LMFDB - Embedded newform 525.2.bh.a.13.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(13,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19, 10]))

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

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

chi := DirichletCharacter("525.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bh (of order $20$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.14
Character	$\chi$	$=$	525.13
Dual form			525.2.bh.a.202.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.44172 + 0.228346i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.124296 - 0.0403862i) q^{4} +(-1.71338 - 1.43678i) q^{5} +(-1.38825 - 0.451069i) q^{6} +(-2.28073 - 1.34100i) q^{7} +(2.43121 - 1.23876i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})$	\(q+(-1.44172 + 0.228346i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.124296 - 0.0403862i) q^{4} +(-1.71338 - 1.43678i) q^{5} +(-1.38825 - 0.451069i) q^{6} +(-2.28073 - 1.34100i) q^{7} +(2.43121 - 1.23876i) q^{8} +(0.587785 + 0.809017i) q^{9} +(2.79829 + 1.68019i) q^{10} +(0.336688 + 0.244618i) q^{11} +(0.129083 + 0.0204448i) q^{12} +(-0.293555 + 1.85344i) q^{13} +(3.59438 + 1.41255i) q^{14} +(-0.874345 - 2.05804i) q^{15} +(-3.43371 + 2.49474i) q^{16} +(4.14136 - 2.11013i) q^{17} +(-1.03216 - 1.03216i) q^{18} +(-2.57638 + 7.92929i) q^{19} +(-0.270992 - 0.109389i) q^{20} +(-1.42334 - 2.23027i) q^{21} +(-0.541267 - 0.275789i) q^{22} +(1.30750 + 8.25521i) q^{23} +2.72861 q^{24} +(0.871321 + 4.92349i) q^{25} -2.73916i q^{26} +(0.156434 + 0.987688i) q^{27} +(-0.337643 - 0.0745709i) q^{28} +(-0.248653 + 0.0807922i) q^{29} +(1.73050 + 2.76746i) q^{30} +(-5.95543 - 1.93504i) q^{31} +(0.521950 - 0.521950i) q^{32} +(0.188937 + 0.370810i) q^{33} +(-5.48883 + 3.98787i) q^{34} +(1.98102 + 5.57454i) q^{35} +(0.105732 + 0.0768191i) q^{36} +(-0.140783 + 0.888869i) q^{37} +(1.90380 - 12.0201i) q^{38} +(-1.10300 + 1.51815i) q^{39} +(-5.94540 - 1.37065i) q^{40} +(-2.97536 - 4.09523i) q^{41} +(2.56133 + 2.89040i) q^{42} +(2.51007 + 2.51007i) q^{43} +(0.0517281 + 0.0168075i) q^{44} +(0.155282 - 2.23067i) q^{45} +(-3.77008 - 11.6031i) q^{46} +(2.12998 - 4.18032i) q^{47} +(-4.19205 + 0.663955i) q^{48} +(3.40344 + 6.11691i) q^{49} +(-2.38046 - 6.89933i) q^{50} +4.64796 q^{51} +(0.0383655 + 0.242230i) q^{52} +(-2.34029 + 4.59308i) q^{53} +(-0.451069 - 1.38825i) q^{54} +(-0.225411 - 0.902870i) q^{55} +(-7.20610 - 0.434971i) q^{56} +(-5.89540 + 5.89540i) q^{57} +(0.340039 - 0.173258i) q^{58} +(1.18568 - 0.861445i) q^{59} +(-0.191794 - 0.220494i) q^{60} +(-8.19257 + 11.2761i) q^{61} +(9.02790 + 1.42988i) q^{62} +(-0.255686 - 2.63337i) q^{63} +(4.35616 - 5.99574i) q^{64} +(3.16595 - 2.75386i) q^{65} +(-0.357066 - 0.491460i) q^{66} +(2.81639 + 5.52747i) q^{67} +(0.429534 - 0.429534i) q^{68} +(-2.58280 + 7.94904i) q^{69} +(-4.12900 - 7.58456i) q^{70} +(3.66863 + 11.2909i) q^{71} +(2.43121 + 1.23876i) q^{72} +(15.4942 - 2.45404i) q^{73} -1.31365i q^{74} +(-1.45887 + 4.78244i) q^{75} +1.08963i q^{76} +(-0.439861 - 1.00941i) q^{77} +(1.24355 - 2.44061i) q^{78} +(-13.5111 + 4.39003i) q^{79} +(9.46764 + 0.659066i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(5.22475 + 5.22475i) q^{82} +(-0.854913 - 1.67786i) q^{83} +(-0.266988 - 0.219730i) q^{84} +(-10.1275 - 2.33478i) q^{85} +(-4.19198 - 3.04565i) q^{86} +(-0.258230 - 0.0408996i) q^{87} +(1.12158 + 0.177641i) q^{88} +(3.53223 + 2.56631i) q^{89} +(0.285490 + 3.25145i) q^{90} +(3.15498 - 3.83353i) q^{91} +(0.495913 + 0.973284i) q^{92} +(-4.42784 - 4.42784i) q^{93} +(-2.11627 + 6.51321i) q^{94} +(15.8070 - 9.88416i) q^{95} +(0.702021 - 0.228101i) q^{96} +(-0.339728 + 0.666753i) q^{97} +(-6.30357 - 8.04170i) q^{98} +0.416169i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 8 q^{7} - 24 q^{8}+O(q^{10}) $ 320 * q + 8 * q^7 - 24 * q^8	$ 320 q + 8 q^{7} - 24 q^{8} - 8 q^{15} + 80 q^{16} - 24 q^{22} + 36 q^{28} - 40 q^{29} - 32 q^{30} - 48 q^{32} + 28 q^{35} + 80 q^{36} - 32 q^{37} + 16 q^{42} - 144 q^{43} - 288 q^{50} + 136 q^{53} - 8 q^{57} - 32 q^{58} - 40 q^{60} - 8 q^{63} - 120 q^{64} - 40 q^{65} + 32 q^{67} - 40 q^{70} - 24 q^{72} + 24 q^{77} + 8 q^{78} + 80 q^{81} - 80 q^{84} - 48 q^{85} - 56 q^{88} + 40 q^{92} + 96 q^{93} - 88 q^{95} - 184 q^{98}+O(q^{100}) $ 320 * q + 8 * q^7 - 24 * q^8 - 8 * q^15 + 80 * q^16 - 24 * q^22 + 36 * q^28 - 40 * q^29 - 32 * q^30 - 48 * q^32 + 28 * q^35 + 80 * q^36 - 32 * q^37 + 16 * q^42 - 144 * q^43 - 288 * q^50 + 136 * q^53 - 8 * q^57 - 32 * q^58 - 40 * q^60 - 8 * q^63 - 120 * q^64 - 40 * q^65 + 32 * q^67 - 40 * q^70 - 24 * q^72 + 24 * q^77 + 8 * q^78 + 80 * q^81 - 80 * q^84 - 48 * q^85 - 56 * q^88 + 40 * q^92 + 96 * q^93 - 88 * q^95 - 184 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$1$	$-1$

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 $

$2$	−1.44172	+	0.228346i	−1.01945	+	0.161465i	−0.643717	−	0.765264i	$-0.722609\pi$
$2$	−1.44172	+	0.228346i	−1.01945	+	0.161465i	−0.375732	+	0.926729i	$0.622609\pi$
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$3$	0.891007	+	0.453990i	0.514423	+	0.262112i
$4$	0.124296	−	0.0403862i	0.0621479	−	0.0201931i
$5$	−1.71338	−	1.43678i	−0.766245	−	0.642548i
$5$	−1.71338	−	1.43678i	−0.766245	−	0.642548i
$6$	−1.38825	−	0.451069i	−0.566749	−	0.184148i
$7$	−2.28073	−	1.34100i	−0.862034	−	0.506850i
$7$	−2.28073	−	1.34100i	−0.862034	−	0.506850i
$8$	2.43121	−	1.23876i	0.859562	−	0.437969i
$9$	0.587785	+	0.809017i	0.195928	+	0.269672i
$10$	2.79829	+	1.68019i	0.884897	+	0.531323i
$11$	0.336688	+	0.244618i	0.101515	+	0.0737551i	0.637385	−	0.770546i	$-0.280016\pi$
$11$	0.336688	+	0.244618i	0.101515	+	0.0737551i	−0.535870	+	0.844301i	$0.680016\pi$
$12$	0.129083	+	0.0204448i	0.0372632	+	0.00590191i
$13$	−0.293555	+	1.85344i	−0.0814176	+	0.514051i	0.912951	+	0.408070i	$0.133798\pi$
$13$	−0.293555	+	1.85344i	−0.0814176	+	0.514051i	−0.994368	+	0.105981i	$0.966202\pi$
$14$	3.59438	+	1.41255i	0.960638	+	0.377520i
$15$	−0.874345	−	2.05804i	−0.225755	−	0.531383i
$16$	−3.43371	+	2.49474i	−0.858429	+	0.623685i
$17$	4.14136	−	2.11013i	1.00443	−	0.511781i	0.127211	−	0.991876i	$-0.459398\pi$
$17$	4.14136	−	2.11013i	1.00443	−	0.511781i	0.877217	+	0.480094i	$0.159398\pi$
$18$	−1.03216	−	1.03216i	−0.243282	−	0.243282i
$19$	−2.57638	+	7.92929i	−0.591063	+	1.81910i	−0.0176392	+	0.999844i	$0.505615\pi$
$19$	−2.57638	+	7.92929i	−0.591063	+	1.81910i	−0.573423	+	0.819259i	$0.694385\pi$
$20$	−0.270992	−	0.109389i	−0.0605956	−	0.0244602i
$21$	−1.42334	−	2.23027i	−0.310599	−	0.486685i
$22$	−0.541267	−	0.275789i	−0.115398	−	0.0587984i
$23$	1.30750	+	8.25521i	0.272632	+	1.72133i	0.620861	+	0.783921i	$0.286783\pi$
$23$	1.30750	+	8.25521i	0.272632	+	1.72133i	−0.348229	+	0.937409i	$0.613217\pi$
$24$	2.72861			0.556975
$25$	0.871321	+	4.92349i	0.174264	+	0.984699i
$26$		−	2.73916i		−	0.537194i
$27$	0.156434	+	0.987688i	0.0301058	+	0.190081i
$28$	−0.337643	−	0.0745709i	−0.0638085	−	0.0140926i
$29$	−0.248653	+	0.0807922i	−0.0461737	+	0.0150027i	−0.332013	−	0.943275i	$-0.607728\pi$
$29$	−0.248653	+	0.0807922i	−0.0461737	+	0.0150027i	0.285839	+	0.958278i	$0.407728\pi$
$30$	1.73050	+	2.76746i	0.315945	+	0.505266i
$31$	−5.95543	−	1.93504i	−1.06963	−	0.347543i	−0.279284	−	0.960209i	$-0.590097\pi$
$31$	−5.95543	−	1.93504i	−1.06963	−	0.347543i	−0.790342	+	0.612666i	$0.790097\pi$
$32$	0.521950	−	0.521950i	0.0922686	−	0.0922686i
$33$	0.188937	+	0.370810i	0.0328897	+	0.0645496i
$34$	−5.48883	+	3.98787i	−0.941327	+	0.683914i
$35$	1.98102	+	5.57454i	0.334854	+	0.942270i
$36$	0.105732	+	0.0768191i	0.0176221	+	0.0128032i
$37$	−0.140783	+	0.888869i	−0.0231446	+	0.146129i	−0.996554	−	0.0829413i	$-0.973569\pi$
$37$	−0.140783	+	0.888869i	−0.0231446	+	0.146129i	0.973410	+	0.229070i	$0.0735686\pi$
$38$	1.90380	−	12.0201i	0.308837	−	1.94992i
$39$	−1.10300	+	1.51815i	−0.176622	+	0.243099i
$40$	−5.94540	−	1.37065i	−0.940051	−	0.216718i
$41$	−2.97536	−	4.09523i	−0.464673	−	0.639567i	0.510797	−	0.859701i	$-0.329350\pi$
$41$	−2.97536	−	4.09523i	−0.464673	−	0.639567i	−0.975470	+	0.220134i	$0.929350\pi$
$42$	2.56133	+	2.89040i	0.395222	+	0.445999i
$43$	2.51007	+	2.51007i	0.382783	+	0.382783i	0.872104	−	0.489321i	$-0.162755\pi$
$43$	2.51007	+	2.51007i	0.382783	+	0.382783i	−0.489321	+	0.872104i	$0.662755\pi$
$44$	0.0517281	+	0.0168075i	0.00779831	+	0.00253382i
$45$	0.155282	−	2.23067i	0.0231481	−	0.332529i
$46$	−3.77008	−	11.6031i	−0.555868	−	1.71079i
$47$	2.12998	−	4.18032i	0.310689	−	0.609762i	−0.681877	−	0.731467i	$-0.738836\pi$
$47$	2.12998	−	4.18032i	0.310689	−	0.609762i	0.992566	+	0.121705i	$0.0388362\pi$
$48$	−4.19205	+	0.663955i	−0.605070	+	0.0958337i
$49$	3.40344	+	6.11691i	0.486205	+	0.873845i
$50$	−2.38046	−	6.89933i	−0.336648	−	0.975712i
$51$	4.64796			0.650844
$52$	0.0383655	+	0.242230i	0.00532033	+	0.0335913i
$53$	−2.34029	+	4.59308i	−0.321464	+	0.630908i	−0.994027	−	0.109131i	$-0.965193\pi$
$53$	−2.34029	+	4.59308i	−0.321464	+	0.630908i	0.672564	+	0.740039i	$0.265193\pi$
$54$	−0.451069	−	1.38825i	−0.0613827	−	0.188916i
$55$	−0.225411	−	0.902870i	−0.0303944	−	0.121743i
$56$	−7.20610	−	0.434971i	−0.962956	−	0.0581255i
$57$	−5.89540	+	5.89540i	−0.780864	+	0.780864i
$58$	0.340039	−	0.173258i	0.0446493	−	0.0227499i
$59$	1.18568	−	0.861445i	0.154362	−	0.112151i	−0.507923	−	0.861402i	$-0.669587\pi$
$59$	1.18568	−	0.861445i	0.154362	−	0.112151i	0.662285	+	0.749252i	$0.269587\pi$
$60$	−0.191794	−	0.220494i	−0.0247605	−	0.0284657i
$61$	−8.19257	+	11.2761i	−1.04895	+	1.44376i	−0.159236	+	0.987241i	$0.550903\pi$
