LMFDB - Embedded newform 153.2.n.a.106.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(4,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(12))

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

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

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

chi := DirichletCharacter("153.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.n (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:	$1.22171115093$
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			106.5
Character	$\chi$	$=$	153.106
Dual form			153.2.n.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11815 - 0.645565i) q^{2} +(0.962729 - 1.43984i) q^{3} +(-0.166493 - 0.288374i) q^{4} +(2.55532 + 0.684695i) q^{5} +(-2.00599 + 0.988459i) q^{6} +(2.18547 - 0.585596i) q^{7} +3.01219i q^{8} +(-1.14630 - 2.77236i) q^{9} +(-2.41521 - 2.41521i) q^{10} +(-1.94899 + 0.522230i) q^{11} +(-0.575501 - 0.0379023i) q^{12} +(-1.81218 - 3.13879i) q^{13} +(-2.82173 - 0.756080i) q^{14} +(3.44593 - 3.02008i) q^{15} +(1.61157 - 2.79133i) q^{16} +(-1.30148 + 3.91231i) q^{17} +(-0.507997 + 3.83993i) q^{18} +0.423344i q^{19} +(-0.227993 - 0.850883i) q^{20} +(1.26085 - 3.71051i) q^{21} +(2.51640 + 0.674267i) q^{22} +(-0.239930 + 0.895433i) q^{23} +(4.33708 + 2.89992i) q^{24} +(1.73071 + 0.999225i) q^{25} +4.67953i q^{26} +(-5.09535 - 1.01853i) q^{27} +(-0.532736 - 0.532736i) q^{28} +(0.150365 + 0.561171i) q^{29} +(-5.80273 + 1.15234i) q^{30} +(8.25989 + 2.21323i) q^{31} +(1.61329 - 0.931434i) q^{32} +(-1.12442 + 3.30901i) q^{33} +(3.98090 - 3.53436i) q^{34} +5.98553 q^{35} +(-0.608625 + 0.792142i) q^{36} +(-6.04219 + 6.04219i) q^{37} +(0.273296 - 0.473363i) q^{38} +(-6.26402 - 0.412546i) q^{39} +(-2.06243 + 7.69709i) q^{40} +(-2.60151 + 9.70896i) q^{41} +(-3.80520 + 3.33495i) q^{42} +(6.86536 + 3.96372i) q^{43} +(0.475090 + 0.475090i) q^{44} +(-1.03095 - 7.86913i) q^{45} +(0.846338 - 0.846338i) q^{46} +(2.62775 - 4.55140i) q^{47} +(-2.46757 - 5.00771i) q^{48} +(-1.62881 + 0.940391i) q^{49} +(-1.29013 - 2.23457i) q^{50} +(4.38014 + 5.64042i) q^{51} +(-0.603431 + 1.04517i) q^{52} -9.13365i q^{53} +(5.03984 + 4.42825i) q^{54} -5.33785 q^{55} +(1.76392 + 6.58305i) q^{56} +(0.609550 + 0.407566i) q^{57} +(0.194141 - 0.724544i) q^{58} +(9.53349 - 5.50416i) q^{59} +(-1.44464 - 0.490895i) q^{60} +(-5.71685 + 1.53183i) q^{61} +(-7.80701 - 7.80701i) q^{62} +(-4.12870 - 5.38765i) q^{63} -8.85150 q^{64} +(-2.48159 - 9.26140i) q^{65} +(3.39345 - 2.97408i) q^{66} +(3.03393 + 5.25493i) q^{67} +(1.34489 - 0.276059i) q^{68} +(1.05830 + 1.20752i) q^{69} +(-6.69273 - 3.86405i) q^{70} +(-3.46822 + 3.46822i) q^{71} +(8.35087 - 3.45288i) q^{72} +(8.18845 - 8.18845i) q^{73} +(10.6567 - 2.85546i) q^{74} +(3.10493 - 1.52997i) q^{75} +(0.122081 - 0.0704837i) q^{76} +(-3.95365 + 2.28264i) q^{77} +(6.73779 + 4.50512i) q^{78} +(4.15030 - 1.11207i) q^{79} +(6.02929 - 6.02929i) q^{80} +(-6.37197 + 6.35594i) q^{81} +(9.17664 - 9.17664i) q^{82} +(-11.2414 - 6.49024i) q^{83} +(-1.27994 + 0.254176i) q^{84} +(-6.00443 + 9.10607i) q^{85} +(-5.11767 - 8.86407i) q^{86} +(0.952760 + 0.323753i) q^{87} +(-1.57305 - 5.87072i) q^{88} -3.03877 q^{89} +(-3.92727 + 9.46442i) q^{90} +(-5.79854 - 5.79854i) q^{91} +(0.298166 - 0.0798933i) q^{92} +(11.1387 - 9.76221i) q^{93} +(-5.87644 + 3.39277i) q^{94} +(-0.289862 + 1.08178i) q^{95} +(0.212042 - 3.21961i) q^{96} +(-3.33832 - 12.4588i) q^{97} +2.42833 q^{98} +(3.68195 + 4.80467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30}+ \cdots + 6 q^{99}+O(q^{100}) $ 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.11815	−	0.645565i	−0.790652	−	0.456483i	0.0495401	−	0.998772i	$-0.484224\pi$
$2$	−1.11815	−	0.645565i	−0.790652	−	0.456483i	−0.840192	+	0.542289i	$0.817558\pi$
$3$	0.962729	−	1.43984i	0.555832	−	0.831295i
$3$	0.962729	−	1.43984i	0.555832	−	0.831295i
$4$	−0.166493	−	0.288374i	−0.0832464	−	0.144187i
$5$	2.55532	+	0.684695i	1.14277	+	0.306205i	0.780065	−	0.625698i	$-0.215186\pi$
$5$	2.55532	+	0.684695i	1.14277	+	0.306205i	0.362707	+	0.931903i	$0.381853\pi$
$6$	−2.00599	+	0.988459i	−0.818942	+	0.403537i
$7$	2.18547	−	0.585596i	0.826031	−	0.221334i	0.179050	−	0.983840i	$-0.442698\pi$
$7$	2.18547	−	0.585596i	0.826031	−	0.221334i	0.646982	+	0.762506i	$0.276031\pi$
$8$			3.01219i			1.06497i
$9$	−1.14630	−	2.77236i	−0.382102	−	0.924120i
$10$	−2.41521	−	2.41521i	−0.763758	−	0.763758i
$11$	−1.94899	+	0.522230i	−0.587643	+	0.157458i	−0.540376	−	0.841424i	$-0.681718\pi$
$11$	−1.94899	+	0.522230i	−0.587643	+	0.157458i	−0.0472670	+	0.998882i	$0.515051\pi$
$12$	−0.575501	−	0.0379023i	−0.166133	−	0.0109415i
$13$	−1.81218	−	3.13879i	−0.502609	−	0.870545i	−0.999995	−	0.00301546i	$-0.999040\pi$
$13$	−1.81218	−	3.13879i	−0.502609	−	0.870545i	0.497386	−	0.867529i	$-0.334293\pi$
$14$	−2.82173	−	0.756080i	−0.754139	−	0.202071i
$15$	3.44593	−	3.02008i	0.889736	−	0.779782i
$16$	1.61157	−	2.79133i	0.402894	−	0.697832i
$17$	−1.30148	+	3.91231i	−0.315655	+	0.948874i
$17$	−1.30148	+	3.91231i	−0.315655	+	0.948874i
$18$	−0.507997	+	3.83993i	−0.119736	+	0.905080i
$19$			0.423344i			0.0971218i	0.998820	+	0.0485609i	$0.0154635\pi$
$19$			0.423344i			0.0971218i	−0.998820	+	0.0485609i	$0.984536\pi$
$20$	−0.227993	−	0.850883i	−0.0509809	−	0.190263i
$21$	1.26085	−	3.71051i	0.275141	−	0.809700i
$22$	2.51640	+	0.674267i	0.536498	+	0.143754i
$23$	−0.239930	+	0.895433i	−0.0500290	+	0.186711i	−0.986418	−	0.164252i	$-0.947479\pi$
$23$	−0.239930	+	0.895433i	−0.0500290	+	0.186711i	0.936389	+	0.350963i	$0.114146\pi$
$24$	4.33708	+	2.89992i	0.885303	+	0.591944i
$25$	1.73071	+	0.999225i	0.346142	+	0.199845i
$26$			4.67953i			0.917730i
$27$	−5.09535	−	1.01853i	−0.980601	−	0.196017i
$28$	−0.532736	−	0.532736i	−0.100678	−	0.100678i
$29$	0.150365	+	0.561171i	0.0279221	+	0.104207i	0.978481	−	0.206339i	$-0.0661549\pi$
$29$	0.150365	+	0.561171i	0.0279221	+	0.104207i	−0.950558	+	0.310546i	$0.899488\pi$
$30$	−5.80273	+	1.15234i	−1.05943	+	0.210387i
$31$	8.25989	+	2.21323i	1.48352	+	0.397508i	0.907543	−	0.419959i	$-0.137955\pi$
$31$	8.25989	+	2.21323i	1.48352	+	0.397508i	0.575976	+	0.817466i	$0.304622\pi$
$32$	1.61329	−	0.931434i	0.285192	−	0.164656i
$33$	−1.12442	+	3.30901i	−0.195736	+	0.576024i
$34$	3.98090	−	3.53436i	0.682718	−	0.606138i
$35$	5.98553			1.01174
$36$	−0.608625	+	0.792142i	−0.101438	+	0.132024i
$37$	−6.04219	+	6.04219i	−0.993330	+	0.993330i	−0.999978	−	0.00664758i	$-0.997884\pi$
$37$	−6.04219	+	6.04219i	−0.993330	+	0.993330i	0.00664758	+	0.999978i	$0.497884\pi$
$38$	0.273296	−	0.473363i	0.0443345	−	0.0767896i
$39$	−6.26402	−	0.412546i	−1.00305	−	0.0660603i
$40$	−2.06243	+	7.69709i	−0.326099	+	1.21702i
$41$	−2.60151	+	9.70896i	−0.406287	+	1.51628i	0.395382	+	0.918517i	$0.370612\pi$
$41$	−2.60151	+	9.70896i	−0.406287	+	1.51628i	−0.801669	+	0.597768i	$0.796055\pi$
$42$	−3.80520	+	3.33495i	−0.587155	+	0.514594i
$43$	6.86536	+	3.96372i	1.04696	+	0.604462i	0.921796	−	0.387675i	$-0.126722\pi$
$43$	6.86536	+	3.96372i	1.04696	+	0.604462i	0.125162	+	0.992136i	$0.460055\pi$
$44$	0.475090	+	0.475090i	0.0716225	+	0.0716225i
$45$	−1.03095	−	7.86913i	−0.153685	−	1.17306i
$46$	0.846338	−	0.846338i	0.124786	−	0.124786i
$47$	2.62775	−	4.55140i	0.383297	−	0.663890i	−0.608234	−	0.793757i	$-0.708122\pi$
$47$	2.62775	−	4.55140i	0.383297	−	0.663890i	0.991531	+	0.129868i	$0.0414553\pi$
$48$	−2.46757	−	5.00771i	−0.356163	−	0.722801i
$49$	−1.62881	+	0.940391i	−0.232687	+	0.134342i
$50$	−1.29013	−	2.23457i	−0.182452	−	0.316016i
$51$	4.38014	+	5.64042i	0.613343	+	0.789817i
$52$	−0.603431	+	1.04517i	−0.0836808	+	0.144939i
$53$		−	9.13365i		−	1.25460i	−0.778776	−	0.627302i	$-0.784159\pi$
$53$		−	9.13365i		−	1.25460i	0.778776	−	0.627302i	$-0.215841\pi$
$54$	5.03984	+	4.42825i	0.685835	+	0.602609i
$55$	−5.33785			−0.719756
$56$	1.76392	+	6.58305i	0.235714	+	0.879697i
$57$	0.609550	+	0.407566i	0.0807369	+	0.0539834i
$58$	0.194141	−	0.724544i	0.0254920	−	0.0951373i
$59$	9.53349	−	5.50416i	1.24115	−	0.716581i	0.271825	−	0.962347i	$-0.412373\pi$
$59$	9.53349	−	5.50416i	1.24115	−	0.716581i	0.969329	+	0.245766i	$0.0790395\pi$
$60$	−1.44464	−	0.490895i	−0.186502	−	0.0633743i
$61$	−5.71685	+	1.53183i	−0.731967	+	0.196130i	−0.605505	−	0.795841i	$-0.707029\pi$
$61$	−5.71685	+	1.53183i	−0.731967	+	0.196130i	−0.126462	+	0.991971i	$0.540362\pi$
$62$	−7.80701	−	7.80701i	−0.991492	−	0.991492i
$63$	−4.12870	−	5.38765i	−0.520168	−	0.678780i
$64$	−8.85150			−1.10644
$65$	−2.48159	−	9.26140i	−0.307803	−	1.14874i
$66$	3.39345	−	2.97408i	0.417705	−	0.366085i
$67$	3.03393	+	5.25493i	0.370654	+	0.641992i	0.989666	−	0.143390i	$-0.0458002\pi$
$67$	3.03393	+	5.25493i	0.370654	+	0.641992i	−0.619012	+	0.785381i	$0.712467\pi$
$68$	1.34489	−	0.276059i	0.163092	−	0.0334770i
$69$	1.05830	+	1.20752i	0.127404	+	0.145369i
$70$	−6.69273	−	3.86405i	−0.799934	−	0.461842i
$71$	−3.46822	+	3.46822i	−0.411603	+	0.411603i	−0.882297	−	0.470694i	$-0.844004\pi$
$71$	−3.46822	+	3.46822i	−0.411603	+	0.411603i	0.470694	+	0.882297i	$0.344004\pi$
$72$	8.35087	−	3.45288i	0.984159	−	0.406926i
$73$	8.18845	−	8.18845i	0.958385	−	0.958385i	−0.0407828	−	0.999168i	$-0.512985\pi$
$73$	8.18845	−	8.18845i	0.958385	−	0.958385i	0.999168	+	0.0407828i	$0.0129852\pi$
