LMFDB - Embedded newform 210.2.x.a.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(23,210)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("210.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.x (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	210.53
Dual form			210.2.x.a.107.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.46139 + 0.929705i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11774 + 0.717755i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(-1.05770 - 2.42513i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.27130 - 2.71732i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.46139 + 0.929705i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11774 + 0.717755i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(-1.05770 - 2.42513i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.27130 - 2.71732i) q^{9} +(-0.145187 - 2.23135i) q^{10} +(2.50087 + 1.44388i) q^{11} +(1.73045 - 0.0744552i) q^{12} +(-4.54633 - 4.54633i) q^{13} +(2.61625 - 0.393987i) q^{14} +(2.42754 - 3.01779i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.39193 + 0.372965i) q^{17} +(2.29569 + 1.93127i) q^{18} +(-1.42086 + 0.820335i) q^{19} +(2.19290 + 0.437276i) q^{20} +(3.80036 + 2.56071i) q^{21} +(-2.04195 + 2.04195i) q^{22} +(-4.76396 - 1.27650i) q^{23} +(-0.375955 + 1.69076i) q^{24} +(3.96965 - 3.04004i) q^{25} +(5.56810 - 3.21474i) q^{26} +(0.668446 + 5.15298i) q^{27} +(-0.296574 + 2.62908i) q^{28} -10.5746 q^{29} +(2.28667 + 3.12588i) q^{30} +(0.155334 - 0.269046i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-4.99712 + 0.215009i) q^{33} -1.44103i q^{34} +(3.98058 + 4.37664i) q^{35} +(-2.45963 + 1.71762i) q^{36} +(-2.82183 - 0.756107i) q^{37} +(-0.424637 - 1.58477i) q^{38} +(10.8707 + 2.41720i) q^{39} +(-0.989939 + 2.00500i) q^{40} -8.54006i q^{41} +(-3.45706 + 3.00811i) q^{42} +(6.09579 + 6.09579i) q^{43} +(-1.44388 - 2.50087i) q^{44} +(-0.741911 + 6.66705i) q^{45} +(2.46601 - 4.27125i) q^{46} +(-1.51442 + 5.65190i) q^{47} +(-1.53584 - 0.800745i) q^{48} +(-4.76255 + 5.13012i) q^{49} +(1.90903 + 4.62121i) q^{50} +(1.68739 - 1.83913i) q^{51} +(1.66407 + 6.21041i) q^{52} +(0.138948 + 0.518562i) q^{53} +(-5.15040 - 0.688020i) q^{54} +(-6.33255 - 1.26275i) q^{55} +(-2.46273 - 0.966923i) q^{56} +(1.31376 - 2.51981i) q^{57} +(2.73692 - 10.2143i) q^{58} +(-3.20862 + 5.55749i) q^{59} +(-3.61120 + 1.39972i) q^{60} +(0.348669 + 0.603912i) q^{61} +(0.219675 + 0.219675i) q^{62} +(-7.93450 - 0.208967i) q^{63} -1.00000i q^{64} +(12.8911 + 6.36480i) q^{65} +(1.08567 - 4.88250i) q^{66} +(-0.216388 - 0.807572i) q^{67} +(1.39193 + 0.372965i) q^{68} +(8.14875 - 2.56362i) q^{69} +(-5.25776 + 2.71219i) q^{70} -2.72315i q^{71} +(-1.02249 - 2.82038i) q^{72} +(0.180414 - 0.0483418i) q^{73} +(1.46069 - 2.52998i) q^{74} +(-2.97486 + 8.13328i) q^{75} +1.64067 q^{76} +(0.856433 - 7.59214i) q^{77} +(-5.14838 + 9.87467i) q^{78} +(8.11986 - 4.68800i) q^{79} +(-1.68046 - 1.47514i) q^{80} +(-5.76761 - 6.90903i) q^{81} +(8.24906 + 2.21033i) q^{82} +(2.26907 - 2.26907i) q^{83} +(-2.01086 - 4.11782i) q^{84} +(2.68004 - 1.78891i) q^{85} +(-7.46579 + 4.31038i) q^{86} +(15.4536 - 9.83128i) q^{87} +(2.78936 - 0.747407i) q^{88} +(-3.60206 - 6.23895i) q^{89} +(-6.24786 - 2.44219i) q^{90} +(-6.21682 + 15.8341i) q^{91} +(3.48746 + 3.48746i) q^{92} +(0.0231308 + 0.537594i) q^{93} +(-5.06736 - 2.92564i) q^{94} +(2.42022 - 2.75709i) q^{95} +(1.17097 - 1.27626i) q^{96} +(4.75522 - 4.75522i) q^{97} +(-3.72268 - 5.92804i) q^{98} +(7.10283 - 4.96006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) $ 64 * q + 8 * q^6 + 4 * q^7	$ 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) $ 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.46139	+	0.929705i	−0.843732	+	0.536765i
$3$	−1.46139	+	0.929705i	−0.843732	+	0.536765i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.11774	+	0.717755i	−0.947083	+	0.320990i
$5$	−2.11774	+	0.717755i	−0.947083	+	0.320990i
$6$	−0.519792	−	1.65222i	−0.212204	−	0.674514i
$7$	−1.05770	−	2.42513i	−0.399772	−	0.916614i
$7$	−1.05770	−	2.42513i	−0.399772	−	0.916614i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	1.27130	−	2.71732i	0.423766	−	0.905772i
$10$	−0.145187	−	2.23135i	−0.0459121	−	0.705615i
$11$	2.50087	+	1.44388i	0.754041	+	0.435346i	0.827152	−	0.561978i	$-0.189959\pi$
$11$	2.50087	+	1.44388i	0.754041	+	0.435346i	−0.0731108	+	0.997324i	$0.523293\pi$
$12$	1.73045	−	0.0744552i	0.499538	−	0.0214934i
$13$	−4.54633	−	4.54633i	−1.26093	−	1.26093i	−0.950645	−	0.310281i	$-0.899577\pi$
$13$	−4.54633	−	4.54633i	−1.26093	−	1.26093i	−0.310281	−	0.950645i	$-0.600423\pi$
$14$	2.61625	−	0.393987i	0.699223	−	0.105297i
$15$	2.42754	−	3.01779i	0.626787	−	0.779191i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.39193	+	0.372965i	−0.337592	+	0.0904574i	−0.423632	−	0.905834i	$-0.639245\pi$
$17$	−1.39193	+	0.372965i	−0.337592	+	0.0904574i	0.0860407	+	0.996292i	$0.472578\pi$
$18$	2.29569	+	1.93127i	0.541099	+	0.455205i
$19$	−1.42086	+	0.820335i	−0.325968	+	0.188198i	−0.654050	−	0.756452i	$-0.726931\pi$
$19$	−1.42086	+	0.820335i	−0.325968	+	0.188198i	0.328081	+	0.944649i	$0.393598\pi$
$20$	2.19290	+	0.437276i	0.490346	+	0.0977779i
$21$	3.80036	+	2.56071i	0.829307	+	0.558793i
$22$	−2.04195	+	2.04195i	−0.435346	+	0.435346i
$23$	−4.76396	−	1.27650i	−0.993354	−	0.266168i	−0.274695	−	0.961531i	$-0.588577\pi$
$23$	−4.76396	−	1.27650i	−0.993354	−	0.266168i	−0.718659	+	0.695363i	$0.755244\pi$
$24$	−0.375955	+	1.69076i	−0.0767415	+	0.345124i
$25$	3.96965	−	3.04004i	0.793931	−	0.608008i
$26$	5.56810	−	3.21474i	1.09199	−	0.630463i
$27$	0.668446	+	5.15298i	0.128642	+	0.991691i
$28$	−0.296574	+	2.62908i	−0.0560472	+	0.496849i
$29$	−10.5746			−1.96366			−0.981830	−	0.189765i	$-0.939227\pi$
$29$	−10.5746			−1.96366			−0.981830	+	0.189765i	$0.939227\pi$
$30$	2.28667	+	3.12588i	0.417487	+	0.570705i
$31$	0.155334	−	0.269046i	0.0278988	−	0.0483221i	−0.851739	−	0.523966i	$-0.824452\pi$
$31$	0.155334	−	0.269046i	0.0278988	−	0.0483221i	0.879638	+	0.475644i	$0.157785\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−4.99712	+	0.215009i	−0.869887	+	0.0374282i
$34$		−	1.44103i		−	0.247134i
$35$	3.98058	+	4.37664i	0.672841	+	0.739787i
$36$	−2.45963	+	1.71762i	−0.409939	+	0.286269i
$37$	−2.82183	−	0.756107i	−0.463906	−	0.124303i	0.0192930	−	0.999814i	$-0.493858\pi$
$37$	−2.82183	−	0.756107i	−0.463906	−	0.124303i	−0.483199	+	0.875511i	$0.660525\pi$
$38$	−0.424637	−	1.58477i	−0.0688852	−	0.257083i
$39$	10.8707	+	2.41720i	1.74070	+	0.387062i
$40$	−0.989939	+	2.00500i	−0.156523	+	0.317018i
$41$		−	8.54006i		−	1.33373i	−0.745177	−	0.666867i	$-0.767635\pi$
$41$		−	8.54006i		−	1.33373i	0.745177	−	0.666867i	$-0.232365\pi$
$42$	−3.45706	+	3.00811i	−0.533436	+	0.464161i
$43$	6.09579	+	6.09579i	0.929600	+	0.929600i	0.997680	−	0.0680801i	$-0.0216874\pi$
$43$	6.09579	+	6.09579i	0.929600	+	0.929600i	−0.0680801	+	0.997680i	$0.521687\pi$
$44$	−1.44388	−	2.50087i	−0.217673	−	0.377021i
$45$	−0.741911	+	6.66705i	−0.110598	+	0.993865i
$46$	2.46601	−	4.27125i	0.363593	−	0.629761i
$47$	−1.51442	+	5.65190i	−0.220901	+	0.824415i	0.763104	+	0.646276i	$0.223674\pi$
$47$	−1.51442	+	5.65190i	−0.220901	+	0.824415i	−0.984005	+	0.178139i	$0.942992\pi$
$48$	−1.53584	−	0.800745i	−0.221680	−	0.115578i
$49$	−4.76255	+	5.13012i	−0.680364	+	0.732874i
$50$	1.90903	+	4.62121i	0.269978	+	0.653538i
$51$	1.68739	−	1.83913i	0.236282	−	0.257529i
$52$	1.66407	+	6.21041i	0.230765	+	0.861228i
$53$	0.138948	+	0.518562i	0.0190860	+	0.0712300i	0.974812	−	0.223028i	$-0.0715942\pi$
$53$	0.138948	+	0.518562i	0.0190860	+	0.0712300i	−0.955726	+	0.294258i	$0.904927\pi$
$54$	−5.15040	−	0.688020i	−0.700881	−	0.0936277i
$55$	−6.33255	−	1.26275i	−0.853881	−	0.170269i
$56$	−2.46273	−	0.966923i	−0.329097	−	0.129211i
$57$	1.31376	−	2.51981i	0.174012	−	0.333757i
$58$	2.73692	−	10.2143i	0.359375	−	1.34120i
$59$	−3.20862	+	5.55749i	−0.417726	+	0.723523i	−0.995710	−	0.0925249i	$-0.970506\pi$
$59$	−3.20862	+	5.55749i	−0.417726	+	0.723523i	0.577984	+	0.816048i	$0.303840\pi$
$60$	−3.61120	+	1.39972i	−0.466204	+	0.180703i
$61$	0.348669	+	0.603912i	0.0446425	+	0.0773230i	0.887483	−	0.460840i	$-0.152452\pi$
$61$	0.348669	+	0.603912i	0.0446425	+	0.0773230i	−0.842841	+	0.538163i	$0.819118\pi$
$62$	0.219675	+	0.219675i	0.0278988	+	0.0278988i
$63$	−7.93450	−	0.208967i	−0.999653	−	0.0263274i
$64$		−	1.00000i		−	0.125000i
$65$	12.8911	+	6.36480i	1.59895	+	0.789456i
$66$	1.08567	−	4.88250i	0.133636	−	0.600994i
$67$	−0.216388	−	0.807572i	−0.0264360	−	0.0986606i	0.951447	−	0.307812i	$-0.0995966\pi$
$67$	−0.216388	−	0.807572i	−0.0264360	−	0.0986606i	−0.977883	+	0.209151i	$0.932930\pi$
$68$	1.39193	+	0.372965i	0.168796	+	0.0452287i
$69$	8.14875	−	2.56362i	0.980994	−	0.308623i
$70$	−5.25776	+	2.71219i	−0.628422	+	0.324169i
$71$		−	2.72315i		−	0.323179i	−0.986858	−	0.161589i	$-0.948338\pi$
$71$		−	2.72315i		−	0.323179i	0.986858	−	0.161589i	$-0.0516620\pi$
$72$	−1.02249	−	2.82038i	−0.120502	−	0.332384i
$73$	0.180414	−	0.0483418i	0.0211159	−	0.00565798i	−0.248246	−	0.968697i	$-0.579854\pi$
$73$	0.180414	−	0.0483418i	0.0211159	−	0.00565798i	0.269362	+	0.963039i	$0.413187\pi$
$74$	1.46069	−	2.52998i	0.169801	−	0.294104i
$75$	−2.97486	+	8.13328i	−0.343507	+	0.939150i
$76$	1.64067			0.188198
$77$	0.856433	−	7.59214i	0.0975996	−	0.865205i
