LMFDB - Embedded newform 230.2.l.a.33.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			33.5
Character	$\chi$	$=$	230.33
Dual form			230.2.l.a.7.5

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{22}\right)$

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
$3$	0.184045	+	0.846041i	0.106258	+	0.488462i	0.999262	+	0.0384123i	$0.0122300\pi$
$3$	0.184045	+	0.846041i	0.106258	+	0.488462i	−0.893004	+	0.450050i	$0.851406\pi$
$4$	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	−0.879367	−	0.476145i	$-0.842034\pi$
$7$	−2.12852	−	3.89809i	−0.804504	−	1.47334i	0.0748635	−	0.997194i	$-0.476148\pi$
$8$	−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	0.724761	−	0.689000i	$-0.241950\pi$
$11$	0.483957	+	0.419351i	0.145919	+	0.126439i	−0.578843	+	0.815439i	$0.696495\pi$
$12$	0.0617674	+	0.863622i	0.0178307	+	0.249306i
$13$	1.16156	+	0.634258i	0.322158	+	0.175912i	0.632188	−	0.774815i	$-0.282157\pi$
$13$	1.16156	+	0.634258i	0.322158	+	0.175912i	−0.310030	+	0.950727i	$0.600339\pi$
$14$	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	−0.665765	−	0.746161i	$-0.731895\pi$
$17$	0.980222	−	1.30942i	0.237739	−	0.317582i	0.903504	+	0.428579i	$0.140986\pi$
$18$	−2.10846	+	0.786414i	−0.496968	+	0.185360i
$19$	−0.660894	+	4.59662i	−0.151619	+	1.05454i	0.761886	+	0.647711i	$0.224273\pi$
$19$	−0.660894	+	4.59662i	−0.151619	+	1.05454i	−0.913506	+	0.406826i	$0.866636\pi$
$20$	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	0.119283	−	0.992860i	$-0.461941\pi$
$29$	2.76504	−	0.397553i	0.513455	−	0.0738237i	0.394172	+	0.919037i	$0.371031\pi$
$30$	−0.832110	−	1.74811i	−0.151922	−	0.319159i
$31$	−0.176248	+	0.113268i	−0.0316550	+	0.0203435i	−0.556373	−	0.830933i	$-0.687807\pi$
$31$	−0.176248	+	0.113268i	−0.0316550	+	0.0203435i	0.524718	+	0.851276i	$0.324171\pi$
$32$	−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	0.328257	+	0.944589i	$0.393539\pi$
$37$	−3.27494	+	8.78046i	−0.538397	+	1.44350i	−0.866654	+	0.498910i	$0.833734\pi$
$38$	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	−0.961410	−	0.275120i	$-0.911282\pi$
$41$	−0.793335	+	1.73716i	−0.123898	+	0.271299i	0.837512	+	0.546419i	$0.184010\pi$
$42$	−3.07844	+	2.30449i	−0.475014	+	0.355591i
$43$	−12.2355	+	2.66167i	−1.86590	+	0.405901i	−0.996155	−	0.0876049i	$-0.972079\pi$
$43$	−12.2355	+	2.66167i	−1.86590	+	0.405901i	−0.869742	+	0.493506i	$0.835715\pi$
$44$	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	−0.162244	−	0.986751i	$-0.551873\pi$
$47$	5.65253	−	5.65253i	0.824506	−	0.824506i	0.986751	+	0.162244i	$0.0518733\pi$
$48$	−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	−0.862081	−	0.506770i	$-0.830839\pi$
$53$	−6.56546	+	3.58501i	−0.901836	+	0.492440i	−0.0397544	+	0.999209i	$0.512658\pi$
$54$	−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	0.982353	−	0.187037i	$-0.0598885\pi$
$59$	0.421120	+	1.43420i	0.0548252	+	0.186717i	−0.927528	+	0.373754i	$0.878070\pi$
$60$	0.705281	+	1.80302i	0.0910514	+	0.232768i
$61$	−2.82825	−	4.40084i	−0.362120	−	0.563470i	0.611614	−	0.791156i	$-0.290520\pi$
$61$	−2.82825	−	4.40084i	−0.362120	−	0.563470i	−0.973735	+	0.227686i	$0.926884\pi$
$62$	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	0.724056	+	0.689741i	$0.242276\pi$
$67$	−0.743153	+	10.3906i	−0.0907906	+	1.26942i	−0.814846	+	0.579677i	$0.803179\pi$
$68$	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	0.354978	−	0.934875i	$-0.384488\pi$
$71$	−5.23180	−	6.03781i	−0.620900	−	0.716557i	−0.975878	+	0.218318i	$0.929943\pi$
$72$	−2.19892	+	0.478345i	−0.259145	+	0.0563735i
$73$	4.53424	−	3.39429i	0.530692	−	0.397271i	−0.300054	−	0.953922i	$-0.597005\pi$
$73$	4.53424	−	3.39429i	0.530692	−	0.397271i	0.830747	+	0.556651i	$0.187914\pi$
$74$	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	−0.278083	−	0.960557i	$-0.589699\pi$
$79$	0.0648320	−	0.0190364i	0.00729418	−	0.00214176i	0.285378	+	0.958415i	$0.407881\pi$
