LMFDB - Embedded newform 416.2.bg.a.77.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [416,2,Mod(77,416)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(416, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 7, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("416.77"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bg (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			77.20
Character	$\chi$	$=$	416.77
Dual form			416.2.bg.a.389.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.544463 + 1.30521i) q^{2} +(1.26194 - 3.04659i) q^{3} +(-1.40712 - 1.42127i) q^{4} +(-0.106710 - 0.257621i) q^{5} +(3.28935 + 3.30585i) q^{6} +(-1.31255 - 1.31255i) q^{7} +(2.62118 - 1.06275i) q^{8} +(-5.56791 - 5.56791i) q^{9} +(0.394348 + 0.000986456i) q^{10} +(-2.43966 + 1.01054i) q^{11} +(-6.10573 + 2.49336i) q^{12} +(-0.345385 - 3.58897i) q^{13} +(2.42779 - 0.998515i) q^{14} -0.919528 q^{15} +(-0.0400230 + 3.99980i) q^{16} +4.27020i q^{17} +(10.2988 - 4.23575i) q^{18} +(-2.82693 + 6.82481i) q^{19} +(-0.215995 + 0.514168i) q^{20} +(-5.65518 + 2.34245i) q^{21} +(0.00934168 - 3.73445i) q^{22} +(2.19360 + 2.19360i) q^{23} +(0.0699936 - 9.32678i) q^{24} +(3.48055 - 3.48055i) q^{25} +(4.87239 + 1.50326i) q^{26} +(-14.8497 + 6.15097i) q^{27} +(-0.0185732 + 3.71242i) q^{28} +(3.60050 - 8.69237i) q^{29} +(0.500649 - 1.20017i) q^{30} -6.29543i q^{31} +(-5.19877 - 2.22998i) q^{32} +8.70788i q^{33} +(-5.57349 - 2.32497i) q^{34} +(-0.198079 + 0.478204i) q^{35} +(-0.0787885 + 15.7482i) q^{36} +(-2.77739 - 6.70521i) q^{37} +(-7.36862 - 7.40557i) q^{38} +(-11.3700 - 3.47682i) q^{39} +(-0.553493 - 0.561863i) q^{40} +(4.14002 - 4.14002i) q^{41} +(0.0216542 - 8.65655i) q^{42} +(0.742131 + 1.79166i) q^{43} +(4.86914 + 2.04546i) q^{44} +(-0.840258 + 2.02856i) q^{45} +(-4.05743 + 1.66877i) q^{46} +6.29123 q^{47} +(12.1353 + 5.16944i) q^{48} -3.55441i q^{49} +(2.64780 + 6.43787i) q^{50} +(13.0096 + 5.38874i) q^{51} +(-4.61490 + 5.54100i) q^{52} +(0.00163576 + 0.00394907i) q^{53} +(0.0568611 - 22.7309i) q^{54} +(0.520672 + 0.520672i) q^{55} +(-4.83535 - 2.04551i) q^{56} +(17.2250 + 17.2250i) q^{57} +(9.38499 + 9.43206i) q^{58} +(-2.46429 - 5.94933i) q^{59} +(1.29389 + 1.30690i) q^{60} +(1.72617 - 4.16733i) q^{61} +(8.21683 + 3.42763i) q^{62} +14.6164i q^{63} +(5.74112 - 5.57132i) q^{64} +(-0.887738 + 0.471958i) q^{65} +(-11.3656 - 4.74112i) q^{66} +(-0.878730 - 0.363982i) q^{67} +(6.06912 - 6.00869i) q^{68} +(9.45120 - 3.91482i) q^{69} +(-0.516308 - 0.518898i) q^{70} +(5.11691 + 5.11691i) q^{71} +(-20.5118 - 8.67716i) q^{72} +(-4.05532 + 4.05532i) q^{73} +(10.2639 + 0.0256749i) q^{74} +(-6.21158 - 14.9961i) q^{75} +(13.6777 - 5.58550i) q^{76} +(4.52857 + 1.87579i) q^{77} +(10.7285 - 12.9472i) q^{78} +2.54997i q^{79} +(1.03470 - 0.416508i) q^{80} +29.3806i q^{81} +(3.14949 + 7.65766i) q^{82} +(3.51752 - 8.49205i) q^{83} +(11.2868 + 4.74143i) q^{84} +(1.10009 - 0.455674i) q^{85} +(-2.74255 - 0.00686045i) q^{86} +(-21.9385 - 21.9385i) q^{87} +(-5.32082 + 5.24155i) q^{88} +(3.42337 + 3.42337i) q^{89} +(-2.19020 - 2.20119i) q^{90} +(-4.25738 + 5.16405i) q^{91} +(0.0310405 - 6.20436i) q^{92} +(-19.1796 - 7.94446i) q^{93} +(-3.42534 + 8.21134i) q^{94} +2.05988 q^{95} +(-13.3544 + 13.0244i) q^{96} +3.98025i q^{97} +(4.63923 + 1.93524i) q^{98} +(19.2104 + 7.95720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$

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 $

$2$	−0.544463	+	1.30521i	−0.384993	+	0.922919i
$2$	−0.544463	+	1.30521i	−0.384993	+	0.922919i
$3$	1.26194	−	3.04659i	0.728581	−	1.75895i	0.0813128	−	0.996689i	$-0.474089\pi$
$3$	1.26194	−	3.04659i	0.728581	−	1.75895i	0.647268	−	0.762262i	$-0.275911\pi$
$4$	−1.40712	−	1.42127i	−0.703560	−	0.710636i
$5$	−0.106710	−	0.257621i	−0.0477222	−	0.115212i	0.898221	−	0.439545i	$-0.144860\pi$
$5$	−0.106710	−	0.257621i	−0.0477222	−	0.115212i	−0.945943	+	0.324333i	$0.894860\pi$
$6$	3.28935	+	3.30585i	1.34287	+	1.34961i
$7$	−1.31255	−	1.31255i	−0.496099	−	0.496099i	0.414123	−	0.910221i	$-0.364089\pi$
$7$	−1.31255	−	1.31255i	−0.496099	−	0.496099i	−0.910221	+	0.414123i	$0.864089\pi$
$8$	2.62118	−	1.06275i	0.926725	−	0.375740i
$9$	−5.56791	−	5.56791i	−1.85597	−	1.85597i
$10$	0.394348		0.000986456i	0.124704		0.000311945i
$11$	−2.43966	+	1.01054i	−0.735584	+	0.304689i	−0.718844	−	0.695171i	$-0.755329\pi$
$11$	−2.43966	+	1.01054i	−0.735584	+	0.304689i	−0.0167397	+	0.999860i	$0.505329\pi$
$12$	−6.10573	+	2.49336i	−1.76257	+	0.719772i
$13$	−0.345385	−	3.58897i	−0.0957926	−	0.995401i
$13$	−0.345385	−	3.58897i	−0.0957926	−	0.995401i
$14$	2.42779	−	0.998515i	0.648854	−	0.266864i
$15$	−0.919528			−0.237421
$16$	−0.0400230	+	3.99980i	−0.0100058	+	0.999950i
$17$			4.27020i			1.03568i	0.855479	+	0.517838i	$0.173263\pi$
$17$			4.27020i			1.03568i	−0.855479	+	0.517838i	$0.826737\pi$
$18$	10.2988	−	4.23575i	2.42745	−	0.998375i
$19$	−2.82693	+	6.82481i	−0.648542	+	1.56572i	0.166326	+	0.986071i	$0.446810\pi$
$19$	−2.82693	+	6.82481i	−0.648542	+	1.56572i	−0.814867	+	0.579647i	$0.803190\pi$
$20$	−0.215995	+	0.514168i	−0.0482980	+	0.114971i
$21$	−5.65518	+	2.34245i	−1.23406	+	0.511165i
$22$	0.00934168	−	3.73445i	0.00199165	−	0.796188i
$23$	2.19360	+	2.19360i	0.457398	+	0.457398i	0.897800	−	0.440403i	$-0.145164\pi$
$23$	2.19360	+	2.19360i	0.457398	+	0.457398i	−0.440403	+	0.897800i	$0.645164\pi$
$24$	0.0699936	−	9.32678i	0.0142874	−	1.90382i
$25$	3.48055	−	3.48055i	0.696110	−	0.696110i
$26$	4.87239	+	1.50326i	0.955555	+	0.294814i
$27$	−14.8497	+	6.15097i	−2.85783	+	1.18375i
$28$	−0.0185732	+	3.71242i	−0.00351001	+	0.701581i
$29$	3.60050	−	8.69237i	0.668596	−	1.61413i	−0.115366	−	0.993323i	$-0.536804\pi$
$29$	3.60050	−	8.69237i	0.668596	−	1.61413i	0.783961	−	0.620809i	$-0.213196\pi$
$30$	0.500649	−	1.20017i	0.0914055	−	0.219120i
$31$		−	6.29543i		−	1.13069i	−0.824854	−	0.565346i	$-0.808742\pi$
$31$		−	6.29543i		−	1.13069i	0.824854	−	0.565346i	$-0.191258\pi$
$32$	−5.19877	−	2.22998i	−0.919021	−	0.394209i
$33$			8.70788i			1.51585i
$34$	−5.57349	−	2.32497i	−0.955846	−	0.398728i
$35$	−0.198079	+	0.478204i	−0.0334814	+	0.0808313i
$36$	−0.0787885	+	15.7482i	−0.0131314	+	2.62471i
$37$	−2.77739	−	6.70521i	−0.456600	−	1.10233i	−0.969765	−	0.244040i	$-0.921527\pi$
$37$	−2.77739	−	6.70521i	−0.456600	−	1.10233i	0.513165	−	0.858290i	$-0.328473\pi$
$38$	−7.36862	−	7.40557i	−1.19535	−	1.20134i
$39$	−11.3700	−	3.47682i	−1.82065	−	0.556736i
$40$	−0.553493	−	0.561863i	−0.0875149	−	0.0888384i
$41$	4.14002	−	4.14002i	0.646562	−	0.646562i	−0.305598	−	0.952161i	$-0.598856\pi$
$41$	4.14002	−	4.14002i	0.646562	−	0.646562i	0.952161	+	0.305598i	$0.0988565\pi$
$42$	0.0216542	−	8.65655i	0.00334132	−	1.33573i
$43$	0.742131	+	1.79166i	0.113174	+	0.273226i	0.970310	−	0.241864i	$-0.0777586\pi$
$43$	0.742131	+	1.79166i	0.113174	+	0.273226i	−0.857136	+	0.515090i	$0.827759\pi$
$44$	4.86914	+	2.04546i	0.734051	+	0.308365i
$45$	−0.840258	+	2.02856i	−0.125258	+	0.302400i
$46$	−4.05743	+	1.66877i	−0.598236	+	0.246046i
$47$	6.29123			0.917670			0.458835	−	0.888522i	$-0.348267\pi$
$47$	6.29123			0.917670			0.458835	+	0.888522i	$0.348267\pi$
$48$	12.1353	+	5.16944i	1.75157	+	0.746144i
$49$		−	3.55441i		−	0.507772i
$50$	2.64780	+	6.43787i	0.374456	+	0.910452i
$51$	13.0096	+	5.38874i	1.82170	+	0.754574i
$52$	−4.61490	+	5.54100i	−0.639972	+	0.768399i
$53$	0.00163576	+	0.00394907i	0.000224689	+	0.000542446i	0.923992	−	0.382412i	$-0.124907\pi$
$53$	0.00163576	+	0.00394907i	0.000224689	+	0.000542446i	−0.923767	+	0.382955i	$0.874907\pi$
$54$	0.0568611	−	22.7309i	0.00773782	−	3.09329i
$55$	0.520672	+	0.520672i	0.0702074	+	0.0702074i
$56$	−4.83535	−	2.04551i	−0.646151	−	0.273343i
$57$	17.2250	+	17.2250i	2.28151	+	2.28151i
$58$	9.38499	+	9.43206i	1.23231	+	1.23849i
$59$	−2.46429	−	5.94933i	−0.320823	−	0.774536i	−0.999207	−	0.0398279i	$-0.987319\pi$
$59$	−2.46429	−	5.94933i	−0.320823	−	0.774536i	0.678383	−	0.734708i	$-0.262681\pi$
$60$	1.29389	+	1.30690i	0.167040	+	0.168720i
$61$	1.72617	−	4.16733i	0.221013	−	0.533572i	−0.774015	−	0.633167i	$-0.781755\pi$
$61$	1.72617	−	4.16733i	0.221013	−	0.533572i	0.995028	+	0.0995947i	$0.0317546\pi$
$62$	8.21683	+	3.42763i	1.04354	+	0.435309i
$63$			14.6164i			1.84149i
$64$	5.74112	−	5.57132i	0.717640	−	0.696415i
$65$	−0.887738	+	0.471958i	−0.110110	+	0.0585392i
$66$	−11.3656	−	4.74112i	−1.39900	−	0.583591i
$67$	−0.878730	−	0.363982i	−0.107354	−	0.0444675i	0.328360	−	0.944553i	$-0.393504\pi$
$67$	−0.878730	−	0.363982i	−0.107354	−	0.0444675i	−0.435714	+	0.900085i	$0.643504\pi$
$68$	6.06912	−	6.00869i	0.735988	−	0.728661i
$69$	9.45120	−	3.91482i	1.13779	−	0.471288i
$70$	−0.516308	−	0.518898i	−0.0617106	−	0.0620201i
$71$	5.11691	+	5.11691i	0.607265	+	0.607265i	0.942230	−	0.334965i	$-0.108725\pi$
$71$	5.11691	+	5.11691i	0.607265	+	0.607265i	−0.334965	+	0.942230i	$0.608725\pi$
$72$	−20.5118	−	8.67716i	−2.41734	−	1.02261i
$73$	−4.05532	+	4.05532i	−0.474639	+	0.474639i	−0.903412	−	0.428773i	$-0.858946\pi$
$73$	−4.05532	+	4.05532i	−0.474639	+	0.474639i	0.428773	+	0.903412i	$0.358946\pi$
