LMFDB - Embedded newform 690.2.w.b.493.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.9
Character	$\chi$	$=$	690.493
Dual form			690.2.w.b.7.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.0285953 - 2.23589i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.81898 - 3.33121i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.0285953 - 2.23589i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.81898 - 3.33121i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(0.188029 - 2.22815i) q^{10} +(-0.824208 - 0.714181i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(1.85393 + 1.01232i) q^{13} +(-1.57670 - 3.45249i) q^{14} +(2.19087 - 0.447330i) q^{15} +(0.959493 + 0.281733i) q^{16} +(4.77311 - 6.37613i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(0.435879 - 3.03161i) q^{19} +(0.346504 - 2.20906i) q^{20} +(2.86843 - 2.48551i) q^{21} +(-0.771159 - 0.771159i) q^{22} +(-1.64562 + 4.50466i) q^{23} +1.00000i q^{24} +(-4.99836 - 0.127872i) q^{25} +(1.77699 + 1.14200i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(-1.32638 - 3.55617i) q^{28} +(3.03728 - 0.436695i) q^{29} +(2.21720 - 0.289895i) q^{30} +(4.68740 - 3.01241i) q^{31} +(0.936950 + 0.349464i) q^{32} +(0.522661 - 0.957183i) q^{33} +(5.21582 - 6.01938i) q^{34} +(-7.50022 + 3.97177i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.45951 + 3.91310i) q^{37} +(0.651041 - 2.99279i) q^{38} +(-0.595107 + 2.02675i) q^{39} +(0.503213 - 2.17871i) q^{40} +(-3.28427 + 7.19155i) q^{41} +(3.03844 - 2.27455i) q^{42} +(-7.16354 + 1.55833i) q^{43} +(-0.714181 - 0.824208i) q^{44} +(0.902809 + 2.04571i) q^{45} +(-1.96278 + 4.37578i) q^{46} +(2.60941 - 2.60941i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(-4.00380 + 6.23003i) q^{49} +(-4.97651 - 0.484125i) q^{50} +(7.24502 + 3.30869i) q^{51} +(1.69099 + 1.26586i) q^{52} +(8.56066 - 4.67447i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-1.62039 + 1.82241i) q^{55} +(-1.06931 - 3.64173i) q^{56} +(3.05498 - 0.218496i) q^{57} +(3.06070 - 0.218905i) q^{58} +(2.33393 + 7.94863i) q^{59} +(2.23223 - 0.130984i) q^{60} +(2.89919 + 4.51123i) q^{61} +(4.89036 - 2.67034i) q^{62} +(3.03844 + 2.27455i) q^{63} +(0.909632 + 0.415415i) q^{64} +(2.31645 - 4.11623i) q^{65} +(0.589614 - 0.917457i) q^{66} +(-0.00898434 + 0.125617i) q^{67} +(5.63195 - 5.63195i) q^{68} +(-4.75151 - 0.650474i) q^{69} +(-7.76445 + 3.42659i) q^{70} +(4.04850 + 4.67221i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(3.31190 - 2.47926i) q^{73} +(-1.73495 + 3.79901i) q^{74} +(-0.937529 - 4.91132i) q^{75} +(0.862885 - 2.93872i) q^{76} +(-0.879869 + 4.04469i) q^{77} +(-0.738178 + 1.97913i) q^{78} +(-14.2008 + 4.16973i) q^{79} +(0.657359 - 2.13726i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-3.78894 + 6.93893i) q^{82} +(-1.10240 - 0.411173i) q^{83} +(3.19296 - 2.05199i) q^{84} +(-14.1198 - 10.8545i) q^{85} +(-7.25646 + 1.04332i) q^{86} +(1.07234 + 2.87504i) q^{87} +(-0.653563 - 0.873057i) q^{88} +(1.56947 + 1.00864i) q^{89} +(0.754569 + 2.10490i) q^{90} -8.01724i q^{91} +(-2.26995 + 4.22461i) q^{92} +(3.93995 + 3.93995i) q^{93} +(2.78891 - 2.41661i) q^{94} +(-6.76586 - 1.06127i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-6.93649 + 2.58718i) q^{97} +(-4.43804 + 5.92853i) q^{98} +(1.04641 + 0.307253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$2$	0.997452	+	0.0713392i	0.705305	+	0.0504444i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	0.0285953	−	2.23589i	0.0127882	−	0.999918i
$5$	0.0285953	−	2.23589i	0.0127882	−	0.999918i
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	−1.81898	−	3.33121i	−0.687509	−	1.25908i	−0.955310	−	0.295605i	$-0.904479\pi$
$7$	−1.81898	−	3.33121i	−0.687509	−	1.25908i	0.267801	−	0.963474i	$-0.413703\pi$
$8$	0.977147	+	0.212565i	0.345474	+	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	0.188029	−	2.22815i	0.0594599	−	0.704602i
$11$	−0.824208	−	0.714181i	−0.248508	−	0.215334i	0.521695	−	0.853132i	$-0.325300\pi$
$11$	−0.824208	−	0.714181i	−0.248508	−	0.215334i	−0.770203	+	0.637798i	$0.779845\pi$
$12$	0.0713392	+	0.997452i	0.0205938	+	0.287940i
$13$	1.85393	+	1.01232i	0.514189	+	0.280768i	0.715321	−	0.698796i	$-0.246280\pi$
$13$	1.85393	+	1.01232i	0.514189	+	0.280768i	−0.201133	+	0.979564i	$0.564462\pi$
$14$	−1.57670	−	3.45249i	−0.421390	−	0.922716i
$15$	2.19087	−	0.447330i	0.565679	−	0.115500i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	4.77311	−	6.37613i	1.15765	−	1.54644i	0.371467	−	0.928446i	$-0.378855\pi$
$17$	4.77311	−	6.37613i	1.15765	−	1.54644i	0.786183	−	0.617994i	$-0.212054\pi$
$18$	−0.936950	+	0.349464i	−0.220841	+	0.0823695i
$19$	0.435879	−	3.03161i	0.0999975	−	0.695498i	−0.876725	−	0.480992i	$-0.840277\pi$
$19$	0.435879	−	3.03161i	0.0999975	−	0.695498i	0.976723	−	0.214506i	$-0.0688142\pi$
$20$	0.346504	−	2.20906i	0.0774806	−	0.493960i
$21$	2.86843	−	2.48551i	0.625943	−	0.542383i
$22$	−0.771159	−	0.771159i	−0.164412	−	0.164412i
$23$	−1.64562	+	4.50466i	−0.343135	+	0.939286i
$23$	−1.64562	+	4.50466i	−0.343135	+	0.939286i
$24$			1.00000i			0.204124i
$25$	−4.99836	−	0.127872i	−0.999673	−	0.0255743i
$26$	1.77699	+	1.14200i	0.348497	+	0.223965i
$27$	−0.599278	−	0.800541i	−0.115331	−	0.154064i
$28$	−1.32638	−	3.55617i	−0.250663	−	0.672053i
$29$	3.03728	−	0.436695i	0.564009	−	0.0810923i	0.145588	−	0.989345i	$-0.453493\pi$
$29$	3.03728	−	0.436695i	0.564009	−	0.0810923i	0.418421	+	0.908253i	$0.362584\pi$
$30$	2.21720	−	0.289895i	0.404803	−	0.0529274i
$31$	4.68740	−	3.01241i	0.841883	−	0.541045i	−0.0471506	−	0.998888i	$-0.515014\pi$
$31$	4.68740	−	3.01241i	0.841883	−	0.541045i	0.889033	+	0.457843i	$0.151378\pi$
$32$	0.936950	+	0.349464i	0.165631	+	0.0617771i
$33$	0.522661	−	0.957183i	0.0909836	−	0.166624i
$34$	5.21582	−	6.01938i	0.894506	−	1.03231i
$35$	−7.50022	+	3.97177i	−1.26777	+	0.671352i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−1.45951	+	3.91310i	−0.239942	+	0.643309i	−0.999978	−	0.00657114i	$-0.997908\pi$
$37$	−1.45951	+	3.91310i	−0.239942	+	0.643309i	0.760036	+	0.649880i	$0.225181\pi$
$38$	0.651041	−	2.99279i	0.105613	−	0.485494i
$39$	−0.595107	+	2.02675i	−0.0952935	+	0.324540i
$40$	0.503213	−	2.17871i	0.0795650	−	0.344484i
$41$	−3.28427	+	7.19155i	−0.512917	+	1.12313i	0.459135	+	0.888367i	$0.348159\pi$
$41$	−3.28427	+	7.19155i	−0.512917	+	1.12313i	−0.972052	+	0.234765i	$0.924568\pi$
$42$	3.03844	−	2.27455i	0.468841	−	0.350970i
$43$	−7.16354	+	1.55833i	−1.09243	+	0.237644i	−0.722469	−	0.691404i	$-0.756993\pi$
$43$	−7.16354	+	1.55833i	−1.09243	+	0.237644i	−0.369961	+	0.929047i	$0.620629\pi$
$44$	−0.714181	−	0.824208i	−0.107667	−	0.124254i
$45$	0.902809	+	2.04571i	0.134583	+	0.304957i
$46$	−1.96278	+	4.37578i	−0.289396	+	0.645174i
$47$	2.60941	−	2.60941i	0.380621	−	0.380621i	−0.490705	−	0.871326i	$-0.663261\pi$
$47$	2.60941	−	2.60941i	0.380621	−	0.380621i	0.871326	+	0.490705i	$0.163261\pi$
$48$	−0.0713392	+	0.997452i	−0.0102969	+	0.143970i
$49$	−4.00380	+	6.23003i	−0.571971	+	0.890005i
$50$	−4.97651	−	0.484125i	−0.703784	−	0.0684656i
$51$	7.24502	+	3.30869i	1.01451	+	0.463309i
$52$	1.69099	+	1.26586i	0.234499	+	0.175544i
$53$	8.56066	−	4.67447i	1.17590	−	0.642089i	0.232125	−	0.972686i	$-0.425432\pi$
$53$	8.56066	−	4.67447i	1.17590	−	0.642089i	0.943772	+	0.330597i	$0.107250\pi$
$54$	−0.540641	−	0.841254i	−0.0735719	−	0.114480i
$55$	−1.62039	+	1.82241i	−0.218494	+	0.245734i
$56$	−1.06931	−	3.64173i	−0.142893	−	0.486647i
$57$	3.05498	−	0.218496i	0.404641	−	0.0289405i
$58$	3.06070	−	0.218905i	0.401889	−	0.0287437i
$59$	2.33393	+	7.94863i	0.303852	+	1.03482i	0.959955	+	0.280153i	$0.0903852\pi$
$59$	2.33393	+	7.94863i	0.303852	+	1.03482i	−0.656104	+	0.754671i	$0.727797\pi$
$60$	2.23223	−	0.130984i	0.288179	−	0.0169099i
$61$	2.89919	+	4.51123i	0.371204	+	0.577604i	0.975729	−	0.218982i	$-0.0702735\pi$
$61$	2.89919	+	4.51123i	0.371204	+	0.577604i	−0.604525	+	0.796586i	$0.706637\pi$
$62$	4.89036	−	2.67034i	0.621077	−	0.339134i
$63$	3.03844	+	2.27455i	0.382807	+	0.286566i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	2.31645	−	4.11623i	0.287321	−	0.510556i
$66$	0.589614	−	0.917457i	0.0725765	−	0.112931i
$67$	−0.00898434	+	0.125617i	−0.00109761	+	0.0153466i	−0.997971	−	0.0636638i	$-0.979721\pi$
$67$	−0.00898434	+	0.125617i	−0.00109761	+	0.0153466i	0.996874	+	0.0790104i	$0.0251760\pi$
$68$	5.63195	−	5.63195i	0.682974	−	0.682974i
$69$	−4.75151	−	0.650474i	−0.572015	−	0.0783079i
$70$	−7.76445	+	3.42659i	−0.928030	+	0.409556i
$71$	4.04850	+	4.67221i	0.480468	+	0.554490i	0.943294	−	0.331960i	$-0.107710\pi$
$71$	4.04850	+	4.67221i	0.480468	+	0.554490i	−0.462826	+	0.886449i	$0.653164\pi$
$72$	−0.977147	+	0.212565i	−0.115158	+	0.0250511i
$73$	3.31190	−	2.47926i	0.387629	−	0.290175i	−0.387635	−	0.921813i	$-0.626708\pi$
$73$	3.31190	−	2.47926i	0.387629	−	0.290175i	0.775264	+	0.631638i	$0.217617\pi$
$74$	−1.73495	+	3.79901i	−0.201684	+	0.441626i
$75$	−0.937529	−	4.91132i	−0.108257	−	0.567110i
$76$	0.862885	−	2.93872i	0.0989797	−	0.337094i
$77$	−0.879869	+	4.04469i	−0.100270	+	0.460935i
$78$	−0.738178	+	1.97913i	−0.0835822	+	0.224093i
$79$	−14.2008	+	4.16973i	−1.59771	+	0.469131i	−0.954909	−	0.296900i	$-0.904047\pi$
$79$	−14.2008	+	4.16973i	−1.59771	+	0.469131i	−0.642804	+	0.766030i	$0.722229\pi$
