LMFDB - Embedded newform 230.2.l.a.113.7

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			113.7
Character	$\chi$	$=$	230.113
Dual form			230.2.l.a.57.7

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{22}\right)$

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	−0.382462	+	0.923971i	$0.624924\pi$
$3$	−2.01135	+	2.68685i	−1.16125	+	1.55125i	−0.778792	+	0.627282i	$0.784167\pi$
$4$	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	−0.804525	−	0.593918i	$-0.797580\pi$
$7$	−4.01185	+	0.286933i	−1.51634	+	0.108451i	−0.711813	+	0.702369i	$0.752126\pi$
$8$	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	0.920780	−	0.390083i	$-0.127554\pi$
$11$	0.608409	+	0.946702i	0.183442	+	0.285442i	−0.737338	+	0.675524i	$0.763917\pi$
$12$	−0.713431	+	3.27959i	−0.205950	+	0.946736i
$13$	−0.125198	+	1.75050i	−0.0347237	+	0.485500i	0.950100	+	0.311944i	$0.100980\pi$
$13$	−0.125198	+	1.75050i	−0.0347237	+	0.485500i	−0.984824	+	0.173556i	$0.944474\pi$
$14$	−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	−0.256117	−	0.966646i	$-0.582443\pi$
$17$	0.755932	−	0.281948i	0.183341	−	0.0683825i	0.439458	+	0.898263i	$0.355171\pi$
$18$	−3.96085	−	7.25375i	−0.933580	−	1.70972i
$19$	2.21800	+	4.85675i	0.508845	+	1.11421i	0.973493	+	0.228719i	$0.0734536\pi$
$19$	2.21800	+	4.85675i	0.508845	+	1.11421i	−0.464648	+	0.885495i	$0.653819\pi$
$20$	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	0.643638	−	0.765330i	$-0.277424\pi$
$29$	2.62114	+	1.19703i	0.486733	+	0.222283i	−0.156905	+	0.987614i	$0.550152\pi$
$30$	−7.50202	+	0.207567i	−1.36968	+	0.0378963i
$31$	0.498555	−	3.46753i	0.0895432	−	0.622786i	−0.894793	−	0.446482i	$-0.852677\pi$
$31$	0.498555	−	3.46753i	0.0895432	−	0.622786i	0.984336	−	0.176304i	$-0.0564142\pi$
$32$	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	0.643308	−	0.765607i	$-0.277561\pi$
$37$	2.11094	+	1.15266i	0.347037	+	0.189496i	−0.296271	+	0.955104i	$0.595743\pi$
$38$	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	0.454454	−	0.890770i	$-0.349834\pi$
$41$	2.27425	+	0.667780i	0.355178	+	0.104290i	−0.0992759	+	0.995060i	$0.531653\pi$
$42$	4.71754	−	12.6482i	0.727932	−	1.95166i
$43$	−3.32960	−	2.49251i	−0.507759	−	0.380104i	0.314464	−	0.949269i	$-0.398175\pi$
$43$	−3.32960	−	2.49251i	−0.507759	−	0.380104i	−0.822223	+	0.569166i	$0.807266\pi$
$44$	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	−0.458377	−	0.888758i	$-0.651569\pi$
$47$	2.95054	−	2.95054i	0.430380	−	0.430380i	0.888758	+	0.458377i	$0.151569\pi$
$48$	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	−0.916949	−	0.399005i	$-0.869356\pi$
$53$	−0.481343	−	6.73006i	−0.0661176	−	0.924445i	0.850831	−	0.525439i	$-0.176099\pi$
$54$	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	−0.808664	−	0.588271i	$-0.799809\pi$
$59$	−2.62284	+	2.27270i	−0.341465	+	0.295881i	0.467199	+	0.884152i	$0.345263\pi$
$60$	−7.28646	+	1.79749i	−0.940678	+	0.232055i
$61$	11.6181	+	1.67044i	1.48755	+	0.213877i	0.837677	−	0.546166i	$-0.183913\pi$
$61$	11.6181	+	1.67044i	1.48755	+	0.213877i	0.649873	+	0.760043i	$0.274822\pi$
$62$	−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	0.991172	−	0.132582i	$-0.0423267\pi$
$67$	0.282344	+	1.29791i	0.0344938	+	0.158565i	−0.956678	+	0.291147i	$0.905963\pi$
$68$	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	−0.987371	−	0.158423i	$-0.949359\pi$
$71$	−12.9901	−	8.34826i	−1.54165	−	0.990756i	−0.554275	−	0.832333i	$-0.687005\pi$
$72$	−6.61623	−	4.95285i	−0.779730	−	0.583698i
$73$	2.52331	−	6.76526i	0.295331	−	0.791813i	−0.701530	−	0.712640i	$-0.747499\pi$
$73$	2.52331	−	6.76526i	0.295331	−	0.791813i	0.996861	−	0.0791731i	$-0.0252280\pi$
$74$	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	0.986116	−	0.166058i	$-0.0531038\pi$
$79$	6.05650	+	6.98957i	0.681410	+	0.786389i	−0.304706	+	0.952446i	$0.598558\pi$
