LMFDB - Embedded newform 57.2.j.b.53.4

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			53.4
Character	$\chi$	$=$	57.53
Dual form			57.2.j.b.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.08555 + 0.759077i) q^{2} +(-1.69575 - 0.352748i) q^{3} +(2.24122 + 1.88060i) q^{4} +(-1.78018 - 2.12154i) q^{5} +(-3.26880 - 2.02288i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(1.02725 + 1.77924i) q^{8} +(2.75114 + 1.19634i) q^{9} +O(q^{10})$	\(q+(2.08555 + 0.759077i) q^{2} +(-1.69575 - 0.352748i) q^{3} +(2.24122 + 1.88060i) q^{4} +(-1.78018 - 2.12154i) q^{5} +(-3.26880 - 2.02288i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(1.02725 + 1.77924i) q^{8} +(2.75114 + 1.19634i) q^{9} +(-2.10224 - 5.77587i) q^{10} +(2.03664 - 1.17586i) q^{11} +(-3.13716 - 3.97962i) q^{12} +(-0.115554 - 0.0203753i) q^{13} +(-5.81156 + 4.87648i) q^{14} +(2.27038 + 4.22556i) 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} +(3.94249 - 4.41703i) q^{21} +(5.14008 - 0.906334i) q^{22} +(-4.79880 + 5.71899i) q^{23} +(-1.11433 - 3.37951i) q^{24} +(-0.463638 + 2.62942i) q^{25} +(-0.225527 - 0.130208i) q^{26} +(-4.24323 - 2.99916i) q^{27} +(-9.39767 + 3.42047i) q^{28} +(-1.69319 + 0.616270i) q^{29} +(1.52745 + 10.5360i) q^{30} +(-1.23287 - 0.711795i) q^{31} +(1.21132 - 6.86975i) q^{32} +(-3.86842 + 1.27554i) q^{33} +(2.16579 - 2.58109i) q^{34} +(9.32295 - 1.64389i) q^{35} +(3.91605 + 7.85507i) 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} +(11.5751 - 6.21927i) q^{42} +(3.60739 - 3.02696i) q^{43} +(6.77588 + 1.19477i) q^{44} +(-2.35944 - 7.96636i) q^{45} +(-14.3493 + 8.28456i) q^{46} +(2.61102 + 7.17373i) q^{47} +(-0.0683620 + 2.23621i) q^{48} +(-2.34224 - 4.05687i) q^{49} +(-2.96287 + 5.13184i) q^{50} +(-1.38373 + 2.23599i) q^{51} +(-0.220664 - 0.262977i) q^{52} +(-2.93617 - 2.46374i) q^{53} +(-6.57287 - 9.47583i) q^{54} +(-6.12022 - 2.22758i) q^{55} -7.02278 q^{56} +(-4.83031 - 5.80242i) q^{57} -3.99901 q^{58} +(-10.5343 - 3.83419i) q^{59} +(-2.85819 + 13.7401i) q^{60} +(6.58405 + 5.52467i) q^{61} +(-2.03089 - 2.42032i) q^{62} +(-8.24358 + 6.09948i) q^{63} +(6.44925 - 11.1704i) q^{64} +(0.162480 + 0.281424i) q^{65} +(-9.03600 - 0.276235i) q^{66} +(-0.0605694 - 0.166413i) q^{67} +(3.84659 - 2.22083i) q^{68} +(10.1549 - 8.00521i) q^{69} +(20.6913 + 3.64843i) q^{70} +(5.60649 - 4.70441i) q^{71} +(0.697508 + 6.12388i) 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} +(0.336506 + 0.300354i) q^{78} +(-6.89453 + 1.21569i) q^{79} +(-2.29942 + 2.74034i) q^{80} +(6.13752 + 6.58262i) q^{81} +(1.40984 - 7.99558i) q^{82} +(-0.836326 - 0.482853i) q^{83} +(17.1427 - 2.48526i) q^{84} +(-3.95092 + 1.43802i) q^{85} +(9.82108 - 3.57458i) q^{86} +(3.08861 - 0.447771i) q^{87} +(4.18427 + 2.41579i) q^{88} +(-2.02208 + 11.4678i) q^{89} +(1.12637 - 18.4052i) q^{90} +(0.257813 - 0.307250i) q^{91} +(-21.5103 + 3.79285i) q^{92} +(1.83955 + 1.64192i) 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} +(7.00981 - 0.798416i) 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	0.949373	−	0.314150i	$-0.101719\pi$
$2$	2.08555	+	0.759077i	1.47470	+	0.536748i	0.525331	+	0.850898i	$0.323942\pi$
$3$	−1.69575	−	0.352748i	−0.979042	−	0.203659i
$3$	−1.69575	−	0.352748i	−0.979042	−	0.203659i
$4$	2.24122	+	1.88060i	1.12061	+	0.940302i
$5$	−1.78018	−	2.12154i	−0.796122	−	0.948781i	0.203418	−	0.979092i	$-0.434795\pi$
$5$	−1.78018	−	2.12154i	−0.796122	−	0.948781i	−0.999541	+	0.0303104i	$0.990350\pi$
$6$	−3.26880	−	2.02288i	−1.33448	−	0.825836i
$7$	−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
$9$	2.75114	+	1.19634i	0.917046	+	0.398782i
$10$	−2.10224	−	5.77587i	−0.664788	−	1.82649i
$11$	2.03664	−	1.17586i	0.614071	−	0.354534i	−0.160486	−	0.987038i	$-0.551306\pi$
$11$	2.03664	−	1.17586i	0.614071	−	0.354534i	0.774557	+	0.632504i	$0.217973\pi$
$12$	−3.13716	−	3.97962i	−0.905621	−	1.14882i
$13$	−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
$15$	2.27038	+	4.22556i	0.586209	+	1.09103i
$16$	−0.224297	−	1.27205i	−0.0560744	−	0.318013i
$17$	0.519239	−	1.42660i	0.125934	−	0.346001i	−0.860663	−	0.509174i	$-0.829951\pi$
$17$	0.519239	−	1.42660i	0.125934	−	0.346001i	0.986597	+	0.163174i	$0.0521731\pi$
$18$	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
$21$	3.94249	−	4.41703i	0.860322	−	0.963875i
$22$	5.14008	−	0.906334i	1.09587	−	0.193231i
$23$	−4.79880	+	5.71899i	−1.00062	+	1.19249i	−0.0193576	+	0.999813i	$0.506162\pi$
$23$	−4.79880	+	5.71899i	−1.00062	+	1.19249i	−0.981262	+	0.192679i	$0.938282\pi$
$24$	−1.11433	−	3.37951i	−0.227461	−	0.689840i
$25$	−0.463638	+	2.62942i	−0.0927276	+	0.525884i
$26$	−0.225527	−	0.130208i	−0.0442294	−	0.0255359i
$27$	−4.24323	−	2.99916i	−0.816611	−	0.577189i
$28$	−9.39767	+	3.42047i	−1.77599	+	0.646409i
$29$	−1.69319	+	0.616270i	−0.314417	+	0.114438i	−0.494408	−	0.869230i	$-0.664615\pi$
$29$	−1.69319	+	0.616270i	−0.314417	+	0.114438i	0.179991	+	0.983668i	$0.442393\pi$
$30$	1.52745	+	10.5360i	0.278874	+	1.92360i
$31$	−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
$33$	−3.86842	+	1.27554i	−0.673405	+	0.222042i
$34$	2.16579	−	2.58109i	0.371431	−	0.442654i
$35$	9.32295	−	1.64389i	1.57587	−	0.277868i
$36$	3.91605	+	7.85507i	0.652674	+	1.30918i
$37$		−	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	$-0.963344\pi$
$41$	−0.635235	−	3.60260i	−0.0992071	−	0.562631i	0.894170	−	0.447728i	$-0.147767\pi$
$42$	11.5751	−	6.21927i	1.78608	−	0.959654i
$43$	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
$45$	−2.35944	−	7.96636i	−0.351724	−	1.18756i
$46$	−14.3493	+	8.28456i	−2.11569	+	1.22149i
$47$	2.61102	+	7.17373i	0.380857	+	1.04640i	0.970996	+	0.239094i	$0.0768505\pi$
$47$	2.61102	+	7.17373i	0.380857	+	1.04640i	−0.590139	+	0.807301i	$0.700927\pi$
$48$	−0.0683620	+	2.23621i	−0.00986720	+	0.322769i
$49$	−2.34224	−	4.05687i	−0.334605	−	0.579553i
$50$	−2.96287	+	5.13184i	−0.419013	+	0.725752i
$51$	−1.38373	+	2.23599i	−0.193761	+	0.313102i
$52$	−0.220664	−	0.262977i	−0.0306005	−	0.0364683i
$53$	−2.93617	−	2.46374i	−0.403314	−	0.338421i	0.418459	−	0.908236i	$-0.362570\pi$
$53$	−2.93617	−	2.46374i	−0.403314	−	0.338421i	−0.821773	+	0.569815i	$0.807015\pi$
$54$	−6.57287	−	9.47583i	−0.894454	−	1.28950i
$55$	−6.12022	−	2.22758i	−0.825251	−	0.300367i
$56$	−7.02278			−0.938458
$57$	−4.83031	−	5.80242i	−0.639790	−	0.768550i
$58$	−3.99901			−0.525096
$59$	−10.5343	−	3.83419i	−1.37145	−	0.499169i	−0.451878	−	0.892080i	$-0.649246\pi$
$59$	−10.5343	−	3.83419i	−1.37145	−	0.499169i	−0.919576	+	0.392911i	$0.871468\pi$
$60$	−2.85819	+	13.7401i	−0.368991	+	1.77384i
$61$	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
$63$	−8.24358	+	6.09948i	−1.03859	+	0.768462i
$64$	6.44925	−	11.1704i	0.806157	−	1.39630i
$65$	0.162480	+	0.281424i	0.0201532	+	0.0349064i
$66$	−9.03600	−	0.276235i	−1.11225	−	0.0340022i
$67$	−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
$69$	10.1549	−	8.00521i	1.22251	−	0.963714i
$70$	20.6913	+	3.64843i	2.47308	+	0.436071i
