LMFDB - Embedded newform 57.2.j.b.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(2,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 1]))

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

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

chi := DirichletCharacter("57.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.j (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			53.1
Character	$\chi$	$=$	57.53
Dual form			57.2.j.b.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08555 - 0.759077i) q^{2} +(-1.47284 + 0.911455i) q^{3} +(2.24122 + 1.88060i) q^{4} +(1.78018 + 2.12154i) q^{5} +(3.76353 - 0.782886i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(-1.02725 - 1.77924i) q^{8} +(1.33850 - 2.68485i) q^{9} +O(q^{10})$	\(q+(-2.08555 - 0.759077i) q^{2} +(-1.47284 + 0.911455i) q^{3} +(2.24122 + 1.88060i) q^{4} +(1.78018 + 2.12154i) q^{5} +(3.76353 - 0.782886i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(-1.02725 - 1.77924i) q^{8} +(1.33850 - 2.68485i) q^{9} +(-2.10224 - 5.77587i) q^{10} +(-2.03664 + 1.17586i) q^{11} +(-5.01503 - 0.727055i) q^{12} +(-0.115554 - 0.0203753i) q^{13} +(5.81156 - 4.87648i) q^{14} +(-4.55561 - 1.50212i) q^{15} +(-0.224297 - 1.27205i) q^{16} +(-0.519239 + 1.42660i) q^{17} +(-4.82951 + 4.58336i) q^{18} +(3.41260 + 2.71186i) q^{19} +8.10265i q^{20} +(-0.180911 - 5.91783i) q^{21} +(5.14008 - 0.906334i) q^{22} +(4.79880 - 5.71899i) q^{23} +(3.13467 + 1.68425i) q^{24} +(-0.463638 + 2.62942i) q^{25} +(0.225527 + 0.130208i) q^{26} +(0.475732 + 5.17433i) q^{27} +(-9.39767 + 3.42047i) q^{28} +(1.69319 - 0.616270i) q^{29} +(8.36070 + 6.59081i) q^{30} +(-1.23287 - 0.711795i) q^{31} +(-1.21132 + 6.86975i) q^{32} +(1.92790 - 3.58815i) q^{33} +(2.16579 - 2.58109i) q^{34} +(-9.32295 + 1.64389i) q^{35} +(8.04901 - 3.50015i) q^{36} -3.31937i q^{37} +(-5.05862 - 8.24613i) q^{38} +(0.188763 - 0.0753128i) q^{39} +(1.94605 - 5.34672i) q^{40} +(0.635235 + 3.60260i) q^{41} +(-4.11479 + 12.4792i) q^{42} +(3.60739 - 3.02696i) q^{43} +(-6.77588 - 1.19477i) q^{44} +(8.07879 - 1.93985i) q^{45} +(-14.3493 + 8.28456i) q^{46} +(-2.61102 - 7.17373i) q^{47} +(1.48977 + 1.66909i) q^{48} +(-2.34224 - 4.05687i) q^{49} +(2.96287 - 5.13184i) q^{50} +(-0.535525 - 2.57441i) q^{51} +(-0.220664 - 0.262977i) q^{52} +(2.93617 + 2.46374i) q^{53} +(2.93555 - 11.1524i) q^{54} +(-6.12022 - 2.22758i) q^{55} +7.02278 q^{56} +(-7.49794 - 0.883697i) q^{57} -3.99901 q^{58} +(10.5343 + 3.83419i) q^{59} +(-7.38520 - 11.9339i) q^{60} +(6.58405 + 5.52467i) q^{61} +(2.03089 + 2.42032i) q^{62} +(5.66029 + 8.55110i) q^{63} +(6.44925 - 11.1704i) q^{64} +(-0.162480 - 0.281424i) q^{65} +(-6.74441 + 6.01983i) q^{66} +(-0.0605694 - 0.166413i) q^{67} +(-3.84659 + 2.22083i) q^{68} +(-1.85525 + 12.7970i) q^{69} +(20.6913 + 3.64843i) q^{70} +(-5.60649 + 4.70441i) q^{71} +(-6.15197 + 0.376489i) q^{72} +(0.838249 + 4.75394i) q^{73} +(-2.51966 + 6.92270i) q^{74} +(-1.71374 - 4.29529i) q^{75} +(2.54844 + 12.4956i) q^{76} -8.03875i q^{77} +(-0.450843 + 0.0137825i) q^{78} +(-6.89453 + 1.21569i) q^{79} +(2.29942 - 2.74034i) q^{80} +(-5.41684 - 7.18734i) q^{81} +(1.40984 - 7.99558i) q^{82} +(0.836326 + 0.482853i) q^{83} +(10.7236 - 13.6034i) q^{84} +(-3.95092 + 1.43802i) q^{85} +(-9.82108 + 3.57458i) q^{86} +(-1.93209 + 2.45093i) q^{87} +(4.18427 + 2.41579i) q^{88} +(2.02208 - 11.4678i) q^{89} +(-18.3212 - 2.08678i) q^{90} +(0.257813 - 0.307250i) q^{91} +(21.5103 - 3.79285i) q^{92} +(2.46458 - 0.0753434i) q^{93} +16.9431i q^{94} +(0.321731 + 12.0676i) q^{95} +(-4.47739 - 11.2221i) q^{96} +(1.73122 - 4.75650i) q^{97} +(1.80536 + 10.2387i) q^{98} +(0.430956 + 7.04196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	$ 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−2.08555	−	0.759077i	−1.47470	−	0.536748i	−0.525331	−	0.850898i	$-0.676058\pi$
$2$	−2.08555	−	0.759077i	−1.47470	−	0.536748i	−0.949373	+	0.314150i	$0.898281\pi$
$3$	−1.47284	+	0.911455i	−0.850343	+	0.526229i
$3$	−1.47284	+	0.911455i	−0.850343	+	0.526229i
$4$	2.24122	+	1.88060i	1.12061	+	0.940302i
$5$	1.78018	+	2.12154i	0.796122	+	0.948781i	0.999541	−	0.0303104i	$-0.00964959\pi$
$5$	1.78018	+	2.12154i	0.796122	+	0.948781i	−0.203418	+	0.979092i	$0.565205\pi$
$6$	3.76353	−	0.782886i	1.53646	−	0.319612i
$7$	−1.70913	+	2.96030i	−0.645990	+	1.11889i	0.338082	+	0.941117i	$0.390222\pi$
$7$	−1.70913	+	2.96030i	−0.645990	+	1.11889i	−0.984072	+	0.177770i	$0.943112\pi$
$8$	−1.02725	−	1.77924i	−0.363186	−	0.629057i
$9$	1.33850	−	2.68485i	0.446166	−	0.894950i
$10$	−2.10224	−	5.77587i	−0.664788	−	1.82649i
$11$	−2.03664	+	1.17586i	−0.614071	+	0.354534i	−0.774557	−	0.632504i	$-0.782027\pi$
$11$	−2.03664	+	1.17586i	−0.614071	+	0.354534i	0.160486	+	0.987038i	$0.448694\pi$
$12$	−5.01503	−	0.727055i	−1.44772	−	0.209883i
$13$	−0.115554	−	0.0203753i	−0.0320489	−	0.00565108i	0.157601	−	0.987503i	$-0.449624\pi$
$13$	−0.115554	−	0.0203753i	−0.0320489	−	0.00565108i	−0.189650	+	0.981852i	$0.560735\pi$
$14$	5.81156	−	4.87648i	1.55320	−	1.30329i
$15$	−4.55561	−	1.50212i	−1.17625	−	0.387847i
$16$	−0.224297	−	1.27205i	−0.0560744	−	0.318013i
$17$	−0.519239	+	1.42660i	−0.125934	+	0.346001i	−0.986597	−	0.163174i	$-0.947827\pi$
$17$	−0.519239	+	1.42660i	−0.125934	+	0.346001i	0.860663	+	0.509174i	$0.170049\pi$
$18$	−4.82951	+	4.58336i	−1.13833	+	1.08031i
$19$	3.41260	+	2.71186i	0.782903	+	0.622143i
$19$	3.41260	+	2.71186i	0.782903	+	0.622143i
$20$			8.10265i			1.81181i
$21$	−0.180911	−	5.91783i	−0.0394780	−	1.29138i
$22$	5.14008	−	0.906334i	1.09587	−	0.193231i
$23$	4.79880	−	5.71899i	1.00062	−	1.19249i	0.0193576	−	0.999813i	$-0.493838\pi$
$23$	4.79880	−	5.71899i	1.00062	−	1.19249i	0.981262	−	0.192679i	$-0.0617177\pi$
$24$	3.13467	+	1.68425i	0.639861	+	0.343795i
$25$	−0.463638	+	2.62942i	−0.0927276	+	0.525884i
$26$	0.225527	+	0.130208i	0.0442294	+	0.0255359i
$27$	0.475732	+	5.17433i	0.0915546	+	0.995800i
$28$	−9.39767	+	3.42047i	−1.77599	+	0.646409i
$29$	1.69319	−	0.616270i	0.314417	−	0.114438i	−0.179991	−	0.983668i	$-0.557607\pi$
$29$	1.69319	−	0.616270i	0.314417	−	0.114438i	0.494408	+	0.869230i	$0.335385\pi$
$30$	8.36070	+	6.59081i	1.52645	+	1.20331i
$31$	−1.23287	−	0.711795i	−0.221429	−	0.127842i	0.385183	−	0.922840i	$-0.374138\pi$
$31$	−1.23287	−	0.711795i	−0.221429	−	0.127842i	−0.606612	+	0.794998i	$0.707472\pi$
$32$	−1.21132	+	6.86975i	−0.214133	+	1.21441i
$33$	1.92790	−	3.58815i	0.335605	−	0.624617i
$34$	2.16579	−	2.58109i	0.371431	−	0.442654i
$35$	−9.32295	+	1.64389i	−1.57587	+	0.277868i
$36$	8.04901	−	3.50015i	1.34150	−	0.583358i
$37$		−	3.31937i		−	0.545701i	−0.962056	−	0.272851i	$-0.912034\pi$
$37$		−	3.31937i		−	0.545701i	0.962056	−	0.272851i	$-0.0879665\pi$
$38$	−5.05862	−	8.24613i	−0.820617	−	1.33770i
$39$	0.188763	−	0.0753128i	0.0302263	−	0.0120597i
$40$	1.94605	−	5.34672i	0.307697	−	0.845391i
$41$	0.635235	+	3.60260i	0.0992071	+	0.562631i	0.993377	+	0.114903i	$0.0366557\pi$
$41$	0.635235	+	3.60260i	0.0992071	+	0.562631i	−0.894170	+	0.447728i	$0.852233\pi$
$42$	−4.11479	+	12.4792i	−0.634925	+	1.92559i
$43$	3.60739	−	3.02696i	0.550122	−	0.461607i	−0.324860	−	0.945762i	$-0.605317\pi$
$43$	3.60739	−	3.02696i	0.550122	−	0.461607i	0.874982	+	0.484155i	$0.160873\pi$
$44$	−6.77588	−	1.19477i	−1.02150	−	0.180118i
$45$	8.07879	−	1.93985i	1.20431	−	0.289176i
$46$	−14.3493	+	8.28456i	−2.11569	+	1.22149i
$47$	−2.61102	−	7.17373i	−0.380857	−	1.04640i	−0.970996	−	0.239094i	$-0.923149\pi$
$47$	−2.61102	−	7.17373i	−0.380857	−	1.04640i	0.590139	−	0.807301i	$-0.299073\pi$
$48$	1.48977	+	1.66909i	0.215030	+	0.240913i
$49$	−2.34224	−	4.05687i	−0.334605	−	0.579553i
$50$	2.96287	−	5.13184i	0.419013	−	0.725752i
$51$	−0.535525	−	2.57441i	−0.0749886	−	0.360489i
$52$	−0.220664	−	0.262977i	−0.0306005	−	0.0364683i
$53$	2.93617	+	2.46374i	0.403314	+	0.338421i	0.821773	−	0.569815i	$-0.192985\pi$
$53$	2.93617	+	2.46374i	0.403314	+	0.338421i	−0.418459	+	0.908236i	$0.637430\pi$
$54$	2.93555	−	11.1524i	0.399478	−	1.51765i
$55$	−6.12022	−	2.22758i	−0.825251	−	0.300367i
$56$	7.02278			0.938458
$57$	−7.49794	−	0.883697i	−0.993126	−	0.117049i
$58$	−3.99901			−0.525096
$59$	10.5343	+	3.83419i	1.37145	+	0.499169i	0.919576	−	0.392911i	$-0.128532\pi$
$59$	10.5343	+	3.83419i	1.37145	+	0.499169i	0.451878	+	0.892080i	$0.350754\pi$
$60$	−7.38520	−	11.9339i	−0.953426	−	1.54066i
$61$	6.58405	+	5.52467i	0.843001	+	0.707362i	0.958237	−	0.285976i	$-0.0923178\pi$
$61$	6.58405	+	5.52467i	0.843001	+	0.707362i	−0.115236	+	0.993338i	$0.536762\pi$
$62$	2.03089	+	2.42032i	0.257923	+	0.307381i
$63$	5.66029	+	8.55110i	0.713129	+	1.07734i
$64$	6.44925	−	11.1704i	0.806157	−	1.39630i
$65$	−0.162480	−	0.281424i	−0.0201532	−	0.0349064i
$66$	−6.74441	+	6.01983i	−0.830180	+	0.740990i
$67$	−0.0605694	−	0.166413i	−0.00739974	−	0.0203306i	0.935938	−	0.352165i	$-0.114555\pi$
$67$	−0.0605694	−	0.166413i	−0.00739974	−	0.0203306i	−0.943338	+	0.331835i	$0.892332\pi$
$68$	−3.84659	+	2.22083i	−0.466468	+	0.269315i
$69$	−1.85525	+	12.7970i	−0.223346	+	1.54058i
$70$	20.6913	+	3.64843i	2.47308	+	0.436071i
$71$	−5.60649	+	4.70441i	−0.665368	+	0.558310i	−0.911690	−	0.410878i	$-0.865222\pi$
$71$	−5.60649	+	4.70441i	−0.665368	+	0.558310i	0.246322	+	0.969188i	$0.420778\pi$
$72$	−6.15197	+	0.376489i	−0.725016	+	0.0443697i
$73$	0.838249	+	4.75394i	0.0981096	+	0.556407i	0.993750	+	0.111628i	$0.0356066\pi$
$73$	0.838249	+	4.75394i	0.0981096	+	0.556407i	−0.895640	+	0.444779i	$0.853282\pi$
$74$	−2.51966	+	6.92270i	−0.292904	+	0.804748i
