LMFDB - Embedded newform 210.2.x.a.137.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,2,Mod(23,210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

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

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

Self dual:	no
Analytic conductor:	$1.67685844245$
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			137.6
Character	$\chi$	$=$	210.137
Dual form			210.2.x.a.23.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.929705 + 1.46139i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.68046 + 1.47514i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(2.42513 - 1.05770i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.27130 + 2.71732i) q^{9} +(2.00500 - 0.989939i) q^{10} +(2.50087 + 1.44388i) q^{11} +(0.0744552 + 1.73045i) q^{12} +(-4.54633 + 4.54633i) q^{13} +(-2.61625 + 0.393987i) q^{14} +(-3.71809 - 1.08436i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.372965 - 1.39193i) q^{17} +(1.93127 - 2.29569i) 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} +(-1.27650 + 4.76396i) q^{23} +(0.375955 - 1.69076i) q^{24} +(0.647925 - 4.95784i) q^{25} +(5.56810 - 3.21474i) q^{26} +(-5.15298 + 0.668446i) q^{27} +(2.62908 + 0.296574i) q^{28} +10.5746 q^{29} +(3.31074 + 2.00973i) q^{30} +(0.155334 - 0.269046i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.215009 + 4.99712i) q^{33} +1.44103i q^{34} +(-2.51510 + 5.35484i) q^{35} +(-2.45963 + 1.71762i) q^{36} +(0.756107 - 2.82183i) q^{37} +(-1.58477 + 0.424637i) q^{38} +(-10.8707 - 2.41720i) q^{39} +(2.23135 + 0.145187i) q^{40} -8.54006i q^{41} +(-3.00811 - 3.45706i) q^{42} +(6.09579 - 6.09579i) q^{43} +(1.44388 + 2.50087i) q^{44} +(-1.87205 - 6.44169i) q^{45} +(2.46601 - 4.27125i) q^{46} +(-5.65190 - 1.51442i) q^{47} +(-0.800745 + 1.53584i) q^{48} +(4.76255 - 5.13012i) q^{49} +(-1.90903 + 4.62121i) q^{50} +(1.68739 - 1.83913i) q^{51} +(-6.21041 + 1.66407i) q^{52} +(0.518562 - 0.138948i) q^{53} +(5.15040 + 0.688020i) q^{54} +(-6.33255 + 1.26275i) q^{55} +(-2.46273 - 0.966923i) q^{56} +(2.51981 + 1.31376i) q^{57} +(-10.2143 - 2.73692i) q^{58} +(3.20862 - 5.55749i) q^{59} +(-2.67777 - 2.79813i) q^{60} +(0.348669 + 0.603912i) q^{61} +(-0.219675 + 0.219675i) q^{62} +(-0.208967 + 7.93450i) q^{63} +1.00000i q^{64} +(0.933476 - 14.3464i) q^{65} +(1.08567 - 4.88250i) q^{66} +(0.807572 - 0.216388i) q^{67} +(0.372965 - 1.39193i) q^{68} +(-8.14875 + 2.56362i) q^{69} +(3.81533 - 4.52142i) q^{70} -2.72315i q^{71} +(2.82038 - 1.02249i) q^{72} +(-0.0483418 - 0.180414i) q^{73} +(-1.46069 + 2.52998i) q^{74} +(7.84770 - 3.66246i) q^{75} +1.64067 q^{76} +(7.59214 + 0.856433i) q^{77} +(9.87467 + 5.14838i) q^{78} +(-8.11986 + 4.68800i) q^{79} +(-2.11774 - 0.717755i) q^{80} +(-5.76761 - 6.90903i) q^{81} +(-2.21033 + 8.24906i) 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} +(9.83128 + 15.4536i) q^{87} +(-0.747407 - 2.78936i) q^{88} +(3.60206 + 6.23895i) q^{89} +(0.141028 + 6.70672i) q^{90} +(-6.21682 + 15.8341i) q^{91} +(-3.48746 + 3.48746i) q^{92} +(0.537594 - 0.0231308i) q^{93} +(5.06736 + 2.92564i) q^{94} +(-1.17760 + 3.47452i) q^{95} +(1.17097 - 1.27626i) q^{96} +(4.75522 + 4.75522i) q^{97} +(-5.92804 + 3.72268i) q^{98} +(-7.10283 + 4.96006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

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

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

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.929705	+	1.46139i	0.536765	+	0.843732i
$3$	0.929705	+	1.46139i	0.536765	+	0.843732i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.68046	+	1.47514i	−0.751527	+	0.659703i
$5$	−1.68046	+	1.47514i	−0.751527	+	0.659703i
$6$	−0.519792	−	1.65222i	−0.212204	−	0.674514i
$7$	2.42513	−	1.05770i	0.916614	−	0.399772i
$7$	2.42513	−	1.05770i	0.916614	−	0.399772i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.27130	+	2.71732i	−0.423766	+	0.905772i
$10$	2.00500	−	0.989939i	0.634036	−	0.313046i
$11$	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	$0.523293\pi$
$12$	0.0744552	+	1.73045i	0.0214934	+	0.499538i
$13$	−4.54633	+	4.54633i	−1.26093	+	1.26093i	−0.310281	+	0.950645i	$0.600423\pi$
$13$	−4.54633	+	4.54633i	−1.26093	+	1.26093i	−0.950645	+	0.310281i	$0.899577\pi$
$14$	−2.61625	+	0.393987i	−0.699223	+	0.105297i
$15$	−3.71809	−	1.08436i	−0.960005	−	0.279981i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.372965	−	1.39193i	−0.0904574	−	0.337592i	0.905834	−	0.423632i	$-0.139245\pi$
$17$	−0.372965	−	1.39193i	−0.0904574	−	0.337592i	−0.996292	+	0.0860407i	$0.972578\pi$
$18$	1.93127	−	2.29569i	0.455205	−	0.541099i
$19$	1.42086	−	0.820335i	0.325968	−	0.188198i	−0.328081	−	0.944649i	$-0.606402\pi$
$19$	1.42086	−	0.820335i	0.325968	−	0.188198i	0.654050	+	0.756452i	$0.273069\pi$
$20$	−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
$23$	−1.27650	+	4.76396i	−0.266168	+	0.993354i	0.695363	+	0.718659i	$0.255244\pi$
$23$	−1.27650	+	4.76396i	−0.266168	+	0.993354i	−0.961531	+	0.274695i	$0.911423\pi$
$24$	0.375955	−	1.69076i	0.0767415	−	0.345124i
$25$	0.647925	−	4.95784i	0.129585	−	0.991568i
$26$	5.56810	−	3.21474i	1.09199	−	0.630463i
$27$	−5.15298	+	0.668446i	−0.991691	+	0.128642i
$28$	2.62908	+	0.296574i	0.496849	+	0.0560472i
$29$	10.5746			1.96366			0.981830	−	0.189765i	$-0.0607726\pi$
$29$	10.5746			1.96366			0.981830	+	0.189765i	$0.0607726\pi$
$30$	3.31074	+	2.00973i	0.604456	+	0.366924i
$31$	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	$0.157785\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.215009	+	4.99712i	0.0374282	+	0.869887i
$34$			1.44103i			0.247134i
$35$	−2.51510	+	5.35484i	−0.425130	+	0.905133i
$36$	−2.45963	+	1.71762i	−0.409939	+	0.286269i
$37$	0.756107	−	2.82183i	0.124303	−	0.463906i	−0.875511	−	0.483199i	$-0.839475\pi$
$37$	0.756107	−	2.82183i	0.124303	−	0.463906i	0.999814	+	0.0192930i	$0.00614152\pi$
$38$	−1.58477	+	0.424637i	−0.257083	+	0.0688852i
$39$	−10.8707	−	2.41720i	−1.74070	−	0.387062i
$40$	2.23135	+	0.145187i	0.352807	+	0.0229560i
$41$		−	8.54006i		−	1.33373i	−0.745177	−	0.666867i	$-0.767635\pi$
$41$		−	8.54006i		−	1.33373i	0.745177	−	0.666867i	$-0.232365\pi$
$42$	−3.00811	−	3.45706i	−0.464161	−	0.533436i
$43$	6.09579	−	6.09579i	0.929600	−	0.929600i	−0.0680801	−	0.997680i	$-0.521687\pi$
$43$	6.09579	−	6.09579i	0.929600	−	0.929600i	0.997680	+	0.0680801i	$0.0216874\pi$
$44$	1.44388	+	2.50087i	0.217673	+	0.377021i
$45$	−1.87205	−	6.44169i	−0.279069	−	0.960271i
$46$	2.46601	−	4.27125i	0.363593	−	0.629761i
$47$	−5.65190	−	1.51442i	−0.824415	−	0.220901i	−0.178139	−	0.984005i	$-0.557008\pi$
$47$	−5.65190	−	1.51442i	−0.824415	−	0.220901i	−0.646276	+	0.763104i	$0.723674\pi$
$48$	−0.800745	+	1.53584i	−0.115578	+	0.221680i
$49$	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
$52$	−6.21041	+	1.66407i	−0.861228	+	0.230765i
$53$	0.518562	−	0.138948i	0.0712300	−	0.0190860i	−0.223028	−	0.974812i	$-0.571594\pi$
$53$	0.518562	−	0.138948i	0.0712300	−	0.0190860i	0.294258	+	0.955726i	$0.404927\pi$
$54$	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
$57$	2.51981	+	1.31376i	0.333757	+	0.174012i
$58$	−10.2143	−	2.73692i	−1.34120	−	0.359375i
$59$	3.20862	−	5.55749i	0.417726	−	0.723523i	−0.577984	−	0.816048i	$-0.696160\pi$
$59$	3.20862	−	5.55749i	0.417726	−	0.723523i	0.995710	+	0.0925249i	$0.0294938\pi$
$60$	−2.67777	−	2.79813i	−0.345699	−	0.361237i
$61$	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
$63$	−0.208967	+	7.93450i	−0.0263274	+	0.999653i
$64$			1.00000i			0.125000i
$65$	0.933476	−	14.3464i	0.115783	−	1.77946i
$66$	1.08567	−	4.88250i	0.133636	−	0.600994i
$67$	0.807572	−	0.216388i	0.0986606	−	0.0264360i	−0.209151	−	0.977883i	$-0.567070\pi$
$67$	0.807572	−	0.216388i	0.0986606	−	0.0264360i	0.307812	+	0.951447i	$0.400403\pi$
$68$	0.372965	−	1.39193i	0.0452287	−	0.168796i
$69$	−8.14875	+	2.56362i	−0.980994	+	0.308623i
$70$	3.81533	−	4.52142i	0.456020	−	0.540413i
$71$		−	2.72315i		−	0.323179i	−0.986858	−	0.161589i	$-0.948338\pi$
$71$		−	2.72315i		−	0.323179i	0.986858	−	0.161589i	$-0.0516620\pi$
$72$	2.82038	−	1.02249i	0.332384	−	0.120502i
$73$	−0.0483418	−	0.180414i	−0.00565798	−	0.0211159i	0.963039	−	0.269362i	$-0.0868127\pi$
$73$	−0.0483418	−	0.180414i	−0.00565798	−	0.0211159i	−0.968697	+	0.248246i	$0.920146\pi$
$74$	−1.46069	+	2.52998i	−0.169801	+	0.294104i
$75$	7.84770	−	3.66246i	0.906174	−	0.422905i
$76$	1.64067			0.188198
