LMFDB - Embedded newform 570.2.bf.a.59.8

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			59.8
Character	$\chi$	$=$	570.59
Dual form			570.2.bf.a.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(-0.977341 + 1.42997i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.640862 - 2.14226i) q^{5} +(1.21080 - 1.23853i) q^{6} +(1.22822 - 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.08961 - 2.79513i) q^{9} +O(q^{10})$	\(q+(-0.984808 - 0.173648i) q^{2} +(-0.977341 + 1.42997i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.640862 - 2.14226i) q^{5} +(1.21080 - 1.23853i) q^{6} +(1.22822 - 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.08961 - 2.79513i) q^{9} +(-1.00313 + 1.99843i) q^{10} +(-4.15895 - 2.40117i) q^{11} +(-1.40748 + 1.00946i) q^{12} +(-4.38640 + 3.68062i) q^{13} +(-1.33269 + 0.485061i) q^{14} +(2.43703 + 3.01013i) 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} +(-0.186381 + 2.44935i) q^{21} +(3.67881 + 3.08688i) q^{22} +(-4.49116 - 1.63465i) q^{23} +(1.56139 - 0.749717i) q^{24} +(-4.17859 - 2.74579i) q^{25} +(4.95889 - 2.86302i) q^{26} +(5.06186 + 1.17369i) q^{27} +(1.39668 - 0.246272i) q^{28} +(0.843948 + 4.78627i) q^{29} +(-1.87730 - 3.38759i) q^{30} +(-8.38379 + 4.84038i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(7.49830 - 3.60040i) q^{33} +(1.71169 - 4.70282i) q^{34} +(-0.731986 - 3.08561i) q^{35} +(-0.0679076 - 2.99923i) q^{36} -6.32334 q^{37} +(-4.19241 + 1.19320i) q^{38} +(-0.976165 - 9.86962i) q^{39} +(-1.62614 + 1.53482i) q^{40} +(-3.61797 - 3.03584i) q^{41} +(0.608875 - 2.37978i) q^{42} +(-3.09131 - 8.49330i) q^{43} +(-3.08688 - 3.67881i) q^{44} +(-6.68620 + 0.542938i) q^{45} +(4.13907 + 2.38969i) q^{46} +(-0.195215 - 1.10712i) q^{47} +(-1.66785 + 0.467196i) q^{48} +(-2.49432 + 4.32029i) q^{49} +(3.63831 + 3.42968i) q^{50} +(-6.19839 - 6.05964i) q^{51} +(-5.38071 + 1.95842i) q^{52} +(-0.0601527 + 0.165268i) q^{53} +(-4.78115 - 2.03484i) q^{54} +(-7.80925 + 7.37075i) q^{55} -1.41822 q^{56} +(-1.11132 + 7.46759i) q^{57} -4.86010i q^{58} +(0.697387 - 3.95508i) q^{59} +(1.26053 + 3.66211i) q^{60} +(0.668904 + 0.243461i) q^{61} +(9.09695 - 3.31102i) q^{62} +(-3.32034 - 2.66037i) q^{63} +(0.500000 + 0.866025i) q^{64} +(5.07379 + 11.7556i) q^{65} +(-8.00959 + 2.24363i) q^{66} +(-2.07512 - 11.7686i) q^{67} +(-2.50232 + 4.33414i) q^{68} +(6.72688 - 4.82460i) q^{69} +(0.185055 + 3.16584i) q^{70} +(11.1500 - 4.05828i) q^{71} +(-0.453935 + 2.96546i) 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} +(-0.752507 + 9.88919i) q^{78} +(6.74377 - 8.03691i) q^{79} +(1.86795 - 1.22913i) q^{80} +(-6.62550 + 6.09120i) q^{81} +(3.03584 + 3.61797i) q^{82} +(-1.06491 - 1.84448i) q^{83} +(-1.01287 + 2.23789i) q^{84} +(10.0014 + 5.02029i) q^{85} +(1.56950 + 8.90107i) q^{86} +(-7.66903 - 3.47100i) q^{87} +(2.40117 + 4.15895i) q^{88} +(-0.424481 + 0.356182i) q^{89} +(6.67890 + 0.626356i) q^{90} +(-2.77747 + 7.63105i) q^{91} +(-3.66122 - 3.07213i) q^{92} +(1.27223 - 16.7192i) q^{93} +1.12420i q^{94} +(-1.56374 - 9.62054i) q^{95} +(1.72364 - 0.170478i) q^{96} +(-3.40129 + 19.2897i) q^{97} +(3.20664 - 3.82152i) q^{98} +(-2.17995 + 14.2411i) 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
$3$	−0.977341	+	1.42997i	−0.564268	+	0.825592i
$3$	−0.977341	+	1.42997i	−0.564268	+	0.825592i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	0.640862	−	2.14226i	0.286602	−	0.958050i
$5$	0.640862	−	2.14226i	0.286602	−	0.958050i
$6$	1.21080	−	1.23853i	0.494309	−	0.505627i
$7$	1.22822	−	0.709111i	0.464222	−	0.268019i	−0.249596	−	0.968350i	$-0.580298\pi$
$7$	1.22822	−	0.709111i	0.464222	−	0.268019i	0.713818	+	0.700331i	$0.246964\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−1.08961	−	2.79513i	−0.363203	−	0.931710i
$10$	−1.00313	+	1.99843i	−0.317216	+	0.631960i
$11$	−4.15895	−	2.40117i	−1.25397	−	0.723980i	−0.282075	−	0.959392i	$-0.591023\pi$
$11$	−4.15895	−	2.40117i	−1.25397	−	0.723980i	−0.971896	+	0.235413i	$0.924356\pi$
$12$	−1.40748	+	1.00946i	−0.406304	+	0.291406i
$13$	−4.38640	+	3.68062i	−1.21657	+	1.02082i	−0.217570	+	0.976045i	$0.569813\pi$
$13$	−4.38640	+	3.68062i	−1.21657	+	1.02082i	−0.998997	+	0.0447764i	$0.985742\pi$
$14$	−1.33269	+	0.485061i	−0.356177	+	0.129638i
$15$	2.43703	+	3.01013i	0.629237	+	0.777213i
$16$	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
$21$	−0.186381	+	2.44935i	−0.0406716	+	0.534493i
$22$	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	$0.777148\pi$
$24$	1.56139	−	0.749717i	0.318716	−	0.153035i
$25$	−4.17859	−	2.74579i	−0.835718	−	0.549159i
$26$	4.95889	−	2.86302i	0.972518	−	0.561484i
$27$	5.06186	+	1.17369i	0.974156	+	0.225876i
$28$	1.39668	−	0.246272i	0.263947	−	0.0465410i
$29$	0.843948	+	4.78627i	0.156717	+	0.888787i	0.957199	+	0.289430i	$0.0934659\pi$
$29$	0.843948	+	4.78627i	0.156717	+	0.888787i	−0.800482	+	0.599357i	$0.795423\pi$
$30$	−1.87730	−	3.38759i	−0.342746	−	0.618486i
$31$	−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
$33$	7.49830	−	3.60040i	1.30529	−	0.626749i
$34$	1.71169	−	4.70282i	0.293552	−	0.806527i
$35$	−0.731986	−	3.08561i	−0.123728	−	0.521563i
$36$	−0.0679076	−	2.99923i	−0.0113179	−	0.499872i
$37$	−6.32334			−1.03955			−0.519775	−	0.854303i	$-0.673984\pi$
$37$	−6.32334			−1.03955			−0.519775	+	0.854303i	$0.673984\pi$
$38$	−4.19241	+	1.19320i	−0.680098	+	0.193563i
$39$	−0.976165	−	9.86962i	−0.156311	−	1.58040i
$40$	−1.62614	+	1.53482i	−0.257115	+	0.242677i
$41$	−3.61797	−	3.03584i	−0.565032	−	0.474118i	0.314961	−	0.949105i	$-0.398008\pi$
$41$	−3.61797	−	3.03584i	−0.565032	−	0.474118i	−0.879993	+	0.474987i	$0.842453\pi$
$42$	0.608875	−	2.37978i	0.0939514	−	0.367208i
$43$	−3.09131	−	8.49330i	−0.471420	−	1.29522i	−0.916611	−	0.399781i	$-0.869086\pi$
$43$	−3.09131	−	8.49330i	−0.471420	−	1.29522i	0.445190	−	0.895436i	$-0.353136\pi$
$44$	−3.08688	−	3.67881i	−0.465365	−	0.554601i
$45$	−6.68620	+	0.542938i	−0.996719	+	0.0809364i
$46$	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	$0.970572\pi$
$48$	−1.66785	+	0.467196i	−0.240734	+	0.0674339i
$49$	−2.49432	+	4.32029i	−0.356332	+	0.617185i
$50$	3.63831	+	3.42968i	0.514534	+	0.485030i
$51$	−6.19839	−	6.05964i	−0.867948	−	0.848519i
$52$	−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	$0.114956\pi$
$54$	−4.78115	−	2.03484i	−0.650632	−	0.276907i
$55$	−7.80925	+	7.37075i	−1.05300	+	0.993871i
$56$	−1.41822			−0.189518
$57$	−1.11132	+	7.46759i	−0.147198	+	0.989107i
$58$		−	4.86010i		−	0.638163i
$59$	0.697387	−	3.95508i	0.0907921	−	0.514907i	−0.905164	−	0.425063i	$-0.860252\pi$
$59$	0.697387	−	3.95508i	0.0907921	−	0.514907i	0.995956	−	0.0898444i	$-0.0286370\pi$
$60$	1.26053	+	3.66211i	0.162733	+	0.472777i
$61$	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
$63$	−3.32034	−	2.66037i	−0.418323	−	0.335175i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	5.07379	+	11.7556i	0.629326	+	1.45810i
$66$	−8.00959	+	2.24363i	−0.985912	+	0.276172i
$67$	−2.07512	−	11.7686i	−0.253516	−	1.43776i	−0.799852	−	0.600197i	$-0.795089\pi$
$67$	−2.07512	−	11.7686i	−0.253516	−	1.43776i	0.546336	−	0.837566i	$-0.316022\pi$
$68$	−2.50232	+	4.33414i	−0.303451	+	0.525592i
$69$	6.72688	−	4.82460i	0.809821	−	0.580813i
$70$	0.185055	+	3.16584i	0.0221183	+	0.378390i
$71$	11.1500	−	4.05828i	1.32327	−	0.481630i	0.418763	−	0.908096i	$-0.362464\pi$
$71$	11.1500	−	4.05828i	1.32327	−	0.481630i	0.904504	+	0.426466i	$0.140242\pi$
$72$	−0.453935	+	2.96546i	−0.0534968	+	0.349483i
$73$	0.496670	−	0.591909i	0.0581309	−	0.0692777i	−0.736195	−	0.676769i	$-0.763380\pi$
