LMFDB - Embedded newform 230.2.l.a.67.9

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			67.9
Character	$\chi$	$=$	230.67
Dual form			230.2.l.a.103.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212565 + 0.977147i) q^{2} +(-0.985673 - 0.737866i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(1.29447 - 1.82328i) q^{5} +(0.511483 - 1.11999i) q^{6} +(-0.0864458 - 1.20867i) q^{7} +(-0.599278 - 0.800541i) q^{8} +(-0.418092 - 1.42389i) q^{9} +(2.05677 + 0.877326i) q^{10} +(-1.71419 - 2.66733i) q^{11} +(1.20312 + 0.261723i) q^{12} +(5.12881 + 0.366820i) q^{13} +(1.16267 - 0.341392i) q^{14} +(-2.62126 + 0.842007i) q^{15} +(0.654861 - 0.755750i) q^{16} +(1.27205 + 3.41051i) q^{17} +(1.30248 - 0.711206i) q^{18} +(-0.552811 - 1.21049i) q^{19} +(-0.420079 + 2.19625i) q^{20} +(-0.806629 + 1.25514i) q^{21} +(2.24200 - 2.24200i) q^{22} +(3.64105 - 3.12134i) q^{23} +1.23126i q^{24} +(-1.64867 - 4.72037i) q^{25} +(0.731770 + 5.08957i) q^{26} +(-1.92938 + 5.17287i) q^{27} +(0.580734 + 1.06353i) q^{28} +(0.381814 + 0.174369i) q^{29} +(-1.37995 - 2.38238i) q^{30} +(-0.00687467 + 0.0478144i) q^{31} +(0.877679 + 0.479249i) q^{32} +(-0.278502 + 3.89396i) q^{33} +(-3.06217 + 1.96794i) q^{34} +(-2.31564 - 1.40698i) q^{35} +(0.971814 + 1.12153i) q^{36} +(-3.33816 + 6.11338i) q^{37} +(1.06532 - 0.797485i) q^{38} +(-4.78467 - 4.14594i) q^{39} +(-2.23536 + 0.0563686i) q^{40} +(-7.66309 - 2.25009i) q^{41} +(-1.39792 - 0.521396i) q^{42} +(-7.09311 + 9.47529i) 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} +(-1.20312 + 0.261723i) q^{48} +(5.47534 - 0.787235i) q^{49} +(4.26204 - 2.61438i) q^{50} +(1.26267 - 4.30025i) q^{51} +(-4.81771 + 1.79691i) q^{52} +(10.3439 - 0.739812i) q^{53} +(-5.46477 - 0.785715i) q^{54} +(-7.08226 - 0.327351i) q^{55} +(-0.915785 + 0.793533i) q^{56} +(-0.348286 + 1.60105i) q^{57} +(-0.0892234 + 0.410153i) q^{58} +(-1.43884 + 1.24677i) q^{59} +(2.03460 - 1.85483i) q^{60} +(3.22324 + 0.463432i) q^{61} +(-0.0481830 + 0.00344611i) q^{62} +(-1.68487 + 0.628424i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(7.30793 - 8.87640i) q^{65} +(-3.86417 + 0.555584i) q^{66} +(4.80982 - 1.04631i) 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} +(-0.889329 + 1.18800i) q^{72} +(11.1774 + 4.16896i) q^{73} +(-6.68325 - 1.96238i) q^{74} +(-1.85795 + 5.86924i) q^{75} +(1.00571 + 0.871452i) q^{76} +(-3.07574 + 2.30247i) q^{77} +(3.03414 - 5.55661i) q^{78} +(9.78605 + 11.2937i) q^{79} +(-0.530240 - 2.17229i) q^{80} +(1.97336 - 1.26820i) q^{81} +(0.569758 - 7.96626i) q^{82} +(-5.45048 - 2.97619i) q^{83} +(0.212332 - 1.47680i) q^{84} +(7.86494 + 2.09551i) q^{85} +(-10.7665 - 4.91689i) q^{86} +(-0.247683 - 0.453598i) q^{87} +(-1.10803 + 2.97075i) q^{88} +(0.260623 + 1.81268i) q^{89} +(0.389298 - 3.29541i) q^{90} -6.23075i q^{91} +(-2.01536 + 4.35182i) q^{92} +(0.0420568 - 0.0420568i) q^{93} +(0.603889 - 0.939669i) q^{94} +(-2.92265 - 0.559018i) q^{95} +(-0.511483 - 1.11999i) q^{96} +(-2.35850 + 1.28784i) q^{97} +(1.93311 + 5.18287i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.212565	+	0.977147i	0.150306	+	0.690947i
$2$	0.212565	+	0.977147i	0.150306	+	0.690947i
$3$	−0.985673	−	0.737866i	−0.569079	−	0.426007i	0.275606	−	0.961271i	$-0.411121\pi$
$3$	−0.985673	−	0.737866i	−0.569079	−	0.426007i	−0.844685	+	0.535264i	$0.820212\pi$
$4$	−0.909632	+	0.415415i	−0.454816	+	0.207708i
$5$	1.29447	−	1.82328i	0.578907	−	0.815394i
$5$	1.29447	−	1.82328i	0.578907	−	0.815394i
$6$	0.511483	−	1.11999i	0.208812	−	0.457235i
$7$	−0.0864458	−	1.20867i	−0.0326734	−	0.456834i	−0.987283	−	0.158974i	$-0.949181\pi$
$7$	−0.0864458	−	1.20867i	−0.0326734	−	0.456834i	0.954609	−	0.297861i	$-0.0962731\pi$
$8$	−0.599278	−	0.800541i	−0.211877	−	0.283034i
$9$	−0.418092	−	1.42389i	−0.139364	−	0.474630i
$10$	2.05677	+	0.877326i	0.650407	+	0.277435i
$11$	−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	$0.976818\pi$
$12$	1.20312	+	0.261723i	0.347311	+	0.0755529i
$13$	5.12881	+	0.366820i	1.42248	+	0.101738i	0.761255	−	0.648453i	$-0.224584\pi$
$13$	5.12881	+	0.366820i	1.42248	+	0.101738i	0.661222	+	0.750191i	$0.270038\pi$
$14$	1.16267	−	0.341392i	0.310737	−	0.0912407i
$15$	−2.62126	+	0.842007i	−0.676807	+	0.217405i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	1.27205	+	3.41051i	0.308518	+	0.827170i	0.994986	+	0.100010i	$0.0318874\pi$
$17$	1.27205	+	3.41051i	0.308518	+	0.827170i	−0.686468	+	0.727160i	$0.740840\pi$
$18$	1.30248	−	0.711206i	0.306997	−	0.167633i
$19$	−0.552811	−	1.21049i	−0.126824	−	0.277705i	0.835560	−	0.549399i	$-0.185143\pi$
$19$	−0.552811	−	1.21049i	−0.126824	−	0.277705i	−0.962384	+	0.271694i	$0.912416\pi$
$20$	−0.420079	+	2.19625i	−0.0939325	+	0.491097i
$21$	−0.806629	+	1.25514i	−0.176021	+	0.273894i
$22$	2.24200	−	2.24200i	0.477996	−	0.477996i
$23$	3.64105	−	3.12134i	0.759211	−	0.650845i
$23$	3.64105	−	3.12134i	0.759211	−	0.650845i
$24$			1.23126i			0.251330i
$25$	−1.64867	−	4.72037i	−0.329734	−	0.944074i
$26$	0.731770	+	5.08957i	0.143512	+	0.998148i
$27$	−1.92938	+	5.17287i	−0.371309	+	0.995519i
$28$	0.580734	+	1.06353i	0.109748	+	0.200989i
$29$	0.381814	+	0.174369i	0.0709011	+	0.0323795i	0.450550	−	0.892751i	$-0.351228\pi$
$29$	0.381814	+	0.174369i	0.0709011	+	0.0323795i	−0.379649	+	0.925131i	$0.623955\pi$
$30$	−1.37995	−	2.38238i	−0.251944	−	0.434961i
$31$	−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	$0.0468354\pi$
$32$	0.877679	+	0.479249i	0.155153	+	0.0847201i
$33$	−0.278502	+	3.89396i	−0.0484809	+	0.677852i
$34$	−3.06217	+	1.96794i	−0.525158	+	0.337499i
$35$	−2.31564	−	1.40698i	−0.391415	−	0.237823i
$36$	0.971814	+	1.12153i	0.161969	+	0.186922i
$37$	−3.33816	+	6.11338i	−0.548790	+	1.00503i	0.445186	+	0.895438i	$0.353138\pi$
$37$	−3.33816	+	6.11338i	−0.548790	+	1.00503i	−0.993976	+	0.109596i	$0.965044\pi$
$38$	1.06532	−	0.797485i	0.172817	−	0.129369i
$39$	−4.78467	−	4.14594i	−0.766160	−	0.663882i
$40$	−2.23536	+	0.0563686i	−0.353441	+	0.00891266i
$41$	−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	$0.805260\pi$
$42$	−1.39792	−	0.521396i	−0.215703	−	0.0804532i
$43$	−7.09311	+	9.47529i	−1.08169	+	1.44497i	−0.196050	+	0.980594i	$0.562811\pi$
$43$	−7.09311	+	9.47529i	−1.08169	+	1.44497i	−0.885639	+	0.464374i	$0.846280\pi$
$44$	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	$0.775960\pi$
$48$	−1.20312	+	0.261723i	−0.173656	+	0.0377764i
$49$	5.47534	−	0.787235i	0.782191	−	0.112462i
$50$	4.26204	−	2.61438i	0.602744	−	0.369729i
$51$	1.26267	−	4.30025i	0.176809	−	0.602156i
$52$	−4.81771	+	1.79691i	−0.668097	+	0.249187i
$53$	10.3439	−	0.739812i	1.42085	−	0.101621i	0.660348	−	0.750960i	$-0.270409\pi$
$53$	10.3439	−	0.739812i	1.42085	−	0.101621i	0.760499	+	0.649339i	$0.224954\pi$
$54$	−5.46477	−	0.785715i	−0.743661	−	0.106922i
$55$	−7.08226	−	0.327351i	−0.954972	−	0.0441400i
$56$	−0.915785	+	0.793533i	−0.122377	+	0.106040i
$57$	−0.348286	+	1.60105i	−0.0461316	+	0.212064i
$58$	−0.0892234	+	0.410153i	−0.0117156	+	0.0538558i
$59$	−1.43884	+	1.24677i	−0.187322	+	0.162315i	−0.743473	−	0.668766i	$-0.766823\pi$
$59$	−1.43884	+	1.24677i	−0.187322	+	0.162315i	0.556151	+	0.831081i	$0.312277\pi$
$60$	2.03460	−	1.85483i	0.262666	−	0.239457i
$61$	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	$0.478607\pi$
$62$	−0.0481830	+	0.00344611i	−0.00611924	+	0.000437657i
$63$	−1.68487	+	0.628424i	−0.212274	+	0.0791740i
$64$	−0.281733	+	0.959493i	−0.0352166	+	0.119937i
$65$	7.30793	−	8.87640i	0.906437	−	1.10098i
$66$	−3.86417	+	0.555584i	−0.475647	+	0.0683877i
$67$	4.80982	−	1.04631i	0.587613	−	0.127827i	0.0910773	−	0.995844i	$-0.470969\pi$
$67$	4.80982	−	1.04631i	0.587613	−	0.127827i	0.496535	+	0.868017i	$0.334605\pi$
$68$	−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	$0.835854\pi$
$72$	−0.889329	+	1.18800i	−0.104808	+	0.140008i
$73$	11.1774	+	4.16896i	1.30822	+	0.487940i	0.904316	−	0.426863i	$-0.140381\pi$
$73$	11.1774	+	4.16896i	1.30822	+	0.487940i	0.403901	+	0.914803i	$0.367654\pi$
$74$	−6.68325	−	1.96238i	−0.776912	−	0.228122i
$75$	−1.85795	+	5.86924i	−0.214537	+	0.677722i
$76$	1.00571	+	0.871452i	0.115363	+	0.0999624i
$77$	−3.07574	+	2.30247i	−0.350513	+	0.262391i
$78$	3.03414	−	5.55661i	0.343548	−	0.629162i
$79$	9.78605	+	11.2937i	1.10102	+	1.27064i	0.959807	+	0.280662i	$0.0905538\pi$
$79$	9.78605	+	11.2937i	1.10102	+	1.27064i	0.141210	+	0.989980i	$0.454901\pi$
$80$	−0.530240	−	2.17229i	−0.0592826	−	0.242869i
$81$	1.97336	−	1.26820i	0.219262	−	0.140911i
$82$	0.569758	−	7.96626i	0.0629193	−	0.879726i
