LMFDB - Embedded newform 230.2.l.a.57.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			57.7
Character	$\chi$	$=$	230.57
Dual form			230.2.l.a.113.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.977147 + 0.212565i) q^{2} +(-2.01135 - 2.68685i) q^{3} +(0.909632 + 0.415415i) q^{4} +(0.984796 - 2.00753i) q^{5} +(-1.39425 - 3.05299i) q^{6} +(-4.01185 - 0.286933i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-2.32843 + 7.92991i) q^{9} +(1.38902 - 1.75232i) q^{10} +(0.608409 - 0.946702i) q^{11} +(-0.713431 - 3.27959i) q^{12} +(-0.125198 - 1.75050i) q^{13} +(-3.85918 - 1.13316i) q^{14} +(-7.37470 + 1.39185i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.755932 + 0.281948i) q^{17} +(-3.96085 + 7.25375i) q^{18} +(2.21800 - 4.85675i) q^{19} +(1.72976 - 1.41701i) q^{20} +(7.29830 + 11.3564i) q^{21} +(0.795741 - 0.795741i) q^{22} +(2.43518 - 4.13157i) q^{23} -3.35629i q^{24} +(-3.06035 - 3.95402i) q^{25} +(0.249758 - 1.73710i) q^{26} +(16.5558 - 6.17498i) q^{27} +(-3.53011 - 1.92759i) q^{28} +(2.62114 - 1.19703i) q^{29} +(-7.50202 - 0.207567i) q^{30} +(0.498555 + 3.46753i) q^{31} +(0.479249 + 0.877679i) q^{32} +(-3.76737 + 0.269448i) q^{33} +(0.678725 + 0.436190i) q^{34} +(-4.52689 + 7.77135i) q^{35} +(-5.41222 + 6.24604i) q^{36} +(2.11094 - 1.15266i) q^{37} +(3.19969 - 4.27428i) q^{38} +(-4.45150 + 3.85725i) q^{39} +(1.99144 - 1.01694i) q^{40} +(2.27425 - 0.667780i) q^{41} +(4.71754 + 12.6482i) q^{42} +(-3.32960 + 2.49251i) q^{43} +(0.946702 - 0.608409i) q^{44} +(13.6265 + 12.4837i) q^{45} +(3.25776 - 3.51952i) q^{46} +(2.95054 + 2.95054i) q^{47} +(0.713431 - 3.27959i) q^{48} +(9.08389 + 1.30607i) q^{49} +(-2.14993 - 4.51418i) q^{50} +(-0.762893 - 2.59817i) q^{51} +(0.613298 - 1.64432i) q^{52} +(-0.481343 + 6.73006i) q^{53} +(17.4900 - 2.51468i) q^{54} +(-1.30137 - 2.15371i) q^{55} +(-3.03970 - 2.63392i) q^{56} +(-17.5105 + 3.80918i) q^{57} +(2.81568 - 0.612514i) q^{58} +(-2.62284 - 2.27270i) q^{59} +(-7.28646 - 1.79749i) q^{60} +(11.6181 - 1.67044i) q^{61} +(-0.249914 + 3.49426i) q^{62} +(11.6167 - 31.1456i) q^{63} +(0.281733 + 0.959493i) q^{64} +(-3.63747 - 1.47254i) q^{65} +(-3.73855 - 0.537522i) q^{66} +(0.282344 - 1.29791i) q^{67} +(0.570495 + 0.570495i) q^{68} +(-15.9989 + 1.76708i) q^{69} +(-6.07535 + 6.63149i) q^{70} +(-12.9901 + 8.34826i) q^{71} +(-6.61623 + 4.95285i) q^{72} +(2.52331 + 6.76526i) q^{73} +(2.30772 - 0.677607i) q^{74} +(-4.46840 + 16.1756i) q^{75} +(4.03513 - 3.49646i) q^{76} +(-2.71249 + 3.62346i) q^{77} +(-5.16969 + 2.82286i) q^{78} +(6.05650 - 6.98957i) q^{79} +(2.16209 - 0.570393i) q^{80} +(-29.0326 - 18.6581i) q^{81} +(2.36422 - 0.169092i) q^{82} +(-2.15217 - 3.94140i) q^{83} +(1.92116 + 13.3619i) q^{84} +(1.31046 - 1.23990i) q^{85} +(-3.78333 + 1.72779i) q^{86} +(-8.48827 - 4.63494i) q^{87} +(1.05439 - 0.393269i) q^{88} +(0.442275 - 3.07609i) q^{89} +(10.6615 + 15.0950i) q^{90} +7.05866i q^{91} +(3.93144 - 2.74660i) q^{92} +(8.31396 - 8.31396i) q^{93} +(2.25593 + 3.51029i) q^{94} +(-7.56579 - 9.23561i) q^{95} +(1.39425 - 3.05299i) q^{96} +(8.91998 - 16.3357i) q^{97} +(8.59867 + 3.20714i) q^{98} +(6.09063 + 7.02896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$3$	−2.01135	−	2.68685i	−1.16125	−	1.55125i	−0.778792	−	0.627282i	$-0.784167\pi$
$3$	−2.01135	−	2.68685i	−1.16125	−	1.55125i	−0.382462	−	0.923971i	$-0.624924\pi$
$4$	0.909632	+	0.415415i	0.454816	+	0.207708i
$5$	0.984796	−	2.00753i	0.440414	−	0.897795i
$5$	0.984796	−	2.00753i	0.440414	−	0.897795i
$6$	−1.39425	−	3.05299i	−0.569202	−	1.24638i
$7$	−4.01185	−	0.286933i	−1.51634	−	0.108451i	−0.711813	−	0.702369i	$-0.752126\pi$
$7$	−4.01185	−	0.286933i	−1.51634	−	0.108451i	−0.804525	+	0.593918i	$0.797580\pi$
$8$	0.800541	+	0.599278i	0.283034	+	0.211877i
$9$	−2.32843	+	7.92991i	−0.776144	+	2.64330i
$10$	1.38902	−	1.75232i	0.439247	−	0.554132i
$11$	0.608409	−	0.946702i	0.183442	−	0.285442i	−0.737338	−	0.675524i	$-0.763917\pi$
$11$	0.608409	−	0.946702i	0.183442	−	0.285442i	0.920780	+	0.390083i	$0.127554\pi$
$12$	−0.713431	−	3.27959i	−0.205950	−	0.946736i
$13$	−0.125198	−	1.75050i	−0.0347237	−	0.485500i	−0.984824	−	0.173556i	$-0.944474\pi$
$13$	−0.125198	−	1.75050i	−0.0347237	−	0.485500i	0.950100	−	0.311944i	$-0.100980\pi$
$14$	−3.85918	−	1.13316i	−1.03141	−	0.302849i
$15$	−7.37470	+	1.39185i	−1.90414	+	0.359373i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	0.755932	+	0.281948i	0.183341	+	0.0683825i	0.439458	−	0.898263i	$-0.355171\pi$
$17$	0.755932	+	0.281948i	0.183341	+	0.0683825i	−0.256117	+	0.966646i	$0.582443\pi$
$18$	−3.96085	+	7.25375i	−0.933580	+	1.70972i
$19$	2.21800	−	4.85675i	0.508845	−	1.11421i	−0.464648	−	0.885495i	$-0.653819\pi$
$19$	2.21800	−	4.85675i	0.508845	−	1.11421i	0.973493	−	0.228719i	$-0.0734536\pi$
$20$	1.72976	−	1.41701i	0.386786	−	0.316854i
$21$	7.29830	+	11.3564i	1.59262	+	2.47816i
$22$	0.795741	−	0.795741i	0.169652	−	0.169652i
$23$	2.43518	−	4.13157i	0.507770	−	0.861493i
$23$	2.43518	−	4.13157i	0.507770	−	0.861493i
$24$		−	3.35629i		−	0.685100i
$25$	−3.06035	−	3.95402i	−0.612071	−	0.790803i
$26$	0.249758	−	1.73710i	0.0489816	−	0.340674i
$27$	16.5558	−	6.17498i	3.18616	−	1.18837i
$28$	−3.53011	−	1.92759i	−0.667129	−	0.364280i
$29$	2.62114	−	1.19703i	0.486733	−	0.222283i	−0.156905	−	0.987614i	$-0.550152\pi$
$29$	2.62114	−	1.19703i	0.486733	−	0.222283i	0.643638	+	0.765330i	$0.277424\pi$
$30$	−7.50202	−	0.207567i	−1.36968	−	0.0378963i
$31$	0.498555	+	3.46753i	0.0895432	+	0.622786i	0.984336	+	0.176304i	$0.0564142\pi$
$31$	0.498555	+	3.46753i	0.0895432	+	0.622786i	−0.894793	+	0.446482i	$0.852677\pi$
$32$	0.479249	+	0.877679i	0.0847201	+	0.155153i
$33$	−3.76737	+	0.269448i	−0.655815	+	0.0469048i
$34$	0.678725	+	0.436190i	0.116400	+	0.0748059i
$35$	−4.52689	+	7.77135i	−0.765183	+	1.31360i
$36$	−5.41222	+	6.24604i	−0.902037	+	1.04101i
$37$	2.11094	−	1.15266i	0.347037	−	0.189496i	−0.296271	−	0.955104i	$-0.595743\pi$
$37$	2.11094	−	1.15266i	0.347037	−	0.189496i	0.643308	+	0.765607i	$0.277561\pi$
$38$	3.19969	−	4.27428i	0.519058	−	0.693381i
$39$	−4.45150	+	3.85725i	−0.712811	+	0.617654i
$40$	1.99144	−	1.01694i	0.314874	−	0.160793i
$41$	2.27425	−	0.667780i	0.355178	−	0.104290i	−0.0992759	−	0.995060i	$-0.531653\pi$
$41$	2.27425	−	0.667780i	0.355178	−	0.104290i	0.454454	+	0.890770i	$0.349834\pi$
$42$	4.71754	+	12.6482i	0.727932	+	1.95166i
$43$	−3.32960	+	2.49251i	−0.507759	+	0.380104i	−0.822223	−	0.569166i	$-0.807266\pi$
$43$	−3.32960	+	2.49251i	−0.507759	+	0.380104i	0.314464	+	0.949269i	$0.398175\pi$
$44$	0.946702	−	0.608409i	0.142721	−	0.0917211i
$45$	13.6265	+	12.4837i	2.03132	+	1.86097i
$46$	3.25776	−	3.51952i	0.480330	−	0.518925i
$47$	2.95054	+	2.95054i	0.430380	+	0.430380i	0.888758	−	0.458377i	$-0.151569\pi$
$47$	2.95054	+	2.95054i	0.430380	+	0.430380i	−0.458377	+	0.888758i	$0.651569\pi$
$48$	0.713431	−	3.27959i	0.102975	−	0.473368i
$49$	9.08389	+	1.30607i	1.29770	+	0.186581i
$50$	−2.14993	−	4.51418i	−0.304046	−	0.638401i
$51$	−0.762893	−	2.59817i	−0.106826	−	0.363817i
$52$	0.613298	−	1.64432i	0.0850492	−	0.228026i
$53$	−0.481343	+	6.73006i	−0.0661176	+	0.924445i	0.850831	+	0.525439i	$0.176099\pi$
$53$	−0.481343	+	6.73006i	−0.0661176	+	0.924445i	−0.916949	+	0.399005i	$0.869356\pi$
$54$	17.4900	−	2.51468i	2.38009	−	0.342205i
$55$	−1.30137	−	2.15371i	−0.175477	−	0.290406i
$56$	−3.03970	−	2.63392i	−0.406197	−	0.351972i
$57$	−17.5105	+	3.80918i	−2.31933	+	0.504539i
$58$	2.81568	−	0.612514i	0.369717	−	0.0804270i
$59$	−2.62284	−	2.27270i	−0.341465	−	0.295881i	0.467199	−	0.884152i	$-0.345263\pi$
$59$	−2.62284	−	2.27270i	−0.341465	−	0.295881i	−0.808664	+	0.588271i	$0.799809\pi$
$60$	−7.28646	−	1.79749i	−0.940678	−	0.232055i
$61$	11.6181	−	1.67044i	1.48755	−	0.213877i	0.649873	−	0.760043i	$-0.274822\pi$
$61$	11.6181	−	1.67044i	1.48755	−	0.213877i	0.837677	+	0.546166i	$0.183913\pi$
$62$	−0.249914	+	3.49426i	−0.0317392	+	0.443771i
$63$	11.6167	−	31.1456i	1.46357	−	3.92397i
$64$	0.281733	+	0.959493i	0.0352166	+	0.119937i
$65$	−3.63747	−	1.47254i	−0.451172	−	0.182647i
$66$	−3.73855	−	0.537522i	−0.460184	−	0.0661644i
$67$	0.282344	−	1.29791i	0.0344938	−	0.158565i	−0.956678	−	0.291147i	$-0.905963\pi$
$67$	0.282344	−	1.29791i	0.0344938	−	0.158565i	0.991172	+	0.132582i	$0.0423267\pi$
$68$	0.570495	+	0.570495i	0.0691827	+	0.0691827i
$69$	−15.9989	+	1.76708i	−1.92604	+	0.212731i
$70$	−6.07535	+	6.63149i	−0.726143	+	0.792614i
$71$	−12.9901	+	8.34826i	−1.54165	+	0.990756i	−0.554275	+	0.832333i	$0.687005\pi$
$71$	−12.9901	+	8.34826i	−1.54165	+	0.990756i	−0.987371	+	0.158423i	$0.949359\pi$
$72$	−6.61623	+	4.95285i	−0.779730	+	0.583698i
$73$	2.52331	+	6.76526i	0.295331	+	0.791813i	0.996861	+	0.0791731i	$0.0252280\pi$
$73$	2.52331	+	6.76526i	0.295331	+	0.791813i	−0.701530	+	0.712640i	$0.747499\pi$
$74$	2.30772	−	0.677607i	0.268267	−	0.0787702i
$75$	−4.46840	+	16.1756i	−0.515967	+	1.86780i
$76$	4.03513	−	3.49646i	0.462861	−	0.401072i
$77$	−2.71249	+	3.62346i	−0.309117	+	0.412931i
$78$	−5.16969	+	2.82286i	−0.585352	+	0.319626i
$79$	6.05650	−	6.98957i	0.681410	−	0.786389i	−0.304706	−	0.952446i	$-0.598558\pi$
$79$	6.05650	−	6.98957i	0.681410	−	0.786389i	0.986116	+	0.166058i	$0.0531038\pi$
$80$	2.16209	−	0.570393i	0.241729	−	0.0637719i
