LMFDB - Embedded newform 546.2.bz.b.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.b.187.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.05962 + 0.819823i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.47842 + 0.925986i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.05962 + 0.819823i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.47842 + 0.925986i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.58378 + 2.74318i) q^{10} +(-0.0343612 - 0.128238i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.467804 + 3.57507i) q^{13} +(-0.252972 - 2.63363i) q^{14} +(2.23980 + 2.23980i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.61860 + 2.80350i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(3.22495 + 0.864122i) q^{19} +(-2.23980 - 2.23980i) q^{20} +(-2.60936 - 0.437281i) q^{21} +0.132761 q^{22} +(1.82480 - 1.05355i) q^{23} +(0.965926 - 0.258819i) q^{24} +(4.35904 + 2.51669i) q^{25} +(-3.33218 - 1.37716i) q^{26} +1.00000i q^{27} +(2.60936 + 0.437281i) q^{28} +2.41342 q^{29} +(-2.74318 + 1.58378i) q^{30} +(-0.494026 - 1.84373i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.0343612 - 0.128238i) q^{33} +(-2.28905 - 2.28905i) q^{34} +(-8.34216 + 0.801303i) q^{35} -1.00000i q^{36} +(6.30977 + 1.69070i) q^{37} +(-1.66935 + 2.89141i) q^{38} +(-2.19267 + 2.86220i) q^{39} +(2.74318 - 1.58378i) q^{40} +(-4.28763 + 4.28763i) q^{41} +(1.09773 - 2.40728i) q^{42} -6.94294i q^{43} +(-0.0343612 + 0.128238i) q^{44} +(0.819823 + 3.05962i) q^{45} +(0.545357 + 2.03530i) q^{46} +(2.06016 - 7.68863i) q^{47} +1.00000i q^{48} +(5.28510 - 4.58996i) q^{49} +(-3.55914 + 3.55914i) q^{50} +(-2.80350 + 1.61860i) q^{51} +(2.19267 - 2.86220i) q^{52} +(-4.30897 + 7.46335i) q^{53} +(-0.965926 - 0.258819i) q^{54} -0.420528i q^{55} +(-1.09773 + 2.40728i) q^{56} +(2.36082 + 2.36082i) q^{57} +(-0.624639 + 2.33118i) q^{58} +(-6.58136 + 1.76347i) q^{59} +(-0.819823 - 3.05962i) q^{60} +(-9.51563 + 5.49385i) q^{61} +1.90877 q^{62} +(-2.04114 - 1.68338i) q^{63} -1.00000i q^{64} +(-4.36223 + 10.5549i) q^{65} +(0.114975 + 0.0663807i) q^{66} +(12.2828 - 3.29118i) q^{67} +(2.80350 - 1.61860i) q^{68} +2.10710 q^{69} +(1.38511 - 8.26530i) q^{70} +(-7.99048 - 7.99048i) q^{71} +(0.965926 + 0.258819i) q^{72} +(6.08308 - 1.62996i) q^{73} +(-3.26618 + 5.65719i) q^{74} +(2.51669 + 4.35904i) q^{75} +(-2.36082 - 2.36082i) q^{76} +(0.203908 + 0.286008i) q^{77} +(-2.19717 - 2.85875i) q^{78} +(-6.51047 - 11.2765i) q^{79} +(0.819823 + 3.05962i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.03181 - 5.25125i) q^{82} +(-0.334721 + 0.334721i) q^{83} +(2.04114 + 1.68338i) q^{84} +(-7.25067 + 7.25067i) q^{85} +(6.70636 + 1.79696i) q^{86} +(2.09008 + 1.20671i) q^{87} +(-0.114975 - 0.0663807i) q^{88} +(4.46531 - 16.6648i) q^{89} -3.16755 q^{90} +(-2.15106 - 9.29371i) q^{91} -2.10710 q^{92} +(0.494026 - 1.84373i) q^{93} +(6.89344 + 3.97993i) q^{94} +(9.15868 + 5.28777i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(4.12633 - 4.12633i) q^{97} +(3.06568 + 6.29298i) q^{98} +(0.0938764 - 0.0938764i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	3.05962	+	0.819823i	1.36830	+	0.366636i	0.866859	−	0.498554i	$-0.166135\pi$
$5$	3.05962	+	0.819823i	1.36830	+	0.366636i	0.501445	+	0.865190i	$0.332802\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−2.47842	+	0.925986i	−0.936754	+	0.349990i
$7$	−2.47842	+	0.925986i	−0.936754	+	0.349990i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.58378	+	2.74318i	−0.500834	+	0.867470i
$11$	−0.0343612	−	0.128238i	−0.0103603	−	0.0386651i	0.960552	−	0.278100i	$-0.0897046\pi$
$11$	−0.0343612	−	0.128238i	−0.0103603	−	0.0386651i	−0.970912	+	0.239435i	$0.923038\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−0.467804	+	3.57507i	−0.129746	+	0.991547i
$13$	−0.467804	+	3.57507i	−0.129746	+	0.991547i
$14$	−0.252972	−	2.63363i	−0.0676097	−	0.703867i
$15$	2.23980	+	2.23980i	0.578313	+	0.578313i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.61860	+	2.80350i	−0.392568	+	0.679948i	−0.992787	−	0.119887i	$-0.961747\pi$
$17$	−1.61860	+	2.80350i	−0.392568	+	0.679948i	0.600219	+	0.799835i	$0.295080\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	3.22495	+	0.864122i	0.739853	+	0.198243i	0.609013	−	0.793160i	$-0.291566\pi$
$19$	3.22495	+	0.864122i	0.739853	+	0.198243i	0.130840	+	0.991403i	$0.458232\pi$
$20$	−2.23980	−	2.23980i	−0.500834	−	0.500834i
$21$	−2.60936	−	0.437281i	−0.569410	−	0.0954225i
$22$	0.132761			0.0283048
$23$	1.82480	−	1.05355i	0.380497	−	0.219680i	−0.297537	−	0.954710i	$-0.596165\pi$
$23$	1.82480	−	1.05355i	0.380497	−	0.219680i	0.678035	+	0.735030i	$0.262832\pi$
$24$	0.965926	−	0.258819i	0.197169	−	0.0528312i
$25$	4.35904	+	2.51669i	0.871807	+	0.503338i
$26$	−3.33218	−	1.37716i	−0.653494	−	0.270084i
$27$			1.00000i			0.192450i
$28$	2.60936	+	0.437281i	0.493124	+	0.0826383i
$29$	2.41342			0.448161			0.224080	−	0.974571i	$-0.428062\pi$
$29$	2.41342			0.448161			0.224080	+	0.974571i	$0.428062\pi$
$30$	−2.74318	+	1.58378i	−0.500834	+	0.289157i
$31$	−0.494026	−	1.84373i	−0.0887297	−	0.331144i	0.907265	−	0.420560i	$-0.138166\pi$
$31$	−0.494026	−	1.84373i	−0.0887297	−	0.331144i	−0.995994	+	0.0894164i	$0.971500\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.0343612	−	0.128238i	0.00598151	−	0.0223233i
$34$	−2.28905	−	2.28905i	−0.392568	−	0.392568i
$35$	−8.34216	+	0.801303i	−1.41008	+	0.135445i
$36$		−	1.00000i		−	0.166667i
$37$	6.30977	+	1.69070i	1.03732	+	0.277949i	0.737003	−	0.675890i	$-0.236241\pi$
$37$	6.30977	+	1.69070i	1.03732	+	0.277949i	0.300318	+	0.953839i	$0.402907\pi$
$38$	−1.66935	+	2.89141i	−0.270805	+	0.469048i
$39$	−2.19267	+	2.86220i	−0.351108	+	0.458319i
$40$	2.74318	−	1.58378i	0.433735	−	0.250417i
$41$	−4.28763	+	4.28763i	−0.669615	+	0.669615i	−0.957627	−	0.288012i	$-0.907006\pi$
$41$	−4.28763	+	4.28763i	−0.669615	+	0.669615i	0.288012	+	0.957627i	$0.407006\pi$
$42$	1.09773	−	2.40728i	0.169384	−	0.371451i
$43$		−	6.94294i		−	1.05879i	−0.848376	−	0.529394i	$-0.822419\pi$
$43$		−	6.94294i		−	1.05879i	0.848376	−	0.529394i	$-0.177581\pi$
$44$	−0.0343612	+	0.128238i	−0.00518014	+	0.0193325i
$45$	0.819823	+	3.05962i	0.122212	+	0.456101i
$46$	0.545357	+	2.03530i	0.0804086	+	0.300089i
$47$	2.06016	−	7.68863i	0.300506	−	1.12150i	−0.636240	−	0.771491i	$-0.719511\pi$
$47$	2.06016	−	7.68863i	0.300506	−	1.12150i	0.936746	−	0.350011i	$-0.113822\pi$
$48$			1.00000i			0.144338i
$49$	5.28510	−	4.58996i	0.755014	−	0.655708i
$50$	−3.55914	+	3.55914i	−0.503338	+	0.503338i
$51$	−2.80350	+	1.61860i	−0.392568	+	0.226649i
$52$	2.19267	−	2.86220i	0.304068	−	0.396916i
$53$	−4.30897	+	7.46335i	−0.591882	+	1.02517i	0.402097	+	0.915597i	$0.368282\pi$
$53$	−4.30897	+	7.46335i	−0.591882	+	1.02517i	−0.993979	+	0.109573i	$0.965052\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$		−	0.420528i		−	0.0567040i
$56$	−1.09773	+	2.40728i	−0.146691	+	0.321686i
$57$	2.36082	+	2.36082i	0.312699	+	0.312699i
$58$	−0.624639	+	2.33118i	−0.0820191	+	0.306099i
$59$	−6.58136	+	1.76347i	−0.856820	+	0.229584i	−0.660380	−	0.750932i	$-0.729605\pi$
$59$	−6.58136	+	1.76347i	−0.856820	+	0.229584i	−0.196440	+	0.980516i	$0.562938\pi$
$60$	−0.819823	−	3.05962i	−0.105839	−	0.394995i
$61$	−9.51563	+	5.49385i	−1.21835	+	0.703416i	−0.964565	−	0.263844i	$-0.915009\pi$
$61$	−9.51563	+	5.49385i	−1.21835	+	0.703416i	−0.253787	+	0.967260i	$0.581676\pi$
$62$	1.90877			0.242414
$63$	−2.04114	−	1.68338i	−0.257159	−	0.212086i
$64$		−	1.00000i		−	0.125000i
$65$	−4.36223	+	10.5549i	−0.541068	+	1.30917i
$66$	0.114975	+	0.0663807i	0.0141524	+	0.00817090i
$67$	12.2828	−	3.29118i	1.50059	−	0.402081i	0.587291	−	0.809376i	$-0.300195\pi$
$67$	12.2828	−	3.29118i	1.50059	−	0.402081i	0.913297	+	0.407295i	$0.133528\pi$
$68$	2.80350	−	1.61860i	0.339974	−	0.196284i
$69$	2.10710			0.253665
$70$	1.38511	−	8.26530i	0.165552	−	0.987892i
$71$	−7.99048	−	7.99048i	−0.948296	−	0.948296i	0.0504317	−	0.998728i	$-0.483940\pi$
$71$	−7.99048	−	7.99048i	−0.948296	−	0.948296i	−0.998728	+	0.0504317i	$0.983940\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	6.08308	−	1.62996i	0.711970	−	0.190772i	0.115384	−	0.993321i	$-0.463190\pi$
$73$	6.08308	−	1.62996i	0.711970	−	0.190772i	0.596586	+	0.802549i	$0.296523\pi$
$74$	−3.26618	+	5.65719i	−0.379686	+	0.657635i
$75$	2.51669	+	4.35904i	0.290602	+	0.503338i
$76$	−2.36082	−	2.36082i	−0.270805	−	0.270805i
$77$	0.203908	+	0.286008i	0.0232374	+	0.0325937i
$78$	−2.19717	−	2.85875i	−0.248781	−	0.323689i
$79$	−6.51047	−	11.2765i	−0.732485	−	1.26870i	−0.955818	−	0.293959i	$-0.905027\pi$
$79$	−6.51047	−	11.2765i	−0.732485	−	1.26870i	0.223333	−	0.974742i	$-0.428306\pi$
$80$	0.819823	+	3.05962i	0.0916590	+	0.342076i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.03181	−	5.25125i	−0.334808	−	0.579904i
$83$	−0.334721	+	0.334721i	−0.0367404	+	0.0367404i	−0.725238	−	0.688498i	$-0.758270\pi$
$83$	−0.334721	+	0.334721i	−0.0367404	+	0.0367404i	0.688498	+	0.725238i	$0.258270\pi$
