LMFDB - Embedded newform 429.2.y.b.116.3

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			116.3
Character	$\chi$	$=$	429.116
Dual form			429.2.y.b.233.3

$q$-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} +(-1.71440 + 0.246677i) q^{3} +(2.41336 - 1.75341i) q^{4} +(-0.370527 + 1.14036i) q^{5} +(3.46954 - 1.70631i) q^{6} +(-1.00158 + 0.727691i) q^{7} +(-1.28990 + 1.77539i) q^{8} +(2.87830 - 0.845805i) 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} +(0.353927 - 2.04643i) q^{15} +(-0.329845 + 1.01516i) q^{16} +(0.806644 - 2.48260i) q^{17} +(-5.52726 + 3.78115i) 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} +(1.77345 - 3.36191i) q^{24} +(2.88195 + 2.09386i) q^{25} +(-3.93535 + 7.02090i) q^{26} +(-4.72590 + 2.16006i) q^{27} +(-1.14124 + 3.51236i) q^{28} +(-5.90780 + 4.29226i) q^{29} +(0.660260 + 4.58877i) q^{30} +(-7.06787 + 2.29649i) q^{31} -6.77175i q^{32} +(-0.872754 - 5.67788i) q^{33} +5.82705i q^{34} +(-0.458720 - 1.41180i) q^{35} +(5.46333 - 7.08807i) q^{36} +(-6.20330 - 8.53811i) q^{37} +(-13.8493 - 4.49991i) q^{38} +(-3.93718 + 4.84754i) q^{39} +(-1.54665 - 2.12878i) q^{40} +(1.36738 - 1.88204i) q^{41} +(-2.23336 + 4.23377i) 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} +(0.315068 - 1.82175i) q^{48} +(-1.68949 + 5.19971i) q^{49} +(-7.56281 - 2.45731i) q^{50} +(-0.770506 + 4.45513i) 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} +(-9.99360 - 5.27174i) q^{57} +(9.58154 - 13.1879i) q^{58} +(-3.98724 + 2.89690i) q^{59} +(-2.73408 - 5.55936i) q^{60} +(-0.891049 - 0.289519i) q^{61} +(13.4211 - 9.75102i) q^{62} +(-2.26737 + 2.94166i) q^{63} +(4.01155 + 12.3463i) q^{64} +(1.80849 + 3.92679i) q^{65} +(5.76955 + 11.4522i) q^{66} +6.41925i q^{67} +(-2.40628 - 7.40578i) q^{68} +(-0.00711431 - 0.0494441i) q^{69} +(1.94775 + 2.68085i) q^{70} +(1.81204 - 5.57687i) q^{71} +(-2.21108 + 6.20112i) q^{72} +(-3.73166 + 2.71121i) q^{73} +(19.0595 + 13.8475i) q^{74} +(-5.45730 - 2.87879i) q^{75} +19.4597 q^{76} +(-2.44530 - 3.29852i) q^{77} +(5.01485 - 13.0074i) q^{78} +(4.58446 - 1.48958i) q^{79} +(-1.03543 - 0.752286i) q^{80} +(7.56923 - 4.86896i) q^{81} +(-1.60473 + 4.93885i) q^{82} +(8.01043 + 2.60275i) q^{83} +(1.09011 - 6.30309i) 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} +(-2.26389 - 7.70410i) q^{90} +(-0.872475 + 4.37766i) q^{91} +(0.0505693 + 0.0696026i) q^{92} +(11.5506 - 5.68058i) q^{93} +(-3.64611 - 1.18469i) q^{94} +(-6.32801 + 4.59757i) q^{95} +(1.67044 + 11.6095i) q^{96} +(-2.58498 + 0.839911i) q^{97} -12.2046i q^{98} +(2.89685 + 9.51884i) 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$	$-1$

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	$-0.889520\pi$
$2$	−2.12303	+	0.689813i	−1.50121	+	0.487771i	−0.560836	+	0.827927i	$0.689520\pi$
$3$	−1.71440	+	0.246677i	−0.989806	+	0.142419i
$3$	−1.71440	+	0.246677i	−0.989806	+	0.142419i
$4$	2.41336	−	1.75341i	1.20668	−	0.876705i
$5$	−0.370527	+	1.14036i	−0.165705	+	0.509986i	−0.999088	−	0.0427099i	$-0.986401\pi$
$5$	−0.370527	+	1.14036i	−0.165705	+	0.509986i	0.833383	+	0.552696i	$0.186401\pi$
$6$	3.46954	−	1.70631i	1.41643	−	0.696600i
$7$	−1.00158	+	0.727691i	−0.378562	+	0.275041i	−0.760752	−	0.649042i	$-0.775170\pi$
$7$	−1.00158	+	0.727691i	−0.378562	+	0.275041i	0.382190	+	0.924084i	$0.375170\pi$
$8$	−1.28990	+	1.77539i	−0.456048	+	0.627696i
$9$	2.87830	−	0.845805i	0.959433	−	0.281935i
$10$		−	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
$15$	0.353927	−	2.04643i	0.0913835	−	0.528387i
$16$	−0.329845	+	1.01516i	−0.0824613	+	0.253790i
$17$	0.806644	−	2.48260i	0.195640	−	0.602118i	−0.804329	−	0.594185i	$-0.797475\pi$
$17$	0.806644	−	2.48260i	0.195640	−	0.602118i	0.999969	−	0.00793315i	$-0.00252523\pi$
$18$	−5.52726	+	3.78115i	−1.30279	+	0.891227i
$19$	5.27752	+	3.83434i	1.21075	+	0.879659i	0.995298	−	0.0968563i	$-0.0308787\pi$
$19$	5.27752	+	3.83434i	1.21075	+	0.879659i	0.215448	+	0.976515i	$0.430879\pi$
$20$	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	$0.999043\pi$
$24$	1.77345	−	3.36191i	0.362003	−	0.686248i
$25$	2.88195	+	2.09386i	0.576389	+	0.418771i
$26$	−3.93535	+	7.02090i	−0.771785	+	1.37691i
$27$	−4.72590	+	2.16006i	−0.909500	+	0.415703i
$28$	−1.14124	+	3.51236i	−0.215673	+	0.663774i
$29$	−5.90780	+	4.29226i	−1.09705	+	0.797054i	−0.980576	−	0.196140i	$-0.937159\pi$
$29$	−5.90780	+	4.29226i	−1.09705	+	0.797054i	−0.116474	+	0.993194i	$0.537159\pi$
$30$	0.660260	+	4.58877i	0.120547	+	0.837792i
$31$	−7.06787	+	2.29649i	−1.26943	+	0.412462i	−0.864845	−	0.502040i	$-0.832583\pi$
$31$	−7.06787	+	2.29649i	−1.26943	+	0.412462i	−0.404583	+	0.914501i	$0.632583\pi$
$32$		−	6.77175i		−	1.19709i
$33$	−0.872754	−	5.67788i	−0.151927	−	0.988392i
$34$			5.82705i			0.999330i
$35$	−0.458720	−	1.41180i	−0.0775378	−	0.238637i
$36$	5.46333	−	7.08807i	0.910556	−	1.18135i
$37$	−6.20330	−	8.53811i	−1.01982	−	1.40366i	−0.912333	−	0.409450i	$-0.865721\pi$
$37$	−6.20330	−	8.53811i	−1.01982	−	1.40366i	−0.107484	−	0.994207i	$-0.534279\pi$
$38$	−13.8493	−	4.49991i	−2.24665	−	0.729982i
$39$	−3.93718	+	4.84754i	−0.630454	+	0.776227i
$40$	−1.54665	−	2.12878i	−0.244547	−	0.336590i
$41$	1.36738	−	1.88204i	0.213549	−	0.293925i	−0.688782	−	0.724968i	$-0.741854\pi$
$41$	1.36738	−	1.88204i	0.213549	−	0.293925i	0.902331	+	0.431043i	$0.141854\pi$
$42$	−2.23336	+	4.23377i	−0.344615	+	0.653284i
$43$			5.93753i			0.905465i	0.891646	+	0.452733i	$0.149551\pi$
$43$			5.93753i			0.905465i	−0.891646	+	0.452733i	$0.850449\pi$
$44$	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	$-0.260025\pi$
$47$	1.38942	+	1.00947i	0.202667	+	0.147246i	−0.481823	+	0.876269i	$0.660025\pi$
$48$	0.315068	−	1.82175i	0.0454761	−	0.262947i
$49$	−1.68949	+	5.19971i	−0.241356	+	0.742816i
$50$	−7.56281	−	2.45731i	−1.06954	−	0.347516i
$51$	−0.770506	+	4.45513i	−0.107892	+	0.623843i
$52$	2.10227	−	10.5482i	0.291533	−	1.46277i
$53$	−12.9952	+	4.22238i	−1.78502	+	0.579989i	−0.999257	−	0.0385362i	$-0.987731\pi$
$53$	−12.9952	+	4.22238i	−1.78502	+	0.579989i	−0.785765	+	0.618525i	$0.787731\pi$
$54$	8.54318	−	7.84584i	1.16258	−	1.06768i
$55$	−3.79380	−	1.19249i	−0.511555	−	0.160795i
$56$		−	2.71685i		−	0.363054i
$57$	−9.99360	−	5.27174i	−1.32369	−	0.698258i
$58$	9.58154	−	13.1879i	1.25812	−	1.73165i
$59$	−3.98724	+	2.89690i	−0.519095	+	0.377144i	−0.816263	−	0.577681i	$-0.803958\pi$
$59$	−3.98724	+	2.89690i	−0.519095	+	0.377144i	0.297168	+	0.954825i	$0.403958\pi$
$60$	−2.73408	−	5.55936i	−0.352969	−	0.717711i
$61$	−0.891049	−	0.289519i	−0.114087	−	0.0370691i	0.251417	−	0.967879i	$-0.419103\pi$
$61$	−0.891049	−	0.289519i	−0.114087	−	0.0370691i	−0.365504	+	0.930810i	$0.619103\pi$
$62$	13.4211	−	9.75102i	1.70448	−	1.23838i
$63$	−2.26737	+	2.94166i	−0.285661	+	0.370614i
$64$	4.01155	+	12.3463i	0.501444	+	1.54329i
$65$	1.80849	+	3.92679i	0.224316	+	0.487059i
$66$	5.76955	+	11.4522i	0.710183	+	1.40967i
$67$			6.41925i			0.784237i	0.919915	+	0.392118i	$0.128258\pi$
$67$			6.41925i			0.784237i	−0.919915	+	0.392118i	$0.871742\pi$
$68$	−2.40628	−	7.40578i	−0.291805	−	0.898082i
$69$	−0.00711431	−	0.0494441i	−0.000856463	−	0.00595237i
$70$	1.94775	+	2.68085i	0.232800	+	0.320422i
$71$	1.81204	−	5.57687i	0.215049	−	0.661853i	−0.784101	−	0.620633i	$-0.786876\pi$
$71$	1.81204	−	5.57687i	0.215049	−	0.661853i	0.999150	−	0.0412197i	$-0.0131244\pi$
$72$	−2.21108	+	6.20112i	−0.260578	+	0.730809i
$73$	−3.73166	+	2.71121i	−0.436757	+	0.317323i	−0.784345	−	0.620325i	$-0.787001\pi$
$73$	−3.73166	+	2.71121i	−0.436757	+	0.317323i	0.347588	+	0.937647i	$0.387001\pi$
$74$	19.0595	+	13.8475i	2.21562	+	1.60974i
$75$	−5.45730	−	2.87879i	−0.630155	−	0.332414i
$76$	19.4597			2.23219
$77$	−2.44530	−	3.29852i	−0.278667	−	0.375901i
$78$	5.01485	−	13.0074i	0.567819	−	1.47279i