$77$	7.59214	+	0.856433i	0.865205	+	0.0975996i
$78$	9.87467	+	5.14838i	1.11809	+	0.582939i
$79$	−8.11986	+	4.68800i	−0.913555	+	0.527441i	−0.881573	−	0.472047i	$-0.843515\pi$
$79$	−8.11986	+	4.68800i	−0.913555	+	0.527441i	−0.0319820	+	0.999488i	$0.510182\pi$
$80$	−2.11774	−	0.717755i	−0.236771	−	0.0802475i
$81$	−5.76761	−	6.90903i	−0.640845	−	0.767670i
$82$	−2.21033	+	8.24906i	−0.244090	+	0.910957i
$83$	−2.26907	−	2.26907i	−0.249062	−	0.249062i	0.571523	−	0.820586i	$-0.306353\pi$
$83$	−2.26907	−	2.26907i	−0.249062	−	0.249062i	−0.820586	+	0.571523i	$0.806353\pi$
$84$	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
$87$	9.83128	+	15.4536i	1.05402	+	1.65680i
$88$	−0.747407	−	2.78936i	−0.0796739	−	0.297347i
$89$	3.60206	+	6.23895i	0.381818	+	0.661327i	0.991322	−	0.131455i	$-0.0419649\pi$
$89$	3.60206	+	6.23895i	0.381818	+	0.661327i	−0.609505	+	0.792783i	$0.708632\pi$
$90$	0.141028	+	6.70672i	0.0148657	+	0.706951i
$91$	−6.21682	+	15.8341i	−0.651700	+	1.65987i
$92$	−3.48746	+	3.48746i	−0.363593	+	0.363593i
$93$	0.537594	−	0.0231308i	0.0557460	−	0.00239855i
$94$	5.06736	+	2.92564i	0.522658	+	0.301757i
$95$	−1.17760	+	3.47452i	−0.120819	+	0.356478i
$96$	1.17097	−	1.27626i	0.119511	−	0.130258i
$97$	4.75522	+	4.75522i	0.482819	+	0.482819i	0.906031	−	0.423212i	$-0.139097\pi$
$97$	4.75522	+	4.75522i	0.482819	+	0.482819i	−0.423212	+	0.906031i	$0.639097\pi$
$98$	−5.92804	+	3.72268i	−0.598823	+	0.376047i
$99$	−7.10283	+	4.96006i	−0.713861	+	0.498505i
$100$	3.04004	−	3.96965i	0.304004	−	0.396965i
$101$	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	$0.498898\pi$
$102$	−2.10590	+	1.33973i	−0.208515	+	0.132653i
$103$	4.89972	+	1.31288i	0.482784	+	0.129362i	0.491999	−	0.870596i	$-0.336266\pi$
$103$	4.89972	+	1.31288i	0.482784	+	0.129362i	−0.00921457	+	0.999958i	$0.502933\pi$
$104$	6.42949			0.630463
$105$	−10.1638	+	1.30289i	−0.991884	+	0.127149i
$106$	−0.536855			−0.0521440
$107$	6.58921	+	1.76557i	0.637003	+	0.170684i	0.562846	−	0.826562i	$-0.309707\pi$
$107$	6.58921	+	1.76557i	0.637003	+	0.170684i	0.0741574	+	0.997247i	$0.476373\pi$
$108$	−4.79683	−	1.99760i	−0.461575	−	0.192219i
$109$	7.88184	+	4.55058i	0.754943	+	0.435867i	0.827477	−	0.561499i	$-0.189775\pi$
$109$	7.88184	+	4.55058i	0.754943	+	0.435867i	−0.0725341	+	0.997366i	$0.523109\pi$
$110$	6.44360	+	0.419264i	0.614373	+	0.0399753i
$111$	4.82674	−	1.51850i	0.458134	−	0.144130i
$112$	2.12856	+	1.57138i	0.201130	+	0.148481i
$113$	−8.08570	−	8.08570i	−0.760639	−	0.760639i	0.215799	−	0.976438i	$-0.430764\pi$
$113$	−8.08570	−	8.08570i	−0.760639	−	0.760639i	−0.976438	+	0.215799i	$0.930764\pi$
$114$	−2.09392	−	1.92117i	−0.196114	−	0.179934i
$115$	−4.88239	−	9.88868i	−0.455286	−	0.922124i
$116$	9.15790	+	5.28731i	0.850289	+	0.490915i
$117$	−6.57408	−	18.1336i	−0.607774	−	1.67645i
$118$	−4.53767	+	4.53767i	−0.417726	+	0.417726i
$119$	−2.37673	−	2.98112i	−0.217874	−	0.273279i
$120$	1.86232	+	3.39584i	0.170006	+	0.309997i
$121$	−1.33042	−	2.30436i	−0.120948	−	0.209487i
$122$	−0.180484	−	0.673576i	−0.0163403	−	0.0609827i
$123$	12.4803	−	7.93974i	1.12531	−	0.715902i
$124$	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	0.685155	−	0.728397i	$-0.259735\pi$
$127$	−0.487319	−	0.487319i	−0.0432425	−	0.0432425i	−0.728397	+	0.685155i	$0.759735\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	14.5756	+	3.24102i	1.28331	+	0.285356i
$130$	−4.61480	+	13.6160i	−0.404745	+	1.19420i
$131$	−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	$0.457668\pi$
$132$	−2.31236	+	4.43514i	−0.201265	+	0.386029i
$133$	2.57812	−	3.49227i	0.223551	−	0.302818i
$134$	−0.836060			−0.0722246
$135$	7.67335	−	8.72466i	0.660417	−	0.750899i
$136$	−0.720514	+	1.24797i	−0.0617836	+	0.107012i
$137$	−4.35805	−	16.2645i	−0.372333	−	1.38957i	−0.857202	−	0.514980i	$-0.827799\pi$
$137$	−4.35805	−	16.2645i	−0.372333	−	1.38957i	0.484869	−	0.874587i	$-0.338867\pi$
$138$	8.53460	−	0.367214i	0.726514	−	0.0312593i
$139$			15.2003i			1.28927i	0.764490	+	0.644636i	$0.222991\pi$
$139$			15.2003i			1.28927i	−0.764490	+	0.644636i	$0.777009\pi$
$140$	−4.85556	+	3.37987i	−0.410370	+	0.285652i
$141$	−3.04145	−	9.66758i	−0.256136	−	0.814157i
$142$	−0.704804	+	2.63036i	−0.0591458	+	0.220735i
$143$	−17.9342	+	4.80544i	−1.49973	+	0.401851i
$144$	−2.98891	+	0.257682i	−0.249076	+	0.0214735i
$145$	−17.7703	+	15.5991i	−1.47574	+	1.29543i
$146$			0.186778i			0.0154579i
$147$	11.9248	+	2.19043i	0.983545	+	0.180663i
$148$	2.06572	−	2.06572i	0.169801	−	0.169801i
$149$	−6.69548	−	11.5969i	−0.548515	−	0.950056i	−0.998377	−	0.0569574i	$-0.981860\pi$
$149$	−6.69548	−	11.5969i	−0.548515	−	0.950056i	0.449862	−	0.893098i	$-0.351473\pi$
$150$	−8.52821	+	1.50653i	−0.696325	+	0.123008i
$151$	−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	$0.187917\pi$
$152$	−1.58477	−	0.424637i	−0.128542	−	0.0344426i
$153$	4.25645	+	0.756087i	0.344114	+	0.0611260i
$154$	−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
$157$	−13.1343	+	3.51932i	−1.04823	+	0.280872i	−0.741520	−	0.670931i	$-0.765895\pi$
$157$	−13.1343	+	3.51932i	−1.04823	+	0.280872i	−0.306710	+	0.951803i	$0.599228\pi$
$158$	9.05652	−	2.42669i	0.720498	−	0.193057i
$159$	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
$162$	3.78289	+	8.16638i	0.297212	+	0.641611i
$163$	0.168401	+	0.0451230i	0.0131902	+	0.00353430i	0.265408	−	0.964136i	$-0.414493\pi$
$163$	0.168401	+	0.0451230i	0.0131902	+	0.00353430i	−0.252218	+	0.967670i	$0.581160\pi$
$164$	4.27003	−	7.39591i	0.333433	−	0.577523i
$165$	−7.73277	−	8.08032i	−0.601995	−	0.629052i
$166$	1.60447	+	2.77903i	0.124531	+	0.215694i
$167$	1.62165	−	1.62165i	0.125487	−	0.125487i	−0.641574	−	0.767061i	$-0.721718\pi$
$167$	1.62165	−	1.62165i	0.125487	−	0.125487i	0.767061	+	0.641574i	$0.221718\pi$
$168$	−0.876568	−	4.49796i	−0.0676287	−	0.347025i
$169$		−	28.3383i		−	2.17987i
$170$	−2.12572	−	2.42160i	−0.163035	−	0.185728i
$171$	0.422771	+	4.90382i	0.0323301	+	0.375005i
$172$	8.32701	−	2.23122i	0.634928	−	0.170129i
$173$	−0.986574	+	3.68194i	−0.0750078	+	0.279933i	−0.993235	−	0.116121i	$-0.962954\pi$
$173$	−0.986574	+	3.68194i	−0.0750078	+	0.279933i	0.918227	+	0.396054i	$0.129621\pi$
$174$	−5.49660	−	17.4716i	−0.416696	−	1.32452i
$175$	−3.67260	−	12.7087i	−0.277622	−	0.960690i
$176$			2.88776i			0.217673i
$177$	11.1047	−	0.477796i	0.834680	−	0.0359134i
$178$	−1.86456	−	6.95864i	−0.139755	−	0.521572i
$179$	−4.40852	+	7.63578i	−0.329508	+	0.570725i	−0.982414	−	0.186714i	$-0.940216\pi$
$179$	−4.40852	+	7.63578i	−0.329508	+	0.570725i	0.652906	+	0.757439i	$0.273550\pi$
$180$	1.59960	−	6.51470i	0.119227	−	0.485577i
$181$	−5.31549			−0.395097			−0.197549	−	0.980293i	$-0.563298\pi$
$181$	−5.31549			−0.395097			−0.197549	+	0.980293i	$0.563298\pi$
$182$	10.1032	−	13.6855i	0.748896	−	1.01444i
$183$	−0.558389	+	1.07100i	−0.0412773	+	0.0791706i
$184$	4.27125	−	2.46601i	0.314881	−	0.181796i
$185$	2.89198	+	5.85735i	0.212623	+	0.430641i
$186$	−0.525263	−	0.116797i	−0.0385142	−	0.00856398i
$187$	1.07703	−	4.01955i	0.0787606	−	0.293938i
$188$	−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	$0.634669\pi$
$192$	−1.46139	+	0.929705i	−0.105466	+	0.0670957i
$193$	4.26527	+	15.9182i	0.307021	+	1.14582i	0.931192	+	0.364529i	$0.118770\pi$
$193$	4.26527	+	15.9182i	0.307021	+	1.14582i	−0.624171	+	0.781287i	$0.714563\pi$
$194$	−3.36245	−	5.82393i	−0.241410	−	0.418134i
$195$	21.8335	−	11.9738i	1.56353	−	0.857460i
$196$	6.68955	−	2.06154i	0.477825	−	0.147253i
$197$	−1.01237	+	1.01237i	−0.0721282	+	0.0721282i	−0.742251	−	0.670122i	$-0.766242\pi$
$197$	−1.01237	+	1.01237i	−0.0721282	+	0.0721282i	0.670122	+	0.742251i	$0.266242\pi$
$198$	8.14456	−	2.95270i	0.578809	−	0.209839i
$199$	−7.66182	−	4.42355i	−0.543132	−	0.313577i	0.203215	−	0.979134i	$-0.434861\pi$
$199$	−7.66182	−	4.42355i	−0.543132	−	0.313577i	−0.746347	+	0.665557i	$0.768194\pi$
$200$	−3.96388	+	3.04757i	−0.280288	+	0.215496i
$201$	1.06703	+	0.978997i	0.0752625	+	0.0690531i
$202$	−7.14891	−	7.14891i	−0.502996	−	0.502996i
$203$	25.6449	−	11.1848i	1.79992	−	0.785016i
$204$	2.38089	−	0.749034i	0.166696	−	0.0524429i
$205$	12.5978	+	14.3513i	0.879867	+	1.00234i
$206$	−4.39297	−	2.53628i	−0.306073	−	0.176711i
$207$	−11.3224	−	9.52506i	−0.786959	−	0.662037i
$208$	−6.21041	−	1.66407i	−0.430614	−	0.115383i
$209$	4.73786			0.327725
$210$	10.1547	+	1.37209i	0.700739	+	0.0946832i
$211$	−13.5047			−0.929702			−0.464851	−	0.885389i	$-0.653892\pi$