$74$	10.6567	−	2.85546i	1.23882	−	0.331940i
$75$	3.10493	−	1.52997i	0.358527	−	0.176665i
$76$	0.122081	−	0.0704837i	0.0140037	−	0.00808504i
$77$	−3.95365	+	2.28264i	−0.450560	+	0.260131i
$78$	6.73779	+	4.50512i	0.762904	+	0.510104i
$79$	4.15030	−	1.11207i	0.466945	−	0.125118i	−0.0176723	−	0.999844i	$-0.505626\pi$
$79$	4.15030	−	1.11207i	0.466945	−	0.125118i	0.484617	+	0.874726i	$0.338959\pi$
$80$	6.02929	−	6.02929i	0.674095	−	0.674095i
$81$	−6.37197	+	6.35594i	−0.707997	+	0.706216i
$82$	9.17664	−	9.17664i	1.01339	−	1.01339i
$83$	−11.2414	−	6.49024i	−1.23391	−	0.712396i	−0.266065	−	0.963955i	$-0.585723\pi$
$83$	−11.2414	−	6.49024i	−1.23391	−	0.712396i	−0.967842	+	0.251559i	$0.919057\pi$
$84$	−1.27994	+	0.254176i	−0.139653	+	0.0277329i
$85$	−6.00443	+	9.10607i	−0.651271	+	0.987692i
$86$	−5.11767	−	8.86407i	−0.551853	−	0.955837i
$87$	0.952760	+	0.323753i	0.102147	+	0.0347100i
$88$	−1.57305	−	5.87072i	−0.167688	−	0.625821i
$89$	−3.03877			−0.322109			−0.161054	−	0.986946i	$-0.551489\pi$
$89$	−3.03877			−0.322109			−0.161054	+	0.986946i	$0.551489\pi$
$90$	−3.92727	+	9.46442i	−0.413971	+	0.997637i
$91$	−5.79854	−	5.79854i	−0.607852	−	0.607852i
$92$	0.298166	−	0.0798933i	0.0310860	−	0.00832946i
$93$	11.1387	−	9.76221i	1.15503	−	1.01229i
$94$	−5.87644	+	3.39277i	−0.606109	+	0.349937i
$95$	−0.289862	+	1.08178i	−0.0297392	+	0.110988i
$96$	0.212042	−	3.21961i	0.0216415	−	0.328600i
$97$	−3.33832	−	12.4588i	−0.338955	−	1.26500i	−0.899518	−	0.436884i	$-0.856082\pi$
$97$	−3.33832	−	12.4588i	−0.338955	−	1.26500i	0.560563	−	0.828112i	$-0.310585\pi$
$98$	2.42833			0.245299
$99$	3.68195	+	4.80467i	0.370050	+	0.482887i
$100$		−	0.665455i		−	0.0665455i
$101$	−9.50685	+	16.4663i	−0.945967	+	1.63846i	−0.192162	+	0.981363i	$0.561550\pi$
$101$	−9.50685	+	16.4663i	−0.945967	+	1.63846i	−0.753804	+	0.657099i	$0.771783\pi$
$102$	−1.25641	−	9.13451i	−0.124403	−	0.904451i
$103$	−3.99894	−	6.92636i	−0.394027	−	0.682475i	0.598949	−	0.800787i	$-0.295585\pi$
$103$	−3.99894	−	6.92636i	−0.394027	−	0.682475i	−0.992976	+	0.118312i	$0.962252\pi$
$104$	9.45463	−	5.45863i	0.927103	−	0.535263i
$105$	5.76245	−	8.61823i	0.562357	−	0.841054i
$106$	−5.89636	+	10.2128i	−0.572705	+	0.991955i
$107$	−5.62573	+	5.62573i	−0.543860	+	0.543860i	−0.924658	−	0.380798i	$-0.875649\pi$
$107$	−5.62573	+	5.62573i	−0.543860	+	0.543860i	0.380798	+	0.924658i	$0.375649\pi$
$108$	0.554620	+	1.63894i	0.0533684	+	0.157707i
$109$	13.1012	+	13.1012i	1.25487	+	1.25487i	0.953510	+	0.301360i	$0.0974406\pi$
$109$	13.1012	+	13.1012i	1.25487	+	1.25487i	0.301360	+	0.953510i	$0.402559\pi$
$110$	5.96853	+	3.44593i	0.569077	+	0.328556i
$111$	2.88282	+	14.5168i	0.273625	+	1.37787i
$112$	1.88746	−	7.04411i	0.178349	−	0.665606i
$113$	−0.440775	+	1.64499i	−0.0414646	+	0.154748i	−0.983554	−	0.180613i	$-0.942192\pi$
$113$	−0.440775	+	1.64499i	−0.0414646	+	0.154748i	0.942090	+	0.335361i	$0.108858\pi$
$114$	−0.418459	−	0.849224i	−0.0391922	−	0.0795371i
$115$	−1.22620	+	2.12383i	−0.114343	+	0.198049i
$116$	0.136792	−	0.136792i	0.0127008	−	0.0127008i
$117$	−6.62455	+	8.62204i	−0.612440	+	0.797108i
$118$	−14.2132			−1.30843
$119$	−0.553314	+	9.31239i	−0.0507222	+	0.853665i
$120$	9.09705	+	10.3798i	0.830443	+	0.947541i
$121$	−6.00044	+	3.46436i	−0.545495	+	0.314942i
$122$	7.38119	+	1.97778i	0.668262	+	0.179060i
$123$	11.4748	+	13.0929i	1.03465	+	1.18054i
$124$	−0.736973	−	2.75042i	−0.0661822	−	0.246995i
$125$	−5.61476	−	5.61476i	−0.502200	−	0.502200i
$126$	1.13843	+	8.68955i	0.101420	+	0.774127i
$127$			15.2792i			1.35581i	0.735148	+	0.677906i	$0.237113\pi$
$127$			15.2792i			1.35581i	−0.735148	+	0.677906i	$0.762887\pi$
$128$	6.67073	+	3.85135i	0.589615	+	0.340414i
$129$	12.3166	−	6.06907i	1.08442	−	0.534352i
$130$	−3.20405	+	11.9577i	−0.281014	+	1.04876i
$131$	−3.45059	−	0.924584i	−0.301480	−	0.0807812i	0.104908	−	0.994482i	$-0.466545\pi$
$131$	−3.45059	−	0.924584i	−0.301480	−	0.0807812i	−0.406388	+	0.913701i	$0.633212\pi$
$132$	1.14144	−	0.226673i	0.0993495	−	0.0197293i
$133$	0.247909	+	0.925208i	0.0214964	+	0.0802257i
$134$		−	7.83440i		−	0.676789i
$135$	−12.3228	−	6.09143i	−1.06058	−	0.524267i
$136$	−11.7846	−	3.92029i	−1.01052	−	0.336162i
$137$	4.06354	−	7.03826i	0.347172	−	0.601319i	−0.638574	−	0.769560i	$-0.720475\pi$
$137$	4.06354	−	7.03826i	0.347172	−	0.601319i	0.985746	+	0.168241i	$0.0538088\pi$
$138$	−0.403801	−	2.03339i	−0.0343738	−	0.173094i
$139$	6.23183	+	1.66982i	0.528577	+	0.141632i	0.513231	−	0.858250i	$-0.328448\pi$
$139$	6.23183	+	1.66982i	0.528577	+	0.141632i	0.0153461	+	0.999882i	$0.495115\pi$
$140$	−0.996547	−	1.72607i	−0.0842236	−	0.145880i
$141$	−4.02349	−	8.16532i	−0.338839	−	0.687644i
$142$	6.11696	−	1.63903i	0.513324	−	0.137545i
$143$	5.17110	+	5.17110i	0.432429	+	0.432429i
$144$	−9.58593	−	1.26815i	−0.798827	−	0.105679i
$145$			1.53692i			0.127635i
$146$	−14.4421	+	3.86975i	−1.19524	+	0.320262i
$147$	−0.214082	+	3.25057i	−0.0176571	+	0.268102i
$148$	2.74839	+	0.736429i	0.225916	+	0.0605341i
$149$	−8.62880	−	14.9455i	−0.706899	−	1.22438i	−0.966002	−	0.258535i	$-0.916760\pi$
$149$	−8.62880	−	14.9455i	−0.706899	−	1.22438i	0.259103	−	0.965850i	$-0.416573\pi$
$150$	−4.45947	−	0.293700i	−0.364115	−	0.0239805i
$151$	2.89921	+	1.67386i	0.235934	+	0.136217i	0.613307	−	0.789845i	$-0.289839\pi$
$151$	2.89921	+	1.67386i	0.235934	+	0.136217i	−0.377373	+	0.926062i	$0.623172\pi$
$152$	−1.27519			−0.103432
$153$	12.3382	−	0.876530i	0.997486	−	0.0708632i
$154$	5.89437			0.474982
$155$	19.5912	+	11.3110i	1.57361	+	0.908522i
$156$	0.923946	+	1.87506i	0.0739749	+	0.150125i
$157$	−10.7662	−	18.6475i	−0.859233	−	1.48823i	−0.872662	−	0.488325i	$-0.837608\pi$
$157$	−10.7662	−	18.6475i	−0.859233	−	1.48823i	0.0134293	−	0.999910i	$-0.495725\pi$
$158$	−5.35857	−	1.43582i	−0.426305	−	0.114228i
$159$	−13.1510	−	8.79323i	−1.04295	−	0.697349i
$160$	4.76022	−	1.27550i	0.376328	−	0.100837i
$161$			2.09745i			0.165302i
$162$	11.2280	−	2.99338i	0.882155	−	0.235182i
$163$	−10.7896	−	10.7896i	−0.845106	−	0.845106i	0.144412	−	0.989518i	$-0.453871\pi$
$163$	−10.7896	−	10.7896i	−0.845106	−	0.845106i	−0.989518	+	0.144412i	$0.953871\pi$
$164$	3.23294	−	0.866264i	0.252450	−	0.0676439i
$165$	−5.13891	+	7.68568i	−0.400063	+	0.598329i
$166$	8.37974	+	14.5141i	0.650394	+	1.12652i
$167$	3.45125	+	0.924759i	0.267066	+	0.0715600i	0.389867	−	0.920871i	$-0.372521\pi$
$167$	3.45125	+	0.924759i	0.267066	+	0.0715600i	−0.122801	+	0.992431i	$0.539188\pi$
$168$	11.1768	+	3.79792i	0.862305	+	0.293016i
$169$	−0.0680160	+	0.117807i	−0.00523200	+	0.00906209i
$170$	12.5924	−	6.30571i	0.965794	−	0.483626i
$171$	1.17366	−	0.485281i	0.0897523	−	0.0371104i
$172$		−	2.63972i		−	0.201277i
$173$	−5.41196	−	20.1977i	−0.411463	−	1.53560i	−0.791815	−	0.610761i	$-0.790864\pi$
$173$	−5.41196	−	20.1977i	−0.411463	−	1.53560i	0.380352	−	0.924842i	$-0.375803\pi$
$174$	−0.856325	−	0.977072i	−0.0649179	−	0.0740717i
$175$	4.36756	+	1.17028i	0.330156	+	0.0884651i
$176$	−1.68323	+	6.28189i	−0.126878	+	0.473515i
$177$	1.25303	−	19.0258i	0.0941835	−	1.43006i
$178$	3.39780	+	1.96172i	0.254676	+	0.147037i
$179$			0.809264i			0.0604872i	0.999543	+	0.0302436i	$0.00962831\pi$
$179$			0.809264i			0.0604872i	−0.999543	+	0.0302436i	$0.990372\pi$
$180$	−2.09761	+	1.60745i	−0.156346	+	0.119812i
$181$	13.9977	+	13.9977i	1.04044	+	1.04044i	0.999147	+	0.0412974i	$0.0131491\pi$
$181$	13.9977	+	13.9977i	1.04044	+	1.04044i	0.0412974	+	0.999147i	$0.486851\pi$
$182$	2.74031	+	10.2270i	0.203125	+	0.758074i
$183$	−3.29819	+	9.70611i	−0.243809	+	0.717496i
$184$	−2.69721	−	0.722715i	−0.198841	−	0.0532793i
$185$	−19.5768	+	11.3027i	−1.43931	+	0.830988i
$186$	−18.7569	+	3.72485i	−1.37532	+	0.273119i
$187$	0.493442	−	8.30472i	0.0360840	−	0.607301i
$188$	−1.75001			−0.127632
$189$	−11.7322	+	0.757840i	−0.853392	+	0.0551247i
$190$	1.02247	−	1.02247i	0.0741775	−	0.0741775i
$191$	−2.13533	+	3.69850i	−0.154507	+	0.267614i	−0.932879	−	0.360189i	$-0.882712\pi$
$191$	−2.13533	+	3.69850i	−0.154507	+	0.267614i	0.778372	+	0.627803i	$0.216046\pi$
$192$	−8.52160	+	12.7448i	−0.614994	+	0.919776i
$193$	−0.256009	+	0.955437i	−0.0184279	+	0.0687739i	−0.974527	−	0.224268i	$-0.928001\pi$
$193$	−0.256009	+	0.955437i	−0.0184279	+	0.0687739i	0.956100	+	0.293042i	$0.0946676\pi$
$194$	−4.31020	+	16.0859i	−0.309454	+	1.15490i
$195$	−15.7241	−	5.34313i	−1.12602	−	0.382629i
$196$	0.542369	+	0.313137i	0.0387406	+	0.0223669i
$197$	−6.96209	−	6.96209i	−0.496028	−	0.496028i	0.414171	−	0.910199i	$-0.364072\pi$
$197$	−6.96209	−	6.96209i	−0.496028	−	0.496028i	−0.910199	+	0.414171i	$0.864072\pi$
$198$	−1.01525	−	7.74928i	−0.0721505	−	0.550717i
$199$	5.42664	−	5.42664i	0.384684	−	0.384684i	−0.488102	−	0.872786i	$-0.662311\pi$
$199$	5.42664	−	5.42664i	0.384684	−	0.384684i	0.872786	+	0.488102i	$0.162311\pi$
$200$	−3.00985	+	5.21321i	−0.212829	+	0.368630i
$201$	10.4871	+	0.690680i	0.739706	+	0.0487168i
$202$	21.2602	−	12.2746i	1.49586	−	0.863636i
$203$	0.657239	+	1.13837i	0.0461291	+	0.0798979i
$204$	0.897287	−	2.20221i	0.0628227	−	0.154185i
$205$	−13.2953	+	23.0282i	−0.928587	+	1.60836i
$206$			10.3263i			0.719467i
$207$	2.75750	−	0.361265i	0.191659	−	0.0251096i
$208$	−11.6819			−0.809992
$209$	−0.221083	−	0.825094i	−0.0152926	−	0.0570729i
