LMFDB - Embedded newform 483.2.v.a.377.43

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			377.43
Character	$\chi$	$=$	483.377
Dual form			483.2.v.a.41.43

$q$-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} +(-0.712905 + 1.57853i) q^{3} +(-0.504143 + 0.323993i) q^{4} +(-0.562316 - 3.91099i) q^{5} +(-2.76568 - 0.385811i) q^{6} +(-1.48783 - 2.18778i) q^{7} +(1.70670 + 1.47886i) q^{8} +(-1.98353 - 2.25069i) q^{9} +(5.79458 - 2.64630i) q^{10} +(0.644839 - 2.19612i) q^{11} +(-0.152028 - 1.02678i) q^{12} +(1.76874 - 0.807755i) q^{13} +(2.70852 - 3.29528i) q^{14} +(6.57451 + 1.90053i) q^{15} +(-2.01037 + 4.40209i) q^{16} +(6.25396 + 4.01918i) q^{17} +(2.58068 - 4.09067i) q^{18} +(-2.11893 - 3.29712i) q^{19} +(1.55062 + 1.78951i) q^{20} +(4.51416 - 0.788909i) 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} +(4.96686 - 1.52655i) q^{27} +(1.45890 + 0.620907i) q^{28} +(0.791187 - 1.23111i) q^{29} +(0.0462820 + 11.0335i) q^{30} +(-4.87912 - 4.22778i) q^{31} +(-3.25223 - 0.467600i) q^{32} +(3.00694 + 2.58352i) q^{33} +(-3.37669 + 11.5000i) q^{34} +(-7.71975 + 7.04910i) q^{35} +(1.72919 + 0.492018i) q^{36} +(0.362545 - 2.52156i) q^{37} +(4.13793 - 4.77542i) q^{38} +(0.0141271 + 3.36786i) q^{39} +(4.82411 - 7.50647i) q^{40} +(-0.875678 - 6.09047i) q^{41} +(3.27079 + 6.62471i) 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} +(-5.51565 - 6.31170i) q^{48} +(-2.57274 + 6.51007i) q^{49} +(-9.24985 - 14.3930i) q^{50} +(-10.8029 + 7.00680i) q^{51} +(-0.629989 + 0.980282i) q^{52} +(4.87250 + 2.22520i) q^{53} +(4.61748 + 6.98995i) q^{54} +(-8.95161 - 1.28705i) q^{55} +(0.696148 - 5.93417i) q^{56} +(6.71521 - 0.994269i) q^{57} +(2.26380 + 0.664712i) q^{58} +(5.91969 + 12.9623i) q^{59} +(-3.93025 + 1.17196i) q^{60} +(10.9041 + 9.44842i) q^{61} +(4.32386 - 9.46794i) q^{62} +(-1.97285 + 7.68816i) q^{63} +(0.623565 + 4.33699i) q^{64} +(-4.15371 - 6.46330i) q^{65} +(-2.63070 + 5.82498i) q^{66} +(-8.41744 + 2.47158i) q^{67} -4.45508 q^{68} +(2.85960 + 7.79889i) q^{69} +(-14.4108 - 8.74002i) q^{70} +(-1.65586 - 5.63935i) q^{71} +(-0.0568357 - 6.77462i) q^{72} +(0.871295 + 1.35576i) q^{73} +(4.06533 - 0.584506i) q^{74} +(2.53950 - 18.2043i) q^{75} +(2.13649 + 0.975701i) q^{76} +(-5.76403 + 1.85668i) q^{77} +(-5.20340 + 1.55159i) q^{78} +(-5.26762 - 11.5345i) q^{79} +(18.3470 + 5.38717i) q^{80} +(-1.13119 + 8.92863i) q^{81} +(9.02373 - 4.12100i) q^{82} +(-0.586751 + 4.08094i) q^{83} +(-2.02018 + 1.86028i) q^{84} +(12.2023 - 26.7192i) q^{85} +(3.31598 - 5.15976i) q^{86} +(1.37931 + 2.12658i) q^{87} +(4.34830 - 2.79449i) q^{88} +(4.01990 + 4.63921i) q^{89} +(-17.4497 - 7.79277i) 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} +(3.05665 - 4.80040i) q^{96} +(-3.81751 + 0.548876i) q^{97} +(-11.2391 - 1.02283i) q^{98} +(-6.22184 + 2.90475i) 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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{11}\right)$

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	0.948947	+	0.315437i	$0.102151\pi$
$2$	0.454217	+	1.54692i	0.321180	+	1.09384i	−0.627767	+	0.778401i	$0.716031\pi$
$3$	−0.712905	+	1.57853i	−0.411596	+	0.911367i
$3$	−0.712905	+	1.57853i	−0.411596	+	0.911367i
$4$	−0.504143	+	0.323993i	−0.252072	+	0.161997i
$5$	−0.562316	−	3.91099i	−0.251475	−	1.74905i	−0.589369	−	0.807864i	$-0.700623\pi$
$5$	−0.562316	−	3.91099i	−0.251475	−	1.74905i	0.337893	−	0.941184i	$-0.390286\pi$
$6$	−2.76568	−	0.385811i	−1.12908	−	0.157507i
$7$	−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
$9$	−1.98353	−	2.25069i	−0.661178	−	0.750229i
$10$	5.79458	−	2.64630i	1.83241	−	0.836832i
$11$	0.644839	−	2.19612i	0.194426	−	0.662155i	−0.803350	−	0.595507i	$-0.796951\pi$
$11$	0.644839	−	2.19612i	0.194426	−	0.662155i	0.997777	−	0.0666483i	$-0.0212306\pi$
$12$	−0.152028	−	1.02678i	−0.0438867	−	0.296407i
$13$	1.76874	−	0.807755i	0.490559	−	0.224031i	−0.154748	−	0.987954i	$-0.549457\pi$
$13$	1.76874	−	0.807755i	0.490559	−	0.224031i	0.645307	+	0.763923i	$0.276729\pi$
$14$	2.70852	−	3.29528i	0.723883	−	0.880700i
$15$	6.57451	+	1.90053i	1.69753	+	0.490715i
$16$	−2.01037	+	4.40209i	−0.502592	+	1.10052i
$17$	6.25396	+	4.01918i	1.51681	+	0.974794i	0.992363	+	0.123350i	$0.0393637\pi$
$17$	6.25396	+	4.01918i	1.51681	+	0.974794i	0.524445	+	0.851444i	$0.324273\pi$
$18$	2.58068	−	4.09067i	0.608272	−	0.964180i
$19$	−2.11893	−	3.29712i	−0.486116	−	0.756411i	0.508386	−	0.861129i	$-0.330242\pi$
$19$	−2.11893	−	3.29712i	−0.486116	−	0.756411i	−0.994502	+	0.104718i	$0.966606\pi$
$20$	1.55062	+	1.78951i	0.346730	+	0.400147i
$21$	4.51416	−	0.788909i	0.985070	−	0.172154i
$22$	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
$27$	4.96686	−	1.52655i	0.955872	−	0.293784i
$28$	1.45890	+	0.620907i	0.275707	+	0.117340i
$29$	0.791187	−	1.23111i	0.146920	−	0.228612i	−0.759992	−	0.649933i	$-0.774797\pi$
$29$	0.791187	−	1.23111i	0.146920	−	0.228612i	0.906912	+	0.421321i	$0.138433\pi$
$30$	0.0462820	+	11.0335i	0.00844990	+	2.01443i
$31$	−4.87912	−	4.22778i	−0.876316	−	0.759332i	0.0954117	−	0.995438i	$-0.469583\pi$
$31$	−4.87912	−	4.22778i	−0.876316	−	0.759332i	−0.971727	+	0.236106i	$0.924129\pi$
$32$	−3.25223	−	0.467600i	−0.574919	−	0.0826608i
$33$	3.00694	+	2.58352i	0.523441	+	0.449734i
$34$	−3.37669	+	11.5000i	−0.579098	+	1.97223i
$35$	−7.71975	+	7.04910i	−1.30488	+	1.19152i
$36$	1.72919	+	0.492018i	0.288199	+	0.0820029i
$37$	0.362545	−	2.52156i	0.0596021	−	0.414542i	−0.938076	−	0.346431i	$-0.887394\pi$
$37$	0.362545	−	2.52156i	0.0596021	−	0.414542i	0.997678	−	0.0681112i	$-0.0216973\pi$
$38$	4.13793	−	4.77542i	0.671260	−	0.774676i
$39$	0.0141271	+	3.36786i	0.00226215	+	0.539289i
$40$	4.82411	−	7.50647i	0.762759	−	1.18688i
$41$	−0.875678	−	6.09047i	−0.136758	−	0.951172i	−0.936460	−	0.350775i	$-0.885918\pi$
$41$	−0.875678	−	6.09047i	−0.136758	−	0.951172i	0.799702	−	0.600397i	$-0.204991\pi$
$42$	3.27079	+	6.62471i	0.504693	+	1.02221i
$43$	−2.49130	−	2.87511i	−0.379919	−	0.438450i	0.533296	−	0.845929i	$-0.320953\pi$
$43$	−2.49130	−	2.87511i	−0.379919	−	0.438450i	−0.913215	+	0.407479i	$0.866408\pi$
$44$	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	$-0.561556\pi$
$47$	−2.63505			−0.384362			−0.192181	+	0.981359i	$0.561556\pi$
$48$	−5.51565	−	6.31170i	−0.796115	−	0.911016i
$49$	−2.57274	+	6.51007i	−0.367534	+	0.930010i
$50$	−9.24985	−	14.3930i	−1.30813	−	2.03548i
$51$	−10.8029	+	7.00680i	−1.51271	+	0.981148i
$52$	−0.629989	+	0.980282i	−0.0873638	+	0.135941i
$53$	4.87250	+	2.22520i	0.669289	+	0.305654i	0.720926	−	0.693012i	$-0.243717\pi$
$53$	4.87250	+	2.22520i	0.669289	+	0.305654i	−0.0516370	+	0.998666i	$0.516444\pi$
$54$	4.61748	+	6.98995i	0.628359	+	0.951211i
$55$	−8.95161	−	1.28705i	−1.20703	−	0.173545i
$56$	0.696148	−	5.93417i	0.0930267	−	0.792986i
$57$	6.71521	−	0.994269i	0.889451	−	0.131694i
$58$	2.26380	+	0.664712i	0.297252	+	0.0872810i
$59$	5.91969	+	12.9623i	0.770678	+	1.68755i	0.725154	+	0.688586i	$0.241768\pi$
$59$	5.91969	+	12.9623i	0.770678	+	1.68755i	0.0455235	+	0.998963i	$0.485504\pi$
$60$	−3.93025	+	1.17196i	−0.507393	+	0.151299i
$61$	10.9041	+	9.44842i	1.39612	+	1.20975i	0.949001	+	0.315272i	$0.102096\pi$
$61$	10.9041	+	9.44842i	1.39612	+	1.20975i	0.447120	+	0.894474i	$0.352450\pi$
$62$	4.32386	−	9.46794i	0.549131	−	1.20243i
$63$	−1.97285	+	7.68816i	−0.248555	+	0.968618i
$64$	0.623565	+	4.33699i	0.0779456	+	0.542124i
$65$	−4.15371	−	6.46330i	−0.515204	−	0.801673i
$66$	−2.63070	+	5.82498i	−0.323817	+	0.717005i
$67$	−8.41744	+	2.47158i	−1.02835	+	0.301952i	−0.752041	−	0.659116i	$-0.770931\pi$
$67$	−8.41744	+	2.47158i	−1.02835	+	0.301952i	−0.276312	+	0.961068i	$0.589112\pi$
$68$	−4.45508			−0.540258
$69$	2.85960	+	7.79889i	0.344255	+	0.938876i
$70$	−14.4108	−	8.74002i	−1.72243	−	1.04463i
$71$	−1.65586	−	5.63935i	−0.196515	−	0.669268i	−0.997505	−	0.0705909i	$-0.977512\pi$
$71$	−1.65586	−	5.63935i	−0.196515	−	0.669268i	0.800991	−	0.598677i	$-0.204307\pi$
$72$	−0.0568357	−	6.77462i	−0.00669816	−	0.798396i
$73$	0.871295	+	1.35576i	0.101977	+	0.158680i	0.888493	−	0.458891i	$-0.151753\pi$
$73$	0.871295	+	1.35576i	0.101977	+	0.158680i	−0.786515	+	0.617571i	$0.788117\pi$
$74$	4.06533	−	0.584506i	0.472584	−	0.0679474i
$75$	2.53950	−	18.2043i	0.293236	−	2.10206i
$76$	2.13649	+	0.975701i	0.245072	+	0.111921i
$77$	−5.76403	+	1.85668i	−0.656872	+	0.211589i
$78$	−5.20340	+	1.55159i	−0.589169	+	0.175683i
$79$	−5.26762	−	11.5345i	−0.592653	−	1.29773i	−0.933825	−	0.357729i	$-0.883551\pi$
$79$	−5.26762	−	11.5345i	−0.592653	−	1.29773i	0.341172	−	0.940001i	$-0.389176\pi$
$80$	18.3470	+	5.38717i	2.05126	+	0.602304i