$80$	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	−0.0265807	−	0.999647i	$-0.508462\pi$
$83$	−6.38913	−	2.38302i	−0.701298	−	0.261571i	−0.674718	+	0.738076i	$0.735735\pi$
$84$	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	0.570105	−	0.821572i	$-0.306902\pi$
$89$	0.562341	+	0.361394i	0.0596080	+	0.0383077i	−0.510497	+	0.859879i	$0.670539\pi$
$90$	−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	−0.777956	+	0.628319i	$0.783743\pi$
$97$	−17.5049	+	6.52900i	−1.77736	+	0.662920i	−0.999401	+	0.0346011i	$0.988984\pi$
$98$	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	0.992751	−	0.120192i	$-0.0383512\pi$
$101$	2.53058	+	5.54119i	0.251802	+	0.551369i	−0.740949	+	0.671562i	$0.765624\pi$
$102$	−1.24298	−	0.678717i	−0.123073	−	0.0672030i
$103$	1.09170	+	15.2639i	0.107568	+	1.50400i	0.709076	+	0.705132i	$0.249112\pi$
$103$	1.09170	+	15.2639i	0.107568	+	1.50400i	−0.601507	+	0.798867i	$0.705433\pi$
$104$	−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	0.484093	−	0.875016i	$-0.339150\pi$
$107$	5.80246	+	1.26225i	0.560945	+	0.122026i	0.0768517	+	0.997043i	$0.475513\pi$
$108$	2.17861	+	3.98983i	0.209637	+	0.383922i
$109$	−1.08696	−	7.55997i	−0.104112	−	0.724114i	−0.973284	−	0.229605i	$-0.926257\pi$
$109$	−1.08696	−	7.55997i	−0.104112	−	0.724114i	0.869172	−	0.494510i	$-0.164652\pi$
$110$	−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	0.887766	−	0.460295i	$-0.152256\pi$
$113$	18.0818	+	1.29323i	1.70099	+	0.121657i	0.813223	+	0.581952i	$0.197711\pi$
$114$	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	−0.861066	−	0.508493i	$-0.830203\pi$
$127$	−0.914294	−	12.7835i	−0.0811305	−	1.13435i	0.779936	−	0.625859i	$-0.215252\pi$
$128$	−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	0.212867	−	0.977081i	$-0.431720\pi$
$131$	−1.56010	−	0.458088i	−0.136307	−	0.0400233i	−0.349174	+	0.937058i	$0.613538\pi$
$132$	−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	0.986964	−	0.160943i	$-0.0514536\pi$
$137$	9.66832	+	9.66832i	0.826020	+	0.826020i	−0.160943	+	0.986964i	$0.551454\pi$
$138$	−4.03256	−	0.990247i	−0.343274	−	0.0842954i
$139$			22.4821i			1.90691i	0.301540	+	0.953453i	$0.402499\pi$
$139$			22.4821i			1.90691i	−0.301540	+	0.953453i	$0.597501\pi$
$140$	−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	−0.183421	+	0.983035i	$0.558717\pi$
$149$	−13.7976	+	15.9233i	−1.13035	+	1.30449i	−0.946925	+	0.321454i	$0.895828\pi$
$150$	−2.93738	−	3.18013i	−0.239836	−	0.259656i
$151$	4.47832	−	1.31495i	0.364440	−	0.107009i	−0.0943851	−	0.995536i	$-0.530088\pi$
$151$	4.47832	−	1.31495i	0.364440	−	0.107009i	0.458826	+	0.888526i	$0.348270\pi$
$152$	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	0.492886	−	0.870094i	$-0.335942\pi$
$157$	18.3764	−	13.7564i	1.46660	−	1.09788i	0.973711	−	0.227787i	$-0.0731491\pi$
$158$	−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	0.752872	+	0.658167i	$0.228668\pi$
$163$	−1.09802	+	15.3524i	−0.0860037	+	1.20249i	−0.838876	+	0.544322i	$0.816787\pi$
$164$	−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	0.895340	−	0.445383i	$-0.146932\pi$
$167$	9.30762	+	6.96760i	0.720245	+	0.539169i	−0.175095	+	0.984552i	$0.556023\pi$
$168$	−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	−0.247277	−	0.968945i	$-0.579536\pi$
$173$	−4.65800	+	0.333147i	−0.354141	+	0.0253287i	−0.106865	+	0.994274i	$0.534081\pi$
$174$	−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	0.0480473	−	0.998845i	$-0.484700\pi$
$179$	−9.03577	−	4.12650i	−0.675365	−	0.308429i	−0.723412	+	0.690416i	$0.757427\pi$
$180$	4.18941	−	2.78729i	0.312261	−	0.207753i
$181$	−10.0747	+	15.6766i	−0.748849	+	1.16523i	0.232425	+	0.972614i	$0.425334\pi$
$181$	−10.0747	+	15.6766i	−0.748849	+	1.16523i	−0.981274	+	0.192617i	$0.938302\pi$
$182$	−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	0.686958	+	0.726697i	$0.258945\pi$