$61$	−8.19257	+	11.2761i	−1.04895	+	1.44376i	−0.889715	+	0.456517i	$0.849097\pi$
$62$	9.02790	+	1.42988i	1.14654	+	0.181595i
$63$	−0.255686	−	2.63337i	−0.0322134	−	0.331773i
$64$	4.35616	−	5.99574i	0.544520	−	0.749467i
$65$	3.16595	−	2.75386i	0.392688	−	0.341574i
$66$	−0.357066	−	0.491460i	−0.0439518	−	0.0604945i
$67$	2.81639	+	5.52747i	0.344076	+	0.675288i	0.996592	−	0.0824874i	$-0.0262864\pi$
$67$	2.81639	+	5.52747i	0.344076	+	0.675288i	−0.652516	+	0.757775i	$0.726286\pi$
$68$	0.429534	−	0.429534i	0.0520886	−	0.0520886i
$69$	−2.58280	+	7.94904i	−0.310932	+	0.956952i
$70$	−4.12900	−	7.58456i	−0.493510	−	0.906529i
$71$	3.66863	+	11.2909i	0.435386	+	1.33998i	0.892690	+	0.450671i	$0.148815\pi$
$71$	3.66863	+	11.2909i	0.435386	+	1.33998i	−0.457304	+	0.889311i	$0.651185\pi$
$72$	2.43121	+	1.23876i	0.286521	+	0.145990i
$73$	15.4942	−	2.45404i	1.81346	−	0.287223i	0.844700	−	0.535240i	$-0.179779\pi$
$73$	15.4942	−	2.45404i	1.81346	−	0.287223i	0.968756	+	0.248016i	$0.0797787\pi$
$74$		−	1.31365i		−	0.152708i
$75$	−1.45887	+	4.78244i	−0.168455	+	0.552228i
$76$			1.08963i			0.124989i
$77$	−0.439861	−	1.00941i	−0.0501268	−	0.115032i
$78$	1.24355	−	2.44061i	0.140805	−	0.276345i
$79$	−13.5111	+	4.39003i	−1.52012	+	0.493917i	−0.945810	−	0.324720i	$-0.894730\pi$
$79$	−13.5111	+	4.39003i	−1.52012	+	0.493917i	−0.574311	+	0.818637i	$0.694730\pi$
$80$	9.46764	+	0.659066i	1.05851	+	0.0736858i
$81$	−0.309017	+	0.951057i	−0.0343352	+	0.105673i
$82$	5.22475	+	5.22475i	0.576977	+	0.576977i
$83$	−0.854913	−	1.67786i	−0.0938389	−	0.184169i	0.839316	−	0.543644i	$-0.182956\pi$
$83$	−0.854913	−	1.67786i	−0.0938389	−	0.184169i	−0.933155	+	0.359475i	$0.882956\pi$
$84$	−0.266988	−	0.219730i	−0.0291307	−	0.0239745i
$85$	−10.1275	−	2.33478i	−1.09848	−	0.253243i
$86$	−4.19198	−	3.04565i	−0.452033	−	0.328421i
$87$	−0.258230	−	0.0408996i	−0.0276852	−	0.00438490i
$88$	1.12158	+	0.177641i	0.119561	+	0.0189366i
$89$	3.53223	+	2.56631i	0.374415	+	0.272029i	0.759039	−	0.651045i	$-0.225669\pi$
$89$	3.53223	+	2.56631i	0.374415	+	0.272029i	−0.384624	+	0.923073i	$0.625669\pi$
$90$	0.285490	+	3.25145i	0.0300933	+	0.342733i
$91$	3.15498	−	3.83353i	0.330732	−	0.401863i
$92$	0.495913	+	0.973284i	0.0517025	+	0.101472i
$93$	−4.42784	−	4.42784i	−0.459145	−	0.459145i
$94$	−2.11627	+	6.51321i	−0.218277	+	0.671786i
$95$	15.8070	−	9.88416i	1.62176	−	1.01409i
$96$	0.702021	−	0.228101i	0.0716498	−	0.0232804i
$97$	−0.339728	+	0.666753i	−0.0344941	+	0.0676985i	−0.907610	−	0.419814i	$-0.862095\pi$
$97$	−0.339728	+	0.666753i	−0.0344941	+	0.0676985i	0.873116	+	0.487512i	$0.162095\pi$
$98$	−6.30357	−	8.04170i	−0.636756	−	0.812335i
$99$			0.416169i			0.0418266i
$100$	0.307143	+	0.576781i	0.0307143	+	0.0576781i
$101$			5.35018i			0.532363i	0.963923	+	0.266181i	$0.0857620\pi$
$101$			5.35018i			0.532363i	−0.963923	+	0.266181i	$0.914238\pi$
$102$	−6.70104	+	1.06134i	−0.663502	+	0.105088i
$103$	−10.4125	−	5.30542i	−1.02597	−	0.522758i	−0.141787	−	0.989897i	$-0.545285\pi$
$103$	−10.4125	−	5.30542i	−1.02597	−	0.522758i	−0.884184	+	0.467139i	$0.845285\pi$
$104$	1.58227	+	4.86973i	0.155155	+	0.477517i
$105$	−0.765686	+	5.86632i	−0.0747233	+	0.572494i
$106$	2.32523	−	7.15632i	0.225846	−	0.695083i
$107$	4.60673	−	4.60673i	0.445349	−	0.445349i	−0.448456	−	0.893805i	$-0.648026\pi$
$107$	4.60673	−	4.60673i	0.445349	−	0.445349i	0.893805	+	0.448456i	$0.148026\pi$
$108$	0.0593331	+	0.116448i	0.00570933	+	0.0112052i
$109$	3.39694	+	4.67549i	0.325368	+	0.447831i	0.940097	−	0.340908i	$-0.110734\pi$
$109$	3.39694	+	4.67549i	0.325368	+	0.447831i	−0.614728	+	0.788739i	$0.710734\pi$
$110$	0.531145	+	1.25021i	0.0506427	+	0.119203i
$111$	−0.528977	+	0.728074i	−0.0502082	+	0.0691057i
$112$	11.1768	−	1.08521i	1.05611	−	0.102543i
$113$	−2.06217	−	0.326616i	−0.193993	−	0.0307254i	0.0586820	−	0.998277i	$-0.481310\pi$
$113$	−2.06217	−	0.326616i	−0.193993	−	0.0307254i	−0.252675	+	0.967551i	$0.581310\pi$
$114$	7.15331	−	9.84568i	0.669969	−	0.922133i
$115$	9.62069	−	16.0229i	0.897134	−	1.49414i
$116$	−0.0276436	+	0.0200843i	−0.00256665	+	0.00186478i
$117$	−1.67201	+	0.851931i	−0.154577	+	0.0787611i
$118$	−1.51271	+	1.51271i	−0.139256	+	0.139256i
$119$	−12.2750	−	0.740937i	−1.12525	−	0.0679216i
$120$	−4.67513	−	3.92041i	−0.426779	−	0.357883i
$121$	−3.34567	−	10.2969i	−0.304151	−	0.936082i
$122$	9.23652	−	18.1277i	0.836236	−	1.64120i
$123$	−0.791868	−	4.99966i	−0.0714003	−	0.450804i
$124$	−0.818384			−0.0734930
$125$	5.58108	−	9.68770i	0.499187	−	0.866494i
$126$	0.969945	+	3.73819i	0.0864096	+	0.333024i
$127$	18.8890	−	2.99172i	1.67612	−	0.265472i	0.755279	−	0.655403i	$-0.227501\pi$
$127$	18.8890	−	2.99172i	1.67612	−	0.265472i	0.920844	+	0.389931i	$0.127501\pi$
$128$	−5.58148	+	10.9543i	−0.493338	+	0.968229i
$129$	1.09694	+	3.37604i	0.0965804	+	0.297244i
$130$	−3.93558	+	4.69322i	−0.345173	+	0.411623i
$131$	−11.4089	−	3.70697i	−0.996798	−	0.323879i	−0.235213	−	0.971944i	$-0.575579\pi$
$131$	−11.4089	−	3.70697i	−0.996798	−	0.323879i	−0.761585	+	0.648065i	$0.775579\pi$
$132$	0.0384597	+	0.0384597i	0.00334748	+	0.00334748i
$133$	16.5092	−	14.6296i	1.43153	−	1.26855i
$134$	−5.32261	−	7.32594i	−0.459803	−	0.632865i
$135$	1.15106	−	1.91704i	0.0990675	−	0.164993i
$136$	7.45456	−	10.2603i	0.639223	−	0.879815i
$137$	1.28211	−	8.09490i	0.109538	−	0.691594i	−0.870408	−	0.492331i	$-0.836145\pi$
$137$	1.28211	−	8.09490i	0.109538	−	0.691594i	0.979946	−	0.199264i	$-0.0638550\pi$
$138$	1.90854	−	12.0500i	0.162466	−	1.02577i
$139$	7.25124	+	5.26833i	0.615042	+	0.446854i	0.851186	−	0.524864i	$-0.175884\pi$
$139$	7.25124	+	5.26833i	0.615042	+	0.446854i	−0.236144	+	0.971718i	$0.575884\pi$
$140$	0.471368	+	0.612887i	0.0398378	+	0.0517984i
$141$	3.79565	−	2.75770i	0.319651	−	0.232240i
$142$	−7.86736	−	15.4406i	−0.660214	−	1.29574i
$143$	−0.552221	+	0.552221i	−0.0461790	+	0.0461790i
$144$	−4.03657	−	1.31156i	−0.336381	−	0.109297i
$145$	0.542117	+	0.218832i	0.0450203	+	0.0181730i
$146$	−21.7779	+	7.07606i	−1.80235	+	0.585619i
$147$	0.255464	+	6.99534i	0.0210703	+	0.576966i
$148$	0.0183993	+	0.116168i	0.00151241	+	0.00954899i
$149$		−	12.1978i		−	0.999285i	−0.866232	−	0.499642i	$-0.833465\pi$
$149$		−	12.1978i		−	0.999285i	0.866232	−	0.499642i	$-0.166535\pi$
$150$	1.01123	−	7.22805i	0.0825662	−	0.590168i
$151$	−11.7130			−0.953189			−0.476594	−	0.879123i	$-0.658129\pi$
$151$	−11.7130			−0.953189			−0.476594	+	0.879123i	$0.658129\pi$
$152$	3.55878	+	22.4693i	0.288655	+	1.82250i
$153$	4.14136	+	2.11013i	0.334809	+	0.170594i
$154$	0.864648	+	1.35484i	0.0696754	+	0.109176i
$155$	7.42367	+	11.8721i	0.596283	+	0.953589i
$156$	−0.0757863	+	0.233246i	−0.00606776	+	0.0186746i
$157$	4.27702	+	4.27702i	0.341343	+	0.341343i	0.856872	−	0.515529i	$-0.172404\pi$
$157$	4.27702	+	4.27702i	0.341343	+	0.341343i	−0.515529	+	0.856872i	$0.672404\pi$
$158$	18.4768	−	9.41440i	1.46994	−	0.748970i
$159$	−4.17043	+	3.02999i	−0.330737	+	0.240294i
$160$	−1.64423	+	0.144369i	−0.129987	+	0.0114134i
$161$	8.08819	−	20.5812i	0.637439	−	1.62203i
$162$	0.228346	−	1.44172i	0.0179405	−	0.113272i
$163$	−0.731741	−	0.115896i	−0.0573144	−	0.00907771i	0.127711	−	0.991811i	$-0.459237\pi$
$163$	−0.731741	−	0.115896i	−0.0573144	−	0.00907771i	−0.185026	+	0.982734i	$0.559237\pi$
$164$	−0.535215	−	0.388857i	−0.0417933	−	0.0303646i
$165$	0.209052	−	0.906797i	0.0162747	−	0.0705941i
$166$	1.61568	+	2.22379i	0.125401	+	0.172599i
$167$	−15.7649	+	8.03262i	−1.21992	+	0.621583i	−0.940895	−	0.338700i	$-0.890013\pi$
$167$	−15.7649	+	8.03262i	−1.21992	+	0.621583i	−0.279030	+	0.960282i	$0.590013\pi$
$168$	−6.22321	−	3.65906i	−0.480131	−	0.282303i
$169$	9.01468	+	2.92905i	0.693437	+	0.225311i
$170$	15.1341	+	1.05353i	1.16074	+	0.0808017i
$171$	−7.92929	+	2.57638i	−0.606368	+	0.197021i
$172$	0.413364	+	0.210619i	0.0315187	+	0.0160596i
$173$	5.22746	−	0.827948i	0.397436	−	0.0629477i	0.0454827	−	0.998965i	$-0.485517\pi$
$173$	5.22746	−	0.827948i	0.397436	−	0.0629477i	0.351954	+	0.936017i	$0.385517\pi$
$174$	0.381634			0.0289316
$175$	4.61516	−	12.3976i	0.348873	−	0.937170i
$176$	−1.76635			−0.133144
$177$	1.44753	−	0.229267i	0.108803	−	0.0172328i
$178$	−5.67848	−	2.89333i	−0.425620	−	0.216864i
$179$	−18.9700	+	6.16371i	−1.41788	+	0.460697i	−0.914928	−	0.403617i	$-0.867753\pi$
$179$	−18.9700	+	6.16371i	−1.41788	+	0.460697i	−0.502953	+	0.864314i	$0.667753\pi$
$180$	−0.0707873	−	0.283534i	−0.00527617	−	0.0211334i
$181$	−7.43938	−	2.41720i	−0.552965	−	0.179669i	0.0191884	−	0.999816i	$-0.493892\pi$
$181$	−7.43938	−	2.41720i	−0.552965	−	0.179669i	−0.572153	+	0.820147i	$0.693892\pi$
$182$	−3.67322	+	6.24729i	−0.272277	+	0.463080i
$183$	−12.4189	+	6.32773i	−0.918030	+	0.467760i
$184$	13.4050	+	18.4504i	0.988232	+	1.36019i
$185$	1.51832	−	1.32069i	0.111629	−	0.0970993i
$186$	7.39477	+	5.37261i	0.542211	+	0.393939i
$187$	1.91052	+	0.302597i	0.139711	+	0.0221281i
$188$	0.0959204	−	0.605618i	0.00699572	−	0.0441692i
$189$	0.967706	−	2.46243i	0.0703903	−	0.179115i
$190$	−20.5322	+	17.8596i	−1.48956	+	1.29567i
$191$	6.20010	−	4.50464i	0.448623	−	0.325944i	−0.340429	−	0.940270i	$-0.610572\pi$
$191$	6.20010	−	4.50464i	0.448623	−	0.325944i	0.789052	+	0.614326i	$0.210572\pi$
$192$	6.60337	−	3.36459i	0.476558	−	0.242818i
$193$	−9.74471	−	9.74471i	−0.701440	−	0.701440i	0.263280	−	0.964720i	$-0.415196\pi$
$193$	−9.74471	−	9.74471i	−0.701440	−	0.701440i	−0.964720	+	0.263280i	$0.915196\pi$
$194$	0.337541	−	1.03885i	0.0242341	−	0.0745848i
$195$	4.07111	−	1.01639i	0.291538	−	0.0727855i
$196$	0.670072	+	0.622855i	0.0478623	+	0.0444897i
$197$	−19.7937	−	10.0854i	−1.41024	−	0.718555i	−0.427584	−	0.903975i	$-0.640635\pi$
