LMFDB - Embedded newform 230.2.l.a.67.12

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			67.12
Character	$\chi$	$=$	230.67
Dual form			230.2.l.a.103.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.212565 + 0.977147i) q^{2} +(2.68685 + 2.01135i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(-1.91382 + 1.15642i) q^{5} +(-1.39425 + 3.05299i) q^{6} +(-0.286933 - 4.01185i) q^{7} +(-0.599278 - 0.800541i) q^{8} +(2.32843 + 7.92991i) q^{9} +(-1.53680 - 1.62426i) q^{10} +(0.608409 + 0.946702i) q^{11} +(-3.27959 - 0.713431i) q^{12} +(1.75050 + 0.125198i) q^{13} +(3.85918 - 1.13316i) q^{14} +(-7.46810 - 0.742226i) q^{15} +(0.654861 - 0.755750i) q^{16} +(0.281948 + 0.755932i) q^{17} +(-7.25375 + 3.96085i) q^{18} +(-2.21800 - 4.85675i) q^{19} +(1.26047 - 1.84695i) q^{20} +(7.29830 - 11.3564i) q^{21} +(-0.795741 + 0.795741i) q^{22} +(4.13157 - 2.43518i) q^{23} -3.35629i q^{24} +(2.32538 - 4.42635i) q^{25} +(0.249758 + 1.73710i) q^{26} +(-6.17498 + 16.5558i) q^{27} +(1.92759 + 3.53011i) q^{28} +(-2.62114 - 1.19703i) q^{29} +(-0.862196 - 7.45520i) q^{30} +(0.498555 - 3.46753i) q^{31} +(0.877679 + 0.479249i) q^{32} +(-0.269448 + 3.76737i) q^{33} +(-0.678725 + 0.436190i) q^{34} +(5.18853 + 7.34613i) q^{35} +(-5.41222 - 6.24604i) q^{36} +(-1.15266 + 2.11094i) q^{37} +(4.27428 - 3.19969i) q^{38} +(4.45150 + 3.85725i) q^{39} +(2.07267 + 0.839071i) q^{40} +(2.27425 + 0.667780i) q^{41} +(12.6482 + 4.71754i) q^{42} +(-2.49251 + 3.32960i) 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} +(3.27959 - 0.713431i) q^{48} +(-9.08389 + 1.30607i) q^{49} +(4.81949 + 1.33135i) q^{50} +(-0.762893 + 2.59817i) q^{51} +(-1.64432 + 0.613298i) q^{52} +(-6.73006 + 0.481343i) q^{53} +(-17.4900 - 2.51468i) q^{54} +(-2.25917 - 1.10824i) q^{55} +(-3.03970 + 2.63392i) q^{56} +(3.80918 - 17.5105i) q^{57} +(0.612514 - 2.81568i) q^{58} +(2.62284 - 2.27270i) q^{59} +(7.10156 - 2.42721i) q^{60} +(11.6181 + 1.67044i) q^{61} +(3.49426 - 0.249914i) q^{62} +(31.1456 - 11.6167i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(-3.49491 + 1.78470i) q^{65} +(-3.73855 + 0.537522i) q^{66} +(-1.29791 + 0.282344i) 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} +(4.95285 - 6.61623i) q^{72} +(-6.76526 - 2.52331i) q^{73} +(-2.30772 - 0.677607i) q^{74} +(15.1509 - 7.21578i) q^{75} +(4.03513 + 3.49646i) q^{76} +(3.62346 - 2.71249i) q^{77} +(-2.82286 + 5.16969i) q^{78} +(-6.05650 - 6.98957i) q^{79} +(-0.379318 + 2.20366i) q^{80} +(-29.0326 + 18.6581i) q^{81} +(-0.169092 + 2.36422i) q^{82} +(3.94140 + 2.15217i) q^{83} +(-1.92116 + 13.3619i) q^{84} +(-1.41377 - 1.12066i) q^{85} +(-3.78333 - 1.72779i) q^{86} +(-4.63494 - 8.48827i) q^{87} +(0.393269 - 1.05439i) q^{88} +(-0.442275 - 3.07609i) q^{89} +(9.30193 - 15.9687i) q^{90} -7.05866i q^{91} +(-2.74660 + 3.93144i) q^{92} +(8.31396 - 8.31396i) q^{93} +(-2.25593 + 3.51029i) q^{94} +(9.86129 + 6.72998i) q^{95} +(1.39425 + 3.05299i) q^{96} +(-16.3357 + 8.91998i) q^{97} +(-3.20714 - 8.59867i) 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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.212565	+	0.977147i	0.150306	+	0.690947i
$2$	0.212565	+	0.977147i	0.150306	+	0.690947i
$3$	2.68685	+	2.01135i	1.55125	+	1.16125i	0.923971	+	0.382462i	$0.124924\pi$
$3$	2.68685	+	2.01135i	1.55125	+	1.16125i	0.627282	+	0.778792i	$0.284167\pi$
$4$	−0.909632	+	0.415415i	−0.454816	+	0.207708i
$5$	−1.91382	+	1.15642i	−0.855884	+	0.517167i
$5$	−1.91382	+	1.15642i	−0.855884	+	0.517167i
$6$	−1.39425	+	3.05299i	−0.569202	+	1.24638i
$7$	−0.286933	−	4.01185i	−0.108451	−	1.51634i	−0.702369	−	0.711813i	$-0.747874\pi$
$7$	−0.286933	−	4.01185i	−0.108451	−	1.51634i	0.593918	−	0.804525i	$-0.297580\pi$
$8$	−0.599278	−	0.800541i	−0.211877	−	0.283034i
$9$	2.32843	+	7.92991i	0.776144	+	2.64330i
$10$	−1.53680	−	1.62426i	−0.485980	−	0.513637i
$11$	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	$0.763917\pi$
$12$	−3.27959	−	0.713431i	−0.946736	−	0.205950i
$13$	1.75050	+	0.125198i	0.485500	+	0.0347237i	0.311944	−	0.950100i	$-0.399020\pi$
$13$	1.75050	+	0.125198i	0.485500	+	0.0347237i	0.173556	+	0.984824i	$0.444474\pi$
$14$	3.85918	−	1.13316i	1.03141	−	0.302849i
$15$	−7.46810	−	0.742226i	−1.92826	−	0.191642i
$16$	0.654861	−	0.755750i	0.163715	−	0.188937i
$17$	0.281948	+	0.755932i	0.0683825	+	0.183341i	0.966646	−	0.256117i	$-0.0824433\pi$
$17$	0.281948	+	0.755932i	0.0683825	+	0.183341i	−0.898263	+	0.439458i	$0.855171\pi$
$18$	−7.25375	+	3.96085i	−1.70972	+	0.933580i
$19$	−2.21800	−	4.85675i	−0.508845	−	1.11421i	−0.973493	−	0.228719i	$-0.926546\pi$
$19$	−2.21800	−	4.85675i	−0.508845	−	1.11421i	0.464648	−	0.885495i	$-0.346181\pi$
$20$	1.26047	−	1.84695i	0.281850	−	0.412989i
$21$	7.29830	−	11.3564i	1.59262	−	2.47816i
$22$	−0.795741	+	0.795741i	−0.169652	+	0.169652i
$23$	4.13157	−	2.43518i	0.861493	−	0.507770i
$23$	4.13157	−	2.43518i	0.861493	−	0.507770i
$24$		−	3.35629i		−	0.685100i
$25$	2.32538	−	4.42635i	0.465076	−	0.885270i
$26$	0.249758	+	1.73710i	0.0489816	+	0.340674i
$27$	−6.17498	+	16.5558i	−1.18837	+	3.18616i
$28$	1.92759	+	3.53011i	0.364280	+	0.667129i
$29$	−2.62114	−	1.19703i	−0.486733	−	0.222283i	0.156905	−	0.987614i	$-0.449848\pi$
$29$	−2.62114	−	1.19703i	−0.486733	−	0.222283i	−0.643638	+	0.765330i	$0.722576\pi$
$30$	−0.862196	−	7.45520i	−0.157415	−	1.36113i
$31$	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	$-0.0564142\pi$
$32$	0.877679	+	0.479249i	0.155153	+	0.0847201i
$33$	−0.269448	+	3.76737i	−0.0469048	+	0.655815i
$34$	−0.678725	+	0.436190i	−0.116400	+	0.0748059i
$35$	5.18853	+	7.34613i	0.877021	+	1.24172i
$36$	−5.41222	−	6.24604i	−0.902037	−	1.04101i
$37$	−1.15266	+	2.11094i	−0.189496	+	0.347037i	−0.955104	−	0.296271i	$-0.904257\pi$
$37$	−1.15266	+	2.11094i	−0.189496	+	0.347037i	0.765607	+	0.643308i	$0.222439\pi$
$38$	4.27428	−	3.19969i	0.693381	−	0.519058i
$39$	4.45150	+	3.85725i	0.712811	+	0.617654i
$40$	2.07267	+	0.839071i	0.327718	+	0.132669i
$41$	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	$0.531653\pi$
$42$	12.6482	+	4.71754i	1.95166	+	0.727932i
$43$	−2.49251	+	3.32960i	−0.380104	+	0.507759i	−0.949269	−	0.314464i	$-0.898175\pi$
$43$	−2.49251	+	3.32960i	−0.380104	+	0.507759i	0.569166	+	0.822223i	$0.307266\pi$
$44$	−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	$0.651569\pi$
$48$	3.27959	−	0.713431i	0.473368	−	0.102975i
$49$	−9.08389	+	1.30607i	−1.29770	+	0.186581i
$50$	4.81949	+	1.33135i	0.681579	+	0.188282i
$51$	−0.762893	+	2.59817i	−0.106826	+	0.363817i
$52$	−1.64432	+	0.613298i	−0.228026	+	0.0850492i
$53$	−6.73006	+	0.481343i	−0.924445	+	0.0661176i	−0.525439	−	0.850831i	$-0.676099\pi$
$53$	−6.73006	+	0.481343i	−0.924445	+	0.0661176i	−0.399005	+	0.916949i	$0.630644\pi$
$54$	−17.4900	−	2.51468i	−2.38009	−	0.342205i
$55$	−2.25917	−	1.10824i	−0.304626	−	0.149435i
$56$	−3.03970	+	2.63392i	−0.406197	+	0.351972i
$57$	3.80918	−	17.5105i	0.504539	−	2.31933i
$58$	0.612514	−	2.81568i	0.0804270	−	0.369717i
$59$	2.62284	−	2.27270i	0.341465	−	0.295881i	−0.467199	−	0.884152i	$-0.654737\pi$
$59$	2.62284	−	2.27270i	0.341465	−	0.295881i	0.808664	+	0.588271i	$0.200191\pi$
$60$	7.10156	−	2.42721i	0.916807	−	0.313351i
$61$	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	$0.274822\pi$
$62$	3.49426	−	0.249914i	0.443771	−	0.0317392i
$63$	31.1456	−	11.6167i	3.92397	−	1.46357i
$64$	−0.281733	+	0.959493i	−0.0352166	+	0.119937i
$65$	−3.49491	+	1.78470i	−0.433490	+	0.221365i
$66$	−3.73855	+	0.537522i	−0.460184	+	0.0661644i
$67$	−1.29791	+	0.282344i	−0.158565	+	0.0344938i	−0.291147	−	0.956678i	$-0.594037\pi$
$67$	−1.29791	+	0.282344i	−0.158565	+	0.0344938i	0.132582	+	0.991172i	$0.457673\pi$
$68$	−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	$-0.687005\pi$
$72$	4.95285	−	6.61623i	0.583698	−	0.779730i
$73$	−6.76526	−	2.52331i	−0.791813	−	0.295331i	−0.0791731	−	0.996861i	$-0.525228\pi$
$73$	−6.76526	−	2.52331i	−0.791813	−	0.295331i	−0.712640	+	0.701530i	$0.752501\pi$
$74$	−2.30772	−	0.677607i	−0.268267	−	0.0787702i
$75$	15.1509	−	7.21578i	1.74948	−	0.833207i
$76$	4.03513	+	3.49646i	0.462861	+	0.401072i
$77$	3.62346	−	2.71249i	0.412931	−	0.309117i
$78$	−2.82286	+	5.16969i	−0.319626	+	0.585352i
$79$	−6.05650	−	6.98957i	−0.681410	−	0.786389i	0.304706	−	0.952446i	$-0.401442\pi$
$79$	−6.05650	−	6.98957i	−0.681410	−	0.786389i	−0.986116	+	0.166058i	$0.946896\pi$
$80$	−0.379318	+	2.20366i	−0.0424091	+	0.246377i