$74$	10.2639	+	0.0256749i	1.19315	+	0.00298465i
$75$	−6.21158	−	14.9961i	−0.717251	−	1.73160i
$76$	13.6777	−	5.58550i	1.56894	−	0.640700i
$77$	4.52857	+	1.87579i	0.516078	+	0.213767i
$78$	10.7285	−	12.9472i	1.21476	−	1.46598i
$79$			2.54997i			0.286894i	0.989658	+	0.143447i	$0.0458187\pi$
$79$			2.54997i			0.286894i	−0.989658	+	0.143447i	$0.954181\pi$
$80$	1.03470	−	0.416508i	0.115683	−	0.0465670i
$81$			29.3806i			3.26451i
$82$	3.14949	+	7.65766i	0.347803	+	0.845647i
$83$	3.51752	−	8.49205i	0.386098	−	0.932124i	−0.604660	−	0.796484i	$-0.706691\pi$
$83$	3.51752	−	8.49205i	0.386098	−	0.932124i	0.990758	−	0.135640i	$-0.0433090\pi$
$84$	11.2868	+	4.74143i	1.23149	+	0.517332i
$85$	1.10009	−	0.455674i	0.119322	−	0.0494248i
$86$	−2.74255	−	0.00686045i	−0.295737	−	0.000739781i
$87$	−21.9385	−	21.9385i	−2.35205	−	2.35205i
$88$	−5.32082	+	5.24155i	−0.567201	+	0.558751i
$89$	3.42337	+	3.42337i	0.362876	+	0.362876i	0.864871	−	0.501994i	$-0.167400\pi$
$89$	3.42337	+	3.42337i	0.362876	+	0.362876i	−0.501994	+	0.864871i	$0.667400\pi$
$90$	−2.19020	−	2.20119i	−0.230868	−	0.232025i
$91$	−4.25738	+	5.16405i	−0.446295	+	0.541340i
$92$	0.0310405	−	6.20436i	0.00323619	−	0.646850i
$93$	−19.1796	−	7.94446i	−1.98883	−	0.823802i
$94$	−3.42534	+	8.21134i	−0.353297	+	0.846935i
$95$	2.05988			0.211339
$96$	−13.3544	+	13.0244i	−1.36297	+	1.32930i
$97$			3.98025i			0.404133i	0.979372	+	0.202067i	$0.0647658\pi$
$97$			3.98025i			0.404133i	−0.979372	+	0.202067i	$0.935234\pi$
$98$	4.63923	+	1.93524i	0.468633	+	0.195489i
$99$	19.2104	+	7.95720i	1.93072	+	0.799729i
$100$	−9.84437	−	0.0492514i	−0.984437	−	0.00492514i
$101$	4.22829	−	1.75142i	0.420731	−	0.174272i	−0.162266	−	0.986747i	$-0.551880\pi$
$101$	4.22829	−	1.75142i	0.420731	−	0.174272i	0.582997	+	0.812475i	$0.301880\pi$
$102$	−14.1166	+	14.0462i	−1.39775	+	1.39078i
$103$	−1.88555	+	1.88555i	−0.185789	+	0.185789i	−0.793873	−	0.608084i	$-0.791938\pi$
$103$	−1.88555	+	1.88555i	−0.185789	+	0.185789i	0.608084	+	0.793873i	$0.291938\pi$
$104$	−4.71950	−	9.04026i	−0.462785	−	0.886471i
$105$	1.20693	+	1.20693i	0.117784	+	0.117784i
$106$	−0.00604495		1.51214e-5i	−0.000587138		1.46872e-6i
$107$	0.0720591	+	0.173966i	0.00696622	+	0.0168179i	0.927324	−	0.374259i	$-0.122103\pi$
$107$	0.0720591	+	0.173966i	0.00696622	+	0.0168179i	−0.920358	+	0.391077i	$0.872103\pi$
$108$	29.6376	+	12.4504i	2.85188	+	1.19804i
$109$	−2.26579	+	5.47011i	−0.217024	+	0.523941i	−0.994472	−	0.105006i	$-0.966514\pi$
$109$	−2.26579	+	5.47011i	−0.217024	+	0.523941i	0.777448	+	0.628947i	$0.216514\pi$
$110$	−0.963070	+	0.396097i	−0.0918252	+	0.0377664i
$111$	−23.9329			−2.27161
$112$	5.30248	−	5.19742i	0.501038	−	0.491110i
$113$			8.71704i			0.820030i	0.912079	+	0.410015i	$0.134476\pi$
$113$			8.71704i			0.820030i	−0.912079	+	0.410015i	$0.865524\pi$
$114$	−31.8605	+	13.1038i	−2.98401	+	1.22728i
$115$	0.331038	−	0.799197i	0.0308695	−	0.0745255i
$116$	−17.4205	+	7.11393i	−1.61746	+	0.660512i
$117$	−18.0600	+	21.9061i	−1.66965	+	2.02522i
$118$	9.10680	+	0.0227805i	0.838349	+	0.00209712i
$119$	5.60487	−	5.60487i	0.513798	−	0.513798i
$120$	−2.41024	+	0.977230i	−0.220024	+	0.0892085i
$121$	−2.84744	+	2.84744i	−0.258858	+	0.258858i
$122$	4.49939	+	4.52196i	0.407356	+	0.409399i
$123$	−7.38849	−	17.8374i	−0.666198	−	1.60834i
$124$	−8.94752	+	8.85843i	−0.803511	+	0.795511i
$125$	−2.55618	−	1.05880i	−0.228632	−	0.0947023i
$126$	−19.0774	−	7.95807i	−1.69955	−	0.708961i
$127$	15.3846			1.36516			0.682581	−	0.730810i	$-0.260857\pi$
$127$	15.3846			1.36516			0.682581	+	0.730810i	$0.260857\pi$
$128$	4.14589	+	10.5267i	0.366448	+	0.930438i
$129$	6.39499			0.563047
$130$	−0.132662	−	1.41564i	−0.0116352	−	0.124160i
$131$	0.877018	−	2.11731i	0.0766254	−	0.184990i	−0.880925	−	0.473256i	$-0.843079\pi$
$131$	0.877018	−	2.11731i	0.0766254	−	0.184990i	0.957550	+	0.288266i	$0.0930786\pi$
$132$	12.3763	−	12.2530i	1.07721	−	1.06649i
$133$	12.6684	−	5.24743i	1.09849	−	0.455010i
$134$	0.953507	−	0.948749i	0.0823705	−	0.0819594i
$135$	3.16924	+	3.16924i	0.272764	+	0.272764i
$136$	4.53817	+	11.1929i	0.389144	+	0.959787i
$137$	8.45003	−	8.45003i	0.721935	−	0.721935i	−0.247064	−	0.968999i	$-0.579466\pi$
$137$	8.45003	−	8.45003i	0.721935	−	0.721935i	0.968999	+	0.247064i	$0.0794660\pi$
$138$	−0.0361896	+	14.4672i	−0.00308066	+	1.23153i
$139$	6.31437	+	15.2442i	0.535578	+	1.29300i	0.927782	+	0.373122i	$0.121713\pi$
$139$	6.31437	+	15.2442i	0.535578	+	1.29300i	−0.392204	+	0.919878i	$0.628287\pi$
$140$	0.958378	−	0.391367i	0.0809977	−	0.0330766i
$141$	7.93915	−	19.1668i	0.668597	−	1.61414i
$142$	−9.46458	+	3.89265i	−0.794250	+	0.326664i
$143$	4.46942	+	8.40683i	0.373751	+	0.703015i
$144$	22.4934	−	22.0477i	1.87445	−	1.83731i
$145$	−2.62355			−0.217874
$146$	−3.08505	−	7.50099i	−0.255321	−	0.620786i
$147$	−10.8288	−	4.48545i	−0.893146	−	0.369953i
$148$	−5.62180	+	13.3825i	−0.462109	+	1.10003i
$149$	22.1955	−	9.19368i	1.81833	−	0.753175i	0.841131	−	0.540832i	$-0.181890\pi$
$149$	22.1955	−	9.19368i	1.81833	−	0.753175i	0.977195	−	0.212344i	$-0.0681096\pi$
$150$	22.9549	+	0.0574214i	1.87426	+	0.00468844i
$151$	−2.76378	+	2.76378i	−0.224913	+	0.224913i	−0.810564	−	0.585650i	$-0.800839\pi$
$151$	−2.76378	+	2.76378i	−0.224913	+	0.224913i	0.585650	+	0.810564i	$0.300839\pi$
$152$	−0.156796	+	20.8933i	−0.0127178	+	1.69467i
$153$	23.7761	−	23.7761i	1.92218	−	1.92218i
$154$	−4.91393	+	4.88941i	−0.395976	+	0.394000i
$155$	−1.62184	+	0.671786i	−0.130269	+	0.0539592i
$156$	11.0574	+	21.0521i	0.885304	+	1.68552i
$157$	−6.64904	+	16.0522i	−0.530651	+	1.28111i	0.400441	+	0.916323i	$0.368857\pi$
$157$	−6.64904	+	16.0522i	−0.530651	+	1.28111i	−0.931092	+	0.364783i	$0.881143\pi$
$158$	−3.32823	−	1.38836i	−0.264780	−	0.110452i
$159$	0.0140954			0.00111784
$160$	−0.0197286	+	1.57727i	−0.00155968	+	0.124694i
$161$		−	5.75844i		−	0.453829i
$162$	−38.3477	−	15.9967i	−3.01288	−	1.25682i
$163$	−19.7581	−	8.18407i	−1.54757	−	0.641026i	−0.564698	−	0.825298i	$-0.691007\pi$
$163$	−19.7581	−	8.18407i	−1.54757	−	0.641026i	−0.982875	+	0.184272i	$0.941007\pi$
$164$	−11.7096	−	0.0585831i	−0.914366	−	0.00457457i
$165$	2.24333	−	0.929219i	0.174643	−	0.0723396i
$166$	9.16871	+	9.21469i	0.711630	+	0.715199i
$167$	−6.78517	−	6.78517i	−0.525052	−	0.525052i	0.394041	−	0.919093i	$-0.371077\pi$
$167$	−6.78517	−	6.78517i	−0.525052	−	0.525052i	−0.919093	+	0.394041i	$0.871077\pi$
$168$	−12.3338	+	12.1500i	−0.951571	+	0.937395i
$169$	−12.7614	+	2.47915i	−0.981648	+	0.190704i
$170$	−0.00421237	+	1.68395i	−0.000323074	+	0.129153i
$171$	53.7400	−	22.2598i	4.10960	−	1.70225i
$172$	1.50217	−	3.57586i	0.114539	−	0.272656i
$173$	2.15316	+	0.891869i	0.163702	+	0.0678075i	0.463030	−	0.886343i	$-0.346762\pi$
$173$	2.15316	+	0.891869i	0.163702	+	0.0678075i	−0.299328	+	0.954150i	$0.596762\pi$
$174$	40.5789	−	16.6895i	3.07628	−	1.26523i
$175$	−9.13682			−0.690679
$176$	−3.94431	−	9.79858i	−0.297314	−	0.738596i
$177$	−21.2350			−1.59612
$178$	−6.33210	+	2.60430i	−0.474611	+	0.195201i
$179$	−11.1383	−	4.61364i	−0.832516	−	0.344839i	−0.0746178	−	0.997212i	$-0.523774\pi$
$179$	−11.1383	−	4.61364i	−0.832516	−	0.344839i	−0.757898	+	0.652373i	$0.773774\pi$
$180$	4.06548	−	1.66020i	0.303023	−	0.123744i
$181$	−2.68516	−	6.48255i	−0.199586	−	0.481844i	0.792120	−	0.610365i	$-0.208977\pi$
$181$	−2.68516	−	6.48255i	−0.199586	−	0.481844i	−0.991707	+	0.128521i	$0.958977\pi$
$182$	−4.42216	−	8.36839i	−0.327793	−	0.620306i
$183$	−10.5178	−	10.5178i	−0.777502	−	0.777502i
$184$	8.08107	+	3.41856i	0.595744	+	0.252020i
$185$	−1.43103	+	1.43103i	−0.105211	+	0.105211i
$186$	20.8117	−	20.7079i	1.52599	−	1.51837i
$187$	−4.31521	−	10.4178i	−0.315559	−	0.761827i
$188$	−8.85251	−	8.94154i	−0.645636	−	0.652129i
$189$	27.5646	+	11.4176i	2.00503	+	0.830509i
$190$	−1.12153	+	2.68856i	−0.0813640	+	0.195049i
$191$	−4.94756			−0.357993			−0.178996	−	0.983850i	$-0.557285\pi$
$191$	−4.94756			−0.357993			−0.178996	+	0.983850i	$0.557285\pi$
$192$	−9.72859	−	24.5215i	−0.702100	−	1.76969i
$193$		−	5.14485i		−	0.370334i	−0.982707	−	0.185167i	$-0.940717\pi$
$193$		−	5.14485i		−	0.370334i	0.982707	−	0.185167i	$-0.0592827\pi$
$194$	−5.19504	−	2.16710i	−0.372982	−	0.155589i
$195$	0.317591	+	3.30016i	0.0227432	+	0.236329i
$196$	−5.05177	+	5.00148i	−0.360841	+	0.357248i
$197$	5.89826	+	14.2397i	0.420234	+	1.01453i	0.982279	+	0.187427i	$0.0600148\pi$
$197$	5.89826	+	14.2397i	0.420234	+	1.01453i	−0.562045	+	0.827107i	$0.689985\pi$
$198$	−20.8451	+	20.7411i	−1.48140	+	1.47401i
$199$	−6.93422	+	6.93422i	−0.491554	+	0.491554i	−0.908796	−	0.417242i	$-0.862997\pi$
$199$	−6.93422	+	6.93422i	−0.491554	+	0.491554i	0.417242	+	0.908796i	$0.362997\pi$
$200$	5.42417	−	12.8221i	0.383547	−	0.906659i
$201$	−2.21781	+	2.21781i	−0.156432	+	0.156432i
$202$	−0.0161905	+	6.47237i	−0.00113916	+	0.455394i
$203$	−16.1350	+	6.68336i	−1.13246	+	0.469080i
$204$	−10.6472	−	26.0727i	−0.745451	−	1.82546i
$205$	−1.50834	−	0.624774i	−0.105347	−	0.0436361i
$206$	−1.43442	−	3.48764i	−0.0999407	−	0.242996i
$207$		−	24.4276i		−	1.69783i
