LMFDB - Embedded newform 242.2.e.a.221.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [242,2,Mod(23,242)] 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("242.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	242.e (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [50] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.93237972891$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$5$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			221.1
Character	$\chi$	$=$	242.221
Dual form			242.2.e.a.23.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.415415 - 0.909632i) q^{2} -3.35440 q^{3} +(-0.654861 + 0.755750i) q^{4} +(-2.65093 + 0.778384i) q^{5} +(1.39347 + 3.05127i) q^{6} +(0.220513 - 1.53370i) q^{7} +(0.959493 + 0.281733i) q^{8} +8.25199 q^{9} +(1.80928 + 2.08802i) q^{10} +(-2.27514 + 2.41325i) q^{11} +(2.19666 - 2.53509i) q^{12} +(2.22394 - 2.56656i) q^{13} +(-1.48671 + 0.436537i) q^{14} +(8.89229 - 2.61101i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.31131 - 1.48539i) q^{17} +(-3.42800 - 7.50628i) q^{18} +(3.92714 + 2.52382i) q^{19} +(1.14773 - 2.51318i) q^{20} +(-0.739689 + 5.14465i) q^{21} +(3.14029 + 1.06704i) q^{22} +(0.583386 + 4.05754i) q^{23} +(-3.21852 - 0.945043i) q^{24} +(2.21530 - 1.42369i) q^{25} +(-3.25848 - 0.956776i) q^{26} -17.6173 q^{27} +(1.01469 + 1.17101i) q^{28} +(5.34655 + 3.43602i) q^{29} +(-6.06905 - 7.00406i) q^{30} +(-5.39897 - 6.23074i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(7.63172 - 8.09499i) q^{33} +(-2.31131 - 1.48539i) q^{34} +(0.609244 + 4.23738i) q^{35} +(-5.40391 + 6.23644i) q^{36} +(1.69822 + 1.95985i) q^{37} +(0.664355 - 4.62069i) q^{38} +(-7.45997 + 8.60927i) q^{39} -2.76285 q^{40} +(3.44639 + 7.54654i) q^{41} +(4.98701 - 1.46432i) q^{42} +(7.18911 + 2.11091i) q^{43} +(-0.333911 - 3.29977i) q^{44} +(-21.8755 + 6.42322i) q^{45} +(3.44852 - 2.21623i) q^{46} +(3.05516 - 6.68988i) q^{47} +(0.477381 + 3.32026i) q^{48} +(4.41284 + 1.29573i) q^{49} +(-2.21530 - 1.42369i) q^{50} +(-7.75307 + 4.98260i) q^{51} +(0.483308 + 3.36148i) q^{52} +(0.267741 - 1.86218i) q^{53} +(7.31848 + 16.0252i) q^{54} +(4.15280 - 8.16828i) q^{55} +(0.643674 - 1.40945i) q^{56} +(-13.1732 - 8.46590i) q^{57} +(0.904476 - 6.29077i) q^{58} +(-4.12044 + 9.02251i) q^{59} +(-3.84994 + 8.43019i) q^{60} +(0.103549 - 0.226740i) q^{61} +(-3.42487 + 7.49942i) q^{62} +(1.81967 - 12.6561i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-3.89774 + 8.53486i) q^{65} +(-10.5338 - 3.57927i) q^{66} +(-1.16072 - 2.54162i) q^{67} +(-0.391005 + 2.71950i) q^{68} +(-1.95691 - 13.6106i) q^{69} +(3.60137 - 2.31446i) q^{70} +(4.09100 + 2.62913i) q^{71} +(7.91773 + 2.32486i) q^{72} +(-0.342626 - 2.38302i) q^{73} +(1.07728 - 2.35890i) q^{74} +(-7.43099 + 4.77561i) q^{75} +(-4.47911 + 1.31518i) q^{76} +(3.19950 + 4.02153i) q^{77} +(10.9302 + 3.20941i) q^{78} +(10.2228 - 3.00169i) q^{79} +(1.14773 + 2.51318i) q^{80} +34.3394 q^{81} +(5.43289 - 6.26989i) q^{82} +(1.78902 - 12.4429i) q^{83} +(-3.40367 - 3.92805i) q^{84} +(-4.97093 + 5.73676i) q^{85} +(-1.06631 - 7.41635i) q^{86} +(-17.9345 - 11.5258i) q^{87} +(-2.86287 + 1.67451i) q^{88} +(-5.82201 + 3.74158i) q^{89} +(14.9302 + 17.2303i) q^{90} +(-3.44593 - 3.97681i) q^{91} +(-3.44852 - 2.21623i) q^{92} +(18.1103 + 20.9004i) q^{93} -7.35449 q^{94} +(-12.3751 - 3.63366i) q^{95} +(2.82190 - 1.81353i) q^{96} +(5.55980 + 1.63250i) q^{97} +(-0.654525 - 4.55232i) q^{98} +(-18.7744 + 19.9141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 5 q^{2} - 10 q^{3} - 5 q^{4} + q^{5} - q^{6} + 5 q^{8} + 40 q^{9} - q^{10} + 11 q^{11} + q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} - 5 q^{16} - 2 q^{17} + 4 q^{18} - q^{19} + q^{20} - 2 q^{21}+ \cdots - 22 q^{99}+O(q^{100}) $ 50 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 + q^5 - q^6 + 5 * q^8 + 40 * q^9 - q^10 + 11 * q^11 + q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 - 5 * q^16 - 2 * q^17 + 4 * q^18 - q^19 + q^20 - 2 * q^21 + 22 * q^22 - 31 * q^23 - q^24 - 2 * q^25 + q^26 - 106 * q^27 - 3 * q^29 - 13 * q^30 - 18 * q^31 + 5 * q^32 + 2 * q^34 - 4 * q^35 - 4 * q^36 - 17 * q^37 + 34 * q^38 - 103 * q^39 + 10 * q^40 - 6 * q^41 - 42 * q^42 - 5 * q^43 - 11 * q^44 - 39 * q^45 - 46 * q^46 - 7 * q^47 + q^48 + 43 * q^49 + 2 * q^50 + 25 * q^51 - q^52 + 25 * q^53 - 4 * q^54 + 22 * q^55 - 11 * q^56 - 41 * q^57 - 8 * q^58 - 30 * q^59 - 31 * q^60 - 40 * q^61 - 4 * q^62 + 45 * q^63 - 5 * q^64 - 43 * q^65 - 55 * q^66 + 64 * q^67 - 2 * q^68 + 8 * q^69 + 15 * q^70 - 5 * q^71 + 4 * q^72 - 34 * q^73 - 5 * q^74 + 11 * q^75 + 10 * q^76 - 22 * q^77 + 4 * q^78 + 47 * q^79 + q^80 + 18 * q^81 + 28 * q^82 - 9 * q^83 - 46 * q^84 + 100 * q^85 + 5 * q^86 - 87 * q^87 + 11 * q^88 - 3 * q^89 + 28 * q^90 + q^91 + 46 * q^92 + 47 * q^93 + 18 * q^94 - 129 * q^95 - q^96 + 3 * q^97 + 45 * q^98 - 22 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{4}{11}\right)$

Coefficient data

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

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

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

$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$2$	−0.415415	−	0.909632i	−0.293743	−	0.643207i
$3$	−3.35440			−1.93666			−0.968332	−	0.249667i	$-0.919679\pi$
$3$	−3.35440			−1.93666			−0.968332	+	0.249667i	$0.919679\pi$
$4$	−0.654861	+	0.755750i	−0.327430	+	0.377875i
$5$	−2.65093	+	0.778384i	−1.18553	+	0.348104i	−0.814305	−	0.580437i	$-0.802882\pi$
$5$	−2.65093	+	0.778384i	−1.18553	+	0.348104i	−0.371229	+	0.928541i	$0.621063\pi$
$6$	1.39347	+	3.05127i	0.568881	+	1.24568i
$7$	0.220513	−	1.53370i	0.0833461	−	0.579685i	−0.904761	−	0.425919i	$-0.859951\pi$
$7$	0.220513	−	1.53370i	0.0833461	−	0.579685i	0.988107	−	0.153766i	$-0.0491401\pi$
$8$	0.959493	+	0.281733i	0.339232	+	0.0996075i
$9$	8.25199			2.75066
$10$	1.80928	+	2.08802i	0.572145	+	0.660290i
$11$	−2.27514	+	2.41325i	−0.685980	+	0.727621i
$11$	−2.27514	+	2.41325i	−0.685980	+	0.727621i
$12$	2.19666	−	2.53509i	0.634122	−	0.731816i
$13$	2.22394	−	2.56656i	0.616809	−	0.711836i	−0.358289	−	0.933611i	$-0.616640\pi$
$13$	2.22394	−	2.56656i	0.616809	−	0.711836i	0.975098	+	0.221775i	$0.0711851\pi$
$14$	−1.48671	+	0.436537i	−0.397339	+	0.116669i
$15$	8.89229	−	2.61101i	2.29598	−	0.674160i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	2.31131	−	1.48539i	0.560576	−	0.360260i	−0.229463	−	0.973317i	$-0.573697\pi$
$17$	2.31131	−	1.48539i	0.560576	−	0.360260i	0.790039	+	0.613057i	$0.210060\pi$
$18$	−3.42800	−	7.50628i	−0.807988	−	1.76925i
$19$	3.92714	+	2.52382i	0.900948	+	0.579004i	0.907071	−	0.420977i	$-0.138313\pi$
$19$	3.92714	+	2.52382i	0.900948	+	0.579004i	−0.00612312	+	0.999981i	$0.501949\pi$
$20$	1.14773	−	2.51318i	0.256640	−	0.561963i
$21$	−0.739689	+	5.14465i	−0.161413	+	1.12265i
$22$	3.14029	+	1.06704i	0.669512	+	0.227493i
$23$	0.583386	+	4.05754i	0.121644	+	0.846056i	0.955693	+	0.294365i	$0.0951081\pi$
$23$	0.583386	+	4.05754i	0.121644	+	0.846056i	−0.834049	+	0.551691i	$0.813983\pi$
$24$	−3.21852	−	0.945043i	−0.656978	−	0.192906i
$25$	2.21530	−	1.42369i	0.443060	−	0.284737i
$26$	−3.25848	−	0.956776i	−0.639041	−	0.187639i
$27$	−17.6173			−3.39045
$28$	1.01469	+	1.17101i	0.191758	+	0.221301i
$29$	5.34655	+	3.43602i	0.992829	+	0.638053i	0.932895	−	0.360150i	$-0.117274\pi$
$29$	5.34655	+	3.43602i	0.992829	+	0.638053i	0.0599348	+	0.998202i	$0.480911\pi$
$30$	−6.06905	−	7.00406i	−1.10805	−	1.27876i
$31$	−5.39897	−	6.23074i	−0.969684	−	1.11907i	−0.992853	−	0.119343i	$-0.961921\pi$
$31$	−5.39897	−	6.23074i	−0.969684	−	1.11907i	0.0231692	−	0.999732i	$-0.492624\pi$
$32$	−0.841254	+	0.540641i	−0.148714	+	0.0955727i
$33$	7.63172	−	8.09499i	1.32851	−	1.40916i
$34$	−2.31131	−	1.48539i	−0.396387	−	0.254743i
$35$	0.609244	+	4.23738i	0.102981	+	0.716249i
$36$	−5.40391	+	6.23644i	−0.900651	+	1.03941i
$37$	1.69822	+	1.95985i	0.279185	+	0.322197i	0.877972	−	0.478711i	$-0.158896\pi$
$37$	1.69822	+	1.95985i	0.279185	+	0.322197i	−0.598787	+	0.800908i	$0.704350\pi$
$38$	0.664355	−	4.62069i	0.107773	−	0.749574i
$39$	−7.45997	+	8.60927i	−1.19455	+	1.37859i
$40$	−2.76285			−0.436845
$41$	3.44639	+	7.54654i	0.538236	+	1.17857i	0.962063	+	0.272829i	$0.0879592\pi$
$41$	3.44639	+	7.54654i	0.538236	+	1.17857i	−0.423827	+	0.905743i	$0.639314\pi$
$42$	4.98701	−	1.46432i	0.769513	−	0.225949i
$43$	7.18911	+	2.11091i	1.09633	+	0.321911i	0.779393	−	0.626536i	$-0.215528\pi$
$43$	7.18911	+	2.11091i	1.09633	+	0.321911i	0.316936	+	0.948447i	$0.397346\pi$
$44$	−0.333911	−	3.29977i	−0.0503390	−	0.497460i
$45$	−21.8755	+	6.42322i	−3.26101	+	0.957517i
$46$	3.44852	−	2.21623i	0.508457	−	0.326765i
$47$	3.05516	−	6.68988i	0.445641	−	0.975819i	−0.544887	−	0.838510i	$-0.683427\pi$
$47$	3.05516	−	6.68988i	0.445641	−	0.975819i	0.990528	−	0.137309i	$-0.0438453\pi$
$48$	0.477381	+	3.32026i	0.0689040	+	0.479238i
$49$	4.41284	+	1.29573i	0.630405	+	0.185104i
$50$	−2.21530	−	1.42369i	−0.313290	−	0.201340i
$51$	−7.75307	+	4.98260i	−1.08565	+	0.697703i
$52$	0.483308	+	3.36148i	0.0670227	+	0.466153i
$53$	0.267741	−	1.86218i	0.0367770	−	0.255790i	−0.963136	−	0.269017i	$-0.913301\pi$
$53$	0.267741	−	1.86218i	0.0367770	−	0.255790i	0.999913	+	0.0132270i	$0.00421041\pi$
$54$	7.31848	+	16.0252i	0.995920	+	2.18076i
$55$	4.15280	−	8.16828i	0.559964	−	1.10141i
$56$	0.643674	−	1.40945i	0.0860146	−	0.188346i
$57$	−13.1732	−	8.46590i	−1.74483	−	1.12134i
$58$	0.904476	−	6.29077i	0.118763	−	0.826018i