$81$	−1.13119	+	8.92863i	−0.125688	+	0.992070i
$82$	9.02373	−	4.12100i	0.996505	−	0.455088i
$83$	−0.586751	+	4.08094i	−0.0644043	+	0.447942i	0.931947	+	0.362595i	$0.118109\pi$
$83$	−0.586751	+	4.08094i	−0.0644043	+	0.447942i	−0.996351	+	0.0853471i	$0.972800\pi$
$84$	−2.02018	+	1.86028i	−0.220420	+	0.202973i
$85$	12.2023	−	26.7192i	1.32352	−	2.89811i
$86$	3.31598	−	5.15976i	0.357571	−	0.556391i
$87$	1.37931	+	2.12658i	0.147877	+	0.227993i
$88$	4.34830	−	2.79449i	0.463531	−	0.297893i
$89$	4.01990	+	4.63921i	0.426108	+	0.491755i	0.927688	−	0.373356i	$-0.121793\pi$
$89$	4.01990	+	4.63921i	0.426108	+	0.491755i	−0.501580	+	0.865111i	$0.667248\pi$
$90$	−17.4497	−	7.79277i	−1.83936	−	0.821430i
$91$	−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
$96$	3.05665	−	4.80040i	0.311968	−	0.489939i
$97$	−3.81751	+	0.548876i	−0.387610	+	0.0557299i	−0.333365	−	0.942798i	$-0.608184\pi$
$97$	−3.81751	+	0.548876i	−0.387610	+	0.0557299i	−0.0542447	+	0.998528i	$0.517275\pi$
$98$	−11.2391	−	1.02283i	−1.13532	−	0.103322i
$99$	−6.22184	+	2.90475i	−0.625319	+	0.291938i
$100$	4.16462	−	4.80623i	0.416462	−	0.480623i
$101$	1.42485	−	9.91007i	0.141778	−	0.986089i	−0.787396	−	0.616447i	$-0.788571\pi$
$101$	1.42485	−	9.91007i	0.141778	−	0.986089i	0.929174	−	0.369642i	$-0.120520\pi$
$102$	−15.7458	−	13.5286i	−1.55907	−	1.33953i
$103$	0.865956	−	2.94918i	0.0853252	−	0.290591i	−0.905766	−	0.423779i	$-0.860703\pi$
$103$	0.865956	−	2.94918i	0.0853252	−	0.290591i	0.991091	+	0.133188i	$0.0425215\pi$
$104$	4.21326	+	1.23712i	0.413144	+	0.121310i
$105$	−5.62380	−	17.2112i	−0.548826	−	1.67964i
$106$	−1.22903	+	8.54809i	−0.119374	+	0.830264i
$107$	−0.964960	−	0.836142i	−0.0932862	−	0.0808329i	0.606969	−	0.794725i	$-0.292385\pi$
$107$	−0.964960	−	0.836142i	−0.0932862	−	0.0808329i	−0.700255	+	0.713892i	$0.746931\pi$
$108$	−2.00942	+	2.37883i	−0.193356	+	0.228903i
$109$	0.501212	+	0.322109i	0.0480074	+	0.0308525i	0.564424	−	0.825485i	$-0.309098\pi$
$109$	0.501212	+	0.322109i	0.0480074	+	0.0308525i	−0.516417	+	0.856337i	$0.672735\pi$
$110$	−2.07501	−	14.4320i	−0.197845	−	1.37604i
$111$	3.72190	+	2.36992i	0.353267	+	0.224943i
$112$	12.6219	−	2.15132i	1.19266	−	0.203280i
$113$	3.09744	+	10.5489i	0.291382	+	0.992358i	0.966930	+	0.255041i	$0.0820891\pi$
$113$	3.09744	+	10.5489i	0.291382	+	0.992358i	−0.675548	+	0.737316i	$0.736093\pi$
$114$	4.58821	+	9.93628i	0.429726	+	0.930618i
$115$	−15.0583	−	11.5033i	−1.40419	−	1.07268i
$116$			0.876995i			0.0814270i
$117$	−5.32635	−	2.37866i	−0.492421	−	0.219908i
$118$	−17.3628	+	15.0450i	−1.59838	+	1.38500i
$119$	−0.511755	−	19.6621i	−0.0469125	−	1.80242i
$120$	8.41007	+	12.9664i	0.767731	+	1.18367i
$121$	4.84666	+	3.11476i	0.440606	+	0.283160i
$122$	−9.66315	+	21.1593i	−0.874860	+	1.91568i
$123$	10.2383	+	2.95964i	0.923156	+	0.266862i
$124$	3.82955	+	0.550606i	0.343903	+	0.0494459i
$125$	9.21158	+	20.1705i	0.823908	+	1.80411i
$126$	−12.7891	+	0.440258i	−1.13934	+	0.0392213i
$127$	1.43939	+	0.422643i	0.127725	+	0.0375035i	0.344970	−	0.938614i	$-0.387889\pi$
$127$	1.43939	+	0.422643i	0.127725	+	0.0375035i	−0.217245	+	0.976117i	$0.569707\pi$
$128$	−12.4033	+	5.66438i	−1.09630	+	0.500665i
$129$	6.31451	−	1.88291i	0.555962	−	0.165781i
$130$	8.11152	−	9.36120i	0.711428	−	0.821031i
$131$	−2.05279	+	4.49498i	−0.179353	+	0.392729i	−0.977861	−	0.209256i	$-0.932896\pi$
$131$	−2.05279	+	4.49498i	−0.179353	+	0.392729i	0.798508	+	0.601984i	$0.205623\pi$
$132$	−2.35297	−	0.328238i	−0.204800	−	0.0285695i
$133$	−4.06076	+	9.54129i	−0.352112	+	0.827335i
$134$	−7.64669	−	11.8985i	−0.660573	−	1.02787i
$135$	−8.76325	−	18.5669i	−0.754221	−	1.59799i
$136$	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	$-0.0762921\pi$
$138$	−10.7654	+	7.96596i	−0.916411	+	0.678107i
$139$			10.7889i			0.915102i	0.889183	+	0.457551i	$0.151273\pi$
$139$			10.7889i			0.915102i	−0.889183	+	0.457551i	$0.848727\pi$
$140$	1.60800	−	6.05490i	0.135901	−	0.511733i
$141$	1.87854	−	4.15952i	0.158202	−	0.350295i
$142$	7.97151	−	5.12298i	0.668954	−	0.429911i
$143$	−0.633376	−	4.40523i	−0.0529656	−	0.368384i
$144$	13.8954	−	4.20699i	1.15795	−	0.350582i
$145$	−5.25976	−	2.40205i	−0.436799	−	0.199480i
$146$	−1.70150	+	1.96363i	−0.140817	+	0.162512i
$147$	−8.44225	−	8.70221i	−0.696305	−	0.717746i
$148$	0.634193	+	1.38869i	0.0521303	+	0.114150i
$149$	−2.07958	+	7.08239i	−0.170366	+	0.580212i	0.829402	+	0.558652i	$0.188681\pi$
$149$	−2.07958	+	7.08239i	−0.170366	+	0.580212i	−0.999768	+	0.0215597i	$0.993137\pi$
$150$	29.3141	−	4.34032i	2.39349	−	0.354386i
$151$	9.49248	+	20.7856i	0.772487	+	1.69151i	0.721100	+	0.692831i	$0.243637\pi$
$151$	9.49248	+	20.7856i	0.772487	+	1.69151i	0.0513872	+	0.998679i	$0.483636\pi$
$152$	1.25961	−	8.76079i	0.102168	−	0.710594i
$153$	−3.35903	−	22.0479i	−0.271562	−	1.78247i
$154$	−5.49026	−	8.07316i	−0.442418	−	0.650554i
$155$	−13.7912	+	21.4595i	−1.10774	+	1.72367i
$156$	−1.09829	−	1.69331i	−0.0879332	−	0.135573i
$157$	8.34739	+	12.9888i	0.666194	+	1.03662i	0.995715	+	0.0924706i	$0.0294764\pi$
$157$	8.34739	+	12.9888i	0.666194	+	1.03662i	−0.329521	+	0.944148i	$0.606887\pi$
$158$	15.4503	−	13.3877i	1.22916	−	1.06507i
$159$	−6.98617	+	6.10505i	−0.554040	+	0.484162i
$160$			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	0.544636	−	0.838673i	$-0.316668\pi$
$163$	18.5919	−	5.45909i	1.45623	−	0.427589i	0.911598	+	0.411084i	$0.134850\pi$
$164$	2.41474	+	2.78676i	0.188559	+	0.217609i
$165$	8.41329	−	13.2129i	0.654974	−	1.02862i
$166$	−6.57941	+	0.945976i	−0.510661	+	0.0734220i
$167$	−9.49508	−	6.10212i	−0.734752	−	0.472196i	0.118988	−	0.992896i	$-0.462035\pi$
$167$	−9.49508	−	6.10212i	−0.734752	−	0.472196i	−0.853740	+	0.520699i	$0.825671\pi$
$168$	8.87099	+	5.32939i	0.684412	+	0.411171i
$169$	−6.03723	+	6.96734i	−0.464402	+	0.535949i
$170$	46.8750	+	6.73961i	3.59515	+	0.516905i
$171$	−3.21782	+	11.3090i	−0.246073	+	0.864820i
$172$	2.18749	+	0.642304i	0.166794	+	0.0489752i
$173$	0.752596	+	0.220982i	0.0572188	+	0.0168010i	0.310217	−	0.950666i	$-0.399598\pi$
$173$	0.752596	+	0.220982i	0.0572188	+	0.0168010i	−0.252998	+	0.967467i	$0.581417\pi$
$174$	−2.66314	+	3.09961i	−0.201892	+	0.234981i
$175$	21.6903	+	17.8281i	1.63963	+	1.34768i
$176$	8.37116	+	7.25365i	0.631000	+	0.546765i
$177$	−24.6816	+	0.103532i	−1.85518	+	0.00778191i
$178$	−5.35058	+	8.32567i	−0.401043	+	0.624036i
$179$	−9.98792	+	1.43605i	−0.746532	+	0.107335i	−0.505074	−	0.863076i	$-0.668535\pi$
$179$	−9.98792	+	1.43605i	−0.746532	+	0.107335i	−0.241458	+	0.970411i	$0.577626\pi$
$180$	0.951925	−	7.03953i	0.0709523	−	0.524695i
$181$	9.69675	−	8.40229i	0.720754	−	0.624537i	−0.215237	−	0.976562i	$-0.569052\pi$
$181$	9.69675	−	8.40229i	0.720754	−	0.624537i	0.935991	+	0.352025i	$0.114507\pi$
$182$	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
$186$	11.8630	+	13.5751i	0.869834	+	0.995375i
$187$	12.8594	−	11.1427i	0.940372	−	0.814837i
$188$	1.32844	−	0.853740i	0.0968868	−	0.0622654i
$189$	−10.7296	−	8.59513i	−0.780461	−	0.625204i
$190$	−21.0035	−	13.4981i	−1.52375	−	0.979255i
$191$	17.5987	+	8.03706i	1.27340	+	0.581541i	0.933384	−	0.358879i	$-0.116841\pi$
$191$	17.5987	+	8.03706i	1.27340	+	0.581541i	0.340014	+	0.940420i	$0.389568\pi$
$192$	−7.29062	−	2.10754i	−0.526155	−	0.152099i
$193$	0.398204	−	2.76957i	0.0286634	−	0.199358i	−0.970458	−	0.241270i	$-0.922436\pi$
$193$	0.398204	−	2.76957i	0.0286634	−	0.199358i	0.999121	+	0.0419124i	$0.0133450\pi$
$194$	−2.58305	−	5.65608i	−0.185452	−	0.406083i
$195$	13.1637	−	1.94905i	0.942674	−	0.139574i
$196$	−0.812191	−	4.11556i	−0.0580137	−	0.293968i
$197$	−0.0671716	+	0.0306763i	−0.00478578	+	0.00218559i	−0.417806	−	0.908536i	$-0.637201\pi$
$197$	−0.0671716	+	0.0306763i	−0.00478578	+	0.00218559i	0.413021	+	0.910722i	$0.364474\pi$
$198$	−7.31948	−	8.30531i	−0.520173	−	0.590233i
$199$	−8.20455	−	7.10929i	−0.581605	−	0.503964i	0.313637	−	0.949543i	$-0.398452\pi$
$199$	−8.20455	−	7.10929i	−0.581605	−	0.503964i	−0.895243	+	0.445579i	$0.852998\pi$
$200$	−21.7994	−	9.95544i	−1.54145	−	0.703956i
$201$	2.09936	−	15.0492i	0.148077	−	1.06149i
$202$	15.9773	−	2.29719i	1.12416	−	0.161630i
$203$	−3.87055	+	0.100741i	−0.271659	+	0.00707060i
$204$	3.17605	−	7.03249i	0.222368	−	0.492373i
$205$	−23.3274	+	6.84954i	−1.62926	+	0.478393i
$206$	4.95547			0.345264
$207$	−14.3494	−	1.04590i	−0.997354	−	0.0726948i
$208$			9.41002i			0.652468i
$209$	−8.60724	+	2.52731i	−0.595375	+	0.174818i
$210$	24.0700	−	16.5172i	1.66099	−	1.13979i
$211$	−12.3018	+	7.90587i	−0.846889	+	0.544263i	−0.890603	−	0.454781i	$-0.849717\pi$
