LMFDB - Embedded newform 570.2.bf.a.89.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.19
Character	$\chi$	$=$	570.89
Dual form			570.2.bf.a.269.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(1.61017 + 0.638236i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.09284 + 1.95082i) q^{5} +(-0.546082 - 1.64371i) q^{6} +(1.53910 + 0.888602i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.18531 + 2.05534i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(1.61017 + 0.638236i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.09284 + 1.95082i) q^{5} +(-0.546082 - 1.64371i) q^{6} +(1.53910 + 0.888602i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.18531 + 2.05534i) q^{9} +(0.791952 - 2.09113i) q^{10} +(-3.70867 + 2.14120i) q^{11} +(-0.908143 + 1.47488i) q^{12} +(2.04162 - 0.743090i) q^{13} +(-0.308608 - 1.75020i) q^{14} +(0.514576 + 3.83865i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.583489 + 0.489606i) q^{17} +(0.169790 - 2.99519i) q^{18} +(-4.17277 + 1.26015i) q^{19} +(-2.11095 + 0.737480i) q^{20} +(1.91109 + 2.41311i) q^{21} +(4.02414 + 1.46467i) q^{22} +(1.10821 - 6.28498i) q^{23} +(1.71357 - 0.252358i) q^{24} +(-2.61141 + 4.26387i) q^{25} +(-1.88157 - 1.08633i) q^{26} +(2.20694 + 4.70419i) q^{27} +(-1.14237 + 1.36142i) q^{28} +(1.06570 + 0.894225i) q^{29} +(2.60981 - 2.86162i) q^{30} +(-4.34123 - 2.50641i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-7.33819 + 1.08070i) q^{33} +(0.750120 + 0.132266i) q^{34} +(-0.0515108 + 3.97362i) q^{35} +(-2.40359 + 1.79521i) q^{36} +7.40103 q^{37} +(3.64754 + 2.38652i) q^{38} +(3.76163 + 0.106533i) q^{39} +(1.92184 + 1.14304i) q^{40} +(3.10582 + 1.13043i) q^{41} +(0.620130 - 3.01510i) q^{42} +(0.00915669 - 0.00161457i) q^{43} +(-1.46467 - 4.02414i) q^{44} +(-1.62141 + 6.50930i) q^{45} +(-5.52692 + 3.19097i) q^{46} +(3.61602 + 3.03420i) q^{47} +(-1.29478 - 1.15046i) q^{48} +(-1.92077 - 3.32687i) q^{49} +(4.94489 - 0.740308i) q^{50} +(-1.25200 + 0.415946i) q^{51} +(0.377277 + 2.13964i) q^{52} +(0.204353 + 0.0360329i) q^{53} +(2.18503 - 4.71441i) q^{54} +(-8.23008 - 4.89497i) q^{55} +1.77720 q^{56} +(-7.52315 - 0.634147i) q^{57} -1.39117i q^{58} +(9.23350 - 7.74782i) q^{59} +(-3.86968 - 0.159816i) q^{60} +(1.87217 - 10.6176i) q^{61} +(0.870468 + 4.93667i) q^{62} +(1.53704 + 5.10525i) q^{63} +(0.500000 - 0.866025i) q^{64} +(3.68080 + 3.17076i) q^{65} +(5.54476 + 4.92672i) q^{66} +(3.11150 + 2.61086i) q^{67} +(-0.380846 - 0.659644i) q^{68} +(5.79571 - 9.41260i) q^{69} +(3.07708 - 2.51473i) q^{70} +(2.40783 + 13.6555i) q^{71} +(2.92020 + 0.687320i) q^{72} +(2.88136 - 7.91647i) q^{73} +(-4.75729 - 5.66952i) q^{74} +(-6.92617 + 5.19887i) q^{75} +(-0.516415 - 4.32820i) q^{76} -7.61071 q^{77} +(-2.33632 - 2.95006i) q^{78} +(1.48419 - 4.07778i) q^{79} +(-0.359713 - 2.20695i) q^{80} +(0.551166 + 8.98311i) q^{81} +(-1.13043 - 3.10582i) q^{82} +(5.46707 - 9.46924i) q^{83} +(-2.70831 + 1.46302i) q^{84} +(-1.59279 - 0.603223i) q^{85} +(-0.00712264 - 0.00597661i) q^{86} +(1.14523 + 2.12002i) q^{87} +(-2.14120 + 3.70867i) q^{88} +(4.59546 - 1.67261i) q^{89} +(6.02864 - 2.94203i) q^{90} +(3.80258 + 0.670498i) q^{91} +(5.99706 + 2.18275i) q^{92} +(-5.39045 - 6.80648i) q^{93} -4.72038i q^{94} +(-7.01850 - 6.76318i) q^{95} +(-0.0490338 + 1.73136i) q^{96} +(-2.62714 + 2.20443i) q^{97} +(-1.31389 + 3.60987i) q^{98} +(-12.5055 - 2.94338i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	1.61017	+	0.638236i	0.929634	+	0.368485i
$3$	1.61017	+	0.638236i	0.929634	+	0.368485i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	1.09284	+	1.95082i	0.488732	+	0.872434i
$5$	1.09284	+	1.95082i	0.488732	+	0.872434i
$6$	−0.546082	−	1.64371i	−0.222937	−	0.671043i
$7$	1.53910	+	0.888602i	0.581727	+	0.335860i	0.761819	−	0.647790i	$-0.224306\pi$
$7$	1.53910	+	0.888602i	0.581727	+	0.335860i	−0.180093	+	0.983650i	$0.557640\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	2.18531	+	2.05534i	0.728437	+	0.685113i
$10$	0.791952	−	2.09113i	0.250437	−	0.661272i
$11$	−3.70867	+	2.14120i	−1.11821	+	0.645597i	−0.940943	−	0.338566i	$-0.890058\pi$
$11$	−3.70867	+	2.14120i	−1.11821	+	0.645597i	−0.177264	+	0.984163i	$0.556725\pi$
$12$	−0.908143	+	1.47488i	−0.262158	+	0.425762i
$13$	2.04162	−	0.743090i	0.566245	−	0.206096i	−0.0430048	−	0.999075i	$-0.513693\pi$
$13$	2.04162	−	0.743090i	0.566245	−	0.206096i	0.609249	+	0.792979i	$0.291471\pi$
$14$	−0.308608	−	1.75020i	−0.0824790	−	0.467762i
$15$	0.514576	+	3.83865i	0.132863	+	0.991134i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−0.583489	+	0.489606i	−0.141517	+	0.118747i	−0.710798	−	0.703396i	$-0.751666\pi$
$17$	−0.583489	+	0.489606i	−0.141517	+	0.118747i	0.569281	+	0.822143i	$0.307222\pi$
$18$	0.169790	−	2.99519i	0.0400199	−	0.705973i
$19$	−4.17277	+	1.26015i	−0.957299	+	0.289099i
$19$	−4.17277	+	1.26015i	−0.957299	+	0.289099i
$20$	−2.11095	+	0.737480i	−0.472023	+	0.164906i
$21$	1.91109	+	2.41311i	0.417033	+	0.526585i
$22$	4.02414	+	1.46467i	0.857951	+	0.312268i
$23$	1.10821	−	6.28498i	0.231078	−	1.31051i	−0.619640	−	0.784886i	$-0.712721\pi$
$23$	1.10821	−	6.28498i	0.231078	−	1.31051i	0.850718	−	0.525623i	$-0.176168\pi$
$24$	1.71357	−	0.252358i	0.349781	−	0.0515124i
$25$	−2.61141	+	4.26387i	−0.522281	+	0.852773i
$26$	−1.88157	−	1.08633i	−0.369006	−	0.213046i
$27$	2.20694	+	4.70419i	0.424725	+	0.905322i
$28$	−1.14237	+	1.36142i	−0.215887	+	0.257284i
$29$	1.06570	+	0.894225i	0.197895	+	0.166053i	0.736350	−	0.676600i	$-0.236548\pi$
$29$	1.06570	+	0.894225i	0.197895	+	0.166053i	−0.538456	+	0.842654i	$0.680992\pi$
$30$	2.60981	−	2.86162i	0.476484	−	0.522458i
$31$	−4.34123	−	2.50641i	−0.779708	−	0.450165i	0.0566186	−	0.998396i	$-0.481968\pi$
$31$	−4.34123	−	2.50641i	−0.779708	−	0.450165i	−0.836327	+	0.548231i	$0.815301\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	−7.33819	+	1.08070i	−1.27742	+	0.188126i
$34$	0.750120	+	0.132266i	0.128644	+	0.0226835i
$35$	−0.0515108	+	3.97362i	−0.00870691	+	0.671664i
$36$	−2.40359	+	1.79521i	−0.400598	+	0.299201i
$37$	7.40103			1.21672			0.608361	−	0.793661i	$-0.291827\pi$
$37$	7.40103			1.21672			0.608361	+	0.793661i	$0.291827\pi$
$38$	3.64754	+	2.38652i	0.591709	+	0.387144i
$39$	3.76163	+	0.106533i	0.602343	+	0.0170590i
$40$	1.92184	+	1.14304i	0.303869	+	0.180731i
$41$	3.10582	+	1.13043i	0.485048	+	0.176543i	0.572957	−	0.819586i	$-0.305796\pi$
$41$	3.10582	+	1.13043i	0.485048	+	0.176543i	−0.0879090	+	0.996129i	$0.528018\pi$
$42$	0.620130	−	3.01510i	0.0956882	−	0.465239i
$43$	0.00915669	−	0.00161457i	0.00139638	−	0.000246220i	−0.172950	−	0.984931i	$-0.555330\pi$
$43$	0.00915669	−	0.00161457i	0.00139638	−	0.000246220i	0.174346	+	0.984684i	$0.444219\pi$
$44$	−1.46467	−	4.02414i	−0.220807	−	0.606663i
$45$	−1.62141	+	6.50930i	−0.241705	+	0.970350i
$46$	−5.52692	+	3.19097i	−0.814900	+	0.470483i
$47$	3.61602	+	3.03420i	0.527451	+	0.442584i	0.867220	−	0.497925i	$-0.165904\pi$
$47$	3.61602	+	3.03420i	0.527451	+	0.442584i	−0.339769	+	0.940509i	$0.610349\pi$
$48$	−1.29478	−	1.15046i	−0.186885	−	0.166054i
$49$	−1.92077	−	3.32687i	−0.274396	−	0.475268i
$50$	4.94489	−	0.740308i	0.699313	−	0.104695i
$51$	−1.25200	+	0.415946i	−0.175315	+	0.0582441i
$52$	0.377277	+	2.13964i	0.0523189	+	0.296715i
$53$	0.204353	+	0.0360329i	0.0280700	+	0.00494950i	0.187666	−	0.982233i	$-0.439908\pi$
$53$	0.204353	+	0.0360329i	0.0280700	+	0.00494950i	−0.159596	+	0.987182i	$0.551019\pi$
$54$	2.18503	−	4.71441i	0.297345	−	0.641550i
$55$	−8.23008	−	4.89497i	−1.10974	−	0.660037i
$56$	1.77720			0.237489
$57$	−7.52315	−	0.634147i	−0.996466	−	0.0839948i
$58$		−	1.39117i		−	0.182669i
$59$	9.23350	−	7.74782i	1.20210	−	1.00868i	0.202531	−	0.979276i	$-0.435083\pi$
$59$	9.23350	−	7.74782i	1.20210	−	1.00868i	0.999568	−	0.0294050i	$-0.00936127\pi$
$60$	−3.86968	−	0.159816i	−0.499574	−	0.0206321i
$61$	1.87217	−	10.6176i	0.239707	−	1.35945i	−0.592764	−	0.805376i	$-0.701963\pi$
$61$	1.87217	−	10.6176i	0.239707	−	1.35945i	0.832471	−	0.554069i	$-0.186926\pi$
$62$	0.870468	+	4.93667i	0.110549	+	0.626957i
$63$	1.53704	+	5.10525i	0.193649	+	0.643201i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	3.68080	+	3.17076i	0.456547	+	0.393285i
$66$	5.54476	+	4.92672i	0.682513	+	0.606438i
$67$	3.11150	+	2.61086i	0.380130	+	0.318967i	0.812754	−	0.582608i	$-0.197968\pi$
$67$	3.11150	+	2.61086i	0.380130	+	0.318967i	−0.432623	+	0.901575i	$0.642412\pi$
$68$	−0.380846	−	0.659644i	−0.0461843	−	0.0799936i
$69$	5.79571	−	9.41260i	0.697722	−	1.13314i
$70$	3.07708	−	2.51473i	0.367781	−	0.300568i
$71$	2.40783	+	13.6555i	0.285757	+	1.62061i	0.702569	+	0.711616i	$0.252036\pi$
$71$	2.40783	+	13.6555i	0.285757	+	1.62061i	−0.416812	+	0.908993i	$0.636853\pi$
$72$	2.92020	+	0.687320i	0.344149	+	0.0810015i
$73$	2.88136	−	7.91647i	0.337238	−	0.926552i	−0.648937	−	0.760842i	$-0.724786\pi$
$73$	2.88136	−	7.91647i	0.337238	−	0.926552i	0.986174	−	0.165710i	$-0.0529917\pi$
$74$	−4.75729	−	5.66952i	−0.553023	−	0.659068i
$75$	−6.92617	+	5.19887i	−0.799765	+	0.600314i
$76$	−0.516415	−	4.32820i	−0.0592368	−	0.496479i
$77$	−7.61071			−0.867321
$78$	−2.33632	−	2.95006i	−0.264536	−	0.334028i
$79$	1.48419	−	4.07778i	0.166985	−	0.458786i	−0.827771	−	0.561066i	$-0.810391\pi$
$79$	1.48419	−	4.07778i	0.166985	−	0.458786i	0.994756	+	0.102280i	$0.0326137\pi$
