6.66426i) q^{90} +(13.5983 - 23.5529i) q^{91} +(0.0790051 - 0.294851i) q^{92} +(3.70563 + 15.7556i) q^{93} +5.41853i q^{94} +(-1.06523 - 9.68841i) q^{95} +(0.819416 + 1.52596i) q^{96} +(-12.3406 - 3.30664i) q^{97} +(16.3609 + 4.38389i) q^{98} +(4.97901 + 9.99938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) $ 144 * q - 4 * q^3 + 8 * q^6	$ 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) $ 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−0.396548	−	1.68605i	−0.228947	−	0.973439i
$3$	−0.396548	−	1.68605i	−0.228947	−	0.973439i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.12625	+	0.692155i	0.950886	+	0.309541i
$5$	2.12625	+	0.692155i	0.950886	+	0.309541i
$6$	1.73123	+	0.0533452i	0.706771	+	0.0217781i
$7$	−3.45963	+	3.45963i	−1.30762	+	1.30762i	−0.384484	+	0.923131i	$0.625621\pi$
$7$	−3.45963	+	3.45963i	−1.30762	+	1.30762i	−0.923131	+	0.384484i	$0.874379\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.68550	+	1.33719i	−0.895167	+	0.445732i
$10$	−1.21888	+	1.87465i	−0.385445	+	0.592817i
$11$		−	3.72347i		−	1.12267i	−0.827589	−	0.561334i	$-0.810288\pi$
$11$		−	3.72347i		−	1.12267i	0.827589	−	0.561334i	$-0.189712\pi$
$12$	−0.499603	+	1.65843i	−0.144223	+	0.478748i
$13$	−5.36924	+	1.43868i	−1.48916	+	0.399019i	−0.909453	−	0.415807i	$-0.863499\pi$
$13$	−5.36924	+	1.43868i	−1.48916	+	0.399019i	−0.579706	+	0.814826i	$0.696833\pi$
$14$	−2.44633	−	4.23716i	−0.653808	−	1.13243i
$15$	0.323848	−	3.85942i	0.0836172	−	0.996498i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.844879	+	3.15313i	−0.204913	+	0.764747i	0.784563	+	0.620049i	$0.212887\pi$
$17$	−0.844879	+	3.15313i	−0.204913	+	0.764747i	−0.989476	+	0.144697i	$0.953779\pi$
$18$	−0.596572	−	2.94009i	−0.140613	−	0.692985i
$19$	−1.79416	−	3.97253i	−0.411609	−	0.911360i
$19$	−1.79416	−	3.97253i	−0.411609	−	0.911360i
$20$	−1.49531	−	1.66255i	−0.334360	−	0.371757i
$21$	7.20499	+	4.46118i	1.57226	+	0.973510i
$22$	3.59660	+	0.963705i	0.766797	+	0.205463i
$23$	0.0790051	+	0.294851i	0.0164737	+	0.0614807i	0.973673	−	0.227948i	$-0.0732015\pi$
$23$	0.0790051	+	0.294851i	0.0164737	+	0.0614807i	−0.957200	+	0.289428i	$0.906535\pi$
$24$	−1.47262	−	0.911813i	−0.300596	−	0.186123i
$25$	4.04184	+	2.94338i	0.808368	+	0.588677i
$26$		−	5.55864i		−	1.09014i
$27$	3.31950	+	3.99761i	0.638838	+	0.769341i
$28$	4.72594	−	1.26631i	0.893118	−	0.239310i
$29$	−2.67316	+	4.63005i	−0.496394	+	0.859779i	−0.999991	−	0.00415924i	$-0.998676\pi$
$29$	−2.67316	+	4.63005i	−0.496394	+	0.859779i	0.503598	+	0.863938i	$0.332009\pi$
$30$	3.64410	+	1.31170i	0.665318	+	0.239483i
$31$	−9.34472			−1.67836			−0.839181	−	0.543853i	$-0.816965\pi$
$31$	−9.34472			−1.67836			−0.839181	+	0.543853i	$0.816965\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−6.27794	+	1.47653i	−1.09285	+	0.257031i
$34$	−2.82702	−	1.63218i	−0.484830	−	0.279917i
$35$	−9.75062	+	4.96142i	−1.64815	+	0.838633i
$36$	2.99431	+	0.184705i	0.499051	+	0.0307842i
$37$	−0.548978	+	0.548978i	−0.0902514	+	0.0902514i	−0.750791	−	0.660540i	$-0.770328\pi$
$37$	−0.548978	+	0.548978i	−0.0902514	+	0.0902514i	0.660540	+	0.750791i	$0.270328\pi$
$38$	4.30153	−	0.704863i	0.697800	−	0.114344i
$39$	4.55484	+	8.48227i	0.729359	+	1.35825i
$40$	1.99291	−	1.01405i	0.315107	−	0.160336i
$41$	−5.45339	+	3.14852i	−0.851677	+	0.491716i	−0.861216	−	0.508238i	$-0.830297\pi$
$41$	−5.45339	+	3.14852i	−0.851677	+	0.491716i	0.00953922	+	0.999955i	$0.496964\pi$
$42$	−6.17396	+	5.80485i	−0.952663	+	0.895708i
$43$	−0.0182401	+	0.0680730i	−0.00278159	+	0.0103810i	−0.967303	−	0.253625i	$-0.918377\pi$
$43$	−0.0182401	+	0.0680730i	−0.00278159	+	0.0103810i	0.964521	+	0.264006i	$0.0850438\pi$
$44$	−1.86174	+	3.22462i	−0.280667	+	0.486130i
$45$	−6.63558	+	0.984421i	−0.989174	+	0.146749i
$46$	−0.305252			−0.0450070
$47$	5.23390	−	1.40242i	0.763442	−	0.204564i	0.143970	−	0.989582i	$-0.454013\pi$
$47$	5.23390	−	1.40242i	0.763442	−	0.204564i	0.619472	+	0.785018i	$0.287347\pi$
$48$	1.26188	−	1.18644i	0.182137	−	0.171248i
$49$		−	16.9380i		−	2.41972i
$50$	−3.88920	+	3.14232i	−0.550016	+	0.444390i
$51$	5.65136	+	0.174138i	0.791348	+	0.0243842i
$52$	5.36924	+	1.43868i	0.744579	+	0.199509i
$53$	0.254873	+	0.951199i	0.0350095	+	0.130657i	0.981219	−	0.192898i	$-0.0617886\pi$
$53$	0.254873	+	0.951199i	0.0350095	+	0.130657i	−0.946209	+	0.323555i	$0.895122\pi$
$54$	−4.72055	+	2.17173i	−0.642385	+	0.295535i
$55$	2.57722	−	7.91701i	0.347512	−	1.06753i
$56$			4.89265i			0.653808i
$57$	−5.98639	+	4.60034i	−0.792917	+	0.609330i
$58$	−3.78042	−	3.78042i	−0.496394	−	0.496394i
$59$	1.56772	+	2.71537i	0.204100	+	0.353511i	0.949846	−	0.312719i	$-0.101240\pi$
$59$	1.56772	+	2.71537i	0.204100	+	0.353511i	−0.745746	+	0.666231i	$0.767907\pi$
$60$	−2.21017	+	3.18043i	−0.285332	+	0.410592i
$61$	−1.34339	+	2.32681i	−0.172003	+	0.297918i	−0.939120	−	0.343589i	$-0.888357\pi$
$61$	−1.34339	+	2.32681i	−0.172003	+	0.297918i	0.767117	+	0.641507i	$0.221691\pi$
$62$	2.41859	−	9.02631i	0.307161	−	1.14634i
$63$	4.66463	−	13.9170i	0.587688	−	1.75338i
$64$		−	1.00000i		−	0.125000i
$65$	−12.4121	−	0.657354i	−1.53953	−	0.0815347i
$66$	0.198629	−	6.44618i	0.0244496	−	0.793470i
$67$	2.21885	+	8.28088i	0.271076	+	1.01167i	0.958425	+	0.285343i	$0.0921075\pi$
$67$	2.21885	+	8.28088i	0.271076	+	1.01167i	−0.687349	+	0.726327i	$0.741226\pi$
$68$	2.30825	−	2.30825i	0.279917	−	0.279917i
$69$	0.465803	−	0.250129i	0.0560761	−	0.0301120i
$70$	−2.26872	−	10.7025i	−0.271163	−	1.27919i
$71$	−4.14476	+	2.39298i	−0.491893	+	0.283994i	−0.725359	−	0.688370i	$-0.758326\pi$
$71$	−4.14476	+	2.39298i	−0.491893	+	0.283994i	0.233467	+	0.972365i	$0.424993\pi$
$72$	−0.953396	+	2.84447i	−0.112359	+	0.335225i
$73$	−1.61314	+	6.02031i	−0.188803	+	0.704624i	0.804981	+	0.593301i	$0.202175\pi$
$73$	−1.61314	+	6.02031i	−0.188803	+	0.704624i	−0.993784	+	0.111323i	$0.964491\pi$
$74$	−0.388186	−	0.672358i	−0.0451257	−	0.0781600i
$75$	3.35990	−	7.98192i	0.387968	−	0.921673i
$76$	−0.432473	+	4.33739i	−0.0496081	+	0.497533i
$77$	12.8818	+	12.8818i	1.46802	+	1.46802i
$78$	−9.37213	+	2.20427i	−1.06118	+	0.249584i
$79$	−1.14768	+	0.662611i	−0.129124	+	0.0745496i	−0.563170	−	0.826341i	$-0.690419\pi$
$79$	−1.14768	+	0.662611i	−0.129124	+	0.0745496i	0.434047	+	0.900890i	$0.357085\pi$
$80$	0.463699	+	2.18746i	0.0518431	+	0.244566i
$81$	5.42382	−	7.18207i	0.602647	−	0.798008i
$82$	−1.62979	−	6.08247i	−0.179981	−	0.671697i
$83$	9.89021	−	9.89021i	1.08559	−	1.08559i	0.0896149	−	0.995976i	$-0.471436\pi$
$83$	9.89021	−	9.89021i	1.08559	−	1.08559i	0.995976	−	0.0896149i	$-0.0285636\pi$
$84$	−4.00912	−	7.46599i	−0.437431	−	0.814607i
$85$	−3.97888	+	6.11954i	−0.431570	+	0.663758i
$86$	−0.0610325	−	0.0352372i	−0.00658131	−	0.00379972i
$87$	8.86651	+	2.67104i	0.950590	+	0.286365i
$88$	−2.63289	−	2.63289i	−0.280667	−	0.280667i
$89$	7.15944	−	12.4005i	0.758899	−	1.31445i	−0.184514	−	0.982830i	$-0.559071\pi$
$89$	7.15944	−	12.4005i	0.758899	−	1.31445i	0.943412	−	0.331622i	$-0.107596\pi$
$90$	0.766536	−	6.66426i	0.0808000	−	0.702475i
$91$	13.5983	−	23.5529i	1.42548	−	2.46901i
$92$	0.0790051	−	0.294851i	0.00823685	−	0.0307403i
$93$	3.70563	+	15.7556i	0.384256	+	1.63378i
$94$			5.41853i			0.558878i
$95$	−1.06523	−	9.68841i	−0.109290	−	0.994010i
$96$	0.819416	+	1.52596i	0.0836313	+	0.155743i
$97$	−12.3406	−	3.30664i	−1.25299	−	0.335739i	−0.429501	−	0.903066i	$-0.641311\pi$
$97$	−12.3406	−	3.30664i	−1.25299	−	0.335739i	−0.823492	+	0.567328i	$0.807977\pi$
$98$	16.3609	+	4.38389i	1.65270	+	0.442839i
$99$	4.97901	+	9.99938i	0.500409	+	1.00498i
$100$	−2.02865	−	4.56997i	−0.202865	−	0.456997i
$101$	6.50940	+	3.75821i	0.647710	+	0.373956i	0.787578	−	0.616215i	$-0.211335\pi$
$101$	6.50940	+	3.75821i	0.647710	+	0.373956i	−0.139868	+	0.990170i	$0.544668\pi$
$102$	−1.63088	+	5.41372i	−0.161482	+	0.536038i
$103$	2.37027	+	2.37027i	0.233549	+	0.233549i	0.814172	−	0.580623i	$-0.197191\pi$
$103$	2.37027	+	2.37027i	0.233549	+	0.233549i	−0.580623	+	0.814172i	$0.697191\pi$
$104$	−2.77932	+	4.81393i	−0.272535	+	0.472044i
$105$	12.2318	+	14.4725i	1.19370	+	1.41238i
$106$	−0.984753			−0.0956477
$107$	−8.22080	−	8.22080i	−0.794735	−	0.794735i	0.187525	−	0.982260i	$-0.439954\pi$
$107$	−8.22080	−	8.22080i	−0.794735	−	0.794735i	−0.982260	+	0.187525i	$0.939954\pi$
$108$	−0.875964	−	5.12179i	−0.0842897	−	0.492844i
$109$	7.19215	−	4.15239i	0.688883	−	0.397727i	−0.114311	−	0.993445i	$-0.536466\pi$
$109$	7.19215	−	4.15239i	0.688883	−	0.397727i	0.803193	+	0.595718i	$0.203133\pi$
$110$	6.98021	+	4.53848i	0.665537	+	0.432727i
$111$	1.14330	+	0.707906i	0.108517	+	0.0671914i
$112$	−4.72594	−	1.26631i	−0.446559	−	0.119655i
$113$	−6.18962	+	6.18962i	−0.582270	+	0.582270i	−0.935527	−	0.353256i	$-0.885074\pi$
$113$	−6.18962	+	6.18962i	−0.582270	+	0.582270i	0.353256	+	0.935527i	$0.385074\pi$
$114$	−2.89419	−	6.97307i	−0.271066	−	0.653087i