$81$	−29.0326	+	18.6581i	−3.22584	+	2.07312i
$82$	−0.169092	+	2.36422i	−0.0186731	+	0.261085i
$83$	3.94140	+	2.15217i	0.432625	+	0.236231i	0.680778	−	0.732490i	$-0.261642\pi$
$83$	3.94140	+	2.15217i	0.432625	+	0.236231i	−0.248153	+	0.968721i	$0.579824\pi$
$84$	−1.92116	+	13.3619i	−0.209615	+	1.45791i
$85$	−1.41377	−	1.12066i	−0.153345	−	0.121553i
$86$	−3.78333	−	1.72779i	−0.407967	−	0.186312i
$87$	−4.63494	−	8.48827i	−0.496918	−	0.910038i
$88$	0.393269	−	1.05439i	0.0419226	−	0.112399i
$89$	−0.442275	−	3.07609i	−0.0468811	−	0.326065i	−0.999743	−	0.0226615i	$-0.992786\pi$
$89$	−0.442275	−	3.07609i	−0.0468811	−	0.326065i	0.952862	−	0.303404i	$-0.0981231\pi$
$90$	9.30193	−	15.9687i	0.980510	−	1.68325i
$91$		−	7.05866i		−	0.739949i
$92$	−2.74660	+	3.93144i	−0.286353	+	0.409880i
$93$	8.31396	−	8.31396i	0.862117	−	0.862117i
$94$	−2.25593	+	3.51029i	−0.232681	+	0.362059i
$95$	9.86129	+	6.72998i	1.01175	+	0.690481i
$96$	1.39425	+	3.05299i	0.142300	+	0.311594i
$97$	−16.3357	+	8.91998i	−1.65864	+	0.905686i	−0.672436	+	0.740155i	$0.734752\pi$
$97$	−16.3357	+	8.91998i	−1.65864	+	0.905686i	−0.986205	+	0.165531i	$0.947066\pi$
$98$	−3.20714	−	8.59867i	−0.323970	−	0.868597i
$99$	−6.09063	+	7.02896i	−0.612131	+	0.706437i
$100$	−0.276469	+	4.99235i	−0.0276469	+	0.499235i
$101$	−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	$0.672563\pi$
$102$	−2.70096	−	0.193177i	−0.267435	−	0.0191273i
$103$	−11.0288	−	2.39916i	−1.08670	−	0.236397i	−0.366677	−	0.930348i	$-0.619504\pi$
$103$	−11.0288	−	2.39916i	−1.08670	−	0.236397i	−0.720022	+	0.693952i	$0.755868\pi$
$104$	−0.948807	−	1.47637i	−0.0930382	−	0.144770i
$105$	−0.834854	+	30.1739i	−0.0814734	+	2.94467i
$106$	−1.90092	−	6.47394i	−0.184634	−	0.628804i
$107$	7.90654	+	10.5619i	0.764354	+	1.02106i	0.998802	+	0.0489288i	$0.0155807\pi$
$107$	7.90654	+	10.5619i	0.764354	+	1.02106i	−0.234448	+	0.972129i	$0.575328\pi$
$108$	−1.26055	−	17.6248i	−0.121297	−	1.69595i
$109$	0.619116	−	1.35567i	0.0593006	−	0.129850i	−0.877662	−	0.479281i	$-0.840898\pi$
$109$	0.619116	−	1.35567i	0.0593006	−	0.129850i	0.936962	+	0.349430i	$0.113625\pi$
$110$	0.602690	−	2.44311i	0.0574643	−	0.232942i
$111$	−7.34287	+	3.35338i	−0.696955	+	0.318288i
$112$	−3.21986	−	2.41036i	−0.304248	−	0.227757i
$113$	0.933242	+	4.29005i	0.0877920	+	0.403573i	0.999981	−	0.00619676i	$-0.00197250\pi$
$113$	0.933242	+	4.29005i	0.0877920	+	0.403573i	−0.912189	+	0.409770i	$0.865609\pi$
$114$	17.9201			1.67837
$115$	−5.09098	+	9.43832i	−0.474736	+	0.880128i
$116$	2.88153			0.267544
$117$	3.08310	+	14.1728i	0.285033	+	1.31028i
$118$	2.77829	+	2.07980i	0.255762	+	0.191461i
$119$	2.95179	−	1.34804i	0.270590	−	0.123574i
$120$	3.88128	+	6.42332i	0.354311	+	0.586367i
$121$	4.04348	−	8.85399i	0.367589	−	0.804908i
$122$	0.837351	+	11.7077i	0.0758102	+	1.05997i
$123$	4.76742	+	6.36853i	0.429864	+	0.574231i
$124$	0.986961	+	3.36128i	0.0886317	+	0.301852i
$125$	0.668372	+	11.1603i	0.0597810	+	0.998212i
$126$	17.9717	+	27.9645i	1.60104	+	2.49127i
$127$	16.6004	+	3.61120i	1.47305	+	0.320442i	0.876214	−	0.481923i	$-0.160061\pi$
$127$	16.6004	+	3.61120i	1.47305	+	0.320442i	0.596834	+	0.802365i	$0.296425\pi$
$128$	−0.997452	−	0.0713392i	−0.0881631	−	0.00630555i
$129$	−13.3940	+	3.93283i	−1.17927	+	0.346266i
$130$	−2.48681	−	3.03567i	−0.218108	−	0.266246i
$131$	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	$0.0316600\pi$
$132$	−1.31992	−	3.53885i	−0.114885	−	0.308018i
$133$	−18.8481	+	10.2919i	−1.63434	+	0.892418i
$134$	−0.551783	−	1.20824i	−0.0476668	−	0.104376i
$135$	−7.32765	−	38.8255i	−0.630663	−	3.34157i
$136$	0.436190	−	0.678725i	0.0374030	−	0.0582001i
$137$	2.39740	−	2.39740i	0.204824	−	0.204824i	−0.597239	−	0.802063i	$-0.703736\pi$
$137$	2.39740	−	2.39740i	0.204824	−	0.204824i	0.802063	+	0.597239i	$0.203736\pi$
$138$	1.67412	+	16.0089i	0.142510	+	1.36277i
$139$			2.52428i			0.214107i	0.994253	+	0.107053i	$0.0341416\pi$
$139$			2.52428i			0.214107i	−0.994253	+	0.107053i	$0.965858\pi$
$140$	−7.77135	−	4.52689i	−0.656799	−	0.382592i
$141$	1.99309	+	13.8622i	0.167848	+	1.16741i
$142$	5.39622	−	14.4678i	0.452841	−	1.21411i
$143$	0.946492	+	1.73337i	0.0791496	+	0.144952i
$144$	7.51783	+	3.43328i	0.626486	+	0.286106i
$145$	6.40064	−	0.740235i	0.531544	−	0.0614732i
$146$	1.02759	−	7.14702i	0.0850436	−	0.591491i
$147$	−27.0340	−	14.7617i	−2.22973	−	1.21752i
$148$	0.171581	−	2.39901i	0.0141039	−	0.197198i
$149$	8.61031	−	5.53351i	0.705384	−	0.453323i	−0.138141	−	0.990413i	$-0.544113\pi$
$149$	8.61031	−	5.53351i	0.705384	−	0.453323i	0.843525	+	0.537090i	$0.180476\pi$
$150$	10.2714	+	13.2708i	0.838659	+	1.08356i
$151$	−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	$0.869322\pi$
$152$	−2.55883	+	4.68614i	−0.207548	+	0.380096i
$153$	−5.33798	+	3.99596i	−0.431550	+	0.323054i
$154$	3.42072	+	2.96407i	0.275649	+	0.238852i
$155$	3.05578	+	7.21275i	0.245446	+	0.579342i
$156$	−5.65159	−	1.65946i	−0.452489	−	0.132863i
$157$	−6.46301	−	2.41058i	−0.515804	−	0.192385i	0.0780624	−	0.996948i	$-0.475127\pi$
$157$	−6.46301	−	2.41058i	−0.515804	−	0.192385i	−0.593867	+	0.804563i	$0.702399\pi$
$158$	5.54244	−	7.40383i	0.440933	−	0.589017i
$159$	−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
$163$	7.78812	−	1.69420i	0.610012	−	0.132700i	0.103061	−	0.994675i	$-0.467136\pi$
$163$	7.78812	−	1.69420i	0.610012	−	0.132700i	0.506951	+	0.861975i	$0.330773\pi$
$164$	−2.34613	+	0.337323i	−0.183202	+	0.0263405i
$165$	−3.84099	−	7.52165i	−0.299021	−	0.585559i
$166$	−1.26518	+	4.30881i	−0.0981970	+	0.334428i
$167$	−1.00736	+	0.375727i	−0.0779522	+	0.0290747i	−0.388138	−	0.921601i	$-0.626882\pi$
$167$	−1.00736	+	0.375727i	−0.0779522	+	0.0290747i	0.310186	+	0.950676i	$0.399609\pi$
$168$	−13.4650	+	0.963032i	−1.03884	+	0.0742996i
$169$	−9.81912	−	1.41178i	−0.755317	−	0.108598i
$170$	0.794535	−	1.61968i	0.0609380	−	0.124224i
$171$	33.3491	−	28.8972i	2.55027	−	2.20982i
$172$	0.884098	−	4.06413i	0.0674119	−	0.309887i
$173$	−4.87405	+	22.4057i	−0.370567	+	1.70347i	0.293634	+	0.955918i	$0.405135\pi$
$173$	−4.87405	+	22.4057i	−0.370567	+	1.70347i	−0.664202	+	0.747553i	$0.731228\pi$
$174$	7.30906	−	6.33333i	0.554098	−	0.480129i
$175$	−18.4251	−	8.05903i	−1.39281	−	0.609205i
$176$	1.11389	+	0.160154i	0.0839628	+	0.0120720i
$177$	11.6184	−	0.830963i	0.873291	−	0.0624590i
$178$	2.91178	−	1.08604i	0.218247	−	0.0814020i
$179$	−3.00324	+	10.2281i	−0.224472	+	0.764483i	0.767831	+	0.640653i	$0.221336\pi$
$179$	−3.00324	+	10.2281i	−0.224472	+	0.764483i	−0.992303	+	0.123830i	$0.960482\pi$
$180$	17.5810	+	5.69496i	1.31041	+	0.424477i
$181$	−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	$0.528816\pi$
$182$	6.89735	−	1.50043i	0.511265	−	0.111219i
$183$	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
$187$	−0.544103	+	0.726837i	−0.0397888	+	0.0531516i
$188$	−3.90960	−	1.45821i	−0.285137	−	0.106351i
$189$	68.1911	+	20.0227i	4.96017	+	1.45644i
$190$	−4.48001	+	11.0665i	−0.325014	+	0.802847i
$191$	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	$0.472256\pi$
$192$	−2.68685	+	2.01135i	−0.193907	+	0.145157i
$193$	7.77598	−	14.2406i	0.559727	−	1.02506i	−0.432619	−	0.901577i	$-0.642410\pi$
$193$	7.77598	−	14.2406i	0.559727	−	1.02506i	0.992346	−	0.123487i	$-0.0394077\pi$
$194$	−12.1885	−	14.0663i	−0.875086	−	1.00990i
$195$	−12.9800	−	2.23426i	−0.929514	−	0.159998i
$196$	7.72044	−	4.96162i	0.551460	−	0.354402i
$197$	0.522575	−	7.30656i	0.0372320	−	0.520571i	−0.944277	−	0.329153i	$-0.893237\pi$
$197$	0.522575	−	7.30656i	0.0372320	−	0.520571i	0.981509	−	0.191418i	$-0.0613086\pi$
$198$	−8.16298	−	4.45733i	−0.580118	−	0.316768i
$199$	−0.206468	+	1.43602i	−0.0146361	+	0.101796i	−0.995830	−	0.0912283i	$-0.970921\pi$
$199$	−0.206468	+	1.43602i	−0.0146361	+	0.101796i	0.981194	+	0.193025i	$0.0618298\pi$
$200$	−4.93703	+	0.791050i	−0.349101	+	0.0559357i
$201$	−4.05519	−	1.85195i	−0.286031	−	0.130626i
$202$	−7.09350	−	12.9908i	−0.499097	−	0.914028i
$203$	−4.05023	+	10.8591i	−0.284270	+	0.762158i
$204$	−0.385369	−	2.68030i	−0.0269812	−	0.187658i
$205$	−5.12473	+	1.35198i	−0.357926	+	0.0944264i
$206$		−	11.2867i		−	0.786383i
$207$	28.9309	+	27.0929i	2.01083	+	1.88308i
$208$	1.24095	−	1.24095i	0.0860444	−	0.0860444i
$209$	3.24844	−	5.05467i	0.224699	−	0.349639i
$210$	−29.6618	+	5.59815i	−2.04686	+	0.386309i
$211$	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	$0.675875\pi$
$212$	5.92192	−	3.23361i	0.406719	−	0.222085i