$191$	−3.92260	+	13.3592i	−0.283830	+	0.966635i	−0.970788	+	0.239938i	$0.922873\pi$
$192$	−0.184045	+	0.846041i	−0.0132823	+	0.0610577i
$193$	−4.51772	+	12.1125i	−0.325192	+	0.871875i	0.666761	+	0.745272i	$0.267680\pi$
$193$	−4.51772	+	12.1125i	−0.325192	+	0.871875i	−0.991953	+	0.126603i	$0.959593\pi$
$194$	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	−0.817484	−	0.575951i	$-0.804632\pi$
$197$	1.52992	−	2.80183i	0.109002	−	0.199622i	0.926486	+	0.376329i	$0.122814\pi$
$198$	−1.35019	−	0.503593i	−0.0959536	−	0.0357888i
$199$	17.2379	−	11.0781i	1.22196	−	0.785307i	0.239341	−	0.970936i	$-0.423069\pi$
$199$	17.2379	−	11.0781i	1.22196	−	0.785307i	0.982620	+	0.185629i	$0.0594322\pi$
$200$	−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	−0.930364	−	0.366637i	$-0.880509\pi$
$211$	0.953001	−	6.62827i	0.0656073	−	0.456309i	0.995971	−	0.0896717i	$-0.0285818\pi$
$212$	−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	0.978756	−	0.205029i	$-0.0657290\pi$
$223$	4.13827	+	7.57867i	0.277119	+	0.507505i	−0.701637	+	0.712535i	$0.747547\pi$
$224$	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	−0.865360	−	0.501151i	$-0.832910\pi$
$227$	−4.31485	−	19.8350i	−0.286386	−	1.31650i	0.578973	−	0.815346i	$-0.303453\pi$
$228$	−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	0.999991	+	0.00420857i	$0.00133963\pi$
$233$	1.40608	+	6.46366i	0.0921155	+	0.423448i	−0.907876	+	0.419240i	$0.862297\pi$
$234$	−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	−0.764232	−	0.644941i	$-0.776882\pi$
$239$	−12.0165	+	5.48776i	−0.777284	+	0.354974i	−0.0130520	+	0.999915i	$0.504155\pi$
$240$	0.441507	+	1.88504i	0.0284991	+	0.121679i
$241$	−13.9561	−	12.0930i	−0.898989	−	0.778979i	0.0769470	−	0.997035i	$-0.475483\pi$
$241$	−13.9561	−	12.0930i	−0.898989	−	0.778979i	−0.975936	+	0.218057i	$0.930028\pi$
$242$	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	0.424224	−	0.905557i	$-0.360547\pi$
$251$	21.8782	−	18.9575i	1.38094	−	1.19659i	0.956713	−	0.291032i	$-0.0939986\pi$
$252$	−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	0.880194	−	0.474614i	$-0.157412\pi$
$257$	2.83473	+	3.78676i	0.176826	+	0.236212i	−0.703368	+	0.710826i	$0.748321\pi$
$258$	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	−0.788678	−	0.614806i	$-0.789234\pi$
$263$	2.51241	−	4.60113i	0.154922	−	0.283718i	0.943600	+	0.331089i	$0.107416\pi$
$264$	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	−0.533606	−	0.845733i	$-0.679163\pi$
$269$	6.10994	−	20.8086i	0.372530	−	1.26872i	0.906136	−	0.422987i	$-0.139018\pi$
$270$	−7.78680	−	6.53386i	−0.473890	−	0.397638i
$271$	−1.82164	+	3.98883i	−0.110657	+	0.242304i	−0.956856	−	0.290562i	$-0.906158\pi$
$271$	−1.82164	+	3.98883i	−0.110657	+	0.242304i	0.846200	+	0.532866i	$0.178885\pi$
$272$	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	−0.132743	−	0.991151i	$-0.542378\pi$
$277$	14.2868	−	14.2868i	0.858408	−	0.858408i	0.991151	+	0.132743i	$0.0423784\pi$
$278$	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	−0.282259	−	0.959338i	$-0.591084\pi$
$281$	−19.9836	−	9.12619i	−1.19212	−	0.544423i	−0.909860	+	0.414916i	$0.863811\pi$
$282$	−5.54081	−	4.14780i	−0.329950	−	0.246998i
$283$	−8.84049	+	4.82727i	−0.525512	+	0.286952i	−0.720025	−	0.693949i	$-0.755869\pi$
$283$	−8.84049	+	4.82727i	−0.525512	+	0.286952i	0.194512	+	0.980900i	$0.437688\pi$
$284$	−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	0.680619	−	0.732637i	$-0.261711\pi$
$293$	2.89986	+	2.17081i	0.169412	+	0.126820i	−0.511208	+	0.859457i	$0.670802\pi$
$294$	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	−0.802200	−	0.597056i	$-0.796337\pi$
$307$	3.07558	−	14.1382i	0.175533	−	0.806911i	0.977732	−	0.209855i	$-0.0672993\pi$
$308$	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	−0.133511	−	0.991047i	$-0.542625\pi$
$311$	15.2800	−	17.6341i	0.866449	−	0.999936i	0.999960	−	0.00888825i	$-0.00282925\pi$