$80$	−0.359713	−	2.20695i	−0.0402171	−	0.246744i
$81$	0.551166	+	8.98311i	0.0612406	+	0.998123i
$82$	−1.13043	−	3.10582i	−0.124835	−	0.342981i
$83$	5.46707	−	9.46924i	0.600089	−	1.03938i	−0.392718	−	0.919659i	$-0.628465\pi$
$83$	5.46707	−	9.46924i	0.600089	−	1.03938i	0.992807	−	0.119725i	$-0.0382014\pi$
$84$	−2.70831	+	1.46302i	−0.295501	+	0.159628i
$85$	−1.59279	−	0.603223i	−0.172763	−	0.0654287i
$86$	−0.00712264	−	0.00597661i	−0.000768054	−	0.000644474i
$87$	1.14523	+	2.12002i	0.122781	+	0.227290i
$88$	−2.14120	+	3.70867i	−0.228253	+	0.395346i
$89$	4.59546	−	1.67261i	0.487117	−	0.177296i	−0.0867734	−	0.996228i	$-0.527656\pi$
$89$	4.59546	−	1.67261i	0.487117	−	0.177296i	0.573891	+	0.818932i	$0.305433\pi$
$90$	6.02864	−	2.94203i	0.635474	−	0.310117i
$91$	3.80258	+	0.670498i	0.398619	+	0.0702873i
$92$	5.99706	+	2.18275i	0.625237	+	0.227568i
$93$	−5.39045	−	6.80648i	−0.558964	−	0.705799i
$94$		−	4.72038i		−	0.486870i
$95$	−7.01850	−	6.76318i	−0.720083	−	0.693888i
$96$	−0.0490338	+	1.73136i	−0.00500450	+	0.176706i
$97$	−2.62714	+	2.20443i	−0.266746	+	0.223826i	−0.766343	−	0.642432i	$-0.777926\pi$
$97$	−2.62714	+	2.20443i	−0.266746	+	0.223826i	0.499598	+	0.866258i	$0.333481\pi$
$98$	−1.31389	+	3.60987i	−0.132722	+	0.364652i
$99$	−12.5055	−	2.94338i	−1.25685	−	0.295821i
$100$	−3.74562	−	3.31215i	−0.374562	−	0.331215i
$101$	2.96211	+	8.13833i	0.294741	+	0.809794i	0.995357	+	0.0962551i	$0.0306865\pi$
$101$	2.96211	+	8.13833i	0.294741	+	0.809794i	−0.700616	+	0.713539i	$0.747091\pi$
$102$	1.12340	+	0.691725i	0.111234	+	0.0684909i
$103$	−0.296628	−	0.513775i	−0.0292276	−	0.0506237i	0.851042	−	0.525098i	$-0.175971\pi$
$103$	−0.296628	−	0.513775i	−0.0292276	−	0.0506237i	−0.880269	+	0.474475i	$0.842638\pi$
$104$	1.39655	−	1.66435i	0.136943	−	0.163203i
$105$	−2.61904	+	6.36533i	−0.255593	+	0.621193i
$106$	−0.103753	−	0.179705i	−0.0100774	−	0.0174545i
$107$	0.321885	+	0.185840i	0.0311178	+	0.0179658i	0.515478	−	0.856903i	$-0.327614\pi$
$107$	0.321885	+	0.185840i	0.0311178	+	0.0179658i	−0.484360	+	0.874869i	$0.660948\pi$
$108$	−5.01596	+	1.35653i	−0.482661	+	0.130533i
$109$	−0.724000	+	0.127661i	−0.0693466	+	0.0122277i	−0.208214	−	0.978083i	$-0.566765\pi$
$109$	−0.724000	+	0.127661i	−0.0693466	+	0.0122277i	0.138867	+	0.990311i	$0.455654\pi$
$110$	1.54044	+	9.45103i	0.146875	+	0.901121i
$111$	11.9169	+	4.72360i	1.13110	+	0.448344i
$112$	−1.14237	−	1.36142i	−0.107943	−	0.128642i
$113$		−	3.03444i		−	0.285456i	−0.989762	−	0.142728i	$-0.954413\pi$
$113$		−	3.03444i		−	0.285456i	0.989762	−	0.142728i	$-0.0455874\pi$
$114$	4.35001	+	6.17069i	0.407415	+	0.577938i
$115$	13.4720	−	4.70655i	1.25627	−	0.438888i
$116$	−1.06570	+	0.894225i	−0.0989474	+	0.0830267i
$117$	5.98888	+	2.57235i	0.553673	+	0.237813i
$118$	−11.8704	−	2.09306i	−1.09275	−	0.192682i
$119$	−1.33312	+	0.235064i	−0.122207	+	0.0215483i
$120$	2.36496	+	3.06708i	0.215890	+	0.279985i
$121$	3.66950	−	6.35576i	0.333591	−	0.577796i
$122$	−9.33697	+	5.39070i	−0.845330	+	0.488051i
$123$	4.27943	+	3.80243i	0.385863	+	0.342853i
$124$	3.22218	−	3.84004i	0.289360	−	0.344846i
$125$	−11.1719	−	0.434665i	−0.999244	−	0.0388776i
$126$	2.92286	−	4.45904i	0.260389	−	0.397242i
$127$	−19.3431	+	7.04033i	−1.71643	+	0.624728i	−0.997520	−	0.0703789i	$-0.977579\pi$
$127$	−19.3431	+	7.04033i	−1.71643	+	0.624728i	−0.718906	+	0.695107i	$0.755357\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	0.0157743	+	0.00324439i	0.00138885	+	0.000285652i
$130$	0.0629725	−	4.85779i	0.00552305	−	0.426056i
$131$	−12.0666	−	14.3804i	−1.05426	−	1.25642i	−0.965509	−	0.260370i	$-0.916155\pi$
$131$	−12.0666	−	14.3804i	−1.05426	−	1.25642i	−0.0887559	−	0.996053i	$-0.528289\pi$
$132$	0.209983	−	7.41437i	0.0182767	−	0.645338i
$133$	−7.54210	−	1.76843i	−0.653983	−	0.153342i
$134$		−	4.06178i		−	0.350884i
$135$	−6.76521	+	9.44626i	−0.582257	+	0.813005i
$136$	−0.260514	+	0.715756i	−0.0223389	+	0.0613756i
$137$	−0.288585	+	1.63665i	−0.0246555	+	0.139828i	−0.994651	−	0.103296i	$-0.967061\pi$
$137$	−0.288585	+	1.63665i	−0.0246555	+	0.139828i	0.969995	+	0.243124i	$0.0781722\pi$
$138$	−10.9359	+	1.61053i	−0.930924	+	0.137098i
$139$	−16.6451	+	6.05832i	−1.41182	+	0.513860i	−0.931663	−	0.363323i	$-0.881642\pi$
$139$	−16.6451	+	6.05832i	−1.41182	+	0.513860i	−0.480156	+	0.877183i	$0.659420\pi$
$140$	−3.90430	−	0.740739i	−0.329974	−	0.0626039i
$141$	3.88589	+	7.19347i	0.327251	+	0.605799i
$142$	8.91299	−	10.6221i	0.747961	−	0.891386i
$143$	−5.98061	+	7.12741i	−0.500123	+	0.596024i
$144$	−1.35055	−	2.67881i	−0.112546	−	0.223234i
$145$	−0.579839	+	3.05623i	−0.0481530	+	0.253806i
$146$	−7.91647	+	2.88136i	−0.655172	+	0.238463i
$147$	−0.969444	−	6.58275i	−0.0799584	−	0.542936i
$148$	−1.28517	+	7.28859i	−0.105641	+	0.599118i
$149$	4.87268	−	13.3876i	0.399185	−	1.09675i	−0.563497	−	0.826118i	$-0.690544\pi$
$149$	4.87268	−	13.3876i	0.399185	−	1.09675i	0.962682	−	0.270634i	$-0.0872334\pi$
$150$	8.43462	+	1.96398i	0.688684	+	0.160358i
$151$		−	22.1194i		−	1.80005i	−0.435841	−	0.900024i	$-0.643549\pi$
$151$		−	22.1194i		−	1.80005i	0.435841	−	0.900024i	$-0.356451\pi$
$152$	−2.98365	+	3.17771i	−0.242006	+	0.257746i
$153$	−2.28141	−	0.129328i	−0.184441	−	0.0104555i
$154$	4.89207	+	5.83014i	0.394214	+	0.469806i
$155$	0.145292	−	11.2081i	0.0116702	−	0.900254i
$156$	−0.758116	+	3.68599i	−0.0606978	+	0.295115i
$157$	−14.9429	+	2.63483i	−1.19257	+	0.210283i	−0.734485	−	0.678625i	$-0.762576\pi$
$157$	−14.9429	+	2.63483i	−1.19257	+	0.210283i	−0.458087	+	0.888907i	$0.651465\pi$
$158$	−4.07778	+	1.48419i	−0.324411	+	0.118076i
$159$	0.306046	+	0.188445i	0.0242710	+	0.0149446i
$160$	−1.45940	+	1.69415i	−0.115376	+	0.133935i
$161$	7.29050	−	8.68848i	0.574572	−	0.684748i
$162$	6.52718	−	6.19645i	0.512823	−	0.486839i
$163$	17.8199	−	10.2883i	1.39576	−	0.805842i	0.401815	−	0.915721i	$-0.368380\pi$
$163$	17.8199	−	10.2883i	1.39576	−	0.805842i	0.993945	+	0.109879i	$0.0350463\pi$
$164$	−1.65257	+	2.86234i	−0.129044	+	0.223511i
$165$	−10.1277	−	13.1345i	−0.788442	−	1.02252i
$166$	−10.7680	+	1.89869i	−0.835761	+	0.147367i
$167$	−23.0744	−	4.06863i	−1.78555	−	0.314840i	−0.819476	−	0.573113i	$-0.805736\pi$
$167$	−23.0744	−	4.06863i	−1.78555	−	0.314840i	−0.966072	+	0.258272i	$0.916847\pi$
$168$	2.86161	+	1.13428i	0.220778	+	0.0875112i
$169$	−6.34253	+	5.32202i	−0.487887	+	0.409386i
$170$	0.561732	+	1.60789i	0.0430829	+	0.123320i
$171$	−11.7088	−	5.82263i	−0.895398	−	0.445268i
$172$			0.00929795i			0.000708962i
$173$	14.5800	+	17.3758i	1.10850	+	1.32105i	0.942227	+	0.334974i	$0.108728\pi$
$173$	14.5800	+	17.3758i	1.10850	+	1.32105i	0.166269	+	0.986080i	$0.446828\pi$
$174$	0.887893	−	2.24002i	0.0673110	−	0.169815i
$175$	−7.80811	+	4.24203i	−0.590237	+	0.320668i
$176$	4.21735	−	0.743632i	0.317894	−	0.0560534i
$177$	19.8125	−	6.58219i	1.48920	−	0.494747i
$178$	−4.23519	−	2.44519i	−0.317441	−	0.183275i
$179$	−9.33334	−	16.1658i	−0.697606	−	1.20829i	−0.969294	−	0.245904i	$-0.920915\pi$
$179$	−9.33334	−	16.1658i	−0.697606	−	1.20829i	0.271688	−	0.962385i	$-0.412418\pi$
$180$	−6.12886	−	2.72710i	−0.456818	−	0.203266i
$181$	−8.85324	+	10.5509i	−0.658056	+	0.784241i	−0.987105	−	0.160072i	$-0.948827\pi$
$181$	−8.85324	+	10.5509i	−0.658056	+	0.784241i	0.329049	+	0.944313i	$0.393272\pi$
$182$	−1.93062	−	3.34394i	−0.143107	−	0.247869i
$183$	9.79105	−	15.9013i	0.723776	−	1.17546i
$184$	−2.18275	−	5.99706i	−0.160915	−	0.442109i
$185$	8.08813	+	14.4381i	0.594651	+	1.06151i
$186$	−1.74915	+	8.50445i	−0.128254	+	0.623576i
$187$	1.11563	−	3.06516i	0.0815826	−	0.224146i
$188$	−3.61602	+	3.03420i	−0.263726	+	0.221292i
$189$	−0.783450	+	9.20133i	−0.0569876	+	0.669298i
$190$	−0.669495	+	9.72377i	−0.0485702	+	0.705437i
$191$			5.95196i			0.430669i	0.976540	+	0.215334i	$0.0690841\pi$
$191$			5.95196i			0.430669i	−0.976540	+	0.215334i	$0.930916\pi$
$192$	1.35781	−	1.07533i	0.0979918	−	0.0776054i
$193$	14.6660	+	5.33800i	1.05568	+	0.384238i	0.810805	−	0.585316i	$-0.199029\pi$
$193$	14.6660	+	5.33800i	1.05568	+	0.384238i	0.244879	+	0.969554i	$0.421252\pi$
$194$	3.37738	+	0.595524i	0.242482	+	0.0427561i
$195$	3.90303	+	7.45470i	0.279502	+	0.533842i
$196$	3.60987	−	1.31389i	0.257848	−	0.0938490i
$197$	3.69707	−	6.40351i	0.263405	−	0.456231i	−0.703740	−	0.710458i	$-0.748488\pi$
$197$	3.69707	−	6.40351i	0.263405	−	0.456231i	0.967145	+	0.254227i	$0.0818211\pi$
$198$	5.78362	+	11.4717i	0.411024	+	0.815261i
$199$	−4.62609	−	3.88175i	−0.327935	−	0.275170i	0.463923	−	0.885876i	$-0.346441\pi$
$199$	−4.62609	−	3.88175i	−0.327935	−	0.275170i	−0.791858	+	0.610706i	$0.790886\pi$
$200$	−0.129610	+	4.99832i	−0.00916483	+	0.353435i
$201$	3.34371	+	6.18980i	0.235847	+	0.436595i
$202$	4.33031	−	7.50032i	0.304680	−	0.527721i
$203$	0.845607	+	2.32329i	0.0593500	+	0.163063i
$204$	−0.192219	−	1.30521i	−0.0134580	−	0.0913830i
$205$	1.18890	+	7.29428i	0.0830366	+	0.509454i
$206$	−0.202906	+	0.557478i	−0.0141371	+	0.0388414i
$207$	15.3396	−	11.4569i	1.06617	−	0.796309i
$208$	−2.17265			−0.150646
$209$	12.7772	−	13.6082i	0.883817	−	0.941302i
$210$	6.55962	−	2.08525i	0.452657	−	0.143896i
$211$	6.34031	+	7.55609i	0.436485	+	0.520183i	0.938782	−	0.344513i	$-0.111956\pi$
$211$	6.34031	+	7.55609i	0.436485	+	0.520183i	−0.502297	+	0.864695i	$0.667511\pi$
$212$	−0.0709710	+	0.194991i	−0.00487431	+	0.0133921i