$213$	−18.1113	−	48.5583i	−1.24097	−	3.32716i
$214$	−8.63987	+	9.97094i	−0.590609	+	0.681600i
$215$	0.919781	−	9.25462i	0.0627286	−	0.631160i
$216$	16.9541	−	4.97817i	1.15358	−	0.338722i
$217$	−14.0543	−	1.00518i	−0.954066	−	0.0682361i
$218$	1.45630	+	0.316798i	0.0986328	+	0.0214563i
$219$	−13.1020	−	20.3871i	−0.885349	−	1.37763i
$220$	2.51539	+	0.0695960i	0.169588	+	0.00469216i
$221$	0.398908	+	1.35856i	0.0268335	+	0.0913864i
$222$	−4.83758	−	6.46225i	−0.324677	−	0.433718i
$223$	1.35322	+	18.9205i	0.0906184	+	1.26701i	0.815752	+	0.578402i	$0.196323\pi$
$223$	1.35322	+	18.9205i	0.0906184	+	1.26701i	−0.725134	+	0.688608i	$0.758222\pi$
$224$	1.67084	−	3.65863i	0.111638	−	0.244453i
$225$	40.5151	+	8.13362i	2.70101	+	0.542241i
$226$	−3.99363	+	1.82383i	−0.265652	+	0.121319i
$227$	10.5681	+	7.91120i	0.701431	+	0.525085i	0.889422	−	0.457086i	$-0.151107\pi$
$227$	10.5681	+	7.91120i	0.701431	+	0.525085i	−0.187992	+	0.982171i	$0.560198\pi$
$228$	3.80918	+	17.5105i	0.252269	+	1.15966i
$229$	−0.731530			−0.0483408			−0.0241704	−	0.999708i	$-0.507694\pi$
$229$	−0.731530			−0.0483408			−0.0241704	+	0.999708i	$0.507694\pi$
$230$	−10.3048	−	2.96837i	−0.679478	−	0.195729i
$231$	15.1915			0.999524
$232$	0.612514	+	2.81568i	0.0402135	+	0.184859i
$233$	−17.6633	−	13.2225i	−1.15716	−	0.866238i	−0.164403	−	0.986393i	$-0.552570\pi$
$233$	−17.6633	−	13.2225i	−1.15716	−	0.866238i	−0.992755	+	0.120156i	$0.961661\pi$
$234$	−13.1935	+	6.02529i	−0.862489	+	0.393886i
$235$	−9.05885	−	2.23472i	−0.590934	−	0.145777i
$236$	−1.44170	+	3.15689i	−0.0938470	+	0.205496i
$237$	−2.21442	−	30.9617i	−0.143842	−	2.01118i
$238$	1.94468	+	2.59779i	0.126055	+	0.168389i
$239$	−0.137096	−	0.466906i	−0.00886800	−	0.0302016i	0.954940	−	0.296798i	$-0.0959190\pi$
$239$	−0.137096	−	0.466906i	−0.00886800	−	0.0302016i	−0.963808	+	0.266597i	$0.914101\pi$
$240$	−5.45150	+	5.15796i	−0.351893	+	0.332945i
$241$	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	$0.655582\pi$
$242$	9.51115	+	2.06902i	0.611400	+	0.133002i
$243$	−62.6596	−	4.48150i	−4.01961	−	0.287489i
$244$	−11.2622	+	3.30687i	−0.720985	+	0.211700i
$245$	15.8745	−	13.0044i	1.01419	−	0.830819i
$246$	−5.20960	+	6.01220i	−0.332152	+	0.383324i
$247$	−3.27455	−	8.77941i	−0.208355	−	0.558620i
$248$	−3.07467	+	1.67890i	−0.195242	+	0.106610i
$249$	6.26119	+	13.7101i	0.396787	+	0.868842i
$250$	−10.7632	+	3.02540i	−0.680726	+	0.191343i
$251$	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
$253$	4.81908	+	2.42979i	0.302973	+	0.152759i
$254$			16.9887i			1.06596i
$255$	−1.54455	−	5.85465i	−0.0967232	−	0.366632i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−0.554053	+	1.48547i	−0.0345609	+	0.0926614i	−0.953084	−	0.302706i	$-0.902110\pi$
$257$	−0.554053	+	1.48547i	−0.0345609	+	0.0926614i	0.918523	+	0.395367i	$0.129383\pi$
$258$	−6.69004	−	12.2519i	−0.416504	−	0.762770i
$259$	8.79953	+	4.01861i	0.546776	+	0.249704i
$260$	2.43769	−	3.07526i	0.151179	−	0.190720i
$261$	3.38923	−	23.5726i	0.209788	−	1.45911i
$262$	11.5840	+	6.32537i	0.715665	+	0.390782i
$263$	−1.05926	+	14.8104i	−0.0653167	+	0.913247i	0.854137	+	0.520048i	$0.174086\pi$
$263$	−1.05926	+	14.8104i	−0.0653167	+	0.913247i	−0.919454	+	0.393199i	$0.871368\pi$
$264$	3.17741	−	2.04200i	0.195556	−	0.125676i
$265$	12.3235	−	8.70398i	0.757024	−	0.534681i
$266$	−14.0631	−	16.2297i	−0.862265	−	0.995107i
$267$	4.99877	−	9.15457i	0.305920	−	0.560251i
$268$	1.06333	−	0.796002i	0.0649535	−	0.0486236i
$269$	−8.95770	−	7.76189i	−0.546161	−	0.473251i	0.337535	−	0.941313i	$-0.390407\pi$
$269$	−8.95770	−	7.76189i	−0.546161	−	0.473251i	−0.883696	+	0.468062i	$0.844952\pi$
$270$	36.3806	−	15.4131i	2.21406	−	0.938014i
$271$	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	$0.449657\pi$
$272$	0.755932	+	0.281948i	0.0458351	+	0.0170956i
$273$	14.1974	−	18.9656i	0.859268	−	1.14785i
$274$	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	$0.503109\pi$
$278$	−2.46659	+	0.536575i	−0.147936	+	0.0321816i
$279$	28.6580	−	4.12041i	1.71571	−	0.246682i
$280$	2.77151	−	8.55601i	0.165630	−	0.511319i
$281$	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	$0.00374291\pi$
$282$	−13.1218	+	4.89417i	−0.781390	+	0.291443i
$283$	7.68752	−	0.549822i	0.456975	−	0.0326835i	0.159046	−	0.987271i	$-0.449158\pi$
$283$	7.68752	−	0.549822i	0.456975	−	0.0326835i	0.297930	+	0.954588i	$0.403704\pi$
$284$	15.2842	+	2.19754i	0.906953	+	0.130400i
$285$	12.9595	+	37.9169i	0.767652	+	2.24601i
$286$	−1.49257	+	1.29332i	−0.0882573	+	0.0764754i
$287$	2.02648	−	9.31556i	0.119619	−	0.549880i
$288$	−1.75679	+	8.07582i	−0.103520	+	0.475872i
$289$	12.3558	−	10.7064i	0.726812	−	0.629786i
$290$	2.08387	+	6.09702i	0.122369	+	0.358029i
$291$	−61.8328	−	8.89022i	−3.62470	−	0.521154i
$292$	7.20211	−	0.515105i	0.421472	−	0.0301443i
$293$	−2.89925	+	1.08136i	−0.169376	+	0.0631739i	−0.432722	−	0.901528i	$-0.642447\pi$
$293$	−2.89925	+	1.08136i	−0.169376	+	0.0631739i	0.263346	+	0.964701i	$0.415174\pi$
$294$	8.67784	−	29.5540i	0.506102	−	1.72363i
$295$	−2.39143	+	7.38265i	−0.139235	+	0.429834i
$296$	2.38066	−	0.342287i	0.138373	−	0.0198950i
$297$	−19.4303	+	4.22680i	−1.12746	+	0.245264i
$298$	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
$302$	4.40111	−	5.87919i	0.253255	−	0.338310i
$303$	−46.5452	−	17.3605i	−2.67395	−	0.997333i
$304$	−5.12297	−	1.50424i	−0.293822	−	0.0862740i
$305$	−24.1667	+	10.2385i	−1.38378	+	0.586257i
$306$	−5.03931	−	4.36659i	−0.288078	−	0.249621i
$307$	0.128581	−	0.0962544i	0.00733849	−	0.00549353i	−0.595602	−	0.803280i	$-0.703086\pi$
$307$	0.128581	−	0.0962544i	0.00733849	−	0.00549353i	0.602941	+	0.797786i	$0.293996\pi$
$308$	−2.16921	+	3.97260i	−0.123602	+	0.226360i
$309$	−24.8071	−	28.6289i	−1.41123	−	1.62864i
$310$	−6.39836	+	4.51912i	−0.363403	+	0.256669i
$311$	−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	$0.469052\pi$
$312$	0.420201	−	5.87518i	0.0237892	−	0.332616i
$313$	18.9071	+	10.3241i	1.06869	+	0.583550i	0.914540	−	0.404497i	$-0.132553\pi$
$313$	18.9071	+	10.3241i	1.06869	+	0.583550i	0.154153	+	0.988047i	$0.450735\pi$
$314$	0.981677	−	6.82772i	0.0553993	−	0.385310i
$315$	−46.1731	+	58.2496i	−2.60156	+	3.28199i
$316$	8.41276	+	3.84198i	0.473255	+	0.216128i
$317$	5.10233	+	9.34421i	0.286575	+	0.524823i	0.980820	−	0.194916i	$-0.0624433\pi$
$317$	5.10233	+	9.34421i	0.286575	+	0.524823i	−0.694245	+	0.719739i	$0.744262\pi$
$318$	7.91387	−	21.2179i	0.443788	−	1.18984i
$319$	−0.461488	−	3.20972i	−0.0258384	−	0.179710i
$320$	−0.570393	−	2.16209i	−0.0318860	−	0.120865i
$321$			44.2811i			2.47153i
$322$	13.1850	−	14.0795i	0.734773	−	0.784621i
$323$	3.04601	−	3.04601i	0.169485	−	0.169485i
$324$	18.6581	−	29.0326i	1.03656	−	1.61292i
$325$	4.62474	−	7.45718i	0.256535	−	0.413650i
$326$	3.31097	+	7.25001i	0.183377	+	0.401541i
$327$	4.39021	−	2.39724i	0.242779	−	0.132567i
$328$	−0.828321	−	2.22081i	−0.0457364	−	0.122624i
$329$	10.9905	−	12.6837i	0.605927	−	0.699277i
$330$	6.53329	−	5.35205i	0.359646	−	0.294621i
$331$	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	$0.122365\pi$
$332$	−4.47927	−	0.320364i	−0.245832	−	0.0175822i
$333$	−19.4235	−	4.22532i	−1.06440	−	0.231546i
$334$	−0.581271	−	0.904476i	−0.0318058	−	0.0494907i
$335$	2.15746	−	2.04129i	0.117875	−	0.111528i
$336$	−3.80321	−	12.9525i	−0.207482	−	0.706618i
$337$	−10.8981	−	14.5581i	−0.593655	−	0.793030i	0.398617	−	0.917118i	$-0.369490\pi$
$337$	−10.8981	−	14.5581i	−0.593655	−	0.793030i	−0.992271	+	0.124088i	$0.960400\pi$
$338$	−0.707691	−	9.89481i	−0.0384933	−	0.538207i
$339$	−6.12130	+	13.4038i	−0.332464	+	0.727994i
$340$	1.75155	+	0.432090i	0.0949913	+	0.0234334i
$341$	3.58604	−	1.63769i	0.194195	−	0.0886859i
$342$	35.3256	+	26.4444i	1.91019	+	1.42995i
$343$	1.86150	+	8.55720i	0.100512	+	0.462045i
$344$	4.15918			0.224248
$345$	−32.6625	+	15.1196i	−1.75849	+	0.814013i
$346$	−22.9297			−1.23271
$347$	2.22238	+	10.2161i	0.119303	+	0.548429i	0.997534	+	0.0701906i	$0.0223607\pi$
$347$	2.22238	+	10.2161i	0.119303	+	0.548429i	−0.878230	+	0.478238i	$0.841276\pi$
$348$	7.74225	+	5.79577i	0.415028	+	0.310686i
$349$	−10.1639	+	4.64172i	−0.544063	+	0.248465i	−0.668435	−	0.743770i	$-0.733036\pi$
$349$	−10.1639	+	4.64172i	−0.544063	+	0.248465i	0.124372	+	0.992236i	$0.460308\pi$
$350$	3.95831	−	19.7171i	0.211581	−	1.05392i
$351$	−12.8820	+	28.2077i	−0.687591	+	1.50562i
$352$	0.0802814	+	1.12248i	0.00427901	+	0.0598284i