$211$	−12.3018	+	7.90587i	−0.846889	+	0.544263i	0.0437139	+	0.999044i	$0.486081\pi$
$212$	−3.17739	+	0.456839i	−0.218224	+	0.0313758i
$213$	10.0824	+	1.40649i	0.690833	+	0.0963708i
$214$	0.855145	−	1.87251i	0.0584565	−	0.128002i
$215$	−9.84363	+	11.3602i	−0.671330	+	0.774756i
$216$	10.7345	+	4.73994i	0.730388	+	0.322512i
$217$	−1.99015	+	16.9646i	−0.135100	+	1.15163i
$218$	−0.270619	+	0.921643i	−0.0183286	+	0.0624215i
$219$	−2.76127	+	0.408839i	−0.186589	+	0.0276268i
$220$	4.92989	−	2.25140i	0.332373	−	0.151790i
$221$	14.3081	+	2.05720i	0.962468	+	0.138382i
$222$	−1.97553	+	6.83395i	−0.132589	+	0.458665i
$223$	6.54427	+	2.98867i	0.438237	+	0.200136i	0.622301	−	0.782778i	$-0.286198\pi$
$223$	6.54427	+	2.98867i	0.438237	+	0.200136i	−0.184064	+	0.982914i	$0.558925\pi$
$224$	3.81576	+	7.81087i	0.254951	+	0.521885i
$225$	26.9257	+	16.9866i	1.79505	+	1.13244i
$226$	−14.9114	+	9.58298i	−0.991892	+	0.637450i
$227$	−4.29773	−	4.95984i	−0.285250	−	0.329196i	0.594982	−	0.803739i	$-0.297159\pi$
$227$	−4.29773	−	4.95984i	−0.285250	−	0.329196i	−0.880233	+	0.474542i	$0.842614\pi$
$228$	−3.06329	+	2.67693i	−0.202871	+	0.177284i
$229$		−	9.13789i		−	0.603849i	−0.953332	−	0.301924i	$-0.902371\pi$
$229$		−	9.13789i		−	0.603849i	0.953332	−	0.301924i	$-0.0976290\pi$
$230$	10.9549	−	28.5190i	0.722344	−	1.88048i
$231$	1.17837	−	10.4224i	0.0775308	−	0.685741i
$232$	3.17096	−	0.931078i	0.208184	−	0.0611283i
$233$	14.8787	−	12.8924i	0.974734	−	0.844611i	−0.0131334	−	0.999914i	$-0.504181\pi$
$233$	14.8787	−	12.8924i	0.974734	−	0.844611i	0.987867	+	0.155302i	$0.0496352\pi$
$234$	1.26029	−	9.31987i	0.0823874	−	0.609259i
$235$	1.48173	+	10.3057i	0.0966575	+	0.672268i
$236$	−7.18407	−	4.61692i	−0.467643	−	0.300536i
$237$	21.9629	−	0.0921273i	1.42664	−	0.00598431i
$238$	30.1833	−	9.72251i	1.95649	−	0.630217i
$239$	1.65420	+	0.237838i	0.107001	+	0.0153845i	0.195607	−	0.980682i	$-0.437332\pi$
$239$	1.65420	+	0.237838i	0.107001	+	0.0153845i	−0.0886061	+	0.996067i	$0.528241\pi$
$240$	−21.5835	+	25.1208i	−1.39321	+	1.62154i
$241$	1.16325	−	3.96167i	0.0749317	−	0.255194i	−0.913505	−	0.406827i	$-0.866635\pi$
$241$	1.16325	−	3.96167i	0.0749317	−	0.255194i	0.988437	+	0.151633i	$0.0484533\pi$
$242$	−2.61685	+	8.91218i	−0.168218	+	0.572896i
$243$	−13.2877	−	8.15088i	−0.852407	−	0.522879i
$244$	−8.55843	−	1.23052i	−0.547897	−	0.0787757i
$245$	26.9075	+	6.40123i	1.71906	+	0.408960i
$246$	0.0720737	+	17.1821i	0.00459525	+	1.09549i
$247$	−6.41109	−	4.12016i	−0.407928	−	0.262159i
$248$	−2.07488	−	14.4311i	−0.131755	−	0.916375i
$249$	−6.02361	−	3.83553i	−0.381731	−	0.243067i
$250$	−27.0182	+	23.4114i	−1.70878	+	1.48067i
$251$	10.7783	−	3.16480i	0.680322	−	0.199761i	0.0767275	−	0.997052i	$-0.475553\pi$
$251$	10.7783	−	3.16480i	0.680322	−	0.199761i	0.603594	+	0.797292i	$0.293735\pi$
$252$	−1.49632	−	4.51513i	−0.0942590	−	0.284426i
$253$	−5.16648	−	9.68499i	−0.324814	−	0.608890i
$254$			2.41860i			0.151756i
$255$	33.4782	+	38.3100i	2.09648	+	2.39906i
$256$	−8.65745	−	9.99123i	−0.541091	−	0.624452i
$257$	1.56773	−	1.00752i	0.0977926	−	0.0628475i	−0.490831	−	0.871255i	$-0.663307\pi$
$257$	1.56773	−	1.00752i	0.0977926	−	0.0628475i	0.588623	+	0.808408i	$0.299670\pi$
$258$	5.78088	+	8.91279i	0.359902	+	0.554886i
$259$	−6.05601	+	2.95848i	−0.376302	+	0.183831i
$260$	4.18813	+	1.91265i	0.259737	+	0.118618i
$261$	−4.34019	+	0.661235i	−0.268651	+	0.0409294i
$262$	−7.88580	−	1.13381i	−0.487186	−	0.0700468i
$263$	−0.486657	+	0.222249i	−0.0300085	+	0.0137044i	−0.430363	−	0.902656i	$-0.641614\pi$
$263$	−0.486657	+	0.222249i	−0.0300085	+	0.0137044i	0.400354	+	0.916360i	$0.368887\pi$
$264$	1.31126	+	8.85614i	0.0807025	+	0.545058i
$265$	5.96284	−	20.3076i	0.366294	−	1.24748i
$266$	−16.6041	−	1.94786i	−1.01806	−	0.119431i
$267$	−10.1890	+	3.03823i	−0.623554	+	0.185937i
$268$	3.44282	−	3.97322i	0.210304	−	0.242703i
$269$	−10.0050	+	21.9080i	−0.610017	+	1.33575i	0.312545	+	0.949903i	$0.398819\pi$
$269$	−10.0050	+	21.9080i	−0.610017	+	1.33575i	−0.922562	+	0.385849i	$0.873909\pi$
$270$	24.7411	−	21.9895i	1.50570	−	1.33824i
$271$	1.47587	−	0.212198i	0.0896529	−	0.0128901i	−0.0973424	−	0.995251i	$-0.531034\pi$
$271$	1.47587	−	0.212198i	0.0896529	−	0.0128901i	0.186995	+	0.982361i	$0.440125\pi$
$272$	−30.2656	+	19.4505i	−1.83512	+	1.17936i
$273$	7.34711	−	5.04170i	0.444667	−	0.305138i
$274$	8.59650	−	2.52416i	0.519334	−	0.152490i
$275$			24.2892i			1.46470i
$276$	−3.96843	−	3.00527i	−0.238872	−	0.180896i
$277$	−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
$279$	0.162482	+	19.3673i	0.00972757	+	1.15949i
$280$	−23.5999	+	0.614247i	−1.41037	+	0.0367083i
$281$	−2.34483	+	0.337136i	−0.139881	+	0.0201118i	−0.211900	−	0.977291i	$-0.567965\pi$
$281$	−2.34483	+	0.337136i	−0.139881	+	0.0201118i	0.0720186	+	0.997403i	$0.477056\pi$
$282$	7.28771	+	1.01663i	0.433977	+	0.0605396i
$283$	8.94976	+	4.08722i	0.532008	+	0.242960i	0.663260	−	0.748389i	$-0.269172\pi$
$283$	8.94976	+	4.08722i	0.532008	+	0.242960i	−0.131252	+	0.991349i	$0.541900\pi$
$284$	2.66190	+	2.30655i	0.157955	+	0.136869i
$285$	−7.66464	−	25.7040i	−0.454014	−	1.52257i
$286$	6.52685	−	2.98071i	0.385941	−	0.176253i
$287$	−12.0217	+	10.9774i	−0.709621	+	0.647973i
$288$	5.39849	+	8.24726i	0.318109	+	0.485974i
$289$	15.8962	+	34.8078i	0.935071	+	2.04752i
$290$	1.32671	−	9.22749i	0.0779072	−	0.541857i
$291$	1.85511	−	6.41737i	0.108748	−	0.376193i
$292$	−0.878515	−	0.401205i	−0.0514112	−	0.0234787i
$293$	9.40045	+	6.04130i	0.549180	+	0.352937i	0.785620	−	0.618710i	$-0.212344\pi$
$293$	9.40045	+	6.04130i	0.549180	+	0.352937i	−0.236440	+	0.971646i	$0.575981\pi$
$294$	9.62702	−	17.0122i	0.561459	−	0.992170i
$295$	47.3668	−	30.4408i	2.75780	−	1.77233i
$296$	4.34779	−	3.76738i	0.252710	−	0.218975i
$297$	−0.149659	−	11.8922i	−0.00868409	−	0.690055i
$298$	−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
$303$	14.6276	+	9.31412i	0.840333	+	0.535082i
$304$	18.7740	−	2.69930i	1.07677	−	0.154815i
$305$	30.8212	−	47.9587i	1.76481	−	2.74611i
$306$	32.5806	−	15.2107i	1.86251	−	0.869537i
$307$	−4.52710	−	3.92276i	−0.258375	−	0.223884i	0.516034	−	0.856568i	$-0.327408\pi$
$307$	−4.52710	−	3.92276i	−0.258375	−	0.223884i	−0.774410	+	0.632684i	$0.781953\pi$
$308$	2.30434	−	2.80354i	0.131302	−	0.159747i
$309$	4.03803	+	3.46942i	0.229715	+	0.197369i
$310$	−39.4604	−	11.5866i	−2.24120	−	0.658076i
$311$	1.31450	+	0.385971i	0.0745384	+	0.0218864i	0.318789	−	0.947826i	$-0.396724\pi$
$311$	1.31450	+	0.385971i	0.0745384	+	0.0218864i	−0.244251	+	0.969712i	$0.578542\pi$
$312$	−4.95649	+	5.76881i	−0.280606	+	0.326595i
$313$	−1.83700	−	0.264121i	−0.103834	−	0.0149290i	0.0902021	−	0.995923i	$-0.471249\pi$
$313$	−1.83700	−	0.264121i	−0.103834	−	0.0149290i	−0.194036	+	0.980994i	$0.562158\pi$
$314$	−16.3011	+	18.8125i	−0.919925	+	1.06165i
$315$	31.1777	+	3.39261i	1.75666	+	0.191152i
$316$	6.39273	+	4.10836i	0.359619	+	0.231113i
$317$	−9.46678	+	1.36112i	−0.531707	+	0.0764480i	−0.402939	−	0.915227i	$-0.632011\pi$
$317$	−9.46678	+	1.36112i	−0.531707	+	0.0764480i	−0.128768	+	0.991675i	$0.541102\pi$
$318$	−12.6173	−	8.03404i	−0.707541	−	0.450527i
$319$	−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
$324$	−2.32253	−	4.86781i	−0.129030	−	0.270434i
$325$	−15.5946	+	13.5128i	−0.865033	+	0.749556i
$326$	16.8896	+	26.2807i	0.935426	+	1.45555i
$327$	−0.865777	+	0.561547i	−0.0478776	+	0.0310536i
$328$	7.51245	−	11.6896i	0.414806	−	0.645451i
$329$	3.92051	+	5.76491i	0.216145	+	0.317830i
$330$	24.2607	+	7.01319i	1.33551	+	0.386063i
$331$	−0.601305	+	4.18217i	−0.0330507	+	0.229873i	−0.999651	−	0.0264158i	$-0.991591\pi$
$331$	−0.601305	+	4.18217i	−0.0330507	+	0.229873i	0.966600	+	0.256289i	$0.0824997\pi$
$332$	−1.02639	−	2.24748i	−0.0563305	−	0.123347i
$333$	−6.39436	+	4.18562i	−0.350409	+	0.229371i
$334$	5.12667	−	17.4598i	0.280519	−	0.955359i
$335$	14.3996	+	31.5307i	0.786734	+	1.72271i
$336$	−5.60227	+	21.4577i	−0.305629	+	1.17062i
$337$	2.74821	−	3.17160i	0.149704	−	0.172768i	−0.675944	−	0.736953i	$-0.736264\pi$
$337$	2.74821	−	3.17160i	0.149704	−	0.172768i	0.825649	+	0.564185i	$0.190809\pi$
$338$	−13.5201	−	6.17443i	−0.735398	−	0.335845i
$339$	−18.8600	−	2.63096i	−1.02433	−	0.142894i
$340$	2.50516	+	17.4238i	0.135861	+	0.944937i
$341$	−12.4310	+	7.98889i	−0.673174	+	0.432623i
$342$	−18.9557	+	0.159029i	−1.02501	+	0.00859931i
$343$	18.0704	−	4.05729i	0.975708	−	0.219073i
$344$		−	8.59122i		−	0.463208i
$345$	28.8934	−	15.5693i	1.55557	−	0.838223i
$346$			1.26458i			0.0679843i
$347$	6.03419	+	20.5506i	0.323932	+	1.10321i	0.947051	+	0.321085i	$0.104047\pi$
$347$	6.03419	+	20.5506i	0.323932	+	1.10321i	−0.623118	+	0.782128i	$0.714134\pi$
