LMFDB - Embedded newform 546.2.by.b.115.2

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			115.2
Character	$\chi$	$=$	546.115
Dual form			546.2.by.b.19.2

$q$-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 $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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	−0.0616062	−	0.998101i	$-0.519622\pi$
$5$	−1.37297	−	0.367885i	−0.614009	−	0.164523i	−0.552403	+	0.833577i	$0.686289\pi$
$6$	−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	−0.164046	−	0.986453i	$-0.552454\pi$
$11$	2.72762	−	2.72762i	0.822407	−	0.822407i	0.986453	+	0.164046i	$0.0524545\pi$
$12$	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	0.972910	−	0.231185i	$-0.0742604\pi$
$17$	1.18021	+	2.04418i	0.286243	+	0.495787i	−0.686667	+	0.726972i	$0.740927\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	−4.27628	+	4.27628i	−0.981045	+	0.981045i	−0.999824	−	0.0187787i	$-0.994022\pi$
$19$	−4.27628	+	4.27628i	−0.981045	+	0.981045i	0.0187787	+	0.999824i	$0.494022\pi$
$20$	−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	−0.464924	−	0.885351i	$-0.653918\pi$
$23$	−7.02168	−	4.05397i	−1.46412	−	0.845311i	−0.999198	+	0.0400397i	$0.987252\pi$
$24$	−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	0.844802	−	0.535078i	$-0.179718\pi$
$29$	−0.220739	−	0.382331i	−0.0409902	−	0.0709971i	−0.885793	+	0.464081i	$0.846385\pi$
$30$			1.42140i			0.259511i
$31$	0.855281	+	3.19195i	0.153613	+	0.573292i	0.999220	+	0.0394858i	$0.0125720\pi$
$31$	0.855281	+	3.19195i	0.153613	+	0.573292i	−0.845607	+	0.533806i	$0.820761\pi$
$32$	−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	0.916466	+	0.400112i	$0.131029\pi$
$37$	1.96375	+	7.32883i	0.322839	+	1.20485i	−0.593627	+	0.804740i	$0.702305\pi$
$38$	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	0.153127	−	0.988206i	$-0.451066\pi$
$41$	−1.33418	−	0.357492i	−0.208364	−	0.0558309i	−0.361491	+	0.932376i	$0.617732\pi$
$42$	2.60383	−	0.469134i	0.401779	−	0.0723889i
$43$	−7.53977	−	4.35309i	−1.14980	−	0.663840i	−0.200964	−	0.979599i	$-0.564408\pi$
$43$	−7.53977	−	4.35309i	−1.14980	−	0.663840i	−0.948839	+	0.315759i	$0.897741\pi$
$44$	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	0.735566	+	0.677453i	$0.236916\pi$
$47$	−1.64659	+	6.14515i	−0.240179	+	0.896362i	−0.975745	+	0.218909i	$0.929750\pi$
$48$	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	0.436327	+	0.899788i	$0.356279\pi$
$53$	−4.08469	+	7.07489i	−0.561076	+	0.971811i	−0.997403	+	0.0720233i	$0.977054\pi$
$54$	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	−0.667251	−	0.744833i	$-0.732529\pi$
$59$	2.17393	−	8.11322i	0.283022	−	1.05625i	0.950273	−	0.311419i	$-0.100804\pi$
$60$	−0.367885	−	1.37297i	−0.0474938	−	0.177249i
$61$		−	10.6572i		−	1.36451i	−0.731112	−	0.682257i	$-0.760998\pi$
$61$		−	10.6572i		−	1.36451i	0.731112	−	0.682257i	$-0.239002\pi$
$62$	−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	0.705403	−	0.708807i	$-0.250766\pi$
$67$	−0.0278660	−	0.0278660i	−0.00340438	−	0.00340438i	−0.708807	+	0.705403i	$0.750766\pi$
$68$	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	−0.897440	−	0.441137i	$-0.854575\pi$
$71$	−12.2523	+	3.28299i	−1.45408	+	0.389619i	−0.556637	+	0.830756i	$0.687909\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	7.72484	−	2.06986i	0.904124	−	0.242259i	0.223337	−	0.974741i	$-0.428305\pi$
$73$	7.72484	−	2.06986i	0.904124	−	0.242259i	0.680786	+	0.732482i	$0.261638\pi$
$74$	−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	0.971359	+	0.237618i	$0.0763666\pi$