$79$	4.58446	−	1.48958i	0.515792	−	0.167591i	−0.0395428	−	0.999218i	$-0.512590\pi$
$79$	4.58446	−	1.48958i	0.515792	−	0.167591i	0.555335	+	0.831627i	$0.312590\pi$
$80$	−1.03543	−	0.752286i	−0.115765	−	0.0841082i
$81$	7.56923	−	4.86896i	0.841025	−	0.540996i
$82$	−1.60473	+	4.93885i	−0.177213	+	0.545405i
$83$	8.01043	+	2.60275i	0.879259	+	0.285689i	0.713650	−	0.700503i	$-0.247041\pi$
$83$	8.01043	+	2.60275i	0.879259	+	0.285689i	0.165609	+	0.986191i	$0.447041\pi$
$84$	1.09011	−	6.30309i	0.118941	−	0.687724i
$85$	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	$-0.417593\pi$
$89$	4.83030			0.512011			0.256006	+	0.966675i	$0.417593\pi$
$90$	−2.26389	−	7.70410i	−0.238635	−	0.812083i
$91$	−0.872475	+	4.37766i	−0.0914602	+	0.458903i
$92$	0.0505693	+	0.0696026i	0.00527221	+	0.00725658i
$93$	11.5506	−	5.68058i	1.19774	−	0.589048i
$94$	−3.64611	−	1.18469i	−0.376068	−	0.122192i
$95$	−6.32801	+	4.59757i	−0.649240	+	0.471700i
$96$	1.67044	+	11.6095i	0.170488	+	1.18489i
$97$	−2.58498	+	0.839911i	−0.262465	+	0.0852800i	−0.437293	−	0.899319i	$-0.644063\pi$
$97$	−2.58498	+	0.839911i	−0.262465	+	0.0852800i	0.174829	+	0.984599i	$0.444063\pi$
$98$		−	12.2046i		−	1.23285i
$99$	2.89685	+	9.51884i	0.291144	+	0.956679i
$100$	10.6266			1.06266
$101$	1.68746	+	5.19346i	0.167908	+	0.516769i	0.999239	−	0.0390096i	$-0.0124203\pi$
$101$	1.68746	+	5.19346i	0.167908	+	0.516769i	−0.831330	+	0.555778i	$0.812420\pi$
$102$	−1.43740	−	9.98986i	−0.142324	−	0.989144i
$103$	−13.4845	+	9.79704i	−1.32866	+	0.965331i	−0.328884	+	0.944370i	$0.606672\pi$
$103$	−13.4845	+	9.79704i	−1.32866	+	0.965331i	−0.999780	+	0.0209605i	$0.993328\pi$
$104$	0.927060	+	7.85791i	0.0909057	+	0.770531i
$105$	1.13469	+	2.30722i	0.110734	+	0.225161i
$106$	24.6764	−	17.9285i	2.39678	−	1.74137i
$107$	8.61592	+	6.25983i	0.832933	+	0.605161i	0.920387	−	0.391008i	$-0.127873\pi$
$107$	8.61592	+	6.25983i	0.832933	+	0.605161i	−0.0874549	+	0.996168i	$0.527873\pi$
$108$	−7.61785	+	13.4994i	−0.733028	+	1.29898i
$109$	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	−0.191500	−	0.981493i	$-0.561335\pi$
$113$	8.51615	−	11.7215i	0.801132	−	1.10266i	0.992632	−	0.121171i	$-0.0386649\pi$
$114$	24.8532	+	4.29831i	2.32771	+	0.402574i
$115$	−0.0328887	−	0.0106862i	−0.00306689	−	0.000996492i
$116$	−6.73155	+	20.7176i	−0.625008	+	1.92358i
$117$	5.55411	−	9.28180i	0.513477	−	0.858103i
$118$	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
$123$	−1.87998	+	3.56386i	−0.169512	+	0.321342i
$124$	−13.0306	+	17.9351i	−1.17019	+	1.61062i
$125$	−8.30585	+	6.03455i	−0.742898	+	0.539747i
$126$	2.78448	−	7.80927i	0.248061	−	0.695705i
$127$	3.10225	+	1.00798i	0.275280	+	0.0894440i	0.443404	−	0.896322i	$-0.353771\pi$
$127$	3.10225	+	1.00798i	0.275280	+	0.0894440i	−0.168124	+	0.985766i	$0.553771\pi$
$128$	−9.07258	−	12.4873i	−0.801910	−	1.10373i
$129$	−1.46466	−	10.1793i	−0.128956	−	0.896235i
$130$	−6.54823	−	7.08916i	−0.574317	−	0.621760i
$131$	9.43941			0.824725			0.412362	−	0.911020i	$-0.364704\pi$
$131$	9.43941			0.824725			0.412362	+	0.911020i	$0.364704\pi$
$132$	−12.0619	−	12.1725i	−1.04985	−	1.05948i
$133$	−8.07608			−0.700285
$134$	−4.42808	−	13.6282i	−0.382528	−	1.17730i
$135$	−0.712177	−	6.18960i	−0.0612944	−	0.532716i
$136$	3.36709	+	4.63441i	0.288726	+	0.397397i
$137$	−5.94800	+	18.3061i	−0.508172	+	1.56399i	0.287200	+	0.957871i	$0.407275\pi$
$137$	−5.94800	+	18.3061i	−0.508172	+	1.56399i	−0.795372	+	0.606121i	$0.792725\pi$
$138$	0.0492110	+	0.100063i	0.00418912	+	0.00851797i
$139$	−9.99794	−	13.7610i	−0.848014	−	1.16719i	−0.984297	−	0.176521i	$-0.943516\pi$
$139$	−9.99794	−	13.7610i	−0.848014	−	1.16719i	0.136283	−	0.990670i	$-0.456484\pi$
$140$	−3.58251	−	2.60285i	−0.302778	−	0.219981i
$141$	−2.63102	−	1.38789i	−0.221572	−	0.116882i
$142$			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
$147$	1.61380	−	9.33112i	0.133104	−	0.769618i
$148$	−29.9416	−	9.72862i	−2.46118	−	0.799687i
$149$	−4.54811	−	1.47777i	−0.372596	−	0.121064i	0.116732	−	0.993163i	$-0.462758\pi$
$149$	−4.54811	−	1.47777i	−0.372596	−	0.121064i	−0.489328	+	0.872100i	$0.662758\pi$
$150$	13.5718	+	2.34722i	1.10813	+	0.191650i
$151$	−1.98728	−	1.44385i	−0.161723	−	0.117499i	0.503980	−	0.863715i	$-0.331868\pi$
$151$	−1.98728	−	1.44385i	−0.161723	−	0.117499i	−0.665703	+	0.746217i	$0.731868\pi$
$152$	−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
$156$	−1.00213	+	18.6023i	−0.0802344	+	1.48938i
$157$	4.39969	+	3.19656i	0.351134	+	0.255113i	0.749344	−	0.662180i	$-0.230369\pi$
$157$	4.39969	+	3.19656i	0.351134	+	0.255113i	−0.398211	+	0.917294i	$0.630369\pi$
$158$	−8.70539	+	6.32484i	−0.692564	+	0.503177i
$159$	21.2373	−	10.4444i	1.68422	−	0.828298i
$160$	7.72226	+	2.50911i	0.610498	+	0.198363i
$161$	−0.0209870	−	0.0288861i	−0.00165401	−	0.00227655i
$162$	−12.7110	+	15.5583i	−0.998669	+	1.22237i
$163$	−8.70818	+	2.82946i	−0.682077	+	0.221620i	−0.629505	−	0.776997i	$-0.716742\pi$
$163$	−8.70818	+	2.82946i	−0.682077	+	0.221620i	−0.0525726	+	0.998617i	$0.516742\pi$
$164$		−	6.93962i		−	0.541893i
$165$	6.79822	+	1.10855i	0.529241	+	0.0863004i
$166$	−18.8018			−1.45930
$167$	−3.23388	+	1.05075i	−0.250245	+	0.0813096i	−0.431454	−	0.902135i	$-0.641999\pi$
$167$	−3.23388	+	1.05075i	−0.250245	+	0.0813096i	0.181208	+	0.983445i	$0.441999\pi$
$168$	0.670185	+	4.65775i	0.0517059	+	0.359353i
$169$	1.02968	−	12.9592i	0.0792061	−	0.996858i
$170$	−6.64495	−	2.15908i	−0.509645	−	0.165594i
$171$	18.4334	+	6.57264i	1.40964	+	0.502622i
$172$	10.4109	+	14.3294i	0.793826	+	1.09261i
$173$	−5.56312	−	4.04184i	−0.422956	−	0.307296i	0.355870	−	0.934535i	$-0.384185\pi$
$173$	−5.56312	−	4.04184i	−0.422956	−	0.307296i	−0.778826	+	0.627240i	$0.784185\pi$
$174$	−13.1734	+	24.9728i	−0.998673	+	1.89318i
$175$	−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	0.174442	+	0.984668i	$0.444188\pi$
$179$	−10.9165	+	15.0253i	−0.815938	+	1.12304i	−0.990380	+	0.138375i	$0.955812\pi$
$180$	6.05867	+	8.85651i	0.451586	+	0.660125i
$181$	−3.87273	+	11.9190i	−0.287858	+	0.885934i	0.697670	+	0.716419i	$0.254220\pi$
$181$	−3.87273	+	11.9190i	−0.287858	+	0.885934i	−0.985528	+	0.169515i	$0.945780\pi$
$182$	−1.16748	−	9.89572i	−0.0865391	−	0.733519i
$183$	1.59903	+	0.276549i	0.118204	+	0.0204431i
$184$	−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
$189$	3.16152	−	5.60247i	0.229967	−	0.407520i
$190$	10.2631	−	14.1259i	0.744561	−	1.02480i
$191$	−13.4900	−	18.5673i	−0.976099	−	1.34348i	−0.938905	−	0.344176i	$-0.888158\pi$
$191$	−13.4900	−	18.5673i	−0.976099	−	1.34348i	−0.0371935	−	0.999308i	$-0.511842\pi$
$192$	−9.92293	−	20.1768i	−0.716126	−	1.45614i
$193$	2.04695	−	6.29985i	0.147342	−	0.453473i	−0.849962	−	0.526843i	$-0.823375\pi$
$193$	2.04695	−	6.29985i	0.147342	−	0.453473i	0.997305	+	0.0733702i	$0.0233755\pi$
$194$	4.90860	−	3.56630i	0.352417	−	0.256046i
$195$	−4.06912	−	6.28596i	−0.291396	−	0.450147i
$196$	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	$0.956305\pi$
$198$	−12.7163	−	18.2104i	−0.903708	−	1.29416i
$199$	−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
$201$	−1.58349	−	11.0051i	−0.111690	−	0.776243i
$202$	−7.16503	−	9.86182i	−0.504130	−	0.693875i
$203$	2.79369	−	8.59810i	0.196079	−	0.603468i
$204$	5.95216	+	12.1029i	0.416734	+	0.847369i
$205$	1.63956	+	2.25666i	0.114512	+	0.157612i
$206$	21.8697	−	30.1011i	1.52374	−	2.09724i
$207$	0.0243935	+	0.0830117i	0.00169546	+	0.00576971i
$208$	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	−0.500022	−	0.866012i	$-0.666675\pi$
$211$	−5.74526	+	1.86675i	−0.395520	+	0.128512i	0.104503	+	0.994525i	$0.466675\pi$
$212$	−23.9584	+	32.9760i	−1.64547	+	2.26480i
$213$	−1.73086	+	10.0079i	−0.118596	+	0.685733i
$214$	−22.6099	−	7.34641i	−1.54558	−	0.502190i