$75$	−1.71374	−	4.29529i	−0.197885	−	0.495978i
$76$	2.54844	+	12.4956i	0.292326	+	1.43334i
$77$		−	8.03875i		−	0.916101i
$78$	−0.450843	+	0.0137825i	−0.0510479	+	0.00156056i
$79$	−6.89453	+	1.21569i	−0.775695	+	0.136776i	−0.547462	−	0.836830i	$-0.684406\pi$
$79$	−6.89453	+	1.21569i	−0.775695	+	0.136776i	−0.228233	+	0.973606i	$0.573295\pi$
$80$	2.29942	−	2.74034i	0.257083	−	0.306380i
$81$	−5.41684	−	7.18734i	−0.601872	−	0.798593i
$82$	1.40984	−	7.99558i	0.155690	−	0.882964i
$83$	0.836326	+	0.482853i	0.0917987	+	0.0530000i	0.545197	−	0.838308i	$-0.316455\pi$
$83$	0.836326	+	0.482853i	0.0917987	+	0.0530000i	−0.453398	+	0.891308i	$0.649788\pi$
$84$	10.7236	−	13.6034i	1.17004	−	1.48425i
$85$	−3.95092	+	1.43802i	−0.428538	+	0.155975i
$86$	−9.82108	+	3.57458i	−1.05903	+	0.385457i
$87$	−1.93209	+	2.45093i	−0.207141	+	0.262767i
$88$	4.18427	+	2.41579i	0.446044	+	0.257524i
$89$	2.02208	−	11.4678i	0.214340	−	1.21558i	−0.667709	−	0.744423i	$-0.732725\pi$
$89$	2.02208	−	11.4678i	0.214340	−	1.21558i	0.882048	−	0.471159i	$-0.156164\pi$
$90$	−18.3212	−	2.08678i	−1.93122	−	0.219966i
$91$	0.257813	−	0.307250i	0.0270262	−	0.0322085i
$92$	21.5103	−	3.79285i	2.24260	−	0.395432i
$93$	2.46458	−	0.0753434i	0.255565	−	0.00781275i
$94$			16.9431i			1.74755i
$95$	0.321731	+	12.0676i	0.0330089	+	1.23811i
$96$	−4.47739	−	11.2221i	−0.456971	−	1.14535i
$97$	1.73122	−	4.75650i	0.175779	−	0.482949i	−0.820247	−	0.572009i	$-0.806164\pi$
$97$	1.73122	−	4.75650i	0.175779	−	0.482949i	0.996026	+	0.0890602i	$0.0283864\pi$
$98$	1.80536	+	10.2387i	0.182369	+	1.03427i
$99$	0.430956	+	7.04196i	0.0433127	+	0.707744i
$100$	−5.98401	+	5.02118i	−0.598401	+	0.502118i
$101$	−15.9166	−	2.80652i	−1.58376	−	0.279259i	−0.688644	−	0.725099i	$-0.741794\pi$
$101$	−15.9166	−	2.80652i	−1.58376	−	0.279259i	−0.895113	+	0.445840i	$0.852905\pi$
$102$	−0.837311	+	5.77555i	−0.0829061	+	0.571865i
$103$	6.51129	−	3.75930i	0.641577	−	0.370414i	−0.143645	−	0.989629i	$-0.545882\pi$
$103$	6.51129	−	3.75930i	0.641577	−	0.370414i	0.785222	+	0.619215i	$0.212549\pi$
$104$	0.0824498	+	0.226529i	0.00808487	+	0.0222130i
$105$	12.2329	−	10.9186i	1.19380	−	1.06555i
$106$	−4.25335	−	7.36702i	−0.413122	−	0.715548i
$107$	7.01577	−	12.1517i	0.678241	−	1.17475i	−0.297270	−	0.954794i	$-0.596076\pi$
$107$	7.01577	−	12.1517i	0.678241	−	1.17475i	0.975510	−	0.219954i	$-0.0705906\pi$
$108$	−8.66465	+	12.4915i	−0.833756	+	1.20199i
$109$	4.37755	+	5.21696i	0.419293	+	0.499694i	0.933802	−	0.357791i	$-0.116470\pi$
$109$	4.37755	+	5.21696i	0.419293	+	0.499694i	−0.514508	+	0.857485i	$0.672026\pi$
$110$	11.0731	+	9.29144i	1.05578	+	0.885904i
$111$	3.02546	+	4.88889i	0.287164	+	0.464033i
$112$	4.14901	+	1.51012i	0.392044	+	0.142693i
$113$	−7.78182			−0.732052			−0.366026	−	0.930605i	$-0.619282\pi$
$113$	−7.78182			−0.732052			−0.366026	+	0.930605i	$0.619282\pi$
$114$	14.9665	+	7.53450i	1.40174	+	0.705671i
$115$	20.6758			1.92803
$116$	4.95376	+	1.80302i	0.459945	+	0.167406i
$117$	−0.209373	+	0.282973i	−0.0193566	+	0.0261608i
$118$	−19.0594	−	15.9927i	−1.75456	−	1.47225i
$119$	−3.33571	−	3.97534i	−0.305784	−	0.364419i
$120$	2.00709	+	9.64859i	0.183221	+	0.880791i
$121$	−2.73472	+	4.73668i	−0.248611	+	0.430607i
$122$	−9.53769	−	16.5198i	−0.863502	−	1.49563i
$123$	−4.21920	−	4.72705i	−0.380433	−	0.426224i
$124$	−1.42451	−	3.91382i	−0.127925	−	0.351471i
$125$	5.58839	−	3.22646i	0.499841	−	0.288583i
$126$	−5.31385	−	22.1303i	−0.473395	−	1.97153i
$127$	−18.3814	−	3.24113i	−1.63108	−	0.287604i	−0.718203	−	0.695833i	$-0.755035\pi$
$127$	−18.3814	−	3.24113i	−1.63108	−	0.287604i	−0.912879	+	0.408230i	$0.866146\pi$
$128$	−11.2420	+	9.43317i	−0.993663	+	0.833782i
$129$	−2.55416	+	7.74620i	−0.224881	+	0.682015i
$130$	0.125238	+	0.710258i	0.0109841	+	0.0622937i
$131$	−3.39721	+	9.33375i	−0.296815	+	0.815493i	0.698212	+	0.715891i	$0.253979\pi$
$131$	−3.39721	+	9.33375i	−0.296815	+	0.815493i	−0.995027	+	0.0996023i	$0.968243\pi$
$132$	11.0687	−	4.41621i	0.963410	−	0.384382i
$133$	−13.8605	+	5.46738i	−1.20186	+	0.474082i
$134$			0.393039i			0.0339534i
$135$	−10.1307	+	10.2205i	−0.871908	+	0.879644i
$136$	3.07165	−	0.541615i	0.263392	−	0.0464431i
$137$	−2.76198	+	3.29160i	−0.235972	+	0.281220i	−0.871015	−	0.491256i	$-0.836538\pi$
$137$	−2.76198	+	3.29160i	−0.235972	+	0.281220i	0.635043	+	0.772477i	$0.280982\pi$
$138$	13.5831	−	25.2805i	1.15627	−	2.15202i
$139$	3.20674	−	18.1863i	0.271992	−	1.54255i	−0.476364	−	0.879248i	$-0.658045\pi$
$139$	3.20674	−	18.1863i	0.271992	−	1.54255i	0.748356	−	0.663297i	$-0.230844\pi$
$140$	−23.9862	−	13.8485i	−2.02721	−	1.17041i
$141$	10.3841	+	8.18590i	0.874503	+	0.689377i
$142$	15.2636	−	5.55550i	1.28089	−	0.466207i
$143$	0.259300	−	0.0943777i	0.0216838	−	0.00789226i
$144$	−3.71550	−	1.10044i	−0.309625	−	0.0917031i
$145$	4.32162	+	2.49509i	0.358891	+	0.207206i
$146$	1.86040	−	10.5509i	0.153968	−	0.873196i
$147$	7.14739	+	3.84027i	0.589507	+	0.316740i
$148$	6.24242	−	7.43943i	0.513124	−	0.611517i
$149$	−4.17566	+	0.736281i	−0.342083	+	0.0603185i	−0.342051	−	0.939682i	$-0.611121\pi$
$149$	−4.17566	+	0.736281i	−0.342083	+	0.0603185i	−3.24291e−5		1.00000i	$0.500010\pi$
$150$	0.313620	+	10.2589i	0.0256069	+	0.837635i
$151$		−	11.5897i		−	0.943157i	−0.881824	−	0.471579i	$-0.843684\pi$
$151$		−	11.5897i		−	0.943157i	0.881824	−	0.471579i	$-0.156316\pi$
$152$	1.31948	−	8.85759i	0.107024	−	0.718445i
$153$	3.13520	+	3.30358i	0.253466	+	0.267078i
$154$	−6.10203	+	16.7652i	−0.491716	+	1.35098i
$155$	−0.684625	−	3.88270i	−0.0549904	−	0.311866i
$156$	0.564693	+	0.186197i	0.0452116	+	0.0149077i
$157$	−5.99170	+	5.02764i	−0.478190	+	0.401249i	−0.849771	−	0.527151i	$-0.823260\pi$
$157$	−5.99170	+	5.02764i	−0.478190	+	0.401249i	0.371581	+	0.928400i	$0.378816\pi$
$158$	15.3017	+	2.69810i	1.21734	+	0.214649i
$159$	−6.57009	−	0.952498i	−0.521042	−	0.0755380i
$160$	−16.7308	+	9.65954i	−1.32269	+	0.763654i
$161$	8.72814	+	23.9804i	0.687874	+	1.88992i
$162$	5.84134	+	19.1013i	0.458939	+	1.50074i
$163$	8.86563	+	15.3557i	0.694410	+	1.20275i	0.970379	+	0.241587i	$0.0776679\pi$
$163$	8.86563	+	15.3557i	0.694410	+	1.20275i	−0.275969	+	0.961166i	$0.588999\pi$
$164$	−5.35136	+	9.26883i	−0.417871	+	0.723774i
$165$	11.0444	−	2.29745i	0.859808	−	0.178856i
$166$	−1.37767	−	1.64185i	−0.106928	−	0.127432i
$167$	1.47243	+	1.23552i	0.113940	+	0.0956071i	0.697978	−	0.716120i	$-0.254083\pi$
$167$	1.47243	+	1.23552i	0.113940	+	0.0956071i	−0.584038	+	0.811727i	$0.698528\pi$
$168$	−10.3434	+	6.40095i	−0.798011	+	0.493844i
$169$	−12.2031	−	4.44155i	−0.938697	−	0.341658i
$170$	9.33140			0.715686
$171$	11.8487	−	5.53249i	0.906092	−	0.423080i
$172$	13.7775			1.05052
$173$	14.7484	+	5.36798i	1.12130	+	0.408120i	0.835126	−	0.550058i	$-0.185395\pi$
$173$	14.7484	+	5.36798i	1.12130	+	0.408120i	0.286173	+	0.958178i	$0.407617\pi$
$174$	5.88990	−	3.64492i	0.446512	−	0.276321i
$175$	−6.99145	−	5.86652i	−0.528504	−	0.443467i
$176$	1.95257	+	2.32698i	0.147180	+	0.175403i
$177$	−19.0101	+	3.95445i	−1.42888	+	0.297235i
$178$	−12.9221	+	22.3817i	−0.968549	+	1.67758i
$179$	7.73482	+	13.3971i	0.578127	+	1.00135i	0.995694	+	0.0926997i	$0.0295497\pi$
$179$	7.73482	+	13.3971i	0.578127	+	1.00135i	−0.417567	+	0.908646i	$0.637117\pi$
$180$	21.7544	+	10.8454i	1.62148	+	0.808367i
$181$	−0.349717	−	0.960840i	−0.0259943	−	0.0714186i	0.926017	−	0.377482i	$-0.123210\pi$
$181$	−0.349717	−	0.960840i	−0.0259943	−	0.0714186i	−0.952011	+	0.306064i	$0.900988\pi$
$182$	−0.770908	+	0.445084i	−0.0571435	+	0.0329918i
$183$	−14.7327	−	2.13588i	−1.08907	−	0.157889i
$184$	−15.1050	−	2.66342i	−1.11356	−	0.196350i
$185$	7.04218	−	5.90909i	0.517751	−	0.434445i
$186$	−5.19719	−	1.71367i	−0.381076	−	0.125653i
$187$	−0.619969	−	3.51602i	−0.0453366	−	0.257117i
$188$	7.63907	−	20.9882i	0.557137	−	1.53072i
$189$	−16.1306	−	7.43528i	−1.17333	−	0.540837i
$190$	8.48922	−	25.4117i	0.615873	−	1.84356i
$191$		−	11.9539i		−	0.864957i	−0.901644	−	0.432478i	$-0.857639\pi$
$191$		−	11.9539i		−	0.864957i	0.901644	−	0.432478i	$-0.142361\pi$
$192$	0.682653	+	22.3304i	0.0492662	+	1.61156i
$193$	11.9048	−	2.09914i	0.856926	−	0.151099i	0.272111	−	0.962266i	$-0.412278\pi$
$193$	11.9048	−	2.09914i	0.856926	−	0.151099i	0.584815	+	0.811167i	$0.301167\pi$
$194$	−7.22109	+	8.60576i	−0.518444	+	0.617858i
$195$	0.495812	+	0.266398i	0.0355059	+	0.0190772i
$196$	2.37991	−	13.4971i	0.169994	−	0.964082i
$197$	1.82224	+	1.05207i	0.129829	+	0.0749568i	0.563508	−	0.826111i	$-0.309451\pi$
$197$	1.82224	+	1.05207i	0.129829	+	0.0749568i	−0.433679	+	0.901067i	$0.642785\pi$
$198$	4.44661	−	15.0135i	0.316007	−	1.06696i
$199$	5.43706	−	1.97893i	0.385423	−	0.140283i	−0.142039	−	0.989861i	$-0.545366\pi$
$199$	5.43706	−	1.97893i	0.385423	−	0.140283i	0.527462	+	0.849578i	$0.323144\pi$
$200$	5.15465	−	1.87614i	0.364489	−	0.132663i
$201$	0.240887	+	0.189893i	0.0169909	+	0.0133940i
$202$	31.0644	+	17.9350i	2.18568	+	1.26190i
$203$	−1.06953	+	6.06562i	−0.0750664	+	0.425723i
$204$	3.64122	−	6.77692i	0.254936	−	0.474479i
$205$	−6.51222	+	7.76096i	−0.454833	+	0.542049i
$206$	−16.4332	+	2.89762i	−1.14496	+	0.201886i
$207$	−8.93144	−	20.5389i	−0.620778	−	1.42755i
$208$			0.151561i			0.0105089i
$209$	−10.1390	−	1.51036i	−0.701329	−	0.104474i
$210$	−33.8003	+	13.4856i	−2.33244	+	0.930597i
$211$	8.09042	−	22.2282i	0.556967	−	1.53025i	−0.267046	−	0.963684i	$-0.586047\pi$
$211$	8.09042	−	22.2282i	0.556967	−	1.53025i	0.824013	−	0.566571i	$-0.191730\pi$
$212$	1.94727	+	11.0435i	0.133739	+	0.758474i