$78$	−5.14838	+	9.87467i	−0.582939	+	1.11809i
$79$	8.11986	−	4.68800i	0.913555	−	0.527441i	0.0319820	−	0.999488i	$-0.489818\pi$
$79$	8.11986	−	4.68800i	0.913555	−	0.527441i	0.881573	+	0.472047i	$0.156485\pi$
$80$	−1.68046	−	1.47514i	−0.187882	−	0.164926i
$81$	−5.76761	−	6.90903i	−0.640845	−	0.767670i
$82$	8.24906	+	2.21033i	0.910957	+	0.244090i
$83$	2.26907	−	2.26907i	0.249062	−	0.249062i	−0.571523	−	0.820586i	$-0.693647\pi$
$83$	2.26907	−	2.26907i	0.249062	−	0.249062i	0.820586	+	0.571523i	$0.193647\pi$
$84$	−2.01086	−	4.11782i	−0.219402	−	0.449291i
$85$	2.68004	−	1.78891i	0.290691	−	0.194034i
$86$	−7.46579	+	4.31038i	−0.805057	+	0.464800i
$87$	15.4536	−	9.83128i	1.65680	−	1.05402i
$88$	2.78936	−	0.747407i	0.297347	−	0.0796739i
$89$	−3.60206	−	6.23895i	−0.381818	−	0.661327i	0.609505	−	0.792783i	$-0.291368\pi$
$89$	−3.60206	−	6.23895i	−0.381818	−	0.661327i	−0.991322	+	0.131455i	$0.958035\pi$
$90$	−6.24786	−	2.44219i	−0.658582	−	0.257430i
$91$	−6.21682	+	15.8341i	−0.651700	+	1.65987i
$92$	3.48746	+	3.48746i	0.363593	+	0.363593i
$93$	0.0231308	+	0.537594i	0.00239855	+	0.0557460i
$94$	−5.06736	−	2.92564i	−0.522658	−	0.301757i
$95$	2.42022	−	2.75709i	0.248309	−	0.282871i
$96$	1.17097	−	1.27626i	0.119511	−	0.130258i
$97$	4.75522	−	4.75522i	0.482819	−	0.482819i	−0.423212	−	0.906031i	$-0.639097\pi$
$97$	4.75522	−	4.75522i	0.482819	−	0.482819i	0.906031	+	0.423212i	$0.139097\pi$
$98$	−3.72268	−	5.92804i	−0.376047	−	0.598823i
$99$	7.10283	−	4.96006i	0.713861	−	0.498505i
$100$	−4.95784	+	0.647925i	−0.495784	+	0.0647925i
$101$	8.75559	+	5.05504i	0.871214	+	0.502996i	0.867752	−	0.496998i	$-0.165564\pi$
$101$	8.75559	+	5.05504i	0.871214	+	0.502996i	0.00346260	+	0.999994i	$0.498898\pi$
$102$	1.33973	+	2.10590i	0.132653	+	0.208515i
$103$	−1.31288	+	4.89972i	−0.129362	+	0.482784i	−0.999958	−	0.00921457i	$-0.997067\pi$
$103$	−1.31288	+	4.89972i	−0.129362	+	0.482784i	0.870596	+	0.491999i	$0.163734\pi$
$104$	−6.42949			−0.630463
$105$	−9.88615	−	2.69519i	−0.964789	−	0.263023i
$106$	−0.536855			−0.0521440
$107$	1.76557	−	6.58921i	0.170684	−	0.637003i	−0.826562	−	0.562846i	$-0.809707\pi$
$107$	1.76557	−	6.58921i	0.170684	−	0.637003i	0.997247	−	0.0741574i	$-0.0236267\pi$
$108$	1.99760	−	4.79683i	0.192219	−	0.461575i
$109$	−7.88184	−	4.55058i	−0.754943	−	0.435867i	0.0725341	−	0.997366i	$-0.476891\pi$
$109$	−7.88184	−	4.55058i	−0.754943	−	0.435867i	−0.827477	+	0.561499i	$0.810225\pi$
$110$	2.85871	−	5.78995i	0.272567	−	0.552050i
$111$	4.82674	−	1.51850i	0.458134	−	0.144130i
$112$	1.57138	−	2.12856i	0.148481	−	0.201130i
$113$	8.08570	−	8.08570i	0.760639	−	0.760639i	−0.215799	−	0.976438i	$-0.569236\pi$
$113$	8.08570	−	8.08570i	0.760639	−	0.760639i	0.976438	+	0.215799i	$0.0692355\pi$
$114$	2.09392	+	1.92117i	0.196114	+	0.179934i
$115$	11.0050	−	0.716063i	1.02623	−	0.0667732i
$116$	9.15790	+	5.28731i	0.850289	+	0.490915i
$117$	−18.1336	+	6.57408i	−1.67645	+	0.607774i
$118$	−4.53767	−	4.53767i	−0.417726	−	0.417726i
$119$	2.37673	+	2.98112i	0.217874	+	0.273279i
$120$	−0.417374	−	3.85043i	−0.0381008	−	0.351494i
$121$	−1.33042	−	2.30436i	−0.120948	−	0.209487i
$122$	−0.673576	+	0.180484i	−0.0609827	+	0.0163403i
$123$	7.93974	+	12.4803i	0.715902	+	1.12531i
$124$	−0.269046	+	0.155334i	−0.0241610	+	0.0139494i
$125$	−6.22470	+	9.28726i	−0.556754	+	0.830678i
$126$	2.25545	−	7.61006i	0.200931	−	0.677958i
$127$	−0.487319	+	0.487319i	−0.0432425	+	0.0432425i	−0.728397	−	0.685155i	$-0.759735\pi$
$127$	−0.487319	+	0.487319i	−0.0432425	+	0.0432425i	0.685155	+	0.728397i	$0.259735\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−14.5756	−	3.24102i	−1.28331	−	0.285356i
$130$	−9.48439	+	10.8045i	−0.831836	+	0.947620i
$131$	−7.54813	+	4.35792i	−0.659483	+	0.380753i	−0.792080	−	0.610417i	$-0.791002\pi$
$131$	−7.54813	+	4.35792i	−0.659483	+	0.380753i	0.132597	+	0.991170i	$0.457668\pi$
$132$	4.43514	+	2.31236i	0.386029	+	0.201265i
$133$	3.49227	+	2.57812i	0.302818	+	0.223551i
$134$	0.836060			0.0722246
$135$	−5.11417	−	10.4329i	−0.440158	−	0.897920i
$136$	−0.720514	+	1.24797i	−0.0617836	+	0.107012i
$137$	−16.2645	+	4.35805i	−1.38957	+	0.372333i	−0.874587	−	0.484869i	$-0.838867\pi$
$137$	−16.2645	+	4.35805i	−1.38957	+	0.372333i	−0.514980	+	0.857202i	$0.672201\pi$
$138$	0.367214	+	8.53460i	0.0312593	+	0.726514i
$139$		−	15.2003i		−	1.28927i	−0.764490	−	0.644636i	$-0.777009\pi$
$139$		−	15.2003i		−	1.28927i	0.764490	−	0.644636i	$-0.222991\pi$
$140$	−1.25897	−	5.78057i	−0.106402	−	0.488547i
$141$	−3.04145	−	9.66758i	−0.256136	−	0.814157i
$142$	2.63036	+	0.704804i	0.220735	+	0.0591458i
$143$	−4.80544	−	17.9342i	−0.401851	−	1.49973i
$144$	2.98891	−	0.257682i	0.249076	−	0.0214735i
$145$	22.3943	−	7.59000i	1.85975	−	0.630315i
$146$			0.186778i			0.0154579i
$147$	2.19043	−	11.9248i	0.180663	−	0.983545i
$148$	2.06572	+	2.06572i	0.169801	+	0.169801i
$149$	6.69548	+	11.5969i	0.548515	+	0.950056i	0.998377	+	0.0569574i	$0.0181399\pi$
$149$	6.69548	+	11.5969i	0.548515	+	0.950056i	−0.449862	+	0.893098i	$0.648527\pi$
$150$	−7.08619	−	4.97854i	−0.578585	−	0.406496i
$151$	−0.819732	+	1.41982i	−0.0667088	+	0.115543i	−0.897451	−	0.441115i	$-0.854583\pi$
$151$	−0.819732	+	1.41982i	−0.0667088	+	0.115543i	0.830742	+	0.556658i	$0.187917\pi$
$152$	−0.424637	+	1.58477i	−0.0344426	+	0.128542i
$153$	−0.756087	+	4.25645i	−0.0611260	+	0.344114i
$154$	7.11178	+	2.79224i	0.573084	+	0.225005i
$155$	−0.135847	+	0.681261i	−0.0109115	+	0.0547202i
$156$	−8.20570	−	7.52870i	−0.656982	−	0.602779i
$157$	3.51932	+	13.1343i	0.280872	+	1.04823i	0.951803	+	0.306710i	$0.0992281\pi$
$157$	3.51932	+	13.1343i	0.280872	+	1.04823i	−0.670931	+	0.741520i	$0.734105\pi$
$158$	2.42669	+	9.05652i	0.193057	+	0.720498i
$159$	−0.685167	−	0.628638i	−0.0543373	−	0.0498543i
$160$	1.85981	−	1.24141i	0.147031	−	0.0981421i
$161$	1.94315	+	12.9034i	0.153142	+	1.01693i
$162$	8.16638	−	3.78289i	0.641611	−	0.297212i
$163$	−0.0451230	+	0.168401i	−0.00353430	+	0.0131902i	−0.967670	−	0.252218i	$-0.918840\pi$
$163$	−0.0451230	+	0.168401i	−0.00353430	+	0.0131902i	0.964136	+	0.265408i	$0.0855067\pi$
$164$	−4.27003	+	7.39591i	−0.333433	+	0.577523i
$165$	10.4283	−	4.04204i	0.811841	−	0.314673i
$166$	1.60447	+	2.77903i	0.124531	+	0.215694i
$167$	−1.62165	−	1.62165i	−0.125487	−	0.125487i	0.641574	−	0.767061i	$-0.278282\pi$
$167$	−1.62165	−	1.62165i	−0.125487	−	0.125487i	−0.767061	+	0.641574i	$0.778282\pi$
$168$	4.49796	−	0.876568i	0.347025	−	0.0676287i
$169$			28.3383i			2.17987i
$170$	1.03431	+	3.05172i	0.0793276	+	0.234057i
$171$	0.422771	+	4.90382i	0.0323301	+	0.375005i
$172$	−2.23122	−	8.32701i	−0.170129	−	0.634928i
$173$	−3.68194	−	0.986574i	−0.279933	−	0.0750078i	0.116121	−	0.993235i	$-0.462954\pi$
$173$	−3.68194	−	0.986574i	−0.279933	−	0.0750078i	−0.396054	+	0.918227i	$0.629621\pi$
$174$	5.49660	+	17.4716i	0.416696	+	1.32452i
$175$	−11.5712	−	6.41150i	−0.874700	−	0.484664i
$176$			2.88776i			0.217673i
$177$	−0.477796	−	11.1047i	−0.0359134	−	0.834680i
$178$	6.95864	−	1.86456i	0.521572	−	0.139755i
$179$	4.40852	−	7.63578i	0.329508	−	0.570725i	−0.652906	−	0.757439i	$-0.726450\pi$
$179$	4.40852	−	7.63578i	0.329508	−	0.570725i	0.982414	+	0.186714i	$0.0597838\pi$
$180$	3.97604	−	5.40288i	0.296356	−	0.402707i
$181$	−5.31549			−0.395097			−0.197549	−	0.980293i	$-0.563298\pi$
$181$	−5.31549			−0.395097			−0.197549	+	0.980293i	$0.563298\pi$
$182$	−13.6855	−	10.1032i	−1.01444	−	0.748896i
$183$	−1.07100	−	0.558389i	−0.0791706	−	0.0412773i
$184$	−4.27125	+	2.46601i	−0.314881	+	0.181796i
$185$	6.51860	−	0.424144i	0.479257	−	0.0311837i
$186$	−0.525263	−	0.116797i	−0.0385142	−	0.00856398i
$187$	−4.01955	−	1.07703i	−0.293938	−	0.0787606i
$188$	4.13748	−	4.13748i	0.301757	−	0.301757i
$189$	11.7896	−	7.07136i	0.857571	−	0.514366i
$190$	2.03675	+	3.05134i	0.147761	+	0.221367i
$191$	−19.4247	+	11.2148i	−1.40552	+	0.811477i	−0.994952	−	0.100354i	$-0.968003\pi$
$191$	−19.4247	+	11.2148i	−1.40552	+	0.811477i	−0.410567	+	0.911830i	$0.634669\pi$
$192$	0.929705	+	1.46139i	0.0670957	+	0.105466i
$193$	−15.9182	+	4.26527i	−1.14582	+	0.307021i	−0.781287	−	0.624171i	$-0.785437\pi$
$193$	−15.9182	+	4.26527i	−1.14582	+	0.307021i	−0.364529	+	0.931192i	$0.618770\pi$
$194$	3.36245	+	5.82393i	0.241410	+	0.418134i
$195$	−24.7563	+	2.68350i	−1.77283	+	0.192169i
$196$	6.68955	−	2.06154i	0.477825	−	0.147253i
$197$	1.01237	+	1.01237i	0.0721282	+	0.0721282i	0.742251	−	0.670122i	$-0.233758\pi$
$197$	1.01237	+	1.01237i	0.0721282	+	0.0721282i	−0.670122	+	0.742251i	$0.733758\pi$
$198$	2.95270	+	8.14456i	0.209839	+	0.578809i
$199$	7.66182	+	4.42355i	0.543132	+	0.313577i	0.746347	−	0.665557i	$-0.231806\pi$
$199$	7.66182	+	4.42355i	0.543132	+	0.313577i	−0.203215	+	0.979134i	$0.565139\pi$
$200$	0.657337	−	4.95660i	0.0464807	−	0.350485i
$201$	1.06703	+	0.978997i	0.0752625	+	0.0690531i
$202$	−7.14891	+	7.14891i	−0.502996	+	0.502996i
$203$	11.1848	+	25.6449i	0.785016	+	1.79992i
$204$	−2.38089	+	0.749034i	−0.166696	+	0.0524429i
$205$	6.12967	+	18.0856i	0.428115	+	1.26316i
$206$	−4.39297	−	2.53628i	−0.306073	−	0.176711i
$207$	−9.52506	+	11.3224i	−0.662037	+	0.786959i
$208$	1.66407	−	6.21041i	0.115383	−	0.430614i
$209$	−4.73786			−0.327725
$210$	5.16208	−	8.85172i	0.356217	−	0.610827i
$211$	−13.5047			−0.929702			−0.464851	−	0.885389i	$-0.653892\pi$
$211$	−13.5047			−0.929702			−0.464851	+	0.885389i	$0.653892\pi$
$212$	0.138948	−	0.518562i	0.00954301	−	0.0356150i