$210$	−12.0069	+	5.91645i	−0.828556	+	0.408274i
$211$	6.82729	−	25.4798i	0.470010	−	1.75410i	−0.169709	−	0.985494i	$-0.554283\pi$
$211$	6.82729	−	25.4798i	0.470010	−	1.75410i	0.639720	−	0.768608i	$-0.279050\pi$
$212$	−2.63391	+	1.52069i	−0.180897	+	0.104441i
$213$	1.65474	+	8.33267i	0.113381	+	0.570945i
$214$	9.92219	−	2.65864i	0.678267	−	0.181741i
$215$	14.8292	+	14.8292i	1.01135	+	1.01135i
$216$	3.06801	−	15.3481i	0.208752	−	1.04431i
$217$	19.3478			1.31342
$218$	−6.19146	−	23.1068i	−0.419339	−	1.56499i
$219$	−3.90683	−	19.6733i	−0.263999	−	1.32940i
$220$	0.888714	+	1.53930i	0.0599171	+	0.103779i
$221$	14.6384	−	3.00475i	0.984688	−	0.202121i
$222$	6.14811	−	18.0930i	0.412634	−	1.21432i
$223$	−7.91623	−	4.57043i	−0.530110	−	0.306059i	0.210951	−	0.977497i	$-0.432344\pi$
$223$	−7.91623	−	4.57043i	−0.530110	−	0.306059i	−0.741061	+	0.671438i	$0.765677\pi$
$224$	2.98036	−	2.98036i	0.199134	−	0.199134i
$225$	0.786293	−	5.94356i	0.0524195	−	0.396238i
$226$	1.55480	−	1.55480i	0.103424	−	0.103424i
$227$	2.72262	−	0.729523i	0.180706	−	0.0484202i	−0.167331	−	0.985901i	$-0.553515\pi$
$227$	2.72262	−	0.729523i	0.180706	−	0.0484202i	0.348037	+	0.937481i	$0.386848\pi$
$228$	0.0160457	−	0.243635i	0.00106265	−	0.0161351i
$229$	−17.5962	+	10.1592i	−1.16279	+	0.671338i	−0.951972	−	0.306186i	$-0.900947\pi$
$229$	−17.5962	+	10.1592i	−1.16279	+	0.671338i	−0.210821	+	0.977525i	$0.567614\pi$
$230$	2.74214	−	1.58318i	0.180812	−	0.104392i
$231$	−0.519647	+	7.89021i	−0.0341902	+	0.519137i
$232$	−1.69035	+	0.452928i	−0.110977	+	0.0297362i
$233$	4.86165	−	4.86165i	0.318497	−	0.318497i	−0.529692	−	0.848190i	$-0.677693\pi$
$233$	4.86165	−	4.86165i	0.318497	−	0.318497i	0.848190	+	0.529692i	$0.177693\pi$
$234$	12.9733	−	5.36416i	0.848093	−	0.350666i
$235$	9.83106	−	9.83106i	0.641307	−	0.641307i
$236$	−3.17451	−	1.83281i	−0.206643	−	0.119305i
$237$	2.39441	−	7.04641i	0.155533	−	0.457713i
$238$	6.63044	−	10.0555i	0.429787	−	0.651798i
$239$	−2.70693	−	4.68855i	−0.175097	−	0.303277i	0.765098	−	0.643914i	$-0.222691\pi$
$239$	−2.70693	−	4.68855i	−0.175097	−	0.303277i	−0.940195	+	0.340637i	$0.889357\pi$
$240$	−2.87667	−	14.4858i	−0.185688	−	0.935056i
$241$	1.45479	+	5.42934i	0.0937110	+	0.349734i	0.996821	−	0.0796753i	$-0.0253883\pi$
$241$	1.45479	+	5.42934i	0.0937110	+	0.349734i	−0.903110	+	0.429410i	$0.858722\pi$
$242$	8.94587			0.575062
$243$	3.01708	+	15.2937i	0.193546	+	0.981091i
$244$	1.39355	+	1.39355i	0.0892130	+	0.0892130i
$245$	−4.80600	+	1.28776i	−0.307044	+	0.0822721i
$246$	−4.37831	−	22.0475i	−0.279151	−	1.40570i
$247$	1.32879	−	0.767177i	0.0845489	−	0.0488143i
$248$	−6.66666	+	24.8803i	−0.423333	+	1.57990i
$249$	−20.1674	+	9.93756i	−1.27806	+	0.629767i
$250$	2.65346	+	9.90285i	0.167820	+	0.626311i
$251$	3.43338			0.216713			0.108356	−	0.994112i	$-0.465441\pi$
$251$	3.43338			0.216713			0.108356	+	0.994112i	$0.465441\pi$
$252$	−0.866259	+	2.08761i	−0.0545692	+	0.131507i
$253$		−	1.87049i		−	0.117597i
$254$	9.86373	−	17.0845i	0.618906	−	1.07198i
$255$	7.33069	+	17.4121i	0.459066	+	1.09039i
$256$	3.87891	+	6.71848i	0.242432	+	0.419905i
$257$	8.11028	−	4.68247i	0.505905	−	0.292085i	−0.225244	−	0.974302i	$-0.572318\pi$
$257$	8.11028	−	4.68247i	0.505905	−	0.292085i	0.731149	+	0.682218i	$0.238984\pi$
$258$	−17.6898	−	1.16505i	−1.10132	−	0.0725326i
$259$	−9.66677	+	16.7433i	−0.600664	+	1.04038i
$260$	−2.25758	+	2.25758i	−0.140009	+	0.140009i
$261$	1.38340	−	1.06014i	0.0856305	−	0.0656210i
$262$	3.26140	+	3.26140i	0.201490	+	0.201490i
$263$	0.747005	+	0.431284i	0.0460623	+	0.0265941i	0.522854	−	0.852422i	$-0.324867\pi$
$263$	0.747005	+	0.431284i	0.0460623	+	0.0265941i	−0.476792	+	0.879016i	$0.658201\pi$
$264$	−9.96735	−	3.38696i	−0.613448	−	0.208453i
$265$	6.25377	−	23.3394i	0.384166	−	1.43373i
$266$	0.320082	−	1.19456i	0.0196255	−	0.0732433i
$267$	−2.92551	+	4.37535i	−0.179038	+	0.267767i
$268$	1.01026	−	1.74982i	0.0617112	−	0.106887i
$269$	6.31660	−	6.31660i	0.385130	−	0.385130i	−0.487816	−	0.872946i	$-0.662206\pi$
$269$	6.31660	−	6.31660i	0.385130	−	0.385130i	0.872946	+	0.487816i	$0.162206\pi$
$270$	9.84639	+	14.7663i	0.599232	+	0.898651i
$271$	13.4602			0.817646			0.408823	−	0.912614i	$-0.365939\pi$
$271$	13.4602			0.817646			0.408823	+	0.912614i	$0.365939\pi$
$272$	8.82311	+	9.93783i	0.534980	+	0.602570i
$273$	−13.9314	+	2.76657i	−0.843168	+	0.167441i
$274$	−9.08730	+	5.24656i	−0.548984	+	0.316956i
$275$	−3.89496	−	1.04365i	−0.234875	−	0.0629345i
$276$	0.172019	−	0.506228i	0.0103543	−	0.0304714i
$277$	3.54689	+	13.2372i	0.213112	+	0.795345i	0.986823	+	0.161806i	$0.0517318\pi$
$277$	3.54689	+	13.2372i	0.213112	+	0.795345i	−0.773711	+	0.633539i	$0.781602\pi$
$278$	−5.89016	−	5.89016i	−0.353268	−	0.353268i
$279$	−3.33247	−	25.4364i	−0.199510	−	1.52284i
$280$			18.0295i			1.07747i
$281$	−7.69934	−	4.44522i	−0.459304	−	0.265179i	0.252447	−	0.967611i	$-0.418765\pi$
$281$	−7.69934	−	4.44522i	−0.459304	−	0.265179i	−0.711752	+	0.702431i	$0.752098\pi$
$282$	−0.772368	+	11.7275i	−0.0459939	+	0.698361i
$283$	4.81143	−	17.9565i	0.286010	−	1.06740i	−0.662089	−	0.749425i	$-0.730330\pi$
$283$	4.81143	−	17.9565i	0.286010	−	1.06740i	0.948098	−	0.317977i	$-0.103004\pi$
$284$	1.57758	+	0.422711i	0.0936121	+	0.0250833i
$285$	1.27853	+	1.45882i	0.0757339	+	0.0864128i
$286$	−2.44379	−	9.12035i	−0.144504	−	0.539297i
$287$			22.7421i			1.34242i
$288$	−4.43160	−	3.40492i	−0.261134	−	0.200637i
$289$	−13.6123	−	10.1836i	−0.800724	−	0.599033i
$290$	0.992183	−	1.71851i	0.0582630	−	0.100914i
$291$	−21.1526	−	7.18776i	−1.23999	−	0.421354i
$292$	−3.72465	−	0.998017i	−0.217969	−	0.0584045i
$293$	5.08353	+	8.80494i	0.296983	+	0.514390i	0.975444	−	0.220246i	$-0.0706862\pi$
$293$	5.08353	+	8.80494i	0.296983	+	0.514390i	−0.678461	+	0.734636i	$0.737353\pi$
$294$	2.33783	−	3.49642i	0.136345	−	0.203916i
$295$	28.1297	−	7.53734i	1.63778	−	0.438841i
$296$	−18.2002	−	18.2002i	−1.05787	−	1.05787i
$297$	10.4627	−	0.675836i	0.607107	−	0.0392160i
$298$			22.2818i			1.29075i
$299$	3.24538	−	0.869596i	0.187685	−	0.0502900i
$300$	−0.958151	−	0.640653i	−0.0553189	−	0.0369881i
$301$	17.3252	+	4.64228i	0.998608	+	0.267576i
$302$	−2.16117	−	3.74325i	−0.124361	−	0.215400i
$303$	14.5565	+	29.5410i	0.836246	+	1.69709i
$304$	1.18169	+	0.682251i	0.0677748	+	0.0391298i
$305$	−15.6572			−0.896528
$306$	−14.3618	−	6.98503i	−0.821012	−	0.399307i
$307$	7.77013			0.443465			0.221732	−	0.975108i	$-0.428829\pi$
$307$	7.77013			0.443465			0.221732	+	0.975108i	$0.428829\pi$
$308$	1.31651	+	0.760086i	0.0750150	+	0.0433099i
$309$	−13.8228	−	0.910364i	−0.786350	−	0.0517888i
$310$	−14.6040	−	25.2948i	−0.829450	−	1.43665i
$311$	9.56982	+	2.56422i	0.542655	+	0.145404i	0.519726	−	0.854333i	$-0.326034\pi$
$311$	9.56982	+	2.56422i	0.542655	+	0.145404i	0.0229290	+	0.999737i	$0.492701\pi$
$312$	1.24267	−	18.8684i	0.0703521	−	1.06821i
$313$	−4.43547	+	1.18848i	−0.250708	+	0.0671770i	−0.381984	−	0.924169i	$-0.624759\pi$
$313$	−4.43547	+	1.18848i	−0.250708	+	0.0671770i	0.131276	+	0.991346i	$0.458092\pi$
$314$			27.8010i			1.56890i
$315$	−6.86124	−	16.5941i	−0.386587	−	0.934969i
$316$	−1.01169	−	1.01169i	−0.0569118	−	0.0569118i
$317$	−0.451728	+	0.121040i	−0.0253716	+	0.00679829i	−0.271483	−	0.962443i	$-0.587514\pi$
$317$	−0.451728	+	0.121040i	−0.0253716	+	0.00679829i	0.246111	+	0.969242i	$0.420847\pi$
$318$	9.02824	+	18.3220i	0.506279	+	1.02745i
$319$	−0.586121	−	1.01519i	−0.0328165	−	0.0568398i
$320$	−22.6184	−	6.06058i	−1.26441	−	0.338797i
$321$	2.68412	+	13.5162i	0.149813	+	0.754403i
$322$	1.35404	−	2.34526i	0.0754575	−	0.130696i
$323$	−1.65625	−	0.550973i	−0.0921564	−	0.0306570i
$324$	2.89377	+	0.779292i	0.160765	+	0.0432940i
$325$		−	7.24311i		−	0.401776i
$326$	5.09901	+	19.0298i	0.282408	+	1.05396i
$327$	31.4767	−	6.25080i	1.74066	−	0.345670i
$328$	−29.2452	−	7.83622i	−1.61479	−	0.432683i
$329$	3.07760	−	11.4858i	0.169674	−	0.633231i
$330$	10.7077	−	5.27625i	0.589438	−	0.290448i
$331$	−23.6199	−	13.6369i	−1.29827	−	0.749555i	−0.318162	−	0.948036i	$-0.603066\pi$
$331$	−23.6199	−	13.6369i	−1.29827	−	0.749555i	−0.980105	+	0.198482i	$0.936399\pi$
$332$			4.32231i			0.237218i
$333$	23.6773	+	9.82495i	1.29751	+	0.538404i
$334$	−3.26202	−	3.26202i	−0.178490	−	0.178490i
$335$	4.15464	+	15.5053i	0.226992	+	0.847147i
$336$	−8.32531	−	9.49922i	−0.454183	−	0.518225i
$337$	6.34815	+	1.70098i	0.345806	+	0.0926583i	0.427542	−	0.903996i	$-0.359380\pi$
$337$	6.34815	+	1.70098i	0.345806	+	0.0926583i	−0.0817360	+	0.996654i	$0.526046\pi$
$338$	0.152104	−	0.0878175i	0.00827338	−	0.00477664i
$339$	1.94419	+	2.21833i	0.105594	+	0.120483i
$340$	3.62565	+	0.215425i	0.196628	+	0.0116831i
$341$	−17.2543			−0.934370
$342$	−1.62561	−	0.215058i	−0.0879031	−	0.0116290i
$343$	−14.2082	+	14.2082i	−0.767169	+	0.767169i
$344$	−11.9395	+	20.6798i	−0.643733	+	1.11498i
$345$	1.87750	+	3.81021i	0.101081	+	0.205135i
$346$	−6.98753	+	26.0778i	−0.375652	+	1.40195i
$347$	−3.35717	+	12.5291i	−0.180222	+	0.672599i	0.815381	+	0.578925i	$0.196528\pi$
$347$	−3.35717	+	12.5291i	−0.180222	+	0.672599i	−0.995603	+	0.0936736i	$0.970139\pi$
$348$	−0.0652657	−	0.328653i	−0.00349861	−	0.0176177i
$349$	−8.88754	−	5.13122i	−0.475739	−	0.274668i	0.242900	−	0.970051i	$-0.421901\pi$