$84$	2.04114	+	1.68338i	0.222706	+	0.183672i
$85$	−7.25067	+	7.25067i	−0.786446	+	0.786446i
$86$	6.70636	+	1.79696i	0.723166	+	0.193772i
$87$	2.09008	+	1.20671i	0.224080	+	0.129373i
$88$	−0.114975	−	0.0663807i	−0.0122563	−	0.00707620i
$89$	4.46531	−	16.6648i	0.473322	−	1.76646i	−0.154386	−	0.988011i	$-0.549340\pi$
$89$	4.46531	−	16.6648i	0.473322	−	1.76646i	0.627707	−	0.778449i	$-0.283993\pi$
$90$	−3.16755			−0.333889
$91$	−2.15106	−	9.29371i	−0.225492	−	0.974245i
$92$	−2.10710			−0.219680
$93$	0.494026	−	1.84373i	0.0512281	−	0.191186i
$94$	6.89344	+	3.97993i	0.711004	+	0.410498i
$95$	9.15868	+	5.28777i	0.939661	+	0.542513i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	4.12633	−	4.12633i	0.418965	−	0.418965i	−0.465882	−	0.884847i	$-0.654263\pi$
$97$	4.12633	−	4.12633i	0.418965	−	0.418965i	0.884847	+	0.465882i	$0.154263\pi$
$98$	3.06568	+	6.29298i	0.309680	+	0.635687i
$99$	0.0938764	−	0.0938764i	0.00943494	−	0.00943494i
$100$	−2.51669	−	4.35904i	−0.251669	−	0.435904i
$101$	3.22882	−	5.59248i	0.321279	−	0.556472i	−0.659473	−	0.751728i	$-0.729221\pi$
$101$	3.22882	−	5.59248i	0.321279	−	0.556472i	0.980752	+	0.195256i	$0.0625538\pi$
$102$	−0.837849	−	3.12690i	−0.0829594	−	0.309609i
$103$	6.04770	+	10.4749i	0.595897	+	1.03212i	0.993420	+	0.114532i	$0.0365369\pi$
$103$	6.04770	+	10.4749i	0.595897	+	1.03212i	−0.397522	+	0.917593i	$0.630130\pi$
$104$	2.19717	+	2.85875i	0.215450	+	0.280323i
$105$	−7.62517	−	3.47713i	−0.744141	−	0.339333i
$106$	−6.09380	−	6.09380i	−0.591882	−	0.591882i
$107$	2.05254	+	3.55510i	0.198426	+	0.343684i	0.948018	−	0.318216i	$-0.103084\pi$
$107$	2.05254	+	3.55510i	0.198426	+	0.343684i	−0.749592	+	0.661900i	$0.769750\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	14.4548	−	3.87315i	1.38452	−	0.370980i	0.511758	−	0.859130i	$-0.328995\pi$
$109$	14.4548	−	3.87315i	1.38452	−	0.370980i	0.872760	+	0.488149i	$0.162328\pi$
$110$	0.406199	+	0.108841i	0.0387296	+	0.0103776i
$111$	4.61908	+	4.61908i	0.438423	+	0.438423i
$112$	−2.04114	−	1.68338i	−0.192869	−	0.159064i
$113$	−8.11684			−0.763568			−0.381784	−	0.924252i	$-0.624690\pi$
$113$	−8.11684			−0.763568			−0.381784	+	0.924252i	$0.624690\pi$
$114$	−2.89141	+	1.66935i	−0.270805	+	0.156349i
$115$	6.44692	−	1.72745i	0.601179	−	0.161085i
$116$	−2.09008	−	1.20671i	−0.194059	−	0.112040i
$117$	−3.33001	+	1.38241i	−0.307859	+	0.127804i
$118$		−	6.81352i		−	0.627236i
$119$	1.41557	−	8.44704i	0.129765	−	0.774339i
$120$	3.16755			0.289157
$121$	9.51102	−	5.49119i	0.864638	−	0.499199i
$122$	−2.84383	−	10.6133i	−0.257468	−	0.960884i
$123$	−5.85701	+	1.56938i	−0.528109	+	0.141506i
$124$	−0.494026	+	1.84373i	−0.0443649	+	0.165572i
$125$	0.0747675	+	0.0747675i	0.00668741	+	0.00668741i
$126$	2.15430	−	1.53590i	0.191921	−	0.136828i
$127$		−	2.15596i		−	0.191311i	−0.995415	−	0.0956554i	$-0.969505\pi$
$127$		−	2.15596i		−	0.191311i	0.995415	−	0.0956554i	$-0.0304947\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	3.47147	−	6.01276i	0.305646	−	0.529394i
$130$	−9.06618	−	6.94539i	−0.795156	−	0.609151i
$131$	16.9467	−	9.78416i	1.48064	−	0.854846i	0.480878	−	0.876788i	$-0.340318\pi$
$131$	16.9467	−	9.78416i	1.48064	−	0.854846i	0.999759	+	0.0219414i	$0.00698473\pi$
$132$	−0.0938764	+	0.0938764i	−0.00817090	+	0.00817090i
$133$	−8.79292	+	0.844601i	−0.762443	+	0.0732362i
$134$			12.7161i			1.09851i
$135$	−0.819823	+	3.05962i	−0.0705591	+	0.263330i
$136$	0.837849	+	3.12690i	0.0718450	+	0.268129i
$137$	−4.91322	−	18.3364i	−0.419764	−	1.56658i	−0.775097	−	0.631842i	$-0.782299\pi$
$137$	−4.91322	−	18.3364i	−0.419764	−	1.56658i	0.355333	−	0.934740i	$-0.384367\pi$
$138$	−0.545357	+	2.03530i	−0.0464239	+	0.173256i
$139$			12.5387i			1.06351i	0.846897	+	0.531757i	$0.178468\pi$
$139$			12.5387i			1.06351i	−0.846897	+	0.531757i	$0.821532\pi$
$140$	7.62517	+	3.47713i	0.644445	+	0.293871i
$141$	5.62847	−	5.62847i	0.474003	−	0.474003i
$142$	9.78630	−	5.65012i	0.821248	−	0.474148i
$143$	0.474533	−	0.0628536i	0.0396825	−	0.00525609i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	7.38414	+	1.97857i	0.613220	+	0.164312i
$146$			6.29766i			0.521198i
$147$	6.87201	−	1.33247i	0.566794	−	0.109900i
$148$	−4.61908	−	4.61908i	−0.379686	−	0.379686i
$149$	−1.47715	+	5.51281i	−0.121013	+	0.451627i	−0.999666	−	0.0258335i	$-0.991776\pi$
$149$	−1.47715	+	5.51281i	−0.121013	+	0.451627i	0.878653	+	0.477461i	$0.158443\pi$
$150$	−4.86187	+	1.30273i	−0.396970	+	0.106368i
$151$	2.46738	+	9.20838i	0.200792	+	0.749367i	0.990691	+	0.136130i	$0.0434664\pi$
$151$	2.46738	+	9.20838i	0.200792	+	0.749367i	−0.789899	+	0.613237i	$0.789867\pi$
$152$	2.89141	−	1.66935i	0.234524	−	0.135403i
$153$	−3.23720			−0.261712
$154$	−0.329038	+	0.122935i	−0.0265146	+	0.00990640i
$155$		−	6.04613i		−	0.485637i
$156$	3.33001	−	1.38241i	0.266614	−	0.110681i
$157$	18.6519	+	10.7687i	1.48859	+	0.859436i	0.999915	−	0.0130320i	$-0.00414833\pi$
$157$	18.6519	+	10.7687i	1.48859	+	0.859436i	0.488672	+	0.872468i	$0.337482\pi$
$158$	12.5773	−	3.37007i	1.00059	−	0.268108i
$159$	−7.46335	+	4.30897i	−0.591882	+	0.341723i
$160$	−3.16755			−0.250417
$161$	−3.54705	+	4.30088i	−0.279546	+	0.338956i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−0.202387	−	0.0542293i	−0.0158521	−	0.00424757i	0.250884	−	0.968017i	$-0.419279\pi$
$163$	−0.202387	−	0.0542293i	−0.0158521	−	0.00424757i	−0.266736	+	0.963770i	$0.585945\pi$
$164$	5.85701	−	1.56938i	0.457356	−	0.122548i
$165$	0.210264	−	0.364188i	0.0163690	−	0.0283520i
$166$	−0.236683	−	0.409947i	−0.0183702	−	0.0318181i
$167$	−2.04064	−	2.04064i	−0.157909	−	0.157909i	0.623730	−	0.781640i	$-0.285616\pi$
$167$	−2.04064	−	2.04064i	−0.157909	−	0.157909i	−0.781640	+	0.623730i	$0.785616\pi$
$168$	−2.15430	+	1.53590i	−0.166208	+	0.118497i
$169$	−12.5623	−	3.34487i	−0.966332	−	0.257298i
$170$	−5.12700	−	8.88022i	−0.393223	−	0.681082i
$171$	0.864122	+	3.22495i	0.0660810	+	0.246618i
$172$	−3.47147	+	6.01276i	−0.264697	+	0.458469i
$173$	6.64527	+	11.5099i	0.505230	+	0.875085i	0.999982	+	0.00605019i	$0.00192585\pi$
$173$	6.64527	+	11.5099i	0.505230	+	0.875085i	−0.494751	+	0.869035i	$0.664741\pi$
$174$	−1.70654	+	1.70654i	−0.129373	+	0.129373i
$175$	−13.1339	−	2.20100i	−0.992832	−	0.166380i
$176$	0.0938764	−	0.0938764i	0.00707620	−	0.00707620i
$177$	−6.58136	−	1.76347i	−0.494685	−	0.132551i
$178$	14.9412	+	8.62631i	1.11989	+	0.646569i
$179$	0.516941	+	0.298456i	0.0386380	+	0.0223077i	0.519195	−	0.854656i	$-0.326232\pi$
$179$	0.516941	+	0.298456i	0.0386380	+	0.0223077i	−0.480557	+	0.876964i	$0.659565\pi$
$180$	0.819823	−	3.05962i	0.0611060	−	0.228051i
$181$	−8.83889			−0.656989			−0.328495	−	0.944506i	$-0.606541\pi$
$181$	−8.83889			−0.656989			−0.328495	+	0.944506i	$0.606541\pi$
$182$	9.53376	+	0.327628i	0.706690	+	0.0242854i
$183$	−10.9877			−0.812235
$184$	0.545357	−	2.03530i	0.0402043	−	0.150044i
$185$	17.9194	+	10.3458i	1.31746	+	0.760638i
$186$	1.65304	+	0.954385i	0.121207	+	0.0699789i
$187$	0.415131	+	0.111234i	0.0303574	+	0.00813423i
$188$	−5.62847	+	5.62847i	−0.410498	+	0.410498i
$189$	−0.925986	−	2.47842i	−0.0673556	−	0.180278i
$190$	−7.47803	+	7.47803i	−0.542513	+	0.542513i
$191$	−7.84119	−	13.5813i	−0.567369	−	0.982711i	−0.996825	−	0.0796236i	$-0.974628\pi$
$191$	−7.84119	−	13.5813i	−0.567369	−	0.982711i	0.429456	−	0.903088i	$-0.358705\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−4.57224	−	17.0638i	−0.329117	−	1.22828i	−0.910108	−	0.414372i	$-0.864001\pi$
$193$	−4.57224	−	17.0638i	−0.329117	−	1.22828i	0.580990	−	0.813910i	$-0.302665\pi$
$194$	2.91776	+	5.05370i	0.209483	+	0.362835i
$195$	−9.05523	+	6.95966i	−0.648458	+	0.498391i
$196$	−6.87201	+	1.33247i	−0.490858	+	0.0951765i
$197$	−5.05240	−	5.05240i	−0.359969	−	0.359969i	0.503833	−	0.863801i	$-0.331923\pi$
$197$	−5.05240	−	5.05240i	−0.359969	−	0.359969i	−0.863801	+	0.503833i	$0.831923\pi$
$198$	0.0663807	+	0.114975i	0.00471747	+	0.00817090i
$199$	7.81296	−	13.5324i	0.553846	−	0.959289i	−0.444147	−	0.895954i	$-0.646493\pi$
$199$	7.81296	−	13.5324i	0.553846	−	0.959289i	0.997992	−	0.0633348i	$-0.0201736\pi$
$200$	4.86187	−	1.30273i	0.343786	−	0.0921173i
$201$	12.2828	+	3.29118i	0.866365	+	0.232142i
$202$	4.56624	+	4.56624i	0.321279	+	0.321279i
$203$	−5.98146	+	2.23479i	−0.419816	+	0.156852i
$204$	3.23720			0.226649
$205$	−16.6336	+	9.60342i	−1.16174	+	0.670732i
$206$	−11.6833	+	3.13052i	−0.814011	+	0.218114i
$207$	1.82480	+	1.05355i	0.126832	+	0.0732268i
$208$	−3.33001	+	1.38241i	−0.230894	+	0.0958527i
$209$		−	0.443252i		−	0.0306604i
$210$	5.33219	−	6.46540i	0.367956	−	0.446155i
$211$	−23.0121			−1.58422			−0.792110	−	0.610379i	$-0.791017\pi$
$211$	−23.0121			−1.58422			−0.792110	+	0.610379i	$0.791017\pi$
$212$	7.46335	−	4.30897i	0.512585	−	0.295941i
$213$	−2.92472	−	10.9152i	−0.200398	−	0.747897i
$214$	−3.96520	+	1.06247i	−0.271055	+	0.0726291i
$215$	5.69198	−	21.2427i	0.388190	−	1.44874i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	2.93167	+	4.11207i	0.199015	+	0.279146i