$83$	−5.45048	−	2.97619i	−0.598268	−	0.326679i	0.151421	−	0.988469i	$-0.451615\pi$
$83$	−5.45048	−	2.97619i	−0.598268	−	0.326679i	−0.749689	+	0.661790i	$0.769797\pi$
$84$	0.212332	−	1.47680i	0.0231673	−	0.161132i
$85$	7.86494	+	2.09551i	0.853072	+	0.227290i
$86$	−10.7665	−	4.91689i	−1.16098	−	0.530202i
$87$	−0.247683	−	0.453598i	−0.0265544	−	0.0486308i
$88$	−1.10803	+	2.97075i	−0.118117	+	0.316683i
$89$	0.260623	+	1.81268i	0.0276260	+	0.192143i	0.998961	−	0.0455713i	$-0.0145108\pi$
$89$	0.260623	+	1.81268i	0.0276260	+	0.192143i	−0.971335	+	0.237715i	$0.923602\pi$
$90$	0.389298	−	3.29541i	0.0410356	−	0.347367i
$91$		−	6.23075i		−	0.653160i
$92$	−2.01536	+	4.35182i	−0.210116	+	0.453709i
$93$	0.0420568	−	0.0420568i	0.00436108	−	0.00436108i
$94$	0.603889	−	0.939669i	0.0622864	−	0.0969195i
$95$	−2.92265	−	0.559018i	−0.299858	−	0.0573540i
$96$	−0.511483	−	1.11999i	−0.0522031	−	0.114309i
$97$	−2.35850	+	1.28784i	−0.239469	+	0.130760i	−0.594503	−	0.804093i	$-0.702651\pi$
$97$	−2.35850	+	1.28784i	−0.239469	+	0.130760i	0.355034	+	0.934853i	$0.384469\pi$
$98$	1.93311	+	5.18287i	0.195274	+	0.523549i
$99$	−3.08130	+	3.55601i	−0.309682	+	0.357392i
$100$	3.46060	+	3.60892i	0.346060	+	0.360892i
$101$	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	$0.240689\pi$
$102$	4.47038	+	0.319728i	0.442633	+	0.0316578i
$103$	10.9932	+	2.39142i	1.08319	+	0.235634i	0.718523	−	0.695503i	$-0.244818\pi$
$103$	10.9932	+	2.39142i	1.08319	+	0.235634i	0.364669	+	0.931137i	$0.381182\pi$
$104$	−2.77993	−	4.32565i	−0.272594	−	0.424165i
$105$	1.24431	+	3.09545i	0.121432	+	0.302085i
$106$	2.92166	+	9.95027i	0.283777	+	0.966456i
$107$	1.80852	+	2.41590i	0.174836	+	0.233554i	0.879396	−	0.476090i	$-0.157946\pi$
$107$	1.80852	+	2.41590i	0.174836	+	0.233554i	−0.704560	+	0.709644i	$0.748856\pi$
$108$	−0.393861	−	5.50690i	−0.0378993	−	0.529902i
$109$	−7.43710	+	16.2850i	−0.712345	+	1.55982i	0.111986	+	0.993710i	$0.464279\pi$
$109$	−7.43710	+	16.2850i	−0.712345	+	1.55982i	−0.824331	+	0.566108i	$0.808449\pi$
$110$	−1.18557	−	6.98999i	−0.113040	−	0.666470i
$111$	7.80119	−	3.56269i	0.740457	−	0.338155i
$112$	−0.970062	−	0.726179i	−0.0916622	−	0.0686175i
$113$	0.835857	+	3.84237i	0.0786308	+	0.361460i	0.999603	−	0.0281679i	$-0.00896731\pi$
$113$	0.835857	+	3.84237i	0.0786308	+	0.361460i	−0.920972	+	0.389628i	$0.872604\pi$
$114$	−1.63849			−0.153459
$115$	−0.977831	−	10.6791i	−0.0911832	−	0.995834i
$116$	−0.419746			−0.0389724
$117$	−1.62200	−	7.45622i	−0.149954	−	0.689328i
$118$	−1.52412	−	1.14094i	−0.140307	−	0.105032i
$119$	4.01222	−	1.83232i	0.367799	−	0.167968i
$120$	2.24492	+	1.59383i	0.204933	+	0.145496i
$121$	0.393350	−	0.861316i	0.0357591	−	0.0783015i
$122$	0.232308	+	3.24809i	0.0210322	+	0.294068i
$123$	5.89305	+	7.87219i	0.531358	+	0.709811i
$124$	−0.0136094	−	0.0463493i	−0.00122216	−	0.00416229i
$125$	−10.7407	−	3.10441i	−0.960677	−	0.277667i
$126$	−0.972208	−	1.51278i	−0.0866111	−	0.134770i
$127$	12.7015	+	2.76305i	1.12708	+	0.245181i	0.737193	−	0.675682i	$-0.236151\pi$
$127$	12.7015	+	2.76305i	1.12708	+	0.245181i	0.389886	+	0.920863i	$0.372515\pi$
$128$	−0.997452	−	0.0713392i	−0.0881631	−	0.00630555i
$129$	13.9830	−	4.10577i	1.23113	−	0.361493i
$130$	10.2270	+	5.25410i	0.896964	+	0.460815i
$131$	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	$0.0510544\pi$
$132$	−1.36428	−	3.65777i	−0.118745	−	0.318368i
$133$	−1.41529	+	0.772808i	−0.122721	+	0.0670110i
$134$	2.04480	+	4.47749i	0.176644	+	0.386796i
$135$	6.93403	+	10.2139i	0.596787	+	0.879076i
$136$	1.96794	−	3.06217i	0.168749	−	0.262579i
$137$	7.15888	−	7.15888i	0.611624	−	0.611624i	−0.331745	−	0.943369i	$-0.607637\pi$
$137$	7.15888	−	7.15888i	0.611624	−	0.611624i	0.943369	+	0.331745i	$0.107637\pi$
$138$	−1.63355	−	5.67446i	−0.139057	−	0.483042i
$139$			6.26942i			0.531765i	0.964005	+	0.265883i	$0.0856633\pi$
$139$			6.26942i			0.531765i	−0.964005	+	0.265883i	$0.914337\pi$
$140$	2.69086	+	0.317880i	0.227419	+	0.0268658i
$141$	0.195726	+	1.36130i	0.0164831	+	0.114642i
$142$	2.73998	−	7.34618i	0.229934	−	0.616477i
$143$	−7.81333	−	14.3090i	−0.653383	−	1.19658i
$144$	−1.34990	−	0.616477i	−0.112491	−	0.0513730i
$145$	0.812171	−	0.470437i	0.0674471	−	0.0390677i
$146$	−1.69776	+	11.8081i	−0.140507	+	0.977249i
$147$	−5.97777	−	3.26411i	−0.493038	−	0.269219i
$148$	0.496906	−	6.94765i	0.0408454	−	0.571093i
$149$	−6.29025	+	4.04250i	−0.515317	+	0.331174i	−0.772317	−	0.635237i	$-0.780902\pi$
$149$	−6.29025	+	4.04250i	−0.515317	+	0.331174i	0.257000	+	0.966411i	$0.417266\pi$
$150$	−6.13005	−	0.567890i	−0.500516	−	0.0463680i
$151$	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	$0.689554\pi$
$152$	−0.637758	+	1.16797i	−0.0517290	+	0.0947346i
$153$	4.32435	−	3.23717i	0.349603	−	0.261710i
$154$	−2.90365	−	2.51603i	−0.233983	−	0.202747i
$155$	0.0782797	+	0.0744289i	0.00628758	+	0.00597827i
$156$	6.07457	+	1.78366i	0.486355	+	0.142807i
$157$	−20.0250	−	7.46894i	−1.59817	−	0.596087i	−0.616615	−	0.787265i	$-0.711496\pi$
$157$	−20.0250	−	7.46894i	−1.59817	−	0.596087i	−0.981555	+	0.191179i	$0.938769\pi$
$158$	−8.95543	+	11.9631i	−0.712456	+	0.951730i
$159$	−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
$163$	−18.5356	+	4.03217i	−1.45182	+	0.315824i	−0.868205	−	0.496206i	$-0.834726\pi$
$163$	−18.5356	+	4.03217i	−1.45182	+	0.315824i	−0.583616	+	0.812030i	$0.698363\pi$
$164$	7.90532	−	1.13661i	0.617301	−	0.0887545i
$165$	6.73926	+	5.54842i	0.524650	+	0.431944i
$166$	1.74959	−	5.95856i	0.135795	−	0.462474i
$167$	−5.92884	+	2.21134i	−0.458787	+	0.171119i	−0.568222	−	0.822875i	$-0.692369\pi$
$167$	−5.92884	+	2.21134i	−0.458787	+	0.171119i	0.109435	+	0.993994i	$0.465096\pi$
$168$	1.48819	−	0.106437i	0.114816	−	0.00821181i
$169$	13.3025	+	1.91261i	1.02327	+	0.147124i
$170$	−0.375808	+	8.13063i	−0.0288231	+	0.623591i
$171$	−1.49247	+	1.29324i	−0.114132	+	0.0988963i
$172$	2.51594	−	11.5656i	0.191839	−	0.881869i
$173$	4.47160	−	20.5556i	0.339969	−	1.56281i	−0.416717	−	0.909036i	$-0.636819\pi$
$173$	4.47160	−	20.5556i	0.339969	−	1.56281i	0.756686	−	0.653778i	$-0.226817\pi$
$174$	0.390583	−	0.338442i	0.0296100	−	0.0256572i
$175$	−5.56285	+	2.40076i	−0.420512	+	0.181480i
$176$	−3.13839	−	0.451233i	−0.236565	−	0.0340129i
$177$	2.33818	−	0.167230i	0.175748	−	0.0125698i
$178$	−1.71585	+	0.639979i	−0.128608	+	0.0479685i
$179$	4.10434	−	13.9781i	0.306773	−	1.04477i	−0.651436	−	0.758704i	$-0.725833\pi$
$179$	4.10434	−	13.9781i	0.306773	−	1.04477i	0.958209	−	0.286069i	$-0.0923488\pi$
$180$	3.30285	−	0.320090i	0.246180	−	0.0238581i
$181$	−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	$0.799966\pi$
$182$	6.08836	−	1.32444i	0.451299	−	0.0981741i
$183$	−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
$187$	6.91642	−	9.23925i	0.505779	−	0.675641i
$188$	1.04656	+	0.390347i	0.0763283	+	0.0284690i
$189$	6.41908	+	1.88481i	0.466919	+	0.137100i
$190$	−0.0750122	−	2.97469i	−0.00544196	−	0.215807i
$191$	−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	$0.953545\pi$
$192$	0.985673	−	0.737866i	0.0711349	−	0.0532509i
$193$	0.282576	−	0.517500i	0.0203403	−	0.0372504i	−0.867311	−	0.497766i	$-0.834154\pi$
$193$	0.282576	−	0.517500i	0.0203403	−	0.0372504i	0.887651	+	0.460516i	$0.152336\pi$
$194$	−1.75974	−	2.03085i	−0.126342	−	0.145806i
$195$	−13.7528	+	3.35696i	−0.984860	+	0.240397i
$196$	−4.65351	+	2.99063i	−0.332394	+	0.213617i
$197$	−1.53141	+	21.4119i	−0.109109	+	1.52554i	0.588171	+	0.808737i	$0.299848\pi$
$197$	−1.53141	+	21.4119i	−0.109109	+	1.52554i	−0.697279	+	0.716800i	$0.745606\pi$
$198$	−4.12972	−	2.25500i	−0.293486	−	0.160256i
$199$	2.94488	−	20.4821i	0.208757	−	1.45194i	−0.568463	−	0.822709i	$-0.692462\pi$
$199$	2.94488	−	20.4821i	0.208757	−	1.45194i	0.777220	−	0.629229i	$-0.216629\pi$
$200$	−2.79084	+	4.14864i	−0.197342	+	0.293353i
$201$	−5.51295	−	2.51768i	−0.388853	−	0.177583i
$202$	4.86181	+	8.90374i	0.342076	+	0.626465i
$203$	0.177748	−	0.476561i	0.0124755	−	0.0334480i
$204$	0.637826	+	4.43618i	0.0446568	+	0.310595i
$205$	−14.0222	+	11.0593i	−0.979354	+	0.772412i
$206$			11.2503i			0.783846i
$207$	−5.96674	−	3.87944i	−0.414717	−	0.269640i
$208$	3.63588	−	3.63588i	0.252103	−	0.252103i
$209$	−2.28115	+	3.54954i	−0.157790	+	0.245527i
$210$	−2.76022	+	1.87386i	−0.190473	+	0.129308i
$211$	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	$0.519247\pi$
$212$	−9.10183	+	4.96998i	−0.625117	+	0.341339i
$213$	3.37363	+	9.04504i	0.231157	+	0.619756i
$214$	−1.97626	+	2.28073i	−0.135095	+	0.155907i
