LMFDB - Embedded newform 90.2.l.a.23.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,2,Mod(23,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("90.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$90 = 2 \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	90.l (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:	$0.718653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{4} + 1$ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	90.23
Dual form			90.2.l.a.47.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(1.62484 + 0.599900i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(2.20711 - 0.358719i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-4.40508 - 1.18034i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.28024 + 1.94949i) q^{9} +(-0.224745 + 2.22474i) q^{10} +(-0.550510 + 0.317837i) q^{11} +(-1.10721 - 1.33195i) q^{12} +(-3.34607 + 0.896575i) q^{13} +(2.28024 - 3.94949i) q^{14} +(3.80140 + 0.741181i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.317837 + 0.317837i) q^{17} +(-2.47323 + 1.69798i) q^{18} -6.44949i q^{19} +(-2.09077 - 0.792893i) q^{20} +(-6.44949 - 4.56048i) q^{21} +(-0.164525 - 0.614014i) q^{22} +(-0.258819 - 0.965926i) q^{23} +(1.57313 - 0.724745i) q^{24} +(4.74264 - 1.58346i) q^{25} -3.46410i q^{26} +(2.53553 + 4.53553i) q^{27} +(3.22474 + 3.22474i) q^{28} +(-0.158919 - 0.275255i) q^{29} +(-1.69980 + 3.48004i) q^{30} +(-0.224745 + 0.389270i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.08516 + 0.186185i) q^{33} +(-0.389270 + 0.224745i) q^{34} +(-10.1459 - 1.02494i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-3.00000 + 3.00000i) q^{37} +(6.22973 + 1.66925i) q^{38} +(-5.97469 - 0.550510i) q^{39} +(1.30701 - 1.81431i) q^{40} +(6.39898 + 3.69445i) q^{41} +(6.07433 - 5.04939i) q^{42} +(-0.896575 + 3.34607i) q^{43} +0.635674 q^{44} +(5.73205 + 3.48477i) q^{45} +1.00000 q^{46} +(-2.32937 + 8.69333i) q^{47} +(0.292893 + 1.70711i) q^{48} +(11.9494 + 6.89898i) q^{49} +(0.302023 + 4.99087i) q^{50} +(0.325765 + 0.707107i) q^{51} +(3.34607 + 0.896575i) q^{52} +(3.78194 - 3.78194i) q^{53} +(-5.03723 + 1.27526i) q^{54} +(-1.10102 + 0.898979i) q^{55} +(-3.94949 + 2.28024i) q^{56} +(3.86905 - 10.4794i) q^{57} +(0.307007 - 0.0822623i) q^{58} +(-4.48905 + 7.77526i) q^{59} +(-2.92152 - 2.54258i) q^{60} +(0.275255 + 0.476756i) q^{61} +(-0.317837 - 0.317837i) q^{62} +(-7.74358 - 11.2791i) q^{63} -1.00000i q^{64} +(-7.06350 + 3.17914i) q^{65} +(0.101021 - 1.09638i) q^{66} +(-1.71089 - 6.38512i) q^{67} +(-0.116337 - 0.434174i) q^{68} +(0.158919 - 1.72474i) q^{69} +(3.61597 - 9.53491i) q^{70} -6.29253i q^{71} +(2.99087 - 0.233875i) q^{72} +(-6.89898 - 6.89898i) q^{73} +(-2.12132 - 3.67423i) q^{74} +(8.65597 + 0.272229i) q^{75} +(-3.22474 + 5.58542i) q^{76} +(2.80020 - 0.750311i) q^{77} +(2.07812 - 5.62863i) q^{78} +(-2.12132 + 1.22474i) q^{79} +(1.41421 + 1.73205i) q^{80} +(1.39898 + 8.89060i) q^{81} +(-5.22474 + 5.22474i) q^{82} +(5.26380 + 1.41043i) q^{83} +(3.30518 + 7.17423i) q^{84} +(0.815515 + 0.587486i) q^{85} +(-3.00000 - 1.73205i) q^{86} +(-0.0930924 - 0.542582i) q^{87} +(-0.164525 + 0.614014i) q^{88} -8.02458 q^{89} +(-4.84959 + 4.63481i) q^{90} +15.7980 q^{91} +(-0.258819 + 0.965926i) q^{92} +(-0.598698 + 0.497678i) q^{93} +(-7.79423 - 4.50000i) q^{94} +(-2.31356 - 14.2347i) q^{95} +(-1.72474 - 0.158919i) q^{96} +(-2.59405 - 0.695075i) q^{97} +(-9.75663 + 9.75663i) q^{98} +(-1.87492 - 0.348469i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{10} - 24 q^{11} - 4 q^{12} + 16 q^{15} + 4 q^{16} - 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{25} - 8 q^{27} + 16 q^{28} - 12 q^{30} + 8 q^{31} + 16 q^{33}+ \cdots + 12 q^{97}+O(q^{100})$ 8 * q + 4 * q^3 + 12 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^10 - 24 * q^11 - 4 * q^12 + 16 * q^15 + 4 * q^16 - 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^25 - 8 * q^27 + 16 * q^28 - 12 * q^30 + 8 * q^31 + 16 * q^33 - 8 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^40 + 12 * q^41 + 20 * q^42 + 32 * q^45 + 8 * q^46 + 8 * q^48 + 24 * q^50 + 32 * q^51 - 48 * q^55 - 12 * q^56 + 28 * q^57 - 4 * q^58 - 8 * q^60 + 12 * q^61 - 32 * q^63 - 24 * q^65 + 40 * q^66 + 4 * q^67 - 12 * q^68 - 16 * q^70 + 8 * q^72 - 16 * q^73 + 8 * q^75 - 16 * q^76 + 24 * q^77 - 24 * q^78 - 28 * q^81 - 32 * q^82 + 12 * q^83 - 20 * q^85 - 24 * q^86 - 8 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 - 20 * q^93 - 24 * q^95 - 4 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$ .

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	1.62484	+	0.599900i	0.938104	+	0.346353i
$3$	1.62484	+	0.599900i	0.938104	+	0.346353i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$5$	2.20711	−	0.358719i	0.987048	−	0.160424i
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	−4.40508	−	1.18034i	−1.66497	−	0.446126i	−0.701219	−	0.712946i	$-0.747360\pi$
$7$	−4.40508	−	1.18034i	−1.66497	−	0.446126i	−0.963746	+	0.266820i	$0.914027\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.28024	+	1.94949i	0.760080	+	0.649830i
$10$	−0.224745	+	2.22474i	−0.0710706	+	0.703526i
$11$	−0.550510	+	0.317837i	−0.165985	+	0.0958315i	−0.580691	−	0.814124i	$-0.697218\pi$
$11$	−0.550510	+	0.317837i	−0.165985	+	0.0958315i	0.414706	+	0.909955i	$0.363884\pi$
$12$	−1.10721	−	1.33195i	−0.319623	−	0.384501i
$13$	−3.34607	+	0.896575i	−0.928032	+	0.248665i	−0.691015	−	0.722840i	$-0.742836\pi$
$13$	−3.34607	+	0.896575i	−0.928032	+	0.248665i	−0.237016	+	0.971506i	$0.576170\pi$
$14$	2.28024	−	3.94949i	0.609419	−	1.05555i
$15$	3.80140	+	0.741181i	0.981518	+	0.191372i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.317837	+	0.317837i	0.0770869	+	0.0770869i	0.744599	−	0.667512i	$-0.232641\pi$
$17$	0.317837	+	0.317837i	0.0770869	+	0.0770869i	−0.667512	+	0.744599i	$0.732641\pi$
$18$	−2.47323	+	1.69798i	−0.582946	+	0.400217i
$19$		−	6.44949i		−	1.47961i	−0.672819	−	0.739807i	$-0.734917\pi$
$19$		−	6.44949i		−	1.47961i	0.672819	−	0.739807i	$-0.265083\pi$
$20$	−2.09077	−	0.792893i	−0.467510	−	0.177296i
$21$	−6.44949	−	4.56048i	−1.40739	−	0.995178i
$22$	−0.164525	−	0.614014i	−0.0350768	−	0.130908i
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	0.933678	−	0.358113i	$-0.116580\pi$
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	−0.987646	+	0.156704i	$0.949913\pi$
$24$	1.57313	−	0.724745i	0.321114	−	0.147938i
$25$	4.74264	−	1.58346i	0.948528	−	0.316693i
$26$		−	3.46410i		−	0.679366i
$27$	2.53553	+	4.53553i	0.487964	+	0.872864i
$28$	3.22474	+	3.22474i	0.609419	+	0.609419i
$29$	−0.158919	−	0.275255i	−0.0295104	−	0.0511136i	0.850893	−	0.525339i	$-0.176061\pi$
$29$	−0.158919	−	0.275255i	−0.0295104	−	0.0511136i	−0.880403	+	0.474225i	$0.842728\pi$
$30$	−1.69980	+	3.48004i	−0.310340	+	0.635365i
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	−0.885502	−	0.464635i	$-0.846186\pi$
$31$	−0.224745	+	0.389270i	−0.0403654	+	0.0699149i	0.845137	+	0.534550i	$0.179519\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−1.08516	+	0.186185i	−0.188903	+	0.0324106i
$34$	−0.389270	+	0.224745i	−0.0667592	+	0.0385434i
$35$	−10.1459	−	1.02494i	−1.71497	−	0.173247i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$	6.22973	+	1.66925i	1.01060	+	0.270788i
$39$	−5.97469	−	0.550510i	−0.956716	−	0.0881522i
$40$	1.30701	−	1.81431i	0.206656	−	0.286868i
$41$	6.39898	+	3.69445i	0.999353	+	0.576977i	0.908057	−	0.418847i	$-0.137566\pi$
$41$	6.39898	+	3.69445i	0.999353	+	0.576977i	0.0912960	+	0.995824i	$0.470899\pi$
$42$	6.07433	−	5.04939i	0.937290	−	0.779138i
$43$	−0.896575	+	3.34607i	−0.136726	+	0.510270i	0.863258	+	0.504762i	$0.168420\pi$
$43$	−0.896575	+	3.34607i	−0.136726	+	0.510270i	−0.999985	+	0.00550783i	$0.998247\pi$
$44$	0.635674			0.0958315
$45$	5.73205	+	3.48477i	0.854484	+	0.519478i
$46$	1.00000			0.147442
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	0.558827	+	0.829285i	$0.311252\pi$
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	−0.898600	+	0.438768i	$0.855415\pi$
$48$	0.292893	+	1.70711i	0.0422755	+	0.246400i
$49$	11.9494	+	6.89898i	1.70705	+	0.985568i
$50$	0.302023	+	4.99087i	0.0427126	+	0.705816i
$51$	0.325765	+	0.707107i	0.0456163	+	0.0990148i
$52$	3.34607	+	0.896575i	0.464016	+	0.124333i
$53$	3.78194	−	3.78194i	0.519489	−	0.519489i	−0.397928	−	0.917417i	$-0.630270\pi$
$53$	3.78194	−	3.78194i	0.519489	−	0.519489i	0.917417	+	0.397928i	$0.130270\pi$
$54$	−5.03723	+	1.27526i	−0.685481	+	0.173540i
$55$	−1.10102	+	0.898979i	−0.148462	+	0.121218i
$56$	−3.94949	+	2.28024i	−0.527773	+	0.304710i
$57$	3.86905	−	10.4794i	0.512468	−	1.38803i
$58$	0.307007	−	0.0822623i	0.0403120	−	0.0108016i
$59$	−4.48905	+	7.77526i	−0.584424	+	1.01225i	0.410523	+	0.911850i	$0.365346\pi$
$59$	−4.48905	+	7.77526i	−0.584424	+	1.01225i	−0.994947	+	0.100402i	$0.967987\pi$
$60$	−2.92152	−	2.54258i	−0.377167	−	0.328246i
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	0.883109	−	0.469168i	$-0.155446\pi$
$61$	0.275255	+	0.476756i	0.0352428	+	0.0610423i	−0.847866	+	0.530211i	$0.822113\pi$
