LMFDB - Embedded newform 210.2.x.a.23.12

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			23.12
Character	$\chi$	$=$	210.23
Dual form			210.2.x.a.137.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.0744552 - 1.73045i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.68046 + 1.47514i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(2.42513 + 1.05770i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98891 + 0.257682i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.0744552 - 1.73045i) 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} +(-2.98891 + 0.257682i) q^{9} +(2.00500 + 0.989939i) q^{10} +(-2.50087 + 1.44388i) q^{11} +(-0.929705 - 1.46139i) 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} +(0.372965 - 1.39193i) q^{17} +(-2.82038 + 1.02249i) q^{18} +(1.42086 + 0.820335i) q^{19} +(2.19290 + 0.437276i) q^{20} +(1.64973 - 4.27532i) q^{21} +(-2.04195 + 2.04195i) q^{22} +(1.27650 + 4.76396i) q^{23} +(-1.27626 - 1.17097i) q^{24} +(0.647925 + 4.95784i) q^{25} +(-5.56810 - 3.21474i) q^{26} +(0.668446 + 5.15298i) q^{27} +(2.62908 - 0.296574i) q^{28} -10.5746 q^{29} +(1.56376 - 3.54326i) q^{30} +(0.155334 + 0.269046i) q^{31} +(0.258819 - 0.965926i) q^{32} +(2.68476 + 4.22013i) 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} +(-7.52870 + 8.20570i) q^{39} +(2.23135 - 0.145187i) q^{40} -8.54006i q^{41} +(0.486981 - 4.55663i) q^{42} +(6.09579 + 6.09579i) q^{43} +(-1.44388 + 2.50087i) q^{44} +(-5.40288 - 3.97604i) q^{45} +(2.46601 + 4.27125i) q^{46} +(5.65190 - 1.51442i) q^{47} +(-1.53584 - 0.800745i) q^{48} +(4.76255 + 5.13012i) q^{49} +(1.90903 + 4.62121i) q^{50} +(-2.43643 - 0.541762i) q^{51} +(-6.21041 - 1.66407i) q^{52} +(-0.518562 - 0.138948i) q^{53} +(1.97936 + 4.80439i) q^{54} +(-6.33255 - 1.26275i) q^{55} +(2.46273 - 0.966923i) q^{56} +(1.31376 - 2.51981i) q^{57} +(-10.2143 + 2.73692i) q^{58} +(-3.20862 - 5.55749i) q^{59} +(0.593412 - 3.82725i) q^{60} +(0.348669 - 0.603912i) q^{61} +(0.219675 + 0.219675i) q^{62} +(-7.52106 - 2.53645i) q^{63} -1.00000i q^{64} +(-0.933476 - 14.3464i) q^{65} +(3.68553 + 3.38146i) 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} +(-1.93127 + 2.29569i) q^{72} +(-0.0483418 + 0.180414i) q^{73} +(1.46069 + 2.52998i) q^{74} +(8.53105 - 1.49034i) q^{75} +1.64067 q^{76} +(-7.59214 + 0.856433i) q^{77} +(-5.14838 + 9.87467i) q^{78} +(-8.11986 - 4.68800i) q^{79} +(2.11774 - 0.717755i) q^{80} +(8.86720 - 1.54038i) q^{81} +(-2.21033 - 8.24906i) q^{82} +(2.26907 - 2.26907i) q^{83} +(-0.708954 - 4.52740i) q^{84} +(2.68004 - 1.78891i) q^{85} +(7.46579 + 4.31038i) q^{86} +(0.787336 + 18.2989i) q^{87} +(-0.747407 + 2.78936i) 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} +(0.454005 - 0.288829i) q^{93} +(5.06736 - 2.92564i) q^{94} +(1.17760 + 3.47452i) q^{95} +(-1.69076 - 0.375955i) 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}+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 $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.0744552	−	1.73045i	−0.0429867	−	0.999076i
$3$	−0.0744552	−	1.73045i	−0.0429867	−	0.999076i
$4$	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
$9$	−2.98891	+	0.257682i	−0.996304	+	0.0858940i
$10$	2.00500	+	0.989939i	0.634036	+	0.313046i
$11$	−2.50087	+	1.44388i	−0.754041	+	0.435346i	−0.827152	−	0.561978i	$-0.810041\pi$
$11$	−2.50087	+	1.44388i	−0.754041	+	0.435346i	0.0731108	+	0.997324i	$0.476707\pi$
$12$	−0.929705	−	1.46139i	−0.268383	−	0.421866i
$13$	−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
$17$	0.372965	−	1.39193i	0.0904574	−	0.337592i	−0.905834	−	0.423632i	$-0.860755\pi$
$17$	0.372965	−	1.39193i	0.0904574	−	0.337592i	0.996292	+	0.0860407i	$0.0274215\pi$
$18$	−2.82038	+	1.02249i	−0.664769	+	0.241003i
$19$	1.42086	+	0.820335i	0.325968	+	0.188198i	0.654050	−	0.756452i	$-0.273069\pi$
$19$	1.42086	+	0.820335i	0.325968	+	0.188198i	−0.328081	+	0.944649i	$0.606402\pi$
$20$	2.19290	+	0.437276i	0.490346	+	0.0977779i
$21$	1.64973	−	4.27532i	0.360000	−	0.932952i
$22$	−2.04195	+	2.04195i	−0.435346	+	0.435346i
$23$	1.27650	+	4.76396i	0.266168	+	0.993354i	0.961531	+	0.274695i	$0.0885770\pi$
$23$	1.27650	+	4.76396i	0.266168	+	0.993354i	−0.695363	+	0.718659i	$0.744756\pi$
$24$	−1.27626	−	1.17097i	−0.260516	−	0.239022i
$25$	0.647925	+	4.95784i	0.129585	+	0.991568i
$26$	−5.56810	−	3.21474i	−1.09199	−	0.630463i
$27$	0.668446	+	5.15298i	0.128642	+	0.991691i
$28$	2.62908	−	0.296574i	0.496849	−	0.0560472i
$29$	−10.5746			−1.96366			−0.981830	−	0.189765i	$-0.939227\pi$
$29$	−10.5746			−1.96366			−0.981830	+	0.189765i	$0.939227\pi$
$30$	1.56376	−	3.54326i	0.285502	−	0.646907i
$31$	0.155334	+	0.269046i	0.0278988	+	0.0483221i	0.879638	−	0.475644i	$-0.157785\pi$
$31$	0.155334	+	0.269046i	0.0278988	+	0.0483221i	−0.851739	+	0.523966i	$0.824452\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	2.68476	+	4.22013i	0.467357	+	0.734630i
$34$		−	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	0.999814	−	0.0192930i	$-0.00614152\pi$
$37$	0.756107	+	2.82183i	0.124303	+	0.463906i	−0.875511	+	0.483199i	$0.839475\pi$
$38$	1.58477	+	0.424637i	0.257083	+	0.0688852i
$39$	−7.52870	+	8.20570i	−1.20556	+	1.31396i
$40$	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	$-0.232365\pi$
$42$	0.486981	−	4.55663i	0.0751428	−	0.703103i
$43$	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
$45$	−5.40288	−	3.97604i	−0.805414	−	0.592713i
$46$	2.46601	+	4.27125i	0.363593	+	0.629761i
$47$	5.65190	−	1.51442i	0.824415	−	0.220901i	0.178139	−	0.984005i	$-0.442992\pi$
$47$	5.65190	−	1.51442i	0.824415	−	0.220901i	0.646276	+	0.763104i	$0.276326\pi$
$48$	−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
$51$	−2.43643	−	0.541762i	−0.341168	−	0.0758618i
$52$	−6.21041	−	1.66407i	−0.861228	−	0.230765i
$53$	−0.518562	−	0.138948i	−0.0712300	−	0.0190860i	0.223028	−	0.974812i	$-0.428406\pi$
$53$	−0.518562	−	0.138948i	−0.0712300	−	0.0190860i	−0.294258	+	0.955726i	$0.595073\pi$
$54$	1.97936	+	4.80439i	0.269356	+	0.653794i
$55$	−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
$58$	−10.2143	+	2.73692i	−1.34120	+	0.359375i
$59$	−3.20862	−	5.55749i	−0.417726	−	0.723523i	0.577984	−	0.816048i	$-0.303840\pi$
$59$	−3.20862	−	5.55749i	−0.417726	−	0.723523i	−0.995710	+	0.0925249i	$0.970506\pi$
$60$	0.593412	−	3.82725i	0.0766092	−	0.494096i
$61$	0.348669	−	0.603912i	0.0446425	−	0.0773230i	−0.842841	−	0.538163i	$-0.819118\pi$
$61$	0.348669	−	0.603912i	0.0446425	−	0.0773230i	0.887483	+	0.460840i	$0.152452\pi$
$62$	0.219675	+	0.219675i	0.0278988	+	0.0278988i
$63$	−7.52106	−	2.53645i	−0.947565	−	0.319563i
$64$		−	1.00000i		−	0.125000i
$65$	−0.933476	−	14.3464i	−0.115783	−	1.77946i
$66$	3.68553	+	3.38146i	0.453658	+	0.416230i
$67$	0.807572	+	0.216388i	0.0986606	+	0.0264360i	0.307812	−	0.951447i	$-0.400403\pi$
$67$	0.807572	+	0.216388i	0.0986606	+	0.0264360i	−0.209151	+	0.977883i	$0.567070\pi$
$68$	−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	$-0.0516620\pi$
$72$	−1.93127	+	2.29569i	−0.227603	+	0.270550i
$73$	−0.0483418	+	0.180414i	−0.00565798	+	0.0211159i	−0.968697	−	0.248246i	$-0.920146\pi$
$73$	−0.0483418	+	0.180414i	−0.00565798	+	0.0211159i	0.963039	+	0.269362i	$0.0868127\pi$
$74$	1.46069	+	2.52998i	0.169801	+	0.294104i
$75$	8.53105	−	1.49034i	0.985081	−	0.172089i