$218$			14.9647i			1.01354i
$219$	6.08308	+	1.62996i	0.411056	+	0.110142i
$220$	−0.210264	+	0.364188i	−0.0141760	+	0.0245536i
$221$	−9.26553	−	7.09810i	−0.623267	−	0.477470i
$222$	−5.65719	+	3.26618i	−0.379686	+	0.219212i
$223$	4.37796	−	4.37796i	0.293170	−	0.293170i	−0.545161	−	0.838331i	$-0.683532\pi$
$223$	4.37796	−	4.37796i	0.293170	−	0.293170i	0.838331	+	0.545161i	$0.183532\pi$
$224$	2.15430	−	1.53590i	0.143940	−	0.102621i
$225$			5.03338i			0.335559i
$226$	2.10079	−	7.84026i	0.139743	−	0.521527i
$227$	−1.95657	−	7.30201i	−0.129862	−	0.484651i	0.870104	−	0.492868i	$-0.164051\pi$
$227$	−1.95657	−	7.30201i	−0.129862	−	0.484651i	−0.999966	+	0.00821638i	$0.997385\pi$
$228$	−0.864122	−	3.22495i	−0.0572279	−	0.213577i
$229$	−3.97504	+	14.8351i	−0.262678	+	0.980328i	0.700978	+	0.713183i	$0.252747\pi$
$229$	−3.97504	+	14.8351i	−0.262678	+	0.980328i	−0.963656	+	0.267145i	$0.913920\pi$
$230$			6.67435i			0.440093i
$231$	0.0335849	+	0.349644i	0.00220973	+	0.0230049i
$232$	1.70654	−	1.70654i	0.112040	−	0.112040i
$233$	−20.1700	+	11.6452i	−1.32138	+	0.762900i	−0.983949	−	0.178450i	$-0.942892\pi$
$233$	−20.1700	+	11.6452i	−1.32138	+	0.762900i	−0.337432	+	0.941350i	$0.609558\pi$
$234$	−0.473433	−	3.57433i	−0.0309493	−	0.233661i
$235$	12.6066	−	21.8353i	0.822366	−	1.42438i
$236$	6.58136	+	1.76347i	0.428410	+	0.114792i
$237$		−	13.0209i		−	0.845800i
$238$	7.79284	+	3.55359i	0.505134	+	0.230345i
$239$	−9.93729	−	9.93729i	−0.642790	−	0.642790i	0.308450	−	0.951240i	$-0.400190\pi$
$239$	−9.93729	−	9.93729i	−0.642790	−	0.642790i	−0.951240	+	0.308450i	$0.900190\pi$
$240$	−0.819823	+	3.05962i	−0.0529193	+	0.197498i
$241$	−3.56773	+	0.955972i	−0.229818	+	0.0615795i	−0.371890	−	0.928277i	$-0.621290\pi$
$241$	−3.56773	+	0.955972i	−0.229818	+	0.0615795i	0.142072	+	0.989856i	$0.454624\pi$
$242$	2.84245	+	10.6082i	0.182719	+	0.681918i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	10.9877			0.703416
$245$	19.9333	−	9.71068i	1.27349	−	0.620393i
$246$		−	6.06362i		−	0.386603i
$247$	−4.59794	+	11.1252i	−0.292560	+	0.707878i
$248$	−1.65304	−	0.954385i	−0.104968	−	0.0606035i
$249$	−0.457237	+	0.122516i	−0.0289762	+	0.00776415i
$250$	−0.0915711	+	0.0528686i	−0.00579147	+	0.00334371i
$251$	−11.9846			−0.756463			−0.378231	−	0.925711i	$-0.623468\pi$
$251$	−11.9846			−0.756463			−0.378231	+	0.925711i	$0.623468\pi$
$252$	0.925986	+	2.47842i	0.0583316	+	0.156126i
$253$	−0.197807	−	0.197807i	−0.0124360	−	0.0124360i
$254$	2.08250	+	0.558004i	0.130668	+	0.0350123i
$255$	−9.90460	+	2.65393i	−0.620250	+	0.166196i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.1709	+	26.2767i	0.946334	+	1.63910i	0.753059	+	0.657953i	$0.228577\pi$
$257$	15.1709	+	26.2767i	0.946334	+	1.63910i	0.193275	+	0.981145i	$0.438089\pi$
$258$	4.90940	+	4.90940i	0.305646	+	0.305646i
$259$	−17.2038	+	1.65251i	−1.06899	+	0.102682i
$260$	9.05523	−	6.95966i	0.561581	−	0.431620i
$261$	1.20671	+	2.09008i	0.0746934	+	0.129373i
$262$	5.06466	+	18.9015i	0.312895	+	1.16774i
$263$	−12.5802	+	21.7895i	−0.775727	+	1.34360i	0.158659	+	0.987333i	$0.449283\pi$
$263$	−12.5802	+	21.7895i	−0.775727	+	1.34360i	−0.934385	+	0.356264i	$0.884050\pi$
$264$	−0.0663807	−	0.114975i	−0.00408545	−	0.00707620i
$265$	−19.3024	+	19.3024i	−1.18574	+	1.18574i
$266$	1.45995	−	8.71191i	0.0895155	−	0.534162i
$267$	12.1994	−	12.1994i	0.746594	−	0.746594i
$268$	−12.2828	−	3.29118i	−0.750294	−	0.201041i
$269$	−3.86820	−	2.23331i	−0.235848	−	0.136167i	0.377419	−	0.926043i	$-0.376812\pi$
$269$	−3.86820	−	2.23331i	−0.235848	−	0.136167i	−0.613267	+	0.789876i	$0.710145\pi$
$270$	−2.74318	−	1.58378i	−0.166945	−	0.0963855i
$271$	1.35201	−	5.04576i	0.0821287	−	0.306508i	−0.912626	−	0.408795i	$-0.865949\pi$
$271$	1.35201	−	5.04576i	0.0821287	−	0.306508i	0.994755	+	0.102286i	$0.0326158\pi$
$272$	−3.23720			−0.196284
$273$	2.78398	−	9.12411i	0.168494	−	0.552216i
$274$	18.9832			1.14682
$275$	0.172953	−	0.645469i	0.0104294	−	0.0389232i
$276$	−1.82480	−	1.05355i	−0.109840	−	0.0634162i
$277$	2.68824	+	1.55206i	0.161521	+	0.0932541i	0.578582	−	0.815625i	$-0.303606\pi$
$277$	2.68824	+	1.55206i	0.161521	+	0.0932541i	−0.417061	+	0.908879i	$0.636940\pi$
$278$	−12.1114	−	3.24524i	−0.726394	−	0.194637i
$279$	1.34970	−	1.34970i	0.0808047	−	0.0808047i
$280$	−5.33219	+	6.46540i	−0.318659	+	0.386382i
$281$	7.08699	−	7.08699i	0.422774	−	0.422774i	−0.463384	−	0.886158i	$-0.653365\pi$
$281$	7.08699	−	7.08699i	0.422774	−	0.422774i	0.886158	+	0.463384i	$0.153365\pi$
$282$	3.97993	+	6.89344i	0.237001	+	0.410498i
$283$	−15.5041	+	26.8539i	−0.921622	+	1.59630i	−0.124717	+	0.992192i	$0.539802\pi$
$283$	−15.5041	+	26.8539i	−0.921622	+	1.59630i	−0.796905	+	0.604104i	$0.793531\pi$
$284$	2.92472	+	10.9152i	0.173550	+	0.647698i
$285$	5.28777	+	9.15868i	0.313220	+	0.542513i
$286$	−0.0621063	+	0.474632i	−0.00367242	+	0.0280656i
$287$	6.65625	−	14.5968i	0.392906	−	0.861623i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	3.26027	+	5.64695i	0.191780	+	0.332173i
$290$	−3.82231	+	6.62044i	−0.224454	+	0.388766i
$291$	5.63667	−	1.51034i	0.330427	−	0.0885378i
$292$	−6.08308	−	1.62996i	−0.355985	−	0.0953859i
$293$	8.56363	+	8.56363i	0.500293	+	0.500293i	0.911529	−	0.411236i	$-0.134903\pi$
$293$	8.56363	+	8.56363i	0.500293	+	0.500293i	−0.411236	+	0.911529i	$0.634903\pi$
$294$	−0.491539	+	6.98272i	−0.0286671	+	0.407241i
$295$	−21.5822			−1.25656
$296$	5.65719	−	3.26618i	0.328817	−	0.189843i
$297$	0.128238	−	0.0343612i	0.00744110	−	0.00199384i
$298$	−4.94265	−	2.85364i	−0.286320	−	0.165307i
$299$	2.91287	+	7.01666i	0.168456	+	0.405784i
$300$		−	5.03338i		−	0.290602i
$301$	6.42906	+	17.2075i	0.370565	+	0.991823i
$302$	−9.53321			−0.548575
$303$	5.59248	−	3.22882i	0.321279	−	0.185491i
$304$	0.864122	+	3.22495i	0.0495608	+	0.184963i
$305$	−33.6182	+	9.00797i	−1.92497	+	0.515795i
$306$	0.837849	−	3.12690i	0.0478966	−	0.178753i
$307$	6.97645	+	6.97645i	0.398167	+	0.398167i	0.877586	−	0.479419i	$-0.159153\pi$
$307$	6.97645	+	6.97645i	0.398167	+	0.398167i	−0.479419	+	0.877586i	$0.659153\pi$
$308$	−0.0335849	−	0.349644i	−0.00191368	−	0.0199228i
$309$			12.0954i			0.688083i
$310$	5.84011	+	1.56485i	0.331696	+	0.0888777i
$311$	−11.2510	+	19.4873i	−0.637986	+	1.10502i	0.347888	+	0.937536i	$0.386899\pi$
$311$	−11.2510	+	19.4873i	−0.637986	+	1.10502i	−0.985874	+	0.167489i	$0.946434\pi$
$312$	0.473433	+	3.57433i	0.0268029	+	0.202357i
$313$	22.7282	−	13.1221i	1.28467	−	0.741706i	0.306973	−	0.951718i	$-0.400684\pi$
$313$	22.7282	−	13.1221i	1.28467	−	0.741706i	0.977699	+	0.210012i	$0.0673504\pi$
$314$	−15.2292	+	15.2292i	−0.859436	+	0.859436i
$315$	−4.86503	−	6.82387i	−0.274113	−	0.384481i
$316$			13.0209i			0.732485i
$317$	−6.87739	+	25.6668i	−0.386272	+	1.44159i	0.449879	+	0.893090i	$0.351467\pi$
$317$	−6.87739	+	25.6668i	−0.386272	+	1.44159i	−0.836151	+	0.548499i	$0.815200\pi$
$318$	−2.23049	−	8.32429i	−0.125079	−	0.466803i
$319$	−0.0829279	−	0.309491i	−0.00464307	−	0.0173282i
$320$	0.819823	−	3.05962i	0.0458295	−	0.171038i
$321$			4.10507i			0.229123i
$322$	−3.23628	−	4.53933i	−0.180351	−	0.252967i
$323$	−7.64246	+	7.64246i	−0.425238	+	0.425238i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−11.0365	+	14.4066i	−0.612197	+	0.799132i
$326$	0.104763	−	0.181455i	0.00580228	−	0.0100499i
$327$	14.4548	+	3.87315i	0.799352	+	0.214186i
$328$			6.06362i			0.334808i
$329$	2.01362	+	20.9633i	0.111015	+	1.15575i
$330$	0.297358	+	0.297358i	0.0163690	+	0.0163690i
$331$	−2.21671	+	8.27289i	−0.121842	+	0.454719i	−0.999707	−	0.0241875i	$-0.992300\pi$
$331$	−2.21671	+	8.27289i	−0.121842	+	0.454719i	0.877866	+	0.478907i	$0.158967\pi$
$332$	0.457237	−	0.122516i	0.0250941	−	0.00672395i
$333$	1.69070	+	6.30977i	0.0926497	+	0.345774i
$334$	2.49926	−	1.44295i	0.136754	−	0.0789547i
$335$	40.2790			2.20068
$336$	−0.925986	−	2.47842i	−0.0505167	−	0.135209i
$337$		−	7.59201i		−	0.413563i	−0.978387	−	0.206782i	$-0.933701\pi$
$337$		−	7.59201i		−	0.413563i	0.978387	−	0.206782i	$-0.0662990\pi$
$338$	6.48226	−	11.2686i	0.352589	−	0.612928i
$339$	−7.02939	−	4.05842i	−0.381784	−	0.220423i
$340$	9.90460	−	2.65393i	0.537152	−	0.143930i
$341$	−0.219460	+	0.126705i	−0.0118844	+	0.00686149i
$342$	−3.33871			−0.180537
$343$	−8.84844	+	16.2698i	−0.477771	+	0.878484i
$344$	−4.90940	−	4.90940i	−0.264697	−	0.264697i
$345$	6.44692	+	1.72745i	0.347091	+	0.0930027i
$346$	−12.8377	+	3.43984i	−0.690158	+	0.184927i
$347$	−2.00675	+	3.47579i	−0.107728	+	0.186590i	−0.914849	−	0.403795i	$-0.867691\pi$
$347$	−2.00675	+	3.47579i	−0.107728	+	0.186590i	0.807122	+	0.590385i	$0.201024\pi$
$348$	−1.20671	−	2.09008i	−0.0646864	−	0.112040i
$349$	−14.9823	−	14.9823i	−0.801986	−	0.801986i	0.181420	−	0.983406i	$-0.441931\pi$
$349$	−14.9823	−	14.9823i	−0.801986	−	0.801986i	−0.983406	+	0.181420i	$0.941931\pi$
$350$	5.52532	−	12.1167i	0.295341	−	0.647667i
$351$	−3.57507	−	0.467804i	−0.190823	−	0.0249695i
$352$	0.0663807	+	0.114975i	0.00353810	+	0.00612817i
