LMFDB - Embedded newform 847.2.f.y.372.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.2
Character	$\chi$	$=$	847.372
Dual form			847.2.f.y.148.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.254493 + 0.783248i) q^{2} +(0.777181 - 0.564655i) q^{3} +(1.06932 + 0.776908i) q^{4} +(0.922616 + 2.83952i) q^{5} +(0.244478 + 0.752427i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.21319 + 1.60798i) q^{8} +(-0.641876 + 1.97549i) q^{9} +O(q^{10})$	\(q+(-0.254493 + 0.783248i) q^{2} +(0.777181 - 0.564655i) q^{3} +(1.06932 + 0.776908i) q^{4} +(0.922616 + 2.83952i) q^{5} +(0.244478 + 0.752427i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.21319 + 1.60798i) q^{8} +(-0.641876 + 1.97549i) q^{9} -2.45885 q^{10} +1.26974 q^{12} +(0.680283 - 2.09370i) q^{13} +(0.666271 - 0.484074i) q^{14} +(2.32039 + 1.68586i) q^{15} +(0.120686 + 0.371434i) q^{16} +(1.36174 + 4.19102i) q^{17} +(-1.38395 - 1.00550i) q^{18} +(1.39606 - 1.01430i) q^{19} +(-1.21947 + 3.75315i) q^{20} -0.960649 q^{21} -8.39774 q^{23} +(-0.812097 + 2.49938i) q^{24} +(-3.16657 + 2.30065i) q^{25} +(1.46676 + 1.06566i) q^{26} +(1.50719 + 4.63865i) q^{27} +(-0.408445 - 1.25706i) q^{28} +(-2.66405 - 1.93555i) q^{29} +(-1.91097 + 1.38840i) q^{30} +(2.31013 - 7.10984i) q^{31} -5.79294 q^{32} -3.62916 q^{34} +(0.922616 - 2.83952i) q^{35} +(-2.22115 + 1.61376i) q^{36} +(7.10374 + 5.16117i) q^{37} +(0.439159 + 1.35159i) q^{38} +(-0.653514 - 2.01131i) q^{39} +(-6.60780 - 4.80085i) q^{40} +(-4.36344 + 3.17023i) q^{41} +(0.244478 - 0.752427i) q^{42} +9.44629 q^{43} -6.20165 q^{45} +(2.13716 - 6.57751i) q^{46} +(4.36600 - 3.17208i) q^{47} +(0.303527 + 0.220525i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.996109 - 3.06571i) q^{50} +(3.42480 + 2.48826i) q^{51} +(2.35405 - 1.71032i) q^{52} +(2.90406 - 8.93778i) q^{53} -4.01678 q^{54} +2.73565 q^{56} +(0.512264 - 1.57659i) q^{57} +(2.19400 - 1.59403i) q^{58} +(-2.81102 - 2.04233i) q^{59} +(1.17149 + 3.60546i) q^{60} +(4.01544 + 12.3582i) q^{61} +(4.98086 + 3.61881i) q^{62} +(1.68045 - 1.22092i) q^{63} +(1.23289 - 3.79444i) q^{64} +6.57274 q^{65} +4.32138 q^{67} +(-1.79989 + 5.53950i) q^{68} +(-6.52656 + 4.74183i) q^{69} +(1.98925 + 1.44527i) q^{70} +(1.35982 + 4.18508i) q^{71} +(-1.75595 - 5.40425i) q^{72} +(-11.9338 - 8.67038i) q^{73} +(-5.85033 + 4.25051i) q^{74} +(-1.16193 + 3.57604i) q^{75} +2.28086 q^{76} +1.74167 q^{78} +(-2.22111 + 6.83589i) q^{79} +(-0.943348 + 0.685382i) q^{80} +(-1.25076 - 0.908732i) q^{81} +(-1.37261 - 4.22446i) q^{82} +(2.35917 + 7.26079i) q^{83} +(-1.02724 - 0.746336i) q^{84} +(-10.6441 + 7.73340i) q^{85} +(-2.40401 + 7.39879i) q^{86} -3.16337 q^{87} +10.8428 q^{89} +(1.57828 - 4.85743i) q^{90} +(-1.78101 + 1.29398i) q^{91} +(-8.97989 - 6.52427i) q^{92} +(-2.21922 - 6.83007i) q^{93} +(1.37341 + 4.22693i) q^{94} +(4.16815 + 3.02834i) q^{95} +(-4.50217 + 3.27102i) q^{96} +(0.882237 - 2.71525i) q^{97} -0.823556 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.254493	+	0.783248i	−0.179954	+	0.553840i	−0.999825	−	0.0187075i	$-0.994045\pi$
$2$	−0.254493	+	0.783248i	−0.179954	+	0.553840i	0.819871	+	0.572548i	$0.194045\pi$
$3$	0.777181	−	0.564655i	0.448706	−	0.326004i	−0.340379	−	0.940288i	$-0.610555\pi$
$3$	0.777181	−	0.564655i	0.448706	−	0.326004i	0.789085	+	0.614285i	$0.210555\pi$
$4$	1.06932	+	0.776908i	0.534661	+	0.388454i
$5$	0.922616	+	2.83952i	0.412606	+	1.26987i	0.914374	+	0.404870i	$0.132683\pi$
$5$	0.922616	+	2.83952i	0.412606	+	1.26987i	−0.501768	+	0.865002i	$0.667317\pi$
$6$	0.244478	+	0.752427i	0.0998078	+	0.307177i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−2.21319	+	1.60798i	−0.782480	+	0.568505i
$9$	−0.641876	+	1.97549i	−0.213959	+	0.658497i
$10$	−2.45885			−0.777556
$11$		0			0
$11$		0			0
$12$	1.26974			0.366543
$13$	0.680283	−	2.09370i	0.188677	−	0.580687i	−0.811316	−	0.584608i	$-0.801248\pi$
$13$	0.680283	−	2.09370i	0.188677	−	0.580687i	0.999992	+	0.00392126i	$0.00124818\pi$
$14$	0.666271	−	0.484074i	0.178068	−	0.129374i
$15$	2.32039	+	1.68586i	0.599122	+	0.435288i
$16$	0.120686	+	0.371434i	0.0301716	+	0.0928585i
$17$	1.36174	+	4.19102i	0.330271	+	1.01647i	0.969005	+	0.247042i	$0.0794587\pi$
$17$	1.36174	+	4.19102i	0.330271	+	1.01647i	−0.638733	+	0.769428i	$0.720541\pi$
$18$	−1.38395	−	1.00550i	−0.326199	−	0.236998i
$19$	1.39606	−	1.01430i	0.320278	−	0.232696i	−0.416016	−	0.909357i	$-0.636574\pi$
$19$	1.39606	−	1.01430i	0.320278	−	0.232696i	0.736294	+	0.676662i	$0.236574\pi$
$20$	−1.21947	+	3.75315i	−0.272682	+	0.839230i
$21$	−0.960649			−0.209631
$22$		0			0
$23$	−8.39774			−1.75105			−0.875525	−	0.483173i	$-0.839484\pi$
$23$	−8.39774			−1.75105			−0.875525	+	0.483173i	$0.839484\pi$
$24$	−0.812097	+	2.49938i	−0.165769	+	0.510183i
$25$	−3.16657	+	2.30065i	−0.633314	+	0.460130i
$26$	1.46676	+	1.06566i	0.287655	+	0.208993i
$27$	1.50719	+	4.63865i	0.290058	+	0.892708i
$28$	−0.408445	−	1.25706i	−0.0771888	−	0.237563i
$29$	−2.66405	−	1.93555i	−0.494702	−	0.359422i	0.312288	−	0.949988i	$-0.398905\pi$
$29$	−2.66405	−	1.93555i	−0.494702	−	0.359422i	−0.806990	+	0.590566i	$0.798905\pi$
$30$	−1.91097	+	1.38840i	−0.348894	+	0.253486i
$31$	2.31013	−	7.10984i	0.414911	−	1.27697i	−0.497419	−	0.867511i	$-0.665719\pi$
$31$	2.31013	−	7.10984i	0.414911	−	1.27697i	0.912330	−	0.409455i	$-0.134281\pi$
$32$	−5.79294			−1.02406
$33$		0			0
$34$	−3.62916			−0.622396
$35$	0.922616	−	2.83952i	0.155951	−	0.479967i
$36$	−2.22115	+	1.61376i	−0.370191	+	0.268960i
$37$	7.10374	+	5.16117i	1.16785	+	0.848491i	0.990750	−	0.135702i	$-0.0433290\pi$
$37$	7.10374	+	5.16117i	1.16785	+	0.848491i	0.177098	+	0.984193i	$0.443329\pi$
$38$	0.439159	+	1.35159i	0.0712411	+	0.219257i
$39$	−0.653514	−	2.01131i	−0.104646	−	0.322067i
$40$	−6.60780	−	4.80085i	−1.04479	−	0.759081i
$41$	−4.36344	+	3.17023i	−0.681456	+	0.495106i	−0.873840	−	0.486213i	$-0.838378\pi$
$41$	−4.36344	+	3.17023i	−0.681456	+	0.495106i	0.192385	+	0.981320i	$0.438378\pi$
$42$	0.244478	−	0.752427i	0.0377238	−	0.116102i
$43$	9.44629			1.44055			0.720273	−	0.693691i	$-0.244017\pi$
$43$	9.44629			1.44055			0.720273	+	0.693691i	$0.244017\pi$
$44$		0			0
$45$	−6.20165			−0.924487
$46$	2.13716	−	6.57751i	0.315108	−	0.969801i
$47$	4.36600	−	3.17208i	0.636846	−	0.462696i	−0.221919	−	0.975065i	$-0.571232\pi$
$47$	4.36600	−	3.17208i	0.636846	−	0.462696i	0.858765	+	0.512369i	$0.171232\pi$
$48$	0.303527	+	0.220525i	0.0438104	+	0.0318301i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.996109	−	3.06571i	−0.140871	−	0.433557i
$51$	3.42480	+	2.48826i	0.479568	+	0.348427i
$52$	2.35405	−	1.71032i	0.326448	−	0.237179i
$53$	2.90406	−	8.93778i	0.398903	−	1.22770i	−0.526976	−	0.849880i	$-0.676674\pi$
$53$	2.90406	−	8.93778i	0.398903	−	1.22770i	0.925880	−	0.377818i	$-0.123326\pi$
$54$	−4.01678			−0.546615
$55$		0			0
$56$	2.73565			0.365567
$57$	0.512264	−	1.57659i	0.0678510	−	0.208824i
$58$	2.19400	−	1.59403i	0.288086	−	0.209307i
$59$	−2.81102	−	2.04233i	−0.365964	−	0.265889i	0.389571	−	0.920996i	$-0.372623\pi$
$59$	−2.81102	−	2.04233i	−0.365964	−	0.265889i	−0.755535	+	0.655108i	$0.772623\pi$
$60$	1.17149	+	3.60546i	0.151238	+	0.465463i
$61$	4.01544	+	12.3582i	0.514124	+	1.58231i	0.784870	+	0.619660i	$0.212730\pi$
$61$	4.01544	+	12.3582i	0.514124	+	1.58231i	−0.270746	+	0.962651i	$0.587270\pi$
$62$	4.98086	+	3.61881i	0.632570	+	0.459589i
$63$	1.68045	−	1.22092i	0.211717	−	0.153821i
$64$	1.23289	−	3.79444i	0.154111	−	0.474305i
$65$	6.57274			0.815248
$66$		0			0
$67$	4.32138			0.527940			0.263970	−	0.964531i	$-0.414968\pi$
$67$	4.32138			0.527940			0.263970	+	0.964531i	$0.414968\pi$
$68$	−1.79989	+	5.53950i	−0.218269	+	0.671763i
$69$	−6.52656	+	4.74183i	−0.785706	+	0.570849i
$70$	1.98925	+	1.44527i	0.237761	+	0.172743i
$71$	1.35982	+	4.18508i	0.161380	+	0.496678i	0.998751	−	0.0499571i	$-0.0159085\pi$
$71$	1.35982	+	4.18508i	0.161380	+	0.496678i	−0.837371	+	0.546635i	$0.815908\pi$
$72$	−1.75595	−	5.40425i	−0.206941	−	0.636897i
$73$	−11.9338	−	8.67038i	−1.39674	−	1.01479i	−0.995087	−	0.0989997i	$-0.968436\pi$
$73$	−11.9338	−	8.67038i	−1.39674	−	1.01479i	−0.401653	−	0.915792i	$-0.631564\pi$
$74$	−5.85033	+	4.25051i	−0.680087	+	0.494112i
$75$	−1.16193	+	3.57604i	−0.134168	+	0.412926i
$76$	2.28086			0.261632
$77$		0			0
$78$	1.74167			0.197205
$79$	−2.22111	+	6.83589i	−0.249895	+	0.769097i	0.744898	+	0.667178i	$0.232498\pi$
$79$	−2.22111	+	6.83589i	−0.249895	+	0.769097i	−0.994793	+	0.101919i	$0.967502\pi$