$213$	3.96959	−	12.0389i	0.271992	−	0.824891i
$214$	−23.8558	+	20.0174i	−1.63075	+	1.36836i
$215$	12.8436	+	2.26468i	0.875929	+	0.154450i
$216$	8.71769	−	6.16175i	0.593164	−	0.419254i
$217$	4.21425	−	2.43310i	0.286082	−	0.165169i
$218$	−5.16951	−	14.2031i	−0.350123	−	0.961956i
$219$	−5.56761	−	6.23776i	−0.376224	−	0.421509i
$220$	−9.52755	−	16.5022i	−0.642347	−	1.11258i
$221$	0.0890674	−	0.154269i	0.00599132	−	0.0103773i
$222$	−2.59869	−	12.4926i	−0.174413	−	0.838446i
$223$	3.50193	+	4.17344i	0.234506	+	0.279474i	0.870445	−	0.492266i	$-0.163831\pi$
$223$	3.50193	+	4.17344i	0.234506	+	0.279474i	−0.635938	+	0.771740i	$0.719387\pi$
$224$	−18.2662	−	15.3271i	−1.22046	−	1.02409i
$225$	6.43902	+	4.76427i	0.429268	+	0.317618i
$226$	16.2293	+	5.90700i	1.07956	+	0.392928i
$227$	2.88851			0.191717			0.0958584	−	0.995395i	$-0.469440\pi$
$227$	2.88851			0.191717			0.0958584	+	0.995395i	$0.469440\pi$
$228$	−15.1426	−	16.0812i	−1.00284	−	1.06500i
$229$	−28.8455			−1.90616			−0.953081	−	0.302714i	$-0.902107\pi$
$229$	−28.8455			−1.90616			−0.953081	+	0.302714i	$0.902107\pi$
$230$	−43.1204	−	15.6945i	−2.84327	−	1.03487i
$231$	7.32697	+	11.8398i	0.482079	+	0.779000i
$232$	−2.83581	−	2.37953i	−0.186180	−	0.156224i
$233$	2.52237	+	3.00604i	0.165246	+	0.196932i	0.842313	−	0.538989i	$-0.181194\pi$
$233$	2.52237	+	3.00604i	0.165246	+	0.196932i	−0.677067	+	0.735922i	$0.736749\pi$
$234$	0.651456	−	0.431222i	0.0425870	−	0.0281899i
$235$	10.5712	−	18.3099i	0.689592	−	1.19441i
$236$	16.3992	+	28.4042i	1.06749	+	1.84895i
$237$	9.04647	−	8.07457i	0.587632	−	0.524500i
$238$	3.93918	+	10.8228i	0.255339	+	0.701539i
$239$	0.756613	−	0.436831i	0.0489412	−	0.0282562i	−0.475330	−	0.879808i	$-0.657671\pi$
$239$	0.756613	−	0.436831i	0.0489412	−	0.0282562i	0.524271	+	0.851552i	$0.324338\pi$
$240$	−0.888973	+	6.13190i	−0.0573829	+	0.395813i
$241$	5.29239	+	0.933191i	0.340913	+	0.0601121i	0.341484	−	0.939888i	$-0.389071\pi$
$241$	5.29239	+	0.933191i	0.340913	+	0.0601121i	−0.000570854		1.00000i	$0.500182\pi$
$242$	9.29890	−	7.80270i	0.597756	−	0.501577i
$243$	14.5291	+	5.64856i	0.932040	+	0.362355i
$244$	4.36656	+	24.7640i	0.279540	+	1.58535i
$245$	4.43720	−	12.1911i	0.283483	−	0.778862i
$246$	5.21115	+	13.0612i	0.332251	+	0.832751i
$247$	−0.339084	−	0.382899i	−0.0215754	−	0.0243633i
$248$			2.92476i			0.185722i
$249$	−1.67187	+	0.0511099i	−0.105950	+	0.00323896i
$250$	−14.1040	+	2.48691i	−0.892014	+	0.157286i
$251$	5.16327	−	6.15335i	0.325903	−	0.388396i	−0.578069	−	0.815988i	$-0.696194\pi$
$251$	5.16327	−	6.15335i	0.325903	−	0.388396i	0.903972	+	0.427592i	$0.140638\pi$
$252$	−3.39531	+	29.8096i	−0.213884	+	1.87783i
$253$	−3.04874	+	17.2902i	−0.191672	+	1.08703i
$254$	35.8749	+	20.7124i	2.25099	+	1.29961i
$255$	4.50838	−	5.71906i	0.282326	−	0.358141i
$256$	6.36496	−	2.31666i	0.397810	−	0.144791i
$257$	−9.31791	+	3.39144i	−0.581235	+	0.211552i	−0.615870	−	0.787848i	$-0.711195\pi$
$257$	−9.31791	+	3.39144i	−0.581235	+	0.211552i	0.0346349	+	0.999400i	$0.488973\pi$
$258$	11.2068	−	14.2162i	0.697703	−	0.885065i
$259$	9.82632	+	5.67323i	0.610578	+	0.352517i
$260$	0.165094	−	0.936293i	0.0102387	−	0.0580664i
$261$	0.611736	−	5.37083i	0.0378655	−	0.332446i
$262$	14.1701	−	16.8872i	0.875429	−	1.04330i
$263$	−21.1995	+	3.73805i	−1.30722	+	0.230498i	−0.783500	−	0.621392i	$-0.786567\pi$
$263$	−21.1995	+	3.73805i	−1.30722	+	0.230498i	−0.523720	+	0.851890i	$0.675456\pi$
$264$	−8.36463	+	0.255711i	−0.514807	+	0.0157379i
$265$			10.6151i			0.652081i
$266$	33.0568	−	0.881321i	2.02684	−	0.0540373i
$267$	7.47417	+	18.7332i	0.457412	+	1.14645i
$268$	0.177208	−	0.486875i	0.0108247	−	0.0297406i
$269$	−3.21162	−	18.2140i	−0.195816	−	1.11053i	−0.911252	−	0.411849i	$-0.864883\pi$
$269$	−3.21162	−	18.2140i	−0.195816	−	1.11053i	0.715436	−	0.698678i	$-0.246228\pi$
$270$	28.8861	−	13.6255i	1.75795	−	0.829219i
$271$	2.34190	−	1.96508i	0.142260	−	0.119370i	−0.568881	−	0.822420i	$-0.692623\pi$
$271$	2.34190	−	1.96508i	0.142260	−	0.119370i	0.711141	+	0.703050i	$0.248179\pi$
$272$	1.93117	+	0.340518i	0.117095	+	0.0206469i
$273$	−0.0996724	+	0.687514i	−0.00603245	+	0.0416103i
$274$	8.25881	−	4.76823i	0.498933	−	0.288059i
$275$	−2.14756	−	5.90036i	−0.129503	−	0.355805i
$276$	−28.2242	+	25.1919i	−1.69890	+	1.51638i
$277$	−13.3273	−	23.0835i	−0.800757	−	1.38695i	−0.919118	−	0.393982i	$-0.871097\pi$
$277$	−13.3273	−	23.0835i	−0.800757	−	1.38695i	0.118361	−	0.992971i	$-0.462236\pi$
$278$	−20.4926	+	35.4943i	−1.22907	+	2.12881i
$279$	−3.56125	+	2.35732i	−0.213207	+	0.141129i
$280$	12.5018	+	14.8991i	0.747128	+	0.890392i
$281$	−18.8698	−	15.8337i	−1.12568	−	0.944558i	−0.126803	−	0.991928i	$-0.540471\pi$
$281$	−18.8698	−	15.8337i	−1.12568	−	0.944558i	−0.998877	+	0.0473703i	$0.984916\pi$
$282$	−15.4429	−	24.9544i	−0.919610	−	1.48602i
$283$	−10.4668	−	3.80961i	−0.622187	−	0.226458i	0.0116400	−	0.999932i	$-0.496295\pi$
$283$	−10.4668	−	3.80961i	−0.622187	−	0.226458i	−0.633827	+	0.773475i	$0.718517\pi$
$284$	−21.4125			−1.27060
$285$	−11.4729	−	17.4803i	−0.679596	−	1.03544i
$286$	−0.612423			−0.0362133
$287$	−11.7505	−	4.27682i	−0.693607	−	0.252452i
$288$	16.8229	+	12.4474i	0.991298	+	0.733468i
$289$	11.2572	+	9.44590i	0.662187	+	0.555641i
$290$	−7.11898	−	8.48407i	−0.418041	−	0.498202i
$291$	1.78552	+	8.58348i	0.104669	+	0.503172i
$292$	−7.06159	+	12.2310i	−0.413248	+	0.715767i
$293$	−14.2154	−	24.6217i	−0.830470	−	1.43842i	−0.897666	−	0.440677i	$-0.854738\pi$
$293$	−14.2154	−	24.6217i	−0.830470	−	1.43842i	0.0671953	−	0.997740i	$-0.478595\pi$
$294$	−11.9912	−	13.4345i	−0.699338	−	0.783514i
$295$	10.6187	+	29.1746i	0.618243	+	1.69861i
$296$	−5.90597	+	3.40981i	−0.343277	+	0.198191i
$297$	−7.05316	−	9.97887i	−0.409266	−	0.579033i
$298$	9.26742	+	1.63410i	0.536847	+	0.0946606i
$299$	−0.671046	+	0.563075i	−0.0388076	+	0.0325635i
$300$	4.23689	−	12.8495i	0.244617	−	0.741869i
$301$	2.79521	+	15.8524i	0.161113	+	0.913718i
$302$	−8.79748	+	24.1709i	−0.506238	+	1.39088i
$303$	26.0005	−	10.3737i	1.49369	−	0.595953i
$304$	2.68419	−	4.94927i	0.153949	−	0.283860i
$305$			23.8033i			1.36297i
$306$	−4.03094	−	9.26962i	−0.230433	−	0.529909i
$307$	1.21691	−	0.214574i	0.0694529	−	0.0122464i	−0.138814	−	0.990319i	$-0.544329\pi$
$307$	1.21691	−	0.214574i	0.0694529	−	0.0122464i	0.208267	+	0.978072i	$0.433218\pi$
$308$	15.1177	−	18.0166i	0.861412	−	1.02659i
$309$	−6.16364	+	11.4716i	−0.350637	+	0.652596i
$310$	−1.51945	+	8.61723i	−0.0862990	+	0.489426i
$311$	12.9378	+	7.46964i	0.733635	+	0.423564i	0.819750	−	0.572721i	$-0.194112\pi$
$311$	12.9378	+	7.46964i	0.733635	+	0.423564i	−0.0861156	+	0.996285i	$0.527445\pi$
$312$	−0.327906	−	0.258491i	−0.0185640	−	0.0146342i
$313$	24.0296	−	8.74606i	1.35823	−	0.494356i	0.442725	−	0.896657i	$-0.354012\pi$
$313$	24.0296	−	8.74606i	1.35823	−	0.494356i	0.915507	+	0.402301i	$0.131789\pi$
$314$	16.3123	−	5.93720i	0.920558	−	0.335056i
$315$	−8.06516	+	27.2311i	−0.454420	+	1.53430i
$316$	−17.7384	−	10.2413i	−0.997862	−	0.576116i
$317$	−5.48089	+	31.0837i	−0.307837	+	1.74583i	0.302003	+	0.953307i	$0.402345\pi$
$317$	−5.48089	+	31.0837i	−0.307837	+	1.74583i	−0.609840	+	0.792525i	$0.708766\pi$
$318$	12.9792	+	6.97368i	0.727837	+	0.391065i
$319$	−2.72377	+	3.24607i	−0.152502	+	0.181745i
$320$	35.1794	−	6.20307i	1.96659	−	0.346762i
$321$	0.742619	+	24.2920i	0.0414490	+	1.35585i
$322$		−	56.6375i		−	3.15628i
$323$	−5.64069	+	3.46030i	−0.313856	+	0.192536i
$324$	1.37621	−	26.2953i	0.0764561	−	1.46085i
$325$	0.107150	−	0.294393i	0.00594363	−	0.0163300i
$326$	−6.83351	−	38.7548i	−0.378473	−	2.14643i
$327$	−11.2024	−	3.69379i	−0.619497	−	0.204267i
$328$	5.75735	−	4.83099i	0.317897	−	0.266747i
$329$	25.6989	+	4.53141i	1.41683	+	0.249825i
$330$	−24.7776	−	3.59213i	−1.36396	−	0.197740i
$331$	−12.6919	+	7.32765i	−0.697608	+	0.402764i	−0.806456	−	0.591294i	$-0.798617\pi$
$331$	−12.6919	+	7.32765i	−0.697608	+	0.402764i	0.108848	+	0.994058i	$0.465284\pi$
$332$	0.966332	+	2.65498i	0.0530344	+	0.145711i
$333$	−8.91202	−	4.44297i	−0.488375	−	0.243473i
$334$	−2.13297	−	3.69442i	−0.116711	−	0.202149i
$335$	0.245228	−	0.424746i	0.0133982	−	0.0232064i
$336$	−7.48722	+	1.55748i	−0.408461	+	0.0849676i
$337$	8.29663	+	9.88754i	0.451946	+	0.538609i	0.943120	−	0.332453i	$-0.107876\pi$
$337$	8.29663	+	9.88754i	0.451946	+	0.538609i	−0.491173	+	0.871062i	$0.663432\pi$
$338$	22.0786	+	18.5261i	1.20092	+	1.00769i
$339$	11.4614	−	7.09278i	0.622495	−	0.385227i
$340$	−11.5592	−	4.20721i	−0.626887	−	0.228168i
$341$	3.34788			0.181298
$342$	−28.9106	+	2.54421i	−1.56331	+	0.137575i
$343$	−7.91507			−0.427374
$344$	−9.09138	−	3.30899i	−0.490174	−	0.178409i
$345$	−30.4521	+	18.8451i	−1.63949	+	1.01459i
$346$	−26.6837	−	22.3903i	−1.43453	−	1.20371i
$347$	4.93290	+	5.87880i	0.264812	+	0.315590i	0.882022	−	0.471208i	$-0.156182\pi$
$347$	4.93290	+	5.87880i	0.264812	+	0.315590i	−0.617211	+	0.786798i	$0.711737\pi$
$348$	−8.93945	+	1.85957i	−0.479205	+	0.0996836i
$349$	−2.39476	+	4.14784i	−0.128188	+	0.222029i	−0.922975	−	0.384860i	$-0.874250\pi$
$349$	−2.39476	+	4.14784i	−0.128188	+	0.222029i	0.794786	+	0.606889i	$0.207583\pi$
$350$	10.1278	+	17.5419i	0.541356	+	0.937657i
$351$	0.0504557	−	0.607607i	0.00269313	−	0.0324317i
$352$	−5.61080	−	15.4156i	−0.299057	−	0.821652i
$353$	26.2583	−	15.1602i	1.39759	−	0.806897i	0.403447	−	0.915003i	$-0.367812\pi$
$353$	26.2583	−	15.1602i	1.39759	−	0.806897i	0.994139	+	0.108106i	$0.0344786\pi$
$354$	42.6481	+	6.18291i	2.26672	+	0.328618i
