LMFDB - Embedded newform 230.2.l.a.57.10

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			57.10
Character	$\chi$	$=$	230.57
Dual form			230.2.l.a.113.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.977147 + 0.212565i) q^{2} +(0.737866 + 0.985673i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-0.103244 + 2.23368i) q^{5} +(0.511483 + 1.11999i) q^{6} +(-1.20867 - 0.0864458i) q^{7} +(0.800541 + 0.599278i) q^{8} +(0.418092 - 1.42389i) q^{9} +(-0.575688 + 2.16069i) q^{10} +(-1.71419 + 2.66733i) q^{11} +(0.261723 + 1.20312i) q^{12} +(-0.366820 - 5.12881i) q^{13} +(-1.16267 - 0.341392i) q^{14} +(-2.27786 + 1.54639i) q^{15} +(0.654861 + 0.755750i) q^{16} +(3.41051 + 1.27205i) q^{17} +(0.711206 - 1.30248i) q^{18} +(0.552811 - 1.21049i) q^{19} +(-1.02182 + 1.98894i) q^{20} +(-0.806629 - 1.25514i) q^{21} +(-2.24200 + 2.24200i) q^{22} +(3.12134 - 3.64105i) q^{23} +1.23126i q^{24} +(-4.97868 - 0.461227i) q^{25} +(0.731770 - 5.08957i) q^{26} +(5.17287 - 1.92938i) q^{27} +(-1.06353 - 0.580734i) q^{28} +(-0.381814 + 0.174369i) q^{29} +(-2.55452 + 1.02686i) q^{30} +(-0.00687467 - 0.0478144i) q^{31} +(0.479249 + 0.877679i) q^{32} +(-3.89396 + 0.278502i) q^{33} +(3.06217 + 1.96794i) q^{34} +(0.317880 - 2.69086i) q^{35} +(0.971814 - 1.12153i) q^{36} +(6.11338 - 3.33816i) q^{37} +(0.797485 - 1.06532i) q^{38} +(4.78467 - 4.14594i) q^{39} +(-1.42125 + 1.72628i) q^{40} +(-7.66309 + 2.25009i) q^{41} +(-0.521396 - 1.39792i) q^{42} +(-9.47529 + 7.09311i) q^{43} +(-2.66733 + 1.71419i) q^{44} +(3.13735 + 1.08089i) q^{45} +(3.82397 - 2.89435i) q^{46} +(-0.789829 - 0.789829i) q^{47} +(-0.261723 + 1.20312i) q^{48} +(-5.47534 - 0.787235i) q^{49} +(-4.76686 - 1.50898i) q^{50} +(1.26267 + 4.30025i) q^{51} +(1.79691 - 4.81771i) q^{52} +(0.739812 - 10.3439i) q^{53} +(5.46477 - 0.785715i) q^{54} +(-5.78100 - 4.10434i) q^{55} +(-0.915785 - 0.793533i) q^{56} +(1.60105 - 0.348286i) q^{57} +(-0.410153 + 0.0892234i) q^{58} +(1.43884 + 1.24677i) q^{59} +(-2.71441 + 0.460392i) q^{60} +(3.22324 - 0.463432i) q^{61} +(0.00344611 - 0.0481830i) q^{62} +(-0.628424 + 1.68487i) q^{63} +(0.281733 + 0.959493i) q^{64} +(11.4940 - 0.289842i) q^{65} +(-3.86417 - 0.555584i) q^{66} +(-1.04631 + 4.80982i) q^{67} +(2.57388 + 2.57388i) q^{68} +(5.89202 + 0.390022i) q^{69} +(0.882599 - 2.56180i) q^{70} +(-6.59587 + 4.23891i) q^{71} +(1.18800 - 0.889329i) q^{72} +(-4.16896 - 11.1774i) q^{73} +(6.68325 - 1.96238i) q^{74} +(-3.21898 - 5.24768i) q^{75} +(1.00571 - 0.871452i) q^{76} +(2.30247 - 3.07574i) q^{77} +(5.55661 - 3.03414i) q^{78} +(-9.78605 + 11.2937i) q^{79} +(-1.75572 + 1.38473i) q^{80} +(1.97336 + 1.26820i) q^{81} +(-7.96626 + 0.569758i) q^{82} +(2.97619 + 5.45048i) q^{83} +(-0.212332 - 1.47680i) q^{84} +(-3.19348 + 7.48666i) q^{85} +(-10.7665 + 4.91689i) q^{86} +(-0.453598 - 0.247683i) q^{87} +(-2.97075 + 1.10803i) q^{88} +(-0.260623 + 1.81268i) q^{89} +(2.83589 + 1.72308i) q^{90} +6.23075i q^{91} +(4.35182 - 2.01536i) q^{92} +(0.0420568 - 0.0420568i) q^{93} +(-0.603889 - 0.939669i) q^{94} +(2.64677 + 1.35978i) q^{95} +(-0.511483 + 1.11999i) q^{96} +(1.28784 - 2.35850i) q^{97} +(-5.18287 - 1.93311i) q^{98} +(3.08130 + 3.55601i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$3$	0.737866	+	0.985673i	0.426007	+	0.569079i	0.961271	−	0.275606i	$-0.0888786\pi$
$3$	0.737866	+	0.985673i	0.426007	+	0.569079i	−0.535264	+	0.844685i	$0.679788\pi$
$4$	0.909632	+	0.415415i	0.454816	+	0.207708i
$5$	−0.103244	+	2.23368i	−0.0461719	+	0.998934i
$5$	−0.103244	+	2.23368i	−0.0461719	+	0.998934i
$6$	0.511483	+	1.11999i	0.208812	+	0.457235i
$7$	−1.20867	−	0.0864458i	−0.456834	−	0.0326734i	−0.158974	−	0.987283i	$-0.550819\pi$
$7$	−1.20867	−	0.0864458i	−0.456834	−	0.0326734i	−0.297861	+	0.954609i	$0.596273\pi$
$8$	0.800541	+	0.599278i	0.283034	+	0.211877i
$9$	0.418092	−	1.42389i	0.139364	−	0.474630i
$10$	−0.575688	+	2.16069i	−0.182048	+	0.683270i
$11$	−1.71419	+	2.66733i	−0.516848	+	0.804231i	−0.997349	−	0.0727629i	$-0.976818\pi$
$11$	−1.71419	+	2.66733i	−0.516848	+	0.804231i	0.480501	+	0.876994i	$0.340455\pi$
$12$	0.261723	+	1.20312i	0.0755529	+	0.347311i
$13$	−0.366820	−	5.12881i	−0.101738	−	1.42248i	−0.750191	−	0.661222i	$-0.770038\pi$
$13$	−0.366820	−	5.12881i	−0.101738	−	1.42248i	0.648453	−	0.761255i	$-0.275416\pi$
$14$	−1.16267	−	0.341392i	−0.310737	−	0.0912407i
$15$	−2.27786	+	1.54639i	−0.588142	+	0.399277i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	3.41051	+	1.27205i	0.827170	+	0.308518i	0.727160	−	0.686468i	$-0.240840\pi$
$17$	3.41051	+	1.27205i	0.827170	+	0.308518i	0.100010	+	0.994986i	$0.468113\pi$
$18$	0.711206	−	1.30248i	0.167633	−	0.306997i
$19$	0.552811	−	1.21049i	0.126824	−	0.277705i	−0.835560	−	0.549399i	$-0.814857\pi$
$19$	0.552811	−	1.21049i	0.126824	−	0.277705i	0.962384	+	0.271694i	$0.0875839\pi$
$20$	−1.02182	+	1.98894i	−0.228486	+	0.444741i
$21$	−0.806629	−	1.25514i	−0.176021	−	0.273894i
$22$	−2.24200	+	2.24200i	−0.477996	+	0.477996i
$23$	3.12134	−	3.64105i	0.650845	−	0.759211i
$23$	3.12134	−	3.64105i	0.650845	−	0.759211i
$24$			1.23126i			0.251330i
$25$	−4.97868	−	0.461227i	−0.995736	−	0.0922454i
$26$	0.731770	−	5.08957i	0.143512	−	0.998148i
$27$	5.17287	−	1.92938i	0.995519	−	0.371309i
$28$	−1.06353	−	0.580734i	−0.200989	−	0.109748i
$29$	−0.381814	+	0.174369i	−0.0709011	+	0.0323795i	−0.450550	−	0.892751i	$-0.648772\pi$
$29$	−0.381814	+	0.174369i	−0.0709011	+	0.0323795i	0.379649	+	0.925131i	$0.376045\pi$
$30$	−2.55452	+	1.02686i	−0.466389	+	0.187478i
$31$	−0.00687467	−	0.0478144i	−0.00123473	−	0.00858771i	0.989195	−	0.146607i	$-0.0468354\pi$
$31$	−0.00687467	−	0.0478144i	−0.00123473	−	0.00858771i	−0.990429	+	0.138020i	$0.955926\pi$
$32$	0.479249	+	0.877679i	0.0847201	+	0.155153i
$33$	−3.89396	+	0.278502i	−0.677852	+	0.0484809i
$34$	3.06217	+	1.96794i	0.525158	+	0.337499i
$35$	0.317880	−	2.69086i	0.0537315	−	0.454839i
$36$	0.971814	−	1.12153i	0.161969	−	0.186922i
$37$	6.11338	−	3.33816i	1.00503	−	0.548790i	0.109596	−	0.993976i	$-0.465044\pi$
$37$	6.11338	−	3.33816i	1.00503	−	0.548790i	0.895438	+	0.445186i	$0.146862\pi$
$38$	0.797485	−	1.06532i	0.129369	−	0.172817i
$39$	4.78467	−	4.14594i	0.766160	−	0.663882i
$40$	−1.42125	+	1.72628i	−0.224719	+	0.272949i
$41$	−7.66309	+	2.25009i	−1.19677	+	0.351405i	−0.818619	−	0.574337i	$-0.805260\pi$
$41$	−7.66309	+	2.25009i	−1.19677	+	0.351405i	−0.378156	+	0.925742i	$0.623442\pi$
$42$	−0.521396	−	1.39792i	−0.0804532	−	0.215703i
$43$	−9.47529	+	7.09311i	−1.44497	+	1.08169i	−0.464374	+	0.885639i	$0.653720\pi$
$43$	−9.47529	+	7.09311i	−1.44497	+	1.08169i	−0.980594	+	0.196050i	$0.937189\pi$
$44$	−2.66733	+	1.71419i	−0.402116	+	0.258424i
$45$	3.13735	+	1.08089i	0.467689	+	0.161130i
$46$	3.82397	−	2.89435i	0.563814	−	0.426748i
$47$	−0.789829	−	0.789829i	−0.115208	−	0.115208i	0.647152	−	0.762361i	$-0.275960\pi$
$47$	−0.789829	−	0.789829i	−0.115208	−	0.115208i	−0.762361	+	0.647152i	$0.775960\pi$
$48$	−0.261723	+	1.20312i	−0.0377764	+	0.173656i
$49$	−5.47534	−	0.787235i	−0.782191	−	0.112462i
$50$	−4.76686	−	1.50898i	−0.674136	−	0.213402i
$51$	1.26267	+	4.30025i	0.176809	+	0.602156i
$52$	1.79691	−	4.81771i	0.249187	−	0.668097i
$53$	0.739812	−	10.3439i	0.101621	−	1.42085i	−0.649339	−	0.760499i	$-0.724954\pi$
$53$	0.739812	−	10.3439i	0.101621	−	1.42085i	0.750960	−	0.660348i	$-0.229591\pi$
$54$	5.46477	−	0.785715i	0.743661	−	0.106922i
$55$	−5.78100	−	4.10434i	−0.779510	−	0.553430i
$56$	−0.915785	−	0.793533i	−0.122377	−	0.106040i
$57$	1.60105	−	0.348286i	0.212064	−	0.0461316i
$58$	−0.410153	+	0.0892234i	−0.0538558	+	0.0117156i
$59$	1.43884	+	1.24677i	0.187322	+	0.162315i	0.743473	−	0.668766i	$-0.233177\pi$
$59$	1.43884	+	1.24677i	0.187322	+	0.162315i	−0.556151	+	0.831081i	$0.687723\pi$
$60$	−2.71441	+	0.460392i	−0.350429	+	0.0594363i
$61$	3.22324	−	0.463432i	0.412693	−	0.0593364i	0.0671587	−	0.997742i	$-0.478607\pi$
$61$	3.22324	−	0.463432i	0.412693	−	0.0593364i	0.345535	+	0.938406i	$0.387698\pi$
$62$	0.00344611	−	0.0481830i	0.000437657	−	0.00611924i
$63$	−0.628424	+	1.68487i	−0.0791740	+	0.212274i
$64$	0.281733	+	0.959493i	0.0352166	+	0.119937i
$65$	11.4940	−	0.289842i	1.42566	−	0.0359505i
$66$	−3.86417	−	0.555584i	−0.475647	−	0.0683877i
$67$	−1.04631	+	4.80982i	−0.127827	+	0.587613i	0.868017	+	0.496535i	$0.165395\pi$
$67$	−1.04631	+	4.80982i	−0.127827	+	0.587613i	−0.995844	+	0.0910773i	$0.970969\pi$
$68$	2.57388	+	2.57388i	0.312128	+	0.312128i
$69$	5.89202	+	0.390022i	0.709315	+	0.0469531i
$70$	0.882599	−	2.56180i	0.105491	−	0.306193i
$71$	−6.59587	+	4.23891i	−0.782786	+	0.503066i	−0.869957	−	0.493128i	$-0.835854\pi$
$71$	−6.59587	+	4.23891i	−0.782786	+	0.503066i	0.0871715	+	0.996193i	$0.472217\pi$
$72$	1.18800	−	0.889329i	0.140008	−	0.104808i
$73$	−4.16896	−	11.1774i	−0.487940	−	1.30822i	−0.914803	−	0.403901i	$-0.867654\pi$
$73$	−4.16896	−	11.1774i	−0.487940	−	1.30822i	0.426863	−	0.904316i	$-0.359619\pi$
$74$	6.68325	−	1.96238i	0.776912	−	0.228122i
$75$	−3.21898	−	5.24768i	−0.371696	−	0.605950i
$76$	1.00571	−	0.871452i	0.115363	−	0.0999624i
$77$	2.30247	−	3.07574i	0.262391	−	0.350513i
$78$	5.55661	−	3.03414i	0.629162	−	0.343548i
$79$	−9.78605	+	11.2937i	−1.10102	+	1.27064i	−0.141210	+	0.989980i	$0.545099\pi$
$79$	−9.78605	+	11.2937i	−1.10102	+	1.27064i	−0.959807	+	0.280662i	$0.909446\pi$