$349$	−8.88754	−	5.13122i	−0.475739	−	0.274668i	−0.718639	+	0.695383i	$0.755235\pi$
$350$	−4.12809	−	4.12809i	−0.220656	−	0.220656i
$351$	6.03674	+	17.8390i	0.322218	+	0.952176i
$352$	−2.65787	+	2.65787i	−0.141665	+	0.141665i
$353$	−6.88387	+	11.9232i	−0.366391	+	0.634608i	−0.988998	−	0.147926i	$-0.952740\pi$
$353$	−6.88387	+	11.9232i	−0.366391	+	0.634608i	0.622607	+	0.782535i	$0.286073\pi$
$354$	−13.6834	+	20.4647i	−0.727266	+	1.08769i
$355$	−11.2371	+	6.48774i	−0.596403	+	0.344333i
$356$	0.505932	+	0.876301i	0.0268144	+	0.0464438i
$357$	12.8757	+	9.76199i	0.681454	+	0.516659i
$358$	0.522432	−	0.904879i	0.0276114	−	0.0478243i
$359$			23.7307i			1.25246i	0.779639	+	0.626229i	$0.215402\pi$
$359$			23.7307i			1.25246i	−0.779639	+	0.626229i	$0.784598\pi$
$360$	23.7033	−	3.10541i	1.24927	−	0.163670i
$361$	18.8208			0.990567
$362$	−6.61514	−	24.6880i	−0.347684	−	1.29757i
$363$	−0.788666	+	11.9749i	−0.0413942	+	0.628522i
$364$	−0.706733	+	2.63756i	−0.0370429	+	0.138246i
$365$	26.5307	−	15.3175i	1.38868	−	0.801754i
$366$	9.95379	−	8.72370i	0.520293	−	0.455995i
$367$	−31.5599	+	8.45645i	−1.64741	+	0.441423i	−0.958887	−	0.283789i	$-0.908408\pi$
$367$	−31.5599	+	8.45645i	−1.64741	+	0.441423i	−0.688526	+	0.725212i	$0.741742\pi$
$368$	2.11278	+	2.11278i	0.110136	+	0.110136i
$369$	29.8989	−	3.91710i	1.55647	−	0.203916i
$370$	29.1864			1.51733
$371$	−5.34863	−	19.9614i	−0.277687	−	1.03634i
$372$	−4.66969	−	1.58678i	−0.242112	−	0.0822710i
$373$	−0.467282	−	0.809356i	−0.0241950	−	0.0419069i	0.853674	−	0.520807i	$-0.174369\pi$
$373$	−0.467282	−	0.809356i	−0.0241950	−	0.0419069i	−0.877869	+	0.478900i	$0.841036\pi$
$374$	−5.91298	+	8.96738i	−0.305753	+	0.463692i
$375$	−13.4899	+	2.67889i	−0.696615	+	0.138337i
$376$	13.7097	+	7.91528i	0.707022	+	0.408199i
$377$	1.48891	−	1.48891i	0.0766827	−	0.0766827i
$378$	13.6076	+	6.72651i	0.699900	+	0.345975i
$379$	7.79837	−	7.79837i	0.400576	−	0.400576i	−0.477860	−	0.878436i	$-0.658587\pi$
$379$	7.79837	−	7.79837i	0.400576	−	0.400576i	0.878436	+	0.477860i	$0.158587\pi$
$380$	0.360216	−	0.0965197i	0.0184787	−	0.00495136i
$381$	21.9997	+	14.7098i	1.12708	+	0.753604i
$382$	4.77524	−	2.75698i	0.244322	−	0.141060i
$383$	16.2084	−	9.35795i	0.828213	−	0.478169i	−0.0250275	−	0.999687i	$-0.507967\pi$
$383$	16.2084	−	9.35795i	0.828213	−	0.478169i	0.853240	+	0.521518i	$0.174634\pi$
$384$	11.9675	−	5.89701i	0.610711	−	0.300931i
$385$	−11.6657	+	3.12583i	−0.594541	+	0.159307i
$386$	0.903053	−	0.903053i	0.0459642	−	0.0459642i
$387$	3.11906	−	23.5769i	0.158551	−	1.19848i
$388$	−3.03698	+	3.03698i	−0.154179	+	0.154179i
$389$	−1.02593	−	0.592318i	−0.0520165	−	0.0300317i	0.473766	−	0.880651i	$-0.342894\pi$
$389$	−1.02593	−	0.592318i	−0.0520165	−	0.0300317i	−0.525783	+	0.850619i	$0.676227\pi$
$390$	14.1326	+	16.1253i	0.715630	+	0.816538i
$391$	−3.19094	−	2.10407i	−0.161373	−	0.106407i
$392$	−2.83263	−	4.90627i	−0.143070	−	0.247804i
$393$	−4.65324	+	4.07819i	−0.234725	+	0.205718i
$394$	3.29019	+	12.2791i	0.165757	+	0.618614i
$395$	11.3668			0.571923
$396$	0.772523	−	1.86172i	0.0388208	−	0.0935549i
$397$	−1.66536	−	1.66536i	−0.0835821	−	0.0835821i	0.664080	−	0.747662i	$-0.268824\pi$
$397$	−1.66536	−	1.66536i	−0.0835821	−	0.0835821i	−0.747662	+	0.664080i	$0.768824\pi$
$398$	−9.57104	+	2.56455i	−0.479753	+	0.128549i
$399$	1.57082	+	0.533775i	0.0786396	+	0.0267222i
$400$	5.57833	−	3.22065i	0.278917	−	0.161033i
$401$	−0.902578	+	3.36847i	−0.0450726	+	0.168213i	−0.984793	−	0.173729i	$-0.944418\pi$
$401$	−0.902578	+	3.36847i	−0.0450726	+	0.168213i	0.939721	+	0.341943i	$0.111085\pi$
$402$	−11.2803	−	7.54241i	−0.562611	−	0.376181i
$403$	−8.02156	−	29.9369i	−0.399582	−	1.49126i
$404$	6.33128			0.314993
$405$	−20.6343	+	11.8786i	−1.02533	+	0.590252i
$406$		−	1.69716i		−	0.0842286i
$407$	8.62076	−	14.9316i	0.427315	−	0.740131i
$408$	−16.9900	+	13.1938i	−0.841130	+	0.653191i
$409$	−0.801688	−	1.38856i	−0.0396409	−	0.0686601i	0.845524	−	0.533937i	$-0.179288\pi$
$409$	−0.801688	−	1.38856i	−0.0396409	−	0.0686601i	−0.885165	+	0.465277i	$0.845955\pi$
$410$	29.7324	−	17.1660i	1.46838	−	0.847769i
$411$	−6.22191	−	12.6268i	−0.306904	−	0.622834i
$412$	−1.33159	+	2.30638i	−0.0656026	+	0.113627i
$413$	17.6120	−	17.6120i	0.866628	−	0.866628i
$414$	−3.31652	−	1.37619i	−0.162998	−	0.0676362i
$415$	−24.2816	−	24.2816i	−1.19194	−	1.19194i
$416$	−5.84716	−	3.37586i	−0.286681	−	0.165515i
$417$	8.40384	−	7.36529i	0.411538	−	0.360680i
$418$	−0.285447	+	1.06530i	−0.0139617	+	0.0521056i
$419$	8.12736	−	30.3317i	0.397048	−	1.48180i	−0.421217	−	0.906960i	$-0.638397\pi$
$419$	8.12736	−	30.3317i	0.397048	−	1.48180i	0.818264	−	0.574842i	$-0.194937\pi$
$420$	−3.44468	−	0.226866i	−0.168083	−	0.0110699i
$421$	−7.09251	+	12.2846i	−0.345668	+	0.598714i	−0.985475	−	0.169821i	$-0.945681\pi$
$421$	−7.09251	+	12.2846i	−0.345668	+	0.598714i	0.639807	+	0.768536i	$0.279014\pi$
$422$	−24.0828	+	24.0828i	−1.17233	+	1.17233i
$423$	−15.6303	−	2.06779i	−0.759972	−	0.100539i
$424$	27.5123			1.33611
$425$	−6.16175	+	5.47059i	−0.298889	+	0.265363i
$426$	3.52902	−	10.3854i	0.170982	−	0.503175i
$427$	−11.5970	+	6.69553i	−0.561218	+	0.324019i
$428$	2.55896	+	0.685670i	0.123692	+	0.0331431i
$429$	12.4239	−	2.46721i	0.599834	−	0.119118i
$430$	−7.00809	−	26.1546i	−0.337960	−	1.26128i
$431$	−15.0327	−	15.0327i	−0.724101	−	0.724101i	0.245337	−	0.969438i	$-0.421102\pi$
$431$	−15.0327	−	15.0327i	−0.724101	−	0.724101i	−0.969438	+	0.245337i	$0.921102\pi$
$432$	−11.0546	+	12.5814i	−0.531865	+	0.605321i
$433$			32.9977i			1.58577i	0.609372	+	0.792884i	$0.291422\pi$
$433$			32.9977i			1.58577i	−0.609372	+	0.792884i	$0.708578\pi$
$434$	−21.6338	−	12.4903i	−1.03845	−	0.599552i
$435$	2.21293	+	1.47964i	0.106102	+	0.0709434i
$436$	1.59679	−	5.95931i	0.0764725	−	0.285399i
$437$	−0.379076	−	0.101573i	−0.0181337	−	0.00485890i
$438$	−8.33199	+	24.5199i	−0.398118	+	1.17161i
$439$	9.70185	+	36.2078i	0.463044	+	1.72810i	0.663293	+	0.748359i	$0.269158\pi$
$439$	9.70185	+	36.2078i	0.463044	+	1.72810i	−0.200249	+	0.979745i	$0.564175\pi$
$440$		−	16.0786i		−	0.766518i
$441$	4.47421	+	3.43766i	0.213058	+	0.163698i
$442$	−18.3077	−	6.09030i	−0.870811	−	0.289686i
$443$	15.0603	−	26.0853i	0.715539	−	1.23935i	−0.247213	−	0.968961i	$-0.579515\pi$
$443$	15.0603	−	26.0853i	0.715539	−	1.23935i	0.962751	−	0.270388i	$-0.0871521\pi$
$444$	3.70630	−	3.24827i	0.175893	−	0.154156i
$445$	−7.76501	−	2.08063i	−0.368097	−	0.0986312i
$446$	5.90102	+	10.2209i	0.279421	+	0.483972i
$447$	−29.8264	−	1.96436i	−1.41074	−	0.0929110i
$448$	−19.3447	+	5.18340i	−0.913952	+	0.244893i
$449$	−6.94280	−	6.94280i	−0.327651	−	0.327651i	0.524042	−	0.851693i	$-0.324424\pi$
$449$	−6.94280	−	6.94280i	−0.327651	−	0.327651i	−0.851693	+	0.524042i	$0.824424\pi$
$450$	−4.71615	+	6.13820i	−0.222321	+	0.289357i
$451$		−	20.2812i		−	0.955006i
$452$	0.547759	−	0.146772i	0.0257644	−	0.00690355i
$453$	5.20124	−	2.56293i	0.244376	−	0.120417i
$454$	−3.51525	−	0.941909i	−0.164979	−	0.0442060i
$455$	−10.8469	−	18.7873i	−0.508510	−	0.880764i
$456$	−1.22766	+	1.83608i	−0.0574906	+	0.0859822i
$457$	−6.94723	−	4.01099i	−0.324978	−	0.187626i	0.328631	−	0.944458i	$-0.393413\pi$
$457$	−6.94723	−	4.01099i	−0.324978	−	0.187626i	−0.653609	+	0.756832i	$0.726746\pi$
$458$	26.2337			1.22582
$459$	10.6163	−	18.6090i	0.495526	−	0.868593i
$460$	0.816611			0.0380747
$461$	15.5998	+	9.00658i	0.726557	+	0.419478i	0.817161	−	0.576409i	$-0.195546\pi$
$461$	15.5998	+	9.00658i	0.726557	+	0.419478i	−0.0906041	+	0.995887i	$0.528880\pi$
$462$	5.67468	−	8.48697i	0.264010	−	0.394850i
$463$	−3.19249	−	5.52955i	−0.148367	−	0.256980i	0.782257	−	0.622956i	$-0.214068\pi$
$463$	−3.19249	−	5.52955i	−0.148367	−	0.256980i	−0.930624	+	0.365976i	$0.880735\pi$
$464$	1.80874	+	0.484650i	0.0839685	+	0.0224993i
$465$	35.1471	−	17.3189i	1.62991	−	0.803145i
$466$	−8.57457	+	2.29755i	−0.397209	+	0.106432i
$467$		−	25.4787i		−	1.17901i	−0.807763	−	0.589507i	$-0.799322\pi$
$467$		−	25.4787i		−	1.17901i	0.807763	−	0.589507i	$-0.200678\pi$
$468$	3.58931	+	0.474841i	0.165916	+	0.0219496i
$469$	9.70785	+	9.70785i	0.448267	+	0.448267i
$470$	−17.3392	+	4.64602i	−0.799797	+	0.214305i
$471$	−37.2144	−	2.45093i	−1.71475	−	0.112933i
$472$	16.5796	+	28.7166i	0.763136	+	1.32179i
$473$	−15.4505	−	4.13995i	−0.710415	−	0.190355i
$474$	−7.22622	+	6.33320i	−0.331911	+	0.290893i
$475$	−0.423016	+	0.732685i	−0.0194093	+	0.0336179i
$476$	2.77757	−	1.39088i	0.127310	−	0.0637510i
$477$	−25.3218	+	10.4699i	−1.15940	+	0.479386i
$478$			6.99000i			0.319715i
$479$	7.77954	+	29.0337i	0.355456	+	1.32658i	0.879909	+	0.475142i	$0.157603\pi$
$479$	7.77954	+	29.0337i	0.355456	+	1.32658i	−0.524453	+	0.851440i	$0.675730\pi$
$480$	2.74628	−	8.08193i	0.125350	−	0.368888i
$481$	29.9148	+	8.01563i	1.36400	+	0.365481i
$482$	1.87832	−	7.00997i	0.0855550	−	0.319296i
$483$	3.02000	+	2.01927i	0.137415	+	0.0918801i
$484$	1.99806	+	1.15358i	0.0908209	+	0.0524355i
$485$		−	34.1218i		−	1.54939i
$486$	6.49952	−	19.0484i	0.294824	−	0.864052i
$487$	−10.8606	−	10.8606i	−0.492139	−	0.492139i	0.416841	−	0.908980i	$-0.363137\pi$
$487$	−10.8606	−	10.8606i	−0.492139	−	0.492139i	−0.908980	+	0.416841i	$0.863137\pi$
$488$	−4.61414	−	17.2202i	−0.208872	−	0.779522i