$79$	6.14585	+	10.6449i	0.691462	+	1.19765i	−0.279896	+	0.960030i	$0.590300\pi$
$80$	−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	−0.0298777	+	0.999554i	$0.509512\pi$
$83$	−9.37857	+	9.37857i	−1.02943	+	1.02943i	−0.999554	+	0.0298777i	$0.990488\pi$
$84$	−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	−0.151714	−	0.988424i	$-0.548479\pi$
$89$	1.99161	−	0.533652i	0.211111	−	0.0565670i	0.362824	+	0.931858i	$0.381812\pi$
$90$	−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	0.863889	+	0.503681i	$0.168021\pi$
$97$	3.62024	+	13.5109i	0.367580	+	1.37183i	−0.496310	+	0.868146i	$0.665312\pi$
$98$	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	0.989767	+	0.142694i	$0.0455764\pi$
$103$	6.27668	+	10.8715i	0.618460	+	1.07120i	−0.371307	+	0.928510i	$0.621090\pi$
$104$	−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	−0.879569	−	0.475772i	$-0.842169\pi$
$107$	−0.287091	+	0.497256i	−0.0277541	+	0.0480716i	0.851815	+	0.523843i	$0.175502\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	18.8390	−	5.04790i	1.80445	−	0.483501i	0.809791	−	0.586718i	$-0.199580\pi$
$109$	18.8390	−	5.04790i	1.80445	−	0.483501i	0.994659	+	0.103218i	$0.0329138\pi$
$110$	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	−0.503101	−	0.864227i	$-0.667808\pi$
$113$	5.28204	−	9.14876i	0.496892	−	0.860643i	0.999994	+	0.00358469i	$0.00114104\pi$
$114$	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	0.245232	−	0.969465i	$-0.421136\pi$
$127$	13.6070	−	7.85602i	1.20743	−	0.697109i	0.962197	+	0.272355i	$0.0878027\pi$
$128$	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	0.128662	−	0.991688i	$-0.458932\pi$
$131$	12.0386	−	6.95051i	1.05182	−	0.607269i	0.923159	+	0.384420i	$0.125598\pi$
$132$	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	0.669379	−	0.742921i	$-0.266560\pi$
$137$	10.2723	+	2.75244i	0.877618	+	0.235157i	0.208239	+	0.978078i	$0.433227\pi$
$138$	−2.09849	+	7.83167i	−0.178635	+	0.666676i
$139$	4.31229	+	2.48970i	0.365764	+	0.211174i	0.671606	−	0.740908i	$-0.265605\pi$
$139$	4.31229	+	2.48970i	0.365764	+	0.211174i	−0.305842	+	0.952082i	$0.598938\pi$
$140$	−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	0.441584	−	0.897220i	$-0.354417\pi$
$149$	−5.56174	−	5.56174i	−0.455636	−	0.455636i	−0.897220	+	0.441584i	$0.854417\pi$
$150$	−0.771184	+	2.87810i	−0.0629669	+	0.234996i
$151$	3.98554	+	14.8742i	0.324338	+	1.21045i	0.914975	+	0.403510i	$0.132210\pi$
$151$	3.98554	+	14.8742i	0.324338	+	1.21045i	−0.590637	+	0.806937i	$0.701123\pi$
$152$		−	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	0.101754	−	0.994810i	$-0.467555\pi$
$157$	−8.88249	−	5.12831i	−0.708900	−	0.409283i	−0.810653	+	0.585526i	$0.800888\pi$
$158$	−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	−0.656052	−	0.754715i	$-0.727775\pi$
$163$	1.25964	−	1.25964i	0.0986630	−	0.0986630i	0.754715	+	0.656052i	$0.227775\pi$
$164$	−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	−0.941618	−	0.336683i	$-0.890695\pi$
$167$	0.545200	−	2.03471i	0.0421888	−	0.157451i	0.983807	+	0.179233i	$0.0573615\pi$
$168$	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	$0.321989\pi$
$179$			22.6818i			1.69532i	−0.530540	+	0.847660i	$0.678011\pi$
$180$	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	−0.586813	−	0.809722i	$-0.699618\pi$
$193$	3.09675	−	3.09675i	0.222909	−	0.222909i	0.809722	+	0.586813i	$0.199618\pi$
$194$	−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	0.797022	+	0.603950i	$0.206407\pi$