$76$	1.64067			0.188198
$77$	−7.59214	+	0.856433i	−0.865205	+	0.0975996i
$78$	−5.14838	+	9.87467i	−0.582939	+	1.11809i
$79$	−8.11986	−	4.68800i	−0.913555	−	0.527441i	−0.0319820	−	0.999488i	$-0.510182\pi$
$79$	−8.11986	−	4.68800i	−0.913555	−	0.527441i	−0.881573	+	0.472047i	$0.843515\pi$
$80$	2.11774	−	0.717755i	0.236771	−	0.0802475i
$81$	8.86720	−	1.54038i	0.985244	−	0.171153i
$82$	−2.21033	−	8.24906i	−0.244090	−	0.910957i
$83$	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	$0.193647\pi$
$84$	−0.708954	−	4.52740i	−0.0773532	−	0.493980i
$85$	2.68004	−	1.78891i	0.290691	−	0.194034i
$86$	7.46579	+	4.31038i	0.805057	+	0.464800i
$87$	0.787336	+	18.2989i	0.0844113	+	1.96184i
$88$	−0.747407	+	2.78936i	−0.0796739	+	0.297347i
$89$	−3.60206	+	6.23895i	−0.381818	+	0.661327i	−0.991322	−	0.131455i	$-0.958035\pi$
$89$	−3.60206	+	6.23895i	−0.381818	+	0.661327i	0.609505	+	0.792783i	$0.291368\pi$
$90$	−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
$93$	0.454005	−	0.288829i	0.0470781	−	0.0299502i
$94$	5.06736	−	2.92564i	0.522658	−	0.301757i
$95$	1.17760	+	3.47452i	0.120819	+	0.356478i
$96$	−1.69076	−	0.375955i	−0.172562	−	0.0383708i
$97$	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	$0.139097\pi$
$98$	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	$-0.834436\pi$
$101$	−8.75559	+	5.05504i	−0.871214	+	0.502996i	−0.00346260	+	0.999994i	$0.501102\pi$
$102$	−2.49363	+	0.107292i	−0.246906	+	0.0106235i
$103$	4.89972	−	1.31288i	0.482784	−	0.129362i	−0.00921457	−	0.999958i	$-0.502933\pi$
$103$	4.89972	−	1.31288i	0.482784	−	0.129362i	0.491999	+	0.870596i	$0.336266\pi$
$104$	−6.42949			−0.630463
$105$	9.07901	−	4.75095i	0.886021	−	0.463645i
$106$	−0.536855			−0.0521440
$107$	−6.58921	+	1.76557i	−0.637003	+	0.170684i	−0.562846	−	0.826562i	$-0.690293\pi$
$107$	−6.58921	+	1.76557i	−0.637003	+	0.170684i	−0.0741574	+	0.997247i	$0.523627\pi$
$108$	3.15538	+	4.12839i	0.303627	+	0.397254i
$109$	7.88184	−	4.55058i	0.754943	−	0.435867i	−0.0725341	−	0.997366i	$-0.523109\pi$
$109$	7.88184	−	4.55058i	0.754943	−	0.435867i	0.827477	+	0.561499i	$0.189775\pi$
$110$	−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	$-0.569236\pi$
$113$	8.08570	−	8.08570i	0.760639	−	0.760639i	0.976438	+	0.215799i	$0.0692355\pi$
$114$	0.616819	−	2.77397i	0.0577704	−	0.259807i
$115$	−4.88239	+	9.88868i	−0.455286	+	0.922124i
$116$	−9.15790	+	5.28731i	−0.850289	+	0.490915i
$117$	14.7601	+	12.4171i	1.36457	+	1.14796i
$118$	−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
$122$	0.180484	−	0.673576i	0.0163403	−	0.0609827i
$123$	−14.7781	+	0.635852i	−1.33250	+	0.0573328i
$124$	0.269046	+	0.155334i	0.0241610	+	0.0139494i
$125$	−6.22470	+	9.28726i	−0.556754	+	0.830678i
$126$	−7.92127	−	0.503432i	−0.705683	−	0.0448493i
$127$	−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	$0.259735\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	10.0946	−	11.0023i	0.888780	−	0.968701i
$130$	−4.61480	−	13.6160i	−0.404745	−	1.19420i
$131$	7.54813	+	4.35792i	0.659483	+	0.380753i	0.792080	−	0.610417i	$-0.208998\pi$
$131$	7.54813	+	4.35792i	0.659483	+	0.380753i	−0.132597	+	0.991170i	$0.542332\pi$
$132$	4.43514	+	2.31236i	0.386029	+	0.201265i
$133$	2.57812	+	3.49227i	0.223551	+	0.302818i
$134$	0.836060			0.0722246
$135$	−6.47806	+	9.64545i	−0.557543	+	0.830148i
$136$	−0.720514	−	1.24797i	−0.0617836	−	0.107012i
$137$	4.35805	−	16.2645i	0.372333	−	1.38957i	−0.484869	−	0.874587i	$-0.661133\pi$
$137$	4.35805	−	16.2645i	0.372333	−	1.38957i	0.857202	−	0.514980i	$-0.172201\pi$
$138$	7.20758	−	4.58532i	0.613550	−	0.390328i
$139$		−	15.2003i		−	1.28927i	−0.764490	−	0.644636i	$-0.777009\pi$
$139$		−	15.2003i		−	1.28927i	0.764490	−	0.644636i	$-0.222991\pi$
$140$	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
$144$	−1.27130	+	2.71732i	−0.105941	+	0.226443i
$145$	−17.7703	−	15.5991i	−1.47574	−	1.29543i
$146$			0.186778i			0.0154579i
$147$	8.52282	−	8.62332i	0.702950	−	0.711239i
$148$	2.06572	+	2.06572i	0.169801	+	0.169801i
$149$	6.69548	−	11.5969i	0.548515	−	0.950056i	−0.449862	−	0.893098i	$-0.648527\pi$
$149$	6.69548	−	11.5969i	0.548515	−	0.950056i	0.998377	−	0.0569574i	$-0.0181399\pi$
$150$	7.85464	−	3.64756i	0.641329	−	0.297822i
$151$	−0.819732	−	1.41982i	−0.0667088	−	0.115543i	0.830742	−	0.556658i	$-0.187917\pi$
$151$	−0.819732	−	1.41982i	−0.0667088	−	0.115543i	−0.897451	+	0.441115i	$0.854583\pi$
$152$	1.58477	−	0.424637i	0.128542	−	0.0344426i
$153$	−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
$156$	−2.41720	+	10.8707i	−0.193531	+	0.870352i
$157$	−13.1343	−	3.51932i	−1.04823	−	0.280872i	−0.306710	−	0.951803i	$-0.599228\pi$
$157$	−13.1343	−	3.51932i	−1.04823	−	0.280872i	−0.741520	+	0.670931i	$0.765895\pi$
$158$	−9.05652	−	2.42669i	−0.720498	−	0.193057i
$159$	−0.201833	+	0.907691i	−0.0160064	+	0.0719846i
$160$	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
$163$	0.168401	−	0.0451230i	0.0131902	−	0.00353430i	−0.252218	−	0.967670i	$-0.581160\pi$
$163$	0.168401	−	0.0451230i	0.0131902	−	0.00353430i	0.265408	+	0.964136i	$0.414493\pi$
$164$	−4.27003	−	7.39591i	−0.333433	−	0.577523i
$165$	−1.71363	+	11.0522i	−0.133406	+	0.860411i
$166$	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	$0.778282\pi$
$168$	−1.85658	−	4.18965i	−0.143238	−	0.323238i
$169$			28.3383i			2.17987i
$170$	2.12572	−	2.42160i	0.163035	−	0.185728i
$171$	−4.45822	−	2.08578i	−0.340929	−	0.159504i
$172$	8.32701	+	2.23122i	0.634928	+	0.170129i
$173$	0.986574	+	3.68194i	0.0750078	+	0.279933i	0.993235	−	0.116121i	$-0.0370460\pi$
$173$	0.986574	+	3.68194i	0.0750078	+	0.279933i	−0.918227	+	0.396054i	$0.870379\pi$
$174$	5.49660	+	17.4716i	0.416696	+	1.32452i
$175$	−3.67260	+	12.7087i	−0.277622	+	0.960690i
$176$			2.88776i			0.217673i
$177$	−9.37805	+	5.96613i	−0.704898	+	0.448442i
$178$	−1.86456	+	6.95864i	−0.139755	+	0.521572i
$179$	4.40852	+	7.63578i	0.329508	+	0.570725i	0.982414	−	0.186714i	$-0.0597838\pi$
$179$	4.40852	+	7.63578i	0.329508	+	0.570725i	−0.652906	+	0.757439i	$0.726450\pi$
$180$	−6.66705	−	0.741911i	−0.496933	−	0.0552988i
$181$	−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
$183$	−1.07100	−	0.558389i	−0.0791706	−	0.0412773i
$184$	4.27125	+	2.46601i	0.314881	+	0.181796i
$185$	−2.89198	+	5.85735i	−0.212623	+	0.430641i
$186$	0.363781	−	0.396493i	0.0266737	−	0.0290723i
$187$	1.07703	+	4.01955i	0.0787606	+	0.293938i
$188$	4.13748	−	4.13748i	0.301757	−	0.301757i
$189$	−3.82922	+	13.2037i	−0.278535	+	0.960426i
$190$	2.03675	+	3.05134i	0.147761	+	0.221367i
$191$	19.4247	+	11.2148i	1.40552	+	0.811477i	0.994952	−	0.100354i	$-0.0319975\pi$
$191$	19.4247	+	11.2148i	1.40552	+	0.811477i	0.410567	+	0.911830i	$0.365331\pi$
$192$	−1.73045	+	0.0744552i	−0.124884	+	0.00537334i
$193$	4.26527	−	15.9182i	0.307021	−	1.14582i	−0.624171	−	0.781287i	$-0.714563\pi$
$193$	4.26527	−	15.9182i	0.307021	−	1.14582i	0.931192	−	0.364529i	$-0.118770\pi$
$194$	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	$0.733758\pi$
$198$	5.57705	−	6.62940i	0.396344	−	0.471131i
$199$	−7.66182	+	4.42355i	−0.543132	+	0.313577i	−0.746347	−	0.665557i	$-0.768194\pi$
$199$	−7.66182	+	4.42355i	−0.543132	+	0.313577i	0.203215	+	0.979134i	$0.434861\pi$
$200$	3.96388	+	3.04757i	0.280288	+	0.215496i
$201$	0.314321	−	1.41357i	0.0221705	−	0.0997058i