$59$	−4.12044	+	9.02251i	−0.536436	+	1.17463i	0.426398	+	0.904536i	$0.359782\pi$
$59$	−4.12044	+	9.02251i	−0.536436	+	1.17463i	−0.962834	+	0.270095i	$0.912945\pi$
$60$	−3.84994	+	8.43019i	−0.497025	+	1.08833i
$61$	0.103549	−	0.226740i	0.0132581	−	0.0290311i	−0.902887	−	0.429878i	$-0.858557\pi$
$61$	0.103549	−	0.226740i	0.0132581	−	0.0290311i	0.916145	+	0.400847i	$0.131284\pi$
$62$	−3.42487	+	7.49942i	−0.434959	+	0.952428i
$63$	1.81967	−	12.6561i	0.229257	−	1.59452i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−3.89774	+	8.53486i	−0.483455	+	1.05862i
$66$	−10.5338	−	3.57927i	−1.29662	−	0.440578i
$67$	−1.16072	−	2.54162i	−0.141804	−	0.310509i	0.825383	−	0.564574i	$-0.190959\pi$
$67$	−1.16072	−	2.54162i	−0.141804	−	0.310509i	−0.967187	+	0.254065i	$0.918232\pi$
$68$	−0.391005	+	2.71950i	−0.0474163	+	0.329788i
$69$	−1.95691	−	13.6106i	−0.235584	−	1.63853i
$70$	3.60137	−	2.31446i	0.430446	−	0.276631i
$71$	4.09100	+	2.62913i	0.485512	+	0.312020i	0.760398	−	0.649457i	$-0.225004\pi$
$71$	4.09100	+	2.62913i	0.485512	+	0.312020i	−0.274886	+	0.961477i	$0.588640\pi$
$72$	7.91773	+	2.32486i	0.933113	+	0.273987i
$73$	−0.342626	−	2.38302i	−0.0401014	−	0.278911i	0.959898	−	0.280351i	$-0.0904508\pi$
$73$	−0.342626	−	2.38302i	−0.0401014	−	0.278911i	−0.999999	+	0.00143969i	$0.999542\pi$
$74$	1.07728	−	2.35890i	0.125231	−	0.274217i
$75$	−7.43099	+	4.77561i	−0.858057	+	0.551440i
$76$	−4.47911	+	1.31518i	−0.513789	+	0.150862i
$77$	3.19950	+	4.02153i	0.364617	+	0.458296i
$78$	10.9302	+	3.20941i	1.23761	+	0.363394i
$79$	10.2228	−	3.00169i	1.15016	−	0.337717i	0.349557	−	0.936915i	$-0.386332\pi$
$79$	10.2228	−	3.00169i	1.15016	−	0.337717i	0.800601	+	0.599198i	$0.204514\pi$
$80$	1.14773	+	2.51318i	0.128320	+	0.280982i
$81$	34.3394			3.81549
$82$	5.43289	−	6.26989i	0.599963	−	0.692394i
$83$	1.78902	−	12.4429i	0.196371	−	1.36579i	−0.618335	−	0.785915i	$-0.712193\pi$
$83$	1.78902	−	12.4429i	0.196371	−	1.36579i	0.814706	−	0.579874i	$-0.196898\pi$
$84$	−3.40367	−	3.92805i	−0.371371	−	0.428585i
$85$	−4.97093	+	5.73676i	−0.539174	+	0.622239i
$86$	−1.06631	−	7.41635i	−0.114983	−	0.799725i
$87$	−17.9345	−	11.5258i	−1.92278	−	1.23569i
$88$	−2.86287	+	1.67451i	−0.305183	+	0.178504i
$89$	−5.82201	+	3.74158i	−0.617132	+	0.396606i	−0.811525	−	0.584317i	$-0.801362\pi$
$89$	−5.82201	+	3.74158i	−0.617132	+	0.396606i	0.194394	+	0.980924i	$0.437726\pi$
$90$	14.9302	+	17.2303i	1.57378	+	1.81624i
$91$	−3.44593	−	3.97681i	−0.361232	−	0.416883i
$92$	−3.44852	−	2.21623i	−0.359533	−	0.231058i
$93$	18.1103	+	20.9004i	1.87795	+	2.16727i
$94$	−7.35449			−0.758557
$95$	−12.3751	−	3.63366i	−1.26966	−	0.372805i
$96$	2.82190	−	1.81353i	0.288009	−	0.185092i
$97$	5.55980	+	1.63250i	0.564512	+	0.165756i	0.551523	−	0.834160i	$-0.314047\pi$
$97$	5.55980	+	1.63250i	0.564512	+	0.165756i	0.0129894	+	0.999916i	$0.495865\pi$
$98$	−0.654525	−	4.55232i	−0.0661170	−	0.459854i
$99$	−18.7744	+	19.9141i	−1.88690	+	2.00144i
$100$	−0.374762	+	2.60653i	−0.0374762	+	0.260653i
$101$	5.18223	−	11.3475i	0.515651	−	1.12912i	−0.455409	−	0.890282i	$-0.650507\pi$
$101$	5.18223	−	11.3475i	0.515651	−	1.12912i	0.971060	−	0.238836i	$-0.0767657\pi$
$102$	7.75307	+	4.98260i	0.767668	+	0.493350i
$103$	3.85916	+	8.45037i	0.380254	+	0.832640i	0.998896	+	0.0469672i	$0.0149556\pi$
$103$	3.85916	+	8.45037i	0.380254	+	0.832640i	−0.618643	+	0.785673i	$0.712317\pi$
$104$	2.85693	−	1.83604i	0.280146	−	0.180039i
$105$	−2.04365	−	14.2139i	−0.199440	−	1.38713i
$106$	−1.80512	+	0.530031i	−0.175329	+	0.0514811i
$107$	−2.33146	+	0.684577i	−0.225390	+	0.0661806i	−0.392478	−	0.919762i	$-0.628382\pi$
$107$	−2.33146	+	0.684577i	−0.225390	+	0.0661806i	0.167087	+	0.985942i	$0.446564\pi$
$108$	11.5369	−	13.3143i	1.11014	−	1.28116i
$109$	−4.89191	+	5.64557i	−0.468560	+	0.540747i	−0.940011	−	0.341145i	$-0.889185\pi$
$109$	−4.89191	+	5.64557i	−0.468560	+	0.540747i	0.471450	+	0.881893i	$0.343731\pi$
$110$	−9.15527	−	0.384296i	−0.872921	−	0.0366412i
$111$	−5.69650	−	6.57411i	−0.540688	−	0.623987i
$112$	−1.54947			−0.146411
$113$	0.674353	+	0.198008i	0.0634378	+	0.0186270i	0.313297	−	0.949655i	$-0.398566\pi$
$113$	0.674353	+	0.198008i	0.0634378	+	0.0186270i	−0.249860	+	0.968282i	$0.580384\pi$
$114$	−2.22851	+	15.4996i	−0.208719	+	1.45167i
$115$	−4.70485	−	10.3022i	−0.438729	−	0.960683i
$116$	−6.09801	+	1.79054i	−0.566186	+	0.166247i
$117$	18.3519	−	21.1792i	1.69663	−	1.95802i
$118$	9.91886			0.913105
$119$	−1.76847	−	3.87241i	−0.162116	−	0.354984i
$120$	9.26770			0.846021
$121$	−0.647505	−	10.9809i	−0.0588641	−	0.998266i
$122$	−0.249266			−0.0225675
$123$	−11.5606	−	25.3141i	−1.04238	−	2.28250i
$124$	8.24446			0.740374
$125$	4.28197	−	4.94166i	0.382991	−	0.441995i
$126$	−12.2683	+	3.60230i	−1.09295	+	0.320918i
$127$	6.37798	+	13.9658i	0.565955	+	1.23927i	0.948923	+	0.315506i	$0.102174\pi$
$127$	6.37798	+	13.9658i	0.565955	+	1.23927i	−0.382969	+	0.923761i	$0.625098\pi$
$128$	0.142315	−	0.989821i	0.0125790	−	0.0874887i
$129$	−24.1151	−	7.08084i	−2.12322	−	0.623434i
$130$	9.38276			0.822922
$131$	6.59469	+	7.61068i	0.576181	+	0.664948i	0.966779	−	0.255613i	$-0.0822773\pi$
$131$	6.59469	+	7.61068i	0.576181	+	0.664948i	−0.390598	+	0.920561i	$0.627732\pi$
$132$	1.12007	+	11.0688i	0.0974898	+	0.963412i
$133$	4.73677	−	5.46653i	0.410730	−	0.474008i
$134$	−1.82976	+	2.11166i	−0.158067	+	0.182419i
$135$	46.7022	−	13.7130i	4.01949	−	1.18023i
$136$	2.63617	−	0.774050i	0.226050	−	0.0663742i
$137$	2.67734	+	18.6213i	0.228741	+	1.59093i	0.703423	+	0.710771i	$0.251654\pi$
$137$	2.67734	+	18.6213i	0.228741	+	1.59093i	−0.474682	+	0.880157i	$0.657437\pi$
$138$	−11.5677	+	7.43412i	−0.984710	+	0.632835i
$139$	3.48681	+	7.63505i	0.295747	+	0.647597i	0.997924	−	0.0644065i	$-0.0205154\pi$
$139$	3.48681	+	7.63505i	0.295747	+	0.647597i	−0.702176	+	0.712003i	$0.747788\pi$
$140$	−3.60137	−	2.31446i	−0.304371	−	0.195608i
$141$	−10.2482	+	22.4405i	−0.863057	+	1.88983i
$142$	0.692074	−	4.81348i	0.0580776	−	0.403938i
$143$	1.13398	+	11.2062i	0.0948280	+	0.937108i
$144$	−1.17438	−	8.16800i	−0.0978651	−	0.680667i
$145$	−16.8479	−	4.94699i	−1.39914	−	0.410825i
$146$	−2.02534	+	1.30161i	−0.167618	+	0.107722i
$147$	−14.8024	−	4.34638i	−1.22088	−	0.358484i
$148$	−2.59325			−0.213164
$149$	−10.4477	−	12.0573i	−0.855910	−	0.987773i	0.144088	−	0.989565i	$-0.453975\pi$
$149$	−10.4477	−	12.0573i	−0.855910	−	0.987773i	−0.999998	+	0.00179168i	$0.999430\pi$
$150$	7.43099	+	4.77561i	0.606738	+	0.389927i
$151$	8.01820	+	9.25350i	0.652512	+	0.753039i	0.981535	−	0.191283i	$-0.0612648\pi$
$151$	8.01820	+	9.25350i	0.652512	+	0.753039i	−0.329023	+	0.944322i	$0.606719\pi$
$152$	3.05702	+	3.52799i	0.247957	+	0.286158i
$153$	19.0729	−	12.2574i	1.54196	−	0.990955i
$154$	2.32899	−	4.58097i	0.187676	−	0.369145i
$155$	19.1622	+	12.3148i	1.53915	+	0.989150i
$156$	−1.62121	−	11.2757i	−0.129800	−	0.902782i
$157$	−12.4968	+	14.4220i	−0.997351	+	1.15100i	−0.00882365	+	0.999961i	$0.502809\pi$
$157$	−12.4968	+	14.4220i	−0.997351	+	1.15100i	−0.988527	+	0.151043i	$0.951737\pi$
$158$	−6.97715	−	8.05206i	−0.555073	−	0.640588i
$159$	−0.898109	+	6.24648i	−0.0712247	+	0.495378i
$160$	1.80928	−	2.08802i	0.143036	−	0.165073i
$161$	6.35170			0.500584
$162$	−14.2651	−	31.2362i	−1.12077	−	2.45415i
$163$	19.2102	−	5.64063i	1.50466	−	0.441808i	0.577474	−	0.816409i	$-0.304038\pi$
$163$	19.2102	−	5.64063i	1.50466	−	0.441808i	0.927186	+	0.374600i	$0.122220\pi$
$164$	−7.96020	−	2.33733i	−0.621587	−	0.182514i
$165$	−13.9302	+	27.3997i	−1.08446	+	2.13306i
$166$	−12.0617	+	3.54163i	−0.936167	+	0.274884i
$167$	−18.0183	+	11.5797i	−1.39430	+	0.896060i	−0.999740	−	0.0228110i	$-0.992738\pi$
$167$	−18.0183	+	11.5797i	−1.39430	+	0.896060i	−0.394557	+	0.918871i	$0.629102\pi$
$168$	−2.15914	+	4.72786i	−0.166581	+	0.364762i
$169$	0.208759	+	1.45195i	0.0160584	+	0.111688i
$170$	7.28334	+	2.13858i	0.558607	+	0.164022i
$171$	32.4068	+	20.8266i	2.47821	+	1.59265i
$172$	−6.30319	+	4.05081i	−0.480613	+	0.308872i
$173$	−0.913068	−	6.35053i	−0.0694193	−	0.482822i	−0.994641	−	0.103394i	$-0.967030\pi$
$173$	−0.913068	−	6.35053i	−0.0694193	−	0.482822i	0.925221	−	0.379428i	$-0.123879\pi$
$174$	−3.03397	+	21.1017i	−0.230005	+	1.59972i
$175$	−1.69501	−	3.71155i	−0.128130	−	0.280567i
$176$	2.71247	+	1.90854i	0.204460	+	0.143862i
$177$	13.8216	−	30.2651i	1.03890	−	2.27486i
$178$	5.82201	+	3.74158i	0.436378	+	0.280443i
$179$	1.86541	−	12.9742i	0.139428	−	0.969740i	−0.793216	−	0.608941i	$-0.791595\pi$
$179$	1.86541	−	12.9742i	0.139428	−	0.969740i	0.932643	−	0.360799i	$-0.117496\pi$
$180$	9.47105	−	20.7387i	0.705930	−	1.54577i
$181$	−0.00635402	+	0.0139134i	−0.000472291	+	0.00103417i	−0.909868	−	0.414898i	$-0.863817\pi$
$181$	−0.00635402	+	0.0139134i	−0.000472291	+	0.00103417i	0.909396	+	0.415932i	$0.136545\pi$
$182$	−2.18595	+	4.78656i	−0.162033	+	0.354803i
$183$	−0.347344	+	0.760577i	−0.0256764	+	0.0562235i
$184$	−0.583386	+	4.05754i	−0.0430078	+	0.299126i
$185$	−6.02738	−	3.87356i	−0.443142	−	0.284790i
$186$	11.4884	−	25.1561i	0.842369	−	1.84453i
$187$	−1.67394	+	8.95724i	−0.122411	+	0.655018i
$188$	3.05516	+	6.68988i	0.222821	+	0.487909i
$189$	−3.88484	+	27.0197i	−0.282581	+	1.96539i
$190$	1.83551	+	12.7663i	0.133162	+	0.926162i
$191$	0.778012	−	0.499998i	0.0562950	−	0.0361786i	−0.512191	−	0.858872i	$-0.671166\pi$
$191$	0.778012	−	0.499998i	0.0562950	−	0.0361786i	0.568486	+	0.822693i	$0.307530\pi$
$192$	−2.82190	−	1.81353i	−0.203653	−	0.130880i
