LMFDB - Embedded newform 546.2.by.b.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			19.2
Character	$\chi$	$=$	546.19
Dual form			546.2.by.b.115.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.37297 + 0.367885i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.220772 - 2.63652i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.37297 + 0.367885i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.220772 - 2.63652i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.42140 q^{10} +(2.72762 + 2.72762i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.74539 - 3.15494i) q^{13} +(-0.469134 + 2.60383i) q^{14} +(0.367885 + 1.37297i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.18021 - 2.04418i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-4.27628 - 4.27628i) q^{19} +(-1.37297 - 0.367885i) q^{20} +(-2.63652 + 0.220772i) q^{21} +(-1.92872 - 3.34063i) q^{22} +(-7.02168 + 4.05397i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.58043 + 1.48981i) q^{25} +(0.869355 + 3.49917i) q^{26} +1.00000i q^{27} +(1.12707 - 2.39368i) q^{28} +(-0.220739 + 0.382331i) q^{29} -1.42140i q^{30} +(0.855281 - 3.19195i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.72762 - 2.72762i) q^{33} +(-1.66907 + 1.66907i) q^{34} +(1.27305 + 3.53864i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(1.96375 - 7.32883i) q^{37} +(3.02378 + 5.23735i) q^{38} +(-3.15494 + 1.74539i) q^{39} +(1.23097 + 0.710699i) q^{40} +(-1.33418 + 0.357492i) q^{41} +(2.60383 + 0.469134i) q^{42} +(-7.53977 + 4.35309i) q^{43} +(0.998376 + 3.72599i) q^{44} +(1.37297 - 0.367885i) q^{45} +(7.83167 - 2.09849i) q^{46} +(-1.64659 - 6.14515i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.90252 + 1.16414i) q^{49} +(2.87810 - 0.771184i) q^{50} +(-2.04418 - 1.18021i) q^{51} +(0.0659206 - 3.60495i) q^{52} +(-4.08469 - 7.07489i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-4.74837 - 2.74147i) q^{55} +(-1.70820 + 2.02041i) q^{56} +(-4.27628 + 4.27628i) q^{57} +(0.312172 - 0.312172i) q^{58} +(2.17393 + 8.11322i) q^{59} +(-0.367885 + 1.37297i) q^{60} +10.6572i q^{61} +(-1.65228 + 2.86183i) q^{62} +(0.220772 + 2.63652i) q^{63} +1.00000i q^{64} +(3.55701 + 3.68952i) q^{65} +(-3.34063 + 1.92872i) q^{66} +(-0.0278660 + 0.0278660i) q^{67} +(2.04418 - 1.18021i) q^{68} +(4.05397 + 7.02168i) q^{69} +(-0.313804 - 3.74755i) q^{70} +(-12.2523 - 3.28299i) q^{71} +(0.707107 + 0.707107i) q^{72} +(7.72484 + 2.06986i) q^{73} +(-3.79368 + 6.57085i) q^{74} +(1.48981 + 2.58043i) q^{75} +(-1.56523 - 5.84150i) q^{76} +(6.58924 - 7.79360i) q^{77} +(3.49917 - 0.869355i) q^{78} +(6.14585 - 10.6449i) q^{79} +(-1.00508 - 1.00508i) q^{80} +1.00000 q^{81} +1.38124 q^{82} +(-9.37857 - 9.37857i) q^{83} +(-2.39368 - 1.12707i) q^{84} +(-0.868362 + 3.24077i) q^{85} +(8.40952 - 2.25332i) q^{86} +(0.382331 + 0.220739i) q^{87} -3.85743i q^{88} +(1.99161 + 0.533652i) q^{89} -1.42140 q^{90} +(-7.93274 + 5.29827i) q^{91} -8.10794 q^{92} +(-3.19195 - 0.855281i) q^{93} +6.36192i q^{94} +(7.44436 + 4.29800i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(3.62024 - 13.5109i) q^{97} +(6.96862 + 0.662032i) q^{98} +(-2.72762 - 2.72762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.37297	+	0.367885i	−0.614009	+	0.164523i	−0.552403	−	0.833577i	$-0.686289\pi$
$5$	−1.37297	+	0.367885i	−0.614009	+	0.164523i	−0.0616062	+	0.998101i	$0.519622\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	−0.220772	−	2.63652i	−0.0834438	−	0.996512i
$7$	−0.220772	−	2.63652i	−0.0834438	−	0.996512i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−1.00000			−0.333333
$10$	1.42140			0.449486
$11$	2.72762	+	2.72762i	0.822407	+	0.822407i	0.986453	−	0.164046i	$-0.0524545\pi$
$11$	2.72762	+	2.72762i	0.822407	+	0.822407i	−0.164046	+	0.986453i	$0.552454\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.74539	−	3.15494i	−0.484083	−	0.875022i
$13$	−1.74539	−	3.15494i	−0.484083	−	0.875022i
$14$	−0.469134	+	2.60383i	−0.125381	+	0.695902i
$15$	0.367885	+	1.37297i	0.0949875	+	0.354498i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.18021	−	2.04418i	0.286243	−	0.495787i	−0.686667	−	0.726972i	$-0.740927\pi$
$17$	1.18021	−	2.04418i	0.286243	−	0.495787i	0.972910	+	0.231185i	$0.0742604\pi$
$18$	0.965926	+	0.258819i	0.227671	+	0.0610042i
$19$	−4.27628	−	4.27628i	−0.981045	−	0.981045i	0.0187787	−	0.999824i	$-0.494022\pi$
$19$	−4.27628	−	4.27628i	−0.981045	−	0.981045i	−0.999824	+	0.0187787i	$0.994022\pi$
$20$	−1.37297	−	0.367885i	−0.307005	−	0.0822616i
$21$	−2.63652	+	0.220772i	−0.575337	+	0.0481763i
$22$	−1.92872	−	3.34063i	−0.411203	−	0.712225i
$23$	−7.02168	+	4.05397i	−1.46412	+	0.845311i	−0.999198	−	0.0400397i	$-0.987252\pi$
$23$	−7.02168	+	4.05397i	−1.46412	+	0.845311i	−0.464924	+	0.885351i	$0.653918\pi$
$24$	−0.707107	+	0.707107i	−0.144338	+	0.144338i
$25$	−2.58043	+	1.48981i	−0.516086	+	0.297962i
$26$	0.869355	+	3.49917i	0.170495	+	0.686245i
$27$			1.00000i			0.192450i
$28$	1.12707	−	2.39368i	0.212996	−	0.452364i
$29$	−0.220739	+	0.382331i	−0.0409902	+	0.0709971i	−0.885793	−	0.464081i	$-0.846385\pi$
$29$	−0.220739	+	0.382331i	−0.0409902	+	0.0709971i	0.844802	+	0.535078i	$0.179718\pi$
$30$		−	1.42140i		−	0.259511i
$31$	0.855281	−	3.19195i	0.153613	−	0.573292i	−0.845607	−	0.533806i	$-0.820761\pi$
$31$	0.855281	−	3.19195i	0.153613	−	0.573292i	0.999220	−	0.0394858i	$-0.0125720\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	2.72762	−	2.72762i	0.474817	−	0.474817i
$34$	−1.66907	+	1.66907i	−0.286243	+	0.286243i
$35$	1.27305	+	3.53864i	0.215185	+	0.598139i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	1.96375	−	7.32883i	0.322839	−	1.20485i	−0.593627	−	0.804740i	$-0.702305\pi$
$37$	1.96375	−	7.32883i	0.322839	−	1.20485i	0.916466	−	0.400112i	$-0.131029\pi$
$38$	3.02378	+	5.23735i	0.490522	+	0.849610i
$39$	−3.15494	+	1.74539i	−0.505194	+	0.279485i
$40$	1.23097	+	0.710699i	0.194633	+	0.112371i
$41$	−1.33418	+	0.357492i	−0.208364	+	0.0558309i	−0.361491	−	0.932376i	$-0.617732\pi$
$41$	−1.33418	+	0.357492i	−0.208364	+	0.0558309i	0.153127	+	0.988206i	$0.451066\pi$
$42$	2.60383	+	0.469134i	0.401779	+	0.0723889i
$43$	−7.53977	+	4.35309i	−1.14980	+	0.663840i	−0.948839	−	0.315759i	$-0.897741\pi$
$43$	−7.53977	+	4.35309i	−1.14980	+	0.663840i	−0.200964	+	0.979599i	$0.564408\pi$
$44$	0.998376	+	3.72599i	0.150511	+	0.561714i
$45$	1.37297	−	0.367885i	0.204670	−	0.0548411i
$46$	7.83167	−	2.09849i	1.15472	−	0.309405i
$47$	−1.64659	−	6.14515i	−0.240179	−	0.896362i	−0.975745	−	0.218909i	$-0.929750\pi$
$47$	−1.64659	−	6.14515i	−0.240179	−	0.896362i	0.735566	−	0.677453i	$-0.236916\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−6.90252	+	1.16414i	−0.986074	+	0.166306i
$50$	2.87810	−	0.771184i	0.407024	−	0.109062i
$51$	−2.04418	−	1.18021i	−0.286243	−	0.165262i
$52$	0.0659206	−	3.60495i	0.00914154	−	0.499916i
$53$	−4.08469	−	7.07489i	−0.561076	−	0.971811i	−0.997403	−	0.0720233i	$-0.977054\pi$
$53$	−4.08469	−	7.07489i	−0.561076	−	0.971811i	0.436327	−	0.899788i	$-0.356279\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	−4.74837	−	2.74147i	−0.640270	−	0.369660i
$56$	−1.70820	+	2.02041i	−0.228267	+	0.269989i
$57$	−4.27628	+	4.27628i	−0.566407	+	0.566407i
$58$	0.312172	−	0.312172i	0.0409902	−	0.0409902i
$59$	2.17393	+	8.11322i	0.283022	+	1.05625i	0.950273	+	0.311419i	$0.100804\pi$
$59$	2.17393	+	8.11322i	0.283022	+	1.05625i	−0.667251	+	0.744833i	$0.732529\pi$
$60$	−0.367885	+	1.37297i	−0.0474938	+	0.177249i
$61$			10.6572i			1.36451i	0.731112	+	0.682257i	$0.239002\pi$
$61$			10.6572i			1.36451i	−0.731112	+	0.682257i	$0.760998\pi$
$62$	−1.65228	+	2.86183i	−0.209839	+	0.363452i
$63$	0.220772	+	2.63652i	0.0278146	+	0.332171i
$64$			1.00000i			0.125000i
$65$	3.55701	+	3.68952i	0.441193	+	0.457629i
$66$	−3.34063	+	1.92872i	−0.411203	+	0.237408i
$67$	−0.0278660	+	0.0278660i	−0.00340438	+	0.00340438i	−0.708807	−	0.705403i	$-0.750766\pi$
$67$	−0.0278660	+	0.0278660i	−0.00340438	+	0.00340438i	0.705403	+	0.708807i	$0.250766\pi$
$68$	2.04418	−	1.18021i	0.247893	−	0.143121i
$69$	4.05397	+	7.02168i	0.488041	+	0.845311i
$70$	−0.313804	−	3.74755i	−0.0375068	−	0.447918i
$71$	−12.2523	−	3.28299i	−1.45408	−	0.389619i	−0.556637	−	0.830756i	$-0.687909\pi$
$71$	−12.2523	−	3.28299i	−1.45408	−	0.389619i	−0.897440	+	0.441137i	$0.854575\pi$
$72$	0.707107	+	0.707107i	0.0833333	+	0.0833333i
$73$	7.72484	+	2.06986i	0.904124	+	0.242259i	0.680786	−	0.732482i	$-0.261638\pi$
$73$	7.72484	+	2.06986i	0.904124	+	0.242259i	0.223337	+	0.974741i	$0.428305\pi$
$74$	−3.79368	+	6.57085i	−0.441006	+	0.763846i
$75$	1.48981	+	2.58043i	0.172029	+	0.297962i
$76$	−1.56523	−	5.84150i	−0.179544	−	0.670066i
$77$	6.58924	−	7.79360i	0.750914	−	0.888163i
$78$	3.49917	−	0.869355i	0.396203	−	0.0984351i
$79$	6.14585	−	10.6449i	0.691462	−	1.19765i	−0.279896	−	0.960030i	$-0.590300\pi$
$79$	6.14585	−	10.6449i	0.691462	−	1.19765i	0.971359	−	0.237618i	$-0.0763666\pi$
$80$	−1.00508	−	1.00508i	−0.112371	−	0.112371i
$81$	1.00000			0.111111