$80$	0.657359	−	2.13726i	0.0734949	−	0.238953i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−3.78894	+	6.93893i	−0.418419	+	0.766277i
$83$	−1.10240	−	0.411173i	−0.121004	−	0.0451321i	0.288233	−	0.957560i	$-0.406932\pi$
$83$	−1.10240	−	0.411173i	−0.121004	−	0.0451321i	−0.409237	+	0.912428i	$0.634205\pi$
$84$	3.19296	−	2.05199i	0.348380	−	0.223891i
$85$	−14.1198	−	10.8545i	−1.53151	−	1.17733i
$86$	−7.25646	+	1.04332i	−0.782484	+	0.112504i
$87$	1.07234	+	2.87504i	0.114967	+	0.308237i
$88$	−0.653563	−	0.873057i	−0.0696700	−	0.0930682i
$89$	1.56947	+	1.00864i	0.166363	+	0.106915i	0.621173	−	0.783673i	$-0.286656\pi$
$89$	1.56947	+	1.00864i	0.166363	+	0.106915i	−0.454810	+	0.890589i	$0.650293\pi$
$90$	0.754569	+	2.10490i	0.0795386	+	0.221876i
$91$		−	8.01724i		−	0.840435i
$92$	−2.26995	+	4.22461i	−0.236658	+	0.440446i
$93$	3.93995	+	3.93995i	0.408554	+	0.408554i
$94$	2.78891	−	2.41661i	0.287654	−	0.249254i
$95$	−6.76586	−	1.06127i	−0.694162	−	0.108884i
$96$	−0.142315	+	0.989821i	−0.0145249	+	0.101023i
$97$	−6.93649	+	2.58718i	−0.704294	+	0.262688i	−0.675990	−	0.736911i	$-0.736284\pi$
$97$	−6.93649	+	2.58718i	−0.704294	+	0.262688i	−0.0283047	+	0.999599i	$0.509011\pi$
$98$	−4.43804	+	5.92853i	−0.448310	+	0.598872i
$99$	1.04641	+	0.307253i	0.105168	+	0.0308801i
$100$	−4.92929	−	0.837912i	−0.492929	−	0.0837912i
$101$	3.99386	+	8.74532i	0.397404	+	0.870192i	0.997527	+	0.0702849i	$0.0223908\pi$
$101$	3.99386	+	8.74532i	0.397404	+	0.870192i	−0.600123	+	0.799907i	$0.704882\pi$
$102$	6.99052	+	3.81711i	0.692165	+	0.377950i
$103$	−1.15648	−	16.1698i	−0.113952	−	1.59325i	−0.657223	−	0.753696i	$-0.728269\pi$
$103$	−1.15648	−	16.1698i	−0.113952	−	1.59325i	0.543271	−	0.839557i	$-0.317186\pi$
$104$	1.59638	+	1.38327i	0.156538	+	0.135641i
$105$	−5.47529	−	6.48456i	−0.534334	−	0.632828i
$106$	8.87232	−	4.05185i	0.861756	−	0.393551i
$107$	0.587265	+	0.127752i	0.0567731	+	0.0123502i	0.240862	−	0.970559i	$-0.422570\pi$
$107$	0.587265	+	0.127752i	0.0567731	+	0.0123502i	−0.184089	+	0.982910i	$0.558933\pi$
$108$	−0.479249	−	0.877679i	−0.0461158	−	0.0844547i
$109$	1.18599	+	8.24871i	0.113597	+	0.790084i	0.964371	+	0.264552i	$0.0852242\pi$
$109$	1.18599	+	8.24871i	0.113597	+	0.790084i	−0.850774	+	0.525531i	$0.823867\pi$
$110$	−1.74627	+	1.70217i	−0.166501	+	0.162296i
$111$	−4.13391	−	0.594367i	−0.392374	−	0.0564148i
$112$	−0.806787	−	3.70874i	−0.0762342	−	0.350443i
$113$	18.0022	+	1.28754i	1.69351	+	0.121122i	0.884458	−	0.466620i	$-0.154528\pi$
$113$	18.0022	+	1.28754i	1.69351	+	0.121122i	0.809048	+	0.587742i	$0.199983\pi$
$114$	3.06278			0.286856
$115$	10.0248	+	3.80822i	0.934821	+	0.355118i
$116$	3.06852			0.284904
$117$	−2.10693	−	0.150691i	−0.194786	−	0.0139314i
$118$	1.76093	+	8.09488i	0.162107	+	0.745194i
$119$	−29.9224	−	4.30220i	−2.74299	−	0.394382i
$120$	2.23589	+	0.0285953i	0.204107	+	0.00261038i
$121$	−1.39620	−	9.71077i	−0.126927	−	0.882797i
$122$	2.56998	+	4.70657i	0.232675	+	0.426113i
$123$	−7.72533	−	1.68054i	−0.696569	−	0.151529i
$124$	5.06840	−	2.31466i	0.455156	−	0.207863i
$125$	−0.428836	+	11.1721i	−0.0383563	+	0.999264i
$126$	2.86843	+	2.48551i	0.255540	+	0.221427i
$127$	0.457526	+	6.39705i	0.0405989	+	0.567646i	0.976519	+	0.215433i	$0.0691163\pi$
$127$	0.457526	+	6.39705i	0.0405989	+	0.567646i	−0.935920	+	0.352213i	$0.885429\pi$
$128$	0.877679	+	0.479249i	0.0775766	+	0.0423600i
$129$	−3.04544	−	6.66858i	−0.268136	−	0.587136i
$130$	2.60420	−	3.94049i	0.228404	−	0.345604i
$131$	−19.1601	−	5.62592i	−1.67403	−	0.491539i	−0.699279	−	0.714849i	$-0.746495\pi$
$131$	−19.1601	−	5.62592i	−1.67403	−	0.491539i	−0.974747	+	0.223310i	$0.928314\pi$
$132$	0.653563	−	0.873057i	0.0568853	−	0.0759899i
$133$	−10.8918	+	4.06242i	−0.944436	+	0.352257i
$134$	−0.0179229	+	0.124656i	−0.00154830	+	0.0107687i
$135$	−1.80705	+	1.31702i	−0.155527	+	0.113351i
$136$	6.01938	−	5.21582i	0.516157	−	0.447253i
$137$	6.93959	+	6.93959i	0.592889	+	0.592889i	0.938411	−	0.345521i	$-0.112298\pi$
$137$	6.93959	+	6.93959i	0.592889	+	0.592889i	−0.345521	+	0.938411i	$0.612298\pi$
$138$	−4.69300	−	0.987786i	−0.399495	−	0.0840859i
$139$			6.28479i			0.533069i	0.963825	+	0.266535i	$0.0858787\pi$
$139$			6.28479i			0.533069i	−0.963825	+	0.266535i	$0.914121\pi$
$140$	−7.98912	+	2.86395i	−0.675204	+	0.242048i
$141$	3.10445	+	1.99511i	0.261441	+	0.168018i
$142$	3.70487	+	4.94913i	0.310906	+	0.415321i
$143$	−0.805045	−	2.15841i	−0.0673212	−	0.180495i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	−0.889548	−	6.80350i	−0.0738730	−	0.565000i
$146$	3.48033	−	2.23667i	0.288034	−	0.185108i
$147$	−6.93873	−	2.58801i	−0.572296	−	0.213456i
$148$	−2.00155	+	3.66556i	−0.164526	+	0.301307i
$149$	−10.4930	+	12.1096i	−0.859623	+	0.992058i	0.140375	+	0.990098i	$0.455169\pi$
$149$	−10.4930	+	12.1096i	−0.859623	+	0.992058i	−0.999998	+	0.00195920i	$0.999376\pi$
$150$	−0.584771	−	4.96569i	−0.0477464	−	0.405447i
$151$	−12.0029	+	3.52436i	−0.976780	+	0.286809i	−0.730895	−	0.682490i	$-0.760897\pi$
$151$	−12.0029	+	3.52436i	−0.976780	+	0.286809i	−0.245886	+	0.969299i	$0.579079\pi$
$152$	1.07033	−	2.86967i	0.0868154	−	0.232761i
$153$	−1.69304	+	7.78276i	−0.136874	+	0.629199i
$154$	−1.16617	+	3.97162i	−0.0939728	+	0.320042i
$155$	−6.60137	−	10.5666i	−0.530235	−	0.848733i
$156$	−0.877487	+	1.92143i	−0.0702552	+	0.153837i
$157$	5.68305	−	4.25428i	0.453557	−	0.339529i	−0.347951	−	0.937513i	$-0.613122\pi$
$157$	5.68305	−	4.25428i	0.453557	−	0.339529i	0.801508	+	0.597984i	$0.204031\pi$
$158$	−14.4621	+	3.14603i	−1.15054	+	0.250285i
$159$	6.38735	+	7.37139i	0.506550	+	0.584589i
$160$	0.808154	−	2.08492i	0.0638902	−	0.164827i
$161$	17.9993	−	2.71199i	1.41854	−	0.213734i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	1.20151	−	16.7993i	0.0941095	−	1.31582i	−0.702654	−	0.711531i	$-0.748002\pi$
$163$	1.20151	−	16.7993i	0.0941095	−	1.31582i	0.796764	−	0.604291i	$-0.206543\pi$
$164$	−4.27431	+	6.65095i	−0.333767	+	0.519352i
$165$	−2.12520	−	1.19598i	−0.165447	−	0.0931070i
$166$	−1.07026	−	0.488769i	−0.0830679	−	0.0379358i
$167$	20.0297	+	14.9940i	1.54994	+	1.16027i	0.925225	+	0.379420i	$0.123876\pi$
$167$	20.0297	+	14.9940i	1.54994	+	1.16027i	0.624717	+	0.780852i	$0.285214\pi$
$168$	3.33121	−	1.81898i	0.257009	−	0.140337i
$169$	−4.61606	−	7.18273i	−0.355082	−	0.552518i
$170$	−13.3095	−	11.8341i	−1.02079	−	0.907634i
$171$	0.862885	+	2.93872i	0.0659864	+	0.224729i
$172$	−7.31240	+	0.522993i	−0.557565	+	0.0398779i
$173$	14.8690	−	1.06345i	1.13047	−	0.0808526i	0.506454	−	0.862267i	$-0.330956\pi$
$173$	14.8690	−	1.06345i	1.13047	−	0.0808526i	0.624013	+	0.781414i	$0.285501\pi$
$174$	0.864501	+	2.94422i	0.0655376	+	0.223201i
$175$	8.66595	+	16.8832i	0.655084	+	1.27625i
$176$	−0.589614	−	0.917457i	−0.0444438	−	0.0691560i
$177$	−7.27087	+	3.97019i	−0.546512	+	0.298418i
$178$	1.49351	+	1.11803i	0.111944	+	0.0838000i
$179$	20.9679	+	9.57570i	1.56721	+	0.715721i	0.994569	−	0.104084i	$-0.0331910\pi$
$179$	20.9679	+	9.57570i	1.56721	+	0.715721i	0.572643	+	0.819805i	$0.305918\pi$
$180$	0.602485	+	2.15337i	0.0449066	+	0.160503i
$181$	−1.31753	+	2.05012i	−0.0979314	+	0.152384i	−0.886762	−	0.462227i	$-0.847051\pi$
$181$	−1.31753	+	2.05012i	−0.0979314	+	0.152384i	0.788830	+	0.614611i	$0.210687\pi$
$182$	0.571943	−	7.99681i	0.0423953	−	0.592763i
$183$	−3.79187	+	3.79187i	−0.280303	+	0.280303i
$184$	−2.56554	+	4.05191i	−0.189134	+	0.298711i
$185$	8.70750	+	3.37519i	0.640188	+	0.248149i
$186$	3.64884	+	4.21098i	0.267546	+	0.308764i
$187$	−8.48775	+	1.84640i	−0.620686	+	0.135022i
$188$	2.95421	−	2.21149i	0.215458	−	0.161290i
$189$	−1.57670	+	3.45249i	−0.114688	+	0.251132i
$190$	−6.67291	−	1.54123i	−0.484104	−	0.111813i
$191$	1.75293	−	5.96993i	0.126838	−	0.431969i	−0.871449	−	0.490486i	$-0.836819\pi$
$191$	1.75293	−	5.96993i	0.126838	−	0.431969i	0.998286	+	0.0585174i	$0.0186373\pi$
$192$	−0.212565	+	0.977147i	−0.0153406	+	0.0705195i
$193$	4.15606	−	11.1428i	0.299160	−	0.802078i	−0.697204	−	0.716873i	$-0.745573\pi$
$193$	4.15606	−	11.1428i	0.299160	−	0.802078i	0.996363	−	0.0852053i	$-0.0271546\pi$
$194$	−7.10339	+	2.08574i	−0.509994	+	0.149748i
$195$	4.51456	+	1.38855i	0.323295	+	0.0994360i
$196$	−4.84967	+	5.59682i	−0.346405	+	0.399773i
$197$	5.07045	−	9.28584i	0.361255	−	0.661589i	−0.632327	−	0.774701i	$-0.717900\pi$
$197$	5.07045	−	9.28584i	0.361255	−	0.661589i	0.993582	+	0.113112i	$0.0360820\pi$
$198$	1.02182	+	0.381120i	0.0726177	+	0.0270850i
$199$	−17.8524	+	11.4731i	−1.26553	+	0.813304i	−0.989030	−	0.147711i	$-0.952809\pi$
$199$	−17.8524	+	11.4731i	−1.26553	+	0.813304i	−0.276495	+	0.961015i	$0.589173\pi$
$200$	−4.85696	−	1.18743i	−0.343439	−	0.0839639i
$201$	−0.124656	+	0.0179229i	−0.00879259	+	0.00126418i
$202$	3.35980	+	9.00796i	0.236394	+	0.633798i
$203$	−6.97948	−	9.32349i	−0.489863	−	0.654381i
$204$	6.70040	+	4.30609i	0.469122	+	0.301486i
$205$	15.9856	+	7.54890i	1.11648	+	0.527238i
$206$		−	16.2111i		−	1.12948i
$207$	−0.374398	−	4.78120i	−0.0260225	−	0.332316i
$208$	1.49363	+	1.49363i	0.103565	+	0.103565i
$209$	−2.52437	+	2.18738i	−0.174614	+	0.151304i
$210$	−4.99874	−	6.85864i	−0.344946	−	0.473291i
$211$	0.312855	−	2.17596i	0.0215379	−	0.149799i	−0.976215	−	0.216806i	$-0.930436\pi$
$211$	0.312855	−	2.17596i	0.0215379	−	0.149799i	0.997752	+	0.0670073i	$0.0213451\pi$
$212$	9.13877	−	3.40859i	0.627654	−	0.234103i