$62$	−0.317837	−	0.317837i	−0.0403654	−	0.0403654i
$63$	−7.74358	−	11.2791i	−0.975600	−	1.42104i
$64$		−	1.00000i		−	0.125000i
$65$	−7.06350	+	3.17914i	−0.876120	+	0.394323i
$66$	0.101021	−	1.09638i	0.0124348	−	0.134955i
$67$	−1.71089	−	6.38512i	−0.209018	−	0.780067i	−0.988187	−	0.153253i	$-0.951025\pi$
$67$	−1.71089	−	6.38512i	−0.209018	−	0.780067i	0.779169	−	0.626814i	$-0.215642\pi$
$68$	−0.116337	−	0.434174i	−0.0141079	−	0.0526513i
$69$	0.158919	−	1.72474i	0.0191316	−	0.207635i
$70$	3.61597	−	9.53491i	0.432191	−	1.13964i
$71$		−	6.29253i		−	0.746786i	−0.927673	−	0.373393i	$-0.878194\pi$
$71$		−	6.29253i		−	0.746786i	0.927673	−	0.373393i	$-0.121806\pi$
$72$	2.99087	−	0.233875i	0.352477	−	0.0275624i
$73$	−6.89898	−	6.89898i	−0.807464	−	0.807464i	0.176785	−	0.984249i	$-0.443430\pi$
$73$	−6.89898	−	6.89898i	−0.807464	−	0.807464i	−0.984249	+	0.176785i	$0.943430\pi$
$74$	−2.12132	−	3.67423i	−0.246598	−	0.427121i
$75$	8.65597	+	0.272229i	0.999506	+	0.0314343i
$76$	−3.22474	+	5.58542i	−0.369904	+	0.640692i
$77$	2.80020	−	0.750311i	0.319112	−	0.0855059i
$78$	2.07812	−	5.62863i	0.235300	−	0.637316i
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	−0.614564	−	0.788867i	$-0.710668\pi$
$79$	−2.12132	+	1.22474i	−0.238667	+	0.137795i	0.375897	+	0.926662i	$0.377335\pi$
$80$	1.41421	+	1.73205i	0.158114	+	0.193649i
$81$	1.39898	+	8.89060i	0.155442	+	0.987845i
$82$	−5.22474	+	5.22474i	−0.576977	+	0.576977i
$83$	5.26380	+	1.41043i	0.577777	+	0.154815i	0.535861	−	0.844306i	$-0.319987\pi$
$83$	5.26380	+	1.41043i	0.577777	+	0.154815i	0.0419163	+	0.999121i	$0.486654\pi$
$84$	3.30518	+	7.17423i	0.360625	+	0.782773i
$85$	0.815515	+	0.587486i	0.0884550	+	0.0637218i
$86$	−3.00000	−	1.73205i	−0.323498	−	0.186772i
$87$	−0.0930924	−	0.542582i	−0.00998055	−	0.0581709i
$88$	−0.164525	+	0.614014i	−0.0175384	+	0.0654542i
$89$	−8.02458			−0.850604			−0.425302	−	0.905052i	$-0.639832\pi$
$89$	−8.02458			−0.850604			−0.425302	+	0.905052i	$0.639832\pi$
$90$	−4.84959	+	4.63481i	−0.511192	+	0.488552i
$91$	15.7980			1.65608
$92$	−0.258819	+	0.965926i	−0.0269838	+	0.100705i
$93$	−0.598698	+	0.497678i	−0.0620821	+	0.0516068i
$94$	−7.79423	−	4.50000i	−0.803913	−	0.464140i
$95$	−2.31356	−	14.2347i	−0.237366	−	1.46045i
$96$	−1.72474	−	0.158919i	−0.176031	−	0.0162196i
$97$	−2.59405	−	0.695075i	−0.263386	−	0.0705741i	0.124709	−	0.992193i	$-0.460200\pi$
$97$	−2.59405	−	0.695075i	−0.263386	−	0.0705741i	−0.388095	+	0.921619i	$0.626867\pi$
$98$	−9.75663	+	9.75663i	−0.985568	+	0.985568i
$99$	−1.87492	−	0.348469i	−0.188436	−	0.0350225i
$100$	−4.89898	−	1.00000i	−0.489898	−	0.100000i
$101$	10.8990	−	6.29253i	1.08449	−	0.626130i	0.152385	−	0.988321i	$-0.451305\pi$
$101$	10.8990	−	6.29253i	1.08449	−	0.626130i	0.932104	+	0.362191i	$0.117971\pi$
$102$	−0.767327	+	0.131652i	−0.0759767	+	0.0130355i
$103$	9.42418	−	2.52520i	0.928592	−	0.248816i	0.237338	−	0.971427i	$-0.423725\pi$
$103$	9.42418	−	2.52520i	0.928592	−	0.248816i	0.691254	+	0.722612i	$0.257058\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$	−15.8706	−	7.75190i	−1.54882	−	0.756508i
$106$	2.67423	+	4.63191i	0.259745	+	0.449891i
$107$	13.6100	+	13.6100i	1.31573	+	1.31573i	0.917122	+	0.398606i	$0.130506\pi$
$107$	13.6100	+	13.6100i	1.31573	+	1.31573i	0.398606	+	0.917122i	$0.369494\pi$
$108$	0.0719302	−	5.19565i	0.00692148	−	0.499952i
$109$			5.65153i			0.541318i	0.962675	+	0.270659i	$0.0872417\pi$
$109$			5.65153i			0.541318i	−0.962675	+	0.270659i	$0.912758\pi$
$110$	−0.583382	−	1.29618i	−0.0556233	−	0.123586i
$111$	−6.67423	+	3.07483i	−0.633490	+	0.291850i
$112$	−1.18034	−	4.40508i	−0.111532	−	0.416241i
$113$	−1.50062	−	5.60040i	−0.141167	−	0.526841i	−0.999896	−	0.0144120i	$-0.995412\pi$
$113$	−1.50062	−	5.60040i	−0.141167	−	0.526841i	0.858729	−	0.512429i	$-0.171254\pi$
$114$	9.12096	+	6.44949i	0.854256	+	0.604050i
$115$	−0.917738	−	2.03906i	−0.0855795	−	0.190143i
$116$			0.317837i			0.0295104i
$117$	−9.37769	−	4.47871i	−0.866968	−	0.414057i
$118$	−6.34847	−	6.34847i	−0.584424	−	0.584424i
$119$	−1.02494	−	1.77526i	−0.0939565	−	0.162737i
$120$	3.21209	−	2.16390i	0.293222	−	0.197536i
$121$	−5.29796	+	9.17633i	−0.481633	+	0.834212i
$122$	−0.531752	+	0.142483i	−0.0481426	+	0.0128998i
$123$	8.18104	+	9.84166i	0.737660	+	0.887393i
$124$	0.389270	−	0.224745i	0.0349574	−	0.0201827i
$125$	9.89949	−	5.19615i	0.885438	−	0.464758i
$126$	12.8990	−	4.56048i	1.14913	−	0.406280i
$127$	1.87628	−	1.87628i	0.166493	−	0.166493i	−0.618943	−	0.785436i	$-0.712439\pi$
$127$	1.87628	−	1.87628i	0.166493	−	0.166493i	0.785436	+	0.618943i	$0.212439\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−3.46410	+	4.89898i	−0.304997	+	0.431331i
$130$	−1.24264	−	7.64564i	−0.108987	−	0.670567i
$131$	−3.12372	−	1.80348i	−0.272921	−	0.157571i	0.357293	−	0.933992i	$-0.383700\pi$
$131$	−3.12372	−	1.80348i	−0.272921	−	0.157571i	−0.630214	+	0.776421i	$0.717033\pi$
$132$	1.03287	+	0.381341i	0.0899000	+	0.0331915i
$133$	−7.61258	+	28.4105i	−0.660095	+	2.46351i
$134$	6.61037			0.571049
$135$	7.22318	+	9.10086i	0.621672	+	0.783278i
$136$	0.449490			0.0385434
$137$	5.64173	−	21.0552i	0.482005	−	1.79887i	−0.111178	−	0.993801i	$-0.535462\pi$
$137$	5.64173	−	21.0552i	0.482005	−	1.79887i	0.593183	−	0.805068i	$-0.297871\pi$
$138$	1.62484	+	0.599900i	0.138316	+	0.0510669i
$139$	2.68556	+	1.55051i	0.227786	+	0.131513i	0.609550	−	0.792747i	$-0.291350\pi$
$139$	2.68556	+	1.55051i	0.227786	+	0.131513i	−0.381764	+	0.924260i	$0.624683\pi$
$140$	8.27414	+	5.96058i	0.699292	+	0.503761i
$141$	−9.00000	+	12.7279i	−0.757937	+	1.07188i
$142$	6.07812	+	1.62863i	0.510064	+	0.136671i
$143$	1.55708	−	1.55708i	0.130209	−	0.130209i
$144$	−0.548188	+	2.94949i	−0.0456823	+	0.245791i
$145$	−0.449490	−	0.550510i	−0.0373281	−	0.0457174i
$146$	8.44949	−	4.87832i	0.699285	−	0.403732i
$147$	15.2772	+	18.3782i	1.26004	+	1.51581i
$148$	4.09808	−	1.09808i	0.336860	−	0.0902613i
$149$	2.20881	−	3.82577i	0.180952	−	0.313419i	−0.761253	−	0.648455i	$-0.775415\pi$
$149$	2.20881	−	3.82577i	0.180952	−	0.313419i	0.942205	+	0.335036i	$0.108749\pi$
$150$	−2.50328	+	8.29057i	−0.204392	+	0.676922i
$151$	−8.79796	−	15.2385i	−0.715968	−	1.24009i	−0.962585	−	0.270980i	$-0.912652\pi$
$151$	−8.79796	−	15.2385i	−0.715968	−	1.24009i	0.246617	−	0.969113i	$-0.420681\pi$
$152$	−4.56048	−	4.56048i	−0.369904	−	0.369904i
$153$	0.105124	+	1.34437i	0.00849881	+	0.108685i
$154$			2.89898i			0.233606i
$155$	−0.356397	+	0.939780i	−0.0286265	+	0.0754849i
$156$	4.89898	+	3.46410i	0.392232	+	0.277350i
$157$	−3.78780	−	14.1363i	−0.302300	−	1.12820i	−0.935245	−	0.354001i	$-0.884821\pi$
$157$	−3.78780	−	14.1363i	−0.302300	−	1.12820i	0.632945	−	0.774196i	$-0.281846\pi$
$158$	−0.633975	−	2.36603i	−0.0504363	−	0.188231i
$159$	8.41385	−	3.87628i	0.667262	−	0.307409i
$160$	−2.03906	+	0.917738i	−0.161202	+	0.0725535i
$161$			4.56048i			0.359416i
$162$	−8.94975	−	0.949747i	−0.703159	−	0.0746192i
$163$	4.44949	+	4.44949i	0.348511	+	0.348511i	0.859555	−	0.511044i	$-0.170741\pi$
$163$	4.44949	+	4.44949i	0.348511	+	0.348511i	−0.511044	+	0.859555i	$0.670741\pi$
$164$	−3.69445	−	6.39898i	−0.288488	−	0.499676i
$165$	−2.32829	+	0.800199i	−0.181257	+	0.0622954i
$166$	−2.72474	+	4.71940i	−0.211481	+	0.366296i
$167$	−8.49818	+	2.27708i	−0.657609	+	0.176206i	−0.572167	−	0.820137i	$-0.693897\pi$
$167$	−8.49818	+	2.27708i	−0.657609	+	0.176206i	−0.0854420	+	0.996343i	$0.527230\pi$
$168$	−7.78522	+	1.33573i	−0.600643	+	0.103054i
$169$	−0.866025	+	0.500000i	−0.0666173	+	0.0384615i
$170$	−0.778539	+	0.635674i	−0.0597112	+	0.0487540i
$171$	12.5732	−	14.7064i	0.961498	−	1.12462i
$172$	2.44949	−	2.44949i	0.186772	−	0.186772i
$173$	−12.4595	−	3.33850i	−0.947275	−	0.253822i	−0.248069	−	0.968742i	$-0.579796\pi$
$173$	−12.4595	−	3.33850i	−0.947275	−	0.253822i	−0.699206	+	0.714921i	$0.746463\pi$
$174$	0.548188	+	0.0505103i	0.0415580	+	0.00382917i
$175$	−22.7608	+	1.37737i	−1.72055	+	0.104119i
$176$	−0.550510	−	0.317837i	−0.0414963	−	0.0239579i
$177$	−11.9584	+	9.94060i	−0.898847	+	0.747181i
$178$	2.07691	−	7.75115i	0.155671	−	0.580973i
$179$	10.6780			0.798114			0.399057	−	0.916926i	$-0.369338\pi$
$179$	10.6780			0.798114			0.399057	+	0.916926i	$0.369338\pi$
$180$	−3.22172	−	5.88392i	−0.240133	−	0.438562i
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$	−4.08881	+	15.2597i	−0.303083	+	1.13112i
$183$	0.161241	+	0.939780i	0.0119193	+	0.0694705i
$184$	−0.866025	−	0.500000i	−0.0638442	−	0.0368605i
$185$	−5.54516	+	7.69748i	−0.407688	+	0.565930i
$186$	−0.325765	−	0.707107i	−0.0238863	−	0.0518476i
$187$	−0.275993	−	0.0739521i	−0.0201826	−	0.00540792i
$188$	6.36396	−	6.36396i	0.464140	−	0.464140i
$189$	−5.81577	−	22.9722i	−0.423035	−	1.67098i
$190$	14.3485	+	1.44949i	1.04095	+	0.105157i
$191$	−15.1237	+	8.73169i	−1.09431	+	0.631803i	−0.934722	−	0.355380i	$-0.884351\pi$
$191$	−15.1237	+	8.73169i	−1.09431	+	0.631803i	−0.159593	+	0.987183i	$0.551018\pi$
$192$	0.599900	−	1.62484i	0.0432941	−	0.117263i
$193$	16.7303	−	4.48288i	1.20428	−	0.322685i	0.399762	−	0.916619i	$-0.369093\pi$