$82$	1.38124			0.152533
$83$	−9.37857	−	9.37857i	−1.02943	−	1.02943i	−0.999554	−	0.0298777i	$-0.990488\pi$
$83$	−9.37857	−	9.37857i	−1.02943	−	1.02943i	−0.0298777	−	0.999554i	$-0.509512\pi$
$84$	−2.39368	−	1.12707i	−0.261172	−	0.122973i
$85$	−0.868362	+	3.24077i	−0.0941871	+	0.351511i
$86$	8.40952	−	2.25332i	0.906822	−	0.242982i
$87$	0.382331	+	0.220739i	0.0409902	+	0.0236657i
$88$		−	3.85743i		−	0.411203i
$89$	1.99161	+	0.533652i	0.211111	+	0.0565670i	0.362824	−	0.931858i	$-0.381812\pi$
$89$	1.99161	+	0.533652i	0.211111	+	0.0565670i	−0.151714	+	0.988424i	$0.548479\pi$
$90$	−1.42140			−0.149829
$91$	−7.93274	+	5.29827i	−0.831577	+	0.555410i
$92$	−8.10794			−0.845311
$93$	−3.19195	−	0.855281i	−0.330990	−	0.0886885i
$94$			6.36192i			0.656182i
$95$	7.44436	+	4.29800i	0.763775	+	0.440966i
$96$	−0.965926	+	0.258819i	−0.0985844	+	0.0264156i
$97$	3.62024	−	13.5109i	0.367580	−	1.37183i	−0.496310	−	0.868146i	$-0.665312\pi$
$97$	3.62024	−	13.5109i	0.367580	−	1.37183i	0.863889	−	0.503681i	$-0.168021\pi$
$98$	6.96862	+	0.662032i	0.703937	+	0.0668753i
$99$	−2.72762	−	2.72762i	−0.274136	−	0.274136i
$100$	−2.97962			−0.297962
$101$	4.61068			0.458780			0.229390	−	0.973335i	$-0.426327\pi$
$101$	4.61068			0.458780			0.229390	+	0.973335i	$0.426327\pi$
$102$	1.66907	+	1.66907i	0.165262	+	0.165262i
$103$	6.27668	−	10.8715i	0.618460	−	1.07120i	−0.371307	−	0.928510i	$-0.621090\pi$
$103$	6.27668	−	10.8715i	0.618460	−	1.07120i	0.989767	−	0.142694i	$-0.0455764\pi$
$104$	−0.996704	+	3.46505i	−0.0977348	+	0.339776i
$105$	3.53864	−	1.27305i	0.345336	−	0.124237i
$106$	2.11439	+	7.89102i	0.205368	+	0.766443i
$107$	−0.287091	−	0.497256i	−0.0277541	−	0.0480716i	0.851815	−	0.523843i	$-0.175502\pi$
$107$	−0.287091	−	0.497256i	−0.0277541	−	0.0480716i	−0.879569	+	0.475772i	$0.842169\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	18.8390	+	5.04790i	1.80445	+	0.483501i	0.994659	−	0.103218i	$-0.0329138\pi$
$109$	18.8390	+	5.04790i	1.80445	+	0.483501i	0.809791	+	0.586718i	$0.199580\pi$
$110$	3.87703	+	3.87703i	0.369660	+	0.369660i
$111$	−7.32883	−	1.96375i	−0.695622	−	0.186391i
$112$	2.17291	−	1.50946i	0.205321	−	0.142630i
$113$	5.28204	+	9.14876i	0.496892	+	0.860643i	0.999994	−	0.00358469i	$-0.00114104\pi$
$113$	5.28204	+	9.14876i	0.496892	+	0.860643i	−0.503101	+	0.864227i	$0.667808\pi$
$114$	5.23735	−	3.02378i	0.490522	−	0.283203i
$115$	8.14913	−	8.14913i	0.759911	−	0.759911i
$116$	−0.382331	+	0.220739i	−0.0354986	+	0.0204951i
$117$	1.74539	+	3.15494i	0.161361	+	0.291674i
$118$		−	8.39942i		−	0.773230i
$119$	−5.65009	−	2.66035i	−0.517943	−	0.243874i
$120$	0.710699	−	1.23097i	0.0648777	−	0.112371i
$121$			3.87977i			0.352706i
$122$	2.75829	−	10.2941i	0.249724	−	0.931981i
$123$	0.357492	+	1.33418i	0.0322340	+	0.120299i
$124$	2.33667	−	2.33667i	0.209839	−	0.209839i
$125$	8.02017	−	8.02017i	0.717346	−	0.717346i
$126$	0.469134	−	2.60383i	0.0417938	−	0.231967i
$127$	13.6070	+	7.85602i	1.20743	+	0.697109i	0.962197	−	0.272355i	$-0.0878027\pi$
$127$	13.6070	+	7.85602i	1.20743	+	0.697109i	0.245232	+	0.969465i	$0.421136\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	4.35309	+	7.53977i	0.383268	+	0.663840i
$130$	−2.48089	−	4.48442i	−0.217588	−	0.393310i
$131$	12.0386	+	6.95051i	1.05182	+	0.607269i	0.923159	−	0.384420i	$-0.125598\pi$
$131$	12.0386	+	6.95051i	1.05182	+	0.607269i	0.128662	+	0.991688i	$0.458932\pi$
$132$	3.72599	−	0.998376i	0.324306	−	0.0868975i
$133$	−10.3304	+	12.2186i	−0.895761	+	1.05949i
$134$	0.0341288	−	0.0197043i	0.00294828	−	0.00170219i
$135$	−0.367885	−	1.37297i	−0.0316625	−	0.118166i
$136$	−2.27999	+	0.610921i	−0.195507	+	0.0523860i
$137$	10.2723	−	2.75244i	0.877618	−	0.235157i	0.208239	−	0.978078i	$-0.433227\pi$
$137$	10.2723	−	2.75244i	0.877618	−	0.235157i	0.669379	+	0.742921i	$0.266560\pi$
$138$	−2.09849	−	7.83167i	−0.178635	−	0.666676i
$139$	4.31229	−	2.48970i	0.365764	−	0.211174i	−0.305842	−	0.952082i	$-0.598938\pi$
$139$	4.31229	−	2.48970i	0.365764	−	0.211174i	0.671606	+	0.740908i	$0.265605\pi$
$140$	−0.666826	+	3.70108i	−0.0563571	+	0.312798i
$141$	−6.14515	+	1.64659i	−0.517515	+	0.138668i
$142$	10.9851	+	6.34224i	0.921848	+	0.532229i
$143$	3.84472	−	13.3662i	0.321511	−	1.11774i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.162413	−	0.606134i	0.0134877	−	0.0503367i
$146$	−6.92590	−	3.99867i	−0.573192	−	0.330932i
$147$	1.16414	+	6.90252i	0.0960166	+	0.569310i
$148$	5.36507	−	5.36507i	0.441006	−	0.441006i
$149$	−5.56174	+	5.56174i	−0.455636	+	0.455636i	−0.897220	−	0.441584i	$-0.854417\pi$
$149$	−5.56174	+	5.56174i	−0.455636	+	0.455636i	0.441584	+	0.897220i	$0.354417\pi$
$150$	−0.771184	−	2.87810i	−0.0629669	−	0.234996i
$151$	3.98554	−	14.8742i	0.324338	−	1.21045i	−0.590637	−	0.806937i	$-0.701123\pi$
$151$	3.98554	−	14.8742i	0.324338	−	1.21045i	0.914975	−	0.403510i	$-0.132210\pi$
$152$			6.04757i			0.490522i
$153$	−1.18021	+	2.04418i	−0.0954142	+	0.165262i
$154$	−8.38185	+	5.82262i	−0.675429	+	0.469200i
$155$			4.69709i			0.377279i
$156$	−3.60495	−	0.0659206i	−0.288627	−	0.00527787i
$157$	−8.88249	+	5.12831i	−0.708900	+	0.409283i	−0.810653	−	0.585526i	$-0.800888\pi$
$157$	−8.88249	+	5.12831i	−0.708900	+	0.409283i	0.101754	+	0.994810i	$0.467555\pi$
$158$	−8.69155	+	8.69155i	−0.691462	+	0.691462i
$159$	−7.07489	+	4.08469i	−0.561076	+	0.323937i
$160$	0.710699	+	1.23097i	0.0561857	+	0.0973165i
$161$	12.2386	+	17.6178i	0.964535	+	1.38848i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	1.25964	+	1.25964i	0.0986630	+	0.0986630i	0.754715	−	0.656052i	$-0.227775\pi$
$163$	1.25964	+	1.25964i	0.0986630	+	0.0986630i	−0.656052	+	0.754715i	$0.727775\pi$
$164$	−1.33418	−	0.357492i	−0.104182	−	0.0279154i
$165$	−2.74147	+	4.74837i	−0.213423	+	0.369660i
$166$	6.63165	+	11.4863i	0.514716	+	0.891514i
$167$	0.545200	+	2.03471i	0.0421888	+	0.157451i	0.983807	−	0.179233i	$-0.0573615\pi$
$167$	0.545200	+	2.03471i	0.0421888	+	0.157451i	−0.941618	+	0.336683i	$0.890695\pi$
$168$	2.02041	+	1.70820i	0.155878	+	0.131790i
$169$	−6.90726	+	11.0132i	−0.531328	+	0.847166i
$170$	1.67755	−	2.90560i	0.128662	−	0.222849i
$171$	4.27628	+	4.27628i	0.327015	+	0.327015i
$172$	−8.70617			−0.663840
$173$	4.41458			0.335634			0.167817	−	0.985818i	$-0.446328\pi$
$173$	4.41458			0.335634			0.167817	+	0.985818i	$0.446328\pi$
$174$	−0.312172	−	0.312172i	−0.0236657	−	0.0236657i
$175$	4.49761	+	6.47446i	0.339988	+	0.489423i
$176$	−0.998376	+	3.72599i	−0.0752555	+	0.280857i
$177$	8.11322	−	2.17393i	0.609827	−	0.163403i
$178$	−1.78563	−	1.03094i	−0.133839	−	0.0772719i
$179$		−	22.6818i		−	1.69532i	−0.530540	−	0.847660i	$-0.678011\pi$
$179$		−	22.6818i		−	1.69532i	0.530540	−	0.847660i	$-0.321989\pi$
$180$	1.37297	+	0.367885i	0.102335	+	0.0274205i
$181$	−4.69879			−0.349259			−0.174629	−	0.984634i	$-0.555873\pi$
$181$	−4.69879			−0.349259			−0.174629	+	0.984634i	$0.555873\pi$
$182$	9.03373	−	3.06459i	0.669625	−	0.227163i
$183$	10.6572			0.787803
$184$	7.83167	+	2.09849i	0.577358	+	0.154703i
$185$			10.7847i			0.792905i
$186$	2.86183	+	1.65228i	0.209839	+	0.121151i
$187$	8.79489	−	2.35658i	0.643146	−	0.172330i
$188$	1.64659	−	6.14515i	0.120090	−	0.448181i
$189$	2.63652	−	0.220772i	0.191779	−	0.0160588i
$190$	−6.07829	−	6.07829i	−0.440966	−	0.440966i
$191$	−23.0096			−1.66491			−0.832457	−	0.554089i	$-0.813067\pi$
$191$	−23.0096			−1.66491			−0.832457	+	0.554089i	$0.813067\pi$
$192$	1.00000			0.0721688
$193$	3.09675	+	3.09675i	0.222909	+	0.222909i	0.809722	−	0.586813i	$-0.199618\pi$
$193$	3.09675	+	3.09675i	0.222909	+	0.222909i	−0.586813	+	0.809722i	$0.699618\pi$
$194$	−6.99377	+	12.1136i	−0.502124	+	0.869703i
$195$	3.68952	−	3.55701i	0.264212	−	0.254723i
$196$	−6.55983	−	2.44309i	−0.468559	−	0.174506i
$197$	−2.73968	−	10.2246i	−0.195194	−	0.728476i	−0.992216	−	0.124525i	$-0.960259\pi$
$197$	−2.73968	−	10.2246i	−0.195194	−	0.728476i	0.797022	−	0.603950i	$-0.206407\pi$
$198$	1.92872	+	3.34063i	0.137068	+	0.237408i
$199$	5.14342	−	8.90867i	0.364608	−	0.631519i	−0.624105	−	0.781340i	$-0.714536\pi$
$199$	5.14342	−	8.90867i	0.364608	−	0.631519i	0.988713	+	0.149821i	$0.0478698\pi$
$200$	2.87810	+	0.771184i	0.203512	+	0.0545309i
$201$	0.0278660	+	0.0278660i	0.00196552	+	0.00196552i
$202$	−4.45357	−	1.19333i	−0.313352	−	0.0839625i
$203$	1.05676	+	0.497576i	0.0741699	+	0.0349230i
$204$	−1.18021	−	2.04418i	−0.0826311	−	0.143121i
$205$	1.70027	−	0.981649i	0.118752	−	0.0685613i
$206$	−8.87657	+	8.87657i	−0.618460	+	0.618460i
$207$	7.02168	−	4.05397i	0.488041	−	0.281770i
$208$	1.85956	−	3.08902i	0.128938	−	0.214185i
$209$		−	23.3281i		−	1.61364i
$210$	−3.74755	+	0.313804i	−0.258606	+	0.0216546i
$211$	−5.66861	+	9.81832i	−0.390243	+	0.675921i	−0.992481	−	0.122395i	$-0.960942\pi$
$211$	−5.66861	+	9.81832i	−0.390243	+	0.675921i	0.602238	+	0.798317i	$0.294276\pi$
$212$		−	8.16938i		−	0.561076i
$213$	−3.28299	+	12.2523i	−0.224946	+	0.839512i
$214$	0.148609	+	0.554617i	0.0101587	+	0.0379129i