$215$	−6.77095	−	2.20001i	−0.461775	−	0.150040i
$216$	2.26099	−	11.1766i	0.153841	−	0.760471i
$217$	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
$222$	−36.0913	−	19.0386i	−2.42229	−	1.27778i
$223$	−13.9752	+	19.2352i	−0.935847	+	1.28808i	0.0216871	+	0.999765i	$0.493096\pi$
$223$	−13.9752	+	19.2352i	−0.935847	+	1.28808i	−0.957535	+	0.288319i	$0.906904\pi$
$224$	4.92774	+	6.78246i	0.329249	+	0.453172i
$225$	10.0661	+	3.58918i	0.671073	+	0.239279i
$226$	−9.99438	+	30.7595i	−0.664816	+	2.04609i
$227$	11.2136	+	15.4342i	0.744273	+	1.02440i	0.998361	+	0.0572227i	$0.0182245\pi$
$227$	11.2136	+	15.4342i	0.744273	+	1.02440i	−0.254089	+	0.967181i	$0.581776\pi$
$228$	−33.3617	+	4.80028i	−2.20943	+	0.317906i
$229$	25.6971	−	8.34949i	1.69811	−	0.551750i	0.709828	−	0.704375i	$-0.248773\pi$
$229$	25.6971	−	8.34949i	1.69811	−	0.551750i	0.988284	+	0.152625i	$0.0487726\pi$
$230$	0.0771950			0.00509009
$231$	5.00588	+	5.05176i	0.329362	+	0.332381i
$232$		−	16.0252i		−	1.05211i
$233$	−2.33718	−	7.19309i	−0.153114	−	0.471235i	0.844851	−	0.535001i	$-0.179689\pi$
$233$	−2.33718	−	7.19309i	−0.153114	−	0.471235i	−0.997965	+	0.0637661i	$0.979689\pi$
$234$	−5.38880	+	23.5368i	−0.352277	+	1.53865i
$235$	−1.66598	+	1.21040i	−0.108676	+	0.0789581i
$236$	−4.54320	+	13.9825i	−0.295737	+	0.910186i
$237$	−7.49213	+	3.68461i	−0.486666	+	0.239341i
$238$	−4.24029	−	5.83626i	−0.274857	−	0.378309i
$239$	13.3747	−	18.4088i	0.865140	−	1.19076i	−0.115179	−	0.993345i	$-0.536744\pi$
$239$	13.3747	−	18.4088i	0.865140	−	1.19076i	0.980319	−	0.197418i	$-0.0632557\pi$
$240$	1.96071	+	1.03430i	0.126564	+	0.0667637i
$241$	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
$246$	1.53284	−	8.86300i	0.0977302	−	0.565084i
$247$	23.3584	−	2.75577i	1.48626	−	0.175346i
$248$	5.03966	−	15.5105i	0.320019	−	0.984917i
$249$	−14.3751	−	2.48614i	−0.910984	−	0.157553i
$250$	13.4708	−	18.5410i	0.851969	−	1.17264i
$251$	1.72205	−	0.559527i	0.108695	−	0.0353170i	−0.254165	−	0.967161i	$-0.581801\pi$
$251$	1.72205	−	0.559527i	0.108695	−	0.0353170i	0.362859	+	0.931844i	$0.381801\pi$
$252$	−0.314045	+	11.0749i	−0.0197830	+	0.697653i
$253$	−0.0956488		0.000919436i	−0.00601339		5.78045e-5i
$254$	−7.28148			−0.456881
$255$	−4.79498	−	2.52940i	−0.300273	−	0.158397i
$256$	6.87047	+	4.99169i	0.429405	+	0.311981i
$257$	6.66937	+	9.17960i	0.416024	+	0.572607i	0.964675	−	0.263444i	$-0.0848584\pi$
$257$	6.66937	+	9.17960i	0.416024	+	0.572607i	−0.548651	+	0.836051i	$0.684858\pi$
$258$	10.1313	+	20.6005i	0.630747	+	1.28253i
$259$	12.4262	+	4.03752i	0.772127	+	0.250879i
$260$	11.2498	+	6.30574i	0.697684	+	0.391065i
$261$	−13.3740	+	17.3513i	−0.827829	+	1.07402i
$262$	−20.0401	+	6.51142i	−1.23808	+	0.402277i
$263$	−2.68308			−0.165446			−0.0827230	−	0.996573i	$-0.526362\pi$
$263$	−2.68308			−0.165446			−0.0827230	+	0.996573i	$0.526362\pi$
$264$	11.2062	+	5.77441i	0.689696	+	0.355390i
$265$		−	16.3837i		−	1.00644i
$266$	17.1457	−	5.57099i	1.05127	−	0.341579i
$267$	−8.28105	+	1.19153i	−0.506792	+	0.0729203i
$268$	11.2556	+	15.4920i	0.687544	+	0.946323i
$269$	30.3194	+	9.85136i	1.84861	+	0.600648i	0.997083	+	0.0763300i	$0.0243203\pi$
$269$	30.3194	+	9.85136i	1.84861	+	0.600648i	0.851522	+	0.524318i	$0.175680\pi$
$270$	5.78164	+	12.6494i	0.351859	+	0.769819i
$271$	6.44173	−	4.68019i	0.391307	−	0.284302i	−0.374684	−	0.927153i	$-0.622249\pi$
$271$	6.44173	−	4.68019i	0.391307	−	0.284302i	0.765991	+	0.642851i	$0.222249\pi$
$272$	2.25416	+	1.63774i	0.136679	+	0.0993028i
$273$	0.415898	−	7.72025i	0.0251713	−	0.467251i
$274$		−	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	0.445920	−	0.895073i	$-0.352877\pi$
$277$	22.1820	−	7.20737i	1.33279	−	0.433049i	0.886867	+	0.462024i	$0.152877\pi$
$278$	30.7184	+	22.3182i	1.84237	+	1.33856i
$279$	−18.4011	+	12.5880i	−1.10164	+	0.753626i
$280$	3.09819	+	1.00666i	0.185152	+	0.0601597i
$281$	−8.61790	−	2.80012i	−0.514101	−	0.167041i	0.0404657	−	0.999181i	$-0.487116\pi$
$281$	−8.61790	−	2.80012i	−0.514101	−	0.167041i	−0.554566	+	0.832139i	$0.687116\pi$
$282$	6.54312	+	1.13162i	0.389637	+	0.0673870i
$283$	−10.0137	+	13.7827i	−0.595255	+	0.819298i	−0.995264	−	0.0972130i	$-0.969007\pi$
$283$	−10.0137	+	13.7827i	−0.595255	+	0.819298i	0.400008	+	0.916511i	$0.369007\pi$
$284$	−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
$288$	−5.72758	−	19.4911i	−0.337501	−	1.14853i
$289$	8.24068	+	5.98721i	0.484746	+	0.352189i
$290$	11.4887	+	15.8129i	0.674642	+	0.928565i
$291$	4.22449	−	2.07759i	0.247644	−	0.121791i
$292$	−4.25198	+	13.0862i	−0.248828	+	0.765814i
$293$	11.3560	+	15.6302i	0.663427	+	0.913128i	0.999589	−	0.0286757i	$-0.00912902\pi$
$293$	11.3560	+	15.6302i	0.663427	+	0.913128i	−0.336162	+	0.941804i	$0.609129\pi$
$294$	3.01059	+	20.9234i	0.175581	+	1.22028i
$295$	−1.82614	−	5.62028i	−0.106322	−	0.327226i
$296$	23.1601			1.34616
$297$	−7.31443	−	15.6045i	−0.424426	−	0.905463i
$298$	10.6751			0.618395
$299$	0.0705572	+	0.0763857i	0.00408043	+	0.00441750i
$300$	−18.2181	+	2.62133i	−1.05182	+	0.151343i
$301$	−4.32069	−	5.94692i	−0.249040	−	0.342775i
$302$	5.21504	+	1.69447i	0.300092	+	0.0975057i
$303$	−4.17408	−	8.48739i	−0.239795	−	0.487588i
$304$	−5.63323	+	4.09278i	−0.323088	+	0.234737i
$305$	0.660314	−	0.908845i	0.0378095	−	0.0520403i
$306$	4.92855	+	16.7720i	0.281746	+	0.958791i
$307$	−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	$-0.898629\pi$
$311$	−6.32137	+	8.70063i	−0.358452	+	0.493367i	0.591264	+	0.806478i	$0.298629\pi$
$312$	−3.52772	−	13.2429i	−0.199718	−	0.749730i
$313$	0.859994	−	2.64679i	0.0486098	−	0.149605i	−0.923805	−	0.382862i	$-0.874938\pi$
$313$	0.859994	−	2.64679i	0.0486098	−	0.149605i	0.972415	+	0.233257i	$0.0749383\pi$
$314$	−11.5457	−	3.75142i	−0.651561	−	0.211705i
$315$	−2.51444	−	3.67558i	−0.141673	−	0.207096i
$316$	8.45211	−	11.6333i	0.475468	−	0.654426i
$317$	−4.10244	−	12.6260i	−0.230416	−	0.709148i	−0.997696	−	0.0678359i	$-0.978391\pi$
$317$	−4.10244	−	12.6260i	−0.230416	−	0.709148i	0.767280	−	0.641312i	$-0.221609\pi$
$318$	−37.8825	+	36.8236i	−2.12435	+	2.06496i
$319$	−14.4235	−	19.4562i	−0.807562	−	1.08934i
$320$	−15.5656			−0.870146
$321$	−16.3153	−	8.60647i	−0.910629	−	0.480366i
$322$	0.0644820	+	0.0468489i	0.00359344	+	0.00261079i
$323$	13.7762	−	10.0090i	0.766529	−	0.556916i
$324$	9.72999	−	25.0225i	0.540555	−	1.39014i
$325$	12.7555	−	1.50487i	0.707549	−	0.0834752i
$326$	16.5359	−	12.0140i	0.915838	−	0.665395i
$327$	−0.472830	+	0.0680336i	−0.0261476	+	0.00376227i
$328$	1.57758	+	4.85528i	0.0871071	+	0.268088i
$329$	−2.12620			−0.117221
$330$	−15.1975	+	2.33603i	−0.836594	+	0.128594i
$331$			4.44175i			0.244141i	0.992521	+	0.122070i	$0.0389534\pi$
$331$			4.44175i			0.244141i	−0.992521	+	0.122070i	$0.961047\pi$
$332$	23.8957	−	7.76420i	1.31145	−	0.426116i
$333$	−25.0765	−	19.3285i	−1.37419	−	1.05919i
$334$	6.14079	−	4.46154i	0.336009	−	0.244125i
$335$	−7.32028	−	2.37850i	−0.399950	−	0.129952i
$336$	1.01010	+	2.05390i	0.0551057	+	0.112049i
$337$	−15.0265	−	20.6823i	−0.818548	−	1.12663i	−0.989948	−	0.141433i	$-0.954829\pi$
$337$	−15.0265	−	20.6823i	−0.818548	−	1.12663i	0.171400	−	0.985202i	$-0.445171\pi$
$338$	6.75336	+	28.2229i	0.367334	+	1.53512i
$339$	−11.7086	+	22.1960i	−0.635925	+	1.20552i
$340$	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
$345$	0.0590203	+	0.0102074i	0.00317754	+	0.000549550i
$346$	14.5988	+	4.74342i	0.784834	+	0.255008i
$347$	−4.91854	+	15.1377i	−0.264041	+	0.812635i	0.727872	+	0.685714i	$0.240510\pi$
$347$	−4.91854	+	15.1377i	−0.264041	+	0.812635i	−0.991913	+	0.126922i	$0.959490\pi$
$348$	6.42997	−	37.1786i	0.344683	−	1.99298i
$349$	27.2856	+	19.8241i	1.46056	+	1.06116i	0.983216	+	0.182446i	$0.0584015\pi$
$349$	27.2856	+	19.8241i	1.46056	+	1.06116i	0.477347	+	0.878715i	$0.341598\pi$