$211$	−13.5047			−0.929702			−0.464851	+	0.885389i	$0.653892\pi$
$212$	0.518562	+	0.138948i	0.0356150	+	0.00954301i
$213$	3.97958	−	2.53173i	0.272676	−	0.173471i
$214$	−5.90772	−	3.41083i	−0.403844	−	0.233159i
$215$	−1.25162	+	19.2359i	−0.0853597	+	1.31188i
$216$	4.11637	+	3.17104i	0.280083	+	0.215762i
$217$	0.0921358	−	0.816769i	0.00625459	−	0.0554459i
$218$	−6.43549	−	6.43549i	−0.435867	−	0.435867i
$219$	0.218711	−	0.238378i	0.0147791	−	0.0161081i
$220$	−6.11553	−	2.07270i	−0.412309	−	0.139742i
$221$	8.02378	+	4.63253i	0.539738	+	0.311618i
$222$	−5.05529	+	0.217511i	−0.339289	+	0.0145984i
$223$	20.0690	−	20.0690i	1.34392	−	1.34392i	0.451807	−	0.892116i	$-0.350780\pi$
$223$	20.0690	−	20.0690i	1.34392	−	1.34392i	0.892116	−	0.451807i	$-0.149220\pi$
$224$	−1.64933	−	2.06875i	−0.110200	−	0.138224i
$225$	12.6483	+	8.06351i	0.843221	+	0.537567i
$226$	5.71746	+	9.90292i	0.380319	+	0.658733i
$227$	2.06654	+	7.71245i	0.137161	+	0.511893i	0.999980	+	0.00637896i	$0.00203050\pi$
$227$	2.06654	+	7.71245i	0.137161	+	0.511893i	−0.862818	+	0.505514i	$0.831303\pi$
$228$	1.52534	+	2.39765i	0.101018	+	0.158788i
$229$	−13.5382	+	7.81631i	−0.894632	+	0.516516i	−0.875455	−	0.483300i	$-0.839438\pi$
$229$	−13.5382	+	7.81631i	−0.894632	+	0.516516i	−0.0191773	+	0.999816i	$0.506105\pi$
$230$	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
$233$	1.90807	−	7.12102i	0.125002	−	0.466514i	−0.874838	−	0.484416i	$-0.839032\pi$
$233$	1.90807	−	7.12102i	0.125002	−	0.466514i	0.999840	+	0.0179022i	$0.00569877\pi$
$234$	1.65676	+	19.2172i	0.108306	+	1.25627i
$235$	11.7318	−	5.79241i	0.765299	−	0.377855i
$236$	5.55749	−	3.20862i	0.361762	−	0.208863i
$237$	−14.4001	−	7.50779i	−0.935384	−	0.487683i
$238$	1.52417	+	3.49469i	0.0987974	+	0.226527i
$239$	3.91525			0.253256			0.126628	−	0.991950i	$-0.459584\pi$
$239$	3.91525			0.253256			0.126628	+	0.991950i	$0.459584\pi$
$240$	−0.919957	−	3.76214i	−0.0593830	−	0.242845i
$241$	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	$-0.0262109\pi$
$242$	0.688678	+	2.57018i	0.0442699	+	0.165218i
$243$	4.73459	−	14.8521i	0.303724	−	0.952760i
$244$			0.697338i			0.0446425i
$245$	−0.435655	+	15.6464i	−0.0278330	+	0.999613i
$246$	−14.1100	+	4.43905i	−0.899622	+	0.283024i
$247$	−2.73020	+	10.1892i	−0.173718	+	0.648325i
$248$	−0.300082	+	0.0804067i	−0.0190552	+	0.00510583i
$249$	1.20642	−	5.42554i	0.0764537	−	0.343830i
$250$	−3.60887	−	10.5819i	−0.228245	−	0.669256i
$251$		−	16.5267i		−	1.04316i	−0.853203	−	0.521579i	$-0.825343\pi$
$251$		−	16.5267i		−	1.04316i	0.853203	−	0.521579i	$-0.174657\pi$
$252$	−4.14822	+	6.76700i	−0.261313	+	0.426281i
$253$	−10.0709	+	10.0709i	−0.633155	+	0.633155i
$254$	0.344586	+	0.596841i	0.0216213	+	0.0374491i
$255$	−0.122635	+	5.57973i	−0.00767973	+	0.349416i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	21.9442	+	5.87993i	1.36884	+	0.366780i	0.867056	−	0.498211i	$-0.166010\pi$
$257$	21.9442	+	5.87993i	1.36884	+	0.366780i	0.501786	+	0.864992i	$0.332676\pi$
$258$	−13.2401	−	6.90302i	−0.824293	−	0.429763i
$259$	−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
$262$	8.41885	−	2.25582i	0.520118	−	0.139365i
$263$	−27.7833	+	7.44452i	−1.71319	+	0.459049i	−0.976204	−	0.216856i	$-0.930420\pi$
$263$	−27.7833	+	7.44452i	−1.71319	+	0.459049i	−0.736989	+	0.675905i	$0.763753\pi$
$264$	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
$267$	−5.76866	+	11.0644i	−0.353036	+	0.677129i
$268$	0.807572	+	0.216388i	0.0493303	+	0.0132180i
$269$	−2.82801	+	4.89825i	−0.172427	+	0.298652i	−0.939268	−	0.343185i	$-0.888494\pi$
$269$	−2.82801	+	4.89825i	−0.172427	+	0.298652i	0.766841	+	0.641837i	$0.221827\pi$
$270$	−9.66999	+	6.44137i	−0.588497	+	0.392009i
$271$	−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
$273$	−28.9196	+	5.63588i	−1.75029	+	0.341099i
$274$			16.8382i			1.01723i
$275$	8.77890	−	11.4634i	0.529388	−	0.691269i
$276$	−8.33883	−	1.85422i	−0.501939	−	0.111611i
$277$	16.2847	−	4.36346i	0.978450	−	0.262175i	0.266058	−	0.963957i	$-0.414279\pi$
$277$	16.2847	−	4.36346i	0.978450	−	0.262175i	0.712392	+	0.701782i	$0.247612\pi$
$278$	3.93413	−	14.6824i	0.235953	−	0.880589i
$279$	0.533607	+	0.764128i	0.0319462	+	0.0457472i
$280$	5.56489	−	2.00800i	0.332566	−	0.120001i
$281$			24.5854i			1.46664i	0.679883	+	0.733321i	$0.262031\pi$
$281$			24.5854i			1.46664i	−0.679883	+	0.733321i	$0.737969\pi$
$282$	0.435658	+	10.1253i	0.0259431	+	0.602956i
$283$	6.93967	+	25.8992i	0.412520	+	1.53955i	0.789751	+	0.613428i	$0.210210\pi$
$283$	6.93967	+	25.8992i	0.412520	+	1.53955i	−0.377230	+	0.926119i	$0.623124\pi$
$284$	1.36158	−	2.35832i	0.0807947	−	0.139941i
$285$	−6.17243	+	1.50935i	−0.365623	+	0.0894060i
$286$	18.5668			1.09788
$287$	−9.03280	−	20.7108i	−0.533190	−	1.22252i
$288$	2.95376	+	0.524686i	0.174052	+	0.0309174i
$289$	12.9241	−	7.46172i	0.760240	−	0.438925i
$290$	21.2021	−	10.4682i	1.24503	−	0.614716i
$291$	−2.52826	+	11.3702i	−0.148209	+	0.666530i
$292$	0.0483418	−	0.180414i	0.00282899	−	0.0105579i
$293$	−13.8738	−	13.8738i	−0.810518	−	0.810518i	0.174193	−	0.984712i	$-0.444268\pi$
$293$	−13.8738	−	13.8738i	−0.810518	−	0.810518i	−0.984712	+	0.174193i	$0.944268\pi$
$294$	−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
$297$	−13.8521	−	5.76858i	−0.803780	−	0.334727i
$298$	3.46583	+	12.9347i	0.200770	+	0.749285i
$299$	−15.8552	−	27.4619i	−0.916927	−	1.58816i
$300$	8.62754	+	0.752064i	0.498111	+	0.0434204i
$301$	8.33561	−	21.2306i	0.480456	−	1.22371i
$302$	1.15928	−	1.15928i	0.0667088	−	0.0667088i
$303$	0.752748	+	17.4950i	0.0432443	+	1.00506i
$304$	1.42086	+	0.820335i	0.0814921	+	0.0470495i
$305$	−1.47678	−	0.500518i	−0.0845602	−	0.0286596i
$306$	−3.91573	−	1.83197i	−0.223847	−	0.104727i
$307$	7.49848	+	7.49848i	0.427961	+	0.427961i	0.887933	−	0.459972i	$-0.152141\pi$
$307$	7.49848	+	7.49848i	0.427961	+	0.427961i	−0.459972	+	0.887933i	$0.652141\pi$
$308$	6.14677	+	4.53776i	0.350245	+	0.258563i
$309$	2.63668	+	8.38098i	0.149995	+	0.476777i
$310$	0.0451048	−	0.693208i	0.00256178	−	0.0393716i
$311$	−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	$0.821721\pi$
$312$	5.97752	+	9.39596i	0.338411	+	0.531941i
$313$	−13.9316	−	3.73296i	−0.787460	−	0.210999i	−0.157389	−	0.987537i	$-0.550308\pi$
$313$	−13.9316	−	3.73296i	−0.787460	−	0.210999i	−0.630071	+	0.776537i	$0.716974\pi$
$314$	13.5976			0.767357
$315$	−11.3533	−	13.6419i	−0.639688	−	0.768635i
$316$	−9.37600			−0.527441
$317$	23.3356	+	6.25275i	1.31066	+	0.351189i	0.845470	−	0.534023i	$-0.179320\pi$
$317$	23.3356	+	6.25275i	1.31066	+	0.351189i	0.465187	+	0.885212i	$0.345987\pi$
$318$	−0.499117	−	0.784552i	−0.0279891	−	0.0439955i
$319$	26.4458	+	15.2685i	1.48068	+	0.854871i
$320$	−1.47514	−	1.68046i	−0.0824628	−	0.0939408i
$321$	3.54584	+	11.2708i	0.197909	+	0.629077i
$322$	1.46271	−	12.9666i	0.0815134	−	0.722603i
$323$	−1.67178	−	1.67178i	−0.0930203	−	0.0930203i
$324$	−1.54038	−	8.86720i	−0.0855765	−	0.492622i
$325$	19.5943	+	25.4857i	1.08690	+	1.41369i
$326$	−0.150984	−	0.0871709i	−0.00836225	−	0.00482795i
$327$	0.677629	+	15.7491i	0.0374729	+	0.870927i
$328$	−6.03873	+	6.03873i	−0.333433	+	0.333433i
$329$	−15.3084	+	2.30533i	−0.843981	+	0.127097i
$330$	5.37794	+	9.80638i	0.296046	+	0.539823i
$331$	−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	$0.979448\pi$
$332$	−0.830536	−	3.09960i	−0.0455816	−	0.170113i
$333$	6.70656	+	5.64196i	0.367517	+	0.309178i
$334$	−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	0.860466	−	0.509507i	$-0.170172\pi$
$337$	6.44276	+	6.44276i	0.350959	+	0.350959i	−0.509507	+	0.860466i	$0.670172\pi$
$338$	−7.33449	+	27.3727i	−0.398944	+	1.48888i
$339$	4.29901	−	19.3337i	0.233490	−	1.05006i
$340$	1.42653	+	2.88926i	0.0773645	+	0.156692i
$341$	0.776940	−	0.448566i	0.0420737	−	0.0242912i
$342$	0.860837	−	4.84615i	0.0465487	−	0.262050i
$343$	6.12371	−	17.4786i	0.330649	−	0.943754i
$344$	−8.62075			−0.464800
$345$	9.91199	−	16.3286i	0.533644	−	0.879103i
$346$	1.90591	−	3.30114i	0.102463	−	0.177470i
$347$	−2.45074	−	9.14627i	−0.131562	−	0.490998i	0.868426	−	0.495819i	$-0.165132\pi$
$347$	−2.45074	−	9.14627i	−0.131562	−	0.490998i	−0.999988	+	0.00482121i	$0.998465\pi$
$348$	0.787336	+	18.2989i	0.0422056	+	0.980922i
$349$		−	19.7917i		−	1.05942i	−0.848177	−	0.529712i	$-0.822300\pi$
$349$		−	19.7917i		−	1.05942i	0.848177	−	0.529712i	$-0.177700\pi$
$350$	0.258191	+	13.2262i	0.0138009	+	0.706972i
