LMFDB - Embedded newform 230.2.l.a.7.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(7,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([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("230.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (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:	$1.83655924649$
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			7.5
Character	$\chi$	$=$	230.7
Dual form			230.2.l.a.33.5

$q$-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} +(0.184045 - 0.846041i) q^{3} +(0.989821 - 0.142315i) q^{4} +(2.13522 + 0.663941i) q^{5} +(-0.123220 + 0.857015i) q^{6} +(-2.12852 + 3.89809i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(2.04698 + 0.934826i) q^{9} +(-2.17715 - 0.509924i) q^{10} +(0.483957 - 0.419351i) q^{11} +(0.0617674 - 0.863622i) q^{12} +(1.16156 - 0.634258i) q^{13} +(1.84501 - 4.04000i) q^{14} +(0.954698 - 1.68429i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.980222 + 1.30942i) q^{17} +(-2.10846 - 0.786414i) q^{18} +(-0.660894 - 4.59662i) q^{19} +(2.20798 + 0.353309i) q^{20} +(2.90620 + 2.51823i) q^{21} +(-0.452808 + 0.452808i) q^{22} +(1.79488 + 4.44729i) q^{23} +0.865828i q^{24} +(4.11836 + 2.83533i) q^{25} +(-1.11335 + 0.715507i) q^{26} +(2.72425 - 3.63917i) q^{27} +(-1.55210 + 4.16133i) q^{28} +(2.76504 + 0.397553i) q^{29} +(-0.832110 + 1.74811i) q^{30} +(-0.176248 - 0.113268i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-0.265718 - 0.486627i) q^{33} +(-1.07114 - 1.23616i) q^{34} +(-7.13296 + 6.91008i) q^{35} +(2.15919 + 0.633995i) q^{36} +(-3.27494 - 8.78046i) q^{37} +(0.987129 + 4.53776i) q^{38} +(-0.322830 - 1.09946i) q^{39} +(-2.22756 - 0.194894i) q^{40} +(-0.793335 - 1.73716i) q^{41} +(-3.07844 - 2.30449i) q^{42} +(-12.2355 - 2.66167i) q^{43} +(0.419351 - 0.483957i) q^{44} +(3.75010 + 3.35514i) q^{45} +(-2.10758 - 4.30791i) q^{46} +(5.65253 + 5.65253i) q^{47} +(-0.0617674 - 0.863622i) q^{48} +(-6.88001 - 10.7055i) q^{49} +(-4.31014 - 2.53430i) q^{50} +(1.28823 - 0.588315i) q^{51} +(1.05947 - 0.793109i) q^{52} +(-6.56546 - 3.58501i) q^{53} +(-2.45769 + 3.82425i) q^{54} +(1.31178 - 0.574090i) q^{55} +(1.25128 - 4.26145i) q^{56} +(-4.01056 - 0.286841i) q^{57} +(-2.78635 - 0.199284i) q^{58} +(0.421120 - 1.43420i) q^{59} +(0.705281 - 1.80302i) q^{60} +(-2.82825 + 4.40084i) q^{61} +(0.183879 + 0.100406i) q^{62} +(-8.00107 + 5.98953i) q^{63} +(0.909632 - 0.415415i) q^{64} +(2.90129 - 0.583078i) q^{65} +(0.299757 + 0.466431i) q^{66} +(-0.743153 - 10.3906i) q^{67} +(1.15660 + 1.15660i) q^{68} +(4.09293 - 0.700044i) q^{69} +(6.62183 - 7.40133i) q^{70} +(-5.23180 + 6.03781i) q^{71} +(-2.19892 - 0.478345i) q^{72} +(4.53424 + 3.39429i) q^{73} +(3.89299 + 8.52446i) q^{74} +(3.15677 - 2.96248i) q^{75} +(-1.30833 - 4.45578i) q^{76} +(0.604557 + 2.77910i) q^{77} +(0.400441 + 1.07362i) q^{78} +(0.0648320 + 0.0190364i) q^{79} +(2.23579 + 0.0354848i) q^{80} +(1.84348 + 2.12749i) q^{81} +(0.915241 + 1.67614i) q^{82} +(-6.38913 + 2.38302i) q^{83} +(3.23500 + 2.07901i) q^{84} +(1.22361 + 3.44672i) q^{85} +(12.3942 + 1.78202i) q^{86} +(0.845237 - 2.26617i) q^{87} +(-0.383758 + 0.512640i) q^{88} +(0.562341 - 0.361394i) q^{89} +(-3.97990 - 3.07906i) q^{90} +5.87788i q^{91} +(2.40953 + 4.14658i) q^{92} +(-0.128266 + 0.128266i) q^{93} +(-6.04138 - 5.23488i) q^{94} +(1.64073 - 10.2536i) q^{95} +(0.123220 + 0.857015i) q^{96} +(-17.5049 - 6.52900i) q^{97} +(7.62621 + 10.1874i) q^{98} +(1.38267 - 0.405989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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
$3$	0.184045	−	0.846041i	0.106258	−	0.488462i	−0.893004	−	0.450050i	$-0.851406\pi$
$3$	0.184045	−	0.846041i	0.106258	−	0.488462i	0.999262	−	0.0384123i	$-0.0122300\pi$
$4$	0.989821	−	0.142315i	0.494911	−	0.0711574i
$5$	2.13522	+	0.663941i	0.954901	+	0.296924i
$5$	2.13522	+	0.663941i	0.954901	+	0.296924i
$6$	−0.123220	+	0.857015i	−0.0503044	+	0.349875i
$7$	−2.12852	+	3.89809i	−0.804504	+	1.47334i	0.0748635	+	0.997194i	$0.476148\pi$
$7$	−2.12852	+	3.89809i	−0.804504	+	1.47334i	−0.879367	+	0.476145i	$0.842034\pi$
$8$	−0.977147	+	0.212565i	−0.345474	+	0.0751532i
$9$	2.04698	+	0.934826i	0.682328	+	0.311609i
$10$	−2.17715	−	0.509924i	−0.688475	−	0.161252i
$11$	0.483957	−	0.419351i	0.145919	−	0.126439i	−0.578843	−	0.815439i	$-0.696495\pi$
$11$	0.483957	−	0.419351i	0.145919	−	0.126439i	0.724761	+	0.689000i	$0.241950\pi$
$12$	0.0617674	−	0.863622i	0.0178307	−	0.249306i
$13$	1.16156	−	0.634258i	0.322158	−	0.175912i	−0.310030	−	0.950727i	$-0.600339\pi$
$13$	1.16156	−	0.634258i	0.322158	−	0.175912i	0.632188	+	0.774815i	$0.282157\pi$
$14$	1.84501	−	4.04000i	0.493099	−	1.07974i
$15$	0.954698	−	1.68429i	0.246502	−	0.434882i
$16$	0.959493	−	0.281733i	0.239873	−	0.0704331i
$17$	0.980222	+	1.30942i	0.237739	+	0.317582i	0.903504	−	0.428579i	$-0.140986\pi$
$17$	0.980222	+	1.30942i	0.237739	+	0.317582i	−0.665765	+	0.746161i	$0.731895\pi$
$18$	−2.10846	−	0.786414i	−0.496968	−	0.185360i
$19$	−0.660894	−	4.59662i	−0.151619	−	1.05454i	−0.913506	−	0.406826i	$-0.866636\pi$
$19$	−0.660894	−	4.59662i	−0.151619	−	1.05454i	0.761886	−	0.647711i	$-0.224273\pi$
$20$	2.20798	+	0.353309i	0.493719	+	0.0790023i
$21$	2.90620	+	2.51823i	0.634184	+	0.549524i
$22$	−0.452808	+	0.452808i	−0.0965389	+	0.0965389i
$23$	1.79488	+	4.44729i	0.374259	+	0.927324i
$23$	1.79488	+	4.44729i	0.374259	+	0.927324i
$24$			0.865828i			0.176736i
$25$	4.11836	+	2.83533i	0.823673	+	0.567065i
$26$	−1.11335	+	0.715507i	−0.218346	+	0.140322i
$27$	2.72425	−	3.63917i	0.524282	−	0.700359i
$28$	−1.55210	+	4.16133i	−0.293318	+	0.786417i
$29$	2.76504	+	0.397553i	0.513455	+	0.0738237i	0.394172	−	0.919037i	$-0.371031\pi$
$29$	2.76504	+	0.397553i	0.513455	+	0.0738237i	0.119283	+	0.992860i	$0.461941\pi$
$30$	−0.832110	+	1.74811i	−0.151922	+	0.319159i
$31$	−0.176248	−	0.113268i	−0.0316550	−	0.0203435i	0.524718	−	0.851276i	$-0.324171\pi$
$31$	−0.176248	−	0.113268i	−0.0316550	−	0.0203435i	−0.556373	+	0.830933i	$0.687807\pi$
$32$	−0.936950	+	0.349464i	−0.165631	+	0.0617771i
$33$	−0.265718	−	0.486627i	−0.0462556	−	0.0847108i
$34$	−1.07114	−	1.23616i	−0.183699	−	0.212000i
$35$	−7.13296	+	6.91008i	−1.20569	+	1.16802i
$36$	2.15919	+	0.633995i	0.359865	+	0.105666i
$37$	−3.27494	−	8.78046i	−0.538397	−	1.44350i	−0.866654	−	0.498910i	$-0.833734\pi$
$37$	−3.27494	−	8.78046i	−0.538397	−	1.44350i	0.328257	−	0.944589i	$-0.393539\pi$
$38$	0.987129	+	4.53776i	0.160133	+	0.736122i
$39$	−0.322830	−	1.09946i	−0.0516941	−	0.176054i
$40$	−2.22756	−	0.194894i	−0.352208	−	0.0308154i
$41$	−0.793335	−	1.73716i	−0.123898	−	0.271299i	0.837512	−	0.546419i	$-0.184010\pi$
$41$	−0.793335	−	1.73716i	−0.123898	−	0.271299i	−0.961410	+	0.275120i	$0.911282\pi$
$42$	−3.07844	−	2.30449i	−0.475014	−	0.355591i
$43$	−12.2355	−	2.66167i	−1.86590	−	0.405901i	−0.869742	−	0.493506i	$-0.835715\pi$
$43$	−12.2355	−	2.66167i	−1.86590	−	0.405901i	−0.996155	+	0.0876049i	$0.972079\pi$
$44$	0.419351	−	0.483957i	0.0632196	−	0.0729593i
$45$	3.75010	+	3.35514i	0.559032	+	0.500155i
$46$	−2.10758	−	4.30791i	−0.310745	−	0.635167i
$47$	5.65253	+	5.65253i	0.824506	+	0.824506i	0.986751	−	0.162244i	$-0.0518733\pi$
$47$	5.65253	+	5.65253i	0.824506	+	0.824506i	−0.162244	+	0.986751i	$0.551873\pi$
$48$	−0.0617674	−	0.863622i	−0.00891536	−	0.124653i
$49$	−6.88001	−	10.7055i	−0.982859	−	1.52936i
$50$	−4.31014	−	2.53430i	−0.609546	−	0.358404i
$51$	1.28823	−	0.588315i	0.180388	−	0.0823806i
$52$	1.05947	−	0.793109i	0.146922	−	0.109984i
$53$	−6.56546	−	3.58501i	−0.901836	−	0.492440i	−0.0397544	−	0.999209i	$-0.512658\pi$
$53$	−6.56546	−	3.58501i	−0.901836	−	0.492440i	−0.862081	+	0.506770i	$0.830839\pi$
$54$	−2.45769	+	3.82425i	−0.334450	+	0.520414i
$55$	1.31178	−	0.574090i	0.176881	−	0.0774102i
$56$	1.25128	−	4.26145i	0.167209	−	0.569460i
$57$	−4.01056	−	0.286841i	−0.531212	−	0.0379930i
$58$	−2.78635	−	0.199284i	−0.365866	−	0.0261673i
$59$	0.421120	−	1.43420i	0.0548252	−	0.186717i	−0.927528	−	0.373754i	$-0.878070\pi$
$59$	0.421120	−	1.43420i	0.0548252	−	0.186717i	0.982353	+	0.187037i	$0.0598885\pi$
$60$	0.705281	−	1.80302i	0.0910514	−	0.232768i
$61$	−2.82825	+	4.40084i	−0.362120	+	0.563470i	−0.973735	−	0.227686i	$-0.926884\pi$
$61$	−2.82825	+	4.40084i	−0.362120	+	0.563470i	0.611614	+	0.791156i	$0.290520\pi$
$62$	0.183879	+	0.100406i	0.0233527	+	0.0127515i
$63$	−8.00107	+	5.98953i	−1.00804	+	0.754609i
$64$	0.909632	−	0.415415i	0.113704	−	0.0519269i
$65$	2.90129	−	0.583078i	0.359861	−	0.0723219i
$66$	0.299757	+	0.466431i	0.0368975	+	0.0574137i
$67$	−0.743153	−	10.3906i	−0.0907906	−	1.26942i	−0.814846	−	0.579677i	$-0.803179\pi$
$67$	−0.743153	−	10.3906i	−0.0907906	−	1.26942i	0.724056	−	0.689741i	$-0.242276\pi$
$68$	1.15660	+	1.15660i	0.140258	+	0.140258i
$69$	4.09293	−	0.700044i	0.492731	−	0.0842754i
$70$	6.62183	−	7.40133i	0.791460	−	0.884628i
$71$	−5.23180	+	6.03781i	−0.620900	+	0.716557i	−0.975878	−	0.218318i	$-0.929943\pi$
$71$	−5.23180	+	6.03781i	−0.620900	+	0.716557i	0.354978	+	0.934875i	$0.384488\pi$
$72$	−2.19892	−	0.478345i	−0.259145	−	0.0563735i
$73$	4.53424	+	3.39429i	0.530692	+	0.397271i	0.830747	−	0.556651i	$-0.187914\pi$
$73$	4.53424	+	3.39429i	0.530692	+	0.397271i	−0.300054	+	0.953922i	$0.597005\pi$
$74$	3.89299	+	8.52446i	0.452551	+	0.990948i
$75$	3.15677	−	2.96248i	0.364512	−	0.342077i
$76$	−1.30833	−	4.45578i	−0.150076	−	0.511112i