$81$	−29.0326	−	18.6581i	−3.22584	−	2.07312i
$82$	2.36422	−	0.169092i	0.261085	−	0.0186731i
$83$	−2.15217	−	3.94140i	−0.236231	−	0.432625i	0.732490	−	0.680778i	$-0.238358\pi$
$83$	−2.15217	−	3.94140i	−0.236231	−	0.432625i	−0.968721	+	0.248153i	$0.920176\pi$
$84$	1.92116	+	13.3619i	0.209615	+	1.45791i
$85$	1.31046	−	1.23990i	0.142139	−	0.134486i
$86$	−3.78333	+	1.72779i	−0.407967	+	0.186312i
$87$	−8.48827	−	4.63494i	−0.910038	−	0.496918i
$88$	1.05439	−	0.393269i	0.112399	−	0.0419226i
$89$	0.442275	−	3.07609i	0.0468811	−	0.326065i	−0.952862	−	0.303404i	$-0.901877\pi$
$89$	0.442275	−	3.07609i	0.0468811	−	0.326065i	0.999743	−	0.0226615i	$-0.00721400\pi$
$90$	10.6615	+	15.0950i	1.12382	+	1.59115i
$91$			7.05866i			0.739949i
$92$	3.93144	−	2.74660i	0.409880	−	0.286353i
$93$	8.31396	−	8.31396i	0.862117	−	0.862117i
$94$	2.25593	+	3.51029i	0.232681	+	0.362059i
$95$	−7.56579	−	9.23561i	−0.776233	−	0.947554i
$96$	1.39425	−	3.05299i	0.142300	−	0.311594i
$97$	8.91998	−	16.3357i	0.905686	−	1.65864i	0.165531	−	0.986205i	$-0.447066\pi$
$97$	8.91998	−	16.3357i	0.905686	−	1.65864i	0.740155	−	0.672436i	$-0.234752\pi$
$98$	8.59867	+	3.20714i	0.868597	+	0.323970i
$99$	6.09063	+	7.02896i	0.612131	+	0.706437i
$100$	−1.14124	−	4.86802i	−0.114124	−	0.486802i
$101$	−14.2017	−	4.17000i	−1.41312	−	0.414931i	−0.515954	−	0.856616i	$-0.672563\pi$
$101$	−14.2017	−	4.17000i	−1.41312	−	0.414931i	−0.897170	+	0.441685i	$0.854381\pi$
$102$	−0.193177	−	2.70096i	−0.0191273	−	0.267435i
$103$	2.39916	+	11.0288i	0.236397	+	1.08670i	0.930348	+	0.366677i	$0.119504\pi$
$103$	2.39916	+	11.0288i	0.236397	+	1.08670i	−0.693952	+	0.720022i	$0.744132\pi$
$104$	0.948807	−	1.47637i	0.0930382	−	0.144770i
$105$	29.9856	−	3.46784i	2.92629	−	0.338426i
$106$	−1.90092	+	6.47394i	−0.184634	+	0.628804i
$107$	10.5619	+	7.90654i	1.02106	+	0.764354i	0.972129	−	0.234448i	$-0.0753284\pi$
$107$	10.5619	+	7.90654i	1.02106	+	0.764354i	0.0489288	+	0.998802i	$0.484419\pi$
$108$	17.6248	+	1.26055i	1.69595	+	0.121297i
$109$	−0.619116	−	1.35567i	−0.0593006	−	0.129850i	0.877662	−	0.479281i	$-0.159102\pi$
$109$	−0.619116	−	1.35567i	−0.0593006	−	0.129850i	−0.936962	+	0.349430i	$0.886375\pi$
$110$	−0.813831	−	2.38112i	−0.0775957	−	0.227030i
$111$	−7.34287	−	3.35338i	−0.696955	−	0.318288i
$112$	−2.41036	−	3.21986i	−0.227757	−	0.304248i
$113$	−4.29005	−	0.933242i	−0.403573	−	0.0877920i	0.00619676	−	0.999981i	$-0.498027\pi$
$113$	−4.29005	−	0.933242i	−0.403573	−	0.0877920i	−0.409770	+	0.912189i	$0.634391\pi$
$114$	−17.9201			−1.67837
$115$	−5.89610	−	8.95745i	−0.549814	−	0.835287i
$116$	2.88153			0.267544
$117$	14.1728	+	3.08310i	1.31028	+	0.285033i
$118$	−2.07980	−	2.77829i	−0.191461	−	0.255762i
$119$	−2.95179	−	1.34804i	−0.270590	−	0.123574i
$120$	−6.73786	−	3.30526i	−0.615079	−	0.301728i
$121$	4.04348	+	8.85399i	0.367589	+	0.804908i
$122$	11.7077	+	0.837351i	1.05997	+	0.0758102i
$123$	−6.36853	−	4.76742i	−0.574231	−	0.429864i
$124$	−0.986961	+	3.36128i	−0.0886317	+	0.301852i
$125$	−10.9516	+	2.24985i	−0.979543	+	0.201233i
$126$	17.9717	−	27.9645i	1.60104	−	2.49127i
$127$	3.61120	+	16.6004i	0.320442	+	1.47305i	0.802365	+	0.596834i	$0.203575\pi$
$127$	3.61120	+	16.6004i	0.320442	+	1.47305i	−0.481923	+	0.876214i	$0.660061\pi$
$128$	0.0713392	+	0.997452i	0.00630555	+	0.0881631i
$129$	13.3940	+	3.93283i	1.17927	+	0.346266i
$130$	−3.24133	−	2.21209i	−0.284283	−	0.194013i
$131$	8.64318	+	9.97476i	0.755158	+	0.871499i	0.995058	−	0.0992990i	$-0.0316600\pi$
$131$	8.64318	+	9.97476i	0.755158	+	0.871499i	−0.239900	+	0.970798i	$0.577115\pi$
$132$	−3.53885	−	1.31992i	−0.308018	−	0.114885i
$133$	−10.2919	+	18.8481i	−0.892418	+	1.63434i
$134$	0.551783	−	1.20824i	0.0476668	−	0.104376i
$135$	3.90759	−	39.3173i	0.336312	−	3.38389i
$136$	0.436190	+	0.678725i	0.0374030	+	0.0582001i
$137$	−2.39740	+	2.39740i	−0.204824	+	0.204824i	−0.802063	−	0.597239i	$-0.796264\pi$
$137$	−2.39740	+	2.39740i	−0.204824	+	0.204824i	0.597239	+	0.802063i	$0.296264\pi$
$138$	−16.0089	−	1.67412i	−1.36277	−	0.142510i
$139$			2.52428i			0.214107i	0.994253	+	0.107053i	$0.0341416\pi$
$139$			2.52428i			0.214107i	−0.994253	+	0.107053i	$0.965858\pi$
$140$	−7.34613	+	5.18853i	−0.620862	+	0.438511i
$141$	1.99309	−	13.8622i	0.167848	−	1.16741i
$142$	−14.4678	+	5.39622i	−1.21411	+	0.452841i
$143$	−1.73337	−	0.946492i	−0.144952	−	0.0791496i
$144$	−7.51783	+	3.43328i	−0.626486	+	0.286106i
$145$	0.178206	−	6.44084i	0.0147992	−	0.534883i
$146$	1.02759	+	7.14702i	0.0850436	+	0.591491i
$147$	−14.7617	−	27.0340i	−1.21752	−	2.22973i
$148$	2.39901	−	0.171581i	0.197198	−	0.0141039i
$149$	−8.61031	−	5.53351i	−0.705384	−	0.453323i	0.138141	−	0.990413i	$-0.455887\pi$
$149$	−8.61031	−	5.53351i	−0.705384	−	0.453323i	−0.843525	+	0.537090i	$0.819524\pi$
$150$	−7.80466	+	14.8561i	−0.637248	+	1.21300i
$151$	−4.80931	+	5.55024i	−0.391376	+	0.451672i	−0.916906	−	0.399103i	$-0.869322\pi$
$151$	−4.80931	+	5.55024i	−0.391376	+	0.451672i	0.525530	+	0.850775i	$0.323867\pi$
$152$	4.68614	−	2.55883i	0.380096	−	0.207548i
$153$	−3.99596	+	5.33798i	−0.323054	+	0.431550i
$154$	−3.42072	+	2.96407i	−0.275649	+	0.238852i
$155$	7.45214	+	2.41394i	0.598570	+	0.193893i
$156$	−5.65159	+	1.65946i	−0.452489	+	0.132863i
$157$	−2.41058	−	6.46301i	−0.192385	−	0.515804i	0.804563	−	0.593867i	$-0.202399\pi$
$157$	−2.41058	−	6.46301i	−0.192385	−	0.515804i	−0.996948	+	0.0780624i	$0.975127\pi$
$158$	7.40383	−	5.54244i	0.589017	−	0.440933i
$159$	19.0508	−	12.2432i	1.51083	−	0.970950i
$160$	2.23393	−	0.0977718i	0.176608	−	0.00772954i
$161$	−10.9551	+	15.8765i	−0.863381	+	1.25125i
$162$	−24.4030	−	24.4030i	−1.91728	−	1.91728i
$163$	1.69420	−	7.78812i	0.132700	−	0.610012i	−0.861975	−	0.506951i	$-0.830773\pi$
$163$	1.69420	−	7.78812i	0.132700	−	0.610012i	0.994675	−	0.103061i	$-0.0328638\pi$
$164$	2.34613	+	0.337323i	0.183202	+	0.0263405i
$165$	−3.16917	+	7.82846i	−0.246719	+	0.609445i
$166$	−1.26518	−	4.30881i	−0.0981970	−	0.334428i
$167$	0.375727	−	1.00736i	0.0290747	−	0.0779522i	−0.921601	−	0.388138i	$-0.873118\pi$
$167$	0.375727	−	1.00736i	0.0290747	−	0.0779522i	0.950676	+	0.310186i	$0.100391\pi$
$168$	−0.963032	+	13.4650i	−0.0742996	+	1.03884i
$169$	9.81912	−	1.41178i	0.755317	−	0.108598i
$170$	1.54407	−	0.933002i	0.118425	−	0.0715580i
$171$	33.3491	+	28.8972i	2.55027	+	2.20982i
$172$	−4.06413	+	0.884098i	−0.309887	+	0.0674119i
$173$	−22.4057	+	4.87405i	−1.70347	+	0.370567i	−0.955918	−	0.293634i	$-0.905135\pi$
$173$	−22.4057	+	4.87405i	−1.70347	+	0.370567i	−0.747553	+	0.664202i	$0.768772\pi$
$174$	−7.30906	−	6.33333i	−0.554098	−	0.480129i
$175$	11.1431	+	16.7411i	0.842343	+	1.26550i
$176$	1.11389	−	0.160154i	0.0839628	−	0.0120720i
$177$	−0.830963	+	11.6184i	−0.0624590	+	0.873291i
$178$	1.08604	−	2.91178i	0.0814020	−	0.218247i
$179$	3.00324	+	10.2281i	0.224472	+	0.764483i	0.992303	+	0.123830i	$0.0395179\pi$
$179$	3.00324	+	10.2281i	0.224472	+	0.764483i	−0.767831	+	0.640653i	$0.778664\pi$
$180$	7.20917	+	17.0163i	0.537340	+	1.26832i
$181$	−6.15811	−	0.885402i	−0.457728	−	0.0658114i	−0.0904058	−	0.995905i	$-0.528816\pi$
$181$	−6.15811	−	0.885402i	−0.457728	−	0.0658114i	−0.367323	+	0.930094i	$0.619725\pi$
$182$	−1.50043	+	6.89735i	−0.111219	+	0.511265i
$183$	−27.8564	−	27.8564i	−2.05920	−	2.05920i
$184$	4.42542	−	1.84815i	0.326246	−	0.136247i
$185$	−0.235155	−	5.37292i	−0.0172889	−	0.395025i
$186$	9.89121	−	6.35670i	0.725259	−	0.466096i
$187$	0.726837	−	0.544103i	0.0531516	−	0.0397888i
$188$	1.45821	+	3.90960i	0.106351	+	0.285137i
$189$	−68.1911	+	20.0227i	−4.96017	+	1.45644i
$190$	−5.42971	−	10.6328i	−0.393913	−	0.771382i
$191$	15.0020	−	12.9993i	1.08550	−	0.940595i	0.0870515	−	0.996204i	$-0.472256\pi$
$191$	15.0020	−	12.9993i	1.08550	−	0.940595i	0.998453	+	0.0556092i	$0.0177101\pi$
$192$	2.01135	−	2.68685i	0.145157	−	0.193907i
$193$	14.2406	−	7.77598i	1.02506	−	0.559727i	0.123487	−	0.992346i	$-0.460592\pi$
$193$	14.2406	−	7.77598i	1.02506	−	0.559727i	0.901577	+	0.432619i	$0.142410\pi$
$194$	12.1885	−	14.0663i	0.875086	−	1.00990i
$195$	3.35972	+	12.7351i	0.240595	+	0.911982i
$196$	7.72044	+	4.96162i	0.551460	+	0.354402i
$197$	−7.30656	+	0.522575i	−0.520571	+	0.0372320i	−0.329153	−	0.944277i	$-0.606763\pi$
$197$	−7.30656	+	0.522575i	−0.520571	+	0.0372320i	−0.191418	+	0.981509i	$0.561309\pi$
$198$	4.45733	+	8.16298i	0.316768	+	0.580118i
$199$	0.206468	+	1.43602i	0.0146361	+	0.101796i	0.995830	−	0.0912283i	$-0.0290793\pi$
$199$	0.206468	+	1.43602i	0.0146361	+	0.101796i	−0.981194	+	0.193025i	$0.938170\pi$
$200$	−0.0803856	−	4.99935i	−0.00568412	−	0.353508i
$201$	−4.05519	+	1.85195i	−0.286031	+	0.130626i
$202$	−12.9908	−	7.09350i	−0.914028	−	0.499097i
$203$	−10.8591	+	4.05023i	−0.762158	+	0.284270i
$204$	0.385369	−	2.68030i	0.0269812	−	0.187658i
$205$	0.899084	−	5.22325i	0.0627947	−	0.364807i
$206$			11.2867i			0.786383i
$207$	27.0929	+	28.9309i	1.88308	+	2.01083i
$208$	1.24095	−	1.24095i	0.0860444	−	0.0860444i
$209$	−3.24844	−	5.05467i	−0.224699	−	0.349639i
$210$	30.0375	+	2.98531i	2.07278	+	0.206006i
$211$	6.71315	−	14.6998i	0.462152	−	1.01197i	−0.524839	−	0.851201i	$-0.675875\pi$
$211$	6.71315	−	14.6998i	0.462152	−	1.01197i	0.986992	−	0.160771i	$-0.0513982\pi$
$212$	−3.23361	+	5.92192i	−0.222085	+	0.406719i