$312$	0.549158	−	1.00571i	0.0310900	−	0.0569370i
$313$	−4.48829	−	1.67405i	−0.253693	−	0.0946227i	0.219400	−	0.975635i	$-0.429590\pi$
$313$	−4.48829	−	1.67405i	−0.253693	−	0.0946227i	−0.473093	+	0.881012i	$0.656863\pi$
$314$	−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	0.955795	+	0.294034i	$0.0949978\pi$
$317$	7.58479	+	20.3356i	0.426004	+	1.14216i	−0.529791	+	0.848129i	$0.677729\pi$
$318$	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	−0.998983	−	0.0450899i	$-0.985643\pi$
$331$	−6.89284	−	15.0932i	−0.378865	−	0.829598i	0.620118	−	0.784509i	$-0.287085\pi$
$332$	−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	−0.159858	−	0.987140i	$-0.551104\pi$
$337$	−13.1319	−	2.85668i	−0.715342	−	0.155613i	−0.555484	+	0.831527i	$0.687467\pi$
$338$	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	0.164159	−	0.986434i	$-0.447509\pi$
$347$	3.46971	+	0.248159i	0.186264	+	0.0133219i	0.0221044	+	0.999756i	$0.492963\pi$
$348$	0.514124	+	2.36339i	0.0275600	+	0.126691i
$349$	4.68836	+	0.674084i	0.250962	+	0.0360829i	0.266648	−	0.963794i	$-0.414084\pi$
$349$	4.68836	+	0.674084i	0.250962	+	0.0360829i	−0.0156856	+	0.999877i	$0.504993\pi$
$350$	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	−0.820090	−	0.572235i	$-0.806077\pi$
$353$	−33.8900	−	7.37233i	−1.80378	−	0.392389i	−0.983695	+	0.179845i	$0.942440\pi$
$354$	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	0.988472	+	0.151402i	$0.0483789\pi$
$359$	8.63206	+	18.9016i	0.455583	+	0.997587i	−0.532889	+	0.846185i	$0.678894\pi$
$360$	−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	0.570554	−	0.821260i	$-0.306728\pi$
$367$	−4.80283	−	4.80283i	−0.250706	−	0.250706i	−0.821260	+	0.570554i	$0.806728\pi$
$368$	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	−0.966200	−	0.257792i	$-0.917005\pi$
$373$	−7.81824	−	20.9615i	−0.404813	−	1.08535i	0.561387	−	0.827553i	$-0.310268\pi$
$374$	−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	−0.439101	−	0.898438i	$-0.644703\pi$
$379$	9.98086	−	11.5185i	0.512682	−	0.591667i	0.951783	+	0.306771i	$0.0992485\pi$
$380$	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	−0.932226	−	0.361878i	$-0.882136\pi$
$383$	1.29333	−	5.94535i	0.0660861	−	0.303793i	0.998312	+	0.0580848i	$0.0184994\pi$
$384$	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	0.268619	−	0.963247i	$-0.413433\pi$
$389$	−14.2608	−	16.4579i	−0.723052	−	0.834446i	−0.991671	+	0.128800i	$0.958887\pi$
$390$	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	0.121639	−	0.992574i	$-0.461185\pi$
$397$	−15.8694	−	11.8796i	−0.796460	−	0.596222i	−0.918099	+	0.396352i	$0.870276\pi$
$398$	−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	−0.969730	−	0.244178i	$-0.921482\pi$
$401$	−5.72622	−	19.5017i	−0.285954	−	0.973869i	0.683777	−	0.729691i	$-0.260336\pi$
$402$	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	−0.409133	−	0.912475i	$-0.634169\pi$
$409$	−27.6390	−	12.6223i	−1.36666	−	0.624133i	−0.957527	+	0.288342i	$0.906896\pi$
$410$	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	−0.497533	−	0.867445i	$-0.665761\pi$
$419$	9.90423	−	21.6872i	0.483853	−	1.05949i	0.981386	−	0.192046i	$-0.0615122\pi$
$420$	5.52711	−	6.58700i	0.269695	−	0.321412i
$421$	−1.17415	+	3.99878i	−0.0572245	+	0.194889i	−0.983144	−	0.182831i	$-0.941474\pi$
$421$	−1.17415	+	3.99878i	−0.0572245	+	0.194889i	0.925920	+	0.377720i	$0.123292\pi$
$422$	−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	0.417082	−	0.908869i	$-0.363053\pi$
$431$	22.2829	−	3.20379i	1.07333	−	0.154321i	0.656245	+	0.754548i	$0.272144\pi$
$432$	1.58863	+	4.25927i	0.0764328	+	0.204924i
$433$	5.21785	+	6.97024i	0.250754	+	0.334968i	0.908202	−	0.418531i	$-0.137455\pi$
$433$	5.21785	+	6.97024i	0.250754	+	0.334968i	−0.657448	+	0.753500i	$0.728364\pi$
$434$	−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	−0.582564	−	0.812785i	$-0.697950\pi$