$353$	5.64841	+	7.54539i	0.300634	+	0.401600i	0.925266	−	0.379319i	$-0.123842\pi$
$353$	5.64841	+	7.54539i	0.300634	+	0.401600i	−0.624632	+	0.780920i	$0.714751\pi$
$354$	3.28164	+	11.1762i	0.174417	+	0.594010i
$355$	34.5148	+	0.954959i	1.83186	+	0.0506840i
$356$	1.68016	+	2.61439i	0.0890485	+	0.138562i
$357$	10.6424	+	2.31511i	0.563255	+	0.122529i
$358$	−10.6327	−	0.760467i	−0.561957	−	0.0401920i
$359$	−13.4794	+	3.95790i	−0.711413	+	0.208890i	−0.617364	−	0.786678i	$-0.711799\pi$
$359$	−13.4794	+	3.95790i	−0.711413	+	0.208890i	−0.0940495	+	0.995568i	$0.529981\pi$
$360$	−1.82769	+	18.3898i	−0.0963279	+	0.969228i
$361$	−6.22610	+	7.18531i	−0.327690	+	0.378174i
$362$	−2.17417	−	5.82917i	−0.114272	−	0.306374i
$363$	28.6727	−	15.6565i	1.50493	−	0.821752i
$364$	2.93227	+	6.42078i	0.153693	+	0.336540i
$365$	15.8655	−	2.99433i	0.830436	−	0.156730i
$366$	−21.2985	+	33.1410i	−1.11329	+	1.73231i
$367$	6.23193	−	6.23193i	0.325304	−	0.325304i	−0.525493	−	0.850798i	$-0.676119\pi$
$367$	6.23193	−	6.23193i	0.325304	−	0.325304i	0.850798	+	0.525493i	$0.176119\pi$
$368$	0.865219	−	4.71714i	0.0451026	−	0.245898i
$369$			19.5895i			1.01979i
$370$	5.20014	−	1.37188i	0.270343	−	0.0713205i
$371$	3.86216	+	26.8619i	0.200513	+	1.39460i
$372$	−4.10890	+	11.0164i	−0.213036	+	0.571173i
$373$	1.18421	+	2.16872i	0.0613162	+	0.112292i	0.906539	−	0.422121i	$-0.138714\pi$
$373$	1.18421	+	2.16872i	0.0613162	+	0.112292i	−0.845223	+	0.534413i	$0.820533\pi$
$374$	−0.825884	−	0.377169i	−0.0427054	−	0.0195029i
$375$	−20.6515	+	31.3305i	−1.06644	+	1.61790i
$376$	0.593836	−	4.13022i	0.0306247	−	0.213000i
$377$	−4.43842	−	2.42356i	−0.228590	−	0.124820i
$378$	−5.07007	+	70.8888i	−0.260776	+	3.64613i
$379$	24.4487	−	15.7123i	1.25585	−	0.807084i	0.268137	−	0.963381i	$-0.413592\pi$
$379$	24.4487	−	15.7123i	1.25585	−	0.807084i	0.987710	+	0.156296i	$0.0499555\pi$
$380$	−11.7659	−	2.02527i	−0.603577	−	0.103894i
$381$	37.3394	+	43.0920i	1.91296	+	2.20767i
$382$	−9.51331	+	17.4223i	−0.486743	+	0.891403i
$383$	−0.636090	+	0.476171i	−0.0325027	+	0.0243312i	−0.615406	−	0.788211i	$-0.711008\pi$
$383$	−0.636090	+	0.476171i	−0.0325027	+	0.0243312i	0.582903	+	0.812542i	$0.301917\pi$
$384$	−2.53652	−	2.19790i	−0.129441	−	0.112161i
$385$	−3.79786	+	9.38144i	−0.193557	+	0.478123i
$386$	15.5681	+	4.57121i	0.792395	+	0.232668i
$387$	−32.2071	−	12.0126i	−1.63718	−	0.610635i
$388$	11.1540	−	14.9000i	0.566258	−	0.756433i
$389$	−21.3772	−	13.7383i	−1.08387	−	0.696559i	−0.128420	−	0.991720i	$-0.540990\pi$
$389$	−21.3772	−	13.7383i	−1.08387	−	0.696559i	−0.955448	+	0.295161i	$0.904627\pi$
$390$	−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
$393$	43.2857	−	9.41622i	2.18347	−	0.474985i
$394$	7.25066	−	1.04249i	0.365283	−	0.0525198i
$395$	19.6739	+	6.37290i	0.989902	+	0.320655i
$396$	2.62030	−	8.92391i	0.131675	−	0.448443i
$397$	4.46867	−	1.66673i	0.224276	−	0.0836506i	−0.234814	−	0.972040i	$-0.575448\pi$
$397$	4.46867	−	1.66673i	0.224276	−	0.0836506i	0.459090	+	0.888390i	$0.348175\pi$
$398$	−1.44709	+	0.103498i	−0.0725359	+	0.00518787i
$399$	−71.3427	−	10.2575i	−3.57160	−	0.513519i
$400$	−1.82241	−	4.65605i	−0.0911206	−	0.232803i
$401$	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	$0.236318\pi$
$402$	0.947629	−	4.35618i	0.0472634	−	0.217266i
$403$	1.30685	−	6.00748i	0.0650987	−	0.299254i
$404$	11.1861	−	9.69278i	0.556527	−	0.482234i
$405$	33.9864	−	69.2820i	1.68880	−	3.44265i
$406$	−11.4719	−	1.64940i	−0.569339	−	0.0818585i
$407$	−2.69972	+	0.193088i	−0.133820	+	0.00957102i
$408$	2.53713	−	0.946300i	0.125607	−	0.0468488i
$409$	−1.49209	+	5.08159i	−0.0737790	+	0.251268i	−0.988122	−	0.153673i	$-0.950890\pi$
$409$	−1.49209	+	5.08159i	−0.0737790	+	0.251268i	0.914343	+	0.404941i	$0.132708\pi$
$410$	−2.41042	−	4.72023i	−0.119042	−	0.233115i
$411$	11.2635	−	1.61944i	0.555586	−	0.0798812i
$412$	11.0288	−	2.39916i	0.543349	−	0.118198i
$413$	−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
$417$	−5.07721	+	6.78236i	−0.248632	+	0.332134i
$418$	5.62967	+	2.09976i	0.275356	+	0.102702i
$419$	−32.1950	−	9.45330i	−1.57283	−	0.461824i	−0.625005	−	0.780621i	$-0.714903\pi$
$419$	−32.1950	−	9.45330i	−1.57283	−	0.461824i	−0.947823	+	0.318797i	$0.896721\pi$
$420$	−11.7753	−	27.7940i	−0.574575	−	1.35621i
$421$	−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	$0.797120\pi$
$422$	−12.9368	+	9.68439i	−0.629755	+	0.471429i
$423$	−16.5274	+	30.2676i	−0.803589	+	1.47166i
$424$	4.41851	+	5.09923i	0.214582	+	0.247641i
$425$	4.00166	+	0.509830i	0.194109	+	0.0247304i
$426$	43.5987	−	28.0192i	2.11236	−	1.35753i
$427$	3.36791	−	47.0896i	0.162985	−	2.27882i
$428$	−11.5796	−	6.32295i	−0.559722	−	0.305631i
$429$	−0.943334	+	6.56103i	−0.0455446	+	0.316770i
$430$	9.23864	−	1.06845i	0.445527	−	0.0515252i
$431$	−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	$0.863010\pi$
$432$	8.46825	+	15.5084i	0.407429	+	0.746151i
$433$	−4.16945	+	11.1787i	−0.200371	+	0.537215i	−0.997807	−	0.0661879i	$-0.978916\pi$
$433$	−4.16945	+	11.1787i	−0.200371	+	0.537215i	0.797436	+	0.603403i	$0.206189\pi$
$434$	−2.00524	−	13.9467i	−0.0962546	−	0.669465i
$435$	18.6864	+	10.8850i	0.895946	+	0.521897i
$436$			1.49036i			0.0713751i
$437$	−20.9909	−	14.6648i	−1.00413	−	0.701511i
$438$	17.1361	−	17.1361i	0.818796	−	0.818796i
$439$	14.8072	−	23.0404i	0.706707	−	1.09966i	−0.283354	−	0.959015i	$-0.591447\pi$
$439$	14.8072	−	23.0404i	0.706707	−	1.09966i	0.990061	−	0.140642i	$-0.0449166\pi$
$440$	0.466679	+	2.47270i	0.0222481	+	0.117881i
$441$	−31.5082	−	68.9934i	−1.50039	−	3.28540i
$442$	−1.24271	+	0.678574i	−0.0591099	+	0.0322765i
$443$	6.47712	+	17.3658i	0.307737	+	0.825076i	0.995110	+	0.0987712i	$0.0314912\pi$
$443$	6.47712	+	17.3658i	0.307737	+	0.825076i	−0.687373	+	0.726305i	$0.741236\pi$
$444$	5.28627	−	6.10068i	0.250875	−	0.289525i
$445$	4.40369	+	5.37562i	0.208755	+	0.254829i
$446$	−18.2005	+	5.34414i	−0.861817	+	0.253052i
$447$	34.2644	+	2.45064i	1.62065	+	0.115911i
$448$	3.93018	+	0.854959i	0.185684	+	0.0403930i
$449$	9.09528	+	14.1525i	0.429233	+	0.667899i	0.986747	−	0.162268i	$-0.0518810\pi$
$449$	9.09528	+	14.1525i	0.429233	+	0.667899i	−0.557514	+	0.830168i	$0.688245\pi$
$450$	0.664362	+	41.3181i	0.0313183	+	1.94775i
$451$	0.751484	+	2.55932i	0.0353860	+	0.120514i
$452$	−2.63106	−	3.51468i	−0.123754	−	0.165317i
$453$	−1.75842	−	24.5859i	−0.0826177	−	1.15515i
$454$	−5.48399	+	12.0083i	−0.257376	+	0.563575i
$455$	8.16278	+	13.5090i	0.382677	+	0.633310i
$456$	−16.3007	+	7.44426i	−0.763348	+	0.348609i
$457$	3.84616	+	2.87920i	0.179916	+	0.134683i	0.685440	−	0.728129i	$-0.259610\pi$
$457$	3.84616	+	2.87920i	0.179916	+	0.134683i	−0.505524	+	0.862812i	$0.668701\pi$
$458$	−0.155498	−	0.714812i	−0.00726593	−	0.0334010i
$459$	−14.2561			−0.665416
$460$	0.710095	−	10.7003i	0.0331084	−	0.498903i
$461$	−17.4657			−0.813461			−0.406730	−	0.913548i	$-0.633331\pi$
$461$	−17.4657			−0.813461			−0.406730	+	0.913548i	$0.633331\pi$
$462$	3.22918	+	14.8443i	0.150235	+	0.690618i
$463$	−10.5582	−	7.90376i	−0.490681	−	0.367319i	0.325101	−	0.945679i	$-0.394602\pi$
$463$	−10.5582	−	7.90376i	−0.490681	−	0.367319i	−0.815781	+	0.578360i	$0.803693\pi$
$464$	−2.62114	+	1.19703i	−0.121683	+	0.0555708i
$465$	−6.29695	+	25.5258i	−0.292014	+	1.18373i
$466$	9.16577	−	20.0702i	0.424596	−	0.929736i
$467$	2.03837	+	28.5002i	0.0943247	+	1.31883i	0.795548	+	0.605890i	$0.207183\pi$
$467$	2.03837	+	28.5002i	0.0943247	+	1.31883i	−0.701223	+	0.712942i	$0.747362\pi$
$468$	−8.69208	−	11.6113i	−0.401792	−	0.536731i
$469$	1.50514	+	5.12603i	0.0695008	+	0.236698i
$470$	0.258056	−	9.32685i	0.0119032	−	0.430216i
$471$	−12.5166	−	19.4762i	−0.576735	−	0.897418i
$472$	−3.39120	−	0.737711i	−0.156093	−	0.0339559i
$473$	−4.66860	−	0.333905i	−0.214663	−	0.0153530i
$474$	29.7834	−	8.74520i	1.36800	−	0.401680i
$475$	−26.6554	−	1.47614i	−1.22303	−	0.0677297i
$476$	−2.12505	+	2.45244i	−0.0974014	+	0.112407i
$477$	−19.4875	−	52.2480i	−0.892271	−	2.39227i
$478$	0.427094	−	0.233211i	0.0195348	−	0.0106668i
$479$	13.8117	+	30.2434i	0.631073	+	1.38186i	0.907185	+	0.420732i	$0.138227\pi$
$479$	13.8117	+	30.2434i	0.631073	+	1.38186i	−0.276112	+	0.961125i	$0.589046\pi$
$480$	−6.19889	−	4.23052i	−0.282939	−	0.193096i
$481$	−2.28202	+	3.55089i	−0.104051	+	0.161906i
$482$	−10.7334	+	10.7334i	−0.488895	+	0.488895i
$483$	2.49864	−	64.6924i	0.113692	−	2.94360i
$484$			9.73359i			0.442436i
$485$	20.9483	−	35.9622i	0.951214	−	1.63296i