$71$	5.60649	−	4.70441i	0.665368	−	0.558310i	−0.246322	−	0.969188i	$-0.579222\pi$
$71$	5.60649	−	4.70441i	0.665368	−	0.558310i	0.911690	+	0.410878i	$0.134778\pi$
$72$	0.697508	+	6.12388i	0.0822021	+	0.721706i
$73$	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
$78$	0.336506	+	0.300354i	0.0381018	+	0.0340084i
$79$	−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
$81$	6.13752	+	6.58262i	0.681947	+	0.731402i
$82$	1.40984	−	7.99558i	0.155690	−	0.882964i
$83$	−0.836326	−	0.482853i	−0.0917987	−	0.0530000i	0.453398	−	0.891308i	$-0.350212\pi$
$83$	−0.836326	−	0.482853i	−0.0917987	−	0.0530000i	−0.545197	+	0.838308i	$0.683545\pi$
$84$	17.1427	−	2.48526i	1.87042	−	0.271164i
$85$	−3.95092	+	1.43802i	−0.428538	+	0.155975i
$86$	9.82108	−	3.57458i	1.05903	−	0.385457i
$87$	3.08861	−	0.447771i	0.331134	−	0.0480061i
$88$	4.18427	+	2.41579i	0.446044	+	0.257524i
$89$	−2.02208	+	11.4678i	−0.214340	+	1.21558i	0.667709	+	0.744423i	$0.267275\pi$
$89$	−2.02208	+	11.4678i	−0.214340	+	1.21558i	−0.882048	+	0.471159i	$0.843836\pi$
$90$	1.12637	−	18.4052i	0.118729	−	1.94008i
$91$	0.257813	−	0.307250i	0.0270262	−	0.0322085i
$92$	−21.5103	+	3.79285i	−2.24260	+	0.395432i
$93$	1.83955	+	1.64192i	0.190752	+	0.170259i
$94$			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
$99$	7.00981	−	0.798416i	0.704513	−	0.0802438i
$100$	−5.98401	+	5.02118i	−0.598401	+	0.502118i
$101$	15.9166	+	2.80652i	1.58376	+	0.279259i	0.895113	−	0.445840i	$-0.147095\pi$
$101$	15.9166	+	2.80652i	1.58376	+	0.279259i	0.688644	+	0.725099i	$0.258206\pi$
$102$	−4.58312	+	3.61291i	−0.453797	+	0.357731i
$103$	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
$105$	−16.3893	−	0.501028i	−1.59943	−	0.0488953i
$106$	−4.25335	−	7.36702i	−0.413122	−	0.715548i
$107$	−7.01577	+	12.1517i	−0.678241	+	1.17475i	0.297270	+	0.954794i	$0.403924\pi$
$107$	−7.01577	+	12.1517i	−0.678241	+	1.17475i	−0.975510	+	0.219954i	$0.929409\pi$
$108$	−3.86978	−	14.7016i	−0.372369	−	1.41466i
$109$	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
$111$	−1.17090	+	5.62882i	−0.111137	+	0.534264i
$112$	4.14901	+	1.51012i	0.392044	+	0.142693i
$113$	7.78182			0.732052			0.366026	−	0.930605i	$-0.380718\pi$
$113$	7.78182			0.732052			0.366026	+	0.930605i	$0.380718\pi$
$114$	−5.66935	−	15.7678i	−0.530983	−	1.47679i
$115$	20.6758			1.92803
$116$	−4.95376	−	1.80302i	−0.459945	−	0.167406i
$117$	−0.293529	−	0.194298i	−0.0271368	−	0.0179628i
$118$	−19.0594	−	15.9927i	−1.75456	−	1.47225i
$119$	3.33571	+	3.97534i	0.305784	+	0.364419i
$120$	−5.18606	+	8.38024i	−0.473420	+	0.765008i
$121$	−2.73472	+	4.73668i	−0.248611	+	0.430607i
$122$	9.53769	+	16.5198i	0.863502	+	1.49563i
$123$	−0.193609	+	6.33318i	−0.0174571	+	0.571044i
$124$	−1.42451	−	3.91382i	−0.127925	−	0.351471i
$125$	−5.58839	+	3.22646i	−0.499841	+	0.288583i
$126$	−21.8223	+	6.46323i	−1.94409	+	0.575790i
$127$	−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
$129$	−7.18499	+	3.86047i	−0.632603	+	0.339895i
$130$	0.125238	+	0.710258i	0.0109841	+	0.0622937i
$131$	3.39721	−	9.33375i	0.296815	−	0.815493i	−0.698212	−	0.715891i	$-0.746021\pi$
$131$	3.39721	−	9.33375i	0.296815	−	0.815493i	0.995027	−	0.0996023i	$-0.0317570\pi$
$132$	−11.0687	−	4.41621i	−0.963410	−	0.384382i
$133$	−13.8605	+	5.46738i	−1.20186	+	0.474082i
$134$		−	0.393039i		−	0.0339534i
$135$	1.19090	+	14.3412i	0.102496	+	1.23430i
$136$	3.07165	−	0.541615i	0.263392	−	0.0464431i
$137$	2.76198	−	3.29160i	0.235972	−	0.281220i	−0.635043	−	0.772477i	$-0.719018\pi$
$137$	2.76198	−	3.29160i	0.235972	−	0.281220i	0.871015	+	0.491256i	$0.163462\pi$
$138$	27.2551	−	8.98686i	2.32011	−	0.765013i
$139$	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
$141$	−1.89713	−	13.0859i	−0.159767	−	1.10203i
$142$	15.2636	−	5.55550i	1.28089	−	0.466207i
$143$	−0.259300	+	0.0943777i	−0.0216838	+	0.00789226i
$144$	0.904742	−	3.76793i	0.0753952	−	0.313994i
$145$	4.32162	+	2.49509i	0.358891	+	0.207206i
$146$	−1.86040	+	10.5509i	−0.153968	+	0.873196i
$147$	2.54079	+	7.70566i	0.209561	+	0.635552i
$148$	6.24242	−	7.43943i	0.513124	−	0.611517i
$149$	4.17566	−	0.736281i	0.342083	−	0.0603185i	3.24291e−5	−	1.00000i	$-0.499990\pi$
$149$	4.17566	−	0.736281i	0.342083	−	0.0603185i	0.342051	+	0.939682i	$0.388879\pi$
$150$	6.83453	−	7.65718i	0.558037	−	0.625206i
$151$		−	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
$156$	0.281426	+	0.523781i	0.0225321	+	0.0419361i
$157$	−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
$159$	4.10993	+	5.21361i	0.325939	+	0.413466i
$160$	−16.7308	+	9.65954i	−1.32269	+	0.763654i
$161$	−8.72814	−	23.9804i	−0.687874	−	1.88992i
$162$	7.80337	+	18.3872i	0.613090	+	1.44464i
$163$	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
$165$	9.59260	+	5.93631i	0.746783	+	0.462141i
$166$	−1.37767	−	1.64185i	−0.106928	−	0.127432i
$167$	−1.47243	−	1.23552i	−0.113940	−	0.0956071i	0.584038	−	0.811727i	$-0.301472\pi$
$167$	−1.47243	−	1.23552i	−0.113940	−	0.0956071i	−0.697978	+	0.716120i	$0.745917\pi$
$168$	11.9089	+	2.47727i	0.918790	+	0.191126i
$169$	−12.2031	−	4.44155i	−0.938697	−	0.341658i
$170$	−9.33140			−0.715686
$171$	6.14421	+	11.5433i	0.469859	+	0.882741i
$172$	13.7775			1.05052
$173$	−14.7484	−	5.36798i	−1.12130	−	0.408120i	−0.286173	−	0.958178i	$-0.592383\pi$
$173$	−14.7484	−	5.36798i	−1.12130	−	0.408120i	−0.835126	+	0.550058i	$0.814605\pi$
$174$	6.78133	+	1.41064i	0.514091	+	0.106941i
$175$	−6.99145	−	5.86652i	−0.528504	−	0.443467i
$176$	−1.95257	−	2.32698i	−0.147180	−	0.175403i
$177$	16.5111	+	10.2178i	1.24105	+	0.768016i
$178$	−12.9221	+	22.3817i	−0.968549	+	1.67758i
$179$	−7.73482	−	13.3971i	−0.578127	−	1.00135i	−0.995694	−	0.0926997i	$-0.970450\pi$
$179$	−7.73482	−	13.3971i	−0.578127	−	1.00135i	0.417567	−	0.908646i	$-0.362883\pi$
$180$	9.69356	−	22.2915i	0.722516	−	1.66151i
$181$	−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
$183$	−9.21609	−	11.6910i	−0.681273	−	0.864222i
$184$	−15.1050	−	2.66342i	−1.11356	−	0.196350i
$185$	−7.04218	+	5.90909i	−0.517751	+	0.434445i
$186$	2.59012	+	4.82065i	0.189917	+	0.353467i
$187$	−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	$0.142361\pi$
$191$			11.9539i			0.864957i	−0.901644	+	0.432478i	$0.857639\pi$
$192$	−14.8767	+	16.6673i	−1.07363	+	1.20286i
$193$	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
$195$	−0.176254	−	0.534539i	−0.0126218	−	0.0382792i
$196$	2.37991	−	13.4971i	0.169994	−	0.964082i
$197$	−1.82224	−	1.05207i	−0.129829	−	0.0749568i	0.433679	−	0.901067i	$-0.357215\pi$
$197$	−1.82224	−	1.05207i	−0.129829	−	0.0749568i	−0.563508	+	0.826111i	$0.690549\pi$
$198$	15.2254	+	3.65585i	1.08202	+	0.259810i
$199$	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
$201$	0.0440088	+	0.303561i	0.00310414	+	0.0214115i
$202$	31.0644	+	17.9350i	2.18568	+	1.26190i
$203$	1.06953	−	6.06562i	0.0750664	−	0.425723i
$204$	−7.30625	+	2.40910i	−0.511540	+	0.168671i
$205$	−6.51222	+	7.76096i	−0.454833	+	0.542049i
