LMFDB - Embedded newform 847.2.f.z.372.5

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			372.5
Character	$\chi$	$=$	847.372
Dual form			847.2.f.z.148.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.254493 - 0.783248i) q^{2} +(0.777181 - 0.564655i) q^{3} +(1.06932 + 0.776908i) q^{4} +(0.922616 + 2.83952i) q^{5} +(-0.244478 - 0.752427i) q^{6} +(0.809017 + 0.587785i) q^{7} +(2.21319 - 1.60798i) q^{8} +(-0.641876 + 1.97549i) q^{9} +O(q^{10})$	\(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	−0.819871	−	0.572548i	$-0.805955\pi$
$2$	0.254493	−	0.783248i	0.179954	−	0.553840i	0.999825	+	0.0187075i	$0.00595514\pi$
$3$	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	−0.999992	−	0.00392126i	$-0.998752\pi$
$13$	−0.680283	+	2.09370i	−0.188677	+	0.580687i	0.811316	+	0.584608i	$0.198752\pi$
$14$	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	$-0.920541\pi$
$17$	−1.36174	−	4.19102i	−0.330271	−	1.01647i	0.638733	−	0.769428i	$-0.279459\pi$
$18$	1.38395	+	1.00550i	0.326199	+	0.236998i
$19$	−1.39606	+	1.01430i	−0.320278	+	0.232696i	−0.736294	−	0.676662i	$-0.763426\pi$
$19$	−1.39606	+	1.01430i	−0.320278	+	0.232696i	0.416016	+	0.909357i	$0.363426\pi$
$20$	−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	0.806990	−	0.590566i	$-0.201095\pi$
$29$	2.66405	+	1.93555i	0.494702	+	0.359422i	−0.312288	+	0.949988i	$0.601095\pi$
$30$	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	−0.192385	−	0.981320i	$-0.561622\pi$
$41$	4.36344	−	3.17023i	0.681456	−	0.495106i	0.873840	+	0.486213i	$0.161622\pi$
$42$	0.244478	−	0.752427i	0.0377238	−	0.116102i
$43$	−9.44629			−1.44055			−0.720273	−	0.693691i	$-0.755983\pi$
$43$	−9.44629			−1.44055			−0.720273	+	0.693691i	$0.755983\pi$
$44$		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	$-0.787270\pi$
$61$	−4.01544	−	12.3582i	−0.514124	−	1.58231i	0.270746	−	0.962651i	$-0.412730\pi$
$62$	−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	$0.0315643\pi$
$73$	11.9338	+	8.67038i	1.39674	+	1.01479i	0.401653	+	0.915792i	$0.368436\pi$
$74$	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	$-0.767502\pi$
$79$	2.22111	−	6.83589i	0.249895	−	0.769097i	0.994793	−	0.101919i	$-0.0324982\pi$
$80$	−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	$-0.962383\pi$
$83$	−2.35917	−	7.26079i	−0.258953	−	0.796976i	0.734072	−	0.679072i	$-0.237617\pi$
$84$	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	$-0.641176\pi$
$101$	4.51200	−	13.8865i	0.448961	−	1.38176i	0.878081	−	0.478512i	$-0.158824\pi$
$102$	−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	−0.754553	−	0.656239i	$-0.772146\pi$
$107$	−3.76114	+	2.73263i	−0.363603	+	0.264173i	0.390950	+	0.920412i	$0.372146\pi$
$108$	−1.99213	+	6.13116i	−0.191693	+	0.589971i
$109$	−3.23140			−0.309512			−0.154756	−	0.987953i	$-0.549459\pi$
$109$	−3.23140			−0.309512			−0.154756	+	0.987953i	$0.549459\pi$
$110$		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	$0.246854\pi$
$127$	6.17421	+	19.0023i	0.547872	+	1.68618i	−0.166188	+	0.986094i	$0.553146\pi$
$128$	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	$-0.620426\pi$
$131$	−8.45523			−0.738737			−0.369368	+	0.929283i	$0.620426\pi$
$132$		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	−0.0454990	−	0.998964i	$-0.514488\pi$
$139$	−11.9034	−	8.64830i	−1.00963	−	0.733540i	−0.964132	+	0.265425i	$0.914488\pi$
$140$	−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	$-0.982022\pi$
$149$	−2.73255	−	8.40992i	−0.223859	−	0.688968i	0.774546	−	0.632517i	$-0.217978\pi$
$150$	2.50523	+	1.82015i	0.204551	+	0.148615i
$151$	−16.1560	+	11.7380i	−1.31476	+	0.955225i	−0.314773	+	0.949167i	$0.601929\pi$
$151$	−16.1560	+	11.7380i	−1.31476	+	0.955225i	−0.999982	+	0.00605860i	$0.998071\pi$
$152$	−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	$0.271298\pi$