$213$	2.53173	+	3.97958i	0.173471	+	0.272676i
$214$	5.90772	+	3.41083i	0.403844	+	0.233159i
$215$	−17.2846	−	8.53402i	−1.17880	−	0.582016i
$216$	4.11637	+	3.17104i	0.280083	+	0.215762i
$217$	−0.816769	−	0.0921358i	−0.0554459	−	0.00625459i
$218$	6.43549	−	6.43549i	0.435867	−	0.435867i
$219$	−0.218711	+	0.238378i	−0.0147791	+	0.0161081i
$220$	4.85278	+	4.25985i	0.327174	+	0.287199i
$221$	8.02378	+	4.63253i	0.539738	+	0.311618i
$222$	0.217511	+	5.05529i	0.0145984	+	0.339289i
$223$	20.0690	+	20.0690i	1.34392	+	1.34392i	0.892116	+	0.451807i	$0.149220\pi$
$223$	20.0690	+	20.0690i	1.34392	+	1.34392i	0.451807	+	0.892116i	$0.350780\pi$
$224$	1.64933	+	2.06875i	0.110200	+	0.138224i
$225$	−3.21414	−	14.6516i	−0.214276	−	0.976773i
$226$	5.71746	+	9.90292i	0.380319	+	0.658733i
$227$	7.71245	−	2.06654i	0.511893	−	0.137161i	0.00637896	−	0.999980i	$-0.497970\pi$
$227$	7.71245	−	2.06654i	0.511893	−	0.137161i	0.505514	+	0.862818i	$0.331303\pi$
$228$	−2.39765	+	1.52534i	−0.158788	+	0.101018i
$229$	13.5382	−	7.81631i	0.894632	−	0.516516i	0.0191773	−	0.999816i	$-0.493895\pi$
$229$	13.5382	−	7.81631i	0.894632	−	0.516516i	0.875455	+	0.483300i	$0.160562\pi$
$230$	−2.15665	+	10.8154i	−0.142205	+	0.713146i
$231$	5.80687	+	11.8913i	0.382064	+	0.782389i
$232$	−7.47739	+	7.47739i	−0.490915	+	0.490915i
$233$	7.12102	+	1.90807i	0.466514	+	0.125002i	0.484416	−	0.874838i	$-0.339032\pi$
$233$	7.12102	+	1.90807i	0.466514	+	0.125002i	−0.0179022	+	0.999840i	$0.505699\pi$
$234$	−1.65676	−	19.2172i	−0.108306	−	1.25627i
$235$	−0.849528	−	13.0563i	−0.0554171	−	0.851696i
$236$	5.55749	−	3.20862i	0.361762	−	0.208863i
$237$	−7.50779	+	14.4001i	−0.487683	+	0.935384i
$238$	−3.49469	+	1.52417i	−0.226527	+	0.0987974i
$239$	−3.91525			−0.253256			−0.126628	−	0.991950i	$-0.540416\pi$
$239$	−3.91525			−0.253256			−0.126628	+	0.991950i	$0.540416\pi$
$240$	3.82725	+	0.593412i	0.247048	+	0.0383046i
$241$	8.84160	−	15.3141i	0.569537	−	0.986468i	−0.427074	−	0.904217i	$-0.640456\pi$
$241$	8.84160	−	15.3141i	0.569537	−	0.986468i	0.996612	−	0.0822510i	$-0.0262109\pi$
$242$	2.57018	−	0.688678i	0.165218	−	0.0442699i
$243$	14.8521	+	4.73459i	0.952760	+	0.303724i
$244$		−	0.697338i		−	0.0446425i
$245$	6.40368	−	14.2826i	0.409116	−	0.912482i
$246$	−14.1100	+	4.43905i	−0.899622	+	0.283024i
$247$	10.1892	+	2.73020i	0.648325	+	0.173718i
$248$	−0.0804067	−	0.300082i	−0.00510583	−	0.0190552i
$249$	−1.20642	+	5.42554i	−0.0764537	+	0.343830i
$250$	−7.35973	−	8.41631i	−0.465470	−	0.532294i
$251$		−	16.5267i		−	1.04316i	−0.853203	−	0.521579i	$-0.825343\pi$
$251$		−	16.5267i		−	1.04316i	0.853203	−	0.521579i	$-0.174657\pi$
$252$	6.76700	+	4.14822i	0.426281	+	0.261313i
$253$	−10.0709	−	10.0709i	−0.633155	−	0.633155i
$254$	−0.344586	−	0.596841i	−0.0216213	−	0.0374491i
$255$	−2.25342	+	5.10593i	−0.141115	+	0.319746i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.87993	−	21.9442i	0.366780	−	1.36884i	−0.498211	−	0.867056i	$-0.666010\pi$
$257$	5.87993	−	21.9442i	0.366780	−	1.36884i	0.864992	−	0.501786i	$-0.167324\pi$
$258$	6.90302	−	13.2401i	0.429763	−	0.824293i
$259$	1.15098	+	7.64305i	0.0715186	+	0.474916i
$260$	−7.98163	−	11.9576i	−0.495000	−	0.741581i
$261$	−13.4435	+	28.7346i	−0.832132	+	1.77863i
$262$	−2.25582	−	8.41885i	−0.139365	−	0.520118i
$263$	−7.44452	−	27.7833i	−0.459049	−	1.71319i	−0.675905	−	0.736989i	$-0.736247\pi$
$263$	−7.44452	−	27.7833i	−0.459049	−	1.71319i	0.216856	−	0.976204i	$-0.430420\pi$
$264$	−3.38146	+	3.68553i	−0.208115	+	0.226829i
$265$	−0.666457	−	0.998449i	−0.0409401	−	0.0613342i
$266$	−3.39413	+	2.70601i	−0.208108	+	0.165916i
$267$	11.0644	+	5.76866i	0.677129	+	0.353036i
$268$	−0.216388	+	0.807572i	−0.0132180	+	0.0493303i
$269$	2.82801	−	4.89825i	0.172427	−	0.298652i	−0.766841	−	0.641837i	$-0.778173\pi$
$269$	2.82801	−	4.89825i	0.172427	−	0.298652i	0.939268	+	0.343185i	$0.111506\pi$
$270$	11.4010	−	2.23968i	0.693846	−	0.136303i
$271$	−11.4291	−	19.7958i	−0.694270	−	1.20251i	−0.970426	−	0.241399i	$-0.922394\pi$
$271$	−11.4291	−	19.7958i	−0.694270	−	1.20251i	0.276156	−	0.961113i	$-0.410939\pi$
$272$	−1.01896	−	1.01896i	−0.0617836	−	0.0617836i
$273$	−5.63588	−	28.9196i	−0.341099	−	1.75029i
$274$		−	16.8382i		−	1.01723i
$275$	14.3171	−	1.87105i	0.863351	−	0.112829i
$276$	−8.33883	−	1.85422i	−0.501939	−	0.111611i
$277$	−4.36346	−	16.2847i	−0.262175	−	0.978450i	−0.963957	−	0.266058i	$-0.914279\pi$
$277$	−4.36346	−	16.2847i	−0.262175	−	0.978450i	0.701782	−	0.712392i	$-0.252388\pi$
$278$	14.6824	+	3.93413i	0.880589	+	0.235953i
$279$	−0.533607	−	0.764128i	−0.0319462	−	0.0457472i
$280$	5.90945	+	0.280053i	0.353157	+	0.0167363i
$281$			24.5854i			1.46664i	0.679883	+	0.733321i	$0.262031\pi$
$281$			24.5854i			1.46664i	−0.679883	+	0.733321i	$0.737969\pi$
$282$	10.1253	−	0.435658i	0.602956	−	0.0259431i
$283$	−25.8992	+	6.93967i	−1.53955	+	0.412520i	−0.926119	−	0.377230i	$-0.876876\pi$
$283$	−25.8992	+	6.93967i	−1.53955	+	0.412520i	−0.613428	+	0.789751i	$0.710210\pi$
$284$	−1.36158	+	2.35832i	−0.0807947	+	0.139941i
$285$	−0.973594	+	6.27926i	−0.0576707	+	0.371951i
$286$	18.5668			1.09788
$287$	−20.7108	+	9.03280i	−1.22252	+	0.533190i
$288$	−0.524686	+	2.95376i	−0.0309174	+	0.174052i
$289$	−12.9241	+	7.46172i	−0.760240	+	0.438925i
$290$	1.53530	+	23.5957i	0.0901556	+	1.38559i
$291$	−2.52826	+	11.3702i	−0.148209	+	0.666530i
$292$	−0.180414	−	0.0483418i	−0.0105579	−	0.00282899i
$293$	13.8738	−	13.8738i	0.810518	−	0.810518i	−0.174193	−	0.984712i	$-0.555732\pi$
$293$	13.8738	−	13.8738i	0.810518	−	0.810518i	0.984712	+	0.174193i	$0.0557317\pi$
$294$	10.9516	+	5.20217i	0.638710	+	0.303397i
$295$	2.80610	−	14.0723i	0.163378	−	0.819322i
$296$	−2.52998	+	1.46069i	−0.147052	+	0.0849007i
$297$	−5.76858	+	13.8521i	−0.334727	+	0.803780i
$298$	−12.9347	+	3.46583i	−0.749285	+	0.200770i
$299$	15.8552	+	27.4619i	0.916927	+	1.58816i
$300$	6.64294	−	5.55620i	0.383530	−	0.320787i
$301$	8.33561	−	21.2306i	0.480456	−	1.22371i
$302$	−1.15928	−	1.15928i	−0.0667088	−	0.0667088i
$303$	−17.4950	+	0.752748i	−1.00506	+	0.0432443i
$304$	−1.42086	−	0.820335i	−0.0814921	−	0.0470495i
$305$	−1.17185	−	1.02867i	−0.0671000	−	0.0589015i
$306$	−3.91573	−	1.83197i	−0.223847	−	0.104727i
$307$	7.49848	−	7.49848i	0.427961	−	0.427961i	−0.459972	−	0.887933i	$-0.652141\pi$
$307$	7.49848	−	7.49848i	0.427961	−	0.427961i	0.887933	+	0.459972i	$0.152141\pi$
$308$	−4.53776	+	6.14677i	−0.258563	+	0.350245i
$309$	−2.63668	−	8.38098i	−0.149995	−	0.476777i
$310$	−0.622888	−	0.307542i	−0.0353777	−	0.0174672i
$311$	−14.2976	−	8.25471i	−0.810741	−	0.468082i	0.0364719	−	0.999335i	$-0.488388\pi$
$311$	−14.2976	−	8.25471i	−0.810741	−	0.468082i	−0.847213	+	0.531253i	$0.821721\pi$
$312$	9.39596	−	5.97752i	0.531941	−	0.338411i
$313$	3.73296	−	13.9316i	0.210999	−	0.787460i	−0.776537	−	0.630071i	$-0.783026\pi$
$313$	3.73296	−	13.9316i	0.210999	−	0.787460i	0.987537	−	0.157389i	$-0.0503076\pi$
$314$	−13.5976			−0.767357
$315$	16.9532	−	5.25249i	0.955205	−	0.295944i
$316$	−9.37600			−0.527441
$317$	6.25275	−	23.3356i	0.351189	−	1.31066i	−0.534023	−	0.845470i	$-0.679320\pi$
$317$	6.25275	−	23.3356i	0.351189	−	1.31066i	0.885212	−	0.465187i	$-0.154013\pi$
$318$	0.784552	−	0.499117i	0.0439955	−	0.0279891i
$319$	−26.4458	−	15.2685i	−1.48068	−	0.854871i
$320$	0.717755	+	2.11774i	0.0401237	+	0.118385i
$321$	3.54584	+	11.2708i	0.197909	+	0.629077i
$322$	−12.9666	−	1.46271i	−0.722603	−	0.0815134i
$323$	1.67178	−	1.67178i	0.0930203	−	0.0930203i
$324$	1.54038	+	8.86720i	0.0855765	+	0.492622i
$325$	−31.8684	−	4.22634i	−1.76774	−	0.234435i
$326$	−0.150984	−	0.0871709i	−0.00836225	−	0.00482795i
$327$	15.7491	−	0.677629i	0.870927	−	0.0374729i
$328$	−6.03873	−	6.03873i	−0.333433	−	0.333433i
$329$	15.3084	−	2.30533i	0.843981	−	0.127097i
$330$	1.20528	+	11.1191i	0.0663482	+	0.612087i
$331$	−8.06115	−	13.9623i	−0.443081	−	0.767439i	0.554835	−	0.831960i	$-0.312781\pi$
$331$	−8.06115	−	13.9623i	−0.443081	−	0.767439i	−0.997916	+	0.0645213i	$0.979448\pi$
$332$	−3.09960	+	0.830536i	−0.170113	+	0.0455816i
$333$	−5.64196	+	6.70656i	−0.309178	+	0.367517i
$334$	1.98610	−	1.14668i	0.108675	−	0.0627433i
$335$	1.03789	+	1.55491i	0.0567062	+	0.0849540i
$336$	−0.317457	+	4.57157i	−0.0173187	+	0.249399i
$337$	6.44276	−	6.44276i	0.350959	−	0.350959i	−0.509507	−	0.860466i	$-0.670172\pi$
$337$	6.44276	−	6.44276i	0.350959	−	0.350959i	0.860466	+	0.509507i	$0.170172\pi$
$338$	−27.3727	−	7.33449i	−1.48888	−	0.398944i
$339$	−4.29901	+	19.3337i	−0.233490	+	1.05006i
$340$	−3.21544	+	0.209218i	−0.174382	+	0.0113464i
$341$	0.776940	−	0.448566i	0.0420737	−	0.0242912i
$342$	−4.84615	−	0.860837i	−0.262050	−	0.0465487i
$343$	17.4786	+	6.12371i	0.943754	+	0.330649i
$344$	8.62075			0.464800
$345$	−15.4169	+	11.2779i	−0.830018	+	0.607181i
$346$	1.90591	−	3.30114i	0.102463	−	0.177470i
$347$	−9.14627	+	2.45074i	−0.490998	+	0.131562i	−0.495819	−	0.868426i	$-0.665132\pi$
$347$	−9.14627	+	2.45074i	−0.490998	+	0.131562i	0.00482121	+	0.999988i	$0.498465\pi$
$348$	−18.2989	+	0.787336i	−0.980922	+	0.0422056i
$349$			19.7917i			1.05942i	0.848177	+	0.529712i	$0.177700\pi$
$349$			19.7917i			1.05942i	−0.848177	+	0.529712i	$0.822300\pi$
$350$	9.18788	−	9.51750i	0.491113	−	0.508732i
$351$	20.3882	−	26.4661i	1.08824	−	1.41266i
$352$	−2.78936	−	0.747407i	−0.148673	−	0.0398369i
$353$	0.588034	+	2.19457i	0.0312979	+	0.116805i	0.979808	−	0.199943i	$-0.0640757\pi$