$77$	0.604557	+	2.77910i	0.0688956	+	0.316708i
$78$	0.400441	+	1.07362i	0.0453411	+	0.121564i
$79$	0.0648320	+	0.0190364i	0.00729418	+	0.00214176i	0.285378	−	0.958415i	$-0.407881\pi$
$79$	0.0648320	+	0.0190364i	0.00729418	+	0.00214176i	−0.278083	+	0.960557i	$0.589699\pi$
$80$	2.23579	+	0.0354848i	0.249969	+	0.00396732i
$81$	1.84348	+	2.12749i	0.204831	+	0.236388i
$82$	0.915241	+	1.67614i	0.101072	+	0.185099i
$83$	−6.38913	+	2.38302i	−0.701298	+	0.261571i	−0.674718	−	0.738076i	$-0.735735\pi$
$83$	−6.38913	+	2.38302i	−0.701298	+	0.261571i	−0.0265807	+	0.999647i	$0.508462\pi$
$84$	3.23500	+	2.07901i	0.352967	+	0.226838i
$85$	1.22361	+	3.44672i	0.132720	+	0.373850i
$86$	12.3942	+	1.78202i	1.33650	+	0.192160i
$87$	0.845237	−	2.26617i	0.0906189	−	0.242959i
$88$	−0.383758	+	0.512640i	−0.0409087	+	0.0546476i
$89$	0.562341	−	0.361394i	0.0596080	−	0.0383077i	−0.510497	−	0.859879i	$-0.670539\pi$
$89$	0.562341	−	0.361394i	0.0596080	−	0.0383077i	0.570105	+	0.821572i	$0.306902\pi$
$90$	−3.97990	−	3.07906i	−0.419518	−	0.324562i
$91$			5.87788i			0.616169i
$92$	2.40953	+	4.14658i	0.251211	+	0.432311i
$93$	−0.128266	+	0.128266i	−0.0133006	+	0.0133006i
$94$	−6.04138	−	5.23488i	−0.623120	−	0.539937i
$95$	1.64073	−	10.2536i	0.168335	−	1.05200i
$96$	0.123220	+	0.857015i	0.0125761	+	0.0874687i
$97$	−17.5049	−	6.52900i	−1.77736	−	0.662920i	−0.999401	−	0.0346011i	$-0.988984\pi$
$97$	−17.5049	−	6.52900i	−1.77736	−	0.662920i	−0.777956	−	0.628319i	$-0.783743\pi$
$98$	7.62621	+	10.1874i	0.770363	+	1.02908i
$99$	1.38267	−	0.405989i	0.138964	−	0.0408035i
$100$	4.47995	+	2.22036i	0.447995	+	0.222036i
$101$	2.53058	−	5.54119i	0.251802	−	0.551369i	−0.740949	−	0.671562i	$-0.765624\pi$
$101$	2.53058	−	5.54119i	0.251802	−	0.551369i	0.992751	+	0.120192i	$0.0383512\pi$
$102$	−1.24298	+	0.678717i	−0.123073	+	0.0672030i
$103$	1.09170	−	15.2639i	0.107568	−	1.50400i	−0.601507	−	0.798867i	$-0.705433\pi$
$103$	1.09170	−	15.2639i	0.107568	−	1.50400i	0.709076	−	0.705132i	$-0.249112\pi$
$104$	−1.00019	+	0.866670i	−0.0980768	+	0.0849840i
$105$	4.53342	+	7.30654i	0.442417	+	0.713045i
$106$	6.80449	+	3.10751i	0.660910	+	0.301828i
$107$	5.80246	−	1.26225i	0.560945	−	0.122026i	0.0768517	−	0.997043i	$-0.475513\pi$
$107$	5.80246	−	1.26225i	0.560945	−	0.122026i	0.484093	+	0.875016i	$0.339150\pi$
$108$	2.17861	−	3.98983i	0.209637	−	0.383922i
$109$	−1.08696	+	7.55997i	−0.104112	+	0.724114i	0.869172	+	0.494510i	$0.164652\pi$
$109$	−1.08696	+	7.55997i	−0.104112	+	0.724114i	−0.973284	+	0.229605i	$0.926257\pi$
$110$	−1.26748	+	0.666208i	−0.120850	+	0.0635205i
$111$	−8.03136	+	1.15474i	−0.762303	+	0.109603i
$112$	−0.944079	+	4.33986i	−0.0892070	+	0.410078i
$113$	18.0818	−	1.29323i	1.70099	−	0.121657i	0.813223	−	0.581952i	$-0.197711\pi$
$113$	18.0818	−	1.29323i	1.70099	−	0.121657i	0.887766	+	0.460295i	$0.152256\pi$
$114$	4.02080			0.376583
$115$	0.879741	+	10.6877i	0.0820363	+	0.996629i
$116$	2.79347			0.259367
$117$	2.97061	−	0.212462i	0.274633	−	0.0196421i
$118$	−0.317732	+	1.46059i	−0.0292496	+	0.134458i
$119$	−7.19067	+	1.03386i	−0.659167	+	0.0947739i
$120$	−0.574859	+	1.84874i	−0.0524772	+	0.168766i
$121$	−1.50710	+	10.4821i	−0.137009	+	0.952922i
$122$	2.50709	−	4.59140i	0.226981	−	0.415686i
$123$	−1.61572	+	0.351478i	−0.145684	+	0.0316917i
$124$	−0.190573	−	0.0870320i	−0.0171140	−	0.00781570i
$125$	6.91114	+	8.78841i	0.618151	+	0.786059i
$126$	7.55340	−	6.54506i	0.672910	−	0.583080i
$127$	−0.914294	+	12.7835i	−0.0811305	+	1.13435i	0.779936	+	0.625859i	$0.215252\pi$
$127$	−0.914294	+	12.7835i	−0.0811305	+	1.13435i	−0.861066	+	0.508493i	$0.830203\pi$
$128$	−0.877679	+	0.479249i	−0.0775766	+	0.0423600i
$129$	−4.50377	+	9.86187i	−0.396534	+	0.868289i
$130$	−2.85231	+	0.788568i	−0.250164	+	0.0691620i
$131$	−1.56010	+	0.458088i	−0.136307	+	0.0400233i	−0.349174	−	0.937058i	$-0.613538\pi$
$131$	−1.56010	+	0.458088i	−0.136307	+	0.0400233i	0.212867	+	0.977081i	$0.431720\pi$
$132$	−0.332268	−	0.443858i	−0.0289202	−	0.0386329i
$133$	19.3247	+	7.20775i	1.67567	+	0.624992i
$134$	1.48252	+	10.3111i	0.128070	+	0.890748i
$135$	8.23308	−	5.96171i	0.708591	−	0.513102i
$136$	−1.23616	−	1.07114i	−0.106000	−	0.0918493i
$137$	9.66832	−	9.66832i	0.826020	−	0.826020i	−0.160943	−	0.986964i	$-0.551454\pi$
$137$	9.66832	−	9.66832i	0.826020	−	0.826020i	0.986964	+	0.160943i	$0.0514536\pi$
$138$	−4.03256	+	0.990247i	−0.343274	+	0.0842954i
$139$		−	22.4821i		−	1.90691i	−0.301540	−	0.953453i	$-0.597501\pi$
$139$		−	22.4821i		−	1.90691i	0.301540	−	0.953453i	$-0.402499\pi$
$140$	−6.07695	+	7.85487i	−0.513596	+	0.663858i
$141$	5.82259	−	3.74195i	0.490351	−	0.315129i
$142$	4.78773	−	6.39566i	0.401778	−	0.536712i
$143$	0.296167	−	0.794054i	0.0247667	−	0.0664021i
$144$	2.22744	+	0.320257i	0.185620	+	0.0266881i
$145$	5.64003	+	2.68469i	0.468379	+	0.222951i
$146$	−4.76483	−	3.06217i	−0.394340	−	0.253427i
$147$	−10.3235	+	3.85048i	−0.851470	+	0.317582i
$148$	−4.49120	−	8.22501i	−0.369174	−	0.676092i
$149$	−13.7976	−	15.9233i	−1.13035	−	1.30449i	−0.946925	−	0.321454i	$-0.895828\pi$
$149$	−13.7976	−	15.9233i	−1.13035	−	1.30449i	−0.183421	−	0.983035i	$-0.558717\pi$
$150$	−2.93738	+	3.18013i	−0.239836	+	0.259656i
$151$	4.47832	+	1.31495i	0.364440	+	0.107009i	0.458826	−	0.888526i	$-0.348270\pi$
$151$	4.47832	+	1.31495i	0.364440	+	0.107009i	−0.0943851	+	0.995536i	$0.530088\pi$
$152$	1.62287	+	4.35109i	0.131632	+	0.352920i
$153$	0.782415	+	3.59671i	0.0632545	+	0.290776i
$154$	−0.801275	−	2.72889i	−0.0645686	−	0.219900i
$155$	−0.301125	−	0.358870i	−0.0241870	−	0.0288251i
$156$	−0.476013	−	1.04232i	−0.0381115	−	0.0834526i
$157$	18.3764	+	13.7564i	1.46660	+	1.09788i	0.973711	+	0.227787i	$0.0731491\pi$
$157$	18.3764	+	13.7564i	1.46660	+	1.09788i	0.492886	+	0.870094i	$0.335942\pi$
$158$	−0.0660249	−	0.0143628i	−0.00525266	−	0.00114265i
$159$	−4.24141	+	4.89485i	−0.336366	+	0.388187i
$160$	−2.23262	+	0.124105i	−0.176504	+	0.00981134i
$161$	−21.1564	−	2.46951i	−1.66736	−	0.194625i
$162$	−1.99055	−	1.99055i	−0.156393	−	0.156393i
$163$	−1.09802	−	15.3524i	−0.0860037	−	1.20249i	−0.838876	−	0.544322i	$-0.816787\pi$
$163$	−1.09802	−	15.3524i	−0.0860037	−	1.20249i	0.752872	−	0.658167i	$-0.228668\pi$
$164$	−1.03248	−	1.60658i	−0.0806235	−	0.125453i
$165$	−0.244277	−	1.21548i	−0.0190169	−	0.0946249i
$166$	6.20285	−	2.83275i	0.481435	−	0.219864i
$167$	9.30762	−	6.96760i	0.720245	−	0.539169i	−0.175095	−	0.984552i	$-0.556023\pi$
$167$	9.30762	−	6.96760i	0.720245	−	0.539169i	0.895340	+	0.445383i	$0.146932\pi$
$168$	−3.37507	−	1.84293i	−0.260392	−	0.142185i
$169$	−6.08140	+	9.46284i	−0.467800	+	0.727911i
$170$	−1.46638	−	3.35065i	−0.112466	−	0.256983i
$171$	2.94420	−	10.0270i	0.225149	−	0.766785i
$172$	−12.4898	−	0.893286i	−0.952336	−	0.0681124i
$173$	−4.65800	−	0.333147i	−0.354141	−	0.0253287i	−0.106865	−	0.994274i	$-0.534081\pi$
$173$	−4.65800	−	0.333147i	−0.354141	−	0.0253287i	−0.247277	+	0.968945i	$0.579536\pi$
$174$	−0.681417	+	2.32069i	−0.0516581	+	0.175931i
$175$	−19.8184	+	10.0187i	−1.49813	+	0.757343i
$176$	0.346208	−	0.538711i	0.0260964	−	0.0406069i
$177$	−1.13589	−	0.620242i	−0.0853787	−	0.0466203i
$178$	−0.535126	+	0.400591i	−0.0401094	+	0.0300255i
$179$	−9.03577	+	4.12650i	−0.675365	+	0.308429i	−0.723412	−	0.690416i	$-0.757427\pi$
$179$	−9.03577	+	4.12650i	−0.675365	+	0.308429i	0.0480473	+	0.998845i	$0.484700\pi$
$180$	4.18941	+	2.78729i	0.312261	+	0.207753i
$181$	−10.0747	−	15.6766i	−0.748849	−	1.16523i	−0.981274	−	0.192617i	$-0.938302\pi$
$181$	−10.0747	−	15.6766i	−0.748849	−	1.16523i	0.232425	−	0.972614i	$-0.425334\pi$
$182$	−0.419323	−	5.86290i	−0.0310823	−	0.434587i
$183$	3.20277	+	3.20277i	0.236755	+	0.236755i
$184$	−2.69921	−	3.96413i	−0.198988	−	0.292239i
$185$	−1.16303	−	20.9226i	−0.0855074	−	1.53826i
$186$	0.118789	−	0.137090i	0.00871005	−	0.0100519i
$187$	1.02349	+	0.222647i	0.0748453	+	0.0162816i
$188$	6.39944	+	4.79056i	0.466727	+	0.349387i
$189$	8.38720	+	18.3654i	0.610079	+	1.33589i
$190$	−0.905063	+	10.3445i	−0.0656602	+	0.750471i
$191$	−3.92260	−	13.3592i	−0.283830	−	0.966635i	−0.970788	−	0.239938i	$-0.922873\pi$
$191$	−3.92260	−	13.3592i	−0.283830	−	0.966635i	0.686958	−	0.726697i	$-0.258945\pi$
$192$	−0.184045	−	0.846041i	−0.0132823	−	0.0610577i
$193$	−4.51772	−	12.1125i	−0.325192	−	0.871875i	−0.991953	−	0.126603i	$-0.959593\pi$
$193$	−4.51772	−	12.1125i	−0.325192	−	0.871875i	0.666761	−	0.745272i	$-0.267680\pi$
$194$	17.9261	+	5.26358i	1.28702	+	0.377903i
$195$	0.0406611	−	2.56193i	0.00291180	−	0.183463i
$196$	−8.33354	−	9.61741i	−0.595253	−	0.686958i
$197$	1.52992	+	2.80183i	0.109002	+	0.199622i	0.926486	−	0.376329i	$-0.122814\pi$
$197$	1.52992	+	2.80183i	0.109002	+	0.199622i	−0.817484	+	0.575951i	$0.804632\pi$
$198$	−1.35019	+	0.503593i	−0.0959536	+	0.0357888i
$199$	17.2379	+	11.0781i	1.22196	+	0.785307i	0.982620	−	0.185629i	$-0.0594322\pi$
$199$	17.2379	+	11.0781i	1.22196	+	0.785307i	0.239341	+	0.970936i	$0.423069\pi$
$200$	−4.62694	−	1.89511i	−0.327174	−	0.134004i
$201$	−8.92768	−	1.28361i	−0.629710	−	0.0905386i
$202$	−2.12883	+	5.70760i	−0.149784	+	0.401586i
$203$	−7.43512	+	9.93216i	−0.521843	+	0.697101i
$204$	1.19139	−	0.765661i	0.0834141	−	0.0536070i
$205$	−0.540575	−	4.23596i	−0.0377554	−	0.295852i
$206$			15.3029i			1.06620i
$207$	−0.483344	+	10.7814i	−0.0335947	+	0.749362i
$208$	0.935815	−	0.935815i	0.0648871	−	0.0648871i