$193$	16.7303	−	4.48288i	1.20428	−	0.322685i	0.804513	+	0.593934i	$0.202426\pi$
$194$	1.34278	−	2.32577i	0.0964061	−	0.166980i
$195$	−13.3843	+	0.928203i	−0.958467	+	0.0664700i
$196$	−6.89898	−	11.9494i	−0.492784	−	0.853527i
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	0.909443	−	0.415829i	$-0.136508\pi$
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	−0.415829	+	0.909443i	$0.636508\pi$
$198$	0.821859	−	1.72084i	0.0584070	−	0.122295i
$199$		−	8.44949i		−	0.598968i	−0.954101	−	0.299484i	$-0.903185\pi$
$199$		−	8.44949i		−	0.598968i	0.954101	−	0.299484i	$-0.0968146\pi$
$200$	2.23388	−	4.47323i	0.157959	−	0.316305i
$201$	1.05051	−	11.4012i	0.0740973	−	0.804178i
$202$	3.25725	+	12.1562i	0.229179	+	0.855310i
$203$	0.375156	+	1.40010i	0.0263308	+	0.0982677i
$204$	0.0714323	−	0.775255i	0.00500126	−	0.0542787i
$205$	15.4485	+	5.85861i	1.07897	+	0.409183i
$206$			9.75663i			0.679777i
$207$	1.29289	−	2.70711i	0.0898623	−	0.188157i
$208$	−2.44949	−	2.44949i	−0.169842	−	0.169842i
$209$	2.04989	+	3.55051i	0.141794	+	0.245594i
$210$	11.5954	−	13.3235i	0.800158	−	0.919411i
$211$	−4.55051	+	7.88171i	−0.313270	+	0.542600i	−0.979068	−	0.203532i	$-0.934758\pi$
$211$	−4.55051	+	7.88171i	−0.313270	+	0.542600i	0.665798	+	0.746132i	$0.268091\pi$
$212$	−5.16622	+	1.38429i	−0.354818	+	0.0950731i
$213$	3.77489	−	10.2244i	0.258651	−	0.700563i
$214$	−16.6688	+	9.62372i	−1.13945	+	0.657864i
$215$	−0.778539	+	7.70674i	−0.0530959	+	0.525595i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	1.44949	−	1.44949i	0.0983978	−	0.0983978i
$218$	−5.45896	−	1.46272i	−0.369727	−	0.0990682i
$219$	−7.07107	−	15.3485i	−0.477818	−	1.03715i
$220$	1.40300	−	0.228029i	0.0945903	−	0.0153737i
$221$	−1.34847	−	0.778539i	−0.0907079	−	0.0523702i
$222$	−1.24264	−	7.24264i	−0.0834006	−	0.486094i
$223$	6.63374	−	24.7575i	0.444228	−	1.65788i	−0.273738	−	0.961804i	$-0.588260\pi$
$223$	6.63374	−	24.7575i	0.444228	−	1.65788i	0.717966	−	0.696078i	$-0.245073\pi$
$224$	4.56048			0.304710
$225$	13.9013	+	5.63505i	0.926753	+	0.375670i
$226$	5.79796			0.385674
$227$	6.44433	−	24.0506i	0.427725	−	1.59629i	−0.330174	−	0.943920i	$-0.607107\pi$
$227$	6.44433	−	24.0506i	0.427725	−	1.59629i	0.757899	−	0.652372i	$-0.226226\pi$
$228$	−8.59041	+	7.14092i	−0.568914	+	0.472919i
$229$	−1.43027	−	0.825765i	−0.0945147	−	0.0545681i	0.451998	−	0.892019i	$-0.350712\pi$
$229$	−1.43027	−	0.825765i	−0.0945147	−	0.0545681i	−0.546512	+	0.837451i	$0.684045\pi$
$230$	2.20711	−	0.358719i	0.145532	−	0.0236533i
$231$	5.00000	+	0.460702i	0.328976	+	0.0303120i
$232$	−0.307007	−	0.0822623i	−0.0201560	−	0.00540079i
$233$	−14.4600	+	14.4600i	−0.947304	+	0.947304i	−0.998679	−	0.0513751i	$-0.983640\pi$
$233$	−14.4600	+	14.4600i	−0.947304	+	0.947304i	0.0513751	+	0.998679i	$0.483640\pi$
$234$	6.75323	−	7.89898i	0.441472	−	0.516372i
$235$	−2.02270	+	20.0227i	−0.131947	+	1.30614i
$236$	7.77526	−	4.48905i	0.506126	−	0.292212i
$237$	−4.18154	+	0.717439i	−0.271620	+	0.0466027i
$238$	1.98004	−	0.530550i	0.128347	−	0.0343905i
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	0.449485	+	0.893288i	$0.351607\pi$
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	−0.998353	+	0.0573782i	$0.981726\pi$
$240$	1.25882	+	3.66270i	0.0812564	+	0.236426i
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$	−7.49245	−	7.49245i	−0.481633	−	0.481633i
$243$	−3.06035	+	15.2851i	−0.196322	+	0.980540i
$244$		−	0.550510i		−	0.0352428i
$245$	28.8484	+	10.9403i	1.84305	+	0.698951i
$246$	−11.6237	+	5.35507i	−0.741102	+	0.341427i
$247$	5.78245	+	21.5804i	0.367929	+	1.37313i
$248$	0.116337	+	0.434174i	0.00738738	+	0.0275701i
$249$	7.70674	+	5.44949i	0.488395	+	0.345347i
$250$	2.45692	+	10.9070i	0.155389	+	0.689822i
$251$		−	2.68556i		−	0.169511i	−0.996402	−	0.0847556i	$-0.972989\pi$
$251$		−	2.68556i		−	0.169511i	0.996402	−	0.0847556i	$-0.0270110\pi$
$252$	1.06658	+	13.6398i	0.0671883	+	0.859226i
$253$	0.449490	+	0.449490i	0.0282592	+	0.0282592i
$254$	1.32673	+	2.29796i	0.0832463	+	0.144187i
$255$	0.972652	+	1.44380i	0.0609098	+	0.0904144i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.4305	+	4.67050i	−1.08729	+	0.291337i	−0.757578	−	0.652745i	$-0.773617\pi$
$257$	−17.4305	+	4.67050i	−1.08729	+	0.291337i	−0.329709	+	0.944083i	$0.606951\pi$
$258$	−3.83548	−	4.61401i	−0.238786	−	0.287256i
$259$	16.7563	−	9.67423i	1.04118	−	0.601128i
$260$	7.70674	+	0.778539i	0.477952	+	0.0482829i
$261$	0.174235	−	0.937458i	0.0107849	−	0.0580272i
$262$	2.55051	−	2.55051i	0.157571	−	0.157571i
$263$	16.1280	+	4.32149i	0.994495	+	0.266474i	0.719138	−	0.694868i	$-0.244537\pi$
$263$	16.1280	+	4.32149i	0.994495	+	0.266474i	0.275358	+	0.961342i	$0.411204\pi$
$264$	−0.635674	+	0.898979i	−0.0391231	+	0.0553284i
$265$	6.99049	−	9.70380i	0.429422	−	0.596100i
$266$	−25.4722	−	14.7064i	−1.56180	−	0.901706i
$267$	−13.0387	−	4.81395i	−0.797955	−	0.294609i
$268$	−1.71089	+	6.38512i	−0.104509	+	0.390033i
$269$	−15.0956			−0.920398			−0.460199	−	0.887816i	$-0.652222\pi$
$269$	−15.0956			−0.920398			−0.460199	+	0.887816i	$0.652222\pi$
$270$	−10.6603	+	4.62158i	−0.648762	+	0.281260i
$271$	28.0454			1.70364			0.851819	−	0.523837i	$-0.175500\pi$
$271$	28.0454			1.70364			0.851819	+	0.523837i	$0.175500\pi$
$272$	−0.116337	+	0.434174i	−0.00705394	+	0.0263257i
$273$	25.6692	+	9.47720i	1.55357	+	0.573586i
$274$	18.8776	+	10.8990i	1.14044	+	0.658431i
$275$	−2.10759	+	2.37910i	−0.127092	+	0.143465i
$276$	−1.00000	+	1.41421i	−0.0601929	+	0.0851257i
$277$	27.1825	+	7.28353i	1.63324	+	0.437625i	0.954852	−	0.297080i	$-0.0960129\pi$
$277$	27.1825	+	7.28353i	1.63324	+	0.437625i	0.678386	+	0.734705i	$0.262680\pi$
$278$	−2.19275	+	2.19275i	−0.131513	+	0.131513i
$279$	−1.27135	+	0.449490i	−0.0761137	+	0.0269102i
$280$	−7.89898	+	6.44949i	−0.472054	+	0.385431i
$281$	−14.8485	+	8.57277i	−0.885785	+	0.511408i	−0.872562	−	0.488504i	$-0.837543\pi$
$281$	−14.8485	+	8.57277i	−0.885785	+	0.511408i	−0.0132238	+	0.999913i	$0.504209\pi$
$282$	−9.96486	−	11.9876i	−0.593399	−	0.713849i
$283$	−23.3914	+	6.26772i	−1.39048	+	0.372577i	−0.874916	−	0.484275i	$-0.839083\pi$
$283$	−23.3914	+	6.26772i	−1.39048	+	0.372577i	−0.515561	+	0.856853i	$0.672417\pi$
$284$	−3.14626	+	5.44949i	−0.186696	+	0.323368i
$285$	4.78024	−	24.5171i	0.283157	−	1.45227i
$286$	1.10102	+	1.90702i	0.0651047	+	0.112765i
$287$	−23.8273	−	23.8273i	−1.40648	−	1.40648i
$288$	−2.70711	−	1.29289i	−0.159518	−	0.0761845i
$289$		−	16.7980i		−	0.988115i
$290$	0.648089	−	0.291691i	0.0380571	−	0.0171287i
$291$	−3.79796	−	2.68556i	−0.222640	−	0.157430i
$292$	2.52520	+	9.42418i	0.147776	+	0.551508i
$293$	5.70577	+	21.2942i	0.333335	+	1.24402i	0.905663	+	0.423998i	$0.139374\pi$
$293$	5.70577	+	21.2942i	0.333335	+	1.24402i	−0.572329	+	0.820024i	$0.693960\pi$
$294$	−21.7060	+	10.0000i	−1.26592	+	0.583212i
$295$	−7.11867	+	18.7711i	−0.414465	+	1.09290i
$296$			4.24264i			0.246598i
$297$	−2.83740	−	1.69097i	−0.164643	−	0.0981201i
$298$	3.12372	+	3.12372i	0.180952	+	0.180952i
$299$	1.73205	+	3.00000i	0.100167	+	0.173494i
$300$	−7.36018	−	4.56374i	−0.424940	−	0.263488i
$301$	7.89898	−	13.6814i	0.455290	−	0.788585i
$302$	16.9964	−	4.55416i	0.978030	−	0.262062i
$303$	21.4840	−	3.68608i	1.23423	−	0.211760i
$304$	5.58542	−	3.22474i	0.320346	−	0.184952i
$305$	0.778539	+	0.953512i	0.0445790	+	0.0545979i
$306$	−1.32577	−	0.246405i	−0.0757890	−	0.0140860i
$307$	−6.67423	+	6.67423i	−0.380919	+	0.380919i	−0.871433	−	0.490514i	$-0.836809\pi$
$307$	−6.67423	+	6.67423i	−0.380919	+	0.380919i	0.490514	+	0.871433i	$0.336809\pi$
$308$	−2.80020	−	0.750311i	−0.159556	−	0.0427529i
$309$	16.8277	+	1.55051i	0.957294	+	0.0882054i
$310$	−0.815515	−	0.587486i	−0.0463181	−	0.0333670i
$311$	23.8207	+	13.7529i	1.35075	+	0.779853i	0.988354	−	0.152172i	$-0.0486269\pi$
$311$	23.8207	+	13.7529i	1.35075	+	0.779853i	0.362392	+	0.932026i	$0.381960\pi$
$312$	−4.61401	+	3.83548i	−0.261217	+	0.217141i
$313$	3.09273	−	11.5422i	0.174811	−	0.652405i	−0.821772	−	0.569816i	$-0.807015\pi$
$313$	3.09273	−	11.5422i	0.174811	−	0.652405i	0.996584	−	0.0825888i	$-0.0263188\pi$
$314$	14.6349			0.825898
$315$	−21.1370	−	22.1164i	−1.19093	−	1.24612i
$316$	2.44949			0.137795
$317$	−2.82086	+	10.5276i	−0.158435	+	0.591289i	0.840351	+	0.542042i	$0.182349\pi$
$317$	−2.82086	+	10.5276i	−0.158435	+	0.591289i	−0.998787	+	0.0492469i	$0.984318\pi$
$318$	1.56653	+	9.13041i	0.0878467	+	0.512008i
$319$	0.174973	+	0.101021i	0.00979659	+	0.00565606i
$320$	−0.358719	−	2.20711i	−0.0200530	−	0.123381i
$321$	13.9495	+	30.2788i	0.778585	+	1.69000i
$322$	−4.40508	−	1.18034i	−0.245486	−	0.0657777i
$323$	2.04989	−	2.04989i	0.114059	−	0.114059i
$324$	3.23375	−	8.39898i	0.179653	−	0.466610i
$325$	−14.4495	+	9.55051i	−0.801513	+	0.529767i
$326$	−5.44949	+	3.14626i	−0.301819	+	0.174255i
$327$	−3.39036	+	9.18286i	−0.187487	+	0.507813i
$328$	7.13713	−	1.91239i	0.394082	−	0.105594i
$329$	20.5222	−	35.5454i	1.13142	−	1.95968i
$330$	−0.170328	−	2.45606i	−0.00937627	−	0.135202i
$331$	−0.224745	−	0.389270i	−0.0123531	−	0.0213962i	0.859783	−	0.510660i	$-0.170599\pi$