$73$	0.496670	−	0.591909i	0.0581309	−	0.0692777i	0.794326	+	0.607491i	$0.207824\pi$
$74$	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
$78$	−0.752507	+	9.88919i	−0.0852047	+	1.11973i
$79$	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	$0.0212752\pi$
$80$	1.86795	−	1.22913i	0.208843	−	0.137421i
$81$	−6.62550	+	6.09120i	−0.736167	+	0.676800i
$82$	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	$0.870626\pi$
$84$	−1.01287	+	2.23789i	−0.110513	+	0.244174i
$85$	10.0014	+	5.02029i	1.08481	+	0.544526i
$86$	1.56950	+	8.90107i	0.169243	+	0.959827i
$87$	−7.66903	−	3.47100i	−0.822206	−	0.372130i
$88$	2.40117	+	4.15895i	0.255966	+	0.443345i
$89$	−0.424481	+	0.356182i	−0.0449949	+	0.0377552i	−0.665008	−	0.746836i	$-0.731572\pi$
$89$	−0.424481	+	0.356182i	−0.0449949	+	0.0377552i	0.620013	+	0.784592i	$0.287127\pi$
$90$	6.67890	+	0.626356i	0.704018	+	0.0660237i
$91$	−2.77747	+	7.63105i	−0.291158	+	0.799951i
$92$	−3.66122	−	3.07213i	−0.381709	−	0.320292i
$93$	1.27223	−	16.7192i	0.131924	−	1.73371i
$94$			1.12420i			0.115952i
$95$	−1.56374	−	9.62054i	−0.160436	−	0.987046i
$96$	1.72364	−	0.170478i	0.175918	−	0.0173994i
$97$	−3.40129	+	19.2897i	−0.345349	+	1.95857i	−0.0685236	+	0.997649i	$0.521829\pi$
$97$	−3.40129	+	19.2897i	−0.345349	+	1.95857i	−0.276825	+	0.960920i	$0.589282\pi$
$98$	3.20664	−	3.82152i	0.323919	−	0.386032i
$99$	−2.17995	+	14.2411i	−0.219093	+	1.43129i
$100$	−2.98747	−	4.00936i	−0.298747	−	0.400936i
$101$	4.90930	+	5.85068i	0.488494	+	0.582164i	0.952834	−	0.303493i	$-0.0981529\pi$
$101$	4.90930	+	5.85068i	0.488494	+	0.582164i	−0.464340	+	0.885657i	$0.653708\pi$
$102$	5.05198	+	7.04391i	0.500220	+	0.697452i
$103$	−7.05809	+	12.2250i	−0.695454	+	1.20456i	0.274573	+	0.961566i	$0.411463\pi$
$103$	−7.05809	+	12.2250i	−0.695454	+	1.20456i	−0.970027	+	0.242996i	$0.921870\pi$
$104$	5.63904	−	0.994315i	0.552953	−	0.0975006i
$105$	5.12772	+	1.96898i	0.500414	+	0.192152i
$106$	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	$0.383681\pi$
$108$	4.35517	+	2.83417i	0.419076	+	0.272718i
$109$	−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	$-0.389365\pi$
$110$	8.97053	−	5.90270i	0.855306	−	0.562801i
$111$	6.18006	−	9.04217i	0.586585	−	0.858245i
$112$	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	$-0.0942519\pi$
$114$	2.39117	−	7.16117i	0.223954	−	0.670705i
$115$	−6.38006	+	8.57366i	−0.594944	+	0.799498i
$116$	−0.843948	+	4.78627i	−0.0783586	+	0.444394i
$117$	15.0673	+	8.25010i	1.39297	+	0.762722i
$118$	−1.37358	+	3.77389i	−0.126449	+	0.347415i
$119$	2.42755	+	6.66965i	0.222533	+	0.611406i
$120$	−0.605459	−	3.82537i	−0.0552706	−	0.349206i
$121$	6.03123	+	10.4464i	0.548294	+	0.949673i
$122$	−0.616465	−	0.355916i	−0.0558121	−	0.0322231i
$123$	7.87713	−	2.20653i	0.710257	−	0.198956i
$124$	−9.53370	+	1.68105i	−0.856151	+	0.150963i
$125$	−8.56012	+	7.19197i	−0.765640	+	0.643269i
$126$	2.80792	+	3.19652i	0.250150	+	0.284769i
$127$	3.40159	−	2.85428i	0.301843	−	0.253276i	−0.479268	−	0.877669i	$-0.659098\pi$
$127$	3.40159	−	2.85428i	0.301843	−	0.253276i	0.781111	+	0.624393i	$0.214653\pi$
$128$	−0.342020	−	0.939693i	−0.0302306	−	0.0830579i
$129$	15.1664	+	3.88038i	1.33533	+	0.341649i
$130$	−2.95537	−	12.4581i	−0.259203	−	1.09264i
$131$	−8.85370	−	1.56115i	−0.773551	−	0.136398i	−0.227080	−	0.973876i	$-0.572918\pi$
$131$	−8.85370	−	1.56115i	−0.773551	−	0.136398i	−0.546471	+	0.837478i	$0.684029\pi$
$132$	8.27751	−	0.818695i	0.720465	−	0.0712583i
$133$	3.46698	−	5.11818i	0.300625	−	0.443803i
$134$			11.9501i			1.03234i
$135$	5.75831	−	10.0917i	0.495596	−	0.868553i
$136$	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	$0.547509\pi$
$138$	−7.46247	+	3.58319i	−0.635247	+	0.305021i
$139$	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	$0.243628\pi$
$140$	0.367498	−	3.14988i	0.0310593	−	0.266213i
$141$	1.77393	+	0.802882i	0.149392	+	0.0676148i
$142$	−11.6854	+	2.06044i	−0.980614	+	0.172909i
$143$	27.0806	−	4.77504i	2.26459	−	0.399309i
$144$	0.961985	−	2.84158i	0.0801654	−	0.236798i
$145$	10.7943	+	1.25938i	0.896418	+	0.104586i
$146$	−0.591909	+	0.496670i	−0.0489867	+	0.0411047i
$147$	−3.74007	−	7.78920i	−0.308476	−	0.642442i
$148$	−5.94200	−	2.16271i	−0.488429	−	0.177774i
$149$	7.24242	−	8.63118i	0.593322	−	0.707094i	−0.382919	−	0.923782i	$-0.625081\pi$
$149$	7.24242	−	8.63118i	0.593322	−	0.707094i	0.976241	+	0.216688i	$0.0695255\pi$
$150$	−8.46020	+	1.85069i	−0.690772	+	0.151108i
$151$			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
$155$	4.99652	+	21.0623i	0.401330	+	1.69177i
$156$	2.45831	−	9.60828i	0.196823	−	0.769278i
$157$	−5.00142	−	13.7413i	−0.399157	−	1.09667i	−0.962696	−	0.270585i	$-0.912783\pi$
$157$	−5.00142	−	13.7413i	−0.399157	−	1.09667i	0.563539	−	0.826089i	$-0.309439\pi$
$158$	−8.03691	+	6.74377i	−0.639382	+	0.536505i
$159$	−0.177538	−	0.247540i	−0.0140797	−	0.0196312i
$160$	−2.05301	+	0.886092i	−0.162305	+	0.0700517i
$161$	−6.67526	+	1.17703i	−0.526084	+	0.0927628i
$162$	7.58257	−	4.84816i	0.595743	−	0.380907i
$163$	−1.16357	−	0.671789i	−0.0911381	−	0.0526186i	0.453738	−	0.891135i	$-0.350090\pi$
$163$	−1.16357	−	0.671789i	−0.0911381	−	0.0526186i	−0.544876	+	0.838516i	$0.683423\pi$
$164$	−2.36146	−	4.09017i	−0.184399	−	0.319389i
$165$	−2.90762	−	18.3707i	−0.226358	−	1.43016i
$166$	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	$0.0878296\pi$
$168$	1.38609	−	2.02801i	0.106939	−	0.156464i
$169$	3.43605	−	19.4868i	0.264312	−	1.49899i
$170$	−8.97773	−	6.68075i	−0.688560	−	0.512390i
$171$	−9.59227	−	8.88754i	−0.733539	−	0.679647i
$172$		−	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	$0.505476\pi$
$174$	6.94978	+	4.74998i	0.526862	+	0.360095i
$175$	−7.07929	−	0.409344i	−0.535144	−	0.0309435i
$176$	−1.64250	−	4.51272i	−0.123808	−	0.340159i
$177$	4.97405	+	4.86270i	0.373872	+	0.365503i
$178$	0.479883	−	0.277060i	0.0359687	−	0.0207666i
$179$	−6.18641	+	10.7152i	−0.462394	+	0.800890i	−0.999080	−	0.0428923i	$-0.986343\pi$
$179$	−6.18641	+	10.7152i	−0.462394	+	0.800890i	0.536686	+	0.843782i	$0.319676\pi$
$180$	−6.46866	−	1.77662i	−0.482146	−	0.132421i
$181$	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
$183$	−1.00189	+	0.718565i	−0.0740617	+	0.0531179i
$184$	3.07213	+	3.66122i	0.226481	+	0.269909i
$185$	−4.05239	+	13.5463i	−0.297938	+	0.995941i
$186$	−4.15617	+	16.2443i	−0.304745	+	1.19109i
$187$	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
$190$	−0.130604	+	9.74592i	−0.00947502	+	0.707043i
$191$			22.4414i			1.62380i	0.583795	+	0.811901i	$0.301567\pi$
$191$			22.4414i			1.62380i	−0.583795	+	0.811901i	$0.698433\pi$
$192$	−1.72706	−	0.131419i	−0.124640	−	0.00948432i
$193$	7.75600	+	6.50806i	0.558289	+	0.468460i	0.877736	−	0.479144i	$-0.159053\pi$
$193$	7.75600	+	6.50806i	0.558289	+	0.468460i	−0.319447	+	0.947604i	$0.603497\pi$
$194$	6.69923	−	18.4060i	0.480977	−	1.32147i
$195$	−21.7689	−	4.23387i	−1.55891	−	0.303194i
$196$	−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	$0.842295\pi$
$198$	4.61978	−	13.6462i	0.328313	−	0.969796i
$199$	−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	$-0.226485\pi$
$200$	2.24587	+	4.46722i	0.158807	+	0.315880i
$201$	18.8568	+	8.53458i	1.33006	+	0.601983i
$202$	−3.81876	−	6.61428i	−0.268687	−	0.465379i
$203$	4.43055	+	5.28012i	0.310963	+	0.370592i
$204$	−3.75206	−	7.81417i	−0.262697	−	0.547101i
$205$	−8.82218	+	5.80509i	−0.616168	+	0.405445i
$206$	9.07370	−	10.8136i	0.632195	−	0.753420i
$207$	0.324557	+	14.3345i	0.0225583	+	0.996316i
