LMFDB - Embedded newform 429.2.y.b.233.42

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [429,2,Mod(116,429)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(429, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 9, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("429.116"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.y (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [176] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			233.42
Character	$\chi$	$=$	429.233
Dual form			429.2.y.b.116.42

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.12303 + 0.689813i) q^{2} +(-0.295173 + 1.70671i) q^{3} +(2.41336 + 1.75341i) q^{4} +(0.370527 + 1.14036i) q^{5} +(-1.80397 + 3.41978i) q^{6} +(-1.00158 - 0.727691i) q^{7} +(1.28990 + 1.77539i) q^{8} +(-2.82575 - 1.00755i) q^{9} +2.67661i q^{10} +(-0.0318800 + 3.31647i) q^{11} +(-3.70493 + 3.60136i) q^{12} +(2.64855 + 2.44646i) q^{13} +(-1.62441 - 2.23581i) q^{14} +(-2.05564 + 0.295778i) q^{15} +(-0.329845 - 1.01516i) q^{16} +(-0.806644 - 2.48260i) q^{17} +(-5.30411 - 4.08829i) q^{18} +(5.27752 - 3.83434i) q^{19} +(-1.10531 + 3.40179i) q^{20} +(1.53760 - 1.49462i) q^{21} +(-2.35543 + 7.01896i) q^{22} +0.0288405i q^{23} +(-3.41083 + 1.67744i) q^{24} +(2.88195 - 2.09386i) q^{25} +(3.93535 + 7.02090i) q^{26} +(2.55369 - 4.52534i) q^{27} +(-1.14124 - 3.51236i) q^{28} +(5.90780 + 4.29226i) q^{29} +(-4.56822 - 0.790064i) q^{30} +(-7.06787 - 2.29649i) q^{31} -6.77175i q^{32} +(-5.65086 - 1.03334i) q^{33} -5.82705i q^{34} +(0.458720 - 1.41180i) q^{35} +(-5.05289 - 7.38628i) q^{36} +(-6.20330 + 8.53811i) q^{37} +(13.8493 - 4.49991i) q^{38} +(-4.95719 + 3.79820i) q^{39} +(-1.54665 + 2.12878i) q^{40} +(-1.36738 - 1.88204i) q^{41} +(4.29537 - 2.11245i) q^{42} -5.93753i q^{43} +(-5.89207 + 7.94794i) q^{44} +(0.101961 - 3.59570i) q^{45} +(-0.0198946 + 0.0612292i) q^{46} +(-1.38942 + 1.00947i) q^{47} +(1.82995 - 0.263304i) q^{48} +(-1.68949 - 5.19971i) q^{49} +(7.56281 - 2.45731i) q^{50} +(4.47518 - 0.643916i) q^{51} +(2.10227 + 10.5482i) q^{52} +(12.9952 + 4.22238i) q^{53} +(8.54318 - 7.84584i) q^{54} +(-3.79380 + 1.19249i) q^{55} -2.71685i q^{56} +(4.98635 + 10.1390i) q^{57} +(9.58154 + 13.1879i) q^{58} +(3.98724 + 2.89690i) q^{59} +(-5.47963 - 2.89056i) q^{60} +(-0.891049 + 0.289519i) q^{61} +(-13.4211 - 9.75102i) q^{62} +(2.09703 + 3.06541i) q^{63} +(4.01155 - 12.3463i) q^{64} +(-1.80849 + 3.92679i) q^{65} +(-11.2841 - 6.09185i) q^{66} -6.41925i q^{67} +(2.40628 - 7.40578i) q^{68} +(-0.0492226 - 0.00851295i) q^{69} +(1.94775 - 2.68085i) q^{70} +(-1.81204 - 5.57687i) q^{71} +(-1.85613 - 6.31645i) q^{72} +(-3.73166 - 2.71121i) q^{73} +(-19.0595 + 13.8475i) q^{74} +(2.72294 + 5.53671i) q^{75} +19.4597 q^{76} +(2.44530 - 3.29852i) q^{77} +(-13.1443 + 4.64414i) q^{78} +(4.58446 + 1.48958i) q^{79} +(1.03543 - 0.752286i) q^{80} +(6.96968 + 5.69417i) q^{81} +(-1.60473 - 4.93885i) q^{82} +(-8.01043 + 2.60275i) q^{83} +(6.33146 - 0.911009i) q^{84} +(2.53218 - 1.83974i) q^{85} +(4.09579 - 12.6055i) q^{86} +(-9.06949 + 8.81596i) q^{87} +(-5.92916 + 4.22131i) q^{88} -4.83030 q^{89} +(2.69683 - 7.56343i) q^{90} +(-0.872475 - 4.37766i) q^{91} +(-0.0505693 + 0.0696026i) q^{92} +(6.00570 - 11.3850i) q^{93} +(-3.64611 + 1.18469i) q^{94} +(6.32801 + 4.59757i) q^{95} +(11.5574 + 1.99884i) q^{96} +(-2.58498 - 0.839911i) q^{97} -12.2046i q^{98} +(3.43160 - 9.33939i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 6 q^{3} + 20 q^{4} + 6 q^{9} + 12 q^{12} - 10 q^{13} + 36 q^{16} - 96 q^{22} - 20 q^{25} + 6 q^{27} - 100 q^{30} - 116 q^{36} + 50 q^{39} + 60 q^{40} + 52 q^{42} + 32 q^{48} - 88 q^{49} - 90 q^{51}+ \cdots - 180 q^{94}+O(q^{100}) $ 176 * q - 6 * q^3 + 20 * q^4 + 6 * q^9 + 12 * q^12 - 10 * q^13 + 36 * q^16 - 96 * q^22 - 20 * q^25 + 6 * q^27 - 100 * q^30 - 116 * q^36 + 50 * q^39 + 60 * q^40 + 52 * q^42 + 32 * q^48 - 88 * q^49 - 90 * q^51 + 210 * q^52 - 20 * q^55 - 92 * q^64 - 62 * q^66 + 96 * q^69 + 166 * q^75 - 112 * q^78 - 60 * q^79 + 70 * q^81 - 144 * q^82 - 148 * q^88 + 100 * q^90 + 62 * q^91 - 180 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$	$-1$

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 $

$2$	2.12303	+	0.689813i	1.50121	+	0.487771i	0.940369	−	0.340155i	$-0.110480\pi$
$2$	2.12303	+	0.689813i	1.50121	+	0.487771i	0.560836	+	0.827927i	$0.310480\pi$
$3$	−0.295173	+	1.70671i	−0.170418	+	0.985372i
$3$	−0.295173	+	1.70671i	−0.170418	+	0.985372i
$4$	2.41336	+	1.75341i	1.20668	+	0.876705i
$5$	0.370527	+	1.14036i	0.165705	+	0.509986i	0.999088	−	0.0427099i	$-0.0135991\pi$
$5$	0.370527	+	1.14036i	0.165705	+	0.509986i	−0.833383	+	0.552696i	$0.813599\pi$
$6$	−1.80397	+	3.41978i	−0.736469	+	1.39612i
$7$	−1.00158	−	0.727691i	−0.378562	−	0.275041i	0.382190	−	0.924084i	$-0.375170\pi$
$7$	−1.00158	−	0.727691i	−0.378562	−	0.275041i	−0.760752	+	0.649042i	$0.775170\pi$
$8$	1.28990	+	1.77539i	0.456048	+	0.627696i
$9$	−2.82575	−	1.00755i	−0.941915	−	0.335851i
$10$			2.67661i			0.846420i
$11$	−0.0318800	+	3.31647i	−0.00961218	+	0.999954i
$11$	−0.0318800	+	3.31647i	−0.00961218	+	0.999954i
$12$	−3.70493	+	3.60136i	−1.06952	+	1.03962i
$13$	2.64855	+	2.44646i	0.734577	+	0.678526i
$13$	2.64855	+	2.44646i	0.734577	+	0.678526i
$14$	−1.62441	−	2.23581i	−0.434142	−	0.597545i
$15$	−2.05564	+	0.295778i	−0.530765	+	0.0763697i
$16$	−0.329845	−	1.01516i	−0.0824613	−	0.253790i
$17$	−0.806644	−	2.48260i	−0.195640	−	0.602118i	−0.999969	−	0.00793315i	$-0.997475\pi$
$17$	−0.806644	−	2.48260i	−0.195640	−	0.602118i	0.804329	−	0.594185i	$-0.202525\pi$
$18$	−5.30411	−	4.08829i	−1.25019	−	0.963620i
$19$	5.27752	−	3.83434i	1.21075	−	0.879659i	0.215448	−	0.976515i	$-0.430879\pi$
$19$	5.27752	−	3.83434i	1.21075	−	0.879659i	0.995298	+	0.0968563i	$0.0308787\pi$
$20$	−1.10531	+	3.40179i	−0.247155	+	0.760664i
$21$	1.53760	−	1.49462i	0.335532	−	0.326152i
$22$	−2.35543	+	7.01896i	−0.502179	+	1.49645i
$23$			0.0288405i			0.00601367i	0.999995	+	0.00300683i	$0.000957107\pi$
$23$			0.0288405i			0.00601367i	−0.999995	+	0.00300683i	$0.999043\pi$
$24$	−3.41083	+	1.67744i	−0.696233	+	0.342406i
$25$	2.88195	−	2.09386i	0.576389	−	0.418771i
$26$	3.93535	+	7.02090i	0.771785	+	1.37691i
$27$	2.55369	−	4.52534i	0.491457	−	0.870902i
$28$	−1.14124	−	3.51236i	−0.215673	−	0.663774i
$29$	5.90780	+	4.29226i	1.09705	+	0.797054i	0.980576	−	0.196140i	$-0.0628408\pi$
$29$	5.90780	+	4.29226i	1.09705	+	0.797054i	0.116474	+	0.993194i	$0.462841\pi$
$30$	−4.56822	−	0.790064i	−0.834038	−	0.144245i
$31$	−7.06787	−	2.29649i	−1.26943	−	0.412462i	−0.404583	−	0.914501i	$-0.632583\pi$
$31$	−7.06787	−	2.29649i	−1.26943	−	0.412462i	−0.864845	+	0.502040i	$0.832583\pi$
$32$		−	6.77175i		−	1.19709i
$33$	−5.65086	−	1.03334i	−0.983688	−	0.179882i
$34$		−	5.82705i		−	0.999330i
$35$	0.458720	−	1.41180i	0.0775378	−	0.238637i
$36$	−5.05289	−	7.38628i	−0.842149	−	1.23105i
$37$	−6.20330	+	8.53811i	−1.01982	+	1.40366i	−0.107484	+	0.994207i	$0.534279\pi$
$37$	−6.20330	+	8.53811i	−1.01982	+	1.40366i	−0.912333	+	0.409450i	$0.865721\pi$
$38$	13.8493	−	4.49991i	2.24665	−	0.729982i
$39$	−4.95719	+	3.79820i	−0.793785	+	0.608198i
$40$	−1.54665	+	2.12878i	−0.244547	+	0.336590i
$41$	−1.36738	−	1.88204i	−0.213549	−	0.293925i	0.688782	−	0.724968i	$-0.258146\pi$
$41$	−1.36738	−	1.88204i	−0.213549	−	0.293925i	−0.902331	+	0.431043i	$0.858146\pi$
$42$	4.29537	−	2.11245i	0.662790	−	0.325959i
$43$		−	5.93753i		−	0.905465i	−0.891646	−	0.452733i	$-0.850449\pi$
$43$		−	5.93753i		−	0.905465i	0.891646	−	0.452733i	$-0.149551\pi$
$44$	−5.89207	+	7.94794i	−0.888263	+	1.19820i
$45$	0.101961	−	3.59570i	0.0151995	−	0.536016i
$46$	−0.0198946	+	0.0612292i	−0.00293329	+	0.00902775i
$47$	−1.38942	+	1.00947i	−0.202667	+	0.147246i	−0.684490	−	0.729022i	$-0.739975\pi$
$47$	−1.38942	+	1.00947i	−0.202667	+	0.147246i	0.481823	+	0.876269i	$0.339975\pi$
$48$	1.82995	−	0.263304i	0.264130	−	0.0380046i
$49$	−1.68949	−	5.19971i	−0.241356	−	0.742816i
$50$	7.56281	−	2.45731i	1.06954	−	0.347516i
$51$	4.47518	−	0.643916i	0.626651	−	0.0901663i
$52$	2.10227	+	10.5482i	0.291533	+	1.46277i
$53$	12.9952	+	4.22238i	1.78502	+	0.579989i	0.999257	−	0.0385362i	$-0.0122695\pi$
$53$	12.9952	+	4.22238i	1.78502	+	0.579989i	0.785765	+	0.618525i	$0.212269\pi$
$54$	8.54318	−	7.84584i	1.16258	−	1.06768i
$55$	−3.79380	+	1.19249i	−0.511555	+	0.160795i
$56$		−	2.71685i		−	0.363054i
$57$	4.98635	+	10.1390i	0.660458	+	1.34295i
$58$	9.58154	+	13.1879i	1.25812	+	1.73165i
$59$	3.98724	+	2.89690i	0.519095	+	0.377144i	0.816263	−	0.577681i	$-0.196042\pi$
$59$	3.98724	+	2.89690i	0.519095	+	0.377144i	−0.297168	+	0.954825i	$0.596042\pi$
$60$	−5.47963	−	2.89056i	−0.707417	−	0.373170i
$61$	−0.891049	+	0.289519i	−0.114087	+	0.0370691i	−0.365504	−	0.930810i	$-0.619103\pi$
$61$	−0.891049	+	0.289519i	−0.114087	+	0.0370691i	0.251417	+	0.967879i	$0.419103\pi$
$62$	−13.4211	−	9.75102i	−1.70448	−	1.23838i
$63$	2.09703	+	3.06541i	0.264201	+	0.386206i
$64$	4.01155	−	12.3463i	0.501444	−	1.54329i
$65$	−1.80849	+	3.92679i	−0.224316	+	0.487059i
$66$	−11.2841	−	6.09185i	−1.38898	−	0.749855i
$67$		−	6.41925i		−	0.784237i	−0.919915	−	0.392118i	$-0.871742\pi$
$67$		−	6.41925i		−	0.784237i	0.919915	−	0.392118i	$-0.128258\pi$