$115$	−0.0360985	+	0.681610i	−0.00336620	+	0.0635604i
$116$	4.63005	−	2.67316i	0.429890	−	0.248197i
$117$	12.4953	−	11.0433i	1.15519	−	1.02095i
$118$	−3.02860	+	0.811512i	−0.278805	+	0.0747057i
$119$	−7.98569	−	13.8316i	−0.732047	−	1.26794i
$120$	−2.50003	−	2.95802i	−0.228220	−	0.270029i
$121$	−2.86424			−0.260385
$122$	−1.89984	−	1.89984i	−0.172003	−	0.172003i
$123$	7.47108	+	7.94613i	0.673644	+	0.716479i
$124$	8.09276	+	4.67236i	0.726752	+	0.419590i
$125$	6.55667	+	9.05594i	0.586446	+	0.809988i
$126$	12.2355	+	8.10768i	1.09003	+	0.722289i
$127$	−0.778814	−	2.90657i	−0.0691086	−	0.257917i	0.922724	−	0.385460i	$-0.125957\pi$
$127$	−0.778814	−	2.90657i	−0.0691086	−	0.257917i	−0.991833	+	0.127544i	$0.959291\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	0.122007	+	0.00375946i	0.0107421	+	0.000331002i
$130$	3.84745	−	11.8190i	0.337443	−	1.03660i
$131$	−5.51651	+	3.18496i	−0.481979	+	0.278271i	−0.721241	−	0.692684i	$-0.756428\pi$
$131$	−5.51651	+	3.18496i	−0.481979	+	0.278271i	0.239262	+	0.970955i	$0.423095\pi$
$132$	6.17512	+	1.86026i	0.537476	+	0.161914i
$133$	19.9506	+	7.53633i	1.72994	+	0.653483i
$134$	−8.57299			−0.740594
$135$	4.29110	+	10.7975i	0.369319	+	0.929303i
$136$	1.63218	+	2.82702i	0.139958	+	0.242415i
$137$	−0.355815	+	0.0953402i	−0.0303993	+	0.00814547i	−0.273987	−	0.961733i	$-0.588342\pi$
$137$	−0.355815	+	0.0953402i	−0.0303993	+	0.00814547i	0.243587	+	0.969879i	$0.421676\pi$
$138$	0.121047	+	0.514669i	0.0103042	+	0.0438116i
$139$	1.03884	+	0.599776i	0.0881134	+	0.0508723i	0.543409	−	0.839468i	$-0.317133\pi$
$139$	1.03884	+	0.599776i	0.0881134	+	0.0508723i	−0.455296	+	0.890340i	$0.650467\pi$
$140$	10.9250	+	0.578595i	0.923330	+	0.0489002i
$141$	−4.44003	−	8.26846i	−0.373918	−	0.696330i
$142$	−1.23870	−	4.62288i	−0.103949	−	0.387944i
$143$	5.35689	+	19.9922i	0.447966	+	1.67183i
$144$	−2.50079	−	1.65711i	−0.208400	−	0.138093i
$145$	−8.88851	+	7.99438i	−0.738151	+	0.663898i
$146$	−5.39766	−	3.11634i	−0.446713	−	0.257910i
$147$	−28.5583	+	6.71674i	−2.35545	+	0.553987i
$148$	0.749917	−	0.200940i	0.0616428	−	0.0165171i
$149$	10.6138	+	18.3837i	0.869520	+	1.50605i	0.862488	+	0.506078i	$0.168905\pi$
$149$	10.6138	+	18.3837i	0.869520	+	1.50605i	0.00703248	+	0.999975i	$0.497761\pi$
$150$	6.84034	+	5.31129i	0.558511	+	0.433665i
$151$	14.1280			1.14972			0.574862	−	0.818251i	$-0.305056\pi$
$151$	14.1280			1.14972			0.574862	+	0.818251i	$0.305056\pi$
$152$	−4.07767	−	1.54034i	−0.330742	−	0.124938i
$153$	−1.94743	−	9.59750i	−0.157440	−	0.775912i
$154$	−15.7769	+	9.10882i	−1.27134	+	0.734010i
$155$	−19.8692	−	6.46800i	−1.59593	−	0.519522i
$156$	0.296527	−	9.62329i	0.0237411	−	0.770480i
$157$	−7.27832	−	1.95022i	−0.580873	−	0.155645i	−0.0435946	−	0.999049i	$-0.513881\pi$
$157$	−7.27832	−	1.95022i	−0.580873	−	0.155645i	−0.537279	+	0.843405i	$0.680548\pi$
$158$	−0.342993	−	1.28007i	−0.0272870	−	0.101837i
$159$	1.50270	−	0.806923i	0.119171	−	0.0639932i
$160$	−2.23294	−	0.118258i	−0.176529	−	0.00934911i
$161$	−1.29340	−	0.746746i	−0.101934	−	0.0588519i
$162$	5.53356	+	7.09787i	0.434758	+	0.557661i
$163$	−11.2570	−	11.2570i	−0.881714	−	0.881714i	0.111995	−	0.993709i	$-0.464276\pi$
$163$	−11.2570	−	11.2570i	−0.881714	−	0.881714i	−0.993709	+	0.111995i	$0.964276\pi$
$164$	6.29704			0.491716
$165$	−14.3704	−	1.20584i	−1.11874	−	0.0938744i
$166$	6.99343	+	12.1130i	0.542796	+	0.940150i
$167$	−15.5788	+	4.17434i	−1.20553	+	0.323020i	−0.805006	−	0.593267i	$-0.797838\pi$
$167$	−15.5788	+	4.17434i	−1.20553	+	0.323020i	−0.400522	+	0.916287i	$0.631171\pi$
$168$	8.24923	−	1.94017i	0.636442	−	0.149687i
$169$	15.5006	−	8.94926i	1.19235	−	0.688405i
$170$	−4.88122	−	5.42715i	−0.374372	−	0.416244i
$171$	10.1303	+	8.26908i	0.774681	+	0.632352i
$172$	0.0498329	−	0.0498329i	0.00379972	−	0.00379972i
$173$	−4.03066	−	1.08001i	−0.306446	−	0.0821118i	0.102319	−	0.994752i	$-0.467374\pi$
$173$	−4.03066	−	1.08001i	−0.306446	−	0.0821118i	−0.408765	+	0.912640i	$0.634040\pi$
$174$	−4.87485	+	7.87308i	−0.369561	+	0.596857i
$175$	−24.1663	+	3.80025i	−1.82680	+	0.287272i
$176$	3.22462	−	1.86174i	0.243065	−	0.140334i
$177$	3.95656	−	3.72002i	0.297394	−	0.279614i
$178$	10.1250	+	10.1250i	0.758899	+	0.758899i
$179$	18.5837			1.38901			0.694505	−	0.719488i	$-0.255623\pi$
$179$	18.5837			1.38901			0.694505	+	0.719488i	$0.255623\pi$
$180$	6.23879	+	2.46526i	0.465012	+	0.183749i
$181$	5.40099	−	9.35478i	0.401452	−	0.695335i	−0.592449	−	0.805608i	$-0.701839\pi$
$181$	5.40099	−	9.35478i	0.401452	−	0.695335i	0.993901	+	0.110272i	$0.0351723\pi$
$182$	19.2308	+	19.2308i	1.42548	+	1.42548i
$183$	4.45583	+	1.34232i	0.329385	+	0.0992271i
$184$	0.264356	+	0.152626i	0.0194886	+	0.0112517i
$185$	−1.54724	+	0.787284i	−0.113755	+	0.0578822i
$186$	−16.1779	−	0.498496i	−1.18622	−	0.0365515i
$187$	11.7406	+	3.14588i	0.858557	+	0.230050i
$188$	−5.23390	−	1.40242i	−0.381721	−	0.102282i
$189$	−25.3145	−	2.34602i	−1.84136	−	0.170648i
$190$	9.63399	+	1.47862i	0.698923	+	0.107270i
$191$		−	17.3703i		−	1.25687i	−0.777862	−	0.628435i	$-0.783696\pi$
$191$		−	17.3703i		−	1.25687i	0.777862	−	0.628435i	$-0.216304\pi$
$192$	−1.68605	+	0.396548i	−0.121680	+	0.0286184i
$193$	0.916884	−	3.42186i	0.0659987	−	0.246311i	−0.925043	−	0.379862i	$-0.875971\pi$
$193$	0.916884	−	3.42186i	0.0659987	−	0.246311i	0.991042	+	0.133551i	$0.0426381\pi$
$194$	6.38794	−	11.0642i	0.458628	−	0.794366i
$195$	3.81367	+	21.1881i	0.273102	+	1.51731i
$196$	−8.46902	+	14.6688i	−0.604930	+	1.04777i
$197$	11.2779	+	11.2779i	0.803514	+	0.803514i	0.983643	−	0.180129i	$-0.0576516\pi$
$197$	11.2779	+	11.2779i	0.803514	+	0.803514i	−0.180129	+	0.983643i	$0.557652\pi$
$198$	−10.9473	+	2.22132i	−0.777992	+	0.157862i
$199$	−6.98482	−	4.03269i	−0.495141	−	0.285870i	0.231564	−	0.972820i	$-0.425616\pi$
$199$	−6.98482	−	4.03269i	−0.495141	−	0.285870i	−0.726705	+	0.686950i	$0.758949\pi$
$200$	4.93930	−	0.776726i	0.349261	−	0.0549228i
$201$	13.0821	−	7.02485i	0.922737	−	0.495495i
$202$	−5.31491	+	5.31491i	−0.373956	+	0.373956i
$203$	−6.77011	−	25.2664i	−0.475169	−	1.77335i
$204$	−4.80715	−	2.97649i	−0.336568	−	0.208396i
$205$	−13.7745	+	2.91993i	−0.962054	+	0.203937i
$206$	−2.90297	+	1.67603i	−0.202260	+	0.116775i
$207$	−0.606441	−	0.686177i	−0.0421506	−	0.0476926i
$208$	−3.93056	−	3.93056i	−0.272535	−	0.272535i
$209$	−14.7916	+	6.68051i	−1.02316	+	0.462101i
$210$	−17.1452	+	8.06920i	−1.18313	+	0.556828i
$211$	−1.16046	−	2.00998i	−0.0798896	−	0.138373i	0.823313	−	0.567588i	$-0.192123\pi$
$211$	−1.16046	−	2.00998i	−0.0798896	−	0.138373i	−0.903202	+	0.429215i	$0.858790\pi$
$212$	0.254873	−	0.951199i	0.0175047	−	0.0653286i
$213$	5.67827	+	6.03933i	0.389069	+	0.413808i
$214$	10.0684	−	5.81299i	0.688261	−	0.397368i
$215$	−0.0859000	+	0.132115i	−0.00585833	+	0.00901016i
$216$	5.17398	+	0.479499i	0.352045	+	0.0326258i
$217$	32.3292	−	32.3292i	2.19465	−	2.19465i
$218$	2.14943	+	8.02180i	0.145578	+	0.543305i
$219$	10.7902	+	0.332483i	0.729134	+	0.0224671i
$220$	−6.19045	+	5.56773i	−0.417360	+	0.375376i
$221$		−	18.1454i		−	1.22059i
$222$	−0.979691	+	0.921121i	−0.0657526	+	0.0618216i
$223$	−1.95802	+	7.30743i	−0.131119	+	0.489342i	−0.999984	−	0.00570723i	$-0.998183\pi$
$223$	−1.95802	+	7.30743i	−0.131119	+	0.489342i	0.868865	+	0.495049i	$0.164850\pi$
$224$	2.44633	−	4.23716i	0.163452	−	0.283107i
$225$	−14.7902	−	2.49973i	−0.986016	−	0.166649i
$226$	−4.37672	−	7.58070i	−0.291135	−	0.504261i
$227$	9.03878	+	9.03878i	0.599925	+	0.599925i	0.940292	−	0.340368i	$-0.110552\pi$
$227$	9.03878	+	9.03878i	0.599925	+	0.599925i	−0.340368	+	0.940292i	$0.610552\pi$
$228$	7.48454	−	0.990813i	0.495676	−	0.0656182i
$229$			10.5901i			0.699813i	0.936785	+	0.349907i	$0.113787\pi$
$229$			10.5901i			0.699813i	−0.936785	+	0.349907i	$0.886213\pi$
$230$	−0.649041	−	0.211282i	−0.0427965	−	0.0139315i
$231$	16.6111	−	26.8276i	1.09293	−	1.76513i
$232$	1.38373	+	5.16415i	0.0908463	+	0.339043i
$233$	21.2229	+	5.68665i	1.39036	+	0.372545i	0.874872	−	0.484353i	$-0.160945\pi$
$233$	21.2229	+	5.68665i	1.39036	+	0.372545i	0.515485	+	0.856899i	$0.327612\pi$
$234$	7.43299	+	14.9277i	0.485910	+	0.975857i
$235$	12.0992	+	0.640784i	0.789267	+	0.0418001i
$236$		−	3.13544i		−	0.204100i
$237$	1.57230	+	1.67228i	0.102132	+	0.108626i
$238$	15.4272	−	4.13370i	0.999995	−	0.267948i
$239$	−21.0944			−1.36448			−0.682242	−	0.731127i	$-0.738995\pi$
$239$	−21.0944			−1.36448			−0.682242	+	0.731127i	$0.738995\pi$
$240$	3.50428	−	1.64925i	0.226200	−	0.106459i
$241$	−3.14290	+	5.44367i	−0.202452	+	0.350657i	−0.949318	−	0.314317i	$-0.898224\pi$
$241$	−3.14290	+	5.44367i	−0.202452	+	0.350657i	0.746866	+	0.664975i	$0.231558\pi$
$242$	0.741319	−	2.76664i	0.0476538	−	0.177846i
$243$	−14.2601	−	6.29677i	−0.914786	−	0.403938i
$244$	2.32681	−	1.34339i	0.148959	−	0.0860015i
$245$	11.7238	−	36.0144i	0.749003	−	2.30088i
