LMFDB - Embedded newform 560.2.t.a.43.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(43,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3, 0]))

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

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

chi := DirichletCharacter("560.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.t (of order $4$, degree $2$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.5
Character	$\chi$	$=$	560.43
Dual form			560.2.t.a.547.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39923 + 0.205299i) q^{2} -0.670195i q^{3} +(1.91570 - 0.574522i) q^{4} +(-1.47177 - 1.68342i) q^{5} +(0.137590 + 0.937758i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.56257 + 1.19718i) q^{8} +2.55084 q^{9} +O(q^{10})$	\(q+(-1.39923 + 0.205299i) q^{2} -0.670195i q^{3} +(1.91570 - 0.574522i) q^{4} +(-1.47177 - 1.68342i) q^{5} +(0.137590 + 0.937758i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.56257 + 1.19718i) q^{8} +2.55084 q^{9} +(2.40495 + 2.05334i) q^{10} +(0.646620 - 0.646620i) q^{11} +(-0.385041 - 1.28389i) q^{12} -0.237545 q^{13} +(0.844239 - 1.13458i) q^{14} +(-1.12822 + 0.986373i) q^{15} +(3.33985 - 2.20123i) q^{16} +(3.27870 - 3.27870i) q^{17} +(-3.56922 + 0.523684i) q^{18} +(0.695701 - 0.695701i) q^{19} +(-3.78664 - 2.37936i) q^{20} +(0.473899 + 0.473899i) q^{21} +(-0.772022 + 1.03752i) q^{22} +(-5.31623 - 5.31623i) q^{23} +(0.802344 + 1.71742i) q^{24} +(-0.667779 + 4.95521i) q^{25} +(0.332381 - 0.0487677i) q^{26} -3.72014i q^{27} +(-0.948360 + 1.76086i) q^{28} +(-4.50136 - 4.50136i) q^{29} +(1.37614 - 1.61179i) q^{30} +0.891710i q^{31} +(-4.22132 + 3.76570i) q^{32} +(-0.433361 - 0.433361i) q^{33} +(-3.91455 + 5.26077i) q^{34} +(2.23105 + 0.149655i) q^{35} +(4.88666 - 1.46551i) q^{36} -5.96763 q^{37} +(-0.830621 + 1.11627i) q^{38} +0.159201i q^{39} +(5.78687 + 2.55189i) q^{40} -4.65612i q^{41} +(-0.760386 - 0.565804i) q^{42} -10.7848 q^{43} +(0.867236 - 1.61023i) q^{44} +(-3.75425 - 4.29412i) q^{45} +(8.53005 + 6.34722i) q^{46} +(7.56463 + 7.56463i) q^{47} +(-1.47525 - 2.23835i) q^{48} -1.00000i q^{49} +(-0.0829195 - 7.07058i) q^{50} +(-2.19737 - 2.19737i) q^{51} +(-0.455066 + 0.136475i) q^{52} -8.96841i q^{53} +(0.763741 + 5.20535i) q^{54} +(-2.04021 - 0.136854i) q^{55} +(0.965475 - 2.65854i) q^{56} +(-0.466255 - 0.466255i) q^{57} +(7.22257 + 5.37433i) q^{58} +(-4.94848 - 4.94848i) q^{59} +(-1.59464 + 2.53778i) q^{60} +(7.96277 - 7.96277i) q^{61} +(-0.183067 - 1.24771i) q^{62} +(-1.80372 + 1.80372i) q^{63} +(5.13351 - 6.13572i) q^{64} +(0.349612 + 0.399887i) q^{65} +(0.695342 + 0.517405i) q^{66} +2.11902 q^{67} +(4.39733 - 8.16470i) q^{68} +(-3.56291 + 3.56291i) q^{69} +(-3.15249 + 0.248630i) q^{70} -11.8668 q^{71} +(-6.53670 + 3.05382i) q^{72} +(5.20281 - 5.20281i) q^{73} +(8.35011 - 1.22515i) q^{74} +(3.32095 + 0.447542i) q^{75} +(0.933063 - 1.73245i) q^{76} +0.914459i q^{77} +(-0.0326838 - 0.222760i) q^{78} -0.134481 q^{79} +(-8.62108 - 2.38265i) q^{80} +5.15930 q^{81} +(0.955896 + 6.51500i) q^{82} -2.61757i q^{83} +(1.18012 + 0.635586i) q^{84} +(-10.3449 - 0.693919i) q^{85} +(15.0905 - 2.21411i) q^{86} +(-3.01679 + 3.01679i) q^{87} +(-0.882887 + 2.43113i) q^{88} +6.29488 q^{89} +(6.13465 + 5.23774i) q^{90} +(0.167970 - 0.167970i) q^{91} +(-13.2386 - 7.13003i) q^{92} +0.597619 q^{93} +(-12.1377 - 9.03167i) q^{94} +(-2.19507 - 0.147242i) q^{95} +(2.52375 + 2.82910i) q^{96} +(4.21488 - 4.21488i) q^{97} +(0.205299 + 1.39923i) q^{98} +(1.64942 - 1.64942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) $ 144 * q + 8 * q^4 - 144 * q^9	$ 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) $ 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.39923	+	0.205299i	−0.989407	+	0.145168i
$2$	−1.39923	+	0.205299i	−0.989407	+	0.145168i
$3$		−	0.670195i		−	0.386937i	−0.981106	−	0.193469i	$-0.938026\pi$
$3$		−	0.670195i		−	0.386937i	0.981106	−	0.193469i	$-0.0619737\pi$
$4$	1.91570	−	0.574522i	0.957852	−	0.287261i
$5$	−1.47177	−	1.68342i	−0.658196	−	0.752847i
$5$	−1.47177	−	1.68342i	−0.658196	−	0.752847i
$6$	0.137590	+	0.937758i	0.0561709	+	0.382838i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−2.56257	+	1.19718i	−0.906005	+	0.423267i
$9$	2.55084			0.850280
$10$	2.40495	+	2.05334i	0.760513	+	0.649323i
$11$	0.646620	−	0.646620i	0.194963	−	0.194963i	−0.602874	−	0.797837i	$-0.705978\pi$
$11$	0.646620	−	0.646620i	0.194963	−	0.194963i	0.797837	+	0.602874i	$0.205978\pi$
$12$	−0.385041	−	1.28389i	−0.111152	−	0.370629i
$13$	−0.237545			−0.0658831			−0.0329415	−	0.999457i	$-0.510488\pi$
$13$	−0.237545			−0.0658831			−0.0329415	+	0.999457i	$0.510488\pi$
$14$	0.844239	−	1.13458i	0.225632	−	0.303228i
$15$	−1.12822	+	0.986373i	−0.291304	+	0.254680i
$16$	3.33985	−	2.20123i	0.834963	−	0.550307i
$17$	3.27870	−	3.27870i	0.795201	−	0.795201i	−0.187133	−	0.982334i	$-0.559920\pi$
$17$	3.27870	−	3.27870i	0.795201	−	0.795201i	0.982334	+	0.187133i	$0.0599197\pi$
$18$	−3.56922	+	0.523684i	−0.841273	+	0.123434i
$19$	0.695701	−	0.695701i	0.159605	−	0.159605i	−0.622787	−	0.782392i	$-0.714000\pi$
$19$	0.695701	−	0.695701i	0.159605	−	0.159605i	0.782392	+	0.622787i	$0.214000\pi$
$20$	−3.78664	−	2.37936i	−0.846718	−	0.532042i
$21$	0.473899	+	0.473899i	0.103413	+	0.103413i
$22$	−0.772022	+	1.03752i	−0.164596	+	0.221200i
$23$	−5.31623	−	5.31623i	−1.10851	−	1.10851i	−0.993347	−	0.115163i	$-0.963261\pi$
$23$	−5.31623	−	5.31623i	−1.10851	−	1.10851i	−0.115163	−	0.993347i	$-0.536739\pi$
$24$	0.802344	+	1.71742i	0.163778	+	0.350567i
$25$	−0.667779	+	4.95521i	−0.133556	+	0.991041i
$26$	0.332381	−	0.0487677i	0.0651852	−	0.00956413i
$27$		−	3.72014i		−	0.715942i
$28$	−0.948360	+	1.76086i	−0.179223	+	0.332770i
$29$	−4.50136	−	4.50136i	−0.835882	−	0.835882i	0.152432	−	0.988314i	$-0.451289\pi$
$29$	−4.50136	−	4.50136i	−0.835882	−	0.835882i	−0.988314	+	0.152432i	$0.951289\pi$
$30$	1.37614	−	1.61179i	0.251247	−	0.294271i
$31$			0.891710i			0.160156i	0.996789	+	0.0800779i	$0.0255169\pi$
$31$			0.891710i			0.160156i	−0.996789	+	0.0800779i	$0.974483\pi$
$32$	−4.22132	+	3.76570i	−0.746231	+	0.665687i
$33$	−0.433361	−	0.433361i	−0.0754385	−	0.0754385i
$34$	−3.91455	+	5.26077i	−0.671340	+	0.902215i
$35$	2.23105	+	0.149655i	0.377117	+	0.0252964i
$36$	4.88666	−	1.46551i	0.814443	−	0.244252i
$37$	−5.96763			−0.981073			−0.490537	−	0.871421i	$-0.663199\pi$
$37$	−5.96763			−0.981073			−0.490537	+	0.871421i	$0.663199\pi$
$38$	−0.830621	+	1.11627i	−0.134745	+	0.181084i
$39$			0.159201i			0.0254926i
$40$	5.78687	+	2.55189i	0.914984	+	0.403490i
$41$		−	4.65612i		−	0.727164i	−0.931562	−	0.363582i	$-0.881554\pi$
$41$		−	4.65612i		−	0.727164i	0.931562	−	0.363582i	$-0.118446\pi$
$42$	−0.760386	−	0.565804i	−0.117330	−	0.0873055i
$43$	−10.7848			−1.64467			−0.822336	−	0.569002i	$-0.807330\pi$
$43$	−10.7848			−1.64467			−0.822336	+	0.569002i	$0.807330\pi$
$44$	0.867236	−	1.61023i	0.130741	−	0.242751i
$45$	−3.75425	−	4.29412i	−0.559651	−	0.640130i
$46$	8.53005	+	6.34722i	1.25769	+	0.935847i
$47$	7.56463	+	7.56463i	1.10341	+	1.10341i	0.993996	+	0.109419i	$0.0348991\pi$
$47$	7.56463	+	7.56463i	1.10341	+	1.10341i	0.109419	+	0.993996i	$0.465101\pi$
$48$	−1.47525	−	2.23835i	−0.212934	−	0.323078i
$49$		−	1.00000i		−	0.142857i
$50$	−0.0829195	−	7.07058i	−0.0117266	−	0.999931i
$51$	−2.19737	−	2.19737i	−0.307693	−	0.307693i
$52$	−0.455066	+	0.136475i	−0.0631063	+	0.0189256i
$53$		−	8.96841i		−	1.23191i	−0.787783	−	0.615953i	$-0.788771\pi$
$53$		−	8.96841i		−	1.23191i	0.787783	−	0.615953i	$-0.211229\pi$
$54$	0.763741	+	5.20535i	0.103932	+	0.708358i
$55$	−2.04021	−	0.136854i	−0.275101	−	0.0184534i
$56$	0.965475	−	2.65854i	0.129017	−	0.355263i
$57$	−0.466255	−	0.466255i	−0.0617570	−	0.0617570i
$58$	7.22257	+	5.37433i	0.948370	+	0.705684i
$59$	−4.94848	−	4.94848i	−0.644237	−	0.644237i	0.307357	−	0.951594i	$-0.400555\pi$
$59$	−4.94848	−	4.94848i	−0.644237	−	0.644237i	−0.951594	+	0.307357i	$0.900555\pi$
$60$	−1.59464	+	2.53778i	−0.205867	+	0.327627i
$61$	7.96277	−	7.96277i	1.01953	−	1.01953i	0.0197231	−	0.999805i	$-0.493722\pi$
$61$	7.96277	−	7.96277i	1.01953	−	1.01953i	0.999805	−	0.0197231i	$-0.00627846\pi$
$62$	−0.183067	−	1.24771i	−0.0232495	−	0.158459i
$63$	−1.80372	+	1.80372i	−0.227247	+	0.227247i
$64$	5.13351	−	6.13572i	0.641689	−	0.766965i
$65$	0.349612	+	0.399887i	0.0433640	+	0.0495999i
$66$	0.695342	+	0.517405i	0.0855907	+	0.0636881i
$67$	2.11902			0.258879			0.129440	−	0.991587i	$-0.458682\pi$
$67$	2.11902			0.258879			0.129440	+	0.991587i	$0.458682\pi$
$68$	4.39733	−	8.16470i	0.533255	−	0.990115i
$69$	−3.56291	+	3.56291i	−0.428923	+	0.428923i
$70$	−3.15249	+	0.248630i	−0.376794	+	0.0297169i
$71$	−11.8668			−1.40834			−0.704168	−	0.710034i	$-0.748680\pi$
$71$	−11.8668			−1.40834			−0.704168	+	0.710034i	$0.748680\pi$
$72$	−6.53670	+	3.05382i	−0.770358	+	0.359896i
$73$	5.20281	−	5.20281i	0.608943	−	0.608943i	−0.333727	−	0.942670i	$-0.608306\pi$