$331$	−0.224745	−	0.389270i	−0.0123531	−	0.0213962i	−0.872136	+	0.489264i	$0.837266\pi$
$332$	−3.85337	−	3.85337i	−0.211481	−	0.211481i
$333$	−12.6892	+	0.992248i	−0.695363	+	0.0543748i
$334$		−	8.79796i		−	0.481403i
$335$	−6.06658	−	13.4789i	−0.331453	−	0.736432i
$336$	0.724745	−	7.86566i	0.0395381	−	0.429107i
$337$	−0.806003	−	3.00804i	−0.0439058	−	0.163859i	0.940492	−	0.339816i	$-0.110365\pi$
$337$	−0.806003	−	3.00804i	−0.0439058	−	0.163859i	−0.984398	+	0.175957i	$0.943698\pi$
$338$	−0.258819	−	0.965926i	−0.0140779	−	0.0525394i
$339$	0.921404	−	10.0000i	0.0500438	−	0.543125i
$340$	−0.412514	−	0.916536i	−0.0223717	−	0.0497061i
$341$		−	0.285729i		−	0.0154731i
$342$	10.9511	+	15.9511i	0.592167	+	0.862536i
$343$	−21.9217	−	21.9217i	−1.18366	−	1.18366i
$344$	1.73205	+	3.00000i	0.0933859	+	0.161749i
$345$	−0.267949	−	3.86370i	−0.0144259	−	0.208015i
$346$	6.44949	−	11.1708i	0.346727	−	0.600548i
$347$	22.9871	−	6.15937i	1.23401	−	0.330652i	0.417870	−	0.908507i	$-0.362777\pi$
$347$	22.9871	−	6.15937i	1.23401	−	0.330652i	0.816140	+	0.577855i	$0.196110\pi$
$348$	−0.190671	+	0.516436i	−0.0102210	+	0.0276839i
$349$	−25.1541	+	14.5227i	−1.34647	+	0.777383i	−0.987747	−	0.156063i	$-0.950120\pi$
$349$	−25.1541	+	14.5227i	−1.34647	+	0.777383i	−0.358719	+	0.933446i	$0.616786\pi$
$350$	4.56048	−	22.3417i	0.243768	−	1.19421i
$351$	−12.5505	−	12.9029i	−0.669897	−	0.688706i
$352$	0.449490	−	0.449490i	0.0239579	−	0.0239579i
$353$	−33.1244	−	8.87564i	−1.76303	−	0.472403i	−0.775704	−	0.631097i	$-0.782605\pi$
$353$	−33.1244	−	8.87564i	−1.76303	−	0.472403i	−0.987328	+	0.158694i	$0.949272\pi$
$354$	−6.50683	−	14.1237i	−0.345834	−	0.750667i
$355$	−2.25725	−	13.8883i	−0.119803	−	0.737114i
$356$	6.94949	+	4.01229i	0.368322	+	0.212651i
$357$	−0.600398	−	3.49938i	−0.0317764	−	0.185207i
$358$	−2.76368	+	10.3142i	−0.146065	+	0.545122i
$359$	3.32124			0.175288			0.0876441	−	0.996152i	$-0.472066\pi$
$359$	3.32124			0.175288			0.0876441	+	0.996152i	$0.472066\pi$
$360$	6.51727	−	1.58907i	0.343490	−	0.0837514i
$361$	−22.5959			−1.18926
$362$	3.99862	−	14.9231i	0.210163	−	0.784339i
$363$	−14.1132	+	11.7319i	−0.740753	+	0.615763i
$364$	−13.6814	−	7.89898i	−0.717102	−	0.414019i
$365$	−17.7016	−	12.7520i	−0.926543	−	0.667469i
$366$	−0.949490	−	0.0874863i	−0.0496306	−	0.00457298i
$367$	3.96008	+	1.06110i	0.206714	+	0.0553890i	0.360690	−	0.932686i	$-0.382541\pi$
$367$	3.96008	+	1.06110i	0.206714	+	0.0553890i	−0.153976	+	0.988075i	$0.549208\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$	7.38891	+	20.8990i	0.384651	+	1.08796i
$370$	−6.00000	−	7.34847i	−0.311925	−	0.382029i
$371$	−21.1237	+	12.1958i	−1.09669	+	0.633174i
$372$	0.767327	−	0.131652i	0.0397841	−	0.00682586i
$373$	0.476018	−	0.127549i	0.0246473	−	0.00660422i	−0.246474	−	0.969149i	$-0.579272\pi$
$373$	0.476018	−	0.127549i	0.0246473	−	0.00660422i	0.271122	+	0.962545i	$0.412605\pi$
$374$	0.142865	−	0.247449i	0.00738735	−	0.0127953i
$375$	19.2023	−	2.50423i	0.991603	−	0.129318i
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	0.778539	+	0.778539i	0.0400968	+	0.0400968i
$378$	23.6947	+	0.328036i	1.21872	+	0.0168724i
$379$			21.3485i			1.09660i	0.836283	+	0.548299i	$0.184724\pi$
$379$			21.3485i			1.09660i	−0.836283	+	0.548299i	$0.815276\pi$
$380$	−5.11376	+	13.4844i	−0.262330	+	0.691735i
$381$	4.17423	−	1.92308i	0.213853	−	0.0985222i
$382$	−4.51985	−	16.8683i	−0.231256	−	0.863058i
$383$	−2.12284	−	7.92256i	−0.108472	−	0.404824i	0.890244	−	0.455485i	$-0.150534\pi$
$383$	−2.12284	−	7.92256i	−0.108472	−	0.404824i	−0.998716	+	0.0506606i	$0.983867\pi$
$384$	1.41421	+	1.00000i	0.0721688	+	0.0510310i
$385$	5.91119	−	2.66050i	0.301262	−	0.135592i
$386$			17.3205i			0.881591i
$387$	−8.56753	+	5.88196i	−0.435512	+	0.298997i
$388$	1.89898	+	1.89898i	0.0964061	+	0.0964061i
$389$	18.4008	+	31.8712i	0.932959	+	1.61593i	0.778233	+	0.627975i	$0.216116\pi$
$389$	18.4008	+	31.8712i	0.932959	+	1.61593i	0.154726	+	0.987957i	$0.450551\pi$
$390$	2.56753	−	13.1684i	0.130012	−	0.666810i
$391$	0.224745	−	0.389270i	0.0113658	−	0.0196862i
$392$	13.3278	−	3.57117i	0.673156	−	0.180372i
$393$	−3.99366	−	4.80430i	−0.201453	−	0.242345i
$394$	−8.48528	+	4.89898i	−0.427482	+	0.246807i
$395$	−4.24264	+	3.46410i	−0.213470	+	0.174298i
$396$	1.44949	+	1.23924i	0.0728396	+	0.0622742i
$397$	10.5505	−	10.5505i	0.529515	−	0.529515i	−0.390913	−	0.920428i	$-0.627841\pi$
$397$	10.5505	−	10.5505i	0.529515	−	0.529515i	0.920428	+	0.390913i	$0.127841\pi$
$398$	8.16158	+	2.18689i	0.409103	+	0.109619i
$399$	−29.4128	+	41.5959i	−1.47248	+	2.08240i
$400$	3.74264	+	3.31552i	0.187132	+	0.165776i
$401$	7.65153	+	4.41761i	0.382099	+	0.220605i	0.678731	−	0.734387i	$-0.262530\pi$
$401$	7.65153	+	4.41761i	0.382099	+	0.220605i	−0.296632	+	0.954992i	$0.595863\pi$
$402$	10.7408	+	3.96556i	0.535703	+	0.197784i
$403$	0.403001	−	1.50402i	0.0200749	−	0.0749207i
$404$	−12.5851			−0.626130
$405$	6.27693	+	19.1207i	0.311903	+	0.950114i
$406$	−1.44949			−0.0719370
$407$	0.698019	−	2.60504i	0.0345995	−	0.129127i
$408$	0.730351	+	0.269649i	0.0361578	+	0.0133496i
$409$	−25.0273	−	14.4495i	−1.23752	−	0.714481i	−0.268932	−	0.963159i	$-0.586671\pi$
$409$	−25.0273	−	14.4495i	−1.23752	−	0.714481i	−0.968586	+	0.248678i	$0.920004\pi$
$410$	−9.65735	+	13.4058i	−0.476943	+	0.662065i
$411$	21.7980	−	30.8270i	1.07521	−	1.52058i
$412$	−9.42418	−	2.52520i	−0.464296	−	0.124408i
$413$	28.9521	−	28.9521i	1.42464	−	1.42464i
$414$	2.28024	+	1.94949i	0.112068	+	0.0958122i
$415$	12.1237	+	1.22474i	0.595130	+	0.0601204i
$416$	3.00000	−	1.73205i	0.147087	−	0.0849208i
$417$	3.43347	+	4.13041i	0.168138	+	0.202267i
$418$	−3.96008	+	1.06110i	−0.193694	+	0.0519001i
$419$	2.51059	−	4.34847i	0.122650	−	0.212437i	−0.798162	−	0.602443i	$-0.794194\pi$
$419$	2.51059	−	4.34847i	0.122650	−	0.212437i	0.920812	+	0.390007i	$0.127527\pi$
$420$	9.86843	+	14.6487i	0.481530	+	0.714782i
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	0.921461	−	0.388471i	$-0.126997\pi$
$421$	2.55051	+	4.41761i	0.124304	+	0.215301i	−0.797157	+	0.603773i	$0.793663\pi$
$422$	−6.43539	−	6.43539i	−0.313270	−	0.313270i
$423$	−22.2591	+	15.2818i	−1.08227	+	0.743026i
$424$		−	5.34847i		−	0.259745i
$425$	2.01067	+	1.00410i	0.0975319	+	0.0487062i
$426$	8.89898	+	6.29253i	0.431157	+	0.304874i
$427$	−0.649788	−	2.42504i	−0.0314455	−	0.117356i
$428$	−4.98161	−	18.5916i	−0.240795	−	0.898659i
$429$	3.46410	−	1.59592i	0.167248	−	0.0770516i
$430$	−7.24264	−	2.74666i	−0.349271	−	0.132456i
$431$			15.5563i			0.749323i	0.927162	+	0.374661i	$0.122241\pi$
$431$			15.5563i			0.749323i	−0.927162	+	0.374661i	$0.877759\pi$
$432$	−2.66012	+	4.46360i	−0.127985	+	0.214755i
$433$	13.4495	+	13.4495i	0.646341	+	0.646341i	0.952107	−	0.305766i	$-0.0989124\pi$
$433$	13.4495	+	13.4495i	0.646341	+	0.646341i	−0.305766	+	0.952107i	$0.598912\pi$
$434$	1.02494	+	1.77526i	0.0491989	+	0.0852150i
$435$	−0.400100	−	1.16414i	−0.0191833	−	0.0558164i
$436$	2.82577	−	4.89437i	0.135330	−	0.234398i
$437$	−6.22973	+	1.66925i	−0.298008	+	0.0798511i
$438$	16.6556	−	2.85765i	0.795836	−	0.136544i
$439$	−25.8058	+	14.8990i	−1.23164	+	0.711089i	−0.967372	−	0.253359i	$-0.918465\pi$
$439$	−25.8058	+	14.8990i	−1.23164	+	0.711089i	−0.264271	+	0.964449i	$0.585131\pi$
$440$	−0.142865	+	1.41421i	−0.00681080	+	0.0674200i
$441$	13.7980	+	39.0265i	0.657046	+	1.85841i
$442$	1.10102	−	1.10102i	0.0523702	−	0.0523702i
$443$	−5.26380	−	1.41043i	−0.250091	−	0.0670116i	0.131596	−	0.991303i	$-0.457990\pi$
$443$	−5.26380	−	1.41043i	−0.250091	−	0.0670116i	−0.381687	+	0.924292i	$0.624657\pi$
$444$	7.31747	+	0.674235i	0.347272	+	0.0319978i
$445$	−17.7111	+	2.87857i	−0.839587	+	0.136457i
$446$	22.1969	+	12.8154i	1.05106	+	0.606827i
$447$	5.88405	−	4.89121i	0.278306	−	0.231346i
$448$	−1.18034	+	4.40508i	−0.0557658	+	0.208121i
$449$	0.921404			0.0434837			0.0217419	−	0.999764i	$-0.493079\pi$
$449$	0.921404			0.0434837			0.0217419	+	0.999764i	$0.493079\pi$
$450$	−9.04096	+	11.9692i	−0.426195	+	0.564232i
$451$	−4.69694			−0.221170
$452$	−1.50062	+	5.60040i	−0.0705833	+	0.263421i
$453$	−5.15373	−	30.0381i	−0.242143	−	1.41131i
$454$	21.5631	+	12.4495i	1.01201	+	0.584284i
$455$	34.8678	−	5.66704i	1.63463	−	0.265675i
$456$	−4.67423	−	10.1459i	−0.218891	−	0.475125i
$457$	14.1363	+	3.78780i	0.661267	+	0.177186i	0.573818	−	0.818983i	$-0.305462\pi$
$457$	14.1363	+	3.78780i	0.661267	+	0.177186i	0.0874492	+	0.996169i	$0.472128\pi$
$458$	1.16781	−	1.16781i	0.0545681	−	0.0545681i
$459$	−0.635674	+	2.24745i	−0.0296707	+	0.104902i
$460$	−0.224745	+	2.22474i	−0.0104788	+	0.103729i
$461$	28.6237	−	16.5259i	1.33314	−	0.769689i	0.347360	−	0.937732i	$-0.387078\pi$
$461$	28.6237	−	16.5259i	1.33314	−	0.769689i	0.985780	+	0.168043i	$0.0537448\pi$
$462$	−1.73910	+	4.71039i	−0.0809102	+	0.219147i
$463$	11.8182	−	3.16668i	0.549239	−	0.147168i	0.0264810	−	0.999649i	$-0.491570\pi$
$463$	11.8182	−	3.16668i	0.549239	−	0.147168i	0.522758	+	0.852481i	$0.324903\pi$
$464$	0.158919	−	0.275255i	0.00737761	−	0.0127784i
$465$	−1.14286	+	1.31319i	−0.0529991	+	0.0608979i