$246$	−9.60903	+	5.15990i	−0.612650	+	0.328983i
$247$	15.3485	+	18.7482i	0.976602	+	1.19292i
$248$	−6.60771	+	6.60771i	−0.419590	+	0.419590i
$249$	−20.5973	−	12.7534i	−1.30530	−	0.808214i
$250$	−10.4444	+	3.98941i	−0.660559	+	0.252312i
$251$	−10.7902	−	6.22970i	−0.681069	−	0.393215i	0.119189	−	0.992872i	$-0.461971\pi$
$251$	−10.7902	−	6.22970i	−0.681069	−	0.393215i	−0.800258	+	0.599656i	$0.795304\pi$
$252$	−10.9982	+	9.72018i	−0.692822	+	0.612314i
$253$	1.09787	−	0.294173i	0.0690225	−	0.0184945i
$254$	3.00911			0.188808
$255$	11.8956	+	4.28188i	0.744934	+	0.268142i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.4565	+	3.33772i	−0.777017	+	0.208201i	−0.625469	−	0.780249i	$-0.715092\pi$
$257$	−12.4565	+	3.33772i	−0.777017	+	0.208201i	−0.151548	+	0.988450i	$0.548426\pi$
$258$	−0.0352091	+	0.116877i	−0.00219203	+	0.00727644i
$259$		−	3.79852i		−	0.236028i
$260$	10.4205	+	6.77534i	0.646254	+	0.420189i
$261$	0.987495	−	16.0085i	0.0611244	−	0.990904i
$262$	−1.64866	−	6.15286i	−0.101854	−	0.380125i
$263$	−14.2306	−	3.81309i	−0.877499	−	0.235125i	−0.208171	−	0.978092i	$-0.566751\pi$
$263$	−14.2306	−	3.81309i	−0.877499	−	0.235125i	−0.669328	+	0.742967i	$0.733418\pi$
$264$	−3.39511	+	5.48324i	−0.208954	+	0.337470i
$265$	−0.116455	+	2.19889i	−0.00715377	+	0.135077i
$266$	−12.4431	+	17.3203i	−0.762937	+	1.06197i
$267$	−23.7469	−	7.15375i	−1.45329	−	0.437802i
$268$	2.21885	−	8.28088i	0.135538	−	0.505835i
$269$	7.40050	+	12.8180i	0.451216	+	0.781529i	0.998462	−	0.0554426i	$-0.0176570\pi$
$269$	7.40050	+	12.8180i	0.451216	+	0.781529i	−0.547246	+	0.836972i	$0.684324\pi$
$270$	−11.5402	+	1.35028i	−0.702316	+	0.0821756i
$271$	4.16451	+	7.21314i	0.252976	+	0.438167i	0.964344	−	0.264653i	$-0.0852574\pi$
$271$	4.16451	+	7.21314i	0.252976	+	0.438167i	−0.711368	+	0.702820i	$0.751924\pi$
$272$	−3.15313	+	0.844879i	−0.191187	+	0.0512283i
$273$	−45.1036	−	13.5874i	−2.72979	−	0.822349i
$274$		−	0.368366i		−	0.0222538i
$275$	10.9596	−	15.0497i	0.660889	−	0.907530i
$276$	−0.528462	−	0.0162837i	−0.0318097	−	0.000980165i
$277$	−20.9905	+	20.9905i	−1.26120	+	1.26120i	−0.310687	+	0.950512i	$0.600559\pi$
$277$	−20.9905	+	20.9905i	−1.26120	+	1.26120i	−0.950512	+	0.310687i	$0.899441\pi$
$278$	−0.848211	+	0.848211i	−0.0508723	+	0.0508723i
$279$	25.0952	−	12.4957i	1.50241	−	0.748099i
$280$	−3.38647	+	10.4030i	−0.202381	+	0.621697i
$281$	−23.0152	−	13.2878i	−1.37297	−	0.792684i	−0.381669	−	0.924299i	$-0.624650\pi$
$281$	−23.0152	−	13.2878i	−1.37297	−	0.792684i	−0.991301	+	0.131615i	$0.957984\pi$
$282$	9.13589	−	2.14870i	0.544034	−	0.127953i
$283$	−3.05511	+	11.4018i	−0.181607	+	0.677767i	0.813724	+	0.581251i	$0.197437\pi$
$283$	−3.05511	+	11.4018i	−0.181607	+	0.677767i	−0.995331	+	0.0965162i	$0.969230\pi$
$284$	4.78596			0.283994
$285$	−15.9127	+	5.63793i	−0.942586	+	0.333962i
$286$	−20.6975			−1.22387
$287$	7.97401	−	29.7594i	0.470691	−	1.75664i
$288$	2.24790	−	1.98669i	0.132459	−	0.117067i
$289$	5.49402	+	3.17197i	0.323177	+	0.186587i
$290$	−5.42147	−	10.6547i	−0.318359	−	0.625668i
$291$	−0.681531	+	22.1180i	−0.0399521	+	1.29658i
$292$	4.40717	−	4.40717i	0.257910	−	0.257910i
$293$	−2.08370	+	2.08370i	−0.121731	+	0.121731i	−0.765348	−	0.643617i	$-0.777433\pi$
$293$	−2.08370	+	2.08370i	−0.121731	+	0.121731i	0.643617	+	0.765348i	$0.277433\pi$
$294$	0.903562	−	29.3236i	0.0526968	−	1.71019i
$295$	1.45390	+	6.85865i	0.0846493	+	0.399326i
$296$			0.776372i			0.0451257i
$297$	14.8850	−	12.3601i	0.863715	−	0.717204i
$298$	−20.5044	+	5.49413i	−1.18779	+	0.318266i
$299$	−0.848394	−	1.46946i	−0.0490639	−	0.0849812i
$300$	−6.90072	+	5.23260i	−0.398413	+	0.302104i
$301$	−0.172403	−	0.298611i	−0.00993715	−	0.0172116i
$302$	−3.65661	+	13.6466i	−0.210414	+	0.785276i
$303$	3.75522	−	12.4655i	0.215732	−	0.716122i
$304$	2.54323	−	3.54005i	0.145864	−	0.203036i
$305$	−4.46689	+	4.01755i	−0.255773	+	0.230044i
$306$	9.77451	+	0.602945i	0.558771	+	0.0344681i
$307$	−17.5354	−	4.69861i	−1.00080	−	0.268164i	−0.279020	−	0.960285i	$-0.590009\pi$
$307$	−17.5354	−	4.69861i	−1.00080	−	0.268164i	−0.721781	+	0.692122i	$0.756676\pi$
$308$	−4.71507	−	17.5969i	−0.268666	−	1.00268i
$309$	3.05645	−	4.93630i	0.173876	−	0.280816i
$310$	11.3901	−	17.5181i	0.646916	−	0.994961i
$311$			1.92696i			0.109268i	0.998506	+	0.0546338i	$0.0173992\pi$
$311$			1.92696i			0.109268i	−0.998506	+	0.0546338i	$0.982601\pi$
$312$	9.21864	+	2.77711i	0.521902	+	0.157223i
$313$	−19.0132	+	5.09458i	−1.07469	+	0.287963i	−0.752420	−	0.658684i	$-0.771113\pi$
$313$	−19.0132	+	5.09458i	−1.07469	+	0.287963i	−0.322273	+	0.946647i	$0.604447\pi$
$314$	3.76754	−	6.52556i	0.212614	−	0.368259i
$315$	19.5509	−	26.3624i	1.10157	−	1.48535i
$316$	1.32522			0.0745496
$317$	6.70528	−	1.79667i	0.376606	−	0.100911i	−0.0655504	−	0.997849i	$-0.520880\pi$
$317$	6.70528	−	1.79667i	0.376606	−	0.100911i	0.442156	+	0.896938i	$0.354214\pi$
$318$	0.390502	+	1.66034i	0.0218982	+	0.0931072i
$319$	17.2399	+	9.95344i	0.965247	+	0.557286i
$320$	0.692155	−	2.12625i	0.0386927	−	0.118861i
$321$	−10.6007	+	17.1206i	−0.591674	+	0.955578i
$322$	1.05606	−	1.05606i	0.0588519	−	0.0588519i
$323$	14.0418	−	2.30093i	0.781304	−	0.128027i
$324$	−8.28820	+	3.50795i	−0.460456	+	0.194886i
$325$	−25.9362	−	9.98881i	−1.43868	−	0.554079i
$326$	13.7869	−	7.95988i	0.763587	−	0.440857i
$327$	−9.85315	−	10.4797i	−0.544880	−	0.579527i
$328$	−1.62979	+	6.08247i	−0.0899903	+	0.335848i
$329$	−13.2555	+	22.9592i	−0.730798	+	1.26578i
$330$	4.88409	−	13.5687i	0.268861	−	0.746931i
$331$	−23.9317			−1.31540			−0.657702	−	0.753278i	$-0.728471\pi$
$331$	−23.9317			−1.31540			−0.657702	+	0.753278i	$0.728471\pi$
$332$	−13.5103	+	3.62007i	−0.741473	+	0.198677i
$333$	0.740189	−	2.20837i	0.0405621	−	0.121018i
$334$		−	16.1284i		−	0.882507i
$335$	−1.01382	+	19.1430i	−0.0553911	+	1.04589i
$336$	−0.260999	+	8.47030i	−0.0142387	+	0.462093i
$337$	−24.7686	−	6.63672i	−1.34923	−	0.361525i	−0.489379	−	0.872071i	$-0.662777\pi$
$337$	−24.7686	−	6.63672i	−1.34923	−	0.361525i	−0.859850	+	0.510546i	$0.829443\pi$
$338$	4.63248	+	17.2887i	0.251974	+	0.940379i
$339$	12.8905	+	7.98150i	0.700114	+	0.433496i
$340$	6.50558	−	3.31024i	0.352815	−	0.179523i
$341$			34.7948i			1.88424i
$342$	−10.6092	+	7.64489i	−0.573681	+	0.413388i
$343$	34.3819	+	34.3819i	1.85645	+	1.85645i
$344$	0.0352372	+	0.0610325i	0.00189986	+	0.00329065i
$345$	1.16354	−	0.209427i	0.0626429	−	0.0112752i
$346$	2.08642	−	3.61379i	0.112167	−	0.194279i
$347$	0.937970	−	3.50055i	0.0503529	−	0.187920i	−0.936169	−	0.351551i	$-0.885654\pi$
$347$	0.937970	−	3.50055i	0.0503529	−	0.187920i	0.986521	+	0.163632i	$0.0523209\pi$
$348$	−6.34311	−	6.74644i	−0.340026	−	0.361647i
$349$		−	2.19272i		−	0.117374i	−0.998276	−	0.0586868i	$-0.981309\pi$
$349$		−	2.19272i		−	0.117374i	0.998276	−	0.0586868i	$-0.0186913\pi$
$350$	2.58393	−	24.3264i	0.138117	−	1.30030i
$351$	−23.5745	−	16.6884i	−1.25831	−	0.890763i
$352$	0.963705	+	3.59660i	0.0513657	+	0.191699i
$353$	19.5877	−	19.5877i	1.04255	−	1.04255i	0.0434971	−	0.999054i	$-0.486150\pi$
$353$	19.5877	−	19.5877i	1.04255	−	1.04255i	0.999054	−	0.0434971i	$-0.0138499\pi$
$354$	2.56923	+	4.78456i	0.136553	+	0.254296i
$355$	−10.4691	+	2.21924i	−0.555642	+	0.117785i
$356$	−12.4005	+	7.15944i	−0.657226	+	0.379449i
$357$	−20.1540	+	18.9491i	−1.06666	+	1.00289i
$358$	−4.80981	+	17.9505i	−0.254207	+	0.948712i
$359$	9.07673	+	15.7214i	0.479052	+	0.829742i	0.999711	−	0.0240226i	$-0.00764736\pi$
$359$	9.07673	+	15.7214i	0.479052	+	0.829742i	−0.520660	+	0.853764i	$0.674314\pi$
$360$	−3.99597	+	5.38815i	−0.210606	+	0.283981i
$361$	−12.5620	+	14.2547i	−0.661156	+	0.750249i
$362$	7.63815	+	7.63815i	0.401452	+	0.401452i
$363$	1.13581	+	4.82923i	0.0596144	+	0.253469i
$364$	−23.5529	+	13.5983i	−1.23451	+	0.712742i
$365$	−7.59691	+	11.6841i	−0.397641	+	0.611574i
$366$	−2.44984	+	3.95659i	−0.128055	+	0.206814i
$367$	5.63455	+	21.0284i	0.294121	+	1.09767i	0.941913	+	0.335857i	$0.109026\pi$
$367$	5.63455	+	21.0284i	0.294121	+	1.09767i	−0.647792	+	0.761817i	$0.724307\pi$
$368$	−0.215846	+	0.215846i	−0.0112517	+	0.0112517i
$369$	10.4349	−	15.7476i	0.543220	−	0.819787i
$370$	−0.360003	−	1.69828i	−0.0187156	−	0.0882895i
$371$	−4.17256	−	2.40903i	−0.216628	−	0.125070i
$372$	4.66865	−	15.4976i	0.242058	−	0.803512i
$373$	5.16921	+	5.16921i	0.267651	+	0.267651i	0.828153	−	0.560502i	$-0.189392\pi$
$373$	5.16921	+	5.16921i	0.267651	+	0.267651i	−0.560502	+	0.828153i	$0.689392\pi$
$374$	−6.07738	+	10.5263i	−0.314254	+	0.544303i
$375$	12.6687	−	14.6460i	0.654209	−	0.756314i
$376$	2.70926	−	4.69258i	0.139720	−	0.242001i
$377$	7.69167	−	28.7057i	0.396141	−	1.47842i
$378$	8.81795	−	23.8447i	0.453547	−	1.22644i
$379$			7.79782i			0.400547i	0.979740	+	0.200274i	$0.0641831\pi$
$379$			7.79782i			0.400547i	−0.979740	+	0.200274i	$0.935817\pi$
$380$	−3.92169	+	8.92302i	−0.201179	+	0.457741i