$351$	20.3882	−	26.4661i	1.08824	−	1.41266i
$352$	0.747407	−	2.78936i	0.0398369	−	0.148673i
$353$	2.19457	−	0.588034i	0.116805	−	0.0312979i	−0.199943	−	0.979808i	$-0.564076\pi$
$353$	2.19457	−	0.588034i	0.116805	−	0.0312979i	0.316748	+	0.948510i	$0.397409\pi$
$354$	−10.8500	−	2.41259i	−0.576670	−	0.128228i
$355$	4.01703	+	4.57616i	0.213202	+	0.242878i
$356$			7.20412i			0.381818i
$357$	2.14691	−	6.24488i	0.113627	−	0.330514i
$358$	6.23458	−	6.23458i	0.329508	−	0.329508i
$359$	5.97213	+	10.3440i	0.315197	+	0.545937i	0.979479	−	0.201545i	$-0.0645961\pi$
$359$	5.97213	+	10.3440i	0.315197	+	0.545937i	−0.664282	+	0.747482i	$0.731263\pi$
$360$	−3.23123	+	5.87871i	−0.170301	+	0.309835i
$361$	−8.15410	+	14.1233i	−0.429163	+	0.743332i
$362$	5.13437	+	1.37575i	0.269856	+	0.0723078i
$363$	2.13066	−	4.08664i	0.111831	−	0.214493i
$364$	−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
$367$	−11.7329	+	3.14381i	−0.612451	+	0.164106i	−0.551694	−	0.834047i	$-0.686018\pi$
$367$	−11.7329	+	3.14381i	−0.612451	+	0.164106i	−0.0607572	+	0.998153i	$0.519352\pi$
$368$	−4.76396	+	1.27650i	−0.248339	+	0.0665421i
$369$	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
$372$	0.477136	+	0.248765i	0.0247383	+	0.0128979i
$373$	−18.9572	−	5.07958i	−0.981569	−	0.263011i	−0.267864	−	0.963457i	$-0.586318\pi$
$373$	−18.9572	−	5.07958i	−0.981569	−	0.263011i	−0.713705	+	0.700446i	$0.752984\pi$
$374$	−2.08067	+	3.60383i	−0.107589	+	0.186349i
$375$	−7.78514	+	17.7311i	−0.402023	+	0.915630i
$376$	2.92564	+	5.06736i	0.150878	+	0.261329i
$377$	−48.0758	+	48.0758i	−2.47603	+	2.47603i
$378$	13.2181	−	3.77903i	0.679867	−	0.194372i
$379$		−	9.32087i		−	0.478781i	−0.970923	−	0.239391i	$-0.923052\pi$
$379$		−	9.32087i		−	0.478781i	0.970923	−	0.239391i	$-0.0769476\pi$
$380$	−2.75709	+	2.42022i	−0.141436	+	0.124155i
$381$	0.259098	−	1.16522i	0.0132740	−	0.0596962i
$382$	21.6654	−	5.80522i	1.10850	−	0.297021i
$383$	2.69851	−	10.0710i	0.137887	−	0.514603i	−0.862082	−	0.506769i	$-0.830840\pi$
$383$	2.69851	−	10.0710i	0.137887	−	0.514603i	0.999969	−	0.00783388i	$-0.00249363\pi$
$384$	1.65222	−	0.519792i	0.0843143	−	0.0265255i
$385$	−14.0217	+	9.76026i	−0.714611	+	0.497429i
$386$		−	16.4797i		−	0.838796i
$387$	8.81463	+	24.3138i	0.448073	+	1.23594i
$388$	1.74053	+	6.49575i	0.0883620	+	0.329772i
$389$	−1.52599	+	2.64309i	−0.0773708	+	0.134010i	−0.902115	−	0.431496i	$-0.857986\pi$
$389$	−1.52599	+	2.64309i	−0.0773708	+	0.134010i	0.824744	+	0.565506i	$0.191319\pi$
$390$	−24.1886	+	5.91485i	−1.22484	+	0.299510i
$391$	7.10717			0.359425
$392$	−6.99517	+	0.259910i	−0.353310	+	0.0131275i
$393$	−13.3861	−	6.97916i	−0.675241	−	0.352052i
$394$	1.23989	−	0.715852i	0.0624649	−	0.0360641i
$395$	6.72968	−	19.8559i	0.338607	−	0.999061i
$396$	−8.63126	+	0.744123i	−0.433737	+	0.0373936i
$397$	3.34711	−	12.4916i	0.167987	−	0.626935i	−0.829654	−	0.558279i	$-0.811462\pi$
$397$	3.34711	−	12.4916i	0.167987	−	0.626935i	0.997640	−	0.0686566i	$-0.0218713\pi$
$398$	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	$0.152645\pi$
$402$	−0.777289	−	1.22181i	−0.0387676	−	0.0609381i
$403$	0.516973	+	1.92937i	0.0257523	+	0.0961088i
$404$	5.05504	+	8.75559i	0.251498	+	0.435607i
$405$	19.8840	+	3.10236i	0.988046	+	0.154157i
$406$	−27.6659	+	4.16627i	−1.37304	+	0.206768i
$407$	5.96531	−	5.96531i	0.295689	−	0.295689i
$408$	−2.49363	+	0.107292i	−0.123453	+	0.00531174i
$409$	−6.31608	−	3.64659i	−0.312310	−	0.180312i	0.335650	−	0.941987i	$-0.391044\pi$
$409$	−6.31608	−	3.64659i	−0.312310	−	0.180312i	−0.647960	+	0.761675i	$0.724377\pi$
$410$	−8.45414	−	17.1228i	−0.417520	−	0.845635i
$411$	19.7170	−	21.4899i	0.972566	−	1.06002i
$412$	3.58685	+	3.58685i	0.176711	+	0.176711i
$413$	1.90318	−	16.8714i	0.0936495	−	0.830187i
$414$	8.47130	+	12.1309i	0.416342	+	0.596204i
$415$	7.16027	+	0.465896i	0.351484	+	0.0228699i
$416$	5.56810	+	3.21474i	0.272998	+	0.157616i
$417$	−22.2135	+	14.1318i	−1.08780	+	0.692037i
$418$	−4.57642	−	1.22625i	−0.223840	−	0.0599778i
$419$	29.6118			1.44663			0.723316	−	0.690517i	$-0.242617\pi$
$419$	29.6118			1.44663			0.723316	+	0.690517i	$0.242617\pi$
$420$	−9.45354	−	3.95356i	−0.461285	−	0.192914i
$421$	3.88093			0.189145			0.0945725	−	0.995518i	$-0.469852\pi$
$421$	3.88093			0.189145			0.0945725	+	0.995518i	$0.469852\pi$
$422$	13.0445	+	3.49527i	0.634998	+	0.170147i
$423$	11.3004	−	13.4327i	0.549445	−	0.653121i
$424$	−0.464930	−	0.268427i	−0.0225790	−	0.0130360i
$425$	−7.14260	+	0.947241i	−0.346467	+	0.0459479i
$426$	−4.49924	+	1.41547i	−0.217989	+	0.0685798i
$427$	1.48432	+	1.09578i	0.0718315	+	0.0530286i
$428$	4.82364	+	4.82364i	0.233159	+	0.233159i
$429$	−23.6961	−	21.7411i	−1.14406	−	1.04967i
$430$	6.18759	−	18.2565i	0.298392	−	0.880408i
$431$	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	$0.436545\pi$
$432$	−3.15538	−	4.12839i	−0.151813	−	0.198627i
$433$	18.1378	−	18.1378i	0.871649	−	0.871649i	−0.121003	−	0.992652i	$-0.538611\pi$
$433$	18.1378	−	18.1378i	0.871649	−	0.871649i	0.992652	+	0.121003i	$0.0386110\pi$
$434$	−0.300392	+	0.765091i	−0.0144193	+	0.0367256i
$435$	−39.3174	−	11.4667i	−1.88512	−	0.549788i
$436$	4.55058	+	7.88184i	0.217933	+	0.377472i
$437$	2.09431	+	7.81609i	0.100185	+	0.373894i
$438$	−0.272955	+	0.173649i	−0.0130423	+	0.00829726i
$439$	−20.3735	+	11.7627i	−0.972376	+	0.561402i	−0.899960	−	0.435973i	$-0.856404\pi$
$439$	−20.3735	+	11.7627i	−0.972376	+	0.561402i	−0.0724163	+	0.997374i	$0.523071\pi$
$440$	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
$443$	−5.45289	+	20.3505i	−0.259075	+	0.966880i	0.706703	+	0.707510i	$0.250182\pi$
$443$	−5.45289	+	20.3505i	−0.259075	+	0.966880i	−0.965778	+	0.259370i	$0.916485\pi$
$444$	4.93933	+	1.09830i	0.234410	+	0.0521232i
$445$	−15.2565	−	5.17079i	−0.723225	−	0.245119i
$446$	−24.5795	+	14.1910i	−1.16387	+	0.671961i
$447$	10.7227	−	20.5664i	0.507168	−	0.972756i
$448$	1.05770	+	2.42513i	0.0499715	+	0.114577i
$449$	2.55651			0.120649			0.0603246	−	0.998179i	$-0.480786\pi$
$449$	2.55651			0.120649			0.0603246	+	0.998179i	$0.480786\pi$
$450$	−10.1303	−	11.0624i	−0.477549	−	0.521485i
$451$	12.3308	−	21.3576i	0.580636	−	1.00569i
$452$	−2.95957	−	11.0453i	−0.139207	−	0.519526i
$453$	−2.83701	+	0.122067i	−0.133294	+	0.00573519i
$454$		−	7.98451i		−	0.374732i
$455$	−12.9104	−	35.7794i	−0.605248	−	1.67736i
$456$	−0.852807	−	2.71074i	−0.0399363	−	0.126942i
$457$	2.81562	−	10.5080i	0.131709	−	0.491546i	−0.868280	−	0.496074i	$-0.834775\pi$
$457$	2.81562	−	10.5080i	0.131709	−	0.491546i	0.999990	+	0.00452783i	$0.00144126\pi$
$458$	15.0999	−	4.04602i	0.705574	−	0.189058i
$459$	2.85231	+	6.92326i	0.133134	+	0.323150i
$460$	0.716063	−	11.0050i	0.0333866	−	0.513113i
$461$		−	33.6432i		−	1.56692i	−0.621441	−	0.783461i	$-0.713453\pi$
$461$		−	33.6432i		−	1.56692i	0.621441	−	0.783461i	$-0.286547\pi$
$462$	−2.53132	−	12.9890i	−0.117768	−	0.604304i
$463$	7.63888	−	7.63888i	0.355009	−	0.355009i	−0.506960	−	0.861969i	$-0.669231\pi$
$463$	7.63888	−	7.63888i	0.355009	−	0.355009i	0.861969	+	0.506960i	$0.169231\pi$
$464$	5.28731	+	9.15790i	0.245457	+	0.425145i
$465$	−0.869287	+	0.831898i	−0.0403122	+	0.0385783i
$466$	−3.68611	+	6.38454i	−0.170756	+	0.295758i
$467$	−31.5447	−	8.45237i	−1.45971	−	0.391129i	−0.560323	−	0.828274i	$-0.689323\pi$
$467$	−31.5447	−	8.45237i	−1.45971	−	0.391129i	−0.899391	+	0.437145i	$0.855990\pi$
$468$	3.37346	−	18.9912i	0.155938	−	0.877867i
$469$	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
$472$	−6.19857	+	1.66090i	−0.285312	+	0.0764492i
$473$	24.0464	−	6.44321i	1.10565	−	0.296259i
$474$	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
$477$	−0.281680	+	1.58574i	−0.0128973	+	0.0726061i
$478$	−3.78184	−	1.01334i	−0.172977	−	0.0463491i
$479$	−13.9213	+	24.1124i	−0.636080	+	1.10172i	0.350205	+	0.936673i	$0.386112\pi$
$479$	−13.9213	+	24.1124i	−0.636080	+	1.10172i	−0.986285	+	0.165050i	$0.947222\pi$
$480$	−0.0851028	+	3.87205i	−0.00388439	+	0.176734i
$481$	9.39146	+	16.2665i	0.428214	+	0.741688i
$482$	−12.5039	+	12.5039i	−0.569537	+	0.569537i
$483$	−17.0503	+	14.8360i	−0.775815	+	0.675063i
$484$		−	2.66085i		−	0.120948i
$485$	−15.0056	−	0.976365i	−0.681368	−	0.0443344i
$486$	−8.41726	+	13.1206i	−0.381815	+	0.595162i
$487$	−30.4561	+	8.16069i	−1.38010	+	0.369796i	−0.871157	−	0.491005i	$-0.836630\pi$
$487$	−30.4561	+	8.16069i	−1.38010	+	0.369796i	−0.508941	+	0.860801i	$0.669963\pi$