$209$	−2.24744	−	1.94742i	−0.155459	−	0.134706i
$210$	−5.04312	−	6.96451i	−0.348008	−	0.480597i
$211$	0.953001	+	6.62827i	0.0656073	+	0.456309i	0.995971	+	0.0896717i	$0.0285818\pi$
$211$	0.953001	+	6.62827i	0.0656073	+	0.456309i	−0.930364	+	0.366637i	$0.880509\pi$
$212$	−7.00884	−	2.61416i	−0.481369	−	0.179541i
$213$	4.14535	+	5.53754i	0.284035	+	0.379426i
$214$	−5.69763	+	1.67297i	−0.389482	+	0.114362i
$215$	−24.3584	−	13.8069i	−1.66123	−	0.941625i
$216$	−1.88843	+	4.13509i	−0.128491	+	0.281357i
$217$	0.816673	−	0.445937i	0.0554394	−	0.0302722i
$218$	0.544868	−	7.61826i	0.0369031	−	0.515973i
$219$	3.70621	−	3.21145i	0.250442	−	0.217010i
$220$	1.21673	−	0.754932i	0.0820318	−	0.0508975i
$221$	1.96910	+	0.899256i	0.132456	+	0.0604905i
$222$	7.92852	−	1.72474i	0.532128	−	0.115757i
$223$	4.13827	−	7.57867i	0.277119	−	0.507505i	−0.701637	−	0.712535i	$-0.747547\pi$
$223$	4.13827	−	7.57867i	0.277119	−	0.507505i	0.978756	+	0.205029i	$0.0657290\pi$
$224$	0.632071	−	4.39615i	0.0422320	−	0.293730i
$225$	5.77969	+	9.65382i	0.385312	+	0.643588i
$226$	−17.9434	+	2.57988i	−1.19358	+	0.171611i
$227$	−4.31485	+	19.8350i	−0.286386	+	1.31650i	0.578973	+	0.815346i	$0.303453\pi$
$227$	−4.31485	+	19.8350i	−0.286386	+	1.31650i	−0.865360	+	0.501151i	$0.832910\pi$
$228$	−4.01056	+	0.286841i	−0.265606	+	0.0189965i
$229$	1.47455			0.0974410			0.0487205	−	0.998812i	$-0.484486\pi$
$229$	1.47455			0.0974410			0.0487205	+	0.998812i	$0.484486\pi$
$230$	−1.63995	−	10.5977i	−0.108135	−	0.698790i
$231$	2.46250			0.162021
$232$	−2.78635	+	0.199284i	−0.182933	+	0.0130836i
$233$	1.40608	−	6.46366i	0.0921155	−	0.423448i	−0.907876	−	0.419240i	$-0.862297\pi$
$233$	1.40608	−	6.46366i	0.0921155	−	0.423448i	0.999991	−	0.00420857i	$-0.00133963\pi$
$234$	−2.94788	+	0.423842i	−0.192709	+	0.0277074i
$235$	8.31647	+	15.8224i	0.542507	+	1.03214i
$236$	0.212725	−	1.47954i	0.0138472	−	0.0963096i
$237$	0.0280376	−	0.0513470i	0.00182124	−	0.00333535i
$238$	7.09859	−	1.54420i	0.460133	−	0.100096i
$239$	−12.0165	−	5.48776i	−0.777284	−	0.354974i	−0.0130520	−	0.999915i	$-0.504155\pi$
$239$	−12.0165	−	5.48776i	−0.777284	−	0.354974i	−0.764232	+	0.644941i	$0.776882\pi$
$240$	0.441507	−	1.88504i	0.0284991	−	0.121679i
$241$	−13.9561	+	12.0930i	−0.898989	+	0.778979i	−0.975936	−	0.218057i	$-0.930028\pi$
$241$	−13.9561	+	12.0930i	−0.898989	+	0.778979i	0.0769470	+	0.997035i	$0.475483\pi$
$242$	0.755477	−	10.5629i	0.0485639	−	0.679012i
$243$	14.1087	−	7.70395i	0.905075	−	0.494208i
$244$	−2.17316	+	4.75855i	−0.139122	+	0.304635i
$245$	−7.58254	−	27.4266i	−0.484431	−	1.75222i
$246$	1.58653	−	0.465847i	0.101153	−	0.0297013i
$247$	−3.68311	−	4.92006i	−0.234351	−	0.313056i
$248$	0.196297	+	0.0732149i	0.0124649	+	0.00464915i
$249$	0.840247	+	5.84405i	0.0532485	+	0.370352i
$250$	−7.52049	−	8.27298i	−0.475637	−	0.523229i
$251$	21.8782	+	18.9575i	1.38094	+	1.19659i	0.956713	+	0.291032i	$0.0939986\pi$
$251$	21.8782	+	18.9575i	1.38094	+	1.19659i	0.424224	+	0.905557i	$0.360547\pi$
$252$	−7.06723	+	7.06723i	−0.445194	+	0.445194i
$253$	2.73362	+	1.39961i	0.171861	+	0.0879927i
$254$		−	12.8162i		−	0.804157i
$255$	3.14127	−	0.400875i	0.196714	−	0.0251038i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	2.83473	−	3.78676i	0.176826	−	0.236212i	−0.703368	−	0.710826i	$-0.748321\pi$
$257$	2.83473	−	3.78676i	0.176826	−	0.236212i	0.880194	+	0.474614i	$0.157412\pi$
$258$	3.78875	−	10.1580i	0.235877	−	0.632412i
$259$	41.1978	+	5.92334i	2.55990	+	0.368059i
$260$	2.78878	−	0.990040i	0.172953	−	0.0613997i
$261$	5.28835	+	3.39861i	0.327340	+	0.210369i
$262$	1.52345	−	0.568218i	0.0941191	−	0.0351046i
$263$	2.51241	+	4.60113i	0.154922	+	0.283718i	0.943600	−	0.331089i	$-0.107416\pi$
$263$	2.51241	+	4.60113i	0.154922	+	0.283718i	−0.788678	+	0.614806i	$0.789234\pi$
$264$	0.363086	+	0.419023i	0.0223464	+	0.0257891i
$265$	−11.6385	−	12.0139i	−0.714947	−	0.738007i
$266$	−19.7897	−	5.81078i	−1.21338	−	0.356282i
$267$	−0.202258	−	0.542276i	−0.0123780	−	0.0331867i
$268$	−2.21433	−	10.1791i	−0.135262	−	0.621788i
$269$	6.10994	+	20.8086i	0.372530	+	1.26872i	0.906136	+	0.422987i	$0.139018\pi$
$269$	6.10994	+	20.8086i	0.372530	+	1.26872i	−0.533606	+	0.845733i	$0.679163\pi$
$270$	−7.78680	+	6.53386i	−0.473890	+	0.397638i
$271$	−1.82164	−	3.98883i	−0.110657	−	0.242304i	0.846200	−	0.532866i	$-0.178885\pi$
$271$	−1.82164	−	3.98883i	−0.110657	−	0.242304i	−0.956856	+	0.290562i	$0.906158\pi$
$272$	1.30942	+	0.980222i	0.0793955	+	0.0594347i
$273$	4.97292	+	1.08179i	0.300975	+	0.0654731i
$274$	−8.95396	+	10.3334i	−0.540928	+	0.624265i
$275$	3.18211	−	0.354864i	0.191888	−	0.0213991i
$276$	3.95164	−	1.27540i	0.237861	−	0.0767703i
$277$	14.2868	+	14.2868i	0.858408	+	0.858408i	0.991151	−	0.132743i	$-0.0423784\pi$
$277$	14.2868	+	14.2868i	0.858408	+	0.858408i	−0.132743	+	0.991151i	$0.542378\pi$
$278$	1.60385	+	22.4248i	0.0961928	+	1.34495i
$279$	−0.254891	−	0.396618i	−0.0152599	−	0.0237449i
$280$	5.50111	−	8.26838i	0.328754	−	0.494130i
$281$	−19.9836	+	9.12619i	−1.19212	+	0.544423i	−0.909860	−	0.414916i	$-0.863811\pi$
$281$	−19.9836	+	9.12619i	−1.19212	+	0.544423i	−0.282259	+	0.959338i	$0.591084\pi$
$282$	−5.54081	+	4.14780i	−0.329950	+	0.246998i
$283$	−8.84049	−	4.82727i	−0.525512	−	0.286952i	0.194512	−	0.980900i	$-0.437688\pi$
$283$	−8.84049	−	4.82727i	−0.525512	−	0.286952i	−0.720025	+	0.693949i	$0.755869\pi$
$284$	−4.31927	+	6.72092i	−0.256302	+	0.398813i
$285$	−8.37300	−	3.27525i	−0.495974	−	0.194009i
$286$	−0.238765	+	0.813159i	−0.0141185	+	0.0480831i
$287$	8.46023	+	0.605088i	0.499392	+	0.0357172i
$288$	−2.24461	−	0.160538i	−0.132265	−	0.00945977i
$289$	4.03570	−	13.7443i	0.237394	−	0.808490i
$290$	−5.81718	−	2.27549i	−0.341596	−	0.133621i
$291$	−8.74550	+	13.6083i	−0.512670	+	0.797730i
$292$	4.97114	+	2.71445i	0.290914	+	0.158851i
$293$	2.89986	−	2.17081i	0.169412	−	0.126820i	−0.511208	−	0.859457i	$-0.670802\pi$
$293$	2.89986	−	2.17081i	0.169412	−	0.126820i	0.680619	+	0.732637i	$0.261711\pi$
$294$	10.0225	−	4.57714i	0.584526	−	0.266944i
$295$	1.85141	−	2.78275i	0.107793	−	0.162018i
$296$	5.06652	+	7.88366i	0.294486	+	0.458228i
$297$	−0.207671	−	2.90362i	−0.0120503	−	0.168485i
$298$	14.8984	+	14.8984i	0.863043	+	0.863043i
$299$	4.90559	+	4.02736i	0.283698	+	0.232908i
$300$	2.70303	−	3.38158i	0.156060	−	0.195235i
$301$	36.4189	−	42.0297i	2.09915	−	2.42255i
$302$	−4.56072	−	0.992123i	−0.262440	−	0.0570903i
$303$	−4.22233	−	3.16080i	−0.242567	−	0.181583i
$304$	−1.92914	−	4.22423i	−0.110644	−	0.242276i
$305$	−8.96085	+	7.51900i	−0.513097	+	0.430537i
$306$	−1.03701	−	3.53172i	−0.0592818	−	0.201895i
$307$	3.07558	+	14.1382i	0.175533	+	0.806911i	0.977732	+	0.209855i	$0.0672993\pi$
$307$	3.07558	+	14.1382i	0.175533	+	0.806911i	−0.802200	+	0.597056i	$0.796337\pi$
$308$	0.993910	+	2.66478i	0.0566333	+	0.151840i
$309$	−12.7130	−	3.73287i	−0.723216	−	0.212356i
$310$	0.325960	+	0.336473i	0.0185133	+	0.0191104i
$311$	15.2800	+	17.6341i	0.866449	+	0.999936i	0.999960	+	0.00888825i	$0.00282925\pi$
$311$	15.2800	+	17.6341i	0.866449	+	0.999936i	−0.133511	+	0.991047i	$0.542625\pi$
$312$	0.549158	+	1.00571i	0.0310900	+	0.0569370i
$313$	−4.48829	+	1.67405i	−0.253693	+	0.0946227i	−0.473093	−	0.881012i	$-0.656863\pi$
$313$	−4.48829	+	1.67405i	−0.253693	+	0.0946227i	0.219400	+	0.975635i	$0.429590\pi$
$314$	−19.3110	−	12.4104i	−1.08978	−	0.700360i
$315$	−21.0608	+	7.47674i	−1.18664	+	0.421267i
$316$	0.0668813	+	0.00961608i	0.00376237	+	0.000540947i
$317$	7.58479	−	20.3356i	0.426004	−	1.14216i	−0.529791	−	0.848129i	$-0.677729\pi$
$317$	7.58479	−	20.3356i	0.426004	−	1.14216i	0.955795	−	0.294034i	$-0.0949978\pi$
$318$	3.88141	−	5.18495i	0.217658	−	0.290758i
$319$	1.50487	−	0.967124i	0.0842567	−	0.0541485i
$320$	2.21808	−	0.283062i	0.123994	−	0.0158236i
$321$		−	5.14143i		−	0.286967i
$322$	21.2786	+	0.953945i	1.18581	+	0.0531613i
$323$	5.37110	−	5.37110i	0.298856	−	0.298856i
$324$	2.12749	+	1.84348i	0.118194	+	0.102415i
$325$	6.58204	+	0.681288i	0.365106	+	0.0377911i
$326$	2.19045	+	15.2349i	0.121318	+	0.843783i
$327$	6.19600	+	2.31099i	0.342639	+	0.127798i
$328$	1.14447	+	1.52883i	0.0631925	+	0.0844153i
$329$	−34.0656	+	10.0026i	−1.87810	+	0.551458i
$330$	0.330365	+	1.19495i	0.0181860	+	0.0657801i
$331$	−6.89284	+	15.0932i	−0.378865	+	0.829598i	0.620118	+	0.784509i	$0.287085\pi$
$331$	−6.89284	+	15.0932i	−0.378865	+	0.829598i	−0.998983	+	0.0450899i	$0.985643\pi$
$332$	−5.98496	+	3.26804i	−0.328467	+	0.179357i
$333$	1.50445	−	21.0350i	0.0824433	−	1.15271i
$334$	−8.78684	+	7.61384i	−0.480795	+	0.416611i
$335$	5.31198	−	22.6798i	0.290224	−	1.23913i
$336$	3.49794	+	1.59746i	0.190829	+	0.0871485i
$337$	−13.1319	+	2.85668i	−0.715342	+	0.155613i	−0.555484	−	0.831527i	$-0.687467\pi$
$337$	−13.1319	+	2.85668i	−0.715342	+	0.155613i	−0.159858	+	0.987140i	$0.551104\pi$
$338$	5.39083	−	9.87257i	0.293223	−	0.536997i
$339$	2.23373	−	15.5359i	0.121319	−	0.843796i
$340$	1.70168	+	3.23750i	0.0922865	+	0.175578i
$341$	−0.132795	+	0.0190931i	−0.00719126	+	0.00103395i
$342$	−2.22138	+	10.2115i	−0.120118	+	0.552175i
$343$	25.3649	−	1.81414i	1.36958	−	0.0979541i
$344$	12.5217			0.675123
$345$	9.20411	+	1.22271i	0.495532	+	0.0658286i
$346$	4.66990			0.251055
$347$	3.46971	−	0.248159i	0.186264	−	0.0133219i	0.0221044	−	0.999756i	$-0.492963\pi$
$347$	3.46971	−	0.248159i	0.186264	−	0.0133219i	0.164159	+	0.986434i	$0.447509\pi$