$68$	2.40628	−	7.40578i	0.291805	−	0.898082i
$69$	−0.0492226	−	0.00851295i	−0.00592570	−	0.00102484i
$70$	1.94775	−	2.68085i	0.232800	−	0.320422i
$71$	−1.81204	−	5.57687i	−0.215049	−	0.661853i	−0.999150	−	0.0412197i	$-0.986876\pi$
$71$	−1.81204	−	5.57687i	−0.215049	−	0.661853i	0.784101	−	0.620633i	$-0.213124\pi$
$72$	−1.85613	−	6.31645i	−0.218746	−	0.744401i
$73$	−3.73166	−	2.71121i	−0.436757	−	0.317323i	0.347588	−	0.937647i	$-0.387001\pi$
$73$	−3.73166	−	2.71121i	−0.436757	−	0.317323i	−0.784345	+	0.620325i	$0.787001\pi$
$74$	−19.0595	+	13.8475i	−2.21562	+	1.60974i
$75$	2.72294	+	5.53671i	0.314418	+	0.639324i
$76$	19.4597			2.23219
$77$	2.44530	−	3.29852i	0.278667	−	0.375901i
$78$	−13.1443	+	4.64414i	−1.48830	+	0.525845i
$79$	4.58446	+	1.48958i	0.515792	+	0.167591i	0.555335	−	0.831627i	$-0.312590\pi$
$79$	4.58446	+	1.48958i	0.515792	+	0.167591i	−0.0395428	+	0.999218i	$0.512590\pi$
$80$	1.03543	−	0.752286i	0.115765	−	0.0841082i
$81$	6.96968	+	5.69417i	0.774409	+	0.632686i
$82$	−1.60473	−	4.93885i	−0.177213	−	0.545405i
$83$	−8.01043	+	2.60275i	−0.879259	+	0.285689i	−0.713650	−	0.700503i	$-0.752959\pi$
$83$	−8.01043	+	2.60275i	−0.879259	+	0.285689i	−0.165609	+	0.986191i	$0.552959\pi$
$84$	6.33146	−	0.911009i	0.690819	−	0.0993992i
$85$	2.53218	−	1.83974i	0.274653	−	0.199547i
$86$	4.09579	−	12.6055i	0.441660	−	1.35929i
$87$	−9.06949	+	8.81596i	−0.972351	+	0.945170i
$88$	−5.92916	+	4.22131i	−0.632051	+	0.449993i
$89$	−4.83030			−0.512011			−0.256006	−	0.966675i	$-0.582407\pi$
$89$	−4.83030			−0.512011			−0.256006	+	0.966675i	$0.582407\pi$
$90$	2.69683	−	7.56343i	0.284271	−	0.797256i
$91$	−0.872475	−	4.37766i	−0.0914602	−	0.458903i
$92$	−0.0505693	+	0.0696026i	−0.00527221	+	0.00725658i
$93$	6.00570	−	11.3850i	0.622762	−	1.18057i
$94$	−3.64611	+	1.18469i	−0.376068	+	0.122192i
$95$	6.32801	+	4.59757i	0.649240	+	0.471700i
$96$	11.5574	+	1.99884i	1.17958	+	0.204006i
$97$	−2.58498	−	0.839911i	−0.262465	−	0.0852800i	0.174829	−	0.984599i	$-0.444063\pi$
$97$	−2.58498	−	0.839911i	−0.262465	−	0.0852800i	−0.437293	+	0.899319i	$0.644063\pi$
$98$		−	12.2046i		−	1.23285i
$99$	3.43160	−	9.33939i	0.344889	−	0.938644i
$100$	10.6266			1.06266
$101$	−1.68746	+	5.19346i	−0.167908	+	0.516769i	−0.999239	−	0.0390096i	$-0.987580\pi$
$101$	−1.68746	+	5.19346i	−0.167908	+	0.516769i	0.831330	+	0.555778i	$0.187580\pi$
$102$	9.94510	+	1.71999i	0.984712	+	0.170304i
$103$	−13.4845	−	9.79704i	−1.32866	−	0.965331i	−0.999780	−	0.0209605i	$-0.993328\pi$
$103$	−13.4845	−	9.79704i	−1.32866	−	0.965331i	−0.328884	−	0.944370i	$-0.606672\pi$
$104$	−0.927060	+	7.85791i	−0.0909057	+	0.770531i
$105$	2.27413	+	1.19963i	0.221932	+	0.117072i
$106$	24.6764	+	17.9285i	2.39678	+	1.74137i
$107$	−8.61592	+	6.25983i	−0.832933	+	0.605161i	−0.920387	−	0.391008i	$-0.872127\pi$
$107$	−8.61592	+	6.25983i	−0.832933	+	0.605161i	0.0874549	+	0.996168i	$0.472127\pi$
$108$	14.0977	−	6.44362i	1.35656	−	0.620037i
$109$	0.275800			0.0264168			0.0132084	−	0.999913i	$-0.495796\pi$
$109$	0.275800			0.0264168			0.0132084	+	0.999913i	$0.495796\pi$
$110$	−8.87692	−	0.0853305i	−0.846381	−	0.00813594i
$111$	−12.7411	−	13.1075i	−1.20933	−	1.24411i
$112$	−0.408355	+	1.25679i	−0.0385860	+	0.118755i
$113$	−8.51615	−	11.7215i	−0.801132	−	1.10266i	−0.992632	−	0.121171i	$-0.961335\pi$
$113$	−8.51615	−	11.7215i	−0.801132	−	1.10266i	0.191500	−	0.981493i	$-0.438665\pi$
$114$	3.59212	+	24.9650i	0.336433	+	2.33819i
$115$	−0.0328887	+	0.0106862i	−0.00306689	+	0.000996492i
$116$	6.73155	+	20.7176i	0.625008	+	1.92358i
$117$	−5.01921	−	9.58163i	−0.464026	−	0.885822i
$118$	6.46670	+	8.90065i	0.595308	+	0.819371i
$119$	−0.998643	+	3.07351i	−0.0915455	+	0.281748i
$120$	−3.17669	−	3.26805i	−0.289991	−	0.298331i
$121$	−10.9980	−	0.211458i	−0.999815	−	0.0192235i
$122$	−2.09143			−0.189349
$123$	3.61572	−	1.77820i	0.326018	−	0.160335i
$124$	−13.0306	−	17.9351i	−1.17019	−	1.61062i
$125$	8.30585	+	6.03455i	0.742898	+	0.539747i
$126$	2.33748	+	7.95451i	0.208239	+	0.708644i
$127$	3.10225	−	1.00798i	0.275280	−	0.0894440i	−0.168124	−	0.985766i	$-0.553771\pi$
$127$	3.10225	−	1.00798i	0.275280	−	0.0894440i	0.443404	+	0.896322i	$0.353771\pi$
$128$	9.07258	−	12.4873i	0.801910	−	1.10373i
$129$	10.1337	+	1.75260i	0.892220	+	0.154308i
$130$	−6.54823	+	7.08916i	−0.574317	+	0.621760i
$131$	−9.43941			−0.824725			−0.412362	−	0.911020i	$-0.635296\pi$
$131$	−9.43941			−0.824725			−0.412362	+	0.911020i	$0.635296\pi$
$132$	−11.8257	−	12.4021i	−1.02929	−	1.07946i
$133$	−8.07608			−0.700285
$134$	4.42808	−	13.6282i	0.382528	−	1.17730i
$135$	6.10674	+	1.23537i	0.525584	+	0.106324i
$136$	3.36709	−	4.63441i	0.288726	−	0.397397i
$137$	5.94800	+	18.3061i	0.508172	+	1.56399i	0.795372	+	0.606121i	$0.207275\pi$
$137$	5.94800	+	18.3061i	0.508172	+	1.56399i	−0.287200	+	0.957871i	$0.592725\pi$
$138$	−0.0986284	−	0.0520276i	−0.00839581	−	0.00442888i
$139$	−9.99794	+	13.7610i	−0.848014	+	1.16719i	0.136283	+	0.990670i	$0.456484\pi$
$139$	−9.99794	+	13.7610i	−0.848014	+	1.16719i	−0.984297	+	0.176521i	$0.943516\pi$
$140$	3.58251	−	2.60285i	0.302778	−	0.219981i
$141$	−1.31276	−	2.66931i	−0.110554	−	0.224796i
$142$		−	13.0898i		−	1.09847i
$143$	−8.19805	+	8.70586i	−0.685555	+	0.728021i
$144$	−0.0907666	+	3.20092i	−0.00756388	+	0.266743i
$145$	−2.70575	+	8.32743i	−0.224700	+	0.691556i
$146$	−6.05218	−	8.33011i	−0.500882	−	0.689404i
$147$	9.37311	−	1.34866i	0.773081	−	0.111236i
$148$	−29.9416	+	9.72862i	−2.46118	+	0.799687i
$149$	4.54811	−	1.47777i	0.372596	−	0.121064i	−0.116732	−	0.993163i	$-0.537242\pi$
$149$	4.54811	−	1.47777i	0.372596	−	0.121064i	0.489328	+	0.872100i	$0.337242\pi$
$150$	1.96158	+	13.6329i	0.160163	+	1.11312i
$151$	−1.98728	+	1.44385i	−0.161723	+	0.117499i	−0.665703	−	0.746217i	$-0.731868\pi$
$151$	−1.98728	+	1.44385i	−0.161723	+	0.117499i	0.503980	+	0.863715i	$0.331868\pi$
$152$	13.6149	+	4.42376i	1.10432	+	0.358814i
$153$	−0.221972	+	7.82792i	−0.0179454	+	0.632850i
$154$	7.46679	−	5.31604i	0.601691	−	0.428378i
$155$		−	8.91085i		−	0.715737i
$156$	−18.6233	+	0.474440i	−1.49106	+	0.0379856i
$157$	4.39969	−	3.19656i	0.351134	−	0.255113i	−0.398211	−	0.917294i	$-0.630369\pi$
$157$	4.39969	−	3.19656i	0.351134	−	0.255113i	0.749344	+	0.662180i	$0.230369\pi$
$158$	8.70539	+	6.32484i	0.692564	+	0.503177i
$159$	−11.0422	+	20.9327i	−0.875705	+	1.66007i
$160$	7.72226	−	2.50911i	0.610498	−	0.198363i
$161$	0.0209870	−	0.0288861i	0.00165401	−	0.00227655i
$162$	10.8689	+	16.8966i	0.853941	+	1.32753i
$163$	−8.70818	−	2.82946i	−0.682077	−	0.221620i	−0.0525726	−	0.998617i	$-0.516742\pi$
$163$	−8.70818	−	2.82946i	−0.682077	−	0.221620i	−0.629505	+	0.776997i	$0.716742\pi$
$164$		−	6.93962i		−	0.541893i
$165$	−0.915407	−	6.82691i	−0.0712643	−	0.531474i
$166$	−18.8018			−1.45930
$167$	3.23388	+	1.05075i	0.250245	+	0.0813096i	0.431454	−	0.902135i	$-0.358001\pi$
$167$	3.23388	+	1.05075i	0.250245	+	0.0813096i	−0.181208	+	0.983445i	$0.558001\pi$
$168$	4.63688	+	0.801940i	0.357743	+	0.0618710i
$169$	1.02968	+	12.9592i	0.0792061	+	0.996858i
$170$	6.64495	−	2.15908i	0.509645	−	0.165594i
$171$	−18.7762	+	5.51751i	−1.43585	+	0.421934i
$172$	10.4109	−	14.3294i	0.793826	−	1.09261i
$173$	5.56312	−	4.04184i	0.422956	−	0.307296i	−0.355870	−	0.934535i	$-0.615815\pi$
$173$	5.56312	−	4.04184i	0.422956	−	0.307296i	0.778826	+	0.627240i	$0.215815\pi$
$174$	−25.3361	+	12.4603i	−1.92073	+	0.944609i
$175$	−4.41018			−0.333379
$176$	3.37726	−	1.06156i	0.254571	−	0.0800180i
$177$	−6.12111	+	5.95000i	−0.460091	+	0.447229i
$178$	−10.2549	−	3.33200i	−0.768634	−	0.249744i
$179$	10.9165	+	15.0253i	0.815938	+	1.12304i	0.990380	+	0.138375i	$0.0441880\pi$
$179$	10.9165	+	15.0253i	0.815938	+	1.12304i	−0.174442	+	0.984668i	$0.555812\pi$
$180$	6.55081	−	8.49895i	0.488268	−	0.633474i
$181$	−3.87273	−	11.9190i	−0.287858	−	0.885934i	−0.985528	−	0.169515i	$-0.945780\pi$
$181$	−3.87273	−	11.9190i	−0.287858	−	0.885934i	0.697670	−	0.716419i	$-0.254220\pi$
$182$	1.16748	−	9.89572i	0.0865391	−	0.733519i
$183$	−0.231113	−	1.60622i	−0.0170844	−	0.118735i
$184$	−0.0512033	+	0.0372014i	−0.00377476	+	0.00274252i
$185$	−12.0350	−	3.91042i	−0.884833	−	0.287500i
$186$	20.6037	−	20.0278i	1.51074	−	1.46851i
$187$	8.25917	−	2.59607i	0.603971	−	0.189843i
$188$	−5.12318			−0.373646
$189$	−5.85077	+	2.67420i	−0.425581	+	0.194519i
$190$	10.2631	+	14.1259i	0.744561	+	1.02480i
$191$	13.4900	−	18.5673i	0.976099	−	1.34348i	0.0371935	−	0.999308i	$-0.488158\pi$
$191$	13.4900	−	18.5673i	0.976099	−	1.34348i	0.938905	−	0.344176i	$-0.111842\pi$
$192$	19.8875	+	10.4909i	1.43525	+	0.757113i
$193$	2.04695	+	6.29985i	0.147342	+	0.453473i	0.997305	−	0.0733702i	$-0.0233755\pi$
$193$	2.04695	+	6.29985i	0.147342	+	0.453473i	−0.849962	+	0.526843i	$0.823375\pi$
$194$	−4.90860	−	3.56630i	−0.352417	−	0.256046i
$195$	−6.16809	−	4.24566i	−0.441706	−	0.304038i
$196$	5.03988	−	15.5111i	0.359991	−	1.10794i
$197$			3.84132i			0.273682i	0.990593	+	0.136841i	$0.0436950\pi$
$197$			3.84132i			0.273682i	−0.990593	+	0.136841i	$0.956305\pi$
$198$	13.7278	−	17.4606i	0.975593	−	1.24087i
$199$	−7.24986			−0.513929			−0.256965	−	0.966421i	$-0.582722\pi$
$199$	−7.24986			−0.513929			−0.256965	+	0.966421i	$0.582722\pi$
$200$	7.43484	+	2.41572i	0.525722	+	0.170818i