$80$	−0.943348	+	0.685382i	−0.105469	+	0.0766280i
$81$	−1.25076	−	0.908732i	−0.138974	−	0.100970i
$82$	−1.37261	−	4.22446i	−0.151579	−	0.466514i
$83$	2.35917	+	7.26079i	0.258953	+	0.796976i	0.993025	+	0.117904i	$0.0376175\pi$
$83$	2.35917	+	7.26079i	0.258953	+	0.796976i	−0.734072	+	0.679072i	$0.762383\pi$
$84$	−1.02724	−	0.746336i	−0.112081	−	0.0814320i
$85$	−10.6441	+	7.73340i	−1.15452	+	0.838805i
$86$	−2.40401	+	7.39879i	−0.259231	+	0.797832i
$87$	−3.16337			−0.339149
$88$		0			0
$89$	10.8428			1.14934			0.574668	−	0.818386i	$-0.305131\pi$
$89$	10.8428			1.14934			0.574668	+	0.818386i	$0.305131\pi$
$90$	1.57828	−	4.85743i	0.166365	−	0.512018i
$91$	−1.78101	+	1.29398i	−0.186700	+	0.135646i
$92$	−8.97989	−	6.52427i	−0.936218	−	0.680202i
$93$	−2.21922	−	6.83007i	−0.230123	−	0.708245i
$94$	1.37341	+	4.22693i	0.141657	+	0.435975i
$95$	4.16815	+	3.02834i	0.427643	+	0.310701i
$96$	−4.50217	+	3.27102i	−0.459500	+	0.333847i
$97$	0.882237	−	2.71525i	0.0895776	−	0.275692i	−0.896225	−	0.443600i	$-0.853701\pi$
$97$	0.882237	−	2.71525i	0.0895776	−	0.275692i	0.985803	+	0.167908i	$0.0537012\pi$
$98$	−0.823556			−0.0831917
$99$		0			0
$100$	−5.17348			−0.517348
$101$	−4.51200	+	13.8865i	−0.448961	+	1.38176i	0.429120	+	0.903247i	$0.358824\pi$
$101$	−4.51200	+	13.8865i	−0.448961	+	1.38176i	−0.878081	+	0.478512i	$0.841176\pi$
$102$	−2.82052	+	2.04922i	−0.279273	+	0.202903i
$103$	0.0871857	+	0.0633441i	0.00859066	+	0.00624148i	0.592072	−	0.805885i	$-0.298310\pi$
$103$	0.0871857	+	0.0633441i	0.00859066	+	0.00624148i	−0.583482	+	0.812126i	$0.698310\pi$
$104$	1.86102	+	5.72763i	0.182488	+	0.561640i
$105$	−0.886310	−	2.72778i	−0.0864950	−	0.266204i
$106$	6.26144	+	4.54920i	0.608165	+	0.441857i
$107$	3.76114	−	2.73263i	0.363603	−	0.264173i	−0.390950	−	0.920412i	$-0.627854\pi$
$107$	3.76114	−	2.73263i	0.363603	−	0.264173i	0.754553	+	0.656239i	$0.227854\pi$
$108$	−1.99213	+	6.13116i	−0.191693	+	0.589971i
$109$	3.23140			0.309512			0.154756	−	0.987953i	$-0.450541\pi$
$109$	3.23140			0.309512			0.154756	+	0.987953i	$0.450541\pi$
$110$		0			0
$111$	8.43518			0.800632
$112$	0.120686	−	0.371434i	0.0114038	−	0.0350972i
$113$	9.15760	−	6.65338i	0.861474	−	0.625898i	−0.0668114	−	0.997766i	$-0.521283\pi$
$113$	9.15760	−	6.65338i	0.861474	−	0.625898i	0.928286	+	0.371868i	$0.121283\pi$
$114$	1.10449	+	0.802460i	0.103445	+	0.0751572i
$115$	−7.74789	−	23.8455i	−0.722494	−	2.22361i
$116$	−1.34499	−	4.13945i	−0.124879	−	0.384338i
$117$	3.69942	+	2.68779i	0.342012	+	0.248486i
$118$	2.31504	−	1.68197i	0.213116	−	0.154838i
$119$	1.36174	−	4.19102i	0.124831	−	0.384190i
$120$	−7.84629			−0.716265
$121$		0			0
$122$	−10.7015			−0.968866
$123$	−1.60110	+	4.92768i	−0.144366	+	0.444314i
$124$	7.99397	−	5.80796i	0.717880	−	0.521570i
$125$	2.62294	+	1.90567i	0.234602	+	0.170449i
$126$	0.528621	+	1.62693i	0.0470933	+	0.144938i
$127$	−6.17421	−	19.0023i	−0.547872	−	1.68618i	−0.714061	−	0.700084i	$-0.753146\pi$
$127$	−6.17421	−	19.0023i	−0.547872	−	1.68618i	0.166188	−	0.986094i	$-0.446854\pi$
$128$	−6.71495	−	4.87869i	−0.593523	−	0.431220i
$129$	7.34148	−	5.33390i	0.646381	−	0.469624i
$130$	−1.67271	+	5.14808i	−0.146707	+	0.451517i
$131$	8.45523			0.738737			0.369368	−	0.929283i	$-0.379574\pi$
$131$	8.45523			0.738737			0.369368	+	0.929283i	$0.379574\pi$
$132$		0			0
$133$	−1.72563			−0.149631
$134$	−1.09976	+	3.38471i	−0.0950048	+	0.292395i
$135$	−11.7810	+	8.55938i	−1.01395	+	0.736674i
$136$	−9.75285	−	7.08586i	−0.836300	−	0.607607i
$137$	2.58170	+	7.94566i	0.220570	+	0.678844i	0.998711	+	0.0507547i	$0.0161627\pi$
$137$	2.58170	+	7.94566i	0.220570	+	0.678844i	−0.778141	+	0.628089i	$0.783837\pi$
$138$	−2.05306	−	6.31868i	−0.174768	−	0.537882i
$139$	11.9034	+	8.64830i	1.00963	+	0.733540i	0.964132	−	0.265425i	$-0.0855122\pi$
$139$	11.9034	+	8.64830i	1.00963	+	0.733540i	0.0454990	+	0.998964i	$0.485512\pi$
$140$	3.19262	−	2.31958i	0.269826	−	0.196040i
$141$	1.60204	−	4.93057i	0.134916	−	0.415229i
$142$	−3.62402			−0.304121
$143$		0			0
$144$	−0.811230			−0.0676025
$145$	3.03813	−	9.35039i	0.252303	−	0.776508i
$146$	9.82812	−	7.14055i	0.813381	−	0.590956i
$147$	0.777181	+	0.564655i	0.0641008	+	0.0465720i
$148$	3.58644	+	11.0379i	0.294803	+	0.907311i
$149$	2.73255	+	8.40992i	0.223859	+	0.688968i	0.998405	+	0.0564503i	$0.0179783\pi$
$149$	2.73255	+	8.40992i	0.223859	+	0.688968i	−0.774546	+	0.632517i	$0.782022\pi$
$150$	−2.50523	−	1.82015i	−0.204551	−	0.148615i
$151$	16.1560	−	11.7380i	1.31476	−	0.955225i	0.314773	−	0.949167i	$-0.398071\pi$
$151$	16.1560	−	11.7380i	1.31476	−	0.955225i	0.999982	−	0.00605860i	$-0.00192852\pi$
$152$	−1.45878	+	4.48966i	−0.118323	+	0.364160i
$153$	−9.15338			−0.740007
$154$		0			0
$155$	22.3199			1.79278
$156$	0.863785	−	2.65846i	0.0691582	−	0.212847i
$157$	−10.5590	+	7.67158i	−0.842702	+	0.612259i	−0.923124	−	0.384502i	$-0.874373\pi$
$157$	−10.5590	+	7.67158i	−0.842702	+	0.612259i	0.0804223	+	0.996761i	$0.474373\pi$
$158$	−4.78894	−	3.47937i	−0.380987	−	0.276804i
$159$	−2.78978	−	8.58607i	−0.221244	−	0.680920i
$160$	−5.34466	−	16.4492i	−0.422533	−	1.30042i
$161$	6.79391	+	4.93607i	0.535435	+	0.389017i
$162$	1.03007	−	0.748392i	0.0809302	−	0.0587992i
$163$	1.84312	−	5.67255i	0.144365	−	0.444308i	−0.852564	−	0.522623i	$-0.824954\pi$
$163$	1.84312	−	5.67255i	0.144365	−	0.444308i	0.996929	+	0.0783141i	$0.0249537\pi$
$164$	−7.12891			−0.556674
$165$		0			0
$166$	−6.28740			−0.487997
$167$	4.09360	−	12.5988i	0.316772	−	0.974924i	−0.658247	−	0.752802i	$-0.728702\pi$
$167$	4.09360	−	12.5988i	0.316772	−	0.974924i	0.975019	−	0.222122i	$-0.0712983\pi$
$168$	2.12610	−	1.54470i	0.164032	−	0.119176i
$169$	6.59644	+	4.79259i	0.507418	+	0.368661i
$170$	−3.34832	−	10.3051i	−0.256804	−	0.790363i
$171$	1.10764	+	3.40896i	0.0847032	+	0.260690i
$172$	10.1011	+	7.33890i	0.770204	+	0.559586i
$173$	0.418841	−	0.304306i	0.0318439	−	0.0231359i	−0.571749	−	0.820428i	$-0.693735\pi$
$173$	0.418841	−	0.304306i	0.0318439	−	0.0231359i	0.603593	+	0.797292i	$0.293735\pi$
$174$	0.805054	−	2.47770i	0.0610310	−	0.187834i
$175$	3.91410			0.295878
$176$		0			0
$177$	−3.33789			−0.250891
$178$	−2.75942	+	8.49262i	−0.206827	+	0.636549i
$179$	−1.37221	+	0.996972i	−0.102564	+	0.0745172i	−0.637885	−	0.770131i	$-0.720191\pi$
$179$	−1.37221	+	0.996972i	−0.102564	+	0.0745172i	0.535321	+	0.844649i	$0.320191\pi$
$180$	−6.63157	−	4.81811i	−0.494288	−	0.359121i
$181$	−3.05494	−	9.40214i	−0.227072	−	0.698855i	−0.998075	−	0.0620236i	$-0.980245\pi$
$181$	−3.05494	−	9.40214i	−0.227072	−	0.698855i	0.771003	−	0.636832i	$-0.219755\pi$
$182$	−0.560251	−	1.72428i	−0.0415286	−	0.127812i
$183$	10.0989	+	7.33726i	0.746530	+	0.542386i
$184$	18.5858	−	13.5034i	1.37016	−	0.995481i
$185$	−8.10122	+	24.9330i	−0.595614	+	1.83311i
$186$	5.91441			0.433666
$187$		0			0
$188$	7.13308			0.520233
$189$	1.50719	−	4.63865i	0.109632	−	0.337412i
$190$	−3.43270	+	2.49400i	−0.249034	+	0.180934i
$191$	−18.7149	−	13.5972i	−1.35416	−	0.983857i	−0.998792	−	0.0491310i	$-0.984355\pi$
$191$	−18.7149	−	13.5972i	−1.35416	−	0.983857i	−0.355370	−	0.934726i	$-0.615645\pi$
$192$	−1.18437	−	3.64513i	−0.0854748	−	0.263064i
$193$	−7.13483	−	21.9587i	−0.513576	−	1.58062i	−0.785858	−	0.618407i	$-0.787778\pi$
$193$	−7.13483	−	21.9587i	−0.513576	−	1.58062i	0.272282	−	0.962217i	$-0.412222\pi$
$194$	1.90219	+	1.38202i	0.136569	+	0.0992234i
$195$	5.10821	−	3.71133i	0.365806	−	0.265774i
$196$	−0.408445	+	1.25706i	−0.0291746	+	0.0897903i
$197$	6.68989			0.476635			0.238318	−	0.971187i	$-0.423404\pi$
$197$	6.68989			0.476635			0.238318	+	0.971187i	$0.423404\pi$
$198$		0			0
$199$	−15.8233			−1.12169			−0.560844	−	0.827922i	$-0.689523\pi$
$199$	−15.8233			−1.12169			−0.560844	+	0.827922i	$0.689523\pi$
$200$	3.30883	−	10.1835i	0.233970	−	0.720085i
$201$	3.35849	−	2.44009i	0.236890	−	0.172111i
$202$	−9.72832	−	7.06803i	−0.684482	−	0.497305i
$203$	1.01758	+	3.13178i	0.0714199	+	0.219808i
$204$	1.72906	+	5.32151i	0.121059	+	0.372580i
$205$	−13.0277	−	9.46519i	−0.909895	−	0.661077i
$206$	−0.0718023	+	0.0521674i	−0.00500270	+	0.00363468i
$207$	5.39030	−	16.5897i	0.374652	−	1.15306i
$208$	0.859771			0.0596144
$209$		0			0
$210$	2.36209			0.163000
$211$	3.50811	−	10.7969i	0.241508	−	0.743286i	−0.754683	−	0.656090i	$-0.772209\pi$
$211$	3.50811	−	10.7969i	0.241508	−	0.743286i	0.996191	−	0.0871965i	$-0.0277908\pi$
$212$	10.0492	−	7.30118i	0.690183	−	0.501447i