$80$	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	−0.968721	−	0.248153i	$-0.920176\pi$
$83$	−2.15217	+	3.94140i	−0.236231	+	0.432625i	0.732490	+	0.680778i	$0.238358\pi$
$84$	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	0.999743	+	0.0226615i	$0.00721400\pi$
$89$	0.442275	+	3.07609i	0.0468811	+	0.326065i	−0.952862	+	0.303404i	$0.901877\pi$
$90$	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	0.740155	+	0.672436i	$0.234752\pi$
$97$	8.91998	+	16.3357i	0.905686	+	1.65864i	0.165531	+	0.986205i	$0.447066\pi$
$98$	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	−0.897170	−	0.441685i	$-0.854381\pi$
$101$	−14.2017	+	4.17000i	−1.41312	+	0.414931i	−0.515954	+	0.856616i	$0.672563\pi$
$102$	−0.193177	+	2.70096i	−0.0191273	+	0.267435i
$103$	2.39916	−	11.0288i	0.236397	−	1.08670i	−0.693952	−	0.720022i	$-0.744132\pi$
$103$	2.39916	−	11.0288i	0.236397	−	1.08670i	0.930348	−	0.366677i	$-0.119504\pi$
$104$	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	0.0489288	−	0.998802i	$-0.484419\pi$
$107$	10.5619	−	7.90654i	1.02106	−	0.764354i	0.972129	+	0.234448i	$0.0753284\pi$
$108$	17.6248	−	1.26055i	1.69595	−	0.121297i
$109$	−0.619116	+	1.35567i	−0.0593006	+	0.129850i	−0.936962	−	0.349430i	$-0.886375\pi$
$109$	−0.619116	+	1.35567i	−0.0593006	+	0.129850i	0.877662	+	0.479281i	$0.159102\pi$
$110$	−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	−0.409770	−	0.912189i	$-0.634391\pi$
$113$	−4.29005	+	0.933242i	−0.403573	+	0.0877920i	0.00619676	+	0.999981i	$0.498027\pi$
$114$	−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	−0.481923	−	0.876214i	$-0.660061\pi$
$127$	3.61120	−	16.6004i	0.320442	−	1.47305i	0.802365	−	0.596834i	$-0.203575\pi$
$128$	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	−0.239900	−	0.970798i	$-0.577115\pi$
$131$	8.64318	−	9.97476i	0.755158	−	0.871499i	0.995058	+	0.0992990i	$0.0316600\pi$
$132$	−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	0.597239	−	0.802063i	$-0.296264\pi$
$137$	−2.39740	−	2.39740i	−0.204824	−	0.204824i	−0.802063	+	0.597239i	$0.796264\pi$
$138$	−16.0089	+	1.67412i	−1.36277	+	0.142510i
$139$		−	2.52428i		−	0.214107i	−0.994253	−	0.107053i	$-0.965858\pi$
$139$		−	2.52428i		−	0.214107i	0.994253	−	0.107053i	$-0.0341416\pi$
$140$	−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	−0.843525	−	0.537090i	$-0.819524\pi$
$149$	−8.61031	+	5.53351i	−0.705384	+	0.453323i	0.138141	+	0.990413i	$0.455887\pi$
$150$	−7.80466	−	14.8561i	−0.637248	−	1.21300i
$151$	−4.80931	−	5.55024i	−0.391376	−	0.451672i	0.525530	−	0.850775i	$-0.323867\pi$
$151$	−4.80931	−	5.55024i	−0.391376	−	0.451672i	−0.916906	+	0.399103i	$0.869322\pi$
$152$	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	−0.996948	−	0.0780624i	$-0.975127\pi$
$157$	−2.41058	+	6.46301i	−0.192385	+	0.515804i	0.804563	+	0.593867i	$0.202399\pi$
$158$	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	0.994675	+	0.103061i	$0.0328638\pi$
$163$	1.69420	+	7.78812i	0.132700	+	0.610012i	−0.861975	+	0.506951i	$0.830773\pi$
$164$	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	0.950676	−	0.310186i	$-0.100391\pi$
$167$	0.375727	+	1.00736i	0.0290747	+	0.0779522i	−0.921601	+	0.388138i	$0.873118\pi$
$168$	−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	−0.747553	−	0.664202i	$-0.768772\pi$
$173$	−22.4057	−	4.87405i	−1.70347	−	0.370567i	−0.955918	+	0.293634i	$0.905135\pi$
$174$	−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	−0.767831	−	0.640653i	$-0.778664\pi$
$179$	3.00324	−	10.2281i	0.224472	−	0.764483i	0.992303	−	0.123830i	$-0.0395179\pi$
$180$	7.20917	−	17.0163i	0.537340	−	1.26832i
$181$	−6.15811	+	0.885402i	−0.457728	+	0.0658114i	−0.367323	−	0.930094i	$-0.619725\pi$
$181$	−6.15811	+	0.885402i	−0.457728	+	0.0658114i	−0.0904058	+	0.995905i	$0.528816\pi$
$182$	−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	0.998453	−	0.0556092i	$-0.0177101\pi$