$167$	−4.09360	+	12.5988i	−0.316772	+	0.974924i	−0.975019	+	0.222122i	$0.928702\pi$
$168$	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	−0.603593	−	0.797292i	$-0.706265\pi$
$173$	−0.418841	+	0.304306i	−0.0318439	+	0.0231359i	0.571749	+	0.820428i	$0.306265\pi$
$174$	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	$0.212222\pi$
$193$	7.13483	+	21.9587i	0.513576	+	1.58062i	−0.272282	+	0.962217i	$0.587778\pi$
$194$	−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	$-0.576596\pi$
$197$	−6.68989			−0.476635			−0.238318	+	0.971187i	$0.576596\pi$
$198$		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	$0.227791\pi$
$211$	−3.50811	+	10.7969i	−0.241508	+	0.743286i	−0.996191	+	0.0871965i	$0.972209\pi$
$212$	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	0.482892	−	0.875680i	$-0.339586\pi$
$227$	−3.02397	−	2.19704i	−0.200708	−	0.145823i	−0.683600	+	0.729857i	$0.739586\pi$
$228$	−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	−0.982537	−	0.186068i	$-0.940426\pi$
$233$	−1.19489	+	3.67750i	−0.0782800	+	0.240921i	0.904257	+	0.426989i	$0.140426\pi$
$234$	−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	−0.819257	−	0.573426i	$-0.805614\pi$
$239$	−8.14816	+	5.91998i	−0.527060	+	0.382932i	0.292197	+	0.956358i	$0.405614\pi$
$240$	−0.346147	+	1.06533i	−0.0223437	+	0.0687669i
$241$	−13.4265			−0.864878			−0.432439	−	0.901663i	$-0.642347\pi$
$241$	−13.4265			−0.864878			−0.432439	+	0.901663i	$0.642347\pi$
$242$		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	$-0.650737\pi$
$263$	−14.7919			−0.912107			−0.456053	+	0.889952i	$0.650737\pi$
$264$		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	0.302389	−	0.953185i	$-0.402216\pi$
$271$	−8.40718	−	6.10818i	−0.510700	−	0.371045i	−0.813089	+	0.582139i	$0.802216\pi$
$272$	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	$0.420160\pi$
$277$	−8.68764	+	26.7378i	−0.521990	+	1.60652i	−0.770193	+	0.637811i	$0.779840\pi$
$278$	−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	0.823276	−	0.567641i	$-0.192144\pi$
$281$	−2.95732	−	9.10171i	−0.176419	−	0.542962i	−0.999695	+	0.0246786i	$0.992144\pi$
$282$	−3.45415	−	2.50959i	−0.205692	−	0.149444i
$283$	−1.33913	+	0.972935i	−0.0796030	+	0.0578350i	−0.626875	−	0.779120i	$-0.715666\pi$
$283$	−1.33913	+	0.972935i	−0.0796030	+	0.0578350i	0.547272	+	0.836955i	$0.315666\pi$
$284$	−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	0.692903	−	0.721031i	$-0.256331\pi$
$293$	3.78772	+	2.75194i	0.221281	+	0.160770i	−0.471622	+	0.881801i	$0.656331\pi$
$294$	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	$-0.338953\pi$
$307$	16.9829			0.969266			0.484633	+	0.874718i	$0.338953\pi$
$308$		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	0.841788	−	0.539809i	$-0.181503\pi$
$337$	10.8039	+	7.84949i	0.588526	+	0.427589i	−0.253262	+	0.967398i	$0.581503\pi$
$338$	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	0.963397	−	0.268080i	$-0.0863892\pi$
$347$	0.492129	+	1.51462i	0.0264189	+	0.0813089i	−0.936978	+	0.349389i	$0.886389\pi$
$348$	3.38266	+	2.45765i	0.181330	+	0.131744i
$349$	5.36763	−	3.89981i	0.287323	−	0.208752i	−0.434782	−	0.900536i	$-0.643175\pi$
$349$	5.36763	−	3.89981i	0.287323	−	0.208752i	0.722105	+	0.691783i	$0.243175\pi$
$350$	−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	0.875526	−	0.483171i	$-0.160515\pi$
$359$	13.0084	+	9.45113i	0.686555	+	0.498811i	−0.188971	+	0.981983i	$0.560515\pi$
$360$	−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	$-0.514332\pi$
$373$	−1.73856			−0.0900192			−0.0450096	+	0.998987i	$0.514332\pi$
$374$		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	$-0.538368\pi$
$409$	11.3365	−	34.8903i	0.560556	−	1.72521i	0.680800	−	0.732470i	$-0.261632\pi$
$410$	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	$-0.662254\pi$
