LMFDB - Embedded newform 483.2.v.a.41.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(41,483)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.v (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$600$
Relative dimension:	$60$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			41.17
Character	$\chi$	$=$	483.41
Dual form			483.2.v.a.377.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.454217 + 1.54692i) q^{2} +(-1.66392 - 0.481000i) q^{3} +(-0.504143 - 0.323993i) q^{4} +(0.562316 - 3.91099i) q^{5} +(1.49985 - 2.35548i) q^{6} +(-1.48783 + 2.18778i) q^{7} +(-1.70670 + 1.47886i) q^{8} +(2.53728 + 1.60069i) q^{9} +(5.79458 + 2.64630i) q^{10} +(-0.644839 - 2.19612i) q^{11} +(0.683015 + 0.781592i) q^{12} +(1.76874 + 0.807755i) q^{13} +(-2.70852 - 3.29528i) q^{14} +(-2.81684 + 6.23711i) q^{15} +(-2.01037 - 4.40209i) q^{16} +(-6.25396 + 4.01918i) q^{17} +(-3.62862 + 3.19791i) q^{18} +(-2.11893 + 3.29712i) q^{19} +(-1.55062 + 1.78951i) q^{20} +(3.52795 - 2.92465i) q^{21} +3.69012 q^{22} +(-3.42406 - 3.35795i) q^{23} +(3.55115 - 1.63979i) q^{24} +(-10.1822 - 2.98976i) q^{25} +(-2.05292 + 2.36920i) q^{26} +(-3.45190 - 3.88386i) q^{27} +(1.45890 - 0.620907i) q^{28} +(-0.791187 - 1.23111i) q^{29} +(-8.36887 - 7.19042i) q^{30} +(-4.87912 + 4.22778i) q^{31} +(3.25223 - 0.467600i) q^{32} +(0.0166292 + 3.96434i) q^{33} +(-3.37669 - 11.5000i) q^{34} +(7.71975 + 7.04910i) q^{35} +(-0.760538 - 1.62904i) q^{36} +(0.362545 + 2.52156i) q^{37} +(-4.13793 - 4.77542i) q^{38} +(-2.55451 - 2.19480i) q^{39} +(4.82411 + 7.50647i) q^{40} +(0.875678 - 6.09047i) q^{41} +(2.92174 + 6.78588i) q^{42} +(-2.49130 + 2.87511i) q^{43} +(-0.386437 + 1.31608i) q^{44} +(7.68705 - 9.02318i) q^{45} +(6.74974 - 3.77152i) q^{46} +2.63505 q^{47} +(1.22769 + 8.29173i) q^{48} +(-2.57274 - 6.51007i) q^{49} +(9.24985 - 14.3930i) q^{50} +(12.3393 - 3.67945i) q^{51} +(-0.629989 - 0.980282i) q^{52} +(-4.87250 + 2.22520i) q^{53} +(7.57594 - 3.57570i) q^{54} +(-8.95161 + 1.28705i) q^{55} +(-0.696148 - 5.93417i) q^{56} +(5.11165 - 4.46695i) q^{57} +(2.26380 - 0.664712i) q^{58} +(-5.91969 + 12.9623i) q^{59} +(3.44087 - 2.23176i) q^{60} +(10.9041 - 9.44842i) q^{61} +(-4.32386 - 9.46794i) q^{62} +(-7.27699 + 3.16944i) q^{63} +(0.623565 - 4.33699i) q^{64} +(4.15371 - 6.46330i) q^{65} +(-6.14008 - 1.77495i) q^{66} +(-8.41744 - 2.47158i) q^{67} +4.45508 q^{68} +(4.08220 + 7.23434i) q^{69} +(-14.4108 + 8.74002i) q^{70} +(1.65586 - 5.63935i) q^{71} +(-6.69757 + 1.02039i) q^{72} +(0.871295 - 1.35576i) q^{73} +(-4.06533 - 0.584506i) q^{74} +(15.5043 + 9.87236i) q^{75} +(2.13649 - 0.975701i) q^{76} +(5.76403 + 1.85668i) q^{77} +(4.55549 - 2.95471i) q^{78} +(-5.26762 + 11.5345i) q^{79} +(-18.3470 + 5.38717i) q^{80} +(3.87556 + 8.12281i) q^{81} +(9.02373 + 4.12100i) q^{82} +(0.586751 + 4.08094i) q^{83} +(-2.72616 + 0.331409i) q^{84} +(12.2023 + 26.7192i) q^{85} +(-3.31598 - 5.15976i) q^{86} +(0.724310 + 2.42903i) q^{87} +(4.34830 + 2.79449i) q^{88} +(-4.01990 + 4.63921i) q^{89} +(10.4666 + 15.9897i) q^{90} +(-4.39876 + 2.66780i) q^{91} +(0.638266 + 2.80226i) q^{92} +(10.1520 - 4.68785i) q^{93} +(-1.19689 + 4.07622i) q^{94} +(11.7035 + 10.1411i) q^{95} +(-5.63638 - 0.786272i) q^{96} +(-3.81751 - 0.548876i) q^{97} +(11.2391 - 1.02283i) q^{98} +(1.87918 - 6.60436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) $ 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{6}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.454217	+	1.54692i	−0.321180	+	1.09384i	0.627767	+	0.778401i	$0.283969\pi$
$2$	−0.454217	+	1.54692i	−0.321180	+	1.09384i	−0.948947	+	0.315437i	$0.897849\pi$
$3$	−1.66392	−	0.481000i	−0.960666	−	0.277705i
$3$	−1.66392	−	0.481000i	−0.960666	−	0.277705i
$4$	−0.504143	−	0.323993i	−0.252072	−	0.161997i
$5$	0.562316	−	3.91099i	0.251475	−	1.74905i	−0.337893	−	0.941184i	$-0.609714\pi$
$5$	0.562316	−	3.91099i	0.251475	−	1.74905i	0.589369	−	0.807864i	$-0.299377\pi$
$6$	1.49985	−	2.35548i	0.612311	−	0.961620i
$7$	−1.48783	+	2.18778i	−0.562346	+	0.826902i
$7$	−1.48783	+	2.18778i	−0.562346	+	0.826902i
$8$	−1.70670	+	1.47886i	−0.603409	+	0.522857i
$9$	2.53728	+	1.60069i	0.845759	+	0.533564i
$10$	5.79458	+	2.64630i	1.83241	+	0.836832i
$11$	−0.644839	−	2.19612i	−0.194426	−	0.662155i	−0.997777	−	0.0666483i	$-0.978769\pi$
$11$	−0.644839	−	2.19612i	−0.194426	−	0.662155i	0.803350	−	0.595507i	$-0.203049\pi$
$12$	0.683015	+	0.781592i	0.197169	+	0.225626i
$13$	1.76874	+	0.807755i	0.490559	+	0.224031i	0.645307	−	0.763923i	$-0.276729\pi$
$13$	1.76874	+	0.807755i	0.490559	+	0.224031i	−0.154748	+	0.987954i	$0.549457\pi$
$14$	−2.70852	−	3.29528i	−0.723883	−	0.880700i
$15$	−2.81684	+	6.23711i	−0.727304	+	1.61042i
$16$	−2.01037	−	4.40209i	−0.502592	−	1.10052i
$17$	−6.25396	+	4.01918i	−1.51681	+	0.974794i	−0.524445	+	0.851444i	$0.675727\pi$
$17$	−6.25396	+	4.01918i	−1.51681	+	0.974794i	−0.992363	+	0.123350i	$0.960636\pi$
$18$	−3.62862	+	3.19791i	−0.855274	+	0.753754i
$19$	−2.11893	+	3.29712i	−0.486116	+	0.756411i	−0.994502	−	0.104718i	$-0.966606\pi$
$19$	−2.11893	+	3.29712i	−0.486116	+	0.756411i	0.508386	+	0.861129i	$0.330242\pi$
$20$	−1.55062	+	1.78951i	−0.346730	+	0.400147i
$21$	3.52795	−	2.92465i	0.769862	−	0.638210i
$22$	3.69012			0.786736
$23$	−3.42406	−	3.35795i	−0.713966	−	0.700180i
$23$	−3.42406	−	3.35795i	−0.713966	−	0.700180i
$24$	3.55115	−	1.63979i	0.724875	−	0.334721i
$25$	−10.1822	−	2.98976i	−2.03644	−	0.597952i
$26$	−2.05292	+	2.36920i	−0.402611	+	0.464638i
$27$	−3.45190	−	3.88386i	−0.664319	−	0.747449i
$28$	1.45890	−	0.620907i	0.275707	−	0.117340i
$29$	−0.791187	−	1.23111i	−0.146920	−	0.228612i	0.759992	−	0.649933i	$-0.225203\pi$
$29$	−0.791187	−	1.23111i	−0.146920	−	0.228612i	−0.906912	+	0.421321i	$0.861567\pi$
$30$	−8.36887	−	7.19042i	−1.52794	−	1.31279i
$31$	−4.87912	+	4.22778i	−0.876316	+	0.759332i	−0.971727	−	0.236106i	$-0.924129\pi$
$31$	−4.87912	+	4.22778i	−0.876316	+	0.759332i	0.0954117	+	0.995438i	$0.469583\pi$
$32$	3.25223	−	0.467600i	0.574919	−	0.0826608i
$33$	0.0166292	+	3.96434i	0.00289477	+	0.690103i
$34$	−3.37669	−	11.5000i	−0.579098	−	1.97223i
$35$	7.71975	+	7.04910i	1.30488	+	1.19152i
$36$	−0.760538	−	1.62904i	−0.126756	−	0.271507i
$37$	0.362545	+	2.52156i	0.0596021	+	0.414542i	0.997678	+	0.0681112i	$0.0216973\pi$
$37$	0.362545	+	2.52156i	0.0596021	+	0.414542i	−0.938076	+	0.346431i	$0.887394\pi$
$38$	−4.13793	−	4.77542i	−0.671260	−	0.774676i
$39$	−2.55451	−	2.19480i	−0.409049	−	0.351450i
$40$	4.82411	+	7.50647i	0.762759	+	1.18688i
$41$	0.875678	−	6.09047i	0.136758	−	0.951172i	−0.799702	−	0.600397i	$-0.795009\pi$
$41$	0.875678	−	6.09047i	0.136758	−	0.951172i	0.936460	−	0.350775i	$-0.114082\pi$
$42$	2.92174	+	6.78588i	0.450835	+	1.04708i
$43$	−2.49130	+	2.87511i	−0.379919	+	0.438450i	−0.913215	−	0.407479i	$-0.866408\pi$
$43$	−2.49130	+	2.87511i	−0.379919	+	0.438450i	0.533296	+	0.845929i	$0.320953\pi$
$44$	−0.386437	+	1.31608i	−0.0582575	+	0.198407i
$45$	7.68705	−	9.02318i	1.14592	−	1.34510i
$46$	6.74974	−	3.77152i	0.995195	−	0.556080i
$47$	2.63505			0.384362			0.192181	−	0.981359i	$-0.438444\pi$
$47$	2.63505			0.384362			0.192181	+	0.981359i	$0.438444\pi$
$48$	1.22769	+	8.29173i	0.177202	+	1.19681i
$49$	−2.57274	−	6.51007i	−0.367534	−	0.930010i
$50$	9.24985	−	14.3930i	1.30813	−	2.03548i
$51$	12.3393	−	3.67945i	1.72785	−	0.515226i
$52$	−0.629989	−	0.980282i	−0.0873638	−	0.135941i
$53$	−4.87250	+	2.22520i	−0.669289	+	0.305654i	−0.720926	−	0.693012i	$-0.756283\pi$
$53$	−4.87250	+	2.22520i	−0.669289	+	0.305654i	0.0516370	+	0.998666i	$0.483556\pi$
$54$	7.57594	−	3.57570i	1.03095	−	0.486592i
$55$	−8.95161	+	1.28705i	−1.20703	+	0.173545i
$56$	−0.696148	−	5.93417i	−0.0930267	−	0.792986i
$57$	5.11165	−	4.46695i	0.677054	−	0.591661i
$58$	2.26380	−	0.664712i	0.297252	−	0.0872810i
$59$	−5.91969	+	12.9623i	−0.770678	+	1.68755i	−0.0455235	+	0.998963i	$0.514496\pi$
$59$	−5.91969	+	12.9623i	−0.770678	+	1.68755i	−0.725154	+	0.688586i	$0.758232\pi$
$60$	3.44087	−	2.23176i	0.444215	−	0.288119i
$61$	10.9041	−	9.44842i	1.39612	−	1.20975i	0.447120	−	0.894474i	$-0.352450\pi$
$61$	10.9041	−	9.44842i	1.39612	−	1.20975i	0.949001	−	0.315272i	$-0.102096\pi$
$62$	−4.32386	−	9.46794i	−0.549131	−	1.20243i
$63$	−7.27699	+	3.16944i	−0.916815	+	0.399312i
$64$	0.623565	−	4.33699i	0.0779456	−	0.542124i
$65$	4.15371	−	6.46330i	0.515204	−	0.801673i
$66$	−6.14008	−	1.77495i	−0.755791	−	0.218481i
$67$	−8.41744	−	2.47158i	−1.02835	−	0.301952i	−0.276312	−	0.961068i	$-0.589112\pi$
$67$	−8.41744	−	2.47158i	−1.02835	−	0.301952i	−0.752041	+	0.659116i	$0.770931\pi$
$68$	4.45508			0.540258
$69$	4.08220	+	7.23434i	0.491440	+	0.870912i
$70$	−14.4108	+	8.74002i	−1.72243	+	1.04463i
$71$	1.65586	−	5.63935i	0.196515	−	0.669268i	−0.800991	−	0.598677i	$-0.795693\pi$
$71$	1.65586	−	5.63935i	0.196515	−	0.669268i	0.997505	−	0.0705909i	$-0.0224885\pi$
$72$	−6.69757	+	1.02039i	−0.789316	+	0.120254i
$73$	0.871295	−	1.35576i	0.101977	−	0.158680i	−0.786515	−	0.617571i	$-0.788117\pi$
$73$	0.871295	−	1.35576i	0.101977	−	0.158680i	0.888493	+	0.458891i	$0.151753\pi$
$74$	−4.06533	−	0.584506i	−0.472584	−	0.0679474i
$75$	15.5043	+	9.87236i	1.79028	+	1.13996i
$76$	2.13649	−	0.975701i	0.245072	−	0.111921i
$77$	5.76403	+	1.85668i	0.656872	+	0.211589i
$78$	4.55549	−	2.95471i	0.515807	−	0.334555i
$79$	−5.26762	+	11.5345i	−0.592653	+	1.29773i	0.341172	+	0.940001i	$0.389176\pi$