$489$	−25.9228	+	5.14788i	−1.17227	+	0.232795i
$490$	6.20516	+	1.66267i	0.280321	+	0.0751117i
$491$	16.1525	−	9.32567i	0.728954	−	0.420862i	−0.0890857	−	0.996024i	$-0.528394\pi$
$491$	16.1525	−	9.32567i	0.728954	−	0.420862i	0.818039	+	0.575162i	$0.195061\pi$
$492$	1.86516	−	5.48891i	0.0840880	−	0.247459i
$493$	−2.39117	−	0.142076i	−0.107693	−	0.00639879i
$494$	−1.98105			−0.0891317
$495$	6.11881	+	14.7985i	0.275020	+	0.665141i
$496$	19.4893	−	19.4893i	0.875095	−	0.875095i
$497$	−5.54873	+	9.61069i	−0.248895	+	0.431098i
$498$	28.9655	+	1.90766i	1.29798	+	0.0854843i
$499$	−6.15029	+	22.9532i	−0.275325	+	1.02753i	0.680299	+	0.732935i	$0.261850\pi$
$499$	−6.15029	+	22.9532i	−0.275325	+	1.02753i	−0.955624	+	0.294591i	$0.904817\pi$
$500$	−0.684334	+	2.55397i	−0.0306043	+	0.114217i
$501$	4.65413	−	4.07897i	0.207931	−	0.182235i
$502$	−3.83903	−	2.21647i	−0.171345	−	0.0989258i
$503$	3.40357	+	3.40357i	0.151758	+	0.151758i	0.778903	−	0.627145i	$-0.215777\pi$
$503$	3.40357	+	3.40357i	0.151758	+	0.151758i	−0.627145	+	0.778903i	$0.715777\pi$
$504$	16.2286	−	12.4364i	0.722879	−	0.553962i
$505$	−35.5674	+	35.5674i	−1.58273	+	1.58273i
$506$	−1.20752	+	2.09149i	−0.0536808	+	0.0929779i
$507$	0.104143	+	0.211349i	0.00462515	+	0.00938634i
$508$	4.40613	−	2.54388i	0.195490	−	0.112866i
$509$	4.35413	+	7.54158i	0.192993	+	0.334275i	0.946241	−	0.323463i	$-0.104847\pi$
$509$	4.35413	+	7.54158i	0.192993	+	0.334275i	−0.753247	+	0.657737i	$0.771514\pi$
$510$	3.04383	−	24.2018i	0.134783	−	1.07167i
$511$	13.1005	−	22.6908i	0.579533	−	1.00378i
$512$		−	25.4218i		−	1.12349i
$513$	0.431190	−	2.15709i	0.0190375	−	0.0952377i
$514$	−12.0913			−0.533327
$515$	−5.47610	−	20.4371i	−0.241306	−	0.900566i
$516$	−3.80079	−	2.54134i	−0.167320	−	0.111876i
$517$	−2.74458	+	10.2429i	−0.120707	+	0.450483i
$518$	21.6178	−	12.4810i	0.949832	−	0.548386i
$519$	−34.2918	−	11.6525i	−1.50524	−	0.511490i
$520$	27.8971	−	7.47500i	1.22337	−	0.327800i
$521$	22.7777	+	22.7777i	0.997911	+	0.997911i	0.999998	−	0.00208654i	$-0.000664166\pi$
$521$	22.7777	+	22.7777i	0.997911	+	0.997911i	−0.00208654	+	0.999998i	$0.500664\pi$
$522$	−2.23124	+	0.292319i	−0.0976588	+	0.0127945i
$523$	−23.6945			−1.03609			−0.518044	−	0.855354i	$-0.673340\pi$
$523$	−23.6945			−1.03609			−0.518044	+	0.855354i	$0.673340\pi$
$524$	0.307873	+	1.14900i	0.0134495	+	0.0501942i
$525$	5.88980	−	5.16194i	0.257052	−	0.225285i
$526$	−0.556843	−	0.964480i	−0.0242795	−	0.0420533i
$527$	−19.4089	+	29.4348i	−0.845465	+	1.28220i
$528$	7.42445	+	8.47134i	0.323108	+	0.368668i
$529$	19.1744	+	11.0703i	0.833667	+	0.481318i
$530$	−22.0597	+	22.0597i	−0.958213	+	0.958213i
$531$	−26.1878	−	20.1208i	−1.13645	−	0.873169i
$532$	0.225531	−	0.225531i	0.00977800	−	0.00977800i
$533$	35.1888	−	9.42881i	1.52420	−	0.408407i
$534$	6.09573	−	3.00370i	0.263788	−	0.129983i
$535$	−18.2274	+	10.5236i	−0.788041	+	0.454975i
$536$	−15.8288	+	9.13878i	−0.683701	+	0.394735i
$537$	1.16521	+	0.779102i	0.0502827	+	0.0336207i
$538$	−11.1407	+	2.98514i	−0.480309	+	0.128698i
$539$	2.68342	−	2.68342i	0.115583	−	0.115583i
$540$	0.295054	+	4.56777i	0.0126971	+	0.196565i
$541$	10.3465	−	10.3465i	0.444833	−	0.444833i	−0.448800	−	0.893632i	$-0.648148\pi$
$541$	10.3465	−	10.3465i	0.444833	−	0.444833i	0.893632	+	0.448800i	$0.148148\pi$
$542$	−15.0505	−	8.68940i	−0.646474	−	0.373242i
$543$	33.6306	−	6.67854i	1.44323	−	0.286604i
$544$	1.54439	+	7.52393i	0.0662154	+	0.322586i
$545$	24.5074	+	42.4481i	1.04978	+	1.81828i
$546$	17.3634	+	5.90019i	0.743086	+	0.252505i
$547$	−5.56060	−	20.7525i	−0.237754	−	0.887311i	−0.976888	−	0.213752i	$-0.931431\pi$
$547$	−5.56060	−	20.7525i	−0.237754	−	0.887311i	0.739134	−	0.673559i	$-0.235235\pi$
$548$	−2.70620			−0.115603
$549$	10.8000	+	14.0932i	0.460934	+	0.601484i
$550$	3.68141	+	3.68141i	0.156976	+	0.156976i
$551$	−0.237568	+	0.0636563i	−0.0101208	+	0.00271185i
$552$	−3.63728	+	3.18778i	−0.154813	+	0.135681i
$553$	8.41914	−	4.86079i	0.358018	−	0.206702i
$554$	4.57950	−	17.0909i	0.194564	−	0.726123i
$555$	−2.57307	+	39.0689i	−0.109221	+	1.65838i
$556$	−0.556024	−	2.07511i	−0.0235807	−	0.0880043i
$557$	21.6471			0.917217			0.458609	−	0.888638i	$-0.348348\pi$
$557$	21.6471			0.917217			0.458609	+	0.888638i	$0.348348\pi$
$558$	−12.6946	+	30.5931i	−0.537407	+	1.29511i
$559$		−	28.7319i		−	1.21523i
$560$	9.64613	−	16.7076i	0.407623	−	0.706025i
$561$	−11.4825	−	8.70568i	−0.484790	−	0.367554i
$562$	5.73935	+	9.94084i	0.242100	+	0.419329i
$563$	−30.5737	+	17.6517i	−1.28853	+	0.743931i	−0.978391	−	0.206761i	$-0.933708\pi$
$563$	−30.5737	+	17.6517i	−1.28853	+	0.743931i	−0.310135	+	0.950692i	$0.600374\pi$
$564$	−1.68478	+	2.51974i	−0.0709421	+	0.106100i
$565$	−2.25264	+	3.90168i	−0.0947692	+	0.164145i
$566$	−16.9720	+	16.9720i	−0.713385	+	0.713385i
$567$	−10.2038	+	17.6221i	−0.428518	+	0.740060i
$568$	−10.4469	−	10.4469i	−0.438344	−	0.438344i
$569$	8.28016	+	4.78055i	0.347122	+	0.200411i	0.663417	−	0.748250i	$-0.269106\pi$
$569$	8.28016	+	4.78055i	0.347122	+	0.200411i	−0.316295	+	0.948661i	$0.602439\pi$
$570$	−0.487835	−	2.45655i	−0.0204331	−	0.102894i
$571$	1.07726	−	4.02039i	0.0450819	−	0.168248i	−0.939715	−	0.341960i	$-0.888909\pi$
$571$	1.07726	−	4.02039i	0.0450819	−	0.168248i	0.984797	+	0.173712i	$0.0555760\pi$
$572$	0.630259	−	2.35216i	0.0263525	−	0.0983488i
$573$	3.26952	+	6.63519i	0.136586	+	0.277189i
$574$	14.6815	−	25.4291i	0.612794	−	1.06139i
$575$	−1.30999	+	1.30999i	−0.0546303	+	0.0546303i
$576$	10.1465	+	24.5396i	0.422772	+	1.02248i
$577$	29.6804			1.23561			0.617806	−	0.786330i	$-0.288022\pi$
$577$	29.6804			1.23561			0.617806	+	0.786330i	$0.288022\pi$
$578$	8.64646	+	20.1744i	0.359645	+	0.839144i
$579$	1.12921	+	1.28844i	0.0469285	+	0.0535458i
$580$	0.443208	−	0.255887i	0.0184032	−	0.0106251i
$581$	−28.3685	−	7.60131i	−1.17692	−	0.315356i
$582$	19.0116	+	21.6924i	0.788057	+	0.899177i
$583$	4.76987	+	17.8014i	0.197548	+	0.737258i
$584$	24.6651	+	24.6651i	1.02065	+	1.02065i
$585$	−22.8313	+	17.4962i	−0.943958	+	0.723381i
$586$		−	13.1270i		−	0.542271i
$587$	35.8435	+	20.6942i	1.47942	+	0.854143i	0.999729	−	0.0232951i	$-0.00741573\pi$
$587$	35.8435	+	20.6942i	1.47942	+	0.854143i	0.479690	+	0.877438i	$0.340749\pi$
$588$	0.973022	−	0.479461i	0.0401268	−	0.0197726i
$589$	−0.936958	+	3.49678i	−0.0386067	+	0.144082i
$590$	−36.3191	−	9.73168i	−1.49524	−	0.400647i
$591$	−16.7269	+	3.32172i	−0.688054	+	0.136637i
$592$	7.12831	+	26.6032i	0.292972	+	1.09338i
$593$			24.3871i			1.00146i	0.865604	+	0.500728i	$0.166934\pi$
$593$			24.3871i			1.00146i	−0.865604	+	0.500728i	$0.833066\pi$
$594$	−12.1352	−	5.99866i	−0.497912	−	0.246128i
$595$	−7.79004	+	23.4172i	−0.319360	+	0.960013i
$596$	−2.87327	+	4.97664i	−0.117694	+	0.203851i
$597$	−2.58913	−	13.0379i	−0.105966	−	0.533605i
$598$	−4.19020	−	1.12276i	−0.171350	−	0.0459131i
$599$	−3.58487	−	6.20919i	−0.146474	−	0.253700i	0.783448	−	0.621457i	$-0.213459\pi$
$599$	−3.58487	−	6.20919i	−0.146474	−	0.253700i	−0.929922	+	0.367757i	$0.880126\pi$
$600$	4.60855	+	9.35263i	0.188143	+	0.381820i
$601$	6.57071	−	1.76062i	0.268025	−	0.0718170i	−0.122304	−	0.992493i	$-0.539028\pi$
$601$	6.57071	−	1.76062i	0.268025	−	0.0718170i	0.390328	+	0.920676i	$0.372361\pi$
$602$	−16.3753	−	16.3753i	−0.667408	−	0.667408i
$603$	11.0907	−	14.4349i	0.451650	−	0.587835i
$604$		−	1.11474i		−	0.0453581i
$605$	−17.7051	+	4.74406i	−0.719813	+	0.192873i
$606$	2.79432	−	42.4284i	0.113512	−	1.72354i
$607$	17.0572	+	4.57046i	0.692330	+	0.185509i	0.587793	−	0.809012i	$-0.299997\pi$
$607$	17.0572	+	4.57046i	0.692330	+	0.185509i	0.104538	+	0.994521i	$0.466664\pi$
$608$	0.394317	+	0.682978i	0.0159917	+	0.0276984i
$609$	2.27182	+	0.149621i	0.0920588	+	0.00606296i
$610$	17.5071	+	10.1077i	0.708842	+	0.409250i
$611$	−19.0479			−0.770594
$612$	−2.30699	−	3.41208i	−0.0932546	−	0.137925i
$613$	−12.5392			−0.506453			−0.253226	−	0.967407i	$-0.581492\pi$
$613$	−12.5392			−0.506453			−0.253226	+	0.967407i	$0.581492\pi$
$614$	−8.68818	−	5.01612i	−0.350626	−	0.202434i
$615$	20.3572	+	41.3132i	0.820883	+	1.66591i
$616$	−6.87574	−	11.9091i	−0.277031	−	0.479832i
$617$	−10.7025	−	2.86771i	−0.430864	−	0.115450i	0.0368674	−	0.999320i	$-0.488262\pi$
$617$	−10.7025	−	2.86771i	−0.430864	−	0.115450i	−0.467732	+	0.883870i	$0.654929\pi$
$618$	14.8683	+	9.94142i	0.598089	+	0.399903i
$619$	−8.63138	+	2.31277i	−0.346925	+	0.0929582i	−0.428074	−	0.903744i	$-0.640808\pi$
$619$	−8.63138	+	2.31277i	−0.346925	+	0.0929582i	0.0811491	+	0.996702i	$0.474141\pi$
$620$		−	7.53280i		−	0.302525i
$621$	2.13456	−	4.31817i	0.0856568	−	0.173282i
$622$	−9.04513	−	9.04513i	−0.362676	−	0.362676i
$623$	−6.64114	+	1.77949i	−0.266072	+	0.0712937i
$624$	−11.2465	+	16.8201i	−0.450220	+	0.673342i
$625$	−15.4992	−	26.8454i	−0.619969	−	1.07382i
$626$	5.72677	+	1.53448i	0.228888	+	0.0613303i
$627$	−1.40085	−	0.476016i	−0.0559445	−	0.0190103i
$628$	−3.58497	+	6.20935i	−0.143056	+	0.247780i
$629$	−15.7751	−	31.5027i	−0.628996	−	1.25609i
$630$	−3.04063	+	22.9840i	−0.121142	+	0.915706i
$631$			29.3068i			1.16668i	0.812226	+	0.583342i	$0.198255\pi$
$631$			29.3068i			1.16668i	−0.812226	+	0.583342i	$0.801745\pi$
$632$	3.34976	+	12.5015i	0.133246	+	0.497282i
$633$	−30.1141	−	34.3604i	−1.19693	−	1.36570i