$213$	−4.83840	+	23.5245i	−0.331521	+	1.61187i
$214$	−0.0645416	−	0.366034i	−0.00441197	−	0.0250215i
$215$	0.0131565	+	0.0160986i	0.000897268	+	0.00109792i
$216$	4.26336	+	2.97048i	0.290085	+	0.202116i
$217$	−4.45441	−	7.71526i	−0.302385	−	0.523746i
$218$	0.563172	+	0.472558i	0.0381428	+	0.0320056i
$219$	9.69206	−	10.9079i	0.654928	−	0.737087i
$220$	6.24974	−	7.25505i	0.421357	−	0.489135i
$221$	−0.827445	+	1.43318i	−0.0556600	+	0.0964059i
$222$	−4.04157	−	12.1652i	−0.271252	−	0.816473i
$223$	−2.25169	−	12.7700i	−0.150784	−	0.855140i	−0.962539	−	0.271142i	$-0.912599\pi$
$223$	−2.25169	−	12.7700i	−0.150784	−	0.855140i	0.811755	−	0.583998i	$-0.198512\pi$
$224$	−0.308608	+	1.75020i	−0.0206198	+	0.116940i
$225$	−14.4704	+	3.95055i	−0.964695	+	0.263370i
$226$	−2.32451	+	1.95050i	−0.154624	+	0.129745i
$227$			9.21420i			0.611568i	0.952101	+	0.305784i	$0.0989185\pi$
$227$			9.21420i			0.611568i	−0.952101	+	0.305784i	$0.901081\pi$
$228$	1.93089	−	7.29874i	0.127877	−	0.483371i
$229$	25.2683			1.66978			0.834888	−	0.550419i	$-0.185532\pi$
$229$	25.2683			1.66978			0.834888	+	0.550419i	$0.185532\pi$
$230$	−12.2650	−	7.29482i	−0.808733	−	0.481006i
$231$	−12.2546	−	4.85743i	−0.806291	−	0.319595i
$232$	1.37003	+	0.241574i	0.0899470	+	0.0158601i
$233$	−0.839783	−	4.76264i	−0.0550160	−	0.312011i	0.944865	−	0.327461i	$-0.106193\pi$
$233$	−0.839783	−	4.76264i	−0.0550160	−	0.312011i	−0.999881	+	0.0154499i	$0.995082\pi$
$234$	−1.87905	−	6.24122i	−0.122837	−	0.408002i
$235$	−1.96746	+	10.3701i	−0.128343	+	0.676472i
$236$	6.02674	+	10.4386i	0.392307	+	0.679496i
$237$	4.99239	−	5.61867i	0.324290	−	0.364972i
$238$	1.03698	+	0.870130i	0.0672174	+	0.0564021i
$239$	−18.3835	+	10.6137i	−1.18913	+	0.686546i	−0.958109	−	0.286402i	$-0.907541\pi$
$239$	−18.3835	+	10.6137i	−1.18913	+	0.686546i	−0.231023	+	0.972948i	$0.574207\pi$
$240$	0.829351	−	3.78314i	0.0535344	−	0.244201i
$241$	−6.62459	−	18.2009i	−0.426728	−	1.17242i	−0.947787	−	0.318904i	$-0.896685\pi$
$241$	−6.62459	−	18.2009i	−0.426728	−	1.17242i	0.521060	−	0.853520i	$-0.325537\pi$
$242$	−7.22750	+	1.27440i	−0.464601	+	0.0819218i
$243$	−4.84587	+	14.8161i	−0.310863	+	0.950455i
$244$	10.1312	+	3.68746i	0.648584	+	0.236065i
$245$	4.39104	−	7.38282i	0.280533	−	0.471671i
$246$	0.162064	−	5.72239i	0.0103328	−	0.364846i
$247$	−7.58282	+	5.67350i	−0.482483	+	0.360996i
$248$	−5.01282			−0.318315
$249$	14.8465	−	11.7578i	0.940860	−	0.745122i
$250$	6.84818	+	8.83756i	0.433117	+	0.558936i
$251$	−3.79741	−	0.669586i	−0.239690	−	0.0422639i	0.0525124	−	0.998620i	$-0.483277\pi$
$251$	−3.79741	−	0.669586i	−0.239690	−	0.0422639i	−0.292203	+	0.956356i	$0.594388\pi$
$252$	−5.29460	+	0.627173i	−0.333528	+	0.0395082i
$253$	9.34743	+	25.6818i	0.587668	+	1.61460i
$254$	17.8267	+	10.2923i	1.11855	+	0.645795i
$255$	−2.17967	−	1.98787i	−0.136496	−	0.124485i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−2.41397	+	2.87686i	−0.150579	+	0.179453i	−0.836061	−	0.548636i	$-0.815147\pi$
$257$	−2.41397	+	2.87686i	−0.150579	+	0.179453i	0.685482	+	0.728090i	$0.259592\pi$
$258$	−0.00765420	−	0.0141693i	−0.000476530	−	0.000882141i
$259$	11.3910	+	6.57657i	0.707799	+	0.408648i
$260$	−3.76176	+	3.07429i	−0.233294	+	0.190659i
$261$	0.490941	+	4.14453i	0.0303885	+	0.256540i
$262$	−3.25978	+	18.4871i	−0.201390	+	1.14214i
$263$	−14.2813	−	5.19798i	−0.880625	−	0.320521i	−0.138163	−	0.990410i	$-0.544120\pi$
$263$	−14.2813	−	5.19798i	−0.880625	−	0.320521i	−0.742462	+	0.669888i	$0.766342\pi$
$264$	−5.81471	+	4.60501i	−0.357871	+	0.283419i
$265$	0.153031	+	0.438034i	0.00940062	+	0.0269082i
$266$	3.49328	+	6.91431i	0.214187	+	0.423943i
$267$	8.46699	+	0.239794i	0.518172	+	0.0146752i
$268$	−3.11150	+	2.61086i	−0.190065	+	0.159484i
$269$	7.56447	+	2.75324i	0.461214	+	0.167868i	0.562168	−	0.827023i	$-0.309967\pi$
$269$	7.56447	+	2.75324i	0.461214	+	0.167868i	−0.100954	+	0.994891i	$0.532190\pi$
$270$	11.5849	−	0.889489i	0.705032	−	0.0541326i
$271$	5.24820	+	29.7640i	0.318805	+	1.80803i	0.550042	+	0.835137i	$0.314612\pi$
$271$	5.24820	+	29.7640i	0.318805	+	1.80803i	−0.231237	+	0.972897i	$0.574277\pi$
$272$	0.715756	−	0.260514i	0.0433991	−	0.0157960i
$273$	5.69488	+	3.50656i	0.344670	+	0.212227i
$274$	1.43924	−	0.830947i	0.0869478	−	0.0501993i
$275$	0.555044	−	21.4048i	0.0334704	−	1.29076i
$276$	8.26319	+	7.34214i	0.497386	+	0.441945i
$277$	16.8444	−	9.72509i	1.01208	−	0.584324i	0.100279	−	0.994959i	$-0.468026\pi$
$277$	16.8444	−	9.72509i	1.01208	−	0.584324i	0.911800	+	0.410635i	$0.134693\pi$
$278$	15.3402	+	8.85667i	0.920045	+	0.531188i
$279$	−4.33542	−	14.4000i	−0.259555	−	0.862105i
$280$	1.94220	+	3.46701i	0.116069	+	0.207193i
$281$	3.16143	−	17.9294i	0.188595	−	1.06958i	−0.732654	−	0.680602i	$-0.761719\pi$
$281$	3.16143	−	17.9294i	0.188595	−	1.06958i	0.921249	−	0.388974i	$-0.127170\pi$
$282$	3.01272	−	7.60063i	0.179405	−	0.452611i
$283$	12.6817	+	15.1135i	0.753850	+	0.898403i	0.997442	−	0.0714743i	$-0.0227704\pi$
$283$	12.6817	+	15.1135i	0.753850	+	0.898403i	−0.243592	+	0.969878i	$0.578326\pi$
$284$	−13.8661			−0.822805
$285$	−6.98449	−	15.3693i	−0.413726	−	0.910402i
$286$	9.30417			0.550167
$287$	3.77568	+	4.49968i	0.222872	+	0.265608i
$288$	−1.18397	+	2.75649i	−0.0697659	+	0.162428i
$289$	−2.85127	+	16.1704i	−0.167722	+	0.951198i
$290$	2.71392	−	1.52032i	0.159367	−	0.0892764i
$291$	−5.63709	+	1.87278i	−0.330452	+	0.109784i
$292$	7.29586	+	4.21226i	0.426958	+	0.246504i
$293$	12.9559	−	7.48008i	0.756890	−	0.436991i	−0.0712879	−	0.997456i	$-0.522711\pi$
$293$	12.9559	−	7.48008i	0.756890	−	0.436991i	0.828178	+	0.560465i	$0.189378\pi$
$294$	−4.41953	+	4.97395i	−0.257752	+	0.290086i
$295$	25.2053	+	9.54578i	1.46751	+	0.555777i
$296$	6.40948	−	3.70051i	0.372543	−	0.215088i
$297$	−18.2574	−	12.7208i	−1.05940	−	0.738136i
$298$	−13.3876	+	4.87268i	−0.775521	+	0.282267i
$299$	−2.40776	−	13.6551i	−0.139244	−	0.789693i
$300$	−3.91717	−	7.72372i	−0.226158	−	0.445929i
$301$	0.0155278	+	0.00565166i	0.000895008	+	0.000325756i
$302$	−16.9444	+	14.2180i	−0.975041	+	0.818157i
$303$	−0.424664	+	14.9946i	−0.0243963	+	0.861419i
$304$	4.35212	+	0.243015i	0.249611	+	0.0139379i
$305$	22.7590	−	7.95107i	1.30318	−	0.455277i
$306$	1.36739	+	1.83079i	0.0781686	+	0.104659i
$307$	13.1823	+	4.79797i	0.752354	+	0.273835i	0.689596	−	0.724194i	$-0.257788\pi$
$307$	13.1823	+	4.79797i	0.752354	+	0.273835i	0.0627582	+	0.998029i	$0.480010\pi$
$308$	1.32159	−	7.49509i	0.0753043	−	0.427072i
$309$	−0.149713	−	1.01658i	−0.00851687	−	0.0578315i
$310$	−8.67927	+	7.09311i	−0.492950	+	0.402861i
$311$	0.786255	+	0.453945i	0.0445844	+	0.0257408i	0.522127	−	0.852868i	$-0.325139\pi$
$311$	0.786255	+	0.453945i	0.0445844	+	0.0257408i	−0.477542	+	0.878609i	$0.658472\pi$
$312$	3.31094	−	1.78856i	0.187445	−	0.101257i
$313$	5.20150	−	6.19891i	0.294006	−	0.350383i	−0.598739	−	0.800944i	$-0.704331\pi$
$313$	5.20150	−	6.19891i	0.294006	−	0.350383i	0.892746	+	0.450561i	$0.148776\pi$
$314$	11.6235	+	9.75328i	0.655952	+	0.550409i
$315$	−8.27969	+	8.57771i	−0.466508	+	0.483299i
$316$	3.75810	+	2.16974i	0.211410	+	0.122058i
$317$	10.0330	+	27.5654i	0.563508	+	1.54822i	0.814457	+	0.580225i	$0.197035\pi$
$317$	10.0330	+	27.5654i	0.563508	+	1.54822i	−0.250949	+	0.968000i	$0.580743\pi$
$318$	−0.0523656	−	0.355575i	−0.00293652	−	0.0199396i
$319$	−5.86704	−	1.03452i	−0.328491	−	0.0579218i
$320$	2.23588	+	0.0289842i	0.124989	+	0.00162026i
$321$	0.399680	+	0.504673i	0.0223080	+	0.0281681i
$322$	−11.3420			−0.632065
$323$	1.81779	−	2.77830i	0.101145	−	0.154589i
$324$	−8.94234	−	1.01711i	−0.496797	−	0.0565060i
$325$	−2.16307	+	10.6457i	−0.119986	+	0.590518i
$326$	−19.3357	−	7.03762i	−1.07090	−	0.389777i
$327$	−1.24724	−	0.256527i	−0.0689727	−	0.0141860i
$328$	3.25493	−	0.573933i	0.179724	−	0.0316901i
$329$	2.86924	+	7.88316i	0.158186	+	0.434613i
$330$	−3.55162	+	16.2010i	−0.195510	+	0.891833i
$331$	−10.3520	+	5.97673i	−0.568998	+	0.328511i	−0.756749	−	0.653706i	$-0.773213\pi$
$331$	−10.3520	+	5.97673i	−0.568998	+	0.328511i	0.187751	+	0.982217i	$0.439880\pi$
$332$	8.37603	+	7.02833i	0.459695	+	0.385730i
$333$	16.1735	+	15.2116i	0.886305	+	0.833591i
$334$	11.7152	+	20.2913i	0.641025	+	1.11029i
$335$	−1.69295	+	8.92323i	−0.0924957	+	0.487528i
$336$	−0.970500	−	2.92122i	−0.0529451	−	0.159365i
$337$	−3.44453	−	19.5349i	−0.187636	−	1.06413i	−0.922522	−	0.385944i	$-0.873876\pi$
$337$	−3.44453	−	19.5349i	−0.187636	−	1.06413i	0.734887	−	0.678190i	$-0.237235\pi$
$338$	8.15380	+	1.43774i	0.443508	+	0.0782025i
$339$	1.93669	−	4.88597i	0.105186	−	0.265369i
$340$	0.870645	−	1.46385i	0.0472173	−	0.0793882i
$341$	21.4669			1.16250
$342$	3.06590	+	12.7122i	0.165785	+	0.687397i
$343$		−	19.2676i		−	1.04035i
$344$	0.00712264	−	0.00597661i	0.000384027	−	0.000322237i
$345$	24.6961	+	1.01993i	1.32959	+	0.0549114i
$346$	3.93876	−	22.3378i	0.211749	−	1.20089i
$347$	−5.53827	−	31.4091i	−0.297310	−	1.68613i	−0.657664	−	0.753311i	$-0.728455\pi$
$347$	−5.53827	−	31.4091i	−0.297310	−	1.68613i	0.360354	−	0.932815i	$-0.382656\pi$
$348$	−2.28668	+	0.759692i	−0.122579	+	0.0407237i
$349$	−5.09466	+	8.82421i	−0.272711	+	0.472349i	−0.969555	−	0.244874i	$-0.921254\pi$
$349$	−5.09466	+	8.82421i	−0.272711	+	0.472349i	0.696844	+	0.717223i	$0.254587\pi$
$350$	8.26854	+	3.25463i	0.441972	+	0.173967i
$351$	8.00137	+	7.96424i	0.427082	+	0.425100i