$350$	9.36293	−	3.04220i	0.500470	−	0.162612i
$351$	−7.23232	+	17.2828i	−0.386033	+	0.922485i
$352$	22.4583	−	0.215883i	1.19703	−	0.0115066i
$353$	−16.8155			−0.894997			−0.447498	−	0.894285i	$-0.647685\pi$
$353$	−16.8155			−0.894997			−0.447498	+	0.894285i	$0.647685\pi$
$354$	−8.89089	+	16.8544i	−0.472545	+	0.895802i
$355$	5.68825	+	4.13276i	0.301901	+	0.219344i
$356$	11.6573	−	8.46950i	0.617834	−	0.448883i
$357$	−2.47023	−	5.02286i	−0.130739	−	0.265838i
$358$	12.8114	−	39.4294i	0.677103	−	2.08391i
$359$	10.0032	+	13.7682i	0.527946	+	0.726656i	0.986816	−	0.161848i	$-0.0517455\pi$
$359$	10.0032	+	13.7682i	0.527946	+	0.726656i	−0.458870	+	0.888504i	$0.651745\pi$
$360$	−6.25226	−	4.81911i	−0.329523	−	0.253990i
$361$	7.27872	+	22.4016i	0.383091	+	1.17903i
$362$		−	27.9759i		−	1.47038i
$363$	18.8027	−	3.07547i	0.986886	−	0.161421i
$364$	5.57023	+	12.0947i	0.291959	+	0.633933i
$365$	−1.70908	−	5.26002i	−0.0894575	−	0.275322i
$366$	−3.58554	+	0.515909i	−0.187419	+	0.0269670i
$367$	4.42012	−	3.21140i	0.230728	−	0.167634i	−0.466414	−	0.884566i	$-0.654454\pi$
$367$	4.42012	−	3.21140i	0.230728	−	0.167634i	0.697143	+	0.716932i	$0.254454\pi$
$368$	−0.0292777	−	0.00951291i	−0.00152621	−	0.000495895i
$369$	2.34390	−	6.57361i	0.122018	−	0.342209i
$370$	−22.8532	+	16.6038i	−1.18808	+	0.863193i
$371$	9.94311	−	13.6855i	0.516221	−	0.710517i
$372$	17.9155	−	33.9623i	0.928874	−	1.76086i
$373$		−	30.2082i		−	1.56412i	−0.623203	−	0.782060i	$-0.714169\pi$
$373$		−	30.2082i		−	1.56412i	0.623203	−	0.782060i	$-0.285831\pi$
$374$	−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
$378$	−2.84733	+	14.0750i	−0.146451	+	0.723942i
$379$	25.9847	+	8.44296i	1.33475	+	0.433686i	0.887534	−	0.460742i	$-0.152417\pi$
$379$	25.9847	+	8.44296i	1.33475	+	0.433686i	0.447213	+	0.894428i	$0.352417\pi$
$380$	−7.21035	+	22.1912i	−0.369883	+	1.13838i
$381$	−5.56713	−	0.962825i	−0.285213	−	0.0493270i
$382$	41.4475	+	30.1134i	2.12064	+	1.54073i
$383$	−5.01987	−	15.4496i	−0.256503	−	0.789436i	−0.993530	−	0.113572i	$-0.963771\pi$
$383$	−5.01987	−	15.4496i	−0.256503	−	0.789436i	0.737026	−	0.675864i	$-0.236229\pi$
$384$	18.6343	+	19.1702i	0.950929	+	0.978276i
$385$	4.66755	−	1.56634i	0.237881	−	0.0798281i
$386$			14.7868i			0.752626i
$387$	5.02200	+	17.0900i	0.255282	+	0.868734i
$388$	−4.76578	+	6.55953i	−0.241946	+	0.333010i
$389$	6.11625	+	8.41830i	0.310106	+	0.426825i	0.935414	−	0.353553i	$-0.115027\pi$
$389$	6.11625	+	8.41830i	0.310106	+	0.426825i	−0.625308	+	0.780378i	$0.715027\pi$
$390$	12.9750	+	10.5383i	0.657014	+	0.533628i
$391$	0.0715994	+	0.0232641i	0.00362094	+	0.00117651i
$392$	−7.05226	−	9.70661i	−0.356193	−	0.490258i
$393$	−16.1829	+	2.32849i	−0.816318	+	0.117457i
$394$	−2.64979	−	8.15521i	−0.133494	−	0.410854i
$395$			5.77988i			0.290817i
$396$	23.6816	+	17.8930i	1.19004	+	0.899158i
$397$			28.8424i			1.44756i	0.690032	+	0.723779i	$0.257597\pi$
$397$			28.8424i			1.44756i	−0.690032	+	0.723779i	$0.742403\pi$
$398$	15.3916	−	5.00105i	0.771513	−	0.250680i
$399$	13.8456	−	1.99219i	0.693147	−	0.0997342i
$400$	−3.07619	+	2.23498i	−0.153810	+	0.111749i
$401$	6.65395	−	20.4788i	0.332283	−	1.02266i	−0.635763	−	0.771885i	$-0.719314\pi$
$401$	6.65395	−	20.4788i	0.332283	−	1.02266i	0.968045	−	0.250776i	$-0.0806857\pi$
$402$	10.9533	+	22.2719i	0.546299	+	1.11082i
$403$	−13.1014	+	23.3736i	−0.652626	+	1.16432i
$404$	13.1787	+	9.57490i	0.655665	+	0.476369i
$405$	2.74779	+	10.4357i	0.136539	+	0.518557i
$406$			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	0.929027	−	0.370012i	$-0.120647\pi$
$409$	−0.810153	−	2.49339i	−0.0400595	−	0.123290i	−0.969086	+	0.246722i	$0.920647\pi$
$410$	−5.03749	−	3.65995i	−0.248784	−	0.180752i
$411$	5.68153	−	32.8510i	0.280249	−	1.62042i
$412$	−15.3647	+	47.2876i	−0.756963	+	2.32969i
$413$	1.88550	−	5.80296i	0.0927792	−	0.285545i
$414$	−0.109051	−	0.159409i	−0.00535954	−	0.00783453i
$415$	−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	$-0.0917309\pi$
$420$	6.78390	+	3.57858i	0.331021	+	0.174617i
$421$	21.0728	−	29.0043i	1.02703	−	1.41358i	0.119869	−	0.992790i	$-0.461752\pi$
$421$	21.0728	−	29.0043i	1.02703	−	1.41358i	0.907157	−	0.420791i	$-0.138248\pi$
$422$	10.9096	−	7.92630i	0.531072	−	0.385846i
$423$	4.85297	+	1.73038i	0.235960	+	0.0841341i
$424$	9.26605	−	28.5180i	0.449999	−	1.38495i
$425$	7.52290	−	5.46571i	0.364914	−	0.265126i
$426$	−3.22896	−	22.4411i	−0.156444	−	1.08727i
$427$	1.10314	−	0.358431i	0.0533846	−	0.0173457i
$428$	31.7694			1.53563
$429$	−16.2022	−	12.9030i	−0.782251	−	0.622963i
$430$	15.8925			0.766404
$431$	−24.4522	+	7.94501i	−1.17782	+	0.382698i	−0.831557	−	0.555439i	$-0.812550\pi$
$431$	−24.4522	+	7.94501i	−1.17782	+	0.382698i	−0.346265	+	0.938137i	$0.612550\pi$
$432$	−0.633984	−	5.51003i	−0.0305026	−	0.265101i
$433$	20.8944	−	15.1807i	1.00412	−	0.729536i	0.0411524	−	0.999153i	$-0.486897\pi$
$433$	20.8944	−	15.1807i	1.00412	−	0.729536i	0.962968	+	0.269617i	$0.0868971\pi$
$434$	−6.34661	+	19.5329i	−0.304647	+	0.937607i
$435$	6.69291	+	13.6091i	0.320900	+	0.652505i
$436$	0.665605	−	0.483590i	0.0318767	−	0.0231598i
$437$	−0.110585	+	0.152207i	−0.00528998	+	0.00728103i
$438$	−8.32097	+	15.7740i	−0.397591	+	0.753712i
$439$			15.1625i			0.723668i	0.932242	+	0.361834i	$0.117849\pi$
$439$			15.1625i			0.723668i	−0.932242	+	0.361834i	$0.882151\pi$
$440$	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	$-0.798385\pi$
$443$	0.125536	−	0.172786i	0.00596440	−	0.00820929i	0.811989	+	0.583673i	$0.198385\pi$
$444$	53.7316	+	9.29277i	2.54999	+	0.441015i
$445$	−1.78976	+	5.50830i	−0.0848425	+	0.261119i
$446$	16.4010	−	50.4770i	0.776609	−	2.39016i
$447$	8.16180	+	1.41157i	0.386040	+	0.0667648i
$448$	−13.0022	−	9.44663i	−0.614295	−	0.446311i
$449$	−4.57403	−	14.0774i	−0.215862	−	0.664354i	−0.999091	−	0.0426216i	$-0.986429\pi$
$449$	−4.57403	−	14.0774i	−0.215862	−	0.664354i	0.783229	−	0.621733i	$-0.213571\pi$
$450$	−23.8465	−	0.676200i	−1.12413	−	0.0318764i
$451$	6.28532	+	4.47488i	0.295964	+	0.210714i
$452$		−	43.2204i		−	2.03292i
$453$	3.76315	+	1.98510i	0.176808	+	0.0932684i
$454$	−34.4535	−	25.0319i	−1.61698	−	1.17481i
$455$	−4.66884	−	2.61698i	−0.218879	−	0.122686i
$456$	22.2501	−	10.9426i	1.04196	−	0.512433i
$457$	−6.69523	+	20.6058i	−0.313190	+	0.963899i	0.663303	+	0.748351i	$0.269154\pi$
$457$	−6.69523	+	20.6058i	−0.313190	+	0.963899i	−0.976493	+	0.215548i	$0.930846\pi$
$458$	−48.7960	+	35.4524i	−2.28009	+	1.65658i
$459$	1.55042	+	13.4749i	0.0723676	+	0.628955i
$460$	−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	$0.991781\pi$
$462$	−14.1124	−	7.27190i	−0.656567	−	0.338319i
$463$		−	18.5721i		−	0.863120i	−0.902084	−	0.431560i	$-0.857963\pi$
$463$		−	18.5721i		−	0.863120i	0.902084	−	0.431560i	$-0.142037\pi$
$464$	−2.40867	−	7.41313i	−0.111820	−	0.344146i
$465$	2.19811	+	15.2767i	0.101935	+	0.708441i
$466$	9.92377	+	13.6589i	0.459710	+	0.632736i
$467$	−6.31071	−	2.05047i	−0.292025	−	0.0948846i	0.159341	−	0.987224i	$-0.449063\pi$
$467$	−6.31071	−	2.05047i	−0.292025	−	0.0948846i	−0.451366	+	0.892339i	$0.649063\pi$
$468$	−2.87074	−	32.1390i	−0.132700	−	1.48562i
$469$	−4.67123	−	6.42940i	−0.215698	−	0.296882i
$470$	2.70196	−	3.71893i	0.124632	−	0.171542i
$471$	−8.33133	−	4.39487i	−0.383887	−	0.202505i
$472$		−	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
$477$	−33.8327	+	23.1447i	−1.54909	+	1.05972i
$478$	−15.6963	+	48.3083i	−0.717933	+	2.20957i
$479$	−24.3291	−	7.90499i	−1.11162	−	0.361188i	−0.305058	−	0.952334i	$-0.598676\pi$
$479$	−24.3291	−	7.90499i	−1.11162	−	0.361188i	−0.806565	+	0.591146i	$0.798676\pi$
$480$	−13.8579	−	2.39670i	−0.632526	−	0.109394i
$481$	−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