$488$	0.180484	−	0.673576i	0.00817014	−	0.0304914i
$489$	0.0906214	+	0.288050i	0.00409804	+	0.0130261i
$490$	4.47040	−	15.0005i	0.201952	−	0.677654i
$491$		−	1.52495i		−	0.0688199i	−0.999408	−	0.0344099i	$-0.989045\pi$
$491$		−	1.52495i		−	0.0688199i	0.999408	−	0.0344099i	$-0.0109552\pi$
$492$	14.7781	−	0.635852i	0.666250	−	0.0286664i
$493$	−3.94397	−	14.7191i	−0.177628	−	0.662915i
$494$	5.27433	−	9.13542i	0.237304	−	0.411022i
$495$	4.61927	−	18.8129i	0.207621	−	0.845576i
$496$	0.310667			0.0139494
$497$	−2.88027	−	6.60401i	−0.129198	−	0.296230i
$498$	−2.56954	+	4.92843i	−0.115144	+	0.220848i
$499$	9.28878	−	5.36288i	0.415823	−	0.240075i	−0.277466	−	0.960736i	$-0.589494\pi$
$499$	9.28878	−	5.36288i	0.415823	−	0.240075i	0.693289	+	0.720660i	$0.256161\pi$
$500$	0.747115	+	11.1553i	0.0334120	+	0.498882i
$501$	3.87750	+	0.862198i	0.173234	+	0.0385202i
$502$	−4.27743	+	15.9636i	−0.190911	+	0.712490i
$503$	29.8137	+	29.8137i	1.32933	+	1.32933i	0.905955	+	0.423373i	$0.139154\pi$
$503$	29.8137	+	29.8137i	1.32933	+	1.32933i	0.423373	+	0.905955i	$0.360846\pi$
$504$	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
$507$	41.4132	−	26.3462i	1.83922	−	1.17008i
$508$	−0.178371	−	0.665690i	−0.00791393	−	0.0295352i
$509$	14.1129	+	24.4442i	0.625543	+	1.08347i	0.988436	+	0.151641i	$0.0484557\pi$
$509$	14.1129	+	24.4442i	0.625543	+	1.08347i	−0.362893	+	0.931831i	$0.618211\pi$
$510$	1.56260	−	5.35786i	0.0691930	−	0.237250i
$511$	−0.308059	−	0.386397i	−0.0136277	−	0.0170932i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−6.77332	+	5.17694i	−0.299050	+	0.228567i
$514$	−19.6746	−	11.3592i	−0.867811	−	0.501031i
$515$	−10.1705	+	5.02153i	−0.448165	+	0.221275i
$516$	11.0023	+	10.0946i	0.484350	+	0.444390i
$517$	−11.9480	−	11.9480i	−0.525474	−	0.525474i
$518$	−0.866402	+	7.68051i	−0.0380675	+	0.337462i
$519$	−6.29796	+	1.98136i	−0.276450	+	0.0869719i
$520$	−10.8045	+	9.48439i	−0.473810	+	0.415918i
$521$	−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	$0.885678\pi$
$522$	20.4225	−	24.2761i	0.893868	−	1.06253i
$523$	13.0137	+	3.48700i	0.569047	+	0.152476i	0.531860	−	0.846833i	$-0.321493\pi$
$523$	13.0137	+	3.48700i	0.569047	+	0.152476i	0.0371877	+	0.999308i	$0.488160\pi$
$524$	−8.71583			−0.380753
$525$	15.1579	−	17.1825i	0.661547	−	0.749904i
$526$	28.7634			1.25414
$527$	−0.432426	−	0.115868i	−0.0188368	−	0.00504730i
$528$	−4.22013	+	2.68476i	−0.183658	+	0.116839i
$529$	−1.14728	−	0.662381i	−0.0498816	−	0.0287992i
$530$	0.902166	−	0.791936i	0.0391876	−	0.0343995i
$531$	11.0223	+	15.7840i	0.478329	+	0.684969i
$532$	3.97885	−	1.73533i	0.172505	−	0.0752363i
$533$	38.8260	+	38.8260i	1.68174	+	1.68174i
$534$	8.43577	−	9.19433i	0.365052	−	0.397878i
$535$	−13.6774	+	6.75302i	−0.591326	+	0.291959i
$536$	−0.724049	−	0.418030i	−0.0312742	−	0.0180561i
$537$	−15.2574	+	0.656474i	−0.658407	+	0.0283289i
$538$	3.99940	−	3.99940i	0.172427	−	0.172427i
$539$	19.3178	−	5.95323i	0.832077	−	0.256424i
$540$	11.0076	−	3.71911i	0.473694	−	0.160045i
$541$	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	$0.742921\pi$
$542$	5.91616	+	22.0794i	0.254121	+	0.948391i
$543$	−4.94184	−	7.76798i	−0.212074	−	0.333356i
$544$	−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	0.917063	−	0.398742i	$-0.130553\pi$
$547$	12.1225	+	12.1225i	0.518321	+	0.518321i	−0.398742	+	0.917063i	$0.630553\pi$
$548$	4.35805	−	16.2645i	0.186167	−	0.694784i
$549$	−2.08428	+	0.179691i	−0.0889549	+	0.00766904i
$550$	−11.4467	+	8.80065i	−0.488090	+	0.375261i
$551$	15.0251	−	8.67474i	0.640091	−	0.369556i
$552$	7.57479	+	3.94928i	0.322404	+	0.168093i
$553$	−14.7333	+	19.9574i	−0.626522	+	0.848675i
$554$	−16.8591			−0.716275
$555$	−5.87116	+	9.67191i	−0.249217	+	0.410550i
$556$	−7.60015	+	13.1638i	−0.322318	+	0.558271i
$557$	−10.1456	−	37.8640i	−0.429884	−	1.60435i	−0.753022	−	0.657996i	$-0.771405\pi$
$557$	−10.1456	−	37.8640i	−0.429884	−	1.60435i	0.323138	−	0.946352i	$-0.395262\pi$
$558$	−0.317654	−	0.876199i	−0.0134474	−	0.0370925i
$559$			55.4270i			2.34431i
$560$	−5.89497	+	0.499278i	−0.249108	+	0.0210983i
$561$	6.87543	−	2.16303i	0.290281	−	0.0913232i
$562$	6.36317	−	23.7477i	0.268414	−	1.00173i
$563$	−12.2809	+	3.29065i	−0.517577	+	0.138684i	−0.508146	−	0.861271i	$-0.669669\pi$
$563$	−12.2809	+	3.29065i	−0.517577	+	0.138684i	−0.00943155	+	0.999956i	$0.503002\pi$
$564$	2.19982	−	9.89309i	0.0926291	−	0.416574i
$565$	25.5153	+	1.66020i	1.07344	+	0.0698450i
$566$		−	26.8128i		−	1.12703i
$567$	−21.2949	−	10.6549i	−0.894301	−	0.447466i
$568$	−1.92556	+	1.92556i	−0.0807947	+	0.0807947i
$569$	−10.6592	−	18.4623i	−0.446858	−	0.773981i	0.551322	−	0.834293i	$-0.314124\pi$
$569$	−10.6592	−	18.4623i	−0.446858	−	0.773981i	−0.998180	+	0.0603121i	$0.980790\pi$
$570$	6.35276	+	0.139626i	0.266088	+	0.00584827i
$571$	−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	$0.273285\pi$
$572$	−17.9342	−	4.80544i	−0.749865	−	0.200926i
$573$	−34.4484	−	17.9604i	−1.43910	−	0.750308i
$574$	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
$577$	13.7052	−	3.67230i	0.570556	−	0.152880i	0.0380044	−	0.999278i	$-0.487900\pi$
$577$	13.7052	−	3.67230i	0.570556	−	0.152880i	0.532552	+	0.846398i	$0.321233\pi$
$578$	−14.4149	+	3.86247i	−0.599582	+	0.160658i
$579$	−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
$582$	5.38492	−	10.3284i	0.223212	−	0.428124i
$583$	1.49748	+	0.401249i	0.0620194	+	0.0166180i
$584$	−0.0933892	+	0.161755i	−0.00386447	+	0.00669347i
$585$	37.7971	+	20.7751i	1.56272	+	0.858946i
$586$	9.81029	+	16.9919i	0.405259	+	0.701930i
$587$	−5.73739	+	5.73739i	−0.236807	+	0.236807i	−0.815527	−	0.578719i	$-0.803553\pi$
$587$	−5.73739	+	5.73739i	−0.236807	+	0.236807i	0.578719	+	0.815527i	$0.303553\pi$
$588$	9.23201	+	7.85939i	0.380722	+	0.324116i
$589$		−	0.509703i		−	0.0210019i
$590$	0.931697	−	14.3191i	0.0383574	−	0.589508i
$591$	−2.42066	−	0.538257i	−0.0995728	−	0.0221409i
$592$	2.82183	−	0.756107i	0.115976	−	0.0310758i
$593$	4.82157	−	17.9944i	0.197998	−	0.738940i	−0.793472	−	0.608607i	$-0.791729\pi$
$593$	4.82157	−	17.9944i	0.197998	−	0.738940i	0.991470	−	0.130333i	$-0.0416046\pi$
$594$	11.8871	+	9.15721i	0.487733	+	0.375725i
$595$	8.39158	+	1.50366i	0.344021	+	0.0616442i
$596$		−	13.3910i		−	0.548515i
$597$	−0.658713	−	15.3095i	−0.0269593	−	0.626575i
$598$	8.20723	+	30.6298i	0.335619	+	1.25255i
$599$	−18.3356	+	31.7582i	−0.749174	+	1.29761i	0.199046	+	0.979990i	$0.436216\pi$
$599$	−18.3356	+	31.7582i	−0.749174	+	1.29761i	−0.948219	+	0.317616i	$0.897118\pi$
$600$	−8.13891	−	2.95941i	−0.332270	−	0.120817i
$601$	−30.3187			−1.23673			−0.618363	−	0.785893i	$-0.712204\pi$
$601$	−30.3187			−1.23673			−0.618363	+	0.785893i	$0.712204\pi$
$602$	−13.5465	+	18.3498i	−0.552113	+	0.747882i
$603$	−0.438669	+	2.46952i	−0.0178640	+	0.100567i
$604$	−1.41982	+	0.819732i	−0.0577715	+	0.0333544i
$605$	5.63499	+	1.90984i	0.229095	+	0.0776459i
$606$	3.80094	−	17.0937i	0.154403	−	0.694384i
$607$	1.69076	−	6.31001i	0.0686259	−	0.256115i	−0.923087	−	0.384592i	$-0.874342\pi$
$607$	1.69076	−	6.31001i	0.0686259	−	0.256115i	0.991713	+	0.128477i	$0.0410088\pi$
$608$	−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
$612$	3.30815	+	2.78302i	0.133724	+	0.112497i
$613$	−9.94374	−	37.1106i	−0.401624	−	1.49888i	−0.810198	−	0.586156i	$-0.800640\pi$
$613$	−9.94374	−	37.1106i	−0.401624	−	1.49888i	0.408574	−	0.912725i	$-0.366026\pi$
$614$	−5.30223	−	9.18373i	−0.213980	−	0.370625i
$615$	−9.26052	+	31.7527i	−0.373420	+	1.28039i
$616$	−4.76286	−	5.97404i	−0.191901	−	0.240701i
$617$	−6.69009	+	6.69009i	−0.269333	+	0.269333i	−0.828831	−	0.559498i	$-0.810994\pi$
$617$	−6.69009	+	6.69009i	−0.269333	+	0.269333i	0.559498	+	0.828831i	$0.310994\pi$
$618$	−0.377679	−	8.77782i	−0.0151925	−	0.353096i
$619$	−1.57421	−	0.908870i	−0.0632728	−	0.0365306i	0.468030	−	0.883713i	$-0.344964\pi$
$619$	−1.57421	−	0.908870i	−0.0632728	−	0.0365306i	−0.531303	+	0.847182i	$0.678297\pi$
$620$	−0.222983	+	0.657913i	−0.00895522	+	0.0264224i
$621$	3.39332	−	25.4018i	0.136169	−	1.01934i
$622$	11.6739	+	11.6739i	0.468082	+	0.468082i
$623$	15.3344	+	11.3204i	0.614360	+	0.453542i
$624$	−3.34199	−	10.6229i	−0.133787	−	0.425256i
$625$	−24.1604	−	6.42461i	−0.966416	−	0.256985i
$626$	12.4907	+	7.21152i	0.499230	+	0.288230i
$627$	4.40481	+	6.92384i	0.175911	+	0.276512i
$628$	−13.1343	−	3.51932i	−0.524115	−	0.140436i
$629$	−4.20978			−0.167855
$630$	7.43570	+	16.1155i	0.296245	+	0.642058i