$201$	10.9558	+	1.89479i	0.772765	+	0.133648i
$202$	−7.16503	+	9.86182i	−0.504130	+	0.693875i
$203$	−2.79369	−	8.59810i	−0.196079	−	0.603468i
$204$	11.9293	+	6.29282i	0.835216	+	0.440586i
$205$	1.63956	−	2.25666i	0.114512	−	0.157612i
$206$	−21.8697	−	30.1011i	−1.52374	−	2.09724i
$207$	0.0290583	−	0.0814960i	0.00201969	−	0.00566437i
$208$	1.60993	−	3.49566i	0.111629	−	0.242380i
$209$	12.5482	+	17.6250i	0.867980	+	1.21915i
$210$	4.00051	+	4.11556i	0.276062	+	0.284001i
$211$	−5.74526	−	1.86675i	−0.395520	−	0.128512i	0.104503	−	0.994525i	$-0.466675\pi$
$211$	−5.74526	−	1.86675i	−0.395520	−	0.128512i	−0.500022	+	0.866012i	$0.666675\pi$
$212$	23.9584	+	32.9760i	1.64547	+	2.26480i
$213$	10.0530	−	1.44648i	0.688819	−	0.0991115i
$214$	−22.6099	+	7.34641i	−1.54558	+	0.502190i
$215$	6.77095	−	2.20001i	0.461775	−	0.150040i
$216$	11.3283	−	1.30343i	0.770790	−	0.0886872i
$217$	5.40791	+	7.44335i	0.367113	+	0.505287i
$218$	0.585530	+	0.190250i	0.0396571	+	0.0128854i
$219$	5.72874	−	5.56860i	0.387112	−	0.376291i
$220$	−11.2467	−	3.77418i	−0.758253	−	0.254455i
$221$	3.93713	−	8.54871i	0.264840	−	0.575049i
$222$	−18.0079	−	36.6165i	−1.20861	−	2.45754i
$223$	−13.9752	−	19.2352i	−0.935847	−	1.28808i	−0.957535	−	0.288319i	$-0.906904\pi$
$223$	−13.9752	−	19.2352i	−0.935847	−	1.28808i	0.0216871	−	0.999765i	$-0.493096\pi$
$224$	−4.92774	+	6.78246i	−0.329249	+	0.453172i
$225$	−10.2533	+	3.01300i	−0.683554	+	0.200866i
$226$	−9.99438	−	30.7595i	−0.664816	−	2.04609i
$227$	−11.2136	+	15.4342i	−0.744273	+	1.02440i	0.254089	+	0.967181i	$0.418224\pi$
$227$	−11.2136	+	15.4342i	−0.744273	+	1.02440i	−0.998361	+	0.0572227i	$0.981776\pi$
$228$	−5.74399	+	33.2122i	−0.380405	+	2.19953i
$229$	25.6971	+	8.34949i	1.69811	+	0.551750i	0.988284	−	0.152625i	$-0.0487726\pi$
$229$	25.6971	+	8.34949i	1.69811	+	0.551750i	0.709828	+	0.704375i	$0.248773\pi$
$230$	−0.0771950			−0.00509009
$231$	4.90784	+	5.14706i	0.322912	+	0.338651i
$232$			16.0252i			1.05211i
$233$	2.33718	−	7.19309i	0.153114	−	0.471235i	−0.844851	−	0.535001i	$-0.820311\pi$
$233$	2.33718	−	7.19309i	0.153114	−	0.471235i	0.997965	+	0.0637661i	$0.0203112\pi$
$234$	−4.04638	−	23.8043i	−0.264520	−	1.55614i
$235$	−1.66598	−	1.21040i	−0.108676	−	0.0789581i
$236$	4.54320	+	13.9825i	0.295737	+	0.910186i
$237$	−3.89550	+	7.38468i	−0.253040	+	0.479686i
$238$	−4.24029	+	5.83626i	−0.274857	+	0.378309i
$239$	−13.3747	−	18.4088i	−0.865140	−	1.19076i	−0.980319	−	0.197418i	$-0.936744\pi$
$239$	−13.3747	−	18.4088i	−0.865140	−	1.19076i	0.115179	−	0.993345i	$-0.463256\pi$
$240$	0.978306	+	1.98924i	0.0631494	+	0.128405i
$241$	5.11788			0.329671			0.164836	−	0.986321i	$-0.447291\pi$
$241$	5.11788			0.329671			0.164836	+	0.986321i	$0.447291\pi$
$242$	−23.2031	−	8.03547i	−1.49155	−	0.516540i
$243$	−11.7756	+	10.2145i	−0.755404	+	0.655259i
$244$	−2.65807	−	0.863659i	−0.170165	−	0.0552901i
$245$	5.30356	−	3.85326i	0.338832	−	0.246176i
$246$	8.90288	−	1.28100i	0.567627	−	0.0816736i
$247$	23.3584	+	2.75577i	1.48626	+	0.175346i
$248$	−5.03966	−	15.5105i	−0.320019	−	0.984917i
$249$	−2.07768	−	14.4398i	−0.131668	−	0.915083i
$250$	13.4708	+	18.5410i	0.851969	+	1.17264i
$251$	−1.72205	−	0.559527i	−0.108695	−	0.0353170i	0.254165	−	0.967161i	$-0.418199\pi$
$251$	−1.72205	−	0.559527i	−0.108695	−	0.0353170i	−0.362859	+	0.931844i	$0.618199\pi$
$252$	−0.314045	+	11.0749i	−0.0197830	+	0.697653i
$253$	−0.0956488		0.000919436i	−0.00601339		5.78045e-5i
$254$	7.28148			0.456881
$255$	2.39247	+	4.86474i	0.149822	+	0.304642i
$256$	6.87047	−	4.99169i	0.429405	−	0.311981i
$257$	−6.66937	+	9.17960i	−0.416024	+	0.572607i	−0.964675	−	0.263444i	$-0.915142\pi$
$257$	−6.66937	+	9.17960i	−0.416024	+	0.572607i	0.548651	+	0.836051i	$0.315142\pi$
$258$	20.3051	+	10.7111i	1.26414	+	0.666847i
$259$	12.4262	−	4.03752i	0.772127	−	0.250879i
$260$	−11.2498	+	6.30574i	−0.697684	+	0.391065i
$261$	−12.3693	−	18.0813i	−0.765637	−	1.11920i
$262$	−20.0401	−	6.51142i	−1.23808	−	0.402277i
$263$	2.68308			0.165446			0.0827230	−	0.996573i	$-0.473638\pi$
$263$	2.68308			0.165446			0.0827230	+	0.996573i	$0.473638\pi$
$264$	−5.45445	−	11.3654i	−0.335698	−	0.699492i
$265$			16.3837i			1.00644i
$266$	−17.1457	−	5.57099i	−1.05127	−	0.341579i
$267$	1.42577	−	8.24395i	0.0872560	−	0.504521i
$268$	11.2556	−	15.4920i	0.687544	−	0.946323i
$269$	−30.3194	+	9.85136i	−1.84861	+	0.600648i	−0.851522	+	0.524318i	$0.824320\pi$
$269$	−30.3194	+	9.85136i	−1.84861	+	0.600648i	−0.997083	+	0.0763300i	$0.975680\pi$
$270$	12.1126	+	6.83523i	0.737148	+	0.415979i
$271$	6.44173	+	4.68019i	0.391307	+	0.284302i	0.765991	−	0.642851i	$-0.222249\pi$
$271$	6.44173	+	4.68019i	0.391307	+	0.284302i	−0.374684	+	0.927153i	$0.622249\pi$
$272$	−2.25416	+	1.63774i	−0.136679	+	0.0993028i
$273$	7.72894	−	0.196900i	0.467777	−	0.0119169i
$274$			42.9672i			2.59575i
$275$	6.85234	+	9.62464i	0.413212	+	0.580388i
$276$	−0.103865	−	0.106852i	−0.00625195	−	0.00643174i
$277$	22.1820	+	7.20737i	1.33279	+	0.433049i	0.886867	−	0.462024i	$-0.152877\pi$
$277$	22.1820	+	7.20737i	1.33279	+	0.433049i	0.445920	+	0.895073i	$0.352877\pi$
$278$	−30.7184	+	22.3182i	−1.84237	+	1.33856i
$279$	17.6582	+	13.6105i	1.05717	+	0.814842i
$280$	3.09819	−	1.00666i	0.185152	−	0.0601597i
$281$	8.61790	−	2.80012i	0.514101	−	0.167041i	−0.0404657	−	0.999181i	$-0.512884\pi$
$281$	8.61790	−	2.80012i	0.514101	−	0.167041i	0.554566	+	0.832139i	$0.312884\pi$
$282$	−0.945700	−	6.57256i	−0.0563156	−	0.391390i
$283$	−10.0137	−	13.7827i	−0.595255	−	0.819298i	0.400008	−	0.916511i	$-0.369007\pi$
$283$	−10.0137	−	13.7827i	−0.595255	−	0.819298i	−0.995264	+	0.0972130i	$0.969007\pi$
$284$	5.40544	−	16.6362i	0.320754	−	0.987179i
$285$	−9.71459	+	9.44302i	−0.575443	+	0.559356i
$286$	−23.4101	+	12.8276i	−1.38427	+	0.758515i
$287$			2.88005i			0.170004i
$288$	−6.82289	+	19.1353i	−0.402043	+	1.12756i
$289$	8.24068	−	5.98721i	0.484746	−	0.352189i
$290$	−11.4887	+	15.8129i	−0.674642	+	0.928565i
$291$	2.19650	−	4.16390i	0.128761	−	0.244092i
$292$	−4.25198	−	13.0862i	−0.248828	−	0.765814i
$293$	−11.3560	+	15.6302i	−0.663427	+	0.913128i	−0.999589	−	0.0286757i	$-0.990871\pi$
$293$	−11.3560	+	15.6302i	−0.663427	+	0.913128i	0.336162	+	0.941804i	$0.390871\pi$
$294$	20.8297	+	3.60245i	1.21481	+	0.210099i
$295$	−1.82614	+	5.62028i	−0.106322	+	0.327226i
$296$	−23.1601			−1.34616
$297$	14.9267	+	8.61350i	0.866138	+	0.499806i
$298$	10.6751			0.618395
$299$	−0.0705572	+	0.0763857i	−0.00408043	+	0.00441750i
$300$	−3.13667	+	18.1365i	−0.181096	+	1.04711i
$301$	−4.32069	+	5.94692i	−0.249040	+	0.342775i
$302$	−5.21504	+	1.69447i	−0.300092	+	0.0975057i
$303$	−8.36566	−	4.41298i	−0.480595	−	0.253519i
$304$	−5.63323	−	4.09278i	−0.323088	−	0.234737i
$305$	−0.660314	−	0.908845i	−0.0378095	−	0.0520403i
$306$	−5.87105	+	16.4658i	−0.335626	+	0.941285i
$307$	−12.6449			−0.721683			−0.360841	−	0.932627i	$-0.617510\pi$
$307$	−12.6449			−0.721683			−0.360841	+	0.932627i	$0.617510\pi$
$308$	11.6850	−	3.67290i	0.665817	−	0.209283i
$309$	20.7010	−	20.1223i	1.17764	−	1.14472i
$310$	6.14682	−	18.9180i	0.349116	−	1.07447i
$311$	6.32137	+	8.70063i	0.358452	+	0.493367i	0.949717	−	0.313111i	$-0.101371\pi$
$311$	6.32137	+	8.70063i	0.358452	+	0.493367i	−0.591264	+	0.806478i	$0.701371\pi$
$312$	−13.1376	−	3.90167i	−0.743768	−	0.220888i
$313$	0.859994	+	2.64679i	0.0486098	+	0.149605i	0.972415	−	0.233257i	$-0.0749383\pi$
$313$	0.859994	+	2.64679i	0.0486098	+	0.149605i	−0.923805	+	0.382862i	$0.874938\pi$
$314$	11.5457	−	3.75142i	0.651561	−	0.211705i
$315$	−2.71868	+	3.52719i	−0.153180	+	0.198735i
$316$	8.45211	+	11.6333i	0.475468	+	0.654426i
$317$	4.10244	−	12.6260i	0.230416	−	0.709148i	−0.767280	−	0.641312i	$-0.778391\pi$
$317$	4.10244	−	12.6260i	0.230416	−	0.709148i	0.997696	−	0.0678359i	$-0.0216094\pi$
$318$	−37.8825	+	36.8236i	−2.12435	+	2.06496i
$319$	−14.4235	+	19.4562i	−0.807562	+	1.08934i
$320$	15.5656			0.870146
$321$	−8.14056	−	16.5526i	−0.454362	−	0.923879i
$322$	0.0644820	−	0.0468489i	0.00359344	−	0.00261079i
$323$	−13.7762	−	10.0090i	−0.766529	−	0.556916i
$324$	6.83614	+	25.9628i	0.379786	+	1.44238i
$325$	12.7555	+	1.50487i	0.707549	+	0.0834752i
$326$	−16.5359	−	12.0140i	−0.915838	−	0.665395i
$327$	−0.0814087	+	0.470711i	−0.00450191	+	0.0260304i
$328$	1.57758	−	4.85528i	0.0871071	−	0.268088i
$329$	2.12620			0.117221
$330$	2.76586	−	15.1252i	0.152256	−	0.832613i
$331$		−	4.44175i		−	0.244141i	−0.992521	−	0.122070i	$-0.961047\pi$
$331$		−	4.44175i		−	0.244141i	0.992521	−	0.122070i	$-0.0389534\pi$
$332$	−23.8957	−	7.76420i	−1.31145	−	0.426116i
$333$	26.1315	−	17.8764i	1.43200	−	0.979620i
$334$	6.14079	+	4.46154i	0.336009	+	0.244125i
$335$	7.32028	−	2.37850i	0.399950	−	0.129952i
$336$	−2.02444	−	1.06792i	−0.110442	−	0.0582596i
$337$	−15.0265	+	20.6823i	−0.818548	+	1.12663i	0.171400	+	0.985202i	$0.445171\pi$
$337$	−15.0265	+	20.6823i	−0.818548	+	1.12663i	−0.989948	+	0.141433i	$0.954829\pi$
$338$	−6.75336	+	28.2229i	−0.367334	+	1.53512i
$339$	22.5189	−	11.0748i	1.22306	−	0.601499i
$340$	9.33687			0.506363
$341$	7.84157	−	23.3672i	0.424645	−	1.26540i
$342$	−43.6685	−	1.23828i	−2.36132	−	0.0669586i
$343$	−4.76961	+	14.6794i	−0.257535	+	0.792611i
$344$	10.5415	−	7.65882i	0.568357	−	0.412936i
$345$	−0.00853041	−	0.0592859i	−0.000459262	−	0.00319184i