$197$	−19.7937	−	10.0854i	−1.41024	−	0.718555i	−0.982659	+	0.185420i	$0.940635\pi$
$198$	−0.0950305	−	0.599999i	−0.00675352	−	0.0426400i
$199$	−7.50163			−0.531776			−0.265888	−	0.964004i	$-0.585665\pi$
$199$	−7.50163			−0.531776			−0.265888	+	0.964004i	$0.585665\pi$
$200$	8.21740	+	10.8907i	0.581058	+	0.770087i
$201$			6.20362i			0.437570i
$202$	−1.22169	−	7.71345i	−0.0859578	−	0.542716i
$203$	0.675452	+	0.149178i	0.0474074	+	0.0104703i
$204$	0.577722	−	0.187713i	0.0404486	−	0.0131426i
$205$	−0.786037	+	11.2916i	−0.0548992	+	0.788640i
$206$	16.2233	+	5.27127i	1.13033	+	0.367267i
$207$	−5.91008	+	5.91008i	−0.410779	+	0.410779i
$208$	−3.61586	−	7.09652i	−0.250714	−	0.492055i
$209$	−2.80708	+	2.03947i	−0.194170	+	0.141073i
$210$	−0.235645	−	8.63242i	−0.0162611	−	0.595694i
$211$	16.2422	+	11.8007i	1.11816	+	0.812391i	0.983929	−	0.178559i	$-0.0571434\pi$
$211$	16.2422	+	11.8007i	1.11816	+	0.812391i	0.134232	+	0.990950i	$0.457143\pi$
$212$	−0.105392	+	0.665416i	−0.00723832	+	0.0457010i
$213$	−1.85718	+	11.7258i	−0.127252	+	0.803437i
$214$	−5.58968	+	7.69353i	−0.382102	+	0.525919i
$215$	−0.694276	−	7.90713i	−0.0473492	−	0.539261i
$216$	1.60384	+	2.20749i	0.109127	+	0.150201i
$217$	10.9878	+	12.3995i	0.745902	+	0.841734i
$218$	−5.96507	−	5.96507i	−0.404005	−	0.404005i
$219$	14.9195	+	4.84765i	1.00817	+	0.327574i
$220$	−0.0644811	−	0.103120i	−0.00434731	−	0.00695232i
$221$	2.69527	+	8.29519i	0.181303	+	0.557995i
$222$	0.596383	−	1.17047i	0.0400266	−	0.0785566i
$223$	−17.7503	+	2.81136i	−1.18864	+	0.188263i	−0.719266	−	0.694734i	$-0.755522\pi$
$223$	−17.7503	+	2.81136i	−1.18864	+	0.188263i	−0.469378	+	0.882997i	$0.655522\pi$
$224$	−1.89036	+	0.490491i	−0.126305	+	0.0327723i
$225$	−3.47104	+	3.59887i	−0.231403	+	0.239925i
$226$	3.04765			0.202727
$227$	0.636153	+	4.01651i	0.0422230	+	0.266585i	0.999764	−	0.0217107i	$-0.00691126\pi$
$227$	0.636153	+	4.01651i	0.0422230	+	0.266585i	−0.957541	+	0.288296i	$0.906911\pi$
$228$	−0.494681	+	0.970866i	−0.0327610	+	0.0642972i
$229$	−1.56516	−	4.81708i	−0.103429	−	0.318322i	0.885930	−	0.463820i	$-0.153522\pi$
$229$	−1.56516	−	4.81708i	−0.103429	−	0.318322i	−0.989359	+	0.145498i	$0.953522\pi$
$230$	−10.2116	+	25.2973i	−0.673331	+	1.66805i
$231$	0.0663421	−	1.09908i	0.00436499	−	0.0723141i
$232$	−0.504444	+	0.504444i	−0.0331184	+	0.0331184i
$233$	−10.3393	+	5.26816i	−0.677353	+	0.345129i	−0.758592	−	0.651566i	$-0.774112\pi$
$233$	−10.3393	+	5.26816i	−0.677353	+	0.345129i	0.0812388	+	0.996695i	$0.474112\pi$
$234$	2.21603	−	1.61004i	0.144866	−	0.105252i
$235$	−9.65565	+	4.10215i	−0.629865	+	0.267594i
$236$	0.112584	−	0.154959i	0.00732862	−	0.0100870i
$237$	−14.0315	−	2.22238i	−0.911447	−	0.144359i
$238$	17.8663	−	1.73472i	1.15810	−	0.112445i
$239$	14.2563	−	19.6221i	0.922165	−	1.26925i	−0.0406738	−	0.999172i	$-0.512950\pi$
$239$	14.2563	−	19.6221i	0.922165	−	1.26925i	0.962838	−	0.270078i	$-0.0870496\pi$
$240$	8.13652	+	4.88545i	0.525210	+	0.315355i
$241$	0.453353	+	0.623986i	0.0292030	+	0.0401945i	0.823369	−	0.567507i	$-0.192092\pi$
$241$	0.453353	+	0.623986i	0.0292030	+	0.0401945i	−0.794166	+	0.607701i	$0.792092\pi$
$242$	7.17476	+	14.0813i	0.461211	+	0.905178i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−0.562904	+	1.73244i	−0.0360362	+	0.110908i
$245$	2.95729	−	15.3706i	0.188935	−	0.981990i
$246$	2.28330	+	7.02728i	0.145578	+	0.448043i
$247$	−13.9401	−	7.10285i	−0.886989	−	0.451943i
$248$	−16.8759	+	2.67288i	−1.07162	+	0.169728i
$249$		−	1.88311i		−	0.119337i
$250$	−5.83420	+	15.2413i	−0.368987	+	0.963947i
$251$			24.1536i			1.52456i	0.647245	+	0.762282i	$0.275921\pi$
$251$			24.1536i			1.52456i	−0.647245	+	0.762282i	$0.724079\pi$
$252$	−0.138132	−	0.316991i	−0.00870152	−	0.0199685i
$253$	−1.57916	+	3.09927i	−0.0992807	+	0.194849i
$254$	−26.5494	+	8.62642i	−1.66586	+	0.541270i
$255$	−7.96370	−	6.67810i	−0.498706	−	0.418199i
$256$	0.965220	−	2.97064i	0.0603262	−	0.185665i
$257$	−3.65966	−	3.65966i	−0.228283	−	0.228283i	0.583692	−	0.811975i	$-0.301608\pi$
$257$	−3.65966	−	3.65966i	−0.228283	−	0.228283i	−0.811975	+	0.583692i	$0.801608\pi$
$258$	−2.35239	−	4.61682i	−0.146453	−	0.287430i
$259$	1.51306	−	1.83848i	0.0940170	−	0.114237i
$260$	0.282297	−	0.470154i	0.0175073	−	0.0291577i
$261$	−0.211517	−	0.153676i	−0.0130926	−	0.00951230i
$262$	17.2949	+	2.73924i	1.06848	+	0.169231i
$263$	17.6459	+	2.79484i	1.08810	+	0.172337i	0.674611	−	0.738174i	$-0.264312\pi$
$263$	17.6459	+	2.79484i	1.08810	+	0.172337i	0.413485	+	0.910511i	$0.364312\pi$
$264$	0.918690	+	0.667467i	0.0565414	+	0.0410798i
$265$	10.6090	−	4.50719i	0.651709	−	0.276875i
$266$	−20.4610	+	24.8616i	−1.25454	+	1.52436i
$267$	1.98216	+	3.89020i	0.121306	+	0.238076i
$268$	0.573298	+	0.573298i	0.0350198	+	0.0350198i
$269$	3.47264	−	10.6877i	0.211730	−	0.651639i	−0.787639	−	0.616137i	$-0.788697\pi$
$269$	3.47264	−	10.6877i	0.211730	−	0.651639i	0.999370	−	0.0355024i	$-0.0113032\pi$
$270$	−1.22176	+	3.02668i	−0.0743537	+	0.184198i
$271$	21.9035	−	7.11688i	1.33054	−	0.432320i	0.444441	−	0.895808i	$-0.353402\pi$
$271$	21.9035	−	7.11688i	1.33054	−	0.432320i	0.886103	+	0.463488i	$0.153402\pi$
$272$	−8.95603	+	17.5772i	−0.543039	+	1.06577i
$273$	4.55149	−	1.98337i	0.275469	−	0.120039i
$274$			11.9633i			0.722731i
$275$	−0.911013	+	1.87082i	−0.0549361	+	0.112815i
$276$			1.09234i			0.0657513i
$277$	−3.46408	+	0.548656i	−0.208136	+	0.0329655i	−0.259632	−	0.965708i	$-0.583601\pi$
$277$	−3.46408	+	0.548656i	−0.208136	+	0.0329655i	0.0514956	+	0.998673i	$0.483601\pi$
$278$	−11.6572	−	5.93966i	−0.699155	−	0.356237i
$279$	−1.93504	−	5.95543i	−0.115848	−	0.356542i
$280$	11.7218	+	11.0989i	0.700512	+	0.663284i
$281$	−7.05813	+	21.7227i	−0.421053	+	1.29587i	0.485670	+	0.874142i	$0.338576\pi$
$281$	−7.05813	+	21.7227i	−0.421053	+	1.29587i	−0.906723	+	0.421726i	$0.861424\pi$
$282$	−4.84254	+	4.84254i	−0.288369	+	0.288369i
$283$	9.18616	+	18.0289i	0.546061	+	1.07170i	0.984898	+	0.173138i	$0.0553905\pi$
$283$	9.18616	+	18.0289i	0.546061	+	1.07170i	−0.438837	+	0.898567i	$0.644609\pi$
$284$	0.911992	+	1.25525i	0.0541167	+	0.0744853i
$285$	18.5714	−	1.63064i	1.10008	−	0.0965910i
$286$	0.670049	−	0.922244i	0.0396208	−	0.0545334i
$287$	1.29428	+	13.3301i	0.0763988	+	0.786848i
$288$	0.729061	+	0.115472i	0.0429603	+	0.00680425i
$289$	2.70587	−	3.72431i	0.159169	−	0.219077i
$290$	−0.831549	−	0.191704i	−0.0488302	−	0.0112573i
$291$	−0.605399	+	0.439848i	−0.0354891	+	0.0257844i
$292$	1.82675	−	0.930777i	0.106903	−	0.0544696i
$293$	−4.47042	+	4.47042i	−0.261165	+	0.261165i	−0.825527	−	0.564363i	$-0.809122\pi$
$293$	−4.47042	+	4.47042i	−0.261165	+	0.261165i	0.564363	+	0.825527i	$0.309122\pi$
$294$	−1.96566	−	10.0270i	−0.114640	−	0.584785i
$295$	−3.26922	−	0.227579i	−0.190341	−	0.0132501i
$296$	0.758824	+	2.33542i	0.0441058	+	0.135744i
$297$	−0.188937	+	0.370810i	−0.0109632	+	0.0215165i
$298$	2.78532	+	17.5858i	0.161349	+	1.01872i
$299$	−15.6843			−0.907048
$300$	0.0118132	+	0.653355i	0.000682037	+	0.0377215i
$301$	−2.35878	−	9.09080i	−0.135958	−	0.523985i
$302$	16.8868	−	2.67461i	0.971727	−	0.153906i
$303$	−2.42893	+	4.76704i	−0.139538	+	0.273859i
$304$	−10.9349	−	33.6543i	−0.627162	−	1.93021i
$305$	30.2383	−	7.54929i	1.73144	−	0.432271i
$306$	−6.45251	−	2.09655i	−0.368866	−	0.119852i
$307$	−0.580979	−	0.580979i	−0.0331582	−	0.0331582i	0.690333	−	0.723491i	$-0.257464\pi$
$307$	−0.580979	−	0.580979i	−0.0331582	−	0.0331582i	−0.723491	+	0.690333i	$0.757464\pi$
$308$	−0.0954389	−	0.107701i	−0.00543814	−	0.00613682i
$309$	−6.86897	−	9.45432i	−0.390762	−	0.537838i
$310$	−13.4138	−	15.4210i	−0.761851	−	0.875856i
$311$	−16.7207	+	23.0141i	−0.948144	+	1.30501i	0.00420336	+	0.999991i	$0.498662\pi$
$311$	−16.7207	+	23.0141i	−0.948144	+	1.30501i	−0.952347	+	0.305017i	$0.901338\pi$
$312$	−0.800998	+	5.05730i	−0.0453476	+	0.286313i
$313$	−1.81024	+	11.4294i	−0.102321	+	0.646027i	0.882216	+	0.470846i	$0.156051\pi$
$313$	−1.81024	+	11.4294i	−0.102321	+	0.646027i	−0.984536	+	0.175181i	$0.943949\pi$
$314$	−7.14290	−	5.18962i	−0.403097	−	0.292867i
$315$	−3.34549	+	4.87932i	−0.188497	+	0.274918i
$316$	−1.50208	+	1.09133i	−0.0844987	+	0.0613919i
$317$	−5.32979	−	10.4603i	−0.299351	−	0.587509i	0.691515	−	0.722362i	$-0.256944\pi$
$317$	−5.32979	−	10.4603i	−0.299351	−	0.587509i	−0.990866	+	0.134853i	$0.956944\pi$
$318$	5.32070	−	5.32070i	0.298370	−	0.298370i
$319$	−0.103482	−	0.0336232i	−0.00579386	−	0.00188254i
$320$	−16.0783	+	4.01411i	−0.898805	+	0.224396i
$321$	6.19604	−	2.01321i	0.345829	−	0.112367i
$322$	−6.96126	+	31.5192i	−0.387936	+	1.75650i
$323$	6.06209	+	38.2745i	0.337304	+	2.12965i
$324$			0.130692i			0.00726069i
$325$	−9.38117	+	0.169620i	−0.520373	+	0.00940880i
$326$	1.08143			0.0598948
$327$	0.904070	+	5.70808i	0.0499952	+	0.315657i
$328$	−12.3067	−	6.27059i	−0.679525	−	0.346235i
$329$	−10.4637	+	6.67786i	−0.576883	+	0.368162i
$330$	−0.0943306	+	1.35508i	−0.00519273	+	0.0745948i
$331$	6.86717	−	21.1350i	0.377454	−	1.16168i	−0.564355	−	0.825533i	$-0.690875\pi$
$331$	6.86717	−	21.1350i	0.377454	−	1.16168i	0.941808	−	0.336151i	$-0.109125\pi$
$332$	−0.174025	−	0.174025i	−0.00955084	−	0.00955084i
$333$	−0.801860	+	0.408568i	−0.0439417	+	0.0223894i
$334$	20.8943	−	15.1806i	1.14329	−	0.830646i
$335$	3.11623	−	13.5172i	0.170258	−	0.738522i
$336$	10.4513	+	4.10724i	0.570165	+	0.224068i
$337$	4.23714	−	26.7523i	0.230812	−	1.45729i	−0.551381	−	0.834253i	$-0.685899\pi$
$337$	4.23714	−	26.7523i	0.230812	−	1.45729i	0.782193	−	0.623036i	$-0.214101\pi$
$338$	−13.6655	−	2.16440i	−0.743303	−	0.117728i
$339$	−1.68913	−	1.22722i	−0.0917407	−	0.0666535i