$208$	−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
$213$	−5.09418	+	19.9105i	−0.349048	+	1.36425i
$214$	3.06213	−	1.11452i	0.209323	−	0.0761872i
$215$	−20.1760	+	1.17936i	−1.37599	+	0.0804318i
$216$	−3.79686	−	3.54738i	−0.258343	−	0.241368i
$217$	−6.86474	+	11.8901i	−0.466009	+	0.807151i
$218$	2.78107	+	15.7722i	0.188358	+	1.06823i
$219$	0.360994	+	1.28872i	0.0243937	+	0.0870836i
$220$	−9.85924	+	4.25531i	−0.664710	+	0.286893i
$221$	−14.3284	−	24.8174i	−0.963830	−	1.66940i
$222$	−7.65633	+	7.83164i	−0.513859	+	0.525625i
$223$	18.9999	−	6.91541i	1.27233	−	0.463090i	0.384442	−	0.923149i	$-0.374394\pi$
$223$	18.9999	−	6.91541i	1.27233	−	0.463090i	0.887888	+	0.460059i	$0.152172\pi$
$224$	−1.33269	−	0.485061i	−0.0890443	−	0.0324095i
$225$	−3.12182	+	14.6715i	−0.208121	+	0.978103i
$226$	−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	$-0.344794\pi$
$228$	−3.59837	+	6.63715i	−0.238308	+	0.439556i
$229$	20.0431			1.32448			0.662241	−	0.749291i	$-0.269605\pi$
$229$	20.0431			1.32448			0.662241	+	0.749291i	$0.269605\pi$
$230$	7.77193	−	7.33552i	0.512466	−	0.483690i
$231$	6.65646	−	9.73920i	0.437963	−	0.640792i
$232$	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	$0.414935\pi$
$234$	−13.4058	−	10.7412i	−0.876362	−	0.702172i
$235$	−2.49685	−	0.291309i	−0.162876	−	0.0190029i
$236$	2.00805	−	3.47804i	0.130713	−	0.226401i
$237$	4.90155	+	17.4982i	0.318390	+	1.13663i
$238$	−1.23250	−	6.98986i	−0.0798912	−	0.453085i
$239$	−12.5280	−	7.23302i	−0.810367	−	0.467865i	0.0367166	−	0.999326i	$-0.488310\pi$
$239$	−12.5280	−	7.23302i	−0.810367	−	0.467865i	−0.847083	+	0.531460i	$0.821643\pi$
$240$	−0.0680073	+	3.87239i	−0.00438985	+	0.249961i
$241$	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
$243$	−2.23484	−	15.4274i	−0.143365	−	0.989670i
$244$	0.545295	+	0.457557i	0.0349089	+	0.0292921i
$245$	7.65669	+	8.11221i	0.489168	+	0.518270i
$246$	−8.14062	+	0.805156i	−0.519027	+	0.0513349i
$247$	−10.1968	+	22.7813i	−0.648808	+	1.44954i
$248$	9.68077			0.614729
$249$	3.67833	+	0.279898i	0.233104	+	0.0177378i
$250$	9.67894	−	5.59626i	0.612150	−	0.353938i
$251$	−8.28066	+	22.7509i	−0.522670	+	1.43602i	0.344866	+	0.938652i	$0.387924\pi$
$251$	−8.28066	+	22.7509i	−0.522670	+	1.43602i	−0.867537	+	0.497373i	$0.834298\pi$
$252$	−2.21019	−	3.63555i	−0.139229	−	0.229018i
$253$	14.7534	+	17.5824i	0.927540	+	1.10540i
$254$	−3.84556	+	2.22023i	−0.241292	+	0.139310i
$255$	−16.9537	+	9.39519i	−1.06168	+	0.588350i
$256$	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	$0.701691\pi$
$258$	−14.2622	−	6.45505i	−0.887924	−	0.401874i
$259$	−7.76643	+	4.48395i	−0.482583	+	0.278619i
$260$	0.747154	+	12.7820i	0.0463365	+	0.792705i
$261$	12.4587	−	7.57411i	0.771172	−	0.468825i
$262$	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	$0.766496\pi$
$264$	−8.29392	−	0.631117i	−0.510455	−	0.0388426i
$265$	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	0.568906	−	0.822403i	$-0.307367\pi$
$269$	−2.33247	−	1.95718i	−0.142213	−	0.119331i	−0.711119	+	0.703072i	$0.751811\pi$
$270$	−7.42323	+	8.93844i	−0.451763	+	0.543976i
$271$	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
$273$	−8.19760	−	11.4298i	−0.496141	−	0.691765i
$274$	−4.02390	−	2.32320i	−0.243093	−	0.140350i
$275$	10.7854	+	21.4531i	0.650386	+	1.29367i
$276$	7.97131	−	2.23291i	0.479816	−	0.134405i
$277$	3.83354	+	2.21329i	0.230335	+	0.132984i	0.610727	−	0.791842i	$-0.290877\pi$
$277$	3.83354	+	2.21329i	0.230335	+	0.132984i	−0.380392	+	0.924825i	$0.624211\pi$
$278$	−2.18662	+	1.26244i	−0.131145	+	0.0757164i
$279$	22.6646	+	18.1597i	1.35689	+	1.08719i
$280$	−0.908886	+	3.03821i	−0.0543163	+	0.181568i
$281$	−28.9911	−	10.5519i	−1.72946	−	0.629472i	−0.730869	−	0.682518i	$-0.760885\pi$
$281$	−28.9911	−	10.5519i	−1.72946	−	0.629472i	−0.998592	+	0.0530452i	$0.983107\pi$
$282$	−1.60757	−	1.09872i	−0.0957292	−	0.0654281i
$283$	−11.7937	−	2.07954i	−0.701060	−	0.123616i	−0.188254	−	0.982120i	$-0.560283\pi$
$283$	−11.7937	−	2.07954i	−0.701060	−	0.123616i	−0.512806	+	0.858505i	$0.671394\pi$
$284$	11.8656			0.704095
$285$	15.2854	+	7.16644i	0.905426	+	0.424504i
$286$	−27.4984			−1.62601
$287$	−6.59639	−	1.16312i	−0.389373	−	0.0686569i
$288$	−1.44081	+	2.63136i	−0.0849003	+	0.155055i
$289$	−7.56114	−	2.75203i	−0.444773	−	0.161884i
$290$	−10.4116	−	3.11466i	−0.611391	−	0.182899i
$291$	−24.2594	−	23.7163i	−1.42211	−	1.39028i
$292$	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	$0.677473\pi$
$294$	2.33067	+	8.32032i	0.135928	+	0.485251i
$295$	−8.02589	−	4.02865i	−0.467286	−	0.234557i
$296$	5.47617	+	3.16167i	0.318296	+	0.183768i
$297$	−18.2338	−	17.0357i	−1.05803	−	0.988512i
$298$	−8.63118	+	7.24242i	−0.499991	+	0.419542i
$299$	25.7165	−	9.36004i	1.48722	−	0.541305i
$300$	8.65304	−	0.353474i	0.499583	−	0.0204078i
$301$	−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
$306$	−15.0101	+	0.339853i	−0.858068	+	0.0194281i
$307$	6.69443	+	5.61729i	0.382071	+	0.320596i	0.813515	−	0.581544i	$-0.197551\pi$
$307$	6.69443	+	5.61729i	0.382071	+	0.320596i	−0.431444	+	0.902140i	$0.641996\pi$
$308$	−6.40005	−	2.32943i	−0.364676	−	0.132731i
$309$	−10.5831	−	22.0408i	−0.602054	−	1.25386i
$310$	−1.26318	−	21.6100i	−0.0717439	−	1.22736i
$311$	15.1358	−	8.73866i	0.858273	−	0.495524i	−0.00516087	−	0.999987i	$-0.501643\pi$
$311$	15.1358	−	8.73866i	0.858273	−	0.495524i	0.863433	+	0.504463i	$0.168309\pi$
$312$	−4.08943	+	9.03543i	−0.231518	+	0.511530i
$313$	−10.9107	+	1.92385i	−0.616709	+	0.108742i	−0.473271	−	0.880917i	$-0.656927\pi$
$313$	−10.9107	+	1.92385i	−0.616709	+	0.108742i	−0.143438	+	0.989659i	$0.545816\pi$
$314$	2.53929	+	14.4010i	0.143300	+	0.812696i
$315$	−7.82709	+	5.40810i	−0.441007	+	0.304712i
$316$	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	$0.867625\pi$
$318$	0.131856	+	0.274608i	0.00739414	+	0.0153993i
$319$	7.98270	−	21.9323i	0.446946	−	1.22797i
$320$	2.17569	−	0.516129i	0.121625	−	0.0288525i
$321$	0.428247	−	5.62787i	0.0239024	−	0.314117i
$322$	6.77824			0.377736
$323$	5.97154	+	20.9815i	0.332265	+	1.16744i
$324$	−8.30925	+	3.45780i	−0.461625	+	0.192100i
$325$	28.4352	−	3.33568i	1.57730	−	0.185030i
$326$	1.02924	+	0.863636i	0.0570044	+	0.0478324i
$327$	26.8740	+	6.87582i	1.48614	+	0.380234i
$328$	1.61533	+	4.43810i	0.0891919	+	0.245053i
$329$	−1.02484	−	1.22135i	−0.0565011	−	0.0673354i
$330$	−0.326594	+	18.5965i	−0.0179784	+	1.02370i
$331$	−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
$333$	6.88998	+	17.6746i	0.377568	+	0.968560i
$334$	−0.944346	+	1.63566i	−0.0516723	+	0.0894991i
$335$	−26.5413	−	3.09659i	−1.45011	−	0.169185i
$336$	−1.71719	+	1.75651i	−0.0936804	+	0.0958255i
$337$	13.7974	−	5.02183i	0.751590	−	0.273557i	0.0623155	−	0.998056i	$-0.480151\pi$
$337$	13.7974	−	5.02183i	0.751590	−	0.273557i	0.689275	+	0.724500i	$0.257929\pi$
$338$	−6.76771	+	18.5941i	−0.368115	+	1.01139i
$339$	8.87096	+	6.06304i	0.481804	+	0.329299i
$340$	7.68124	+	8.13822i	0.416574	+	0.441357i
$341$	46.4903			2.51759
$342$	7.90324	+	10.4182i	0.427358	+	0.563352i
$343$			17.0026i			0.918052i
$344$	−1.56950	+	8.90107i	−0.0846217	+	0.479914i
$345$	−6.02455	−	17.5027i	−0.324351	−	0.942311i
$346$	−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	$0.273857\pi$
$348$	−6.01938	−	5.88463i	−0.322672	−	0.315449i
$349$	−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	$0.835734\pi$
$350$	6.90066	+	1.63243i	0.368856	+	0.0872571i
$351$	−26.5232	+	13.4825i	−1.41571	+	0.719645i
$352$	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	$0.130591\pi$