$634$	0.583239	+	0.156278i	0.0231634	+	0.00620661i
$635$	−10.4616	+	39.0433i	−0.415156	+	1.54939i
$636$	−0.346187	+	5.25642i	−0.0137272	+	0.208431i
$637$	5.90339	+	3.40832i	0.233901	+	0.135043i
$638$			1.51351i			0.0599206i
$639$	13.5908	+	5.63953i	0.537644	+	0.223096i
$640$	14.4088	+	14.4088i	0.569559	+	0.569559i
$641$	8.55683	+	31.9345i	0.337974	+	1.26134i	0.900608	+	0.434631i	$0.143121\pi$
$641$	8.55683	+	31.9345i	0.337974	+	1.26134i	−0.562634	+	0.826706i	$0.690212\pi$
$642$	5.72435	−	16.8460i	0.225922	−	0.664857i
$643$	12.9994	+	3.48317i	0.512645	+	0.137363i	0.505862	−	0.862614i	$-0.331174\pi$
$643$	12.9994	+	3.48317i	0.512645	+	0.137363i	0.00678258	+	0.999977i	$0.497841\pi$
$644$	0.604849	−	0.349210i	0.0238344	−	0.0137608i
$645$	35.6283	−	7.07526i	1.40286	−	0.278588i
$646$	1.49625	+	1.68529i	0.0588692	+	0.0663068i
$647$	−15.5667			−0.611990			−0.305995	−	0.952033i	$-0.598989\pi$
$647$	−15.5667			−0.611990			−0.305995	+	0.952033i	$0.598989\pi$
$648$	−19.1453	−	19.1936i	−0.752097	−	0.753994i
$649$	−15.7062	+	15.7062i	−0.616523	+	0.616523i
$650$	−4.67590	+	8.09889i	−0.183404	+	0.317665i
$651$	18.6267	−	27.8579i	0.730039	−	1.09184i
$652$	−1.31505	+	4.90782i	−0.0515012	+	0.192205i
$653$	5.14779	−	19.2118i	0.201449	−	0.751817i	−0.789054	−	0.614324i	$-0.789429\pi$
$653$	5.14779	−	19.2118i	0.201449	−	0.751817i	0.990503	−	0.137493i	$-0.0439044\pi$
$654$	−39.2310	−	13.3309i	−1.53405	−	0.521279i
$655$	−8.18430	−	4.72521i	−0.319787	−	0.184629i
$656$	22.9084	+	22.9084i	0.894422	+	0.894422i
$657$	−32.0878	−	13.3149i	−1.25186	−	0.519463i
$658$	−10.8560	+	10.8560i	−0.423212	+	0.423212i
$659$	11.4840	−	19.8908i	0.447352	−	0.774836i	−0.550861	−	0.834597i	$-0.685701\pi$
$659$	11.4840	−	19.8908i	0.447352	−	0.774836i	0.998213	+	0.0597610i	$0.0190339\pi$
$660$	3.07194	+	0.202317i	0.119575	+	0.00787518i
$661$	−12.5958	+	7.27221i	−0.489922	+	0.282856i	−0.724542	−	0.689231i	$-0.757949\pi$
$661$	−12.5958	+	7.27221i	−0.489922	+	0.282856i	0.234620	+	0.972087i	$0.424615\pi$
$662$	17.6071	+	30.4963i	0.684318	+	1.18527i
$663$	9.76649	−	23.9698i	0.379299	−	0.930912i
$664$	19.5498	−	33.8613i	0.758680	−	1.31407i
$665$			2.53394i			0.0982620i
$666$	−20.1322	−	26.2710i	−0.780106	−	1.01798i
$667$	−0.538568			−0.0208534
$668$	−0.307931	−	1.14922i	−0.0119142	−	0.0444645i
$669$	−14.2019	+	6.99804i	−0.549077	+	0.270560i
$670$	5.36418	−	20.0194i	0.207236	−	0.773416i
$671$	10.3421	−	5.97102i	0.399253	−	0.230509i
$672$	−1.42198	−	7.16054i	−0.0548539	−	0.276224i
$673$	15.2459	−	4.08513i	0.587686	−	0.157470i	0.0472908	−	0.998881i	$-0.484941\pi$
$673$	15.2459	−	4.08513i	0.587686	−	0.157470i	0.540396	+	0.841411i	$0.318275\pi$
$674$	−6.00009	−	6.00009i	−0.231115	−	0.231115i
$675$	−7.80082	−	6.85418i	−0.300254	−	0.263818i
$676$	0.0452967			0.00174218
$677$	9.11573	+	34.0204i	0.350346	+	1.30751i	0.886241	+	0.463224i	$0.153308\pi$
$677$	9.11573	+	34.0204i	0.350346	+	1.30751i	−0.535895	+	0.844285i	$0.680026\pi$
$678$	−0.741820	−	3.73553i	−0.0284894	−	0.143462i
$679$	−14.5916	−	25.2734i	−0.559974	−	0.969904i
$680$	−27.4292	−	18.0864i	−1.05186	−	0.693584i
$681$	1.57074	−	4.62248i	0.0601910	−	0.177134i
$682$	19.2929	+	11.1387i	0.738761	+	0.426524i
$683$	28.1642	−	28.1642i	1.07767	−	1.07767i	0.0809552	−	0.996718i	$-0.474203\pi$
$683$	28.1642	−	28.1642i	1.07767	−	1.07767i	0.996718	−	0.0809552i	$-0.0257971\pi$
$684$	−0.335349	−	0.257658i	−0.0128224	−	0.00985180i
$685$	15.2027	−	15.2027i	0.580865	−	0.580865i
$686$	25.0592	−	6.71458i	0.956763	−	0.256364i
$687$	−2.31276	+	35.1164i	−0.0882371	+	1.33977i
$688$	22.1281	−	12.7757i	0.843626	−	0.487068i
$689$	−28.6686	+	16.5518i	−1.09219	+	0.630575i
$690$	0.360413	−	5.47243i	0.0137207	−	0.208332i
$691$	25.6447	−	6.87147i	0.975570	−	0.261403i	0.264392	−	0.964415i	$-0.414829\pi$
$691$	25.6447	−	6.87147i	0.975570	−	0.261403i	0.711178	+	0.703012i	$0.248162\pi$
$692$	−4.92344	+	4.92344i	−0.187161	+	0.187161i
$693$	10.8604	+	8.34434i	0.412552	+	0.316975i
$694$	11.8422	−	11.8422i	0.449523	−	0.449523i
$695$	14.7810	+	8.53381i	0.560675	+	0.323706i
$696$	−0.975204	+	2.86989i	−0.0369650	+	0.108783i
$697$	−34.5986	−	22.8139i	−1.31052	−	0.864138i
$698$	6.62507	+	11.4750i	0.250763	+	0.434334i
$699$	−2.31957	−	11.6805i	−0.0877341	−	0.441796i
$700$	−0.389687	−	1.45433i	−0.0147288	−	0.0549686i
$701$	−9.93026			−0.375061			−0.187530	−	0.982259i	$-0.560048\pi$
$701$	−9.93026			−0.375061			−0.187530	+	0.982259i	$0.560048\pi$
$702$	4.76625	−	23.8438i	0.179890	−	0.899927i
$703$	−2.55793	−	2.55793i	−0.0964741	−	0.0964741i
$704$	17.2515	−	4.62252i	0.650190	−	0.174218i
$705$	−4.69055	−	23.6198i	−0.176656	−	0.889575i
$706$	15.3944	−	8.88796i	0.579376	−	0.334503i
$707$	−11.1343	+	41.5539i	−0.418750	+	1.56280i
$708$	−5.69515	+	2.80631i	−0.214037	+	0.105468i
$709$	0.750499	+	2.80090i	0.0281856	+	0.105190i	0.978586	−	0.205840i	$-0.0659927\pi$
$709$	0.750499	+	2.80090i	0.0281856	+	0.105190i	−0.950400	+	0.311030i	$0.899326\pi$
$710$	16.7530			0.628729
$711$	−7.84056	−	10.2314i	−0.294044	−	0.383706i
$712$		−	9.15333i		−	0.343035i
$713$	−3.96360	+	6.86515i	−0.148438	+	0.257102i
$714$	−8.09497	−	19.2275i	−0.302947	−	0.719570i
$715$	9.67317	+	16.7544i	0.361756	+	0.626580i
$716$	0.233370	−	0.134737i	0.00872146	−	0.00503534i
$717$	−9.35682	−	0.616237i	−0.349437	−	0.0230138i
$718$	15.3197	−	26.5345i	0.571726	−	0.990258i
$719$	2.82342	−	2.82342i	0.105296	−	0.105296i	−0.652496	−	0.757792i	$-0.726278\pi$
$719$	2.82342	−	2.82342i	0.105296	−	0.105296i	0.757792	+	0.652496i	$0.226278\pi$
$720$	−23.6268	−	9.80397i	−0.880518	−	0.365372i
$721$	−12.7956	−	12.7956i	−0.476534	−	0.476534i
$722$	−21.0445	−	12.1500i	−0.783194	−	0.452177i
$723$	9.21797	+	3.13231i	0.342820	+	0.116492i
$724$	1.70606	−	6.36711i	0.0634053	−	0.236632i
$725$	−0.300497	+	1.12147i	−0.0111602	+	0.0416504i
$726$	8.61245	−	12.8807i	0.319638	−	0.478046i
$727$	9.53899	−	16.5220i	0.353782	−	0.612768i	−0.633127	−	0.774048i	$-0.718229\pi$
$727$	9.53899	−	16.5220i	0.353782	−	0.612768i	0.986909	+	0.161280i	$0.0515623\pi$
$728$	17.4663	−	17.4663i	0.647344	−	0.647344i
$729$	24.9252	+	10.3796i	0.923155	+	0.384428i
$730$	−39.5537			−1.46395
$731$	−24.4424	+	21.7007i	−0.904035	+	0.802630i
$732$	3.34811	−	0.664885i	0.123750	−	0.0245749i
$733$	−13.5434	+	7.81930i	−0.500238	+	0.288812i	−0.728812	−	0.684714i	$-0.759927\pi$
$733$	−13.5434	+	7.81930i	−0.500238	+	0.288812i	0.228574	+	0.973527i	$0.426594\pi$
$734$	40.7479	+	10.9184i	1.50403	+	0.403004i
$735$	−2.77269	+	8.15965i	−0.102272	+	0.300973i
$736$	0.446959	+	1.66807i	0.0164751	+	0.0614860i
$737$	−8.65739	−	8.65739i	−0.318899	−	0.318899i
$738$	−35.9602	−	14.9217i	−1.32371	−	0.549276i
$739$		−	49.1273i		−	1.80718i	−0.428400	−	0.903589i	$-0.640923\pi$
$739$		−	49.1273i		−	1.80718i	0.428400	−	0.903589i	$-0.359077\pi$
$740$	6.51878	+	3.76362i	0.239635	+	0.138353i
$741$	0.174649	−	2.65184i	0.00641589	−	0.0974176i
$742$	−6.90577	+	25.7727i	−0.253519	+	0.946145i
$743$	−26.8616	−	7.19753i	−0.985455	−	0.264052i	−0.270115	−	0.962828i	$-0.587062\pi$
$743$	−26.8616	−	7.19753i	−0.985455	−	0.264052i	−0.715340	+	0.698776i	$0.753728\pi$
$744$	29.4056	+	33.5520i	1.07806	+	1.23007i
$745$	−11.8162	−	44.0986i	−0.432912	−	1.61565i
$746$			1.20664i			0.0441783i
$747$	−5.10719	+	38.6051i	−0.186862	+	1.41249i
$748$	−2.47702	+	1.24038i	−0.0905688	+	0.0453528i
$749$	−9.00048	+	15.5893i	−0.328870	+	0.569620i
$750$	16.8131	+	5.71319i	0.613928	+	0.208616i
$751$	27.0630	+	7.25150i	0.987542	+	0.264611i	0.716218	−	0.697877i	$-0.245872\pi$
$751$	27.0630	+	7.25150i	0.987542	+	0.264611i	0.271324	+	0.962488i	$0.412538\pi$
$752$	−8.46964	−	14.6698i	−0.308856	−	0.534954i
$753$	3.30541	−	4.94353i	0.120456	−	0.180152i
$754$	−2.62601	+	0.703638i	−0.0956337	+	0.0256250i
$755$	6.26231	+	6.26231i	0.227909	+	0.227909i
$756$	2.17187	+	3.25709i	0.0789900	+	0.118459i
$757$		−	14.7045i		−	0.534446i	−0.963635	−	0.267223i	$-0.913894\pi$
$757$		−	14.7045i		−	0.534446i	0.963635	−	0.267223i	$-0.0861060\pi$
$758$	−13.7541	+	3.68540i	−0.499572	+	0.133860i
$759$	−2.69321	−	1.80077i	−0.0977574	−	0.0653639i
$760$	−3.25852	−	0.873117i	−0.118199	−	0.0316713i
$761$	−19.2342	−	33.3146i	−0.697240	−	1.20765i	−0.969420	−	0.245408i	$-0.921078\pi$
$761$	−19.2342	−	33.3146i	−0.697240	−	1.20765i	0.272180	−	0.962246i	$-0.412255\pi$
$762$	−15.1029	−	30.6500i	−0.547120	−	1.11033i
$763$	36.3044	+	20.9604i	1.31431	+	0.758816i
$764$	1.42207			0.0514485
$765$	32.1282	+	6.20811i	1.16160	+	0.224455i
$766$	−24.1646			−0.873104
$767$	−34.5528	−	19.9491i	−1.24763	−	0.720320i
$768$	13.4079	+	0.883041i	0.483816	+	0.0318640i
$769$	19.5798	+	33.9133i	0.706067	+	1.22294i	0.966305	+	0.257399i	$0.0828655\pi$
$769$	19.5798	+	33.9133i	0.706067	+	1.22294i	−0.260238	+	0.965544i	$0.583801\pi$
$770$	15.0620	+	4.03584i	0.542796	+	0.145442i
$771$	1.06597	−	16.1855i	0.0383900	−	0.582906i
$772$	0.318147	−	0.0852472i	0.0114504	−	0.00306811i
$773$			48.3356i			1.73851i	0.494362	+	0.869256i	$0.335402\pi$
$773$			48.3356i			1.73851i	−0.494362	+	0.869256i	$0.664598\pi$
$774$	−18.7080	+	24.3490i	−0.672445	+	0.875206i
$775$	12.0839	+	12.0839i	0.434068	+	0.434068i
$776$	37.5281	−	10.0556i	1.34718	−	0.360976i
$777$	14.8013	+	30.0379i	0.530994	+	1.07761i
$778$	0.764759	+	1.32460i	0.0274180	+	0.0474893i