$206$	16.4332	−	2.89762i	1.14496	−	0.201886i
$207$	−20.0440	+	9.99271i	−1.39316	+	0.694541i
$208$			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
$213$	−11.1667	+	5.99982i	−0.765128	+	0.411101i
$214$	−23.8558	+	20.0174i	−1.63075	+	1.36836i
$215$	−12.8436	−	2.26468i	−0.875929	−	0.154450i
$216$	0.977387	−	10.6306i	0.0665027	−	0.723322i
$217$	4.21425	−	2.43310i	0.286082	−	0.165169i
$218$	5.16951	+	14.2031i	0.350123	+	0.961956i
$219$	0.255484	−	8.35719i	0.0172640	−	0.564727i
$220$	−9.52755	−	16.5022i	−0.642347	−	1.11258i
$221$	−0.0890674	+	0.154269i	−0.00599132	+	0.0103773i
$222$	−6.71468	+	10.8504i	−0.450660	+	0.728229i
$223$	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
$225$	−4.42123	+	6.67923i	−0.294748	+	0.445282i
$226$	16.2293	+	5.90700i	1.07956	+	0.392928i
$227$	−2.88851			−0.191717			−0.0958584	−	0.995395i	$-0.530560\pi$
$227$	−2.88851			−0.191717			−0.0958584	+	0.995395i	$0.530560\pi$
$228$	0.0862887	−	22.0884i	0.00571461	−	1.46284i
$229$	−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
$231$	2.83565	−	13.6317i	0.186572	−	0.896901i
$232$	−2.83581	−	2.37953i	−0.186180	−	0.156224i
$233$	−2.52237	−	3.00604i	−0.165246	−	0.196932i	0.677067	−	0.735922i	$-0.263251\pi$
$233$	−2.52237	−	3.00604i	−0.165246	−	0.196932i	−0.842313	+	0.538989i	$0.818806\pi$
$234$	−0.464681	−	0.628027i	−0.0303772	−	0.0410554i
$235$	10.5712	−	18.3099i	0.689592	−	1.19441i
$236$	−16.3992	−	28.4042i	−1.06749	−	1.84895i
$237$	12.1202	+	0.370522i	0.787294	+	0.0240680i
$238$	3.93918	+	10.8228i	0.255339	+	0.701539i
$239$	−0.756613	+	0.436831i	−0.0489412	+	0.0282562i	−0.524271	−	0.851552i	$-0.675662\pi$
$239$	−0.756613	+	0.436831i	−0.0489412	+	0.0282562i	0.475330	+	0.879808i	$0.342329\pi$
$240$	4.86590	−	3.83582i	0.314092	−	0.247601i
$241$	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
$243$	−8.08569	−	13.3275i	−0.518697	−	0.854958i
$244$	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
$249$	1.24787	+	1.11381i	0.0790808	+	0.0705848i
$250$	−14.1040	+	2.48691i	−0.892014	+	0.157286i
$251$	−5.16327	+	6.15335i	−0.325903	+	0.388396i	−0.903972	−	0.427592i	$-0.859362\pi$
$251$	−5.16327	+	6.15335i	−0.325903	+	0.388396i	0.578069	+	0.815988i	$0.303806\pi$
$252$	−29.9464	−	1.83266i	−1.88644	−	0.115447i
$253$	−3.04874	+	17.2902i	−0.191672	+	1.08703i
$254$	−35.8749	−	20.7124i	−2.25099	−	1.29961i
$255$	7.20704	−	1.04484i	0.451322	−	0.0654305i
$256$	6.36496	−	2.31666i	0.397810	−	0.144791i
$257$	9.31791	−	3.39144i	0.581235	−	0.211552i	−0.0346349	−	0.999400i	$-0.511027\pi$
$257$	9.31791	−	3.39144i	0.581235	−	0.211552i	0.615870	+	0.787848i	$0.288805\pi$
$258$	−17.9150	+	2.59723i	−1.11534	+	0.161696i
$259$	9.82632	+	5.67323i	0.610578	+	0.352517i
$260$	−0.165094	+	0.936293i	−0.0102387	+	0.0580664i
$261$	−5.39546	−	0.330193i	−0.333971	−	0.0204384i
$262$	14.1701	−	16.8872i	0.875429	−	1.04330i
$263$	21.1995	−	3.73805i	1.30722	−	0.230498i	0.523720	−	0.851890i	$-0.324544\pi$
$263$	21.1995	−	3.73805i	1.30722	−	0.230498i	0.783500	+	0.621392i	$0.213433\pi$
$264$	−6.24331	−	5.57256i	−0.384249	−	0.342968i
$265$			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	$0.135117\pi$
$269$	3.21162	+	18.2140i	0.195816	+	1.11053i	−0.715436	+	0.698678i	$0.753772\pi$
$270$	−8.40243	+	30.8133i	−0.511356	+	1.87524i
$271$	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
$273$	−0.545569	+	0.430076i	−0.0330193	+	0.0260294i
$274$	8.25881	−	4.76823i	0.498933	−	0.288059i
$275$	2.14756	+	5.90036i	0.129503	+	0.355805i
$276$	37.8140	+	1.15599i	2.27614	+	0.0695827i
$277$	−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
$279$	−2.54023	−	3.43318i	−0.152080	−	0.205539i
$280$	12.5018	+	14.8991i	0.747128	+	0.890392i
$281$	18.8698	+	15.8337i	1.12568	+	0.944558i	0.998877	−	0.0473703i	$-0.0150841\pi$
$281$	18.8698	+	15.8337i	1.12568	+	0.944558i	0.126803	+	0.991928i	$0.459529\pi$
$282$	5.97665	−	28.7313i	0.355904	−	1.71092i
$283$	−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
$285$	−3.71123	+	20.5771i	−0.219835	+	1.21888i
$286$	−0.612423			−0.0362133
$287$	11.7505	+	4.27682i	0.693607	+	0.252452i
$288$	11.5511	−	17.4505i	0.680655	−	1.02828i
$289$	11.2572	+	9.44590i	0.662187	+	0.555641i
$290$	7.11898	+	8.48407i	0.418041	+	0.498202i
$291$	−4.61357	+	7.45514i	−0.270452	+	0.437028i
$292$	−7.06159	+	12.2310i	−0.413248	+	0.715767i
$293$	14.2154	+	24.6217i	0.830470	+	1.43842i	0.897666	+	0.440677i	$0.145262\pi$
$293$	14.2154	+	24.6217i	0.830470	+	1.43842i	−0.0671953	+	0.997740i	$0.521405\pi$
$294$	−0.550244	+	17.9992i	−0.0320909	+	1.04973i
$295$	10.6187	+	29.1746i	0.618243	+	1.69861i
$296$	5.90597	−	3.40981i	0.343277	−	0.198191i
$297$	−12.1685	−	1.11878i	−0.706090	−	0.0649184i
$298$	9.26742	+	1.63410i	0.536847	+	0.0946606i
$299$	0.671046	−	0.563075i	0.0388076	−	0.0325635i
$300$	11.9186	−	6.40382i	0.688121	−	0.369725i
$301$	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
$306$	9.04628	−	4.50991i	0.517141	−	0.257814i
$307$	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
$309$	−12.3676	+	4.07798i	−0.703569	+	0.231988i
$310$	−1.51945	+	8.61723i	−0.0862990	+	0.489426i
$311$	−12.9378	−	7.46964i	−0.733635	−	0.423564i	0.0861156	−	0.996285i	$-0.472555\pi$
$311$	−12.9378	−	7.46964i	−0.733635	−	0.423564i	−0.819750	+	0.572721i	$0.805888\pi$
$312$	0.0599066	+	0.413220i	0.00339155	+	0.0233940i
$313$	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
$315$	27.6154	+	6.63090i	1.55595	+	0.373609i
$316$	−17.7384	−	10.2413i	−0.997862	−	0.576116i
$317$	5.48089	−	31.0837i	0.307837	−	1.74583i	−0.302003	−	0.953307i	$-0.597655\pi$
$317$	5.48089	−	31.0837i	0.307837	−	1.74583i	0.609840	−	0.792525i	$-0.291234\pi$
$318$	4.61392	+	13.9930i	0.258736	+	0.784688i
$319$	−2.72377	+	3.24607i	−0.152502	+	0.181745i
$320$	−35.1794	+	6.20307i	−1.96659	+	0.346762i
$321$	16.1835	−	18.1314i	0.903274	−	1.01200i
$322$		−	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
$327$	−5.58296	−	10.3908i	−0.308738	−	0.574615i
$328$	5.75735	−	4.83099i	0.317897	−	0.266747i
$329$	−25.6989	−	4.53141i	−1.41683	−	0.249825i
$330$	15.4997	+	19.6620i	0.853230	+	1.08236i
$331$	−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
$333$	3.97111	−	9.13205i	0.217616	−	0.500433i
$334$	−2.13297	−	3.69442i	−0.116711	−	0.202149i
$335$	−0.245228	+	0.424746i	−0.0133982	+	0.0232064i
$336$	−6.50299	−	4.02433i	−0.354767	−	0.219545i
$337$	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
$339$	−13.1960	−	2.74502i	−0.716710	−	0.149089i
$340$	−11.5592	−	4.20721i	−0.626887	−	0.228168i
$341$	−3.34788			−0.181298
$342$	4.05174	+	28.7381i	0.219093	+	1.55398i
$343$	−7.91507			−0.427374
$344$	9.09138	+	3.30899i	0.490174	+	0.178409i
$345$	−35.0610	−	7.29335i	−1.88762	−	0.392661i
$346$	−26.6837	−	22.3903i	−1.43453	−	1.20371i
$347$	−4.93290	−	5.87880i	−0.264812	−	0.315590i	0.617211	−	0.786798i	$-0.288263\pi$
$347$	−4.93290	−	5.87880i	−0.264812	−	0.315590i	−0.882022	+	0.471208i	$0.843818\pi$
$348$	7.76432	+	4.80490i	0.416211	+	0.257570i