$213$	48.5583	+	18.1113i	3.32716	+	1.24097i
$214$	8.63987	+	9.97094i	0.590609	+	0.681600i
$215$	1.72481	+	9.13888i	0.117631	+	0.623266i
$216$	16.9541	+	4.97817i	1.15358	+	0.338722i
$217$	−1.00518	−	14.0543i	−0.0682361	−	0.954066i
$218$	−0.316798	−	1.45630i	−0.0214563	−	0.0986328i
$219$	13.1020	−	20.3871i	0.885349	−	1.37763i
$220$	−0.289090	−	2.49969i	−0.0194904	−	0.168529i
$221$	0.398908	−	1.35856i	0.0268335	−	0.0913864i
$222$	−6.46225	−	4.83758i	−0.433718	−	0.324677i
$223$	−18.9205	−	1.35322i	−1.26701	−	0.0906184i	−0.578402	−	0.815752i	$-0.696323\pi$
$223$	−18.9205	−	1.35322i	−1.26701	−	0.0906184i	−0.688608	+	0.725134i	$0.741778\pi$
$224$	−1.67084	−	3.65863i	−0.111638	−	0.244453i
$225$	38.4808	−	15.0617i	2.56539	−	1.00411i
$226$	−3.99363	−	1.82383i	−0.265652	−	0.121319i
$227$	7.91120	+	10.5681i	0.525085	+	0.701431i	0.982171	−	0.187992i	$-0.0601978\pi$
$227$	7.91120	+	10.5681i	0.525085	+	0.701431i	−0.457086	+	0.889422i	$0.651107\pi$
$228$	−17.5105	−	3.80918i	−1.15966	−	0.252269i
$229$	0.731530			0.0483408			0.0241704	−	0.999708i	$-0.492306\pi$
$229$	0.731530			0.0483408			0.0241704	+	0.999708i	$0.492306\pi$
$230$	−3.85731	−	10.0061i	−0.254344	−	0.659780i
$231$	15.1915			0.999524
$232$	2.81568	+	0.612514i	0.184859	+	0.0402135i
$233$	13.2225	+	17.6633i	0.866238	+	1.15716i	0.986393	+	0.164403i	$0.0525698\pi$
$233$	13.2225	+	17.6633i	0.866238	+	1.15716i	−0.120156	+	0.992755i	$0.538339\pi$
$234$	13.1935	+	6.02529i	0.862489	+	0.393886i
$235$	8.82897	−	3.01762i	0.575939	−	0.196848i
$236$	−1.44170	−	3.15689i	−0.0938470	−	0.205496i
$237$	−30.9617	−	2.21442i	−2.01118	−	0.143842i
$238$	−2.59779	−	1.94468i	−0.168389	−	0.126055i
$239$	0.137096	−	0.466906i	0.00886800	−	0.0302016i	−0.954940	−	0.296798i	$-0.904081\pi$
$239$	0.137096	−	0.466906i	0.00886800	−	0.0302016i	0.963808	+	0.266597i	$0.0858992\pi$
$240$	−5.88129	−	4.66196i	−0.379636	−	0.300928i
$241$	8.20660	−	12.7697i	0.528633	−	0.822570i	−0.469545	−	0.882909i	$-0.655582\pi$
$241$	8.20660	−	12.7697i	0.528633	−	0.822570i	0.998178	+	0.0603392i	$0.0192182\pi$
$242$	2.06902	+	9.51115i	0.133002	+	0.611400i
$243$	4.48150	+	62.6596i	0.287489	+	4.01961i
$244$	11.2622	+	3.30687i	0.720985	+	0.211700i
$245$	11.5677	−	16.9500i	0.739036	−	1.08289i
$246$	−5.20960	−	6.01220i	−0.332152	−	0.383324i
$247$	−8.77941	−	3.27455i	−0.558620	−	0.208355i
$248$	−1.67890	+	3.07467i	−0.106610	+	0.195242i
$249$	−6.26119	+	13.7101i	−0.396787	+	0.868842i
$250$	−11.1796	−	0.129501i	−0.707059	−	0.00819038i
$251$	1.35410	+	2.10703i	0.0854703	+	0.132994i	0.881356	−	0.472452i	$-0.156631\pi$
$251$	1.35410	+	2.10703i	0.0854703	+	0.132994i	−0.795886	+	0.605446i	$0.792995\pi$
$252$	23.5052	−	23.5052i	1.48069	−	1.48069i
$253$	−2.42979	−	4.81908i	−0.152759	−	0.302973i
$254$			16.9887i			1.06596i
$255$	−5.96720	−	1.02714i	−0.373681	−	0.0643221i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	1.48547	−	0.554053i	0.0926614	−	0.0345609i	−0.302706	−	0.953084i	$-0.597890\pi$
$257$	1.48547	−	0.554053i	0.0926614	−	0.0345609i	0.395367	+	0.918523i	$0.370617\pi$
$258$	12.2519	+	6.69004i	0.762770	+	0.416504i
$259$	−8.79953	+	4.01861i	−0.546776	+	0.249704i
$260$	−2.69704	−	2.85053i	−0.167263	−	0.176782i
$261$	3.38923	+	23.5726i	0.209788	+	1.45911i
$262$	6.32537	+	11.5840i	0.390782	+	0.715665i
$263$	−14.8104	+	1.05926i	−0.913247	+	0.0653167i	−0.520048	−	0.854137i	$-0.674086\pi$
$263$	−14.8104	+	1.05926i	−0.913247	+	0.0653167i	−0.393199	+	0.919454i	$0.628632\pi$
$264$	−3.17741	−	2.04200i	−0.195556	−	0.125676i
$265$	13.0368	+	7.59405i	0.800842	+	0.466499i
$266$	−14.0631	+	16.2297i	−0.862265	+	0.995107i
$267$	−9.15457	+	4.99877i	−0.560251	+	0.305920i
$268$	0.796002	−	1.06333i	0.0486236	−	0.0649535i
$269$	8.95770	−	7.76189i	0.546161	−	0.473251i	−0.337535	−	0.941313i	$-0.609593\pi$
$269$	8.95770	−	7.76189i	0.546161	−	0.473251i	0.883696	+	0.468062i	$0.155048\pi$
$270$	12.1758	−	37.5881i	0.740994	−	2.28754i
$271$	13.5629	−	3.98242i	0.823887	−	0.241915i	0.157498	−	0.987519i	$-0.449657\pi$
$271$	13.5629	−	3.98242i	0.823887	−	0.241915i	0.666389	+	0.745604i	$0.267839\pi$
$272$	0.281948	+	0.755932i	0.0170956	+	0.0458351i
$273$	18.9656	−	14.1974i	1.14785	−	0.859268i
$274$	−2.85222	+	1.83301i	−0.172309	+	0.110736i
$275$	−5.60522	+	0.491586i	−0.338008	+	0.0296438i
$276$	−15.2872	−	5.03880i	−0.920181	−	0.303300i
$277$	16.4799	+	16.4799i	0.990184	+	0.990184i	0.999952	−	0.00976828i	$-0.00310939\pi$
$277$	16.4799	+	16.4799i	0.990184	+	0.990184i	−0.00976828	+	0.999952i	$0.503109\pi$
$278$	−0.536575	+	2.46659i	−0.0321816	+	0.147936i
$279$	−28.6580	−	4.12041i	−1.71571	−	0.246682i
$280$	−8.28115	+	3.50842i	−0.494894	+	0.209668i
$281$	2.55433	+	8.69924i	0.152378	+	0.518953i	0.999931	−	0.0117584i	$-0.00374291\pi$
$281$	2.55433	+	8.69924i	0.152378	+	0.518953i	−0.847552	+	0.530712i	$0.821925\pi$
$282$	4.89417	−	13.1218i	0.291443	−	0.781390i
$283$	0.549822	−	7.68752i	0.0326835	−	0.456975i	−0.954588	−	0.297930i	$-0.903704\pi$
$283$	0.549822	−	7.68752i	0.0326835	−	0.456975i	0.987271	−	0.159046i	$-0.0508417\pi$
$284$	−15.2842	+	2.19754i	−0.906953	+	0.130400i
$285$	−9.59725	+	38.9042i	−0.568492	+	2.30448i
$286$	−1.49257	−	1.29332i	−0.0882573	−	0.0764754i
$287$	−9.31556	+	2.02648i	−0.549880	+	0.119619i
$288$	−8.07582	+	1.75679i	−0.475872	+	0.103520i
$289$	−12.3558	−	10.7064i	−0.726812	−	0.629786i
$290$	1.54323	−	6.25577i	0.0906217	−	0.367351i
$291$	−61.8328	+	8.89022i	−3.62470	+	0.521154i
$292$	−0.515105	+	7.20211i	−0.0301443	+	0.421472i
$293$	−1.08136	+	2.89925i	−0.0631739	+	0.169376i	−0.964701	−	0.263346i	$-0.915174\pi$
$293$	−1.08136	+	2.89925i	−0.0631739	+	0.169376i	0.901528	+	0.432722i	$0.142447\pi$
$294$	−8.67784	−	29.5540i	−0.506102	−	1.72363i
$295$	−7.14549	+	3.02728i	−0.416026	+	0.176255i
$296$	2.38066	+	0.342287i	0.138373	+	0.0198950i
$297$	4.22680	−	19.4303i	0.245264	−	1.12746i
$298$	−7.23731	−	7.23731i	−0.419246	−	0.419246i
$299$	−7.53718	−	3.74551i	−0.435887	−	0.216608i
$300$	−10.7842	+	12.8576i	−0.622626	+	0.742335i
$301$	14.0730	−	9.04420i	0.811157	−	0.521299i
$302$	−5.87919	+	4.40111i	−0.338310	+	0.253255i
$303$	17.3605	+	46.5452i	0.997333	+	2.67395i
$304$	5.12297	−	1.50424i	0.293822	−	0.0862740i
$305$	8.08805	−	24.9688i	0.463120	−	1.42971i
$306$	−5.03931	+	4.36659i	−0.288078	+	0.249621i
$307$	−0.0962544	+	0.128581i	−0.00549353	+	0.00733849i	−0.803280	−	0.595602i	$-0.796914\pi$
$307$	−0.0962544	+	0.128581i	−0.00549353	+	0.00733849i	0.797786	+	0.602941i	$0.206004\pi$
$308$	−3.97260	+	2.16921i	−0.226360	+	0.123602i
$309$	24.8071	−	28.6289i	1.41123	−	1.62864i
$310$	6.76871	+	3.94284i	0.384437	+	0.223938i
$311$	−13.5427	−	8.70338i	−0.767937	−	0.493523i	0.0970731	−	0.995277i	$-0.469052\pi$
$311$	−13.5427	−	8.70338i	−0.767937	−	0.493523i	−0.865010	+	0.501754i	$0.832688\pi$
$312$	−5.87518	+	0.420201i	−0.332616	+	0.0237892i
$313$	−10.3241	−	18.9071i	−0.583550	−	1.06869i	−0.988047	−	0.154153i	$-0.950735\pi$
$313$	−10.3241	−	18.9071i	−0.583550	−	1.06869i	0.404497	−	0.914540i	$-0.367447\pi$
$314$	−0.981677	−	6.82772i	−0.0553993	−	0.385310i
$315$	−51.0856	−	53.9929i	−2.87834	−	3.04215i
$316$	8.41276	−	3.84198i	0.473255	−	0.216128i
$317$	9.34421	+	5.10233i	0.524823	+	0.286575i	0.719739	−	0.694245i	$-0.244262\pi$
$317$	9.34421	+	5.10233i	0.524823	+	0.286575i	−0.194916	+	0.980820i	$0.562443\pi$
$318$	21.2179	−	7.91387i	1.18984	−	0.443788i
$319$	0.461488	−	3.20972i	0.0258384	−	0.179710i
$320$	2.20366	+	0.379318i	0.123188	+	0.0212045i
$321$		−	44.2811i		−	2.47153i
$322$	−14.0795	+	13.1850i	−0.784621	+	0.734773i
$323$	3.04601	−	3.04601i	0.169485	−	0.169485i
$324$	−18.6581	−	29.0326i	−1.03656	−	1.61292i
$325$	−6.53834	+	5.85217i	−0.362682	+	0.324620i
$326$	3.31097	−	7.25001i	0.183377	−	0.401541i
$327$	−2.39724	+	4.39021i	−0.132567	+	0.242779i
$328$	2.22081	+	0.828321i	0.122624	+	0.0457364i
$329$	−10.9905	−	12.6837i	−0.605927	−	0.699277i
$330$	−4.76080	+	6.97590i	−0.262073	+	0.384011i
$331$	27.3650	+	8.03509i	1.50412	+	0.441649i	0.927015	−	0.375024i	$-0.122365\pi$
$331$	27.3650	+	8.03509i	1.50412	+	0.441649i	0.577102	+	0.816672i	$0.304184\pi$
$332$	−0.320364	−	4.47927i	−0.0175822	−	0.245832i
$333$	4.22532	+	19.4235i	0.231546	+	1.06440i
$334$	0.581271	−	0.904476i	0.0318058	−	0.0494907i
$335$	−2.32755	−	1.84500i	−0.127168	−	0.100803i
$336$	−3.80321	+	12.9525i	−0.207482	+	0.706618i
$337$	−14.5581	−	10.8981i	−0.793030	−	0.593655i	0.124088	−	0.992271i	$-0.460400\pi$
$337$	−14.5581	−	10.8981i	−0.793030	−	0.593655i	−0.917118	+	0.398617i	$0.869490\pi$
$338$	9.89481	+	0.707691i	0.538207	+	0.0384933i
$339$	6.12130	+	13.4038i	0.332464	+	0.727994i
$340$	1.70711	−	0.583464i	0.0925808	−	0.0316428i
$341$	3.58604	+	1.63769i	0.194195	+	0.0886859i
$342$	26.4444	+	35.3256i	1.42995	+	1.91019i
$343$	−8.55720	−	1.86150i	−0.462045	−	0.100512i
$344$	−4.15918			−0.224248
$345$	−12.2082	+	33.8585i	−0.657268	+	1.82288i
$346$	−22.9297			−1.23271
$347$	10.2161	+	2.22238i	0.548429	+	0.119303i	0.478238	−	0.878230i	$-0.341276\pi$
$347$	10.2161	+	2.22238i	0.548429	+	0.119303i	0.0701906	+	0.997534i	$0.477639\pi$
$348$	−5.79577	−	7.74225i	−0.310686	−	0.415028i
$349$	10.1639	+	4.64172i	0.544063	+	0.248465i	0.668435	−	0.743770i	$-0.266964\pi$