$340$	−1.35310	+	0.118807i	−0.0733821	+	0.00644324i
$341$	−1.53178	−	2.10831i	−0.0829503	−	0.114171i
$342$	10.8435	−	5.52504i	0.586349	−	0.298760i
$343$	0.440470	−	18.5150i	0.0237832	−	0.999717i
$344$	9.21189	+	2.99312i	0.496672	+	0.161378i
$345$	15.8463	−	9.90878i	0.853138	−	0.533471i
$346$	−7.34746	+	2.38734i	−0.395002	+	0.128344i
$347$	4.10191	+	2.09003i	0.220202	+	0.112199i	0.560612	−	0.828078i	$-0.310566\pi$
$347$	4.10191	+	2.09003i	0.220202	+	0.112199i	−0.340410	+	0.940277i	$0.610566\pi$
$348$	−0.0337487	+	0.00534527i	−0.00180912	+	0.000286537i
$349$	−6.93398			−0.371167			−0.185584	−	0.982628i	$-0.559418\pi$
$349$	−6.93398			−0.371167			−0.185584	+	0.982628i	$0.559418\pi$
$350$	−3.82282	+	18.9277i	−0.204339	+	1.01173i
$351$	−1.87654			−0.100162
$352$	0.303413	−	0.0480559i	0.0161720	−	0.00256139i
$353$	−7.71310	−	3.93002i	−0.410527	−	0.209174i	0.236516	−	0.971628i	$-0.423995\pi$
$353$	−7.71310	−	3.93002i	−0.410527	−	0.209174i	−0.647043	+	0.762454i	$0.723995\pi$
$354$	−2.03458	+	0.661077i	−0.108137	+	0.0351358i
$355$	9.93678	−	24.6166i	0.527390	−	1.30651i
$356$	0.542685	+	0.176329i	0.0287622	+	0.00934542i
$357$	−10.6007	−	6.23291i	−0.561050	−	0.329881i
$358$	25.9419	−	13.2180i	1.37107	−	0.698595i
$359$	14.6124	+	20.1122i	0.771212	+	1.06148i	0.996198	+	0.0871204i	$0.0277665\pi$
$359$	14.6124	+	20.1122i	0.771212	+	1.06148i	−0.224986	+	0.974362i	$0.572234\pi$
$360$	−2.38575	−	5.61558i	−0.125740	−	0.295967i
$361$	−40.8646	−	29.6898i	−2.15077	−	1.56262i
$362$	11.2774	+	1.78617i	0.592730	+	0.0938791i
$363$	1.69369	−	10.6935i	0.0888954	−	0.561264i
$364$	0.237329	−	0.603909i	0.0124394	−	0.0316534i
$365$	−30.0733	−	18.0570i	−1.57411	−	0.945149i
$366$	16.4596	−	11.9586i	0.860357	−	0.625086i
$367$	−21.2245	+	10.8144i	−1.10791	+	0.564510i	−0.909540	−	0.415617i	$-0.863566\pi$
$367$	−21.2245	+	10.8144i	−1.10791	+	0.564510i	−0.198373	+	0.980127i	$0.563566\pi$
$368$	−25.0842	−	25.0842i	−1.30760	−	1.30760i
$369$	1.56424	−	4.81423i	0.0814309	−	0.250619i
$370$	−1.88742	+	2.25077i	−0.0981223	+	0.117012i
$371$	11.4969	−	7.33723i	0.596889	−	0.380930i
$372$	−0.729185	−	0.371538i	−0.0378065	−	0.0192634i
$373$	1.95355	+	12.3342i	0.101151	+	0.638643i	0.985221	+	0.171288i	$0.0547929\pi$
$373$	1.95355	+	12.3342i	0.101151	+	0.638643i	−0.884070	+	0.467355i	$0.845207\pi$
$374$	−2.82353			−0.146001
$375$	9.37090	−	6.09805i	0.483911	−	0.314902i
$376$		−	12.8017i		−	0.660200i
$377$	−0.0767498	−	0.484579i	−0.00395282	−	0.0249571i
$378$	−0.832875	+	3.77110i	−0.0428384	+	0.193964i
$379$	−9.17764	+	2.98200i	−0.471424	+	0.153175i	−0.535088	−	0.844797i	$-0.679721\pi$
$379$	−9.17764	+	2.98200i	−0.471424	+	0.153175i	0.0636639	+	0.997971i	$0.479721\pi$
$380$	1.56556	−	1.86694i	0.0803114	−	0.0957722i
$381$	18.1884	+	5.90977i	0.931819	+	0.302767i
$382$	−7.91018	+	7.91018i	−0.404720	+	0.404720i
$383$	4.84427	+	9.50742i	0.247531	+	0.485807i	0.981023	−	0.193891i	$-0.0621109\pi$
$383$	4.84427	+	9.50742i	0.247531	+	0.485807i	−0.733492	+	0.679698i	$0.762111\pi$
$384$	−9.94626	+	7.22638i	−0.507568	+	0.368770i
$385$	−0.696648	+	2.36148i	−0.0355045	+	0.120352i
$386$	16.2743	+	11.8240i	0.828339	+	0.601824i
$387$	−0.555308	+	3.50608i	−0.0282279	+	0.178224i
$388$	−0.0152991	+	0.0965950i	−0.000776696	+	0.00490387i
$389$	20.9363	−	28.8163i	1.06151	−	1.46105i	0.183129	−	0.983089i	$-0.441378\pi$
$389$	20.9363	−	28.8163i	1.06151	−	1.46105i	0.878383	−	0.477957i	$-0.158622\pi$
$390$	−5.63731	+	2.39498i	−0.285456	+	0.121274i
$391$	22.8344	+	31.4288i	1.15478	+	1.58942i
$392$	15.8519	+	10.6554i	0.800640	+	0.538181i
$393$	−8.48246	−	8.48246i	−0.427883	−	0.427883i
$394$	30.8399	+	10.0205i	1.55369	+	0.504825i
$395$	29.4572	+	11.8908i	1.48215	+	0.598289i
$396$	0.0168075	+	0.0517281i	0.000844608	+	0.00259944i
$397$	−8.45498	+	16.5938i	−0.424343	+	0.832820i	0.575544	+	0.817771i	$0.304791\pi$
$397$	−8.45498	+	16.5938i	−0.424343	+	0.832820i	−0.999887	+	0.0150493i	$0.995209\pi$
$398$	10.8152	−	1.71296i	0.542118	−	0.0858631i
$399$	21.3515	−	5.54006i	1.06891	−	0.277350i
$400$	−15.2747	−	14.7322i	−0.763735	−	0.736608i
$401$	6.35860			0.317533			0.158767	−	0.987316i	$-0.449248\pi$
$401$	6.35860			0.317533			0.158767	+	0.987316i	$0.449248\pi$
$402$	−1.41657	−	8.94387i	−0.0706521	−	0.446080i
$403$	5.33471	−	10.4700i	0.265741	−	0.521546i
$404$	0.216073	+	0.665005i	0.0107500	+	0.0330852i
$405$	1.89592	−	1.18553i	0.0942091	−	0.0589094i
$406$	−1.00788	−	0.0608368i	−0.0500200	−	0.00301928i
$407$	−0.264833	+	0.264833i	−0.0131273	+	0.0131273i
$408$	11.3001	−	5.75771i	0.559441	−	0.285049i
$409$	−24.6484	+	17.9081i	−1.21878	+	0.885499i	−0.995999	−	0.0893688i	$-0.971515\pi$
$409$	−24.6484	+	17.9081i	−1.21878	+	0.885499i	−0.222786	+	0.974867i	$0.571515\pi$
$410$	−1.44515	−	16.4588i	−0.0713707	−	0.812842i
$411$	4.81738	−	6.63055i	0.237624	−	0.327061i
$412$	−1.50849	−	0.238922i	−0.0743181	−	0.0117708i
$413$	−3.85941	+	0.374728i	−0.189909	+	0.0184392i
$414$	7.17112	−	9.87021i	0.352442	−	0.485094i
$415$	−0.945931	+	4.10313i	−0.0464339	+	0.201415i
$416$	0.814180	+	1.12062i	0.0399185	+	0.0549431i
$417$	4.06913	+	7.98611i	0.199266	+	0.391082i
$418$	3.58132	−	3.58132i	0.175168	−	0.175168i
$419$	8.14767	−	25.0759i	0.398040	−	1.22504i	−0.528529	−	0.848915i	$-0.677256\pi$
$419$	8.14767	−	25.0759i	0.398040	−	1.22504i	0.926569	−	0.376125i	$-0.122744\pi$
$420$	0.141747	+	0.760083i	0.00691653	+	0.0370882i
$421$	3.53800	+	10.8889i	0.172432	+	0.530690i	0.999507	−	0.0314010i	$-0.00999691\pi$
$421$	3.53800	+	10.8889i	0.172432	+	0.530690i	−0.827075	+	0.562091i	$0.809997\pi$
$422$	−26.1113	−	13.3044i	−1.27108	−	0.647648i
$423$	4.63392	−	0.733940i	0.225309	−	0.0356854i
$424$			14.0658i			0.683095i
$425$	13.9977	+	18.5514i	0.678986	+	0.899873i
$426$		−	17.3293i		−	0.839609i
$427$	33.8063	−	14.7315i	1.63600	−	0.712906i
$428$	0.386549	−	0.758646i	0.0186846	−	0.0366705i
$429$	−0.742735	+	0.241329i	−0.0358596	+	0.0116515i
$430$	2.80651	+	11.2413i	0.135342	+	0.542104i
$431$	9.96766	−	30.6773i	0.480125	−	1.47767i	−0.358794	−	0.933417i	$-0.616812\pi$
$431$	9.96766	−	30.6773i	0.480125	−	1.47767i	0.838919	−	0.544256i	$-0.183188\pi$
$432$	−3.00118	−	3.00118i	−0.144394	−	0.144394i
$433$	16.0348	+	31.4700i	0.770582	+	1.51235i	0.856556	+	0.516055i	$0.172600\pi$
$433$	16.0348	+	31.4700i	0.770582	+	1.51235i	−0.0859739	+	0.996297i	$0.527400\pi$
$434$	−18.6727	−	15.3676i	−0.896319	−	0.737668i
$435$	0.383682	+	0.441097i	0.0183961	+	0.0211490i
$436$	0.611052	+	0.443955i	0.0292641	+	0.0212616i
$437$	−68.8266	−	10.9011i	−3.29242	−	0.521468i
$438$	−22.6167	−	3.58213i	−1.08067	−	0.171161i
$439$	6.83761	+	4.96781i	0.326341	+	0.237101i	0.738877	−	0.673841i	$-0.235357\pi$
$439$	6.83761	+	4.96781i	0.326341	+	0.237101i	−0.412535	+	0.910942i	$0.635357\pi$
$440$	−1.66646	−	1.91583i	−0.0794454	−	0.0913338i
$441$	−2.94820	+	6.34887i	−0.140390	+	0.302327i
$442$	−5.77999	−	11.3439i	−0.274926	−	0.539573i
$443$	−15.6780	−	15.6780i	−0.744885	−	0.744885i	0.228629	−	0.973514i	$-0.426576\pi$
$443$	−15.6780	−	15.6780i	−0.744885	−	0.744885i	−0.973514	+	0.228629i	$0.926576\pi$
$444$	−0.0363455	+	0.111860i	−0.00172488	+	0.00530864i
$445$	−2.36481	−	9.47210i	−0.112103	−	0.449021i
$446$	24.9489	−	8.10639i	1.18136	−	0.383849i
$447$	5.53770	−	10.8683i	0.261924	−	0.514055i
$448$	−17.9755	+	7.83304i	−0.849263	+	0.370076i
$449$		−	31.4142i		−	1.48253i	−0.671213	−	0.741265i	$-0.734226\pi$
$449$		−	31.4142i		−	1.48253i	0.671213	−	0.741265i	$-0.265774\pi$
$450$	4.18248	−	5.98115i	0.197164	−	0.281954i
$451$		−	2.10664i		−	0.0991978i
$452$	−0.269510	+	0.0426862i	−0.0126767	+	0.00200779i
$453$	−10.4363	−	5.31758i	−0.490342	−	0.249842i
$454$	−1.83431	−	5.64542i	−0.0860883	−	0.264953i
$455$	−10.9136	+	2.03526i	−0.511638	+	0.0954145i
$456$	−7.02994	+	21.6359i	−0.329207	+	1.01319i
$457$	−0.136665	+	0.136665i	−0.00639294	+	0.00639294i	−0.710296	−	0.703903i	$-0.751439\pi$
$457$	−0.136665	+	0.136665i	−0.00639294	+	0.00639294i	0.703903	+	0.710296i	$0.251439\pi$
$458$	3.35649	+	6.58747i	0.156838	+	0.307812i
$459$	2.73200	+	3.76028i	0.127519	+	0.175515i
$460$	0.548710	−	2.38012i	0.0255837	−	0.110974i
$461$	17.4049	−	23.9558i	0.810626	−	1.11573i	−0.180600	−	0.983557i	$-0.557804\pi$
$461$	17.4049	−	23.9558i	0.810626	−	1.11573i	0.991226	−	0.132175i	$-0.0421959\pi$
$462$	0.155324	+	1.59971i	0.00722631	+	0.0744253i
$463$	3.99339	+	0.632491i	0.185589	+	0.0293943i	0.248537	−	0.968622i	$-0.420050\pi$
$463$	3.99339	+	0.632491i	0.185589	+	0.0293943i	−0.0629482	+	0.998017i	$0.520050\pi$
$464$	0.652247	−	0.897741i	0.0302798	−	0.0416766i
$465$	1.22472	+	13.9484i	0.0567951	+	0.646841i
$466$	13.7035	−	9.95615i	0.634801	−	0.461210i
$467$	14.2499	−	7.26070i	0.659408	−	0.335985i	−0.0920612	−	0.995753i	$-0.529346\pi$
$467$	14.2499	−	7.26070i	0.659408	−	0.335985i	0.751469	+	0.659768i	$0.229346\pi$
$468$	−0.173418	+	0.173418i	−0.00801623	+	0.00801623i
$469$	0.988928	−	16.3834i	0.0456644	−	0.756516i
$470$	12.9840	−	8.11896i	0.598908	−	0.374500i
$471$	1.86913	+	5.75258i	0.0861248	+	0.265065i
$472$	1.81550	−	3.56313i	0.0835653	−	0.164006i
$473$	0.231102	+	1.45912i	0.0106261	+	0.0670904i
$474$	20.7370			0.952482
$475$	−41.2847	−	5.77585i	−1.89427	−	0.265014i
$476$	−1.55566	+	0.403645i	−0.0713033	+	0.0185010i
$477$	−5.09147	+	0.806409i	−0.233122	+	0.0369229i
$478$	−16.0730	+	31.5450i	−0.735160	+	1.44283i
$479$	9.00398	+	27.7114i	0.411402	+	1.26617i	0.915430	+	0.402478i	$0.131851\pi$
$479$	9.00398	+	27.7114i	0.411402	+	1.26617i	−0.504027	+	0.863688i	$0.668149\pi$
$480$	−1.53056	−	0.617829i	−0.0698601	−	0.0281999i
$481$	−1.60613	−	0.521865i	−0.0732334	−	0.0237950i