$486$	17.9538	−	29.8086i	0.814400	−	1.35214i
$487$	8.32526	−	11.4587i	0.377253	−	0.519245i	−0.577601	−	0.816319i	$-0.696011\pi$
$487$	8.32526	−	11.4587i	0.377253	−	0.519245i	0.954854	+	0.297074i	$0.0960110\pi$
$488$	1.66337	−	1.20851i	0.0752974	−	0.0547067i
$489$	14.2313	−	6.99892i	0.643561	−	0.316502i
$490$	13.9176	+	4.52211i	0.628734	+	0.204288i
$491$	−17.7099	+	12.8670i	−0.799235	+	0.580678i	−0.910690	−	0.413091i	$-0.864449\pi$
$491$	−17.7099	+	12.8670i	−0.799235	+	0.580678i	0.111455	+	0.993770i	$0.464449\pi$
$492$	1.71185	+	11.8972i	0.0771761	+	0.536369i
$493$	5.89047	+	18.1290i	0.265293	+	0.816489i
$494$	−47.6894	+	21.9635i	−2.14565	+	0.988183i
$495$	−11.9283	−	0.223521i	−0.536137	−	0.0100465i
$496$		−	7.93250i		−	0.356180i
$497$	2.24334	+	6.90429i	0.100628	+	0.309700i
$498$	32.2336	−	4.63797i	1.44442	−	0.207832i
$499$	5.32294	+	7.32640i	0.238288	+	0.327975i	0.911366	−	0.411596i	$-0.135029\pi$
$499$	5.32294	+	7.32640i	0.238288	+	0.327975i	−0.673079	+	0.739571i	$0.735029\pi$
$500$	−9.46397	+	29.1271i	−0.423242	+	1.30260i
$501$	5.28495	−	2.59913i	0.236114	−	0.116121i
$502$	−3.26998	+	2.37578i	−0.145946	+	0.106036i
$503$	−10.1392	−	7.36658i	−0.452086	−	0.328460i	0.338333	−	0.941026i	$-0.390137\pi$
$503$	−10.1392	−	7.36658i	−0.452086	−	0.328460i	−0.790419	+	0.612567i	$0.790137\pi$
$504$	−2.29792	−	7.81990i	−0.102358	−	0.348326i
$505$	−6.54768			−0.291368
$506$	0.202431	−	0.0679318i	0.00899914	−	0.00301994i
$507$	1.43146	+	22.4711i	0.0635732	+	0.997977i
$508$	9.25426	−	3.00689i	0.410591	−	0.133409i
$509$	15.7439	+	11.4386i	0.697835	+	0.507007i	0.879226	−	0.476404i	$-0.158060\pi$
$509$	15.7439	+	11.4386i	0.697835	+	0.507007i	−0.181391	+	0.983411i	$0.558060\pi$
$510$	11.9247	+	2.06235i	0.528033	+	0.0913223i
$511$	1.76463	−	5.43099i	0.0780628	−	0.240253i
$512$	11.3299	+	3.68132i	0.500718	+	0.162693i
$513$	−33.2235	−	6.72099i	−1.46685	−	0.296739i
$514$	−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
$519$	10.5344	+	5.55702i	0.462409	+	0.243926i
$520$	−9.30437	−	1.85438i	−0.408024	−	0.0813199i
$521$	−18.7666	−	25.8300i	−0.822178	−	1.13163i	−0.989329	−	0.145700i	$-0.953457\pi$
$521$	−18.7666	−	25.8300i	−0.822178	−	1.13163i	0.167151	−	0.985931i	$-0.446543\pi$
$522$	16.4242	−	46.0627i	0.718867	−	2.01611i
$523$	−34.8885	−	11.3360i	−1.52557	−	0.495687i	−0.578216	−	0.815883i	$-0.696251\pi$
$523$	−34.8885	−	11.3360i	−1.52557	−	0.495687i	−0.947351	+	0.320196i	$0.896251\pi$
$524$	22.7807	−	16.5511i	0.995179	−	0.723040i
$525$	7.56080	−	1.08789i	0.329980	−	0.0474795i
$526$	5.69625	−	1.85082i	0.248368	−	0.0806998i
$527$			19.3991i			0.845039i
$528$	6.05182	+	0.986836i	0.263372	+	0.0429465i
$529$	22.9992			0.999964
$530$	11.3017	+	34.7830i	0.490914	+	1.51088i
$531$	−9.02627	+	11.7106i	−0.391707	+	0.508196i
$532$	−19.4905	+	14.1607i	−0.845021	+	0.613943i
$533$	−0.982747	−	8.32992i	−0.0425675	−	0.360809i
$534$	16.7589	−	8.24201i	0.725230	−	0.356667i
$535$	−10.3309	+	7.50585i	−0.446644	+	0.324506i
$536$	−11.3967	−	8.28019i	−0.492263	−	0.357650i
$537$	15.0088	−	28.4521i	0.647678	−	1.22780i
$538$	−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	0.964208	+	0.265148i	$0.0854208\pi$
$541$	7.90813	+	24.3387i	0.339997	+	1.04640i	−0.624211	+	0.781256i	$0.714579\pi$
$542$	−10.4475	+	14.3798i	−0.448759	+	0.617664i
$543$	3.69923	−	21.3892i	0.158749	−	0.917900i
$544$	−16.8115	−	5.46240i	−0.720788	−	0.234198i
$545$	−0.102191	+	0.314512i	−0.00437739	+	0.0134722i
$546$	4.44257	+	16.6772i	0.190124	+	0.713717i
$547$	19.3057	−	26.5720i	0.825451	−	1.13614i	−0.163301	−	0.986576i	$-0.552214\pi$
$547$	19.3057	−	26.5720i	0.825451	−	1.13614i	0.988753	−	0.149560i	$-0.0477857\pi$
$548$	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
$552$	0.0969594	+	0.0511471i	0.00412687	+	0.00217697i
$553$	−3.50775	+	4.82801i	−0.149165	+	0.205308i
$554$	−42.1212	+	30.6029i	−1.78956	+	1.30019i
$555$	−19.6682	+	9.67278i	−0.834868	+	0.410587i
$556$	−48.2573	−	15.6797i	−2.04656	−	0.664969i
$557$	15.6453	+	21.5339i	0.662912	+	0.912421i	0.999573	−	0.0292053i	$-0.00929766\pi$
$557$	15.6453	+	21.5339i	0.662912	+	0.912421i	−0.336661	+	0.941626i	$0.609298\pi$
$558$	30.3826	−	39.4180i	1.28620	−	1.66870i
$559$	14.5259	+	15.7259i	0.614381	+	0.665134i
$560$	1.58450			0.0669575
$561$	−14.7999	−	2.41333i	−0.624851	−	0.101891i
$562$	20.2276			0.853249
$563$	12.4173	+	38.2165i	0.523327	+	1.61063i	0.767601	+	0.640928i	$0.221450\pi$
$563$	12.4173	+	38.2165i	0.523327	+	1.61063i	−0.244275	+	0.969706i	$0.578550\pi$
$564$	−8.78315	+	1.26377i	−0.369837	+	0.0532144i
$565$	10.2113	+	14.0546i	0.429592	+	0.591282i
$566$	11.7519	−	36.1687i	0.493970	−	1.52028i
$567$	−4.03809	+	10.3847i	−0.169584	+	0.436117i
$568$	7.56380	+	10.4107i	0.317370	+	0.436822i
$569$	−21.0115	−	15.2657i	−0.880848	−	0.639973i	0.0526278	−	0.998614i	$-0.483240\pi$
$569$	−21.0115	−	15.2657i	−0.880848	−	0.639973i	−0.933476	+	0.358641i	$0.883240\pi$
$570$	−14.1104	+	26.7490i	−0.591020	+	1.12039i
$571$		−	36.4013i		−	1.52335i	−0.647960	−	0.761675i	$-0.724378\pi$
$571$		−	36.4013i		−	1.52335i	0.647960	−	0.761675i	$-0.275622\pi$
$572$	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
$576$	21.9890	+	32.1433i	0.916208	+	1.33931i
$577$	−12.8606	−	4.17868i	−0.535396	−	0.173961i	0.0288252	−	0.999584i	$-0.490823\pi$
$577$	−12.8606	−	4.17868i	−0.535396	−	0.173961i	−0.564221	+	0.825624i	$0.690823\pi$
$578$	−21.6252	−	7.02646i	−0.899491	−	0.292262i
$579$	−1.95524	+	11.3054i	−0.0812571	+	0.469835i
$580$	−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
$585$	8.52669	+	9.77286i	0.352535	+	0.404058i
$586$	−34.8911	−	25.3499i	−1.44134	−	1.04719i
$587$	35.0275	−	25.4490i	1.44574	−	1.05039i	0.458936	−	0.888470i	$-0.348231\pi$
$587$	35.0275	−	25.4490i	1.44574	−	1.05039i	0.986804	−	0.161921i	$-0.0517691\pi$
$588$	−12.4666	−	25.3490i	−0.514114	−	1.04538i
$589$	−46.1064	−	14.9809i	−1.89978	−	0.617276i
$590$	7.75389	+	10.6723i	0.319223	+	0.439372i
$591$	−0.947566	−	6.58553i	−0.0389777	−	0.270893i
$592$	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	$0.661116\pi$
$594$	26.2929	+	28.0831i	1.07881	+	1.15226i
$595$	−3.87494			−0.158857
$596$	−13.5674	+	4.40831i	−0.555742	+	0.180571i
$597$	12.4291	−	1.78838i	0.508690	−	0.0731934i
$598$	−0.202487	−	0.113498i	−0.00828029	−	0.00464126i
$599$	17.4014	+	5.65405i	0.711001	+	0.231018i	0.642117	−	0.766606i	$-0.278056\pi$
$599$	17.4014	+	5.65405i	0.711001	+	0.231018i	0.0688838	+	0.997625i	$0.478056\pi$
$600$	12.1503	−	5.97551i	0.496036	−	0.243949i
$601$	13.3670	+	18.3982i	0.545253	+	0.750477i	0.989359	−	0.145498i	$-0.0464784\pi$
$601$	13.3670	+	18.3982i	0.545253	+	0.750477i	−0.444105	+	0.895975i	$0.646478\pi$
$602$	13.2752	+	9.64500i	0.541057	+	0.393101i
$603$	5.42944	+	18.4765i	0.221104	+	0.752423i
$604$	−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	−0.330108	−	0.943943i	$-0.607085\pi$
$607$	−1.04302	+	0.338897i	−0.0423348	+	0.0137554i	0.287773	+	0.957699i	$0.407085\pi$
$608$	25.9652	−	35.7381i	1.05303	−	1.44937i
$609$	−2.66853	+	15.4297i	−0.108134	+	0.625242i
$610$	−0.774931	+	2.38499i	−0.0313761	+	0.0965656i
$611$	6.14957	−	0.725514i	0.248785	−	0.0293512i
$612$	−13.1899	−	19.2808i	−0.533168	−	0.779380i
$613$	4.01628	+	2.91800i	0.162216	+	0.117857i	0.665932	−	0.746013i	$-0.268034\pi$
$613$	4.01628	+	2.91800i	0.162216	+	0.117857i	−0.503716	+	0.863869i	$0.668034\pi$
$614$	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	$-0.310712\pi$
$617$	27.8317			1.12046			0.560231	+	0.828336i	$0.310712\pi$
$618$	−30.0681	+	57.0000i	−1.20952	+	2.29288i
$619$	14.5929	−	20.0854i	0.586538	−	0.807300i	−0.407855	−	0.913047i	$-0.633723\pi$
$619$	14.5929	−	20.0854i	0.586538	−	0.807300i	0.994393	+	0.105746i	$0.0337231\pi$
$620$	−15.6244	−	21.5051i	−0.627490	−	0.863666i