$631$	−0.0416272			−0.00165715			−0.000828576	−	1.00000i	$-0.500264\pi$
$631$	−0.0416272			−0.00165715			−0.000828576		1.00000i	$0.500264\pi$
$632$	9.05652	+	2.42669i	0.360249	+	0.0965285i
$633$	−12.5554	−	19.7356i	−0.499032	−	0.784419i
$634$	−20.9221	−	12.0794i	−0.830923	−	0.479734i
$635$	1.53779	+	0.100059i	0.0610251	+	0.00397071i
$636$	0.279053	+	0.887000i	0.0110652	+	0.0351718i
$637$	1.67109	+	44.9754i	0.0662110	+	1.78199i
$638$	−21.5929	−	21.5929i	−0.854871	−	0.854871i
$639$	7.39967	+	3.46194i	0.292726	+	0.136952i
$640$	0.989939	+	2.00500i	0.0391308	+	0.0792545i
$641$	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	$0.650443\pi$
$642$	−0.507907	−	11.8045i	−0.0200455	−	0.465887i
$643$	−14.7760	+	14.7760i	−0.582709	+	0.582709i	−0.935647	−	0.352938i	$-0.885183\pi$
$643$	−14.7760	+	14.7760i	−0.582709	+	0.582709i	0.352938	+	0.935647i	$0.385183\pi$
$644$	−4.76888	+	12.1462i	−0.187920	+	0.478629i
$645$	−29.2747	+	16.0546i	−1.15269	+	0.632150i
$646$	1.18213	+	2.04750i	0.0465101	+	0.0805579i
$647$	1.62567	+	6.06708i	0.0639116	+	0.238521i	0.990491	−	0.137578i	$-0.0439318\pi$
$647$	1.62567	+	6.06708i	0.0639116	+	0.238521i	−0.926579	+	0.376099i	$0.877265\pi$
$648$	−0.807110	+	8.96374i	−0.0317063	+	0.352129i
$649$	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
$653$	−11.3516	+	42.3647i	−0.444222	+	1.65786i	0.273761	+	0.961798i	$0.411732\pi$
$653$	−11.3516	+	42.3647i	−0.444222	+	1.65786i	−0.717983	+	0.696061i	$0.754934\pi$
$654$	3.42163	−	15.3878i	0.133796	−	0.601712i
$655$	6.25583	−	18.4579i	0.244436	−	0.721209i
$656$	7.39591	−	4.27003i	0.288762	−	0.166717i
$657$	0.551699	+	0.0980000i	0.0215238	+	0.00382335i
$658$	15.3835	+	1.73534i	0.599710	+	0.0676504i
$659$	−8.17474			−0.318443			−0.159221	−	0.987243i	$-0.550898\pi$
$659$	−8.17474			−0.318443			−0.159221	+	0.987243i	$0.550898\pi$
$660$	−2.65661	−	10.8641i	−0.103409	−	0.422886i
$661$	−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	$0.309843\pi$
$662$	4.17276	+	15.5730i	0.162179	+	0.605260i
$663$	0.689832	+	16.0327i	0.0267909	+	0.622660i
$664$			3.20894i			0.124531i
$665$	0.819150	+	9.67171i	0.0317653	+	0.375053i
$666$	−5.01779	−	7.18550i	−0.194436	−	0.278433i
$667$	−13.4985	+	50.3771i	−0.522664	+	1.95061i
$668$	2.21521	−	0.593563i	0.0857090	−	0.0229657i
$669$	47.9869	+	10.6703i	1.85528	+	0.412539i
$670$	1.40497	−	1.23331i	0.0542787	−	0.0476467i
$671$			2.01374i			0.0777397i
$672$	1.48985	−	4.33363i	0.0574722	−	0.167173i
$673$	−28.3904	+	28.3904i	−1.09437	+	1.09437i	−0.0993124	+	0.995056i	$0.531664\pi$
$673$	−28.3904	+	28.3904i	−1.09437	+	1.09437i	−0.995056	+	0.0993124i	$0.968336\pi$
$674$	−4.55572	−	7.89073i	−0.175480	−	0.303940i
$675$	−0.0246934	+	25.9808i	−0.000950448	+	1.00000i
$676$	14.1691	−	24.5417i	0.544967	−	0.943911i
$677$	37.5247	+	10.0547i	1.44219	+	0.386434i	0.893300	−	0.449460i	$-0.148384\pi$
$677$	37.5247	+	10.0547i	1.44219	+	0.386434i	0.548891	+	0.835894i	$0.315050\pi$
$678$	−9.15645	+	17.5622i	−0.351651	+	0.674472i
$679$	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
$682$	−0.866564	+	0.232195i	−0.0331824	+	0.00889121i
$683$	20.1417	−	5.39696i	0.770702	−	0.206509i	0.148020	−	0.988984i	$-0.452710\pi$
$683$	20.1417	−	5.39696i	0.770702	−	0.206509i	0.622681	+	0.782475i	$0.286043\pi$
$684$	−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
$687$	−24.0092	−	12.5177i	−0.916009	−	0.477581i
$688$	8.32701	+	2.23122i	0.317464	+	0.0850643i
$689$	−1.72585	+	2.98926i	−0.0657497	+	0.113882i
$690$	−13.8004	+	13.2068i	−0.525373	+	0.502775i
$691$	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
$693$	−11.9791	+	19.5415i	−0.455047	+	0.742319i
$694$			9.46892i			0.359435i
$695$	−22.4226	−	25.5436i	−0.850536	−	0.968922i
$696$	3.97559	−	17.8791i	0.150694	−	0.677706i
$697$	−11.8871	+	3.18515i	−0.450257	+	0.120646i
$698$	−5.12246	+	19.1173i	−0.193888	+	0.723600i
$699$	12.1805	−	3.83202i	0.460709	−	0.144940i
$700$	3.17381	−	12.8424i	0.119959	−	0.485397i
$701$			3.17238i			0.119819i	0.998204	+	0.0599096i	$0.0190812\pi$
$701$			3.17238i			0.119819i	−0.998204	+	0.0599096i	$0.980919\pi$
$702$	−26.5434	+	20.2875i	−1.00182	+	0.765701i
$703$	−1.24052	−	4.62969i	−0.0467872	−	0.174612i
$704$	−1.44388	+	2.50087i	−0.0544183	+	0.0942552i
$705$	19.3721	+	11.7595i	0.729595	+	0.442887i
$706$	−2.27199			−0.0855074
$707$	26.5802	+	2.99839i	0.999651	+	0.112766i
$708$	9.85585	+	5.13857i	0.370406	+	0.193119i
$709$	2.89790	−	1.67311i	0.108833	−	0.0628348i	−0.444595	−	0.895731i	$-0.646653\pi$
$709$	2.89790	−	1.67311i	0.108833	−	0.0628348i	0.553429	+	0.832897i	$0.313319\pi$
$710$	−2.69576	−	5.45992i	−0.101170	−	0.204907i
$711$	−2.41603	−	28.0241i	−0.0906081	−	1.05098i
$712$	1.86456	−	6.95864i	0.0698775	−	0.260786i
$713$	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
$717$	3.64003	+	5.72169i	0.135939	+	0.213680i
$718$	−3.09140	−	11.5373i	−0.115370	−	0.430567i
$719$	−9.77351	−	16.9282i	−0.364491	−	0.631316i	0.624204	−	0.781262i	$-0.285424\pi$
$719$	−9.77351	−	16.9282i	−0.364491	−	0.631316i	−0.988694	+	0.149945i	$0.952090\pi$
$720$	4.64265	−	4.84209i	0.173021	−	0.180454i
$721$	13.2711	−	1.99853i	0.494242	−	0.0744290i
$722$	11.5316	−	11.5316i	0.429163	−	0.429163i
$723$	30.5999	−	1.31661i	1.13802	−	0.0489651i
$724$	−4.60335	−	2.65774i	−0.171082	−	0.0987743i
$725$	6.85156	−	52.4273i	0.254461	−	1.94710i
$726$	−3.11576	+	3.39593i	−0.115637	+	0.126035i
$727$	−35.4505	−	35.4505i	−1.31479	−	1.31479i	−0.917842	−	0.396946i	$-0.870070\pi$
$727$	−35.4505	−	35.4505i	−1.31479	−	1.31479i	−0.396946	−	0.917842i	$-0.629930\pi$
$728$	15.5924	−	6.80045i	0.577891	−	0.252042i
$729$	26.1064	−	6.88897i	0.966902	−	0.255147i
$730$	−0.275524	−	0.313875i	−0.0101976	−	0.0116170i
$731$	−10.7584	−	6.21137i	−0.397914	−	0.229736i
$732$	−1.01908	+	0.648318i	−0.0376663	+	0.0239625i
$733$	22.8943	+	6.13452i	0.845622	+	0.226584i	0.655517	−	0.755180i	$-0.272451\pi$
$733$	22.8943	+	6.13452i	0.845622	+	0.226584i	0.190105	+	0.981764i	$0.439117\pi$
$734$	12.1468			0.448345
$735$	−23.2705	+	13.9099i	−0.858344	+	0.513074i
$736$	4.93201			0.181796
$737$	2.33207	+	0.624877i	0.0859030	+	0.0230176i
$738$	−19.6053	−	16.4932i	−0.721682	−	0.607122i
$739$	−27.8766	−	16.0945i	−1.02546	−	0.592047i	−0.109776	−	0.993956i	$-0.535013\pi$
$739$	−27.8766	−	16.0945i	−1.02546	−	0.592047i	−0.915680	+	0.401909i	$0.868347\pi$
$740$	−0.424144	+	6.51860i	−0.0155919	+	0.239629i
$741$	−17.4287	+	5.48311i	−0.640258	+	0.201427i
$742$	−1.30195	+	0.567830i	−0.0477959	+	0.0208457i
$743$	−7.19137	−	7.19137i	−0.263826	−	0.263826i	0.562781	−	0.826606i	$-0.309732\pi$
$743$	−7.19137	−	7.19137i	−0.263826	−	0.263826i	−0.826606	+	0.562781i	$0.809732\pi$
$744$	−0.396493	−	0.363781i	−0.0145361	−	0.0133368i
$745$	28.3586	+	9.61143i	1.03898	+	0.352136i
$746$	16.9966	+	9.81299i	0.622290	+	0.359279i
$747$	9.05042	−	3.28111i	0.331138	−	0.120050i
$748$	2.94251	−	2.94251i	0.107589	−	0.107589i
$749$	17.8472	−	2.68764i	0.652121	−	0.0982043i
$750$	12.1090	−	15.1120i	0.442159	−	0.551811i
$751$	−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	$-0.398866\pi$
$752$	−1.51442	−	5.65190i	−0.0552253	−	0.206104i
$753$	24.1519	−	15.3650i	0.880145	−	0.559931i
$754$	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	0.326073	−	0.945344i	$-0.394274\pi$
$757$	−17.0384	−	17.0384i	−0.619271	−	0.619271i	−0.945344	+	0.326073i	$0.894274\pi$
$758$	−2.41242	+	9.00327i	−0.0876230	+	0.327014i
$759$	−24.0805	−	5.35453i	−0.874068	−	0.194357i
$760$	3.28954	−	1.62416i	0.119324	−	0.0589146i
$761$	−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	$0.357811\pi$
$762$	−0.551851	+	1.05846i	−0.0199915	+	0.0383439i
$763$	23.9277	+	2.69916i	0.866239	+	0.0977163i
$764$	−22.4297			−0.811477
$765$	−8.26815	+	5.00828i	−0.298936	+	0.181075i
$766$	−5.21312	+	9.02939i	−0.188358	+	0.326245i
$767$	10.6787	+	39.8536i	0.385587	+	1.43903i
$768$	−1.73045	+	0.0744552i	−0.0624422	+	0.00268667i
$769$		−	9.91452i		−	0.357527i	−0.983892	−	0.178763i	$-0.942790\pi$
$769$		−	9.91452i		−	0.357527i	0.983892	−	0.178763i	$-0.0572097\pi$
$770$	16.0700	−	5.79861i	0.579124	−	0.208967i
$771$	11.8088	+	37.5356i	0.425283	+	1.35181i
$772$	−4.26527	+	15.9182i	−0.153510	+	0.572908i
$773$	6.65181	−	1.78235i	0.239249	−	0.0641066i	−0.137202	−	0.990543i	$-0.543811\pi$
$773$	6.65181	−	1.78235i	0.239249	−	0.0641066i	0.376451	+	0.926436i	$0.377144\pi$
$774$	−2.22141	−	25.7667i	−0.0798470	−	0.926164i
$775$	−1.23324	−	0.944442i	−0.0442994	−	0.0339253i