$80$	−1.75572	+	1.38473i	−0.196295	+	0.154817i
$81$	1.97336	+	1.26820i	0.219262	+	0.140911i
$82$	−7.96626	+	0.569758i	−0.879726	+	0.0629193i
$83$	2.97619	+	5.45048i	0.326679	+	0.598268i	0.988469	−	0.151421i	$-0.0483849\pi$
$83$	2.97619	+	5.45048i	0.326679	+	0.598268i	−0.661790	+	0.749689i	$0.730203\pi$
$84$	−0.212332	−	1.47680i	−0.0231673	−	0.161132i
$85$	−3.19348	+	7.48666i	−0.346381	+	0.812043i
$86$	−10.7665	+	4.91689i	−1.16098	+	0.530202i
$87$	−0.453598	−	0.247683i	−0.0486308	−	0.0265544i
$88$	−2.97075	+	1.10803i	−0.316683	+	0.118117i
$89$	−0.260623	+	1.81268i	−0.0276260	+	0.192143i	−0.998961	−	0.0455713i	$-0.985489\pi$
$89$	−0.260623	+	1.81268i	−0.0276260	+	0.192143i	0.971335	+	0.237715i	$0.0763983\pi$
$90$	2.83589	+	1.72308i	0.298929	+	0.181629i
$91$			6.23075i			0.653160i
$92$	4.35182	−	2.01536i	0.453709	−	0.210116i
$93$	0.0420568	−	0.0420568i	0.00436108	−	0.00436108i
$94$	−0.603889	−	0.939669i	−0.0622864	−	0.0969195i
$95$	2.64677	+	1.35978i	0.271553	+	0.139510i
$96$	−0.511483	+	1.11999i	−0.0522031	+	0.114309i
$97$	1.28784	−	2.35850i	0.130760	−	0.239469i	−0.804093	−	0.594503i	$-0.797349\pi$
$97$	1.28784	−	2.35850i	0.130760	−	0.239469i	0.934853	+	0.355034i	$0.115531\pi$
$98$	−5.18287	−	1.93311i	−0.523549	−	0.195274i
$99$	3.08130	+	3.55601i	0.309682	+	0.357392i
$100$	−4.33717	−	2.48777i	−0.433717	−	0.248777i
$101$	9.73371	+	2.85808i	0.968541	+	0.284389i	0.727486	−	0.686122i	$-0.240689\pi$
$101$	9.73371	+	2.85808i	0.968541	+	0.284389i	0.241055	+	0.970512i	$0.422507\pi$
$102$	0.319728	+	4.47038i	0.0316578	+	0.442633i
$103$	−2.39142	−	10.9932i	−0.235634	−	1.08319i	−0.931137	−	0.364669i	$-0.881182\pi$
$103$	−2.39142	−	10.9932i	−0.235634	−	1.08319i	0.695503	−	0.718523i	$-0.255182\pi$
$104$	2.77993	−	4.32565i	0.272594	−	0.424165i
$105$	2.88686	−	1.67217i	0.281729	−	0.163187i
$106$	2.92166	−	9.95027i	0.283777	−	0.966456i
$107$	2.41590	+	1.80852i	0.233554	+	0.174836i	0.709644	−	0.704560i	$-0.248856\pi$
$107$	2.41590	+	1.80852i	0.233554	+	0.174836i	−0.476090	+	0.879396i	$0.657946\pi$
$108$	5.50690	+	0.393861i	0.529902	+	0.0378993i
$109$	7.43710	+	16.2850i	0.712345	+	1.55982i	0.824331	+	0.566108i	$0.191551\pi$
$109$	7.43710	+	16.2850i	0.712345	+	1.55982i	−0.111986	+	0.993710i	$0.535721\pi$
$110$	−4.77644	−	5.23939i	−0.455416	−	0.499556i
$111$	7.80119	+	3.56269i	0.740457	+	0.338155i
$112$	−0.726179	−	0.970062i	−0.0686175	−	0.0916622i
$113$	−3.84237	−	0.835857i	−0.361460	−	0.0786308i	0.0281679	−	0.999603i	$-0.491033\pi$
$113$	−3.84237	−	0.835857i	−0.361460	−	0.0786308i	−0.389628	+	0.920972i	$0.627396\pi$
$114$	1.63849			0.153459
$115$	7.81068	+	7.34801i	0.728350	+	0.685205i
$116$	−0.419746			−0.0389724
$117$	−7.45622	−	1.62200i	−0.689328	−	0.149954i
$118$	1.14094	+	1.52412i	0.105032	+	0.140307i
$119$	−4.01222	−	1.83232i	−0.367799	−	0.167968i
$120$	−2.75024	−	0.127120i	−0.251062	−	0.0116044i
$121$	0.393350	+	0.861316i	0.0357591	+	0.0783015i
$122$	3.24809	+	0.232308i	0.294068	+	0.0210322i
$123$	−7.87219	−	5.89305i	−0.709811	−	0.531358i
$124$	0.0136094	−	0.0463493i	0.00122216	−	0.00416229i
$125$	1.54425	−	11.0732i	0.138122	−	0.990415i
$126$	−0.972208	+	1.51278i	−0.0866111	+	0.134770i
$127$	2.76305	+	12.7015i	0.245181	+	1.12708i	0.920863	+	0.389886i	$0.127485\pi$
$127$	2.76305	+	12.7015i	0.245181	+	1.12708i	−0.675682	+	0.737193i	$0.736151\pi$
$128$	0.0713392	+	0.997452i	0.00630555	+	0.0881631i
$129$	−13.9830	−	4.10577i	−1.23113	−	0.361493i
$130$	11.2929	+	2.16001i	0.990457	+	0.189445i
$131$	7.88135	+	9.09556i	0.688597	+	0.794683i	0.987165	−	0.159705i	$-0.0510544\pi$
$131$	7.88135	+	9.09556i	0.688597	+	0.794683i	−0.298568	+	0.954388i	$0.596509\pi$
$132$	−3.65777	−	1.36428i	−0.318368	−	0.118745i
$133$	−0.772808	+	1.41529i	−0.0670110	+	0.122721i
$134$	−2.04480	+	4.47749i	−0.176644	+	0.386796i
$135$	3.77556	+	11.7537i	0.324948	+	1.01160i
$136$	1.96794	+	3.06217i	0.168749	+	0.262579i
$137$	−7.15888	+	7.15888i	−0.611624	+	0.611624i	−0.943369	−	0.331745i	$-0.892363\pi$
$137$	−7.15888	+	7.15888i	−0.611624	+	0.611624i	0.331745	+	0.943369i	$0.392363\pi$
$138$	5.67446	+	1.63355i	0.483042	+	0.139057i
$139$			6.26942i			0.531765i	0.964005	+	0.265883i	$0.0856633\pi$
$139$			6.26942i			0.531765i	−0.964005	+	0.265883i	$0.914337\pi$
$140$	1.40698	−	2.31564i	0.118911	−	0.195707i
$141$	0.195726	−	1.36130i	0.0164831	−	0.114642i
$142$	−7.34618	+	2.73998i	−0.616477	+	0.229934i
$143$	14.3090	+	7.81333i	1.19658	+	0.653383i
$144$	1.34990	−	0.616477i	0.112491	−	0.0513730i
$145$	−0.350065	−	0.870854i	−0.0290713	−	0.0723205i
$146$	−1.69776	−	11.8081i	−0.140507	−	0.977249i
$147$	−3.26411	−	5.97777i	−0.269219	−	0.493038i
$148$	6.94765	−	0.496906i	0.571093	−	0.0408454i
$149$	6.29025	+	4.04250i	0.515317	+	0.331174i	0.772317	−	0.635237i	$-0.219098\pi$
$149$	6.29025	+	4.04250i	0.515317	+	0.331174i	−0.257000	+	0.966411i	$0.582734\pi$
$150$	−2.02994	−	5.81200i	−0.165744	−	0.474547i
$151$	4.15764	−	4.79818i	0.338344	−	0.390470i	−0.560924	−	0.827867i	$-0.689554\pi$
$151$	4.15764	−	4.79818i	0.338344	−	0.390470i	0.899268	+	0.437397i	$0.144100\pi$
$152$	1.16797	−	0.637758i	0.0947346	−	0.0517290i
$153$	3.23717	−	4.32435i	0.261710	−	0.349603i
$154$	2.90365	−	2.51603i	0.233983	−	0.202747i
$155$	0.107512	−	0.0104193i	0.00863556	−	0.000836899i
$156$	6.07457	−	1.78366i	0.486355	−	0.142807i
$157$	−7.46894	−	20.0250i	−0.596087	−	1.59817i	−0.787265	−	0.616615i	$-0.788504\pi$
$157$	−7.46894	−	20.0250i	−0.596087	−	1.59817i	0.191179	−	0.981555i	$-0.438769\pi$
$158$	−11.9631	+	8.95543i	−0.951730	+	0.712456i
$159$	10.7416	−	6.90322i	0.851865	−	0.547461i
$160$	−2.00994	+	0.979876i	−0.158899	+	0.0774660i
$161$	−4.08743	+	4.13100i	−0.322134	+	0.325568i
$162$	1.65868	+	1.65868i	0.130319	+	0.130319i
$163$	−4.03217	+	18.5356i	−0.315824	+	1.45182i	0.496206	+	0.868205i	$0.334726\pi$
$163$	−4.03217	+	18.5356i	−0.315824	+	1.45182i	−0.812030	+	0.583616i	$0.801637\pi$
$164$	−7.90532	−	1.13661i	−0.617301	−	0.0887545i
$165$	−0.220058	−	8.72663i	−0.0171315	−	0.679367i
$166$	1.74959	+	5.95856i	0.135795	+	0.462474i
$167$	2.21134	−	5.92884i	0.171119	−	0.458787i	−0.822875	−	0.568222i	$-0.807631\pi$
$167$	2.21134	−	5.92884i	0.171119	−	0.458787i	0.993994	+	0.109435i	$0.0349041\pi$
$168$	0.106437	−	1.48819i	0.00821181	−	0.114816i
$169$	−13.3025	+	1.91261i	−1.02327	+	0.147124i
$170$	−4.71190	+	6.63675i	−0.361386	+	0.509015i
$171$	−1.49247	−	1.29324i	−0.114132	−	0.0988963i
$172$	−11.5656	+	2.51594i	−0.881869	+	0.191839i
$173$	20.5556	−	4.47160i	1.56281	−	0.339969i	0.653778	−	0.756686i	$-0.273183\pi$
$173$	20.5556	−	4.47160i	1.56281	−	0.339969i	0.909036	+	0.416717i	$0.136819\pi$
$174$	−0.390583	−	0.338442i	−0.0296100	−	0.0256572i
$175$	5.97771	+	0.987857i	0.451873	+	0.0746750i
$176$	−3.13839	+	0.451233i	−0.236565	+	0.0340129i
$177$	−0.167230	+	2.33818i	−0.0125698	+	0.175748i
$178$	−0.639979	+	1.71585i	−0.0479685	+	0.128608i
$179$	−4.10434	−	13.9781i	−0.306773	−	1.04477i	−0.958209	−	0.286069i	$-0.907651\pi$
$179$	−4.10434	−	13.9781i	−0.306773	−	1.04477i	0.651436	−	0.758704i	$-0.274167\pi$
$180$	2.40482	+	2.28652i	0.179244	+	0.170427i
$181$	−23.5541	−	3.38657i	−1.75076	−	0.251722i	−0.808954	−	0.587872i	$-0.799966\pi$
$181$	−23.5541	−	3.38657i	−1.75076	−	0.251722i	−0.941808	+	0.336150i	$0.890875\pi$
$182$	−1.32444	+	6.08836i	−0.0981741	+	0.451299i
$183$	2.83511	+	2.83511i	0.209577	+	0.209577i
$184$	4.68076	−	1.04426i	0.345070	−	0.0769836i
$185$	6.82523	+	14.0000i	0.501801	+	1.02930i
$186$	0.0500354	−	0.0321558i	0.00366878	−	0.00235778i
$187$	−9.23925	+	6.91642i	−0.675641	+	0.505779i
$188$	−0.390347	−	1.04656i	−0.0284690	−	0.0763283i
$189$	−6.41908	+	1.88481i	−0.466919	+	0.137100i
$190$	2.29724	+	1.89132i	0.166659	+	0.137211i
$191$	−13.6299	+	11.8104i	−0.986228	+	0.854571i	−0.989369	−	0.145424i	$-0.953545\pi$
$191$	−13.6299	+	11.8104i	−0.986228	+	0.854571i	0.00314163	+	0.999995i	$0.499000\pi$
$192$	−0.737866	+	0.985673i	−0.0532509	+	0.0711349i
$193$	0.517500	−	0.282576i	0.0372504	−	0.0203403i	−0.460516	−	0.887651i	$-0.652336\pi$
$193$	0.517500	−	0.282576i	0.0372504	−	0.0203403i	0.497766	+	0.867311i	$0.334154\pi$
$194$	1.75974	−	2.03085i	0.126342	−	0.145806i
$195$	8.76673	+	11.1155i	0.627798	+	0.795996i
$196$	−4.65351	−	2.99063i	−0.332394	−	0.213617i
$197$	21.4119	−	1.53141i	1.52554	−	0.109109i	0.716800	−	0.697279i	$-0.245606\pi$
$197$	21.4119	−	1.53141i	1.52554	−	0.109109i	0.808737	+	0.588171i	$0.200152\pi$
$198$	2.25500	+	4.12972i	0.160256	+	0.293486i
$199$	−2.94488	−	20.4821i	−0.208757	−	1.45194i	−0.777220	−	0.629229i	$-0.783371\pi$
$199$	−2.94488	−	20.4821i	−0.208757	−	1.45194i	0.568463	−	0.822709i	$-0.307538\pi$
$200$	−3.70924	−	3.35284i	−0.262283	−	0.237082i
$201$	−5.51295	+	2.51768i	−0.388853	+	0.177583i
$202$	8.90374	+	4.86181i	0.626465	+	0.342076i
$203$	0.476561	−	0.177748i	0.0334480	−	0.0124755i
$204$	−0.637826	+	4.43618i	−0.0446568	+	0.310595i
$205$	−4.23482	−	17.3492i	−0.295772	−	1.21172i
$206$		−	11.2503i		−	0.783846i
$207$	−3.87944	−	5.96674i	−0.269640	−	0.414717i
$208$	3.63588	−	3.63588i	0.252103	−	0.252103i
$209$	2.28115	+	3.54954i	0.157790	+	0.245527i
$210$	3.17633	−	1.02031i	0.219188	−	0.0704079i
$211$	10.6549	−	23.3309i	0.733511	−	1.60617i	−0.0604304	−	0.998172i	$-0.519247\pi$
$211$	10.6549	−	23.3309i	0.733511	−	1.60617i	0.793942	−	0.607994i	$-0.208025\pi$