$352$	−3.28051	−	2.75268i	−0.174852	−	0.146718i
$353$	−9.43899	−	16.3488i	−0.502387	−	0.870159i	−0.999996	−	0.00275791i	$-0.999122\pi$
$353$	−9.43899	−	16.3488i	−0.502387	−	0.870159i	0.497610	−	0.867401i	$-0.334211\pi$
$354$	−17.7775	−	10.9463i	−0.944861	−	0.581788i
$355$	−24.0080	+	19.6205i	−1.27421	+	1.04135i
$356$	0.849206	+	4.81609i	0.0450078	+	0.255252i
$357$	−2.29657	−	0.472348i	−0.121548	−	0.0249993i
$358$	−6.38438	+	17.5409i	−0.337425	+	0.927067i
$359$	−5.06268	−	6.03347i	−0.267198	−	0.318434i	0.615717	−	0.787968i	$-0.288867\pi$
$359$	−5.06268	−	6.03347i	−0.267198	−	0.318434i	−0.882915	+	0.469533i	$0.844422\pi$
$360$	1.85047	+	6.44793i	0.0975286	+	0.339836i
$361$	15.8240	−	10.5167i	0.832844	−	0.553508i
$362$	13.7732			0.723903
$363$	9.96500	−	7.89186i	0.523027	−	0.414215i
$364$	−1.32062	+	3.62838i	−0.0692195	+	0.190179i
$365$	18.5925	−	3.03041i	0.973175	−	0.158619i
$366$	−18.4747	+	2.72077i	−0.965686	+	0.142217i
$367$	10.9918	+	30.1996i	0.573765	+	1.57641i	0.798506	+	0.601987i	$0.205624\pi$
$367$	10.9918	+	30.1996i	0.573765	+	1.57641i	−0.224741	+	0.974419i	$0.572154\pi$
$368$	−3.19097	+	5.52692i	−0.166341	+	0.288111i
$369$	4.46378	+	8.85385i	0.232375	+	0.460913i
$370$	5.86126	−	15.4765i	0.304712	−	0.804584i
$371$	0.282501	+	0.237047i	0.0146667	+	0.0123069i
$372$	7.63912	−	4.12662i	0.396070	−	0.213956i
$373$	4.80246	−	8.31810i	0.248662	−	0.430695i	−0.714493	−	0.699643i	$-0.753343\pi$
$373$	4.80246	−	8.31810i	0.248662	−	0.430695i	0.963155	+	0.268948i	$0.0866759\pi$
$374$	−3.06516	+	1.11563i	−0.158495	+	0.0576876i
$375$	−17.7112	−	7.83018i	−0.914605	−	0.404349i
$376$	4.64867	+	0.819686i	0.239737	+	0.0422721i
$377$	2.84024	+	1.03376i	0.146280	+	0.0532415i
$378$	7.55222	−	5.31434i	0.388444	−	0.273340i
$379$		−	10.2857i		−	0.528342i	−0.964476	−	0.264171i	$-0.914902\pi$
$379$		−	10.2857i		−	0.528342i	0.964476	−	0.264171i	$-0.0850984\pi$
$380$	7.87919	−	5.73746i	0.404194	−	0.294325i
$381$	−35.6392	−	1.00934i	−1.82585	−	0.0517100i
$382$	4.55946	−	3.82585i	0.233282	−	0.195747i
$383$	10.2712	−	28.2199i	0.524834	−	1.44197i	−0.340246	−	0.940337i	$-0.610510\pi$
$383$	10.2712	−	28.2199i	0.524834	−	1.44197i	0.865080	−	0.501634i	$-0.167268\pi$
$384$	−1.69654	−	0.348936i	−0.0865761	−	0.0178066i
$385$	−8.31728	−	14.8471i	−0.423888	−	0.756680i
$386$	−5.33800	−	14.6660i	−0.271697	−	0.746482i
$387$	0.0233287	+	0.0152918i	0.00118586	+	0.000777324i
$388$	−1.71474	−	2.97002i	−0.0870529	−	0.150780i
$389$	−7.40884	+	8.82951i	−0.375643	+	0.447674i	−0.920434	−	0.390898i	$-0.872165\pi$
$389$	−7.40884	+	8.82951i	−0.375643	+	0.447674i	0.544791	+	0.838572i	$0.316609\pi$
$390$	3.20181	−	7.78168i	0.162130	−	0.394041i
$391$	2.43053	+	4.20981i	0.122917	+	0.212899i
$392$	−3.32687	−	1.92077i	−0.168033	−	0.0970136i
$393$	−10.2512	−	30.8563i	−0.517106	−	1.55649i
$394$	−7.28180	+	1.28398i	−0.366852	+	0.0646858i
$395$	9.57700	−	1.56097i	0.481871	−	0.0785408i
$396$	5.07022	−	11.8044i	0.254788	−	0.593193i
$397$	−20.7497	−	24.7285i	−1.04140	−	1.24109i	−0.969863	−	0.243649i	$-0.921655\pi$
$397$	−20.7497	−	24.7285i	−1.04140	−	1.24109i	−0.0715325	−	0.997438i	$-0.522789\pi$
$398$			6.03893i			0.302704i
$399$	−11.0154	−	7.66111i	−0.551461	−	0.383535i
$400$	3.91225	−	3.11357i	0.195612	−	0.155679i
$401$	−1.26880	+	1.06465i	−0.0633608	+	0.0531660i	−0.673918	−	0.738806i	$-0.735390\pi$
$401$	−1.26880	+	1.06465i	−0.0633608	+	0.0531660i	0.610557	+	0.791972i	$0.290946\pi$
$402$	2.59237	−	6.54016i	0.129296	−	0.326193i
$403$	−10.7257	−	1.89122i	−0.534283	−	0.0942085i
$404$	−8.52905	+	1.50390i	−0.424336	+	0.0748219i
$405$	−16.9221	+	10.8923i	−0.840866	+	0.541244i
$406$	1.23619	−	2.14115i	0.0613513	−	0.106264i
$407$	−27.4480	+	15.8471i	−1.36055	+	0.785511i
$408$	−0.876293	+	0.986221i	−0.0433830	+	0.0488252i
$409$	−5.05226	+	6.02104i	−0.249818	+	0.297721i	−0.876351	−	0.481674i	$-0.840029\pi$
$409$	−5.05226	+	6.02104i	−0.249818	+	0.297721i	0.626533	+	0.779395i	$0.284473\pi$
$410$	4.82353	−	5.59942i	0.238217	−	0.276536i
$411$	−1.50924	+	2.45110i	−0.0744452	+	0.120904i
$412$	0.557478	−	0.202906i	0.0274650	−	0.00999644i
$413$	21.0960	−	3.71980i	1.03807	−	0.183040i
$414$	−18.6366	−	4.38643i	−0.915937	−	0.215581i
$415$	24.4474	+	0.316917i	1.20008	+	0.0155568i
$416$	1.39655	+	1.66435i	0.0684716	+	0.0816013i
$417$	−30.6681	−	0.868554i	−1.50182	−	0.0425333i
$418$	−18.6375	−	1.04069i	−0.911592	−	0.0509017i
$419$			20.7310i			1.01277i	0.862306	+	0.506387i	$0.169019\pi$
$419$			20.7310i			1.01277i	−0.862306	+	0.506387i	$0.830981\pi$
$420$	−5.81384	−	3.68458i	−0.283686	−	0.179789i
$421$	−9.31585	+	25.5951i	−0.454027	+	1.24743i	0.475840	+	0.879532i	$0.342144\pi$
$421$	−9.31585	+	25.5951i	−0.454027	+	1.24743i	−0.929867	+	0.367896i	$0.880078\pi$
$422$	1.71283	−	9.71392i	0.0833791	−	0.472866i
$423$	1.66582	+	14.0628i	0.0809949	+	0.683758i
$424$	0.194991	−	0.0709710i	0.00946961	−	0.00344666i
$425$	−0.563886	−	3.76648i	−0.0273525	−	0.182701i
$426$	21.1308	−	11.4148i	1.02379	−	0.553049i
$427$	12.3163	−	14.6780i	0.596027	−	0.710318i
$428$	−0.238912	+	0.284724i	−0.0115482	+	0.0137626i
$429$	−14.1788	+	7.65932i	−0.684558	+	0.369796i
$430$	0.00387539	−	0.0204265i	0.000186888	−	0.000985052i
$431$	−30.6120	+	11.1419i	−1.47453	+	0.536684i	−0.949326	−	0.314293i	$-0.898233\pi$
$431$	−30.6120	+	11.1419i	−1.47453	+	0.536684i	−0.525202	+	0.850977i	$0.676010\pi$
$432$	−0.464914	−	5.17531i	−0.0223682	−	0.248997i
$433$	−5.99363	+	33.9916i	−0.288035	+	1.63353i	0.406201	+	0.913784i	$0.366853\pi$
$433$	−5.99363	+	33.9916i	−0.288035	+	1.63353i	−0.694237	+	0.719747i	$0.744258\pi$
$434$	−3.04699	+	8.37154i	−0.146260	+	0.401847i
$435$	−2.88423	+	4.55098i	−0.138288	+	0.218203i
$436$		−	0.735169i		−	0.0352082i
$437$	3.29573	+	27.6223i	0.157656	+	1.32135i
$438$	−14.5859	−	0.413087i	−0.696940	−	0.0197381i
$439$	−4.60712	−	5.49056i	−0.219886	−	0.262050i	0.644813	−	0.764340i	$-0.276935\pi$
$439$	−4.60712	−	5.49056i	−0.219886	−	0.262050i	−0.864699	+	0.502290i	$0.832491\pi$
$440$	−9.57495	−	0.124122i	−0.456468	−	0.00591728i
$441$	2.64037	−	11.2181i	0.125732	−	0.534195i
$442$	1.62975	−	0.287369i	0.0775192	−	0.0136687i
$443$	−33.3331	+	12.1323i	−1.58370	+	0.576421i	−0.976005	−	0.217747i	$-0.930129\pi$
$443$	−33.3331	+	12.1323i	−1.58370	+	0.576421i	−0.607698	+	0.794168i	$0.707907\pi$
$444$	−6.72119	+	10.9156i	−0.318974	+	0.518033i
$445$	8.28505	+	7.13702i	0.392749	+	0.338327i
$446$	−8.33500	+	9.93327i	−0.394674	+	0.470354i
$447$	16.3903	−	18.4464i	0.775233	−	0.872484i
$448$	1.53910	−	0.888602i	0.0727158	−	0.0419825i
$449$	−18.4631	+	31.9789i	−0.871325	+	1.50918i	−0.0106992	+	0.999943i	$0.503406\pi$
$449$	−18.4631	+	31.9789i	−0.871325	+	1.50918i	−0.860626	+	0.509237i	$0.829928\pi$
$450$	12.3277	+	8.54562i	0.581134	+	0.402845i
$451$	−13.9389	+	2.45781i	−0.656359	+	0.115734i
$452$	2.98834	+	0.526925i	0.140560	+	0.0247845i
$453$	14.1174	−	35.6160i	0.663291	−	1.67338i
$454$	7.05849	−	5.92277i	0.331271	−	0.277970i
$455$	2.84759	+	8.15091i	0.133497	+	0.382120i
$456$	−6.83232	+	3.21239i	−0.319953	+	0.150434i
$457$		−	25.5668i		−	1.19597i	−0.801509	−	0.597983i	$-0.795969\pi$
$457$		−	25.5668i		−	1.19597i	0.801509	−	0.597983i	$-0.204031\pi$
$458$	−16.2422	−	19.3566i	−0.758946	−	0.904477i
$459$	−3.59092	−	1.66432i	−0.167610	−	0.0776837i
$460$	2.29566	+	14.0846i	0.107036	+	0.656697i
$461$	−22.0151	+	3.88185i	−1.02534	+	0.180796i	−0.660935	−	0.750443i	$-0.729840\pi$
$461$	−22.0151	+	3.88185i	−1.02534	+	0.180796i	−0.364409	+	0.931239i	$0.618729\pi$
$462$	4.15607	+	12.5098i	0.193358	+	0.582010i
$463$	−0.0527706	−	0.0304671i	−0.00245246	−	0.00141593i	0.498773	−	0.866732i	$-0.333784\pi$
$463$	−0.0527706	−	0.0304671i	−0.00245246	−	0.00141593i	−0.501226	+	0.865317i	$0.667117\pi$
$464$	−0.695584	−	1.20479i	−0.0322917	−	0.0559308i
$465$	7.38734	−	17.9542i	0.342579	−	0.832606i
$466$	−3.10859	+	3.70468i	−0.144003	+	0.171616i
$467$	6.86983	+	11.8989i	0.317898	+	0.550615i	0.980049	−	0.198755i	$-0.0636898\pi$
$467$	6.86983	+	11.8989i	0.317898	+	0.550615i	−0.662151	+	0.749370i	$0.730356\pi$
$468$	−3.57322	+	5.45122i	−0.165172	+	0.251983i
$469$	2.46891	+	6.78327i	0.114004	+	0.313222i
$470$	9.20863	−	5.15862i	0.424762	−	0.237949i
$471$	−25.7423	−	5.29455i	−1.18614	−	0.243960i
$472$	4.12253	−	11.3266i	0.189755	−	0.521347i
$473$	−0.0305020	+	0.0255942i	−0.00140249	+	0.00117682i
$474$	−7.51319	−	0.212782i	−0.345092	−	0.00977338i
$475$	5.52367	−	21.0829i	0.253443	−	0.967350i
$476$		−	1.35368i		−	0.0620459i
$477$	0.372515	+	0.498758i	0.0170563	+	0.0228365i
$478$	19.9473	+	7.26023i	0.912369	+	0.332075i
$479$	5.40172	+	0.952469i	0.246811	+	0.0435194i	0.295685	−	0.955286i	$-0.404452\pi$
$479$	5.40172	+	0.952469i	0.246811	+	0.0435194i	−0.0488739	+	0.998805i	$0.515563\pi$
$480$	−3.43115	+	1.79644i	−0.156610	+	0.0819958i
$481$	15.1101	−	5.49963i	0.688962	−	0.250762i
$482$	−9.68451	+	16.7741i	−0.441117	+	0.764037i
$483$	17.2843	−	9.33690i	0.786461	−	0.424843i
$484$	5.62200	+	4.71742i	0.255545	+	0.214428i
$485$	−7.17149	−	2.71599i	−0.325641	−	0.123327i
$486$	14.4647	−	5.81147i	0.656131	−	0.263614i
$487$	−13.1225	+	22.7288i	−0.594636	+	1.02994i	0.398962	+	0.916968i	$0.369371\pi$
$487$	−13.1225	+	22.7288i	−0.594636	+	1.02994i	−0.993598	+	0.112973i	$0.963963\pi$
$488$	−3.68746	−	10.1312i	−0.166923	−	0.458618i
$489$	35.2594	−	5.19267i	1.59449	−	0.234821i