$193$	−10.1444	−	2.97866i	−0.730209	−	0.214409i	−0.104566	−	0.994518i	$-0.533345\pi$
$193$	−10.1444	−	2.97866i	−0.730209	−	0.214409i	−0.625643	+	0.780109i	$0.715163\pi$
$194$	−0.824646	−	5.73554i	−0.0592061	−	0.411788i
$195$	13.0746	−	28.6293i	0.936289	−	2.05019i
$196$	−3.86904	+	2.48648i	−0.276360	+	0.177606i
$197$	−0.248587	+	0.0729917i	−0.0177111	+	0.00520044i	−0.290576	−	0.956852i	$-0.593847\pi$
$197$	−0.248587	+	0.0729917i	−0.0177111	+	0.00520044i	0.272865	+	0.962052i	$0.412029\pi$
$198$	25.9137	+	8.80520i	1.84160	+	0.625758i
$199$	13.8658	+	4.07136i	0.982918	+	0.288611i	0.733428	−	0.679767i	$-0.237919\pi$
$199$	13.8658	+	4.07136i	0.982918	+	0.288611i	0.249490	+	0.968377i	$0.419737\pi$
$200$	2.52666	−	0.741895i	0.178662	−	0.0524599i
$201$	3.89352	+	8.52561i	0.274628	+	0.601350i
$202$	−12.4748			−0.877725
$203$	6.44881	−	7.44232i	0.452618	−	0.522349i
$204$	1.31159	−	9.12229i	0.0918294	−	0.638688i
$205$	−15.0103	−	17.3228i	−1.04836	−	1.20987i
$206$	6.08358	−	7.02082i	0.423863	−	0.489164i
$207$	4.81410	+	33.4828i	0.334603	+	2.32722i
$208$	−2.85693	−	1.83604i	−0.198093	−	0.127307i
$209$	−15.0254	+	3.73512i	−1.03933	+	0.258364i
$210$	−12.0804	+	7.76363i	−0.833629	+	0.535741i
$211$	−0.995207	−	1.14853i	−0.0685129	−	0.0790680i	0.720458	−	0.693498i	$-0.243931\pi$
$211$	−0.995207	−	1.14853i	−0.0685129	−	0.0790680i	−0.788971	+	0.614430i	$0.789386\pi$
$212$	1.23201	+	1.42181i	0.0846146	+	0.0976504i
$213$	−13.7228	−	8.81914i	−0.940274	−	0.604277i
$214$	1.59124	+	1.83638i	0.108775	+	0.125533i
$215$	−20.7010			−1.41179
$216$	−16.9037	−	4.96336i	−1.15015	−	0.337714i
$217$	−10.7466	+	6.90645i	−0.729530	+	0.468840i
$218$	7.16756	+	2.10459i	0.485448	+	0.142541i
$219$	1.14931	+	7.99359i	0.0776629	+	0.540157i
$220$	3.45367	+	8.48757i	0.232846	+	0.572232i
$221$	1.32787	−	9.23554i	0.0893222	−	0.621250i
$222$	−3.61361	+	7.91270i	−0.242530	+	0.531066i
$223$	−8.62898	−	5.54551i	−0.577840	−	0.371355i	0.218836	−	0.975762i	$-0.429774\pi$
$223$	−8.62898	−	5.54551i	−0.577840	−	0.371355i	−0.796676	+	0.604407i	$0.793410\pi$
$224$	0.643674	+	1.40945i	0.0430073	+	0.0941728i
$225$	18.2806	−	11.7482i	1.21871	−	0.783216i
$226$	−0.100022	−	0.695668i	−0.00665337	−	0.0462752i
$227$	−1.71247	+	0.502827i	−0.113661	+	0.0333738i	−0.338068	−	0.941122i	$-0.609773\pi$
$227$	−1.71247	+	0.502827i	−0.113661	+	0.0333738i	0.224408	+	0.974495i	$0.427955\pi$
$228$	15.0247	−	4.41165i	0.995036	−	0.292169i
$229$	6.87698	−	7.93645i	0.454443	−	0.524456i	−0.481576	−	0.876404i	$-0.659935\pi$
$229$	6.87698	−	7.93645i	0.454443	−	0.524456i	0.936019	+	0.351949i	$0.114481\pi$
$230$	−7.41672	+	8.55936i	−0.489044	+	0.564387i
$231$	−10.7324	−	13.4898i	−0.706140	−	0.887565i
$232$	4.16194	+	4.80313i	0.273245	+	0.315341i
$233$	−5.29786			−0.347074			−0.173537	−	0.984827i	$-0.555520\pi$
$233$	−5.29786			−0.347074			−0.173537	+	0.984827i	$0.555520\pi$
$234$	−26.8890	−	7.89531i	−1.75779	−	0.516133i
$235$	−2.89174	+	20.1125i	−0.188636	+	1.31200i
$236$	−4.12044	−	9.02251i	−0.268218	−	0.587316i
$237$	−34.2915	+	10.0689i	−2.22747	+	0.654044i
$238$	−2.78782	+	3.21732i	−0.180708	+	0.208548i
$239$	−3.09682			−0.200317			−0.100158	−	0.994971i	$-0.531935\pi$
$239$	−3.09682			−0.200317			−0.100158	+	0.994971i	$0.531935\pi$
$240$	−3.84994	−	8.43019i	−0.248513	−	0.544167i
$241$	−12.0273			−0.774748			−0.387374	−	0.921923i	$-0.626618\pi$
$241$	−12.0273			−0.774748			−0.387374	+	0.921923i	$0.626618\pi$
$242$	−9.71962	+	5.15063i	−0.624801	+	0.331095i
$243$	−62.3363			−3.99887
$244$	0.103549	+	0.226740i	0.00662903	+	0.0145155i
$245$	−12.7067			−0.811802
$246$	−18.2241	+	21.0317i	−1.16193	+	1.34093i
$247$	15.2113	−	4.46643i	0.967869	−	0.284192i
$248$	−3.42487	−	7.49942i	−0.217480	−	0.476214i
$249$	−6.00110	+	41.7386i	−0.380304	+	2.64507i
$250$	−6.27388	−	1.84218i	−0.396795	−	0.116510i
$251$	−9.76662			−0.616463			−0.308232	−	0.951311i	$-0.599737\pi$
$251$	−9.76662			−0.616463			−0.308232	+	0.951311i	$0.599737\pi$
$252$	8.37321	+	9.66320i	0.527462	+	0.608724i
$253$	−11.1191	−	7.82361i	−0.699054	−	0.491866i
$254$	10.0543	−	11.6032i	0.630860	−	0.728052i
$255$	16.6745	−	19.2434i	1.04420	−	1.20507i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	−14.2366	+	4.18024i	−0.888054	+	0.260756i	−0.693776	−	0.720191i	$-0.744054\pi$
$257$	−14.2366	+	4.18024i	−0.888054	+	0.260756i	−0.194277	+	0.980947i	$0.562236\pi$
$258$	3.57683	+	24.8774i	0.222684	+	1.54880i
$259$	3.38030	−	2.17239i	0.210042	−	0.134986i
$260$	−3.89774	−	8.53486i	−0.241727	−	0.529309i
$261$	44.1197	+	28.3540i	2.73094	+	1.75507i
$262$	4.18338	−	9.16033i	0.258450	−	0.565927i
$263$	0.585911	−	4.07510i	0.0361288	−	0.251282i	−0.963751	−	0.266805i	$-0.914032\pi$
$263$	0.585911	−	4.07510i	0.0361288	−	0.251282i	0.999880	+	0.0155229i	$0.00494128\pi$
$264$	9.60320	−	5.61698i	0.591036	−	0.345701i
$265$	0.739727	+	5.14491i	0.0454410	+	0.316049i
$266$	−6.94026	−	2.03784i	−0.425534	−	0.124948i
$267$	19.5293	−	12.5507i	1.19518	−	0.768093i
$268$	2.68094	+	0.787195i	0.163764	+	0.0480856i
$269$	23.4406			1.42920			0.714599	−	0.699535i	$-0.246609\pi$
$269$	23.4406			1.42920			0.714599	+	0.699535i	$0.246609\pi$
$270$	−31.8746	−	36.7853i	−1.93983	−	2.23868i
$271$	17.7649	+	11.4168i	1.07914	+	0.693521i	0.954359	−	0.298663i	$-0.0965406\pi$
$271$	17.7649	+	11.4168i	1.07914	+	0.693521i	0.124782	+	0.992184i	$0.460177\pi$
$272$	−1.79921	−	2.07639i	−0.109093	−	0.125900i
$273$	11.5590	+	13.3398i	0.699584	+	0.807363i
$274$	15.8264	−	10.1710i	0.956105	−	0.614452i
$275$	−1.60440	+	8.58514i	−0.0967492	+	0.517703i
$276$	11.5677	+	7.43412i	0.696295	+	0.447482i
$277$	0.00770609	+	0.0535971i	0.000463014	+	0.00322034i	0.990052	−	0.140704i	$-0.0449367\pi$
$277$	0.00770609	+	0.0535971i	0.000463014	+	0.00322034i	−0.989589	+	0.143925i	$0.954028\pi$
$278$	5.49661	−	6.34343i	0.329665	−	0.380454i
$279$	−44.5523	−	51.4161i	−2.66728	−	3.07820i
$280$	−0.609244	+	4.23738i	−0.0364093	+	0.253232i
$281$	15.6911	−	18.1085i	0.936055	−	1.08026i	−0.0605692	−	0.998164i	$-0.519292\pi$
$281$	15.6911	−	18.1085i	0.936055	−	1.08026i	0.996624	−	0.0821009i	$-0.0261630\pi$
$282$	24.6699			1.46907
$283$	8.12609	+	17.7937i	0.483046	+	1.05772i	0.981615	+	0.190873i	$0.0611318\pi$
$283$	8.12609	+	17.7937i	0.483046	+	1.05772i	−0.498569	+	0.866850i	$0.666141\pi$
$284$	−4.66600	+	1.37006i	−0.276876	+	0.0812981i
$285$	41.5110	+	12.1887i	2.45890	+	0.721998i
$286$	9.72243	−	5.68672i	0.574899	−	0.336263i
$287$	12.3341	−	3.62162i	0.728060	−	0.213778i
$288$	−6.94202	+	4.46136i	−0.409062	+	0.262888i
$289$	−3.92627	+	8.59733i	−0.230957	+	0.505725i
$290$	2.49893	+	17.3804i	0.146742	+	1.02061i
$291$	−18.6498	−	5.47607i	−1.09327	−	0.321013i
$292$	2.02534	+	1.30161i	0.118524	+	0.0761707i
$293$	−3.73674	+	2.40146i	−0.218303	+	0.140295i	−0.645222	−	0.763995i	$-0.723235\pi$
$293$	−3.73674	+	2.40146i	−0.218303	+	0.140295i	0.426919	+	0.904290i	$0.359599\pi$
$294$	2.19554	+	15.2703i	0.128046	+	0.890582i
$295$	3.90004	−	27.1254i	0.227069	−	1.57930i
$296$	1.07728	+	2.35890i	0.0626153	+	0.137108i
$297$	40.0817	−	42.5148i	2.32578	−	2.46696i
$298$	−6.62757	+	14.5124i	−0.383925	+	0.840679i
$299$	11.7113	+	7.52642i	0.677284	+	0.435264i
$300$	1.25710	−	8.74333i	0.0725788	−	0.504796i
$301$	4.82280	−	10.5605i	0.277982	−	0.608695i
$302$	5.08640	−	11.1377i	0.292689	−	0.640900i
$303$	−17.3833	+	38.0640i	−0.998642	+	2.18672i
$304$	1.93924	−	4.24635i	0.111223	−	0.243545i
$305$	−0.0980099	+	0.681674i	−0.00561203	+	0.0390325i
$306$	−19.0729	−	12.2574i	−1.09033	−	0.700711i
$307$	10.5635	−	23.1309i	0.602893	−	1.32015i	−0.324438	−	0.945907i	$-0.605175\pi$
$307$	10.5635	−	23.1309i	0.602893	−	1.32015i	0.927330	−	0.374244i	$-0.122098\pi$
$308$	−5.13450	−	0.215522i	−0.292565	−	0.0122805i
$309$	−12.9451	−	28.3459i	−0.736424	−	1.61254i
$310$	3.24167	−	22.5463i	0.184115	−	1.28055i
$311$	0.740146	+	5.14783i	0.0419698	+	0.291906i	0.999987	+	0.00519402i	$0.00165331\pi$
$311$	0.740146	+	5.14783i	0.0419698	+	0.291906i	−0.958017	+	0.286712i	$0.907438\pi$
$312$	−9.58330	+	6.15881i	−0.542548	+	0.348674i
$313$	−18.5401	−	11.9150i	−1.04795	−	0.673476i	−0.101009	−	0.994886i	$-0.532207\pi$
$313$	−18.5401	−	11.9150i	−1.04795	−	0.673476i	−0.946940	+	0.321410i	$0.895843\pi$
$314$	18.3101	+	5.37633i	1.03330	+	0.303404i
$315$	5.02748	+	34.9669i	0.283266	+	1.97016i
$316$	−4.42600	+	9.69159i	−0.248982	+	0.545195i
$317$	6.96811	−	4.47814i	0.391368	−	0.251517i	−0.330127	−	0.943937i	$-0.607092\pi$
$317$	6.96811	−	4.47814i	0.391368	−	0.251517i	0.721495	+	0.692419i	$0.243455\pi$
$318$	6.05509	−	1.77793i	0.339553	−	0.0997016i
$319$	−20.4561	+	5.08512i	−1.14532	+	0.284712i
$320$	−2.65093	−	0.778384i	−0.148192	−	0.0435130i
$321$	7.82063	−	2.29635i	0.436505	−	0.128169i
$322$	−2.63859	−	5.77771i	−0.147043	−	0.321979i
$323$	12.8257			0.713642
$324$	−22.4875	+	25.9520i	−1.24931	+	1.44178i
$325$	1.27271	−	8.85188i	0.0705972	−	0.491014i
$326$	−13.1111	−	15.1310i	−0.726157	−	0.838030i
$327$	16.4094	−	18.9375i	0.907443	−	1.04725i
$328$	1.18068	+	8.21181i	0.0651922	+	0.453422i
$329$	−9.58657	−	6.16091i	−0.528525	−	0.339662i
$330$	30.7104	+	1.28908i	1.69055	+	0.0709616i
$331$	−16.1983	+	10.4100i	−0.890338	+	0.572186i	−0.903910	−	0.427722i	$-0.859316\pi$
$331$	−16.1983	+	10.4100i	−0.890338	+	0.572186i	0.0135719	+	0.999908i	$0.495680\pi$
$332$	8.23218	+	9.50044i	0.451799	+	0.521404i
$333$	14.0137	+	16.1727i	0.767945	+	0.886256i
$334$	18.0183	+	11.5797i	0.985917	+	0.633610i
$335$	5.05535	+	5.83418i	0.276203	+	0.318756i
$336$	5.19755			0.283550