$213$	3.41995	+	2.48474i	0.234331	+	0.170252i
$214$	1.18314	+	3.64134i	0.0808780	+	0.248917i
$215$	8.71530	+	26.8229i	0.594379	+	1.82931i
$216$	−10.7945	−	7.84268i	−0.734474	−	0.533627i
$217$	−6.04800	+	4.39413i	−0.410565	+	0.298293i
$218$	−0.822369	+	2.53099i	−0.0556979	+	0.171420i
$219$	−14.1705			−0.957552
$220$		0			0
$221$	9.70109			0.652566
$222$	−2.14669	+	6.60684i	−0.144077	+	0.443422i
$223$	8.64827	−	6.28334i	0.579131	−	0.420764i	−0.259280	−	0.965802i	$-0.583485\pi$
$223$	8.64827	−	6.28334i	0.579131	−	0.420764i	0.838411	+	0.545039i	$0.183485\pi$
$224$	4.68659	+	3.40501i	0.313136	+	0.227507i
$225$	−2.51236	−	7.73226i	−0.167491	−	0.515484i
$226$	2.88071	+	8.86591i	0.191622	+	0.589752i
$227$	3.02397	+	2.19704i	0.200708	+	0.145823i	0.683600	−	0.729857i	$-0.260414\pi$
$227$	3.02397	+	2.19704i	0.200708	+	0.145823i	−0.482892	+	0.875680i	$0.660414\pi$
$228$	1.77264	−	1.28790i	0.117396	−	0.0852931i
$229$	−7.31088	+	22.5006i	−0.483116	+	1.48688i	0.351574	+	0.936160i	$0.385647\pi$
$229$	−7.31088	+	22.5006i	−0.483116	+	1.48688i	−0.834690	+	0.550719i	$0.814353\pi$
$230$	20.6488			1.36154
$231$		0			0
$232$	9.00836			0.591428
$233$	1.19489	−	3.67750i	0.0782800	−	0.240921i	−0.904257	−	0.426989i	$-0.859574\pi$
$233$	1.19489	−	3.67750i	0.0782800	−	0.240921i	0.982537	+	0.186068i	$0.0595744\pi$
$234$	−3.04668	+	2.21354i	−0.199168	+	0.144704i
$235$	13.0353	+	9.47072i	0.850331	+	0.617802i
$236$	−1.41919	−	4.36782i	−0.0923814	−	0.284321i
$237$	2.13371	+	6.56689i	0.138599	+	0.426565i
$238$	2.93605	+	2.13317i	0.190316	+	0.138273i
$239$	8.14816	−	5.91998i	0.527060	−	0.382932i	−0.292197	−	0.956358i	$-0.594386\pi$
$239$	8.14816	−	5.91998i	0.527060	−	0.382932i	0.819257	+	0.573426i	$0.194386\pi$
$240$	−0.346147	+	1.06533i	−0.0223437	+	0.0687669i
$241$	13.4265			0.864878			0.432439	−	0.901663i	$-0.357653\pi$
$241$	13.4265			0.864878			0.432439	+	0.901663i	$0.357653\pi$
$242$		0			0
$243$	−16.1173			−1.03392
$244$	−5.30743	+	16.3346i	−0.339773	+	1.04571i
$245$	−2.41544	+	1.75492i	−0.154317	+	0.112118i
$246$	−3.45213	−	2.50812i	−0.220100	−	0.159912i
$247$	−1.17391	−	3.61294i	−0.0746944	−	0.229886i
$248$	6.31971	+	19.4501i	0.401302	+	1.23508i
$249$	5.93335	+	4.31083i	0.376011	+	0.273188i
$250$	−2.16013	+	1.56943i	−0.136619	+	0.0992594i
$251$	0.0236235	−	0.0727055i	0.00149110	−	0.00458913i	−0.950308	−	0.311311i	$-0.899232\pi$
$251$	0.0236235	−	0.0727055i	0.00149110	−	0.00458913i	0.951799	+	0.306722i	$0.0992320\pi$
$252$	2.74549			0.172950
$253$		0			0
$254$	16.4548			1.03246
$255$	−3.90570	+	12.0205i	−0.244584	+	0.752753i
$256$	11.9856	−	8.70807i	0.749102	−	0.544254i
$257$	−7.69532	−	5.59098i	−0.480021	−	0.348755i	0.321313	−	0.946973i	$-0.395876\pi$
$257$	−7.69532	−	5.59098i	−0.480021	−	0.348755i	−0.801334	+	0.598218i	$0.795876\pi$
$258$	2.30941	+	7.10764i	0.143778	+	0.442502i
$259$	−2.71339	−	8.35095i	−0.168602	−	0.518903i
$260$	7.02838	+	5.10641i	0.435881	+	0.316686i
$261$	5.53364	−	4.02043i	0.342524	−	0.248858i
$262$	−2.15179	+	6.62254i	−0.132938	+	0.409142i
$263$	14.7919			0.912107			0.456053	−	0.889952i	$-0.349263\pi$
$263$	14.7919			0.912107			0.456053	+	0.889952i	$0.349263\pi$
$264$		0			0
$265$	28.0583			1.72361
$266$	0.439159	−	1.35159i	0.0269266	−	0.0828715i
$267$	8.42684	−	6.12245i	0.515714	−	0.374688i
$268$	4.62095	+	3.35732i	0.282269	+	0.205081i
$269$	−9.28770	−	28.5846i	−0.566281	−	1.74283i	−0.664115	−	0.747631i	$-0.731191\pi$
$269$	−9.28770	−	28.5846i	−0.566281	−	1.74283i	0.0978340	−	0.995203i	$-0.468809\pi$
$270$	−3.70595	−	11.4057i	−0.225537	−	0.694131i
$271$	8.40718	+	6.10818i	0.510700	+	0.371045i	0.813089	−	0.582139i	$-0.197784\pi$
$271$	8.40718	+	6.10818i	0.510700	+	0.371045i	−0.302389	+	0.953185i	$0.597784\pi$
$272$	−1.39234	+	1.01160i	−0.0844231	+	0.0613370i
$273$	−0.653514	+	2.01131i	−0.0395524	+	0.121730i
$274$	−6.88045			−0.415663
$275$		0			0
$276$	−10.6630			−0.641835
$277$	8.68764	−	26.7378i	0.521990	−	1.60652i	−0.248203	−	0.968708i	$-0.579840\pi$
$277$	8.68764	−	26.7378i	0.521990	−	1.60652i	0.770193	−	0.637811i	$-0.220160\pi$
$278$	−9.80309	+	7.12236i	−0.587950	+	0.427171i
$279$	12.5626	+	9.12727i	0.752104	+	0.546436i
$280$	2.52396	+	7.76794i	0.150835	+	0.464223i
$281$	2.95732	+	9.10171i	0.176419	+	0.542962i	0.999695	−	0.0246786i	$-0.00785623\pi$
$281$	2.95732	+	9.10171i	0.176419	+	0.542962i	−0.823276	+	0.567641i	$0.807856\pi$
$282$	3.45415	+	2.50959i	0.205692	+	0.149444i
$283$	1.33913	−	0.972935i	0.0796030	−	0.0578350i	−0.547272	−	0.836955i	$-0.684334\pi$
$283$	1.33913	−	0.972935i	0.0796030	−	0.0578350i	0.626875	+	0.779120i	$0.284334\pi$
$284$	−1.79734	+	5.53166i	−0.106653	+	0.328244i
$285$	4.94937			0.293176
$286$		0			0
$287$	5.39351			0.318369
$288$	3.71835	−	11.4439i	0.219106	−	0.674338i
$289$	−1.95698	+	1.42183i	−0.115116	+	0.0836369i
$290$	6.55050	+	4.75922i	0.384659	+	0.279471i
$291$	−0.847520	−	2.60840i	−0.0496825	−	0.152907i
$292$	−6.02495	−	18.5429i	−0.352583	−	1.08514i
$293$	−3.78772	−	2.75194i	−0.221281	−	0.160770i	0.471622	−	0.881801i	$-0.343669\pi$
$293$	−3.78772	−	2.75194i	−0.221281	−	0.160770i	−0.692903	+	0.721031i	$0.743669\pi$
$294$	−0.640052	+	0.465025i	−0.0373286	+	0.0271208i
$295$	3.20574	−	9.86625i	0.186645	−	0.574435i
$296$	−24.0210			−1.39619
$297$		0			0
$298$	−7.28247			−0.421862
$299$	−5.71284	+	17.5823i	−0.330382	+	1.01681i
$300$	−4.02073	+	2.92123i	−0.232137	+	0.168657i
$301$	−7.64221	−	5.55239i	−0.440490	−	0.320034i
$302$	5.08219	+	15.6414i	0.292447	+	0.900060i
$303$	4.33445	+	13.3401i	0.249008	+	0.766367i
$304$	0.545230	+	0.396133i	0.0312711	+	0.0227198i
$305$	−31.3868	+	22.8038i	−1.79720	+	1.30574i
$306$	2.32947	−	7.16937i	0.133167	−	0.409846i
$307$	−16.9829			−0.969266			−0.484633	−	0.874718i	$-0.661047\pi$
$307$	−16.9829			−0.969266			−0.484633	+	0.874718i	$0.661047\pi$
$308$		0			0
$309$	0.103527			0.00588942
$310$	−5.68026	+	17.4820i	−0.322617	+	0.992913i
$311$	17.7382	−	12.8876i	1.00584	−	0.730787i	0.0425095	−	0.999096i	$-0.486465\pi$
$311$	17.7382	−	12.8876i	1.00584	−	0.730787i	0.963333	+	0.268309i	$0.0864647\pi$
$312$	4.68048	+	3.40057i	0.264980	+	0.192519i
$313$	3.10731	+	9.56331i	0.175636	+	0.540551i	0.999662	−	0.0260009i	$-0.00827727\pi$
$313$	3.10731	+	9.56331i	0.175636	+	0.540551i	−0.824026	+	0.566551i	$0.808277\pi$
$314$	−3.32156	−	10.2227i	−0.187446	−	0.576900i
$315$	5.01724	+	3.64524i	0.282689	+	0.205386i
$316$	−7.68594	+	5.58417i	−0.432368	+	0.314134i
$317$	7.28049	−	22.4070i	0.408913	−	1.25851i	−0.508670	−	0.860961i	$-0.669863\pi$
$317$	7.28049	−	22.4070i	0.408913	−	1.25851i	0.917583	−	0.397544i	$-0.130137\pi$
$318$	7.43500			0.416934
$319$		0			0
$320$	11.9119			0.665895
$321$	1.38009	−	4.24749i	0.0770293	−	0.237072i
$322$	−5.59517	+	4.06513i	−0.311806	+	0.226541i
$323$	6.15201	+	4.46970i	0.342307	+	0.248701i
$324$	−0.631467	−	1.94346i	−0.0350815	−	0.107970i
$325$	2.66269	+	8.19493i	0.147700	+	0.454573i
$326$	3.97395	+	2.88725i	0.220097	+	0.159910i
$327$	2.51139	−	1.82463i	0.138880	−	0.100902i
$328$	4.55948	−	14.0326i	0.251755	−	0.774822i
$329$	−5.39667			−0.297528
$330$		0			0
$331$	−20.8607			−1.14661			−0.573304	−	0.819343i	$-0.694339\pi$
$331$	−20.8607			−1.14661			−0.573304	+	0.819343i	$0.694339\pi$
$332$	−3.11825	+	9.59699i	−0.171136	+	0.526704i
$333$	−14.7556	+	10.7205i	−0.808600	+	0.587482i
$334$	8.82619	+	6.41260i	0.482948	+	0.350882i
$335$	3.98697	+	12.2706i	0.217832	+	0.670417i
$336$	−0.115937	−	0.356818i	−0.00632489	−	0.0194660i
$337$	−10.8039	−	7.84949i	−0.588526	−	0.427589i	0.253262	−	0.967398i	$-0.418497\pi$
$337$	−10.8039	−	7.84949i	−0.588526	−	0.427589i	−0.841788	+	0.539809i	$0.818497\pi$
$338$	−5.43254	+	3.94697i	−0.295491	+	0.214687i
$339$	3.36025	−	10.3418i	0.182503	−	0.561688i
$340$	−17.3901			−0.943112
$341$		0			0
$342$	−2.95195			−0.159623
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−20.9064	+	15.1894i	−1.12720	+	0.818958i
$345$	−19.4860	−	14.1574i	−1.04909	−	0.762210i
$346$	0.131755	+	0.405500i	0.00708319	+	0.0217998i
$347$	−0.492129	−	1.51462i	−0.0264189	−	0.0813089i	0.936978	−	0.349389i	$-0.113611\pi$
$347$	−0.492129	−	1.51462i	−0.0264189	−	0.0813089i	−0.963397	+	0.268080i	$0.913611\pi$
$348$	−3.38266	−	2.45765i	−0.181330	−	0.131744i
$349$	−5.36763	+	3.89981i	−0.287323	+	0.208752i	−0.722105	−	0.691783i	$-0.756825\pi$
$349$	−5.36763	+	3.89981i	−0.287323	+	0.208752i	0.434782	+	0.900536i	$0.356825\pi$
$350$	−0.996109	+	3.06571i	−0.0532443	+	0.163869i