$354$	−4.05408	−	5.65256i	−0.215472	−	0.300430i
$355$	−1.54827	−	26.4871i	−0.0821737	−	1.40579i
$356$	−0.520703	+	0.189521i	−0.0275972	+	0.0100446i
$357$	−11.9099	−	3.04720i	−0.630340	−	0.161275i
$358$	7.95310	−	9.47813i	0.420334	−	0.500935i
$359$	4.39502	+	0.774960i	0.231960	+	0.0409008i	0.288420	−	0.957504i	$-0.406870\pi$
$359$	4.39502	+	0.774960i	0.231960	+	0.0409008i	−0.0564597	+	0.998405i	$0.517981\pi$
$360$	6.06188	+	2.87290i	0.319489	+	0.151415i
$361$	11.7566	−	14.9259i	0.618768	−	0.785574i
$362$	−9.08379			−0.477433
$363$	−20.8326	−	1.58523i	−1.09343	−	0.0832031i
$364$	−5.21994	+	6.22088i	−0.273599	+	0.326063i
$365$	−0.949728	−	1.44333i	−0.0497110	−	0.0755474i
$366$	1.11144	−	0.533673i	0.0580961	−	0.0278955i
$367$	−3.08143	−	3.67231i	−0.160850	−	0.191693i	0.679600	−	0.733583i	$-0.262153\pi$
$367$	−3.08143	−	3.67231i	−0.160850	−	0.191693i	−0.840449	+	0.541890i	$0.817709\pi$
$368$	−2.38969	−	4.13907i	−0.124571	−	0.215764i
$369$	−4.54338	+	13.4206i	−0.236519	+	0.698647i
$370$	6.34311	−	12.6368i	0.329763	−	0.656955i
$371$	0.0433130	+	0.245640i	0.00224870	+	0.0127530i
$372$	6.91383	−	15.2758i	0.358465	−	0.792015i
$373$	−7.49476	−	12.9813i	−0.388064	−	0.672147i	0.604125	−	0.796890i	$-0.293523\pi$
$373$	−7.49476	−	12.9813i	−0.388064	−	0.672147i	−0.992189	+	0.124743i	$0.960189\pi$
$374$	−18.4111	+	15.4487i	−0.952015	+	0.798835i
$375$	−1.91812	−	19.2697i	−0.0990515	−	0.995082i
$376$	−0.384498	+	1.05640i	−0.0198290	+	0.0544797i
$377$	−21.3183	−	17.8882i	−1.09795	−	0.921289i
$378$	−7.31522	+	0.891144i	−0.376254	+	0.0458355i
$379$			16.5268i			0.848924i	0.905446	+	0.424462i	$0.139537\pi$
$379$			16.5268i			0.848924i	−0.905446	+	0.424462i	$0.860463\pi$
$380$	1.82098	−	9.57518i	0.0934144	−	0.491196i
$381$	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	$0.163419\pi$
$384$	1.67800	+	0.429323i	0.0856301	+	0.0219088i
$385$	−4.36478	+	14.5905i	−0.222450	+	0.743601i
$386$	−6.50806	−	7.75600i	−0.331251	−	0.394770i
$387$	−20.3716	+	17.8950i	−1.03554	+	0.909654i
$388$	−9.79363	+	16.9631i	−0.497196	+	0.861169i
$389$	−25.3831	+	4.47573i	−1.28697	+	0.226928i	−0.774939	−	0.632036i	$-0.782219\pi$
$389$	−25.3831	+	4.47573i	−1.28697	+	0.226928i	−0.512036	+	0.858964i	$0.671108\pi$
$390$	20.7030	+	7.94968i	1.04834	+	0.402548i
$391$	11.9596	−	20.7146i	0.604821	−	1.04758i
$392$	4.32029	−	2.49432i	0.218208	−	0.125982i
$393$	10.8855	−	11.1347i	0.549099	−	0.561672i
$394$	0.270268	+	0.742556i	0.0136159	+	0.0374094i
$395$	−12.8954	−	19.5975i	−0.648836	−	0.986056i
$396$	−6.91924	+	12.6367i	−0.347705	+	0.635018i
$397$	28.0894	+	4.95291i	1.40976	+	0.248580i	0.826150	−	0.563451i	$-0.190527\pi$
$397$	28.0894	+	4.95291i	1.40976	+	0.248580i	0.583615	+	0.812030i	$0.301638\pi$
$398$			14.4327i			0.723446i
$399$	3.93041	+	9.95987i	0.196767	+	0.498617i
$400$	−1.43602	−	4.78935i	−0.0718012	−	0.239467i
$401$	0.583919	−	3.31157i	0.0291595	−	0.165372i	−0.966751	−	0.255721i	$-0.917687\pi$
$401$	0.583919	−	3.31157i	0.0291595	−	0.165372i	0.995910	+	0.0903491i	$0.0287983\pi$
$402$	−17.0883	−	11.6794i	−0.852288	−	0.582514i
$403$	18.9590	−	52.0894i	0.944415	−	2.59476i
$404$	2.61218	+	7.17692i	0.129961	+	0.357065i
$405$	8.80293	+	18.0972i	0.437421	+	0.899257i
$406$	−3.44635	−	5.96926i	−0.171040	−	0.296249i
$407$	26.2984	+	15.1834i	1.30357	+	0.752614i
$408$	2.33814	+	8.34699i	0.115755	+	0.413238i
$409$	−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	$0.789964\pi$
$410$	9.69620	−	4.18494i	0.478861	−	0.206680i
$411$	−6.53971	+	4.69035i	−0.322580	+	0.231358i
$412$	−10.8136	+	9.07370i	−0.532749	+	0.447029i
$413$	−1.94805	−	5.35222i	−0.0958572	−	0.263366i
$414$	2.16953	−	14.1731i	0.106627	−	0.696569i
$415$	−4.63383	+	1.09926i	−0.227466	+	0.0539607i
$416$	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	$-0.993844\pi$
$419$		−	0.791705i		−	0.0386773i	0.999813	−	0.0193387i	$-0.00615607\pi$
$420$	4.14505	+	3.60401i	0.202258	+	0.175858i
$421$	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
$423$	−2.88183	+	1.75198i	−0.140120	+	0.0851841i
$424$	0.134728	−	0.113050i	0.00654297	−	0.00549020i
$425$	17.1643	−	18.2084i	0.832592	−	0.883237i
$426$	8.47421	−	18.7234i	0.410577	−	0.907153i
$427$	0.994199	−	0.175304i	0.0481127	−	0.00848356i
$428$	−3.20914	+	0.565858i	−0.155120	+	0.0273518i
$429$	−19.6388	+	43.3912i	−0.948171	+	2.09495i
$430$	20.0743	+	2.34208i	0.968068	+	0.112945i
$431$	7.47680	−	6.27378i	0.360145	−	0.302197i	−0.444704	−	0.895678i	$-0.646691\pi$
$431$	7.47680	−	6.27378i	0.360145	−	0.302197i	0.804848	+	0.593480i	$0.202247\pi$
$432$	3.12318	+	4.15280i	0.150264	+	0.199802i
$433$	17.3942	+	6.33098i	0.835913	+	0.304247i	0.724283	−	0.689503i	$-0.242171\pi$
$433$	17.3942	+	6.33098i	0.835913	+	0.304247i	0.111629	+	0.993750i	$0.464393\pi$
$434$	8.82514	−	10.5174i	0.423620	−	0.504851i
$435$	−12.3506	+	14.2046i	−0.592165	+	0.681061i
$436$		−	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	$0.691065\pi$
$440$	10.4484	−	2.47863i	0.498107	−	0.118164i
$441$	14.7936	+	2.26452i	0.704458	+	0.107834i
$442$	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	$0.221365\pi$
$444$	8.89996	−	6.38315i	0.422373	−	0.302931i
$445$	0.491002	+	1.13761i	0.0232757	+	0.0539281i
$446$	−19.9121	+	3.51105i	−0.942867	+	0.166253i
$447$	5.26399	+	18.7920i	0.248978	+	0.888832i
$448$	1.22822	+	0.709111i	0.0580278	+	0.0335024i
$449$	−3.42022	−	5.92399i	−0.161410	−	0.279570i	0.773965	−	0.633229i	$-0.218271\pi$
$449$	−3.42022	−	5.92399i	−0.161410	−	0.279570i	−0.935375	+	0.353658i	$0.884938\pi$
$450$	5.62208	−	13.9066i	0.265027	−	0.655561i
$451$	7.75739	+	21.3132i	0.365281	+	1.00360i
$452$	2.12176	−	5.82949i	0.0997992	−	0.274196i
$453$	−28.0414	−	19.1655i	−1.31750	−	0.900474i
$454$	−4.62276	+	26.2170i	−0.216957	+	1.23042i
$455$	14.5677	+	10.8405i	0.682946	+	0.508212i
$456$	4.69623	−	5.91147i	0.219921	−	0.276830i
$457$		−	1.24574i		−	0.0582734i	−0.999575	−	0.0291367i	$-0.990724\pi$
$457$		−	1.24574i		−	0.0582734i	0.999575	−	0.0291367i	$-0.00927581\pi$
$458$	−19.7386	−	3.48044i	−0.922322	−	0.162630i
$459$	−10.1836	+	23.9279i	−0.475332	+	1.11686i
$460$	−8.92766	+	5.87449i	−0.416254	+	0.273900i
$461$	4.17855	+	11.4805i	0.194614	+	0.534699i	0.998166	−	0.0605363i	$-0.0192811\pi$
$461$	4.17855	+	11.4805i	0.194614	+	0.534699i	−0.803552	+	0.595235i	$0.797059\pi$
$462$	−8.24653	+	8.43536i	−0.383663	+	0.392448i
$463$	5.36979	−	3.10025i	0.249555	−	0.144081i	−0.370005	−	0.929030i	$-0.620644\pi$
$463$	5.36979	−	3.10025i	0.249555	−	0.144081i	0.619561	+	0.784949i	$0.287311\pi$
$464$	−2.43005	+	4.20897i	−0.112812	+	0.195397i
$465$	−35.0017	−	13.4402i	−1.62317	−	0.623274i
$466$	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	$-0.0933933\pi$
$468$	11.3369	+	12.9059i	0.524049	+	0.596574i
$469$	−10.8939	−	12.9829i	−0.503036	−	0.599494i
$470$	2.40833	+	0.720456i	0.111088	+	0.0332322i
$471$	24.5377	+	6.27806i	1.13064	+	0.289278i
$472$	−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
$475$	−21.6119	−	2.81549i	−0.991621	−	0.129184i
$476$			7.09769i			0.325322i
$477$	0.527489	−	0.0119432i	0.0241521	−	0.000546844i
$478$	11.0816	+	9.29859i	0.506862	+	0.425308i
$479$	−1.99506	+	5.48139i	−0.0911568	+	0.250451i	−0.976890	−	0.213744i	$-0.931434\pi$
$479$	−1.99506	+	5.48139i	−0.0911568	+	0.250451i	0.885733	+	0.464195i	$0.153656\pi$
$480$	0.739407	−	3.80175i	0.0337492	−	0.173525i
$481$	27.7367	−	23.2738i	1.26468	−	1.06120i
$482$	−7.00029	−	12.1249i	−0.318855	−	0.552272i
$483$	4.84089	−	10.6958i	0.220268	−	0.486674i