$346$	14.5988	−	4.74342i	0.784834	−	0.255008i
$347$	4.91854	+	15.1377i	0.264041	+	0.812635i	0.991913	+	0.126922i	$0.0405097\pi$
$347$	4.91854	+	15.1377i	0.264041	+	0.812635i	−0.727872	+	0.685714i	$0.759490\pi$
$348$	−37.3459	+	5.37356i	−2.00195	+	0.288053i
$349$	27.2856	−	19.8241i	1.46056	−	1.06116i	0.477347	−	0.878715i	$-0.341598\pi$
$349$	27.2856	−	19.8241i	1.46056	−	1.06116i	0.983216	−	0.182446i	$-0.0584015\pi$
$350$	−9.36293	−	3.04220i	−0.500470	−	0.162612i
$351$	17.8346	−	5.73812i	0.951942	−	0.306278i
$352$	22.4583	+	0.215883i	1.19703	+	0.0115066i
$353$	16.8155			0.894997			0.447498	−	0.894285i	$-0.352315\pi$
$353$	16.8155			0.894997			0.447498	+	0.894285i	$0.352315\pi$
$354$	−17.0997	+	8.40957i	−0.908836	+	0.446964i
$355$	5.68825	−	4.13276i	0.301901	−	0.219344i
$356$	−11.6573	−	8.46950i	−0.617834	−	0.448883i
$357$	−4.95083	−	2.61162i	−0.262026	−	0.138221i
$358$	12.8114	+	39.4294i	0.677103	+	2.08391i
$359$	−10.0032	+	13.7682i	−0.527946	+	0.726656i	−0.986816	−	0.161848i	$-0.948255\pi$
$359$	−10.0032	+	13.7682i	−0.527946	+	0.726656i	0.458870	+	0.888504i	$0.348255\pi$
$360$	6.51530	−	4.45707i	0.343387	−	0.234908i
$361$	7.27872	−	22.4016i	0.383091	−	1.17903i
$362$		−	27.9759i		−	1.47038i
$363$	3.60720	−	18.7080i	0.189329	−	0.981914i
$364$	5.57023	−	12.0947i	0.291959	−	0.633933i
$365$	1.70908	−	5.26002i	0.0894575	−	0.275322i
$366$	0.617335	−	3.56948i	0.0322686	−	0.186580i
$367$	4.42012	+	3.21140i	0.230728	+	0.167634i	0.697143	−	0.716932i	$-0.254454\pi$
$367$	4.42012	+	3.21140i	0.230728	+	0.167634i	−0.466414	+	0.884566i	$0.654454\pi$
$368$	0.0292777	−	0.00951291i	0.00152621	−	0.000495895i
$369$	1.96762	+	6.69587i	0.102430	+	0.348573i
$370$	−22.8532	−	16.6038i	−1.18808	−	0.863193i
$371$	−9.94311	−	13.6855i	−0.516221	−	0.710517i
$372$	34.4564	−	16.9456i	1.78648	−	0.878589i
$373$			30.2082i			1.56412i	0.623203	+	0.782060i	$0.285831\pi$
$373$			30.2082i			1.56412i	−0.623203	+	0.782060i	$0.714169\pi$
$374$	19.3252	+	0.185766i	0.999284	+	0.00960574i
$375$	−12.7509	+	12.3945i	−0.658455	+	0.640048i
$376$	−3.58441	−	1.16465i	−0.184852	−	0.0600621i
$377$	5.14627	+	25.8215i	0.265046	+	1.32987i
$378$	−14.2660	+	1.64145i	−0.733766	+	0.0844272i
$379$	25.9847	−	8.44296i	1.33475	−	0.433686i	0.447213	−	0.894428i	$-0.352417\pi$
$379$	25.9847	−	8.44296i	1.33475	−	0.433686i	0.887534	+	0.460742i	$0.152417\pi$
$380$	7.21035	+	22.1912i	0.369883	+	1.13838i
$381$	0.804637	+	5.59219i	0.0412228	+	0.286496i
$382$	41.4475	−	30.1134i	2.12064	−	1.54073i
$383$	5.01987	−	15.4496i	0.256503	−	0.789436i	−0.737026	−	0.675864i	$-0.763771\pi$
$383$	5.01987	−	15.4496i	0.256503	−	0.789436i	0.993530	−	0.113572i	$-0.0362293\pi$
$384$	18.6343	+	19.1702i	0.950929	+	0.978276i
$385$	4.66755	+	1.56634i	0.237881	+	0.0798281i
$386$			14.7868i			0.752626i
$387$	−5.98237	+	16.7780i	−0.304101	+	0.852872i
$388$	−4.76578	−	6.55953i	−0.241946	−	0.333010i
$389$	−6.11625	+	8.41830i	−0.310106	+	0.426825i	−0.935414	−	0.353553i	$-0.884973\pi$
$389$	−6.11625	+	8.41830i	−0.310106	+	0.426825i	0.625308	+	0.780378i	$0.284973\pi$
$390$	−10.1663	−	13.2685i	−0.514791	−	0.671876i
$391$	0.0715994	−	0.0232641i	0.00362094	−	0.00117651i
$392$	7.05226	−	9.70661i	0.356193	−	0.490258i
$393$	2.78626	−	16.1104i	0.140548	−	0.812661i
$394$	−2.64979	+	8.15521i	−0.133494	+	0.410854i
$395$			5.77988i			0.290817i
$396$	24.6575	−	16.5223i	1.23908	−	0.830277i
$397$		−	28.8424i		−	1.44756i	−0.690032	−	0.723779i	$-0.742403\pi$
$397$		−	28.8424i		−	1.44756i	0.690032	−	0.723779i	$-0.257597\pi$
$398$	−15.3916	−	5.00105i	−0.771513	−	0.250680i
$399$	2.38384	−	13.7836i	0.119341	−	0.690041i
$400$	−3.07619	−	2.23498i	−0.153810	−	0.111749i
$401$	−6.65395	−	20.4788i	−0.332283	−	1.02266i	−0.968045	−	0.250776i	$-0.919314\pi$
$401$	−6.65395	−	20.4788i	−0.332283	−	1.02266i	0.635763	−	0.771885i	$-0.280686\pi$
$402$	21.9525	+	11.5802i	1.09489	+	0.577566i
$403$	−13.1014	−	23.3736i	−0.652626	−	1.16432i
$404$	−13.1787	+	9.57490i	−0.655665	+	0.476369i
$405$	−3.91097	+	10.0578i	−0.194338	+	0.499777i
$406$		−	20.1811i		−	1.00157i
$407$	−28.1186	−	20.8453i	−1.39379	−	1.03326i
$408$	6.91573	+	7.11462i	0.342380	+	0.352226i
$409$	−0.810153	+	2.49339i	−0.0400595	+	0.123290i	−0.969086	−	0.246722i	$-0.920647\pi$
$409$	−0.810153	+	2.49339i	−0.0400595	+	0.123290i	0.929027	+	0.370012i	$0.120647\pi$
$410$	5.03749	−	3.65995i	0.248784	−	0.180752i
$411$	−32.9989	+	4.74808i	−1.62772	+	0.234205i
$412$	−15.3647	−	47.2876i	−0.756963	−	2.32969i
$413$	−1.88550	−	5.80296i	−0.0927792	−	0.285545i
$414$	0.117909	−	0.152973i	0.00579489	−	0.00751823i
$415$	−5.93615	−	8.17041i	−0.291394	−	0.401070i
$416$	16.5668	−	17.9354i	0.812255	−	0.879353i
$417$	−20.5349	−	21.1255i	−1.00560	−	1.03452i
$418$	14.4823	+	46.0742i	0.708353	+	2.25357i
$419$		−	11.6352i		−	0.568417i	−0.958762	−	0.284209i	$-0.908269\pi$
$419$		−	11.6352i		−	0.568417i	0.958762	−	0.284209i	$-0.0917309\pi$
$420$	3.38486	+	6.88261i	0.165164	+	0.335837i
$421$	21.0728	+	29.0043i	1.02703	+	1.41358i	0.907157	+	0.420791i	$0.138248\pi$
$421$	21.0728	+	29.0043i	1.02703	+	1.41358i	0.119869	+	0.992790i	$0.461752\pi$
$422$	−10.9096	−	7.92630i	−0.531072	−	0.385846i
$423$	4.94323	−	1.45260i	0.240348	−	0.0706277i
$424$	9.26605	+	28.5180i	0.449999	+	1.38495i
$425$	−7.52290	−	5.46571i	−0.364914	−	0.265126i
$426$	22.3406	+	3.86376i	1.08240	+	0.187200i
$427$	1.10314	+	0.358431i	0.0533846	+	0.0173457i
$428$	−31.7694			−1.53563
$429$	−12.4386	−	16.5615i	−0.600540	−	0.799595i
$430$	15.8925			0.766404
$431$	24.4522	+	7.94501i	1.17782	+	0.382698i	0.831557	−	0.555439i	$-0.187450\pi$
$431$	24.4522	+	7.94501i	1.17782	+	0.382698i	0.346265	+	0.938137i	$0.387450\pi$
$432$	−5.43626	−	1.09974i	−0.261552	−	0.0529111i
$433$	20.8944	+	15.1807i	1.00412	+	0.729536i	0.962968	−	0.269617i	$-0.0868971\pi$
$433$	20.8944	+	15.1807i	1.00412	+	0.729536i	0.0411524	+	0.999153i	$0.486897\pi$
$434$	6.34661	+	19.5329i	0.304647	+	0.937607i
$435$	−13.4139	−	7.07597i	−0.643146	−	0.339267i
$436$	0.665605	+	0.483590i	0.0318767	+	0.0231598i
$437$	0.110585	+	0.152207i	0.00528998	+	0.00728103i
$438$	16.0035	−	7.87051i	0.764679	−	0.376068i
$439$		−	15.1625i		−	0.723668i	−0.932242	−	0.361834i	$-0.882151\pi$
$439$		−	15.1625i		−	0.723668i	0.932242	−	0.361834i	$-0.117849\pi$
$440$	−7.01074	−	5.19729i	−0.334224	−	0.247771i
$441$	−0.464913	+	16.3953i	−0.0221387	+	0.780729i
$442$	14.2556	−	15.4333i	0.678071	−	0.734085i
$443$	−0.125536	−	0.172786i	−0.00596440	−	0.00820929i	0.806024	−	0.591882i	$-0.201615\pi$
$443$	−0.125536	−	0.172786i	−0.00596440	−	0.00820929i	−0.811989	+	0.583673i	$0.801615\pi$
$444$	−7.76602	−	53.9734i	−0.368559	−	2.56146i
$445$	−1.78976	−	5.50830i	−0.0848425	−	0.261119i
$446$	−16.4010	−	50.4770i	−0.776609	−	2.39016i
$447$	1.17965	+	8.19853i	0.0557957	+	0.387777i
$448$	−13.0022	+	9.44663i	−0.614295	+	0.446311i
$449$	4.57403	−	14.0774i	0.215862	−	0.664354i	−0.783229	−	0.621733i	$-0.786429\pi$
$449$	4.57403	−	14.0774i	0.215862	−	0.664354i	0.999091	−	0.0426216i	$-0.0135710\pi$
$450$	−23.8465	−	0.676200i	−1.12413	−	0.0318764i
$451$	6.28532	−	4.47488i	0.295964	−	0.210714i
$452$		−	43.2204i		−	2.03292i
$453$	−1.87764	−	3.81791i	−0.0882193	−	0.179381i
$454$	−34.4535	+	25.0319i	−1.61698	+	1.17481i
$455$	4.66884	−	2.61698i	0.218879	−	0.122686i
$456$	−11.5689	+	21.9310i	−0.541761	+	1.02701i
$457$	−6.69523	−	20.6058i	−0.313190	−	0.963899i	−0.976493	−	0.215548i	$-0.930846\pi$
$457$	−6.69523	−	20.6058i	−0.313190	−	0.963899i	0.663303	−	0.748351i	$-0.269154\pi$
$458$	48.7960	+	35.4524i	2.28009	+	1.65658i
$459$	−13.2945	−	2.68943i	−0.620534	−	0.125532i
$460$	−0.0981096	−	0.0318777i	−0.00457438	−	0.00148631i
$461$			1.10864i			0.0516344i	0.999667	+	0.0258172i	$0.00821878\pi$
$461$			1.10864i			0.0516344i	−0.999667	+	0.0258172i	$0.991781\pi$
$462$	6.86896	+	14.3128i	0.319573	+	0.665893i
$463$			18.5721i			0.863120i	0.902084	+	0.431560i	$0.142037\pi$
$463$			18.5721i			0.863120i	−0.902084	+	0.431560i	$0.857963\pi$
$464$	2.40867	−	7.41313i	0.111820	−	0.344146i
$465$	15.2083	+	2.63024i	0.705267	+	0.121975i
$466$	9.92377	−	13.6589i	0.459710	−	0.632736i
$467$	6.31071	−	2.05047i	0.292025	−	0.0948846i	−0.159341	−	0.987224i	$-0.550937\pi$
$467$	6.31071	−	2.05047i	0.292025	−	0.0948846i	0.451366	+	0.892339i	$0.350937\pi$
$468$	4.68735	−	31.9246i	0.216673	−	1.47572i
$469$	−4.67123	+	6.42940i	−0.215698	+	0.296882i
$470$	−2.70196	−	3.71893i	−0.124632	−	0.171542i
$471$	4.15695	+	8.45255i	0.191542	+	0.389473i
$472$			10.8156i			0.497830i
$473$	19.6917	+	0.189289i	0.905424	+	0.00870350i
$474$	−13.3643	+	12.9907i	−0.613842	+	0.596682i
$475$	7.18097	−	22.1007i	0.329485	−	1.01405i
$476$	−7.79921	+	5.66645i	−0.357476	+	0.259722i
$477$	−32.4667	−	25.0247i	−1.48655	−	1.14580i
$478$	−15.6963	−	48.3083i	−0.717933	−	2.20957i
$479$	24.3291	−	7.90499i	1.11162	−	0.361188i	0.305058	−	0.952334i	$-0.401324\pi$
$479$	24.3291	−	7.90499i	1.11162	−	0.361188i	0.806565	+	0.591146i	$0.201324\pi$
$480$	2.00294	+	13.9203i	0.0914212	+	0.635372i
$481$	−37.3179	+	7.43753i	−1.70155	+	0.339122i
$482$	10.8654	+	3.53038i	0.494905	+	0.160804i
$483$	0.0431056	+	0.0443452i	0.00196137	+	0.00201778i
$484$	−26.1713	−	19.7943i	−1.18960	−	0.899739i
$485$		−	3.25903i		−	0.147985i