$439$	2.91323	−	2.52433i	0.139041	−	0.120479i	0.721605	+	0.692306i	$0.243405\pi$
$440$	−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	−0.988777	−	0.149402i	$-0.952265\pi$
$443$	−11.9309	+	15.9379i	−0.566856	+	0.757231i	0.421920	+	0.906633i	$0.361356\pi$
$444$	−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	0.910456	−	0.413606i	$-0.135731\pi$
$449$	13.3628	+	11.5790i	0.630631	+	0.546445i	−0.279825	+	0.960051i	$0.590276\pi$
$450$	−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	0.976294	−	0.216451i	$-0.0694481\pi$
$457$	−0.0361530	−	0.166193i	−0.00169117	−	0.00777417i	−0.977985	+	0.208677i	$0.933084\pi$
$458$	−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	−0.986216	−	0.165464i	$-0.947088\pi$
$463$	−3.39671	−	15.6144i	−0.157859	−	0.725664i	0.828357	−	0.560200i	$-0.189276\pi$
$464$	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	0.968508	−	0.248983i	$-0.0800965\pi$
$467$	5.08779	+	9.31759i	0.235435	+	0.431167i	−0.733073	+	0.680150i	$0.761915\pi$
$468$	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	−0.994421	−	0.105486i	$-0.966360\pi$
$479$	−0.231166	+	1.60779i	−0.0105622	+	0.0734619i	0.983859	+	0.178948i	$0.0572693\pi$
$480$	−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	−0.995704	−	0.0925982i	$-0.970483\pi$
$487$	−17.7434	−	23.7024i	−0.804029	−	1.07406i	0.191675	−	0.981458i	$-0.438608\pi$
$488$	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	−0.762157	−	0.647392i	$-0.775860\pi$
$491$	−10.8550	+	6.97610i	−0.489880	+	0.314827i	0.272277	+	0.962219i	$0.412223\pi$
$492$	−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	0.583317	+	0.812245i	$0.301755\pi$
$499$	−7.74097	+	26.3633i	−0.346533	+	1.18018i	−0.929850	+	0.367939i	$0.880064\pi$
$500$	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	0.153233	−	0.988190i	$-0.451031\pi$
$503$	15.7695	−	3.43045i	0.703128	−	0.152956i	0.549895	+	0.835234i	$0.314668\pi$
$504$	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	−0.863970	−	0.503543i	$-0.832030\pi$
$509$	−1.06094	+	1.65085i	−0.0470253	+	0.0731728i	0.816945	+	0.576716i	$0.195666\pi$
$510$	−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	−0.998231	−	0.0594579i	$-0.981063\pi$
$521$	−14.5543	−	22.6469i	−0.637636	−	0.992180i	0.360595	−	0.932722i	$-0.382574\pi$
$522$	−5.51733	+	3.01269i	−0.241487	+	0.131862i
$523$	−26.2670	−	19.6632i	−1.14858	−	0.859813i	−0.156778	−	0.987634i	$-0.550111\pi$
$523$	−26.2670	−	19.6632i	−1.14858	−	0.859813i	−0.991797	+	0.127821i	$0.959202\pi$
$524$	−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	−0.838260	−	0.545271i	$-0.816427\pi$
$541$	−4.16906	+	4.81135i	−0.179242	+	0.206856i	0.659018	+	0.752127i	$0.270972\pi$
$542$	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	0.999491	−	0.0319164i	$-0.0101610\pi$
$547$	5.22080	+	13.9975i	0.223225	+	0.598490i	−0.776265	+	0.630406i	$0.782888\pi$
$548$	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	−0.876743	−	0.480959i	$-0.840288\pi$
$557$	−28.8964	+	10.7778i	−1.22438	+	0.456670i	−0.347637	+	0.937629i	$0.613016\pi$
$558$	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	−0.747273	−	0.664517i	$-0.768637\pi$
$563$	−2.42441	−	33.8977i	−0.102177	−	1.42862i	0.645096	−	0.764101i	$-0.276817\pi$
$564$	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	0.764700	+	0.644386i	$0.222887\pi$
$569$	5.06940	+	35.2585i	0.212520	+	1.47811i	−0.552180	+	0.833725i	$0.686204\pi$
$570$	8.58532	−	2.66958i	0.359599	−	0.111816i
$571$	31.9169	+	4.58896i	1.33568	+	0.192042i	0.772881	−	0.634551i	$-0.218815\pi$
$571$	31.9169	+	4.58896i	1.33568	+	0.192042i	0.562800	+	0.826593i	$0.309724\pi$
$572$	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	0.305150	−	0.952304i	$-0.401293\pi$
$577$	11.3298	+	0.810326i	0.471667	+	0.0337343i	0.166517	+	0.986039i	$0.446748\pi$
$578$	−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	−0.920708	−	0.390252i	$-0.872388\pi$