$202$	−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
$207$	−5.04293	−	13.9101i	−0.350508	−	0.966821i
$208$	−6.21041	+	1.66407i	−0.430614	+	0.115383i
$209$	−4.73786			−0.327725
$210$	7.54002	−	6.93889i	0.520311	−	0.478829i
$211$	−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
$213$	−4.71228	+	0.202753i	−0.322880	+	0.0138924i
$214$	−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
$219$	0.315797	+	0.0702203i	0.0213396	+	0.00474505i
$220$	−6.11553	+	2.07270i	−0.412309	+	0.139742i
$221$	−8.02378	+	4.63253i	−0.539738	+	0.311618i
$222$	4.26925	−	2.71601i	0.286533	−	0.182287i
$223$	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
$227$	−2.06654	+	7.71245i	−0.137161	+	0.511893i	0.862818	+	0.505514i	$0.168697\pi$
$227$	−2.06654	+	7.71245i	−0.137161	+	0.511893i	−0.999980	+	0.00637896i	$0.997970\pi$
$228$	−0.122156	−	2.83910i	−0.00809001	−	0.188024i
$229$	−13.5382	−	7.81631i	−0.894632	−	0.516516i	−0.0191773	−	0.999816i	$-0.506105\pi$
$229$	−13.5382	−	7.81631i	−0.894632	−	0.516516i	−0.875455	+	0.483300i	$0.839438\pi$
$230$	−2.15665	+	10.8154i	−0.142205	+	0.713146i
$231$	2.04729	+	13.0741i	0.134702	+	0.860209i
$232$	−7.47739	+	7.47739i	−0.490915	+	0.490915i
$233$	−1.90807	−	7.12102i	−0.125002	−	0.466514i	0.874838	−	0.484416i	$-0.160968\pi$
$233$	−1.90807	−	7.12102i	−0.125002	−	0.466514i	−0.999840	+	0.0179022i	$0.994301\pi$
$234$	17.4709	+	8.17379i	1.14211	+	0.534337i
$235$	11.7318	+	5.79241i	0.765299	+	0.377855i
$236$	−5.55749	−	3.20862i	−0.361762	−	0.208863i
$237$	−7.50779	+	14.4001i	−0.487683	+	0.935384i
$238$	1.52417	−	3.49469i	0.0987974	−	0.226527i
$239$	−3.91525			−0.253256			−0.126628	−	0.991950i	$-0.540416\pi$
$239$	−3.91525			−0.253256			−0.126628	+	0.991950i	$0.540416\pi$
$240$	−1.39972	−	3.61120i	−0.0903513	−	0.233102i
$241$	8.84160	+	15.3141i	0.569537	+	0.986468i	0.996612	+	0.0822510i	$0.0262109\pi$
$241$	8.84160	+	15.3141i	0.569537	+	0.986468i	−0.427074	+	0.904217i	$0.640456\pi$
$242$	−0.688678	+	2.57018i	−0.0442699	+	0.165218i
$243$	−3.32575	−	15.2296i	−0.213347	−	0.976976i
$244$		−	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
$249$	−4.09545	−	3.75756i	−0.259538	−	0.238126i
$250$	−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	$-0.174657\pi$
$252$	−7.78166	+	1.56390i	−0.490198	+	0.0985163i
$253$	−10.0709	−	10.0709i	−0.633155	−	0.633155i
$254$	−0.344586	+	0.596841i	−0.0216213	+	0.0374491i
$255$	−3.29516	−	4.50448i	−0.206351	−	0.282082i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−21.9442	+	5.87993i	−1.36884	+	0.366780i	−0.867056	−	0.498211i	$-0.833990\pi$
$257$	−21.9442	+	5.87993i	−1.36884	+	0.366780i	−0.501786	+	0.864992i	$0.667324\pi$
$258$	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
$261$	31.6066	−	2.72489i	1.95640	−	0.168666i
$262$	8.41885	+	2.25582i	0.520118	+	0.139365i
$263$	27.7833	+	7.44452i	1.71319	+	0.459049i	0.976204	−	0.216856i	$-0.0695803\pi$
$263$	27.7833	+	7.44452i	1.71319	+	0.459049i	0.736989	+	0.675905i	$0.236247\pi$
$264$	4.88250	+	1.08567i	0.300497	+	0.0668182i
$265$	−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
$268$	0.807572	−	0.216388i	0.0493303	−	0.0132180i
$269$	2.82801	+	4.89825i	0.172427	+	0.298652i	0.939268	−	0.343185i	$-0.111506\pi$
$269$	2.82801	+	4.89825i	0.172427	+	0.298652i	−0.766841	+	0.641837i	$0.778173\pi$
$270$	−3.76090	+	10.9934i	−0.228881	+	0.669039i
$271$	−11.4291	+	19.7958i	−0.694270	+	1.20251i	0.276156	+	0.961113i	$0.410939\pi$
$271$	−11.4291	+	19.7958i	−0.694270	+	1.20251i	−0.970426	+	0.241399i	$0.922394\pi$
$272$	−1.01896	−	1.01896i	−0.0617836	−	0.0617836i
$273$	−26.9373	+	11.9368i	−1.63032	+	0.722450i
$274$		−	16.8382i		−	1.01723i
$275$	−8.77890	−	11.4634i	−0.529388	−	0.691269i
$276$	5.77522	−	6.29453i	0.347627	−	0.378886i
$277$	16.2847	+	4.36346i	0.978450	+	0.262175i	0.712392	−	0.701782i	$-0.247612\pi$
$277$	16.2847	+	4.36346i	0.978450	+	0.262175i	0.266058	+	0.963957i	$0.414279\pi$
$278$	−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	$0.737969\pi$
$282$	−5.43996	−	8.55098i	−0.323945	−	0.509203i
$283$	6.93967	−	25.8992i	0.412520	−	1.53955i	−0.377230	−	0.926119i	$-0.623124\pi$
$283$	6.93967	−	25.8992i	0.412520	−	1.53955i	0.789751	−	0.613428i	$-0.210210\pi$
$284$	−1.36158	−	2.35832i	−0.0807947	−	0.139941i
$285$	5.92480	−	2.29647i	0.350955	−	0.136031i
$286$	18.5668			1.09788
$287$	9.03280	−	20.7108i	0.533190	−	1.22252i
$288$	−0.524686	+	2.95376i	−0.0309174	+	0.174052i
$289$	12.9241	+	7.46172i	0.760240	+	0.438925i
$290$	−21.2021	−	10.4682i	−1.24503	−	0.614716i
$291$	−8.58271	−	7.87461i	−0.503128	−	0.461618i
$292$	0.0483418	+	0.180414i	0.00282899	+	0.0105579i
$293$	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	$0.0557317\pi$
$294$	6.00053	−	10.5354i	0.349958	−	0.614434i
$295$	2.80610	−	14.0723i	0.163378	−	0.819322i
$296$	2.52998	+	1.46069i	0.147052	+	0.0849007i
$297$	−9.11198	−	11.9218i	−0.528731	−	0.691772i
$298$	3.46583	−	12.9347i	0.200770	−	0.749285i
$299$	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
$303$	9.39940	+	14.7747i	0.539981	+	0.848787i
$304$	1.42086	−	0.820335i	0.0814921	−	0.0470495i
$305$	1.47678	−	0.500518i	0.0845602	−	0.0286596i
$306$	0.371327	+	4.30711i	0.0212273	+	0.246221i
$307$	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	$0.152141\pi$
$308$	−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	$-0.511612\pi$
$311$	14.2976	−	8.25471i	0.810741	−	0.468082i	0.847213	+	0.531253i	$0.178279\pi$
$312$	0.478708	+	11.1259i	0.0271015	+	0.629880i
$313$	−13.9316	+	3.73296i	−0.787460	+	0.210999i	−0.630071	−	0.776537i	$-0.716974\pi$
$313$	−13.9316	+	3.73296i	−0.787460	+	0.210999i	−0.157389	+	0.987537i	$0.550308\pi$
$314$	−13.5976			−0.767357
$315$	−8.89726	−	15.3570i	−0.501304	−	0.865271i
$316$	−9.37600			−0.527441
$317$	−23.3356	+	6.25275i	−1.31066	+	0.351189i	−0.845470	−	0.534023i	$-0.820680\pi$
$317$	−23.3356	+	6.25275i	−1.31066	+	0.351189i	−0.465187	+	0.885212i	$0.654013\pi$
$318$	0.0399716	+	0.929000i	0.00224150	+	0.0520958i
$319$	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
$324$	6.90903	−	5.76761i	0.383835	−	0.320423i
$325$	19.5943	−	25.4857i	1.08690	−	1.41369i
$326$	0.150984	−	0.0871709i	0.00836225	−	0.00482795i
$327$	−8.46139	−	13.3003i	−0.467916	−	0.735509i
$328$	−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	−0.997916	−	0.0645213i	$-0.979448\pi$
$331$	−8.06115	+	13.9623i	−0.443081	+	0.767439i	0.554835	+	0.831960i	$0.312781\pi$
$332$	0.830536	−	3.09960i	0.0455816	−	0.170113i
$333$	−2.98707	−	8.23937i	−0.163690	−	0.451514i
$334$	−1.98610	−	1.14668i	−0.108675	−	0.0627433i
$335$	1.03789	+	1.55491i	0.0567062	+	0.0849540i
$336$	−2.87767	−	3.56637i	−0.156990	−	0.194561i
$337$	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	$0.170172\pi$
$338$	7.33449	+	27.3727i	0.398944	+	1.48888i
$339$	−14.5939	−	13.3899i	−0.792633	−	0.727239i
$340$	1.42653	−	2.88926i	0.0773645	−	0.156692i
$341$	−0.776940	−	0.448566i	−0.0420737	−	0.0242912i
$342$	−4.84615	−	0.860837i	−0.262050	−	0.0465487i
$343$	6.12371	+	17.4786i	0.330649	+	0.943754i
$344$	8.62075			0.464800
$345$	17.4754	+	7.71248i	0.940843	+	0.415226i
$346$	1.90591	+	3.30114i	0.102463	+	0.177470i
$347$	2.45074	−	9.14627i	0.131562	−	0.490998i	−0.868426	−	0.495819i	$-0.834868\pi$
$347$	2.45074	−	9.14627i	0.131562	−	0.490998i	0.999988	+	0.00482121i	$0.00153464\pi$