$353$	0.588034	+	2.19457i	0.0312979	+	0.116805i	−0.948510	+	0.316748i	$0.897409\pi$
$354$	10.8500	+	2.41259i	0.576670	+	0.128228i
$355$	1.95456	+	5.76693i	0.103737	+	0.306077i
$356$			7.20412i			0.381818i
$357$	−6.24488	−	2.14691i	−0.330514	−	0.113627i
$358$	6.23458	+	6.23458i	0.329508	+	0.329508i
$359$	−5.97213	−	10.3440i	−0.315197	−	0.545937i	0.664282	−	0.747482i	$-0.268737\pi$
$359$	−5.97213	−	10.3440i	−0.315197	−	0.545937i	−0.979479	+	0.201545i	$0.935404\pi$
$360$	4.18971	+	5.23893i	0.220817	+	0.276116i
$361$	−8.15410	+	14.1233i	−0.429163	+	0.743332i
$362$	1.37575	−	5.13437i	0.0723078	−	0.269856i
$363$	4.08664	+	2.13066i	0.214493	+	0.111831i
$364$	13.3010	−	10.6043i	0.697161	−	0.555818i
$365$	−0.347373	+	0.231869i	−0.0181823	+	0.0121366i
$366$	0.816558	−	0.889984i	0.0426822	−	0.0465202i
$367$	3.14381	+	11.7329i	0.164106	+	0.612451i	0.998153	+	0.0607572i	$0.0193515\pi$
$367$	3.14381	+	11.7329i	0.164106	+	0.612451i	−0.834047	+	0.551694i	$0.813982\pi$
$368$	−1.27650	−	4.76396i	−0.0665421	−	0.248339i
$369$	−23.2060	−	10.8570i	−1.20806	−	0.565191i
$370$	−1.27745	+	6.40626i	−0.0664113	+	0.333046i
$371$	1.11062	−	0.885450i	0.0576604	−	0.0459703i
$372$	0.248765	−	0.477136i	0.0128979	−	0.0247383i
$373$	5.07958	−	18.9572i	0.263011	−	0.981569i	−0.700446	−	0.713705i	$-0.747016\pi$
$373$	5.07958	−	18.9572i	0.263011	−	0.981569i	0.963457	−	0.267864i	$-0.0863177\pi$
$374$	2.08067	−	3.60383i	0.107589	−	0.186349i
$375$	0.462272	−	19.3594i	0.0238716	−	0.999715i
$376$	2.92564	+	5.06736i	0.150878	+	0.261329i
$377$	48.0758	+	48.0758i	2.47603	+	2.47603i
$378$	3.77903	+	13.2181i	0.194372	+	0.679867i
$379$			9.32087i			0.478781i	0.970923	+	0.239391i	$0.0769476\pi$
$379$			9.32087i			0.478781i	−0.970923	+	0.239391i	$0.923052\pi$
$380$	−3.47452	+	1.17760i	−0.178239	+	0.0604096i
$381$	0.259098	−	1.16522i	0.0132740	−	0.0596962i
$382$	−5.80522	−	21.6654i	−0.297021	−	1.10850i
$383$	10.0710	+	2.69851i	0.514603	+	0.137887i	0.506769	−	0.862082i	$-0.330840\pi$
$383$	10.0710	+	2.69851i	0.514603	+	0.137887i	0.00783388	+	0.999969i	$0.497506\pi$
$384$	−1.65222	+	0.519792i	−0.0843143	+	0.0265255i
$385$	3.63560	+	16.6929i	0.185287	+	0.850749i
$386$		−	16.4797i		−	0.838796i
$387$	24.3138	−	8.81463i	1.23594	−	0.448073i
$388$	−6.49575	+	1.74053i	−0.329772	+	0.0883620i
$389$	1.52599	−	2.64309i	0.0773708	−	0.134010i	−0.824744	−	0.565506i	$-0.808681\pi$
$389$	1.52599	−	2.64309i	0.0773708	−	0.134010i	0.902115	+	0.431496i	$0.142014\pi$
$390$	3.81533	−	24.6073i	0.193197	−	1.24604i
$391$	7.10717			0.359425
$392$	0.259910	+	6.99517i	0.0131275	+	0.353310i
$393$	6.97916	−	13.3861i	0.352052	−	0.675241i
$394$	−1.23989	+	0.715852i	−0.0624649	+	0.0360641i
$395$	−13.8309	+	15.7560i	−0.695909	+	0.792773i
$396$	−8.63126	+	0.744123i	−0.433737	+	0.0373936i
$397$	−12.4916	−	3.34711i	−0.626935	−	0.167987i	−0.0686566	−	0.997640i	$-0.521871\pi$
$397$	−12.4916	−	3.34711i	−0.626935	−	0.167987i	−0.558279	+	0.829654i	$0.688538\pi$
$398$	−6.25585	+	6.25585i	−0.313577	+	0.313577i
$399$	−7.50044	−	0.520843i	−0.375491	−	0.0260748i
$400$	4.61758	+	1.91780i	0.230879	+	0.0958901i
$401$	18.6481	−	10.7665i	0.931240	−	0.537652i	0.0440366	−	0.999030i	$-0.485978\pi$
$401$	18.6481	−	10.7665i	0.931240	−	0.537652i	0.887204	+	0.461378i	$0.152645\pi$
$402$	−1.22181	+	0.777289i	−0.0609381	+	0.0387676i
$403$	−1.92937	+	0.516973i	−0.0961088	+	0.0257523i
$404$	−5.05504	−	8.75559i	−0.251498	−	0.435607i
$405$	17.1733	+	10.4918i	0.853348	+	0.521342i
$406$	−27.6659	+	4.16627i	−1.37304	+	0.206768i
$407$	−5.96531	−	5.96531i	−0.295689	−	0.295689i
$408$	−0.107292	−	2.49363i	−0.00531174	−	0.123453i
$409$	6.31608	+	3.64659i	0.312310	+	0.180312i	0.647960	−	0.761675i	$-0.275623\pi$
$409$	6.31608	+	3.64659i	0.312310	+	0.180312i	−0.335650	+	0.941987i	$0.608956\pi$
$410$	−19.0559	+	1.23990i	−0.941102	+	0.0612344i
$411$	19.7170	−	21.4899i	0.972566	−	1.06002i
$412$	3.58685	−	3.58685i	0.176711	−	0.176711i
$413$	16.8714	+	1.90318i	0.830187	+	0.0936495i
$414$	−8.47130	−	12.1309i	−0.416342	−	0.596204i
$415$	−3.17666	+	6.43393i	−0.155936	+	0.315829i
$416$	5.56810	+	3.21474i	0.272998	+	0.157616i
$417$	14.1318	+	22.2135i	0.692037	+	1.08780i
$418$	1.22625	−	4.57642i	0.0599778	−	0.223840i
$419$	−29.6118			−1.44663			−0.723316	−	0.690517i	$-0.757383\pi$
$419$	−29.6118			−1.44663			−0.723316	+	0.690517i	$0.757383\pi$
$420$	7.21406	+	7.27718i	0.352010	+	0.355090i
$421$	3.88093			0.189145			0.0945725	−	0.995518i	$-0.469852\pi$
$421$	3.88093			0.189145			0.0945725	+	0.995518i	$0.469852\pi$
$422$	3.49527	−	13.0445i	0.170147	−	0.634998i
$423$	13.4327	+	11.3004i	0.653121	+	0.549445i
$424$	0.464930	+	0.268427i	0.0225790	+	0.0130360i
$425$	−4.39164	+	5.71205i	−0.213026	+	0.277075i
$426$	−4.49924	+	1.41547i	−0.217989	+	0.0685798i
$427$	1.09578	−	1.48432i	0.0530286	−	0.0718315i
$428$	−4.82364	+	4.82364i	−0.233159	+	0.233159i
$429$	23.6961	+	21.7411i	1.14406	+	1.04967i
$430$	12.7168	−	14.4869i	0.613259	−	0.698619i
$431$	23.7899	+	13.7351i	1.14592	+	0.661598i	0.947890	−	0.318598i	$-0.103212\pi$
$431$	23.7899	+	13.7351i	1.14592	+	0.661598i	0.198031	+	0.980196i	$0.436545\pi$
$432$	−4.12839	+	3.15538i	−0.198627	+	0.151813i
$433$	18.1378	+	18.1378i	0.871649	+	0.871649i	0.992652	−	0.121003i	$-0.0386110\pi$
$433$	18.1378	+	18.1378i	0.871649	+	0.871649i	−0.121003	+	0.992652i	$0.538611\pi$
$434$	0.300392	−	0.765091i	0.0144193	−	0.0367256i
$435$	−25.6703	+	31.9120i	−1.23080	+	1.53006i
$436$	4.55058	+	7.88184i	0.217933	+	0.377472i
$437$	7.81609	−	2.09431i	0.373894	−	0.100185i
$438$	−0.173649	−	0.272955i	−0.00829726	−	0.0130423i
$439$	20.3735	−	11.7627i	0.972376	−	0.561402i	0.0724163	−	0.997374i	$-0.476929\pi$
$439$	20.3735	−	11.7627i	0.972376	−	0.561402i	0.899960	+	0.435973i	$0.143596\pi$
$440$	−5.37069	+	3.58489i	−0.256038	+	0.170903i
$441$	7.88553	+	19.4633i	0.375502	+	0.926822i
$442$	−6.55139	+	6.55139i	−0.311618	+	0.311618i
$443$	−20.3505	−	5.45289i	−0.966880	−	0.259075i	−0.259370	−	0.965778i	$-0.583515\pi$
$443$	−20.3505	−	5.45289i	−0.966880	−	0.259075i	−0.707510	+	0.706703i	$0.750182\pi$
$444$	−4.93933	−	1.09830i	−0.234410	−	0.0521232i
$445$	12.1063	+	10.6271i	0.573892	+	0.503772i
$446$	−24.5795	+	14.1910i	−1.16387	+	0.671961i
$447$	−20.5664	−	10.7227i	−0.972756	−	0.507168i
$448$	−2.42513	+	1.05770i	−0.114577	+	0.0499715i
$449$	−2.55651			−0.120649			−0.0603246	−	0.998179i	$-0.519214\pi$
$449$	−2.55651			−0.120649			−0.0603246	+	0.998179i	$0.519214\pi$
$450$	14.9842	+	0.687496i	0.706364	+	0.0324089i
$451$	12.3308	−	21.3576i	0.580636	−	1.00569i
$452$	−11.0453	+	2.95957i	−0.519526	+	0.139207i
$453$	−0.122067	−	2.83701i	−0.00573519	−	0.133294i
$454$			7.98451i			0.374732i
$455$	1.80059	−	37.9947i	0.0844131	−	1.78122i
$456$	−0.852807	−	2.71074i	−0.0399363	−	0.126942i
$457$	−10.5080	−	2.81562i	−0.491546	−	0.131709i	0.00452783	−	0.999990i	$-0.498559\pi$
$457$	−10.5080	−	2.81562i	−0.491546	−	0.131709i	−0.496074	+	0.868280i	$0.665225\pi$
$458$	4.04602	+	15.0999i	0.189058	+	0.705574i
$459$	−2.85231	−	6.92326i	−0.133134	−	0.323150i
$460$	−9.88868	−	4.88239i	−0.461062	−	0.227643i
$461$		−	33.6432i		−	1.56692i	−0.621441	−	0.783461i	$-0.713453\pi$
$461$		−	33.6432i		−	1.56692i	0.621441	−	0.783461i	$-0.286547\pi$
$462$	−12.9890	+	2.53132i	−0.604304	+	0.117768i
$463$	7.63888	+	7.63888i	0.355009	+	0.355009i	0.861969	−	0.506960i	$-0.169231\pi$
$463$	7.63888	+	7.63888i	0.355009	+	0.355009i	−0.506960	+	0.861969i	$0.669231\pi$
$464$	−5.28731	−	9.15790i	−0.245457	−	0.425145i
$465$	−0.434846	−	1.12188i	−0.0201655	−	0.0520261i
$466$	−3.68611	+	6.38454i	−0.170756	+	0.295758i
$467$	−8.45237	+	31.5447i	−0.391129	+	1.45971i	0.437145	+	0.899391i	$0.355990\pi$
$467$	−8.45237	+	31.5447i	−0.391129	+	1.45971i	−0.828274	+	0.560323i	$0.810677\pi$
$468$	18.9912	+	3.37346i	0.877867	+	0.155938i
$469$	−1.72960	+	1.37894i	−0.0798653	+	0.0636734i
$470$	12.8312	+	2.55863i	0.591861	+	0.118021i
$471$	−17.3541	−	15.9223i	−0.799634	−	0.733662i
$472$	1.66090	+	6.19857i	0.0764492	+	0.285312i
$473$	6.44321	+	24.0464i	0.296259	+	1.10565i
$474$	−11.9662	−	10.9790i	−0.549627	−	0.504281i
$475$	−3.14648	+	7.57593i	−0.144370	+	0.347607i
$476$	−0.567746	−	3.77009i	−0.0260226	−	0.172802i
$477$	1.58574	+	0.281680i	0.0726061	+	0.0128973i
$478$	1.01334	−	3.78184i	0.0463491	−	0.172977i
$479$	13.9213	−	24.1124i	0.636080	−	1.10172i	−0.350205	−	0.936673i	$-0.613888\pi$
$479$	13.9213	−	24.1124i	0.636080	−	1.10172i	0.986285	−	0.165050i	$-0.0527785\pi$
$480$	−1.56376	+	3.54326i	−0.0713755	+	0.161727i
$481$	9.39146	+	16.2665i	0.428214	+	0.741688i
$482$	12.5039	+	12.5039i	0.569537	+	0.569537i
$483$	−14.8360	−	17.0503i	−0.675063	−	0.775815i
$484$			2.66085i			0.120948i
$485$	−6.65723	+	13.4834i	−0.302289	+	0.612250i
$486$	−8.41726	+	13.1206i	−0.381815	+	0.595162i
$487$	8.16069	+	30.4561i	0.369796	+	1.38010i	0.860801	+	0.508941i	$0.169963\pi$
$487$	8.16069	+	30.4561i	0.369796	+	1.38010i	−0.491005	+	0.871157i	$0.663370\pi$
$488$	0.673576	+	0.180484i	0.0304914	+	0.00817014i
$489$	−0.0906214	−	0.288050i	−0.00409804	−	0.0130261i
$490$	12.1385	+	9.88209i	0.548364	+	0.446427i
$491$		−	1.52495i		−	0.0688199i	−0.999408	−	0.0344099i	$-0.989045\pi$
$491$		−	1.52495i		−	0.0688199i	0.999408	−	0.0344099i	$-0.0109552\pi$
$492$	−0.635852	−	14.7781i	−0.0286664	−	0.666250i
$493$	14.7191	−	3.94397i	0.662915	−	0.177628i
$494$	−5.27433	+	9.13542i	−0.237304	+	0.411022i