$381$	−4.59178	+	2.46571i	−0.235244	+	0.126322i
$382$	16.7784	+	4.49576i	0.858458	+	0.230023i
$383$	−23.7749	−	6.37046i	−1.21484	−	0.325515i	−0.406181	−	0.913793i	$-0.633140\pi$
$383$	−23.7749	−	6.37046i	−1.21484	−	0.325515i	−0.808659	+	0.588278i	$0.799806\pi$
$384$	0.0533452	−	1.73123i	0.00272226	−	0.0883464i
$385$	18.4737	+	36.3061i	0.941507	+	1.85033i
$386$	3.06795	+	1.77128i	0.156155	+	0.0901560i
$387$	−0.0420430	−	0.207200i	−0.00213717	−	0.0105326i
$388$	9.03391	+	9.03391i	0.458628	+	0.458628i
$389$	−11.6425	+	20.1653i	−0.590296	+	1.02242i	0.403897	+	0.914805i	$0.367656\pi$
$389$	−11.6425	+	20.1653i	−0.590296	+	1.02242i	−0.994192	+	0.107618i	$0.965678\pi$
$390$	−21.4531	−	1.80016i	−1.08632	−	0.0911544i
$391$	−0.996454			−0.0503928
$392$	−11.9770	−	11.9770i	−0.604930	−	0.604930i
$393$	7.55754	+	8.03810i	0.381228	+	0.405468i
$394$	−13.8125	+	7.97465i	−0.695863	+	0.401757i
$395$	−2.89887	+	0.614504i	−0.145858	+	0.0309190i
$396$	0.687745	−	11.1492i	0.0345605	−	0.560269i
$397$	−15.5489	−	4.16632i	−0.780377	−	0.209101i	−0.153426	−	0.988160i	$-0.549031\pi$
$397$	−15.5489	−	4.16632i	−0.780377	−	0.209101i	−0.626951	+	0.779059i	$0.715697\pi$
$398$	5.70308	−	5.70308i	0.285870	−	0.285870i
$399$	4.79523	−	36.6261i	0.240062	−	1.83360i
$400$	−0.528125	+	4.97203i	−0.0264063	+	0.248602i
$401$	−20.6315	+	11.9116i	−1.03029	+	0.594836i	−0.917066	−	0.398734i	$-0.869450\pi$
$401$	−20.6315	+	11.9116i	−1.03029	+	0.594836i	−0.113219	+	0.993570i	$0.536116\pi$
$402$	3.39960	+	14.4545i	0.169557	+	0.720923i
$403$	50.1740	−	13.4441i	2.49935	−	0.669698i
$404$	−3.75821	−	6.50940i	−0.186978	−	0.323855i
$405$	16.5035	−	11.5167i	0.820065	−	0.572271i
$406$	26.1577			1.29818
$407$	2.04410	+	2.04410i	0.101322	+	0.101322i
$408$	4.11925	−	3.87298i	0.203933	−	0.191741i
$409$	28.1287	+	16.2401i	1.39087	+	0.803022i	0.993412	−	0.114596i	$-0.0365574\pi$
$409$	28.1287	+	16.2401i	1.39087	+	0.803022i	0.397463	+	0.917618i	$0.369891\pi$
$410$	0.744674	−	14.0609i	0.0367768	−	0.694418i
$411$	0.301845	+	0.562113i	0.0148889	+	0.0277270i
$412$	−0.867577	−	3.23784i	−0.0427425	−	0.159517i
$413$	−14.8179	−	3.97044i	−0.729141	−	0.195373i
$414$	0.819755	−	0.408182i	0.0402888	−	0.0200610i
$415$	27.8746	−	14.1835i	1.36831	−	0.696238i
$416$	4.81393	−	2.77932i	0.236022	−	0.136267i
$417$	0.599299	−	1.98937i	0.0293478	−	0.0974201i
$418$	−2.62454	−	16.0166i	−0.128370	−	0.783399i
$419$	17.1402			0.837351			0.418676	−	0.908136i	$-0.362494\pi$
$419$	17.1402			0.837351			0.418676	+	0.908136i	$0.362494\pi$
$420$	−3.35674	−	18.6495i	−0.163792	−	0.910001i
$421$	−0.299791	−	0.519253i	−0.0146109	−	0.0253068i	0.858628	−	0.512600i	$-0.171318\pi$
$421$	−0.299791	−	0.519253i	−0.0146109	−	0.0253068i	−0.873238	+	0.487293i	$0.837984\pi$
$422$	2.24184	−	0.600700i	0.109131	−	0.0292416i
$423$	−12.1803	+	10.7649i	−0.592227	+	0.523409i
$424$	0.852821	+	0.492377i	0.0414167	+	0.0239119i
$425$	−12.6957	+	10.2577i	−0.615834	+	0.497569i
$426$	−7.30319	+	3.92169i	−0.353841	+	0.190007i
$427$	−3.40229	−	12.6975i	−0.164648	−	0.614476i
$428$	3.00902	+	11.2298i	0.145447	+	0.542814i
$429$	31.5835	−	16.9598i	1.52487	−	0.818828i
$430$	−0.105381	−	0.117167i	−0.00508190	−	0.00565029i
$431$	25.8995	+	14.9531i	1.24753	+	0.720265i	0.970617	−	0.240629i	$-0.0773537\pi$
$431$	25.8995	+	14.9531i	1.24753	+	0.720265i	0.276918	+	0.960894i	$0.410687\pi$
$432$	−1.80229	+	4.87358i	−0.0867125	+	0.234480i
$433$	−2.01789	+	0.540691i	−0.0969735	+	0.0259840i	−0.306980	−	0.951716i	$-0.599318\pi$
$433$	−2.01789	+	0.540691i	−0.0969735	+	0.0259840i	0.210006	+	0.977700i	$0.432652\pi$
$434$	22.8602	+	39.5951i	1.09733	+	1.90062i
$435$	17.0036	+	11.8163i	0.815261	+	0.566548i
$436$	−8.30478			−0.397727
$437$	1.02956	−	0.842861i	0.0492503	−	0.0403195i
$438$	−3.11386	+	10.3365i	−0.148786	+	0.493896i
$439$	−34.2500	+	19.7743i	−1.63466	+	0.943774i	−0.652037	+	0.758187i	$0.726085\pi$
$439$	−34.2500	+	19.7743i	−1.63466	+	0.943774i	−0.982628	+	0.185587i	$0.940581\pi$
$440$	−3.77580	−	7.42054i	−0.180004	−	0.353761i
$441$	22.6494	+	45.4871i	1.07855	+	2.16605i
$442$	17.5271	+	4.69638i	0.833681	+	0.223384i
$443$	9.99111	+	37.2873i	0.474692	+	1.77158i	0.622564	+	0.782569i	$0.286091\pi$
$443$	9.99111	+	37.2873i	0.474692	+	1.77158i	−0.147872	+	0.989007i	$0.547242\pi$
$444$	−0.636172	−	1.18471i	−0.0301914	−	0.0562240i
$445$	23.8058	−	21.4111i	1.12850	−	1.01498i
$446$	−6.55167	−	3.78261i	−0.310230	−	0.179112i
$447$	26.7869	−	25.1855i	1.26698	−	1.19123i
$448$	3.45963	+	3.45963i	0.163452	+	0.163452i
$449$	31.1275			1.46900			0.734499	−	0.678610i	$-0.237417\pi$
$449$	31.1275			1.46900			0.734499	+	0.678610i	$0.237417\pi$
$450$	6.24255	−	13.6393i	0.294277	−	0.642963i
$451$	11.7234	+	20.3056i	0.552034	+	0.956151i
$452$	8.45518	−	2.26556i	0.397698	−	0.106563i
$453$	−5.60244	−	23.8205i	−0.263226	−	1.11919i
$454$	−11.0702	+	6.39138i	−0.519550	+	0.299962i
$455$	45.2155	−	40.6671i	2.11973	−	1.90650i
$456$	−0.980089	+	7.48595i	−0.0458969	+	0.350562i
$457$	4.03775	−	4.03775i	0.188878	−	0.188878i	−0.606333	−	0.795211i	$-0.707360\pi$
$457$	4.03775	−	4.03775i	0.188878	−	0.188878i	0.795211	+	0.606333i	$0.207360\pi$
$458$	−10.2292	−	2.74092i	−0.477981	−	0.128075i
$459$	−15.4096	+	7.08932i	−0.719258	+	0.330901i
$460$	0.372067	−	0.572242i	0.0173477	−	0.0266809i
$461$	−1.52175	+	0.878583i	−0.0708750	+	0.0409197i	−0.535019	−	0.844840i	$-0.679695\pi$
$461$	−1.52175	+	0.878583i	−0.0708750	+	0.0409197i	0.464144	+	0.885760i	$0.346362\pi$
$462$	21.6142	+	22.9886i	1.00558	+	1.06952i
$463$	−7.69757	−	7.69757i	−0.357736	−	0.357736i	0.505242	−	0.862978i	$-0.331403\pi$
$463$	−7.69757	−	7.69757i	−0.357736	−	0.357736i	−0.862978	+	0.505242i	$0.831403\pi$
$464$	−5.34632			−0.248197
$465$	−3.02627	+	36.0652i	−0.140340	+	1.67248i
$466$	−10.9858	+	19.0279i	−0.508906	+	0.881451i
$467$	−4.61421	−	4.61421i	−0.213520	−	0.213520i	0.592241	−	0.805761i	$-0.298243\pi$
$467$	−4.61421	−	4.61421i	−0.213520	−	0.213520i	−0.805761	+	0.592241i	$0.798243\pi$
$468$	−16.3429	+	3.31613i	−0.755450	+	0.153288i
$469$	−36.3251	−	20.9723i	−1.67734	−	0.968412i
$470$	−3.75046	+	11.5211i	−0.172996	+	0.531430i
$471$	−0.401960	+	13.0449i	−0.0185213	+	0.601079i
$472$	3.02860	+	0.811512i	0.139403	+	0.0373529i
$473$	0.253468	+	0.0679165i	0.0116545	+	0.00312280i
$474$	−2.02224	+	1.08591i	−0.0928844	+	0.0498774i
$475$	4.44095	−	21.3372i	0.203765	−	0.979020i
$476$			15.9714i			0.732047i
$477$	−1.95640	−	2.21363i	−0.0895774	−	0.101355i
$478$	5.45963	−	20.3756i	0.249718	−	0.931959i
$479$	−15.3426	+	26.5741i	−0.701020	+	1.21420i	0.267089	+	0.963672i	$0.413938\pi$
$479$	−15.3426	+	26.5741i	−0.701020	+	1.21420i	−0.968109	+	0.250530i	$0.919395\pi$
$480$	0.686078	+	3.81173i	0.0313150	+	0.173981i
$481$	2.15779	−	3.73740i	0.0983866	−	0.170411i
$482$	−4.44473	−	4.44473i	−0.202452	−	0.202452i
$483$	−0.746153	+	2.47686i	−0.0339511	+	0.112701i
$484$	2.48050	+	1.43212i	0.112750	+	0.0650963i
$485$	−23.9503	−	15.5723i	−1.08753	−	0.707102i
$486$	9.77300	−	12.1445i	0.443312	−	0.550885i
$487$	4.16789	−	4.16789i	0.188865	−	0.188865i	−0.606340	−	0.795205i	$-0.707363\pi$
$487$	4.16789	−	4.16789i	0.188865	−	0.188865i	0.795205	+	0.606340i	$0.207363\pi$
$488$	0.695388	+	2.59522i	0.0314788	+	0.117480i
$489$	−14.5158	+	23.4437i	−0.656429	+	1.06016i
$490$	31.7529	+	20.6455i	1.43445	+	0.932668i
$491$	−27.3394	+	15.7844i	−1.23381	+	0.712340i	−0.967822	−	0.251637i	$-0.919031\pi$
$491$	−27.3394	+	15.7844i	−1.23381	+	0.712340i	−0.265987	+	0.963977i	$0.585698\pi$
$492$	−2.49708	−	10.6171i	−0.112577	−	0.478656i
$493$	−12.3407	−	12.3407i	−0.555796	−	0.555796i
$494$	−22.0819	+	9.97312i	−0.993510	+	0.448712i
$495$	3.66546	+	24.7074i	0.164750	+	1.11051i
$496$	−4.67236	−	8.09276i	−0.209795	−	0.363376i
$497$	6.06051	−	22.6181i	0.271851	−	1.01456i
$498$	17.6498	−	16.5946i	0.790907	−	0.743623i
$499$	−20.1799	+	11.6509i	−0.903379	+	0.521566i	−0.878295	−	0.478119i	$-0.841319\pi$
$499$	−20.1799	+	11.6509i	−0.903379	+	0.521566i	−0.0250838	+	0.999685i	$0.507985\pi$
$500$	−1.15027	−	11.1210i	−0.0514417	−	0.497347i
$501$	13.2159	+	24.6113i	0.590442	+	1.09955i
$502$	8.81013	−	8.81013i	0.393215	−	0.393215i
$503$	3.39616	+	12.6746i	0.151427	+	0.565134i	0.999385	+	0.0350700i	$0.0111654\pi$
$503$	3.39616	+	12.6746i	0.151427	+	0.565134i	−0.847958	+	0.530064i	$0.822168\pi$
$504$	−6.54243	−	13.1392i	−0.291423	−	0.585267i
$505$	11.2393	+	12.4964i	0.500144	+	0.556082i
$506$			1.13660i			0.0505279i
$507$	−21.2356	−	22.5859i	−0.943106	−	1.00307i
$508$	−0.778814	+	2.90657i	−0.0345543	+	0.128958i
$509$	9.39122	−	16.2661i	0.416258	−	0.720981i	−0.579301	−	0.815114i	$-0.696675\pi$
$509$	9.39122	−	16.2661i	0.416258	−	0.720981i	0.995560	+	0.0941329i	$0.0300079\pi$
$510$	−7.21480	+	10.3821i	−0.319477	+	0.459726i
$511$	−15.2472	−	26.4089i	−0.674495	−	1.16826i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	9.92491	−	20.3592i	0.438195	−	0.898880i