$351$	10.7372			0.573111
$352$		0			0
$353$	−25.4141			−1.35265			−0.676327	−	0.736601i	$-0.736430\pi$
$353$	−25.4141			−1.35265			−0.676327	+	0.736601i	$0.736430\pi$
$354$	0.849468	−	2.61439i	0.0451487	−	0.138954i
$355$	−10.6290	+	7.72245i	−0.564131	+	0.409865i
$356$	11.5945	+	8.42388i	0.614506	+	0.446465i
$357$	−1.30816	−	4.02609i	−0.0692350	−	0.213084i
$358$	−0.431658	−	1.32851i	−0.0228138	−	0.0702138i
$359$	−13.0084	−	9.45113i	−0.686555	−	0.498811i	0.188971	−	0.981983i	$-0.439485\pi$
$359$	−13.0084	−	9.45113i	−0.686555	−	0.498811i	−0.875526	+	0.483171i	$0.839485\pi$
$360$	13.7254	−	9.97210i	0.723393	−	0.525576i
$361$	−4.95114	+	15.2380i	−0.260586	+	0.802002i
$362$	8.14167			0.427916
$363$		0			0
$364$	−2.90977			−0.152513
$365$	13.6095	−	41.8856i	0.712351	−	2.19239i
$366$	−8.31699	+	6.04264i	−0.434736	+	0.315854i
$367$	2.44814	+	1.77868i	0.127792	+	0.0928461i	0.649845	−	0.760067i	$-0.274834\pi$
$367$	2.44814	+	1.77868i	0.127792	+	0.0928461i	−0.522053	+	0.852913i	$0.674834\pi$
$368$	−1.01349	−	3.11921i	−0.0528319	−	0.162600i
$369$	−3.46197	−	10.6548i	−0.180223	−	0.554669i
$370$	−17.4670	−	12.6905i	−0.908067	−	0.659750i
$371$	−7.60293	+	5.52385i	−0.394724	+	0.286784i
$372$	2.93327	−	9.02768i	0.152083	−	0.468063i
$373$	1.73856			0.0900192			0.0450096	−	0.998987i	$-0.485668\pi$
$373$	1.73856			0.0900192			0.0450096	+	0.998987i	$0.485668\pi$
$374$		0			0
$375$	3.11455			0.160834
$376$	−4.56214	+	14.0408i	−0.235275	+	0.724101i
$377$	−5.86476	+	4.26100i	−0.302050	+	0.219452i
$378$	3.24964	+	2.36100i	0.167144	+	0.121437i
$379$	6.04831	+	18.6148i	0.310681	+	0.956178i	0.977496	+	0.210954i	$0.0676571\pi$
$379$	6.04831	+	18.6148i	0.310681	+	0.956178i	−0.666815	+	0.745223i	$0.732343\pi$
$380$	2.10435	+	6.47654i	0.107951	+	0.332239i
$381$	−15.5282	−	11.2819i	−0.795534	−	0.577989i
$382$	15.4128	−	11.1980i	0.788586	−	0.572941i
$383$	1.47238	−	4.53152i	0.0752351	−	0.231550i	−0.906366	−	0.422494i	$-0.861155\pi$
$383$	1.47238	−	4.53152i	0.0752351	−	0.231550i	0.981601	+	0.190944i	$0.0611548\pi$
$384$	−7.97351			−0.406897
$385$		0			0
$386$	19.0149			0.967833
$387$	−6.06335	+	18.6611i	−0.308217	+	0.948595i
$388$	3.05289	−	2.21806i	0.154987	−	0.112605i
$389$	1.15049	+	0.835879i	0.0583321	+	0.0423807i	0.616569	−	0.787301i	$-0.288522\pi$
$389$	1.15049	+	0.835879i	0.0583321	+	0.0423807i	−0.558237	+	0.829681i	$0.688522\pi$
$390$	1.60689	+	4.94550i	0.0813681	+	0.250425i
$391$	−11.4356	−	35.1950i	−0.578321	−	1.77989i
$392$	−2.21319	−	1.60798i	−0.111783	−	0.0812150i
$393$	6.57125	−	4.77429i	0.331476	−	0.240831i
$394$	−1.70253	+	5.23985i	−0.0857722	+	0.263980i
$395$	−21.4599			−1.07976
$396$		0			0
$397$	−18.3969			−0.923314			−0.461657	−	0.887059i	$-0.652745\pi$
$397$	−18.3969			−0.923314			−0.461657	+	0.887059i	$0.652745\pi$
$398$	4.02693	−	12.3936i	0.201852	−	0.621236i
$399$	−1.34112	+	0.974384i	−0.0671402	+	0.0487802i
$400$	−1.23670	−	0.898516i	−0.0618350	−	0.0449258i
$401$	−0.510706	−	1.57179i	−0.0255034	−	0.0784915i	0.937495	−	0.348000i	$-0.113139\pi$
$401$	−0.510706	−	1.57179i	−0.0255034	−	0.0784915i	−0.962998	+	0.269508i	$0.913139\pi$
$402$	1.05648	+	3.25152i	0.0526926	+	0.162171i
$403$	−13.3143	−	9.67342i	−0.663233	−	0.481867i
$404$	−15.6133	+	11.3438i	−0.776792	+	0.564373i
$405$	1.42639	−	4.38998i	0.0708779	−	0.218140i
$406$	−2.71193			−0.134591
$407$		0			0
$408$	−11.5808			−0.573335
$409$	−11.3365	+	34.8903i	−0.560556	+	1.72521i	0.120244	+	0.992744i	$0.461632\pi$
$409$	−11.3365	+	34.8903i	−0.560556	+	1.72521i	−0.680800	+	0.732470i	$0.738368\pi$
$410$	10.7290	−	7.79511i	0.529870	−	0.384973i
$411$	6.49301	+	4.71745i	0.320277	+	0.232695i
$412$	0.0440170	+	0.135471i	0.00216856	+	0.00667415i
$413$	1.07372	+	3.30456i	0.0528341	+	0.162607i
$414$	11.6220	+	8.44389i	0.571191	+	0.414995i
$415$	−18.4406	+	13.3979i	−0.905211	+	0.657675i
$416$	−3.94084	+	12.1287i	−0.193216	+	0.594657i
$417$	14.1344			0.692164
$418$		0			0
$419$	−17.3452			−0.847366			−0.423683	−	0.905810i	$-0.639263\pi$
$419$	−17.3452			−0.847366			−0.423683	+	0.905810i	$0.639263\pi$
$420$	1.17149	−	3.60546i	0.0571626	−	0.175929i
$421$	−4.30950	+	3.13103i	−0.210032	+	0.152597i	−0.687828	−	0.725874i	$-0.741436\pi$
$421$	−4.30950	+	3.13103i	−0.210032	+	0.152597i	0.477796	+	0.878471i	$0.341436\pi$
$422$	7.56383	+	5.49545i	0.368202	+	0.267514i
$423$	3.46399	+	10.6611i	0.168425	+	0.518359i
$424$	7.94450	+	24.4507i	0.385819	+	1.18743i
$425$	−13.9541	−	10.1383i	−0.676874	−	0.491778i
$426$	−2.81652	+	2.04632i	−0.136461	+	0.0991447i
$427$	4.01544	−	12.3582i	0.194321	−	0.598057i
$428$	6.14487			0.297024
$429$		0			0
$430$	−23.2270			−1.12011
$431$	−8.71677	+	26.8275i	−0.419872	+	1.29223i	0.487948	+	0.872873i	$0.337746\pi$
$431$	−8.71677	+	26.8275i	−0.419872	+	1.29223i	−0.907820	+	0.419361i	$0.862254\pi$
$432$	−1.54105	+	1.11964i	−0.0741440	+	0.0538688i
$433$	−14.3244	−	10.4073i	−0.688388	−	0.500143i	0.187742	−	0.982218i	$-0.439883\pi$
$433$	−14.3244	−	10.4073i	−0.688388	−	0.500143i	−0.876130	+	0.482075i	$0.839883\pi$
$434$	−1.90252	−	5.85536i	−0.0913239	−	0.281066i
$435$	−2.91857	−	8.98245i	−0.139935	−	0.430675i
$436$	3.45541	+	2.51051i	0.165484	+	0.120231i
$437$	−11.7238	+	8.51781i	−0.560823	+	0.407462i
$438$	3.60628	−	11.0990i	0.172315	−	0.530331i
$439$	−25.1189			−1.19886			−0.599430	−	0.800427i	$-0.704606\pi$
$439$	−25.1189			−1.19886			−0.599430	+	0.800427i	$0.704606\pi$
$440$		0			0
$441$	−2.07715			−0.0989121
$442$	−2.46886	+	7.59836i	−0.117432	+	0.361417i
$443$	21.8084	−	15.8448i	1.03615	−	0.752807i	0.0666201	−	0.997778i	$-0.478778\pi$
$443$	21.8084	−	15.8448i	1.03615	−	0.752807i	0.969530	+	0.244971i	$0.0787785\pi$
$444$	9.01993	+	6.55336i	0.428067	+	0.311009i
$445$	10.0038	+	30.7884i	0.474224	+	1.45951i
$446$	2.72049	+	8.37281i	0.128819	+	0.396464i
$447$	6.87239	+	4.99309i	0.325053	+	0.236165i
$448$	−3.22775	+	2.34510i	−0.152497	+	0.110795i
$449$	−6.51913	+	20.0638i	−0.307657	+	0.946871i	0.671015	+	0.741443i	$0.265858\pi$
$449$	−6.51913	+	20.0638i	−0.307657	+	0.946871i	−0.978672	+	0.205427i	$0.934142\pi$
$450$	6.69566			0.315636
$451$		0			0
$452$	14.9615			0.703730
$453$	5.92820	−	18.2451i	0.278531	−	0.857231i
$454$	−2.49041	+	1.80939i	−0.116881	+	0.0849188i
$455$	−5.31746	−	3.86336i	−0.249286	−	0.181117i
$456$	1.40138	+	4.31299i	0.0656254	+	0.201974i
$457$	−0.588232	−	1.81039i	−0.0275163	−	0.0846866i	0.936355	−	0.351054i	$-0.114177\pi$
$457$	−0.588232	−	1.81039i	−0.0275163	−	0.0846866i	−0.963872	+	0.266367i	$0.914177\pi$
$458$	−15.7630	−	11.4525i	−0.736555	−	0.535139i
$459$	−17.3882	+	12.6333i	−0.811613	+	0.589672i
$460$	10.2408	−	31.5180i	0.477480	−	1.46953i
$461$	25.0440			1.16641			0.583207	−	0.812324i	$-0.301798\pi$
$461$	25.0440			1.16641			0.583207	+	0.812324i	$0.301798\pi$
$462$		0			0
$463$	−21.1721			−0.983952			−0.491976	−	0.870609i	$-0.663725\pi$
$463$	−21.1721			−0.983952			−0.491976	+	0.870609i	$0.663725\pi$
$464$	0.397414	−	1.22311i	0.0184495	−	0.0567816i
$465$	17.3466	−	12.6031i	0.804430	−	0.584453i
$466$	2.57630	+	1.87179i	0.119345	+	0.0867092i
$467$	5.14465	+	15.8336i	0.238066	+	0.732692i	0.996700	+	0.0811746i	$0.0258671\pi$
$467$	5.14465	+	15.8336i	0.238066	+	0.732692i	−0.758634	+	0.651517i	$0.774133\pi$
$468$	1.86771	+	5.74822i	0.0863350	+	0.265712i
$469$	−3.49607	−	2.54004i	−0.161433	−	0.117288i
$470$	−10.7353	+	7.79967i	−0.495184	+	0.359772i
$471$	−3.87448	+	11.9244i	−0.178527	+	0.549448i
$472$	9.50534			0.437519
$473$		0			0
$474$	−5.68652			−0.261190
$475$	−2.08718	+	6.42369i	−0.0957665	+	0.294739i
$476$	4.71218	−	3.42360i	0.215982	−	0.156920i
$477$	15.7925	+	11.4739i	0.723087	+	0.525353i
$478$	2.56317	+	7.88862i	0.117237	+	0.360817i
$479$	6.69371	+	20.6011i	0.305843	+	0.941289i	0.979361	+	0.202118i	$0.0647825\pi$
$479$	6.69371	+	20.6011i	0.305843	+	0.941289i	−0.673518	+	0.739171i	$0.735217\pi$
$480$	−13.4419	−	9.76610i	−0.613535	−	0.445760i
$481$	15.6385	−	11.3620i	0.713054	−	0.518064i
$482$	−3.41695	+	10.5163i	−0.155638	+	0.479004i
$483$	8.06728			0.367074
$484$		0			0
$485$	8.52397			0.387053
$486$	4.10173	−	12.6238i	0.186058	−	0.572629i
$487$	2.27605	−	1.65365i	0.103138	−	0.0749339i	−0.535021	−	0.844839i	$-0.679696\pi$
$487$	2.27605	−	1.65365i	0.103138	−	0.0749339i	0.638159	+	0.769905i	$0.279696\pi$
$488$	−28.7587	−	20.8944i	−1.30184	−	0.945845i
$489$	−1.77059	−	5.44933i	−0.0800690	−	0.246427i
$490$	−0.759826	−	2.33850i	−0.0343254	−	0.105643i