$212$	4.96998	−	9.10183i	0.341339	−	0.625117i
$213$	−9.04504	−	3.37363i	−0.619756	−	0.231157i
$214$	1.97626	+	2.28073i	0.135095	+	0.155907i
$215$	−14.8655	−	21.8971i	−1.01382	−	1.49337i
$216$	5.29733	+	1.55544i	0.360438	+	0.105834i
$217$	0.00417585	+	0.0583861i	0.000283476	+	0.00396351i
$218$	3.80552	+	17.4937i	0.257742	+	1.18482i
$219$	7.94114	−	12.3567i	0.536613	−	0.834986i
$220$	−3.55357	−	6.13496i	−0.239582	−	0.413619i
$221$	5.27308	−	17.9585i	0.354706	−	1.20802i
$222$	6.86561	+	5.13953i	0.460790	+	0.344943i
$223$	−7.73159	−	0.552974i	−0.517745	−	0.0370299i	−0.189978	−	0.981788i	$-0.560842\pi$
$223$	−7.73159	−	0.552974i	−0.517745	−	0.0370299i	−0.327767	+	0.944758i	$0.606296\pi$
$224$	−0.503382	−	1.10225i	−0.0336336	−	0.0736474i
$225$	−2.73828	+	6.89626i	−0.182552	+	0.459750i
$226$	−3.57689	−	1.63351i	−0.237931	−	0.108659i
$227$	1.80240	+	2.40772i	0.119629	+	0.159806i	0.856358	−	0.516382i	$-0.172722\pi$
$227$	1.80240	+	2.40772i	0.119629	+	0.159806i	−0.736729	+	0.676188i	$0.763631\pi$
$228$	1.60105	+	0.348286i	0.106032	+	0.0230658i
$229$	−8.82281			−0.583028			−0.291514	−	0.956567i	$-0.594159\pi$
$229$	−8.82281			−0.583028			−0.291514	+	0.956567i	$0.594159\pi$
$230$	6.07025	+	8.84036i	0.400261	+	0.582916i
$231$	4.73059			0.311250
$232$	−0.410153	−	0.0892234i	−0.0269279	−	0.00585780i
$233$	4.72883	+	6.31698i	0.309796	+	0.413839i	0.928235	−	0.371993i	$-0.121326\pi$
$233$	4.72883	+	6.31698i	0.309796	+	0.413839i	−0.618439	+	0.785833i	$0.712235\pi$
$234$	−6.94104	−	3.16987i	−0.453750	−	0.207221i
$235$	1.84577	−	1.68268i	0.120405	−	0.109766i
$236$	0.790894	+	1.73182i	0.0514828	+	0.112732i
$237$	−18.3527	−	1.31261i	−1.19214	−	0.0852633i
$238$	−3.53104	−	2.64330i	−0.228883	−	0.171340i
$239$	1.70779	−	5.81620i	0.110468	−	0.376219i	−0.885639	−	0.464374i	$-0.846279\pi$
$239$	1.70779	−	5.81620i	0.110468	−	0.376219i	0.996107	+	0.0881559i	$0.0280974\pi$
$240$	−2.66037	−	0.708821i	−0.171726	−	0.0457542i
$241$	0.603307	−	0.938764i	0.0388624	−	0.0604711i	−0.821279	−	0.570527i	$-0.806739\pi$
$241$	0.603307	−	0.938764i	0.0388624	−	0.0604711i	0.860141	+	0.510056i	$0.170375\pi$
$242$	0.201275	+	0.925245i	0.0129384	+	0.0594770i
$243$	−0.975542	−	13.6399i	−0.0625810	−	0.874997i
$244$	3.12448	+	0.917429i	0.200024	+	0.0587324i
$245$	2.32373	−	12.1489i	0.148457	−	0.776165i
$246$	−6.43963	−	7.43172i	−0.410576	−	0.473829i
$247$	−6.41114	−	2.39123i	−0.407931	−	0.152151i
$248$	0.0231506	−	0.0423972i	0.00147007	−	0.00269223i
$249$	−3.17637	+	6.95528i	−0.201294	+	0.440773i
$250$	3.86273	−	10.4919i	0.244301	−	0.663564i
$251$	−14.8573	−	23.1184i	−0.937785	−	1.45922i	−0.887671	−	0.460479i	$-0.847678\pi$
$251$	−14.8573	−	23.1184i	−0.937785	−	1.45922i	−0.0501147	−	0.998743i	$-0.515959\pi$
$252$	−1.27156	+	1.27156i	−0.0801004	+	0.0801004i
$253$	4.36130	+	14.5671i	0.274193	+	0.915826i
$254$			12.9986i			0.815604i
$255$	−9.73576	+	2.37643i	−0.609677	+	0.148818i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	0.916115	−	0.341693i	0.0571457	−	0.0213142i	−0.320729	−	0.947171i	$-0.603928\pi$
$257$	0.916115	−	0.341693i	0.0571457	−	0.0213142i	0.377874	+	0.925857i	$0.376655\pi$
$258$	−12.7907	−	6.98424i	−0.796313	−	0.434820i
$259$	−7.67764	+	3.50626i	−0.477065	+	0.217868i
$260$	10.5757	+	4.51113i	0.655879	+	0.279769i
$261$	0.0886484	+	0.616563i	0.00548720	+	0.0381643i
$262$	5.76783	+	10.5630i	0.356338	+	0.652584i
$263$	−6.78749	+	0.485451i	−0.418535	+	0.0299342i	−0.279019	−	0.960286i	$-0.590009\pi$
$263$	−6.78749	+	0.485451i	−0.418535	+	0.0299342i	−0.139516	+	0.990220i	$0.544555\pi$
$264$	−3.28418	−	2.11061i	−0.202127	−	0.129899i
$265$	23.0287	+	2.72045i	1.41464	+	0.167116i
$266$	−1.05599	+	1.21868i	−0.0647468	+	0.0747218i
$267$	−1.97901	+	1.08062i	−0.121114	+	0.0661330i
$268$	−2.94983	+	3.94051i	−0.180189	+	0.240705i
$269$	11.2785	−	9.77286i	0.687661	−	0.595862i	−0.239333	−	0.970938i	$-0.576929\pi$
$269$	11.2785	−	9.77286i	0.687661	−	0.595862i	0.926994	+	0.375076i	$0.122383\pi$
$270$	1.19084	+	12.2877i	0.0724720	+	0.747805i
$271$	0.0740959	−	0.0217565i	0.00450100	−	0.00132161i	−0.279481	−	0.960151i	$-0.590162\pi$
$271$	0.0740959	−	0.0217565i	0.00450100	−	0.00132161i	0.283982	+	0.958830i	$0.408344\pi$
$272$	1.27205	+	3.41051i	0.0771296	+	0.206792i
$273$	−6.14149	+	4.59746i	−0.371700	+	0.278251i
$274$	−8.51700	+	5.47355i	−0.514531	+	0.330669i
$275$	9.76466	−	12.4892i	0.588831	−	0.753125i
$276$	5.19754	+	2.80241i	0.312855	+	0.168685i
$277$	−22.3713	−	22.3713i	−1.34416	−	1.34416i	−0.891871	−	0.452291i	$-0.850607\pi$
$277$	−22.3713	−	22.3713i	−1.34416	−	1.34416i	−0.452291	−	0.891871i	$-0.649393\pi$
$278$	−1.33266	+	6.12614i	−0.0799277	+	0.367422i
$279$	−0.0709566	−	0.0102020i	−0.00424806	−	0.000610779i
$280$	1.86705	−	1.96365i	0.111578	−	0.117350i
$281$	3.03938	+	10.3512i	0.181314	+	0.617500i	0.999118	+	0.0420020i	$0.0133736\pi$
$281$	3.03938	+	10.3512i	0.181314	+	0.617500i	−0.817803	+	0.575498i	$0.804808\pi$
$282$	0.480618	−	1.28859i	0.0286204	−	0.0767342i
$283$	−0.653259	+	9.13376i	−0.0388322	+	0.542946i	0.940382	+	0.340119i	$0.110467\pi$
$283$	−0.653259	+	9.13376i	−0.0388322	+	0.542946i	−0.979215	+	0.202827i	$0.934987\pi$
$284$	−7.76072	+	1.11582i	−0.460514	+	0.0662119i
$285$	0.612663	+	3.61219i	0.0362911	+	0.213968i
$286$	12.3212	+	10.6764i	0.728568	+	0.631307i
$287$	9.45666	−	2.05717i	0.558209	−	0.121431i
$288$	1.45009	−	0.315447i	0.0854472	−	0.0185879i
$289$	−2.83430	−	2.45593i	−0.166724	−	0.144467i
$290$	−0.156951	−	0.925364i	−0.00921649	−	0.0543393i
$291$	3.27496	−	0.470868i	0.191981	−	0.0276028i
$292$	0.851046	−	11.8992i	0.0498037	−	0.696347i
$293$	−11.2200	+	30.0821i	−0.655482	+	1.75742i	−0.00255239	+	0.999997i	$0.500812\pi$
$293$	−11.2200	+	30.0821i	−0.655482	+	1.75742i	−0.652930	+	0.757419i	$0.726460\pi$
$294$	−1.91885	−	6.53500i	−0.111909	−	0.381129i
$295$	−2.93343	+	3.08520i	−0.170791	+	0.179627i
$296$	6.89450	+	0.991280i	0.400735	+	0.0576170i
$297$	−3.72098	+	17.1051i	−0.215913	+	0.992538i
$298$	5.28720	+	5.28720i	0.306279	+	0.306279i
$299$	−19.8192	−	14.6732i	−1.14617	−	0.848572i
$300$	−0.748123	−	6.11067i	−0.0431929	−	0.352800i
$301$	12.0657	−	7.75413i	0.695453	−	0.446941i
$302$	5.08255	−	3.80475i	0.292468	−	0.218939i
$303$	4.36505	+	11.7031i	0.250765	+	0.672328i
$304$	1.27684	−	0.374914i	0.0732318	−	0.0215028i
$305$	0.702381	+	7.24754i	0.0402182	+	0.414993i
$306$	4.08240	−	3.53742i	0.233375	−	0.202221i
$307$	−11.2654	+	15.0488i	−0.642951	+	0.858882i	−0.997084	−	0.0763127i	$-0.975685\pi$
$307$	−11.2654	+	15.0488i	−0.642951	+	0.858882i	0.354133	+	0.935195i	$0.384776\pi$
$308$	3.37211	−	1.84131i	0.192144	−	0.104918i
$309$	9.07116	−	10.4687i	0.516040	−	0.595542i
$310$	0.107270	+	0.0126721i	0.00609251	+	0.000719727i
$311$	21.3640	+	13.7298i	1.21144	+	0.778548i	0.980900	−	0.194514i	$-0.0623130\pi$
$311$	21.3640	+	13.7298i	1.21144	+	0.778548i	0.230544	+	0.973062i	$0.425949\pi$
$312$	6.31489	−	0.451650i	0.357510	−	0.0255697i
$313$	2.71406	+	4.97042i	0.153407	+	0.280945i	0.943069	−	0.332599i	$-0.107925\pi$
$313$	2.71406	+	4.97042i	0.153407	+	0.280945i	−0.789661	+	0.613543i	$0.789744\pi$
$314$	−3.04163	−	21.1550i	−0.171649	−	1.19385i
$315$	−3.69859	−	1.57765i	−0.208392	−	0.0888906i
$316$	−13.5933	+	6.20784i	−0.764682	+	0.349218i
$317$	7.62748	+	4.16492i	0.428402	+	0.233925i	0.678958	−	0.734177i	$-0.262432\pi$
$317$	7.62748	+	4.16492i	0.428402	+	0.233925i	−0.250556	+	0.968102i	$0.580614\pi$
$318$	11.9635	−	4.46216i	0.670881	−	0.250226i
$319$	0.189403	−	1.31733i	0.0106045	−	0.0737561i
$320$	−2.17229	+	0.530240i	−0.121435	+	0.0296413i
$321$			3.71574i			0.207392i
$322$	−4.87212	+	3.16774i	−0.271513	+	0.176532i
$323$	3.42517	−	3.42517i	0.190582	−	0.190582i
$324$	1.26820	+	1.97336i	0.0704555	+	0.109631i
$325$	−0.539266	+	25.7039i	−0.0299131	+	1.42580i
$326$	−7.88005	+	17.2549i	−0.436436	+	0.955661i
$327$	−10.5641	+	19.3467i	−0.584195	+	1.06987i
$328$	−7.48305	−	2.79103i	−0.413182	−	0.154109i
$329$	0.886365	+	1.02292i	0.0488669	+	0.0563954i
$330$	1.63995	−	8.57398i	0.0902763	−	0.471982i
$331$	26.2869	+	7.71854i	1.44486	+	0.424249i	0.907839	−	0.419319i	$-0.137731\pi$
$331$	26.2869	+	7.71854i	1.44486	+	0.424249i	0.537022	+	0.843568i	$0.319549\pi$
$332$	0.443024	+	6.19429i	0.0243141	+	0.339956i
$333$	−2.19722	−	10.1004i	−0.120407	−	0.553501i
$334$	3.42107	−	5.32329i	0.187193	−	0.291278i
$335$	−10.6356	−	2.83371i	−0.581084	−	0.154822i
$336$	0.420341	−	1.43155i	0.0229315	−	0.0780975i
$337$	13.0283	+	9.75289i	0.709699	+	0.531274i	0.892037	−	0.451962i	$-0.149276\pi$
$337$	13.0283	+	9.75289i	0.709699	+	0.531274i	−0.182338	+	0.983236i	$0.558367\pi$
$338$	−13.4050	−	0.958746i	−0.729137	−	0.0521489i
$339$	−2.01127	−	4.40407i	−0.109237	−	0.239196i
$340$	−6.01496	+	5.48349i	−0.326207	+	0.297384i
$341$	0.139321	+	0.0636259i	0.00754467	+	0.00344554i
$342$	−1.18347	−	1.58093i	−0.0639947	−	0.0854869i
$343$	14.8383	+	3.22787i	0.801192	+	0.174289i
$344$	−11.8361			−0.638160
$345$	−1.47950	+	13.1206i	−0.0796535	+	0.706391i
$346$	21.0364			1.13092
$347$	25.3729	+	5.51954i	1.36209	+	0.296304i	0.833475	−	0.552558i	$-0.186348\pi$
$347$	25.3729	+	5.51954i	1.36209	+	0.296304i	0.528615	+	0.848862i	$0.322712\pi$
$348$	−0.309716	−	0.413732i	−0.0166025	−	0.0221784i
$349$	7.99964	+	3.65331i	0.428211	+	0.195557i	0.617849	−	0.786297i	$-0.288004\pi$
$349$	7.99964	+	3.65331i	0.428211	+	0.195557i	−0.189638	+	0.981854i	$0.560732\pi$