$486$	−8.94017	−	62.1802i	−0.405534	−	2.82055i
$487$	5.35025	−	14.3446i	0.242443	−	0.650015i	−0.757553	−	0.652774i	$-0.773605\pi$
$487$	5.35025	−	14.3446i	0.242443	−	0.650015i	0.999996	+	0.00275839i	$0.000878025\pi$
$488$	−5.62524	−	10.3019i	−0.254642	−	0.466343i
$489$	24.3331	+	11.1126i	1.10038	+	0.502528i
$490$	16.0816	+	12.7475i	0.726491	+	0.575872i
$491$	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	$-0.261767\pi$
$492$	−6.98219	−	3.81256i	−0.314781	−	0.171884i
$493$	0.165851	−	2.31890i	0.00746956	−	0.104438i
$494$	7.88271	−	5.06591i	0.354660	−	0.227926i
$495$	3.52791	−	20.4955i	0.158568	−	0.921203i
$496$	−2.29410	−	2.64753i	−0.103008	−	0.118878i
$497$	−29.7647	+	54.5100i	−1.33513	+	2.44511i
$498$	−12.0659	+	9.03240i	−0.540685	+	0.404751i
$499$	28.1456	+	24.3883i	1.25997	+	1.09177i	0.991719	+	0.128424i	$0.0409917\pi$
$499$	28.1456	+	24.3883i	1.25997	+	1.09177i	0.268253	+	0.963349i	$0.413554\pi$
$500$	−5.24415	−	9.87415i	−0.234525	−	0.441586i
$501$	−3.46235	−	1.01664i	−0.154687	−	0.0454201i
$502$	2.34671	+	0.875278i	0.104739	+	0.0390656i
$503$	11.0599	−	14.7742i	0.493135	−	0.658751i	−0.483075	−	0.875579i	$-0.660480\pi$
$503$	11.0599	−	14.7742i	0.493135	−	0.658751i	0.976210	+	0.216828i	$0.0695711\pi$
$504$	−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
$508$	−16.6004	+	3.61120i	−0.736524	+	0.160221i
$509$	0.380645	−	0.0547284i	0.0168718	−	0.00242579i	−0.133874	−	0.990998i	$-0.542742\pi$
$509$	0.380645	−	0.0547284i	0.0168718	−	0.00242579i	0.150746	+	0.988573i	$0.451833\pi$
$510$	5.39254	−	2.75374i	0.238786	−	0.121938i
$511$	−8.18197	+	27.8652i	−0.361949	+	1.23269i
$512$	0.936950	−	0.349464i	0.0414077	−	0.0154443i
$513$	94.1032	−	6.73039i	4.15476	−	0.297154i
$514$	−1.56930	−	0.225631i	−0.0692188	−	0.00995217i
$515$	23.8815	−	8.16235i	1.05234	−	0.359676i
$516$	10.5498	−	9.14149i	0.464431	−	0.402431i
$517$	−0.998149	+	4.58842i	−0.0438985	+	0.201798i
$518$	−2.05630	+	9.45265i	−0.0903485	+	0.415325i
$519$	−58.1615	+	50.3972i	−2.55301	+	2.21219i
$520$	3.52315	+	1.72829i	0.154500	+	0.0757903i
$521$	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	$0.392374\pi$
$522$	23.7543	−	1.69894i	1.03970	−	0.0743607i
$523$	−1.77957	+	0.663744i	−0.0778150	+	0.0290235i	−0.388070	−	0.921630i	$-0.626858\pi$
$523$	−1.77957	+	0.663744i	−0.0778150	+	0.0290235i	0.310255	+	0.950653i	$0.399585\pi$
$524$	−3.71845	+	12.6639i	−0.162441	+	0.553224i
$525$	−33.2960	−	58.7127i	−1.45316	−	2.56243i
$526$	−14.6971	+	2.11312i	−0.640823	+	0.0921364i
$527$	2.76178	−	0.600789i	0.120305	−	0.0261708i
$528$	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
$532$	12.8695	−	17.1916i	0.557963	−	0.745351i
$533$	3.89746	+	1.45368i	0.168818	+	0.0629657i
$534$	10.0079	+	2.93859i	0.433085	+	0.127165i
$535$	−27.3457	−	11.0702i	−1.18226	−	0.478608i
$536$	1.00384	+	0.869832i	0.0433593	+	0.0375710i
$537$	−28.6415	+	21.4408i	−1.23597	+	0.925237i
$538$	5.68041	−	10.4029i	0.244900	−	0.448501i
$539$	−6.76317	−	7.80512i	−0.291311	−	0.336190i
$540$	22.7942	+	32.2729i	0.980905	+	1.38881i
$541$	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	$0.135655\pi$
$542$	−1.00841	+	14.0995i	−0.0433151	+	0.605624i
$543$	−18.3268	−	10.0072i	−0.786476	−	0.429449i
$544$	−0.114820	+	0.798589i	−0.00492286	+	0.0342392i
$545$	0.382856	+	3.31047i	0.0163998	+	0.141805i
$546$	21.5500	+	9.84156i	0.922256	+	0.421180i
$547$	−16.6046	−	30.4091i	−0.709963	−	1.30020i	−0.944634	−	0.328126i	$-0.893583\pi$
$547$	−16.6046	−	30.4091i	−0.709963	−	1.30020i	0.234671	−	0.972075i	$-0.424599\pi$
$548$	−1.18484	+	3.17667i	−0.0506137	+	0.135701i
$549$	13.8056	+	96.0203i	0.589210	+	4.09805i
$550$	1.67183	+	5.37263i	0.0712870	+	0.229090i
$551$			15.3852i			0.655432i
$552$	−8.17317	−	13.8668i	−0.347873	−	0.590209i
$553$	−26.3033	+	26.3033i	−1.11853	+	1.11853i
$554$	−12.6003	+	19.6064i	−0.535334	+	0.832996i
$555$	10.1750	−	14.9092i	0.431904	−	0.632860i
$556$	−1.04862	−	2.29617i	−0.0444716	−	0.0973792i
$557$	3.47955	−	1.89998i	0.147433	−	0.0805045i	−0.403839	−	0.914830i	$-0.632324\pi$
$557$	3.47955	−	1.89998i	0.147433	−	0.0805045i	0.551272	+	0.834326i	$0.314143\pi$
$558$	10.1179	+	27.1273i	0.428327	+	1.14839i
$559$	−4.77998	+	5.51639i	−0.202172	+	0.233319i
$560$	8.94960	+	0.889466i	0.378190	+	0.0375868i
$561$	−2.92385	+	0.858519i	−0.123445	+	0.0362467i
$562$	9.04340	+	0.646797i	0.381473	+	0.0272835i
$563$	−5.49198	−	1.19471i	−0.231460	−	0.0503509i	0.0953394	−	0.995445i	$-0.469606\pi$
$563$	−5.49198	−	1.19471i	−0.231460	−	0.0503509i	−0.326799	+	0.945094i	$0.605970\pi$
$564$	−7.57155	−	11.7816i	−0.318820	−	0.496093i
$565$	−6.74715	−	7.13114i	−0.283855	−	0.300009i
$566$	2.17136	+	7.39496i	0.0912689	+	0.310833i
$567$	83.1839	+	111.121i	3.49340	+	4.66663i
$568$	1.10158	+	15.4021i	0.0462212	+	0.646257i
$569$	−0.0158620	+	0.0347329i	−0.000664969	+	0.00145608i	−0.909964	−	0.414687i	$-0.863891\pi$
$569$	−0.0158620	+	0.0347329i	−0.000664969	+	0.00145608i	0.909299	+	0.416143i	$0.136618\pi$
$570$	−34.2957	+	20.7231i	−1.43649	+	0.867996i
$571$	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	$0.0813305\pi$
$572$	−1.58103	−	1.18354i	−0.0661061	−	0.0494864i
$573$	14.1619	+	65.1013i	0.591623	+	2.71965i
$574$	9.53343			0.397918
$575$	−1.17148	−	23.9505i	−0.0488540	−	0.998806i
$576$	−8.26469			−0.344362
$577$	5.07853	+	23.3456i	0.211422	+	0.971891i	0.953457	+	0.301530i	$0.0974973\pi$
$577$	5.07853	+	23.3456i	0.211422	+	0.971891i	−0.742035	+	0.670361i	$0.766139\pi$
$578$	13.0881	+	9.79763i	0.544393	+	0.407528i
$579$	49.5358	−	22.6222i	2.05864	−	0.940148i
$580$	−5.51472	+	3.33227i	−0.228986	+	0.138365i
$581$	7.50327	−	16.4299i	0.311288	−	0.681626i
$582$	−4.45646	−	62.3095i	−0.184726	−	2.58281i
$583$	−4.55031	−	6.07851i	−0.188455	−	0.251746i
$584$	2.03425	+	6.92803i	0.0841780	+	0.286684i
$585$	−22.2902	−	23.5588i	−0.921587	−	0.974035i
$586$	−1.67293	−	2.60313i	−0.0691081	−	0.107534i
$587$	−46.1163	−	10.0320i	−1.90342	−	0.414065i	−0.903530	−	0.428526i	$-0.859033\pi$
$587$	−46.1163	−	10.0320i	−1.90342	−	0.414065i	−0.999895	+	0.0144611i	$0.995397\pi$
$588$	30.7232	+	2.19737i	1.26700	+	0.0906179i
$589$	−17.9467	+	5.26963i	−0.739481	+	0.217131i
$590$	−7.72226	−	0.767486i	−0.317921	−	0.0315969i
$591$	16.1001	−	18.5805i	0.662271	−	0.764302i
$592$	0.840511	+	2.25350i	0.0345448	+	0.0926181i
$593$	−24.9575	+	13.6278i	−1.02488	+	0.559628i	−0.901522	−	0.432734i	$-0.857549\pi$
$593$	−24.9575	+	13.6278i	−1.02488	+	0.559628i	−0.123361	+	0.992362i	$0.539367\pi$
$594$	−8.26041	−	18.0878i	−0.338929	−	0.742150i
$595$	−4.09028	+	5.99341i	−0.167685	+	0.245706i
$596$	−5.53351	+	8.61031i	−0.226661	+	0.352692i
$597$	−3.44308	+	3.44308i	−0.140916	+	0.140916i
$598$	5.26206	+	6.56877i	0.215181	+	0.268617i
$599$			1.22147i			0.0499078i	0.999689	+	0.0249539i	$0.00794390\pi$
$599$			1.22147i			0.0499078i	−0.999689	+	0.0249539i	$0.992056\pi$
$600$	−14.8561	−	7.80466i	−0.606499	−	0.318624i
$601$	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	$0.928917\pi$
$602$	−5.84607	+	15.6739i	−0.238268	+	0.638821i
$603$	−5.26107	−	9.63493i	−0.214247	−	0.392365i
$604$	6.68036	+	3.05082i	0.271820	+	0.124136i
$605$	2.50046	+	21.6209i	0.101658	+	0.879013i
$606$	7.06983	−	49.1718i	0.287192	−	1.99747i
$607$	15.6912	+	8.56803i	0.636885	+	0.347765i	0.765034	−	0.643989i	$-0.222722\pi$
$607$	15.6912	+	8.56803i	0.636885	+	0.347765i	−0.128150	+	0.991755i	$0.540904\pi$
$608$	0.380897	−	5.32564i	0.0154474	−	0.215983i
$609$	−32.7238	+	21.0303i	−1.32603	+	0.852190i
$610$	−15.1416	−	21.4381i	−0.613064	−	0.868001i
$611$	4.79551	+	5.53431i	0.194005	+	0.223894i
$612$	3.19562	−	5.85233i	0.129175	−	0.236567i
$613$	28.6038	−	21.4125i	1.15529	−	0.864843i	0.162743	−	0.986668i	$-0.447966\pi$
$613$	28.6038	−	21.4125i	1.15529	−	0.864843i	0.992551	+	0.121826i	$0.0388749\pi$
$614$	0.121386	+	0.105182i	0.00489876	+	0.00424480i
$615$	−16.4887	−	6.67505i	−0.664888	−	0.269164i
$616$	−4.34292	−	1.27520i	−0.174981	−	0.0513791i
$617$	18.1861	+	6.78308i	0.732147	+	0.273077i	0.687760	−	0.725938i	$-0.258594\pi$
$617$	18.1861	+	6.78308i	0.732147	+	0.273077i	0.0443863	+	0.999014i	$0.485867\pi$
$618$	22.7015	−	30.3257i	0.913190	−	1.21988i
$619$	−6.27874	−	4.03510i	−0.252364	−	0.162184i	0.408343	−	0.912829i	$-0.366107\pi$
$619$	−6.27874	−	4.03510i	−0.252364	−	0.162184i	−0.660706	+	0.750644i	$0.729743\pi$
$620$	−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
$623$	−12.2139	+	2.65698i	−0.489341	+	0.106450i