$355$	−19.9612	−	3.51969i	−1.05943	−	0.186806i
$356$	26.0983	−	21.8990i	1.38320	−	1.16065i
$357$	8.53630	+	2.81468i	0.451789	+	0.148969i
$358$	−5.96189	−	33.8116i	−0.315096	−	1.78700i
$359$	10.5174	−	28.8964i	0.555089	−	1.52510i	−0.271585	−	0.962414i	$-0.587548\pi$
$359$	10.5174	−	28.8964i	0.555089	−	1.52510i	0.826674	−	0.562681i	$-0.190230\pi$
$360$	−11.7504	−	12.3814i	−0.619299	−	0.652558i
$361$	4.29164	+	18.5090i	0.225876	+	0.974156i
$362$			2.26934i			0.119274i
$363$	−0.289470	−	9.46894i	−0.0151932	−	0.496990i
$364$	1.15563	−	0.203769i	0.0605715	−	0.0106804i
$365$	−8.59345	+	10.2413i	−0.449802	+	0.536053i
$366$	29.1045	+	15.6377i	1.52132	+	0.817398i
$367$	−0.382670	+	2.17023i	−0.0199752	+	0.113285i	−0.993165	−	0.116718i	$-0.962763\pi$
$367$	−0.382670	+	2.17023i	−0.0199752	+	0.113285i	0.973190	+	0.230003i	$0.0738737\pi$
$368$	−8.35122	−	4.82158i	−0.435338	−	0.251342i
$369$	10.5227	+	3.11656i	0.547790	+	0.162242i
$370$	−19.1722	+	6.97813i	−0.996717	+	0.362775i
$371$	−12.3117	+	4.48109i	−0.639191	+	0.232646i
$372$	5.66535	+	4.46604i	0.293735	+	0.231553i
$373$	−22.9106	−	13.2274i	−1.18627	−	0.684891i	−0.228810	−	0.973471i	$-0.573484\pi$
$373$	−22.9106	−	13.2274i	−1.18627	−	0.684891i	−0.957456	+	0.288580i	$0.906817\pi$
$374$	−1.37595	+	7.80343i	−0.0711489	+	0.403506i
$375$	−5.29002	+	9.84562i	−0.273175	+	0.508425i
$376$	−10.0816	+	12.0148i	−0.519921	+	0.619617i
$377$	−0.208211	+	0.0367132i	−0.0107234	+	0.00189083i
$378$	27.9972	+	27.7510i	1.44002	+	1.42736i
$379$			29.7135i			1.52628i	0.646234	+	0.763139i	$0.276343\pi$
$379$			29.7135i			1.52628i	−0.646234	+	0.763139i	$0.723657\pi$
$380$	−21.9732	+	27.6511i	−1.12720	+	1.41847i
$381$	30.0269	−	11.9801i	1.53832	−	0.613761i
$382$	−9.07396	+	24.9305i	−0.464264	+	1.27555i
$383$	−1.03686	−	5.88035i	−0.0529813	−	0.300472i	0.946790	−	0.321852i	$-0.104305\pi$
$383$	−1.03686	−	5.88035i	−0.0529813	−	0.300472i	−0.999771	+	0.0213797i	$0.993194\pi$
$384$	7.95974	−	24.1401i	0.406194	−	1.23189i
$385$	17.0545	−	14.3105i	0.869180	−	0.729328i
$386$	−26.4214	−	4.65881i	−1.34481	−	0.237127i
$387$	−3.29845	−	13.7369i	−0.167670	−	0.698285i
$388$	12.8251	−	7.40459i	0.651097	−	0.375911i
$389$	4.73660	+	13.0137i	0.240155	+	0.659821i	0.999953	+	0.00966178i	$0.00307549\pi$
$389$	4.73660	+	13.0137i	0.240155	+	0.659821i	−0.759798	+	0.650159i	$0.774702\pi$
$390$	−0.831823	−	0.931945i	−0.0421210	−	0.0471909i
$391$	5.66697	+	9.81548i	0.286591	+	0.496390i
$392$	−4.81211	+	8.33481i	−0.243048	+	0.420971i
$393$	−3.50376	−	16.8435i	−0.176741	−	0.849642i
$394$	−3.00176	−	3.57735i	−0.151226	−	0.180225i
$395$	−14.8527	−	12.4629i	−0.747319	−	0.627075i
$396$	−12.2773	+	16.5930i	−0.616957	+	0.833831i
$397$	11.1519	+	4.05896i	0.559697	+	0.203713i	0.606350	−	0.795198i	$-0.292633\pi$
$397$	11.1519	+	4.05896i	0.559697	+	0.203713i	−0.0466525	+	0.998911i	$0.514855\pi$
$398$	−12.8414			−0.643682
$399$	15.4309	−	20.6858i	0.772513	−	1.03558i
$400$	3.44876			0.172438
$401$	−22.3703	−	8.14211i	−1.11712	−	0.406597i	−0.283518	−	0.958967i	$-0.591502\pi$
$401$	−22.3703	−	8.14211i	−1.11712	−	0.406597i	−0.833599	+	0.552370i	$0.813724\pi$
$402$	−0.358238	−	0.578883i	−0.0178673	−	0.0288721i
$403$	0.127959	+	0.107371i	0.00637411	+	0.00534852i
$404$	−30.3945	−	36.2228i	−1.51218	−	1.80215i
$405$	5.60524	−	24.2868i	0.278527	−	1.20682i
$406$	6.83483	−	11.8383i	0.339207	−	0.587523i
$407$	3.90310	+	6.76037i	0.193470	+	0.335099i
$408$	−4.03038	+	3.59738i	−0.199534	+	0.178097i
$409$	−11.2638	−	30.9472i	−0.556961	−	1.53024i	−0.824022	−	0.566559i	$-0.808275\pi$
$409$	−11.2638	−	30.9472i	−0.556961	−	1.53024i	0.267060	−	0.963680i	$-0.413948\pi$
$410$	19.4727	−	11.2426i	0.961688	−	0.555231i
$411$	1.06780	−	7.36541i	0.0526707	−	0.363309i
$412$	21.6630	+	3.81977i	1.06726	+	0.188186i
$413$	−29.3549	+	24.6317i	−1.44446	+	1.21204i
$414$	3.03632	+	49.6145i	0.149227	+	2.43842i
$415$	0.464421	+	2.63386i	0.0227976	+	0.129291i
$416$	0.279946	−	0.769145i	0.0137255	−	0.0377104i
$417$	11.8530	+	29.7083i	0.580445	+	1.45482i
$418$	19.9989	+	10.8462i	0.978177	+	0.530506i
$419$		−	10.4846i		−	0.512206i	−0.966649	−	0.256103i	$-0.917561\pi$
$419$		−	10.4846i		−	0.512206i	0.966649	−	0.256103i	$-0.0824387\pi$
$420$	47.9501	−	1.46586i	2.33972	−	0.0715266i
$421$	8.46790	−	1.49312i	0.412700	−	0.0727702i	0.0365568	−	0.999332i	$-0.488361\pi$
$421$	8.46790	−	1.49312i	0.412700	−	0.0727702i	0.376144	+	0.926561i	$0.377250\pi$
$422$	−33.7459	+	40.2168i	−1.64272	+	1.95772i
$423$	−22.7552	−	2.59181i	−1.10640	−	0.126018i
$424$	1.36742	−	7.75502i	0.0664078	−	0.376617i
$425$	−3.51039	−	2.02672i	−0.170279	−	0.0983105i
$426$	−17.4172	+	22.0944i	−0.843867	+	1.07048i
$427$	−27.6077	+	10.0484i	−1.33603	+	0.486274i
$428$	38.5764	−	14.0406i	1.86466	−	0.678680i
$429$	−0.295886	+	0.375344i	−0.0142855	+	0.0181218i
$430$	−25.0669	−	14.4724i	−1.20883	−	0.697921i
$431$	2.37538	−	13.4715i	0.114418	−	0.648897i	−0.872619	−	0.488402i	$-0.837580\pi$
$431$	2.37538	−	13.4715i	0.114418	−	0.648897i	0.987037	−	0.160495i	$-0.0513090\pi$
$432$	6.47532	−	1.76574i	0.311544	−	0.0849544i
$433$	21.1358	−	25.1887i	1.01572	−	1.21049i	0.0382849	−	0.999267i	$-0.487811\pi$
$433$	21.1358	−	25.1887i	1.01572	−	1.21049i	0.977438	−	0.211224i	$-0.0677450\pi$
$434$	−10.6359	+	1.87540i	−0.510540	+	0.0900221i
$435$	−8.63921	+	0.264105i	−0.414218	+	0.0126629i
$436$			19.9248i			0.954224i
$437$	31.8855	−	6.50293i	1.52529	−	0.311077i
$438$	6.87657	+	17.2354i	0.328575	+	0.823538i
$439$	−12.9069	+	35.4614i	−0.616012	+	1.69248i	0.100529	+	0.994934i	$0.467946\pi$
$439$	−12.9069	+	35.4614i	−0.616012	+	1.69248i	−0.716541	+	0.697545i	$0.754276\pi$
$440$	2.32357	+	13.1776i	0.110772	+	0.628219i
$441$	−14.0272	+	0.858438i	−0.667960	+	0.0408780i
$442$	−0.302857	+	0.254127i	−0.0144054	+	0.0120876i
$443$	5.09078	+	0.897641i	0.241870	+	0.0426482i	0.293269	−	0.956030i	$-0.405257\pi$
$443$	5.09078	+	0.897641i	0.241870	+	0.0426482i	−0.0513989	+	0.998678i	$0.516368\pi$
$444$	−2.41336	+	16.6468i	−0.114533	+	0.790020i
$445$	27.9290	−	16.1248i	1.32396	−	0.764390i
$446$	−4.13548	−	11.3621i	−0.195820	−	0.538012i
$447$	5.47897	−	4.89035i	0.259147	−	0.231305i
$448$	22.0452	+	38.1834i	1.04154	+	1.80400i
$449$	14.3628	−	24.8771i	0.677823	−	1.17402i	−0.297812	−	0.954625i	$-0.596257\pi$
$449$	14.3628	−	24.8771i	0.677823	−	1.17402i	0.975635	−	0.219399i	$-0.0704098\pi$
$450$	−9.81243	−	14.8238i	−0.462562	−	0.698802i
$451$	−5.52988	−	6.59026i	−0.260392	−	0.310323i
$452$	−17.4407	−	14.6345i	−0.820344	−	0.688350i
$453$	10.5635	+	17.0698i	0.496317	+	0.802007i
$454$	−6.02411	−	2.19260i	−0.282726	−	0.102904i
$455$	1.11080			0.0520750
$456$	6.12992	+	14.2484i	0.287060	+	0.667244i
$457$	5.68893			0.266117			0.133058	−	0.991108i	$-0.457520\pi$
$457$	5.68893			0.266117			0.133058	+	0.991108i	$0.457520\pi$
$458$	60.1586	+	21.8959i	2.81103	+	1.02313i
$459$	−7.62870	−	2.00804i	−0.356077	−	0.0937271i
$460$	46.3390	+	38.8830i	2.16057	+	1.81293i
$461$	18.8457	+	22.4594i	0.877732	+	1.04604i	0.998575	+	0.0533689i	$0.0169959\pi$
$461$	18.8457	+	22.4594i	0.877732	+	1.04604i	−0.120843	+	0.992672i	$0.538560\pi$
$462$	−6.29343	−	30.2541i	−0.292797	−	1.40755i
$463$	7.50134	−	12.9927i	0.348617	−	0.603822i	−0.637387	−	0.770544i	$-0.719985\pi$
$463$	7.50134	−	12.9927i	0.348617	−	0.603822i	0.986004	+	0.166722i	$0.0533182\pi$
$464$	−1.16371	−	2.01560i	−0.0540237	−	0.0935717i
$465$	4.54725	+	5.09458i	0.210874	+	0.236255i
$466$	−2.97870	−	8.18391i	−0.137986	−	0.379112i
$467$	−35.4175	+	20.4483i	−1.63893	+	0.946235i	−0.657724	+	0.753259i	$0.728481\pi$
$467$	−35.4175	+	20.4483i	−1.63893	+	0.946235i	−0.981203	+	0.192976i	$0.938186\pi$
$468$	−1.00141	+	0.240455i	−0.0462902	+	0.0111150i
$469$	0.596153	+	0.105118i	0.0275278	+	0.00485389i
$470$	−35.9455	+	30.1618i	−1.65804	+	1.39126i
$471$	4.24234	−	12.8661i	0.195477	−	0.592837i
$472$	−3.99941	−	22.6818i	−0.184088	−	1.04401i
$473$	−3.78770	+	10.4066i	−0.174158	+	0.478496i
$474$	−24.9961	+	9.97293i	−1.14811	+	0.458072i
$475$	−8.71283	+	7.71583i	−0.399772	+	0.354027i
$476$		−	15.1827i		−	0.695900i
$477$	10.5448	−	4.58547i	0.482814	−	0.209954i
$478$	−1.90954	+	0.336703i	−0.0873403	+	0.0154004i
$479$	−15.6062	+	18.5987i	−0.713063	+	0.849796i	−0.993937	−	0.109949i	$-0.964931\pi$
$479$	−15.6062	+	18.5987i	−0.713063	+	0.849796i	0.280874	+	0.959745i	$0.409376\pi$
$480$	15.8375	−	29.4763i	0.722881	−	1.34540i
$481$	−0.0676331	+	0.383566i	−0.00308380	+	0.0174891i
$482$	−10.3292	−	5.96354i	−0.470480	−	0.271632i
$483$	−34.7122	−	27.3639i	−1.57946	−	1.24510i
$484$	−15.0369	+	5.47300i	−0.683497	+	0.248773i
$485$	13.1730	−	4.79458i	0.598155	−	0.217711i
$486$	−26.0133	−	22.8090i	−1.17999	−	1.03464i
$487$	16.1964	+	9.35100i	0.733930	+	0.423734i	0.819858	−	0.572567i	$-0.194052\pi$
$487$	16.1964	+	9.35100i	0.733930	+	0.423734i	−0.0859284	+	0.996301i	$0.527386\pi$
$488$	3.06629	−	17.3898i	0.138805	−	0.787200i
$489$	−27.0537	−	14.5359i	−1.22341	−	0.657334i
$490$	−18.5080	+	22.0570i	−0.836106	+	0.996432i
$491$	34.3949	−	6.06475i	1.55222	−	0.273698i	0.669218	−	0.743066i	$-0.266629\pi$
$491$	34.3949	−	6.06475i	1.55222	−	0.273698i	0.883003	+	0.469368i	$0.155518\pi$
$492$	−0.566441	−	18.5290i	−0.0255371	−	0.835352i
$493$			2.73549i			0.123200i
$494$	0.416526	+	1.05594i	0.0187404	+	0.0475091i
$495$	−14.1726	+	13.4503i	−0.637012	+	0.604545i
$496$	−0.628913	+	1.72793i	−0.0282390	+	0.0775861i
$497$	−4.34422	−	24.6373i	−0.194865	−	1.10513i
$498$	3.52556	+	1.16249i	0.157984	+	0.0520922i