$514$		−	12.8960i		−	0.568816i
$515$	3.39918	+	6.68036i	0.149786	+	0.294372i
$516$	−0.103782	−	0.0642594i	−0.00456873	−	0.00282886i
$517$	−5.22186	−	19.4883i	−0.229657	−	0.857093i
$518$	3.66908	+	0.983128i	0.161210	+	0.0431962i
$519$	−0.222601	+	7.22416i	−0.00977111	+	0.317105i
$520$	−9.24151	+	8.31187i	−0.405267	+	0.364500i
$521$		−	21.4803i		−	0.941067i	−0.882382	−	0.470533i	$-0.844062\pi$
$521$		−	21.4803i		−	0.941067i	0.882382	−	0.470533i	$-0.155938\pi$
$522$	15.2075	+	5.09716i	0.665613	+	0.223097i
$523$	−19.6241	+	5.25825i	−0.858100	+	0.229927i	−0.660935	−	0.750443i	$-0.729840\pi$
$523$	−19.6241	+	5.25825i	−0.858100	+	0.229927i	−0.197165	+	0.980370i	$0.563174\pi$
$524$	6.36991			0.278271
$525$	15.9905	+	39.2385i	0.697882	+	1.71251i
$526$	7.36632	−	12.7588i	0.321187	−	0.556312i
$527$	7.89516	−	29.4651i	0.343918	−	1.28352i
$528$	−4.41769	−	4.69859i	−0.192255	−	0.204480i
$529$	19.8379	−	11.4534i	0.862517	−	0.497974i
$530$	−2.09383	−	0.681602i	−0.0909501	−	0.0296069i
$531$	−7.84109	−	5.19578i	−0.340274	−	0.225478i
$532$	−13.5096	−	16.5020i	−0.585714	−	0.715450i
$533$	24.7509	−	24.7509i	1.07208	−	1.07208i
$534$	13.0561	−	21.0862i	0.564994	−	0.912489i
$535$	−11.7894	−	23.1695i	−0.509699	−	1.00171i
$536$	7.42443	+	4.28650i	0.320687	+	0.185148i
$537$	−7.36932	−	31.3330i	−0.318010	−	1.35212i
$538$	−14.2967	+	3.83078i	−0.616373	+	0.165157i
$539$	−63.0683			−2.71654
$540$	1.68256	−	11.4965i	0.0724057	−	0.494730i
$541$	14.0493	−	24.3342i	0.604028	−	1.04621i	−0.388176	−	0.921585i	$-0.626895\pi$
$541$	14.0493	−	24.3342i	0.604028	−	1.04621i	0.992204	−	0.124622i	$-0.0397719\pi$
$542$	−8.04521	+	2.15571i	−0.345571	+	0.0925956i
$543$	−17.9143	−	5.39669i	−0.768778	−	0.231594i
$544$		−	3.26436i		−	0.139958i
$545$	18.1664	−	3.85091i	0.778162	−	0.164955i
$546$	24.7981	−	40.0500i	1.06126	−	1.71398i
$547$	3.35772	+	12.5312i	0.143566	+	0.535795i	0.999815	+	0.0192320i	$0.00612212\pi$
$547$	3.35772	+	12.5312i	0.143566	+	0.535795i	−0.856249	+	0.516563i	$0.827211\pi$
$548$	0.355815	+	0.0953402i	0.0151996	+	0.00407273i
$549$	0.496262	−	8.04503i	0.0211799	−	0.343354i
$550$	11.7003	+	14.4813i	0.498903	+	0.617485i
$551$	23.1891	+	2.31214i	0.987889	+	0.0985005i
$552$	0.152505	−	0.506240i	0.00649104	−	0.0215470i
$553$	1.67814	−	6.26292i	0.0713619	−	0.266326i
$554$	−14.8426	−	25.7081i	−0.630600	−	1.09223i
$555$	1.94095	+	2.29652i	0.0823887	+	0.0974819i
$556$	−0.599776	−	1.03884i	−0.0254362	−	0.0440567i
$557$	−26.1675	+	7.01155i	−1.10875	+	0.297089i	−0.766323	−	0.642455i	$-0.777916\pi$
$557$	−26.1675	+	7.01155i	−1.10875	+	0.297089i	−0.342428	+	0.939544i	$0.611249\pi$
$558$	5.57480	+	27.4743i	0.236000	+	1.16308i
$559$		−	0.391742i		−	0.0165689i
$560$	−9.17202	−	5.96357i	−0.387589	−	0.252007i
$561$	0.648397	−	21.0427i	0.0273754	−	0.888422i
$562$	18.7918	−	18.7918i	0.792684	−	0.792684i
$563$	−18.7414	+	18.7414i	−0.789857	+	0.789857i	−0.981470	−	0.191614i	$-0.938628\pi$
$563$	−18.7414	+	18.7414i	−0.789857	+	0.789857i	0.191614	+	0.981470i	$0.438628\pi$
$564$	−0.289052	+	9.38071i	−0.0121713	+	0.394999i
$565$	−17.4448	+	8.87647i	−0.733909	+	0.373436i
$566$	−10.2226	−	5.90201i	−0.429687	−	0.248080i
$567$	6.08290	+	43.6117i	0.255458	+	1.83152i
$568$	−1.23870	+	4.62288i	−0.0519746	+	0.193972i
$569$	12.4416			0.521577			0.260788	−	0.965396i	$-0.416017\pi$
$569$	12.4416			0.521577			0.260788	+	0.965396i	$0.416017\pi$
$570$	−1.32732	−	16.8297i	−0.0555953	−	0.704918i
$571$	20.3986			0.853654			0.426827	−	0.904333i	$-0.359631\pi$
$571$	20.3986			0.853654			0.426827	+	0.904333i	$0.359631\pi$
$572$	5.35689	−	19.9922i	0.223983	−	0.835916i
$573$	−29.2871	+	6.88815i	−1.22349	+	0.287756i
$574$	26.6816	+	15.4046i	1.11367	+	0.642976i
$575$	−0.548534	+	1.42428i	−0.0228755	+	0.0593967i
$576$	1.33719	+	2.68550i	0.0557164	+	0.111896i
$577$	−10.5331	+	10.5331i	−0.438499	+	0.438499i	−0.891506	−	0.453008i	$-0.850351\pi$
$577$	−10.5331	+	10.5331i	−0.438499	+	0.438499i	0.453008	+	0.891506i	$0.350351\pi$
$578$	−4.48585	+	4.48585i	−0.186587	+	0.186587i
$579$	−6.13299	−	0.188979i	−0.254879	−	0.00785369i
$580$	11.6949	−	2.47908i	0.485603	−	0.102938i
$581$			68.4329i			2.83907i
$582$	−21.1879	−	6.38286i	−0.878268	−	0.264578i
$583$	3.54176	−	0.949012i	0.146685	−	0.0393041i
$584$	3.11634	+	5.39766i	0.128955	+	0.223357i
$585$	34.2117	−	14.8321i	1.41448	−	0.613231i
$586$	−1.47340	−	2.55200i	−0.0608654	−	0.105422i
$587$	−7.12616	+	26.5952i	−0.294128	+	1.09770i	0.647779	+	0.761828i	$0.275698\pi$
$587$	−7.12616	+	26.5952i	−0.294128	+	1.09770i	−0.941907	+	0.335873i	$0.890969\pi$
$588$	28.0906	+	8.46228i	1.15844	+	0.348979i
$589$	16.7660	+	37.1222i	0.690829	+	1.52959i
$590$	−7.00125	−	0.370791i	−0.288237	−	0.0152652i
$591$	14.5428	−	23.4872i	0.598210	−	0.966133i
$592$	−0.749917	−	0.200940i	−0.0308214	−	0.00825857i
$593$	−1.79179	−	6.68705i	−0.0735800	−	0.274604i	0.919328	−	0.393493i	$-0.128733\pi$
$593$	−1.79179	−	6.68705i	−0.0735800	−	0.274604i	−0.992908	+	0.118889i	$0.962067\pi$
$594$	8.08638	+	17.5768i	0.331788	+	0.721186i
$595$	−7.40591	−	34.9368i	−0.303613	−	1.43227i
$596$		−	21.2277i		−	0.869520i
$597$	−4.02948	+	13.3759i	−0.164916	+	0.547438i
$598$	1.63897	−	0.439161i	0.0670226	−	0.0179586i
$599$	21.0760	−	36.5047i	0.861141	−	1.49154i	−0.00968759	−	0.999953i	$-0.503084\pi$
$599$	21.0760	−	36.5047i	0.861141	−	1.49154i	0.870829	−	0.491587i	$-0.163583\pi$
$600$	−3.26826	−	8.01988i	−0.133426	−	0.327410i
$601$	30.5006			1.24415			0.622073	−	0.782960i	$-0.286291\pi$
$601$	30.5006			1.24415			0.622073	+	0.782960i	$0.286291\pi$
$602$	0.333057	−	0.0892424i	0.0135744	−	0.00363725i
$603$	−17.0319	−	19.2713i	−0.693592	−	0.784786i
$604$	−12.2352	−	7.06402i	−0.497845	−	0.287431i
$605$	−6.09007	−	1.98250i	−0.247597	−	0.0806000i
$606$	11.0688	+	6.85356i	0.449639	+	0.278407i
$607$	28.7965	−	28.7965i	1.16881	−	1.16881i	0.186326	−	0.982488i	$-0.440342\pi$
$607$	28.7965	−	28.7965i	1.16881	−	1.16881i	0.982488	−	0.186326i	$-0.0596581\pi$
$608$	2.76119	+	3.37280i	0.111981	+	0.136785i
$609$	−39.9156	+	21.4340i	−1.61746	+	0.868551i
$610$	−2.72454	−	5.35450i	−0.110313	−	0.216797i
$611$	−26.0844	+	15.0598i	−1.05526	+	0.609256i
$612$	−3.11223	+	9.28539i	−0.125804	+	0.375340i
$613$	6.12820	−	22.8708i	0.247516	−	0.923741i	−0.724587	−	0.689184i	$-0.757969\pi$
$613$	6.12820	−	22.8708i	0.247516	−	0.923741i	0.972102	−	0.234557i	$-0.0753641\pi$
$614$	9.07701	−	15.7218i	0.366318	−	0.634482i
$615$	10.3854	+	22.0666i	0.418779	+	0.889810i
$616$	18.2176			0.734010
$617$	36.4183	−	9.75826i	1.46615	−	0.392853i	0.564539	−	0.825407i	$-0.309054\pi$
$617$	36.4183	−	9.75826i	1.46615	−	0.392853i	0.901608	+	0.432554i	$0.142387\pi$
$618$	3.97703	+	4.22992i	0.159980	+	0.170152i
$619$		−	9.78109i		−	0.393135i	−0.980490	−	0.196568i	$-0.937020\pi$
$619$		−	9.78109i		−	0.393135i	0.980490	−	0.196568i	$-0.0629795\pi$
$620$	13.9732	+	15.5360i	0.561178	+	0.623942i
$621$	−0.916443	+	1.29459i	−0.0367756	+	0.0519501i
$622$	−1.86130	−	0.498733i	−0.0746312	−	0.0199974i
$623$	18.1322	+	67.6701i	0.726449	+	2.71115i
$624$	−5.06844	+	8.18575i	−0.202900	+	0.327692i
$625$	7.67297	+	23.7934i	0.306919	+	0.951736i
$626$		−	19.6840i		−	0.786729i
$627$	17.1292	+	22.2902i	0.684075	+	0.890183i
$628$	5.32810	+	5.32810i	0.212614	+	0.212614i
$629$	−1.26718	−	2.19482i	−0.0505257	−	0.0875131i
$630$	20.4039	+	25.7078i	0.812912	+	1.02422i
$631$	−0.633854	+	1.09787i	−0.0252333	+	0.0437054i	−0.878366	−	0.477988i	$-0.841366\pi$
$631$	−0.633854	+	1.09787i	−0.0252333	+	0.0437054i	0.853133	+	0.521693i	$0.174700\pi$
$632$	−0.342993	+	1.28007i	−0.0136435	+	0.0509183i
$633$	−2.92874	+	2.75365i	−0.116407	+	0.109448i
$634$			6.94181i			0.275695i
$635$	0.355851	−	6.71915i	0.0141215	−	0.266641i
$636$	−1.70483	−	0.0525318i	−0.0676011	−	0.00208302i
$637$	24.3685	+	90.9443i	0.965514	+	3.60335i
$638$	−14.0763	+	14.0763i	−0.557286	+	0.557286i
$639$	7.93088	−	11.9687i	0.313741	−	0.473475i
$640$	1.87465	+	1.21888i	0.0741022	+	0.0481806i
$641$	9.33554	−	5.38988i	0.368732	−	0.212887i	−0.304173	−	0.952617i	$-0.598380\pi$
$641$	9.33554	−	5.38988i	0.368732	−	0.212887i	0.672904	+	0.739730i	$0.265047\pi$
$642$	−13.7936	−	14.6706i	−0.544388	−	0.579004i
$643$	3.76108	−	14.0366i	0.148323	−	0.553548i	−0.851262	−	0.524740i	$-0.824162\pi$
$643$	3.76108	−	14.0366i	0.148323	−	0.553548i	0.999585	−	0.0288074i	$-0.00917094\pi$
$644$	0.746746	+	1.29340i	0.0294259	+	0.0509672i
$645$	0.256815	+	0.0924415i	0.0101121	+	0.00363988i
$646$	−1.41175	+	14.1588i	−0.0555445	+	0.557071i
$647$	−2.02525	−	2.02525i	−0.0796210	−	0.0796210i	0.666175	−	0.745796i	$-0.267930\pi$
$647$	−2.02525	−	2.02525i	−0.0796210	−	0.0796210i	−0.745796	+	0.666175i	$0.767930\pi$
$648$	−1.24327	−	8.91371i	−0.0488404	−	0.350164i
$649$	10.1106	−	5.83736i	0.396876	−	0.229136i
$650$	16.3612	−	22.4672i	0.641740	−	0.881235i