$624$	5.83023	−	0.838260i	0.233396	−	0.0335573i
$625$	−14.1852	−	20.5859i	−0.567408	−	0.823437i
$626$	−6.06913	+	20.6696i	−0.242571	+	0.826122i
$627$	18.8948	−	7.04740i	0.754586	−	0.281446i
$628$	6.88035	−	0.492092i	0.274556	−	0.0196366i
$629$	−1.92072	−	0.276158i	−0.0765841	−	0.0110111i
$630$	−66.7332	−	32.7360i	−2.65871	−	1.30423i
$631$	−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	$0.929876\pi$
$632$	−1.96592	+	9.03717i	−0.0782000	+	0.359480i
$633$	−11.5291	+	52.9985i	−0.458242	+	2.10650i
$634$	−8.04609	+	6.97198i	−0.319551	+	0.276893i
$635$	−35.9462	+	12.2859i	−1.42648	+	0.487551i
$636$	22.4152	+	3.22282i	0.888822	+	0.127793i
$637$	−16.0648	+	1.14898i	−0.636512	+	0.0455242i
$638$	3.03827	−	1.13322i	0.120286	−	0.0448645i
$639$	35.9543	−	122.449i	1.42233	−	4.84401i
$640$	1.99144	−	1.01694i	0.0787185	−	0.0401982i
$641$	−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	$0.794834\pi$
$642$	−43.2691	+	9.41262i	−1.70769	+	0.371486i
$643$	−6.37779	−	6.37779i	−0.251515	−	0.251515i	0.570076	−	0.821592i	$-0.306914\pi$
$643$	−6.37779	−	6.37779i	−0.251515	−	0.251515i	−0.821592	+	0.570076i	$0.806914\pi$
$644$	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
$647$	26.7356	−	35.7146i	1.05108	−	1.40408i	0.140830	−	0.990034i	$-0.455023\pi$
$647$	26.7356	−	35.7146i	1.05108	−	1.40408i	0.910254	−	0.414050i	$-0.135886\pi$
$648$	32.3351	+	12.0604i	1.27024	+	0.473776i
$649$	3.74733	+	1.10032i	0.147096	+	0.0431912i
$650$	8.26982	+	2.93392i	0.324369	+	0.115078i
$651$	−35.7399	−	30.9688i	−1.40076	−	1.21376i
$652$	−6.38052	+	4.77640i	−0.249881	+	0.187058i
$653$	2.21675	−	4.05967i	0.0867480	−	0.158867i	−0.830703	−	0.556716i	$-0.812061\pi$
$653$	2.21675	−	4.05967i	0.0867480	−	0.158867i	0.917451	+	0.397849i	$0.130243\pi$
$654$	3.27566	+	3.78031i	0.128088	+	0.147822i
$655$	−5.00643	+	29.0850i	−0.195618	+	1.13644i
$656$	1.99399	−	1.28146i	0.0778522	−	0.0500326i
$657$	4.25719	−	59.5233i	0.166089	−	2.32222i
$658$	14.7301	+	8.04323i	0.574238	+	0.313558i
$659$	0.705668	−	4.90803i	0.0274889	−	0.191190i	−0.971450	−	0.237244i	$-0.923756\pi$
$659$	0.705668	−	4.90803i	0.0274889	−	0.191190i	0.998939	+	0.0460547i	$0.0146649\pi$
$660$	6.61849	+	5.24633i	0.257625	+	0.204213i
$661$	−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	$0.876860\pi$
$662$	13.6683	+	25.0316i	0.531234	+	0.972883i
$663$	−1.66073	+	4.45258i	−0.0644973	+	0.172924i
$664$	−0.639095	−	4.44500i	−0.0248017	−	0.172500i
$665$	24.1701	−	41.4931i	0.937278	−	1.60903i
$666$		−	19.8778i		−	0.770247i
$667$	−13.7444	+	1.43731i	−0.532185	+	0.0556528i
$668$	0.760248	−	0.760248i	0.0294149	−	0.0294149i
$669$	−34.4198	+	53.5583i	−1.33075	+	2.07068i
$670$	2.45324	+	1.67425i	0.0947770	+	0.0646819i
$671$	5.48717	+	12.0152i	0.211830	+	0.463843i
$672$	11.8481	−	6.46955i	0.457050	−	0.249568i
$673$	−9.30633	−	24.9512i	−0.358733	−	0.961799i	−0.983487	−	0.180978i	$-0.942074\pi$
$673$	−9.30633	−	24.9512i	−0.358733	−	0.961799i	0.624754	−	0.780821i	$-0.285199\pi$
$674$	11.9088	−	13.7435i	0.458712	−	0.529381i
$675$	58.9224	+	65.8311i	2.26792	+	2.53384i
$676$	9.51825	−	2.79481i	0.366087	−	0.107493i
$677$	22.5473	+	1.61261i	0.866562	+	0.0619777i	0.497538	−	0.867442i	$-0.334237\pi$
$677$	22.5473	+	1.61261i	0.866562	+	0.0619777i	0.369024	+	0.929420i	$0.379692\pi$
$678$	−14.3986	−	3.13223i	−0.552977	−	0.120293i
$679$	40.4729	+	62.9771i	1.55321	+	2.41684i
$680$	−0.0498958	+	1.80337i	−0.00191342	+	0.0691562i
$681$	12.4828	+	42.5124i	0.478341	+	1.62908i
$682$	2.36253	+	3.15597i	0.0904660	+	0.120848i
$683$	0.401705	+	5.61656i	0.0153708	+	0.214912i	0.999332	+	0.0365319i	$0.0116311\pi$
$683$	0.401705	+	5.61656i	0.0153708	+	0.214912i	−0.983962	+	0.178380i	$0.942914\pi$
$684$	−18.3311	+	40.1395i	−0.700907	+	1.53477i
$685$	−1.81578	+	7.36059i	−0.0693774	+	0.281234i
$686$	−7.96595	+	3.63793i	−0.304141	+	0.138897i
$687$	−1.96551	−	1.47136i	−0.0749889	−	0.0561360i
$688$	0.884098	+	4.06413i	0.0337059	+	0.154944i
$689$	−11.8412			−0.451114
$690$	−21.7170	−	28.7021i	−0.826752	−	1.09267i
$691$	25.2537			0.960697			0.480348	−	0.877078i	$-0.340510\pi$
$691$	25.2537			0.960697			0.480348	+	0.877078i	$0.340510\pi$
$692$	−4.87405	−	22.4057i	−0.185284	−	0.851736i
$693$	29.9468	+	22.4179i	1.13758	+	0.851585i
$694$	−9.51022	+	4.34317i	−0.361003	+	0.164865i
$695$	−2.91913	−	4.83101i	−0.110729	−	0.183251i
$696$	−4.01759	+	8.79729i	−0.152286	+	0.333461i
$697$	0.136424	+	1.90746i	0.00516743	+	0.0722501i
$698$	−6.69614	−	8.94499i	−0.253453	−	0.338573i
$699$	−20.8633	−	71.0540i	−0.789124	−	2.68751i
$700$	20.1079	−	0.323319i	0.760008	−	0.0122203i
$701$	−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	$-0.594013\pi$
$702$	−30.3013	−	6.59165i	−1.14365	−	0.248786i
$703$	12.8089	+	0.916112i	0.483097	+	0.0345518i
$704$	−1.07976	+	0.317047i	−0.0406951	+	0.0119492i
$705$	−19.8450	−	24.2249i	−0.747404	−	0.912362i
$706$	−6.17230	+	7.12321i	−0.232297	+	0.268086i
$707$	20.8044	+	55.7787i	0.782430	+	2.09778i
$708$	−10.2233	+	5.58232i	−0.384214	+	0.209797i
$709$	13.4931	+	29.5458i	0.506744	+	1.10962i	0.974218	+	0.225608i	$0.0724369\pi$
$709$	13.4931	+	29.5458i	0.506744	+	1.10962i	−0.467474	+	0.884007i	$0.654836\pi$
$710$	6.40352	+	33.9291i	0.240320	+	1.27334i
$711$	41.3246	−	64.3023i	1.54979	−	2.41152i
$712$	−2.19749	+	2.19749i	−0.0823546	+	0.0823546i
$713$	−6.38424	−	15.5404i	−0.239092	−	0.581993i
$714$			10.8913i			0.407596i
$715$	−3.81592	−	2.22281i	−0.142707	−	0.0831284i
$716$	−1.51706	−	10.5514i	−0.0566952	−	0.394324i
$717$	0.570755	−	1.53025i	0.0213152	−	0.0571484i
$718$	−6.73269	−	12.3300i	−0.251262	−	0.460152i
$719$	−14.0335	−	6.40887i	−0.523360	−	0.239011i	0.136174	−	0.990685i	$-0.456519\pi$
$719$	−14.0335	−	6.40887i	−0.523360	−	0.239011i	−0.659534	+	0.751674i	$0.729247\pi$
$720$	−18.3581	+	2.12311i	−0.684164	+	0.0791237i
$721$	−6.46057	+	44.9343i	−0.240604	+	1.67344i
$722$	−8.34455	−	4.55647i	−0.310552	−	0.169574i
$723$	−3.63448	+	50.8166i	−0.135168	+	1.88989i
$724$	5.23380	−	3.36356i	0.194513	−	0.125006i
$725$	−11.3936	+	8.81851i	−0.423149	+	0.327511i
$726$	21.3935	+	24.6894i	0.793987	+	0.916310i
$727$	−2.57514	+	4.71602i	−0.0955066	+	0.174907i	−0.921064	−	0.389410i	$-0.872679\pi$
$727$	−2.57514	+	4.71602i	−0.0955066	+	0.174907i	0.825558	+	0.564318i	$0.190861\pi$
$728$	−5.65075	+	4.23010i	−0.209431	+	0.156778i
$729$	−81.0979	−	70.2717i	−3.00363	−	2.60266i
$730$	6.29835	+	14.8664i	0.233112	+	0.550230i
$731$	−3.21971	−	0.945392i	−0.119085	−	0.0349666i
$732$	−36.9110	−	13.7671i	−1.36427	−	0.508846i
$733$	3.76683	−	5.03190i	0.139131	−	0.185857i	−0.725564	−	0.688155i	$-0.758421\pi$
$733$	3.76683	−	5.03190i	0.139131	−	0.185857i	0.864695	+	0.502298i	$0.167512\pi$
$734$	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
$738$	−19.1418	+	4.16404i	−0.704619	+	0.153281i
$739$	−52.0089	+	7.47775i	−1.91318	+	0.275073i	−0.993156	−	0.116794i	$-0.962738\pi$
$739$	−52.0089	+	7.47775i	−1.91318	+	0.275073i	−0.920022	+	0.391868i	$0.871829\pi$
$740$	2.44589	+	4.78969i	0.0899129	+	0.176072i
$741$	8.86024	−	30.1752i	0.325489	−	1.10851i
$742$	−25.4271	+	9.48380i	−0.933457	+	0.348161i
$743$	−45.6968	+	3.26830i	−1.67645	+	0.119902i	−0.876894	−	0.480685i	$-0.840388\pi$
$743$	−45.6968	+	3.26830i	−1.67645	+	0.119902i	−0.799559	+	0.600587i	$0.794934\pi$
$744$	−11.6380	−	1.67330i	−0.426671	−	0.0613460i
$745$	−10.0795	+	20.5473i	−0.369284	+	0.752793i
$746$	−1.86744	+	1.61814i	−0.0683717	+	0.0592445i
$747$	−7.88922	+	36.2662i	−0.288652	+	1.32691i
$748$	0.192995	−	0.887183i	0.00705659	−	0.0324386i
$749$	40.1041	−	34.7504i	1.46537	−	1.26975i
$750$	−35.0043	−	13.5198i	−1.27818	−	0.493674i
$751$	−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	$0.762918\pi$
$752$	4.16206	−	0.297676i	0.151775	−	0.0108551i
$753$	7.87625	−	2.93769i	0.287026	−	0.107055i
$754$	1.42472	−	4.85215i	0.0518853	−	0.176705i
$755$	15.6226	+	5.06056i	0.568563	+	0.184172i
$756$	−70.3465	+	10.1143i	−2.55848	+	0.367854i
$757$	38.2518	−	8.32118i	1.39029	−	0.302438i	0.545755	−	0.837945i	$-0.316243\pi$
$757$	38.2518	−	8.32118i	1.39029	−	0.302438i	0.844531	+	0.535506i	$0.179879\pi$
$758$	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	$0.902200\pi$
$762$	−34.1701	+	45.6460i	−1.23785	+	1.65358i
$763$	−5.61642	−	2.09481i	−0.203328	−	0.0758374i
$764$	−19.0464	−	5.59252i	−0.689073	−	0.202330i
$765$	5.59490	−	13.8205i	0.202284	−	0.499681i
$766$	−0.600500	−	0.520336i	−0.0216969	−	0.0188005i
$767$	4.87581	−	3.64999i	0.176055	−	0.131793i