$197$	−2.73968	+	10.2246i	−0.195194	+	0.728476i	−0.992216	+	0.124525i	$0.960259\pi$
$198$	1.92872	−	3.34063i	0.137068	−	0.237408i
$199$	5.14342	+	8.90867i	0.364608	+	0.631519i	0.988713	−	0.149821i	$-0.0478698\pi$
$199$	5.14342	+	8.90867i	0.364608	+	0.631519i	−0.624105	+	0.781340i	$0.714536\pi$
$200$	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	0.602238	−	0.798317i	$-0.294276\pi$
$211$	−5.66861	−	9.81832i	−0.390243	−	0.675921i	−0.992481	+	0.122395i	$0.960942\pi$
$212$			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	0.0968232	−	0.995302i	$-0.469132\pi$
$223$	−4.73346	−	1.26833i	−0.316976	−	0.0849335i	−0.413799	+	0.910368i	$0.635799\pi$
$224$	−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	0.0152274	−	0.999884i	$-0.495153\pi$
$227$	−7.10428	−	1.90358i	−0.471527	−	0.126345i	−0.486755	+	0.873539i	$0.661819\pi$
$228$	−5.84150	−	1.56523i	−0.386863	−	0.103660i
$229$	1.29668	−	4.83929i	0.0856873	−	0.319789i	−0.909756	−	0.415143i	$-0.863732\pi$
$229$	1.29668	−	4.83929i	0.0856873	−	0.319789i	0.995443	+	0.0953536i	$0.0303982\pi$
$230$	−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	−0.775238	−	0.631669i	$-0.782370\pi$
$233$	−9.40002	+	5.42710i	−0.615816	+	0.355541i	0.159422	+	0.987210i	$0.449037\pi$
$234$	−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	0.881596	−	0.472006i	$-0.156470\pi$
$239$	6.33211	+	6.33211i	0.409590	+	0.409590i	−0.472006	+	0.881596i	$0.656470\pi$
$240$	−1.00508	−	1.00508i	−0.0648777	−	0.0648777i
$241$	−5.26545	+	19.6509i	−0.339177	+	1.26583i	0.560092	+	0.828430i	$0.310766\pi$
$241$	−5.26545	+	19.6509i	−0.339177	+	1.26583i	−0.899269	+	0.437396i	$0.855901\pi$
$242$	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	−0.836545	−	0.547898i	$-0.815428\pi$
$251$	0.890713	−	1.54276i	0.0562213	−	0.0973782i	0.892766	+	0.450520i	$0.148761\pi$
$252$	−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	−0.798916	−	0.601443i	$-0.794593\pi$
$257$	1.94630	−	3.37109i	0.121407	−	0.210283i	0.920323	+	0.391160i	$0.127926\pi$
$258$	−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	−0.112800	−	0.993618i	$-0.535982\pi$
$269$	11.3381	−	6.54607i	0.691297	−	0.399121i	0.804098	+	0.594497i	$0.202649\pi$
$270$		−	1.42140i		−	0.0865036i
$271$	−23.4390	+	6.28045i	−1.42382	+	0.381510i	−0.886836	−	0.462085i	$-0.847102\pi$
$271$	−23.4390	+	6.28045i	−1.42382	+	0.381510i	−0.536980	+	0.843595i	$0.680435\pi$
$272$	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	0.559506	−	0.828827i	$-0.310991\pi$
$277$	25.9144	−	14.9617i	1.55704	−	0.898959i	0.997538	−	0.0701328i	$-0.0223423\pi$
$278$	−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	−0.989057	−	0.147535i	$-0.952866\pi$
$281$	−14.1065	+	14.1065i	−0.841521	+	0.841521i	0.147535	+	0.989057i	$0.452866\pi$
$282$	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	0.844796	−	0.535089i	$-0.179722\pi$
$293$	31.5634	−	8.45739i	1.84395	−	0.494086i	0.999159	+	0.0410025i	$0.0130552\pi$
$294$	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	0.605982	−	0.795478i	$-0.292780\pi$
$307$	−3.32023	−	3.32023i	−0.189496	−	0.189496i	−0.795478	+	0.605982i	$0.792780\pi$
$308$	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	0.189749	+	0.981833i	$0.439232\pi$
$311$	−13.3219	+	23.0743i	−0.755417	+	1.30842i	−0.945167	+	0.326588i	$0.894101\pi$
$312$	3.46505	−	0.996704i	0.196170	−	0.0564272i
$313$	6.79782	−	3.92473i	0.384236	−	0.221839i	−0.295424	−	0.955366i	$-0.595461\pi$
$313$	6.79782	−	3.92473i	0.384236	−	0.221839i	0.679660	+	0.733528i	$0.262128\pi$