$337$	−1.29308	−	0.379684i	−0.0704388	−	0.0206827i	0.246323	−	0.969188i	$-0.420777\pi$
$337$	−1.29308	−	0.379684i	−0.0704388	−	0.0206827i	−0.316762	+	0.948505i	$0.602596\pi$
$338$	1.23402	−	0.793055i	0.0671217	−	0.0431365i
$339$	−2.26205	−	0.664197i	−0.122858	−	0.0360743i
$340$	−1.08029	−	7.51356i	−0.0585868	−	0.407480i
$341$	27.3197	+	1.14676i	1.47945	+	0.0621003i
$342$	5.48225	−	38.1299i	0.296446	−	2.06183i
$343$	7.46606	−	16.3484i	0.403130	−	0.882731i
$344$	6.30319	+	4.05081i	0.339845	+	0.218405i
$345$	15.7819	+	34.5576i	0.849671	+	1.86052i
$346$	−5.39734	+	3.46866i	−0.290163	+	0.186476i
$347$	−1.71186	−	11.9063i	−0.0918976	−	0.639162i	−0.982760	−	0.184888i	$-0.940808\pi$
$347$	−1.71186	−	11.9063i	−0.0918976	−	0.639162i	0.890862	−	0.454274i	$-0.150101\pi$
$348$	20.4552	−	6.00618i	1.09651	−	0.321965i
$349$	−1.43056	+	0.420051i	−0.0765763	+	0.0224848i	−0.319796	−	0.947486i	$-0.603614\pi$
$349$	−1.43056	+	0.420051i	−0.0765763	+	0.0224848i	0.243220	+	0.969971i	$0.421796\pi$
$350$	−2.67201	+	3.08366i	−0.142825	+	0.164829i
$351$	−39.1797	+	45.2158i	−2.09126	+	2.41344i
$352$	0.609268	−	3.26018i	0.0324741	−	0.173768i
$353$	19.3967	+	22.3850i	1.03238	+	1.19144i	0.981249	+	0.192744i	$0.0617385\pi$
$353$	19.3967	+	22.3850i	1.03238	+	1.19144i	0.0511354	+	0.998692i	$0.483716\pi$
$354$	−33.2718			−1.76838
$355$	−12.8914	−	3.78527i	−0.684206	−	0.200901i
$356$	0.984909	−	6.85019i	0.0522001	−	0.363060i
$357$	5.93216	+	12.9896i	0.313963	+	0.687484i
$358$	−12.5767	+	3.69285i	−0.664699	+	0.195173i
$359$	18.3599	−	21.1885i	0.968999	−	1.11828i	−0.0239465	−	0.999713i	$-0.507623\pi$
$359$	18.3599	−	21.1885i	0.968999	−	1.11828i	0.992946	−	0.118571i	$-0.0378314\pi$
$360$	−22.7990			−1.20161
$361$	1.15989	+	2.53980i	0.0610467	+	0.133674i
$362$	0.0152956			0.000803919
$363$	2.17199	+	36.8344i	0.114000	+	1.93331i
$364$	5.26208			0.275808
$365$	2.76318	+	6.05053i	0.144632	+	0.316699i
$366$	0.836137			0.0437056
$367$	8.07128	−	9.31476i	0.421318	−	0.486226i	−0.504920	−	0.863166i	$-0.668478\pi$
$367$	8.07128	−	9.31476i	0.421318	−	0.486226i	0.926238	+	0.376940i	$0.123024\pi$
$368$	3.93322	−	1.15490i	0.205033	−	0.0602032i
$369$	28.4396	+	62.2740i	1.48051	+	3.24186i
$370$	−1.01965	+	7.09183i	−0.0530091	+	0.368687i
$371$	−2.79698	−	0.821268i	−0.145212	−	0.0426381i
$372$	−27.6552			−1.43386
$373$	1.83449	+	2.11711i	0.0949860	+	0.109620i	0.801252	−	0.598326i	$-0.204167\pi$
$373$	1.83449	+	2.11711i	0.0949860	+	0.109620i	−0.706266	+	0.707946i	$0.749622\pi$
$374$	8.84317	−	2.19830i	0.457269	−	0.113671i
$375$	−14.3634	+	16.5763i	−0.741725	+	0.855996i
$376$	4.81616	−	5.55815i	0.248375	−	0.286640i
$377$	20.7091	−	6.08075i	1.06657	−	0.313175i
$378$	26.1918	−	7.69060i	1.34716	−	0.395562i
$379$	−1.86174	−	12.9487i	−0.0956309	−	0.665128i	−0.980096	−	0.198522i	$-0.936386\pi$
$379$	−1.86174	−	12.9487i	−0.0956309	−	0.665128i	0.884465	−	0.466606i	$-0.154523\pi$
$380$	10.8501	−	6.97293i	0.556598	−	0.357704i
$381$	−21.3943	−	46.8470i	−1.09606	−	2.40004i
$382$	−0.778012	−	0.499998i	−0.0398065	−	0.0255821i
$383$	2.69760	−	5.90692i	0.137841	−	0.301830i	−0.828105	−	0.560573i	$-0.810581\pi$
$383$	2.69760	−	5.90692i	0.137841	−	0.301830i	0.965946	+	0.258743i	$0.0833083\pi$
$384$	−0.477381	+	3.32026i	−0.0243612	+	0.169436i
$385$	−11.6120	−	8.17037i	−0.591800	−	0.416401i
$386$	1.50465	+	10.4650i	0.0765845	+	0.532657i
$387$	59.3245	+	17.4192i	3.01563	+	0.885470i
$388$	−4.87466	+	3.13275i	−0.247473	+	0.159041i
$389$	19.7385	+	5.79575i	1.00078	+	0.293856i	0.740777	−	0.671751i	$-0.234457\pi$
$389$	19.7385	+	5.79575i	1.00078	+	0.293856i	0.260006	+	0.965607i	$0.416276\pi$
$390$	−31.4735			−1.59372
$391$	7.37543	+	8.51170i	0.372991	+	0.430455i
$392$	3.86904	+	2.48648i	0.195416	+	0.125586i
$393$	−22.1212	−	25.5293i	−1.11587	−	1.28778i
$394$	0.169662	+	0.195801i	0.00854747	+	0.00986430i
$395$	−24.7636	+	15.9146i	−1.24599	+	0.800749i
$396$	−2.75543	−	27.2297i	−0.138466	−	1.36834i
$397$	−10.8311	−	6.96074i	−0.543599	−	0.349350i	0.239846	−	0.970811i	$-0.422903\pi$
$397$	−10.8311	−	6.96074i	−0.543599	−	0.349350i	−0.783445	+	0.621461i	$0.786539\pi$
$398$	−2.05661	−	14.3040i	−0.103089	−	0.716997i
$399$	−15.8890	+	18.3369i	−0.795446	+	0.917994i
$400$	−1.72446	−	1.99014i	−0.0862232	−	0.0995069i
$401$	2.27613	−	15.8308i	0.113665	−	0.790554i	−0.850638	−	0.525752i	$-0.823784\pi$
$401$	2.27613	−	15.8308i	0.113665	−	0.790554i	0.964303	−	0.264803i	$-0.0853068\pi$
$402$	6.13775	−	7.08334i	0.306123	−	0.353285i
$403$	−27.9985			−1.39471
$404$	5.18223	+	11.3475i	0.257825	+	0.564559i
$405$	−91.0315	+	26.7293i	−4.52339	+	1.32819i
$406$	−9.44871	−	2.77439i	−0.468932	−	0.137691i
$407$	−8.59327	−	0.360706i	−0.425953	−	0.0178795i
$408$	−8.84278	+	2.59647i	−0.437783	+	0.128545i
$409$	−15.5823	+	10.0141i	−0.770494	+	0.495167i	−0.865867	−	0.500275i	$-0.833232\pi$
$409$	−15.5823	+	10.0141i	−0.770494	+	0.495167i	0.0953722	+	0.995442i	$0.469596\pi$
$410$	−9.52185	+	20.8499i	−0.470251	+	1.02971i
$411$	−8.98088	−	62.4634i	−0.442994	−	3.08109i
$412$	−8.91357	−	2.61726i	−0.439140	−	0.128943i
$413$	12.9292	+	8.30911i	0.636206	+	0.408865i
$414$	28.4572	−	18.2883i	1.39859	−	0.898822i
$415$	4.94280	+	34.3779i	0.242632	+	1.68755i
$416$	−0.483308	+	3.36148i	−0.0236961	+	0.164810i
$417$	−11.6962	−	25.6110i	−0.572763	−	1.25418i
$418$	9.63935	+	12.1159i	0.471476	+	0.592610i
$419$	12.4633	−	27.2908i	0.608871	−	1.33324i	−0.314473	−	0.949267i	$-0.601828\pi$
$419$	12.4633	−	27.2908i	0.608871	−	1.33324i	0.923344	−	0.383975i	$-0.125445\pi$
$420$	12.0804	+	7.76363i	0.589465	+	0.378826i
$421$	−2.29826	+	15.9847i	−0.112010	+	0.779047i	0.853950	+	0.520355i	$0.174201\pi$
$421$	−2.29826	+	15.9847i	−0.112010	+	0.779047i	−0.965960	+	0.258692i	$0.916709\pi$
$422$	−0.631316	+	1.38239i	−0.0307320	+	0.0672936i
$423$	25.2112	−	55.2048i	1.22581	−	2.68415i
$424$	0.781531	−	1.71131i	0.0379545	−	0.0831088i
$425$	3.00552	−	6.58117i	0.145789	−	0.319234i
$426$	−2.32149	+	16.1463i	−0.112477	+	0.782293i
$427$	−0.324918	−	0.208812i	−0.0157239	−	0.0101051i
$428$	1.00941	−	2.21030i	0.0487917	−	0.106839i
$429$	−3.80381	−	37.5900i	−0.183650	−	1.81486i
$430$	8.59949	+	18.8302i	0.414704	+	0.908075i
$431$	3.03517	−	21.1100i	0.146199	−	1.01683i	−0.776170	−	0.630524i	$-0.782840\pi$
$431$	3.03517	−	21.1100i	0.146199	−	1.01683i	0.922369	−	0.386311i	$-0.126251\pi$
$432$	2.50720	+	17.4380i	0.120628	+	0.838985i
$433$	2.42427	−	1.55798i	0.116503	−	0.0748718i	−0.481092	−	0.876670i	$-0.659760\pi$
$433$	2.42427	−	1.55798i	0.116503	−	0.0748718i	0.597595	+	0.801798i	$0.296123\pi$
$434$	10.7466	+	6.90645i	0.515855	+	0.331520i
$435$	56.5145	+	16.5942i	2.70967	+	0.795629i
$436$	−1.06311	−	7.39412i	−0.0509139	−	0.354114i
$437$	−7.94947	+	17.4069i	−0.380275	+	0.832685i
$438$	6.79379	−	4.36610i	0.324620	−	0.208621i
$439$	12.8306	−	3.76740i	0.612370	−	0.179808i	0.0391823	−	0.999232i	$-0.487525\pi$
$439$	12.8306	−	3.76740i	0.612370	−	0.179808i	0.573188	+	0.819424i	$0.305706\pi$
$440$	6.28586	−	6.66743i	0.299666	−	0.317857i
$441$	36.4147	+	10.6923i	1.73403	+	0.509158i
$442$	−8.95256	+	2.62871i	−0.425830	+	0.125035i
$443$	7.76562	+	17.0043i	0.368956	+	0.807900i	0.999496	+	0.0317436i	$0.0101060\pi$
$443$	7.76562	+	17.0043i	0.368956	+	0.807900i	−0.630540	+	0.776156i	$0.717167\pi$
$444$	8.69880			0.412827
$445$	12.5214	−	14.4504i	0.593570	−	0.685016i
$446$	−1.45977	+	10.1529i	−0.0691219	+	0.480753i
$447$	35.0458	+	40.4450i	1.65761	+	1.91298i
$448$	1.01469	−	1.17101i	0.0479395	−	0.0553252i
$449$	−0.528856	−	3.67827i	−0.0249583	−	0.173588i	0.973530	−	0.228561i	$-0.0734020\pi$
$449$	−0.528856	−	3.67827i	−0.0249583	−	0.173588i	−0.998488	+	0.0549724i	$0.982493\pi$
$450$	−18.2806	−	11.7482i	−0.861757	−	0.553818i
$451$	−26.0527	−	8.85243i	−1.22677	−	0.416845i
$452$	−0.591252	+	0.379974i	−0.0278101	+	0.0178725i
$453$	−26.8962	−	31.0399i	−1.26370	−	1.45838i
$454$	1.16877	+	1.34884i	0.0548532	+	0.0633040i
$455$	12.2304	+	7.86001i	0.573371	+	0.368483i
$456$	−10.2545	−	11.8343i	−0.480210	−	0.554192i
$457$	−27.3644			−1.28005			−0.640026	−	0.768353i	$-0.721076\pi$
$457$	−27.3644			−1.28005			−0.640026	+	0.768353i	$0.721076\pi$
$458$	−10.0761	−	2.95860i	−0.470823	−	0.138246i
$459$	−40.7191	+	26.1686i	−1.90060	+	1.22144i
$460$	10.8669	+	3.19080i	0.506671	+	0.148772i
$461$	−3.17435	−	22.0781i	−0.147844	−	1.02828i	−0.919739	−	0.392529i	$-0.871600\pi$
$461$	−3.17435	−	22.0781i	−0.147844	−	1.02828i	0.771895	−	0.635750i	$-0.219309\pi$
$462$	−7.81238	+	15.3664i	−0.363465	+	0.714910i
$463$	3.37601	−	23.4807i	0.156897	−	1.09124i	−0.747412	−	0.664361i	$-0.768704\pi$
$463$	3.37601	−	23.4807i	0.156897	−	1.09124i	0.904309	−	0.426879i	$-0.140387\pi$
$464$	2.64015	−	5.78113i	0.122566	−	0.268382i
$465$	−64.2778	−	41.3088i	−2.98081	−	1.91565i
$466$	2.20081	+	4.81910i	0.101951	+	0.223241i
$467$	−18.8574	+	12.1189i	−0.872618	+	0.560797i	−0.898552	−	0.438866i	$-0.855380\pi$
$467$	−18.8574	+	12.1189i	−0.872618	+	0.560797i	0.0259345	+	0.999664i	$0.491744\pi$
$468$	3.98825	+	27.7389i	0.184357	+	1.28223i
$469$	−4.15404	+	1.21974i	−0.191816	+	0.0563222i
$470$	19.4963	−	5.72462i	0.899295	−	0.264057i
$471$	41.9192	−	48.3773i	1.93153	−	2.22911i
$472$	−6.49547	+	7.49617i	−0.298978	+	0.345039i
$473$	−21.4504	+	12.5465i	−0.986288	+	0.576887i
$474$	23.4042	+	27.0098i	1.07499	+	1.24060i
$475$	12.2929			0.564038
$476$	4.08468	+	1.19937i	0.187221	+	0.0549730i
$477$	2.20939	−	15.3667i	0.101161	−	0.703592i
$478$	1.28647	+	2.81697i	0.0588417	+	0.128845i