$621$	−0.0622972	−	0.136298i	−0.00249990	−	0.00546943i
$622$	7.41864	−	22.8322i	0.297460	−	0.915488i
$623$	−4.83794	+	3.51497i	−0.193828	+	0.140824i
$624$	−3.62236	−	5.59580i	−0.145010	−	0.224011i
$625$	1.69998	+	5.23200i	0.0679993	+	0.209280i
$626$			6.21244i			0.248299i
$627$	17.1650	−	33.3116i	0.685503	−	1.33034i
$628$	16.2229			0.647365
$629$	−26.2005	+	8.51307i	−1.04468	+	0.339438i
$630$	7.87368	+	6.06886i	0.313695	+	0.241789i
$631$	11.8895	+	16.3645i	0.473313	+	0.651459i	0.977203	−	0.212309i	$-0.0680983\pi$
$631$	11.8895	+	16.3645i	0.473313	+	0.651459i	−0.503890	+	0.863768i	$0.668098\pi$
$632$	−3.26890	+	10.0606i	−0.130030	+	0.400190i
$633$	9.38916	−	4.61757i	0.373185	−	0.183532i
$634$	17.4192	+	23.9754i	0.691804	+	0.952186i
$635$	−2.29893	+	3.16421i	−0.0912304	+	0.125568i
$636$	32.9398	−	62.4438i	1.30615	−	2.47606i
$637$	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	$-0.842219\pi$
$641$	−3.93606	+	5.41753i	−0.155465	+	0.213979i	0.724179	+	0.689612i	$0.242219\pi$
$642$	40.5745	+	7.01729i	1.60135	+	0.276950i
$643$	20.0932	+	6.52868i	0.792399	+	0.257466i	0.677125	−	0.735868i	$-0.263226\pi$
$643$	20.0932	+	6.52868i	0.792399	+	0.257466i	0.115274	+	0.993334i	$0.463226\pi$
$644$	−0.101298	−	0.0329139i	−0.00399172	−	0.00129699i
$645$	12.1508	+	2.10145i	0.478436	+	0.0827446i
$646$	−22.3429	+	30.7524i	−0.879070	+	1.20994i
$647$	8.66732	−	2.81618i	0.340747	−	0.110716i	−0.133644	−	0.991029i	$-0.542668\pi$
$647$	8.66732	−	2.81618i	0.340747	−	0.110716i	0.474392	+	0.880314i	$0.342668\pi$
$648$	−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
$651$	−7.43519	+	14.0948i	−0.291408	+	0.552421i
$652$	−16.0548	+	22.0975i	−0.628754	+	0.865405i
$653$	6.04944	+	8.32635i	0.236733	+	0.325835i	0.910810	−	0.412826i	$-0.135458\pi$
$653$	6.04944	+	8.32635i	0.236733	+	0.325835i	−0.674077	+	0.738661i	$0.735458\pi$
$654$	0.956899	−	0.470601i	0.0374177	−	0.0184020i
$655$	−3.49755	+	10.7644i	−0.136661	+	0.420598i
$656$	1.45954	+	2.00889i	0.0569856	+	0.0784340i
$657$	−8.44768	+	10.9599i	−0.329575	+	0.427587i
$658$	4.51397	−	1.46668i	0.175973	−	0.0571770i
$659$	36.7889			1.43309			0.716546	−	0.697540i	$-0.245722\pi$
$659$	36.7889			1.43309			0.716546	+	0.697540i	$0.245722\pi$
$660$	18.3503	−	9.24474i	0.714285	−	0.359851i
$661$			32.6701i			1.27072i	0.772217	+	0.635359i	$0.219148\pi$
$661$			32.6701i			1.27072i	−0.772217	+	0.635359i	$0.780852\pi$
$662$	−3.06398	−	9.42995i	−0.119085	−	0.366506i
$663$	8.85857	+	13.6847i	0.344038	+	0.531468i
$664$	−14.9535	+	10.8644i	−0.580310	+	0.421620i
$665$	2.99240	−	9.20967i	0.116040	−	0.357136i
$666$	66.5711	+	23.7367i	2.57958	+	0.919778i
$667$	−0.123791	−	0.170384i	−0.00479322	−	0.00659730i
$668$	−5.96212	+	8.20616i	−0.230682	+	0.317506i
$669$	19.2141	−	36.4241i	0.742860	−	1.40824i
$670$	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	−0.541907	−	0.840438i	$-0.682298\pi$
$673$	−12.6163	+	4.09928i	−0.486322	+	0.158016i	0.0555852	+	0.998454i	$0.482298\pi$
$674$	46.1686	+	33.5435i	1.77835	+	1.29205i
$675$	−18.1426	−	3.67020i	−0.698311	−	0.141266i
$676$	−20.2377	−	33.0806i	−0.778374	−	1.27233i
$677$	3.79563	−	11.6818i	0.145878	−	0.448966i	−0.851245	−	0.524769i	$-0.824152\pi$
$677$	3.79563	−	11.6818i	0.145878	−	0.448966i	0.997123	+	0.0758024i	$0.0241518\pi$
$678$	9.54663	−	55.1994i	0.366636	−	2.11992i
$679$	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	$-0.408492\pi$
$683$	14.8201			0.567074			0.283537	+	0.958961i	$0.408492\pi$
$684$	56.0110	−	16.4592i	2.14163	−	0.629331i
$685$	−18.6717	−	13.5658i	−0.713408	−	0.518321i
$686$	20.2520	+	27.8745i	0.773226	+	1.06425i
$687$	−41.9954	+	20.6532i	−1.60222	+	0.787970i
$688$	−6.02754	−	1.95847i	−0.229798	−	0.0746658i
$689$	−24.0885	+	42.9753i	−0.917699	+	1.63723i
$690$	−0.132343	+	0.0190423i	−0.00503820	+	0.000724927i
$691$	−38.0035	+	12.3481i	−1.44572	+	0.469743i	−0.923676	−	0.383174i	$-0.874831\pi$
$691$	−38.0035	+	12.3481i	−1.44572	+	0.469743i	−0.522045	+	0.852918i	$0.674831\pi$
$692$	−20.5128			−0.779780
$693$	−9.82820	−	7.42587i	−0.373343	−	0.282086i
$694$		−	35.5306i		−	1.34872i
$695$	19.3970	−	6.30248i	0.735771	−	0.239067i
$696$	3.95307	+	27.4736i	0.149841	+	1.04138i
$697$	−3.56935	−	4.91279i	−0.135199	−	0.186085i
$698$	−71.6029	−	23.2652i	−2.71021	−	0.880600i
$699$	5.78122	+	11.7553i	0.218666	+	0.444625i
$700$	−10.6434	+	7.73286i	−0.402281	+	0.292274i
$701$	9.47103	+	6.88111i	0.357716	+	0.259896i	0.752099	−	0.659050i	$-0.229042\pi$
$701$	9.47103	+	6.88111i	0.357716	+	0.259896i	−0.394383	+	0.918946i	$0.629042\pi$
$702$	3.43254	−	41.6807i	0.129553	−	1.57314i
$703$		−	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
$708$	4.33967	−	25.0923i	0.163095	−	0.943026i
$709$	−20.2217	−	6.57042i	−0.759441	−	0.246757i	−0.0964022	−	0.995342i	$-0.530733\pi$
$709$	−20.2217	−	6.57042i	−0.759441	−	0.246757i	−0.663039	+	0.748585i	$0.730733\pi$
$710$	−14.9271	−	4.85012i	−0.560205	−	0.182022i
$711$	11.9356	−	8.16502i	0.447618	−	0.306212i
$712$	−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
$717$	−18.3886	+	34.8591i	−0.686733	+	1.30184i
$718$	−30.7344	−	22.3298i	−1.14700	−	0.833342i
$719$	12.1614	+	16.7387i	0.453543	+	0.624248i	0.973154	−	0.230155i	$-0.0739233\pi$
$719$	12.1614	+	16.7387i	0.453543	+	0.624248i	−0.519611	+	0.854403i	$0.673923\pi$
$720$	−3.61658	−	1.28953i	−0.134782	−	0.0480580i
$721$	6.37657	−	19.6251i	0.237476	−	0.730875i
$722$	−30.9058	−	42.5382i	−1.15020	−	1.58311i
$723$	−8.77406	+	1.26246i	−0.326311	+	0.0469516i
$724$	11.5526	+	35.5554i	0.429351	+	1.32141i
$725$	−26.0133			−0.966111
$726$	−37.7971	+	19.4996i	−1.40278	+	0.723700i
$727$	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
$729$	17.6683	−	20.4164i	0.654382	−	0.756164i
$730$	7.25686	+	9.98821i	0.268588	+	0.369680i
$731$	14.7405	+	4.78948i	0.545197	+	0.177145i
$732$	4.34393	−	2.13634i	0.160556	−	0.0789613i
$733$	2.62799	−	1.90934i	0.0970669	−	0.0705232i	−0.538193	−	0.842822i	$-0.680893\pi$
$733$	2.62799	−	1.90934i	0.0970669	−	0.0705232i	0.635260	+	0.772298i	$0.280893\pi$
$734$	−7.16875	+	9.86694i	−0.264603	+	0.364195i
$735$	10.0429	+	5.29775i	0.370438	+	0.195410i
$736$	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	−0.964905	−	0.262598i	$-0.915421\pi$
$739$	−9.20555	−	28.3318i	−0.338632	−	1.04220i	0.626274	−	0.779603i	$-0.284579\pi$
$740$	22.1883	−	30.5396i	0.815659	−	1.12266i
$741$	−39.3657	+	10.4865i	−1.44613	+	0.385230i
$742$	−11.6690	+	35.9136i	−0.428384	+	1.31843i
$743$	19.6389	+	6.38108i	0.720483	+	0.234099i	0.646233	−	0.763141i	$-0.276344\pi$
$743$	19.6389	+	6.38108i	0.720483	+	0.234099i	0.0742504	+	0.997240i	$0.476344\pi$
$744$	−4.81389	+	27.8343i	−0.176486	+	1.02045i
$745$	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
$750$	−18.5207	+	35.1095i	−0.676279	+	1.28202i
$751$	36.3678	+	26.4227i	1.32708	+	0.964180i	0.999815	+	0.0192471i	$0.00612693\pi$
$751$	36.3678	+	26.4227i	1.32708	+	0.964180i	0.327265	+	0.944933i	$0.393873\pi$
$752$	−1.48307	+	1.07751i	−0.0540818	+	0.0392927i
$753$	−2.81425	+	1.38404i	−0.102557	+	0.0504373i
$754$	−6.88632	−	58.3696i	−0.250785	−	2.12570i
$755$	2.38285	−	1.73124i	0.0867208	−	0.0630064i
$756$	−2.19353	−	19.0642i	−0.0797780	−	0.693359i
$757$	−9.57470	−	29.4679i	−0.347998	−	1.07103i	−0.959959	−	0.280141i	$-0.909619\pi$
$757$	−9.57470	−	29.4679i	−0.347998	−	1.07103i	0.611961	−	0.790888i	$-0.290381\pi$
$758$	−60.9903			−2.21527
$759$	0.163753	−	0.0251707i	0.00594386	−	0.000913638i
$760$		−	17.1651i		−	0.622644i
$761$	48.6784	−	15.8166i	1.76459	−	0.573350i	0.766930	−	0.641730i	$-0.221783\pi$
$761$	48.6784	−	15.8166i	1.76459	−	0.573350i	0.997659	+	0.0683802i	$0.0217831\pi$
$762$	12.4833	−	1.79618i	0.452223	−	0.0650686i
$763$	−0.276236	+	0.200697i	−0.0100004	+	0.00726572i
$764$	−65.1122	−	21.1562i	−2.35568	−	0.765406i