$348$	9.83128	+	15.4536i	0.527012	+	0.828401i
$349$			19.7917i			1.05942i	0.848177	+	0.529712i	$0.177700\pi$
$349$			19.7917i			1.05942i	−0.848177	+	0.529712i	$0.822300\pi$
$350$	−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	$-0.435924\pi$
$353$	−2.19457	−	0.588034i	−0.116805	−	0.0312979i	−0.316748	+	0.948510i	$0.602591\pi$
$354$	−7.51436	+	8.19006i	−0.399383	+	0.435297i
$355$	4.01703	−	4.57616i	0.213202	−	0.242878i
$356$			7.20412i			0.381818i
$357$	−5.33564	−	3.89085i	−0.282392	−	0.205926i
$358$	6.23458	+	6.23458i	0.329508	+	0.329508i
$359$	−5.97213	+	10.3440i	−0.315197	+	0.545937i	−0.979479	−	0.201545i	$-0.935404\pi$
$359$	−5.97213	+	10.3440i	−0.315197	+	0.545937i	0.664282	+	0.747482i	$0.268737\pi$
$360$	−6.63190	+	1.00893i	−0.349532	+	0.0531752i
$361$	−8.15410	−	14.1233i	−0.429163	−	0.743332i
$362$	−5.13437	+	1.37575i	−0.269856	+	0.0723078i
$363$	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
$366$	−1.17903	−	0.262168i	−0.0616288	−	0.0137037i
$367$	−11.7329	−	3.14381i	−0.612451	−	0.164106i	−0.0607572	−	0.998153i	$-0.519352\pi$
$367$	−11.7329	−	3.14381i	−0.612451	−	0.164106i	−0.551694	+	0.834047i	$0.686018\pi$
$368$	4.76396	+	1.27650i	0.248339	+	0.0665421i
$369$	2.20062	+	25.5255i	0.114560	+	1.32880i
$370$	−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
$373$	−18.9572	+	5.07958i	−0.981569	+	0.263011i	−0.713705	−	0.700446i	$-0.752984\pi$
$373$	−18.9572	+	5.07958i	−0.981569	+	0.263011i	−0.267864	+	0.963457i	$0.586318\pi$
$374$	2.08067	+	3.60383i	0.107589	+	0.186349i
$375$	16.5346	+	10.0800i	0.853843	+	0.520531i
$376$	2.92564	−	5.06736i	0.150878	−	0.261329i
$377$	48.0758	+	48.0758i	2.47603	+	2.47603i
$378$	−0.281384	+	13.7448i	−0.0144728	+	0.706959i
$379$			9.32087i			0.478781i	0.970923	+	0.239391i	$0.0769476\pi$
$379$			9.32087i			0.478781i	−0.970923	+	0.239391i	$0.923052\pi$
$380$	2.75709	+	2.42022i	0.141436	+	0.124155i
$381$	0.879564	+	0.806997i	0.0450614	+	0.0413437i
$382$	21.6654	+	5.80522i	1.10850	+	0.297021i
$383$	−2.69851	−	10.0710i	−0.137887	−	0.514603i	−0.999969	−	0.00783388i	$-0.997506\pi$
$383$	−2.69851	−	10.0710i	−0.137887	−	0.514603i	0.862082	−	0.506769i	$-0.169160\pi$
$384$	−1.65222	+	0.519792i	−0.0843143	+	0.0265255i
$385$	−14.0217	−	9.76026i	−0.714611	−	0.497429i
$386$		−	16.4797i		−	0.838796i
$387$	−19.7906	−	16.6490i	−1.00601	−	0.846317i
$388$	1.74053	−	6.49575i	0.0883620	−	0.329772i
$389$	1.52599	+	2.64309i	0.0773708	+	0.134010i	0.902115	−	0.431496i	$-0.142014\pi$
$389$	1.52599	+	2.64309i	0.0773708	+	0.134010i	−0.824744	+	0.565506i	$0.808681\pi$
$390$	−23.2182	+	8.99946i	−1.17570	+	0.455705i
$391$	7.10717			0.359425
$392$	6.99517	+	0.259910i	0.353310	+	0.0131275i
$393$	6.97916	−	13.3861i	0.352052	−	0.675241i
$394$	1.23989	+	0.715852i	0.0624649	+	0.0360641i
$395$	−6.72968	−	19.8559i	−0.338607	−	0.999061i
$396$	3.67120	−	7.84695i	0.184485	−	0.394324i
$397$	3.34711	+	12.4916i	0.167987	+	0.626935i	0.997640	+	0.0686566i	$0.0218713\pi$
$397$	3.34711	+	12.4916i	0.167987	+	0.626935i	−0.829654	+	0.558279i	$0.811462\pi$
$398$	−6.25585	+	6.25585i	−0.313577	+	0.313577i
$399$	5.85124	−	4.72132i	0.292928	−	0.236361i
$400$	4.61758	+	1.91780i	0.230879	+	0.0958901i
$401$	−18.6481	−	10.7665i	−0.931240	−	0.537652i	−0.0440366	−	0.999030i	$-0.514022\pi$
$401$	−18.6481	−	10.7665i	−0.931240	−	0.537652i	−0.887204	+	0.461378i	$0.847355\pi$
$402$	−0.0622490	−	1.44676i	−0.00310470	−	0.0721578i
$403$	0.516973	−	1.92937i	0.0257523	−	0.0961088i
$404$	−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
$408$	−2.10590	+	1.33973i	−0.104257	+	0.0663266i
$409$	−6.31608	+	3.64659i	−0.312310	+	0.180312i	−0.647960	−	0.761675i	$-0.724377\pi$
$409$	−6.31608	+	3.64659i	−0.312310	+	0.180312i	0.335650	+	0.941987i	$0.391044\pi$
$410$	8.45414	−	17.1228i	0.417520	−	0.845635i
$411$	−28.4693	−	6.33041i	−1.40429	−	0.312256i
$412$	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
$417$	−26.3033	+	1.13174i	−1.28808	+	0.0554216i
$418$	−4.57642	+	1.22625i	−0.223840	+	0.0599778i
$419$	−29.6118			−1.44663			−0.723316	−	0.690517i	$-0.757383\pi$
$419$	−29.6118			−1.44663			−0.723316	+	0.690517i	$0.757383\pi$
$420$	5.48718	−	8.65395i	0.267747	−	0.422270i
$421$	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
$423$	−16.5028	+	5.98287i	−0.802394	+	0.290897i
$424$	−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
$429$	6.98029	−	31.3919i	0.337011	−	1.51562i
$430$	6.18759	+	18.2565i	0.298392	+	0.880408i
$431$	−23.7899	+	13.7351i	−1.14592	+	0.661598i	−0.947890	−	0.318598i	$-0.896788\pi$
$431$	−23.7899	+	13.7351i	−1.14592	+	0.661598i	−0.198031	+	0.980196i	$0.563455\pi$
$432$	4.79683	+	1.99760i	0.230788	+	0.0961095i
$433$	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
$437$	−2.09431	+	7.81609i	−0.100185	+	0.373894i
$438$	0.323211	−	0.0139066i	0.0154436	−	0.000664484i
$439$	−20.3735	−	11.7627i	−0.972376	−	0.561402i	−0.0724163	−	0.997374i	$-0.523071\pi$
$439$	−20.3735	−	11.7627i	−0.972376	−	0.561402i	−0.899960	+	0.435973i	$0.856404\pi$
$440$	−5.37069	+	3.58489i	−0.256038	+	0.170903i
$441$	−15.5568	−	14.1063i	−0.740799	−	0.671726i
$442$	−6.55139	+	6.55139i	−0.311618	+	0.311618i
$443$	5.45289	+	20.3505i	0.259075	+	0.966880i	0.965778	+	0.259370i	$0.0835150\pi$
$443$	5.45289	+	20.3505i	0.259075	+	0.966880i	−0.706703	+	0.707510i	$0.749818\pi$
$444$	3.42082	−	3.72843i	0.162345	−	0.176944i
$445$	−15.2565	+	5.17079i	−0.723225	+	0.245119i
$446$	24.5795	+	14.1910i	1.16387	+	0.671961i
$447$	−20.5664	−	10.7227i	−0.972756	−	0.507168i
$448$	1.05770	−	2.42513i	0.0499715	−	0.114577i
$449$	−2.55651			−0.120649			−0.0603246	−	0.998179i	$-0.519214\pi$
$449$	−2.55651			−0.120649			−0.0603246	+	0.998179i	$0.519214\pi$
$450$	−6.89673	−	13.3205i	−0.325115	−	0.627933i
$451$	12.3308	+	21.3576i	0.580636	+	1.00569i
$452$	2.95957	−	11.0453i	0.139207	−	0.519526i
$453$	−2.39589	+	1.52422i	−0.112569	+	0.0716140i
$454$			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	0.999990	−	0.00452783i	$-0.00144126\pi$
$457$	2.81562	+	10.5080i	0.131709	+	0.491546i	−0.868280	+	0.496074i	$0.834775\pi$
$458$	−15.0999	−	4.04602i	−0.705574	−	0.189058i
$459$	7.42187	+	0.991456i	0.346423	+	0.0462772i
$460$	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	$-0.286547\pi$
$462$	5.36134	+	12.0987i	0.249432	+	0.562882i
$463$	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
$465$	1.18900	+	0.184354i	0.0551387	+	0.00854920i
$466$	−3.68611	−	6.38454i	−0.170756	−	0.295758i
$467$	31.5447	−	8.45237i	1.45971	−	0.391129i	0.560323	−	0.828274i	$-0.310677\pi$
$467$	31.5447	−	8.45237i	1.45971	−	0.391129i	0.899391	+	0.437145i	$0.144010\pi$
$468$	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
$471$	−5.11209	+	22.9902i	−0.235553	+	1.05933i
$472$	−6.19857	−	1.66090i	−0.285312	−	0.0764492i
$473$	−24.0464	−	6.44321i	−1.10565	−	0.296259i
$474$	−3.52496	+	15.8525i	−0.161907	+	0.728131i
$475$	−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
$478$	−3.78184	+	1.01334i	−0.172977	+	0.0463491i
$479$	13.9213	+	24.1124i	0.636080	+	1.10172i	0.986285	+	0.165050i	$0.0527785\pi$
$479$	13.9213	+	24.1124i	0.636080	+	1.10172i	−0.350205	+	0.936673i	$0.613888\pi$
$480$	−2.28667	−	3.12588i	−0.104372	−	0.142676i
$481$	9.39146	−	16.2665i	0.428214	−	0.741688i
$482$	12.5039	+	12.5039i	0.569537	+	0.569537i