$73$	5.20281	−	5.20281i	0.608943	−	0.608943i	0.942670	+	0.333727i	$0.108306\pi$
$74$	8.35011	−	1.22515i	0.970681	−	0.142421i
$75$	3.32095	+	0.447542i	0.383471	+	0.0516777i
$76$	0.933063	−	1.73245i	0.107030	−	0.198726i
$77$			0.914459i			0.104212i
$78$	−0.0326838	−	0.222760i	−0.00370071	−	0.0252226i
$79$	−0.134481			−0.0151303			−0.00756514	−	0.999971i	$-0.502408\pi$
$79$	−0.134481			−0.0151303			−0.00756514	+	0.999971i	$0.502408\pi$
$80$	−8.62108	−	2.38265i	−0.963866	−	0.266389i
$81$	5.15930			0.573255
$82$	0.955896	+	6.51500i	0.105561	+	0.719461i
$83$		−	2.61757i		−	0.287315i	−0.989627	−	0.143658i	$-0.954114\pi$
$83$		−	2.61757i		−	0.287315i	0.989627	−	0.143658i	$-0.0458864\pi$
$84$	1.18012	+	0.635586i	0.128761	+	0.0693481i
$85$	−10.3449	−	0.693919i	−1.12206	−	0.0752661i
$86$	15.0905	−	2.21411i	1.62725	−	0.238754i
$87$	−3.01679	+	3.01679i	−0.323433	+	0.323433i
$88$	−0.882887	+	2.43113i	−0.0941160	+	0.259159i
$89$	6.29488			0.667256			0.333628	−	0.942705i	$-0.391727\pi$
$89$	6.29488			0.667256			0.333628	+	0.942705i	$0.391727\pi$
$90$	6.13465	+	5.23774i	0.646649	+	0.552106i
$91$	0.167970	−	0.167970i	0.0176080	−	0.0176080i
$92$	−13.2386	−	7.13003i	−1.38022	−	0.743357i
$93$	0.597619			0.0619702
$94$	−12.1377	−	9.03167i	−1.25191	−	0.931546i
$95$	−2.19507	−	0.147242i	−0.225209	−	0.0151067i
$96$	2.52375	+	2.82910i	0.257579	+	0.288744i
$97$	4.21488	−	4.21488i	0.427957	−	0.427957i	−0.459975	−	0.887932i	$-0.652142\pi$
$97$	4.21488	−	4.21488i	0.427957	−	0.427957i	0.887932	+	0.459975i	$0.152142\pi$
$98$	0.205299	+	1.39923i	0.0207383	+	0.141344i
$99$	1.64942	−	1.64942i	0.165773	−	0.165773i
$100$	1.56761	+	9.87637i	0.156761	+	0.987637i
$101$	0.475532	+	0.475532i	0.0473172	+	0.0473172i	0.730370	−	0.683052i	$-0.239348\pi$
$101$	0.475532	+	0.475532i	0.0473172	+	0.0473172i	−0.683052	+	0.730370i	$0.739348\pi$
$102$	3.52574	+	2.62351i	0.349100	+	0.259766i
$103$	0.933945	+	0.933945i	0.0920243	+	0.0920243i	0.751620	−	0.659596i	$-0.229273\pi$
$103$	0.933945	+	0.933945i	0.0920243	+	0.0920243i	−0.659596	+	0.751620i	$0.729273\pi$
$104$	0.608725	−	0.284384i	0.0596904	−	0.0278862i
$105$	0.100298	−	1.49524i	0.00978811	−	0.145921i
$106$	1.84120	+	12.5489i	0.178834	+	1.21886i
$107$			6.16986i			0.596463i	0.954494	+	0.298231i	$0.0963967\pi$
$107$			6.16986i			0.596463i	−0.954494	+	0.298231i	$0.903603\pi$
$108$	−2.13730	−	7.12669i	−0.205662	−	0.685767i
$109$	11.6754	+	11.6754i	1.11830	+	1.11830i	0.991991	+	0.126305i	$0.0403120\pi$
$109$	11.6754	+	11.6754i	1.11830	+	1.11830i	0.126305	+	0.991991i	$0.459688\pi$
$110$	2.88282	−	0.227362i	0.274866	−	0.0216781i
$111$			3.99948i			0.379614i
$112$	−0.805128	+	3.91813i	−0.0760774	+	0.370229i
$113$	−10.0429	−	10.0429i	−0.944758	−	0.944758i	0.0537940	−	0.998552i	$-0.482869\pi$
$113$	−10.0429	−	10.0429i	−0.944758	−	0.944758i	−0.998552	+	0.0537940i	$0.982869\pi$
$114$	0.748121	+	0.556678i	0.0700680	+	0.0521377i
$115$	−1.12515	+	16.7737i	−0.104921	+	1.56415i
$116$	−11.2094	−	6.03715i	−1.04077	−	0.560535i
$117$	−0.605939			−0.0560191
$118$	7.93999	+	5.90816i	0.730936	+	0.543890i
$119$			4.63678i			0.425053i
$120$	1.71026	−	3.87833i	0.156125	−	0.354041i
$121$			10.1638i			0.923979i
$122$	−9.50703	+	12.7765i	−0.860726	+	1.15673i
$123$	−3.12051			−0.281367
$124$	0.512307	+	1.70825i	0.0460065	+	0.153406i
$125$	9.32449	−	6.16878i	0.834008	−	0.551752i
$126$	2.15352	−	2.89412i	0.191851	−	0.257829i
$127$	13.1989	+	13.1989i	1.17122	+	1.17122i	0.981920	+	0.189295i	$0.0606203\pi$
$127$	13.1989	+	13.1989i	1.17122	+	1.17122i	0.189295	+	0.981920i	$0.439380\pi$
$128$	−5.92333	+	9.63920i	−0.523553	+	0.851993i
$129$			7.22794i			0.636385i
$130$	−0.571284	−	0.487760i	−0.0501050	−	0.0427794i
$131$	8.16738	+	8.16738i	0.713587	+	0.713587i	0.967284	−	0.253697i	$-0.0816465\pi$
$131$	8.16738	+	8.16738i	0.713587	+	0.713587i	−0.253697	+	0.967284i	$0.581646\pi$
$132$	−1.07917	−	0.581217i	−0.0939295	−	0.0505884i
$133$			0.983870i			0.0853124i
$134$	−2.96500	+	0.435031i	−0.256137	+	0.0375810i
$135$	−6.26255	+	5.47520i	−0.538994	+	0.471230i
$136$	−4.47669	+	12.3271i	−0.383873	+	1.05704i
$137$	13.0505	+	13.0505i	1.11498	+	1.11498i	0.992467	+	0.122512i	$0.0390951\pi$
$137$	13.0505	+	13.0505i	1.11498	+	1.11498i	0.122512	+	0.992467i	$0.460905\pi$
$138$	4.25387	−	5.71679i	0.362114	−	0.486646i
$139$	4.03001	+	4.03001i	0.341821	+	0.341821i	0.857051	−	0.515231i	$-0.172294\pi$
$139$	4.03001	+	4.03001i	0.341821	+	0.341821i	−0.515231	+	0.857051i	$0.672294\pi$
$140$	4.36002	−	0.995093i	0.368489	−	0.0841007i
$141$	5.06977	−	5.06977i	0.426952	−	0.426952i
$142$	16.6045	−	2.43625i	1.39342	−	0.204445i
$143$	−0.153601	+	0.153601i	−0.0128448	+	0.0128448i
$144$	8.51942	−	5.61498i	0.709952	−	0.467915i
$145$	−0.952689	+	14.2026i	−0.0791166	+	1.17946i
$146$	−6.21181	+	8.34807i	−0.514093	+	0.690891i
$147$	−0.670195			−0.0552767
$148$	−11.4322	+	3.42853i	−0.939723	+	0.281824i
$149$	2.16490	−	2.16490i	0.177356	−	0.177356i	−0.612846	−	0.790202i	$-0.709976\pi$
$149$	2.16490	−	2.16490i	0.177356	−	0.177356i	0.790202	+	0.612846i	$0.209976\pi$
$150$	−4.73867	+	0.0555722i	−0.386910	+	0.00453745i
$151$	−1.82616			−0.148611			−0.0743054	−	0.997236i	$-0.523674\pi$
$151$	−1.82616			−0.148611			−0.0743054	+	0.997236i	$0.523674\pi$
$152$	−0.949902	+	2.61566i	−0.0770472	+	0.212158i
$153$	8.36343	−	8.36343i	0.676143	−	0.676143i
$154$	−0.187737	−	1.27954i	−0.0151283	−	0.103108i
$155$	1.50112	−	1.31239i	0.120573	−	0.105414i
$156$	0.0914646	+	0.304983i	0.00732303	+	0.0244182i
$157$		−	22.1094i		−	1.76453i	−0.470757	−	0.882263i	$-0.656019\pi$
$157$		−	22.1094i		−	1.76453i	0.470757	−	0.882263i	$-0.343981\pi$
$158$	0.188170	−	0.0276087i	0.0149700	−	0.00219643i
$159$	−6.01058			−0.476670
$160$	12.5520	+	1.56399i	0.992327	+	0.123644i
$161$	7.51828			0.592523
$162$	−7.21906	+	1.05920i	−0.567183	+	0.0832184i
$163$		−	6.71607i		−	0.526043i	−0.964790	−	0.263022i	$-0.915281\pi$
$163$		−	6.71607i		−	0.526043i	0.964790	−	0.263022i	$-0.0847191\pi$
$164$	−2.67504	−	8.91976i	−0.208886	−	0.696516i
$165$	−0.0917187	+	1.36734i	−0.00714029	+	0.106447i
$166$	0.537383	+	3.66259i	0.0417090	+	0.284272i
$167$	−14.9948	+	14.9948i	−1.16033	+	1.16033i	−0.175925	+	0.984404i	$0.556292\pi$
$167$	−14.9948	+	14.9948i	−1.16033	+	1.16033i	−0.984404	+	0.175925i	$0.943708\pi$
$168$	−1.78174	−	0.647056i	−0.137464	−	0.0499214i
$169$	−12.9436			−0.995659
$170$	14.6174	−	1.15284i	1.12110	−	0.0884189i
$171$	1.77462	−	1.77462i	0.135709	−	0.135709i
$172$	−20.6606	+	6.19612i	−1.57535	+	0.472450i
$173$	2.64406			0.201024			0.100512	−	0.994936i	$-0.467952\pi$
$173$	2.64406			0.201024			0.100512	+	0.994936i	$0.467952\pi$
$174$	3.60184	−	4.84053i	0.273055	−	0.366960i
$175$	−3.03167	−	3.97605i	−0.229173	−	0.300561i
$176$	0.736256	−	3.58297i	0.0554974	−	0.270077i
$177$	−3.31645	+	3.31645i	−0.249279	+	0.249279i
$178$	−8.80800	+	1.29233i	−0.660188	+	0.0968643i
$179$	1.89516	−	1.89516i	0.141651	−	0.141651i	−0.632725	−	0.774376i	$-0.718064\pi$
$179$	1.89516	−	1.89516i	0.141651	−	0.141651i	0.774376	+	0.632725i	$0.218064\pi$
$180$	−9.65910	−	6.06937i	−0.719947	−	0.452384i
$181$	−3.68616	−	3.68616i	−0.273990	−	0.273990i	0.556714	−	0.830704i	$-0.312062\pi$
$181$	−3.68616	−	3.68616i	−0.273990	−	0.273990i	−0.830704	+	0.556714i	$0.812062\pi$
$182$	−0.200545	+	0.269512i	−0.0148654	+	0.0199776i
$183$	−5.33661	−	5.33661i	−0.394493	−	0.394493i
$184$	19.9877	+	7.25871i	1.47351	+	0.535119i
$185$	8.78299	+	10.0460i	0.645739	+	0.738598i
$186$	−0.836209	+	0.122691i	−0.0613138	+	0.00899610i
$187$		−	4.24014i		−	0.310070i
$188$	18.8376	+	10.1456i	1.37388	+	0.739941i
$189$	2.63054	+	2.63054i	0.191343	+	0.191343i
$190$	3.10164	−	0.244619i	0.225017	−	0.0177466i
$191$		−	5.80442i		−	0.419993i	−0.977702	−	0.209997i	$-0.932655\pi$
$191$		−	5.80442i		−	0.419993i	0.977702	−	0.209997i	$-0.0673453\pi$
$192$	−4.11212	−	3.44045i	−0.296767	−	0.248293i
$193$	7.00472	+	7.00472i	0.504211	+	0.504211i	0.912744	−	0.408533i	$-0.133960\pi$
$193$	7.00472	+	7.00472i	0.504211	+	0.504211i	−0.408533	+	0.912744i	$0.633960\pi$
$194$	−5.03229	+	6.76291i	−0.361298	+	0.485549i
$195$	0.268002	−	0.234308i	0.0191920	−	0.0167791i
$196$	−0.574522	−	1.91570i	−0.0410373	−	0.136836i
$197$	15.4945			1.10394			0.551969	−	0.833865i	$-0.313877\pi$
$197$	15.4945			1.10394			0.551969	+	0.833865i	$0.313877\pi$
$198$	−1.96930	+	2.64655i	−0.139952	+	0.188082i
$199$		−	22.0804i		−	1.56524i	−0.622502	−	0.782618i	$-0.713884\pi$
$199$		−	22.0804i		−	1.56524i	0.622502	−	0.782618i	$-0.286116\pi$
$200$	−4.22105	−	13.4975i	−0.298473	−	0.954418i
$201$		−	1.42015i		−	0.100170i
$202$	−0.763007	−	0.567754i	−0.0536850	−	0.0399471i
$203$	6.36588			0.446797
$204$	−5.47194	−	2.94707i	−0.383112	−	0.206336i
$205$	−7.83819	+	6.85275i	−0.547443	+	0.478617i
$206$	−1.49854	−	1.11507i	−0.104408	−	0.0776905i
$207$	−13.5608	−	13.5608i	−0.942543	−	0.942543i
$208$	−0.793364	+	0.522890i	−0.0550099	+	0.0362559i
$209$		−	0.899709i		−	0.0622342i