$490$	−8.47808	+	1.38185i	−0.383000	+	0.0624257i
$491$	12.7898	−	35.1398i	0.577197	−	1.58584i	−0.215686	−	0.976463i	$-0.569199\pi$
$491$	12.7898	−	35.1398i	0.577197	−	1.58584i	0.792884	−	0.609373i	$-0.208579\pi$
$492$	−4.48778	+	3.55413i	−0.202325	+	0.160233i
$493$	−1.05964			−0.0477238
$494$	9.22030	+	2.16192i	0.414841	+	0.0972693i
$495$	−7.92448	−	27.6126i	−0.356179	−	1.24110i
$496$	3.22218	+	3.84004i	0.144680	+	0.172423i
$497$	−8.42840	+	23.1568i	−0.378065	+	1.03873i
$498$	−18.5502	−	3.81531i	−0.831254	−	0.170968i
$499$	−6.59648	−	37.4105i	−0.295299	−	1.67472i	−0.665985	−	0.745965i	$-0.731988\pi$
$499$	−6.59648	−	37.4105i	−0.295299	−	1.67472i	0.370686	−	0.928758i	$-0.379123\pi$
$500$	2.36804	−	10.9267i	0.105902	−	0.488656i
$501$	−34.5570	−	21.2781i	−1.54389	−	0.950635i
$502$	1.92800	+	3.33939i	0.0860507	+	0.149044i
$503$	−6.88143	−	5.77421i	−0.306828	−	0.257459i	0.476352	−	0.879255i	$-0.341959\pi$
$503$	−6.88143	−	5.77421i	−0.306828	−	0.257459i	−0.783179	+	0.621796i	$0.786403\pi$
$504$	3.88374	+	3.65276i	0.172996	+	0.162707i
$505$	−12.6393	+	14.6724i	−0.562442	+	0.652914i
$506$	13.6650	−	23.6685i	0.607484	−	1.05219i
$507$	−13.6093	+	4.52134i	−0.604409	+	0.200800i
$508$	−3.57447	−	20.2718i	−0.158591	−	0.899417i
$509$	−4.64448	+	26.3401i	−0.205863	+	1.16751i	0.690214	+	0.723606i	$0.257517\pi$
$509$	−4.64448	+	26.3401i	−0.205863	+	1.16751i	−0.896076	+	0.443900i	$0.853595\pi$
$510$	−0.121730	+	2.94751i	−0.00539031	+	0.130518i
$511$	11.4693	−	9.62389i	0.507372	−	0.425736i
$512$		−	1.00000i		−	0.0441942i
$513$	−15.1370	−	16.8484i	−0.668317	−	0.743877i
$514$	3.75547			0.165647
$515$	0.678116	−	1.14014i	0.0298814	−	0.0502406i
$516$	−0.00593428	+	0.0149713i	−0.000261242	+	0.000659075i
$517$	−19.9075	−	3.51023i	−0.875531	−	0.154380i
$518$	−2.28402	−	12.9533i	−0.100354	−	0.569136i
$519$	12.3865	+	37.2834i	0.543706	+	1.63656i
$520$	4.77305	+	0.905562i	0.209312	+	0.0397115i
$521$	13.1034	+	22.6958i	0.574071	+	0.994320i	0.996142	+	0.0877571i	$0.0279699\pi$
$521$	13.1034	+	22.6958i	0.574071	+	0.994320i	−0.422071	+	0.906563i	$0.638697\pi$
$522$	2.85932	−	3.04013i	0.125149	−	0.133063i
$523$	−23.0996	−	19.3829i	−1.01008	−	0.847555i	−0.0217287	−	0.999764i	$-0.506917\pi$
$523$	−23.0996	−	19.3829i	−1.01008	−	0.847555i	−0.988348	+	0.152209i	$0.951361\pi$
$524$	16.2573	−	9.38616i	0.710204	−	0.410036i
$525$	−15.2798	+	1.84700i	−0.666866	+	0.0806095i
$526$	5.19798	+	14.2813i	0.226643	+	0.622696i
$527$	3.76022	−	0.663028i	0.163798	−	0.0288819i
$528$	7.26527	+	1.49428i	0.316180	+	0.0650304i
$529$	−16.6599	−	6.06372i	−0.724345	−	0.263640i
$530$	0.237187	−	0.398791i	0.0103028	−	0.0173224i
$531$	36.1025	+	2.04656i	1.56671	+	0.0888132i
$532$	3.05123	−	7.12044i	0.132288	−	0.308710i
$533$	7.18093			0.311041
$534$	−5.25879	−	6.64023i	−0.227570	−	0.287351i
$535$	−0.0107728	+	0.831033i	−0.000465751	+	0.0359287i
$536$	4.00007	+	0.705320i	0.172777	+	0.0304652i
$537$	−4.71068	−	31.9866i	−0.203281	−	1.38032i
$538$	−2.75324	−	7.56447i	−0.118701	−	0.326128i
$539$	14.2470	+	8.22552i	0.613663	+	0.354298i
$540$	−8.12799	−	8.30276i	−0.349773	−	0.357294i
$541$	5.19668	+	4.36054i	0.223423	+	0.187474i	0.747628	−	0.664118i	$-0.231193\pi$
$541$	5.19668	+	4.36054i	0.223423	+	0.187474i	−0.524205	+	0.851592i	$0.675637\pi$
$542$	19.4271	−	23.1523i	0.834464	−	0.994476i
$543$	−20.9892	+	11.3383i	−0.900733	+	0.486573i
$544$	−0.659644	−	0.380846i	−0.0282820	−	0.0163286i
$545$	−1.04026	−	1.27288i	−0.0445598	−	0.0545243i
$546$	−0.974416	−	6.61651i	−0.0417012	−	0.283160i
$547$	−5.83161	+	33.0727i	−0.249342	+	1.41409i	0.560848	+	0.827919i	$0.310475\pi$
$547$	−5.83161	+	33.0727i	−0.249342	+	1.41409i	−0.810190	+	0.586168i	$0.800636\pi$
$548$	−1.56167	−	0.568401i	−0.0667112	−	0.0242809i
$549$	25.9141	−	19.3548i	1.10599	−	0.826044i
$550$	−16.7538	+	13.3336i	−0.714386	+	0.568545i
$551$	−5.57377	−	2.38846i	−0.237450	−	0.101752i
$552$	0.312931	−	11.0494i	0.0133192	−	0.470294i
$553$	5.90785	−	4.95727i	0.251227	−	0.210805i
$554$	−18.2772	−	6.65235i	−0.776524	−	0.282631i
$555$	3.80839	+	28.4099i	0.161657	+	1.20593i
$556$	−3.07589	−	17.4442i	−0.130447	−	0.739801i
$557$	10.0444	−	3.65587i	0.425596	−	0.154904i	−0.120337	−	0.992733i	$-0.538398\pi$
$557$	10.0444	−	3.65587i	0.425596	−	0.154904i	0.545933	+	0.837829i	$0.316175\pi$
$558$	−8.24428	+	12.5773i	−0.349008	+	0.532438i
$559$	0.0174947	−	0.0101006i	0.000739949	−	0.000427210i
$560$	1.40746	−	3.71636i	0.0594761	−	0.157045i
$561$	3.75264	−	4.22340i	0.158437	−	0.178312i
$562$	−15.7668	+	9.10297i	−0.665083	+	0.383986i
$563$	12.1664	+	7.02426i	0.512752	+	0.296037i	0.733964	−	0.679188i	$-0.237668\pi$
$563$	12.1664	+	7.02426i	0.512752	+	0.296037i	−0.221212	+	0.975226i	$0.571001\pi$
$564$	−7.75896	+	2.57772i	−0.326711	+	0.108541i
$565$	5.91965	−	3.31615i	0.249041	−	0.139512i
$566$	3.42595	−	19.4295i	0.144003	−	0.816684i
$567$	−7.13411	+	14.3157i	−0.299604	+	0.601203i
$568$	8.91299	+	10.6221i	0.373981	+	0.445693i
$569$	−15.7947			−0.662149			−0.331074	−	0.943605i	$-0.607411\pi$
$569$	−15.7947			−0.662149			−0.331074	+	0.943605i	$0.607411\pi$
$570$	−7.28406	+	15.2297i	−0.305096	+	0.637900i
$571$	16.6332			0.696078			0.348039	−	0.937480i	$-0.386848\pi$
$571$	16.6332			0.696078			0.348039	+	0.937480i	$0.386848\pi$
$572$	−5.98061	−	7.12741i	−0.250062	−	0.298012i
$573$	−3.79875	+	9.58368i	−0.158695	+	0.400364i
$574$	1.02000	−	5.78468i	0.0425738	−	0.241448i
$575$	23.9043	+	21.1379i	0.996880	+	0.881511i
$576$	2.87263	−	0.864865i	0.119693	−	0.0360361i
$577$	21.7458	+	12.5549i	0.905288	+	0.522668i	0.878912	−	0.476984i	$-0.158270\pi$
$577$	21.7458	+	12.5549i	0.905288	+	0.522668i	0.0263761	+	0.999652i	$0.491603\pi$
$578$	14.2200	−	8.20991i	0.591473	−	0.341487i
$579$	20.2080	+	17.9555i	0.839814	+	0.746205i
$580$	−2.90911	−	1.10174i	−0.120794	−	0.0457472i
$581$	16.8288	−	9.71610i	0.698175	−	0.403092i
$582$	5.05809	+	3.11446i	0.209664	+	0.129099i
$583$	−0.835032	+	0.303927i	−0.0345835	+	0.0125874i
$584$	−1.46290	−	8.29654i	−0.0605354	−	0.343313i
$585$	1.52670	+	14.4944i	0.0631213	+	0.599270i
$586$	−14.0579	−	5.11667i	−0.580728	−	0.211368i
$587$	−18.1425	+	15.2234i	−0.748822	+	0.628336i	−0.935191	−	0.354144i	$-0.884772\pi$
$587$	−18.1425	+	15.2234i	−0.748822	+	0.628336i	0.186369	+	0.982480i	$0.440328\pi$
$588$	6.65108	+	0.188366i	0.274286	+	0.00776807i
$589$	21.2734	+	4.98806i	0.876556	+	0.205530i
$590$	−8.88919	−	25.4443i	−0.365962	−	1.04753i
$591$	10.0399	−	7.95115i	0.412985	−	0.327067i
$592$	−6.95469	−	2.53130i	−0.285836	−	0.104036i
$593$	0.865939	−	4.91098i	0.0355599	−	0.201670i	−0.961852	−	0.273571i	$-0.911795\pi$
$593$	0.865939	−	4.91098i	0.0355599	−	0.201670i	0.997412	+	0.0719006i	$0.0229064\pi$
$594$	1.99095	+	22.1628i	0.0816896	+	0.909350i
$595$	−1.91545	−	2.34378i	−0.0785258	−	0.0960857i
$596$	12.3380	+	7.12338i	0.505386	+	0.291785i
$597$	−4.97133	−	9.20282i	−0.203463	−	0.376646i
$598$	−8.91271	+	10.6218i	−0.364468	+	0.434356i
$599$	3.60400	+	3.02411i	0.147255	+	0.123562i	0.713439	−	0.700717i	$-0.247136\pi$
$599$	3.60400	+	3.02411i	0.147255	+	0.123562i	−0.566184	+	0.824279i	$0.691581\pi$
$600$	−3.39880	+	7.96544i	−0.138755	+	0.325188i
$601$	15.7532	+	9.09510i	0.642585	+	0.370997i	0.785610	−	0.618722i	$-0.212349\pi$
$601$	15.7532	+	9.09510i	0.642585	+	0.370997i	−0.143024	+	0.989719i	$0.545683\pi$
$602$	−0.00565166	−	0.0155278i	−0.000230345	−	0.000632866i
$603$	1.43340	+	12.1007i	0.0583724	+	0.492780i
$604$	21.7833	+	3.84099i	0.886350	+	0.156287i
$605$	16.4091	+	0.212715i	0.667125	+	0.00864808i
$606$	11.7595	−	9.31305i	0.477698	−	0.378317i
$607$	−6.34256			−0.257437			−0.128718	−	0.991681i	$-0.541086\pi$
$607$	−6.34256			−0.257437			−0.128718	+	0.991681i	$0.541086\pi$
$608$	−2.61133	−	3.49012i	−0.105903	−	0.141543i
$609$	−0.121231	+	4.28059i	−0.00491252	+	0.173458i
$610$	−20.7201	−	12.3236i	−0.838932	−	0.498967i
$611$	9.63725	+	3.50767i	0.389881	+	0.141905i
$612$	0.523526	−	2.22429i	0.0211623	−	0.0899118i
$613$	−14.0354	+	2.47482i	−0.566883	+	0.0999568i	−0.449742	−	0.893158i	$-0.648484\pi$
$613$	−14.0354	+	2.47482i	−0.566883	+	0.0999568i	−0.117141	+	0.993115i	$0.537373\pi$
$614$	−4.79797	−	13.1823i	−0.193630	−	0.531995i
$615$	−2.74113	+	12.5038i	−0.110533	+	0.504204i
$616$	−6.59107	+	3.80536i	−0.265562	+	0.153322i
$617$	20.0114	+	16.7916i	0.805630	+	0.676004i	0.949561	−	0.313584i	$-0.101530\pi$
$617$	20.0114	+	16.7916i	0.805630	+	0.676004i	−0.143930	+	0.989588i	$0.545974\pi$
$618$	−0.682515	+	0.768135i	−0.0274548	+	0.0308989i
$619$	−7.82506	−	13.5534i	−0.314516	−	0.544757i	0.664819	−	0.747005i	$-0.268509\pi$
$619$	−7.82506	−	13.5534i	−0.314516	−	0.544757i	−0.979334	+	0.202248i	$0.935175\pi$
$620$	11.0126	+	2.08935i	0.442275	+	0.0839102i
$621$	32.0115	−	8.65731i	1.28458	−	0.347406i
$622$	−0.157653	−	0.894096i	−0.00632132	−	0.0358500i
$623$	8.55917	+	1.50921i	0.342916	+	0.0604653i
$624$	−3.49834	−	1.38666i	−0.140046	−	0.0555109i
$625$	−11.3611	−	22.2694i	−0.454445	−	0.890775i
$626$	−8.09210			−0.323425
$627$	29.2587	−	13.7568i	1.16848	−	0.549392i
$628$		−	15.1734i		−	0.605485i
$629$	−4.31842	+	3.62359i	−0.172187	+	0.144482i
$630$	11.8930	+	0.828966i	0.473828	+	0.0330268i
$631$	−4.43669	+	25.1617i	−0.176622	+	1.00167i	0.759633	+	0.650352i	$0.225379\pi$
$631$	−4.43669	+	25.1617i	−0.176622	+	1.00167i	−0.936255	+	0.351321i	$0.885733\pi$
