LMFDB - Embedded newform 570.2.s.b.521.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (of order $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.9
Character	$\chi$	$=$	570.521
Dual form			570.2.s.b.221.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(1.00317 + 1.41197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.72438 - 0.162784i) q^{6} +3.36569 q^{7} -1.00000 q^{8} +(-0.987311 + 2.83288i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(1.00317 + 1.41197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.72438 - 0.162784i) q^{6} +3.36569 q^{7} -1.00000 q^{8} +(-0.987311 + 2.83288i) q^{9} +(-0.866025 + 0.500000i) q^{10} +0.795353i q^{11} +(0.721217 - 1.57475i) q^{12} +(1.59822 - 0.922734i) q^{13} +(1.68284 - 2.91477i) q^{14} +(-0.162784 - 1.72438i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.17887 + 3.56737i) q^{17} +(1.95969 + 2.27148i) q^{18} +(-0.831025 - 4.27895i) q^{19} +1.00000i q^{20} +(3.37635 + 4.75224i) q^{21} +(0.688796 + 0.397676i) q^{22} +(1.72727 - 0.997241i) q^{23} +(-1.00317 - 1.41197i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.84547i q^{26} +(-4.99038 + 1.44780i) q^{27} +(-1.68284 - 2.91477i) q^{28} +(-1.95032 - 3.37805i) q^{29} +(-1.57475 - 0.721217i) q^{30} +8.28909i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.12301 + 0.797872i) q^{33} +(6.17887 - 3.56737i) q^{34} +(-2.91477 - 1.68284i) q^{35} +(2.94700 - 0.561404i) q^{36} -3.63511i q^{37} +(-4.12119 - 1.41979i) q^{38} +(2.90616 + 1.33098i) q^{39} +(0.866025 + 0.500000i) q^{40} +(2.08497 - 3.61128i) q^{41} +(5.80374 - 0.547880i) q^{42} +(-1.75379 + 3.03766i) q^{43} +(0.688796 - 0.397676i) q^{44} +(2.27148 - 1.95969i) q^{45} -1.99448i q^{46} +(3.13074 - 1.80753i) q^{47} +(-1.72438 + 0.162784i) q^{48} +4.32785 q^{49} +1.00000 q^{50} +(1.16142 + 12.3030i) q^{51} +(-1.59822 - 0.922734i) q^{52} +(-3.21210 - 5.56351i) q^{53} +(-1.24136 + 5.04569i) q^{54} +(0.397676 - 0.688796i) q^{55} -3.36569 q^{56} +(5.20808 - 5.46588i) q^{57} -3.90064 q^{58} +(-4.40416 + 7.62824i) q^{59} +(-1.41197 + 1.00317i) q^{60} +(-3.34905 - 5.80073i) q^{61} +(7.17856 + 4.14455i) q^{62} +(-3.32298 + 9.53459i) q^{63} +1.00000 q^{64} -1.84547 q^{65} +(0.129471 + 1.37149i) q^{66} +(-3.16763 + 1.82883i) q^{67} -7.13474i q^{68} +(3.14081 + 1.43845i) q^{69} +(-2.91477 + 1.68284i) q^{70} +(-0.800066 + 1.38576i) q^{71} +(0.987311 - 2.83288i) q^{72} +(-7.05458 + 12.2189i) q^{73} +(-3.14810 - 1.81755i) q^{74} +(-0.721217 + 1.57475i) q^{75} +(-3.29017 + 2.85916i) q^{76} +2.67691i q^{77} +(2.60574 - 1.85131i) q^{78} +(-10.3514 - 5.97636i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-7.05043 - 5.59387i) q^{81} +(-2.08497 - 3.61128i) q^{82} -13.9932i q^{83} +(2.42739 - 5.30012i) q^{84} +(-3.56737 - 6.17887i) q^{85} +(1.75379 + 3.03766i) q^{86} +(2.81321 - 6.14254i) q^{87} -0.795353i q^{88} +(1.83681 + 3.18145i) q^{89} +(-0.561404 - 2.94700i) q^{90} +(5.37912 - 3.10563i) q^{91} +(-1.72727 - 0.997241i) q^{92} +(-11.7039 + 8.31535i) q^{93} -3.61507i q^{94} +(-1.41979 + 4.12119i) q^{95} +(-0.721217 + 1.57475i) q^{96} +(-15.9344 - 9.19973i) q^{97} +(2.16392 - 3.74803i) q^{98} +(-2.25314 - 0.785261i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.00317	+	1.41197i	0.579179	+	0.815201i
$3$	1.00317	+	1.41197i	0.579179	+	0.815201i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.72438	−	0.162784i	0.703977	−	0.0664562i
$7$	3.36569			1.27211			0.636055	−	0.771644i	$-0.280565\pi$
$7$	3.36569			1.27211			0.636055	+	0.771644i	$0.280565\pi$
$8$	−1.00000			−0.353553
$9$	−0.987311	+	2.83288i	−0.329104	+	0.944294i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$			0.795353i			0.239808i	0.992785	+	0.119904i	$0.0382587\pi$
$11$			0.795353i			0.239808i	−0.992785	+	0.119904i	$0.961741\pi$
$12$	0.721217	−	1.57475i	0.208197	−	0.454592i
$13$	1.59822	−	0.922734i	0.443267	−	0.255920i	−0.261715	−	0.965145i	$-0.584288\pi$
$13$	1.59822	−	0.922734i	0.443267	−	0.255920i	0.704982	+	0.709225i	$0.250955\pi$
$14$	1.68284	−	2.91477i	0.449759	−	0.779005i
$15$	−0.162784	−	1.72438i	−0.0420306	−	0.445234i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.17887	+	3.56737i	1.49860	+	0.865214i	0.999999	−	0.00161968i	$-0.000515560\pi$
$17$	6.17887	+	3.56737i	1.49860	+	0.865214i	0.498597	+	0.866834i	$0.333849\pi$
$18$	1.95969	+	2.27148i	0.461904	+	0.535392i
$19$	−0.831025	−	4.27895i	−0.190650	−	0.981658i
$19$	−0.831025	−	4.27895i	−0.190650	−	0.981658i
$20$			1.00000i			0.223607i
$21$	3.37635	+	4.75224i	0.736779	+	1.03702i
$22$	0.688796	+	0.397676i	0.146852	+	0.0847849i
$23$	1.72727	−	0.997241i	0.360161	−	0.207939i	−0.308990	−	0.951065i	$-0.599991\pi$
$23$	1.72727	−	0.997241i	0.360161	−	0.207939i	0.669151	+	0.743126i	$0.266658\pi$
$24$	−1.00317	−	1.41197i	−0.204771	−	0.288217i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	1.84547i		−	0.361926i
$27$	−4.99038	+	1.44780i	−0.960399	+	0.278629i
$28$	−1.68284	−	2.91477i	−0.318028	−	0.550840i
$29$	−1.95032	−	3.37805i	−0.362165	−	0.627288i	0.626152	−	0.779701i	$-0.284629\pi$
$29$	−1.95032	−	3.37805i	−0.362165	−	0.627288i	−0.988317	+	0.152413i	$0.951296\pi$
$30$	−1.57475	−	0.721217i	−0.287509	−	0.131676i
$31$			8.28909i			1.48876i	0.667753	+	0.744382i	$0.267256\pi$
$31$			8.28909i			1.48876i	−0.667753	+	0.744382i	$0.732744\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.12301	+	0.797872i	−0.195492	+	0.138892i
$34$	6.17887	−	3.56737i	1.05967	−	0.611799i
$35$	−2.91477	−	1.68284i	−0.492686	−	0.284452i
$36$	2.94700	−	0.561404i	0.491167	−	0.0935673i