$215$	8.75041	−	8.75041i	0.596773	−	0.596773i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−8.60448	−	1.55028i	−0.584110	−	0.105240i
$218$	−16.8906	−	9.75179i	−1.14398	−	0.660474i
$219$	2.06986	−	7.72484i	0.139868	−	0.521996i
$220$	−2.74147	−	4.74837i	−0.184830	−	0.320135i
$221$	−8.50918	−	0.155600i	−0.572389	−	0.0104668i
$222$	6.57085	+	3.79368i	0.441006	+	0.254615i
$223$	−4.73346	+	1.26833i	−0.316976	+	0.0849335i	−0.413799	−	0.910368i	$-0.635799\pi$
$223$	−4.73346	+	1.26833i	−0.316976	+	0.0849335i	0.0968232	+	0.995302i	$0.469132\pi$
$224$	−2.48955	+	0.895632i	−0.166340	+	0.0598419i
$225$	2.58043	−	1.48981i	0.172029	−	0.0993208i
$226$	−2.73418	−	10.2041i	−0.181875	−	0.678768i
$227$	−7.10428	+	1.90358i	−0.471527	+	0.126345i	−0.486755	−	0.873539i	$-0.661819\pi$
$227$	−7.10428	+	1.90358i	−0.471527	+	0.126345i	0.0152274	+	0.999884i	$0.495153\pi$
$228$	−5.84150	+	1.56523i	−0.386863	+	0.103660i
$229$	1.29668	+	4.83929i	0.0856873	+	0.319789i	0.995443	−	0.0953536i	$-0.0303982\pi$
$229$	1.29668	+	4.83929i	0.0856873	+	0.319789i	−0.909756	+	0.415143i	$0.863732\pi$
$230$	−9.98061	+	5.76231i	−0.658102	+	0.379955i
$231$	−7.79360	−	6.58924i	−0.512781	−	0.433540i
$232$	0.426435	−	0.114263i	0.0279968	−	0.00750173i
$233$	−9.40002	−	5.42710i	−0.615816	−	0.355541i	0.159422	−	0.987210i	$-0.449037\pi$
$233$	−9.40002	−	5.42710i	−0.615816	−	0.355541i	−0.775238	+	0.631669i	$0.782370\pi$
$234$	−0.869355	−	3.49917i	−0.0568315	−	0.228748i
$235$	4.52142	+	7.83132i	0.294945	+	0.510859i
$236$	−2.17393	+	8.11322i	−0.141511	+	0.528126i
$237$	−10.6449	−	6.14585i	−0.691462	−	0.399216i
$238$	4.76902	+	4.03205i	0.309129	+	0.261359i
$239$	6.33211	−	6.33211i	0.409590	−	0.409590i	−0.472006	−	0.881596i	$-0.656470\pi$
$239$	6.33211	−	6.33211i	0.409590	−	0.409590i	0.881596	+	0.472006i	$0.156470\pi$
$240$	−1.00508	+	1.00508i	−0.0648777	+	0.0648777i
$241$	−5.26545	−	19.6509i	−0.339177	−	1.26583i	−0.899269	−	0.437396i	$-0.855901\pi$
$241$	−5.26545	−	19.6509i	−0.339177	−	1.26583i	0.560092	−	0.828430i	$-0.310766\pi$
$242$	1.00416	−	3.74757i	0.0645497	−	0.240903i
$243$		−	1.00000i		−	0.0641500i
$244$	−5.32860	+	9.22941i	−0.341129	+	0.590852i
$245$	9.04866	−	4.13766i	0.578097	−	0.264345i
$246$		−	1.38124i		−	0.0880649i
$247$	−6.02763	+	20.9551i	−0.383529	+	1.33334i
$248$	−2.86183	+	1.65228i	−0.181726	+	0.104920i
$249$	−9.37857	+	9.37857i	−0.594342	+	0.594342i
$250$	−9.82266	+	5.67112i	−0.621240	+	0.358673i
$251$	0.890713	+	1.54276i	0.0562213	+	0.0973782i	0.892766	−	0.450520i	$-0.148761\pi$
$251$	0.890713	+	1.54276i	0.0562213	+	0.0973782i	−0.836545	+	0.547898i	$0.815428\pi$
$252$	−1.12707	+	2.39368i	−0.0709986	+	0.150788i
$253$	−30.2101	−	8.09478i	−1.89929	−	0.508914i
$254$	−11.1101	−	11.1101i	−0.697109	−	0.697109i
$255$	3.24077	+	0.868362i	0.202945	+	0.0543789i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.94630	+	3.37109i	0.121407	+	0.210283i	0.920323	−	0.391160i	$-0.127926\pi$
$257$	1.94630	+	3.37109i	0.121407	+	0.210283i	−0.798916	+	0.601443i	$0.794593\pi$
$258$	−2.25332	−	8.40952i	−0.140286	−	0.523554i
$259$	−19.7562	−	3.55949i	−1.22759	−	0.221176i
$260$	1.23570	+	4.97372i	0.0766349	+	0.308457i
$261$	0.220739	−	0.382331i	0.0136634	−	0.0236657i
$262$	−9.82951	−	9.82951i	−0.607269	−	0.607269i
$263$	3.32390			0.204960			0.102480	−	0.994735i	$-0.467322\pi$
$263$	3.32390			0.204960			0.102480	+	0.994735i	$0.467322\pi$
$264$	−3.85743			−0.237408
$265$	8.21089	+	8.21089i	0.504391	+	0.504391i
$266$	13.1408	−	9.12854i	0.805716	−	0.559706i
$267$	0.533652	−	1.99161i	0.0326589	−	0.121885i
$268$	−0.0380657	+	0.0101997i	−0.00232523	+	0.000623044i
$269$	11.3381	+	6.54607i	0.691297	+	0.399121i	0.804098	−	0.594497i	$-0.202649\pi$
$269$	11.3381	+	6.54607i	0.691297	+	0.399121i	−0.112800	+	0.993618i	$0.535982\pi$
$270$			1.42140i			0.0865036i
$271$	−23.4390	−	6.28045i	−1.42382	−	0.381510i	−0.536980	−	0.843595i	$-0.680435\pi$
$271$	−23.4390	−	6.28045i	−1.42382	−	0.381510i	−0.886836	+	0.462085i	$0.847102\pi$
$272$	2.36042			0.143121
$273$	5.29827	+	7.93274i	0.320666	+	0.480111i
$274$	−10.6346			−0.642461
$275$	−11.1021	−	2.97479i	−0.669479	−	0.179386i
$276$			8.10794i			0.488041i
$277$	25.9144	+	14.9617i	1.55704	+	0.898959i	0.997538	+	0.0701328i	$0.0223423\pi$
$277$	25.9144	+	14.9617i	1.55704	+	0.898959i	0.559506	+	0.828827i	$0.310991\pi$
$278$	−4.80974	+	1.28877i	−0.288469	+	0.0772950i
$279$	−0.855281	+	3.19195i	−0.0512043	+	0.191097i
$280$	1.60201	−	3.40238i	0.0957386	−	0.203331i
$281$	−14.1065	−	14.1065i	−0.841521	−	0.841521i	0.147535	−	0.989057i	$-0.452866\pi$
$281$	−14.1065	−	14.1065i	−0.841521	−	0.841521i	−0.989057	+	0.147535i	$0.952866\pi$
$282$	6.36192			0.378847
$283$	−16.6838			−0.991749			−0.495874	−	0.868394i	$-0.665152\pi$
$283$	−16.6838			−0.991749			−0.495874	+	0.868394i	$0.665152\pi$
$284$	−8.96928	−	8.96928i	−0.532229	−	0.532229i
$285$	4.29800	−	7.44436i	0.254592	−	0.440966i
$286$	−7.17314	+	11.9157i	−0.424156	+	0.704588i
$287$	1.23709	+	3.43867i	0.0730228	+	0.202978i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	5.71422	+	9.89731i	0.336130	+	0.582195i
$290$	−0.313758	+	0.543445i	−0.0184245	+	0.0319122i
$291$	−13.5109	−	3.62024i	−0.792025	−	0.212222i
$292$	5.65497	+	5.65497i	0.330932	+	0.330932i
$293$	31.5634	+	8.45739i	1.84395	+	0.494086i	0.999159	−	0.0410025i	$-0.0130552\pi$
$293$	31.5634	+	8.45739i	1.84395	+	0.494086i	0.844796	+	0.535089i	$0.179722\pi$
$294$	0.662032	−	6.96862i	0.0386105	−	0.406418i
$295$	−5.96947	−	10.3394i	−0.347556	−	0.601984i
$296$	−6.57085	+	3.79368i	−0.381923	+	0.220503i
$297$	−2.72762	+	2.72762i	−0.158272	+	0.158272i
$298$	6.81171	−	3.93275i	0.394592	−	0.227818i
$299$	25.0456	+	15.0772i	1.44842	+	0.871938i
$300$			2.97962i			0.172029i
$301$	13.1416	+	18.9177i	0.757468	+	1.09040i
$302$	−7.69947	+	13.3359i	−0.443054	+	0.767393i
$303$		−	4.61068i		−	0.264877i
$304$	1.56523	−	5.84150i	0.0897718	−	0.335033i
$305$	−3.92063	−	14.6320i	−0.224494	−	0.837824i
$306$	1.66907	−	1.66907i	0.0954142	−	0.0954142i
$307$	−3.32023	+	3.32023i	−0.189496	+	0.189496i	−0.795478	−	0.605982i	$-0.792780\pi$
$307$	−3.32023	+	3.32023i	−0.189496	+	0.189496i	0.605982	+	0.795478i	$0.292780\pi$
$308$	9.60325	−	3.45484i	0.547196	−	0.196858i
$309$	−10.8715	−	6.27668i	−0.618460	−	0.357068i
$310$	1.21570	−	4.53704i	0.0690469	−	0.257686i
$311$	−13.3219	−	23.0743i	−0.755417	−	1.30842i	−0.945167	−	0.326588i	$-0.894101\pi$
$311$	−13.3219	−	23.0743i	−0.755417	−	1.30842i	0.189749	−	0.981833i	$-0.439232\pi$
$312$	3.46505	+	0.996704i	0.196170	+	0.0564272i
$313$	6.79782	+	3.92473i	0.384236	+	0.221839i	0.679660	−	0.733528i	$-0.262128\pi$
$313$	6.79782	+	3.92473i	0.384236	+	0.221839i	−0.295424	+	0.955366i	$0.595461\pi$
$314$	9.90713	−	2.65461i	0.559091	−	0.149808i
$315$	−1.27305	−	3.53864i	−0.0717282	−	0.199380i
$316$	10.6449	−	6.14585i	0.598824	−	0.345731i
$317$	1.29502	+	4.83309i	0.0727358	+	0.271454i	0.992710	−	0.120524i	$-0.0384576\pi$
$317$	1.29502	+	4.83309i	0.0727358	+	0.271454i	−0.919975	+	0.391978i	$0.871791\pi$
$318$	7.89102	−	2.11439i	0.442506	−	0.118569i
$319$	−1.64494	+	0.440761i	−0.0920992	+	0.0246779i
$320$	−0.367885	−	1.37297i	−0.0205654	−	0.0767511i
$321$	−0.497256	+	0.287091i	−0.0277541	+	0.0160239i
$322$	−7.26173	−	20.1851i	−0.404680	−	1.12487i
$323$	−13.7884	+	3.69458i	−0.767206	+	0.205572i
$324$	0.866025	+	0.500000i	0.0481125	+	0.0277778i
$325$	9.20411	+	5.54080i	0.510552	+	0.307348i
$326$	−0.890703	−	1.54274i	−0.0493315	−	0.0854447i
$327$	5.04790	−	18.8390i	0.279149	−	1.04180i
$328$	1.19619	+	0.690622i	0.0660487	+	0.0381332i
$329$	−15.8383	+	5.69794i	−0.873194	+	0.314138i
$330$	3.87703	−	3.87703i	0.213423	−	0.213423i
$331$	−4.93829	+	4.93829i	−0.271433	+	0.271433i	−0.829677	−	0.558244i	$-0.811475\pi$
$331$	−4.93829	+	4.93829i	−0.271433	+	0.271433i	0.558244	+	0.829677i	$0.311475\pi$
$332$	−3.43279	−	12.8114i	−0.188399	−	0.703115i
$333$	−1.96375	+	7.32883i	−0.107613	+	0.401617i
$334$		−	2.10649i		−	0.115262i
$335$	0.0280076	−	0.0485106i	0.00153022	−	0.00265042i
$336$	−1.50946	−	2.17291i	−0.0823476	−	0.118542i
$337$			11.2260i			0.611518i	0.952109	+	0.305759i	$0.0989101\pi$
$337$			11.2260i			0.611518i	−0.952109	+	0.305759i	$0.901090\pi$
$338$	9.52232	−	8.85017i	0.517946	−	0.481386i
$339$	9.14876	−	5.28204i	0.496892	−	0.286881i
$340$	−2.37241	+	2.37241i	−0.128662	+	0.128662i
$341$	11.0393	−	6.37354i	0.597811	−	0.345147i
$342$	−3.02378	−	5.23735i	−0.163507	−	0.283203i
$343$	4.59316	+	17.9417i	0.248007	+	0.968758i
$344$	8.40952	+	2.25332i	0.453411	+	0.121491i
$345$	−8.14913	−	8.14913i	−0.438735	−	0.438735i
$346$	−4.26416	−	1.14258i	−0.229243	−	0.0614254i
$347$	−16.1101	+	27.9035i	−0.864836	+	1.49794i	0.00237486	+	0.999997i	$0.499244\pi$
$347$	−16.1101	+	27.9035i	−0.864836	+	1.49794i	−0.867210	+	0.497942i	$0.834089\pi$
$348$	0.220739	+	0.382331i	0.0118329	+	0.0204951i
$349$	0.290712	+	1.08495i	0.0155614	+	0.0580761i	0.973270	−	0.229664i	$-0.0737627\pi$
$349$	0.290712	+	1.08495i	0.0155614	+	0.0580761i	−0.957709	+	0.287740i	$0.907096\pi$
$350$	−2.66865	−	7.41792i	−0.142645	−	0.396504i