$348$	0.514124	−	2.36339i	0.0275600	−	0.126691i
$349$	4.68836	−	0.674084i	0.250962	−	0.0360829i	−0.0156856	−	0.999877i	$-0.504993\pi$
$349$	4.68836	−	0.674084i	0.250962	−	0.0360829i	0.266648	+	0.963794i	$0.414084\pi$
$350$	19.0531	−	11.4070i	1.01843	−	0.609730i
$351$	0.856198	−	5.95499i	0.0457005	−	0.317854i
$352$	−0.306895	+	0.562036i	−0.0163576	+	0.0299566i
$353$	−33.8900	+	7.37233i	−1.80378	+	0.392389i	−0.983695	−	0.179845i	$-0.942440\pi$
$353$	−33.8900	+	7.37233i	−1.80378	+	0.392389i	−0.820090	+	0.572235i	$0.806077\pi$
$354$	1.17724	+	0.537629i	0.0625697	+	0.0285746i
$355$	−15.1798	+	9.41848i	−0.805661	+	0.499881i
$356$	0.505185	−	0.437745i	0.0267748	−	0.0232005i
$357$	−0.448716	+	6.27387i	−0.0237486	+	0.332049i
$358$	8.71837	−	4.76059i	0.460780	−	0.251605i
$359$	8.63206	−	18.9016i	0.455583	−	0.997587i	−0.532889	−	0.846185i	$-0.678894\pi$
$359$	8.63206	−	18.9016i	0.455583	−	0.997587i	0.988472	−	0.151402i	$-0.0483789\pi$
$360$	−4.37758	−	2.48132i	−0.230719	−	0.130777i
$361$	−2.46174	+	0.722833i	−0.129565	+	0.0380438i
$362$	11.1674	+	14.9179i	0.586946	+	0.784068i
$363$	8.59094	+	3.20426i	0.450908	+	0.168180i
$364$	0.836509	+	5.81805i	0.0438450	+	0.304949i
$365$	7.42801	+	10.2580i	0.388800	+	0.536930i
$366$	−3.42309	−	2.96613i	−0.178928	−	0.155042i
$367$	−4.80283	+	4.80283i	−0.250706	+	0.250706i	−0.821260	−	0.570554i	$-0.806728\pi$
$367$	−4.80283	+	4.80283i	−0.250706	+	0.250706i	0.570554	+	0.821260i	$0.306728\pi$
$368$	2.97513	+	3.76147i	0.155089	+	0.196080i
$369$		−	4.29757i		−	0.223723i
$370$	2.65267	+	20.7863i	0.137905	+	1.08063i
$371$	27.9494	−	17.9620i	1.45106	−	0.932540i
$372$	−0.108707	+	0.145215i	−0.00563618	+	0.00752905i
$373$	−7.81824	+	20.9615i	−0.404813	+	1.08535i	0.561387	+	0.827553i	$0.310268\pi$
$373$	−7.81824	+	20.9615i	−0.404813	+	1.08535i	−0.966200	+	0.257792i	$0.917005\pi$
$374$	−1.03677	−	0.149065i	−0.0536101	−	0.00770796i
$375$	8.70731	−	4.22964i	0.449644	−	0.218418i
$376$	−6.72488	−	4.32182i	−0.346809	−	0.222881i
$377$	3.46390	−	1.29197i	0.178400	−	0.0665398i
$378$	−9.67600	−	17.7203i	−0.497680	−	0.911433i
$379$	9.98086	+	11.5185i	0.512682	+	0.591667i	0.951783	−	0.306771i	$-0.0992485\pi$
$379$	9.98086	+	11.5185i	0.512682	+	0.591667i	−0.439101	+	0.898438i	$0.644703\pi$
$380$	0.164787	−	10.3827i	0.00845342	−	0.532623i
$381$	10.6471	+	3.12627i	0.545467	+	0.160164i
$382$	4.86564	+	13.0453i	0.248948	+	0.667455i
$383$	1.29333	+	5.94535i	0.0660861	+	0.303793i	0.998312	−	0.0580848i	$-0.0184994\pi$
$383$	1.29333	+	5.94535i	0.0660861	+	0.303793i	−0.932226	+	0.361878i	$0.882136\pi$
$384$	0.243932	+	0.830755i	0.0124481	+	0.0423943i
$385$	−0.554297	+	6.33540i	−0.0282496	+	0.322882i
$386$	5.37030	+	11.7593i	0.273341	+	0.598533i
$387$	−22.5577	−	16.8865i	−1.14667	−	0.858388i
$388$	−18.2559	−	3.97134i	−0.926805	−	0.201614i
$389$	−14.2608	+	16.4579i	−0.723052	+	0.834446i	−0.991671	−	0.128800i	$-0.958887\pi$
$389$	−14.2608	+	16.4579i	−0.723052	+	0.834446i	0.268619	+	0.963247i	$0.413433\pi$
$390$	0.142208	+	2.55830i	0.00720099	+	0.129545i
$391$	−4.06400	+	6.70960i	−0.205525	+	0.339319i
$392$	8.99840	+	8.99840i	0.454488	+	0.454488i
$393$	0.100432	+	1.40422i	0.00506612	+	0.0708336i
$394$	−1.72590	−	2.68555i	−0.0869495	−	0.135296i
$395$	0.125792	+	0.0836917i	0.00632928	+	0.00421098i
$396$	1.31082	−	0.598632i	0.0658712	−	0.0300824i
$397$	−15.8694	+	11.8796i	−0.796460	+	0.596222i	−0.918099	−	0.396352i	$-0.870276\pi$
$397$	−15.8694	+	11.8796i	−0.796460	+	0.596222i	0.121639	+	0.992574i	$0.461185\pi$
$398$	−17.9843	−	9.82015i	−0.901470	−	0.492240i
$399$	9.65467	−	15.0230i	0.483338	−	0.752089i
$400$	4.75035	+	1.56020i	0.237517	+	0.0780099i
$401$	−5.72622	+	19.5017i	−0.285954	+	0.973869i	0.683777	+	0.729691i	$0.260336\pi$
$401$	−5.72622	+	19.5017i	−0.285954	+	0.973869i	−0.969730	+	0.244178i	$0.921482\pi$
$402$	8.99650	+	0.643442i	0.448705	+	0.0320920i
$403$	−0.276563	−	0.0197802i	−0.0137766	−	0.000985320i
$404$	1.71623	−	5.84493i	0.0853854	−	0.290796i
$405$	2.52371	+	5.76662i	0.125404	+	0.286546i
$406$	6.70763	−	10.4373i	0.332894	−	0.517993i
$407$	−5.26703	−	2.87601i	−0.261077	−	0.142559i
$408$	−1.13373	+	0.848703i	−0.0561282	+	0.0420171i
$409$	−27.6390	+	12.6223i	−1.36666	+	0.624133i	−0.957527	−	0.288342i	$-0.906896\pi$
$409$	−27.6390	+	12.6223i	−1.36666	+	0.624133i	−0.409133	+	0.912475i	$0.634169\pi$
$410$	0.841387	+	4.18660i	0.0415532	+	0.206761i
$411$	−6.40039	−	9.95920i	−0.315708	−	0.491251i
$412$	−1.09170	−	15.2639i	−0.0537841	−	0.752000i
$413$	4.69429	+	4.69429i	0.230991	+	0.230991i
$414$	−0.287026	−	10.7884i	−0.0141066	−	0.530223i
$415$	−15.2244	+	0.846280i	−0.747337	+	0.0415422i
$416$	−0.866670	+	1.00019i	−0.0424920	+	0.0490384i
$417$	−19.0208	−	4.13772i	−0.931451	−	0.202625i
$418$	2.38064	+	1.78213i	0.116441	+	0.0871666i
$419$	9.90423	+	21.6872i	0.483853	+	1.05949i	0.981386	+	0.192046i	$0.0615122\pi$
$419$	9.90423	+	21.6872i	0.483853	+	1.05949i	−0.497533	+	0.867445i	$0.665761\pi$
$420$	5.52711	+	6.58700i	0.269695	+	0.321412i
$421$	−1.17415	−	3.99878i	−0.0572245	−	0.194889i	0.925920	−	0.377720i	$-0.123292\pi$
$421$	−1.17415	−	3.99878i	−0.0572245	−	0.194889i	−0.983144	+	0.182831i	$0.941474\pi$
$422$	−1.42343	−	6.54339i	−0.0692914	−	0.318527i
$423$	6.28650	+	16.8548i	0.305660	+	0.819507i
$424$	7.17747	+	2.10750i	0.348569	+	0.102349i
$425$	0.324268	+	8.17193i	0.0157293	+	0.396397i
$426$	−4.52983	−	5.22771i	−0.219471	−	0.253283i
$427$	−11.1349	−	20.3920i	−0.538855	−	0.986840i
$428$	5.56376	−	2.07518i	0.268935	−	0.100307i
$429$	−0.617294	−	0.396711i	−0.0298032	−	0.0191534i
$430$	25.2813	+	12.0340i	1.21917	+	0.580333i
$431$	22.2829	+	3.20379i	1.07333	+	0.154321i	0.656245	−	0.754548i	$-0.272144\pi$
$431$	22.2829	+	3.20379i	1.07333	+	0.154321i	0.417082	+	0.908869i	$0.363053\pi$
$432$	1.58863	−	4.25927i	0.0764328	−	0.204924i
$433$	5.21785	−	6.97024i	0.250754	−	0.334968i	−0.657448	−	0.753500i	$-0.728364\pi$
$433$	5.21785	−	6.97024i	0.250754	−	0.334968i	0.908202	+	0.418531i	$0.137455\pi$
$434$	−0.782779	+	0.503062i	−0.0375746	+	0.0241477i
$435$	3.30937	−	4.27759i	0.158672	−	0.205095i
$436$			7.63772i			0.365780i
$437$	19.2563	−	11.1896i	0.921152	−	0.535270i
$438$	−3.46766	+	3.46766i	−0.165691	+	0.165691i
$439$	2.91323	+	2.52433i	0.139041	+	0.120479i	0.721605	−	0.692306i	$-0.243405\pi$
$439$	2.91323	+	2.52433i	0.139041	+	0.120479i	−0.582564	+	0.812785i	$0.697950\pi$
$440$	−1.15977	+	0.839809i	−0.0552899	+	0.0400363i
$441$	−4.07548	−	28.3456i	−0.194071	−	1.34979i
$442$	−2.02823	−	0.756491i	−0.0964731	−	0.0359826i
$443$	−11.9309	−	15.9379i	−0.566856	−	0.757231i	0.421920	−	0.906633i	$-0.361356\pi$
$443$	−11.9309	−	15.9379i	−0.566856	−	0.757231i	−0.988777	+	0.149402i	$0.952265\pi$
$444$	−7.78528	+	2.28596i	−0.369473	+	0.108487i
$445$	1.44067	−	0.398297i	0.0682942	−	0.0188811i
$446$	−3.58707	+	7.85458i	−0.169853	+	0.371925i
$447$	−16.0112	+	8.74275i	−0.757302	+	0.413518i
$448$	−0.316843	+	4.43004i	−0.0149694	+	0.209300i
$449$	13.3628	−	11.5790i	0.630631	−	0.546445i	−0.279825	−	0.960051i	$-0.590276\pi$
$449$	13.3628	−	11.5790i	0.630631	−	0.546445i	0.910456	+	0.413606i	$0.135731\pi$
$450$	−6.45366	−	9.21691i	−0.304228	−	0.434489i
$451$	−1.11242	−	0.508025i	−0.0523818	−	0.0239220i
$452$	17.7137	−	3.85337i	0.833181	−	0.181247i
$453$	1.93672	−	3.54683i	0.0909948	−	0.166645i
$454$	2.88884	−	20.0923i	0.135580	−	0.942979i
$455$	−3.90257	+	12.5506i	−0.182955	+	0.588381i
$456$	3.97988	−	0.572220i	0.186375	−	0.0267967i
$457$	−0.0361530	+	0.166193i	−0.00169117	+	0.00777417i	−0.977985	−	0.208677i	$-0.933084\pi$
$457$	−0.0361530	+	0.166193i	−0.00169117	+	0.00777417i	0.976294	+	0.216451i	$0.0694481\pi$
$458$	−1.47079	+	0.105193i	−0.0687256	+	0.00491535i
$459$	7.43559			0.347064
$460$	2.39180	+	10.4537i	0.111518	+	0.487405i
$461$	−13.3460			−0.621587			−0.310794	−	0.950477i	$-0.600595\pi$
$461$	−13.3460			−0.621587			−0.310794	+	0.950477i	$0.600595\pi$
$462$	−2.45622	+	0.175673i	−0.114274	+	0.00817303i
$463$	−3.39671	+	15.6144i	−0.157859	+	0.725664i	0.828357	+	0.560200i	$0.189276\pi$
$463$	−3.39671	+	15.6144i	−0.157859	+	0.725664i	−0.986216	+	0.165464i	$0.947088\pi$
$464$	2.76504	−	0.397553i	0.128364	−	0.0184559i
$465$	−0.359039	+	0.188716i	−0.0166500	+	0.00875151i
$466$	−0.941388	+	6.54750i	−0.0436089	+	0.303307i
$467$	5.08779	−	9.31759i	0.235435	−	0.431167i	−0.733073	−	0.680150i	$-0.761915\pi$
$467$	5.08779	−	9.31759i	0.235435	−	0.431167i	0.968508	+	0.248983i	$0.0800965\pi$
$468$	2.91014	−	0.633061i	0.134521	−	0.0292633i
$469$	42.0854	+	19.2198i	1.94332	+	0.887486i
$470$	−9.42404	−	15.1888i	−0.434698	−	0.700605i
$471$	15.0206	−	13.0154i	0.692111	−	0.599718i
$472$	−0.106634	+	1.49094i	−0.00490824	+	0.0686262i
$473$	−7.03763	+	3.84284i	−0.323591	+	0.176694i
$474$	−0.0243031	+	0.0532163i	−0.00111628	+	0.00244431i
$475$	10.3111	−	20.8044i	0.473106	−	0.954571i
$476$	−6.97034	+	2.04668i	−0.319485	+	0.0938093i
$477$	−10.0880	−	13.4760i	−0.461899	−	0.617025i
$478$	12.3774	+	4.61653i	0.566129	+	0.211155i
$479$	−0.231166	−	1.60779i	−0.0105622	−	0.0734619i	0.983859	−	0.178948i	$-0.0572693\pi$
$479$	−0.231166	−	1.60779i	−0.0105622	−	0.0734619i	−0.994421	+	0.105486i	$0.966360\pi$
$480$	−0.305905	+	1.91173i	−0.0139626	+	0.0872581i
$481$	−9.37311	−	8.12185i	−0.427377	−	0.370324i
$482$	13.0578	−	13.0578i	0.594767	−	0.594767i
$483$	−5.98303	+	17.4446i	−0.272237	+	0.793759i