$486$	−32.0459	+	13.5627i	−1.45363	+	0.615215i
$487$	8.32526	+	11.4587i	0.377253	+	0.519245i	0.954854	−	0.297074i	$-0.0960110\pi$
$487$	8.32526	+	11.4587i	0.377253	+	0.519245i	−0.577601	+	0.816319i	$0.696011\pi$
$488$	−1.66337	−	1.20851i	−0.0752974	−	0.0547067i
$489$	7.39950	−	14.0272i	0.334617	−	0.634332i
$490$	13.9176	−	4.52211i	0.628734	−	0.204288i
$491$	17.7099	+	12.8670i	0.799235	+	0.580678i	0.910690	−	0.413091i	$-0.135551\pi$
$491$	17.7099	+	12.8670i	0.799235	+	0.580678i	−0.111455	+	0.993770i	$0.535551\pi$
$492$	11.8439	+	2.04839i	0.533966	+	0.0923485i
$493$	5.89047	−	18.1290i	0.265293	−	0.816489i
$494$	47.6894	+	21.9635i	2.14565	+	0.988183i
$495$	11.9218	+	0.452783i	0.535845	+	0.0203511i
$496$			7.93250i			0.356180i
$497$	−2.24334	+	6.90429i	−0.100628	+	0.309700i
$498$	5.54977	−	32.0892i	0.248691	−	1.43795i
$499$	5.32294	−	7.32640i	0.238288	−	0.327975i	−0.673079	−	0.739571i	$-0.735029\pi$
$499$	5.32294	−	7.32640i	0.238288	−	0.327975i	0.911366	+	0.411596i	$0.135029\pi$
$500$	9.46397	+	29.1271i	0.423242	+	1.30260i
$501$	−2.74789	+	5.20916i	−0.122767	+	0.232728i
$502$	−3.26998	−	2.37578i	−0.145946	−	0.106036i
$503$	10.1392	−	7.36658i	0.452086	−	0.328460i	−0.338333	−	0.941026i	$-0.609863\pi$
$503$	10.1392	−	7.36658i	0.452086	−	0.328460i	0.790419	+	0.612567i	$0.209863\pi$
$504$	−2.73736	+	7.67712i	−0.121932	+	0.341966i
$505$	−6.54768			−0.291368
$506$	−0.202431	−	0.0679318i	−0.00899914	−	0.00301994i
$507$	−22.4215	−	2.06783i	−0.995774	−	0.0918353i
$508$	9.25426	+	3.00689i	0.410591	+	0.133409i
$509$	−15.7439	+	11.4386i	−0.697835	+	0.507007i	−0.879226	−	0.476404i	$-0.841940\pi$
$509$	−15.7439	+	11.4386i	−0.697835	+	0.507007i	0.181391	+	0.983411i	$0.441940\pi$
$510$	1.72351	+	11.9783i	0.0763185	+	0.530410i
$511$	1.76463	+	5.43099i	0.0780628	+	0.240253i
$512$	−11.3299	+	3.68132i	−0.500718	+	0.162693i
$513$	−3.87457	−	33.6743i	−0.171066	−	1.48676i
$514$	−20.4914	+	14.8879i	−0.903838	+	0.656677i
$515$	6.17583	−	19.0073i	0.272140	−	0.837560i
$516$	21.3832	+	21.9981i	0.941342	+	0.968414i
$517$	−3.30359	−	4.64014i	−0.145292	−	0.204073i
$518$	29.1663			1.28149
$519$	5.25619	+	10.6877i	0.230721	+	0.469138i
$520$	−9.30437	+	1.85438i	−0.408024	+	0.0813199i
$521$	18.7666	−	25.8300i	0.822178	−	1.13163i	−0.167151	−	0.985931i	$-0.553457\pi$
$521$	18.7666	−	25.8300i	0.822178	−	1.13163i	0.989329	−	0.145700i	$-0.0465434\pi$
$522$	−13.7875	−	46.9194i	−0.603465	−	2.05361i
$523$	−34.8885	+	11.3360i	−1.52557	+	0.495687i	−0.947351	−	0.320196i	$-0.896251\pi$
$523$	−34.8885	+	11.3360i	−1.52557	+	0.495687i	−0.578216	+	0.815883i	$0.696251\pi$
$524$	−22.7807	−	16.5511i	−0.995179	−	0.723040i
$525$	1.30177	−	7.52692i	0.0568138	−	0.328502i
$526$	5.69625	+	1.85082i	0.248368	+	0.0806998i
$527$			19.3991i			0.845039i
$528$	0.814901	+	6.07736i	0.0354640	+	0.264483i
$529$	22.9992			0.999964
$530$	−11.3017	+	34.7830i	−0.490914	+	1.51088i
$531$	−8.34816	−	12.2033i	−0.362279	−	0.529576i
$532$	−19.4905	−	14.1607i	−0.845021	−	0.613943i
$533$	0.982747	−	8.32992i	0.0425675	−	0.360809i
$534$	8.71374	−	16.5186i	0.377080	−	0.714829i
$535$	−10.3309	−	7.50585i	−0.446644	−	0.324506i
$536$	11.3967	−	8.28019i	0.492263	−	0.357650i
$537$	−28.8661	+	14.1963i	−1.24567	+	0.612616i
$538$	−71.1644			−3.06812
$539$	17.2986	−	5.43738i	0.745102	−	0.234204i
$540$	12.5717	+	13.6890i	0.540998	+	0.589081i
$541$	7.90813	−	24.3387i	0.339997	−	1.04640i	−0.624211	−	0.781256i	$-0.714579\pi$
$541$	7.90813	−	24.3387i	0.339997	−	1.04640i	0.964208	−	0.265148i	$-0.0854208\pi$
$542$	10.4475	+	14.3798i	0.448759	+	0.617664i
$543$	21.4855	−	3.09146i	0.922031	−	0.132667i
$544$	−16.8115	+	5.46240i	−0.720788	+	0.234198i
$545$	0.102191	+	0.314512i	0.00437739	+	0.0134722i
$546$	16.5446	+	4.91350i	0.708042	+	0.210278i
$547$	19.3057	+	26.5720i	0.825451	+	1.13614i	0.988753	+	0.149560i	$0.0477857\pi$
$547$	19.3057	+	26.5720i	0.825451	+	1.13614i	−0.163301	+	0.986576i	$0.552214\pi$
$548$	−17.7433	+	54.6084i	−0.757958	+	2.33276i
$549$	2.80958	+	0.0796698i	0.119910	+	0.00340022i
$550$	7.90849	+	25.1602i	0.337219	+	1.07283i
$551$	47.6365			2.02939
$552$	−0.0483783	−	0.0983702i	−0.00205912	−	0.00418692i
$553$	−3.50775	−	4.82801i	−0.149165	−	0.205308i
$554$	42.1212	+	30.6029i	1.78956	+	1.30019i
$555$	10.2264	−	19.3861i	0.434086	−	0.822895i
$556$	−48.2573	+	15.6797i	−2.04656	+	0.664969i
$557$	−15.6453	+	21.5339i	−0.662912	+	0.912421i	−0.999573	−	0.0292053i	$-0.990702\pi$
$557$	−15.6453	+	21.5339i	−0.662912	+	0.912421i	0.336661	+	0.941626i	$0.390702\pi$
$558$	28.1000	+	41.0764i	1.18957	+	1.73890i
$559$	14.5259	−	15.7259i	0.614381	−	0.665134i
$560$	−1.58450			−0.0669575
$561$	1.99286	+	14.8623i	0.0841386	+	0.627488i
$562$	20.2276			0.853249
$563$	−12.4173	+	38.2165i	−0.523327	+	1.61063i	0.244275	+	0.969706i	$0.421450\pi$
$563$	−12.4173	+	38.2165i	−0.523327	+	1.61063i	−0.767601	+	0.640928i	$0.778550\pi$
$564$	1.51222	−	8.74380i	0.0636761	−	0.368181i
$565$	10.2113	−	14.0546i	0.429592	−	0.591282i
$566$	−11.7519	−	36.1687i	−0.493970	−	1.52028i
$567$	−2.83710	−	10.7749i	−0.119147	−	0.452505i
$568$	7.56380	−	10.4107i	0.317370	−	0.436822i
$569$	21.0115	−	15.2657i	0.880848	−	0.639973i	−0.0526278	−	0.998614i	$-0.516760\pi$
$569$	21.0115	−	15.2657i	0.880848	−	0.639973i	0.933476	+	0.358641i	$0.116760\pi$
$570$	−27.1382	+	13.3465i	−1.13670	+	0.559025i
$571$			36.4013i			1.52335i	0.647960	+	0.761675i	$0.275622\pi$
$571$			36.4013i			1.52335i	−0.647960	+	0.761675i	$0.724378\pi$
$572$	−35.0498	+	6.63585i	−1.46551	+	0.277459i
$573$	27.7072	+	28.5041i	1.15749	+	1.19077i
$574$	−1.98669	+	6.11441i	−0.0829229	+	0.255211i
$575$	0.0603880	+	0.0831169i	0.00251835	+	0.00346621i
$576$	−23.7751	+	30.8456i	−0.990631	+	1.28523i
$577$	−12.8606	+	4.17868i	−0.535396	+	0.173961i	−0.564221	−	0.825624i	$-0.690823\pi$
$577$	−12.8606	+	4.17868i	−0.535396	+	0.173961i	0.0288252	+	0.999584i	$0.490823\pi$
$578$	21.6252	−	7.02646i	0.899491	−	0.292262i
$579$	−11.3562	+	1.63401i	−0.471950	+	0.0679069i
$580$	−21.1313	+	15.3528i	−0.877431	+	0.637491i
$581$	9.91709	+	3.22226i	0.411430	+	0.133682i
$582$	7.53555	−	7.32489i	0.312358	−	0.303627i
$583$	−14.4177	+	42.9635i	−0.597120	+	1.77936i
$584$		−	10.1223i		−	0.418865i
$585$	9.06679	−	9.27397i	0.374865	−	0.383431i
$586$	−34.8911	+	25.3499i	−1.44134	+	1.04719i
$587$	−35.0275	−	25.4490i	−1.44574	−	1.05039i	−0.986804	−	0.161921i	$-0.948231\pi$
$587$	−35.0275	−	25.4490i	−1.44574	−	1.05039i	−0.458936	−	0.888470i	$-0.651769\pi$
$588$	24.9855	+	13.1801i	1.03038	+	0.543538i
$589$	−46.1064	+	14.9809i	−1.89978	+	0.617276i
$590$	−7.75389	+	10.6723i	−0.319223	+	0.439372i
$591$	−6.55603	−	1.13385i	−0.269679	−	0.0466405i
$592$	10.7137	+	3.48108i	0.440329	+	0.143072i
$593$			42.5964i			1.74923i	0.484822	+	0.874613i	$0.338884\pi$
$593$			42.5964i			1.74923i	−0.484822	+	0.874613i	$0.661116\pi$
$594$	25.7482	+	28.5833i	1.05646	+	1.17279i
$595$	−3.87494			−0.158857
$596$	13.5674	+	4.40831i	0.555742	+	0.180571i
$597$	2.13996	−	12.3734i	0.0875829	−	0.506411i
$598$	−0.202487	+	0.113498i	−0.00828029	+	0.00464126i
$599$	−17.4014	+	5.65405i	−0.711001	+	0.231018i	−0.642117	−	0.766606i	$-0.721944\pi$
$599$	−17.4014	+	5.65405i	−0.711001	+	0.231018i	−0.0688838	+	0.997625i	$0.521944\pi$
$600$	−6.31751	+	11.9761i	−0.257911	+	0.488922i
$601$	13.3670	−	18.3982i	0.545253	−	0.750477i	−0.444105	−	0.895975i	$-0.646478\pi$
$601$	13.3670	−	18.3982i	0.545253	−	0.750477i	0.989359	+	0.145498i	$0.0464784\pi$
$602$	−13.2752	+	9.64500i	−0.541057	+	0.393101i
$603$	−6.46773	+	18.1392i	−0.263386	+	0.738685i
$604$	−7.32769			−0.298159
$605$	−3.83390	−	12.6200i	−0.155870	−	0.513077i
$606$	−14.7164	−	15.1396i	−0.597812	−	0.615005i
$607$	−1.04302	−	0.338897i	−0.0423348	−	0.0137554i	0.287773	−	0.957699i	$-0.407085\pi$
$607$	−1.04302	−	0.338897i	−0.0423348	−	0.0137554i	−0.330108	+	0.943943i	$0.607085\pi$
$608$	−25.9652	−	35.7381i	−1.05303	−	1.44937i
$609$	15.4991	−	2.23011i	0.628056	−	0.0903685i
$610$	−0.774931	−	2.38499i	−0.0313761	−	0.0965656i
$611$	−6.14957	−	0.725514i	−0.248785	−	0.0293512i
$612$	−14.2612	+	18.5024i	−0.576477	+	0.747915i
$613$	4.01628	−	2.91800i	0.162216	−	0.117857i	−0.503716	−	0.863869i	$-0.668034\pi$
$613$	4.01628	−	2.91800i	0.162216	−	0.117857i	0.665932	+	0.746013i	$0.268034\pi$
$614$	−26.8455	−	8.72262i	−1.08339	−	0.352016i
$615$	3.36752	+	3.46436i	0.135791	+	0.139696i
$616$	9.01035	+	0.0866131i	0.363037	+	0.00348974i
$617$	−27.8317			−1.12046			−0.560231	−	0.828336i	$-0.689288\pi$
$617$	−27.8317			−1.12046			−0.560231	+	0.828336i	$0.689288\pi$
$618$	57.8294	−	28.4404i	2.32624	−	1.14404i
$619$	14.5929	+	20.0854i	0.586538	+	0.807300i	0.994393	−	0.105746i	$-0.0337231\pi$
$619$	14.5929	+	20.0854i	0.586538	+	0.807300i	−0.407855	+	0.913047i	$0.633723\pi$
$620$	15.6244	−	21.5051i	0.627490	−	0.863666i
$621$	0.130513	+	0.0736497i	0.00523731	+	0.00295546i
$622$	7.41864	+	22.8322i	0.297460	+	0.915488i
$623$	4.83794	+	3.51497i	0.193828	+	0.140824i
$624$	5.49088	+	3.77952i	0.219811	+	0.151302i
$625$	1.69998	−	5.23200i	0.0679993	−	0.209280i
$626$			6.21244i			0.248299i
$627$	−33.7847	+	16.2138i	−1.34923	+	0.647519i
$628$	16.2229			0.647365
$629$	26.2005	+	8.51307i	1.04468	+	0.339438i
$630$	−8.20493	+	5.61293i	−0.326892	+	0.223625i