$479$	30.5328	−	8.96524i	1.39508	−	0.409632i	0.504088	−	0.863652i	$-0.331829\pi$
$479$	30.5328	−	8.96524i	1.39508	−	0.409632i	0.890992	+	0.454020i	$0.150010\pi$
$480$	−6.06905	+	7.00406i	−0.277013	+	0.319690i
$481$	8.80679			0.401555
$482$	4.99633	+	10.9404i	0.227577	+	0.498323i
$483$	−21.3061			−0.969463
$484$	8.72286	+	6.70163i	0.396493	+	0.304619i
$485$	−16.0094			−0.726948
$486$	25.8954	+	56.7031i	1.17464	+	2.57210i
$487$	−20.5709			−0.932156			−0.466078	−	0.884744i	$-0.654333\pi$
$487$	−20.5709			−0.932156			−0.466078	+	0.884744i	$0.654333\pi$
$488$	0.163234	−	0.188383i	0.00738927	−	0.00852768i
$489$	−64.4388	+	18.9209i	−2.91402	+	0.855634i
$490$	5.27856	+	11.5584i	0.238461	+	0.522157i
$491$	−1.32511	+	9.21632i	−0.0598012	+	0.415927i	0.937828	+	0.347102i	$0.112834\pi$
$491$	−1.32511	+	9.21632i	−0.0598012	+	0.415927i	−0.997629	+	0.0688251i	$0.978075\pi$
$492$	26.7017	+	7.84032i	1.20381	+	0.353469i
$493$	17.4614			0.786421
$494$	−10.3818	−	11.9812i	−0.467099	−	0.539061i
$495$	34.2689	−	67.4046i	1.54027	−	3.02961i
$496$	−5.39897	+	6.23074i	−0.242421	+	0.279769i
$497$	4.93441	−	5.69462i	0.221339	−	0.255438i
$498$	40.4597	−	11.8800i	1.81304	−	0.532357i
$499$	−4.31142	+	1.26595i	−0.193006	+	0.0566715i	−0.376807	−	0.926292i	$-0.622978\pi$
$499$	−4.31142	+	1.26595i	−0.193006	+	0.0566715i	0.183801	+	0.982963i	$0.441160\pi$
$500$	0.930561	+	6.47219i	0.0416160	+	0.289445i
$501$	60.4405	−	38.8428i	2.70028	−	1.73537i
$502$	4.05720	+	8.88403i	0.181082	+	0.396514i
$503$	−27.2759	−	17.5292i	−1.21617	−	0.781588i	−0.234493	−	0.972118i	$-0.575343\pi$
$503$	−27.2759	−	17.5292i	−1.21617	−	0.781588i	−0.981681	+	0.190530i	$0.938979\pi$
$504$	5.31160	−	11.6308i	0.236597	−	0.518076i
$505$	−4.90503	+	34.1152i	−0.218271	+	1.51811i
$506$	−2.49755	+	13.3644i	−0.111030	+	0.594118i
$507$	−0.700260	−	4.87041i	−0.0310996	−	0.216303i
$508$	−14.7314	−	4.32552i	−0.653599	−	0.191914i
$509$	−9.16446	+	5.88964i	−0.406208	+	0.261054i	−0.727752	−	0.685841i	$-0.759435\pi$
$509$	−9.16446	+	5.88964i	−0.406208	+	0.261054i	0.321544	+	0.946895i	$0.395798\pi$
$510$	−24.4312	−	7.17366i	−1.08183	−	0.317655i
$511$	−3.73039			−0.165023
$512$	0.654861	+	0.755750i	0.0289410	+	0.0333997i
$513$	−69.1856	−	44.4629i	−3.05462	−	1.96308i
$514$	9.71657	+	11.2135i	0.428579	+	0.494607i
$515$	−16.8080	−	19.3975i	−0.740649	−	0.854754i
$516$	21.1434	−	13.5880i	0.930786	−	0.598180i
$517$	9.19339	+	22.5932i	0.404325	+	0.993650i
$518$	−3.38030	−	2.17239i	−0.148522	−	0.0954492i
$519$	3.06279	+	21.3022i	0.134442	+	0.935063i
$520$	−6.14440	+	7.09101i	−0.269450	+	0.310962i
$521$	23.1355	+	26.6998i	1.01359	+	1.16974i	0.985420	+	0.170137i	$0.0544211\pi$
$521$	23.1355	+	26.6998i	1.01359	+	1.16974i	0.0281656	+	0.999603i	$0.491033\pi$
$522$	7.46373	−	51.9114i	0.326678	−	2.27210i
$523$	−18.0758	+	20.8606i	−0.790399	+	0.912170i	−0.997814	−	0.0660835i	$-0.978950\pi$
$523$	−18.0758	+	20.8606i	−0.790399	+	0.912170i	0.207415	+	0.978253i	$0.433495\pi$
$524$	−10.0704			−0.439926
$525$	5.68573	+	12.4500i	0.248146	+	0.543363i
$526$	−3.95024	+	1.15990i	−0.172239	+	0.0505738i
$527$	−21.7338	−	6.38162i	−0.946740	−	0.277988i
$528$	−9.09870	−	6.40200i	−0.395970	−	0.278611i
$529$	5.94503	−	1.74562i	0.258480	−	0.0758965i
$530$	4.37268	−	2.81015i	0.189937	−	0.122065i
$531$	−34.0019	+	74.4537i	−1.47556	+	3.23102i
$532$	1.02940	+	7.15963i	0.0446301	+	0.310409i
$533$	27.0332	+	7.93766i	1.17094	+	0.343818i
$534$	−19.5293	−	12.5507i	−0.845117	−	0.543124i
$535$	5.64767	−	3.62954i	0.244170	−	0.156919i
$536$	−0.397645	−	2.76568i	−0.0171756	−	0.119459i
$537$	−6.25734	+	43.5208i	−0.270024	+	1.87806i
$538$	−9.73757	−	21.3223i	−0.419816	−	0.919270i
$539$	−13.1667	+	7.70130i	−0.567130	+	0.331719i
$540$	−20.2199	+	44.2753i	−0.870124	+	1.90531i
$541$	5.94487	+	3.82054i	0.255590	+	0.164258i	0.662161	−	0.749361i	$-0.269639\pi$
$541$	5.94487	+	3.82054i	0.255590	+	0.164258i	−0.406571	+	0.913619i	$0.633276\pi$
$542$	3.00529	−	20.9022i	0.129088	−	0.897827i
$543$	0.0213139	−	0.0466710i	0.000914668	−	0.00200284i
$544$	−1.14134	+	2.49918i	−0.0489345	+	0.107152i
$545$	8.57371	−	18.7738i	0.367257	−	0.804181i
$546$	7.33254	−	16.0560i	0.313804	−	0.687134i
$547$	2.81626	−	19.5875i	0.120414	−	0.837500i	−0.836673	−	0.547702i	$-0.815503\pi$
$547$	2.81626	−	19.5875i	0.120414	−	0.837500i	0.957088	−	0.289798i	$-0.0935882\pi$
$548$	−15.8264	−	10.1710i	−0.676069	−	0.434483i
$549$	0.854484	−	1.87106i	0.0364685	−	0.0798548i
$550$	8.47581	−	2.10698i	0.361410	−	0.0898419i
$551$	12.3248	+	26.9875i	0.525053	+	1.14970i
$552$	1.95691	−	13.6106i	0.0832917	−	0.579306i
$553$	−2.34944	−	16.3407i	−0.0999081	−	0.694876i
$554$	0.0455524	−	0.0292747i	0.00193533	−	0.00124376i
$555$	20.2182	+	12.9935i	0.858216	+	0.551542i
$556$	−8.05356	−	2.36474i	−0.341547	−	0.100287i
$557$	1.79489	+	12.4837i	0.0760519	+	0.528953i	0.991860	+	0.127336i	$0.0406426\pi$
$557$	1.79489	+	12.4837i	0.0760519	+	0.528953i	−0.915808	+	0.401617i	$0.868448\pi$
$558$	−28.2620	+	61.8852i	−1.19643	+	2.61981i
$559$	21.4059	−	13.7567i	0.905373	−	0.581848i
$560$	4.10755	−	1.20609i	0.173576	−	0.0509664i
$561$	5.61507	−	30.0461i	0.237068	−	1.26855i
$562$	−22.9904	−	6.75060i	−0.969793	−	0.284757i
$563$	27.0876	−	7.95363i	1.14160	−	0.335205i	0.344346	−	0.938843i	$-0.388101\pi$
$563$	27.0876	−	7.95363i	1.14160	−	0.335205i	0.797259	+	0.603637i	$0.206283\pi$
$564$	−10.2482	−	22.4405i	−0.431529	−	0.944916i
$565$	−1.94179			−0.0816918
$566$	12.8100	−	14.7835i	0.538444	−	0.621397i
$567$	7.57229	−	52.6664i	0.318006	−	2.21178i
$568$	3.18458	+	3.67520i	0.133622	+	0.154208i
$569$	−26.5371	+	30.6254i	−1.11249	+	1.28388i	−0.157413	+	0.987533i	$0.550315\pi$
$569$	−26.5371	+	30.6254i	−1.11249	+	1.28388i	−0.955079	+	0.296351i	$0.904230\pi$
$570$	−6.15704	−	42.8231i	−0.257890	−	1.79366i
$571$	−22.0834	−	14.1922i	−0.924163	−	0.593924i	−0.0103006	−	0.999947i	$-0.503279\pi$
$571$	−22.0834	−	14.1922i	−0.924163	−	0.593924i	−0.913863	+	0.406023i	$0.866915\pi$
$572$	−9.21166	−	6.48148i	−0.385159	−	0.271004i
$573$	−2.60976	+	1.67719i	−0.109024	+	0.0700657i
$574$	−8.41812	−	9.71503i	−0.351366	−	0.405497i
$575$	7.06904	+	8.15811i	0.294799	+	0.340217i
$576$	6.94202	+	4.46136i	0.289251	+	0.185890i
$577$	−0.158661	−	0.183105i	−0.00660515	−	0.00762275i	0.752437	−	0.658664i	$-0.228878\pi$
$577$	−0.158661	−	0.183105i	−0.00660515	−	0.00762275i	−0.759043	+	0.651041i	$0.774333\pi$
$578$	9.45144			0.393128
$579$	34.0283	+	9.99162i	1.41417	+	0.415238i
$580$	14.7717	−	9.49320i	0.613362	−	0.394184i
$581$	−18.6892	−	5.48765i	−0.775360	−	0.227666i
$582$	2.76619	+	19.2393i	0.114662	+	0.797494i
$583$	3.88474	+	4.88283i	0.160890	+	0.202226i
$584$	0.342626	−	2.38302i	0.0141780	−	0.0986100i
$585$	−32.1641	+	70.4296i	−1.32982	+	2.91190i
$586$	3.73674	+	2.40146i	0.154363	+	0.0992033i
$587$	17.8339	+	39.0508i	0.736085	+	1.61180i	0.789890	+	0.613249i	$0.210138\pi$
$587$	17.8339	+	39.0508i	0.736085	+	1.61180i	−0.0538051	+	0.998551i	$0.517135\pi$
$588$	12.9783	−	8.34065i	0.535216	−	0.343962i
$589$	−5.47724	−	38.0951i	−0.225686	−	1.56968i
$590$	−26.2942	+	7.72068i	−1.08252	+	0.317856i
$591$	0.833860	−	0.244843i	0.0343004	−	0.0100715i
$592$	1.69822	−	1.95985i	0.0697963	−	0.0805492i
$593$	−16.7325	+	19.3103i	−0.687121	+	0.792979i	−0.986952	−	0.161013i	$-0.948524\pi$
$593$	−16.7325	+	19.3103i	−0.687121	+	0.792979i	0.299832	+	0.953992i	$0.403069\pi$
$594$	−55.3234	−	18.7983i	−2.26995	−	0.771305i
$595$	7.70233	+	8.88896i	0.315765	+	0.364412i
$596$	15.9541			0.653506
$597$	−46.5113	−	13.6570i	−1.90358	−	0.558942i
$598$	1.98121	−	13.7796i	0.0810176	−	0.563490i
$599$	0.351305	+	0.769250i	0.0143539	+	0.0314307i	0.916673	−	0.399638i	$-0.130864\pi$
$599$	0.351305	+	0.769250i	0.0143539	+	0.0314307i	−0.902319	+	0.431068i	$0.858137\pi$
$600$	−8.47543	+	2.48861i	−0.346008	+	0.101597i
$601$	−14.2315	+	16.4240i	−0.580515	+	0.669950i	−0.967715	−	0.252046i	$-0.918897\pi$
$601$	−14.2315	+	16.4240i	−0.580515	+	0.669950i	0.387200	+	0.921996i	$0.373442\pi$
$602$	−11.6096			−0.473172
$603$	−9.57825	−	20.9734i	−0.390057	−	0.854105i
$604$	−12.2441			−0.498207
$605$	10.2639	+	28.6057i	0.417286	+	1.16299i
$606$	41.8455			1.69986
$607$	19.7887	+	43.3312i	0.803198	+	1.75876i	0.634243	+	0.773133i	$0.281312\pi$
$607$	19.7887	+	43.3312i	0.803198	+	1.75876i	0.168954	+	0.985624i	$0.445961\pi$
$608$	−4.66820			−0.189321
$609$	−21.6319	+	24.9645i	−0.876568	+	1.01161i
$610$	0.660787	−	0.194025i	0.0267545	−	0.00785582i
$611$	−10.3755	−	22.7191i	−0.419747	−	0.919117i
$612$	−3.22657	+	22.4413i	−0.130426	+	0.907135i
$613$	13.0785	+	3.84019i	0.528235	+	0.155104i	0.534966	−	0.844874i	$-0.320324\pi$
$613$	13.0785	+	3.84019i	0.528235	+	0.155104i	−0.00673125	+	0.999977i	$0.502143\pi$
$614$	−25.4289			−1.02623
$615$	50.3504	+	58.1075i	2.03032	+	2.34312i
$616$	1.93690	+	4.76004i	0.0780400	+	0.191787i
$617$	−23.2139	+	26.7903i	−0.934558	+	1.07854i	0.0621986	+	0.998064i	$0.480189\pi$
$617$	−23.2139	+	26.7903i	−0.934558	+	1.07854i	−0.996757	+	0.0804738i	$0.974357\pi$
$618$	−20.4067	+	23.5506i	−0.820880	+	0.947346i
$619$	27.1076	−	7.95951i	1.08955	−	0.319920i	0.312855	−	0.949801i	$-0.398715\pi$
$619$	27.1076	−	7.95951i	1.08955	−	0.319920i	0.776692	+	0.629881i	$0.216896\pi$
$620$	−21.8555	+	6.41736i	−0.877738	+	0.257727i
$621$	−10.2777	−	71.4829i	−0.412429	−	2.86851i
$622$	4.37516	−	2.81174i	0.175428	−	0.112741i
$623$	4.45463	+	9.75429i	0.178471	+	0.390797i
$624$	9.58330	+	6.15881i	0.383639	+	0.246550i