$351$	3.15494	−	1.74539i	0.168398	−	0.0931618i
$352$	1.92872	−	3.34063i	0.102801	−	0.178056i
$353$	6.28449	+	6.28449i	0.334490	+	0.334490i	0.854289	−	0.519799i	$-0.173993\pi$
$353$	6.28449	+	6.28449i	0.334490	+	0.334490i	−0.519799	+	0.854289i	$0.673993\pi$
$354$	−8.39942			−0.446424
$355$	18.0297			0.956917
$356$	1.45796	+	1.45796i	0.0772719	+	0.0772719i
$357$	−2.66035	+	5.65009i	−0.140801	+	0.299034i
$358$	−5.87049	+	21.9090i	−0.310265	+	1.15792i
$359$	9.34329	−	2.50353i	0.493120	−	0.132131i	−0.00368517	−	0.999993i	$-0.501173\pi$
$359$	9.34329	−	2.50353i	0.493120	−	0.132131i	0.496805	+	0.867862i	$0.334506\pi$
$360$	−1.23097	−	0.710699i	−0.0648777	−	0.0374572i
$361$			17.5731i			0.924898i
$362$	4.53869	+	1.21614i	0.238548	+	0.0639187i
$363$	3.87977			0.203635
$364$	−9.51909	+	0.622069i	−0.498936	+	0.0326053i
$365$	−11.3674			−0.594997
$366$	−10.2941	−	2.75829i	−0.538079	−	0.144178i
$367$		−	26.5746i		−	1.38718i	−0.720369	−	0.693591i	$-0.756027\pi$
$367$		−	26.5746i		−	1.38718i	0.720369	−	0.693591i	$-0.243973\pi$
$368$	−7.02168	−	4.05397i	−0.366030	−	0.211328i
$369$	1.33418	−	0.357492i	0.0694546	−	0.0186103i
$370$	2.79128	−	10.4172i	0.145112	−	0.541564i
$371$	−17.7513	+	12.3313i	−0.921604	+	0.640210i
$372$	−2.33667	−	2.33667i	−0.121151	−	0.121151i
$373$	−9.75113			−0.504894			−0.252447	−	0.967611i	$-0.581235\pi$
$373$	−9.75113			−0.504894			−0.252447	+	0.967611i	$0.581235\pi$
$374$	−9.10514			−0.470816
$375$	−8.02017	−	8.02017i	−0.414160	−	0.414160i
$376$	−3.18096	+	5.50959i	−0.164046	+	0.284135i
$377$	1.59151	+	0.0291025i	0.0819667	+	0.00149885i
$378$	−2.60383	−	0.469134i	−0.133926	−	0.0241296i
$379$	7.08824	+	26.4537i	0.364098	+	1.35883i	0.868639	+	0.495445i	$0.164995\pi$
$379$	7.08824	+	26.4537i	0.364098	+	1.35883i	−0.504541	+	0.863388i	$0.668338\pi$
$380$	4.29800	+	7.44436i	0.220483	+	0.381888i
$381$	7.85602	−	13.6070i	0.402476	−	0.697109i
$382$	22.2255	+	5.95532i	1.13716	+	0.304701i
$383$	−21.6913	−	21.6913i	−1.10837	−	1.10837i	−0.993365	−	0.115007i	$-0.963311\pi$
$383$	−21.6913	−	21.6913i	−1.10837	−	1.10837i	−0.115007	−	0.993365i	$-0.536689\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−6.17966	+	13.1244i	−0.314944	+	0.668883i
$386$	−2.18973	−	3.79273i	−0.111455	−	0.193045i
$387$	7.53977	−	4.35309i	0.383268	−	0.221280i
$388$	9.89069	−	9.89069i	0.502124	−	0.502124i
$389$	2.94763	−	1.70182i	0.149451	−	0.0862855i	−0.423410	−	0.905938i	$-0.639167\pi$
$389$	2.94763	−	1.70182i	0.149451	−	0.0862855i	0.572861	+	0.819653i	$0.305834\pi$
$390$	−4.48442	+	2.48089i	−0.227078	+	0.125625i
$391$			19.1381i			0.967856i
$392$	5.70399	+	4.05765i	0.288095	+	0.204942i
$393$	6.95051	−	12.0386i	0.350607	−	0.607269i
$394$			10.5853i			0.533281i
$395$	−4.52194	+	16.8761i	−0.227523	+	0.849128i
$396$	−0.998376	−	3.72599i	−0.0501703	−	0.187238i
$397$	18.0810	−	18.0810i	0.907458	−	0.907458i	−0.0886087	−	0.996067i	$-0.528242\pi$
$397$	18.0810	−	18.0810i	0.907458	−	0.907458i	0.996067	+	0.0886087i	$0.0282421\pi$
$398$	−7.27390	+	7.27390i	−0.364608	+	0.364608i
$399$	12.2186	+	10.3304i	0.611694	+	0.517168i
$400$	−2.58043	−	1.48981i	−0.129022	−	0.0744906i
$401$	−0.553681	+	2.06637i	−0.0276495	+	0.103189i	−0.978372	−	0.206855i	$-0.933677\pi$
$401$	−0.553681	+	2.06637i	−0.0276495	+	0.103189i	0.950722	+	0.310044i	$0.100344\pi$
$402$	−0.0197043	−	0.0341288i	−0.000982759	−	0.00170219i
$403$	−11.5632	+	2.87283i	−0.576004	+	0.143106i
$404$	3.99296	+	2.30534i	0.198657	+	0.114695i
$405$	−1.37297	+	0.367885i	−0.0682232	+	0.0182804i
$406$	−0.891968	−	0.754131i	−0.0442676	−	0.0374269i
$407$	25.3466	−	14.6339i	1.25638	−	0.725373i
$408$	0.610921	+	2.27999i	0.0302451	+	0.112876i
$409$	−17.8921	+	4.79418i	−0.884709	+	0.237057i	−0.672438	−	0.740154i	$-0.734753\pi$
$409$	−17.8921	+	4.79418i	−0.884709	+	0.237057i	−0.212271	+	0.977211i	$0.568086\pi$
$410$	−1.89640	+	0.508139i	−0.0936565	+	0.0250952i
$411$	−2.75244	−	10.2723i	−0.135768	−	0.506693i
$412$	10.8715	−	6.27668i	0.535602	−	0.309230i
$413$	20.9108	−	7.52279i	1.02895	−	0.370172i
$414$	−7.83167	+	2.09849i	−0.384905	+	0.103135i
$415$	16.3267	+	9.42622i	0.801445	+	0.462715i
$416$	−2.59570	+	2.50247i	−0.127264	+	0.122694i
$417$	−2.48970	−	4.31229i	−0.121921	−	0.211174i
$418$	−6.03775	+	22.5332i	−0.295316	+	1.10213i
$419$	−28.4741	−	16.4395i	−1.39105	−	0.803124i	−0.397620	−	0.917550i	$-0.630164\pi$
$419$	−28.4741	−	16.4395i	−1.39105	−	0.803124i	−0.993432	+	0.114426i	$0.963497\pi$
$420$	3.70108	+	0.666826i	0.180594	+	0.0325378i
$421$	11.1258	−	11.1258i	0.542238	−	0.542238i	−0.381946	−	0.924185i	$-0.624746\pi$
$421$	11.1258	−	11.1258i	0.542238	−	0.542238i	0.924185	+	0.381946i	$0.124746\pi$
$422$	8.01663	−	8.01663i	0.390243	−	0.390243i
$423$	1.64659	+	6.14515i	0.0800598	+	0.298787i
$424$	−2.11439	+	7.89102i	−0.102684	+	0.383222i
$425$			7.03316i			0.341158i
$426$	6.34224	−	10.9851i	0.307283	−	0.532229i
$427$	28.0980	−	2.35281i	1.35976	−	0.113860i
$428$		−	0.574182i		−	0.0277541i
$429$	−13.3662	−	3.84472i	−0.645326	−	0.185625i
$430$	−10.7170	+	6.18747i	−0.516821	+	0.298386i
$431$	−8.40355	+	8.40355i	−0.404785	+	0.404785i	−0.879915	−	0.475131i	$-0.842401\pi$
$431$	−8.40355	+	8.40355i	−0.404785	+	0.404785i	0.475131	+	0.879915i	$0.342401\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	−1.73495	−	3.00502i	−0.0833765	−	0.144412i	0.821322	−	0.570465i	$-0.193237\pi$
$433$	−1.73495	−	3.00502i	−0.0833765	−	0.144412i	−0.904698	+	0.426053i	$0.859904\pi$
$434$	7.91005	+	3.72446i	0.379695	+	0.178780i
$435$	−0.606134	−	0.162413i	−0.0290619	−	0.00778712i
$436$	13.7911	+	13.7911i	0.660474	+	0.660474i
$437$	47.3625	+	12.6908i	2.26566	+	0.607081i
$438$	−3.99867	+	6.92590i	−0.191064	+	0.330932i
$439$	−8.44641	−	14.6296i	−0.403125	−	0.698233i	0.590976	−	0.806689i	$-0.298743\pi$
$439$	−8.44641	−	14.6296i	−0.403125	−	0.698233i	−0.994101	+	0.108456i	$0.965409\pi$
$440$	1.41909	+	5.29612i	0.0676525	+	0.252483i
$441$	6.90252	−	1.16414i	0.328691	−	0.0554352i
$442$	8.17896	+	2.35264i	0.389034	+	0.111903i
$443$	0.108413	−	0.187777i	0.00515086	−	0.00892155i	−0.863438	−	0.504454i	$-0.831694\pi$
$443$	0.108413	−	0.187777i	0.00515086	−	0.00892155i	0.868589	+	0.495533i	$0.165027\pi$
$444$	−5.36507	−	5.36507i	−0.254615	−	0.254615i
$445$	−2.93074			−0.138930
$446$	4.90044			0.232043
$447$	5.56174	+	5.56174i	0.263061	+	0.263061i
$448$	2.63652	−	0.220772i	0.124564	−	0.0104305i
$449$	2.07566	−	7.74645i	0.0979562	−	0.365578i	−0.899495	−	0.436931i	$-0.856065\pi$
$449$	2.07566	−	7.74645i	0.0979562	−	0.365578i	0.997451	+	0.0713537i	$0.0227319\pi$
$450$	−2.87810	+	0.771184i	−0.135675	+	0.0363539i
$451$	−4.61423	−	2.66403i	−0.217275	−	0.125444i
$452$			10.5641i			0.496892i
$453$	−14.8742	−	3.98554i	−0.698852	−	0.187257i
$454$	7.35489			0.345182
$455$	8.94222	−	10.1927i	0.419218	−	0.477840i
$456$	6.04757			0.283203
$457$	−30.0661	−	8.05618i	−1.40643	−	0.376852i	−0.525782	−	0.850619i	$-0.676227\pi$
$457$	−30.0661	−	8.05618i	−1.40643	−	0.376852i	−0.880650	+	0.473767i	$0.842894\pi$
$458$		−	5.01000i		−	0.234102i
$459$	2.04418	+	1.18021i	0.0954142	+	0.0550874i
$460$	11.1319	−	2.98279i	0.519029	−	0.139073i
$461$	10.2018	−	38.0738i	0.475147	−	1.77327i	−0.145689	−	0.989331i	$-0.546540\pi$
$461$	10.2018	−	38.0738i	0.475147	−	1.77327i	0.620835	−	0.783941i	$-0.286794\pi$
$462$	5.82262	+	8.38185i	0.270893	+	0.389959i
$463$	6.13141	+	6.13141i	0.284951	+	0.284951i	0.835080	−	0.550129i	$-0.185421\pi$
$463$	6.13141	+	6.13141i	0.284951	+	0.284951i	−0.550129	+	0.835080i	$0.685421\pi$
$464$	−0.441478			−0.0204951
$465$	4.69709			0.217822
$466$	7.67508	+	7.67508i	0.355541	+	0.355541i
$467$	6.52135	−	11.2953i	0.301772	−	0.522684i	−0.674765	−	0.738032i	$-0.735755\pi$
$467$	6.52135	−	11.2953i	0.301772	−	0.522684i	0.976537	+	0.215348i	$0.0690886\pi$
$468$	−0.0659206	+	3.60495i	−0.00304718	+	0.166639i
$469$	0.0796215	+	0.0673174i	0.00367658	+	0.00310843i
$470$	−2.34046	−	8.73470i	−0.107957	−	0.402902i
$471$	5.12831	+	8.88249i	0.236300	+	0.409283i
$472$	4.19971	−	7.27411i	0.193307	−	0.334818i
$473$	−32.4391	−	8.69204i	−1.49155	−	0.399660i
$474$	8.69155	+	8.69155i	0.399216	+	0.399216i
$475$	17.4055	+	4.66379i	0.798618	+	0.213989i
$476$	−3.56294	−	5.12898i	−0.163307	−	0.235086i
$477$	4.08469	+	7.07489i	0.187025	+	0.323937i
$478$	−7.75521	+	4.47748i	−0.354715	+	0.204795i
$479$	−24.7228	+	24.7228i	−1.12961	+	1.12961i	−0.139374	+	0.990240i	$0.544509\pi$
$479$	−24.7228	+	24.7228i	−1.12961	+	1.12961i	−0.990240	+	0.139374i	$0.955491\pi$
$480$	1.23097	−	0.710699i	0.0561857	−	0.0324388i
$481$	−26.5495	+	6.59611i	−1.21055	+	0.300757i
$482$			20.3441i			0.926649i
$483$	17.6178	−	12.2386i	0.801639	−	0.556875i
$484$	−1.93988	+	3.35998i	−0.0881765	+	0.152726i
$485$			19.8819i			0.902790i
$486$	−0.258819	+	0.965926i	−0.0117403	+	0.0438153i
$487$	−8.54456	−	31.8887i	−0.387191	−	1.44502i	−0.834684	−	0.550729i	$-0.814350\pi$
$487$	−8.54456	−	31.8887i	−0.387191	−	1.44502i	0.447493	−	0.894288i	$-0.352317\pi$
$488$	7.53578	−	7.53578i	0.341129	−	0.341129i