$631$	11.8895	−	16.3645i	0.473313	−	0.651459i	−0.503890	−	0.863768i	$-0.668098\pi$
$631$	11.8895	−	16.3645i	0.473313	−	0.651459i	0.977203	+	0.212309i	$0.0680983\pi$
$632$	3.26890	+	10.0606i	0.130030	+	0.400190i
$633$	4.88185	−	9.25450i	0.194036	−	0.367833i
$634$	17.4192	−	23.9754i	0.691804	−	0.952186i
$635$	2.29893	+	3.16421i	0.0912304	+	0.125568i
$636$	−63.3524	+	31.1566i	−2.51209	+	1.23544i
$637$	8.24618	−	17.9050i	0.326726	−	0.709421i
$638$	−44.0426	+	31.3565i	−1.74366	+	1.24141i
$639$	−0.498635	+	17.5845i	−0.0197257	+	0.695634i
$640$	17.6017	+	5.71915i	0.695769	+	0.226069i
$641$	3.93606	+	5.41753i	0.155465	+	0.213979i	0.879644	−	0.475633i	$-0.157781\pi$
$641$	3.93606	+	5.41753i	0.155465	+	0.213979i	−0.724179	+	0.689612i	$0.757781\pi$
$642$	−5.86438	−	40.7571i	−0.231449	−	1.60856i
$643$	20.0932	−	6.52868i	0.792399	−	0.257466i	0.115274	−	0.993334i	$-0.463226\pi$
$643$	20.0932	−	6.52868i	0.792399	−	0.257466i	0.677125	+	0.735868i	$0.263226\pi$
$644$	0.101298	−	0.0329139i	0.00399172	−	0.00129699i
$645$	1.75619	+	12.2055i	0.0691501	+	0.480589i
$646$	−22.3429	−	30.7524i	−0.879070	−	1.20994i
$647$	−8.66732	−	2.81618i	−0.340747	−	0.110716i	0.133644	−	0.991029i	$-0.457332\pi$
$647$	−8.66732	−	2.81618i	−0.340747	−	0.110716i	−0.474392	+	0.880314i	$0.657332\pi$
$648$	−1.11921	+	19.7188i	−0.0439668	+	0.774629i
$649$	−9.73461	+	13.1312i	−0.382117	+	0.515446i
$650$	26.0422	+	11.9938i	1.02146	+	0.470436i
$651$	−14.2999	+	7.03268i	−0.560459	+	0.275632i
$652$	−16.0548	−	22.0975i	−0.628754	−	0.865405i
$653$	−6.04944	+	8.32635i	−0.236733	+	0.325835i	−0.910810	−	0.412826i	$-0.864542\pi$
$653$	−6.04944	+	8.32635i	−0.236733	+	0.325835i	0.674077	+	0.738661i	$0.264542\pi$
$654$	−0.497535	+	0.943176i	−0.0194552	+	0.0368811i
$655$	−3.49755	−	10.7644i	−0.136661	−	0.420598i
$656$	−1.45954	+	2.00889i	−0.0569856	+	0.0784340i
$657$	7.81303	+	11.4210i	0.304815	+	0.445576i
$658$	4.51397	+	1.46668i	0.175973	+	0.0571770i
$659$	−36.7889			−1.43309			−0.716546	−	0.697540i	$-0.754278\pi$
$659$	−36.7889			−1.43309			−0.716546	+	0.697540i	$0.754278\pi$
$660$	9.76117	−	18.0809i	0.379953	−	0.703798i
$661$		−	32.6701i		−	1.27072i	−0.772217	−	0.635359i	$-0.780852\pi$
$661$		−	32.6701i		−	1.27072i	0.772217	−	0.635359i	$-0.219148\pi$
$662$	3.06398	−	9.42995i	0.119085	−	0.366506i
$663$	13.4281	+	9.24290i	0.521503	+	0.358964i
$664$	−14.9535	−	10.8644i	−0.580310	−	0.421620i
$665$	−2.99240	−	9.20967i	−0.116040	−	0.357136i
$666$	67.8093	−	19.9261i	2.62756	−	0.772123i
$667$	−0.123791	+	0.170384i	−0.00479322	+	0.00659730i
$668$	5.96212	+	8.20616i	0.230682	+	0.317506i
$669$	36.9541	−	18.1739i	1.42873	−	0.702645i
$670$	17.1819			0.663794
$671$	−0.931776	−	2.96437i	−0.0359708	−	0.114438i
$672$	−10.1212	−	10.4122i	−0.390433	−	0.401661i
$673$	−12.6163	−	4.09928i	−0.486322	−	0.158016i	0.0555852	−	0.998454i	$-0.482298\pi$
$673$	−12.6163	−	4.09928i	−0.486322	−	0.158016i	−0.541907	+	0.840438i	$0.682298\pi$
$674$	−46.1686	+	33.5435i	−1.77835	+	1.29205i
$675$	−2.11582	−	18.3888i	−0.0814380	−	0.707787i
$676$	−20.2377	+	33.0806i	−0.778374	+	1.27233i
$677$	−3.79563	−	11.6818i	−0.145878	−	0.448966i	0.851245	−	0.524769i	$-0.175848\pi$
$677$	−3.79563	−	11.6818i	−0.145878	−	0.448966i	−0.997123	+	0.0758024i	$0.975848\pi$
$678$	55.4478	−	7.97816i	2.12946	−	0.306400i
$679$	1.97787	+	2.72231i	0.0759037	+	0.104472i
$680$	6.53251	+	2.12254i	0.250510	+	0.0813957i
$681$	−23.0318	−	23.6942i	−0.882581	−	0.907962i
$682$	32.7668	−	44.1999i	1.25471	−	1.69250i
$683$	−14.8201			−0.567074			−0.283537	−	0.958961i	$-0.591508\pi$
$683$	−14.8201			−0.567074			−0.283537	+	0.958961i	$0.591508\pi$
$684$	−54.9883	−	19.6067i	−2.10253	−	0.749681i
$685$	−18.6717	+	13.5658i	−0.713408	+	0.518321i
$686$	−20.2520	+	27.8745i	−0.773226	+	1.06425i
$687$	−21.8353	+	41.3931i	−0.833068	+	1.57924i
$688$	−6.02754	+	1.95847i	−0.229798	+	0.0746658i
$689$	24.0885	+	42.9753i	0.917699	+	1.63723i
$690$	0.0227859	−	0.131750i	0.000867444	−	0.00501563i
$691$	−38.0035	−	12.3481i	−1.44572	−	0.469743i	−0.522045	−	0.852918i	$-0.674831\pi$
$691$	−38.0035	−	12.3481i	−1.44572	−	0.469743i	−0.923676	+	0.383174i	$0.874831\pi$
$692$	20.5128			0.779780
$693$	−10.2332	+	6.85700i	−0.388728	+	0.260476i
$694$			35.5306i			1.34872i
$695$	−19.3970	−	6.30248i	−0.735771	−	0.239067i
$696$	−27.3505	−	4.73022i	−1.03672	−	0.179299i
$697$	−3.56935	+	4.91279i	−0.135199	+	0.186085i
$698$	71.6029	−	23.2652i	2.71021	−	0.880600i
$699$	11.5867	+	6.11210i	0.438248	+	0.231181i
$700$	−10.6434	−	7.73286i	−0.402281	−	0.292274i
$701$	−9.47103	+	6.88111i	−0.357716	+	0.259896i	−0.752099	−	0.659050i	$-0.770958\pi$
$701$	−9.47103	+	6.88111i	−0.357716	+	0.259896i	0.394383	+	0.918946i	$0.370958\pi$
$702$	41.8216	+	0.120392i	1.57845	+	0.00454389i
$703$			68.8457i			2.59656i
$704$	40.8182	+	13.6978i	1.53839	+	0.516255i
$705$	2.55757	−	2.48607i	0.0963235	−	0.0936309i
$706$	35.6997	+	11.5995i	1.34357	+	0.436554i
$707$	5.46936	−	3.97372i	0.205697	−	0.149447i
$708$	−25.2052	+	3.62668i	−0.947270	+	0.136299i
$709$	−20.2217	+	6.57042i	−0.759441	+	0.246757i	−0.663039	−	0.748585i	$-0.730733\pi$
$709$	−20.2217	+	6.57042i	−0.759441	+	0.246757i	−0.0964022	+	0.995342i	$0.530733\pi$
$710$	14.9271	−	4.85012i	0.560205	−	0.182022i
$711$	−11.4537	−	8.82826i	−0.429547	−	0.331085i
$712$	−6.23060	−	8.57569i	−0.233502	−	0.321387i
$713$	0.0662320	−	0.203841i	0.00248041	−	0.00763391i
$714$	−8.70921	−	8.95967i	−0.325934	−	0.335307i
$715$	−12.9654	−	6.12300i	−0.484880	−	0.228987i
$716$			55.4025i			2.07049i
$717$	35.3663	−	17.3931i	1.32078	−	0.649557i
$718$	−30.7344	+	22.3298i	−1.14700	+	0.833342i
$719$	−12.1614	+	16.7387i	−0.453543	+	0.624248i	−0.973154	−	0.230155i	$-0.926077\pi$
$719$	−12.1614	+	16.7387i	−0.453543	+	0.624248i	0.519611	+	0.854403i	$0.326077\pi$
$720$	−3.68384	+	1.08252i	−0.137289	+	0.0403430i
$721$	6.37657	+	19.6251i	0.237476	+	0.730875i
$722$	30.9058	−	42.5382i	1.15020	−	1.58311i
$723$	−1.51066	+	8.73475i	−0.0561820	+	0.324849i
$724$	11.5526	−	35.5554i	0.429351	−	1.32141i
$725$	26.0133			0.966111
$726$	20.5632	−	37.2292i	0.763171	−	1.38171i
$727$	39.7266			1.47338			0.736688	−	0.676233i	$-0.236389\pi$
$727$	39.7266			1.47338			0.736688	+	0.676233i	$0.236389\pi$
$728$	6.64666	−	7.19572i	0.246341	−	0.266691i
$729$	−13.9574	−	23.1126i	−0.516940	−	0.856022i
$730$	7.25686	−	9.98821i	0.268588	−	0.369680i
$731$	−14.7405	+	4.78948i	−0.545197	+	0.177145i
$732$	2.25861	−	4.28163i	0.0834806	−	0.158254i
$733$	2.62799	+	1.90934i	0.0970669	+	0.0705232i	0.635260	−	0.772298i	$-0.280893\pi$
$733$	2.62799	+	1.90934i	0.0970669	+	0.0705232i	−0.538193	+	0.842822i	$0.680893\pi$
$734$	7.16875	+	9.86694i	0.264603	+	0.364195i
$735$	5.01095	+	10.1890i	0.184832	+	0.375828i
$736$	0.195301			0.00719889
$737$	21.2893	+	0.204646i	0.784201	+	0.00753823i
$738$	−0.441589	+	15.5728i	−0.0162551	+	0.573242i
$739$	−9.20555	+	28.3318i	−0.338632	+	1.04220i	0.626274	+	0.779603i	$0.284579\pi$
$739$	−9.20555	+	28.3318i	−0.338632	+	1.04220i	−0.964905	+	0.262598i	$0.915421\pi$
$740$	−22.1883	−	30.5396i	−0.815659	−	1.12266i
$741$	−11.5981	+	39.0526i	−0.426066	+	1.43463i
$742$	−11.6690	−	35.9136i	−0.428384	−	1.31843i
$743$	−19.6389	+	6.38108i	−0.720483	+	0.234099i	−0.646233	−	0.763141i	$-0.723656\pi$
$743$	−19.6389	+	6.38108i	−0.720483	+	0.234099i	−0.0742504	+	0.997240i	$0.523656\pi$
$744$	27.9595	−	4.02299i	1.02505	−	0.147490i
$745$	3.37039	+	4.63895i	0.123482	+	0.169958i
$746$	−20.8380	+	64.1327i	−0.762933	+	2.34806i
$747$	25.2578	+	0.716222i	0.924136	+	0.0262052i
$748$	24.4843	+	8.21647i	0.895236	+	0.300424i
$749$	13.1848			0.481761
$750$	−35.6204	+	17.5180i	−1.30067	+	0.639668i
$751$	36.3678	−	26.4227i	1.32708	−	0.964180i	0.327265	−	0.944933i	$-0.393873\pi$
$751$	36.3678	−	26.4227i	1.32708	−	0.964180i	0.999815	−	0.0192471i	$-0.00612693\pi$
$752$	1.48307	+	1.07751i	0.0540818	+	0.0392927i
$753$	1.46325	−	2.77389i	0.0533240	−	0.101086i
$754$	−6.88632	+	58.3696i	−0.250785	+	2.12570i
$755$	−2.38285	−	1.73124i	−0.0867208	−	0.0630064i
$756$	−18.8090	−	3.80499i	−0.684076	−	0.138386i
$757$	−9.57470	+	29.4679i	−0.347998	+	1.07103i	0.611961	+	0.790888i	$0.290381\pi$
$757$	−9.57470	+	29.4679i	−0.347998	+	1.07103i	−0.959959	+	0.280141i	$0.909619\pi$
$758$	60.9903			2.21527
$759$	0.0298022	−	0.162974i	0.00108175	−	0.00591557i
$760$			17.1651i			0.622644i
$761$	−48.6784	−	15.8166i	−1.76459	−	0.573350i	−0.766930	−	0.641730i	$-0.778217\pi$
$761$	−48.6784	−	15.8166i	−1.76459	−	0.573350i	−0.997659	+	0.0683802i	$0.978217\pi$
$762$	−2.14930	+	12.4274i	−0.0778607	+	0.450197i
$763$	−0.276236	−	0.200697i	−0.0100004	−	0.00726572i
$764$	65.1122	−	21.1562i	2.35568	−	0.765406i
$765$	−9.00892	+	2.64732i	−0.325718	+	0.0957142i
$766$	21.3146	−	29.3371i	0.770128	−	1.05999i
$767$	3.47328	+	17.4272i	0.125413	+	0.629261i
$768$	6.49141	+	13.1993i	0.234239	+	0.476290i
$769$	42.6211			1.53696			0.768478	−	0.639876i	$-0.221014\pi$
$769$	42.6211			1.53696			0.768478	+	0.639876i	$0.221014\pi$
$770$	8.82885	+	6.54512i	0.318170	+	0.235870i
$771$	−13.6983	−	14.0923i	−0.493333	−	0.507521i
$772$	−6.10620	+	18.7929i	−0.219767	+	0.676373i
$773$	17.2995	−	12.5688i	0.622219	−	0.452069i	−0.231477	−	0.972840i	$-0.574356\pi$
$773$	17.2995	−	12.5688i	0.622219	−	0.452069i	0.853696	+	0.520772i	$0.174356\pi$