$499$	2.90071	−	2.43398i	0.129853	−	0.108960i	−0.575548	−	0.817768i	$-0.695211\pi$
$499$	2.90071	−	2.43398i	0.129853	−	0.108960i	0.705401	+	0.708808i	$0.250767\pi$
$500$	18.5925	+	3.27836i	0.831481	+	0.146613i
$501$	−3.29477	−	0.477659i	−0.147199	−	0.0213402i
$502$	−15.4391	+	8.91377i	−0.689081	+	0.397841i
$503$	0.0977650	+	0.268607i	0.00435912	+	0.0119766i	0.941853	−	0.336025i	$-0.109083\pi$
$503$	0.0977650	+	0.268607i	0.00435912	+	0.0119766i	−0.937494	+	0.348001i	$0.886860\pi$
$504$	9.39998	−	18.8551i	0.418708	−	0.839874i
$505$	−22.3803	−	38.7637i	−0.995908	−	1.72496i
$506$	19.4829	−	33.7454i	0.866121	−	1.50016i
$507$	22.0214	−	4.58087i	0.978005	−	0.203443i
$508$	−35.1013	−	41.8321i	−1.55737	−	1.85600i
$509$	−3.00696	−	2.52314i	−0.133281	−	0.111836i	0.573710	−	0.819058i	$-0.305504\pi$
$509$	−3.00696	−	2.52314i	−0.133281	−	0.111836i	−0.706991	+	0.707222i	$0.749948\pi$
$510$	−13.7436	+	8.50516i	−0.608578	+	0.376615i
$511$	−15.5058	−	5.64363i	−0.685934	−	0.249660i
$512$	14.3179			0.632766
$513$	−12.4086	+	18.9480i	−0.547852	+	0.836575i
$514$	22.0073			0.970700
$515$	19.5668	+	7.12173i	0.862216	+	0.313821i
$516$	−20.2920	+	12.5575i	−0.893303	+	0.552815i
$517$	13.7530	+	11.5401i	0.604856	+	0.507534i
$518$	−16.1868	−	19.2907i	−0.711209	−	0.847585i
$519$	−26.6146	+	5.53635i	−1.16825	+	0.243019i
$520$	−0.333814	+	0.578183i	−0.0146387	+	0.0253550i
$521$	−4.18609	−	7.25051i	−0.183396	−	0.317651i	0.759639	−	0.650345i	$-0.225376\pi$
$521$	−4.18609	−	7.25051i	−0.183396	−	0.317651i	−0.943035	+	0.332694i	$0.892042\pi$
$522$	−5.35267	+	10.7368i	−0.234280	+	0.469935i
$523$	1.52796	+	4.19803i	0.0668130	+	0.183567i	0.968606	−	0.248601i	$-0.0799708\pi$
$523$	1.52796	+	4.19803i	0.0668130	+	0.183567i	−0.901793	+	0.432168i	$0.857749\pi$
$524$	−25.1670	+	14.5302i	−1.09942	+	0.634753i
$525$	15.6443	+	2.26804i	0.682775	+	0.0989853i
$526$	47.0501	+	8.29620i	2.05148	+	0.361732i
$527$	1.65560	−	1.38921i	0.0721190	−	0.0605150i
$528$	−4.99675	−	1.64758i	−0.217456	−	0.0717018i
$529$	−5.68443	−	32.2380i	−0.247149	−	1.40165i
$530$	8.05768	−	22.1383i	0.350003	−	0.961626i
$531$	24.3944	−	23.1511i	1.05863	−	1.00467i
$532$	−41.3463	−	13.8125i	−1.79259	−	0.598846i
$533$		−	0.429237i		−	0.0185923i
$534$	−1.36780	−	44.7424i	−0.0591904	−	1.93619i
$535$	38.2696	−	6.74797i	1.65454	−	0.291740i
$536$	−0.233870	+	0.278715i	−0.0101016	+	0.0120387i
$537$	−23.6030	−	12.6818i	−1.01854	−	0.547260i
$538$	−7.12784	+	40.4240i	−0.307303	+	1.74280i
$539$	9.54059	+	5.50826i	0.410942	+	0.237258i
$540$	−41.9258	+	3.85469i	−1.80420	+	0.165879i
$541$	2.61046	−	0.950130i	0.112232	−	0.0408493i	−0.285294	−	0.958440i	$-0.592091\pi$
$541$	2.61046	−	0.950130i	0.112232	−	0.0408493i	0.397526	+	0.917591i	$0.369869\pi$
$542$	−6.37578	+	2.32059i	−0.273863	+	0.0996781i
$543$	1.39084	+	1.09641i	0.0596866	+	0.0470514i
$544$	−9.17140	−	5.29511i	−0.393220	−	0.227026i
$545$	−3.27515	+	18.5743i	−0.140292	+	0.795635i
$546$	0.729748	−	1.35818i	0.0312303	−	0.0581249i
$547$	−23.7660	+	28.3232i	−1.01616	+	1.21101i	−0.0388403	+	0.999245i	$0.512366\pi$
$547$	−23.7660	+	28.3232i	−1.01616	+	1.21101i	−0.977320	+	0.211767i	$0.932078\pi$
$548$	−12.3804	+	2.18300i	−0.528864	+	0.0932530i
$549$	23.6457	−	10.2824i	1.00917	−	0.438843i
$550$			13.9356i			0.594218i
$551$	7.44940	+	2.48860i	0.317355	+	0.106018i
$552$	24.6748	−	9.84477i	1.05023	−	0.419021i
$553$	8.18483	−	22.4876i	0.348054	−	0.956271i
$554$	10.2725	+	58.2581i	0.436436	+	2.47515i
$555$	−4.98611	+	15.1218i	−0.211649	+	0.641883i
$556$	41.3883	−	34.7289i	1.75526	−	1.47283i
$557$	−1.21307	−	0.213897i	−0.0513994	−	0.00906310i	0.147889	−	0.989004i	$-0.452752\pi$
$557$	−1.21307	−	0.213897i	−0.0513994	−	0.00906310i	−0.199289	+	0.979941i	$0.563863\pi$
$558$	9.21654	−	2.21304i	0.390167	−	0.0936855i
$559$	−0.478523	+	0.276276i	−0.0202394	+	0.0116852i
$560$	4.18223	+	11.4906i	0.176731	+	0.485565i
$561$	4.11781	+	4.61345i	0.173854	+	0.194780i
$562$	27.3349	+	47.3455i	1.15305	+	1.99715i
$563$	−18.4158	+	31.8971i	−0.776134	+	1.34430i	0.158020	+	0.987436i	$0.449489\pi$
$563$	−18.4158	+	31.8971i	−0.776134	+	1.34430i	−0.934155	+	0.356868i	$0.883845\pi$
$564$	7.87868	+	37.8748i	0.331752	+	1.59482i
$565$	−13.8531	−	16.5094i	−0.582803	−	0.694557i
$566$	18.9372	+	15.8902i	0.795991	+	0.667916i
$567$	30.5347	−	3.75139i	1.28234	−	0.157544i
$568$	14.1295	+	5.14273i	0.592862	+	0.215784i
$569$	33.1970			1.39169			0.695846	−	0.718191i	$-0.255029\pi$
$569$	33.1970			1.39169			0.695846	+	0.718191i	$0.255029\pi$
$570$	10.6584	+	45.1648i	0.446430	+	1.89175i
$571$	−20.3097			−0.849935			−0.424967	−	0.905209i	$-0.639714\pi$
$571$	−20.3097			−0.849935			−0.424967	+	0.905209i	$0.639714\pi$
$572$	0.758636	+	0.276121i	0.0317201	+	0.0115452i
$573$	10.8955	+	17.6062i	0.455165	+	0.735510i
$574$	21.2597	+	17.8390i	0.887362	+	0.744585i
$575$	12.8127	+	15.2696i	0.534328	+	0.636787i
$576$	−21.3586	−	32.2669i	−0.889943	−	1.34445i
$577$	−17.7982	+	30.8274i	−0.740949	+	1.28336i	0.211115	+	0.977461i	$0.432290\pi$
$577$	−17.7982	+	30.8274i	−0.740949	+	1.28336i	−0.952064	+	0.305899i	$0.901043\pi$
$578$	−16.3072	−	28.2449i	−0.678291	−	1.17483i
$579$	−15.6206	+	13.9424i	−0.649168	+	0.579426i
$580$	4.99342	+	13.7193i	0.207340	+	0.569663i
$581$	−2.85877	+	1.65051i	−0.118602	+	0.0684749i
$582$	2.79172	−	19.2566i	0.115721	−	0.798211i
$583$	−8.87693	−	1.56524i	−0.367645	−	0.0648257i
$584$	7.59733	−	6.37492i	0.314380	−	0.263796i
$585$	−0.973061	+	0.0595496i	−0.0402311	+	0.00246207i
$586$	10.9570	+	62.1403i	0.452630	+	2.56699i
$587$	1.44221	−	3.96244i	0.0595265	−	0.163548i	−0.906365	−	0.422496i	$-0.861154\pi$
$587$	1.44221	−	3.96244i	0.0595265	−	0.163548i	0.965891	+	0.258949i	$0.0833761\pi$
$588$	8.79682	+	22.0483i	0.362775	+	0.909256i
$589$	−2.27698	−	5.77243i	−0.0938215	−	0.237849i
$590$		−	68.9053i		−	2.83679i
$591$	−3.64277	+	0.111361i	−0.149844	+	0.00458079i
$592$	−4.22242	+	0.744526i	−0.173540	+	0.0305998i
$593$	−4.95391	+	5.90384i	−0.203433	+	0.242442i	−0.858109	−	0.513468i	$-0.828361\pi$
$593$	−4.95391	+	5.90384i	−0.203433	+	0.242442i	0.654676	+	0.755910i	$0.272805\pi$
$594$	7.13497	+	26.1653i	0.292751	+	1.07357i
$595$	2.49567	−	14.1537i	0.102313	−	0.580244i
$596$	−10.7432	−	6.20259i	−0.440059	−	0.254068i
$597$	−6.20420	+	7.87028i	−0.253921	+	0.322109i
$598$	1.82692	−	0.664943i	0.0747081	−	0.0271915i
$599$	−25.3361	+	9.22158i	−1.03520	+	0.376783i	−0.803060	−	0.595898i	$-0.796796\pi$
$599$	−25.3361	+	9.22158i	−1.03520	+	0.376783i	−0.232144	+	0.972681i	$0.574574\pi$
$600$	−5.88194	+	7.46148i	−0.240129	+	0.304614i
$601$	9.17267	+	5.29585i	0.374161	+	0.216022i	0.675275	−	0.737566i	$-0.264025\pi$
$601$	9.17267	+	5.29585i	0.374161	+	0.216022i	−0.301114	+	0.953588i	$0.597358\pi$
$602$	6.20366	−	35.1827i	0.252842	−	1.43394i
$603$	−0.527867	−	0.0601239i	−0.0214964	−	0.00244843i
$604$	21.7957	−	25.9751i	0.886853	−	1.05691i
$605$	−14.9174	+	2.63033i	−0.606477	+	0.106938i
$606$	−62.0997	+	1.89842i	−2.52263	+	0.0771180i
$607$		−	20.9280i		−	0.849442i	−0.905324	−	0.424721i	$-0.860372\pi$
$607$		−	20.9280i		−	0.849442i	0.905324	−	0.424721i	$-0.139628\pi$
$608$	−22.7635	+	20.1587i	−0.923183	+	0.817545i
$609$	−3.95329	−	9.90850i	−0.160196	−	0.401513i
$610$	18.0685	−	49.6428i	0.731572	−	2.00998i
$611$	0.155547	+	0.882153i	0.00629277	+	0.0356881i
$612$	0.813943	+	13.3001i	0.0329017	+	0.537625i
$613$	−5.91704	+	4.96499i	−0.238987	+	0.200534i	−0.754413	−	0.656400i	$-0.772078\pi$
$613$	−5.91704	+	4.96499i	−0.238987	+	0.200534i	0.515426	+	0.856934i	$0.327634\pi$
$614$	−2.70081	−	0.476225i	−0.108996	−	0.0192189i
$615$	2.51767	−	17.3662i	0.101522	−	0.700274i
$616$	−14.3029	+	8.25778i	−0.576280	+	0.332715i
$617$	−2.76356	−	7.59281i	−0.111257	−	0.305675i	0.871552	−	0.490303i	$-0.163114\pi$
$617$	−2.76356	−	7.59281i	−0.111257	−	0.305675i	−0.982808	+	0.184629i	$0.940892\pi$
$618$	21.5624	−	19.2458i	0.867366	−	0.774181i
$619$	20.8358	+	36.0886i	0.837460	+	1.45052i	0.892012	+	0.452012i	$0.149293\pi$
$619$	20.8358	+	36.0886i	0.837460	+	1.45052i	−0.0545523	+	0.998511i	$0.517373\pi$
$620$	5.76743	−	9.98948i	0.231625	−	0.401187i
$621$	31.8749	+	22.1099i	1.27909	+	0.887239i
$622$	−21.3123	−	25.3991i	−0.854547	−	1.01841i
$623$	30.4920	+	25.5858i	1.22164	+	1.02508i
$624$	−0.138141	−	0.223225i	−0.00553007	−	0.00893613i
$625$	29.3382	+	10.6782i	1.17353	+	0.427130i
$626$	−56.7537			−2.26834
$627$	16.3097	−	7.01672i	0.651348	−	0.280221i
$628$	−22.8837			−0.913159
$629$	4.73541	+	1.72355i	0.188813	+	0.0687223i
$630$	37.4907	−	50.6696i	1.49367	−	2.01872i
$631$	−14.6394	−	12.2839i	−0.582786	−	0.489016i	0.303075	−	0.952967i	$-0.401987\pi$
$631$	−14.6394	−	12.2839i	−0.582786	−	0.489016i	−0.885861	+	0.463951i	$0.846431\pi$
$632$	9.24539	+	11.0182i	0.367762	+	0.438282i
$633$	8.34418	+	40.1126i	0.331651	+	1.59433i
$634$	35.0255	−	60.6660i	1.39104	−	2.40935i
$635$	−25.8460	−	44.7666i	−1.02567	−	1.77651i
$636$	−12.9337	−	14.4905i	−0.512855	−	0.574585i
$637$	0.187995	+	0.516511i	0.00744862	+	0.0204649i
$638$	8.14456	−	4.70227i	0.322446	−	0.186165i
$639$	5.12635	+	21.3494i	0.202795	+	0.844571i
$640$	−40.0257	−	7.05761i	−1.58215	−	0.278976i
$641$	25.7120	−	21.5750i	1.01556	−	0.852159i	0.0265004	−	0.999649i	$-0.491564\pi$
$641$	25.7120	−	21.5750i	1.01556	−	0.852159i	0.989064	+	0.147489i	$0.0471192\pi$
$642$	16.8907	−	51.2258i	0.666624	−	2.02172i
$643$	−0.140117	−	0.794641i	−0.00552566	−	0.0313376i	0.981920	−	0.189295i	$-0.0606202\pi$
$643$	−0.140117	−	0.794641i	−0.00552566	−	0.0313376i	−0.987446	+	0.157957i	$0.949509\pi$