$484$	2.09463	+	11.8792i	0.0952102	+	0.539964i
$485$	39.1438	+	19.6485i	1.77743	+	0.892192i
$486$	−0.478053	+	15.5811i	−0.0216849	+	0.706774i
$487$	2.75503	+	4.77186i	0.124842	+	0.216234i	0.921671	−	0.387972i	$-0.126824\pi$
$487$	2.75503	+	4.77186i	0.124842	+	0.216234i	−0.796829	+	0.604205i	$0.793491\pi$
$488$	−0.457557	−	0.545295i	−0.0207126	−	0.0246844i
$489$	2.09784	−	1.00730i	0.0948678	−	0.0455519i
$490$	−6.13170	−	9.31854i	−0.277002	−	0.420969i
$491$	11.0236	−	13.1374i	0.497489	−	0.592885i	−0.457617	−	0.889150i	$-0.651297\pi$
$491$	11.0236	−	13.1374i	0.497489	−	0.592885i	0.955106	+	0.296265i	$0.0957412\pi$
$492$	8.15676	+	0.620680i	0.367735	+	0.0279824i
$493$	−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
$498$	−3.57384	−	0.914381i	−0.160148	−	0.0409744i
$499$	−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	$0.589692\pi$
$500$	−10.5037	+	3.83051i	−0.469739	+	0.171305i
$501$	1.90656	+	2.65829i	0.0851787	+	0.118764i
$502$	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	$-0.354658\pi$
$504$	1.54531	+	3.96412i	0.0688335	+	0.176576i
$505$	15.6799	−	6.76754i	0.697746	−	0.301152i
$506$	−11.4761	−	19.8772i	−0.510176	−	0.883651i
$507$	24.5073	+	23.9587i	1.08841	+	1.06404i
$508$	4.17267	−	1.51873i	0.185132	−	0.0673827i
$509$	18.8278	+	6.85277i	0.834529	+	0.303744i	0.723716	−	0.690098i	$-0.242432\pi$
$509$	18.8278	+	6.85277i	0.834529	+	0.303744i	0.110813	+	0.993841i	$0.464655\pi$
$510$	18.3275	−	6.30849i	0.811557	−	0.279345i
$511$	0.190290	−	1.07919i	0.00841792	−	0.0477404i
$512$		−	1.00000i		−	0.0441942i
$513$	22.0838	−	5.03048i	0.975024	−	0.222101i
$514$	23.1818			1.02251
$515$	21.6658	+	22.9548i	0.954711	+	1.01151i
$516$	12.9246	+	8.83358i	0.568973	+	0.388877i
$517$	−1.84649	+	5.07319i	−0.0812086	+	0.223119i
$518$	8.42707	−	3.06720i	0.370264	−	0.134765i
$519$	−4.99054	+	5.10482i	−0.219060	+	0.224077i
$520$	1.48376	−	12.7175i	0.0650674	−	0.557701i
$521$	−14.2673	+	24.7117i	−0.625061	+	1.08264i	0.363468	+	0.931607i	$0.381593\pi$
$521$	−14.2673	+	24.7117i	−0.625061	+	1.08264i	−0.988529	+	0.151031i	$0.951741\pi$
$522$	−13.5846	+	5.29561i	−0.594582	+	0.231783i
$523$	1.42189	+	8.06393i	0.0621748	+	0.352611i	0.999985	+	0.00546262i	$0.00173881\pi$
$523$	1.42189	+	8.06393i	0.0621748	+	0.352611i	−0.937810	+	0.347148i	$0.887150\pi$
$524$	−7.78581	−	4.49514i	−0.340125	−	0.196371i
$525$	7.50422	−	9.72308i	0.327511	−	0.424350i
$526$	2.89049	+	3.44475i	0.126031	+	0.150198i
$527$	−16.5704	−	45.5269i	−0.721820	−	1.98318i
$528$	8.05832	+	2.06175i	0.350694	+	0.0897263i
$529$	−0.120610	−	0.101204i	−0.00524392	−	0.00440017i
$530$	−0.269937	−	0.285996i	−0.0117253	−	0.0124229i
$531$	−11.8148	+	2.36021i	−0.512720	+	0.102424i
$532$	5.00842	−	3.62374i	0.217142	−	0.157109i
$533$	27.0436			1.17139
$534$	−0.0728218	+	0.956999i	−0.00315131	+	0.0414134i
$535$	1.68188	+	7.08980i	0.0727141	+	0.306519i
$536$	−4.08719	+	11.2295i	−0.176540	+	0.485039i
$537$	−9.27612	−	19.3187i	−0.400294	−	0.833665i
$538$	1.95718	+	2.33247i	0.0843798	+	0.100560i
$539$	20.7475	−	11.9786i	0.893659	−	0.515954i
$540$	8.86260	−	7.51361i	0.381385	−	0.323334i
$541$	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
$543$	−6.48747	+	14.3338i	−0.278404	+	0.615123i
$544$	4.33414	−	2.50232i	0.185825	−	0.107286i
$545$	−35.7508	+	2.08976i	−1.53139	+	0.0895157i
$546$	6.08829	+	12.6797i	0.260555	+	0.542640i
$547$	−17.2181	−	6.26689i	−0.736194	−	0.267953i	−0.0534097	−	0.998573i	$-0.517009\pi$
$547$	−17.2181	−	6.26689i	−0.736194	−	0.267953i	−0.682784	+	0.730620i	$0.739231\pi$
$548$	3.55935	+	2.98665i	0.152048	+	0.127583i
$549$	−0.0483388	−	2.13495i	−0.00206305	−	0.0911174i
$550$	−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
$555$	−15.4101	−	19.0341i	−0.654124	−	0.807953i
$556$	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	$0.368956\pi$
$558$	−19.1668	−	21.8194i	−0.811397	−	0.923690i
$559$	44.8204	+	25.8770i	1.89570	+	1.09448i
$560$	1.42266	−	2.83422i	0.0601182	−	0.119768i
$561$	11.2286	+	40.0851i	0.474070	+	1.69239i
$562$	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	$0.627880\pi$
$564$	1.39235	+	1.36118i	0.0586286	+	0.0573162i
$565$	−13.2898	−	3.97566i	−0.559105	−	0.167257i
$566$	11.2534	+	4.09589i	0.473015	+	0.172163i
$567$	−3.81821	+	12.1795i	−0.160350	+	0.511492i
$568$	−11.6854	−	2.06044i	−0.490307	−	0.0864543i
$569$	17.7730			0.745083			0.372542	−	0.928016i	$-0.378486\pi$
$569$	17.7730			0.745083			0.372542	+	0.928016i	$0.378486\pi$
$570$	−13.8087	−	9.71184i	−0.578383	−	0.406784i
$571$	−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
$573$	−32.0905	−	21.9329i	−1.34060	−	0.916260i
$574$	6.29421	+	2.29090i	0.262715	+	0.0956205i
$575$	14.2783	+	19.1623i	0.595446	+	0.799123i
$576$	1.87585	−	2.34119i	0.0781604	−	0.0975498i
$577$	−3.11745	+	1.79986i	−0.129781	+	0.0749292i	−0.563485	−	0.826126i	$-0.690540\pi$
$577$	−3.11745	+	1.79986i	−0.129781	+	0.0749292i	0.433704	+	0.901055i	$0.357206\pi$
$578$	6.96839	+	4.02320i	0.289847	+	0.167343i
$579$	−16.8866	+	4.73023i	−0.701781	+	0.196582i
$580$	9.71259	+	4.87530i	0.403293	+	0.202436i
$581$	−2.61588	−	1.51028i	−0.108525	−	0.0626570i
$582$	19.7725	+	27.5686i	0.819598	+	1.14276i
$583$	0.647009	−	0.542905i	0.0267964	−	0.0224848i
$584$	−0.726084	+	0.264273i	−0.0300456	+	0.0109357i
$585$	27.3299	−	26.9909i	1.12995	−	1.11594i
$586$	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
$591$	1.36474	+	0.103849i	0.0561380	+	0.00427176i
$592$	−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	$0.461190\pi$
$594$	14.9986	+	19.9432i	0.615399	+	0.818278i
$595$	15.8439	−	0.926133i	0.649535	−	0.0379678i
$596$	9.75769	−	5.63360i	0.399690	−	0.230761i
$597$	22.7742	+	10.3076i	0.932085	+	0.421861i
$598$	−26.9512	+	4.75222i	−1.10212	+	0.194333i
$599$	4.39302	+	24.9141i	0.179494	+	1.01796i	0.932828	+	0.360323i	$0.117333\pi$
$599$	4.39302	+	24.9141i	0.179494	+	1.01796i	−0.753334	+	0.657638i	$0.771556\pi$
$600$	−8.58296	−	1.15448i	−0.350398	−	0.0471315i
$601$	−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
$603$	−30.6337	+	18.6234i	−1.24750	+	0.758404i
$604$	−6.70696	+	18.4272i	−0.272902	+	0.749793i
$605$	26.2441	−	6.22579i	1.06698	−	0.253114i
$606$	13.1904	+	1.00371i	0.535825	+	0.0407730i
$607$	−22.8014			−0.925482			−0.462741	−	0.886493i	$-0.653134\pi$
$607$	−22.8014			−0.925482			−0.462741	+	0.886493i	$0.653134\pi$
$608$	−3.97854	−	1.78078i	−0.161351	−	0.0722202i
$609$	−11.8805	+	1.17506i	−0.481424	+	0.0476157i
$610$	−1.15754	+	1.09254i	−0.0468672	+	0.0442355i
$611$	4.93118	+	4.13775i	0.199494	+	0.167395i
$612$	14.8410	+	2.27178i	0.599914	+	0.0918313i
$613$	2.80974	+	7.71971i	0.113484	+	0.311796i	0.983413	−	0.181382i	$-0.0580572\pi$
$613$	2.80974	+	7.71971i	0.113484	+	0.311796i	−0.869928	+	0.493178i	$0.835835\pi$
$614$	−5.61729	−	6.69443i	−0.226696	−	0.270165i
$615$	0.321193	−	18.2890i	0.0129518	−	0.737483i
$616$	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	$0.672016\pi$
$618$	6.59501	+	23.5437i	0.265290	+	0.947066i
$619$	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	$0.0426235\pi$
$620$	−2.50854	+	21.5010i	−0.100745	+	0.863501i
$621$	−20.8150	−	13.5456i	−0.835279	−	0.543565i
$622$	−16.4233	+	5.97759i	−0.658515	+	0.239680i
$623$	−0.268782	+	0.738473i	−0.0107685	+	0.0295863i
$624$	5.59629	−	8.18804i	0.224031	−	0.327784i
$625$	9.92124	+	22.9471i	0.396850	+	0.917884i
$626$	11.0790			0.442806
$627$	22.5529	−	28.3889i	0.900676	−	1.13374i
$628$		−	14.6232i		−	0.583528i
$629$	5.49528	−	31.1653i	0.219111	−	1.24264i