$314$	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	−0.919975	−	0.391978i	$-0.871791\pi$
$317$	1.29502	−	4.83309i	0.0727358	−	0.271454i	0.992710	+	0.120524i	$0.0384576\pi$
$318$	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	0.558244	−	0.829677i	$-0.311475\pi$
$331$	−4.93829	−	4.93829i	−0.271433	−	0.271433i	−0.829677	+	0.558244i	$0.811475\pi$
$332$	−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	$-0.901090\pi$
$337$		−	11.2260i		−	0.611518i	0.952109	−	0.305759i	$-0.0989101\pi$
$338$	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	−0.867210	−	0.497942i	$-0.834089\pi$
$347$	−16.1101	−	27.9035i	−0.864836	−	1.49794i	0.00237486	−	0.999997i	$-0.499244\pi$
$348$	0.220739	−	0.382331i	0.0118329	−	0.0204951i
$349$	0.290712	−	1.08495i	0.0155614	−	0.0580761i	−0.957709	−	0.287740i	$-0.907096\pi$
$349$	0.290712	−	1.08495i	0.0155614	−	0.0580761i	0.973270	+	0.229664i	$0.0737627\pi$
$350$	−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	−0.519799	−	0.854289i	$-0.673993\pi$
$353$	6.28449	−	6.28449i	0.334490	−	0.334490i	0.854289	+	0.519799i	$0.173993\pi$
$354$	−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	0.496805	−	0.867862i	$-0.334506\pi$
$359$	9.34329	+	2.50353i	0.493120	+	0.132131i	−0.00368517	+	0.999993i	$0.501173\pi$
$360$	−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	$0.243973\pi$
$367$			26.5746i			1.38718i	−0.720369	+	0.693591i	$0.756027\pi$
$368$	−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	−0.504541	−	0.863388i	$-0.668338\pi$
$379$	7.08824	−	26.4537i	0.364098	−	1.35883i	0.868639	−	0.495445i	$-0.164995\pi$
$380$	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	−0.115007	+	0.993365i	$0.536689\pi$
$383$	−21.6913	+	21.6913i	−1.10837	+	1.10837i	−0.993365	+	0.115007i	$0.963311\pi$
$384$	−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	0.572861	−	0.819653i	$-0.305834\pi$
$389$	2.94763	+	1.70182i	0.149451	+	0.0862855i	−0.423410	+	0.905938i	$0.639167\pi$
$390$	−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	0.996067	−	0.0886087i	$-0.0282421\pi$
$397$	18.0810	+	18.0810i	0.907458	+	0.907458i	−0.0886087	+	0.996067i	$0.528242\pi$
$398$	−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	0.950722	−	0.310044i	$-0.100344\pi$
$401$	−0.553681	−	2.06637i	−0.0276495	−	0.103189i	−0.978372	+	0.206855i	$0.933677\pi$
$402$	−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	−0.212271	−	0.977211i	$-0.568086\pi$
$409$	−17.8921	−	4.79418i	−0.884709	−	0.237057i	−0.672438	+	0.740154i	$0.734753\pi$
$410$	−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	−0.993432	−	0.114426i	$-0.963497\pi$
$419$	−28.4741	+	16.4395i	−1.39105	+	0.803124i	−0.397620	+	0.917550i	$0.630164\pi$
$420$	3.70108	−	0.666826i	0.180594	−	0.0325378i
$421$	11.1258	+	11.1258i	0.542238	+	0.542238i	0.924185	−	0.381946i	$-0.124746\pi$
$421$	11.1258	+	11.1258i	0.542238	+	0.542238i	−0.381946	+	0.924185i	$0.624746\pi$
$422$	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	0.475131	−	0.879915i	$-0.342401\pi$
$431$	−8.40355	−	8.40355i	−0.404785	−	0.404785i	−0.879915	+	0.475131i	$0.842401\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−1.73495	+	3.00502i	−0.0833765	+	0.144412i	−0.904698	−	0.426053i	$-0.859904\pi$
$433$	−1.73495	+	3.00502i	−0.0833765	+	0.144412i	0.821322	+	0.570465i	$0.193237\pi$
$434$	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	−0.994101	−	0.108456i	$-0.965409\pi$
$439$	−8.44641	+	14.6296i	−0.403125	+	0.698233i	0.590976	+	0.806689i	$0.298743\pi$