$79$	−5.26762	+	11.5345i	−0.592653	+	1.29773i	−0.933825	+	0.357729i	$0.883551\pi$
$80$	−18.3470	+	5.38717i	−2.05126	+	0.602304i
$81$	3.87556	+	8.12281i	0.430618	+	0.902534i
$82$	9.02373	+	4.12100i	0.996505	+	0.455088i
$83$	0.586751	+	4.08094i	0.0644043	+	0.447942i	0.996351	+	0.0853471i	$0.0271999\pi$
$83$	0.586751	+	4.08094i	0.0644043	+	0.447942i	−0.931947	+	0.362595i	$0.881891\pi$
$84$	−2.72616	+	0.331409i	−0.297448	+	0.0361597i
$85$	12.2023	+	26.7192i	1.32352	+	2.89811i
$86$	−3.31598	−	5.15976i	−0.357571	−	0.556391i
$87$	0.724310	+	2.42903i	0.0776542	+	0.260420i
$88$	4.34830	+	2.79449i	0.463531	+	0.297893i
$89$	−4.01990	+	4.63921i	−0.426108	+	0.491755i	−0.927688	−	0.373356i	$-0.878207\pi$
$89$	−4.01990	+	4.63921i	−0.426108	+	0.491755i	0.501580	+	0.865111i	$0.332752\pi$
$90$	10.4666	+	15.9897i	1.10327	+	1.68547i
$91$	−4.39876	+	2.66780i	−0.461116	+	0.279661i
$92$	0.638266	+	2.80226i	0.0665439	+	0.292156i
$93$	10.1520	−	4.68785i	1.05272	−	0.486107i
$94$	−1.19689	+	4.07622i	−0.123449	+	0.420430i
$95$	11.7035	+	10.1411i	1.20075	+	1.04046i
$96$	−5.63638	−	0.786272i	−0.575260	−	0.0802485i
$97$	−3.81751	−	0.548876i	−0.387610	−	0.0557299i	−0.0542447	−	0.998528i	$-0.517275\pi$
$97$	−3.81751	−	0.548876i	−0.387610	−	0.0557299i	−0.333365	+	0.942798i	$0.608184\pi$
$98$	11.2391	−	1.02283i	1.13532	−	0.103322i
$99$	1.87918	−	6.60436i	0.188865	−	0.663763i
$100$	4.16462	+	4.80623i	0.416462	+	0.480623i
$101$	−1.42485	−	9.91007i	−0.141778	−	0.986089i	−0.929174	−	0.369642i	$-0.879480\pi$
$101$	−1.42485	−	9.91007i	−0.141778	−	0.986089i	0.787396	−	0.616447i	$-0.211429\pi$
$102$	0.0870784	+	20.7592i	0.00862205	+	2.05547i
$103$	0.865956	+	2.94918i	0.0853252	+	0.290591i	0.991091	−	0.133188i	$-0.0425215\pi$
$103$	0.865956	+	2.94918i	0.0853252	+	0.290591i	−0.905766	+	0.423779i	$0.860703\pi$
$104$	−4.21326	+	1.23712i	−0.413144	+	0.121310i
$105$	−9.45445	−	15.4424i	−0.922660	−	1.50702i
$106$	−1.22903	−	8.54809i	−0.119374	−	0.830264i
$107$	0.964960	−	0.836142i	0.0932862	−	0.0808329i	−0.606969	−	0.794725i	$-0.707615\pi$
$107$	0.964960	−	0.836142i	0.0932862	−	0.0808329i	0.700255	+	0.713892i	$0.253069\pi$
$108$	0.481909	+	3.07641i	0.0463717	+	0.296028i
$109$	0.501212	−	0.322109i	0.0480074	−	0.0308525i	−0.516417	−	0.856337i	$-0.672735\pi$
$109$	0.501212	−	0.322109i	0.0480074	−	0.0308525i	0.564424	+	0.825485i	$0.309098\pi$
$110$	2.07501	−	14.4320i	0.197845	−	1.37604i
$111$	0.609622	−	4.37006i	0.0578627	−	0.414788i
$112$	12.6219	+	2.15132i	1.19266	+	0.203280i
$113$	−3.09744	+	10.5489i	−0.291382	+	0.992358i	0.675548	+	0.737316i	$0.263907\pi$
$113$	−3.09744	+	10.5489i	−0.291382	+	0.992358i	−0.966930	+	0.255041i	$0.917911\pi$
$114$	4.58821	+	9.93628i	0.429726	+	0.930618i
$115$	−15.0583	+	11.5033i	−1.40419	+	1.07268i
$116$			0.876995i			0.0814270i
$117$	3.19481	+	4.88070i	0.295360	+	0.451221i
$118$	−17.3628	−	15.0450i	−1.59838	−	1.38500i
$119$	0.511755	−	19.6621i	0.0469125	−	1.80242i
$120$	−4.41634	−	14.8106i	−0.403155	−	1.35201i
$121$	4.84666	−	3.11476i	0.440606	−	0.283160i
$122$	9.66315	+	21.1593i	0.874860	+	1.91568i
$123$	−4.38658	+	9.71288i	−0.395524	+	0.875781i
$124$	3.82955	−	0.550606i	0.343903	−	0.0494459i
$125$	−9.21158	+	20.1705i	−0.823908	+	1.80411i
$126$	−1.59754	−	12.6965i	−0.142321	−	1.13110i
$127$	1.43939	−	0.422643i	0.127725	−	0.0375035i	−0.217245	−	0.976117i	$-0.569707\pi$
$127$	1.43939	−	0.422643i	0.127725	−	0.0375035i	0.344970	+	0.938614i	$0.387889\pi$
$128$	12.4033	+	5.66438i	1.09630	+	0.500665i
$129$	5.52825	−	3.58565i	0.486735	−	0.315699i
$130$	8.11152	+	9.36120i	0.711428	+	0.821031i
$131$	2.05279	+	4.49498i	0.179353	+	0.392729i	0.977861	−	0.209256i	$-0.0671042\pi$
$131$	2.05279	+	4.49498i	0.179353	+	0.392729i	−0.798508	+	0.601984i	$0.794377\pi$
$132$	1.27604	−	2.00398i	0.111065	−	0.174424i
$133$	−4.06076	−	9.54129i	−0.352112	−	0.827335i
$134$	7.64669	−	11.8985i	0.660573	−	1.02787i
$135$	−17.1308	+	11.3164i	−1.47438	+	0.973961i
$136$	4.72981	−	16.1083i	0.405578	−	1.38127i
$137$		−	5.55717i		−	0.474781i	−0.971414	−	0.237391i	$-0.923708\pi$
$137$		−	5.55717i		−	0.474781i	0.971414	−	0.237391i	$-0.0762921\pi$
$138$	−13.0451	+	3.02889i	−1.11048	+	0.257836i
$139$		−	10.7889i		−	0.915102i	−0.889183	−	0.457551i	$-0.848727\pi$
$139$		−	10.7889i		−	0.915102i	0.889183	−	0.457551i	$-0.151273\pi$
$140$	−1.60800	−	6.05490i	−0.135901	−	0.511733i
$141$	−4.38453	−	1.26746i	−0.369244	−	0.106739i
$142$	7.97151	+	5.12298i	0.668954	+	0.429911i
$143$	0.633376	−	4.40523i	0.0529656	−	0.368384i
$144$	1.94553	−	14.3873i	0.162128	−	1.19894i
$145$	−5.25976	+	2.40205i	−0.436799	+	0.199480i
$146$	1.70150	+	1.96363i	0.140817	+	0.162512i
$147$	1.14949	+	12.0697i	0.0948085	+	0.995496i
$148$	0.634193	−	1.38869i	0.0521303	−	0.114150i
$149$	2.07958	+	7.08239i	0.170366	+	0.580212i	0.999768	+	0.0215597i	$0.00686319\pi$
$149$	2.07958	+	7.08239i	0.170366	+	0.580212i	−0.829402	+	0.558652i	$0.811319\pi$
$150$	−22.3141	+	19.4997i	−1.82194	+	1.59215i
$151$	9.49248	−	20.7856i	0.772487	−	1.69151i	0.0513872	−	0.998679i	$-0.483636\pi$
$151$	9.49248	−	20.7856i	0.772487	−	1.69151i	0.721100	−	0.692831i	$-0.243637\pi$
$152$	−1.25961	−	8.76079i	−0.102168	−	0.710594i
$153$	−22.3015	+	0.187099i	−1.80297	+	0.0151260i
$154$	−5.49026	+	8.07316i	−0.442418	+	0.650554i
$155$	13.7912	+	21.4595i	1.10774	+	1.72367i
$156$	0.576738	+	1.93414i	0.0461760	+	0.154855i
$157$	8.34739	−	12.9888i	0.666194	−	1.03662i	−0.329521	−	0.944148i	$-0.606887\pi$
$157$	8.34739	−	12.9888i	0.666194	−	1.03662i	0.995715	−	0.0924706i	$-0.0294764\pi$
$158$	−15.4503	−	13.3877i	−1.22916	−	1.06507i
$159$	9.17778	−	1.35888i	0.727845	−	0.107766i
$160$		−	12.9824i		−	1.02635i
$161$	12.4409	−	2.49504i	0.980476	−	0.196637i
$162$	−14.3257	+	2.30567i	−1.12553	+	0.181151i
$163$	18.5919	+	5.45909i	1.45623	+	0.427589i	0.911598	−	0.411084i	$-0.134850\pi$
$163$	18.5919	+	5.45909i	1.45623	+	0.427589i	0.544636	+	0.838673i	$0.316668\pi$
$164$	−2.41474	+	2.78676i	−0.188559	+	0.217609i
$165$	15.5139	+	2.16418i	1.20775	+	0.168481i
$166$	−6.57941	−	0.945976i	−0.510661	−	0.0734220i
$167$	9.49508	−	6.10212i	0.734752	−	0.472196i	−0.118988	−	0.992896i	$-0.537965\pi$
$167$	9.49508	−	6.10212i	0.734752	−	0.472196i	0.853740	+	0.520699i	$0.174329\pi$
$168$	−1.69600	+	10.2088i	−0.130849	+	0.787629i
$169$	−6.03723	−	6.96734i	−0.464402	−	0.535949i
$170$	−46.8750	+	6.73961i	−3.59515	+	0.516905i
$171$	−10.6540	+	4.97395i	−0.814731	+	0.380368i
$172$	2.18749	−	0.642304i	0.166794	−	0.0489752i
$173$	−0.752596	+	0.220982i	−0.0572188	+	0.0168010i	−0.310217	−	0.950666i	$-0.600402\pi$
$173$	−0.752596	+	0.220982i	−0.0572188	+	0.0168010i	0.252998	+	0.967467i	$0.418583\pi$
$174$	−4.08652	+	0.0171416i	−0.309798	+	0.00129950i
$175$	21.6903	−	17.8281i	1.63963	−	1.34768i
$176$	−8.37116	+	7.25365i	−0.631000	+	0.546765i
$177$	16.0848	−	18.7209i	1.20901	−	1.40715i
$178$	−5.35058	−	8.32567i	−0.401043	−	0.624036i
$179$	9.98792	+	1.43605i	0.746532	+	0.107335i	0.505074	−	0.863076i	$-0.331465\pi$
$179$	9.98792	+	1.43605i	0.746532	+	0.107335i	0.241458	+	0.970411i	$0.422374\pi$
$180$	−6.79882	+	2.05842i	−0.506754	+	0.153426i
$181$	9.69675	+	8.40229i	0.720754	+	0.624537i	0.935991	−	0.352025i	$-0.114507\pi$
$181$	9.69675	+	8.40229i	0.720754	+	0.624537i	−0.215237	+	0.976562i	$0.569052\pi$
$182$	−2.12888	−	8.01629i	−0.157803	−	0.594207i
$183$	−22.6882	+	10.4766i	−1.67716	+	0.774452i
$184$	10.8098	+	0.667283i	0.796907	+	0.0491927i
$185$	10.0657			0.740042
$186$	2.64050	+	17.8337i	0.193611	+	1.30763i
$187$	12.8594	+	11.1427i	0.940372	+	0.814837i
$188$	−1.32844	−	0.853740i	−0.0968868	−	0.0622654i
$189$	13.6329	−	1.77348i	0.991644	−	0.129002i
$190$	−21.0035	+	13.4981i	−1.52375	+	0.979255i
$191$	−17.5987	+	8.03706i	−1.27340	+	0.581541i	−0.933384	−	0.358879i	$-0.883159\pi$
$191$	−17.5987	+	8.03706i	−1.27340	+	0.581541i	−0.340014	+	0.940420i	$0.610432\pi$
$192$	−3.12365	+	6.91648i	−0.225430	+	0.499154i
$193$	0.398204	+	2.76957i	0.0286634	+	0.199358i	0.999121	−	0.0419124i	$-0.0133450\pi$
$193$	0.398204	+	2.76957i	0.0286634	+	0.199358i	−0.970458	+	0.241270i	$0.922436\pi$
$194$	2.58305	−	5.65608i	0.185452	−	0.406083i
$195$	−10.0203	+	8.75650i	−0.717568	+	0.627066i
$196$	−0.812191	+	4.11556i	−0.0580137	+	0.293968i
$197$	0.0671716	+	0.0306763i	0.00478578	+	0.00218559i	0.417806	−	0.908536i	$-0.362799\pi$
$197$	0.0671716	+	0.0306763i	0.00478578	+	0.00218559i	−0.413021	+	0.910722i	$0.635526\pi$
$198$	9.36286	+	5.90675i	0.665390	+	0.419774i
$199$	−8.20455	+	7.10929i	−0.581605	+	0.503964i	−0.895243	−	0.445579i	$-0.852998\pi$
$199$	−8.20455	+	7.10929i	−0.581605	+	0.503964i	0.313637	+	0.949543i	$0.398452\pi$
$200$	21.7994	−	9.95544i	1.54145	−	0.703956i
$201$	12.8171	+	8.16131i	0.904051	+	0.575654i
$202$	15.9773	+	2.29719i	1.12416	+	0.161630i
$203$	3.87055	+	0.100741i	0.271659	+	0.00707060i
$204$	−7.41291	−	2.14289i	−0.519007	−	0.150032i
$205$	−23.3274	−	6.84954i	−1.62926	−	0.478393i
$206$	−4.95547			−0.345264
$207$	−3.31276	−	14.0009i	−0.230253	−	0.973131i
$208$		−	9.41002i		−	0.652468i
$209$	8.60724	+	2.52731i	0.595375	+	0.174818i
$210$	28.1825	−	7.61110i	1.94478	−	0.525216i
$211$	−12.3018	−	7.90587i	−0.846889	−	0.544263i	0.0437139	−	0.999044i	$-0.486081\pi$
$211$	−12.3018	−	7.90587i	−0.846889	−	0.544263i	−0.890603	+	0.454781i	$0.849717\pi$
$212$	3.17739	+	0.456839i	0.218224	+	0.0313758i