$37$		−	3.63511i		−	0.597608i	−0.954314	−	0.298804i	$-0.903412\pi$
$37$		−	3.63511i		−	0.597608i	0.954314	−	0.298804i	$-0.0965877\pi$
$38$	−4.12119	−	1.41979i	−0.668545	−	0.230320i
$39$	2.90616	+	1.33098i	0.465357	+	0.213128i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	2.08497	−	3.61128i	0.325618	−	0.563987i	−0.656019	−	0.754744i	$-0.727761\pi$
$41$	2.08497	−	3.61128i	0.325618	−	0.563987i	0.981637	+	0.190757i	$0.0610944\pi$
$42$	5.80374	−	0.547880i	0.895536	−	0.0845397i
$43$	−1.75379	+	3.03766i	−0.267451	+	0.463238i	−0.968203	−	0.250167i	$-0.919515\pi$
$43$	−1.75379	+	3.03766i	−0.267451	+	0.463238i	0.700752	+	0.713405i	$0.252848\pi$
$44$	0.688796	−	0.397676i	0.103840	−	0.0599520i
$45$	2.27148	−	1.95969i	0.338612	−	0.292134i
$46$		−	1.99448i		−	0.294070i
$47$	3.13074	−	1.80753i	0.456665	−	0.263656i	−0.253976	−	0.967211i	$-0.581738\pi$
$47$	3.13074	−	1.80753i	0.456665	−	0.263656i	0.710641	+	0.703555i	$0.248405\pi$
$48$	−1.72438	+	0.162784i	−0.248893	+	0.0234958i
$49$	4.32785			0.618264
$50$	1.00000			0.141421
$51$	1.16142	+	12.3030i	0.162631	+	1.72277i
$52$	−1.59822	−	0.922734i	−0.221634	−	0.127960i
$53$	−3.21210	−	5.56351i	−0.441215	−	0.764207i	0.556565	−	0.830804i	$-0.312119\pi$
$53$	−3.21210	−	5.56351i	−0.441215	−	0.764207i	−0.997780	+	0.0665970i	$0.978786\pi$
$54$	−1.24136	+	5.04569i	−0.168927	+	0.686632i
$55$	0.397676	−	0.688796i	0.0536227	−	0.0928772i
$56$	−3.36569			−0.449759
$57$	5.20808	−	5.46588i	0.689828	−	0.723974i
$58$	−3.90064			−0.512179
$59$	−4.40416	+	7.62824i	−0.573373	+	0.993112i	0.422843	+	0.906203i	$0.361032\pi$
$59$	−4.40416	+	7.62824i	−0.573373	+	0.993112i	−0.996216	+	0.0869089i	$0.972301\pi$
$60$	−1.41197	+	1.00317i	−0.182284	+	0.129508i
$61$	−3.34905	−	5.80073i	−0.428802	−	0.742707i	0.567965	−	0.823053i	$-0.307731\pi$
$61$	−3.34905	−	5.80073i	−0.428802	−	0.742707i	−0.996767	+	0.0803454i	$0.974398\pi$
$62$	7.17856	+	4.14455i	0.911679	+	0.526358i
$63$	−3.32298	+	9.53459i	−0.418656	+	1.20125i
$64$	1.00000			0.125000
$65$	−1.84547			−0.228902
$66$	0.129471	+	1.37149i	0.0159367	+	0.168819i
$67$	−3.16763	+	1.82883i	−0.386987	+	0.223427i	−0.680854	−	0.732419i	$-0.738391\pi$
$67$	−3.16763	+	1.82883i	−0.386987	+	0.223427i	0.293867	+	0.955846i	$0.405058\pi$
$68$		−	7.13474i		−	0.865214i
$69$	3.14081	+	1.43845i	0.378110	+	0.173170i
$70$	−2.91477	+	1.68284i	−0.348382	+	0.201138i
$71$	−0.800066	+	1.38576i	−0.0949504	+	0.164459i	−0.909588	−	0.415512i	$-0.863603\pi$
$71$	−0.800066	+	1.38576i	−0.0949504	+	0.164459i	0.814637	+	0.579970i	$0.196936\pi$
$72$	0.987311	−	2.83288i	0.116356	−	0.333858i
$73$	−7.05458	+	12.2189i	−0.825676	+	1.43011i	0.0757258	+	0.997129i	$0.475873\pi$
$73$	−7.05458	+	12.2189i	−0.825676	+	1.43011i	−0.901402	+	0.432984i	$0.857461\pi$