$348$	−1.38437	−	0.625214i	−0.0742098	−	0.0335150i
$349$	−15.7133	−	24.4504i	−0.841116	−	1.30880i	−0.949204	−	0.314660i	$-0.898109\pi$
$349$	−15.7133	−	24.4504i	−0.841116	−	1.30880i	0.108088	−	0.994141i	$-0.465527\pi$
$350$	−17.7266	+	41.6510i	−0.947526	+	2.22634i
$351$	7.55198	−	6.71206i	0.403095	−	0.358263i
$352$	−3.12407	+	6.84077i	−0.166514	+	0.364614i
$353$	17.7678	−	20.5052i	0.945686	−	1.09138i	−0.0500149	−	0.998748i	$-0.515927\pi$
$353$	17.7678	−	20.5052i	0.945686	−	1.09138i	0.995701	−	0.0926309i	$-0.0295277\pi$
$354$	−11.3710	−	38.1335i	−0.604360	−	2.02677i
$355$	−21.1243	+	9.64716i	−1.12116	+	0.512018i
$356$	−3.52968	−	1.03641i	−0.187073	−	0.0549295i
$357$	31.4021	+	13.2094i	1.66198	+	0.699115i
$358$	−6.75813	−	14.7982i	−0.357178	−	0.782112i
$359$	10.5648	+	1.51899i	0.557590	+	0.0801693i	0.415348	−	0.909663i	$-0.363660\pi$
$359$	10.5648	+	1.51899i	0.557590	+	0.0801693i	0.142242	+	0.989832i	$0.454569\pi$
$360$	−26.4635	+	4.03176i	−1.39475	+	0.212492i
$361$	1.51176	−	3.31028i	0.0795661	−	0.174226i
$362$	17.4021	+	11.1836i	0.914634	+	0.587800i
$363$	−8.37196	+	5.43009i	−0.439414	+	0.285006i
$364$	3.08196	−	0.0802155i	0.161538	−	0.00420444i
$365$	4.81243	−	4.16999i	0.251894	−	0.218268i
$366$	−26.5118	−	30.3382i	−1.38579	−	1.58580i
$367$			4.41784i			0.230609i	0.993330	+	0.115305i	$0.0367844\pi$
$367$			4.41784i			0.230609i	−0.993330	+	0.115305i	$0.963216\pi$
$368$	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
$372$	−3.59925	+	5.65254i	−0.186613	+	0.293070i
$373$	−1.54402	−	10.7389i	−0.0799462	−	0.556038i	−0.989948	−	0.141433i	$-0.954829\pi$
$373$	−1.54402	−	10.7389i	−0.0799462	−	0.556038i	0.910002	−	0.414605i	$-0.136080\pi$
$374$	23.0779	+	14.8313i	1.19333	+	0.766906i
$375$	−38.4068	+	0.161105i	−1.98332	+	0.00831940i
$376$	−4.49724	−	3.89688i	−0.231927	−	0.200966i
$377$	0.404965	−	2.81660i	0.0208568	−	0.145062i
$378$	8.42244	−	20.5018i	0.433203	−	1.05450i
$379$	−17.3778	−	5.10258i	−0.892638	−	0.262102i	−0.196922	−	0.980419i	$-0.563095\pi$
$379$	−17.3778	−	5.10258i	−0.892638	−	0.262102i	−0.695716	+	0.718317i	$0.744913\pi$
$380$	2.61458	−	8.90444i	0.134125	−	0.456788i
$381$	−1.69331	+	1.97082i	−0.0867507	+	0.100968i
$382$	−4.43906	+	30.8744i	−0.227122	+	1.57967i
$383$	22.4663	−	25.9275i	1.14797	−	1.32483i	0.210169	−	0.977665i	$-0.432598\pi$
$383$	22.4663	−	25.9275i	1.14797	−	1.32483i	0.937804	−	0.347166i	$-0.112856\pi$
$384$	−0.0990663	−	23.6171i	−0.00505546	−	1.20521i
$385$	10.5027	+	21.4990i	0.535266	+	1.09569i
$386$	4.46518	−	0.641995i	0.227271	−	0.0326767i
$387$	−1.52940	+	11.3100i	−0.0777439	+	0.574920i
$388$	1.74674	−	1.51356i	0.0886774	−	0.0768394i
$389$	7.29732	+	24.8524i	0.369989	+	1.26007i	0.908656	+	0.417547i	$0.137110\pi$
$389$	7.29732	+	24.8524i	0.369989	+	1.26007i	−0.538667	+	0.842519i	$0.681072\pi$
$390$	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
$393$	−5.63204	−	6.44489i	−0.284099	−	0.325102i
$394$	−0.0779642	−	0.0899755i	−0.00392778	−	0.00453290i
$395$	−42.1492	+	27.0876i	−2.12075	+	1.36293i
$396$	2.19558	−	3.48024i	0.110332	−	0.174889i
$397$	−15.3953	+	23.9556i	−0.772669	+	1.20230i	0.202162	+	0.979352i	$0.435203\pi$
$397$	−15.3953	+	23.9556i	−0.772669	+	1.20230i	−0.974831	+	0.222944i	$0.928433\pi$
$398$	7.27085	−	15.9209i	0.364455	−	0.798045i
$399$	−12.1663	−	13.2121i	−0.609077	−	0.661431i
$400$	7.30875	−	50.8335i	0.365437	−	2.54167i
$401$	17.4416	−	7.96532i	0.870993	−	0.397769i	0.0707849	−	0.997492i	$-0.477450\pi$
$401$	17.4416	−	7.96532i	0.870993	−	0.397769i	0.800208	+	0.599722i	$0.204722\pi$
$402$	24.2335	−	3.58807i	1.20866	−	0.178956i
$403$	−12.0449	−	3.53670i	−0.599998	−	0.176175i
$404$	2.49247	+	5.45774i	0.124005	+	0.271533i
$405$	35.5559	−	0.596635i	1.76679	−	0.0296470i
$406$	−1.91391	−	5.94167i	−0.0949855	−	0.294880i
$407$	−5.30386	−	2.42219i	−0.262903	−	0.120064i
$408$	−28.7993	−	4.01749i	−1.42578	−	0.198896i
$409$	2.75918	−	0.396710i	0.136433	−	0.0196161i	−0.0737601	−	0.997276i	$-0.523500\pi$
$409$	2.75918	−	0.396710i	0.136433	−	0.0196161i	0.210193	+	0.977660i	$0.432591\pi$
$410$	−21.1914	−	32.9744i	−1.04657	−	1.62849i
$411$	8.77218	+	3.96173i	0.432700	+	0.195418i
$412$	0.518947	+	1.76737i	0.0255667	+	0.0870721i
$413$	19.5512	−	32.2367i	0.962050	−	1.58626i
$414$	−4.89983	−	22.6725i	−0.240814	−	1.11429i
$415$	16.2905			0.799668
$416$	−6.13005	+	1.79994i	−0.300550	+	0.0882495i
$417$	−17.0306	−	7.69146i	−0.833994	−	0.376652i
$418$	−7.81911	−	12.1668i	−0.382445	−	0.595096i
$419$	−2.70970	−	18.8464i	−0.132378	−	0.920707i	−0.942443	−	0.334367i	$-0.891478\pi$
$419$	−2.70970	−	18.8464i	−0.132378	−	0.920707i	0.810065	−	0.586340i	$-0.199432\pi$
$420$	8.41152	+	6.85485i	0.410440	+	0.334482i
$421$	−12.4077	+	27.1691i	−0.604714	+	1.32414i	0.321418	+	0.946938i	$0.395841\pi$
$421$	−12.4077	+	27.1691i	−0.604714	+	1.32414i	−0.926131	+	0.377201i	$0.876887\pi$
$422$	−17.8174	−	15.4389i	−0.867339	−	0.751553i
$423$	5.22672	+	5.93068i	0.254132	+	0.288360i
$424$	5.02513	+	11.0035i	0.244042	+	0.534377i
$425$	−75.6954	−	22.2262i	−3.67177	−	1.07813i
$426$	2.40386	+	16.2355i	0.116468	+	0.786612i
$427$	4.44767	−	37.9133i	0.215238	−	1.83475i
$428$	0.757382	+	0.108895i	0.0366095	+	0.00526365i
$429$	7.40534	+	2.14070i	0.357533	+	0.103354i
$430$	−22.0444	−	10.0673i	−1.06308	−	0.485490i
$431$	−5.91406	+	9.20246i	−0.284870	+	0.443267i	−0.953968	−	0.299907i	$-0.903044\pi$
$431$	−5.91406	+	9.20246i	−0.284870	+	0.443267i	0.669098	+	0.743174i	$0.266681\pi$
$432$	−3.26521	+	24.9335i	−0.157097	+	1.19961i
$433$	−19.8983	−	30.9624i	−0.956252	−	1.48796i	−0.870813	−	0.491614i	$-0.836407\pi$
$433$	−19.8983	−	30.9624i	−0.956252	−	1.48796i	−0.0854384	−	0.996343i	$-0.527229\pi$
$434$	−27.1469	+	4.62702i	−1.30309	+	0.222104i
$435$	7.54143	−	6.59027i	0.361584	−	0.315979i
$436$	−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	0.986423	−	0.164222i	$-0.0525114\pi$
$439$	1.42069	+	4.83844i	0.0678060	+	0.230926i	−0.918617	+	0.395148i	$0.870693\pi$
$440$	−13.3743	−	15.4348i	−0.637596	−	0.735825i
$441$	19.7552	−	7.12252i	0.940726	−	0.339168i
$442$	3.31667	+	23.0679i	0.157758	+	1.09723i
$443$	−0.489932	+	0.762349i	−0.0232774	+	0.0362203i	−0.852697	−	0.522405i	$-0.825035\pi$
$443$	−0.489932	+	0.762349i	−0.0232774	+	0.0362203i	0.829420	+	0.558626i	$0.188671\pi$
$444$	−2.64421	+	0.0110916i	−0.125489	+	0.000526385i
$445$	15.8835	−	18.3305i	0.752948	−	0.868949i
$446$	−1.65071	+	11.4810i	−0.0781636	+	0.543640i
$447$	−9.69725	−	8.33175i	−0.458664	−	0.394078i
$448$	8.56061	−	7.81691i	0.404451	−	0.369314i
$449$	−5.57247	+	18.9781i	−0.262981	+	0.895632i	0.717089	+	0.696981i	$0.245474\pi$
$449$	−5.57247	+	18.9781i	−0.262981	+	0.895632i	−0.980070	+	0.198650i	$0.936344\pi$
$450$	−14.0469	+	49.3676i	−0.662175	+	2.32721i
$451$	−13.9401	−	2.00428i	−0.656413	−	0.0943780i
$452$	−4.97933	−	4.31461i	−0.234208	−	0.202942i
$453$	−39.5780	+	0.166017i	−1.85954	+	0.00780017i
$454$	5.72038	−	8.90109i	0.268471	−	0.417749i
$455$	−7.96025	+	18.7037i	−0.373182	+	0.876841i
$456$	12.9312	+	8.23395i	0.605560	+	0.385590i
$457$	−21.3038	−	24.5858i	−0.996547	−	1.15008i	−0.988670	−	0.150108i	$-0.952038\pi$
$457$	−21.3038	−	24.5858i	−0.996547	−	1.15008i	−0.00787784	−	0.999969i	$-0.502508\pi$
$458$	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	$-0.545128\pi$
$461$	−6.06769			−0.282600			−0.141300	+	0.989967i	$0.545128\pi$
$462$	16.6578	−	2.91117i	0.774990	−	0.135440i
$463$	22.1809	+	25.5981i	1.03083	+	1.18965i	0.981618	+	0.190857i	$0.0611268\pi$
$463$	22.1809	+	25.5981i	1.03083	+	1.18965i	0.0492159	+	0.998788i	$0.484328\pi$
$464$	3.82889	+	5.95786i	0.177752	+	0.276587i
$465$	−24.0428	−	37.0685i	−1.11496	−	1.71901i
$466$	26.7017	+	17.1601i	1.23693	+	0.794928i
$467$	1.89678	−	4.15338i	0.0877727	−	0.192195i	−0.860655	−	0.509188i	$-0.829946\pi$
$467$	1.89678	−	4.15338i	0.0877727	−	0.192195i	0.948428	+	0.316993i	$0.102673\pi$
$468$	3.45591	−	0.526514i	0.159750	−	0.0243381i
$469$	17.9310	+	14.7382i	0.827975	+	0.680546i
$470$	−15.2690	+	6.97313i	−0.704308	+	0.321647i
$471$	−26.4541	+	3.91686i	−1.21894	+	0.180479i
$472$	−9.06635	+	30.8772i	−0.417313	+	1.42124i
$473$	−7.92057	+	3.61720i	−0.364188	+	0.166319i
$474$	10.1184	+	33.9330i	0.464754	+	1.55859i
$475$	31.4329	+	27.2368i	1.44224	+	1.24971i
$476$	6.62839	+	9.74672i	0.303812	+	0.446740i
$477$	−4.65655	−	15.3802i	−0.213209	−	0.704212i
$478$	0.383449	+	2.66695i	0.0175386	+	0.121983i
$479$	20.7002	−	13.3032i	0.945816	−	0.607839i	0.0257778	−	0.999668i	$-0.491794\pi$
$479$	20.7002	−	13.3032i	0.945816	−	0.607839i	0.920038	+	0.391829i	$0.128157\pi$