$489$	1.25964	−	1.25964i	0.0569631	−	0.0569631i
$490$	−9.81123	+	1.65471i	−0.443226	+	0.0747520i
$491$	36.0599	+	20.8192i	1.62736	+	0.939556i	0.984877	+	0.173256i	$0.0554287\pi$
$491$	36.0599	+	20.8192i	1.62736	+	0.939556i	0.642482	+	0.766301i	$0.277905\pi$
$492$	−0.357492	+	1.33418i	−0.0161170	+	0.0601494i
$493$	0.521036	+	0.902461i	0.0234663	+	0.0406448i
$494$	11.2458	−	18.6810i	0.505974	−	0.840500i
$495$	4.74837	+	2.74147i	0.213423	+	0.123220i
$496$	3.19195	−	0.855281i	0.143323	−	0.0384033i
$497$	−5.95072	+	33.0282i	−0.266926	+	1.48152i
$498$	11.4863	−	6.63165i	0.514716	−	0.297171i
$499$	1.75918	+	6.56533i	0.0787515	+	0.293905i	0.994058	−	0.108854i	$-0.0347181\pi$
$499$	1.75918	+	6.56533i	0.0787515	+	0.293905i	−0.915306	+	0.402759i	$0.868051\pi$
$500$	10.9558	−	2.93559i	0.489956	−	0.131283i
$501$	2.03471	−	0.545200i	0.0909043	−	0.0243577i
$502$	−0.461067	−	1.72073i	−0.0205784	−	0.0767997i
$503$	7.14428	−	4.12475i	0.318548	−	0.183914i	−0.332197	−	0.943210i	$-0.607790\pi$
$503$	7.14428	−	4.12475i	0.318548	−	0.183914i	0.650745	+	0.759296i	$0.274457\pi$
$504$	1.70820	−	2.02041i	0.0760891	−	0.0899964i
$505$	−6.33030	+	1.69620i	−0.281695	+	0.0754799i
$506$	27.0856	+	15.6379i	1.20410	+	0.695190i
$507$	11.0132	+	6.90726i	0.489112	+	0.306762i
$508$	7.85602	+	13.6070i	0.348555	+	0.603714i
$509$	−8.86288	+	33.0767i	−0.392840	+	1.46610i	0.432588	+	0.901592i	$0.357600\pi$
$509$	−8.86288	+	33.0767i	−0.392840	+	1.46610i	−0.825428	+	0.564507i	$0.809066\pi$
$510$	−2.90560	−	1.67755i	−0.128662	−	0.0742830i
$511$	3.75182	−	20.8237i	0.165971	−	0.921186i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	4.27628	−	4.27628i	0.188802	−	0.188802i
$514$	−1.00748	−	3.75996i	−0.0444380	−	0.165845i
$515$	−4.61820	+	17.2353i	−0.203502	+	0.759480i
$516$			8.70617i			0.383268i
$517$	12.2703	−	21.2528i	0.539649	−	0.934699i
$518$	18.1617	+	8.55147i	0.797981	+	0.375730i
$519$		−	4.41458i		−	0.193779i
$520$	0.0936995	−	5.12407i	0.00410899	−	0.224705i
$521$	18.7607	−	10.8315i	0.821921	−	0.474536i	−0.0291576	−	0.999575i	$-0.509282\pi$
$521$	18.7607	−	10.8315i	0.821921	−	0.474536i	0.851078	+	0.525039i	$0.175949\pi$
$522$	−0.312172	+	0.312172i	−0.0136634	+	0.0136634i
$523$	−26.0748	+	15.0543i	−1.14017	+	0.658277i	−0.946473	−	0.322784i	$-0.895381\pi$
$523$	−26.0748	+	15.0543i	−1.14017	+	0.658277i	−0.193697	+	0.981061i	$0.562048\pi$
$524$	6.95051	+	12.0386i	0.303634	+	0.525910i
$525$	6.47446	−	4.49761i	0.282569	−	0.196292i
$526$	−3.21064	−	0.860288i	−0.139990	−	0.0375103i
$527$	−5.51552	−	5.51552i	−0.240260	−	0.240260i
$528$	3.72599	+	0.998376i	0.162153	+	0.0434488i
$529$	21.3693	−	37.0128i	0.929102	−	1.60925i
$530$	−5.80598	−	10.0562i	−0.252195	−	0.436815i
$531$	−2.17393	−	8.11322i	−0.0943406	−	0.352084i
$532$	−15.0557	+	5.41639i	−0.652748	+	0.234830i
$533$	3.45652	+	3.58529i	0.149719	+	0.155296i
$534$	−1.03094	+	1.78563i	−0.0446129	+	0.0772719i
$535$	0.577099	+	0.577099i	0.0249502	+	0.0249502i
$536$	0.0394085			0.00170219
$537$	−22.6818			−0.978793
$538$	−9.25754	−	9.25754i	−0.399121	−	0.399121i
$539$	−22.0027	−	15.6521i	−0.947725	−	0.674183i
$540$	0.367885	−	1.37297i	0.0158313	−	0.0590830i
$541$	−1.32311	+	0.354527i	−0.0568850	+	0.0152423i	−0.287149	−	0.957886i	$-0.592708\pi$
$541$	−1.32311	+	0.354527i	−0.0568850	+	0.0152423i	0.230264	+	0.973128i	$0.426041\pi$
$542$	21.0148	+	12.1329i	0.902663	+	0.521153i
$543$			4.69879i			0.201644i
$544$	−2.27999	−	0.610921i	−0.0977536	−	0.0261930i
$545$	−27.7224			−1.18750
$546$	−3.06459	−	9.03373i	−0.131152	−	0.386608i
$547$	13.2992			0.568632			0.284316	−	0.958731i	$-0.408233\pi$
$547$	13.2992			0.568632			0.284316	+	0.958731i	$0.408233\pi$
$548$	10.2723	+	2.75244i	0.438809	+	0.117579i
$549$		−	10.6572i		−	0.454838i
$550$	9.95383	+	5.74685i	0.424433	+	0.245046i
$551$	2.57889	−	0.691013i	0.109865	−	0.0294381i
$552$	2.09849	−	7.83167i	0.0893176	−	0.333338i
$553$	−29.4224	−	13.8536i	−1.25117	−	0.589115i
$554$	−21.1590	−	21.1590i	−0.898959	−	0.898959i
$555$	10.7847			0.457784
$556$	4.97941			0.211174
$557$	12.4410	+	12.4410i	0.527141	+	0.527141i	0.919719	−	0.392578i	$-0.128417\pi$
$557$	12.4410	+	12.4410i	0.527141	+	0.527141i	−0.392578	+	0.919719i	$0.628417\pi$
$558$	1.65228	−	2.86183i	0.0699464	−	0.121151i
$559$	26.8935	+	16.1897i	1.13747	+	0.684751i
$560$	−2.42803	+	2.87181i	−0.102603	+	0.121356i
$561$	−2.35658	−	8.79489i	−0.0994951	−	0.371321i
$562$	9.97478	+	17.2768i	0.420761	+	0.728779i
$563$	−10.3723	+	17.9653i	−0.437140	+	0.757149i	−0.997468	−	0.0711225i	$-0.977342\pi$
$563$	−10.3723	+	17.9653i	−0.437140	+	0.757149i	0.560328	+	0.828271i	$0.310675\pi$
$564$	−6.14515	−	1.64659i	−0.258757	−	0.0693338i
$565$	−10.6178	−	10.6178i	−0.446692	−	0.446692i
$566$	16.1153	+	4.31808i	0.677377	+	0.181503i
$567$	−0.220772	−	2.63652i	−0.00927153	−	0.110724i
$568$	6.34224	+	10.9851i	0.266114	+	0.460924i
$569$	6.00413	−	3.46648i	0.251706	−	0.145323i	−0.368839	−	0.929493i	$-0.620245\pi$
$569$	6.00413	−	3.46648i	0.251706	−	0.145323i	0.620545	+	0.784171i	$0.286911\pi$
$570$	−6.07829	+	6.07829i	−0.254592	+	0.254592i
$571$	25.9520	−	14.9834i	1.08606	−	0.627035i	0.153533	−	0.988144i	$-0.450935\pi$
$571$	25.9520	−	14.9834i	1.08606	−	0.627035i	0.932524	+	0.361108i	$0.117602\pi$
$572$	10.0127	−	9.65311i	0.418653	−	0.403617i
$573$			23.0096i			0.961239i
$574$	−0.304939	−	3.64168i	−0.0127279	−	0.152001i
$575$	12.0793	−	20.9220i	0.503742	−	0.872507i
$576$		−	1.00000i		−	0.0416667i
$577$	6.46820	−	24.1396i	0.269275	−	1.00495i	−0.690307	−	0.723516i	$-0.742525\pi$
$577$	6.46820	−	24.1396i	0.269275	−	1.00495i	0.959582	−	0.281430i	$-0.0908087\pi$
$578$	−2.95790	−	11.0390i	−0.123032	−	0.459163i
$579$	3.09675	−	3.09675i	0.128697	−	0.128697i
$580$	0.443721	−	0.443721i	0.0184245	−	0.0184245i
$581$	−22.6563	+	26.7973i	−0.939941	+	1.11174i
$582$	12.1136	+	6.99377i	0.502124	+	0.289901i
$583$	8.15612	−	30.4391i	0.337792	−	1.26066i
$584$	−3.99867	−	6.92590i	−0.165466	−	0.286596i
$585$	−3.55701	−	3.68952i	−0.147064	−	0.152543i
$586$	−28.2990	−	16.3384i	−1.16902	−	0.674934i
$587$	16.4638	−	4.41145i	0.679532	−	0.182080i	0.0974873	−	0.995237i	$-0.468919\pi$
$587$	16.4638	−	4.41145i	0.679532	−	0.182080i	0.582045	+	0.813157i	$0.302253\pi$
$588$	−2.44309	+	6.55983i	−0.100751	+	0.270523i
$589$	−17.3071	+	9.99225i	−0.713126	+	0.411724i
$590$	3.09002	+	11.5321i	0.127214	+	0.474770i
$591$	−10.2246	+	2.73968i	−0.420586	+	0.112696i
$592$	7.32883	−	1.96375i	0.301213	−	0.0807098i
$593$	−10.8717	−	40.5737i	−0.446447	−	1.66616i	−0.712089	−	0.702090i	$-0.752251\pi$
$593$	−10.8717	−	40.5737i	−0.446447	−	1.66616i	0.265642	−	0.964072i	$-0.414416\pi$
$594$	3.34063	−	1.92872i	0.137068	−	0.0791361i
$595$	8.73608	+	1.57399i	0.358144	+	0.0645272i
$596$	−7.59748	+	2.03574i	−0.311205	+	0.0833871i
$597$	−8.90867	−	5.14342i	−0.364608	−	0.210506i
$598$	−20.2899	−	21.0457i	−0.829715	−	0.860625i
$599$	11.3993	+	19.7442i	0.465764	+	0.806727i	0.999236	−	0.0390909i	$-0.0124462\pi$
$599$	11.3993	+	19.7442i	0.465764	+	0.806727i	−0.533472	+	0.845818i	$0.679113\pi$
$600$	0.771184	−	2.87810i	0.0314834	−	0.117498i
$601$	24.1075	+	13.9185i	0.983364	+	0.567745i	0.903284	−	0.429043i	$-0.141149\pi$
$601$	24.1075	+	13.9185i	0.983364	+	0.567745i	0.0800799	+	0.996788i	$0.474482\pi$
$602$	−7.79753	−	21.6744i	−0.317803	−	0.883384i
$603$	0.0278660	−	0.0278660i	0.00113479	−	0.00113479i
$604$	10.8887	−	10.8887i	0.443054	−	0.443054i
$605$	−1.42731	−	5.32679i	−0.0580284	−	0.216565i
$606$	−1.19333	+	4.45357i	−0.0484758	+	0.180914i
$607$		−	41.3512i		−	1.67839i	−0.543829	−	0.839196i	$-0.683026\pi$
$607$		−	41.3512i		−	1.67839i	0.543829	−	0.839196i	$-0.316974\pi$
$608$	−3.02378	+	5.23735i	−0.122631	+	0.212402i
$609$	0.497576	−	1.05676i	0.0201628	−	0.0428220i
$610$			15.1481i			0.613330i
$611$	−16.5136	+	15.9205i	−0.668070	+	0.644075i
$612$	−2.04418	+	1.18021i	−0.0826311	+	0.0477071i
$613$	−12.8048	+	12.8048i	−0.517182	+	0.517182i	−0.916718	−	0.399536i	$-0.869171\pi$
$613$	−12.8048	+	12.8048i	−0.517182	+	0.517182i	0.399536	+	0.916718i	$0.369171\pi$
$614$	4.06644	−	2.34776i	0.164108	−	0.0947478i
$615$	−0.981649	−	1.70027i	−0.0395839	−	0.0685613i
$616$	−10.1702	+	0.851611i	−0.409769	+	0.0343124i
$617$	32.3546	+	8.66940i	1.30255	+	0.349017i	0.842413	−	0.538832i	$-0.181134\pi$
$617$	32.3546	+	8.66940i	1.30255	+	0.349017i	0.460135	+	0.887849i	$0.347801\pi$
$618$	8.87657	+	8.87657i	0.357068	+	0.357068i
$619$	42.1473	+	11.2933i	1.69404	+	0.453917i	0.971428	−	0.237335i	$-0.0762741\pi$
$619$	42.1473	+	11.2933i	1.69404	+	0.453917i	0.722613	+	0.691252i	$0.242941\pi$
$620$	−2.34854	+	4.06780i	−0.0943198	+	0.163367i
$621$	−4.05397	−	7.02168i	−0.162680	−	0.281770i
$622$	6.89594	+	25.7360i	0.276502	+	1.03192i
$623$	0.967293	−	5.36876i	0.0387538	−	0.215095i
$624$	−3.08902	−	1.85956i	−0.123660	−	0.0744421i
$625$	−0.611855	+	1.05976i	−0.0244742	+	0.0423906i
$626$	−5.55040	−	5.55040i	−0.221839	−	0.221839i
$627$	−23.3281			−0.931633
$628$	−10.2566			−0.409283