$191$	15.0020	+	12.9993i	1.08550	+	0.940595i	0.0870515	+	0.996204i	$0.472256\pi$
$192$	2.01135	+	2.68685i	0.145157	+	0.193907i
$193$	14.2406	+	7.77598i	1.02506	+	0.559727i	0.901577	−	0.432619i	$-0.142410\pi$
$193$	14.2406	+	7.77598i	1.02506	+	0.559727i	0.123487	+	0.992346i	$0.460592\pi$
$194$	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	−0.191418	−	0.981509i	$-0.561309\pi$
$197$	−7.30656	−	0.522575i	−0.520571	−	0.0372320i	−0.329153	+	0.944277i	$0.606763\pi$
$198$	4.45733	−	8.16298i	0.316768	−	0.580118i
$199$	0.206468	−	1.43602i	0.0146361	−	0.101796i	−0.981194	−	0.193025i	$-0.938170\pi$
$199$	0.206468	−	1.43602i	0.0146361	−	0.101796i	0.995830	+	0.0912283i	$0.0290793\pi$
$200$	−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	0.986992	+	0.160771i	$0.0513982\pi$
$211$	6.71315	+	14.6998i	0.462152	+	1.01197i	−0.524839	+	0.851201i	$0.675875\pi$
$212$	−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	−0.688608	−	0.725134i	$-0.741778\pi$
$223$	−18.9205	+	1.35322i	−1.26701	+	0.0906184i	−0.578402	+	0.815752i	$0.696323\pi$
$224$	−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	−0.457086	−	0.889422i	$-0.651107\pi$
$227$	7.91120	−	10.5681i	0.525085	−	0.701431i	0.982171	+	0.187992i	$0.0601978\pi$
$228$	−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	−0.120156	−	0.992755i	$-0.538339\pi$
$233$	13.2225	−	17.6633i	0.866238	−	1.15716i	0.986393	−	0.164403i	$-0.0525698\pi$
$234$	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	0.963808	−	0.266597i	$-0.0858992\pi$
$239$	0.137096	+	0.466906i	0.00886800	+	0.0302016i	−0.954940	+	0.296798i	$0.904081\pi$
$240$	−5.88129	+	4.66196i	−0.379636	+	0.300928i
$241$	8.20660	+	12.7697i	0.528633	+	0.822570i	0.998178	−	0.0603392i	$-0.0192182\pi$
$241$	8.20660	+	12.7697i	0.528633	+	0.822570i	−0.469545	+	0.882909i	$0.655582\pi$
$242$	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	−0.795886	−	0.605446i	$-0.792995\pi$
$251$	1.35410	−	2.10703i	0.0854703	−	0.132994i	0.881356	+	0.472452i	$0.156631\pi$
$252$	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	0.395367	−	0.918523i	$-0.370617\pi$
$257$	1.48547	+	0.554053i	0.0926614	+	0.0345609i	−0.302706	+	0.953084i	$0.597890\pi$
$258$	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	−0.393199	−	0.919454i	$-0.628632\pi$
$263$	−14.8104	−	1.05926i	−0.913247	−	0.0653167i	−0.520048	+	0.854137i	$0.674086\pi$
$264$	−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	0.883696	−	0.468062i	$-0.155048\pi$
$269$	8.95770	+	7.76189i	0.546161	+	0.473251i	−0.337535	+	0.941313i	$0.609593\pi$
$270$	12.1758	+	37.5881i	0.740994	+	2.28754i
$271$	13.5629	+	3.98242i	0.823887	+	0.241915i	0.666389	−	0.745604i	$-0.267839\pi$
$271$	13.5629	+	3.98242i	0.823887	+	0.241915i	0.157498	+	0.987519i	$0.449657\pi$
$272$	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	−0.00976828	−	0.999952i	$-0.503109\pi$
$277$	16.4799	−	16.4799i	0.990184	−	0.990184i	0.999952	+	0.00976828i	$0.00310939\pi$
$278$	−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	−0.847552	−	0.530712i	$-0.821925\pi$
$281$	2.55433	−	8.69924i	0.152378	−	0.518953i	0.999931	+	0.0117584i	$0.00374291\pi$
$282$	4.89417	+	13.1218i	0.291443	+	0.781390i
$283$	0.549822	+	7.68752i	0.0326835	+	0.456975i	0.987271	+	0.159046i	$0.0508417\pi$
$283$	0.549822	+	7.68752i	0.0326835	+	0.456975i	−0.954588	+	0.297930i	$0.903704\pi$
$284$	−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	0.901528	−	0.432722i	$-0.142447\pi$
$293$	−1.08136	−	2.89925i	−0.0631739	−	0.169376i	−0.964701	+	0.263346i	$0.915174\pi$
$294$	−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	0.797786	−	0.602941i	$-0.206004\pi$
$307$	−0.0962544	−	0.128581i	−0.00549353	−	0.00733849i	−0.803280	+	0.595602i	$0.796914\pi$
$308$	−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	−0.865010	−	0.501754i	$-0.832688\pi$
$311$	−13.5427	+	8.70338i	−0.767937	+	0.493523i	0.0970731	+	0.995277i	$0.469052\pi$