$349$	−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
$351$	0.429214	+	0.433022i	0.0229097	+	0.0231130i
$352$	−5.61080	−	15.4156i	−0.299057	−	0.821652i
$353$	−26.2583	+	15.1602i	−1.39759	+	0.806897i	−0.994139	−	0.108106i	$-0.965521\pi$
$353$	−26.2583	+	15.1602i	−1.39759	+	0.806897i	−0.403447	+	0.915003i	$0.632188\pi$
$354$	26.6786	+	33.8429i	1.41795	+	1.79873i
$355$	−19.9612	−	3.51969i	−1.05943	−	0.186806i
$356$	−26.0983	+	21.8990i	−1.38320	+	1.16065i
$357$	−4.25423	−	7.91785i	−0.225158	−	0.419057i
$358$	−5.96189	−	33.8116i	−0.315096	−	1.78700i
$359$	−10.5174	+	28.8964i	−0.555089	+	1.52510i	0.271585	+	0.962414i	$0.412452\pi$
$359$	−10.5174	+	28.8964i	−0.555089	+	1.52510i	−0.826674	+	0.562681i	$0.809770\pi$
$360$	11.7504	−	12.3814i	0.619299	−	0.652558i
$361$	4.29164	+	18.5090i	0.225876	+	0.974156i
$362$		−	2.26934i		−	0.119274i
$363$	6.30826	−	7.06756i	0.331098	−	0.370951i
$364$	1.15563	−	0.203769i	0.0605715	−	0.0106804i
$365$	8.59345	−	10.2413i	0.449802	−	0.536053i
$366$	−10.3462	−	31.3778i	−0.540806	−	1.64014i
$367$	−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
$369$	2.56233	−	10.6712i	0.133390	−	0.555521i
$370$	−19.1722	+	6.97813i	−0.996717	+	0.362775i
$371$	12.3117	−	4.48109i	0.639191	−	0.232646i
$372$	1.03503	+	7.13935i	0.0536637	+	0.370158i
$373$	−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
$375$	10.6146	−	3.49998i	0.548138	−	0.180738i
$376$	−10.0816	+	12.0148i	−0.519921	+	0.619617i
$377$	0.208211	−	0.0367132i	0.0107234	−	0.00189083i
$378$	39.2851	−	3.26224i	2.02061	−	0.167791i
$379$			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	0.999771	−	0.0213797i	$-0.00680588\pi$
$383$	1.03686	+	5.88035i	0.0529813	+	0.300472i	−0.946790	+	0.321852i	$0.895695\pi$
$384$	−22.3912	+	12.0307i	−1.14264	+	0.613939i
$385$	17.0545	−	14.3105i	0.869180	−	0.729328i
$386$	26.4214	+	4.65881i	1.34481	+	0.237127i
$387$	13.5457	−	4.01190i	0.688568	−	0.203936i
$388$	12.8251	−	7.40459i	0.651097	−	0.375911i
$389$	−4.73660	−	13.0137i	−0.240155	−	0.659821i	−0.999953	−	0.00966178i	$-0.996925\pi$
$389$	−4.73660	−	13.0137i	−0.240155	−	0.659821i	0.759798	−	0.650159i	$-0.225298\pi$
$390$	0.0381702	−	1.24860i	0.00193283	−	0.0632252i
$391$	5.66697	+	9.81548i	0.286591	+	0.496390i
$392$	4.81211	−	8.33481i	0.243048	−	0.420971i
$393$	−9.05327	+	14.6293i	−0.456677	+	0.737953i
$394$	−3.00176	−	3.57735i	−0.151226	−	0.180225i
$395$	14.8527	+	12.4629i	0.747319	+	0.627075i
$396$	17.2120	+	11.3933i	0.864936	+	0.572533i
$397$	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
$399$	25.4325	−	4.38207i	1.27322	−	0.219378i
$400$	3.44876			0.172438
$401$	22.3703	+	8.14211i	1.11712	+	0.406597i	0.833599	−	0.552370i	$-0.186276\pi$
$401$	22.3703	+	8.14211i	1.11712	+	0.406597i	0.283518	+	0.958967i	$0.408498\pi$
$402$	−0.138644	+	0.666496i	−0.00691492	+	0.0332418i
$403$	0.127959	+	0.107371i	0.00637411	+	0.00534852i
$404$	30.3945	+	36.2228i	1.51218	+	1.80215i
$405$	3.03938	−	24.7393i	0.151028	−	1.22930i
$406$	6.83483	−	11.8383i	0.339207	−	0.587523i
$407$	−3.90310	−	6.76037i	−0.193470	−	0.335099i
$408$	−5.39980	−	0.165075i	−0.267330	−	0.00817242i
$409$	−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
$411$	−5.84473	+	4.60745i	−0.288299	+	0.227269i
$412$	21.6630	+	3.81977i	1.06726	+	0.188186i
$413$	29.3549	−	24.6317i	1.44446	−	1.21204i
$414$	−49.3880	+	5.62528i	−2.42729	+	0.276467i
$415$	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	$0.0824387\pi$
$419$			10.4846i			0.512206i	−0.966649	+	0.256103i	$0.917561\pi$
$420$	−35.7897	−	31.9446i	−1.74636	−	1.55874i
$421$	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
$423$	−1.39897	+	22.8596i	−0.0680201	+	1.11147i
$424$	1.36742	−	7.75502i	0.0664078	−	0.376617i
$425$	3.51039	+	2.02672i	0.170279	+	0.0983105i
$426$	−27.8430	+	4.03653i	−1.34900	+	0.195571i
$427$	−27.6077	+	10.0484i	−1.33603	+	0.486274i
$428$	−38.5764	+	14.0406i	−1.86466	+	0.678680i
$429$	0.473000	−	0.0685732i	0.0228367	−	0.00331075i
$430$	−25.0669	−	14.4724i	−1.20883	−	0.697921i
$431$	−2.37538	+	13.4715i	−0.114418	+	0.648897i	0.872619	+	0.488402i	$0.162420\pi$
$431$	−2.37538	+	13.4715i	−0.114418	+	0.648897i	−0.987037	+	0.160495i	$0.948691\pi$
$432$	−2.86335	+	6.07033i	−0.137763	+	0.292059i
$433$	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
$435$	−6.44826	−	5.75549i	−0.309170	−	0.275955i
$436$			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
$441$	−1.59040	−	13.9631i	−0.0757332	−	0.664911i
$442$	−0.302857	+	0.254127i	−0.0144054	+	0.0120876i
$443$	−5.09078	−	0.897641i	−0.241870	−	0.0426482i	0.0513989	−	0.998678i	$-0.483632\pi$
$443$	−5.09078	−	0.897641i	−0.241870	−	0.0426482i	−0.293269	+	0.956030i	$0.594743\pi$
$444$	−13.2098	+	10.4134i	−0.626911	+	0.494199i
$445$	27.9290	−	16.1248i	1.32396	−	0.764390i
$446$	4.13548	+	11.3621i	0.195820	+	0.538012i
$447$	−7.34059	−	0.224406i	−0.347198	−	0.0106140i
$448$	22.0452	+	38.1834i	1.04154	+	1.80400i
$449$	−14.3628	+	24.8771i	−0.677823	+	1.17402i	0.297812	+	0.954625i	$0.403743\pi$
$449$	−14.3628	+	24.8771i	−0.677823	+	1.17402i	−0.975635	+	0.219399i	$0.929590\pi$
$450$	−14.2907	+	10.5738i	−0.673671	+	0.498453i
$451$	−5.52988	−	6.59026i	−0.260392	−	0.310323i
$452$	17.4407	+	14.6345i	0.820344	+	0.688350i
$453$	−4.08825	+	19.6533i	−0.192083	+	0.923390i
$454$	−6.02411	−	2.19260i	−0.282726	−	0.102904i
$455$	−1.11080			−0.0520750
$456$	5.36200	−	14.5548i	0.251099	−	0.681591i
$457$	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
$459$	−6.48185	+	4.49611i	−0.302547	+	0.209860i
$460$	46.3390	+	38.8830i	2.16057	+	1.81293i
$461$	−18.8457	−	22.4594i	−0.877732	−	1.04604i	−0.998575	−	0.0533689i	$-0.983004\pi$
$461$	−18.8457	−	22.4594i	−0.877732	−	1.04604i	0.120843	−	0.992672i	$-0.461440\pi$
$462$	16.2614	−	26.2771i	0.756549	−	1.22252i
$463$	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
$465$	0.208662	−	6.82559i	0.00967645	−	0.316529i
$466$	−2.97870	−	8.18391i	−0.137986	−	0.379112i
$467$	35.4175	−	20.4483i	1.63893	−	0.946235i	0.657724	−	0.753259i	$-0.271519\pi$
$467$	35.4175	−	20.4483i	1.63893	−	0.946235i	0.981203	−	0.192976i	$-0.0618141\pi$
$468$	−0.292465	−	0.987475i	−0.0135192	−	0.0456460i
$469$	0.596153	+	0.105118i	0.0275278	+	0.00485389i
$470$	35.9455	−	30.1618i	1.65804	−	1.39126i
$471$	11.9339	−	6.41205i	0.549886	−	0.295452i
$472$	−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
$477$	−5.13033	−	10.2908i	−0.234901	−	0.471181i
$478$	−1.90954	+	0.336703i	−0.0873403	+	0.0154004i
$479$	15.6062	−	18.5987i	0.713063	−	0.849796i	−0.280874	−	0.959745i	$-0.590624\pi$
$479$	15.6062	−	18.5987i	0.713063	−	0.849796i	0.993937	+	0.109949i	$0.0350687\pi$
$480$	31.7787	−	10.4784i	1.45049	−	0.478272i
$481$	−0.0676331	+	0.383566i	−0.00308380	+	0.0174891i
$482$	10.3292	+	5.96354i	0.470480	+	0.271632i
$483$	6.34172	+	43.7435i	0.288558	+	1.99040i
$484$	−15.0369	+	5.47300i	−0.683497	+	0.248773i
$485$	−13.1730	+	4.79458i	−0.598155	+	0.217711i
$486$	−6.74651	−	33.9327i	−0.306028	−	1.53922i