$779$	−4.11023	−	1.10133i	−0.147264	−	0.0394594i
$780$	1.07713	+	5.42400i	0.0385673	+	0.194211i
$781$	4.94832	−	8.57075i	0.177065	−	0.306685i
$782$	2.20964	+	4.41262i	0.0790167	+	0.157795i
$783$	−0.194593	−	3.01251i	−0.00695418	−	0.107658i
$784$			6.06205i			0.216502i
$785$	−14.7431	−	55.0219i	−0.526203	−	1.96381i
$786$	7.83577	−	1.55607i	0.279492	−	0.0555030i
$787$	42.1167	+	11.2851i	1.50130	+	0.402272i	0.913535	−	0.406761i	$-0.133342\pi$
$787$	42.1167	+	11.2851i	1.50130	+	0.402272i	0.587764	+	0.809032i	$0.300008\pi$
$788$	−0.848548	+	3.16682i	−0.0302283	+	0.112813i
$789$	1.34015	−	0.660362i	0.0477104	−	0.0235095i
$790$	−12.7097	−	7.33797i	−0.452192	−	0.261073i
$791$			3.85321i			0.137004i
$792$	−14.4726	+	11.0907i	−0.514260	+	0.394091i
$793$	15.1681	+	15.1681i	0.538634	+	0.538634i
$794$	0.787027	+	2.93722i	0.0279305	+	0.104238i
$795$	−27.5844	−	31.4739i	−0.978317	−	1.11627i
$796$	−2.46840	−	0.661405i	−0.0874900	−	0.0234429i
$797$	16.6610	−	9.61921i	0.590162	−	0.340730i	−0.175000	−	0.984568i	$-0.555992\pi$
$797$	16.6610	−	9.61921i	0.590162	−	0.340730i	0.765161	+	0.643838i	$0.222659\pi$
$798$	−1.41183	−	1.61091i	−0.0499783	−	0.0570256i
$799$	14.3865	+	16.2041i	0.508958	+	0.573261i
$800$	3.72285			0.131623
$801$	3.48335	+	8.42456i	0.123078	+	0.297667i
$802$	3.18378	−	3.18378i	0.112423	−	0.112423i
$803$	−11.6829	+	20.2355i	−0.412282	+	0.714094i
$804$	−1.54686	−	3.13921i	−0.0545535	−	0.110711i
$805$	−1.43611	+	5.35964i	−0.0506163	+	0.188902i
$806$	−10.3569	+	38.6523i	−0.364805	+	1.36147i
$807$	−3.01375	−	15.1761i	−0.106089	−	0.534224i
$808$	−49.5997	−	28.6364i	−1.74491	−	1.00742i
$809$	13.6338	+	13.6338i	0.479339	+	0.479339i	0.904920	−	0.425581i	$-0.139930\pi$
$809$	13.6338	+	13.6338i	0.479339	+	0.479339i	−0.425581	+	0.904920i	$0.639930\pi$
$810$	30.7406	+	0.0387180i	1.08012	+	0.00136041i
$811$	−3.95207	+	3.95207i	−0.138776	+	0.138776i	−0.773082	−	0.634306i	$-0.781286\pi$
$811$	−3.95207	+	3.95207i	−0.138776	+	0.138776i	0.634306	+	0.773082i	$0.281286\pi$
$812$	0.218851	−	0.379061i	0.00768016	−	0.0133024i
$813$	12.9585	−	19.3805i	0.454474	−	0.679705i
$814$	−19.2786	+	11.1305i	−0.675715	+	0.390124i
$815$	−20.1832	−	34.9584i	−0.706988	−	1.22454i
$816$	22.8032	−	3.13647i	0.798272	−	0.109798i
$817$	−1.67802	+	2.90641i	−0.0587064	+	0.101682i
$818$			2.07016i			0.0723816i
$819$	−9.42876	+	22.7226i	−0.329467	+	0.793990i
$820$	8.85431			0.309206
$821$	−12.9504	−	48.3314i	−0.451971	−	1.68678i	−0.696843	−	0.717223i	$-0.745413\pi$
$821$	−12.9504	−	48.3314i	−0.451971	−	1.68678i	0.244872	−	0.969555i	$-0.421254\pi$
$822$	−1.19439	+	18.1353i	−0.0416590	+	0.632542i
$823$	−6.46517	+	24.1284i	−0.225362	+	0.841062i	0.756897	+	0.653534i	$0.226714\pi$
$823$	−6.46517	+	24.1284i	−0.225362	+	0.841062i	−0.982259	+	0.187528i	$0.939952\pi$
$824$	20.8635	−	12.0455i	0.726814	−	0.419626i
$825$	−5.25248	+	4.60338i	−0.182868	+	0.160269i
$826$	−31.0625	+	8.32317i	−1.08080	+	0.289600i
$827$	−19.2646	−	19.2646i	−0.669896	−	0.669896i	0.287795	−	0.957692i	$-0.407078\pi$
$827$	−19.2646	−	19.2646i	−0.669896	−	0.669896i	−0.957692	+	0.287795i	$0.907078\pi$
$828$	−0.563282	−	0.735042i	−0.0195754	−	0.0255445i
$829$	−8.93195			−0.310220			−0.155110	−	0.987897i	$-0.549573\pi$
$829$	−8.93195			−0.310220			−0.155110	+	0.987897i	$0.549573\pi$
$830$	11.4751	+	42.8258i	0.398308	+	1.48650i
$831$	22.4742	+	7.63685i	0.779621	+	0.264919i
$832$	16.0405	+	27.7830i	0.556106	+	0.963204i
$833$	−1.55925	−	7.59629i	−0.0540247	−	0.263196i
$834$	−14.1515	+	2.81028i	−0.490028	+	0.0973122i
$835$	8.18585	+	4.72610i	0.283283	+	0.163554i
$836$	−0.201127	+	0.201127i	−0.00695611	+	0.00695611i
$837$	−39.8328	−	19.6901i	−1.37682	−	0.680591i
$838$	−28.6687	+	28.6687i	−0.990344	+	0.990344i
$839$	−29.8162	+	7.98922i	−1.02937	+	0.275818i	−0.733701	−	0.679473i	$-0.762209\pi$
$839$	−29.8162	+	7.98922i	−1.02937	+	0.275818i	−0.295667	+	0.955291i	$0.595542\pi$
$840$	25.9597	+	17.3576i	0.895695	+	0.598893i
$841$	24.8224	−	14.3312i	0.855946	−	0.494181i
$842$	15.8610	−	9.15735i	0.546606	−	0.315583i
$843$	−13.8128	+	6.80631i	−0.475738	+	0.234422i
$844$	−8.48441	+	2.27339i	−0.292045	+	0.0782533i
$845$	−0.254464	+	0.254464i	−0.00875384	+	0.00875384i
$846$	16.1422	+	12.4025i	0.554979	+	0.426406i
$847$	−11.0851	+	11.0851i	−0.380888	+	0.380888i
$848$	−25.4950	−	14.7196i	−0.875503	−	0.505472i
$849$	−21.2225	−	24.2149i	−0.728353	−	0.831055i
$850$	10.4214	−	2.13914i	0.357451	−	0.0733718i
$851$	−3.96067	−	6.86008i	−0.135770	−	0.235161i
$852$	2.12742	−	1.86451i	0.0728842	−	0.0638772i
$853$	−9.61776	−	35.8940i	−0.329306	−	1.22899i	−0.909912	−	0.414802i	$-0.863851\pi$
$853$	−9.61776	−	35.8940i	−0.329306	−	1.22899i	0.580606	−	0.814185i	$-0.302816\pi$
$854$	17.2896			0.591637
$855$	3.33135	−	0.436446i	0.113930	−	0.0149262i
$856$	−16.9457	−	16.9457i	−0.579194	−	0.579194i
$857$	30.2796	−	8.11340i	1.03433	−	0.277149i	0.298570	−	0.954388i	$-0.403490\pi$
$857$	30.2796	−	8.11340i	1.03433	−	0.277149i	0.735763	+	0.677239i	$0.236824\pi$
$858$	−15.4846	−	5.26175i	−0.528635	−	0.179633i
$859$	−6.01084	+	3.47036i	−0.205087	+	0.118407i	−0.599026	−	0.800729i	$-0.704445\pi$
$859$	−6.01084	+	3.47036i	−0.205087	+	0.118407i	0.393939	+	0.919137i	$0.371112\pi$
$860$	1.80740	−	6.74533i	0.0616320	−	0.230014i
$861$	32.7451	+	21.8945i	1.11595	+	0.746162i
$862$	7.10426	+	26.5135i	0.241972	+	0.903052i
$863$	29.9759			1.02039			0.510195	−	0.860059i	$-0.329573\pi$
$863$	29.9759			1.02039			0.510195	+	0.860059i	$0.329573\pi$
$864$	−9.16898	+	3.10279i	−0.311935	+	0.105559i
$865$		−	55.3170i		−	1.88084i
$866$	21.3022	−	36.8964i	0.723877	−	1.25379i
$867$	−27.7677	+	9.79559i	−0.943041	+	0.332676i
$868$	−3.22127	−	5.57941i	−0.109337	−	0.189377i
$869$	−7.50813	+	4.33482i	−0.254696	+	0.147049i
$870$	−1.51919	−	3.08305i	−0.0515052	−	0.104525i
$871$	10.9961	−	19.0458i	0.372588	−	0.645342i
$872$	−39.4633	+	39.4633i	−1.33640	+	1.33640i
$873$	−30.7135	+	23.5366i	−1.03949	+	0.796592i
$874$	0.358292	+	0.358292i	0.0121194	+	0.0121194i
$875$	−15.5589	−	8.98294i	−0.525987	−	0.303679i
$876$	−5.02282	+	4.40210i	−0.169705	+	0.148733i
$877$	3.50577	−	13.0837i	0.118381	−	0.441806i	−0.881136	−	0.472863i	$-0.843221\pi$
$877$	3.50577	−	13.0837i	0.118381	−	0.441806i	0.999518	+	0.0310571i	$0.00988736\pi$
$878$	12.5263	−	46.7490i	0.422744	−	1.57770i
$879$	17.5718	+	1.15727i	0.592682	+	0.0390339i
$880$	−8.60235	+	14.8997i	−0.289985	+	0.502269i
$881$	−3.84653	+	3.84653i	−0.129593	+	0.129593i	−0.768928	−	0.639335i	$-0.779210\pi$
$881$	−3.84653	+	3.84653i	−0.129593	+	0.129593i	0.639335	+	0.768928i	$0.279210\pi$
$882$	−2.78361	−	6.73222i	−0.0937290	−	0.226686i
$883$	0.406755			0.0136884			0.00684419	−	0.999977i	$-0.497821\pi$
$883$	0.406755			0.0136884			0.00684419	+	0.999977i	$0.497821\pi$
$884$	−3.30369	−	3.72108i	−0.111115	−	0.125153i
$885$	16.2287	−	47.7589i	0.545523	−	1.60540i
$886$	−33.6795	+	19.4449i	−1.13148	+	0.653263i
$887$	39.3980	+	10.5567i	1.32286	+	0.354458i	0.850047	−	0.526707i	$-0.176574\pi$
$887$	39.3980	+	10.5567i	1.32286	+	0.354458i	0.472808	+	0.881165i	$0.343240\pi$
$888$	−43.7273	+	8.68360i	−1.46739	+	0.291402i
$889$	8.94746	+	33.3924i	0.300088	+	1.11994i
$890$	7.33927	+	7.33927i	0.246013	+	0.246013i
$891$	9.09964	−	15.7153i	0.304850	−	0.526482i
$892$			3.04378i			0.101913i
$893$	1.92681	+	1.11244i	0.0644782	+	0.0372265i
$894$	32.0823	+	21.4513i	1.07299	+	0.717440i
$895$	−0.554099	+	2.06792i	−0.0185215	+	0.0691231i
$896$	16.8340	+	4.51067i	0.562386	+	0.150691i
$897$	1.87234	−	5.51002i	0.0625155	−	0.183974i
$898$	3.28107	+	12.2451i	0.109491	+	0.408625i
$899$			4.96800i			0.165692i
$900$	−1.84488	+	0.762814i	−0.0614960	+	0.0254271i
$901$	35.7337	+	11.8872i	1.19046	+	0.396022i
$902$	−13.0929	+	22.6775i	−0.435944	+	0.755078i
$903$	23.3636	−	20.4764i	0.777493	−	0.681410i
$904$	−4.95503	−	1.32770i	−0.164802	−	0.0441585i
$905$	26.1845	+	45.3529i	0.870402	+	1.50758i
$906$	−7.47031	−	0.491993i	−0.248185	−	0.0163454i
$907$	47.3114	−	12.6771i	1.57095	−	0.420935i	0.634840	−	0.772644i	$-0.281066\pi$
$907$	47.3114	−	12.6771i	1.57095	−	0.420935i	0.936109	+	0.351709i	$0.114399\pi$
$908$	−0.663671	−	0.663671i	−0.0220247	−	0.0220247i
$909$	56.5484	+	7.48097i	1.87559	+	0.248128i
$910$			28.0094i			0.928504i
$911$	25.1368	−	6.73538i	0.832819	−	0.223153i	0.182876	−	0.983136i	$-0.441459\pi$
$911$	25.1368	−	6.73538i	0.832819	−	0.223153i	0.649943	+	0.759983i	$0.274793\pi$
$912$	2.11999	−	1.04463i	0.0701998	−	0.0345912i
$913$	25.2988	+	6.77880i	0.837269	+	0.224345i
$914$	5.17870	+	8.96978i	0.171296	+	0.296694i
$915$	−15.0736	+	22.5439i	−0.498319	+	0.745279i
$916$	5.85929	+	3.38286i	0.193596	+	0.111773i
$917$	−8.08261			−0.266911
$918$	−23.8839	+	13.9541i	−0.788287	+	0.460555i
$919$	10.9358			0.360739			0.180370	−	0.983599i	$-0.442271\pi$
$919$	10.9358			0.360739			0.180370	+	0.983599i	$0.442271\pi$
$920$	−6.39738	−	3.69353i	−0.210915	−	0.121772i
$921$	7.48053	−	11.1878i	0.246492	−	0.368650i
$922$	−11.6287	−	20.1414i	−0.382969	−	0.663322i
$923$	17.1711	+	4.60098i	0.565194	+	0.151443i
$924$	2.36185	−	1.16381i	0.0776990	−	0.0382865i
$925$	−16.4948	+	4.41976i	−0.542345	+	0.145321i
$926$			8.24383i			0.270909i
$927$	−14.6184	+	19.0262i	−0.480131	+	0.624903i
$928$	0.765277	+	0.765277i	0.0251214	+	0.0251214i