$312$	−5.87518	−	0.420201i	−0.332616	−	0.0237892i
$313$	−10.3241	+	18.9071i	−0.583550	+	1.06869i	0.404497	+	0.914540i	$0.367447\pi$
$313$	−10.3241	+	18.9071i	−0.583550	+	1.06869i	−0.988047	+	0.154153i	$0.950735\pi$
$314$	−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	−0.194916	−	0.980820i	$-0.562443\pi$
$317$	9.34421	−	5.10233i	0.524823	−	0.286575i	0.719739	+	0.694245i	$0.244262\pi$
$318$	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	0.577102	−	0.816672i	$-0.304184\pi$
$331$	27.3650	−	8.03509i	1.50412	−	0.441649i	0.927015	+	0.375024i	$0.122365\pi$
$332$	−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	−0.917118	−	0.398617i	$-0.869490\pi$
$337$	−14.5581	+	10.8981i	−0.793030	+	0.593655i	0.124088	+	0.992271i	$0.460400\pi$
$338$	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	0.0701906	−	0.997534i	$-0.477639\pi$
$347$	10.2161	−	2.22238i	0.548429	−	0.119303i	0.478238	+	0.878230i	$0.341276\pi$
$348$	−5.79577	+	7.74225i	−0.310686	+	0.415028i
$349$	10.1639	−	4.64172i	0.544063	−	0.248465i	−0.124372	−	0.992236i	$-0.539692\pi$
$349$	10.1639	−	4.64172i	0.544063	−	0.248465i	0.668435	+	0.743770i	$0.266964\pi$
$350$	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	−0.780920	−	0.624632i	$-0.785249\pi$
$353$	−7.54539	+	5.64841i	−0.401600	+	0.300634i	0.379319	+	0.925266i	$0.376158\pi$
$354$	−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	0.0940495	−	0.995568i	$-0.470019\pi$
$359$	13.4794	−	3.95790i	0.711413	−	0.208890i	0.617364	+	0.786678i	$0.288201\pi$
$360$	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	0.525493	−	0.850798i	$-0.323881\pi$
$367$	−6.23193	−	6.23193i	−0.325304	−	0.325304i	−0.850798	+	0.525493i	$0.823881\pi$
$368$	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	−0.534413	−	0.845223i	$-0.679467\pi$
$373$	−2.16872	+	1.18421i	−0.112292	+	0.0613162i	0.422121	+	0.906539i	$0.361286\pi$
$374$	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	−0.987710	−	0.156296i	$-0.950044\pi$
$379$	−24.4487	+	15.7123i	−1.25585	+	0.807084i	−0.268137	+	0.963381i	$0.586408\pi$
$380$	−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	0.788211	−	0.615406i	$-0.211008\pi$
$383$	−0.476171	−	0.636090i	−0.0243312	−	0.0325027i	−0.812542	+	0.582903i	$0.801917\pi$
$384$	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	0.955448	−	0.295161i	$-0.0953732\pi$
$389$	21.3772	+	13.7383i	1.08387	+	0.696559i	0.128420	+	0.991720i	$0.459010\pi$
$390$	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	0.888390	−	0.459090i	$-0.151825\pi$
$397$	−1.66673	−	4.46867i	−0.0836506	−	0.224276i	−0.972040	+	0.234814i	$0.924552\pi$
$398$	−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	−0.564326	−	0.825552i	$-0.690864\pi$
$401$	3.45453	−	2.99337i	0.172511	−	0.149482i	0.736837	+	0.676070i	$0.236318\pi$
$402$	−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	−0.914343	−	0.404941i	$-0.867292\pi$
$409$	1.49209	−	5.08159i	0.0737790	−	0.251268i	0.988122	+	0.153673i	$0.0491102\pi$
$410$	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	0.947823	−	0.318797i	$-0.103279\pi$
$419$	32.1950	+	9.45330i	1.57283	+	0.461824i	0.625005	+	0.780621i	$0.285097\pi$
$420$	28.7164	−	9.30201i	1.40122	−	0.453892i
$421$	−6.75083	−	5.84962i	−0.329015	−	0.285093i	0.474651	−	0.880174i	$-0.342574\pi$
$421$	−6.75083	−	5.84962i	−0.329015	−	0.285093i	−0.803666	+	0.595081i	$0.797120\pi$
$422$	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	−0.279844	−	0.960046i	$-0.590283\pi$
$431$	−24.6772	−	11.2697i	−1.18866	−	0.542841i	−0.908813	+	0.417204i	$0.863010\pi$
$432$	15.5084	−	8.46825i	0.746151	−	0.407429i
$433$	−11.1787	−	4.16945i	−0.537215	−	0.200371i	0.0661879	−	0.997807i	$-0.478916\pi$
$433$	−11.1787	−	4.16945i	−0.537215	−	0.200371i	−0.603403	+	0.797436i	$0.706189\pi$
$434$	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	0.283354	+	0.959015i	$0.408553\pi$
