LMFDB - Embedded newform 570.2.bf.a.59.5

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			59.5
Character	$\chi$	$=$	570.59
Dual form			570.2.bf.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(-1.23853 + 1.21080i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.86795 + 1.22913i) q^{5} +(1.42997 - 0.977341i) q^{6} +(-1.22822 + 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0679076 - 2.99923i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.23853 + 1.21080i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.86795 + 1.22913i) q^{5} +(1.42997 - 0.977341i) q^{6} +(-1.22822 + 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0679076 - 2.99923i) q^{9} +(-1.62614 - 1.53482i) q^{10} +(4.15895 + 2.40117i) q^{11} +(-1.57796 + 0.714182i) q^{12} +(4.38640 - 3.68062i) q^{13} +(1.33269 - 0.485061i) q^{14} +(-3.80175 + 0.739407i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.869046 + 4.92861i) q^{17} +(-0.587687 + 2.94187i) q^{18} +(3.92152 - 1.90308i) q^{19} +(1.33491 + 1.79388i) q^{20} +(0.662587 - 2.36538i) q^{21} +(-3.67881 - 3.08688i) q^{22} +(-4.49116 - 1.63465i) q^{23} +(1.67800 - 0.429323i) q^{24} +(1.97847 + 4.59191i) q^{25} +(-4.95889 + 2.86302i) q^{26} +(3.54738 + 3.79686i) q^{27} +(-1.39668 + 0.246272i) q^{28} +(-0.843948 - 4.78627i) q^{29} +(3.87239 - 0.0680073i) q^{30} +(-8.38379 + 4.84038i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-8.05832 + 2.06175i) q^{33} +(1.71169 - 4.70282i) q^{34} +(-3.16584 - 0.185055i) q^{35} +(1.08961 - 2.79513i) q^{36} +6.32334 q^{37} +(-4.19241 + 1.19320i) q^{38} +(-0.976165 + 9.86962i) q^{39} +(-1.00313 - 1.99843i) q^{40} +(3.61797 + 3.03584i) q^{41} +(-1.06327 + 2.21439i) q^{42} +(3.09131 + 8.49330i) q^{43} +(3.08688 + 3.67881i) q^{44} +(3.81330 - 5.51895i) q^{45} +(4.13907 + 2.38969i) q^{46} +(-0.195215 - 1.10712i) q^{47} +(-1.72706 + 0.131419i) q^{48} +(-2.49432 + 4.32029i) q^{49} +(-1.15104 - 4.86571i) q^{50} +(-4.89124 - 7.15647i) q^{51} +(5.38071 - 1.95842i) q^{52} +(-0.0601527 + 0.165268i) q^{53} +(-2.83417 - 4.35517i) q^{54} +(4.81735 + 9.59716i) q^{55} +1.41822 q^{56} +(-2.55266 + 7.10520i) q^{57} +4.86010i q^{58} +(-0.697387 + 3.95508i) q^{59} +(-3.82537 - 0.605459i) q^{60} +(0.668904 + 0.243461i) q^{61} +(9.09695 - 3.31102i) q^{62} +(2.04338 + 3.73186i) q^{63} +(0.500000 + 0.866025i) q^{64} +(12.7175 - 1.48376i) q^{65} +(8.29392 - 0.631117i) q^{66} +(2.07512 + 11.7686i) q^{67} +(-2.50232 + 4.33414i) q^{68} +(7.54166 - 3.41335i) q^{69} +(3.08561 + 0.731986i) q^{70} +(-11.1500 + 4.05828i) q^{71} +(-1.55843 + 2.56346i) q^{72} +(-0.496670 + 0.591909i) q^{73} +(-6.22728 - 1.09804i) q^{74} +(-8.01030 - 3.29167i) q^{75} +(4.33591 - 0.447070i) q^{76} -6.81079 q^{77} +(2.67518 - 9.55017i) q^{78} +(6.74377 - 8.03691i) q^{79} +(0.640862 + 2.14226i) q^{80} +(-8.99078 - 0.407341i) q^{81} +(-3.03584 - 3.61797i) q^{82} +(-1.06491 - 1.84448i) q^{83} +(1.43164 - 1.99612i) q^{84} +(-7.68124 + 8.13822i) q^{85} +(-1.56950 - 8.90107i) q^{86} +(6.84048 + 4.90607i) q^{87} +(-2.40117 - 4.15895i) q^{88} +(0.424481 - 0.356182i) q^{89} +(-4.71372 + 4.77293i) q^{90} +(-2.77747 + 7.63105i) q^{91} +(-3.66122 - 3.07213i) q^{92} +(4.52281 - 16.1461i) q^{93} +1.12420i q^{94} +(9.66433 + 1.26520i) q^{95} +(1.72364 + 0.170478i) q^{96} +(3.40129 - 19.2897i) q^{97} +(3.20664 - 3.82152i) q^{98} +(7.48409 - 12.3106i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$2$	−0.984808	−	0.173648i	−0.696364	−	0.122788i
$3$	−1.23853	+	1.21080i	−0.715065	+	0.699058i
$3$	−1.23853	+	1.21080i	−0.715065	+	0.699058i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	1.86795	+	1.22913i	0.835373	+	0.549684i
$5$	1.86795	+	1.22913i	0.835373	+	0.549684i
$6$	1.42997	−	0.977341i	0.583781	−	0.398998i
$7$	−1.22822	+	0.709111i	−0.464222	+	0.268019i	−0.713818	−	0.700331i	$-0.753036\pi$
$7$	−1.22822	+	0.709111i	−0.464222	+	0.268019i	0.249596	+	0.968350i	$0.419702\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	0.0679076	−	2.99923i	0.0226359	−	0.999744i
$10$	−1.62614	−	1.53482i	−0.514229	−	0.485354i
$11$	4.15895	+	2.40117i	1.25397	+	0.723980i	0.971896	−	0.235413i	$-0.0756441\pi$
$11$	4.15895	+	2.40117i	1.25397	+	0.723980i	0.282075	+	0.959392i	$0.408977\pi$
$12$	−1.57796	+	0.714182i	−0.455517	+	0.206166i
$13$	4.38640	−	3.68062i	1.21657	−	1.02082i	0.217570	−	0.976045i	$-0.430187\pi$
$13$	4.38640	−	3.68062i	1.21657	−	1.02082i	0.998997	−	0.0447764i	$-0.0142575\pi$
$14$	1.33269	−	0.485061i	0.356177	−	0.129638i
$15$	−3.80175	+	0.739407i	−0.981607	+	0.190914i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.869046	+	4.92861i	−0.210775	+	1.19536i	0.677315	+	0.735693i	$0.263143\pi$
$17$	−0.869046	+	4.92861i	−0.210775	+	1.19536i	−0.888090	+	0.459670i	$0.847968\pi$
$18$	−0.587687	+	2.94187i	−0.138519	+	0.693406i
$19$	3.92152	−	1.90308i	0.899658	−	0.436596i
$19$	3.92152	−	1.90308i	0.899658	−	0.436596i
$20$	1.33491	+	1.79388i	0.298495	+	0.401124i
$21$	0.662587	−	2.36538i	0.144588	−	0.516169i
$22$	−3.67881	−	3.08688i	−0.784324	−	0.658126i
$23$	−4.49116	−	1.63465i	−0.936471	−	0.340847i	−0.171700	−	0.985149i	$-0.554926\pi$
$23$	−4.49116	−	1.63465i	−0.936471	−	0.340847i	−0.764771	+	0.644302i	$0.777148\pi$
$24$	1.67800	−	0.429323i	0.342520	−	0.0876351i
$25$	1.97847	+	4.59191i	0.395695	+	0.918382i
$26$	−4.95889	+	2.86302i	−0.972518	+	0.561484i
$27$	3.54738	+	3.79686i	0.682693	+	0.730706i
$28$	−1.39668	+	0.246272i	−0.263947	+	0.0465410i
$29$	−0.843948	−	4.78627i	−0.156717	−	0.888787i	−0.957199	−	0.289430i	$-0.906534\pi$
$29$	−0.843948	−	4.78627i	−0.156717	−	0.888787i	0.800482	−	0.599357i	$-0.204577\pi$
$30$	3.87239	−	0.0680073i	0.706998	−	0.0124164i
$31$	−8.38379	+	4.84038i	−1.50577	+	0.869359i	−0.505796	+	0.862653i	$0.668801\pi$
$31$	−8.38379	+	4.84038i	−1.50577	+	0.869359i	−0.999978	+	0.00670539i	$0.997866\pi$
$32$	−0.642788	−	0.766044i	−0.113630	−	0.135419i
$33$	−8.05832	+	2.06175i	−1.40277	+	0.358905i
$34$	1.71169	−	4.70282i	0.293552	−	0.806527i
$35$	−3.16584	−	0.185055i	−0.535124	−	0.0312800i
$36$	1.08961	−	2.79513i	0.181602	−	0.465855i
$37$	6.32334			1.03955			0.519775	−	0.854303i	$-0.326016\pi$
$37$	6.32334			1.03955			0.519775	+	0.854303i	$0.326016\pi$
$38$	−4.19241	+	1.19320i	−0.680098	+	0.193563i
$39$	−0.976165	+	9.86962i	−0.156311	+	1.58040i
$40$	−1.00313	−	1.99843i	−0.158608	−	0.315980i
$41$	3.61797	+	3.03584i	0.565032	+	0.474118i	0.879993	−	0.474987i	$-0.157547\pi$
$41$	3.61797	+	3.03584i	0.565032	+	0.474118i	−0.314961	+	0.949105i	$0.601992\pi$
$42$	−1.06327	+	2.21439i	−0.164065	+	0.341688i
$43$	3.09131	+	8.49330i	0.471420	+	1.29522i	0.916611	+	0.399781i	$0.130914\pi$
$43$	3.09131	+	8.49330i	0.471420	+	1.29522i	−0.445190	+	0.895436i	$0.646864\pi$
$44$	3.08688	+	3.67881i	0.465365	+	0.554601i
$45$	3.81330	−	5.51895i	0.568453	−	0.822716i
$46$	4.13907	+	2.38969i	0.610273	+	0.352341i
$47$	−0.195215	−	1.10712i	−0.0284750	−	0.161490i	0.967254	−	0.253808i	$-0.0816833\pi$
$47$	−0.195215	−	1.10712i	−0.0284750	−	0.161490i	−0.995730	+	0.0923186i	$0.970572\pi$
$48$	−1.72706	+	0.131419i	−0.249279	+	0.0189686i
$49$	−2.49432	+	4.32029i	−0.356332	+	0.617185i
$50$	−1.15104	−	4.86571i	−0.162782	−	0.688115i
$51$	−4.89124	−	7.15647i	−0.684910	−	1.00211i
$52$	5.38071	−	1.95842i	0.746170	−	0.271584i
$53$	−0.0601527	+	0.165268i	−0.00826261	+	0.0227013i	−0.943755	−	0.330645i	$-0.892734\pi$
$53$	−0.0601527	+	0.165268i	−0.00826261	+	0.0227013i	0.935493	+	0.353346i	$0.114956\pi$
$54$	−2.83417	−	4.35517i	−0.385681	−	0.592664i
$55$	4.81735	+	9.59716i	0.649572	+	1.29408i
$56$	1.41822			0.189518
$57$	−2.55266	+	7.10520i	−0.338108	+	0.941107i
$58$			4.86010i			0.638163i
$59$	−0.697387	+	3.95508i	−0.0907921	+	0.514907i	0.905164	+	0.425063i	$0.139748\pi$
$59$	−0.697387	+	3.95508i	−0.0907921	+	0.514907i	−0.995956	+	0.0898444i	$0.971363\pi$
$60$	−3.82537	−	0.605459i	−0.493853	−	0.0781644i
$61$	0.668904	+	0.243461i	0.0856443	+	0.0311720i	0.384487	−	0.923130i	$-0.374378\pi$
$61$	0.668904	+	0.243461i	0.0856443	+	0.0311720i	−0.298843	+	0.954302i	$0.596601\pi$
$62$	9.09695	−	3.31102i	1.15531	−	0.420500i
$63$	2.04338	+	3.73186i	0.257442	+	0.470170i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	12.7175	−	1.48376i	1.57742	−	0.184038i
$66$	8.29392	−	0.631117i	1.02091	−	0.0776851i
$67$	2.07512	+	11.7686i	0.253516	+	1.43776i	0.799852	+	0.600197i	$0.204911\pi$
$67$	2.07512	+	11.7686i	0.253516	+	1.43776i	−0.546336	+	0.837566i	$0.683978\pi$
$68$	−2.50232	+	4.33414i	−0.303451	+	0.525592i
$69$	7.54166	−	3.41335i	0.907910	−	0.410919i
$70$	3.08561	+	0.731986i	0.368801	+	0.0874890i
$71$	−11.1500	+	4.05828i	−1.32327	+	0.481630i	−0.904504	−	0.426466i	$-0.859758\pi$
$71$	−11.1500	+	4.05828i	−1.32327	+	0.481630i	−0.418763	+	0.908096i	$0.637536\pi$
$72$	−1.55843	+	2.56346i	−0.183662	+	0.302106i
$73$	−0.496670	+	0.591909i	−0.0581309	+	0.0692777i	−0.794326	−	0.607491i	$-0.792176\pi$
$73$	−0.496670	+	0.591909i	−0.0581309	+	0.0692777i	0.736195	+	0.676769i	$0.236620\pi$
$74$	−6.22728	−	1.09804i	−0.723906	−	0.127644i
$75$	−8.01030	−	3.29167i	−0.924950	−	0.380089i
$76$	4.33591	−	0.447070i	0.497363	−	0.0512824i
$77$	−6.81079			−0.776161
$78$	2.67518	−	9.55017i	0.302904	−	1.08134i
$79$	6.74377	−	8.03691i	0.758733	−	0.904223i	−0.239034	−	0.971011i	$-0.576831\pi$