$440$	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	0.868589	−	0.495533i	$-0.165027\pi$
$443$	0.108413	+	0.187777i	0.00515086	+	0.00892155i	−0.863438	+	0.504454i	$0.831694\pi$
$444$	−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	0.997451	−	0.0713537i	$-0.0227319\pi$
$449$	2.07566	+	7.74645i	0.0979562	+	0.365578i	−0.899495	+	0.436931i	$0.856065\pi$
$450$	−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	−0.880650	−	0.473767i	$-0.842894\pi$
$457$	−30.0661	+	8.05618i	−1.40643	+	0.376852i	−0.525782	+	0.850619i	$0.676227\pi$
$458$			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	0.620835	+	0.783941i	$0.286794\pi$
$461$	10.2018	+	38.0738i	0.475147	+	1.77327i	−0.145689	+	0.989331i	$0.546540\pi$
$462$	5.82262	−	8.38185i	0.270893	−	0.389959i
$463$	6.13141	−	6.13141i	0.284951	−	0.284951i	−0.550129	−	0.835080i	$-0.685421\pi$
$463$	6.13141	−	6.13141i	0.284951	−	0.284951i	0.835080	+	0.550129i	$0.185421\pi$
$464$	−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	0.976537	−	0.215348i	$-0.0690886\pi$
$467$	6.52135	+	11.2953i	0.301772	+	0.522684i	−0.674765	+	0.738032i	$0.735755\pi$
$468$	−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	−0.990240	−	0.139374i	$-0.955491\pi$
$479$	−24.7228	−	24.7228i	−1.12961	−	1.12961i	−0.139374	−	0.990240i	$-0.544509\pi$
$480$	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	0.447493	+	0.894288i	$0.352317\pi$
$487$	−8.54456	+	31.8887i	−0.387191	+	1.44502i	−0.834684	+	0.550729i	$0.814350\pi$
$488$	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	0.642482	−	0.766301i	$-0.277905\pi$
$491$	36.0599	−	20.8192i	1.62736	−	0.939556i	0.984877	−	0.173256i	$-0.0554287\pi$
$492$	−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	−0.915306	−	0.402759i	$-0.868051\pi$
$499$	1.75918	−	6.56533i	0.0787515	−	0.293905i	0.994058	+	0.108854i	$0.0347181\pi$
$500$	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	0.650745	−	0.759296i	$-0.274457\pi$
$503$	7.14428	+	4.12475i	0.318548	+	0.183914i	−0.332197	+	0.943210i	$0.607790\pi$
$504$	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	−0.825428	−	0.564507i	$-0.809066\pi$
$509$	−8.86288	−	33.0767i	−0.392840	−	1.46610i	0.432588	−	0.901592i	$-0.357600\pi$
$510$	−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	0.851078	−	0.525039i	$-0.175949\pi$
$521$	18.7607	+	10.8315i	0.821921	+	0.474536i	−0.0291576	+	0.999575i	$0.509282\pi$
$522$	−0.312172	−	0.312172i	−0.0136634	−	0.0136634i
$523$	−26.0748	−	15.0543i	−1.14017	−	0.658277i	−0.193697	−	0.981061i	$-0.562048\pi$
$523$	−26.0748	−	15.0543i	−1.14017	−	0.658277i	−0.946473	+	0.322784i	$0.895381\pi$
$524$	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	0.230264	−	0.973128i	$-0.426041\pi$
$541$	−1.32311	−	0.354527i	−0.0568850	−	0.0152423i	−0.287149	+	0.957886i	$0.592708\pi$
$542$	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	−0.392578	−	0.919719i	$-0.628417\pi$
$557$	12.4410	−	12.4410i	0.527141	−	0.527141i	0.919719	+	0.392578i	$0.128417\pi$
$558$	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	0.560328	−	0.828271i	$-0.310675\pi$
$563$	−10.3723	−	17.9653i	−0.437140	−	0.757149i	−0.997468	+	0.0711225i	$0.977342\pi$
$564$	−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	0.620545	−	0.784171i	$-0.286911\pi$
$569$	6.00413	+	3.46648i	0.251706	+	0.145323i	−0.368839	+	0.929493i	$0.620245\pi$
$570$	−6.07829	−	6.07829i	−0.254592	−	0.254592i
$571$	25.9520	+	14.9834i	1.08606	+	0.627035i	0.932524	−	0.361108i	$-0.117602\pi$
$571$	25.9520	+	14.9834i	1.08606	+	0.627035i	0.153533	+	0.988144i	$0.450935\pi$