$215$	8.09421	+	25.1982i	0.552021	+	1.71850i
$216$	5.29733	−	1.55544i	0.360438	−	0.105834i
$217$	0.0583861	+	0.00417585i	0.00396351	+	0.000283476i
$218$	−17.4937	−	3.80552i	−1.18482	−	0.257742i
$219$	−7.94114	−	12.3567i	−0.536613	−	0.834986i
$220$	6.57824	−	2.64431i	0.443505	−	0.178279i
$221$	5.27308	+	17.9585i	0.354706	+	1.20802i
$222$	5.13953	+	6.86561i	0.344943	+	0.460790i
$223$	0.552974	+	7.73159i	0.0370299	+	0.517745i	0.981788	+	0.189978i	$0.0608417\pi$
$223$	0.552974	+	7.73159i	0.0370299	+	0.517745i	−0.944758	+	0.327767i	$0.893704\pi$
$224$	0.503382	−	1.10225i	0.0336336	−	0.0736474i
$225$	−6.03199	+	4.32107i	−0.402132	+	0.288072i
$226$	−3.57689	+	1.63351i	−0.237931	+	0.108659i
$227$	2.40772	+	1.80240i	0.159806	+	0.119629i	0.676188	−	0.736729i	$-0.263631\pi$
$227$	2.40772	+	1.80240i	0.159806	+	0.119629i	−0.516382	+	0.856358i	$0.672722\pi$
$228$	−0.348286	−	1.60105i	−0.0230658	−	0.106032i
$229$	8.82281			0.583028			0.291514	−	0.956567i	$-0.405841\pi$
$229$	8.82281			0.583028			0.291514	+	0.956567i	$0.405841\pi$
$230$	10.2272	−	3.22550i	0.674363	−	0.212683i
$231$	4.73059			0.311250
$232$	−0.0892234	−	0.410153i	−0.00585780	−	0.0269279i
$233$	−6.31698	−	4.72883i	−0.413839	−	0.309796i	0.371993	−	0.928235i	$-0.378674\pi$
$233$	−6.31698	−	4.72883i	−0.413839	−	0.309796i	−0.785833	+	0.618439i	$0.787765\pi$
$234$	6.94104	−	3.16987i	0.453750	−	0.207221i
$235$	−2.46249	+	0.417663i	−0.160635	+	0.0272453i
$236$	0.790894	−	1.73182i	0.0514828	−	0.112732i
$237$	−1.31261	−	18.3527i	−0.0852633	−	1.19214i
$238$	2.64330	+	3.53104i	0.171340	+	0.228883i
$239$	−1.70779	−	5.81620i	−0.110468	−	0.376219i	0.885639	−	0.464374i	$-0.153721\pi$
$239$	−1.70779	−	5.81620i	−0.110468	−	0.376219i	−0.996107	+	0.0881559i	$0.971903\pi$
$240$	−1.08022	+	2.53241i	−0.0697276	+	0.163467i
$241$	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	$0.806739\pi$
$242$	0.925245	+	0.201275i	0.0594770	+	0.0129384i
$243$	13.6399	+	0.975542i	0.874997	+	0.0625810i
$244$	−3.12448	+	0.917429i	−0.200024	+	0.0587324i
$245$	5.65234	−	11.0021i	0.361115	−	0.702899i
$246$	−6.43963	+	7.43172i	−0.410576	+	0.473829i
$247$	−2.39123	−	6.41114i	−0.152151	−	0.407931i
$248$	0.0423972	−	0.0231506i	0.00269223	−	0.00147007i
$249$	3.17637	+	6.95528i	0.201294	+	0.440773i
$250$	0.750365	−	11.1551i	0.0474573	−	0.705512i
$251$	−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
$253$	−14.5671	−	4.36130i	−0.915826	−	0.274193i
$254$			12.9986i			0.815604i
$255$	−6.20606	−	7.86876i	−0.388638	−	0.492761i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−0.341693	+	0.916115i	−0.0213142	+	0.0571457i	−0.947171	−	0.320729i	$-0.896072\pi$
$257$	−0.341693	+	0.916115i	−0.0213142	+	0.0571457i	0.925857	+	0.377874i	$0.123345\pi$
$258$	6.98424	+	12.7907i	0.434820	+	0.796313i
$259$	7.67764	+	3.50626i	0.477065	+	0.217868i
$260$	−2.96014	+	11.1101i	−0.183580	+	0.689018i
$261$	0.0886484	−	0.616563i	0.00548720	−	0.0381643i
$262$	10.5630	+	5.76783i	0.652584	+	0.356338i
$263$	−0.485451	+	6.78749i	−0.0299342	+	0.418535i	0.960286	+	0.279019i	$0.0900092\pi$
$263$	−0.485451	+	6.78749i	−0.0299342	+	0.418535i	−0.990220	+	0.139516i	$0.955445\pi$
$264$	3.28418	−	2.11061i	0.202127	−	0.129899i
$265$	12.0411	−	19.8175i	0.739677	−	1.21738i
$266$	−1.05599	−	1.21868i	−0.0647468	−	0.0747218i
$267$	1.08062	−	1.97901i	0.0661330	−	0.121114i
$268$	−3.94051	+	2.94983i	−0.240705	+	0.180189i
$269$	−11.2785	−	9.77286i	−0.687661	−	0.595862i	0.239333	−	0.970938i	$-0.423071\pi$
$269$	−11.2785	−	9.77286i	−0.687661	−	0.595862i	−0.926994	+	0.375076i	$0.877617\pi$
$270$	−8.50658	+	8.94670i	−0.517694	+	0.544479i
$271$	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	$0.590162\pi$
$272$	3.41051	+	1.27205i	0.206792	+	0.0771296i
$273$	−4.59746	+	6.14149i	−0.278251	+	0.371700i
$274$	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	$-0.649393\pi$
$278$	−6.12614	+	1.33266i	−0.367422	+	0.0799277i
$279$	0.0709566	−	0.0102020i	0.00424806	−	0.000610779i
$280$	0.261368	+	2.69694i	0.0156197	+	0.161173i
$281$	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	$-0.0133736\pi$
$282$	−1.28859	+	0.480618i	−0.0767342	+	0.0286204i
$283$	−9.13376	+	0.653259i	−0.542946	+	0.0388322i	−0.340119	−	0.940382i	$-0.610467\pi$
$283$	−9.13376	+	0.653259i	−0.542946	+	0.0388322i	−0.202827	+	0.979215i	$0.565013\pi$
$284$	7.76072	+	1.11582i	0.460514	+	0.0662119i
$285$	2.46830	+	2.70754i	0.146210	+	0.160381i
$286$	12.3212	−	10.6764i	0.728568	−	0.631307i
$287$	−2.05717	+	9.45666i	−0.121431	+	0.558209i
$288$	0.315447	−	1.45009i	0.0185879	−	0.0854472i
$289$	2.83430	−	2.45593i	0.166724	−	0.144467i
$290$	0.632325	+	0.693612i	0.0371314	+	0.0407303i
$291$	3.27496	+	0.470868i	0.191981	+	0.0276028i
$292$	−11.8992	+	0.851046i	−0.696347	+	0.0498037i
$293$	−30.0821	+	11.2200i	−1.75742	+	0.655482i	−0.757419	+	0.652930i	$0.773540\pi$
$293$	−30.0821	+	11.2200i	−1.75742	+	0.655482i	−0.999997	+	0.00255239i	$0.999188\pi$
$294$	1.91885	−	6.53500i	0.111909	−	0.381129i
$295$	0.410651	+	4.23732i	0.0239090	+	0.246706i
$296$	6.89450	−	0.991280i	0.400735	−	0.0576170i
$297$	17.1051	−	3.72098i	0.992538	−	0.215913i
$298$	−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
$302$	−3.80475	+	5.08255i	−0.218939	+	0.292468i
$303$	−11.7031	−	4.36505i	−0.672328	−	0.250765i
$304$	−1.27684	−	0.374914i	−0.0732318	−	0.0215028i
$305$	5.01736	−	5.27695i	0.287293	−	0.302158i
$306$	4.08240	+	3.53742i	0.233375	+	0.202221i
$307$	15.0488	−	11.2654i	0.858882	−	0.642951i	−0.0763127	−	0.997084i	$-0.524315\pi$
$307$	15.0488	−	11.2654i	0.858882	−	0.642951i	0.935195	+	0.354133i	$0.115224\pi$
$308$	1.84131	−	3.37211i	0.104918	−	0.192144i
$309$	−9.07116	−	10.4687i	−0.516040	−	0.595542i
$310$	−0.0560884	+	0.0923118i	−0.00318561	+	0.00524296i
$311$	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	$0.0623130\pi$
$312$	−0.451650	+	6.31489i	−0.0255697	+	0.357510i
$313$	−4.97042	−	2.71406i	−0.280945	−	0.153407i	0.332599	−	0.943069i	$-0.392075\pi$
$313$	−4.97042	−	2.71406i	−0.280945	−	0.153407i	−0.613543	+	0.789661i	$0.710256\pi$
$314$	3.04163	−	21.1550i	0.171649	−	1.19385i
$315$	−1.03523	+	3.88546i	−0.0583286	+	0.218921i
$316$	−13.5933	−	6.20784i	−0.764682	−	0.349218i
$317$	4.16492	+	7.62748i	0.233925	+	0.428402i	0.968102	−	0.250556i	$-0.0806135\pi$
$317$	4.16492	+	7.62748i	0.233925	+	0.428402i	−0.734177	+	0.678958i	$0.762432\pi$
$318$	4.46216	−	11.9635i	0.250226	−	0.670881i
$319$	−0.189403	−	1.31733i	−0.0106045	−	0.0737561i
$320$	1.38473	+	1.75572i	0.0774085	+	0.0981475i
$321$		−	3.71574i		−	0.207392i
$322$	3.16774	−	4.87212i	0.176532	−	0.271513i
$323$	3.42517	−	3.42517i	0.190582	−	0.190582i
$324$	−1.26820	+	1.97336i	−0.0704555	+	0.109631i
$325$	−6.72420	−	24.8146i	−0.372992	−	1.37647i
$326$	−7.88005	−	17.2549i	−0.436436	−	0.955661i
$327$	19.3467	−	10.5641i	1.06987	−	0.584195i
$328$	2.79103	+	7.48305i	0.154109	+	0.413182i
$329$	−0.886365	+	1.02292i	−0.0488669	+	0.0563954i
$330$	−3.98909	+	7.76464i	−0.219592	+	0.427430i
$331$	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	$0.137731\pi$
$332$	6.19429	+	0.443024i	0.339956	+	0.0243141i
$333$	10.1004	+	2.19722i	0.553501	+	0.120407i
$334$	−3.42107	−	5.32329i	−0.187193	−	0.291278i
$335$	4.31847	−	10.1240i	0.235943	−	0.553136i
$336$	0.420341	+	1.43155i	0.0229315	+	0.0780975i
$337$	9.75289	+	13.0283i	0.531274	+	0.709699i	0.983236	−	0.182338i	$-0.0583667\pi$
$337$	9.75289	+	13.0283i	0.531274	+	0.709699i	−0.451962	+	0.892037i	$0.649276\pi$
$338$	0.958746	+	13.4050i	0.0521489	+	0.729137i
$339$	2.01127	−	4.40407i	0.109237	−	0.239196i
$340$	−8.02471	+	1.36107i	−0.435201	+	0.0738144i
$341$	0.139321	−	0.0636259i	0.00754467	−	0.00344554i
$342$	−1.58093	−	1.18347i	−0.0854869	−	0.0639947i
$343$	−3.22787	−	14.8383i	−0.174289	−	0.801192i
$344$	11.8361			0.638160
$345$	−6.91594	+	11.2476i	−0.372342	+	0.605553i
$346$	21.0364			1.13092
$347$	5.51954	+	25.3729i	0.296304	+	1.36209i	0.848862	+	0.528615i	$0.177288\pi$
$347$	5.51954	+	25.3729i	0.296304	+	1.36209i	−0.552558	+	0.833475i	$0.686348\pi$
$348$	0.413732	+	0.309716i	0.0221784	+	0.0166025i
$349$	−7.99964	+	3.65331i	−0.428211	+	0.195557i	−0.617849	−	0.786297i	$-0.711996\pi$
$349$	−7.99964	+	3.65331i	−0.428211	+	0.195557i	0.189638	+	0.981854i	$0.439268\pi$
$350$	−3.52836	−	4.92540i	−0.188599	−	0.263274i
$351$	−11.7929	+	25.8229i	−0.629460	+	1.37833i
$352$	−0.226193	−	3.16259i	−0.0120561	−	0.168566i
$353$	−3.54542	−	4.73613i	−0.188704	−	0.252079i	0.696205	−	0.717843i	$-0.254870\pi$