$487$	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
$489$	−9.61720	−	29.1668i	−0.434905	−	1.31897i
$490$	−18.5080	+	22.0570i	−0.836106	+	0.996432i
$491$	−34.3949	+	6.06475i	−1.55222	+	0.273698i	−0.883003	−	0.469368i	$-0.844482\pi$
$491$	−34.3949	+	6.06475i	−1.55222	+	0.273698i	−0.669218	+	0.743066i	$0.733371\pi$
$492$	−12.3441	+	13.8299i	−0.556516	+	0.623502i
$493$			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
$498$	1.75703	+	3.27013i	0.0787345	+	0.146538i
$499$	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
$501$	2.06105	+	2.61452i	0.0920809	+	0.116808i
$502$	−15.4391	+	8.91377i	−0.689081	+	0.397841i
$503$	−0.0977650	−	0.268607i	−0.00435912	−	0.0119766i	0.937494	−	0.348001i	$-0.113140\pi$
$503$	−0.0977650	−	0.268607i	−0.00435912	−	0.0119766i	−0.941853	+	0.336025i	$0.890917\pi$
$504$	−19.3206	−	8.40167i	−0.860610	−	0.374240i
$505$	−22.3803	−	38.7637i	−0.995908	−	1.72496i
$506$	−19.4829	+	33.7454i	−0.866121	+	1.50016i
$507$	19.1266	+	11.8364i	0.849442	+	0.525672i
$508$	−35.1013	−	41.8321i	−1.55737	−	1.85600i
$509$	3.00696	+	2.52314i	0.133281	+	0.111836i	0.706991	−	0.707222i	$-0.250052\pi$
$509$	3.00696	+	2.52314i	0.133281	+	0.111836i	−0.573710	+	0.819058i	$0.694496\pi$
$510$	15.8237	+	3.29163i	0.700686	+	0.145756i
$511$	−15.5058	−	5.64363i	−0.685934	−	0.249660i
$512$	−14.3179			−0.632766
$513$	−6.34715	−	21.7420i	−0.280234	−	0.959932i
$514$	22.0073			0.970700
$515$	−19.5668	−	7.12173i	−0.862216	−	0.313821i
$516$	−23.3631	−	4.85997i	−1.02850	−	0.213948i
$517$	13.7530	+	11.5401i	0.604856	+	0.507534i
$518$	16.1868	+	19.2907i	0.711209	+	0.847585i
$519$	23.1160	+	14.3052i	1.01468	+	0.627929i
$520$	−0.333814	+	0.578183i	−0.0146387	+	0.0253550i
$521$	4.18609	+	7.25051i	0.183396	+	0.317651i	0.943035	−	0.332694i	$-0.107958\pi$
$521$	4.18609	+	7.25051i	0.183396	+	0.317651i	−0.759639	+	0.650345i	$0.774624\pi$
$522$	−11.0018	−	4.78420i	−0.481538	−	0.209399i
$523$	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
$525$	9.78635	+	12.4144i	0.427111	+	0.541808i
$526$	47.0501	+	8.29620i	2.05148	+	0.361732i
$527$	−1.65560	+	1.38921i	−0.0721190	+	0.0605150i
$528$	2.49023	+	4.63474i	0.108373	+	0.201701i
$529$	−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
$534$	29.8077	−	33.3955i	1.28990	−	1.44516i
$535$	38.2696	−	6.74797i	1.65454	−	0.291740i
$536$	0.233870	−	0.278715i	0.0101016	−	0.0120387i
$537$	8.39052	+	25.4466i	0.362078	+	1.09810i
$538$	−7.12784	+	40.4240i	−0.307303	+	1.74280i
$539$	−9.54059	−	5.50826i	−0.410942	−	0.237258i
$540$	−24.3011	+	34.3814i	−1.04575	+	1.47954i
$541$	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
$543$	0.254099	+	1.75271i	0.0109044	+	0.0752158i
$544$	−9.17140	−	5.29511i	−0.393220	−	0.227026i
$545$	3.27515	−	18.5743i	0.140292	−	0.795635i
$546$	−1.46427	+	0.482815i	−0.0626649	+	0.0206626i
$547$	−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
$549$	11.5042	+	23.0759i	0.490988	+	0.984857i
$550$			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
$555$	14.0262	−	7.53623i	0.595379	−	0.319895i
$556$	41.3883	−	34.7289i	1.75526	−	1.47283i
$557$	1.21307	+	0.213897i	0.0513994	+	0.00906310i	0.199289	−	0.979941i	$-0.436137\pi$
$557$	1.21307	+	0.213897i	0.0513994	+	0.00906310i	−0.147889	+	0.989004i	$0.547248\pi$
$558$	−2.69172	−	9.08828i	−0.113950	−	0.384738i
$559$	−0.478523	+	0.276276i	−0.0202394	+	0.0116852i
$560$	−4.18223	−	11.4906i	−0.176731	−	0.485565i
$561$	−0.188956	+	6.18099i	−0.00797772	+	0.260961i
$562$	27.3349	+	47.3455i	1.15305	+	1.99715i
$563$	18.4158	−	31.8971i	0.776134	−	1.34430i	−0.158020	−	0.987436i	$-0.550511\pi$
$563$	18.4158	−	31.8971i	0.776134	−	1.34430i	0.934155	−	0.356868i	$-0.116155\pi$
$564$	20.3575	−	32.8960i	0.857205	−	1.38517i
$565$	−13.8531	−	16.5094i	−0.582803	−	0.694557i
$566$	−18.9372	−	15.8902i	−0.795991	−	0.667916i
$567$	−29.9763	+	6.91834i	−1.25889	+	0.290543i
$568$	14.1295	+	5.14273i	0.592862	+	0.215784i
$569$	−33.1970			−1.39169			−0.695846	−	0.718191i	$-0.744971\pi$
$569$	−33.1970			−1.39169			−0.695846	+	0.718191i	$0.744971\pi$
$570$	−23.3595	+	40.0973i	−0.978423	+	1.67949i
$571$	−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
$573$	4.21673	−	20.2709i	0.176156	−	0.846829i
$574$	21.2597	+	17.8390i	0.887362	+	0.744585i
$575$	−12.8127	−	15.2696i	−0.534328	−	0.636787i
$576$	31.1065	−	23.0159i	1.29610	−	0.958995i
$577$	−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
$579$	−20.9280	−	0.639781i	−0.869740	−	0.0265884i
$580$	4.99342	+	13.7193i	0.207340	+	0.569663i
$581$	2.85877	−	1.65051i	0.118602	−	0.0684749i
$582$	−15.2808	+	12.0460i	−0.633411	+	0.499323i
$583$	−8.87693	−	1.56524i	−0.367645	−	0.0648257i
$584$	−7.59733	+	6.37492i	−0.314380	+	0.263796i
$585$	0.110325	+	0.968619i	0.00456139	+	0.0400474i
$586$	10.9570	+	62.1403i	0.452630	+	2.56699i
$587$	−1.44221	+	3.96244i	−0.0595265	+	0.163548i	−0.965891	−	0.258949i	$-0.916624\pi$
$587$	−1.44221	+	3.96244i	−0.0595265	+	0.163548i	0.906365	+	0.422496i	$0.138846\pi$
$588$	−8.79682	+	22.0483i	−0.362775	+	0.909256i
$589$	−2.27698	−	5.77243i	−0.0938215	−	0.237849i
$590$			68.9053i			2.83679i
$591$	2.71894	+	2.42684i	0.111842	+	0.0998267i
$592$	−4.22242	+	0.744526i	−0.173540	+	0.0305998i
$593$	4.95391	−	5.90384i	0.203433	−	0.242442i	−0.654676	−	0.755910i	$-0.727195\pi$
$593$	4.95391	−	5.90384i	0.203433	−	0.242442i	0.858109	+	0.513468i	$0.171639\pi$
$594$	−24.5288	−	11.5701i	−1.00643	−	0.474728i
$595$	2.49567	−	14.1537i	0.102313	−	0.580244i
$596$	10.7432	+	6.20259i	0.440059	+	0.254068i
$597$	−9.91797	+	1.43786i	−0.405915	+	0.0588476i
$598$	1.82692	−	0.664943i	0.0747081	−	0.0271915i
$599$	25.3361	−	9.22158i	1.03520	−	0.376783i	0.232144	−	0.972681i	$-0.425426\pi$
$599$	25.3361	−	9.22158i	1.03520	−	0.376783i	0.803060	+	0.595898i	$0.203204\pi$
$600$	9.40280	−	1.36317i	0.383868	−	0.0556512i
$601$	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
$603$	0.0324526	−	0.530288i	0.00132157	−	0.0215950i
$604$	21.7957	−	25.9751i	0.886853	−	1.05691i
$605$	14.9174	−	2.63033i	0.606477	−	0.106938i
$606$	−46.3509	−	41.3712i	−1.88287	−	1.68059i
$607$		−	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
$612$	13.2394	−	1.50796i	0.535170	−	0.0609558i
$613$	−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
$615$	13.7808	−	10.8635i	0.555694	−	0.438058i
$616$	−14.3029	+	8.25778i	−0.576280	+	0.332715i
$617$	2.76356	+	7.59281i	0.111257	+	0.305675i	0.982808	−	0.184629i	$-0.0591082\pi$
$617$	2.76356	+	7.59281i	0.111257	+	0.305675i	−0.871552	+	0.490303i	$0.836886\pi$
$618$	−28.8887	−	0.883143i	−1.16207	−	0.0355252i
$619$	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
$621$	37.5146	−	9.87464i	1.50541	−	0.396256i
$622$	−21.3123	−	25.3991i	−0.854547	−	1.01841i
$623$	−30.4920	−	25.5858i	−1.22164	−	1.02508i
$624$	0.0534628	−	0.257010i	0.00214023	−	0.0102886i
$625$	29.3382	+	10.6782i	1.17353	+	0.427130i
$626$	56.7537			2.26834
$627$	−16.6604	−	6.13771i	−0.665353	−	0.245117i
$628$	−22.8837			−0.913159
$629$	−4.73541	−	1.72355i	−0.188813	−	0.0687223i