$439$	−14.8072	+	23.0404i	−0.706707	+	1.09966i	−0.990061	+	0.140642i	$0.955083\pi$
$440$	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	−0.726305	−	0.687373i	$-0.758764\pi$
$443$	−17.3658	+	6.47712i	−0.825076	+	0.307737i	−0.0987712	+	0.995110i	$0.531491\pi$
$444$	−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	0.557514	−	0.830168i	$-0.311755\pi$
$449$	−9.09528	−	14.1525i	−0.429233	−	0.667899i	−0.986747	+	0.162268i	$0.948119\pi$
$450$	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	−0.728129	−	0.685440i	$-0.759610\pi$
$457$	2.87920	−	3.84616i	0.134683	−	0.179916i	0.862812	+	0.505524i	$0.168701\pi$
$458$	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	−0.578360	−	0.815781i	$-0.696307\pi$
$463$	7.90376	−	10.5582i	0.367319	−	0.490681i	0.945679	+	0.325101i	$0.105398\pi$
$464$	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	0.605890	−	0.795548i	$-0.292817\pi$
$467$	28.5002	−	2.03837i	1.31883	−	0.0943247i	0.712942	+	0.701223i	$0.247362\pi$
$468$	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	−0.907185	−	0.420732i	$-0.861773\pi$
$479$	−13.8117	−	30.2434i	−0.631073	−	1.38186i	0.276112	−	0.961125i	$-0.410954\pi$
$480$	−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	0.00275839	−	0.999996i	$-0.499122\pi$
$487$	−14.3446	−	5.35025i	−0.650015	−	0.242443i	−0.652774	+	0.757553i	$0.726395\pi$
$488$	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	−0.446484	−	0.894791i	$-0.647324\pi$
$491$	5.18523	−	36.0641i	0.234006	−	1.62755i	0.680491	−	0.732757i	$-0.261767\pi$
$492$	−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	−0.991719	−	0.128424i	$-0.959008\pi$
$499$	−28.1456	−	24.3883i	−1.25997	−	1.09177i	−0.268253	−	0.963349i	$-0.586446\pi$
$500$	−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	0.875579	−	0.483075i	$-0.160480\pi$
$503$	14.7742	+	11.0599i	0.658751	+	0.493135i	−0.216828	+	0.976210i	$0.569571\pi$
$504$	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	−0.150746	−	0.988573i	$-0.548167\pi$
$509$	−0.380645	+	0.0547284i	−0.0168718	+	0.00242579i	0.133874	+	0.990998i	$0.457258\pi$
$510$	−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	0.584055	−	0.811714i	$-0.301465\pi$
$521$	20.9027	+	3.00536i	0.915765	+	0.131667i	0.331710	+	0.943381i	$0.392374\pi$
$522$	−1.69894	−	23.7543i	−0.0743607	−	1.03970i
$523$	−0.663744	−	1.77957i	−0.0290235	−	0.0778150i	0.921630	−	0.388070i	$-0.126858\pi$
$523$	−0.663744	−	1.77957i	−0.0290235	−	0.0778150i	−0.950653	+	0.310255i	$0.899585\pi$
$524$	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	0.00222653	−	0.999998i	$-0.499291\pi$
$541$	21.2307	−	13.6442i	0.912781	−	0.586609i	0.910555	+	0.413389i	$0.135655\pi$
$542$	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	−0.972075	−	0.234671i	$-0.924599\pi$
$547$	−30.4091	+	16.6046i	−1.30020	+	0.709963i	−0.328126	+	0.944634i	$0.606417\pi$
$548$	−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	0.834326	−	0.551272i	$-0.185857\pi$
$557$	−1.89998	−	3.47955i	−0.0805045	−	0.147433i	−0.914830	+	0.403839i	$0.867676\pi$
$558$	−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	−0.945094	−	0.326799i	$-0.894030\pi$
$563$	1.19471	−	5.49198i	0.0503509	−	0.231460i	0.995445	+	0.0953394i	$0.0303936\pi$
$564$	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	−0.909299	−	0.416143i	$-0.863382\pi$
$569$	0.0158620	−	0.0347329i	0.000664969	−	0.00145608i	0.909964	+	0.414687i	$0.136109\pi$
$570$	−17.6476	−	35.9751i	−0.739177	−	1.50683i
$571$	33.6959	−	15.3884i	1.41013	−	0.643985i	0.442595	−	0.896721i	$-0.354058\pi$
$571$	33.6959	−	15.3884i	1.41013	−	0.643985i	0.967535	+	0.252736i	$0.0813305\pi$
$572$	−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	0.301530	−	0.953457i	$-0.402503\pi$
$577$	23.3456	−	5.07853i	0.971891	−	0.211422i	0.670361	+	0.742035i	$0.266139\pi$
$578$	−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	0.0144611	+	0.999895i	$0.495397\pi$