$774$	−24.2744	+	31.4933i	−0.872525	+	1.13200i
$775$	−25.1777	+	8.18075i	−0.904411	+	0.293861i
$776$	−1.84319	−	5.67275i	−0.0661667	−	0.203640i
$777$	3.22301	+	22.3998i	0.115625	+	0.803587i
$778$	−18.7920	+	13.6532i	−0.673726	+	0.489491i
$779$	−14.4328	−	4.68949i	−0.517108	−	0.168018i
$780$	−7.44145	−	21.0615i	−0.266447	−	0.754123i
$781$	18.5533	−	5.83177i	0.663889	−	0.208677i
$782$	0.168055			0.00600964
$783$	34.5106	−	15.7737i	1.23331	−	0.563705i
$784$	−4.72126	+	3.43020i	−0.168617	+	0.122507i
$785$	5.27545	+	3.83284i	0.188289	+	0.136800i
$786$	17.0284	−	32.2807i	0.607384	−	1.15142i
$787$	0.226708	+	0.697737i	0.00808128	+	0.0248716i	0.955016	−	0.296555i	$-0.0958377\pi$
$787$	0.226708	+	0.697737i	0.00808128	+	0.0248716i	−0.946935	+	0.321426i	$0.895838\pi$
$788$	−6.73540	+	9.27048i	−0.239939	+	0.330247i
$789$	−0.791973	+	4.57925i	−0.0281950	+	0.163026i
$790$	−3.98703	+	12.2708i	−0.141852	+	0.436576i
$791$			17.9371i			0.637771i
$792$	21.0075	−	5.95442i	0.746469	−	0.211581i
$793$	−3.06829	−	1.41311i	−0.108958	−	0.0501809i
$794$	19.8959	−	61.2331i	0.706077	−	2.17308i
$795$	−27.9623	−	4.83603i	−0.991721	−	0.171516i
$796$	−17.4965	−	12.7120i	−0.620148	−	0.450564i
$797$	−2.83292	+	0.920472i	−0.100347	+	0.0326048i	−0.358760	−	0.933430i	$-0.616800\pi$
$797$	−2.83292	+	0.920472i	−0.100347	+	0.0326048i	0.258413	+	0.966035i	$0.416800\pi$
$798$	14.5690	−	27.6185i	0.515738	−	0.977683i
$799$	3.62687	+	2.63508i	0.128310	+	0.0932223i
$800$	−14.1791	−	19.5158i	−0.501306	−	0.689989i
$801$	13.6492	+	4.86678i	0.482271	+	0.171959i
$802$		−	48.0669i		−	1.69730i
$803$	9.11061	−	12.2895i	0.321506	−	0.433687i
$804$	23.1180	+	23.7829i	0.815310	+	0.838757i
$805$	0.0407169	+	0.0132297i	0.00143508	+	0.000466287i
$806$	−11.6911	−	58.6603i	−0.411802	−	2.06622i
$807$	−7.86400	−	54.6544i	−0.276826	−	1.92392i
$808$	−11.3971	+	3.70314i	−0.400948	+	0.130276i
$809$	−15.7650	−	48.5195i	−0.554266	−	1.70586i	−0.697874	−	0.716221i	$-0.745870\pi$
$809$	−15.7650	−	48.5195i	−0.554266	−	1.70586i	0.143607	−	0.989635i	$-0.454130\pi$
$810$	−15.2411	+	18.6551i	−0.535518	+	0.655475i
$811$	23.4422	−	17.0317i	0.823166	−	0.598065i	−0.0944518	−	0.995529i	$-0.530110\pi$
$811$	23.4422	−	17.0317i	0.823166	−	0.598065i	0.917618	+	0.397465i	$0.130110\pi$
$812$	8.33380	−	25.6488i	0.292459	−	0.900097i
$813$	−9.88918	+	9.61273i	−0.346829	+	0.337133i
$814$	−45.3173	−	63.6516i	−1.58837	−	2.23099i
$815$		−	10.9789i		−	0.384573i
$816$	−2.12979	−	4.33063i	−0.0745577	−	0.151602i
$817$	−22.7666	−	31.3355i	−0.796501	−	1.09629i
$818$	−3.43995	+	4.73468i	−0.120275	+	0.165544i
$819$	−1.94532	+	13.2492i	−0.0679750	+	0.462965i
$820$	7.91369	−	2.57131i	0.276358	−	0.0897941i
$821$	−2.51822	+	3.46603i	−0.0878865	+	0.120965i	−0.850696	−	0.525658i	$-0.823819\pi$
$821$	−2.51822	+	3.46603i	−0.0878865	+	0.120965i	0.762810	+	0.646623i	$0.223819\pi$
$822$	−73.3328	−	12.6828i	−2.55777	−	0.442362i
$823$	5.05957	−	15.5718i	0.176366	−	0.542797i	−0.823328	−	0.567566i	$-0.807885\pi$
$823$	5.05957	−	15.5718i	0.176366	−	0.542797i	0.999693	+	0.0247690i	$0.00788501\pi$
$824$		−	36.5774i		−	1.27423i
$825$	−18.4491	+	8.85405i	−0.642317	+	0.308258i
$826$		−	13.6205i		−	0.473917i
$827$	−9.96320	−	3.23724i	−0.346455	−	0.112570i	0.130621	−	0.991432i	$-0.458303\pi$
$827$	−9.96320	−	3.23724i	−0.346455	−	0.112570i	−0.477075	+	0.878863i	$0.658303\pi$
$828$	0.213024	−	0.145728i	0.00740310	−	0.00506440i
$829$	−2.81250	−	2.04340i	−0.0976822	−	0.0709702i	0.537872	−	0.843026i	$-0.319228\pi$
$829$	−2.81250	−	2.04340i	−0.0976822	−	0.0709702i	−0.635554	+	0.772056i	$0.719228\pi$
$830$	−6.96655	−	21.4408i	−0.241812	−	0.744222i
$831$	−18.8484	+	35.7309i	−0.653845	+	1.23949i
$832$	40.8295	−	22.8857i	1.41551	−	0.793419i
$833$	−11.5460	+	8.38864i	−0.400044	+	0.290649i
$834$	−29.0236	−	59.0152i	−1.00500	−	2.04353i
$835$			4.07713i			0.141095i
$836$	−0.620376	+	64.5377i	−0.0214562	+	2.23208i
$837$	−28.4415	+	26.1200i	−0.983083	+	0.902839i
$838$	8.02612	−	24.7019i	0.277258	−	0.853311i
$839$	2.88863	−	2.09871i	0.0997265	−	0.0724555i	−0.536805	−	0.843707i	$-0.680369\pi$
$839$	2.88863	−	2.09871i	0.0997265	−	0.0724555i	0.636531	+	0.771251i	$0.280369\pi$
$840$	0.803585	+	5.58487i	0.0277263	+	0.192696i
$841$	7.51702	+	23.1350i	0.259208	+	0.797759i
$842$	24.7306	+	76.1131i	0.852274	+	2.62303i
$843$	2.23524	+	15.5348i	0.0769858	+	0.535047i
$844$	−10.5922	−	14.5789i	−0.364599	−	0.501827i
$845$	−14.3966	+	5.97592i	−0.495259	+	0.205578i
$846$	11.4966	+	0.326003i	0.395262	+	0.0112082i
$847$	10.8615	+	8.21492i	0.373205	+	0.282268i
$848$		−	14.5849i		−	0.500847i
$849$	26.4790	−	13.0223i	0.908756	−	0.446924i
$850$	−12.2010	−	16.7932i	−0.418491	−	0.576003i
$851$	−0.246244	−	0.178907i	−0.00844113	−	0.00613284i
$852$	26.7978	+	14.1361i	0.918076	+	0.484295i
$853$	0.738763	+	2.27368i	0.0252948	+	0.0778493i	0.962907	−	0.269833i	$-0.0869686\pi$
$853$	0.738763	+	2.27368i	0.0252948	+	0.0778493i	−0.937612	+	0.347683i	$0.886969\pi$
$854$	2.09474	+	1.52192i	0.0716805	+	0.0520789i
$855$	−13.2491	−	19.3674i	−0.453108	−	0.662349i
$856$	−22.2273	−	7.22210i	−0.759714	−	0.246846i
$857$	−31.0326			−1.06006			−0.530028	−	0.847980i	$-0.677818\pi$
$857$	−31.0326			−1.06006			−0.530028	+	0.847980i	$0.677818\pi$
$858$	−14.9831	−	43.7407i	−0.511515	−	1.49328i
$859$	2.10662			0.0718769			0.0359384	−	0.999354i	$-0.488558\pi$
$859$	2.10662			0.0718769			0.0359384	+	0.999354i	$0.488558\pi$
$860$	20.1983	+	6.56281i	0.688755	+	0.223790i
$861$	−4.91541	−	0.850112i	−0.167517	−	0.0289717i
$862$	46.4321	+	33.7349i	1.58148	+	1.14902i
$863$	−2.88584	−	8.88170i	−0.0982351	−	0.302337i	0.889848	−	0.456257i	$-0.150810\pi$
$863$	−2.88584	−	8.88170i	−0.0982351	−	0.302337i	−0.988083	+	0.153920i	$0.950810\pi$
$864$	−30.6445	−	17.2929i	−1.04255	−	0.588317i
$865$	6.67045	+	4.84637i	0.226802	+	0.164781i
$866$	33.8875	+	46.6421i	1.15154	+	1.58496i
$867$	7.78602	+	15.8317i	0.264427	+	0.537674i
$868$			27.4458i			0.931570i
$869$	−5.08631	+	15.1567i	−0.172541	+	0.514157i
$870$	−23.5969	−	24.2755i	−0.800010	−	0.823017i
$871$	15.7044	−	17.0017i	0.532125	−	0.576082i
$872$	0.355754	+	0.489653i	0.0120473	+	0.0165817i
$873$	6.45824	+	4.97787i	0.218578	+	0.168476i
$874$	0.129780	+	0.399421i	0.00438987	+	0.0135106i
$875$	−3.92769	−	12.0882i	−0.132780	−	0.408655i
$876$	23.5895	−	3.39421i	0.797017	−	0.114680i
$877$	−20.6549	+	15.0066i	−0.697466	+	0.506738i	−0.879106	−	0.476627i	$-0.841859\pi$
$877$	−20.6549	+	15.0066i	−0.697466	+	0.506738i	0.181640	+	0.983365i	$0.441859\pi$
$878$	10.4593	−	32.1904i	0.352985	−	1.08637i
$879$	−23.3244	−	23.9951i	−0.786711	−	0.809336i
$880$	2.46193	+	3.45797i	0.0829915	+	0.116568i
$881$			29.7416i			1.00202i	0.865441	+	0.501010i	$0.167038\pi$
$881$			29.7416i			1.00202i	−0.865441	+	0.501010i	$0.832962\pi$
$882$	−12.2967	+	34.4870i	−0.414052	+	1.16124i
$883$	−37.3884	+	27.1643i	−1.25822	+	0.914151i	−0.998669	−	0.0515779i	$-0.983575\pi$
$883$	−37.3884	+	27.1643i	−1.25822	+	0.914151i	−0.259552	+	0.965729i	$0.583575\pi$
$884$	24.4911	−	13.7277i	0.823725	−	0.461714i
$885$	−9.05319	−	4.77566i	−0.304320	−	0.160532i
$886$	−0.147327	−	0.453425i	−0.00494953	−	0.0152331i
$887$	−37.6070	−	27.3231i	−1.26272	−	0.917419i	−0.263831	−	0.964569i	$-0.584986\pi$
$887$	−37.6070	−	27.3231i	−1.26272	−	0.917419i	−0.998888	+	0.0471496i	$0.984986\pi$
$888$	6.83624	−	39.5277i	0.229409	−	1.32646i
$889$	−3.84066	−	1.24790i	−0.128811	−	0.0418534i
$890$		−	12.9289i		−	0.433376i
$891$	−19.1067	+	22.9332i	−0.640100	+	0.768292i
$892$		−	70.9257i		−	2.37477i
$893$	−3.46202	+	10.6550i	−0.115852	+	0.356556i
$894$	−3.15101	+	18.2194i	−0.105386	+	0.609349i
$895$	−13.0894	+	18.0161i	−0.437531	+	0.602210i
$896$	−18.1738	+	5.90504i	−0.607145	+	0.197273i
$897$	−0.109542	−	0.142968i	−0.00365750	−	0.00477356i
$898$	19.4216	−	26.7315i	0.648106	−	0.892041i
$899$	−31.8984	−	43.9044i	−1.06387	−	1.46429i
$900$	−30.0280	−	10.7068i	−1.00093	−	0.356894i
$901$		−	35.6677i		−	1.18826i
$902$	16.4307	−	5.16459i	0.547083	−	0.171962i
$903$	−8.87434	−	9.12955i	−0.295320	−	0.303813i
$904$	9.82526	−	30.2390i	0.326783	−	1.00574i
$905$	12.1571	−	8.83263i	0.404115	−	0.293607i
$906$	−1.35264	−	9.40074i	−0.0449383	−	0.312319i
$907$	4.84805	+	14.9208i	0.160977	+	0.495436i	0.998717	−	0.0506325i	$-0.0161237\pi$
$907$	4.84805	+	14.9208i	0.160977	+	0.495436i	−0.837740	+	0.546069i	$0.816124\pi$
$908$	−54.1249	+	17.5863i	−1.79620	+	0.583620i
$909$	10.0010	−	12.9752i	0.331713	−	0.430360i
$910$	11.7173	−	2.33528i	0.388425	−	0.0774138i
$911$	8.58762	+	2.79029i	0.284520	+	0.0924463i	0.447801	−	0.894133i	$-0.352207\pi$
$911$	8.58762	+	2.79029i	0.284520	+	0.0924463i	−0.163280	+	0.986580i	$0.552207\pi$
$912$	8.64799	−	8.40624i	0.286364	−	0.278358i
$913$	−8.37656	−	26.6493i	−0.277224	−	0.881964i
$914$		−	48.3651i		−	1.59978i
$915$	1.74605	−	0.858701i	0.0577225	−	0.0283878i
$916$	47.3763	+	65.2079i	1.56536	+	2.15453i
$917$	9.45433	+	6.86897i	0.312209	+	0.226833i
$918$	−26.3694	−	14.8805i	−0.870319	−	0.491128i
$919$	−7.52402	+	2.44470i	−0.248194	+	0.0806432i	−0.430472	−	0.902604i	$-0.641653\pi$
$919$	−7.52402	+	2.44470i	−0.248194	+	0.0806432i	0.182278	+	0.983247i	$0.441653\pi$
$920$	−0.0613953	−	0.0446063i	−0.00202414	−	0.00147063i