$484$			10.5899i			0.481360i
$485$	−33.0421	−	25.5631i	−1.50036	−	1.16076i
$486$	−13.5232	+	8.69082i	−0.613424	+	0.394224i
$487$	−17.7434	+	23.7024i	−0.804029	+	1.07406i	0.191675	+	0.981458i	$0.438608\pi$
$487$	−17.7434	+	23.7024i	−0.804029	+	1.07406i	−0.995704	+	0.0925982i	$0.970483\pi$
$488$	1.82815	−	4.90146i	0.0827565	−	0.221879i
$489$	−13.1908	−	1.89655i	−0.596509	−	0.0857650i
$490$	9.51981	+	26.8158i	0.430061	+	1.21141i
$491$	−10.8550	−	6.97610i	−0.489880	−	0.314827i	0.272277	−	0.962219i	$-0.412223\pi$
$491$	−10.8550	−	6.97610i	−0.489880	−	0.314827i	−0.762157	+	0.647392i	$0.775860\pi$
$492$	−1.54925	+	0.577841i	−0.0698457	+	0.0260511i
$493$	2.18979	+	4.01030i	0.0986231	+	0.180615i
$494$	4.02472	+	4.64477i	0.181081	+	0.208978i
$495$	3.22187	+	0.0511352i	0.144812	+	0.00229836i
$496$	−0.201020	−	0.0590247i	−0.00902605	−	0.00265029i
$497$	−12.4000	−	33.2456i	−0.556214	−	1.49127i
$498$	−1.25502	−	5.76922i	−0.0562386	−	0.258525i
$499$	−7.74097	−	26.3633i	−0.346533	−	1.18018i	−0.929850	−	0.367939i	$-0.880064\pi$
$499$	−7.74097	−	26.3633i	−0.346533	−	1.18018i	0.583317	−	0.812245i	$-0.301755\pi$
$500$	8.09152	+	7.71540i	0.361864	+	0.345043i
$501$	−4.18185	−	9.15698i	−0.186831	−	0.409103i
$502$	−23.1748	−	17.3485i	−1.03434	−	0.774300i
$503$	15.7695	+	3.43045i	0.703128	+	0.152956i	0.549895	−	0.835234i	$-0.314668\pi$
$503$	15.7695	+	3.43045i	0.703128	+	0.152956i	0.153233	+	0.988190i	$0.451031\pi$
$504$	6.54506	−	7.55340i	0.291540	−	0.336455i
$505$	9.08238	−	10.1515i	0.404160	−	0.451737i
$506$	−2.82650	−	1.20103i	−0.125653	−	0.0533923i
$507$	6.88670	+	6.88670i	0.305849	+	0.305849i
$508$	0.914294	+	12.7835i	0.0405652	+	0.567176i
$509$	−1.06094	−	1.65085i	−0.0470253	−	0.0731728i	0.816945	−	0.576716i	$-0.195666\pi$
$509$	−1.06094	−	1.65085i	−0.0470253	−	0.0731728i	−0.863970	+	0.503543i	$0.832030\pi$
$510$	−3.10467	+	0.623949i	−0.137477	+	0.0276289i
$511$	−22.8824	+	10.4501i	−1.01226	+	0.462283i
$512$	−0.800541	+	0.599278i	−0.0353793	+	0.0264846i
$513$	−18.5283	−	10.1172i	−0.818046	−	0.446687i
$514$	−2.55737	+	3.97934i	−0.112801	+	0.175521i
$515$	12.4654	−	31.8671i	0.549290	−	1.40423i
$516$	−3.05443	+	10.4024i	−0.134464	+	0.457942i
$517$	5.10598	+	0.365187i	0.224561	+	0.0160609i
$518$	−41.5154	−	2.96924i	−1.82408	−	0.130461i
$519$	−1.13914	+	3.87955i	−0.0500026	+	0.170293i
$520$	−2.71105	+	1.18647i	−0.118887	+	0.0520300i
$521$	−14.5543	+	22.6469i	−0.637636	+	0.992180i	0.360595	+	0.932722i	$0.382574\pi$
$521$	−14.5543	+	22.6469i	−0.637636	+	0.992180i	−0.998231	+	0.0594579i	$0.981063\pi$
$522$	−5.51733	−	3.01269i	−0.241487	−	0.131862i
$523$	−26.2670	+	19.6632i	−1.14858	+	0.859813i	−0.991797	−	0.127821i	$-0.959202\pi$
$523$	−26.2670	+	19.6632i	−1.14858	+	0.859813i	−0.156778	+	0.987634i	$0.550111\pi$
$524$	−1.47903	+	0.675452i	−0.0646118	+	0.0295072i
$525$	4.82876	+	18.6110i	0.210744	+	0.812252i
$526$	−2.83424	−	4.41017i	−0.123579	−	0.192293i
$527$	−0.0244468	−	0.341810i	−0.00106492	−	0.0148895i
$528$	−0.392053	−	0.392053i	−0.0170619	−	0.0170619i
$529$	−16.5568	+	15.9647i	−0.719860	+	0.694119i
$530$	12.4659	+	11.1530i	0.541484	+	0.484455i
$531$	2.20276	−	2.54212i	0.0955915	−	0.110318i
$532$	20.1538	+	4.38419i	0.873778	+	0.190079i
$533$	−2.02331	−	1.51463i	−0.0876394	−	0.0656060i
$534$	0.240429	+	0.526465i	0.0104044	+	0.0227824i
$535$	13.2276	+	1.15731i	0.571879	+	0.0500349i
$536$	2.93486	+	9.99521i	0.126767	+	0.431727i
$537$	1.82820	+	8.40409i	0.0788926	+	0.362663i
$538$	−7.57884	−	20.3197i	−0.326747	−	0.876043i
$539$	−7.81900	−	2.29586i	−0.336788	−	0.0988899i
$540$	7.30084	−	7.07272i	0.314178	−	0.304361i
$541$	−4.16906	−	4.81135i	−0.179242	−	0.206856i	0.659018	−	0.752127i	$-0.270972\pi$
$541$	−4.16906	−	4.81135i	−0.179242	−	0.206856i	−0.838260	+	0.545271i	$0.816427\pi$
$542$	2.10155	+	3.84871i	0.0902695	+	0.165316i
$543$	−15.1172	+	5.63844i	−0.648742	+	0.241968i
$544$	−1.37602	−	0.884311i	−0.0589962	−	0.0379145i
$545$	−7.34028	+	15.4206i	−0.314423	+	0.660544i
$546$	−5.03743	−	0.724273i	−0.215582	−	0.0309960i
$547$	5.22080	−	13.9975i	0.223225	−	0.598490i	−0.776265	−	0.630406i	$-0.782888\pi$
$547$	5.22080	−	13.9975i	0.223225	−	0.598490i	0.999491	+	0.0319164i	$0.0101610\pi$
$548$	8.19397	−	10.9459i	0.350029	−	0.467584i
$549$	−9.90341	+	6.36453i	−0.422667	+	0.271632i
$550$	−3.14868	+	0.580969i	−0.134260	+	0.0247726i
$551$		−	12.9726i		−	0.552650i
$552$	−3.85059	+	1.55406i	−0.163892	+	0.0661452i
$553$	−0.212202	+	0.212202i	−0.00902373	+	0.00902373i
$554$	−15.2696	−	13.2311i	−0.648741	−	0.562138i
$555$	−17.9154	−	2.86673i	−0.760468	−	0.121686i
$556$	−3.19954	−	22.2533i	−0.135691	−	0.943749i
$557$	−28.8964	−	10.7778i	−1.22438	−	0.456670i	−0.347637	−	0.937629i	$-0.613016\pi$
$557$	−28.8964	−	10.7778i	−1.22438	−	0.456670i	−0.876743	+	0.480959i	$0.840288\pi$
$558$	0.282536	+	0.377424i	0.0119607	+	0.0159776i
$559$	−15.9004	+	4.66879i	−0.672516	+	0.197469i
$560$	−4.89723	+	8.63976i	−0.206946	+	0.365096i
$561$	0.376737	−	0.824940i	0.0159059	−	0.0348290i
$562$	19.2816	−	10.5285i	0.813345	−	0.444120i
$563$	−2.42441	+	33.8977i	−0.102177	+	1.42862i	0.645096	+	0.764101i	$0.276817\pi$
$563$	−2.42441	+	33.8977i	−0.102177	+	1.42862i	−0.747273	+	0.664517i	$0.768637\pi$
$564$	5.23079	−	4.53251i	0.220256	−	0.190853i
$565$	39.4673	+	9.24389i	1.66040	+	0.388893i
$566$	9.16234	+	4.18430i	0.385122	+	0.175879i
$567$	−12.2170	+	2.65765i	−0.513066	+	0.111611i
$568$	3.82880	−	7.01193i	0.160653	−	0.294214i
$569$	5.06940	−	35.2585i	0.212520	−	1.47811i	−0.552180	−	0.833725i	$-0.686204\pi$
$569$	5.06940	−	35.2585i	0.212520	−	1.47811i	0.764700	−	0.644386i	$-0.222887\pi$
$570$	8.58532	+	2.66958i	0.359599	+	0.111816i
$571$	31.9169	−	4.58896i	1.33568	−	0.192042i	0.562800	−	0.826593i	$-0.309724\pi$
$571$	31.9169	−	4.58896i	1.33568	−	0.192042i	0.772881	+	0.634551i	$0.218815\pi$
$572$	0.180147	−	0.828120i	0.00753231	−	0.0346255i
$573$	−12.0243	+	0.859997i	−0.502324	+	0.0359269i
$574$	−8.48184			−0.354025
$575$	−5.21753	+	23.4046i	−0.217586	+	0.976041i
$576$	2.25034			0.0937643
$577$	11.3298	−	0.810326i	0.471667	−	0.0337343i	0.166517	−	0.986039i	$-0.446748\pi$
$577$	11.3298	−	0.810326i	0.471667	−	0.0337343i	0.305150	+	0.952304i	$0.401293\pi$
$578$	−3.04491	+	13.9972i	−0.126651	+	0.582207i
$579$	−11.0791	+	1.59293i	−0.460432	+	0.0662001i
$580$	5.96469	+	1.85470i	0.247670	+	0.0770123i
$581$	4.31014	−	29.9777i	0.178815	−	1.24368i
$582$	7.75241	−	14.1975i	0.321348	−	0.588505i
$583$	−4.68078	+	1.01824i	−0.193858	+	0.0421713i
$584$	−5.15212	−	2.35290i	−0.213196	−	0.0973635i
$585$	6.48398	+	1.51866i	0.268080	+	0.0627887i
$586$	−2.73761	+	2.37215i	−0.113090	+	0.0979928i
$587$	−1.57265	+	21.9885i	−0.0649102	+	0.907563i	0.855798	+	0.517311i	$0.173067\pi$
$587$	−1.57265	+	21.9885i	−0.0649102	+	0.907563i	−0.920708	+	0.390252i	$0.872388\pi$
$588$	−9.67047	+	5.28048i	−0.398803	+	0.217763i
$589$	−0.404167	+	0.885001i	−0.0166534	+	0.0364658i
$590$	−1.64818	+	2.90773i	−0.0678543	+	0.119710i
$591$	2.65204	−	0.778708i	0.109090	−	0.0320318i
$592$	−5.61603	−	7.50213i	−0.230817	−	0.308336i
$593$	36.6050	+	13.6530i	1.50319	+	0.560659i	0.960257	−	0.279119i	$-0.0900423\pi$
$593$	36.6050	+	13.6530i	1.50319	+	0.560659i	0.542930	+	0.839778i	$0.317315\pi$
$594$	0.414284	+	2.88141i	0.0169983	+	0.118226i
$595$	−16.0401	−	2.56665i	−0.657580	−	0.105223i
$596$	−15.9233	−	13.7976i	−0.652244	−	0.565173i
$597$	12.5451	−	12.5451i	0.513436	−	0.513436i
$598$	−5.18040	−	3.66714i	−0.211842	−	0.149960i
$599$		−	25.5351i		−	1.04334i	−0.853148	−	0.521669i	$-0.825310\pi$
$599$		−	25.5351i		−	1.04334i	0.853148	−	0.521669i	$-0.174690\pi$
$600$	−2.45490	+	3.56579i	−0.100221	+	0.145573i
$601$	17.4019	−	11.1835i	0.709838	−	0.456185i	−0.135250	−	0.990811i	$-0.543184\pi$
$601$	17.4019	−	11.1835i	0.709838	−	0.456185i	0.845089	+	0.534626i	$0.179548\pi$
$602$	−33.3278	+	44.5207i	−1.35834	+	1.81453i
$603$	8.19222	−	21.9642i	0.333613	−	0.894451i
$604$	4.61987	+	0.664238i	0.187980	+	0.0270274i
$605$	−10.1775	+	21.3811i	−0.413775	+	0.869265i
$606$	4.43706	+	2.85153i	0.180243	+	0.115835i
$607$	33.2647	−	12.4071i	1.35017	−	0.503588i	0.432754	−	0.901512i	$-0.357542\pi$
$607$	33.2647	−	12.4071i	1.35017	−	0.503588i	0.917418	+	0.397924i	$0.130269\pi$
$608$	2.22558	+	4.07584i	0.0902591	+	0.165297i
$609$	7.03462	+	8.11838i	0.285057	+	0.328973i
$610$	8.40162	−	8.13910i	0.340172	−	0.329543i
$611$	10.1509	+	2.98057i	0.410661	+	0.120581i
$612$	1.28632	+	3.44875i	0.0519962	+	0.139407i
$613$	0.574635	+	2.64155i	0.0232093	+	0.106691i	0.987294	−	0.158903i	$-0.0507956\pi$
$613$	0.574635	+	2.64155i	0.0232093	+	0.106691i	−0.964085	+	0.265594i	$0.914432\pi$
$614$	−4.07635	−	13.8828i	−0.164508	−	0.560264i
$615$	−3.68328	−	0.322258i	−0.148524	−	0.0129947i
$616$	−1.18148	−	2.58708i	−0.0476032	−	0.104237i
$617$	−19.4148	−	14.5337i	−0.781609	−	0.585106i	0.132212	−	0.991221i	$-0.457792\pi$
$617$	−19.4148	−	14.5337i	−0.781609	−	0.585106i	−0.913822	+	0.406116i	$0.866883\pi$
$618$	12.9469	+	2.81642i	0.520800	+	0.113293i
$619$	−2.13986	+	2.46953i	−0.0860082	+	0.0992588i	−0.797122	−	0.603818i	$-0.793645\pi$
$619$	−2.13986	+	2.46953i	−0.0860082	+	0.0992588i	0.711114	+	0.703077i	$0.248191\pi$
$620$	−0.349133	−	0.312362i	−0.0140215	−	0.0125448i
$621$	21.0742	+	5.58364i	0.845678	+	0.224064i
$622$	−16.4991	−	16.4991i	−0.661552	−	0.661552i
$623$	0.211795	+	2.96129i	0.00848540	+	0.118641i