$765$	8.84443	+	3.15358i	0.319771	+	0.114018i
$766$	21.3146	+	29.3371i	0.770128	+	1.05999i
$767$	−3.47328	+	17.4272i	−0.125413	+	0.629261i
$768$	−13.0100	−	6.86294i	−0.469460	−	0.247645i
$769$	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	$-0.425644\pi$
$773$	−17.2995	−	12.5688i	−0.622219	−	0.452069i	−0.853696	+	0.520772i	$0.825644\pi$
$774$	−22.4507	−	32.8183i	−0.806975	−	1.17963i
$775$	−25.1777	−	8.18075i	−0.904411	−	0.293861i
$776$	1.84319	−	5.67275i	0.0661667	−	0.203640i
$777$	−22.2994	−	3.85664i	−0.799987	−	0.138356i
$778$	−18.7920	−	13.6532i	−0.673726	−	0.489491i
$779$	14.4328	−	4.68949i	0.517108	−	0.168018i
$780$	−20.8421	−	8.03545i	−0.746268	−	0.287715i
$781$	18.5533	+	5.83177i	0.663889	+	0.208677i
$782$	−0.168055			−0.00600964
$783$	18.6481	−	33.0460i	0.666430	−	1.18097i
$784$	−4.72126	−	3.43020i	−0.168617	−	0.122507i
$785$	−5.27545	+	3.83284i	−0.188289	+	0.136800i
$786$	32.7504	−	16.1066i	1.16817	−	0.574503i
$787$	0.226708	−	0.697737i	0.00808128	−	0.0248716i	−0.946935	−	0.321426i	$-0.895838\pi$
$787$	0.226708	−	0.697737i	0.00808128	−	0.0248716i	0.955016	+	0.296555i	$0.0958377\pi$
$788$	6.73540	+	9.27048i	0.239939	+	0.330247i
$789$	4.59986	−	0.661856i	0.163759	−	0.0235627i
$790$	−3.98703	−	12.2708i	−0.141852	−	0.436576i
$791$			17.9371i			0.637771i
$792$	−20.6363	−	7.13529i	−0.733280	−	0.253541i
$793$	−3.06829	+	1.41311i	−0.108958	+	0.0501809i
$794$	−19.8959	−	61.2331i	−0.706077	−	2.17308i
$795$	4.04149	+	28.0881i	0.143337	+	0.996184i
$796$	−17.4965	+	12.7120i	−0.620148	+	0.450564i
$797$	2.83292	+	0.920472i	0.100347	+	0.0326048i	0.358760	−	0.933430i	$-0.383200\pi$
$797$	2.83292	+	0.920472i	0.100347	+	0.0326048i	−0.258413	+	0.966035i	$0.583200\pi$
$798$	−28.0203	+	13.7803i	−0.991909	+	0.487819i
$799$	3.62687	−	2.63508i	0.128310	−	0.0932223i
$800$	14.1791	−	19.5158i	0.501306	−	0.689989i
$801$	13.9031	−	4.08550i	0.491241	−	0.144354i
$802$			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
$807$	−54.4095	−	9.41002i	−1.91531	−	0.331248i
$808$	−11.3971	−	3.70314i	−0.400948	−	0.130276i
$809$	15.7650	−	48.5195i	0.554266	−	1.70586i	−0.143607	−	0.989635i	$-0.545870\pi$
$809$	15.7650	−	48.5195i	0.554266	−	1.70586i	0.697874	−	0.716221i	$-0.254130\pi$
$810$	−13.0323	−	20.2599i	−0.457910	−	0.711860i
$811$	23.4422	+	17.0317i	0.823166	+	0.598065i	0.917618	−	0.397465i	$-0.130110\pi$
$811$	23.4422	+	17.0317i	0.823166	+	0.598065i	−0.0944518	+	0.995529i	$0.530110\pi$
$812$	−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
$816$	−4.26852	−	2.25169i	−0.149428	−	0.0788249i
$817$	−22.7666	+	31.3355i	−0.796501	+	1.09629i
$818$	3.43995	+	4.73468i	0.120275	+	0.165544i
$819$	1.19140	+	13.3382i	0.0416309	+	0.466073i
$820$	7.91369	+	2.57131i	0.276358	+	0.0897941i
$821$	2.51822	+	3.46603i	0.0878865	+	0.120965i	0.850696	−	0.525658i	$-0.176181\pi$
$821$	2.51822	+	3.46603i	0.0878865	+	0.120965i	−0.762810	+	0.646623i	$0.776181\pi$
$822$	10.5990	+	73.6628i	0.369684	+	2.56929i
$823$	5.05957	+	15.5718i	0.176366	+	0.542797i	0.999693	−	0.0247690i	$-0.00788501\pi$
$823$	5.05957	+	15.5718i	0.176366	+	0.542797i	−0.823328	+	0.567566i	$0.807885\pi$
$824$		−	36.5774i		−	1.27423i
$825$	9.37343	−	18.1908i	0.326341	−	0.633321i
$826$			13.6205i			0.473917i
$827$	9.96320	−	3.23724i	0.346455	−	0.112570i	−0.130621	−	0.991432i	$-0.541697\pi$
$827$	9.96320	−	3.23724i	0.346455	−	0.112570i	0.477075	+	0.878863i	$0.341697\pi$
$828$	0.204424	+	0.157566i	0.00710422	+	0.00547578i
$829$	−2.81250	+	2.04340i	−0.0976822	+	0.0709702i	−0.635554	−	0.772056i	$-0.719228\pi$
$829$	−2.81250	+	2.04340i	−0.0976822	+	0.0709702i	0.537872	+	0.843026i	$0.319228\pi$
$830$	6.96655	−	21.4408i	0.241812	−	0.744222i
$831$	−36.2508	+	17.8281i	−1.25753	+	0.618449i
$832$	40.8295	+	22.8857i	1.41551	+	0.793419i
$833$	11.5460	+	8.38864i	0.400044	+	0.290649i
$834$	−58.1688	−	30.6847i	−2.01422	−	1.06252i
$835$		−	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	$-0.319631\pi$
$839$	−2.88863	−	2.09871i	−0.0997265	−	0.0724555i	−0.636531	+	0.771251i	$0.719631\pi$
$840$	−5.55985	−	0.961565i	−0.191833	−	0.0331772i
$841$	7.51702	−	23.1350i	0.259208	−	0.797759i
$842$	−24.7306	+	76.1131i	−0.852274	+	2.62303i
$843$	15.4652	+	2.67468i	0.532650	+	0.0921208i
$844$	−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
$849$	13.7676	−	26.0992i	0.472503	−	0.895723i
$850$	−12.2010	+	16.7932i	−0.418491	+	0.576003i
$851$	0.246244	−	0.178907i	0.00844113	−	0.00613284i
$852$	13.3709	+	27.1877i	0.458078	+	0.931435i
$853$	0.738763	−	2.27368i	0.0252948	−	0.0778493i	−0.937612	−	0.347683i	$-0.886969\pi$
$853$	0.738763	−	2.27368i	0.0252948	−	0.0778493i	0.962907	+	0.269833i	$0.0869686\pi$
$854$	−2.09474	+	1.52192i	−0.0716805	+	0.0520789i
$855$	−14.3253	+	18.5854i	−0.489914	+	0.635609i
$856$	−22.2273	+	7.22210i	−0.759714	+	0.246846i
$857$	31.0326			1.06006			0.530028	−	0.847980i	$-0.322182\pi$
$857$	31.0326			1.06006			0.530028	+	0.847980i	$0.322182\pi$
$858$	43.2984	+	16.2169i	1.47818	+	0.553636i
$859$	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
$861$	−0.710442	−	4.93754i	−0.0242118	−	0.168271i
$862$	46.4321	−	33.7349i	1.58148	−	1.14902i
$863$	2.88584	−	8.88170i	0.0982351	−	0.302337i	−0.889848	−	0.456257i	$-0.849190\pi$
$863$	2.88584	−	8.88170i	0.0982351	−	0.302337i	0.988083	+	0.153920i	$0.0491899\pi$
$864$	14.6274	+	32.0026i	0.497633	+	1.08875i
$865$	6.67045	−	4.84637i	0.226802	−	0.164781i
$866$	−33.8875	+	46.6421i	−1.15154	+	1.58496i
$867$	−15.6047	−	8.23164i	−0.529963	−	0.279561i
$868$		−	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
$873$	−6.72995	+	4.60390i	−0.227774	+	0.155819i
$874$	0.129780	−	0.399421i	0.00438987	−	0.0135106i
$875$	3.92769	−	12.0882i	0.132780	−	0.408655i
$876$	4.06149	−	23.4839i	0.137225	−	0.793446i
$877$	−20.6549	−	15.0066i	−0.697466	−	0.506738i	0.181640	−	0.983365i	$-0.441859\pi$
$877$	−20.6549	−	15.0066i	−0.697466	−	0.506738i	−0.879106	+	0.476627i	$0.841859\pi$
$878$	−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	$0.832962\pi$
$882$	−10.3227	−	35.1284i	−0.347583	−	1.18283i
$883$	−37.3884	−	27.1643i	−1.25822	−	0.914151i	−0.259552	−	0.965729i	$-0.583575\pi$
$883$	−37.3884	−	27.1643i	−1.25822	−	0.914151i	−0.998669	+	0.0515779i	$0.983575\pi$
$884$	−24.4911	−	13.7277i	−0.823725	−	0.461714i
$885$	4.51713	+	9.18492i	0.151842	+	0.308748i
$886$	−0.147327	+	0.453425i	−0.00494953	+	0.0152331i
$887$	37.6070	−	27.3231i	1.26272	−	0.917419i	0.263831	−	0.964569i	$-0.415014\pi$
$887$	37.6070	−	27.3231i	1.26272	−	0.917419i	0.998888	+	0.0471496i	$0.0150138\pi$
$888$	−39.7056	+	5.71308i	−1.33243	+	0.191719i
$889$	−3.84066	+	1.24790i	−0.128811	+	0.0418534i
$890$		−	12.9289i		−	0.433376i
$891$	16.3891	+	24.9479i	0.549055	+	0.835786i
$892$			70.9257i			2.37477i
$893$	3.46202	+	10.6550i	0.115852	+	0.356556i
$894$	−18.3014	+	2.63332i	−0.612091	+	0.0880713i
$895$	−13.0894	−	18.0161i	−0.437531	−	0.602210i
$896$	18.1738	+	5.90504i	0.607145	+	0.197273i
$897$	−0.139806	−	0.113550i	−0.00466797	−	0.00379134i
$898$	19.4216	+	26.7315i	0.648106	+	0.892041i
$899$	31.8984	−	43.9044i	1.06387	−	1.46429i
$900$	30.5864	−	8.98800i	1.01955	−	0.299600i
$901$			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
$906$	−9.35862	−	1.61856i	−0.310919	−	0.0537729i
$907$	4.84805	−	14.9208i	0.160977	−	0.495436i	−0.837740	−	0.546069i	$-0.816124\pi$
$907$	4.84805	−	14.9208i	0.160977	−	0.495436i	0.998717	+	0.0506325i	$0.0161237\pi$
$908$	54.1249	+	17.5863i	1.79620	+	0.583620i
$909$	9.24967	+	13.5211i	0.306792	+	0.448466i
$910$	11.7173	+	2.33528i	0.388425	+	0.0774138i
$911$	−8.58762	+	2.79029i	−0.284520	+	0.0924463i	−0.447801	−	0.894133i	$-0.647793\pi$
$911$	−8.58762	+	2.79029i	−0.284520	+	0.0924463i	0.163280	+	0.986580i	$0.447793\pi$
$912$	8.64799	−	8.40624i	0.286364	−	0.278358i