$79$	6.74377	−	8.03691i	0.758733	−	0.904223i	0.997767	+	0.0667883i	$0.0212752\pi$
$80$	0.640862	+	2.14226i	0.0716506	+	0.239512i
$81$	−8.99078	−	0.407341i	−0.998975	−	0.0452602i
$82$	−3.03584	−	3.61797i	−0.335252	−	0.399538i
$83$	−1.06491	−	1.84448i	−0.116889	−	0.202458i	0.801644	−	0.597801i	$-0.203959\pi$
$83$	−1.06491	−	1.84448i	−0.116889	−	0.202458i	−0.918533	+	0.395343i	$0.870626\pi$
$84$	1.43164	−	1.99612i	0.156204	−	0.217794i
$85$	−7.68124	+	8.13822i	−0.833147	+	0.882714i
$86$	−1.56950	−	8.90107i	−0.169243	−	0.959827i
$87$	6.84048	+	4.90607i	0.733377	+	0.525986i
$88$	−2.40117	−	4.15895i	−0.255966	−	0.443345i
$89$	0.424481	−	0.356182i	0.0449949	−	0.0377552i	−0.620013	−	0.784592i	$-0.712873\pi$
$89$	0.424481	−	0.356182i	0.0449949	−	0.0377552i	0.665008	+	0.746836i	$0.268428\pi$
$90$	−4.71372	+	4.77293i	−0.496870	+	0.503111i
$91$	−2.77747	+	7.63105i	−0.291158	+	0.799951i
$92$	−3.66122	−	3.07213i	−0.381709	−	0.320292i
$93$	4.52281	−	16.1461i	0.468994	−	1.67427i
$94$			1.12420i			0.115952i
$95$	9.66433	+	1.26520i	0.991539	+	0.129807i
$96$	1.72364	+	0.170478i	0.175918	+	0.0173994i
$97$	3.40129	−	19.2897i	0.345349	−	1.95857i	0.0685236	−	0.997649i	$-0.478171\pi$
$97$	3.40129	−	19.2897i	0.345349	−	1.95857i	0.276825	−	0.960920i	$-0.410718\pi$
$98$	3.20664	−	3.82152i	0.323919	−	0.386032i
$99$	7.48409	−	12.3106i	0.752179	−	1.23726i
$100$	0.288632	+	4.99166i	0.0288632	+	0.499166i
$101$	−4.90930	−	5.85068i	−0.488494	−	0.582164i	0.464340	−	0.885657i	$-0.346292\pi$
$101$	−4.90930	−	5.85068i	−0.488494	−	0.582164i	−0.952834	+	0.303493i	$0.901847\pi$
$102$	3.57422	+	7.89710i	0.353901	+	0.781929i
$103$	7.05809	−	12.2250i	0.695454	−	1.20456i	−0.274573	−	0.961566i	$-0.588537\pi$
$103$	7.05809	−	12.2250i	0.695454	−	1.20456i	0.970027	−	0.242996i	$-0.0781301\pi$
$104$	−5.63904	+	0.994315i	−0.552953	+	0.0975006i
$105$	4.14505	−	3.60401i	0.404515	−	0.351716i
$106$	0.0879374	−	0.152312i	0.00854124	−	0.0147939i
$107$	−2.82207	+	1.62932i	−0.272820	+	0.157513i	−0.630168	−	0.776458i	$-0.717014\pi$
$107$	−2.82207	+	1.62932i	−0.272820	+	0.157513i	0.357348	+	0.933971i	$0.383681\pi$
$108$	2.03484	+	4.78115i	0.195803	+	0.460067i
$109$	−5.47763	−	15.0497i	−0.524662	−	1.44150i	−0.865277	−	0.501294i	$-0.832858\pi$
$109$	−5.47763	−	15.0497i	−0.524662	−	1.44150i	0.340615	−	0.940203i	$-0.389365\pi$
$110$	−3.07764	−	10.2879i	−0.293441	−	0.980911i
$111$	−7.83164	+	7.65633i	−0.743346	+	0.726706i
$112$	−1.39668	−	0.246272i	−0.131974	−	0.0232705i
$113$		−	6.20361i		−	0.583587i	−0.956481	−	0.291793i	$-0.905748\pi$
$113$		−	6.20361i		−	0.583587i	0.956481	−	0.291793i	$-0.0942519\pi$
$114$	3.74768	−	6.55400i	0.351003	−	0.613838i
$115$	−6.38006	−	8.57366i	−0.594944	−	0.799498i
$116$	0.843948	−	4.78627i	0.0783586	−	0.444394i
$117$	−10.7412	−	13.4058i	−0.993021	−	1.23936i
$118$	1.37358	−	3.77389i	0.126449	−	0.347415i
$119$	−2.42755	−	6.66965i	−0.222533	−	0.611406i
$120$	3.66211	+	1.26053i	0.334304	+	0.115070i
$121$	6.03123	+	10.4464i	0.548294	+	0.949673i
$122$	−0.616465	−	0.355916i	−0.0558121	−	0.0322231i
$123$	−8.15676	+	0.620680i	−0.735470	+	0.0559648i
$124$	−9.53370	+	1.68105i	−0.856151	+	0.150963i
$125$	−1.94837	+	11.0093i	−0.174267	+	0.984698i
$126$	−1.36431	−	4.02999i	−0.121542	−	0.359020i
$127$	−3.40159	+	2.85428i	−0.301843	+	0.253276i	−0.781111	−	0.624393i	$-0.785347\pi$
$127$	−3.40159	+	2.85428i	−0.301843	+	0.253276i	0.479268	+	0.877669i	$0.340902\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	−14.1124	−	6.77623i	−1.24253	−	0.596614i
$130$	−12.7820	−	0.747154i	−1.12105	−	0.0655297i
$131$	8.85370	+	1.56115i	0.773551	+	0.136398i	0.546471	−	0.837478i	$-0.315971\pi$
$131$	8.85370	+	1.56115i	0.773551	+	0.136398i	0.227080	+	0.973876i	$0.427082\pi$
$132$	−8.27751	−	0.818695i	−0.720465	−	0.0712583i
$133$	−3.46698	+	5.11818i	−0.300625	+	0.443803i
$134$		−	11.9501i		−	1.03234i
$135$	1.95948	+	11.4525i	0.168646	+	0.985677i
$136$	3.21692	−	3.83378i	0.275849	−	0.328744i
$137$	4.36619	+	1.58916i	0.373029	+	0.135771i	0.521730	−	0.853111i	$-0.325287\pi$
$137$	4.36619	+	1.58916i	0.373029	+	0.135771i	−0.148701	+	0.988882i	$0.547509\pi$
$138$	−8.01981	+	2.05190i	−0.682692	+	0.174669i
$139$	1.93418	−	1.62297i	0.164055	−	0.137658i	−0.557064	−	0.830469i	$-0.688072\pi$
$139$	1.93418	−	1.62297i	0.164055	−	0.137658i	0.721119	+	0.692811i	$0.243628\pi$
$140$	−2.91162	−	1.25668i	−0.246077	−	0.106208i
$141$	1.58228	+	1.13483i	0.133252	+	0.0955701i
$142$	11.6854	−	2.06044i	0.980614	−	0.172909i
$143$	27.0806	−	4.77504i	2.26459	−	0.399309i
$144$	1.97989	−	2.25389i	0.164991	−	0.187825i
$145$	4.30650	−	9.97783i	0.357635	−	0.828613i
$146$	0.591909	−	0.496670i	0.0489867	−	0.0411047i
$147$	−2.14174	−	8.37094i	−0.176648	−	0.690424i
$148$	5.94200	+	2.16271i	0.488429	+	0.177774i
$149$	−7.24242	+	8.63118i	−0.593322	+	0.707094i	−0.976241	−	0.216688i	$-0.930475\pi$
$149$	−7.24242	+	8.63118i	−0.593322	+	0.707094i	0.382919	+	0.923782i	$0.374919\pi$
$150$	7.31701	+	4.63264i	0.597432	+	0.378253i
$151$			19.6099i			1.59583i	0.602772	+	0.797914i	$0.294063\pi$
$151$			19.6099i			1.59583i	−0.602772	+	0.797914i	$0.705937\pi$
$152$	−4.34767	−	0.312645i	−0.352643	−	0.0253589i
$153$	14.7230	+	2.94116i	1.19029	+	0.237779i
$154$	6.70732	+	1.18268i	0.540491	+	0.0953031i
$155$	−21.6100	−	1.26318i	−1.73575	−	0.101461i
$156$	−4.29290	+	8.94054i	−0.343707	+	0.715816i
$157$	5.00142	+	13.7413i	0.399157	+	1.09667i	0.962696	+	0.270585i	$0.0872172\pi$
$157$	5.00142	+	13.7413i	0.399157	+	1.09667i	−0.563539	+	0.826089i	$0.690561\pi$
$158$	−8.03691	+	6.74377i	−0.639382	+	0.536505i
$159$	−0.125607	−	0.277523i	−0.00996125	−	0.0220090i
$160$	−0.259126	−	2.22100i	−0.0204857	−	0.175586i
$161$	6.67526	−	1.17703i	0.526084	−	0.0927628i
$162$	8.78345	+	1.96239i	0.690093	+	0.154180i
$163$	1.16357	+	0.671789i	0.0911381	+	0.0526186i	0.544876	−	0.838516i	$-0.316577\pi$
$163$	1.16357	+	0.671789i	0.0911381	+	0.0526186i	−0.453738	+	0.891135i	$0.649910\pi$
$164$	2.36146	+	4.09017i	0.184399	+	0.319389i
$165$	−17.5867	−	6.05348i	−1.36912	−	0.471263i
$166$	0.728442	+	2.00138i	0.0565381	+	0.155337i
$167$	0.645971	−	1.77479i	0.0499867	−	0.137337i	−0.912187	−	0.409774i	$-0.865607\pi$
$167$	0.645971	−	1.77479i	0.0499867	−	0.137337i	0.962174	+	0.272437i	$0.0878296\pi$
$168$	−1.75651	+	1.71719i	−0.135518	+	0.132484i
$169$	3.43605	−	19.4868i	0.264312	−	1.49899i
$170$	8.97773	−	6.68075i	0.688560	−	0.512390i
$171$	−5.44147	−	11.8908i	−0.416119	−	0.909310i
$172$			9.03839i			0.689170i
$173$	4.05906	+	0.715722i	0.308605	+	0.0544153i	0.325806	−	0.945437i	$-0.394364\pi$
$173$	4.05906	+	0.715722i	0.308605	+	0.0544153i	−0.0172012	+	0.999852i	$0.505476\pi$
$174$	−5.88463	−	6.01938i	−0.446113	−	0.456328i
$175$	−5.68617	−	4.23690i	−0.429834	−	0.320280i
$176$	1.64250	+	4.51272i	0.123808	+	0.340159i
$177$	−3.92509	−	5.74288i	−0.295028	−	0.431661i
$178$	−0.479883	+	0.277060i	−0.0359687	+	0.0207666i
$179$	6.18641	−	10.7152i	0.462394	−	0.800890i	−0.536686	−	0.843782i	$-0.680324\pi$
$179$	6.18641	−	10.7152i	0.462394	−	0.800890i	0.999080	+	0.0428923i	$0.0136572\pi$
$180$	5.47092	−	3.88189i	0.407778	−	0.289339i
$181$	8.94578	−	1.57738i	0.664935	−	0.117246i	0.169014	−	0.985614i	$-0.445942\pi$
$181$	8.94578	−	1.57738i	0.664935	−	0.117246i	0.495921	+	0.868368i	$0.334831\pi$
$182$	4.06039	−	7.03281i	0.300976	−	0.521306i
$183$	−1.12324	+	0.508378i	−0.0830323	+	0.0375804i
$184$	3.07213	+	3.66122i	0.226481	+	0.269909i
$185$	11.8117	+	7.77222i	0.868412	+	0.571425i
$186$	−7.25784	+	15.1154i	−0.532170	+	1.10832i
$187$	−15.4487	+	18.4111i	−1.12972	+	1.34635i
$188$	0.195215	−	1.10712i	0.0142375	−	0.0807450i
$189$	−7.04934	−	2.14788i	−0.512764	−	0.156235i
$190$	−9.29781	−	2.92418i	−0.674534	−	0.212142i
$191$		−	22.4414i		−	1.62380i	−0.583795	−	0.811901i	$-0.698433\pi$
$191$		−	22.4414i		−	1.62380i	0.583795	−	0.811901i	$-0.301567\pi$
$192$	−1.66785	−	0.467196i	−0.120367	−	0.0337169i
$193$	−7.75600	−	6.50806i	−0.558289	−	0.468460i	0.319447	−	0.947604i	$-0.396503\pi$
$193$	−7.75600	−	6.50806i	−0.558289	−	0.468460i	−0.877736	+	0.479144i	$0.840947\pi$
$194$	−6.69923	+	18.4060i	−0.480977	+	1.32147i
$195$	−13.9545	+	17.2361i	−0.999302	+	1.23430i
$196$	−3.82152	+	3.20664i	−0.272966	+	0.229046i
$197$	−0.395106	−	0.684343i	−0.0281501	−	0.0487574i	0.851607	−	0.524181i	$-0.175628\pi$
$197$	−0.395106	−	0.684343i	−0.0281501	−	0.0487574i	−0.879757	+	0.475423i	$0.842295\pi$
$198$	−9.50810	+	10.8240i	−0.675711	+	0.769226i
$199$	−2.50621	−	14.2134i	−0.177661	−	1.00756i	−0.935028	−	0.354575i	$-0.884626\pi$
$199$	−2.50621	−	14.2134i	−0.177661	−	1.00756i	0.757367	−	0.652989i	$-0.226485\pi$
$200$	0.582546	−	4.96595i	0.0411923	−	0.351146i
$201$	−16.8196	−	12.0632i	−1.18636	−	0.850871i
$202$	3.81876	+	6.61428i	0.268687	+	0.465379i
$203$	4.43055	+	5.28012i	0.310963	+	0.370592i
$204$	−2.14860	−	8.39778i	−0.150432	−	0.587962i
$205$	3.02674	+	10.1177i	0.211397	+	0.706654i
$206$	−9.07370	+	10.8136i	−0.632195	+	0.753420i
$207$	−5.20767	+	13.3590i	−0.361958	+	0.928515i
$208$	5.72603			0.397029
$209$	20.8790	+	1.50143i	1.44423	+	0.103856i
$210$	−4.70790	+	2.82948i	−0.324876	+	0.195253i
$211$	−12.2236	−	2.15536i	−0.841510	−	0.148381i	−0.263753	−	0.964590i	$-0.584961\pi$
$211$	−12.2236	−	2.15536i	−0.841510	−	0.148381i	−0.577756	+	0.816209i	$0.696072\pi$
$212$	−0.113050	+	0.134728i	−0.00776432	+	0.00925315i