$210$	0.166630	+	2.11278i	0.0114986	+	0.145796i
$211$	4.11458	+	4.11458i	0.283260	+	0.283260i	0.834408	−	0.551148i	$-0.185810\pi$
$211$	4.11458	+	4.11458i	0.283260	+	0.283260i	−0.551148	+	0.834408i	$0.685810\pi$
$212$	−5.15255	−	17.1808i	−0.353878	−	1.17998i
$213$			7.95309i			0.544937i
$214$	−1.26666	−	8.63307i	−0.0865874	−	0.590145i
$215$	15.8728	+	18.1554i	1.08252	+	1.23819i
$216$	4.45368	+	9.53312i	0.303035	+	0.648647i
$217$	−0.630534	−	0.630534i	−0.0428035	−	0.0428035i
$218$	−18.7335	−	13.9396i	−1.26879	−	0.944110i
$219$	−3.48689	−	3.48689i	−0.235622	−	0.235622i
$220$	−3.98706	+	0.909972i	−0.268808	+	0.0613503i
$221$	−0.778838	+	0.778838i	−0.0523903	+	0.0523903i
$222$	−0.821088	−	5.59620i	−0.0551078	−	0.375592i
$223$	−6.05558	+	6.05558i	−0.405512	+	0.405512i	−0.880170	−	0.474658i	$-0.842572\pi$
$223$	−6.05558	+	6.05558i	−0.405512	+	0.405512i	0.474658	+	0.880170i	$0.342572\pi$
$224$	0.322173	−	5.64767i	0.0215261	−	0.377351i
$225$	−1.70340	+	12.6399i	−0.113560	+	0.842662i
$226$	16.1142	+	11.9906i	1.07190	+	0.797601i
$227$	−5.44592			−0.361458			−0.180729	−	0.983533i	$-0.557846\pi$
$227$	−5.44592			−0.361458			−0.180729	+	0.983533i	$0.557846\pi$
$228$	−1.16108	−	0.625334i	−0.0768945	−	0.0414137i
$229$	−20.7193	+	20.7193i	−1.36917	+	1.36917i	−0.507546	+	0.861625i	$0.669447\pi$
$229$	−20.7193	+	20.7193i	−1.36917	+	1.36917i	−0.861625	+	0.507546i	$0.830553\pi$
$230$	−1.86927	−	23.7013i	−0.123256	−	1.56282i
$231$	0.612865			0.0403236
$232$	16.9240	+	6.14610i	1.11111	+	0.403511i
$233$	1.92905	−	1.92905i	0.126376	−	0.126376i	−0.641090	−	0.767466i	$-0.721517\pi$
$233$	1.92905	−	1.92905i	0.126376	−	0.126376i	0.767466	+	0.641090i	$0.221517\pi$
$234$	0.847849	−	0.124398i	0.0554256	−	0.00813218i
$235$	1.60101	−	23.8678i	0.104439	−	1.55697i
$236$	−12.3228	−	6.63682i	−0.802148	−	0.432020i
$237$			0.0901283i			0.00585446i
$238$	−0.951925	−	6.48793i	−0.0617041	−	0.420550i
$239$	1.59720			0.103314			0.0516572	−	0.998665i	$-0.483550\pi$
$239$	1.59720			0.103314			0.0516572	+	0.998665i	$0.483550\pi$
$240$	−1.59684	+	5.77780i	−0.103076	+	0.372955i
$241$	5.90184			0.380171			0.190086	−	0.981768i	$-0.439123\pi$
$241$	5.90184			0.380171			0.190086	+	0.981768i	$0.439123\pi$
$242$	−2.08661	−	14.2215i	−0.134132	−	0.914191i
$243$		−	14.6182i		−	0.937755i
$244$	10.6795	−	19.8291i	0.683687	−	1.26943i
$245$	−1.68342	+	1.47177i	−0.107550	+	0.0940280i
$246$	4.36632	−	0.640637i	0.278386	−	0.0408455i
$247$	−0.165260	+	0.165260i	−0.0105153	+	0.0105153i
$248$	−1.06754	−	2.28507i	−0.0677888	−	0.145102i
$249$	−1.75428			−0.111173
$250$	−11.7807	+	10.5459i	−0.745076	+	0.666979i
$251$	−12.3581	+	12.3581i	−0.780034	+	0.780034i	−0.979836	−	0.199802i	$-0.935970\pi$
$251$	−12.3581	+	12.3581i	−0.780034	+	0.780034i	0.199802	+	0.979836i	$0.435970\pi$
$252$	−2.41911	+	4.49166i	−0.152390	+	0.282948i
$253$	−6.87516			−0.432237
$254$	−21.1781	−	15.7586i	−1.32883	−	0.988785i
$255$	−0.465061	+	6.93310i	−0.0291232	+	0.434168i
$256$	6.30920	−	14.7035i	0.394325	−	0.918971i
$257$	19.1648	−	19.1648i	1.19547	−	1.19547i	0.219956	−	0.975510i	$-0.429409\pi$
$257$	19.1648	−	19.1648i	1.19547	−	1.19547i	0.975510	−	0.219956i	$-0.0705914\pi$
$258$	−1.48389	−	10.1136i	−0.0923828	−	0.629644i
$259$	4.21976	−	4.21976i	0.262203	−	0.262203i
$260$	0.899496	+	0.565206i	0.0557844	+	0.0350526i
$261$	−11.4822	−	11.4822i	−0.710733	−	0.710733i
$262$	−13.1048	−	9.75131i	−0.809618	−	0.602438i
$263$	20.2717	+	20.2717i	1.25001	+	1.25001i	0.955717	+	0.294289i	$0.0950827\pi$
$263$	20.2717	+	20.2717i	1.25001	+	1.25001i	0.294289	+	0.955717i	$0.404917\pi$
$264$	1.62933	+	0.591706i	0.100278	+	0.0364170i
$265$	−15.0976	+	13.1995i	−0.927436	+	0.810836i
$266$	−0.201987	−	1.37666i	−0.0123846	−	0.0844087i
$267$		−	4.21879i		−	0.258186i
$268$	4.05941	−	1.21742i	0.247968	−	0.0743658i
$269$	−6.96087	−	6.96087i	−0.424412	−	0.424412i	0.462308	−	0.886720i	$-0.347022\pi$
$269$	−6.96087	−	6.96087i	−0.424412	−	0.424412i	−0.886720	+	0.462308i	$0.847022\pi$
$270$	7.63871	−	8.94677i	0.464877	−	0.544483i
$271$		−	22.6311i		−	1.37474i	−0.726306	−	0.687372i	$-0.758764\pi$
$271$		−	22.6311i		−	1.37474i	0.726306	−	0.687372i	$-0.241236\pi$
$272$	3.73320	−	18.1675i	0.226358	−	1.10157i
$273$	−0.112572	−	0.112572i	−0.00681319	−	0.00681319i
$274$	−20.9399	−	15.5814i	−1.26503	−	0.941309i
$275$	2.77234	+	3.63594i	0.167178	+	0.219255i
$276$	−4.77851	+	8.87244i	−0.287632	+	0.534058i
$277$	6.60010			0.396562			0.198281	−	0.980145i	$-0.436464\pi$
$277$	6.60010			0.396562			0.198281	+	0.980145i	$0.436464\pi$
$278$	−6.46627	−	4.81156i	−0.387821	−	0.288578i
$279$			2.27461i			0.136177i
$280$	−5.89639	+	2.28747i	−0.352377	+	0.136703i
$281$			0.364224i			0.0217278i	0.999941	+	0.0108639i	$0.00345815\pi$
$281$			0.364224i			0.0217278i	−0.999941	+	0.0108639i	$0.996542\pi$
$282$	−6.05298	+	8.13461i	−0.360449	+	0.484409i
$283$	21.0825			1.25323			0.626613	−	0.779331i	$-0.284441\pi$
$283$	21.0825			1.25323			0.626613	+	0.779331i	$0.284441\pi$
$284$	−22.7334	+	6.81776i	−1.34898	+	0.404559i
$285$	−0.0986805	+	1.47112i	−0.00584533	+	0.0871418i
$286$	0.183390	−	0.246458i	0.0108441	−	0.0145734i
$287$	3.29238	+	3.29238i	0.194343	+	0.194343i
$288$	−10.7679	+	9.60569i	−0.634505	+	0.566021i
$289$		−	4.49972i		−	0.264689i
$290$	−1.58275	−	20.0684i	−0.0929422	−	1.17846i
$291$	−2.82479	−	2.82479i	−0.165592	−	0.165592i
$292$	6.97792	−	12.9562i	0.408352	−	0.758203i
$293$		−	5.54977i		−	0.324221i	−0.986773	−	0.162110i	$-0.948170\pi$
$293$		−	5.54977i		−	0.324221i	0.986773	−	0.162110i	$-0.0518301\pi$
$294$	0.937758	−	0.137590i	0.0546912	−	0.00802442i
$295$	−1.04732	+	15.6134i	−0.0609773	+	0.909046i
$296$	15.2925	−	7.14434i	0.888857	−	0.415256i
$297$	−2.40552	−	2.40552i	−0.139582	−	0.139582i
$298$	−2.58475	+	3.47365i	−0.149730	+	0.201223i
$299$	1.26284	+	1.26284i	0.0730320	+	0.0730320i
$300$	6.61909	−	1.05060i	0.382153	−	0.0606565i
$301$	7.62603	−	7.62603i	0.439557	−	0.439557i
$302$	2.55522	−	0.374908i	0.147037	−	0.0215736i
$303$	0.318699	−	0.318699i	0.0183088	−	0.0183088i
$304$	0.792141	−	3.85493i	0.0454324	−	0.221096i
$305$	−25.1240	−	1.68528i	−1.43860	−	0.0964988i
$306$	−9.98538	+	13.4194i	−0.570826	+	0.767135i
$307$	29.5084			1.68413			0.842067	−	0.539374i	$-0.181339\pi$
$307$	29.5084			1.68413			0.842067	+	0.539374i	$0.181339\pi$
$308$	0.525376	+	1.75183i	0.0299361	+	0.0998200i
$309$	0.625925	−	0.625925i	0.0356076	−	0.0356076i
$310$	−1.83098	+	2.14452i	−0.103993	+	0.121801i
$311$	−18.3324			−1.03954			−0.519768	−	0.854308i	$-0.673982\pi$
$311$	−18.3324			−1.03954			−0.519768	+	0.854308i	$0.673982\pi$
$312$	−0.190593	−	0.407964i	−0.0107902	−	0.0230964i
$313$	−2.36215	+	2.36215i	−0.133517	+	0.133517i	−0.770707	−	0.637190i	$-0.780097\pi$
$313$	−2.36215	+	2.36215i	−0.133517	+	0.133517i	0.637190	+	0.770707i	$0.280097\pi$
$314$	4.53904	+	30.9363i	0.256153	+	1.74583i
$315$	5.69106	+	0.381747i	0.320655	+	0.0215090i
$316$	−0.257626	+	0.0772621i	−0.0144926	+	0.00434633i
$317$			3.17455i			0.178300i	0.996018	+	0.0891502i	$0.0284151\pi$
$317$			3.17455i			0.178300i	−0.996018	+	0.0891502i	$0.971585\pi$
$318$	8.41020	−	1.23396i	0.471621	−	0.0691973i
$319$	−5.82134			−0.325932
$320$	−17.8843	+	0.388532i	−0.999764	+	0.0217196i
$321$	4.13501			0.230794
$322$	−10.5198	+	1.54349i	−0.586247	+	0.0860155i
$323$		−	4.56199i		−	0.253836i
$324$	9.88369	−	2.96413i	0.549094	−	0.164674i
$325$	0.158627	−	1.17708i	0.00879907	−	0.0652929i
$326$	1.37880	+	9.39735i	0.0763648	+	0.520471i
$327$	7.82476	−	7.82476i	0.432710	−	0.432710i
$328$	5.57422	+	11.9316i	0.307785	+	0.658814i
$329$	−10.6980			−0.589800
$330$	−0.152377	−	1.93205i	−0.00838806	−	0.106356i
$331$	11.5366	−	11.5366i	0.634107	−	0.634107i	−0.314989	−	0.949095i	$-0.602001\pi$
$331$	11.5366	−	11.5366i	0.634107	−	0.634107i	0.949095	+	0.314989i	$0.102001\pi$
$332$	−1.50385	−	5.01449i	−0.0825344	−	0.275206i
$333$	−15.2225			−0.834187
$334$	17.9027	−	24.0596i	0.979595	−	1.31648i
$335$	−3.11871	−	3.56719i	−0.170393	−	0.194896i
$336$	2.62591	+	0.539592i	0.143255	+	0.0294372i
$337$	4.48987	−	4.48987i	0.244579	−	0.244579i	−0.574163	−	0.818741i	$-0.694672\pi$
$337$	4.48987	−	4.48987i	0.244579	−	0.244579i	0.818741	+	0.574163i	$0.194672\pi$
$338$	18.1111	−	2.65730i	0.985112	−	0.144538i
$339$	−6.73071	+	6.73071i	−0.365562	+	0.365562i
$340$	−20.2165	+	4.61403i	−1.09639	+	0.250231i
$341$	0.576598	+	0.576598i	0.0312245	+	0.0312245i
$342$	−2.11878	+	2.84744i	−0.114571	+	0.153972i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	27.6369	−	12.9114i	1.49008	−	0.696137i
$345$	11.2416	+	0.754071i	0.605229	+	0.0405978i
$346$	−3.69966	+	0.542823i	−0.198895	+	0.0291823i
$347$		−	17.4590i		−	0.937246i	−0.883398	−	0.468623i	$-0.844750\pi$
$347$		−	17.4590i		−	0.937246i	0.883398	−	0.468623i	$-0.155250\pi$
$348$	−4.04606	+	7.51248i	−0.216892	+	0.402711i
$349$	17.8737	+	17.8737i	0.956755	+	0.956755i	0.999103	−	0.0423483i	$-0.0134839\pi$
$349$	17.8737	+	17.8737i	0.956755	+	0.956755i	−0.0423483	+	0.999103i	$0.513484\pi$