$350$	5.63112	+	2.23594i	0.300996	+	0.119516i
$351$	−11.7929	−	25.8229i	−0.629460	−	1.37833i
$352$	−3.16259	−	0.226193i	−0.168566	−	0.0120561i
$353$	4.73613	+	3.54542i	0.252079	+	0.188704i	0.717843	−	0.696205i	$-0.245130\pi$
$353$	4.73613	+	3.54542i	0.252079	+	0.188704i	−0.465764	+	0.884909i	$0.654220\pi$
$354$	−0.660423	+	2.24920i	−0.0351011	+	0.119543i
$355$	−8.78739	−	15.1707i	−0.466386	−	0.805178i
$356$	−0.990084	+	1.54060i	−0.0524743	+	0.0816517i
$357$	−1.15441	−	5.30674i	−0.0610979	−	0.280862i
$358$	−1.03929	−	14.5311i	−0.0549279	−	0.767993i
$359$	−12.6602	−	3.71736i	−0.668178	−	0.196195i	−0.0699863	−	0.997548i	$-0.522296\pi$
$359$	−12.6602	−	3.71736i	−0.668178	−	0.196195i	−0.598191	+	0.801353i	$0.704114\pi$
$360$	1.86383	+	2.74544i	0.0982322	+	0.144698i
$361$	11.2827	+	13.0209i	0.593825	+	0.685311i
$362$	−22.2959	−	8.31596i	−1.17185	−	0.437077i
$363$	−0.558737	+	1.02325i	−0.0293261	+	0.0537067i
$364$	−2.58835	+	5.66769i	−0.135666	+	0.297068i
$365$	25.3972	−	8.15814i	1.32935	−	0.427016i
$366$	2.16767	+	3.37297i	0.113306	+	0.176308i
$367$	19.3819	−	19.3819i	1.01173	−	1.01173i	0.0117981	−	0.999930i	$-0.496244\pi$
$367$	19.3819	−	19.3819i	1.01173	−	1.01173i	0.999930	−	0.0117981i	$-0.00375552\pi$
$368$	4.79576	−	0.0254238i	0.249996	−	0.00132530i
$369$			11.8521i			0.616998i
$370$	3.69333	+	15.1309i	0.192007	+	0.786616i
$371$	−1.78838	+	12.4384i	−0.0928479	+	0.645772i
$372$	0.0557272	−	0.0207852i	0.00288932	−	0.00107766i
$373$	23.5016	+	12.8328i	1.21687	+	0.664459i	0.953836	−	0.300329i	$-0.0970963\pi$
$373$	23.5016	+	12.8328i	1.21687	+	0.664459i	0.263030	+	0.964788i	$0.415278\pi$
$374$	−10.4983	+	4.79441i	−0.542854	+	0.247913i
$375$	12.0540	−	6.64839i	0.622465	−	0.343322i
$376$	−0.158964	−	1.10562i	−0.00819793	−	0.0570179i
$377$	1.03436	+	1.89429i	0.0532723	+	0.0975609i
$378$	−6.67303	+	0.477264i	−0.343224	+	0.0245478i
$379$	14.4150	+	9.26396i	0.740449	+	0.475858i	0.855696	−	0.517479i	$-0.173130\pi$
$379$	14.4150	+	9.26396i	0.740449	+	0.475858i	−0.115247	+	0.993337i	$0.536766\pi$
$380$	1.84272	+	2.33641i	0.0945293	+	0.119855i
$381$	−10.4808	+	12.0955i	−0.536948	+	0.619671i
$382$	−15.8289	+	8.64325i	−0.809879	+	0.442227i
$383$	−4.72698	+	6.31451i	−0.241538	+	0.322656i	−0.904886	−	0.425654i	$-0.860044\pi$
$383$	−4.72698	+	6.31451i	−0.241538	+	0.322656i	0.663348	+	0.748311i	$0.269135\pi$
$384$	−0.930523	+	0.806303i	−0.0474856	+	0.0411465i
$385$	6.63252	+	5.46054i	0.338024	+	0.278295i
$386$	0.565739	−	0.166116i	0.0287954	−	0.00845508i
$387$	6.13827	+	16.4573i	0.312026	+	0.836573i
$388$	2.15121	−	1.61038i	0.109211	−	0.0817545i
$389$	−13.5196	+	8.68853i	−0.685472	+	0.440526i	−0.836473	−	0.548007i	$-0.815387\pi$
$389$	−13.5196	+	8.68853i	−0.685472	+	0.440526i	0.151001	+	0.988534i	$0.451750\pi$
$390$	6.20362	+	12.7250i	0.314132	+	0.644353i
$391$	15.2770	−	8.44730i	0.772590	−	0.427198i
$392$	−3.91146	−	3.91146i	−0.197559	−	0.197559i
$393$	−3.14987	+	14.4797i	−0.158890	+	0.730406i
$394$	21.2481	+	3.05502i	1.07047	+	0.153910i
$395$	−24.2162	−	23.0249i	−1.21845	−	1.15851i
$396$	1.32563	+	4.51468i	0.0666153	+	0.226871i
$397$	5.48239	−	14.6989i	0.275153	−	0.737715i	−0.723713	−	0.690102i	$-0.757566\pi$
$397$	5.48239	−	14.6989i	0.275153	−	0.737715i	0.998866	−	0.0476130i	$-0.0151614\pi$
$398$	1.47620	−	20.6400i	0.0739953	−	1.03459i
$399$	−1.96524	+	0.282560i	−0.0983853	+	0.0141457i
$400$	−2.91177	−	4.06468i	−0.145589	−	0.203234i
$401$	−7.31309	−	6.33683i	−0.365198	−	0.316446i	0.452860	−	0.891582i	$-0.350404\pi$
$401$	−7.31309	−	6.33683i	−0.365198	−	0.316446i	−0.818058	+	0.575136i	$0.804949\pi$
$402$	−5.92213	+	1.28828i	−0.295369	+	0.0642536i
$403$	−0.242709	+	0.0527981i	−0.0120902	+	0.00263006i
$404$	7.66681	+	6.64333i	0.381438	+	0.330518i
$405$	−3.03649	+	4.27692i	−0.150885	+	0.212522i
$406$	0.503453	−	0.0723856i	0.0249860	−	0.00359244i
$407$	−1.57552	+	22.0287i	−0.0780957	+	1.09192i
$408$	−1.56623	+	4.19922i	−0.0775398	+	0.207892i
$409$	2.00025	+	6.81224i	0.0989062	+	0.336844i	0.994049	−	0.108937i	$-0.0347445\pi$
$409$	2.00025	+	6.81224i	0.0989062	+	0.336844i	−0.895143	+	0.445780i	$0.852926\pi$
$410$	−0.450194	−	17.8529i	−0.0222335	−	0.881693i
$411$	−12.3386	−	1.77402i	−0.608619	−	0.0875062i
$412$	2.39142	−	10.9932i	0.117817	−	0.541596i
$413$	−1.63131	−	1.63131i	−0.0802716	−	0.0802716i
$414$	−2.52246	−	6.65501i	−0.123972	−	0.327076i
$415$	−12.4819	+	6.08514i	−0.612714	+	0.298708i
$416$	4.32565	−	2.77993i	0.212083	−	0.136297i
$417$	−6.17960	+	4.62599i	−0.302616	+	0.226536i
$418$	1.47451	+	3.95331i	0.0721206	+	0.193363i
$419$	3.58100	−	1.05148i	0.174943	−	0.0513680i	−0.193088	−	0.981181i	$-0.561850\pi$
$419$	3.58100	−	1.05148i	0.174943	−	0.0513680i	0.368031	+	0.929814i	$0.380032\pi$
$420$	3.32063	−	0.321812i	0.162030	−	0.0157028i
$421$	8.27799	−	7.17292i	0.403445	−	0.349587i	−0.429380	−	0.903124i	$-0.641268\pi$
$421$	8.27799	−	7.17292i	0.403445	−	0.349587i	0.832824	+	0.553537i	$0.186722\pi$
$422$	15.3707	−	20.5329i	0.748235	−	0.999524i
$423$	−1.45485	+	0.794408i	−0.0707372	+	0.0386254i
$424$	6.79113	−	7.83738i	0.329807	−	0.380617i
$425$	−16.3931	−	7.90617i	−0.795183	−	0.383505i
$426$	−8.12122	−	5.21919i	−0.393474	−	0.252871i
$427$	−3.93589	+	0.281501i	−0.190471	+	0.0136228i
$428$	1.44629	+	2.64869i	0.0699093	+	0.128029i
$429$	2.85676	+	19.8692i	0.137926	+	0.959296i
$430$	−9.87121	−	24.5566i	−0.476032	−	1.18422i
$431$	−5.78004	+	2.63966i	−0.278415	+	0.127148i	−0.549729	−	0.835343i	$-0.685269\pi$
$431$	−5.78004	+	2.63966i	−0.278415	+	0.127148i	0.271314	+	0.962491i	$0.412542\pi$
$432$	4.84564	+	2.64592i	0.233136	+	0.127302i
$433$	10.6427	−	3.96952i	0.511455	−	0.190763i	−0.0804685	−	0.996757i	$-0.525642\pi$
$433$	10.6427	−	3.96952i	0.511455	−	0.190763i	0.591923	+	0.805994i	$0.298369\pi$
$434$	−0.00833043	+	0.0579394i	−0.000399873	+	0.00278118i
$435$	0.600077	−	0.987623i	0.0287715	−	0.0473529i
$436$			17.9028i			0.857389i
$437$	−2.68193	−	5.79116i	−0.128294	−	0.277029i
$438$	10.3863	−	10.3863i	0.496275	−	0.496275i
$439$	−6.15393	−	9.57570i	−0.293711	−	0.457023i	0.662768	−	0.748825i	$-0.269382\pi$
$439$	−6.15393	−	9.57570i	−0.293711	−	0.457023i	−0.956479	+	0.291802i	$0.905745\pi$
$440$	−2.16829	−	6.75012i	−0.103369	−	0.321799i
$441$	−3.41013	+	7.46714i	−0.162387	+	0.355578i
$442$	8.96992	−	16.4272i	0.426656	−	0.781361i
$443$	−19.8383	−	7.39932i	−0.942548	−	0.351552i	−0.169234	−	0.985576i	$-0.554129\pi$
$443$	−19.8383	−	7.39932i	−0.942548	−	0.351552i	−0.773314	+	0.634024i	$0.781402\pi$
$444$	5.61622	+	6.48147i	0.266534	+	0.307597i
$445$	−4.02204	−	0.769297i	−0.190663	−	0.0364682i
$446$	−7.43735	−	2.18380i	−0.352169	−	0.103406i
$447$	0.656778	+	9.18295i	0.0310645	+	0.434339i
$448$	−0.257578	−	1.18407i	−0.0121694	−	0.0559418i
$449$	−16.3926	+	25.5074i	−0.773616	+	1.20377i	0.200935	+	0.979605i	$0.435602\pi$
$449$	−16.3926	+	25.5074i	−0.773616	+	1.20377i	−0.974551	+	0.224165i	$0.928034\pi$
$450$	−4.14161	+	6.15659i	−0.195237	+	0.290224i
$451$	7.13427	−	24.2971i	0.335940	−	1.14411i
$452$	−3.14792	−	2.35650i	−0.148066	−	0.110840i
$453$	7.79722	+	0.557668i	0.366345	+	0.0262015i
$454$	1.24941	+	2.73582i	0.0586376	+	0.128399i
$455$	−13.9175	−	0.643285i	−0.652464	−	0.0301577i
$456$	1.49042	+	0.680654i	0.0697955	+	0.0318745i
$457$	−2.52719	−	3.37593i	−0.118217	−	0.157919i	0.737529	−	0.675315i	$-0.235992\pi$
$457$	−2.52719	−	3.37593i	−0.118217	−	0.157919i	−0.855746	+	0.517396i	$0.826901\pi$
$458$	−8.62118	−	1.87542i	−0.402841	−	0.0876327i
$459$	20.0964			0.938019
$460$	4.05238	+	9.92866i	0.188943	+	0.462926i
$461$	−34.8411			−1.62271			−0.811355	−	0.584554i	$-0.801269\pi$
$461$	−34.8411			−1.62271			−0.811355	+	0.584554i	$0.801269\pi$
$462$	4.62248	+	1.00556i	0.215057	+	0.0467829i
$463$	−19.8543	−	26.5222i	−0.922706	−	1.23259i	−0.972280	−	0.233820i	$-0.924877\pi$
$463$	−19.8543	−	26.5222i	−0.922706	−	1.23259i	0.0495744	−	0.998770i	$-0.484214\pi$
$464$	−0.381814	−	0.174369i	−0.0177253	−	0.00809486i
$465$	0.0895994	+	0.0982836i	0.00415507	+	0.00455779i
$466$	3.27799	+	7.17780i	0.151850	+	0.332505i
$467$	−23.3960	−	1.67331i	−1.08264	−	0.0774317i	−0.481399	−	0.876502i	$-0.659871\pi$
$467$	−23.3960	−	1.67331i	−1.08264	−	0.0774317i	−0.601238	+	0.799070i	$0.705326\pi$
$468$	−6.10861	−	4.57285i	−0.282371	−	0.211380i
$469$	1.68043	−	5.72303i	0.0775952	−	0.264265i
$470$	2.16127	−	1.25188i	0.0996920	−	0.0577450i
$471$	14.2270	−	22.1377i	0.655548	−	1.02005i
$472$	0.404696	+	1.86036i	0.0186276	+	0.0856298i
$473$	−2.67724	−	37.4327i	−0.123100	−	1.72116i
$474$	−17.6543	−	5.18376i	−0.810887	−	0.238098i
$475$	−3.31058	+	5.77166i	−0.151900	+	0.264822i
$476$	−2.88847	−	3.33347i	−0.132393	−	0.152789i
$477$	−14.4193	−	5.37812i	−0.660214	−	0.246247i
$478$	2.90508	−	5.32026i	0.132875	−	0.243343i
$479$	−3.27451	+	7.17018i	−0.149616	+	0.327614i	−0.969569	−	0.244817i	$-0.921272\pi$
$479$	−3.27451	+	7.17018i	−0.149616	+	0.327614i	0.819953	+	0.572431i	$0.193999\pi$
$480$	−2.44890	−	1.25812i	−0.111777	−	0.0574252i
$481$	−19.3633	−	30.1299i	−0.882891	−	1.37380i
$482$	0.789068	−	0.789068i	0.0359411	−	0.0359411i
$483$	−7.08779	−	0.980748i	−0.322506	−	0.0446256i
$484$			0.946884i			0.0430402i
$485$	5.13517	+	3.12012i	0.233176	+	0.141677i
$486$	1.94611	−	13.5355i	0.0882774	−	0.613983i