$572$	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	0.959582	+	0.281430i	$0.0908087\pi$
$577$	6.46820	+	24.1396i	0.269275	+	1.00495i	−0.690307	+	0.723516i	$0.742525\pi$
$578$	−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	0.582045	−	0.813157i	$-0.302253\pi$
$587$	16.4638	+	4.41145i	0.679532	+	0.182080i	0.0974873	+	0.995237i	$0.468919\pi$
$588$	−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	0.265642	+	0.964072i	$0.414416\pi$
$593$	−10.8717	+	40.5737i	−0.446447	+	1.66616i	−0.712089	+	0.702090i	$0.752251\pi$
$594$	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	−0.533472	−	0.845818i	$-0.679113\pi$
$599$	11.3993	−	19.7442i	0.465764	−	0.806727i	0.999236	+	0.0390909i	$0.0124462\pi$
$600$	0.771184	+	2.87810i	0.0314834	+	0.117498i
$601$	24.1075	−	13.9185i	0.983364	−	0.567745i	0.0800799	−	0.996788i	$-0.474482\pi$
$601$	24.1075	−	13.9185i	0.983364	−	0.567745i	0.903284	+	0.429043i	$0.141149\pi$
$602$	−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	$0.316974\pi$
$607$			41.3512i			1.67839i	−0.543829	+	0.839196i	$0.683026\pi$
$608$	−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	0.399536	−	0.916718i	$-0.369171\pi$
$613$	−12.8048	−	12.8048i	−0.517182	−	0.517182i	−0.916718	+	0.399536i	$0.869171\pi$
$614$	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	0.460135	−	0.887849i	$-0.347801\pi$
$617$	32.3546	−	8.66940i	1.30255	−	0.349017i	0.842413	+	0.538832i	$0.181134\pi$
$618$	8.87657	−	8.87657i	0.357068	−	0.357068i
$619$	42.1473	−	11.2933i	1.69404	−	0.453917i	0.722613	−	0.691252i	$-0.242941\pi$
$619$	42.1473	−	11.2933i	1.69404	−	0.453917i	0.971428	+	0.237335i	$0.0762741\pi$
$620$	−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	−0.999536	−	0.0304680i	$-0.990300\pi$
$631$	−3.74651	−	13.9822i	−0.149146	−	0.556622i	0.850389	−	0.526154i	$-0.176366\pi$
$632$	−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	−0.853874	−	0.520480i	$-0.825753\pi$
$641$	−21.0155	+	12.1333i	−0.830061	+	0.479236i	0.0238123	+	0.999716i	$0.492420\pi$
$642$	0.554617	+	0.148609i	0.0218890	+	0.00586514i
$643$	−0.634628	−	2.36846i	−0.0250273	−	0.0934031i	0.952283	−	0.305218i	$-0.0987293\pi$
$643$	−0.634628	−	2.36846i	−0.0250273	−	0.0934031i	−0.977310	+	0.211815i	$0.932063\pi$
$644$	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	0.497383	+	0.867531i	$0.334294\pi$
$653$	−12.8437	+	22.2459i	−0.502612	+	0.870550i	−0.999995	+	0.00301925i	$0.999039\pi$
$654$	−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	−0.140747	−	0.990046i	$-0.544950\pi$
$659$	20.2039	−	34.9941i	0.787031	−	1.36318i	0.927778	−	0.373133i	$-0.121716\pi$
$660$	−4.74837	−	2.74147i	−0.184830	−	0.106712i
$661$	5.92024	+	5.92024i	0.230271	+	0.230271i	0.812806	−	0.582535i	$-0.197939\pi$
$661$	5.92024	+	5.92024i	0.230271	+	0.230271i	−0.582535	+	0.812806i	$0.697939\pi$
$662$	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	−0.493454	−	0.869772i	$-0.664266\pi$
$673$	0.338909	−	0.195669i	0.0130640	−	0.00754250i	0.506518	+	0.862230i	$0.330932\pi$
$674$	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	−0.00995355	−	0.999950i	$-0.503168\pi$
$677$	22.1437	−	12.7847i	0.851052	−	0.491355i	0.861006	+	0.508595i	$0.169835\pi$
$678$	−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	0.155711	−	0.987803i	$-0.450233\pi$
$683$	−5.31418	−	1.42393i	−0.203341	−	0.0544852i	−0.359052	+	0.933318i	$0.616900\pi$
$684$	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	−0.961972	−	0.273149i	$-0.911935\pi$