$483$	22.4733	+	2.40180i	1.02257	+	0.109286i
$484$			2.66085i			0.120948i
$485$	15.0056	−	0.976365i	0.681368	−	0.0443344i
$486$	−7.15413	−	13.8499i	−0.324518	−	0.628242i
$487$	−30.4561	−	8.16069i	−1.38010	−	0.369796i	−0.508941	−	0.860801i	$-0.669963\pi$
$487$	−30.4561	−	8.16069i	−1.38010	−	0.369796i	−0.871157	+	0.491005i	$0.836630\pi$
$488$	−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	$-0.0109552\pi$
$492$	−12.4803	+	7.93974i	−0.562656	+	0.357951i
$493$	−3.94397	+	14.7191i	−0.177628	+	0.662915i
$494$	−5.27433	−	9.13542i	−0.237304	−	0.411022i
$495$	19.2528	+	2.14246i	0.865351	+	0.0962964i
$496$	0.310667			0.0139494
$497$	2.88027	−	6.60401i	0.129198	−	0.296230i
$498$	−4.92843	−	2.56954i	−0.220848	−	0.115144i
$499$	9.28878	+	5.36288i	0.415823	+	0.240075i	0.693289	−	0.720660i	$-0.256161\pi$
$499$	9.28878	+	5.36288i	0.415823	+	0.240075i	−0.277466	+	0.960736i	$0.589494\pi$
$500$	−0.747115	+	11.1553i	−0.0334120	+	0.498882i
$501$	−2.68544	+	2.92692i	−0.119976	+	0.130765i
$502$	−4.27743	−	15.9636i	−0.190911	−	0.712490i
$503$	−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	$0.860846\pi$
$504$	−7.11174	+	3.52465i	−0.316782	+	0.157000i
$505$	−22.1704	−	4.42090i	−0.986568	−	0.196728i
$506$	−12.3343	−	7.12123i	−0.548328	−	0.316577i
$507$	49.0380	−	2.10993i	2.17785	−	0.0937054i
$508$	−0.178371	+	0.665690i	−0.00791393	+	0.0295352i
$509$	−14.1129	+	24.4442i	−0.625543	+	1.08347i	0.362893	+	0.931831i	$0.381789\pi$
$509$	−14.1129	+	24.4442i	−0.625543	+	1.08347i	−0.988436	+	0.151641i	$0.951544\pi$
$510$	−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
$513$	−3.27740	+	7.87002i	−0.144701	+	0.347470i
$514$	−19.6746	+	11.3592i	−0.867811	+	0.501031i
$515$	10.1705	+	5.02153i	0.448165	+	0.221275i
$516$	3.24102	−	14.5756i	0.142678	−	0.641655i
$517$	−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	$-0.447655\pi$
$521$	25.1057	−	14.4948i	1.09990	−	0.635028i	0.936195	+	0.351481i	$0.114322\pi$
$522$	29.8244	−	10.8124i	1.30538	−	0.473248i
$523$	13.0137	−	3.48700i	0.569047	−	0.152476i	0.0371877	−	0.999308i	$-0.488160\pi$
$523$	13.0137	−	3.48700i	0.569047	−	0.152476i	0.531860	+	0.846833i	$0.321493\pi$
$524$	8.71583			0.380753
$525$	22.2653	+	5.40901i	0.971736	+	0.236069i
$526$	28.7634			1.25414
$527$	0.432426	−	0.115868i	0.0188368	−	0.00504730i
$528$	4.99712	−	0.215009i	0.217472	−	0.00935705i
$529$	−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
$534$	12.1804	+	2.70843i	0.527098	+	0.117205i
$535$	−13.6774	−	6.75302i	−0.591326	−	0.291959i
$536$	0.724049	−	0.418030i	0.0312742	−	0.0180561i
$537$	12.8851	−	8.19724i	0.556033	−	0.353737i
$538$	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	−0.691207	−	0.722656i	$-0.742921\pi$
$541$	6.51810	−	11.2897i	0.280235	−	0.485382i	0.971443	+	0.237275i	$0.0762542\pi$
$542$	−5.91616	+	22.0794i	−0.254121	+	0.948391i
$543$	0.395766	+	9.19819i	0.0169839	+	0.394732i
$544$	−1.24797	−	0.720514i	−0.0535061	−	0.0308918i
$545$	19.9579	+	3.97972i	0.854902	+	0.170473i
$546$	−22.9299	+	18.5020i	−0.981310	+	0.791811i
$547$	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	$0.130553\pi$
$548$	−4.35805	−	16.2645i	−0.186167	−	0.694784i
$549$	−0.886523	+	1.89489i	−0.0378359	+	0.0808718i
$550$	−11.4467	−	8.80065i	−0.488090	−	0.375261i
$551$	−15.0251	−	8.67474i	−0.640091	−	0.369556i
$552$	3.94928	−	7.57479i	0.168093	−	0.322404i
$553$	−14.7333	−	19.9574i	−0.626522	−	0.848675i
$554$	16.8591			0.716275
$555$	10.3512	+	4.56832i	0.439383	+	0.193914i
$556$	−7.60015	−	13.1638i	−0.322318	−	0.558271i
$557$	10.1456	−	37.8640i	0.429884	−	1.60435i	−0.323138	−	0.946352i	$-0.604738\pi$
$557$	10.1456	−	37.8640i	0.429884	−	1.60435i	0.753022	−	0.657996i	$-0.228595\pi$
$558$	−0.713196	−	0.599983i	−0.0301920	−	0.0253993i
$559$		−	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	$-0.330331\pi$
$563$	12.2809	+	3.29065i	0.517577	+	0.138684i	0.00943155	+	0.999956i	$0.496998\pi$
$564$	−7.46776	−	6.85165i	−0.314449	−	0.288506i
$565$	25.5153	−	1.66020i	1.07344	−	0.0698450i
$566$		−	26.8128i		−	1.12703i
$567$	23.1334	+	5.64320i	0.971512	+	0.236992i
$568$	−1.92556	−	1.92556i	−0.0807947	−	0.0807947i
$569$	10.6592	−	18.4623i	0.446858	−	0.773981i	−0.551322	−	0.834293i	$-0.685876\pi$
$569$	10.6592	−	18.4623i	0.446858	−	0.773981i	0.998180	+	0.0603121i	$0.0192096\pi$
$570$	5.12854	−	3.75167i	0.214811	−	0.157140i
$571$	−7.85503	−	13.6053i	−0.328723	−	0.569365i	0.653536	−	0.756896i	$-0.273285\pi$
$571$	−7.85503	−	13.6053i	−0.328723	−	0.569365i	−0.982259	+	0.187531i	$0.939952\pi$
$572$	17.9342	−	4.80544i	0.749865	−	0.200926i
$573$	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
$576$	0.257682	+	2.98891i	0.0107367	+	0.124538i
$577$	13.7052	+	3.67230i	0.570556	+	0.152880i	0.532552	−	0.846398i	$-0.321233\pi$
$577$	13.7052	+	3.67230i	0.570556	+	0.152880i	0.0380044	+	0.999278i	$0.487900\pi$
$578$	14.4149	+	3.86247i	0.599582	+	0.160658i
$579$	−27.8632	−	6.19564i	−1.15796	−	0.257482i
$580$	−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
$583$	1.49748	−	0.401249i	0.0620194	−	0.0166180i
$584$	0.0933892	+	0.161755i	0.00386447	+	0.00669347i
$585$	6.48689	+	42.6397i	0.268200	+	1.76293i
$586$	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	$0.696447\pi$
$588$	3.06932	−	11.7294i	0.126576	−	0.483713i
$589$			0.509703i			0.0210019i
$590$	−0.931697	−	14.3191i	−0.0383574	−	0.589508i
$591$	1.67648	−	1.82723i	0.0689610	−	0.0751621i
$592$	2.82183	+	0.756107i	0.115976	+	0.0310758i
$593$	−4.82157	−	17.9944i	−0.197998	−	0.738940i	−0.991470	−	0.130333i	$-0.958395\pi$
$593$	−4.82157	−	17.9944i	−0.197998	−	0.738940i	0.793472	−	0.608607i	$-0.208271\pi$
$594$	−11.8871	−	9.15721i	−0.487733	−	0.375725i
$595$	8.39158	−	1.50366i	0.344021	−	0.0616442i
$596$		−	13.3910i		−	0.548515i
$597$	8.22520	+	12.9290i	0.336635	+	0.529150i
$598$	8.20723	−	30.6298i	0.335619	−	1.25255i
$599$	18.3356	+	31.7582i	0.749174	+	1.29761i	0.948219	+	0.317616i	$0.102882\pi$
$599$	18.3356	+	31.7582i	0.749174	+	1.29761i	−0.199046	+	0.979990i	$0.563784\pi$
$600$	4.97854	−	7.08619i	0.203248	−	0.289293i
$601$	−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
$603$	−2.46952	−	0.438669i	−0.100567	−	0.0178640i
$604$	−1.41982	−	0.819732i	−0.0577715	−	0.0333544i
$605$	−5.63499	+	1.90984i	−0.229095	+	0.0776459i
$606$	12.9031	+	11.8386i	0.524153	+	0.480909i
$607$	1.69076	+	6.31001i	0.0686259	+	0.256115i	0.991713	−	0.128477i	$-0.0410088\pi$
$607$	1.69076	+	6.31001i	0.0686259	+	0.256115i	−0.923087	+	0.384592i	$0.874342\pi$
$608$	1.16013	−	1.16013i	0.0470495	−	0.0470495i
$609$	−17.4453	+	45.2100i	−0.706918	+	1.83200i
$610$	1.29692	−	0.865682i	0.0525106	−	0.0350504i
$611$	−32.5805	−	18.8104i	−1.31807	−	0.760986i
$612$	1.47344	+	4.06424i	0.0595601	+	0.164287i
$613$	−9.94374	+	37.1106i	−0.401624	+	1.49888i	0.408574	+	0.912725i	$0.366026\pi$
$613$	−9.94374	+	37.1106i	−0.401624	+	1.49888i	−0.810198	+	0.586156i	$0.800640\pi$
$614$	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	$0.689006\pi$
$618$	−4.71599	−	7.41298i	−0.189705	−	0.298194i
$619$	−1.57421	+	0.908870i	−0.0632728	+	0.0365306i	−0.531303	−	0.847182i	$-0.678297\pi$
$619$	−1.57421	+	0.908870i	−0.0632728	+	0.0365306i	0.468030	+	0.883713i	$0.344964\pi$
$620$	0.222983	+	0.657913i	0.00895522	+	0.0264224i
$621$	−23.6953	+	9.76222i	−0.950860	+	0.391744i