$625$	−12.9743	+	28.4098i	−0.518973	+	1.13639i
$626$	−3.13643	+	21.8143i	−0.125357	+	0.871877i
$627$	50.4011	−	12.5291i	2.01283	−	0.500363i
$628$	−2.71581	−	18.8889i	−0.108373	−	0.753747i
$629$	6.83626	+	2.00731i	0.272579	+	0.0800365i
$630$	29.7185	−	19.0989i	1.18401	−	0.760919i
$631$	−40.5394	−	11.9035i	−1.61385	−	0.473869i	−0.654493	−	0.756068i	$-0.727118\pi$
$631$	−40.5394	−	11.9035i	−1.61385	−	0.473869i	−0.959356	+	0.282199i	$0.908936\pi$
$632$	10.6544			0.423810
$633$	3.33832	+	3.85263i	0.132686	+	0.153128i
$634$	−6.96811	−	4.47814i	−0.276739	−	0.177849i
$635$	−27.7784	−	32.0580i	−1.10235	−	1.27218i
$636$	−4.13264	−	4.76932i	−0.163870	−	0.189116i
$637$	13.1394	−	8.44420i	0.520603	−	0.334571i
$638$	13.1234	+	16.4951i	0.519559	+	0.653046i
$639$	33.7589	+	21.6955i	1.33548	+	0.858262i
$640$	0.393194	+	2.73473i	0.0155424	+	0.108100i
$641$	−6.33488	+	7.31084i	−0.250213	+	0.288761i	−0.866936	−	0.498419i	$-0.833914\pi$
$641$	−6.33488	+	7.31084i	−0.250213	+	0.288761i	0.616724	+	0.787180i	$0.288460\pi$
$642$	−5.33764	−	6.15996i	−0.210660	−	0.243114i
$643$	−4.59604	+	31.9661i	−0.181250	+	1.26062i	0.672562	+	0.740040i	$0.265194\pi$
$643$	−4.59604	+	31.9661i	−0.181250	+	1.26062i	−0.853812	+	0.520581i	$0.825715\pi$
$644$	−4.15948	+	4.80030i	−0.163906	+	0.189158i
$645$	69.4393			2.73417
$646$	−5.32800	−	11.6667i	−0.209627	−	0.459020i
$647$	−23.3656	+	6.86076i	−0.918596	+	0.269724i	−0.706655	−	0.707558i	$-0.749797\pi$
$647$	−23.3656	+	6.86076i	−0.918596	+	0.269724i	−0.211941	+	0.977282i	$0.567979\pi$
$648$	32.9484	+	9.67453i	1.29434	+	0.380052i
$649$	−12.3990	−	30.4711i	−0.486702	−	1.19609i
$650$	−8.58066	+	2.51951i	−0.336561	+	0.0988232i
$651$	36.0485	−	23.1670i	1.41285	−	0.907986i
$652$	−8.31712	+	18.2119i	−0.325723	+	0.713235i
$653$	−5.25474	−	36.5475i	−0.205634	−	1.43022i	−0.787191	−	0.616710i	$-0.788465\pi$
$653$	−5.25474	−	36.5475i	−0.205634	−	1.43022i	0.581557	−	0.813506i	$-0.302444\pi$
$654$	−24.0429	−	7.05962i	−0.940150	−	0.276053i
$655$	−23.4061	−	15.0422i	−0.914553	−	0.587747i
$656$	6.97926	−	4.48530i	0.272494	−	0.175121i
$657$	−2.82735	−	19.6647i	−0.110305	−	0.767191i
$658$	−1.62176	+	11.2796i	−0.0632228	+	0.439724i
$659$	−1.15380	−	2.52646i	−0.0449455	−	0.0984169i	0.885827	−	0.464015i	$-0.153592\pi$
$659$	−1.15380	−	2.52646i	−0.0449455	−	0.0984169i	−0.930773	+	0.365598i	$0.880864\pi$
$660$	−11.5850	−	28.4707i	−0.450945	−	1.10822i
$661$	4.49409	−	9.84069i	0.174800	−	0.382759i	−0.801872	−	0.597496i	$-0.796162\pi$
$661$	4.49409	−	9.84069i	0.174800	−	0.382759i	0.976672	+	0.214738i	$0.0688896\pi$
$662$	16.1983	+	10.4100i	0.629564	+	0.404596i
$663$	−4.45421	+	30.9797i	−0.172987	+	1.20315i
$664$	5.22213	−	11.4349i	0.202658	−	0.443759i
$665$	−8.30181	+	18.1784i	−0.321930	+	0.704929i
$666$	8.88967	−	19.4657i	0.344468	−	0.754279i
$667$	−10.8227	+	23.6984i	−0.419056	+	0.917605i
$668$	3.04815	−	21.2004i	0.117937	−	0.820267i
$669$	28.9451	+	18.6019i	1.11908	+	0.719189i
$670$	3.20689	−	7.02212i	0.123893	−	0.271288i
$671$	0.311592	+	0.765753i	0.0120289	+	0.0295616i
$672$	−2.15914	−	4.72786i	−0.0832907	−	0.182381i
$673$	−2.35967	+	16.4118i	−0.0909585	+	0.632630i	0.892439	+	0.451167i	$0.148992\pi$
$673$	−2.35967	+	16.4118i	−0.0909585	+	0.632630i	−0.983398	+	0.181463i	$0.941917\pi$
$674$	0.191794	+	1.33396i	0.00738763	+	0.0513821i
$675$	−39.0275	+	25.0815i	−1.50217	+	0.965386i
$676$	−1.23402	−	0.793055i	−0.0474622	−	0.0305021i
$677$	−16.0852	−	4.72304i	−0.618205	−	0.181521i	−0.0423895	−	0.999101i	$-0.513497\pi$
$677$	−16.0852	−	4.72304i	−0.618205	−	0.181521i	−0.575815	+	0.817580i	$0.695315\pi$
$678$	0.335514	+	2.33355i	0.0128853	+	0.0896194i
$679$	3.72978	−	8.16708i	0.143136	−	0.313424i
$680$	−6.38581	+	4.10391i	−0.244885	+	0.157378i
$681$	5.74431	−	1.68668i	0.220122	−	0.0646338i
$682$	−10.3059	−	25.3273i	−0.394633	−	0.969831i
$683$	−16.9287	−	4.97072i	−0.647759	−	0.190199i	−0.0586830	−	0.998277i	$-0.518690\pi$
$683$	−16.9287	−	4.97072i	−0.647759	−	0.190199i	−0.589076	+	0.808077i	$0.700508\pi$
$684$	−36.9616	+	10.8529i	−1.41326	+	0.414971i
$685$	−21.5920	−	47.2799i	−0.824989	−	1.80647i
$686$	−17.9725			−0.686195
$687$	−23.0681	+	26.6220i	−0.880104	+	1.01569i
$688$	1.06631	−	7.41635i	0.0406527	−	0.282746i
$689$	−4.18395	−	4.82854i	−0.159396	−	0.183953i
$690$	24.8787	−	28.7115i	0.947114	−	1.09303i
$691$	3.41142	+	23.7269i	0.129776	+	0.902614i	0.945836	+	0.324646i	$0.105245\pi$
$691$	3.41142	+	23.7269i	0.129776	+	0.902614i	−0.816059	+	0.577968i	$0.803846\pi$
$692$	5.39734	+	3.46866i	0.205176	+	0.131859i
$693$	26.4023	+	33.1857i	1.00294	+	1.26062i
$694$	−10.1192	+	6.50321i	−0.384119	+	0.246858i
$695$	−15.1863	−	17.5259i	−0.576050	−	0.664797i
$696$	−13.9608	−	16.1116i	−0.529183	−	0.610710i
$697$	19.1753	+	12.3232i	0.726315	+	0.466774i
$698$	0.976370	+	1.12679i	0.0369561	+	0.0426497i
$699$	17.7711			0.672166
$700$	3.91499	+	1.14955i	0.147973	+	0.0434487i
$701$	30.4742	−	19.5846i	1.15099	−	0.739699i	0.181158	−	0.983454i	$-0.442016\pi$
$701$	30.4742	−	19.5846i	1.15099	−	0.739699i	0.969837	+	0.243755i	$0.0783791\pi$
$702$	57.4056	+	16.8558i	2.16663	+	0.636181i
$703$	1.72284	+	11.9826i	0.0649781	+	0.451932i
$704$	−3.21867	+	0.800119i	−0.121308	+	0.0301556i
$705$	9.70006	−	67.4654i	0.365325	−	2.54089i
$706$	12.3044	−	26.9430i	0.463084	−	1.01401i
$707$	−16.2609	−	10.4503i	−0.611555	−	0.393022i
$708$	13.8216	+	30.2651i	0.519448	+	1.13743i
$709$	1.72801	−	1.11052i	0.0648967	−	0.0417066i	−0.507790	−	0.861481i	$-0.669537\pi$
$709$	1.72801	−	1.11052i	0.0648967	−	0.0417066i	0.572687	+	0.819774i	$0.305901\pi$
$710$	1.91210	+	13.2989i	0.0717597	+	0.499100i
$711$	84.3587	−	24.7700i	3.16370	−	0.928946i
$712$	−6.64030	+	1.94977i	−0.248856	+	0.0730707i
$713$	22.1318	−	25.5415i	0.828843	−	0.956536i
$714$	9.35147	−	10.7922i	0.349970	−	0.403887i
$715$	−11.7288	−	28.8242i	−0.438633	−	1.07796i
$716$	8.58369	+	9.90610i	0.320787	+	0.370208i
$717$	10.3880			0.387946
$718$	−26.9007	−	7.89876i	−1.00392	−	0.294779i
$719$	2.79772	−	19.4586i	0.104337	−	0.725682i	−0.868751	−	0.495249i	$-0.835077\pi$
$719$	2.79772	−	19.4586i	0.104337	−	0.725682i	0.973088	−	0.230433i	$-0.0740142\pi$
$720$	9.47105	+	20.7387i	0.352965	+	0.772886i
$721$	13.8113	−	4.05538i	0.514361	−	0.151030i
$722$	1.82845	−	2.11014i	0.0680478	−	0.0785313i
$723$	40.3445			1.50043
$724$	−0.00635402	−	0.0139134i	−0.000236145	−	0.000517086i
$725$	16.7360			0.621560
$726$	32.6035	−	17.2773i	1.21003	−	0.641220i
$727$	25.2513			0.936519			0.468260	−	0.883591i	$-0.344881\pi$
$727$	25.2513			0.936519			0.468260	+	0.883591i	$0.344881\pi$
$728$	−2.18595	−	4.78656i	−0.0810166	−	0.177402i
$729$	106.082			3.92898
$730$	4.35589	−	5.02696i	0.161219	−	0.186056i
$731$	19.7518	−	5.79966i	0.730547	−	0.214508i
$732$	−0.347344	−	0.760577i	−0.0128382	−	0.0281117i
$733$	−5.84664	+	40.6643i	−0.215951	+	1.50197i	0.536826	+	0.843693i	$0.319623\pi$
$733$	−5.84664	+	40.6643i	−0.215951	+	1.50197i	−0.752776	+	0.658277i	$0.771286\pi$
$734$	−11.8259	−	3.47241i	−0.436503	−	0.128169i
$735$	42.6234			1.57219
$736$	−2.68445	−	3.09802i	−0.0989501	−	0.114194i
$737$	8.77435	+	2.98144i	0.323207	+	0.109823i
$738$	44.8322	−	51.7391i	1.65030	−	1.90454i
$739$	−34.9541	+	40.3392i	−1.28581	+	1.48390i	−0.499140	+	0.866521i	$0.666351\pi$
$739$	−34.9541	+	40.3392i	−1.28581	+	1.48390i	−0.786667	+	0.617378i	$0.788195\pi$
$740$	6.87453	−	2.01855i	0.252713	−	0.0742032i
$741$	−51.0246	+	14.9822i	−1.87444	+	0.550384i
$742$	0.414857	+	2.88539i	0.0152299	+	0.105926i
$743$	−9.04131	+	5.81050i	−0.331693	+	0.213166i	−0.695877	−	0.718161i	$-0.744984\pi$
$743$	−9.04131	+	5.81050i	−0.331693	+	0.213166i	0.364184	+	0.931327i	$0.381348\pi$
$744$	11.4884	+	25.1561i	0.421185	+	0.922266i
$745$	37.0814	+	23.8308i	1.35856	+	0.873092i
$746$	1.16372	−	2.54819i	0.0426067	−	0.0932957i
$747$	14.7630	−	102.679i	0.540150	−	3.75683i
$748$	−5.67323	−	7.13082i	−0.207434	−	0.260729i
$749$	0.535821	+	3.72672i	0.0195785	+	0.136171i
$750$	21.0451	+	6.17940i	0.768459	+	0.225640i
$751$	15.0156	−	9.64996i	0.547928	−	0.352132i	−0.237204	−	0.971460i	$-0.576231\pi$
$751$	15.0156	−	9.64996i	0.547928	−	0.352132i	0.785133	+	0.619328i	$0.212595\pi$
$752$	−7.05658	−	2.07200i	−0.257327	−	0.0755580i
$753$	32.7611			1.19388
$754$	−14.1341	−	16.3117i	−0.514735	−	0.594035i
$755$	−28.4585	−	18.2892i	−1.03571	−	0.665611i
$756$	−17.8761	−	20.6301i	−0.650146	−	0.750309i
$757$	−4.78737	−	5.52491i	−0.174000	−	0.200806i	0.662051	−	0.749459i	$-0.269686\pi$
$757$	−4.78737	−	5.52491i	−0.174000	−	0.200806i	−0.836050	+	0.548653i	$0.815141\pi$
$758$	−11.0051	+	7.07256i	−0.399724	+	0.256887i
$759$	37.2980	+	26.2435i	1.35383	+	0.952579i
$760$	−10.8501	−	6.97293i	−0.393574	−	0.252935i
$761$	5.06224	+	35.2086i	0.183506	+	1.27631i	0.848392	+	0.529368i	$0.177571\pi$
$761$	5.06224	+	35.2086i	0.183506	+	1.27631i	−0.664886	+	0.746944i	$0.731520\pi$
$762$	−33.7260	+	38.9219i	−1.22176	+	1.40999i
$763$	7.57988	+	8.74765i	0.274410	+	0.316686i
$764$	−0.131616	+	0.915411i	−0.00476171	+	0.0331184i
$765$	−41.0201	+	47.3397i	−1.48309	+	1.71157i
$766$	−6.49375			−0.234629
$767$	13.9932	+	30.6409i	0.505266	+	1.10638i
$768$	3.21852	−	0.945043i	0.116138	−	0.0341013i
$769$	13.0147	+	3.82146i	0.469322	+	0.137806i	0.507838	−	0.861452i	$-0.330445\pi$
$769$	13.0147	+	3.82146i	0.469322	+	0.137806i	−0.0385157	+	0.999258i	$0.512263\pi$
$770$	−2.60825	+	13.9567i	−0.0939948	+	0.502965i
$771$	47.7552	−	14.0222i	1.71986	−	0.504997i
$772$	8.89428	−	5.71601i	0.320112	−	0.205724i