$353$	−6.28543	−	23.4575i	−0.334540	−	1.24852i	−0.904367	−	0.426755i	$-0.859657\pi$
$353$	−6.28543	−	23.4575i	−0.334540	−	1.24852i	0.569828	−	0.821764i	$-0.307010\pi$
$354$	3.40676	−	5.90069i	0.181067	−	0.313618i
$355$	−17.8971	−	30.9986i	−0.949877	−	1.64524i
$356$	−12.1994	+	12.1994i	−0.646569	+	0.646569i
$357$	5.44943	−	6.60757i	0.288415	−	0.349709i
$358$	−0.422081	+	0.422081i	−0.0223077	+	0.0223077i
$359$	−10.3732	−	2.77948i	−0.547475	−	0.146695i	−0.0255289	−	0.999674i	$-0.508127\pi$
$359$	−10.3732	−	2.77948i	−0.547475	−	0.146695i	−0.521946	+	0.852979i	$0.674794\pi$
$360$	2.74318	+	1.58378i	0.144578	+	0.0834723i
$361$	−6.80091	−	3.92651i	−0.357943	−	0.206658i
$362$	2.28767	−	8.53771i	0.120237	−	0.448732i
$363$	10.9824			0.576425
$364$	−2.78398	+	9.12411i	−0.145920	+	0.478233i
$365$	19.9482			1.04414
$366$	2.84383	−	10.6133i	0.148649	−	0.554767i
$367$	0.979626	+	0.565587i	0.0511361	+	0.0295234i	0.525350	−	0.850886i	$-0.323934\pi$
$367$	0.979626	+	0.565587i	0.0511361	+	0.0295234i	−0.474214	+	0.880410i	$0.657268\pi$
$368$	1.82480	+	1.05355i	0.0951244	+	0.0549201i
$369$	−5.85701	−	1.56938i	−0.304904	−	0.0816987i
$370$	−14.6312	+	14.6312i	−0.760638	+	0.760638i
$371$	3.76846	−	22.4873i	0.195649	−	1.16748i
$372$	−1.34970	+	1.34970i	−0.0699789	+	0.0699789i
$373$	14.6335	+	25.3460i	0.757693	+	1.31236i	0.944024	+	0.329877i	$0.107007\pi$
$373$	14.6335	+	25.3460i	0.757693	+	1.31236i	−0.186331	+	0.982487i	$0.559660\pi$
$374$	−0.214888	+	0.372196i	−0.0111116	+	0.0192458i
$375$	0.0273668	+	0.102134i	0.00141322	+	0.00527419i
$376$	−3.97993	−	6.89344i	−0.205249	−	0.355502i
$377$	−1.12901	+	8.62815i	−0.0581468	+	0.444372i
$378$	2.63363	−	0.252972i	0.135459	−	0.0130115i
$379$	−9.42782	−	9.42782i	−0.484275	−	0.484275i	0.422219	−	0.906494i	$-0.361251\pi$
$379$	−9.42782	−	9.42782i	−0.484275	−	0.484275i	−0.906494	+	0.422219i	$0.861251\pi$
$380$	−5.28777	−	9.15868i	−0.271257	−	0.469830i
$381$	1.07798	−	1.86712i	0.0552267	−	0.0956554i
$382$	15.1480	−	4.05890i	0.775040	−	0.207671i
$383$	14.8301	+	3.97371i	0.757782	+	0.203047i	0.616967	−	0.786989i	$-0.288361\pi$
$383$	14.8301	+	3.97371i	0.757782	+	0.203047i	0.140815	+	0.990036i	$0.455028\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	0.389403	+	1.04224i	0.0198458	+	0.0531177i
$386$	17.6658			0.899165
$387$	6.01276	−	3.47147i	0.305646	−	0.176465i
$388$	−5.63667	+	1.51034i	−0.286159	+	0.0766760i
$389$	18.9577	+	10.9452i	0.961192	+	0.554944i	0.896540	−	0.442963i	$-0.146073\pi$
$389$	18.9577	+	10.9452i	0.961192	+	0.554944i	0.0646522	+	0.997908i	$0.479406\pi$
$390$	−4.37885	−	10.5480i	−0.221731	−	0.534117i
$391$			6.82110i			0.344958i
$392$	0.491539	−	6.98272i	0.0248265	−	0.352681i
$393$	19.5683			0.987091
$394$	6.18790	−	3.57259i	0.311742	−	0.179984i
$395$	−10.6749	−	39.8391i	−0.537110	−	2.00452i
$396$	−0.128238	+	0.0343612i	−0.00644418	+	0.00172671i
$397$	2.86371	−	10.6875i	0.143726	−	0.536391i	−0.856083	−	0.516838i	$-0.827109\pi$
$397$	2.86371	−	10.6875i	0.143726	−	0.536391i	0.999809	−	0.0195531i	$-0.00622435\pi$
$398$	11.0492	+	11.0492i	0.553846	+	0.553846i
$399$	−8.03720	−	3.66502i	−0.402363	−	0.183480i
$400$			5.03338i			0.251669i
$401$	−8.03917	−	2.15409i	−0.401457	−	0.107570i	0.0524404	−	0.998624i	$-0.483300\pi$
$401$	−8.03917	−	2.15409i	−0.401457	−	0.107570i	−0.453897	+	0.891054i	$0.649967\pi$
$402$	−6.35806	+	11.0125i	−0.317111	+	0.549253i
$403$	6.82258	−	0.903676i	0.339857	−	0.0450153i
$404$	−5.59248	+	3.22882i	−0.278236	+	0.160640i
$405$	−2.23980	+	2.23980i	−0.111296	+	0.111296i
$406$	−0.610528	−	6.35605i	−0.0303000	−	0.315445i
$407$		−	0.867245i		−	0.0429877i
$408$	−0.837849	+	3.12690i	−0.0414797	+	0.154804i
$409$	−6.63609	−	24.7662i	−0.328134	−	1.22461i	−0.911124	−	0.412132i	$-0.864784\pi$
$409$	−6.63609	−	24.7662i	−0.328134	−	1.22461i	0.582990	−	0.812479i	$-0.301883\pi$
$410$	−4.97110	−	18.5524i	−0.245505	−	0.916237i
$411$	4.91322	−	18.3364i	0.242351	−	0.904466i
$412$		−	12.0954i		−	0.595897i
$413$	14.6784	−	10.4649i	0.722277	−	0.514942i
$414$	−1.48994	+	1.48994i	−0.0732268	+	0.0732268i
$415$	−1.29853	+	0.749706i	−0.0637423	+	0.0368016i
$416$	−0.473433	−	3.57433i	−0.0232120	−	0.175246i
$417$	−6.26933	+	10.8588i	−0.307010	+	0.531757i
$418$	0.428148	+	0.114722i	0.0209414	+	0.00561123i
$419$		−	17.9834i		−	0.878545i	−0.898354	−	0.439273i	$-0.855236\pi$
$419$		−	17.9834i		−	0.878545i	0.898354	−	0.439273i	$-0.144764\pi$
$420$	4.86503	+	6.82387i	0.237389	+	0.332971i
$421$	7.80826	+	7.80826i	0.380552	+	0.380552i	0.871301	−	0.490749i	$-0.163277\pi$
$421$	7.80826	+	7.80826i	0.380552	+	0.380552i	−0.490749	+	0.871301i	$0.663277\pi$
$422$	5.95597	−	22.2280i	0.289932	−	1.08204i
$423$	7.68863	−	2.06016i	0.373834	−	0.100169i
$424$	2.23049	+	8.32429i	0.108322	+	0.404263i
$425$	−14.1111	+	8.14703i	−0.684488	+	0.395189i
$426$	11.3002			0.547499
$427$	18.4965	−	22.4274i	0.895107	−	1.08534i
$428$		−	4.10507i		−	0.198426i
$429$	0.442385	+	0.182834i	0.0213585	+	0.00882730i
$430$	19.0457	+	10.9961i	0.918466	+	0.530277i
$431$	3.27342	−	0.877111i	0.157675	−	0.0422489i	−0.179118	−	0.983828i	$-0.557324\pi$
$431$	3.27342	−	0.877111i	0.157675	−	0.0422489i	0.336793	+	0.941579i	$0.390658\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−3.14209			−0.150999			−0.0754996	−	0.997146i	$-0.524055\pi$
$433$	−3.14209			−0.150999			−0.0754996	+	0.997146i	$0.524055\pi$
$434$	−4.73073	+	1.76749i	−0.227082	+	0.0848425i
$435$	5.40557	+	5.40557i	0.259177	+	0.259177i
$436$	−14.4548	−	3.87315i	−0.692259	−	0.185490i
$437$	6.79528	−	1.82079i	0.325062	−	0.0871002i
$438$	−3.14883	+	5.45394i	−0.150457	+	0.260599i
$439$	19.5705	+	33.8970i	0.934047	+	1.61782i	0.776324	+	0.630334i	$0.217082\pi$
$439$	19.5705	+	33.8970i	0.934047	+	1.61782i	0.157723	+	0.987483i	$0.449585\pi$
$440$	−0.297358	−	0.297358i	−0.0141760	−	0.0141760i
$441$	6.61757	+	2.28205i	0.315122	+	0.108669i
$442$	9.25434	−	7.11269i	0.440184	−	0.338316i
$443$	−14.2259	−	24.6399i	−0.675892	−	1.17068i	−0.976207	−	0.216839i	$-0.930425\pi$
$443$	−14.2259	−	24.6399i	−0.675892	−	1.17068i	0.300316	−	0.953840i	$-0.402908\pi$
$444$	−1.69070	−	6.30977i	−0.0802370	−	0.299449i
$445$	27.3243	−	47.3270i	1.29530	−	2.24352i
$446$	3.09569	+	5.36189i	0.146585	+	0.253893i
$447$	−4.03566	+	4.03566i	−0.190880	+	0.190880i
$448$	0.925986	+	2.47842i	0.0437487	+	0.117094i
$449$	−2.60464	+	2.60464i	−0.122921	+	0.122921i	−0.765891	−	0.642970i	$-0.777702\pi$
$449$	−2.60464	+	2.60464i	−0.122921	+	0.122921i	0.642970	+	0.765891i	$0.277702\pi$
$450$	−4.86187	−	1.30273i	−0.229191	−	0.0614115i
$451$	0.697163	+	0.402507i	0.0328281	+	0.0189533i
$452$	7.02939	+	4.05842i	0.330635	+	0.190892i
$453$	−2.46738	+	9.20838i	−0.115927	+	0.432647i
$454$	7.55959			0.354789
$455$	1.03778	−	30.1987i	0.0486518	−	1.41574i
$456$	3.33871			0.156349
$457$	6.86319	−	25.6138i	0.321046	−	1.19816i	−0.597181	−	0.802107i	$-0.703712\pi$
$457$	6.86319	−	25.6138i	0.321046	−	1.19816i	0.918227	−	0.396054i	$-0.129621\pi$
$458$	−13.3007	−	7.67919i	−0.621503	−	0.358825i
$459$	−2.80350	−	1.61860i	−0.130856	−	0.0755498i
$460$	−6.44692	−	1.72745i	−0.300589	−	0.0805427i
$461$	11.5349	−	11.5349i	0.537233	−	0.537233i	−0.385482	−	0.922715i	$-0.625965\pi$
$461$	11.5349	−	11.5349i	0.537233	−	0.537233i	0.922715	+	0.385482i	$0.125965\pi$
$462$	−0.346423	−	0.0580540i	−0.0161170	−	0.00270092i
$463$	−1.46395	+	1.46395i	−0.0680358	+	0.0680358i	−0.740306	−	0.672270i	$-0.765319\pi$
$463$	−1.46395	+	1.46395i	−0.0680358	+	0.0680358i	0.672270	+	0.740306i	$0.265319\pi$
$464$	1.20671	+	2.09008i	0.0560201	+	0.0970296i
$465$	3.02306	−	5.23610i	0.140191	−	0.242818i
$466$	−6.02798	−	22.4967i	−0.279241	−	1.04214i
$467$	−14.4242	−	24.9834i	−0.667471	−	1.15609i	−0.978609	−	0.205729i	$-0.934043\pi$
$467$	−14.4242	−	24.9834i	−0.667471	−	1.15609i	0.311138	−	0.950365i	$-0.399290\pi$
$468$	3.57507	+	0.467804i	0.165258	+	0.0216243i
$469$	−27.3944	+	19.5306i	−1.26496	+	0.901841i
$470$	17.8285	+	17.8285i	0.822366	+	0.822366i
$471$	10.7687	+	18.6519i	0.496196	+	0.859436i
$472$	−3.40676	+	5.90069i	−0.156809	+	0.271601i
$473$	−0.890346	+	0.238567i	−0.0409381	+	0.0109693i
$474$	12.5773	+	3.37007i	0.577692	+	0.154792i
$475$	11.8829	+	11.8829i	0.545226	+	0.545226i
$476$	−5.44943	+	6.60757i	−0.249774	+	0.302857i
$477$	−8.61793			−0.394588
$478$	12.1706	−	7.02673i	0.556673	−	0.321395i
$479$	−31.0160	+	8.31070i	−1.41716	+	0.379726i	−0.884474	−	0.466590i	$-0.845482\pi$
$479$	−31.0160	+	8.31070i	−1.41716	+	0.379726i	−0.532682	+	0.846316i	$0.678816\pi$
$480$	−2.74318	−	1.58378i	−0.125208	−	0.0722891i
$481$	−8.99611	+	21.7670i	−0.410187	+	0.992490i
$482$		−	3.69359i		−	0.168238i
$483$	−5.22227	+	1.95114i	−0.237622	+	0.0887801i
$484$	−10.9824			−0.499199
$485$	16.0079	−	9.24214i	0.726879	−	0.419664i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	−14.3435	+	3.84333i	−0.649967	+	0.174158i	−0.568714	−	0.822536i	$-0.692559\pi$
$487$	−14.3435	+	3.84333i	−0.649967	+	0.174158i	−0.0812528	+	0.996694i	$0.525892\pi$