$208$	14.3690	−	1.23783i	0.996310	−	0.0858281i
$209$		−	19.5069i		−	1.34932i
$210$	−2.23242	+	0.918162i	−0.154052	+	0.0633592i
$211$	21.6907	+	8.98456i	1.49325	+	0.618523i	0.972020	−	0.234896i	$-0.0754750\pi$
$211$	21.6907	+	8.98456i	1.49325	+	0.618523i	0.521226	+	0.853419i	$0.325475\pi$
$212$	0.00331099	−	0.00788167i	0.000227400	−	0.000541315i
$213$	22.0464	−	9.13190i	1.51059	−	0.625707i
$214$	−0.266295		0.000666133i	−0.0182036		4.55359e-5i
$215$	0.382377	−	0.382377i	0.0260779	−	0.0260779i
$216$	−32.3868	+	31.9044i	−2.20364	+	2.17082i
$217$	−8.26309	+	8.26309i	−0.560935	+	0.560935i
$218$	−5.90597	−	5.93559i	−0.400003	−	0.402009i
$219$	7.23733	+	17.4725i	0.489054	+	1.18068i
$220$	0.00736775	−	1.47266i	0.000496733	−	0.0992870i
$221$	15.3256	−	1.47486i	1.03091	−	0.0992101i
$222$	13.0306	−	31.2374i	0.874556	−	2.09652i
$223$			4.92251i			0.329636i	0.986324	+	0.164818i	$0.0527036\pi$
$223$			4.92251i			0.329636i	−0.986324	+	0.164818i	$0.947296\pi$
$224$	3.89669	+	9.75063i	0.260359	+	0.651491i
$225$	−38.7588			−2.58392
$226$	−11.3775	−	4.74610i	−0.756821	−	0.315706i
$227$	19.3949	+	8.03365i	1.28729	+	0.533212i	0.918176	−	0.396173i	$-0.129662\pi$
$227$	19.3949	+	8.03365i	1.28729	+	0.533212i	0.369111	+	0.929385i	$0.379662\pi$
$228$	0.243741	−	48.7190i	0.0161422	−	3.22650i
$229$	−7.52387	−	18.1642i	−0.497191	−	1.20033i	−0.950990	−	0.309222i	$-0.899932\pi$
$229$	−7.52387	−	18.1642i	−0.497191	−	1.20033i	0.453799	−	0.891104i	$-0.350068\pi$
$230$	0.862878	+	0.867206i	0.0568965	+	0.0571819i
$231$	11.4296	−	11.4296i	0.752010	−	0.752010i
$232$	0.199702	−	26.6107i	0.0131111	−	1.74708i
$233$	−7.65415	−	7.65415i	−0.501440	−	0.501440i	0.410445	−	0.911885i	$-0.365373\pi$
$233$	−7.65415	−	7.65415i	−0.501440	−	0.501440i	−0.911885	+	0.410445i	$0.865373\pi$
$234$	−18.7590	−	35.4991i	−1.22632	−	2.32065i
$235$	−0.671337	−	1.62075i	−0.0437932	−	0.105726i
$236$	−4.98805	+	11.8738i	−0.324694	+	0.772921i
$237$	7.76872	+	3.21791i	0.504633	+	0.209026i
$238$	4.26386	+	10.3671i	0.276385	+	0.672002i
$239$	10.2714			0.664401			0.332201	−	0.943209i	$-0.392209\pi$
$239$	10.2714			0.664401			0.332201	+	0.943209i	$0.392209\pi$
$240$	0.0368023	−	3.67793i	0.00237558	−	0.237409i
$241$	13.3698			0.861222			0.430611	−	0.902538i	$-0.358298\pi$
$241$	13.3698			0.861222			0.430611	+	0.902538i	$0.358298\pi$
$242$	−2.16617	−	5.26681i	−0.139246	−	0.338564i
$243$	44.9615	+	18.6237i	2.88428	+	1.19471i
$244$	−8.35183	+	3.41059i	−0.534671	+	0.218341i
$245$	−0.915690	+	0.379291i	−0.0585013	+	0.0242320i
$246$	27.3042	+	0.0683011i	1.74085	+	0.00435472i
$247$	25.4704	+	7.78857i	1.62064	+	0.495575i
$248$	−6.69048	−	16.5014i	−0.424846	−	1.04784i
$249$	−21.4329	−	21.4329i	−1.35826	−	1.35826i
$250$	2.77370	−	2.75986i	0.175424	−	0.174549i
$251$	4.09594	−	1.69659i	0.258533	−	0.107088i	−0.249652	−	0.968336i	$-0.580316\pi$
$251$	4.09594	−	1.69659i	0.258533	−	0.107088i	0.508186	+	0.861248i	$0.330316\pi$
$252$	20.7738	−	20.5670i	1.30863	−	1.29560i
$253$	−7.56835	−	3.13492i	−0.475818	−	0.197090i
$254$	−8.37634	+	20.0801i	−0.525578	+	1.25993i
$255$		−	3.92657i		−	0.245891i
$256$	−15.9968	−	0.320168i	−0.999800	−	0.0200105i
$257$	14.9068			0.929862			0.464931	−	0.885347i	$-0.346079\pi$
$257$	14.9068			0.929862			0.464931	+	0.885347i	$0.346079\pi$
$258$	−3.48183	+	8.34677i	−0.216770	+	0.519647i
$259$	−5.15548	+	12.4464i	−0.320346	+	0.773383i
$260$	1.91993	+	0.597615i	0.119069	+	0.0370625i
$261$	−68.4456	+	28.3511i	−4.23668	+	1.75489i
$262$	2.28602	+	2.29748i	0.141231	+	0.141939i
$263$	−21.4367	+	21.4367i	−1.32184	+	1.32184i	−0.409557	+	0.912285i	$0.634317\pi$
$263$	−21.4367	+	21.4367i	−1.32184	+	1.32184i	−0.912285	+	0.409557i	$0.865683\pi$
$264$	9.25431	+	22.8249i	0.569564	+	1.40477i
$265$	0.000842811	0	0.000842811i	5.17735e−5	0	5.17735e-5i
$266$	−0.0485086	+	19.3919i	−0.00297425	+	1.18899i
$267$	14.7497	−	6.10952i	0.902667	−	0.373897i
$268$	0.719162	+	1.76108i	0.0439298	+	0.107575i
$269$	2.56690	+	1.06325i	0.156507	+	0.0648272i	0.459562	−	0.888146i	$-0.348007\pi$
$269$	2.56690	+	1.06325i	0.156507	+	0.0648272i	−0.303055	+	0.952973i	$0.598007\pi$
$270$	−5.86203	+	2.41097i	−0.356752	+	0.146727i
$271$	0.802240			0.0487326			0.0243663	−	0.999703i	$-0.492243\pi$
$271$	0.802240			0.0487326			0.0243663	+	0.999703i	$0.492243\pi$
$272$	−17.0800	−	0.170906i	−1.03562	−	0.0103627i
$273$	10.3602	+	19.4872i	0.627028	+	1.17942i
$274$	6.42829	+	15.6297i	0.388347	+	0.944227i
$275$	−4.97412	+	12.0086i	−0.299951	+	0.724145i
$276$	−18.8630	−	7.92410i	−1.13542	−	0.476975i
$277$	−6.56181	−	15.8416i	−0.394261	−	0.951830i	−0.989001	−	0.147912i	$-0.952745\pi$
$277$	−6.56181	−	15.8416i	−0.394261	−	0.951830i	0.594740	−	0.803918i	$-0.297255\pi$
$278$	−23.3348	−	0.0583717i	−1.39953	−	0.00350090i
$279$	−35.0524	+	35.0524i	−2.09853	+	2.09853i
$280$	−0.0109864	+	1.46397i	−0.000656566	+	0.0874887i
$281$	13.4920	+	13.4920i	0.804867	+	0.804867i	0.983852	−	0.178985i	$-0.0572814\pi$
$281$	13.4920	+	13.4920i	0.804867	+	0.804867i	−0.178985	+	0.983852i	$0.557281\pi$
$282$	20.6940	+	20.7978i	1.23231	+	1.23849i
$283$	8.06403	−	3.34023i	0.479357	−	0.198556i	−0.129903	−	0.991527i	$-0.541467\pi$
$283$	8.06403	−	3.34023i	0.479357	−	0.198556i	0.609260	+	0.792971i	$0.291467\pi$
$284$	0.0724066	−	14.4726i	0.00429654	−	0.858792i
$285$	2.59944	−	6.27560i	0.153977	−	0.371735i
$286$	−13.4061	+	1.25630i	−0.792717	+	0.0742865i
$287$	−10.8680			−0.641517
$288$	16.5299	+	41.3626i	0.974036	+	2.43732i
$289$	−1.23463			−0.0726252
$290$	1.42842	−	3.42427i	0.0838799	−	0.201080i
$291$	12.1262	+	5.02284i	0.710850	+	0.294444i
$292$	11.4700	+	0.0573846i	0.671233	+	0.00335818i
$293$	1.70636	+	4.11951i	0.0996865	+	0.240665i	0.965853	−	0.259091i	$-0.0834231\pi$
$293$	1.70636	+	4.11951i	0.0996865	+	0.240665i	−0.866166	+	0.499756i	$0.833423\pi$
$294$	11.7503	−	11.6917i	0.685292	−	0.681873i
$295$	−1.26971	+	1.26971i	−0.0739252	+	0.0739252i
$296$	−14.4060	−	14.6239i	−0.837332	−	0.849995i
$297$	30.0125	−	30.0125i	1.74150	−	1.74150i
$298$	−0.0849887	+	33.9753i	−0.00492326	+	1.96814i
$299$	7.11513	−	8.63041i	0.411479	−	0.499109i
$300$	−12.5730	+	29.9296i	−0.725905	+	1.72799i
$301$	1.37757	−	3.32574i	0.0794016	−	0.191692i
$302$	−2.10253	−	5.11208i	−0.120987	−	0.294167i
$303$		−	15.0921i		−	0.867017i
$304$	−27.1847	−	11.5803i	−1.55915	−	0.664175i
$305$	−1.25779			−0.0720209
$306$	18.0875	+	43.9779i	1.03399	+	2.51405i
$307$	10.6163	−	25.6300i	0.605903	−	1.46278i	−0.261515	−	0.965200i	$-0.584222\pi$
$307$	10.6163	−	25.6300i	0.605903	−	1.46278i	0.867418	−	0.497580i	$-0.165778\pi$
$308$	−3.70623	−	9.07579i	−0.211182	−	0.517141i
$309$	3.36505	+	8.12396i	0.191431	+	0.462156i
$310$	0.00621017	−	2.48259i	0.000352714	−	0.141002i
$311$	10.7135	+	10.7135i	0.607507	+	0.607507i	0.942294	−	0.334787i	$-0.108664\pi$
$311$	10.7135	+	10.7135i	0.607507	+	0.607507i	−0.334787	+	0.942294i	$0.608664\pi$
$312$	−33.4977	+	2.97013i	−1.89643	+	0.168150i
$313$	10.4176	−	10.4176i	0.588836	−	0.588836i	−0.348480	−	0.937316i	$-0.613302\pi$
$313$	10.4176	−	10.4176i	0.588836	−	0.588836i	0.937316	+	0.348480i	$0.113302\pi$
$314$	−17.3313	−	17.4182i	−0.978060	−	0.982966i
$315$	3.76548	−	1.55971i	0.212161	−	0.0878799i
$316$	3.62420	−	3.58812i	0.203877	−	0.201847i
$317$	−24.4979	−	10.1474i	−1.37594	−	0.569933i	−0.432548	−	0.901611i	$-0.642385\pi$
$317$	−24.4979	−	10.1474i	−1.37594	−	0.569933i	−0.943393	+	0.331678i	$0.892385\pi$
$318$	−0.00767444	+	0.0183974i	−0.000430361	+	0.00103168i
$319$			24.8448i			1.39104i
$320$	−2.04792	−	0.884516i	−0.114482	−	0.0494460i
$321$	0.620938			0.0346574
$322$	7.51594	+	3.13526i	0.418847	+	0.174721i
$323$	−29.1433	−	12.0716i	−1.62158	−	0.671679i
$324$	41.7578	−	41.3421i	2.31988	−	2.29678i
$325$	−13.6937	−	11.2895i	−0.759592	−	0.626227i
$326$	21.4394	−	21.3324i	1.18742	−	1.18149i
$327$	13.8059	+	13.8059i	0.763467	+	0.763467i
$328$	6.45190	−	15.2515i	0.356247	−	0.842124i
$329$	−8.25757	−	8.25757i	−0.455255	−	0.455255i
$330$	−0.00858994	+	3.43393i	−0.000472861	+	0.189032i
$331$	−29.2619	+	12.1207i	−1.60838	+	0.666212i	−0.992569	−	0.121684i	$-0.961171\pi$
$331$	−29.2619	+	12.1207i	−1.60838	+	0.666212i	−0.615809	+	0.787896i	$0.711171\pi$
$332$	−17.0191	+	6.94999i	−0.934044	+	0.381430i
$333$	−21.8698	+	52.7983i	−1.19846	+	2.89333i
$334$	12.5503	−	5.16176i	0.686722	−	0.282439i
$335$			0.265220i			0.0144905i
$336$	−9.14300	−	22.7133i	−0.498792	−	1.23911i
$337$			6.84061i			0.372632i	0.982490	+	0.186316i	$0.0596548\pi$
$337$			6.84061i			0.372632i	−0.982490	+	0.186316i	$0.940345\pi$
$338$	3.71231	−	18.0061i	0.201923	−	0.979401i
$339$	26.5572	+	11.0004i	1.44239	+	0.597458i
$340$	−2.19560	−	0.922344i	−0.119073	−	0.0500211i
$341$	6.36178	+	15.3587i	0.344510	+	0.831720i
$342$	−0.205776	+	82.2614i	−0.0111271	+	4.44819i
$343$	−13.8532	+	13.8532i	−0.748004	+	0.748004i
$344$	3.84935	+	3.90756i	0.207543	+	0.210682i
$345$	−2.01708	−	2.01708i	−0.108596	−	0.108596i
$346$	−2.33639	+	2.32473i	−0.125605	+	0.124978i
$347$	−9.62644	+	3.98740i	−0.516774	+	0.214055i	−0.625799	−	0.779984i	$-0.715227\pi$