$495$	−11.4818	+	15.6022i	−0.516070	+	0.701267i
$496$	0.310667			0.0139494
$497$	−6.60401	+	2.88027i	−0.296230	+	0.129198i
$498$	−4.92843	−	2.56954i	−0.220848	−	0.115144i
$499$	−9.28878	+	5.36288i	−0.415823	+	0.240075i	−0.693289	−	0.720660i	$-0.743839\pi$
$499$	−9.28878	+	5.36288i	−0.415823	+	0.240075i	0.277466	+	0.960736i	$0.410506\pi$
$500$	10.0344	−	4.93065i	0.448751	−	0.220506i
$501$	3.87750	+	0.862198i	0.173234	+	0.0385202i
$502$	15.9636	+	4.27743i	0.712490	+	0.190911i
$503$	−29.8137	+	29.8137i	−1.32933	+	1.32933i	−0.423373	+	0.905955i	$0.639154\pi$
$503$	−29.8137	+	29.8137i	−1.32933	+	1.32933i	−0.905955	+	0.423373i	$0.860846\pi$
$504$	−5.75830	+	5.46278i	−0.256495	+	0.243331i
$505$	−22.1704	−	4.42090i	−0.986568	−	0.196728i
$506$	12.3343	−	7.12123i	0.548328	−	0.316577i
$507$	−26.3462	−	41.4132i	−1.17008	−	1.83922i
$508$	0.665690	−	0.178371i	0.0295352	−	0.00791393i
$509$	−14.1129	−	24.4442i	−0.625543	−	1.08347i	−0.988436	−	0.151641i	$-0.951544\pi$
$509$	−14.1129	−	24.4442i	−0.625543	−	1.08347i	0.362893	−	0.931831i	$-0.381789\pi$
$510$	−4.34872	−	3.49815i	−0.192565	−	0.154901i
$511$	−0.308059	−	0.386397i	−0.0136277	−	0.0170932i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−5.17694	−	6.77332i	−0.228567	−	0.299050i
$514$	19.6746	+	11.3592i	0.867811	+	0.501031i
$515$	−0.736469	−	11.3187i	−0.0324527	−	0.498760i
$516$	11.0023	+	10.0946i	0.484350	+	0.444390i
$517$	−11.9480	+	11.9480i	−0.525474	+	0.525474i
$518$	−7.68051	−	0.866402i	−0.337462	−	0.0380675i
$519$	6.29796	−	1.98136i	0.276450	−	0.0869719i
$520$	13.6160	−	4.61480i	0.597100	−	0.202372i
$521$	−25.1057	−	14.4948i	−1.09990	−	0.635028i	−0.163706	−	0.986509i	$-0.552345\pi$
$521$	−25.1057	−	14.4948i	−1.09990	−	0.635028i	−0.936195	+	0.351481i	$0.885678\pi$
$522$	−24.2761	−	20.4225i	−1.06253	−	0.893868i
$523$	−3.48700	+	13.0137i	−0.152476	+	0.569047i	0.846833	+	0.531860i	$0.178507\pi$
$523$	−3.48700	+	13.0137i	−0.152476	+	0.569047i	−0.999308	+	0.0371877i	$0.988160\pi$
$524$	8.71583			0.380753
$525$	22.8708	−	1.38813i	0.998163	−	0.0605828i
$526$	28.7634			1.25414
$527$	−0.115868	+	0.432426i	−0.00504730	+	0.0188368i
$528$	−2.68476	−	4.22013i	−0.116839	−	0.183658i
$529$	1.14728	+	0.662381i	0.0498816	+	0.0287992i
$530$	1.13692	−	0.385330i	0.0493846	−	0.0167377i
$531$	11.0223	+	15.7840i	0.478329	+	0.684969i
$532$	−1.73533	−	3.97885i	−0.0752363	−	0.172505i
$533$	−38.8260	+	38.8260i	−1.68174	+	1.68174i
$534$	−8.43577	+	9.19433i	−0.365052	+	0.397878i
$535$	0.990413	+	15.2215i	0.0428193	+	0.658082i
$536$	−0.724049	−	0.418030i	−0.0312742	−	0.0180561i
$537$	0.656474	+	15.2574i	0.0283289	+	0.658407i
$538$	3.99940	+	3.99940i	0.172427	+	0.172427i
$539$	−19.3178	+	5.95323i	−0.832077	+	0.256424i
$540$	−0.787443	+	11.5922i	−0.0338862	+	0.498850i
$541$	6.51810	+	11.2897i	0.280235	+	0.485382i	0.971443	−	0.237275i	$-0.0762542\pi$
$541$	6.51810	+	11.2897i	0.280235	+	0.485382i	−0.691207	+	0.722656i	$0.742921\pi$
$542$	22.0794	−	5.91616i	0.948391	−	0.254121i
$543$	7.76798	−	4.94184i	0.333356	−	0.212074i
$544$	1.24797	−	0.720514i	0.0535061	−	0.0308918i
$545$	19.9579	+	3.97972i	0.854902	+	0.170473i
$546$	29.3928	+	2.04109i	1.25790	+	0.0873505i
$547$	12.1225	−	12.1225i	0.518321	−	0.518321i	−0.398742	−	0.917063i	$-0.630553\pi$
$547$	12.1225	−	12.1225i	0.518321	−	0.518321i	0.917063	+	0.398742i	$0.130553\pi$
$548$	16.2645	+	4.35805i	0.694784	+	0.186167i
$549$	2.08428	−	0.179691i	0.0889549	−	0.00766904i
$550$	−1.89823	+	14.3135i	−0.0809408	+	0.610329i
$551$	15.0251	−	8.67474i	0.640091	−	0.369556i
$552$	3.94928	−	7.57479i	0.168093	−	0.322404i
$553$	−19.9574	−	14.7333i	−0.848675	−	0.626522i
$554$	16.8591			0.716275
$555$	−9.13186	+	6.68022i	−0.387626	+	0.283559i
$556$	−7.60015	+	13.1638i	−0.322318	+	0.558271i
$557$	−37.8640	+	10.1456i	−1.60435	+	0.429884i	−0.946352	−	0.323138i	$-0.895262\pi$
$557$	−37.8640	+	10.1456i	−1.60435	+	0.429884i	−0.657996	+	0.753022i	$0.728595\pi$
$558$	0.876199	−	0.317654i	0.0370925	−	0.0134474i
$559$		−	55.4270i		−	2.34431i
$560$	−1.79999	+	5.63561i	−0.0760634	+	0.238148i
$561$	6.87543	−	2.16303i	0.290281	−	0.0913232i
$562$	−23.7477	−	6.36317i	−1.00173	−	0.268414i
$563$	−3.29065	−	12.2809i	−0.138684	−	0.517577i	−0.999956	−	0.00943155i	$-0.996998\pi$
$563$	−3.29065	−	12.2809i	−0.138684	−	0.517577i	0.861271	−	0.508146i	$-0.169669\pi$
$564$	−2.19982	+	9.89309i	−0.0926291	+	0.416574i
$565$	−11.3199	+	22.9270i	−0.476230	+	0.964545i
$566$		−	26.8128i		−	1.12703i
$567$	−10.6549	+	21.2949i	−0.447466	+	0.894301i
$568$	−1.92556	−	1.92556i	−0.0807947	−	0.0807947i
$569$	10.6592	+	18.4623i	0.446858	+	0.773981i	0.998180	−	0.0603121i	$-0.0192096\pi$
$569$	10.6592	+	18.4623i	0.446858	+	0.773981i	−0.551322	+	0.834293i	$0.685876\pi$
$570$	−5.81332	−	2.56561i	−0.243493	−	0.107462i
$571$	−7.85503	+	13.6053i	−0.328723	+	0.569365i	−0.982259	−	0.187531i	$-0.939952\pi$
$571$	−7.85503	+	13.6053i	−0.328723	+	0.569365i	0.653536	+	0.756896i	$0.273285\pi$
$572$	−4.80544	+	17.9342i	−0.200926	+	0.749865i
$573$	17.9604	−	34.4484i	0.750308	−	1.43910i
$574$	−3.36467	−	22.3429i	−0.140439	−	0.932577i
$575$	−22.7919	+	9.41537i	−0.950487	+	0.392648i
$576$	−2.71732	−	1.27130i	−0.113221	−	0.0529707i
$577$	−3.67230	−	13.7052i	−0.152880	−	0.570556i	−0.999278	−	0.0380044i	$-0.987900\pi$
$577$	−3.67230	−	13.7052i	−0.152880	−	0.570556i	0.846398	−	0.532552i	$-0.178767\pi$
$578$	−3.86247	−	14.4149i	−0.160658	−	0.599582i
$579$	19.2972	−	21.0324i	0.801964	−	0.874078i
$580$	−23.1891	−	4.62403i	−0.962873	−	0.192003i
$581$	−7.90277	−	3.10280i	−0.327862	−	0.128726i
$582$	−10.3284	−	5.38492i	−0.428124	−	0.223212i
$583$	−0.401249	+	1.49748i	−0.0166180	+	0.0620194i
$584$	0.0933892	−	0.161755i	0.00386447	−	0.00669347i
$585$	33.6836	−	26.9377i	1.39265	−	1.11374i
$586$	9.81029	+	16.9919i	0.405259	+	0.701930i
$587$	5.73739	+	5.73739i	0.236807	+	0.236807i	0.815527	−	0.578719i	$-0.196447\pi$
$587$	5.73739	+	5.73739i	0.236807	+	0.236807i	−0.578719	+	0.815527i	$0.696447\pi$
$588$	−7.85939	+	9.23201i	−0.324116	+	0.380722i
$589$			0.509703i			0.0210019i
$590$	12.8665	+	6.35267i	0.529707	+	0.261535i
$591$	−2.42066	−	0.538257i	−0.0995728	−	0.0221409i
$592$	−0.756107	−	2.82183i	−0.0310758	−	0.115976i
$593$	17.9944	+	4.82157i	0.738940	+	0.197998i	0.608607	−	0.793472i	$-0.291729\pi$
$593$	17.9944	+	4.82157i	0.738940	+	0.197998i	0.130333	+	0.991470i	$0.458395\pi$
$594$	−11.8871	−	9.15721i	−0.487733	−	0.375725i
$595$	−7.17301	−	4.60734i	−0.294065	−	0.188882i
$596$		−	13.3910i		−	0.548515i
$597$	−15.3095	+	0.658713i	−0.626575	+	0.0269593i
$598$	−30.6298	+	8.20723i	−1.25255	+	0.335619i
$599$	18.3356	−	31.7582i	0.749174	−	1.29761i	−0.199046	−	0.979990i	$-0.563784\pi$
$599$	18.3356	−	31.7582i	0.749174	−	1.29761i	0.948219	−	0.317616i	$-0.102882\pi$
$600$	3.64756	+	7.85464i	0.148911	+	0.320664i
$601$	−30.3187			−1.23673			−0.618363	−	0.785893i	$-0.712204\pi$
$601$	−30.3187			−1.23673			−0.618363	+	0.785893i	$0.712204\pi$
$602$	18.3498	+	13.5465i	0.747882	+	0.552113i
$603$	−2.46952	−	0.438669i	−0.100567	−	0.0178640i
$604$	1.41982	−	0.819732i	0.0577715	−	0.0333544i
$605$	4.47146	+	3.92512i	0.181791	+	0.159579i
$606$	3.80094	−	17.0937i	0.154403	−	0.694384i
$607$	−6.31001	−	1.69076i	−0.256115	−	0.0686259i	0.128477	−	0.991713i	$-0.458991\pi$
$607$	−6.31001	−	1.69076i	−0.256115	−	0.0686259i	−0.384592	+	0.923087i	$0.625658\pi$
$608$	1.16013	−	1.16013i	0.0470495	−	0.0470495i
$609$	−40.1874	−	27.0786i	−1.62848	−	1.09728i
$610$	1.29692	−	0.865682i	0.0525106	−	0.0350504i
$611$	32.5805	−	18.8104i	1.31807	−	0.760986i
$612$	2.78302	−	3.30815i	0.112497	−	0.133724i
$613$	37.1106	−	9.94374i	1.49888	−	0.401624i	0.586156	−	0.810198i	$-0.300640\pi$
$613$	37.1106	−	9.94374i	1.49888	−	0.401624i	0.912725	+	0.408574i	$0.133974\pi$
$614$	5.30223	+	9.18373i	0.213980	+	0.370625i
$615$	−25.7721	−	20.7313i	−1.03923	−	0.835967i
$616$	−4.76286	−	5.97404i	−0.191901	−	0.240701i
$617$	6.69009	+	6.69009i	0.269333	+	0.269333i	0.828831	−	0.559498i	$-0.189006\pi$
$617$	6.69009	+	6.69009i	0.269333	+	0.269333i	−0.559498	+	0.828831i	$0.689006\pi$
$618$	8.77782	−	0.377679i	0.353096	−	0.0151925i
$619$	1.57421	+	0.908870i	0.0632728	+	0.0365306i	0.531303	−	0.847182i	$-0.321703\pi$
$619$	1.57421	+	0.908870i	0.0632728	+	0.0365306i	−0.468030	+	0.883713i	$0.655036\pi$
$620$	0.458278	−	0.522066i	0.0184049	−	0.0209667i
$621$	3.39332	−	25.4018i	0.136169	−	1.01934i
$622$	11.6739	−	11.6739i	0.468082	−	0.468082i
$623$	−11.3204	+	15.3344i	−0.453542	+	0.614360i
$624$	3.34199	+	10.6229i	0.133787	+	0.425256i
$625$	6.51631	−	24.1358i	0.260653	−	0.965433i
$626$	12.4907	+	7.21152i	0.499230	+	0.288230i
$627$	6.92384	−	4.40481i	0.276512	−	0.175911i
$628$	3.51932	−	13.1343i	0.140436	−	0.524115i
$629$	4.20978			0.167855
$630$	0.685705	+	17.7350i	0.0273191	+	0.706579i
$631$	−0.0416272			−0.00165715			−0.000828576	−	1.00000i	$-0.500264\pi$
$631$	−0.0416272			−0.00165715			−0.000828576		1.00000i	$0.500264\pi$
$632$	2.42669	−	9.05652i	0.0965285	−	0.360249i
$633$	19.7356	−	12.5554i	0.784419	−	0.499032i
$634$	20.9221	+	12.0794i	0.830923	+	0.479734i
$635$	0.682239	−	1.38179i	0.0270738	−	0.0548347i
$636$	0.279053	+	0.887000i	0.0110652	+	0.0351718i
$637$	44.9754	−	1.67109i	1.78199	−	0.0662110i
$638$	21.5929	−	21.5929i	0.854871	−	0.854871i
$639$	−7.39967	−	3.46194i	−0.292726	−	0.136952i
$640$	−2.23135	+	0.145187i	−0.0882018	+	0.00573901i
