LMFDB - Embedded newform 230.2.l.a.113.10

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			113.10
Character	$\chi$	$=$	230.113
Dual form			230.2.l.a.57.10

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

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{22}\right)$

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	−0.535264	−	0.844685i	$-0.679788\pi$
$3$	0.737866	−	0.985673i	0.426007	−	0.569079i	0.961271	+	0.275606i	$0.0888786\pi$
$4$	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	−0.297861	−	0.954609i	$-0.596273\pi$
$7$	−1.20867	+	0.0864458i	−0.456834	+	0.0326734i	−0.158974	+	0.987283i	$0.550819\pi$
$8$	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	0.480501	−	0.876994i	$-0.340455\pi$
$11$	−1.71419	−	2.66733i	−0.516848	−	0.804231i	−0.997349	+	0.0727629i	$0.976818\pi$
$12$	0.261723	−	1.20312i	0.0755529	−	0.347311i
$13$	−0.366820	+	5.12881i	−0.101738	+	1.42248i	0.648453	+	0.761255i	$0.275416\pi$
$13$	−0.366820	+	5.12881i	−0.101738	+	1.42248i	−0.750191	+	0.661222i	$0.770038\pi$
$14$	−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	0.100010	−	0.994986i	$-0.468113\pi$
$17$	3.41051	−	1.27205i	0.827170	−	0.308518i	0.727160	+	0.686468i	$0.240840\pi$
$18$	0.711206	+	1.30248i	0.167633	+	0.306997i
$19$	0.552811	+	1.21049i	0.126824	+	0.277705i	0.962384	−	0.271694i	$-0.0875839\pi$
$19$	0.552811	+	1.21049i	0.126824	+	0.277705i	−0.835560	+	0.549399i	$0.814857\pi$
$20$	−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	0.379649	−	0.925131i	$-0.376045\pi$
$29$	−0.381814	−	0.174369i	−0.0709011	−	0.0323795i	−0.450550	+	0.892751i	$0.648772\pi$
$30$	−2.55452	−	1.02686i	−0.466389	−	0.187478i
$31$	−0.00687467	+	0.0478144i	−0.00123473	+	0.00858771i	−0.990429	−	0.138020i	$-0.955926\pi$
$31$	−0.00687467	+	0.0478144i	−0.00123473	+	0.00858771i	0.989195	+	0.146607i	$0.0468354\pi$
$32$	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	0.895438	−	0.445186i	$-0.146862\pi$
$37$	6.11338	+	3.33816i	1.00503	+	0.548790i	0.109596	+	0.993976i	$0.465044\pi$
$38$	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	−0.378156	−	0.925742i	$-0.623442\pi$
$41$	−7.66309	−	2.25009i	−1.19677	−	0.351405i	−0.818619	+	0.574337i	$0.805260\pi$
$42$	−0.521396	+	1.39792i	−0.0804532	+	0.215703i
$43$	−9.47529	−	7.09311i	−1.44497	−	1.08169i	−0.980594	−	0.196050i	$-0.937189\pi$
$43$	−9.47529	−	7.09311i	−1.44497	−	1.08169i	−0.464374	−	0.885639i	$-0.653720\pi$
$44$	−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	−0.762361	−	0.647152i	$-0.775960\pi$
$47$	−0.789829	+	0.789829i	−0.115208	+	0.115208i	0.647152	+	0.762361i	$0.275960\pi$
$48$	−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	0.750960	+	0.660348i	$0.229591\pi$
$53$	0.739812	+	10.3439i	0.101621	+	1.42085i	−0.649339	+	0.760499i	$0.724954\pi$
$54$	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	−0.556151	−	0.831081i	$-0.687723\pi$
$59$	1.43884	−	1.24677i	0.187322	−	0.162315i	0.743473	+	0.668766i	$0.233177\pi$
$60$	−2.71441	−	0.460392i	−0.350429	−	0.0594363i
$61$	3.22324	+	0.463432i	0.412693	+	0.0593364i	0.345535	−	0.938406i	$-0.387698\pi$
$61$	3.22324	+	0.463432i	0.412693	+	0.0593364i	0.0671587	+	0.997742i	$0.478607\pi$
$62$	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	−0.995844	−	0.0910773i	$-0.970969\pi$
$67$	−1.04631	−	4.80982i	−0.127827	−	0.587613i	0.868017	−	0.496535i	$-0.165395\pi$
$68$	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	0.0871715	−	0.996193i	$-0.472217\pi$
$71$	−6.59587	−	4.23891i	−0.782786	−	0.503066i	−0.869957	+	0.493128i	$0.835854\pi$
$72$	1.18800	+	0.889329i	0.140008	+	0.104808i
$73$	−4.16896	+	11.1774i	−0.487940	+	1.30822i	0.426863	+	0.904316i	$0.359619\pi$
$73$	−4.16896	+	11.1774i	−0.487940	+	1.30822i	−0.914803	+	0.403901i	$0.867654\pi$
$74$	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	−0.959807	−	0.280662i	$-0.909446\pi$