$921$	3.73243	−	21.5812i	0.122988	−	0.711126i
$922$	−0.764752	+	2.35367i	−0.0251858	+	0.0775139i
$923$	8.84431	−	19.2037i	0.291114	−	0.632098i
$924$	2.81949	+	21.0272i	0.0927543	+	0.691743i
$925$			37.5952i			1.23612i
$926$	−12.8113	+	39.4291i	−0.421005	+	1.29572i
$927$	28.2327	+	41.2702i	0.927282	+	1.35549i
$928$	29.0662	−	40.0061i	0.954143	−	1.31327i
$929$	7.78936	+	23.9732i	0.255561	+	0.786535i	0.993719	+	0.111907i	$0.0356959\pi$
$929$	7.78936	+	23.9732i	0.255561	+	0.786535i	−0.738158	+	0.674628i	$0.764304\pi$
$930$	30.4732	+	16.0749i	0.999255	+	0.527118i
$931$	−28.8538	−	20.9635i	−0.945645	−	0.687052i
$932$	18.2529	−	13.2615i	0.597893	−	0.434395i
$933$	−16.7154	+	8.22059i	−0.547237	+	0.269130i
$934$	14.8122			0.484671
$935$	6.02070	+	8.45655i	0.196898	+	0.276559i
$936$	10.5369	−	21.2704i	0.344409	−	0.695245i
$937$	−17.9996	−	5.84842i	−0.588021	−	0.191060i	−0.000130176	−	1.00000i	$-0.500041\pi$
$937$	−17.9996	−	5.84842i	−0.588021	−	0.191060i	−0.587891	+	0.808940i	$0.700041\pi$
$938$	−14.3522	+	10.4275i	−0.468617	+	0.340470i
$939$	−4.77116	+	0.686504i	−0.155701	+	0.0224032i
$940$	−1.89827	−	5.84229i	−0.0619149	−	0.190554i
$941$	−10.7067	+	3.47881i	−0.349028	+	0.113406i	−0.478284	−	0.878205i	$-0.658741\pi$
$941$	−10.7067	+	3.47881i	−0.349028	+	0.113406i	0.129256	+	0.991611i	$0.458741\pi$
$942$	2.99463	+	20.8125i	0.0975703	+	0.678108i
$943$	0.0542790	−	0.0394360i	0.00176757	−	0.00128421i
$944$	1.62564	−	5.00321i	0.0529102	−	0.162841i
$945$	−5.21742	−	5.68115i	−0.169723	−	0.184808i
$946$	41.6753	+	13.9854i	1.35498	+	0.454705i
$947$	30.0619			0.976882			0.488441	−	0.872597i	$-0.337566\pi$
$947$	30.0619			0.976882			0.488441	+	0.872597i	$0.337566\pi$
$948$	−22.3496	+	10.9915i	−0.725881	+	0.356987i
$949$	−3.25064	−	16.3101i	−0.105520	−	0.529449i
$950$	30.4908	−	41.9669i	0.989251	−	1.36159i
$951$	20.3381	+	10.7286i	0.659507	+	0.347897i
$952$	−6.74484	+	2.19153i	−0.218601	+	0.0710279i
$953$	−9.64010	−	7.00394i	−0.312273	−	0.226880i	0.420598	−	0.907247i	$-0.361820\pi$
$953$	−9.64010	−	7.00394i	−0.312273	−	0.226880i	−0.732871	+	0.680367i	$0.761820\pi$
$954$	−51.6654	−	75.5240i	−1.67273	−	2.44518i
$955$	26.1719	+	8.50376i	0.846902	+	0.275175i
$956$		−	67.8784i		−	2.19534i
$957$	−28.9487	−	30.3598i	−0.935780	−	0.981392i
$958$	57.1042			1.84495
$959$	7.36375	−	22.6633i	0.237788	−	0.731836i
$960$	−4.59456	+	26.5661i	−0.148289	+	0.857417i
$961$	19.6014	+	14.2413i	0.632304	+	0.459395i
$962$	−84.3574	−	9.95231i	−2.71979	−	0.320875i
$963$	30.6535	−	9.00771i	0.987796	−	0.290269i
$964$	12.3513	+	8.97373i	0.397808	+	0.289024i
$965$	−6.42567	+	4.66852i	−0.206850	+	0.150285i
$966$	0.0609243	+	0.123881i	0.00196021	+	0.00398580i
$967$	50.2118			1.61470			0.807351	−	0.590071i	$-0.200900\pi$
$967$	50.2118			1.61470			0.807351	+	0.590071i	$0.200900\pi$
$968$	−13.8108	−	19.7985i	−0.443897	−	0.636347i
$969$	21.1489	−	20.5577i	0.679400	−	0.660407i
$970$	2.24812	−	6.91899i	0.0721827	−	0.222155i
$971$	3.78214	+	5.20567i	0.121375	+	0.167058i	0.865381	−	0.501115i	$-0.167077\pi$
$971$	3.78214	+	5.20567i	0.121375	+	0.167058i	−0.744006	+	0.668173i	$0.767077\pi$
$972$	−46.3289	+	4.00382i	−1.48600	+	0.128423i
$973$	20.0275	−	6.50733i	0.642052	−	0.208615i
$974$	9.77035	+	30.0701i	0.313062	+	0.963507i
$975$	−6.33347	+	21.3258i	−0.202833	+	0.682973i
$976$	0.587816	+	0.809059i	0.0188155	+	0.0258974i
$977$	−15.3441	+	47.2243i	−0.490901	+	1.51084i	0.332347	+	0.943157i	$0.392160\pi$
$977$	−15.3441	+	47.2243i	−0.490901	+	1.51084i	−0.823248	+	0.567682i	$0.807840\pi$
$978$	25.3855	−	24.6758i	0.811737	−	0.789046i
$979$	0.153990	−	16.0196i	0.00492154	−	0.511987i
$980$	19.5558			0.624686
$981$	−0.779340	−	0.277883i	−0.0248824	−	0.00887211i
$982$	28.7227	+	39.5334i	0.916578	+	1.26156i
$983$	5.33308	+	3.87471i	0.170099	+	0.123584i	0.669578	−	0.742742i	$-0.266475\pi$
$983$	5.33308	+	3.87471i	0.170099	+	0.123584i	−0.499479	+	0.866326i	$0.666475\pi$
$984$	7.82092	+	4.12562i	0.249322	+	0.131520i
$985$	−4.38050	+	1.42331i	−0.139574	+	0.0453504i
$986$	25.0112	−	34.4250i	0.796520	−	1.09632i
$987$	−0.627596	+	3.62881i	−0.0199766	+	0.115506i
$988$	51.5402	+	47.6075i	1.63971	+	1.51459i
$989$	0.171242			0.00544517
$990$	24.9979	+	9.18507i	0.794486	+	0.291921i
$991$	−47.7227			−1.51596			−0.757980	−	0.652278i	$-0.773814\pi$
$991$	−47.7227			−1.51596			−0.757980	+	0.652278i	$0.773814\pi$
$992$	−15.5513	+	47.8619i	−0.493753	+	1.51962i
$993$	7.58080	+	1.31109i	0.240569	+	0.0416060i
$994$	−9.52533	+	13.1105i	−0.302125	+	0.415840i
$995$	−2.68627	−	8.26748i	−0.0851604	−	0.262097i
$996$	20.3046	−	38.4914i	0.643377	−	1.21965i
$997$	−33.8859	+	46.6400i	−1.07318	+	1.47710i	−0.206362	+	0.978476i	$0.566162\pi$
$997$	−33.8859	+	46.6400i	−1.07318	+	1.47710i	−0.866817	+	0.498627i	$0.833838\pi$
$998$	16.3546	−	11.8823i	0.517695	−	0.376128i
$999$	22.7966	+	49.8757i	0.721251	+	1.57800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.y.b.233.42	yes	176
3.2	odd	2	inner	429.2.y.b.233.3	yes	176
11.6	odd	10	inner	429.2.y.b.116.41	yes	176
13.12	even	2	inner	429.2.y.b.233.4	yes	176
33.17	even	10	inner	429.2.y.b.116.4	yes	176
39.38	odd	2	inner	429.2.y.b.233.41	yes	176
143.116	odd	10	inner	429.2.y.b.116.3	✓	176
429.116	even	10	inner	429.2.y.b.116.42	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.b.116.3	✓	176	143.116	odd	10	inner
429.2.y.b.116.4	yes	176	33.17	even	10	inner
429.2.y.b.116.41	yes	176	11.6	odd	10	inner
429.2.y.b.116.42	yes	176	429.116	even	10	inner
429.2.y.b.233.3	yes	176	3.2	odd	2	inner
429.2.y.b.233.4	yes	176	13.12	even	2	inner
429.2.y.b.233.41	yes	176	39.38	odd	2	inner
429.2.y.b.233.42	yes	176	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.12303 + 0.689813i) q^{2} +(-0.295173 + 1.70671i) q^{3} +(2.41336 + 1.75341i) q^{4} +(0.370527 + 1.14036i) q^{5} +(-1.80397 + 3.41978i) q^{6} +(-1.00158 - 0.727691i) q^{7} +(1.28990 + 1.77539i) q^{8} +(-2.82575 - 1.00755i) q^{9} +2.67661i q^{10} +(-0.0318800 + 3.31647i) q^{11} +(-3.70493 + 3.60136i) q^{12} +(2.64855 + 2.44646i) q^{13} +(-1.62441 - 2.23581i) q^{14} +(-2.05564 + 0.295778i) q^{15} +(-0.329845 - 1.01516i) q^{16} +(-0.806644 - 2.48260i) q^{17} +(-5.30411 - 4.08829i) q^{18} +(5.27752 - 3.83434i) q^{19} +(-1.10531 + 3.40179i) q^{20} +(1.53760 - 1.49462i) q^{21} +(-2.35543 + 7.01896i) q^{22} +0.0288405i q^{23} +(-3.41083 + 1.67744i) q^{24} +(2.88195 - 2.09386i) q^{25} +(3.93535 + 7.02090i) q^{26} +(2.55369 - 4.52534i) q^{27} +(-1.14124 - 3.51236i) q^{28} +(5.90780 + 4.29226i) q^{29} +(-4.56822 - 0.790064i) q^{30} +(-7.06787 - 2.29649i) q^{31} -6.77175i q^{32} +(-5.65086 - 1.03334i) q^{33} -5.82705i q^{34} +(0.458720 - 1.41180i) q^{35} +(-5.05289 - 7.38628i) q^{36} +(-6.20330 + 8.53811i) q^{37} +(13.8493 - 4.49991i) q^{38} +(-4.95719 + 3.79820i) q^{39} +(-1.54665 + 2.12878i) q^{40} +(-1.36738 - 1.88204i) q^{41} +(4.29537 - 2.11245i) q^{42} -5.93753i q^{43} +(-5.89207 + 7.94794i) q^{44} +(0.101961 - 3.59570i) q^{45} +(-0.0198946 + 0.0612292i) q^{46} +(-1.38942 + 1.00947i) q^{47} +(1.82995 - 0.263304i) q^{48} +(-1.68949 - 5.19971i) q^{49} +(7.56281 - 2.45731i) q^{50} +(4.47518 - 0.643916i) q^{51} +(2.10227 + 10.5482i) q^{52} +(12.9952 + 4.22238i) q^{53} +(8.54318 - 7.84584i) q^{54} +(-3.79380 + 1.19249i) q^{55} -2.71685i q^{56} +(4.98635 + 10.1390i) q^{57} +(9.58154 + 13.1879i) q^{58} +(3.98724 + 2.89690i) q^{59} +(-5.47963 - 2.89056i) q^{60} +(-0.891049 + 0.289519i) q^{61} +(-13.4211 - 9.75102i) q^{62} +(2.09703 + 3.06541i) q^{63} +(4.01155 - 12.3463i) q^{64} +(-1.80849 + 3.92679i) q^{65} +(-11.2841 - 6.09185i) q^{66} -6.41925i q^{67} +(2.40628 - 7.40578i) q^{68} +(-0.0492226 - 0.00851295i) q^{69} +(1.94775 - 2.68085i) q^{70} +(-1.81204 - 5.57687i) q^{71} +(-1.85613 - 6.31645i) q^{72} +(-3.73166 - 2.71121i) q^{73} +(-19.0595 + 13.8475i) q^{74} +(2.72294 + 5.53671i) q^{75} +19.4597 q^{76} +(2.44530 - 3.29852i) q^{77} +(-13.1443 + 4.64414i) q^{78} +(4.58446 + 1.48958i) q^{79} +(1.03543 - 0.752286i) q^{80} +(6.96968 + 5.69417i) q^{81} +(-1.60473 - 4.93885i) q^{82} +(-8.01043 + 2.60275i) q^{83} +(6.33146 - 0.911009i) q^{84} +(2.53218 - 1.83974i) q^{85} +(4.09579 - 12.6055i) q^{86} +(-9.06949 + 8.81596i) q^{87} +(-5.92916 + 4.22131i) q^{88} -4.83030 q^{89} +(2.69683 - 7.56343i) q^{90} +(-0.872475 - 4.37766i) q^{91} +(-0.0505693 + 0.0696026i) q^{92} +(6.00570 - 11.3850i) q^{93} +(-3.64611 + 1.18469i) q^{94} +(6.32801 + 4.59757i) q^{95} +(11.5574 + 1.99884i) q^{96} +(-2.58498 - 0.839911i) q^{97} -12.2046i q^{98} +(3.43160 - 9.33939i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 6 q^{3} + 20 q^{4} + 6 q^{9} + 12 q^{12} - 10 q^{13} + 36 q^{16} - 96 q^{22} - 20 q^{25} + 6 q^{27} - 100 q^{30} - 116 q^{36} + 50 q^{39} + 60 q^{40} + 52 q^{42} + 32 q^{48} - 88 q^{49} - 90 q^{51}+ \cdots - 180 q^{94}+O(q^{100}) \) 176 * q - 6 * q^3 + 20 * q^4 + 6 * q^9 + 12 * q^12 - 10 * q^13 + 36 * q^16 - 96 * q^22 - 20 * q^25 + 6 * q^27 - 100 * q^30 - 116 * q^36 + 50 * q^39 + 60 * q^40 + 52 * q^42 + 32 * q^48 - 88 * q^49 - 90 * q^51 + 210 * q^52 - 20 * q^55 - 92 * q^64 - 62 * q^66 + 96 * q^69 + 166 * q^75 - 112 * q^78 - 60 * q^79 + 70 * q^81 - 144 * q^82 - 148 * q^88 + 100 * q^90 + 62 * q^91 - 180 * q^94

Introduction

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