$213$	−3.70487	+	4.94913i	−0.253853	+	0.339108i
$214$	0.576655	+	0.169321i	0.0394193	+	0.0115746i
$215$	3.27941	+	16.0614i	0.223654	+	1.09538i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−18.5613	−	10.1352i	−1.26002	−	0.688024i
$218$	0.594508	+	8.31230i	0.0402651	+	0.562980i
$219$	3.12660	+	2.70921i	0.211276	+	0.183071i
$220$	−1.86326	+	1.57326i	−0.125621	+	0.106069i
$221$	15.3038	−	6.98899i	1.02944	−	0.470130i
$222$	−4.08098	−	0.887762i	−0.273897	−	0.0595827i
$223$	4.01570	+	7.35421i	0.268911	+	0.492474i	0.976885	−	0.213764i	$-0.0685724\pi$
$223$	4.01570	+	7.35421i	0.268911	+	0.492474i	−0.707974	+	0.706238i	$0.750391\pi$
$224$	−0.540153	−	3.75685i	−0.0360905	−	0.251015i
$225$	4.59979	−	1.96008i	0.306653	−	0.130672i
$226$	17.8645	+	2.56853i	1.18833	+	0.170856i
$227$	1.67691	+	7.70864i	0.111301	+	0.511640i	0.998716	+	0.0506688i	$0.0161353\pi$
$227$	1.67691	+	7.70864i	0.111301	+	0.511640i	−0.887415	+	0.460971i	$0.847501\pi$
$228$	3.05498	+	0.218496i	0.202321	+	0.0144703i
$229$	4.27189			0.282295			0.141147	−	0.989989i	$-0.454921\pi$
$229$	4.27189			0.282295			0.141147	+	0.989989i	$0.454921\pi$
$230$	9.72762	+	4.51368i	0.641421	+	0.297623i
$231$	−4.13929			−0.272345
$232$	3.06070	+	0.218905i	0.200945	+	0.0143718i
$233$	−5.89002	−	27.0760i	−0.385868	−	1.77381i	−0.603080	−	0.797681i	$-0.706060\pi$
$233$	−5.89002	−	27.0760i	−0.385868	−	1.77381i	0.217212	−	0.976124i	$-0.430304\pi$
$234$	−2.09081	−	0.300614i	−0.136681	−	0.0196517i
$235$	−5.75972	−	5.90896i	−0.375723	−	0.385458i
$236$	1.17896	+	8.19988i	0.0767441	+	0.533767i
$237$	−7.09303	−	12.9899i	−0.460742	−	0.843785i
$238$	−29.5393	−	6.42588i	−1.91475	−	0.416528i
$239$	15.7615	−	7.19805i	1.01953	−	0.465603i	0.165711	−	0.986174i	$-0.447008\pi$
$239$	15.7615	−	7.19805i	1.01953	−	0.465603i	0.853818	+	0.520571i	$0.174281\pi$
$240$	2.22815	+	0.188029i	0.143826	+	0.0121372i
$241$	14.8123	+	12.8350i	0.954146	+	0.826772i	0.984965	−	0.172753i	$-0.0552661\pi$
$241$	14.8123	+	12.8350i	0.954146	+	0.826772i	−0.0308190	+	0.999525i	$0.509812\pi$
$242$	−0.699882	−	9.78563i	−0.0449901	−	0.629044i
$243$	0.877679	+	0.479249i	0.0563031	+	0.0307438i
$244$	2.22767	+	4.87792i	0.142612	+	0.312277i
$245$	13.8151	+	9.13018i	0.882617	+	0.583306i
$246$	−7.58576	−	2.22738i	−0.483650	−	0.142012i
$247$	3.87706	−	5.17914i	0.246691	−	0.329541i
$248$	5.22062	−	1.94719i	0.331509	−	0.123647i
$249$	0.167445	−	1.16460i	0.0106114	−	0.0738038i
$250$	−1.22475	+	11.1131i	−0.0774602	+	0.702851i
$251$	1.57174	−	1.36192i	0.0992073	−	0.0859636i	−0.603845	−	0.797102i	$-0.706365\pi$
$251$	1.57174	−	1.36192i	0.0992073	−	0.0859636i	0.703052	+	0.711138i	$0.251820\pi$
$252$	2.68381	+	2.68381i	0.169064	+	0.169064i
$253$	4.57347	−	2.53751i	0.287532	−	0.159532i
$254$			6.41339i			0.402412i
$255$	7.60502	−	16.1044i	0.476245	−	1.00850i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−4.67810	−	6.24922i	−0.291812	−	0.389815i	0.630546	−	0.776152i	$-0.282831\pi$
$257$	−4.67810	−	6.24922i	−0.291812	−	0.389815i	−0.922358	+	0.386337i	$0.873740\pi$
$258$	−2.56195	−	6.86885i	−0.159500	−	0.427636i
$259$	15.6902	−	2.25591i	0.974940	−	0.140175i
$260$	2.87868	−	3.74467i	0.178528	−	0.232235i
$261$	−2.58140	+	1.65896i	−0.159785	+	0.102687i
$262$	−18.7099	−	6.97845i	−1.15590	−	0.431130i
$263$	−9.46011	+	17.3249i	−0.583335	+	1.06830i	0.404755	+	0.914425i	$0.367357\pi$
$263$	−9.46011	+	17.3249i	−0.583335	+	1.06830i	−0.988091	+	0.153874i	$0.950825\pi$
$264$	0.714181	−	0.824208i	0.0439548	−	0.0507265i
$265$	−10.2068	−	19.2743i	−0.626998	−	1.18401i
$266$	−11.1538	+	3.27506i	−0.683885	+	0.200807i
$267$	−0.651971	+	1.74800i	−0.0399000	+	0.106976i
$268$	−0.0267701	+	0.123060i	−0.00163524	+	0.00751710i
$269$	−5.03648	+	17.1527i	−0.307080	+	1.04582i	0.650943	+	0.759126i	$0.274374\pi$
$269$	−5.03648	+	17.1527i	−0.307080	+	1.04582i	−0.958023	+	0.286691i	$0.907445\pi$
$270$	−1.89641	+	1.18475i	−0.115412	+	0.0721019i
$271$	−12.1619	+	26.6308i	−0.738783	+	1.61771i	0.0467636	+	0.998906i	$0.485109\pi$
$271$	−12.1619	+	26.6308i	−0.738783	+	1.61771i	−0.785546	+	0.618803i	$0.787618\pi$
$272$	6.37613	−	4.77311i	0.386610	−	0.289413i
$273$	7.83402	−	1.70419i	0.474137	−	0.103142i
$274$	6.42685	+	7.41698i	0.388260	+	0.448076i
$275$	4.02837	+	3.67513i	0.242920	+	0.221619i
$276$	−4.61058	−	1.32006i	−0.277524	−	0.0794585i
$277$	−1.08385	+	1.08385i	−0.0651220	+	0.0651220i	−0.738918	−	0.673796i	$-0.764663\pi$
$277$	−1.08385	+	1.08385i	−0.0651220	+	0.0651220i	0.673796	+	0.738918i	$0.264663\pi$
$278$	−0.448352	+	6.26878i	−0.0268904	+	0.375976i
$279$	−3.01241	+	4.68740i	−0.180348	+	0.280628i
$280$	−8.17308	+	2.28672i	−0.488435	+	0.136657i
$281$	2.00639	+	0.916286i	0.119691	+	0.0546611i	0.474360	−	0.880331i	$-0.342679\pi$
$281$	2.00639	+	0.916286i	0.119691	+	0.0546611i	−0.354669	+	0.934992i	$0.615407\pi$
$282$	2.95421	+	2.21149i	0.175920	+	0.131692i
$283$	1.72980	−	0.944545i	0.102826	−	0.0561474i	−0.427013	−	0.904246i	$-0.640434\pi$
$283$	1.72980	−	0.944545i	0.102826	−	0.0561474i	0.529839	+	0.848098i	$0.322252\pi$
$284$	3.34236	+	5.20082i	0.198333	+	0.308612i
$285$	−0.401174	−	6.83682i	−0.0237635	−	0.404978i
$286$	−0.649015	−	2.21034i	−0.0383770	−	0.130700i
$287$	29.9306	−	2.14068i	1.76675	−	0.126360i
$288$	−0.997452	+	0.0713392i	−0.0587754	+	0.00420370i
$289$	−13.0830	−	44.5567i	−0.769589	−	2.62098i
$290$	−0.401926	−	6.84963i	−0.0236019	−	0.402224i
$291$	−4.00251	−	6.22803i	−0.234631	−	0.365094i
$292$	3.63103	−	1.98269i	0.212490	−	0.116028i
$293$	−3.41712	−	2.55802i	−0.199630	−	0.149441i	0.494786	−	0.869015i	$-0.335246\pi$
$293$	−3.41712	−	2.55802i	−0.199630	−	0.149441i	−0.694416	+	0.719574i	$0.744337\pi$
$294$	−6.73642	−	3.07642i	−0.392876	−	0.179420i
$295$	17.8390	−	4.99110i	1.03862	−	0.290593i
$296$	−2.25794	+	3.51343i	−0.131240	+	0.204214i
$297$	−0.0778014	+	1.08781i	−0.00451449	+	0.0631209i
$298$	−11.3302	+	11.3302i	−0.656340	+	0.656340i
$299$	−7.61104	+	6.68544i	−0.440158	+	0.386629i
$300$	−0.229033	−	4.99475i	−0.0132232	−	0.288372i
$301$	18.2215	+	21.0287i	1.05027	+	1.21207i
$302$	−12.2237	+	2.65911i	−0.703396	+	0.153014i
$303$	−7.69651	+	5.76154i	−0.442153	+	0.330992i
$304$	1.27232	−	2.78600i	0.0729728	−	0.159788i
$305$	10.1695	−	6.35327i	0.582304	−	0.363787i
$306$	−2.24394	+	7.64215i	−0.128277	+	0.436873i
$307$	4.44894	−	20.4515i	0.253915	−	1.16723i	−0.656759	−	0.754100i	$-0.728073\pi$
$307$	4.44894	−	20.4515i	0.253915	−	1.16723i	0.910674	−	0.413126i	$-0.135563\pi$
$308$	−1.44653	+	3.87830i	−0.0824238	+	0.220987i
$309$	15.5544	−	4.56718i	0.884859	−	0.259818i
$310$	−5.83073	−	11.0107i	−0.331163	−	0.625363i
$311$	4.09723	−	4.72846i	0.232333	−	0.268126i	−0.627597	−	0.778538i	$-0.715962\pi$
$311$	4.09723	−	4.72846i	0.232333	−	0.268126i	0.859930	+	0.510412i	$0.170507\pi$
$312$	−1.01232	+	1.85393i	−0.0573116	+	0.104958i
$313$	−25.2039	−	9.40056i	−1.42461	−	0.531351i	−0.485275	−	0.874361i	$-0.661281\pi$
$313$	−25.2039	−	9.40056i	−1.42461	−	0.531351i	−0.939332	+	0.343010i	$0.888553\pi$
$314$	5.97207	−	3.83802i	0.337023	−	0.216592i
$315$	5.17251	−	6.72855i	0.291438	−	0.379111i
$316$	−14.6497	+	2.10630i	−0.824107	+	0.118489i
$317$	0.874729	+	2.34524i	0.0491297	+	0.131722i	0.959197	−	0.282739i	$-0.0912430\pi$
$317$	0.874729	+	2.34524i	0.0491297	+	0.131722i	−0.910067	+	0.414461i	$0.863970\pi$
$318$	5.84520	+	7.80828i	0.327783	+	0.437867i
$319$	−2.81523	−	1.80924i	−0.157623	−	0.101298i
$320$	0.954831	−	2.02195i	0.0533767	−	0.113031i
$321$			0.601000i			0.0335445i
$322$	18.1469	−	1.42102i	1.01129	−	0.0791904i
$323$	−17.2494	−	17.2494i	−0.959784	−	0.959784i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	−9.13719	−	5.29703i	−0.506840	−	0.293826i
$326$	2.39690	−	16.6708i	0.132752	−	0.923309i
$327$	−7.80811	+	2.91227i	−0.431789	+	0.161049i
$328$	−4.73789	+	6.32908i	−0.261606	+	0.349465i
$329$	−13.4390	−	3.94603i	−0.740914	−	0.217552i
$330$	−2.03447	−	1.34454i	−0.111994	−	0.0740147i
$331$	9.44956	+	20.6916i	0.519395	+	1.13732i	0.969668	+	0.244425i	$0.0785993\pi$
$331$	9.44956	+	20.6916i	0.519395	+	1.13732i	−0.450273	+	0.892891i	$0.648673\pi$
$332$	−1.03266	−	0.563875i	−0.0566746	−	0.0309467i
$333$	−0.297943	−	4.16578i	−0.0163272	−	0.228283i
$334$	18.9090	+	16.3847i	1.03465	+	0.896531i
$335$	0.280609	+	0.0236800i	0.0153313	+	0.00129378i
$336$	3.45249	−	1.57670i	0.188349	−	0.0860160i
$337$	23.2975	+	5.06805i	1.26909	+	0.276074i	0.796194	−	0.605042i	$-0.206844\pi$
$337$	23.2975	+	5.06805i	1.26909	+	0.276074i	0.472900	+	0.881116i	$0.343207\pi$
$338$	−4.09189	−	7.49374i	−0.222570	−	0.407606i
$339$	2.56853	+	17.8645i	0.139503	+	0.970266i
$340$	−12.4313	−	12.7534i	−0.674184	−	0.691652i
$341$	−6.01480	−	0.864798i	−0.325720	−	0.0468314i
$342$	0.651041	+	2.99279i	0.0352042	+	0.161831i
$343$	1.53573	+	0.109838i	0.0829216	+	0.00593067i
$344$	−7.33108			−0.395265
$345$	−1.59026	+	10.6052i	−0.0856165	+	0.570967i
$346$	14.9070			0.801403
$347$	−10.8491	−	0.775945i	−0.582412	−	0.0416549i	−0.222975	−	0.974824i	$-0.571577\pi$
$347$	−10.8491	−	0.775945i	−0.582412	−	0.0416549i	−0.359437	+	0.933169i	$0.617031\pi$
$348$	0.652260	+	2.99839i	0.0349648	+	0.160731i
$349$	6.80667	+	0.978651i	0.364353	+	0.0523860i	0.322060	−	0.946719i	$-0.395625\pi$
$349$	6.80667	+	0.978651i	0.364353	+	0.0523860i	0.0422926	+	0.999105i	$0.486534\pi$
$350$	7.43944	+	17.4584i	0.397655	+	0.933191i