$622$	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
$627$	0.352758	+	8.19863i	0.0140878	+	0.327422i
$628$	−13.1343	+	3.51932i	−0.524115	+	0.140436i
$629$	4.20978			0.167855
$630$	−12.5688	−	12.5310i	−0.500752	−	0.499246i
$631$	−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
$633$	1.00549	+	23.3692i	0.0399648	+	0.928842i
$634$	−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
$639$	0.701707	+	8.13927i	0.0277591	+	0.321984i
$640$	0.989939	−	2.00500i	0.0391308	−	0.0792545i
$641$	−2.23407	+	1.28984i	−0.0882404	+	0.0509456i	−0.543471	−	0.839428i	$-0.682890\pi$
$641$	−2.23407	+	1.28984i	−0.0882404	+	0.0509456i	0.455231	+	0.890374i	$0.349557\pi$
$642$	6.34212	+	9.96907i	0.250304	+	0.393448i
$643$	−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
$647$	−1.62567	+	6.06708i	−0.0639116	+	0.238521i	−0.990491	−	0.137578i	$-0.956068\pi$
$647$	−1.62567	+	6.06708i	−0.0639116	+	0.238521i	0.926579	+	0.376099i	$0.122735\pi$
$648$	5.18085	−	7.35927i	0.203523	−	0.289099i
$649$	16.0487	+	9.26571i	0.629966	+	0.363711i
$650$	12.3305	−	29.6887i	0.483641	−	1.16449i
$651$	1.40652	−	0.220249i	0.0551258	−	0.00863224i
$652$	0.123278	−	0.123278i	0.00482795	−	0.00482795i
$653$	11.3516	+	42.3647i	0.444222	+	1.65786i	0.717983	+	0.696061i	$0.245066\pi$
$653$	11.3516	+	42.3647i	0.444222	+	1.65786i	−0.273761	+	0.961798i	$0.588268\pi$
$654$	−11.6155	−	10.6571i	−0.454200	−	0.416727i
$655$	6.25583	+	18.4579i	0.244436	+	0.721209i
$656$	−7.39591	−	4.27003i	−0.288762	−	0.166717i
$657$	0.0980000	−	0.551699i	0.00382335	−	0.0215238i
$658$	15.3835	−	1.73534i	0.599710	−	0.0676504i
$659$	8.17474			0.318443			0.159221	−	0.987243i	$-0.449102\pi$
$659$	8.17474			0.318443			0.159221	+	0.987243i	$0.449102\pi$
$660$	4.04204	+	10.4283i	0.157336	+	0.405921i
$661$	−11.1783	−	19.3615i	−0.434787	−	0.753074i	0.562491	−	0.826803i	$-0.309843\pi$
$661$	−11.1783	−	19.3615i	−0.434787	−	0.753074i	−0.997278	+	0.0737297i	$0.976510\pi$
$662$	−4.17276	+	15.5730i	−0.162179	+	0.605260i
$663$	8.61378	+	13.5398i	0.334531	+	0.525844i
$664$		−	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
$669$	33.2342	−	36.2227i	1.28491	−	1.40045i
$670$	1.40497	+	1.23331i	0.0542787	+	0.0476467i
$671$			2.01374i			0.0777397i
$672$	−3.70266	−	2.70005i	−0.142833	−	0.104157i
$673$	−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
$675$	−25.1145	+	6.65279i	−0.966659	+	0.256066i
$676$	14.1691	+	24.5417i	0.544967	+	0.943911i
$677$	−37.5247	+	10.0547i	−1.44219	+	0.386434i	−0.893300	−	0.449460i	$-0.851616\pi$
$677$	−37.5247	+	10.0547i	−1.44219	+	0.386434i	−0.548891	+	0.835894i	$0.684950\pi$
$678$	−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
$681$	13.4999	+	3.00182i	0.517316	+	0.115030i
$682$	−0.866564	−	0.232195i	−0.0331824	−	0.00889121i
$683$	−20.1417	−	5.39696i	−0.770702	−	0.206509i	−0.148020	−	0.988984i	$-0.547290\pi$
$683$	−20.1417	−	5.39696i	−0.770702	−	0.206509i	−0.622681	+	0.782475i	$0.713957\pi$
$684$	−4.90382	+	0.422771i	−0.187502	+	0.0161651i
$685$	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
$688$	8.32701	−	2.23122i	0.317464	−	0.0850643i
$689$	1.72585	+	2.98926i	0.0657497	+	0.113882i
$690$	18.8761	+	2.92672i	0.718599	+	0.111418i
$691$	6.25756	−	10.8384i	0.238049	−	0.412313i	−0.722105	−	0.691783i	$-0.756825\pi$
$691$	6.25756	−	10.8384i	0.238049	−	0.412313i	0.960154	+	0.279470i	$0.0901588\pi$
$692$	2.69537	+	2.69537i	0.102463	+	0.102463i
$693$	22.4716	−	4.51616i	0.853624	−	0.171555i
$694$		−	9.46892i		−	0.359435i
$695$	22.4226	−	25.5436i	0.850536	−	0.968922i
$696$	13.4960	+	12.3825i	0.511564	+	0.469358i
$697$	−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	$0.980919\pi$
$702$	12.8435	−	30.8412i	0.484748	−	1.16402i
$703$	−1.24052	+	4.62969i	−0.0467872	+	0.174612i
$704$	1.44388	+	2.50087i	0.0544183	+	0.0942552i
$705$	9.14999	−	20.7326i	0.344608	−	0.780834i
$706$	−2.27199			−0.0855074
$707$	−26.5802	+	2.99839i	−0.999651	+	0.112766i
$708$	−5.13857	+	9.85585i	−0.193119	+	0.370406i
$709$	2.89790	+	1.67311i	0.108833	+	0.0628348i	0.553429	−	0.832897i	$-0.313319\pi$
$709$	2.89790	+	1.67311i	0.108833	+	0.0628348i	−0.444595	+	0.895731i	$0.646653\pi$
$710$	2.69576	−	5.45992i	0.101170	−	0.204907i
$711$	25.4776	+	11.9197i	0.955483	+	0.447023i
$712$	1.86456	+	6.95864i	0.0698775	+	0.260786i
$713$	−1.08344	+	1.08344i	−0.0405752	+	0.0405752i
$714$	−6.16086	−	2.37731i	−0.230564	−	0.0889684i
$715$	23.0490	+	34.5308i	0.861985	+	1.29138i
$716$	7.63578	+	4.40852i	0.285362	+	0.164754i
$717$	0.291511	+	6.77514i	0.0108867	+	0.253022i
$718$	−3.09140	+	11.5373i	−0.115370	+	0.430567i
$719$	9.77351	−	16.9282i	0.364491	−	0.631316i	−0.624204	−	0.781262i	$-0.714576\pi$
$719$	9.77351	−	16.9282i	0.364491	−	0.631316i	0.988694	+	0.149945i	$0.0479098\pi$
$720$	−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
$723$	25.8420	−	16.4402i	0.961073	−	0.611416i
$724$	−4.60335	+	2.65774i	−0.171082	+	0.0987743i
$725$	−6.85156	−	52.4273i	−0.254461	−	1.94710i
$726$	4.49885	+	1.00036i	0.166968	+	0.0371268i
$727$	−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	$0.870070\pi$
$728$	−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
$732$	−1.20671	+	0.0519204i	−0.0446012	+	0.00191903i
$733$	22.8943	−	6.13452i	0.845622	−	0.226584i	0.190105	−	0.981764i	$-0.439117\pi$
$733$	22.8943	−	6.13452i	0.845622	−	0.226584i	0.655517	+	0.755180i	$0.272451\pi$
$734$	−12.1468			−0.448345
$735$	27.0429	−	1.91884i	0.997492	−	0.0707773i
$736$	4.93201			0.181796
$737$	−2.33207	+	0.624877i	−0.0859030	+	0.0230176i
$738$	8.73212	+	24.0862i	0.321434	+	0.886624i
$739$	−27.8766	+	16.0945i	−1.02546	+	0.592047i	−0.915680	−	0.401909i	$-0.868347\pi$
$739$	−27.8766	+	16.0945i	−1.02546	+	0.592047i	−0.109776	+	0.993956i	$0.535013\pi$
$740$	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	$-0.690268\pi$
$743$	7.19137	−	7.19137i	0.263826	−	0.263826i	0.826606	+	0.562781i	$0.190268\pi$
$744$	0.116797	−	0.525263i	0.00428199	−	0.0192571i
$745$	28.3586	−	9.61143i	1.03898	−	0.352136i
$746$	−16.9966	+	9.81299i	−0.622290	+	0.359279i
$747$	−6.19734	+	7.36674i	−0.226749	+	0.269535i
$748$	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	0.312404	+	0.949949i	$0.398866\pi$
$751$	−18.2644	+	31.6349i	−0.666478	+	1.15437i	−0.978882	+	0.204424i	$0.934468\pi$
$752$	1.51442	−	5.65190i	0.0552253	−	0.206104i
$753$	−28.5987	+	1.23050i	−1.04219	+	0.0448419i
$754$	58.8806	+	33.9947i	2.14430	+	1.23801i
$755$	0.716898	−	3.59517i	0.0260906	−	0.130842i
$756$	3.28563	+	13.3493i	0.119497	+	0.485510i
$757$	−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	$0.394274\pi$
$758$	2.41242	+	9.00327i	0.0876230	+	0.327014i
$759$	−16.6774	+	18.1771i	−0.605352	+	0.659787i
$760$	3.28954	+	1.62416i	0.119324	+	0.0589146i
$761$	3.67071	+	2.11929i	0.133063	+	0.0768240i	0.565054	−	0.825054i	$-0.308855\pi$
$761$	3.67071	+	2.11929i	0.133063	+	0.0768240i	−0.431991	+	0.901878i	$0.642189\pi$
$762$	1.05846	+	0.551851i	0.0383439	+	0.0199915i
$763$	23.9277	−	2.69916i	0.866239	−	0.0977163i
$764$	22.4297			0.811477
$765$	−7.54944	+	6.03748i	−0.272951	+	0.218286i
$766$	−5.21312	−	9.02939i	−0.188358	−	0.326245i
$767$	−10.6787	+	39.8536i	−0.385587	+	1.43903i
$768$	−1.46139	+	0.929705i	−0.0527332	+	0.0335478i
$769$			9.91452i			0.357527i	0.983892	+	0.178763i	$0.0572097\pi$
$769$			9.91452i			0.357527i	−0.983892	+	0.178763i	$0.942790\pi$