$213$	−5.46775	+	8.58697i	−0.374644	+	0.588370i
$214$	0.855145	+	1.87251i	0.0584565	+	0.128002i
$215$	9.84363	+	11.3602i	0.671330	+	0.774756i
$216$	11.6350	+	1.52369i	0.791665	+	0.103674i
$217$	−1.99015	−	16.9646i	−0.135100	−	1.15163i
$218$	0.270619	+	0.921643i	0.0183286	+	0.0624215i
$219$	−2.10189	+	1.83679i	−0.142033	+	0.124119i
$220$	4.92989	+	2.25140i	0.332373	+	0.151790i
$221$	−14.3081	+	2.05720i	−0.962468	+	0.138382i
$222$	6.48324	+	2.92799i	0.435127	+	0.196514i
$223$	6.54427	−	2.98867i	0.438237	−	0.200136i	−0.184064	−	0.982914i	$-0.558925\pi$
$223$	6.54427	−	2.98867i	0.438237	−	0.200136i	0.622301	+	0.782778i	$0.286198\pi$
$224$	−3.81576	+	7.81087i	−0.254951	+	0.521885i
$225$	−21.0494	−	23.8844i	−1.40329	−	1.59229i
$226$	−14.9114	−	9.58298i	−0.991892	−	0.637450i
$227$	4.29773	−	4.95984i	0.285250	−	0.329196i	−0.594982	−	0.803739i	$-0.702841\pi$
$227$	4.29773	−	4.95984i	0.285250	−	0.329196i	0.880233	+	0.474542i	$0.157386\pi$
$228$	−4.02426	+	0.595842i	−0.266513	+	0.0394606i
$229$			9.13789i			0.603849i	0.953332	+	0.301924i	$0.0976290\pi$
$229$			9.13789i			0.603849i	−0.953332	+	0.301924i	$0.902371\pi$
$230$	−10.9549	−	28.5190i	−0.722344	−	1.88048i
$231$	−8.69784	−	5.86188i	−0.572276	−	0.385683i
$232$	3.17096	+	0.931078i	0.208184	+	0.0611283i
$233$	−14.8787	−	12.8924i	−0.974734	−	0.844611i	0.0131334	−	0.999914i	$-0.495819\pi$
$233$	−14.8787	−	12.8924i	−0.974734	−	0.844611i	−0.987867	+	0.155302i	$0.950365\pi$
$234$	−9.00119	+	2.72522i	−0.588426	+	0.178153i
$235$	1.48173	−	10.3057i	0.0966575	−	0.672268i
$236$	7.18407	−	4.61692i	0.467643	−	0.300536i
$237$	14.3130	−	16.6588i	0.929729	−	1.08210i
$238$	30.1833	+	9.72251i	1.95649	+	0.630217i
$239$	−1.65420	+	0.237838i	−0.107001	+	0.0153845i	−0.195607	−	0.980682i	$-0.562668\pi$
$239$	−1.65420	+	0.237838i	−0.107001	+	0.0153845i	0.0886061	+	0.996067i	$0.471759\pi$
$240$	33.1192	−	0.138925i	2.13784	−	0.00896755i
$241$	1.16325	+	3.96167i	0.0749317	+	0.255194i	0.988437	−	0.151633i	$-0.0484533\pi$
$241$	1.16325	+	3.96167i	0.0749317	+	0.255194i	−0.913505	+	0.406827i	$0.866635\pi$
$242$	2.61685	+	8.91218i	0.168218	+	0.572896i
$243$	−2.54157	−	15.3799i	−0.163042	−	0.986619i
$244$	−8.55843	+	1.23052i	−0.547897	+	0.0787757i
$245$	−26.9075	+	6.40123i	−1.71906	+	0.408960i
$246$	−13.0326	−	11.1974i	−0.830928	−	0.713923i
$247$	−6.41109	+	4.12016i	−0.407928	+	0.262159i
$248$	2.07488	−	14.4311i	0.131755	−	0.916375i
$249$	0.986624	−	7.07260i	0.0625248	−	0.448208i
$250$	−27.0182	−	23.4114i	−1.70878	−	1.48067i
$251$	−10.7783	−	3.16480i	−0.680322	−	0.199761i	−0.0767275	−	0.997052i	$-0.524447\pi$
$251$	−10.7783	−	3.16480i	−0.680322	−	0.199761i	−0.603594	+	0.797292i	$0.706265\pi$
$252$	4.69553	+	0.759843i	0.295790	+	0.0478656i
$253$	−5.16648	+	9.68499i	−0.324814	+	0.608890i
$254$			2.41860i			0.151756i
$255$	−7.45168	−	50.3280i	−0.466643	−	3.15166i
$256$	−8.65745	+	9.99123i	−0.541091	+	0.624452i
$257$	−1.56773	−	1.00752i	−0.0977926	−	0.0628475i	0.490831	−	0.871255i	$-0.336693\pi$
$257$	−1.56773	−	1.00752i	−0.0977926	−	0.0628475i	−0.588623	+	0.808408i	$0.700330\pi$
$258$	3.03569	+	10.1804i	0.188993	+	0.633806i
$259$	−6.05601	−	2.95848i	−0.376302	−	0.183831i
$260$	−4.18813	+	1.91265i	−0.259737	+	0.118618i
$261$	−0.0368310	−	4.39012i	−0.00227978	−	0.271742i
$262$	−7.88580	+	1.13381i	−0.487186	+	0.0700468i
$263$	0.486657	+	0.222249i	0.0300085	+	0.0137044i	0.430363	−	0.902656i	$-0.358386\pi$
$263$	0.486657	+	0.222249i	0.0300085	+	0.0137044i	−0.400354	+	0.916360i	$0.631113\pi$
$264$	−5.89110	−	6.74134i	−0.362572	−	0.414901i
$265$	5.96284	+	20.3076i	0.366294	+	1.24748i
$266$	16.6041	−	1.94786i	1.01806	−	0.119431i
$267$	8.92026	−	5.78572i	0.545911	−	0.354080i
$268$	3.44282	+	3.97322i	0.210304	+	0.242703i
$269$	10.0050	+	21.9080i	0.610017	+	1.33575i	0.922562	+	0.385849i	$0.126091\pi$
$269$	10.0050	+	21.9080i	0.610017	+	1.33575i	−0.312545	+	0.949903i	$0.601181\pi$
$270$	−9.72448	−	31.6401i	−0.591813	−	1.92555i
$271$	1.47587	+	0.212198i	0.0896529	+	0.0128901i	0.186995	−	0.982361i	$-0.440125\pi$
$271$	1.47587	+	0.212198i	0.0896529	+	0.0128901i	−0.0973424	+	0.995251i	$0.531034\pi$
$272$	30.2656	+	19.4505i	1.83512	+	1.17936i
$273$	8.60241	−	2.32321i	0.520642	−	0.140607i
$274$	8.59650	+	2.52416i	0.519334	+	0.152490i
$275$			24.2892i			1.46470i
$276$	0.285860	−	4.96975i	0.0172067	−	0.299144i
$277$	−20.9607			−1.25941			−0.629703	−	0.776836i	$-0.716823\pi$
$277$	−20.9607			−1.25941			−0.629703	+	0.776836i	$0.716823\pi$
$278$	16.6896	+	4.90050i	1.00097	+	0.293912i
$279$	−19.1471	+	2.91709i	−1.14630	+	0.174641i
$280$	−23.5999	−	0.614247i	−1.41037	−	0.0367083i
$281$	2.34483	+	0.337136i	0.139881	+	0.0201118i	0.211900	−	0.977291i	$-0.432035\pi$
$281$	2.34483	+	0.337136i	0.139881	+	0.0201118i	−0.0720186	+	0.997403i	$0.522944\pi$
$282$	3.95219	−	6.20681i	0.235349	−	0.369610i
$283$	8.94976	−	4.08722i	0.532008	−	0.242960i	−0.131252	−	0.991349i	$-0.541900\pi$
$283$	8.94976	−	4.08722i	0.532008	−	0.242960i	0.663260	+	0.748389i	$0.269172\pi$
$284$	−2.66190	+	2.30655i	−0.157955	+	0.136869i
$285$	−14.5958	−	22.5034i	−0.864582	−	1.33299i
$286$	6.52685	+	2.98071i	0.385941	+	0.176253i
$287$	12.0217	+	10.9774i	0.709621	+	0.647973i
$288$	9.00030	+	4.01939i	0.530348	+	0.236845i
$289$	15.8962	−	34.8078i	0.935071	−	2.04752i
$290$	−1.32671	−	9.22749i	−0.0779072	−	0.541857i
$291$	6.08804	+	2.74951i	0.356887	+	0.161179i
$292$	−0.878515	+	0.401205i	−0.0514112	+	0.0234787i
$293$	−9.40045	+	6.04130i	−0.549180	+	0.352937i	−0.785620	−	0.618710i	$-0.787656\pi$
$293$	−9.40045	+	6.04130i	−0.549180	+	0.352937i	0.236440	+	0.971646i	$0.424019\pi$
$294$	−19.1931	−	3.70411i	−1.11936	−	0.216028i
$295$	47.3668	+	30.4408i	2.75780	+	1.77233i
$296$	−4.34779	−	3.76738i	−0.252710	−	0.218975i
$297$	−6.30350	+	10.0853i	−0.365766	+	0.585206i
$298$	−11.9005			−0.689376
$299$	−3.34387	−	8.70512i	−0.193381	−	0.503430i
$300$	−4.61781	−	10.0004i	−0.266610	−	0.577372i
$301$	−2.58348	−	9.72807i	−0.148909	−	0.560716i
$302$	27.8421	+	24.1253i	1.60213	+	1.38825i
$303$	−2.39590	+	17.1750i	−0.137641	+	0.986675i
$304$	18.7740	+	2.69930i	1.07677	+	0.154815i
$305$	−30.8212	−	47.9587i	−1.76481	−	2.74611i
$306$	9.84030	−	34.5837i	0.562532	−	1.97702i
$307$	−4.52710	+	3.92276i	−0.258375	+	0.223884i	−0.774410	−	0.632684i	$-0.781953\pi$
$307$	−4.52710	+	3.92276i	−0.258375	+	0.223884i	0.516034	+	0.856568i	$0.327408\pi$
$308$	−2.30434	−	2.80354i	−0.131302	−	0.159747i
$309$	−0.0223314	−	5.32373i	−0.00127039	−	0.302856i
$310$	−39.4604	+	11.5866i	−2.24120	+	0.658076i
$311$	−1.31450	+	0.385971i	−0.0745384	+	0.0218864i	−0.318789	−	0.947826i	$-0.603276\pi$
$311$	−1.31450	+	0.385971i	−0.0745384	+	0.0218864i	0.244251	+	0.969712i	$0.421458\pi$
$312$	7.60559	−	0.0319030i	0.430582	−	0.00180615i
$313$	−1.83700	+	0.264121i	−0.103834	+	0.0149290i	−0.194036	−	0.980994i	$-0.562158\pi$
$313$	−1.83700	+	0.264121i	−0.103834	+	0.0149290i	0.0902021	+	0.995923i	$0.471249\pi$
$314$	16.3011	+	18.8125i	0.919925	+	1.06165i
$315$	8.30370	+	30.2425i	0.467861	+	1.70397i
$316$	6.39273	−	4.10836i	0.359619	−	0.231113i
$317$	9.46678	+	1.36112i	0.531707	+	0.0764480i	0.402939	−	0.915227i	$-0.367989\pi$
$317$	9.46678	+	1.36112i	0.531707	+	0.0764480i	0.128768	+	0.991675i	$0.458898\pi$
$318$	−2.06662	+	14.8145i	−0.115890	+	0.830757i
$319$	−2.19348	+	2.53141i	−0.122811	+	0.141732i
$320$	−16.6113	−	4.87751i	−0.928599	−	0.272661i
$321$	−2.00780	+	0.927131i	−0.112065	+	0.0517474i
$322$	−1.79122	+	20.3783i	−0.0998206	+	1.13564i
$323$		−	29.1364i		−	1.62119i
$324$	0.677895	−	5.35072i	0.0376608	−	0.297262i
$325$	−15.5946	−	13.5128i	−0.865033	−	0.749556i
$326$	−16.8896	+	26.2807i	−0.935426	+	1.45555i
$327$	−0.988913	+	0.294882i	−0.0546870	+	0.0163070i
$328$	7.51245	+	11.6896i	0.414806	+	0.645451i
$329$	−3.92051	+	5.76491i	−0.216145	+	0.317830i
$330$	−10.3945	+	23.0157i	−0.572196	+	1.26697i
$331$	−0.601305	−	4.18217i	−0.0330507	−	0.229873i	0.966600	−	0.256289i	$-0.0824997\pi$
$331$	−0.601305	−	4.18217i	−0.0330507	−	0.229873i	−0.999651	+	0.0264158i	$0.991591\pi$
$332$	1.02639	−	2.24748i	0.0563305	−	0.123347i
$333$	−3.11636	+	6.97822i	−0.170776	+	0.382404i
$334$	5.12667	+	17.4598i	0.280519	+	0.955359i
$335$	−14.3996	+	31.5307i	−0.786734	+	1.72271i
$336$	−19.9670	−	9.65075i	−1.08929	−	0.526491i
$337$	2.74821	+	3.17160i	0.149704	+	0.172768i	0.825649	−	0.564185i	$-0.190809\pi$
$337$	2.74821	+	3.17160i	0.149704	+	0.172768i	−0.675944	+	0.736953i	$0.736264\pi$
$338$	13.5201	−	6.17443i	0.735398	−	0.335845i
$339$	10.2279	−	16.0627i	0.555504	−	0.872406i
$340$	2.50516	−	17.4238i	0.135861	−	0.944937i
$341$	12.4310	+	7.98889i	0.673174	+	0.432623i
$342$	−2.85509	−	18.7401i	−0.154385	−	1.01335i
$343$	18.0704	+	4.05729i	0.975708	+	0.219073i
$344$		−	8.59122i		−	0.463208i
$345$	30.5889	−	11.8975i	1.64685	−	0.640539i
$346$		−	1.26458i		−	0.0679843i
$347$	−6.03419	+	20.5506i	−0.323932	+	1.10321i	0.623118	+	0.782128i	$0.285866\pi$
$347$	−6.03419	+	20.5506i	−0.323932	+	1.10321i	−0.947051	+	0.321085i	$0.895953\pi$
$348$	0.421835	−	1.45925i	0.0226127	−	0.0782242i
$349$	−15.7133	+	24.4504i	−0.841116	+	1.30880i	0.108088	+	0.994141i	$0.465527\pi$
$349$	−15.7133	+	24.4504i	−0.841116	+	1.30880i	−0.949204	+	0.314660i	$0.898109\pi$
$350$	17.7266	+	41.6510i	0.947526	+	2.22634i
$351$	−2.96830	−	9.65781i	−0.158436	−	0.515496i
$352$	−3.12407	−	6.84077i	−0.166514	−	0.364614i