$587$	−10.0320	+	46.1163i	−0.414065	+	1.90342i	−0.428526	+	0.903530i	$0.640967\pi$
$588$	−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	−0.992362	−	0.123361i	$-0.960633\pi$
$593$	−13.6278	−	24.9575i	−0.559628	−	1.02488i	0.432734	−	0.901522i	$-0.357549\pi$
$594$	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	$-0.992056\pi$
$599$		−	1.22147i		−	0.0499078i	0.999689	−	0.0249539i	$-0.00794390\pi$
$600$	−13.2708	−	10.2714i	−0.541779	−	0.419330i
$601$	0.561196	+	3.90321i	0.0228917	+	0.159215i	0.998061	−	0.0622463i	$-0.0198264\pi$
$601$	0.561196	+	3.90321i	0.0228917	+	0.159215i	−0.975169	+	0.221461i	$0.928917\pi$
$602$	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	−0.643989	−	0.765034i	$-0.722722\pi$
$607$	8.56803	−	15.6912i	0.347765	−	0.636885i	0.991755	+	0.128150i	$0.0409037\pi$
$608$	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	0.986668	+	0.162743i	$0.0520342\pi$
$613$	21.4125	+	28.6038i	0.864843	+	1.15529i	−0.121826	+	0.992551i	$0.538875\pi$
$614$	−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	−0.725938	−	0.687760i	$-0.758594\pi$
$617$	6.78308	−	18.1861i	0.273077	−	0.732147i	0.999014	−	0.0443863i	$-0.0141332\pi$
$618$	30.3257	+	22.7015i	1.21988	+	0.913190i
$619$	6.27874	+	4.03510i	0.252364	+	0.162184i	0.660706	−	0.750644i	$-0.270257\pi$
$619$	6.27874	+	4.03510i	0.252364	+	0.162184i	−0.408343	+	0.912829i	$0.633893\pi$
$620$	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	−0.355175	+	0.934800i	$0.615579\pi$
$631$	−33.4345	+	28.9712i	−1.33101	+	1.15332i	−0.975832	+	0.218524i	$0.929876\pi$
$632$	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	−0.936266	−	0.351291i	$-0.885743\pi$
$641$	−43.9428	+	6.31803i	−1.73564	+	0.249547i	−0.799371	+	0.600838i	$0.794834\pi$
$642$	9.41262	+	43.2691i	0.371486	+	1.70769i
$643$	6.37779	−	6.37779i	0.251515	−	0.251515i	−0.570076	−	0.821592i	$-0.693086\pi$
$643$	6.37779	−	6.37779i	0.251515	−	0.251515i	0.821592	+	0.570076i	$0.193086\pi$
$644$	−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	−0.990034	−	0.140830i	$-0.955023\pi$
$647$	−35.7146	−	26.7356i	−1.40408	−	1.05108i	−0.414050	−	0.910254i	$-0.635886\pi$
$648$	−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	0.556716	−	0.830703i	$-0.312061\pi$
$653$	4.05967	+	2.21675i	0.158867	+	0.0867480i	−0.397849	+	0.917451i	$0.630243\pi$
$654$	−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	−0.998939	−	0.0460547i	$-0.985335\pi$
$659$	−0.705668	+	4.90803i	−0.0274889	+	0.191190i	0.971450	+	0.237244i	$0.0762442\pi$
$660$	−6.13484	−	5.80450i	−0.238798	−	0.225940i
$661$	−32.0716	−	14.6466i	−1.24744	−	0.569687i	−0.321340	−	0.946964i	$-0.604133\pi$
$661$	−32.0716	−	14.6466i	−1.24744	−	0.569687i	−0.926100	+	0.377277i	$0.876860\pi$
$662$	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	0.180978	−	0.983487i	$-0.442074\pi$
$673$	24.9512	−	9.30633i	0.961799	−	0.358733i	0.780821	+	0.624754i	$0.214801\pi$
$674$	−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	−0.867442	−	0.497538i	$-0.834237\pi$
$677$	1.61261	−	22.5473i	0.0619777	−	0.866562i	0.929420	−	0.369024i	$-0.120308\pi$
$678$	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	−0.178380	−	0.983962i	$-0.557086\pi$
$683$	−5.61656	+	0.401705i	−0.214912	+	0.0153708i	−0.0365319	+	0.999332i	$0.511631\pi$
$684$	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	−0.749329	−	0.662198i	$-0.769624\pi$
$701$	−27.5461	−	42.8626i	−1.04040	−	1.61890i	−0.291074	−	0.956701i	$-0.594013\pi$
$702$	−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	−0.974218	−	0.225608i	$-0.927563\pi$
$709$	−13.4931	−	29.5458i	−0.506744	−	1.10962i	0.467474	−	0.884007i	$-0.345164\pi$
$710$	−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	0.659534	−	0.751674i	$-0.270753\pi$
$719$	14.0335	+	6.40887i	0.523360	+	0.239011i	−0.136174	+	0.990685i	$0.543481\pi$