$770$	−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	$-0.456189\pi$
$773$	−6.65181	−	1.78235i	−0.239249	−	0.0641066i	−0.376451	+	0.926436i	$0.622856\pi$
$774$	−23.4253	−	10.9595i	−0.842005	−	0.393933i
$775$	−1.23324	+	0.944442i	−0.0442994	+	0.0339253i
$776$		−	6.72489i		−	0.241410i
$777$	13.3116	+	1.42265i	0.477551	+	0.0510374i
$778$	2.15808	+	2.15808i	0.0773708	+	0.0773708i
$779$	7.00571	−	12.1343i	0.251006	−	0.434755i
$780$	−20.0978	+	14.7021i	−0.719617	+	0.526420i
$781$	3.93191	+	6.81026i	0.140695	+	0.243690i
$782$	6.86500	−	1.83947i	0.245492	−	0.0657793i
$783$	−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
$786$	3.27676	−	14.7363i	0.116878	−	0.525628i
$787$	−11.0089	−	2.94983i	−0.392425	−	0.105150i	0.0572104	−	0.998362i	$-0.481779\pi$
$787$	−11.0089	−	2.94983i	−0.392425	−	0.105150i	−0.449635	+	0.893212i	$0.648446\pi$
$788$	1.38292	+	0.370552i	0.0492645	+	0.0132004i
$789$	10.8138	−	48.6319i	0.384980	−	1.73134i
$790$	−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
$793$	−4.33075	+	1.16042i	−0.153789	+	0.0412078i
$794$	6.46613	+	11.1997i	0.229474	+	0.397461i
$795$	−1.67815	+	1.22761i	−0.0595177	+	0.0435389i
$796$	−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	$-0.515421\pi$
$798$	4.42990	−	6.07485i	0.156817	−	0.215047i
$799$		−	8.43186i		−	0.298298i
$800$	4.95660	+	0.657337i	0.175242	+	0.0232404i
$801$	9.15858	−	19.5759i	0.323602	−	0.691679i
$802$	−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
$807$	8.26562	−	5.25842i	0.290964	−	0.185105i
$808$	−2.61668	+	9.76560i	−0.0920546	+	0.343552i
$809$	−12.3778	−	21.4390i	−0.435181	−	0.753756i	0.562129	−	0.827050i	$-0.309982\pi$
$809$	−12.3778	−	21.4390i	−0.435181	−	0.753756i	−0.997310	+	0.0732932i	$0.976649\pi$
$810$	19.3036	+	5.68954i	0.678260	+	0.199910i
$811$	−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
$813$	35.1067	+	18.3036i	1.23124	+	0.641937i
$814$	−7.30598	−	4.21811i	−0.256074	−	0.147845i
$815$	0.349555	+	0.172588i	0.0122444	+	0.00604549i
$816$	−1.68739	+	1.83913i	−0.0590706	+	0.0643823i
$817$	3.66069	+	13.6619i	0.128071	+	0.477969i
$818$	−5.15705	+	5.15705i	−0.180312	+	0.180312i
$819$	22.6617	+	45.7248i	0.791864	+	1.59775i
$820$	3.73436	−	18.7275i	0.130410	−	0.653991i
$821$	37.5263	+	21.6658i	1.30968	+	0.756143i	0.982042	−	0.188661i	$-0.0604148\pi$
$821$	37.5263	+	21.6658i	1.30968	+	0.756143i	0.327636	+	0.944804i	$0.393748\pi$
$822$	−29.1377	+	1.25369i	−1.01629	+	0.0437275i
$823$	−12.0052	+	44.8040i	−0.418474	+	1.56177i	0.359298	+	0.933223i	$0.383016\pi$
$823$	−12.0052	+	44.8040i	−0.418474	+	1.56177i	−0.777773	+	0.628545i	$0.783651\pi$
$824$	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	$0.423522\pi$
$828$	−11.3224	−	9.52506i	−0.393480	−	0.331019i
$829$	−26.7949	+	15.4700i	−0.930624	+	0.537296i	−0.887009	−	0.461752i	$-0.847221\pi$
$829$	−26.7949	+	15.4700i	−0.930624	+	0.537296i	−0.0436151	+	0.999048i	$0.513888\pi$
$830$	6.79571	−	2.30324i	0.235883	−	0.0799465i
$831$	6.33827	−	28.5047i	0.219872	−	0.988816i
$832$	−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
$837$	−1.28256	+	0.980274i	−0.0443316	+	0.0338832i
$838$	−28.6028	+	7.66410i	−0.988068	+	0.264752i
$839$	5.32218			0.183742			0.0918710	−	0.995771i	$-0.470715\pi$
$839$	5.32218			0.183742			0.0918710	+	0.995771i	$0.470715\pi$
$840$	3.06040	−	9.77926i	0.105594	−	0.337417i
$841$	82.8228			2.85596
$842$	3.74869	−	1.00446i	0.129188	−	0.0346159i
$843$	42.5438	−	1.83051i	1.46529	−	0.0630461i
$844$	−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
$849$	−45.3339	−	10.0804i	−1.55586	−	0.345959i
$850$	7.14439	−	0.933677i	0.245050	−	0.0320249i
$851$	−12.4779	+	7.20412i	−0.427737	+	0.246954i
$852$	−3.97958	+	2.53173i	−0.136338	+	0.0867356i
$853$	−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
$857$	11.3844	−	42.4872i	0.388884	−	1.45133i	−0.443069	−	0.896487i	$-0.646110\pi$
$857$	11.3844	−	42.4872i	0.388884	−	1.45133i	0.831953	−	0.554846i	$-0.187223\pi$
$858$	−1.38239	−	32.1289i	−0.0471942	−	1.09686i
$859$	23.4854	+	13.5593i	0.801311	+	0.462637i	0.843929	−	0.536454i	$-0.180237\pi$
$859$	23.4854	+	13.5593i	0.801311	+	0.462637i	−0.0426185	+	0.999091i	$0.513570\pi$
$860$	10.7019	+	16.0330i	0.364931	+	0.546720i
$861$	−36.5115	−	14.0888i	−1.24431	−	0.480145i
$862$	−19.4244	+	19.4244i	−0.661598	+	0.661598i
$863$	−10.0628	−	37.5548i	−0.342541	−	1.27838i	−0.895458	−	0.445145i	$-0.853152\pi$
$863$	−10.0628	−	37.5548i	−0.342541	−	1.27838i	0.552917	−	0.833236i	$-0.313515\pi$
$864$	5.15040	+	0.688020i	0.175220	+	0.0234069i
$865$	−3.77348	+	7.64271i	−0.128302	+	0.259860i
$866$	22.2142	+	12.8254i	0.754870	+	0.435825i
$867$	11.9499	−	22.9200i	0.405839	−	0.778405i
$868$	0.488176	+	0.661274i	0.0165698	+	0.0224451i
$869$	27.0756			0.918478
$870$	−16.5362	+	37.4686i	−0.560628	+	1.27030i
$871$	−2.68772	−	4.65526i	−0.0910698	−	0.157738i
$872$	2.35555	−	8.79105i	0.0797691	−	0.297702i
$873$	−12.9876	+	15.4383i	−0.439563	+	0.522506i
$874$			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	0.894248	+	0.447572i	$0.147711\pi$
$877$	10.1752	+	37.9744i	0.343592	+	1.28230i	−0.550656	+	0.834732i	$0.685622\pi$
$878$	−22.7237	−	6.08881i	−0.766889	−	0.205487i
$879$	−25.0410	−	22.9750i	−0.844611	−	0.774928i
$880$	−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	$-0.140648\pi$
$882$	−18.6777	−	9.59920i	−0.628910	−	0.323222i
$883$	−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
$885$	−24.5604	−	3.80806i	−0.825588	−	0.128007i
$886$	10.5342	+	18.2457i	0.353903	+	0.612978i
$887$	−10.2169	+	2.73762i	−0.343051	+	0.0919202i	−0.426231	−	0.904614i	$-0.640159\pi$
$887$	−10.2169	+	2.73762i	−0.343051	+	0.0919202i	0.0831802	+	0.996535i	$0.473492\pi$
$888$	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
$891$	−19.9516	+	16.6555i	−0.668404	+	0.557979i
$892$	27.4148	+	7.34578i	0.917916	+	0.245955i
$893$	9.27291	+	2.48467i	0.310306	+	0.0831463i
$894$	−22.6408	−	5.03440i	−0.757223	−	0.168375i
$895$	−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
$898$	−2.46940	+	0.661674i	−0.0824049	+	0.0220803i
$899$	−1.64260	−	2.84506i	−0.0547837	−	0.0948881i
$900$	−10.1093	−	11.0816i	−0.336977	−	0.369386i
$901$	−0.386811	+	0.669977i	−0.0128866	+	0.0223202i
$902$	17.4384	+	17.4384i	0.580636	+	0.580636i
$903$	36.1179	−	16.0051i	1.20193	−	0.532616i
$904$		−	11.4349i		−	0.380319i
$905$	−8.93249	−	7.84109i	−0.296926	−	0.260647i
$906$	−1.91975	+	2.09238i	−0.0637796	+	0.0695147i
$907$	25.4126	+	6.80928i	0.843811	+	0.226098i	0.654730	−	0.755863i	$-0.272782\pi$
$907$	25.4126	+	6.80928i	0.843811	+	0.226098i	0.189081	+	0.981961i	$0.439449\pi$
$908$	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	$0.775643\pi$
$912$	−1.52534	−	2.39765i	−0.0505090	−	0.0793942i
$913$	−2.39839	+	8.95090i	−0.0793750	+	0.296232i
$914$	5.43937	+	9.42126i	0.179918	+	0.311628i
$915$	−0.976075	−	2.51823i	−0.0322680	−	0.0832500i
$916$	−15.6326			−0.516516
$917$	13.6959	+	18.5522i	0.452277	+	0.612647i
$918$	7.42558	−	0.963249i	0.245081	−	0.0317919i
$919$	47.4211	+	27.3786i	1.56428	+	0.903137i	0.996816	+	0.0797385i	$0.0254085\pi$
$919$	47.4211	+	27.3786i	1.56428	+	0.903137i	0.567464	+	0.823399i	$0.307925\pi$
$920$	3.53998	+	10.4447i	0.116710	+	0.344353i
$921$	−13.5340	−	12.4174i	−0.445962	−	0.409169i
$922$	−8.70751	−	32.4969i	−0.286766	−	1.07023i