$351$	−0.300614	−	2.09081i	−0.0160456	−	0.111599i
$352$	−0.522661	−	0.957183i	−0.0278579	−	0.0510180i
$353$	−9.42090	−	2.04939i	−0.501424	−	0.109078i	−0.0452625	−	0.998975i	$-0.514412\pi$
$353$	−9.42090	−	2.04939i	−0.501424	−	0.109078i	−0.456162	+	0.889897i	$0.650776\pi$
$354$	−7.53557	+	3.44138i	−0.400511	+	0.182907i
$355$	10.5623	−	8.91837i	0.560589	−	0.473338i
$356$	1.40995	+	1.22173i	0.0747272	+	0.0647515i
$357$	−2.15659	−	30.1531i	−0.114139	−	1.59587i
$358$	20.2313	+	11.0471i	1.06926	+	0.583859i
$359$	6.38997	+	13.9921i	0.337250	+	0.738474i	0.999946	−	0.0104144i	$-0.00331507\pi$
$359$	6.38997	+	13.9921i	0.337250	+	0.738474i	−0.662696	+	0.748889i	$0.730588\pi$
$360$	0.447330	+	2.19087i	0.0235763	+	0.115469i
$361$	9.22973	+	2.71009i	0.485775	+	0.142636i
$362$	−1.46043	+	1.95090i	−0.0767584	+	0.102537i
$363$	9.19206	−	3.42846i	0.482458	−	0.179948i
$364$	1.14097	−	7.93564i	0.0598032	−	0.415940i
$365$	−5.44863	−	7.47593i	−0.285195	−	0.391308i
$366$	−4.05272	+	3.51170i	−0.211839	+	0.183560i
$367$	−9.77773	−	9.77773i	−0.510394	−	0.510394i	0.404253	−	0.914647i	$-0.367531\pi$
$367$	−9.77773	−	9.77773i	−0.510394	−	0.510394i	−0.914647	+	0.404253i	$0.867531\pi$
$368$	−2.84807	+	3.85856i	−0.148466	+	0.201142i
$369$		−	7.90600i		−	0.411570i
$370$	8.44453	+	3.98778i	0.439010	+	0.207315i
$371$	−31.1433	−	20.0146i	−1.61688	−	1.03911i
$372$	3.33913	+	4.46056i	0.173126	+	0.231269i
$373$	−2.21892	−	5.94914i	−0.114891	−	0.308035i	0.866759	−	0.498728i	$-0.166199\pi$
$373$	−2.21892	−	5.94914i	−0.114891	−	0.308035i	−0.981650	+	0.190693i	$0.938927\pi$
$374$	−8.59785	+	1.23618i	−0.444584	+	0.0639215i
$375$	−11.0080	+	1.95577i	−0.568448	+	0.100995i
$376$	3.10445	−	1.99511i	0.160100	−	0.102890i
$377$	6.07300	+	2.26511i	0.312775	+	0.116659i
$378$	−1.81898	+	3.33121i	−0.0935582	+	0.171339i
$379$	−1.35947	+	1.56891i	−0.0698313	+	0.0805896i	−0.789590	−	0.613634i	$-0.789707\pi$
$379$	−1.35947	+	1.56891i	−0.0698313	+	0.0805896i	0.719759	+	0.694224i	$0.244252\pi$
$380$	−6.54596	−	2.01334i	−0.335800	−	0.103282i
$381$	−6.15360	+	1.80686i	−0.315259	+	0.0925683i
$382$	2.17435	−	5.82967i	0.111250	−	0.298272i
$383$	0.187281	−	0.860916i	0.00956961	−	0.0439908i	−0.972114	−	0.234507i	$-0.924652\pi$
$383$	0.187281	−	0.860916i	0.00956961	−	0.0439908i	0.981684	+	0.190516i	$0.0610161\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	9.01831	+	2.08294i	0.459615	+	0.106157i
$386$	4.94039	−	10.8179i	0.251459	−	0.550619i
$387$	5.86883	−	4.39335i	0.298329	−	0.223327i
$388$	−7.23409	+	1.57368i	−0.367255	+	0.0798914i
$389$	−20.4642	−	23.6169i	−1.03757	−	1.19742i	−0.979982	−	0.199085i	$-0.936203\pi$
$389$	−20.4642	−	23.6169i	−1.03757	−	1.19742i	−0.0575923	−	0.998340i	$-0.518342\pi$
$390$	4.40400	+	1.70707i	0.223005	+	0.0864411i
$391$	20.8676	+	31.9939i	1.05532	+	1.61800i
$392$	−5.23659	+	5.23659i	−0.264488	+	0.264488i
$393$	1.42457	−	19.9181i	0.0718601	−	1.00474i
$394$	5.71998	−	8.90046i	0.288168	−	0.448399i
$395$	8.91695	+	31.8706i	0.448661	+	1.60358i
$396$	0.992030	+	0.453045i	0.0498514	+	0.0227664i
$397$	−2.12060	−	1.58746i	−0.106430	−	0.0796724i	0.544737	−	0.838607i	$-0.316629\pi$
$397$	−2.12060	−	1.58746i	−0.106430	−	0.0796724i	−0.651167	+	0.758934i	$0.725720\pi$
$398$	−18.6254	+	10.1703i	−0.933608	+	0.509789i
$399$	−6.28479	−	9.77933i	−0.314633	−	0.489579i
$400$	−4.75987	−	1.53089i	−0.237994	−	0.0765447i
$401$	−9.24389	−	31.4818i	−0.461618	−	1.57213i	−0.781020	−	0.624506i	$-0.785300\pi$
$401$	−9.24389	−	31.4818i	−0.461618	−	1.57213i	0.319402	−	0.947619i	$-0.396518\pi$
$402$	−0.125617	+	0.00898434i	−0.00626523	+	0.000448098i
$403$	11.7397	−	0.839638i	0.584795	−	0.0418253i
$404$	2.70861	+	9.22469i	0.134759	+	0.458946i
$405$	−1.67104	−	1.48580i	−0.0830348	−	0.0738302i
$406$	−6.29656	−	9.79764i	−0.312493	−	0.486249i
$407$	3.99760	−	2.18285i	0.198154	−	0.108200i
$408$	6.37613	+	4.77311i	0.315666	+	0.236304i
$409$	19.8746	+	9.07644i	0.982738	+	0.448801i	0.840960	−	0.541097i	$-0.181991\pi$
$409$	19.8746	+	9.07644i	0.982738	+	0.448801i	0.141778	+	0.989899i	$0.454718\pi$
$410$	15.4063	+	8.67007i	0.760864	+	0.428184i
$411$	−5.30588	+	8.25612i	−0.261720	+	0.407244i
$412$	1.15648	−	16.1698i	0.0569759	−	0.796627i
$413$	22.2332	−	22.2332i	1.09402	−	1.09402i
$414$	−0.0323578	−	4.79572i	−0.00159030	−	0.235697i
$415$	−0.950858	+	2.45307i	−0.0466758	+	0.120417i
$416$	1.38327	+	1.59638i	0.0678204	+	0.0782690i
$417$	−6.14117	+	1.33593i	−0.300734	+	0.0654207i
$418$	−2.67398	+	2.00172i	−0.130789	+	0.0979072i
$419$	15.6924	−	34.3616i	0.766625	−	1.67867i	0.0326800	−	0.999466i	$-0.489596\pi$
$419$	15.6924	−	34.3616i	0.766625	−	1.67867i	0.733945	−	0.679209i	$-0.237677\pi$
$420$	−4.49671	−	7.19777i	−0.219417	−	0.351215i
$421$	6.28059	−	21.3897i	0.306097	−	1.04247i	−0.652520	−	0.757772i	$-0.726288\pi$
$421$	6.28059	−	21.3897i	0.306097	−	1.04247i	0.958617	−	0.284699i	$-0.0918937\pi$
$422$	0.467289	−	2.14809i	0.0227473	−	0.104568i
$423$	−1.28961	+	3.45759i	−0.0627032	+	0.168114i
$424$	9.35865	−	2.74795i	0.454496	−	0.133452i
$425$	−24.6731	+	31.2599i	−1.19682	+	1.51633i
$426$	−4.04850	+	4.67221i	−0.196150	+	0.226369i
$427$	9.75430	−	17.8637i	0.472044	−	0.864484i
$428$	0.563107	+	0.210028i	0.0272188	+	0.0101521i
$429$	1.93796	−	1.24545i	0.0935655	−	0.0601309i
$430$	2.12525	+	16.2544i	0.102488	+	0.783859i
$431$	−36.8541	+	5.29881i	−1.77520	+	0.255235i	−0.950585	−	0.310463i	$-0.899516\pi$
$431$	−36.8541	+	5.29881i	−1.77520	+	0.255235i	−0.824612	+	0.565698i	$0.808607\pi$
$432$	−0.349464	−	0.936950i	−0.0168136	−	0.0450790i
$433$	21.2526	+	28.3901i	1.02133	+	1.36434i	0.929605	+	0.368559i	$0.120149\pi$
$433$	21.2526	+	28.3901i	1.02133	+	1.36434i	0.0917295	+	0.995784i	$0.470760\pi$
$434$	−17.7909	−	11.4335i	−0.853992	−	0.548828i
$435$	6.45893	−	2.31541i	0.309682	−	0.111015i
$436$			8.33354i			0.399104i
$437$	12.9391	+	6.95234i	0.618959	+	0.332576i
$438$	2.92536	+	2.92536i	0.139779	+	0.139779i
$439$	−7.09371	+	6.14673i	−0.338564	+	0.293367i	−0.807503	−	0.589863i	$-0.799182\pi$
$439$	−7.09371	+	6.14673i	−0.338564	+	0.293367i	0.468939	+	0.883230i	$0.344636\pi$
$440$	−1.97074	+	1.43633i	−0.0939516	+	0.0684741i
$441$	1.05393	−	7.33028i	0.0501874	−	0.349061i
$442$	15.7633	−	5.87942i	0.749786	−	0.279656i
$443$	18.0481	−	24.1095i	0.857492	−	1.14548i	−0.130573	−	0.991439i	$-0.541682\pi$
$443$	18.0481	−	24.1095i	0.857492	−	1.14548i	0.988065	−	0.154037i	$-0.0492275\pi$
$444$	−4.00725	−	1.17663i	−0.190176	−	0.0558406i
$445$	2.30007	−	3.48031i	0.109034	−	0.164982i
$446$	3.48083	+	7.62195i	0.164822	+	0.360910i
$447$	−14.0633	−	7.67915i	−0.665172	−	0.363211i
$448$	−0.270766	−	3.78581i	−0.0127925	−	0.178863i
$449$	10.4448	+	9.05050i	0.492922	+	0.427119i	0.865521	−	0.500873i	$-0.166988\pi$
$449$	10.4448	+	9.05050i	0.492922	+	0.427119i	−0.372599	+	0.927993i	$0.621533\pi$
$450$	4.72790	−	1.62694i	0.222875	−	0.0766947i
$451$	7.84299	−	3.58177i	0.369312	−	0.168659i
$452$	17.6357	+	3.83642i	0.829516	+	0.180450i
$453$	−5.99522	−	10.9794i	−0.281680	−	0.515858i
$454$	1.12271	+	7.80863i	0.0526914	+	0.366477i
$455$	−17.9256	−	0.229256i	−0.840366	−	0.0107477i
$456$	3.03161	+	0.435879i	0.141968	+	0.0204119i
$457$	6.53397	+	30.0362i	0.305646	+	1.40503i	0.832004	+	0.554769i	$0.187193\pi$
$457$	6.53397	+	30.0362i	0.305646	+	1.40503i	−0.526358	+	0.850263i	$0.676443\pi$
$458$	4.26101	+	0.304753i	0.199104	+	0.0142402i
$459$	−7.96478			−0.371764
$460$	9.38084	+	5.19614i	0.437384	+	0.242271i
$461$	29.9499			1.39491			0.697453	−	0.716630i	$-0.254316\pi$
$461$	29.9499			1.39491			0.697453	+	0.716630i	$0.254316\pi$
$462$	−4.12874	−	0.295293i	−0.192086	−	0.0137383i
$463$	−3.18494	−	14.6409i	−0.148017	−	0.680423i	−0.990017	−	0.140946i	$-0.954986\pi$
$463$	−3.18494	−	14.6409i	−0.148017	−	0.680423i	0.842000	−	0.539477i	$-0.181378\pi$
$464$	3.03728	+	0.436695i	0.141002	+	0.0202731i
$465$	8.92194	−	8.69661i	0.413745	−	0.403295i
$466$	−3.94343	−	27.4272i	−0.182676	−	1.27054i
$467$	12.5931	+	23.0625i	0.582739	+	1.06721i	0.988211	+	0.153099i	$0.0489252\pi$
$467$	12.5931	+	23.0625i	0.582739	+	1.06721i	−0.405472	+	0.914107i	$0.632893\pi$
$468$	−2.06404	−	0.449005i	−0.0954103	−	0.0207552i
$469$	0.434801	−	0.198567i	0.0200772	−	0.00916896i
$470$	−5.32351	−	6.30479i	−0.245555	−	0.290818i
$471$	5.36508	+	4.64887i	0.247210	+	0.214208i
$472$	0.590988	+	8.26309i	0.0272024	+	0.380340i
$473$	7.01718	+	3.83167i	0.322650	+	0.176180i
$474$	−6.14827	−	13.4628i	−0.282399	−	0.618368i
$475$	−2.56634	+	15.0973i	−0.117752	+	0.692713i
$476$	−29.0056	−	8.51682i	−1.32947	−	0.390368i
$477$	−5.84520	+	7.80828i	−0.267634	+	0.357517i
$478$	16.2349	−	6.05530i	0.742566	−	0.276963i
$479$	−3.67809	+	25.5817i	−0.168056	+	1.16886i	0.714840	+	0.699288i	$0.246499\pi$
$479$	−3.67809	+	25.5817i	−0.168056	+	1.16886i	−0.882896	+	0.469568i	$0.844410\pi$
$480$	2.20906	+	0.346504i	0.100829	+	0.0158157i
$481$	−6.66716	+	5.77712i	−0.303996	+	0.263414i
$482$	13.8590	+	13.8590i	0.631258	+	0.631258i
$483$	6.47604	+	17.0115i	0.294670	+	0.774050i
$484$		−	9.81063i		−	0.445938i
$485$	5.58628	+	15.5832i	0.253660	+	0.707596i
$486$	0.841254	+	0.540641i	0.0381600	+	0.0245240i
$487$	11.4835	+	15.3401i	0.520366	+	0.695128i	0.981339	−	0.192286i	$-0.0615902\pi$
$487$	11.4835	+	15.3401i	0.520366	+	0.695128i	−0.460973	+	0.887414i	$0.652499\pi$
$488$	1.87401	+	5.02441i	0.0848323	+	0.227444i