$632$	−0.753543	−	4.27356i	−0.0299744	−	0.169993i
$633$	5.38643	+	16.2132i	0.214091	+	0.644418i
$634$	14.6672	−	25.4044i	0.582510	−	1.00894i
$635$	−34.8734	−	30.0411i	−1.38391	−	1.19214i
$636$	−0.238726	+	0.268673i	−0.00946610	+	0.0106536i
$637$	−6.39366	−	5.36492i	−0.253326	−	0.212566i
$638$	2.97877	+	5.15938i	0.117931	+	0.204262i
$639$	−22.8048	+	34.7904i	−0.902144	+	1.37629i
$640$	−1.41499	−	1.73141i	−0.0559325	−	0.0684402i
$641$	0.791320	+	4.48780i	0.0312553	+	0.177258i	0.996439	−	0.0843148i	$-0.0268701\pi$
$641$	0.791320	+	4.48780i	0.0312553	+	0.177258i	−0.965184	+	0.261572i	$0.915759\pi$
$642$	0.129693	−	0.630570i	0.00511856	−	0.0248866i
$643$	9.60424	−	26.3874i	0.378754	−	1.04062i	−0.593119	−	0.805115i	$-0.702104\pi$
$643$	9.60424	−	26.3874i	0.378754	−	1.04062i	0.971873	−	0.235504i	$-0.0756742\pi$
$644$	7.29050	+	8.68848i	0.287286	+	0.342374i
$645$	0.0109096	+	0.0343185i	0.000429564	+	0.00135129i
$646$	−3.29675	+	0.393349i	−0.129709	+	0.0154761i
$647$	−25.2337			−0.992038			−0.496019	−	0.868312i	$-0.665205\pi$
$647$	−25.2337			−0.992038			−0.496019	+	0.868312i	$0.665205\pi$
$648$	4.96888	+	7.50402i	0.195196	+	0.294786i
$649$	−17.6544	+	48.5049i	−0.692994	+	1.90398i
$650$	9.54549	−	5.18593i	0.374405	−	0.203409i
$651$	−2.24821	−	15.2659i	−0.0881143	−	0.598316i
$652$	7.03762	+	19.3357i	0.275614	+	0.757244i
$653$	1.74619	−	3.02449i	0.0683337	−	0.118357i	−0.829834	−	0.558010i	$-0.811565\pi$
$653$	1.74619	−	3.02449i	0.0683337	−	0.118357i	0.898168	+	0.439653i	$0.144898\pi$
$654$	0.605201	+	1.12034i	0.0236652	+	0.0438086i
$655$	14.8668	−	39.2553i	0.580893	−	1.53383i
$656$	−2.53189	−	2.12451i	−0.0988537	−	0.0829481i
$657$	22.5677	−	11.3778i	0.880449	−	0.443889i
$658$	4.19454	−	7.26516i	0.163520	−	0.283226i
$659$	15.8542	−	5.77046i	0.617593	−	0.224785i	−0.0142295	−	0.999899i	$-0.504530\pi$
$659$	15.8542	−	5.77046i	0.617593	−	0.224785i	0.631822	+	0.775113i	$0.282307\pi$
$660$	14.6936	−	7.69308i	0.571947	−	0.299453i
$661$	−15.1762	−	2.67598i	−0.590287	−	0.104083i	−0.129477	−	0.991582i	$-0.541330\pi$
$661$	−15.1762	−	2.67598i	−0.590287	−	0.104083i	−0.460810	+	0.887499i	$0.652441\pi$
$662$	11.2326	+	4.08833i	0.436567	+	0.158897i
$663$	−2.24703	+	1.77956i	−0.0872675	+	0.0691122i
$664$		−	10.9341i		−	0.424327i
$665$	−4.79242	−	16.6459i	−0.185842	−	0.645500i
$666$	1.25662	−	22.1675i	0.0486931	−	0.858973i
$667$	6.80121	−	5.70689i	0.263344	−	0.220972i
$668$	8.01365	−	22.0173i	0.310057	−	0.851875i
$669$	4.52464	−	21.9990i	0.174933	−	0.850529i
$670$	7.92380	−	4.43887i	0.306123	−	0.171488i
$671$	15.7912	+	43.3859i	0.609612	+	1.67490i
$672$	−1.61396	+	2.62117i	−0.0622597	+	0.101114i
$673$	6.12370	+	10.6066i	0.236051	+	0.408853i	0.959578	−	0.281444i	$-0.0908133\pi$
$673$	6.12370	+	10.6066i	0.236051	+	0.408853i	−0.723526	+	0.690297i	$0.757480\pi$
$674$	−12.7505	+	15.1955i	−0.491131	+	0.585307i
$675$	−25.8213	−	2.87447i	−0.993861	−	0.110638i
$676$	−4.13979	−	7.17033i	−0.159223	−	0.275782i
$677$	−20.1922	−	11.6580i	−0.776048	−	0.448051i	0.0589800	−	0.998259i	$-0.481215\pi$
$677$	−20.1922	−	11.6580i	−0.776048	−	0.448051i	−0.835028	+	0.550208i	$0.814549\pi$
$678$	−4.98775	+	1.65705i	−0.191553	+	0.0636387i
$679$	−6.00230	+	1.05837i	−0.230347	+	0.0406164i
$680$	−1.68101	+	0.273990i	−0.0644638	+	0.0105070i
$681$	−5.88083	+	14.8365i	−0.225354	+	0.568534i
$682$	−13.7987	−	16.4446i	−0.528379	−	0.629697i
$683$			0.376958i			0.0144239i	0.999974	+	0.00721196i	$0.00229566\pi$
$683$			0.376958i			0.0144239i	−0.999974	+	0.00721196i	$0.997704\pi$
$684$	7.76739	−	10.5199i	0.296994	−	0.402237i
$685$	−3.50818	+	1.22561i	−0.134041	+	0.0468283i
$686$	−14.7599	+	12.3850i	−0.563534	+	0.472862i
$687$	40.6863	+	16.1271i	1.55228	+	0.615288i
$688$	−0.00915669	−	0.00161457i	−0.000349096	−	6.15550e-5i
$689$	0.443987	−	0.0782870i	0.0169146	−	0.00298250i
$690$	−15.0930	−	19.5739i	−0.574582	−	0.745166i
$691$	8.77928	−	15.2062i	0.333979	−	0.578469i	−0.649309	−	0.760525i	$-0.724942\pi$
$691$	8.77928	−	15.2062i	0.333979	−	0.578469i	0.983288	+	0.182055i	$0.0582750\pi$
$692$	−19.6436	+	11.3412i	−0.746737	+	0.431129i
$693$	−16.6318	−	15.6426i	−0.631789	−	0.594213i
$694$	−20.5008	+	24.4319i	−0.778200	+	0.927423i
$695$	−30.0091	−	25.8508i	−1.13831	−	0.980578i
$696$	2.05181	+	1.26338i	0.0777736	+	0.0478883i
$697$	−2.36568	+	0.861036i	−0.0896064	+	0.0326141i
$698$	10.0345	−	1.76936i	0.379812	−	0.0669711i
$699$	1.68749	−	8.20466i	0.0638269	−	0.310329i
$700$	−2.82172	−	8.42611i	−0.106651	−	0.318477i
$701$	6.98342	+	8.32252i	0.263760	+	0.314337i	0.881628	−	0.471945i	$-0.156448\pi$
$701$	6.98342	+	8.32252i	0.263760	+	0.314337i	−0.617868	+	0.786282i	$0.712003\pi$
$702$	0.957776	−	11.2487i	0.0361489	−	0.424556i
$703$	−30.8828	+	9.32643i	−1.16477	+	0.351753i
$704$			4.28241i			0.161399i
$705$	−9.78652	+	15.4420i	−0.368582	+	0.581578i
$706$	−6.45665	+	17.7395i	−0.242999	+	0.667635i
$707$	−2.67274	+	15.1579i	−0.100519	+	0.570070i
$708$	3.04179	+	20.6544i	0.114318	+	0.776242i
$709$	−0.548054	+	0.199475i	−0.0205826	+	0.00749146i	−0.352291	−	0.935891i	$-0.614597\pi$
$709$	−0.548054	+	0.199475i	−0.0205826	+	0.00749146i	0.331708	+	0.943382i	$0.392375\pi$
$710$	30.4622	+	5.77942i	1.14323	+	0.216898i
$711$	11.6246	−	5.86070i	0.435958	−	0.219794i
$712$	3.14348	−	3.74625i	0.117807	−	0.140397i
$713$	−20.5638	+	24.5069i	−0.770119	+	0.917792i
$714$	1.11437	+	2.06290i	0.0417042	+	0.0772020i
$715$	−20.4401	−	3.87798i	−0.764418	−	0.145028i
$716$	17.5409	−	6.38438i	0.655536	−	0.238595i
$717$	−36.3747	+	5.35693i	−1.35844	+	0.200058i
$718$	−1.36768	+	7.75648i	−0.0510412	+	0.289469i
$719$	−16.2739	+	44.7123i	−0.606916	+	1.66749i	0.130009	+	0.991513i	$0.458499\pi$
$719$	−16.2739	+	44.7123i	−0.606916	+	1.66749i	−0.736925	+	0.675975i	$0.763723\pi$
$720$	3.74994	−	5.56219i	0.139752	−	0.207291i
$721$		−	1.05434i		−	0.0392656i
$722$	−18.2277	−	5.36193i	−0.678365	−	0.199550i
$723$	0.949737	−	33.5347i	0.0353211	−	1.24717i
$724$	−8.85324	−	10.5509i	−0.329028	−	0.392121i
$725$	−6.59582	+	2.20880i	−0.244963	+	0.0820328i
$726$	−12.4509	−	2.56084i	−0.462096	−	0.0950416i
$727$	29.9296	−	5.27739i	1.11003	−	0.195728i	0.411569	−	0.911379i	$-0.364981\pi$
$727$	29.9296	−	5.27739i	1.11003	−	0.195728i	0.698458	+	0.715651i	$0.253870\pi$
$728$	3.62838	−	1.32062i	0.134477	−	0.0489456i
$729$	−17.2589	+	20.7637i	−0.639217	+	0.769026i
$730$	−14.2724	−	12.2948i	−0.528247	−	0.455049i
$731$	−0.00455233	+	0.00542525i	−0.000168374	+	0.000200660i
$732$	13.9595	+	12.4035i	0.515959	+	0.458448i
$733$	22.0169	−	12.7114i	0.813212	−	0.469508i	−0.0348584	−	0.999392i	$-0.511098\pi$
$733$	22.0169	−	12.7114i	0.813212	−	0.469508i	0.848070	+	0.529884i	$0.177765\pi$
$734$	16.0689	−	27.8321i	0.593113	−	1.02730i
$735$	11.7823	−	9.08510i	0.434597	−	0.335109i
$736$	6.28498	−	1.10821i	0.231667	−	0.0408492i
$737$	−17.1299	−	3.02047i	−0.630988	−	0.111260i
$738$	3.91318	−	9.11060i	0.144046	−	0.335366i
$739$	−16.6031	+	13.9317i	−0.610755	+	0.512484i	−0.894882	−	0.446302i	$-0.852741\pi$
$739$	−16.6031	+	13.9317i	−0.610755	+	0.512484i	0.284127	+	0.958787i	$0.408296\pi$
$740$	−15.6232	+	5.45811i	−0.574321	+	0.200644i
$741$	−15.8307	+	4.29569i	−0.581555	+	0.157806i
$742$		−	0.368779i		−	0.0135383i
$743$	−14.9004	−	17.7576i	−0.546641	−	0.651462i	0.420022	−	0.907514i	$-0.362023\pi$
$743$	−14.9004	−	17.7576i	−0.546641	−	0.651462i	−0.966663	+	0.256052i	$0.917578\pi$
$744$	−8.07151	−	3.19936i	−0.295916	−	0.117294i
$745$	31.4418	−	5.12474i	1.15194	−	0.187756i
$746$	−9.45899	+	1.66788i	−0.346318	+	0.0610653i
$747$	31.4097	−	9.45655i	1.14922	−	0.345997i
$748$	2.82486	+	1.63094i	0.103287	+	0.0596329i
$749$	0.330276	+	0.572055i	0.0120680	+	0.0209024i
$750$	5.38630	+	18.6007i	0.196680	+	0.679203i
$751$	0.0322560	−	0.0384412i	0.00117704	−	0.00140274i	−0.765456	−	0.643489i	$-0.777486\pi$
$751$	0.0322560	−	0.0384412i	0.00117704	−	0.00140274i	0.766633	+	0.642086i	$0.221931\pi$
$752$	−2.36019	−	4.08797i	−0.0860674	−	0.149073i
$753$	−5.68713	−	3.50179i	−0.207251	−	0.127612i
$754$	−1.03376	−	2.84024i	−0.0376474	−	0.103435i
$755$	43.1509	−	24.1729i	1.57042	−	0.879742i
$756$	−8.92550	−	2.36934i	−0.324617	−	0.0861722i
$757$	−10.0370	+	27.5764i	−0.364801	+	1.00228i	0.612508	+	0.790464i	$0.290161\pi$
$757$	−10.0370	+	27.5764i	−0.364801	+	1.00228i	−0.977309	+	0.211818i	$0.932062\pi$
$758$	−7.87932	+	6.61154i	−0.286190	+	0.240142i
$759$	−1.34010	+	47.3180i	−0.0486424	+	1.71754i
$760$	−9.45979	−	2.34784i	−0.343143	−	0.0851651i
$761$			2.19617i			0.0796110i	0.999207	+	0.0398055i	$0.0126738\pi$
$761$			2.19617i			0.0796110i	−0.999207	+	0.0398055i	$0.987326\pi$
$762$	22.1352	+	27.9500i	0.801875	+	1.01252i
$763$	−1.22775	−	0.446865i	−0.0444476	−	0.0161776i
$764$	−5.86153	−	1.03355i	−0.212063	−	0.0373924i
$765$	−2.24092	−	4.59196i	−0.0810206	−	0.166023i
$766$	−28.2199	+	10.2712i	−1.01963	+	0.371114i
$767$	13.0940	−	22.6795i	0.472797	−	0.818908i
$768$	0.823214	+	1.52392i	0.0297052	+	0.0549896i
$769$	−24.4931	−	20.5521i	−0.883243	−	0.741129i	0.0836006	−	0.996499i	$-0.473358\pi$
$769$	−24.4931	−	20.5521i	−0.883243	−	0.741129i	−0.966843	+	0.255371i	$0.917802\pi$
$770$	−6.02732	+	15.9150i	−0.217209	+	0.573535i
$771$	−5.72302	+	3.09156i	−0.206110	+	0.111340i
$772$	−7.80364	+	13.5163i	−0.280859	+	0.486462i
$773$	5.58848	+	15.3542i	0.201004	+	0.552253i	0.998709	−	0.0507940i	$-0.0161752\pi$