$466$	−10.2247	−	17.7098i	−0.473652	−	0.820390i
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	0.769514	−	0.638630i	$-0.220499\pi$
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	−0.638630	+	0.769514i	$0.720499\pi$
$468$	5.88196	+	8.56753i	0.271894	+	0.396034i
$469$			30.1464i			1.39203i
$470$	−18.8169	−	7.13604i	−0.867960	−	0.329161i
$471$	2.32577	−	25.2415i	0.107166	−	1.16307i
$472$	2.32370	+	8.67217i	0.106957	+	0.399169i
$473$	−0.569930	−	2.12701i	−0.0262054	−	0.0977999i
$474$	0.389270	−	4.22474i	0.0178797	−	0.194049i
$475$	−10.2125	−	30.5876i	−0.468583	−	1.40346i
$476$			2.04989i			0.0939565i
$477$	15.9966	−	1.25087i	0.732433	−	0.0572736i
$478$	−12.0000	−	12.0000i	−0.548867	−	0.548867i
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	0.773879	−	0.633333i	$-0.218314\pi$
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	−0.935422	+	0.353533i	$0.884980\pi$
$480$	−3.86370	+	0.267949i	−0.176353	+	0.0122302i
$481$	7.34847	−	12.7279i	0.335061	−	0.580343i
$482$	18.3526	−	4.91756i	0.835938	−	0.223989i
$483$	−2.73583	+	7.41007i	−0.124485	+	0.337170i
$484$	9.17633	−	5.29796i	0.417106	−	0.240816i
$485$	−5.97469	−	0.603566i	−0.271297	−	0.0274065i
$486$	−13.9722	−	6.91215i	−0.633792	−	0.313541i
$487$	−12.0000	+	12.0000i	−0.543772	+	0.543772i	−0.924632	−	0.380861i	$-0.875628\pi$
$487$	−12.0000	+	12.0000i	−0.543772	+	0.543772i	0.380861	+	0.924632i	$0.375628\pi$
$488$	0.531752	+	0.142483i	0.0240713	+	0.00644988i
$489$	4.56048	+	9.89898i	0.206232	+	0.447647i
$490$	−18.0340	+	25.0338i	−0.814695	+	1.13091i
$491$	−24.2474	−	13.9993i	−1.09427	−	0.631778i	−0.159561	−	0.987188i	$-0.551008\pi$
$491$	−24.2474	−	13.9993i	−1.09427	−	0.631778i	−0.934711	+	0.355410i	$0.884341\pi$
$492$	−2.16416	−	12.6136i	−0.0975679	−	0.568667i
$493$	0.0369761	−	0.137997i	0.00166532	−	0.00621505i
$494$	−22.3417			−1.00520
$495$	−4.26314	−	0.0965401i	−0.191614	−	0.00433916i
$496$	−0.449490			−0.0201827
$497$	−7.42731	+	27.7191i	−0.333161	+	1.24337i
$498$	−7.25845	+	6.03371i	−0.325259	+	0.270377i
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	0.517325	−	0.855789i	$-0.326928\pi$
$499$	0.778539	+	0.449490i	0.0348522	+	0.0201219i	−0.482473	+	0.875911i	$0.660261\pi$
$500$	−11.1713	−	0.449747i	−0.499595	−	0.0201133i
$501$	−15.1742	−	1.39816i	−0.677935	−	0.0624652i
$502$	2.59405	+	0.695075i	0.115778	+	0.0310227i
$503$	4.02834	−	4.02834i	0.179615	−	0.179615i	−0.611573	−	0.791188i	$-0.709463\pi$
$503$	4.02834	−	4.02834i	0.179615	−	0.179615i	0.791188	+	0.611573i	$0.209463\pi$
$504$	−13.4511	−	2.50000i	−0.599159	−	0.111359i
$505$	21.7980	−	17.7980i	0.969996	−	0.791999i
$506$	−0.550510	+	0.317837i	−0.0244732	+	0.0141296i
$507$	−1.70711	+	0.292893i	−0.0758153	+	0.0130078i
$508$	−2.56304	+	0.686765i	−0.113717	+	0.0304702i
$509$	−4.22659	+	7.32066i	−0.187340	+	0.324483i	−0.944363	−	0.328906i	$-0.893320\pi$
$509$	−4.22659	+	7.32066i	−0.187340	+	0.324483i	0.757022	+	0.653389i	$0.226653\pi$
$510$	−1.64635	+	0.565826i	−0.0729014	+	0.0250552i
$511$	22.2474	+	38.5337i	0.984169	+	1.70463i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	29.2519	−	16.3529i	1.29150	−	0.721998i
$514$		−	18.0454i		−	0.795949i
$515$	19.8943	−	8.95403i	0.876649	−	0.394562i
$516$	5.44949	−	2.51059i	0.239900	−	0.110523i
$517$	−1.48072	−	5.52613i	−0.0651221	−	0.243039i
$518$	5.00775	+	18.6892i	0.220028	+	0.821156i
$519$	−18.2419	−	12.8990i	−0.800731	−	0.566202i
$520$	−2.74666	+	7.24264i	−0.120449	+	0.317611i
$521$		−	29.4449i		−	1.29000i	−0.764181	−	0.645001i	$-0.776857\pi$
$521$		−	29.4449i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$522$	0.860419	+	0.410930i	0.0376595	+	0.0179859i
$523$	4.22474	+	4.22474i	0.184735	+	0.184735i	0.793416	−	0.608680i	$-0.208301\pi$
$523$	4.22474	+	4.22474i	0.184735	+	0.184735i	−0.608680	+	0.793416i	$0.708301\pi$
$524$	1.80348	+	3.12372i	0.0787855	+	0.136461i
$525$	−37.8090	−	11.4162i	−1.65012	−	0.498243i
$526$	−8.34847	+	14.4600i	−0.364011	+	0.630485i
$527$	−0.195157	+	0.0522921i	−0.00850116	+	0.00227788i
$528$	−0.703823	−	0.846687i	−0.0306300	−	0.0368473i
$529$	19.0526	−	11.0000i	0.828372	−	0.478261i
$530$	7.56388	+	9.26382i	0.328554	+	0.402395i
$531$	−25.3939	+	8.97809i	−1.10200	+	0.389616i
$532$	20.7980	−	20.7980i	0.901706	−	0.901706i
$533$	−24.7238	−	6.62471i	−1.07090	−	0.286948i
$534$	8.02458	−	11.3485i	0.347258	−	0.491096i
$535$	34.9209	+	25.1566i	1.50976	+	1.08761i
$536$	−5.72474	−	3.30518i	−0.247271	−	0.142762i
$537$	17.3501	+	6.40576i	0.748714	+	0.276429i
$538$	3.90704	−	14.5813i	0.168444	−	0.628643i
$539$	−8.77101			−0.377794
$540$	−1.70502	−	11.4932i	−0.0733726	−	0.494587i
$541$	27.9444			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$541$	27.9444			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$542$	−7.25869	+	27.0898i	−0.311787	+	1.16361i
$543$	−25.1030	−	9.26816i	−1.07727	−	0.397735i
$544$	−0.389270	−	0.224745i	−0.0166898	−	0.00963586i
$545$	2.02731	+	12.4735i	0.0868406	+	0.534307i
$546$	−15.7980	+	22.3417i	−0.676090	+	0.956136i
$547$	3.92907	+	1.05279i	0.167995	+	0.0450140i	0.341836	−	0.939760i	$-0.388951\pi$
$547$	3.92907	+	1.05279i	0.167995	+	0.0450140i	−0.173841	+	0.984774i	$0.555618\pi$
$548$	−15.4135	+	15.4135i	−0.658431	+	0.658431i
$549$	−0.301783	+	1.62372i	−0.0128798	+	0.0692989i
$550$	−1.75255	−	2.65153i	−0.0747290	−	0.113062i
$551$	−1.77526	+	1.02494i	−0.0756284	+	0.0436641i
$552$	−1.10721	−	1.33195i	−0.0471258	−	0.0566916i
$553$	10.7902	−	2.89123i	0.458846	−	0.122947i
$554$	−14.0707	+	24.3712i	−0.597807	+	1.03543i
$555$	−13.6277	+	9.18066i	−0.578466	+	0.389697i
$556$	−1.55051	−	2.68556i	−0.0657563	−	0.113893i
$557$	−7.88171	−	7.88171i	−0.333959	−	0.333959i	0.520129	−	0.854088i	$-0.325884\pi$
$557$	−7.88171	−	7.88171i	−0.333959	−	0.333959i	−0.854088	+	0.520129i	$0.825884\pi$
$558$	−0.105124	−	1.34437i	−0.00445027	−	0.0569115i
$559$		−	12.0000i		−	0.507546i
$560$	−4.18532	−	9.29908i	−0.176862	−	0.392958i
$561$	−0.404082	−	0.285729i	−0.0170604	−	0.0120635i
$562$	−4.43759	−	16.5613i	−0.187188	−	0.698597i
$563$	5.08619	+	18.9819i	0.214357	+	0.799993i	0.986392	+	0.164412i	$0.0525726\pi$
$563$	5.08619	+	18.9819i	0.214357	+	0.799993i	−0.772034	+	0.635581i	$0.780761\pi$
$564$	14.1582	−	6.52270i	0.596167	−	0.274655i
$565$	−5.32101	−	11.8224i	−0.223856	−	0.497371i
$566$		−	24.2166i		−	1.01790i
$567$	4.33130	−	40.8151i	0.181898	−	1.71407i
$568$	−4.44949	−	4.44949i	−0.186696	−	0.186696i
$569$	−9.58166	−	16.5959i	−0.401684	−	0.695737i	0.592245	−	0.805758i	$-0.298242\pi$
$569$	−9.58166	−	16.5959i	−0.401684	−	0.695737i	−0.993929	+	0.110021i	$0.964908\pi$
$570$	22.4445	+	10.9628i	0.940096	+	0.459183i
$571$	−18.4495	+	31.9555i	−0.772087	+	1.33729i	0.164330	+	0.986405i	$0.447454\pi$
$571$	−18.4495	+	31.9555i	−0.772087	+	1.33729i	−0.936417	+	0.350889i	$0.885880\pi$
$572$	−2.12701	+	0.569930i	−0.0889347	+	0.0238300i
$573$	−29.8118	+	5.11490i	−1.24541	+	0.213678i
$574$	29.1824	−	16.8485i	1.21805	−	0.703242i
$575$	−2.75699	−	4.17121i	−0.114975	−	0.173951i
$576$	1.94949	−	2.28024i	0.0812287	−	0.0950100i
$577$	−17.0000	+	17.0000i	−0.707719	+	0.707719i	−0.966055	−	0.258336i	$-0.916826\pi$
$577$	−17.0000	+	17.0000i	−0.707719	+	0.707719i	0.258336	+	0.966055i	$0.416826\pi$
$578$	16.2256	+	4.34763i	0.674895	+	0.180838i
$579$	29.8735	+	2.75255i	1.24150	+	0.114392i
$580$	0.114014	+	0.701501i	0.00473419	+	0.0291282i
$581$	−21.5227	−	12.4261i	−0.892912	−	0.515523i
$582$	3.57704	−	2.97347i	0.148273	−	0.123254i
$583$	−0.879955	+	3.28404i	−0.0364440	+	0.136011i
$584$	−9.75663			−0.403732
$585$	−22.3042	−	6.52104i	−0.922164	−	0.269612i
$586$	−22.0454			−0.910687
$587$	3.37640	−	12.6009i	0.139359	−	0.520095i	−0.860583	−	0.509310i	$-0.829901\pi$
$587$	3.37640	−	12.6009i	0.139359	−	0.520095i	0.999942	−	0.0107843i	$-0.00343281\pi$
$588$	−4.04133	−	23.5546i	−0.166662	−	0.971375i
$589$	2.51059	+	1.44949i	0.103447	+	0.0597252i
$590$	−16.2891	−	11.7344i	−0.670610	−	0.483099i
$591$	7.10102	+	15.4135i	0.292097	+	0.634026i
$592$	−4.09808	−	1.09808i	−0.168430	−	0.0451307i
$593$	−7.24604	+	7.24604i	−0.297559	+	0.297559i	−0.840057	−	0.542498i	$-0.817479\pi$
$593$	−7.24604	+	7.24604i	−0.297559	+	0.297559i	0.542498	+	0.840057i	$0.317479\pi$
$594$	2.36773	−	2.30306i	0.0971489	−	0.0944958i
$595$	−2.89898	−	3.55051i	−0.118847	−	0.145557i
$596$	−3.82577	+	2.20881i	−0.156709	+	0.0904762i
$597$	5.06885	−	13.7291i	0.207454	−	0.561895i
$598$	−3.34607	+	0.896575i	−0.136831	+	0.0366637i
$599$	9.97093	−	17.2702i	0.407401	−	0.705639i	−0.587197	−	0.809444i	$-0.699768\pi$
$599$	9.97093	−	17.2702i	0.407401	−	0.705639i	0.994598	+	0.103805i	$0.0331018\pi$
$600$	6.31319	−	5.92820i	0.257735	−	0.242018i
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	0.806866	−	0.590735i	$-0.201162\pi$
$601$	−2.65153	−	4.59259i	−0.108158	−	0.187335i	−0.915024	+	0.403399i	$0.867829\pi$
$602$	11.1708	+	11.1708i	0.455290	+	0.455290i
$603$	8.54650	−	17.8950i	0.348040	−	0.728739i
$604$			17.5959i			0.715968i
$605$	−8.40143	+	22.1536i	−0.341567	+	0.900673i
$606$	−2.00000	+	21.7060i	−0.0812444	+	0.881747i