$624$	−0.619505	−	0.963969i	−0.0248001	−	0.0385897i
$625$	8.92184	+	23.3538i	0.356874	+	0.934153i
$626$	4.35743	−	1.98997i	0.174158	−	0.0795353i
$627$	−2.06123	+	1.54301i	−0.0823174	+	0.0616220i
$628$	20.1471	+	11.0012i	0.803957	+	0.438994i
$629$	8.28717	−	12.8951i	0.330431	−	0.514161i
$630$	20.4737	−	8.96015i	0.815693	−	0.356981i
$631$	−1.11462	+	3.79606i	−0.0443725	+	0.151119i	−0.978699	−	0.205298i	$-0.934184\pi$
$631$	−1.11462	+	3.79606i	−0.0443725	+	0.151119i	0.934327	+	0.356417i	$0.116002\pi$
$632$	−0.0673969	−	0.00482032i	−0.00268091	−	0.000191742i
$633$	5.78318	+	0.413621i	0.229861	+	0.0164400i
$634$	−6.11474	+	20.8249i	−0.242847	+	0.827062i
$635$	−10.4397	+	26.6886i	−0.414287	+	1.05910i
$636$	−3.50163	+	5.44864i	−0.138849	+	0.216053i
$637$	−14.7816	−	8.07136i	−0.585668	−	0.319799i
$638$	−1.43205	+	1.07202i	−0.0566952	+	0.0424415i
$639$	−16.3537	+	7.46849i	−0.646943	+	0.295449i
$640$	−2.19223	+	0.440577i	−0.0866557	+	0.0174153i
$641$	2.40679	+	3.74504i	0.0950626	+	0.147920i	0.885527	−	0.464587i	$-0.153797\pi$
$641$	2.40679	+	3.74504i	0.0950626	+	0.147920i	−0.790465	+	0.612508i	$0.790161\pi$
$642$	0.366785	+	5.12833i	0.0144759	+	0.202399i
$643$	9.24567	+	9.24567i	0.364614	+	0.364614i	0.865508	−	0.500895i	$-0.166996\pi$
$643$	9.24567	+	9.24567i	0.364614	+	0.364614i	−0.500895	+	0.865508i	$0.666996\pi$
$644$	−21.2925	+	0.566486i	−0.839041	+	0.0223227i
$645$	−16.1643	+	18.0671i	−0.636467	+	0.711390i
$646$	−4.97424	+	5.74058i	−0.195709	+	0.225860i
$647$	38.5584	+	8.38787i	1.51589	+	0.329761i	0.892102	−	0.451834i	$-0.149230\pi$
$647$	38.5584	+	8.38787i	1.51589	+	0.329761i	0.623786	+	0.781595i	$0.285594\pi$
$648$	−2.25358	−	1.68701i	−0.0885290	−	0.0662719i
$649$	−0.397631	−	0.870690i	−0.0156084	−	0.0341776i
$650$	−6.61388	−	0.209994i	−0.259418	−	0.00823666i
$651$	−0.226977	−	0.773011i	−0.00889591	−	0.0302967i
$652$	−3.27171	−	15.0398i	−0.128130	−	0.589005i
$653$	11.7762	+	31.5732i	0.460838	+	1.23556i	0.934852	+	0.355038i	$0.115532\pi$
$653$	11.7762	+	31.5732i	0.460838	+	1.23556i	−0.474013	+	0.880518i	$0.657195\pi$
$654$	−6.34507	−	1.86308i	−0.248112	−	0.0728523i
$655$	−3.63532	−	0.0576972i	−0.142044	−	0.00225442i
$656$	−1.25061	−	1.44329i	−0.0488283	−	0.0563509i
$657$	6.10844	+	11.1868i	0.238313	+	0.436438i
$658$	33.2652	−	12.4073i	1.29681	−	0.483686i
$659$	19.4189	+	12.4798i	0.756453	+	0.486143i	0.861144	−	0.508362i	$-0.169749\pi$
$659$	19.4189	+	12.4798i	0.756453	+	0.486143i	−0.104690	+	0.994505i	$0.533385\pi$
$660$	−0.414771	−	1.16834i	−0.0161449	−	0.0454777i
$661$	5.09759	+	0.732922i	0.198273	+	0.0285074i	0.240736	−	0.970591i	$-0.422611\pi$
$661$	5.09759	+	0.732922i	0.198273	+	0.0285074i	−0.0424627	+	0.999098i	$0.513520\pi$
$662$	5.79854	−	15.5465i	0.225367	−	0.604232i
$663$	1.12321	−	1.50043i	0.0436218	−	0.0582720i
$664$	5.73657	−	3.68667i	0.222622	−	0.143071i
$665$	36.4771	+	28.2207i	1.41452	+	1.09435i
$666$			21.0887i			0.817170i
$667$	3.19489	+	13.0105i	0.123707	+	0.503768i
$668$	8.22129	−	8.22129i	0.318091	−	0.318091i
$669$	−5.65024	−	4.89596i	−0.218451	−	0.189289i
$670$	−3.68049	+	23.0009i	−0.142190	+	0.888603i
$671$	0.476747	+	3.31585i	0.0184046	+	0.128007i
$672$	−3.60299	−	1.34385i	−0.138989	−	0.0518400i
$673$	−28.7147	−	38.3584i	−1.10687	−	1.47861i	−0.860513	−	0.509428i	$-0.829857\pi$
$673$	−28.7147	−	38.3584i	−1.10687	−	1.47861i	−0.246358	−	0.969179i	$-0.579234\pi$
$674$	12.8947	−	3.78622i	0.496685	−	0.145840i
$675$	21.5377	−	7.26330i	0.828987	−	0.279565i
$676$	−4.67280	+	10.2320i	−0.179723	+	0.393538i
$677$	28.3792	−	15.4962i	1.09070	−	0.595568i	0.169845	−	0.985471i	$-0.445673\pi$
$677$	28.3792	−	15.4962i	1.09070	−	0.595568i	0.920856	+	0.389903i	$0.127492\pi$
$678$	−1.11972	+	15.6557i	−0.0430025	+	0.601253i
$679$	62.7102	−	54.3387i	2.40660	−	2.08533i
$680$	−1.92830	−	3.10786i	−0.0739471	−	0.119181i
$681$	15.9871	+	7.30107i	0.612628	+	0.279778i
$682$	0.131095	−	0.0285179i	0.00501988	−	0.00109201i
$683$	2.42858	−	4.44760i	0.0929269	−	0.170183i	−0.827081	−	0.562083i	$-0.810000\pi$
$683$	2.42858	−	4.44760i	0.0929269	−	0.170183i	0.920008	+	0.391900i	$0.128182\pi$
$684$	1.48724	−	10.3440i	0.0568659	−	0.395511i
$685$	27.0632	−	14.2248i	1.03403	−	0.543503i
$686$	−25.1709	+	3.61903i	−0.961029	+	0.138175i
$687$	0.271383	−	1.24753i	0.0103539	−	0.0475962i
$688$	−12.4898	+	0.893286i	−0.476168	+	0.0340562i
$689$	−9.89998			−0.377159
$690$	−9.26788	−	0.562983i	−0.352822	−	0.0214324i
$691$	−0.0185681			−0.000706364			−0.000353182	−	1.00000i	$-0.500112\pi$
$691$	−0.0185681			−0.000706364			−0.000353182		1.00000i	$0.500112\pi$
$692$	−4.65800	+	0.333147i	−0.177071	+	0.0126643i
$693$	−1.36046	+	6.25393i	−0.0516796	+	0.237567i
$694$	−3.44317	+	0.495053i	−0.130701	+	0.0187919i
$695$	14.9268	−	48.0043i	0.566206	−	1.82091i
$696$	−0.344212	+	2.39405i	−0.0130473	+	0.0907461i
$697$	1.49704	−	2.74162i	0.0567043	−	0.103846i
$698$	−4.62832	+	1.00683i	−0.175185	+	0.0381091i
$699$	−5.20973	−	2.37921i	−0.197050	−	0.0899898i
$700$	−18.1908	+	12.7372i	−0.687548	+	0.481420i
$701$	18.8681	−	16.3493i	0.712638	−	0.617504i	−0.221188	−	0.975231i	$-0.570994\pi$
$701$	18.8681	−	16.3493i	0.712638	−	0.617504i	0.933826	+	0.357727i	$0.116448\pi$
$702$	−0.429192	+	6.00089i	−0.0161988	+	0.226489i
$703$	−38.1960	+	20.8566i	−1.44059	+	0.786622i
$704$	0.266018	−	0.582498i	0.0100259	−	0.0219537i
$705$	14.9170	−	4.12405i	0.561806	−	0.155321i
$706$	33.2778	−	9.77123i	1.25242	−	0.367745i
$707$	16.2137	+	21.6589i	0.609778	+	0.814568i
$708$	−1.21260	−	0.452275i	−0.0455722	−	0.0169975i
$709$	4.28341	+	29.7917i	0.160867	+	1.11885i	0.897005	+	0.442021i	$0.145738\pi$
$709$	4.28341	+	29.7917i	0.160867	+	1.11885i	−0.736138	+	0.676831i	$0.763353\pi$
$710$	14.4692	−	10.4774i	0.543020	−	0.393210i
$711$	0.114914	+	0.0995739i	0.00430963	+	0.00373431i
$712$	−0.472670	+	0.472670i	−0.0177140	+	0.0177140i
$713$	0.187389	−	0.987127i	0.00701779	−	0.0369682i
$714$		−	6.28990i		−	0.235394i
$715$	1.15959	−	1.49885i	0.0433661	−	0.0560536i
$716$	−8.35654	+	5.37042i	−0.312298	+	0.200702i
$717$	−6.85445	+	9.15647i	−0.255984	+	0.341955i
$718$	−7.26165	+	19.4692i	−0.271002	+	0.726585i
$719$	−14.6266	−	2.10298i	−0.545479	−	0.0784281i	−0.135934	−	0.990718i	$-0.543404\pi$
$719$	−14.6266	−	2.10298i	−0.545479	−	0.0784281i	−0.409545	+	0.912290i	$0.634313\pi$
$720$	4.54345	+	2.16271i	0.169324	+	0.0805994i
$721$	57.1764	+	36.7451i	2.12936	+	1.36846i
$722$	2.40390	−	0.896610i	0.0894640	−	0.0333684i
$723$	7.66263	+	14.0331i	0.284976	+	0.521895i
$724$	−12.2032	−	14.0832i	−0.453528	−	0.523399i
$725$	10.2602	+	9.47705i	0.381056	+	0.351969i
$726$	−8.79764	−	2.58322i	−0.326511	−	0.0958723i
$727$	2.29485	+	6.15274i	0.0851114	+	0.228192i	0.972532	−	0.232767i	$-0.0747780\pi$
$727$	2.29485	+	6.15274i	0.0851114	+	0.228192i	−0.887421	+	0.460960i	$0.847505\pi$
$728$	−1.24943	−	5.74355i	−0.0463071	−	0.212870i
$729$	−1.54192	−	5.25131i	−0.0571083	−	0.194493i
$730$	−8.14088	−	9.70199i	−0.301307	−	0.359087i
$731$	−8.50826	−	18.6305i	−0.314689	−	0.689074i
$732$	3.62597	+	2.71437i	0.134020	+	0.100326i
$733$	−16.7692	−	3.64792i	−0.619384	−	0.134739i	−0.108085	−	0.994142i	$-0.534472\pi$
$733$	−16.7692	−	3.64792i	−0.619384	−	0.134739i	−0.511299	+	0.859403i	$0.670836\pi$
$734$	4.44796	−	5.13322i	0.164177	−	0.189471i
$735$	−24.5995	+	1.36741i	−0.907368	+	0.0504379i
$736$	−3.23589	−	3.53964i	−0.119276	−	0.130473i
$737$	−4.71698	−	4.71698i	−0.173752	−	0.173752i
$738$	0.306585	+	4.28662i	0.0112856	+	0.157793i
$739$	−8.70552	−	13.5461i	−0.320238	−	0.498300i	0.643393	−	0.765536i	$-0.277526\pi$
$739$	−8.70552	−	13.5461i	−0.320238	−	0.498300i	−0.963631	+	0.267236i	$0.913890\pi$
$740$	−4.12879	−	20.5441i	−0.151777	−	0.755218i
$741$	−4.84042	+	2.21055i	−0.177817	+	0.0812065i
$742$	−26.5968	+	19.9101i	−0.976399	+	0.730923i
$743$	26.4475	+	14.4414i	0.970266	+	0.529805i	0.884515	−	0.466512i	$-0.154489\pi$
$743$	26.4475	+	14.4414i	0.970266	+	0.529805i	0.0857505	+	0.996317i	$0.472671\pi$
$744$	0.0980702	−	0.152600i	0.00359543	−	0.00559459i
$745$	−18.8889	−	43.1607i	−0.692035	−	1.58128i
$746$	6.30294	−	21.4658i	0.230767	−	0.785920i
$747$	−15.3062	−	1.09472i	−0.560023	−	0.0400536i
$748$	1.04476	+	0.0747228i	0.0382003	+	0.00273214i
$749$	−7.43028	+	25.3052i	−0.271496	+	0.924632i
$750$	−8.38339	+	4.84004i	−0.306118	+	0.176733i
$751$	0.941316	−	1.46472i	0.0343491	−	0.0534483i	−0.823654	−	0.567092i	$-0.808068\pi$
$751$	0.941316	−	1.46472i	0.0343491	−	0.0534483i	0.858004	+	0.513644i	$0.171705\pi$
$752$	7.01607	+	3.83106i	0.255850	+	0.139704i
$753$	20.0654	−	15.0208i	0.731224	−	0.547388i
$754$	−3.36291	+	1.53579i	−0.122470	+	0.0559301i
$755$	8.68916	+	5.78106i	0.316231	+	0.210394i
$756$	10.9155	+	16.9849i	0.396993	+	0.617733i
$757$	0.306709	+	4.28835i	0.0111475	+	0.155863i	0.999977	+	0.00681020i	$0.00216777\pi$
$757$	0.306709	+	4.28835i	0.0111475	+	0.155863i	−0.988829	+	0.149052i	$0.952378\pi$
$758$	−10.7771	−	10.7771i	−0.391444	−	0.391444i
$759$	1.68724	−	2.05516i	0.0612428	−	0.0745978i
$760$	0.576328	+	10.3680i	0.0209056	+	0.376088i
$761$	−25.0554	+	28.9155i	−0.908257	+	1.04818i	0.0903754	+	0.995908i	$0.471193\pi$
$761$	−25.0554	+	28.9155i	−0.908257	+	1.04818i	−0.998633	+	0.0522769i	$0.983352\pi$
$762$	−10.8430	−	2.35875i	−0.392800	−	0.0854484i
$763$	−27.1558	−	20.3286i	−0.983107	−	0.735945i
$764$	−5.78388	−	12.6649i	−0.209254	−	0.458201i