$347$	−9.62644	+	3.98740i	−0.516774	+	0.214055i	0.109025	+	0.994039i	$0.465227\pi$
$348$	−0.310440	+	62.0507i	−0.0166413	+	3.32626i
$349$	15.3354	+	6.35214i	0.820886	+	0.340022i	0.753288	−	0.657691i	$-0.228467\pi$
$349$	15.3354	+	6.35214i	0.820886	+	0.340022i	0.0675978	+	0.997713i	$0.478467\pi$
$350$	4.97466	−	11.9254i	0.265907	−	0.637441i
$351$	27.2045	+	51.1708i	1.45207	+	2.73130i
$352$	14.9367	+	0.186829i	0.796128	+	0.00995802i
$353$			34.5024i			1.83638i	0.396145	+	0.918188i	$0.370348\pi$
$353$			34.5024i			1.83638i	−0.396145	+	0.918188i	$0.629652\pi$
$354$	11.5616	−	27.7160i	0.614494	−	1.47309i
$355$	0.772197	−	1.86425i	0.0409840	−	0.0989440i
$356$	0.0484422	−	9.68263i	0.00256743	−	0.513178i
$357$	−10.0027	−	24.1488i	−0.529401	−	1.27809i
$358$	12.0861	−	12.0258i	0.638772	−	0.635584i
$359$	−10.1113	−	10.1113i	−0.533653	−	0.533653i	0.388005	−	0.921657i	$-0.373164\pi$
$359$	−10.1113	−	10.1113i	−0.533653	−	0.533653i	−0.921657	+	0.388005i	$0.873164\pi$
$360$	−0.0466050	+	6.21021i	−0.00245630	+	0.327307i
$361$	−25.1515	−	25.1515i	−1.32376	−	1.32376i
$362$	9.92303	+	0.0248223i	0.521543	+	0.00130463i
$363$	5.08169	+	12.2683i	0.266719	+	0.643918i
$364$	13.3302	−	1.21555i	0.698691	−	0.0637124i
$365$	1.47748	+	0.611992i	0.0773348	+	0.0320331i
$366$	19.4545	−	8.00137i	1.01690	−	0.418238i
$367$		−	10.8908i		−	0.568495i	−0.958751	−	0.284248i	$-0.908256\pi$
$367$		−	10.8908i		−	0.568495i	0.958751	−	0.284248i	$-0.0917438\pi$
$368$	−8.86176	+	8.68617i	−0.461951	+	0.452798i
$369$	−46.1025			−2.40000
$370$	−1.08864	−	2.64693i	−0.0565959	−	0.137607i
$371$	0.00303634	−	0.00733038i	0.000157639	−	0.000380575i
$372$	15.6968	+	38.4382i	0.813841	+	1.99293i
$373$	−14.4949	−	34.9939i	−0.750519	−	1.81191i	−0.556354	−	0.830945i	$-0.687800\pi$
$373$	−14.4949	−	34.9939i	−0.750519	−	1.81191i	−0.194165	−	0.980969i	$-0.562200\pi$
$374$	15.9469	+	0.0398909i	0.824593	+	0.00206271i
$375$	−6.45149	+	6.45149i	−0.333153	+	0.333153i
$376$	16.4904	−	6.68601i	0.850428	−	0.344805i
$377$	−32.4402	−	9.91986i	−1.67076	−	0.510899i
$378$	−29.9102	+	29.7609i	−1.53841	+	1.53074i
$379$	2.65359	+	6.40632i	0.136306	+	0.329071i	0.977263	−	0.212030i	$-0.0680076\pi$
$379$	2.65359	+	6.40632i	0.136306	+	0.329071i	−0.840958	+	0.541101i	$0.818008\pi$
$380$	−2.89849	−	2.92764i	−0.148690	−	0.150185i
$381$	19.4144	−	46.8706i	0.994632	−	2.40125i
$382$	2.69376	−	6.45758i	0.137825	−	0.330398i
$383$			11.3109i			0.577960i	0.957335	+	0.288980i	$0.0933161\pi$
$383$			11.3109i			0.577960i	−0.957335	+	0.288980i	$0.906684\pi$
$384$	37.3025	+	0.653246i	1.90358	+	0.0333358i
$385$		−	1.36682i		−	0.0696596i
$386$	6.71508	+	2.80118i	0.341789	+	0.142576i
$387$	5.84370	−	14.1079i	0.297052	−	0.717147i
$388$	5.65702	−	5.60069i	0.287191	−	0.284332i
$389$	−15.3615	+	6.36295i	−0.778860	+	0.322614i	−0.736455	−	0.676486i	$-0.763502\pi$
$389$	−15.3615	+	6.36295i	−0.778860	+	0.322614i	−0.0424047	+	0.999101i	$0.513502\pi$
$390$	−4.48030	−	1.38229i	−0.226869	−	0.0699950i
$391$	−9.36712	+	9.36712i	−0.473716	+	0.473716i
$392$	−3.77745	−	9.31672i	−0.190790	−	0.470565i
$393$	−5.34383	−	5.34383i	−0.269561	−	0.269561i
$394$	−21.7971	−	0.0545250i	−1.09812	−	0.00274693i
$395$	0.656926	−	0.272108i	0.0330535	−	0.0136912i
$396$	−15.7220	−	38.4999i	−0.790060	−	1.93469i
$397$	6.31349	−	15.2421i	0.316865	−	0.764979i	−0.682552	−	0.730837i	$-0.739130\pi$
$397$	6.31349	−	15.2421i	0.316865	−	0.764979i	0.999417	−	0.0341425i	$-0.0108700\pi$
$398$	−5.27516	−	12.8260i	−0.264420	−	0.642910i
$399$		−	45.2175i		−	2.26370i
$400$	13.7822	+	14.0608i	0.689111	+	0.703041i
$401$	26.7135			1.33401			0.667004	−	0.745054i	$-0.267577\pi$
$401$	26.7135			1.33401			0.667004	+	0.745054i	$0.267577\pi$
$402$	−1.68718	−	4.10221i	−0.0841490	−	0.204600i
$403$	−22.5941	+	2.17435i	−1.12549	+	0.108312i
$404$	−8.43896	−	3.54510i	−0.419854	−	0.176375i
$405$	7.56906	−	3.13521i	0.376110	−	0.155790i
$406$	0.0617827	−	24.6984i	0.00306622	−	1.22576i
$407$	13.5518	+	13.5518i	0.671736	+	0.671736i
$408$	39.8272	+	0.298887i	1.97174	+	0.0147971i
$409$	15.8299	+	15.8299i	0.782740	+	0.782740i	0.980292	−	0.197552i	$-0.0632992\pi$
$409$	15.8299	+	15.8299i	0.782740	+	0.782740i	−0.197552	+	0.980292i	$0.563299\pi$
$410$	1.63669	−	1.62852i	0.0808304	−	0.0804270i
$411$	−15.0804	−	36.4072i	−0.743859	−	1.79584i
$412$	5.33308	+	0.0266814i	0.262742	+	0.00131450i
$413$	−4.57429	+	11.0433i	−0.225086	+	0.543406i
$414$	31.8830	+	13.2999i	1.56696	+	0.653654i
$415$	−2.56309			−0.125817
$416$	−6.20776	+	19.4284i	−0.304360	+	0.952557i
$417$	54.4113			2.66454
$418$	25.4605	+	10.6208i	1.24531	+	0.519480i
$419$	−2.24236	+	5.41354i	−0.109547	+	0.264469i	−0.969141	−	0.246509i	$-0.920717\pi$
$419$	−2.24236	+	5.41354i	−0.109547	+	0.264469i	0.859594	+	0.510978i	$0.170717\pi$
$420$	0.0170786	−	3.41367i	0.000833350	−	0.166570i
$421$	−9.51868	−	22.9801i	−0.463912	−	1.11998i	−0.966778	−	0.255618i	$-0.917721\pi$
$421$	−9.51868	−	22.9801i	−0.463912	−	1.11998i	0.502866	−	0.864364i	$-0.332279\pi$
$422$	−23.5364	+	23.4190i	−1.14574	+	1.14002i
$423$	−35.0290	−	35.0290i	−1.70317	−	1.70317i
$424$	0.00848449	+	0.00861280i	0.000412043	+	0.000418274i
$425$	14.8627	+	14.8627i	0.720945	+	0.720945i
$426$	−0.0844176	+	33.7470i	−0.00409005	+	1.63505i
$427$	−7.73553	+	3.20416i	−0.374349	+	0.155060i
$428$	0.145857	−	0.347207i	0.00705027	−	0.0167829i
$429$	31.2523	−	3.00757i	1.50888	−	0.145207i
$430$	0.290890	+	0.707271i	0.0140280	+	0.0341076i
$431$	31.8965			1.53640			0.768201	−	0.640209i	$-0.221152\pi$
$431$	31.8965			1.53640			0.768201	+	0.640209i	$0.221152\pi$
$432$	−24.0083	−	59.6422i	−1.15510	−	2.86954i
$433$			1.56360i			0.0751418i	0.999294	+	0.0375709i	$0.0119620\pi$
$433$			1.56360i			0.0751418i	−0.999294	+	0.0375709i	$0.988038\pi$
$434$	−6.28608	−	15.2840i	−0.301742	−	0.733654i
$435$	−3.31076	+	7.99288i	−0.158739	+	0.383229i
$436$	10.9627	−	4.47679i	0.525020	−	0.214400i
$437$	−21.1721	+	8.76976i	−1.01280	+	0.419514i
$438$	−26.7456	−	0.0669038i	−1.27795	−	0.00319679i
$439$	10.9641	+	10.9641i	0.523289	+	0.523289i	0.918563	−	0.395274i	$-0.129350\pi$
$439$	10.9641	+	10.9641i	0.523289	+	0.523289i	−0.395274	+	0.918563i	$0.629350\pi$
$440$	1.91812	+	0.811427i	0.0914427	+	0.0386833i
$441$	−19.7906	+	19.7906i	−0.942410	+	0.942410i
$442$	−6.41923	+	20.8061i	−0.305332	+	0.989645i
$443$	22.5755	−	9.35108i	1.07259	−	0.444283i	0.224689	−	0.974431i	$-0.427863\pi$
$443$	22.5755	−	9.35108i	1.07259	−	0.444283i	0.847905	+	0.530148i	$0.177863\pi$
$444$	33.6765	+	34.0152i	1.59822	+	1.61429i
$445$	0.516624	−	1.24724i	0.0244903	−	0.0591248i
$446$	−6.42488	−	2.68012i	−0.304227	−	0.126907i
$447$		−	79.2225i		−	3.74710i
$448$	−14.8482	−	0.222871i	−0.701510	−	0.0105297i
$449$			14.5949i			0.688774i	0.938828	+	0.344387i	$0.111913\pi$
$449$			14.5949i			0.688774i	−0.938828	+	0.344387i	$0.888087\pi$
$450$	21.1027	−	50.5882i	0.994792	−	2.38475i
$451$	−5.91657	+	14.2839i	−0.278601	+	0.672601i
$452$	12.3893	−	12.2659i	0.582742	−	0.576940i
$453$	4.93239	+	11.9078i	0.231744	+	0.559479i
$454$	−21.0454	+	20.9403i	−0.987708	+	0.982779i
$455$	1.78467	+	0.545734i	0.0836668	+	0.0255844i
$456$	63.4556	+	26.8438i	2.97158	+	1.25708i
$457$	7.21546	−	7.21546i	0.337525	−	0.337525i	−0.517910	−	0.855435i	$-0.673290\pi$
$457$	7.21546	−	7.21546i	0.337525	−	0.337525i	0.855435	+	0.517910i	$0.173290\pi$
$458$	27.8045	+	0.0695526i	1.29922	+	0.00324998i
$459$	−26.2659	−	63.4114i	−1.22599	−	2.95979i
$460$	−1.60169	+	0.654072i	−0.0746790	+	0.0304963i
$461$	−2.67079	+	6.44786i	−0.124391	+	0.300307i	−0.973792	−	0.227442i	$-0.926964\pi$
$461$	−2.67079	+	6.44786i	−0.124391	+	0.300307i	0.849400	+	0.527749i	$0.176964\pi$
$462$	8.69495	+	21.1409i	0.404526	+	0.983563i
$463$	8.93410			0.415203			0.207601	−	0.978213i	$-0.433434\pi$
$463$	8.93410			0.415203			0.207601	+	0.978213i	$0.433434\pi$
$464$	34.6236	+	14.7492i	1.60736	+	0.684713i
$465$			5.78882i			0.268450i
$466$	14.1576	−	5.82283i	0.655839	−	0.269738i
$467$	−6.31559	−	2.61600i	−0.292251	−	0.121054i	0.231741	−	0.972777i	$-0.425558\pi$
$467$	−6.31559	−	2.61600i	−0.292251	−	0.121054i	−0.523992	+	0.851723i	$0.675558\pi$
$468$	56.5472	−	5.15644i	2.61389	−	0.238356i
$469$	0.675635	+	1.63113i	0.0311979	+	0.0753184i
$470$	2.48093	+	0.00620602i	0.114437	+	0.000286262i
$471$	40.5138	+	40.5138i	1.86678	+	1.86678i
$472$	−12.7820	−	12.9753i	−0.588339	−	0.597236i
$473$	−3.62109	−	3.62109i	−0.166498	−	0.166498i
$474$	−8.42981	+	8.38774i	−0.387194	+	0.385262i
$475$	13.9148	+	33.5934i	0.638456	+	1.54137i
$476$	−15.8528	−	0.0793115i	−0.726610	−	0.00363523i
$477$	0.0128803	−	0.0310958i	0.000589749	−	0.00142378i
$478$	−5.59239	+	13.4063i	−0.255790	+	0.613189i
$479$		−	25.9100i		−	1.18386i	−0.805990	−	0.591929i	$-0.798366\pi$
$479$		−	25.9100i		−	1.18386i	0.805990	−	0.591929i	$-0.201634\pi$
$480$	4.78041	+	2.05053i	0.218195	+	0.0935934i
$481$	−23.1055	+	12.2839i	−1.05352	+	0.560095i
$482$	−7.27934	+	17.4503i	−0.331565	+	0.794839i
$483$	−17.5436	−	7.26680i	−0.798262	−	0.330651i
$484$	8.05367	+	0.0402925i	0.366076	+	0.00183148i
$485$	1.02540	−	0.424733i	0.0465608	−	0.0192861i
$486$	−48.7876	+	48.5441i	−2.21305	+	2.20201i