$353$	−3.54542	−	4.73613i	−0.188704	−	0.252079i	−0.884909	+	0.465764i	$0.845780\pi$
$354$	0.660423	+	2.24920i	0.0351011	+	0.119543i
$355$	−16.2669	+	6.53893i	−0.863356	+	0.347051i
$356$	−0.990084	−	1.54060i	−0.0524743	−	0.0816517i
$357$	−5.30674	−	1.15441i	−0.280862	−	0.0610979i
$358$	14.5311	+	1.03929i	0.767993	+	0.0549279i
$359$	12.6602	−	3.71736i	0.668178	−	0.196195i	0.0699863	−	0.997548i	$-0.477704\pi$
$359$	12.6602	−	3.71736i	0.668178	−	0.196195i	0.598191	+	0.801353i	$0.295886\pi$
$360$	1.01485	+	3.15933i	0.0534871	+	0.166512i
$361$	11.2827	−	13.0209i	0.593825	−	0.685311i
$362$	−8.31596	−	22.2959i	−0.437077	−	1.17185i
$363$	−1.02325	+	0.558737i	−0.0537067	+	0.0293261i
$364$	2.58835	+	5.66769i	0.135666	+	0.297068i
$365$	22.0700	−	14.9829i	1.15520	−	0.784241i
$366$	2.16767	−	3.37297i	0.113306	−	0.176308i
$367$	−19.3819	+	19.3819i	−1.01173	+	1.01173i	−0.0117981	+	0.999930i	$0.503756\pi$
$367$	−19.3819	+	19.3819i	−1.01173	+	1.01173i	−0.999930	+	0.0117981i	$0.996244\pi$
$368$	0.0254238	−	4.79576i	0.00132530	−	0.249996i
$369$			11.8521i			0.616998i
$370$	−12.2293	+	9.64516i	−0.635769	+	0.501428i
$371$	−1.78838	−	12.4384i	−0.0928479	−	0.645772i
$372$	−0.0207852	+	0.0557272i	−0.00107766	+	0.00288932i
$373$	−12.8328	−	23.5016i	−0.664459	−	1.21687i	−0.964788	−	0.263030i	$-0.915278\pi$
$373$	−12.8328	−	23.5016i	−0.664459	−	1.21687i	0.300329	−	0.953836i	$-0.402904\pi$
$374$	10.4983	+	4.79441i	0.542854	+	0.247913i
$375$	8.29618	+	10.9851i	0.428413	+	0.567270i
$376$	−0.158964	+	1.10562i	−0.00819793	+	0.0570179i
$377$	1.89429	+	1.03436i	0.0975609	+	0.0532723i
$378$	−0.477264	+	6.67303i	−0.0245478	+	0.343224i
$379$	−14.4150	+	9.26396i	−0.740449	+	0.475858i	−0.855696	−	0.517479i	$-0.826870\pi$
$379$	−14.4150	+	9.26396i	−0.740449	+	0.475858i	0.115247	+	0.993337i	$0.463234\pi$
$380$	2.89076	−	0.705614i	0.148293	−	0.0361972i
$381$	−10.4808	−	12.0955i	−0.536948	−	0.619671i
$382$	8.64325	−	15.8289i	0.442227	−	0.809879i
$383$	−6.31451	+	4.72698i	−0.322656	+	0.241538i	−0.748311	−	0.663348i	$-0.769135\pi$
$383$	−6.31451	+	4.72698i	−0.322656	+	0.241538i	0.425654	+	0.904886i	$0.360044\pi$
$384$	0.930523	+	0.806303i	0.0474856	+	0.0411465i
$385$	0.216573	+	8.58842i	0.0110376	+	0.437706i
$386$	0.565739	+	0.166116i	0.0287954	+	0.00845508i
$387$	16.4573	+	6.13827i	0.836573	+	0.312026i
$388$	1.61038	−	2.15121i	0.0817545	−	0.109211i
$389$	13.5196	+	8.68853i	0.685472	+	0.440526i	0.836473	−	0.548007i	$-0.184613\pi$
$389$	13.5196	+	8.68853i	0.685472	+	0.440526i	−0.151001	+	0.988534i	$0.548250\pi$
$390$	−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
$393$	−14.4797	+	3.14987i	−0.730406	+	0.158890i
$394$	−21.2481	+	3.05502i	−1.07047	+	0.153910i
$395$	33.2593	−	3.22326i	1.67346	−	0.162180i
$396$	1.32563	−	4.51468i	0.0666153	−	0.226871i
$397$	−14.6989	+	5.48239i	−0.737715	+	0.275153i	−0.690102	−	0.723713i	$-0.742434\pi$
$397$	−14.6989	+	5.48239i	−0.737715	+	0.275153i	−0.0476130	+	0.998866i	$0.515161\pi$
$398$	20.6400	−	1.47620i	1.03459	−	0.0739953i
$399$	1.96524	+	0.282560i	0.0983853	+	0.0141457i
$400$	−4.64707	−	1.84520i	−0.232353	−	0.0922600i
$401$	−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	$0.350404\pi$
$402$	1.28828	−	5.92213i	0.0642536	−	0.295369i
$403$	−0.0527981	+	0.242709i	−0.00263006	+	0.0120902i
$404$	−7.66681	+	6.64333i	−0.381438	+	0.330518i
$405$	0.242182	−	5.23963i	0.0120341	−	0.260359i
$406$	0.503453	+	0.0723856i	0.0249860	+	0.00359244i
$407$	22.0287	−	1.57552i	1.09192	−	0.0780957i
$408$	−4.19922	+	1.56623i	−0.207892	+	0.0775398i
$409$	−2.00025	+	6.81224i	−0.0989062	+	0.336844i	−0.994049	−	0.108937i	$-0.965255\pi$
$409$	−2.00025	+	6.81224i	−0.0989062	+	0.336844i	0.895143	+	0.445780i	$0.147074\pi$
$410$	−13.7872	−	11.3509i	−0.680899	−	0.560583i
$411$	−12.3386	+	1.77402i	−0.608619	+	0.0875062i
$412$	−10.9932	+	2.39142i	−0.541596	+	0.117817i
$413$	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
$417$	4.62599	−	6.17960i	0.226536	−	0.302616i
$418$	−3.95331	−	1.47451i	−0.193363	−	0.0721206i
$419$	−3.58100	−	1.05148i	−0.174943	−	0.0513680i	0.193088	−	0.981181i	$-0.438150\pi$
$419$	−3.58100	−	1.05148i	−0.174943	−	0.0513680i	−0.368031	+	0.929814i	$0.619968\pi$
$420$	−2.41776	−	2.29882i	−0.117975	−	0.112171i
$421$	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	$0.641268\pi$
$422$	−20.5329	+	15.3707i	−0.999524	+	0.748235i
$423$	−0.794408	+	1.45485i	−0.0386254	+	0.0707372i
$424$	−6.79113	−	7.83738i	−0.329807	−	0.380617i
$425$	14.0017	−	11.6274i	0.679180	−	0.564010i
$426$	−8.12122	+	5.21919i	−0.393474	+	0.252871i
$427$	0.281501	−	3.93589i	0.0136228	−	0.190471i
$428$	−2.64869	−	1.44629i	−0.128029	−	0.0699093i
$429$	−2.85676	+	19.8692i	−0.137926	+	0.959296i
$430$	−22.9018	+	13.2655i	−1.10442	+	0.639719i
$431$	−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	$0.685269\pi$
$432$	2.64592	+	4.84564i	0.127302	+	0.233136i
$433$	3.96952	−	10.6427i	0.190763	−	0.511455i	−0.805994	−	0.591923i	$-0.798369\pi$
$433$	3.96952	−	10.6427i	0.190763	−	0.511455i	0.996757	+	0.0804685i	$0.0256416\pi$
$434$	0.00833043	+	0.0579394i	0.000399873	+	0.00278118i
$435$	−1.14765	−	0.135576i	−0.0550258	−	0.00650038i
$436$		−	17.9028i		−	0.857389i
$437$	−5.79116	−	2.68193i	−0.277029	−	0.128294i
$438$	10.3863	−	10.3863i	0.496275	−	0.496275i
$439$	6.15393	−	9.57570i	0.293711	−	0.457023i	−0.662768	−	0.748825i	$-0.730618\pi$
$439$	6.15393	−	9.57570i	0.293711	−	0.457023i	0.956479	+	0.291802i	$0.0942547\pi$
$440$	3.98218	+	5.86582i	0.189843	+	0.279642i
$441$	−3.41013	−	7.46714i	−0.162387	−	0.355578i
$442$	−16.4272	+	8.96992i	−0.781361	+	0.426656i
$443$	7.39932	+	19.8383i	0.351552	+	0.942548i	0.985576	+	0.169234i	$0.0541294\pi$
$443$	7.39932	+	19.8383i	0.351552	+	0.942548i	−0.634024	+	0.773314i	$0.718598\pi$
$444$	−5.61622	+	6.48147i	−0.266534	+	0.307597i
$445$	3.64238	+	1.87127i	0.172665	+	0.0887069i
$446$	−7.43735	+	2.18380i	−0.352169	+	0.103406i
$447$	9.18295	+	0.656778i	0.434339	+	0.0310645i
$448$	1.18407	+	0.257578i	0.0559418	+	0.0121694i
$449$	16.3926	+	25.5074i	0.773616	+	1.20377i	0.974551	+	0.224165i	$0.0719655\pi$
$449$	16.3926	+	25.5074i	0.773616	+	1.20377i	−0.200935	+	0.979605i	$0.564398\pi$
$450$	−5.50451	−	4.97563i	−0.259485	−	0.234553i
$451$	7.13427	+	24.2971i	0.335940	+	1.14411i
$452$	−2.35650	−	3.14792i	−0.110840	−	0.148066i
$453$	−0.557668	−	7.79722i	−0.0262015	−	0.366345i
$454$	−1.24941	+	2.73582i	−0.0586376	+	0.128399i
$455$	−11.3604	−	8.06555i	−0.532583	−	0.378119i
$456$	1.49042	−	0.680654i	0.0697955	−	0.0318745i
$457$	−3.37593	−	2.52719i	−0.157919	−	0.118217i	0.517396	−	0.855746i	$-0.326901\pi$
$457$	−3.37593	−	2.52719i	−0.157919	−	0.118217i	−0.675315	+	0.737529i	$0.735992\pi$
$458$	1.87542	+	8.62118i	0.0876327	+	0.402841i
$459$	−20.0964			−0.938019
$460$	5.32574	+	9.30787i	0.248314	+	0.433982i
$461$	−34.8411			−1.62271			−0.811355	−	0.584554i	$-0.801269\pi$
$461$	−34.8411			−1.62271			−0.811355	+	0.584554i	$0.801269\pi$
$462$	1.00556	+	4.62248i	0.0467829	+	0.215057i
$463$	26.5222	+	19.8543i	1.23259	+	0.922706i	0.998770	−	0.0495744i	$-0.0157865\pi$
$463$	26.5222	+	19.8543i	1.23259	+	0.922706i	0.233820	+	0.972280i	$0.424877\pi$
$464$	0.381814	−	0.174369i	0.0177253	−	0.00809486i
$465$	−0.0222397	−	0.131123i	−0.00103134	−	0.00608066i
$466$	3.27799	−	7.17780i	0.151850	−	0.332505i
$467$	−1.67331	−	23.3960i	−0.0774317	−	1.08264i	−0.876502	−	0.481399i	$-0.840129\pi$
$467$	−1.67331	−	23.3960i	−0.0774317	−	1.08264i	0.799070	−	0.601238i	$-0.205326\pi$
$468$	4.57285	+	6.10861i	0.211380	+	0.282371i
$469$	−1.68043	−	5.72303i	−0.0775952	−	0.264265i
$470$	−0.931558	−	2.31743i	−0.0429696	−	0.106895i
$471$	14.2270	+	22.1377i	0.655548	+	1.02005i
$472$	1.86036	+	0.404696i	0.0856298	+	0.0186276i
$473$	37.4327	+	2.67724i	1.72116	+	0.123100i
$474$	17.6543	−	5.18376i	0.810887	−	0.238098i
$475$	−4.80254	+	4.60517i	−0.220356	+	0.211300i
$476$	−2.88847	+	3.33347i	−0.132393	+	0.152789i
$477$	−5.37812	−	14.4193i	−0.246247	−	0.660214i
$478$	5.32026	−	2.90508i	0.243343	−	0.132875i
$479$	3.27451	+	7.17018i	0.149616	+	0.327614i	0.969569	−	0.244817i	$-0.0787278\pi$
$479$	3.27451	+	7.17018i	0.149616	+	0.327614i	−0.819953	+	0.572431i	$0.806001\pi$
$480$	−2.70416	−	0.517226i	−0.123427	−	0.0236080i
$481$	−19.3633	+	30.1299i	−0.882891	+	1.37380i
$482$	−0.789068	+	0.789068i	−0.0359411	+	0.0359411i
$483$	0.980748	+	7.08779i	0.0446256	+	0.322506i
$484$			0.946884i			0.0430402i
$485$	−0.704931	+	5.96726i	−0.0320093	+	0.270959i
$486$	1.94611	+	13.5355i	0.0882774	+	0.613983i