$480$	−20.4931	−	9.25521i	−0.935379	−	0.422441i
$481$	−1.39555	−	4.75282i	−0.0636318	−	0.216710i
$482$	6.65676			0.303207
$483$	12.8076	−	17.8596i	0.582768	−	0.812639i
$484$	−3.45257			−0.156935
$485$	4.29330	+	14.6216i	0.194949	+	0.663934i
$486$	6.57327	−	24.2573i	0.298169	−	1.10033i
$487$	14.9737	−	9.62299i	0.678522	−	0.436060i	−0.155467	−	0.987841i	$-0.549688\pi$
$487$	14.9737	−	9.62299i	0.678522	−	0.436060i	0.833989	+	0.551782i	$0.186052\pi$
$488$	4.63702	+	32.2512i	0.209908	+	1.45994i
$489$	−4.63694	+	33.2398i	−0.209690	+	1.50316i
$490$	2.31965	+	44.5313i	0.104791	+	2.01172i
$491$	11.4454	+	9.91745i	0.516521	+	0.447568i	0.873698	−	0.486468i	$-0.161715\pi$
$491$	11.4454	+	9.91745i	0.516521	+	0.447568i	−0.357177	+	0.934037i	$0.616261\pi$
$492$	−6.12047	+	1.82505i	−0.275932	+	0.0822798i
$493$	9.89611	−	4.51940i	0.445698	−	0.203544i
$494$	3.46153	−	11.7889i	0.155742	−	0.530407i
$495$	14.8591	+	22.7002i	0.667866	+	1.02030i
$496$	28.4199	−	12.9789i	1.27609	−	0.582771i
$497$	−9.87400	+	12.0130i	−0.442910	+	0.538859i
$498$	3.19724	−	11.0602i	0.143272	−	0.495620i
$499$	−9.37653	+	20.5317i	−0.419751	+	0.919127i	0.575129	+	0.818063i	$0.304952\pi$
$499$	−9.37653	+	20.5317i	−0.419751	+	0.919127i	−0.994880	+	0.101064i	$0.967775\pi$
$500$	−11.1791	−	7.18435i	−0.499943	−	0.321294i
$501$	16.4015	−	10.6381i	0.732765	−	0.475274i
$502$	9.79140	+	15.2357i	0.437011	+	0.680003i
$503$	11.8191	+	13.6400i	0.526987	+	0.608176i	0.955366	−	0.295423i	$-0.0954607\pi$
$503$	11.8191	+	13.6400i	0.526987	+	0.608176i	−0.428379	+	0.903599i	$0.640915\pi$
$504$	−14.7368	+	10.2038i	−0.656429	+	0.454514i
$505$	−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	$-0.306379\pi$
$509$	−7.26808	−	8.38782i	−0.322152	−	0.371783i	−0.893607	+	0.448850i	$0.851834\pi$
$510$	−44.0561	+	69.1891i	−1.95084	+	3.06374i
$511$	1.66977	−	3.92334i	0.0738662	−	0.173558i
$512$	−3.22050	+	5.01119i	−0.142327	+	0.221465i
$513$	−15.5576	−	13.1417i	−0.686886	−	0.580219i
$514$	2.27065	+	1.96753i	0.100154	+	0.0867839i
$515$	−12.0211	−	1.72838i	−0.529715	−	0.0761615i
$516$	−2.57337	+	2.99512i	−0.113286	+	0.131853i
$517$	−1.69919	+	5.78690i	−0.0747301	+	0.254507i
$518$	−7.32727	−	8.02438i	−0.321942	−	0.352571i
$519$	−0.885357	+	1.03046i	−0.0388629	+	0.0452321i
$520$	2.46920	−	17.1737i	0.108282	−	0.753115i
$521$	−10.6478	+	12.2883i	−0.466490	+	0.538359i	−0.939432	−	0.342735i	$-0.888647\pi$
$521$	−10.6478	+	12.2883i	−0.466490	+	0.538359i	0.472942	+	0.881094i	$0.343192\pi$
$522$	−2.99427	−	6.41359i	−0.131055	−	0.280715i
$523$	2.77927	−	4.32462i	0.121529	−	0.189103i	−0.775159	−	0.631767i	$-0.782330\pi$
$523$	2.77927	−	4.32462i	0.121529	−	0.189103i	0.896688	+	0.442664i	$0.145967\pi$
$524$	−0.421444	−	2.93121i	−0.0184109	−	0.128050i
$525$	−43.6054	+	21.5291i	−1.90309	+	0.939606i
$526$	−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
$531$	17.4322	−	39.0346i	0.756494	−	1.69396i
$532$	−1.04411	−	6.12583i	−0.0452679	−	0.265589i
$533$	−6.46845	−	10.0651i	−0.280180	−	0.435968i
$534$	−9.32789	−	14.3815i	−0.403657	−	0.622348i
$535$	−2.72753	+	4.24412i	−0.117922	+	0.183490i
$536$	−18.0212	−	8.22999i	−0.778395	−	0.355481i
$537$	4.85359	−	16.7900i	0.209448	−	0.724543i
$538$	−38.4343	−	5.52602i	−1.65702	−	0.238244i
$539$	12.6379	+	9.84799i	0.544353	+	0.424183i
$540$	10.4335	+	6.52116i	0.448986	+	0.280626i
$541$	23.7024	+	6.95965i	1.01904	+	0.299219i	0.748249	−	0.663418i	$-0.230895\pi$
$541$	23.7024	+	6.95965i	1.01904	+	0.299219i	0.270796	+	0.962637i	$0.412713\pi$
$542$	0.998620	+	2.18667i	0.0428944	+	0.0939257i
$543$	6.35042	+	21.2967i	0.272523	+	0.913928i
$544$	−18.4600	−	15.9957i	−0.791465	−	0.685808i
$545$	0.977928	−	2.14136i	0.0418898	−	0.0917259i
$546$	11.1363	+	9.07537i	0.476589	+	0.388390i
$547$	−0.0951187	−	0.661565i	−0.00406698	−	0.0282865i	0.987687	−	0.156444i	$-0.0500029\pi$
$547$	−0.0951187	−	0.661565i	−0.00406698	−	0.0282865i	−0.991754	+	0.128157i	$0.959094\pi$
$548$	1.80049	+	2.80161i	0.0769129	+	0.119679i
$549$	−0.363122	−	43.2829i	−0.0154977	−	1.84727i
$550$	−37.5735	+	11.0326i	−1.60214	+	0.470431i
$551$	−5.73559			−0.244344
$552$	−6.65301	+	17.5393i	−0.283171	+	0.746522i
$553$	−17.3976	+	28.6857i	−0.739819	+	1.21984i
$554$	−9.52070	−	32.4245i	−0.404496	−	1.37759i
$555$	7.17586	−	15.8890i	0.304598	−	0.674449i
$556$	−3.49553	−	5.43915i	−0.148243	−	0.230671i
$557$	32.9057	−	4.73112i	1.39426	−	0.200464i	0.596100	−	0.802911i	$-0.296716\pi$
$557$	32.9057	−	4.73112i	1.39426	−	0.200464i	0.798159	+	0.602446i	$0.205807\pi$
$558$	−29.8859	+	9.04831i	−1.26517	+	0.383045i
$559$	−6.72883	−	3.07295i	−0.284599	−	0.129972i
$560$	−15.5113	−	48.1543i	−0.655471	−	2.03489i
$561$	8.42164	+	28.2427i	0.355562	+	1.19241i
$562$	−1.58659	−	3.47414i	−0.0669261	−	0.146548i
$563$	−5.98132	−	1.75627i	−0.252083	−	0.0740181i	0.153250	−	0.988187i	$-0.451026\pi$
$563$	−5.98132	−	1.75627i	−0.252083	−	0.0740181i	−0.405332	+	0.914169i	$0.632844\pi$
$564$	0.400602	+	2.70563i	0.0168684	+	0.113928i
$565$	39.5149	−	18.0459i	1.66241	−	0.759195i
$566$	−2.25747	+	15.7011i	−0.0948886	+	0.659964i
$567$	21.2169	−	10.8095i	0.891025	−	0.453955i
$568$	5.51376	−	12.0735i	0.231352	−	0.506591i
$569$	−11.5554	+	17.9805i	−0.484426	+	0.753782i	−0.994317	−	0.106457i	$-0.966049\pi$
$569$	−11.5554	+	17.9805i	−0.484426	+	0.753782i	0.509891	+	0.860239i	$0.329686\pi$
$570$	36.2807	−	23.5318i	1.51963	−	0.985638i
$571$	−33.5143	+	21.5383i	−1.40253	+	0.901352i	−0.999902	−	0.0140118i	$-0.995540\pi$
$571$	−33.5143	+	21.5383i	−1.40253	+	0.901352i	−0.402629	+	0.915363i	$0.631903\pi$
$572$	1.74658	+	2.01566i	0.0730280	+	0.0842788i
$573$	−25.2330	+	22.0505i	−1.05412	+	0.921172i
$574$	−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	−0.980442	−	0.196807i	$-0.936943\pi$
$577$	−6.29451	−	21.4371i	−0.262044	−	0.892439i	0.718399	−	0.695632i	$-0.244875\pi$
$578$	−46.6246	+	40.4005i	−1.93933	+	1.68044i
$579$	4.08798	+	2.60302i	0.169891	+	0.108178i
$580$	3.42992	−	0.493148i	0.142420	−	0.0204769i
$581$	9.80118	−	4.78806i	0.406621	−	0.198642i
$582$	10.7698	−	0.0451758i	0.446422	−	0.00187260i
$583$	8.02878	−	9.26570i	0.332518	−	0.383746i
$584$	−0.517947	+	3.60240i	−0.0214328	+	0.149068i
$585$	−6.30784	+	22.1689i	−0.260797	+	0.916570i
$586$	−5.07557	+	17.2858i	−0.209670	+	0.714070i
$587$	−0.0377979	−	0.0110985i	−0.00156008	−	0.000458082i	0.280952	−	0.959722i	$-0.409350\pi$
$587$	−0.0377979	−	0.0110985i	−0.00156008	−	0.000458082i	−0.282513	+	0.959264i	$0.591168\pi$
$588$	7.07556	+	1.65193i	0.291791	+	0.0681245i
$589$	−3.60099	+	25.0454i	−0.148376	+	1.03198i
$590$	68.6042	+	59.4459i	2.82439	+	2.44735i
$591$	−0.000536508	−	0.127902i	−2.20690e−5	−	0.00526118i
$592$	10.3713	+	6.66522i	0.426257	+	0.273939i
$593$	2.69979	+	18.7774i	0.110867	+	0.771097i	0.967080	+	0.254474i	$0.0819022\pi$
$593$	2.69979	+	18.7774i	0.110867	+	0.771097i	−0.856213	+	0.516623i	$0.827189\pi$
$594$	18.3283	−	5.63314i	0.752019	−	0.231131i
$595$	−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	$0.936141\pi$
$600$	31.2559	−	27.3137i	1.27602	−	1.11508i
$601$	23.1540	−	20.0631i	0.944471	−	0.818389i	−0.0390396	−	0.999238i	$-0.512430\pi$
$601$	23.1540	−	20.0631i	0.944471	−	0.818389i	0.983511	+	0.180849i	$0.0578844\pi$
$602$	−16.2220	+	0.422218i	−0.661160	+	0.0172083i
$603$	22.2590	+	14.0426i	0.906458	+	0.571857i
$604$	−11.5200	−	7.40343i	−0.468741	−	0.301241i
$605$	9.45645	−	20.7067i	0.384459	−	0.841848i
$606$	−7.76410	+	26.8584i	−0.315395	+	1.09105i
$607$	−44.7437	−	6.43317i	−1.81609	−	0.261114i	−0.851403	−	0.524512i	$-0.824248\pi$
$607$	−44.7437	−	6.43317i	−1.81609	−	0.261114i	−0.964687	+	0.263398i	$0.915157\pi$
$608$	5.34952	+	11.7138i	0.216952	+	0.475058i
$609$	2.60031	−	6.18160i	0.105370	−	0.250491i
$610$	88.1877	+	25.8943i	3.57062	+	1.04843i
$611$	−4.66071	+	2.12848i	−0.188552	+	0.0861090i
$612$	8.83680	+	10.0270i	0.357206	+	0.405317i
$613$	26.0111	−	30.0184i	1.05058	−	1.21243i	0.0740014	−	0.997258i	$-0.476423\pi$
$613$	26.0111	−	30.0184i	1.05058	−	1.21243i	0.976576	−	0.215173i	$-0.0690315\pi$
$614$	4.01191	−	8.78485i	0.161907	−	0.354528i
$615$	5.81798	−	41.7061i	0.234604	−	1.68175i
$616$	−12.5832	−	5.35541i	−0.506993	−	0.215775i
$617$	−18.5417	−	28.8515i	−0.746463	−	1.16152i	−0.981858	−	0.189619i	$-0.939275\pi$
$617$	−18.5417	−	28.8515i	−0.746463	−	1.16152i	0.235395	−	0.971900i	$-0.424362\pi$
$618$	−3.53278	+	7.82238i	−0.142109	+	0.314662i
$619$	−1.58338	−	5.39250i	−0.0636414	−	0.216743i	0.921533	−	0.388301i	$-0.126938\pi$
$619$	−1.58338	−	5.39250i	−0.0636414	−	0.216743i	−0.985174	+	0.171558i	$0.945120\pi$
$620$		−	15.2869i		−	0.613938i
$621$	11.8808	−	21.9054i	0.476758	−	0.879034i