$773$	5.58848	+	15.3542i	0.201004	+	0.552253i	−0.797705	+	0.603047i	$0.793953\pi$
$774$	−0.00328124	−	0.0277002i	−0.000117942	−	0.000995662i
$775$	22.0237	−	11.9652i	0.791115	−	0.429802i
$776$	−1.17295	+	3.22266i	−0.0421066	+	0.115687i
$777$	14.1440	+	17.8595i	0.507413	+	0.640707i
$778$	11.5261			0.413231
$779$	−14.3844	−	0.803200i	−0.515374	−	0.0287776i
$780$	−8.01920	+	2.54924i	−0.287133	+	0.0912775i
$781$	−38.1690	−	45.4881i	−1.36580	−	1.62769i
$782$	1.66258	−	4.56791i	0.0594538	−	0.163348i
$783$	−1.85468	+	6.98674i	−0.0662810	+	0.249686i
$784$	0.667077	+	3.78318i	0.0238242	+	0.135114i
$785$	−21.4703	−	26.2715i	−0.766307	−	0.937668i
$786$	−17.0479	+	27.6869i	−0.608080	+	0.987561i
$787$	15.2643	+	26.4386i	0.544114	+	0.942433i	0.998662	+	0.0517107i	$0.0164674\pi$
$787$	15.2643	+	26.4386i	0.544114	+	0.942433i	−0.454548	+	0.890722i	$0.650199\pi$
$788$	5.66423	+	4.75286i	0.201780	+	0.169313i
$789$	−19.6779	−	17.4845i	−0.700551	−	0.622465i
$790$	−7.35175	−	6.33304i	−0.261564	−	0.225319i
$791$	2.69641	−	4.67032i	0.0958733	−	0.166057i
$792$	−12.3018	+	3.70370i	−0.437124	+	0.131605i
$793$	−4.06757	−	23.0684i	−0.144444	−	0.819181i
$794$	−5.60549	+	31.7903i	−0.198932	+	1.12820i
$795$	−0.0331626	+	0.802980i	−0.00117616	+	0.0284788i
$796$	4.62609	−	3.88175i	0.163967	−	0.137585i
$797$		−	29.2971i		−	1.03776i	−0.854848	−	0.518878i	$-0.826350\pi$
$797$		−	29.2971i		−	1.03776i	0.854848	−	0.518878i	$-0.173650\pi$
$798$	1.21182	+	13.3628i	0.0428980	+	0.473037i
$799$	−3.59548			−0.127199
$800$	−4.89988	−	0.995590i	−0.173237	−	0.0351994i
$801$	13.4803	+	5.79005i	0.476302	+	0.204581i
$802$	1.63114	+	0.287613i	0.0575974	+	0.0101560i
$803$	6.26475	+	35.5292i	0.221078	+	1.25380i
$804$	−6.67639	+	2.21806i	−0.235458	+	0.0782250i
$805$	24.9170	+	4.72735i	0.878209	+	0.166617i
$806$	5.44556	+	9.43198i	0.191812	+	0.332227i
$807$	10.4229	+	9.26111i	0.366903	+	0.326007i
$808$	6.63442	+	5.56694i	0.233398	+	0.195844i
$809$	−6.10815	+	3.52654i	−0.214751	+	0.123987i	−0.603518	−	0.797350i	$-0.706235\pi$
$809$	−6.10815	+	3.52654i	−0.214751	+	0.123987i	0.388766	+	0.921336i	$0.372901\pi$
$810$	19.2213	+	5.96163i	0.675368	+	0.209470i
$811$	12.0809	+	33.1921i	0.424218	+	1.16553i	0.949271	+	0.314461i	$0.101824\pi$
$811$	12.0809	+	33.1921i	0.424218	+	1.16553i	−0.525052	+	0.851070i	$0.675954\pi$
$812$	−2.43483	+	0.429326i	−0.0854457	+	0.0150664i
$813$	−10.5459	+	51.2748i	−0.369862	+	1.79828i
$814$	29.7828	+	10.8401i	1.04389	+	0.379944i
$815$	39.5449	+	23.5199i	1.38520	+	0.823867i
$816$	1.31876	+	0.0373487i	0.0461658	+	0.00130746i
$817$	−0.0361742	+	0.0182761i	−0.00126557	+	0.000639399i
$818$	7.85991			0.274815
$819$	6.93173	+	9.28084i	0.242214	+	0.324299i
$820$	−7.38991	−	0.0957969i	−0.258067	−	0.00334537i
$821$	−39.0306	−	6.88215i	−1.36218	−	0.240189i	−0.555666	−	0.831406i	$-0.687537\pi$
$821$	−39.0306	−	6.88215i	−1.36218	−	0.240189i	−0.806512	+	0.591217i	$0.798648\pi$
$822$	2.84777	−	0.419392i	0.0993273	−	0.0146280i
$823$	5.66550	+	15.5658i	0.197487	+	0.542591i	0.998422	−	0.0561608i	$-0.0178859\pi$
$823$	5.66550	+	15.5658i	0.197487	+	0.542591i	−0.800935	+	0.598751i	$0.795664\pi$
$824$	−0.513775	−	0.296628i	−0.0178982	−	0.0103335i
$825$	14.5550	−	34.1112i	0.506741	−	1.18760i
$826$	−16.4098	−	13.7695i	−0.570970	−	0.479101i
$827$	2.61739	−	3.11928i	0.0910156	−	0.108468i	−0.718614	−	0.695409i	$-0.755223\pi$
$827$	2.61739	−	3.11928i	0.0910156	−	0.108468i	0.809630	+	0.586941i	$0.199668\pi$
$828$	8.61914	+	17.0960i	0.299536	+	0.594126i
$829$	13.6505	+	7.88112i	0.474102	+	0.273723i	0.717955	−	0.696089i	$-0.245078\pi$
$829$	13.6505	+	7.88112i	0.474102	+	0.273723i	−0.243853	+	0.969812i	$0.578412\pi$
$830$	−15.4717	−	18.9315i	−0.537031	−	0.657123i
$831$	33.3292	−	4.90841i	1.15618	−	0.170271i
$832$	0.377277	−	2.13964i	0.0130797	−	0.0741788i
$833$	2.74961	+	1.00078i	0.0952683	+	0.0346748i
$834$	19.0477	+	24.0514i	0.659569	+	0.832833i
$835$	−17.2794	−	49.4603i	−0.597978	−	1.71165i
$836$	11.1828	+	14.9461i	0.386764	+	0.516923i
$837$	2.20982	−	25.9535i	0.0763825	−	0.897084i
$838$	15.8808	−	13.3256i	0.548594	−	0.460325i
$839$	30.3943	+	11.0626i	1.04933	+	0.381924i	0.808409	−	0.588622i	$-0.200329\pi$
$839$	30.3943	+	11.0626i	1.04933	+	0.381924i	0.240918	+	0.970545i	$0.422551\pi$
$840$	0.914507	+	6.82206i	0.0315535	+	0.235383i
$841$	−4.69973	−	26.6535i	−0.162060	−	0.919086i
$842$	25.5951	−	9.31585i	0.882065	−	0.321045i
$843$	16.5336	−	26.8516i	0.569447	−	0.924819i
$844$	−8.54228	+	4.93189i	−0.294037	+	0.169763i
$845$	−17.3137	−	6.55704i	−0.595608	−	0.225569i
$846$	9.70199	−	10.3155i	0.333561	−	0.354654i
$847$	11.2955	−	6.52145i	0.388117	−	0.224080i
$848$	−0.179705	−	0.103753i	−0.00617109	−	0.00356288i
$849$	10.7738	+	32.4292i	0.369756	+	1.11297i
$850$	−2.52283	+	2.85301i	−0.0865324	+	0.0978574i
$851$	8.20190	−	46.5153i	0.281158	−	1.59452i
$852$	−22.3269	−	8.84987i	−0.764907	−	0.303192i
$853$	19.8835	+	23.6962i	0.680798	+	0.811344i	0.990210	−	0.139584i	$-0.0445766\pi$
$853$	19.8835	+	23.6962i	0.680798	+	0.811344i	−0.309412	+	0.950928i	$0.600132\pi$
$854$	−19.1608			−0.655668
$855$	−1.43697	−	29.2051i	−0.0491433	−	0.998792i
$856$	0.371680			0.0127038
$857$	21.2563	+	25.3322i	0.726100	+	0.865332i	0.995208	−	0.0977776i	$-0.0311734\pi$
$857$	21.2563	+	25.3322i	0.726100	+	0.865332i	−0.269108	+	0.963110i	$0.586729\pi$
$858$	14.9813	+	5.93825i	0.511454	+	0.202729i
$859$	1.55429	−	8.81482i	0.0530317	−	0.300758i	−0.946743	−	0.321991i	$-0.895648\pi$
$859$	1.55429	−	8.81482i	0.0530317	−	0.300758i	0.999775	+	0.0212328i	$0.00675912\pi$
$860$	−0.0181386	+	0.0101612i	−0.000618522	+	0.000346493i
$861$	3.20764	+	9.65504i	0.109316	+	0.329043i
$862$	28.2122	+	16.2883i	0.960911	+	0.554782i
$863$	−12.8707	+	7.43090i	−0.438123	+	0.252951i	−0.702801	−	0.711386i	$-0.748068\pi$
$863$	−12.8707	+	7.43090i	−0.438123	+	0.252951i	0.264678	+	0.964337i	$0.414734\pi$
$864$	−3.66568	+	3.68277i	−0.124709	+	0.125290i
$865$	−17.9634	+	47.4319i	−0.610774	+	1.61273i
$866$	29.8917	−	17.2580i	1.01576	−	0.586450i
$867$	−14.9115	+	24.2173i	−0.506423	+	0.822463i
$868$	8.37154	−	3.04699i	0.284149	−	0.103422i
$869$	3.22698	+	18.3011i	0.109468	+	0.620822i
$870$	5.34020	−	0.715861i	0.181050	−	0.0242700i
$871$	8.29262	+	3.01827i	0.280985	+	0.102270i
$872$	−0.563172	+	0.472558i	−0.0190714	+	0.0160028i
$873$	−10.2720	−	0.582293i	−0.347653	−	0.0197076i
$874$	19.0415	−	20.2799i	0.644087	−	0.685979i
$875$	−16.8085	−	10.5964i	−0.568229	−	0.358222i
$876$	9.05917	+	11.4389i	0.306081	+	0.386486i
$877$	23.5786	+	8.58191i	0.796193	+	0.289791i	0.707908	−	0.706305i	$-0.249639\pi$
$877$	23.5786	+	8.58191i	0.796193	+	0.289791i	0.0882851	+	0.996095i	$0.471861\pi$
$878$	−1.24461	+	7.05852i	−0.0420035	+	0.238214i
$879$	25.6352	−	3.77531i	0.864655	−	0.127338i
$880$	6.05957	+	7.41462i	0.204268	+	0.249947i
$881$	−50.4770	−	29.1429i	−1.70061	−	0.981850i	−0.945137	−	0.326674i	$-0.894072\pi$
$881$	−50.4770	−	29.1429i	−1.70061	−	0.981850i	−0.755477	−	0.655176i	$-0.772595\pi$
$882$	−10.2908	+	5.18821i	−0.346508	+	0.174696i
$883$	−0.899037	+	1.07143i	−0.0302550	+	0.0360565i	−0.780960	−	0.624581i	$-0.785270\pi$
$883$	−0.899037	+	1.07143i	−0.0302550	+	0.0360565i	0.750705	+	0.660638i	$0.229714\pi$
$884$	−1.26772	−	1.06374i	−0.0426380	−	0.0357775i
$885$	34.4925	+	31.4573i	1.15945	+	1.05743i
$886$	30.7199	+	17.7362i	1.03206	+	0.595858i
$887$	14.9371	+	41.0393i	0.501538	+	1.37797i	0.889772	+	0.456405i	$0.150863\pi$
$887$	14.9371	+	41.0393i	0.501538	+	1.37797i	−0.388234	+	0.921561i	$0.626915\pi$
$888$	12.6822	−	1.86771i	0.425585	−	0.0626762i
$889$	−36.0272	−	6.35256i	−1.20831	−	0.213058i
$890$	0.141744	−	10.9343i	0.00475126	−	0.366519i
$891$	−21.2787	−	32.1352i	−0.712865	−	1.07657i
$892$	12.9670			0.434166
$893$	−18.9124	−	8.10429i	−0.632879	−	0.271200i
$894$	−24.6662	−	0.698573i	−0.824961	−	0.0233638i
$895$	21.3368	−	35.8743i	0.713210	−	1.19915i
$896$	−1.67003	−	0.607840i	−0.0557917	−	0.0203065i
$897$	4.83825	−	23.5237i	0.161544	−	0.785435i
$898$	36.3651	−	6.41215i	1.21352	−	0.213976i
$899$	−2.38514	−	6.55311i	−0.0795488	−	0.218559i
$900$	−1.37777	−	14.9366i	−0.0459257	−	0.497886i
$901$	−0.136880	+	0.0790275i	−0.00456012	+	0.00263279i
$902$	10.8426	+	9.09800i	0.361018	+	0.302930i
$903$	0.0213954	+	0.0190106i	0.000711993	+	0.000632632i
$904$	−1.51722	−	2.62790i	−0.0504620	−	0.0874027i
$905$	−30.2581	−	5.74067i	−1.00581	−	0.190826i
$906$	−36.3579	+	12.0790i	−1.20791	+	0.401297i
$907$	0.905180	+	5.13353i	0.0300560	+	0.170456i	0.996141	−	0.0877686i	$-0.0279736\pi$
$907$	0.905180	+	5.13353i	0.0300560	+	0.170456i	−0.966085	+	0.258225i	$0.916863\pi$
$908$	−9.07422	−	1.60003i	−0.301138	−	0.0530988i
$909$	−10.2539	+	23.8729i	−0.340100	+	0.791814i
$910$	4.41356	−	7.42068i	0.146308	−	0.245993i
$911$	51.2970			1.69955			0.849773	−	0.527149i	$-0.176739\pi$
$911$	51.2970			1.69955			0.849773	+	0.527149i	$0.176739\pi$
$912$	6.85256	+	3.16897i	0.226911	+	0.104935i
$913$			46.8244i			1.54966i
$914$	−19.5853	+	16.4340i	−0.647825	+	0.543590i
$915$	41.7206	+	1.72304i	1.37924	+	0.0569619i
$916$	−4.38780	+	24.8844i	−0.144977	+	0.822204i
$917$	−5.79329	−	32.8554i	−0.191311	−	1.08498i
$918$	1.03326	+	3.82061i	0.0341027	+	0.126099i
$919$	13.5313	−	23.4369i	0.446356	−	0.773111i	−0.551790	−	0.833983i	$-0.686055\pi$