$630$	8.64729	−	3.96678i	0.344516	−	0.158040i
$631$	−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
$633$	15.0287	−	15.3729i	0.597339	−	0.611017i
$634$	4.95910	+	8.58942i	0.196951	+	0.341129i
$635$	−3.93466	−	9.11631i	−0.156142	−	0.361770i
$636$	−0.0821679	−	0.293333i	−0.00325817	−	0.0116314i
$637$	−4.96028	−	28.1312i	−0.196534	−	1.11460i
$638$	−11.6699	+	20.2129i	−0.462017	+	0.800237i
$639$	−23.4926	−	26.7439i	−0.929354	−	1.05797i
$640$	−2.23226	+	0.130484i	−0.0882377	+	0.00515782i
$641$	−13.3177	+	4.84724i	−0.526017	+	0.191455i	−0.591359	−	0.806408i	$-0.701408\pi$
$641$	−13.3177	+	4.84724i	−0.526017	+	0.191455i	0.0653420	+	0.997863i	$0.479186\pi$
$642$	−1.39901	+	5.46801i	−0.0552146	+	0.215805i
$643$	−10.8475	+	12.9275i	−0.427782	+	0.509811i	−0.936281	−	0.351252i	$-0.885756\pi$
$643$	−10.8475	+	12.9275i	−0.427782	+	0.509811i	0.508499	+	0.861063i	$0.330201\pi$
$644$	−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	$0.533556\pi$
$648$	8.78345	−	1.96239i	0.345047	−	0.0770898i
$649$	−12.3972	+	14.7744i	−0.486633	+	0.579947i
$650$	−28.5824	−	1.65271i	−1.12109	−	0.0648248i
$651$	−10.2932	−	21.4370i	−0.403423	−	0.840183i
$652$	−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	$-0.405857\pi$
$654$	−25.2718	−	11.4380i	−0.988205	−	0.447261i
$655$	−9.01839	+	17.9665i	−0.352378	+	0.702008i
$656$	−0.820127	−	4.65117i	−0.0320206	−	0.181598i
$657$	−2.19564	−	0.743309i	−0.0856600	−	0.0289992i
$658$	0.797182	+	1.38076i	0.0310774	+	0.0538276i
$659$	−6.36176	+	5.33815i	−0.247819	+	0.207945i	−0.758232	−	0.651984i	$-0.773937\pi$
$659$	−6.36176	+	5.33815i	−0.247819	+	0.207945i	0.510414	+	0.859929i	$0.329492\pi$
$660$	3.55088	−	18.2573i	0.138218	−	0.710664i
$661$	−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
$663$	49.4918	+	3.76603i	1.92210	+	0.146260i
$664$			2.12982i			0.0826531i
$665$	−8.74264	−	10.7072i	−0.339025	−	0.415209i
$666$	−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
$669$	−8.68061	+	33.9280i	−0.335612	+	1.31173i
$670$	25.6004	+	7.65840i	0.989029	+	0.295870i
$671$	−2.19734	−	2.61869i	−0.0848275	−	0.101094i
$672$	1.99612	−	1.43164i	0.0770019	−	0.0552266i
$673$	−7.25134	+	12.5597i	−0.279519	+	0.484141i	−0.971265	−	0.238000i	$-0.923508\pi$
$673$	−7.25134	+	12.5597i	−0.279519	+	0.484141i	0.691747	+	0.722140i	$0.256842\pi$
$674$	−14.4598	+	2.54965i	−0.556970	+	0.0982088i
$675$	−17.9287	−	18.8032i	−0.690078	−	0.723735i
$676$	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	$0.520778\pi$
$678$	−7.68335	−	7.51136i	−0.295077	−	0.288472i
$679$	9.50100	+	26.1038i	0.364615	+	1.00177i
$680$	−6.15136	−	9.34841i	−0.235894	−	0.358495i
$681$	38.0677	+	26.0182i	1.45876	+	0.997019i
$682$	−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	$-0.166582\pi$
$684$	−5.97407	−	11.6323i	−0.228424	−	0.444772i
$685$	6.20253	−	8.33510i	0.236987	−	0.318468i
$686$	2.95246	−	16.7443i	0.112726	−	0.639299i
$687$	−19.5889	+	28.6609i	−0.747363	+	1.09348i
$688$	3.09131	−	8.49330i	0.117855	−	0.323804i
$689$	−0.344437	−	0.946332i	−0.0131220	−	0.0360524i
$690$	2.89372	+	18.2829i	0.110162	+	0.696018i
$691$	−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
$693$	7.42110	+	19.0370i	0.281904	+	0.723157i
$694$	−12.9724	+	2.28738i	−0.492424	+	0.0868277i
$695$	−2.23728	−	5.18362i	−0.0848650	−	0.196626i
$696$	4.90607	+	6.84048i	0.185964	+	0.259288i
$697$	18.1066	−	15.1933i	0.685837	−	0.575486i
$698$	0.0963803	+	0.264803i	0.00364805	+	0.0100229i
$699$	1.07126	−	4.18701i	0.0405188	−	0.158367i
$700$	−6.51235	−	2.80592i	−0.246144	−	0.106054i
$701$	−46.1368	−	8.13516i	−1.74256	−	0.307261i	−0.790341	−	0.612667i	$-0.790097\pi$
$701$	−46.1368	−	8.13516i	−1.74256	−	0.307261i	−0.952222	+	0.305407i	$0.901208\pi$
$702$	28.4615	−	8.67200i	1.07421	−	0.327304i
$703$	−24.7971	+	12.0338i	−0.935240	+	0.453864i
$704$		−	4.80234i		−	0.180995i
$705$	2.85683	−	3.28570i	0.107595	−	0.123747i
$706$	−2.73163	+	3.25543i	−0.102806	+	0.122520i
$707$	10.1785	+	3.70466i	0.382801	+	0.139328i
$708$	3.01093	+	6.27067i	0.113158	+	0.235666i
$709$	−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	$0.430036\pi$
$710$	−3.07469	+	26.3536i	−0.115391	+	0.989033i
$711$	−29.8123	−	10.0926i	−1.11805	−	0.378502i
$712$	0.545703	−	0.0962221i	0.0204511	−	0.00360608i
$713$	45.5652	−	8.03438i	1.70643	−	0.300890i
$714$	11.1998	+	5.06904i	0.419144	+	0.189704i
$715$	7.12554	−	61.0739i	0.266480	−	2.28404i
$716$	−9.47813	+	7.95310i	−0.354214	+	0.297221i
$717$	22.5871	−	10.8454i	0.843530	−	0.405030i
$718$	−4.19368	−	1.52637i	−0.156507	−	0.0569638i
$719$	−3.90235	+	4.65064i	−0.145533	+	0.173439i	−0.833887	−	0.551936i	$-0.813889\pi$
$719$	−3.90235	+	4.65064i	−0.145533	+	0.173439i	0.688354	+	0.725375i	$0.258334\pi$
$720$	−5.47092	−	3.88189i	−0.203889	−	0.144669i
$721$			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
$725$	9.61558	−	22.3172i	0.357114	−	0.828838i
$726$	20.2408	+	5.17869i	0.751207	+	0.192199i
$727$	8.98220	+	24.6784i	0.333131	+	0.915270i	0.987292	+	0.158915i	$0.0507996\pi$
$727$	8.98220	+	24.6784i	0.333131	+	0.915270i	−0.654161	+	0.756355i	$0.726978\pi$
$728$	6.22088	−	5.21994i	0.230561	−	0.193464i
$729$	24.2449	+	11.8821i	0.897960	+	0.440078i
$730$	0.684667	+	1.58632i	0.0253407	+	0.0587124i
$731$	44.5466	−	7.85478i	1.64762	−	0.290519i
$732$	−1.18723	+	0.332565i	−0.0438813	+	0.0122920i
$733$	9.94353	+	5.74090i	0.367273	+	0.212045i	0.672266	−	0.740309i	$-0.265321\pi$
$733$	9.94353	+	5.74090i	0.367273	+	0.212045i	−0.304994	+	0.952354i	$0.598654\pi$
$734$	2.39693	+	4.15160i	0.0884723	+	0.153238i
$735$	−19.0834	+	3.02042i	−0.703901	+	0.111410i
$736$	1.63465	+	4.49116i	0.0602539	+	0.165546i
$737$	−19.6281	+	53.9277i	−0.723010	+	1.98645i
$738$	6.80481	−	12.4277i	0.250489	−	0.457471i
$739$	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
$741$	−22.6107	−	36.8462i	−0.830625	−	1.35358i
$742$		−	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	$0.676069\pi$
$744$	−9.46141	+	13.8432i	−0.346872	+	0.507515i
$745$	−13.8489	−	21.0466i	−0.507383	−	0.771087i
$746$	5.12672	+	14.0855i	0.187703	+	0.515708i
$747$	−3.99522	+	4.98633i	−0.146178	+	0.182440i
$748$	20.8140	−	12.0170i	0.761036	−	0.439385i
$749$	−2.31074	+	4.00233i	−0.0844328	+	0.146242i
$750$	−1.45716	+	19.3100i	−0.0532080	+	0.705102i
$751$	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
$753$	−24.4400	−	34.0765i	−0.890644	−	1.24182i
$754$	17.8882	+	21.3183i	0.651450	+	0.776368i
$755$	42.0095	+	12.5672i	1.52888	+	0.457368i
$756$	7.35883	+	0.392669i	0.267638	+	0.0142813i
$757$	−26.0578	+	31.0544i	−0.947086	+	1.12869i	0.0444701	+	0.999011i	$0.485840\pi$
$757$	−26.0578	+	31.0544i	−0.947086	+	1.12869i	−0.991556	+	0.129682i	$0.958604\pi$
$758$	2.86985	−	16.2757i	0.104238	−	0.591161i
$759$	−39.5614	+	3.91286i	−1.43599	+	0.142028i
$760$	−3.45603	+	9.11350i	−0.125363	+	0.330581i
$761$		−	35.7467i		−	1.29582i	−0.761719	−	0.647908i	$-0.775644\pi$
$761$		−	35.7467i		−	1.29582i	0.761719	−	0.647908i	$-0.224356\pi$
$762$	0.583560	−	7.66894i	0.0211401	−	0.277816i
$763$	−17.3996	−	14.6000i	−0.629908	−	0.528556i
$764$	−7.67541	+	21.0880i	−0.277687	+	0.762938i
$765$	3.13469	−	33.4255i	0.113335	−	1.20850i
$766$	−5.50756	+	4.62139i	−0.198996	+	0.166978i
$767$	11.4981	+	19.9154i	0.415174	+	0.719102i
$768$	−1.57796	−	0.714182i	−0.0569396	−	0.0257708i
$769$	−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	$-0.122890\pi$
$770$	6.83208	−	13.6109i	0.246211	−	0.490503i
$771$	16.5560	−	36.5798i	0.596250	−	1.31739i
$772$	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	$0.585131\pi$