$773$	15.6593	−	34.2890i	0.563224	−	1.23329i	−0.387103	−	0.922037i	$-0.626524\pi$
$773$	15.6593	−	34.2890i	0.563224	−	1.23329i	0.950327	−	0.311253i	$-0.100749\pi$
$774$	−8.79918	−	61.1997i	−0.316280	−	2.19978i
$775$	−20.8310	−	6.11652i	−0.748270	−	0.219712i
$776$	4.87466	+	3.13275i	0.174990	+	0.112459i
$777$	−11.3389	+	7.28705i	−0.406780	+	0.261422i
$778$	−2.92768	−	20.3624i	−0.104962	−	0.730029i
$779$	−5.51166	+	38.3344i	−0.197476	+	1.37347i
$780$	13.0746	+	28.6293i	0.468145	+	1.02509i
$781$	−15.6523	+	3.89096i	−0.560084	+	0.139230i
$782$	4.67865	−	10.2448i	0.167308	−	0.366354i
$783$	−94.1917	−	60.5333i	−3.36614	−	2.16328i
$784$	0.654525	−	4.55232i	0.0233759	−	0.162583i
$785$	21.9022	−	47.9592i	0.781724	−	1.71174i
$786$	−14.0327	+	30.7274i	−0.500531	+	1.09601i
$787$	−2.95525	+	6.47110i	−0.105343	+	0.230670i	−0.954962	−	0.296727i	$-0.904105\pi$
$787$	−2.95525	+	6.47110i	−0.105343	+	0.230670i	0.849619	+	0.527397i	$0.176832\pi$
$788$	0.107626	−	0.235669i	0.00383403	−	0.00839536i
$789$	−1.96538	+	13.6695i	−0.0699694	+	0.486648i
$790$	24.7636	+	15.9146i	0.881048	+	0.566215i
$791$	0.452389	−	0.990593i	0.0160851	−	0.0352214i
$792$	−23.6244	+	13.8181i	−0.839455	+	0.491003i
$793$	−0.351656	−	0.770020i	−0.0124877	−	0.0273442i
$794$	−1.83230	+	12.7439i	−0.0650259	+	0.452265i
$795$	−2.48134	−	17.2581i	−0.0880040	−	0.612081i
$796$	−12.1571	+	7.81288i	−0.430896	+	0.276920i
$797$	−19.8720	−	12.7709i	−0.703901	−	0.452370i	0.139102	−	0.990278i	$-0.455578\pi$
$797$	−19.8720	−	12.7709i	−0.703901	−	0.452370i	−0.843003	+	0.537908i	$0.819215\pi$
$798$	23.2804	+	6.83574i	0.824117	+	0.241983i
$799$	−2.87564	−	20.0005i	−0.101733	−	0.707567i
$800$	−1.09392	+	2.39536i	−0.0386761	+	0.0846888i
$801$	−48.0432	+	30.8755i	−1.69752	+	1.09093i
$802$	−15.3458	+	4.50593i	−0.541878	+	0.159110i
$803$	6.53033	+	4.59485i	0.230450	+	0.162149i
$804$	−8.99294	−	2.64057i	−0.317157	−	0.0931256i
$805$	−16.8379	+	4.94407i	−0.593459	+	0.174255i
$806$	11.6310	+	25.4684i	0.409685	+	0.897085i
$807$	−78.6290			−2.76787
$808$	8.16927	−	9.42784i	0.287394	−	0.331670i
$809$	4.11164	−	28.5971i	0.144558	−	1.00542i	−0.780381	−	0.625305i	$-0.784975\pi$
$809$	4.11164	−	28.5971i	0.144558	−	1.00542i	0.924939	−	0.380117i	$-0.124116\pi$
$810$	62.1297	+	71.7014i	2.18301	+	2.51933i
$811$	−16.8538	+	19.4503i	−0.591816	+	0.682992i	−0.970102	−	0.242697i	$-0.921968\pi$
$811$	−16.8538	+	19.4503i	−0.591816	+	0.682992i	0.378286	+	0.925689i	$0.376513\pi$
$812$	1.40146	+	9.74737i	0.0491816	+	0.342066i
$813$	−59.5905	−	38.2965i	−2.08993	−	1.34312i
$814$	3.24166	+	7.96656i	0.113620	+	0.279228i
$815$	−46.5344	+	29.9059i	−1.63003	+	1.04756i
$816$	6.03526	+	6.96506i	0.211276	+	0.243826i
$817$	22.9051	+	26.4339i	0.801348	+	0.924804i
$818$	15.5823	+	10.0141i	0.544822	+	0.350136i
$819$	−28.4358	−	32.8166i	−0.993627	−	1.14671i
$820$	22.9213			0.800447
$821$	14.0467	+	4.12449i	0.490234	+	0.143946i	0.517501	−	0.855683i	$-0.326862\pi$
$821$	14.0467	+	4.12449i	0.490234	+	0.143946i	−0.0272672	+	0.999628i	$0.508681\pi$
$822$	−53.0879	+	34.1175i	−1.85165	+	1.18999i
$823$	4.33069	+	1.27160i	0.150958	+	0.0443254i	0.356339	−	0.934357i	$-0.384025\pi$
$823$	4.33069	+	1.27160i	0.150958	+	0.0443254i	−0.205380	+	0.978682i	$0.565843\pi$
$824$	1.32209	+	9.19532i	0.0460571	+	0.320334i
$825$	5.38181	−	28.7980i	0.187371	−	1.00262i
$826$	2.18724	−	15.2126i	0.0761037	−	0.529313i
$827$	−16.2662	+	35.6180i	−0.565631	+	1.23856i	0.383460	+	0.923557i	$0.374732\pi$
$827$	−16.2662	+	35.6180i	−0.565631	+	1.23856i	−0.949091	+	0.315002i	$0.897995\pi$
$828$	−28.4572	−	18.2883i	−0.988956	−	0.635563i
$829$	−10.2343	−	22.4100i	−0.355452	−	0.778331i	−0.999906	−	0.0136882i	$-0.995643\pi$
$829$	−10.2343	−	22.4100i	−0.355452	−	0.778331i	0.644455	−	0.764643i	$-0.277084\pi$
$830$	29.2179	−	18.7772i	1.01417	−	0.651767i
$831$	−0.0258493	−	0.179786i	−0.000896703	−	0.00623671i
$832$	3.25848	−	0.956776i	0.112968	−	0.0331703i
$833$	12.1241	−	3.55996i	0.420076	−	0.123345i
$834$	−18.4378	+	21.2784i	−0.638450	+	0.736811i
$835$	38.7519	−	44.7220i	1.34106	−	1.54767i
$836$	7.01672	−	13.8014i	0.242678	−	0.477332i
$837$	95.1152	+	109.769i	3.28766	+	3.79416i
$838$	−30.0020			−1.03640
$839$	17.5203	+	5.14442i	0.604868	+	0.177605i	0.569805	−	0.821780i	$-0.307019\pi$
$839$	17.5203	+	5.14442i	0.604868	+	0.177605i	0.0350628	+	0.999385i	$0.488837\pi$
$840$	2.04365	−	14.2139i	0.0705125	−	0.490425i
$841$	4.73233	+	10.3624i	0.163184	+	0.357323i
$842$	15.4949	−	4.54972i	0.533991	−	0.156794i
$843$	−52.6343	+	60.7433i	−1.81282	+	2.09211i
$844$	1.51972			0.0523110
$845$	−1.68358	−	3.68652i	−0.0579169	−	0.126820i
$846$	−60.6892			−2.08654
$847$	−16.9842	−	1.42836i	−0.583586	−	0.0490789i
$848$	−1.88133			−0.0646050
$849$	−27.2582	−	59.6870i	−0.935497	−	2.04845i
$850$	−7.23498			−0.248158
$851$	−6.96145	+	8.03394i	−0.238635	+	0.275400i
$852$	15.6516	−	4.59573i	0.536215	−	0.157447i
$853$	8.37758	+	18.3443i	0.286843	+	0.628098i	0.997121	−	0.0758226i	$-0.0241583\pi$
$853$	8.37758	+	18.3443i	0.286843	+	0.628098i	−0.710279	+	0.703921i	$0.751431\pi$
$854$	−0.0549663	+	0.382299i	−0.00188091	+	0.0130820i
$855$	−102.119	−	29.9849i	−3.49240	−	1.02546i
$856$	−2.42988			−0.0830517
$857$	−31.8484	−	36.7550i	−1.08792	−	1.25553i	−0.964757	−	0.263141i	$-0.915242\pi$
$857$	−31.8484	−	36.7550i	−1.08792	−	1.25553i	−0.123163	−	0.992386i	$-0.539304\pi$
$858$	−32.6129	+	19.0755i	−1.11339	+	0.651228i
$859$	28.8918	−	33.3429i	0.985774	−	1.13764i	−0.00470595	−	0.999989i	$-0.501498\pi$
$859$	28.8918	−	33.3429i	0.985774	−	1.13764i	0.990480	−	0.137655i	$-0.0439566\pi$
$860$	13.5562	−	15.6447i	0.462264	−	0.533481i
$861$	−41.3735	+	12.1484i	−1.41001	+	0.414015i
$862$	−20.4632	+	6.00854i	−0.696980	+	0.204652i
$863$	−2.69846	−	18.7682i	−0.0918565	−	0.638876i	−0.982788	−	0.184738i	$-0.940856\pi$
$863$	−2.69846	−	18.7682i	−0.0918565	−	0.638876i	0.890931	−	0.454138i	$-0.150053\pi$
$864$	14.8206	−	9.52462i	0.504207	−	0.324034i
$865$	7.36363	+	16.1241i	0.250371	+	0.548236i
$866$	−2.42427	−	1.55798i	−0.0823799	−	0.0529424i
$867$	13.1703	−	28.8389i	0.447286	−	0.979420i
$868$	1.81801	−	12.6445i	0.0617073	−	0.429183i
$869$	−16.0145	+	31.4995i	−0.543255	+	1.06855i
$870$	−8.38240	−	58.3009i	−0.284190	−	1.97659i
$871$	−9.10459	−	2.67335i	−0.308497	−	0.0905830i
$872$	−6.28429	+	4.03867i	−0.212813	+	0.136767i
$873$	45.8794	+	13.4714i	1.55278	+	0.455938i
$874$	19.1362			0.647292
$875$	−6.63480	−	7.65696i	−0.224297	−	0.258853i
$876$	−6.79379	−	4.36610i	−0.229541	−	0.147517i
$877$	11.0498	+	12.7522i	0.373126	+	0.430610i	0.910995	−	0.412418i	$-0.135316\pi$
$877$	11.0498	+	12.7522i	0.373126	+	0.430610i	−0.537869	+	0.843029i	$0.680770\pi$
$878$	−8.75696	−	10.1061i	−0.295533	−	0.341063i
$879$	12.5345	−	8.05545i	0.422779	−	0.271703i
$880$	−8.67615	−	2.94807i	−0.292473	−	0.0993793i
$881$	8.17449	+	5.25343i	0.275406	+	0.176992i	0.671052	−	0.741411i	$-0.265843\pi$
$881$	8.17449	+	5.25343i	0.275406	+	0.176992i	−0.395646	+	0.918403i	$0.629479\pi$
$882$	−5.40114	−	37.5657i	−0.181866	−	1.26490i
$883$	21.9550	−	25.3374i	0.738844	−	0.852672i	−0.254593	−	0.967048i	$-0.581942\pi$
$883$	21.9550	−	25.3374i	0.738844	−	0.852672i	0.993437	+	0.114376i	$0.0364870\pi$
$884$	6.11019	+	7.05153i	0.205508	+	0.237169i
$885$	−13.0823	+	90.9893i	−0.439756	+	3.05857i
$886$	12.2417	−	14.1277i	0.411269	−	0.474630i
$887$	−3.95548			−0.132812			−0.0664059	−	0.997793i	$-0.521153\pi$
$887$	−3.95548			−0.132812			−0.0664059	+	0.997793i	$0.521153\pi$
$888$	−3.61361	−	7.91270i	−0.121265	−	0.265533i
$889$	22.8258	−	6.70227i	0.765554	−	0.224787i
$890$	−18.3461	−	5.38691i	−0.614964	−	0.180570i
$891$	−78.1269	+	82.8695i	−2.61735	+	2.77623i
$892$	9.84180	−	2.88981i	0.329528	−	0.0967581i
$893$	28.8821	−	18.5614i	0.966503	−	0.621134i
$894$	22.2315	−	48.6803i	0.743534	−	1.62811i
$895$	5.15385	+	35.8458i	0.172274	+	1.19819i
$896$	−1.48671	−	0.436537i	−0.0496674	−	0.0145837i
$897$	−39.2845	−	25.2466i	−1.31167	−	0.842960i
$898$	−3.12618	+	2.00907i	−0.104322	+	0.0670437i
$899$	−7.45691	−	51.8639i	−0.248702	−	1.72976i
$900$	−3.09253	+	21.5090i	−0.103084	+	0.716968i
$901$	−2.14723	−	4.70177i	−0.0715346	−	0.156639i
$902$	2.77021	+	27.3758i	0.0922381	+	0.911513i
$903$	−16.1776	+	35.4240i	−0.538357	+	1.17884i
$904$	0.591252	+	0.379974i	0.0196647	+	0.0126378i
$905$	0.00601414	−	0.0418293i	0.000199917	−	0.00139045i
$906$	−17.0618	+	37.3601i	−0.566840	+	1.24121i
$907$	−11.1579	+	24.4324i	−0.370493	+	0.811265i	0.628936	+	0.777457i	$0.283491\pi$
$907$	−11.1579	+	24.4324i	−0.370493	+	0.811265i	−0.999428	+	0.0338082i	$0.989236\pi$
$908$	0.741418	−	1.62348i	0.0246048	−	0.0538771i
$909$	42.7637	−	93.6394i	1.41838	−	3.10582i
$910$	2.06902	−	14.3903i	0.0685873	−	0.477035i
$911$	−31.2535	−	20.0854i	−1.03547	−	0.665458i	−0.0916101	−	0.995795i	$-0.529201\pi$
$911$	−31.2535	−	20.0854i	−1.03547	−	0.665458i	−0.943863	+	0.330337i	$0.892838\pi$
$912$	−6.50499	+	14.2439i	−0.215402	+	0.471664i
$913$	25.9576	+	32.6267i	0.859070	+	1.07979i
$914$	11.3676	+	24.8915i	0.376006	+	0.823338i
$915$	0.328764	−	2.28661i	0.0108686	−	0.0755929i
$916$	1.49451	+	10.3945i	0.0493800	+	0.343445i
$917$	13.1267	−	8.43603i	0.433483	−	0.278582i
$918$	40.7191	+	26.1686i	1.34393	+	0.863691i
$919$	−26.4342	−	7.76179i	−0.871985	−	0.256038i	−0.185025	−	0.982734i	$-0.559237\pi$
$919$	−26.4342	−	7.76179i	−0.871985	−	0.256038i	−0.686959	+	0.726696i	$0.741055\pi$
$920$	−1.61181	−	11.2104i	−0.0531397	−	0.369595i
$921$	−35.4343	+	77.5903i	−1.16760	+	2.55669i