$641$	2.23407	+	1.28984i	0.0882404	+	0.0509456i	0.543471	−	0.839428i	$-0.317110\pi$
$641$	2.23407	+	1.28984i	0.0882404	+	0.0509456i	−0.455231	+	0.890374i	$0.650443\pi$
$642$	−11.8045	+	0.507907i	−0.465887	+	0.0200455i
$643$	−14.7760	−	14.7760i	−0.582709	−	0.582709i	0.352938	−	0.935647i	$-0.385183\pi$
$643$	−14.7760	−	14.7760i	−0.582709	−	0.582709i	−0.935647	+	0.352938i	$0.885183\pi$
$644$	4.76888	−	12.1462i	0.187920	−	0.478629i
$645$	33.1936	−	3.59808i	1.30700	−	0.141674i
$646$	1.18213	+	2.04750i	0.0465101	+	0.0805579i
$647$	6.06708	−	1.62567i	0.238521	−	0.0639116i	−0.137578	−	0.990491i	$-0.543932\pi$
$647$	6.06708	−	1.62567i	0.238521	−	0.0639116i	0.376099	+	0.926579i	$0.377265\pi$
$648$	−8.96374	−	0.807110i	−0.352129	−	0.0317063i
$649$	−16.0487	+	9.26571i	−0.629966	+	0.363711i
$650$	12.3305	−	29.6887i	0.483641	−	1.16449i
$651$	1.27927	−	0.624708i	0.0501387	−	0.0244842i
$652$	0.123278	−	0.123278i	0.00482795	−	0.00482795i
$653$	−42.3647	−	11.3516i	−1.65786	−	0.444222i	−0.696061	−	0.717983i	$-0.745066\pi$
$653$	−42.3647	−	11.3516i	−1.65786	−	0.444222i	−0.961798	+	0.273761i	$0.911732\pi$
$654$	−3.42163	+	15.3878i	−0.133796	+	0.601712i
$655$	12.8571	−	14.6466i	0.502367	−	0.572292i
$656$	7.39591	−	4.27003i	0.288762	−	0.166717i
$657$	0.0980000	−	0.551699i	0.00382335	−	0.0215238i
$658$	−1.73534	+	15.3835i	−0.0676504	+	0.599710i
$659$	8.17474			0.318443			0.159221	−	0.987243i	$-0.449102\pi$
$659$	8.17474			0.318443			0.159221	+	0.987243i	$0.449102\pi$
$660$	−11.0522	−	1.71363i	−0.430206	−	0.0667030i
$661$	−11.1783	+	19.3615i	−0.434787	+	0.753074i	−0.997278	−	0.0737297i	$-0.976510\pi$
$661$	−11.1783	+	19.3615i	−0.434787	+	0.753074i	0.562491	+	0.826803i	$0.309843\pi$
$662$	15.5730	−	4.17276i	0.605260	−	0.162179i
$663$	−16.0327	+	0.689832i	−0.622660	+	0.0267909i
$664$		−	3.20894i		−	0.124531i
$665$	−9.24617	−	2.95319i	−0.358551	−	0.114520i
$666$	−5.01779	−	7.18550i	−0.194436	−	0.278433i
$667$	50.3771	+	13.4985i	1.95061	+	0.522664i
$668$	0.593563	+	2.21521i	0.0229657	+	0.0857090i
$669$	−47.9869	−	10.6703i	−1.85528	−	0.412539i
$670$	−1.77056	+	0.600086i	−0.0684026	+	0.0231834i
$671$			2.01374i			0.0777397i
$672$	−4.33363	−	1.48985i	−0.167173	−	0.0574722i
$673$	−28.3904	−	28.3904i	−1.09437	−	1.09437i	−0.995056	−	0.0993124i	$-0.968336\pi$
$673$	−28.3904	−	28.3904i	−1.09437	−	1.09437i	−0.0993124	−	0.995056i	$-0.531664\pi$
$674$	4.55572	+	7.89073i	0.175480	+	0.303940i
$675$	18.3188	+	18.4234i	0.705089	+	0.709119i
$676$	14.1691	−	24.5417i	0.544967	−	0.943911i
$677$	10.0547	−	37.5247i	0.386434	−	1.44219i	−0.449460	−	0.893300i	$-0.648384\pi$
$677$	10.0547	−	37.5247i	0.386434	−	1.44219i	0.835894	−	0.548891i	$-0.184950\pi$
$678$	−17.5622	−	9.15645i	−0.674472	−	0.351651i
$679$	−16.5616	−	6.50245i	−0.635577	−	0.249541i
$680$	0.630127	−	3.16002i	0.0241643	−	0.121181i
$681$	−9.34959	+	10.1903i	−0.358277	+	0.390494i
$682$	0.232195	+	0.866564i	0.00889121	+	0.0331824i
$683$	5.39696	+	20.1417i	0.206509	+	0.770702i	0.988984	+	0.148020i	$0.0472900\pi$
$683$	5.39696	+	20.1417i	0.206509	+	0.770702i	−0.782475	+	0.622681i	$0.786043\pi$
$684$	2.08578	−	4.45822i	0.0797518	−	0.170464i
$685$	31.3159	−	20.9031i	1.19652	−	0.798667i
$686$	−10.4388	+	15.2981i	−0.398556	+	0.584083i
$687$	−12.5177	+	24.0092i	−0.477581	+	0.916009i
$688$	−2.23122	+	8.32701i	−0.0850643	+	0.317464i
$689$	1.72585	−	2.98926i	0.0657497	−	0.113882i
$690$	−6.90342	−	17.8105i	−0.262809	−	0.678034i
$691$	6.25756	+	10.8384i	0.238049	+	0.412313i	0.960154	−	0.279470i	$-0.0901588\pi$
$691$	6.25756	+	10.8384i	0.238049	+	0.412313i	−0.722105	+	0.691783i	$0.756825\pi$
$692$	2.69537	+	2.69537i	0.102463	+	0.102463i
$693$	−19.5415	−	11.9791i	−0.742319	−	0.455047i
$694$		−	9.46892i		−	0.359435i
$695$	10.9101	+	32.1903i	0.413843	+	1.22105i
$696$	3.97559	−	17.8791i	0.150694	−	0.677706i
$697$	3.18515	+	11.8871i	0.120646	+	0.450257i
$698$	−19.1173	−	5.12246i	−0.723600	−	0.193888i
$699$	−12.1805	+	3.83202i	−0.460709	+	0.144940i
$700$	6.81520	+	11.3381i	0.257590	+	0.428541i
$701$			3.17238i			0.119819i	0.998204	+	0.0599096i	$0.0190812\pi$
$701$			3.17238i			0.119819i	−0.998204	+	0.0599096i	$0.980919\pi$
$702$	20.2875	+	26.5434i	0.765701	+	1.00182i
$703$	4.62969	−	1.24052i	0.174612	−	0.0467872i
$704$	1.44388	−	2.50087i	0.0544183	−	0.0942552i
$705$	13.3800	+	18.2904i	0.503918	+	0.688857i
$706$	−2.27199			−0.0855074
$707$	2.99839	−	26.5802i	0.112766	−	0.999651i
$708$	−5.13857	+	9.85585i	−0.193119	+	0.370406i
$709$	−2.89790	+	1.67311i	−0.108833	+	0.0628348i	−0.553429	−	0.832897i	$-0.686681\pi$
$709$	−2.89790	+	1.67311i	−0.108833	+	0.0628348i	0.444595	+	0.895731i	$0.353347\pi$
$710$	−6.07631	+	0.395366i	−0.228040	+	0.0148378i
$711$	−2.41603	−	28.0241i	−0.0906081	−	1.05098i
$712$	−6.95864	−	1.86456i	−0.260786	−	0.0698775i
$713$	−1.08344	+	1.08344i	−0.0405752	+	0.0405752i
$714$	3.69005	−	5.47643i	0.138097	−	0.204950i
$715$	23.0490	+	34.5308i	0.861985	+	1.29138i
$716$	−7.63578	+	4.40852i	−0.285362	+	0.164754i
$717$	5.72169	−	3.64003i	0.213680	−	0.135939i
$718$	11.5373	−	3.09140i	0.430567	−	0.115370i
$719$	9.77351	+	16.9282i	0.364491	+	0.631316i	0.988694	−	0.149945i	$-0.0479098\pi$
$719$	9.77351	+	16.9282i	0.364491	+	0.631316i	−0.624204	+	0.781262i	$0.714576\pi$
$720$	−6.14479	+	2.69101i	−0.229003	+	0.100288i
$721$	13.2711	−	1.99853i	0.494242	−	0.0744290i
$722$	−11.5316	−	11.5316i	−0.429163	−	0.429163i
$723$	1.31661	+	30.5999i	0.0489651	+	1.13802i
$724$	4.60335	+	2.65774i	0.171082	+	0.0987743i
$725$	−41.9776	+	32.1473i	−1.55901	+	1.19392i
$726$	−3.11576	+	3.39593i	−0.115637	+	0.126035i
$727$	−35.4505	+	35.4505i	−1.31479	+	1.31479i	−0.396946	+	0.917842i	$0.629930\pi$
$727$	−35.4505	+	35.4505i	−1.31479	+	1.31479i	−0.917842	+	0.396946i	$0.870070\pi$
$728$	6.80045	+	15.5924i	0.252042	+	0.577891i
$729$	−26.1064	+	6.88897i	−0.966902	+	0.255147i
$730$	−0.134061	−	0.395548i	−0.00496183	−	0.0146399i
$731$	−10.7584	−	6.21137i	−0.397914	−	0.229736i
$732$	0.648318	+	1.01908i	0.0239625	+	0.0376663i
$733$	−6.13452	+	22.8943i	−0.226584	+	0.845622i	0.755180	+	0.655517i	$0.227549\pi$
$733$	−6.13452	+	22.8943i	−0.226584	+	0.845622i	−0.981764	+	0.190105i	$0.939117\pi$
$734$	−12.1468			−0.448345
$735$	3.92037	+	26.8259i	0.144605	+	0.989489i
$736$	4.93201			0.181796
$737$	0.624877	−	2.33207i	0.0230176	−	0.0859030i
$738$	16.4932	−	19.6053i	0.607122	−	0.721682i
$739$	27.8766	+	16.0945i	1.02546	+	0.592047i	0.915680	−	0.401909i	$-0.131653\pi$
$739$	27.8766	+	16.0945i	1.02546	+	0.592047i	0.109776	+	0.993956i	$0.464987\pi$
$740$	−5.85735	−	2.89198i	−0.215320	−	0.106311i
$741$	−17.4287	+	5.48311i	−0.640258	+	0.201427i
$742$	0.567830	+	1.30195i	0.0208457	+	0.0477959i
$743$	7.19137	−	7.19137i	0.263826	−	0.263826i	−0.562781	−	0.826606i	$-0.690268\pi$
$743$	7.19137	−	7.19137i	0.263826	−	0.263826i	0.826606	+	0.562781i	$0.190268\pi$
$744$	0.396493	+	0.363781i	0.0145361	+	0.0133368i
$745$	−22.5030	−	19.7535i	−0.824447	−	0.723713i
$746$	16.9966	+	9.81299i	0.622290	+	0.359279i
$747$	−3.28111	−	9.05042i	−0.120050	−	0.331138i
$748$	2.94251	+	2.94251i	0.107589	+	0.107589i
$749$	−17.8472	+	2.68764i	−0.652121	+	0.0982043i
$750$	18.5801	+	5.45710i	0.678449	+	0.199265i
$751$	−18.2644	−	31.6349i	−0.666478	−	1.15437i	−0.978882	−	0.204424i	$-0.934468\pi$
$751$	−18.2644	−	31.6349i	−0.666478	−	1.15437i	0.312404	−	0.949949i	$-0.398866\pi$
$752$	−5.65190	+	1.51442i	−0.206104	+	0.0552253i
$753$	15.3650	+	24.1519i	0.559931	+	0.880145i
$754$	−58.8806	+	33.9947i	−2.14430	+	1.23801i
$755$	0.716898	−	3.59517i	0.0260906	−	0.130842i
$756$	−13.7458	+	0.229157i	−0.499931	+	0.00833437i
$757$	−17.0384	+	17.0384i	−0.619271	+	0.619271i	−0.945344	−	0.326073i	$-0.894274\pi$
$757$	−17.0384	+	17.0384i	−0.619271	+	0.619271i	0.326073	+	0.945344i	$0.394274\pi$
$758$	−9.00327	−	2.41242i	−0.327014	−	0.0876230i
$759$	24.0805	+	5.35453i	0.874068	+	0.194357i
$760$	−0.238204	−	3.66091i	−0.00864055	−	0.132795i
$761$	−3.67071	+	2.11929i	−0.133063	+	0.0768240i	−0.565054	−	0.825054i	$-0.691145\pi$
$761$	−3.67071	+	2.11929i	−0.133063	+	0.0768240i	0.431991	+	0.901878i	$0.357811\pi$
$762$	1.05846	+	0.551851i	0.0383439	+	0.0199915i
$763$	−2.69916	+	23.9277i	−0.0977163	+	0.866239i
$764$	22.4297			0.811477
$765$	−1.45389	−	9.55675i	−0.0525657	−	0.345525i
$766$	−5.21312	+	9.02939i	−0.188358	+	0.326245i
$767$	39.8536	−	10.6787i	1.43903	−	0.385587i
$768$	−0.0744552	−	1.73045i	−0.00268667	−	0.0624422i
$769$			9.91452i			0.357527i	0.983892	+	0.178763i	$0.0572097\pi$
$769$			9.91452i			0.357527i	−0.983892	+	0.178763i	$0.942790\pi$
$770$	−17.0651	−	0.808724i	−0.614982	−	0.0291444i
$771$	11.8088	+	37.5356i	0.425283	+	1.35181i
$772$	15.9182	+	4.26527i	0.572908	+	0.153510i
$773$	1.78235	+	6.65181i	0.0641066	+	0.239249i	0.990543	−	0.137202i	$-0.0438109\pi$
$773$	1.78235	+	6.65181i	0.0641066	+	0.239249i	−0.926436	+	0.376451i	$0.877144\pi$
$774$	2.22141	+	25.7667i	0.0798470	+	0.926164i
$775$	−0.201289	−	1.54024i	−0.00723052	−	0.0553271i
$776$		−	6.72489i		−	0.241410i
$777$	−8.78781	−	10.0994i	−0.315261	−	0.362313i
$778$	2.15808	+	2.15808i	0.0773708	+	0.0773708i
$779$	7.00571	+	12.1343i	0.251006	+	0.434755i
$780$	22.7813	+	10.0542i	0.815702	+	0.359997i
$781$	3.93191	−	6.81026i	0.140695	−	0.243690i
$782$	−1.83947	+	6.86500i	−0.0657793	+	0.245492i
$783$	−7.06856	−	54.4908i	−0.252610	−	1.94734i
$784$	−6.82409	−	1.55943i	−0.243717	−	0.0556939i