$765$	−0.717369	+	8.19925i	−0.0259365	+	0.296445i
$766$	−1.71417	−	5.83793i	−0.0619355	−	0.210933i
$767$	−0.420500	−	1.93301i	−0.0151834	−	0.0697969i
$768$	−0.302576	−	0.811237i	−0.0109183	−	0.0292730i
$769$	43.1597	+	12.6728i	1.55638	+	0.456994i	0.942999	−	0.332795i	$-0.107992\pi$
$769$	43.1597	+	12.6728i	1.55638	+	0.456994i	0.613379	+	0.789789i	$0.289810\pi$
$770$	0.100922	−	6.35880i	0.00363699	−	0.229155i
$771$	−2.68204	−	3.09523i	−0.0965911	−	0.111472i
$772$	−6.19552	−	11.3462i	−0.222982	−	0.408360i
$773$	−27.0428	+	10.0864i	−0.972661	+	0.362784i	−0.785031	−	0.619456i	$-0.787353\pi$
$773$	−27.0428	+	10.0864i	−0.972661	+	0.362784i	−0.187629	+	0.982240i	$0.560080\pi$
$774$	23.7049	+	15.2342i	0.852054	+	0.547582i
$775$	−0.404702	−	0.966197i	−0.0145373	−	0.0347068i
$776$	18.4927	+	2.65885i	0.663850	+	0.0954473i
$777$	12.5936	−	33.7648i	0.451794	−	1.21131i
$778$	13.0504	−	17.4333i	0.467879	−	0.625013i
$779$	−7.46076	+	4.79474i	−0.267309	+	0.171789i
$780$	−0.324353	−	2.54164i	−0.0116137	−	0.0910052i
$781$			5.11600i			0.183065i
$782$	3.57499	−	6.98242i	0.127841	−	0.249691i
$783$	8.97942	−	8.97942i	0.320898	−	0.320898i
$784$	−9.61741	−	8.33354i	−0.343479	−	0.297626i
$785$	30.1043	+	41.5739i	1.07447	+	1.48384i
$786$	−0.200352	−	1.39348i	−0.00714632	−	0.0497037i
$787$	4.24741	+	1.58420i	0.151404	+	0.0564707i	0.424024	−	0.905651i	$-0.360617\pi$
$787$	4.24741	+	1.58420i	0.151404	+	0.0564707i	−0.272620	+	0.962122i	$0.587890\pi$
$788$	1.91308	+	2.55558i	0.0681508	+	0.0910388i
$789$	4.35514	−	1.27878i	0.155047	−	0.0455259i
$790$	−0.131442	−	0.0745045i	−0.00467649	−	0.00265075i
$791$	−33.4462	+	73.2370i	−1.18921	+	2.60401i
$792$	−1.26477	+	0.690619i	−0.0449418	+	0.0245401i
$793$	−0.493904	+	6.90567i	−0.0175390	+	0.245228i
$794$	14.9814	−	12.9815i	0.531671	−	0.460696i
$795$	−12.3062	+	7.63555i	−0.436458	+	0.270805i
$796$	18.6390	+	8.51215i	0.660642	+	0.301705i
$797$	−44.1182	+	9.59733i	−1.56275	+	0.339955i	−0.909013	−	0.416769i	$-0.863163\pi$
$797$	−44.1182	+	9.59733i	−1.56275	+	0.339955i	−0.653735	+	0.756723i	$0.726799\pi$
$798$	−8.55835	+	15.6734i	−0.302962	+	0.554834i
$799$	−1.86082	+	12.9423i	−0.0658311	+	0.457865i
$800$	−4.84955	−	1.21734i	−0.171457	−	0.0430394i
$801$	1.48894	−	0.214078i	0.0526092	−	0.00756406i
$802$	4.32039	−	19.8605i	0.152558	−	0.701300i
$803$	3.61777	−	0.258748i	0.127668	−	0.00913103i
$804$	−9.01948			−0.318093
$805$	−43.5340	−	19.3196i	−1.53437	−	0.680925i
$806$	0.277269			0.00976639
$807$	18.7294	−	1.33955i	0.659306	−	0.0471545i
$808$	−1.29488	+	5.95247i	−0.0455537	+	0.209407i
$809$	43.3227	−	6.22886i	1.52314	−	0.218995i	0.670667	−	0.741759i	$-0.266008\pi$
$809$	43.3227	−	6.22886i	1.52314	−	0.218995i	0.852478	+	0.522764i	$0.175099\pi$
$810$	−2.92867	−	5.57189i	−0.102903	−	0.195776i
$811$	−0.844780	+	5.87558i	−0.0296642	+	0.206319i	−0.999263	−	0.0383801i	$-0.987780\pi$
$811$	−0.844780	+	5.87558i	−0.0296642	+	0.206319i	0.969599	+	0.244699i	$0.0786893\pi$
$812$	−5.94595	+	10.8892i	−0.208662	+	0.382136i
$813$	−3.70997	+	0.807055i	−0.130114	+	0.0283047i
$814$	5.45878	+	2.49294i	0.191330	+	0.0873775i
$815$	7.84854	−	33.5097i	0.274922	−	1.17379i
$816$	1.07030	−	0.927421i	0.0374680	−	0.0324662i
$817$	−4.14832	+	58.0010i	−0.145131	+	2.02920i
$818$	26.6681	−	14.5619i	0.932428	−	0.509144i
$819$	−5.49479	+	12.0319i	−0.192004	+	0.420429i
$820$	−1.13791	−	4.11591i	−0.0397376	−	0.143734i
$821$	−17.5582	+	5.15556i	−0.612786	+	0.179930i	−0.573375	−	0.819293i	$-0.694366\pi$
$821$	−17.5582	+	5.15556i	−0.612786	+	0.179930i	−0.0394106	+	0.999223i	$0.512548\pi$
$822$	7.09456	+	9.47723i	0.247451	+	0.330556i
$823$	−30.9397	−	11.5399i	−1.07849	−	0.402256i	−0.253461	−	0.967346i	$-0.581569\pi$
$823$	−30.9397	−	11.5399i	−1.07849	−	0.402256i	−0.825029	+	0.565090i	$0.808842\pi$
$824$	2.17783	+	15.1472i	0.0758684	+	0.527676i
$825$	0.285421	−	2.75750i	0.00993709	−	0.0960040i
$826$	−5.01721	−	4.34744i	−0.174571	−	0.151267i
$827$	10.7227	−	10.7227i	0.372864	−	0.372864i	−0.495655	−	0.868519i	$-0.665072\pi$
$827$	10.7227	−	10.7227i	0.372864	−	0.372864i	0.868519	+	0.495655i	$0.165072\pi$
$828$	1.05593	+	10.7405i	0.0366962	+	0.373258i
$829$			25.9627i			0.901722i	0.892594	+	0.450861i	$0.148883\pi$
$829$			25.9627i			0.901722i	−0.892594	+	0.450861i	$0.851117\pi$
$830$	15.1253	−	1.93022i	0.525005	−	0.0669990i
$831$	14.7166	−	9.45777i	0.510513	−	0.328086i
$832$	0.793109	−	1.05947i	0.0274961	−	0.0367305i
$833$	7.27410	−	19.5026i	0.252033	−	0.675726i
$834$	19.2675	+	2.77025i	0.667179	+	0.0959258i
$835$	24.4999	−	8.69767i	0.847855	−	0.300995i
$836$	−2.50171	−	1.60775i	−0.0865235	−	0.0556053i
$837$	−0.892343	+	0.332827i	−0.0308439	+	0.0115042i
$838$	−11.4261	−	20.9254i	−0.394710	−	0.722857i
$839$	4.99582	+	5.76549i	0.172475	+	0.199047i	0.835405	−	0.549634i	$-0.185233\pi$
$839$	4.99582	+	5.76549i	0.172475	+	0.199047i	−0.662930	+	0.748681i	$0.730687\pi$
$840$	−5.98294	−	6.17591i	−0.206431	−	0.213089i
$841$	−20.3379	−	5.97175i	−0.701307	−	0.205922i
$842$	1.45643	+	3.90483i	0.0501918	+	0.134569i
$843$	4.04325	+	18.5865i	0.139257	+	0.640154i
$844$	1.88660	+	6.42517i	0.0649395	+	0.221164i
$845$	−19.2679	+	16.1676i	−0.662837	+	0.556182i
$846$	−7.47289	−	16.3634i	−0.256923	−	0.562584i
$847$	−37.6524	−	28.1862i	−1.29375	−	0.968490i
$848$	−7.30953	−	1.59009i	−0.251010	−	0.0546040i
$849$	−5.71112	+	6.59098i	−0.196005	+	0.226202i
$850$	−0.906421	−	8.12798i	−0.0310900	−	0.278787i
$851$	33.1711	−	30.3245i	1.13709	−	1.03951i
$852$	4.89123	+	4.89123i	0.167571	+	0.167571i
$853$	0.131406	+	1.83730i	0.00449926	+	0.0629078i	0.999206	−	0.0398498i	$-0.0126879\pi$
$853$	0.131406	+	1.83730i	0.00449926	+	0.0629078i	−0.994706	+	0.102758i	$0.967233\pi$
$854$	12.5613	+	19.5457i	0.429838	+	0.668841i
$855$	12.9439	−	19.4552i	0.442671	−	0.665352i
$856$	−5.40155	+	2.46680i	−0.184621	+	0.0843136i
$857$	0.187124	−	0.140079i	0.00639202	−	0.00478500i	−0.596077	−	0.802927i	$-0.703275\pi$
$857$	0.187124	−	0.140079i	0.00639202	−	0.00478500i	0.602469	+	0.798142i	$0.294184\pi$
$858$	0.644022	+	0.351663i	0.0219866	+	0.0120056i
$859$	13.2769	−	20.6592i	0.453001	−	0.704883i	−0.537366	−	0.843349i	$-0.680581\pi$
$859$	13.2769	−	20.6592i	0.453001	−	0.704883i	0.990367	+	0.138466i	$0.0442171\pi$
$860$	−26.0754	−	10.1998i	−0.889162	−	0.347811i
$861$	2.06899	−	7.04634i	0.0705110	−	0.240139i
$862$	−22.4546	−	1.60599i	−0.764808	−	0.0547002i
$863$	−10.2618	−	0.733939i	−0.349316	−	0.0249836i	−0.104421	−	0.994533i	$-0.533299\pi$
$863$	−10.2618	−	0.733939i	−0.349316	−	0.0249836i	−0.244895	+	0.969550i	$0.578753\pi$
$864$	−1.28073	+	4.36175i	−0.0435712	+	0.148390i
$865$	−9.72469	−	3.80398i	−0.330649	−	0.129339i
$866$	−4.70731	+	7.32472i	−0.159961	+	0.248904i
$867$	−10.8855	−	5.94394i	−0.369691	−	0.201867i
$868$	0.744897	−	0.557623i	0.0252835	−	0.0189270i
$869$	0.0393589	−	0.0179746i	0.00133516	−	0.000609746i
$870$	−2.99578	+	4.50278i	−0.101566	+	0.152658i
$871$	−7.45356	−	11.5980i	−0.252554	−	0.392982i
$872$	−0.544868	−	7.61826i	−0.0184516	−	0.257987i
$873$	−29.7288	−	29.7288i	−1.00617	−	1.00617i
$874$	−18.4089	+	12.5348i	−0.622692	+	0.423996i
$875$	−48.9685	+	8.23395i	−1.65544	+	0.278358i
$876$	3.21145	−	3.70621i	0.108505	−	0.125221i
$877$	−17.8109	−	3.87453i	−0.601432	−	0.130833i	−0.0984669	−	0.995140i	$-0.531394\pi$
$877$	−17.8109	−	3.87453i	−0.601432	−	0.130833i	−0.502965	+	0.864307i	$0.667757\pi$
$878$	−3.08589	−	2.31007i	−0.104144	−	0.0779610i
$879$	−1.30289	−	2.85293i	−0.0439454	−	0.0962269i
$880$	1.09690	−	0.920406i	0.0369767	−	0.0310269i
$881$	−4.62296	−	15.7444i	−0.155752	−	0.530441i	0.844233	−	0.535976i	$-0.180056\pi$
$881$	−4.62296	−	15.7444i	−0.155752	−	0.530441i	−0.999985	+	0.00553503i	$0.998238\pi$
$882$	6.08725	+	27.9827i	0.204968	+	0.942225i
$883$	−12.1721	−	32.6348i	−0.409625	−	1.09825i	−0.963982	−	0.265968i	$-0.914308\pi$
$883$	−12.1721	−	32.6348i	−0.409625	−	1.09825i	0.554357	−	0.832279i	$-0.312964\pi$
$884$	2.07703	+	0.609871i	0.0698581	+	0.0205122i
$885$	−2.01357	−	2.07852i	−0.0676855	−	0.0698687i
$886$	13.0375	+	15.0461i	0.438005	+	0.505484i
$887$	11.4695	+	21.0048i	0.385107	+	0.705271i	0.996275	−	0.0862298i	$-0.0274819\pi$
$887$	11.4695	+	21.0048i	0.385107	+	0.705271i	−0.611168	+	0.791501i	$0.709300\pi$
$888$	7.60236	−	2.83554i	0.255119	−	0.0951543i
$889$	−47.8851	−	30.7739i	−1.60601	−	1.03212i
$890$	−1.40858	+	0.500058i	−0.0472158	+	0.0167620i
$891$	1.78433	+	0.256548i	0.0597773	+	0.00859467i
$892$	3.01759	−	8.09047i	0.101036	−	0.270889i
$893$	22.2468	−	29.7182i	0.744461	−	0.994483i
$894$	15.3467	−	9.86270i	0.513269	−	0.329858i
$895$	−22.0331	+	2.81178i	−0.736487	+	0.0939874i
$896$		−	4.44136i		−	0.148375i
$897$	4.31016	−	3.40911i	0.143912	−	0.113827i
$898$	−12.5027	+	12.5027i	−0.417222	+	0.417222i
$899$	−0.442302	−	0.383257i	−0.0147516	−	0.0127823i
$900$	7.09474	+	8.73302i	0.236491	+	0.291101i
$901$	−1.74131	−	12.1111i	−0.0580115	−	0.403479i
$902$	1.14583	+	0.427372i	0.0381519	+	0.0142299i
$903$	−28.8561	−	38.5472i	−0.960271	−	1.28277i
$904$	−17.3936	+	5.10724i	−0.578504	+	0.169864i
$905$	−11.1035	−	40.1620i	−0.369092	−	1.33503i
$906$	−1.67875	+	3.67596i	−0.0557728	+	0.122125i
$907$	−37.9535	+	20.7242i	−1.26023	+	0.688136i	−0.963725	−	0.266897i	$-0.914002\pi$
$907$	−37.9535	+	20.7242i	−1.26023	+	0.688136i	−0.296501	+	0.955033i	$0.595820\pi$
$908$	−1.44811	+	20.2472i	−0.0480572	+	0.671927i
$909$	10.3601	−	8.97708i	0.343623	−	0.297751i