$350$	5.05829	+	4.94102i	0.270377	+	0.264109i
$351$			0.883701i			0.0471684i
$352$	−0.294614	+	5.16456i	−0.0157030	+	0.275272i
$353$	19.1456	+	19.1456i	1.01902	+	1.01902i	0.999816	+	0.0191994i	$0.00611175\pi$
$353$	19.1456	+	19.1456i	1.01902	+	1.01902i	0.0191994	+	0.999816i	$0.493888\pi$
$354$	3.95962	−	5.32134i	0.210451	−	0.282826i
$355$	17.4653	+	19.9768i	0.926961	+	1.06026i
$356$	12.0591	−	3.61654i	0.639133	−	0.191676i
$357$	3.10754			0.164469
$358$	−2.26270	+	3.04085i	−0.119587	+	0.160714i
$359$		−	3.20756i		−	0.169288i	−0.996411	−	0.0846442i	$-0.973025\pi$
$359$		−	3.20756i		−	0.169288i	0.996411	−	0.0846442i	$-0.0269754\pi$
$360$	14.7614	+	6.50947i	0.777993	+	0.343079i
$361$			18.0320i			0.949053i
$362$	5.91456	+	4.40103i	0.310862	+	0.231313i
$363$	6.81170			0.357522
$364$	0.225278	−	0.418282i	0.0118078	−	0.0219239i
$365$	−16.4158	−	1.10115i	−0.859244	−	0.0576367i
$366$	8.56275	+	6.37156i	0.447582	+	0.333047i
$367$	19.6218	+	19.6218i	1.02425	+	1.02425i	0.999699	+	0.0245524i	$0.00781605\pi$
$367$	19.6218	+	19.6218i	1.02425	+	1.02425i	0.0245524	+	0.999699i	$0.492184\pi$
$368$	−29.4576	−	6.05318i	−1.53558	−	0.315544i
$369$		−	11.8770i		−	0.618293i
$370$	−14.3519	−	12.2536i	−0.746119	−	0.637033i
$371$	6.34163	+	6.34163i	0.329241	+	0.329241i
$372$	1.14486	−	0.343345i	0.0593583	−	0.0178016i
$373$		−	7.56437i		−	0.391668i	−0.980637	−	0.195834i	$-0.937259\pi$
$373$		−	7.56437i		−	0.391668i	0.980637	−	0.195834i	$-0.0627414\pi$
$374$	0.870496	+	5.93295i	0.0450123	+	0.306785i
$375$	−4.13428	−	6.24922i	−0.213493	−	0.322709i
$376$	−28.4411	−	10.3287i	−1.46674	−	0.532659i
$377$	1.06927	+	1.06927i	0.0550705	+	0.0550705i
$378$	−4.22078	−	3.14069i	−0.217094	−	0.161540i
$379$	−11.5791	−	11.5791i	−0.594780	−	0.594780i	0.344139	−	0.938919i	$-0.388171\pi$
$379$	−11.5791	−	11.5791i	−0.594780	−	0.594780i	−0.938919	+	0.344139i	$0.888171\pi$
$380$	−4.28970	+	0.979042i	−0.220057	+	0.0502238i
$381$	8.84585	−	8.84585i	0.453187	−	0.453187i
$382$	1.19164	+	8.12174i	0.0609696	+	0.415544i
$383$	3.47914	−	3.47914i	0.177776	−	0.177776i	−0.612610	−	0.790386i	$-0.709880\pi$
$383$	3.47914	−	3.47914i	0.177776	−	0.177776i	0.790386	+	0.612610i	$0.209880\pi$
$384$	6.46014	+	3.96978i	0.329668	+	0.202582i
$385$	1.53941	−	1.34587i	0.0784558	−	0.0685921i
$386$	−11.2393	−	8.36317i	−0.572065	−	0.425674i
$387$	−27.5104			−1.39843
$388$	5.65293	−	10.4960i	0.286984	−	0.532854i
$389$	−9.43342	+	9.43342i	−0.478294	+	0.478294i	−0.904586	−	0.426292i	$-0.859820\pi$
$389$	−9.43342	+	9.43342i	−0.478294	+	0.478294i	0.426292	+	0.904586i	$0.359820\pi$
$390$	−0.326894	+	0.382872i	−0.0165529	+	0.0193875i
$391$	−34.8606			−1.76298
$392$	1.19718	+	2.56257i	0.0604668	+	0.129429i
$393$	5.47373	−	5.47373i	0.276113	−	0.276113i
$394$	−21.6804	+	3.18100i	−1.09224	+	0.160257i
$395$	0.197925	+	0.226387i	0.00995869	+	0.0113908i
$396$	2.21218	−	4.10744i	0.111166	−	0.206407i
$397$			12.6111i			0.632933i	0.948604	+	0.316466i	$0.102496\pi$
$397$			12.6111i			0.632933i	−0.948604	+	0.316466i	$0.897504\pi$
$398$	4.53308	+	30.8956i	0.227223	+	1.54866i
$399$	0.659384			0.0330105
$400$	8.67725	+	18.0196i	0.433863	+	0.900979i
$401$	−25.7324			−1.28501			−0.642507	−	0.766280i	$-0.722106\pi$
$401$	−25.7324			−1.28501			−0.642507	+	0.766280i	$0.722106\pi$
$402$	0.291556	+	1.98712i	0.0145415	+	0.0991088i
$403$		−	0.211821i		−	0.0105516i
$404$	1.18418	+	0.637776i	0.0589153	+	0.0317306i
$405$	−7.59331	−	8.68525i	−0.377314	−	0.431573i
$406$	−8.90735	+	1.30691i	−0.442065	+	0.0648608i
$407$	−3.85879	+	3.85879i	−0.191273	+	0.191273i
$408$	8.26154	+	3.00025i	0.409007	+	0.148535i
$409$	6.63937			0.328295			0.164148	−	0.986436i	$-0.447513\pi$
$409$	6.63937			0.328295			0.164148	+	0.986436i	$0.447513\pi$
$410$	9.56060	−	11.1978i	0.472164	−	0.553018i
$411$	8.74637	−	8.74637i	0.431427	−	0.431427i
$412$	2.32573	+	1.25259i	0.114581	+	0.0617107i
$413$	6.99821			0.344359
$414$	21.7588	+	16.1907i	1.06939	+	0.795732i
$415$	−4.40645	+	3.85246i	−0.216304	+	0.189110i
$416$	1.00275	−	0.894522i	0.0491640	−	0.0438575i
$417$	2.70089	−	2.70089i	0.132263	−	0.132263i
$418$	0.184709	+	1.25890i	0.00903442	+	0.0615749i
$419$	−8.08017	+	8.08017i	−0.394742	+	0.394742i	−0.876374	−	0.481632i	$-0.840044\pi$
$419$	−8.08017	+	8.08017i	−0.394742	+	0.394742i	0.481632	+	0.876374i	$0.340044\pi$
$420$	−0.666906	−	2.92206i	−0.0325417	−	0.142582i
$421$	−16.3305	−	16.3305i	−0.795902	−	0.795902i	0.186545	−	0.982446i	$-0.440271\pi$
$421$	−16.3305	−	16.3305i	−0.795902	−	0.795902i	−0.982446	+	0.186545i	$0.940271\pi$
$422$	−6.60198	−	4.91254i	−0.321379	−	0.239139i
$423$	19.2962	+	19.2962i	0.938211	+	0.938211i
$424$	10.7368	+	22.9822i	0.521426	+	1.11611i
$425$	14.0572	+	18.4361i	0.681873	+	0.894281i
$426$	−1.63276	−	11.1282i	−0.0791075	−	0.539164i
$427$			11.2611i			0.544961i
$428$	3.54472	+	11.8196i	0.171340	+	0.571323i
$429$	0.102943	+	0.102943i	0.00497012	+	0.00497012i
$430$	−25.9370	−	22.1449i	−1.25080	−	1.06792i
$431$			2.86113i			0.137816i	0.997623	+	0.0689079i	$0.0219515\pi$
$431$			2.86113i			0.137816i	−0.997623	+	0.0689079i	$0.978049\pi$
$432$	−8.18888	−	12.4247i	−0.393988	−	0.597784i
$433$	−23.5560	−	23.5560i	−1.13203	−	1.13203i	−0.989840	−	0.142187i	$-0.954586\pi$
$433$	−23.5560	−	23.5560i	−1.13203	−	1.13203i	−0.142187	−	0.989840i	$-0.545414\pi$
$434$	1.01171	+	0.752816i	0.0485637	+	0.0361363i
$435$	9.51853	+	0.638487i	0.456378	+	0.0306131i
$436$	29.0743	+	15.6588i	1.39241	+	0.749921i
$437$	−7.39701			−0.353847
$438$	5.59483	+	4.16312i	0.267331	+	0.198922i
$439$		−	8.07806i		−	0.385545i	−0.981244	−	0.192772i	$-0.938252\pi$
$439$		−	8.07806i		−	0.385545i	0.981244	−	0.192772i	$-0.0617479\pi$
$440$	5.39201	−	2.09180i	0.257054	−	0.0997227i
$441$		−	2.55084i		−	0.121469i
$442$	0.929881	−	1.24967i	0.0442299	−	0.0594407i
$443$	−5.71739			−0.271641			−0.135821	−	0.990733i	$-0.543367\pi$
$443$	−5.71739			−0.271641			−0.135821	+	0.990733i	$0.543367\pi$
$444$	2.29779	+	7.66182i	0.109048	+	0.363614i
$445$	−9.26462	−	10.5969i	−0.439185	−	0.502341i
$446$	7.22997	−	9.71637i	0.342349	−	0.460084i
$447$	−1.45090	−	1.45090i	−0.0686254	−	0.0686254i
$448$	0.708665	+	7.96855i	0.0334813	+	0.376479i
$449$			5.72789i			0.270316i	0.990824	+	0.135158i	$0.0431542\pi$
$449$			5.72789i			0.270316i	−0.990824	+	0.135158i	$0.956846\pi$
$450$	−0.211514	−	18.0359i	−0.00997088	−	0.850221i
$451$	−3.01074	−	3.01074i	−0.141770	−	0.141770i
$452$	−25.0091	−	13.4694i	−1.17633	−	0.633547i
$453$			1.22388i			0.0575030i
$454$	7.62011	−	1.11804i	0.357629	−	0.0524722i
$455$	−0.529975	−	0.0355499i	−0.0248456	−	0.00166660i
$456$	1.75300	+	0.636619i	0.0820919	+	0.0298124i
$457$	−0.428797	−	0.428797i	−0.0200583	−	0.0200583i	0.697007	−	0.717065i	$-0.254515\pi$
$457$	−0.428797	−	0.428797i	−0.0200583	−	0.0200583i	−0.717065	+	0.697007i	$0.754515\pi$
$458$	24.7375	−	33.2448i	1.15591	−	1.55343i
$459$	−12.1972	−	12.1972i	−0.569318	−	0.569318i
$460$	7.48139	+	32.7799i	0.348821	+	1.52837i
$461$	−18.2257	+	18.2257i	−0.848855	+	0.848855i	−0.989990	−	0.141135i	$-0.954925\pi$
$461$	−18.2257	+	18.2257i	−0.848855	+	0.848855i	0.141135	+	0.989990i	$0.454925\pi$
$462$	−0.857541	+	0.125820i	−0.0398964	+	0.00585370i
$463$	3.55354	−	3.55354i	0.165147	−	0.165147i	−0.619695	−	0.784842i	$-0.712744\pi$
$463$	3.55354	−	3.55354i	0.165147	−	0.165147i	0.784842	+	0.619695i	$0.212744\pi$
$464$	−24.9424	−	5.12535i	−1.15792	−	0.237938i
$465$	−0.879559	−	1.00604i	−0.0407886	−	0.0466541i
$466$	−2.30315	+	3.09521i	−0.106692	+	0.143383i
$467$	0.912671			0.0422334			0.0211167	−	0.999777i	$-0.493278\pi$
$467$	0.912671			0.0422334			0.0211167	+	0.999777i	$0.493278\pi$
$468$	−1.16080	+	0.348125i	−0.0536580	+	0.0160921i
$469$	−1.49837	+	1.49837i	−0.0691883	+	0.0691883i
$470$	2.65984	+	33.7253i	0.122689	+	1.55563i
$471$	−14.8176			−0.682760
$472$	18.6050	+	6.75659i	0.856367	+	0.310997i
$473$	−6.97369	+	6.97369i	−0.320651	+	0.320651i
$474$	−0.0185032	−	0.126110i	−0.000849881	−	0.00579245i
$475$	2.98277	+	3.91192i	0.136859	+	0.179491i
$476$	2.66393	+	8.88270i	0.122101	+	0.407138i
$477$		−	22.8770i		−	1.04746i
$478$	−2.23486	+	0.327903i	−0.102220	+	0.0149979i
$479$	37.5934			1.71768			0.858842	−	0.512240i	$-0.171184\pi$
$479$	37.5934			1.71768			0.858842	+	0.512240i	$0.171184\pi$
$480$	1.04818	−	8.41232i	0.0478426	−	0.383968i
$481$	1.41758			0.0646361
$482$	−8.25805	+	1.21164i	−0.376144	+	0.0551887i
$483$		−	5.03871i		−	0.229269i
$484$	5.83930	+	19.4708i	0.265423	+	0.885035i
$485$	−13.2987	−	0.892058i	−0.603865	−	0.0405063i
$486$	3.00109	+	20.4542i	0.136132	+	0.927822i
$487$	18.2469	−	18.2469i	0.826848	−	0.826848i	−0.160231	−	0.987079i	$-0.551224\pi$
$487$	18.2469	−	18.2469i	0.826848	−	0.826848i	0.987079	+	0.160231i	$0.0512240\pi$
$488$	−10.8723	+	29.9380i	−0.492164	+	1.35523i
$489$	−4.50108			−0.203546
$490$	2.05334	−	2.40495i	0.0927604	−	0.108645i
$491$	−9.60974	+	9.60974i	−0.433681	+	0.433681i	−0.889879	−	0.456197i	$-0.849211\pi$