$919$	13.5313	−	23.4369i	0.446356	−	0.773111i	0.998146	+	0.0608721i	$0.0193882\pi$
$920$	9.31379	−	10.8120i	0.307067	−	0.356460i
$921$	18.1636	+	16.1390i	0.598510	+	0.531797i
$922$	17.1247	+	14.3693i	0.563971	+	0.473228i
$923$	15.0631	+	26.0901i	0.495810	+	0.858767i
$924$	6.91161	−	11.2249i	0.227375	−	0.369272i
$925$	−19.3271	+	31.5570i	−0.635471	+	1.03759i
$926$	0.0105811	+	0.0600085i	0.000347717	+	0.00197200i
$927$	0.407757	−	1.73243i	0.0133925	−	0.0569004i
$928$	−0.475807	+	1.30727i	−0.0156191	+	0.0429132i
$929$	−22.3527	−	26.6389i	−0.733369	−	0.873995i	0.262487	−	0.964935i	$-0.415457\pi$
$929$	−22.3527	−	26.6389i	−0.733369	−	0.873995i	−0.995856	+	0.0909401i	$0.971013\pi$
$930$	−18.5022	+	5.88171i	−0.606711	+	0.192869i
$931$	12.2073	+	11.4618i	0.400079	+	0.375646i
$932$	4.83612			0.158412
$933$	0.976283	+	1.23275i	0.0319621	+	0.0403583i
$934$	4.69924	−	12.9111i	0.153764	−	0.422463i
$935$	7.19877	−	1.17334i	0.235425	−	0.0383722i
$936$	6.47270	−	0.766726i	0.211567	−	0.0250612i
$937$	−13.1131	−	36.0279i	−0.428385	−	1.17698i	−0.946792	−	0.321845i	$-0.895697\pi$
$937$	−13.1131	−	36.0279i	−0.428385	−	1.17698i	0.518407	−	0.855134i	$-0.326525\pi$
$938$	3.60930	−	6.25150i	0.117848	−	0.204119i
$939$	12.3317	−	6.66153i	0.402429	−	0.217391i
$940$	−9.87092	−	3.73832i	−0.321954	−	0.121931i
$941$	−43.3229	−	36.3522i	−1.41229	−	1.18505i	−0.955324	−	0.295562i	$-0.904493\pi$
$941$	−43.3229	−	36.3522i	−1.41229	−	1.18505i	−0.456962	−	0.889486i	$-0.651062\pi$
$942$	12.4910	+	23.1230i	0.406977	+	0.753388i
$943$	10.5466	−	18.2673i	0.343445	−	0.594864i
$944$	−11.3266	+	4.12253i	−0.368648	+	0.134177i
$945$	−18.8063	+	8.52720i	−0.611770	+	0.277390i
$946$	0.0392127	+	0.00691425i	0.00127491	+	0.000224802i
$947$	−34.1860	−	12.4427i	−1.11090	−	0.404333i	−0.279574	−	0.960124i	$-0.590193\pi$
$947$	−34.1860	−	12.4427i	−1.11090	−	0.404333i	−0.831322	+	0.555791i	$0.812416\pi$
$948$	4.66639	+	5.89221i	0.151557	+	0.191370i
$949$		−	18.3036i		−	0.594159i
$950$	−19.7010	+	9.32046i	−0.639185	+	0.302396i
$951$	−1.43838	+	50.7884i	−0.0466427	+	1.64693i
$952$	−1.03698	+	0.870130i	−0.0336087	+	0.0282011i
$953$	−13.9821	+	38.4155i	−0.452924	+	1.24440i	0.477732	+	0.878506i	$0.341459\pi$
$953$	−13.9821	+	38.4155i	−0.452924	+	1.24440i	−0.930656	+	0.365894i	$0.880763\pi$
$954$	0.142623	−	0.605958i	0.00461758	−	0.0196186i
$955$	−11.6112	+	6.50453i	−0.375730	+	0.210482i
$956$	−7.26023	−	19.9473i	−0.234813	−	0.645142i
$957$	−8.78667	−	5.41030i	−0.284033	−	0.174890i
$958$	−2.74253	−	4.75019i	−0.0886070	−	0.153472i
$959$	−1.89849	+	2.26253i	−0.0613054	+	0.0730609i
$960$	3.58165	+	1.47369i	0.115597	+	0.0475631i
$961$	−2.93580	−	5.08496i	−0.0947034	−	0.164031i
$962$	−13.9256	−	8.03992i	−0.448978	−	0.259217i
$963$	0.321453	+	1.06770i	0.0103587	+	0.0344062i
$964$	19.0748	−	3.36339i	0.614356	−	0.108328i
$965$	5.61414	+	34.4444i	0.180725	+	1.10880i
$966$	−18.2626	−	7.23887i	−0.587589	−	0.232907i
$967$	25.7133	+	30.6439i	0.826883	+	0.985441i	1.00000		0.000539394i	$0.000171694\pi$
$967$	25.7133	+	30.6439i	0.826883	+	0.985441i	−0.173117	+	0.984901i	$0.555384\pi$
$968$		−	7.33900i		−	0.235884i
$969$	4.70016	−	3.31336i	0.150991	−	0.106441i
$970$	2.52918	+	7.23949i	0.0812070	+	0.232446i
$971$	32.3924	−	27.1805i	1.03952	−	0.872263i	0.0475693	−	0.998868i	$-0.484853\pi$
$971$	32.3924	−	27.1805i	1.03952	−	0.872263i	0.991953	+	0.126605i	$0.0404081\pi$
$972$	−13.7496	−	7.34504i	−0.441017	−	0.235592i
$973$	−31.0020	−	5.46649i	−0.993878	−	0.175248i
$974$	25.8462	−	4.55739i	0.828167	−	0.146028i
$975$	−10.2774	+	15.7609i	−0.329140	+	0.504753i
$976$	−5.39070	+	9.33697i	−0.172552	+	0.298869i
$977$	9.77099	−	5.64129i	0.312602	−	0.180481i	−0.335488	−	0.942044i	$-0.608901\pi$
$977$	9.77099	−	5.64129i	0.312602	−	0.180481i	0.648090	+	0.761564i	$0.275568\pi$
$978$	−26.6421	−	23.6725i	−0.851922	−	0.756963i
$979$	−13.4616	+	16.0430i	−0.430236	+	0.512735i
$980$	6.50816	+	5.60635i	0.207896	+	0.179088i
$981$	−1.84455	−	1.20909i	−0.0588920	−	0.0386032i
$982$	−35.1398	+	12.7898i	−1.12136	+	0.408140i
$983$	−33.6212	+	5.92833i	−1.07235	+	0.189084i	−0.681831	−	0.731510i	$-0.738816\pi$
$983$	−33.6212	+	5.92833i	−1.07235	+	0.189084i	−0.390520	+	0.920594i	$0.627705\pi$
$984$	5.60731	+	1.15328i	0.178754	+	0.0367654i
$985$	16.5324	+	0.214313i	0.526766	+	0.00682857i
$986$	0.681124	+	0.811732i	0.0216914	+	0.0258508i
$987$	−0.411349	+	14.5245i	−0.0130934	+	0.462320i
$988$	−4.27057	−	8.45281i	−0.135865	−	0.268920i
$989$		−	0.0593389i		−	0.00188687i
$990$	−16.0587	+	23.8196i	−0.510380	+	0.757035i
$991$	−11.4538	+	31.4692i	−0.363843	+	0.999651i	0.613815	+	0.789450i	$0.289634\pi$
$991$	−11.4538	+	31.4692i	−0.363843	+	0.999651i	−0.977658	+	0.210201i	$0.932588\pi$
$992$	0.870468	−	4.93667i	0.0276374	−	0.156739i
$993$	−20.4831	+	3.01655i	−0.650011	+	0.0957274i
$994$	23.1568	−	8.42840i	0.734490	−	0.267332i
$995$	2.51703	−	13.2668i	0.0797951	−	0.420586i
$996$	9.00113	+	16.6627i	0.285212	+	0.527978i
$997$	13.3750	−	15.9398i	0.423592	−	0.504817i	−0.511470	−	0.859301i	$-0.670899\pi$
$997$	13.3750	−	15.9398i	0.423592	−	0.504817i	0.935062	+	0.354484i	$0.115343\pi$
$998$	−24.4180	+	29.1002i	−0.772937	+	0.921151i
$999$	16.3336	+	34.8159i	0.516772	+	1.10152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.89.19	yes	240
3.2	odd	2	inner	570.2.bf.a.89.38	yes	240
5.4	even	2	inner	570.2.bf.a.89.22	yes	240
15.14	odd	2	inner	570.2.bf.a.89.3	✓	240
19.3	odd	18	inner	570.2.bf.a.269.3	yes	240
57.41	even	18	inner	570.2.bf.a.269.22	yes	240
95.79	odd	18	inner	570.2.bf.a.269.38	yes	240
285.269	even	18	inner	570.2.bf.a.269.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.89.3	✓	240	15.14	odd	2	inner
570.2.bf.a.89.19	yes	240	1.1	even	1	trivial
570.2.bf.a.89.22	yes	240	5.4	even	2	inner
570.2.bf.a.89.38	yes	240	3.2	odd	2	inner
570.2.bf.a.269.3	yes	240	19.3	odd	18	inner
570.2.bf.a.269.19	yes	240	285.269	even	18	inner
570.2.bf.a.269.22	yes	240	57.41	even	18	inner
570.2.bf.a.269.38	yes	240	95.79	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(1.61017 + 0.638236i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.09284 + 1.95082i) q^{5} +(-0.546082 - 1.64371i) q^{6} +(1.53910 + 0.888602i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.18531 + 2.05534i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(1.61017 + 0.638236i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.09284 + 1.95082i) q^{5} +(-0.546082 - 1.64371i) q^{6} +(1.53910 + 0.888602i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.18531 + 2.05534i) q^{9} +(0.791952 - 2.09113i) q^{10} +(-3.70867 + 2.14120i) q^{11} +(-0.908143 + 1.47488i) q^{12} +(2.04162 - 0.743090i) q^{13} +(-0.308608 - 1.75020i) q^{14} +(0.514576 + 3.83865i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-0.583489 + 0.489606i) q^{17} +(0.169790 - 2.99519i) q^{18} +(-4.17277 + 1.26015i) q^{19} +(-2.11095 + 0.737480i) q^{20} +(1.91109 + 2.41311i) q^{21} +(4.02414 + 1.46467i) q^{22} +(1.10821 - 6.28498i) q^{23} +(1.71357 - 0.252358i) q^{24} +(-2.61141 + 4.26387i) q^{25} +(-1.88157 - 1.08633i) q^{26} +(2.20694 + 4.70419i) q^{27} +(-1.14237 + 1.36142i) q^{28} +(1.06570 + 0.894225i) q^{29} +(2.60981 - 2.86162i) q^{30} +(-4.34123 - 2.50641i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-7.33819 + 1.08070i) q^{33} +(0.750120 + 0.132266i) q^{34} +(-0.0515108 + 3.97362i) q^{35} +(-2.40359 + 1.79521i) q^{36} +7.40103 q^{37} +(3.64754 + 2.38652i) q^{38} +(3.76163 + 0.106533i) q^{39} +(1.92184 + 1.14304i) q^{40} +(3.10582 + 1.13043i) q^{41} +(0.620130 - 3.01510i) q^{42} +(0.00915669 - 0.00161457i) q^{43} +(-1.46467 - 4.02414i) q^{44} +(-1.62141 + 6.50930i) q^{45} +(-5.52692 + 3.19097i) q^{46} +(3.61602 + 3.03420i) q^{47} +(-1.29478 - 1.15046i) q^{48} +(-1.92077 - 3.32687i) q^{49} +(4.94489 - 0.740308i) q^{50} +(-1.25200 + 0.415946i) q^{51} +(0.377277 + 2.13964i) q^{52} +(0.204353 + 0.0360329i) q^{53} +(2.18503 - 4.71441i) q^{54} +(-8.23008 - 4.89497i) q^{55} +1.77720 q^{56} +(-7.52315 - 0.634147i) q^{57} -1.39117i q^{58} +(9.23350 - 7.74782i) q^{59} +(-3.86968 - 0.159816i) q^{60} +(1.87217 - 10.6176i) q^{61} +(0.870468 + 4.93667i) q^{62} +(1.53704 + 5.10525i) q^{63} +(0.500000 - 0.866025i) q^{64} +(3.68080 + 3.17076i) q^{65} +(5.54476 + 4.92672i) q^{66} +(3.11150 + 2.61086i) q^{67} +(-0.380846 - 0.659644i) q^{68} +(5.79571 - 9.41260i) q^{69} +(3.07708 - 2.51473i) q^{70} +(2.40783 + 13.6555i) q^{71} +(2.92020 + 0.687320i) q^{72} +(2.88136 - 7.91647i) q^{73} +(-4.75729 - 5.66952i) q^{74} +(-6.92617 + 5.19887i) q^{75} +(-0.516415 - 4.32820i) q^{76} -7.61071 q^{77} +(-2.33632 - 2.95006i) q^{78} +(1.48419 - 4.07778i) q^{79} +(-0.359713 - 2.20695i) q^{80} +(0.551166 + 8.98311i) q^{81} +(-1.13043 - 3.10582i) q^{82} +(5.46707 - 9.46924i) q^{83} +(-2.70831 + 1.46302i) q^{84} +(-1.59279 - 0.603223i) q^{85} +(-0.00712264 - 0.00597661i) q^{86} +(1.14523 + 2.12002i) q^{87} +(-2.14120 + 3.70867i) q^{88} +(4.59546 - 1.67261i) q^{89} +(6.02864 - 2.94203i) q^{90} +(3.80258 + 0.670498i) q^{91} +(5.99706 + 2.18275i) q^{92} +(-5.39045 - 6.80648i) q^{93} -4.72038i q^{94} +(-7.01850 - 6.76318i) q^{95} +(-0.0490338 + 1.73136i) q^{96} +(-2.62714 + 2.20443i) q^{97} +(-1.31389 + 3.60987i) q^{98} +(-12.5055 - 2.94338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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