$489$	16.6708	−	2.39690i	0.753878	−	0.108391i
$490$	13.1286	+	10.0925i	0.593090	+	0.455932i
$491$	−14.4234	+	9.26936i	−0.650919	+	0.418321i	−0.824002	−	0.566587i	$-0.808264\pi$
$491$	−14.4234	+	9.26936i	−0.650919	+	0.418321i	0.173083	+	0.984907i	$0.444627\pi$
$492$	−7.40753	−	2.76287i	−0.333957	−	0.124560i
$493$	11.7129	−	21.4505i	0.527521	−	0.966083i
$494$	4.23665	−	4.88936i	0.190616	−	0.219983i
$495$	0.716905	−	2.33086i	0.0322225	−	0.104764i
$496$	5.34623	−	1.56979i	0.240053	−	0.0704858i
$497$	8.20000	−	21.9851i	0.367820	−	0.986164i
$498$	0.250100	−	1.14969i	0.0112073	−	0.0515189i
$499$	−0.625577	+	2.13052i	−0.0280047	+	0.0953752i	−0.972310	−	0.233697i	$-0.924918\pi$
$499$	−0.625577	+	2.13052i	−0.0280047	+	0.0953752i	0.944305	+	0.329072i	$0.106736\pi$
$500$	−2.01443	+	10.9974i	−0.0900880	+	0.491817i
$501$	−10.3937	+	22.7591i	−0.464358	+	1.01680i
$502$	1.66489	−	1.24632i	0.0743078	−	0.0556261i
$503$	−18.2372	+	3.96725i	−0.813155	+	0.176891i	−0.599868	−	0.800099i	$-0.704780\pi$
$503$	−18.2372	+	3.96725i	−0.813155	+	0.176891i	−0.213286	+	0.976990i	$0.568417\pi$
$504$	2.48551	+	2.86843i	0.110713	+	0.127770i
$505$	19.6677	−	8.67973i	0.875203	−	0.386243i
$506$	4.74284	−	2.20478i	0.210845	−	0.0980143i
$507$	6.03737	−	6.03737i	0.268129	−	0.268129i
$508$	−0.457526	+	6.39705i	−0.0202994	+	0.283823i
$509$	−0.766973	+	1.19343i	−0.0339955	+	0.0528980i	−0.857835	−	0.513925i	$-0.828191\pi$
$509$	−0.766973	+	1.19343i	−0.0339955	+	0.0528980i	0.823840	+	0.566823i	$0.191827\pi$
$510$	8.73452	−	15.5208i	0.386771	−	0.687275i
$511$	−14.2832	−	6.52293i	−0.631852	−	0.288557i
$512$	0.800541	+	0.599278i	0.0353793	+	0.0264846i
$513$	−2.68814	+	1.46783i	−0.118684	+	0.0648065i
$514$	−4.22037	−	6.56703i	−0.186153	−	0.289659i
$515$	−36.1868	+	2.12339i	−1.59458	+	0.0935675i
$516$	−2.06540	−	7.03412i	−0.0909243	−	0.309660i
$517$	−4.01429	+	0.287107i	−0.176548	+	0.0126270i
$518$	15.8111	−	1.13083i	0.694701	−	0.0496860i
$519$	4.19978	+	14.3031i	0.184350	+	0.627837i
$520$	3.13848	−	3.52977i	0.137632	−	0.154791i
$521$	−4.24600	−	6.60690i	−0.186021	−	0.289454i	0.735701	−	0.677307i	$-0.236853\pi$
$521$	−4.24600	−	6.60690i	−0.186021	−	0.289454i	−0.921721	+	0.387853i	$0.873217\pi$
$522$	−2.69317	+	1.47058i	−0.117877	+	0.0643657i
$523$	19.4783	+	14.5813i	0.851728	+	0.637595i	0.933310	−	0.359071i	$-0.116907\pi$
$523$	19.4783	+	14.5813i	0.851728	+	0.637595i	−0.0815825	+	0.996667i	$0.525997\pi$
$524$	−18.1644	−	8.29542i	−0.793517	−	0.362387i
$525$	−14.6553	+	12.0567i	−0.639609	+	0.526197i
$526$	−10.6719	+	16.6059i	−0.465319	+	0.724051i
$527$	3.16597	−	44.2661i	0.137912	−	1.92826i
$528$	0.771159	−	0.771159i	0.0335604	−	0.0335604i
$529$	−17.5839	−	14.8259i	−0.764517	−	0.644603i
$530$	−8.80577	−	19.9534i	−0.382498	−	0.866719i
$531$	−5.42500	−	6.26078i	−0.235425	−	0.271695i
$532$	−11.3591	+	2.47101i	−0.492477	+	0.107132i
$533$	−13.3690	+	10.0079i	−0.579076	+	0.433491i
$534$	−0.775011	+	1.69704i	−0.0335380	+	0.0734380i
$535$	0.302431	−	1.30940i	0.0130752	−	0.0566105i
$536$	−0.0354809	+	0.120837i	−0.00153254	+	0.00521936i
$537$	−4.89983	+	22.5241i	−0.211443	+	0.971988i
$538$	−6.24731	+	16.7497i	−0.269341	+	0.722130i
$539$	7.74933	−	2.27541i	0.333787	−	0.0980088i
$540$	−1.97609	+	1.04645i	−0.0850375	+	0.0450320i
$541$	−3.13026	+	3.61251i	−0.134580	+	0.155314i	−0.819039	−	0.573737i	$-0.805493\pi$
$541$	−3.13026	+	3.61251i	−0.134580	+	0.155314i	0.684459	+	0.729051i	$0.260039\pi$
$542$	−14.0307	+	25.6954i	−0.602672	+	1.10371i
$543$	−2.28333	−	0.851638i	−0.0979870	−	0.0365473i
$544$	6.70040	−	4.30609i	0.287277	−	0.184622i
$545$	18.4771	−	2.41585i	0.791472	−	0.103484i
$546$	7.93564	−	1.14097i	0.339614	−	0.0488291i
$547$	0.461173	+	1.23645i	0.0197183	+	0.0528668i	0.946436	−	0.322892i	$-0.104655\pi$
$547$	0.461173	+	1.23645i	0.0197183	+	0.0528668i	−0.926718	+	0.375759i	$0.877382\pi$
$548$	5.88135	+	7.85656i	0.251239	+	0.335616i
$549$	−4.51123	−	2.89919i	−0.192535	−	0.123735i
$550$	3.75593	+	3.95314i	0.160153	+	0.168563i
$551$		−	9.39819i		−	0.400376i
$552$	−4.50466	−	1.64562i	−0.191731	−	0.0700420i
$553$	39.7212	+	39.7212i	1.68912	+	1.68912i
$554$	−1.15841	+	1.00376i	−0.0492160	+	0.0426459i
$555$	−1.44715	+	9.22596i	−0.0614280	+	0.391620i
$556$	−0.894419	+	6.22082i	−0.0379318	+	0.263822i
$557$	−38.1643	+	14.2345i	−1.61707	+	0.603137i	−0.985120	−	0.171869i	$-0.945019\pi$
$557$	−38.1643	+	14.2345i	−1.61707	+	0.603137i	−0.631954	+	0.775006i	$0.717747\pi$
$558$	−3.33913	+	4.46056i	−0.141357	+	0.188830i
$559$	−14.8583	−	4.36278i	−0.628438	−	0.184526i
$560$	−8.31539	+	1.69783i	−0.351389	+	0.0717464i
$561$	−3.60840	−	7.90130i	−0.152347	−	0.333593i
$562$	1.93591	+	1.05709i	0.0816613	+	0.0445905i
$563$	−3.24999	−	45.4407i	−0.136971	−	1.91510i	−0.347787	−	0.937574i	$-0.613067\pi$
$563$	−3.24999	−	45.4407i	−0.136971	−	1.91510i	0.210816	−	0.977526i	$-0.432388\pi$
$564$	2.78891	+	2.41661i	0.117434	+	0.101758i
$565$	3.39358	−	40.2141i	0.142769	−	1.69182i
$566$	1.79278	−	0.818735i	0.0753562	−	0.0344140i
$567$	−3.70874	−	0.806787i	−0.155752	−	0.0338819i
$568$	2.96282	+	5.42601i	0.124317	+	0.227670i
$569$	−2.37460	−	16.5157i	−0.0995483	−	0.692374i	−0.977083	−	0.212860i	$-0.931722\pi$
$569$	−2.37460	−	16.5157i	−0.0995483	−	0.692374i	0.877534	−	0.479514i	$-0.159187\pi$
$570$	0.0875812	−	6.84802i	0.00366837	−	0.286832i
$571$	46.9340	+	6.74809i	1.96413	+	0.282399i	0.999847	+	0.0175182i	$0.00557651\pi$
$571$	46.9340	+	6.74809i	1.96413	+	0.282399i	0.964281	+	0.264881i	$0.0853326\pi$
$572$	−0.489677	−	2.25101i	−0.0204744	−	0.0941194i
$573$	6.20611	+	0.443870i	0.259264	+	0.0185429i
$574$	30.0071			1.25247
$575$	8.80141	−	22.3055i	0.367044	−	0.930204i
$576$	−1.00000			−0.0416667
$577$	−45.0321	−	3.22076i	−1.87471	−	0.134082i	−0.912966	−	0.408035i	$-0.866214\pi$
$577$	−45.0321	−	3.22076i	−1.87471	−	0.134082i	−0.961743	+	0.273953i	$0.911669\pi$
$578$	−9.87105	−	45.3765i	−0.410581	−	1.88741i
$579$	11.7716	+	1.69250i	0.489212	+	0.0703380i
$580$	0.0877452	−	6.86085i	0.00364342	−	0.284881i
$581$	0.635533	+	4.42023i	0.0263664	+	0.183382i
$582$	−3.54801	−	6.49770i	−0.147070	−	0.269338i
$583$	−10.3942	−	2.26112i	−0.430483	−	0.0936459i
$584$	3.76322	−	1.71860i	0.155723	−	0.0711164i
$585$	−0.397176	+	4.70655i	−0.0164212	+	0.194592i
$586$	−3.22592	−	2.79528i	−0.133262	−	0.115472i
$587$	−1.67825	−	23.4650i	−0.0692689	−	0.968505i	−0.906649	−	0.421885i	$-0.861369\pi$
$587$	−1.67825	−	23.4650i	−0.0692689	−	0.968505i	0.837380	−	0.546620i	$-0.184086\pi$
$588$	−6.49979	−	3.54915i	−0.268047	−	0.146365i
$589$	−7.08930	−	15.5234i	−0.292110	−	0.639631i
$590$	18.1496	−	3.70577i	0.747206	−	0.152564i
$591$	10.1514	+	2.98073i	0.417574	+	0.122611i
$592$	−2.50284	+	3.34340i	−0.102866	+	0.137413i
$593$	5.41564	−	2.01993i	0.222394	−	0.0829486i	−0.235797	−	0.971802i	$-0.575770\pi$
$593$	5.41564	−	2.01993i	0.222394	−	0.0829486i	0.458191	+	0.888854i	$0.348497\pi$
$594$	−0.155206	+	1.07948i	−0.00636819	+	0.0442917i
$595$	−10.4749	+	66.7801i	−0.429428	+	2.73772i
$596$	−12.1096	+	10.4930i	−0.496029	+	0.429811i
$597$	−15.0057	−	15.0057i	−0.614141	−	0.614141i
$598$	−8.06858	+	6.12544i	−0.329949	+	0.250488i
$599$		−	4.93153i		−	0.201497i	−0.994912	−	0.100748i	$-0.967876\pi$
$599$		−	4.93153i		−	0.201497i	0.994912	−	0.100748i	$-0.0321237\pi$
$600$	0.127872	−	4.99836i	0.00522034	−	0.204057i
$601$	−26.3091	−	16.9078i	−1.07317	−	0.689685i	−0.120200	−	0.992750i	$-0.538354\pi$
$601$	−26.3091	−	16.9078i	−1.07317	−	0.689685i	−0.952970	+	0.303065i	$0.901990\pi$
$602$	16.6749	+	22.2750i	0.679617	+	0.907862i
$603$	−0.0440109	−	0.117998i	−0.00179226	−	0.00480524i
$604$	−12.3823	+	1.78030i	−0.503828	+	0.0724395i
$605$	−21.7521	+	2.84406i	−0.884348	+	0.115627i
$606$	−8.08792	+	5.19779i	−0.328549	+	0.211146i
$607$	−35.4558	−	13.2243i	−1.43910	−	0.536758i	−0.495727	−	0.868479i	$-0.665098\pi$
$607$	−35.4558	−	13.2243i	−1.43910	−	0.536758i	−0.943378	+	0.331720i	$0.892371\pi$
$608$	1.46783	−	2.68814i	0.0595285	−	0.109018i
$609$	7.62682	−	8.80182i	0.309055	−	0.356668i
$610$	10.5968	−	5.61159i	0.429053	−	0.227207i
$611$	7.47924	−	2.19610i	0.302578	−	0.0888448i
$612$	−2.78341	+	7.46260i	−0.112512	+	0.301658i
$613$	−7.23397	+	33.2540i	−0.292177	+	1.34312i	0.563718	+	0.825967i	$0.309370\pi$
$613$	−7.23397	+	33.2540i	−0.292177	+	1.34312i	−0.855895	+	0.517149i	$0.826993\pi$
$614$	5.89660	−	20.0820i	0.237967	−	0.810442i
$615$	−3.97841	+	17.2249i	−0.160425	+	0.694575i
$616$	−1.71952	+	3.76523i	−0.0692815	+	0.151705i
$617$	−26.4408	+	19.7933i	−1.06447	+	0.796849i	−0.979884	−	0.199568i	$-0.936046\pi$
$617$	−26.4408	+	19.7933i	−1.06447	+	0.796849i	−0.0845811	+	0.996417i	$0.526955\pi$
$618$	15.8406	−	3.44591i	0.637202	−	0.138615i
$619$	−9.56034	−	11.0332i	−0.384262	−	0.443462i	0.530359	−	0.847773i	$-0.322057\pi$
$619$	−9.56034	−	11.0332i	−0.384262	−	0.443462i	−0.914622	+	0.404310i	$0.867512\pi$
$620$	−5.03039	−	11.3986i	−0.202025	−	0.457777i
$621$	4.59235	−	1.38216i	0.184284	−	0.0554641i
$622$	4.42412	−	4.42412i	0.177391	−	0.177391i
$623$	0.505150	−	7.06292i	0.0202384	−	0.282970i
$624$	−1.14200	+	1.77699i	−0.0457167	+	0.0711366i
$625$	24.9673	+	1.27830i	0.998692	+	0.0511320i
$626$	−24.4690	−	11.1746i	−0.977979	−	0.446628i
$627$	−2.67398	−	2.00172i	−0.106789	−	0.0799409i
$628$	6.23066	−	3.40220i	0.248630	−	0.135762i