$913$	−8.37656	+	26.6493i	−0.277224	+	0.881964i
$914$		−	48.3651i		−	1.59978i
$915$	−0.907848	+	1.72100i	−0.0300125	+	0.0568946i
$916$	47.3763	−	65.2079i	1.56536	−	2.15453i
$917$	−9.45433	+	6.86897i	−0.312209	+	0.226833i
$918$	−12.5868	−	27.5381i	−0.415425	−	0.908891i
$919$	−7.52402	−	2.44470i	−0.248194	−	0.0806432i	0.182278	−	0.983247i	$-0.441653\pi$
$919$	−7.52402	−	2.44470i	−0.248194	−	0.0806432i	−0.430472	+	0.902604i	$0.641653\pi$
$920$	0.0613953	−	0.0446063i	0.00202414	−	0.00147063i
$921$	21.6784	−	3.11921i	0.714326	−	0.102782i
$922$	−0.764752	−	2.35367i	−0.0251858	−	0.0775139i
$923$	−8.84431	−	19.2037i	−0.291114	−	0.632098i
$924$	20.9388	+	3.41437i	0.688835	+	0.112325i
$925$		−	37.5952i		−	1.23612i
$926$	12.8113	+	39.4291i	0.421005	+	1.29572i
$927$	−30.5260	+	39.6041i	−1.00260	+	1.30077i
$928$	29.0662	+	40.0061i	0.954143	+	1.31327i
$929$	−7.78936	+	23.9732i	−0.255561	+	0.786535i	0.738158	+	0.674628i	$0.235696\pi$
$929$	−7.78936	+	23.9732i	−0.255561	+	0.786535i	−0.993719	+	0.111907i	$0.964304\pi$
$930$	−15.2047	−	30.9166i	−0.498582	−	1.01379i
$931$	−28.8538	+	20.9635i	−0.945645	+	0.687052i
$932$	−18.2529	−	13.2615i	−0.597893	−	0.434395i
$933$	8.69108	−	16.4756i	0.284533	−	0.539389i
$934$	14.8122			0.484671
$935$	−6.02070	+	8.45655i	−0.196898	+	0.276559i
$936$	9.31462	+	21.8333i	0.304458	+	0.713644i
$937$	−17.9996	+	5.84842i	−0.588021	+	0.191060i	−0.587891	−	0.808940i	$-0.700041\pi$
$937$	−17.9996	+	5.84842i	−0.588021	+	0.191060i	−0.000130176		1.00000i	$0.500041\pi$
$938$	14.3522	+	10.4275i	0.468617	+	0.340470i
$939$	−0.821466	+	4.74979i	−0.0268075	+	0.155003i
$940$	−1.89827	+	5.84229i	−0.0619149	+	0.190554i
$941$	10.7067	+	3.47881i	0.349028	+	0.113406i	0.478284	−	0.878205i	$-0.341259\pi$
$941$	10.7067	+	3.47881i	0.349028	+	0.113406i	−0.129256	+	0.991611i	$0.541259\pi$
$942$	20.7193	+	3.58336i	0.675070	+	0.116752i
$943$	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	$-0.662434\pi$
$947$	−30.0619			−0.976882			−0.488441	+	0.872597i	$0.662434\pi$
$948$	−11.6206	+	22.0291i	−0.377419	+	0.715471i
$949$	−3.25064	+	16.3101i	−0.105520	+	0.529449i
$950$	−30.4908	−	41.9669i	−0.989251	−	1.36159i
$951$	10.1478	+	20.6340i	0.329064	+	0.669103i
$952$	−6.74484	−	2.19153i	−0.218601	−	0.0710279i
$953$	9.64010	−	7.00394i	0.312273	−	0.226880i	−0.420598	−	0.907247i	$-0.638180\pi$
$953$	9.64010	−	7.00394i	0.312273	−	0.226880i	0.732871	+	0.680367i	$0.238180\pi$
$954$	55.8621	−	72.4749i	1.80860	−	2.34646i
$955$	26.1719	−	8.50376i	0.846902	−	0.275175i
$956$		−	67.8784i		−	2.19534i
$957$	29.5270	+	29.7977i	0.954473	+	0.963221i
$958$	57.1042			1.84495
$959$	−7.36375	−	22.6633i	−0.237788	−	0.731836i
$960$	26.6856	−	3.83969i	0.861276	−	0.123926i
$961$	19.6014	−	14.2413i	0.632304	−	0.459395i
$962$	84.3574	−	9.95231i	2.71979	−	0.320875i
$963$	30.0938	+	10.7303i	0.969759	+	0.345779i
$964$	12.3513	−	8.97373i	0.397808	−	0.289024i
$965$	6.42567	+	4.66852i	0.206850	+	0.150285i
$966$	−0.122104	−	0.0644113i	−0.00392864	−	0.00207240i
$967$	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	$-0.832923\pi$
$971$	−3.78214	+	5.20567i	−0.121375	+	0.167058i	0.744006	+	0.668173i	$0.232923\pi$
$972$	−10.5086	+	45.2987i	−0.337062	+	1.45295i
$973$	20.0275	+	6.50733i	0.642052	+	0.208615i
$974$	−9.77035	+	30.0701i	−0.313062	+	0.963507i
$975$	−21.4968	+	5.72644i	−0.688448	+	0.183393i
$976$	0.587816	−	0.809059i	0.0188155	−	0.0258974i
$977$	15.3441	+	47.2243i	0.490901	+	1.51084i	0.823248	+	0.567682i	$0.192160\pi$
$977$	15.3441	+	47.2243i	0.490901	+	1.51084i	−0.332347	+	0.943157i	$0.607840\pi$
$978$	−25.3855	+	24.6758i	−0.811737	+	0.789046i
$979$	0.153990	+	16.0196i	0.00492154	+	0.511987i
$980$	−19.5558			−0.624686
$981$	0.793835	−	0.233273i	0.0253452	−	0.00744783i
$982$	28.7227	−	39.5334i	0.916578	−	1.26156i
$983$	−5.33308	+	3.87471i	−0.170099	+	0.123584i	−0.669578	−	0.742742i	$-0.733525\pi$
$983$	−5.33308	+	3.87471i	−0.170099	+	0.123584i	0.499479	+	0.866326i	$0.333525\pi$
$984$	−3.90228	−	7.93471i	−0.124400	−	0.252949i
$985$	−4.38050	−	1.42331i	−0.139574	−	0.0453504i
$986$	−25.0112	−	34.4250i	−0.796520	−	1.09632i
$987$	3.64514	−	0.524485i	0.116026	−	0.0166945i
$988$	51.5402	−	47.6075i	1.63971	−	1.51459i
$989$	−0.171242			−0.00544517
$990$	25.4783	−	7.75375i	0.809752	−	0.246430i
$991$	−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
$993$	−1.09568	−	7.61492i	−0.0347704	−	0.241652i
$994$	−9.52533	−	13.1105i	−0.302125	−	0.415840i
$995$	2.68627	−	8.26748i	0.0851604	−	0.262097i
$996$	−39.0515	+	19.2054i	−1.23739	+	0.608548i
$997$	−33.8859	−	46.6400i	−1.07318	−	1.47710i	−0.866817	−	0.498627i	$-0.833838\pi$
$997$	−33.8859	−	46.6400i	−1.07318	−	1.47710i	−0.206362	−	0.978476i	$-0.566162\pi$
$998$	−16.3546	−	11.8823i	−0.517695	−	0.376128i
$999$	47.7590	+	26.9508i	1.51103	+	0.852686i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.y.b.116.3	✓	176	1.1	even	1	trivial
429.2.y.b.116.4	yes	176	39.38	odd	2	inner
429.2.y.b.116.41	yes	176	13.12	even	2	inner
429.2.y.b.116.42	yes	176	3.2	odd	2	inner
429.2.y.b.233.3	yes	176	429.233	even	10	inner
429.2.y.b.233.4	yes	176	11.2	odd	10	inner
429.2.y.b.233.41	yes	176	33.2	even	10	inner
429.2.y.b.233.42	yes	176	143.90	odd	10	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12303 + 0.689813i) q^{2} +(-1.71440 + 0.246677i) q^{3} +(2.41336 - 1.75341i) q^{4} +(-0.370527 + 1.14036i) q^{5} +(3.46954 - 1.70631i) q^{6} +(-1.00158 + 0.727691i) q^{7} +(-1.28990 + 1.77539i) q^{8} +(2.87830 - 0.845805i) 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} +(0.353927 - 2.04643i) q^{15} +(-0.329845 + 1.01516i) q^{16} +(0.806644 - 2.48260i) q^{17} +(-5.52726 + 3.78115i) 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} +(1.77345 - 3.36191i) q^{24} +(2.88195 + 2.09386i) q^{25} +(-3.93535 + 7.02090i) q^{26} +(-4.72590 + 2.16006i) q^{27} +(-1.14124 + 3.51236i) q^{28} +(-5.90780 + 4.29226i) q^{29} +(0.660260 + 4.58877i) q^{30} +(-7.06787 + 2.29649i) q^{31} -6.77175i q^{32} +(-0.872754 - 5.67788i) q^{33} +5.82705i q^{34} +(-0.458720 - 1.41180i) q^{35} +(5.46333 - 7.08807i) q^{36} +(-6.20330 - 8.53811i) q^{37} +(-13.8493 - 4.49991i) q^{38} +(-3.93718 + 4.84754i) q^{39} +(-1.54665 - 2.12878i) q^{40} +(1.36738 - 1.88204i) q^{41} +(-2.23336 + 4.23377i) 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} +(0.315068 - 1.82175i) q^{48} +(-1.68949 + 5.19971i) q^{49} +(-7.56281 - 2.45731i) q^{50} +(-0.770506 + 4.45513i) 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} +(-9.99360 - 5.27174i) q^{57} +(9.58154 - 13.1879i) q^{58} +(-3.98724 + 2.89690i) q^{59} +(-2.73408 - 5.55936i) q^{60} +(-0.891049 - 0.289519i) q^{61} +(13.4211 - 9.75102i) q^{62} +(-2.26737 + 2.94166i) q^{63} +(4.01155 + 12.3463i) q^{64} +(1.80849 + 3.92679i) q^{65} +(5.76955 + 11.4522i) q^{66} +6.41925i q^{67} +(-2.40628 - 7.40578i) q^{68} +(-0.00711431 - 0.0494441i) q^{69} +(1.94775 + 2.68085i) q^{70} +(1.81204 - 5.57687i) q^{71} +(-2.21108 + 6.20112i) q^{72} +(-3.73166 + 2.71121i) q^{73} +(19.0595 + 13.8475i) q^{74} +(-5.45730 - 2.87879i) q^{75} +19.4597 q^{76} +(-2.44530 - 3.29852i) q^{77} +(5.01485 - 13.0074i) q^{78} +(4.58446 - 1.48958i) q^{79} +(-1.03543 - 0.752286i) q^{80} +(7.56923 - 4.86896i) q^{81} +(-1.60473 + 4.93885i) q^{82} +(8.01043 + 2.60275i) q^{83} +(1.09011 - 6.30309i) 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} +(-2.26389 - 7.70410i) q^{90} +(-0.872475 + 4.37766i) q^{91} +(0.0505693 + 0.0696026i) q^{92} +(11.5506 - 5.68058i) q^{93} +(-3.64611 - 1.18469i) q^{94} +(-6.32801 + 4.59757i) q^{95} +(1.67044 + 11.6095i) q^{96} +(-2.58498 + 0.839911i) q^{97} -12.2046i q^{98} +(2.89685 + 9.51884i) 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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