$482$	−0.796091	−	0.796091i	−0.0362610	−	0.0362610i
$483$	16.5503	−	14.6661i	0.753066	−	0.667329i
$484$	−0.831705	−	1.14474i	−0.0378048	−	0.0520338i
$485$	1.54006	−	0.654285i	0.0699305	−	0.0297096i
$486$	0.857984	−	1.18091i	0.0389189	−	0.0535673i
$487$	2.10750	−	13.3062i	0.0955001	−	0.602964i	−0.892801	−	0.450451i	$-0.851263\pi$
$487$	2.10750	−	13.3062i	0.0955001	−	0.602964i	0.988301	−	0.152513i	$-0.0487366\pi$
$488$	−5.94943	+	37.5632i	−0.269318	+	1.70041i
$489$	−0.599370	−	0.435468i	−0.0271045	−	0.0196925i
$490$	−0.753780	+	22.8353i	−0.0340523	+	1.03159i
$491$	−5.14602	+	3.73880i	−0.232237	+	0.168730i	−0.697818	−	0.716276i	$-0.745845\pi$
$491$	−5.14602	+	3.73880i	−0.232237	+	0.168730i	0.465581	+	0.885005i	$0.345845\pi$
$492$	−0.300343	−	0.589456i	−0.0135405	−	0.0265747i
$493$	−0.859279	+	0.859279i	−0.0387000	+	0.0387000i
$494$	21.7196	+	7.05713i	0.977212	+	0.317516i
$495$	0.597944	−	0.713055i	0.0268756	−	0.0320494i
$496$	25.2766	−	8.21288i	1.13495	−	0.368769i
$497$	6.77393	−	30.6711i	0.303852	−	1.37579i
$498$	0.430000	+	2.71491i	0.0192687	+	0.121658i
$499$			35.6786i			1.59719i	0.601867	+	0.798597i	$0.294424\pi$
$499$			35.6786i			1.59719i	−0.601867	+	0.798597i	$0.705576\pi$
$500$	0.302456	−	1.42954i	0.0135263	−	0.0639310i
$501$	−17.6934			−0.790481
$502$	−5.51538	−	34.8227i	−0.246163	−	1.55421i
$503$	24.5666	+	12.5173i	1.09537	+	0.558118i	0.905781	−	0.423745i	$-0.139285\pi$
$503$	24.5666	+	12.5173i	1.09537	+	0.558118i	0.189588	+	0.981864i	$0.439285\pi$
$504$	−3.88374	−	6.08553i	−0.172996	−	0.271071i
$505$	7.68703	−	9.16687i	0.342068	−	0.407920i
$506$	1.56899	−	4.82886i	0.0697502	−	0.214669i
$507$	6.70238	+	6.70238i	0.297663	+	0.297663i
$508$	2.22700	−	1.13471i	0.0988069	−	0.0503446i
$509$	14.3025	−	10.3914i	0.633949	−	0.460591i	−0.223817	−	0.974631i	$-0.571852\pi$
$509$	14.3025	−	10.3914i	0.633949	−	0.460591i	0.857766	+	0.514040i	$0.171852\pi$
$510$	13.0063	+	7.80945i	0.575930	+	0.345808i
$511$	−38.6289	−	15.1807i	−1.70884	−	0.671555i
$512$	3.13325	−	19.7826i	0.138471	−	0.874274i
$513$	−8.23470	−	1.30425i	−0.363571	−	0.0575840i
$514$	6.11187	+	4.44053i	0.269583	+	0.195863i
$515$	10.2178	+	24.0506i	0.450248	+	1.05980i
$516$	0.272691	+	0.375327i	0.0120045	+	0.0165228i
$517$	1.73972	−	0.886431i	0.0765127	−	0.0389852i
$518$	−1.76160	+	2.99607i	−0.0774002	+	0.131640i
$519$	5.03358	+	1.63551i	0.220950	+	0.0717909i
$520$	4.28571	−	10.6171i	0.187941	−	0.465589i
$521$	−21.4046	+	6.95477i	−0.937751	+	0.304694i	−0.737729	−	0.675097i	$-0.764102\pi$
$521$	−21.4046	+	6.95477i	−0.937751	+	0.304694i	−0.200023	+	0.979791i	$0.564102\pi$
$522$	0.340039	+	0.173258i	0.0148831	+	0.00758331i
$523$	10.8475	−	1.71807i	0.474327	−	0.0751260i	0.0853057	−	0.996355i	$-0.472813\pi$
$523$	10.8475	−	1.71807i	0.474327	−	0.0751260i	0.389021	+	0.921229i	$0.372813\pi$
$524$	−1.56779			−0.0684891
$525$	9.74053	−	8.95110i	0.425111	−	0.390658i
$526$	−26.0787			−1.13708
$527$	−28.7467	+	4.55304i	−1.25223	+	0.198333i
$528$	−1.57383	−	0.801906i	−0.0684921	−	0.0348985i
$529$	−44.5646	+	14.4799i	−1.93759	+	0.629562i
$530$	−14.2661	+	8.92063i	−0.619678	+	0.387487i
$531$	1.39385	+	0.452889i	0.0604879	+	0.0196537i
$532$	1.46119	−	2.48514i	0.0633507	−	0.107745i
$533$	8.46367	−	4.31246i	0.366602	−	0.186793i
$534$	−3.74602	−	5.15595i	−0.162106	−	0.223120i
$535$	−14.5119	+	1.27420i	−0.627405	+	0.0550886i
$536$	13.6944	+	9.94959i	0.591509	+	0.429757i
$537$	−19.7006	−	3.12027i	−0.850144	−	0.134650i
$538$	−2.56608	+	16.2016i	−0.110631	+	0.698500i
$539$	−0.350412	+	2.89203i	−0.0150933	+	0.124569i
$540$	0.0656500	−	0.284768i	0.00282513	−	0.0122544i
$541$	−1.76714	+	1.28390i	−0.0759752	+	0.0551992i	−0.625125	−	0.780525i	$-0.714952\pi$
$541$	−1.76714	+	1.28390i	−0.0759752	+	0.0551992i	0.549149	+	0.835724i	$0.314952\pi$
$542$	−29.9536	+	15.2621i	−1.28662	+	0.655564i
$543$	−5.53115	−	5.53115i	−0.237364	−	0.237364i
$544$	1.06020	−	3.26297i	0.0454558	−	0.139898i
$545$	0.897413	−	12.8915i	0.0384409	−	0.552213i
$546$	−6.10907	+	3.89877i	−0.261444	+	0.166852i
$547$	16.6659	+	8.49172i	0.712584	+	0.363080i	0.772406	−	0.635129i	$-0.219053\pi$
$547$	16.6659	+	8.49172i	0.712584	+	0.363080i	−0.0598216	+	0.998209i	$0.519053\pi$
$548$	−0.167562	−	1.05794i	−0.00715788	−	0.0451931i
$549$	−13.9380			−0.594861
$550$	0.886229	−	2.90522i	0.0377889	−	0.123879i
$551$		−	2.17979i		−	0.0928622i
$552$	3.56765	+	22.5252i	0.151849	+	0.958737i
$553$	36.7023	+	8.10597i	1.56074	+	0.344701i
$554$	4.86894	−	1.58201i	0.206861	−	0.0672133i
$555$	1.95242	−	0.487441i	0.0828756	−	0.0206907i
$556$	1.11407	+	0.361982i	0.0472470	+	0.0153515i
$557$	8.99916	−	8.99916i	0.381307	−	0.381307i	−0.490266	−	0.871573i	$-0.663100\pi$
$557$	8.99916	−	8.99916i	0.381307	−	0.381307i	0.871573	+	0.490266i	$0.163100\pi$
$558$	4.14967	+	8.14419i	0.175670	+	0.344771i
$559$	−5.38911	+	3.91541i	−0.227935	+	0.165604i
$560$	−20.7093	−	14.1993i	−0.875128	−	0.600028i
$561$	1.56491	+	1.13697i	0.0660706	+	0.0480031i
$562$	5.21555	−	32.9297i	0.220005	−	1.38906i
$563$	−1.35290	+	8.54188i	−0.0570180	+	0.359997i	0.942639	+	0.333813i	$0.108336\pi$
$563$	−1.35290	+	8.54188i	−0.0570180	+	0.359997i	−0.999657	+	0.0261840i	$0.991664\pi$
$564$	0.360410	−	0.496062i	0.0151760	−	0.0208880i
$565$	3.06400	+	3.52250i	0.128903	+	0.148193i
$566$	−17.3607	−	23.8949i	−0.729723	−	1.00438i
$567$	1.98015	−	1.75471i	0.0831585	−	0.0736908i
$568$	22.9059	+	22.9059i	0.961111	+	0.961111i
$569$	28.6110	+	9.29629i	1.19944	+	0.389721i	0.839554	−	0.543277i	$-0.182816\pi$
$569$	28.6110	+	9.29629i	1.19944	+	0.389721i	0.359883	+	0.932997i	$0.382816\pi$
$570$	−26.4024	+	6.59163i	−1.10588	+	0.276093i
$571$	11.3398	+	34.9004i	0.474557	+	1.46054i	0.846554	+	0.532302i	$0.178673\pi$
$571$	11.3398	+	34.9004i	0.474557	+	1.46054i	−0.371998	+	0.928234i	$0.621327\pi$
$572$	−0.0463367	+	0.0909409i	−0.00193743	+	0.00380243i
$573$	7.56939	−	1.19887i	0.316216	−	0.0500837i
$574$	−4.90984	−	18.9226i	−0.204933	−	0.789815i
$575$	−39.5052	+	13.6304i	−1.64748	+	0.568427i
$576$	7.41114			0.308798
$577$	−1.91178	−	12.0705i	−0.0795883	−	0.502501i	−0.994991	−	0.0999621i	$-0.968128\pi$
$577$	−1.91178	−	12.0705i	−0.0795883	−	0.502501i	0.915403	−	0.402539i	$-0.131872\pi$
$578$	−3.05067	+	5.98728i	−0.126891	+	0.249038i
$579$	−4.25860	−	13.1066i	−0.176981	−	0.544692i
$580$	0.0762207	+	0.00530591i	0.00316489	+	0.000220316i
$581$	−0.300189	+	4.97319i	−0.0124539	+	0.206323i
$582$	0.772378	−	0.772378i	0.0320161	−	0.0320161i
$583$	−1.91150	+	0.973957i	−0.0791662	+	0.0403372i
$584$	34.6296	−	25.1599i	1.43298	−	1.04112i
$585$	4.08882	+	0.942632i	0.169052	+	0.0389730i
$586$	5.42428	−	7.46588i	0.224075	−	0.308413i
$587$	6.20023	+	0.982020i	0.255911	+	0.0405323i	0.283072	−	0.959099i	$-0.408647\pi$
$587$	6.20023	+	0.982020i	0.255911	+	0.0405323i	−0.0271607	+	0.999631i	$0.508647\pi$
$588$	0.314268	+	0.859174i	0.0129602	+	0.0354318i
$589$	30.6869	−	42.2369i	1.26443	−	1.74034i
$590$	4.76526	−	0.418408i	0.196183	−	0.0172256i
$591$	−13.0577	−	17.9723i	−0.537120	−	0.739282i
$592$	−1.73409	−	3.40334i	−0.0712706	−	0.139876i
$593$	22.1761	−	22.1761i	0.910661	−	0.910661i	−0.0856628	−	0.996324i	$-0.527301\pi$
$593$	22.1761	−	22.1761i	0.910661	−	0.910661i	0.996324	+	0.0856628i	$0.0273008\pi$
$594$	0.187721	−	0.577746i	0.00770228	−	0.0237052i
$595$	19.9671	+	18.9060i	0.818573	+	0.775070i
$596$	−0.492624	−	1.51614i	−0.0201787	−	0.0621035i
$597$	−6.68400	−	3.40567i	−0.273558	−	0.139385i
$598$	22.6124	−	3.58145i	0.924689	−	0.146456i
$599$			17.5767i			0.718164i	0.933306	+	0.359082i	$0.116910\pi$
$599$			17.5767i			0.718164i	−0.933306	+	0.359082i	$0.883090\pi$
$600$	2.37749	+	13.4343i	0.0970608	+	0.548452i
$601$		−	17.6745i		−	0.720959i	−0.932767	−	0.360480i	$-0.882613\pi$
$601$		−	17.6745i		−	0.720959i	0.932767	−	0.360480i	$-0.117387\pi$
$602$	5.47655	+	12.5678i	0.223207	+	0.512223i
$603$	−2.81639	+	5.52747i	−0.114692	+	0.225096i
$604$	−1.45588	+	0.473043i	−0.0592387	+	0.0192478i
$605$	−9.06200	+	22.4495i	−0.368423	+	0.912700i
$606$	2.41330	−	7.42737i	0.0980335	−	0.301716i
$607$	−14.4849	−	14.4849i	−0.587923	−	0.587923i	0.349146	−	0.937068i	$-0.386472\pi$
$607$	−14.4849	−	14.4849i	−0.587923	−	0.587923i	−0.937068	+	0.349146i	$0.886472\pi$
$608$	2.79395	+	5.48344i	0.113310	+	0.222383i
$609$	0.534106	+	0.439568i	0.0216431	+	0.0178122i
$610$	−41.8712	+	17.7887i	−1.69531	+	0.720244i
$611$	7.12268	+	5.17493i	0.288153	+	0.209355i
$612$	0.599974	+	0.0950265i	0.0242525	+	0.00384122i
$613$	35.1774	+	5.57155i	1.42080	+	0.225033i	0.819083	−	0.573676i	$-0.194483\pi$
$613$	35.1774	+	5.57155i	1.42080	+	0.225033i	0.601718	+	0.798708i	$0.294483\pi$
$614$	0.970271	+	0.704943i	0.0391570	+	0.0284492i
$615$	−5.82664	+	9.70404i	−0.234953	+	0.391305i
$616$	−2.31981	−	1.90919i	−0.0934677	−	0.0769236i
$617$	3.02224	+	5.93148i	0.121671	+	0.238792i	0.943806	−	0.330500i	$-0.107217\pi$
$617$	3.02224	+	5.93148i	0.121671	+	0.238792i	−0.822135	+	0.569292i	$0.807217\pi$
$618$	12.0620	+	12.0620i	0.485203	+	0.485203i
$619$	−9.66535	+	29.7469i	−0.388483	+	1.19563i	0.545439	+	0.838151i	$0.316363\pi$
$619$	−9.66535	+	29.7469i	−0.388483	+	1.19563i	−0.933922	+	0.357477i	$0.883637\pi$
$620$	1.40220	+	1.17584i	0.0563137	+	0.0472228i
$621$	−7.94904	+	2.58280i	−0.318984	+	0.103644i
$622$	18.8514	−	36.9979i	0.755871	−	1.48348i
$623$	−4.61462	−	10.5898i	−0.184881	−	0.424271i
$624$		−	7.96461i		−	0.318839i
$625$	−23.4816	+	8.57989i	−0.939264	+	0.343196i
$626$		−	16.8913i		−	0.675112i
$627$	−3.42703	+	0.542788i	−0.136862	+	0.0216769i
$628$	0.704349	+	0.358884i	0.0281066	+	0.0143210i
$629$	1.29259	+	3.97820i	0.0515391	+	0.158621i
$630$	3.70908	−	7.79852i	0.147773	−	0.310701i