$74$	−3.14810	−	1.81755i	−0.365959	−	0.211286i
$75$	−0.721217	+	1.57475i	−0.0832790	+	0.181837i
$76$	−3.29017	+	2.85916i	−0.377408	+	0.327968i
$77$			2.67691i			0.305062i
$78$	2.60574	−	1.85131i	0.295042	−	0.209620i
$79$	−10.3514	−	5.97636i	−1.16462	−	0.672394i	−0.212213	−	0.977223i	$-0.568067\pi$
$79$	−10.3514	−	5.97636i	−1.16462	−	0.672394i	−0.952407	+	0.304830i	$0.901400\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−7.05043	−	5.59387i	−0.783381	−	0.621541i
$82$	−2.08497	−	3.61128i	−0.230247	−	0.398799i
$83$		−	13.9932i		−	1.53595i	−0.640479	−	0.767976i	$-0.721264\pi$
$83$		−	13.9932i		−	1.53595i	0.640479	−	0.767976i	$-0.278736\pi$
$84$	2.42739	−	5.30012i	0.264850	−	0.578291i
$85$	−3.56737	−	6.17887i	−0.386936	−	0.670192i
$86$	1.75379	+	3.03766i	0.189116	+	0.327559i
$87$	2.81321	−	6.14254i	0.301607	−	0.658549i
$88$		−	0.795353i		−	0.0847849i
$89$	1.83681	+	3.18145i	0.194701	+	0.337233i	0.946803	−	0.321815i	$-0.104293\pi$
$89$	1.83681	+	3.18145i	0.194701	+	0.337233i	−0.752101	+	0.659048i	$0.770960\pi$
$90$	−0.561404	−	2.94700i	−0.0591772	−	0.310641i
$91$	5.37912	−	3.10563i	0.563885	−	0.325559i
$92$	−1.72727	−	0.997241i	−0.180080	−	0.103970i
$93$	−11.7039	+	8.31535i	−1.21364	+	0.862261i
$94$		−	3.61507i		−	0.372866i
$95$	−1.41979	+	4.12119i	−0.145667	+	0.422825i
$96$	−0.721217	+	1.57475i	−0.0736089	+	0.160723i
$97$	−15.9344	−	9.19973i	−1.61789	−	0.934092i	−0.987464	−	0.157846i	$-0.949545\pi$
$97$	−15.9344	−	9.19973i	−1.61789	−	0.934092i	−0.630430	−	0.776246i	$-0.717121\pi$
$98$	2.16392	−	3.74803i	0.218589	−	0.378608i
$99$	−2.25314	−	0.785261i	−0.226449	−	0.0789217i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−1.03574	+	0.597984i	−0.103060	+	0.0595017i	−0.550644	−	0.834740i	$-0.685618\pi$
$101$	−1.03574	+	0.597984i	−0.103060	+	0.0595017i	0.447584	+	0.894242i	$0.352284\pi$
$102$	11.2355	+	5.14570i	1.11248	+	0.509500i
$103$		−	2.19200i		−	0.215984i	−0.994152	−	0.107992i	$-0.965558\pi$
$103$		−	2.19200i		−	0.215984i	0.994152	−	0.107992i	$-0.0344421\pi$
$104$	−1.59822	+	0.922734i	−0.156719	+	0.0904815i
$105$	−0.547880	−	5.80374i	−0.0534676	−	0.566387i
$106$	−6.42419			−0.623973
$107$	1.07225			0.103659			0.0518293	−	0.998656i	$-0.483495\pi$
$107$	1.07225			0.103659			0.0518293	+	0.998656i	$0.483495\pi$
$108$	3.74902	+	3.59789i	0.360750	+	0.346207i
$109$	0.897440	+	0.518137i	0.0859592	+	0.0496285i	0.542363	−	0.840144i	$-0.317530\pi$
$109$	0.897440	+	0.518137i	0.0859592	+	0.0496285i	−0.456404	+	0.889773i	$0.650863\pi$
$110$	−0.397676	−	0.688796i	−0.0379170	−	0.0656741i
$111$	5.13266	−	3.64662i	0.487171	−	0.346122i
$112$	−1.68284	+	2.91477i	−0.159014	+	0.275420i
$113$	−11.7127			−1.10183			−0.550917	−	0.834560i	$-0.685722\pi$