$488$	−2.84383	+	10.6133i	−0.128734	+	0.480442i
$489$	−0.148157	−	0.148157i	−0.00669990	−	0.00669990i
$490$	4.22067	+	21.7674i	0.190670	+	0.983353i
$491$			9.86395i			0.445154i	0.974915	+	0.222577i	$0.0714469\pi$
$491$			9.86395i			0.445154i	−0.974915	+	0.222577i	$0.928553\pi$
$492$	5.85701	+	1.56938i	0.264054	+	0.0707532i
$493$	−3.90636	+	6.76601i	−0.175934	+	0.304726i
$494$	−9.55607	−	7.32068i	−0.429948	−	0.329373i
$495$	0.364188	−	0.210264i	0.0163690	−	0.00945067i
$496$	1.34970	−	1.34970i	0.0606035	−	0.0606035i
$497$	27.2028	+	12.4047i	1.22021	+	0.556426i
$498$		−	0.473366i		−	0.0212121i
$499$	−1.63939	+	6.11829i	−0.0733892	+	0.273892i	−0.992863	−	0.119258i	$-0.961948\pi$
$499$	−1.63939	+	6.11829i	−0.0733892	+	0.273892i	0.919474	+	0.393151i	$0.128615\pi$
$500$	−0.0273668	−	0.102134i	−0.00122388	−	0.00456759i
$501$	−0.746926	−	2.78756i	−0.0333702	−	0.124539i
$502$	3.10185	−	11.5763i	0.138442	−	0.516674i
$503$			9.84473i			0.438955i	0.975618	+	0.219477i	$0.0704352\pi$
$503$			9.84473i			0.438955i	−0.975618	+	0.219477i	$0.929565\pi$
$504$	−2.63363	+	0.252972i	−0.117311	+	0.0112683i
$505$	14.4638	−	14.4638i	0.643630	−	0.643630i
$506$	0.242263	−	0.139871i	0.0107699	−	0.00621801i
$507$	−9.20685	−	9.17790i	−0.408891	−	0.407605i
$508$	−1.07798	+	1.86712i	−0.0478277	+	0.0828400i
$509$	−19.5576	−	5.24046i	−0.866877	−	0.232279i	−0.202140	−	0.979357i	$-0.564790\pi$
$509$	−19.5576	−	5.24046i	−0.866877	−	0.232279i	−0.664737	+	0.747077i	$0.731456\pi$
$510$		−	10.2540i		−	0.454055i
$511$	−13.5671	+	9.67255i	−0.600172	+	0.427889i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.864122	+	3.22495i	−0.0381519	+	0.142385i
$514$	−29.3079	+	7.85303i	−1.29272	+	0.346382i
$515$	9.91608	+	37.0073i	0.436955	+	1.63074i
$516$	−6.01276	+	3.47147i	−0.264697	+	0.152823i
$517$	−1.05676			−0.0464763
$518$	2.85648	−	17.0453i	0.125506	−	0.748928i
$519$			13.2905i			0.583390i
$520$	4.37885	+	10.5480i	0.192025	+	0.462559i
$521$	2.42079	+	1.39765i	0.106057	+	0.0612319i	0.552090	−	0.833784i	$-0.313830\pi$
$521$	2.42079	+	1.39765i	0.106057	+	0.0612319i	−0.446033	+	0.895016i	$0.647164\pi$
$522$	−2.33118	+	0.624639i	−0.102033	+	0.0273397i
$523$	−28.8220	+	16.6404i	−1.26030	+	0.727633i	−0.973132	−	0.230248i	$-0.926046\pi$
$523$	−28.8220	+	16.6404i	−1.26030	+	0.727633i	−0.287165	+	0.957881i	$0.592713\pi$
$524$	−19.5683			−0.854846
$525$	−10.2738	−	8.47309i	−0.448386	−	0.369796i
$526$	−17.7910	−	17.7910i	−0.775727	−	0.775727i
$527$	5.96853	+	1.59926i	0.259993	+	0.0696649i
$528$	0.128238	−	0.0343612i	0.00558083	−	0.00149538i
$529$	−9.28007	+	16.0735i	−0.403481	+	0.698850i
$530$	−13.6489	−	23.6405i	−0.592869	−	1.02688i
$531$	−4.81789	−	4.81789i	−0.209079	−	0.209079i
$532$	8.03720	+	3.66502i	0.348457	+	0.158899i
$533$	−13.3228	−	17.3344i	−0.577076	−	0.750835i
$534$	8.62631	+	14.9412i	0.373297	+	0.646569i
$535$	3.36543	+	12.5600i	0.145500	+	0.543015i
$536$	6.35806	−	11.0125i	0.274627	−	0.475667i
$537$	0.298456	+	0.516941i	0.0128793	+	0.0223077i
$538$	3.15837	−	3.15837i	0.136167	−	0.136167i
$539$	−0.770207	−	0.520032i	−0.0331752	−	0.0223994i
$540$	2.23980	−	2.23980i	0.0963855	−	0.0963855i
$541$	18.8598	+	5.05346i	0.810845	+	0.217265i	0.640340	−	0.768092i	$-0.278793\pi$
$541$	18.8598	+	5.05346i	0.810845	+	0.217265i	0.170505	+	0.985357i	$0.445460\pi$
$542$	4.52391	+	2.61188i	0.194319	+	0.112190i
$543$	−7.65470	−	4.41944i	−0.328495	−	0.189656i
$544$	0.837849	−	3.12690i	0.0359225	−	0.134065i
$545$	47.4015			2.03046
$546$	8.09267	+	5.05062i	0.346334	+	0.216146i
$547$	26.5031			1.13319			0.566594	−	0.823997i	$-0.308261\pi$
$547$	26.5031			1.13319			0.566594	+	0.823997i	$0.308261\pi$
$548$	−4.91322	+	18.3364i	−0.209882	+	0.783291i
$549$	−9.51563	−	5.49385i	−0.406117	−	0.234472i
$550$	0.578711	+	0.334119i	0.0246763	+	0.0142469i
$551$	7.78314	+	2.08549i	0.331573	+	0.0888447i
$552$	1.48994	−	1.48994i	0.0634162	−	0.0634162i
$553$	26.5775	+	21.9192i	1.13019	+	0.932098i
$554$	−2.19494	+	2.19494i	−0.0932541	+	0.0932541i
$555$	10.3458	+	17.9194i	0.439154	+	0.760638i
$556$	6.26933	−	10.8588i	0.265879	−	0.460515i
$557$	−0.997371	−	3.72224i	−0.0422600	−	0.157716i	0.941571	−	0.336813i	$-0.109349\pi$
$557$	−0.997371	−	3.72224i	−0.0422600	−	0.157716i	−0.983831	+	0.179097i	$0.942682\pi$
$558$	0.954385	+	1.65304i	0.0404024	+	0.0699789i
$559$	24.8215	+	3.24794i	1.04984	+	0.137373i
$560$	−4.86503	−	6.82387i	−0.205585	−	0.288361i
$561$	0.303897	+	0.303897i	0.0128305	+	0.0128305i
$562$	5.01126	+	8.67975i	0.211387	+	0.366133i
$563$	14.9206	−	25.8432i	0.628826	−	1.08916i	−0.358961	−	0.933352i	$-0.616869\pi$
$563$	14.9206	−	25.8432i	0.628826	−	1.08916i	0.987788	−	0.155807i	$-0.0497977\pi$
$564$	−7.68863	+	2.06016i	−0.323750	+	0.0867485i
$565$	−24.8344	−	6.65437i	−1.04479	−	0.279951i
$566$	−21.9261	−	21.9261i	−0.921622	−	0.921622i
$567$	0.437281	−	2.60936i	0.0183641	−	0.109583i
$568$	−11.3002			−0.474148
$569$	−5.44783	+	3.14531i	−0.228385	+	0.131858i	−0.609827	−	0.792535i	$-0.708761\pi$
$569$	−5.44783	+	3.14531i	−0.228385	+	0.131858i	0.381442	+	0.924393i	$0.375428\pi$
$570$	−10.2152	+	2.73715i	−0.427867	+	0.114647i
$571$	−5.12924	−	2.96137i	−0.214652	−	0.123929i	0.388820	−	0.921314i	$-0.372883\pi$
$571$	−5.12924	−	2.96137i	−0.214652	−	0.123929i	−0.603472	+	0.797385i	$0.706216\pi$
$572$	−0.442385	−	0.182834i	−0.0184970	−	0.00764467i
$573$		−	15.6824i		−	0.655141i
$574$	12.3767	+	10.2074i	0.516593	+	0.426048i
$575$	10.6058			0.442294
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	−1.33194	−	4.97088i	−0.0554496	−	0.206941i	0.932643	−	0.360800i	$-0.117496\pi$
$577$	−1.33194	−	4.97088i	−0.0554496	−	0.206941i	−0.988093	+	0.153859i	$0.950830\pi$
$578$	−6.29835	+	1.68764i	−0.261977	+	0.0701965i
$579$	4.57224	−	17.0638i	0.190016	−	0.709149i
$580$	−5.40557	−	5.40557i	−0.224454	−	0.224454i
$581$	0.519630	−	1.13952i	0.0215579	−	0.0472754i
$582$			5.83551i			0.241890i
$583$	1.10514	+	0.296122i	0.0457704	+	0.0122641i
$584$	3.14883	−	5.45394i	0.130300	−	0.225686i
$585$	−11.3219	+	1.49962i	−0.468102	+	0.0620018i
$586$	−10.4883	+	6.05540i	−0.433266	+	0.250146i
$587$	21.2729	−	21.2729i	0.878027	−	0.878027i	−0.115304	−	0.993330i	$-0.536784\pi$
$587$	21.2729	−	21.2729i	0.878027	−	0.878027i	0.993330	+	0.115304i	$0.0367841\pi$
$588$	−6.61757	−	2.28205i	−0.272904	−	0.0941102i
$589$		−	6.37283i		−	0.262588i
$590$	5.58588	−	20.8468i	0.229967	−	0.858249i
$591$	−1.84931	−	6.90171i	−0.0760704	−	0.283898i
$592$	1.69070	+	6.30977i	0.0694873	+	0.259330i
$593$	−11.2846	+	42.1148i	−0.463404	+	1.72945i	0.198721	+	0.980056i	$0.436321\pi$
$593$	−11.2846	+	42.1148i	−0.463404	+	1.72945i	−0.662126	+	0.749393i	$0.730345\pi$
$594$			0.132761i			0.00544726i
$595$	11.2562	−	24.6842i	0.461458	−	1.01195i
$596$	4.03566	−	4.03566i	0.165307	−	0.165307i
$597$	13.5324	−	7.81296i	0.553846	−	0.319763i
$598$	−7.53148	+	0.997571i	−0.307985	+	0.0407937i
$599$	−5.94701	+	10.3005i	−0.242988	+	0.420868i	−0.961564	−	0.274581i	$-0.911461\pi$
$599$	−5.94701	+	10.3005i	−0.242988	+	0.420868i	0.718576	+	0.695449i	$0.244794\pi$
$600$	4.86187	+	1.30273i	0.198485	+	0.0531839i
$601$		−	35.7070i		−	1.45652i	−0.685301	−	0.728260i	$-0.740329\pi$
$601$		−	35.7070i		−	1.45652i	0.685301	−	0.728260i	$-0.259671\pi$
$602$	−18.2851	+	1.75637i	−0.745246	+	0.0715843i
$603$	8.99166	+	8.99166i	0.366169	+	0.366169i
$604$	2.46738	−	9.20838i	0.100396	−	0.374683i
$605$	33.6019	−	9.00360i	1.36611	−	0.366048i
$606$	1.67136	+	6.23760i	0.0678943	+	0.253385i
$607$	−12.4957	+	7.21439i	−0.507185	+	0.292823i	−0.731676	−	0.681653i	$-0.761261\pi$
$607$	−12.4957	+	7.21439i	−0.507185	+	0.292823i	0.224491	+	0.974476i	$0.427928\pi$
$608$	−3.33871			−0.135403
$609$	−6.29749	−	1.05534i	−0.255187	−	0.0427646i
$610$		−	34.8041i		−	1.40918i
$611$	26.5237	+	10.9620i	1.07303	+	0.443476i
$612$	2.80350	+	1.61860i	0.113325	+	0.0654280i
$613$	6.40358	−	1.71583i	0.258638	−	0.0693019i	−0.127170	−	0.991881i	$-0.540589\pi$
$613$	6.40358	−	1.71583i	0.258638	−	0.0693019i	0.385808	+	0.922579i	$0.373923\pi$
$614$	−8.54437	+	4.93310i	−0.344823	+	0.199084i
$615$	−19.2068			−0.774495
$616$	0.346423	+	0.0580540i	0.0139578	+	0.00233906i
$617$	27.5574	+	27.5574i	1.10942	+	1.10942i	0.993227	+	0.116192i	$0.0370687\pi$
$617$	27.5574	+	27.5574i	1.10942	+	1.10942i	0.116192	+	0.993227i	$0.462931\pi$
$618$	−11.6833	−	3.13052i	−0.469969	−	0.125928i
$619$	44.3183	−	11.8751i	1.78130	−	0.477299i	0.790484	−	0.612483i	$-0.209829\pi$
$619$	44.3183	−	11.8751i	1.78130	−	0.477299i	0.990821	+	0.135184i	$0.0431624\pi$
$620$	−3.02306	+	5.23610i	−0.121409	+	0.210287i
$621$	1.05355	+	1.82480i	0.0422775	+	0.0732268i
$622$	−15.9113	−	15.9113i	−0.637986	−	0.637986i
$623$	4.36444	+	45.4370i	0.174857	+	1.82040i
$624$	−3.57507	−	0.467804i	−0.143118	−	0.0187272i
$625$	−12.4160	−	21.5051i	−0.496640	−	0.860205i
$626$	6.79251	+	25.3500i	0.271483	+	1.01319i
$627$	0.221626	−	0.383867i	0.00885088	−	0.0153302i
$628$	−10.7687	−	18.6519i	−0.429718	−	0.744293i