$487$	−18.7582	−	18.7582i	−0.850015	−	0.850015i	0.140120	−	0.990135i	$-0.455251\pi$
$487$	−18.7582	−	18.7582i	−0.850015	−	0.850015i	−0.990135	+	0.140120i	$0.955251\pi$
$488$	0.0957419	−	12.7578i	0.00433403	−	0.577518i
$489$	−49.8670	+	49.8670i	−2.25507	+	2.25507i
$490$	0.00350626	−	1.40167i	0.000158397	−	0.0633211i
$491$	−7.56728	−	18.2690i	−0.341506	−	0.824470i	−0.997564	−	0.0697586i	$-0.977777\pi$
$491$	−7.56728	−	18.2690i	−0.341506	−	0.824470i	0.656057	−	0.754711i	$-0.272223\pi$
$492$	−14.9553	+	35.6004i	−0.674236	+	1.60499i
$493$	37.1182	+	15.3749i	1.67172	+	0.692449i
$494$	−24.0334	+	29.0035i	−1.08131	+	1.30493i
$495$		−	5.79811i		−	0.260606i
$496$	25.1805	+	0.251962i	1.13064	+	0.0113134i
$497$		−	13.4324i		−	0.602527i
$498$	39.6438	−	16.3049i	1.77648	−	0.730641i
$499$	−8.87615	+	21.4289i	−0.397351	+	0.959290i	0.590941	+	0.806715i	$0.298757\pi$
$499$	−8.87615	+	21.4289i	−0.397351	+	0.959290i	−0.988292	+	0.152575i	$0.951243\pi$
$500$	2.09200	+	5.12289i	0.0935573	+	0.229102i
$501$	−29.2341	+	12.1092i	−1.30608	+	0.540998i
$502$	−0.0156837	+	6.26977i	−0.000699999	+	0.279833i
$503$	−9.78693	−	9.78693i	−0.436378	−	0.436378i	0.454413	−	0.890791i	$-0.349849\pi$
$503$	−9.78693	−	9.78693i	−0.436378	−	0.436378i	−0.890791	+	0.454413i	$0.849849\pi$
$504$	15.5336	+	38.3120i	0.691920	+	1.70655i
$505$	−0.902403	−	0.902403i	−0.0401564	−	0.0401564i
$506$	8.21239	−	8.17141i	0.365085	−	0.363263i
$507$	−8.55117	+	42.0074i	−0.379771	+	1.86561i
$508$	−21.6480	−	21.8657i	−0.960474	−	0.970133i
$509$	9.08863	+	3.76463i	0.402846	+	0.166864i	0.574901	−	0.818223i	$-0.305041\pi$
$509$	9.08863	+	3.76463i	0.402846	+	0.166864i	−0.172055	+	0.985087i	$0.555041\pi$
$510$	5.12498	+	2.13787i	0.226938	+	0.0946665i
$511$	10.6456			0.470936
$512$	9.12754	−	20.7048i	0.403384	−	0.915031i
$513$		−	118.735i		−	5.24228i
$514$	−8.11621	+	19.4565i	−0.357991	+	0.858188i
$515$	0.686965	+	0.284550i	0.0302713	+	0.0125388i
$516$	−8.99852	−	9.08901i	−0.396138	−	0.400122i
$517$	−15.3484	+	6.35753i	−0.675023	+	0.279604i
$518$	−13.4382	−	13.5056i	−0.590439	−	0.593401i
$519$	5.43432	−	5.43432i	0.238540	−	0.238540i
$520$	−1.82534	+	2.18053i	−0.0800466	+	0.0956225i
$521$	16.9151	+	16.9151i	0.741063	+	0.741063i	0.972783	−	0.231720i	$-0.0744352\pi$
$521$	16.9151	+	16.9151i	0.741063	+	0.741063i	−0.231720	+	0.972783i	$0.574435\pi$
$522$	0.262085	−	104.772i	0.0114711	−	4.58573i
$523$	−13.2048	−	31.8792i	−0.577405	−	1.39398i	−0.895134	−	0.445797i	$-0.852920\pi$
$523$	−13.2048	−	31.8792i	−0.577405	−	1.39398i	0.317729	−	0.948181i	$-0.397080\pi$
$524$	−4.24334	+	1.73283i	−0.185371	+	0.0756989i
$525$	−11.5301	+	27.8362i	−0.503216	+	1.21487i
$526$	−16.3078	−	39.6507i	−0.711053	−	1.72885i
$527$	26.8828			1.17103
$528$	−34.8298	−	0.348516i	−1.51577	−	0.0151672i
$529$		−	13.3762i		−	0.581575i
$530$	0.000641162		0.00155892i	2.78503e−5		6.77152e-5i
$531$	−19.4044	+	46.8463i	−0.842077	+	2.03295i
$532$	−25.2840	−	10.6215i	−1.09620	−	0.460500i
$533$	−16.2883	−	13.4285i	−0.705525	−	0.581653i
$534$	−0.0564780	+	22.5778i	−0.00244404	+	0.977036i
$535$	0.0371279	−	0.0371279i	0.00160518	−	0.00160518i
$536$	−2.69013	−	0.0201883i	−0.116196	−	0.000872002i
$537$	−28.1117	+	28.1117i	−1.21311	+	1.21311i
$538$	−2.78533	+	2.77143i	−0.120084	+	0.119485i
$539$	3.59187	+	8.67153i	0.154713	+	0.373509i
$540$	0.0448461	−	8.96384i	0.00192987	−	0.385742i
$541$	21.7755	+	9.01970i	0.936201	+	0.387787i	0.798028	−	0.602621i	$-0.205877\pi$
$541$	21.7755	+	9.01970i	0.936201	+	0.387787i	0.138173	+	0.990408i	$0.455877\pi$
$542$	−0.436790	+	1.04709i	−0.0187617	+	0.0449763i
$543$	−23.1382			−0.992955
$544$	9.52247	−	22.1998i	0.408272	−	0.951808i
$545$	1.65100			0.0707209
$546$	−31.0756	+	2.91213i	−1.32991	+	0.124628i
$547$	−4.71202	+	11.3758i	−0.201471	+	0.486395i	−0.992032	−	0.125989i	$-0.959789\pi$
$547$	−4.71202	+	11.3758i	−0.201471	+	0.486395i	0.790560	+	0.612384i	$0.209789\pi$
$548$	−23.9000	−	0.119572i	−1.02096	−	0.00510785i
$549$	−32.8145	+	13.5922i	−1.40049	+	0.580101i
$550$	−12.9654	−	13.0305i	−0.552848	−	0.555621i
$551$	49.1454	+	49.1454i	2.09366	+	2.09366i
$552$	20.6128	−	20.3057i	0.877338	−	0.864268i
$553$	3.34697	−	3.34697i	0.142328	−	0.142328i
$554$	24.2492	+	0.0606591i	1.03025	+	0.00257716i
$555$	2.55389	+	6.16563i	0.108406	+	0.261716i
$556$	12.7811	−	30.4249i	0.542040	−	1.29030i
$557$	−6.68007	+	16.1271i	−0.283044	+	0.683328i	−0.999904	−	0.0138892i	$-0.995579\pi$
$557$	−6.68007	+	16.1271i	−0.283044	+	0.683328i	0.716860	+	0.697217i	$0.245579\pi$
$558$	−26.6658	−	64.8353i	−1.12886	−	2.74470i
$559$	6.17390	−	3.28230i	0.261128	−	0.138827i
$560$	−1.90479	−	0.811414i	−0.0804922	−	0.0342885i
$561$	−37.1844			−1.56993
$562$	−24.9558	+	10.2640i	−1.05270	+	0.432959i
$563$	−22.4854	−	9.31375i	−0.947646	−	0.392528i	−0.145301	−	0.989388i	$-0.546415\pi$
$563$	−22.4854	−	9.31375i	−0.947646	−	0.392528i	−0.802346	+	0.596860i	$0.796415\pi$
$564$	−38.4126	+	15.6863i	−1.61746	+	0.660513i
$565$	2.24569	−	0.930196i	0.0944769	−	0.0391336i
$566$	−0.0308779	+	12.3438i	−0.00129790	+	0.518850i
$567$	38.5636	−	38.5636i	1.61952	−	1.61952i
$568$	18.8503	+	7.97431i	0.790941	+	0.334594i
$569$	−25.0232	+	25.0232i	−1.04903	+	1.04903i	−0.0502918	+	0.998735i	$0.516015\pi$
$569$	−25.0232	+	25.0232i	−1.04903	+	1.04903i	−0.998735	+	0.0502918i	$0.983985\pi$
$570$	6.77565	+	6.80963i	0.283801	+	0.285224i
$571$	30.3157	−	12.5572i	1.26867	−	0.525502i	0.356113	−	0.934443i	$-0.384102\pi$
$571$	30.3157	−	12.5572i	1.26867	−	0.525502i	0.912561	+	0.408941i	$0.134102\pi$
$572$	5.65938	−	18.1817i	0.236631	−	0.760214i
$573$	−6.24352	+	15.0732i	−0.260827	+	0.629692i
$574$	5.91722	−	14.1850i	0.246980	−	0.592069i
$575$	15.2699			0.636798
$576$	−62.9866	−	0.945430i	−2.62444	−	0.0393929i
$577$			10.1315i			0.421780i	0.977510	+	0.210890i	$0.0676362\pi$
$577$			10.1315i			0.421780i	−0.977510	+	0.210890i	$0.932364\pi$
$578$	0.672210	−	1.61144i	0.0279602	−	0.0670272i
$579$	−15.6743	−	6.49249i	−0.651400	−	0.269819i
$580$	3.69165	+	3.72877i	0.153287	+	0.154829i
$581$	−15.7632	+	6.52934i	−0.653968	+	0.270882i
$582$	−13.1581	+	13.0924i	−0.545421	+	0.542699i
$583$	−0.00798138	−	0.00798138i	−0.000330555	−	0.000330555i
$584$	−6.31990	+	14.9395i	−0.261519	+	0.618201i
$585$	7.57067	+	2.31503i	0.313009	+	0.0957146i
$586$	−6.30586	−	0.0157740i	−0.260493	−	0.000651619i
$587$	−11.8645	+	4.91445i	−0.489702	+	0.202841i	−0.613850	−	0.789422i	$-0.710380\pi$
$587$	−11.8645	+	4.91445i	−0.489702	+	0.202841i	0.124148	+	0.992264i	$0.460380\pi$
$588$	8.86243	+	21.7023i	0.365480	+	0.894986i
$589$	42.9651	+	17.7967i	1.77035	+	0.733302i
$590$	−0.965919	−	2.34853i	−0.0397663	−	0.0966877i
$591$	50.8257			2.09069
$592$	26.9307	−	10.8406i	1.10684	−	0.445548i
$593$	30.8111			1.26526			0.632631	−	0.774453i	$-0.281975\pi$
$593$	30.8111			1.26526			0.632631	+	0.774453i	$0.281975\pi$
$594$	22.8318	+	55.5131i	0.936799	+	2.27773i
$595$	−2.04203	−	0.845836i	−0.0837150	−	0.0346759i
$596$	−44.2984	−	18.6092i	−1.81454	−	0.762263i
$597$	12.3752	+	29.8763i	0.506482	+	1.22276i
$598$	7.39053	+	13.9856i	0.302221	+	0.571916i
$599$	−0.873102	−	0.873102i	−0.0356740	−	0.0356740i	0.689045	−	0.724719i	$-0.258030\pi$
$599$	−0.873102	−	0.873102i	−0.0356740	−	0.0356740i	−0.724719	+	0.689045i	$0.758030\pi$
$600$	−32.2187	−	32.7060i	−1.31532	−	1.33522i
$601$	−17.4459	+	17.4459i	−0.711634	+	0.711634i	−0.966877	−	0.255243i	$-0.917845\pi$
$601$	−17.4459	+	17.4459i	−0.711634	+	0.711634i	0.255243	+	0.966877i	$0.417845\pi$
$602$	3.59074	+	3.60875i	0.146348	+	0.147082i
$603$	2.86607	+	6.91931i	0.116716	+	0.281776i
$604$	7.81706	+	0.0391088i	0.318072	+	0.00159131i
$605$	1.03741	+	0.429709i	0.0421767	+	0.0174702i
$606$	19.6982	+	8.21707i	0.800187	+	0.333796i
$607$	−26.9196			−1.09263			−0.546317	−	0.837579i	$-0.683971\pi$
$607$	−26.9196			−1.09263			−0.546317	+	0.837579i	$0.683971\pi$
$608$	29.9157	−	29.1766i	1.21324	−	1.18327i
$609$			57.5909i			2.33370i
$610$	0.684821	−	1.64168i	0.0277276	−	0.0664695i
$611$	−2.17290	−	22.5790i	−0.0879060	−	0.913450i
$612$	−67.2481	−	0.336443i	−2.71835	−	0.0135999i
$613$	6.54210	+	15.7940i	0.264233	+	0.637915i	0.999192	−	0.0401971i	$-0.0127986\pi$
$613$	6.54210	+	15.7940i	0.264233	+	0.637915i	−0.734959	+	0.678112i	$0.762799\pi$
$614$	27.6722	+	27.8110i	1.11676	+	1.12236i
$615$	−3.80686	+	3.80686i	−0.153507	+	0.153507i
$616$	13.8637	+	0.104041i	0.558583	+	0.00419193i
$617$	−26.3628	+	26.3628i	−1.06133	+	1.06133i	−0.0633327	+	0.997992i	$0.520173\pi$
$617$	−26.3628	+	26.3628i	−1.06133	+	1.06133i	−0.997992	+	0.0633327i	$0.979827\pi$
$618$	−12.4356	−	0.0311074i	−0.500232	−	0.00125132i
$619$	−12.0457	+	4.98948i	−0.484156	+	0.200544i	−0.611391	−	0.791329i	$-0.709390\pi$
$619$	−12.0457	+	4.98948i	−0.484156	+	0.200544i	0.127235	+	0.991873i	$0.459390\pi$
$620$	3.23691	+	1.35978i	0.129997	+	0.0546102i
$621$	−46.0672	−	19.0817i	−1.84861	−	0.765720i
$622$	−19.8164	+	8.15021i	−0.794566	+	0.326794i
$623$		−	8.98671i		−	0.360045i
$624$	14.3616	−	45.3385i	0.574925	−	1.81499i
$625$		−	23.8397i		−	0.953588i
$626$	7.92508	+	19.2690i	0.316750	+	0.770146i