$785$	−16.8802	−	25.2890i	−0.602481	−	0.902603i
$786$	11.1237	+	10.2059i	0.396768	+	0.364034i
$787$	2.94983	+	11.0089i	0.105150	+	0.392425i	0.998362	−	0.0572104i	$-0.0182206\pi$
$787$	2.94983	+	11.0089i	0.105150	+	0.392425i	−0.893212	+	0.449635i	$0.851554\pi$
$788$	−0.370552	−	1.38292i	−0.0132004	−	0.0492645i
$789$	36.7096	+	33.6809i	1.30690	+	1.19907i
$790$	−11.6395	−	17.4376i	−0.414114	−	0.620402i
$791$	−28.1611	−	11.0567i	−1.00130	−	0.393130i
$792$	1.51517	−	8.52975i	0.0538391	−	0.303091i
$793$	1.16042	−	4.33075i	0.0412078	−	0.153789i
$794$	6.46613	−	11.1997i	0.229474	−	0.397461i
$795$	1.90221	+	0.839511i	0.0674646	+	0.0297744i
$796$	−4.42355	−	7.66182i	−0.156789	−	0.271566i
$797$	−29.5652	−	29.5652i	−1.04725	−	1.04725i	−0.998827	−	0.0484262i	$-0.984579\pi$
$797$	−29.5652	−	29.5652i	−1.04725	−	1.04725i	−0.0484262	−	0.998827i	$-0.515421\pi$
$798$	2.44435	−	7.11006i	0.0865291	−	0.251693i
$799$		−	8.43186i		−	0.298298i
$800$	−3.04757	+	3.96388i	−0.107748	+	0.140144i
$801$	−21.5325	+	1.85637i	−0.760813	+	0.0655916i
$802$	5.57313	+	20.7992i	0.196794	+	0.734446i
$803$	0.520993	+	0.139600i	0.0183854	+	0.00492636i
$804$	−0.434577	−	1.38135i	−0.0153263	−	0.0487165i
$805$	−13.3766	−	25.9313i	−0.471462	−	0.913959i
$806$		−	1.99743i		−	0.0703565i
$807$	0.421119	+	9.78745i	0.0148241	+	0.344534i
$808$	9.76560	−	2.61668i	0.343552	−	0.0920546i
$809$	−12.3778	+	21.4390i	−0.435181	+	0.753756i	−0.997310	−	0.0732932i	$-0.976649\pi$
$809$	−12.3778	+	21.4390i	−0.435181	+	0.753756i	0.562129	+	0.827050i	$0.309982\pi$
$810$	−14.5791	+	13.8726i	−0.512257	+	0.487435i
$811$	−28.9643			−1.01707			−0.508537	−	0.861040i	$-0.669813\pi$
$811$	−28.9643			−1.01707			−0.508537	+	0.861040i	$0.669813\pi$
$812$	3.13616	−	27.8015i	0.110058	−	0.975642i
$813$	35.1067	+	18.3036i	1.23124	+	0.641937i
$814$	7.30598	−	4.21811i	0.256074	−	0.147845i
$815$	−0.0253121	−	0.389017i	−0.000886644	−	0.0136267i
$816$	2.43643	+	0.541762i	0.0852920	+	0.0189655i
$817$	−13.6619	−	3.66069i	−0.477969	−	0.128071i
$818$	−5.15705	+	5.15705i	−0.180312	+	0.180312i
$819$	35.1229	+	37.0229i	1.22729	+	1.29369i
$820$	3.73436	−	18.7275i	0.130410	−	0.653991i
$821$	−37.5263	+	21.6658i	−1.30968	+	0.756143i	−0.982042	−	0.188661i	$-0.939585\pi$
$821$	−37.5263	+	21.6658i	−1.30968	+	0.756143i	−0.327636	+	0.944804i	$0.606252\pi$
$822$	15.6546	+	24.6071i	0.546016	+	0.858272i
$823$	44.8040	−	12.0052i	1.56177	−	0.418474i	0.628545	−	0.777773i	$-0.283651\pi$
$823$	44.8040	−	12.0052i	1.56177	−	0.418474i	0.933223	+	0.359298i	$0.116984\pi$
$824$	2.53628	+	4.39297i	0.0883556	+	0.153036i
$825$	−19.1832	+	16.0450i	−0.667874	+	0.558614i
$826$	−6.20497	+	15.8039i	−0.215899	+	0.549889i
$827$	34.7746	+	34.7746i	1.20923	+	1.20923i	0.971276	+	0.237957i	$0.0764779\pi$
$827$	34.7746	+	34.7746i	1.20923	+	1.20923i	0.237957	+	0.971276i	$0.423522\pi$
$828$	13.9101	−	5.04293i	0.483410	−	0.175254i
$829$	26.7949	+	15.4700i	0.930624	+	0.537296i	0.887009	−	0.461752i	$-0.152779\pi$
$829$	26.7949	+	15.4700i	0.930624	+	0.537296i	0.0436151	+	0.999048i	$0.486112\pi$
$830$	−5.39252	−	4.73364i	−0.187177	−	0.164307i
$831$	21.5166	+	19.7414i	0.746404	+	0.684823i
$832$	−4.54633	+	4.54633i	−0.157616	+	0.157616i
$833$	4.71576	−	8.91701i	0.163391	−	0.308956i
$834$	−25.1142	+	7.90098i	−0.869632	+	0.273589i
$835$	4.59817	+	2.27028i	0.159126	+	0.0785663i
$836$	4.10311	+	2.36893i	0.141909	+	0.0819312i
$837$	1.49022	+	0.620589i	0.0515095	+	0.0214507i
$838$	7.66410	−	28.6028i	0.264752	−	0.988068i
$839$	5.32218			0.183742			0.0918710	−	0.995771i	$-0.470715\pi$
$839$	5.32218			0.183742			0.0918710	+	0.995771i	$0.470715\pi$
$840$	−8.89635	+	5.08478i	−0.306953	+	0.175442i
$841$	82.8228			2.85596
$842$	−1.00446	+	3.74869i	−0.0346159	+	0.129188i
$843$	−22.8572	−	35.9287i	−0.787242	−	1.23745i
$844$	11.6954	+	6.75235i	0.402573	+	0.232425i
$845$	−20.3400	−	60.0132i	−0.699716	−	2.06452i
$846$	−14.3920	+	10.0503i	−0.494807	+	0.345535i
$847$	−4.18120	+	5.66377i	−0.143668	+	0.194610i
$848$	−0.379614	+	0.379614i	−0.0130360	+	0.0130360i
$849$	31.3969	−	34.2201i	1.07754	−	1.17443i
$850$	−4.38078	−	5.72038i	−0.150260	−	0.196208i
$851$	12.4779	+	7.20412i	0.427737	+	0.246954i
$852$	−0.202753	−	4.71228i	−0.00694620	−	0.161440i
$853$	−12.3820	−	12.3820i	−0.423953	−	0.423953i	0.462609	−	0.886562i	$-0.346913\pi$
$853$	−12.3820	−	12.3820i	−0.423953	−	0.423953i	−0.886562	+	0.462609i	$0.846913\pi$
$854$	1.15014	+	1.44262i	0.0393569	+	0.0493653i
$855$	−4.41506	−	10.0816i	−0.150992	−	0.344783i
$856$	−3.41083	−	5.90772i	−0.116580	−	0.201922i
$857$	−42.4872	+	11.3844i	−1.45133	+	0.388884i	−0.896487	−	0.443069i	$-0.853890\pi$
$857$	−42.4872	+	11.3844i	−1.45133	+	0.388884i	−0.554846	+	0.831953i	$0.687223\pi$
$858$	−27.1333	+	17.2617i	−0.926314	+	0.589303i
$859$	−23.4854	+	13.5593i	−0.801311	+	0.462637i	−0.843929	−	0.536454i	$-0.819763\pi$
$859$	−23.4854	+	13.5593i	−0.801311	+	0.462637i	0.0426185	+	0.999091i	$0.486430\pi$
$860$	10.7019	+	16.0330i	0.364931	+	0.546720i
$861$	21.8686	−	32.4553i	0.745280	−	1.10607i
$862$	−19.4244	+	19.4244i	−0.661598	+	0.661598i
$863$	37.5548	+	10.0628i	1.27838	+	0.342541i	0.833236	−	0.552917i	$-0.186485\pi$
$863$	37.5548	+	10.0628i	1.27838	+	0.342541i	0.445145	+	0.895458i	$0.353152\pi$
$864$	−1.97936	−	4.80439i	−0.0673391	−	0.163449i
$865$	8.50552	−	0.553427i	0.289196	−	0.0188171i
$866$	−22.2142	+	12.8254i	−0.754870	+	0.435825i
$867$	11.9499	−	22.9200i	0.405839	−	0.778405i
$868$	0.661274	+	0.488176i	0.0224451	+	0.0165698i
$869$	27.0756			0.918478
$870$	−24.1807	−	33.0550i	−0.819802	−	1.12067i
$871$	−2.68772	+	4.65526i	−0.0910698	+	0.157738i
$872$	−8.79105	+	2.35555i	−0.297702	+	0.0797691i
$873$	−6.87613	−	18.9667i	−0.232722	−	0.641926i
$874$			8.09181i			0.273710i
$875$	29.1067	+	5.27261i	0.983986	+	0.178247i
$876$	0.308598	−	0.0970859i	0.0104266	−	0.00328023i
$877$	−37.9744	−	10.1752i	−1.28230	−	0.343592i	−0.447572	−	0.894248i	$-0.647711\pi$
$877$	−37.9744	−	10.1752i	−1.28230	−	0.343592i	−0.834732	+	0.550656i	$0.814378\pi$
$878$	6.08881	+	22.7237i	0.205487	+	0.766889i
$879$	−7.37646	+	33.1736i	−0.248802	+	1.11892i
$880$	−2.07270	−	6.11553i	−0.0698709	−	0.206154i
$881$		−	25.3849i		−	0.855240i	−0.903959	−	0.427620i	$-0.859352\pi$
$881$		−	25.3849i		−	0.855240i	0.903959	−	0.427620i	$-0.140648\pi$
$882$	−20.8410	+	2.57938i	−0.701753	+	0.0868522i
$883$	−26.1956	−	26.1956i	−0.881550	−	0.881550i	0.112142	−	0.993692i	$-0.464229\pi$
$883$	−26.1956	−	26.1956i	−0.881550	−	0.881550i	−0.993692	+	0.112142i	$0.964229\pi$
$884$	−4.63253	−	8.02378i	−0.155809	−	0.269869i
$885$	8.98231	+	23.1739i	0.301937	+	0.778983i
$886$	10.5342	−	18.2457i	0.353903	−	0.612978i
$887$	2.73762	−	10.2169i	0.0919202	−	0.343051i	−0.904614	−	0.426231i	$-0.859841\pi$
$887$	2.73762	−	10.2169i	0.0919202	−	0.343051i	0.996535	+	0.0831802i	$0.0265077\pi$
$888$	2.33927	−	4.48676i	0.0785009	−	0.150566i
$889$	1.69725	+	0.666377i	0.0569239	+	0.0223496i
$890$	−13.3983	+	8.94327i	−0.449112	+	0.299779i
$891$	−4.44824	−	25.6063i	−0.149022	−	0.857845i
$892$	−7.34578	−	27.4148i	−0.245955	−	0.917916i
$893$	−2.48467	−	9.27291i	−0.0831463	−	0.310306i
$894$	15.6803	−	17.0903i	0.524429	−	0.571587i
$895$	−3.85548	+	19.3348i	−0.128874	+	0.646292i
$896$	−0.393987	−	2.61625i	−0.0131622	−	0.0874028i
$897$	−48.7020	−	25.3919i	−1.62611	−	0.847810i
$898$	0.661674	−	2.46940i	0.0220803	−	0.0824049i
$899$	−1.64260	+	2.84506i	−0.0547837	+	0.0948881i
$900$	−4.54228	+	14.2957i	−0.151409	+	0.476524i
$901$	−0.386811	−	0.669977i	−0.0128866	−	0.0223202i
$902$	17.4384	+	17.4384i	0.580636	+	0.580636i
$903$	7.55668	+	38.7758i	0.251470	+	1.29038i
$904$		−	11.4349i		−	0.380319i
$905$	11.2568	−	3.81522i	0.374190	−	0.126822i
$906$	2.77193	+	0.616365i	0.0920913	+	0.0204773i
$907$	−6.80928	−	25.4126i	−0.226098	−	0.843811i	−0.981961	−	0.189081i	$-0.939449\pi$
$907$	−6.80928	−	25.4126i	−0.226098	−	0.843811i	0.755863	−	0.654730i	$-0.227218\pi$
$908$	−7.71245	−	2.06654i	−0.255947	−	0.0685807i
$909$	24.8671	−	17.3652i	0.824790	−	0.575969i
$910$	36.2340	+	11.5730i	1.20115	+	0.383641i
$911$			39.1115i			1.29582i	0.761716	+	0.647911i	$0.224357\pi$
$911$			39.1115i			1.29582i	−0.761716	+	0.647911i	$0.775643\pi$
$912$	2.83910	−	0.122156i	0.0940119	−	0.00404500i
$913$	8.95090	−	2.39839i	0.296232	−	0.0793750i
$914$	5.43937	−	9.42126i	0.179918	−	0.311628i
$915$	2.66889	+	0.413808i	0.0882307	+	0.0136801i
$916$	−15.6326			−0.516516
$917$	18.5522	+	13.6959i	0.612647	+	0.452277i
$918$	7.42558	−	0.963249i	0.245081	−	0.0317919i
$919$	−47.4211	+	27.3786i	−1.56428	+	0.903137i	−0.567464	+	0.823399i	$0.692075\pi$
$919$	−47.4211	+	27.3786i	−1.56428	+	0.903137i	−0.996816	+	0.0797385i	$0.974591\pi$
$920$	7.27541	−	8.28808i	0.239863	−	0.273250i
$921$	−3.98680	+	17.9296i	−0.131370	+	0.590799i
$922$	32.4969	+	8.70751i	1.07023	+	0.286766i
$923$	−12.3804	+	12.3804i	−0.407505	+	0.407505i
$924$	0.916741	−	13.2016i	0.0301586	−	0.434300i
$925$	−13.5003	+	5.57699i	−0.443886	+	0.183370i
$926$	−9.35568	+	5.40151i	−0.307447	+	0.177505i
$927$	11.6450	+	9.79651i	0.382473	+	0.321760i
$928$	10.2143	−	2.73692i	0.335301	−	0.0898436i
$929$	8.26043	+	14.3075i	0.271016	+	0.469414i	0.969122	−	0.246581i	$-0.0793070\pi$
$929$	8.26043	+	14.3075i	0.271016	+	0.469414i	−0.698106	+	0.715994i	$0.745974\pi$
$930$	1.19620	−	0.129664i	0.0392250	−	0.00425187i
$931$	2.55851	−	11.1961i	0.0838518	−	0.366937i
$932$	−5.21295	−	5.21295i	−0.170756	−	0.170756i