$629$	−14.9529	+	14.9529i	−0.596210	+	0.596210i
$630$	7.85051	−	2.93311i	0.312772	−	0.116858i
$631$	−30.4681	+	30.4681i	−1.21291	+	1.21291i	−0.242850	+	0.970064i	$0.578082\pi$
$631$	−30.4681	+	30.4681i	−1.21291	+	1.21291i	−0.970064	+	0.242850i	$0.921918\pi$
$632$	−12.5773	−	3.37007i	−0.500296	−	0.134054i
$633$	−19.9291	−	11.5061i	−0.792110	−	0.457325i
$634$	−23.0122	−	13.2861i	−0.913930	−	0.527658i
$635$	1.76751	−	6.59643i	0.0701414	−	0.261771i
$636$	8.61793			0.341723
$637$	13.9371	+	21.0418i	0.552206	+	0.833708i
$638$	0.320409			0.0126851
$639$	2.92472	−	10.9152i	0.115700	−	0.431799i
$640$	2.74318	+	1.58378i	0.108434	+	0.0626042i
$641$	−3.02599	−	1.74706i	−0.119519	−	0.0690045i	0.439048	−	0.898463i	$-0.355316\pi$
$641$	−3.02599	−	1.74706i	−0.119519	−	0.0690045i	−0.558568	+	0.829459i	$0.688649\pi$
$642$	−3.96520	−	1.06247i	−0.156494	−	0.0419324i
$643$	−10.5150	+	10.5150i	−0.414670	+	0.414670i	−0.883362	−	0.468692i	$-0.844725\pi$
$643$	−10.5150	+	10.5150i	−0.414670	+	0.414670i	0.468692	+	0.883362i	$0.344725\pi$
$644$	5.22227	−	1.95114i	0.205786	−	0.0768859i
$645$	15.5508	−	15.5508i	0.612311	−	0.612311i
$646$	−5.40404	−	9.36006i	−0.212619	−	0.368267i
$647$	−2.59053	+	4.48692i	−0.101844	+	0.176399i	−0.912444	−	0.409201i	$-0.865808\pi$
$647$	−2.59053	+	4.48692i	−0.101844	+	0.176399i	0.810600	+	0.585600i	$0.199141\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	0.452286	+	0.783383i	0.0177538	+	0.0307505i
$650$	−11.0592	−	14.3892i	−0.433778	−	0.564389i
$651$	0.482866	+	5.02700i	0.0189250	+	0.197023i
$652$	0.148157	+	0.148157i	0.00580228	+	0.00580228i
$653$	−0.687303	−	1.19044i	−0.0268962	−	0.0465857i	0.852264	−	0.523112i	$-0.175229\pi$
$653$	−0.687303	−	1.19044i	−0.0268962	−	0.0465857i	−0.879160	+	0.476526i	$0.841896\pi$
$654$	−7.48235	+	12.9598i	−0.292583	+	0.506769i
$655$	59.8716	−	16.0426i	2.33938	−	0.626834i
$656$	−5.85701	−	1.56938i	−0.228678	−	0.0612741i
$657$	4.45312	+	4.45312i	0.173733	+	0.173733i
$658$	−20.7702	−	3.48070i	−0.809706	−	0.135692i
$659$	−41.5643			−1.61911			−0.809557	−	0.587042i	$-0.800293\pi$
$659$	−41.5643			−1.61911			−0.809557	+	0.587042i	$0.800293\pi$
$660$	−0.364188	+	0.210264i	−0.0141760	+	0.00818452i
$661$	−25.4902	+	6.83007i	−0.991453	+	0.265659i	−0.717861	−	0.696187i	$-0.754879\pi$
$661$	−25.4902	+	6.83007i	−0.991453	+	0.265659i	−0.273592	+	0.961846i	$0.588212\pi$
$662$	−7.41727	−	4.28236i	−0.288280	−	0.166439i
$663$	−4.47513	−	10.7799i	−0.173800	−	0.418657i
$664$			0.473366i			0.0183702i
$665$	−27.5954	−	4.62448i	−1.07010	−	0.179330i
$666$	−6.53236			−0.253124
$667$	4.40401	−	2.54266i	0.170524	−	0.0984520i
$668$	0.746926	+	2.78756i	0.0288994	+	0.107854i
$669$	5.98041	−	1.60245i	0.231216	−	0.0619541i
$670$	−10.4250	+	38.9065i	−0.402752	+	1.50309i
$671$	1.03149	+	1.03149i	0.0398201	+	0.0398201i
$672$	2.63363	−	0.252972i	0.101594	−	0.00975862i
$673$		−	14.1537i		−	0.545587i	−0.962073	−	0.272793i	$-0.912052\pi$
$673$		−	14.1537i		−	0.545587i	0.962073	−	0.272793i	$-0.0879476\pi$
$674$	7.33332	+	1.96496i	0.282469	+	0.0756873i
$675$	−2.51669	+	4.35904i	−0.0968675	+	0.167779i
$676$	9.20685	+	9.17790i	0.354110	+	0.352996i
$677$	−32.5882	+	18.8148i	−1.25247	+	0.723113i	−0.971599	−	0.236634i	$-0.923956\pi$
$677$	−32.5882	+	18.8148i	−1.25247	+	0.723113i	−0.280869	+	0.959746i	$0.590623\pi$
$678$	5.73947	−	5.73947i	0.220423	−	0.220423i
$679$	−6.40584	+	14.0477i	−0.245834	+	0.539101i
$680$			10.2540i			0.393223i
$681$	1.95657	−	7.30201i	0.0749758	−	0.279813i
$682$	−0.0655876	−	0.244776i	−0.00251148	−	0.00937296i
$683$	−11.1509	−	41.6157i	−0.426677	−	1.59238i	−0.760233	−	0.649651i	$-0.774915\pi$
$683$	−11.1509	−	41.6157i	−0.426677	−	1.59238i	0.333555	−	0.942731i	$-0.391752\pi$
$684$	0.864122	−	3.22495i	0.0330405	−	0.123309i
$685$		−	60.1303i		−	2.29746i
$686$	−13.4252	−	12.7579i	−0.512578	−	0.487097i
$687$	−10.8600	+	10.8600i	−0.414335	+	0.414335i
$688$	6.01276	−	3.47147i	0.229234	−	0.132349i
$689$	−24.6663	−	18.8963i	−0.939710	−	0.719890i
$690$	−3.33717	+	5.78015i	−0.127044	+	0.220047i
$691$	34.2331	+	9.17273i	1.30229	+	0.348947i	0.842315	−	0.538985i	$-0.181192\pi$
$691$	34.2331	+	9.17273i	1.30229	+	0.348947i	0.459974	+	0.887933i	$0.347859\pi$
$692$		−	13.2905i		−	0.505230i
$693$	−0.145737	+	0.319593i	−0.00553608	+	0.0121403i
$694$	−2.83797	−	2.83797i	−0.107728	−	0.107728i
$695$	−10.2795	+	38.3635i	−0.389923	+	1.45521i
$696$	2.33118	−	0.624639i	0.0883633	−	0.0236769i
$697$	−5.08040	−	18.9603i	−0.192434	−	0.718173i
$698$	18.3495	−	10.5941i	0.694540	−	0.400993i
$699$	−23.2903			−0.880921
$700$	10.2738	+	8.47309i	0.388314	+	0.320253i
$701$		−	22.0570i		−	0.833081i	−0.909117	−	0.416540i	$-0.863242\pi$
$701$		−	22.0570i		−	0.833081i	0.909117	−	0.416540i	$-0.136758\pi$
$702$	1.37716	−	3.33218i	0.0519776	−	0.125765i
$703$	18.8877	+	10.9048i	0.712364	+	0.411283i
$704$	−0.128238	+	0.0343612i	−0.00483314	+	0.00129504i
$705$	21.8353	−	12.6066i	0.822366	−	0.474793i
$706$	24.2850			0.913979
$707$	−2.82380	+	16.8503i	−0.106200	+	0.633722i
$708$	4.81789	+	4.81789i	0.181067	+	0.181067i
$709$	−30.1207	−	8.07082i	−1.13121	−	0.303106i	−0.355796	−	0.934564i	$-0.615790\pi$
$709$	−30.1207	−	8.07082i	−1.13121	−	0.303106i	−0.775410	+	0.631458i	$0.782457\pi$
$710$	34.5745	−	9.26420i	1.29756	−	0.347679i
$711$	6.51047	−	11.2765i	0.244162	−	0.422900i
$712$	−8.62631	−	14.9412i	−0.323285	−	0.559945i
$713$	−2.84396	−	2.84396i	−0.106507	−	0.106507i
$714$	4.97200	+	6.97391i	0.186072	+	0.260992i
$715$	1.50342	+	0.196725i	0.0562247	+	0.00735709i
$716$	−0.298456	−	0.516941i	−0.0111538	−	0.0193190i
$717$	−3.63730	−	13.5746i	−0.135838	−	0.506953i
$718$	5.36954	−	9.30032i	0.200390	−	0.347085i
$719$	12.7941	+	22.1601i	0.477141	+	0.826433i	0.999657	−	0.0261969i	$-0.00833968\pi$
$719$	12.7941	+	22.1601i	0.477141	+	0.826433i	−0.522516	+	0.852630i	$0.675006\pi$
$720$	−2.23980	+	2.23980i	−0.0834723	+	0.0834723i
$721$	−24.6883	−	20.3611i	−0.919442	−	0.758288i
$722$	5.55292	−	5.55292i	0.206658	−	0.206658i
$723$	−3.56773	−	0.955972i	−0.132685	−	0.0355530i
$724$	7.65470	+	4.41944i	0.284485	+	0.164247i
$725$	10.5202	+	6.07383i	0.390710	+	0.225576i
$726$	−2.84245	+	10.6082i	−0.105493	+	0.393706i
$727$	4.02875			0.149418			0.0747090	−	0.997205i	$-0.476197\pi$
$727$	4.02875			0.149418			0.0747090	+	0.997205i	$0.476197\pi$
$728$	−8.09267	−	5.05062i	−0.299934	−	0.187188i
$729$	−1.00000			−0.0370370
$730$	−5.16297	+	19.2685i	−0.191090	+	0.713158i
$731$	19.4645	+	11.2378i	0.719921	+	0.415646i
$732$	9.51563	+	5.49385i	0.351708	+	0.203059i
$733$	−4.34392	−	1.16395i	−0.160446	−	0.0429914i	0.177702	−	0.984084i	$-0.443134\pi$
$733$	−4.34392	−	1.16395i	−0.160446	−	0.0429914i	−0.338148	+	0.941093i	$0.609800\pi$
$734$	−0.799861	+	0.799861i	−0.0295234	+	0.0295234i
$735$	22.1181	+	1.55698i	0.815839	+	0.0574299i
$736$	−1.48994	+	1.48994i	−0.0549201	+	0.0549201i
$737$	−0.844105	−	1.46203i	−0.0310930	−	0.0538547i
$738$	3.03181	−	5.25125i	0.111603	−	0.193301i
$739$	3.72751	+	13.9113i	0.137119	+	0.511734i	0.999980	+	0.00629360i	$0.00200333\pi$
$739$	3.72751	+	13.9113i	0.137119	+	0.511734i	−0.862861	+	0.505441i	$0.831330\pi$
$740$	−10.3458	−	17.9194i	−0.380319	−	0.658732i
$741$	−9.54453	+	7.33572i	−0.350627	+	0.269484i
$742$	20.7457	+	9.46020i	0.761600	+	0.347295i
$743$	28.8005	+	28.8005i	1.05659	+	1.05659i	0.998300	+	0.0582865i	$0.0185637\pi$
$743$	28.8005	+	28.8005i	1.05659	+	1.05659i	0.0582865	+	0.998300i	$0.481436\pi$
$744$	−0.954385	−	1.65304i	−0.0349895	−	0.0606035i
$745$	−9.03905	+	15.6561i	−0.331165	+	0.573595i
$746$	−28.2697	+	7.57485i	−1.03503	+	0.277335i
$747$	−0.457237	−	0.122516i	−0.0167294	−	0.00448263i
$748$	−0.303897	−	0.303897i	−0.0111116	−	0.0111116i
$749$	−8.37901	−	6.91040i	−0.306163	−	0.252500i
$750$	−0.105737			−0.00386098
$751$	−22.0684	+	12.7412i	−0.805286	+	0.464932i	−0.845316	−	0.534267i	$-0.820588\pi$
$751$	−22.0684	+	12.7412i	−0.805286	+	0.464932i	0.0400304	+	0.999198i	$0.487255\pi$
$752$	7.68863	−	2.06016i	0.280376	−	0.0751264i
$753$	−10.3790	−	5.99231i	−0.378231	−	0.218372i
$754$	−8.04195	−	3.32367i	−0.292870	−	0.121041i
$755$			30.1969i			1.09898i
$756$	−0.437281	+	2.60936i	−0.0159038	+	0.0949017i
$757$	31.4162			1.14184			0.570921	−	0.821005i	$-0.306586\pi$
$757$	31.4162			1.14184			0.570921	+	0.821005i	$0.306586\pi$
$758$	11.5467	−	6.66648i	0.419394	−	0.242137i
$759$	−0.0724024	−	0.270209i	−0.00262804	−	0.00980798i
$760$	10.2152	−	2.73715i	0.370544	−	0.0992869i
$761$	−7.19283	+	26.8440i	−0.260740	+	0.973095i	0.704067	+	0.710134i	$0.251366\pi$
$761$	−7.19283	+	26.8440i	−0.260740	+	0.973095i	−0.964807	+	0.262961i	$0.915301\pi$
$762$	1.52450	+	1.52450i	0.0552267	+	0.0552267i
$763$	−32.2385	+	22.9842i	−1.16711	+	0.832084i
$764$			15.6824i			0.567369i
$765$	−9.90460	−	2.65393i	−0.358102	−	0.0959530i
$766$	−7.67662	+	13.2963i	−0.277368	+	0.480415i
$767$	−3.22575	−	24.3538i	−0.116475	−	0.879365i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	35.0151	−	35.0151i	1.26268	−	1.26268i	0.312889	−	0.949790i	$-0.398703\pi$