$627$	−59.4296	−	24.6165i	−2.37339	−	0.983090i
$628$	32.1705	−	13.1373i	1.28374	−	0.524235i
$629$	28.6326	−	11.8600i	1.14166	−	0.472890i
$630$	−0.0144184	+	5.76393i	−0.000574443	+	0.229641i
$631$	16.0696	−	16.0696i	0.639720	−	0.639720i	−0.310767	−	0.950486i	$-0.600586\pi$
$631$	16.0696	−	16.0696i	0.639720	−	0.639720i	0.950486	+	0.310767i	$0.100586\pi$
$632$	2.70999	+	6.68392i	0.107797	+	0.265872i
$633$	54.7446	−	54.7446i	2.17590	−	2.17590i
$634$	26.5826	−	26.4500i	1.05573	−	1.05046i
$635$	−1.64169	−	3.96340i	−0.0651486	−	0.157283i
$636$	−0.0198340	−	0.0200334i	−0.000786468	−	0.000794377i
$637$	−12.7567	+	1.22764i	−0.505437	+	0.0486408i
$638$	−32.4276	−	13.5271i	−1.28382	−	0.535543i
$639$		−	56.9810i		−	2.25413i
$640$	2.26949	−	2.19137i	0.0897096	−	0.0866217i
$641$	28.6903			1.13320			0.566600	−	0.823993i	$-0.308259\pi$
$641$	28.6903			1.13320			0.566600	+	0.823993i	$0.308259\pi$
$642$	−0.338078	+	0.810452i	−0.0133429	+	0.0319860i
$643$	27.5763	+	11.4225i	1.08750	+	0.450459i	0.853136	−	0.521689i	$-0.174698\pi$
$643$	27.5763	+	11.4225i	1.08750	+	0.450459i	0.234369	+	0.972148i	$0.424698\pi$
$644$	−8.18430	+	8.10282i	−0.322507	+	0.319296i
$645$	−0.682410	−	1.64748i	−0.0268699	−	0.0648696i
$646$	31.6233	−	31.4655i	1.24420	−	1.23799i
$647$	−20.7700	+	20.7700i	−0.816554	+	0.816554i	−0.985607	−	0.169053i	$-0.945929\pi$
$647$	−20.7700	+	20.7700i	−0.816554	+	0.816554i	0.169053	+	0.985607i	$0.445929\pi$
$648$	31.2243	+	77.0117i	1.22661	+	3.02531i
$649$	12.0240	+	12.0240i	0.471985	+	0.471985i
$650$	22.1908	−	11.7264i	0.870395	−	0.459949i
$651$	14.7467	+	35.6018i	0.577971	+	1.39534i
$652$	16.1702	+	39.5976i	0.633275	+	1.55076i
$653$	−0.575546	−	0.238399i	−0.0225228	−	0.00932927i	0.371394	−	0.928476i	$-0.378880\pi$
$653$	−0.575546	−	0.238399i	−0.0225228	−	0.00932927i	−0.393916	+	0.919146i	$0.628880\pi$
$654$	−25.5363	+	10.5027i	−0.998549	+	0.410689i
$655$	−0.639050			−0.0249697
$656$	16.3935	+	16.7249i	0.640060	+	0.652999i
$657$	45.1593			1.76183
$658$	15.2738	−	6.28188i	0.595433	−	0.244893i
$659$	−18.9694	−	7.85740i	−0.738944	−	0.306081i	−0.0187226	−	0.999825i	$-0.505960\pi$
$659$	−18.9694	−	7.85740i	−0.738944	−	0.306081i	−0.720222	+	0.693744i	$0.755960\pi$
$660$	−4.47731	−	1.88086i	−0.174279	−	0.0732124i
$661$	37.3996	−	15.4914i	1.45468	−	0.602547i	0.491370	−	0.870951i	$-0.336496\pi$
$661$	37.3996	−	15.4914i	1.45468	−	0.602547i	0.963306	+	0.268404i	$0.0864962\pi$
$662$	0.112047	−	44.7920i	0.00435481	−	1.74089i
$663$	14.8467	−	48.5521i	0.576598	−	1.88561i
$664$	0.195100	−	25.9974i	0.00757134	−	1.00890i
$665$	−2.70370	−	2.70370i	−0.104845	−	0.104845i
$666$	−57.0053	−	57.2912i	−2.20891	−	2.21999i
$667$	26.9657	−	11.1695i	1.04411	−	0.432486i
$668$	−0.0960132	+	19.1911i	−0.00371486	+	0.742526i
$669$	14.9969	+	6.21191i	0.579813	+	0.240166i
$670$	−0.346166	−	0.144402i	−0.0133736	−	0.00557875i
$671$			11.9112i			0.459828i
$672$	34.6236	+	0.433074i	1.33563	+	0.0167062i
$673$	−32.9544			−1.27030			−0.635150	−	0.772389i	$-0.719062\pi$
$673$	−32.9544			−1.27030			−0.635150	+	0.772389i	$0.719062\pi$
$674$	−8.92840	−	3.72446i	−0.343909	−	0.143461i
$675$	−30.2766	+	73.0941i	−1.16535	+	2.81339i
$676$	21.4804	+	14.6490i	0.826169	+	0.563422i
$677$	28.0187	−	11.6057i	1.07685	−	0.446045i	0.227445	−	0.973791i	$-0.426963\pi$
$677$	28.0187	−	11.6057i	1.07685	−	0.446045i	0.849402	+	0.527746i	$0.176963\pi$
$678$	−28.8172	+	28.6734i	−1.10672	+	1.10119i
$679$	5.22429	−	5.22429i	0.200490	−	0.200490i
$680$	2.39927	−	2.36353i	0.0920078	−	0.0906371i
$681$	48.9505	−	48.9505i	1.87579	−	1.87579i
$682$	−23.5100	−	0.0588099i	−0.900244	−	0.00225195i
$683$	−14.1590	+	5.86484i	−0.541778	+	0.224412i	−0.636753	−	0.771068i	$-0.719723\pi$
$683$	−14.1590	+	5.86484i	−0.541778	+	0.224412i	0.0949748	+	0.995480i	$0.469723\pi$
$684$	−107.256	−	45.0568i	−4.10103	−	1.72279i
$685$	−3.07861	−	1.27520i	−0.117628	−	0.0487229i
$686$	−10.5387	−	25.6239i	−0.402371	−	0.978324i
$687$	−64.8337			−2.47356
$688$	−7.19599	+	2.89667i	−0.274345	+	0.110434i
$689$	0.0136081	−	0.00723464i	0.000518428	−	0.000275618i
$690$	3.73092	−	1.53448i	0.142034	−	0.0584165i
$691$	3.35012	−	8.08790i	0.127445	−	0.307678i	−0.847259	−	0.531180i	$-0.821749\pi$
$691$	3.35012	−	8.08790i	0.127445	−	0.307678i	0.974704	+	0.223502i	$0.0717488\pi$
$692$	−1.76217	−	4.31519i	−0.0669877	−	0.164039i
$693$	−14.7704	−	35.6589i	−0.561081	−	1.35457i
$694$	0.0368606	−	14.7355i	0.00139921	−	0.559351i
$695$	3.25343	−	3.25343i	0.123410	−	0.123410i
$696$	−80.8198	−	34.1895i	−3.06347	−	1.29595i
$697$	17.6787	+	17.6787i	0.669629	+	0.669629i
$698$	−16.6404	+	16.5574i	−0.629849	+	0.626705i
$699$	−32.9781	+	13.6600i	−1.24735	+	0.516668i
$700$	12.8566	+	12.9859i	0.485934	+	0.490821i
$701$	−15.9928	+	38.6099i	−0.604038	+	1.45828i	0.265352	+	0.964152i	$0.414512\pi$
$701$	−15.9928	+	38.6099i	−0.604038	+	1.45828i	−0.869391	+	0.494126i	$0.835488\pi$
$702$	−81.6003	+	7.64686i	−3.07980	+	0.288612i
$703$	53.6133			2.02206
$704$	−8.37632	+	19.3937i	−0.315695	+	0.730928i
$705$	−5.78496			−0.217874
$706$	−45.0327	−	18.7853i	−1.69483	−	0.706992i
$707$	−7.84869	−	3.25103i	−0.295180	−	0.122268i
$708$	29.8801	+	30.1806i	1.12296	+	1.13426i
$709$	9.14517	+	22.0784i	0.343454	+	0.829172i	0.997361	+	0.0725969i	$0.0231286\pi$
$709$	9.14517	+	22.0784i	0.343454	+	0.829172i	−0.653907	+	0.756575i	$0.726871\pi$
$710$	2.01279	+	2.02289i	0.0755388	+	0.0759177i
$711$	14.1980	−	14.1980i	0.532467	−	0.532467i
$712$	12.6114	+	5.33506i	0.472634	+	0.199940i
$713$	13.8097	−	13.8097i	0.517176	−	0.517176i
$714$	36.9652	+	0.0924680i	1.38339	+	0.00346053i
$715$	1.68884	−	2.04851i	0.0631592	−	0.0766099i
$716$	9.11571	+	22.3225i	0.340670	+	0.834231i
$717$	12.9619	−	31.2928i	0.484070	−	1.16865i
$718$	18.7025	−	7.69208i	0.697971	−	0.287066i
$719$			27.8409i			1.03829i	0.854686	+	0.519145i	$0.173750\pi$
$719$			27.8409i			1.03829i	−0.854686	+	0.519145i	$0.826250\pi$
$720$	−8.08022	−	3.44205i	−0.301132	−	0.128278i
$721$	4.94978			0.184339
$722$	46.5218	−	19.1338i	1.73136	−	0.712085i
$723$	16.8718	−	40.7322i	0.627470	−	1.51485i
$724$	−5.43512	+	12.9381i	−0.201995	+	0.480840i
$725$	−17.7225	−	42.7860i	−0.658198	−	1.58903i
$726$	−18.7794	−	0.0469764i	−0.696969	−	0.00174346i
$727$	−7.08604	−	7.08604i	−0.262806	−	0.262806i	0.563387	−	0.826193i	$-0.309498\pi$
$727$	−7.08604	−	7.08604i	−0.262806	−	0.262806i	−0.826193	+	0.563387i	$0.809498\pi$
$728$	−5.67123	+	18.0604i	−0.210190	+	0.669364i
$729$	51.1518	−	51.1518i	1.89451	−	1.89451i
$730$	−1.60321	+	1.59521i	−0.0593373	+	0.0590412i
$731$	−7.65076	+	3.16905i	−0.282974	+	0.117212i
$732$	−0.148832	+	29.7486i	−0.00550100	+	1.09954i
$733$	−40.5640	−	16.8022i	−1.49827	−	0.620602i	−0.525170	−	0.850998i	$-0.675998\pi$
$733$	−40.5640	−	16.8022i	−1.49827	−	0.620602i	−0.973097	+	0.230395i	$0.925998\pi$
$734$	14.2147	+	5.92964i	0.524675	+	0.218867i
$735$			3.26837i			0.120556i
$736$	−6.51234	−	16.2957i	−0.240048	−	0.600668i
$737$	2.51162			0.0925167
$738$	25.1011	−	60.1732i	0.923984	−	2.21501i
$739$	−23.7569	−	9.84042i	−0.873910	−	0.361986i	−0.0997783	−	0.995010i	$-0.531813\pi$
$739$	−23.7569	−	9.84042i	−0.873910	−	0.361986i	−0.774132	+	0.633024i	$0.781813\pi$
$740$	4.04751	+	0.0202497i	0.148789	+	0.000744394i
$741$	55.8707	−	67.7692i	2.05246	−	2.48957i
$742$	0.00791448	+	0.00795417i	0.000290550	+	0.000292007i
$743$	4.18794	+	4.18794i	0.153641	+	0.153641i	0.779742	−	0.626101i	$-0.215350\pi$
$743$	4.18794	+	4.18794i	0.153641	+	0.153641i	−0.626101	+	0.779742i	$0.715350\pi$
$744$	−58.7161	−	0.440640i	−2.15264	−	0.0161546i
$745$	−4.73697	−	4.73697i	−0.173549	−	0.173549i
$746$	53.5661	+	0.133995i	1.96120	+	0.00490590i
$747$	−66.8682	+	27.6977i	−2.44658	+	1.01341i
$748$	−8.73454	+	20.7922i	−0.319367	+	0.760239i
$749$	0.133758	−	0.322921i	0.00488743	−	0.0117993i
$750$	−4.90792	−	11.9331i	−0.179212	−	0.435735i
$751$		−	19.6220i		−	0.716016i	−0.933718	−	0.358008i	$-0.883456\pi$
$751$		−	19.6220i		−	0.716016i	0.933718	−	0.358008i	$-0.116544\pi$
$752$	−0.251794	+	25.1636i	−0.00918198	+	0.917624i
$753$		−	14.6196i		−	0.532769i
$754$	30.6099	−	36.9401i	1.11475	−	1.34528i
$755$	1.00693	+	0.417085i	0.0366460	+	0.0151793i
$756$	−22.5591	−	55.2427i	−0.820468	−	2.00916i
$757$	−16.4279	−	39.6604i	−0.597082	−	1.44148i	−0.876542	−	0.481325i	$-0.840156\pi$
$757$	−16.4279	−	39.6604i	−0.597082	−	1.44148i	0.279461	−	0.960157i	$-0.409844\pi$
$758$	−9.80634	−	0.0245304i	−0.356182	−	0.000890985i
$759$	−19.1016	+	19.1016i	−0.693345	+	0.693345i
$760$	5.39929	−	2.18914i	0.195853	−	0.0794083i
$761$	−10.9565	−	10.9565i	−0.397174	−	0.397174i	0.480061	−	0.877235i	$-0.340615\pi$
$761$	−10.9565	−	10.9565i	−0.397174	−	0.397174i	−0.877235	+	0.480061i	$0.840615\pi$
$762$	50.6053	+	50.8591i	1.83324	+	1.84243i
$763$	10.1538	−	4.20583i	0.367592	−	0.152261i
$764$	6.96181	+	7.03182i	0.251870	+	0.254402i
$765$	−8.66238	−	3.58807i	−0.313189	−	0.129727i
$766$	−14.7630	−	6.15836i	−0.533410	−	0.222511i
$767$	−20.5008	+	10.8991i	−0.740242	+	0.393543i
$768$	−21.1624	+	48.3317i	−0.763633	+	1.74402i