$629$	−12.6638	−	12.6638i	−0.504939	−	0.504939i
$630$	0.313804	+	3.74755i	0.0125023	+	0.149306i
$631$	−3.74651	+	13.9822i	−0.149146	+	0.556622i	0.850389	+	0.526154i	$0.176366\pi$
$631$	−3.74651	+	13.9822i	−0.149146	+	0.556622i	−0.999536	+	0.0304680i	$0.990300\pi$
$632$	−11.8729	+	3.18133i	−0.472278	+	0.126546i
$633$	9.81832	+	5.66861i	0.390243	+	0.225307i
$634$		−	5.00359i		−	0.198718i
$635$	−21.5721	−	5.78023i	−0.856063	−	0.229381i
$636$	−8.16938			−0.323937
$637$	15.7203	+	19.7451i	0.622863	+	0.782331i
$638$	1.70297			0.0674213
$639$	12.2523	+	3.28299i	0.484692	+	0.129873i
$640$			1.42140i			0.0561857i
$641$	−21.0155	−	12.1333i	−0.830061	−	0.479236i	0.0238123	−	0.999716i	$-0.492420\pi$
$641$	−21.0155	−	12.1333i	−0.830061	−	0.479236i	−0.853874	+	0.520480i	$0.825753\pi$
$642$	0.554617	−	0.148609i	0.0218890	−	0.00586514i
$643$	−0.634628	+	2.36846i	−0.0250273	+	0.0934031i	−0.977310	−	0.211815i	$-0.932063\pi$
$643$	−0.634628	+	2.36846i	−0.0250273	+	0.0934031i	0.952283	+	0.305218i	$0.0987293\pi$
$644$	1.79000	+	21.3768i	0.0705360	+	0.842363i
$645$	−8.75041	−	8.75041i	−0.344547	−	0.344547i
$646$	14.2748			0.561634
$647$	−1.85066			−0.0727568			−0.0363784	−	0.999338i	$-0.511582\pi$
$647$	−1.85066			−0.0727568			−0.0363784	+	0.999338i	$0.511582\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	−16.2001	+	28.0594i	−0.635909	+	1.10143i
$650$	−7.45642	−	7.73420i	−0.292465	−	0.303360i
$651$	−1.55028	+	8.60448i	−0.0607602	+	0.337236i
$652$	0.461062	+	1.72071i	0.0180566	+	0.0673881i
$653$	−12.8437	−	22.2459i	−0.502612	−	0.870550i	−0.999995	−	0.00301925i	$-0.999039\pi$
$653$	−12.8437	−	22.2459i	−0.502612	−	0.870550i	0.497383	−	0.867531i	$-0.334294\pi$
$654$	−9.75179	+	16.8906i	−0.381325	+	0.660474i
$655$	−19.0856	−	5.11398i	−0.745737	−	0.199820i
$656$	−0.976687	−	0.976687i	−0.0381332	−	0.0381332i
$657$	−7.72484	−	2.06986i	−0.301375	−	0.0807531i
$658$	16.7734	−	1.40453i	0.653894	−	0.0547543i
$659$	20.2039	+	34.9941i	0.787031	+	1.36318i	0.927778	+	0.373133i	$0.121716\pi$
$659$	20.2039	+	34.9941i	0.787031	+	1.36318i	−0.140747	+	0.990046i	$0.544950\pi$
$660$	−4.74837	+	2.74147i	−0.184830	+	0.106712i
$661$	5.92024	−	5.92024i	0.230271	−	0.230271i	−0.582535	−	0.812806i	$-0.697939\pi$
$661$	5.92024	−	5.92024i	0.230271	−	0.230271i	0.812806	+	0.582535i	$0.197939\pi$
$662$	6.04814	−	3.49190i	0.235068	−	0.135716i
$663$	−0.155600	+	8.50918i	−0.00604301	+	0.330469i
$664$			13.2633i			0.514716i
$665$	9.68829	−	20.5761i	0.375696	−	0.797907i
$666$	3.79368	−	6.57085i	0.147002	−	0.254615i
$667$		−	3.57948i		−	0.138598i
$668$	−0.545200	+	2.03471i	−0.0210944	+	0.0787254i
$669$	1.26833	+	4.73346i	0.0490364	+	0.183006i
$670$	−0.0396088	+	0.0396088i	−0.00153022	+	0.00153022i
$671$	−29.0687	+	29.0687i	−1.12219	+	1.12219i
$672$	0.895632	+	2.48955i	0.0345497	+	0.0960364i
$673$	0.338909	+	0.195669i	0.0130640	+	0.00754250i	0.506518	−	0.862230i	$-0.330932\pi$
$673$	0.338909	+	0.195669i	0.0130640	+	0.00754250i	−0.493454	+	0.869772i	$0.664266\pi$
$674$	2.90550	−	10.8435i	0.111916	−	0.417674i
$675$	−1.48981	−	2.58043i	−0.0573429	−	0.0993208i
$676$	−11.4884	+	6.08405i	−0.441863	+	0.234002i
$677$	22.1437	+	12.7847i	0.851052	+	0.491355i	0.861006	−	0.508595i	$-0.169835\pi$
$677$	22.1437	+	12.7847i	0.851052	+	0.491355i	−0.00995355	+	0.999950i	$0.503168\pi$
$678$	−10.2041	+	2.73418i	−0.391887	+	0.105006i
$679$	−36.4211	−	6.56203i	−1.39772	−	0.251828i
$680$	2.90560	−	1.67755i	0.111425	−	0.0643310i
$681$	1.90358	+	7.10428i	0.0729455	+	0.272236i
$682$	−12.3127	+	3.29919i	−0.471479	+	0.126332i
$683$	−5.31418	+	1.42393i	−0.203341	+	0.0544852i	−0.359052	−	0.933318i	$-0.616900\pi$
$683$	−5.31418	+	1.42393i	−0.203341	+	0.0544852i	0.155711	+	0.987803i	$0.450233\pi$
$684$	1.56523	+	5.84150i	0.0598479	+	0.223355i
$685$	−13.0909	+	7.55802i	−0.500177	+	0.288777i
$686$	0.206989	−	18.5191i	0.00790287	−	0.707063i
$687$	4.83929	−	1.29668i	0.184631	−	0.0494716i
$688$	−7.53977	−	4.35309i	−0.287451	−	0.165960i
$689$	−15.1915	+	25.2354i	−0.578749	+	0.961391i
$690$	5.76231	+	9.98061i	0.219367	+	0.379955i
$691$	−6.97796	+	26.0421i	−0.265454	+	0.990688i	0.696518	+	0.717540i	$0.254732\pi$
$691$	−6.97796	+	26.0421i	−0.265454	+	0.990688i	−0.961972	+	0.273149i	$0.911935\pi$
$692$	3.82314	+	2.20729i	0.145334	+	0.0839086i
$693$	−6.58924	+	7.79360i	−0.250305	+	0.296054i
$694$	22.7831	−	22.7831i	0.864836	−	0.864836i
$695$	−5.00471	+	5.00471i	−0.189839	+	0.189839i
$696$	−0.114263	−	0.426435i	−0.00433113	−	0.0161640i
$697$	−0.843830	+	3.14922i	−0.0319624	+	0.119285i
$698$		−	1.12322i		−	0.0425147i
$699$	−5.42710	+	9.40002i	−0.205272	+	0.355541i
$700$	0.657816	+	7.85585i	0.0248631	+	0.296923i
$701$		−	41.8639i		−	1.58118i	−0.612348	−	0.790588i	$-0.709775\pi$
$701$		−	41.8639i		−	1.58118i	0.612348	−	0.790588i	$-0.290225\pi$
$702$	−3.49917	+	0.869355i	−0.132068	+	0.0328117i
$703$	−39.7376	+	22.9425i	−1.49873	+	0.865294i
$704$	−2.72762	+	2.72762i	−0.102801	+	0.102801i
$705$	7.83132	−	4.52142i	0.294945	−	0.170286i
$706$	−4.44381	−	7.69690i	−0.167245	−	0.289677i
$707$	−1.01791	−	12.1562i	−0.0382823	−	0.457180i
$708$	8.11322	+	2.17393i	0.304913	+	0.0817013i
$709$	7.12529	+	7.12529i	0.267596	+	0.267596i	0.828131	−	0.560535i	$-0.189404\pi$
$709$	7.12529	+	7.12529i	0.267596	+	0.267596i	−0.560535	+	0.828131i	$0.689404\pi$
$710$	−17.4154	−	4.66643i	−0.653587	−	0.175128i
$711$	−6.14585	+	10.6449i	−0.230487	+	0.399216i
$712$	−1.03094	−	1.78563i	−0.0386359	−	0.0669194i
$713$	6.93457	+	25.8802i	0.259702	+	0.969220i
$714$	4.03205	−	4.76902i	0.150896	−	0.178476i
$715$	−0.361439	+	19.7657i	−0.0135171	+	0.739197i
$716$	11.3409	−	19.6430i	0.423830	−	0.734095i
$717$	−6.33211	−	6.33211i	−0.236477	−	0.236477i
$718$	−9.67289			−0.360989
$719$	−42.4068			−1.58151			−0.790753	−	0.612136i	$-0.790311\pi$
$719$	−42.4068			−1.58151			−0.790753	+	0.612136i	$0.790311\pi$
$720$	1.00508	+	1.00508i	0.0374572	+	0.0374572i
$721$	−30.0488	−	14.1485i	−1.11907	−	0.526918i
$722$	4.54825	−	16.9743i	0.169268	−	0.631717i
$723$	−19.6509	+	5.26545i	−0.730825	+	0.195824i
$724$	−4.06927	−	2.34940i	−0.151233	−	0.0873146i
$725$		−	1.31544i		−	0.0488542i
$726$	−3.74757	−	1.00416i	−0.139085	−	0.0372678i
$727$	−16.8790			−0.626008			−0.313004	−	0.949752i	$-0.601335\pi$
$727$	−16.8790			−0.626008			−0.313004	+	0.949752i	$0.601335\pi$
$728$	9.35574	+	1.86285i	0.346747	+	0.0690418i
$729$	−1.00000			−0.0370370
$730$	10.9801	+	2.94210i	0.406391	+	0.108892i
$731$			20.5502i			0.760077i
$732$	9.22941	+	5.32860i	0.341129	+	0.196951i
$733$	13.8883	−	3.72135i	0.512975	−	0.137451i	0.00695978	−	0.999976i	$-0.497785\pi$
$733$	13.8883	−	3.72135i	0.512975	−	0.137451i	0.506015	+	0.862525i	$0.331118\pi$
$734$	−6.87801	+	25.6691i	−0.253872	+	0.947463i
$735$	−4.13766	−	9.04866i	−0.152620	−	0.333765i
$736$	5.73318	+	5.73318i	0.211328	+	0.211328i
$737$	−0.152016			−0.00559957
$738$	−1.38124			−0.0508443
$739$	−11.5720	−	11.5720i	−0.425684	−	0.425684i	0.461471	−	0.887155i	$-0.347322\pi$
$739$	−11.5720	−	11.5720i	−0.425684	−	0.425684i	−0.887155	+	0.461471i	$0.847322\pi$
$740$	−5.39233	+	9.33980i	−0.198226	+	0.343338i
$741$	20.9551	+	6.02763i	0.769806	+	0.221431i
$742$	20.3381	−	7.31676i	0.746634	−	0.268607i
$743$	−0.834271	−	3.11354i	−0.0306064	−	0.114225i	0.948933	−	0.315479i	$-0.102165\pi$
$743$	−0.834271	−	3.11354i	−0.0306064	−	0.114225i	−0.979539	+	0.201254i	$0.935498\pi$
$744$	1.65228	+	2.86183i	0.0605754	+	0.104920i
$745$	5.59000	−	9.68216i	0.204802	−	0.354727i
$746$	9.41887	+	2.52378i	0.344849	+	0.0924021i
$747$	9.37857	+	9.37857i	0.343144	+	0.343144i
$748$	8.79489	+	2.35658i	0.321573	+	0.0861652i
$749$	−1.24765	+	0.866703i	−0.0455880	+	0.0316686i
$750$	5.67112	+	9.82266i	0.207080	+	0.358673i
$751$	18.2107	−	10.5140i	0.664518	−	0.383660i	−0.129478	−	0.991582i	$-0.541330\pi$
$751$	18.2107	−	10.5140i	0.664518	−	0.383660i	0.793996	+	0.607922i	$0.207997\pi$
$752$	4.49856	−	4.49856i	0.164046	−	0.164046i
$753$	1.54276	−	0.890713i	0.0562213	−	0.0324594i
$754$	−1.52974	−	0.440023i	−0.0557100	−	0.0160247i
$755$			21.8880i			0.796587i
$756$	2.39368	+	1.12707i	0.0870574	+	0.0409911i
$757$	25.1659	−	43.5887i	0.914672	−	1.58426i	0.107290	−	0.994228i	$-0.465783\pi$
$757$	25.1659	−	43.5887i	0.914672	−	1.58426i	0.807381	−	0.590030i	$-0.200884\pi$
$758$		−	27.3868i		−	0.994735i
$759$	−8.09478	+	30.2101i	−0.293822	+	1.09656i
$760$	−2.22481	−	8.30310i	−0.0807023	−	0.301185i
$761$	11.7335	−	11.7335i	0.425340	−	0.425340i	−0.461698	−	0.887037i	$-0.652760\pi$
$761$	11.7335	−	11.7335i	0.425340	−	0.425340i	0.887037	+	0.461698i	$0.152760\pi$
$762$	−11.1101	+	11.1101i	−0.402476	+	0.402476i
$763$	9.14979	−	50.7839i	0.331245	−	1.83850i
$764$	−19.9269	−	11.5048i	−0.720929	−	0.416229i
$765$	0.868362	−	3.24077i	0.0313957	−	0.117170i
$766$	15.3380	+	26.5663i	0.554186	+	0.959878i
$767$	21.8024	−	21.0193i	0.787237	−	0.758963i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	13.0827	−	3.50549i	0.471773	−	0.126411i	−0.0150963	−	0.999886i	$-0.504805\pi$