$630$	52.5598	+	34.7912i	2.09403	+	1.38612i
$631$	−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
$633$	−21.5603	+	34.8397i	−0.856945	+	1.38475i
$634$	35.0255	−	60.6660i	1.39104	−	2.40935i
$635$	25.8460	+	44.7666i	1.02567	+	1.77651i
$636$	−0.593495	+	19.4140i	−0.0235336	+	0.769815i
$637$	0.187995	+	0.516511i	0.00744862	+	0.0204649i
$638$	−8.14456	+	4.70227i	−0.322446	+	0.186165i
$639$	21.0523	−	6.23517i	0.832817	−	0.246660i
$640$	−40.0257	−	7.05761i	−1.58215	−	0.278976i
$641$	−25.7120	+	21.5750i	−1.01556	+	0.852159i	−0.989064	−	0.147489i	$-0.952881\pi$
$641$	−25.7120	+	21.5750i	−1.01556	+	0.852159i	−0.0265004	+	0.999649i	$0.508436\pi$
$642$	47.5145	−	25.5294i	1.87525	−	1.00756i
$643$	−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	$-0.833574\pi$
$647$		−	25.4029i		−	0.998690i	0.866403	−	0.499345i	$-0.166426\pi$
$648$	−5.40733	+	17.6821i	−0.212420	+	0.694619i
$649$	−25.9631	+	4.57800i	−1.01914	+	0.179702i
$650$	0.446934	−	0.532635i	0.0175302	−	0.0208917i
$651$	−8.00458	+	2.63936i	−0.313724	+	0.103445i
$652$	−9.00824	+	51.0883i	−0.352790	+	2.00077i
$653$	38.7229	+	22.3567i	1.51534	+	0.874884i	0.999838	+	0.0179975i	$0.00572909\pi$
$653$	38.7229	+	22.3567i	1.51534	+	0.874884i	0.515505	+	0.856886i	$0.327604\pi$
$654$	−3.75608	−	25.9085i	−0.146874	−	1.01310i
$655$	−25.8496	+	9.40847i	−1.01003	+	0.367619i
$656$	−4.44022	+	1.61611i	−0.173361	+	0.0630984i
$657$	−3.38122	+	14.0816i	−0.131914	+	0.549375i
$658$	−50.1566	−	28.9579i	−1.95531	−	1.12890i
$659$	−4.52313	+	25.6520i	−0.176196	+	0.999258i	0.760558	+	0.649270i	$0.224926\pi$
$659$	−4.52313	+	25.6520i	−0.176196	+	0.999258i	−0.936754	+	0.349988i	$0.886186\pi$
$660$	10.3352	+	31.3444i	0.402298	+	1.22008i
$661$	−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
$663$	0.205454	−	0.230184i	0.00797918	−	0.00893960i
$664$		−	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
$669$	−4.46622	−	8.31240i	−0.172674	−	0.321376i
$670$	−0.833848	+	0.699682i	−0.0322144	+	0.0270311i
$671$	19.9056	+	3.50989i	0.768446	+	0.135498i
$672$	−25.5683	−	32.4344i	−0.986317	−	1.25118i
$673$	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
$675$	9.85338	−	9.76673i	0.379257	−	0.375921i
$676$	−18.9969	−	32.9036i	−0.730651	−	1.26552i
$677$	8.46982	−	14.6702i	0.325522	−	0.563820i	−0.656096	−	0.754677i	$-0.727793\pi$
$677$	8.46982	−	14.6702i	0.325522	−	0.563820i	0.981618	+	0.190857i	$0.0611267\pi$
$678$	−25.4372	−	15.7417i	−0.976911	−	0.604555i
$679$	11.1218	+	13.2544i	0.426814	+	0.508657i
$680$	−6.61716	−	5.55245i	−0.253756	−	0.212927i
$681$	4.89818	+	1.01891i	0.187699	+	0.0390449i
$682$	−6.98215	−	2.54129i	−0.267360	−	0.0973112i
$683$	31.1308			1.19119			0.595593	−	0.803287i	$-0.296917\pi$
$683$	31.1308			1.19119			0.595593	+	0.803287i	$0.296917\pi$
$684$	−7.93796	+	37.4259i	−0.303515	+	1.43102i
$685$	−11.9001			−0.454679
$686$	−16.5072	−	6.00815i	−0.630249	−	0.229392i
$687$	48.9147	+	10.1752i	1.86621	+	0.388207i
$688$	−4.65959	−	3.90986i	−0.177645	−	0.149062i
$689$	0.289087	+	0.344520i	0.0110133	+	0.0131252i
$690$	−67.5852	−	41.8246i	−2.57292	−	1.59224i
$691$	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
$693$	−9.61712	+	22.1157i	−0.365324	+	0.840107i
$694$	−5.82532	−	16.0049i	−0.221126	−	0.607540i
$695$	−44.2917	+	25.5718i	−1.68008	+	0.969994i
$696$	3.96946	+	5.03541i	0.150462	+	0.190867i
$697$	−5.46930	−	0.964384i	−0.207164	−	0.0365287i
$698$	−8.14291	+	6.83271i	−0.308214	+	0.258622i
$699$	3.21693	+	5.98726i	0.121676	+	0.226459i
$700$	−4.63675	−	26.2963i	−0.175253	−	0.993906i
$701$	0.663693	−	1.82348i	0.0250673	−	0.0688719i	−0.926528	−	0.376226i	$-0.877221\pi$
$701$	0.663693	−	1.82348i	0.0250673	−	0.0688719i	0.951595	+	0.307354i	$0.0994437\pi$
$702$	0.566448	+	1.22889i	0.0213792	+	0.0463816i
$703$	9.00167	−	11.3277i	0.339504	−	0.427231i
$704$		−	30.3336i		−	1.14324i
$705$	−24.3850	+	27.3201i	−0.918392	+	1.02893i
$706$	−66.2706	+	11.6853i	−2.49413	+	0.439782i
$707$	−35.5116	+	42.3210i	−1.33555	+	1.59165i
$708$	17.7894	+	53.9511i	0.668565	+	2.02761i
$709$	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
$711$	−20.4222	−	4.90370i	−0.765892	−	0.183903i
$712$	−22.4811	+	8.18246i	−0.842516	+	0.306651i
$713$	9.98703	−	3.63498i	0.374017	−	0.136131i
$714$	−2.86214	−	19.7423i	−0.107113	−	0.738838i
$715$	0.661828	+	0.382107i	0.0247510	+	0.0142900i
$716$	7.85923	−	44.5719i	0.293713	−	1.66573i
$717$	1.43712	−	0.473862i	0.0536701	−	0.0176967i
$718$	−43.8692	+	52.2813i	−1.63718	+	1.95112i
$719$	11.9507	−	2.10723i	0.445685	−	0.0785864i	0.0536985	−	0.998557i	$-0.482899\pi$
$719$	11.9507	−	2.10723i	0.445685	−	0.0785864i	0.391987	+	0.919971i	$0.371788\pi$
$720$	−9.60443	+	4.78816i	−0.357936	+	0.178444i
$721$			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
$726$	18.5210	−	9.95127i	0.687379	−	0.369326i
$727$	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
$729$	9.01008	+	25.4523i	0.333707	+	0.942677i
$730$	25.6959	−	14.8356i	0.951049	−	0.549089i
$731$	−2.44516	−	6.71801i	−0.0904374	−	0.248475i
$732$	1.33085	−	43.5338i	0.0491897	−	1.60906i
$733$	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
$735$	11.8248	−	19.1079i	0.436164	−	0.704805i
$736$	33.4751	+	39.8941i	1.23391	+	1.47052i
$737$	−0.319036	−	0.267703i	−0.0117519	−	0.00986098i
$738$	13.4441	−	20.3103i	0.494885	−	0.747632i
$739$	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
$741$	0.439935	+	0.768912i	0.0161614	+	0.0282467i
$742$	29.0781			1.06749
$743$	36.8666	+	13.4183i	1.35250	+	0.492271i	0.913728	−	0.406326i	$-0.133190\pi$
$743$	36.8666	+	13.4183i	1.35250	+	0.492271i	0.438775	+	0.898597i	$0.355412\pi$
$744$	−1.03170	+	4.95966i	−0.0378240	+	0.181830i
$745$	−8.99548	−	7.54811i	−0.329569	−	0.276541i
$746$	−37.7405	−	44.9773i	−1.38178	−	1.64674i
$747$	−1.72319	−	2.32893i	−0.0630482	−	0.0852110i
$748$	5.22276	−	9.04608i	0.190963	−	0.330757i
$749$	−23.9817	−	41.5375i	−0.876273	−	1.51775i
$750$	24.7941	+	0.757967i	0.905352	+	0.0276771i
$751$	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
$753$	10.9262	−	8.61321i	0.398173	−	0.313883i
$754$	0.462102	+	0.0814810i	0.0168288	+	0.00296736i
$755$	−24.5880	+	20.6318i	−0.894850	+	0.750868i
$756$	50.1351	+	13.6713i	1.82339	+	0.497219i
$757$	−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	$-0.939261\pi$
$761$		−	10.4640i		−	0.379320i	0.981850	−	0.189660i	$-0.0607385\pi$
$762$	53.5287	+	47.7779i	1.93914	+	1.73081i
$763$	−22.9255	+	4.04239i	−0.829960	+	0.146344i
$764$	−22.4806	+	26.7914i	−0.813320	+	0.969278i
$765$	−12.5899	−	0.770480i	−0.455189	−	0.0278567i
$766$	−2.30121	+	13.0508i	−0.0831461	+	0.471545i
$767$	1.13916	+	0.657695i	0.0411328	+	0.0237480i
$768$	−11.6106	+	1.68324i	−0.418961	+	0.0607388i
$769$	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
$771$	−16.9972	+	2.46416i	−0.612138	+	0.0887447i
$772$	30.6289	+	17.6836i	1.10236	+	0.636447i
$773$	2.18041	−	12.3657i	0.0784238	−	0.444763i	−0.920159	−	0.391545i	$-0.871941\pi$