$629$	17.9840	+	27.9837i	0.717070	+	1.11578i
$630$	5.63934	−	6.34241i	0.224677	−	0.252688i
$631$	−2.78203	−	9.47471i	−0.110751	−	0.377182i	0.885401	−	0.464828i	$-0.153884\pi$
$631$	−2.78203	−	9.47471i	−0.110751	−	0.377182i	−0.996152	+	0.0876457i	$0.972066\pi$
$632$	−14.7626	+	1.05584i	−0.587224	+	0.0419991i
$633$	2.19273	−	0.156827i	0.0871533	−	0.00623332i
$634$	0.705193	+	2.40167i	0.0280068	+	0.0953824i
$635$	14.3161	−	0.840050i	0.568119	−	0.0333364i
$636$	5.27328	+	8.20538i	0.209099	+	0.325364i
$637$	−13.7296	+	7.49692i	−0.543986	+	0.297039i
$638$	−2.67899	−	2.00547i	−0.106062	−	0.0793972i
$639$	−5.62355	−	2.56819i	−0.222464	−	0.101596i
$640$	1.09664	−	1.94869i	0.0433486	−	0.0770285i
$641$	−9.98047	+	15.5299i	−0.394205	+	0.613395i	−0.980457	−	0.196734i	$-0.936967\pi$
$641$	−9.98047	+	15.5299i	−0.394205	+	0.613395i	0.586252	+	0.810129i	$0.300603\pi$
$642$	−0.0428748	+	0.599468i	−0.00169213	+	0.0236591i
$643$	−19.2620	+	19.2620i	−0.759621	+	0.759621i	−0.976253	−	0.216632i	$-0.930493\pi$
$643$	−19.2620	+	19.2620i	−0.759621	+	0.759621i	0.216632	+	0.976253i	$0.430493\pi$
$644$	18.2021	−	0.122813i	0.717262	−	0.00483952i
$645$	−14.9973	+	6.61856i	−0.590517	+	0.260606i
$646$	−15.9749	−	18.4360i	−0.628525	−	0.725356i
$647$	−33.0727	+	7.19453i	−1.30022	+	0.282846i	−0.808805	−	0.588077i	$-0.799885\pi$
$647$	−33.0727	+	7.19453i	−1.30022	+	0.282846i	−0.491419	+	0.870923i	$0.663522\pi$
$648$	0.800541	−	0.599278i	0.0314482	−	0.0235419i
$649$	3.75311	−	8.21817i	0.147323	−	0.322592i
$650$	−8.73602	−	5.93537i	−0.342655	−	0.232805i
$651$	5.95812	−	20.2915i	0.233517	−	0.795286i
$652$	3.58007	−	16.4573i	0.140206	−	0.644518i
$653$	−15.3873	+	41.2548i	−0.602150	+	1.61443i	0.174616	+	0.984637i	$0.444131\pi$
$653$	−15.3873	+	41.2548i	−0.602150	+	1.61443i	−0.776766	+	0.629789i	$0.783141\pi$
$654$	−7.99597	+	2.34783i	−0.312667	+	0.0918074i
$655$	−13.1268	+	42.6789i	−0.512906	+	1.66760i
$656$	−5.17733	+	5.97496i	−0.202141	+	0.233283i
$657$	−1.98269	+	3.63103i	−0.0773521	+	0.141660i
$658$	−13.1232	−	4.89470i	−0.511596	−	0.190815i
$659$	−16.8484	+	10.8278i	−0.656320	+	0.421791i	−0.825971	−	0.563713i	$-0.809372\pi$
$659$	−16.8484	+	10.8278i	−0.656320	+	0.421791i	0.169651	+	0.985504i	$0.445736\pi$
$660$	−1.93337	−	1.48626i	−0.0752562	−	0.0578524i
$661$	27.0339	−	3.88689i	1.05150	−	0.151183i	0.405169	−	0.914242i	$-0.367213\pi$
$661$	27.0339	−	3.88689i	1.05150	−	0.151183i	0.646328	+	0.763059i	$0.276304\pi$
$662$	7.94936	+	21.3131i	0.308961	+	0.828355i
$663$	10.0823	+	13.4684i	0.391565	+	0.523069i
$664$	−0.989802	−	0.636107i	−0.0384118	−	0.0246858i
$665$	8.77165	+	24.4689i	0.340150	+	0.948864i
$666$		−	4.17642i		−	0.161833i
$667$	−3.03104	+	14.4006i	−0.117362	+	0.557592i
$668$	17.6919	+	17.6919i	0.684521	+	0.684521i
$669$	−6.33254	+	5.48718i	−0.244830	+	0.212147i
$670$	0.278205	+	0.0436381i	0.0107480	+	0.00168589i
$671$	0.832296	−	5.78875i	0.0321304	−	0.223472i
$672$	3.55617	−	1.32638i	0.137182	−	0.0511664i
$673$	−17.8557	+	23.8524i	−0.688285	+	0.919441i	−0.999523	−	0.0308910i	$-0.990166\pi$
$673$	−17.8557	+	23.8524i	−0.688285	+	0.919441i	0.311238	+	0.950332i	$0.399256\pi$
$674$	22.8766	+	6.71716i	0.881172	+	0.258735i
$675$	2.89304	+	4.07803i	0.111353	+	0.156963i
$676$	−3.54687	−	7.76656i	−0.136418	−	0.298714i
$677$	−10.8817	−	5.94184i	−0.418217	−	0.228363i	0.256340	−	0.966587i	$-0.417483\pi$
$677$	−10.8817	−	5.94184i	−0.418217	−	0.228363i	−0.674557	+	0.738223i	$0.735665\pi$
$678$	1.28754	+	18.0022i	0.0494478	+	0.691371i
$679$	21.2358	+	18.4009i	0.814954	+	0.706162i
$680$	−11.4899	−	13.6078i	−0.440616	−	0.521835i
$681$	−7.17602	+	3.27718i	−0.274986	+	0.125582i
$682$	−5.93778	−	1.29169i	−0.227369	−	0.0494612i
$683$	−13.4641	−	24.6577i	−0.515191	−	0.943502i	−0.997711	−	0.0676172i	$-0.978460\pi$
$683$	−13.4641	−	24.6577i	−0.515191	−	0.943502i	0.482520	−	0.875885i	$-0.339721\pi$
$684$	0.435879	+	3.03161i	0.0166663	+	0.115916i
$685$	15.7146	−	15.3177i	0.600423	−	0.585259i
$686$	1.52398	+	0.219115i	0.0581859	+	0.00836586i
$687$	0.908056	+	4.17427i	0.0346445	+	0.159258i
$688$	−7.31240	−	0.522993i	−0.278783	−	0.0199389i
$689$	20.6030			0.784911
$690$	−2.34277	+	10.4648i	−0.0891879	+	0.398387i
$691$	−21.1019			−0.802754			−0.401377	−	0.915913i	$-0.631468\pi$
$691$	−21.1019			−0.802754			−0.401377	+	0.915913i	$0.631468\pi$
$692$	14.8690	+	1.06345i	0.565234	+	0.0404263i
$693$	−0.879869	−	4.04469i	−0.0334234	−	0.153645i
$694$	−10.7661	−	1.54794i	−0.408677	−	0.0587588i
$695$	14.0521	+	0.179716i	0.533026	+	0.00681701i
$696$	0.436695	+	3.03728i	0.0165529	+	0.115128i
$697$	30.1781	+	55.2671i	1.14308	+	2.09339i
$698$	6.71951	+	1.46174i	0.254337	+	0.0553277i
$699$	25.2052	−	11.5108i	0.953347	−	0.435379i
$700$	6.17502	+	17.9447i	0.233394	+	0.678244i
$701$	15.2422	+	13.2075i	0.575691	+	0.498839i	0.893347	−	0.449367i	$-0.148350\pi$
$701$	15.2422	+	13.2075i	0.575691	+	0.498839i	−0.317656	+	0.948206i	$0.602896\pi$
$702$	−0.150691	−	2.10693i	−0.00568745	−	0.0795210i
$703$	11.2268	+	6.13030i	0.423427	+	0.231208i
$704$	−0.453045	−	0.992030i	−0.0170748	−	0.0373885i
$705$	4.54960	−	6.88413i	0.171348	−	0.259271i
$706$	−9.25070	−	2.71625i	−0.348155	−	0.102227i
$707$	21.8678	−	29.2119i	0.822423	−	1.09863i
$708$	−7.76188	+	2.89503i	−0.291709	+	0.108802i
$709$	−1.20391	+	8.37338i	−0.0452138	+	0.314469i	0.954646	+	0.297742i	$0.0962336\pi$
$709$	−1.20391	+	8.37338i	−0.0452138	+	0.314469i	−0.999860	+	0.0167267i	$0.994675\pi$
$710$	11.1716	−	8.14214i	0.419263	−	0.305569i
$711$	11.1853	−	9.69214i	0.419482	−	0.363483i
$712$	1.31920	+	1.31920i	0.0494391	+	0.0494391i
$713$	5.85622	+	26.0724i	0.219317	+	0.976420i
$714$		−	30.2301i		−	1.13133i
$715$	−4.84897	+	1.73827i	−0.181341	+	0.0650075i
$716$	19.3917	+	12.4623i	0.724701	+	0.465737i
$717$	10.3839	+	13.8713i	0.387794	+	0.518032i
$718$	5.37551	+	14.4123i	0.200612	+	0.537862i
$719$	−10.9257	+	1.57088i	−0.407461	+	0.0585840i	−0.342998	−	0.939336i	$-0.611442\pi$
$719$	−10.9257	+	1.57088i	−0.407461	+	0.0585840i	−0.0644627	+	0.997920i	$0.520533\pi$
$720$	0.289895	+	2.21720i	0.0108038	+	0.0826300i
$721$	−51.7613	+	33.2649i	−1.92769	+	1.23885i
$722$	9.01288	+	3.36163i	0.335425	+	0.125107i
$723$	−9.39305	+	17.2021i	−0.349331	+	0.639753i
$724$	−1.59588	+	1.84175i	−0.0593105	+	0.0684480i
$725$	−15.2373	+	1.79438i	−0.565899	+	0.0666416i
$726$	9.41323	−	2.76397i	0.349358	−	0.102581i
$727$	−2.13903	+	5.73497i	−0.0793324	+	0.212698i	−0.970561	−	0.240857i	$-0.922572\pi$
$727$	−2.13903	+	5.73497i	−0.0793324	+	0.212698i	0.891228	+	0.453555i	$0.149844\pi$
$728$	1.70419	−	7.83402i	0.0631614	−	0.290348i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	−4.90142	−	7.84558i	−0.181410	−	0.290378i
$731$	−24.2563	+	53.1138i	−0.897150	+	1.96448i
$732$	−4.29291	+	3.21364i	−0.158671	+	0.118779i
$733$	−10.2800	+	2.23627i	−0.379699	+	0.0825985i	−0.398364	−	0.917227i	$-0.630422\pi$
$733$	−10.2800	+	2.23627i	−0.379699	+	0.0825985i	0.0186651	+	0.999826i	$0.494058\pi$
$734$	−9.05529	−	10.4504i	−0.334237	−	0.385730i
$735$	−5.98491	+	15.4402i	−0.220757	+	0.569520i
$736$	−3.11608	+	3.64555i	−0.114860	+	0.134377i
$737$	0.0971185	−	0.0971185i	0.00357741	−	0.00357741i
$738$	0.564008	−	7.88586i	0.0207614	−	0.290283i
$739$	20.1826	−	31.4048i	0.742431	−	1.15524i	−0.240389	−	0.970677i	$-0.577275\pi$
$739$	20.1826	−	31.4048i	0.742431	−	1.15524i	0.982820	−	0.184568i	$-0.0590886\pi$
$740$	8.13853	+	4.58005i	0.299178	+	0.168366i
$741$	5.88491	+	2.68755i	0.216188	+	0.0987296i
$742$	−29.6362	−	22.1853i	−1.08798	−	0.814450i
$743$	−28.3267	+	15.4676i	−1.03921	+	0.567449i	−0.905841	−	0.423618i	$-0.860760\pi$
$743$	−28.3267	+	15.4676i	−1.03921	+	0.567449i	−0.133365	+	0.991067i	$0.542578\pi$
$744$	3.01241	+	4.68740i	0.110440	+	0.171849i
$745$	26.7756	+	23.8075i	0.980983	+	0.872239i
$746$	−1.78886	−	6.09228i	−0.0654947	−	0.223054i
$747$	1.17358	−	0.0839363i	0.0429391	−	0.00307107i
$748$	−8.66413	+	0.619671i	−0.316792	+	0.0226574i
$749$	−0.642655	−	2.18868i	−0.0234821	−	0.0799727i
$750$	−11.1194	+	1.16549i	−0.406024	+	0.0425575i
$751$	−9.24313	−	14.3826i	−0.337287	−	0.524828i	0.630635	−	0.776079i	$-0.282794\pi$
$751$	−9.24313	−	14.3826i	−0.337287	−	0.524828i	−0.967922	+	0.251251i	$0.919158\pi$
$752$	3.23887	−	1.76855i	0.118109	−	0.0644925i
$753$	1.66489	+	1.24632i	0.0606721	+	0.0454185i
$754$	5.89593	+	2.69258i	0.214717	+	0.0980580i
$755$	7.53684	+	26.9378i	0.274294	+	0.980368i
$756$	−2.05199	+	3.19296i	−0.0746302	+	0.116127i
$757$	2.32344	−	32.4860i	0.0844470	−	1.18072i	−0.761757	−	0.647863i	$-0.775663\pi$
$757$	2.32344	−	32.4860i	0.0844470	−	1.18072i	0.846204	−	0.532860i	$-0.178883\pi$
$758$	−1.46793	+	1.46793i	−0.0533177	+	0.0533177i
$759$	3.45168	+	3.92956i	0.125288	+	0.142634i
$760$	−6.38565	−	2.47520i	−0.231632	−	0.0897849i
$761$	−14.0132	−	16.1721i	−0.507980	−	0.586240i	0.442600	−	0.896719i	$-0.354056\pi$
$761$	−14.0132	−	16.1721i	−0.507980	−	0.586240i	−0.950580	+	0.310479i	$0.899511\pi$
$762$	−6.26682	+	1.36326i	−0.227023	+	0.0493858i
$763$	25.3209	−	18.9550i	0.916679	−	0.686217i
$764$	2.58470	−	5.65970i	0.0935111	−	0.204761i
$765$	17.3529	+	4.00798i	0.627397	+	0.144909i
$766$	0.248221	−	0.845362i	0.00896858	−	0.0305442i
$767$	−3.71964	+	17.0989i	−0.134309	+	0.617406i
$768$	−0.349464	+	0.936950i	−0.0126102	+	0.0338093i
$769$	−28.6559	+	8.41413i	−1.03336	+	0.303421i	−0.754075	−	0.656788i	$-0.771915\pi$