$491$	−9.60974	+	9.60974i	−0.433681	+	0.433681i	0.456197	+	0.889879i	$0.349211\pi$
$492$	−5.97797	+	1.79280i	−0.269508	+	0.0808256i
$493$	−29.5172			−1.32939
$494$	0.197310	−	0.265165i	0.00887739	−	0.0119304i
$495$	−5.20424	−	0.349092i	−0.233913	−	0.0156905i
$496$	1.96286	+	2.97818i	0.0881349	+	0.133724i
$497$	8.39113	−	8.39113i	0.376393	−	0.376393i
$498$	2.45465	−	0.360151i	0.109995	−	0.0161388i
$499$	19.6872	−	19.6872i	0.881321	−	0.881321i	−0.112348	−	0.993669i	$-0.535837\pi$
$499$	19.6872	−	19.6872i	0.881321	−	0.881321i	0.993669	+	0.112348i	$0.0358371\pi$
$500$	14.3189	−	17.1747i	0.640360	−	0.768075i
$501$	10.0494	+	10.0494i	0.448974	+	0.448974i
$502$	14.7547	−	19.8289i	0.658535	−	0.885007i
$503$	22.7324	+	22.7324i	1.01359	+	1.01359i	0.999906	+	0.0136822i	$0.00435530\pi$
$503$	22.7324	+	22.7324i	1.01359	+	1.01359i	0.0136822	+	0.999906i	$0.495645\pi$
$504$	2.46277	−	6.78152i	0.109701	−	0.302073i
$505$	0.100644	−	1.50039i	0.00447860	−	0.0667667i
$506$	9.61994	−	1.41146i	0.427659	−	0.0627471i
$507$			8.67471i			0.385257i
$508$	32.8683	+	17.7022i	1.45830	+	0.785407i
$509$	28.8900	+	28.8900i	1.28053	+	1.28053i	0.940368	+	0.340158i	$0.110481\pi$
$509$	28.8900	+	28.8900i	1.28053	+	1.28053i	0.340158	+	0.940368i	$0.389519\pi$
$510$	−0.772628	−	9.79650i	−0.0342125	−	0.433796i
$511$			7.35788i			0.325494i
$512$	−5.80942	+	21.8689i	−0.256742	+	0.966480i
$513$	−2.58811	−	2.58811i	−0.114268	−	0.114268i
$514$	−22.8815	+	30.7505i	−1.00926	+	1.35635i
$515$	0.197665	−	2.94677i	0.00871014	−	0.129850i
$516$	4.15261	+	13.8466i	0.182808	+	0.609563i
$517$	9.78288			0.430251
$518$	−5.03811	+	6.77073i	−0.221362	+	0.297489i
$519$		−	1.77204i		−	0.0777838i
$520$	−1.37464	−	0.606189i	−0.0602820	−	0.0265831i
$521$			8.18880i			0.358758i	0.983780	+	0.179379i	$0.0574088\pi$
$521$			8.18880i			0.358758i	−0.983780	+	0.179379i	$0.942591\pi$
$522$	18.4236	+	13.7090i	0.806380	+	0.600029i
$523$	−4.18582			−0.183033			−0.0915166	−	0.995804i	$-0.529171\pi$
$523$	−4.18582			−0.183033			−0.0915166	+	0.995804i	$0.529171\pi$
$524$	20.3386	+	10.9540i	0.888497	+	0.478526i
$525$	−2.66473	+	2.03181i	−0.116298	+	0.0886754i
$526$	−32.5265	−	24.2030i	−1.41822	−	1.05530i
$527$	2.92365	+	2.92365i	0.127356	+	0.127356i
$528$	−2.40129	−	0.493435i	−0.104503	−	0.0214740i
$529$			33.5245i			1.45759i
$530$	18.4152	−	21.5686i	0.799904	−	0.936881i
$531$	−12.6228	−	12.6228i	−0.547782	−	0.547782i
$532$	0.565255	+	1.88480i	0.0245069	+	0.0817167i
$533$			1.10604i			0.0479078i
$534$	0.866113	+	5.90308i	0.0374804	+	0.255451i
$535$	10.3864	−	9.08062i	0.449045	−	0.392590i
$536$	−5.43012	+	2.53685i	−0.234546	+	0.109575i
$537$	−1.27013	−	1.27013i	−0.0548100	−	0.0548100i
$538$	11.1689	+	8.31082i	0.481527	+	0.358305i
$539$	−0.646620	−	0.646620i	−0.0278519	−	0.0278519i
$540$	−8.85157	+	14.0868i	−0.380911	+	0.606201i
$541$	−1.19461	+	1.19461i	−0.0513603	+	0.0513603i	−0.732320	−	0.680960i	$-0.761563\pi$
$541$	−1.19461	+	1.19461i	−0.0513603	+	0.0513603i	0.680960	+	0.732320i	$0.261563\pi$
$542$	4.64614	+	31.6662i	0.199569	+	1.36018i
$543$	−2.47044	+	2.47044i	−0.106017	+	0.106017i
$544$	−1.49385	+	26.1870i	−0.0640481	+	1.12276i
$545$	2.47103	−	36.8380i	0.105847	−	1.57796i
$546$	0.180626	+	0.134404i	0.00773007	+	0.00575196i
$547$	−28.0595			−1.19974			−0.599870	−	0.800098i	$-0.704781\pi$
$547$	−28.0595			−1.19974			−0.599870	+	0.800098i	$0.704781\pi$
$548$	32.4987	+	17.5031i	1.38828	+	0.747696i
$549$	20.3118	−	20.3118i	0.866884	−	0.866884i
$550$	−4.62560	−	4.51836i	−0.197236	−	0.192664i
$551$	−6.26320			−0.266821
$552$	4.86475	−	13.3956i	0.207057	−	0.570156i
$553$	0.0950923	−	0.0950923i	0.00404374	−	0.00404374i
$554$	−9.23508	+	1.35499i	−0.392361	+	0.0575681i
$555$	6.73278	−	5.88631i	0.285791	−	0.249860i
$556$	10.0356	+	5.40498i	0.425606	+	0.229222i
$557$			45.7677i			1.93924i	0.244621	+	0.969619i	$0.421337\pi$
$557$			45.7677i			1.93924i	−0.244621	+	0.969619i	$0.578663\pi$
$558$	−0.466974	−	3.18271i	−0.0197686	−	0.134735i
$559$	2.56188			0.108356
$560$	7.78081	−	4.41123i	0.328799	−	0.186409i
$561$	−2.84172			−0.119978
$562$	−0.0747747	−	0.509634i	−0.00315418	−	0.0214976i
$563$			11.5402i			0.486361i	0.969981	+	0.243180i	$0.0781907\pi$
$563$			11.5402i			0.486361i	−0.969981	+	0.243180i	$0.921809\pi$
$564$	6.79950	−	12.6249i	0.286310	−	0.531604i
$565$	−2.12553	+	31.6873i	−0.0894218	+	1.33309i
$566$	−29.4993	+	4.32821i	−1.23995	+	0.181928i
$567$	−3.64817	+	3.64817i	−0.153209	+	0.153209i
$568$	30.4096	−	14.2068i	1.27596	−	0.596102i
$569$	−13.2739			−0.556469			−0.278234	−	0.960513i	$-0.589749\pi$
$569$	−13.2739			−0.556469			−0.278234	+	0.960513i	$0.589749\pi$
$570$	−0.163943	−	2.07870i	−0.00686680	−	0.0870672i
$571$	31.0625	−	31.0625i	1.29993	−	1.29993i	0.371488	−	0.928438i	$-0.378848\pi$
$571$	31.0625	−	31.0625i	1.29993	−	1.29993i	0.928438	−	0.371488i	$-0.121152\pi$
$572$	−0.206007	+	0.382502i	−0.00861360	+	0.0159932i
$573$	−3.89009			−0.162511
$574$	−5.28272	−	3.93088i	−0.220497	−	0.164072i
$575$	29.8931	−	22.7929i	1.24663	−	0.950531i
$576$	13.0948	−	15.6512i	0.545615	−	0.652135i
$577$	−12.7749	+	12.7749i	−0.531825	+	0.531825i	−0.921115	−	0.389290i	$-0.872720\pi$
$577$	−12.7749	+	12.7749i	−0.531825	+	0.531825i	0.389290	+	0.921115i	$0.372720\pi$
$578$	0.923786	+	6.29615i	0.0384245	+	0.261885i
$579$	4.69452	−	4.69452i	0.195098	−	0.195098i
$580$	6.33465	+	27.7554i	0.263032	+	1.15248i
$581$	1.85090	+	1.85090i	0.0767883	+	0.0767883i
$582$	4.53247	+	3.37262i	0.187877	+	0.139799i
$583$	−5.79916	−	5.79916i	−0.240176	−	0.240176i
$584$	−7.10385	+	19.5613i	−0.293959	+	0.809451i
$585$	0.891803	+	1.02005i	0.0368715	+	0.0421737i
$586$	1.13936	+	7.76542i	0.0470666	+	0.320786i
$587$			18.8003i			0.775973i	0.921665	+	0.387987i	$0.126829\pi$
$587$			18.8003i			0.775973i	−0.921665	+	0.387987i	$0.873171\pi$
$588$	−1.28389	+	0.385041i	−0.0529469	+	0.0158788i
$589$	0.620364	+	0.620364i	0.0255616	+	0.0255616i
$590$	−1.73996	−	22.0618i	−0.0716332	−	0.908269i
$591$		−	10.3843i		−	0.427154i
$592$	−19.9310	+	13.1361i	−0.819159	+	0.539891i
$593$	−21.1159	−	21.1159i	−0.867125	−	0.867125i	0.125028	−	0.992153i	$-0.460098\pi$
$593$	−21.1159	−	21.1159i	−0.867125	−	0.867125i	−0.992153	+	0.125028i	$0.960098\pi$
$594$	3.85973	+	2.87203i	0.158367	+	0.117841i
$595$	7.80563	−	6.82428i	0.320000	−	0.279768i
$596$	2.90353	−	5.39109i	0.118933	−	0.220828i
$597$	−14.7982			−0.605648
$598$	−2.02627	−	1.50775i	−0.0828603	−	0.0616565i
$599$		−	38.7982i		−	1.58525i	−0.609707	−	0.792627i	$-0.708713\pi$
$599$		−	38.7982i		−	1.58525i	0.609707	−	0.792627i	$-0.291287\pi$
$600$	−9.04596	+	2.82893i	−0.369300	+	0.115490i
$601$		−	16.6788i		−	0.680341i	−0.940364	−	0.340171i	$-0.889515\pi$
$601$		−	16.6788i		−	0.680341i	0.940364	−	0.340171i	$-0.110485\pi$
$602$	−9.10498	+	12.2362i	−0.371091	+	0.498711i
$603$	5.40527			0.220120
$604$	−3.49838	+	1.04917i	−0.142347	+	0.0426901i
$605$	17.1098	−	14.9587i	0.695614	−	0.608159i
$606$	−0.380506	+	0.511363i	−0.0154570	+	0.0207727i
$607$	−31.6490	−	31.6490i	−1.28459	−	1.28459i	−0.938024	−	0.346569i	$-0.887347\pi$
$607$	−31.6490	−	31.6490i	−1.28459	−	1.28459i	−0.346569	−	0.938024i	$-0.612653\pi$
$608$	−0.316977	+	5.55658i	−0.0128551	+	0.225349i
$609$		−	4.26638i		−	0.172882i
$610$	35.5004	−	2.79984i	1.43737	−	0.113362i
$611$	−1.79694	−	1.79694i	−0.0726964	−	0.0726964i
$612$	11.2169	−	20.8268i	0.453416	−	0.841875i
$613$		−	16.6369i		−	0.671958i	−0.941869	−	0.335979i	$-0.890933\pi$
$613$		−	16.6369i		−	0.671958i	0.941869	−	0.335979i	$-0.109067\pi$
$614$	−41.2891	+	6.05804i	−1.66629	+	0.244482i
$615$	4.59267	+	5.25311i	0.185195	+	0.211826i
$616$	−1.09477	−	2.34336i	−0.0441097	−	0.0944168i
$617$	5.93685	+	5.93685i	0.239008	+	0.239008i	0.816439	−	0.577431i	$-0.195945\pi$
$617$	5.93685	+	5.93685i	0.239008	+	0.239008i	−0.577431	+	0.816439i	$0.695945\pi$
$618$	−0.747313	+	1.00432i	−0.0300613	+	0.0403995i
$619$	3.97762	+	3.97762i	0.159874	+	0.159874i	0.782511	−	0.622637i	$-0.213939\pi$
$619$	3.97762	+	3.97762i	0.159874	+	0.159874i	−0.622637	+	0.782511i	$0.713939\pi$
$620$	2.12170	−	3.37658i	0.0852096	−	0.135607i
$621$	−19.7771	+	19.7771i	−0.793628	+	0.793628i
$622$	25.6513	−	3.76362i	1.02852	−	0.150907i
$623$	−4.45115	+	4.45115i	−0.178332	+	0.178332i
$624$	0.350438	+	0.531708i	0.0140288	+	0.0212854i
$625$	−24.1081	−	6.61797i	−0.964326	−	0.264719i
$626$	2.82026	−	3.79015i	0.112720	−	0.151485i
$627$	−0.602980			−0.0240807
$628$	−12.7024	−	42.3552i	−0.506879	−	1.69016i
$629$	−19.5661	+	19.5661i	−0.780150	+	0.780150i
$630$	−8.04149	+	0.634215i	−0.320381	+	0.0252677i
$631$	25.3759			1.01020			0.505098	−	0.863062i	$-0.331456\pi$
$631$	25.3759			1.01020			0.505098	+	0.863062i	$0.331456\pi$
$632$	0.344616	−	0.160998i	0.0137081	−	0.00640415i
$633$	2.75757	−	2.75757i	0.109604	−	0.109604i
$634$	−0.651731	−	4.44193i	−0.0258835	−	0.176412i
$635$	2.79348	−	41.6451i	0.110856	−	1.65263i
$636$	−11.5145	+	3.45321i	−0.456580	+	0.136929i
$637$			0.237545i			0.00941187i