$773$	2.18041	−	12.3657i	0.0784238	−	0.444763i	0.998583	−	0.0532187i	$-0.0169480\pi$
$774$	31.2956	+	1.91523i	1.12490	+	0.0688416i
$775$	2.44321	−	2.91171i	0.0877628	−	0.104592i
$776$	10.2414	−	1.80583i	0.367643	−	0.0648254i
$777$	−14.6618	−	13.0866i	−0.525988	−	0.469479i
$778$		−	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
$783$	9.03288	+	2.46316i	0.322809	+	0.0880262i
$784$	−4.63520	+	3.88940i	−0.165543	+	0.138907i
$785$	21.3327	+	3.76152i	0.761395	+	0.134255i
$786$	−29.9858	+	23.6381i	−1.06956	+	0.843141i
$787$	−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
$789$	−37.2677	−	1.13929i	−1.32677	−	0.0405599i
$790$	21.5157	+	37.2662i	0.765493	+	1.32587i
$791$	−13.3001	+	23.0365i	−0.472898	+	0.819083i
$792$	8.62138	+	11.6520i	0.306347	+	0.414035i
$793$	−0.648246	−	0.772550i	−0.0230199	−	0.0274340i
$794$	20.1767	+	16.9303i	0.716045	+	0.600833i
$795$	3.74446	−	18.0006i	0.132802	−	0.638414i
$796$	15.9072	+	5.78975i	0.563816	+	0.205212i
$797$	−19.4024			−0.687269			−0.343635	−	0.939103i	$-0.611658\pi$
$797$	−19.4024			−0.687269			−0.343635	+	0.939103i	$0.611658\pi$
$798$	56.3670	+	10.1662i	1.99537	+	0.359880i
$799$	11.5898			0.410017
$800$	17.5018	+	6.37015i	0.618783	+	0.225219i
$801$	−19.2824	+	29.1303i	−0.681311	+	1.02927i
$802$	40.4737	+	33.9615i	1.42918	+	1.19922i
$803$	7.29717	+	8.69643i	0.257511	+	0.306890i
$804$	−0.472245	+	0.763109i	−0.0166548	+	0.0269128i
$805$	−35.3376	+	61.2065i	−1.24549	+	2.15725i
$806$	0.185363	+	0.321058i	0.00652912	+	0.0113088i
$807$	0.978846	−	32.0193i	0.0344570	−	1.12713i
$808$	11.3567	+	31.2024i	0.399529	+	1.09770i
$809$	−0.787555	+	0.454695i	−0.0276890	+	0.0159862i	−0.513781	−	0.857922i	$-0.671755\pi$
$809$	−0.787555	+	0.454695i	−0.0276890	+	0.0159862i	0.486092	+	0.873908i	$0.338422\pi$
$810$	25.1178	−	49.2877i	0.882548	−	1.73179i
$811$	−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
$813$	−4.66445	+	2.50619i	−0.163589	+	0.0878960i
$814$	−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
$819$	1.07686	−	0.536853i	0.0376284	−	0.0187592i
$820$	−29.1906	+	5.14709i	−1.01938	+	0.179744i
$821$	−4.15443	+	4.95106i	−0.144991	+	0.172793i	−0.833652	−	0.552290i	$-0.813754\pi$
$821$	−4.15443	+	4.95106i	−0.144991	+	0.172793i	0.688661	+	0.725083i	$0.258199\pi$
$822$	−15.6869	+	5.17244i	−0.547142	+	0.180410i
$823$	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
$825$	−1.56038	−	10.7631i	−0.0543254	−	0.374723i
$826$	79.9182	−	29.0879i	2.78071	−	1.01210i
$827$	−15.6661	+	5.70199i	−0.544764	+	0.198278i	−0.599718	−	0.800211i	$-0.704721\pi$
$827$	−15.6661	+	5.70199i	−0.544764	+	0.198278i	0.0549548	+	0.998489i	$0.482499\pi$
$828$	−63.7154	−	15.2991i	−2.21426	−	0.531680i
$829$	−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
$831$	14.4570	+	43.8450i	0.501510	+	1.52097i
$832$	−0.972837	+	1.15938i	−0.0337271	+	0.0401944i
$833$	−7.00370	+	1.23494i	−0.242664	+	0.0427882i
$834$	−47.2709	+	52.9607i	−1.63686	+	1.83388i
$835$			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	$-0.826872\pi$
$839$	−6.62128	−	37.5512i	−0.228592	−	1.29641i	0.627106	−	0.778934i	$-0.284239\pi$
$840$	−15.9444	−	29.6752i	−0.550133	−	1.02389i
$841$	−19.7282	+	16.5539i	−0.680283	+	0.570825i
$842$	18.7936	+	3.31382i	0.647670	+	0.114202i
$843$	−26.4132	−	33.5062i	−0.909720	−	1.15402i
$844$	59.9349	−	34.6034i	2.06304	−	1.19110i
$845$	12.3008	+	33.7961i	0.423159	+	1.16262i
$846$	−20.2698	+	46.6128i	−0.696890	+	1.60258i
$847$	−9.34799	−	16.1912i	−0.321201	−	0.556336i
$848$	−2.47543	+	4.28758i	−0.0850067	+	0.147236i
$849$	16.4053	+	10.1523i	0.563027	+	0.348426i
$850$	5.78264	+	6.89148i	0.198343	+	0.236376i
$851$	18.9835	+	15.9290i	0.650744	+	0.546039i
$852$	−36.3102	−	7.55321i	−1.24397	−	0.258769i
$853$	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
$855$	13.5518	−	33.5844i	0.463463	−	1.14856i
$856$	−28.8277			−0.985311
$857$	−2.73238	−	0.994507i	−0.0933365	−	0.0339717i	0.294930	−	0.955519i	$-0.404704\pi$
$857$	−2.73238	−	0.994507i	−0.0933365	−	0.0339717i	−0.388266	+	0.921547i	$0.626926\pi$
$858$	1.03852	+	0.216031i	0.0354544	+	0.00737517i
$859$	−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
$861$	−18.4172	−	11.3974i	−0.627656	−	0.388421i
$862$	−15.1798	+	26.2922i	−0.517027	+	0.895518i
$863$	−1.75212	−	3.03476i	−0.0596429	−	0.103305i	0.834662	−	0.550762i	$-0.185663\pi$
$863$	−1.75212	−	3.03476i	−0.0596429	−	0.103305i	−0.894305	+	0.447458i	$0.852330\pi$
$864$	−25.7434	+	25.5170i	−0.875808	+	0.868106i
$865$	14.8665	+	40.8453i	0.505475	+	1.38878i
$866$	63.1999	−	36.4885i	2.14762	−	1.23993i
$867$	−15.7574	−	19.9888i	−0.535148	−	0.678856i
$868$	14.0207	+	2.47223i	0.475895	+	0.0839131i
$869$	−12.6122	+	10.5829i	−0.427840	+	0.359001i
$870$	−9.07927	−	16.8981i	−0.307816	−	0.572898i
$871$	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
$876$	16.2892	−	18.2498i	0.550360	−	0.616604i
$877$	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
$879$	−15.4204	−	46.7667i	−0.520119	−	1.57740i
$880$	−1.46085	+	8.28489i	−0.0492453	+	0.279284i
$881$	−18.5886	−	10.7321i	−0.626266	−	0.361575i	0.153038	−	0.988220i	$-0.451094\pi$
$881$	−18.5886	−	10.7321i	−0.626266	−	0.361575i	−0.779305	+	0.626645i	$0.784428\pi$
$882$	7.28224	−	30.3280i	0.245206	−	1.02120i
$883$	−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
$885$	−7.71535	−	53.2185i	−0.259349	−	1.78892i
$886$	−9.93567	−	5.73636i	−0.333795	−	0.192717i
$887$	−1.33715	+	7.58336i	−0.0448971	+	0.254624i	−0.998992	−	0.0448790i	$-0.985710\pi$
$887$	−1.33715	+	7.58336i	−0.0448971	+	0.254624i	0.954095	+	0.299503i	$0.0968209\pi$
$888$	−11.2178	+	3.69887i	−0.376446	+	0.124126i
$889$	41.0108	−	48.8748i	1.37546	−	1.63921i
$890$	70.4872	−	12.4288i	2.36274	−	0.416614i
$891$	20.2401	+	6.18960i	0.678070	+	0.207359i
$892$			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
$897$	−1.33655	+	0.718124i	−0.0446261	+	0.0239775i
$898$	−48.8380	+	40.9799i	−1.62974	+	1.36752i
$899$	2.52613	+	0.445425i	0.0842511	+	0.0148557i
$900$	−22.4699	+	6.65502i	−0.748997	+	0.221834i
$901$	−5.03934	+	2.90946i	−0.167885	+	0.0969283i
$902$	−6.53032	−	17.9419i	−0.217436	−	0.597400i
$903$	0.851931	−	27.8677i	0.0283505	−	0.927380i
$904$	7.99385	+	13.8457i	0.265871	+	0.460503i
$905$	−1.41590	+	2.45241i	−0.0470661	+	0.0815208i
$906$	−23.4446	+	37.8845i	−0.778893	+	1.25863i
$907$	−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
$909$	40.4311	+	26.7628i	1.34101	+	0.887667i
$910$	−2.31662	−	0.843181i	−0.0767952	−	0.0279512i
$911$	13.1248			0.434844			0.217422	−	0.976078i	$-0.430235\pi$
$911$	13.1248			0.434844			0.217422	+	0.976078i	$0.430235\pi$
$912$	−6.29757	+	7.44588i	−0.208533	+	0.246558i
$913$	−2.27106			−0.0751612
$914$	11.8645	+	4.31833i	0.392444	+	0.142838i
$915$	−8.39655	+	40.3644i	−0.277581	+	1.33441i
$916$	−64.6490	−	54.2469i	−2.13606	−	1.79237i
$917$	21.8244	+	26.0093i	0.720705	+	0.858903i
$918$	−16.9311	+	4.45662i	−0.558809	+	0.147090i
$919$	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