$607$	3.04744	+	11.3732i	0.123692	+	0.461624i	0.999790	−	0.0205092i	$-0.00652872\pi$
$607$	3.04744	+	11.3732i	0.123692	+	0.461624i	−0.876098	+	0.482133i	$0.839862\pi$
$608$	1.66925	+	6.22973i	0.0676971	+	0.252649i
$609$	−0.230351	+	2.50000i	−0.00933429	+	0.101305i
$610$	−1.12252	+	0.505224i	−0.0454496	+	0.0204559i
$611$		−	31.1769i		−	1.26128i
$612$	0.581142	−	1.21682i	0.0234913	−	0.0491869i
$613$	6.79796	+	6.79796i	0.274567	+	0.274567i	0.830936	−	0.556369i	$-0.187806\pi$
$613$	6.79796	+	6.79796i	0.274567	+	0.274567i	−0.556369	+	0.830936i	$0.687806\pi$
$614$	−4.71940	−	8.17423i	−0.190459	−	0.329885i
$615$	21.5868	+	18.7869i	0.870465	+	0.757561i
$616$	1.44949	−	2.51059i	0.0584016	−	0.101155i
$617$	−16.3232	+	4.37378i	−0.657146	+	0.176082i	−0.571958	−	0.820283i	$-0.693816\pi$
$617$	−16.3232	+	4.37378i	−0.657146	+	0.176082i	−0.0851882	+	0.996365i	$0.527149\pi$
$618$	−5.85301	+	15.8530i	−0.235442	+	0.637701i
$619$	42.2121	−	24.3712i	1.69665	−	0.979560i	0.747748	−	0.663982i	$-0.231135\pi$
$619$	42.2121	−	24.3712i	1.69665	−	0.979560i	0.948900	−	0.315578i	$-0.102198\pi$
$620$	0.778539	−	0.635674i	0.0312669	−	0.0255293i
$621$	3.72474	−	3.62302i	0.149469	−	0.145387i
$622$	−19.4495	+	19.4495i	−0.779853	+	0.779853i
$623$	35.3489	+	9.47172i	1.41623	+	0.379476i
$624$	−2.51059	−	5.44949i	−0.100504	−	0.218154i
$625$	19.9853	−	15.0196i	0.799411	−	0.600784i
$626$	10.3485	+	5.97469i	0.413608	+	0.238797i
$627$	1.20080	+	6.99876i	0.0479552	+	0.279503i
$628$	−3.78780	+	14.1363i	−0.151150	+	0.564099i
$629$	−1.90702			−0.0760380
$630$	26.8335	−	14.6926i	1.06907	−	0.585366i
$631$	−3.10102			−0.123450			−0.0617248	−	0.998093i	$-0.519660\pi$
$631$	−3.10102			−0.123450			−0.0617248	+	0.998093i	$0.519660\pi$
$632$	−0.633975	+	2.36603i	−0.0252182	+	0.0941154i
$633$	−12.1221	+	10.0767i	−0.481811	+	0.400513i
$634$	−9.43879	−	5.44949i	−0.374862	−	0.216427i
$635$	3.46808	−	4.81420i	0.137627	−	0.191046i
$636$	−9.22474	−	0.849971i	−0.365785	−	0.0337036i
$637$	−46.1689	−	12.3709i	−1.82928	−	0.490153i
$638$	−0.142865	+	0.142865i	−0.00565606	+	0.00565606i
$639$	12.2672	−	14.3485i	0.485284	−	0.567617i
$640$	2.22474	+	0.224745i	0.0879408	+	0.00888382i
$641$	16.7474	−	9.66914i	0.661484	−	0.381908i	−0.131358	−	0.991335i	$-0.541934\pi$
$641$	16.7474	−	9.66914i	0.661484	−	0.381908i	0.792842	+	0.609427i	$0.208600\pi$
$642$	−32.8575	+	5.63745i	−1.29678	+	0.222492i
$643$	−6.10913	+	1.63694i	−0.240921	+	0.0645545i	−0.377259	−	0.926108i	$-0.623133\pi$
$643$	−6.10913	+	1.63694i	−0.240921	+	0.0645545i	0.136338	+	0.990662i	$0.456467\pi$
$644$	2.28024	−	3.94949i	0.0898540	−	0.155632i
$645$	−5.88828	+	12.0552i	−0.231851	+	0.474673i
$646$	1.44949	+	2.51059i	0.0570294	+	0.0987778i
$647$	23.5416	+	23.5416i	0.925516	+	0.925516i	0.997412	−	0.0718961i	$-0.0229050\pi$
$647$	23.5416	+	23.5416i	0.925516	+	0.925516i	−0.0718961	+	0.997412i	$0.522905\pi$
$648$	7.27583	+	5.29738i	0.285822	+	0.208101i
$649$		−	5.70714i		−	0.224025i
$650$	−5.48528	−	16.4290i	−0.215150	−	0.644398i
$651$	3.22474	−	1.48565i	0.126388	−	0.0582271i
$652$	−1.62863	−	6.07812i	−0.0637819	−	0.238037i
$653$	6.84563	+	25.5482i	0.267890	+	0.999780i	0.960457	+	0.278427i	$0.0898129\pi$
$653$	6.84563	+	25.5482i	0.267890	+	0.999780i	−0.692567	+	0.721353i	$0.743520\pi$
$654$	−7.99247	−	5.65153i	−0.312530	−	0.220992i
$655$	−7.54134	−	2.85994i	−0.294664	−	0.111747i
$656$			7.38891i			0.288488i
$657$	−2.28183	−	29.1808i	−0.0890227	−	1.13845i
$658$	29.0227	+	29.0227i	1.13142	+	1.13142i
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	0.954917	−	0.296872i	$-0.0959435\pi$
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	−0.734557	+	0.678546i	$0.762610\pi$
$660$	2.41645	+	0.471150i	0.0940603	+	0.0183395i
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	−0.853076	−	0.521786i	$-0.825266\pi$
$661$	0.651531	−	1.12848i	0.0253416	−	0.0438930i	0.878418	+	0.477893i	$0.158599\pi$
$662$	0.434174	−	0.116337i	0.0168746	−	0.00452155i
$663$	−1.72401	−	2.07395i	−0.0669549	−	0.0805456i
$664$	4.71940	−	2.72474i	0.183148	−	0.105741i
$665$	−6.61037	+	65.4359i	−0.256339	+	2.53749i
$666$	2.32577	−	12.5136i	0.0901216	−	0.484893i
$667$	−0.224745	+	0.224745i	−0.00870216	+	0.00870216i
$668$	8.49818	+	2.27708i	0.328804	+	0.0881028i
$669$	25.6308	−	36.2474i	0.990945	−	1.40141i
$670$	14.5898	−	2.37127i	0.563653	−	0.0916100i
$671$	−0.303062	−	0.174973i	−0.0116996	−	0.00675474i
$672$	7.41007	+	2.73583i	0.285850	+	0.105537i
$673$	−6.02093	+	22.4704i	−0.232090	+	0.866171i	0.747349	+	0.664431i	$0.231326\pi$
$673$	−6.02093	+	22.4704i	−0.232090	+	0.866171i	−0.979439	+	0.201740i	$0.935340\pi$
$674$	3.11416			0.119953
$675$	19.2070	+	17.4955i	0.739277	+	0.673401i
$676$	1.00000			0.0384615
$677$	−11.8011	+	44.0423i	−0.453553	+	1.69268i	0.238755	+	0.971080i	$0.423261\pi$
$677$	−11.8011	+	44.0423i	−0.453553	+	1.69268i	−0.692308	+	0.721602i	$0.743406\pi$
$678$	9.42078	+	3.47820i	0.361803	+	0.133579i
$679$	10.6066	+	6.12372i	0.407044	+	0.235007i
$680$	0.992072	−	0.161241i	0.0380442	−	0.00618330i
$681$	24.8990	−	35.2125i	0.954131	−	1.34934i
$682$	0.275993	+	0.0739521i	0.0105683	+	0.00283177i
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	−0.920632	−	0.390431i	$-0.872326\pi$
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	0.390431	+	0.920632i	$0.372326\pi$
$684$	−18.2419	+	6.44949i	−0.697497	+	0.246602i
$685$	4.89898	−	48.4949i	0.187180	−	1.85289i
$686$	26.8485	−	15.5010i	1.02508	−	0.591830i
$687$	−1.82859	−	2.19976i	−0.0697649	−	0.0839260i
$688$	−3.34607	+	0.896575i	−0.127568	+	0.0341816i
$689$	−9.26382	+	16.0454i	−0.352923	+	0.611281i
$690$	3.80140	+	0.741181i	0.144717	+	0.0282163i
$691$	10.4722	+	18.1384i	0.398381	+	0.690016i	0.993526	−	0.113602i	$-0.0362388\pi$
$691$	10.4722	+	18.1384i	0.398381	+	0.690016i	−0.595145	+	0.803618i	$0.702906\pi$
$692$	9.12096	+	9.12096i	0.346727	+	0.346727i
$693$	7.84785	+	3.74807i	0.298115	+	0.142377i
$694$			23.7980i			0.903358i
$695$	6.48352	+	2.45878i	0.245934	+	0.0932668i
$696$	−0.449490	−	0.317837i	−0.0170379	−	0.0120476i
$697$	0.859599	+	3.20807i	0.0325596	+	0.121514i
$698$	−7.51750	−	28.0557i	−0.284542	−	1.06192i
$699$	−32.1698	+	14.8207i	−1.21677	+	0.560569i
$700$	20.4001	+	10.1875i	0.771050	+	0.385053i
$701$			21.1024i			0.797028i	0.917162	+	0.398514i	$0.130474\pi$
$701$			21.1024i			0.797028i	−0.917162	+	0.398514i	$0.869526\pi$
$702$	15.7116	−	8.78335i	0.592994	−	0.331506i
$703$	19.3485	+	19.3485i	0.729741	+	0.729741i
$704$	0.317837	+	0.550510i	0.0119789	+	0.0207481i
$705$	−15.2982	+	31.3204i	−0.576164	+	1.17959i
$706$	17.1464	−	29.6985i	0.645314	−	1.11772i
$707$	−55.4382	+	14.8546i	−2.08497	+	0.558666i
$708$	15.3266	−	2.62962i	0.576007	−	0.0988272i
$709$	−25.6790	+	14.8258i	−0.964394	+	0.556793i	−0.897523	−	0.440968i	$-0.854635\pi$
$709$	−25.6790	+	14.8258i	−0.964394	+	0.556793i	−0.0668716	+	0.997762i	$0.521302\pi$
$710$	13.9993	+	1.41421i	0.525383	+	0.0530745i
$711$	−7.22474	−	1.34278i	−0.270949	−	0.0503582i
$712$	−5.67423	+	5.67423i	−0.212651	+	0.212651i
$713$	0.434174	+	0.116337i	0.0162599	+	0.00435684i
$714$	3.53553	+	0.325765i	0.132314	+	0.0121915i
$715$	2.87808	−	3.99519i	0.107634	−	0.149412i
$716$	−9.24745	−	5.33902i	−0.345593	−	0.199528i
$717$	−22.6040	+	18.7899i	−0.844160	+	0.701722i
$718$	−0.859599	+	3.20807i	−0.0320800	+	0.119724i
$719$	32.5269			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$719$	32.5269			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$720$	−0.151870	+	6.70648i	−0.00565988	+	0.249936i
$721$	−44.4949			−1.65708
$722$	5.84825	−	21.8260i	0.217649	−	0.812279i
$723$	−5.56497	−	32.4350i	−0.206964	−	1.20627i
$724$	13.3797	+	7.72474i	0.497251	+	0.287088i
$725$	−1.18955	−	1.05379i	−0.0441788	−	0.0391369i
$726$	−7.67934	−	16.6688i	−0.285007	−	0.618636i
$727$	−46.6759	−	12.5068i	−1.73111	−	0.463850i	−0.750674	−	0.660673i	$-0.770271\pi$
$727$	−46.6759	−	12.5068i	−1.73111	−	0.463850i	−0.980439	+	0.196822i	$0.936938\pi$
$728$	11.1708	−	11.1708i	0.414019	−	0.414019i
$729$	−14.1421	+	23.0000i	−0.523783	+	0.851852i
$730$	16.8990	−	13.7980i	0.625459	−	0.510685i
$731$	−1.34847	+	0.778539i	−0.0498749	+	0.0287953i
$732$	0.330251	−	0.894494i	0.0122064	−	0.0330614i
$733$	−32.9846	+	8.83821i	−1.21832	+	0.326447i	−0.810019	−	0.586403i	$-0.800543\pi$
$733$	−32.9846	+	8.83821i	−1.21832	+	0.326447i	−0.408296	+	0.912850i	$0.633877\pi$
$734$	−2.04989	+	3.55051i	−0.0756627	+	0.131052i
$735$	40.3110	+	35.0824i	1.48689	+	1.29404i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	2.97129	+	2.97129i	0.109449	+	0.109449i
$738$	−22.0993	+	1.72808i	−0.813485	+	0.0636115i
$739$		−	28.9444i		−	1.06474i	−0.846513	−	0.532368i	$-0.821302\pi$
$739$		−	28.9444i		−	1.06474i	0.846513	−	0.532368i	$-0.178698\pi$
$740$	8.65099	−	3.89363i	0.318017	−	0.143133i
$741$	−3.55051	+	38.5337i	−0.130431	+	1.41557i
$742$	−6.31300	−	23.5605i	−0.231758	−	0.864931i
$743$	−2.56204	−	9.56168i	−0.0939923	−	0.350784i	0.902872	−	0.429909i	$-0.141454\pi$
$743$	−2.56204	−	9.56168i	−0.0939923	−	0.350784i	−0.996865	+	0.0791245i	$0.974788\pi$
$744$	−0.0714323	+	0.775255i	−0.00261883	+	0.0284222i