$638$	8.14541	−	1.19511i	0.322480	−	0.0473150i
$639$	−30.2704			−1.19748
$640$	24.9446	−	4.21528i	0.986021	−	0.166623i
$641$	−9.09202			−0.359113			−0.179557	−	0.983748i	$-0.557466\pi$
$641$	−9.09202			−0.359113			−0.179557	+	0.983748i	$0.557466\pi$
$642$	−5.78584	+	0.848912i	−0.228349	+	0.0335039i
$643$		−	45.8712i		−	1.80898i	−0.426493	−	0.904491i	$-0.640251\pi$
$643$		−	45.8712i		−	1.80898i	0.426493	−	0.904491i	$-0.359749\pi$
$644$	14.4028	−	4.31941i	0.567550	−	0.170209i
$645$	12.1676	−	10.6379i	0.479100	−	0.418866i
$646$	0.936571	+	6.38328i	0.0368489	+	0.251147i
$647$	5.58972	−	5.58972i	0.219754	−	0.219754i	−0.588641	−	0.808395i	$-0.700337\pi$
$647$	5.58972	−	5.58972i	0.219754	−	0.219754i	0.808395	+	0.588641i	$0.200337\pi$
$648$	−13.2211	+	6.17662i	−0.519372	+	0.242640i
$649$	−6.39957			−0.251205
$650$	0.0196971	+	1.67958i	0.000772583	+	0.0658786i
$651$	−0.422581	+	0.422581i	−0.0165622	+	0.0165622i
$652$	−3.85853	−	12.8660i	−0.151112	−	0.503872i
$653$	−26.6791			−1.04403			−0.522017	−	0.852935i	$-0.674820\pi$
$653$	−26.6791			−1.04403			−0.522017	+	0.852935i	$0.674820\pi$
$654$	−9.34225	+	12.5551i	−0.365311	+	0.490943i
$655$	1.72858	−	25.7696i	0.0675413	−	1.00690i
$656$	−10.2492	−	15.5508i	−0.400163	−	0.607155i
$657$	13.2715	−	13.2715i	0.517772	−	0.517772i
$658$	14.9690	−	2.19629i	0.583552	−	0.0856202i
$659$	−30.0146	+	30.0146i	−1.16920	+	1.16920i	−0.186804	+	0.982397i	$0.559813\pi$
$659$	−30.0146	+	30.0146i	−1.16920	+	1.16920i	−0.982397	+	0.186804i	$0.940187\pi$
$660$	0.609858	+	2.67211i	0.0237387	+	0.104012i
$661$	3.24369	+	3.24369i	0.126165	+	0.126165i	0.767370	−	0.641205i	$-0.221565\pi$
$661$	3.24369	+	3.24369i	0.126165	+	0.126165i	−0.641205	+	0.767370i	$0.721565\pi$
$662$	−13.7739	+	18.5108i	−0.535338	+	0.719442i
$663$	0.521973	+	0.521973i	0.0202717	+	0.0202717i
$664$	3.13370	+	6.70770i	0.121611	+	0.260309i
$665$	1.65626	−	1.44803i	0.0642271	−	0.0561523i
$666$	21.2998	−	3.12516i	0.825350	−	0.121097i
$667$			47.8605i			1.85317i
$668$	−20.1107	+	37.3403i	−0.778107	+	1.44474i
$669$	4.05842	+	4.05842i	0.156908	+	0.156908i
$670$	5.09614	+	4.35106i	0.196881	+	0.168096i
$671$		−	10.2978i		−	0.397541i
$672$	−3.78504	−	0.215919i	−0.146011	−	0.00832925i
$673$	30.3738	+	30.3738i	1.17082	+	1.17082i	0.982014	+	0.188808i	$0.0604625\pi$
$673$	30.3738	+	30.3738i	1.17082	+	1.17082i	0.188808	+	0.982014i	$0.439538\pi$
$674$	−5.36060	+	7.20413i	−0.206483	+	0.277493i
$675$	18.4341	+	2.48423i	0.709528	+	0.0956182i
$676$	−24.7961	+	7.43636i	−0.953695	+	0.286014i
$677$	47.3315			1.81910			0.909550	−	0.415596i	$-0.136427\pi$
$677$	47.3315			1.81910			0.909550	+	0.415596i	$0.136427\pi$
$678$	8.03602	−	10.7996i	0.308622	−	0.414757i
$679$			5.96075i			0.228752i
$680$	27.3403	−	10.6065i	1.04845	−	0.406741i
$681$			3.64982i			0.139862i
$682$	−0.925169	−	0.688420i	−0.0354266	−	0.0263609i
$683$	27.5883			1.05564			0.527819	−	0.849357i	$-0.323010\pi$
$683$	27.5883			1.05564			0.527819	+	0.849357i	$0.323010\pi$
$684$	2.38009	−	4.41921i	0.0910052	−	0.168973i
$685$	2.76207	−	41.1768i	0.105533	−	1.57328i
$686$	−1.13458	−	0.844239i	−0.0433183	−	0.0322332i
$687$	13.8860	+	13.8860i	0.529783	+	0.529783i
$688$	−36.0198	+	23.7399i	−1.37324	+	0.905075i
$689$			2.13040i			0.0811618i
$690$	−15.8845	+	1.25277i	−0.604712	+	0.0476923i
$691$	−22.7396	−	22.7396i	−0.865055	−	0.865055i	0.126865	−	0.991920i	$-0.459508\pi$
$691$	−22.7396	−	22.7396i	−0.865055	−	0.865055i	−0.991920	+	0.126865i	$0.959508\pi$
$692$	5.06525	−	1.51907i	0.192552	−	0.0577464i
$693$			2.33264i			0.0886096i
$694$	3.58430	+	24.4292i	0.136058	+	0.927318i
$695$	0.852930	−	12.7154i	0.0323535	−	0.482324i
$696$	4.11908	−	11.3424i	0.156133	−	0.429931i
$697$	−15.2660	−	15.2660i	−0.578242	−	0.578242i
$698$	−28.6788	−	21.3400i	−1.08551	−	0.807729i
$699$	−1.29284	−	1.29284i	−0.0488995	−	0.0488995i
$700$	−8.09211	−	5.87518i	−0.305853	−	0.222061i
$701$	9.01372	−	9.01372i	0.340444	−	0.340444i	−0.516090	−	0.856534i	$-0.672613\pi$
$701$	9.01372	−	9.01372i	0.340444	−	0.340444i	0.856534	+	0.516090i	$0.172613\pi$
$702$	−0.181423	−	1.23650i	−0.00684736	−	0.0466688i
$703$	−4.15169	+	4.15169i	−0.156584	+	0.156584i
$704$	−0.648045	−	7.28691i	−0.0244241	−	0.274636i
$705$	−15.9961	−	1.07299i	−0.602448	−	0.0404112i
$706$	−30.7196	−	22.8585i	−1.15615	−	0.860292i
$707$	−0.672504			−0.0252921
$708$	−4.44796	+	8.25870i	−0.167165	+	0.310381i
$709$	7.66579	−	7.66579i	0.287895	−	0.287895i	−0.548353	−	0.836247i	$-0.684745\pi$
$709$	7.66579	−	7.66579i	0.287895	−	0.287895i	0.836247	+	0.548353i	$0.184745\pi$
$710$	−28.5392	−	24.3666i	−1.07106	−	0.914464i
$711$	−0.343039			−0.0128650
$712$	−16.1311	+	7.53611i	−0.604537	+	0.282428i
$713$	4.74053	−	4.74053i	0.177534	−	0.177534i
$714$	−4.34818	+	0.637975i	−0.162726	+	0.0238756i
$715$	0.484641	+	0.0325089i	0.0181245	+	0.00121576i
$716$	2.54176	−	4.71938i	0.0949900	−	0.176372i
$717$		−	1.07044i		−	0.0399761i
$718$	0.658507	+	4.48812i	0.0245753	+	0.167495i
$719$	−26.7578			−0.997898			−0.498949	−	0.866631i	$-0.666281\pi$
$719$	−26.7578			−0.997898			−0.498949	+	0.866631i	$0.666281\pi$
$720$	−21.9910	−	6.07777i	−0.819555	−	0.226505i
$721$	−1.32080			−0.0491891
$722$	−3.70195	−	25.2310i	−0.137772	−	0.938999i
$723$		−	3.95538i		−	0.147102i
$724$	−9.17937	−	4.94381i	−0.341148	−	0.183735i
$725$	25.3111	−	19.2993i	0.940030	−	0.716756i
$726$	−9.53115	+	1.39843i	−0.353734	+	0.0519007i
$727$	15.6510	−	15.6510i	0.580465	−	0.580465i	−0.354566	−	0.935031i	$-0.615371\pi$
$727$	15.6510	−	15.6510i	0.580465	−	0.580465i	0.935031	+	0.354566i	$0.115371\pi$
$728$	−0.229344	+	0.631524i	−0.00850004	+	0.0234058i
$729$	5.68088			0.210403
$730$	23.1956	−	1.82939i	0.858509	−	0.0677087i
$731$	−35.3602	+	35.3602i	−1.30785	+	1.30785i
$732$	−13.2894	−	7.15737i	−0.491189	−	0.264544i
$733$	−33.4286			−1.23471			−0.617356	−	0.786684i	$-0.711796\pi$
$733$	−33.4286			−1.23471			−0.617356	+	0.786684i	$0.711796\pi$
$734$	−31.4838	−	23.4272i	−1.16209	−	0.864712i
$735$	0.986373	+	1.12822i	0.0363829	+	0.0416149i
$736$	42.4608	+	2.42219i	1.56513	+	0.0892831i
$737$	1.37020	−	1.37020i	0.0504719	−	0.0504719i
$738$	2.43834	+	16.6187i	0.0897565	+	0.611743i
$739$	−22.8250	+	22.8250i	−0.839632	+	0.839632i	−0.988810	−	0.149178i	$-0.952337\pi$
$739$	−22.8250	+	22.8250i	−0.839632	+	0.839632i	0.149178	+	0.988810i	$0.452337\pi$
$740$	22.5973	+	14.1992i	0.830692	+	0.521972i
$741$	0.110757	+	0.110757i	0.00406874	+	0.00406874i
$742$	−10.1753	−	7.57148i	−0.373548	−	0.277958i
$743$	−1.71892	−	1.71892i	−0.0630612	−	0.0630612i	0.674873	−	0.737934i	$-0.264198\pi$
$743$	−1.71892	−	1.71892i	−0.0630612	−	0.0630612i	−0.737934	+	0.674873i	$0.764198\pi$
$744$	−1.53144	+	0.715459i	−0.0561453	+	0.0262300i
$745$	−6.83067	−	0.458190i	−0.250256	−	0.0167868i
$746$	1.55296	+	10.5843i	0.0568578	+	0.387519i
$747$		−	6.67699i		−	0.244298i
$748$	−2.43605	−	8.12286i	−0.0890709	−	0.297001i
$749$	−4.36275	−	4.36275i	−0.159411	−	0.159411i
$750$	7.06778	+	7.89536i	0.258079	+	0.288298i
$751$		−	16.7879i		−	0.612599i	−0.951935	−	0.306299i	$-0.900909\pi$
$751$		−	16.7879i		−	0.612599i	0.951935	−	0.306299i	$-0.0990908\pi$
$752$	41.9162	+	8.61326i	1.52853	+	0.314093i
$753$	8.28231	+	8.28231i	0.301824	+	0.301824i
$754$	−1.71569	−	1.27664i	−0.0624816	−	0.0464926i
$755$	2.68769	+	3.07419i	0.0978151	+	0.111881i
$756$	6.55063	+	3.52803i	0.238244	+	0.128313i
$757$	42.5556			1.54671			0.773355	−	0.633973i	$-0.218577\pi$
$757$	42.5556			1.54671			0.773355	+	0.633973i	$0.218577\pi$
$758$	18.5791	+	13.8247i	0.674823	+	0.502136i
$759$			4.60769i			0.167249i
$760$	5.80129	−	2.25058i	0.210435	−	0.0816370i
$761$			18.4055i			0.667198i	0.942715	+	0.333599i	$0.108263\pi$
$761$			18.4055i			0.667198i	−0.942715	+	0.333599i	$0.891737\pi$
$762$	−10.5614	+	14.1934i	−0.382598	+	0.514174i
$763$	−16.5115			−0.597755
$764$	−3.33476	−	11.1196i	−0.120648	−	0.402291i
$765$	−26.3882	−	1.77008i	−0.954067	−	0.0639973i
$766$	−4.15387	+	5.58239i	−0.150085	+	0.201700i
$767$	1.17549	+	1.17549i	0.0424443	+	0.0424443i
$768$	−9.85423	−	4.22839i	−0.355584	−	0.152579i
$769$			26.8842i			0.969467i	0.874662	+	0.484734i	$0.161083\pi$
$769$			26.8842i			0.969467i	−0.874662	+	0.484734i	$0.838917\pi$
$770$	−1.87769	+	2.19923i	−0.0676674	+	0.0792548i
$771$	−12.8441	−	12.8441i	−0.462570	−	0.462570i
$772$	17.4433	+	9.39461i	0.627799	+	0.338119i
$773$			8.83135i			0.317642i	0.987307	+	0.158821i	$0.0507692\pi$
$773$			8.83135i			0.317642i	−0.987307	+	0.158821i	$0.949231\pi$
$774$	38.4935	−	5.64785i	1.38362	−	0.203008i
$775$	−4.41861	−	0.595465i	−0.158721	−	0.0213897i
$776$	−5.75495	+	15.8469i	−0.206591	+	0.568871i
$777$	−2.82806	−	2.82806i	−0.101456	−	0.101456i
$778$	11.2629	−	15.1362i	0.403794	−	0.542660i
$779$	−3.23927	−	3.23927i	−0.116059	−	0.116059i
$780$	0.378798	−	0.602838i	0.0135631	−	0.0215850i
$781$	−7.67334	+	7.67334i	−0.274574	+	0.274574i
$782$	48.7781	−	7.15684i	1.74430	−	0.255928i
$783$	−16.7457	+	16.7457i	−0.598442	+	0.598442i