$491$	−2.59355	−	1.88432i	−0.117045	−	0.0850383i	0.527723	−	0.849417i	$-0.323046\pi$
$491$	−2.59355	−	1.88432i	−0.117045	−	0.0850383i	−0.644768	+	0.764378i	$0.723046\pi$
$492$	−5.54045	+	4.02538i	−0.249783	+	0.181478i
$493$	4.48415	−	13.8008i	0.201956	−	0.621557i
$494$	3.12858			0.140762
$495$		0			0
$496$	2.91964			0.131096
$497$	1.35982	−	4.18508i	0.0609961	−	0.187727i
$498$	−4.88645	+	3.55021i	−0.218967	+	0.159089i
$499$	16.2218	+	11.7858i	0.726187	+	0.527605i	0.888355	−	0.459158i	$-0.151849\pi$
$499$	16.2218	+	11.7858i	0.726187	+	0.527605i	−0.162168	+	0.986763i	$0.551849\pi$
$500$	1.32423	+	4.07556i	0.0592214	+	0.182265i
$501$	−3.93251	−	12.1030i	−0.175692	−	0.540723i
$502$	0.0509345	+	0.0370061i	0.00227332	+	0.00165166i
$503$	−28.7273	+	20.8716i	−1.28089	+	0.930618i	−0.999579	−	0.0289998i	$-0.990768\pi$
$503$	−28.7273	+	20.8716i	−1.28089	+	0.930618i	−0.281307	+	0.959618i	$0.590768\pi$
$504$	−1.75595	+	5.40425i	−0.0782162	+	0.240725i
$505$	−43.5939			−1.93990
$506$		0			0
$507$	7.83279			0.347867
$508$	8.16079	−	25.1163i	0.362077	−	1.11436i
$509$	−7.43470	+	5.40163i	−0.329537	+	0.239423i	−0.740234	−	0.672349i	$-0.765285\pi$
$509$	−7.43470	+	5.40163i	−0.329537	+	0.239423i	0.410697	+	0.911772i	$0.365285\pi$
$510$	−8.42107	−	6.11826i	−0.372891	−	0.270921i
$511$	4.55829	+	14.0290i	0.201647	+	0.620605i
$512$	−1.35944	−	4.18392i	−0.0600793	−	0.184905i
$513$	6.80909	+	4.94710i	0.300629	+	0.218420i
$514$	6.33752	−	4.60448i	0.279536	−	0.203095i
$515$	−0.0994279	+	0.306008i	−0.00438132	+	0.0134843i
$516$	11.9944			0.528022
$517$		0			0
$518$	7.23140			0.317730
$519$	0.153688	−	0.473002i	0.00674614	−	0.0207625i
$520$	−14.5467	+	10.5688i	−0.637915	+	0.463473i
$521$	−10.0317	−	7.28844i	−0.439496	−	0.319312i	0.345939	−	0.938257i	$-0.387560\pi$
$521$	−10.0317	−	7.28844i	−0.439496	−	0.319312i	−0.785435	+	0.618945i	$0.787560\pi$
$522$	1.74072	+	5.35739i	0.0761893	+	0.234486i
$523$	7.01794	+	21.5990i	0.306873	+	0.944458i	0.978972	+	0.203997i	$0.0653932\pi$
$523$	7.01794	+	21.5990i	0.306873	+	0.944458i	−0.672098	+	0.740462i	$0.734607\pi$
$524$	9.04137	+	6.56894i	0.394974	+	0.286965i
$525$	3.04196	−	2.21012i	0.132762	−	0.0964573i
$526$	−3.76443	+	11.5857i	−0.164137	+	0.505161i
$527$	32.9433			1.43503
$528$		0			0
$529$	47.5220			2.06617
$530$	−7.14065	+	21.9766i	−0.310170	+	0.954605i
$531$	5.83893	−	4.24223i	0.253388	−	0.184097i
$532$	−1.84525	−	1.34065i	−0.0800018	−	0.0581247i
$533$	3.66912	+	11.2924i	0.158927	+	0.489128i
$534$	2.65083	+	8.15843i	0.114713	+	0.353050i
$535$	11.2294	+	8.15866i	0.485491	+	0.352730i
$536$	−9.56403	+	6.94867i	−0.413103	+	0.300137i
$537$	−0.503514	+	1.54966i	−0.0217282	+	0.0668726i
$538$	24.7525			1.06716
$539$		0			0
$540$	−19.2475			−0.828281
$541$	5.33821	−	16.4293i	0.229508	−	0.706352i	−0.768295	−	0.640096i	$-0.778895\pi$
$541$	5.33821	−	16.4293i	0.229508	−	0.706352i	0.997803	−	0.0662562i	$-0.0211055\pi$
$542$	−6.92379	+	5.03042i	−0.297402	+	0.216075i
$543$	−7.68321	−	5.58218i	−0.329718	−	0.239554i
$544$	−7.88850	−	24.2783i	−0.338217	−	1.04092i
$545$	2.98135	+	9.17564i	0.127707	+	0.393041i
$546$	−1.40904	−	1.02373i	−0.0603013	−	0.0438115i
$547$	10.6580	−	7.74346i	0.455701	−	0.331086i	−0.336141	−	0.941812i	$-0.609122\pi$
$547$	10.6580	−	7.74346i	0.455701	−	0.331086i	0.791843	+	0.610725i	$0.209122\pi$
$548$	−3.41238	+	10.5022i	−0.145770	+	0.448633i
$549$	−26.9910			−1.15195
$550$		0			0
$551$	−5.68240			−0.242078
$552$	6.81978	−	20.9891i	0.290269	−	0.893356i
$553$	5.81495	−	4.22481i	0.247277	−	0.179657i
$554$	18.7314	+	13.6092i	0.795821	+	0.578198i
$555$	7.78243	+	23.9519i	0.330346	+	1.01670i
$556$	6.00960	+	18.4957i	0.254864	+	0.784390i
$557$	10.2111	+	7.41877i	0.432656	+	0.314343i	0.782710	−	0.622386i	$-0.213837\pi$
$557$	10.2111	+	7.41877i	0.432656	+	0.314343i	−0.350054	+	0.936730i	$0.613837\pi$
$558$	−10.3460	+	7.51682i	−0.437982	+	0.318212i
$559$	6.42616	−	19.7777i	0.271797	−	0.836506i
$560$	1.16604			0.0492743
$561$		0			0
$562$	−7.88151			−0.332462
$563$	3.03431	−	9.33865i	0.127881	−	0.393577i	−0.866534	−	0.499118i	$-0.833657\pi$
$563$	3.03431	−	9.33865i	0.127881	−	0.393577i	0.994415	+	0.105541i	$0.0336574\pi$
$564$	5.54369	−	4.02773i	0.233432	−	0.169598i
$565$	27.3414	+	19.8647i	1.15026	+	0.835713i
$566$	0.421251	+	1.29648i	0.0177065	+	0.0544949i
$567$	0.477749	+	1.47036i	0.0200636	+	0.0617493i
$568$	−9.73904	−	7.07583i	−0.408641	−	0.296895i
$569$	−16.4671	+	11.9640i	−0.690335	+	0.501558i	−0.876770	−	0.480910i	$-0.840307\pi$
$569$	−16.4671	+	11.9640i	−0.690335	+	0.501558i	0.186435	+	0.982467i	$0.440307\pi$
$570$	−1.25958	+	3.87659i	−0.0527580	+	0.162372i
$571$	−32.3174			−1.35244			−0.676221	−	0.736699i	$-0.736384\pi$
$571$	−32.3174			−1.35244			−0.676221	+	0.736699i	$0.736384\pi$
$572$		0			0
$573$	−22.2226			−0.928362
$574$	−1.37261	+	4.22446i	−0.0572917	+	0.176326i
$575$	26.5920	−	19.3202i	1.10896	−	0.805710i
$576$	6.70453	+	4.87112i	0.279355	+	0.202963i
$577$	−3.49749	−	10.7642i	−0.145602	−	0.448118i	0.851486	−	0.524378i	$-0.175702\pi$
$577$	−3.49749	−	10.7642i	−0.145602	−	0.448118i	−0.997088	+	0.0762600i	$0.975702\pi$
$578$	−0.615607	−	1.89464i	−0.0256059	−	0.0788068i
$579$	−17.9442	−	13.0372i	−0.745734	−	0.541808i
$580$	10.5131	−	7.63824i	0.436534	−	0.317161i
$581$	2.35917	−	7.26079i	0.0978751	−	0.301228i
$582$	2.25871			0.0936266
$583$		0			0
$584$	40.3534			1.66984
$585$	−4.21888	+	12.9844i	−0.174429	+	0.536838i
$586$	3.11940	−	2.26638i	0.128861	−	0.0936232i
$587$	30.9358	+	22.4762i	1.27686	+	0.927692i	0.999453	−	0.0330612i	$-0.0105256\pi$
$587$	30.9358	+	22.4762i	1.27686	+	0.927692i	0.277405	+	0.960753i	$0.410526\pi$
$588$	0.392372	+	1.20760i	0.0161812	+	0.0498005i
$589$	−3.98642	−	12.2689i	−0.164258	−	0.505533i
$590$	6.91188	+	5.02178i	0.284558	+	0.206743i
$591$	5.19926	−	3.77748i	0.213869	−	0.155385i
$592$	−1.05971	+	3.26145i	−0.0435538	+	0.134045i
$593$	−26.4263			−1.08520			−0.542598	−	0.839992i	$-0.682559\pi$
$593$	−26.4263			−1.08520			−0.542598	+	0.839992i	$0.682559\pi$
$594$		0			0
$595$	13.1568			0.539378
$596$	−3.61176	+	11.1159i	−0.147944	+	0.455323i
$597$	−12.2976	+	8.93474i	−0.503308	+	0.365674i
$598$	−12.3174	−	8.94915i	−0.503698	−	0.365958i
$599$	−6.27287	−	19.3059i	−0.256303	−	0.788818i	−0.993570	−	0.113218i	$-0.963884\pi$
$599$	−6.27287	−	19.3059i	−0.256303	−	0.788818i	0.737268	−	0.675601i	$-0.236116\pi$
$600$	−3.17863	−	9.78280i	−0.129767	−	0.399381i
$601$	4.12121	+	2.99424i	0.168108	+	0.122137i	0.668658	−	0.743570i	$-0.266869\pi$
$601$	4.12121	+	2.99424i	0.168108	+	0.122137i	−0.500550	+	0.865707i	$0.666869\pi$
$602$	6.29379	−	4.57270i	0.256516	−	0.186370i
$603$	−2.77379	+	8.53684i	−0.112957	+	0.347647i
$604$	26.3953			1.07401
$605$		0			0
$606$	−11.5517			−0.469254
$607$	9.46848	−	29.1410i	0.384314	−	1.18280i	−0.552663	−	0.833405i	$-0.686388\pi$
$607$	9.46848	−	29.1410i	0.384314	−	1.18280i	0.936977	−	0.349392i	$-0.113612\pi$
$608$	−8.08730	+	5.87577i	−0.327983	+	0.238294i
$609$	2.55922	+	1.85938i	0.103705	+	0.0753459i
$610$	−9.87335	−	30.3871i	−0.399760	−	1.23034i
$611$	−3.67126	−	11.2990i	−0.148523	−	0.457108i
$612$	−9.78792	−	7.11134i	−0.395653	−	0.287459i
$613$	20.0952	−	14.6000i	0.811639	−	0.589690i	−0.102667	−	0.994716i	$-0.532737\pi$
$613$	20.0952	−	14.6000i	0.811639	−	0.589690i	0.914305	+	0.405026i	$0.132737\pi$
$614$	4.32203	−	13.3018i	0.174423	−	0.536818i
$615$	−15.4695			−0.623789
$616$		0			0
$617$	0.521714			0.0210034			0.0105017	−	0.999945i	$-0.496657\pi$
$617$	0.521714			0.0210034			0.0105017	+	0.999945i	$0.496657\pi$
$618$	−0.0263468	+	0.0810871i	−0.00105982	+	0.00326180i
$619$	−25.4726	+	18.5069i	−1.02383	+	0.743857i	−0.967065	−	0.254531i	$-0.918079\pi$
$619$	−25.4726	+	18.5069i	−1.02383	+	0.743857i	−0.0567663	+	0.998387i	$0.518079\pi$
$620$	23.8672	+	17.3405i	0.958529	+	0.696412i
$621$	−12.6570	−	38.9541i	−0.507907	−	1.56318i
$622$	5.57992	+	17.1732i	0.223734	+	0.688584i
$623$	−8.77202	−	6.37325i	−0.351444	−	0.255339i
$624$	0.668198	−	0.485474i	0.0267493	−	0.0194345i
$625$	−9.03885	+	27.8187i	−0.361554	+	1.11275i
$626$	−8.28124			−0.330985
$627$		0			0
$628$	−17.2511			−0.688395
$629$	−11.9571	+	36.8001i	−0.476760	+	1.46732i
$630$	−4.13198	+	3.00206i	−0.164622	+	0.119605i
$631$	0.0924140	+	0.0671427i	0.00367894	+	0.00267291i	0.589623	−	0.807678i	$-0.299276\pi$
$631$	0.0924140	+	0.0671427i	0.00367894	+	0.00267291i	−0.585944	+	0.810351i	$0.699276\pi$
$632$	−6.07619	−	18.7006i	−0.241698	−	0.743870i