$651$	−67.3287	−	41.6885i	−2.63882	−	1.63390i
$652$	4.12034	+	15.3773i	0.161365	+	0.602222i
$653$	8.20494	−	8.20494i	0.321084	−	0.321084i	−0.528099	−	0.849183i	$-0.677095\pi$
$653$	8.20494	−	8.20494i	0.321084	−	0.321084i	0.849183	+	0.528099i	$0.177095\pi$
$654$	12.6728	−	6.80507i	0.495544	−	0.266099i
$655$	−13.9339	+	2.95372i	−0.544444	+	0.115411i
$656$	−5.45339	−	3.14852i	−0.212919	−	0.122929i
$657$	−3.71825	−	18.3246i	−0.145063	−	0.714911i
$658$	−18.7461	−	18.7461i	−0.730798	−	0.730798i
$659$	0.184438	−	0.319456i	0.00718469	−	0.0124443i	−0.862411	−	0.506209i	$-0.831046\pi$
$659$	0.184438	−	0.319456i	0.00718469	−	0.0124443i	0.869595	+	0.493765i	$0.164380\pi$
$660$	11.8422	+	8.22951i	0.460959	+	0.320333i
$661$	6.14228	−	10.6387i	0.238907	−	0.413799i	−0.721494	−	0.692421i	$-0.756544\pi$
$661$	6.14228	−	10.6387i	0.238907	−	0.413799i	0.960401	+	0.278622i	$0.0898775\pi$
$662$	6.19398	−	23.1162i	0.240736	−	0.898438i
$663$	−30.5940	+	7.19553i	−1.18817	+	0.279451i
$664$		−	13.9869i		−	0.542796i
$665$	37.2036	+	29.8330i	1.44269	+	1.15687i
$666$	1.94155	+	1.28654i	0.0752334	+	0.0498523i
$667$	−1.57637	−	0.422387i	−0.0610373	−	0.0163549i
$668$	15.5788	+	4.17434i	0.602764	+	0.161510i
$669$	13.0971	+	0.403567i	0.506364	+	0.0156028i
$670$	−18.2283	−	5.93384i	−0.704220	−	0.229244i
$671$	8.66383	+	5.00206i	0.334463	+	0.193103i
$672$	−8.11413	−	2.44438i	−0.313009	−	0.0942940i
$673$	−21.0039	−	21.0039i	−0.809642	−	0.809642i	0.174937	−	0.984580i	$-0.444028\pi$
$673$	−21.0039	−	21.0039i	−0.809642	−	0.809642i	−0.984580	+	0.174937i	$0.944028\pi$
$674$	12.8212	−	22.2069i	0.493852	−	0.855377i
$675$	1.65038	+	25.9283i	0.0635230	+	0.997980i
$676$	−17.8985			−0.688405
$677$	−13.6281	−	13.6281i	−0.523772	−	0.523772i	0.394937	−	0.918708i	$-0.370766\pi$
$677$	−13.6281	−	13.6281i	−0.523772	−	0.523772i	−0.918708	+	0.394937i	$0.870766\pi$
$678$	−11.0458	+	10.3855i	−0.424213	+	0.398851i
$679$	54.1335	−	31.2540i	2.07745	−	1.19942i
$680$	1.51368	+	7.14066i	0.0580470	+	0.273832i
$681$	11.6555	−	18.8241i	0.446639	−	0.721341i
$682$	−33.6092	−	9.00556i	−1.28696	−	0.344841i
$683$	1.04280	−	1.04280i	0.0399015	−	0.0399015i	−0.686875	−	0.726776i	$-0.741018\pi$
$683$	1.04280	−	1.04280i	0.0399015	−	0.0399015i	0.726776	+	0.686875i	$0.241018\pi$
$684$	−4.63853	−	12.2264i	−0.177359	−	0.467487i
$685$	−0.822539	−	0.0435622i	−0.0314276	−	0.00166443i
$686$	−42.1090	+	24.3117i	−1.60773	+	0.928223i
$687$	17.8554	−	4.19948i	0.681225	−	0.160220i
$688$	−0.0680730	+	0.0182401i	−0.00259526	+	0.000695397i
$689$	−2.73695	−	4.74053i	−0.104269	−	0.180600i
$690$	−0.0988553	+	1.17810i	−0.00376336	+	0.0448494i
$691$	−35.3243			−1.34380			−0.671900	−	0.740642i	$-0.734522\pi$
$691$	−35.3243			−1.34380			−0.671900	+	0.740642i	$0.734522\pi$
$692$	2.95065	+	2.95065i	0.112167	+	0.112167i
$693$	−51.8196	−	17.3686i	−1.96846	−	0.659779i
$694$	3.13851	+	1.81202i	0.119136	+	0.0687833i
$695$	1.79370	+	1.99431i	0.0680387	+	0.0756485i
$696$	8.15828	−	4.38086i	0.309239	−	0.166056i
$697$	−5.32023	−	19.8554i	−0.201518	−	0.752076i
$698$	2.11801	+	0.567518i	0.0801677	+	0.0214809i
$699$	1.17208	−	38.0378i	0.0443320	−	1.43872i
$700$	22.8287	+	8.79202i	0.862845	+	0.332307i
$701$	31.9857	−	18.4670i	1.20808	−	0.697487i	0.245743	−	0.969335i	$-0.420968\pi$
$701$	31.9857	−	18.4670i	1.20808	−	0.697487i	0.962340	+	0.271848i	$0.0876347\pi$
$702$	22.2213	−	18.4519i	0.838690	−	0.696423i
$703$	3.16578	+	1.19587i	0.119400	+	0.0451032i
$704$	−3.72347			−0.140334
$705$	−3.71753	−	20.6540i	−0.140010	−	0.777874i
$706$	13.8506	+	23.9900i	0.521275	+	0.902875i
$707$	−35.5221	+	9.51812i	−1.33595	+	0.357966i
$708$	−5.28650	+	1.24335i	−0.198679	+	0.0467280i
$709$	−45.3080	−	26.1586i	−1.70158	−	0.982405i	−0.944169	−	0.329463i	$-0.893132\pi$
$709$	−45.3080	−	26.1586i	−1.70158	−	0.982405i	−0.757408	−	0.652942i	$-0.773534\pi$
$710$	0.565977	−	10.6868i	0.0212408	−	0.401067i
$711$	2.19604	−	3.31411i	0.0823581	−	0.124289i
$712$	−3.70600	−	13.8310i	−0.138888	−	0.518338i
$713$	−0.738281	−	2.75530i	−0.0276488	−	0.103187i
$714$	−13.0872	−	24.3717i	−0.489777	−	0.912088i
$715$	−2.44764	+	46.2161i	−0.0915364	+	1.72839i
$716$	−16.0939	−	9.29185i	−0.601459	−	0.347253i
$717$	8.36493	+	35.5661i	0.312394	+	1.32824i
$718$	−17.5349	+	4.69846i	−0.654397	+	0.175345i
$719$	−10.6840	−	18.5052i	−0.398445	−	0.690127i	0.595089	−	0.803660i	$-0.297117\pi$
$719$	−10.6840	−	18.5052i	−0.398445	−	0.690127i	−0.993534	+	0.113533i	$0.963783\pi$
$720$	−4.17032	−	5.25437i	−0.155419	−	0.195819i
$721$	−16.4005			−0.610785
$722$	−10.5177	−	15.8233i	−0.391430	−	0.588883i
$723$	10.4246	+	3.14040i	0.387694	+	0.116793i
$724$	−9.35478	+	5.40099i	−0.347668	+	0.200726i
$725$	−24.4325	+	10.8458i	−0.907401	+	0.402803i
$726$	−4.95865	−	0.152793i	−0.184033	−	0.00567069i
$727$	5.43826	+	1.45718i	0.201694	+	0.0540437i	0.358251	−	0.933625i	$-0.383373\pi$
$727$	5.43826	+	1.45718i	0.201694	+	0.0540437i	−0.156558	+	0.987669i	$0.550040\pi$
$728$	−7.03897	−	26.2698i	−0.260882	−	0.973624i
$729$	−4.96184	+	26.5402i	−0.183772	+	0.982969i
$730$	−9.31976	−	10.3621i	−0.344940	−	0.383519i
$731$	−0.199232	−	0.115027i	−0.00736887	−	0.00425442i
$732$	−3.18770	−	3.39040i	−0.117821	−	0.125313i
$733$	0.898556	+	0.898556i	0.0331889	+	0.0331889i	0.723506	−	0.690318i	$-0.242529\pi$
$733$	0.898556	+	0.898556i	0.0331889	+	0.0331889i	−0.690318	+	0.723506i	$0.742529\pi$
$734$	−21.7702			−0.803554
$735$	−65.3710	−	5.48535i	−2.41124	−	0.202330i
$736$	−0.152626	−	0.264356i	−0.00562587	−	0.00974430i
$737$	30.8336	−	8.26184i	1.13577	−	0.304329i
$738$	12.5103	+	14.1551i	0.460509	+	0.521057i
$739$	−12.4688	+	7.19884i	−0.458671	+	0.264814i	−0.711485	−	0.702701i	$-0.751977\pi$
$739$	−12.4688	+	7.19884i	−0.458671	+	0.264814i	0.252815	+	0.967515i	$0.418644\pi$
$740$	1.73359	+	0.0918121i	0.0637280	+	0.00337508i
$741$	25.5239	−	33.3128i	0.937645	−	1.22378i
$742$	3.40688	−	3.40688i	0.125070	−	0.125070i
$743$	−0.527524	−	0.141350i	−0.0193530	−	0.00518561i	0.249130	−	0.968470i	$-0.419855\pi$
$743$	−0.527524	−	0.141350i	−0.0193530	−	0.00518561i	−0.268483	+	0.963285i	$0.586522\pi$
$744$	13.7612	+	8.52064i	0.504509	+	0.312382i
$745$	9.84325	+	46.4347i	0.360629	+	1.70124i
$746$	−6.33096	+	3.65518i	−0.231793	+	0.133826i
$747$	−13.3350	+	39.7853i	−0.487903	+	1.45567i
$748$	−8.59471	−	8.59471i	−0.314254	−	0.314254i
$749$	56.8818			2.07842
$750$	10.8680	+	16.0277i	0.396843	+	0.585248i
$751$	−19.6556	+	34.0444i	−0.717242	+	1.24230i	0.244847	+	0.969562i	$0.421262\pi$
$751$	−19.6556	+	34.0444i	−0.717242	+	1.24230i	−0.962089	+	0.272737i	$0.912071\pi$
$752$	3.83148	+	3.83148i	0.139720	+	0.139720i
$753$	−6.22475	+	20.6631i	−0.226843	+	0.753005i
$754$	25.7368	+	14.8592i	0.937279	+	0.541139i
$755$	30.0397	+	9.77880i	1.09326	+	0.355887i
$756$	20.7500	+	14.6890i	0.754669	+	0.534232i
$757$	27.4691	+	7.36033i	0.998383	+	0.267516i	0.720768	−	0.693177i	$-0.243789\pi$
$757$	27.4691	+	7.36033i	0.998383	+	0.267516i	0.277615	+	0.960692i	$0.410456\pi$
$758$	−7.53212	−	2.01822i	−0.273579	−	0.0733052i
$759$	−0.931347	−	1.73440i	−0.0338058	−	0.0629549i
$760$	−7.60397	−	6.09751i	−0.275825	−	0.221180i
$761$			38.3903i			1.39165i	0.718213	+	0.695823i	$0.244960\pi$
$761$			38.3903i			1.39165i	−0.718213	+	0.695823i	$0.755040\pi$
$762$	−1.19325	−	5.07349i	−0.0432270	−	0.183793i
$763$	−10.5164	+	39.2479i	−0.380720	+	1.42087i
$764$	−8.68514	+	15.0431i	−0.314217	+	0.544241i
$765$	2.50225	−	21.7546i	0.0904691	−	0.786538i
$766$	12.3068	−	21.3160i	0.444662	−	0.770177i
$767$	−12.3240	−	12.3240i	−0.444995	−	0.444995i
$768$	1.65843	+	0.499603i	0.0598435	+	0.0180279i
$769$	−19.0387	−	10.9920i	−0.686555	−	0.396382i	0.115765	−	0.993277i	$-0.463068\pi$
$769$	−19.0387	−	10.9920i	−0.686555	−	0.396382i	−0.802320	+	0.596894i	$0.796401\pi$
$770$	−39.8504	+	8.44750i	−1.43611	+	0.304427i
$771$	10.5672	+	19.6787i	0.380567	+	0.708712i
$772$	−2.50497	+	2.50497i	−0.0901560	+	0.0901560i
$773$	1.83101	+	6.83343i	0.0658569	+	0.245781i	0.991005	−	0.133825i	$-0.0427261\pi$
$773$	1.83101	+	6.83343i	0.0658569	+	0.245781i	−0.925148	+	0.379606i	$0.876059\pi$
$774$	0.211022	+	0.0130170i	0.00758502	+	0.000467886i
$775$	−37.7699	−	27.5051i	−1.35673	−	0.988013i
$776$	−11.0642	+	6.38794i	−0.397183	+	0.229314i
$777$	−6.40447	+	1.50629i	−0.229759	+	0.0540379i
$778$	−16.4649	−	16.4649i	−0.590296	−	0.590296i
$779$	22.2919	+	16.0148i	0.798689	+	0.573790i
$780$	7.29130	−	20.2562i	0.261070	−	0.725289i
$781$	8.91019	+	15.4329i	0.318832	+	0.552233i
$782$	0.257901	−	0.962500i	0.00922253	−	0.0344189i
$783$	−27.3827	+	4.68319i	−0.978579	+	0.167363i
$784$	14.6688	−	8.46902i	0.523884	−	0.302465i
$785$	−14.1256	−	9.18438i	−0.504166	−	0.327804i
$786$	−9.72024	+	5.21961i	−0.346709	+	0.186177i
$787$	−27.0679	+	27.0679i	−0.964865	+	0.964865i	−0.999403	−	0.0345379i	$-0.989004\pi$
$787$	−27.0679	+	27.0679i	−0.964865	+	0.964865i	0.0345379	+	0.999403i	$0.489004\pi$