$79$	−9.78605	−	11.2937i	−1.10102	−	1.27064i	−0.141210	−	0.989980i	$-0.545099\pi$
$80$	−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	−0.661790	−	0.749689i	$-0.730203\pi$
$83$	2.97619	−	5.45048i	0.326679	−	0.598268i	0.988469	+	0.151421i	$0.0483849\pi$
$84$	−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	0.971335	−	0.237715i	$-0.0763983\pi$
$89$	−0.260623	−	1.81268i	−0.0276260	−	0.192143i	−0.998961	+	0.0455713i	$0.985489\pi$
$90$	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	0.934853	−	0.355034i	$-0.115531\pi$
$97$	1.28784	+	2.35850i	0.130760	+	0.239469i	−0.804093	+	0.594503i	$0.797349\pi$
$98$	−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	0.241055	−	0.970512i	$-0.422507\pi$
$101$	9.73371	−	2.85808i	0.968541	−	0.284389i	0.727486	+	0.686122i	$0.240689\pi$
$102$	0.319728	−	4.47038i	0.0316578	−	0.442633i
$103$	−2.39142	+	10.9932i	−0.235634	+	1.08319i	0.695503	+	0.718523i	$0.255182\pi$
$103$	−2.39142	+	10.9932i	−0.235634	+	1.08319i	−0.931137	+	0.364669i	$0.881182\pi$
$104$	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	−0.476090	−	0.879396i	$-0.657946\pi$
$107$	2.41590	−	1.80852i	0.233554	−	0.174836i	0.709644	+	0.704560i	$0.248856\pi$
$108$	5.50690	−	0.393861i	0.529902	−	0.0378993i
$109$	7.43710	−	16.2850i	0.712345	−	1.55982i	−0.111986	−	0.993710i	$-0.535721\pi$
$109$	7.43710	−	16.2850i	0.712345	−	1.55982i	0.824331	−	0.566108i	$-0.191551\pi$
$110$	−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	−0.389628	−	0.920972i	$-0.627396\pi$
$113$	−3.84237	+	0.835857i	−0.361460	+	0.0786308i	0.0281679	+	0.999603i	$0.491033\pi$
$114$	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	−0.675682	−	0.737193i	$-0.736151\pi$
$127$	2.76305	−	12.7015i	0.245181	−	1.12708i	0.920863	−	0.389886i	$-0.127485\pi$
$128$	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	−0.298568	−	0.954388i	$-0.596509\pi$
$131$	7.88135	−	9.09556i	0.688597	−	0.794683i	0.987165	+	0.159705i	$0.0510544\pi$
$132$	−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	0.331745	−	0.943369i	$-0.392363\pi$
$137$	−7.15888	−	7.15888i	−0.611624	−	0.611624i	−0.943369	+	0.331745i	$0.892363\pi$
$138$	5.67446	−	1.63355i	0.483042	−	0.139057i
$139$		−	6.26942i		−	0.531765i	−0.964005	−	0.265883i	$-0.914337\pi$
$139$		−	6.26942i		−	0.531765i	0.964005	−	0.265883i	$-0.0856633\pi$
$140$	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	−0.257000	−	0.966411i	$-0.582734\pi$
$149$	6.29025	−	4.04250i	0.515317	−	0.331174i	0.772317	+	0.635237i	$0.219098\pi$
$150$	−2.02994	+	5.81200i	−0.165744	+	0.474547i
$151$	4.15764	+	4.79818i	0.338344	+	0.390470i	0.899268	−	0.437397i	$-0.144100\pi$
$151$	4.15764	+	4.79818i	0.338344	+	0.390470i	−0.560924	+	0.827867i	$0.689554\pi$
$152$	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	0.191179	+	0.981555i	$0.438769\pi$
$157$	−7.46894	+	20.0250i	−0.596087	+	1.59817i	−0.787265	+	0.616615i	$0.788504\pi$
$158$	−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	−0.812030	−	0.583616i	$-0.801637\pi$
$163$	−4.03217	−	18.5356i	−0.315824	−	1.45182i	0.496206	−	0.868205i	$-0.334726\pi$
$164$	−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	0.993994	−	0.109435i	$-0.0349041\pi$
$167$	2.21134	+	5.92884i	0.171119	+	0.458787i	−0.822875	+	0.568222i	$0.807631\pi$
$168$	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	0.909036	−	0.416717i	$-0.136819\pi$
$173$	20.5556	+	4.47160i	1.56281	+	0.339969i	0.653778	+	0.756686i	$0.273183\pi$
$174$	−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	0.651436	+	0.758704i	$0.274167\pi$
$179$	−4.10434	+	13.9781i	−0.306773	+	1.04477i	−0.958209	+	0.286069i	$0.907651\pi$
$180$	2.40482	−	2.28652i	0.179244	−	0.170427i
$181$	−23.5541	+	3.38657i	−1.75076	+	0.251722i	−0.941808	−	0.336150i	$-0.890875\pi$
$181$	−23.5541	+	3.38657i	−1.75076	+	0.251722i	−0.808954	+	0.587872i	$0.799966\pi$
$182$	−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	0.00314163	−	0.999995i	$-0.499000\pi$