$431$	8.71677	−	26.8275i	0.419872	−	1.29223i	0.907820	−	0.419361i	$-0.137746\pi$
$432$	−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	$-0.295394\pi$
$439$	25.1189			1.19886			0.599430	+	0.800427i	$0.295394\pi$
$440$		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	0.963872	−	0.266367i	$-0.0858234\pi$
$457$	0.588232	+	1.81039i	0.0275163	+	0.0846866i	−0.936355	+	0.351054i	$0.885823\pi$
$458$	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	$-0.698202\pi$
$461$	−25.0440			−1.16641			−0.583207	+	0.812324i	$0.698202\pi$
$462$		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	$-0.935217\pi$
$479$	−6.69371	−	20.6011i	−0.305843	−	0.941289i	0.673518	−	0.739171i	$-0.264783\pi$
$480$	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	0.644768	−	0.764378i	$-0.276954\pi$
$491$	2.59355	+	1.88432i	0.117045	+	0.0850383i	−0.527723	+	0.849417i	$0.676954\pi$
$492$	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	0.281307	−	0.959618i	$-0.409232\pi$
$503$	28.7273	−	20.8716i	1.28089	−	0.930618i	0.999579	+	0.0289998i	$0.00923222\pi$
$504$	−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	$-0.934607\pi$
$523$	−7.01794	−	21.5990i	−0.306873	−	0.944458i	0.672098	−	0.740462i	$-0.265393\pi$
$524$	−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	$0.221105\pi$
$541$	−5.33821	+	16.4293i	−0.229508	+	0.706352i	−0.997803	+	0.0662562i	$0.978895\pi$
$542$	−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	−0.791843	−	0.610725i	$-0.790878\pi$
$547$	−10.6580	+	7.74346i	−0.455701	+	0.331086i	0.336141	+	0.941812i	$0.390878\pi$
$548$	−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	0.350054	−	0.936730i	$-0.386163\pi$
$557$	−10.2111	−	7.41877i	−0.432656	−	0.314343i	−0.782710	+	0.622386i	$0.786163\pi$
$558$	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	−0.994415	−	0.105541i	$-0.966343\pi$
$563$	−3.03431	+	9.33865i	−0.127881	+	0.393577i	0.866534	+	0.499118i	$0.166343\pi$
$564$	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	−0.186435	−	0.982467i	$-0.559693\pi$
$569$	16.4671	−	11.9640i	0.690335	−	0.501558i	0.876770	+	0.480910i	$0.159693\pi$
$570$	−1.25958	+	3.87659i	−0.0527580	+	0.162372i
$571$	32.3174			1.35244			0.676221	−	0.736699i	$-0.263616\pi$
$571$	32.3174			1.35244			0.676221	+	0.736699i	$0.263616\pi$
$572$		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	$-0.317441\pi$
$593$	26.4263			1.08520			0.542598	+	0.839992i	$0.317441\pi$
$594$		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	0.500550	−	0.865707i	$-0.333131\pi$
$601$	−4.12121	−	2.99424i	−0.168108	−	0.122137i	−0.668658	+	0.743570i	$0.733131\pi$
$602$	−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	$0.313612\pi$
$607$	−9.46848	+	29.1410i	−0.384314	+	1.18280i	−0.936977	+	0.349392i	$0.886388\pi$
$608$	−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	−0.914305	−	0.405026i	$-0.867263\pi$
$613$	−20.0952	+	14.6000i	−0.811639	+	0.589690i	0.102667	+	0.994716i	$0.467263\pi$
$614$	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	$-0.529281\pi$
$659$	−4.71629			−0.183721			−0.0918603	+	0.995772i	$0.529281\pi$
$660$		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	−0.915845	−	0.401532i	$-0.868478\pi$
$673$	1.58517	−	4.87866i	0.0611039	−	0.188058i	0.976949	+	0.213474i	$0.0684778\pi$
$674$	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	$0.344908\pi$
$677$	15.8405	+	48.7521i	0.608800	+	1.87369i	0.140616	+	0.990064i	$0.455092\pi$
$678$	−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	−0.952436	−	0.304737i	$-0.901431\pi$
$701$	−25.3362	+	18.4078i	−0.956933	+	0.695253i	−0.00449682	+	0.999990i	$0.501431\pi$
$702$	−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	−0.0451688	−	0.998979i	$-0.514383\pi$
$733$	−27.3234	−	19.8516i	−1.00921	−	0.733236i	−0.964044	+	0.265743i	$0.914383\pi$
$734$	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	$-0.612064\pi$