$933$	28.5687	−	1.22921i	0.935298	−	0.0402426i
$934$	−28.2822	−	16.3287i	−0.925421	−	0.534292i
$935$	9.28541	−	0.604171i	0.303665	−	0.0197585i
$936$	−8.17379	+	17.4709i	−0.267169	+	0.571056i
$937$	25.3565	−	25.3565i	0.828362	−	0.828362i	−0.158928	−	0.987290i	$-0.550804\pi$
$937$	25.3565	−	25.3565i	0.828362	−	0.828362i	0.987290	+	0.158928i	$0.0508038\pi$
$938$	−0.884299	−	2.02756i	−0.0288734	−	0.0662021i
$939$	7.49697	+	23.8300i	0.244655	+	0.777662i
$940$	−5.79241	+	11.7318i	−0.188928	+	0.382649i
$941$	21.3739	+	12.3402i	0.696768	+	0.402279i	0.806143	−	0.591721i	$-0.201551\pi$
$941$	21.3739	+	12.3402i	0.696768	+	0.402279i	−0.109374	+	0.994001i	$0.534885\pi$
$942$	19.8714	−	12.6418i	0.647444	−	0.411891i
$943$	−10.9014	+	40.6845i	−0.354998	+	1.32487i
$944$	−6.41723			−0.208863
$945$	−19.8919	+	23.4374i	−0.647084	+	0.762419i
$946$	−24.8947			−0.809395
$947$	−3.29765	+	12.3070i	−0.107159	+	0.399923i	−0.998581	−	0.0532508i	$-0.983042\pi$
$947$	−3.29765	+	12.3070i	−0.107159	+	0.399923i	0.891422	+	0.453174i	$0.149708\pi$
$948$	13.7020	−	8.71692i	0.445019	−	0.283112i
$949$	−1.04000	−	0.600445i	−0.0337599	−	0.0194913i
$950$	−6.50341	−	5.00006i	−0.210999	−	0.162223i
$951$	12.5575	+	39.9155i	0.407206	+	1.29435i
$952$	3.78857	+	0.427371i	0.122788	+	0.0138512i
$953$	20.6345	−	20.6345i	0.668417	−	0.668417i	−0.288933	−	0.957349i	$-0.593300\pi$
$953$	20.6345	−	20.6345i	0.668417	−	0.668417i	0.957349	+	0.288933i	$0.0933004\pi$
$954$	−0.682502	+	1.45880i	−0.0220968	+	0.0472305i
$955$	33.0869	−	37.6923i	1.07067	−	1.21969i
$956$	3.39070	+	1.95762i	0.109663	+	0.0633141i
$957$	52.8427	−	2.27364i	1.70816	−	0.0734962i
$958$	19.6877	+	19.6877i	0.636080	+	0.636080i
$959$	27.7717	+	34.8340i	0.896797	+	1.12485i
$960$	−3.01779	−	2.42754i	−0.0973988	−	0.0783484i
$961$	15.4517	+	26.7632i	0.498443	+	0.863329i
$962$	−18.1429	+	4.86138i	−0.584951	+	0.156737i
$963$	−15.6604	−	13.1745i	−0.504649	−	0.424541i
$964$	−15.3141	+	8.84160i	−0.493234	+	0.284769i
$965$	30.6492	−	20.4581i	0.986632	−	0.658570i
$966$	20.3092	−	9.91757i	0.653436	−	0.319093i
$967$	30.4549	−	30.4549i	0.979364	−	0.979364i	−0.0204272	−	0.999791i	$-0.506503\pi$
$967$	30.4549	−	30.4549i	0.979364	−	0.979364i	0.999791	+	0.0204272i	$0.00650265\pi$
$968$	−2.57018	−	0.688678i	−0.0826088	−	0.0221350i
$969$	−0.888853	+	3.99738i	−0.0285541	+	0.128414i
$970$	−11.3009	−	9.92016i	−0.362851	−	0.318517i
$971$	−36.5408	+	21.0969i	−1.17265	+	0.677030i	−0.954303	−	0.298841i	$-0.903400\pi$
$971$	−36.5408	+	21.0969i	−1.17265	+	0.677030i	−0.218348	+	0.975871i	$0.570067\pi$
$972$	−10.4950	−	11.5263i	−0.336626	−	0.369706i
$973$	−36.8628	+	16.0773i	−1.18177	+	0.515415i
$974$	−31.5305			−1.01030
$975$	50.5013	−	23.4519i	1.61734	−	0.751062i
$976$	−0.348669	+	0.603912i	−0.0111606	+	0.0193308i
$977$	6.84676	−	1.83458i	0.219047	−	0.0586936i	−0.147626	−	0.989043i	$-0.547163\pi$
$977$	6.84676	−	1.83458i	0.219047	−	0.0586936i	0.366674	+	0.930350i	$0.380497\pi$
$978$	0.301690	−	0.0129806i	0.00964697	−	0.000415075i
$979$		−	20.8038i		−	0.664891i
$980$	−12.6871	+	9.16726i	−0.405273	+	0.292837i
$981$	−22.3855	+	15.6323i	−0.714715	+	0.499101i
$982$	1.47299	+	0.394685i	0.0470048	+	0.0125949i
$983$	7.06155	+	26.3541i	0.225229	+	0.840564i	0.982313	+	0.187247i	$0.0599565\pi$
$983$	7.06155	+	26.3541i	0.225229	+	0.840564i	−0.757084	+	0.653317i	$0.773377\pi$
$984$	14.4392	+	3.21068i	0.460304	+	0.102353i
$985$	−2.87057	−	1.41730i	−0.0914639	−	0.0451590i
$986$			15.2383i			0.485287i
$987$	−20.2282	+	17.6013i	−0.643872	+	0.560255i
$988$	−7.45904	−	7.45904i	−0.237304	−	0.237304i
$989$	−21.2588	−	36.8214i	−0.675992	−	1.17085i
$990$	−12.0989	−	15.1288i	−0.384527	−	0.480824i
$991$	−20.8255	+	36.0708i	−0.661543	+	1.14583i	0.318667	+	0.947867i	$0.396765\pi$
$991$	−20.8255	+	36.0708i	−0.661543	+	1.14583i	−0.980210	+	0.197960i	$0.936568\pi$
$992$	−0.0804067	+	0.300082i	−0.00255291	+	0.00952761i
$993$	24.7613	+	12.9099i	0.785776	+	0.409682i
$994$	−1.07289	−	7.12445i	−0.0340299	−	0.225974i
$995$	−19.4008	−	3.86863i	−0.615046	−	0.122644i
$996$	3.75756	−	4.09545i	0.119063	−	0.129769i
$997$	−7.66148	−	28.5930i	−0.242641	−	0.905550i	−0.974554	−	0.224152i	$-0.928039\pi$
$997$	−7.66148	−	28.5930i	−0.242641	−	0.905550i	0.731913	−	0.681398i	$-0.238628\pi$
$998$	−2.77603	−	10.3603i	−0.0878737	−	0.327949i
$999$	2.00996	−	15.0462i	0.0635924	−	0.476042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.x.a.53.3	yes	64
3.2	odd	2	inner	210.2.x.a.53.9	yes	64
5.2	odd	4	inner	210.2.x.a.137.6	yes	64
7.2	even	3	inner	210.2.x.a.23.12	yes	64
15.2	even	4	inner	210.2.x.a.137.12	yes	64
21.2	odd	6	inner	210.2.x.a.23.6	✓	64
35.2	odd	12	inner	210.2.x.a.107.9	yes	64
105.2	even	12	inner	210.2.x.a.107.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.6	✓	64	21.2	odd	6	inner
210.2.x.a.23.12	yes	64	7.2	even	3	inner
210.2.x.a.53.3	yes	64	1.1	even	1	trivial
210.2.x.a.53.9	yes	64	3.2	odd	2	inner
210.2.x.a.107.3	yes	64	105.2	even	12	inner
210.2.x.a.107.9	yes	64	35.2	odd	12	inner
210.2.x.a.137.6	yes	64	5.2	odd	4	inner
210.2.x.a.137.12	yes	64	15.2	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.46139 + 0.929705i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11774 + 0.717755i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(-1.05770 - 2.42513i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.27130 - 2.71732i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.46139 + 0.929705i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.11774 + 0.717755i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(-1.05770 - 2.42513i) q^{7} +(0.707107 - 0.707107i) q^{8} +(1.27130 - 2.71732i) q^{9} +(-0.145187 - 2.23135i) q^{10} +(2.50087 + 1.44388i) q^{11} +(1.73045 - 0.0744552i) q^{12} +(-4.54633 - 4.54633i) q^{13} +(2.61625 - 0.393987i) q^{14} +(2.42754 - 3.01779i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.39193 + 0.372965i) q^{17} +(2.29569 + 1.93127i) q^{18} +(-1.42086 + 0.820335i) q^{19} +(2.19290 + 0.437276i) q^{20} +(3.80036 + 2.56071i) q^{21} +(-2.04195 + 2.04195i) q^{22} +(-4.76396 - 1.27650i) q^{23} +(-0.375955 + 1.69076i) q^{24} +(3.96965 - 3.04004i) q^{25} +(5.56810 - 3.21474i) q^{26} +(0.668446 + 5.15298i) q^{27} +(-0.296574 + 2.62908i) q^{28} -10.5746 q^{29} +(2.28667 + 3.12588i) q^{30} +(0.155334 - 0.269046i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-4.99712 + 0.215009i) q^{33} -1.44103i q^{34} +(3.98058 + 4.37664i) q^{35} +(-2.45963 + 1.71762i) q^{36} +(-2.82183 - 0.756107i) q^{37} +(-0.424637 - 1.58477i) q^{38} +(10.8707 + 2.41720i) q^{39} +(-0.989939 + 2.00500i) q^{40} -8.54006i q^{41} +(-3.45706 + 3.00811i) q^{42} +(6.09579 + 6.09579i) q^{43} +(-1.44388 - 2.50087i) q^{44} +(-0.741911 + 6.66705i) q^{45} +(2.46601 - 4.27125i) q^{46} +(-1.51442 + 5.65190i) q^{47} +(-1.53584 - 0.800745i) q^{48} +(-4.76255 + 5.13012i) q^{49} +(1.90903 + 4.62121i) q^{50} +(1.68739 - 1.83913i) q^{51} +(1.66407 + 6.21041i) q^{52} +(0.138948 + 0.518562i) q^{53} +(-5.15040 - 0.688020i) q^{54} +(-6.33255 - 1.26275i) q^{55} +(-2.46273 - 0.966923i) q^{56} +(1.31376 - 2.51981i) q^{57} +(2.73692 - 10.2143i) q^{58} +(-3.20862 + 5.55749i) q^{59} +(-3.61120 + 1.39972i) q^{60} +(0.348669 + 0.603912i) q^{61} +(0.219675 + 0.219675i) q^{62} +(-7.93450 - 0.208967i) q^{63} -1.00000i q^{64} +(12.8911 + 6.36480i) q^{65} +(1.08567 - 4.88250i) q^{66} +(-0.216388 - 0.807572i) q^{67} +(1.39193 + 0.372965i) q^{68} +(8.14875 - 2.56362i) q^{69} +(-5.25776 + 2.71219i) q^{70} -2.72315i q^{71} +(-1.02249 - 2.82038i) q^{72} +(0.180414 - 0.0483418i) q^{73} +(1.46069 - 2.52998i) q^{74} +(-2.97486 + 8.13328i) q^{75} +1.64067 q^{76} +(0.856433 - 7.59214i) q^{77} +(-5.14838 + 9.87467i) q^{78} +(8.11986 - 4.68800i) q^{79} +(-1.68046 - 1.47514i) q^{80} +(-5.76761 - 6.90903i) q^{81} +(8.24906 + 2.21033i) q^{82} +(2.26907 - 2.26907i) q^{83} +(-2.01086 - 4.11782i) q^{84} +(2.68004 - 1.78891i) q^{85} +(-7.46579 + 4.31038i) q^{86} +(15.4536 - 9.83128i) q^{87} +(2.78936 - 0.747407i) q^{88} +(-3.60206 - 6.23895i) q^{89} +(-6.24786 - 2.44219i) q^{90} +(-6.21682 + 15.8341i) q^{91} +(3.48746 + 3.48746i) q^{92} +(0.0231308 + 0.537594i) q^{93} +(-5.06736 - 2.92564i) q^{94} +(2.42022 - 2.75709i) q^{95} +(1.17097 - 1.27626i) q^{96} +(4.75522 - 4.75522i) q^{97} +(-3.72268 - 5.92804i) q^{98} +(7.10283 - 4.96006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 64 * q + 8 * q^6 + 4 * q^7	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43} - 28 q^{45} + 24 q^{46} - 16 q^{55} + 24 q^{57} - 28 q^{58} + 8 q^{60} + 24 q^{61} - 88 q^{63} - 16 q^{67} - 12 q^{70} + 8 q^{72} - 56 q^{73} + 8 q^{75} - 32 q^{76} - 16 q^{78} + 4 q^{81} + 16 q^{82} + 32 q^{85} + 76 q^{87} + 12 q^{88} + 40 q^{90} - 48 q^{91} + 84 q^{93} + 4 q^{96} + 104 q^{97}+O(q^{100}) \) 64 * q + 8 * q^6 + 4 * q^7 + 4 * q^10 - 24 * q^15 + 32 * q^16 - 8 * q^18 + 12 * q^21 - 24 * q^22 - 8 * q^25 - 72 * q^27 + 4 * q^28 - 12 * q^30 + 32 * q^31 - 20 * q^33 - 24 * q^36 - 8 * q^37 - 40 * q^42 - 64 * q^43 - 28 * q^45 + 24 * q^46 - 16 * q^55 + 24 * q^57 - 28 * q^58 + 8 * q^60 + 24 * q^61 - 88 * q^63 - 16 * q^67 - 12 * q^70 + 8 * q^72 - 56 * q^73 + 8 * q^75 - 32 * q^76 - 16 * q^78 + 4 * q^81 + 16 * q^82 + 32 * q^85 + 76 * q^87 + 12 * q^88 + 40 * q^90 - 48 * q^91 + 84 * q^93 + 4 * q^96 + 104 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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