$587$	−1.57265	−	21.9885i	−0.0649102	−	0.907563i	0.855798	−	0.517311i	$-0.173067\pi$
$588$	−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	0.542930	−	0.839778i	$-0.317315\pi$
$593$	36.6050	−	13.6530i	1.50319	−	0.560659i	0.960257	+	0.279119i	$0.0900423\pi$
$594$	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	$0.174690\pi$
$599$			25.5351i			1.04334i	−0.853148	+	0.521669i	$0.825310\pi$
$600$	−2.45490	−	3.56579i	−0.100221	−	0.145573i
$601$	17.4019	+	11.1835i	0.709838	+	0.456185i	0.845089	−	0.534626i	$-0.179548\pi$
$601$	17.4019	+	11.1835i	0.709838	+	0.456185i	−0.135250	+	0.990811i	$0.543184\pi$
$602$	−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	0.917418	−	0.397924i	$-0.130269\pi$
$607$	33.2647	+	12.4071i	1.35017	+	0.503588i	0.432754	+	0.901512i	$0.357542\pi$
$608$	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	−0.964085	−	0.265594i	$-0.914432\pi$
$613$	0.574635	−	2.64155i	0.0232093	−	0.106691i	0.987294	+	0.158903i	$0.0507956\pi$
$614$	−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	−0.913822	−	0.406116i	$-0.866883\pi$
$617$	−19.4148	+	14.5337i	−0.781609	+	0.585106i	0.132212	+	0.991221i	$0.457792\pi$
$618$	12.9469	−	2.81642i	0.520800	−	0.113293i
$619$	−2.13986	−	2.46953i	−0.0860082	−	0.0992588i	0.711114	−	0.703077i	$-0.248191\pi$
$619$	−2.13986	−	2.46953i	−0.0860082	−	0.0992588i	−0.797122	+	0.603818i	$0.793645\pi$
$620$	−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	0.934327	−	0.356417i	$-0.116002\pi$
$631$	−1.11462	−	3.79606i	−0.0443725	−	0.151119i	−0.978699	+	0.205298i	$0.934184\pi$
$632$	−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	−0.790465	−	0.612508i	$-0.790161\pi$
$641$	2.40679	−	3.74504i	0.0950626	−	0.147920i	0.885527	+	0.464587i	$0.153797\pi$
$642$	0.366785	−	5.12833i	0.0144759	−	0.202399i
$643$	9.24567	−	9.24567i	0.364614	−	0.364614i	−0.500895	−	0.865508i	$-0.666996\pi$
$643$	9.24567	−	9.24567i	0.364614	−	0.364614i	0.865508	+	0.500895i	$0.166996\pi$
$644$	−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	0.623786	−	0.781595i	$-0.285594\pi$
$647$	38.5584	−	8.38787i	1.51589	−	0.329761i	0.892102	+	0.451834i	$0.149230\pi$
$648$	−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	−0.474013	−	0.880518i	$-0.657195\pi$
$653$	11.7762	−	31.5732i	0.460838	−	1.23556i	0.934852	−	0.355038i	$-0.115532\pi$
$654$	−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	−0.104690	−	0.994505i	$-0.533385\pi$
$659$	19.4189	−	12.4798i	0.756453	−	0.486143i	0.861144	+	0.508362i	$0.169749\pi$
$660$	−0.414771	+	1.16834i	−0.0161449	+	0.0454777i
$661$	5.09759	−	0.732922i	0.198273	−	0.0285074i	−0.0424627	−	0.999098i	$-0.513520\pi$
$661$	5.09759	−	0.732922i	0.198273	−	0.0285074i	0.240736	+	0.970591i	$0.422611\pi$
$662$	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	−0.246358	+	0.969179i	$0.579234\pi$
$673$	−28.7147	+	38.3584i	−1.10687	+	1.47861i	−0.860513	+	0.509428i	$0.829857\pi$
$674$	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	0.920856	−	0.389903i	$-0.127492\pi$
$677$	28.3792	+	15.4962i	1.09070	+	0.595568i	0.169845	+	0.985471i	$0.445673\pi$
$678$	−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	0.920008	−	0.391900i	$-0.128182\pi$
$683$	2.42858	+	4.44760i	0.0929269	+	0.170183i	−0.827081	+	0.562083i	$0.810000\pi$
$684$	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	0.933826	−	0.357727i	$-0.116448\pi$
$701$	18.8681	+	16.3493i	0.712638	+	0.617504i	−0.221188	+	0.975231i	$0.570994\pi$
$702$	−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	−0.736138	−	0.676831i	$-0.763353\pi$
$709$	4.28341	−	29.7917i	0.160867	−	1.11885i	0.897005	−	0.442021i	$-0.145738\pi$
$710$	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	−0.409545	−	0.912290i	$-0.634313\pi$
$719$	−14.6266	+	2.10298i	−0.545479	+	0.0784281i	−0.135934	+	0.990718i	$0.543404\pi$
$720$	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	−0.887421	−	0.460960i	$-0.847505\pi$