$113$	−11.7127			−1.10183			−0.550917	+	0.834560i	$0.685722\pi$
$114$	−2.12955	−	7.24327i	−0.199451	−	0.678395i
$115$	−1.99448			−0.185986
$116$	−1.95032	+	3.37805i	−0.181083	+	0.313644i
$117$	1.03605	+	5.43860i	0.0957832	+	0.502799i
$118$	4.40416	+	7.62824i	0.405436	+	0.702236i
$119$	20.7961	+	12.0067i	1.90638	+	1.10065i
$120$	0.162784	+	1.72438i	0.0148601	+	0.157414i
$121$	10.3674			0.942492
$122$	−6.69811			−0.606418
$123$	7.19059	−	0.678800i	0.648353	−	0.0612053i
$124$	7.17856	−	4.14455i	0.644654	−	0.372191i
$125$		−	1.00000i		−	0.0894427i
$126$	6.59571	+	7.64508i	0.587592	+	0.681078i
$127$	3.29108	−	1.90011i	0.292036	−	0.168607i	−0.346823	−	0.937930i	$-0.612740\pi$
$127$	3.29108	−	1.90011i	0.292036	−	0.168607i	0.638860	+	0.769323i	$0.279406\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.04842	+	0.570978i	−0.532534	+	0.0502718i
$130$	−0.922734	+	1.59822i	−0.0809291	+	0.140173i
$131$	4.80319	+	2.77312i	0.419656	+	0.242289i	0.694930	−	0.719077i	$-0.255435\pi$
$131$	4.80319	+	2.77312i	0.419656	+	0.242289i	−0.275274	+	0.961366i	$0.588769\pi$
$132$	1.25248	+	0.573622i	0.109015	+	0.0499274i
$133$	−2.79697	−	14.4016i	−0.242528	−	1.24878i
$134$			3.65766i			0.315974i
$135$	5.04569	+	1.24136i	0.434264	+	0.106839i
$136$	−6.17887	−	3.56737i	−0.529833	−	0.305899i
$137$	−17.2616	+	9.96597i	−1.47475	+	0.851450i	−0.999595	−	0.0284500i	$-0.990943\pi$
$137$	−17.2616	+	9.96597i	−1.47475	+	0.851450i	−0.475159	+	0.879900i	$0.657610\pi$
$138$	2.81615	−	2.00080i	0.239726	−	0.170319i
$139$	−5.17049	−	8.95556i	−0.438556	−	0.759600i	0.559023	−	0.829152i	$-0.311176\pi$
$139$	−5.17049	−	8.95556i	−0.438556	−	0.759600i	−0.997578	+	0.0695518i	$0.977843\pi$
$140$			3.36569i			0.284452i
$141$	5.69284	+	2.60725i	0.479423	+	0.219570i
$142$	0.800066	+	1.38576i	0.0671401	+	0.116290i
$143$	0.733899	+	1.27115i	0.0613717	+	0.106299i
$144$	−1.95969	−	2.27148i	−0.163308	−	0.189290i
$145$			3.90064i			0.323930i
$146$	7.05458	+	12.2189i	0.583841	+	1.01124i
$147$	4.34156	+	6.11079i	0.358086	+	0.504009i
$148$	−3.14810	+	1.81755i	−0.258772	+	0.149402i
$149$	7.24356	+	4.18207i	0.593415	+	0.342608i	0.766447	−	0.642308i	$-0.222023\pi$
$149$	7.24356	+	4.18207i	0.593415	+	0.342608i	−0.173031	+	0.984916i	$0.555356\pi$
$150$	1.00317	+	1.41197i	0.0819083	+	0.115287i
$151$		−	22.3534i		−	1.81909i	−0.415601	−	0.909547i	$-0.636429\pi$
$151$		−	22.3534i		−	1.81909i	0.415601	−	0.909547i	$-0.363571\pi$
$152$	0.831025	+	4.27895i	0.0674050	+	0.347069i
$153$	−16.2064	+	13.9819i	−1.31021	+	1.13037i
$154$	2.31827	+	1.33845i	0.186812	+	0.107856i
$155$	4.14455	−	7.17856i	0.332898	−	0.576596i
$156$	−0.300413	−	3.18230i	−0.0240522	−	0.254788i
$157$	−9.07185	+	15.7129i	−0.724013	+	1.25403i	0.235367	+	0.971907i	$0.424371\pi$