$784$	−2.20123	−	3.33985i	−0.0786153	−	0.119280i
$785$	−37.2194	+	32.5400i	−1.32842	+	1.16140i
$786$	−6.53528	+	8.78278i	−0.233106	+	0.313271i
$787$	−40.1397			−1.43083			−0.715414	−	0.698701i	$-0.753762\pi$
$787$	−40.1397			−1.43083			−0.715414	+	0.698701i	$0.753762\pi$
$788$	29.6829	−	8.90193i	1.05741	−	0.317118i
$789$	13.5860	−	13.5860i	0.483673	−	0.483673i
$790$	−0.323420	−	0.276135i	−0.0115068	−	0.00982443i
$791$	14.2028			0.504994
$792$	−2.25210	+	6.20142i	−0.0800250	+	0.220358i
$793$	−1.89152	+	1.89152i	−0.0671697	+	0.0671697i
$794$	−2.58904	−	17.6459i	−0.0918817	−	0.626228i
$795$	8.84620	+	10.1183i	0.313742	+	0.358859i
$796$	−12.6857	−	42.2995i	−0.449631	−	1.49927i
$797$		−	3.95005i		−	0.139918i	−0.997550	−	0.0699589i	$-0.977713\pi$
$797$		−	3.95005i		−	0.139918i	0.997550	−	0.0699589i	$-0.0222868\pi$
$798$	−0.922632	+	0.135371i	−0.0326608	+	0.00479208i
$799$	49.6043			1.75487
$800$	−15.8409	−	23.4322i	−0.560060	−	0.828452i
$801$	16.0572			0.567354
$802$	36.0056	−	5.28283i	1.27140	−	0.186543i
$803$		−	6.72848i		−	0.237443i
$804$	−0.815908	−	2.72059i	−0.0287749	−	0.0959480i
$805$	−11.0652	−	12.6564i	−0.389997	−	0.446079i
$806$	0.0434866	+	0.296387i	0.00153175	+	0.0104398i
$807$	−4.66514	+	4.66514i	−0.164221	+	0.164221i
$808$	−1.78788	−	0.649286i	−0.0628975	−	0.0228418i
$809$	12.6940			0.446299			0.223149	−	0.974784i	$-0.428366\pi$
$809$	12.6940			0.446299			0.223149	+	0.974784i	$0.428366\pi$
$810$	12.4079	+	10.5938i	0.435968	+	0.372228i
$811$	−29.7859	+	29.7859i	−1.04592	+	1.04592i	−0.0470298	+	0.998893i	$0.514976\pi$
$811$	−29.7859	+	29.7859i	−1.04592	+	1.04592i	−0.998893	+	0.0470298i	$0.985024\pi$
$812$	12.1952	−	3.65734i	0.427966	−	0.128347i
$813$	−15.1673			−0.531939
$814$	4.60714	−	6.19155i	0.161480	−	0.217014i
$815$	−11.3059	+	9.88452i	−0.396030	+	0.346240i
$816$	−12.1758	−	2.50197i	−0.426237	−	0.0875865i
$817$	−7.50303	+	7.50303i	−0.262498	+	0.262498i
$818$	−9.29002	+	1.36305i	−0.324818	+	0.0476580i
$819$	0.428463	−	0.428463i	0.0149717	−	0.0149717i
$820$	−11.0786	+	17.6311i	−0.386882	+	0.615703i
$821$	26.4633	+	26.4633i	0.923575	+	0.923575i	0.997280	−	0.0737055i	$-0.0234825\pi$
$821$	26.4633	+	26.4633i	0.923575	+	0.923575i	−0.0737055	+	0.997280i	$0.523482\pi$
$822$	−10.4426	+	14.0338i	−0.364227	+	0.489486i
$823$	4.91678	+	4.91678i	0.171388	+	0.171388i	0.787589	−	0.616201i	$-0.211329\pi$
$823$	4.91678	+	4.91678i	0.171388	+	0.171388i	−0.616201	+	0.787589i	$0.711329\pi$
$824$	−3.51140	−	1.27520i	−0.122325	−	0.0444236i
$825$	2.43678	−	1.85800i	0.0848379	−	0.0646874i
$826$	−9.79212	+	1.43672i	−0.340712	+	0.0499900i
$827$			1.97904i			0.0688181i	0.999408	+	0.0344091i	$0.0109549\pi$
$827$			1.97904i			0.0688181i	−0.999408	+	0.0344091i	$0.989045\pi$
$828$	−33.7696	−	18.1876i	−1.17357	−	0.632062i
$829$	−2.54957	−	2.54957i	−0.0885502	−	0.0885502i	0.661444	−	0.749994i	$-0.269944\pi$
$829$	−2.54957	−	2.54957i	−0.0885502	−	0.0885502i	−0.749994	+	0.661444i	$0.769944\pi$
$830$	5.37475	−	6.29513i	0.186560	−	0.218507i
$831$		−	4.42335i		−	0.153444i
$832$	−1.21944	+	1.45751i	−0.0422765	+	0.0505300i
$833$	−3.27870	−	3.27870i	−0.113600	−	0.113600i
$834$	−3.22468	+	4.33366i	−0.111662	+	0.150062i
$835$	47.3112	+	3.17356i	1.63727	+	0.109826i
$836$	−0.516902	−	1.72358i	−0.0178774	−	0.0596111i
$837$	3.31729			0.114662
$838$	9.64719	−	12.9649i	0.333256	−	0.447864i
$839$		−	41.9916i		−	1.44971i	−0.688902	−	0.724855i	$-0.741907\pi$
$839$		−	41.9916i		−	1.44971i	0.688902	−	0.724855i	$-0.258093\pi$
$840$	1.53305	+	3.95173i	0.0528953	+	0.136348i
$841$			11.5245i			0.397396i
$842$	26.2029	+	19.4976i	0.903010	+	0.671931i
$843$	0.244101			0.00840728
$844$	10.2462	+	5.51841i	0.352690	+	0.189952i
$845$	19.0500	+	21.7894i	0.655339	+	0.749579i
$846$	−30.9613	−	23.0383i	−1.06447	−	0.792074i
$847$	−7.18687	−	7.18687i	−0.246944	−	0.246944i
$848$	−19.7415	−	29.9532i	−0.677926	−	1.02860i
$849$		−	14.1294i		−	0.484919i
$850$	−23.4542	−	22.9104i	−0.804471	−	0.785821i
$851$	31.7253	+	31.7253i	1.08753	+	1.08753i
$852$	4.56922	+	15.2358i	0.156539	+	0.521969i
$853$			24.5799i			0.841601i	0.907153	+	0.420800i	$0.138251\pi$
$853$			24.5799i			0.841601i	−0.907153	+	0.420800i	$0.861749\pi$
$854$	−2.31188	−	15.7568i	−0.0791110	−	0.539188i
$855$	−5.59927	−	0.375590i	−0.191491	−	0.0128449i
$856$	−7.38644	−	15.8107i	−0.252463	−	0.540398i
$857$	−35.0677	−	35.0677i	−1.19789	−	1.19789i	−0.974798	−	0.223091i	$-0.928385\pi$
$857$	−35.0677	−	35.0677i	−1.19789	−	1.19789i	−0.223091	−	0.974798i	$-0.571615\pi$
$858$	−0.165175	−	0.122907i	−0.00563898	−	0.00419597i
$859$	16.5341	+	16.5341i	0.564137	+	0.564137i	0.930480	−	0.366343i	$-0.119390\pi$
$859$	16.5341	+	16.5341i	0.564137	+	0.564137i	−0.366343	+	0.930480i	$0.619390\pi$
$860$	40.8383	+	25.6611i	1.39257	+	0.875035i
$861$	2.20653	−	2.20653i	0.0751984	−	0.0751984i
$862$	−0.587386	−	4.00339i	−0.0200065	−	0.136356i
$863$	−15.2317	+	15.2317i	−0.518492	+	0.518492i	−0.917115	−	0.398623i	$-0.869488\pi$
$863$	−15.2317	+	15.2317i	−0.518492	+	0.518492i	0.398623	+	0.917115i	$0.369488\pi$
$864$	14.0089	+	15.7039i	0.476593	+	0.534258i
$865$	−3.89146	−	4.45106i	−0.132314	−	0.151341i
$866$	37.7963	+	28.1243i	1.28437	+	0.955701i
$867$	−3.01569			−0.102418
$868$	−1.57017	−	0.845662i	−0.0532951	−	0.0287036i
$869$	−0.0869580	+	0.0869580i	−0.00294985	+	0.00294985i
$870$	−13.4497	+	1.06075i	−0.455988	+	0.0359628i
$871$	−0.503361			−0.0170557
$872$	−43.8964	−	15.9414i	−1.48652	−	0.539844i
$873$	10.7515	−	10.7515i	0.363883	−	0.363883i
$874$	10.3501	−	1.51860i	0.350099	−	0.0513673i
$875$	−2.23143	+	10.9554i	−0.0754359	+	0.370360i
$876$	−8.68316	−	4.67656i	−0.293377	−	0.158006i
$877$			37.3027i			1.25962i	0.776748	+	0.629811i	$0.216868\pi$
$877$			37.3027i			1.25962i	−0.776748	+	0.629811i	$0.783132\pi$
$878$	1.65842	+	11.3031i	0.0559688	+	0.381461i
$879$	−3.71942			−0.125453
$880$	−7.11523	+	4.03389i	−0.239854	+	0.135982i
$881$	29.2179			0.984375			0.492188	−	0.870489i	$-0.336197\pi$
$881$	29.2179			0.984375			0.492188	+	0.870489i	$0.336197\pi$
$882$	0.523684	+	3.56922i	0.0176334	+	0.120182i
$883$			1.31852i			0.0443718i	0.999754	+	0.0221859i	$0.00706257\pi$
$883$			1.31852i			0.0443718i	−0.999754	+	0.0221859i	$0.992937\pi$
$884$	−1.04456	+	1.93948i	−0.0351325	+	0.0652318i
$885$	10.4640	+	0.701908i	0.351744	+	0.0235944i
$886$	7.99996	−	1.17377i	0.268764	−	0.0394337i
$887$	28.0560	−	28.0560i	0.942030	−	0.942030i	−0.0563798	−	0.998409i	$-0.517956\pi$
$887$	28.0560	−	28.0560i	0.942030	−	0.942030i	0.998409	+	0.0563798i	$0.0179558\pi$
$888$	−4.78810	−	10.2489i	−0.160678	−	0.343932i
$889$	−18.6661			−0.626041
$890$	15.1389	+	12.9255i	0.507457	+	0.433264i
$891$	3.33611	−	3.33611i	0.111764	−	0.111764i
$892$	−8.12165	+	15.0798i	−0.271933	+	0.504908i
$893$	10.5254			0.352221
$894$	2.32802	+	1.73228i	0.0778607	+	0.0579363i
$895$	−5.97959	−	0.401101i	−0.199876	−	0.0134073i
$896$	−2.62752	−	11.0044i	−0.0877793	−	0.367630i
$897$	0.846350	−	0.846350i	0.0282588	−	0.0282588i
$898$	−1.17593	−	8.01465i	−0.0392412	−	0.267452i
$899$	4.01391	−	4.01391i	0.133871	−	0.133871i
$900$	3.99871	+	25.1930i	0.133290	+	0.839767i
$901$	−29.4047	−	29.4047i	−0.979613	−	0.979613i
$902$	4.83083	+	3.59463i	0.160849	+	0.119688i
$903$	−5.11093	−	5.11093i	−0.170081	−	0.170081i
$904$	37.7588	+	13.7125i	1.25584	+	0.456070i
$905$	−0.780156	+	11.6305i	−0.0259333	+	0.386611i
$906$	−0.251262	−	1.71250i	−0.00834761	−	0.0568939i
$907$			13.6836i			0.454358i	0.973853	+	0.227179i	$0.0729503\pi$
$907$			13.6836i			0.454358i	−0.973853	+	0.227179i	$0.927050\pi$
$908$	−10.4328	+	3.12880i	−0.346224	+	0.103833i
$909$	1.21301	+	1.21301i	0.0402329	+	0.0402329i
$910$	0.748857	−	0.0590607i	0.0248244	−	0.00195784i
$911$			3.73460i			0.123733i	0.998084	+	0.0618664i	$0.0197053\pi$
$911$			3.73460i			0.123733i	−0.998084	+	0.0618664i	$0.980295\pi$
$912$	−2.58356	−	0.530889i	−0.0855501	−	0.0175795i
$913$	−1.69257	−	1.69257i	−0.0560159	−	0.0560159i
$914$	0.688018	+	0.511955i	0.0227576	+	0.0169340i
$915$	−1.12947	+	16.8380i	−0.0373390	+	0.556647i
$916$	−27.7884	+	51.5958i	−0.918154	+	1.70477i
$917$	−11.5504			−0.381428
$918$	19.5708	+	14.5627i	0.645934	+	0.480640i
$919$		−	32.7961i		−	1.08184i	−0.841073	−	0.540921i	$-0.818076\pi$
$919$		−	32.7961i		−	1.08184i	0.841073	−	0.540921i	$-0.181924\pi$
$920$	−17.1979	−	44.3307i	−0.566997	−	1.46154i
$921$		−	19.7764i		−	0.651653i
$922$	21.7603	−	29.2437i	0.716636	−	0.963090i
$923$	2.81891			0.0927855
$924$	1.17407	−	0.352104i	0.0386240	−	0.0115834i
$925$	3.98506	−	29.5709i	0.131028	−	0.972284i
$926$	−4.24269	+	5.70177i	−0.139424	+	0.187372i
$927$	2.38234	+	2.38234i	0.0782464	+	0.0782464i
$928$	35.9524	+	2.05092i	1.18020	+	0.0673247i
$929$		−	32.7466i		−	1.07438i	−0.843461	−	0.537191i	$-0.819486\pi$
$929$		−	32.7466i		−	1.07438i	0.843461	−	0.537191i	$-0.180514\pi$
$930$	1.43725	+	1.22711i	0.0471292	+	0.0402387i
$931$	−0.695701	−	0.695701i	−0.0228007	−	0.0228007i
$932$	2.58720	−	4.80376i	0.0847467	−	0.157352i