$487$	13.1105	−	4.88996i	0.594093	−	0.221585i	−0.0343902	−	0.999408i	$-0.510949\pi$
$487$	13.1105	−	4.88996i	0.594093	−	0.221585i	0.628483	+	0.777823i	$0.283676\pi$
$488$	2.85806	+	1.56062i	0.129378	+	0.0706459i
$489$	−21.2453	+	9.70238i	−0.960744	+	0.438757i
$490$	4.85306	−	11.3773i	0.219239	−	0.513975i
$491$	3.99479	+	27.7843i	0.180282	+	1.25389i	0.856096	+	0.516817i	$0.172883\pi$
$491$	3.99479	+	27.7843i	0.180282	+	1.25389i	−0.675813	+	0.737073i	$0.736208\pi$
$492$	−4.71273	−	8.63073i	−0.212466	−	0.389103i
$493$	−1.52399	+	0.108998i	−0.0686369	+	0.00490901i
$494$	−5.75634	−	3.69937i	−0.258990	−	0.166443i
$495$	−8.26112	+	6.51551i	−0.371310	+	0.292850i
$496$	0.0316337	−	0.0365073i	0.00142040	−	0.00163923i
$497$	8.33867	−	4.55326i	0.374040	−	0.204241i
$498$	−4.58223	+	6.12114i	−0.205335	+	0.274295i
$499$	30.1269	−	26.1051i	1.34867	−	1.16863i	0.378664	−	0.925534i	$-0.376384\pi$
$499$	30.1269	−	26.1051i	1.34867	−	1.16863i	0.970003	−	0.243092i	$-0.0781618\pi$
$500$	6.00467	−	9.43101i	0.268537	−	0.421768i
$501$	7.47557	−	2.19503i	0.333984	−	0.0980665i
$502$	−9.60360	−	25.7483i	−0.428630	−	1.14920i
$503$	−2.58849	+	1.93772i	−0.115415	+	0.0863985i	−0.655426	−	0.755259i	$-0.727511\pi$
$503$	−2.58849	+	1.93772i	−0.115415	+	0.0863985i	0.540011	+	0.841658i	$0.318420\pi$
$504$	−1.51278	+	0.972208i	−0.0673848	+	0.0433056i
$505$	−7.38898	+	21.4470i	−0.328805	+	0.954377i
$506$	1.16517	+	15.1613i	0.0517982	+	0.674001i
$507$	−11.7006	−	11.7006i	−0.519644	−	0.519644i
$508$	−2.76305	+	12.7015i	−0.122590	+	0.563539i
$509$	36.6949	+	5.27593i	1.62647	+	0.233851i	0.894365	−	0.447338i	$-0.147628\pi$
$509$	36.6949	+	5.27593i	1.62647	+	0.233851i	0.732107	+	0.681190i	$0.238537\pi$
$510$	−10.0184	+	0.252633i	−0.443623	+	0.0111868i
$511$	4.07266	+	13.8702i	0.180164	+	0.613581i
$512$	−0.349464	+	0.936950i	−0.0154443	+	0.0414077i
$513$	0.524129	−	7.32828i	0.0231408	−	0.323551i
$514$	0.967811	−	0.139150i	0.0426883	−	0.00613766i
$515$	24.8022	−	4.20671i	1.09292	−	0.185370i
$516$	−11.0138	−	9.54348i	−0.484854	−	0.420128i
$517$	3.46065	−	0.752819i	0.152199	−	0.0331090i
$518$	−8.24749	+	1.79413i	−0.362374	+	0.0788296i
$519$	19.5748	+	16.9617i	0.859239	+	0.744535i
$520$	9.37513	+	6.65607i	0.411126	+	0.291888i
$521$	−18.2694	+	2.62675i	−0.800398	+	0.115080i	−0.530363	−	0.847771i	$-0.677944\pi$
$521$	−18.2694	+	2.62675i	−0.800398	+	0.115080i	−0.270035	+	0.962851i	$0.587035\pi$
$522$	−0.0444374	+	0.621316i	−0.00194497	+	0.0271943i
$523$	10.5477	−	28.2794i	0.461217	−	1.23657i	−0.473379	−	0.880859i	$-0.656966\pi$
$523$	10.5477	−	28.2794i	0.461217	−	1.23657i	0.934596	−	0.355712i	$-0.115761\pi$
$524$	3.39069	+	11.5476i	0.148123	+	0.504461i
$525$	3.43705	+	6.62098i	0.150005	+	0.288963i
$526$	−6.73556	−	0.968428i	−0.293685	−	0.0422255i
$527$	0.0373763	−	0.171816i	0.00162814	−	0.00748443i
$528$	−2.76048	−	2.76048i	−0.120135	−	0.120135i
$529$	−3.51443	−	22.7299i	−0.152801	−	0.988257i
$530$	21.9241	+	7.55337i	0.952323	+	0.328098i
$531$	2.37683	−	1.52749i	0.103145	−	0.0662876i
$532$	−1.29090	+	0.966359i	−0.0559678	+	0.0418970i
$533$	14.3512	+	38.4772i	0.621621	+	1.66663i
$534$	−2.16349	+	0.635257i	−0.0936233	+	0.0274903i
$535$	−4.28909	+	5.20964i	−0.185434	+	0.225232i
$536$	−3.72003	+	3.22343i	−0.160681	+	0.139231i
$537$	10.7494	−	14.3595i	0.463871	−	0.619659i
$538$	13.0981	−	7.15211i	0.564699	−	0.308349i
$539$	11.4856	−	13.2551i	0.494720	−	0.570937i
$540$	−1.44831	+	12.2600i	−0.0623255	+	0.527587i
$541$	−23.9270	−	15.3769i	−1.02870	−	0.661106i	−0.0865334	−	0.996249i	$-0.527579\pi$
$541$	−23.9270	−	15.3769i	−1.02870	−	0.661106i	−0.942167	+	0.335143i	$0.891215\pi$
$542$	0.0770272	−	0.00550910i	0.00330860	−	0.000236636i
$543$	−14.0417	−	25.7155i	−0.602588	−	1.10356i
$544$	0.518028	+	3.60296i	0.0222103	+	0.154476i
$545$	−37.1433	+	14.9308i	−1.59104	+	0.639565i
$546$	−6.97839	+	3.18693i	−0.298648	+	0.136388i
$547$	24.8682	+	13.5791i	1.06329	+	0.580599i	0.912965	−	0.408038i	$-0.133787\pi$
$547$	24.8682	+	13.5791i	1.06329	+	0.580599i	0.150323	+	0.988637i	$0.451969\pi$
$548$	−9.48585	+	3.53804i	−0.405215	+	0.151138i
$549$	0.687734	−	4.78329i	0.0293518	−	0.204146i
$550$	12.1963	−	10.1281i	0.520051	−	0.431865i
$551$			0.558574i			0.0237961i
$552$	4.48307	+	3.84318i	0.190812	+	0.163577i
$553$	12.8044	−	12.8044i	0.544499	−	0.544499i
$554$	−17.1047	−	26.6154i	−0.726708	−	1.13078i
$555$	−8.76334	+	17.0576i	−0.371983	+	0.724054i
$556$	−2.60441	+	5.70286i	−0.110452	+	0.241855i
$557$	3.46034	−	6.33715i	0.146619	−	0.268513i	−0.794040	−	0.607866i	$-0.792026\pi$
$557$	3.46034	−	6.33715i	0.146619	−	0.268513i	0.940659	+	0.339352i	$0.110208\pi$
$558$	−0.0671664	−	0.0250518i	−0.00284338	−	0.00106053i
$559$	39.8549	+	45.9951i	1.68568	+	1.94538i
$560$	2.24178	−	1.52190i	0.0947327	−	0.0643121i
$561$	−13.6347	−	4.00350i	−0.575656	−	0.169028i
$562$	0.769620	+	10.7607i	0.0324645	+	0.453913i
$563$	−4.08178	−	18.7637i	−0.172027	−	0.790794i	−0.979589	−	0.201011i	$-0.935577\pi$
$563$	−4.08178	−	18.7637i	−0.172027	−	0.790794i	0.807562	−	0.589782i	$-0.200786\pi$
$564$	0.743543	−	1.15698i	0.0313088	−	0.0487175i
$565$	2.26374	−	8.49634i	0.0952362	−	0.357444i
$566$	−2.57985	+	8.78616i	−0.108439	+	0.369310i
$567$	−2.27551	−	1.70342i	−0.0955623	−	0.0715371i
$568$	−7.82055	−	0.559337i	−0.328143	−	0.0234692i
$569$	16.3752	+	35.8566i	0.686483	+	1.50319i	0.855625	+	0.517597i	$0.173173\pi$
$569$	16.3752	+	35.8566i	0.686483	+	1.50319i	−0.169142	+	0.985592i	$0.554100\pi$
$570$	−0.169164	+	3.65987i	−0.00708548	+	0.153295i
$571$	−22.8911	−	10.4540i	−0.957962	−	0.437487i	−0.125822	−	0.992053i	$-0.540157\pi$
$571$	−22.8911	−	10.4540i	−0.957962	−	0.437487i	−0.832140	+	0.554566i	$0.812884\pi$
$572$	9.77019	+	13.0514i	0.408512	+	0.545708i
$573$	−21.6983	−	4.72017i	−0.906458	−	0.197188i
$574$	9.67783			0.403945
$575$	−17.2195	+	16.6880i	−0.718104	+	0.695936i
$576$	1.48400			0.0618334
$577$	−21.6642	−	4.71276i	−0.901894	−	0.196195i	−0.262371	−	0.964967i	$-0.584504\pi$
$577$	−21.6642	−	4.71276i	−0.901894	−	0.196195i	−0.639523	+	0.768772i	$0.720868\pi$
$578$	−2.24748	−	3.00228i	−0.0934829	−	0.124879i
$579$	0.660373	+	0.301582i	0.0274442	+	0.0125333i
$580$	0.0433361	−	0.937579i	0.00179943	−	0.0389309i
$581$	−3.12606	−	6.84512i	−0.129691	−	0.283983i
$582$	3.30020	+	0.236035i	0.136798	+	0.00978398i
$583$	26.3225	+	19.7048i	1.09017	+	0.816089i
$584$	3.36095	−	11.4463i	0.139077	−	0.473653i
$585$	4.39285	−	16.4874i	0.181622	−	0.681669i
$586$	−17.3580	+	27.0096i	−0.717054	+	1.11576i
$587$	7.24877	+	33.3220i	0.299189	+	1.37535i	0.843799	+	0.536659i	$0.180314\pi$
$587$	7.24877	+	33.3220i	0.299189	+	1.37535i	−0.544611	+	0.838689i	$0.683323\pi$
$588$	−0.485883	−	6.79353i	−0.0200375	−	0.280161i
$589$	−0.0616791	−	0.0181106i	−0.00254144	−	0.000746235i
$590$	−3.52220	+	2.39115i	−0.145007	+	0.0984421i
$591$	17.3086	+	19.9752i	0.711981	+	0.821670i
$592$	6.52623	+	2.43416i	0.268226	+	0.100043i
$593$	−0.346512	+	0.634590i	−0.0142296	+	0.0260595i	−0.884697	−	0.466166i	$-0.845635\pi$
$593$	−0.346512	+	0.634590i	−0.0142296	+	0.0260595i	0.870467	+	0.492226i	$0.163817\pi$
$594$	−7.27190	+	15.9232i	−0.298370	+	0.653338i
$595$	4.50705	−	8.77284i	0.184771	−	0.359652i
$596$	4.04250	+	6.29025i	0.165587	+	0.257659i
$597$	18.0157	−	18.0157i	0.737335	−	0.737335i
$598$	−16.2473	−	18.5507i	−0.664400	−	0.758595i
$599$		−	32.4930i		−	1.32763i	−0.747898	−	0.663814i	$-0.768937\pi$
$599$		−	32.4930i		−	1.32763i	0.747898	−	0.663814i	$-0.231063\pi$
$600$	0.567890	−	6.13005i	0.0231840	−	0.250258i
$601$	−5.78227	+	40.2166i	−0.235864	+	1.64047i	0.436111	+	0.899893i	$0.356356\pi$
$601$	−5.78227	+	40.2166i	−0.235864	+	1.64047i	−0.671974	+	0.740574i	$0.734553\pi$
$602$	13.4382	−	5.01218i	0.547700	−	0.204281i
$603$	6.41119	+	3.50078i	0.261084	+	0.142563i
$604$	5.77516	−	2.63743i	0.234988	−	0.107315i
$605$	−1.96452	+	0.789694i	−0.0798690	+	0.0321056i
$606$	1.77761	+	12.3635i	0.0722104	+	0.502235i
$607$	−10.4219	−	19.0862i	−0.423010	−	0.774685i	0.576077	−	0.817395i	$-0.304583\pi$
$607$	−10.4219	−	19.0862i	−0.423010	−	0.774685i	−0.999088	+	0.0427098i	$0.986401\pi$
$608$	1.32735	−	0.0949342i	0.0538313	−	0.00385009i
$609$	0.526840	+	0.338579i	0.0213486	+	0.0137199i
$610$	−0.854246	+	7.23121i	−0.0345874	+	0.292783i
$611$	−3.76116	+	4.34061i	−0.152160	+	0.175602i
$612$	4.74103	−	2.58880i	0.191645	−	0.104646i
$613$	−1.67469	+	2.23712i	−0.0676399	+	0.0903563i	−0.833085	−	0.553144i	$-0.813428\pi$
$613$	−1.67469	+	2.23712i	−0.0676399	+	0.0903563i	0.765445	+	0.643501i	$0.222519\pi$
$614$	−14.2068	+	12.3103i	−0.573341	+	0.496803i
$615$	13.9759	−	16.9756i	0.563565	−	0.684520i
$616$	3.68645	−	1.08244i	0.148531	−	0.0436127i
$617$	1.45882	+	3.91125i	0.0587300	+	0.157461i	0.963001	−	0.269498i	$-0.0868577\pi$
$617$	1.45882	+	3.91125i	0.0587300	+	0.157461i	−0.904271	+	0.426959i	$0.859585\pi$
$618$	11.0891	−	8.30122i	0.446070	−	0.333924i
$619$	1.24522	−	0.800257i	0.0500498	−	0.0321650i	−0.515377	−	0.856964i	$-0.672348\pi$
$619$	1.24522	−	0.800257i	0.0500498	−	0.0321650i	0.565426	+	0.824799i	$0.308712\pi$
$620$	0.102125	+	0.0351843i	0.00410142	+	0.00141304i
$621$	9.12134	−	24.8569i	0.366027	−	0.997473i
$622$	17.9573	+	17.9573i	0.720023	+	0.720023i
$623$	0.471706	−	2.16840i	0.0188985	−	0.0868750i
$624$	6.26658	+	0.900999i	0.250864	+	0.0360688i
$625$	24.5745	+	4.59260i	0.982982	+	0.183704i