$191$	−13.6299	−	11.8104i	−0.986228	−	0.854571i	−0.989369	+	0.145424i	$0.953545\pi$
$192$	−0.737866	−	0.985673i	−0.0532509	−	0.0711349i
$193$	0.517500	+	0.282576i	0.0372504	+	0.0203403i	0.497766	−	0.867311i	$-0.334154\pi$
$193$	0.517500	+	0.282576i	0.0372504	+	0.0203403i	−0.460516	+	0.887651i	$0.652336\pi$
$194$	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	0.808737	−	0.588171i	$-0.200152\pi$
$197$	21.4119	+	1.53141i	1.52554	+	0.109109i	0.716800	+	0.697279i	$0.245606\pi$
$198$	2.25500	−	4.12972i	0.160256	−	0.293486i
$199$	−2.94488	+	20.4821i	−0.208757	+	1.45194i	0.568463	+	0.822709i	$0.307538\pi$
$199$	−2.94488	+	20.4821i	−0.208757	+	1.45194i	−0.777220	+	0.629229i	$0.783371\pi$
$200$	−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	0.793942	+	0.607994i	$0.208025\pi$
$211$	10.6549	+	23.3309i	0.733511	+	1.60617i	−0.0604304	+	0.998172i	$0.519247\pi$
$212$	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	−0.327767	−	0.944758i	$-0.606296\pi$
$223$	−7.73159	+	0.552974i	−0.517745	+	0.0370299i	−0.189978	+	0.981788i	$0.560842\pi$
$224$	−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	−0.736729	−	0.676188i	$-0.763631\pi$
$227$	1.80240	−	2.40772i	0.119629	−	0.159806i	0.856358	+	0.516382i	$0.172722\pi$
$228$	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	−0.618439	−	0.785833i	$-0.712235\pi$
$233$	4.72883	−	6.31698i	0.309796	−	0.413839i	0.928235	+	0.371993i	$0.121326\pi$
$234$	−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	0.996107	−	0.0881559i	$-0.0280974\pi$
$239$	1.70779	+	5.81620i	0.110468	+	0.376219i	−0.885639	+	0.464374i	$0.846279\pi$
$240$	−2.66037	+	0.708821i	−0.171726	+	0.0457542i
$241$	0.603307	+	0.938764i	0.0388624	+	0.0604711i	0.860141	−	0.510056i	$-0.170375\pi$
$241$	0.603307	+	0.938764i	0.0388624	+	0.0604711i	−0.821279	+	0.570527i	$0.806739\pi$
$242$	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	−0.0501147	+	0.998743i	$0.515959\pi$
$251$	−14.8573	+	23.1184i	−0.937785	+	1.45922i	−0.887671	+	0.460479i	$0.847678\pi$
$252$	−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	0.377874	−	0.925857i	$-0.376655\pi$
$257$	0.916115	+	0.341693i	0.0571457	+	0.0213142i	−0.320729	+	0.947171i	$0.603928\pi$
$258$	−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	−0.139516	−	0.990220i	$-0.544555\pi$
$263$	−6.78749	−	0.485451i	−0.418535	−	0.0299342i	−0.279019	+	0.960286i	$0.590009\pi$
$264$	−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	0.926994	−	0.375076i	$-0.122383\pi$
$269$	11.2785	+	9.77286i	0.687661	+	0.595862i	−0.239333	+	0.970938i	$0.576929\pi$
$270$	1.19084	−	12.2877i	0.0724720	−	0.747805i
$271$	0.0740959	+	0.0217565i	0.00450100	+	0.00132161i	0.283982	−	0.958830i	$-0.408344\pi$
$271$	0.0740959	+	0.0217565i	0.00450100	+	0.00132161i	−0.279481	+	0.960151i	$0.590162\pi$
$272$	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	−0.452291	+	0.891871i	$0.649393\pi$
$277$	−22.3713	+	22.3713i	−1.34416	+	1.34416i	−0.891871	+	0.452291i	$0.850607\pi$
$278$	−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	−0.817803	−	0.575498i	$-0.804808\pi$
$281$	3.03938	−	10.3512i	0.181314	−	0.617500i	0.999118	−	0.0420020i	$-0.0133736\pi$
$282$	0.480618	+	1.28859i	0.0286204	+	0.0767342i
$283$	−0.653259	−	9.13376i	−0.0388322	−	0.542946i	−0.979215	−	0.202827i	$-0.934987\pi$
$283$	−0.653259	−	9.13376i	−0.0388322	−	0.542946i	0.940382	−	0.340119i	$-0.110467\pi$
$284$	−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	−0.652930	−	0.757419i	$-0.726460\pi$
$293$	−11.2200	−	30.0821i	−0.655482	−	1.75742i	−0.00255239	−	0.999997i	$-0.500812\pi$
$294$	−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	0.354133	−	0.935195i	$-0.384776\pi$
$307$	−11.2654	−	15.0488i	−0.642951	−	0.858882i	−0.997084	+	0.0763127i	$0.975685\pi$
$308$	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	0.230544	−	0.973062i	$-0.425949\pi$