$349$	10.1639	+	4.64172i	0.544063	+	0.248465i	−0.124372	+	0.992236i	$0.539692\pi$
$350$	7.32993	+	18.7271i	0.391801	+	1.00101i
$351$	−12.8820	−	28.2077i	−0.687591	−	1.50562i
$352$	1.12248	+	0.0802814i	0.0598284	+	0.00427901i
$353$	−7.54539	−	5.64841i	−0.401600	−	0.300634i	0.379319	−	0.925266i	$-0.376158\pi$
$353$	−7.54539	−	5.64841i	−0.401600	−	0.300634i	−0.780920	+	0.624632i	$0.785249\pi$
$354$	−3.28164	+	11.1762i	−0.174417	+	0.594010i
$355$	3.96674	+	34.2994i	0.210532	+	1.82043i
$356$	1.68016	−	2.61439i	0.0890485	−	0.138562i
$357$	2.31511	+	10.6424i	0.122529	+	0.563255i
$358$	0.760467	+	10.6327i	0.0401920	+	0.561957i
$359$	13.4794	+	3.95790i	0.711413	+	0.208890i	0.617364	−	0.786678i	$-0.288201\pi$
$359$	13.4794	+	3.95790i	0.711413	+	0.208890i	0.0940495	+	0.995568i	$0.470019\pi$
$360$	3.42735	+	18.1598i	0.180637	+	0.957106i
$361$	−6.22610	−	7.18531i	−0.327690	−	0.378174i
$362$	−5.82917	−	2.17417i	−0.306374	−	0.114272i
$363$	15.6565	−	28.6727i	0.821752	−	1.50493i
$364$	−2.93227	+	6.42078i	−0.153693	+	0.336540i
$365$	16.0664	+	1.59678i	0.840954	+	0.0835792i
$366$	−21.2985	−	33.1410i	−1.11329	−	1.73231i
$367$	−6.23193	+	6.23193i	−0.325304	+	0.325304i	−0.850798	−	0.525493i	$-0.823881\pi$
$367$	−6.23193	+	6.23193i	−0.325304	+	0.325304i	0.525493	+	0.850798i	$0.323881\pi$
$368$	4.71714	−	0.865219i	0.245898	−	0.0451026i
$369$			19.5895i			1.01979i
$370$	0.912314	−	5.30011i	0.0474290	−	0.275540i
$371$	3.86216	−	26.8619i	0.200513	−	1.39460i
$372$	11.0164	−	4.10890i	0.571173	−	0.213036i
$373$	−2.16872	−	1.18421i	−0.112292	−	0.0613162i	0.422121	−	0.906539i	$-0.361286\pi$
$373$	−2.16872	−	1.18421i	−0.112292	−	0.0613162i	−0.534413	+	0.845223i	$0.679467\pi$
$374$	0.825884	−	0.377169i	0.0427054	−	0.0195029i
$375$	28.0726	+	24.9001i	1.44966	+	1.28584i
$376$	0.593836	+	4.13022i	0.0306247	+	0.213000i
$377$	−2.42356	−	4.43842i	−0.124820	−	0.228590i
$378$	−70.8888	+	5.07007i	−3.64613	+	0.260776i
$379$	−24.4487	−	15.7123i	−1.25585	−	0.807084i	−0.268137	−	0.963381i	$-0.586408\pi$
$379$	−24.4487	−	15.7123i	−1.25585	−	0.807084i	−0.987710	+	0.156296i	$0.950044\pi$
$380$	−3.04547	−	11.5439i	−0.156229	−	0.592192i
$381$	37.3394	−	43.0920i	1.91296	−	2.20767i
$382$	17.4223	−	9.51331i	0.891403	−	0.486743i
$383$	−0.476171	+	0.636090i	−0.0243312	+	0.0325027i	−0.812542	−	0.582903i	$-0.801917\pi$
$383$	−0.476171	+	0.636090i	−0.0243312	+	0.0325027i	0.788211	+	0.615406i	$0.211008\pi$
$384$	2.53652	−	2.19790i	0.129441	−	0.112161i
$385$	4.60296	+	9.01377i	0.234588	+	0.459384i
$386$	15.5681	−	4.57121i	0.792395	−	0.232668i
$387$	−12.0126	−	32.2071i	−0.610635	−	1.63718i
$388$	14.9000	−	11.1540i	0.756433	−	0.566258i
$389$	21.3772	−	13.7383i	1.08387	−	0.696559i	0.128420	−	0.991720i	$-0.459010\pi$
$389$	21.3772	−	13.7383i	1.08387	−	0.696559i	0.955448	+	0.295161i	$0.0953732\pi$
$390$	0.575894	+	13.1583i	0.0291615	+	0.666294i
$391$	3.00572	−	2.43660i	0.152006	−	0.123224i
$392$	6.48933	+	6.48933i	0.327761	+	0.327761i
$393$	9.41622	−	43.2857i	0.474985	−	2.18347i
$394$	−7.25066	−	1.04249i	−0.365283	−	0.0525198i
$395$	−8.06736	−	19.0419i	−0.405913	−	0.958103i
$396$	2.62030	+	8.92391i	0.131675	+	0.448443i
$397$	−1.66673	+	4.46867i	−0.0836506	+	0.224276i	−0.972040	−	0.234814i	$-0.924552\pi$
$397$	−1.66673	+	4.46867i	−0.0836506	+	0.224276i	0.888390	+	0.459090i	$0.151825\pi$
$398$	−0.103498	+	1.44709i	−0.00518787	+	0.0725359i
$399$	71.3427	−	10.2575i	3.57160	−	0.513519i
$400$	0.984141	−	4.90219i	0.0492070	−	0.245110i
$401$	3.45453	+	2.99337i	0.172511	+	0.149482i	0.736837	−	0.676070i	$-0.236318\pi$
$401$	3.45453	+	2.99337i	0.172511	+	0.149482i	−0.564326	+	0.825552i	$0.690864\pi$
$402$	−4.35618	+	0.947629i	−0.217266	+	0.0472634i
$403$	6.00748	−	1.30685i	0.299254	−	0.0650987i
$404$	−11.1861	−	9.69278i	−0.556527	−	0.482234i
$405$	−66.0478	+	39.9093i	−3.28194	+	1.98311i
$406$	−11.4719	+	1.64940i	−0.569339	+	0.0818585i
$407$	0.193088	−	2.69972i	0.00957102	−	0.133820i
$408$	0.946300	−	2.53713i	0.0468488	−	0.125607i
$409$	1.49209	+	5.08159i	0.0737790	+	0.251268i	0.988122	−	0.153673i	$-0.0491102\pi$
$409$	1.49209	+	5.08159i	0.0737790	+	0.251268i	−0.914343	+	0.404941i	$0.867292\pi$
$410$	1.98882	−	4.91277i	0.0982207	−	0.242624i
$411$	11.2635	+	1.61944i	0.555586	+	0.0798812i
$412$	−2.39916	+	11.0288i	−0.118198	+	0.543349i
$413$	9.87034	+	9.87034i	0.485688	+	0.485688i
$414$	20.3240	+	34.0287i	0.998871	+	1.67242i
$415$	−10.0319	+	0.439065i	−0.492448	+	0.0215529i
$416$	1.47637	−	0.948807i	0.0723851	−	0.0465191i
$417$	6.78236	−	5.07721i	0.332134	−	0.248632i
$418$	−2.09976	−	5.62967i	−0.102702	−	0.275356i
$419$	32.1950	−	9.45330i	1.57283	−	0.461824i	0.625005	−	0.780621i	$-0.285097\pi$
$419$	32.1950	−	9.45330i	1.57283	−	0.461824i	0.947823	+	0.318797i	$0.103279\pi$
$420$	28.7164	+	9.30201i	1.40122	+	0.453892i
$421$	−6.75083	+	5.84962i	−0.329015	+	0.285093i	−0.803666	−	0.595081i	$-0.797120\pi$
$421$	−6.75083	+	5.84962i	−0.329015	+	0.285093i	0.474651	+	0.880174i	$0.342574\pi$
$422$	9.68439	−	12.9368i	0.471429	−	0.629755i
$423$	−30.2676	+	16.5274i	−1.47166	+	0.803589i
$424$	−4.41851	+	5.09923i	−0.214582	+	0.247641i
$425$	−1.19859	−	3.85183i	−0.0581403	−	0.186841i
$426$	43.5987	+	28.0192i	2.11236	+	1.35753i
$427$	−47.0896	+	3.36791i	−2.27882	+	0.162985i
$428$	6.32295	+	11.5796i	0.305631	+	0.559722i
$429$	0.943334	+	6.56103i	0.0455446	+	0.316770i
$430$	−0.257221	+	9.29666i	−0.0124043	+	0.448325i
$431$	−24.6772	+	11.2697i	−1.18866	+	0.542841i	−0.908813	−	0.417204i	$-0.863010\pi$
$431$	−24.6772	+	11.2697i	−1.18866	+	0.542841i	−0.279844	+	0.960046i	$0.590283\pi$
$432$	15.5084	+	8.46825i	0.746151	+	0.407429i
$433$	−11.1787	+	4.16945i	−0.537215	+	0.200371i	−0.603403	−	0.797436i	$-0.706189\pi$
$433$	−11.1787	+	4.16945i	−0.537215	+	0.200371i	0.0661879	+	0.997807i	$0.478916\pi$
$434$	2.00524	−	13.9467i	0.0962546	−	0.669465i
$435$	−17.6640	+	12.4760i	−0.846924	+	0.598177i
$436$		−	1.49036i		−	0.0713751i
$437$	−14.6648	−	20.9909i	−0.701511	−	1.00413i
$438$	17.1361	−	17.1361i	0.818796	−	0.818796i
$439$	−14.8072	−	23.0404i	−0.706707	−	1.09966i	−0.990061	−	0.140642i	$-0.955083\pi$
$439$	−14.8072	−	23.0404i	−0.706707	−	1.09966i	0.283354	−	0.959015i	$-0.408553\pi$
$440$	0.248865	−	2.50402i	0.0118642	−	0.119374i
$441$	−31.5082	+	68.9934i	−1.50039	+	3.28540i
$442$	0.678574	−	1.24271i	0.0322765	−	0.0591099i
$443$	−17.3658	−	6.47712i	−0.825076	−	0.307737i	−0.0987712	−	0.995110i	$-0.531491\pi$
$443$	−17.3658	−	6.47712i	−0.825076	−	0.307737i	−0.726305	+	0.687373i	$0.758764\pi$
$444$	−5.28627	−	6.10068i	−0.250875	−	0.289525i
$445$	−5.73980	−	3.91721i	−0.272093	−	0.185693i
$446$	−18.2005	−	5.34414i	−0.861817	−	0.253052i
$447$	2.45064	+	34.2644i	0.115911	+	1.62065i
$448$	−0.854959	−	3.93018i	−0.0403930	−	0.185684i
$449$	−9.09528	+	14.1525i	−0.429233	+	0.667899i	−0.986747	−	0.162268i	$-0.948119\pi$
$449$	−9.09528	+	14.1525i	−0.429233	+	0.667899i	0.557514	+	0.830168i	$0.311755\pi$
$450$	40.8030	−	6.53778i	1.92347	−	0.308194i
$451$	0.751484	−	2.55932i	0.0353860	−	0.120514i
$452$	−3.51468	−	2.63106i	−0.165317	−	0.123754i
$453$	24.5859	+	1.75842i	1.15515	+	0.0826177i
$454$	5.48399	+	12.0083i	0.257376	+	0.563575i
$455$	14.1705	+	6.95134i	0.664322	+	0.325884i
$456$	−16.3007	−	7.44426i	−0.763348	−	0.348609i
$457$	2.87920	+	3.84616i	0.134683	+	0.179916i	0.862812	−	0.505524i	$-0.168701\pi$
$457$	2.87920	+	3.84616i	0.134683	+	0.179916i	−0.728129	+	0.685440i	$0.759610\pi$
$458$	0.714812	+	0.155498i	0.0334010	+	0.00726593i
$459$	14.2561			0.665416
$460$	−1.64222	−	10.5973i	−0.0765690	−	0.494102i
$461$	−17.4657			−0.813461			−0.406730	−	0.913548i	$-0.633331\pi$
$461$	−17.4657			−0.813461			−0.406730	+	0.913548i	$0.633331\pi$
$462$	14.8443	+	3.22918i	0.690618	+	0.150235i
$463$	7.90376	+	10.5582i	0.367319	+	0.490681i	0.945679	−	0.325101i	$-0.105398\pi$
$463$	7.90376	+	10.5582i	0.367319	+	0.490681i	−0.578360	+	0.815781i	$0.696307\pi$
$464$	2.62114	+	1.19703i	0.121683	+	0.0555708i
$465$	−8.50296	−	24.8781i	−0.394315	−	1.15369i
$466$	9.16577	+	20.0702i	0.424596	+	0.929736i
$467$	28.5002	+	2.03837i	1.31883	+	0.0943247i	0.712942	−	0.701223i	$-0.247362\pi$
$467$	28.5002	+	2.03837i	1.31883	+	0.0943247i	0.605890	+	0.795548i	$0.292817\pi$
$468$	11.6113	+	8.69208i	0.536731	+	0.401792i
$469$	−1.50514	+	5.12603i	−0.0695008	+	0.236698i
$470$	9.26864	−	1.07192i	0.427531	−	0.0494440i
$471$	−12.5166	+	19.4762i	−0.576735	+	0.897418i
$472$	−0.737711	−	3.39120i	−0.0339559	−	0.156093i
$473$	0.333905	+	4.66860i	0.0153530	+	0.214663i
$474$	−29.7834	−	8.74520i	−1.36800	−	0.401680i
$475$	−25.9915	+	6.09335i	−1.19257	+	0.279582i
$476$	−2.12505	−	2.45244i	−0.0974014	−	0.112407i
$477$	−52.2480	−	19.4875i	−2.39227	−	0.892271i
$478$	0.233211	−	0.427094i	0.0106668	−	0.0195348i
$479$	−13.8117	+	30.2434i	−0.631073	+	1.38186i	0.276112	+	0.961125i	$0.410954\pi$
$479$	−13.8117	+	30.2434i	−0.631073	+	1.38186i	−0.907185	+	0.420732i	$0.861773\pi$
$480$	−4.75591	−	5.80558i	−0.217077	−	0.264987i
$481$	−2.28202	−	3.55089i	−0.104051	−	0.161906i
$482$	10.7334	−	10.7334i	0.488895	−	0.488895i
$483$	64.6924	−	2.49864i	2.94360	−	0.113692i
$484$			9.73359i			0.442436i
$485$	−24.0101	−	33.9945i	−1.09024	−	1.54361i
$486$	−8.94017	+	62.1802i	−0.405534	+	2.82055i
$487$	−14.3446	+	5.35025i	−0.650015	+	0.242443i	−0.652774	−	0.757553i	$-0.726395\pi$