$644$	−25.5359	+	70.1594i	−1.00626	+	2.76467i
$645$	−20.9807	+	8.37090i	−0.826116	+	0.329604i
$646$	14.3905	−	2.93490i	0.566188	−	0.115472i
$647$			25.4029i			0.998690i	0.866403	+	0.499345i	$0.166426\pi$
$647$			25.4029i			0.998690i	−0.866403	+	0.499345i	$0.833574\pi$
$648$	−7.22358	+	17.0210i	−0.283769	+	0.668650i
$649$	−25.9631	+	4.57800i	−1.01914	+	0.179702i
$650$	−0.446934	+	0.532635i	−0.0175302	+	0.0208917i
$651$	−3.98924	+	7.42466i	−0.156351	+	0.290995i
$652$	−9.00824	+	51.0883i	−0.352790	+	2.00077i
$653$	−38.7229	−	22.3567i	−1.51534	−	0.874884i	−0.999838	−	0.0179975i	$-0.994271\pi$
$653$	−38.7229	−	22.3567i	−1.51534	−	0.874884i	−0.515505	−	0.856886i	$-0.672396\pi$
$654$	20.5593	+	16.2071i	0.803934	+	0.633747i
$655$	−25.8496	+	9.40847i	−1.01003	+	0.367619i
$656$	4.44022	−	1.61611i	0.173361	−	0.0630984i
$657$	13.8856	+	4.11257i	0.541730	+	0.160447i
$658$	−50.1566	−	28.9579i	−1.95531	−	1.12890i
$659$	4.52313	−	25.6520i	0.176196	−	0.999258i	−0.760558	−	0.649270i	$-0.775074\pi$
$659$	4.52313	−	25.6520i	0.176196	−	0.999258i	0.936754	−	0.349988i	$-0.113814\pi$
$660$	29.0736	+	15.6211i	1.13169	+	0.608051i
$661$	−9.92400	+	11.8270i	−0.385999	+	0.460016i	−0.923698	−	0.383121i	$-0.874849\pi$
$661$	−9.92400	+	11.8270i	−0.385999	+	0.460016i	0.537699	+	0.843137i	$0.319294\pi$
$662$	32.0317	−	5.64806i	1.24495	−	0.219518i
$663$	0.00942778	+	0.308395i	0.000366145	+	0.0119771i
$664$		−	1.98403i		−	0.0769955i
$665$	−36.2735	−	19.6726i	−1.40662	−	0.762871i
$666$	15.2139	+	16.0309i	0.589525	+	0.621186i
$667$	4.60083	−	12.6407i	0.178145	−	0.489449i
$668$	0.976520	+	5.53812i	0.0377827	+	0.214276i
$669$	−8.96167	−	2.95494i	−0.346478	−	0.114245i
$670$	−0.833848	+	0.699682i	−0.0322144	+	0.0270311i
$671$	−19.9056	−	3.50989i	−0.768446	−	0.135498i
$672$	40.8731	+	5.92558i	1.57671	+	0.228584i
$673$	10.6310	−	6.13783i	0.409796	−	0.236596i	−0.280906	−	0.959735i	$-0.590635\pi$
$673$	10.6310	−	6.13783i	0.409796	−	0.236596i	0.690702	+	0.723139i	$0.257302\pi$
$674$	−9.79761	−	26.9187i	−0.377390	−	1.03687i
$675$	−13.8261	−	1.14812i	−0.532165	−	0.0441910i
$676$	−18.9969	−	32.9036i	−0.730651	−	1.26552i
$677$	−8.46982	+	14.6702i	−0.325522	+	0.563820i	−0.981618	−	0.190857i	$-0.938873\pi$
$677$	−8.46982	+	14.6702i	−0.325522	+	0.563820i	0.656096	+	0.754677i	$0.272207\pi$
$678$	−29.2871	+	6.09228i	−1.12477	+	0.233973i
$679$	11.1218	+	13.2544i	0.426814	+	0.508657i
$680$	6.61716	+	5.55245i	0.253756	+	0.212927i
$681$	−4.25430	+	2.63274i	−0.163025	+	0.100887i
$682$	−6.98215	−	2.54129i	−0.267360	−	0.0973112i
$683$	−31.1308			−1.19119			−0.595593	−	0.803287i	$-0.703083\pi$
$683$	−31.1308			−1.19119			−0.595593	+	0.803287i	$0.703083\pi$
$684$	36.9599	+	9.88318i	1.41320	+	0.377893i
$685$	−11.9001			−0.454679
$686$	16.5072	+	6.00815i	0.630249	+	0.229392i
$687$	42.4847	−	26.2914i	1.62089	−	1.00308i
$688$	−4.65959	−	3.90986i	−0.177645	−	0.149062i
$689$	−0.289087	−	0.344520i	−0.0110133	−	0.0131252i
$690$	77.8141	−	16.1868i	2.96233	−	0.616221i
$691$	3.11327	−	5.39234i	0.118434	−	0.205134i	−0.800713	−	0.599048i	$-0.795546\pi$
$691$	3.11327	−	5.39234i	0.118434	−	0.205134i	0.919147	+	0.393914i	$0.128879\pi$
$692$	22.9593	+	39.7667i	0.872782	+	1.51170i
$693$	−21.5829	−	10.7599i	−0.819865	−	0.408733i
$694$	−5.82532	−	16.0049i	−0.221126	−	0.607540i
$695$	44.2917	−	25.5718i	1.68008	−	0.969994i
$696$	6.34552	+	0.919942i	0.240526	+	0.0348703i
$697$	−5.46930	−	0.964384i	−0.207164	−	0.0365287i
$698$	8.14291	−	6.83271i	0.308214	−	0.258622i
$699$	−6.45491	−	2.12838i	−0.244147	−	0.0805029i
$700$	−4.63675	−	26.2963i	−0.175253	−	0.993906i
$701$	−0.663693	+	1.82348i	−0.0250673	+	0.0688719i	−0.951595	−	0.307354i	$-0.900556\pi$
$701$	−0.663693	+	1.82348i	−0.0250673	+	0.0688719i	0.926528	+	0.376226i	$0.122779\pi$
$702$	−0.566448	+	1.22889i	−0.0213792	+	0.0463816i
$703$	9.00167	−	11.3277i	0.339504	−	0.427231i
$704$			30.3336i			1.14324i
$705$	1.11897	+	36.6028i	0.0421427	+	1.37854i
$706$	−66.2706	+	11.6853i	−2.49413	+	0.439782i
$707$	35.5116	−	42.3210i	1.33555	−	1.59165i
$708$	−50.0424	−	26.8876i	−1.88071	−	1.01050i
$709$	5.57773	−	31.6329i	0.209476	−	1.18800i	−0.680762	−	0.732504i	$-0.738351\pi$
$709$	5.57773	−	31.6329i	0.209476	−	1.18800i	0.890239	−	0.455494i	$-0.150538\pi$
$710$	38.9582	+	22.4925i	1.46208	+	0.844130i
$711$	−5.96437	+	20.1380i	−0.223681	+	0.755234i
$712$	−22.4811	+	8.18246i	−0.842516	+	0.306651i
$713$	−9.98703	+	3.63498i	−0.374017	+	0.136131i
$714$	−15.6663	−	12.3498i	−0.586296	−	0.462181i
$715$	0.661828	+	0.382107i	0.0247510	+	0.0142900i
$716$	−7.85923	+	44.5719i	−0.293713	+	1.66573i
$717$	−0.716216	+	1.33300i	−0.0267476	+	0.0497818i
$718$	−43.8692	+	52.2813i	−1.63718	+	1.95112i
$719$	−11.9507	+	2.10723i	−0.445685	+	0.0785864i	−0.391987	−	0.919971i	$-0.628212\pi$
$719$	−11.9507	+	2.10723i	−0.445685	+	0.0785864i	−0.0536985	+	0.998557i	$0.517101\pi$
$720$	−4.27964	−	9.84155i	−0.159493	−	0.366773i
$721$			25.7005i			0.957136i
$722$	5.09931	−	41.8590i	0.189777	−	1.55783i
$723$	−8.64539	+	3.44934i	−0.321526	+	0.128282i
$724$	1.02317	−	2.81113i	0.0380257	−	0.104475i
$725$	0.835407	+	4.73783i	0.0310262	+	0.175958i
$726$	−6.58395	+	19.9676i	−0.244353	+	0.741069i
$727$	31.3986	−	26.3465i	1.16451	−	0.977139i	0.164552	−	0.986368i	$-0.447382\pi$
$727$	31.3986	−	26.3465i	1.16451	−	0.977139i	0.999957	+	0.00922935i	$0.00293784\pi$
$728$	−0.811510	−	0.143091i	−0.0300766	−	0.00530331i
$729$	−26.5474	+	4.92318i	−0.983236	+	0.182340i
$730$	25.6959	−	14.8356i	0.951049	−	0.549089i
$731$	2.44516	+	6.71801i	0.0904374	+	0.248475i
$732$	−29.0025	−	32.4934i	−1.07196	−	1.20099i
$733$	7.55658	+	13.0884i	0.279109	+	0.483430i	0.971163	−	0.238415i	$-0.0766277\pi$
$733$	7.55658	+	13.0884i	0.279109	+	0.483430i	−0.692055	+	0.721845i	$0.743294\pi$
$734$	2.44544	−	4.23563i	0.0902630	−	0.156340i
$735$	4.57638	+	21.9998i	0.168802	+	0.811477i
$736$	33.4751	+	39.8941i	1.23391	+	1.47052i
$737$	0.319036	+	0.267703i	0.0117519	+	0.00986098i
$738$	−19.5799	−	14.4873i	−0.720745	−	0.533284i
$739$	44.2024	+	16.0884i	1.62601	+	0.591820i	0.984514	−	0.175304i	$-0.0560910\pi$
$739$	44.2024	+	16.0884i	1.62601	+	0.591820i	0.641498	+	0.767125i	$0.278313\pi$
$740$	26.8957			0.988706
$741$	0.848411	+	0.254887i	0.0311671	+	0.00936352i
$742$	29.0781			1.06749
$743$	−36.8666	−	13.4183i	−1.35250	−	0.492271i	−0.438775	−	0.898597i	$-0.644588\pi$
$743$	−36.8666	−	13.4183i	−1.35250	−	0.492271i	−0.913728	+	0.406326i	$0.866810\pi$
$744$	−2.66578	−	4.30769i	−0.0977324	−	0.157928i
$745$	−8.99548	−	7.54811i	−0.329569	−	0.276541i
$746$	37.7405	+	44.9773i	1.38178	+	1.64674i
$747$	2.41581	−	1.59911i	0.0883898	−	0.0585084i
$748$	5.22276	−	9.04608i	0.190963	−	0.330757i
$749$	23.9817	+	41.5375i	0.876273	+	1.51775i
$750$	18.5062	−	16.5180i	0.675749	−	0.603151i
$751$	3.88517	+	10.6744i	0.141772	+	0.389515i	0.990175	−	0.139836i	$-0.0446575\pi$
$751$	3.88517	+	10.6744i	0.141772	+	0.389515i	−0.848403	+	0.529351i	$0.822435\pi$
$752$	−8.53972	+	4.93041i	−0.311412	+	0.179794i
$753$	−1.99616	+	13.7690i	−0.0727440	+	0.501769i
$754$	0.462102	+	0.0814810i	0.0168288	+	0.00296736i
$755$	24.5880	−	20.6318i	0.894850	−	0.750868i
$756$	−22.1694	−	46.9994i	−0.806294	−	1.70935i
$757$	−5.58358	−	31.6660i	−0.202939	−	1.15092i	−0.900651	−	0.434544i	$-0.856910\pi$
$757$	−5.58358	−	31.6660i	−0.202939	−	1.15092i	0.697712	−	0.716378i	$-0.254201\pi$
$758$	22.5548	−	61.9688i	0.819227	−	2.25081i
$759$	−11.2690	−	28.2445i	−0.409038	−	1.02521i
$760$	21.1406	−	12.9688i	0.766851	−	0.470428i
$761$			10.4640i			0.379320i	0.981850	+	0.189660i	$0.0607385\pi$
$761$			10.4640i			0.379320i	−0.981850	+	0.189660i	$0.939261\pi$
$762$	−71.7163	+	2.19240i	−2.59801	+	0.0794224i
$763$	−22.9255	+	4.04239i	−0.829960	+	0.146344i
$764$	22.4806	−	26.7914i	0.813320	−	0.969278i
$765$	−1.42744	+	12.5324i	−0.0516092	+	0.453111i
$766$	−2.30121	+	13.0508i	−0.0831461	+	0.471545i
$767$	−1.13916	−	0.657695i	−0.0411328	−	0.0237480i
$768$	−7.26302	+	9.21343i	−0.262082	+	0.332461i
$769$	17.4417	−	6.34825i	0.628963	−	0.228924i	−0.00781690	−	0.999969i	$-0.502488\pi$
$769$	17.4417	−	6.34825i	0.628963	−	0.228924i	0.636780	+	0.771046i	$0.280266\pi$
$770$	−46.4308	+	16.8994i	−1.67325	+	0.609013i
$771$	10.6326	−	13.4879i	0.382924	−	0.485755i
$772$	30.6289	+	17.6836i	1.10236	+	0.636447i
$773$	−2.18041	+	12.3657i	−0.0784238	+	0.444763i	0.920159	+	0.391545i	$0.128059\pi$
$773$	−2.18041	+	12.3657i	−0.0784238	+	0.444763i	−0.998583	+	0.0532187i	$0.983052\pi$
$774$	−3.54828	+	31.1527i	−0.127540	+	1.11976i
$775$	2.44321	−	2.91171i	0.0877628	−	0.104592i
$776$	−10.2414	+	1.80583i	−0.367643	+	0.0648254i
$777$	−19.6435	+	0.600511i	−0.704705	+	0.0215432i
$778$		−	30.7361i		−	1.10194i
$779$	−7.60194	+	14.0169i	−0.272368	+	0.502207i
$780$	0.610233	+	1.52948i	0.0218499	+	0.0547643i
$781$	5.88672	−	16.1736i	0.210643	−	0.578738i
$782$	−4.36803	−	24.7723i	−0.156200	−	0.885856i
$783$	3.99428	+	8.46793i	0.142744	+	0.302619i
$784$	−4.63520	+	3.88940i	−0.165543	+	0.138907i
$785$	−21.3327	−	3.76152i	−0.761395	−	0.134255i
$786$	−5.47824	+	37.7875i	−0.195402	+	1.34784i
$787$	−19.4460	+	11.2272i	−0.693175	+	0.400205i	−0.804800	−	0.593546i	$-0.797728\pi$
$787$	−19.4460	+	11.2272i	−0.693175	+	0.400205i	0.111625	+	0.993750i	$0.464394\pi$
$788$	2.10550	+	5.78482i	0.0750054	+	0.206076i
$789$	27.8164	−	24.8280i	0.990290	−	0.883899i
$790$	21.5157	+	37.2662i	0.765493	+	1.32587i
$791$	13.3001	−	23.0365i	0.472898	−	0.819083i
$792$	12.0867	−	8.00060i	0.429481	−	0.284289i
$793$	−0.648246	−	0.772550i	−0.0230199	−	0.0274340i