$311$	21.3640	−	13.7298i	1.21144	−	0.778548i	0.980900	+	0.194514i	$0.0623130\pi$
$312$	6.31489	+	0.451650i	0.357510	+	0.0255697i
$313$	2.71406	−	4.97042i	0.153407	−	0.280945i	−0.789661	−	0.613543i	$-0.789744\pi$
$313$	2.71406	−	4.97042i	0.153407	−	0.280945i	0.943069	+	0.332599i	$0.107925\pi$
$314$	−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	−0.250556	−	0.968102i	$-0.580614\pi$
$317$	7.62748	−	4.16492i	0.428402	−	0.233925i	0.678958	+	0.734177i	$0.262432\pi$
$318$	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	0.537022	−	0.843568i	$-0.319549\pi$
$331$	26.2869	−	7.71854i	1.44486	−	0.424249i	0.907839	+	0.419319i	$0.137731\pi$
$332$	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	−0.182338	−	0.983236i	$-0.558367\pi$
$337$	13.0283	−	9.75289i	0.709699	−	0.531274i	0.892037	+	0.451962i	$0.149276\pi$
$338$	−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	0.528615	−	0.848862i	$-0.322712\pi$
$347$	25.3729	−	5.51954i	1.36209	−	0.296304i	0.833475	+	0.552558i	$0.186348\pi$
$348$	−0.309716	+	0.413732i	−0.0166025	+	0.0221784i
$349$	7.99964	−	3.65331i	0.428211	−	0.195557i	−0.189638	−	0.981854i	$-0.560732\pi$
$349$	7.99964	−	3.65331i	0.428211	−	0.195557i	0.617849	+	0.786297i	$0.288004\pi$
$350$	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	−0.465764	−	0.884909i	$-0.654220\pi$
$353$	4.73613	−	3.54542i	0.252079	−	0.188704i	0.717843	+	0.696205i	$0.245130\pi$
$354$	−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	−0.598191	−	0.801353i	$-0.704114\pi$
$359$	−12.6602	+	3.71736i	−0.668178	+	0.196195i	−0.0699863	+	0.997548i	$0.522296\pi$
$360$	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	0.999930	+	0.0117981i	$0.00375552\pi$
$367$	19.3819	+	19.3819i	1.01173	+	1.01173i	0.0117981	+	0.999930i	$0.496244\pi$
$368$	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	0.263030	−	0.964788i	$-0.415278\pi$
$373$	23.5016	−	12.8328i	1.21687	−	0.664459i	0.953836	+	0.300329i	$0.0970963\pi$
$374$	−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	−0.115247	−	0.993337i	$-0.536766\pi$
$379$	14.4150	−	9.26396i	0.740449	−	0.475858i	0.855696	+	0.517479i	$0.173130\pi$
$380$	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	0.663348	−	0.748311i	$-0.269135\pi$
$383$	−4.72698	−	6.31451i	−0.241538	−	0.322656i	−0.904886	+	0.425654i	$0.860044\pi$
$384$	−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	0.151001	−	0.988534i	$-0.451750\pi$
$389$	−13.5196	−	8.68853i	−0.685472	−	0.440526i	−0.836473	+	0.548007i	$0.815387\pi$
$390$	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	0.998866	+	0.0476130i	$0.0151614\pi$
$397$	5.48239	+	14.6989i	0.275153	+	0.737715i	−0.723713	+	0.690102i	$0.757566\pi$
$398$	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	−0.818058	−	0.575136i	$-0.804949\pi$
$401$	−7.31309	+	6.33683i	−0.365198	+	0.316446i	0.452860	+	0.891582i	$0.350404\pi$
$402$	−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	−0.895143	−	0.445780i	$-0.852926\pi$
$409$	2.00025	−	6.81224i	0.0989062	−	0.336844i	0.994049	+	0.108937i	$0.0347445\pi$
$410$	−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	0.368031	−	0.929814i	$-0.380032\pi$
$419$	3.58100	+	1.05148i	0.174943	+	0.0513680i	−0.193088	+	0.981181i	$0.561850\pi$
$420$	3.32063	+	0.321812i	0.162030	+	0.0157028i
$421$	8.27799	+	7.17292i	0.403445	+	0.349587i	0.832824	−	0.553537i	$-0.186722\pi$
$421$	8.27799	+	7.17292i	0.403445	+	0.349587i	−0.429380	+	0.903124i	$0.641268\pi$
$422$	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	0.271314	−	0.962491i	$-0.412542\pi$
$431$	−5.78004	−	2.63966i	−0.278415	−	0.127148i	−0.549729	+	0.835343i	$0.685269\pi$
$432$	4.84564	−	2.64592i	0.233136	−	0.127302i
$433$	10.6427	+	3.96952i	0.511455	+	0.190763i	0.591923	−	0.805994i	$-0.298369\pi$
$433$	10.6427	+	3.96952i	0.511455	+	0.190763i	−0.0804685	+	0.996757i	$0.525642\pi$