$776$		−	6.72489i		−	0.241410i
$777$	10.0994	−	8.78781i	0.362313	−	0.315261i
$778$	2.15808	−	2.15808i	0.0773708	−	0.0773708i
$779$	−7.00571	−	12.1343i	−0.251006	−	0.434755i
$780$	24.8953	+	0.547167i	0.891394	+	0.0195917i
$781$	3.93191	−	6.81026i	0.140695	−	0.243690i
$782$	−6.86500	−	1.83947i	−0.245492	−	0.0657793i
$783$	−54.4908	+	7.06856i	−1.94734	+	0.252610i
$784$	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
$787$	−11.0089	+	2.94983i	−0.392425	+	0.105150i	−0.449635	−	0.893212i	$-0.648446\pi$
$787$	−11.0089	+	2.94983i	−0.392425	+	0.105150i	0.0572104	+	0.998362i	$0.481779\pi$
$788$	−1.38292	+	0.370552i	−0.0492645	+	0.0132004i
$789$	−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
$792$	8.52975	+	1.51517i	0.303091	+	0.0538391i
$793$	−4.33075	−	1.16042i	−0.153789	−	0.0412078i
$794$	−6.46613	+	11.1997i	−0.229474	+	0.397461i
$795$	−2.07873	−	0.0456878i	−0.0737249	−	0.00162038i
$796$	−4.42355	−	7.66182i	−0.156789	−	0.271566i
$797$	29.5652	−	29.5652i	1.04725	−	1.04725i	0.0484262	−	0.998827i	$-0.484579\pi$
$797$	29.5652	−	29.5652i	1.04725	−	1.04725i	0.998827	−	0.0484262i	$-0.0154206\pi$
$798$	−7.11006	−	2.44435i	−0.251693	−	0.0865291i
$799$			8.43186i			0.298298i
$800$	−4.95660	+	0.657337i	−0.175242	+	0.0232404i
$801$	−21.5325	+	1.85637i	−0.760813	+	0.0655916i
$802$	−20.7992	+	5.57313i	−0.734446	+	0.196794i
$803$	0.139600	−	0.520993i	0.00492636	−	0.0183854i
$804$	0.434577	+	1.38135i	0.0153263	+	0.0487165i
$805$	−22.2997	−	18.8173i	−0.785961	−	0.663222i
$806$		−	1.99743i		−	0.0703565i
$807$	−9.78745	+	0.421119i	−0.344534	+	0.0148241i
$808$	−2.61668	−	9.76560i	−0.0920546	−	0.343552i
$809$	12.3778	−	21.4390i	0.435181	−	0.753756i	−0.562129	−	0.827050i	$-0.690018\pi$
$809$	12.3778	−	21.4390i	0.435181	−	0.753756i	0.997310	+	0.0732932i	$0.0233509\pi$
$810$	−18.4036	−	8.14302i	−0.646635	−	0.286117i
$811$	−28.9643			−1.01707			−0.508537	−	0.861040i	$-0.669813\pi$
$811$	−28.9643			−1.01707			−0.508537	+	0.861040i	$0.669813\pi$
$812$	27.8015	+	3.13616i	0.975642	+	0.110058i
$813$	18.3036	−	35.1067i	0.641937	−	1.23124i
$814$	−7.30598	+	4.21811i	−0.256074	+	0.147845i
$815$	−0.349555	+	0.172588i	−0.0122444	+	0.00604549i
$816$	2.43643	+	0.541762i	0.0852920	+	0.0189655i
$817$	3.66069	−	13.6619i	0.128071	−	0.477969i
$818$	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	$0.606252\pi$
$822$	−24.6071	+	15.6546i	−0.858272	+	0.546016i
$823$	−12.0052	−	44.8040i	−0.418474	−	1.56177i	−0.777773	−	0.628545i	$-0.783651\pi$
$823$	−12.0052	−	44.8040i	−0.418474	−	1.56177i	0.359298	−	0.933223i	$-0.383016\pi$
$824$	−2.53628	−	4.39297i	−0.0883556	−	0.153036i
$825$	24.9142	+	2.17178i	0.867403	+	0.0756117i
$826$	−6.20497	+	15.8039i	−0.215899	+	0.549889i
$827$	−34.7746	+	34.7746i	−1.20923	+	1.20923i	−0.237957	+	0.971276i	$0.576478\pi$
$827$	−34.7746	+	34.7746i	−1.20923	+	1.20923i	−0.971276	+	0.237957i	$0.923522\pi$
$828$	−5.04293	−	13.9101i	−0.175254	−	0.483410i
$829$	−26.7949	−	15.4700i	−0.930624	−	0.537296i	−0.0436151	−	0.999048i	$-0.513888\pi$
$829$	−26.7949	−	15.4700i	−0.930624	−	0.537296i	−0.887009	+	0.461752i	$0.847221\pi$
$830$	−6.79571	−	2.30324i	−0.235883	−	0.0799465i
$831$	21.5166	+	19.7414i	0.746404	+	0.684823i
$832$	−4.54633	−	4.54633i	−0.157616	−	0.157616i
$833$	−8.91701	−	4.71576i	−0.308956	−	0.163391i
$834$	25.1142	−	7.90098i	0.869632	−	0.273589i
$835$	−0.332964	+	5.11727i	−0.0115227	+	0.177090i
$836$	4.10311	+	2.36893i	0.141909	+	0.0819312i
$837$	−0.620589	+	1.49022i	−0.0214507	+	0.0515095i
$838$	−28.6028	−	7.66410i	−0.988068	−	0.264752i
$839$	−5.32218			−0.183742			−0.0918710	−	0.995771i	$-0.529285\pi$
$839$	−5.32218			−0.183742			−0.0918710	+	0.995771i	$0.529285\pi$
$840$	8.10816	+	6.26560i	0.279758	+	0.216184i
$841$	82.8228			2.85596
$842$	−3.74869	−	1.00446i	−0.129188	−	0.0346159i
$843$	−35.9287	+	22.8572i	−1.23745	+	0.787242i
$844$	−11.6954	−	6.75235i	−0.402573	−	0.232425i
$845$	41.8029	+	47.6215i	1.43806	+	1.63823i
$846$	−14.3920	+	10.0503i	−0.494807	+	0.345535i
$847$	−5.66377	−	4.18120i	−0.194610	−	0.143668i
$848$	0.379614	+	0.379614i	0.0130360	+	0.0130360i
$849$	−31.3969	+	34.2201i	−1.07754	+	1.17443i
$850$	7.14439	+	0.933677i	0.245050	+	0.0320249i
$851$	12.4779	+	7.20412i	0.427737	+	0.246954i
$852$	4.71228	−	0.202753i	0.161440	−	0.00694620i
$853$	−12.3820	+	12.3820i	−0.423953	+	0.423953i	−0.886562	−	0.462609i	$-0.846913\pi$
$853$	−12.3820	+	12.3820i	−0.423953	+	0.423953i	0.462609	+	0.886562i	$0.346913\pi$
$854$	−1.15014	−	1.44262i	−0.0393569	−	0.0493653i
$855$	−7.94428	−	7.61705i	−0.271688	−	0.260498i
$856$	−3.41083	−	5.90772i	−0.116580	−	0.201922i
$857$	−11.3844	−	42.4872i	−0.388884	−	1.45133i	−0.831953	−	0.554846i	$-0.812777\pi$
$857$	−11.3844	−	42.4872i	−0.388884	−	1.45133i	0.443069	−	0.896487i	$-0.353890\pi$
$858$	17.2617	+	27.1333i	0.589303	+	0.926314i
$859$	23.4854	−	13.5593i	0.801311	−	0.462637i	−0.0426185	−	0.999091i	$-0.513570\pi$
$859$	23.4854	−	13.5593i	0.801311	−	0.462637i	0.843929	+	0.536454i	$0.180237\pi$
$860$	−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
$863$	10.0628	−	37.5548i	0.342541	−	1.27838i	−0.552917	−	0.833236i	$-0.686485\pi$
$863$	10.0628	−	37.5548i	0.342541	−	1.27838i	0.895458	−	0.445145i	$-0.146848\pi$
$864$	1.97936	+	4.80439i	0.0673391	+	0.163449i
$865$	−3.77348	−	7.64271i	−0.128302	−	0.259860i
$866$	−22.2142	+	12.8254i	−0.754870	+	0.435825i
$867$	22.9200	+	11.9499i	0.778405	+	0.405839i
$868$	0.488176	−	0.661274i	0.0165698	−	0.0224451i
$869$	−27.0756			−0.918478
$870$	35.0099	+	21.2521i	1.18695	+	0.720514i
$871$	−2.68772	+	4.65526i	−0.0910698	+	0.157738i
$872$	−2.35555	−	8.79105i	−0.0797691	−	0.297702i
$873$	−18.9667	+	6.87613i	−0.641926	+	0.232722i
$874$		−	8.09181i		−	0.273710i
$875$	24.9188	+	15.9390i	0.842410	+	0.538836i
$876$	0.308598	−	0.0970859i	0.0104266	−	0.00328023i
$877$	10.1752	−	37.9744i	0.343592	−	1.28230i	−0.550656	−	0.834732i	$-0.685622\pi$
$877$	10.1752	−	37.9744i	0.343592	−	1.28230i	0.894248	−	0.447572i	$-0.147711\pi$
$878$	22.7237	−	6.08881i	0.766889	−	0.205487i
$879$	7.37646	−	33.1736i	0.248802	−	1.11892i
$880$	−4.25985	−	4.85278i	−0.143599	−	0.163587i
$881$		−	25.3849i		−	0.855240i	−0.903959	−	0.427620i	$-0.859352\pi$
$881$		−	25.3849i		−	0.855240i	0.903959	−	0.427620i	$-0.140648\pi$
$882$	−2.57938	−	20.8410i	−0.0868522	−	0.701753i
$883$	−26.1956	+	26.1956i	−0.881550	+	0.881550i	−0.993692	−	0.112142i	$-0.964229\pi$
$883$	−26.1956	+	26.1956i	−0.881550	+	0.881550i	0.112142	+	0.993692i	$0.464229\pi$
$884$	4.63253	+	8.02378i	0.155809	+	0.269869i
$885$	−17.9562	+	17.1839i	−0.603592	+	0.577631i
$886$	10.5342	−	18.2457i	0.353903	−	0.612978i
$887$	10.2169	+	2.73762i	0.343051	+	0.0919202i	0.426231	−	0.904614i	$-0.359841\pi$
$887$	10.2169	+	2.73762i	0.343051	+	0.0919202i	−0.0831802	+	0.996535i	$0.526508\pi$
$888$	−4.48676	−	2.33927i	−0.150566	−	0.0785009i
$889$	−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
$892$	27.4148	−	7.34578i	0.917916	−	0.245955i
$893$	−9.27291	+	2.48467i	−0.310306	+	0.0831463i
$894$	−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
$897$	25.3919	−	48.7020i	0.847810	−	1.62611i
$898$	−2.46940	−	0.661674i	−0.0824049	−	0.0220803i
$899$	1.64260	−	2.84506i	0.0547837	−	0.0948881i
$900$	6.92201	+	13.3074i	0.230734	+	0.443579i
$901$	−0.386811	−	0.669977i	−0.0128866	−	0.0223202i
$902$	−17.4384	+	17.4384i	−0.580636	+	0.580636i
$903$	38.7758	−	7.55668i	1.29038	−	0.251470i
$904$			11.4349i			0.380319i
$905$	8.93249	−	7.84109i	0.296926	−	0.260647i
$906$	2.77193	+	0.616365i	0.0920913	+	0.0204773i
$907$	25.4126	−	6.80928i	0.843811	−	0.226098i	0.189081	−	0.981961i	$-0.439449\pi$
$907$	25.4126	−	6.80928i	0.843811	−	0.226098i	0.654730	+	0.755863i	$0.272782\pi$
$908$	−2.06654	+	7.71245i	−0.0685807	+	0.255947i
$909$	−24.8671	+	17.3652i	−0.824790	+	0.575969i
$910$	3.21010	+	37.9017i	0.106414	+	1.25643i
$911$			39.1115i			1.29582i	0.761716	+	0.647911i	$0.224357\pi$
$911$			39.1115i			1.29582i	−0.761716	+	0.647911i	$0.775643\pi$
$912$	0.122156	+	2.83910i	0.00404500	+	0.0940119i
$913$	−2.39839	−	8.95090i	−0.0793750	−	0.296232i
$914$	−5.43937	+	9.42126i	−0.179918	+	0.311628i
$915$	−0.641520	−	2.62348i	−0.0212080	−	0.0867296i
$916$	−15.6326			−0.516516
$917$	−13.6959	+	18.5522i	−0.452277	+	0.612647i
$918$	−0.963249	−	7.42558i	−0.0317919	−	0.245081i
$919$	47.4211	−	27.3786i	1.56428	−	0.903137i	0.567464	−	0.823399i	$-0.307925\pi$