$921$	−2.13927	−	0.0653986i	−0.0704913	−	0.00215496i
$922$	−22.2552	−	61.1455i	−0.732935	−	2.01372i
$923$	−0.743706	+	0.429379i	−0.0244794	+	0.0141332i
$924$	31.9912	−	25.2189i	1.05243	−	0.829641i
$925$	8.72802	+	1.53899i	0.286976	+	0.0506016i
$926$	25.5068	−	21.4028i	0.838207	−	0.703339i
$927$	22.4109	−	2.55259i	0.736070	−	0.0838381i
$928$	2.18262	+	12.3783i	0.0716481	+	0.406336i
$929$	14.0692	−	38.6548i	0.461596	−	1.26822i	−0.462689	−	0.886520i	$-0.653115\pi$
$929$	14.0692	−	38.6548i	0.461596	−	1.26822i	0.924285	−	0.381703i	$-0.124662\pi$
$930$	5.61632	−	14.0767i	0.184166	−	0.461593i
$931$	3.00856	−	20.1963i	0.0986015	−	0.661906i
$932$		−	11.4808i		−	0.376065i
$933$	19.3044	+	17.2304i	0.631996	+	0.564099i
$934$	89.3867	−	15.7613i	2.92482	−	0.515725i
$935$	−6.35572	+	7.57445i	−0.207854	+	0.247711i
$936$	0.0441760	−	0.721851i	0.00144394	−	0.0235944i
$937$	−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
$939$	−43.8333	+	6.35474i	−1.43045	+	0.207379i
$940$	58.1262	−	21.1562i	1.89587	−	0.690039i
$941$	25.8180	−	9.39697i	0.841641	−	0.306332i	0.115014	−	0.993364i	$-0.463309\pi$
$941$	25.8180	−	9.39697i	0.841641	−	0.306332i	0.726628	+	0.687032i	$0.241087\pi$
$942$	29.7560	−	4.31387i	0.969502	−	0.140554i
$943$	23.6516	+	13.6553i	0.770202	+	0.444676i
$944$	−2.51447	+	14.2602i	−0.0818389	+	0.464132i
$945$	−44.4897	−	20.9856i	−1.44725	−	0.682662i
$946$	15.7988	−	18.8283i	0.513664	−	0.612161i
$947$	23.6875	−	4.17674i	0.769739	−	0.135726i	0.225031	−	0.974352i	$-0.427752\pi$
$947$	23.6875	−	4.17674i	0.769739	−	0.135726i	0.544708	+	0.838626i	$0.316641\pi$
$948$	26.4673	+	23.6238i	0.859617	+	0.767265i
$949$		−	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	$-0.885053\pi$
$953$	−5.47213	−	31.0340i	−0.177260	−	1.00529i	0.758244	−	0.651971i	$-0.226058\pi$
$954$	−2.88806	−	25.3562i	−0.0935043	−	0.820936i
$955$	25.3608	−	21.2802i	0.820655	−	0.688611i
$956$	−2.51724	−	0.443857i	−0.0814133	−	0.0143554i
$957$	5.76388	−	4.54371i	0.186320	−	0.146877i
$958$	46.6652	−	26.9422i	1.50768	−	0.870462i
$959$	5.02353	+	13.8020i	0.162218	+	0.445691i
$960$	61.8436	+	1.89059i	1.99599	+	0.0610185i
$961$	−14.4867	−	25.0917i	−0.467313	−	0.809409i
$962$	−0.432208	+	0.748607i	−0.0139350	+	0.0241361i
$963$	−33.8390	+	25.0377i	−1.09045	+	0.806827i
$964$	10.1064	+	12.0444i	0.325506	+	0.387923i
$965$	−25.6461	−	21.5197i	−0.825578	−	0.692742i
$966$	−19.9788	+	96.0430i	−0.642806	+	3.09013i
$967$	−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
$969$	−10.7858	+	3.87806i	−0.346490	+	0.124581i
$970$	−31.1123			−0.998957
$971$	−29.2900	−	10.6607i	−0.939961	−	0.342118i	−0.173810	−	0.984779i	$-0.555608\pi$
$971$	−29.2900	−	10.6607i	−0.939961	−	0.342118i	−0.766150	+	0.642661i	$0.777830\pi$
$972$	6.94191	−	45.0757i	0.222662	−	1.44581i
$973$	48.3562	+	40.5757i	1.55023	+	1.30080i
$974$	26.6802	+	31.7963i	0.854890	+	1.01882i
$975$	−0.285547	+	0.461420i	−0.00914482	+	0.0147773i
$976$	5.55090	−	9.61444i	0.177680	−	0.307751i
$977$	−3.52792	−	6.11054i	−0.112868	−	0.195493i	0.804057	−	0.594552i	$-0.202670\pi$
$977$	−3.52792	−	6.11054i	−0.112868	−	0.195493i	−0.916926	+	0.399058i	$0.869337\pi$
$978$	2.08274	−	68.1289i	0.0665985	−	2.17852i
$979$	9.36620	+	25.7334i	0.299345	+	0.822444i
$980$	−32.8714	+	18.9783i	−1.05004	+	0.606240i
$981$	5.80196	+	19.5896i	0.185242	+	0.625449i
$982$	−76.3358	−	13.4601i	−2.43597	−	0.429528i
$983$	−4.44208	+	3.72735i	−0.141680	+	0.118884i	−0.710873	−	0.703320i	$-0.751700\pi$
$983$	−4.44208	+	3.72735i	−0.141680	+	0.118884i	0.569193	+	0.822204i	$0.307256\pi$
$984$	−11.4672	+	6.16126i	−0.365560	+	0.196414i
$985$	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
$990$	−19.3479	−	38.8093i	−0.614916	−	1.23344i
$991$	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
$993$	24.1071	−	7.94884i	0.765014	−	0.252249i
$994$	−9.64153	+	54.6799i	−0.305811	+	1.73434i
$995$	−13.8773	−	8.01209i	−0.439942	−	0.254000i
$996$	0.702121	+	4.84305i	0.0222475	+	0.153458i
$997$	−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
$999$	−9.95533	+	14.0849i	−0.314973	+	0.445626i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(2.08555 + 0.759077i) q^{2} +(-1.69575 - 0.352748i) q^{3} +(2.24122 + 1.88060i) q^{4} +(-1.78018 - 2.12154i) q^{5} +(-3.26880 - 2.02288i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(1.02725 + 1.77924i) q^{8} +(2.75114 + 1.19634i) q^{9} +O(q^{10})\)	\(q+(2.08555 + 0.759077i) q^{2} +(-1.69575 - 0.352748i) q^{3} +(2.24122 + 1.88060i) q^{4} +(-1.78018 - 2.12154i) q^{5} +(-3.26880 - 2.02288i) q^{6} +(-1.70913 + 2.96030i) q^{7} +(1.02725 + 1.77924i) q^{8} +(2.75114 + 1.19634i) q^{9} +(-2.10224 - 5.77587i) q^{10} +(2.03664 - 1.17586i) q^{11} +(-3.13716 - 3.97962i) q^{12} +(-0.115554 - 0.0203753i) q^{13} +(-5.81156 + 4.87648i) q^{14} +(2.27038 + 4.22556i) 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} +(3.94249 - 4.41703i) q^{21} +(5.14008 - 0.906334i) q^{22} +(-4.79880 + 5.71899i) q^{23} +(-1.11433 - 3.37951i) q^{24} +(-0.463638 + 2.62942i) q^{25} +(-0.225527 - 0.130208i) q^{26} +(-4.24323 - 2.99916i) q^{27} +(-9.39767 + 3.42047i) q^{28} +(-1.69319 + 0.616270i) q^{29} +(1.52745 + 10.5360i) q^{30} +(-1.23287 - 0.711795i) q^{31} +(1.21132 - 6.86975i) q^{32} +(-3.86842 + 1.27554i) q^{33} +(2.16579 - 2.58109i) q^{34} +(9.32295 - 1.64389i) q^{35} +(3.91605 + 7.85507i) 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} +(11.5751 - 6.21927i) q^{42} +(3.60739 - 3.02696i) q^{43} +(6.77588 + 1.19477i) q^{44} +(-2.35944 - 7.96636i) q^{45} +(-14.3493 + 8.28456i) q^{46} +(2.61102 + 7.17373i) q^{47} +(-0.0683620 + 2.23621i) q^{48} +(-2.34224 - 4.05687i) q^{49} +(-2.96287 + 5.13184i) q^{50} +(-1.38373 + 2.23599i) q^{51} +(-0.220664 - 0.262977i) q^{52} +(-2.93617 - 2.46374i) q^{53} +(-6.57287 - 9.47583i) q^{54} +(-6.12022 - 2.22758i) q^{55} -7.02278 q^{56} +(-4.83031 - 5.80242i) q^{57} -3.99901 q^{58} +(-10.5343 - 3.83419i) q^{59} +(-2.85819 + 13.7401i) q^{60} +(6.58405 + 5.52467i) q^{61} +(-2.03089 - 2.42032i) q^{62} +(-8.24358 + 6.09948i) q^{63} +(6.44925 - 11.1704i) q^{64} +(0.162480 + 0.281424i) q^{65} +(-9.03600 - 0.276235i) q^{66} +(-0.0605694 - 0.166413i) q^{67} +(3.84659 - 2.22083i) q^{68} +(10.1549 - 8.00521i) q^{69} +(20.6913 + 3.64843i) q^{70} +(5.60649 - 4.70441i) q^{71} +(0.697508 + 6.12388i) 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} +(0.336506 + 0.300354i) q^{78} +(-6.89453 + 1.21569i) q^{79} +(-2.29942 + 2.74034i) q^{80} +(6.13752 + 6.58262i) q^{81} +(1.40984 - 7.99558i) q^{82} +(-0.836326 - 0.482853i) q^{83} +(17.1427 - 2.48526i) q^{84} +(-3.95092 + 1.43802i) q^{85} +(9.82108 - 3.57458i) q^{86} +(3.08861 - 0.447771i) q^{87} +(4.18427 + 2.41579i) q^{88} +(-2.02208 + 11.4678i) q^{89} +(1.12637 - 18.4052i) q^{90} +(0.257813 - 0.307250i) q^{91} +(-21.5103 + 3.79285i) q^{92} +(1.83955 + 1.64192i) 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} +(7.00981 - 0.798416i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more