$434$	−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	−0.956479	−	0.291802i	$-0.905745\pi$
$439$	−6.15393	+	9.57570i	−0.293711	+	0.457023i	0.662768	+	0.748825i	$0.269382\pi$
$440$	−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	−0.773314	−	0.634024i	$-0.781402\pi$
$443$	−19.8383	+	7.39932i	−0.942548	+	0.351552i	−0.169234	+	0.985576i	$0.554129\pi$
$444$	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	−0.974551	−	0.224165i	$-0.928034\pi$
$449$	−16.3926	−	25.5074i	−0.773616	−	1.20377i	0.200935	−	0.979605i	$-0.435602\pi$
$450$	−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	−0.855746	−	0.517396i	$-0.826901\pi$
$457$	−2.52719	+	3.37593i	−0.118217	+	0.157919i	0.737529	+	0.675315i	$0.235992\pi$
$458$	−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	0.0495744	+	0.998770i	$0.484214\pi$
$463$	−19.8543	+	26.5222i	−0.922706	+	1.23259i	−0.972280	+	0.233820i	$0.924877\pi$
$464$	−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	−0.601238	−	0.799070i	$-0.705326\pi$
$467$	−23.3960	+	1.67331i	−1.08264	+	0.0774317i	−0.481399	+	0.876502i	$0.659871\pi$
$468$	−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	0.819953	−	0.572431i	$-0.193999\pi$
$479$	−3.27451	−	7.17018i	−0.149616	−	0.327614i	−0.969569	+	0.244817i	$0.921272\pi$
$480$	−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	0.628483	−	0.777823i	$-0.283676\pi$
$487$	13.1105	+	4.88996i	0.594093	+	0.221585i	−0.0343902	+	0.999408i	$0.510949\pi$
$488$	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	−0.675813	−	0.737073i	$-0.736208\pi$
$491$	3.99479	−	27.7843i	0.180282	−	1.25389i	0.856096	−	0.516817i	$-0.172883\pi$
$492$	−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	0.970003	+	0.243092i	$0.0781618\pi$
$499$	30.1269	+	26.1051i	1.34867	+	1.16863i	0.378664	+	0.925534i	$0.376384\pi$
$500$	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	0.540011	−	0.841658i	$-0.318420\pi$
$503$	−2.58849	−	1.93772i	−0.115415	−	0.0863985i	−0.655426	+	0.755259i	$0.727511\pi$
$504$	−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	0.732107	−	0.681190i	$-0.238537\pi$
$509$	36.6949	−	5.27593i	1.62647	−	0.233851i	0.894365	+	0.447338i	$0.147628\pi$
$510$	−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	−0.270035	−	0.962851i	$-0.587035\pi$
$521$	−18.2694	−	2.62675i	−0.800398	−	0.115080i	−0.530363	+	0.847771i	$0.677944\pi$
$522$	−0.0444374	−	0.621316i	−0.00194497	−	0.0271943i
$523$	10.5477	+	28.2794i	0.461217	+	1.23657i	0.934596	+	0.355712i	$0.115761\pi$
$523$	10.5477	+	28.2794i	0.461217	+	1.23657i	−0.473379	+	0.880859i	$0.656966\pi$
$524$	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	−0.942167	−	0.335143i	$-0.891215\pi$
$541$	−23.9270	+	15.3769i	−1.02870	+	0.661106i	−0.0865334	+	0.996249i	$0.527579\pi$
$542$	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	0.150323	−	0.988637i	$-0.451969\pi$
$547$	24.8682	−	13.5791i	1.06329	−	0.580599i	0.912965	+	0.408038i	$0.133787\pi$
$548$	−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	0.940659	−	0.339352i	$-0.110208\pi$
$557$	3.46034	+	6.33715i	0.146619	+	0.268513i	−0.794040	+	0.607866i	$0.792026\pi$
$558$	−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	0.807562	+	0.589782i	$0.200786\pi$
$563$	−4.08178	+	18.7637i	−0.172027	+	0.790794i	−0.979589	+	0.201011i	$0.935577\pi$
$564$	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	−0.169142	−	0.985592i	$-0.554100\pi$
$569$	16.3752	−	35.8566i	0.686483	−	1.50319i	0.855625	−	0.517597i	$-0.173173\pi$
$570$	−0.169164	−	3.65987i	−0.00708548	−	0.153295i
$571$	−22.8911	+	10.4540i	−0.957962	+	0.437487i	−0.832140	−	0.554566i	$-0.812884\pi$
$571$	−22.8911	+	10.4540i	−0.957962	+	0.437487i	−0.125822	+	0.992053i	$0.540157\pi$
$572$	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	−0.639523	−	0.768772i	$-0.720868\pi$
$577$	−21.6642	+	4.71276i	−0.901894	+	0.196195i	−0.262371	+	0.964967i	$0.584504\pi$