$774$	23.1695	−	14.0856i	0.832811	−	0.506298i
$775$	48.3231	+	2.79417i	1.73582	+	0.100370i
$776$	12.5904	−	15.0047i	0.451971	−	0.538637i
$777$	1.17855	−	15.4881i	0.0422802	−	0.555632i
$778$	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
$783$	−1.34564	+	25.2180i	−0.0480892	+	0.901216i
$784$	−4.68779	+	1.70622i	−0.167421	+	0.0609363i
$785$	−32.6427	+	1.90809i	−1.16507	+	0.0681025i
$786$	−12.6536	+	9.07532i	−0.451340	+	0.323706i
$787$	−12.8766	+	22.3028i	−0.459000	+	0.795011i	−0.998908	−	0.0467129i	$-0.985125\pi$
$787$	−12.8766	+	22.3028i	−0.459000	+	0.795011i	0.539909	+	0.841724i	$0.318459\pi$
$788$	−0.137219	−	0.778207i	−0.00488822	−	0.0277225i
$789$	7.50000	−	2.10089i	0.267007	−	0.0747935i
$790$	9.29638	+	21.5390i	0.330750	+	0.766323i
$791$	−4.39905	−	7.61938i	−0.156412	−	0.270914i
$792$	9.00846	−	11.2432i	0.320102	−	0.399510i
$793$	−3.83016	+	1.39407i	−0.136013	+	0.0495047i
$794$	−26.8026	−	9.75533i	−0.951187	−	0.346204i
$795$	−0.644073	+	0.221695i	−0.0228429	+	0.00786272i
$796$	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	$-0.143784\pi$
$798$	−2.14119	−	10.4911i	−0.0757972	−	0.371380i
$799$	5.62620			0.199041
$800$	0.582546	+	4.96595i	0.0205961	+	0.175573i
$801$	1.45809	+	0.798381i	0.0515192	+	0.0282094i
$802$	−1.15010	+	3.15986i	−0.0406113	+	0.111579i
$803$	−3.48690	+	1.26913i	−0.123050	+	0.0447866i
$804$	14.8006	+	14.4693i	0.521977	+	0.510292i
$805$	−1.75642	+	15.0545i	−0.0619056	+	0.530601i
$806$	−27.7162	+	48.0059i	−0.976261	+	1.69093i
$807$	5.07831	−	1.42253i	0.178765	−	0.0500754i
$808$	−1.32624	−	7.52149i	−0.0466570	−	0.264605i
$809$	25.2953	+	14.6042i	0.889334	+	0.513458i	0.873725	−	0.486421i	$-0.161698\pi$
$809$	25.2953	+	14.6042i	0.889334	+	0.513458i	0.0156097	+	0.999878i	$0.495031\pi$
$810$	−5.52665	−	19.3509i	−0.194187	−	0.679920i
$811$	−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
$813$	−4.35737	+	17.0307i	−0.152820	+	0.597293i
$814$	−23.2623	−	19.5194i	−0.815345	−	0.684155i
$815$	−2.18484	+	2.06216i	−0.0765316	+	0.0722342i
$816$	−0.853183	−	8.62620i	−0.0298674	−	0.301977i
$817$	−28.2860	−	27.4236i	−0.989603	−	0.959432i
$818$	35.7770			1.25091
$819$	24.3561	−	0.551464i	0.851072	−	0.0192697i
$820$	−10.2756	+	2.43764i	−0.358839	+	0.0851260i
$821$	7.78634	−	21.3928i	0.271745	−	0.746613i	−0.726487	−	0.687180i	$-0.758848\pi$
$821$	7.78634	−	21.3928i	0.271745	−	0.746613i	0.998232	−	0.0594334i	$-0.0189294\pi$
$822$	7.25483	−	3.48349i	0.253041	−	0.121501i
$823$	10.9164	+	13.0096i	0.380521	+	0.453487i	0.921979	−	0.387241i	$-0.126572\pi$
$823$	10.9164	+	13.0096i	0.380521	+	0.453487i	−0.541458	+	0.840728i	$0.682127\pi$
$824$	12.2250	−	7.05809i	0.425877	−	0.245880i
$825$	−41.2183	−	5.54421i	−1.43504	−	0.193025i
$826$	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	$0.509483\pi$
$828$	−4.59770	+	13.5810i	−0.159781	+	0.471973i
$829$	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	$0.160409\pi$
$830$	4.75431	−	0.277907i	0.165025	−	0.00964630i
$831$	−6.91161	+	3.31869i	−0.239761	+	0.115124i
$832$	−5.38071	−	1.95842i	−0.186543	−	0.0678959i
$833$	−19.1253	−	16.0481i	−0.662654	−	0.556033i
$834$	0.331818	−	4.36063i	0.0114899	−	0.150996i
$835$	−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	0.977386	−	0.211464i	$-0.0678231\pi$
$839$	27.1944	+	22.8188i	0.938856	+	0.787793i	−0.0385302	+	0.999257i	$0.512268\pi$
$840$	−3.45624	−	4.26904i	−0.119252	−	0.147296i
$841$	5.05499	−	1.83987i	0.174310	−	0.0634437i
$842$	−14.4380	+	12.1149i	−0.497567	+	0.417508i
$843$	43.4230	−	31.1435i	1.49557	−	1.07264i
$844$	−10.7493	−	6.20610i	−0.370006	−	0.213623i
$845$	−39.5439	−	19.8493i	−1.36035	−	0.682837i
$846$	3.14228	−	1.22494i	0.108034	−	0.0421142i
$847$	14.8153	+	8.55363i	0.509061	+	0.293906i
$848$	−0.152312	+	0.0879374i	−0.00523042	+	0.00301978i
$849$	14.5001	−	14.8321i	0.497642	−	0.509037i
$850$	−20.0654	+	14.9512i	−0.688238	+	0.512823i
$851$	28.3991	+	10.3364i	0.973509	+	0.354328i
$852$	−11.5968	+	16.9675i	−0.397299	+	0.581295i
$853$	−7.64787	−	1.34853i	−0.261858	−	0.0461727i	0.0411776	−	0.999152i	$-0.486889\pi$
$853$	−7.64787	−	1.34853i	−0.261858	−	0.0461727i	−0.303036	+	0.952979i	$0.598000\pi$
$854$	−1.00954			−0.0345456
$855$	−25.1868	+	14.8535i	−0.861370	+	0.507979i
$856$	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	$0.579960\pi$
$858$	26.8753	−	39.3217i	0.917506	−	1.34242i
$859$	−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	$0.795265\pi$
$860$	−19.3626	−	5.79236i	−0.660259	−	0.197518i
$861$	8.11015	−	8.29586i	0.276393	−	0.282722i
$862$	−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	$0.648946\pi$
$864$	−2.35461	−	4.63204i	−0.0801053	−	0.157585i
$865$	4.13456	−	8.23690i	0.140579	−	0.280063i
$866$	−16.0306	−	9.25527i	−0.544742	−	0.314507i
$867$	11.3251	−	8.12251i	0.384622	−	0.275855i
$868$	−10.5174	+	8.82514i	−0.356984	+	0.299545i
$869$	−47.3450	+	17.2322i	−1.60607	+	0.584561i
$870$	14.6296	−	11.8442i	0.495988	−	0.401556i
$871$	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
$876$	−0.101545	+	1.33447i	−0.00343088	+	0.0450875i
$877$	−28.2811	−	23.7307i	−0.954985	−	0.801328i	0.0251450	−	0.999684i	$-0.491995\pi$
$877$	−28.2811	−	23.7307i	−0.954985	−	0.801328i	−0.980130	+	0.198356i	$0.936440\pi$
$878$	16.2618	+	5.91880i	0.548808	+	0.199750i
$879$	1.81426	−	0.871140i	0.0611936	−	0.0293828i
$880$	−10.7201	+	0.626627i	−0.361373	+	0.0211236i
$881$	−2.11328	+	1.22011i	−0.0711984	+	0.0411064i	−0.535177	−	0.844740i	$-0.679755\pi$
$881$	−2.11328	+	1.22011i	−0.0711984	+	0.0411064i	0.463978	+	0.885847i	$0.346422\pi$
$882$	−14.1756	−	4.79900i	−0.477319	−	0.161591i
$883$	15.4179	−	2.71859i	0.518852	−	0.0914877i	0.0919115	−	0.995767i	$-0.470702\pi$
$883$	15.4179	−	2.71859i	0.518852	−	0.0914877i	0.426941	+	0.904280i	$0.359591\pi$
$884$	−4.97619	−	28.2214i	−0.167367	−	0.949187i
$885$	13.6049	−	7.53940i	0.457323	−	0.253434i
$886$	−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	$0.863380\pi$
$888$	−9.87317	+	4.74072i	−0.331322	+	0.159088i
$889$	2.15389	−	5.91778i	0.0722393	−	0.198476i
$890$	−0.285998	−	1.20559i	−0.00958667	−	0.0404116i
$891$	42.1811	−	9.42404i	1.41312	−	0.315717i
$892$	20.2193			0.676993
$893$	−2.87247	−	3.97008i	−0.0961236	−	0.132854i
$894$	−1.92082	−	19.4206i	−0.0642417	−	0.649523i
$895$	18.9901	+	20.1199i	0.634769	+	0.672533i
$896$	−1.08642	−	0.911616i	−0.0362948	−	0.0304549i
$897$	−11.7492	+	45.9217i	−0.392296	+	1.53328i
$898$	2.33957	+	6.42791i	0.0780724	+	0.214502i
$899$	−30.2428	−	36.0420i	−1.00866	−	1.20207i
$900$	−7.95151	+	12.7190i	−0.265050	+	0.423967i
$901$	−0.762267	−	0.440095i	−0.0253948	−	0.0146617i
$902$	−3.93853	−	22.3365i	−0.131139	−	0.743724i
$903$	21.3793	−	5.98872i	0.711457	−	0.199292i
$904$	−3.10181	+	5.37248i	−0.103165	+	0.178686i
$905$	2.35385	−	20.1751i	0.0782445	−	0.670643i
$906$	24.2874	+	23.7437i	0.806894	+	0.788831i
$907$	23.5544	−	8.57310i	0.782111	−	0.284665i	0.0800584	−	0.996790i	$-0.474489\pi$
$907$	23.5544	−	8.57310i	0.782111	−	0.284665i	0.702053	+	0.712125i	$0.252267\pi$
$908$	9.10506	−	25.0159i	0.302162	−	0.830183i
$909$	11.0042	−	20.0971i	0.364986	−	0.666578i
$910$	−12.4640	−	13.2055i	−0.413177	−	0.437758i
$911$	−45.9454			−1.52224			−0.761120	−	0.648612i	$-0.775350\pi$
$911$	−45.9454			−1.52224			−0.761120	+	0.648612i	$0.775350\pi$
$912$	−5.65140	+	5.00617i	−0.187137	+	0.165771i
$913$			10.2281i			0.338502i
$914$	−0.216321	+	1.22682i	−0.00715526	+	0.0405795i
$915$	0.897285	+	2.60681i	0.0296633	+	0.0861785i
$916$	18.8343	+	6.85513i	0.622303	+	0.226500i