$769$	13.0827	−	3.50549i	0.471773	−	0.126411i	0.486869	+	0.873475i	$0.338139\pi$
$770$	9.36594	−	11.0778i	0.337525	−	0.399217i
$771$	3.37109	−	1.94630i	0.121407	−	0.0700943i
$772$	1.13349	+	4.23024i	0.0407952	+	0.152250i
$773$	−36.9356	+	9.89685i	−1.32848	+	0.355965i	−0.852148	−	0.523301i	$-0.824700\pi$
$773$	−36.9356	+	9.89685i	−1.32848	+	0.355965i	−0.476332	+	0.879266i	$0.658034\pi$
$774$	−8.40952	+	2.25332i	−0.302274	+	0.0809941i
$775$	2.54842	+	9.51082i	0.0915418	+	0.341639i
$776$	−12.1136	+	6.99377i	−0.434852	+	0.251062i
$777$	−3.55949	+	19.7562i	−0.127696	+	0.708749i
$778$	−3.28766	+	0.880925i	−0.117868	+	0.0315827i
$779$	7.23405	+	4.17658i	0.259187	+	0.149642i
$780$	4.97372	−	1.23570i	0.178088	−	0.0442452i
$781$	−24.4647	−	42.3742i	−0.875418	−	1.51627i
$782$	4.95331	−	18.4860i	0.177130	−	0.661058i
$783$	−0.382331	−	0.220739i	−0.0136634	−	0.00788857i
$784$	−4.45943	−	5.39569i	−0.159265	−	0.192703i
$785$	10.3087	−	10.3087i	0.367934	−	0.367934i
$786$	−9.82951	+	9.82951i	−0.350607	+	0.350607i
$787$	−7.02900	−	26.2326i	−0.250557	−	0.935091i	−0.970509	−	0.241067i	$-0.922503\pi$
$787$	−7.02900	−	26.2326i	−0.250557	−	0.935091i	0.719952	−	0.694024i	$-0.244164\pi$
$788$	2.73968	−	10.2246i	0.0975972	−	0.364238i
$789$		−	3.32390i		−	0.118334i
$790$	8.73571	−	15.1307i	0.310803	−	0.538326i
$791$	22.9548	−	15.9460i	0.816179	−	0.566975i
$792$			3.85743i			0.137068i
$793$	33.6228	−	18.6009i	1.19398	−	0.660538i
$794$	−22.1446	+	12.7852i	−0.785882	+	0.453729i
$795$	8.21089	−	8.21089i	0.291210	−	0.291210i
$796$	8.90867	−	5.14342i	0.315759	−	0.182304i
$797$	−8.46109	−	14.6550i	−0.299707	−	0.519108i	0.676362	−	0.736570i	$-0.263556\pi$
$797$	−8.46109	−	14.6550i	−0.299707	−	0.519108i	−0.976069	+	0.217462i	$0.930222\pi$
$798$	−9.12854	−	13.1408i	−0.323147	−	0.465180i
$799$	−14.5051	−	3.88663i	−0.513154	−	0.137499i
$800$	2.10691	+	2.10691i	0.0744906	+	0.0744906i
$801$	−1.99161	−	0.533652i	−0.0703702	−	0.0188557i
$802$	1.06963	−	1.85265i	0.0377700	−	0.0654195i
$803$	15.4246	+	26.7162i	0.544322	+	0.942793i
$804$	0.0101997	+	0.0380657i	0.000359715	+	0.00134247i
$805$	−23.2845	−	19.6863i	−0.820670	−	0.693851i
$806$	11.9127	+	0.217838i	0.419608	+	0.00767302i
$807$	6.54607	−	11.3381i	0.230432	−	0.399121i
$808$	−3.26024	−	3.26024i	−0.114695	−	0.114695i
$809$	9.11145			0.320342			0.160171	−	0.987089i	$-0.448796\pi$
$809$	9.11145			0.320342			0.160171	+	0.987089i	$0.448796\pi$
$810$	1.42140			0.0499429
$811$	0.850909	+	0.850909i	0.0298795	+	0.0298795i	0.721889	−	0.692009i	$-0.243274\pi$
$811$	0.850909	+	0.850909i	0.0298795	+	0.0298795i	−0.692009	+	0.721889i	$0.743274\pi$
$812$	0.666392	+	0.959293i	0.0233858	+	0.0336646i
$813$	−6.28045	+	23.4390i	−0.220265	+	0.822040i
$814$	−28.2704	+	7.57504i	−0.990879	+	0.265505i
$815$	−2.19285	−	1.26604i	−0.0768123	−	0.0443476i
$816$		−	2.36042i		−	0.0826311i
$817$	50.8571	+	13.6271i	1.77927	+	0.476753i
$818$	18.5233			0.647652
$819$	7.93274	−	5.29827i	0.277192	−	0.185137i
$820$	1.96330			0.0685613
$821$	−43.0231	−	11.5280i	−1.50152	−	0.402330i	−0.587908	−	0.808928i	$-0.700048\pi$
$821$	−43.0231	−	11.5280i	−1.50152	−	0.402330i	−0.913607	+	0.406598i	$0.866715\pi$
$822$			10.6346i			0.370925i
$823$	44.6477	+	25.7774i	1.55632	+	0.898542i	0.997604	+	0.0691840i	$0.0220396\pi$
$823$	44.6477	+	25.7774i	1.55632	+	0.898542i	0.558717	+	0.829358i	$0.311294\pi$
$824$	−12.1256	+	3.24905i	−0.422416	+	0.113186i
$825$	−2.97479	+	11.1021i	−0.103569	+	0.386524i
$826$	−22.1453	+	1.85435i	−0.770533	+	0.0645212i
$827$	−11.5383	−	11.5383i	−0.401227	−	0.401227i	0.477439	−	0.878665i	$-0.341565\pi$
$827$	−11.5383	−	11.5383i	−0.401227	−	0.401227i	−0.878665	+	0.477439i	$0.841565\pi$
$828$	8.10794			0.281770
$829$	−13.0488			−0.453204			−0.226602	−	0.973987i	$-0.572762\pi$
$829$	−13.0488			−0.453204			−0.226602	+	0.973987i	$0.572762\pi$
$830$	−13.3307	−	13.3307i	−0.462715	−	0.462715i
$831$	14.9617	−	25.9144i	0.519014	−	0.898959i
$832$	3.15494	−	1.74539i	0.109378	−	0.0605104i
$833$	−5.76670	+	15.4839i	−0.199804	+	0.536486i
$834$	1.28877	+	4.80974i	0.0446263	+	0.166548i
$835$	−1.49708	−	2.59302i	−0.0518086	−	0.0897352i
$836$	11.6640	−	20.2027i	0.403409	−	0.698725i
$837$	3.19195	+	0.855281i	0.110330	+	0.0295628i
$838$	23.2490	+	23.2490i	0.803124	+	0.803124i
$839$	−4.77327	−	1.27899i	−0.164792	−	0.0441558i	0.175480	−	0.984483i	$-0.443852\pi$
$839$	−4.77327	−	1.27899i	−0.164792	−	0.0441558i	−0.340272	+	0.940327i	$0.610519\pi$
$840$	−3.40238	−	1.60201i	−0.117393	−	0.0552747i
$841$	14.4025	+	24.9459i	0.496640	+	0.860205i
$842$	−13.6263	+	7.86713i	−0.469592	+	0.271119i
$843$	−14.1065	+	14.1065i	−0.485853	+	0.485853i
$844$	−9.81832	+	5.66861i	−0.337961	+	0.195122i
$845$	5.43185	−	17.6618i	0.186861	−	0.607584i
$846$		−	6.36192i		−	0.218727i
$847$	10.2291	−	0.856542i	0.351476	−	0.0294311i
$848$	4.08469	−	7.07489i	0.140269	−	0.242953i
$849$			16.6838i			0.572587i
$850$	1.82031	−	6.79351i	0.0624363	−	0.233015i
$851$	15.9220	+	59.4217i	0.545799	+	2.03695i
$852$	−8.96928	+	8.96928i	−0.307283	+	0.307283i
$853$	−27.1995	+	27.1995i	−0.931292	+	0.931292i	−0.997787	−	0.0664946i	$-0.978818\pi$
$853$	−27.1995	+	27.1995i	−0.931292	+	0.931292i	0.0664946	+	0.997787i	$0.478818\pi$
$854$	−27.7495	−	4.99965i	−0.949569	−	0.171085i
$855$	−7.44436	−	4.29800i	−0.254592	−	0.146989i
$856$	−0.148609	+	0.554617i	−0.00507936	+	0.0189564i
$857$	2.53008	+	4.38222i	0.0864258	+	0.149694i	0.905998	−	0.423282i	$-0.139122\pi$
$857$	2.53008	+	4.38222i	0.0864258	+	0.149694i	−0.819572	+	0.572976i	$0.805789\pi$
$858$	11.9157	+	7.17314i	0.406794	+	0.244887i
$859$	−47.6367	−	27.5031i	−1.62534	−	0.938393i	−0.985457	−	0.169924i	$-0.945648\pi$
$859$	−47.6367	−	27.5031i	−1.62534	−	0.938393i	−0.639887	−	0.768469i	$-0.721019\pi$
$860$	11.9533	−	3.20287i	0.407604	−	0.109217i
$861$	3.43867	−	1.23709i	0.117190	−	0.0421598i
$862$	10.2922	−	5.94221i	0.350554	−	0.202392i
$863$	0.733228	+	2.73644i	0.0249594	+	0.0931496i	0.977282	−	0.211943i	$-0.0679792\pi$
$863$	0.733228	+	2.73644i	0.0249594	+	0.0931496i	−0.952323	+	0.305093i	$0.901313\pi$
$864$	0.965926	−	0.258819i	0.0328615	−	0.00880520i
$865$	−6.06107	+	1.62406i	−0.206083	+	0.0552197i
$866$	0.898077	+	3.35167i	0.0305179	+	0.113894i
$867$	9.89731	−	5.71422i	0.336130	−	0.194065i
$868$	−6.67656	−	5.64482i	−0.226617	−	0.191598i
$869$	45.7988	−	12.2717i	1.55362	−	0.416291i
$870$	0.543445	+	0.313758i	0.0184245	+	0.0106374i
$871$	0.136553	+	0.0392786i	0.00462691	+	0.00133091i
$872$	−9.75179	−	16.8906i	−0.330237	−	0.571988i
$873$	−3.62024	+	13.5109i	−0.122527	+	0.457276i
$874$	−42.4641	−	24.5167i	−1.43637	−	0.829288i
$875$	−22.9160	−	19.3747i	−0.774702	−	0.654986i
$876$	5.65497	−	5.65497i	0.191064	−	0.191064i
$877$	0.369114	−	0.369114i	0.0124641	−	0.0124641i	−0.700847	−	0.713311i	$-0.747195\pi$
$877$	0.369114	−	0.369114i	0.0124641	−	0.0124641i	0.713311	+	0.700847i	$0.247195\pi$
$878$	4.37218	+	16.3172i	0.147554	+	0.550679i
$879$	8.45739	−	31.5634i	0.285261	−	1.06461i
$880$		−	5.48295i		−	0.184830i
$881$	8.60734	−	14.9083i	0.289989	−	0.502275i	−0.683818	−	0.729653i	$-0.739682\pi$
$881$	8.60734	−	14.9083i	0.289989	−	0.502275i	0.973807	+	0.227378i	$0.0730152\pi$
$882$	−6.96862	−	0.662032i	−0.234646	−	0.0222918i
$883$			2.32270i			0.0781651i	0.999236	+	0.0390825i	$0.0124435\pi$
$883$			2.32270i			0.0781651i	−0.999236	+	0.0390825i	$0.987556\pi$
$884$	−7.29137	−	4.38934i	−0.245235	−	0.147630i
$885$	−10.3394	+	5.96947i	−0.347556	+	0.200661i
$886$	−0.153319	+	0.153319i	−0.00515086	+	0.00515086i
$887$	−15.0990	+	8.71739i	−0.506973	+	0.292701i	−0.731589	−	0.681746i	$-0.761221\pi$
$887$	−15.0990	+	8.71739i	−0.506973	+	0.292701i	0.224615	+	0.974448i	$0.427887\pi$
$888$	3.79368	+	6.57085i	0.127308	+	0.220503i
$889$	17.7085	−	37.6096i	0.593925	−	1.26139i
$890$	2.83088	+	0.758532i	0.0948913	+	0.0254260i
$891$	2.72762	+	2.72762i	0.0913785	+	0.0913785i
$892$	−4.73346	−	1.26833i	−0.158488	−	0.0424668i
$893$	−19.2371	+	33.3196i	−0.643744	+	1.11500i
$894$	−3.93275	−	6.81171i	−0.131531	−	0.227818i
$895$	8.34431	+	31.1414i	0.278919	+	1.04094i
$896$	−2.60383	−	0.469134i	−0.0869877	−	0.0156727i
$897$	15.0772	−	25.0456i	0.503414	−	0.836247i
$898$	−4.00986	+	6.94528i	−0.133811	+	0.231767i
$899$	1.03159	+	1.03159i	0.0344054	+	0.0344054i
$900$	2.97962			0.0993208
$901$	−19.2831			−0.642415
$902$	3.76750	+	3.76750i	0.125444	+	0.125444i
$903$	18.9177	−	13.1416i	0.629543	−	0.437325i
$904$	2.73418	−	10.2041i	0.0909376	−	0.339384i
$905$	6.45128	−	1.72862i	0.214448	−	0.0574611i
$906$	13.3359	+	7.69947i	0.443054	+	0.255798i
$907$		−	26.2722i		−	0.872355i	−0.899861	−	0.436177i	$-0.856332\pi$
$907$		−	26.2722i		−	0.872355i	0.899861	−	0.436177i	$-0.143668\pi$
$908$	−7.10428	−	1.90358i	−0.235764	−	0.0631727i
$909$	−4.61068			−0.152927
$910$	−11.2756	+	7.53096i	−0.373782	+	0.249649i
$911$	16.3508			0.541727			0.270863	−	0.962618i	$-0.412691\pi$
$911$	16.3508			0.541727			0.270863	+	0.962618i	$0.412691\pi$
$912$	−5.84150	−	1.56523i	−0.193431	−	0.0518298i
$913$		−	51.1622i		−	1.69322i