$213$	8.89586	−	18.5268i	0.609535	−	1.26944i
$214$	3.06213	−	1.11452i	0.209323	−	0.0761872i
$215$	−4.66497	+	19.6647i	−0.318148	+	1.34112i
$216$	−1.17369	−	5.06186i	−0.0798594	−	0.344416i
$217$	6.86474	−	11.8901i	0.466009	−	0.807151i
$218$	2.78107	+	15.7722i	0.188358	+	1.06823i
$219$	−0.101545	−	1.33447i	−0.00686176	−	0.0901749i
$220$	1.24441	+	10.6660i	0.0838982	+	0.719102i
$221$	14.3284	+	24.8174i	0.963830	+	1.66940i
$222$	9.04217	−	6.18006i	0.606871	−	0.414778i
$223$	−18.9999	+	6.91541i	−1.27233	+	0.463090i	−0.887888	−	0.460059i	$-0.847828\pi$
$223$	−18.9999	+	6.91541i	−1.27233	+	0.463090i	−0.384442	+	0.923149i	$0.625606\pi$
$224$	1.33269	+	0.485061i	0.0890443	+	0.0324095i
$225$	13.9066	−	5.62208i	0.927104	−	0.374805i
$226$	−1.07725	+	6.10936i	−0.0716573	+	0.406389i
$227$		−	26.6214i		−	1.76692i	−0.468502	−	0.883462i	$-0.655206\pi$
$227$		−	26.6214i		−	1.76692i	0.468502	−	0.883462i	$-0.344794\pi$
$228$	−4.82884	+	5.80365i	−0.319798	+	0.384356i
$229$	20.0431			1.32448			0.662241	−	0.749291i	$-0.269605\pi$
$229$	20.0431			1.32448			0.662241	+	0.749291i	$0.269605\pi$
$230$	4.79433	+	9.55129i	0.316129	+	0.629793i
$231$	8.43536	−	8.24653i	0.555006	−	0.542582i
$232$	−1.66225	+	4.56700i	−0.109132	+	0.299838i
$233$	−2.34476	+	0.853421i	−0.153610	+	0.0559095i	−0.417681	−	0.908594i	$-0.637157\pi$
$233$	−2.34476	+	0.853421i	−0.153610	+	0.0559095i	0.264071	+	0.964503i	$0.414935\pi$
$234$	8.25010	+	15.0673i	0.539326	+	0.984979i
$235$	0.996143	−	2.30799i	0.0649812	−	0.150557i
$236$	−2.00805	+	3.47804i	−0.130713	+	0.226401i
$237$	1.37877	+	18.1193i	0.0895608	+	1.17698i
$238$	1.23250	+	6.98986i	0.0798912	+	0.453085i
$239$	12.5280	+	7.23302i	0.810367	+	0.467865i	0.847083	−	0.531460i	$-0.178357\pi$
$239$	12.5280	+	7.23302i	0.810367	+	0.467865i	−0.0367166	+	0.999326i	$0.511690\pi$
$240$	−3.38759	−	1.87730i	−0.218668	−	0.121179i
$241$	8.99940	+	10.7251i	0.579702	+	0.690862i	0.973592	−	0.228295i	$-0.0733152\pi$
$241$	8.99940	+	10.7251i	0.579702	+	0.690862i	−0.393890	+	0.919158i	$0.628871\pi$
$242$	−4.12561	−	11.3350i	−0.265204	−	0.728642i
$243$	11.6285	−	10.3816i	0.745972	−	0.665978i
$244$	0.545295	+	0.457557i	0.0349089	+	0.0292921i
$245$	−9.96948	+	5.00424i	−0.636926	+	0.319709i
$246$	8.14062	+	0.805156i	0.519027	+	0.0513349i
$247$	10.1968	−	22.7813i	0.648808	−	1.44954i
$248$	9.68077			0.614729
$249$	3.55223	+	0.995044i	0.225113	+	0.0630583i
$250$	3.83051	−	10.5037i	0.242263	−	0.664311i
$251$	8.28066	−	22.7509i	0.522670	−	1.43602i	−0.344866	−	0.938652i	$-0.612076\pi$
$251$	8.28066	−	22.7509i	0.522670	−	1.43602i	0.867537	−	0.497373i	$-0.165702\pi$
$252$	0.643781	+	4.20568i	0.0405544	+	0.264933i
$253$	−14.7534	−	17.5824i	−0.927540	−	1.10540i
$254$	3.84556	−	2.22023i	0.241292	−	0.139310i
$255$	−0.340352	−	19.3799i	−0.0213136	−	1.21362i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−22.8296	+	4.02548i	−1.42407	+	0.251102i	−0.831997	−	0.554780i	$-0.812802\pi$
$257$	−22.8296	+	4.02548i	−1.42407	+	0.251102i	−0.592075	+	0.805883i	$0.701691\pi$
$258$	12.7213	+	9.12388i	0.791995	+	0.568028i
$259$	−7.76643	+	4.48395i	−0.482583	+	0.278619i
$260$	12.4581	+	2.95537i	0.772616	+	0.183284i
$261$	−14.4124	+	2.20617i	−0.892107	+	0.136559i
$262$	−8.44810	−	3.07486i	−0.521925	−	0.189965i
$263$	−3.44475	−	2.89049i	−0.212412	−	0.178235i	0.530374	−	0.847764i	$-0.322052\pi$
$263$	−3.44475	−	2.89049i	−0.212412	−	0.178235i	−0.742786	+	0.669529i	$0.766496\pi$
$264$	8.00959	+	2.24363i	0.492956	+	0.138086i
$265$	−0.315499	+	0.234777i	−0.0193809	+	0.0144223i
$266$	4.30307	−	4.43839i	0.263838	−	0.272135i
$267$	−0.0944657	+	0.955105i	−0.00578120	+	0.0584515i
$268$	−2.07512	+	11.7686i	−0.126758	+	0.718881i
$269$	2.33247	+	1.95718i	0.142213	+	0.119331i	0.711119	−	0.703072i	$-0.248189\pi$
$269$	2.33247	+	1.95718i	0.142213	+	0.119331i	−0.568906	+	0.822403i	$0.692633\pi$
$270$	0.0589951	−	11.6188i	0.00359033	−	0.707098i
$271$	9.53733	−	3.47130i	0.579351	−	0.210867i	−0.0356881	−	0.999363i	$-0.511362\pi$
$271$	9.53733	−	3.47130i	0.579351	−	0.210867i	0.615040	+	0.788496i	$0.289140\pi$
$272$	−3.83378	+	3.21692i	−0.232457	+	0.195054i
$273$	−5.79972	−	12.8142i	−0.351015	−	0.775553i
$274$	−4.02390	−	2.32320i	−0.243093	−	0.140350i
$275$	−2.79759	+	23.8482i	−0.168701	+	1.43810i
$276$	8.25428	−	0.628101i	0.496849	−	0.0378072i
$277$	−3.83354	−	2.21329i	−0.230335	−	0.132984i	0.380392	−	0.924825i	$-0.375789\pi$
$277$	−3.83354	−	2.21329i	−0.230335	−	0.132984i	−0.610727	+	0.791842i	$0.709123\pi$
$278$	−2.18662	+	1.26244i	−0.131145	+	0.0757164i
$279$	13.9481	+	25.4736i	0.835051	+	1.52507i
$280$	2.64917	+	1.74318i	0.158318	+	0.104175i
$281$	28.9911	+	10.5519i	1.72946	+	0.629472i	0.998592	−	0.0530452i	$-0.0168927\pi$
$281$	28.9911	+	10.5519i	1.72946	+	0.629472i	0.730869	+	0.682518i	$0.239115\pi$
$282$	−1.36118	−	1.39235i	−0.0810573	−	0.0829133i
$283$	11.7937	+	2.07954i	0.701060	+	0.123616i	0.512806	−	0.858505i	$-0.328606\pi$
$283$	11.7937	+	2.07954i	0.701060	+	0.123616i	0.188254	+	0.982120i	$0.439717\pi$
$284$	−11.8656			−0.704095
$285$	−13.5015	+	10.1346i	−0.799758	+	0.600323i
$286$	−27.4984			−1.62601
$287$	−6.59639	−	1.16312i	−0.389373	−	0.0686569i
$288$	−2.34119	+	1.87585i	−0.137956	+	0.110535i
$289$	−7.56114	−	2.75203i	−0.444773	−	0.161884i
$290$	−5.97370	+	9.07843i	−0.350788	+	0.533104i
$291$	19.1434	+	28.0091i	1.12221	+	1.64192i
$292$	−0.669162	+	0.386341i	−0.0391598	+	0.0226089i
$293$	−1.00629	−	0.580979i	−0.0587878	−	0.0339412i	0.470318	−	0.882497i	$-0.344139\pi$
$293$	−1.00629	−	0.580979i	−0.0587878	−	0.0339412i	−0.529106	+	0.848556i	$0.677473\pi$
$294$	0.655601	+	8.61568i	0.0382354	+	0.502477i
$295$	−6.16399	+	6.53071i	−0.358882	+	0.380233i
$296$	−5.47617	−	3.16167i	−0.318296	−	0.183768i
$297$	5.63645	+	24.3088i	0.327060	+	1.41054i
$298$	8.63118	−	7.24242i	0.499991	−	0.419542i
$299$	−25.7165	+	9.36004i	−1.48722	+	0.541305i
$300$	−6.40140	−	5.83284i	−0.369585	−	0.336759i
$301$	−9.81950	−	8.23954i	−0.565986	−	0.474919i
$302$	3.40521	−	19.3119i	0.195948	−	1.11128i
$303$	13.1643	+	1.30203i	0.756271	+	0.0747998i
$304$	4.22733	+	1.06286i	0.242454	+	0.0609592i
$305$	0.950233	+	1.27694i	0.0544102	+	0.0731175i
$306$	−13.9886	−	5.45310i	−0.799676	−	0.311733i
$307$	−6.69443	−	5.61729i	−0.382071	−	0.320596i	0.431444	−	0.902140i	$-0.358004\pi$
$307$	−6.69443	−	5.61729i	−0.382071	−	0.320596i	−0.813515	+	0.581544i	$0.802449\pi$
$308$	−6.40005	−	2.32943i	−0.364676	−	0.132731i
$309$	6.06039	+	23.6869i	0.344764	+	1.34750i
$310$	21.0623	+	4.99652i	1.19626	+	0.283783i
$311$	−15.1358	+	8.73866i	−0.858273	+	0.495524i	−0.863433	−	0.504463i	$-0.831691\pi$
$311$	−15.1358	+	8.73866i	−0.858273	+	0.495524i	0.00516087	+	0.999987i	$0.498357\pi$
$312$	5.78019	−	8.05926i	0.327239	−	0.456266i
$313$	10.9107	−	1.92385i	0.616709	−	0.108742i	0.143438	−	0.989659i	$-0.454184\pi$
$313$	10.9107	−	1.92385i	0.616709	−	0.108742i	0.473271	+	0.880917i	$0.343073\pi$
$314$	−2.53929	−	14.4010i	−0.143300	−	0.812696i
$315$	−0.770007	+	9.48251i	−0.0433850	+	0.534279i
$316$	9.08585	−	5.24572i	0.511119	−	0.295095i
$317$	−6.37530	−	7.59779i	−0.358073	−	0.426734i	0.556694	−	0.830718i	$-0.312070\pi$
$317$	−6.37530	−	7.59779i	−0.358073	−	0.426734i	−0.914766	+	0.403984i	$0.867625\pi$
$318$	0.0755070	+	0.295118i	0.00423422	+	0.0165494i
$319$	7.98270	−	21.9323i	0.446946	−	1.22797i
$320$	−0.130484	+	2.23226i	−0.00729426	+	0.124787i
$321$	1.52243	−	5.43494i	0.0849735	−	0.303349i
$322$	−6.77824			−0.377736
$323$	5.97154	+	20.9815i	0.332265	+	1.16744i
$324$	−8.30925	−	3.45780i	−0.461625	−	0.192100i
$325$	25.5795	+	12.8599i	1.41889	+	0.713340i
$326$	−1.02924	−	0.863636i	−0.0570044	−	0.0478324i
$327$	25.0064	+	12.0071i	1.38286	+	0.663995i
$328$	−1.61533	−	4.43810i	−0.0891919	−	0.245053i
$329$	1.02484	+	1.22135i	0.0565011	+	0.0673354i
$330$	16.2684	+	9.01542i	0.895543	+	0.496282i
$331$	−1.54553	−	0.892314i	−0.0849502	−	0.0490460i	0.456923	−	0.889506i	$-0.348951\pi$
$331$	−1.54553	−	0.892314i	−0.0849502	−	0.0490460i	−0.541873	+	0.840460i	$0.682285\pi$
$332$	−0.369840	−	2.09747i	−0.0202976	−	0.115113i
$333$	0.429403	−	18.9652i	0.0235311	−	1.03928i
$334$	−0.944346	+	1.63566i	−0.0516723	+	0.0894991i
$335$	−10.5889	+	24.5337i	−0.578535	+	1.34042i
$336$	2.02801	−	1.38609i	0.110637	−	0.0756172i
$337$	−13.7974	+	5.02183i	−0.751590	+	0.273557i	−0.689275	−	0.724500i	$-0.742071\pi$
$337$	−13.7974	+	5.02183i	−0.751590	+	0.273557i	−0.0623155	+	0.998056i	$0.519849\pi$
$338$	−6.76771	+	18.5941i	−0.368115	+	1.01139i
$339$	7.51136	+	7.68335i	0.407961	+	0.417302i
$340$	−10.0014	+	5.02029i	−0.542404	+	0.272263i
$341$	−46.4903			−2.51759
$342$	3.29399	+	12.6550i	0.178119	+	0.684305i
$343$		−	17.0026i		−	0.918052i
$344$	1.56950	−	8.90107i	0.0846217	−	0.479914i
$345$	18.2829	+	2.89372i	0.984319	+	0.155793i
$346$	−3.87311	−	1.40970i	−0.208220	−	0.0757857i
$347$	12.3781	−	4.50525i	0.664490	−	0.241855i	0.0123165	−	0.999924i	$-0.496079\pi$
$347$	12.3781	−	4.50525i	0.664490	−	0.241855i	0.652174	+	0.758069i	$0.273857\pi$
$348$	4.74998	+	6.94978i	0.254625	+	0.372548i
$349$	−0.140899	−	0.244043i	−0.00754213	−	0.0130633i	0.862230	−	0.506517i	$-0.169067\pi$
$349$	−0.140899	−	0.244043i	−0.00754213	−	0.0130633i	−0.869772	+	0.493454i	$0.835734\pi$
$350$	4.86405	+	5.15993i	0.259995	+	0.275810i