$631$	−9.13014	+	28.0997i	−0.363465	+	1.11863i	0.587472	+	0.809245i	$0.300123\pi$
$631$	−9.13014	+	28.0997i	−0.363465	+	1.11863i	−0.950937	+	0.309386i	$0.899877\pi$
$632$	−27.4102	+	27.4102i	−1.09032	+	1.09032i
$633$	9.11454	+	17.8883i	0.362270	+	0.710996i
$634$	10.0726	+	13.8638i	0.400035	+	0.550601i
$635$	−36.6623	−	22.0133i	−1.45490	−	0.873573i
$636$	−0.395997	+	0.545043i	−0.0157023	+	0.0216124i
$637$	−12.3364	+	4.51240i	−0.488786	+	0.178788i
$638$	0.156869	+	0.0248456i	0.00621051	+	0.000983647i
$639$	−6.97815	+	9.60460i	−0.276051	+	0.379952i
$640$	25.3021	−	10.7494i	1.00015	−	0.424908i
$641$	20.2118	−	14.6847i	0.798318	−	0.580012i	−0.112103	−	0.993697i	$-0.535759\pi$
$641$	20.2118	−	14.6847i	0.798318	−	0.580012i	0.910420	+	0.413685i	$0.135759\pi$
$642$	−8.47323	+	4.31733i	−0.334412	+	0.170391i
$643$	−3.25460	+	3.25460i	−0.128349	+	0.128349i	−0.768363	−	0.640014i	$-0.778928\pi$
$643$	−3.25460	+	3.25460i	−0.128349	+	0.128349i	0.640014	+	0.768363i	$0.278928\pi$
$644$	0.174132	−	2.88481i	0.00686175	−	0.113678i
$645$	2.97116	−	7.36050i	0.116989	−	0.289819i
$646$	−17.4797	−	53.7968i	−0.687728	−	2.11661i
$647$	12.8552	−	25.2298i	0.505390	−	0.991884i	−0.487531	−	0.873106i	$-0.662102\pi$
$647$	12.8552	−	25.2298i	0.505390	−	0.991884i	0.992921	−	0.118778i	$-0.0378978\pi$
$648$	0.426848	+	2.69501i	0.0167682	+	0.105870i
$649$	0.609929			0.0239418
$650$	13.4863	−	2.38669i	0.528975	−	0.0936138i
$651$	4.16096	+	16.0364i	0.163081	+	0.628517i
$652$	−0.0956330	+	0.0151468i	−0.00374528	+	0.000593194i
$653$	−17.0895	+	33.5400i	−0.668763	+	1.31252i	0.268291	+	0.963338i	$0.413541\pi$
$653$	−17.0895	+	33.5400i	−0.668763	+	1.31252i	−0.937054	+	0.349183i	$0.886459\pi$
$654$	−2.60683	−	8.02299i	−0.101935	−	0.313724i
$655$	14.2216	+	22.7435i	0.555684	+	0.888662i
$656$	20.4330	+	6.63910i	0.797776	+	0.259213i
$657$	11.0926	+	11.0926i	0.432764	+	0.432764i
$658$	13.5608	−	12.0169i	0.528657	−	0.468469i
$659$	−5.44817	−	7.49876i	−0.212231	−	0.292110i	0.689609	−	0.724182i	$-0.257783\pi$
$659$	−5.44817	−	7.49876i	−0.212231	−	0.292110i	−0.901839	+	0.432072i	$0.857783\pi$
$660$	−0.0106378	−	0.121154i	−0.000414075	−	0.00471591i
$661$	6.77368	−	9.32317i	0.263465	−	0.362629i	−0.656705	−	0.754148i	$-0.728050\pi$
$661$	6.77368	−	9.32317i	0.263465	−	0.362629i	0.920170	+	0.391519i	$0.128050\pi$
$662$	−5.07444	+	32.0388i	−0.197224	+	1.24522i
$663$	−1.36443	+	8.61469i	−0.0529902	+	0.334567i
$664$	−4.15694	−	3.02020i	−0.161321	−	0.117206i
$665$	−49.3060	+	1.34594i	−1.91201	+	0.0521934i
$666$	1.06276	−	0.772141i	0.0411812	−	0.0299199i
$667$	−0.992069	−	1.94705i	−0.0384131	−	0.0753899i
$668$	−1.63511	+	1.63511i	−0.0632641	+	0.0632641i
$669$	−17.0919	−	5.55350i	−0.660812	−	0.214711i
$670$	−1.40614	+	20.1995i	−0.0543239	+	0.780375i
$671$	−5.51668	+	1.79248i	−0.212969	+	0.0691978i
$672$	−1.90700	−	0.421176i	−0.0735642	−	0.0162472i
$673$	−0.905463	−	5.71687i	−0.0349030	−	0.220369i	0.964072	−	0.265643i	$-0.0855841\pi$
$673$	−0.905463	−	5.71687i	−0.0349030	−	0.220369i	−0.998975	+	0.0452735i	$0.985584\pi$
$674$			39.5368i			1.52290i
$675$	−4.72657	+	1.63080i	−0.181926	+	0.0627694i
$676$	1.23878			0.0476454
$677$	−0.752443	−	4.75074i	−0.0289187	−	0.182586i	0.969001	−	0.247058i	$-0.0794637\pi$
$677$	−0.752443	−	4.75074i	−0.0289187	−	0.182586i	−0.997920	+	0.0644719i	$0.979464\pi$
$678$	2.71547	+	1.38360i	0.104287	+	0.0531370i
$679$	1.66894	−	1.06511i	0.0640481	−	0.0408751i
$680$	−27.5143	+	6.86923i	−1.05513	+	0.263423i
$681$	−1.25664	+	3.86755i	−0.0481546	+	0.148205i
$682$	2.68981	+	2.68981i	0.102998	+	0.102998i
$683$	−6.25039	+	3.18473i	−0.239164	+	0.121860i	−0.569465	−	0.822015i	$-0.692850\pi$
$683$	−6.25039	+	3.18473i	−0.239164	+	0.121860i	0.330301	+	0.943876i	$0.392850\pi$
$684$	−0.881528	+	0.640467i	−0.0337061	+	0.0244889i
$685$	−13.8273	+	12.0275i	−0.528315	+	0.459548i
$686$	3.59279	+	26.7940i	0.137173	+	1.02300i
$687$	0.792337	−	5.00262i	0.0302296	−	0.190862i
$688$	−14.8809	−	2.35690i	−0.567327	−	0.0898558i
$689$	−7.82597	−	5.68590i	−0.298146	−	0.216616i
$690$	−20.5833	+	17.9041i	−0.783593	+	0.681598i
$691$	5.10167	+	7.02184i	0.194077	+	0.267124i	0.894954	−	0.446158i	$-0.147208\pi$
$691$	5.10167	+	7.02184i	0.194077	+	0.267124i	−0.700878	+	0.713282i	$0.747208\pi$
$692$	0.616314	−	0.314028i	0.0234287	−	0.0119375i
$693$	0.558083	−	0.949169i	0.0211998	−	0.0360559i
$694$	−6.39105	−	2.07658i	−0.242601	−	0.0788259i
$695$	−4.85466	−	19.4451i	−0.184148	−	0.737594i
$696$	−0.678476	+	0.220450i	−0.0257176	+	0.00835614i
$697$	−20.9635	−	10.6814i	−0.794048	−	0.404588i
$698$	9.99684	−	1.58334i	0.378386	−	0.0599305i
$699$	−11.6041			−0.438908
$700$	0.0729542	−	1.72736i	0.00275741	−	0.0652880i
$701$	33.2050			1.25414			0.627068	−	0.778964i	$-0.284255\pi$
$701$	33.2050			1.25414			0.627068	+	0.778964i	$0.284255\pi$
$702$	2.70544	−	0.428500i	0.102110	−	0.0161727i
$703$	−6.68539	−	3.40638i	−0.252144	−	0.128474i
$704$	2.93333	−	0.953098i	0.110554	−	0.0359212i
$705$	−10.4656	−	0.728535i	−0.394157	−	0.0274382i
$706$	12.0175	+	3.90473i	0.452285	+	0.146956i
$707$	7.17459	−	12.2023i	0.269828	−	0.458915i
$708$	0.170663	−	0.0869573i	0.00641392	−	0.00326806i
$709$	−9.99873	−	13.7621i	−0.375510	−	0.516846i	0.578878	−	0.815414i	$-0.303491\pi$
$709$	−9.99873	−	13.7621i	−0.375510	−	0.516846i	−0.954388	+	0.298569i	$0.903491\pi$
$710$	−8.70495	+	37.7592i	−0.326691	+	1.41708i
$711$	−11.4933	−	8.35034i	−0.431031	−	0.313162i
$712$	11.7666	+	1.86365i	0.440973	+	0.0698433i
$713$	8.18742	−	51.6933i	0.306621	−	1.93593i
$714$	16.7065	+	6.56547i	0.625225	+	0.245707i
$715$	1.73958	−	0.152742i	0.0650567	−	0.00571223i
$716$	−2.10896	+	1.53225i	−0.0788155	+	0.0572628i
$717$	21.6107	−	11.0112i	0.807068	−	0.411222i
$718$	−25.6595	−	25.6595i	−0.957603	−	0.957603i
$719$	−11.6254	+	35.7792i	−0.433553	+	1.33434i	0.461010	+	0.887395i	$0.347487\pi$
$719$	−11.6254	+	35.7792i	−0.433553	+	1.33434i	−0.894563	+	0.446943i	$0.852513\pi$
$720$	5.03174	+	8.04687i	0.187522	+	0.299889i
$721$	16.6334	+	26.0633i	0.619461	+	0.970649i
$722$	65.6947	+	33.4731i	2.44490	+	1.24574i
$723$	0.120656	+	0.761794i	0.00448726	+	0.0283314i
$724$	−1.02231			−0.0379937
$725$	−0.614436	−	1.15384i	−0.0228196	−	0.0428527i
$726$			15.8038i			0.586533i
$727$	−6.09483	−	38.4812i	−0.226045	−	1.42719i	−0.795892	−	0.605439i	$-0.792998\pi$
$727$	−6.09483	−	38.4812i	−0.226045	−	1.42719i	0.569847	−	0.821751i	$-0.307002\pi$
$728$	2.92158	−	13.2284i	0.108281	−	0.490276i
$729$	−0.951057	+	0.309017i	−0.0352243	+	0.0114451i
$730$	47.4804	+	19.1661i	1.75733	+	0.709368i
$731$	15.6917	+	5.09854i	0.580378	+	0.188576i
$732$	−1.28806	+	1.28806i	−0.0476082	+	0.0476082i
$733$	−0.669247	−	1.31347i	−0.0247192	−	0.0485141i	0.878317	−	0.478079i	$-0.158667\pi$
$733$	−0.669247	−	1.31347i	−0.0247192	−	0.0485141i	−0.903036	+	0.429565i	$0.858667\pi$
$734$	28.1304	−	20.4379i	1.03831	−	0.754377i
$735$	9.61306	−	12.3527i	0.354583	−	0.455636i
$736$	4.99126	+	3.62636i	0.183980	+	0.133669i
$737$	−0.403876	+	2.54997i	−0.0148770	+	0.0939294i
$738$	−1.15588	+	7.29795i	−0.0425486	+	0.268641i
$739$	−21.0866	+	29.0232i	−0.775684	+	1.06764i	0.220061	+	0.975486i	$0.429374\pi$
$739$	−21.0866	+	29.0232i	−0.775684	+	1.06764i	−0.995745	+	0.0921513i	$0.970626\pi$
$740$	0.135384	−	0.225476i	0.00497680	−	0.00828866i
$741$	−9.19611	−	12.6574i	−0.337828	−	0.464980i
$742$	−14.8998	+	13.2035i	−0.546990	+	0.484715i
$743$	−25.4637	−	25.4637i	−0.934173	−	0.934173i	0.0637902	−	0.997963i	$-0.479681\pi$
$743$	−25.4637	−	25.4637i	−0.934173	−	0.934173i	−0.997963	+	0.0637902i	$0.979681\pi$
$744$	−16.2500	−	5.27995i	−0.595755	−	0.193572i
$745$	−17.5256	+	20.8995i	−0.642089	+	0.765698i
$746$	−5.63294	−	17.3364i	−0.206237	−	0.634731i
$747$	0.854913	−	1.67786i	0.0312796	−	0.0613898i
$748$	0.249691	−	0.0395471i	0.00912960	−	0.00144599i
$749$	−16.6843	+	4.32907i	−0.609632	+	0.158181i
$750$	−12.1177	+	10.9315i	−0.442477	+	0.399161i
$751$	38.3937			1.40101			0.700504	−	0.713649i	$-0.252959\pi$
$751$	38.3937			1.40101			0.700504	+	0.713649i	$0.252959\pi$
$752$	3.11507	+	19.6677i	0.113595	+	0.717209i
$753$	−10.9655	+	21.5210i	−0.399606	+	0.784270i
$754$	0.221303	+	0.681101i	0.00805938	+	0.0248042i
$755$	20.0688	+	16.8290i	0.730377	+	0.612470i
$756$	0.0208339	−	0.345151i	0.000757720	−	0.0125530i
$757$	21.8668	−	21.8668i	0.794761	−	0.794761i	−0.187503	−	0.982264i	$-0.560039\pi$
$757$	21.8668	−	21.8668i	0.794761	−	0.794761i	0.982264	+	0.187503i	$0.0600395\pi$
$758$	12.5506	−	6.39487i	0.455860	−	0.232272i
$759$	−2.81408	+	2.04455i	−0.102144	+	0.0742123i
$760$	26.1859	−	43.6115i	0.949862	−	1.58196i
$761$	12.6129	−	17.3601i	0.457216	−	0.629303i	−0.516713	−	0.856159i	$-0.672845\pi$
$761$	12.6129	−	17.3601i	0.457216	−	0.629303i	0.973928	+	0.226856i	$0.0728445\pi$
$762$	−27.5720	−	4.36698i	−0.998828	−	0.158199i
$763$	−1.47767	−	15.2188i	−0.0534952	−	0.550959i
$764$	0.588722	−	0.810306i	0.0212992	−	0.0293158i
$765$	−4.06392	−	9.56567i	−0.146931	−	0.345848i
$766$	−9.15505	−	12.6009i	−0.330786	−	0.455287i
$767$	1.24857	+	2.45046i	0.0450833	+	0.0884810i
$768$	2.20866	−	2.20866i	0.0796981	−	0.0796981i
$769$	14.7100	−	45.2728i	0.530457	−	1.63258i	−0.222808	−	0.974862i	$-0.571522\pi$
$769$	14.7100	−	45.2728i	0.530457	−	1.63258i	0.753265	−	0.657717i	$-0.228478\pi$
$770$	0.465137	−	3.56366i	0.0167624	−	0.128425i
$771$	−1.59933	−	4.92223i	−0.0575985	−	0.177270i
$772$	−1.60478	−	0.817676i	−0.0577573	−	0.0294288i
$773$	19.6082	−	3.10563i	0.705257	−	0.111702i	0.206504	−	0.978446i	$-0.433791\pi$
$773$	19.6082	−	3.10563i	0.705257	−	0.111702i	0.498753	+	0.866744i	$0.333791\pi$