$353$	−17.7678	−	20.5052i	−0.945686	−	1.09138i	−0.995701	−	0.0926309i	$-0.970472\pi$
$353$	−17.7678	−	20.5052i	−0.945686	−	1.09138i	0.0500149	−	0.998748i	$-0.484073\pi$
$354$	21.6538	+	33.3852i	1.15089	+	1.77441i
$355$	−21.1243	−	9.64716i	−1.12116	−	0.512018i
$356$	3.52968	−	1.03641i	0.187073	−	0.0549295i
$357$	−10.3090	+	32.4701i	−0.545610	+	1.71850i
$358$	−6.75813	+	14.7982i	−0.357178	+	0.782112i
$359$	−10.5648	+	1.51899i	−0.557590	+	0.0801693i	−0.415348	−	0.909663i	$-0.636340\pi$
$359$	−10.5648	+	1.51899i	−0.557590	+	0.0801693i	−0.142242	+	0.989832i	$0.545431\pi$
$360$	0.224570	+	26.7679i	0.0118359	+	1.41079i
$361$	1.51176	+	3.31028i	0.0795661	+	0.174226i
$362$	−17.4021	+	11.1836i	−0.914634	+	0.587800i
$363$	−9.56267	+	2.85148i	−0.501910	+	0.149664i
$364$	3.08196	+	0.0802155i	0.161538	+	0.00420444i
$365$	−4.81243	−	4.16999i	−0.251894	−	0.218268i
$366$	−5.90109	−	39.8555i	−0.308455	−	2.08328i
$367$		−	4.41784i		−	0.230609i	−0.993330	−	0.115305i	$-0.963216\pi$
$367$		−	4.41784i		−	0.230609i	0.993330	−	0.115305i	$-0.0367844\pi$
$368$	−7.89836	+	21.8237i	−0.411730	+	1.13764i
$369$	11.9708	−	14.0515i	0.623176	−	0.731494i
$370$	−4.57199	+	15.5708i	−0.237687	+	0.809486i
$371$	2.38121	−	13.9707i	0.123626	−	0.725320i
$372$	−6.63691	−	0.925846i	−0.344108	−	0.0480029i
$373$	−1.54402	+	10.7389i	−0.0799462	+	0.556038i	0.910002	+	0.414605i	$0.136080\pi$
$373$	−1.54402	+	10.7389i	−0.0799462	+	0.556038i	−0.989948	+	0.141433i	$0.954829\pi$
$374$	−23.0779	+	14.8313i	−1.19333	+	0.766906i
$375$	25.0294	−	29.1315i	1.29251	−	1.50434i
$376$	−4.49724	+	3.89688i	−0.231927	+	0.200966i
$377$	−0.404965	−	2.81660i	−0.0208568	−	0.145062i
$378$	−3.44884	+	21.8945i	−0.177389	+	1.12613i
$379$	−17.3778	+	5.10258i	−0.892638	+	0.262102i	−0.695716	−	0.718317i	$-0.744913\pi$
$379$	−17.3778	+	5.10258i	−0.892638	+	0.262102i	−0.196922	+	0.980419i	$0.563095\pi$
$380$	−2.61458	−	8.90444i	−0.134125	−	0.456788i
$381$	−2.59833	+	0.0108992i	−0.133116	+	0.000558381i
$382$	−4.43906	−	30.8744i	−0.227122	−	1.57967i
$383$	−22.4663	−	25.9275i	−1.14797	−	1.32483i	−0.937804	−	0.347166i	$-0.887144\pi$
$383$	−22.4663	−	25.9275i	−1.14797	−	1.32483i	−0.210169	−	0.977665i	$-0.567402\pi$
$384$	−17.9135	−	15.3910i	−0.914144	−	0.785421i
$385$	10.5027	−	21.4990i	0.535266	−	1.09569i
$386$	−4.46518	−	0.641995i	−0.227271	−	0.0326767i
$387$	−10.9233	+	3.30715i	−0.555261	+	0.168112i
$388$	1.74674	+	1.51356i	0.0886774	+	0.0768394i
$389$	−7.29732	+	24.8524i	−0.369989	+	1.26007i	0.538667	+	0.842519i	$0.318928\pi$
$389$	−7.29732	+	24.8524i	−0.369989	+	1.26007i	−0.908656	+	0.417547i	$0.862890\pi$
$390$	−8.99422	−	19.4780i	−0.455440	−	0.986304i
$391$	34.9101	+	7.23855i	1.76548	+	0.366069i
$392$	14.0184	+	7.30600i	0.708035	+	0.369009i
$393$	−1.25360	−	8.46670i	−0.0632357	−	0.427088i
$394$	−0.0779642	+	0.0899755i	−0.00392778	+	0.00453290i
$395$	42.1492	+	27.0876i	2.12075	+	1.36293i
$396$	−3.08714	+	2.72070i	−0.155135	+	0.136720i
$397$	−15.3953	−	23.9556i	−0.772669	−	1.20230i	−0.974831	−	0.222944i	$-0.928433\pi$
$397$	−15.3953	−	23.9556i	−0.772669	−	1.20230i	0.202162	−	0.979352i	$-0.435203\pi$
$398$	−7.27085	−	15.9209i	−0.364455	−	0.798045i
$399$	2.16743	+	17.8292i	0.108507	+	0.892576i
$400$	7.30875	+	50.8335i	0.365437	+	2.54167i
$401$	−17.4416	−	7.96532i	−0.870993	−	0.397769i	−0.0707849	−	0.997492i	$-0.522550\pi$
$401$	−17.4416	−	7.96532i	−0.870993	−	0.397769i	−0.800208	+	0.599722i	$0.795278\pi$
$402$	−18.4467	+	16.1201i	−0.920036	+	0.803997i
$403$	−12.0449	+	3.53670i	−0.599998	+	0.176175i
$404$	−2.49247	+	5.45774i	−0.124005	+	0.271533i
$405$	33.9475	−	10.5897i	1.68687	−	0.526207i
$406$	−1.91391	+	5.94167i	−0.0949855	+	0.294880i
$407$	5.30386	−	2.42219i	0.262903	−	0.120064i
$408$	−15.6181	+	24.5279i	−0.773212	+	1.21431i
$409$	2.75918	+	0.396710i	0.136433	+	0.0196161i	0.210193	−	0.977660i	$-0.432591\pi$
$409$	2.75918	+	0.396710i	0.136433	+	0.0196161i	−0.0737601	+	0.997276i	$0.523500\pi$
$410$	21.1914	−	32.9744i	1.04657	−	1.62849i
$411$	−2.67300	+	9.24670i	−0.131849	+	0.456106i
$412$	0.518947	−	1.76737i	0.0255667	−	0.0870721i
$413$	−19.5512	−	32.2367i	−0.962050	−	1.58626i
$414$	23.1630	+	1.23488i	1.13840	+	0.0606909i
$415$	16.2905			0.799668
$416$	6.13005	+	1.79994i	0.300550	+	0.0882495i
$417$	−5.18946	+	17.9519i	−0.254129	+	0.879108i
$418$	−7.81911	+	12.1668i	−0.382445	+	0.595096i
$419$	2.70970	−	18.8464i	0.132378	−	0.920707i	−0.810065	−	0.586340i	$-0.800568\pi$
$419$	2.70970	−	18.8464i	0.132378	−	0.920707i	0.942443	−	0.334367i	$-0.108522\pi$
$420$	−0.236824	+	10.8483i	−0.0115558	+	0.529345i
$421$	−12.4077	−	27.1691i	−0.604714	−	1.32414i	−0.926131	−	0.377201i	$-0.876887\pi$
$421$	−12.4077	−	27.1691i	−0.604714	−	1.32414i	0.321418	−	0.946938i	$-0.395841\pi$
$422$	17.8174	−	15.4389i	0.867339	−	0.751553i
$423$	6.68587	+	4.21791i	0.325078	+	0.205082i
$424$	5.02513	−	11.0035i	0.244042	−	0.534377i
$425$	75.6954	−	22.2262i	3.67177	−	1.07813i
$426$	−10.7998	−	12.3585i	−0.523253	−	0.598773i
$427$	4.44767	+	37.9133i	0.215238	+	1.83475i
$428$	−0.757382	+	0.108895i	−0.0366095	+	0.00526365i
$429$	−3.17280	+	7.02531i	−0.153184	+	0.339185i
$430$	−22.0444	+	10.0673i	−1.06308	+	0.485490i
$431$	5.91406	+	9.20246i	0.284870	+	0.443267i	0.953968	−	0.299907i	$-0.0969557\pi$
$431$	5.91406	+	9.20246i	0.284870	+	0.443267i	−0.669098	+	0.743174i	$0.733319\pi$
$432$	−10.1575	+	23.0036i	−0.488704	+	1.10676i
$433$	−19.8983	+	30.9624i	−0.956252	+	1.48796i	−0.0854384	+	0.996343i	$0.527229\pi$
$433$	−19.8983	+	30.9624i	−0.956252	+	1.48796i	−0.870813	+	0.491614i	$0.836407\pi$
$434$	27.1469	+	4.62702i	1.30309	+	0.222104i
$435$	9.90722	−	1.46689i	0.475015	−	0.0703318i
$436$	−0.357044			−0.0170993
$437$	18.3269	−	4.17429i	0.876694	−	0.199683i
$438$	−1.88666	−	4.08576i	−0.0901479	−	0.195225i
$439$	1.42069	−	4.83844i	0.0678060	−	0.230926i	−0.918617	−	0.395148i	$-0.870693\pi$
$439$	1.42069	−	4.83844i	0.0678060	−	0.230926i	0.986423	+	0.164222i	$0.0525114\pi$
$440$	13.3743	−	15.4348i	0.637596	−	0.735825i
$441$	3.89288	−	20.6360i	0.185375	−	0.982668i
$442$	3.31667	−	23.0679i	0.157758	−	1.09723i
$443$	0.489932	+	0.762349i	0.0232774	+	0.0362203i	0.852697	−	0.522405i	$-0.174965\pi$
$443$	0.489932	+	0.762349i	0.0232774	+	0.0362203i	−0.829420	+	0.558626i	$0.811329\pi$
$444$	−1.72321	+	2.00562i	−0.0817798	+	0.0951827i
$445$	15.8835	+	18.3305i	0.752948	+	0.868949i
$446$	1.65071	+	11.4810i	0.0781636	+	0.543640i
$447$	−0.0536283	−	12.7848i	−0.00253653	−	0.604702i
$448$	8.56061	+	7.81691i	0.404451	+	0.369314i
$449$	5.57247	+	18.9781i	0.262981	+	0.895632i	0.980070	+	0.198650i	$0.0636558\pi$
$449$	5.57247	+	18.9781i	0.262981	+	0.895632i	−0.717089	+	0.696981i	$0.754526\pi$
$450$	46.5083	−	21.7130i	2.19242	−	1.02356i
$451$	−13.9401	+	2.00428i	−0.656413	+	0.0943780i
$452$	4.97933	−	4.31461i	0.234208	−	0.202942i
$453$	−25.7926	+	30.0198i	−1.21184	+	1.41045i
$454$	5.72038	+	8.90109i	0.268471	+	0.417749i
$455$	7.96025	+	18.7037i	0.373182	+	0.876841i
$456$	−2.11804	+	15.1832i	−0.0991864	+	0.711016i
$457$	−21.3038	+	24.5858i	−0.996547	+	1.15008i	−0.00787784	+	0.999969i	$0.502508\pi$
$457$	−21.3038	+	24.5858i	−0.996547	+	1.15008i	−0.988670	+	0.150108i	$0.952038\pi$
$458$	−14.1356	−	4.15058i	−0.660513	−	0.193944i
$459$	37.1980	+	10.4157i	1.73625	+	0.486163i
$460$	11.3185	−	0.920500i	0.527729	−	0.0429185i
$461$	6.06769			0.282600			0.141300	−	0.989967i	$-0.454872\pi$
$461$	6.06769			0.282600			0.141300	+	0.989967i	$0.454872\pi$
$462$	13.0186	−	10.7923i	0.605678	−	0.502103i
$463$	22.1809	−	25.5981i	1.03083	−	1.18965i	0.0492159	−	0.998788i	$-0.484328\pi$
$463$	22.1809	−	25.5981i	1.03083	−	1.18965i	0.981618	−	0.190857i	$-0.0611268\pi$
$464$	−3.82889	+	5.95786i	−0.177752	+	0.276587i
$465$	−12.6255	−	42.3406i	−0.585492	−	1.96350i
$466$	26.7017	−	17.1601i	1.23693	−	0.794928i
$467$	−1.89678	−	4.15338i	−0.0877727	−	0.192195i	0.860655	−	0.509188i	$-0.170054\pi$
$467$	−1.89678	−	4.15338i	−0.0877727	−	0.192195i	−0.948428	+	0.316993i	$0.897327\pi$
$468$	−0.0293270	−	3.49567i	−0.00135564	−	0.161587i
$469$	17.9310	−	14.7382i	0.827975	−	0.680546i
$470$	15.2690	+	6.97313i	0.704308	+	0.321647i
$471$	−20.1370	+	17.5973i	−0.927865	+	0.810839i
$472$	−9.06635	−	30.8772i	−0.417313	−	1.42124i
$473$	7.92057	+	3.61720i	0.364188	+	0.166319i
$474$	19.2686	+	29.7077i	0.885035	+	1.36452i
$475$	31.4329	−	27.2368i	1.44224	−	1.24971i
$476$	−6.62839	+	9.74672i	−0.303812	+	0.446740i
$477$	−15.9247	−	2.15343i	−0.729144	−	0.0985990i
$478$	0.383449	−	2.66695i	0.0175386	−	0.121983i
$479$	−20.7002	−	13.3032i	−0.945816	−	0.607839i	−0.0257778	−	0.999668i	$-0.508206\pi$
$479$	−20.7002	−	13.3032i	−0.945816	−	0.607839i	−0.920038	+	0.391829i	$0.871843\pi$
$480$	−6.24453	+	21.6017i	−0.285022	+	0.985978i
$481$	−1.39555	+	4.75282i	−0.0636318	+	0.216710i
$482$	−6.65676			−0.303207
$483$	−21.9007	−	1.83249i	−0.996518	−	0.0833813i
$484$	−3.45257			−0.156935
$485$	−4.29330	+	14.6216i	−0.194949	+	0.663934i
$486$	24.9459	+	3.05419i	1.13157	+	0.138541i
$487$	14.9737	+	9.62299i	0.678522	+	0.436060i	0.833989	−	0.551782i	$-0.186052\pi$
$487$	14.9737	+	9.62299i	0.678522	+	0.436060i	−0.155467	+	0.987841i	$0.549688\pi$
$488$	−4.63702	+	32.2512i	−0.209908	+	1.45994i
$489$	−28.3097	−	18.0262i	−1.28021	−	0.815174i
$490$	2.31965	−	44.5313i	0.104791	−	2.01172i
$491$	−11.4454	+	9.91745i	−0.516521	+	0.447568i	−0.873698	−	0.486468i	$-0.838285\pi$