$351$	29.5350	+	3.59797i	1.57646	+	0.192045i
$352$	−0.833918	−	4.72938i	−0.0444480	−	0.252077i
$353$	2.12483	−	3.68032i	0.113093	−	0.195884i	−0.803923	−	0.594734i	$-0.797257\pi$
$353$	2.12483	−	3.68032i	0.113093	−	0.195884i	0.917016	+	0.398850i	$0.130591\pi$
$354$	2.86822	+	6.33722i	0.152444	+	0.336819i
$355$	−25.8159	−	6.12419i	−1.37016	−	0.325038i
$356$	0.520703	−	0.189521i	0.0275972	−	0.0100446i
$357$	11.0822	+	5.32126i	0.586534	+	0.281631i
$358$	−7.95310	+	9.47813i	−0.420334	+	0.500935i
$359$	−4.39502	−	0.774960i	−0.231960	−	0.0409008i	0.0564597	−	0.998405i	$-0.482019\pi$
$359$	−4.39502	−	0.774960i	−0.231960	−	0.0409008i	−0.288420	+	0.957504i	$0.593130\pi$
$360$	−6.06188	+	2.87290i	−0.319489	+	0.151415i
$361$	11.7566	−	14.9259i	0.618768	−	0.785574i
$362$	−9.08379			−0.477433
$363$	−20.1184	−	5.63553i	−1.05594	−	0.295789i
$364$	−5.21994	+	6.22088i	−0.273599	+	0.326063i
$365$	−1.65529	+	0.495183i	−0.0866418	+	0.0259191i
$366$	1.19445	−	0.305606i	0.0624351	−	0.0159743i
$367$	3.08143	+	3.67231i	0.160850	+	0.191693i	0.840449	−	0.541890i	$-0.182291\pi$
$367$	3.08143	+	3.67231i	0.160850	+	0.191693i	−0.679600	+	0.733583i	$0.737847\pi$
$368$	−2.38969	−	4.13907i	−0.124571	−	0.215764i
$369$	9.35086	−	10.6450i	0.486786	−	0.554155i
$370$	−10.2826	−	9.70522i	−0.534567	−	0.504550i
$371$	−0.0433130	−	0.245640i	−0.00224870	−	0.0127530i
$372$	9.77234	−	13.6255i	0.506672	−	0.706447i
$373$	7.49476	+	12.9813i	0.388064	+	0.672147i	0.992189	−	0.124743i	$-0.0398106\pi$
$373$	7.49476	+	12.9813i	0.388064	+	0.672147i	−0.604125	+	0.796890i	$0.706477\pi$
$374$	18.4111	−	15.4487i	0.952015	−	0.798835i
$375$	−10.9169	−	15.9944i	−0.563749	−	0.825946i
$376$	−0.384498	+	1.05640i	−0.0198290	+	0.0544797i
$377$	−21.3183	−	17.8882i	−1.09795	−	0.921289i
$378$	6.56927	+	3.33935i	0.337887	+	0.171758i
$379$			16.5268i			0.848924i	0.905446	+	0.424462i	$0.139537\pi$
$379$			16.5268i			0.848924i	−0.905446	+	0.424462i	$0.860463\pi$
$380$	8.64877	+	4.49430i	0.443673	+	0.230553i
$381$	0.757003	−	7.65377i	0.0387825	−	0.392114i
$382$	−3.89691	+	22.1005i	−0.199383	+	1.13076i
$383$	4.62139	−	5.50756i	0.236142	−	0.281423i	−0.634939	−	0.772562i	$-0.718975\pi$
$383$	4.62139	−	5.50756i	0.236142	−	0.281423i	0.871081	+	0.491139i	$0.163419\pi$
$384$	1.56139	+	0.749717i	0.0796791	+	0.0382588i
$385$	−12.7222	−	8.37135i	−0.648384	−	0.426643i
$386$	6.50806	+	7.75600i	0.331251	+	0.394770i
$387$	25.6833	−	8.69479i	1.30556	−	0.441981i
$388$	9.79363	−	16.9631i	0.497196	−	0.861169i
$389$	25.3831	−	4.47573i	1.28697	−	0.226928i	0.512036	−	0.858964i	$-0.328892\pi$
$389$	25.3831	−	4.47573i	1.28697	−	0.226928i	0.774939	+	0.632036i	$0.217781\pi$
$390$	16.7355	−	14.5511i	0.847435	−	0.736824i
$391$	11.9596	−	20.7146i	0.604821	−	1.04758i
$392$	4.32029	−	2.49432i	0.218208	−	0.125982i
$393$	−12.8558	+	8.78657i	−0.648489	+	0.443224i
$394$	0.270268	+	0.742556i	0.0136159	+	0.0374094i
$395$	22.4754	−	6.72357i	1.13086	−	0.338300i
$396$	11.2432	−	9.00846i	0.564993	−	0.452692i
$397$	−28.0894	−	4.95291i	−1.40976	−	0.248580i	−0.583615	−	0.812030i	$-0.698362\pi$
$397$	−28.0894	−	4.95291i	−1.40976	−	0.248580i	−0.826150	+	0.563451i	$0.809473\pi$
$398$			14.4327i			0.723446i
$399$	−1.90316	−	10.5369i	−0.0952773	−	0.527502i
$400$	−1.43602	+	4.78935i	−0.0718012	+	0.239467i
$401$	−0.583919	+	3.31157i	−0.0291595	+	0.165372i	−0.995910	−	0.0903491i	$-0.971202\pi$
$401$	−0.583919	+	3.31157i	−0.0291595	+	0.165372i	0.966751	+	0.255721i	$0.0823128\pi$
$402$	14.4693	+	14.8006i	0.721662	+	0.738187i
$403$	−18.9590	+	52.0894i	−0.944415	+	2.59476i
$404$	−2.61218	−	7.17692i	−0.129961	−	0.357065i
$405$	−16.2936	−	11.8117i	−0.809638	−	0.586930i
$406$	−3.44635	−	5.96926i	−0.171040	−	0.296249i
$407$	26.2984	+	15.1834i	1.30357	+	0.752614i
$408$	0.657703	+	8.64330i	0.0325611	+	0.427907i
$409$	−35.2334	+	6.21261i	−1.74218	+	0.307194i	−0.952095	−	0.305802i	$-0.901076\pi$
$409$	−35.2334	+	6.21261i	−1.74218	+	0.307194i	−0.790087	+	0.612995i	$0.789964\pi$
$410$	−1.22383	−	10.4896i	−0.0604408	−	0.518046i
$411$	−7.33182	+	3.31838i	−0.361652	+	0.163683i
$412$	10.8136	−	9.07370i	0.532749	−	0.447029i
$413$	−1.94805	−	5.35222i	−0.0958572	−	0.263366i
$414$	7.44832	−	12.2518i	0.366065	−	0.602141i
$415$	0.277907	−	4.75431i	0.0136419	−	0.233380i
$416$	−5.63904	−	0.994315i	−0.276477	−	0.0487503i
$417$	−0.430439	+	4.35200i	−0.0210787	+	0.213118i
$418$	−20.3011	−	5.10422i	−0.992958	−	0.249655i
$419$			0.791705i			0.0386773i	0.999813	+	0.0193387i	$0.00615607\pi$
$419$			0.791705i			0.0386773i	−0.999813	+	0.0193387i	$0.993844\pi$
$420$	5.12772	−	1.96898i	0.250207	−	0.0960761i
$421$	12.1149	−	14.4380i	0.590445	−	0.703665i	−0.385246	−	0.922814i	$-0.625883\pi$
$421$	12.1149	−	14.4380i	0.590445	−	0.703665i	0.975692	+	0.219148i	$0.0703279\pi$
$422$	11.6637	+	4.24522i	0.567778	+	0.206654i
$423$	−3.33376	+	0.510313i	−0.162093	+	0.0248123i
$424$	0.134728	−	0.113050i	0.00654297	−	0.00549020i
$425$	−24.3511	+	5.76054i	−1.18120	+	0.279427i
$426$	−11.9779	+	16.7006i	−0.580329	+	0.809147i
$427$	−0.994199	+	0.175304i	−0.0481127	+	0.00848356i
$428$	−3.20914	+	0.565858i	−0.155120	+	0.0273518i
$429$	−27.7585	+	38.7033i	−1.34019	+	1.86861i
$430$	8.00884	−	18.5559i	0.386220	−	0.894844i
$431$	−7.47680	+	6.27378i	−0.360145	+	0.302197i	−0.804848	−	0.593480i	$-0.797753\pi$
$431$	−7.47680	+	6.27378i	−0.360145	+	0.302197i	0.444704	+	0.895678i	$0.353309\pi$
$432$	0.276874	+	5.18877i	0.0133211	+	0.249645i
$433$	−17.3942	−	6.33098i	−0.835913	−	0.304247i	−0.111629	−	0.993750i	$-0.535607\pi$
$433$	−17.3942	−	6.33098i	−0.835913	−	0.304247i	−0.724283	+	0.689503i	$0.757829\pi$
$434$	−8.82514	+	10.5174i	−0.423620	+	0.504851i
$435$	6.74747	+	17.5721i	0.323517	+	0.842520i
$436$		−	16.0155i		−	0.767004i
$437$	−20.7230	+	2.13672i	−0.991316	+	0.102213i
$438$	−0.131726	+	1.33183i	−0.00629409	+	0.0636371i
$439$	−17.0425	−	3.00505i	−0.813394	−	0.143423i	−0.248548	−	0.968620i	$-0.579953\pi$
$439$	−17.0425	−	3.00505i	−0.813394	−	0.143423i	−0.564846	+	0.825196i	$0.691065\pi$
$440$	0.626627	−	10.7201i	0.0298733	−	0.511059i
$441$	12.7882	+	7.77443i	0.608961	+	0.370211i
$442$	−9.80118	−	26.9285i	−0.466194	−	1.28086i
$443$	5.68509	−	4.77036i	0.270107	−	0.226647i	−0.497666	−	0.867369i	$-0.665809\pi$
$443$	5.68509	−	4.77036i	0.270107	−	0.226647i	0.767773	+	0.640722i	$0.221365\pi$
$444$	−9.97795	+	4.51601i	−0.473533	+	0.214321i
$445$	1.23070	−	0.143587i	0.0583410	−	0.00680669i
$446$	19.9121	−	3.51105i	0.942867	−	0.166253i
$447$	−1.48072	−	19.4591i	−0.0700357	−	0.920385i
$448$	−1.22822	−	0.709111i	−0.0580278	−	0.0335024i
$449$	3.42022	+	5.92399i	0.161410	+	0.279570i	0.935375	−	0.353658i	$-0.115062\pi$
$449$	3.42022	+	5.92399i	0.161410	+	0.279570i	−0.773965	+	0.633229i	$0.781729\pi$
$450$	−14.6715	+	3.12182i	−0.691623	+	0.147164i
$451$	7.75739	+	21.3132i	0.365281	+	1.00360i
$452$	2.12176	−	5.82949i	0.0997992	−	0.274196i
$453$	−23.7437	−	24.2874i	−1.11558	−	1.14112i
$454$	−4.62276	+	26.2170i	−0.216957	+	1.23042i
$455$	−14.5677	+	10.8405i	−0.682946	+	0.508212i
$456$	5.76327	−	4.87696i	0.269890	−	0.228385i
$457$			1.24574i			0.0582734i	0.999575	+	0.0291367i	$0.00927581\pi$
$457$			1.24574i			0.0582734i	−0.999575	+	0.0291367i	$0.990724\pi$
$458$	−19.7386	−	3.48044i	−0.922322	−	0.162630i
$459$	−21.7960	+	14.1840i	−1.01735	+	0.662051i
$460$	−3.06293	−	10.2387i	−0.142810	−	0.477382i
$461$	−4.17855	−	11.4805i	−0.194614	−	0.534699i	0.803552	−	0.595235i	$-0.202941\pi$
$461$	−4.17855	−	11.4805i	−0.194614	−	0.534699i	−0.998166	+	0.0605363i	$0.980719\pi$
$462$	−9.73920	+	6.65646i	−0.453109	+	0.309687i
$463$	−5.36979	+	3.10025i	−0.249555	+	0.144081i	−0.619561	−	0.784949i	$-0.712689\pi$
$463$	−5.36979	+	3.10025i	−0.249555	+	0.144081i	0.370005	+	0.929030i	$0.379356\pi$
$464$	2.43005	−	4.20897i	0.112812	−	0.195397i
$465$	28.2940	−	24.6009i	1.31210	−	1.14084i
$466$	2.45733	−	0.433293i	0.113834	−	0.0200719i
$467$	15.7559	−	27.2901i	0.729097	−	1.26283i	−0.228168	−	0.973622i	$-0.573273\pi$
$467$	15.7559	−	27.2901i	0.729097	−	1.26283i	0.957265	−	0.289212i	$-0.0933933\pi$
$468$	−5.50836	−	16.2710i	−0.254624	−	0.752127i
$469$	−10.8939	−	12.9829i	−0.503036	−	0.599494i
$470$	−1.38179	+	2.09995i	−0.0637371	+	0.0968633i
$471$	−22.8324	−	10.9632i	−1.05206	−	0.505160i
$472$	2.58149	−	3.07651i	0.118823	−	0.141608i
$473$	−7.53727	+	42.7460i	−0.346564	+	1.96546i
$474$	1.78856	−	18.0835i	0.0821515	−	0.830601i
$475$	16.4974	+	14.2421i	0.756952	+	0.653471i
$476$		−	7.09769i		−	0.325322i
$477$	0.491593	+	0.191635i	0.0225085	+	0.00877436i
$478$	−11.0816	−	9.29859i	−0.506862	−	0.425308i
$479$	1.99506	−	5.48139i	0.0911568	−	0.250451i	−0.885733	−	0.464195i	$-0.846344\pi$
$479$	1.99506	−	5.48139i	0.0911568	−	0.250451i	0.976890	+	0.213744i	$0.0685658\pi$
$480$	3.01013	+	2.43703i	0.137393	+	0.111234i
$481$	27.7367	−	23.2738i	1.26468	−	1.06120i
$482$	−7.00029	−	12.1249i	−0.318855	−	0.552272i
$483$	−6.84235	+	9.54021i	−0.311338	+	0.434095i
$484$	2.09463	+	11.8792i	0.0952102	+	0.539964i
$485$	30.0630	−	31.8515i	1.36509	−	1.44630i
$486$	−13.2546	+	8.20457i	−0.601242	+	0.372167i
$487$	−2.75503	−	4.77186i	−0.124842	−	0.216234i	0.796829	−	0.604205i	$-0.206509\pi$
$487$	−2.75503	−	4.77186i	−0.124842	−	0.216234i	−0.921671	+	0.387972i	$0.873176\pi$
$488$	−0.457557	−	0.545295i	−0.0207126	−	0.0246844i