$788$	−4.12798	−	15.4058i	−0.147053	−	0.548810i
$789$	−0.785915	+	25.5056i	−0.0279793	+	0.908022i
$790$	0.156718	−	2.95914i	0.00557577	−	0.105281i
$791$		−	42.8275i		−	1.52277i
$792$	10.5913	+	3.54994i	0.376346	+	0.126142i
$793$	3.86542	−	14.4259i	0.137265	−	0.512280i
$794$	8.04871	−	13.9408i	0.285638	−	0.494739i
$795$	3.75362	−	0.675618i	0.133127	−	0.0239617i
$796$	4.03269	+	6.98482i	0.142935	+	0.247570i
$797$	−17.2528	−	17.2528i	−0.611126	−	0.611126i	0.332114	−	0.943239i	$-0.392238\pi$
$797$	−17.2528	−	17.2528i	−0.611126	−	0.611126i	−0.943239	+	0.332114i	$0.892238\pi$
$798$	34.1370	+	14.1114i	1.20844	+	0.499537i
$799$			17.6880i			0.625758i
$800$	−4.66592	−	1.79699i	−0.164965	−	0.0635330i
$801$	−2.64477	+	42.8751i	−0.0934485	+	1.51492i
$802$	−6.16588	−	23.0114i	−0.217725	−	0.812561i
$803$	22.4164	+	6.00647i	0.791059	+	0.211964i
$804$	−14.8418	−	0.457328i	−0.523430	−	0.0161287i
$805$	−2.23323	−	2.48300i	−0.0787109	−	0.0875143i
$806$			51.9440i			1.82965i
$807$	18.6771	−	17.5605i	0.657467	−	0.618160i
$808$	7.26030	−	1.94539i	0.255416	−	0.0684386i
$809$	32.9170			1.15730			0.578649	−	0.815577i	$-0.303580\pi$
$809$	32.9170			1.15730			0.578649	+	0.815577i	$0.303580\pi$
$810$	6.85289	+	18.9219i	0.240786	+	0.664847i
$811$	10.1940	−	17.6565i	0.357960	−	0.620004i	−0.629660	−	0.776871i	$-0.716806\pi$
$811$	10.1940	−	17.6565i	0.357960	−	0.620004i	0.987620	+	0.156866i	$0.0501392\pi$
$812$	−6.77011	+	25.2664i	−0.237584	+	0.886677i
$813$	10.5103	−	9.88190i	0.368611	−	0.346573i
$814$	−2.50350	+	1.44540i	−0.0877478	+	0.0506612i
$815$	−16.1435	−	31.7267i	−0.565483	−	1.11134i
$816$	2.67487	+	4.98129i	0.0936392	+	0.174380i
$817$	0.303147	−	0.0496747i	0.0106058	−	0.00173790i
$818$	−22.9670	+	22.9670i	−0.803022	+	0.803022i
$819$	−5.02334	+	81.4347i	−0.175530	+	2.84556i
$820$	13.3890	+	4.35853i	0.467566	+	0.152206i
$821$	15.3387	+	8.85578i	0.535323	+	0.309069i	0.743181	−	0.669090i	$-0.233316\pi$
$821$	15.3387	+	8.85578i	0.535323	+	0.309069i	−0.207858	+	0.978159i	$0.566649\pi$
$822$	−0.621082	+	0.146075i	−0.0216627	+	0.00509494i
$823$	5.46105	−	1.46328i	0.190360	−	0.0510069i	−0.162379	−	0.986728i	$-0.551917\pi$
$823$	5.46105	−	1.46328i	0.190360	−	0.0510069i	0.352740	+	0.935722i	$0.385250\pi$
$824$	3.35206			0.116775
$825$	−29.7205	−	12.5105i	−1.03473	−	0.435559i
$826$	7.67031	−	13.2854i	0.266884	−	0.462257i
$827$	−38.6474	+	10.3555i	−1.34390	+	0.360098i	−0.857881	−	0.513849i	$-0.828219\pi$
$827$	−38.6474	+	10.3555i	−1.34390	+	0.360098i	−0.486022	+	0.873947i	$0.661552\pi$
$828$	0.182105	+	0.897468i	0.00632859	+	0.0311892i
$829$		−	15.5487i		−	0.540030i	−0.962856	−	0.270015i	$-0.912971\pi$
$829$		−	15.5487i		−	0.540030i	0.962856	−	0.270015i	$-0.0870286\pi$
$830$	6.48569	+	30.5957i	0.225122	+	1.06199i
$831$	43.7147	+	27.0673i	1.51645	+	0.938953i
$832$	1.43868	+	5.36924i	0.0498774	+	0.186145i
$833$	53.4078	+	14.3106i	1.85047	+	0.495832i
$834$	1.76648	+	1.09377i	0.0611681	+	0.0378740i
$835$	−36.0137	−	1.90731i	−1.24631	−	0.0660052i
$836$	16.1502	+	1.61030i	0.558565	+	0.0556934i
$837$	−31.0198	−	37.3566i	−1.07220	−	1.29123i
$838$	−4.43620	+	16.5561i	−0.153246	+	0.571922i
$839$	−1.70665	−	2.95601i	−0.0589201	−	0.102053i	0.835061	−	0.550158i	$-0.185432\pi$
$839$	−1.70665	−	2.95601i	−0.0589201	−	0.102053i	−0.893981	+	0.448105i	$0.852099\pi$
$840$	18.8828	+	1.58447i	0.651518	+	0.0546696i
$841$	0.208413	+	0.360981i	0.00718665	+	0.0124476i
$842$	0.579151	−	0.155183i	0.0199589	−	0.00534796i
$843$	−13.2772	+	44.0739i	−0.457293	+	1.51798i
$844$			2.32093i			0.0798896i
$845$	39.1523	−	8.29952i	1.34688	−	0.285512i
$846$	−7.24563	−	14.5515i	−0.249110	−	0.500289i
$847$	9.90919	−	9.90919i	0.340484	−	0.340484i
$848$	−0.696326	+	0.696326i	−0.0239119	+	0.0239119i
$849$	20.4355	+	0.629687i	0.701344	+	0.0216108i
$850$	−6.62223	−	14.9180i	−0.227141	−	0.511684i
$851$	−0.205239	−	0.118495i	−0.00703549	−	0.00406194i
$852$	−1.89786	−	8.06935i	−0.0650196	−	0.276451i
$853$	9.73773	−	36.3417i	0.333414	−	1.24432i	−0.572165	−	0.820139i	$-0.693896\pi$
$853$	9.73773	−	36.3417i	0.333414	−	1.24432i	0.905579	−	0.424178i	$-0.139437\pi$
$854$	13.1454			0.449828
$855$	15.8160	+	24.5938i	0.540894	+	0.841091i
$856$	−11.6260			−0.397368
$857$	−9.40220	+	35.0895i	−0.321173	+	1.19863i	0.596931	+	0.802293i	$0.296387\pi$
$857$	−9.40220	+	35.0895i	−0.321173	+	1.19863i	−0.918104	+	0.396341i	$0.870280\pi$
$858$	8.20753	+	34.8968i	0.280200	+	1.19136i
$859$	−13.2982	−	7.67772i	−0.453729	−	0.261960i	0.255675	−	0.966763i	$-0.417702\pi$
$859$	−13.2982	−	7.67772i	−0.453729	−	0.261960i	−0.709404	+	0.704802i	$0.751036\pi$
$860$	0.140449	−	0.0714648i	0.00478927	−	0.00243693i
$861$	−53.3378	−	1.64352i	−1.81775	−	0.0560111i
$862$	−21.1468	+	21.1468i	−0.720265	+	0.720265i
$863$	−4.31936	+	4.31936i	−0.147033	+	0.147033i	−0.776791	−	0.629758i	$-0.783154\pi$
$863$	−4.31936	+	4.31936i	−0.147033	+	0.147033i	0.629758	+	0.776791i	$0.283154\pi$
$864$	−4.24105	−	3.00225i	−0.144283	−	0.102139i
$865$	−7.82264	−	5.08622i	−0.265978	−	0.172937i
$866$		−	2.08907i		−	0.0709895i
$867$	3.16945	−	10.5210i	0.107640	−	0.357312i
$868$	−44.1626	+	11.8333i	−1.49898	+	0.401649i
$869$	2.46721	+	4.27334i	0.0836945	+	0.144963i
$870$	−15.8145	+	13.3660i	−0.536162	+	0.453148i
$871$	−23.8271	−	41.2698i	−0.807351	−	1.39837i
$872$	2.14943	−	8.02180i	0.0727890	−	0.271652i
$873$	37.5622	−	7.62174i	1.27129	−	0.257957i
$874$	0.547672	+	1.21262i	0.0185253	+	0.0410176i
$875$	−54.0138	−	8.64655i	−1.82600	−	0.292307i
$876$	−9.17834	−	5.68304i	−0.310108	−	0.192012i
$877$	−37.4075	−	10.0233i	−1.26316	−	0.338463i	−0.435753	−	0.900066i	$-0.643518\pi$
$877$	−37.4075	−	10.0233i	−1.26316	−	0.338463i	−0.827407	+	0.561603i	$0.810185\pi$
$878$	−10.2359	−	38.2009i	−0.345445	−	1.28922i
$879$	4.33949	+	2.68692i	0.146367	+	0.0906276i
$880$	8.14495	−	1.72657i	0.274566	−	0.0582026i
$881$		−	10.4726i		−	0.352830i	−0.984316	−	0.176415i	$-0.943550\pi$
$881$		−	10.4726i		−	0.352830i	0.984316	−	0.176415i	$-0.0564501\pi$
$882$	−49.7993	+	10.1048i	−1.67683	+	0.340245i
$883$	1.64428	−	0.440584i	0.0553345	−	0.0148268i	−0.231046	−	0.972943i	$-0.574215\pi$
$883$	1.64428	−	0.440584i	0.0553345	−	0.0148268i	0.286380	+	0.958116i	$0.407548\pi$
$884$	−9.07271	+	15.7144i	−0.305148	+	0.528532i
$885$	10.9875	−	5.17112i	0.369339	−	0.173825i
$886$	−38.6027			−1.29688
$887$	46.0525	−	12.3397i	1.54629	−	0.414328i	0.618000	−	0.786178i	$-0.287943\pi$
$887$	46.0525	−	12.3397i	1.54629	−	0.414328i	0.928293	+	0.371851i	$0.121277\pi$
$888$	1.30900	−	0.307868i	0.0439271	−	0.0103314i
$889$	12.7501	+	7.36125i	0.427623	+	0.246889i
$890$	14.5201	+	28.5362i	0.486716	+	0.956537i
$891$	−26.7422	−	20.1954i	−0.895899	−	0.676573i
$892$	5.34941	−	5.34941i	0.179112	−	0.179112i
$893$	−14.9616	−	18.2756i	−0.500671	−	0.611571i
$894$	17.3943	+	32.3926i	0.581753	+	1.08337i
$895$	39.5135	+	12.8628i	1.32079	+	0.429956i
$896$	−4.23716	+	2.44633i	−0.141554	+	0.0817260i
$897$	−2.14115	+	2.01314i	−0.0714910	+	0.0672169i
$898$	−8.05639	+	30.0668i	−0.268845	+	1.00334i
$899$	24.9799	−	43.2665i	0.833128	−	1.44302i
$900$	11.5589	+	9.55995i	0.385295	+	0.318665i
$901$	−3.21459			−0.107094
$902$	−22.6479	+	6.06849i	−0.754093	+	0.202059i
$903$	−0.435106	+	0.409093i	−0.0144794	+	0.0136138i
$904$			8.75344i			0.291135i
$905$	17.9588	−	16.1522i	0.596970	−	0.536919i
$906$	24.4589	+	0.753662i	0.812592	+	0.0250388i
$907$	46.5820	+	12.4816i	1.54673	+	0.414445i	0.928433	−	0.371499i	$-0.121156\pi$
$907$	46.5820	+	12.4816i	1.54673	+	0.414445i	0.618298	+	0.785944i	$0.287823\pi$
$908$	−3.30842	−	12.3472i	−0.109794	−	0.409756i
$909$	−22.5065	−	1.38832i	−0.746492	−	0.0460477i
$910$	27.5788	+	54.2002i	0.914227	+	1.79672i
$911$			22.1407i			0.733553i	0.930309	+	0.366776i	$0.119539\pi$
$911$			22.1407i			0.733553i	−0.930309	+	0.366776i	$0.880461\pi$
$912$	−6.97721	−	2.88420i	−0.231038	−	0.0955054i
$913$	−36.8259	−	36.8259i	−1.21876	−	1.21876i
$914$	2.85512	+	4.94522i	0.0944391	+	0.163573i
$915$	8.54510	+	5.93823i	0.282492	+	0.196312i
$916$	5.29505	−	9.17129i	0.174953	−	0.303028i
$917$	8.06629	−	30.1038i	0.266372	−	0.994116i
$918$	−2.85946	−	16.7194i	−0.0943764	−	0.551821i
$919$			40.5856i			1.33880i	0.742904	+	0.669398i	$0.233448\pi$
$919$			40.5856i			1.33880i	−0.742904	+	0.669398i	$0.766552\pi$
$920$	0.456445	+	0.507496i	0.0150486	+	0.0167317i
$921$	−0.968429	+	31.4288i	−0.0319108	+	1.03561i
$922$	−0.454788	−	1.69729i	−0.0149776	−	0.0558973i
$923$	18.8115	−	18.8115i	0.619187	−	0.619187i
$924$	−27.7994	+	14.9278i	−0.914534	+	0.491090i
$925$	−3.83473	+	0.603028i	−0.126085	+	0.0198274i
$926$	9.42756	−	5.44300i	0.309809	−	0.178868i
$927$	−9.53486	−	3.19584i	−0.313166	−	0.104965i
$928$	1.38373	−	5.16415i	0.0454232	−	0.169522i
$929$	−8.35681	−	14.4744i	−0.274178	−	0.474890i	0.695749	−	0.718285i	$-0.255072\pi$
$929$	−8.35681	−	14.4744i	−0.274178	−	0.474890i	−0.969927	+	0.243394i	$0.921739\pi$