$487$	−14.3446	+	5.35025i	−0.650015	+	0.242443i	0.00275839	+	0.999996i	$0.499122\pi$
$488$	10.3019	+	5.62524i	0.466343	+	0.254642i
$489$	−24.3331	+	11.1126i	−1.10038	+	0.502528i
$490$	14.9064	−	14.1037i	0.673401	−	0.637141i
$491$	5.18523	+	36.0641i	0.234006	+	1.62755i	0.680491	+	0.732757i	$0.261767\pi$
$491$	5.18523	+	36.0641i	0.234006	+	1.62755i	−0.446484	+	0.894791i	$0.647324\pi$
$492$	−3.81256	−	6.98219i	−0.171884	−	0.314781i
$493$	2.31890	−	0.165851i	0.104438	−	0.00746956i
$494$	−7.88271	−	5.06591i	−0.354660	−	0.227926i
$495$	20.1089	−	5.30503i	0.903827	−	0.238443i
$496$	−2.29410	+	2.64753i	−0.103008	+	0.118878i
$497$	54.5100	−	29.7647i	2.44511	−	1.33513i
$498$	−9.03240	+	12.0659i	−0.404751	+	0.540685i
$499$	−28.1456	+	24.3883i	−1.25997	+	1.09177i	−0.268253	+	0.963349i	$0.586446\pi$
$499$	−28.1456	+	24.3883i	−1.25997	+	1.09177i	−0.991719	+	0.128424i	$0.959008\pi$
$500$	−10.8966	−	2.50293i	−0.487310	−	0.111935i
$501$	−3.46235	+	1.01664i	−0.154687	+	0.0454201i
$502$	0.875278	+	2.34671i	0.0390656	+	0.104739i
$503$	14.7742	−	11.0599i	0.658751	−	0.493135i	−0.216828	−	0.976210i	$-0.569571\pi$
$503$	14.7742	−	11.0599i	0.658751	−	0.493135i	0.875579	+	0.483075i	$0.160480\pi$
$504$	27.9645	−	17.9717i	1.24564	−	0.800522i
$505$	−22.3572	+	24.4038i	−0.994883	+	1.08595i
$506$	−1.34989	−	5.22543i	−0.0600099	−	0.232299i
$507$	−23.5429	−	23.5429i	−1.04558	−	1.04558i
$508$	−3.61120	+	16.6004i	−0.160221	+	0.736524i
$509$	−0.380645	−	0.0547284i	−0.0168718	−	0.00242579i	0.133874	−	0.990998i	$-0.457258\pi$
$509$	−0.380645	−	0.0547284i	−0.0168718	−	0.00242579i	−0.150746	+	0.988573i	$0.548167\pi$
$510$	−5.61250	−	2.27209i	−0.248526	−	0.100610i
$511$	−8.18197	−	27.8652i	−0.361949	−	1.23269i
$512$	−0.349464	+	0.936950i	−0.0154443	+	0.0414077i
$513$	6.73039	−	94.1032i	0.297154	−	4.15476i
$514$	1.56930	−	0.225631i	0.0692188	−	0.00995217i
$515$	24.5033	+	6.04471i	1.07974	+	0.266362i
$516$	10.5498	+	9.14149i	0.464431	+	0.402431i
$517$	4.58842	−	0.998149i	0.201798	−	0.0438985i
$518$	−9.45265	+	2.05630i	−0.415325	+	0.0903485i
$519$	58.1615	+	50.3972i	2.55301	+	2.21219i
$520$	−2.02948	−	3.35869i	−0.0889986	−	0.147288i
$521$	20.9027	−	3.00536i	0.915765	−	0.131667i	0.331710	−	0.943381i	$-0.392374\pi$
$521$	20.9027	−	3.00536i	0.915765	−	0.131667i	0.584055	+	0.811714i	$0.301465\pi$
$522$	−1.69894	+	23.7543i	−0.0743607	+	1.03970i
$523$	−0.663744	+	1.77957i	−0.0290235	+	0.0778150i	−0.950653	−	0.310255i	$-0.899585\pi$
$523$	−0.663744	+	1.77957i	−0.0290235	+	0.0778150i	0.921630	+	0.388070i	$0.126858\pi$
$524$	3.71845	+	12.6639i	0.162441	+	0.553224i
$525$	22.5679	−	63.6121i	0.984944	−	2.77626i
$526$	−14.6971	−	2.11312i	−0.640823	−	0.0921364i
$527$	−0.600789	+	2.76178i	−0.0261708	+	0.120305i
$528$	−2.67074	−	2.67074i	−0.116229	−	0.116229i
$529$	−11.1398	−	20.1222i	−0.484339	−	0.874880i
$530$	11.1246	+	10.1917i	0.483222	+	0.442698i
$531$	24.1295	−	15.5071i	1.04713	−	0.672949i
$532$	−17.1916	+	12.8695i	−0.745351	+	0.557963i
$533$	−1.45368	−	3.89746i	−0.0629657	−	0.168818i
$534$	−10.0079	+	2.93859i	−0.433085	+	0.127165i
$535$	26.2739	−	13.4170i	1.13592	−	0.580068i
$536$	1.00384	−	0.869832i	0.0433593	−	0.0375710i
$537$	21.4408	−	28.6415i	0.925237	−	1.23597i
$538$	10.4029	−	5.68041i	0.448501	−	0.244900i
$539$	6.76317	−	7.80512i	0.291311	−	0.336190i
$540$	19.8875	−	34.1410i	0.855820	−	1.46919i
$541$	21.2307	+	13.6442i	0.912781	+	0.586609i	0.910555	−	0.413389i	$-0.135655\pi$
$541$	21.2307	+	13.6442i	0.912781	+	0.586609i	0.00222653	+	0.999998i	$0.499291\pi$
$542$	14.0995	−	1.00841i	0.605624	−	0.0433151i
$543$	10.0072	+	18.3268i	0.429449	+	0.786476i
$544$	0.114820	+	0.798589i	0.00492286	+	0.0342392i
$545$	−3.33126	−	0.0921696i	−0.142696	−	0.00394811i
$546$	21.5500	−	9.84156i	0.922256	−	0.421180i
$547$	−30.4091	−	16.6046i	−1.30020	−	0.709963i	−0.328126	−	0.944634i	$-0.606417\pi$
$547$	−30.4091	−	16.6046i	−1.30020	−	0.709963i	−0.972075	+	0.234671i	$0.924599\pi$
$548$	−3.17667	+	1.18484i	−0.135701	+	0.0506137i
$549$	−13.8056	+	96.0203i	−0.589210	+	4.09805i
$550$	−5.58162	−	0.711124i	−0.238001	−	0.0303224i
$551$		−	15.3852i		−	0.655432i
$552$	−13.8668	−	8.17317i	−0.590209	−	0.347873i
$553$	−26.3033	+	26.3033i	−1.11853	+	1.11853i
$554$	12.6003	+	19.6064i	0.535334	+	0.832996i
$555$	−13.9632	+	11.4386i	−0.592706	+	0.485543i
$556$	−1.04862	+	2.29617i	−0.0444716	+	0.0973792i
$557$	−1.89998	+	3.47955i	−0.0805045	+	0.147433i	−0.914830	−	0.403839i	$-0.867676\pi$
$557$	−1.89998	+	3.47955i	−0.0805045	+	0.147433i	0.834326	+	0.551272i	$0.185857\pi$
$558$	−27.1273	−	10.1179i	−1.14839	−	0.428327i
$559$	4.77998	+	5.51639i	0.202172	+	0.233319i
$560$	−8.83767	+	1.66796i	−0.373460	+	0.0704841i
$561$	−2.92385	−	0.858519i	−0.123445	−	0.0362467i
$562$	0.646797	+	9.04340i	0.0272835	+	0.381473i
$563$	1.19471	+	5.49198i	0.0503509	+	0.231460i	0.995445	−	0.0953394i	$-0.0303936\pi$
$563$	1.19471	+	5.49198i	0.0503509	+	0.231460i	−0.945094	+	0.326799i	$0.894030\pi$
$564$	7.57155	−	11.7816i	0.318820	−	0.496093i
$565$	−6.09833	+	7.69334i	−0.256559	+	0.323661i
$566$	2.17136	−	7.39496i	0.0912689	−	0.310833i
$567$	111.121	+	83.1839i	4.66663	+	3.49340i
$568$	−15.4021	−	1.10158i	−0.646257	−	0.0462212i
$569$	0.0158620	+	0.0347329i	0.000664969	+	0.00145608i	0.909964	−	0.414687i	$-0.136109\pi$
$569$	0.0158620	+	0.0347329i	0.000664969	+	0.00145608i	−0.909299	+	0.416143i	$0.863382\pi$
$570$	−17.6476	+	35.9751i	−0.739177	+	1.50683i
$571$	33.6959	+	15.3884i	1.41013	+	0.643985i	0.967535	−	0.252736i	$-0.0813305\pi$
$571$	33.6959	+	15.3884i	1.41013	+	0.643985i	0.442595	+	0.896721i	$0.354058\pi$
$572$	−1.18354	−	1.58103i	−0.0494864	−	0.0661061i
$573$	−65.1013	−	14.1619i	−2.71965	−	0.591623i
$574$	−9.53343			−0.397918
$575$	−23.7888	+	3.01533i	−0.992062	+	0.125748i
$576$	−8.26469			−0.344362
$577$	23.3456	+	5.07853i	0.971891	+	0.211422i	0.670361	−	0.742035i	$-0.266139\pi$
$577$	23.3456	+	5.07853i	0.971891	+	0.211422i	0.301530	+	0.953457i	$0.402503\pi$
$578$	−9.79763	−	13.0881i	−0.407528	−	0.544393i
$579$	−49.5358	−	22.6222i	−2.05864	−	0.940148i
$580$	2.83772	−	5.78477i	0.117830	−	0.240199i
$581$	7.50327	+	16.4299i	0.311288	+	0.681626i
$582$	−62.3095	−	4.45646i	−2.58281	−	0.184726i
$583$	6.07851	+	4.55031i	0.251746	+	0.188455i
$584$	−2.03425	+	6.92803i	−0.0841780	+	0.286684i
$585$	20.1467	−	25.4161i	0.832965	−	1.05083i
$586$	−1.67293	+	2.60313i	−0.0691081	+	0.107534i
$587$	−10.0320	−	46.1163i	−0.414065	−	1.90342i	−0.428526	−	0.903530i	$-0.640967\pi$
$587$	−10.0320	−	46.1163i	−0.414065	−	1.90342i	0.0144611	−	0.999895i	$-0.495397\pi$
$588$	−2.19737	−	30.7232i	−0.0906179	−	1.26700i
$589$	17.9467	+	5.26963i	0.739481	+	0.217131i
$590$	−7.62568	+	1.43922i	−0.313944	+	0.0592516i
$591$	16.1001	+	18.5805i	0.662271	+	0.764302i
$592$	2.25350	+	0.840511i	0.0926181	+	0.0345448i
$593$	−13.6278	+	24.9575i	−0.559628	+	1.02488i	0.432734	+	0.901522i	$0.357549\pi$
$593$	−13.6278	+	24.9575i	−0.559628	+	1.02488i	−0.992362	+	0.123361i	$0.960633\pi$
$594$	8.26041	−	18.0878i	0.338929	−	0.742150i
$595$	−5.61314	+	4.59826i	−0.230116	+	0.188510i
$596$	−5.53351	−	8.61031i	−0.226661	−	0.352692i
$597$	3.44308	−	3.44308i	0.140916	−	0.140916i
$598$	−6.56877	−	5.26206i	−0.268617	−	0.215181i
$599$			1.22147i			0.0499078i	0.999689	+	0.0249539i	$0.00794390\pi$
$599$			1.22147i			0.0499078i	−0.999689	+	0.0249539i	$0.992056\pi$
$600$	−13.2708	+	10.2714i	−0.541779	+	0.419330i
$601$	0.561196	−	3.90321i	0.0228917	−	0.159215i	−0.975169	−	0.221461i	$-0.928917\pi$
$601$	0.561196	−	3.90321i	0.0228917	−	0.159215i	0.998061	+	0.0622463i	$0.0198264\pi$
$602$	15.6739	−	5.84607i	0.638821	−	0.238268i
$603$	9.63493	+	5.26107i	0.392365	+	0.214247i
$604$	−6.68036	+	3.05082i	−0.271820	+	0.124136i
$605$	21.7567	+	0.601964i	0.884534	+	0.0244733i
$606$	7.06983	+	49.1718i	0.287192	+	1.99747i
$607$	8.56803	+	15.6912i	0.347765	+	0.636885i	0.991755	−	0.128150i	$-0.0409037\pi$
$607$	8.56803	+	15.6912i	0.347765	+	0.636885i	−0.643989	+	0.765034i	$0.722722\pi$
$608$	5.32564	−	0.380897i	0.215983	−	0.0154474i
$609$	32.7238	+	21.0303i	1.32603	+	0.852190i
$610$	13.2107	−	22.6789i	0.534886	−	0.918243i
$611$	4.79551	−	5.53431i	0.194005	−	0.223894i
$612$	−5.85233	+	3.19562i	−0.236567	+	0.129175i
$613$	21.4125	−	28.6038i	0.864843	−	1.15529i	−0.121826	−	0.992551i	$-0.538875\pi$
$613$	21.4125	−	28.6038i	0.864843	−	1.15529i	0.986668	−	0.162743i	$-0.0520342\pi$
$614$	−0.121386	+	0.105182i	−0.00489876	+	0.00424480i
$615$	−15.8425	+	8.09008i	−0.638829	+	0.326224i
$616$	−4.34292	+	1.27520i	−0.174981	+	0.0513791i
$617$	6.78308	+	18.1861i	0.273077	+	0.732147i	0.999014	+	0.0443863i	$0.0141332\pi$
$617$	6.78308	+	18.1861i	0.273077	+	0.732147i	−0.725938	+	0.687760i	$0.758594\pi$
$618$	30.3257	−	22.7015i	1.21988	−	0.913190i
$619$	6.27874	−	4.03510i	0.252364	−	0.162184i	−0.408343	−	0.912829i	$-0.633893\pi$
$619$	6.27874	−	4.03510i	0.252364	−	0.162184i	0.660706	+	0.750644i	$0.270257\pi$
$620$	5.77592	+	5.29153i	0.231966	+	0.212513i
$621$	14.8039	−	83.4385i	0.594059	−	3.34827i
$622$	−11.3832	−	11.3832i	−0.456424	−	0.456424i
$623$	−2.65698	+	12.2139i	−0.106450	+	0.489341i
$624$	−5.83023	−	0.838260i	−0.233396	−	0.0335573i
$625$	−6.26848	+	24.2014i	−0.250739	+	0.968055i