$489$	−2.25452	+	0.576829i	−0.101953	+	0.0260851i
$490$	10.6870	−	3.19704i	0.482789	−	0.144427i
$491$	−11.0236	+	13.1374i	−0.497489	+	0.592885i	−0.955106	−	0.296265i	$-0.904259\pi$
$491$	−11.0236	+	13.1374i	−0.497489	+	0.592885i	0.457617	+	0.889150i	$0.348703\pi$
$492$	−7.87713	−	2.20653i	−0.355129	−	0.0994780i
$493$	24.3231			1.09546
$494$	−13.9978	+	20.6645i	−0.629792	+	0.929741i
$495$	29.1112	−	13.7966i	1.30845	−	0.620113i
$496$	−9.53370	−	1.68105i	−0.428076	−	0.0754813i
$497$	10.8169	−	12.8911i	0.485204	−	0.578244i
$498$	−3.32547	−	1.59676i	−0.149018	−	0.0715527i
$499$	−24.7622	+	9.01269i	−1.10851	+	0.403463i	−0.830445	−	0.557100i	$-0.811914\pi$
$499$	−24.7622	+	9.01269i	−1.10851	+	0.403463i	−0.278061	+	0.960563i	$0.589692\pi$
$500$	−5.59626	+	9.67894i	−0.250272	+	0.432855i
$501$	1.34887	+	2.98027i	0.0602630	+	0.133149i
$502$	−12.1055	+	20.9674i	−0.540295	+	0.935819i
$503$	−6.28854	−	35.6641i	−0.280392	−	1.59018i	−0.721295	−	0.692628i	$-0.756453\pi$
$503$	−6.28854	−	35.6641i	−0.280392	−	1.59018i	0.440903	−	0.897555i	$-0.354658\pi$
$504$	0.0963081	−	4.25358i	0.00428991	−	0.189469i
$505$	−1.97908	−	16.9629i	−0.0880679	−	0.754841i
$506$	11.4761	+	19.8772i	0.510176	+	0.883651i
$507$	19.3391	+	28.2954i	0.858879	+	1.25664i
$508$	−4.17267	+	1.51873i	−0.185132	+	0.0673827i
$509$	−18.8278	−	6.85277i	−0.834529	−	0.303744i	−0.110813	−	0.993841i	$-0.535345\pi$
$509$	−18.8278	−	6.85277i	−0.834529	−	0.303744i	−0.723716	+	0.690098i	$0.757568\pi$
$510$	−3.03010	+	19.1446i	−0.134175	+	0.847736i
$511$	0.190290	−	1.07919i	0.00841792	−	0.0477404i
$512$		−	1.00000i		−	0.0441942i
$513$	21.1368	+	8.13851i	0.933213	+	0.359324i
$514$	23.1818			1.02251
$515$	28.2102	−	14.1603i	1.24309	−	0.623978i
$516$	−10.9437	−	11.1943i	−0.481770	−	0.492802i
$517$	1.84649	−	5.07319i	0.0812086	−	0.223119i
$518$	8.42707	−	3.06720i	0.370264	−	0.134765i
$519$	−5.89386	+	4.02828i	−0.258712	+	0.176822i
$520$	−11.7556	−	5.07379i	−0.515517	−	0.222500i
$521$	14.2673	−	24.7117i	0.625061	−	1.08264i	−0.363468	−	0.931607i	$-0.618407\pi$
$521$	14.2673	−	24.7117i	0.625061	−	1.08264i	0.988529	−	0.151031i	$-0.0482592\pi$
$522$	14.5766	+	0.330038i	0.637999	+	0.0144454i
$523$	−1.42189	−	8.06393i	−0.0621748	−	0.352611i	−0.999985	−	0.00546262i	$-0.998261\pi$
$523$	−1.42189	−	8.06393i	−0.0621748	−	0.352611i	0.937810	−	0.347148i	$-0.112850\pi$
$524$	7.78581	+	4.49514i	0.340125	+	0.196371i
$525$	12.1725	−	1.63731i	0.531253	−	0.0714581i
$526$	2.89049	+	3.44475i	0.126031	+	0.150198i
$527$	−16.5704	−	45.5269i	−0.721820	−	1.98318i
$528$	−7.49830	−	3.60040i	−0.326322	−	0.156687i
$529$	−0.120610	−	0.101204i	−0.00524392	−	0.00440017i
$530$	0.351474	−	0.176425i	0.0152671	−	0.00766340i
$531$	11.8148	+	2.36021i	0.512720	+	0.102424i
$532$	−5.00842	+	3.62374i	−0.217142	+	0.157109i
$533$	27.0436			1.17139
$534$	0.258883	−	0.924191i	0.0112030	−	0.0399937i
$535$	−7.27414	−	0.425200i	−0.314489	−	0.0183830i
$536$	4.08719	−	11.2295i	0.176540	−	0.485039i
$537$	5.31193	+	20.7616i	0.229227	+	0.895929i
$538$	−1.95718	−	2.33247i	−0.0843798	−	0.100560i
$539$	−20.7475	+	11.9786i	−0.893659	+	0.515954i
$540$	−2.07568	+	11.4320i	−0.0893231	+	0.491957i
$541$	0.949568	+	5.38527i	0.0408251	+	0.231531i	0.998392	−	0.0566788i	$-0.0180511\pi$
$541$	0.949568	+	5.38527i	0.0408251	+	0.231531i	−0.957567	+	0.288210i	$0.906940\pi$
$542$	−9.99522	+	1.76243i	−0.429331	+	0.0757027i
$543$	−9.16971	+	12.7852i	−0.393510	+	0.548666i
$544$	4.33414	−	2.50232i	0.185825	−	0.107286i
$545$	8.26607	−	34.8447i	0.354080	−	1.49259i
$546$	3.48644	+	13.6267i	0.149206	+	0.583168i
$547$	17.2181	+	6.26689i	0.736194	+	0.267953i	0.682784	−	0.730620i	$-0.260769\pi$
$547$	17.2181	+	6.26689i	0.736194	+	0.267953i	0.0534097	+	0.998573i	$0.482991\pi$
$548$	3.55935	+	2.98665i	0.152048	+	0.127583i
$549$	0.775619	−	1.98966i	0.0331026	−	0.0849168i
$550$	6.89628	−	23.0001i	0.294058	−	0.980726i
$551$	−12.4182	−	17.1633i	−0.529033	−	0.731182i
$552$	−8.23795	−	0.814783i	−0.350630	−	0.0346794i
$553$	−2.58375	+	14.6531i	−0.109872	+	0.623115i
$554$	3.39096	+	2.84536i	0.144068	+	0.120888i
$555$	−24.0397	+	4.67552i	−1.02043	+	0.198465i
$556$	2.37262	−	0.863563i	0.100622	−	0.0366232i
$557$	−10.2164	+	8.57260i	−0.432884	+	0.363233i	−0.833039	−	0.553215i	$-0.813401\pi$
$557$	−10.2164	+	8.57260i	−0.432884	+	0.363233i	0.400155	+	0.916448i	$0.368956\pi$
$558$	−9.31276	−	27.5087i	−0.394240	−	1.16454i
$559$	44.8204	+	25.8770i	1.89570	+	1.09448i
$560$	−2.30622	−	2.17672i	−0.0974557	−	0.0919833i
$561$	−3.15851	−	41.5081i	−0.133352	−	1.75247i
$562$	−26.7183	−	15.4258i	−1.12704	−	0.650699i
$563$	−32.8298	+	18.9543i	−1.38361	+	0.798829i	−0.992585	−	0.121550i	$-0.961214\pi$
$563$	−32.8298	+	18.9543i	−1.38361	+	0.798829i	−0.391027	+	0.920379i	$0.627880\pi$
$564$	1.09872	+	1.60757i	0.0462647	+	0.0676907i
$565$	7.62505	−	11.5880i	0.320788	−	0.487512i
$566$	−11.2534	−	4.09589i	−0.473015	−	0.172163i
$567$	11.3315	−	5.87516i	0.475877	−	0.246733i
$568$	11.6854	+	2.06044i	0.490307	+	0.0864543i
$569$	−17.7730			−0.745083			−0.372542	−	0.928016i	$-0.621514\pi$
$569$	−17.7730			−0.745083			−0.372542	+	0.928016i	$0.621514\pi$
$570$	15.0562	−	7.63614i	0.630635	−	0.319843i
$571$	−4.65101			−0.194639			−0.0973193	−	0.995253i	$-0.531027\pi$
$571$	−4.65101			−0.194639			−0.0973193	+	0.995253i	$0.531027\pi$
$572$	27.0806	+	4.77504i	1.13230	+	0.199654i
$573$	27.1721	+	27.7943i	1.13513	+	1.16112i
$574$	6.29421	+	2.29090i	0.262715	+	0.0956205i
$575$	−1.37948	−	23.8571i	−0.0575284	−	0.994910i
$576$	2.63136	−	1.44081i	0.109640	−	0.0600336i
$577$	3.11745	−	1.79986i	0.129781	−	0.0749292i	−0.433704	−	0.901055i	$-0.642794\pi$
$577$	3.11745	−	1.79986i	0.129781	−	0.0749292i	0.563485	+	0.826126i	$0.309460\pi$
$578$	6.96839	+	4.02320i	0.289847	+	0.167343i
$579$	17.4860	−	1.33058i	0.726694	−	0.0552970i
$580$	7.45940	−	7.90318i	0.309735	−	0.328162i
$581$	2.61588	+	1.51028i	0.108525	+	0.0626570i
$582$	−13.9889	−	30.9078i	−0.579857	−	1.28117i
$583$	−0.647009	+	0.542905i	−0.0267964	+	0.0224848i
$584$	0.726084	−	0.264273i	0.0300456	−	0.0109357i
$585$	−3.58654	−	38.2436i	−0.148285	−	1.58118i
$586$	0.890112	+	0.746892i	0.0367702	+	0.0308538i
$587$	6.87823	−	39.0084i	0.283895	−	1.61005i	−0.425311	−	0.905047i	$-0.639835\pi$
$587$	6.87823	−	39.0084i	0.283895	−	1.61005i	0.709206	−	0.705001i	$-0.249054\pi$
$588$	0.850456	−	8.59863i	0.0350722	−	0.354602i
$589$	−23.6656	+	34.9367i	−0.975122	+	1.43954i
$590$	7.20440	−	5.36113i	0.296600	−	0.220714i
$591$	1.31796	+	0.369183i	0.0542135	+	0.0151862i
$592$	4.84396	+	4.06457i	0.199086	+	0.167053i
$593$	20.7672	+	7.55865i	0.852807	+	0.310396i	0.731184	−	0.682180i	$-0.238968\pi$
$593$	20.7672	+	7.55865i	0.852807	+	0.310396i	0.121623	+	0.992576i	$0.461190\pi$
$594$	−1.32964	−	24.9182i	−0.0545560	−	1.02241i
$595$	3.66332	−	15.4423i	0.150182	−	0.633075i
$596$	−9.75769	+	5.63360i	−0.399690	+	0.230761i
$597$	20.3137	+	14.5692i	0.831385	+	0.596279i
$598$	26.9512	−	4.75222i	1.10212	−	0.194333i
$599$	−4.39302	−	24.9141i	−0.179494	−	1.01796i	−0.932828	−	0.360323i	$-0.882667\pi$
$599$	−4.39302	−	24.9141i	−0.179494	−	1.01796i	0.753334	−	0.657638i	$-0.228444\pi$
$600$	5.29129	+	6.85582i	0.216016	+	0.279888i
$601$	−39.5222	+	22.8182i	−1.61215	+	0.930773i	−0.623274	+	0.782003i	$0.714198\pi$
$601$	−39.5222	+	22.8182i	−1.61215	+	0.930773i	−0.988872	+	0.148769i	$0.952469\pi$
$602$	8.23954	+	9.81950i	0.335818	+	0.400213i
$603$	35.4377	−	5.42459i	1.44313	−	0.220906i
$604$	−6.70696	+	18.4272i	−0.272902	+	0.749793i
$605$	−1.57396	+	26.9265i	−0.0639904	+	1.09472i
$606$	−12.7382	−	3.56821i	−0.517456	−	0.144949i
$607$	22.8014			0.925482			0.462741	−	0.886493i	$-0.346866\pi$
$607$	22.8014			0.925482			0.462741	+	0.886493i	$0.346866\pi$
$608$	−3.97854	−	1.78078i	−0.161351	−	0.0722202i
$609$	−11.8805	−	1.17506i	−0.481424	−	0.0476157i
$610$	−0.714058	−	1.42255i	−0.0289114	−	0.0575973i
$611$	−4.93118	−	4.13775i	−0.199494	−	0.167395i
$612$	12.8292	+	7.79936i	0.518589	+	0.315270i
$613$	−2.80974	−	7.71971i	−0.113484	−	0.311796i	0.869928	−	0.493178i	$-0.164165\pi$
$613$	−2.80974	−	7.71971i	−0.113484	−	0.311796i	−0.983413	+	0.181382i	$0.941943\pi$
$614$	5.61729	+	6.69443i	0.226696	+	0.270165i
$615$	−15.9993	−	8.86633i	−0.645155	−	0.357525i
$616$	5.89831	+	3.40539i	0.237650	+	0.137207i
$617$	6.51429	+	36.9444i	0.262255	+	1.48732i	0.776738	+	0.629823i	$0.216873\pi$
$617$	6.51429	+	36.9444i	0.262255	+	1.48732i	−0.514483	+	0.857501i	$0.672016\pi$
$618$	−1.85513	−	24.3795i	−0.0746242	−	0.980685i
$619$	9.45192	−	16.3712i	0.379905	−	0.658014i	−0.611143	−	0.791520i	$-0.709290\pi$
$619$	9.45192	−	16.3712i	0.379905	−	0.658014i	0.991048	+	0.133506i	$0.0426235\pi$
$620$	−19.8747	−	8.57805i	−0.798187	−	0.344503i
$621$	−9.72530	−	22.8510i	−0.390263	−	0.916979i
$622$	16.4233	−	5.97759i	0.658515	−	0.239680i
$623$	−0.268782	+	0.738473i	−0.0107685	+	0.0295863i
$624$	−7.09186	+	6.93310i	−0.283901	+	0.277546i
$625$	−17.1713	+	18.1699i	−0.686851	+	0.726798i
$626$	−11.0790			−0.442806
$627$	−27.6772	+	23.4208i	−1.10532	+	0.935337i
$628$			14.6232i			0.583528i
$629$	−5.49528	+	31.1653i	−0.219111	+	1.24264i
$630$	2.40493	−	9.20474i	0.0958147	−	0.366726i
$631$	−1.50942	−	0.549385i	−0.0600891	−	0.0218707i	0.311801	−	0.950148i	$-0.399068\pi$