$919$	47.4211	−	27.3786i	1.56428	−	0.903137i	0.996816	−	0.0797385i	$-0.0254085\pi$
$920$	−3.53998	+	10.4447i	−0.116710	+	0.344353i
$921$	−3.98680	+	17.9296i	−0.131370	+	0.590799i
$922$	−8.70751	+	32.4969i	−0.286766	+	1.07023i
$923$	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
$927$	−9.79651	+	11.6450i	−0.321760	+	0.382473i
$928$	−2.73692	−	10.2143i	−0.0898436	−	0.335301i
$929$	−8.26043	−	14.3075i	−0.271016	−	0.469414i	0.698106	−	0.715994i	$-0.254026\pi$
$929$	−8.26043	−	14.3075i	−0.271016	−	0.469414i	−0.969122	+	0.246581i	$0.920693\pi$
$930$	1.05498	−	0.578563i	0.0345941	−	0.0189718i
$931$	2.55851	−	11.1961i	0.0838518	−	0.366937i
$932$	5.21295	−	5.21295i	0.170756	−	0.170756i
$933$	−1.22921	−	28.5687i	−0.0402426	−	0.935298i
$934$	28.2822	+	16.3287i	0.925421	+	0.534292i
$935$	4.11948	+	8.34348i	0.134721	+	0.272861i
$936$	−8.17379	+	17.4709i	−0.267169	+	0.571056i
$937$	25.3565	+	25.3565i	0.828362	+	0.828362i	0.987290	−	0.158928i	$-0.0508038\pi$
$937$	25.3565	+	25.3565i	0.828362	+	0.828362i	−0.158928	+	0.987290i	$0.550804\pi$
$938$	−2.02756	+	0.884299i	−0.0662021	+	0.0288734i
$939$	−7.49697	−	23.8300i	−0.244655	−	0.777662i
$940$	13.0563	+	0.849528i	0.425848	+	0.0277086i
$941$	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	$0.534885\pi$
$942$	12.6418	+	19.8714i	0.411891	+	0.647444i
$943$	40.6845	+	10.9014i	1.32487	+	0.354998i
$944$	6.41723			0.208863
$945$	9.38084	−	29.2746i	0.305159	−	0.952302i
$946$	−24.8947			−0.809395
$947$	−12.3070	−	3.29765i	−0.399923	−	0.107159i	0.0532508	−	0.998581i	$-0.483042\pi$
$947$	−12.3070	−	3.29765i	−0.399923	−	0.107159i	−0.453174	+	0.891422i	$0.649708\pi$
$948$	−8.71692	−	13.7020i	−0.283112	−	0.445019i
$949$	1.04000	+	0.600445i	0.0337599	+	0.0194913i
$950$	1.07847	+	8.13215i	0.0349903	+	0.263842i
$951$	12.5575	+	39.9155i	0.407206	+	1.29435i
$952$	−0.427371	+	3.78857i	−0.0138512	+	0.122788i
$953$	−20.6345	−	20.6345i	−0.668417	−	0.668417i	0.288933	−	0.957349i	$-0.406700\pi$
$953$	−20.6345	−	20.6345i	−0.668417	−	0.668417i	−0.957349	+	0.288933i	$0.906700\pi$
$954$	0.682502	−	1.45880i	0.0220968	−	0.0472305i
$955$	16.0990	−	47.5002i	0.520952	−	1.53707i
$956$	3.39070	+	1.95762i	0.109663	+	0.0633141i
$957$	2.27364	+	52.8427i	0.0734962	+	1.70816i
$958$	19.6877	−	19.6877i	0.636080	−	0.636080i
$959$	−27.7717	−	34.8340i	−0.896797	−	1.12485i
$960$	1.08436	−	3.71809i	0.0349977	−	0.120001i
$961$	15.4517	+	26.7632i	0.498443	+	0.863329i
$962$	−4.86138	−	18.1429i	−0.156737	−	0.584951i
$963$	−13.1745	+	15.6604i	−0.424541	+	0.504649i
$964$	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	0.999791	−	0.0204272i	$-0.00650265\pi$
$967$	30.4549	+	30.4549i	0.979364	+	0.979364i	−0.0204272	+	0.999791i	$0.506503\pi$
$968$	−0.688678	+	2.57018i	−0.0221350	+	0.0826088i
$969$	0.888853	−	3.99738i	0.0285541	−	0.128414i
$970$	14.2416	+	4.82683i	0.457270	+	0.154980i
$971$	−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	$0.570067\pi$
$972$	11.5263	−	10.4950i	0.369706	−	0.336626i
$973$	16.0773	+	36.8628i	0.515415	+	1.18177i
$974$	31.5305			1.01030
$975$	−19.0275	+	52.3290i	−0.609367	+	1.67587i
$976$	−0.348669	+	0.603912i	−0.0111606	+	0.0193308i
$977$	1.83458	+	6.84676i	0.0586936	+	0.219047i	0.989043	−	0.147626i	$-0.0471633\pi$
$977$	1.83458	+	6.84676i	0.0586936	+	0.219047i	−0.930350	+	0.366674i	$0.880497\pi$
$978$	−0.0129806	−	0.301690i	−0.000415075	−	0.00964697i
$979$			20.8038i			0.664891i
$980$	−8.20049	+	13.3324i	−0.261955	+	0.425887i
$981$	−22.3855	+	15.6323i	−0.714715	+	0.499101i
$982$	−0.394685	+	1.47299i	−0.0125949	+	0.0470048i
$983$	26.3541	−	7.06155i	0.840564	−	0.225229i	0.187247	−	0.982313i	$-0.440043\pi$
$983$	26.3541	−	7.06155i	0.840564	−	0.225229i	0.653317	+	0.757084i	$0.273377\pi$
$984$	−14.4392	−	3.21068i	−0.460304	−	0.102353i
$985$	0.207865	−	3.19463i	0.00662311	−	0.101790i
$986$			15.2383i			0.485287i
$987$	−17.6013	−	20.2282i	−0.560255	−	0.643872i
$988$	−7.45904	+	7.45904i	−0.237304	+	0.237304i
$989$	21.2588	+	36.8214i	0.675992	+	1.17085i
$990$	−9.33100	+	16.9763i	−0.296559	+	0.539542i
$991$	−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	$0.936568\pi$
$992$	−0.300082	−	0.0804067i	−0.00952761	−	0.00255291i
$993$	12.9099	−	24.7613i	0.409682	−	0.785776i
$994$	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
$997$	28.5930	−	7.66148i	0.905550	−	0.242641i	0.224152	−	0.974554i	$-0.428039\pi$
$997$	28.5930	−	7.66148i	0.905550	−	0.242641i	0.681398	+	0.731913i	$0.261372\pi$
$998$	−10.3603	+	2.77603i	−0.327949	+	0.0878737i
$999$	−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.137.6	yes	64
3.2	odd	2	inner	210.2.x.a.137.12	yes	64
5.3	odd	4	inner	210.2.x.a.53.3	yes	64
7.2	even	3	inner	210.2.x.a.107.9	yes	64
15.8	even	4	inner	210.2.x.a.53.9	yes	64
21.2	odd	6	inner	210.2.x.a.107.3	yes	64
35.23	odd	12	inner	210.2.x.a.23.12	yes	64
105.23	even	12	inner	210.2.x.a.23.6	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.6	✓	64	105.23	even	12	inner
210.2.x.a.23.12	yes	64	35.23	odd	12	inner
210.2.x.a.53.3	yes	64	5.3	odd	4	inner
210.2.x.a.53.9	yes	64	15.8	even	4	inner
210.2.x.a.107.3	yes	64	21.2	odd	6	inner
210.2.x.a.107.9	yes	64	7.2	even	3	inner
210.2.x.a.137.6	yes	64	1.1	even	1	trivial
210.2.x.a.137.12	yes	64	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.929705 + 1.46139i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.68046 + 1.47514i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(2.42513 - 1.05770i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-1.27130 + 2.71732i) q^{9} +(2.00500 - 0.989939i) q^{10} +(2.50087 + 1.44388i) q^{11} +(0.0744552 + 1.73045i) q^{12} +(-4.54633 + 4.54633i) q^{13} +(-2.61625 + 0.393987i) q^{14} +(-3.71809 - 1.08436i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.372965 - 1.39193i) q^{17} +(1.93127 - 2.29569i) 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} +(-1.27650 + 4.76396i) q^{23} +(0.375955 - 1.69076i) q^{24} +(0.647925 - 4.95784i) q^{25} +(5.56810 - 3.21474i) q^{26} +(-5.15298 + 0.668446i) q^{27} +(2.62908 + 0.296574i) q^{28} +10.5746 q^{29} +(3.31074 + 2.00973i) q^{30} +(0.155334 - 0.269046i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.215009 + 4.99712i) q^{33} +1.44103i q^{34} +(-2.51510 + 5.35484i) q^{35} +(-2.45963 + 1.71762i) q^{36} +(0.756107 - 2.82183i) q^{37} +(-1.58477 + 0.424637i) q^{38} +(-10.8707 - 2.41720i) q^{39} +(2.23135 + 0.145187i) q^{40} -8.54006i q^{41} +(-3.00811 - 3.45706i) q^{42} +(6.09579 - 6.09579i) q^{43} +(1.44388 + 2.50087i) q^{44} +(-1.87205 - 6.44169i) q^{45} +(2.46601 - 4.27125i) q^{46} +(-5.65190 - 1.51442i) q^{47} +(-0.800745 + 1.53584i) q^{48} +(4.76255 - 5.13012i) q^{49} +(-1.90903 + 4.62121i) q^{50} +(1.68739 - 1.83913i) q^{51} +(-6.21041 + 1.66407i) q^{52} +(0.518562 - 0.138948i) q^{53} +(5.15040 + 0.688020i) q^{54} +(-6.33255 + 1.26275i) q^{55} +(-2.46273 - 0.966923i) q^{56} +(2.51981 + 1.31376i) q^{57} +(-10.2143 - 2.73692i) q^{58} +(3.20862 - 5.55749i) q^{59} +(-2.67777 - 2.79813i) q^{60} +(0.348669 + 0.603912i) q^{61} +(-0.219675 + 0.219675i) q^{62} +(-0.208967 + 7.93450i) q^{63} +1.00000i q^{64} +(0.933476 - 14.3464i) q^{65} +(1.08567 - 4.88250i) q^{66} +(0.807572 - 0.216388i) q^{67} +(0.372965 - 1.39193i) q^{68} +(-8.14875 + 2.56362i) q^{69} +(3.81533 - 4.52142i) q^{70} -2.72315i q^{71} +(2.82038 - 1.02249i) q^{72} +(-0.0483418 - 0.180414i) q^{73} +(-1.46069 + 2.52998i) q^{74} +(7.84770 - 3.66246i) q^{75} +1.64067 q^{76} +(7.59214 + 0.856433i) q^{77} +(9.87467 + 5.14838i) q^{78} +(-8.11986 + 4.68800i) q^{79} +(-2.11774 - 0.717755i) q^{80} +(-5.76761 - 6.90903i) q^{81} +(-2.21033 + 8.24906i) 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} +(9.83128 + 15.4536i) q^{87} +(-0.747407 - 2.78936i) q^{88} +(3.60206 + 6.23895i) q^{89} +(0.141028 + 6.70672i) q^{90} +(-6.21682 + 15.8341i) q^{91} +(-3.48746 + 3.48746i) q^{92} +(0.537594 - 0.0231308i) q^{93} +(5.06736 + 2.92564i) q^{94} +(-1.17760 + 3.47452i) q^{95} +(1.17097 - 1.27626i) q^{96} +(4.75522 + 4.75522i) q^{97} +(-5.92804 + 3.72268i) q^{98} +(-7.10283 + 4.96006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7} + 4 q^{10} - 24 q^{15} + 32 q^{16} - 8 q^{18} + 12 q^{21} - 24 q^{22} - 8 q^{25} - 72 q^{27} + 4 q^{28} - 12 q^{30} + 32 q^{31} - 20 q^{33} - 24 q^{36} - 8 q^{37} - 40 q^{42} - 64 q^{43}+ \cdots + 104 q^{97}+O(q^{100}) \) 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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