$622$			2.20874i			0.0885624i
$623$	4.16864	−	15.6970i	0.167013	−	0.628887i
$624$	−14.8540	−	6.70845i	−0.594637	−	0.268553i
$625$	29.0699	−	18.6821i	1.16279	−	0.747282i
$626$	−0.425824	−	2.96167i	−0.0170193	−	0.118372i
$627$	2.14669	−	15.3885i	0.0857307	−	0.614559i
$628$	−8.41656	−	3.84372i	−0.335857	−	0.153381i
$629$	12.4019	−	14.3126i	0.494498	−	0.570681i
$630$	8.91335	+	49.7704i	0.355116	+	1.98290i
$631$	−13.3365	−	29.2029i	−0.530919	−	1.16255i	−0.965138	−	0.261743i	$-0.915703\pi$
$631$	−13.3365	−	29.2029i	−0.530919	−	1.16255i	0.434219	−	0.900807i	$-0.357025\pi$
$632$	8.06767	−	27.4759i	0.320915	−	1.09293i
$633$	−3.70968	−	25.0549i	−0.147447	−	0.995843i
$634$	−6.40551	−	14.0261i	−0.254395	−	0.557048i
$635$	0.843562	−	5.86710i	0.0334757	−	0.232829i
$636$	1.54404	−	5.34129i	0.0612251	−	0.211796i
$637$	0.708049	+	13.5927i	0.0280539	+	0.538564i
$638$	2.91958	−	4.54295i	0.115587	−	0.179857i
$639$	−9.40796	+	14.9127i	−0.372173	+	0.589936i
$640$	29.1279	+	45.3238i	1.15138	+	1.79158i
$641$	30.2329	−	26.1970i	1.19413	−	1.03472i	0.195589	−	0.980686i	$-0.437338\pi$
$641$	30.2329	−	26.1970i	1.19413	−	1.03472i	0.998539	−	0.0540323i	$-0.0172074\pi$
$642$	2.34618	+	2.68479i	0.0925962	+	0.105960i
$643$			39.3025i			1.54994i	0.631998	+	0.774970i	$0.282235\pi$
$643$			39.3025i			1.54994i	−0.631998	+	0.774970i	$0.717765\pi$
$644$	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	$-0.0391175\pi$
$647$	18.5654	+	21.4256i	0.729882	+	0.842329i	−0.262576	+	0.964911i	$0.584572\pi$
$648$	−15.1348	+	13.5656i	−0.594551	+	0.532907i
$649$	32.2840	−	4.64175i	1.26726	−	0.182204i
$650$	−27.9866	−	17.9859i	−1.09772	−	0.705464i
$651$	−25.3604	−	15.2357i	−0.993954	−	0.597134i
$652$	−7.60430	+	8.77583i	−0.297807	+	0.343688i
$653$	10.0205	+	1.44073i	0.392132	+	0.0563801i	0.335561	−	0.942018i	$-0.391074\pi$
$653$	10.0205	+	1.44073i	0.392132	+	0.0563801i	0.0565712	+	0.998399i	$0.481983\pi$
$654$	−1.26192	−	1.08422i	−0.0493449	−	0.0423965i
$655$	18.7342	+	5.50085i	0.732004	+	0.214936i
$656$	28.5713	+	8.38928i	1.11552	+	0.327546i
$657$	1.32315	−	4.65021i	0.0516211	−	0.181422i
$658$	−7.13710	+	8.68323i	−0.278233	+	0.338508i
$659$	−28.4236	−	24.6292i	−1.10723	−	0.959417i	−0.107830	−	0.994169i	$-0.534390\pi$
$659$	−28.4236	−	24.6292i	−1.10723	−	0.959417i	−0.999396	+	0.0347525i	$0.988936\pi$
$660$	0.0393756	+	9.38703i	0.00153269	+	0.365390i
$661$	−3.82150	+	5.94637i	−0.148639	+	0.231287i	−0.907587	−	0.419865i	$-0.862077\pi$
$661$	−3.82150	+	5.94637i	−0.148639	+	0.231287i	0.758948	+	0.651152i	$0.225714\pi$
$662$	−6.74261	+	0.969440i	−0.262059	+	0.0376784i
$663$	−13.4477	+	21.1193i	−0.522265	+	0.820204i
$664$	−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
$669$	−9.38315	+	8.19971i	−0.362774	+	0.317019i
$670$	−42.2350	+	36.5968i	−1.63168	+	1.41386i
$671$	27.7812	−	17.8539i	1.07248	−	0.689243i
$672$	−15.0500	+	0.454893i	−0.580566	+	0.0175479i
$673$	8.07464	+	5.18925i	0.311254	+	0.200031i	0.686936	−	0.726718i	$-0.258955\pi$
$673$	8.07464	+	5.18925i	0.311254	+	0.200031i	−0.375682	+	0.926749i	$0.622591\pi$
$674$	6.15449	+	2.81066i	0.237062	+	0.108263i
$675$	−46.0095	+	30.3933i	−1.77090	+	1.16984i
$676$	0.786260	−	5.46856i	0.0302408	−	0.210329i
$677$	9.56671	+	20.9482i	0.367679	+	0.805104i	0.999549	+	0.0300299i	$0.00956026\pi$
$677$	9.56671	+	20.9482i	0.367679	+	0.805104i	−0.631870	+	0.775074i	$0.717712\pi$
$678$	−4.49664	−	30.3699i	−0.172692	−	1.16635i
$679$	6.88062	+	7.53524i	0.264054	+	0.289176i
$680$	60.3397	−	27.5562i	2.31392	−	1.05673i
$681$	10.8931	−	3.24821i	0.417426	−	0.124472i
$682$	−18.0045	−	15.6010i	−0.689429	−	0.597394i
$683$	42.2552	+	19.2973i	1.61685	+	0.738391i	0.998857	−	0.0477933i	$-0.0152189\pi$
$683$	42.2552	+	19.2973i	1.61685	+	0.738391i	0.617993	+	0.786184i	$0.287946\pi$
$684$	−2.04180	−	6.74390i	−0.0780700	−	0.257860i
$685$	−21.7340	+	3.12488i	−0.830415	+	0.119396i
$686$	14.4842	+	26.1105i	0.553008	+	0.996905i
$687$	14.4245	+	6.51445i	0.550328	+	0.248542i
$688$	17.6649	−	5.18689i	0.673468	−	0.197748i
$689$	10.4156			0.396802
$690$	37.2083	+	37.6240i	1.41650	+	1.43232i
$691$		−	15.4525i		−	0.587841i	−0.955830	−	0.293920i	$-0.905040\pi$
$691$		−	15.4525i		−	0.587841i	0.955830	−	0.293920i	$-0.0949600\pi$
$692$	−0.451013	+	0.132429i	−0.0171449	+	0.00503421i
$693$	15.6120	+	9.29024i	0.593050	+	0.352907i
$694$	−29.0493	+	18.6688i	−1.10270	+	0.708659i
$695$	42.1953	−	6.06677i	1.60056	−	0.230126i
$696$	−0.790855	+	5.66924i	−0.0299773	+	0.214892i
$697$	19.0022	−	41.6091i	0.719761	−	1.57606i
$698$	30.6856	−	35.4131i	1.16147	−	1.34041i
$699$	9.74406	+	32.6775i	0.368554	+	1.23598i
$700$	−16.7112	−	1.96042i	−0.631624	−	0.0740969i
$701$	−8.77256	+	29.8766i	−0.331335	+	1.12842i	0.610407	+	0.792088i	$0.291006\pi$
$701$	−8.77256	+	29.8766i	−0.331335	+	1.12842i	−0.941742	+	0.336336i	$0.890812\pi$
$702$	13.8133	+	8.63358i	0.521348	+	0.325854i
$703$	−9.08209	+	4.14765i	−0.342537	+	0.156432i
$704$	9.92665	+	1.42724i	0.374125	+	0.0537910i
$705$	−17.3242	−	5.00800i	−0.652466	−	0.188612i
$706$	39.7903	+	18.1716i	1.49753	+	0.683898i
$707$	−23.8010	+	11.6272i	−0.895128	+	0.437287i
$708$	12.4095	−	8.04887i	0.466379	−	0.302495i
$709$	−1.09759	+	0.705378i	−0.0412209	+	0.0264910i	−0.561089	−	0.827756i	$-0.689617\pi$
$709$	−1.09759	+	0.705378i	−0.0412209	+	0.0264910i	0.519868	+	0.854247i	$0.325981\pi$
$710$	−24.5184	−	28.2958i	−0.920160	−	1.06192i
$711$	−15.5120	+	34.7348i	−0.581746	+	1.30266i
$712$			13.8626i			0.519523i
$713$	−30.9031	+	1.90763i	−1.15733	+	0.0714414i
$714$	−6.17051	+	54.5765i	−0.230925	+	2.04248i
$715$	−16.8727	+	4.95426i	−0.631002	+	0.185279i
$716$	4.57007	−	3.95999i	0.170792	−	0.147992i
$717$	−1.55472	+	2.44165i	−0.0580622	+	0.0911853i
$718$	2.44896	+	17.0329i	0.0913943	+	0.635662i
$719$	−1.60029	−	1.02845i	−0.0596808	−	0.0383546i	0.510460	−	0.859901i	$-0.329475\pi$
$719$	−1.60029	−	1.02845i	−0.0596808	−	0.0383546i	−0.570141	+	0.821547i	$0.693111\pi$
$720$	−24.2671	−	51.9790i	−0.904380	−	1.93714i
$721$	−7.74053	+	2.49335i	−0.288273	+	0.0928571i
$722$	5.80741	+	0.834980i	0.216130	+	0.0310747i
$723$	5.42434	+	4.66053i	0.201734	+	0.173327i
$724$	−2.16627	+	7.37764i	−0.0805088	+	0.274188i
$725$	−4.37529	+	14.9009i	−0.162494	+	0.553404i
$726$	−12.2026	−	10.4843i	−0.452881	−	0.389110i
$727$	−23.8393	−	3.42757i	−0.884149	−	0.127121i	−0.314742	−	0.949177i	$-0.601918\pi$
$727$	−23.8393	−	3.42757i	−0.884149	−	0.127121i	−0.569407	+	0.822056i	$0.692827\pi$
$728$	−3.56205	−	11.0583i	−0.132018	−	0.409847i
$729$	22.3393	−	15.1643i	0.827382	−	0.561640i
$730$	8.63654	+	5.55037i	0.319653	+	0.205428i
$731$	−4.02490	−	27.9938i	−0.148866	−	1.03539i
$732$	8.04376	−	12.6325i	0.297306	−	0.466912i
$733$	13.4275	−	11.6350i	0.495954	−	0.429747i	−0.370628	−	0.928782i	$-0.620857\pi$
$733$	13.4275	−	11.6350i	0.495954	−	0.429747i	0.866582	+	0.499035i	$0.166312\pi$
$734$	−6.83405	+	2.00666i	−0.252249	+	0.0740671i
$735$	−29.2871	+	37.9109i	−1.08027	+	1.39837i
$736$	−12.7060	+	9.31972i	−0.468350	+	0.343530i
$737$			20.0795i			0.739637i
$738$	−27.1740	−	12.1355i	−1.00029	−	0.446713i
$739$	−1.61667	−	1.86574i	−0.0594702	−	0.0686323i	0.725235	−	0.688501i	$-0.241731\pi$
$739$	−1.61667	−	1.86574i	−0.0594702	−	0.0686323i	−0.784705	+	0.619869i	$0.787186\pi$
$740$	5.07453	−	3.26121i	0.186544	−	0.119884i
$741$	11.0743	−	7.18284i	0.406825	−	0.263868i
$742$	20.5299	−	10.0292i	0.753676	−	0.368185i
$743$	−30.2153	−	13.7989i	−1.10849	−	0.506231i	−0.224849	−	0.974394i	$-0.572189\pi$
$743$	−30.2153	−	13.7989i	−1.10849	−	0.506231i	−0.883643	+	0.468162i	$0.844916\pi$
$744$	24.2591	+	7.01273i	0.889383	+	0.257099i
$745$	28.8685	+	4.15067i	1.05766	+	0.152069i
$746$	15.9109	−	7.26625i	0.582538	−	0.266036i
$747$	10.3488	−	6.77409i	0.378642	−	0.247851i
$748$	−2.87281	+	9.78389i	−0.105040	+	0.357734i
$749$	−0.393599	+	3.35515i	−0.0143818	+	0.122595i
$750$	−17.6943	−	59.3392i	−0.646103	−	2.16676i
$751$	−2.04295	+	2.35768i	−0.0745481	+	0.0860331i	−0.791798	−	0.610783i	$-0.790855\pi$
$751$	−2.04295	+	2.35768i	−0.0745481	+	0.0860331i	0.717250	+	0.696816i	$0.245400\pi$
$752$	5.29743	−	11.5997i	0.193177	−	0.422999i
$753$	−2.68818	+	19.2701i	−0.0979626	+	0.702243i
$754$	4.54099	−	0.652896i	0.165373	−	0.0237771i
$755$	75.9546	−	48.8131i	2.76427	−	1.77649i
$756$	8.19401	+	0.856870i	0.298013	+	0.0311641i
$757$	33.4008	−	9.80737i	1.21397	−	0.356455i	0.388794	−	0.921325i	$-0.372892\pi$
$757$	33.4008	−	9.80737i	1.21397	−	0.356455i	0.825180	+	0.564870i	$0.191074\pi$
$758$		−	29.1998i		−	1.06058i
$759$	18.9713	−	1.25099i	0.688614	−	0.0454081i
$760$	−34.9717			−1.26856