$631$	−1.50942	−	0.549385i	−0.0600891	−	0.0218707i	−0.371890	+	0.928277i	$0.621290\pi$
$632$	−9.85873	+	3.58828i	−0.392159	+	0.142734i
$633$	17.7490	−	12.1310i	0.705461	−	0.482162i
$634$	4.95910	+	8.58942i	0.196951	+	0.341129i
$635$	−9.86228	+	1.15064i	−0.391373	+	0.0456618i
$636$	−0.0231132	−	0.303746i	−0.000916499	−	0.0120443i
$637$	4.96028	+	28.1312i	0.196534	+	1.11460i
$638$	−11.6699	+	20.2129i	−0.462017	+	0.800237i
$639$	11.4146	+	33.7171i	0.451553	+	1.33383i
$640$	0.516129	−	2.17569i	0.0204018	−	0.0860016i
$641$	13.3177	−	4.84724i	0.526017	−	0.191455i	−0.0653420	−	0.997863i	$-0.520814\pi$
$641$	13.3177	−	4.84724i	0.526017	−	0.191455i	0.591359	+	0.806408i	$0.298592\pi$
$642$	−2.44306	+	5.08801i	−0.0964201	+	0.200808i
$643$	10.8475	−	12.9275i	0.427782	−	0.509811i	−0.508499	−	0.861063i	$-0.669799\pi$
$643$	10.8475	−	12.9275i	0.427782	−	0.509811i	0.936281	+	0.351252i	$0.114244\pi$
$644$	6.67526	+	1.17703i	0.263042	+	0.0463814i
$645$	−18.0324	−	30.0037i	−0.710024	−	1.18139i
$646$	−2.23742	−	21.6997i	−0.0880302	−	0.853762i
$647$	−5.35296			−0.210447			−0.105223	−	0.994449i	$-0.533556\pi$
$647$	−5.35296			−0.210447			−0.105223	+	0.994449i	$0.533556\pi$
$648$	7.58257	+	4.84816i	0.297872	+	0.190454i
$649$	−12.3972	+	14.7744i	−0.486633	+	0.579947i
$650$	−22.9577	−	17.1064i	−0.900477	−	0.670967i
$651$	5.89438	+	23.0381i	0.231019	+	0.902933i
$652$	0.863636	+	1.02924i	0.0338226	+	0.0403082i
$653$	−17.4454	−	30.2163i	−0.682692	−	1.18246i	−0.974156	−	0.225875i	$-0.927476\pi$
$653$	−17.4454	−	30.2163i	−0.682692	−	1.18246i	0.291465	−	0.956582i	$-0.405857\pi$
$654$	−22.5415	−	16.1670i	−0.881442	−	0.632180i
$655$	14.6194	+	13.7985i	0.571228	+	0.539152i
$656$	0.820127	+	4.65117i	0.0320206	+	0.181598i
$657$	1.74154	+	1.52982i	0.0679441	+	0.0596841i
$658$	−0.797182	−	1.38076i	−0.0310774	−	0.0538276i
$659$	6.36176	−	5.33815i	0.247819	−	0.207945i	−0.510414	−	0.859929i	$-0.670508\pi$
$659$	6.36176	−	5.33815i	0.247819	−	0.207945i	0.758232	+	0.651984i	$0.226063\pi$
$660$	−14.4557	−	11.7034i	−0.562687	−	0.455555i
$661$	−7.72468	+	21.2234i	−0.300455	+	0.825493i	0.693966	+	0.720008i	$0.255862\pi$
$661$	−7.72468	+	21.2234i	−0.300455	+	0.825493i	−0.994421	+	0.105485i	$0.966360\pi$
$662$	1.36710	+	1.14714i	0.0531340	+	0.0445847i
$663$	−47.7952	−	13.3883i	−1.85621	−	0.519958i
$664$			2.12982i			0.0826531i
$665$	−12.7671	+	5.29914i	−0.495085	+	0.205492i
$666$	−3.71615	+	18.6025i	−0.143998	+	0.720831i
$667$	−4.03355	+	22.8754i	−0.156180	+	0.885740i
$668$	1.21403	−	1.44682i	0.0469721	−	0.0559792i
$669$	15.1588	−	31.5701i	0.586072	−	1.22057i
$670$	14.6883	−	22.3223i	0.567458	−	0.862385i
$671$	2.19734	+	2.61869i	0.0848275	+	0.101094i
$672$	−2.23789	+	1.01287i	−0.0863286	+	0.0390723i
$673$	7.25134	−	12.5597i	0.279519	−	0.484141i	−0.691747	−	0.722140i	$-0.743158\pi$
$673$	7.25134	−	12.5597i	0.279519	−	0.484141i	0.971265	+	0.238000i	$0.0764918\pi$
$674$	14.4598	−	2.54965i	0.556970	−	0.0982088i
$675$	−10.4164	+	23.8012i	−0.400929	+	0.916109i
$676$	9.89372	−	17.1364i	0.380528	−	0.659094i
$677$	−25.0311	+	14.4517i	−0.962025	+	0.555425i	−0.896796	−	0.442445i	$-0.854111\pi$
$677$	−25.0311	+	14.4517i	−0.962025	+	0.555425i	−0.0652290	+	0.997870i	$0.520778\pi$
$678$	−6.06304	−	8.87096i	−0.232850	−	0.340687i
$679$	9.50100	+	26.1038i	0.364615	+	1.00177i
$680$	10.7213	−	3.20728i	0.411141	−	0.122994i
$681$	32.2333	+	32.9714i	1.23518	+	1.26347i
$682$	45.7840	+	8.07296i	1.75316	+	0.309130i
$683$		−	26.1222i		−	0.999537i	−0.866159	−	0.499768i	$-0.833418\pi$
$683$		−	26.1222i		−	0.999537i	0.866159	−	0.499768i	$-0.166582\pi$
$684$	−1.04642	−	13.0348i	−0.0400110	−	0.498397i
$685$	6.20253	+	8.33510i	0.236987	+	0.318468i
$686$	−2.95246	+	16.7443i	−0.112726	+	0.639299i
$687$	−24.8239	+	24.2682i	−0.947091	+	0.925890i
$688$	−3.09131	+	8.49330i	−0.117855	+	0.323804i
$689$	0.344437	+	0.946332i	0.0131220	+	0.0360524i
$690$	−17.5027	−	6.02455i	−0.666315	−	0.229351i
$691$	−22.3974	−	38.7935i	−0.852038	−	1.47577i	−0.879366	−	0.476146i	$-0.842033\pi$
$691$	−22.3974	−	38.7935i	−0.852038	−	1.47577i	0.0273283	−	0.999627i	$-0.491300\pi$
$692$	3.56948	+	2.06084i	0.135691	+	0.0783413i
$693$	−0.462504	+	20.4271i	−0.0175691	+	0.775962i
$694$	−12.9724	+	2.28738i	−0.492424	+	0.0868277i
$695$	5.60779	−	0.654265i	0.212716	−	0.0248177i
$696$	−3.47100	−	7.66903i	−0.131568	−	0.290694i
$697$	−18.1066	+	15.1933i	−0.685837	+	0.575486i
$698$	0.0963803	+	0.264803i	0.00364805	+	0.0100229i
$699$	1.87072	−	3.89603i	0.0707572	−	0.147361i
$700$	−3.89415	−	5.92617i	−0.147185	−	0.223988i
$701$	46.1368	+	8.13516i	1.74256	+	0.307261i	0.952222	−	0.305407i	$-0.0987924\pi$
$701$	46.1368	+	8.13516i	1.74256	+	0.307261i	0.790341	+	0.612667i	$0.209903\pi$
$702$	−28.4615	−	8.67200i	−1.07421	−	0.327304i
$703$	24.7971	−	12.0338i	0.935240	−	0.453864i
$704$			4.80234i			0.180995i
$705$	1.56077	+	4.06464i	0.0587820	+	0.153083i
$706$	−2.73163	+	3.25543i	−0.102806	+	0.122520i
$707$	10.1785	+	3.70466i	0.382801	+	0.139328i
$708$	−1.72420	−	6.73900i	−0.0647994	−	0.253267i
$709$	−18.7780	+	15.7566i	−0.705222	+	0.591752i	−0.923254	−	0.384190i	$-0.874481\pi$
$709$	−18.7780	+	15.7566i	−0.705222	+	0.591752i	0.218032	+	0.975942i	$0.430036\pi$
$710$	24.3602	+	10.5140i	0.914223	+	0.394585i
$711$	−23.6466	−	20.7719i	−0.886817	−	0.779007i
$712$	−0.545703	+	0.0962221i	−0.0204511	+	0.00360608i
$713$	45.5652	−	8.03438i	1.70643	−	0.300890i
$714$	−9.98984	−	7.16483i	−0.373860	−	0.268137i
$715$	56.4543	+	24.3661i	2.11127	+	0.911239i
$716$	9.47813	−	7.95310i	0.354214	−	0.297221i
$717$	−24.2740	+	6.21060i	−0.906530	+	0.231939i
$718$	4.19368	+	1.52637i	0.156507	+	0.0569638i
$719$	3.90235	−	4.65064i	0.145533	−	0.173439i	−0.688354	−	0.725375i	$-0.741666\pi$
$719$	3.90235	−	4.65064i	0.145533	−	0.173439i	0.833887	+	0.551936i	$0.186111\pi$
$720$	6.46866	−	1.77662i	0.241073	−	0.0662107i
$721$			20.0199i			0.745579i
$722$	−14.1698	+	12.6576i	−0.527347	+	0.471068i
$723$	−24.1320	−	2.38680i	−0.897478	−	0.0887659i
$724$	8.94578	+	1.57738i	0.332467	+	0.0586230i
$725$	20.3084	−	13.3448i	0.754234	−	0.495615i
$726$	18.8342	+	9.04344i	0.699001	+	0.335633i
$727$	−8.98220	−	24.6784i	−0.333131	−	0.915270i	−0.987292	−	0.158915i	$-0.949200\pi$
$727$	−8.98220	−	24.6784i	−0.333131	−	0.915270i	0.654161	−	0.756355i	$-0.273022\pi$
$728$	6.22088	−	5.21994i	0.230561	−	0.193464i
$729$	−1.83225	+	26.9378i	−0.0678612	+	0.997695i
$730$	1.71613	−	0.200222i	0.0635168	−	0.00741055i
$731$	−44.5466	+	7.85478i	−1.64762	+	0.290519i
$732$	−1.22938	+	0.0935480i	−0.0454390	+	0.00345763i
$733$	−9.94353	−	5.74090i	−0.367273	−	0.212045i	0.304994	−	0.952354i	$-0.401346\pi$
$733$	−9.94353	−	5.74090i	−0.367273	−	0.212045i	−0.672266	+	0.740309i	$0.734679\pi$
$734$	−2.39693	−	4.15160i	−0.0884723	−	0.153238i
$735$	6.28833	−	18.2690i	0.231948	−	0.673861i
$736$	1.63465	+	4.49116i	0.0602539	+	0.165546i
$737$	−19.6281	+	53.9277i	−0.723010	+	1.98645i
$738$	−11.0573	+	8.85949i	−0.407024	+	0.326122i
$739$	1.78347	−	10.1146i	0.0656061	−	0.372071i	−0.934274	−	0.356557i	$-0.883951\pi$
$739$	1.78347	−	10.1146i	0.0656061	−	0.372071i	0.999880	−	0.0155136i	$-0.00493833\pi$
$740$	8.44110	+	11.3433i	0.310301	+	0.416989i
$741$	14.9546	+	40.5616i	0.549371	+	1.49007i
$742$			0.249430i			0.00915685i
$743$	−19.8443	−	3.49908i	−0.728016	−	0.128369i	−0.202657	−	0.979250i	$-0.564958\pi$
$743$	−19.8443	−	3.49908i	−0.728016	−	0.128369i	−0.525359	+	0.850881i	$0.676069\pi$
$744$	−11.9899	+	11.7215i	−0.439571	+	0.429731i
$745$	−24.1373	+	7.22073i	−0.884323	+	0.264547i
$746$	−5.12672	−	14.0855i	−0.187703	−	0.515708i
$747$	−5.60434	+	3.06866i	−0.205052	+	0.112276i
$748$	−20.8140	+	12.0170i	−0.761036	+	0.439385i
$749$	2.31074	−	4.00233i	0.0844328	−	0.146242i
$750$	7.97370	+	17.6471i	0.291158	+	0.644381i
$751$	6.32900	−	1.11597i	0.230949	−	0.0407225i	−0.0569760	−	0.998376i	$-0.518146\pi$
$751$	6.32900	−	1.11597i	0.230949	−	0.0407225i	0.287925	+	0.957653i	$0.407035\pi$
$752$	0.562099	−	0.973584i	0.0204976	−	0.0355030i
$753$	17.2911	+	38.2039i	0.630121	+	1.39223i
$754$	17.8882	+	21.3183i	0.651450	+	0.776368i
$755$	−24.1031	+	36.6302i	−0.877201	+	1.33311i
$756$	−5.88960	−	4.42936i	−0.214203	−	0.161094i
$757$	26.0578	−	31.0544i	0.947086	−	1.12869i	−0.0444701	−	0.999011i	$-0.514160\pi$
$757$	26.0578	−	31.0544i	0.947086	−	1.12869i	0.991556	−	0.129682i	$-0.0413956\pi$
$758$	2.86985	−	16.2757i	0.104238	−	0.591161i
$759$	39.5614	+	3.91286i	1.43599	+	0.142028i
$760$	−7.73695	−	5.92786i	−0.280649	−	0.215026i
$761$			35.7467i			1.29582i	0.761719	+	0.647908i	$0.224356\pi$
$761$			35.7467i			1.29582i	−0.761719	+	0.647908i	$0.775644\pi$
$762$	−2.07457	+	7.40604i	−0.0751536	+	0.268292i
$763$	17.3996	+	14.6000i	0.629908	+	0.528556i
$764$	7.67541	−	21.0880i	0.277687	−	0.762938i
$765$	23.8868	+	23.5905i	0.863629	+	0.852915i
$766$	−5.50756	+	4.62139i	−0.198996	+	0.166978i
$767$	11.4981	+	19.9154i	0.415174	+	0.719102i
$768$	−1.40748	−	1.00946i	−0.0507880	−	0.0364257i
$769$	−2.02211	−	11.4680i	−0.0729191	−	0.413545i	−0.999315	−	0.0369950i	$-0.988221\pi$
$769$	−2.02211	−	11.4680i	−0.0729191	−	0.413545i	0.926396	−	0.376550i	$-0.122890\pi$
$770$	11.0753	+	10.4534i	0.399125	+	0.376713i
$771$	23.4011	−	32.6278i	0.842769	−	1.17506i
$772$	−5.06237	−	8.76828i	−0.182199	−	0.315577i
$773$	20.3355	+	24.2349i	0.731417	+	0.871669i	0.995687	−	0.0927798i	$-0.0295753\pi$