$491$	−11.4454	+	9.91745i	−0.516521	+	0.447568i	0.357177	+	0.934037i	$0.383739\pi$
$492$	5.35837	−	3.47546i	0.241574	−	0.156686i
$493$	9.89611	+	4.51940i	0.445698	+	0.203544i
$494$	−3.46153	−	11.7889i	−0.155742	−	0.530407i
$495$	−24.7729	−	11.0632i	−1.11346	−	0.497253i
$496$	28.4199	+	12.9789i	1.27609	+	0.582771i
$497$	9.87400	+	12.0130i	0.442910	+	0.538859i
$498$	10.4926	+	4.73872i	0.470185	+	0.212347i
$499$	−9.37653	−	20.5317i	−0.419751	−	0.919127i	−0.994880	−	0.101064i	$-0.967775\pi$
$499$	−9.37653	−	20.5317i	−0.419751	−	0.919127i	0.575129	−	0.818063i	$-0.304952\pi$
$500$	11.1791	−	7.18435i	0.499943	−	0.321294i
$501$	−18.7342	+	5.58632i	−0.836983	+	0.249579i
$502$	9.79140	−	15.2357i	0.437011	−	0.680003i
$503$	−11.8191	+	13.6400i	−0.526987	+	0.608176i	−0.955366	−	0.295423i	$-0.904539\pi$
$503$	−11.8191	+	13.6400i	−0.526987	+	0.608176i	0.428379	+	0.903599i	$0.359085\pi$
$504$	7.73246	−	16.1710i	0.344431	−	0.720311i
$505$	−39.5594			−1.76037
$506$	−12.6352	−	12.3912i	−0.561703	−	0.550857i
$507$	6.69420	+	14.4970i	0.297300	+	0.643835i
$508$	−0.862593	−	0.253280i	−0.0382714	−	0.0112375i
$509$	7.26808	−	8.38782i	0.322152	−	0.371783i	−0.571455	−	0.820633i	$-0.693621\pi$
$509$	7.26808	−	8.38782i	0.322152	−	0.371783i	0.893607	+	0.448850i	$0.148166\pi$
$510$	81.2382	+	11.3327i	3.59729	+	0.501820i
$511$	1.66977	+	3.92334i	0.0738662	+	0.173558i
$512$	3.22050	+	5.01119i	0.142327	+	0.221465i
$513$	20.1199	−	3.15171i	0.888315	−	0.139151i
$514$	2.27065	−	1.96753i	0.100154	−	0.0867839i
$515$	12.0211	−	1.72838i	0.529715	−	0.0761615i
$516$	−3.94875	+	0.0165638i	−0.173834	+	0.000729180i
$517$	−1.69919	−	5.78690i	−0.0747301	−	0.254507i
$518$	7.32727	−	8.02438i	0.321942	−	0.352571i
$519$	1.35855	−	0.00569871i	0.0596339	−	0.000250146i
$520$	2.46920	+	17.1737i	0.108282	+	0.753115i
$521$	10.6478	+	12.2883i	0.466490	+	0.538359i	0.939432	−	0.342735i	$-0.111353\pi$
$521$	10.6478	+	12.2883i	0.466490	+	0.538359i	−0.472942	+	0.881094i	$0.656808\pi$
$522$	6.80789	+	1.93709i	0.297973	+	0.0847842i
$523$	2.77927	+	4.32462i	0.121529	+	0.189103i	0.896688	−	0.442664i	$-0.145967\pi$
$523$	2.77927	+	4.32462i	0.121529	+	0.189103i	−0.775159	+	0.631767i	$0.782330\pi$
$524$	0.421444	−	2.93121i	0.0184109	−	0.128050i
$525$	−44.6663	+	19.2316i	−1.94940	+	0.839335i
$526$	−0.564849	+	0.651870i	−0.0246286	+	0.0284229i
$527$	13.5216	−	46.0504i	0.589011	−	2.00599i
$528$	17.4180	−	8.04299i	0.758020	−	0.350026i
$529$	0.448403	+	22.9956i	0.0194958	+	0.999810i
$530$	−34.1226			−1.48219
$531$	−35.7686	+	23.4134i	−1.55222	+	1.01605i
$532$	−1.04411	+	6.12583i	−0.0452679	+	0.265589i
$533$	6.46845	−	10.0651i	0.280180	−	0.435968i
$534$	4.89831	+	16.4269i	0.211971	+	0.710862i
$535$	−2.72753	−	4.24412i	−0.117922	−	0.183490i
$536$	18.0212	−	8.22999i	0.778395	−	0.355481i
$537$	−15.9284	−	7.19366i	−0.687361	−	0.310429i
$538$	−38.4343	+	5.52602i	−1.65702	+	0.238244i
$539$	−12.6379	+	9.84799i	−0.544353	+	0.424183i
$540$	12.3028	−	0.154827i	0.529429	−	0.00666267i
$541$	23.7024	−	6.95965i	1.01904	−	0.299219i	0.270796	−	0.962637i	$-0.412713\pi$
$541$	23.7024	−	6.95965i	1.01904	−	0.299219i	0.748249	+	0.663418i	$0.230895\pi$
$542$	−0.998620	+	2.18667i	−0.0428944	+	0.0939257i
$543$	−12.0932	−	18.6449i	−0.518967	−	0.800129i
$544$	−18.4600	+	15.9957i	−0.791465	+	0.685808i
$545$	−0.977928	−	2.14136i	−0.0418898	−	0.0917259i
$546$	−0.313539	+	14.3625i	−0.0134182	+	0.614658i
$547$	−0.0951187	+	0.661565i	−0.00406698	+	0.0282865i	−0.991754	−	0.128157i	$-0.959094\pi$
$547$	−0.0951187	+	0.661565i	−0.00406698	+	0.0282865i	0.987687	+	0.156444i	$0.0500029\pi$
$548$	−1.80049	+	2.80161i	−0.0769129	+	0.119679i
$549$	42.7906	−	6.51922i	1.82626	−	0.278234i
$550$	−37.5735	−	11.0326i	−1.60214	−	0.470431i
$551$	5.73559			0.244344
$552$	−17.6657	−	6.30981i	−0.751901	−	0.268563i
$553$	−17.3976	−	28.6857i	−0.739819	−	1.21984i
$554$	9.52070	−	32.4245i	0.404496	−	1.37759i
$555$	−16.7485	−	4.84158i	−0.710933	−	0.205514i
$556$	−3.49553	+	5.43915i	−0.148243	+	0.230671i
$557$	−32.9057	−	4.73112i	−1.39426	−	0.200464i	−0.596100	−	0.802911i	$-0.703284\pi$
$557$	−32.9057	−	4.73112i	−1.39426	−	0.200464i	−0.798159	+	0.602446i	$0.794193\pi$
$558$	4.18442	−	30.9440i	0.177141	−	1.30996i
$559$	−6.72883	+	3.07295i	−0.284599	+	0.129972i
$560$	15.5113	−	48.1543i	0.655471	−	2.03489i
$561$	−16.0374	−	24.7260i	−0.677099	−	1.04393i
$562$	−1.58659	+	3.47414i	−0.0669261	+	0.146548i
$563$	5.98132	−	1.75627i	0.252083	−	0.0740181i	−0.153250	−	0.988187i	$-0.548974\pi$
$563$	5.98132	−	1.75627i	0.252083	−	0.0740181i	0.405332	+	0.914169i	$0.367156\pi$
$564$	1.79978	+	2.05954i	0.0757844	+	0.0867222i
$565$	39.5149	+	18.0459i	1.66241	+	0.759195i
$566$	2.25747	+	15.7011i	0.0948886	+	0.659964i
$567$	−23.5371	−	3.60647i	−0.988464	−	0.151458i
$568$	5.51376	+	12.0735i	0.231352	+	0.506591i
$569$	11.5554	+	17.9805i	0.484426	+	0.753782i	0.994317	−	0.106457i	$-0.0339506\pi$
$569$	11.5554	+	17.9805i	0.484426	+	0.753782i	−0.509891	+	0.860239i	$0.670314\pi$
$570$	41.4407	−	12.3571i	1.73576	−	0.517584i
$571$	−33.5143	−	21.5383i	−1.40253	−	0.901352i	−0.402629	−	0.915363i	$-0.631903\pi$
$571$	−33.5143	−	21.5383i	−1.40253	−	0.901352i	−0.999902	+	0.0140118i	$0.995540\pi$
$572$	−1.74658	+	2.01566i	−0.0730280	+	0.0842788i
$573$	33.1487	−	4.90807i	1.38481	−	0.205038i
$574$	−22.4416	+	13.6106i	−0.936694	+	0.568094i
$575$	24.8250	+	44.4284i	1.03527	+	1.85279i
$576$	8.52434	−	10.0060i	0.355181	−	0.416917i
$577$	−6.29451	+	21.4371i	−0.262044	+	0.892439i	0.718399	+	0.695632i	$0.244875\pi$
$577$	−6.29451	+	21.4371i	−0.262044	+	0.892439i	−0.980442	+	0.196807i	$0.936943\pi$
$578$	46.6246	+	40.4005i	1.93933	+	1.68044i
$579$	0.669582	−	4.79989i	0.0278269	−	0.199476i
$580$	3.42992	+	0.493148i	0.142420	+	0.0204769i
$581$	−9.80118	−	4.78806i	−0.406621	−	0.198642i
$582$	−7.01856	+	8.16884i	−0.290929	+	0.338609i
$583$	8.02878	+	9.26570i	0.332518	+	0.383746i
$584$	0.517947	+	3.60240i	0.0214328	+	0.149068i
$585$	20.8849	−	9.75037i	0.863483	−	0.403128i
$586$	−5.07557	−	17.2858i	−0.209670	−	0.714070i
$587$	0.0377979	−	0.0110985i	0.00156008	−	0.000458082i	−0.280952	−	0.959722i	$-0.590650\pi$
$587$	0.0377979	−	0.0110985i	0.00156008	−	0.000458082i	0.282513	+	0.959264i	$0.408832\pi$
$588$	3.33101	−	6.45731i	0.137368	−	0.266295i
$589$	−3.60099	−	25.0454i	−0.148376	−	1.03198i
$590$	−68.6042	+	59.4459i	−2.82439	+	2.44735i
$591$	−0.0970132	−	0.0833525i	−0.00399059	−	0.00342866i
$592$	10.3713	−	6.66522i	0.426257	−	0.273939i
$593$	−2.69979	+	18.7774i	−0.110867	+	0.771097i	0.856213	+	0.516623i	$0.172811\pi$
$593$	−2.69979	+	18.7774i	−0.110867	+	0.771097i	−0.967080	+	0.254474i	$0.918098\pi$
$594$	−12.7379	−	14.3319i	−0.522644	−	0.588045i
$595$	−76.6106	−	13.0578i	−3.14073	−	0.535317i
$596$	1.24624	−	4.24431i	0.0510480	−	0.173854i
$597$	17.0713	−	7.88291i	0.698682	−	0.322626i
$598$	14.9850	−	1.21868i	0.612781	−	0.0498356i
$599$			9.75438i			0.398553i	0.979943	+	0.199277i	$0.0638592\pi$
$599$			9.75438i			0.398553i	−0.979943	+	0.199277i	$0.936141\pi$
$600$	−41.0610	+	6.07959i	−1.67631	+	0.248198i
$601$	23.1540	+	20.0631i	0.944471	+	0.818389i	0.983511	−	0.180849i	$-0.0578844\pi$
$601$	23.1540	+	20.0631i	0.944471	+	0.818389i	−0.0390396	+	0.999238i	$0.512430\pi$
$602$	16.2220	+	0.422218i	0.661160	+	0.0172083i
$603$	−17.4011	−	19.7448i	−0.708629	−	0.804072i
$604$	−11.5200	+	7.40343i	−0.468741	+	0.301241i
$605$	−9.45645	−	20.7067i	−0.384459	−	0.841848i
$606$	−25.4800	−	11.5074i	−1.03506	−	0.467457i
$607$	−44.7437	+	6.43317i	−1.81609	+	0.261114i	−0.964687	−	0.263398i	$-0.915157\pi$
$607$	−44.7437	+	6.43317i	−1.81609	+	0.261114i	−0.851403	+	0.524512i	$0.824248\pi$
$608$	−5.34952	+	11.7138i	−0.216952	+	0.475058i
$609$	−6.39183	−	2.02936i	−0.259010	−	0.0822337i
$610$	88.1877	−	25.8943i	3.57062	−	1.04843i
$611$	4.66071	+	2.12848i	0.188552	+	0.0861090i
$612$	11.3038	+	7.13121i	0.456928	+	0.288262i
$613$	26.0111	+	30.0184i	1.05058	+	1.21243i	0.976576	+	0.215173i	$0.0690315\pi$
$613$	26.0111	+	30.0184i	1.05058	+	1.21243i	0.0740014	+	0.997258i	$0.476423\pi$
$614$	−4.01191	−	8.78485i	−0.161907	−	0.354528i
$615$	35.5203	+	22.6176i	1.43232	+	0.912029i
$616$	−12.5832	+	5.35541i	−0.506993	+	0.215775i
$617$	18.5417	−	28.8515i	0.746463	−	1.16152i	−0.235395	−	0.971900i	$-0.575638\pi$
$617$	18.5417	−	28.8515i	0.746463	−	1.16152i	0.981858	−	0.189619i	$-0.0607252\pi$
$618$	8.24553	+	2.38358i	0.331684	+	0.0958817i
$619$	−1.58338	+	5.39250i	−0.0636414	+	0.216743i	−0.985174	−	0.171558i	$-0.945120\pi$
$619$	−1.58338	+	5.39250i	−0.0636414	+	0.216743i	0.921533	+	0.388301i	$0.126938\pi$
$620$		−	15.2869i		−	0.613938i
$621$	−1.22226	+	24.8899i	−0.0490477	+	0.998796i
$622$		−	2.20874i		−	0.0885624i
$623$	−4.16864	−	15.6970i	−0.167013	−	0.628887i
$624$	−4.52622	+	15.6576i	−0.181194	+	0.626804i
$625$	29.0699	+	18.6821i	1.16279	+	0.747282i
$626$	0.425824	−	2.96167i	0.0170193	−	0.118372i
$627$	−13.1061	−	8.34533i	−0.523409	−	0.333281i
$628$	−8.41656	+	3.84372i	−0.335857	+	0.153381i
$629$	−12.4019	−	14.3126i	−0.494498	−	0.570681i
$630$	−50.5544	−	0.891482i	−2.01414	−	0.0355175i
$631$	−13.3365	+	29.2029i	−0.530919	+	1.16255i	0.434219	+	0.900807i	$0.357025\pi$
$631$	−13.3365	+	29.2029i	−0.530919	+	1.16255i	−0.965138	+	0.261743i	$0.915703\pi$
$632$	−8.06767	−	27.4759i	−0.320915	−	1.09293i
$633$	16.6665	+	19.0719i	0.662433	+	0.758040i
$634$	−6.40551	+	14.0261i	−0.254395	+	0.557048i