$914$	26.9565	+	15.5634i	0.891642	+	0.514790i
$915$	−14.6320	+	3.92063i	−0.483718	+	0.129612i
$916$	−1.29668	+	4.83929i	−0.0428437	+	0.159895i
$917$	15.6674	−	33.2746i	0.517383	−	1.09883i
$918$	−1.66907	−	1.66907i	−0.0550874	−	0.0550874i
$919$	−32.7666			−1.08087			−0.540435	−	0.841386i	$-0.681740\pi$
$919$	−32.7666			−1.08087			−0.540435	+	0.841386i	$0.681740\pi$
$920$	−11.5246			−0.379955
$921$	3.32023	+	3.32023i	0.109405	+	0.109405i
$922$	−19.7084	+	34.1360i	−0.649062	+	1.12421i
$923$	11.0273	+	44.3852i	0.362969	+	1.46096i
$924$	−3.45484	−	9.60325i	−0.113656	−	0.315924i
$925$	5.85125	+	21.8372i	0.192388	+	0.718001i
$926$	−4.33556	−	7.50941i	−0.142475	−	0.246775i
$927$	−6.27668	+	10.8715i	−0.206153	+	0.357068i
$928$	0.426435	+	0.114263i	0.0139984	+	0.00375086i
$929$	0.206244	+	0.206244i	0.00676665	+	0.00676665i	0.710482	−	0.703715i	$-0.248477\pi$
$929$	0.206244	+	0.206244i	0.00676665	+	0.00676665i	−0.703715	+	0.710482i	$0.748477\pi$
$930$	−4.53704	−	1.21570i	−0.148775	−	0.0398642i
$931$	34.4953	+	24.5389i	1.13054	+	0.804230i
$932$	−5.42710	−	9.40002i	−0.177771	−	0.307908i
$933$	−23.0743	+	13.3219i	−0.755417	+	0.436140i
$934$	−9.22258	+	9.22258i	−0.301772	+	0.301772i
$935$	−11.2081	+	6.47102i	−0.366545	+	0.211625i
$936$	0.996704	−	3.46505i	0.0325783	−	0.113259i
$937$			6.39250i			0.208834i	0.994534	+	0.104417i	$0.0332976\pi$
$937$			6.39250i			0.208834i	−0.994534	+	0.104417i	$0.966702\pi$
$938$	−0.0594854	−	0.0856312i	−0.00194227	−	0.00279596i
$939$	3.92473	−	6.79782i	0.128079	−	0.221839i
$940$			9.04283i			0.294945i
$941$	−6.27411	+	23.4153i	−0.204530	+	0.763317i	0.785062	+	0.619417i	$0.212631\pi$
$941$	−6.27411	+	23.4153i	−0.204530	+	0.763317i	−0.989592	+	0.143900i	$0.954036\pi$
$942$	−2.65461	−	9.90713i	−0.0864918	−	0.322792i
$943$	7.91892	−	7.91892i	0.257875	−	0.257875i
$944$	−5.93929	+	5.93929i	−0.193307	+	0.193307i
$945$	−3.53864	+	1.27305i	−0.115112	+	0.0414123i
$946$	29.0841	+	16.7917i	0.945607	+	0.545946i
$947$	−14.7845	+	55.1764i	−0.480431	+	1.79299i	0.119377	+	0.992849i	$0.461910\pi$
$947$	−14.7845	+	55.1764i	−0.480431	+	1.79299i	−0.599808	+	0.800144i	$0.704756\pi$
$948$	−6.14585	−	10.6449i	−0.199608	−	0.345731i
$949$	−6.95253	−	27.9841i	−0.225689	−	0.908402i
$950$	−15.6053	−	9.00974i	−0.506304	−	0.292315i
$951$	4.83309	−	1.29502i	0.156724	−	0.0419940i
$952$	2.11406	+	5.87637i	0.0685172	+	0.190454i
$953$	−29.1590	+	16.8350i	−0.944553	+	0.545338i	−0.891385	−	0.453247i	$-0.850265\pi$
$953$	−29.1590	+	16.8350i	−0.944553	+	0.545338i	−0.0531686	+	0.998586i	$0.516932\pi$
$954$	−2.11439	−	7.89102i	−0.0684560	−	0.255481i
$955$	31.5914	−	8.46488i	1.02227	−	0.273917i
$956$	8.64982	−	2.31771i	0.279755	−	0.0749602i
$957$	0.440761	+	1.64494i	0.0142478	+	0.0531735i
$958$	30.2791	−	17.4817i	0.978274	−	0.564807i
$959$	−9.52470	−	26.4754i	−0.307569	−	0.854935i
$960$	−1.37297	+	0.367885i	−0.0443123	+	0.0118734i
$961$	17.3897	+	10.0400i	0.560959	+	0.323870i
$962$	27.3520	+	0.500163i	0.881865	+	0.0161259i
$963$	0.287091	+	0.497256i	0.00925138	+	0.0160239i
$964$	5.26545	−	19.6509i	0.169589	−	0.632913i
$965$	−5.39098	−	3.11249i	−0.173542	−	0.100194i
$966$	−20.1851	+	7.26173i	−0.649445	+	0.233642i
$967$	−6.11427	+	6.11427i	−0.196622	+	0.196622i	−0.798550	−	0.601928i	$-0.794399\pi$
$967$	−6.11427	+	6.11427i	−0.196622	+	0.196622i	0.601928	+	0.798550i	$0.294399\pi$
$968$	2.74341	−	2.74341i	0.0881765	−	0.0881765i
$969$	3.69458	+	13.7884i	0.118687	+	0.442946i
$970$	5.14581	−	19.2044i	0.165222	−	0.616617i
$971$		−	32.1499i		−	1.03174i	−0.856667	−	0.515870i	$-0.827469\pi$
$971$		−	32.1499i		−	1.03174i	0.856667	−	0.515870i	$-0.172531\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−7.51619	−	10.8198i	−0.240958	−	0.346867i
$974$			33.0137i			1.05783i
$975$	5.54080	−	9.20411i	0.177448	−	0.294767i
$976$	−9.22941	+	5.32860i	−0.295426	+	0.170564i
$977$	1.19552	−	1.19552i	0.0382480	−	0.0382480i	−0.687724	−	0.725972i	$-0.741390\pi$
$977$	1.19552	−	1.19552i	0.0382480	−	0.0382480i	0.725972	+	0.687724i	$0.241390\pi$
$978$	−1.54274	+	0.890703i	−0.0493315	+	0.0284816i
$979$	3.97676	+	6.88795i	0.127098	+	0.220140i
$980$	9.90519	+	0.941011i	0.316410	+	0.0300595i
$981$	−18.8390	−	5.04790i	−0.601483	−	0.161167i
$982$	−29.4428	−	29.4428i	−0.939556	−	0.939556i
$983$	−17.7305	−	4.75086i	−0.565514	−	0.151529i	−0.0352757	−	0.999378i	$-0.511231\pi$
$983$	−17.7305	−	4.75086i	−0.565514	−	0.151529i	−0.530238	+	0.847849i	$0.677898\pi$
$984$	0.690622	−	1.19619i	0.0220162	−	0.0381332i
$985$	7.52299	+	13.0302i	0.239702	+	0.415177i
$986$	−0.269708	−	1.00656i	−0.00858926	−	0.0320555i
$987$	5.69794	+	15.8383i	0.181367	+	0.504139i
$988$	−15.6976	+	15.1339i	−0.499409	+	0.481472i
$989$	35.2946	−	61.1320i	1.12230	−	1.94388i
$990$	−3.87703	−	3.87703i	−0.123220	−	0.123220i
$991$	4.43739			0.140958			0.0704791	−	0.997513i	$-0.477547\pi$
$991$	4.43739			0.140958			0.0704791	+	0.997513i	$0.477547\pi$
$992$	−3.30455			−0.104920
$993$	4.93829	+	4.93829i	0.156712	+	0.156712i
$994$	14.2963	−	30.3626i	0.453450	−	0.963044i
$995$	−3.78438	+	14.1235i	−0.119973	+	0.447745i
$996$	−12.8114	+	3.43279i	−0.405943	+	0.108772i
$997$	−31.0524	−	17.9281i	−0.983438	−	0.567788i	−0.0801318	−	0.996784i	$-0.525534\pi$
$997$	−31.0524	−	17.9281i	−0.983438	−	0.567788i	−0.903306	+	0.428996i	$0.858867\pi$
$998$		−	6.79693i		−	0.215153i
$999$	7.32883	+	1.96375i	0.231874	+	0.0621304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.19.2	✓	40
7.3	odd	6		546.2.cg.b.409.7	yes	40
13.11	odd	12		546.2.cg.b.271.7	yes	40
91.24	even	12	inner	546.2.by.b.115.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.2	✓	40	1.1	even	1	trivial
546.2.by.b.115.2	yes	40	91.24	even	12	inner
546.2.cg.b.271.7	yes	40	13.11	odd	12
546.2.cg.b.409.7	yes	40	7.3	odd	6

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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.37297 + 0.367885i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.220772 - 2.63652i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} -1.00000i q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.37297 + 0.367885i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.220772 - 2.63652i) q^{7} +(-0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +1.42140 q^{10} +(2.72762 + 2.72762i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-1.74539 - 3.15494i) q^{13} +(-0.469134 + 2.60383i) q^{14} +(0.367885 + 1.37297i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.18021 - 2.04418i) q^{17} +(0.965926 + 0.258819i) q^{18} +(-4.27628 - 4.27628i) q^{19} +(-1.37297 - 0.367885i) q^{20} +(-2.63652 + 0.220772i) q^{21} +(-1.92872 - 3.34063i) q^{22} +(-7.02168 + 4.05397i) q^{23} +(-0.707107 + 0.707107i) q^{24} +(-2.58043 + 1.48981i) q^{25} +(0.869355 + 3.49917i) q^{26} +1.00000i q^{27} +(1.12707 - 2.39368i) q^{28} +(-0.220739 + 0.382331i) q^{29} -1.42140i q^{30} +(0.855281 - 3.19195i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(2.72762 - 2.72762i) q^{33} +(-1.66907 + 1.66907i) q^{34} +(1.27305 + 3.53864i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(1.96375 - 7.32883i) q^{37} +(3.02378 + 5.23735i) q^{38} +(-3.15494 + 1.74539i) q^{39} +(1.23097 + 0.710699i) q^{40} +(-1.33418 + 0.357492i) q^{41} +(2.60383 + 0.469134i) q^{42} +(-7.53977 + 4.35309i) q^{43} +(0.998376 + 3.72599i) q^{44} +(1.37297 - 0.367885i) q^{45} +(7.83167 - 2.09849i) q^{46} +(-1.64659 - 6.14515i) q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.90252 + 1.16414i) q^{49} +(2.87810 - 0.771184i) q^{50} +(-2.04418 - 1.18021i) q^{51} +(0.0659206 - 3.60495i) q^{52} +(-4.08469 - 7.07489i) q^{53} +(0.258819 - 0.965926i) q^{54} +(-4.74837 - 2.74147i) q^{55} +(-1.70820 + 2.02041i) q^{56} +(-4.27628 + 4.27628i) q^{57} +(0.312172 - 0.312172i) q^{58} +(2.17393 + 8.11322i) q^{59} +(-0.367885 + 1.37297i) q^{60} +10.6572i q^{61} +(-1.65228 + 2.86183i) q^{62} +(0.220772 + 2.63652i) q^{63} +1.00000i q^{64} +(3.55701 + 3.68952i) q^{65} +(-3.34063 + 1.92872i) q^{66} +(-0.0278660 + 0.0278660i) q^{67} +(2.04418 - 1.18021i) q^{68} +(4.05397 + 7.02168i) q^{69} +(-0.313804 - 3.74755i) q^{70} +(-12.2523 - 3.28299i) q^{71} +(0.707107 + 0.707107i) q^{72} +(7.72484 + 2.06986i) q^{73} +(-3.79368 + 6.57085i) q^{74} +(1.48981 + 2.58043i) q^{75} +(-1.56523 - 5.84150i) q^{76} +(6.58924 - 7.79360i) q^{77} +(3.49917 - 0.869355i) q^{78} +(6.14585 - 10.6449i) q^{79} +(-1.00508 - 1.00508i) q^{80} +1.00000 q^{81} +1.38124 q^{82} +(-9.37857 - 9.37857i) q^{83} +(-2.39368 - 1.12707i) q^{84} +(-0.868362 + 3.24077i) q^{85} +(8.40952 - 2.25332i) q^{86} +(0.382331 + 0.220739i) q^{87} -3.85743i q^{88} +(1.99161 + 0.533652i) q^{89} -1.42140 q^{90} +(-7.93274 + 5.29827i) q^{91} -8.10794 q^{92} +(-3.19195 - 0.855281i) q^{93} +6.36192i q^{94} +(7.44436 + 4.29800i) q^{95} +(-0.965926 + 0.258819i) q^{96} +(3.62024 - 13.5109i) q^{97} +(6.96862 + 0.662032i) q^{98} +(-2.72762 - 2.72762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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