$487$	−4.88996	+	13.1105i	−0.221585	+	0.594093i	−0.999408	−	0.0343902i	$-0.989051\pi$
$487$	−4.88996	+	13.1105i	−0.221585	+	0.594093i	0.777823	+	0.628483i	$0.216324\pi$
$488$	−1.56062	−	2.85806i	−0.0706459	−	0.129378i
$489$	21.2453	+	9.70238i	0.960744	+	0.438757i
$490$	11.9522	+	3.18450i	0.539944	+	0.143861i
$491$	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	$-0.172883\pi$
$492$	−8.63073	−	4.71273i	−0.389103	−	0.212466i
$493$	−0.108998	+	1.52399i	−0.00490901	+	0.0686369i
$494$	5.75634	−	3.69937i	0.258990	−	0.166443i
$495$	2.49492	+	10.2212i	0.112138	+	0.459410i
$496$	0.0316337	+	0.0365073i	0.00142040	+	0.00163923i
$497$	−4.55326	+	8.33867i	−0.204241	+	0.374040i
$498$	−6.12114	+	4.58223i	−0.274295	+	0.205335i
$499$	−30.1269	−	26.1051i	−1.34867	−	1.16863i	−0.970003	−	0.243092i	$-0.921838\pi$
$499$	−30.1269	−	26.1051i	−1.34867	−	1.16863i	−0.378664	−	0.925534i	$-0.623616\pi$
$500$	11.0597	−	1.63798i	0.494605	−	0.0732525i
$501$	7.47557	+	2.19503i	0.333984	+	0.0980665i
$502$	−25.7483	−	9.60360i	−1.14920	−	0.428630i
$503$	−1.93772	+	2.58849i	−0.0863985	+	0.115415i	−0.841658	−	0.540011i	$-0.818420\pi$
$503$	−1.93772	+	2.58849i	−0.0863985	+	0.115415i	0.755259	+	0.655426i	$0.227511\pi$
$504$	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
$508$	−12.7015	+	2.76305i	−0.563539	+	0.122590i
$509$	−36.6949	+	5.27593i	−1.62647	+	0.233851i	−0.894365	−	0.447338i	$-0.852372\pi$
$509$	−36.6949	+	5.27593i	−1.62647	+	0.233851i	−0.732107	+	0.681190i	$0.761463\pi$
$510$	6.36974	−	7.73685i	0.282057	−	0.342594i
$511$	4.07266	−	13.8702i	0.180164	−	0.613581i
$512$	0.936950	−	0.349464i	0.0414077	−	0.0154443i
$513$	7.32828	−	0.524129i	0.323551	−	0.0231408i
$514$	−0.967811	−	0.139150i	−0.0426883	−	0.00613766i
$515$	18.5906	−	16.9480i	0.819202	−	0.746818i
$516$	−11.0138	+	9.54348i	−0.484854	+	0.420128i
$517$	−0.752819	+	3.46065i	−0.0331090	+	0.152199i
$518$	−1.79413	+	8.24749i	−0.0788296	+	0.362374i
$519$	−19.5748	+	16.9617i	−0.859239	+	0.744535i
$520$	−11.4854	−	0.530869i	−0.503668	−	0.0232802i
$521$	−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	$0.677944\pi$
$522$	0.621316	−	0.0444374i	0.0271943	−	0.00194497i
$523$	28.2794	−	10.5477i	1.23657	−	0.461217i	0.355712	−	0.934596i	$-0.384239\pi$
$523$	28.2794	−	10.5477i	1.23657	−	0.461217i	0.880859	+	0.473379i	$0.156966\pi$
$524$	−3.39069	+	11.5476i	−0.148123	+	0.504461i
$525$	7.25459	+	1.73827i	0.316616	+	0.0758645i
$526$	−6.73556	+	0.968428i	−0.293685	+	0.0422255i
$527$	−0.171816	+	0.0373763i	−0.00748443	+	0.00162814i
$528$	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
$532$	0.966359	−	1.29090i	0.0418970	−	0.0559678i
$533$	−38.4772	−	14.3512i	−1.66663	−	0.621621i
$534$	2.16349	+	0.635257i	0.0936233	+	0.0274903i
$535$	6.74594	−	0.170111i	0.291652	−	0.00735455i
$536$	−3.72003	−	3.22343i	−0.160681	−	0.139231i
$537$	−14.3595	+	10.7494i	−0.619659	+	0.463871i
$538$	7.15211	−	13.0981i	0.308349	−	0.564699i
$539$	−11.4856	−	13.2551i	−0.494720	−	0.570937i
$540$	−10.5504	−	6.41042i	−0.454019	−	0.275861i
$541$	−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	$0.527579\pi$
$542$	−0.00550910	+	0.0770272i	−0.000236636	+	0.00330860i
$543$	25.7155	+	14.0417i	1.10356	+	0.602588i
$544$	−0.518028	+	3.60296i	−0.0222103	+	0.154476i
$545$	20.0649	+	34.6404i	0.859485	+	1.48383i
$546$	−6.97839	−	3.18693i	−0.298648	−	0.136388i
$547$	13.5791	+	24.8682i	0.580599	+	1.06329i	0.988637	+	0.150323i	$0.0480314\pi$
$547$	13.5791	+	24.8682i	0.580599	+	1.06329i	−0.408038	+	0.912965i	$0.633787\pi$
$548$	−3.53804	+	9.48585i	−0.151138	+	0.405215i
$549$	−0.687734	−	4.78329i	−0.0293518	−	0.204146i
$550$	−14.2794	−	6.88674i	−0.608875	−	0.293652i
$551$		−	0.558574i		−	0.0237961i
$552$	3.84318	+	4.48307i	0.163577	+	0.190812i
$553$	12.8044	−	12.8044i	0.544499	−	0.544499i
$554$	17.1047	−	26.6154i	0.726708	−	1.13078i
$555$	3.60269	−	18.8355i	0.152925	−	0.799524i
$556$	−2.60441	−	5.70286i	−0.110452	−	0.241855i
$557$	−6.33715	+	3.46034i	−0.268513	+	0.146619i	−0.607866	−	0.794040i	$-0.707974\pi$
$557$	−6.33715	+	3.46034i	−0.268513	+	0.146619i	0.339352	+	0.940659i	$0.389792\pi$
$558$	0.0250518	+	0.0671664i	0.00106053	+	0.00284338i
$559$	−39.8549	+	45.9951i	−1.68568	+	1.94538i
$560$	−2.57975	+	0.828670i	−0.109014	+	0.0350177i
$561$	−13.6347	+	4.00350i	−0.575656	+	0.169028i
$562$	10.7607	+	0.769620i	0.453913	+	0.0324645i
$563$	18.7637	+	4.08178i	0.790794	+	0.172027i	0.589782	−	0.807562i	$-0.299214\pi$
$563$	18.7637	+	4.08178i	0.790794	+	0.172027i	0.201011	+	0.979589i	$0.435577\pi$
$564$	−0.743543	−	1.15698i	−0.0313088	−	0.0487175i
$565$	8.08770	+	3.44985i	0.340252	+	0.145136i
$566$	−2.57985	−	8.78616i	−0.108439	−	0.369310i
$567$	−1.70342	−	2.27551i	−0.0715371	−	0.0955623i
$568$	0.559337	+	7.82055i	0.0234692	+	0.328143i
$569$	−16.3752	+	35.8566i	−0.686483	+	1.50319i	0.169142	+	0.985592i	$0.445900\pi$
$569$	−16.3752	+	35.8566i	−0.686483	+	1.50319i	−0.855625	+	0.517597i	$0.826827\pi$
$570$	−2.12098	+	2.98742i	−0.0888383	+	0.125129i
$571$	−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	$0.540157\pi$
$572$	13.0514	+	9.77019i	0.545708	+	0.408512i
$573$	4.72017	+	21.6983i	0.197188	+	0.906458i
$574$	−9.67783			−0.403945
$575$	−20.7368	−	12.0410i	−0.864784	−	0.502145i
$576$	1.48400			0.0618334
$577$	−4.71276	−	21.6642i	−0.196195	−	0.901894i	−0.964967	−	0.262371i	$-0.915496\pi$
$577$	−4.71276	−	21.6642i	−0.196195	−	0.901894i	0.768772	−	0.639523i	$-0.220868\pi$
$578$	3.00228	+	2.24748i	0.124879	+	0.0934829i
$579$	−0.660373	+	0.301582i	−0.0274442	+	0.0125333i
$580$	−0.543350	+	0.765313i	−0.0225614	+	0.0317779i
$581$	−3.12606	+	6.84512i	−0.129691	+	0.283983i
$582$	0.236035	+	3.30020i	0.00978398	+	0.136798i
$583$	−19.7048	−	26.3225i	−0.816089	−	1.09017i
$584$	−3.36095	−	11.4463i	−0.139077	−	0.473653i
$585$	−15.6944	−	6.69453i	−0.648883	−	0.276785i
$586$	−17.3580	−	27.0096i	−0.717054	−	1.11576i
$587$	33.3220	+	7.24877i	1.37535	+	0.299189i	0.838689	−	0.544611i	$-0.183323\pi$
$587$	33.3220	+	7.24877i	1.37535	+	0.299189i	0.536659	+	0.843799i	$0.319686\pi$
$588$	6.79353	+	0.485883i	0.280161	+	0.0200375i
$589$	0.0616791	−	0.0181106i	0.00254144	−	0.000746235i
$590$	−4.05319	+	1.30197i	−0.166867	+	0.0536014i
$591$	17.3086	−	19.9752i	0.711981	−	0.821670i
$592$	2.43416	+	6.52623i	0.100043	+	0.268226i
$593$	−0.634590	+	0.346512i	−0.0260595	+	0.0142296i	−0.492226	−	0.870467i	$-0.663817\pi$
$593$	−0.634590	+	0.346512i	−0.0260595	+	0.0142296i	0.466166	+	0.884697i	$0.345635\pi$
$594$	7.27190	+	15.9232i	0.298370	+	0.653338i
$595$	1.85289	−	9.68727i	0.0759611	−	0.397139i
$596$	4.04250	−	6.29025i	0.165587	−	0.257659i
$597$	−18.0157	+	18.0157i	−0.737335	+	0.737335i
$598$	18.5507	+	16.2473i	0.758595	+	0.664400i
$599$		−	32.4930i		−	1.32763i	−0.747898	−	0.663814i	$-0.768937\pi$
$599$		−	32.4930i		−	1.32763i	0.747898	−	0.663814i	$-0.231063\pi$
$600$	5.81200	−	2.02994i	0.237274	−	0.0828721i
$601$	−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	$-0.356356\pi$
$602$	−5.01218	+	13.4382i	−0.204281	+	0.547700i
$603$	−3.50078	−	6.41119i	−0.142563	−	0.261084i
$604$	−5.77516	−	2.63743i	−0.234988	−	0.107315i
$605$	−1.06124	−	1.83214i	−0.0431454	−	0.0744870i
$606$	1.77761	−	12.3635i	0.0722104	−	0.502235i
$607$	−19.0862	−	10.4219i	−0.774685	−	0.423010i	0.0427098	−	0.999088i	$-0.486401\pi$
$607$	−19.0862	−	10.4219i	−0.774685	−	0.423010i	−0.817395	+	0.576077i	$0.804583\pi$
$608$	0.0949342	−	1.32735i	0.00385009	−	0.0538313i
$609$	−0.526840	+	0.338579i	−0.0213486	+	0.0137199i
$610$	6.22288	+	3.78100i	0.251957	+	0.153088i
$611$	−3.76116	−	4.34061i	−0.152160	−	0.175602i
$612$	−2.58880	+	4.74103i	−0.104646	+	0.191645i
$613$	−2.23712	+	1.67469i	−0.0903563	+	0.0676399i	−0.643501	−	0.765445i	$-0.722519\pi$
$613$	−2.23712	+	1.67469i	−0.0903563	+	0.0676399i	0.553144	+	0.833085i	$0.313428\pi$
$614$	14.2068	+	12.3103i	0.573341	+	0.496803i
$615$	21.9816	−	0.554305i	0.886382	−	0.0223517i
$616$	3.68645	+	1.08244i	0.148531	+	0.0436127i
$617$	3.91125	+	1.45882i	0.157461	+	0.0587300i	0.426959	−	0.904271i	$-0.359585\pi$
$617$	3.91125	+	1.45882i	0.157461	+	0.0587300i	−0.269498	+	0.963001i	$0.586858\pi$
$618$	8.30122	−	11.0891i	0.333924	−	0.446070i
$619$	−1.24522	−	0.800257i	−0.0500498	−	0.0321650i	0.515377	−	0.856964i	$-0.327652\pi$
$619$	−1.24522	−	0.800257i	−0.0500498	−	0.0321650i	−0.565426	+	0.824799i	$0.691288\pi$
$620$	−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
$623$	2.16840	−	0.471706i	0.0868750	−	0.0188985i
$624$	−6.26658	+	0.900999i	−0.250864	+	0.0360688i