$635$	−0.843562	−	5.86710i	−0.0334757	−	0.232829i
$636$	−5.06719	−	2.28847i	−0.200927	−	0.0907436i
$637$	0.708049	−	13.5927i	0.0280539	−	0.538564i
$638$	−2.91958	−	4.54295i	−0.115587	−	0.179857i
$639$	13.2283	−	11.6581i	0.523302	−	0.461186i
$640$	29.1279	−	45.3238i	1.15138	−	1.79158i
$641$	−30.2329	−	26.1970i	−1.19413	−	1.03472i	−0.998539	−	0.0540323i	$-0.982793\pi$
$641$	−30.2329	−	26.1970i	−1.19413	−	1.03472i	−0.195589	−	0.980686i	$-0.562662\pi$
$642$	−0.522220	−	3.52703i	−0.0206104	−	0.139201i
$643$		−	39.3025i		−	1.54994i	−0.631998	−	0.774970i	$-0.717765\pi$
$643$		−	39.3025i		−	1.54994i	0.631998	−	0.774970i	$-0.282235\pi$
$644$	−7.08035	−	2.77289i	−0.279005	−	0.109267i
$645$	−10.9148	−	23.6372i	−0.429770	−	0.930714i
$646$	45.0717	+	13.2342i	1.77332	+	0.520695i
$647$	−18.5654	+	21.4256i	−0.729882	+	0.842329i	−0.992458	−	0.122582i	$-0.960883\pi$
$647$	−18.5654	+	21.4256i	−0.729882	+	0.842329i	0.262576	+	0.964911i	$0.415428\pi$
$648$	−18.6269	−	8.13175i	−0.731735	−	0.319445i
$649$	32.2840	+	4.64175i	1.26726	+	0.182204i
$650$	27.9866	−	17.9859i	1.09772	−	0.705464i
$651$	−4.84853	+	29.1851i	−0.190029	+	1.14385i
$652$	−7.60430	−	8.77583i	−0.297807	−	0.343688i
$653$	−10.0205	+	1.44073i	−0.392132	+	0.0563801i	−0.335561	−	0.942018i	$-0.608926\pi$
$653$	−10.0205	+	1.44073i	−0.392132	+	0.0563801i	−0.0565712	+	0.998399i	$0.518017\pi$
$654$	−0.00697874	−	1.66371i	−0.000272890	−	0.0650562i
$655$	18.7342	−	5.50085i	0.732004	−	0.214936i
$656$	−28.5713	+	8.38928i	−1.11552	+	0.327546i
$657$	4.38088	−	2.04527i	0.170914	−	0.0797936i
$658$	−7.13710	−	8.68323i	−0.278233	−	0.338508i
$659$	28.4236	−	24.6292i	1.10723	−	0.959417i	0.107830	−	0.994169i	$-0.465610\pi$
$659$	28.4236	−	24.6292i	1.10723	−	0.959417i	0.999396	+	0.0347525i	$0.0110643\pi$
$660$	−7.12003	−	6.11744i	−0.277147	−	0.238121i
$661$	−3.82150	−	5.94637i	−0.148639	−	0.231287i	0.758948	−	0.651152i	$-0.225714\pi$
$661$	−3.82150	−	5.94637i	−0.148639	−	0.231287i	−0.907587	+	0.419865i	$0.862077\pi$
$662$	6.74261	+	0.969440i	0.262059	+	0.0376784i
$663$	24.7971	+	3.45918i	0.963040	+	0.134344i
$664$	−7.03656	−	6.09721i	−0.273071	−	0.236618i
$665$	−39.5993	+	10.5164i	−1.53560	+	0.407807i
$666$	−9.37925	−	7.99039i	−0.363438	−	0.309621i
$667$	−1.42493	+	6.87216i	−0.0551735	+	0.266091i
$668$	−6.76393			−0.261704
$669$	−12.3267	+	1.82512i	−0.476578	+	0.0705632i
$670$	−42.2350	−	36.5968i	−1.63168	−	1.41386i
$671$	−27.7812	−	17.8539i	−1.07248	−	0.689243i
$672$	10.1061	−	11.1613i	0.389853	−	0.430557i
$673$	8.07464	−	5.18925i	0.311254	−	0.200031i	−0.375682	−	0.926749i	$-0.622591\pi$
$673$	8.07464	−	5.18925i	0.311254	−	0.200031i	0.686936	+	0.726718i	$0.258955\pi$
$674$	−6.15449	+	2.81066i	−0.237062	+	0.108263i
$675$	23.5361	+	49.8666i	0.905906	+	1.91936i
$676$	0.786260	+	5.46856i	0.0302408	+	0.210329i
$677$	−9.56671	+	20.9482i	−0.367679	+	0.805104i	0.631870	+	0.775074i	$0.282288\pi$
$677$	−9.56671	+	20.9482i	−0.367679	+	0.805104i	−0.999549	+	0.0300299i	$0.990440\pi$
$678$	20.2020	+	23.1177i	0.775854	+	0.887831i
$679$	6.88062	−	7.53524i	0.264054	−	0.289176i
$680$	−60.3397	−	27.5562i	−2.31392	−	1.05673i
$681$	−9.53677	+	6.18559i	−0.365450	+	0.237032i
$682$	−18.0045	+	15.6010i	−0.689429	+	0.597394i
$683$	−42.2552	+	19.2973i	−1.61685	+	0.738391i	−0.998857	−	0.0477933i	$-0.984781\pi$
$683$	−42.2552	+	19.2973i	−1.61685	+	0.738391i	−0.617993	+	0.786184i	$0.712054\pi$
$684$	6.98266	+	0.944235i	0.266989	+	0.0361037i
$685$	−21.7340	−	3.12488i	−0.830415	−	0.119396i
$686$	−14.4842	+	26.1105i	−0.553008	+	0.996905i
$687$	4.39532	−	15.2047i	0.167692	−	0.580097i
$688$	17.6649	+	5.18689i	0.673468	+	0.197748i
$689$	−10.4156			−0.396802
$690$	4.51047	+	52.7227i	0.171710	+	2.00712i
$691$			15.4525i			0.587841i	0.955830	+	0.293920i	$0.0949600\pi$
$691$			15.4525i			0.587841i	−0.955830	+	0.293920i	$0.905040\pi$
$692$	0.451013	+	0.132429i	0.0171449	+	0.00503421i
$693$	11.6530	+	13.9374i	0.442660	+	0.529437i
$694$	−29.0493	−	18.6688i	−1.10270	−	0.708659i
$695$	−42.1953	−	6.06677i	−1.60056	−	0.230126i
$696$	−4.82839	−	3.07447i	−0.183019	−	0.116538i
$697$	19.0022	+	41.6091i	0.719761	+	1.57606i
$698$	−30.6856	−	35.4131i	−1.16147	−	1.34041i
$699$	18.5557	+	28.6086i	0.701841	+	1.08208i
$700$	−16.7112	+	1.96042i	−0.631624	+	0.0740969i
$701$	8.77256	+	29.8766i	0.331335	+	1.12842i	0.941742	+	0.336336i	$0.109188\pi$
$701$	8.77256	+	29.8766i	0.331335	+	1.12842i	−0.610407	+	0.792088i	$0.708994\pi$
$702$	16.2881	−	0.204980i	0.614756	−	0.00773648i
$703$	−9.08209	−	4.14765i	−0.342537	−	0.156432i
$704$	−9.92665	+	1.42724i	−0.374125	+	0.0537910i
$705$	−7.42251	+	16.4351i	−0.279548	+	0.618983i
$706$	39.7903	−	18.1716i	1.49753	−	0.683898i
$707$	23.8010	+	11.6272i	0.895128	+	0.437287i
$708$	−14.1745	+	4.22667i	−0.532710	+	0.158848i
$709$	−1.09759	−	0.705378i	−0.0412209	−	0.0264910i	0.519868	−	0.854247i	$-0.325981\pi$
$709$	−1.09759	−	0.705378i	−0.0412209	−	0.0264910i	−0.561089	+	0.827756i	$0.689617\pi$
$710$	24.5184	−	28.2958i	0.920160	−	1.06192i
$711$	−31.8286	+	20.8343i	−1.19366	+	0.781349i
$712$		−	13.8626i		−	0.519523i
$713$	30.9031	+	1.90763i	1.15733	+	0.0714414i
$714$	−45.5461	−	30.6957i	−1.70452	−	1.14876i
$715$	−16.8727	−	4.95426i	−0.631002	−	0.185279i
$716$	−4.57007	−	3.95999i	−0.170792	−	0.147992i
$717$	2.86686	+	0.399926i	0.107065	+	0.0149355i
$718$	2.44896	−	17.0329i	0.0913943	−	0.635662i
$719$	1.60029	−	1.02845i	0.0596808	−	0.0383546i	−0.510460	−	0.859901i	$-0.670525\pi$
$719$	1.60029	−	1.02845i	0.0596808	−	0.0383546i	0.570141	+	0.821547i	$0.306889\pi$
$720$	−55.1747	−	15.6992i	−2.05624	−	0.585074i
$721$	−7.74053	−	2.49335i	−0.288273	−	0.0928571i
$722$	−5.80741	+	0.834980i	−0.216130	+	0.0310747i
$723$	−0.0299980	−	7.15144i	−0.00111564	−	0.265965i
$724$	−2.16627	−	7.37764i	−0.0805088	−	0.274188i
$725$	4.37529	+	14.9009i	0.162494	+	0.553404i
$726$	−0.0674836	−	16.0879i	−0.00250455	−	0.597077i
$727$	−23.8393	+	3.42757i	−0.884149	+	0.127121i	−0.569407	−	0.822056i	$-0.692827\pi$
$727$	−23.8393	+	3.42757i	−0.884149	+	0.127121i	−0.314742	+	0.949177i	$0.601918\pi$
$728$	3.56205	−	11.0583i	0.132018	−	0.409847i
$729$	−3.16874	+	26.8134i	−0.117361	+	0.993089i
$730$	8.63654	−	5.55037i	0.319653	−	0.205428i
$731$	4.02490	−	27.9938i	0.148866	−	1.03539i
$732$	14.8324	+	2.06912i	0.548223	+	0.0764768i
$733$	13.4275	+	11.6350i	0.495954	+	0.429747i	0.866582	−	0.499035i	$-0.166312\pi$
$733$	13.4275	+	11.6350i	0.495954	+	0.429747i	−0.370628	+	0.928782i	$0.620857\pi$
$734$	6.83405	+	2.00666i	0.252249	+	0.0740671i
$735$	47.8510	+	2.29135i	1.76501	+	0.0845178i
$736$	−12.7060	−	9.31972i	−0.468350	−	0.343530i
$737$			20.0795i			0.739637i
$738$	16.2993	+	24.9004i	0.599984	+	0.916595i
$739$	−1.61667	+	1.86574i	−0.0594702	+	0.0686323i	−0.784705	−	0.619869i	$-0.787186\pi$
$739$	−1.61667	+	1.86574i	−0.0594702	+	0.0686323i	0.725235	+	0.688501i	$0.241731\pi$
$740$	−5.07453	−	3.26121i	−0.186544	−	0.119884i
$741$	12.6494	−	3.77189i	0.464686	−	0.138564i
$742$	20.5299	+	10.0292i	0.753676	+	0.368185i
$743$	30.2153	−	13.7989i	1.10849	−	0.506231i	0.224849	−	0.974394i	$-0.427811\pi$
$743$	30.2153	−	13.7989i	1.10849	−	0.506231i	0.883643	+	0.468162i	$0.155084\pi$
$744$	−10.3938	+	23.0142i	−0.381055	+	0.843742i
$745$	28.8685	−	4.15067i	1.05766	−	0.152069i
$746$	−15.9109	−	7.26625i	−0.582538	−	0.266036i
$747$	−5.04359	+	11.2937i	−0.184535	+	0.413215i
$748$	−2.87281	−	9.78389i	−0.105040	−	0.357734i
$749$	0.393599	+	3.35515i	0.0143818	+	0.122595i
$750$	33.6953	+	51.9505i	1.23038	+	1.89696i
$751$	−2.04295	−	2.35768i	−0.0745481	−	0.0860331i	0.717250	−	0.696816i	$-0.245400\pi$
$751$	−2.04295	−	2.35768i	−0.0745481	−	0.0860331i	−0.791798	+	0.610783i	$0.790855\pi$
$752$	−5.29743	−	11.5997i	−0.193177	−	0.422999i
$753$	16.4120	+	10.4504i	0.598088	+	0.380832i
$754$	4.54099	+	0.652896i	0.165373	+	0.0237771i
$755$	−75.9546	−	48.8131i	−2.76427	−	1.77649i
$756$	−7.44751	−	3.52287i	−0.270863	−	0.128125i
$757$	33.4008	+	9.80737i	1.21397	+	0.356455i	0.825180	−	0.564870i	$-0.191074\pi$
$757$	33.4008	+	9.80737i	1.21397	+	0.356455i	0.388794	+	0.921325i	$0.372892\pi$
$758$		−	29.1998i		−	1.06058i
$759$	13.2551	−	13.6300i	0.481130	−	0.494737i
$760$	−34.9717			−1.26856
$761$	33.3233	+	9.78461i	1.20797	+	0.354692i	0.822895	−	0.568194i	$-0.192358\pi$
$761$	33.3233	+	9.78461i	1.20797	+	0.354692i	0.385074	+	0.922886i	$0.374176\pi$
$762$	1.16334	−	4.02436i	0.0421435	−	0.145787i
$763$	−0.0410137	+	1.57578i	−0.00148479	+	0.0570472i
$764$	11.4762	+	1.65003i	0.415195	+	0.0596961i
$765$	−11.8087	+	87.3262i	−0.426946	+	3.15729i
$766$	50.3123	−	22.9769i	1.81786	−	0.830187i
$767$	−20.9407	+	18.1453i	−0.756126	+	0.655187i
$768$	19.2111	−	12.4604i	0.693221	−	0.449626i
$769$	−10.5939	−	4.83806i	−0.382024	−	0.174465i	0.215141	−	0.976583i	$-0.430979\pi$
$769$	−10.5939	−	4.83806i	−0.382024	−	0.174465i	−0.597165	+	0.802118i	$0.703706\pi$
$770$	28.4868	+	26.0120i	1.02659	+	0.937409i
$771$	2.12397	+	2.43052i	0.0764930	+	0.0875330i
$772$	0.696570	−	1.52528i	0.0250701	−	0.0548959i
$773$	−2.38754	−	16.6057i	−0.0858737	−	0.597265i	−0.986634	−	0.162949i	$-0.947899\pi$
$773$	−2.38754	−	16.6057i	−0.0858737	−	0.597265i	0.900761	−	0.434316i	$-0.143010\pi$
$774$	−0.154364	−	18.3996i	−0.00554849	−	0.661360i
$775$	62.3202	−	28.4607i	2.23861	−	1.02234i
$776$	7.32705	−	4.70881i	0.263026	−	0.169037i
$777$	8.65371	+	7.83562i	0.310450	+	0.281101i