$773$	20.3355	+	24.2349i	0.731417	+	0.871669i	−0.264269	+	0.964449i	$0.585131\pi$
$774$	−26.8030	+	4.10284i	−0.963412	+	0.147474i
$775$	−38.8137	−	28.9210i	−1.39423	−	1.03887i
$776$	−12.5904	+	15.0047i	−0.451971	+	0.538637i
$777$	4.18977	−	14.9571i	0.150307	−	0.536584i
$778$	−25.7747			−0.924067
$779$	19.9654	+	5.01981i	0.715333	+	0.179853i
$780$	−19.0080	+	11.4239i	−0.680597	+	0.409043i
$781$	−56.1171	−	9.89495i	−2.00803	−	0.354069i
$782$	−15.3749	+	18.3231i	−0.549806	+	0.655233i
$783$	15.1790	−	20.1830i	0.542452	−	0.721283i
$784$	−4.68779	+	1.70622i	−0.167421	+	0.0609363i
$785$	−7.54744	+	31.8154i	−0.269380	+	1.13554i
$786$	14.1863	−	6.42069i	0.506007	−	0.229019i
$787$	12.8766	−	22.3028i	0.459000	−	0.795011i	−0.539909	−	0.841724i	$-0.681541\pi$
$787$	12.8766	−	22.3028i	0.459000	−	0.795011i	0.998908	+	0.0467129i	$0.0148746\pi$
$788$	−0.137219	−	0.778207i	−0.00488822	−	0.0277225i
$789$	7.76624	−	0.590963i	0.276485	−	0.0210389i
$790$	−23.3015	+	2.71861i	−0.829031	+	0.0967236i
$791$	4.39905	+	7.61938i	0.156412	+	0.270914i
$792$	−12.6367	+	6.91924i	−0.449026	+	0.245864i
$793$	3.83016	−	1.39407i	0.136013	−	0.0495047i
$794$	26.8026	+	9.75533i	0.951187	+	0.346204i
$795$	0.106485	−	0.672785i	0.00377663	−	0.0238612i
$796$	2.50621	−	14.2134i	0.0888304	−	0.503782i
$797$		−	24.6462i		−	0.873012i	−0.899701	−	0.436506i	$-0.856216\pi$
$797$		−	24.6462i		−	0.873012i	0.899701	−	0.436506i	$-0.143784\pi$
$798$	0.0445445	+	10.7073i	0.00157686	+	0.379033i
$799$	5.62620			0.199041
$800$	2.24587	−	4.46722i	0.0794035	−	0.157940i
$801$	−1.03945	−	1.29731i	−0.0367271	−	0.0458380i
$802$	1.15010	−	3.15986i	0.0406113	−	0.111579i
$803$	−3.48690	+	1.26913i	−0.123050	+	0.0447866i
$804$	−11.6794	−	17.0883i	−0.411899	−	0.602658i
$805$	13.9158	+	6.00614i	0.490467	+	0.211689i
$806$	27.7162	−	48.0059i	0.976261	−	1.69093i
$807$	−5.25859	+	0.400147i	−0.185111	+	0.0140858i
$808$	1.32624	+	7.52149i	0.0466570	+	0.264605i
$809$	−25.2953	−	14.6042i	−0.889334	−	0.513458i	−0.0156097	−	0.999878i	$-0.504969\pi$
$809$	−25.2953	−	14.6042i	−0.889334	−	0.513458i	−0.873725	+	0.486421i	$0.838302\pi$
$810$	13.9950	+	14.4617i	0.491735	+	0.508131i
$811$	−0.663509	−	0.790739i	−0.0232990	−	0.0277666i	0.754269	−	0.656565i	$-0.227991\pi$
$811$	−0.663509	−	0.790739i	−0.0232990	−	0.0277666i	−0.777568	+	0.628799i	$0.783547\pi$
$812$	2.35744	+	6.47702i	0.0827301	+	0.227299i
$813$	−7.60919	+	15.8471i	−0.266866	+	0.555784i
$814$	−23.2623	−	19.5194i	−0.815345	−	0.684155i
$815$	1.34778	+	2.68505i	0.0472107	+	0.0940533i
$816$	0.853183	−	8.62620i	0.0298674	−	0.301977i
$817$	28.2860	+	27.4236i	0.989603	+	0.959432i
$818$	35.7770			1.25091
$819$	22.6987	+	8.84849i	0.793155	+	0.309191i
$820$	−0.616264	+	10.5428i	−0.0215209	+	0.368170i
$821$	−7.78634	+	21.3928i	−0.271745	+	0.746613i	0.726487	+	0.687180i	$0.241152\pi$
$821$	−7.78634	+	21.3928i	−0.271745	+	0.746613i	−0.998232	+	0.0594334i	$0.981071\pi$
$822$	7.79666	−	1.99481i	0.271940	−	0.0695768i
$823$	−10.9164	−	13.0096i	−0.380521	−	0.453487i	0.541458	−	0.840728i	$-0.317873\pi$
$823$	−10.9164	−	13.0096i	−0.380521	−	0.453487i	−0.921979	+	0.387241i	$0.873428\pi$
$824$	−12.2250	+	7.05809i	−0.425877	+	0.245880i
$825$	−25.4106	−	32.9240i	−0.884682	−	1.14627i
$826$	0.989050	+	5.60918i	0.0344135	+	0.195168i
$827$	−11.4929	+	2.02651i	−0.399647	+	0.0704686i	−0.369860	−	0.929088i	$-0.620594\pi$
$827$	−11.4929	+	2.02651i	−0.399647	+	0.0704686i	−0.0297877	+	0.999556i	$0.509483\pi$
$828$	−9.46266	+	10.7722i	−0.328850	+	0.374361i
$829$	25.7790	−	14.8835i	0.895342	−	0.516926i	0.0196563	−	0.999807i	$-0.493743\pi$
$829$	25.7790	−	14.8835i	0.895342	−	0.516926i	0.875686	+	0.482881i	$0.160409\pi$
$830$	−1.09926	+	4.63383i	−0.0381560	+	0.160842i
$831$	7.42781	−	1.90043i	0.257668	−	0.0659253i
$832$	5.38071	+	1.95842i	0.186543	+	0.0678959i
$833$	−19.1253	−	16.0481i	−0.662654	−	0.556033i
$834$	1.17962	−	4.21114i	0.0408468	−	0.145820i
$835$	3.38809	−	2.52124i	0.117250	−	0.0872510i
$836$	19.1063	+	8.55192i	0.660806	+	0.295774i
$837$	−48.1187	−	14.6614i	−1.66323	−	0.506772i
$838$	0.137478	−	0.779677i	0.00474910	−	0.0269335i
$839$	−27.1944	−	22.8188i	−0.938856	−	0.787793i	0.0385302	−	0.999257i	$-0.487732\pi$
$839$	−27.1944	−	22.8188i	−0.938856	−	0.787793i	−0.977386	+	0.211464i	$0.932177\pi$
$840$	−5.39172	+	1.04864i	−0.186032	+	0.0361816i
$841$	5.05499	−	1.83987i	0.174310	−	0.0634437i
$842$	−14.4380	+	12.1149i	−0.497567	+	0.417508i
$843$	−48.6825	+	22.0337i	−1.67671	+	0.758880i
$844$	−10.7493	−	6.20610i	−0.370006	−	0.213623i
$845$	30.3702	−	32.1771i	1.04477	−	1.10692i
$846$	3.37173	+	0.0763416i	0.115922	+	0.00262468i
$847$	−14.8153	−	8.55363i	−0.509061	−	0.293906i
$848$	−0.152312	+	0.0879374i	−0.00523042	+	0.00301978i
$849$	−17.1247	+	11.7042i	−0.587718	+	0.401688i
$850$	24.9815	−	1.44450i	0.856857	−	0.0495458i
$851$	−28.3991	−	10.3364i	−0.973509	−	0.354328i
$852$	14.6959	−	14.3669i	0.503474	−	0.492204i
$853$	7.64787	+	1.34853i	0.261858	+	0.0461727i	0.303036	−	0.952979i	$-0.402000\pi$
$853$	7.64787	+	1.34853i	0.261858	+	0.0461727i	−0.0411776	+	0.999152i	$0.513111\pi$
$854$	1.00954			0.0345456
$855$	4.45092	−	28.8996i	0.152218	−	0.988347i
$856$	3.25865			0.111378
$857$	−4.41642	−	0.778735i	−0.150862	−	0.0266011i	0.0977070	−	0.995215i	$-0.468849\pi$
$857$	−4.41642	−	0.778735i	−0.150862	−	0.0266011i	−0.248569	+	0.968614i	$0.579960\pi$
$858$	34.0575	−	33.2951i	1.16270	−	1.13668i
$859$	−30.1189	−	10.9624i	−1.02764	−	0.374032i	−0.227461	−	0.973787i	$-0.573042\pi$
$859$	−30.1189	−	10.9624i	−1.02764	−	0.374032i	−0.800183	+	0.599755i	$0.795265\pi$
$860$	−11.1094	+	16.8833i	−0.378826	+	0.575714i
$861$	9.57814	−	6.54638i	0.326422	−	0.223100i
$862$	8.45264	−	4.88013i	0.287898	−	0.166218i
$863$	2.83124	+	1.63462i	0.0963766	+	0.0556431i	0.547414	−	0.836862i	$-0.315612\pi$
$863$	2.83124	+	1.63462i	0.0963766	+	0.0556431i	−0.451037	+	0.892505i	$0.648946\pi$
$864$	0.628353	−	5.15802i	0.0213770	−	0.175479i
$865$	6.70240	+	6.32605i	0.227889	+	0.215092i
$866$	16.0306	+	9.25527i	0.544742	+	0.314507i
$867$	12.6969	−	5.74659i	0.431208	−	0.195165i
$868$	10.5174	−	8.82514i	0.356984	−	0.299545i
$869$	47.3450	−	17.2322i	1.60607	−	0.584561i
$870$	−3.59359	−	18.4769i	−0.121834	−	0.626425i
$871$	52.4181	+	43.9840i	1.77612	+	1.49034i
$872$	−2.78107	+	15.7722i	−0.0941788	+	0.534114i
$873$	−57.6232	−	11.5112i	−1.95025	−	0.389594i
$874$	20.7792	+	1.49425i	0.702867	+	0.0505439i
$875$	−5.41377	−	14.9034i	−0.183019	−	0.503826i
$876$	0.360994	−	1.28872i	0.0121968	−	0.0435418i
$877$	28.2811	+	23.7307i	0.954985	+	0.801328i	0.980130	−	0.198356i	$-0.0635603\pi$
$877$	28.2811	+	23.7307i	0.954985	+	0.801328i	−0.0251450	+	0.999684i	$0.508005\pi$
$878$	16.2618	+	5.91880i	0.548808	+	0.199750i
$879$	1.94977	−	0.498855i	0.0657639	−	0.0168260i
$880$	−2.47863	+	10.4484i	−0.0835545	+	0.352215i
$881$	2.11328	−	1.22011i	0.0711984	−	0.0411064i	−0.463978	−	0.885847i	$-0.653578\pi$
$881$	2.11328	−	1.22011i	0.0711984	−	0.0411064i	0.535177	+	0.844740i	$0.320245\pi$
$882$	−11.2439	−	9.87696i	−0.378601	−	0.332575i
$883$	−15.4179	+	2.71859i	−0.518852	+	0.0914877i	−0.426941	−	0.904280i	$-0.640409\pi$
$883$	−15.4179	+	2.71859i	−0.518852	+	0.0914877i	−0.0919115	+	0.995767i	$0.529298\pi$
$884$	4.97619	+	28.2214i	0.167367	+	0.949187i
$885$	−0.273123	−	15.5519i	−0.00918094	−	0.522770i
$886$	−6.42709	+	3.71068i	−0.215922	+	0.124663i
$887$	−10.1730	−	12.1237i	−0.341576	−	0.407074i	0.567722	−	0.823220i	$-0.307825\pi$
$887$	−10.1730	−	12.1237i	−0.341576	−	0.407074i	−0.909298	+	0.416146i	$0.863380\pi$
$888$	10.6106	−	2.71475i	0.356067	−	0.0911011i
$889$	2.15389	−	5.91778i	0.0722393	−	0.198476i
$890$	−1.23694	−	0.0723038i	−0.0414623	−	0.00242363i
$891$	−36.4141	−	23.2825i	−1.21992	−	0.779993i
$892$	−20.2193			−0.676993
$893$	−2.87247	−	3.97008i	−0.0961236	−	0.132854i
$894$	−1.92082	+	19.4206i	−0.0642417	+	0.649523i
$895$	24.7263	−	12.4115i	0.826508	−	0.414871i
$896$	1.08642	+	0.911616i	0.0362948	+	0.0304549i
$897$	20.5175	−	42.7303i	0.685058	−	1.42672i
$898$	−2.33957	−	6.42791i	−0.0780724	−	0.214502i
$899$	30.2428	+	36.0420i	1.00866	+	1.20207i
$900$	14.9908	−	0.526701i	0.499692	−	0.0175567i
$901$	−0.762267	−	0.440095i	−0.0253948	−	0.0146617i
$902$	−3.93853	−	22.3365i	−0.131139	−	0.743724i
$903$	22.1382	−	1.68458i	0.736713	−	0.0560594i
$904$	−3.10181	+	5.37248i	−0.103165	+	0.178686i
$905$	18.6491	+	8.04907i	0.619917	+	0.267560i
$906$	19.1655	+	28.0414i	0.636731	+	0.931614i
$907$	−23.5544	+	8.57310i	−0.782111	+	0.284665i	−0.702053	−	0.712125i	$-0.747733\pi$
$907$	−23.5544	+	8.57310i	−0.782111	+	0.284665i	−0.0800584	+	0.996790i	$0.525511\pi$
$908$	9.10506	−	25.0159i	0.302162	−	0.830183i
$909$	−17.8809	+	14.3268i	−0.593073	+	0.475191i
$910$	16.2289	−	8.14618i	0.537981	−	0.270043i
$911$	45.9454			1.52224			0.761120	−	0.648612i	$-0.224650\pi$
$911$	45.9454			1.52224			0.761120	+	0.648612i	$0.224650\pi$
$912$	−6.52259	+	3.80209i	−0.215984	+	0.125900i
$913$		−	10.2281i		−	0.338502i
$914$	0.216321	−	1.22682i	0.00715526	−	0.0405795i
$915$	−2.72302	−	0.430985i	−0.0900202	−	0.0142479i
$916$	18.8343	+	6.85513i	0.622303	+	0.226500i
$917$	−11.9813	+	4.36083i	−0.395657	+	0.144007i
$918$	23.9279	−	10.1836i	0.789740	−	0.336110i
$919$	14.6787	+	25.4243i	0.484206	+	0.838669i	0.999835	−	0.0181424i	$-0.00577523\pi$