$625$	−19.5638	+	15.5647i	−0.782550	+	0.622587i
$626$	1.59549	−	5.43375i	0.0637687	−	0.217176i
$627$	4.86755	−	1.81550i	0.194391	−	0.0725042i
$628$	21.3181	−	1.52470i	0.850685	−	0.0608422i
$629$	−25.0961	−	3.60827i	−1.00065	−	0.143871i
$630$	−4.01672	−	0.185658i	−0.160030	−	0.00739678i
$631$	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	$0.198875\pi$
$632$	3.17652	−	14.6022i	0.126355	−	0.580844i
$633$	6.71286	−	30.8585i	0.266812	−	1.22652i
$634$	−6.56785	+	5.69108i	−0.260843	+	0.226021i
$635$	21.4796	−	19.5817i	0.852392	−	0.777076i
$636$	12.6386	+	1.81716i	0.501154	+	0.0720550i
$637$	28.3708	−	2.02912i	1.12409	−	0.0803965i
$638$	1.24696	−	0.465093i	0.0493677	−	0.0184132i
$639$	−3.27806	+	11.1640i	−0.129678	+	0.441642i
$640$	−1.42125	+	1.72628i	−0.0561797	+	0.0682374i
$641$	−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	$0.481435\pi$
$642$	3.63082	−	0.789837i	0.143297	−	0.0311724i
$643$	−7.60531	−	7.60531i	−0.299924	−	0.299924i	0.541060	−	0.840984i	$-0.318023\pi$
$643$	−7.60531	−	7.60531i	−0.299924	−	0.299924i	−0.840984	+	0.541060i	$0.818023\pi$
$644$	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
$647$	−26.5562	+	35.4749i	−1.04403	+	1.39466i	−0.128832	+	0.991666i	$0.541123\pi$
$647$	−26.5562	+	35.4749i	−1.04403	+	1.39466i	−0.915201	+	0.402998i	$0.867968\pi$
$648$	−2.19784	−	0.819750i	−0.0863391	−	0.0322028i
$649$	5.79199	+	1.70068i	0.227356	+	0.0667577i
$650$	22.8182	−	11.8453i	0.895004	−	0.464610i
$651$	−0.0544684	−	0.0471971i	−0.00213478	−	0.00184980i
$652$	15.1856	−	11.3678i	0.594712	−	0.445196i
$653$	−12.5687	+	23.0179i	−0.491853	+	0.900761i	0.507385	+	0.861720i	$0.330612\pi$
$653$	−12.5687	+	23.0179i	−0.491853	+	0.900761i	−0.999238	+	0.0390414i	$0.987570\pi$
$654$	14.4351	+	16.6590i	0.564457	+	0.651418i
$655$	−6.38152	−	26.1438i	−0.249346	−	1.02152i
$656$	−6.71876	+	4.31789i	−0.262324	+	0.168585i
$657$	1.26295	−	17.6584i	0.0492725	−	0.688920i
$658$	−1.18795	−	0.648672i	−0.0463113	−	0.0252879i
$659$	4.18317	−	29.0946i	0.162953	−	1.13336i	−0.730077	−	0.683365i	$-0.760516\pi$
$659$	4.18317	−	29.0946i	0.162953	−	1.13336i	0.893030	−	0.449998i	$-0.148575\pi$
$660$	−8.43514	−	2.24743i	−0.328337	−	0.0874812i
$661$	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	$0.542338\pi$
$662$	13.1298	+	24.0455i	0.510306	+	0.934555i
$663$	8.05340	−	21.5920i	0.312768	−	0.838564i
$664$	0.883791	+	6.14690i	0.0342977	+	0.238546i
$665$	−0.423017	+	3.58085i	−0.0164039	+	0.138859i
$666$			10.3367i			0.400538i
$667$	1.93447	−	0.556889i	0.0749029	−	0.0215628i
$668$	4.47444	−	4.47444i	0.173121	−	0.173121i
$669$	5.15982	−	8.02884i	0.199490	−	0.310413i
$670$	10.8106	+	2.06776i	0.417651	+	0.0798844i
$671$	−4.28912	−	9.39186i	−0.165580	−	0.362569i
$672$	−1.30949	+	0.715033i	−0.0505145	+	0.0275830i
$673$	−7.72305	−	20.7063i	−0.297702	−	0.798169i	−0.996557	−	0.0829062i	$-0.973580\pi$
$673$	−7.72305	−	20.7063i	−0.297702	−	0.798169i	0.698856	−	0.715263i	$-0.253693\pi$
$674$	−10.6575	+	12.2994i	−0.410510	+	0.473754i
$675$	27.5988	+	0.579020i	1.06228	+	0.0222865i
$676$	−12.8949	+	3.78628i	−0.495957	+	0.145626i
$677$	38.5801	+	2.75930i	1.48275	+	0.106049i	0.789102	−	0.614262i	$-0.210546\pi$
$677$	38.5801	+	2.75930i	1.48275	+	0.106049i	0.693651	+	0.720311i	$0.256001\pi$
$678$	4.73095	+	1.02916i	0.181691	+	0.0395245i
$679$	1.76045	+	2.73932i	0.0675599	+	0.105125i
$680$	−3.03574	−	7.55200i	−0.116415	−	0.289606i
$681$	−1.04330	−	3.55315i	−0.0399793	−	0.136157i
$682$	0.0917867	+	0.122613i	0.00351470	+	0.00469508i
$683$	2.97437	+	41.5871i	0.113811	+	1.59129i	0.658457	+	0.752619i	$0.271210\pi$
$683$	2.97437	+	41.5871i	0.113811	+	1.59129i	−0.544646	+	0.838666i	$0.683336\pi$
$684$	0.820373	−	1.79637i	0.0313677	−	0.0686858i
$685$	−3.78563	−	22.3196i	−0.144641	−	0.852788i
$686$	13.8130	−	6.30821i	0.527385	−	0.240848i
$687$	−8.69641	−	6.51005i	−0.331789	−	0.248374i
$688$	2.51594	+	11.5656i	0.0959195	+	0.440935i
$689$	53.3234			2.03146
$690$	−12.4607	−	4.36703i	−0.474370	−	0.166250i
$691$	15.4014			0.585897			0.292949	−	0.956128i	$-0.405363\pi$
$691$	15.4014			0.585897			0.292949	+	0.956128i	$0.405363\pi$
$692$	4.47160	+	20.5556i	0.169985	+	0.781407i
$693$	4.56441	+	3.41687i	0.173387	+	0.129796i
$694$	−23.6198	+	10.7868i	−0.896595	+	0.409461i
$695$	11.4309	+	8.11560i	0.433598	+	0.307842i
$696$	−0.214693	+	0.470112i	−0.00813792	+	0.0178196i
$697$	−2.07393	−	28.9973i	−0.0785555	−	1.09835i
$698$	−5.27027	−	7.04025i	−0.199483	−	0.266478i
$699$	2.73724	+	9.32217i	0.103532	+	0.352597i
$700$	4.06283	−	4.49470i	0.153561	−	0.169884i
$701$	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	$0.507738\pi$
$702$	−27.7396	−	6.03437i	−1.04696	−	0.227753i
$703$	9.24555	+	0.661255i	0.348702	+	0.0249397i
$704$	3.04223	−	0.893280i	0.114658	−	0.0336667i
$705$	2.73539	+	1.40531i	0.103021	+	0.0529270i
$706$	3.87426	−	4.47114i	0.145810	−	0.168273i
$707$	−4.29591	−	11.5178i	−0.161564	−	0.433171i
$708$	−2.05741	+	1.12343i	−0.0773222	+	0.0422211i
$709$	9.59066	+	21.0006i	0.360185	+	0.788695i	0.999800	+	0.0199994i	$0.00636644\pi$
$709$	9.59066	+	21.0006i	0.360185	+	0.788695i	−0.639615	+	0.768695i	$0.720906\pi$
$710$	−9.84727	−	14.5052i	−0.369562	−	0.544370i
$711$	11.9895	−	18.6561i	0.449642	−	0.699657i
$712$	1.29494	−	1.29494i	0.0485298	−	0.0485298i
$713$	0.124214	+	0.195552i	0.00465185	+	0.00732350i
$714$		−	5.43085i		−	0.203244i
$715$	−36.2035	−	4.27683i	−1.35393	−	0.159945i
$716$	2.07327	+	14.4199i	0.0774819	+	0.538899i
$717$	−2.60825	+	6.99299i	−0.0974069	+	0.261158i
$718$	6.32352	+	11.5807i	0.235992	+	0.432186i
$719$	−21.9795	−	10.0377i	−0.819699	−	0.374344i	−0.0389906	−	0.999240i	$-0.512414\pi$
$719$	−21.9795	−	10.0377i	−0.819699	−	0.374344i	−0.780708	+	0.624896i	$0.785142\pi$
$720$	−2.87141	+	1.66322i	−0.107011	+	0.0619845i
$721$	1.94013	−	13.4939i	0.0722541	−	0.502538i
$722$	15.1216	+	8.25704i	0.562769	+	0.307295i
$723$	0.0980182	−	1.37047i	0.00364534	−	0.0509685i
$724$	20.0187	−	12.8653i	0.743990	−	0.478134i
$725$	0.193598	−	2.08978i	0.00719005	−	0.0776125i
$726$	−0.763476	−	0.881098i	−0.0283352	−	0.0327006i
$727$	−1.24735	+	2.28435i	−0.0462617	+	0.0847220i	−0.899787	−	0.436329i	$-0.856278\pi$
$727$	−1.24735	+	2.28435i	−0.0462617	+	0.0847220i	0.853525	+	0.521051i	$0.174460\pi$
$728$	−4.98797	+	3.73395i	−0.184867	+	0.138389i
$729$	−18.0430	−	15.6343i	−0.668259	−	0.579049i
$730$	19.3318	+	18.3808i	0.715502	+	0.680305i
$731$	−41.3384	−	12.1380i	−1.52895	−	0.448941i
$732$	3.75665	+	1.40116i	0.138850	+	0.0517884i
$733$	3.30961	−	4.42112i	0.122243	−	0.163298i	−0.735245	−	0.677801i	$-0.762933\pi$
$733$	3.30961	−	4.42112i	0.122243	−	0.163298i	0.857488	+	0.514504i	$0.172024\pi$
$734$	−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
$738$	−11.5813	+	2.51935i	−0.426313	+	0.0927387i
$739$	43.0951	−	6.19614i	1.58528	−	0.227929i	0.707400	−	0.706813i	$-0.249868\pi$
$739$	43.0951	−	6.19614i	1.58528	−	0.227929i	0.877878	+	0.478885i	$0.158959\pi$
$740$	−12.0243	−	9.89955i	−0.442020	−	0.363915i
$741$	−2.37359	+	8.08370i	−0.0871960	+	0.296962i
$742$	11.7740	−	4.39149i	0.432238	−	0.161217i
$743$	−10.3375	+	0.739355i	−0.379247	+	0.0271243i	−0.259662	−	0.965700i	$-0.583611\pi$
$743$	−10.3375	+	0.739355i	−0.379247	+	0.0271243i	−0.119585	+	0.992824i	$0.538157\pi$
$744$	−0.0588719	−	0.00846449i	−0.00215835	−	0.000310323i
$745$	−0.771976	+	16.7018i	−0.0282830	+	0.611905i
$746$	20.2367	−	17.5352i	0.740918	−	0.642009i
$747$	−1.95896	+	9.00520i	−0.0716747	+	0.329483i
$748$	−2.45327	+	11.2775i	−0.0897005	+	0.412346i
$749$	2.76369	−	2.39475i	0.100983	−	0.0875023i
$750$	−8.97061	+	10.4416i	−0.327560	+	0.381275i
$751$	−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	$0.662988\pi$
$752$	−1.11414	+	0.0796849i	−0.0406285	+	0.00290581i
$753$	31.7028	−	11.8245i	1.15531	−	0.430909i
$754$	−0.608062	+	2.07087i	−0.0221443	+	0.0754166i
$755$	14.1304	−	1.36942i	0.514256	−	0.0498382i
$756$	−6.62198	+	0.952097i	−0.240839	+	0.0346274i
$757$	22.7140	−	4.94113i	0.825555	−	0.179589i	0.220110	−	0.975475i	$-0.429359\pi$
$757$	22.7140	−	4.94113i	0.825555	−	0.179589i	0.605446	+	0.795887i	$0.292995\pi$
$758$	−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	$0.592974\pi$
$762$	9.59122	−	12.8124i	0.347453	−	0.464143i
$763$	20.3261	+	7.58123i	0.735853	+	0.274459i
$764$	17.3045	+	5.08105i	0.626053	+	0.183826i
$765$	−0.304491	−	12.0749i	−0.0110089	−	0.436569i
$766$	−5.96120	−	5.16541i	−0.215387	−	0.186634i
$767$	−7.83690	+	5.86663i	−0.282974	+	0.211832i
$768$	−0.590080	+	1.08065i	−0.0212927	+	0.0389946i