$761$	−33.3233	+	9.78461i	−1.20797	+	0.354692i	−0.822895	−	0.568194i	$-0.807642\pi$
$761$	−33.3233	+	9.78461i	−1.20797	+	0.354692i	−0.385074	+	0.922886i	$0.625824\pi$
$762$	−3.81783	−	1.72423i	−0.138305	−	0.0624622i
$763$	−0.0410137	−	1.57578i	−0.00148479	−	0.0570472i
$764$	−11.4762	+	1.65003i	−0.415195	+	0.0596961i
$765$	−84.3403	+	25.5350i	−3.04933	+	0.923220i
$766$	50.3123	+	22.9769i	1.81786	+	0.830187i
$767$	20.9407	+	18.1453i	0.756126	+	0.655187i
$768$	21.9434	−	6.54327i	0.791815	−	0.236110i
$769$	−10.5939	+	4.83806i	−0.382024	+	0.174465i	−0.597165	−	0.802118i	$-0.703706\pi$
$769$	−10.5939	+	4.83806i	−0.382024	+	0.174465i	0.215141	+	0.976583i	$0.430979\pi$
$770$	−28.4868	+	26.0120i	−1.02659	+	0.937409i
$771$	0.472761	+	3.19299i	0.0170261	+	0.114993i
$772$	0.696570	+	1.52528i	0.0250701	+	0.0548959i
$773$	2.38754	−	16.6057i	0.0858737	−	0.597265i	−0.900761	−	0.434316i	$-0.856990\pi$
$773$	2.38754	−	16.6057i	0.0858737	−	0.597265i	0.986634	−	0.162949i	$-0.0521006\pi$
$774$	−18.1904	+	2.77133i	−0.653839	+	0.0996134i
$775$	62.3202	+	28.4607i	2.23861	+	1.02234i
$776$	−7.32705	−	4.70881i	−0.263026	−	0.169037i
$777$	−0.352693	−	11.6687i	−0.0126528	−	0.418613i
$778$	−35.1301	+	22.5767i	−1.25947	+	0.809415i
$779$	−18.2255	+	15.7925i	−0.652997	+	0.565825i
$780$	−6.00493	+	5.24756i	−0.215011	+	0.187893i
$781$	−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
$786$	7.41157	−	11.6397i	0.264362	−	0.415174i
$787$	25.4439	−	3.65828i	0.906977	−	0.130404i	0.326988	−	0.945028i	$-0.393966\pi$
$787$	25.4439	−	3.65828i	0.906977	−	0.130404i	0.579988	+	0.814625i	$0.303057\pi$
$788$	0.0239252	−	0.0372284i	0.000852301	−	0.00132621i
$789$	−0.00388699	−	0.926646i	−0.000138380	−	0.0329895i
$790$	−61.0473	−	52.8978i	−2.17196	−	1.88202i
$791$	18.4702	−	22.4715i	0.656725	−	0.798993i
$792$	−14.9145	−	4.24372i	−0.529964	−	0.150794i
$793$	26.9184	+	7.90396i	0.955901	+	0.280678i
$794$	−44.0502	−	12.9343i	−1.56328	−	0.459021i
$795$	27.8052	+	23.8899i	0.986150	+	0.847288i
$796$	6.43963	+	0.925879i	0.228247	+	0.0328169i
$797$	−18.8976	+	21.8090i	−0.669386	+	0.772513i	−0.984280	−	0.176614i	$-0.943486\pi$
$797$	−18.8976	+	21.8090i	−0.669386	+	0.772513i	0.314894	+	0.949127i	$0.398031\pi$
$798$	14.9119	−	24.8215i	0.527875	−	0.878670i
$799$	−16.4795	−	10.5907i	−0.583004	−	0.374674i
$800$	34.5129	−	4.96220i	1.22021	−	0.175440i
$801$	2.46781	−	18.2496i	0.0871958	−	0.644817i
$802$	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
$807$	−27.4498	−	31.4116i	−0.966279	−	1.10574i
$808$	17.0874	−	14.8063i	0.601134	−	0.520885i
$809$	−12.1987	−	18.9815i	−0.428883	−	0.667354i	0.557807	−	0.829971i	$-0.311643\pi$
$809$	−12.1987	−	18.9815i	−0.428883	−	0.667354i	−0.986689	+	0.162616i	$0.948007\pi$
$810$	17.0730	+	54.7311i	0.599885	+	1.92306i
$811$	−10.2140	+	15.8934i	−0.358664	+	0.558092i	−0.972957	−	0.230986i	$-0.925805\pi$
$811$	−10.2140	+	15.8934i	−0.358664	+	0.558092i	0.614293	+	0.789078i	$0.289441\pi$
$812$	1.91867	−	1.30482i	0.0673321	−	0.0457901i
$813$	−0.717194	+	2.48099i	−0.0251531	+	0.0870121i
$814$	1.33784	−	9.30486i	0.0468911	−	0.326135i
$815$	−31.8050	−	69.6432i	−1.11408	−	2.43950i
$816$	−9.12678	−	61.6415i	−0.319501	−	2.15789i
$817$	−4.20069	+	14.3062i	−0.146964	+	0.500512i
$818$	1.86695	+	4.08804i	0.0652763	+	0.142935i
$819$	2.72071	+	15.1919i	0.0950692	+	0.530848i
$820$	9.54114	−	11.0111i	0.333191	−	0.384523i
$821$	−3.30448	−	1.50911i	−0.115327	−	0.0526682i	0.356916	−	0.934137i	$-0.383828\pi$
$821$	−3.30448	−	1.50911i	−0.115327	−	0.0526682i	−0.472243	+	0.881468i	$0.656556\pi$
$822$	−2.14402	+	15.3693i	−0.0747811	+	0.536068i
$823$	−5.21289	−	36.2565i	−0.181710	−	1.26382i	−0.852718	−	0.522371i	$-0.825048\pi$
$823$	−5.21289	−	36.2565i	−0.181710	−	1.26382i	0.671008	−	0.741450i	$-0.265862\pi$
$824$	5.83935	−	3.75272i	0.203423	−	0.130732i
$825$	−38.3414	−	17.3159i	−1.33487	−	0.602863i
$826$	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	$-0.0123902\pi$
$828$	7.57303	−	4.12184i	0.263181	−	0.143244i
$829$		−	31.0778i		−	1.07938i	−0.841865	−	0.539689i	$-0.818542\pi$
$829$		−	31.0778i		−	1.07938i	0.841865	−	0.539689i	$-0.181458\pi$
$830$	7.39941	+	25.2001i	0.256837	+	0.874707i
$831$	14.9430	−	33.0871i	0.518366	−	1.14778i
$832$	4.60614	+	7.16730i	0.159689	+	0.248481i
$833$	−42.2549	+	30.3735i	−1.46405	+	1.05238i
$834$	4.16247	−	29.8386i	0.144135	−	1.03323i
$835$	−18.5261	+	40.5665i	−0.641122	+	1.40386i
$836$	3.52045	−	4.06281i	0.121757	−	0.140515i
$837$	−30.6878	−	13.5506i	−1.06073	−	0.468376i
$838$	27.9231	−	12.7520i	0.964587	−	0.440512i
$839$	26.7655	+	7.85907i	0.924049	+	0.271325i	0.708943	−	0.705266i	$-0.249172\pi$
$839$	26.7655	+	7.85907i	0.924049	+	0.271325i	0.215106	+	0.976591i	$0.430990\pi$
$840$	15.8549	−	37.6912i	0.547046	−	1.30047i
$841$	11.1574	+	24.4312i	0.384737	+	0.842457i
$842$	−47.6641	−	6.85307i	−1.64262	−	0.236172i
$843$	1.13946	−	3.94174i	0.0392452	−	0.135761i
$844$	3.64041	−	7.97138i	0.125308	−	0.274386i
$845$	30.6440	+	19.6937i	1.05419	+	0.677484i
$846$	−6.80023	+	10.7791i	−0.233797	+	0.370594i
$847$	−0.396597	−	15.2376i	−0.0136272	−	0.523572i
$848$	−19.5910	+	16.9757i	−0.672759	+	0.582949i
$849$	−12.8321	+	11.2137i	−0.440398	+	0.384853i
$850$		−	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	0.875588	+	0.483059i	$0.160474\pi$
$853$	11.6871	+	39.8025i	0.400158	+	1.36281i	−0.475430	+	0.879754i	$0.657707\pi$
$854$	60.6690	−	10.3406i	2.07605	−	0.353850i
$855$	46.0388	+	6.22563i	1.57449	+	0.212912i
$856$	−0.410355	−	2.85408i	−0.0140257	−	0.0975506i
$857$	23.8331	+	15.3166i	0.814123	+	0.523205i	0.880196	−	0.474610i	$-0.157411\pi$
$857$	23.8331	+	15.3166i	0.814123	+	0.523205i	−0.0660737	+	0.997815i	$0.521047\pi$
$858$	0.0521307	+	12.4278i	0.00177971	+	0.424278i
$859$	−2.79686	−	2.42349i	−0.0954275	−	0.0826884i	0.605841	−	0.795586i	$-0.292837\pi$
$859$	−2.79686	−	2.42349i	−0.0954275	−	0.0826884i	−0.701268	+	0.712898i	$0.747382\pi$
$860$	1.28199	−	8.91641i	0.0437154	−	0.304047i
$861$	−8.75778	−	26.8025i	−0.298464	−	0.913428i
$862$	−16.9217	−	4.96867i	−0.576357	−	0.169234i
$863$	4.42496	−	15.0700i	0.150627	−	0.512990i	−0.849260	−	0.527974i	$-0.822952\pi$
$863$	4.42496	−	15.0700i	0.150627	−	0.512990i	0.999888	+	0.0149846i	$0.00476993\pi$
$864$	−16.8672	+	2.64218i	−0.573833	+	0.0898889i
$865$	0.441063	−	3.06766i	0.0149966	−	0.104304i
$866$	38.8582	−	44.8447i	1.32046	−	1.52389i
$867$	−66.2778	+	0.278014i	−2.25091	+	0.00944186i
$868$	−4.49310	−	9.19740i	−0.152506	−	0.312180i
$869$	−28.7279	+	4.13044i	−0.974526	+	0.140116i
$870$	13.6201	+	8.67258i	0.461764	+	0.294028i
$871$	−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
$876$	1.25961	−	1.10074i	0.0425584	−	0.0371907i
$877$	4.18196	+	4.82624i	0.141215	+	0.162970i	0.821951	−	0.569558i	$-0.192886\pi$
$877$	4.18196	+	4.82624i	0.141215	+	0.162970i	−0.680737	+	0.732528i	$0.738340\pi$
$878$	−6.83938	+	4.39540i	−0.230818	+	0.148338i
$879$	−16.2380	+	10.5320i	−0.547695	+	0.355237i
$880$	23.6617	−	36.8184i	0.797637	−	1.24115i
$881$	−23.6193	+	51.7191i	−0.795755	+	1.74246i	−0.136365	+	0.990659i	$0.543542\pi$
$881$	−23.6193	+	51.7191i	−0.795755	+	1.74246i	−0.659390	+	0.751801i	$0.729185\pi$
$882$	19.9911	+	27.3246i	0.673137	+	0.920068i
$883$	−4.06965	+	28.3050i	−0.136955	+	0.952541i	0.799228	+	0.601028i	$0.205242\pi$
$883$	−4.06965	+	28.3050i	−0.136955	+	0.952541i	−0.936183	+	0.351513i	$0.885667\pi$
$884$	−7.87986	+	3.59861i	−0.265028	+	0.121034i
$885$	14.2838	+	96.4714i	0.480144	+	3.24285i
$886$	−1.40183	−	0.411614i	−0.0470953	−	0.0138284i
$887$	7.05187	+	15.4414i	0.236779	+	0.518473i	0.990299	−	0.138951i	$-0.0443732\pi$
$887$	7.05187	+	15.4414i	0.236779	+	0.518473i	−0.753521	+	0.657424i	$0.771646\pi$
$888$	2.84738	+	9.54892i	0.0955517	+	0.320441i
$889$	−1.21692	−	3.77789i	−0.0408141	−	0.126706i
$890$	35.5704	+	16.2444i	1.19232	+	0.544515i
$891$	18.8789	+	8.24176i	0.632467	+	0.276109i
$892$	−4.26756	+	0.613582i	−0.142888	+	0.0205443i
$893$	5.58349	+	8.68808i	0.186844	+	0.290736i
$894$	8.48391	−	18.7853i	0.283744	−	0.628274i
$895$	11.2327	+	38.2552i	0.375469	+	1.27873i
$896$	30.8463	+	18.7079i	1.03050	+	0.624988i
$897$	11.3575	+	11.4843i	0.379215	+	0.383450i
$898$	−31.8887			−1.06414
$899$	−9.06516	+	2.66177i	−0.302340	+	0.0887751i
$900$	−19.0780	+	0.160055i	−0.635933	+	0.00533517i
$901$	21.5290	+	33.4997i	0.717234	+	1.11604i
$902$	−3.23136	−	22.4746i	−0.107592	−	0.748322i
$903$	−13.5143	−	11.0133i	−0.449728	−	0.366499i
$904$	−10.3140	+	22.5845i	−0.343038	+	0.751149i
$905$	−38.3139	−	33.1992i	−1.27360	−	1.10358i
$906$	−18.2338	−	61.1487i	−0.605778	−	2.03153i