$739$	13.2083	−	40.6511i	0.485876	−	1.49537i	0.830708	−	0.556709i	$-0.187936\pi$
$740$	−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	$-0.961646\pi$
$743$	−7.09394	−	21.8329i	−0.260252	−	0.800972i	0.732498	−	0.680769i	$-0.238354\pi$
$744$	−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	$0.348788\pi$
$761$	−12.0096	+	36.9619i	−0.435349	+	1.33987i	−0.892728	+	0.450595i	$0.851212\pi$
$762$	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	$-0.277772\pi$
$769$	35.6509			1.28560			0.642802	+	0.766032i	$0.277772\pi$
$770$		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	0.930889	−	0.365303i	$-0.119035\pi$
$787$	−1.03618	−	3.18904i	−0.0369359	−	0.113677i	−0.967824	+	0.251626i	$0.919035\pi$
$788$	−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	0.981764	−	0.190103i	$-0.0608823\pi$
$809$	2.15484	+	6.63192i	0.0757602	+	0.233166i	−0.906004	+	0.423270i	$0.860882\pi$
$810$	−3.07544	−	2.23443i	−0.108060	−	0.0785100i
$811$	4.80052	−	3.48778i	0.168569	−	0.122473i	−0.500302	−	0.865851i	$-0.666778\pi$
$811$	4.80052	−	3.48778i	0.168569	−	0.122473i	0.668871	+	0.743378i	$0.266778\pi$
$812$	−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	0.992026	−	0.126031i	$-0.0402240\pi$
$821$	33.7739	+	24.5382i	1.17872	+	0.856388i	0.186690	+	0.982419i	$0.440224\pi$
$822$	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	−0.854955	−	0.518703i	$-0.826415\pi$
$827$	4.07219	−	12.5329i	0.141604	−	0.435813i	0.996559	+	0.0828903i	$0.0264151\pi$
$828$	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	0.913304	−	0.407278i	$-0.133522\pi$
$853$	−1.89741	−	5.83963i	−0.0649662	−	0.199945i	−0.978271	+	0.207332i	$0.933522\pi$
$854$	−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	$-0.700401\pi$
$857$	−34.4740			−1.17761			−0.588804	+	0.808276i	$0.700401\pi$
$858$		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	−0.315362	−	0.948971i	$-0.602126\pi$
$877$	14.5024	−	10.5366i	0.489711	−	0.355796i	0.805073	+	0.593176i	$0.202126\pi$
$878$	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	0.878518	−	0.477708i	$-0.158532\pi$
$887$	20.7188	+	15.0531i	0.695668	+	0.505432i	−0.182851	+	0.983141i	$0.558532\pi$
$888$	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	0.998931	−	0.0462365i	$-0.0147228\pi$
$919$	4.95958	+	15.2640i	0.163602	+	0.503514i	−0.835329	+	0.549750i	$0.814723\pi$
$920$	−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	−0.893624	−	0.448816i	$-0.851846\pi$
$937$	2.85107	−	8.77468i	0.0931403	−	0.286656i	0.986765	+	0.162160i	$0.0518459\pi$
$938$	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	$0.235743\pi$
$941$	16.4900	+	50.7508i	0.537557	+	1.65443i	−0.200501	+	0.979693i	$0.564257\pi$
$942$	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	0.942365	−	0.334587i	$-0.108597\pi$
$953$	28.2578	+	20.5305i	0.915361	+	0.665048i	−0.0270043	+	0.999635i	$0.508597\pi$
$954$	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	$-0.391437\pi$
$967$	20.8029			0.668975			0.334488	+	0.942400i	$0.391437\pi$
$968$		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	−0.127968	−	0.991778i	$-0.540845\pi$
$997$	−35.0723	−	25.4815i	−1.11075	−	0.807007i	−0.982782	+	0.184772i	$0.940845\pi$
$998$	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.z.372.5		24
11.2	odd	10		847.2.f.y.729.5		24
11.3	even	5	inner	847.2.f.z.323.2		24
11.4	even	5		847.2.a.m.1.5	✓	6
11.5	even	5	inner	847.2.f.z.148.5		24
11.6	odd	10		847.2.f.y.148.2		24
11.7	odd	10		847.2.a.n.1.2	yes	6
11.8	odd	10		847.2.f.y.323.5		24
11.9	even	5	inner	847.2.f.z.729.2		24
11.10	odd	2		847.2.f.y.372.2		24
33.26	odd	10		7623.2.a.cs.1.2		6
33.29	even	10		7623.2.a.cp.1.5		6
77.48	odd	10		5929.2.a.bj.1.5		6
77.62	even	10		5929.2.a.bm.1.2		6

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

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