$727$	2.29485	−	6.15274i	0.0851114	−	0.228192i	0.972532	+	0.232767i	$0.0747780\pi$
$728$	−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	−0.511299	−	0.859403i	$-0.670836\pi$
$733$	−16.7692	+	3.64792i	−0.619384	+	0.134739i	−0.108085	+	0.994142i	$0.534472\pi$
$734$	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	−0.963631	−	0.267236i	$-0.913890\pi$
$739$	−8.70552	+	13.5461i	−0.320238	+	0.498300i	0.643393	+	0.765536i	$0.277526\pi$
$740$	−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	0.0857505	−	0.996317i	$-0.472671\pi$
$743$	26.4475	−	14.4414i	0.970266	−	0.529805i	0.884515	+	0.466512i	$0.154489\pi$
$744$	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	0.858004	−	0.513644i	$-0.171705\pi$
$751$	0.941316	+	1.46472i	0.0343491	+	0.0534483i	−0.823654	+	0.567092i	$0.808068\pi$
$752$	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	−0.988829	−	0.149052i	$-0.952378\pi$
$757$	0.306709	−	4.28835i	0.0111475	−	0.155863i	0.999977	−	0.00681020i	$-0.00216777\pi$
$758$	−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	−0.998633	−	0.0522769i	$-0.983352\pi$
$761$	−25.0554	−	28.9155i	−0.908257	−	1.04818i	0.0903754	−	0.995908i	$-0.471193\pi$
$762$	−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	0.613379	−	0.789789i	$-0.289810\pi$
$769$	43.1597	−	12.6728i	1.55638	−	0.456994i	0.942999	+	0.332795i	$0.107992\pi$
$770$	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	−0.187629	−	0.982240i	$-0.560080\pi$
$773$	−27.0428	−	10.0864i	−0.972661	−	0.362784i	−0.785031	+	0.619456i	$0.787353\pi$
$774$	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	−0.272620	−	0.962122i	$-0.587890\pi$
$787$	4.24741	−	1.58420i	0.151404	−	0.0564707i	0.424024	+	0.905651i	$0.360617\pi$
$788$	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	−0.653735	−	0.756723i	$-0.726799\pi$
$797$	−44.1182	−	9.59733i	−1.56275	−	0.339955i	−0.909013	+	0.416769i	$0.863163\pi$
$798$	−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	0.852478	−	0.522764i	$-0.175099\pi$
$809$	43.3227	+	6.22886i	1.52314	+	0.218995i	0.670667	+	0.741759i	$0.266008\pi$
$810$	−2.92867	+	5.57189i	−0.102903	+	0.195776i
$811$	−0.844780	−	5.87558i	−0.0296642	−	0.206319i	0.969599	−	0.244699i	$-0.0786893\pi$
$811$	−0.844780	−	5.87558i	−0.0296642	−	0.206319i	−0.999263	+	0.0383801i	$0.987780\pi$
$812$	−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	−0.0394106	−	0.999223i	$-0.512548\pi$
$821$	−17.5582	−	5.15556i	−0.612786	−	0.179930i	−0.573375	+	0.819293i	$0.694366\pi$
$822$	7.09456	−	9.47723i	0.247451	−	0.330556i
$823$	−30.9397	+	11.5399i	−1.07849	+	0.402256i	−0.825029	−	0.565090i	$-0.808842\pi$
$823$	−30.9397	+	11.5399i	−1.07849	+	0.402256i	−0.253461	+	0.967346i	$0.581569\pi$
$824$	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	0.868519	−	0.495655i	$-0.165072\pi$
$827$	10.7227	+	10.7227i	0.372864	+	0.372864i	−0.495655	+	0.868519i	$0.665072\pi$
$828$	1.05593	−	10.7405i	0.0366962	−	0.373258i
$829$		−	25.9627i		−	0.901722i	−0.892594	−	0.450861i	$-0.851117\pi$
$829$		−	25.9627i		−	0.901722i	0.892594	−	0.450861i	$-0.148883\pi$
$830$	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	−0.662930	−	0.748681i	$-0.730687\pi$
$839$	4.99582	−	5.76549i	0.172475	−	0.199047i	0.835405	+	0.549634i	$0.185233\pi$
$840$	−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	−0.994706	−	0.102758i	$-0.967233\pi$
$853$	0.131406	−	1.83730i	0.00449926	−	0.0629078i	0.999206	+	0.0398498i	$0.0126879\pi$
$854$	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	0.602469	−	0.798142i	$-0.294184\pi$
$857$	0.187124	+	0.140079i	0.00639202	+	0.00478500i	−0.596077	+	0.802927i	$0.703275\pi$
$858$	0.644022	−	0.351663i	0.0219866	−	0.0120056i
$859$	13.2769	+	20.6592i	0.453001	+	0.704883i	0.990367	−	0.138466i	$-0.0442171\pi$
$859$	13.2769	+	20.6592i	0.453001	+	0.704883i	−0.537366	+	0.843349i	$0.680581\pi$