$769$			6.54132i			0.235886i	0.993020	+	0.117943i	$0.0376300\pi$
$769$			6.54132i			0.235886i	−0.993020	+	0.117943i	$0.962370\pi$
$770$	1.78398	+	0.744183i	0.0642902	+	0.0268185i
$771$	18.8115	−	45.4150i	0.677480	−	1.63558i
$772$	−7.31222	+	7.23942i	−0.263173	+	0.260553i
$773$	1.74467	+	4.21199i	0.0627512	+	0.151495i	0.952145	−	0.305648i	$-0.0988729\pi$
$773$	1.74467	+	4.21199i	0.0627512	+	0.151495i	−0.889393	+	0.457142i	$0.848873\pi$
$774$	15.2321	+	15.3085i	0.547506	+	0.550252i
$775$	−21.9116	−	21.9116i	−0.787087	−	0.787087i
$776$	4.23002	+	10.4329i	0.151849	+	0.374521i
$777$	31.4133	+	31.4133i	1.12694	+	1.12694i
$778$	0.0588208	−	23.5143i	0.00210883	−	0.843029i
$779$	16.5513	+	39.9584i	0.593012	+	1.43166i
$780$	4.24353	−	5.09510i	0.151943	−	0.182434i
$781$	−17.6543	−	7.31266i	−0.631722	−	0.261668i
$782$	−7.12597	−	17.3261i	−0.254824	−	0.619579i
$783$			151.226i			5.40438i
$784$	14.2169	+	0.142258i	0.507747	+	0.00508065i
$785$	4.84491			0.172922
$786$	9.88431	−	4.06528i	0.352562	−	0.145004i
$787$	−10.2813	+	24.8213i	−0.366490	+	0.884785i	0.627830	+	0.778351i	$0.283943\pi$
$787$	−10.2813	+	24.8213i	−0.366490	+	0.884785i	−0.994320	+	0.106434i	$0.966057\pi$
$788$	11.9389	−	28.4199i	0.425304	−	1.01242i
$789$	38.2570	+	92.3605i	1.36198	+	3.28812i
$790$	−0.00251543	+	1.00558i	−8.94951e−5	+	0.0357768i
$791$	11.4416	−	11.4416i	0.406816	−	0.406816i
$792$	58.8103	+	0.441347i	2.08973	+	0.0156826i
$793$	−15.5526	−	4.75582i	−0.552290	−	0.168884i
$794$	16.4566	+	16.5392i	0.584024	+	0.586953i
$795$	−0.00150412	−	0.00363128i	−5.33458e−5	−	0.000128788i
$796$	19.6127	+	0.0981224i	0.695154	+	0.00347786i
$797$	14.4913	−	34.9850i	0.513307	−	1.23923i	−0.428641	−	0.903475i	$-0.641008\pi$
$797$	14.4913	−	34.9850i	0.513307	−	1.23923i	0.941948	−	0.335758i	$-0.108992\pi$
$798$	59.0181	+	24.6192i	2.08922	+	0.871511i
$799$			26.8648i			0.950409i
$800$	−25.8561	+	10.3330i	−0.914153	+	0.365327i
$801$		−	38.1220i		−	1.34698i
$802$	−14.5445	+	34.8666i	−0.513584	+	1.23118i
$803$	5.79553	−	13.9916i	0.204520	−	0.493754i
$804$	6.27283	+	0.0313830i	0.221226	+	0.00110679i
$805$	−1.48349	+	0.614484i	−0.0522863	+	0.0216577i
$806$	9.46368	−	30.6738i	0.333344	−	1.08044i
$807$	6.47855	−	6.47855i	0.228056	−	0.228056i
$808$	9.22178	−	9.08440i	0.324421	−	0.319588i
$809$	37.9570	+	37.9570i	1.33450	+	1.33450i	0.901299	+	0.433198i	$0.142615\pi$
$809$	37.9570	+	37.9570i	1.33450	+	1.33450i	0.433198	+	0.901299i	$0.357385\pi$
$810$	−0.0289827	+	11.5862i	−0.00101835	+	0.407097i
$811$	19.9179	−	8.25028i	0.699413	−	0.289706i	−0.00450261	−	0.999990i	$-0.501433\pi$
$811$	19.9179	−	8.25028i	0.699413	−	0.289706i	0.703916	+	0.710283i	$0.251433\pi$
$812$	32.2028	+	13.5280i	1.13010	+	0.474739i
$813$	1.01238	−	2.44410i	0.0355057	−	0.0857182i
$814$	−25.0662	+	10.3094i	−0.878572	+	0.361344i
$815$			5.96342i			0.208890i
$816$	−22.0746	+	51.8200i	−0.772764	+	1.81406i
$817$	−14.3257			−0.501193
$818$	−29.2801	+	12.0425i	−1.02376	+	0.421056i
$819$	52.4577	−	5.04828i	1.83302	−	0.176401i
$820$	1.23444	+	3.02289i	0.0431085	+	0.105564i
$821$	−28.0923	+	11.6362i	−0.980429	+	0.406107i	−0.814585	−	0.580045i	$-0.803035\pi$
$821$	−28.0923	+	11.6362i	−0.980429	+	0.406107i	−0.165845	+	0.986152i	$0.553035\pi$
$822$	55.7296	+	0.139407i	1.94379	+	0.00486237i
$823$	2.38875	+	2.38875i	0.0832665	+	0.0832665i	0.747513	−	0.664247i	$-0.231248\pi$
$823$	2.38875	+	2.38875i	0.0832665	+	0.0832665i	−0.664247	+	0.747513i	$0.731248\pi$
$824$	−2.93849	+	6.94623i	−0.102367	+	0.241984i
$825$	30.3082	+	30.3082i	1.05520	+	1.05520i
$826$	−11.9233	−	11.9831i	−0.414864	−	0.416944i
$827$	7.15182	+	17.2660i	0.248693	+	0.600398i	0.998094	−	0.0617187i	$-0.0196582\pi$
$827$	7.15182	+	17.2660i	0.248693	+	0.600398i	−0.749400	+	0.662117i	$0.769658\pi$
$828$	−34.7182	+	34.3725i	−1.20654	+	1.19453i
$829$	14.0725	−	33.9740i	0.488758	−	1.17997i	−0.466588	−	0.884475i	$-0.654517\pi$
$829$	14.0725	−	33.9740i	0.488758	−	1.17997i	0.955346	−	0.295491i	$-0.0954832\pi$
$830$	1.39550	−	3.34535i	0.0484387	−	0.116119i
$831$	−56.5435			−1.96147
$832$	−21.9782	−	18.6804i	−0.761957	−	0.647628i
$833$	15.1780			0.525888
$834$	−29.6250	+	71.0180i	−1.02583	+	2.45915i
$835$	−1.02396	+	2.47205i	−0.0354354	+	0.0855487i
$836$	−27.7246	+	27.4486i	−0.958876	+	0.949329i
$837$	38.7230	+	93.4856i	1.33846	+	3.23133i
$838$	−5.84490	−	5.87421i	−0.201909	−	0.202921i
$839$	−1.08311	−	1.08311i	−0.0373933	−	0.0373933i	0.688163	−	0.725556i	$-0.258417\pi$
$839$	−1.08311	−	1.08311i	−0.0373933	−	0.0373933i	−0.725556	+	0.688163i	$0.758417\pi$
$840$	4.44624	+	1.88091i	0.153410	+	0.0648975i
$841$	−42.0876	−	42.0876i	−1.45130	−	1.45130i
$842$	35.1763	+	0.0879931i	1.21226	+	0.00303244i
$843$	58.1308	−	24.0786i	2.00213	−	0.829310i
$844$	−17.7519	−	43.4707i	−0.611044	−	1.49632i
$845$	2.00045	+	3.02306i	0.0688177	+	0.103996i
$846$	64.7920	−	26.6480i	2.22759	−	0.916178i
$847$	7.47483			0.256838
$848$	−0.0158610	+	0.00638465i	−0.000544667	+	0.000219250i
$849$		−	28.7830i		−	0.987829i
$850$	−27.4910	+	11.3067i	−0.942933	+	0.387815i
$851$	8.61608	−	20.8011i	0.295355	−	0.713051i
$852$	−44.0008	−	18.4842i	−1.50744	−	0.633257i
$853$	16.0563	−	6.65074i	0.549757	−	0.227717i	−0.0904744	−	0.995899i	$-0.528838\pi$
$853$	16.0563	−	6.65074i	0.549757	−	0.227717i	0.640232	+	0.768182i	$0.278838\pi$
$854$	0.0296201	−	11.8410i	0.00101358	−	0.405191i
$855$	−11.4692	−	11.4692i	−0.392238	−	0.392238i
$856$	0.373762	+	0.379415i	0.0127749	+	0.0129681i
$857$	1.78348	−	1.78348i	0.0609226	−	0.0609226i	−0.675989	−	0.736912i	$-0.736283\pi$
$857$	1.78348	−	1.78348i	0.0609226	−	0.0609226i	0.736912	+	0.675989i	$0.236283\pi$
$858$	−13.0902	+	42.4282i	−0.446893	+	1.44847i
$859$	9.94613	−	4.11982i	0.339358	−	0.140567i	−0.206495	−	0.978448i	$-0.566206\pi$
$859$	9.94613	−	4.11982i	0.339358	−	0.140567i	0.545853	+	0.837881i	$0.316206\pi$
$860$	−1.08151	−	0.00541081i	−0.0368793	−	0.000184507i
$861$	−13.7147	+	33.1103i	−0.467397	+	1.12840i
$862$	−17.3665	+	41.6315i	−0.591504	+	1.41797i
$863$		−	4.49783i		−	0.153108i	−0.997065	−	0.0765539i	$-0.975608\pi$
$863$		−	4.49783i		−	0.153108i	0.997065	−	0.0765539i	$-0.0243917\pi$
$864$	90.9169	+	1.13719i	3.09306	+	0.0386881i
$865$		−	0.649871i		−	0.0220963i
$866$	−2.04082	−	0.851322i	−0.0693498	−	0.0289291i
$867$	−1.55803	+	3.76141i	−0.0529134	+	0.127744i
$868$	23.3713	+	0.116927i	0.793272	+	0.00396874i
$869$	−2.57684	−	6.22105i	−0.0874135	−	0.211035i
$870$	−8.62976	−	8.67304i	−0.292576	−	0.294044i
$871$	−1.00282	+	3.27945i	−0.0339793	+	0.111120i
$872$	−0.125672	+	16.7461i	−0.00425580	+	0.567094i
$873$	22.1617	−	22.1617i	0.750059	−	0.750059i
$874$	0.0810699	−	32.4087i	0.00274223	−	1.09624i
$875$	1.96538	+	4.74486i	0.0664421	+	0.160405i
$876$	14.6493	−	34.8721i	0.494954	−	1.17822i
$877$	−12.1690	+	29.3787i	−0.410919	+	0.992047i	0.573972	+	0.818875i	$0.305402\pi$
$877$	−12.1690	+	29.3787i	−0.410919	+	0.992047i	−0.984892	+	0.173172i	$0.944598\pi$
$878$	−20.2800	+	8.34087i	−0.684416	+	0.281491i
$879$	14.7038			0.495947
$880$	−2.10342	+	2.06175i	−0.0709064	+	0.0695014i
$881$			14.5844i			0.491362i	0.969351	+	0.245681i	$0.0790116\pi$
$881$			14.5844i			0.491362i	−0.969351	+	0.245681i	$0.920988\pi$
$882$	−15.0556	−	36.6061i	−0.506947	−	1.23259i
$883$	16.4587	+	6.81741i	0.553879	+	0.229424i	0.642025	−	0.766683i	$-0.278094\pi$
$883$	16.4587	+	6.81741i	0.553879	+	0.229424i	−0.0881464	+	0.996108i	$0.528094\pi$
$884$	−23.6612	−	19.7066i	−0.795812	−	0.662803i
$885$	2.26598	+	5.47057i	0.0761702	+	0.183891i
$886$	−0.0864438	+	34.5570i	−0.00290414	+	1.16096i
$887$	21.5575	+	21.5575i	0.723829	+	0.723829i	0.969383	−	0.245554i	$-0.0789698\pi$
$887$	21.5575	+	21.5575i	0.723829	+	0.723829i	−0.245554	+	0.969383i	$0.578970\pi$
$888$	−62.7324	+	25.4348i	−2.10516	+	0.853535i
$889$	−20.1931	−	20.1931i	−0.677255	−	0.677255i
$890$	1.34662	+	1.35338i	0.0451389	+	0.0453652i
$891$	−29.6903	−	71.6786i	−0.994661	−	2.40132i
$892$	6.99622	−	6.92656i	0.234251	−	0.231918i
$893$	−17.7848	+	42.9364i	−0.595147	+	1.43681i
$894$	103.402	+	43.1337i	3.45827	+	1.44261i
$895$			3.36178i			0.112372i
$896$	8.37517	−	19.2586i	0.279795	−	0.643384i
$897$	−17.3145	−	32.5680i	−0.578113	−	1.08741i
$898$	−19.0493	−	7.94635i	−0.635683	−	0.265173i
$899$	−54.7222	−	22.6667i	−1.82509	−	0.755976i
$900$	54.5383	+	55.0868i	1.81794	+	1.83623i
$901$	−0.0168633	+	0.00698502i	−0.000561799	+	0.000232705i
$902$	−15.4220	−	15.4994i	−0.513497	−	0.516073i
$903$	−8.39377	−	8.39377i	−0.279327	−	0.279327i
$904$	9.26405	+	22.8489i	0.308118	+	0.759942i
$905$	−1.38351	+	1.38351i	−0.0459893	+	0.0459893i
$906$	−18.2277	−	0.0455963i	−0.605574	−	0.00151484i
$907$	4.91772	+	11.8724i	0.163290	+	0.394217i	0.984253	−	0.176764i	$-0.0565629\pi$
$907$	4.91772	+	11.8724i	0.163290	+	0.394217i	−0.820963	+	0.570981i	$0.806563\pi$
$908$	−15.8730	−	38.8698i	−0.526765	−	1.28994i
$909$	−33.2945	−	13.7910i	−1.10431	−	0.457420i
$910$	−1.68398	+	2.03223i	−0.0558235	+	0.0673679i
$911$		−	55.8283i		−	1.84968i	−0.380362	−	0.924838i	$-0.624201\pi$
$911$		−	55.8283i		−	1.84968i	0.380362	−	0.924838i	$-0.375799\pi$