$929$	−30.8676	+	8.27095i	−1.01273	+	0.271361i	−0.726771	−	0.686880i	$-0.758980\pi$
$929$	−30.8676	+	8.27095i	−1.01273	+	0.271361i	−0.285962	+	0.958241i	$0.592313\pi$
$930$	−50.4803	−	3.32462i	−1.65531	−	0.109018i
$931$	−0.398109	−	0.689546i	−0.0130475	−	0.0225989i
$932$	−2.21140	−	0.592543i	−0.0724369	−	0.0194094i
$933$	12.9052	−	11.3104i	0.422498	−	0.370286i
$934$	−16.4482	+	28.4891i	−0.538200	+	0.932190i
$935$	6.94710	−	20.8833i	0.227194	−	0.682958i
$936$	−25.9712	−	19.9544i	−0.848895	−	0.652230i
$937$			31.1066i			1.01621i	0.861295	+	0.508105i	$0.169654\pi$
$937$			31.1066i			1.01621i	−0.861295	+	0.508105i	$0.830346\pi$
$938$	−4.58779	−	17.1219i	−0.149797	−	0.559049i
$939$	−2.55893	+	7.53058i	−0.0835076	+	0.245751i
$940$	−4.47182	−	1.19822i	−0.145855	−	0.0390816i
$941$	6.89056	−	25.7159i	0.224626	−	0.838315i	−0.757928	−	0.652338i	$-0.773788\pi$
$941$	6.89056	−	25.7159i	0.224626	−	0.838315i	0.982554	−	0.185977i	$-0.0595451\pi$
$942$	40.0291	+	26.7648i	1.30422	+	0.872045i
$943$	−8.06954	−	4.65895i	−0.262780	−	0.151716i
$944$		−	35.4815i		−	1.15482i
$945$	−30.4984	−	6.09646i	−0.992112	−	0.198318i
$946$	14.6034	+	14.6034i	0.474797	+	0.474797i
$947$	1.47438	+	5.50246i	0.0479109	+	0.178806i	0.985735	−	0.168305i	$-0.0538294\pi$
$947$	1.47438	+	5.50246i	0.0479109	+	0.178806i	−0.937824	+	0.347111i	$0.887163\pi$
$948$	−2.43065	+	0.482691i	−0.0789439	+	0.0156771i
$949$	−40.5408	−	10.8629i	−1.31601	−	0.352624i
$950$	0.945991	−	0.546168i	0.0306920	−	0.0177200i
$951$	−0.260613	+	0.766947i	−0.00845095	+	0.0248700i
$952$	−28.0506	−	1.66669i	−0.909126	−	0.0540176i
$953$	−3.85323			−0.124818			−0.0624091	−	0.998051i	$-0.519878\pi$
$953$	−3.85323			−0.124818			−0.0624091	+	0.998051i	$0.519878\pi$
$954$	35.0726	+	4.63987i	1.13552	+	0.150221i
$955$	−7.98878	+	7.98878i	−0.258511	+	0.258511i
$956$	−0.901369	+	1.56122i	−0.0291524	+	0.0504934i
$957$	−2.02599	−	0.133431i	−0.0654910	−	0.00431322i
$958$	10.0444	−	37.4862i	0.324520	−	1.21112i
$959$	4.75918	−	17.7615i	0.153682	−	0.573549i
$960$	−30.5017	+	26.7323i	−0.984438	+	0.862780i
$961$	36.4806	+	21.0621i	1.17679	+	0.679421i
$962$	−28.2746	−	28.2746i	−0.911609	−	0.911609i
$963$	22.0454	+	9.14776i	0.710402	+	0.294782i
$964$	1.32347	−	1.32347i	0.0426260	−	0.0426260i
$965$	−1.30837	+	2.26616i	−0.0421178	+	0.0729502i
$966$	−2.07324	−	4.20745i	−0.0667054	−	0.135373i
$967$	−45.8855	+	26.4920i	−1.47558	+	0.851925i	−0.999621	−	0.0275443i	$-0.991231\pi$
$967$	−45.8855	+	26.4920i	−1.47558	+	0.851925i	−0.475956	+	0.879469i	$0.657898\pi$
$968$	−10.4353	−	18.0744i	−0.335403	−	0.580935i
$969$	−2.38784	+	1.85431i	−0.0767084	+	0.0595690i
$970$	−22.0278	+	38.1533i	−0.707271	+	1.22503i
$971$		−	1.60076i		−	0.0513709i	−0.999670	−	0.0256854i	$-0.991823\pi$
$971$		−	1.60076i		−	0.0513709i	0.999670	−	0.0256854i	$-0.00817683\pi$
$972$	3.90798	−	3.41634i	0.125349	−	0.109579i
$973$	14.5973			0.467969
$974$	5.13255	+	19.1549i	0.164457	+	0.613764i
$975$	−10.4290	−	6.97316i	−0.333994	−	0.223320i
$976$	−4.93730	+	18.4263i	−0.158039	+	0.589810i
$977$	14.7424	−	8.51152i	0.471650	−	0.272308i	−0.245280	−	0.969452i	$-0.578880\pi$
$977$	14.7424	−	8.51152i	0.471650	−	0.272308i	0.716930	+	0.697145i	$0.245547\pi$
$978$	32.3089	+	10.9787i	1.03312	+	0.351061i
$979$	5.92252	−	1.58694i	0.189285	−	0.0507187i
$980$	1.17152	+	1.17152i	0.0374228	+	0.0374228i
$981$	21.3033	−	51.3394i	0.680163	−	1.63914i
$982$	−24.0813			−0.768465
$983$	−7.10960	−	26.5334i	−0.226761	−	0.846284i	−0.981691	−	0.190479i	$-0.938996\pi$
$983$	−7.10960	−	26.5334i	−0.226761	−	0.846284i	0.754930	−	0.655805i	$-0.227671\pi$
$984$	−39.4381	+	34.5644i	−1.25724	+	1.10187i
$985$	−13.0234	−	22.5573i	−0.414961	−	0.718734i
$986$	2.58197	+	1.70252i	0.0822266	+	0.0542192i
$987$	−13.5748	−	15.4889i	−0.432091	−	0.493019i
$988$	−0.442468	−	0.255459i	−0.0140768	−	0.00812723i
$989$	−5.19645	+	5.19645i	−0.165238	+	0.165238i
$990$	2.71161	−	20.4970i	0.0861807	−	0.651437i
$991$	−18.4126	+	18.4126i	−0.584894	+	0.584894i	−0.936244	−	0.351350i	$-0.885723\pi$
$991$	−18.4126	+	18.4126i	−0.584894	+	0.584894i	0.351350	+	0.936244i	$0.385723\pi$
$992$	15.3871	−	4.12296i	0.488540	−	0.130904i
$993$	−42.3746	+	20.8803i	−1.34472	+	0.662616i
$994$	12.4086	−	7.16413i	0.393578	−	0.227233i
$995$	17.5824	−	10.1512i	0.557398	−	0.321814i
$996$	6.22346	+	4.16121i	0.197198	+	0.131853i
$997$	−41.0256	+	10.9928i	−1.29929	+	0.348145i	−0.841183	−	0.540751i	$-0.818140\pi$
$997$	−41.0256	+	10.9928i	−1.29929	+	0.348145i	−0.458110	+	0.888895i	$0.651474\pi$
$998$	21.6947	−	21.6947i	0.686734	−	0.686734i
$999$	36.9413	−	24.6329i	1.16877	−	0.779351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.n.a.106.5	yes	64
3.2	odd	2		459.2.o.a.208.12		64
9.4	even	3	inner	153.2.n.a.4.12	✓	64
9.5	odd	6		459.2.o.a.361.5		64
17.13	even	4	inner	153.2.n.a.115.12	yes	64
51.47	odd	4		459.2.o.a.370.5		64
153.13	even	12	inner	153.2.n.a.13.5	yes	64
153.149	odd	12		459.2.o.a.64.12		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.n.a.4.12	✓	64	9.4	even	3	inner
153.2.n.a.13.5	yes	64	153.13	even	12	inner
153.2.n.a.106.5	yes	64	1.1	even	1	trivial
153.2.n.a.115.12	yes	64	17.13	even	4	inner
459.2.o.a.64.12		64	153.149	odd	12
459.2.o.a.208.12		64	3.2	odd	2
459.2.o.a.361.5		64	9.5	odd	6
459.2.o.a.370.5		64	51.47	odd	4

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.n (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11815 - 0.645565i) q^{2} +(0.962729 - 1.43984i) q^{3} +(-0.166493 - 0.288374i) q^{4} +(2.55532 + 0.684695i) q^{5} +(-2.00599 + 0.988459i) q^{6} +(2.18547 - 0.585596i) q^{7} +3.01219i q^{8} +(-1.14630 - 2.77236i) q^{9} +(-2.41521 - 2.41521i) q^{10} +(-1.94899 + 0.522230i) q^{11} +(-0.575501 - 0.0379023i) q^{12} +(-1.81218 - 3.13879i) q^{13} +(-2.82173 - 0.756080i) q^{14} +(3.44593 - 3.02008i) q^{15} +(1.61157 - 2.79133i) q^{16} +(-1.30148 + 3.91231i) q^{17} +(-0.507997 + 3.83993i) q^{18} +0.423344i q^{19} +(-0.227993 - 0.850883i) q^{20} +(1.26085 - 3.71051i) q^{21} +(2.51640 + 0.674267i) q^{22} +(-0.239930 + 0.895433i) q^{23} +(4.33708 + 2.89992i) q^{24} +(1.73071 + 0.999225i) q^{25} +4.67953i q^{26} +(-5.09535 - 1.01853i) q^{27} +(-0.532736 - 0.532736i) q^{28} +(0.150365 + 0.561171i) q^{29} +(-5.80273 + 1.15234i) q^{30} +(8.25989 + 2.21323i) q^{31} +(1.61329 - 0.931434i) q^{32} +(-1.12442 + 3.30901i) q^{33} +(3.98090 - 3.53436i) q^{34} +5.98553 q^{35} +(-0.608625 + 0.792142i) q^{36} +(-6.04219 + 6.04219i) q^{37} +(0.273296 - 0.473363i) q^{38} +(-6.26402 - 0.412546i) q^{39} +(-2.06243 + 7.69709i) q^{40} +(-2.60151 + 9.70896i) q^{41} +(-3.80520 + 3.33495i) q^{42} +(6.86536 + 3.96372i) q^{43} +(0.475090 + 0.475090i) q^{44} +(-1.03095 - 7.86913i) q^{45} +(0.846338 - 0.846338i) q^{46} +(2.62775 - 4.55140i) q^{47} +(-2.46757 - 5.00771i) q^{48} +(-1.62881 + 0.940391i) q^{49} +(-1.29013 - 2.23457i) q^{50} +(4.38014 + 5.64042i) q^{51} +(-0.603431 + 1.04517i) q^{52} -9.13365i q^{53} +(5.03984 + 4.42825i) q^{54} -5.33785 q^{55} +(1.76392 + 6.58305i) q^{56} +(0.609550 + 0.407566i) q^{57} +(0.194141 - 0.724544i) q^{58} +(9.53349 - 5.50416i) q^{59} +(-1.44464 - 0.490895i) q^{60} +(-5.71685 + 1.53183i) q^{61} +(-7.80701 - 7.80701i) q^{62} +(-4.12870 - 5.38765i) q^{63} -8.85150 q^{64} +(-2.48159 - 9.26140i) q^{65} +(3.39345 - 2.97408i) q^{66} +(3.03393 + 5.25493i) q^{67} +(1.34489 - 0.276059i) q^{68} +(1.05830 + 1.20752i) q^{69} +(-6.69273 - 3.86405i) q^{70} +(-3.46822 + 3.46822i) q^{71} +(8.35087 - 3.45288i) q^{72} +(8.18845 - 8.18845i) q^{73} +(10.6567 - 2.85546i) q^{74} +(3.10493 - 1.52997i) q^{75} +(0.122081 - 0.0704837i) q^{76} +(-3.95365 + 2.28264i) q^{77} +(6.73779 + 4.50512i) q^{78} +(4.15030 - 1.11207i) q^{79} +(6.02929 - 6.02929i) q^{80} +(-6.37197 + 6.35594i) q^{81} +(9.17664 - 9.17664i) q^{82} +(-11.2414 - 6.49024i) q^{83} +(-1.27994 + 0.254176i) q^{84} +(-6.00443 + 9.10607i) q^{85} +(-5.11767 - 8.86407i) q^{86} +(0.952760 + 0.323753i) q^{87} +(-1.57305 - 5.87072i) q^{88} -3.03877 q^{89} +(-3.92727 + 9.46442i) q^{90} +(-5.79854 - 5.79854i) q^{91} +(0.298166 - 0.0798933i) q^{92} +(11.1387 - 9.76221i) q^{93} +(-5.87644 + 3.39277i) q^{94} +(-0.289862 + 1.08178i) q^{95} +(0.212042 - 3.21961i) q^{96} +(-3.33832 - 12.4588i) q^{97} +2.42833 q^{98} +(3.68195 + 4.80467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30}+ \cdots + 6 q^{99}+O(q^{100}) \) 64 * q - 6 * q^3 + 24 * q^4 - 2 * q^5 - 10 * q^6 - 2 * q^7 - 16 * q^10 - 24 * q^12 - 4 * q^13 - 16 * q^16 - 8 * q^17 - 8 * q^18 + 18 * q^20 - 16 * q^21 - 4 * q^22 - 8 * q^23 - 2 * q^24 - 10 * q^29 - 36 * q^30 - 2 * q^31 + 12 * q^33 + 20 * q^34 - 128 * q^35 - 8 * q^37 - 24 * q^38 + 34 * q^39 - 20 * q^40 + 32 * q^41 + 20 * q^44 + 20 * q^45 - 40 * q^46 - 64 * q^47 + 62 * q^48 + 48 * q^50 + 40 * q^51 + 36 * q^52 - 46 * q^54 - 16 * q^55 + 12 * q^56 + 72 * q^57 - 10 * q^58 - 2 * q^61 - 28 * q^62 + 64 * q^63 - 8 * q^64 + 8 * q^65 - 4 * q^67 - 60 * q^68 - 24 * q^69 - 84 * q^71 + 72 * q^72 - 44 * q^73 - 14 * q^74 + 46 * q^75 - 56 * q^78 + 10 * q^79 + 204 * q^80 + 44 * q^81 - 52 * q^82 - 60 * q^84 + 22 * q^85 + 32 * q^86 + 16 * q^88 + 128 * q^89 - 66 * q^90 + 44 * q^91 + 136 * q^92 + 4 * q^95 - 2 * q^96 - 44 * q^97 + 208 * q^98 + 6 * q^99

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