$626$	−6.06913	−	20.6696i	−0.242571	−	0.826122i
$627$	−7.04740	+	18.8948i	−0.281446	+	0.754586i
$628$	0.492092	−	6.88035i	0.0196366	−	0.274556i
$629$	1.92072	−	0.276158i	0.0765841	−	0.0110111i
$630$	−38.4411	−	63.6180i	−1.53153	−	2.53460i
$631$	−33.4345	−	28.9712i	−1.33101	−	1.15332i	−0.975832	−	0.218524i	$-0.929876\pi$
$631$	−33.4345	−	28.9712i	−1.33101	−	1.15332i	−0.355175	−	0.934800i	$-0.615579\pi$
$632$	9.03717	−	1.96592i	0.359480	−	0.0782000i
$633$	−52.9985	+	11.5291i	−2.10650	+	0.458242i
$634$	8.04609	+	6.97198i	0.319551	+	0.276893i
$635$	36.8821	+	9.09843i	1.46362	+	0.361060i
$636$	22.4152	−	3.22282i	0.888822	−	0.127793i
$637$	1.14898	−	16.0648i	0.0455242	−	0.636512i
$638$	1.13322	−	3.03827i	0.0448645	−	0.120286i
$639$	−35.9543	−	122.449i	−1.42233	−	4.84401i
$640$	2.07267	+	0.839071i	0.0819295	+	0.0331672i
$641$	−43.9428	−	6.31803i	−1.73564	−	0.249547i	−0.799371	−	0.600838i	$-0.794834\pi$
$641$	−43.9428	−	6.31803i	−1.73564	−	0.249547i	−0.936266	+	0.351291i	$0.885743\pi$
$642$	9.41262	−	43.2691i	0.371486	−	1.70769i
$643$	6.37779	+	6.37779i	0.251515	+	0.251515i	0.821592	−	0.570076i	$-0.193086\pi$
$643$	6.37779	+	6.37779i	0.251515	+	0.251515i	−0.570076	+	0.821592i	$0.693086\pi$
$644$	−16.5604	+	9.89090i	−0.652573	+	0.389756i
$645$	21.0856	−	23.0158i	0.830245	−	0.906245i
$646$	3.62388	−	2.32892i	0.142579	−	0.0916303i
$647$	−35.7146	+	26.7356i	−1.40408	+	1.05108i	−0.414050	+	0.910254i	$0.635886\pi$
$647$	−35.7146	+	26.7356i	−1.40408	+	1.05108i	−0.990034	+	0.140830i	$0.955023\pi$
$648$	−12.0604	−	32.3351i	−0.473776	−	1.27024i
$649$	−3.74733	+	1.10032i	−0.147096	+	0.0431912i
$650$	−7.63289	+	4.32861i	−0.299386	+	0.169782i
$651$	−35.7399	+	30.9688i	−1.40076	+	1.21376i
$652$	4.77640	−	6.38052i	0.187058	−	0.249881i
$653$	4.05967	−	2.21675i	0.158867	−	0.0867480i	−0.397849	−	0.917451i	$-0.630243\pi$
$653$	4.05967	−	2.21675i	0.158867	−	0.0867480i	0.556716	+	0.830703i	$0.312061\pi$
$654$	−3.27566	+	3.78031i	−0.128088	+	0.147822i
$655$	28.5364	−	7.52833i	1.11501	−	0.294156i
$656$	1.99399	+	1.28146i	0.0778522	+	0.0500326i
$657$	−59.5233	+	4.25719i	−2.32222	+	0.166089i
$658$	−8.04323	−	14.7301i	−0.313558	−	0.574238i
$659$	−0.705668	−	4.90803i	−0.0274889	−	0.191190i	0.971450	−	0.237244i	$-0.0762442\pi$
$659$	−0.705668	−	4.90803i	−0.0274889	−	0.191190i	−0.998939	+	0.0460547i	$0.985335\pi$
$660$	−6.13484	+	5.80450i	−0.238798	+	0.225940i
$661$	−32.0716	+	14.6466i	−1.24744	+	0.569687i	−0.926100	−	0.377277i	$-0.876860\pi$
$661$	−32.0716	+	14.6466i	−1.24744	+	0.569687i	−0.321340	+	0.946964i	$0.604133\pi$
$662$	25.0316	+	13.6683i	0.972883	+	0.531234i
$663$	−4.45258	+	1.66073i	−0.172924	+	0.0644973i
$664$	0.639095	−	4.44500i	0.0248017	−	0.172500i
$665$	27.7028	+	39.2228i	1.07427	+	1.52099i
$666$			19.8778i			0.770247i
$667$	1.43731	−	13.7444i	0.0556528	−	0.532185i
$668$	0.760248	−	0.760248i	0.0294149	−	0.0294149i
$669$	34.4198	+	53.5583i	1.33075	+	2.07068i
$670$	−1.88218	−	2.29759i	−0.0727148	−	0.0887636i
$671$	5.48717	−	12.0152i	0.211830	−	0.463843i
$672$	−6.46955	+	11.8481i	−0.249568	+	0.457050i
$673$	24.9512	+	9.30633i	0.961799	+	0.358733i	0.780821	−	0.624754i	$-0.214801\pi$
$673$	24.9512	+	9.30633i	0.961799	+	0.358733i	0.180978	+	0.983487i	$0.442074\pi$
$674$	−11.9088	−	13.7435i	−0.458712	−	0.529381i
$675$	−75.0824	−	46.5641i	−2.88992	−	1.79225i
$676$	9.51825	+	2.79481i	0.366087	+	0.107493i
$677$	1.61261	+	22.5473i	0.0619777	+	0.866562i	0.929420	+	0.369024i	$0.120308\pi$
$677$	1.61261	+	22.5473i	0.0619777	+	0.866562i	−0.867442	+	0.497538i	$0.834237\pi$
$678$	3.13223	+	14.3986i	0.120293	+	0.552977i
$679$	−40.4729	+	62.9771i	−1.55321	+	2.41684i
$680$	1.79212	−	0.207259i	0.0687246	−	0.00794801i
$681$	12.4828	−	42.5124i	0.478341	−	1.62908i
$682$	3.15597	+	2.36253i	0.120848	+	0.0904660i
$683$	−5.61656	−	0.401705i	−0.214912	−	0.0153708i	−0.0365319	−	0.999332i	$-0.511631\pi$
$683$	−5.61656	−	0.401705i	−0.214912	−	0.0153708i	−0.178380	+	0.983962i	$0.557086\pi$
$684$	18.3311	+	40.1395i	0.700907	+	1.53477i
$685$	2.45190	+	7.17380i	0.0936824	+	0.274097i
$686$	−7.96595	−	3.63793i	−0.304141	−	0.138897i
$687$	−1.47136	−	1.96551i	−0.0561360	−	0.0749889i
$688$	−4.06413	−	0.884098i	−0.154944	−	0.0337059i
$689$	11.8412			0.451114
$690$	−19.1264	+	30.4897i	−0.728128	+	1.16072i
$691$	25.2537			0.960697			0.480348	−	0.877078i	$-0.340510\pi$
$691$	25.2537			0.960697			0.480348	+	0.877078i	$0.340510\pi$
$692$	−22.4057	−	4.87405i	−0.851736	−	0.185284i
$693$	−22.4179	−	29.9468i	−0.851585	−	1.13758i
$694$	9.51022	+	4.34317i	0.361003	+	0.164865i
$695$	5.06757	+	2.48590i	0.192224	+	0.0942957i
$696$	−4.01759	−	8.79729i	−0.152286	−	0.333461i
$697$	1.90746	+	0.136424i	0.0722501	+	0.00516743i
$698$	8.94499	+	6.69614i	0.338573	+	0.253453i
$699$	20.8633	−	71.0540i	0.789124	−	2.68751i
$700$	3.18168	+	19.8572i	0.120256	+	0.750533i
$701$	−27.5461	+	42.8626i	−1.04040	+	1.61890i	−0.291074	+	0.956701i	$0.594013\pi$
$701$	−27.5461	+	42.8626i	−1.04040	+	1.61890i	−0.749329	+	0.662198i	$0.769624\pi$
$702$	−6.59165	−	30.3013i	−0.248786	−	1.14365i
$703$	−0.916112	−	12.8089i	−0.0345518	−	0.483097i
$704$	1.07976	+	0.317047i	0.0406951	+	0.0119492i
$705$	−25.8660	−	17.6526i	−0.974171	−	0.664837i
$706$	−6.17230	−	7.12321i	−0.232297	−	0.268086i
$707$	55.7787	+	20.8044i	2.09778	+	0.782430i
$708$	−5.58232	+	10.2233i	−0.209797	+	0.384214i
$709$	−13.4931	+	29.5458i	−0.506744	+	1.10962i	0.467474	+	0.884007i	$0.345164\pi$
$709$	−13.4931	+	29.5458i	−0.506744	+	1.10962i	−0.974218	+	0.225608i	$0.927563\pi$
$710$	−3.41479	+	34.3588i	−0.128155	+	1.28946i
$711$	41.3246	+	64.3023i	1.54979	+	2.41152i
$712$	2.19749	−	2.19749i	0.0823546	−	0.0823546i
$713$	15.5404	+	6.38424i	0.581993	+	0.239092i
$714$			10.8913i			0.407596i
$715$	−3.60713	+	2.54769i	−0.134899	+	0.0952783i
$716$	−1.51706	+	10.5514i	−0.0566952	+	0.394324i
$717$	−1.53025	+	0.570755i	−0.0571484	+	0.0213152i
$718$	12.3300	+	6.73269i	0.460152	+	0.251262i
$719$	14.0335	−	6.40887i	0.523360	−	0.239011i	−0.136174	−	0.990685i	$-0.543481\pi$
$719$	14.0335	−	6.40887i	0.523360	−	0.239011i	0.659534	+	0.751674i	$0.270753\pi$
$720$	−0.511122	+	18.4733i	−0.0190484	+	0.688461i
$721$	−6.46057	−	44.9343i	−0.240604	−	1.67344i
$722$	−4.55647	−	8.34455i	−0.169574	−	0.310552i
$723$	−50.8166	+	3.63448i	−1.88989	+	0.135168i
$724$	−5.23380	−	3.36356i	−0.194513	−	0.125006i
$725$	−12.7547	−	6.70067i	−0.473697	−	0.248857i
$726$	21.3935	−	24.6894i	0.793987	−	0.916310i
$727$	4.71602	−	2.57514i	0.174907	−	0.0955066i	−0.389410	−	0.921064i	$-0.627321\pi$
$727$	4.71602	−	2.57514i	0.174907	−	0.0955066i	0.564318	+	0.825558i	$0.309139\pi$
$728$	−4.23010	+	5.65075i	−0.156778	+	0.209431i
$729$	81.0979	−	70.2717i	3.00363	−	2.60266i
$730$	15.3598	+	4.97544i	0.568492	+	0.184149i
$731$	−3.21971	+	0.945392i	−0.119085	+	0.0349666i
$732$	−13.7671	−	36.9110i	−0.508846	−	1.36427i
$733$	5.03190	−	3.76683i	0.185857	−	0.139131i	−0.502298	−	0.864695i	$-0.667512\pi$
$733$	5.03190	−	3.76683i	0.185857	−	0.139131i	0.688155	+	0.725564i	$0.258421\pi$
$734$	−7.41420	+	4.76482i	−0.273663	+	0.175873i
$735$	−68.8088	+	3.01154i	−2.53805	+	0.111082i
$736$	4.79325	+	0.157254i	0.176682	+	0.00579646i
$737$	−1.05696	−	1.05696i	−0.0389336	−	0.0389336i
$738$	−4.16404	+	19.1418i	−0.153281	+	0.704619i
$739$	52.0089	+	7.47775i	1.91318	+	0.275073i	0.993156	−	0.116794i	$-0.0372618\pi$
$739$	52.0089	+	7.47775i	1.91318	+	0.275073i	0.920022	+	0.391868i	$0.128171\pi$
$740$	2.01809	−	4.98506i	0.0741863	−	0.183255i
$741$	8.86024	+	30.1752i	0.325489	+	1.10851i
$742$	9.48380	−	25.4271i	0.348161	−	0.933457i
$743$	−3.26830	+	45.6968i	−0.119902	+	1.67645i	0.480685	+	0.876894i	$0.340388\pi$
$743$	−3.26830	+	45.6968i	−0.119902	+	1.67645i	−0.600587	+	0.799559i	$0.705066\pi$
$744$	11.6380	−	1.67330i	0.426671	−	0.0613460i
$745$	−19.5881	+	11.8361i	−0.717652	+	0.433640i
$746$	−1.86744	−	1.61814i	−0.0683717	−	0.0592445i
$747$	36.2662	−	7.88922i	1.32691	−	0.288652i
$748$	0.887183	−	0.192995i	0.0324386	−	0.00705659i
$749$	−40.1041	−	34.7504i	−1.46537	−	1.26975i
$750$	22.1381	+	30.2984i	0.808370	+	1.10634i
$751$	−34.2466	+	4.92392i	−1.24968	+	0.179676i	−0.735213	−	0.677836i	$-0.762918\pi$
$751$	−34.2466	+	4.92392i	−1.24968	+	0.179676i	−0.514463	+	0.857512i	$0.672009\pi$
$752$	−0.297676	+	4.16206i	−0.0108551	+	0.151775i
$753$	2.93769	−	7.87625i	0.107055	−	0.287026i
$754$	−1.42472	−	4.85215i	−0.0518853	−	0.176705i
$755$	6.40609	+	15.1207i	0.233141	+	0.550299i
$756$	−70.3465	−	10.1143i	−2.55848	−	0.367854i
$757$	−8.32118	+	38.2518i	−0.302438	+	1.39029i	0.535506	+	0.844531i	$0.320121\pi$
$757$	−8.32118	+	38.2518i	−0.302438	+	1.39029i	−0.837945	+	0.545755i	$0.816243\pi$
$758$	−20.5501	−	20.5501i	−0.746414	−	0.746414i
$759$	−8.06098	+	16.2213i	−0.292595	+	0.588797i
$760$	−0.522027	−	11.9275i	−0.0189359	−	0.432656i
$761$	−29.6283	+	19.0409i	−1.07402	+	0.690233i	−0.953169	−	0.302437i	$-0.902200\pi$
$761$	−29.6283	+	19.0409i	−1.07402	+	0.690233i	−0.120854	+	0.992670i	$0.538563\pi$
$762$	45.6460	−	34.1701i	1.65358	−	1.23785i
$763$	2.09481	+	5.61642i	0.0758374	+	0.203328i
$764$	19.0464	−	5.59252i	0.689073	−	0.202330i
$765$	6.78095	+	13.2788i	0.245166	+	0.480097i
$766$	−0.600500	+	0.520336i	−0.0216969	+	0.0188005i
$767$	−3.64999	+	4.87581i	−0.131793	+	0.176055i