$907$	−4.52283	−	9.90362i	−0.150178	−	0.328844i	0.819559	−	0.572994i	$-0.194218\pi$
$907$	−4.52283	−	9.90362i	−0.150178	−	0.328844i	−0.969737	+	0.244150i	$0.921491\pi$
$908$	3.77363	+	1.10804i	0.125232	+	0.0367715i
$909$	−25.1307	+	16.4501i	−0.833534	+	0.545614i
$910$	−32.5488	−	3.81835i	−1.07898	−	0.126577i
$911$	−45.7113	−	6.57229i	−1.51448	−	0.217750i	−0.665591	−	0.746317i	$-0.731821\pi$
$911$	−45.7113	−	6.57229i	−1.51448	−	0.217750i	−0.848892	+	0.528567i	$0.822730\pi$
$912$	−9.12317	+	31.5598i	−0.302098	+	1.04505i
$913$	8.58388	+	3.92013i	0.284085	+	0.129737i
$914$	28.3558	−	44.1225i	0.937927	−	1.45944i
$915$	53.7318	+	82.8422i	1.77632	+	2.73868i
$916$	2.96061	+	4.60681i	0.0978214	+	0.152213i
$917$	12.8882	−	2.19671i	0.425607	−	0.0725419i
$918$	0.783688	+	62.2733i	0.0258655	+	2.05533i
$919$	−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
$924$	2.78271	+	5.63614i	0.0915443	+	0.185415i
$925$	3.84735	+	26.7589i	0.126500	+	0.879828i
$926$	−29.5233	+	45.9392i	−0.970196	+	1.50966i
$927$	−8.35533	+	3.90079i	−0.274425	+	0.128119i
$928$	−3.14879	+	3.63390i	−0.103364	+	0.119289i
$929$	−5.43248	+	37.7838i	−0.178234	+	1.23964i	0.682613	+	0.730780i	$0.260844\pi$
$929$	−5.43248	+	37.7838i	−0.178234	+	1.23964i	−0.860847	+	0.508865i	$0.830065\pi$
$930$	46.4214	−	54.0294i	1.52222	−	1.77169i
$931$	26.9159	−	5.31176i	0.882134	−	0.174086i
$932$	−3.32392	+	11.3202i	−0.108878	+	0.370806i
$933$	−1.54638	+	1.79982i	−0.0506262	+	0.0589234i
$934$	7.28650	+	1.04764i	0.238422	+	0.0342798i
$935$	−50.8102	−	44.0273i	−1.66167	−	1.43985i
$936$	−5.57275	−	11.9366i	−0.182151	−	0.390160i
$937$	−31.5027	+	49.0191i	−1.02915	+	1.60138i	−0.256505	+	0.966543i	$0.582571\pi$
$937$	−31.5027	+	49.0191i	−1.02915	+	1.60138i	−0.772643	+	0.634841i	$0.781065\pi$
$938$	−14.6543	+	34.4321i	−0.478478	+	1.12425i
$939$	1.72653	−	2.71148i	0.0563433	−	0.0884858i
$940$	−4.08597	−	4.71546i	−0.133270	−	0.153801i
$941$	−42.6511	+	12.5235i	−1.39039	+	0.408255i	−0.889372	−	0.457184i	$-0.848858\pi$
$941$	−42.6511	+	12.5235i	−1.39039	+	0.408255i	−0.501015	+	0.865439i	$0.667040\pi$
$942$	−18.0750	−	39.1434i	−0.588915	−	1.27536i
$943$	−23.4499	−	17.9137i	−0.763632	−	0.583350i
$944$	−68.9620			−2.24452
$945$	−27.5821	+	46.7964i	−0.897245	+	1.52229i
$946$	−9.19318	−	10.6095i	−0.298896	−	0.344944i
$947$	9.28510	+	14.4479i	0.301725	+	0.469493i	0.958700	−	0.284419i	$-0.0918007\pi$
$947$	9.28510	+	14.4479i	0.301725	+	0.469493i	−0.656975	+	0.753912i	$0.728164\pi$
$948$	−11.0426	+	7.16226i	−0.358646	+	0.232619i
$949$	2.63621	+	1.69419i	0.0855751	+	0.0549958i
$950$	−27.8558	+	60.9957i	−0.903761	+	1.97896i
$951$	4.60034	−	15.9140i	0.149176	−	0.516046i
$952$	28.2042	−	34.3141i	0.914102	−	1.11213i
$953$	17.3080	−	7.90430i	0.560661	−	0.256045i	−0.114865	−	0.993381i	$-0.536644\pi$
$953$	17.3080	−	7.90430i	0.560661	−	0.256045i	0.675526	+	0.737336i	$0.263916\pi$
$954$	21.6769	−	14.1893i	0.701816	−	0.459394i
$955$	21.5368	−	73.3478i	0.696916	−	2.37348i
$956$	−0.911012	+	0.416045i	−0.0294642	+	0.0134559i
$957$	5.55966	−	1.65783i	0.179718	−	0.0535899i
$958$	29.9814	+	25.9790i	0.968655	+	0.839344i
$959$	−12.1578	+	8.26811i	−0.392597	+	0.266991i
$960$	−4.14295	+	29.6987i	−0.133713	+	0.958520i
$961$	1.51991	+	10.5712i	0.0490294	+	0.341007i
$962$	6.71835	−	4.31762i	0.216608	−	0.139206i
$963$	0.0321347	+	3.83034i	0.00103553	+	0.123431i
$964$	0.697109	+	2.37414i	0.0224524	+	0.0764658i
$965$	−11.0557			−0.355895
$966$	33.4448	+	11.7003i	1.07607	+	0.376451i
$967$	−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
$969$	45.9928	+	20.7715i	1.47750	+	0.667276i
$970$	−20.6684	+	13.2828i	−0.663622	+	0.426484i
$971$	−2.50655	−	17.4335i	−0.0804391	−	0.559467i	−0.989691	−	0.143220i	$-0.954254\pi$
$971$	−2.50655	−	17.4335i	−0.0804391	−	0.559467i	0.909252	−	0.416247i	$-0.136655\pi$
$972$	9.33974	−	0.195914i	0.299572	−	0.00628394i
$973$	23.6037	−	16.0520i	0.756700	−	0.514604i
$974$	21.6873	+	18.7922i	0.694906	+	0.602139i
$975$	−10.2129	−	34.2500i	−0.327076	−	1.09688i
$976$	−63.5140	+	29.0059i	−2.03303	+	0.928455i
$977$	5.73157	−	19.5199i	0.183369	−	0.624498i	−0.815579	−	0.578646i	$-0.803581\pi$
$977$	5.73157	−	19.5199i	0.183369	−	0.624498i	0.998948	−	0.0458526i	$-0.0146005\pi$
$978$	−53.5255	+	7.92511i	−1.71156	+	0.253417i
$979$	12.7805	−	5.83664i	0.408465	−	0.186540i
$980$	−15.6392	+	5.49072i	−0.499576	+	0.175394i
$981$	−0.269203	−	1.76699i	−0.00859500	−	0.0564155i
$982$	−10.1428	+	22.2097i	−0.323671	+	0.708741i
$983$	−31.5001	−	20.2439i	−1.00470	−	0.645680i	−0.0686819	−	0.997639i	$-0.521879\pi$
$983$	−31.5001	−	20.2439i	−1.00470	−	0.645680i	−0.936015	+	0.351959i	$0.885516\pi$
$984$	13.0968	+	20.1922i	0.417510	+	0.643705i
$985$	0.157746	+	0.245458i	0.00502621	+	0.00782094i
$986$	11.4861	+	13.2557i	0.365793	+	0.422148i
$987$	−11.8950	+	2.07882i	−0.378624	+	0.0661695i
$988$	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	−0.505848	−	0.862623i	$-0.668820\pi$
$991$	−14.6390	+	4.29841i	−0.465025	+	0.136544i	0.0408230	+	0.999166i	$0.487002\pi$
$992$	13.8911	+	16.0312i	0.441043	+	0.508991i
$993$	−6.17302	−	3.93067i	−0.195895	−	0.124736i
$994$	−23.0682	−	9.81777i	−0.731678	−	0.311401i
$995$	−23.1908	+	36.0856i	−0.735198	+	1.14399i
$996$	4.27945	−	0.0179509i	0.135599	−	0.000568797i
$997$	40.8953	+	35.4360i	1.29517	+	1.12227i	0.985179	+	0.171528i	$0.0548704\pi$
$997$	40.8953	+	35.4360i	1.29517	+	1.12227i	0.309988	+	0.950741i	$0.399675\pi$
$998$	−36.0199	−	5.17889i	−1.14019	−	0.163935i
$999$	−2.04857	−	13.0777i	−0.0648138	−	0.413759i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.v.a.41.17	✓	600	161.41	odd	22	inner
483.2.v.a.41.18	yes	600	23.18	even	11	inner
483.2.v.a.41.43	yes	600	483.41	even	22	inner
483.2.v.a.41.44	yes	600	69.41	odd	22	inner
483.2.v.a.377.17	yes	600	3.2	odd	2	inner
483.2.v.a.377.18	yes	600	21.20	even	2	inner
483.2.v.a.377.43	yes	600	1.1	even	1	trivial
483.2.v.a.377.44	yes	600	7.6	odd	2	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} +(-0.712905 + 1.57853i) q^{3} +(-0.504143 + 0.323993i) q^{4} +(-0.562316 - 3.91099i) q^{5} +(-2.76568 - 0.385811i) q^{6} +(-1.48783 - 2.18778i) q^{7} +(1.70670 + 1.47886i) q^{8} +(-1.98353 - 2.25069i) q^{9} +(5.79458 - 2.64630i) q^{10} +(0.644839 - 2.19612i) q^{11} +(-0.152028 - 1.02678i) q^{12} +(1.76874 - 0.807755i) q^{13} +(2.70852 - 3.29528i) q^{14} +(6.57451 + 1.90053i) q^{15} +(-2.01037 + 4.40209i) q^{16} +(6.25396 + 4.01918i) q^{17} +(2.58068 - 4.09067i) q^{18} +(-2.11893 - 3.29712i) q^{19} +(1.55062 + 1.78951i) q^{20} +(4.51416 - 0.788909i) 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} +(4.96686 - 1.52655i) q^{27} +(1.45890 + 0.620907i) q^{28} +(0.791187 - 1.23111i) q^{29} +(0.0462820 + 11.0335i) q^{30} +(-4.87912 - 4.22778i) q^{31} +(-3.25223 - 0.467600i) q^{32} +(3.00694 + 2.58352i) q^{33} +(-3.37669 + 11.5000i) q^{34} +(-7.71975 + 7.04910i) q^{35} +(1.72919 + 0.492018i) q^{36} +(0.362545 - 2.52156i) q^{37} +(4.13793 - 4.77542i) q^{38} +(0.0141271 + 3.36786i) q^{39} +(4.82411 - 7.50647i) q^{40} +(-0.875678 - 6.09047i) q^{41} +(3.27079 + 6.62471i) 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} +(-5.51565 - 6.31170i) q^{48} +(-2.57274 + 6.51007i) q^{49} +(-9.24985 - 14.3930i) q^{50} +(-10.8029 + 7.00680i) q^{51} +(-0.629989 + 0.980282i) q^{52} +(4.87250 + 2.22520i) q^{53} +(4.61748 + 6.98995i) q^{54} +(-8.95161 - 1.28705i) q^{55} +(0.696148 - 5.93417i) q^{56} +(6.71521 - 0.994269i) q^{57} +(2.26380 + 0.664712i) q^{58} +(5.91969 + 12.9623i) q^{59} +(-3.93025 + 1.17196i) q^{60} +(10.9041 + 9.44842i) q^{61} +(4.32386 - 9.46794i) q^{62} +(-1.97285 + 7.68816i) q^{63} +(0.623565 + 4.33699i) q^{64} +(-4.15371 - 6.46330i) q^{65} +(-2.63070 + 5.82498i) q^{66} +(-8.41744 + 2.47158i) q^{67} -4.45508 q^{68} +(2.85960 + 7.79889i) q^{69} +(-14.4108 - 8.74002i) q^{70} +(-1.65586 - 5.63935i) q^{71} +(-0.0568357 - 6.77462i) q^{72} +(0.871295 + 1.35576i) q^{73} +(4.06533 - 0.584506i) q^{74} +(2.53950 - 18.2043i) q^{75} +(2.13649 + 0.975701i) q^{76} +(-5.76403 + 1.85668i) q^{77} +(-5.20340 + 1.55159i) q^{78} +(-5.26762 - 11.5345i) q^{79} +(18.3470 + 5.38717i) q^{80} +(-1.13119 + 8.92863i) q^{81} +(9.02373 - 4.12100i) q^{82} +(-0.586751 + 4.08094i) q^{83} +(-2.02018 + 1.86028i) q^{84} +(12.2023 - 26.7192i) q^{85} +(3.31598 - 5.15976i) q^{86} +(1.37931 + 2.12658i) q^{87} +(4.34830 - 2.79449i) q^{88} +(4.01990 + 4.63921i) q^{89} +(-17.4497 - 7.79277i) 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} +(3.05665 - 4.80040i) q^{96} +(-3.81751 + 0.548876i) q^{97} +(-11.2391 - 1.02283i) q^{98} +(-6.22184 + 2.90475i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more