$768$	1.60850	−	2.94575i	0.0580417	−	0.106295i
$769$	7.93536	+	9.15790i	0.286157	+	0.330242i	0.880569	−	0.473918i	$-0.157161\pi$
$769$	7.93536	+	9.15790i	0.286157	+	0.330242i	−0.594412	+	0.804160i	$0.702615\pi$
$770$	−9.97434	−	1.71689i	−0.359450	−	0.0618726i
$771$	−4.47647	+	2.87685i	−0.161216	+	0.103607i
$772$	−1.15750	+	16.1840i	−0.0416594	+	0.582475i
$773$	16.7429	+	9.14229i	0.602199	+	0.328825i	0.751264	−	0.660002i	$-0.229445\pi$
$773$	16.7429	+	9.14229i	0.602199	+	0.328825i	−0.149065	+	0.988827i	$0.547626\pi$
$774$	4.89198	−	34.0245i	0.175839	−	1.22299i
$775$	−14.1892	−	10.2701i	−0.509690	−	0.368913i
$776$	16.9304	+	7.73187i	0.607767	+	0.277558i
$777$	15.5602	+	28.4963i	0.558218	+	1.02230i
$778$	8.88028	−	23.8089i	0.318373	−	0.853592i
$779$	−1.80105	−	12.5266i	−0.0645294	−	0.448811i
$780$	12.7351	−	3.35972i	0.455991	−	0.120297i
$781$		−	17.3770i		−	0.621796i
$782$	−1.74200	+	3.45497i	−0.0622938	+	0.123549i
$783$	36.0032	−	36.0032i	1.28665	−	1.28665i
$784$	−4.96162	+	7.72044i	−0.177201	+	0.275730i
$785$	15.1567	−	2.86056i	0.540964	−	0.102098i
$786$	18.4021	+	40.2949i	0.656380	+	1.43727i
$787$	−20.5907	+	11.2433i	−0.733978	+	0.400782i	−0.802331	−	0.596879i	$-0.796407\pi$
$787$	−20.5907	+	11.2433i	−0.733978	+	0.400782i	0.0683536	+	0.997661i	$0.478225\pi$
$788$	2.55990	+	6.86337i	0.0911928	+	0.244497i
$789$	−32.6349	+	37.6627i	−1.16183	+	1.34083i
$790$	−2.04526	+	20.5790i	−0.0727672	+	0.732167i
$791$	16.9433	−	4.97499i	0.602433	−	0.176890i
$792$	9.27695	+	0.663501i	0.329642	+	0.0235765i
$793$	20.1284	+	4.37866i	0.714779	+	0.155491i
$794$	2.57852	+	4.01225i	0.0915082	+	0.142390i
$795$	50.6180	+	1.40050i	1.79524	+	0.0496707i
$796$	−0.408733	−	1.39202i	−0.0144871	−	0.0493387i
$797$	3.03770	+	4.05790i	0.107601	+	0.143738i	0.851109	−	0.524989i	$-0.175930\pi$
$797$	3.03770	+	4.05790i	0.107601	+	0.143738i	−0.743508	+	0.668727i	$0.766840\pi$
$798$	−5.14186	−	71.8927i	−0.182020	−	2.54497i
$799$	−1.39851	+	3.06231i	−0.0494757	+	0.108337i
$800$	4.16226	−	2.77048i	0.147158	−	0.0979512i
$801$	23.3633	−	10.6697i	0.825503	−	0.376995i
$802$	3.65927	+	2.73930i	0.129213	+	0.0967280i
$803$	−1.72722	−	7.93989i	−0.0609522	−	0.280193i
$804$	4.45806			0.157224
$805$	39.3259	+	17.7161i	1.38606	+	0.624410i
$806$	6.14798			0.216553
$807$	−8.45611	−	38.8721i	−0.297669	−	1.36836i
$808$	11.8490	+	8.87008i	0.416848	+	0.312048i
$809$	15.0856	−	6.88935i	0.530381	−	0.242217i	−0.132179	−	0.991226i	$-0.542197\pi$
$809$	15.0856	−	6.88935i	0.530381	−	0.242217i	0.662560	+	0.749009i	$0.269470\pi$
$810$	74.9230	+	18.4827i	2.63253	+	0.649417i
$811$	−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	$0.176164\pi$
$812$	−0.826808	−	11.5603i	−0.0290153	−	0.405687i
$813$	28.4314	+	37.9799i	0.997133	+	1.33201i
$814$	−0.762543	−	2.59698i	−0.0267271	−	0.0910242i
$815$	−12.9458	+	12.2487i	−0.453472	+	0.429054i
$816$	1.46398	+	2.27800i	0.0512496	+	0.0797459i
$817$	21.6994	+	4.72042i	0.759166	+	0.165146i
$818$	−5.28262	−	0.377821i	−0.184703	−	0.0132102i
$819$	55.9746	−	16.4356i	1.95591	−	0.574307i
$820$	4.09998	−	3.35869i	0.143178	−	0.117291i
$821$	−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	$0.447625\pi$
$822$	3.97665	+	10.6618i	0.138702	+	0.371874i
$823$	−36.1865	+	19.7593i	−1.26138	+	0.688767i	−0.963977	−	0.265984i	$-0.914303\pi$
$823$	−36.1865	+	19.7593i	−1.26138	+	0.688767i	−0.297405	+	0.954751i	$0.596121\pi$
$824$	4.68867	+	10.2668i	0.163338	+	0.357660i
$825$	16.0491	+	9.95325i	0.558759	+	0.346528i
$826$	7.54668	−	11.7429i	0.262583	−	0.408586i
$827$	−8.59770	+	8.59770i	−0.298971	+	0.298971i	−0.840611	−	0.541640i	$-0.817804\pi$
$827$	−8.59770	+	8.59770i	−0.298971	+	0.298971i	0.541640	+	0.840611i	$0.317804\pi$
$828$	−37.5712	−	12.6262i	−1.30569	−	0.438792i
$829$			15.6632i			0.544005i	0.962297	+	0.272002i	$0.0876859\pi$
$829$			15.6632i			0.544005i	−0.962297	+	0.272002i	$0.912314\pi$
$830$	−2.56147	−	9.70934i	−0.0889100	−	0.337016i
$831$	11.1322	+	77.4261i	0.386171	+	2.68588i
$832$	−0.613298	+	1.64432i	−0.0212623	+	0.0570064i
$833$	−3.54848	−	6.49856i	−0.122948	−	0.225162i
$834$	−7.70661	−	3.51949i	−0.266858	−	0.121870i
$835$	1.49341	−	1.88401i	0.0516816	−	0.0651988i
$836$	−0.855099	+	5.94735i	−0.0295742	+	0.205693i
$837$	54.3290	+	29.6659i	1.87788	+	1.02540i
$838$	2.39373	−	33.4687i	0.0826899	−	1.15616i
$839$	5.83932	−	3.75270i	0.201596	−	0.129558i	−0.435948	−	0.899972i	$-0.643587\pi$
$839$	5.83932	−	3.75270i	0.201596	−	0.129558i	0.637544	+	0.770414i	$0.279951\pi$
$840$	24.6558	−	17.4142i	0.850705	−	0.600847i
$841$	−13.5535	−	15.6416i	−0.467362	−	0.539365i
$842$	4.28095	−	7.83997i	0.147531	−	0.270183i
$843$	24.3603	−	18.2359i	0.839014	−	0.628078i
$844$	−12.2130	−	10.5826i	−0.420389	−	0.364269i
$845$	20.4246	−	8.65315i	0.702627	−	0.297677i
$846$	−33.0891	−	9.71583i	−1.13763	−	0.334037i
$847$	−36.6811	−	13.6813i	−1.26038	−	0.470097i
$848$	−4.04348	+	5.40145i	−0.138854	+	0.185487i
$849$	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
$853$	−12.0085	+	2.61229i	−0.411163	+	0.0894430i	−0.413389	−	0.910555i	$-0.635655\pi$
$853$	−12.0085	+	2.61229i	−0.411163	+	0.0894430i	0.00222628	+	0.999998i	$0.499291\pi$
$854$	46.7293	−	6.71866i	1.59904	−	0.229908i
$855$	−30.4068	+	93.8695i	−1.03989	+	3.21027i
$856$	3.71702	−	12.6590i	0.127045	−	0.432676i
$857$	−31.7083	+	11.8266i	−1.08314	+	0.403989i	−0.826741	−	0.562583i	$-0.809808\pi$
$857$	−31.7083	+	11.8266i	−1.08314	+	0.403989i	−0.256395	+	0.966572i	$0.582535\pi$
$858$	−6.61161	+	0.472872i	−0.225717	+	0.0161436i
$859$	45.5682	+	6.55171i	1.55477	+	0.223542i	0.865478	−	0.500947i	$-0.167015\pi$
$859$	45.5682	+	6.55171i	1.55477	+	0.223542i	0.689287	+	0.724488i	$0.257924\pi$
$860$	3.00785	+	8.80039i	0.102567	+	0.300091i
$861$	24.1817	−	20.9536i	0.824110	−	0.714095i
$862$	5.76663	−	26.5087i	0.196412	−	0.902892i
$863$	1.31001	−	6.02201i	0.0445932	−	0.204992i	−0.949460	−	0.313889i	$-0.898368\pi$
$863$	1.31001	−	6.02201i	0.0445932	−	0.204992i	0.994053	+	0.108897i	$0.0347318\pi$
$864$	−13.3540	+	11.5713i	−0.454311	+	0.393663i
$865$	−16.5823	−	48.5168i	−0.563816	−	1.64962i
$866$	−11.8095	−	1.69796i	−0.401304	−	0.0576989i
$867$	54.7324	−	3.91454i	1.85881	−	0.132945i
$868$	13.2018	−	4.92401i	0.448097	−	0.167132i
$869$	2.93222	−	9.98622i	0.0994687	−	0.338759i
$870$	−6.66419	+	20.5732i	−0.225937	+	0.697496i
$871$	−2.30734	+	0.331746i	−0.0781814	+	0.0112408i
$872$	−1.45630	+	0.316798i	−0.0493164	+	0.0107281i
$873$	−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
$877$	−14.3784	+	19.2073i	−0.485525	+	0.648586i	−0.974678	−	0.223612i	$-0.928215\pi$
$877$	−14.3784	+	19.2073i	−0.485525	+	0.648586i	0.489153	+	0.872198i	$0.337306\pi$
$878$	25.6613	+	9.57118i	0.866028	+	0.323012i
$879$	−9.96484	−	2.92594i	−0.336106	−	0.0986895i
$880$	−2.31699	+	0.981624i	−0.0781057	+	0.0330905i
$881$	−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	$0.875883\pi$
$882$	60.7191	−	45.4538i	2.04452	−	1.53051i
$883$	23.4859	−	43.0112i	0.790363	−	1.44744i	−0.101356	−	0.994850i	$-0.532318\pi$
$883$	23.4859	−	43.0112i	0.790363	−	1.44744i	0.891718	−	0.452591i	$-0.149500\pi$
$884$	−0.927224	−	1.07007i	−0.0311859	−	0.0359905i
$885$	−21.2745	+	15.0261i	−0.715135	+	0.505095i
$886$	−15.5922	+	10.0205i	−0.523829	+	0.336644i
$887$	0.650170	−	9.09057i	0.0218306	−	0.305232i	−0.974792	−	0.223115i	$-0.928377\pi$
$887$	0.650170	−	9.09057i	0.0218306	−	0.305232i	0.996623	−	0.0821166i	$-0.0261680\pi$
$888$	7.08494	+	3.86867i	0.237755	+	0.129824i
$889$	9.72439	−	67.6346i	0.326145	−	2.26839i
$890$	−4.31670	+	5.44572i	−0.144696	+	0.182541i
$891$	−35.3273	−	16.1334i	−1.18351	−	0.540491i
$892$	−9.09079	−	16.6485i	−0.304382	−	0.557434i
$893$	7.78572	−	20.8743i	0.260539	−	0.698532i
$894$	4.88879	+	34.0023i	0.163506	+	1.13721i
$895$	−6.08033	−	23.0477i	−0.203243	−	0.770399i
$896$			4.02210i			0.134369i
$897$	27.7848	+	5.09630i	0.927708	+	0.170160i
$898$	−11.8958	+	11.8958i	−0.396967	+	0.396967i
$899$	−5.45752	+	8.49207i	−0.182019	+	0.283226i
$900$	−40.2327	+	9.43198i	−1.34109	+	0.314399i
$901$	−2.26139	−	4.95175i	−0.0753378	−	0.164967i
$902$	−2.34109	+	1.27833i	−0.0779498	+	0.0425638i
$903$	19.6211	+	52.6062i	0.652950	+	1.75063i
$904$	2.87509	−	3.31803i	0.0956240	−	0.110356i
$905$	10.7616	−	8.81586i	0.357727	−	0.293049i
$906$	23.6502	−	6.94434i	0.785727	−	0.230710i
$907$	−51.1541	−	3.65862i	−1.69855	−	0.121482i	−0.811859	−	0.583854i	$-0.801544\pi$