$768$	2.94575	−	1.60850i	0.106295	−	0.0580417i
$769$	−7.93536	+	9.15790i	−0.286157	+	0.330242i	−0.880569	−	0.473918i	$-0.842839\pi$
$769$	−7.93536	+	9.15790i	−0.286157	+	0.330242i	0.594412	+	0.804160i	$0.297385\pi$
$770$	2.58175	+	9.78620i	0.0930398	+	0.352670i
$771$	−4.47647	−	2.87685i	−0.161216	−	0.103607i
$772$	16.1840	−	1.15750i	0.582475	−	0.0416594i
$773$	−9.14229	−	16.7429i	−0.328825	−	0.602199i	0.660002	−	0.751264i	$-0.270555\pi$
$773$	−9.14229	−	16.7429i	−0.328825	−	0.602199i	−0.988827	+	0.149065i	$0.952374\pi$
$774$	−4.89198	−	34.0245i	−0.175839	−	1.22299i
$775$	12.1849	−	12.5832i	0.437695	−	0.452000i
$776$	16.9304	−	7.73187i	0.607767	−	0.277558i
$777$	28.4963	+	15.5602i	1.02230	+	0.558218i
$778$	23.8089	−	8.88028i	0.853592	−	0.318373i
$779$	1.80105	−	12.5266i	0.0645294	−	0.448811i
$780$	−2.23426	+	12.9800i	−0.0799992	+	0.464757i
$781$			17.3770i			0.621796i
$782$	3.45497	−	1.74200i	0.123549	−	0.0622938i
$783$	36.0032	−	36.0032i	1.28665	−	1.28665i
$784$	4.96162	+	7.72044i	0.177201	+	0.275730i
$785$	−15.3486	−	1.52544i	−0.547816	−	0.0544453i
$786$	18.4021	−	40.2949i	0.656380	−	1.43727i
$787$	11.2433	−	20.5907i	0.400782	−	0.733978i	−0.596879	−	0.802331i	$-0.703593\pi$
$787$	11.2433	−	20.5907i	0.400782	−	0.733978i	0.997661	+	0.0683536i	$0.0217746\pi$
$788$	−6.86337	−	2.55990i	−0.244497	−	0.0911928i
$789$	32.6349	+	37.6627i	1.16183	+	1.34083i
$790$	−3.83535	−	20.3216i	−0.136456	−	0.723010i
$791$	16.9433	+	4.97499i	0.602433	+	0.176890i
$792$	0.663501	+	9.27695i	0.0235765	+	0.329642i
$793$	−4.37866	−	20.1284i	−0.155491	−	0.714779i
$794$	−2.57852	+	4.01225i	−0.0915082	+	0.142390i
$795$	−5.81745	−	50.3021i	−0.206324	−	1.78403i
$796$	−0.408733	+	1.39202i	−0.0144871	+	0.0493387i
$797$	4.05790	+	3.03770i	0.143738	+	0.107601i	0.668727	−	0.743508i	$-0.266840\pi$
$797$	4.05790	+	3.03770i	0.143738	+	0.107601i	−0.524989	+	0.851109i	$0.675930\pi$
$798$	71.8927	+	5.14186i	2.54497	+	0.182020i
$799$	1.39851	+	3.06231i	0.0494757	+	0.108337i
$800$	2.00369	−	4.58097i	0.0708410	−	0.161962i
$801$	23.3633	+	10.6697i	0.825503	+	0.376995i
$802$	2.73930	+	3.65927i	0.0967280	+	0.129213i
$803$	7.93989	+	1.72722i	0.280193	+	0.0609522i
$804$	−4.45806			−0.157224
$805$	21.0841	+	37.6278i	0.743117	+	1.32621i
$806$	6.14798			0.216553
$807$	−38.8721	−	8.45611i	−1.36836	−	0.297669i
$808$	−8.87008	−	11.8490i	−0.312048	−	0.416848i
$809$	−15.0856	−	6.88935i	−0.530381	−	0.242217i	0.132179	−	0.991226i	$-0.457803\pi$
$809$	−15.0856	−	6.88935i	−0.530381	−	0.242217i	−0.662560	+	0.749009i	$0.730530\pi$
$810$	−73.0217	+	24.9578i	−2.56572	+	0.876927i
$811$	−2.95071	−	6.46116i	−0.103614	−	0.226882i	0.850724	−	0.525613i	$-0.176164\pi$
$811$	−2.95071	−	6.46116i	−0.103614	−	0.226882i	−0.954337	+	0.298731i	$0.903437\pi$
$812$	−11.5603	−	0.826808i	−0.405687	−	0.0290153i
$813$	−37.9799	−	28.4314i	−1.33201	−	0.997133i
$814$	0.762543	−	2.59698i	0.0267271	−	0.0910242i
$815$	−13.9664	−	11.0709i	−0.489223	−	0.387796i
$816$	1.46398	−	2.27800i	0.0512496	−	0.0797459i
$817$	4.72042	+	21.6994i	0.165146	+	0.759166i
$818$	0.377821	+	5.28262i	0.0132102	+	0.184703i
$819$	−55.9746	−	16.4356i	−1.95591	−	0.574307i
$820$	2.98765	−	4.37774i	0.104333	−	0.152877i
$821$	−23.9530	−	27.6432i	−0.835966	−	0.964756i	0.163798	−	0.986494i	$-0.447625\pi$
$821$	−23.9530	−	27.6432i	−0.835966	−	0.964756i	−0.999764	+	0.0217382i	$0.993080\pi$
$822$	10.6618	+	3.97665i	0.371874	+	0.138702i
$823$	−19.7593	+	36.1865i	−0.688767	+	1.26138i	0.265984	+	0.963977i	$0.414303\pi$
$823$	−19.7593	+	36.1865i	−0.688767	+	1.26138i	−0.954751	+	0.297405i	$0.903879\pi$
$824$	−4.68867	+	10.2668i	−0.163338	+	0.357660i
$825$	12.5949	+	14.0716i	0.438498	+	0.489911i
$826$	7.54668	+	11.7429i	0.262583	+	0.408586i
$827$	8.59770	−	8.59770i	0.298971	−	0.298971i	−0.541640	−	0.840611i	$-0.682196\pi$
$827$	8.59770	−	8.59770i	0.298971	−	0.298971i	0.840611	+	0.541640i	$0.182196\pi$
$828$	12.6262	+	37.5712i	0.438792	+	1.30569i
$829$			15.6632i			0.544005i	0.962297	+	0.272002i	$0.0876859\pi$
$829$			15.6632i			0.544005i	−0.962297	+	0.272002i	$0.912314\pi$
$830$	−9.89600	−	1.70341i	−0.343495	−	0.0591262i
$831$	11.1322	−	77.4261i	0.386171	−	2.68588i
$832$	1.64432	−	0.613298i	0.0570064	−	0.0212623i
$833$	6.49856	+	3.54848i	0.225162	+	0.122948i
$834$	7.70661	−	3.51949i	0.266858	−	0.121870i
$835$	−1.65230	−	1.74633i	−0.0571801	−	0.0604343i
$836$	−0.855099	−	5.94735i	−0.0295742	−	0.205693i
$837$	29.6659	+	54.3290i	1.02540	+	1.87788i
$838$	33.4687	−	2.39373i	1.15616	−	0.0826899i
$839$	−5.83932	−	3.75270i	−0.201596	−	0.129558i	0.435948	−	0.899972i	$-0.356413\pi$
$839$	−5.83932	−	3.75270i	−0.201596	−	0.129558i	−0.637544	+	0.770414i	$0.720049\pi$
$840$	26.0829	+	15.1935i	0.899946	+	0.524227i
$841$	−13.5535	+	15.6416i	−0.467362	+	0.539365i
$842$	−7.83997	+	4.28095i	−0.270183	+	0.147531i
$843$	18.2359	−	24.3603i	0.628078	−	0.839014i
$844$	12.2130	−	10.5826i	0.420389	−	0.364269i
$845$	6.83565	−	21.1025i	0.235153	−	0.725947i
$846$	−33.0891	+	9.71583i	−1.13763	+	0.334037i
$847$	−13.6813	−	36.6811i	−0.470097	−	1.26038i
$848$	−5.40145	+	4.04348i	−0.185487	+	0.138854i
$849$	−21.7611	+	13.9850i	−0.746839	+	0.479964i
$850$	−0.352436	−	4.01858i	−0.0120884	−	0.137836i
$851$	0.378218	−	11.5284i	0.0129652	−	0.395190i
$852$	36.6464	+	36.6464i	1.25549	+	1.25549i
$853$	−2.61229	+	12.0085i	−0.0894430	+	0.411163i	−0.999998	−	0.00222628i	$-0.999291\pi$
$853$	−2.61229	+	12.0085i	−0.0894430	+	0.411163i	0.910555	+	0.413389i	$0.135655\pi$
$854$	−46.7293	−	6.71866i	−1.59904	−	0.229908i
$855$	90.8540	−	38.4915i	3.10714	−	1.31638i
$856$	3.71702	+	12.6590i	0.127045	+	0.432676i
$857$	11.8266	−	31.7083i	0.403989	−	1.08314i	−0.562583	−	0.826741i	$-0.690192\pi$
$857$	11.8266	−	31.7083i	0.403989	−	1.08314i	0.966572	−	0.256395i	$-0.0825348\pi$
$858$	−0.472872	+	6.61161i	−0.0161436	+	0.225717i
$859$	−45.5682	+	6.55171i	−1.55477	+	0.223542i	−0.865478	−	0.500947i	$-0.832985\pi$
$859$	−45.5682	+	6.55171i	−1.55477	+	0.223542i	−0.689287	+	0.724488i	$0.742076\pi$
$860$	−2.22749	+	9.02953i	−0.0759568	+	0.307904i
$861$	24.1817	+	20.9536i	0.824110	+	0.714095i
$862$	−26.5087	+	5.76663i	−0.902892	+	0.196412i
$863$	6.02201	−	1.31001i	0.204992	−	0.0445932i	−0.108897	−	0.994053i	$-0.534732\pi$
$863$	6.02201	−	1.31001i	0.204992	−	0.0445932i	0.313889	+	0.949460i	$0.398368\pi$
$864$	13.3540	+	11.5713i	0.454311	+	0.393663i
$865$	−12.2802	+	49.7800i	−0.417539	+	1.69257i
$866$	−11.8095	+	1.69796i	−0.401304	+	0.0576989i
$867$	−3.91454	+	54.7324i	−0.132945	+	1.85881i
$868$	4.92401	−	13.2018i	0.167132	−	0.448097i
$869$	−2.93222	−	9.98622i	−0.0994687	−	0.338759i
$870$	−19.9123	+	8.43611i	−0.675090	+	0.286011i
$871$	−2.30734	−	0.331746i	−0.0781814	−	0.0112408i
$872$	0.316798	−	1.45630i	0.0107281	−	0.0493164i
$873$	108.771	+	108.771i	3.68135	+	3.68135i
$874$	−9.86770	−	23.6284i	−0.333780	−	0.799243i
$875$	44.5819	−	5.88369i	1.50714	−	0.198905i
$876$	20.3871	−	13.1020i	0.688815	−	0.442674i
$877$	19.2073	−	14.3784i	0.648586	−	0.485525i	−0.223612	−	0.974678i	$-0.571785\pi$
$877$	19.2073	−	14.3784i	0.648586	−	0.485525i	0.872198	+	0.489153i	$0.162694\pi$
$878$	−9.57118	−	25.6613i	−0.323012	−	0.866028i
$879$	9.96484	−	2.92594i	0.336106	−	0.0986895i
$880$	0.775444	−	2.39389i	0.0261402	−	0.0806981i
$881$	−20.1930	+	17.4974i	−0.680320	+	0.589501i	−0.924938	−	0.380119i	$-0.875883\pi$
$881$	−20.1930	+	17.4974i	−0.680320	+	0.589501i	0.244617	+	0.969620i	$0.421338\pi$
$882$	−45.4538	+	60.7191i	−1.53051	+	2.04452i
$883$	43.0112	−	23.4859i	1.44744	−	0.790363i	0.452591	−	0.891718i	$-0.350500\pi$
$883$	43.0112	−	23.4859i	1.44744	−	0.790363i	0.994850	+	0.101356i	$0.0323180\pi$
$884$	0.927224	−	1.07007i	0.0311859	−	0.0359905i
$885$	22.5059	+	13.1099i	0.756528	+	0.440685i
$886$	−15.5922	−	10.0205i	−0.523829	−	0.336644i
$887$	−9.09057	+	0.650170i	−0.305232	+	0.0218306i	−0.223115	−	0.974792i	$-0.571623\pi$
$887$	−9.09057	+	0.650170i	−0.305232	+	0.0218306i	−0.0821166	+	0.996623i	$0.526168\pi$
$888$	−3.86867	−	7.08494i	−0.129824	−	0.237755i
$889$	−9.72439	−	67.6346i	−0.326145	−	2.26839i
$890$	−4.77596	−	5.04777i	−0.160091	−	0.169202i
$891$	−35.3273	+	16.1334i	−1.18351	+	0.540491i
$892$	−16.6485	−	9.09079i	−0.557434	−	0.304382i
$893$	20.8743	−	7.78572i	0.698532	−	0.260539i
$894$	−4.88879	+	34.0023i	−0.163506	+	1.13721i
$895$	23.4908	+	4.04349i	0.785210	+	0.135159i
$896$		−	4.02210i		−	0.134369i
$897$	5.09630	+	27.7848i	0.170160	+	0.927708i
$898$	−11.8958	+	11.8958i	−0.396967	+	0.396967i
$899$	5.45752	+	8.49207i	0.182019	+	0.283226i
$900$	41.2602	+	2.28493i	1.37534	+	0.0761644i
$901$	−2.26139	+	4.95175i	−0.0753378	+	0.164967i
$902$	1.27833	−	2.34109i	0.0425638	−	0.0779498i
$903$	−52.6062	−	19.6211i	−1.75063	−	0.652950i
$904$	−2.87509	−	3.31803i	−0.0956240	−	0.110356i
$905$	−7.84195	+	11.4906i	−0.260675	+	0.381962i
$906$	23.6502	+	6.94434i	0.785727	+	0.230710i
$907$	−3.65862	−	51.1541i	−0.121482	−	1.69855i	−0.583854	−	0.811859i	$-0.698456\pi$
$907$	−3.65862	−	51.1541i	−0.121482	−	1.69855i	0.462371	−	0.886686i	$-0.346999\pi$
$908$	2.80612	+	12.8995i	0.0931244	+	0.428086i
$909$	66.1355	−	102.909i	2.19358	−	3.41327i
$910$	12.3690	+	9.80463i	0.410029	+	0.325020i
$911$	−0.926807	+	3.15641i	−0.0307065	+	0.104577i	−0.973420	−	0.229026i	$-0.926446\pi$