$578$	−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	−0.544611	−	0.838689i	$-0.683323\pi$
$587$	7.24877	−	33.3220i	0.299189	−	1.37535i	0.843799	−	0.536659i	$-0.180314\pi$
$588$	−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	0.870467	−	0.492226i	$-0.163817\pi$
$593$	−0.346512	−	0.634590i	−0.0142296	−	0.0260595i	−0.884697	+	0.466166i	$0.845635\pi$
$594$	−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	$0.231063\pi$
$599$			32.4930i			1.32763i	−0.747898	+	0.663814i	$0.768937\pi$
$600$	0.567890	+	6.13005i	0.0231840	+	0.250258i
$601$	−5.78227	−	40.2166i	−0.235864	−	1.64047i	−0.671974	−	0.740574i	$-0.734553\pi$
$601$	−5.78227	−	40.2166i	−0.235864	−	1.64047i	0.436111	−	0.899893i	$-0.356356\pi$
$602$	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	−0.999088	−	0.0427098i	$-0.986401\pi$
$607$	−10.4219	+	19.0862i	−0.423010	+	0.774685i	0.576077	+	0.817395i	$0.304583\pi$
$608$	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	0.765445	−	0.643501i	$-0.222519\pi$
$613$	−1.67469	−	2.23712i	−0.0676399	−	0.0903563i	−0.833085	+	0.553144i	$0.813428\pi$
$614$	−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	−0.904271	−	0.426959i	$-0.859585\pi$
$617$	1.45882	−	3.91125i	0.0587300	−	0.157461i	0.963001	+	0.269498i	$0.0868577\pi$
$618$	11.0891	+	8.30122i	0.446070	+	0.333924i
$619$	1.24522	+	0.800257i	0.0500498	+	0.0321650i	0.565426	−	0.824799i	$-0.308712\pi$
$619$	1.24522	+	0.800257i	0.0500498	+	0.0321650i	−0.515377	+	0.856964i	$0.672348\pi$
$620$	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	−0.463538	−	0.886077i	$-0.653420\pi$
$631$	8.73039	−	7.56493i	0.347551	−	0.301155i	0.811090	+	0.584922i	$0.198875\pi$
$632$	−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	−0.225324	−	0.974284i	$-0.572344\pi$
$641$	−4.22893	+	0.608028i	−0.167033	+	0.0240157i	0.0582911	+	0.998300i	$0.481435\pi$
$642$	−0.789837	−	3.63082i	−0.0311724	−	0.143297i
$643$	7.60531	−	7.60531i	0.299924	−	0.299924i	−0.541060	−	0.840984i	$-0.681977\pi$
$643$	7.60531	−	7.60531i	0.299924	−	0.299924i	0.840984	+	0.541060i	$0.181977\pi$
$644$	−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	0.991666	+	0.128832i	$0.0411226\pi$
$647$	35.4749	+	26.5562i	1.39466	+	1.04403i	0.402998	+	0.915201i	$0.367968\pi$
$648$	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	−0.0390414	−	0.999238i	$-0.512430\pi$
$653$	−23.0179	−	12.5687i	−0.900761	−	0.491853i	−0.861720	+	0.507385i	$0.830612\pi$
$654$	−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	0.730077	+	0.683365i	$0.239484\pi$
$659$	−4.18317	+	29.0946i	−0.162953	+	1.13336i	−0.893030	+	0.449998i	$0.851425\pi$
$660$	3.42500	+	8.02944i	0.133318	+	0.312545i
$661$	13.6162	+	6.21833i	0.529611	+	0.241865i	0.662228	−	0.749302i	$-0.269611\pi$
$661$	13.6162	+	6.21833i	0.529611	+	0.241865i	−0.132618	+	0.991167i	$0.542338\pi$
$662$	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	0.0829062	−	0.996557i	$-0.473580\pi$
$673$	20.7063	−	7.72305i	0.798169	−	0.297702i	0.715263	+	0.698856i	$0.246307\pi$
$674$	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	−0.614262	−	0.789102i	$-0.710546\pi$
$677$	2.75930	−	38.5801i	0.106049	−	1.48275i	0.720311	−	0.693651i	$-0.243999\pi$
$678$	−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	−0.838666	−	0.544646i	$-0.816664\pi$
$683$	−41.5871	+	2.97437i	−1.59129	+	0.113811i	−0.752619	+	0.658457i	$0.771210\pi$
$684$	−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	0.919461	+	0.393180i	$0.128625\pi$
$701$	23.7004	+	36.8786i	0.895153	+	1.39288i	−0.0243085	+	0.999705i	$0.507738\pi$
$702$	−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	−0.999800	−	0.0199994i	$-0.993634\pi$
$709$	−9.59066	−	21.0006i	−0.360185	−	0.788695i	0.639615	−	0.768695i	$-0.279094\pi$
$710$	−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	0.780708	−	0.624896i	$-0.214858\pi$