$745$	3.50270	−	9.23621i	0.128329	−	0.338389i
$746$			0.492810i			0.0180431i
$747$	9.25311	+	13.4779i	0.338553	+	0.493129i
$748$	0.202041	+	0.202041i	0.00738735	+	0.00738735i
$749$	−43.8888	−	76.0176i	−1.60366	−	2.77762i
$750$	−2.55103	+	19.1962i	−0.0931503	+	0.700944i
$751$	−10.3485	+	17.9241i	−0.377621	+	0.654059i	−0.990716	−	0.135951i	$-0.956591\pi$
$751$	−10.3485	+	17.9241i	−0.377621	+	0.654059i	0.613095	+	0.790010i	$0.289924\pi$
$752$	−8.69333	+	2.32937i	−0.317013	+	0.0849434i
$753$	1.61107	−	4.36362i	0.0587107	−	0.159019i
$754$	−0.953512	+	0.550510i	−0.0347248	+	0.0200484i
$755$	−24.8844	−	30.4770i	−0.905636	−	1.10917i
$756$	−6.44949	+	22.8024i	−0.234566	+	0.829315i
$757$	22.0454	−	22.0454i	0.801254	−	0.801254i	−0.182038	−	0.983292i	$-0.558269\pi$
$757$	22.0454	−	22.0454i	0.801254	−	0.801254i	0.983292	+	0.182038i	$0.0582693\pi$
$758$	−20.6210	−	5.52539i	−0.748990	−	0.200691i
$759$	0.460702	+	1.00000i	0.0167224	+	0.0362977i
$760$	−11.7014	−	8.42953i	−0.424454	−	0.305771i
$761$	−5.60102	−	3.23375i	−0.203037	−	0.117223i	0.395034	−	0.918666i	$-0.370733\pi$
$761$	−5.60102	−	3.23375i	−0.203037	−	0.117223i	−0.598071	+	0.801443i	$0.704066\pi$
$762$	0.777179	+	4.52973i	0.0281542	+	0.164095i
$763$	6.67072	−	24.8955i	0.241496	−	0.901276i
$764$	17.4634			0.631803
$765$	0.714271	+	2.92945i	0.0258245	+	0.105914i
$766$	8.20204			0.296352
$767$	8.04954	−	30.0413i	0.290652	−	1.08473i
$768$	−1.33195	+	1.10721i	−0.0480627	+	0.0399529i
$769$	−8.39780	−	4.84847i	−0.302832	−	0.174840i	0.340882	−	0.940106i	$-0.389274\pi$
$769$	−8.39780	−	4.84847i	−0.302832	−	0.174840i	−0.643715	+	0.765266i	$0.722608\pi$
$770$	1.03992	+	6.39836i	0.0374761	+	0.230581i
$771$	−31.1237	−	2.86775i	−1.12089	−	0.103280i
$772$	−16.7303	−	4.48288i	−0.602138	−	0.161342i
$773$	30.8270	−	30.8270i	1.10877	−	1.10877i	0.115456	−	0.993313i	$-0.463167\pi$
$773$	30.8270	−	30.8270i	1.10877	−	1.10877i	0.993313	−	0.115456i	$-0.0368331\pi$
$774$	−3.46410	−	9.79796i	−0.124515	−	0.352180i
$775$	−0.449490	+	2.20204i	−0.0161461	+	0.0790996i
$776$	−2.32577	+	1.34278i	−0.0834901	+	0.0482030i
$777$	33.0299	−	5.66704i	1.18494	−	0.203304i
$778$	−35.5477	+	9.52497i	−1.27445	+	0.341487i
$779$	23.8273	−	41.2702i	0.853703	−	1.47866i
$780$	12.0552	+	5.88828i	0.431646	+	0.210834i
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	0.317837	+	0.317837i	0.0113658	+	0.0113658i
$783$	0.845485	−	1.41870i	0.0302152	−	0.0507002i
$784$			13.7980i			0.492784i
$785$	−13.4310	−	29.8415i	−0.479374	−	1.06509i
$786$	5.67423	−	2.61413i	0.202393	−	0.0932429i
$787$	−2.52520	−	9.42418i	−0.0900137	−	0.335936i	0.906203	−	0.422844i	$-0.138968\pi$
$787$	−2.52520	−	9.42418i	−0.0900137	−	0.335936i	−0.996216	+	0.0869079i	$0.972301\pi$
$788$	−2.53590	−	9.46410i	−0.0903376	−	0.337145i
$789$	23.6130	+	16.6969i	0.840646	+	0.594427i
$790$	−2.24799	−	4.99465i	−0.0799799	−	0.177702i
$791$			26.4415i			0.940150i
$792$	−1.57217	+	1.07936i	−0.0558646	+	0.0383534i
$793$	−1.34847	−	1.34847i	−0.0478855	−	0.0478855i
$794$	7.46034	+	12.9217i	0.264757	+	0.458573i
$795$	17.1798	−	11.5736i	0.609304	−	0.410472i
$796$	−4.22474	+	7.31747i	−0.149742	+	0.259361i
$797$	38.4419	−	10.3005i	1.36168	−	0.364861i	0.497248	−	0.867609i	$-0.334344\pi$
$797$	38.4419	−	10.3005i	1.36168	−	0.364861i	0.864433	+	0.502747i	$0.167677\pi$
$798$	−32.5660	−	39.1764i	−1.15282	−	1.38683i
$799$	−3.50343	+	2.02270i	−0.123942	+	0.0715581i
$800$	−4.17121	+	2.75699i	−0.147474	+	0.0974745i
$801$	−18.2980	−	15.6438i	−0.646527	−	0.552748i
$802$	−6.24745	+	6.24745i	−0.220605	+	0.220605i
$803$	5.99071	+	1.60521i	0.211408	+	0.0566465i
$804$	−6.61037	+	9.34847i	−0.233130	+	0.329695i
$805$	1.63593	+	10.0655i	0.0576590	+	0.354761i
$806$	1.34847	+	0.778539i	0.0474978	+	0.0274229i
$807$	−24.5281	−	9.05589i	−0.863429	−	0.318782i
$808$	3.25725	−	12.1562i	0.114590	−	0.427655i
$809$	−19.4490			−0.683792			−0.341896	−	0.939738i	$-0.611069\pi$
$809$	−19.4490			−0.683792			−0.341896	+	0.939738i	$0.611069\pi$
$810$	−20.0937	+	1.11425i	−0.706022	+	0.0391509i
$811$	−39.6413			−1.39200			−0.695998	−	0.718044i	$-0.745038\pi$
$811$	−39.6413			−1.39200			−0.695998	+	0.718044i	$0.745038\pi$
$812$	0.375156	−	1.40010i	0.0131654	−	0.0491339i
$813$	45.5694	+	16.8245i	1.59819	+	0.590059i
$814$	2.33562	+	1.34847i	0.0818633	+	0.0472638i
$815$	11.4166	+	8.22438i	0.399907	+	0.288087i
$816$	−0.449490	+	0.635674i	−0.0157353	+	0.0222531i
$817$	21.5804	+	5.78245i	0.755003	+	0.202302i
$818$	20.4347	−	20.4347i	0.714481	−	0.714481i
$819$	36.0231	+	30.7980i	1.25875	+	1.07617i
$820$	−10.4495	−	12.7980i	−0.364912	−	0.446924i
$821$	19.3207	−	11.1548i	0.674296	−	0.389305i	−0.123407	−	0.992356i	$-0.539382\pi$
$821$	19.3207	−	11.1548i	0.674296	−	0.389305i	0.797702	+	0.603051i	$0.206049\pi$
$822$	24.1348	+	29.0338i	0.841799	+	1.01267i
$823$	−3.23908	+	0.867910i	−0.112907	+	0.0302534i	−0.314830	−	0.949148i	$-0.601948\pi$
$823$	−3.23908	+	0.867910i	−0.112907	+	0.0302534i	0.201923	+	0.979401i	$0.435281\pi$
$824$	4.87832	−	8.44949i	0.169944	−	0.294352i
$825$	−4.85173	+	2.60133i	−0.168915	+	0.0905666i
$826$	20.4722	+	35.4589i	0.712319	+	1.23377i
$827$	31.5662	+	31.5662i	1.09766	+	1.09766i	0.994683	+	0.102980i	$0.0328379\pi$
$827$	31.5662	+	31.5662i	1.09766	+	1.09766i	0.102980	+	0.994683i	$0.467162\pi$
$828$	−2.47323	+	1.69798i	−0.0859507	+	0.0590088i
$829$			10.5505i			0.366434i	0.983072	+	0.183217i	$0.0586512\pi$
$829$			10.5505i			0.366434i	−0.983072	+	0.183217i	$0.941349\pi$
$830$	−4.32086	+	11.3936i	−0.149979	+	0.395479i
$831$	39.7980	+	28.1414i	1.38058	+	0.976215i
$832$	0.896575	+	3.34607i	0.0310832	+	0.116004i
$833$	1.60521	+	5.99071i	0.0556171	+	0.207566i
$834$	−4.87832	+	2.24745i	−0.168922	+	0.0778228i
$835$	−17.9395	+	8.07422i	−0.620824	+	0.279420i
$836$		−	4.09978i		−	0.141794i
$837$	−2.33539	−	0.0323319i	−0.0807230	−	0.00111755i
$838$	3.55051	+	3.55051i	0.122650	+	0.122650i
$839$	0.246405	+	0.426786i	0.00850684	+	0.0147343i	0.870247	−	0.492615i	$-0.163959\pi$
$839$	0.246405	+	0.426786i	0.00850684	+	0.0147343i	−0.861741	+	0.507349i	$0.830625\pi$
$840$	−16.7037	+	5.74082i	−0.576331	+	0.198077i
$841$	14.4495	−	25.0273i	0.498258	−	0.863009i
$842$	−4.92721	+	1.32024i	−0.169803	+	0.0454985i
$843$	−29.2693	+	5.02181i	−1.00809	+	0.172960i
$844$	7.88171	−	4.55051i	0.271300	−	0.156635i
$845$	−1.73205	+	1.41421i	−0.0595844	+	0.0486504i
$846$	−9.00000	−	25.4558i	−0.309426	−	0.875190i
$847$	34.1691	−	34.1691i	1.17407	−	1.17407i
$848$	5.16622	+	1.38429i	0.177409	+	0.0475366i
$849$	−41.7675	−	3.84847i	−1.43346	−	0.132079i
$850$	−1.49029	+	1.68228i	−0.0511165	+	0.0577017i
$851$	3.67423	+	2.12132i	0.125951	+	0.0727179i
$852$	−8.38134	+	6.96713i	−0.287140	+	0.238690i
$853$	−0.641478	+	2.39403i	−0.0219638	+	0.0819700i	−0.976038	−	0.217601i	$-0.930177\pi$
$853$	−0.641478	+	2.39403i	−0.0219638	+	0.0819700i	0.954074	+	0.299571i	$0.0968435\pi$
$854$	2.51059			0.0859106
$855$	22.4750	−	36.9688i	0.768627	−	1.26431i
$856$	19.2474			0.657864
$857$	4.08881	−	15.2597i	0.139671	−	0.521260i	−0.860264	−	0.509849i	$-0.829701\pi$
$857$	4.08881	−	15.2597i	0.139671	−	0.521260i	0.999935	−	0.0114106i	$-0.00363219\pi$
$858$	0.644963	+	3.75912i	0.0220187	+	0.128334i
$859$	−40.2658	−	23.2474i	−1.37385	−	0.793193i	−0.382440	−	0.923980i	$-0.624916\pi$
$859$	−40.2658	−	23.2474i	−1.37385	−	0.793193i	−0.991410	+	0.130788i	$0.958249\pi$
$860$	4.52761	−	6.28497i	0.154390	−	0.214316i
$861$	−24.4217	−	53.0097i	−0.832289	−	1.80657i
$862$	−15.0263	−	4.02628i	−0.511797	−	0.137136i
$863$	−20.7132	+	20.7132i	−0.705085	+	0.705085i	−0.965497	−	0.260413i	$-0.916141\pi$
$863$	−20.7132	+	20.7132i	−0.705085	+	0.705085i	0.260413	+	0.965497i	$0.416141\pi$
$864$	−3.62302	−	3.72474i	−0.123258	−	0.126718i
$865$	−28.6969	−	2.89898i	−0.975725	−	0.0985683i
$866$	−16.4722	+	9.51023i	−0.559748	+	0.323171i
$867$	10.0771	−	27.2941i	0.342236	−	0.926955i
$868$	−1.98004	+	0.530550i	−0.0672069	+	0.0180080i
$869$	0.778539	−	1.34847i	0.0264101	−	0.0457437i
$870$	1.22803	−	0.0851642i	0.0416341	−	0.00288734i
$871$	11.4495	+	19.8311i	0.387951	+	0.671951i
$872$	3.99624	+	3.99624i	0.135330	+	0.135330i
$873$	−4.56002	−	6.64202i	−0.154333	−	0.224798i
$874$		−	6.44949i		−	0.218157i
$875$	−49.7413	+	11.2047i	−1.68156	+	0.378789i
$876$	−1.55051	+	16.8277i	−0.0523869	+	0.568555i
$877$	11.0713	+	41.3188i	0.373852	+	1.39524i	0.855014	+	0.518604i	$0.173548\pi$
$877$	11.0713	+	41.3188i	0.373852	+	1.39524i	−0.481162	+	0.876632i	$0.659785\pi$
$878$	−7.71228	−	28.7826i	−0.260277	−	0.971366i
$879$	−3.50343	+	38.0227i	−0.118168	+	1.28247i
$880$	−1.32905	−	0.504022i	−0.0448022	−	0.0169906i
$881$		−	54.8365i		−	1.84749i	−0.383010	−	0.923744i	$-0.625113\pi$
$881$		−	54.8365i		−	1.84749i	0.383010	−	0.923744i	$-0.374887\pi$
$882$	−41.2679	+	3.22700i	−1.38956	+	0.108659i
$883$	6.27015	+	6.27015i	0.211007	+	0.211007i	0.804695	−	0.593688i	$-0.202329\pi$
$883$	6.27015	+	6.27015i	0.211007	+	0.211007i	−0.593688	+	0.804695i	$0.702329\pi$
$884$	0.778539	+	1.34847i	0.0261851	+	0.0453539i
$885$	−22.8275	+	26.2297i	−0.767339	+	0.881701i