$774$		−	5.18157i		−	0.186248i
$775$	4.33805	−	31.0075i	0.155827	−	1.11382i
$776$			2.04186i			0.0732984i
$777$	2.18280	−	0.951180i	0.0783075	−	0.0341234i
$778$	−23.6041	+	46.3257i	−0.846249	+	1.66086i
$779$	40.1379	−	13.0416i	1.43809	−	0.467264i
$780$	0.464974	−	0.290750i	0.0166487	−	0.0104105i
$781$	−1.52677	+	4.69892i	−0.0546322	+	0.168141i
$782$	−40.0973	−	40.0973i	−1.43388	−	1.43388i
$783$	−0.118695	−	0.232953i	−0.00424183	−	0.00832505i
$784$	−26.9465	−	12.5130i	−0.962376	−	0.446894i
$785$	−1.18301	−	13.4733i	−0.0422233	−	0.480882i
$786$	14.1662	+	10.2924i	0.505293	+	0.367117i
$787$	39.8037	+	6.30429i	1.41885	+	0.224724i	0.818266	−	0.574839i	$-0.194935\pi$
$787$	39.8037	+	6.30429i	1.41885	+	0.224724i	0.600582	+	0.799563i	$0.294935\pi$
$788$	−2.86759	−	0.454181i	−0.102154	−	0.0161795i
$789$	14.4538	+	10.5013i	0.514569	+	0.373857i
$790$	−45.1842	−	10.4167i	−1.60758	−	0.370610i
$791$	4.26525	+	3.51029i	0.151655	+	0.124812i
$792$	0.515535	+	1.01179i	0.0183187	+	0.0359525i
$793$	−18.4946	−	18.4946i	−0.656761	−	0.656761i
$794$	8.40056	−	25.8543i	0.298125	−	0.917534i
$795$	11.4990	+	0.800471i	0.407826	+	0.0283898i
$796$	−0.932421	+	0.302962i	−0.0330488	+	0.0107382i
$797$	3.35389	−	6.58237i	0.118801	−	0.233160i	−0.823947	−	0.566668i	$-0.808232\pi$
$797$	3.35389	−	6.58237i	0.118801	−	0.233160i	0.942747	+	0.333508i	$0.108232\pi$
$798$	−29.5178	+	12.8627i	−1.04492	+	0.455336i
$799$		−	21.8067i		−	0.771466i
$800$	3.02461	+	2.11503i	0.106936	+	0.0747777i
$801$			4.36607i			0.154268i
$802$	−9.16731	+	1.45196i	−0.323709	+	0.0512705i
$803$	5.81700	+	2.96391i	0.205278	+	0.104594i
$804$	0.250541	+	0.771085i	0.00883589	+	0.0271941i
$805$	−43.4289	+	23.6425i	−1.53067	+	0.833287i
$806$	−5.30038	+	16.3129i	−0.186698	+	0.574597i
$807$	7.94625	−	7.94625i	0.279721	−	0.279721i
$808$	6.62760	+	13.0074i	0.233158	+	0.457598i
$809$	2.76300	+	3.80294i	0.0971418	+	0.133704i	0.854821	−	0.518923i	$-0.173667\pi$
$809$	2.76300	+	3.80294i	0.0971418	+	0.133704i	−0.757679	+	0.652627i	$0.773667\pi$
$810$	−2.46268	+	2.14212i	−0.0865296	+	0.0752666i
$811$	−26.2272	+	36.0986i	−0.920961	+	1.26759i	0.0423217	+	0.999104i	$0.486525\pi$
$811$	−26.2272	+	36.0986i	−0.920961	+	1.26759i	−0.963283	+	0.268490i	$0.913475\pi$
$812$	0.0899806	−	0.00873664i	0.00315770	−	0.000306596i
$813$	22.7472	+	3.60280i	0.797778	+	0.126356i
$814$	0.321342	−	0.442289i	0.0112630	−	0.0155022i
$815$	1.08723	+	1.24993i	0.0380840	+	0.0437830i
$816$	−15.9598	+	11.5954i	−0.558703	+	0.405922i
$817$	−26.3700	+	13.4362i	−0.922569	+	0.470073i
$818$	31.4468	−	31.4468i	1.09951	−	1.09951i
$819$	4.95584	+	0.299142i	0.173171	+	0.0104529i
$820$	0.358324	+	1.43524i	0.0125132	+	0.0501209i
$821$	−7.57152	−	23.3027i	−0.264248	−	0.813271i	−0.991866	−	0.127289i	$-0.959373\pi$
$821$	−7.57152	−	23.3027i	−0.264248	−	0.813271i	0.727618	−	0.685983i	$-0.240627\pi$
$822$	−5.43124	+	10.6594i	−0.189436	+	0.371790i
$823$	5.33049	+	33.6554i	0.185809	+	1.17315i	0.887547	+	0.460718i	$0.152408\pi$
$823$	5.33049	+	33.6554i	0.185809	+	1.17315i	−0.701737	+	0.712436i	$0.747592\pi$
$824$	−31.8870			−1.11084
$825$	−1.66105	+	1.25332i	−0.0578305	+	0.0436351i
$826$	5.47861	−	1.42153i	0.190625	−	0.0494614i
$827$	1.28829	−	0.204045i	0.0447981	−	0.00709533i	−0.133995	−	0.990982i	$-0.542781\pi$
$827$	1.28829	−	0.204045i	0.0447981	−	0.00709533i	0.178793	+	0.983887i	$0.442781\pi$
$828$	−0.495913	+	0.973284i	−0.0172342	+	0.0338239i
$829$	−1.23680	−	3.80649i	−0.0429560	−	0.132205i	0.927279	−	0.374372i	$-0.122142\pi$
$829$	−1.23680	−	3.80649i	−0.0429560	−	0.132205i	−0.970235	+	0.242167i	$0.922142\pi$
$830$	0.426833	−	6.13156i	0.0148156	−	0.212830i
$831$	−3.33560	−	1.08380i	−0.115711	−	0.0375967i
$832$	9.83395	+	9.83395i	0.340931	+	0.340931i
$833$	27.0023	+	18.1506i	0.935575	+	0.628883i
$834$	−7.69013	−	10.5846i	−0.266287	−	0.366513i
$835$	38.5523	+	8.88781i	1.33416	+	0.307575i
$836$	−0.266543	+	0.366865i	−0.00921858	+	0.0126883i
$837$	0.979578	−	6.18481i	0.0338592	−	0.213778i
$838$	−6.02066	+	38.0129i	−0.207980	+	1.31313i
$839$	2.22857	+	1.61915i	0.0769388	+	0.0558993i	0.625590	−	0.780152i	$-0.284858\pi$
$839$	2.22857	+	1.61915i	0.0769388	+	0.0558993i	−0.548651	+	0.836051i	$0.684858\pi$
$840$	5.40543	+	15.2107i	0.186505	+	0.524821i
$841$	−23.4062	+	17.0056i	−0.807110	+	0.586400i
$842$	−7.58723	−	14.8908i	−0.261473	−	0.513170i
$843$	−16.1507	+	16.1507i	−0.556261	+	0.556261i
$844$	2.49543	+	0.810813i	0.0858961	+	0.0279093i
$845$	−11.2371	−	17.9707i	−0.386570	−	0.618210i
$846$	−6.51321	+	2.11627i	−0.223929	+	0.0727588i
$847$	−6.17760	+	27.9710i	−0.212265	+	0.961094i
$848$	−3.42265	−	21.6097i	−0.117534	−	0.742081i
$849$			20.2343i			0.694438i
$850$	−24.4168	−	23.5495i	−0.837489	−	0.807742i
$851$	−7.52187			−0.257846
$852$	0.242719	+	1.53247i	0.00831543	+	0.0525016i
$853$	27.6944	+	14.1110i	0.948240	+	0.483152i	0.858500	−	0.512813i	$-0.171397\pi$
$853$	27.6944	+	14.1110i	0.948240	+	0.483152i	0.0897394	+	0.995965i	$0.471397\pi$
$854$	−45.3752	+	28.9582i	−1.55271	+	0.990928i
$855$	17.2876	+	6.97834i	0.591222	+	0.238654i
$856$	5.49327	−	16.9066i	0.187756	−	0.577854i
$857$	−11.7237	−	11.7237i	−0.400474	−	0.400474i	0.477926	−	0.878400i	$-0.341389\pi$
$857$	−11.7237	−	11.7237i	−0.400474	−	0.400474i	−0.878400	+	0.477926i	$0.841389\pi$
$858$	1.01571	−	0.517529i	0.0346757	−	0.0176682i
$859$	7.44362	−	5.40810i	0.253973	−	0.184522i	−0.453513	−	0.891250i	$-0.649829\pi$
$859$	7.44362	−	5.40810i	0.253973	−	0.184522i	0.707486	+	0.706728i	$0.249829\pi$
$860$	−0.405634	−	0.954784i	−0.0138320	−	0.0325579i
$861$	−4.89851	+	12.4648i	−0.166941	+	0.424798i
$862$	−7.36552	+	46.5041i	−0.250871	+	1.58394i
$863$	−34.0160	−	5.38761i	−1.15792	−	0.183396i	−0.452219	−	0.891907i	$-0.649367\pi$
$863$	−34.0160	−	5.38761i	−1.15792	−	0.183396i	−0.705700	+	0.708511i	$0.749367\pi$
$864$	0.597175	+	0.433873i	0.0203163	+	0.0147607i
$865$	−10.1462	−	6.09213i	−0.344981	−	0.207139i
$866$	−30.3037	−	41.7094i	−1.02976	−	1.41734i
$867$	4.10175	−	2.08995i	0.139303	−	0.0709783i
$868$	1.86651	+	1.09745i	0.0633535	+	0.0372500i
$869$	−5.62292	−	1.82700i	−0.190744	−	0.0619766i
$870$	−0.653883	−	0.548325i	−0.0221687	−	0.0185900i
$871$	−11.0716	+	3.59737i	−0.375146	+	0.121892i
$872$	14.0505	+	7.15909i	0.475810	+	0.242437i
$873$	−0.739102	+	0.117062i	−0.0250148	+	0.00396196i
$874$	101.718			3.44065
$875$	−25.7201	+	14.6108i	−0.869499	+	0.493934i
$876$	2.05021			0.0692703
$877$	23.0441	−	3.64982i	0.778143	−	0.123246i	0.245286	−	0.969451i	$-0.421118\pi$
$877$	23.0441	−	3.64982i	0.778143	−	0.123246i	0.532857	+	0.846205i	$0.321118\pi$
$878$	−10.9923	−	5.60085i	−0.370972	−	0.189019i
$879$	−6.01270	+	1.95364i	−0.202803	+	0.0658948i
$880$	3.02642	+	2.53786i	0.102021	+	0.0855511i
$881$	29.3374	+	9.53231i	0.988404	+	0.321152i	0.758222	−	0.651996i	$-0.226068\pi$
$881$	29.3374	+	9.53231i	0.988404	+	0.321152i	0.230181	+	0.973148i	$0.426068\pi$
$882$	2.80073	−	9.82649i	0.0943055	−	0.330875i
$883$	14.7501	−	7.51553i	0.496379	−	0.252918i	−0.187833	−	0.982201i	$-0.560146\pi$
$883$	14.7501	−	7.51553i	0.496379	−	0.252918i	0.684212	+	0.729283i	$0.260146\pi$
$884$	0.670022	+	0.922206i	0.0225353	+	0.0310171i
$885$	−2.80958	−	1.68697i	−0.0944430	−	0.0567069i
$886$	26.1833	+	19.0233i	0.879644	+	0.639099i
$887$	52.8136	+	8.36486i	1.77331	+	0.280864i	0.955578	−	0.294737i	$-0.0952322\pi$
$887$	52.8136	+	8.36486i	1.77331	+	0.280864i	0.817730	+	0.575602i	$0.195232\pi$
$888$	−0.384142	+	2.42537i	−0.0128909	+	0.0813902i
$889$	−47.0924	−	18.5068i	−1.57943	−	0.620698i
$890$	5.57230	+	13.1161i	0.186784	+	0.439653i
$891$	−0.336688	+	0.244618i	−0.0112795	+	0.00819502i
$892$	−2.09274	+	1.06631i	−0.0700702	+	0.0357026i
$893$	27.6593	+	27.6593i	0.925583	+	0.925583i
$894$	−5.50206	+	16.9336i	−0.184016	+	0.566344i
$895$	41.3586	+	16.6949i	1.38246	+	0.558049i
$896$	27.4195	−	17.4989i	0.916021	−	0.584598i
$897$	−13.9748	−	7.12054i	−0.466606	−	0.237748i
$898$	7.17331	+	45.2905i	0.239376	+	1.51136i
$899$	1.63717			0.0546026
$900$	−0.286091	+	0.587507i	−0.00953638	+	0.0195836i
$901$			23.9599i			0.798220i
$902$	0.481042	+	3.03718i	0.0160170	+	0.101127i
$903$	2.02545	−	9.17083i	0.0674026	−	0.305186i
$904$	−5.41816	+	1.76047i	−0.180205	+	0.0585523i
$905$	9.27348	+	14.8303i	0.308261	+	0.492977i
$906$	16.2605	+	5.28336i	0.540219	+	0.175528i
$907$	16.3898	−	16.3898i	0.544215	−	0.544215i	−0.380546	−	0.924762i	$-0.624264\pi$
$907$	16.3898	−	16.3898i	0.544215	−	0.544215i	0.924762	+	0.380546i	$0.124264\pi$
$908$	0.241283	+	0.473544i	0.00800725	+	0.0157151i
$909$	−4.32838	+	3.14476i	−0.143563	+	0.104305i
$910$	15.2696	−	5.42635i	0.506182	−	0.179882i
$911$	3.68609	+	2.67810i	0.122125	+	0.0887294i	0.647171	−	0.762345i	$-0.275952\pi$
$911$	3.68609	+	2.67810i	0.122125	+	0.0887294i	−0.525046	+	0.851074i	$0.675952\pi$
$912$	5.53563	−	34.9506i	0.183303	−	1.15733i
$913$	0.122596	−	0.774043i	0.00405735	−	0.0256171i
$914$	0.165826	−	0.228240i	0.00548504	−	0.00754951i
$915$	30.3698	+	7.00141i	1.00399	+	0.231460i
$916$	−0.389087	−	0.535532i	−0.0128558	−	0.0176945i
$917$	21.0495	+	23.7539i	0.695116	+	0.784423i
$918$	−4.79742	−	4.79742i	−0.158338	−	0.158338i
$919$	−8.27463	−	2.68859i	−0.272955	−	0.0886884i	0.169341	−	0.985557i	$-0.445836\pi$
$919$	−8.27463	−	2.68859i	−0.272955	−	0.0886884i	−0.442296	+	0.896869i	$0.645836\pi$
$920$	3.54137	−	50.8727i	0.116756	−	1.67722i
$921$	−0.253897	−	0.781415i	−0.00836619	−	0.0257485i
$922$	−19.6227	+	38.5118i	−0.646240	+	1.26832i
$923$	−22.0039	+	3.48507i	−0.724267	+	0.114713i
$924$	−0.0361416	−	0.139290i	−0.00118897	−	0.00458232i
$925$	−4.49901	+	0.0813460i	−0.147926	+	0.00267464i