$907$	−51.1541	−	3.65862i	−1.69855	−	0.121482i	−0.886686	+	0.462371i	$0.846999\pi$
$908$	−12.8995	−	2.80612i	−0.428086	−	0.0931244i
$909$	−66.1355	−	102.909i	−2.19358	−	3.41327i
$910$	−11.4651	+	10.8478i	−0.380065	+	0.359600i
$911$	−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	$0.926446\pi$
$912$	−10.7391	−	14.3457i	−0.355607	−	0.475035i
$913$	0.360521	+	5.04074i	0.0119315	+	0.166824i
$914$	−1.99584	+	4.37028i	−0.0660165	+	0.144556i
$915$	−85.5256	−	21.0983i	−2.82739	−	0.697487i
$916$	0.665423	−	0.303888i	0.0219862	−	0.0100408i
$917$	−42.4973	−	31.8131i	−1.40338	−	1.05056i
$918$	−3.03034	−	13.9303i	−0.100016	−	0.459767i
$919$	15.1309			0.499124			0.249562	−	0.968359i	$-0.419713\pi$
$919$	15.1309			0.499124			0.249562	+	0.968359i	$0.419713\pi$
$920$	10.6067	−	1.58064i	0.349692	−	0.0521121i
$921$	0.539079			0.0177632
$922$	−3.71261	−	17.0666i	−0.122268	−	0.562058i
$923$	−21.6940	−	16.2399i	−0.714067	−	0.534544i
$924$	−13.8186	+	6.31076i	−0.454600	+	0.207609i
$925$	6.66339	+	10.0108i	0.219091	+	0.329154i
$926$	5.47883	−	11.9970i	0.180046	−	0.394245i
$927$	−6.65461	−	93.0436i	−0.218566	−	3.05595i
$928$	−1.72684	−	2.30679i	−0.0566863	−	0.0757240i
$929$	3.39678	+	11.5684i	0.111445	+	0.379546i	0.996261	−	0.0863941i	$-0.0275344\pi$
$929$	3.39678	+	11.5684i	0.111445	+	0.379546i	−0.884816	+	0.465940i	$0.845716\pi$
$930$	−26.2810	−	0.727144i	−0.861787	−	0.0238440i
$931$	26.4913	+	41.2213i	0.868218	+	1.35097i
$932$	21.5599	+	4.69007i	0.706218	+	0.153628i
$933$	−53.8928	−	3.85449i	−1.76437	−	0.126190i
$934$	−27.4156	+	8.04995i	−0.897066	+	0.263402i
$935$	0.200784	−	2.02024i	0.00656635	−	0.0660690i
$936$	9.49828	−	10.9616i	0.310461	−	0.358291i
$937$	17.7157	+	47.4977i	0.578747	+	1.55168i	0.814679	+	0.579912i	$0.196913\pi$
$937$	17.7157	+	47.4977i	0.578747	+	1.55168i	−0.235932	+	0.971770i	$0.575814\pi$
$938$	−4.68894	+	2.56036i	−0.153099	+	0.0835986i
$939$	30.0352	+	65.7680i	0.980163	+	2.14626i
$940$	9.16856	−	1.73041i	0.299045	−	0.0564396i
$941$	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
$943$	11.0224	−	2.77922i	0.358938	−	0.0905040i
$944$		−	3.47052i		−	0.112956i
$945$	−153.660	+	40.5378i	−4.99855	+	1.31869i
$946$	−0.666108	−	4.63289i	−0.0216571	−	0.150628i
$947$	12.6352	−	33.8762i	0.410588	−	1.10083i	−0.552940	−	0.833221i	$-0.686494\pi$
$947$	12.6352	−	33.8762i	0.410588	−	1.10083i	0.963528	−	0.267608i	$-0.0862332\pi$
$948$	14.8763	+	27.2438i	0.483158	+	0.884839i
$949$	−11.5266	−	5.26404i	−0.374171	−	0.170878i
$950$	−4.22361	−	26.3600i	−0.137032	−	0.855231i
$951$	−5.08530	+	35.3691i	−0.164902	+	1.14692i
$952$	−2.84810	−	1.55518i	−0.0923075	−	0.0504037i
$953$	3.66560	−	51.2518i	0.118741	−	1.66021i	−0.493655	−	0.869658i	$-0.664339\pi$
$953$	3.66560	−	51.2518i	0.118741	−	1.66021i	0.612395	−	0.790552i	$-0.290206\pi$
$954$	46.9116	−	30.1483i	1.51882	−	0.976086i
$955$	−43.7436	−	7.52964i	−1.41551	−	0.243653i
$956$	0.318667	+	0.367761i	0.0103064	+	0.0118942i
$957$	5.21592	−	9.55225i	0.168607	−	0.308780i
$958$	−26.6164	+	19.9248i	−0.859936	+	0.643740i
$959$	−10.3059	−	8.93012i	−0.332795	−	0.288369i
$960$	2.81617	−	6.95648i	0.0908914	−	0.224520i
$961$	17.9691	+	5.27620i	0.579648	+	0.170200i
$962$	−3.95481	−	1.47507i	−0.127508	−	0.0475581i
$963$	−65.3451	+	87.2908i	−2.10572	+	2.81291i
$964$	−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	$0.757163\pi$
$968$	−9.51115	+	2.06902i	−0.305700	+	0.0665010i
$969$	14.3108	−	2.05758i	0.459728	−	0.0660989i
$970$	39.5932	+	12.8253i	1.27126	+	0.411795i
$971$	−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	$0.128458\pi$
$972$	58.8589	−	21.9532i	1.88790	−	0.704150i
$973$	10.1270	−	0.724301i	0.324658	−	0.0232200i
$974$	15.1540	+	2.17882i	0.485567	+	0.0698140i
$975$	27.4250	−	10.7343i	0.878303	−	0.343774i
$976$	8.87069	−	7.68650i	0.283944	−	0.246039i
$977$	5.91332	−	27.1831i	0.189184	−	0.869665i	−0.780472	−	0.625191i	$-0.785021\pi$
$977$	5.91332	−	27.1831i	0.189184	−	0.869665i	0.969656	−	0.244474i	$-0.0786152\pi$
$978$	−5.68623	+	26.1392i	−0.181826	+	0.835839i
$979$	2.64306	−	2.29023i	0.0844726	−	0.0731959i
$980$	−9.03777	+	18.4237i	−0.288701	+	0.588524i
$981$	12.1920	+	1.75294i	0.389259	+	0.0559670i
$982$	36.3421	−	2.59924i	1.15972	−	0.0829450i
$983$	49.3873	−	18.4205i	1.57521	−	0.587523i	0.598319	−	0.801258i	$-0.295836\pi$
$983$	49.3873	−	18.4205i	1.57521	−	0.587523i	0.976892	+	0.213735i	$0.0685629\pi$
$984$	2.24126	−	7.63304i	0.0714488	−	0.243332i
$985$	7.44934	+	14.5877i	0.237356	+	0.464804i
$986$	2.30116	−	0.330857i	0.0732839	−	0.0105366i
$987$	55.0413	−	11.9735i	1.75198	−	0.381121i
$988$	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	$0.552950\pi$
$992$	2.09938	−	2.80444i	0.0666554	−	0.0890412i
$993$	89.6870	+	33.4515i	2.84613	+	1.06155i
$994$	−59.5912	−	17.4975i	−1.89012	−	0.554989i
$995$	−1.26550	−	2.98703i	−0.0401189	−	0.0946953i
$996$	−11.3908	−	9.87015i	−0.360930	−	0.312748i
$997$	−35.4735	+	26.5551i	−1.12346	+	0.841010i	−0.988706	−	0.149870i	$-0.952115\pi$
$997$	−35.4735	+	26.5551i	−1.12346	+	0.841010i	−0.134752	+	0.990879i	$0.543024\pi$
$998$	−17.8482	+	32.6865i	−0.564975	+	1.03467i
$999$	−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.67.12	yes	240
5.3	odd	4	inner	230.2.l.a.113.7	yes	240
23.11	odd	22	inner	230.2.l.a.57.7	✓	240
115.103	even	44	inner	230.2.l.a.103.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.7	✓	240	23.11	odd	22	inner
230.2.l.a.67.12	yes	240	1.1	even	1	trivial
230.2.l.a.103.12	yes	240	115.103	even	44	inner
230.2.l.a.113.7	yes	240	5.3	odd	4	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+(0.212565 + 0.977147i) q^{2} +(2.68685 + 2.01135i) q^{3} +(-0.909632 + 0.415415i) q^{4} +(-1.91382 + 1.15642i) q^{5} +(-1.39425 + 3.05299i) q^{6} +(-0.286933 - 4.01185i) q^{7} +(-0.599278 - 0.800541i) q^{8} +(2.32843 + 7.92991i) q^{9} +(-1.53680 - 1.62426i) q^{10} +(0.608409 + 0.946702i) q^{11} +(-3.27959 - 0.713431i) q^{12} +(1.75050 + 0.125198i) q^{13} +(3.85918 - 1.13316i) q^{14} +(-7.46810 - 0.742226i) q^{15} +(0.654861 - 0.755750i) q^{16} +(0.281948 + 0.755932i) q^{17} +(-7.25375 + 3.96085i) q^{18} +(-2.21800 - 4.85675i) q^{19} +(1.26047 - 1.84695i) q^{20} +(7.29830 - 11.3564i) q^{21} +(-0.795741 + 0.795741i) q^{22} +(4.13157 - 2.43518i) q^{23} -3.35629i q^{24} +(2.32538 - 4.42635i) q^{25} +(0.249758 + 1.73710i) q^{26} +(-6.17498 + 16.5558i) q^{27} +(1.92759 + 3.53011i) q^{28} +(-2.62114 - 1.19703i) q^{29} +(-0.862196 - 7.45520i) q^{30} +(0.498555 - 3.46753i) q^{31} +(0.877679 + 0.479249i) q^{32} +(-0.269448 + 3.76737i) q^{33} +(-0.678725 + 0.436190i) q^{34} +(5.18853 + 7.34613i) q^{35} +(-5.41222 - 6.24604i) q^{36} +(-1.15266 + 2.11094i) q^{37} +(4.27428 - 3.19969i) q^{38} +(4.45150 + 3.85725i) q^{39} +(2.07267 + 0.839071i) q^{40} +(2.27425 + 0.667780i) q^{41} +(12.6482 + 4.71754i) q^{42} +(-2.49251 + 3.32960i) 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} +(3.27959 - 0.713431i) q^{48} +(-9.08389 + 1.30607i) q^{49} +(4.81949 + 1.33135i) q^{50} +(-0.762893 + 2.59817i) q^{51} +(-1.64432 + 0.613298i) q^{52} +(-6.73006 + 0.481343i) q^{53} +(-17.4900 - 2.51468i) q^{54} +(-2.25917 - 1.10824i) q^{55} +(-3.03970 + 2.63392i) q^{56} +(3.80918 - 17.5105i) q^{57} +(0.612514 - 2.81568i) q^{58} +(2.62284 - 2.27270i) q^{59} +(7.10156 - 2.42721i) q^{60} +(11.6181 + 1.67044i) q^{61} +(3.49426 - 0.249914i) q^{62} +(31.1456 - 11.6167i) q^{63} +(-0.281733 + 0.959493i) q^{64} +(-3.49491 + 1.78470i) q^{65} +(-3.73855 + 0.537522i) q^{66} +(-1.29791 + 0.282344i) 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} +(4.95285 - 6.61623i) q^{72} +(-6.76526 - 2.52331i) q^{73} +(-2.30772 - 0.677607i) q^{74} +(15.1509 - 7.21578i) q^{75} +(4.03513 + 3.49646i) q^{76} +(3.62346 - 2.71249i) q^{77} +(-2.82286 + 5.16969i) q^{78} +(-6.05650 - 6.98957i) q^{79} +(-0.379318 + 2.20366i) q^{80} +(-29.0326 + 18.6581i) q^{81} +(-0.169092 + 2.36422i) q^{82} +(3.94140 + 2.15217i) q^{83} +(-1.92116 + 13.3619i) q^{84} +(-1.41377 - 1.12066i) q^{85} +(-3.78333 - 1.72779i) q^{86} +(-4.63494 - 8.48827i) q^{87} +(0.393269 - 1.05439i) q^{88} +(-0.442275 - 3.07609i) q^{89} +(9.30193 - 15.9687i) q^{90} -7.05866i q^{91} +(-2.74660 + 3.93144i) q^{92} +(8.31396 - 8.31396i) q^{93} +(-2.25593 + 3.51029i) q^{94} +(9.86129 + 6.72998i) q^{95} +(1.39425 + 3.05299i) q^{96} +(-16.3357 + 8.91998i) q^{97} +(-3.20714 - 8.59867i) 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

Related objects

Downloads

Learn more