$769$	−28.1303	−	32.4640i	−1.01440	−	1.17068i	−0.985252	−	0.171108i	$-0.945265\pi$
$769$	−28.1303	−	32.4640i	−1.01440	−	1.17068i	−0.0291508	−	0.999575i	$-0.509280\pi$
$770$	−8.34611	+	2.03722i	−0.300773	+	0.0734164i
$771$	1.01277	−	0.650867i	0.0364740	−	0.0234404i
$772$	−0.0420632	+	0.588121i	−0.00151389	+	0.0211669i
$773$	−15.9567	−	8.71304i	−0.573924	−	0.313386i	0.165947	−	0.986135i	$-0.446932\pi$
$773$	−15.9567	−	8.71304i	−0.573924	−	0.313386i	−0.739871	+	0.672748i	$0.765114\pi$
$774$	−2.49973	+	17.3860i	−0.0898510	+	0.624927i
$775$	0.237035	−	0.0463793i	0.00851457	−	0.00166599i
$776$	2.44436	+	1.11630i	0.0877474	+	0.0400729i
$777$	−4.98049	−	9.12109i	−0.178674	−	0.327217i
$778$	−5.61617	+	15.0575i	−0.201349	+	0.539839i
$779$	1.51254	+	10.5200i	0.0541924	+	0.376916i
$780$	11.1155	−	8.76673i	0.397998	−	0.313899i
$781$			24.8597i			0.889549i
$782$	−5.00690	+	16.7234i	−0.179046	+	0.598029i
$783$	−1.63865	+	1.63865i	−0.0585606	+	0.0585606i
$784$	2.99063	−	4.65351i	0.106808	−	0.166197i
$785$	−39.5398	+	26.8428i	−1.41124	+	0.958060i
$786$	−6.15578	−	13.4793i	−0.219569	−	0.480790i
$787$	−43.6549	+	23.8374i	−1.55613	+	0.849710i	−0.556303	+	0.830979i	$0.687781\pi$
$787$	−43.6549	+	23.8374i	−1.55613	+	0.849710i	−0.999825	+	0.0187306i	$0.994038\pi$
$788$	−7.50182	−	20.1131i	−0.267241	−	0.716501i
$789$	5.48675	−	6.33205i	0.195334	−	0.225427i
$790$	10.2194	+	31.8141i	0.363589	+	1.13190i
$791$	4.57190	−	1.34243i	0.162558	−	0.0477314i
$792$	4.69328	+	0.335670i	0.166769	+	0.0119275i
$793$	16.3614	+	3.55920i	0.581010	+	0.126391i
$794$	−8.48157	−	13.1976i	−0.301000	−	0.468364i
$795$	−26.4912	+	10.6489i	−0.939546	+	0.377677i
$796$	5.82981	+	19.8545i	0.206632	+	0.703725i
$797$	−3.27287	−	4.37205i	−0.115931	−	0.154866i	0.738822	−	0.673901i	$-0.235382\pi$
$797$	−3.27287	−	4.37205i	−0.115931	−	0.154866i	−0.854753	+	0.519035i	$0.826292\pi$
$798$	0.141641	+	1.98039i	0.00501402	+	0.0701052i
$799$	1.68901	−	3.69842i	0.0597530	−	0.130841i
$800$	0.815227	−	4.93309i	0.0288226	−	0.174411i
$801$	2.47208	−	1.12896i	0.0873468	−	0.0398900i
$802$	−7.74653	−	5.79898i	−0.273539	−	0.204769i
$803$	−8.04021	−	36.9603i	−0.283733	−	1.30430i
$804$	6.06063			0.213742
$805$	−12.8230	+	2.10504i	−0.451952	+	0.0741930i
$806$	−0.248385			−0.00874900
$807$	3.90584	+	17.9549i	0.137492	+	0.632041i
$808$	−8.12121	−	6.07946i	−0.285703	−	0.213875i
$809$	−8.94018	+	4.08284i	−0.314320	+	0.143545i	−0.566328	−	0.824180i	$-0.691636\pi$
$809$	−8.94018	+	4.08284i	−0.314320	+	0.143545i	0.252008	+	0.967725i	$0.418909\pi$
$810$	5.17136	−	0.877116i	0.181703	−	0.0308187i
$811$	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	$0.0473155\pi$
$812$	0.0362853	+	0.507334i	0.00127336	+	0.0178039i
$813$	−0.0569810	−	0.0761176i	−0.00199841	−	0.00266956i
$814$	6.22205	+	21.1904i	0.218083	+	0.742721i
$815$	−16.6421	+	39.0151i	−0.582947	+	1.36664i
$816$	−2.42304	−	3.77033i	−0.0848234	−	0.131988i
$817$	15.3909	+	3.34808i	0.538458	+	0.117134i
$818$	−7.08174	−	0.506496i	−0.247607	−	0.0177092i
$819$	−8.87190	+	2.60502i	−0.310009	+	0.0910269i
$820$	8.16087	−	15.8849i	0.284990	−	0.554724i
$821$	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	$-0.0497200\pi$
$822$	−4.35624	−	11.6795i	−0.151941	−	0.407371i
$823$	−34.7538	+	18.9770i	−1.21144	+	0.661497i	−0.952542	−	0.304407i	$-0.901542\pi$
$823$	−34.7538	+	18.9770i	−1.21144	+	0.661497i	−0.258900	+	0.965904i	$0.583360\pi$
$824$	−4.67355	−	10.2336i	−0.162811	−	0.356506i
$825$	18.8401	−	5.10524i	0.655928	−	0.177742i
$826$	−1.24727	+	1.94079i	−0.0433981	+	0.0675287i
$827$	4.83634	−	4.83634i	0.168176	−	0.168176i	−0.618001	−	0.786177i	$-0.712057\pi$
$827$	4.83634	−	4.83634i	0.168176	−	0.168176i	0.786177	+	0.618001i	$0.212057\pi$
$828$	7.03911	+	1.05019i	0.244626	+	0.0364966i
$829$			39.2405i			1.36288i	0.731875	+	0.681439i	$0.238646\pi$
$829$			39.2405i			1.36288i	−0.731875	+	0.681439i	$0.761354\pi$
$830$	−8.59929	−	10.9032i	−0.298486	−	0.378455i
$831$	5.54378	+	38.5578i	0.192312	+	1.33756i
$832$	−1.79691	+	4.81771i	−0.0622968	+	0.167024i
$833$	9.64980	+	17.6723i	0.334346	+	0.612308i
$834$	7.02170	+	3.20670i	0.243142	+	0.111039i
$835$	−3.64284	+	13.6724i	−0.126066	+	0.473154i
$836$	0.600475	−	4.17640i	0.0207679	−	0.144444i
$837$	−0.234074	−	0.127814i	−0.00809077	−	0.00441789i
$838$	0.266251	−	3.72267i	0.00919747	−	0.128597i
$839$	−20.7248	+	13.3190i	−0.715498	+	0.459823i	−0.847068	−	0.531484i	$-0.821634\pi$
$839$	−20.7248	+	13.3190i	−0.715498	+	0.459823i	0.131570	+	0.991307i	$0.457998\pi$
$840$	1.73235	−	2.85115i	0.0597719	−	0.0983742i
$841$	−18.8756	−	21.7836i	−0.650882	−	0.751158i
$842$	−5.24938	+	9.61353i	−0.180906	+	0.331304i
$843$	−10.6336	+	7.96023i	−0.366242	+	0.274165i
$844$	−19.3840	−	16.7963i	−0.667226	−	0.578154i
$845$	20.7069	−	21.7782i	0.712339	−	0.749194i
$846$	−1.59047	−	0.467003i	−0.0546813	−	0.0160559i
$847$	−1.07505	−	0.400973i	−0.0369392	−	0.0137776i
$848$	6.21472	−	8.30189i	0.213414	−	0.285088i
$849$	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
$853$	30.9069	−	6.72339i	1.05823	−	0.230204i	0.350411	−	0.936596i	$-0.386042\pi$
$853$	30.9069	−	6.72339i	1.05823	−	0.230204i	0.707821	+	0.706392i	$0.249678\pi$
$854$	3.90578	−	0.561567i	0.133653	−	0.0192164i
$855$	0.425957	+	4.39525i	0.0145674	+	0.150315i
$856$	0.850223	−	2.89559i	0.0290600	−	0.0989693i
$857$	−28.3994	+	10.5924i	−0.970104	+	0.361830i	−0.784042	−	0.620708i	$-0.786845\pi$
$857$	−28.3994	+	10.5924i	−0.970104	+	0.361830i	−0.186062	+	0.982538i	$0.559573\pi$
$858$	−20.0224	+	1.43203i	−0.683554	+	0.0488887i
$859$	−26.5495	−	3.81725i	−0.905858	−	0.130243i	−0.326388	−	0.945236i	$-0.605831\pi$
$859$	−26.5495	−	3.81725i	−0.905858	−	0.130243i	−0.579470	+	0.814993i	$0.696741\pi$
$860$	−17.8305	−	19.5586i	−0.608014	−	0.666944i
$861$	9.00545	−	7.80327i	0.306905	−	0.265935i
$862$	1.35070	−	6.20905i	0.0460049	−	0.211481i
$863$	−10.6380	+	48.9019i	−0.362120	+	1.66464i	0.330858	+	0.943681i	$0.392662\pi$
$863$	−10.6380	+	48.9019i	−0.362120	+	1.66464i	−0.692978	+	0.720959i	$0.743702\pi$
$864$	−4.17247	+	3.61546i	−0.141950	+	0.123001i
$865$	−31.6902	−	34.7617i	−1.07750	−	1.18193i
$866$	11.2432	+	1.61653i	0.382061	+	0.0549321i
$867$	−4.60585	+	0.329417i	−0.156423	+	0.0111876i
$868$	−0.0548446	+	0.0204560i	−0.00186155	+	0.000694321i
$869$	13.3489	−	45.4622i	0.452831	−	1.54220i
$870$	−0.111474	−	1.15025i	−0.00377932	−	0.0389970i
$871$	25.0524	−	3.60200i	0.848870	−	0.122049i
$872$	17.4937	−	3.80552i	0.592411	−	0.128871i
$873$	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
$877$	4.11061	−	5.49114i	0.138806	−	0.185423i	−0.725752	−	0.687957i	$-0.758508\pi$
$877$	4.11061	−	5.49114i	0.138806	−	0.185423i	0.864557	+	0.502534i	$0.167599\pi$
$878$	10.6650	+	3.97783i	0.359926	+	0.134245i
$879$	37.9300	+	11.1373i	1.27935	+	0.375650i
$880$	−4.88529	+	5.13805i	−0.164683	+	0.173204i
$881$	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	$0.643019\pi$
$882$	6.57162	−	4.91945i	0.221278	−	0.165647i
$883$	−3.56265	+	6.52451i	−0.119893	+	0.219567i	−0.930732	−	0.365701i	$-0.880829\pi$
$883$	−3.56265	+	6.52451i	−0.119893	+	0.219567i	0.810839	+	0.585269i	$0.199011\pi$
$884$	−12.2568	−	14.1451i	−0.412240	−	0.475750i
$885$	2.72180	−	4.47962i	0.0914925	−	0.150581i
$886$	−17.8121	+	11.4472i	−0.598410	+	0.384575i
$887$	3.52211	−	49.2455i	0.118261	−	1.65350i	−0.498895	−	0.866662i	$-0.666261\pi$
$887$	3.52211	−	49.2455i	0.118261	−	1.65350i	0.617156	−	0.786841i	$-0.288285\pi$
$888$	−7.52716	−	4.11014i	−0.252595	−	0.137927i
$889$	2.24162	−	15.5908i	0.0751816	−	0.522899i
$890$	−1.05427	+	3.95691i	−0.0353391	+	0.132636i
$891$	−6.76542	−	3.08966i	−0.226650	−	0.103508i
$892$	−3.71482	−	6.80319i	−0.124381	−	0.227787i
$893$	−0.519452	+	1.39270i	−0.0173828	+	0.0466051i
$894$	1.31021	+	9.11270i	0.0438199	+	0.304774i
$895$	−20.1730	−	25.5777i	−0.674309	−	0.854967i
$896$			1.21176i			0.0404820i
$897$	−30.3621	−	0.160958i	−1.01376	−	0.00537424i
$898$	−21.4400	+	21.4400i	−0.715462	+	0.715462i
$899$	−0.0109622	+	0.0170575i	−0.000365609	+	0.000568899i
$900$	3.69185	−	6.43636i	0.123062	−	0.214545i
$901$	15.6812	+	34.3370i	0.522415	+	1.14393i
$902$	−22.2253	+	12.1360i	−0.740023	+	0.404083i
$903$	−6.17130	−	16.5459i	−0.205368	−	0.550613i
$904$	2.57507	−	2.97178i	0.0856454	−	0.0988401i
$905$	−24.3155	+	47.3295i	−0.808276	+	1.57328i
$906$	7.50049	−	2.20234i	0.249187	−	0.0731679i
$907$	−4.49034	−	0.321155i	−0.149099	−	0.0106638i	−0.00340992	−	0.999994i	$-0.501085\pi$
$907$	−4.49034	−	0.321155i	−0.149099	−	0.0106638i	−0.145689	+	0.989330i	$0.546540\pi$