$923$	−12.3804	+	12.3804i	−0.407505	+	0.407505i
$924$	8.31003	+	10.2988i	0.273380	+	0.338806i
$925$	−13.5003	+	5.57699i	−0.443886	+	0.183370i
$926$	9.35568	+	5.40151i	0.307447	+	0.177505i
$927$	−14.3065	+	5.18665i	−0.469889	+	0.170352i
$928$	−2.73692	+	10.2143i	−0.0898436	+	0.335301i
$929$	8.26043	−	14.3075i	0.271016	−	0.469414i	−0.698106	−	0.715994i	$-0.745974\pi$
$929$	8.26043	−	14.3075i	0.271016	−	0.469414i	0.969122	+	0.246581i	$0.0793070\pi$
$930$	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
$933$	−15.3489	−	24.1266i	−0.502500	−	0.789871i
$934$	28.2822	−	16.3287i	0.925421	−	0.534292i
$935$	−4.11948	+	8.34348i	−0.134721	+	0.272861i
$936$	19.2172	−	1.65676i	0.628133	−	0.0541530i
$937$	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	$0.0508038\pi$
$938$	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	$-0.798449\pi$
$941$	−21.3739	+	12.3402i	−0.696768	+	0.402279i	0.109374	+	0.994001i	$0.465115\pi$
$942$	1.01241	+	23.5300i	0.0329862	+	0.766648i
$943$	40.6845	−	10.9014i	1.32487	−	0.354998i
$944$	−6.41723			−0.208863
$945$	−25.9121	+	16.5397i	−0.842922	+	0.538036i
$946$	−24.8947			−0.809395
$947$	12.3070	−	3.29765i	0.399923	−	0.107159i	−0.0532508	−	0.998581i	$-0.516958\pi$
$947$	12.3070	−	3.29765i	0.399923	−	0.107159i	0.453174	+	0.891422i	$0.350292\pi$
$948$	0.698092	+	16.2247i	0.0226730	+	0.526954i
$949$	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	$-0.593300\pi$
$953$	20.6345	−	20.6345i	0.668417	−	0.668417i	0.957349	+	0.288933i	$0.0933004\pi$
$954$	1.60461	−	0.138338i	0.0519513	−	0.00447885i
$955$	16.0990	+	47.5002i	0.520952	+	1.53707i
$956$	−3.39070	+	1.95762i	−0.109663	+	0.0633141i
$957$	−28.3904	−	44.6263i	−0.917731	−	1.44256i
$958$	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
$962$	4.86138	−	18.1429i	0.156737	−	0.584951i
$963$	19.2396	−	6.97507i	0.619988	−	0.224768i
$964$	15.3141	+	8.84160i	0.493234	+	0.284769i
$965$	30.6492	−	20.4581i	0.986632	−	0.658570i
$966$	22.3292	−	3.49657i	0.718431	−	0.112500i
$967$	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	$0.00650265\pi$
$968$	0.688678	+	2.57018i	0.0221350	+	0.0826088i
$969$	−3.01740	−	2.76846i	−0.0969329	−	0.0889356i
$970$	14.2416	−	4.82683i	0.457270	−	0.154980i
$971$	36.5408	+	21.0969i	1.17265	+	0.677030i	0.954303	−	0.298841i	$-0.0965999\pi$
$971$	36.5408	+	21.0969i	1.17265	+	0.677030i	0.218348	+	0.975871i	$0.429933\pi$
$972$	−10.4950	−	11.5263i	−0.336626	−	0.369706i
$973$	16.0773	−	36.8628i	0.515415	−	1.18177i
$974$	−31.5305			−1.01030
$975$	−45.5606	−	32.0094i	−1.45911	−	1.02512i
$976$	−0.348669	−	0.603912i	−0.0111606	−	0.0193308i
$977$	−1.83458	+	6.84676i	−0.0586936	+	0.219047i	−0.989043	−	0.147626i	$-0.952837\pi$
$977$	−1.83458	+	6.84676i	−0.0586936	+	0.219047i	0.930350	+	0.366674i	$0.119503\pi$
$978$	−0.162086	−	0.254781i	−0.00518295	−	0.00814698i
$979$		−	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	$-0.559957\pi$
$983$	−26.3541	−	7.06155i	−0.840564	−	0.225229i	−0.653317	+	0.757084i	$0.726623\pi$
$984$	−10.0001	+	10.8993i	−0.318792	+	0.347458i
$985$	0.207865	+	3.19463i	0.00662311	+	0.101790i
$986$			15.2383i			0.485287i
$987$	2.84946	−	26.6621i	0.0906994	−	0.848664i
$988$	−7.45904	−	7.45904i	−0.237304	−	0.237304i
$989$	−21.2588	+	36.8214i	−0.675992	+	1.17085i
$990$	19.1513	−	2.91354i	0.608669	−	0.0925985i
$991$	−20.8255	−	36.0708i	−0.661543	−	1.14583i	−0.980210	−	0.197960i	$-0.936568\pi$
$991$	−20.8255	−	36.0708i	−0.661543	−	1.14583i	0.318667	−	0.947867i	$-0.396765\pi$
$992$	0.300082	−	0.0804067i	0.00952761	−	0.00255291i
$993$	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
$996$	−5.42554	−	1.20642i	−0.171915	−	0.0382268i
$997$	28.5930	+	7.66148i	0.905550	+	0.242641i	0.681398	−	0.731913i	$-0.261372\pi$
$997$	28.5930	+	7.66148i	0.905550	+	0.242641i	0.224152	+	0.974554i	$0.428039\pi$
$998$	10.3603	+	2.77603i	0.327949	+	0.0878737i
$999$	−14.0354	+	5.78244i	−0.444061	+	0.182948i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.x.a.23.6	✓	64	3.2	odd	2	inner
210.2.x.a.23.12	yes	64	1.1	even	1	trivial
210.2.x.a.53.3	yes	64	7.4	even	3	inner
210.2.x.a.53.9	yes	64	21.11	odd	6	inner
210.2.x.a.107.3	yes	64	15.2	even	4	inner
210.2.x.a.107.9	yes	64	5.2	odd	4	inner
210.2.x.a.137.6	yes	64	35.32	odd	12	inner
210.2.x.a.137.12	yes	64	105.32	even	12	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)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.0744552 - 1.73045i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.68046 + 1.47514i) q^{5} +(-0.519792 - 1.65222i) q^{6} +(2.42513 + 1.05770i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.98891 + 0.257682i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.0744552 - 1.73045i) 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} +(-2.98891 + 0.257682i) q^{9} +(2.00500 + 0.989939i) q^{10} +(-2.50087 + 1.44388i) q^{11} +(-0.929705 - 1.46139i) 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} +(0.372965 - 1.39193i) q^{17} +(-2.82038 + 1.02249i) q^{18} +(1.42086 + 0.820335i) q^{19} +(2.19290 + 0.437276i) q^{20} +(1.64973 - 4.27532i) q^{21} +(-2.04195 + 2.04195i) q^{22} +(1.27650 + 4.76396i) q^{23} +(-1.27626 - 1.17097i) q^{24} +(0.647925 + 4.95784i) q^{25} +(-5.56810 - 3.21474i) q^{26} +(0.668446 + 5.15298i) q^{27} +(2.62908 - 0.296574i) q^{28} -10.5746 q^{29} +(1.56376 - 3.54326i) q^{30} +(0.155334 + 0.269046i) q^{31} +(0.258819 - 0.965926i) q^{32} +(2.68476 + 4.22013i) 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} +(-7.52870 + 8.20570i) q^{39} +(2.23135 - 0.145187i) q^{40} -8.54006i q^{41} +(0.486981 - 4.55663i) q^{42} +(6.09579 + 6.09579i) q^{43} +(-1.44388 + 2.50087i) q^{44} +(-5.40288 - 3.97604i) q^{45} +(2.46601 + 4.27125i) q^{46} +(5.65190 - 1.51442i) q^{47} +(-1.53584 - 0.800745i) q^{48} +(4.76255 + 5.13012i) q^{49} +(1.90903 + 4.62121i) q^{50} +(-2.43643 - 0.541762i) q^{51} +(-6.21041 - 1.66407i) q^{52} +(-0.518562 - 0.138948i) q^{53} +(1.97936 + 4.80439i) q^{54} +(-6.33255 - 1.26275i) q^{55} +(2.46273 - 0.966923i) q^{56} +(1.31376 - 2.51981i) q^{57} +(-10.2143 + 2.73692i) q^{58} +(-3.20862 - 5.55749i) q^{59} +(0.593412 - 3.82725i) q^{60} +(0.348669 - 0.603912i) q^{61} +(0.219675 + 0.219675i) q^{62} +(-7.52106 - 2.53645i) q^{63} -1.00000i q^{64} +(-0.933476 - 14.3464i) q^{65} +(3.68553 + 3.38146i) 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} +(-1.93127 + 2.29569i) q^{72} +(-0.0483418 + 0.180414i) q^{73} +(1.46069 + 2.52998i) q^{74} +(8.53105 - 1.49034i) q^{75} +1.64067 q^{76} +(-7.59214 + 0.856433i) q^{77} +(-5.14838 + 9.87467i) q^{78} +(-8.11986 - 4.68800i) q^{79} +(2.11774 - 0.717755i) q^{80} +(8.86720 - 1.54038i) q^{81} +(-2.21033 - 8.24906i) q^{82} +(2.26907 - 2.26907i) q^{83} +(-0.708954 - 4.52740i) q^{84} +(2.68004 - 1.78891i) q^{85} +(7.46579 + 4.31038i) q^{86} +(0.787336 + 18.2989i) q^{87} +(-0.747407 + 2.78936i) 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} +(0.454005 - 0.288829i) q^{93} +(5.06736 - 2.92564i) q^{94} +(1.17760 + 3.47452i) q^{95} +(-1.69076 - 0.375955i) q^{96} +(4.75522 - 4.75522i) q^{97} +(5.92804 + 3.72268i) q^{98} +(7.10283 - 4.96006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{6} + 4 q^{7}+O(q^{10}) \) 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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