$691$	−6.97796	−	26.0421i	−0.265454	−	0.990688i	0.696518	−	0.717540i	$-0.254732\pi$
$692$	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	$0.290225\pi$
$701$			41.8639i			1.58118i	−0.612348	+	0.790588i	$0.709775\pi$
$702$	−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	−0.560535	−	0.828131i	$-0.689404\pi$
$709$	7.12529	−	7.12529i	0.267596	−	0.267596i	0.828131	+	0.560535i	$0.189404\pi$
$710$	−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	0.506015	−	0.862525i	$-0.331118\pi$
$733$	13.8883	+	3.72135i	0.512975	+	0.137451i	0.00695978	+	0.999976i	$0.497785\pi$
$734$	−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	−0.887155	−	0.461471i	$-0.847322\pi$
$739$	−11.5720	+	11.5720i	−0.425684	+	0.425684i	0.461471	+	0.887155i	$0.347322\pi$
$740$	−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	−0.979539	−	0.201254i	$-0.935498\pi$
$743$	−0.834271	+	3.11354i	−0.0306064	+	0.114225i	0.948933	+	0.315479i	$0.102165\pi$
$744$	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	0.793996	−	0.607922i	$-0.207997\pi$
$751$	18.2107	+	10.5140i	0.664518	+	0.383660i	−0.129478	+	0.991582i	$0.541330\pi$
$752$	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	0.807381	+	0.590030i	$0.200884\pi$
$757$	25.1659	+	43.5887i	0.914672	+	1.58426i	0.107290	+	0.994228i	$0.465783\pi$
$758$			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	0.887037	−	0.461698i	$-0.152760\pi$
$761$	11.7335	+	11.7335i	0.425340	+	0.425340i	−0.461698	+	0.887037i	$0.652760\pi$
$762$	−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	0.486869	−	0.873475i	$-0.338139\pi$
$769$	13.0827	+	3.50549i	0.471773	+	0.126411i	−0.0150963	+	0.999886i	$0.504805\pi$
$770$	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	−0.476332	−	0.879266i	$-0.658034\pi$
$773$	−36.9356	−	9.89685i	−1.32848	−	0.355965i	−0.852148	+	0.523301i	$0.824700\pi$
$774$	−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	0.719952	+	0.694024i	$0.244164\pi$
$787$	−7.02900	+	26.2326i	−0.250557	+	0.935091i	−0.970509	+	0.241067i	$0.922503\pi$
$788$	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	−0.976069	−	0.217462i	$-0.930222\pi$
$797$	−8.46109	+	14.6550i	−0.299707	+	0.519108i	0.676362	+	0.736570i	$0.263556\pi$
$798$	−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	−0.692009	−	0.721889i	$-0.743274\pi$
$811$	0.850909	−	0.850909i	0.0298795	−	0.0298795i	0.721889	+	0.692009i	$0.243274\pi$
$812$	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	−0.913607	−	0.406598i	$-0.866715\pi$
$821$	−43.0231	+	11.5280i	−1.50152	+	0.402330i	−0.587908	+	0.808928i	$0.700048\pi$
$822$		−	10.6346i		−	0.370925i
$823$	44.6477	−	25.7774i	1.55632	−	0.898542i	0.558717	−	0.829358i	$-0.311294\pi$
$823$	44.6477	−	25.7774i	1.55632	−	0.898542i	0.997604	−	0.0691840i	$-0.0220396\pi$
$824$	−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	−0.878665	−	0.477439i	$-0.841565\pi$
$827$	−11.5383	+	11.5383i	−0.401227	+	0.401227i	0.477439	+	0.878665i	$0.341565\pi$
$828$	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	−0.340272	−	0.940327i	$-0.610519\pi$
$839$	−4.77327	+	1.27899i	−0.164792	+	0.0441558i	0.175480	+	0.984483i	$0.443852\pi$
$840$	−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	0.0664946	−	0.997787i	$-0.478818\pi$
$853$	−27.1995	−	27.1995i	−0.931292	−	0.931292i	−0.997787	+	0.0664946i	$0.978818\pi$
$854$	−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	−0.819572	−	0.572976i	$-0.805789\pi$
$857$	2.53008	−	4.38222i	0.0864258	−	0.149694i	0.905998	+	0.423282i	$0.139122\pi$