$626$	1.59549	+	5.43375i	0.0637687	+	0.217176i
$627$	−1.81550	+	4.86755i	−0.0725042	+	0.194391i
$628$	1.52470	−	21.3181i	0.0608422	−	0.850685i
$629$	25.0961	−	3.60827i	1.00065	−	0.143871i
$630$	−3.27871	−	2.32779i	−0.130627	−	0.0927413i
$631$	8.73039	+	7.56493i	0.347551	+	0.301155i	0.811090	−	0.584922i	$-0.198875\pi$
$631$	8.73039	+	7.56493i	0.347551	+	0.301155i	−0.463538	+	0.886077i	$0.653420\pi$
$632$	−14.6022	+	3.17652i	−0.580844	+	0.126355i
$633$	30.8585	−	6.71286i	1.22652	−	0.266812i
$634$	6.56785	+	5.69108i	0.260843	+	0.226021i
$635$	−28.6565	+	4.86042i	−1.13720	+	0.192880i
$636$	12.6386	−	1.81716i	0.501154	−	0.0720550i
$637$	−2.02912	+	28.3708i	−0.0803965	+	1.12409i
$638$	0.465093	−	1.24696i	0.0184132	−	0.0493677i
$639$	3.27806	+	11.1640i	0.129678	+	0.441642i
$640$	−2.23536	+	0.0563686i	−0.0883603	+	0.00222817i
$641$	−4.22893	−	0.608028i	−0.167033	−	0.0240157i	0.0582911	−	0.998300i	$-0.481435\pi$
$641$	−4.22893	−	0.608028i	−0.167033	−	0.0240157i	−0.225324	+	0.974284i	$0.572344\pi$
$642$	−0.789837	+	3.63082i	−0.0311724	+	0.143297i
$643$	7.60531	+	7.60531i	0.299924	+	0.299924i	0.840984	−	0.541060i	$-0.181977\pi$
$643$	7.60531	+	7.60531i	0.299924	+	0.299924i	−0.541060	+	0.840984i	$0.681977\pi$
$644$	−5.43413	+	2.05971i	−0.214135	+	0.0811638i
$645$	10.6147	−	30.8097i	0.417951	−	1.21313i
$646$	4.07497	−	2.61882i	0.160327	−	0.103036i
$647$	35.4749	−	26.5562i	1.39466	−	1.04403i	0.402998	−	0.915201i	$-0.367968\pi$
$647$	35.4749	−	26.5562i	1.39466	−	1.04403i	0.991666	−	0.128832i	$-0.0411226\pi$
$648$	0.819750	+	2.19784i	0.0322028	+	0.0863391i
$649$	−5.79199	+	1.70068i	−0.227356	+	0.0667577i
$650$	−5.99070	+	25.0019i	−0.234975	+	0.980654i
$651$	−0.0544684	+	0.0471971i	−0.00213478	+	0.00184980i
$652$	−11.3678	+	15.1856i	−0.445196	+	0.594712i
$653$	−23.0179	+	12.5687i	−0.900761	+	0.491853i	−0.861720	−	0.507385i	$-0.830612\pi$
$653$	−23.0179	+	12.5687i	−0.900761	+	0.491853i	−0.0390414	+	0.999238i	$0.512430\pi$
$654$	−14.4351	+	16.6590i	−0.564457	+	0.651418i
$655$	−21.1303	+	16.6654i	−0.825629	+	0.651170i
$656$	−6.71876	−	4.31789i	−0.262324	−	0.168585i
$657$	−17.6584	+	1.26295i	−0.688920	+	0.0492725i
$658$	0.648672	+	1.18795i	0.0252879	+	0.0463113i
$659$	−4.18317	−	29.0946i	−0.162953	−	1.13336i	−0.893030	−	0.449998i	$-0.851425\pi$
$659$	−4.18317	−	29.0946i	−0.162953	−	1.13336i	0.730077	−	0.683365i	$-0.239484\pi$
$660$	3.42500	−	8.02944i	0.133318	−	0.312545i
$661$	13.6162	−	6.21833i	0.529611	−	0.241865i	−0.132618	−	0.991167i	$-0.542338\pi$
$661$	13.6162	−	6.21833i	0.529611	−	0.241865i	0.662228	+	0.749302i	$0.269611\pi$
$662$	24.0455	+	13.1298i	0.934555	+	0.510306i
$663$	21.5920	−	8.05340i	0.838564	−	0.312768i
$664$	−0.883791	+	6.14690i	−0.0342977	+	0.238546i
$665$	−3.08153	−	1.87233i	−0.119496	−	0.0726058i
$666$		−	10.3367i		−	0.400538i
$667$	−0.556889	+	1.93447i	−0.0215628	+	0.0749029i
$668$	4.47444	−	4.47444i	0.173121	−	0.173121i
$669$	−5.15982	−	8.02884i	−0.199490	−	0.310413i
$670$	−9.79018	−	5.02971i	−0.378228	−	0.194315i
$671$	−4.28912	+	9.39186i	−0.165580	+	0.362569i
$672$	0.715033	−	1.30949i	0.0275830	−	0.0505145i
$673$	20.7063	+	7.72305i	0.798169	+	0.297702i	0.715263	−	0.698856i	$-0.246307\pi$
$673$	20.7063	+	7.72305i	0.798169	+	0.297702i	0.0829062	+	0.996557i	$0.473580\pi$
$674$	10.6575	+	12.2994i	0.410510	+	0.473754i
$675$	−26.6439	+	7.21990i	−1.02553	+	0.277894i
$676$	−12.8949	−	3.78628i	−0.495957	−	0.145626i
$677$	2.75930	+	38.5801i	0.106049	+	1.48275i	0.720311	+	0.693651i	$0.243999\pi$
$677$	2.75930	+	38.5801i	0.106049	+	1.48275i	−0.614262	+	0.789102i	$0.710546\pi$
$678$	−1.02916	−	4.73095i	−0.0395245	−	0.181691i
$679$	−1.76045	+	2.73932i	−0.0675599	+	0.105125i
$680$	−7.04310	+	4.07960i	−0.270091	+	0.156446i
$681$	−1.04330	+	3.55315i	−0.0399793	+	0.136157i
$682$	0.122613	+	0.0917867i	0.00469508	+	0.00351470i
$683$	−41.5871	−	2.97437i	−1.59129	−	0.113811i	−0.752619	−	0.658457i	$-0.771210\pi$
$683$	−41.5871	−	2.97437i	−1.59129	−	0.113811i	−0.838666	+	0.544646i	$0.816664\pi$
$684$	−0.820373	−	1.79637i	−0.0313677	−	0.0686858i
$685$	−15.2516	−	16.7298i	−0.582732	−	0.639212i
$686$	13.8130	+	6.30821i	0.527385	+	0.240848i
$687$	−6.51005	−	8.69641i	−0.248374	−	0.331789i
$688$	−11.5656	−	2.51594i	−0.440935	−	0.0959195i
$689$	−53.3234			−2.03146
$690$	−4.23468	+	12.5063i	−0.161211	+	0.476106i
$691$	15.4014			0.585897			0.292949	−	0.956128i	$-0.405363\pi$
$691$	15.4014			0.585897			0.292949	+	0.956128i	$0.405363\pi$
$692$	20.5556	+	4.47160i	0.781407	+	0.169985i
$693$	−3.41687	−	4.56441i	−0.129796	−	0.173387i
$694$	23.6198	+	10.7868i	0.896595	+	0.409461i
$695$	−14.0039	−	0.647277i	−0.531198	−	0.0245526i
$696$	−0.214693	−	0.470112i	−0.00813792	−	0.0178196i
$697$	−28.9973	−	2.07393i	−1.09835	−	0.0785555i
$698$	7.04025	+	5.27027i	0.266478	+	0.199483i
$699$	−2.73724	+	9.32217i	−0.103532	+	0.352597i
$700$	5.02715	+	3.38182i	0.190008	+	0.127821i
$701$	23.7004	−	36.8786i	0.895153	−	1.39288i	−0.0243085	−	0.999705i	$-0.507738\pi$
$701$	23.7004	−	36.8786i	0.895153	−	1.39288i	0.919461	−	0.393180i	$-0.128625\pi$
$702$	−6.03437	−	27.7396i	−0.227753	−	1.04696i
$703$	−0.661255	−	9.24555i	−0.0249397	−	0.348702i
$704$	−3.04223	−	0.893280i	−0.114658	−	0.0336667i
$705$	3.02051	+	0.577735i	0.113759	+	0.0217587i
$706$	3.87426	+	4.47114i	0.145810	+	0.168273i
$707$	−11.5178	−	4.29591i	−0.433171	−	0.161564i
$708$	−1.12343	+	2.05741i	−0.0422211	+	0.0773222i
$709$	−9.59066	+	21.0006i	−0.360185	+	0.788695i	0.639615	+	0.768695i	$0.279094\pi$
$709$	−9.59066	+	21.0006i	−0.360185	+	0.788695i	−0.999800	+	0.0199994i	$0.993634\pi$
$710$	−5.36181	−	16.6919i	−0.201225	−	0.626436i
$711$	11.9895	+	18.6561i	0.449642	+	0.699657i
$712$	−1.29494	+	1.29494i	−0.0485298	+	0.0485298i
$713$	−0.195552	−	0.124214i	−0.00732350	−	0.00465185i
$714$		−	5.43085i		−	0.203244i
$715$	−18.9298	+	31.1552i	−0.707935	+	1.16514i
$716$	2.07327	−	14.4199i	0.0774819	−	0.538899i
$717$	6.99299	−	2.60825i	0.261158	−	0.0974069i
$718$	−11.5807	−	6.32352i	−0.432186	−	0.235992i
$719$	21.9795	−	10.0377i	0.819699	−	0.374344i	0.0389906	−	0.999240i	$-0.487586\pi$
$719$	21.9795	−	10.0377i	0.819699	−	0.374344i	0.780708	+	0.624896i	$0.214858\pi$
$720$	1.23765	+	3.07889i	0.0461243	+	0.114743i
$721$	1.94013	+	13.4939i	0.0722541	+	0.502538i
$722$	8.25704	+	15.1216i	0.307295	+	0.562769i
$723$	1.37047	−	0.0980182i	0.0509685	−	0.00364534i
$724$	−20.0187	−	12.8653i	−0.743990	−	0.478134i
$725$	1.98135	−	0.692023i	0.0735857	−	0.0257011i
$726$	−0.763476	+	0.881098i	−0.0283352	+	0.0327006i
$727$	2.28435	−	1.24735i	0.0847220	−	0.0462617i	−0.436329	−	0.899787i	$-0.643722\pi$
$727$	2.28435	−	1.24735i	0.0847220	−	0.0462617i	0.521051	+	0.853525i	$0.325540\pi$
$728$	−3.73395	+	4.98797i	−0.138389	+	0.184867i
$729$	18.0430	−	15.6343i	0.668259	−	0.579049i
$730$	26.5509	−	2.57313i	0.982694	−	0.0952359i
$731$	−41.3384	+	12.1380i	−1.52895	+	0.448941i
$732$	1.40116	+	3.75665i	0.0517884	+	0.138850i
$733$	4.42112	−	3.30961i	0.163298	−	0.122243i	−0.514504	−	0.857488i	$-0.672024\pi$
$733$	4.42112	−	3.30961i	0.163298	−	0.122243i	0.677801	+	0.735245i	$0.262933\pi$
$734$	23.0589	−	14.8191i	0.851120	−	0.546982i
$735$	13.6894	−	6.67382i	0.504943	−	0.246168i
$736$	4.69157	+	0.994570i	0.172934	+	0.0366603i
$737$	−11.0358	−	11.0358i	−0.406509	−	0.406509i
$738$	−2.51935	+	11.5813i	−0.0927387	+	0.426313i
$739$	−43.0951	−	6.19614i	−1.58528	−	0.227929i	−0.707400	−	0.706813i	$-0.750132\pi$
$739$	−43.0951	−	6.19614i	−1.58528	−	0.227929i	−0.877878	+	0.478885i	$0.841041\pi$
$740$	0.392630	+	15.5702i	0.0144334	+	0.572370i
$741$	−2.37359	−	8.08370i	−0.0871960	−	0.296962i
$742$	−4.39149	+	11.7740i	−0.161217	+	0.432238i
$743$	−0.739355	+	10.3375i	−0.0271243	+	0.379247i	0.965700	+	0.259662i	$0.0836111\pi$
$743$	−0.739355	+	10.3375i	−0.0271243	+	0.379247i	−0.992824	+	0.119585i	$0.961843\pi$
$744$	0.0588719	−	0.00846449i	0.00215835	−	0.000310323i
$745$	−9.67908	+	13.6331i	−0.354614	+	0.499477i
$746$	20.2367	+	17.5352i	0.740918	+	0.642009i
$747$	9.00520	−	1.95896i	0.329483	−	0.0716747i
$748$	−11.2775	+	2.45327i	−0.412346	+	0.0897005i
$749$	−2.76369	−	2.39475i	−0.100983	−	0.0875023i
$750$	13.1917	−	3.93420i	0.481694	−	0.143657i
$751$	−19.5796	+	2.81512i	−0.714470	+	0.102725i	−0.489958	−	0.871746i	$-0.662988\pi$
$751$	−19.5796	+	2.81512i	−0.714470	+	0.102725i	−0.224512	+	0.974471i	$0.572079\pi$
$752$	0.0796849	−	1.11414i	0.00290581	−	0.0406285i
$753$	11.8245	−	31.7028i	0.430909	−	1.15531i
$754$	0.608062	+	2.07087i	0.0221443	+	0.0754166i
$755$	10.2884	+	9.78224i	0.374432	+	0.356012i
$756$	−6.62198	−	0.952097i	−0.240839	−	0.0346274i
$757$	−4.94113	+	22.7140i	−0.179589	+	0.825555i	0.795887	+	0.605446i	$0.207005\pi$
$757$	−4.94113	+	22.7140i	−0.179589	+	0.825555i	−0.975475	+	0.220110i	$0.929359\pi$
$758$	12.1164	+	12.1164i	0.440087	+	0.440087i
$759$	−11.1404	+	15.0474i	−0.404369	+	0.546186i
$760$	1.30396	+	2.67471i	0.0472997	+	0.0970220i
$761$	12.7871	−	8.21780i	0.463533	−	0.297895i	−0.287952	−	0.957645i	$-0.592974\pi$
$761$	12.7871	−	8.21780i	0.463533	−	0.297895i	0.751485	+	0.659750i	$0.229338\pi$
$762$	−12.8124	+	9.59122i	−0.464143	+	0.347453i
$763$	−7.58123	−	20.3261i	−0.274459	−	0.735853i
$764$	−17.3045	+	5.08105i	−0.626053	+	0.183826i
$765$	9.32501	+	7.67727i	0.337146	+	0.277572i
$766$	−5.96120	+	5.16541i	−0.215387	+	0.186634i
$767$	5.86663	−	7.83690i	0.211832	−	0.282974i