$860$	−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	−0.244895	−	0.969550i	$-0.578753\pi$
$863$	−10.2618	+	0.733939i	−0.349316	+	0.0249836i	−0.104421	+	0.994533i	$0.533299\pi$
$864$	−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	−0.502965	−	0.864307i	$-0.667757\pi$
$877$	−17.8109	+	3.87453i	−0.601432	+	0.130833i	−0.0984669	+	0.995140i	$0.531394\pi$
$878$	−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	−0.999985	−	0.00553503i	$-0.998238\pi$
$881$	−4.62296	+	15.7444i	−0.155752	+	0.530441i	0.844233	+	0.535976i	$0.180056\pi$
$882$	6.08725	−	27.9827i	0.204968	−	0.942225i
$883$	−12.1721	+	32.6348i	−0.409625	+	1.09825i	0.554357	+	0.832279i	$0.312964\pi$
$883$	−12.1721	+	32.6348i	−0.409625	+	1.09825i	−0.963982	+	0.265968i	$0.914308\pi$
$884$	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	−0.611168	−	0.791501i	$-0.709300\pi$
$887$	11.4695	−	21.0048i	0.385107	−	0.705271i	0.996275	+	0.0862298i	$0.0274819\pi$
$888$	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	−0.296501	−	0.955033i	$-0.595820\pi$
$907$	−37.9535	−	20.7242i	−1.26023	−	0.688136i	−0.963725	+	0.266897i	$0.914002\pi$
$908$	−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	−0.803592	−	0.595181i	$-0.797080\pi$
$911$	−26.5616	+	12.1303i	−0.880024	+	0.401894i	−0.0764326	+	0.997075i	$0.524353\pi$
$912$	−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	−0.597874	−	0.801590i	$-0.703988\pi$
$929$	−11.6918	+	5.33948i	−0.383597	+	0.175183i	0.214277	+	0.976773i	$0.431260\pi$
$930$	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	−0.744538	−	0.667580i	$-0.767330\pi$
$937$	3.23738	−	4.32464i	0.105761	−	0.141280i	0.850299	+	0.526300i	$0.176421\pi$
$938$	−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	−0.918756	−	0.394825i	$-0.870805\pi$
$941$	−20.2062	+	17.5088i	−0.658703	+	0.570769i	0.260054	+	0.965594i	$0.416260\pi$
$942$	−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	0.823499	−	0.567318i	$-0.192019\pi$
$947$	1.45112	+	1.93847i	0.0471550	+	0.0629917i	−0.776344	+	0.630310i	$0.782928\pi$
$948$	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	−0.397658	−	0.917534i	$-0.630177\pi$
$953$	18.1893	−	33.3113i	0.589211	−	1.07906i	0.986869	−	0.161525i	$-0.0516413\pi$
$954$	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	−0.603908	−	0.797054i	$-0.706391\pi$
$967$	6.00616	−	6.00616i	0.193145	−	0.193145i	0.797054	+	0.603908i	$0.206391\pi$
$968$	−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	−0.108233	−	0.994126i	$-0.534519\pi$
$971$	−28.9927	−	13.2405i	−0.930421	−	0.424909i	−0.822188	+	0.569217i	$0.807247\pi$
$972$	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	0.827278	−	0.561793i	$-0.189888\pi$
$977$	53.9523	−	3.85874i	1.72609	−	0.123452i	0.898809	+	0.438341i	$0.144434\pi$
$978$	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	0.164775	−	0.986331i	$-0.447310\pi$
$983$	−23.0500	−	17.2550i	−0.735180	−	0.550349i	−0.899955	+	0.435982i	$0.856401\pi$
$984$	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	0.838741	−	0.544530i	$-0.183292\pi$
$991$	5.67864	+	6.55350i	0.180388	+	0.208179i	−0.658353	+	0.752709i	$0.728747\pi$
$992$	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	−0.958324	−	0.285684i	$-0.907779\pi$
$997$	1.01280	−	4.65575i	0.0320756	−	0.147449i	0.990399	+	0.138235i	$0.0441429\pi$
$998$	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.33.5	yes	240
5.2	odd	4	inner	230.2.l.a.217.11	yes	240
23.7	odd	22	inner	230.2.l.a.53.11	yes	240
115.7	even	44	inner	230.2.l.a.7.5	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.7.5	✓	240	115.7	even	44	inner
230.2.l.a.33.5	yes	240	1.1	even	1	trivial
230.2.l.a.53.11	yes	240	23.7	odd	22	inner
230.2.l.a.217.11	yes	240	5.2	odd	4	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 $\F_{q}$
Belyi maps

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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