$778$	−35.1301	−	22.5767i	−1.25947	−	0.809415i
$779$	18.2255	+	15.7925i	0.652997	+	0.565825i
$780$	7.88871	−	1.16802i	0.282461	−	0.0418218i
$781$	−13.4525			−0.481367
$782$	−27.0542	+	50.7153i	−0.967458	+	1.81358i
$783$	−2.05036	+	7.32253i	−0.0732740	+	0.261686i
$784$	−23.4858	+	24.4131i	−0.838778	+	0.871895i
$785$	−46.1052	−	39.9504i	−1.64557	−	1.42589i
$786$	13.6667	+	1.90650i	0.487476	+	0.0680026i
$787$	25.4439	+	3.65828i	0.906977	+	0.130404i	0.579988	−	0.814625i	$-0.303057\pi$
$787$	25.4439	+	3.65828i	0.906977	+	0.130404i	0.326988	+	0.945028i	$0.393966\pi$
$788$	−0.0239252	−	0.0372284i	−0.000852301	−	0.00132621i
$789$	−0.702857	−	0.603886i	−0.0250224	−	0.0214989i
$790$	−61.0473	+	52.8978i	−2.17196	+	1.88202i
$791$	−18.4702	−	22.4715i	−0.656725	−	0.798993i
$792$	6.55975	+	14.0507i	0.233090	+	0.499269i
$793$	26.9184	−	7.90396i	0.955901	−	0.280678i
$794$	44.0502	−	12.9343i	1.56328	−	0.459021i
$795$	−0.153770	−	36.6583i	−0.00545367	−	1.30014i
$796$	6.43963	−	0.925879i	0.228247	−	0.0328169i
$797$	18.8976	+	21.8090i	0.669386	+	0.772513i	0.984280	−	0.176614i	$-0.0565144\pi$
$797$	18.8976	+	21.8090i	0.669386	+	0.772513i	−0.314894	+	0.949127i	$0.601969\pi$
$798$	−28.5648	−	4.74548i	−1.01118	−	0.167988i
$799$	−16.4795	+	10.5907i	−0.583004	+	0.374674i
$800$	−34.5129	−	4.96220i	−1.22021	−	0.175440i
$801$	−17.6256	+	5.33635i	−0.622768	+	0.188550i
$802$	20.2440	−	23.3628i	0.714840	−	0.824970i
$803$	−3.53926	−	1.03922i	−0.124898	−	0.0366733i
$804$	−3.81746	−	8.26713i	−0.134632	−	0.291559i
$805$	−2.76239	−	50.0591i	−0.0973615	−	1.76435i
$806$		−	20.2389i		−	0.712885i
$807$	−6.10987	−	41.2656i	−0.215078	−	1.45262i
$808$	17.0874	+	14.8063i	0.601134	+	0.520885i
$809$	12.1987	−	18.9815i	0.428883	−	0.667354i	−0.557807	−	0.829971i	$-0.688357\pi$
$809$	12.1987	−	18.9815i	0.428883	−	0.667354i	0.986689	+	0.162616i	$0.0519933\pi$
$810$	0.961911	+	57.3241i	0.0337981	+	2.01417i
$811$	−10.2140	−	15.8934i	−0.358664	−	0.558092i	0.614293	−	0.789078i	$-0.289441\pi$
$811$	−10.2140	−	15.8934i	−0.358664	−	0.558092i	−0.972957	+	0.230986i	$0.925805\pi$
$812$	−1.91867	−	1.30482i	−0.0673321	−	0.0457901i
$813$	−2.35367	−	1.06298i	−0.0825468	−	0.0372802i
$814$	1.33784	+	9.30486i	0.0468911	+	0.326135i
$815$	31.8050	−	69.6432i	1.11408	−	2.43950i
$816$	−41.0039	−	46.9218i	−1.43542	−	1.64259i
$817$	−4.20069	−	14.3062i	−0.146964	−	0.500512i
$818$	−1.86695	+	4.08804i	−0.0652763	+	0.142935i
$819$	−15.4312	−	0.272116i	−0.539210	−	0.00950849i
$820$	9.54114	+	11.0111i	0.333191	+	0.384523i
$821$	3.30448	−	1.50911i	0.115327	−	0.0526682i	−0.356916	−	0.934137i	$-0.616172\pi$
$821$	3.30448	−	1.50911i	0.115327	−	0.0526682i	0.472243	+	0.881468i	$0.343444\pi$
$822$	−13.0898	−	8.33492i	−0.456559	−	0.290714i
$823$	−5.21289	+	36.2565i	−0.181710	+	1.26382i	0.671008	+	0.741450i	$0.265862\pi$
$823$	−5.21289	+	36.2565i	−0.181710	+	1.26382i	−0.852718	+	0.522371i	$0.825048\pi$
$824$	−5.83935	−	3.75272i	−0.203423	−	0.130732i
$825$	11.6831	−	40.4154i	0.406754	−	1.40708i
$826$	58.7480	−	15.6017i	2.04410	−	0.542852i
$827$		−	2.23822i		−	0.0778305i	−0.999243	−	0.0389153i	$-0.987610\pi$
$827$		−	2.23822i		−	0.0778305i	0.999243	−	0.0389153i	$-0.0123902\pi$
$828$	−2.86610	+	8.13178i	−0.0996037	+	0.282599i
$829$			31.0778i			1.07938i	0.841865	+	0.539689i	$0.181458\pi$
$829$			31.0778i			1.07938i	−0.841865	+	0.539689i	$0.818542\pi$
$830$	−7.39941	+	25.2001i	−0.256837	+	0.874707i
$831$	34.8770	+	10.0821i	1.20987	+	0.349744i
$832$	4.60614	−	7.16730i	0.159689	−	0.248481i
$833$	42.2549	+	30.3735i	1.46405	+	1.05238i
$834$	−25.4130	−	16.1817i	−0.879981	−	0.560328i
$835$	−18.5261	−	40.5665i	−0.641122	−	1.40386i
$836$	−3.52045	−	4.06281i	−0.121757	−	0.140515i
$837$	33.2624	+	4.35593i	1.14972	+	0.150563i
$838$	27.9231	+	12.7520i	0.964587	+	0.440512i
$839$	−26.7655	+	7.85907i	−0.924049	+	0.271325i	−0.708943	−	0.705266i	$-0.750828\pi$
$839$	−26.7655	+	7.85907i	−0.924049	+	0.271325i	−0.215106	+	0.976591i	$0.569010\pi$
$840$	38.9730	+	12.3736i	1.34470	+	0.426930i
$841$	11.1574	−	24.4312i	0.384737	−	0.842457i
$842$	47.6641	−	6.85307i	1.64262	−	0.236172i
$843$	−3.73946	−	1.68883i	−0.128794	−	0.0581665i
$844$	3.64041	+	7.97138i	0.125308	+	0.274386i
$845$	−30.6440	+	19.6937i	−1.05419	+	0.677484i
$846$	−9.56161	+	8.42666i	−0.328735	+	0.289714i
$847$	−0.396597	+	15.2376i	−0.0136272	+	0.523572i
$848$	19.5910	+	16.9757i	0.672759	+	0.582949i
$849$	−16.8577	+	2.49598i	−0.578553	+	0.0856619i
$850$			127.190i			4.36259i
$851$	7.22588	−	9.85138i	0.247700	−	0.337701i
$852$	5.53865	−	2.55755i	0.189751	−	0.0876202i
$853$	11.6871	−	39.8025i	0.400158	−	1.36281i	−0.475430	−	0.879754i	$-0.657707\pi$
$853$	11.6871	−	39.8025i	0.400158	−	1.36281i	0.875588	−	0.483059i	$-0.160474\pi$
$854$	−60.6690	−	10.3406i	−2.07605	−	0.353850i
$855$	13.4622	+	44.4646i	0.460397	+	1.52066i
$856$	−0.410355	+	2.85408i	−0.0140257	+	0.0975506i
$857$	−23.8331	+	15.3166i	−0.814123	+	0.523205i	−0.880196	−	0.474610i	$-0.842589\pi$
$857$	−23.8331	+	15.3166i	−0.814123	+	0.523205i	0.0660737	+	0.997815i	$0.478953\pi$
$858$	−9.42645	−	8.09909i	−0.321814	−	0.276498i
$859$	−2.79686	+	2.42349i	−0.0954275	+	0.0826884i	−0.701268	−	0.712898i	$-0.747382\pi$
$859$	−2.79686	+	2.42349i	−0.0954275	+	0.0826884i	0.605841	+	0.795586i	$0.292837\pi$
$860$	−1.28199	−	8.91641i	−0.0437154	−	0.304047i
$861$	−14.7231	−	24.0479i	−0.501763	−	0.819552i
$862$	−16.9217	+	4.96867i	−0.576357	+	0.169234i
$863$	−4.42496	−	15.0700i	−0.150627	−	0.512990i	0.849260	−	0.527974i	$-0.177048\pi$
$863$	−4.42496	−	15.0700i	−0.150627	−	0.512990i	−0.999888	+	0.0149846i	$0.995230\pi$
$864$	−13.0425	−	11.0171i	−0.443714	−	0.374809i
$865$	0.441063	+	3.06766i	0.0149966	+	0.104304i
$866$	−38.8582	−	44.8447i	−1.32046	−	1.52389i
$867$	−43.1926	+	50.2715i	−1.46690	+	1.70731i
$868$	−4.49310	+	9.19740i	−0.152506	+	0.312180i
$869$	28.7279	+	4.13044i	0.974526	+	0.140116i
$870$	−2.23087	+	15.9920i	−0.0756336	+	0.542179i
$871$	−12.8918	−	11.1708i	−0.436822	−	0.378508i
$872$	−0.379062	+	1.29097i	−0.0128367	+	0.0437177i
$873$	−8.80752	−	7.50332i	−0.298089	−	0.253949i
$874$	−1.86709	+	30.2463i	−0.0631552	+	1.02310i
$875$	−30.4234	−	50.1632i	−1.02850	−	1.69582i
$876$	1.65476	−	0.245008i	0.0559092	−	0.00827804i
$877$	4.18196	−	4.82624i	0.141215	−	0.162970i	−0.680737	−	0.732528i	$-0.738340\pi$
$877$	4.18196	−	4.82624i	0.141215	−	0.162970i	0.821951	+	0.569558i	$0.192886\pi$
$878$	6.83938	+	4.39540i	0.230818	+	0.148338i
$879$	18.5475	−	5.53065i	0.625591	−	0.186544i
$880$	23.6617	+	36.8184i	0.797637	+	1.24115i
$881$	23.6193	+	51.7191i	0.795755	+	1.74246i	0.659390	+	0.751801i	$0.270815\pi$
$881$	23.6193	+	51.7191i	0.795755	+	1.74246i	0.136365	+	0.990659i	$0.456458\pi$
$882$	30.1541	+	15.3952i	1.01534	+	0.518383i
$883$	−4.06965	−	28.3050i	−0.136955	−	0.952541i	−0.936183	−	0.351513i	$-0.885667\pi$
$883$	−4.06965	−	28.3050i	−0.136955	−	0.952541i	0.799228	−	0.601028i	$-0.205242\pi$
$884$	7.87986	+	3.59861i	0.265028	+	0.121034i
$885$	−64.1726	−	73.4345i	−2.15714	−	2.46847i
$886$	−1.40183	+	0.411614i	−0.0470953	+	0.0138284i
$887$	−7.05187	+	15.4414i	−0.236779	+	0.518473i	−0.990299	−	0.138951i	$-0.955627\pi$
$887$	−7.05187	+	15.4414i	−0.236779	+	0.518473i	0.753521	+	0.657424i	$0.228354\pi$
$888$	5.42228	+	8.35992i	0.181960	+	0.280541i
$889$	−1.21692	+	3.77789i	−0.0408141	+	0.126706i
$890$	−35.5704	+	16.2444i	−1.19232	+	0.544515i
$891$	15.3395	−	13.7491i	0.513894	−	0.460612i
$892$	−4.26756	−	0.613582i	−0.142888	−	0.0205443i
$893$	−5.58349	+	8.68808i	−0.186844	+	0.290736i
$894$	19.8015	+	5.72413i	0.662260	+	0.191443i
$895$	11.2327	−	38.2552i	0.375469	−	1.27873i
$896$	−30.8463	+	18.7079i	−1.03050	+	0.624988i
$897$	1.37677	+	16.0930i	0.0459691	+	0.537331i
$898$	−31.8887			−1.06414
$899$	9.06516	+	2.66177i	0.302340	+	0.0887751i
$900$	2.87351	+	18.8610i	0.0957835	+	0.628701i
$901$	21.5290	−	33.4997i	0.717234	−	1.11604i
$902$	3.23136	−	22.4746i	0.107592	−	0.748322i
$903$	−0.380491	+	17.4294i	−0.0126619	+	0.580014i
$904$	−10.3140	−	22.5845i	−0.343038	−	0.751149i
$905$	38.3139	−	33.1992i	1.27360	−	1.10358i
$906$	−34.7228	−	53.5346i	−1.15359	−	1.77857i
$907$	−4.52283	+	9.90362i	−0.150178	+	0.328844i	−0.969737	−	0.244150i	$-0.921491\pi$
$907$	−4.52283	+	9.90362i	−0.150178	+	0.328844i	0.819559	+	0.572994i	$0.194218\pi$
$908$	−3.77363	+	1.10804i	−0.125232	+	0.0367715i
$909$	12.2477	−	27.4254i	0.406232	−	0.909642i
$910$	−32.5488	+	3.81835i	−1.07898	+	0.126577i
$911$	45.7113	−	6.57229i	1.51448	−	0.217750i	0.665591	−	0.746317i	$-0.268179\pi$
$911$	45.7113	−	6.57229i	1.51448	−	0.217750i	0.848892	+	0.528567i	$0.177270\pi$
$912$	−29.9402	−	13.5217i	−0.991419	−	0.447750i
$913$	8.58388	−	3.92013i	0.284085	−	0.129737i
$914$	−28.3558	−	44.1225i	−0.937927	−	1.45944i
$915$	28.2159	+	94.6245i	0.932790	+	3.12819i
$916$	2.96061	−	4.60681i	0.0978214	−	0.152213i
$917$	−12.8882	−	2.19671i	−0.425607	−	0.0725419i
$918$	−33.0082	+	52.8114i	−1.08943	+	1.74303i
$919$	−50.2381			−1.65720			−0.828601	−	0.559840i	$-0.810863\pi$
$919$	−50.2381			−1.65720			−0.828601	+	0.559840i	$0.810863\pi$
$920$	8.68824	−	41.9017i	0.286443	−	1.38146i
$921$	9.41960	−	4.34963i	0.310386	−	0.143325i
$922$	−2.75605	+	9.38623i	−0.0907655	+	0.309119i
$923$	7.48400	−	8.63699i	0.246339	−	0.284290i
$924$	2.48575	+	5.77327i	0.0817751	+	0.189927i
$925$	3.84735	−	26.7589i	0.126500	−	0.879828i
$926$	29.5233	+	45.9392i	0.970196	+	1.50966i