$886$	2.72474	−	4.71940i	0.0915396	−	0.158551i
$887$	−7.92256	+	2.12284i	−0.266014	+	0.0712781i	−0.389360	−	0.921085i	$-0.627304\pi$
$887$	−7.92256	+	2.12284i	−0.266014	+	0.0712781i	0.123347	+	0.992364i	$0.460637\pi$
$888$	−2.54516	+	6.89363i	−0.0854100	+	0.231335i
$889$	−10.4798	+	6.05051i	−0.351481	+	0.202928i
$890$	1.80348	−	17.8526i	0.0604529	−	0.598422i
$891$	−3.59592	−	4.44972i	−0.120468	−	0.149071i
$892$	−18.1237	+	18.1237i	−0.606827	+	0.606827i
$893$	56.0676	+	15.0233i	1.87623	+	0.502734i
$894$	3.20164	+	6.94949i	0.107079	+	0.232426i
$895$	23.5676	−	3.83042i	0.787777	−	0.128037i
$896$	−3.94949	−	2.28024i	−0.131943	−	0.0761774i
$897$	1.01461	+	5.91359i	0.0338769	+	0.197449i
$898$	−0.238477	+	0.890008i	−0.00795807	+	0.0296999i
$899$	0.142865			0.00476480
$900$	−9.22135	−	11.8307i	−0.307378	−	0.394358i
$901$	2.40408			0.0800916
$902$	1.21566	−	4.53689i	0.0404770	−	0.151062i
$903$	21.0421	−	17.4916i	0.700238	−	0.582084i
$904$	−5.02118	−	2.89898i	−0.167002	−	0.0964186i
$905$	−34.0987	+	5.54203i	−1.13348	+	0.184223i
$906$	30.3485	+	2.79632i	1.00826	+	0.0929015i
$907$	3.65307	+	0.978838i	0.121298	+	0.0325018i	0.318957	−	0.947769i	$-0.396667\pi$
$907$	3.65307	+	0.978838i	0.121298	+	0.0325018i	−0.197659	+	0.980271i	$0.563334\pi$
$908$	−17.6062	+	17.6062i	−0.584284	+	0.584284i
$909$	37.1195	+	6.89898i	1.23118	+	0.228825i
$910$	−3.55051	+	35.1464i	−0.117698	+	1.16509i
$911$	−6.12372	+	3.53553i	−0.202888	+	0.117137i	−0.598002	−	0.801495i	$-0.704038\pi$
$911$	−6.12372	+	3.53553i	−0.202888	+	0.117137i	0.395114	+	0.918632i	$0.370705\pi$
$912$	11.0100	−	1.88901i	0.364576	−	0.0625514i
$913$	−3.34607	+	0.896575i	−0.110739	+	0.0296723i
$914$	−7.31747	+	12.6742i	−0.242040	+	0.419226i
$915$	0.692993	+	2.01635i	0.0229096	+	0.0666586i
$916$	0.825765	+	1.43027i	0.0272841	+	0.0472574i
$917$	11.6315	+	11.6315i	0.384107	+	0.384107i
$918$	−2.00634	−	1.19570i	−0.0662192	−	0.0394639i
$919$		−	12.6515i		−	0.417335i	−0.977987	−	0.208668i	$-0.933087\pi$
$919$		−	12.6515i		−	0.417335i	0.977987	−	0.208668i	$-0.0669127\pi$
$920$	−2.09077	−	0.792893i	−0.0689307	−	0.0261409i
$921$	−14.8485	+	6.84072i	−0.489274	+	0.225409i
$922$	8.55444	+	31.9256i	0.281726	+	1.05141i
$923$	5.64173	+	21.0552i	0.185700	+	0.693041i
$924$	−4.09978	−	2.89898i	−0.134873	−	0.0953694i
$925$	−9.47753	+	18.9783i	−0.311619	+	0.624003i
$926$			12.2351i			0.402071i
$927$	26.4122	+	12.6143i	0.867492	+	0.414307i
$928$	0.224745	+	0.224745i	0.00737761	+	0.00737761i
$929$	21.1024	+	36.5505i	0.692349	+	1.19918i	0.971066	+	0.238810i	$0.0767574\pi$
$929$	21.1024	+	36.5505i	0.692349	+	1.19918i	−0.278717	+	0.960373i	$0.589909\pi$
$930$	−0.972652	−	1.44380i	−0.0318945	−	0.0473441i
$931$	44.4949	−	77.0674i	1.45826	−	2.52578i
$932$	19.7527	−	5.29272i	0.647021	−	0.173369i
$933$	30.4545	+	36.6363i	0.997036	+	1.19942i
$934$	−3.46410	+	2.00000i	−0.113349	+	0.0654420i
$935$	−0.635674	−	0.0642162i	−0.0207888	−	0.00210009i
$936$	−9.79796	+	3.46410i	−0.320256	+	0.113228i
$937$	−3.10102	+	3.10102i	−0.101306	+	0.101306i	−0.755943	−	0.654637i	$-0.772821\pi$
$937$	−3.10102	+	3.10102i	−0.101306	+	0.101306i	0.654637	+	0.755943i	$0.272821\pi$
$938$	−29.1192	−	7.80247i	−0.950776	−	0.254760i
$939$	11.9494	−	16.8990i	0.389953	−	0.551477i
$940$	11.7631	−	16.3288i	0.383669	−	0.532587i
$941$	27.5227	+	15.8902i	0.897215	+	0.518007i	0.876295	−	0.481774i	$-0.160007\pi$
$941$	27.5227	+	15.8902i	0.897215	+	0.518007i	0.0209191	+	0.999781i	$0.493341\pi$
$942$	23.7795	+	8.77951i	0.774778	+	0.286052i
$943$	1.91239	−	7.13713i	0.0622760	−	0.232417i
$944$	−8.97809			−0.292212
$945$	−21.0766	−	48.6159i	−0.685622	−	1.58147i
$946$	2.20204			0.0715945
$947$	0.788210	−	2.94164i	0.0256134	−	0.0955904i	−0.951936	−	0.306297i	$-0.900910\pi$
$947$	0.788210	−	2.94164i	0.0256134	−	0.0955904i	0.977549	+	0.210707i	$0.0675765\pi$
$948$	3.98004	+	1.46945i	0.129266	+	0.0477255i
$949$	29.2699	+	16.8990i	0.950141	+	0.548564i
$950$	32.1886	−	1.94790i	1.04433	−	0.0631981i
$951$	−10.8990	+	15.4135i	−0.353424	+	0.499816i
$952$	−1.98004	−	0.530550i	−0.0641735	−	0.0171952i
$953$	−5.79972	+	5.79972i	−0.187871	+	0.187871i	−0.794775	−	0.606904i	$-0.792411\pi$
$953$	−5.79972	+	5.79972i	−0.187871	+	0.187871i	0.606904	+	0.794775i	$0.292411\pi$
$954$	−2.93197	+	15.7753i	−0.0949260	+	0.510743i
$955$	−30.2474	+	24.6969i	−0.978784	+	0.799174i
$956$	14.6969	−	8.48528i	0.475333	−	0.274434i
$957$	0.223701	+	0.269109i	0.00723123	+	0.00869905i
$958$	6.83013	−	1.83013i	0.220671	−	0.0591287i
$959$	−49.7046	+	86.0908i	−1.60504	+	2.78002i
$960$	0.741181	−	3.80140i	0.0239215	−	0.122690i
$961$	15.3990	+	26.6718i	0.496741	+	0.860381i
$962$	10.3923	+	10.3923i	0.335061	+	0.335061i
$963$	4.50150	+	57.5666i	0.145059	+	1.85506i
$964$			19.0000i			0.611949i
$965$	35.3175	−	15.8957i	1.13691	−	0.511700i
$966$	−6.44949	−	4.56048i	−0.207509	−	0.146731i
$967$	−10.3679	−	38.6937i	−0.333411	−	1.24431i	−0.905582	−	0.424172i	$-0.860565\pi$
$967$	−10.3679	−	38.6937i	−0.333411	−	1.24431i	0.572171	−	0.820134i	$-0.306101\pi$
$968$	2.74243	+	10.2349i	0.0881449	+	0.328961i
$969$	4.56048	−	2.10102i	0.146504	−	0.0674945i
$970$	2.12936	−	5.61489i	0.0683698	−	0.180283i
$971$			21.4989i			0.689934i	0.938615	+	0.344967i	$0.112110\pi$
$971$			21.4989i			0.689934i	−0.938615	+	0.344967i	$0.887890\pi$
$972$	10.2929	−	11.7071i	0.330145	−	0.375506i
$973$	−10.0000	−	10.0000i	−0.320585	−	0.320585i
$974$	−8.48528	−	14.6969i	−0.271886	−	0.470920i
$975$	−29.2075	+	6.84984i	−0.935390	+	0.219370i
$976$	−0.275255	+	0.476756i	−0.00881070	+	0.0152606i
$977$	6.27359	−	1.68100i	0.200710	−	0.0537801i	−0.157063	−	0.987589i	$-0.550203\pi$
$977$	6.27359	−	1.68100i	0.200710	−	0.0537801i	0.357773	+	0.933808i	$0.383536\pi$
$978$	−10.7420	+	1.84304i	−0.343492	+	0.0589339i
$979$	4.41761	−	2.55051i	0.141188	−	0.0815147i
$980$	−19.5133	−	23.8988i	−0.623328	−	0.763418i
$981$	−11.0176	+	12.8868i	−0.351765	+	0.411445i
$982$	19.7980	−	19.7980i	0.631778	−	0.631778i
$983$	−26.2752	−	7.04041i	−0.838047	−	0.224554i	−0.185826	−	0.982583i	$-0.559496\pi$
$983$	−26.2752	−	7.04041i	−0.838047	−	0.224554i	−0.652221	+	0.758029i	$0.726163\pi$
$984$	12.7440	+	1.17423i	0.406263	+	0.0374332i
$985$	17.7766	+	12.8060i	0.566408	+	0.408033i
$986$	0.123724	+	0.0714323i	0.00394019	+	0.00227487i
$987$	54.6690	−	45.4445i	1.74013	−	1.44651i
$988$	5.78245	−	21.5804i	0.183964	−	0.686564i
$989$	3.46410			0.110152
$990$	1.19663	−	4.09289i	0.0380315	−	0.130081i
$991$	16.7423			0.531838			0.265919	−	0.963995i	$-0.414325\pi$
$991$	16.7423			0.531838			0.265919	+	0.963995i	$0.414325\pi$
$992$	0.116337	−	0.434174i	0.00369369	−	0.0137850i
$993$	−0.131652	−	0.767327i	−0.00417787	−	0.0243504i
$994$	−24.8523	−	14.3485i	−0.788266	−	0.455106i
$995$	−3.03100	−	18.6489i	−0.0960890	−	0.591211i
$996$	−3.94949	−	8.57277i	−0.125144	−	0.271639i
$997$	6.49211	+	1.73955i	0.205607	+	0.0550922i	0.360153	−	0.932893i	$-0.382725\pi$
$997$	6.49211	+	1.73955i	0.205607	+	0.0550922i	−0.154545	+	0.987986i	$0.549391\pi$
$998$	−0.635674	+	0.635674i	−0.0201219	+	0.0201219i
$999$	−21.2132	−	6.00000i	−0.671156	−	0.189832i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.l.a.23.1	✓	8
3.2	odd	2		270.2.m.a.233.2		8
4.3	odd	2		720.2.cu.a.113.1		8
5.2	odd	4	inner	90.2.l.a.77.1	yes	8
5.3	odd	4		450.2.p.a.257.2		8
5.4	even	2		450.2.p.a.293.2		8
9.2	odd	6	inner	90.2.l.a.83.1	yes	8
9.4	even	3		810.2.f.b.323.1		8
9.5	odd	6		810.2.f.b.323.4		8
9.7	even	3		270.2.m.a.143.2		8
15.2	even	4		270.2.m.a.17.2		8
15.8	even	4		1350.2.q.g.557.1		8
15.14	odd	2		1350.2.q.g.1043.1		8
20.7	even	4		720.2.cu.a.257.1		8
36.11	even	6		720.2.cu.a.353.1		8
45.2	even	12	inner	90.2.l.a.47.1	yes	8
45.7	odd	12		270.2.m.a.197.2		8
45.22	odd	12		810.2.f.b.647.3		8
45.29	odd	6		450.2.p.a.443.2		8
45.32	even	12		810.2.f.b.647.2		8
45.34	even	6		1350.2.q.g.143.1		8
45.38	even	12		450.2.p.a.407.2		8
45.43	odd	12		1350.2.q.g.1007.1		8
180.47	odd	12		720.2.cu.a.497.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	1.1	even	1	trivial
90.2.l.a.47.1	yes	8	45.2	even	12	inner
90.2.l.a.77.1	yes	8	5.2	odd	4	inner
90.2.l.a.83.1	yes	8	9.2	odd	6	inner
270.2.m.a.17.2		8	15.2	even	4
270.2.m.a.143.2		8	9.7	even	3
270.2.m.a.197.2		8	45.7	odd	12
270.2.m.a.233.2		8	3.2	odd	2
450.2.p.a.257.2		8	5.3	odd	4
450.2.p.a.293.2		8	5.4	even	2
450.2.p.a.407.2		8	45.38	even	12
450.2.p.a.443.2		8	45.29	odd	6
720.2.cu.a.113.1		8	4.3	odd	2
720.2.cu.a.257.1		8	20.7	even	4
720.2.cu.a.353.1		8	36.11	even	6
720.2.cu.a.497.1		8	180.47	odd	12
810.2.f.b.323.1		8	9.4	even	3
810.2.f.b.323.4		8	9.5	odd	6
810.2.f.b.647.2		8	45.32	even	12
810.2.f.b.647.3		8	45.22	odd	12
1350.2.q.g.143.1		8	45.34	even	6
1350.2.q.g.557.1		8	15.8	even	4
1350.2.q.g.1007.1		8	45.43	odd	12
1350.2.q.g.1043.1		8	15.14	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

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Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	90.2.l.a.23.1

Level	$90$
Weight	$2$
Character	90.23
Analytic conductor	$0.719$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$