$919$	14.6787	+	25.4243i	0.484206	+	0.838669i	−0.515630	+	0.856812i	$0.672442\pi$
$920$	1.23846	+	10.6150i	0.0408310	+	0.349967i
$921$	15.0927	−	1.14846i	0.497321	−	0.0378431i
$922$	2.12151	+	12.0317i	0.0698681	+	0.396241i
$923$	−33.9715	+	58.8403i	−1.11818	+	1.93675i
$924$	10.7471	−	4.86414i	0.353554	−	0.160018i
$925$	12.5106	+	29.0362i	0.411345	+	0.954705i
$926$	5.82657	−	2.12070i	0.191473	−	0.0696904i
$927$	−36.1862	−	21.9990i	−1.18851	−	0.722542i
$928$	−3.12401	+	3.72305i	−0.102551	+	0.122215i
$929$	6.95259	+	1.22593i	0.228107	+	0.0402214i	0.286533	−	0.958070i	$-0.407497\pi$
$929$	6.95259	+	1.22593i	0.228107	+	0.0402214i	−0.0584262	+	0.998292i	$0.518608\pi$
$930$	−32.1361	+	19.3140i	−1.05378	+	0.633331i
$931$	−1.55968	+	21.6890i	−0.0511163	+	0.710828i
$932$	−2.49524			−0.0817342
$933$	8.16532	−	29.1496i	0.267321	−	0.954314i
$934$	−20.2554	+	24.1395i	−0.662778	+	0.789868i
$935$	−51.4871	+	15.4025i	−1.68381	+	0.503715i
$936$	2.59925	+	16.9803i	0.0849590	+	0.555019i
$937$	15.3123	+	18.2485i	0.500231	+	0.596152i	0.955789	−	0.294054i	$-0.0950047\pi$
$937$	15.3123	+	18.2485i	0.500231	+	0.596152i	−0.455558	+	0.890206i	$0.650560\pi$
$938$	8.47398	+	14.6774i	0.276685	+	0.479233i
$939$	−11.1838	+	15.5935i	−0.364970	+	0.508873i
$940$	1.72545	−	1.82810i	0.0562778	−	0.0596260i
$941$	−6.77146	−	38.4029i	−0.220743	−	1.25190i	−0.870657	−	0.491890i	$-0.836306\pi$
$941$	−6.77146	−	38.4029i	−0.220743	−	1.25190i	0.649914	−	0.760008i	$-0.274805\pi$
$942$	20.5818	+	14.7615i	0.670591	+	0.480956i
$943$	−11.2863	−	19.5485i	−0.367534	−	0.636587i
$944$	−3.07651	+	2.58149i	−0.100132	+	0.0840205i
$945$	−10.5278	−	12.6767i	−0.342469	−	0.412373i
$946$	14.8455	−	40.7877i	0.482670	−	1.32612i
$947$	19.4835	+	16.3486i	0.633128	+	0.531258i	0.901899	−	0.431946i	$-0.142173\pi$
$947$	19.4835	+	16.3486i	0.633128	+	0.531258i	−0.268771	+	0.963204i	$0.586617\pi$
$948$	−4.90155	+	17.4982i	−0.159195	+	0.568314i
$949$			4.42440i			0.143622i
$950$	−13.7736	−	16.8904i	−0.446876	−	0.547998i
$951$	17.0954	+	1.69084i	0.554357	+	0.0548292i
$952$	−1.23250	+	6.98986i	−0.0399456	+	0.226543i
$953$	−19.1150	+	22.7804i	−0.619197	+	0.737930i	−0.980932	−	0.194351i	$-0.937740\pi$
$953$	−19.1150	+	22.7804i	−0.619197	+	0.737930i	0.361735	+	0.932281i	$0.382184\pi$
$954$	−0.450848	−	0.274088i	−0.0145967	−	0.00887392i
$955$	27.5834	−	41.9194i	0.892578	−	1.35648i
$956$	9.29859	+	11.0816i	0.300738	+	0.358406i
$957$	16.6689	+	36.8293i	0.538829	+	1.19052i
$958$	−2.91659	+	5.05168i	−0.0942307	+	0.163212i
$959$	−6.48952	+	1.14428i	−0.209558	+	0.0369507i
$960$	−2.54122	−	2.92271i	−0.0820175	−	0.0943299i
$961$	31.3586	−	54.3147i	1.01157	−	1.75209i
$962$	−31.3568	+	18.1038i	−1.01098	+	0.583691i
$963$	4.69508	+	8.57469i	0.151297	+	0.276316i
$964$	4.78848	+	13.1562i	0.154227	+	0.423734i
$965$	−6.48856	−	21.6899i	−0.208874	−	0.698221i
$966$	8.39504	−	8.20712i	0.270106	−	0.264060i
$967$	41.5722	+	7.33030i	1.33687	+	0.235727i	0.795958	−	0.605352i	$-0.206967\pi$
$967$	41.5722	+	7.33030i	1.33687	+	0.235727i	0.540914	+	0.841078i	$0.318079\pi$
$968$		−	12.0625i		−	0.387702i
$969$	−32.8004	−	18.7558i	−1.05370	−	0.602523i
$970$	−35.1372	+	26.1472i	−1.12819	+	0.839537i
$971$	−6.03347	+	34.2175i	−0.193623	+	1.09809i	0.720742	+	0.693203i	$0.243801\pi$
$971$	−6.03347	+	34.2175i	−0.193623	+	1.09809i	−0.914366	+	0.404889i	$0.867310\pi$
$972$	14.4780	−	5.77828i	0.464381	−	0.185338i
$973$	−1.22472	+	3.36490i	−0.0392629	+	0.107874i
$974$	1.88455	+	5.17777i	0.0603850	+	0.165906i
$975$	−47.2517	+	15.0443i	−1.51327	+	0.481804i
$976$	0.355916	+	0.616465i	0.0113926	+	0.0197326i
$977$	28.2801	+	16.3275i	0.904761	+	0.522364i	0.878742	−	0.477298i	$-0.158384\pi$
$977$	28.2801	+	16.3275i	0.904761	+	0.522364i	0.0260191	+	0.999661i	$0.491717\pi$
$978$	2.32044	−	0.176571i	0.0741994	−	0.00564613i
$979$	2.62065	−	0.462091i	0.0837563	−	0.0147685i
$980$	−11.0798	+	1.29269i	−0.353931	+	0.0412934i
$981$	−45.5094	+	15.4067i	−1.45300	+	0.491898i
$982$	13.1374	−	11.0236i	0.419233	−	0.351778i
$983$	6.55421	+	18.0075i	0.209047	+	0.574352i	0.999259	−	0.0384815i	$-0.0122521\pi$
$983$	6.55421	+	18.0075i	0.209047	+	0.574352i	−0.790212	+	0.612833i	$0.790030\pi$
$984$	7.37430	+	3.54086i	0.235084	+	0.112878i
$985$	0.103110	−	1.76396i	0.00328535	−	0.0562043i
$986$	−23.9535	−	4.22365i	−0.762836	−	0.134509i
$987$	−2.74811	−	0.271804i	−0.0874733	−	0.00865163i
$988$	17.3735	−	17.9199i	0.552726	−	0.570107i
$989$		−	43.1980i		−	1.37362i
$990$	−31.0647	+	8.53193i	−0.987302	+	0.271162i
$991$	9.41330	−	11.2183i	0.299023	−	0.356362i	−0.595522	−	0.803339i	$-0.703055\pi$
$991$	9.41330	−	11.2183i	0.299023	−	0.356362i	0.894546	+	0.446977i	$0.147499\pi$
$992$	9.09695	+	3.31102i	0.288828	+	0.105125i
$993$	2.99460	−	0.766181i	0.0950309	−	0.0243140i
$994$	−12.8911	+	10.8169i	−0.408880	+	0.343091i
$995$	12.7887	−	29.6305i	0.405429	−	0.939349i
$996$	2.99768	+	2.14997i	0.0949850	+	0.0681244i
$997$	−43.8794	+	7.73712i	−1.38967	+	0.245037i	−0.817893	−	0.575370i	$-0.804858\pi$
$997$	−43.8794	+	7.73712i	−1.38967	+	0.245037i	−0.571780	+	0.820407i	$0.693747\pi$
$998$	25.9510	−	4.57586i	0.821465	−	0.144846i
$999$	22.4313	+	24.0088i	0.709694	+	0.759606i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.59.5	yes	240
3.2	odd	2	inner	570.2.bf.a.59.33	yes	240
5.4	even	2	inner	570.2.bf.a.59.36	yes	240
15.14	odd	2	inner	570.2.bf.a.59.8	yes	240
19.10	odd	18	inner	570.2.bf.a.29.8	yes	240
57.29	even	18	inner	570.2.bf.a.29.36	yes	240
95.29	odd	18	inner	570.2.bf.a.29.33	yes	240
285.29	even	18	inner	570.2.bf.a.29.5	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.5	✓	240	285.29	even	18	inner
570.2.bf.a.29.8	yes	240	19.10	odd	18	inner
570.2.bf.a.29.33	yes	240	95.29	odd	18	inner
570.2.bf.a.29.36	yes	240	57.29	even	18	inner
570.2.bf.a.59.5	yes	240	1.1	even	1	trivial
570.2.bf.a.59.8	yes	240	15.14	odd	2	inner
570.2.bf.a.59.33	yes	240	3.2	odd	2	inner
570.2.bf.a.59.36	yes	240	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.23853 + 1.21080i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.86795 + 1.22913i) q^{5} +(1.42997 - 0.977341i) q^{6} +(-1.22822 + 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0679076 - 2.99923i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.23853 + 1.21080i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.86795 + 1.22913i) q^{5} +(1.42997 - 0.977341i) q^{6} +(-1.22822 + 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.0679076 - 2.99923i) q^{9} +(-1.62614 - 1.53482i) q^{10} +(4.15895 + 2.40117i) q^{11} +(-1.57796 + 0.714182i) q^{12} +(4.38640 - 3.68062i) q^{13} +(1.33269 - 0.485061i) q^{14} +(-3.80175 + 0.739407i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.869046 + 4.92861i) q^{17} +(-0.587687 + 2.94187i) q^{18} +(3.92152 - 1.90308i) q^{19} +(1.33491 + 1.79388i) q^{20} +(0.662587 - 2.36538i) q^{21} +(-3.67881 - 3.08688i) q^{22} +(-4.49116 - 1.63465i) q^{23} +(1.67800 - 0.429323i) q^{24} +(1.97847 + 4.59191i) q^{25} +(-4.95889 + 2.86302i) q^{26} +(3.54738 + 3.79686i) q^{27} +(-1.39668 + 0.246272i) q^{28} +(-0.843948 - 4.78627i) q^{29} +(3.87239 - 0.0680073i) q^{30} +(-8.38379 + 4.84038i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(-8.05832 + 2.06175i) q^{33} +(1.71169 - 4.70282i) q^{34} +(-3.16584 - 0.185055i) q^{35} +(1.08961 - 2.79513i) q^{36} +6.32334 q^{37} +(-4.19241 + 1.19320i) q^{38} +(-0.976165 + 9.86962i) q^{39} +(-1.00313 - 1.99843i) q^{40} +(3.61797 + 3.03584i) q^{41} +(-1.06327 + 2.21439i) q^{42} +(3.09131 + 8.49330i) q^{43} +(3.08688 + 3.67881i) q^{44} +(3.81330 - 5.51895i) q^{45} +(4.13907 + 2.38969i) q^{46} +(-0.195215 - 1.10712i) q^{47} +(-1.72706 + 0.131419i) q^{48} +(-2.49432 + 4.32029i) q^{49} +(-1.15104 - 4.86571i) q^{50} +(-4.89124 - 7.15647i) q^{51} +(5.38071 - 1.95842i) q^{52} +(-0.0601527 + 0.165268i) q^{53} +(-2.83417 - 4.35517i) q^{54} +(4.81735 + 9.59716i) q^{55} +1.41822 q^{56} +(-2.55266 + 7.10520i) q^{57} +4.86010i q^{58} +(-0.697387 + 3.95508i) q^{59} +(-3.82537 - 0.605459i) q^{60} +(0.668904 + 0.243461i) q^{61} +(9.09695 - 3.31102i) q^{62} +(2.04338 + 3.73186i) q^{63} +(0.500000 + 0.866025i) q^{64} +(12.7175 - 1.48376i) q^{65} +(8.29392 - 0.631117i) q^{66} +(2.07512 + 11.7686i) q^{67} +(-2.50232 + 4.33414i) q^{68} +(7.54166 - 3.41335i) q^{69} +(3.08561 + 0.731986i) q^{70} +(-11.1500 + 4.05828i) q^{71} +(-1.55843 + 2.56346i) q^{72} +(-0.496670 + 0.591909i) q^{73} +(-6.22728 - 1.09804i) q^{74} +(-8.01030 - 3.29167i) q^{75} +(4.33591 - 0.447070i) q^{76} -6.81079 q^{77} +(2.67518 - 9.55017i) q^{78} +(6.74377 - 8.03691i) q^{79} +(0.640862 + 2.14226i) q^{80} +(-8.99078 - 0.407341i) q^{81} +(-3.03584 - 3.61797i) q^{82} +(-1.06491 - 1.84448i) q^{83} +(1.43164 - 1.99612i) q^{84} +(-7.68124 + 8.13822i) q^{85} +(-1.56950 - 8.90107i) q^{86} +(6.84048 + 4.90607i) q^{87} +(-2.40117 - 4.15895i) q^{88} +(0.424481 - 0.356182i) q^{89} +(-4.71372 + 4.77293i) q^{90} +(-2.77747 + 7.63105i) q^{91} +(-3.66122 - 3.07213i) q^{92} +(4.52281 - 16.1461i) q^{93} +1.12420i q^{94} +(9.66433 + 1.26520i) q^{95} +(1.72364 + 0.170478i) q^{96} +(3.40129 - 19.2897i) q^{97} +(3.20664 - 3.82152i) q^{98} +(7.48409 - 12.3106i) 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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