$768$	−1.08065	+	0.590080i	−0.0389946	+	0.0212927i
$769$	28.1303	−	32.4640i	1.01440	−	1.17068i	0.0291508	−	0.999575i	$-0.490720\pi$
$769$	28.1303	−	32.4640i	1.01440	−	1.17068i	0.985252	−	0.171108i	$-0.0547349\pi$
$770$	5.32022	+	6.74559i	0.191727	+	0.243094i
$771$	1.01277	+	0.650867i	0.0364740	+	0.0234404i
$772$	0.588121	−	0.0420632i	0.0211669	−	0.00151389i
$773$	8.71304	+	15.9567i	0.313386	+	0.573924i	0.986135	−	0.165947i	$-0.0530681\pi$
$773$	8.71304	+	15.9567i	0.313386	+	0.573924i	−0.672748	+	0.739871i	$0.734886\pi$
$774$	2.49973	+	17.3860i	0.0898510	+	0.624927i
$775$	0.0121735	+	0.241223i	0.000437285	+	0.00866500i
$776$	2.44436	−	1.11630i	0.0877474	−	0.0400729i
$777$	−9.12109	−	4.98049i	−0.327217	−	0.178674i
$778$	−15.0575	+	5.61617i	−0.539839	+	0.201349i
$779$	−1.51254	+	10.5200i	−0.0541924	+	0.376916i
$780$	3.35696	+	13.7528i	0.120198	+	0.492430i
$781$		−	24.8597i		−	0.889549i
$782$	16.7234	−	5.00690i	0.598029	−	0.179046i
$783$	−1.63865	+	1.63865i	−0.0585606	+	0.0585606i
$784$	−2.99063	−	4.65351i	−0.106808	−	0.166197i
$785$	45.5007	−	14.6158i	1.62399	−	0.521660i
$786$	−6.15578	+	13.4793i	−0.219569	+	0.480790i
$787$	23.8374	−	43.6549i	0.849710	−	1.55613i	0.0187306	−	0.999825i	$-0.494038\pi$
$787$	23.8374	−	43.6549i	0.849710	−	1.55613i	0.830979	−	0.556303i	$-0.187781\pi$
$788$	20.1131	+	7.50182i	0.716501	+	0.267241i
$789$	−5.48675	−	6.33205i	−0.195334	−	0.225427i
$790$	−18.7685	−	27.6463i	−0.667753	−	0.983610i
$791$	4.57190	+	1.34243i	0.162558	+	0.0477314i
$792$	0.335670	+	4.69328i	0.0119275	+	0.166769i
$793$	−3.55920	−	16.3614i	−0.126391	−	0.581010i
$794$	8.48157	−	13.1976i	0.301000	−	0.468364i
$795$	14.3106	+	24.7061i	0.507544	+	0.876234i
$796$	5.82981	−	19.8545i	0.206632	−	0.703725i
$797$	−4.37205	−	3.27287i	−0.154866	−	0.115931i	0.519035	−	0.854753i	$-0.326292\pi$
$797$	−4.37205	−	3.27287i	−0.154866	−	0.115931i	−0.673901	+	0.738822i	$0.735382\pi$
$798$	−1.98039	−	0.141641i	−0.0701052	−	0.00501402i
$799$	−1.68901	−	3.69842i	−0.0597530	−	0.130841i
$800$	−1.98122	−	4.59073i	−0.0700467	−	0.162307i
$801$	2.47208	+	1.12896i	0.0873468	+	0.0398900i
$802$	−5.79898	−	7.74653i	−0.204769	−	0.273539i
$803$	36.9603	+	8.04021i	1.30430	+	0.283733i
$804$	−6.06063			−0.213742
$805$	−8.80534	−	9.55652i	−0.310347	−	0.336823i
$806$	−0.248385			−0.00874900
$807$	17.9549	+	3.90584i	0.632041	+	0.137492i
$808$	6.07946	+	8.12121i	0.213875	+	0.285703i
$809$	8.94018	+	4.08284i	0.314320	+	0.143545i	0.566328	−	0.824180i	$-0.308364\pi$
$809$	8.94018	+	4.08284i	0.314320	+	0.143545i	−0.252008	+	0.967725i	$0.581091\pi$
$810$	−3.87622	+	3.53373i	−0.136197	+	0.124163i
$811$	6.53308	+	14.3054i	0.229407	+	0.502332i	0.988973	−	0.148099i	$-0.0473155\pi$
$811$	6.53308	+	14.3054i	0.229407	+	0.502332i	−0.759565	+	0.650431i	$0.774588\pi$
$812$	0.507334	+	0.0362853i	0.0178039	+	0.00127336i
$813$	0.0761176	+	0.0569810i	0.00266956	+	0.00199841i
$814$	−6.22205	+	21.1904i	−0.218083	+	0.742721i
$815$	−40.9864	−	10.9203i	−1.43569	−	0.382521i
$816$	−2.42304	+	3.77033i	−0.0848234	+	0.131988i
$817$	3.34808	+	15.3909i	0.117134	+	0.538458i
$818$	0.506496	+	7.08174i	0.0177092	+	0.247607i
$819$	8.87190	+	2.60502i	0.310009	+	0.0910269i
$820$	3.35501	−	17.5406i	0.117162	−	0.612545i
$821$	28.6882	+	33.1080i	1.00123	+	1.15548i	0.987826	+	0.155566i	$0.0497200\pi$
$821$	28.6882	+	33.1080i	1.00123	+	1.15548i	0.0133999	+	0.999910i	$0.495735\pi$
$822$	−11.6795	−	4.35624i	−0.407371	−	0.151941i
$823$	−18.9770	+	34.7538i	−0.661497	+	1.21144i	0.304407	+	0.952542i	$0.401542\pi$
$823$	−18.9770	+	34.7538i	−0.661497	+	1.21144i	−0.965904	+	0.258900i	$0.916640\pi$
$824$	4.67355	−	10.2336i	0.162811	−	0.356506i
$825$	19.5153	+	0.409429i	0.679434	+	0.0142545i
$826$	−1.24727	−	1.94079i	−0.0433981	−	0.0675287i
$827$	−4.83634	+	4.83634i	−0.168176	+	0.168176i	−0.786177	−	0.618001i	$-0.787943\pi$
$827$	−4.83634	+	4.83634i	−0.168176	+	0.168176i	0.618001	+	0.786177i	$0.287943\pi$
$828$	−1.05019	−	7.03911i	−0.0364966	−	0.244626i
$829$			39.2405i			1.36288i	0.731875	+	0.681439i	$0.238646\pi$
$829$			39.2405i			1.36288i	−0.731875	+	0.681439i	$0.761354\pi$
$830$	−13.4902	+	3.29285i	−0.468250	+	0.114296i
$831$	5.54378	−	38.5578i	0.192312	−	1.33756i
$832$	4.81771	−	1.79691i	0.167024	−	0.0622968i
$833$	−17.6723	−	9.64980i	−0.612308	−	0.334346i
$834$	−7.02170	+	3.20670i	−0.243142	+	0.111039i
$835$	13.0148	+	5.55155i	0.450397	+	0.192119i
$836$	0.600475	+	4.17640i	0.0207679	+	0.144444i
$837$	−0.127814	−	0.234074i	−0.00441789	−	0.00809077i
$838$	3.72267	−	0.266251i	0.128597	−	0.00919747i
$839$	20.7248	+	13.3190i	0.715498	+	0.459823i	0.847068	−	0.531484i	$-0.178366\pi$
$839$	20.7248	+	13.3190i	0.715498	+	0.459823i	−0.131570	+	0.991307i	$0.542002\pi$
$840$	3.31315	+	0.391393i	0.114314	+	0.0135043i
$841$	−18.8756	+	21.7836i	−0.650882	+	0.751158i
$842$	9.61353	−	5.24938i	0.331304	−	0.180906i
$843$	−7.96023	+	10.6336i	−0.274165	+	0.366242i
$844$	19.3840	−	16.7963i	0.667226	−	0.578154i
$845$	−2.89876	−	29.9110i	−0.0997204	−	1.02897i
$846$	−1.59047	+	0.467003i	−0.0546813	+	0.0160559i
$847$	−0.400973	−	1.07505i	−0.0137776	−	0.0369392i
$848$	8.30189	−	6.21472i	0.285088	−	0.213414i
$849$	−9.48492	+	6.09559i	−0.325522	+	0.209200i
$850$	−14.3379	−	11.2101i	−0.491786	−	0.384503i
$851$	6.92758	−	32.6787i	0.237474	−	1.12021i
$852$	−6.82621	−	6.82621i	−0.233862	−	0.233862i
$853$	6.72339	−	30.9069i	0.230204	−	1.05823i	−0.706392	−	0.707821i	$-0.749678\pi$
$853$	6.72339	−	30.9069i	0.230204	−	1.05823i	0.936596	−	0.350411i	$-0.113958\pi$
$854$	−3.90578	−	0.561567i	−0.133653	−	0.0192164i
$855$	3.04277	−	3.20020i	0.104061	−	0.109444i
$856$	0.850223	+	2.89559i	0.0290600	+	0.0989693i
$857$	10.5924	−	28.3994i	0.361830	−	0.970104i	−0.620708	−	0.784042i	$-0.713155\pi$
$857$	10.5924	−	28.3994i	0.361830	−	0.970104i	0.982538	−	0.186062i	$-0.0595725\pi$
$858$	−1.43203	+	20.0224i	−0.0488887	+	0.683554i
$859$	26.5495	−	3.81725i	0.905858	−	0.130243i	0.326388	−	0.945236i	$-0.394169\pi$
$859$	26.5495	−	3.81725i	0.905858	−	0.130243i	0.579470	+	0.814993i	$0.303259\pi$
$860$	−4.42575	−	26.0937i	−0.150917	−	0.889786i
$861$	9.00545	+	7.80327i	0.306905	+	0.265935i
$862$	−6.20905	+	1.35070i	−0.211481	+	0.0460049i
$863$	−48.9019	+	10.6380i	−1.66464	+	0.362120i	−0.943681	−	0.330858i	$-0.892662\pi$
$863$	−48.9019	+	10.6380i	−1.66464	+	0.362120i	−0.720959	+	0.692978i	$0.756298\pi$
$864$	4.17247	+	3.61546i	0.141950	+	0.123001i
$865$	7.86590	+	46.3764i	0.267449	+	1.57684i
$866$	11.2432	−	1.61653i	0.382061	−	0.0549321i
$867$	0.329417	−	4.60585i	0.0111876	−	0.156423i
$868$	−0.0204560	+	0.0548446i	−0.000694321	+	0.00186155i
$869$	−13.3489	−	45.4622i	−0.452831	−	1.54220i
$870$	0.796298	−	0.837497i	0.0269970	−	0.0283938i
$871$	25.0524	+	3.60200i	0.848870	+	0.122049i
$872$	−3.80552	+	17.4937i	−0.128871	+	0.592411i
$873$	−2.81980	−	2.81980i	−0.0954359	−	0.0954359i
$874$	−1.38964	−	6.22890i	−0.0470052	−	0.210696i
$875$	−2.82372	+	13.2503i	−0.0954592	+	0.447943i
$876$	12.3567	−	7.94114i	0.417493	−	0.268306i
$877$	−5.49114	+	4.11061i	−0.185423	+	0.138806i	−0.687957	−	0.725752i	$-0.741492\pi$
$877$	−5.49114	+	4.11061i	−0.185423	+	0.138806i	0.502534	+	0.864557i	$0.332401\pi$
$878$	−3.97783	−	10.6650i	−0.134245	−	0.359926i
$879$	−37.9300	+	11.1373i	−1.27935	+	0.375650i
$880$	−0.683892	−	7.05676i	−0.0230540	−	0.237883i
$881$	11.7368	−	10.1700i	0.395422	−	0.342636i	−0.434343	−	0.900747i	$-0.643019\pi$
$881$	11.7368	−	10.1700i	0.395422	−	0.342636i	0.829766	+	0.558112i	$0.188474\pi$
$882$	−4.91945	+	6.57162i	−0.165647	+	0.221278i
$883$	−6.52451	+	3.56265i	−0.219567	+	0.119893i	−0.585269	−	0.810839i	$-0.699011\pi$
$883$	−6.52451	+	3.56265i	−0.219567	+	0.119893i	0.365701	+	0.930732i	$0.380829\pi$
$884$	12.2568	−	14.1451i	0.412240	−	0.475750i
$885$	−5.20548	−	0.614940i	−0.174980	−	0.0206710i
$886$	−17.8121	−	11.4472i	−0.598410	−	0.384575i
$887$	−49.2455	+	3.52211i	−1.65350	+	0.118261i	−0.866662	−	0.498895i	$-0.833739\pi$
$887$	−49.2455	+	3.52211i	−1.65350	+	0.118261i	−0.786841	+	0.617156i	$0.788285\pi$
$888$	4.11014	+	7.52716i	0.137927	+	0.252595i
$889$	−2.24162	−	15.5908i	−0.0751816	−	0.522899i
$890$	−3.76659	−	1.60666i	−0.126256	−	0.0538554i
$891$	−6.76542	+	3.08966i	−0.226650	+	0.103508i
$892$	−6.80319	−	3.71482i	−0.227787	−	0.124381i
$893$	−1.39270	+	0.519452i	−0.0466051	+	0.0173828i
$894$	−1.31021	+	9.11270i	−0.0438199	+	0.304774i
$895$	31.6464	−	7.72465i	1.05782	−	0.258207i
$896$		−	1.21176i		−	0.0404820i
$897$	−0.160958	−	30.3621i	−0.00537424	−	1.01376i
$898$	−21.4400	+	21.4400i	−0.715462	+	0.715462i
$899$	0.0109622	+	0.0170575i	0.000365609	+	0.000568899i
$900$	−5.35564	+	5.13553i	−0.178521	+	0.171184i
$901$	15.6812	−	34.3370i	0.522415	−	1.14393i
$902$	12.1360	−	22.2253i	0.404083	−	0.740023i
$903$	16.5459	+	6.17130i	0.550613	+	0.205368i
$904$	−2.57507	−	2.97178i	−0.0856454	−	0.0988401i
$905$	9.99633	−	52.2628i	0.332289	−	1.73727i
$906$	7.50049	+	2.20234i	0.249187	+	0.0731679i
$907$	−0.321155	−	4.49034i	−0.0106638	−	0.149099i	−0.999994	−	0.00340992i	$-0.998915\pi$
$907$	−0.321155	−	4.49034i	−0.0106638	−	0.149099i	0.989330	−	0.145689i	$-0.0465400\pi$
$908$	0.639314	+	2.93888i	0.0212164	+	0.0975302i
$909$	8.13917	−	12.6648i	0.269959	−	0.420065i
$910$	−13.4627	−	3.58697i	−0.446285	−	0.118907i