$911$	−0.926807	+	3.15641i	−0.0307065	+	0.104577i	0.942714	+	0.333602i	$0.108264\pi$
$912$	−14.3457	−	10.7391i	−0.475035	−	0.355607i
$913$	−5.04074	−	0.360521i	−0.166824	−	0.0119315i
$914$	1.99584	+	4.37028i	0.0660165	+	0.144556i
$915$	−83.3553	+	28.4896i	−2.75564	+	0.941838i
$916$	0.665423	+	0.303888i	0.0219862	+	0.0100408i
$917$	−31.8131	−	42.4973i	−1.05056	−	1.40338i
$918$	13.9303	+	3.03034i	0.459767	+	0.100016i
$919$	−15.1309			−0.499124			−0.249562	−	0.968359i	$-0.580287\pi$
$919$	−15.1309			−0.499124			−0.249562	+	0.968359i	$0.580287\pi$
$920$	0.647930	−	10.7042i	0.0213616	−	0.352907i
$921$	0.539079			0.0177632
$922$	−17.0666	−	3.71261i	−0.562058	−	0.122268i
$923$	16.2399	+	21.6940i	0.534544	+	0.714067i
$924$	13.8186	+	6.31076i	0.454600	+	0.207609i
$925$	−11.0179	−	4.81915i	−0.362265	−	0.158453i
$926$	5.47883	+	11.9970i	0.180046	+	0.394245i
$927$	−93.0436	−	6.65461i	−3.05595	−	0.218566i
$928$	2.30679	+	1.72684i	0.0757240	+	0.0566863i
$929$	−3.39678	+	11.5684i	−0.111445	+	0.379546i	−0.996261	−	0.0863941i	$-0.972466\pi$
$929$	−3.39678	+	11.5684i	−0.111445	+	0.379546i	0.884816	+	0.465940i	$0.154284\pi$
$930$	−3.02043	−	26.1170i	−0.0990438	−	0.856409i
$931$	26.4913	−	41.2213i	0.868218	−	1.35097i
$932$	4.69007	+	21.5599i	0.153628	+	0.706218i
$933$	3.85449	+	53.8928i	0.126190	+	1.76437i
$934$	27.4156	+	8.04995i	0.897066	+	0.263402i
$935$	−0.376517	−	1.99498i	−0.0123134	−	0.0652427i
$936$	9.49828	+	10.9616i	0.310461	+	0.358291i
$937$	47.4977	+	17.7157i	1.55168	+	0.578747i	0.971770	−	0.235932i	$-0.0758142\pi$
$937$	47.4977	+	17.7157i	1.55168	+	0.578747i	0.579912	+	0.814679i	$0.303087\pi$
$938$	−2.56036	+	4.68894i	−0.0835986	+	0.153099i
$939$	−30.0352	+	65.7680i	−0.980163	+	2.14626i
$940$	9.28468	+	0.922769i	0.302833	+	0.0300974i
$941$	3.99751	+	6.22025i	0.130315	+	0.202774i	0.900279	−	0.435313i	$-0.143362\pi$
$941$	3.99751	+	6.22025i	0.130315	+	0.202774i	−0.769964	+	0.638087i	$0.779726\pi$
$942$	−16.3705	+	16.3705i	−0.533381	+	0.533381i
$943$	2.77922	−	11.0224i	0.0905040	−	0.358938i
$944$		−	3.47052i		−	0.112956i
$945$	−26.9581	+	156.614i	−0.876948	+	5.09465i
$946$	−0.666108	+	4.63289i	−0.0216571	+	0.150628i
$947$	−33.8762	+	12.6352i	−1.10083	+	0.410588i	−0.833221	−	0.552940i	$-0.813506\pi$
$947$	−33.8762	+	12.6352i	−1.10083	+	0.410588i	−0.267608	+	0.963528i	$0.586233\pi$
$948$	−27.2438	−	14.8763i	−0.884839	−	0.483158i
$949$	11.5266	−	5.26404i	0.374171	−	0.170878i
$950$	−26.6928	+	0.429198i	−0.866028	+	0.0139250i
$951$	−5.08530	−	35.3691i	−0.164902	−	1.14692i
$952$	−1.55518	−	2.84810i	−0.0504037	−	0.0923075i
$953$	51.2518	−	3.66560i	1.66021	−	0.118741i	0.790552	−	0.612395i	$-0.209794\pi$
$953$	51.2518	−	3.66560i	1.66021	−	0.118741i	0.869658	+	0.493655i	$0.164339\pi$
$954$	−46.9116	−	30.1483i	−1.51882	−	0.976086i
$955$	−11.3226	−	42.9185i	−0.366389	−	1.38881i
$956$	0.318667	−	0.367761i	0.0103064	−	0.0118942i
$957$	−9.55225	+	5.21592i	−0.308780	+	0.168607i
$958$	−19.9248	+	26.6164i	−0.643740	+	0.859936i
$959$	10.3059	−	8.93012i	0.332795	−	0.288369i
$960$	−3.41316	−	6.68385i	−0.110159	−	0.215720i
$961$	17.9691	−	5.27620i	0.579648	−	0.170200i
$962$	−1.47507	−	3.95481i	−0.0475581	−	0.127508i
$963$	−87.2908	+	65.3451i	−2.81291	+	2.10572i
$964$	12.7697	−	8.20660i	0.411285	−	0.264317i
$965$	−1.58638	−	36.2463i	−0.0510674	−	1.16681i
$966$	63.7451	+	11.3098i	2.05096	+	0.363887i
$967$	−0.989496	−	0.989496i	−0.0318200	−	0.0318200i	0.691018	−	0.722838i	$-0.257163\pi$
$967$	−0.989496	−	0.989496i	−0.0318200	−	0.0318200i	−0.722838	+	0.691018i	$0.757163\pi$
$968$	−2.06902	+	9.51115i	−0.0665010	+	0.305700i
$969$	−14.3108	−	2.05758i	−0.459728	−	0.0660989i
$970$	−16.2353	−	38.3213i	−0.521285	−	1.23042i
$971$	−2.06640	−	7.03752i	−0.0663140	−	0.225845i	0.919668	−	0.392697i	$-0.128458\pi$
$971$	−2.06640	−	7.03752i	−0.0663140	−	0.225845i	−0.985982	+	0.166852i	$0.946640\pi$
$972$	−21.9532	+	58.8589i	−0.704150	+	1.88790i
$973$	0.724301	−	10.1270i	0.0232200	−	0.324658i
$974$	−15.1540	+	2.17882i	−0.485567	+	0.0698140i
$975$	28.8748	+	5.79677i	0.924734	+	0.185645i
$976$	8.87069	+	7.68650i	0.283944	+	0.246039i
$977$	−27.1831	+	5.91332i	−0.869665	+	0.189184i	−0.625191	−	0.780472i	$-0.714979\pi$
$977$	−27.1831	+	5.91332i	−0.869665	+	0.189184i	−0.244474	+	0.969656i	$0.578615\pi$
$978$	−26.1392	+	5.68623i	−0.835839	+	0.181826i
$979$	−2.64306	−	2.29023i	−0.0844726	−	0.0731959i
$980$	17.5637	−	10.6128i	0.561051	−	0.339014i
$981$	12.1920	−	1.75294i	0.389259	−	0.0559670i
$982$	−2.59924	+	36.3421i	−0.0829450	+	1.15972i
$983$	18.4205	−	49.3873i	0.587523	−	1.57521i	−0.213735	−	0.976892i	$-0.568563\pi$
$983$	18.4205	−	49.3873i	0.587523	−	1.57521i	0.801258	−	0.598319i	$-0.204164\pi$
$984$	−2.24126	−	7.63304i	−0.0714488	−	0.243332i
$985$	−6.14639	+	15.1828i	−0.195840	+	0.483763i
$986$	2.30116	+	0.330857i	0.0732839	+	0.0105366i
$987$	−11.9735	+	55.0413i	−0.381121	+	1.75198i
$988$	−6.62573	−	6.62573i	−0.210793	−	0.210793i
$989$	2.18980	+	19.8262i	0.0696316	+	0.630436i
$990$	20.7770	−	0.909341i	0.660336	−	0.0289008i
$991$	20.8622	−	13.4073i	0.662709	−	0.425897i	−0.165581	−	0.986196i	$-0.552950\pi$
$991$	20.8622	−	13.4073i	0.662709	−	0.425897i	0.828291	+	0.560299i	$0.189314\pi$
$992$	−2.80444	+	2.09938i	−0.0890412	+	0.0666554i
$993$	−33.4515	−	89.6870i	−1.06155	−	2.84613i
$994$	59.5912	−	17.4975i	1.89012	−	0.554989i
$995$	3.08617	+	0.999692i	0.0978383	+	0.0316924i
$996$	−11.3908	+	9.87015i	−0.360930	+	0.312748i
$997$	26.5551	−	35.4735i	0.841010	−	1.12346i	−0.149870	−	0.988706i	$-0.547885\pi$
$997$	26.5551	−	35.4735i	0.841010	−	1.12346i	0.990879	−	0.134752i	$-0.0430237\pi$
$998$	−32.6865	+	17.8482i	−1.03467	+	0.564975i
$999$	27.8306	−	32.1182i	0.880520	−	1.01617i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.57.7	✓	240
5.3	odd	4	inner	230.2.l.a.103.12	yes	240
23.21	odd	22	inner	230.2.l.a.67.12	yes	240
115.113	even	44	inner	230.2.l.a.113.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.7	✓	240	1.1	even	1	trivial
230.2.l.a.67.12	yes	240	23.21	odd	22	inner
230.2.l.a.103.12	yes	240	5.3	odd	4	inner
230.2.l.a.113.7	yes	240	115.113	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.977147 + 0.212565i) q^{2} +(-2.01135 - 2.68685i) q^{3} +(0.909632 + 0.415415i) q^{4} +(0.984796 - 2.00753i) q^{5} +(-1.39425 - 3.05299i) q^{6} +(-4.01185 - 0.286933i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-2.32843 + 7.92991i) q^{9} +(1.38902 - 1.75232i) q^{10} +(0.608409 - 0.946702i) q^{11} +(-0.713431 - 3.27959i) q^{12} +(-0.125198 - 1.75050i) q^{13} +(-3.85918 - 1.13316i) q^{14} +(-7.37470 + 1.39185i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.755932 + 0.281948i) q^{17} +(-3.96085 + 7.25375i) q^{18} +(2.21800 - 4.85675i) q^{19} +(1.72976 - 1.41701i) q^{20} +(7.29830 + 11.3564i) q^{21} +(0.795741 - 0.795741i) q^{22} +(2.43518 - 4.13157i) q^{23} -3.35629i q^{24} +(-3.06035 - 3.95402i) q^{25} +(0.249758 - 1.73710i) q^{26} +(16.5558 - 6.17498i) q^{27} +(-3.53011 - 1.92759i) q^{28} +(2.62114 - 1.19703i) q^{29} +(-7.50202 - 0.207567i) q^{30} +(0.498555 + 3.46753i) q^{31} +(0.479249 + 0.877679i) q^{32} +(-3.76737 + 0.269448i) q^{33} +(0.678725 + 0.436190i) q^{34} +(-4.52689 + 7.77135i) q^{35} +(-5.41222 + 6.24604i) q^{36} +(2.11094 - 1.15266i) q^{37} +(3.19969 - 4.27428i) q^{38} +(-4.45150 + 3.85725i) q^{39} +(1.99144 - 1.01694i) q^{40} +(2.27425 - 0.667780i) q^{41} +(4.71754 + 12.6482i) q^{42} +(-3.32960 + 2.49251i) q^{43} +(0.946702 - 0.608409i) q^{44} +(13.6265 + 12.4837i) q^{45} +(3.25776 - 3.51952i) q^{46} +(2.95054 + 2.95054i) q^{47} +(0.713431 - 3.27959i) q^{48} +(9.08389 + 1.30607i) q^{49} +(-2.14993 - 4.51418i) q^{50} +(-0.762893 - 2.59817i) q^{51} +(0.613298 - 1.64432i) q^{52} +(-0.481343 + 6.73006i) q^{53} +(17.4900 - 2.51468i) q^{54} +(-1.30137 - 2.15371i) q^{55} +(-3.03970 - 2.63392i) q^{56} +(-17.5105 + 3.80918i) q^{57} +(2.81568 - 0.612514i) q^{58} +(-2.62284 - 2.27270i) q^{59} +(-7.28646 - 1.79749i) q^{60} +(11.6181 - 1.67044i) q^{61} +(-0.249914 + 3.49426i) q^{62} +(11.6167 - 31.1456i) q^{63} +(0.281733 + 0.959493i) q^{64} +(-3.63747 - 1.47254i) q^{65} +(-3.73855 - 0.537522i) q^{66} +(0.282344 - 1.29791i) q^{67} +(0.570495 + 0.570495i) q^{68} +(-15.9989 + 1.76708i) q^{69} +(-6.07535 + 6.63149i) q^{70} +(-12.9901 + 8.34826i) q^{71} +(-6.61623 + 4.95285i) q^{72} +(2.52331 + 6.76526i) q^{73} +(2.30772 - 0.677607i) q^{74} +(-4.46840 + 16.1756i) q^{75} +(4.03513 - 3.49646i) q^{76} +(-2.71249 + 3.62346i) q^{77} +(-5.16969 + 2.82286i) q^{78} +(6.05650 - 6.98957i) q^{79} +(2.16209 - 0.570393i) q^{80} +(-29.0326 - 18.6581i) q^{81} +(2.36422 - 0.169092i) q^{82} +(-2.15217 - 3.94140i) q^{83} +(1.92116 + 13.3619i) q^{84} +(1.31046 - 1.23990i) q^{85} +(-3.78333 + 1.72779i) q^{86} +(-8.48827 - 4.63494i) q^{87} +(1.05439 - 0.393269i) q^{88} +(0.442275 - 3.07609i) q^{89} +(10.6615 + 15.0950i) q^{90} +7.05866i q^{91} +(3.93144 - 2.74660i) q^{92} +(8.31396 - 8.31396i) q^{93} +(2.25593 + 3.51029i) q^{94} +(-7.56579 - 9.23561i) q^{95} +(1.39425 - 3.05299i) q^{96} +(8.91998 - 16.3357i) q^{97} +(8.59867 + 3.20714i) q^{98} +(6.09063 + 7.02896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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