$769$	35.0151	−	35.0151i	1.26268	−	1.26268i	0.949790	−	0.312889i	$-0.101297\pi$
$770$	−1.10752	+	0.106382i	−0.0399121	+	0.00383374i
$771$			30.3418i			1.09273i
$772$	−4.57224	+	17.0638i	−0.164559	+	0.614141i
$773$	9.81954	+	36.6470i	0.353184	+	1.31810i	0.882754	+	0.469835i	$0.155687\pi$
$773$	9.81954	+	36.6470i	0.353184	+	1.31810i	−0.529570	+	0.848266i	$0.677647\pi$
$774$	1.79696	+	6.70636i	0.0645906	+	0.241055i
$775$	2.48662	−	9.28020i	0.0893221	−	0.333355i
$776$		−	5.83551i		−	0.209483i
$777$	−15.7252	−	7.17080i	−0.564138	−	0.257251i
$778$	−15.4789	+	15.4789i	−0.554944	+	0.554944i
$779$	−17.5324	+	10.1223i	−0.628164	+	0.362671i
$780$	11.3219	−	1.49962i	0.405389	−	0.0536952i
$781$	−0.750118	+	1.29924i	−0.0268413	+	0.0464906i
$782$	−6.58868	−	1.76543i	−0.235611	−	0.0631317i
$783$			2.41342i			0.0862485i
$784$	6.61757	+	2.28205i	0.236342	+	0.0815018i
$785$	48.2394	+	48.2394i	1.72174	+	1.72174i
$786$	−5.06466	+	18.9015i	−0.180650	+	0.674196i
$787$	51.6860	−	13.8492i	1.84241	−	0.493671i	0.843361	−	0.537347i	$-0.180573\pi$
$787$	51.6860	−	13.8492i	1.84241	−	0.493671i	0.999046	+	0.0436756i	$0.0139068\pi$
$788$	1.84931	+	6.90171i	0.0658789	+	0.245863i
$789$	−21.7895	+	12.5802i	−0.775727	+	0.447866i
$790$	41.2445			1.46741
$791$	20.1169	−	7.51608i	0.715275	−	0.267241i
$792$		−	0.132761i		−	0.00471747i
$793$	−15.1895	−	36.5891i	−0.539394	−	1.29932i
$794$	9.58216	+	5.53227i	0.340058	+	0.196333i
$795$	−26.3676	+	7.06518i	−0.935162	+	0.250576i
$796$	−13.5324	+	7.81296i	−0.479644	+	0.276923i
$797$	−19.8240			−0.702201			−0.351100	−	0.936338i	$-0.614192\pi$
$797$	−19.8240			−0.702201			−0.351100	+	0.936338i	$0.614192\pi$
$798$	5.62031	−	6.81476i	0.198957	−	0.241240i
$799$	18.2205	+	18.2205i	0.644594	+	0.644594i
$800$	−4.86187	−	1.30273i	−0.171893	−	0.0460586i
$801$	16.6648	−	4.46531i	0.588820	−	0.157774i
$802$	4.16138	−	7.20772i	0.146943	−	0.254513i
$803$	−0.418043	−	0.724072i	−0.0147524	−	0.0255519i
$804$	−8.99166	−	8.99166i	−0.317111	−	0.317111i
$805$	−14.3786	+	10.2511i	−0.506778	+	0.361304i
$806$	−0.892931	+	6.82400i	−0.0314521	+	0.240365i
$807$	−2.23331	−	3.86820i	−0.0786162	−	0.136167i
$808$	−1.67136	−	6.23760i	−0.0587982	−	0.219438i
$809$	−20.8295	+	36.0777i	−0.732326	+	1.26843i	0.223561	+	0.974690i	$0.428232\pi$
$809$	−20.8295	+	36.0777i	−0.732326	+	1.26843i	−0.955887	+	0.293736i	$0.905101\pi$
$810$	−1.58378	−	2.74318i	−0.0556482	−	0.0963855i
$811$	−23.1115	+	23.1115i	−0.811556	+	0.811556i	−0.984867	−	0.173311i	$-0.944553\pi$
$811$	−23.1115	+	23.1115i	−0.811556	+	0.811556i	0.173311	+	0.984867i	$0.444553\pi$
$812$	6.29749	+	1.05534i	0.220999	+	0.0370352i
$813$	3.69376	−	3.69376i	0.129546	−	0.129546i
$814$	0.837694	+	0.224459i	0.0293612	+	0.00786730i
$815$	−0.574767	−	0.331842i	−0.0201332	−	0.0116239i
$816$	−2.80350	−	1.61860i	−0.0981420	−	0.0566623i
$817$	5.99954	−	22.3906i	0.209897	−	0.783348i
$818$	25.6399			0.896478
$819$	6.97306	−	6.50972i	0.243658	−	0.227468i
$820$	19.2068			0.670732
$821$	−8.93697	+	33.3532i	−0.311902	+	1.16404i	0.614937	+	0.788576i	$0.289181\pi$
$821$	−8.93697	+	33.3532i	−0.311902	+	1.16404i	−0.926839	+	0.375459i	$0.877485\pi$
$822$	16.4399	+	9.49160i	0.573409	+	0.331058i
$823$	−10.3596	−	5.98112i	−0.361113	−	0.208489i	0.308456	−	0.951239i	$-0.400188\pi$
$823$	−10.3596	−	5.98112i	−0.361113	−	0.208489i	−0.669569	+	0.742750i	$0.733521\pi$
$824$	11.6833	+	3.13052i	0.407006	+	0.109057i
$825$	0.472516	−	0.472516i	0.0164509	−	0.0164509i
$826$	6.30923	+	16.8868i	0.219526	+	0.587565i
$827$	21.4792	−	21.4792i	0.746906	−	0.746906i	−0.226991	−	0.973897i	$-0.572889\pi$
$827$	21.4792	−	21.4792i	0.746906	−	0.746906i	0.973897	+	0.226991i	$0.0728887\pi$
$828$	−1.05355	−	1.82480i	−0.0366134	−	0.0634162i
$829$	8.11868	−	14.0620i	0.281974	−	0.488392i	−0.689897	−	0.723907i	$-0.742344\pi$
$829$	8.11868	−	14.0620i	0.281974	−	0.488392i	0.971871	+	0.235515i	$0.0756776\pi$
$830$	−0.388076	−	1.44832i	−0.0134703	−	0.0502720i
$831$	1.55206	+	2.68824i	0.0538403	+	0.0932541i
$832$	3.57507	+	0.467804i	0.123943	+	0.0162182i
$833$	4.31347	+	22.2461i	0.149453	+	0.770781i
$834$	−8.86617	−	8.86617i	−0.307010	−	0.307010i
$835$	−4.57062	−	7.91654i	−0.158173	−	0.273963i
$836$	−0.221626	+	0.383867i	−0.00766509	+	0.0132763i
$837$	1.84373	−	0.494026i	0.0637287	−	0.0170760i
$838$	17.3706	+	4.65444i	0.600058	+	0.160785i
$839$	2.56377	+	2.56377i	0.0885113	+	0.0885113i	0.749976	−	0.661465i	$-0.230065\pi$
$839$	2.56377	+	2.56377i	0.0885113	+	0.0885113i	−0.661465	+	0.749976i	$0.730065\pi$
$840$	−7.85051	+	2.93311i	−0.270868	+	0.101202i
$841$	−23.1754			−0.799152
$842$	−9.56313	+	5.52128i	−0.329567	+	0.190276i
$843$	9.68100	−	2.59402i	0.333431	−	0.0893427i
$844$	19.9291	+	11.5061i	0.685987	+	0.396055i
$845$	−35.6937	−	20.5329i	−1.22790	−	0.706353i
$846$			7.95986i			0.273666i
$847$	−18.4875	+	22.4165i	−0.635238	+	0.770241i
$848$	−8.61793			−0.295941
$849$	−26.8539	+	15.5041i	−0.921622	+	0.532099i
$850$	−4.21721	−	15.7389i	−0.144649	−	0.539838i
$851$	13.2953	−	3.56247i	0.455758	−	0.122120i
$852$	−2.92472	+	10.9152i	−0.100199	+	0.373949i
$853$	−17.6718	−	17.6718i	−0.605071	−	0.605071i	0.336583	−	0.941654i	$-0.390729\pi$
$853$	−17.6718	−	17.6718i	−0.605071	−	0.605071i	−0.941654	+	0.336583i	$0.890729\pi$
$854$	16.8760	+	23.6709i	0.577484	+	0.810000i
$855$			10.5755i			0.361676i
$856$	3.96520	+	1.06247i	0.135528	+	0.0363145i
$857$	−18.3964	+	31.8635i	−0.628410	+	1.08844i	0.359461	+	0.933160i	$0.382961\pi$
$857$	−18.3964	+	31.8635i	−0.628410	+	1.08844i	−0.987871	+	0.155278i	$0.950373\pi$
$858$	−0.291101	+	0.379990i	−0.00993804	+	0.0129726i
$859$	0.678380	−	0.391663i	0.0231460	−	0.0133634i	−0.488382	−	0.872630i	$-0.662413\pi$
$859$	0.678380	−	0.391663i	0.0231460	−	0.0133634i	0.511528	+	0.859266i	$0.329080\pi$
$860$	−15.5508	+	15.5508i	−0.530277	+	0.530277i
$861$	13.0629	−	9.31309i	0.445182	−	0.317389i
$862$			3.38889i			0.115426i
$863$	−5.98844	+	22.3491i	−0.203849	+	0.760774i	0.785949	+	0.618292i	$0.212175\pi$
$863$	−5.98844	+	22.3491i	−0.203849	+	0.760774i	−0.989797	+	0.142482i	$0.954492\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	10.8959	+	40.6640i	0.370471	+	1.38262i
$866$	0.813232	−	3.03502i	0.0276348	−	0.103134i
$867$			6.52054i			0.221449i
$868$	−0.482866	−	5.02700i	−0.0163895	−	0.170627i
$869$	−1.22236	+	1.22236i	−0.0414657	+	0.0414657i
$870$	−6.62044	+	3.82231i	−0.224454	+	0.129589i
$871$	6.02024	+	45.4517i	0.203988	+	1.54007i
$872$	7.48235	−	12.9598i	0.253384	−	0.438875i
$873$	5.63667	+	1.51034i	0.190772	+	0.0511173i
$874$			7.03499i			0.237962i
$875$	−0.254539	−	0.116071i	−0.00860498	−	0.00392393i
$876$	−4.45312	−	4.45312i	−0.150457	−	0.150457i
$877$	14.7321	−	54.9809i	0.497467	−	1.85657i	−0.0182827	−	0.999833i	$-0.505820\pi$
$877$	14.7321	−	54.9809i	0.497467	−	1.85657i	0.515750	−	0.856739i	$-0.327513\pi$
$878$	−37.8072	+	10.1304i	−1.27593	+	0.341885i
$879$	3.13451	+	11.6981i	0.105724	+	0.394568i
$880$	0.364188	−	0.210264i	0.0122768	−	0.00708800i
$881$	−36.3094			−1.22329			−0.611647	−	0.791131i	$-0.709493\pi$
$881$	−36.3094			−1.22329			−0.611647	+	0.791131i	$0.709493\pi$
$882$	−3.91705	+	5.80144i	−0.131894	+	0.195345i
$883$		−	48.4701i		−	1.63115i	−0.578653	−	0.815574i	$-0.696421\pi$
$883$		−	48.4701i		−	1.63115i	0.578653	−	0.815574i	$-0.303579\pi$
$884$	4.47513	+	10.7799i	0.150515	+	0.362567i
$885$	−18.6907	−	10.7911i	−0.628282	−	0.362739i
$886$	27.4823	−	7.36386i	0.923285	−	0.247394i
$887$	7.20573	−	4.16023i	0.241945	−	0.139687i	−0.374125	−	0.927378i	$-0.622057\pi$
$887$	7.20573	−	4.16023i	0.241945	−	0.139687i	0.616070	+	0.787691i	$0.288724\pi$
$888$	6.53236			0.219212
$889$	1.99639	+	5.34338i	0.0669568	+	0.179211i
$890$	38.6424	+	38.6424i	1.29530	+	1.29530i
$891$	0.128238	+	0.0343612i	0.00429612	+	0.00115114i
$892$	−5.98041	+	1.60245i	−0.200239	+	0.0536539i
$893$	13.2878	−	23.0152i	0.444660	−	0.770174i
$894$	−2.85364	−	4.94265i	−0.0954400	−	0.165307i
$895$	1.33696	+	1.33696i	0.0446897	+	0.0446897i
$896$	−2.63363	+	0.252972i	−0.0879834	+	0.00845121i
$897$	−0.985710	+	7.53304i	−0.0329119	+	0.251521i
$898$	−1.84176	−	3.19002i	−0.0614604	−	0.106452i
$899$	−1.19229	−	4.44969i	−0.0397652	−	0.148406i
$900$	2.51669	−	4.35904i	0.0838897	−	0.145301i
$901$	−13.9490	−	24.1604i	−0.464708	−	0.804898i
$902$	−0.569232	+	0.569232i	−0.0189533	+	0.0189533i
$903$	−3.03601	+	18.1167i	−0.101032	+	0.602885i
$904$	−5.73947	+	5.73947i	−0.190892	+	0.190892i
$905$	−27.0436	−	7.24632i	−0.898961	−	0.240876i
$906$	−8.25600	−	4.76661i	−0.274287	−	0.158360i
$907$	−37.1412	−	21.4435i	−1.23325	−	0.712019i	−0.265546	−	0.964098i	$-0.585552\pi$
$907$	−37.1412	−	21.4435i	−1.23325	−	0.712019i	−0.967706	+	0.252080i	$0.918886\pi$
$908$	−1.95657	+	7.30201i	−0.0649309	+	0.242326i
$909$	6.45763			0.214186
$910$	28.9011	+	8.81841i	0.958062	+	0.292328i
$911$	−13.3641			−0.442774			−0.221387	−	0.975186i	$-0.571058\pi$
$911$	−13.3641			−0.442774			−0.221387	+	0.975186i	$0.571058\pi$