$769$	−28.6559	+	8.41413i	−1.03336	+	0.303421i	−0.279282	+	0.960209i	$0.590097\pi$
$770$	8.84673	+	2.72100i	0.318814	+	0.0980579i
$771$	5.11200	−	5.89956i	0.184104	−	0.212468i
$772$	5.69955	−	10.4379i	0.205131	−	0.375670i
$773$	46.6602	+	17.4034i	1.67825	+	0.625955i	0.994593	−	0.103848i	$-0.0331155\pi$
$773$	46.6602	+	17.4034i	1.67825	+	0.625955i	0.683657	+	0.729803i	$0.260388\pi$
$774$	6.16730	−	3.96348i	0.221679	−	0.142464i
$775$	−23.8146	+	14.4577i	−0.855444	+	0.519338i
$776$	−7.32792	+	1.05360i	−0.263057	+	0.0378219i
$777$	5.53954	+	14.8521i	0.198730	+	0.532815i
$778$	−18.7272	−	25.0166i	−0.671403	−	0.896890i
$779$	20.3704	+	13.0913i	0.729846	+	0.469043i
$780$	4.27100	+	2.01690i	0.152926	+	0.0722167i
$781$		−	6.74223i		−	0.241256i
$782$	18.5320	+	33.4011i	0.662703	+	1.19442i
$783$	−2.16977	−	2.16977i	−0.0775412	−	0.0775412i
$784$	−5.59682	+	4.84967i	−0.199886	+	0.173203i
$785$	−9.34957	−	12.8283i	−0.333701	−	0.457862i
$786$	2.84188	−	19.7657i	0.101367	−	0.705020i
$787$	−19.5393	+	7.28777i	−0.696500	+	0.259781i	−0.672678	−	0.739935i	$-0.734856\pi$
$787$	−19.5393	+	7.28777i	−0.696500	+	0.259781i	−0.0238217	+	0.999716i	$0.507583\pi$
$788$	6.34036	−	8.46973i	0.225866	−	0.301721i
$789$	−18.9399	−	5.56124i	−0.674277	−	0.197985i
$790$	6.62061	+	32.4255i	0.235551	+	1.15365i
$791$	−28.4566	−	62.3112i	−1.01180	−	2.21553i
$792$	0.957183	+	0.522661i	0.0340120	+	0.0185720i
$793$	0.808081	+	11.2985i	0.0286958	+	0.401220i
$794$	−2.00195	−	1.73470i	−0.0710465	−	0.0615621i
$795$	16.6642	−	14.0706i	0.591020	−	0.499032i
$796$	−19.3035	+	8.81562i	−0.684195	+	0.312461i
$797$	24.1545	+	5.25449i	0.855597	+	0.186124i	0.618910	−	0.785462i	$-0.287575\pi$
$797$	24.1545	+	5.25449i	0.855597	+	0.186124i	0.236687	+	0.971586i	$0.423938\pi$
$798$	−5.57113	−	10.2028i	−0.197216	−	0.361174i
$799$	−4.18294	−	29.0930i	−0.147982	−	1.02923i
$800$	−4.63853	−	1.86656i	−0.163997	−	0.0659928i
$801$	−1.84664	−	0.265507i	−0.0652479	−	0.00938123i
$802$	−6.97445	−	32.0610i	−0.246276	−	1.13211i
$803$	−4.50034	−	0.321870i	−0.158813	−	0.0113586i
$804$	−0.125938			−0.00444150
$805$	−5.54899	−	40.3219i	−0.195576	−	1.42116i
$806$	11.7697			0.414569
$807$	−17.8313	−	1.27532i	−0.627691	−	0.0448933i
$808$	2.04363	+	9.39442i	0.0718947	+	0.330495i
$809$	−51.8542	−	7.45550i	−1.82310	−	0.262122i	−0.856081	−	0.516842i	$-0.827107\pi$
$809$	−51.8542	−	7.45550i	−1.82310	−	0.262122i	−0.967015	+	0.254721i	$0.918017\pi$
$810$	−1.56079	−	1.60123i	−0.0548406	−	0.0562615i
$811$	5.27824	+	36.7109i	0.185344	+	1.28910i	0.843874	+	0.536541i	$0.180269\pi$
$811$	5.27824	+	36.7109i	0.185344	+	1.28910i	−0.658530	+	0.752554i	$0.728822\pi$
$812$	−5.58157	−	10.2219i	−0.195875	−	0.358717i
$813$	−28.6074	−	6.22317i	−1.00331	−	0.218256i
$814$	4.14314	−	1.89211i	0.145217	−	0.0663183i
$815$	−37.5269	−	3.16682i	−1.31451	−	0.110929i
$816$	6.01938	+	5.21582i	0.210720	+	0.182590i
$817$	1.60181	+	22.3963i	0.0560403	+	0.783546i
$818$	19.1765	+	10.4712i	0.670490	+	0.366115i
$819$	3.33048	+	7.29274i	0.116376	+	0.254829i
$820$	14.7485	+	9.74705i	0.515041	+	0.340382i
$821$	−39.0296	−	11.4601i	−1.36214	−	0.399961i	−0.482624	−	0.875828i	$-0.660316\pi$
$821$	−39.0296	−	11.4601i	−1.36214	−	0.399961i	−0.879517	+	0.475867i	$0.842134\pi$
$822$	−5.88135	+	7.85656i	−0.205136	+	0.274029i
$823$	−10.8875	+	4.06082i	−0.379514	+	0.141551i	−0.531979	−	0.846758i	$-0.678551\pi$
$823$	−10.8875	+	4.06082i	−0.379514	+	0.141551i	0.152465	+	0.988309i	$0.451279\pi$
$824$	2.30707	−	16.0461i	0.0803707	−	0.558991i
$825$	−2.73485	+	4.71751i	−0.0952152	+	0.164243i
$826$	23.7627	−	20.5905i	0.826808	−	0.716434i
$827$	−6.04433	−	6.04433i	−0.210182	−	0.210182i	0.594163	−	0.804345i	$-0.297483\pi$
$827$	−6.04433	−	6.04433i	−0.210182	−	0.210182i	−0.804345	+	0.594163i	$0.797483\pi$
$828$	0.309848	−	4.78581i	0.0107679	−	0.166318i
$829$			0.508709i			0.0176682i	0.999961	+	0.00883409i	$0.00281202\pi$
$829$			0.508709i			0.0176682i	−0.999961	+	0.00883409i	$0.997188\pi$
$830$	−1.12344	+	2.37899i	−0.0389950	+	0.0825760i
$831$	−1.28947	−	0.828689i	−0.0447311	−	0.0287469i
$832$	1.26586	+	1.69099i	0.0438859	+	0.0586247i
$833$	20.6129	+	55.2654i	0.714196	+	1.91483i
$834$	−6.22082	+	0.894419i	−0.215409	+	0.0309712i
$835$	34.0976	−	44.3552i	1.18000	−	1.53498i
$836$	−2.80997	+	1.80586i	−0.0971849	+	0.0624569i
$837$	−5.22062	−	1.94719i	−0.180451	−	0.0673047i
$838$	18.1038	−	33.1546i	0.625384	−	1.14531i
$839$	−0.349757	+	0.403641i	−0.0120749	+	0.0139352i	−0.761755	−	0.647865i	$-0.775662\pi$
$839$	−0.349757	+	0.403641i	−0.0120749	+	0.0139352i	0.749680	+	0.661801i	$0.230207\pi$
$840$	−3.97177	−	7.50022i	−0.137039	−	0.258782i
$841$	−18.7909	+	5.51751i	−0.647963	+	0.190259i
$842$	7.79051	−	20.8872i	0.268479	−	0.719819i
$843$	−0.468858	+	2.15531i	−0.0161483	+	0.0742327i
$844$	0.619342	−	2.10928i	0.0213186	−	0.0726046i
$845$	−16.1918	+	10.1156i	−0.557014	+	0.347987i
$846$	−1.53299	+	3.35678i	−0.0527053	+	0.115408i
$847$	−29.8090	+	22.3147i	−1.02425	+	0.766743i
$848$	9.53085	−	2.07331i	0.327291	−	0.0711977i
$849$	1.29066	+	1.48950i	0.0442952	+	0.0511194i
$850$	−26.8403	+	29.4201i	−0.920614	+	1.00910i
$851$	−15.2254	−	13.0140i	−0.521919	−	0.446116i
$852$	−4.37149	+	4.37149i	−0.149765	+	0.149765i
$853$	0.653179	−	9.13264i	0.0223644	−	0.312695i	−0.973940	−	0.226805i	$-0.927172\pi$
$853$	0.653179	−	9.13264i	0.0223644	−	0.312695i	0.996305	−	0.0858904i	$-0.0273735\pi$
$854$	11.0038	−	17.1223i	0.376543	−	0.585913i
$855$	6.59531	−	1.84528i	0.225555	−	0.0631072i
$856$	0.546689	+	0.249664i	0.0186854	+	0.00853335i
$857$	−31.3421	−	23.4624i	−1.07063	−	0.801461i	−0.0897252	−	0.995967i	$-0.528599\pi$
$857$	−31.3421	−	23.4624i	−1.07063	−	0.801461i	−0.980901	+	0.194505i	$0.937690\pi$
$858$	2.02187	−	1.10402i	0.0690255	−	0.0376908i
$859$	−3.29579	−	5.12834i	−0.112451	−	0.174977i	0.780466	−	0.625198i	$-0.214982\pi$
$859$	−3.29579	−	5.12834i	−0.112451	−	0.174977i	−0.892917	+	0.450221i	$0.851345\pi$
$860$	0.960252	+	16.3646i	0.0327443	+	0.558030i
$861$	8.45397	+	28.7916i	0.288110	+	0.981214i
$862$	−37.1382	+	2.65617i	−1.26493	+	0.0904697i
$863$	−4.14074	+	0.296151i	−0.140952	+	0.0100811i	−0.141637	−	0.989919i	$-0.545237\pi$
$863$	−4.14074	+	0.296151i	−0.140952	+	0.0100811i	0.000684728		1.00000i	$0.499782\pi$
$864$	−0.281733	−	0.959493i	−0.00958474	−	0.0326426i
$865$	−1.95257	−	33.2757i	−0.0663893	−	1.13141i
$866$	19.1731	+	29.8339i	0.651529	+	1.01380i
$867$	40.7574	−	22.2552i	1.38419	−	0.755827i
$868$	−16.9300	−	12.6736i	−0.574640	−	0.430170i
$869$	14.6823	+	6.70520i	0.498064	+	0.227458i
$870$	6.60766	−	1.84873i	0.224021	−	0.0626779i
$871$	−0.143822	+	0.223791i	−0.00487322	+	0.00758288i
$872$	−0.594508	+	8.31230i	−0.0201326	+	0.281490i
$873$	5.23490	−	5.23490i	0.177175	−	0.177175i
$874$	12.4101	+	7.85769i	0.419778	+	0.265790i
$875$	37.9967	−	18.8933i	1.28452	−	0.638710i
$876$	2.70921	+	3.12660i	0.0915357	+	0.105638i
$877$	−18.4576	+	4.01522i	−0.623270	+	0.135584i	−0.513100	−	0.858329i	$-0.671503\pi$
$877$	−18.4576	+	4.01522i	−0.623270	+	0.135584i	−0.110170	+	0.993913i	$0.535140\pi$
$878$	−7.51413	+	5.62501i	−0.253590	+	0.189835i
$879$	1.77320	−	3.88277i	0.0598086	−	0.130963i
$880$	−2.06819	+	1.29207i	−0.0697187	+	0.0435558i
$881$	2.25658	−	7.68521i	0.0760261	−	0.258921i	−0.912706	−	0.408617i	$-0.866011\pi$
$881$	2.25658	−	7.68521i	0.0760261	−	0.258921i	0.988732	+	0.149696i	$0.0478294\pi$
$882$	1.57419	−	7.23641i	0.0530056	−	0.243663i
$883$	19.3771	−	51.9520i	0.652091	−	1.74832i	−0.0111731	−	0.999938i	$-0.503557\pi$
$883$	19.3771	−	51.9520i	0.652091	−	1.74832i	0.663264	−	0.748386i	$-0.269171\pi$
$884$	16.1426	−	4.73990i	0.542935	−	0.159420i
$885$	8.66899	+	16.3704i	0.291405	+	0.550283i
$886$	19.7221	−	22.7605i	0.662577	−	0.764654i
$887$	−2.90358	+	5.31750i	−0.0974925	+	0.178544i	−0.921873	−	0.387491i	$-0.873342\pi$
$887$	−2.90358	+	5.31750i	−0.0974925	+	0.178544i	0.824381	+	0.566036i	$0.191524\pi$
$888$	−3.91310	−	1.45951i	−0.131315	−	0.0489779i
$889$	20.4777	−	13.1602i	0.686800	−	0.441379i
$890$	2.54250	−	3.30736i	0.0852247	−	0.110863i
$891$	−1.07948	+	0.155206i	−0.0361640	+	0.00519961i
$892$	2.92821	+	7.85085i	0.0980439	+	0.262866i
$893$	−6.77331	−	9.04808i	−0.226660	−	0.302783i
$894$	−13.4797	−	8.66285i	−0.450827	−	0.289729i
$895$	22.0097	−	46.6079i	0.735705	−	1.55793i
$896$		−	3.79548i		−	0.126798i
$897$	−8.15050	−	6.01601i	−0.272137	−	0.200869i
$898$	9.77257	+	9.77257i	0.326115	+	0.326115i
$899$	12.9215	−	11.1965i	0.430955	−	0.373425i
$900$	4.83192	−	1.28551i	0.161064	−	0.0428503i
$901$	11.0559	−	76.8957i	0.368327	−	2.56177i
$902$	8.07853	−	3.01314i	0.268986	−	0.100326i
$903$	−16.6749	+	22.2750i	−0.554905	+	0.741266i
$904$	17.3171	+	5.08477i	0.575959	+	0.169117i
$905$	4.54616	+	3.00447i	0.151119	+	0.0998721i
$906$	−5.19668	−	11.3791i	−0.172648	−	0.378046i
$907$	13.3314	+	7.27950i	0.442662	+	0.241712i	0.685091	−	0.728457i	$-0.259762\pi$
$907$	13.3314	+	7.27950i	0.442662	+	0.241712i	−0.242429	+	0.970169i	$0.577944\pi$
$908$	0.562789	+	7.86882i	0.0186768	+	0.261136i
$909$	−7.26588	−	6.29592i	−0.240994	−	0.208822i
$910$	−17.8636	−	1.50747i	−0.592173	−	0.0499722i
$911$	25.4849	−	11.6386i	0.844354	−	0.385603i	0.0542132	−	0.998529i	$-0.482735\pi$
$911$	25.4849	−	11.6386i	0.844354	−	0.385603i	0.790140	+	0.612926i	$0.210008\pi$