$911$	−13.3712	+	45.5380i	−0.443007	+	1.50874i	0.371414	+	0.928467i	$0.378873\pi$
$911$	−13.3712	+	45.5380i	−0.443007	+	1.50874i	−0.814421	+	0.580275i	$0.802945\pi$
$912$	1.31168	+	0.981911i	0.0434340	+	0.0325143i
$913$	−19.6400	−	1.40468i	−0.649989	−	0.0464882i
$914$	−1.75183	−	3.83597i	−0.0579454	−	0.126883i
$915$	−6.62545	+	6.04003i	−0.219030	+	0.199677i
$916$	−8.02551	−	3.66513i	−0.265170	−	0.121099i
$917$	−8.73968	−	11.6748i	−0.288610	−	0.385537i
$918$	19.6371	+	4.27179i	0.648121	+	0.140990i
$919$	−41.4667			−1.36786			−0.683930	−	0.729547i	$-0.739731\pi$
$919$	−41.4667			−1.36786			−0.683930	+	0.729547i	$0.739731\pi$
$920$	1.84928	+	10.5632i	0.0609689	+	0.348257i
$921$	−23.1456			−0.762674
$922$	−34.0448	−	7.40600i	−1.12121	−	0.243904i
$923$	24.1600	+	32.2740i	0.795238	+	1.06231i
$924$	4.30310	+	1.96516i	0.141562	+	0.0646490i
$925$	−31.9762	+	13.8000i	−1.05137	+	0.453741i
$926$	−13.7628	−	30.1364i	−0.452275	−	0.990343i
$927$	−16.6529	−	1.19104i	−0.546954	−	0.0391189i
$928$	−0.336024	−	0.251544i	−0.0110305	−	0.00825735i
$929$	0.948223	−	3.22935i	0.0311102	−	0.105952i	−0.942474	−	0.334279i	$-0.891507\pi$
$929$	0.948223	−	3.22935i	0.0311102	−	0.105952i	0.973584	+	0.228327i	$0.0733255\pi$
$930$	0.0666601	+	0.115083i	0.00218587	+	0.00377373i
$931$	−3.97977	+	6.19264i	−0.130432	+	0.202956i
$932$	1.67733	+	7.71056i	0.0549427	+	0.252568i
$933$	2.23066	+	31.1888i	0.0730286	+	1.02107i
$934$	−22.5056	−	6.60824i	−0.736406	−	0.216228i
$935$	−14.4952	−	21.3516i	−0.474043	−	0.698273i
$936$	−4.99698	−	5.76683i	−0.163332	−	0.188495i
$937$	36.6735	+	13.6785i	1.19807	+	0.446857i	0.867745	−	0.497010i	$-0.165569\pi$
$937$	36.6735	+	13.6785i	1.19807	+	0.446857i	0.330325	+	0.943867i	$0.392842\pi$
$938$	2.85855	−	5.23504i	0.0933349	−	0.170930i
$939$	−2.89660	+	6.34268i	−0.0945271	+	0.206985i
$940$	2.37799	−	0.763861i	0.0775613	−	0.0249144i
$941$	20.9705	+	32.6308i	0.683620	+	1.06373i	0.993596	+	0.112989i	$0.0360425\pi$
$941$	20.9705	+	32.6308i	0.683620	+	1.06373i	−0.309976	+	0.950744i	$0.600321\pi$
$942$	18.6076	−	18.6076i	0.606269	−	0.606269i
$943$	−15.7265	+	34.9250i	−0.512125	+	1.13731i
$944$			1.90386i			0.0619655i
$945$	−3.54734	−	14.5328i	−0.115395	−	0.472751i
$946$	5.34083	−	37.1463i	0.173646	−	1.20773i
$947$	−12.0522	+	4.49524i	−0.391644	+	0.146076i	−0.537568	−	0.843220i	$-0.680657\pi$
$947$	−12.0522	+	4.49524i	−0.391644	+	0.146076i	0.145925	+	0.989296i	$0.453384\pi$
$948$	−16.1489	−	8.81798i	−0.524493	−	0.286395i
$949$	−55.7976	+	25.4819i	−1.81127	+	0.827177i
$950$	−4.46178	+	4.93605i	−0.144759	+	0.160146i
$951$	1.52281	+	10.5914i	0.0493804	+	0.343448i
$952$	−2.11388	−	3.87128i	−0.0685111	−	0.125469i
$953$	−25.5275	+	1.82577i	−0.826918	+	0.0591424i	−0.478381	−	0.878153i	$-0.658776\pi$
$953$	−25.5275	+	1.82577i	−0.826918	+	0.0591424i	−0.348537	+	0.937295i	$0.613322\pi$
$954$	−12.9466	−	8.32025i	−0.419160	−	0.269378i
$955$	−24.9735	−	31.6643i	−0.808124	−	1.02463i
$956$	3.96960	−	4.58116i	0.128386	−	0.148165i
$957$	1.43821	−	0.785321i	0.0464907	−	0.0253858i
$958$	−4.72381	+	6.31027i	−0.152619	+	0.203876i
$959$	9.27158	−	8.03387i	0.299395	−	0.259427i
$960$	−2.12550	−	1.74992i	−0.0686003	−	0.0564785i
$961$	29.7420	−	8.73305i	0.959421	−	0.281711i
$962$	−12.5162	−	33.5573i	−0.403539	−	1.08193i
$963$	3.58520	−	2.68385i	0.115532	−	0.0864858i
$964$	0.938764	−	0.603307i	0.0302355	−	0.0194312i
$965$	0.577757	+	1.18510i	0.0185987	+	0.0381499i
$966$	−6.71734	−	2.46495i	−0.216127	−	0.0793085i
$967$	1.78926	+	1.78926i	0.0575386	+	0.0575386i	0.735291	−	0.677752i	$-0.237046\pi$
$967$	1.78926	+	1.78926i	0.0575386	+	0.0575386i	−0.677752	+	0.735291i	$0.737046\pi$
$968$	−0.201275	+	0.925245i	−0.00646922	+	0.0297385i
$969$	5.90342	+	0.848783i	0.189645	+	0.0272669i
$970$	4.35459	+	4.14037i	0.139817	+	0.132939i
$971$	−8.22478	−	28.0110i	−0.263946	−	0.898917i	−0.979684	−	0.200548i	$-0.935728\pi$
$971$	−8.22478	−	28.0110i	−0.263946	−	0.898917i	0.715738	−	0.698369i	$-0.246090\pi$
$972$	4.77882	−	12.8125i	0.153281	−	0.410961i
$973$	0.541965	−	7.57766i	0.0173746	−	0.242929i
$974$	13.8503	−	1.99137i	0.443792	−	0.0638077i
$975$	−25.7336	+	18.4345i	−0.824134	+	0.590376i
$976$	2.46101	+	2.13248i	0.0787750	+	0.0682590i
$977$	52.1102	−	11.3359i	1.66715	−	0.362667i	0.722661	−	0.691203i	$-0.242919\pi$
$977$	52.1102	−	11.3359i	1.66715	−	0.362667i	0.944492	+	0.328536i	$0.106555\pi$
$978$	−22.8221	+	4.96465i	−0.729771	+	0.158752i
$979$	−4.38825	−	3.80244i	−0.140249	−	0.121527i
$980$	7.16057	−	10.0857i	0.228736	−	0.322176i
$981$	26.2974	−	3.78099i	0.839611	−	0.120718i
$982$	−2.00250	+	27.9985i	−0.0639022	+	0.893469i
$983$	19.6575	−	52.7037i	0.626975	−	1.68099i	−0.100573	−	0.994930i	$-0.532068\pi$
$983$	19.6575	−	52.7037i	0.626975	−	1.68099i	0.727548	−	0.686056i	$-0.240660\pi$
$984$	−2.77044	−	9.43525i	−0.0883184	−	0.300785i
$985$	1.21004	+	47.9856i	0.0385552	+	1.52895i
$986$	−1.51233	−	0.217440i	−0.0481623	−	0.00692470i
$987$	−0.354246	+	1.62844i	−0.0112758	+	0.0518340i
$988$	−4.83843	−	4.83843i	−0.153931	−	0.153931i
$989$	−3.74928	+	56.6400i	−0.119220	+	1.80105i
$990$	−9.45730	+	4.61058i	−0.300573	+	0.146534i
$991$	7.69741	−	4.94682i	0.244516	−	0.157141i	−0.412643	−	0.910893i	$-0.635394\pi$
$991$	7.69741	−	4.94682i	0.244516	−	0.157141i	0.657159	+	0.753752i	$0.271758\pi$
$992$	0.0386710	−	0.0289487i	0.00122780	−	0.000919123i
$993$	11.7883	+	31.6056i	0.374090	+	1.00297i
$994$	9.11596	−	2.67669i	0.289141	−	0.0848994i
$995$	46.0546	−	4.46329i	1.46003	−	0.141496i
$996$	−5.77865	+	5.00723i	−0.183104	+	0.158660i
$997$	−22.2021	+	29.6585i	−0.703147	+	0.939295i	−0.999877	−	0.0156666i	$-0.995013\pi$
$997$	−22.2021	+	29.6585i	−0.703147	+	0.939295i	0.296730	+	0.954961i	$0.404104\pi$
$998$	34.9875	−	19.1046i	1.10751	−	0.604746i
$999$	25.1832	−	29.0629i	0.796760	−	0.919510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.57.10	✓	240
5.3	odd	4	inner	230.2.l.a.103.9	yes	240
23.21	odd	22	inner	230.2.l.a.67.9	yes	240
115.113	even	44	inner	230.2.l.a.113.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.10	✓	240	1.1	even	1	trivial
230.2.l.a.67.9	yes	240	23.21	odd	22	inner
230.2.l.a.103.9	yes	240	5.3	odd	4	inner
230.2.l.a.113.10	yes	240	115.113	even	44	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+(0.977147 + 0.212565i) q^{2} +(0.737866 + 0.985673i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-0.103244 + 2.23368i) q^{5} +(0.511483 + 1.11999i) q^{6} +(-1.20867 - 0.0864458i) q^{7} +(0.800541 + 0.599278i) q^{8} +(0.418092 - 1.42389i) q^{9} +(-0.575688 + 2.16069i) q^{10} +(-1.71419 + 2.66733i) q^{11} +(0.261723 + 1.20312i) q^{12} +(-0.366820 - 5.12881i) q^{13} +(-1.16267 - 0.341392i) q^{14} +(-2.27786 + 1.54639i) q^{15} +(0.654861 + 0.755750i) q^{16} +(3.41051 + 1.27205i) q^{17} +(0.711206 - 1.30248i) q^{18} +(0.552811 - 1.21049i) q^{19} +(-1.02182 + 1.98894i) q^{20} +(-0.806629 - 1.25514i) q^{21} +(-2.24200 + 2.24200i) q^{22} +(3.12134 - 3.64105i) q^{23} +1.23126i q^{24} +(-4.97868 - 0.461227i) q^{25} +(0.731770 - 5.08957i) q^{26} +(5.17287 - 1.92938i) q^{27} +(-1.06353 - 0.580734i) q^{28} +(-0.381814 + 0.174369i) q^{29} +(-2.55452 + 1.02686i) q^{30} +(-0.00687467 - 0.0478144i) q^{31} +(0.479249 + 0.877679i) q^{32} +(-3.89396 + 0.278502i) q^{33} +(3.06217 + 1.96794i) q^{34} +(0.317880 - 2.69086i) q^{35} +(0.971814 - 1.12153i) q^{36} +(6.11338 - 3.33816i) q^{37} +(0.797485 - 1.06532i) q^{38} +(4.78467 - 4.14594i) q^{39} +(-1.42125 + 1.72628i) q^{40} +(-7.66309 + 2.25009i) q^{41} +(-0.521396 - 1.39792i) q^{42} +(-9.47529 + 7.09311i) q^{43} +(-2.66733 + 1.71419i) q^{44} +(3.13735 + 1.08089i) q^{45} +(3.82397 - 2.89435i) q^{46} +(-0.789829 - 0.789829i) q^{47} +(-0.261723 + 1.20312i) q^{48} +(-5.47534 - 0.787235i) q^{49} +(-4.76686 - 1.50898i) q^{50} +(1.26267 + 4.30025i) q^{51} +(1.79691 - 4.81771i) q^{52} +(0.739812 - 10.3439i) q^{53} +(5.46477 - 0.785715i) q^{54} +(-5.78100 - 4.10434i) q^{55} +(-0.915785 - 0.793533i) q^{56} +(1.60105 - 0.348286i) q^{57} +(-0.410153 + 0.0892234i) q^{58} +(1.43884 + 1.24677i) q^{59} +(-2.71441 + 0.460392i) q^{60} +(3.22324 - 0.463432i) q^{61} +(0.00344611 - 0.0481830i) q^{62} +(-0.628424 + 1.68487i) q^{63} +(0.281733 + 0.959493i) q^{64} +(11.4940 - 0.289842i) q^{65} +(-3.86417 - 0.555584i) q^{66} +(-1.04631 + 4.80982i) q^{67} +(2.57388 + 2.57388i) q^{68} +(5.89202 + 0.390022i) q^{69} +(0.882599 - 2.56180i) q^{70} +(-6.59587 + 4.23891i) q^{71} +(1.18800 - 0.889329i) q^{72} +(-4.16896 - 11.1774i) q^{73} +(6.68325 - 1.96238i) q^{74} +(-3.21898 - 5.24768i) q^{75} +(1.00571 - 0.871452i) q^{76} +(2.30247 - 3.07574i) q^{77} +(5.55661 - 3.03414i) q^{78} +(-9.78605 + 11.2937i) q^{79} +(-1.75572 + 1.38473i) q^{80} +(1.97336 + 1.26820i) q^{81} +(-7.96626 + 0.569758i) q^{82} +(2.97619 + 5.45048i) q^{83} +(-0.212332 - 1.47680i) q^{84} +(-3.19348 + 7.48666i) q^{85} +(-10.7665 + 4.91689i) q^{86} +(-0.453598 - 0.247683i) q^{87} +(-2.97075 + 1.10803i) q^{88} +(-0.260623 + 1.81268i) q^{89} +(2.83589 + 1.72308i) q^{90} +6.23075i q^{91} +(4.35182 - 2.01536i) q^{92} +(0.0420568 - 0.0420568i) q^{93} +(-0.603889 - 0.939669i) q^{94} +(2.64677 + 1.35978i) q^{95} +(-0.511483 + 1.11999i) q^{96} +(1.28784 - 2.35850i) q^{97} +(-5.18287 - 1.93311i) q^{98} +(3.08130 + 3.55601i) 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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