$926$	−5.90177			−0.193944
$927$	−1.82812	−	11.5423i	−0.0600434	−	0.379099i
$928$	−0.0876149	+	0.171954i	−0.00287610	+	0.00564466i
$929$	−1.60093	−	4.92715i	−0.0525248	−	0.161655i	0.921353	−	0.388726i	$-0.127085\pi$
$929$	−1.60093	−	4.92715i	−0.0525248	−	0.161655i	−0.973878	+	0.227072i	$0.927085\pi$
$930$	−4.95076	−	19.8300i	−0.162342	−	0.650250i
$931$	−57.2713	+	11.2273i	−1.87699	+	0.367961i
$932$	−1.07238	+	1.07238i	−0.0351269	+	0.0351269i
$933$	−25.3464	+	12.9146i	−0.829804	+	0.422806i
$934$	−18.8864	+	13.7218i	−0.617983	+	0.448991i
$935$	−2.83868	−	3.26346i	−0.0928347	−	0.106727i
$936$	−3.00966	+	4.14244i	−0.0983738	+	0.135400i
$937$	10.6398	+	1.68518i	0.347588	+	0.0550525i	0.327788	−	0.944751i	$-0.393697\pi$
$937$	10.6398	+	1.68518i	0.347588	+	0.0550525i	0.0198003	+	0.999804i	$0.493697\pi$
$938$	2.31533	+	23.8461i	0.0755982	+	0.778602i
$939$	−6.80176	+	9.36182i	−0.221967	+	0.305511i
$940$	−1.03449	+	0.899835i	−0.0337413	+	0.0293494i
$941$	30.9497	+	42.5986i	1.00893	+	1.38867i	0.919682	+	0.392665i	$0.128447\pi$
$941$	30.9497	+	42.5986i	1.00893	+	1.38867i	0.0892490	+	0.996009i	$0.471553\pi$
$942$	−4.00833	−	7.86679i	−0.130598	−	0.256314i
$943$	29.9167	−	29.9167i	0.974221	−	0.974221i
$944$	−1.92220	+	5.91592i	−0.0625622	+	0.192547i
$945$	−5.19601	+	2.82868i	−0.169026	+	0.0920171i
$946$	−0.666368	−	2.05087i	−0.0216655	−	0.0666795i
$947$	−27.6661	−	14.0966i	−0.899026	−	0.458077i	−0.0575323	−	0.998344i	$-0.518323\pi$
$947$	−27.6661	−	14.0966i	−0.899026	−	0.458077i	−0.841494	+	0.540267i	$0.818323\pi$
$948$	−1.83382	+	0.290448i	−0.0595596	+	0.00943331i
$949$			29.4379i			0.955594i
$950$	60.8397	−	1.10004i	1.97390	−	0.0356899i
$951$		−	11.7399i		−	0.380692i
$952$	−30.7609	+	13.4044i	−0.996967	+	0.434440i
$953$	2.03269	−	3.98938i	0.0658453	−	0.129229i	−0.855738	−	0.517410i	$-0.826896\pi$
$953$	2.03269	−	3.98938i	0.0658453	−	0.129229i	0.921583	+	0.388181i	$0.126896\pi$
$954$	7.15632	−	2.32523i	0.231694	−	0.0752821i
$955$	−17.0953	−	1.19005i	−0.553190	−	0.0385090i
$956$	0.979538	−	3.01471i	0.0316805	−	0.0975027i
$957$	−0.0769382	−	0.0769382i	−0.00248706	−	0.00248706i
$958$	−19.3090	−	37.8960i	−0.623845	−	1.22436i
$959$	−13.7794	+	16.7430i	−0.444960	+	0.540659i
$960$	−16.1482	−	3.72280i	−0.521182	−	0.120153i
$961$	6.64321	+	4.82658i	0.214297	+	0.155696i
$962$	2.43476	+	0.385628i	0.0784998	+	0.0124331i
$963$	6.43469	+	1.01915i	0.207355	+	0.0328418i
$964$	0.0815503	+	0.0592498i	0.00262656	+	0.00190831i
$965$	2.69535	+	30.6974i	0.0867663	+	0.988184i
$966$	−20.5120	+	24.9235i	−0.659962	+	0.801901i
$967$	−14.8066	−	29.0596i	−0.476149	−	0.934495i	−0.996739	−	0.0806883i	$-0.974288\pi$
$967$	−14.8066	−	29.0596i	−0.476149	−	0.934495i	0.520590	−	0.853807i	$-0.325712\pi$
$968$	−20.8894	−	20.8894i	−0.671411	−	0.671411i
$969$	−11.9749	+	36.8550i	−0.384690	+	1.18395i
$970$	−2.07093	+	1.29496i	−0.0664935	+	0.0415787i
$971$	−20.9739	+	6.81483i	−0.673084	+	0.218698i	−0.625565	−	0.780172i	$-0.715131\pi$
$971$	−20.9739	+	6.81483i	−0.673084	+	0.218698i	−0.0475189	+	0.998870i	$0.515131\pi$
$972$	−0.0593331	+	0.116448i	−0.00190311	+	0.00373506i
$973$	−9.47326	−	21.7395i	−0.303699	−	0.696938i
$974$			19.6651i			0.630110i
$975$	−8.43569	−	4.10783i	−0.270158	−	0.131556i
$976$		−	59.1572i		−	1.89358i
$977$	−17.7059	+	2.80435i	−0.566463	+	0.0897190i	−0.433096	−	0.901348i	$-0.642579\pi$
$977$	−17.7059	+	2.80435i	−0.566463	+	0.0897190i	−0.133367	+	0.991067i	$0.542579\pi$
$978$	0.963560	+	0.490958i	0.0308113	+	0.0156991i
$979$	0.561492	+	1.72809i	0.0179454	+	0.0552301i
$980$	−0.253179	−	2.02993i	−0.00808751	−	0.0648438i
$981$	−1.78588	+	5.49637i	−0.0570187	+	0.175486i
$982$	6.56537	−	6.56537i	0.209509	−	0.209509i
$983$	−20.2940	−	39.8292i	−0.647278	−	1.27036i	−0.948493	−	0.316799i	$-0.897392\pi$
$983$	−20.2940	−	39.8292i	−0.647278	−	1.27036i	0.301215	−	0.953556i	$-0.402608\pi$
$984$	−8.11858	−	11.1743i	−0.258811	−	0.356223i
$985$	19.4236	+	45.7193i	0.618887	+	1.45674i
$986$	1.04263	−	1.43505i	0.0332039	−	0.0457013i
$987$	−12.3549	+	1.19960i	−0.393261	+	0.0381836i
$988$	−2.01956	−	0.319866i	−0.0642507	−	0.0101763i
$989$	−17.4393	+	24.0031i	−0.554536	+	0.763254i
$990$	−0.699244	+	1.16456i	−0.0222234	+	0.0370122i
$991$	−15.7260	+	11.4256i	−0.499552	+	0.362946i	−0.808846	−	0.588021i	$-0.799907\pi$
$991$	−15.7260	+	11.4256i	−0.499552	+	0.362946i	0.309294	+	0.950967i	$0.399907\pi$
$992$	−4.11843	+	2.09844i	−0.130760	+	0.0666257i
$993$	15.7138	−	15.7138i	0.498661	−	0.498661i
$994$	−2.76249	+	45.7658i	−0.0876210	+	1.45160i
$995$	12.8531	+	10.7782i	0.407471	+	0.341692i
$996$	−0.0760516	−	0.234063i	−0.00240979	−	0.00741656i
$997$	−15.8300	+	31.0682i	−0.501342	+	0.983939i	0.492201	+	0.870482i	$0.336193\pi$
$997$	−15.8300	+	31.0682i	−0.501342	+	0.983939i	−0.993543	+	0.113458i	$0.963807\pi$
$998$	−8.14705	−	51.4385i	−0.257890	−	1.62826i
$999$	−0.899949			−0.0284731

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bh.a.13.14	yes	320
7.6	odd	2	inner	525.2.bh.a.13.13	✓	320
25.2	odd	20	inner	525.2.bh.a.202.13	yes	320
175.27	even	20	inner	525.2.bh.a.202.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bh.a.13.13	✓	320	7.6	odd	2	inner
525.2.bh.a.13.14	yes	320	1.1	even	1	trivial
525.2.bh.a.202.13	yes	320	25.2	odd	20	inner
525.2.bh.a.202.14	yes	320	175.27	even	20	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.44172 + 0.228346i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.124296 - 0.0403862i) q^{4} +(-1.71338 - 1.43678i) q^{5} +(-1.38825 - 0.451069i) q^{6} +(-2.28073 - 1.34100i) q^{7} +(2.43121 - 1.23876i) q^{8} +(0.587785 + 0.809017i) q^{9} +O(q^{10})\)	\(q+(-1.44172 + 0.228346i) q^{2} +(0.891007 + 0.453990i) q^{3} +(0.124296 - 0.0403862i) q^{4} +(-1.71338 - 1.43678i) q^{5} +(-1.38825 - 0.451069i) q^{6} +(-2.28073 - 1.34100i) q^{7} +(2.43121 - 1.23876i) q^{8} +(0.587785 + 0.809017i) q^{9} +(2.79829 + 1.68019i) q^{10} +(0.336688 + 0.244618i) q^{11} +(0.129083 + 0.0204448i) q^{12} +(-0.293555 + 1.85344i) q^{13} +(3.59438 + 1.41255i) q^{14} +(-0.874345 - 2.05804i) q^{15} +(-3.43371 + 2.49474i) q^{16} +(4.14136 - 2.11013i) q^{17} +(-1.03216 - 1.03216i) q^{18} +(-2.57638 + 7.92929i) q^{19} +(-0.270992 - 0.109389i) q^{20} +(-1.42334 - 2.23027i) q^{21} +(-0.541267 - 0.275789i) q^{22} +(1.30750 + 8.25521i) q^{23} +2.72861 q^{24} +(0.871321 + 4.92349i) q^{25} -2.73916i q^{26} +(0.156434 + 0.987688i) q^{27} +(-0.337643 - 0.0745709i) q^{28} +(-0.248653 + 0.0807922i) q^{29} +(1.73050 + 2.76746i) q^{30} +(-5.95543 - 1.93504i) q^{31} +(0.521950 - 0.521950i) q^{32} +(0.188937 + 0.370810i) q^{33} +(-5.48883 + 3.98787i) q^{34} +(1.98102 + 5.57454i) q^{35} +(0.105732 + 0.0768191i) q^{36} +(-0.140783 + 0.888869i) q^{37} +(1.90380 - 12.0201i) q^{38} +(-1.10300 + 1.51815i) q^{39} +(-5.94540 - 1.37065i) q^{40} +(-2.97536 - 4.09523i) q^{41} +(2.56133 + 2.89040i) q^{42} +(2.51007 + 2.51007i) q^{43} +(0.0517281 + 0.0168075i) q^{44} +(0.155282 - 2.23067i) q^{45} +(-3.77008 - 11.6031i) q^{46} +(2.12998 - 4.18032i) q^{47} +(-4.19205 + 0.663955i) q^{48} +(3.40344 + 6.11691i) q^{49} +(-2.38046 - 6.89933i) q^{50} +4.64796 q^{51} +(0.0383655 + 0.242230i) q^{52} +(-2.34029 + 4.59308i) q^{53} +(-0.451069 - 1.38825i) q^{54} +(-0.225411 - 0.902870i) q^{55} +(-7.20610 - 0.434971i) q^{56} +(-5.89540 + 5.89540i) q^{57} +(0.340039 - 0.173258i) q^{58} +(1.18568 - 0.861445i) q^{59} +(-0.191794 - 0.220494i) q^{60} +(-8.19257 + 11.2761i) q^{61} +(9.02790 + 1.42988i) q^{62} +(-0.255686 - 2.63337i) q^{63} +(4.35616 - 5.99574i) q^{64} +(3.16595 - 2.75386i) q^{65} +(-0.357066 - 0.491460i) q^{66} +(2.81639 + 5.52747i) q^{67} +(0.429534 - 0.429534i) q^{68} +(-2.58280 + 7.94904i) q^{69} +(-4.12900 - 7.58456i) q^{70} +(3.66863 + 11.2909i) q^{71} +(2.43121 + 1.23876i) q^{72} +(15.4942 - 2.45404i) q^{73} -1.31365i q^{74} +(-1.45887 + 4.78244i) q^{75} +1.08963i q^{76} +(-0.439861 - 1.00941i) q^{77} +(1.24355 - 2.44061i) q^{78} +(-13.5111 + 4.39003i) q^{79} +(9.46764 + 0.659066i) q^{80} +(-0.309017 + 0.951057i) q^{81} +(5.22475 + 5.22475i) q^{82} +(-0.854913 - 1.67786i) q^{83} +(-0.266988 - 0.219730i) q^{84} +(-10.1275 - 2.33478i) q^{85} +(-4.19198 - 3.04565i) q^{86} +(-0.258230 - 0.0408996i) q^{87} +(1.12158 + 0.177641i) q^{88} +(3.53223 + 2.56631i) q^{89} +(0.285490 + 3.25145i) q^{90} +(3.15498 - 3.83353i) q^{91} +(0.495913 + 0.973284i) q^{92} +(-4.42784 - 4.42784i) q^{93} +(-2.11627 + 6.51321i) q^{94} +(15.8070 - 9.88416i) q^{95} +(0.702021 - 0.228101i) q^{96} +(-0.339728 + 0.666753i) q^{97} +(-6.30357 - 8.04170i) q^{98} +0.416169i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 8 q^{7} - 24 q^{8}+O(q^{10}) \) 320 * q + 8 * q^7 - 24 * q^8	\( 320 q + 8 q^{7} - 24 q^{8} - 8 q^{15} + 80 q^{16} - 24 q^{22} + 36 q^{28} - 40 q^{29} - 32 q^{30} - 48 q^{32} + 28 q^{35} + 80 q^{36} - 32 q^{37} + 16 q^{42} - 144 q^{43} - 288 q^{50} + 136 q^{53} - 8 q^{57} - 32 q^{58} - 40 q^{60} - 8 q^{63} - 120 q^{64} - 40 q^{65} + 32 q^{67} - 40 q^{70} - 24 q^{72} + 24 q^{77} + 8 q^{78} + 80 q^{81} - 80 q^{84} - 48 q^{85} - 56 q^{88} + 40 q^{92} + 96 q^{93} - 88 q^{95} - 184 q^{98}+O(q^{100}) \) 320 * q + 8 * q^7 - 24 * q^8 - 8 * q^15 + 80 * q^16 - 24 * q^22 + 36 * q^28 - 40 * q^29 - 32 * q^30 - 48 * q^32 + 28 * q^35 + 80 * q^36 - 32 * q^37 + 16 * q^42 - 144 * q^43 - 288 * q^50 + 136 * q^53 - 8 * q^57 - 32 * q^58 - 40 * q^60 - 8 * q^63 - 120 * q^64 - 40 * q^65 + 32 * q^67 - 40 * q^70 - 24 * q^72 + 24 * q^77 + 8 * q^78 + 80 * q^81 - 80 * q^84 - 48 * q^85 - 56 * q^88 + 40 * q^92 + 96 * q^93 - 88 * q^95 - 184 * q^98

Introduction

L-functions

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