$922$	−18.7643	+	12.0591i	−0.617968	+	0.397144i
$923$	15.8459	−	4.65279i	0.521575	−	0.153148i
$924$	17.2232	+	0.722948i	0.566600	+	0.0237833i
$925$	6.55227	+	1.92392i	0.215437	+	0.0632581i
$926$	−22.7612	+	6.68330i	−0.747980	+	0.219627i
$927$	31.8457	+	69.7324i	1.04595	+	2.29031i
$928$	−6.35546			−0.208628
$929$	16.6249	−	19.1862i	0.545446	−	0.629478i	−0.414370	−	0.910109i	$-0.635998\pi$
$929$	16.6249	−	19.1862i	0.545446	−	0.629478i	0.959816	+	0.280630i	$0.0905435\pi$
$930$	−10.8739	+	75.6294i	−0.356568	+	2.47999i
$931$	14.0597	+	16.2257i	0.460787	+	0.531776i
$932$	3.46936	−	4.00386i	0.113643	−	0.131151i
$933$	−2.48274	−	17.2679i	−0.0812814	−	0.565324i
$934$	18.8574	+	12.1189i	0.617034	+	0.396544i
$935$	−2.53466	−	25.0480i	−0.0828923	−	0.819157i
$936$	23.5754	−	15.1510i	0.770586	−	0.495226i
$937$	−27.7205	−	31.9911i	−0.905588	−	1.04510i	−0.998776	−	0.0494561i	$-0.984251\pi$
$937$	−27.7205	−	31.9911i	−0.905588	−	1.04510i	0.0931879	−	0.995649i	$-0.470294\pi$
$938$	2.83516	+	3.27195i	0.0925714	+	0.106833i
$939$	62.1909	+	39.9677i	2.02952	+	1.30430i
$940$	−13.3063	−	15.3563i	−0.434005	−	0.500868i
$941$	−27.3577			−0.891836			−0.445918	−	0.895074i	$-0.647123\pi$
$941$	−27.3577			−0.891836			−0.445918	+	0.895074i	$0.647123\pi$
$942$	−61.4194	−	18.0344i	−2.00115	−	0.587591i
$943$	−28.6098	+	18.3864i	−0.931664	+	0.598744i
$944$	9.51708	+	2.79447i	0.309754	+	0.0909521i
$945$	−10.7332	−	74.6512i	−0.349152	−	2.42840i
$946$	20.3235	+	14.2999i	0.660773	+	0.464931i
$947$	2.40855	−	16.7519i	0.0782675	−	0.544362i	−0.912530	−	0.409010i	$-0.865874\pi$
$947$	2.40855	−	16.7519i	0.0782675	−	0.544362i	0.990798	−	0.135353i	$-0.0432167\pi$
$948$	14.8466	−	32.5095i	0.482194	−	1.05586i
$949$	−6.87814	−	4.42031i	−0.223274	−	0.143489i
$950$	−5.10666	−	11.1820i	−0.165682	−	0.362793i
$951$	−23.3738	+	15.0215i	−0.757949	+	0.487104i
$952$	−0.605851	−	4.21379i	−0.0196358	−	0.136570i
$953$	24.4803	−	7.18806i	0.792995	−	0.232844i	0.139945	−	0.990159i	$-0.455307\pi$
$953$	24.4803	−	7.18806i	0.792995	−	0.232844i	0.653050	+	0.757315i	$0.273489\pi$
$954$	−14.8958	+	4.37381i	−0.482270	+	0.141607i
$955$	−1.67327	+	1.93105i	−0.0541456	+	0.0624874i
$956$	2.02799	−	2.34042i	0.0655898	−	0.0756947i
$957$	68.6179	−	17.0575i	2.21810	−	0.551392i
$958$	−20.8389	−	24.0493i	−0.673273	−	0.776999i
$959$	29.1500			0.941302
$960$	8.89229	+	2.61101i	0.286997	+	0.0842700i
$961$	−5.26153	+	36.5948i	−0.169727	+	1.18048i
$962$	−3.65847	−	8.01094i	−0.117954	−	0.258283i
$963$	−19.2392	+	5.64913i	−0.619973	+	0.182041i
$964$	7.87622	−	9.08965i	0.253676	−	0.292758i
$965$	29.2106			0.940324
$966$	8.85089	+	19.3808i	0.284773	+	0.623565i
$967$	58.5012			1.88127			0.940636	−	0.339416i	$-0.110229\pi$
$967$	58.5012			1.88127			0.940636	+	0.339416i	$0.110229\pi$
$968$	2.47241	−	10.7185i	0.0794662	−	0.344507i
$969$	−43.0226			−1.38208
$970$	6.65053	+	14.5626i	0.213536	+	0.467578i
$971$	3.98355			0.127838			0.0639190	−	0.997955i	$-0.479640\pi$
$971$	3.98355			0.127838			0.0639190	+	0.997955i	$0.479640\pi$
$972$	40.8216	−	47.1106i	1.30935	−	1.51107i
$973$	12.4788	−	3.66410i	0.400051	−	0.117466i
$974$	8.54545	+	18.7119i	0.273814	+	0.599569i
$975$	−4.26917	+	29.6927i	−0.136723	+	0.950929i
$976$	−0.239169	−	0.0702263i	−0.00765561	−	0.00224789i
$977$	26.4501			0.846213			0.423107	−	0.906080i	$-0.360940\pi$
$977$	26.4501			0.846213			0.423107	+	0.906080i	$0.360940\pi$
$978$	43.9799	+	50.7555i	1.40632	+	1.62298i
$979$	4.21652	−	22.5625i	0.134761	−	0.721102i
$980$	8.32112	−	9.60309i	0.265809	−	0.306759i
$981$	−40.3680	+	46.5872i	−1.28885	+	1.48741i
$982$	8.93393	−	2.62324i	0.285093	−	0.0837109i
$983$	12.2496	−	3.59680i	0.390700	−	0.114720i	−0.0804814	−	0.996756i	$-0.525646\pi$
$983$	12.2496	−	3.59680i	0.390700	−	0.114720i	0.471182	+	0.882036i	$0.343828\pi$
$984$	−3.96047	−	27.5457i	−0.126255	−	0.878125i
$985$	0.602172	−	0.386992i	0.0191868	−	0.0123306i
$986$	−7.25372	−	15.8834i	−0.231006	−	0.505832i
$987$	32.1572	+	20.6662i	1.02357	+	0.657811i
$988$	−6.58575	+	14.4208i	−0.209521	+	0.458786i
$989$	−4.37109	+	30.4016i	−0.138993	+	0.966714i
$990$	−75.5492	−	3.17121i	−2.40111	−	0.100788i
$991$	−3.69872	−	25.7252i	−0.117494	−	0.817187i	−0.960300	−	0.278970i	$-0.910007\pi$
$991$	−3.69872	−	25.7252i	−0.117494	−	0.817187i	0.842806	−	0.538217i	$-0.180902\pi$
$992$	7.91050	+	2.32273i	0.251159	+	0.0737468i
$993$	54.3355	−	34.9193i	1.72429	−	1.10813i
$994$	−7.22983	−	2.12287i	−0.229316	−	0.0673334i
$995$	−39.9263			−1.26575
$996$	−27.6140	−	31.8683i	−0.874983	−	1.00978i
$997$	47.3718	+	30.4440i	1.50028	+	0.964172i	0.994856	+	0.101301i	$0.0323007\pi$
$997$	47.3718	+	30.4440i	1.50028	+	0.964172i	0.505425	+	0.862870i	$0.331336\pi$
$998$	2.94257	+	3.39591i	0.0931455	+	0.107496i
$999$	−29.9180	−	34.5272i	−0.946563	−	1.09239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.e.a.221.1	yes	50
121.23	even	11	inner	242.2.e.a.23.1	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
242.2.e.a.23.1	✓	50	121.23	even	11	inner
242.2.e.a.221.1	yes	50	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:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415415 - 0.909632i) q^{2} -3.35440 q^{3} +(-0.654861 + 0.755750i) q^{4} +(-2.65093 + 0.778384i) q^{5} +(1.39347 + 3.05127i) q^{6} +(0.220513 - 1.53370i) q^{7} +(0.959493 + 0.281733i) q^{8} +8.25199 q^{9} +(1.80928 + 2.08802i) q^{10} +(-2.27514 + 2.41325i) q^{11} +(2.19666 - 2.53509i) q^{12} +(2.22394 - 2.56656i) q^{13} +(-1.48671 + 0.436537i) q^{14} +(8.89229 - 2.61101i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(2.31131 - 1.48539i) q^{17} +(-3.42800 - 7.50628i) q^{18} +(3.92714 + 2.52382i) q^{19} +(1.14773 - 2.51318i) q^{20} +(-0.739689 + 5.14465i) q^{21} +(3.14029 + 1.06704i) q^{22} +(0.583386 + 4.05754i) q^{23} +(-3.21852 - 0.945043i) q^{24} +(2.21530 - 1.42369i) q^{25} +(-3.25848 - 0.956776i) q^{26} -17.6173 q^{27} +(1.01469 + 1.17101i) q^{28} +(5.34655 + 3.43602i) q^{29} +(-6.06905 - 7.00406i) q^{30} +(-5.39897 - 6.23074i) q^{31} +(-0.841254 + 0.540641i) q^{32} +(7.63172 - 8.09499i) q^{33} +(-2.31131 - 1.48539i) q^{34} +(0.609244 + 4.23738i) q^{35} +(-5.40391 + 6.23644i) q^{36} +(1.69822 + 1.95985i) q^{37} +(0.664355 - 4.62069i) q^{38} +(-7.45997 + 8.60927i) q^{39} -2.76285 q^{40} +(3.44639 + 7.54654i) q^{41} +(4.98701 - 1.46432i) q^{42} +(7.18911 + 2.11091i) q^{43} +(-0.333911 - 3.29977i) q^{44} +(-21.8755 + 6.42322i) q^{45} +(3.44852 - 2.21623i) q^{46} +(3.05516 - 6.68988i) q^{47} +(0.477381 + 3.32026i) q^{48} +(4.41284 + 1.29573i) q^{49} +(-2.21530 - 1.42369i) q^{50} +(-7.75307 + 4.98260i) q^{51} +(0.483308 + 3.36148i) q^{52} +(0.267741 - 1.86218i) q^{53} +(7.31848 + 16.0252i) q^{54} +(4.15280 - 8.16828i) q^{55} +(0.643674 - 1.40945i) q^{56} +(-13.1732 - 8.46590i) q^{57} +(0.904476 - 6.29077i) q^{58} +(-4.12044 + 9.02251i) q^{59} +(-3.84994 + 8.43019i) q^{60} +(0.103549 - 0.226740i) q^{61} +(-3.42487 + 7.49942i) q^{62} +(1.81967 - 12.6561i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-3.89774 + 8.53486i) q^{65} +(-10.5338 - 3.57927i) q^{66} +(-1.16072 - 2.54162i) q^{67} +(-0.391005 + 2.71950i) q^{68} +(-1.95691 - 13.6106i) q^{69} +(3.60137 - 2.31446i) q^{70} +(4.09100 + 2.62913i) q^{71} +(7.91773 + 2.32486i) q^{72} +(-0.342626 - 2.38302i) q^{73} +(1.07728 - 2.35890i) q^{74} +(-7.43099 + 4.77561i) q^{75} +(-4.47911 + 1.31518i) q^{76} +(3.19950 + 4.02153i) q^{77} +(10.9302 + 3.20941i) q^{78} +(10.2228 - 3.00169i) q^{79} +(1.14773 + 2.51318i) q^{80} +34.3394 q^{81} +(5.43289 - 6.26989i) q^{82} +(1.78902 - 12.4429i) q^{83} +(-3.40367 - 3.92805i) q^{84} +(-4.97093 + 5.73676i) q^{85} +(-1.06631 - 7.41635i) q^{86} +(-17.9345 - 11.5258i) q^{87} +(-2.86287 + 1.67451i) q^{88} +(-5.82201 + 3.74158i) q^{89} +(14.9302 + 17.2303i) q^{90} +(-3.44593 - 3.97681i) q^{91} +(-3.44852 - 2.21623i) q^{92} +(18.1103 + 20.9004i) q^{93} -7.35449 q^{94} +(-12.3751 - 3.63366i) q^{95} +(2.82190 - 1.81353i) q^{96} +(5.55980 + 1.63250i) q^{97} +(-0.654525 - 4.55232i) q^{98} +(-18.7744 + 19.9141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 5 q^{2} - 10 q^{3} - 5 q^{4} + q^{5} - q^{6} + 5 q^{8} + 40 q^{9} - q^{10} + 11 q^{11} + q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} - 5 q^{16} - 2 q^{17} + 4 q^{18} - q^{19} + q^{20} - 2 q^{21}+ \cdots - 22 q^{99}+O(q^{100}) \) 50 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 + q^5 - q^6 + 5 * q^8 + 40 * q^9 - q^10 + 11 * q^11 + q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 - 5 * q^16 - 2 * q^17 + 4 * q^18 - q^19 + q^20 - 2 * q^21 + 22 * q^22 - 31 * q^23 - q^24 - 2 * q^25 + q^26 - 106 * q^27 - 3 * q^29 - 13 * q^30 - 18 * q^31 + 5 * q^32 + 2 * q^34 - 4 * q^35 - 4 * q^36 - 17 * q^37 + 34 * q^38 - 103 * q^39 + 10 * q^40 - 6 * q^41 - 42 * q^42 - 5 * q^43 - 11 * q^44 - 39 * q^45 - 46 * q^46 - 7 * q^47 + q^48 + 43 * q^49 + 2 * q^50 + 25 * q^51 - q^52 + 25 * q^53 - 4 * q^54 + 22 * q^55 - 11 * q^56 - 41 * q^57 - 8 * q^58 - 30 * q^59 - 31 * q^60 - 40 * q^61 - 4 * q^62 + 45 * q^63 - 5 * q^64 - 43 * q^65 - 55 * q^66 + 64 * q^67 - 2 * q^68 + 8 * q^69 + 15 * q^70 - 5 * q^71 + 4 * q^72 - 34 * q^73 - 5 * q^74 + 11 * q^75 + 10 * q^76 - 22 * q^77 + 4 * q^78 + 47 * q^79 + q^80 + 18 * q^81 + 28 * q^82 - 9 * q^83 - 46 * q^84 + 100 * q^85 + 5 * q^86 - 87 * q^87 + 11 * q^88 - 3 * q^89 + 28 * q^90 + q^91 + 46 * q^92 + 47 * q^93 + 18 * q^94 - 129 * q^95 - q^96 + 3 * q^97 + 45 * q^98 - 22 * q^99

Introduction

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