$912$	−0.864122	+	3.22495i	−0.0286139	+	0.106789i
$913$	0.0544251	+	0.0314224i	0.00180121	+	0.00103993i
$914$	22.9647	+	13.2587i	0.759604	+	0.438557i
$915$	−33.6182	−	9.00797i	−1.11138	−	0.297794i
$916$	10.8600	−	10.8600i	0.358825	−	0.358825i
$917$	−32.9409	+	39.9416i	−1.08780	+	1.31899i
$918$	2.28905	−	2.28905i	0.0755498	−	0.0755498i
$919$	−4.12875	−	7.15121i	−0.136195	−	0.235897i	0.789858	−	0.613289i	$-0.210154\pi$
$919$	−4.12875	−	7.15121i	−0.136195	−	0.235897i	−0.926053	+	0.377393i	$0.876821\pi$
$920$	3.33717	−	5.78015i	0.110023	−	0.190566i
$921$	2.55356	+	9.53001i	0.0841426	+	0.314025i
$922$	8.15640	+	14.1273i	0.268617	+	0.465258i
$923$	32.3046	−	24.8286i	1.06332	−	0.817243i
$924$	0.145737	−	0.319593i	0.00479438	−	0.0105138i
$925$	23.2496	+	23.2496i	0.764441	+	0.764441i
$926$	−1.03517	−	1.79297i	−0.0340179	−	0.0589207i
$927$	−6.04770	+	10.4749i	−0.198632	+	0.344042i
$928$	−2.33118	+	0.624639i	−0.0765248	+	0.0205048i
$929$	42.7488	+	11.4545i	1.40254	+	0.375810i	0.879257	−	0.476347i	$-0.158039\pi$
$929$	42.7488	+	11.4545i	1.40254	+	0.375810i	0.523286	+	0.852157i	$0.324706\pi$
$930$	4.27526	+	4.27526i	0.140191	+	0.140191i
$931$	21.0104	−	10.2354i	0.688589	−	0.335452i
$932$	23.2903			0.762900
$933$	−19.4873	+	11.2510i	−0.637986	+	0.368342i
$934$	27.8654	−	7.46650i	0.911782	−	0.244311i
$935$	1.17895	+	0.680667i	0.0385558	+	0.0222602i
$936$	−1.37716	+	3.33218i	−0.0450139	+	0.108916i
$937$		−	9.36599i		−	0.305973i	−0.988228	−	0.152987i	$-0.951111\pi$
$937$		−	9.36599i		−	0.305973i	0.988228	−	0.152987i	$-0.0488892\pi$
$938$	−11.7750	−	31.5159i	−0.384466	−	1.02903i
$939$	26.2442			0.856448
$940$	−21.8353	+	12.6066i	−0.712190	+	0.411183i
$941$	−5.92312	−	22.1054i	−0.193088	−	0.720615i	−0.992753	−	0.120169i	$-0.961656\pi$
$941$	−5.92312	−	22.1054i	−0.193088	−	0.720615i	0.799665	−	0.600446i	$-0.205010\pi$
$942$	−20.8035	+	5.57429i	−0.677816	+	0.181620i
$943$	−3.30684	+	12.3413i	−0.107686	+	0.401888i
$944$	−4.81789	−	4.81789i	−0.156809	−	0.156809i
$945$	−0.801303	−	8.34216i	−0.0260664	−	0.271370i
$946$		−	0.921754i		−	0.0299688i
$947$	−0.748885	−	0.200663i	−0.0243355	−	0.00652068i	0.246631	−	0.969110i	$-0.420677\pi$
$947$	−0.748885	−	0.200663i	−0.0243355	−	0.00652068i	−0.270966	+	0.962589i	$0.587343\pi$
$948$	−6.51047	+	11.2765i	−0.211450	+	0.366242i
$949$	2.98152	+	22.5100i	0.0967844	+	0.730704i
$950$	−14.5536	+	8.40250i	−0.472180	+	0.272613i
$951$	−18.7894	+	18.7894i	−0.609287	+	0.609287i
$952$	−4.97200	−	6.97391i	−0.161143	−	0.226026i
$953$		−	26.2222i		−	0.849421i	−0.905329	−	0.424711i	$-0.860376\pi$
$953$		−	26.2222i		−	0.849421i	0.905329	−	0.424711i	$-0.139624\pi$
$954$	2.23049	−	8.32429i	0.0722146	−	0.269509i
$955$	−12.8568	−	47.9821i	−0.416035	−	1.55266i
$956$	3.63730	+	13.5746i	0.117639	+	0.439034i
$957$	0.0829279	−	0.309491i	0.00268068	−	0.0100044i
$958$		−	32.1101i		−	1.03743i
$959$	29.1562	+	40.8956i	0.941503	+	1.32059i
$960$	2.23980	−	2.23980i	0.0722891	−	0.0722891i
$961$	23.6915	−	13.6783i	0.764242	−	0.441235i
$962$	−18.6969	−	14.3233i	−0.602814	−	0.461801i
$963$	−2.05254	+	3.55510i	−0.0661421	+	0.114561i
$964$	3.56773	+	0.955972i	0.114909	+	0.0307898i
$965$		−	55.9573i		−	1.80133i
$966$	−0.533038	−	5.54932i	−0.0171502	−	0.178546i
$967$	36.6449	+	36.6449i	1.17842	+	1.17842i	0.980147	+	0.198273i	$0.0635331\pi$
$967$	36.6449	+	36.6449i	1.17842	+	1.17842i	0.198273	+	0.980147i	$0.436467\pi$
$968$	2.84245	−	10.6082i	0.0913597	−	0.340959i
$969$	−10.4398	+	2.79733i	−0.335375	+	0.0898633i
$970$	4.78408	+	17.8544i	0.153608	+	0.573272i
$971$	39.7725	−	22.9627i	1.27636	−	0.736907i	0.300184	−	0.953881i	$-0.402952\pi$
$971$	39.7725	−	22.9627i	1.27636	−	0.736907i	0.976177	+	0.216974i	$0.0696186\pi$
$972$	1.00000			0.0320750
$973$	−11.6106	−	31.0760i	−0.372219	−	0.996251i
$974$		−	14.8495i		−	0.475809i
$975$	−16.7612	+	6.95818i	−0.536788	+	0.222840i
$976$	−9.51563	−	5.49385i	−0.304588	−	0.175854i
$977$	16.6380	−	4.45814i	0.532297	−	0.142629i	0.0173484	−	0.999850i	$-0.494478\pi$
$977$	16.6380	−	4.45814i	0.532297	−	0.142629i	0.514949	+	0.857221i	$0.327811\pi$
$978$	0.181455	−	0.104763i	0.00580228	−	0.00334995i
$979$	−2.29048			−0.0732041
$980$	−22.1181	−	1.55698i	−0.706538	−	0.0497358i
$981$	10.5816	+	10.5816i	0.337846	+	0.337846i
$982$	−9.52785	−	2.55298i	−0.304046	−	0.0814688i
$983$	−40.5638	+	10.8690i	−1.29378	+	0.346668i	−0.839096	−	0.543983i	$-0.816916\pi$
$983$	−40.5638	+	10.8690i	−1.29378	+	0.346668i	−0.454687	+	0.890651i	$0.650249\pi$
$984$	−3.03181	+	5.25125i	−0.0966506	+	0.167404i
$985$	−11.3164	−	19.6005i	−0.360569	−	0.624524i
$986$	−5.52443	−	5.52443i	−0.175934	−	0.175934i
$987$	−8.73781	+	19.1616i	−0.278128	+	0.609920i
$988$	9.54453	−	7.33572i	0.303652	−	0.233380i
$989$	−7.31473	−	12.6695i	−0.232595	−	0.402866i
$990$	0.108841	+	0.406199i	0.00345919	+	0.0129099i
$991$	−28.1761	+	48.8024i	−0.895043	+	1.55026i	−0.0612922	+	0.998120i	$0.519522\pi$
$991$	−28.1761	+	48.8024i	−0.895043	+	1.55026i	−0.833751	+	0.552141i	$0.813811\pi$
$992$	0.954385	+	1.65304i	0.0303018	+	0.0524842i
$993$	−6.05618	+	6.05618i	−0.192187	+	0.192187i
$994$	−19.0226	+	23.0653i	−0.603360	+	0.731588i
$995$	34.9989	−	34.9989i	1.10954	−	1.10954i
$996$	0.457237	+	0.122516i	0.0144881	+	0.00388208i
$997$	4.99140	+	2.88179i	0.158079	+	0.0912671i	0.576953	−	0.816777i	$-0.304242\pi$
$997$	4.99140	+	2.88179i	0.158079	+	0.0912671i	−0.418874	+	0.908045i	$0.637575\pi$
$998$	−5.48551	−	3.16706i	−0.173641	−	0.100252i
$999$	−1.69070	+	6.30977i	−0.0534913	+	0.199632i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.b.73.5	yes	40
7.5	odd	6		546.2.bz.a.229.10	yes	40
13.5	odd	4		546.2.bz.a.31.10	✓	40
91.5	even	12	inner	546.2.bz.b.187.5	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.31.10	✓	40	13.5	odd	4
546.2.bz.a.229.10	yes	40	7.5	odd	6
546.2.bz.b.73.5	yes	40	1.1	even	1	trivial
546.2.bz.b.187.5	yes	40	91.5	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.05962 + 0.819823i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.47842 + 0.925986i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(3.05962 + 0.819823i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.47842 + 0.925986i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.58378 + 2.74318i) q^{10} +(-0.0343612 - 0.128238i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.467804 + 3.57507i) q^{13} +(-0.252972 - 2.63363i) q^{14} +(2.23980 + 2.23980i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.61860 + 2.80350i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(3.22495 + 0.864122i) q^{19} +(-2.23980 - 2.23980i) q^{20} +(-2.60936 - 0.437281i) q^{21} +0.132761 q^{22} +(1.82480 - 1.05355i) q^{23} +(0.965926 - 0.258819i) q^{24} +(4.35904 + 2.51669i) q^{25} +(-3.33218 - 1.37716i) q^{26} +1.00000i q^{27} +(2.60936 + 0.437281i) q^{28} +2.41342 q^{29} +(-2.74318 + 1.58378i) q^{30} +(-0.494026 - 1.84373i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.0343612 - 0.128238i) q^{33} +(-2.28905 - 2.28905i) q^{34} +(-8.34216 + 0.801303i) q^{35} -1.00000i q^{36} +(6.30977 + 1.69070i) q^{37} +(-1.66935 + 2.89141i) q^{38} +(-2.19267 + 2.86220i) q^{39} +(2.74318 - 1.58378i) q^{40} +(-4.28763 + 4.28763i) q^{41} +(1.09773 - 2.40728i) q^{42} -6.94294i q^{43} +(-0.0343612 + 0.128238i) q^{44} +(0.819823 + 3.05962i) q^{45} +(0.545357 + 2.03530i) q^{46} +(2.06016 - 7.68863i) q^{47} +1.00000i q^{48} +(5.28510 - 4.58996i) q^{49} +(-3.55914 + 3.55914i) q^{50} +(-2.80350 + 1.61860i) q^{51} +(2.19267 - 2.86220i) q^{52} +(-4.30897 + 7.46335i) q^{53} +(-0.965926 - 0.258819i) q^{54} -0.420528i q^{55} +(-1.09773 + 2.40728i) q^{56} +(2.36082 + 2.36082i) q^{57} +(-0.624639 + 2.33118i) q^{58} +(-6.58136 + 1.76347i) q^{59} +(-0.819823 - 3.05962i) q^{60} +(-9.51563 + 5.49385i) q^{61} +1.90877 q^{62} +(-2.04114 - 1.68338i) q^{63} -1.00000i q^{64} +(-4.36223 + 10.5549i) q^{65} +(0.114975 + 0.0663807i) q^{66} +(12.2828 - 3.29118i) q^{67} +(2.80350 - 1.61860i) q^{68} +2.10710 q^{69} +(1.38511 - 8.26530i) q^{70} +(-7.99048 - 7.99048i) q^{71} +(0.965926 + 0.258819i) q^{72} +(6.08308 - 1.62996i) q^{73} +(-3.26618 + 5.65719i) q^{74} +(2.51669 + 4.35904i) q^{75} +(-2.36082 - 2.36082i) q^{76} +(0.203908 + 0.286008i) q^{77} +(-2.19717 - 2.85875i) q^{78} +(-6.51047 - 11.2765i) q^{79} +(0.819823 + 3.05962i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.03181 - 5.25125i) q^{82} +(-0.334721 + 0.334721i) q^{83} +(2.04114 + 1.68338i) q^{84} +(-7.25067 + 7.25067i) q^{85} +(6.70636 + 1.79696i) q^{86} +(2.09008 + 1.20671i) q^{87} +(-0.114975 - 0.0663807i) q^{88} +(4.46531 - 16.6648i) q^{89} -3.16755 q^{90} +(-2.15106 - 9.29371i) q^{91} -2.10710 q^{92} +(0.494026 - 1.84373i) q^{93} +(6.89344 + 3.97993i) q^{94} +(9.15868 + 5.28777i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(4.12633 - 4.12633i) q^{97} +(3.06568 + 6.29298i) q^{98} +(0.0938764 - 0.0938764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

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