$633$	−3.37006	−	10.3720i	−0.133948	−	0.412250i
$634$	15.6974	+	11.4049i	0.623425	+	0.452945i
$635$	48.2609	−	35.0636i	1.91517	−	1.39146i
$636$	3.68741	−	11.3487i	0.146215	−	0.450005i
$637$	2.20144			0.0872244
$638$		0			0
$639$	−9.14043			−0.361590
$640$	7.65783	−	23.5684i	0.302702	−	0.931622i
$641$	−10.6905	+	7.76707i	−0.422248	+	0.306781i	−0.778542	−	0.627593i	$-0.784040\pi$
$641$	−10.6905	+	7.76707i	−0.422248	+	0.306781i	0.356294	+	0.934374i	$0.384040\pi$
$642$	2.97562	+	2.16191i	0.117438	+	0.0853239i
$643$	0.758944	+	2.33579i	0.0299298	+	0.0921146i	0.964906	−	0.262597i	$-0.0845790\pi$
$643$	0.758944	+	2.33579i	0.0299298	+	0.0921146i	−0.934976	+	0.354712i	$0.884579\pi$
$644$	3.43001	+	10.5565i	0.135161	+	0.415984i
$645$	21.9191	+	15.9251i	0.863063	+	0.627052i
$646$	−5.06653	+	3.68105i	−0.199340	+	0.144829i
$647$	−5.75130	+	17.7007i	−0.226107	+	0.695886i	0.772070	+	0.635537i	$0.219221\pi$
$647$	−5.75130	+	17.7007i	−0.226107	+	0.695886i	−0.998177	+	0.0603488i	$0.980779\pi$
$648$	4.22939			0.166146
$649$		0			0
$650$	−7.09630			−0.278340
$651$	−2.21922	+	6.83007i	−0.0869782	+	0.267691i
$652$	6.37795	−	4.63385i	0.249780	−	0.181476i
$653$	−15.7339	−	11.4313i	−0.615714	−	0.447343i	0.235708	−	0.971824i	$-0.424259\pi$
$653$	−15.7339	−	11.4313i	−0.615714	−	0.447343i	−0.851422	+	0.524481i	$0.824259\pi$
$654$	0.790008	+	2.43139i	0.0308918	+	0.0950751i
$655$	7.80093	+	24.0088i	0.304808	+	0.938101i
$656$	−1.70414	−	1.23813i	−0.0665354	−	0.0483408i
$657$	24.7882	−	18.0097i	0.967082	−	0.702626i
$658$	1.37341	−	4.22693i	0.0535412	−	0.164783i
$659$	4.71629			0.183721			0.0918603	−	0.995772i	$-0.470719\pi$
$659$	4.71629			0.183721			0.0918603	+	0.995772i	$0.470719\pi$
$660$		0			0
$661$	24.9330			0.969782			0.484891	−	0.874575i	$-0.338859\pi$
$661$	24.9330			0.969782			0.484891	+	0.874575i	$0.338859\pi$
$662$	5.30890	−	16.3391i	0.206336	−	0.635038i
$663$	7.53951	−	5.47777i	0.292810	−	0.212739i
$664$	−16.8965	−	12.2760i	−0.655711	−	0.476402i
$665$	−1.59209	−	4.89995i	−0.0617386	−	0.190012i
$666$	−4.64166	−	14.2856i	−0.179861	−	0.553555i
$667$	22.3720	+	16.2542i	0.866247	+	0.629366i
$668$	14.1655	−	10.2918i	0.548079	−	0.398203i
$669$	3.17336	−	9.76659i	0.122689	−	0.377598i
$670$	−10.6256			−0.410503
$671$		0			0
$672$	5.56498			0.214674
$673$	−1.58517	+	4.87866i	−0.0611039	+	0.188058i	−0.976949	−	0.213474i	$-0.931522\pi$
$673$	−1.58517	+	4.87866i	−0.0611039	+	0.188058i	0.915845	+	0.401532i	$0.131522\pi$
$674$	8.89762	−	6.46450i	0.342723	−	0.249003i
$675$	−15.4445	−	11.2211i	−0.594460	−	0.431900i
$676$	3.33032	+	10.2497i	0.128089	+	0.394218i
$677$	−15.8405	−	48.7521i	−0.608800	−	1.87369i	−0.468185	−	0.883631i	$-0.655092\pi$
$677$	−15.8405	−	48.7521i	−0.608800	−	1.87369i	−0.140616	−	0.990064i	$-0.544908\pi$
$678$	7.24502	+	5.26381i	0.278243	+	0.202156i
$679$	−2.30973	+	1.67812i	−0.0886392	+	0.0644001i
$680$	11.1223	−	34.2309i	0.426521	−	1.31270i
$681$	3.59074			0.137598
$682$		0			0
$683$	−24.9448			−0.954485			−0.477242	−	0.878772i	$-0.658364\pi$
$683$	−24.9448			−0.954485			−0.477242	+	0.878772i	$0.658364\pi$
$684$	−1.46403	+	4.50581i	−0.0559784	+	0.172284i
$685$	−20.1799	+	14.6616i	−0.771036	+	0.560191i
$686$	0.666271	+	0.484074i	0.0254383	+	0.0184820i
$687$	7.02319	+	21.6151i	0.267951	+	0.824669i
$688$	1.14004	+	3.50867i	0.0434635	+	0.133767i
$689$	−16.7374	−	12.1604i	−0.637645	−	0.463276i
$690$	16.0478	−	11.6594i	0.610931	−	0.443867i
$691$	3.64168	−	11.2079i	0.138536	−	0.426370i	−0.857587	−	0.514338i	$-0.828038\pi$
$691$	3.64168	−	11.2079i	0.138536	−	0.426370i	0.996123	+	0.0879687i	$0.0280376\pi$
$692$	0.684294			0.0260130
$693$		0			0
$694$	1.31156			0.0497863
$695$	−13.5748	+	41.7789i	−0.514921	+	1.58476i
$696$	7.00113	−	5.08662i	0.265377	−	0.192808i
$697$	−19.2284	−	13.9702i	−0.728326	−	0.529160i
$698$	−1.68850	−	5.19666i	−0.0639105	−	0.196696i
$699$	−1.14787	−	3.53279i	−0.0434165	−	0.133622i
$700$	4.18543	+	3.04089i	0.158194	+	0.114935i
$701$	25.3362	−	18.4078i	0.956933	−	0.695253i	0.00449682	−	0.999990i	$-0.498569\pi$
$701$	25.3362	−	18.4078i	0.956933	−	0.695253i	0.952436	+	0.304737i	$0.0985686\pi$
$702$	−2.73255	+	8.40992i	−0.103133	+	0.317412i
$703$	15.1522			0.571477
$704$		0			0
$705$	15.4785			0.582954
$706$	6.46770	−	19.9055i	0.243415	−	0.749155i
$707$	11.8126	−	8.58234i	0.444258	−	0.322772i
$708$	−3.56928	−	2.59323i	−0.134142	−	0.0974597i
$709$	−12.8165	−	39.4451i	−0.481334	−	1.48139i	−0.837221	−	0.546865i	$-0.815821\pi$
$709$	−12.8165	−	39.4451i	−0.481334	−	1.48139i	0.355887	−	0.934529i	$-0.384179\pi$
$710$	−3.34358	−	10.2905i	−0.125482	−	0.386195i
$711$	−12.0785	−	8.77558i	−0.452981	−	0.329110i
$712$	−23.9972	+	17.4350i	−0.899333	+	0.653404i
$713$	−19.3999	+	59.7066i	−0.726530	+	2.23603i
$714$	3.48635			0.130473
$715$		0			0
$716$	−2.24190			−0.0837836
$717$	2.98985	−	9.20180i	0.111658	−	0.343647i
$718$	10.7131	−	7.78353i	0.399810	−	0.290479i
$719$	6.38337	+	4.63779i	0.238059	+	0.172960i	0.700418	−	0.713733i	$-0.252997\pi$
$719$	6.38337	+	4.63779i	0.238059	+	0.172960i	−0.462359	+	0.886693i	$0.652997\pi$
$720$	−0.748454	−	2.30350i	−0.0278932	−	0.0858465i
$721$	−0.0333020	−	0.102493i	−0.00124023	−	0.00381703i
$722$	−10.6751	−	7.75594i	−0.397287	−	0.288646i
$723$	10.4348	−	7.58135i	0.388076	−	0.281954i
$724$	4.03788	−	12.4273i	0.150067	−	0.461858i
$725$	12.8889			0.478682
$726$		0			0
$727$	5.12729			0.190161			0.0950803	−	0.995470i	$-0.469689\pi$
$727$	5.12729			0.190161			0.0950803	+	0.995470i	$0.469689\pi$
$728$	1.86102	−	5.72763i	0.0689739	−	0.212280i
$729$	−8.77376	+	6.37451i	−0.324954	+	0.236093i
$730$	29.3433	+	21.3192i	1.08604	+	0.789057i
$731$	12.8634	+	39.5896i	0.475771	+	1.46427i
$732$	5.09857	+	15.6918i	0.188449	+	0.579986i
$733$	27.3234	+	19.8516i	1.00921	+	0.733236i	0.964044	−	0.265743i	$-0.0856174\pi$
$733$	27.3234	+	19.8516i	1.00921	+	0.733236i	0.0451688	+	0.998979i	$0.485617\pi$
$734$	−2.01618	+	1.46484i	−0.0744185	+	0.0540682i
$735$	−0.886310	+	2.72778i	−0.0326920	+	0.100616i
$736$	48.6476			1.79317
$737$		0			0
$738$	9.22643			0.339629
$739$	−13.2083	+	40.6511i	−0.485876	+	1.49537i	0.344831	+	0.938665i	$0.387936\pi$
$739$	−13.2083	+	40.6511i	−0.485876	+	1.49537i	−0.830708	+	0.556709i	$0.812064\pi$
$740$	−28.0335	+	20.3675i	−1.03053	+	0.748725i
$741$	−2.95241	−	2.14505i	−0.108459	−	0.0788004i
$742$	−2.39166	−	7.36076i	−0.0878005	−	0.270222i
$743$	7.09394	+	21.8329i	0.260252	+	0.800972i	0.992749	+	0.120203i	$0.0383544\pi$
$743$	7.09394	+	21.8329i	0.260252	+	0.800972i	−0.732498	+	0.680769i	$0.761646\pi$
$744$	15.8941	+	11.5478i	0.582707	+	0.423362i
$745$	−21.3590	+	15.5183i	−0.782535	+	0.568545i
$746$	−0.442451	+	1.36172i	−0.0161993	+	0.0498563i
$747$	−15.8579			−0.580211
$748$		0			0
$749$	−4.64902			−0.169872
$750$	−0.792629	+	2.43946i	−0.0289427	+	0.0890766i
$751$	0.752967	−	0.547063i	0.0274762	−	0.0199626i	−0.573962	−	0.818882i	$-0.694594\pi$
$751$	0.752967	−	0.547063i	0.0274762	−	0.0199626i	0.601439	+	0.798919i	$0.294594\pi$
$752$	1.70514	+	1.23885i	0.0621799	+	0.0451763i
$753$	−0.0226938	−	0.0698445i	−0.000827010	−	0.00254527i
$754$	−1.84488	−	5.67795i	−0.0671865	−	0.206779i
$755$	48.2361	+	35.0456i	1.75549	+	1.27544i
$756$	5.21547	−	3.78926i	0.189685	−	0.137814i
$757$	−3.54825	+	10.9204i	−0.128963	+	0.396908i	−0.994602	−	0.103760i	$-0.966913\pi$
$757$	−3.54825	+	10.9204i	−0.128963	+	0.396908i	0.865639	+	0.500669i	$0.166913\pi$
$758$	−16.1193			−0.585478
$759$		0			0
$760$	−14.0944			−0.511257
$761$	12.0096	−	36.9619i	0.435349	−	1.33987i	−0.457379	−	0.889272i	$-0.651212\pi$
$761$	12.0096	−	36.9619i	0.435349	−	1.33987i	0.892728	−	0.450595i	$-0.148788\pi$
$762$	12.7883	−	9.29128i	0.463273	−	0.336587i
$763$	−2.61426	−	1.89937i	−0.0946426	−	0.0687619i
$764$	−9.44851	−	29.0795i	−0.341835	−	1.05206i
$765$	−8.44506	−	25.9912i	−0.305332	−	0.939714i
$766$	3.17460	+	2.30648i	0.114703	+	0.0833365i
$767$	−6.18831	+	4.49607i	−0.223447	+	0.162344i
$768$	4.39795	−	13.5355i	0.158697	−	0.488420i
$769$	−35.6509			−1.28560			−0.642802	−	0.766032i	$-0.722228\pi$
$769$	−35.6509			−1.28560			−0.642802	+	0.766032i	$0.722228\pi$
$770$		0			0
$771$	−9.13763			−0.329084
$772$	9.43050	−	29.0241i	0.339411	−	1.04460i
$773$	1.43233	−	1.04065i	0.0515172	−	0.0374294i	−0.561729	−	0.827322i	$-0.689863\pi$
$773$	1.43233	−	1.04065i	0.0515172	−	0.0374294i	0.613246	+	0.789892i	$0.289863\pi$
$774$	−13.0732	−	9.49821i	−0.469905	−	0.341406i