$910$	2.99727	−	12.7970i	0.0993587	−	0.424217i
$911$	−26.5616	−	12.1303i	−0.880024	−	0.401894i	−0.0764326	−	0.997075i	$-0.524353\pi$
$911$	−26.5616	−	12.1303i	−0.880024	−	0.401894i	−0.803592	+	0.595181i	$0.797080\pi$
$912$	−3.92892	+	0.854683i	−0.130099	+	0.0283014i
$913$	−2.09274	+	3.83257i	−0.0692596	+	0.126840i
$914$	0.0242049	−	0.168348i	0.000800625	−	0.00556847i
$915$	4.71218	+	8.96508i	0.155780	+	0.296376i
$916$	1.45954	−	0.209850i	0.0482246	−	0.00693365i
$917$	1.53504	−	7.05647i	0.0506915	−	0.233025i
$918$	−7.41665	+	0.530449i	−0.244786	+	0.0175074i
$919$	−35.9123			−1.18464			−0.592318	−	0.805704i	$-0.701787\pi$
$919$	−35.9123			−1.18464			−0.592318	+	0.805704i	$0.701787\pi$
$920$	−3.13146	−	10.2564i	−0.103241	−	0.338144i
$921$	12.5276			0.412797
$922$	13.3120	−	0.952096i	0.438409	−	0.0313556i
$923$	−2.24750	+	10.3316i	−0.0739772	+	0.340068i
$924$	2.43743	−	0.350450i	0.0801857	−	0.0115290i
$925$	11.4081	−	45.4467i	0.375095	−	1.49428i
$926$	2.27414	−	15.8170i	0.0747328	−	0.519778i
$927$	16.5038	−	30.2245i	0.542056	−	0.992702i
$928$	−2.72963	+	0.593795i	−0.0896046	+	0.0194923i
$929$	−11.6918	−	5.33948i	−0.383597	−	0.175183i	0.214277	−	0.976773i	$-0.431260\pi$
$929$	−11.6918	−	5.33948i	−0.383597	−	0.175183i	−0.597874	+	0.801590i	$0.703988\pi$
$930$	0.344661	−	0.213849i	0.0113019	−	0.00701238i
$931$	−44.6622	+	38.7000i	−1.46374	+	1.26834i
$932$	0.471896	−	6.59797i	0.0154575	−	0.216124i
$933$	17.7313	−	9.68204i	0.580498	−	0.316976i
$934$	−4.41012	+	9.65681i	−0.144303	+	0.315980i
$935$	2.03756	+	1.15494i	0.0666354	+	0.0377706i
$936$	−2.85756	+	0.839055i	−0.0934023	+	0.0274254i
$937$	3.23738	+	4.32464i	0.105761	+	0.141280i	0.850299	−	0.526300i	$-0.176421\pi$
$937$	3.23738	+	4.32464i	0.105761	+	0.141280i	−0.744538	+	0.667580i	$0.767330\pi$
$938$	−43.3493	−	16.1685i	−1.41541	−	0.527919i
$939$	0.590264	+	4.10538i	0.0192625	+	0.133974i
$940$	10.4836	+	14.4778i	0.341937	+	0.472213i
$941$	−20.2062	−	17.5088i	−0.658703	−	0.570769i	0.260054	−	0.965594i	$-0.416260\pi$
$941$	−20.2062	−	17.5088i	−0.658703	−	0.570769i	−0.918756	+	0.394825i	$0.870805\pi$
$942$	−14.0538	+	14.0538i	−0.457897	+	0.457897i
$943$	6.30172	−	6.64620i	0.205212	−	0.216430i
$944$		−	1.49475i		−	0.0486500i
$945$	5.71500	+	44.7829i	0.185909	+	1.45679i
$946$	6.74556	−	4.33511i	0.219317	−	0.140946i
$947$	1.45112	−	1.93847i	0.0471550	−	0.0629917i	−0.776344	−	0.630310i	$-0.782928\pi$
$947$	1.45112	−	1.93847i	0.0471550	−	0.0629917i	0.823499	+	0.567318i	$0.192019\pi$
$948$	0.0204448	−	0.0548145i	0.000664015	−	0.00178029i
$949$	7.41963	+	1.06678i	0.240851	+	0.0346292i
$950$	−8.80067	+	21.4870i	−0.285531	+	0.697129i
$951$	−15.8088	−	10.1597i	−0.512636	−	0.329451i
$952$	6.80657	−	2.53872i	0.220602	−	0.0822804i
$953$	18.1893	+	33.3113i	0.589211	+	1.07906i	0.986869	+	0.161525i	$0.0516413\pi$
$953$	18.1893	+	33.3113i	0.589211	+	1.07906i	−0.397658	+	0.917534i	$0.630177\pi$
$954$	11.0237	+	12.7220i	0.356905	+	0.411891i
$955$	0.494060	−	31.1292i	0.0159874	−	1.00732i
$956$	−12.6752	−	3.72178i	−0.409945	−	0.120371i
$957$	−0.541262	−	1.45118i	−0.0174965	−	0.0469099i
$958$	0.345275	+	1.58720i	0.0111553	+	0.0512802i
$959$	17.1088	+	58.2671i	0.552471	+	1.88154i
$960$	0.168744	−	1.92868i	0.00544620	−	0.0622479i
$961$	−12.8596	−	28.1587i	−0.414827	−	0.908344i
$962$	9.92863	+	7.43248i	0.320112	+	0.239633i
$963$	13.0575	+	2.84049i	0.420773	+	0.0915335i
$964$	−12.0930	+	13.9561i	−0.389489	+	0.449495i
$965$	−1.60437	−	28.8623i	−0.0516465	−	0.929111i
$966$	4.72330	−	17.8270i	0.151970	−	0.573575i
$967$	6.00616	+	6.00616i	0.193145	+	0.193145i	0.797054	−	0.603908i	$-0.206391\pi$
$967$	6.00616	+	6.00616i	0.193145	+	0.193145i	−0.603908	+	0.797054i	$0.706391\pi$
$968$	−0.755477	−	10.5629i	−0.0242819	−	0.339506i
$969$	−3.55564	−	5.53269i	−0.114224	−	0.177736i
$970$	34.7816	+	23.1408i	1.11677	+	0.743007i
$971$	−28.9927	+	13.2405i	−0.930421	+	0.424909i	−0.822188	−	0.569217i	$-0.807247\pi$
$971$	−28.9927	+	13.2405i	−0.930421	+	0.424909i	−0.108233	+	0.994126i	$0.534519\pi$
$972$	12.8687	−	9.63341i	0.412765	−	0.308992i
$973$	87.6372	+	47.8535i	2.80952	+	1.53411i
$974$	16.0073	−	24.9078i	0.512905	−	0.798096i
$975$	1.78779	−	5.44329i	0.0572551	−	0.174325i
$976$	−1.47383	+	5.01939i	−0.0471760	+	0.160667i
$977$	53.9523	+	3.85874i	1.72609	+	0.123452i	0.898809	−	0.438341i	$-0.144434\pi$
$977$	53.9523	+	3.85874i	1.72609	+	0.123452i	0.827278	+	0.561793i	$0.189888\pi$
$978$	13.2925	+	0.950698i	0.425047	+	0.0304000i
$979$	0.120598	−	0.410718i	0.00385431	−	0.0131266i
$980$	−11.4086	−	26.0683i	−0.364433	−	0.832722i
$981$	−9.29225	+	14.4590i	−0.296679	+	0.461641i
$982$	11.3250	+	6.18394i	0.361396	+	0.197337i
$983$	−23.0500	+	17.2550i	−0.735180	+	0.550349i	−0.899955	−	0.435982i	$-0.856401\pi$
$983$	−23.0500	+	17.2550i	−0.735180	+	0.550349i	0.164775	+	0.986331i	$0.447310\pi$
$984$	1.50408	−	0.686891i	0.0479484	−	0.0218973i
$985$	1.40646	+	6.99831i	0.0448136	+	0.222985i
$986$	−2.47030	−	3.84386i	−0.0786704	−	0.122413i
$987$	2.19297	+	30.6618i	0.0698031	+	0.975975i
$988$	−4.34582	−	4.34582i	−0.138259	−	0.138259i
$989$	−10.1241	−	59.1923i	−0.321928	−	1.88220i
$990$	−3.21731	+	0.178841i	−0.102253	+	0.00568392i
$991$	5.67864	−	6.55350i	0.180388	−	0.208179i	−0.658353	−	0.752709i	$-0.728747\pi$
$991$	5.67864	−	6.55350i	0.180388	−	0.208179i	0.838741	+	0.544530i	$0.183292\pi$
$992$	0.204718	+	0.0445337i	0.00649981	+	0.00141395i
$993$	11.5009	+	8.60946i	0.364970	+	0.273213i
$994$	14.7401	+	32.2763i	0.467527	+	1.02374i
$995$	29.4515	+	35.0992i	0.933676	+	1.11272i
$996$	1.66339	+	5.66499i	0.0527065	+	0.179502i
$997$	1.01280	+	4.65575i	0.0320756	+	0.147449i	0.990399	−	0.138235i	$-0.0441429\pi$
$997$	1.01280	+	4.65575i	0.0320756	+	0.147449i	−0.958324	+	0.285684i	$0.907779\pi$
$998$	9.60198	+	25.7439i	0.303945	+	0.814909i
$999$	−40.8754	−	12.0021i	−1.29324	−	0.379729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.7.5	✓	240
5.3	odd	4	inner	230.2.l.a.53.11	yes	240
23.10	odd	22	inner	230.2.l.a.217.11	yes	240
115.33	even	44	inner	230.2.l.a.33.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.5	✓	240	1.1	even	1	trivial
230.2.l.a.33.5	yes	240	115.33	even	44	inner
230.2.l.a.53.11	yes	240	5.3	odd	4	inner
230.2.l.a.217.11	yes	240	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 + 0.0713392i) q^{2} +(0.184045 - 0.846041i) q^{3} +(0.989821 - 0.142315i) q^{4} +(2.13522 + 0.663941i) q^{5} +(-0.123220 + 0.857015i) q^{6} +(-2.12852 + 3.89809i) q^{7} +(-0.977147 + 0.212565i) q^{8} +(2.04698 + 0.934826i) q^{9} +(-2.17715 - 0.509924i) q^{10} +(0.483957 - 0.419351i) q^{11} +(0.0617674 - 0.863622i) q^{12} +(1.16156 - 0.634258i) q^{13} +(1.84501 - 4.04000i) q^{14} +(0.954698 - 1.68429i) q^{15} +(0.959493 - 0.281733i) q^{16} +(0.980222 + 1.30942i) q^{17} +(-2.10846 - 0.786414i) q^{18} +(-0.660894 - 4.59662i) q^{19} +(2.20798 + 0.353309i) q^{20} +(2.90620 + 2.51823i) q^{21} +(-0.452808 + 0.452808i) q^{22} +(1.79488 + 4.44729i) q^{23} +0.865828i q^{24} +(4.11836 + 2.83533i) q^{25} +(-1.11335 + 0.715507i) q^{26} +(2.72425 - 3.63917i) q^{27} +(-1.55210 + 4.16133i) q^{28} +(2.76504 + 0.397553i) q^{29} +(-0.832110 + 1.74811i) q^{30} +(-0.176248 - 0.113268i) q^{31} +(-0.936950 + 0.349464i) q^{32} +(-0.265718 - 0.486627i) q^{33} +(-1.07114 - 1.23616i) q^{34} +(-7.13296 + 6.91008i) q^{35} +(2.15919 + 0.633995i) q^{36} +(-3.27494 - 8.78046i) q^{37} +(0.987129 + 4.53776i) q^{38} +(-0.322830 - 1.09946i) q^{39} +(-2.22756 - 0.194894i) q^{40} +(-0.793335 - 1.73716i) q^{41} +(-3.07844 - 2.30449i) q^{42} +(-12.2355 - 2.66167i) q^{43} +(0.419351 - 0.483957i) q^{44} +(3.75010 + 3.35514i) q^{45} +(-2.10758 - 4.30791i) q^{46} +(5.65253 + 5.65253i) q^{47} +(-0.0617674 - 0.863622i) q^{48} +(-6.88001 - 10.7055i) q^{49} +(-4.31014 - 2.53430i) q^{50} +(1.28823 - 0.588315i) q^{51} +(1.05947 - 0.793109i) q^{52} +(-6.56546 - 3.58501i) q^{53} +(-2.45769 + 3.82425i) q^{54} +(1.31178 - 0.574090i) q^{55} +(1.25128 - 4.26145i) q^{56} +(-4.01056 - 0.286841i) q^{57} +(-2.78635 - 0.199284i) q^{58} +(0.421120 - 1.43420i) q^{59} +(0.705281 - 1.80302i) q^{60} +(-2.82825 + 4.40084i) q^{61} +(0.183879 + 0.100406i) q^{62} +(-8.00107 + 5.98953i) q^{63} +(0.909632 - 0.415415i) q^{64} +(2.90129 - 0.583078i) q^{65} +(0.299757 + 0.466431i) q^{66} +(-0.743153 - 10.3906i) q^{67} +(1.15660 + 1.15660i) q^{68} +(4.09293 - 0.700044i) q^{69} +(6.62183 - 7.40133i) q^{70} +(-5.23180 + 6.03781i) q^{71} +(-2.19892 - 0.478345i) q^{72} +(4.53424 + 3.39429i) q^{73} +(3.89299 + 8.52446i) q^{74} +(3.15677 - 2.96248i) q^{75} +(-1.30833 - 4.45578i) q^{76} +(0.604557 + 2.77910i) q^{77} +(0.400441 + 1.07362i) q^{78} +(0.0648320 + 0.0190364i) q^{79} +(2.23579 + 0.0354848i) q^{80} +(1.84348 + 2.12749i) q^{81} +(0.915241 + 1.67614i) q^{82} +(-6.38913 + 2.38302i) q^{83} +(3.23500 + 2.07901i) q^{84} +(1.22361 + 3.44672i) q^{85} +(12.3942 + 1.78202i) q^{86} +(0.845237 - 2.26617i) q^{87} +(-0.383758 + 0.512640i) q^{88} +(0.562341 - 0.361394i) q^{89} +(-3.97990 - 3.07906i) q^{90} +5.87788i q^{91} +(2.40953 + 4.14658i) q^{92} +(-0.128266 + 0.128266i) q^{93} +(-6.04138 - 5.23488i) q^{94} +(1.64073 - 10.2536i) q^{95} +(0.123220 + 0.857015i) q^{96} +(-17.5049 - 6.52900i) q^{97} +(7.62621 + 10.1874i) q^{98} +(1.38267 - 0.405989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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