$720$	−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	0.564318	−	0.825558i	$-0.309139\pi$
$727$	4.71602	+	2.57514i	0.174907	+	0.0955066i	−0.389410	+	0.921064i	$0.627321\pi$
$728$	−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	0.688155	−	0.725564i	$-0.258421\pi$
$733$	5.03190	+	3.76683i	0.185857	+	0.139131i	−0.502298	+	0.864695i	$0.667512\pi$
$734$	−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	0.920022	−	0.391868i	$-0.128171\pi$
$739$	52.0089	−	7.47775i	1.91318	−	0.275073i	0.993156	+	0.116794i	$0.0372618\pi$
$740$	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	−0.600587	−	0.799559i	$-0.705066\pi$
$743$	−3.26830	−	45.6968i	−0.119902	−	1.67645i	0.480685	−	0.876894i	$-0.340388\pi$
$744$	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	−0.514463	−	0.857512i	$-0.672009\pi$
$751$	−34.2466	−	4.92392i	−1.24968	−	0.179676i	−0.735213	+	0.677836i	$0.762918\pi$
$752$	−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	−0.837945	−	0.545755i	$-0.816243\pi$
$757$	−8.32118	−	38.2518i	−0.302438	−	1.39029i	0.535506	−	0.844531i	$-0.320121\pi$
$758$	−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	−0.120854	−	0.992670i	$-0.538563\pi$
$761$	−29.6283	−	19.0409i	−1.07402	−	0.690233i	−0.953169	+	0.302437i	$0.902200\pi$
$762$	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	0.594412	−	0.804160i	$-0.297385\pi$
$769$	−7.93536	−	9.15790i	−0.286157	−	0.330242i	−0.880569	+	0.473918i	$0.842839\pi$
$770$	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	−0.988827	−	0.149065i	$-0.952374\pi$
$773$	−9.14229	+	16.7429i	−0.328825	+	0.602199i	0.660002	+	0.751264i	$0.270555\pi$
$774$	−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	0.997661	−	0.0683536i	$-0.0217746\pi$
$787$	11.2433	+	20.5907i	0.400782	+	0.733978i	−0.596879	+	0.802331i	$0.703593\pi$
$788$	−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	−0.524989	−	0.851109i	$-0.675930\pi$
$797$	4.05790	−	3.03770i	0.143738	−	0.107601i	0.668727	+	0.743508i	$0.266840\pi$
$798$	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	−0.662560	−	0.749009i	$-0.730530\pi$
$809$	−15.0856	+	6.88935i	−0.530381	+	0.242217i	0.132179	+	0.991226i	$0.457803\pi$
$810$	−73.0217	−	24.9578i	−2.56572	−	0.876927i
$811$	−2.95071	+	6.46116i	−0.103614	+	0.226882i	−0.954337	−	0.298731i	$-0.903437\pi$
$811$	−2.95071	+	6.46116i	−0.103614	+	0.226882i	0.850724	+	0.525613i	$0.176164\pi$
$812$	−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	−0.999764	−	0.0217382i	$-0.993080\pi$
$821$	−23.9530	+	27.6432i	−0.835966	+	0.964756i	0.163798	+	0.986494i	$0.447625\pi$
$822$	10.6618	−	3.97665i	0.371874	−	0.138702i
$823$	−19.7593	−	36.1865i	−0.688767	−	1.26138i	−0.954751	−	0.297405i	$-0.903879\pi$
$823$	−19.7593	−	36.1865i	−0.688767	−	1.26138i	0.265984	−	0.963977i	$-0.414303\pi$
$824$	−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	0.840611	−	0.541640i	$-0.182196\pi$
$827$	8.59770	+	8.59770i	0.298971	+	0.298971i	−0.541640	+	0.840611i	$0.682196\pi$
$828$	12.6262	−	37.5712i	0.438792	−	1.30569i
$829$		−	15.6632i		−	0.544005i	−0.962297	−	0.272002i	$-0.912314\pi$
$829$		−	15.6632i		−	0.544005i	0.962297	−	0.272002i	$-0.0876859\pi$
$830$	−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	−0.637544	−	0.770414i	$-0.720049\pi$
$839$	−5.83932	+	3.75270i	−0.201596	+	0.129558i	0.435948	+	0.899972i	$0.356413\pi$
$840$	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	0.910555	−	0.413389i	$-0.135655\pi$
$853$	−2.61229	−	12.0085i	−0.0894430	−	0.411163i	−0.999998	+	0.00222628i	$0.999291\pi$
$854$	−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	0.966572	+	0.256395i	$0.0825348\pi$
$857$	11.8266	+	31.7083i	0.403989	+	1.08314i	−0.562583	+	0.826741i	$0.690192\pi$
$858$	−0.472872	−	6.61161i	−0.0161436	−	0.225717i
$859$	−45.5682	−	6.55171i	−1.55477	−	0.223542i	−0.689287	−	0.724488i	$-0.742076\pi$