$775$	9.04207	+	27.8286i	0.324801	+	0.999633i
$776$	2.41349	+	7.42797i	0.0866394	+	0.266649i
$777$	−6.82420	−	4.95807i	−0.244817	−	0.177870i
$778$	−0.947492	+	0.688393i	−0.0339692	+	0.0246801i
$779$	−2.87608	+	8.85166i	−0.103046	+	0.317144i
$780$	8.34569			0.298824
$781$		0			0
$782$	30.4767			1.08985
$783$	4.96309	−	15.2748i	0.177366	−	0.545878i
$784$	−0.315961	+	0.229559i	−0.0112843	+	0.00819853i
$785$	−31.5255	−	22.9046i	−1.12519	−	0.817502i
$786$	2.06712	+	6.36194i	0.0737317	+	0.226923i
$787$	1.03618	+	3.18904i	0.0369359	+	0.113677i	0.967824	−	0.251626i	$-0.0809654\pi$
$787$	1.03618	+	3.18904i	0.0369359	+	0.113677i	−0.930889	+	0.365303i	$0.880965\pi$
$788$	7.15366	+	5.19743i	0.254838	+	0.185151i
$789$	11.4960	−	8.35232i	0.409268	−	0.297350i
$790$	5.46138	−	16.8084i	0.194307	−	0.598016i
$791$	−11.3194			−0.402472
$792$		0			0
$793$	28.6061			1.01583
$794$	4.68188	−	14.4093i	0.166154	−	0.511368i
$795$	21.8064	−	15.8433i	0.773394	−	0.561904i
$796$	−16.9203	−	12.2933i	−0.599723	−	0.435724i
$797$	1.52204	+	4.68435i	0.0539134	+	0.165928i	0.974388	−	0.224875i	$-0.0721973\pi$
$797$	1.52204	+	4.68435i	0.0539134	+	0.165928i	−0.920474	+	0.390803i	$0.872197\pi$
$798$	−0.421878	−	1.29841i	−0.0149343	−	0.0459631i
$799$	19.2396	+	13.9784i	0.680649	+	0.494520i
$800$	18.3438	−	13.3275i	0.648550	−	0.471199i
$801$	−6.95974	+	21.4199i	−0.245910	+	0.756834i
$802$	1.36107			0.0480612
$803$		0			0
$804$	5.48704			0.193513
$805$	−7.74789	+	23.8455i	−0.273077	+	0.840445i
$806$	10.9651	−	7.96660i	0.386229	−	0.280612i
$807$	−23.3587	−	16.9711i	−0.822264	−	0.597410i
$808$	−12.3433	−	37.9887i	−0.434235	−	1.33644i
$809$	−2.15484	−	6.63192i	−0.0757602	−	0.233166i	0.906004	−	0.423270i	$-0.139118\pi$
$809$	−2.15484	−	6.63192i	−0.0757602	−	0.233166i	−0.981764	+	0.190103i	$0.939118\pi$
$810$	3.07544	+	2.23443i	0.108060	+	0.0785100i
$811$	−4.80052	+	3.48778i	−0.168569	+	0.122473i	−0.668871	−	0.743378i	$-0.733222\pi$
$811$	−4.80052	+	3.48778i	−0.168569	+	0.122473i	0.500302	+	0.865851i	$0.333222\pi$
$812$	−1.34499	+	4.13945i	−0.0471998	+	0.145266i
$813$	9.98292			0.350116
$814$		0			0
$815$	17.8078			0.623781
$816$	−0.510899	+	1.57239i	−0.0178851	+	0.0550445i
$817$	13.1876	−	9.58135i	0.461376	−	0.335209i
$818$	−24.4427	−	17.7587i	−0.854619	−	0.620917i
$819$	−1.41305	−	4.34893i	−0.0493761	−	0.151964i
$820$	−6.57724	−	20.2427i	−0.229687	−	0.706905i
$821$	−33.7739	−	24.5382i	−1.17872	−	0.856388i	−0.186690	−	0.982419i	$-0.559776\pi$
$821$	−33.7739	−	24.5382i	−1.17872	−	0.856388i	−0.992026	+	0.126031i	$0.959776\pi$
$822$	−5.34736	+	3.88508i	−0.186511	+	0.135508i
$823$	−7.16931	+	22.0649i	−0.249906	+	0.769132i	0.744884	+	0.667194i	$0.232505\pi$
$823$	−7.16931	+	22.0649i	−0.249906	+	0.769132i	−0.994791	+	0.101939i	$0.967495\pi$
$824$	−0.294814			−0.0102703
$825$		0			0
$826$	−2.86154			−0.0995658
$827$	−4.07219	+	12.5329i	−0.141604	+	0.435813i	−0.996559	−	0.0828903i	$-0.973585\pi$
$827$	−4.07219	+	12.5329i	−0.141604	+	0.435813i	0.854955	+	0.518703i	$0.173585\pi$
$828$	18.6526	−	13.5519i	0.648223	−	0.470962i
$829$	−3.47141	−	2.52213i	−0.120567	−	0.0875972i	0.525868	−	0.850566i	$-0.323741\pi$
$829$	−3.47141	−	2.52213i	−0.120567	−	0.0875972i	−0.646435	+	0.762969i	$0.723741\pi$
$830$	−5.80085	−	17.8532i	−0.201351	−	0.619693i
$831$	−8.34577	−	25.6856i	−0.289512	−	0.891025i
$832$	−7.10570	−	5.16259i	−0.246346	−	0.178981i
$833$	−3.56509	+	2.59019i	−0.123523	+	0.0897448i
$834$	−3.59710	+	11.0707i	−0.124557	+	0.383348i
$835$	39.5513			1.36873
$836$		0			0
$837$	36.4619			1.26031
$838$	4.41422	−	13.5856i	0.152487	−	0.469305i
$839$	12.7382	−	9.25486i	0.439772	−	0.319513i	−0.345772	−	0.938318i	$-0.612383\pi$
$839$	12.7382	−	9.25486i	0.439772	−	0.319513i	0.785544	+	0.618805i	$0.212383\pi$
$840$	6.34778	+	4.61193i	0.219019	+	0.159127i
$841$	−5.61066	−	17.2678i	−0.193471	−	0.595443i
$842$	−1.35564	−	4.17223i	−0.0467184	−	0.143785i
$843$	7.43770	+	5.40381i	0.256168	+	0.186117i
$844$	12.1395	−	8.81984i	0.417858	−	0.303592i
$845$	−7.52269	+	23.1524i	−0.258788	+	0.796468i
$846$	−9.23182			−0.317397
$847$		0			0
$848$	3.67028			0.126038
$849$	0.491374	−	1.51229i	0.0168639	−	0.0519018i
$850$	11.4920	−	8.34942i	0.394172	−	0.286383i
$851$	−59.6554	−	43.3422i	−2.04496	−	1.48575i
$852$	1.72662	+	5.31398i	0.0591529	+	0.182054i
$853$	1.89741	+	5.83963i	0.0649662	+	0.199945i	0.978271	−	0.207332i	$-0.0664781\pi$
$853$	1.89741	+	5.83963i	0.0649662	+	0.199945i	−0.913304	+	0.407278i	$0.866478\pi$
$854$	8.65768	+	6.29017i	0.296260	+	0.215245i
$855$	−8.65788	+	6.29032i	−0.296093	+	0.215124i
$856$	−3.93011	+	12.0956i	−0.134328	+	0.413420i
$857$	34.4740			1.17761			0.588804	−	0.808276i	$-0.299599\pi$
$857$	34.4740			1.17761			0.588804	+	0.808276i	$0.299599\pi$
$858$		0			0
$859$	8.21553			0.280310			0.140155	−	0.990130i	$-0.455240\pi$
$859$	8.21553			0.280310			0.140155	+	0.990130i	$0.455240\pi$
$860$	−11.5195	+	35.4534i	−0.392812	+	1.20895i
$861$	4.19174	−	3.04548i	0.142854	−	0.103790i
$862$	−18.7942	−	13.6548i	−0.640133	−	0.465084i
$863$	4.02927	+	12.4008i	0.137158	+	0.422129i	0.995919	−	0.0902468i	$-0.0287656\pi$
$863$	4.02927	+	12.4008i	0.137158	+	0.422129i	−0.858761	+	0.512376i	$0.828766\pi$
$864$	−8.73105	−	26.8714i	−0.297036	−	0.914184i
$865$	1.25051	+	0.908550i	0.0425187	+	0.0308916i
$866$	11.7970	−	8.57100i	0.400877	−	0.291254i
$867$	−0.718084	+	2.21003i	−0.0243874	+	0.0750567i
$868$	−9.88109			−0.335386
$869$		0			0
$870$	7.77824			0.263707
$871$	2.93976	−	9.04766i	0.0996100	−	0.306568i
$872$	−7.15171	+	5.19602i	−0.242187	+	0.175959i
$873$	4.79766	+	3.48570i	0.162376	+	0.117973i
$874$	−3.68795	−	11.3503i	−0.124747	−	0.383931i
$875$	−1.00187	−	3.08345i	−0.0338695	−	0.104239i
$876$	−15.1528	−	11.0092i	−0.511966	−	0.371965i
$877$	−14.5024	+	10.5366i	−0.489711	+	0.355796i	−0.805073	−	0.593176i	$-0.797874\pi$
$877$	−14.5024	+	10.5366i	−0.489711	+	0.355796i	0.315362	+	0.948971i	$0.397874\pi$
$878$	6.39258	−	19.6744i	0.215739	−	0.663977i
$879$	−4.49765			−0.151702
$880$		0			0
$881$	−17.3276			−0.583780			−0.291890	−	0.956452i	$-0.594284\pi$
$881$	−17.3276			−0.583780			−0.291890	+	0.956452i	$0.594284\pi$
$882$	0.528621	−	1.62693i	0.0177996	−	0.0547815i
$883$	−17.6965	+	12.8572i	−0.595534	+	0.432680i	−0.844291	−	0.535885i	$-0.819978\pi$
$883$	−17.6965	+	12.8572i	−0.595534	+	0.432680i	0.248757	+	0.968566i	$0.419978\pi$
$884$	10.3736	+	7.53686i	0.348902	+	0.253492i
$885$	−3.07959	−	9.47800i	−0.103519	−	0.318599i
$886$	6.86029	+	21.1138i	0.230476	+	0.709332i
$887$	−20.7188	−	15.0531i	−0.695668	−	0.505432i	0.182851	−	0.983141i	$-0.441468\pi$
$887$	−20.7188	−	15.0531i	−0.695668	−	0.505432i	−0.878518	+	0.477708i	$0.841468\pi$
$888$	−18.6686	+	13.5636i	−0.626479	+	0.455163i
$889$	−6.17421	+	19.0023i	−0.207076	+	0.637315i
$890$	−26.6608			−0.893674
$891$		0			0
$892$	14.1294			0.473087
$893$	2.87776	−	8.85684i	0.0963006	−	0.296383i
$894$	−5.65980	+	4.11209i	−0.189292	+	0.137529i
$895$	−4.09695	−	2.97661i	−0.136946	−	0.0994971i
$896$	2.56488	+	7.89389i	0.0856867	+	0.263716i
$897$	5.48804	+	16.8904i	0.183240	+	0.563955i
$898$	−14.0559	−	10.2122i	−0.469051	−	0.340786i
$899$	−19.9157	+	14.4696i	−0.664227	+	0.482589i
$900$	3.32073	−	10.2202i	0.110691	−	0.340672i
$901$	41.4130			1.37967
$902$		0			0
$903$	−9.07457			−0.301983
$904$	−9.56901	+	29.4504i	−0.318261	+	0.979505i
$905$	23.8790	−	17.3491i	0.793765	−	0.576704i
$906$	12.7818	+	9.28650i	0.424646	+	0.308523i
$907$	−4.46182	−	13.7321i	−0.148152	−	0.455966i	0.849251	−	0.527990i	$-0.177054\pi$
$907$	−4.46182	−	13.7321i	−0.148152	−	0.455966i	−0.997403	+	0.0720241i	$0.977054\pi$
$908$	1.52670	+	4.69869i	0.0506653	+	0.155932i
$909$	−24.5365	−	17.8268i	−0.813825	−	0.591279i
$910$	4.37922	−	3.18169i	0.145170	−	0.105472i
$911$	11.4910	−	35.3658i	0.380715	−	1.17172i	−0.558827	−	0.829285i	$-0.688748\pi$
$911$	11.4910	−	35.3658i	0.380715	−	1.17172i	0.939541	−	0.342435i	$-0.111252\pi$
$912$	0.647421			0.0214383
$913$		0			0
$914$	1.56769			0.0518545
$915$	−11.5169	+	35.4454i	−0.380738	+	1.17179i
$916$	−25.2986	+	18.3805i	−0.835888	+	0.607308i
$917$	−6.84042	−	4.96986i	−0.225891	−	0.164119i
$918$	−5.46983	−	16.8344i	−0.180531	−	0.555618i
$919$	−4.95958	−	15.2640i	−0.163602	−	0.503514i	0.835329	−	0.549750i	$-0.185277\pi$
$919$	−4.95958	−	15.2640i	−0.163602	−	0.503514i	−0.998931	+	0.0462365i	$0.985277\pi$
$920$	55.4906	+	40.3163i	1.82947	+	1.32919i
$921$	−13.1988	+	9.58949i	−0.434915	+	0.315984i