$912$	2.99279	+	0.651041i	0.0991010	+	0.0215581i
$913$	0.614953	+	1.12620i	0.0203520	+	0.0372719i
$914$	4.37456	+	30.4258i	0.144698	+	1.00639i
$915$	8.36976	+	8.58662i	0.276696	+	0.283865i
$916$	4.22841	+	0.607954i	0.139711	+	0.0200874i
$917$	16.1107	+	74.0598i	0.532023	+	2.44567i
$918$	−7.94449	−	0.568201i	−0.262207	−	0.0187534i
$919$	−14.1690			−0.467394			−0.233697	−	0.972310i	$-0.575082\pi$
$919$	−14.1690			−0.467394			−0.233697	+	0.972310i	$0.575082\pi$
$920$	8.98625	+	5.85212i	0.296268	+	0.192939i
$921$	20.9298			0.689659
$922$	29.8736	+	2.13660i	0.983835	+	0.0703653i
$923$	2.77585	+	12.7604i	0.0913681	+	0.420012i
$924$	−4.09716	−	0.589082i	−0.134787	−	0.0193794i
$925$	7.79554	−	19.3725i	0.256316	−	0.636963i
$926$	−2.13236	−	14.8309i	−0.0700735	−	0.487372i
$927$	7.76913	+	14.2281i	0.255172	+	0.467312i
$928$	2.99839	+	0.652260i	0.0984270	+	0.0214115i
$929$	−18.4390	+	8.42082i	−0.604965	+	0.276278i	−0.694257	−	0.719727i	$-0.744267\pi$
$929$	−18.4390	+	8.42082i	−0.604965	+	0.276278i	0.0892919	+	0.996005i	$0.471540\pi$
$930$	9.51961	−	8.03797i	0.312160	−	0.263575i
$931$	17.1418	+	14.8535i	0.561801	+	0.486803i
$932$	−1.97675	−	27.6386i	−0.0647507	−	0.905333i
$933$	5.49133	+	2.99849i	0.179778	+	0.0981662i
$934$	10.9157	+	23.9021i	0.357174	+	0.782102i
$935$	3.88562	+	19.0304i	0.127073	+	0.622362i
$936$	−2.02675	−	0.595107i	−0.0662464	−	0.0194517i
$937$	−10.3671	+	13.8488i	−0.338677	+	0.452419i	−0.937255	−	0.348645i	$-0.886642\pi$
$937$	−10.3671	+	13.8488i	−0.338677	+	0.452419i	0.598578	+	0.801065i	$0.295733\pi$
$938$	0.447858	−	0.167043i	0.0146231	−	0.00545413i
$939$	3.82826	−	26.6261i	0.124930	−	0.868910i
$940$	−4.86016	−	6.66851i	−0.158521	−	0.217503i
$941$	20.9894	−	18.1874i	0.684235	−	0.592893i	−0.241802	−	0.970326i	$-0.577738\pi$
$941$	20.9894	−	18.1874i	0.684235	−	0.592893i	0.926037	+	0.377433i	$0.123193\pi$
$942$	5.01976	+	5.01976i	0.163553	+	0.163553i
$943$	−26.9908	−	26.6291i	−0.878943	−	0.867162i
$944$			8.28420i			0.269628i
$945$	7.67428	+	3.62404i	0.249644	+	0.117890i
$946$	6.72595	+	4.32251i	0.218680	+	0.140537i
$947$	10.3303	+	13.7997i	0.335690	+	0.448430i	0.936346	−	0.351078i	$-0.114185\pi$
$947$	10.3303	+	13.7997i	0.335690	+	0.448430i	−0.600656	+	0.799508i	$0.705094\pi$
$948$	−5.17217	−	13.8671i	−0.167984	−	0.450384i
$949$	8.64986	−	1.24366i	0.280786	−	0.0403710i
$950$	−3.63683	+	14.8758i	−0.117994	+	0.482634i
$951$	−2.10571	+	1.35326i	−0.0682822	+	0.0438823i
$952$	−28.3241	−	10.5644i	−0.917990	−	0.342393i
$953$	14.3100	−	26.2068i	0.463546	−	0.848922i	−0.536441	−	0.843938i	$-0.680232\pi$
$953$	14.3100	−	26.2068i	0.463546	−	0.848922i	0.999988	−	0.00498415i	$-0.00158651\pi$
$954$	−6.38735	+	7.37139i	−0.206798	+	0.238658i
$955$	−13.2980	−	4.09006i	−0.430312	−	0.132351i
$956$	16.6255	−	4.88169i	0.537707	−	0.157885i
$957$	1.16947	−	3.13548i	0.0378037	−	0.101356i
$958$	−5.49369	+	25.2541i	−0.177493	+	0.815922i
$959$	10.4943	−	35.7402i	0.338878	−	1.15411i
$960$	2.17871	+	0.503213i	0.0703176	+	0.0162411i
$961$	0.0192668	−	0.0421885i	0.000621511	−	0.00136092i
$962$	−7.06231	+	5.28678i	−0.227698	+	0.170452i
$963$	−0.587265	+	0.127752i	−0.0189244	+	0.00411674i
$964$	12.8350	+	14.8123i	0.413386	+	0.477073i
$965$	−24.7952	−	9.61111i	−0.798187	−	0.309392i
$966$	5.24595	+	17.4301i	0.168786	+	0.560806i
$967$	29.2204	−	29.2204i	0.939665	−	0.939665i	−0.0586155	−	0.998281i	$-0.518669\pi$
$967$	29.2204	−	29.2204i	0.939665	−	0.939665i	0.998281	+	0.0586155i	$0.0186686\pi$
$968$	0.699882	−	9.78563i	0.0224951	−	0.314522i
$969$	13.1886	−	20.5218i	0.423679	−	0.659257i
$970$	4.46036	+	15.9420i	0.143213	+	0.511867i
$971$	47.6006	+	21.7385i	1.52758	+	0.697621i	0.989401	−	0.145211i	$-0.0463863\pi$
$971$	47.6006	+	21.7385i	1.52758	+	0.697621i	0.538176	+	0.842832i	$0.319114\pi$
$972$	0.800541	+	0.599278i	0.0256774	+	0.0192218i
$973$	20.9360	−	11.4319i	0.671177	−	0.366490i
$974$	10.3599	+	16.1203i	0.331952	+	0.516527i
$975$	3.23373	−	10.0543i	0.103562	−	0.321997i
$976$	1.51080	+	5.14530i	0.0483594	+	0.164697i
$977$	−28.8711	+	2.06490i	−0.923669	+	0.0660621i	−0.525066	−	0.851061i	$-0.675959\pi$
$977$	−28.8711	+	2.06490i	−0.923669	+	0.0660621i	−0.398603	+	0.917124i	$0.630505\pi$
$978$	16.7993	−	1.20151i	0.537182	−	0.0384200i
$979$	−0.573221	−	1.95221i	−0.0183202	−	0.0623929i
$980$	12.3752	+	11.0034i	0.395310	+	0.351489i
$981$	−4.50545	−	7.01062i	−0.143848	−	0.223832i
$982$	−15.0479	+	8.21679i	−0.480199	+	0.262208i
$983$	−26.9550	−	20.1782i	−0.859730	−	0.643586i	0.0756872	−	0.997132i	$-0.475885\pi$
$983$	−26.9550	−	20.1782i	−0.859730	−	0.643586i	−0.935417	+	0.353546i	$0.884976\pi$
$984$	−7.19155	−	3.28427i	−0.229258	−	0.104699i
$985$	−20.6171	−	11.6025i	−0.656915	−	0.369686i
$986$	13.2133	−	20.5603i	0.420797	−	0.654773i
$987$	0.999199	−	13.9706i	0.0318048	−	0.444690i
$988$	4.57466	−	4.57466i	0.145539	−	0.145539i
$989$	4.76868	−	34.8337i	0.151635	−	1.10765i
$990$	0.881360	−	2.27378i	0.0280115	−	0.0722654i
$991$	−4.55930	−	5.26171i	−0.144831	−	0.167144i	0.678699	−	0.734416i	$-0.262544\pi$
$991$	−4.55930	−	5.26171i	−0.144831	−	0.167144i	−0.823530	+	0.567273i	$0.807999\pi$
$992$	5.44459	−	1.18440i	0.172866	−	0.0376047i
$993$	−18.2101	+	13.6319i	−0.577881	+	0.432596i
$994$	9.74750	−	21.3441i	0.309172	−	0.676992i
$995$	25.1420	+	40.2441i	0.797054	+	1.27582i
$996$	0.331481	−	1.12892i	0.0105034	−	0.0357712i
$997$	−0.681212	+	3.13148i	−0.0215742	+	0.0991750i	−0.986675	−	0.162704i	$-0.947978\pi$
$997$	−0.681212	+	3.13148i	−0.0215742	+	0.0991750i	0.965101	+	0.261879i	$0.0843421\pi$
$998$	−0.775973	+	2.08046i	−0.0245630	+	0.0658559i
$999$	4.00725	−	1.17663i	0.126784	−	0.0372271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.493.9	yes	240
5.2	odd	4	inner	690.2.w.b.217.2	yes	240
23.7	odd	22	inner	690.2.w.b.283.2	yes	240
115.7	even	44	inner	690.2.w.b.7.9	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.7.9	✓	240	115.7	even	44	inner
690.2.w.b.217.2	yes	240	5.2	odd	4	inner
690.2.w.b.283.2	yes	240	23.7	odd	22	inner
690.2.w.b.493.9	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.0285953 - 2.23589i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.81898 - 3.33121i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(0.997452 + 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.0285953 - 2.23589i) q^{5} +(0.142315 + 0.989821i) q^{6} +(-1.81898 - 3.33121i) q^{7} +(0.977147 + 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(0.188029 - 2.22815i) q^{10} +(-0.824208 - 0.714181i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(1.85393 + 1.01232i) q^{13} +(-1.57670 - 3.45249i) q^{14} +(2.19087 - 0.447330i) q^{15} +(0.959493 + 0.281733i) q^{16} +(4.77311 - 6.37613i) q^{17} +(-0.936950 + 0.349464i) q^{18} +(0.435879 - 3.03161i) q^{19} +(0.346504 - 2.20906i) q^{20} +(2.86843 - 2.48551i) q^{21} +(-0.771159 - 0.771159i) q^{22} +(-1.64562 + 4.50466i) q^{23} +1.00000i q^{24} +(-4.99836 - 0.127872i) q^{25} +(1.77699 + 1.14200i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(-1.32638 - 3.55617i) q^{28} +(3.03728 - 0.436695i) q^{29} +(2.21720 - 0.289895i) q^{30} +(4.68740 - 3.01241i) q^{31} +(0.936950 + 0.349464i) q^{32} +(0.522661 - 0.957183i) q^{33} +(5.21582 - 6.01938i) q^{34} +(-7.50022 + 3.97177i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-1.45951 + 3.91310i) q^{37} +(0.651041 - 2.99279i) q^{38} +(-0.595107 + 2.02675i) q^{39} +(0.503213 - 2.17871i) q^{40} +(-3.28427 + 7.19155i) q^{41} +(3.03844 - 2.27455i) q^{42} +(-7.16354 + 1.55833i) q^{43} +(-0.714181 - 0.824208i) q^{44} +(0.902809 + 2.04571i) q^{45} +(-1.96278 + 4.37578i) q^{46} +(2.60941 - 2.60941i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(-4.00380 + 6.23003i) q^{49} +(-4.97651 - 0.484125i) q^{50} +(7.24502 + 3.30869i) q^{51} +(1.69099 + 1.26586i) q^{52} +(8.56066 - 4.67447i) q^{53} +(-0.540641 - 0.841254i) q^{54} +(-1.62039 + 1.82241i) q^{55} +(-1.06931 - 3.64173i) q^{56} +(3.05498 - 0.218496i) q^{57} +(3.06070 - 0.218905i) q^{58} +(2.33393 + 7.94863i) q^{59} +(2.23223 - 0.130984i) q^{60} +(2.89919 + 4.51123i) q^{61} +(4.89036 - 2.67034i) q^{62} +(3.03844 + 2.27455i) q^{63} +(0.909632 + 0.415415i) q^{64} +(2.31645 - 4.11623i) q^{65} +(0.589614 - 0.917457i) q^{66} +(-0.00898434 + 0.125617i) q^{67} +(5.63195 - 5.63195i) q^{68} +(-4.75151 - 0.650474i) q^{69} +(-7.76445 + 3.42659i) q^{70} +(4.04850 + 4.67221i) q^{71} +(-0.977147 + 0.212565i) q^{72} +(3.31190 - 2.47926i) q^{73} +(-1.73495 + 3.79901i) q^{74} +(-0.937529 - 4.91132i) q^{75} +(0.862885 - 2.93872i) q^{76} +(-0.879869 + 4.04469i) q^{77} +(-0.738178 + 1.97913i) q^{78} +(-14.2008 + 4.16973i) q^{79} +(0.657359 - 2.13726i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-3.78894 + 6.93893i) q^{82} +(-1.10240 - 0.411173i) q^{83} +(3.19296 - 2.05199i) q^{84} +(-14.1198 - 10.8545i) q^{85} +(-7.25646 + 1.04332i) q^{86} +(1.07234 + 2.87504i) q^{87} +(-0.653563 - 0.873057i) q^{88} +(1.56947 + 1.00864i) q^{89} +(0.754569 + 2.10490i) q^{90} -8.01724i q^{91} +(-2.26995 + 4.22461i) q^{92} +(3.93995 + 3.93995i) q^{93} +(2.78891 - 2.41661i) q^{94} +(-6.76586 - 1.06127i) q^{95} +(-0.142315 + 0.989821i) q^{96} +(-6.93649 + 2.58718i) q^{97} +(-4.43804 + 5.92853i) q^{98} +(1.04641 + 0.307253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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