$908$	−2.93888	−	0.639314i	−0.0975302	−	0.0212164i
$909$	−8.13917	−	12.6648i	−0.269959	−	0.420065i
$910$	5.46640	−	12.8152i	0.181209	−	0.424820i
$911$	−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	$-0.378873\pi$
$912$	0.981911	+	1.31168i	0.0325143	+	0.0434340i
$913$	1.40468	+	19.6400i	0.0464882	+	0.649989i
$914$	1.75183	−	3.83597i	0.0579454	−	0.126883i
$915$	−8.83917	+	1.49921i	−0.292214	+	0.0495624i
$916$	−8.02551	+	3.66513i	−0.265170	+	0.121099i
$917$	−11.6748	−	8.73968i	−0.385537	−	0.288610i
$918$	−4.27179	−	19.6371i	−0.140990	−	0.648121i
$919$	41.4667			1.36786			0.683930	−	0.729547i	$-0.260269\pi$
$919$	41.4667			1.36786			0.683930	+	0.729547i	$0.260269\pi$
$920$	−7.96309	+	7.18256i	−0.262535	+	0.236802i
$921$	−23.1456			−0.762674
$922$	−7.40600	−	34.0448i	−0.243904	−	1.12121i
$923$	−32.2740	−	24.1600i	−1.06231	−	0.795238i
$924$	−4.30310	+	1.96516i	−0.141562	+	0.0646490i
$925$	34.3610	+	5.67838i	1.12978	+	0.186704i
$926$	−13.7628	+	30.1364i	−0.452275	+	0.990343i
$927$	−1.19104	−	16.6529i	−0.0391189	−	0.546954i
$928$	0.251544	+	0.336024i	0.00825735	+	0.0110305i
$929$	−0.948223	−	3.22935i	−0.0311102	−	0.105952i	0.942474	−	0.334279i	$-0.108493\pi$
$929$	−0.948223	−	3.22935i	−0.0311102	−	0.105952i	−0.973584	+	0.228327i	$0.926674\pi$
$930$	0.123399	−	0.0496035i	0.00404640	−	0.00162656i
$931$	−3.97977	−	6.19264i	−0.130432	−	0.202956i
$932$	7.71056	+	1.67733i	0.252568	+	0.0549427i
$933$	−31.1888	−	2.23066i	−1.02107	−	0.0730286i
$934$	22.5056	−	6.60824i	0.736406	−	0.216228i
$935$	−7.89258	−	24.5705i	−0.258115	−	0.803542i
$936$	−4.99698	+	5.76683i	−0.163332	+	0.188495i
$937$	13.6785	+	36.6735i	0.446857	+	1.19807i	0.943867	+	0.330325i	$0.107158\pi$
$937$	13.6785	+	36.6735i	0.446857	+	1.19807i	−0.497010	+	0.867745i	$0.665569\pi$
$938$	5.23504	−	2.85855i	0.170930	−	0.0933349i
$939$	2.89660	+	6.34268i	0.0945271	+	0.206985i
$940$	2.06646	−	1.40287i	0.0674004	−	0.0457567i
$941$	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
$943$	−34.9250	+	15.7265i	−1.13731	+	0.512125i
$944$			1.90386i			0.0619655i
$945$	11.7459	−	9.26391i	0.382093	−	0.301355i
$946$	5.34083	+	37.1463i	0.173646	+	1.20773i
$947$	4.49524	−	12.0522i	0.146076	−	0.391644i	−0.843220	−	0.537568i	$-0.819343\pi$
$947$	4.49524	−	12.0522i	0.146076	−	0.391644i	0.989296	+	0.145925i	$0.0466157\pi$
$948$	8.81798	+	16.1489i	0.286395	+	0.524493i
$949$	55.7976	+	25.4819i	1.81127	+	0.827177i
$950$	−5.52078	−	3.71389i	−0.179118	−	0.120495i
$951$	1.52281	−	10.5914i	0.0493804	−	0.343448i
$952$	−3.87128	−	2.11388i	−0.125469	−	0.0685111i
$953$	−1.82577	+	25.5275i	−0.0591424	+	0.826918i	0.878153	+	0.478381i	$0.158776\pi$
$953$	−1.82577	+	25.5275i	−0.0591424	+	0.826918i	−0.937295	+	0.348537i	$0.886678\pi$
$954$	12.9466	−	8.32025i	0.419160	−	0.269378i
$955$	−39.1772	+	9.56287i	−1.26775	+	0.309447i
$956$	3.96960	+	4.58116i	0.128386	+	0.148165i
$957$	−0.785321	+	1.43821i	−0.0253858	+	0.0464907i
$958$	−6.31027	+	4.72381i	−0.203876	+	0.152619i
$959$	−9.27158	−	8.03387i	−0.299395	−	0.259427i
$960$	−0.0694044	−	2.75230i	−0.00224002	−	0.0888302i
$961$	29.7420	+	8.73305i	0.959421	+	0.281711i
$962$	−33.5573	−	12.5162i	−1.08193	−	0.403539i
$963$	2.68385	−	3.58520i	0.0864858	−	0.115532i
$964$	−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	$0.737046\pi$
$968$	−0.925245	+	0.201275i	−0.0297385	+	0.00646922i
$969$	−5.90342	+	0.848783i	−0.189645	+	0.0272669i
$970$	−5.98073	+	0.579611i	−0.192030	+	0.0186102i
$971$	−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	$0.935728\pi$
$972$	−12.8125	+	4.77882i	−0.410961	+	0.153281i
$973$	7.57766	−	0.541965i	0.242929	−	0.0173746i
$974$	−13.8503	−	1.99137i	−0.443792	−	0.0638077i
$975$	−11.6820	+	29.4207i	−0.374124	+	0.942216i
$976$	2.46101	−	2.13248i	0.0787750	−	0.0682590i
$977$	−11.3359	+	52.1102i	−0.362667	+	1.66715i	0.328536	+	0.944492i	$0.393445\pi$
$977$	−11.3359	+	52.1102i	−0.362667	+	1.66715i	−0.691203	+	0.722661i	$0.742919\pi$
$978$	−4.96465	+	22.8221i	−0.158752	+	0.729771i
$979$	4.38825	−	3.80244i	0.140249	−	0.121527i
$980$	−0.571107	+	12.3559i	−0.0182433	+	0.394696i
$981$	26.2974	+	3.78099i	0.839611	+	0.120718i
$982$	27.9985	−	2.00250i	0.893469	−	0.0639022i
$983$	52.7037	−	19.6575i	1.68099	−	0.626975i	0.686056	−	0.727548i	$-0.259340\pi$
$983$	52.7037	−	19.6575i	1.68099	−	0.626975i	0.994930	+	0.100573i	$0.0320676\pi$
$984$	2.77044	−	9.43525i	0.0883184	−	0.300785i
$985$	37.0575	+	30.5094i	1.18075	+	0.972110i
$986$	−1.51233	+	0.217440i	−0.0481623	+	0.00692470i
$987$	1.62844	−	0.354246i	0.0518340	−	0.0112758i
$988$	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	$0.635394\pi$
$992$	−0.0289487	+	0.0386710i	−0.000919123	+	0.00122780i
$993$	−31.6056	−	11.7883i	−1.00297	−	0.374090i
$994$	−9.11596	−	2.67669i	−0.289141	−	0.0848994i
$995$	−33.5325	−	31.8829i	−1.06305	−	1.01076i
$996$	−5.77865	−	5.00723i	−0.183104	−	0.158660i
$997$	29.6585	−	22.2021i	0.939295	−	0.703147i	−0.0156666	−	0.999877i	$-0.504987\pi$
$997$	29.6585	−	22.2021i	0.939295	−	0.703147i	0.954961	+	0.296730i	$0.0958961\pi$
$998$	19.1046	−	34.9875i	0.604746	−	1.10751i
$999$	−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.67.9	yes	240
5.3	odd	4	inner	230.2.l.a.113.10	yes	240
23.11	odd	22	inner	230.2.l.a.57.10	✓	240
115.103	even	44	inner	230.2.l.a.103.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.10	✓	240	23.11	odd	22	inner
230.2.l.a.67.9	yes	240	1.1	even	1	trivial
230.2.l.a.103.9	yes	240	115.103	even	44	inner
230.2.l.a.113.10	yes	240	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.212565 + 0.977147i) q^{2} +(-0.985673 - 0.737866i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(1.29447 - 1.82328i) q^{5} +(0.511483 - 1.11999i) q^{6} +(-0.0864458 - 1.20867i) q^{7} +(-0.599278 - 0.800541i) q^{8} +(-0.418092 - 1.42389i) q^{9} +(2.05677 + 0.877326i) q^{10} +(-1.71419 - 2.66733i) q^{11} +(1.20312 + 0.261723i) q^{12} +(5.12881 + 0.366820i) q^{13} +(1.16267 - 0.341392i) q^{14} +(-2.62126 + 0.842007i) q^{15} +(0.654861 - 0.755750i) q^{16} +(1.27205 + 3.41051i) q^{17} +(1.30248 - 0.711206i) q^{18} +(-0.552811 - 1.21049i) q^{19} +(-0.420079 + 2.19625i) q^{20} +(-0.806629 + 1.25514i) q^{21} +(2.24200 - 2.24200i) q^{22} +(3.64105 - 3.12134i) q^{23} +1.23126i q^{24} +(-1.64867 - 4.72037i) q^{25} +(0.731770 + 5.08957i) q^{26} +(-1.92938 + 5.17287i) q^{27} +(0.580734 + 1.06353i) q^{28} +(0.381814 + 0.174369i) q^{29} +(-1.37995 - 2.38238i) q^{30} +(-0.00687467 + 0.0478144i) q^{31} +(0.877679 + 0.479249i) q^{32} +(-0.278502 + 3.89396i) q^{33} +(-3.06217 + 1.96794i) q^{34} +(-2.31564 - 1.40698i) q^{35} +(0.971814 + 1.12153i) q^{36} +(-3.33816 + 6.11338i) q^{37} +(1.06532 - 0.797485i) q^{38} +(-4.78467 - 4.14594i) q^{39} +(-2.23536 + 0.0563686i) q^{40} +(-7.66309 - 2.25009i) q^{41} +(-1.39792 - 0.521396i) q^{42} +(-7.09311 + 9.47529i) 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} +(-1.20312 + 0.261723i) q^{48} +(5.47534 - 0.787235i) q^{49} +(4.26204 - 2.61438i) q^{50} +(1.26267 - 4.30025i) q^{51} +(-4.81771 + 1.79691i) q^{52} +(10.3439 - 0.739812i) q^{53} +(-5.46477 - 0.785715i) q^{54} +(-7.08226 - 0.327351i) q^{55} +(-0.915785 + 0.793533i) q^{56} +(-0.348286 + 1.60105i) q^{57} +(-0.0892234 + 0.410153i) q^{58} +(-1.43884 + 1.24677i) q^{59} +(2.03460 - 1.85483i) q^{60} +(3.22324 + 0.463432i) q^{61} +(-0.0481830 + 0.00344611i) q^{62} +(-1.68487 + 0.628424i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(7.30793 - 8.87640i) q^{65} +(-3.86417 + 0.555584i) q^{66} +(4.80982 - 1.04631i) 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} +(-0.889329 + 1.18800i) q^{72} +(11.1774 + 4.16896i) q^{73} +(-6.68325 - 1.96238i) q^{74} +(-1.85795 + 5.86924i) q^{75} +(1.00571 + 0.871452i) q^{76} +(-3.07574 + 2.30247i) q^{77} +(3.03414 - 5.55661i) q^{78} +(9.78605 + 11.2937i) q^{79} +(-0.530240 - 2.17229i) q^{80} +(1.97336 - 1.26820i) q^{81} +(0.569758 - 7.96626i) q^{82} +(-5.45048 - 2.97619i) q^{83} +(0.212332 - 1.47680i) q^{84} +(7.86494 + 2.09551i) q^{85} +(-10.7665 - 4.91689i) q^{86} +(-0.247683 - 0.453598i) q^{87} +(-1.10803 + 2.97075i) q^{88} +(0.260623 + 1.81268i) q^{89} +(0.389298 - 3.29541i) q^{90} -6.23075i q^{91} +(-2.01536 + 4.35182i) q^{92} +(0.0420568 - 0.0420568i) q^{93} +(0.603889 - 0.939669i) q^{94} +(-2.92265 - 0.559018i) q^{95} +(-0.511483 - 1.11999i) q^{96} +(-2.35850 + 1.28784i) q^{97} +(1.93311 + 5.18287i) 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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