$933$			12.2863i			0.402235i
$934$	−1.27704	+	0.187370i	−0.0417860	+	0.00613094i
$935$	−7.13793	+	6.24052i	−0.233435	+	0.204087i
$936$	1.55276	−	0.725418i	0.0507535	−	0.0237110i
$937$	−36.7133	−	36.7133i	−1.19937	−	1.19937i	−0.974355	−	0.225018i	$-0.927756\pi$
$937$	−36.7133	−	36.7133i	−1.19937	−	1.19937i	−0.225018	−	0.974355i	$-0.572244\pi$
$938$	1.78896	−	2.40418i	0.0584115	−	0.0784994i
$939$	1.58310	+	1.58310i	0.0516626	+	0.0516626i
$940$	−10.6455	−	46.6435i	−0.347218	−	1.52134i
$941$	34.4757	−	34.4757i	1.12387	−	1.12387i	0.132721	−	0.991153i	$-0.457629\pi$
$941$	34.4757	−	34.4757i	1.12387	−	1.12387i	0.991153	−	0.132721i	$-0.0423715\pi$
$942$	20.7333	−	3.04204i	0.675528	−	0.0991151i
$943$	−24.7530	+	24.7530i	−0.806069	+	0.806069i
$944$	−27.4199	−	5.63445i	−0.892442	−	0.183386i
$945$	0.556740	−	8.29984i	0.0181107	−	0.269994i
$946$	8.32613	−	11.1895i	0.270706	−	0.363802i
$947$	−24.6740			−0.801797			−0.400898	−	0.916123i	$-0.631302\pi$
$947$	−24.6740			−0.801797			−0.400898	+	0.916123i	$0.631302\pi$
$948$	0.0517807	+	0.172659i	0.00168176	+	0.00560771i
$949$	−1.23590	+	1.23590i	−0.0401190	+	0.0401190i
$950$	−4.97670	−	4.86133i	−0.161465	−	0.157722i
$951$	2.12757			0.0689910
$952$	−5.55106	−	11.8821i	−0.179911	−	0.385100i
$953$	39.8238	−	39.8238i	1.29002	−	1.29002i	0.355245	−	0.934773i	$-0.384397\pi$
$953$	39.8238	−	39.8238i	1.29002	−	1.29002i	0.934773	−	0.355245i	$-0.115603\pi$
$954$	4.69662	+	32.0102i	0.152059	+	1.03637i
$955$	−9.77125	+	8.54278i	−0.316190	+	0.276438i
$956$	3.05976	−	0.917626i	0.0989599	−	0.0296781i
$957$			3.90143i			0.126115i
$958$	−52.6019	+	7.71787i	−1.69949	+	0.249353i
$959$	−18.4562			−0.595981
$960$	0.260392	+	11.9860i	0.00840412	+	0.386846i
$961$	30.2049			0.974350
$962$	−1.98353	+	0.291028i	−0.0639514	+	0.00938311i
$963$			15.7383i			0.507160i
$964$	11.3062	−	3.39074i	0.364148	−	0.109208i
$965$	1.48251	−	22.1012i	0.0477237	−	0.711463i
$966$	1.03444	+	7.05033i	0.0332826	+	0.226841i
$967$	22.6571	−	22.6571i	0.728605	−	0.728605i	−0.241737	−	0.970342i	$-0.577717\pi$
$967$	22.6571	−	22.6571i	0.728605	−	0.728605i	0.970342	+	0.241737i	$0.0777172\pi$
$968$	−12.1679	−	26.0453i	−0.391090	−	0.837129i
$969$	−3.05742			−0.0982185
$970$	18.7912	−	1.48202i	0.603349	−	0.0475848i
$971$	−40.9369	+	40.9369i	−1.31373	+	1.31373i	−0.395082	+	0.918646i	$0.629284\pi$
$971$	−40.9369	+	40.9369i	−1.31373	+	1.31373i	−0.918646	+	0.395082i	$0.870716\pi$
$972$	−8.39845	−	28.0041i	−0.269380	−	0.898231i
$973$	−5.69929			−0.182711
$974$	−21.7857	+	29.2778i	−0.698057	+	0.938121i
$975$	−0.788875	−	0.106311i	−0.0252642	−	0.00340469i
$976$	9.06659	−	44.1223i	0.290215	−	1.41232i
$977$	−21.7300	+	21.7300i	−0.695206	+	0.695206i	−0.963373	−	0.268167i	$-0.913582\pi$
$977$	−21.7300	+	21.7300i	−0.695206	+	0.695206i	0.268167	+	0.963373i	$0.413582\pi$
$978$	6.29805	−	0.924065i	0.201390	−	0.0295483i
$979$	4.07040	−	4.07040i	0.130090	−	0.130090i
$980$	−2.37936	+	3.78664i	−0.0760060	+	0.120960i
$981$	29.7820	+	29.7820i	0.950865	+	0.950865i
$982$	11.4734	−	15.4191i	0.366131	−	0.492044i
$983$	23.7194	+	23.7194i	0.756533	+	0.756533i	0.975690	−	0.219157i	$-0.0703307\pi$
$983$	23.7194	+	23.7194i	0.756533	+	0.756533i	−0.219157	+	0.975690i	$0.570331\pi$
$984$	7.99652	−	3.73581i	0.254920	−	0.119093i
$985$	−22.8044	−	26.0837i	−0.726607	−	0.831096i
$986$	41.3014	−	6.05984i	1.31531	−	0.192985i
$987$			7.16974i			0.228215i
$988$	−0.221644	+	0.411535i	−0.00705144	+	0.0130927i
$989$	57.3347	+	57.3347i	1.82314	+	1.82314i
$990$	7.35361	−	0.579963i	0.233713	−	0.0184324i
$991$			14.7984i			0.470085i	0.971985	+	0.235043i	$0.0755230\pi$
$991$			14.7984i			0.470085i	−0.971985	+	0.235043i	$0.924477\pi$
$992$	−3.35791	−	3.76419i	−0.106614	−	0.119513i
$993$	−7.73174	−	7.73174i	−0.245359	−	0.245359i
$994$	−10.0184	+	13.4638i	−0.317766	+	0.427047i
$995$	−37.1705	+	32.4973i	−1.17838	+	1.03023i
$996$	−3.36068	+	1.00787i	−0.106487	+	0.0319356i
$997$	−26.4216			−0.836781			−0.418391	−	0.908267i	$-0.637406\pi$
$997$	−26.4216			−0.836781			−0.418391	+	0.908267i	$0.637406\pi$
$998$	−23.5052	+	31.5888i	−0.744046	+	0.999925i
$999$			22.2005i			0.702391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.t.a.43.5	✓	144
5.2	odd	4		560.2.bl.a.267.32	yes	144
16.3	odd	4		560.2.bl.a.323.32	yes	144
80.67	even	4	inner	560.2.t.a.547.5	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.t.a.43.5	✓	144	1.1	even	1	trivial
560.2.t.a.547.5	yes	144	80.67	even	4	inner
560.2.bl.a.267.32	yes	144	5.2	odd	4
560.2.bl.a.323.32	yes	144	16.3	odd	4

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39923 + 0.205299i) q^{2} -0.670195i q^{3} +(1.91570 - 0.574522i) q^{4} +(-1.47177 - 1.68342i) q^{5} +(0.137590 + 0.937758i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.56257 + 1.19718i) q^{8} +2.55084 q^{9} +O(q^{10})\)	\(q+(-1.39923 + 0.205299i) q^{2} -0.670195i q^{3} +(1.91570 - 0.574522i) q^{4} +(-1.47177 - 1.68342i) q^{5} +(0.137590 + 0.937758i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-2.56257 + 1.19718i) q^{8} +2.55084 q^{9} +(2.40495 + 2.05334i) q^{10} +(0.646620 - 0.646620i) q^{11} +(-0.385041 - 1.28389i) q^{12} -0.237545 q^{13} +(0.844239 - 1.13458i) q^{14} +(-1.12822 + 0.986373i) q^{15} +(3.33985 - 2.20123i) q^{16} +(3.27870 - 3.27870i) q^{17} +(-3.56922 + 0.523684i) q^{18} +(0.695701 - 0.695701i) q^{19} +(-3.78664 - 2.37936i) q^{20} +(0.473899 + 0.473899i) q^{21} +(-0.772022 + 1.03752i) q^{22} +(-5.31623 - 5.31623i) q^{23} +(0.802344 + 1.71742i) q^{24} +(-0.667779 + 4.95521i) q^{25} +(0.332381 - 0.0487677i) q^{26} -3.72014i q^{27} +(-0.948360 + 1.76086i) q^{28} +(-4.50136 - 4.50136i) q^{29} +(1.37614 - 1.61179i) q^{30} +0.891710i q^{31} +(-4.22132 + 3.76570i) q^{32} +(-0.433361 - 0.433361i) q^{33} +(-3.91455 + 5.26077i) q^{34} +(2.23105 + 0.149655i) q^{35} +(4.88666 - 1.46551i) q^{36} -5.96763 q^{37} +(-0.830621 + 1.11627i) q^{38} +0.159201i q^{39} +(5.78687 + 2.55189i) q^{40} -4.65612i q^{41} +(-0.760386 - 0.565804i) q^{42} -10.7848 q^{43} +(0.867236 - 1.61023i) q^{44} +(-3.75425 - 4.29412i) q^{45} +(8.53005 + 6.34722i) q^{46} +(7.56463 + 7.56463i) q^{47} +(-1.47525 - 2.23835i) q^{48} -1.00000i q^{49} +(-0.0829195 - 7.07058i) q^{50} +(-2.19737 - 2.19737i) q^{51} +(-0.455066 + 0.136475i) q^{52} -8.96841i q^{53} +(0.763741 + 5.20535i) q^{54} +(-2.04021 - 0.136854i) q^{55} +(0.965475 - 2.65854i) q^{56} +(-0.466255 - 0.466255i) q^{57} +(7.22257 + 5.37433i) q^{58} +(-4.94848 - 4.94848i) q^{59} +(-1.59464 + 2.53778i) q^{60} +(7.96277 - 7.96277i) q^{61} +(-0.183067 - 1.24771i) q^{62} +(-1.80372 + 1.80372i) q^{63} +(5.13351 - 6.13572i) q^{64} +(0.349612 + 0.399887i) q^{65} +(0.695342 + 0.517405i) q^{66} +2.11902 q^{67} +(4.39733 - 8.16470i) q^{68} +(-3.56291 + 3.56291i) q^{69} +(-3.15249 + 0.248630i) q^{70} -11.8668 q^{71} +(-6.53670 + 3.05382i) q^{72} +(5.20281 - 5.20281i) q^{73} +(8.35011 - 1.22515i) q^{74} +(3.32095 + 0.447542i) q^{75} +(0.933063 - 1.73245i) q^{76} +0.914459i q^{77} +(-0.0326838 - 0.222760i) q^{78} -0.134481 q^{79} +(-8.62108 - 2.38265i) q^{80} +5.15930 q^{81} +(0.955896 + 6.51500i) q^{82} -2.61757i q^{83} +(1.18012 + 0.635586i) q^{84} +(-10.3449 - 0.693919i) q^{85} +(15.0905 - 2.21411i) q^{86} +(-3.01679 + 3.01679i) q^{87} +(-0.882887 + 2.43113i) q^{88} +6.29488 q^{89} +(6.13465 + 5.23774i) q^{90} +(0.167970 - 0.167970i) q^{91} +(-13.2386 - 7.13003i) q^{92} +0.597619 q^{93} +(-12.1377 - 9.03167i) q^{94} +(-2.19507 - 0.147242i) q^{95} +(2.52375 + 2.82910i) q^{96} +(4.21488 - 4.21488i) q^{97} +(0.205299 + 1.39923i) q^{98} +(1.64942 - 1.64942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 8 q^{4} - 144 q^{9}+O(q^{10}) \) 144 * q + 8 * q^4 - 144 * q^9	\( 144 q + 8 q^{4} - 144 q^{9} - 16 q^{12} + 8 q^{16} - 28 q^{18} - 16 q^{19} + 4 q^{22} + 32 q^{26} - 36 q^{30} + 32 q^{34} - 32 q^{36} - 56 q^{38} + 8 q^{40} - 20 q^{42} + 64 q^{43} - 56 q^{44} - 32 q^{46} - 80 q^{48} - 48 q^{50} - 16 q^{51} - 16 q^{52} + 32 q^{54} - 24 q^{56} + 52 q^{58} + 72 q^{60} - 32 q^{61} - 40 q^{62} + 32 q^{64} + 32 q^{66} - 24 q^{68} - 32 q^{69} + 80 q^{72} - 16 q^{73} - 32 q^{74} - 88 q^{75} + 76 q^{78} + 128 q^{80} + 144 q^{81} + 56 q^{82} + 32 q^{86} - 112 q^{87} + 88 q^{88} + 88 q^{90} - 136 q^{92} - 8 q^{94} + 80 q^{95} + 32 q^{96} + 64 q^{99}+O(q^{100}) \) 144 * q + 8 * q^4 - 144 * q^9 - 16 * q^12 + 8 * q^16 - 28 * q^18 - 16 * q^19 + 4 * q^22 + 32 * q^26 - 36 * q^30 + 32 * q^34 - 32 * q^36 - 56 * q^38 + 8 * q^40 - 20 * q^42 + 64 * q^43 - 56 * q^44 - 32 * q^46 - 80 * q^48 - 48 * q^50 - 16 * q^51 - 16 * q^52 + 32 * q^54 - 24 * q^56 + 52 * q^58 + 72 * q^60 - 32 * q^61 - 40 * q^62 + 32 * q^64 + 32 * q^66 - 24 * q^68 - 32 * q^69 + 80 * q^72 - 16 * q^73 - 32 * q^74 - 88 * q^75 + 76 * q^78 + 128 * q^80 + 144 * q^81 + 56 * q^82 + 32 * q^86 - 112 * q^87 + 88 * q^88 + 88 * q^90 - 136 * q^92 - 8 * q^94 + 80 * q^95 + 32 * q^96 + 64 * q^99

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