$794$	−20.1767	−	16.9303i	−0.716045	−	0.600833i
$795$	−9.67520	−	15.6343i	−0.343144	−	0.554492i
$796$	15.9072	+	5.78975i	0.563816	+	0.205212i
$797$	19.4024			0.687269			0.343635	−	0.939103i	$-0.388342\pi$
$797$	19.4024			0.687269			0.343635	+	0.939103i	$0.388342\pi$
$798$	−47.8840	+	31.4279i	−1.69508	+	1.11253i
$799$	11.5898			0.410017
$800$	−17.5018	−	6.37015i	−0.618783	−	0.225219i
$801$	−28.0827	−	20.7786i	−0.992254	−	0.734175i
$802$	40.4737	+	33.9615i	1.42918	+	1.19922i
$803$	−7.29717	−	8.69643i	−0.257511	−	0.306890i
$804$	0.182766	+	0.878605i	0.00644567	+	0.0309860i
$805$	−35.3376	+	61.2065i	−1.24549	+	2.15725i
$806$	−0.185363	−	0.321058i	−0.00652912	−	0.0113088i
$807$	21.3314	+	23.8990i	0.750902	+	0.841285i
$808$	11.3567	+	31.2024i	0.399529	+	1.09770i
$809$	0.787555	−	0.454695i	0.0276890	−	0.0159862i	−0.486092	−	0.873908i	$-0.661578\pi$
$809$	0.787555	−	0.454695i	0.0276890	−	0.0159862i	0.513781	+	0.857922i	$0.328245\pi$
$810$	−30.1256	+	46.3965i	−1.05850	+	1.63021i
$811$	−31.1396	−	5.49074i	−1.09346	−	0.192806i	−0.402299	−	0.915509i	$-0.631789\pi$
$811$	−31.1396	−	5.49074i	−1.09346	−	0.192806i	−0.691159	+	0.722702i	$0.742900\pi$
$812$	−13.8041	+	11.5830i	−0.484428	+	0.406483i
$813$	−1.65814	+	5.02878i	−0.0581537	+	0.176367i
$814$	−3.00846	−	17.0618i	−0.105446	−	0.598017i
$815$	−16.7953	+	46.1448i	−0.588315	+	1.61638i
$816$	−3.15467	+	1.25865i	−0.110436	+	0.0440616i
$817$	20.5193	−	0.547060i	0.717878	−	0.0191392i
$818$			73.0918i			2.55560i
$819$	−0.479837	−	1.10344i	−0.0167669	−	0.0385574i
$820$	−29.1906	+	5.14709i	−1.01938	+	0.179744i
$821$	4.15443	−	4.95106i	0.144991	−	0.172793i	−0.688661	−	0.725083i	$-0.741801\pi$
$821$	4.15443	−	4.95106i	0.144991	−	0.172793i	0.833652	+	0.552290i	$0.186246\pi$
$822$	−7.81786	+	14.5504i	−0.272679	+	0.507502i
$823$	6.56313	−	37.2214i	0.228776	−	1.29746i	−0.626556	−	0.779376i	$-0.715536\pi$
$823$	6.56313	−	37.2214i	0.228776	−	1.29746i	0.855332	−	0.518080i	$-0.173353\pi$
$824$	−13.3774	−	7.72345i	−0.466024	−	0.269059i
$825$	8.54092	+	6.73287i	0.297357	+	0.234408i
$826$	79.9182	−	29.0879i	2.78071	−	1.01210i
$827$	15.6661	−	5.70199i	0.544764	−	0.198278i	−0.0549548	−	0.998489i	$-0.517501\pi$
$827$	15.6661	−	5.70199i	0.544764	−	0.198278i	0.599718	+	0.800211i	$0.295279\pi$
$828$	18.6083	−	62.8287i	0.646683	−	2.18345i
$829$	−34.2416	−	19.7694i	−1.18926	−	0.686619i	−0.231121	−	0.972925i	$-0.574239\pi$
$829$	−34.2416	−	19.7694i	−1.18926	−	0.686619i	−0.958138	+	0.286306i	$0.907572\pi$
$830$	1.03073	−	5.84558i	0.0357773	−	0.202903i
$831$	40.6685	+	21.8510i	1.41077	+	0.758003i
$832$	−0.972837	+	1.15938i	−0.0337271	+	0.0401944i
$833$	7.00370	−	1.23494i	0.242664	−	0.0427882i
$834$	−2.16914	−	70.9555i	−0.0751113	−	2.45699i
$835$			5.32327i			0.184219i
$836$	−19.8833	−	22.4525i	−0.687678	−	0.776536i
$837$	3.09655	−	6.71787i	0.107032	−	0.232204i
$838$	−7.95862	+	21.8661i	−0.274926	+	0.755353i
$839$	6.62128	+	37.5512i	0.228592	+	1.29641i	0.855698	+	0.517476i	$0.173128\pi$
$839$	6.62128	+	37.5512i	0.228592	+	1.29641i	−0.627106	+	0.778934i	$0.715761\pi$
$840$	−31.9930	−	10.5491i	−1.10386	−	0.363978i
$841$	−19.7282	+	16.5539i	−0.680283	+	0.570825i
$842$	−18.7936	−	3.31382i	−0.647670	−	0.114202i
$843$	42.2239	+	6.12141i	1.45427	+	0.210832i
$844$	59.9349	−	34.6034i	2.06304	−	1.19110i
$845$	−12.3008	−	33.7961i	−0.423159	−	1.16262i
$846$	45.4897	+	22.6783i	1.56397	+	0.779697i
$847$	−9.34799	−	16.1912i	−0.321201	−	0.556336i
$848$	2.47543	−	4.28758i	0.0850067	−	0.147236i
$849$	18.8882	−	3.92910i	0.648241	−	0.134846i
$850$	5.78264	+	6.89148i	0.198343	+	0.236376i
$851$	−18.9835	−	15.9290i	−0.650744	−	0.546039i
$852$	31.5371	−	19.5165i	1.08044	−	0.668625i
$853$	24.2542	+	8.82779i	0.830447	+	0.302258i	0.722042	−	0.691849i	$-0.243204\pi$
$853$	24.2542	+	8.82779i	0.830447	+	0.302258i	0.108404	+	0.994107i	$0.465426\pi$
$854$	65.2045			2.23125
$855$	32.8303	+	15.2886i	1.12277	+	0.522860i
$856$	−28.8277			−0.985311
$857$	2.73238	+	0.994507i	0.0933365	+	0.0339717i	0.388266	−	0.921547i	$-0.373074\pi$
$857$	2.73238	+	0.994507i	0.0933365	+	0.0339717i	−0.294930	+	0.955519i	$0.595296\pi$
$858$	0.901999	−	0.558196i	0.0307937	−	0.0190565i
$859$	−16.4632	−	13.8142i	−0.561717	−	0.471336i	0.317169	−	0.948369i	$-0.397268\pi$
$859$	−16.4632	−	13.8142i	−0.561717	−	0.471336i	−0.878885	+	0.477033i	$0.841712\pi$
$860$	24.5264	+	29.2294i	0.836343	+	0.996715i
$861$	21.2046	−	4.41096i	0.722652	−	0.150325i
$862$	−15.1798	+	26.2922i	−0.517027	+	0.895518i
$863$	1.75212	+	3.03476i	0.0596429	+	0.103305i	0.894305	−	0.447458i	$-0.147670\pi$
$863$	1.75212	+	3.03476i	0.0596429	+	0.103305i	−0.834662	+	0.550762i	$0.814337\pi$
$864$	−36.1226	−	2.99962i	−1.22892	−	0.102049i
$865$	14.8665	+	40.8453i	0.505475	+	1.38878i
$866$	−63.1999	+	36.4885i	−2.14762	+	1.23993i
$867$	−25.1895	−	3.65185i	−0.855481	−	0.124023i
$868$	14.0207	+	2.47223i	0.475895	+	0.0839131i
$869$	12.6122	−	10.5829i	0.427840	−	0.359001i
$870$	18.2179	+	6.00702i	0.617646	+	0.203657i
$871$	0.00360832	+	0.0204638i	0.000122263	+	0.000693390i
$872$	4.78542	−	13.1478i	0.162055	−	0.445242i
$873$	−10.4532	−	11.0146i	−0.353789	−	0.372789i
$874$	−71.4349	−	10.6414i	−2.41632	−	0.359949i
$875$			22.0577i			0.745687i
$876$	−0.747469	−	24.4506i	−0.0252546	−	0.826111i
$877$	0.463140	−	0.0816641i	0.0156391	−	0.00275760i	−0.165823	−	0.986156i	$-0.553028\pi$
$877$	0.463140	−	0.0816641i	0.0156391	−	0.00275760i	0.181462	+	0.983398i	$0.441917\pi$
$878$	53.8358	−	64.1590i	1.81687	−	2.16526i
$879$	43.3785	+	23.3071i	1.46312	+	0.786130i
$880$	−1.46085	+	8.28489i	−0.0492453	+	0.279284i
$881$	18.5886	+	10.7321i	0.626266	+	0.361575i	0.779305	−	0.626645i	$-0.215572\pi$
$881$	18.5886	+	10.7321i	0.626266	+	0.361575i	−0.153038	+	0.988220i	$0.548906\pi$
$882$	29.9059	+	8.85739i	1.00699	+	0.298244i
$883$	−16.1337	+	5.87220i	−0.542943	+	0.197615i	−0.598908	−	0.800818i	$-0.704399\pi$
$883$	−16.1337	+	5.87220i	−0.542943	+	0.197615i	0.0559653	+	0.998433i	$0.482176\pi$
$884$	0.489739	−	0.178250i	0.0164717	−	0.00599521i
$885$	−42.2309	−	33.2910i	−1.41958	−	1.11906i
$886$	−9.93567	−	5.73636i	−0.333795	−	0.192717i
$887$	1.33715	−	7.58336i	0.0448971	−	0.254624i	−0.954095	−	0.299503i	$-0.903179\pi$
$887$	1.33715	−	7.58336i	0.0448971	−	0.254624i	0.998992	+	0.0448790i	$0.0142902\pi$
$888$	5.59064	−	10.4051i	0.187609	−	0.349173i
$889$	41.0108	−	48.8748i	1.37546	−	1.63921i
$890$	−70.4872	+	12.4288i	−2.36274	+	0.416614i
$891$	19.4835	+	8.26860i	0.652720	+	0.277009i
$892$			15.9393i			0.533688i
$893$	10.5438	−	31.5618i	0.352834	−	1.05617i
$894$	−15.1388	+	6.04008i	−0.506317	+	0.202010i
$895$	−14.6531	+	40.2590i	−0.489798	+	1.34571i
$896$	−8.71093	−	49.4022i	−0.291012	−	1.65041i
$897$	0.475125	−	1.44095i	0.0158639	−	0.0481118i
$898$	−48.8380	+	40.9799i	−1.62974	+	1.36752i
$899$	−2.52613	−	0.445425i	−0.0842511	−	0.0148557i
$900$	5.47153	+	22.7870i	0.182384	+	0.759567i
$901$	−5.03934	+	2.90946i	−0.167885	+	0.0969283i
$902$	6.53032	+	17.9419i	0.217436	+	0.597400i
$903$	−18.5656	−	20.8003i	−0.617826	−	0.692191i
$904$	7.99385	+	13.8457i	0.265871	+	0.460503i
$905$	1.41590	−	2.45241i	0.0470661	−	0.0815208i
$906$	−9.07342	−	43.6183i	−0.301444	−	1.44912i
$907$	−9.58133	−	11.4186i	−0.318143	−	0.379148i	0.583145	−	0.812368i	$-0.301822\pi$
$907$	−9.58133	−	11.4186i	−0.318143	−	0.379148i	−0.901288	+	0.433220i	$0.857377\pi$
$908$	6.47377	+	5.43213i	0.214839	+	0.180272i
$909$	−28.8394	+	38.9771i	−0.956542	+	1.29279i
$910$	−2.31662	−	0.843181i	−0.0767952	−	0.0279512i
$911$	−13.1248			−0.434844			−0.217422	−	0.976078i	$-0.569765\pi$
$911$	−13.1248			−0.434844			−0.217422	+	0.976078i	$0.569765\pi$
$912$	0.557658	+	9.73599i	0.0184659	+	0.322391i
$913$	−2.27106			−0.0751612
$914$	−11.8645	−	4.31833i	−0.392444	−	0.142838i
$915$	−21.6956	−	35.0583i	−0.717235	−	1.15899i
$916$	−64.6490	−	54.2469i	−2.13606	−	1.79237i
$917$	−21.8244	−	26.0093i	−0.720705	−	0.858903i
$918$	14.3858	+	9.97862i	0.474801	+	0.329344i
$919$	10.2468	−	17.7480i	0.338012	−	0.585453i	−0.646047	−	0.763298i	$-0.723579\pi$
$919$	10.2468	−	17.7480i	0.338012	−	0.585453i	0.984059	+	0.177844i	$0.0569123\pi$
$920$	−21.2391	−	36.7873i	−0.700234	−	1.21284i
$921$	−1.59674	+	1.42519i	−0.0526143	+	0.0469618i
$922$	−22.2552	−	61.1455i	−0.732935	−	2.01372i
$923$	0.743706	−	0.429379i	0.0244794	−	0.0141332i
$924$	−5.84461	+	40.3146i	−0.192274	+	1.32625i
$925$	8.72802	+	1.53899i	0.286976	+	0.0506016i
$926$	−25.5068	+	21.4028i	−0.838207	+	0.703339i
$927$	−1.37780	−	22.5137i	−0.0452527	−	0.739446i
$928$	2.18262	+	12.3783i	0.0716481	+	0.406336i
$929$	−14.0692	+	38.6548i	−0.461596	+	1.26822i	0.462689	+	0.886520i	$0.346885\pi$
$929$	−14.0692	+	38.6548i	−0.461596	+	1.26822i	−0.924285	+	0.381703i	$0.875338\pi$
$930$	−5.61632	−	14.0767i	−0.184166	−	0.461593i
$931$	3.00856	−	20.1963i	0.0986015	−	0.661906i
$932$			11.4808i			0.376065i
$933$	−25.8635	+	0.790660i	−0.846733	+	0.0258851i
$934$	89.3867	−	15.7613i	2.92482	−	0.515725i
$935$	6.35572	−	7.57445i	0.207854	−	0.247711i
$936$	0.718555	+	0.0818432i	0.0234867	+	0.00267513i
$937$	−4.72848	+	26.8166i	−0.154473	+	0.876059i	0.804793	+	0.593555i	$0.202276\pi$
$937$	−4.72848	+	26.8166i	−0.154473	+	0.876059i	−0.959266	+	0.282504i	$0.908835\pi$
$938$	−1.16351	−	0.671754i	−0.0379900	−	0.0219336i
$939$	−27.4200	+	34.7834i	−0.894819	+	1.13511i
$940$	58.1262	−	21.1562i	1.89587	−	0.690039i
$941$	−25.8180	+	9.39697i	−0.841641	+	0.306332i	−0.726628	−	0.687032i	$-0.758913\pi$