$930$	−34.0531	−	12.2575i	−1.11664	−	0.401940i
$931$	−67.2868	+	30.3896i	−2.20524	+	0.995979i
$932$	−15.5362	−	15.5362i	−0.508906	−	0.508906i
$933$	3.24894	−	0.764130i	0.106365	−	0.0250165i
$934$	5.65123	−	3.26274i	0.184914	−	0.106760i
$935$	22.7859	+	14.8152i	0.745180	+	0.484510i
$936$	1.02671	−	16.6443i	0.0335591	−	0.544036i
$937$	−14.9416	−	55.7627i	−0.488120	−	1.82169i	−0.565582	−	0.824692i	$-0.691348\pi$
$937$	−14.9416	−	55.7627i	−0.488120	−	1.82169i	0.0774623	−	0.996995i	$-0.475318\pi$
$938$	29.6594	−	29.6594i	0.968412	−	0.968412i
$939$	16.1294	+	30.0370i	0.526362	+	0.980219i
$940$	−10.1579	−	6.60455i	−0.331313	−	0.215417i
$941$	−13.6214	−	7.86433i	−0.444045	−	0.256370i	0.261267	−	0.965267i	$-0.415860\pi$
$941$	−13.6214	−	7.86433i	−0.444045	−	0.256370i	−0.705312	+	0.708897i	$0.749193\pi$
$942$	−12.4964	−	3.76454i	−0.407155	−	0.122655i
$943$	−1.35919	−	1.35919i	−0.0442613	−	0.0442613i
$944$	−1.56772	+	2.71537i	−0.0510249	+	0.0883778i
$945$	−52.2010	−	22.5098i	−1.69810	−	0.732243i
$946$	−0.131205	+	0.227253i	−0.00426583	+	0.00738863i
$947$	6.23968	−	23.2868i	0.202762	−	0.756719i	−0.787358	−	0.616496i	$-0.788552\pi$
$947$	6.23968	−	23.2868i	0.202762	−	0.756719i	0.990120	−	0.140223i	$-0.0447818\pi$
$948$	−0.525514	−	2.23438i	−0.0170679	−	0.0725694i
$949$		−	34.6453i		−	1.12463i
$950$	19.4608	+	9.81212i	0.631391	+	0.318347i
$951$	−5.68824	−	10.5929i	−0.184454	−	0.343500i
$952$	−15.4272	−	4.13370i	−0.499997	−	0.133974i
$953$	−5.66974	−	1.51920i	−0.183661	−	0.0492118i	0.165816	−	0.986157i	$-0.446974\pi$
$953$	−5.66974	−	1.51920i	−0.183661	−	0.0492118i	−0.349477	+	0.936945i	$0.613641\pi$
$954$	2.64456	−	1.31681i	0.0856206	−	0.0426332i
$955$	12.0229	−	36.9335i	0.389053	−	1.19514i
$956$	18.2683	+	10.5472i	0.590839	+	0.341121i
$957$	9.94553	−	33.0142i	0.321493	−	1.06720i
$958$	−21.6977	−	21.6977i	−0.701020	−	0.701020i
$959$	0.901144	−	1.56083i	0.0290995	−	0.0504017i
$960$	−3.85942	−	0.323848i	−0.124562	−	0.0104521i
$961$	56.3238			1.81690
$962$	3.05157	+	3.05157i	0.0983866	+	0.0983866i
$963$	33.0698	+	11.0842i	1.06566	+	0.357182i
$964$	5.44367	−	3.14290i	0.175329	−	0.101226i
$965$	4.31798	−	6.64108i	0.139001	−	0.213784i
$966$	−2.19934	−	1.36179i	−0.0707626	−	0.0438147i
$967$	51.9375	+	13.9166i	1.67020	+	0.447528i	0.965164	−	0.261647i	$-0.0842655\pi$
$967$	51.9375	+	13.9166i	1.67020	+	0.447528i	0.705033	+	0.709175i	$0.250932\pi$
$968$	−2.02532	+	2.02532i	−0.0650963	+	0.0650963i
$969$	−9.44769	−	22.7626i	−0.303504	−	0.731240i
$970$	21.2405	−	19.1038i	0.681992	−	0.613387i
$971$	23.5909	−	13.6202i	0.757069	−	0.437094i	−0.0711734	−	0.997464i	$-0.522674\pi$
$971$	23.5909	−	13.6202i	0.757069	−	0.437094i	0.828242	+	0.560370i	$0.189341\pi$
$972$	9.20123	+	12.5832i	0.295129	+	0.403607i
$973$	−5.66901	+	1.51901i	−0.181740	+	0.0486971i
$974$	2.94715	+	5.10461i	0.0944327	+	0.163562i
$975$	−6.55664	+	47.6907i	−0.209981	+	1.52732i
$976$	−2.68677			−0.0860015
$977$	−7.80906	−	7.80906i	−0.249834	−	0.249834i	0.571068	−	0.820902i	$-0.306529\pi$
$977$	−7.80906	−	7.80906i	−0.249834	−	0.249834i	−0.820902	+	0.571068i	$0.806529\pi$
$978$	−18.8879	−	20.0889i	−0.603968	−	0.642372i
$979$	−46.1729	−	26.6580i	−1.47569	−	0.851992i
$980$	−28.1603	+	25.3275i	−0.899547	+	0.809058i
$981$	−13.7620	+	20.7685i	−0.439386	+	0.663088i
$982$	−8.17061	−	30.4931i	−0.260735	−	0.973075i
$983$	−51.2500	−	13.7324i	−1.63462	−	0.437995i	−0.679371	−	0.733795i	$-0.737747\pi$
$983$	−51.2500	−	13.7324i	−1.63462	−	0.437995i	−0.955250	+	0.295800i	$0.904414\pi$
$984$	10.9016	+	0.335916i	0.347531	+	0.0107086i
$985$	16.1735	+	31.7855i	0.515329	+	1.01277i
$986$	15.1142	−	8.72617i	0.481333	−	0.277898i
$987$	43.9666	+	13.2449i	1.39947	+	0.421591i
$988$	−3.91808	−	23.9107i	−0.124651	−	0.760700i
$989$	−0.0215124			−0.000684056
$990$	−24.8142	−	2.85418i	−0.788647	−	0.0907117i
$991$	−15.5203	−	26.8820i	−0.493020	−	0.853936i	0.506948	−	0.861977i	$-0.330774\pi$
$991$	−15.5203	−	26.8820i	−0.493020	−	0.853936i	−0.999968	+	0.00804105i	$0.997440\pi$
$992$	9.02631	−	2.41859i	0.286586	−	0.0767904i
$993$	9.49005	+	40.3499i	0.301158	+	1.28047i
$994$	20.2789	+	11.7080i	0.643207	+	0.371356i
$995$	−12.0602	−	13.4091i	−0.382334	−	0.425096i
$996$	11.4611	+	21.3434i	0.363158	+	0.676292i
$997$	6.20363	+	23.1523i	0.196471	+	0.733240i	0.991881	+	0.127168i	$0.0405888\pi$
$997$	6.20363	+	23.1523i	0.196471	+	0.733240i	−0.795410	+	0.606072i	$0.792745\pi$
$998$	−6.03095	−	22.5078i	−0.190906	−	0.712472i
$999$	−4.01693	−	0.372270i	−0.127090	−	0.0117781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.v.c.83.9	✓	144
3.2	odd	2	inner	570.2.v.c.83.31	yes	144
5.2	odd	4	inner	570.2.v.c.197.2	yes	144
15.2	even	4	inner	570.2.v.c.197.24	yes	144
19.11	even	3	inner	570.2.v.c.353.24	yes	144
57.11	odd	6	inner	570.2.v.c.353.2	yes	144
95.87	odd	12	inner	570.2.v.c.467.31	yes	144
285.182	even	12	inner	570.2.v.c.467.9	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.c.83.9	✓	144	1.1	even	1	trivial
570.2.v.c.83.31	yes	144	3.2	odd	2	inner
570.2.v.c.197.2	yes	144	5.2	odd	4	inner
570.2.v.c.197.24	yes	144	15.2	even	4	inner
570.2.v.c.353.2	yes	144	57.11	odd	6	inner
570.2.v.c.353.24	yes	144	19.11	even	3	inner
570.2.v.c.467.9	yes	144	285.182	even	12	inner
570.2.v.c.467.31	yes	144	95.87	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.396548 - 1.68605i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.12625 + 0.692155i) q^{5} +(1.73123 + 0.0533452i) q^{6} +(-3.45963 + 3.45963i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.68550 + 1.33719i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.396548 - 1.68605i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.12625 + 0.692155i) q^{5} +(1.73123 + 0.0533452i) q^{6} +(-3.45963 + 3.45963i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.68550 + 1.33719i) q^{9} +(-1.21888 + 1.87465i) q^{10} -3.72347i q^{11} +(-0.499603 + 1.65843i) q^{12} +(-5.36924 + 1.43868i) q^{13} +(-2.44633 - 4.23716i) q^{14} +(0.323848 - 3.85942i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.844879 + 3.15313i) q^{17} +(-0.596572 - 2.94009i) q^{18} +(-1.79416 - 3.97253i) q^{19} +(-1.49531 - 1.66255i) q^{20} +(7.20499 + 4.46118i) q^{21} +(3.59660 + 0.963705i) q^{22} +(0.0790051 + 0.294851i) q^{23} +(-1.47262 - 0.911813i) q^{24} +(4.04184 + 2.94338i) q^{25} -5.55864i q^{26} +(3.31950 + 3.99761i) q^{27} +(4.72594 - 1.26631i) q^{28} +(-2.67316 + 4.63005i) q^{29} +(3.64410 + 1.31170i) q^{30} -9.34472 q^{31} +(-0.965926 + 0.258819i) q^{32} +(-6.27794 + 1.47653i) q^{33} +(-2.82702 - 1.63218i) q^{34} +(-9.75062 + 4.96142i) q^{35} +(2.99431 + 0.184705i) q^{36} +(-0.548978 + 0.548978i) q^{37} +(4.30153 - 0.704863i) q^{38} +(4.55484 + 8.48227i) q^{39} +(1.99291 - 1.01405i) q^{40} +(-5.45339 + 3.14852i) q^{41} +(-6.17396 + 5.80485i) q^{42} +(-0.0182401 + 0.0680730i) q^{43} +(-1.86174 + 3.22462i) q^{44} +(-6.63558 + 0.984421i) q^{45} -0.305252 q^{46} +(5.23390 - 1.40242i) q^{47} +(1.26188 - 1.18644i) q^{48} -16.9380i q^{49} +(-3.88920 + 3.14232i) q^{50} +(5.65136 + 0.174138i) q^{51} +(5.36924 + 1.43868i) q^{52} +(0.254873 + 0.951199i) q^{53} +(-4.72055 + 2.17173i) q^{54} +(2.57722 - 7.91701i) q^{55} +4.89265i q^{56} +(-5.98639 + 4.60034i) q^{57} +(-3.78042 - 3.78042i) q^{58} +(1.56772 + 2.71537i) q^{59} +(-2.21017 + 3.18043i) q^{60} +(-1.34339 + 2.32681i) q^{61} +(2.41859 - 9.02631i) q^{62} +(4.66463 - 13.9170i) q^{63} -1.00000i q^{64} +(-12.4121 - 0.657354i) q^{65} +(0.198629 - 6.44618i) q^{66} +(2.21885 + 8.28088i) q^{67} +(2.30825 - 2.30825i) q^{68} +(0.465803 - 0.250129i) q^{69} +(-2.26872 - 10.7025i) q^{70} +(-4.14476 + 2.39298i) q^{71} +(-0.953396 + 2.84447i) q^{72} +(-1.61314 + 6.02031i) q^{73} +(-0.388186 - 0.672358i) q^{74} +(3.35990 - 7.98192i) q^{75} +(-0.432473 + 4.33739i) q^{76} +(12.8818 + 12.8818i) q^{77} +(-9.37213 + 2.20427i) q^{78} +(-1.14768 + 0.662611i) q^{79} +(0.463699 + 2.18746i) q^{80} +(5.42382 - 7.18207i) q^{81} +(-1.62979 - 6.08247i) q^{82} +(9.89021 - 9.89021i) q^{83} +(-4.00912 - 7.46599i) q^{84} +(-3.97888 + 6.11954i) q^{85} +(-0.0610325 - 0.0352372i) q^{86} +(8.86651 + 2.67104i) q^{87} +(-2.63289 - 2.63289i) q^{88} +(7.15944 - 12.4005i) q^{89} +(0.766536 - 6.66426i) q^{90} +(13.5983 - 23.5529i) q^{91} +(0.0790051 - 0.294851i) q^{92} +(3.70563 + 15.7556i) q^{93} +5.41853i q^{94} +(-1.06523 - 9.68841i) q^{95} +(0.819416 + 1.52596i) q^{96} +(-12.3406 - 3.30664i) q^{97} +(16.3609 + 4.38389i) q^{98} +(4.97901 + 9.99938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) \) 144 * q - 4 * q^3 + 8 * q^6	\( 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) \) 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Introduction

L-functions

Modular forms

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Database

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