$719$	21.9795	+	10.0377i	0.819699	+	0.374344i	0.0389906	+	0.999240i	$0.487586\pi$
$720$	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	0.521051	−	0.853525i	$-0.325540\pi$
$727$	2.28435	+	1.24735i	0.0847220	+	0.0462617i	−0.436329	+	0.899787i	$0.643722\pi$
$728$	−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	0.677801	−	0.735245i	$-0.262933\pi$
$733$	4.42112	+	3.30961i	0.163298	+	0.122243i	−0.514504	+	0.857488i	$0.672024\pi$
$734$	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	−0.877878	−	0.478885i	$-0.841041\pi$
$739$	−43.0951	+	6.19614i	−1.58528	+	0.227929i	−0.707400	+	0.706813i	$0.750132\pi$
$740$	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	−0.992824	−	0.119585i	$-0.961843\pi$
$743$	−0.739355	−	10.3375i	−0.0271243	−	0.379247i	0.965700	−	0.259662i	$-0.0836111\pi$
$744$	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	−0.224512	−	0.974471i	$-0.572079\pi$
$751$	−19.5796	−	2.81512i	−0.714470	−	0.102725i	−0.489958	+	0.871746i	$0.662988\pi$
$752$	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	−0.975475	−	0.220110i	$-0.929359\pi$
$757$	−4.94113	−	22.7140i	−0.179589	−	0.825555i	0.795887	−	0.605446i	$-0.207005\pi$
$758$	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	0.751485	−	0.659750i	$-0.229338\pi$
$761$	12.7871	+	8.21780i	0.463533	+	0.297895i	−0.287952	+	0.957645i	$0.592974\pi$
$762$	−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	0.985252	+	0.171108i	$0.0547349\pi$
$769$	28.1303	+	32.4640i	1.01440	+	1.17068i	0.0291508	+	0.999575i	$0.490720\pi$
$770$	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	−0.672748	−	0.739871i	$-0.734886\pi$
$773$	8.71304	−	15.9567i	0.313386	−	0.573924i	0.986135	+	0.165947i	$0.0530681\pi$
$774$	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	0.830979	+	0.556303i	$0.187781\pi$
$787$	23.8374	+	43.6549i	0.849710	+	1.55613i	0.0187306	+	0.999825i	$0.494038\pi$
$788$	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	−0.673901	−	0.738822i	$-0.735382\pi$
$797$	−4.37205	+	3.27287i	−0.154866	+	0.115931i	0.519035	+	0.854753i	$0.326292\pi$
$798$	−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	−0.252008	−	0.967725i	$-0.581091\pi$
$809$	8.94018	−	4.08284i	0.314320	−	0.143545i	0.566328	+	0.824180i	$0.308364\pi$
$810$	−3.87622	−	3.53373i	−0.136197	−	0.124163i
$811$	6.53308	−	14.3054i	0.229407	−	0.502332i	−0.759565	−	0.650431i	$-0.774588\pi$
$811$	6.53308	−	14.3054i	0.229407	−	0.502332i	0.988973	+	0.148099i	$0.0473155\pi$
$812$	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	0.0133999	−	0.999910i	$-0.495735\pi$
$821$	28.6882	−	33.1080i	1.00123	−	1.15548i	0.987826	−	0.155566i	$-0.0497200\pi$
$822$	−11.6795	+	4.35624i	−0.407371	+	0.151941i
$823$	−18.9770	−	34.7538i	−0.661497	−	1.21144i	−0.965904	−	0.258900i	$-0.916640\pi$
$823$	−18.9770	−	34.7538i	−0.661497	−	1.21144i	0.304407	−	0.952542i	$-0.401542\pi$
$824$	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	0.618001	−	0.786177i	$-0.287943\pi$
$827$	−4.83634	−	4.83634i	−0.168176	−	0.168176i	−0.786177	+	0.618001i	$0.787943\pi$
$828$	−1.05019	+	7.03911i	−0.0364966	+	0.244626i
$829$		−	39.2405i		−	1.36288i	−0.731875	−	0.681439i	$-0.761354\pi$
$829$		−	39.2405i		−	1.36288i	0.731875	−	0.681439i	$-0.238646\pi$
$830$	−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	−0.131570	−	0.991307i	$-0.542002\pi$
$839$	20.7248	−	13.3190i	0.715498	−	0.459823i	0.847068	+	0.531484i	$0.178366\pi$
$840$	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	0.936596	+	0.350411i	$0.113958\pi$
$853$	6.72339	+	30.9069i	0.230204	+	1.05823i	−0.706392	+	0.707821i	$0.749678\pi$
$854$	−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	0.982538	+	0.186062i	$0.0595725\pi$
$857$	10.5924	+	28.3994i	0.361830	+	0.970104i	−0.620708	+	0.784042i	$0.713155\pi$
$858$	−1.43203	−	20.0224i	−0.0488887	−	0.683554i
$859$	26.5495	+	3.81725i	0.905858	+	0.130243i	0.579470	−	0.814993i	$-0.303259\pi$