$917$	−11.9813	+	4.36083i	−0.395657	+	0.144007i
$918$	14.1840	−	21.7960i	0.468141	−	0.719377i
$919$	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	$0.672442\pi$
$920$	9.81212	−	4.23498i	0.323496	−	0.139623i
$921$	−14.5753	+	4.08280i	−0.480272	+	0.134533i
$922$	−2.12151	−	12.0317i	−0.0698681	−	0.396241i
$923$	−33.9715	+	58.8403i	−1.11818	+	1.93675i
$924$	9.58603	−	6.87521i	0.315357	−	0.226178i
$925$	26.4227	+	17.3626i	0.868772	+	0.570878i
$926$	−5.82657	+	2.12070i	−0.191473	+	0.0696904i
$927$	41.8609	+	6.40783i	1.37489	+	0.210461i
$928$	3.12401	−	3.72305i	0.102551	−	0.122215i
$929$	−6.95259	−	1.22593i	−0.228107	−	0.0402214i	0.0584262	−	0.998292i	$-0.481392\pi$
$929$	−6.95259	−	1.22593i	−0.228107	−	0.0402214i	−0.286533	+	0.958070i	$0.592503\pi$
$930$	32.1361	+	19.3140i	1.05378	+	0.633331i
$931$	−1.55968	+	21.6890i	−0.0511163	+	0.710828i
$932$	−2.49524			−0.0817342
$933$	−2.29684	+	30.1843i	−0.0751953	+	0.988191i
$934$	−20.2554	+	24.1395i	−0.662778	+	0.789868i
$935$	−29.5409	−	44.8943i	−0.966091	−	1.46820i
$936$	−8.92359	−	14.6784i	−0.291677	−	0.479780i
$937$	−15.3123	−	18.2485i	−0.500231	−	0.596152i	0.455558	−	0.890206i	$-0.349440\pi$
$937$	−15.3123	−	18.2485i	−0.500231	−	0.596152i	−0.955789	+	0.294054i	$0.904995\pi$
$938$	8.47398	+	14.6774i	0.276685	+	0.479233i
$939$	7.91243	−	17.4822i	0.258212	−	0.570510i
$940$	−2.24664	−	1.12771i	−0.0732772	−	0.0367819i
$941$	6.77146	+	38.4029i	0.220743	+	1.25190i	0.870657	+	0.491890i	$0.163694\pi$
$941$	6.77146	+	38.4029i	0.220743	+	1.25190i	−0.649914	+	0.760008i	$0.725195\pi$
$942$	−23.0747	−	10.4436i	−0.751815	−	0.340271i
$943$	11.2863	+	19.5485i	0.367534	+	0.636587i
$944$	3.07651	−	2.58149i	0.100132	−	0.0840205i
$945$	−0.0836682	−	16.4780i	−0.00272173	−	0.536031i
$946$	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	$0.586617\pi$
$948$	−1.37877	+	18.1193i	−0.0447804	+	0.588488i
$949$			4.42440i			0.143622i
$950$	20.7946	+	6.52558i	0.674667	+	0.211718i
$951$	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	$0.382184\pi$
$954$	−0.521549	−	0.0798358i	−0.0168858	−	0.00258478i
$955$	48.0754	+	14.3818i	1.55568	+	0.465386i
$956$	−9.29859	−	11.0816i	−0.300738	−	0.358406i
$957$	23.5606	+	32.8503i	0.761607	+	1.06190i
$958$	2.91659	−	5.05168i	0.0942307	−	0.163212i
$959$	6.48952	−	1.14428i	0.209558	−	0.0369507i
$960$	−1.38834	+	3.61559i	−0.0448085	+	0.116693i
$961$	31.3586	−	54.3147i	1.01157	−	1.75209i
$962$	−31.3568	+	18.1038i	−1.01098	+	0.583691i
$963$	7.62913	+	6.11273i	0.245845	+	0.196980i
$964$	4.78848	+	13.1562i	0.154227	+	0.423734i
$965$	18.9125	−	12.4446i	0.608815	−	0.400607i
$966$	−6.62465	+	9.69265i	−0.213145	+	0.311856i
$967$	−41.5722	−	7.33030i	−1.33687	−	0.235727i	−0.540914	−	0.841078i	$-0.681921\pi$
$967$	−41.5722	−	7.33030i	−1.33687	−	0.235727i	−0.795958	+	0.605352i	$0.793033\pi$
$968$		−	12.0625i		−	0.387702i
$969$	−35.8390	−	11.9670i	−1.15132	−	0.384434i
$970$	−35.1372	−	26.1472i	−1.12819	−	0.839537i
$971$	6.03347	−	34.2175i	0.193623	−	1.09809i	−0.720742	−	0.693203i	$-0.756199\pi$
$971$	6.03347	−	34.2175i	0.193623	−	1.09809i	0.914366	−	0.404889i	$-0.132690\pi$
$972$	3.17642	−	15.2614i	0.101884	−	0.489510i
$973$	1.22472	−	3.36490i	0.0392629	−	0.107874i
$974$	−1.88455	−	5.17777i	−0.0603850	−	0.165906i
$975$	−23.0210	+	43.9215i	−0.737260	+	1.40661i
$976$	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	$0.491717\pi$
$978$	−2.24089	+	0.627714i	−0.0716558	+	0.0200721i
$979$	2.62065	−	0.462091i	0.0837563	−	0.0147685i
$980$	4.42040	+	10.2417i	0.141204	+	0.327160i
$981$	−36.0973	+	31.7090i	−1.15250	+	1.01239i
$982$	−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	$0.790030\pi$
$984$	−7.92506	−	2.02766i	−0.252642	−	0.0646393i
$985$	−1.71925	+	0.407851i	−0.0547799	+	0.0129952i
$986$	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
$990$	−26.2732	−	18.6422i	−0.835017	−	0.592486i
$991$	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
$993$	2.78649	−	1.33797i	0.0884266	−	0.0424591i
$994$	−12.8911	+	10.8169i	−0.408880	+	0.343091i
$995$	−32.0551	−	3.73989i	−1.01621	−	0.118562i
$996$	3.36077	+	1.52108i	0.106490	+	0.0481973i
$997$	43.8794	−	7.73712i	1.38967	−	0.245037i	0.571780	−	0.820407i	$-0.306253\pi$
$997$	43.8794	−	7.73712i	1.38967	−	0.245037i	0.817893	+	0.575370i	$0.195142\pi$
$998$	25.9510	−	4.57586i	0.821465	−	0.144846i
$999$	−32.0079	−	7.42163i	−1.01268	−	0.234810i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-0.977341 + 1.42997i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.640862 - 2.14226i) q^{5} +(1.21080 - 1.23853i) q^{6} +(1.22822 - 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.08961 - 2.79513i) q^{9} +O(q^{10})\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-0.977341 + 1.42997i) q^{3} +(0.939693 + 0.342020i) q^{4} +(0.640862 - 2.14226i) q^{5} +(1.21080 - 1.23853i) q^{6} +(1.22822 - 0.709111i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.08961 - 2.79513i) q^{9} +(-1.00313 + 1.99843i) q^{10} +(-4.15895 - 2.40117i) q^{11} +(-1.40748 + 1.00946i) q^{12} +(-4.38640 + 3.68062i) q^{13} +(-1.33269 + 0.485061i) q^{14} +(2.43703 + 3.01013i) 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} +(-0.186381 + 2.44935i) q^{21} +(3.67881 + 3.08688i) q^{22} +(-4.49116 - 1.63465i) q^{23} +(1.56139 - 0.749717i) q^{24} +(-4.17859 - 2.74579i) q^{25} +(4.95889 - 2.86302i) q^{26} +(5.06186 + 1.17369i) q^{27} +(1.39668 - 0.246272i) q^{28} +(0.843948 + 4.78627i) q^{29} +(-1.87730 - 3.38759i) q^{30} +(-8.38379 + 4.84038i) q^{31} +(-0.642788 - 0.766044i) q^{32} +(7.49830 - 3.60040i) q^{33} +(1.71169 - 4.70282i) q^{34} +(-0.731986 - 3.08561i) q^{35} +(-0.0679076 - 2.99923i) q^{36} -6.32334 q^{37} +(-4.19241 + 1.19320i) q^{38} +(-0.976165 - 9.86962i) q^{39} +(-1.62614 + 1.53482i) q^{40} +(-3.61797 - 3.03584i) q^{41} +(0.608875 - 2.37978i) q^{42} +(-3.09131 - 8.49330i) q^{43} +(-3.08688 - 3.67881i) q^{44} +(-6.68620 + 0.542938i) q^{45} +(4.13907 + 2.38969i) q^{46} +(-0.195215 - 1.10712i) q^{47} +(-1.66785 + 0.467196i) q^{48} +(-2.49432 + 4.32029i) q^{49} +(3.63831 + 3.42968i) q^{50} +(-6.19839 - 6.05964i) q^{51} +(-5.38071 + 1.95842i) q^{52} +(-0.0601527 + 0.165268i) q^{53} +(-4.78115 - 2.03484i) q^{54} +(-7.80925 + 7.37075i) q^{55} -1.41822 q^{56} +(-1.11132 + 7.46759i) q^{57} -4.86010i q^{58} +(0.697387 - 3.95508i) q^{59} +(1.26053 + 3.66211i) q^{60} +(0.668904 + 0.243461i) q^{61} +(9.09695 - 3.31102i) q^{62} +(-3.32034 - 2.66037i) q^{63} +(0.500000 + 0.866025i) q^{64} +(5.07379 + 11.7556i) q^{65} +(-8.00959 + 2.24363i) q^{66} +(-2.07512 - 11.7686i) q^{67} +(-2.50232 + 4.33414i) q^{68} +(6.72688 - 4.82460i) q^{69} +(0.185055 + 3.16584i) q^{70} +(11.1500 - 4.05828i) q^{71} +(-0.453935 + 2.96546i) 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} +(-0.752507 + 9.88919i) q^{78} +(6.74377 - 8.03691i) q^{79} +(1.86795 - 1.22913i) q^{80} +(-6.62550 + 6.09120i) q^{81} +(3.03584 + 3.61797i) q^{82} +(-1.06491 - 1.84448i) q^{83} +(-1.01287 + 2.23789i) q^{84} +(10.0014 + 5.02029i) q^{85} +(1.56950 + 8.90107i) q^{86} +(-7.66903 - 3.47100i) q^{87} +(2.40117 + 4.15895i) q^{88} +(-0.424481 + 0.356182i) q^{89} +(6.67890 + 0.626356i) q^{90} +(-2.77747 + 7.63105i) q^{91} +(-3.66122 - 3.07213i) q^{92} +(1.27223 - 16.7192i) q^{93} +1.12420i q^{94} +(-1.56374 - 9.62054i) q^{95} +(1.72364 - 0.170478i) q^{96} +(-3.40129 + 19.2897i) q^{97} +(3.20664 - 3.82152i) q^{98} +(-2.17995 + 14.2411i) 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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