$927$	−2.52355	+	8.86901i	−0.0828844	+	0.291297i
$928$	−3.14879	−	3.63390i	−0.103364	−	0.119289i
$929$	5.43248	+	37.7838i	0.178234	+	1.23964i	0.860847	+	0.508865i	$0.169935\pi$
$929$	5.43248	+	37.7838i	0.178234	+	1.23964i	−0.682613	+	0.730780i	$0.739156\pi$
$930$	71.2322	−	0.298797i	2.33580	−	0.00979793i
$931$	26.9159	+	5.31176i	0.882134	+	0.174086i
$932$	3.32392	+	11.3202i	0.108878	+	0.370806i
$933$	2.37288	−	0.00995346i	0.0776845	−	0.000325862i
$934$	7.28650	−	1.04764i	0.238422	−	0.0342798i
$935$	50.8102	−	44.0273i	1.66167	−	1.43985i
$936$	−12.6705	−	3.60520i	−0.414147	−	0.117840i
$937$	−31.5027	−	49.0191i	−1.02915	−	1.60138i	−0.772643	−	0.634841i	$-0.781065\pi$
$937$	−31.5027	−	49.0191i	−1.02915	−	1.60138i	−0.256505	−	0.966543i	$-0.582571\pi$
$938$	14.6543	+	34.4321i	0.478478	+	1.12425i
$939$	3.18368	+	0.444121i	0.103895	+	0.0144933i
$940$	−4.08597	+	4.71546i	−0.133270	+	0.153801i
$941$	42.6511	+	12.5235i	1.39039	+	0.408255i	0.889372	−	0.457184i	$-0.151142\pi$
$941$	42.6511	+	12.5235i	1.39039	+	0.408255i	0.501015	+	0.865439i	$0.332960\pi$
$942$	−18.0750	−	39.1434i	−0.588915	−	1.27536i
$943$	−23.4499	+	17.9137i	−0.763632	+	0.583350i
$944$	68.9620			2.24452
$945$	0.729912	−	54.3152i	0.0237440	−	1.76687i
$946$	−9.19318	+	10.6095i	−0.298896	+	0.344944i
$947$	−9.28510	+	14.4479i	−0.301725	+	0.469493i	−0.958700	−	0.284419i	$-0.908199\pi$
$947$	−9.28510	+	14.4479i	−0.301725	+	0.469493i	0.656975	+	0.753912i	$0.271836\pi$
$948$	−12.6131	+	3.76109i	−0.409655	+	0.122154i
$949$	2.63621	−	1.69419i	0.0855751	−	0.0549958i
$950$	27.8558	+	60.9957i	0.903761	+	1.97896i
$951$	−15.0973	−	6.81831i	−0.489563	−	0.221099i
$952$	28.2042	+	34.3141i	0.914102	+	1.11213i
$953$	−17.3080	−	7.90430i	−0.560661	−	0.256045i	0.114865	−	0.993381i	$-0.463356\pi$
$953$	−17.3080	−	7.90430i	−0.560661	−	0.256045i	−0.675526	+	0.737336i	$0.736084\pi$
$954$	10.5645	−	23.6562i	0.342038	−	0.765897i
$955$	21.5368	+	73.3478i	0.696916	+	2.37348i
$956$	0.911012	+	0.416045i	0.0294642	+	0.0134559i
$957$	4.86739	−	3.15701i	0.157340	−	0.102052i
$958$	29.9814	−	25.9790i	0.968655	−	0.839344i
$959$	12.1578	+	8.26811i	0.392597	+	0.266991i
$960$	25.2938	+	16.1058i	0.816354	+	0.519813i
$961$	1.51991	−	10.5712i	0.0490294	−	0.341007i
$962$	−6.71835	−	4.31762i	−0.216608	−	0.139206i
$963$	3.78678	−	0.576922i	0.122027	−	0.0185910i
$964$	0.697109	−	2.37414i	0.0224524	−	0.0764658i
$965$	11.0557			0.355895
$966$	12.7824	−	33.0463i	0.411267	−	1.06325i
$967$	−0.336156			−0.0108100			−0.00540502	−	0.999985i	$-0.501720\pi$
$967$	−0.336156			−0.0108100			−0.00540502	+	0.999985i	$0.501720\pi$
$968$	−3.66549	+	12.4835i	−0.117813	+	0.401235i
$969$	−14.0146	+	48.4807i	−0.450214	+	1.55743i
$970$	−20.6684	−	13.2828i	−0.663622	−	0.426484i
$971$	2.50655	−	17.4335i	0.0804391	−	0.559467i	−0.909252	−	0.416247i	$-0.863345\pi$
$971$	2.50655	−	17.4335i	0.0804391	−	0.559467i	0.989691	−	0.143220i	$-0.0457456\pi$
$972$	−3.70166	+	8.57711i	−0.118731	+	0.275111i
$973$	23.6037	+	16.0520i	0.756700	+	0.514604i
$974$	−21.6873	+	18.7922i	−0.694906	+	0.602139i
$975$	19.4486	+	29.9853i	0.622853	+	0.960297i
$976$	−63.5140	−	29.0059i	−2.03303	−	0.928455i
$977$	−5.73157	−	19.5199i	−0.183369	−	0.624498i	−0.998948	−	0.0458526i	$-0.985400\pi$
$977$	−5.73157	−	19.5199i	−0.183369	−	0.624498i	0.815579	−	0.578646i	$-0.196419\pi$
$978$	40.7439	−	35.6051i	1.30285	−	1.13853i
$979$	12.7805	+	5.83664i	0.408465	+	0.186540i
$980$	15.6392	+	5.49072i	0.499576	+	0.175394i
$981$	1.78731	−	0.0149947i	0.0570645	−	0.000478744i
$982$	−10.1428	−	22.2097i	−0.323671	−	0.708741i
$983$	31.5001	−	20.2439i	1.00470	−	0.645680i	0.0686819	−	0.997639i	$-0.478121\pi$
$983$	31.5001	−	20.2439i	1.00470	−	0.645680i	0.936015	+	0.351959i	$0.114484\pi$
$984$	−6.87745	−	23.0641i	−0.219245	−	0.735256i
$985$	0.157746	−	0.245458i	0.00502621	−	0.00782094i
$986$	−11.4861	+	13.2557i	−0.365793	+	0.422148i
$987$	9.29634	−	7.70660i	0.295906	−	0.245304i
$988$	4.56701			0.145296
$989$	18.1848	−	1.47891i	0.578243	−	0.0470268i
$990$	28.3661	−	33.2966i	0.901535	−	1.05824i
$991$	−14.6390	−	4.29841i	−0.465025	−	0.136544i	0.0408230	−	0.999166i	$-0.487002\pi$
$991$	−14.6390	−	4.29841i	−0.465025	−	0.136544i	−0.505848	+	0.862623i	$0.668820\pi$
$992$	−13.8911	+	16.0312i	−0.441043	+	0.508991i
$993$	−1.01110	+	7.24803i	−0.0320862	+	0.230009i
$994$	−23.0682	+	9.81777i	−0.731678	+	0.311401i
$995$	23.1908	+	36.0856i	0.735198	+	1.14399i
$996$	−2.78887	+	3.24594i	−0.0883689	+	0.102852i
$997$	40.8953	−	35.4360i	1.29517	−	1.12227i	0.309988	−	0.950741i	$-0.399675\pi$
$997$	40.8953	−	35.4360i	1.29517	−	1.12227i	0.985179	−	0.171528i	$-0.0548704\pi$
$998$	36.0199	−	5.17889i	1.14019	−	0.163935i
$999$	8.54191	−	10.1123i	0.270254	−	0.319937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.v.a.41.17	✓	600
3.2	odd	2	inner	483.2.v.a.41.43	yes	600
7.6	odd	2	inner	483.2.v.a.41.18	yes	600
21.20	even	2	inner	483.2.v.a.41.44	yes	600
23.9	even	11	inner	483.2.v.a.377.44	yes	600
69.32	odd	22	inner	483.2.v.a.377.18	yes	600
161.55	odd	22	inner	483.2.v.a.377.43	yes	600
483.377	even	22	inner	483.2.v.a.377.17	yes	600

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.17	✓	600	1.1	even	1	trivial
483.2.v.a.41.18	yes	600	7.6	odd	2	inner
483.2.v.a.41.43	yes	600	3.2	odd	2	inner
483.2.v.a.41.44	yes	600	21.20	even	2	inner
483.2.v.a.377.17	yes	600	483.377	even	22	inner
483.2.v.a.377.18	yes	600	69.32	odd	22	inner
483.2.v.a.377.43	yes	600	161.55	odd	22	inner
483.2.v.a.377.44	yes	600	23.9	even	11	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.v (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.454217 + 1.54692i) q^{2} +(-1.66392 - 0.481000i) q^{3} +(-0.504143 - 0.323993i) q^{4} +(0.562316 - 3.91099i) q^{5} +(1.49985 - 2.35548i) q^{6} +(-1.48783 + 2.18778i) q^{7} +(-1.70670 + 1.47886i) q^{8} +(2.53728 + 1.60069i) q^{9} +(5.79458 + 2.64630i) q^{10} +(-0.644839 - 2.19612i) q^{11} +(0.683015 + 0.781592i) q^{12} +(1.76874 + 0.807755i) q^{13} +(-2.70852 - 3.29528i) q^{14} +(-2.81684 + 6.23711i) q^{15} +(-2.01037 - 4.40209i) q^{16} +(-6.25396 + 4.01918i) q^{17} +(-3.62862 + 3.19791i) q^{18} +(-2.11893 + 3.29712i) q^{19} +(-1.55062 + 1.78951i) q^{20} +(3.52795 - 2.92465i) q^{21} +3.69012 q^{22} +(-3.42406 - 3.35795i) q^{23} +(3.55115 - 1.63979i) q^{24} +(-10.1822 - 2.98976i) q^{25} +(-2.05292 + 2.36920i) q^{26} +(-3.45190 - 3.88386i) q^{27} +(1.45890 - 0.620907i) q^{28} +(-0.791187 - 1.23111i) q^{29} +(-8.36887 - 7.19042i) q^{30} +(-4.87912 + 4.22778i) q^{31} +(3.25223 - 0.467600i) q^{32} +(0.0166292 + 3.96434i) q^{33} +(-3.37669 - 11.5000i) q^{34} +(7.71975 + 7.04910i) q^{35} +(-0.760538 - 1.62904i) q^{36} +(0.362545 + 2.52156i) q^{37} +(-4.13793 - 4.77542i) q^{38} +(-2.55451 - 2.19480i) q^{39} +(4.82411 + 7.50647i) q^{40} +(0.875678 - 6.09047i) q^{41} +(2.92174 + 6.78588i) q^{42} +(-2.49130 + 2.87511i) q^{43} +(-0.386437 + 1.31608i) q^{44} +(7.68705 - 9.02318i) q^{45} +(6.74974 - 3.77152i) q^{46} +2.63505 q^{47} +(1.22769 + 8.29173i) q^{48} +(-2.57274 - 6.51007i) q^{49} +(9.24985 - 14.3930i) q^{50} +(12.3393 - 3.67945i) q^{51} +(-0.629989 - 0.980282i) q^{52} +(-4.87250 + 2.22520i) q^{53} +(7.57594 - 3.57570i) q^{54} +(-8.95161 + 1.28705i) q^{55} +(-0.696148 - 5.93417i) q^{56} +(5.11165 - 4.46695i) q^{57} +(2.26380 - 0.664712i) q^{58} +(-5.91969 + 12.9623i) q^{59} +(3.44087 - 2.23176i) q^{60} +(10.9041 - 9.44842i) q^{61} +(-4.32386 - 9.46794i) q^{62} +(-7.27699 + 3.16944i) q^{63} +(0.623565 - 4.33699i) q^{64} +(4.15371 - 6.46330i) q^{65} +(-6.14008 - 1.77495i) q^{66} +(-8.41744 - 2.47158i) q^{67} +4.45508 q^{68} +(4.08220 + 7.23434i) q^{69} +(-14.4108 + 8.74002i) q^{70} +(1.65586 - 5.63935i) q^{71} +(-6.69757 + 1.02039i) q^{72} +(0.871295 - 1.35576i) q^{73} +(-4.06533 - 0.584506i) q^{74} +(15.5043 + 9.87236i) q^{75} +(2.13649 - 0.975701i) q^{76} +(5.76403 + 1.85668i) q^{77} +(4.55549 - 2.95471i) q^{78} +(-5.26762 + 11.5345i) q^{79} +(-18.3470 + 5.38717i) q^{80} +(3.87556 + 8.12281i) q^{81} +(9.02373 + 4.12100i) q^{82} +(0.586751 + 4.08094i) q^{83} +(-2.72616 + 0.331409i) q^{84} +(12.2023 + 26.7192i) q^{85} +(-3.31598 - 5.15976i) q^{86} +(0.724310 + 2.42903i) q^{87} +(4.34830 + 2.79449i) q^{88} +(-4.01990 + 4.63921i) q^{89} +(10.4666 + 15.9897i) q^{90} +(-4.39876 + 2.66780i) q^{91} +(0.638266 + 2.80226i) q^{92} +(10.1520 - 4.68785i) q^{93} +(-1.19689 + 4.07622i) q^{94} +(11.7035 + 10.1411i) q^{95} +(-5.63638 - 0.786272i) q^{96} +(-3.81751 - 0.548876i) q^{97} +(11.2391 - 1.02283i) q^{98} +(1.87918 - 6.60436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 600 q + 20 q^{4} - 18 q^{7} - 26 q^{9} - 14 q^{15} - 116 q^{16} - 46 q^{18} - 50 q^{21} - 104 q^{22} - 88 q^{25} - 26 q^{28} + 26 q^{30} - 26 q^{36} - 56 q^{37} - 14 q^{39} + 5 q^{42} - 40 q^{43} - 44 q^{46}+ \cdots - 250 q^{99}+O(q^{100}) \) 600 * q + 20 * q^4 - 18 * q^7 - 26 * q^9 - 14 * q^15 - 116 * q^16 - 46 * q^18 - 50 * q^21 - 104 * q^22 - 88 * q^25 - 26 * q^28 + 26 * q^30 - 26 * q^36 - 56 * q^37 - 14 * q^39 + 5 * q^42 - 40 * q^43 - 44 * q^46 + 74 * q^49 + 14 * q^51 - 66 * q^57 - 76 * q^58 + 22 * q^60 - 44 * q^63 + 44 * q^64 - 92 * q^67 - 92 * q^70 + 178 * q^72 - 182 * q^78 + 68 * q^79 + 106 * q^81 - 87 * q^84 - 4 * q^85 - 220 * q^88 - 24 * q^91 - 44 * q^93 - 250 * q^99

Introduction

L-functions

Modular forms

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