$859$	26.5495	+	3.81725i	0.905858	+	0.130243i	0.326388	+	0.945236i	$0.394169\pi$
$860$	−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	−0.720959	−	0.692978i	$-0.756298\pi$
$863$	−48.9019	−	10.6380i	−1.66464	−	0.362120i	−0.943681	+	0.330858i	$0.892662\pi$
$864$	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	0.502534	−	0.864557i	$-0.332401\pi$
$877$	−5.49114	−	4.11061i	−0.185423	−	0.138806i	−0.687957	+	0.725752i	$0.741492\pi$
$878$	−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	0.829766	−	0.558112i	$-0.188474\pi$
$881$	11.7368	+	10.1700i	0.395422	+	0.342636i	−0.434343	+	0.900747i	$0.643019\pi$
$882$	−4.91945	−	6.57162i	−0.165647	−	0.221278i
$883$	−6.52451	−	3.56265i	−0.219567	−	0.119893i	0.365701	−	0.930732i	$-0.380829\pi$
$883$	−6.52451	−	3.56265i	−0.219567	−	0.119893i	−0.585269	+	0.810839i	$0.699011\pi$
$884$	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	−0.786841	−	0.617156i	$-0.788285\pi$
$887$	−49.2455	−	3.52211i	−1.65350	−	0.118261i	−0.866662	+	0.498895i	$0.833739\pi$
$888$	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	0.989330	+	0.145689i	$0.0465400\pi$
$907$	−0.321155	+	4.49034i	−0.0106638	+	0.149099i	−0.999994	+	0.00340992i	$0.998915\pi$
$908$	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	−0.814421	−	0.580275i	$-0.802945\pi$
$911$	−13.3712	−	45.5380i	−0.443007	−	1.50874i	0.371414	−	0.928467i	$-0.378873\pi$
$912$	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	0.973584	−	0.228327i	$-0.0733255\pi$
$929$	0.948223	+	3.22935i	0.0311102	+	0.105952i	−0.942474	+	0.334279i	$0.891507\pi$
$930$	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	0.330325	−	0.943867i	$-0.392842\pi$
$937$	36.6735	−	13.6785i	1.19807	−	0.446857i	0.867745	+	0.497010i	$0.165569\pi$
$938$	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	−0.309976	−	0.950744i	$-0.600321\pi$
$941$	20.9705	−	32.6308i	0.683620	−	1.06373i	0.993596	−	0.112989i	$-0.0360425\pi$
$942$	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	0.145925	−	0.989296i	$-0.453384\pi$
$947$	−12.0522	−	4.49524i	−0.391644	−	0.146076i	−0.537568	+	0.843220i	$0.680657\pi$
$948$	−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	−0.348537	−	0.937295i	$-0.613322\pi$
$953$	−25.5275	−	1.82577i	−0.826918	−	0.0591424i	−0.478381	+	0.878153i	$0.658776\pi$
$954$	−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	−0.677752	−	0.735291i	$-0.737046\pi$
$967$	1.78926	−	1.78926i	0.0575386	−	0.0575386i	0.735291	+	0.677752i	$0.237046\pi$
$968$	−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	0.715738	+	0.698369i	$0.246090\pi$
$971$	−8.22478	+	28.0110i	−0.263946	+	0.898917i	−0.979684	+	0.200548i	$0.935728\pi$
$972$	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	0.944492	−	0.328536i	$-0.106555\pi$
$977$	52.1102	+	11.3359i	1.66715	+	0.362667i	0.722661	+	0.691203i	$0.242919\pi$
$978$	−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	0.727548	+	0.686056i	$0.240660\pi$
$983$	19.6575	+	52.7037i	0.626975	+	1.68099i	−0.100573	+	0.994930i	$0.532068\pi$
$984$	−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	0.657159	−	0.753752i	$-0.271758\pi$
$991$	7.69741	+	4.94682i	0.244516	+	0.157141i	−0.412643	+	0.910893i	$0.635394\pi$
$992$	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	0.296730	−	0.954961i	$-0.404104\pi$
$997$	−22.2021	−	29.6585i	−0.703147	−	0.939295i	−0.999877	+	0.0156666i	$0.995013\pi$
$998$	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.113.10	yes	240
5.2	odd	4	inner	230.2.l.a.67.9	yes	240
23.11	odd	22	inner	230.2.l.a.103.9	yes	240
115.57	even	44	inner	230.2.l.a.57.10	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.10	✓	240	115.57	even	44	inner
230.2.l.a.67.9	yes	240	5.2	odd	4	inner
230.2.l.a.103.9	yes	240	23.11	odd	22	inner
230.2.l.a.113.10	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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