$859$	−45.5682	−	6.55171i	−1.55477	−	0.223542i	−0.865478	+	0.500947i	$0.832985\pi$
$860$	−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	0.313889	−	0.949460i	$-0.398368\pi$
$863$	6.02201	+	1.31001i	0.204992	+	0.0445932i	−0.108897	+	0.994053i	$0.534732\pi$
$864$	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	0.872198	−	0.489153i	$-0.162694\pi$
$877$	19.2073	+	14.3784i	0.648586	+	0.485525i	−0.223612	+	0.974678i	$0.571785\pi$
$878$	−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	0.244617	−	0.969620i	$-0.421338\pi$
$881$	−20.1930	−	17.4974i	−0.680320	−	0.589501i	−0.924938	+	0.380119i	$0.875883\pi$
$882$	−45.4538	−	60.7191i	−1.53051	−	2.04452i
$883$	43.0112	+	23.4859i	1.44744	+	0.790363i	0.994850	−	0.101356i	$-0.0323180\pi$
$883$	43.0112	+	23.4859i	1.44744	+	0.790363i	0.452591	+	0.891718i	$0.350500\pi$
$884$	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	−0.0821166	−	0.996623i	$-0.526168\pi$
$887$	−9.09057	−	0.650170i	−0.305232	−	0.0218306i	−0.223115	+	0.974792i	$0.571623\pi$
$888$	−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	0.462371	+	0.886686i	$0.346999\pi$
$907$	−3.65862	+	51.1541i	−0.121482	+	1.69855i	−0.583854	+	0.811859i	$0.698456\pi$
$908$	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	0.942714	−	0.333602i	$-0.108264\pi$
$911$	−0.926807	−	3.15641i	−0.0307065	−	0.104577i	−0.973420	+	0.229026i	$0.926446\pi$
$912$	−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	0.884816	−	0.465940i	$-0.154284\pi$
$929$	−3.39678	−	11.5684i	−0.111445	−	0.379546i	−0.996261	+	0.0863941i	$0.972466\pi$
$930$	−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	0.579912	−	0.814679i	$-0.303087\pi$
$937$	47.4977	−	17.7157i	1.55168	−	0.578747i	0.971770	+	0.235932i	$0.0758142\pi$
$938$	−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	−0.769964	−	0.638087i	$-0.779726\pi$
$941$	3.99751	−	6.22025i	0.130315	−	0.202774i	0.900279	+	0.435313i	$0.143362\pi$
$942$	−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	−0.267608	−	0.963528i	$-0.586233\pi$
$947$	−33.8762	−	12.6352i	−1.10083	−	0.410588i	−0.833221	+	0.552940i	$0.813506\pi$
$948$	−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	0.869658	−	0.493655i	$-0.164339\pi$
$953$	51.2518	+	3.66560i	1.66021	+	0.118741i	0.790552	+	0.612395i	$0.209794\pi$
$954$	−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	−0.722838	−	0.691018i	$-0.757163\pi$
$967$	−0.989496	+	0.989496i	−0.0318200	+	0.0318200i	0.691018	+	0.722838i	$0.257163\pi$
$968$	−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	−0.985982	−	0.166852i	$-0.946640\pi$
$971$	−2.06640	+	7.03752i	−0.0663140	+	0.225845i	0.919668	+	0.392697i	$0.128458\pi$
$972$	−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	−0.244474	−	0.969656i	$-0.578615\pi$
$977$	−27.1831	−	5.91332i	−0.869665	−	0.189184i	−0.625191	+	0.780472i	$0.714979\pi$
$978$	−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	0.801258	+	0.598319i	$0.204164\pi$
$983$	18.4205	+	49.3873i	0.587523	+	1.57521i	−0.213735	+	0.976892i	$0.568563\pi$
$984$	−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	0.828291	−	0.560299i	$-0.189314\pi$
$991$	20.8622	+	13.4073i	0.662709	+	0.425897i	−0.165581	+	0.986196i	$0.552950\pi$
$992$	−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	0.990879	+	0.134752i	$0.0430237\pi$
$997$	26.5551	+	35.4735i	0.841010	+	1.12346i	−0.149870	+	0.988706i	$0.547885\pi$
$998$	−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.113.7	yes	240
5.2	odd	4	inner	230.2.l.a.67.12	yes	240
23.11	odd	22	inner	230.2.l.a.103.12	yes	240
115.57	even	44	inner	230.2.l.a.57.7	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.7	✓	240	115.57	even	44	inner
230.2.l.a.67.12	yes	240	5.2	odd	4	inner
230.2.l.a.103.12	yes	240	23.11	odd	22	inner
230.2.l.a.113.7	yes	240	1.1	even	1	trivial

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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