$858$	11.9157	−	7.17314i	0.406794	−	0.244887i
$859$	−47.6367	+	27.5031i	−1.62534	+	0.938393i	−0.639887	+	0.768469i	$0.721019\pi$
$859$	−47.6367	+	27.5031i	−1.62534	+	0.938393i	−0.985457	+	0.169924i	$0.945648\pi$
$860$	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	−0.952323	−	0.305093i	$-0.901313\pi$
$863$	0.733228	−	2.73644i	0.0249594	−	0.0931496i	0.977282	+	0.211943i	$0.0679792\pi$
$864$	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	0.713311	−	0.700847i	$-0.247195\pi$
$877$	0.369114	+	0.369114i	0.0124641	+	0.0124641i	−0.700847	+	0.713311i	$0.747195\pi$
$878$	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	0.973807	−	0.227378i	$-0.0730152\pi$
$881$	8.60734	+	14.9083i	0.289989	+	0.502275i	−0.683818	+	0.729653i	$0.739682\pi$
$882$	−6.96862	+	0.662032i	−0.234646	+	0.0222918i
$883$		−	2.32270i		−	0.0781651i	−0.999236	−	0.0390825i	$-0.987556\pi$
$883$		−	2.32270i		−	0.0781651i	0.999236	−	0.0390825i	$-0.0124435\pi$
$884$	−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	0.224615	−	0.974448i	$-0.427887\pi$
$887$	−15.0990	−	8.71739i	−0.506973	−	0.292701i	−0.731589	+	0.681746i	$0.761221\pi$
$888$	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	$0.143668\pi$
$907$			26.2722i			0.872355i	−0.899861	+	0.436177i	$0.856332\pi$
$908$	−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	−0.703715	−	0.710482i	$-0.748477\pi$
$929$	0.206244	−	0.206244i	0.00676665	−	0.00676665i	0.710482	+	0.703715i	$0.248477\pi$
$930$	−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	$-0.966702\pi$
$937$		−	6.39250i		−	0.208834i	0.994534	−	0.104417i	$-0.0332976\pi$
$938$	−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	−0.989592	−	0.143900i	$-0.954036\pi$
$941$	−6.27411	−	23.4153i	−0.204530	−	0.763317i	0.785062	−	0.619417i	$-0.212631\pi$
$942$	−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	−0.599808	−	0.800144i	$-0.704756\pi$
$947$	−14.7845	−	55.1764i	−0.480431	−	1.79299i	0.119377	−	0.992849i	$-0.461910\pi$
$948$	−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	−0.0531686	−	0.998586i	$-0.516932\pi$
$953$	−29.1590	−	16.8350i	−0.944553	−	0.545338i	−0.891385	+	0.453247i	$0.850265\pi$
$954$	−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	0.601928	−	0.798550i	$-0.294399\pi$
$967$	−6.11427	−	6.11427i	−0.196622	−	0.196622i	−0.798550	+	0.601928i	$0.794399\pi$
$968$	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	$0.172531\pi$
$971$			32.1499i			1.03174i	−0.856667	+	0.515870i	$0.827469\pi$
$972$	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	0.725972	−	0.687724i	$-0.241390\pi$
$977$	1.19552	+	1.19552i	0.0382480	+	0.0382480i	−0.687724	+	0.725972i	$0.741390\pi$
$978$	−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	−0.530238	−	0.847849i	$-0.677898\pi$
$983$	−17.7305	+	4.75086i	−0.565514	+	0.151529i	−0.0352757	+	0.999378i	$0.511231\pi$
$984$	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	−0.903306	−	0.428996i	$-0.858867\pi$
$997$	−31.0524	+	17.9281i	−0.983438	+	0.567788i	−0.0801318	+	0.996784i	$0.525534\pi$
$998$			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.115.2	yes	40
7.5	odd	6		546.2.cg.b.271.7	yes	40
13.6	odd	12		546.2.cg.b.409.7	yes	40
91.19	even	12	inner	546.2.by.b.19.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.2	✓	40	91.19	even	12	inner
546.2.by.b.115.2	yes	40	1.1	even	1	trivial
546.2.cg.b.271.7	yes	40	7.5	odd	6
546.2.cg.b.409.7	yes	40	13.6	odd	12

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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