$912$	−69.5859	+	68.2071i	−2.30422	+	2.25856i
$913$			24.2723i			0.803295i
$914$	5.48911	+	13.3462i	0.181563	+	0.441453i
$915$	−1.58726	+	3.83198i	−0.0524731	+	0.126681i
$916$	−15.2293	+	36.2527i	−0.503190	+	1.19782i
$917$	−3.93021	+	1.62795i	−0.129787	+	0.0537596i
$918$	97.0657	+	0.242808i	3.20365	+	0.00801387i
$919$	−3.66026	−	3.66026i	−0.120741	−	0.120741i	0.644155	−	0.764895i	$-0.277209\pi$
$919$	−3.66026	−	3.66026i	−0.120741	−	0.120741i	−0.764895	+	0.644155i	$0.777209\pi$
$920$	0.0183611	−	2.44665i	0.000605347	−	0.0806636i
$921$	−64.6870	−	64.6870i	−2.13151	−	2.13151i
$922$	−6.96163	−	6.99655i	−0.229269	−	0.230419i
$923$	16.5971	−	20.1317i	0.546301	−	0.662644i
$924$	−32.3273	−	0.161733i	−1.06349	−	0.00532064i
$925$	−33.0047	−	13.6710i	−1.08519	−	0.449499i
$926$	−4.86428	+	11.6608i	−0.159850	+	0.383199i
$927$	20.9972			0.689637
$928$	−38.1020	+	37.1606i	−1.25076	+	1.21986i
$929$		−	36.2528i		−	1.18942i	−0.803941	−	0.594709i	$-0.797267\pi$
$929$		−	36.2528i		−	1.18942i	0.803941	−	0.594709i	$-0.202733\pi$
$930$	−7.55560	−	3.15180i	−0.247758	−	0.103352i
$931$	24.2581	+	10.0480i	0.795028	+	0.329312i
$932$	−0.108310	+	21.6489i	−0.00354780	+	0.709134i
$933$	46.1595	−	19.1199i	1.51119	−	0.625956i
$934$	6.85302	−	6.81882i	0.224238	−	0.223119i
$935$	−2.22338	+	2.22338i	−0.0727121	+	0.0727121i
$936$	−24.0576	+	76.6131i	−0.786348	+	2.50418i
$937$	−1.96588	−	1.96588i	−0.0642223	−	0.0642223i	0.674266	−	0.738488i	$-0.264460\pi$
$937$	−1.96588	−	1.96588i	−0.0642223	−	0.0642223i	−0.738488	+	0.674266i	$0.764460\pi$
$938$	−2.49681	−	0.00624574i	−0.0815238	−	0.000203931i
$939$	−18.5917	−	44.8844i	−0.606718	−	1.46475i
$940$	−1.35888	+	3.23475i	−0.0443216	+	0.105506i
$941$	−4.16502	+	10.0552i	−0.135776	+	0.327792i	−0.977114	−	0.212718i	$-0.931768\pi$
$941$	−4.16502	+	10.0552i	−0.135776	+	0.327792i	0.841338	+	0.540509i	$0.181768\pi$
$942$	−74.9371	+	30.8206i	−2.44158	+	1.00419i
$943$	18.1631			0.591472
$944$	23.8947	−	9.61856i	0.777707	−	0.313058i
$945$		−	8.31958i		−	0.270636i
$946$	6.69781	−	2.75472i	0.217765	−	0.0895636i
$947$	−2.31534	+	5.58973i	−0.0752385	+	0.181642i	−0.957024	−	0.290009i	$-0.906342\pi$
$947$	−2.31534	+	5.58973i	−0.0752385	+	0.181642i	0.881785	+	0.471651i	$0.156342\pi$
$948$	−6.35800	−	15.5694i	−0.206498	−	0.505672i
$949$	15.9551	+	13.1538i	0.517923	+	0.426989i
$950$	−51.4223	−	0.128632i	−1.66836	−	0.00417338i
$951$	−61.8298	+	61.8298i	−2.00497	+	2.00497i
$952$	8.73476	−	20.6479i	0.283095	−	0.669203i
$953$	1.90503	−	1.90503i	0.0617100	−	0.0617100i	−0.675578	−	0.737288i	$-0.736106\pi$
$953$	1.90503	−	1.90503i	0.0617100	−	0.0617100i	0.737288	+	0.675578i	$0.236106\pi$
$954$	0.0335736	+	0.0337420i	0.00108698	+	0.00109244i
$955$	0.527955	+	1.27460i	0.0170842	+	0.0412449i
$956$	−14.4531	−	14.5984i	−0.467446	−	0.472147i
$957$	75.6921	+	31.3527i	2.44678	+	1.01349i
$958$	33.8179	+	14.1070i	1.09261	+	0.455778i
$959$	−22.1822			−0.716302
$960$	−5.27912	+	5.12298i	−0.170383	+	0.165344i
$961$	−8.63246			−0.278467
$962$	−3.45284	−	36.8456i	−0.111324	−	1.18795i
$963$	0.567409	−	1.36985i	0.0182845	−	0.0441427i
$964$	−18.8129	−	19.0021i	−0.605922	−	0.612015i
$965$	−1.32542	+	0.549007i	−0.0426668	+	0.0176732i
$966$	19.0365	−	18.9415i	0.612490	−	0.609433i
$967$	−22.0379	−	22.0379i	−0.708692	−	0.708692i	0.257568	−	0.966260i	$-0.417079\pi$
$967$	−22.0379	−	22.0379i	−0.708692	−	0.708692i	−0.966260	+	0.257568i	$0.917079\pi$
$968$	−4.43751	+	10.4898i	−0.142627	+	0.337153i
$969$	−73.5542	+	73.5542i	−2.36290	+	2.36290i
$970$	−0.00392634	+	1.56960i	−0.000126067	+	0.0503969i
$971$	13.0711	+	31.5565i	0.419472	+	1.01270i	0.982501	+	0.186258i	$0.0596360\pi$
$971$	13.0711	+	31.5565i	0.419472	+	1.01270i	−0.563029	+	0.826437i	$0.690364\pi$
$972$	−36.7970	−	90.1083i	−1.18026	−	2.89022i
$973$	11.7209	−	28.2968i	0.375756	−	0.907155i
$974$	34.6964	−	14.2701i	1.11174	−	0.457245i
$975$	−51.6751	+	27.4726i	−1.65493	+	0.879827i
$976$	16.5994	+	7.07111i	0.531334	+	0.226341i
$977$	−3.58962			−0.114842			−0.0574211	−	0.998350i	$-0.518288\pi$
$977$	−3.58962			−0.114842			−0.0574211	+	0.998350i	$0.518288\pi$
$978$	−37.9360	−	92.2375i	−1.21306	−	2.94943i
$979$	−11.8113	−	4.89240i	−0.377491	−	0.156362i
$980$	1.82756	+	0.767735i	0.0583793	+	0.0245244i
$981$	43.0728	−	17.8413i	1.37521	−	0.569630i
$982$	27.9649	+	0.0699539i	0.892397	+	0.00223232i
$983$	29.7242	−	29.7242i	0.948055	−	0.948055i	−0.0506608	−	0.998716i	$-0.516133\pi$
$983$	29.7242	−	29.7242i	0.948055	−	0.948055i	0.998716	+	0.0506608i	$0.0161327\pi$
$984$	−38.3233	−	38.9028i	−1.22170	−	1.24018i
$985$	3.03903	−	3.03903i	0.0968316	−	0.0968316i
$986$	−40.2768	+	40.0758i	−1.28267	+	1.27627i
$987$	−35.5780	+	14.7369i	−1.13246	+	0.469081i
$988$	−24.7703	−	47.1598i	−0.788047	−	1.50035i
$989$	−2.30225	+	5.55813i	−0.0732074	+	0.176738i
$990$	7.56772	+	3.15686i	0.240518	+	0.100331i
$991$	44.1278			1.40176			0.700882	−	0.713277i	$-0.252790\pi$
$991$	44.1278			1.40176			0.700882	+	0.713277i	$0.252790\pi$
$992$	−14.0387	+	32.7285i	−0.445729	+	1.03913i
$993$			104.445i			3.31445i
$994$	17.5321	+	7.31346i	0.556084	+	0.231969i
$995$	2.52635	+	1.04645i	0.0800908	+	0.0331747i
$996$	−0.303285	+	60.6207i	−0.00960997	+	1.92084i
$997$	−46.1215	+	19.1042i	−1.46068	+	0.605035i	−0.964713	−	0.263305i	$-0.915187\pi$
$997$	−46.1215	+	19.1042i	−1.46068	+	0.605035i	−0.495970	+	0.868340i	$0.665187\pi$
$998$	−23.1364	−	23.2524i	−0.732370	−	0.736043i
$999$	82.4871	+	82.4871i	2.60978	+	2.60978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bg.a.77.20	✓	216
13.12	even	2	inner	416.2.bg.a.77.35	yes	216
32.5	even	8	inner	416.2.bg.a.389.35	yes	216
416.389	even	8	inner	416.2.bg.a.389.20	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bg.a.77.20	✓	216	1.1	even	1	trivial
416.2.bg.a.77.35	yes	216	13.12	even	2	inner
416.2.bg.a.389.20	yes	216	416.389	even	8	inner
416.2.bg.a.389.35	yes	216	32.5	even	8	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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bg (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.544463 + 1.30521i) q^{2} +(1.26194 - 3.04659i) q^{3} +(-1.40712 - 1.42127i) q^{4} +(-0.106710 - 0.257621i) q^{5} +(3.28935 + 3.30585i) q^{6} +(-1.31255 - 1.31255i) q^{7} +(2.62118 - 1.06275i) q^{8} +(-5.56791 - 5.56791i) q^{9} +(0.394348 + 0.000986456i) q^{10} +(-2.43966 + 1.01054i) q^{11} +(-6.10573 + 2.49336i) q^{12} +(-0.345385 - 3.58897i) q^{13} +(2.42779 - 0.998515i) q^{14} -0.919528 q^{15} +(-0.0400230 + 3.99980i) q^{16} +4.27020i q^{17} +(10.2988 - 4.23575i) q^{18} +(-2.82693 + 6.82481i) q^{19} +(-0.215995 + 0.514168i) q^{20} +(-5.65518 + 2.34245i) q^{21} +(0.00934168 - 3.73445i) q^{22} +(2.19360 + 2.19360i) q^{23} +(0.0699936 - 9.32678i) q^{24} +(3.48055 - 3.48055i) q^{25} +(4.87239 + 1.50326i) q^{26} +(-14.8497 + 6.15097i) q^{27} +(-0.0185732 + 3.71242i) q^{28} +(3.60050 - 8.69237i) q^{29} +(0.500649 - 1.20017i) q^{30} -6.29543i q^{31} +(-5.19877 - 2.22998i) q^{32} +8.70788i q^{33} +(-5.57349 - 2.32497i) q^{34} +(-0.198079 + 0.478204i) q^{35} +(-0.0787885 + 15.7482i) q^{36} +(-2.77739 - 6.70521i) q^{37} +(-7.36862 - 7.40557i) q^{38} +(-11.3700 - 3.47682i) q^{39} +(-0.553493 - 0.561863i) q^{40} +(4.14002 - 4.14002i) q^{41} +(0.0216542 - 8.65655i) q^{42} +(0.742131 + 1.79166i) q^{43} +(4.86914 + 2.04546i) q^{44} +(-0.840258 + 2.02856i) q^{45} +(-4.05743 + 1.66877i) q^{46} +6.29123 q^{47} +(12.1353 + 5.16944i) q^{48} -3.55441i q^{49} +(2.64780 + 6.43787i) q^{50} +(13.0096 + 5.38874i) q^{51} +(-4.61490 + 5.54100i) q^{52} +(0.00163576 + 0.00394907i) q^{53} +(0.0568611 - 22.7309i) q^{54} +(0.520672 + 0.520672i) q^{55} +(-4.83535 - 2.04551i) q^{56} +(17.2250 + 17.2250i) q^{57} +(9.38499 + 9.43206i) q^{58} +(-2.46429 - 5.94933i) q^{59} +(1.29389 + 1.30690i) q^{60} +(1.72617 - 4.16733i) q^{61} +(8.21683 + 3.42763i) q^{62} +14.6164i q^{63} +(5.74112 - 5.57132i) q^{64} +(-0.887738 + 0.471958i) q^{65} +(-11.3656 - 4.74112i) q^{66} +(-0.878730 - 0.363982i) q^{67} +(6.06912 - 6.00869i) q^{68} +(9.45120 - 3.91482i) q^{69} +(-0.516308 - 0.518898i) q^{70} +(5.11691 + 5.11691i) q^{71} +(-20.5118 - 8.67716i) q^{72} +(-4.05532 + 4.05532i) q^{73} +(10.2639 + 0.0256749i) q^{74} +(-6.21158 - 14.9961i) q^{75} +(13.6777 - 5.58550i) q^{76} +(4.52857 + 1.87579i) q^{77} +(10.7285 - 12.9472i) q^{78} +2.54997i q^{79} +(1.03470 - 0.416508i) q^{80} +29.3806i q^{81} +(3.14949 + 7.65766i) q^{82} +(3.51752 - 8.49205i) q^{83} +(11.2868 + 4.74143i) q^{84} +(1.10009 - 0.455674i) q^{85} +(-2.74255 - 0.00686045i) q^{86} +(-21.9385 - 21.9385i) q^{87} +(-5.32082 + 5.24155i) q^{88} +(3.42337 + 3.42337i) q^{89} +(-2.19020 - 2.20119i) q^{90} +(-4.25738 + 5.16405i) q^{91} +(0.0310405 - 6.20436i) q^{92} +(-19.1796 - 7.94446i) q^{93} +(-3.42534 + 8.21134i) q^{94} +2.05988 q^{95} +(-13.3544 + 13.0244i) q^{96} +3.98025i q^{97} +(4.63923 + 1.93524i) q^{98} +(19.2104 + 7.95720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38}+ \cdots + 112 q^{95}+O(q^{100}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Introduction

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