$922$	−6.37351	+	19.6156i	−0.209900	+	0.646007i
$923$	9.68736			0.318863
$924$		0			0
$925$	−34.3685			−1.13003
$926$	5.38816	−	16.5830i	0.177066	−	0.544952i
$927$	−0.181098	+	0.131575i	−0.00594804	+	0.00432150i
$928$	15.4327	+	11.2125i	0.506603	+	0.368069i
$929$	10.4730	+	32.2326i	0.343608	+	1.05752i	0.962325	+	0.271903i	$0.0876531\pi$
$929$	10.4730	+	32.2326i	0.343608	+	1.05752i	−0.618716	+	0.785615i	$0.712347\pi$
$930$	5.45673	+	16.7941i	0.178933	+	0.550700i
$931$	1.39606	+	1.01430i	0.0457540	+	0.0332423i
$932$	4.13481	−	3.00411i	0.135440	−	0.0984030i
$933$	6.50878	−	20.0320i	0.213088	−	0.655817i
$934$	−13.7109			−0.448635
$935$		0			0
$936$	−12.5094			−0.408883
$937$	−2.85107	+	8.77468i	−0.0931403	+	0.286656i	−0.986765	−	0.162160i	$-0.948154\pi$
$937$	−2.85107	+	8.77468i	−0.0931403	+	0.286656i	0.893624	+	0.448816i	$0.148154\pi$
$938$	2.87921	−	2.09187i	0.0940095	−	0.0683019i
$939$	7.81492	+	5.67787i	0.255030	+	0.185290i
$940$	6.58109	+	20.2545i	0.214652	+	0.660630i
$941$	−16.4900	−	50.7508i	−0.537557	−	1.65443i	−0.738058	−	0.674737i	$-0.764257\pi$
$941$	−16.4900	−	50.7508i	−0.537557	−	1.65443i	0.200501	−	0.979693i	$-0.435743\pi$
$942$	−8.35375	−	6.06936i	−0.272180	−	0.197750i
$943$	36.6431	−	26.6227i	1.19326	−	0.866956i
$944$	0.419338	−	1.29059i	0.0136483	−	0.0420052i
$945$	14.5621			0.473705
$946$		0			0
$947$	31.0986			1.01057			0.505285	−	0.862953i	$-0.331388\pi$
$947$	31.0986			1.01057			0.505285	+	0.862953i	$0.331388\pi$
$948$	−2.82024	+	8.67982i	−0.0915973	+	0.281907i
$949$	−26.2715	+	19.0874i	−0.852809	+	0.619602i
$950$	−4.50017	−	3.26957i	−0.146005	−	0.106079i
$951$	−6.99400	−	21.5253i	−0.226796	−	0.698006i
$952$	3.72526	+	11.4652i	0.120736	+	0.371588i
$953$	−28.2578	−	20.5305i	−0.915361	−	0.665048i	0.0270043	−	0.999635i	$-0.491403\pi$
$953$	−28.2578	−	20.5305i	−0.915361	−	0.665048i	−0.942365	+	0.334587i	$0.891403\pi$
$954$	−13.0060	+	9.44939i	−0.421084	+	0.305935i
$955$	21.3428	−	65.6863i	0.690636	−	2.12556i
$956$	13.3123			0.430550
$957$		0			0
$958$	−17.8393			−0.576361
$959$	2.58170	−	7.94566i	0.0833675	−	0.256579i
$960$	9.25769	−	6.72611i	0.298791	−	0.217084i
$961$	−20.1337	−	14.6280i	−0.649473	−	0.471870i
$962$	4.91940	+	15.1404i	0.158608	+	0.488145i
$963$	2.98409	+	9.18410i	0.0961611	+	0.295953i
$964$	14.3573	+	10.4312i	0.462417	+	0.335965i
$965$	55.7696	−	40.5190i	1.79529	−	1.30435i
$966$	−2.05306	+	6.31868i	−0.0660563	+	0.203300i
$967$	−20.8029			−0.668975			−0.334488	−	0.942400i	$-0.608563\pi$
$967$	−20.8029			−0.668975			−0.334488	+	0.942400i	$0.608563\pi$
$968$		0			0
$969$	7.30507			0.234673
$970$	−2.16929	+	6.67638i	−0.0696516	+	0.214366i
$971$	32.3856	−	23.5295i	1.03930	−	0.755098i	0.0691539	−	0.997606i	$-0.477970\pi$
$971$	32.3856	−	23.5295i	1.03930	−	0.755098i	0.970149	+	0.242508i	$0.0779700\pi$
$972$	−17.2346	−	12.5216i	−0.552799	−	0.401632i
$973$	−4.54668	−	13.9932i	−0.145760	−	0.448603i
$974$	0.715978	+	2.20355i	0.0229414	+	0.0706064i
$975$	6.69671	+	4.86544i	0.214466	+	0.155819i
$976$	−4.10567	+	2.98294i	−0.131419	+	0.0954816i
$977$	2.00431	−	6.16864i	0.0641237	−	0.197352i	−0.913862	−	0.406025i	$-0.866914\pi$
$977$	2.00431	−	6.16864i	0.0641237	−	0.197352i	0.977985	+	0.208673i	$0.0669144\pi$
$978$	4.71878			0.150890
$979$		0			0
$980$	−3.94630			−0.126060
$981$	−2.07416	+	6.38361i	−0.0662228	+	0.203813i
$982$	2.13593	−	1.55185i	0.0681604	−	0.0495214i
$983$	−8.88154	−	6.45282i	−0.283277	−	0.205813i	0.437068	−	0.899428i	$-0.356017\pi$
$983$	−8.88154	−	6.45282i	−0.283277	−	0.205813i	−0.720346	+	0.693615i	$0.756017\pi$
$984$	−4.38006	−	13.4804i	−0.139631	−	0.429740i
$985$	6.17220	+	18.9961i	0.196663	+	0.605266i
$986$	9.66827	+	7.02441i	0.307900	+	0.223703i
$987$	−4.19419	+	3.04726i	−0.133503	+	0.0969953i
$988$	1.55163	−	4.77542i	0.0493639	−	0.151926i
$989$	−79.3275			−2.52247
$990$		0			0
$991$	−59.2666			−1.88267			−0.941333	−	0.337479i	$-0.890426\pi$
$991$	−59.2666			−1.88267			−0.941333	+	0.337479i	$0.890426\pi$
$992$	−13.3824	+	41.1869i	−0.424893	+	1.30769i
$993$	−16.2126	+	11.7791i	−0.514490	+	0.373799i
$994$	2.93190	+	2.13015i	0.0929941	+	0.0675642i
$995$	−14.5989	−	44.9307i	−0.462816	−	1.42440i
$996$	2.99555	+	9.21934i	0.0949175	+	0.292126i
$997$	35.0723	+	25.4815i	1.11075	+	0.807007i	0.982782	−	0.184772i	$-0.0591545\pi$
$997$	35.0723	+	25.4815i	1.11075	+	0.807007i	0.127968	+	0.991778i	$0.459155\pi$
$998$	−13.3595	+	9.70628i	−0.422889	+	0.307247i
$999$	−13.2342	+	40.7306i	−0.418711	+	1.28866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.372.2		24
11.2	odd	10		847.2.f.z.729.2		24
11.3	even	5	inner	847.2.f.y.323.5		24
11.4	even	5		847.2.a.n.1.2	yes	6
11.5	even	5	inner	847.2.f.y.148.2		24
11.6	odd	10		847.2.f.z.148.5		24
11.7	odd	10		847.2.a.m.1.5	✓	6
11.8	odd	10		847.2.f.z.323.2		24
11.9	even	5	inner	847.2.f.y.729.5		24
11.10	odd	2		847.2.f.z.372.5		24
33.26	odd	10		7623.2.a.cp.1.5		6
33.29	even	10		7623.2.a.cs.1.2		6
77.48	odd	10		5929.2.a.bm.1.2		6
77.62	even	10		5929.2.a.bj.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.5	✓	6	11.7	odd	10
847.2.a.n.1.2	yes	6	11.4	even	5
847.2.f.y.148.2		24	11.5	even	5	inner
847.2.f.y.323.5		24	11.3	even	5	inner
847.2.f.y.372.2		24	1.1	even	1	trivial
847.2.f.y.729.5		24	11.9	even	5	inner
847.2.f.z.148.5		24	11.6	odd	10
847.2.f.z.323.2		24	11.8	odd	10
847.2.f.z.372.5		24	11.10	odd	2
847.2.f.z.729.2		24	11.2	odd	10
5929.2.a.bj.1.5		6	77.62	even	10
5929.2.a.bm.1.2		6	77.48	odd	10
7623.2.a.cp.1.5		6	33.26	odd	10
7623.2.a.cs.1.2		6	33.29	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.254493 + 0.783248i) q^{2} +(0.777181 - 0.564655i) q^{3} +(1.06932 + 0.776908i) q^{4} +(0.922616 + 2.83952i) q^{5} +(0.244478 + 0.752427i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.21319 + 1.60798i) q^{8} +(-0.641876 + 1.97549i) q^{9} +O(q^{10})\)	\(q+(-0.254493 + 0.783248i) q^{2} +(0.777181 - 0.564655i) q^{3} +(1.06932 + 0.776908i) q^{4} +(0.922616 + 2.83952i) q^{5} +(0.244478 + 0.752427i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-2.21319 + 1.60798i) q^{8} +(-0.641876 + 1.97549i) q^{9} -2.45885 q^{10} +1.26974 q^{12} +(0.680283 - 2.09370i) q^{13} +(0.666271 - 0.484074i) q^{14} +(2.32039 + 1.68586i) q^{15} +(0.120686 + 0.371434i) q^{16} +(1.36174 + 4.19102i) q^{17} +(-1.38395 - 1.00550i) q^{18} +(1.39606 - 1.01430i) q^{19} +(-1.21947 + 3.75315i) q^{20} -0.960649 q^{21} -8.39774 q^{23} +(-0.812097 + 2.49938i) q^{24} +(-3.16657 + 2.30065i) q^{25} +(1.46676 + 1.06566i) q^{26} +(1.50719 + 4.63865i) q^{27} +(-0.408445 - 1.25706i) q^{28} +(-2.66405 - 1.93555i) q^{29} +(-1.91097 + 1.38840i) q^{30} +(2.31013 - 7.10984i) q^{31} -5.79294 q^{32} -3.62916 q^{34} +(0.922616 - 2.83952i) q^{35} +(-2.22115 + 1.61376i) q^{36} +(7.10374 + 5.16117i) q^{37} +(0.439159 + 1.35159i) q^{38} +(-0.653514 - 2.01131i) q^{39} +(-6.60780 - 4.80085i) q^{40} +(-4.36344 + 3.17023i) q^{41} +(0.244478 - 0.752427i) q^{42} +9.44629 q^{43} -6.20165 q^{45} +(2.13716 - 6.57751i) q^{46} +(4.36600 - 3.17208i) q^{47} +(0.303527 + 0.220525i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.996109 - 3.06571i) q^{50} +(3.42480 + 2.48826i) q^{51} +(2.35405 - 1.71032i) q^{52} +(2.90406 - 8.93778i) q^{53} -4.01678 q^{54} +2.73565 q^{56} +(0.512264 - 1.57659i) q^{57} +(2.19400 - 1.59403i) q^{58} +(-2.81102 - 2.04233i) q^{59} +(1.17149 + 3.60546i) q^{60} +(4.01544 + 12.3582i) q^{61} +(4.98086 + 3.61881i) q^{62} +(1.68045 - 1.22092i) q^{63} +(1.23289 - 3.79444i) q^{64} +6.57274 q^{65} +4.32138 q^{67} +(-1.79989 + 5.53950i) q^{68} +(-6.52656 + 4.74183i) q^{69} +(1.98925 + 1.44527i) q^{70} +(1.35982 + 4.18508i) q^{71} +(-1.75595 - 5.40425i) q^{72} +(-11.9338 - 8.67038i) q^{73} +(-5.85033 + 4.25051i) q^{74} +(-1.16193 + 3.57604i) q^{75} +2.28086 q^{76} +1.74167 q^{78} +(-2.22111 + 6.83589i) q^{79} +(-0.943348 + 0.685382i) q^{80} +(-1.25076 - 0.908732i) q^{81} +(-1.37261 - 4.22446i) q^{82} +(2.35917 + 7.26079i) q^{83} +(-1.02724 - 0.746336i) q^{84} +(-10.6441 + 7.73340i) q^{85} +(-2.40401 + 7.39879i) q^{86} -3.16337 q^{87} +10.8428 q^{89} +(1.57828 - 4.85743i) q^{90} +(-1.78101 + 1.29398i) q^{91} +(-8.97989 - 6.52427i) q^{92} +(-2.21922 - 6.83007i) q^{93} +(1.37341 + 4.22693i) q^{94} +(4.16815 + 3.02834i) q^{95} +(-4.50217 + 3.27102i) q^{96} +(0.882237 - 2.71525i) q^{97} -0.823556 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Introduction

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