$941$	−25.8180	+	9.39697i	−0.841641	+	0.306332i	−0.115014	+	0.993364i	$0.536691\pi$
$942$	−18.6139	+	23.6125i	−0.606474	+	0.769337i
$943$	23.6516	+	13.6553i	0.770202	+	0.444676i
$944$	2.51447	−	14.2602i	0.0818389	−	0.464132i
$945$	−12.9412	−	47.4579i	−0.420978	−	1.54381i
$946$	15.7988	−	18.8283i	0.513664	−	0.612161i
$947$	−23.6875	+	4.17674i	−0.769739	+	0.135726i	−0.544708	−	0.838626i	$-0.683359\pi$
$947$	−23.6875	+	4.17674i	−0.769739	+	0.135726i	−0.225031	+	0.974352i	$0.572248\pi$
$948$	35.4602	−	1.08404i	1.15169	−	0.0352078i
$949$		−	0.566416i		−	0.0183867i
$950$	24.0279	−	9.47802i	0.779569	−	0.307508i
$951$	−20.2589	−	50.7767i	−0.656940	−	1.64655i
$952$	−3.64650	+	10.0187i	−0.118184	+	0.324707i
$953$	5.47213	+	31.0340i	0.177260	+	1.00529i	0.935503	+	0.353318i	$0.114947\pi$
$953$	5.47213	+	31.0340i	0.177260	+	1.00529i	−0.758244	+	0.651971i	$0.773942\pi$
$954$	−25.4724	+	1.55887i	−0.824701	+	0.0504702i
$955$	25.3608	−	21.2802i	0.820655	−	0.688611i
$956$	2.51724	+	0.443857i	0.0814133	+	0.0143554i
$957$	1.05303	−	7.26352i	0.0340396	−	0.234796i
$958$	46.6652	−	26.9422i	1.50768	−	0.870462i
$959$	−5.02353	−	13.8020i	−0.162218	−	0.445691i
$960$	−46.1597	+	41.2006i	−1.48980	+	1.32974i
$961$	−14.4867	−	25.0917i	−0.467313	−	0.809409i
$962$	0.432208	−	0.748607i	0.0139350	−	0.0241361i
$963$	−23.2348	−	35.1013i	−0.748732	−	1.13112i
$964$	10.1064	+	12.0444i	0.325506	+	0.387923i
$965$	25.6461	+	21.5197i	0.825578	+	0.692742i
$966$	51.6225	+	83.4178i	1.66093	+	2.68392i
$967$	−14.9667	−	5.44744i	−0.481297	−	0.175178i	0.0899658	−	0.995945i	$-0.471324\pi$
$967$	−14.9667	−	5.44744i	−0.481297	−	0.175178i	−0.571263	+	0.820767i	$0.693546\pi$
$968$	11.2369			0.361169
$969$	5.15390	−	10.2377i	0.165567	−	0.328882i
$970$	−31.1123			−0.998957
$971$	29.2900	+	10.6607i	0.939961	+	0.342118i	0.766150	−	0.642661i	$-0.222170\pi$
$971$	29.2900	+	10.6607i	0.939961	+	0.342118i	0.173810	+	0.984779i	$0.444392\pi$
$972$	21.9401	+	39.9831i	0.703728	+	1.28246i
$973$	48.3562	+	40.5757i	1.55023	+	1.30080i
$974$	−26.6802	−	31.7963i	−0.854890	−	1.01882i
$975$	0.110511	+	0.531256i	0.00353919	+	0.0170138i
$976$	5.55090	−	9.61444i	0.177680	−	0.307751i
$977$	3.52792	+	6.11054i	0.112868	+	0.195493i	0.916926	−	0.399058i	$-0.130663\pi$
$977$	3.52792	+	6.11054i	0.112868	+	0.195493i	−0.804057	+	0.594552i	$0.797330\pi$
$978$	45.3879	+	50.8510i	1.45134	+	1.62604i
$979$	9.36620	+	25.7334i	0.299345	+	0.822444i
$980$	32.8714	−	18.9783i	1.05004	−	0.606240i
$981$	19.8661	−	4.77018i	0.634276	−	0.152300i
$982$	−76.3358	−	13.4601i	−2.43597	−	0.429528i
$983$	4.44208	−	3.72735i	0.141680	−	0.118884i	−0.569193	−	0.822204i	$-0.692744\pi$
$983$	4.44208	−	3.72735i	0.141680	−	0.118884i	0.710873	+	0.703320i	$0.248300\pi$
$984$	−4.07641	+	12.3628i	−0.129951	+	0.394113i
$985$	1.01191	+	5.73882i	0.0322421	+	0.182854i
$986$	2.07644	−	5.70499i	0.0661275	−	0.181684i
$987$	−41.9805	+	16.7494i	−1.33625	+	0.533139i
$988$	−0.0398803	−	1.49584i	−0.00126876	−	0.0475891i
$989$		−	35.1564i		−	1.11791i
$990$	39.7675	−	17.2931i	1.26389	−	0.549609i
$991$	12.4052	−	2.18738i	0.394065	−	0.0694844i	0.0268955	−	0.999638i	$-0.491438\pi$
$991$	12.4052	−	2.18738i	0.394065	−	0.0694844i	0.367170	+	0.930154i	$0.380327\pi$
$992$	6.38325	−	7.60726i	0.202668	−	0.241531i
$993$	12.0142	−	22.3605i	0.381260	−	0.709589i
$994$	−9.64153	+	54.6799i	−0.305811	+	1.73434i
$995$	13.8773	+	8.01209i	0.439942	+	0.254000i
$996$	−3.84314	−	3.02958i	−0.121775	−	0.0959958i
$997$	−24.1000	+	8.77169i	−0.763255	+	0.277802i	−0.694172	−	0.719809i	$-0.744229\pi$
$997$	−24.1000	+	8.77169i	−0.763255	+	0.277802i	−0.0690827	+	0.997611i	$0.522007\pi$
$998$	−7.89713	+	2.87432i	−0.249979	+	0.0909851i
$999$	17.1755	−	1.57913i	0.543409	−	0.0499614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.j.b.53.1	yes	24
3.2	odd	2	inner	57.2.j.b.53.4	yes	24
4.3	odd	2		912.2.cc.e.737.3		24
12.11	even	2		912.2.cc.e.737.4		24
19.9	even	9		1083.2.d.d.1082.21		24
19.10	odd	18		1083.2.d.d.1082.3		24
19.14	odd	18	inner	57.2.j.b.14.4	yes	24
57.14	even	18	inner	57.2.j.b.14.1	✓	24
57.29	even	18		1083.2.d.d.1082.22		24
57.47	odd	18		1083.2.d.d.1082.4		24
76.71	even	18		912.2.cc.e.641.4		24
228.71	odd	18		912.2.cc.e.641.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.j.b.14.1	✓	24	57.14	even	18	inner
57.2.j.b.14.4	yes	24	19.14	odd	18	inner
57.2.j.b.53.1	yes	24	1.1	even	1	trivial
57.2.j.b.53.4	yes	24	3.2	odd	2	inner
912.2.cc.e.641.3		24	228.71	odd	18
912.2.cc.e.641.4		24	76.71	even	18
912.2.cc.e.737.3		24	4.3	odd	2
912.2.cc.e.737.4		24	12.11	even	2
1083.2.d.d.1082.3		24	19.10	odd	18
1083.2.d.d.1082.4		24	57.47	odd	18
1083.2.d.d.1082.21		24	19.9	even	9
1083.2.d.d.1082.22		24	57.29	even	18

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08555 - 0.759077i) q^{2} +(-1.47284 + 0.911455i) q^{3} +(2.24122 + 1.88060i) q^{4} +(1.78018 + 2.12154i) q^{5} +(3.76353 - 0.782886i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(-1.02725 - 1.77924i) q^{8} +(1.33850 - 2.68485i) q^{9} +O(q^{10})\)	\(q+(-2.08555 - 0.759077i) q^{2} +(-1.47284 + 0.911455i) q^{3} +(2.24122 + 1.88060i) q^{4} +(1.78018 + 2.12154i) q^{5} +(3.76353 - 0.782886i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(-1.02725 - 1.77924i) q^{8} +(1.33850 - 2.68485i) q^{9} +(-2.10224 - 5.77587i) q^{10} +(-2.03664 + 1.17586i) q^{11} +(-5.01503 - 0.727055i) q^{12} +(-0.115554 - 0.0203753i) q^{13} +(5.81156 - 4.87648i) q^{14} +(-4.55561 - 1.50212i) q^{15} +(-0.224297 - 1.27205i) q^{16} +(-0.519239 + 1.42660i) q^{17} +(-4.82951 + 4.58336i) q^{18} +(3.41260 + 2.71186i) q^{19} +8.10265i q^{20} +(-0.180911 - 5.91783i) q^{21} +(5.14008 - 0.906334i) q^{22} +(4.79880 - 5.71899i) q^{23} +(3.13467 + 1.68425i) q^{24} +(-0.463638 + 2.62942i) q^{25} +(0.225527 + 0.130208i) q^{26} +(0.475732 + 5.17433i) q^{27} +(-9.39767 + 3.42047i) q^{28} +(1.69319 - 0.616270i) q^{29} +(8.36070 + 6.59081i) q^{30} +(-1.23287 - 0.711795i) q^{31} +(-1.21132 + 6.86975i) q^{32} +(1.92790 - 3.58815i) q^{33} +(2.16579 - 2.58109i) q^{34} +(-9.32295 + 1.64389i) q^{35} +(8.04901 - 3.50015i) q^{36} -3.31937i q^{37} +(-5.05862 - 8.24613i) q^{38} +(0.188763 - 0.0753128i) q^{39} +(1.94605 - 5.34672i) q^{40} +(0.635235 + 3.60260i) q^{41} +(-4.11479 + 12.4792i) q^{42} +(3.60739 - 3.02696i) q^{43} +(-6.77588 - 1.19477i) q^{44} +(8.07879 - 1.93985i) q^{45} +(-14.3493 + 8.28456i) q^{46} +(-2.61102 - 7.17373i) q^{47} +(1.48977 + 1.66909i) q^{48} +(-2.34224 - 4.05687i) q^{49} +(2.96287 - 5.13184i) q^{50} +(-0.535525 - 2.57441i) q^{51} +(-0.220664 - 0.262977i) q^{52} +(2.93617 + 2.46374i) q^{53} +(2.93555 - 11.1524i) q^{54} +(-6.12022 - 2.22758i) q^{55} +7.02278 q^{56} +(-7.49794 - 0.883697i) q^{57} -3.99901 q^{58} +(10.5343 + 3.83419i) q^{59} +(-7.38520 - 11.9339i) q^{60} +(6.58405 + 5.52467i) q^{61} +(2.03089 + 2.42032i) q^{62} +(5.66029 + 8.55110i) q^{63} +(6.44925 - 11.1704i) q^{64} +(-0.162480 - 0.281424i) q^{65} +(-6.74441 + 6.01983i) q^{66} +(-0.0605694 - 0.166413i) q^{67} +(-3.84659 + 2.22083i) q^{68} +(-1.85525 + 12.7970i) q^{69} +(20.6913 + 3.64843i) q^{70} +(-5.60649 + 4.70441i) q^{71} +(-6.15197 + 0.376489i) q^{72} +(0.838249 + 4.75394i) q^{73} +(-2.51966 + 6.92270i) q^{74} +(-1.71374 - 4.29529i) q^{75} +(2.54844 + 12.4956i) q^{76} -8.03875i q^{77} +(-0.450843 + 0.0137825i) q^{78} +(-6.89453 + 1.21569i) q^{79} +(2.29942 - 2.74034i) q^{80} +(-5.41684 - 7.18734i) q^{81} +(1.40984 - 7.99558i) q^{82} +(0.836326 + 0.482853i) q^{83} +(10.7236 - 13.6034i) q^{84} +(-3.95092 + 1.43802i) q^{85} +(-9.82108 + 3.57458i) q^{86} +(-1.93209 + 2.45093i) q^{87} +(4.18427 + 2.41579i) q^{88} +(2.02208 - 11.4678i) q^{89} +(-18.3212 - 2.08678i) q^{90} +(0.257813 - 0.307250i) q^{91} +(21.5103 - 3.79285i) q^{92} +(2.46458 - 0.0753434i) q^{93} +16.9431i q^{94} +(0.321731 + 12.0676i) q^{95} +(-4.47739 - 11.2221i) q^{96} +(1.73122 - 4.75650i) q^{97} +(1.80536 + 10.2387i) q^{98} +(0.430956 + 7.04196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9}+O(q^{10}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9	\( 24 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} - 6 q^{10} + 9 q^{12} + 6 q^{13} - 9 q^{15} + 30 q^{16} - 12 q^{19} - 6 q^{21} + 24 q^{22} - 21 q^{24} + 12 q^{25} - 27 q^{27} - 48 q^{28} + 42 q^{30} - 18 q^{31} + 21 q^{33} - 42 q^{34} + 63 q^{36} + 30 q^{40} + 105 q^{42} + 54 q^{43} + 6 q^{45} - 54 q^{46} - 33 q^{48} + 6 q^{49} + 3 q^{51} - 48 q^{52} - 87 q^{54} - 90 q^{55} - 6 q^{57} + 24 q^{58} - 66 q^{60} - 6 q^{61} - 9 q^{63} + 18 q^{64} - 57 q^{66} - 36 q^{69} + 18 q^{70} + 24 q^{72} + 90 q^{73} + 12 q^{76} + 9 q^{78} + 30 q^{79} + 3 q^{81} + 126 q^{82} + 99 q^{84} - 6 q^{85} + 15 q^{87} + 54 q^{88} + 24 q^{90} + 66 q^{91} + 33 q^{93} - 18 q^{96} - 78 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q - 9 * q^3 - 18 * q^4 - 9 * q^6 - 6 * q^7 + 3 * q^9 - 6 * q^10 + 9 * q^12 + 6 * q^13 - 9 * q^15 + 30 * q^16 - 12 * q^19 - 6 * q^21 + 24 * q^22 - 21 * q^24 + 12 * q^25 - 27 * q^27 - 48 * q^28 + 42 * q^30 - 18 * q^31 + 21 * q^33 - 42 * q^34 + 63 * q^36 + 30 * q^40 + 105 * q^42 + 54 * q^43 + 6 * q^45 - 54 * q^46 - 33 * q^48 + 6 * q^49 + 3 * q^51 - 48 * q^52 - 87 * q^54 - 90 * q^55 - 6 * q^57 + 24 * q^58 - 66 * q^60 - 6 * q^61 - 9 * q^63 + 18 * q^64 - 57 * q^66 - 36 * q^69 + 18 * q^70 + 24 * q^72 + 90 * q^73 + 12 * q^76 + 9 * q^78 + 30 * q^79 + 3 * q^81 + 126 * q^82 + 99 * q^84 - 6 * q^85 + 15 * q^87 + 54 * q^88 + 24 * q^90 + 66 * q^91 + 33 * q^93 - 18 * q^96 - 78 * q^97 + 12 * q^99

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