$157$	−9.07185	+	15.7129i	−0.724013	+	1.25403i	−0.959379	+	0.282120i	$0.908962\pi$
$158$	−10.3514	+	5.97636i	−0.823511	+	0.475454i
$159$	4.63324	−	10.1165i	0.367440	−	0.802292i
$160$		−	1.00000i		−	0.0790569i
$161$	5.81345	−	3.35640i	0.458164	−	0.264521i
$162$	−8.36965	+	3.30892i	−0.657582	+	0.259973i
$163$	−18.5170			−1.45037			−0.725184	−	0.688556i	$-0.758245\pi$
$163$	−18.5170			−1.45037			−0.725184	+	0.688556i	$0.758245\pi$
$164$	−4.16994			−0.325618
$165$	1.37149	−	0.129471i	0.106771	−	0.0100793i
$166$	−12.1185	−	6.99659i	−0.940575	−	0.543041i
$167$	9.91145	+	17.1671i	0.766971	+	1.32843i	0.939198	+	0.343376i	$0.111570\pi$
$167$	9.91145	+	17.1671i	0.766971	+	1.32843i	−0.172227	+	0.985057i	$0.555096\pi$
$168$	−3.37635	−	4.75224i	−0.260491	−	0.366644i
$169$	−4.79712	+	8.30886i	−0.369009	+	0.639143i
$170$	−7.13474			−0.547210
$171$	12.9422	+	1.87046i	0.989717	+	0.143038i
$172$	3.50758			0.267451
$173$	3.72918	−	6.45913i	0.283524	−	0.491079i	−0.688726	−	0.725022i	$-0.741830\pi$
$173$	3.72918	−	6.45913i	0.283524	−	0.491079i	0.972250	+	0.233943i	$0.0751630\pi$
$174$	−3.91299	−	5.50758i	−0.296643	−	0.417528i
$175$	1.68284	+	2.91477i	0.127211	+	0.220336i
$176$	−0.688796	−	0.397676i	−0.0519199	−	0.0299760i
$177$	−15.1889	+	1.43385i	−1.14167	+	0.107775i
$178$	3.67362			0.275349
$179$	0.307151			0.0229575			0.0114788	−	0.999934i	$-0.496346\pi$
$179$	0.307151			0.0229575			0.0114788	+	0.999934i	$0.496346\pi$
$180$	−2.83288	−	0.987311i	−0.211151	−	0.0735898i
$181$	11.6567	−	6.72999i	0.866435	−	0.500236i	0.000273100	−	1.00000i	$-0.499913\pi$
$181$	11.6567	−	6.72999i	0.866435	−	0.500236i	0.866162	+	0.499763i	$0.166580\pi$
$182$		−	6.21127i		−	0.460410i
$183$	4.83079	−	10.5479i	0.357102	−	0.779720i
$184$	−1.72727	+	0.997241i	−0.127336	+	0.0735176i
$185$	−1.81755	+	3.14810i	−0.133629	+	0.231453i
$186$	1.34933	+	14.2936i	0.0989377	+	1.04806i
$187$	−2.83732	+	4.91438i	−0.207485	+	0.359375i
$188$	−3.13074	−	1.80753i	−0.228333	−	0.131828i
$189$	−16.7961	+	4.87284i	−1.22173	+	0.354447i
$190$	2.85916	+	3.29017i	0.207425	+	0.238694i
$191$			20.3011i			1.46893i	0.678644	+	0.734467i	$0.262568\pi$
$191$			20.3011i			1.46893i	−0.678644	+	0.734467i	$0.737432\pi$
$192$	1.00317	+	1.41197i	0.0723974	+	0.101900i
$193$	−4.00713	−	2.31352i	−0.288439	−	0.166531i	0.348798	−	0.937198i	$-0.386590\pi$
$193$	−4.00713	−	2.31352i	−0.288439	−	0.166531i	−0.637238	+	0.770667i	$0.719923\pi$
$194$	−15.9344	+	9.19973i	−1.14402	+	0.660502i
$195$	−1.85131	−	2.60574i	−0.132575	−	0.186601i
$196$	−2.16392	−	3.74803i	−0.154566	−	0.267716i
$197$		−	17.5153i		−	1.24791i	−0.781460	−	0.623956i	$-0.785524\pi$
$197$		−	17.5153i		−	1.24791i	0.781460	−	0.623956i	$-0.214476\pi$
$198$	−1.80663	+	1.55865i	−0.128391	+	0.110768i
$199$	−0.637900	−	1.10487i	−0.0452195	−	0.0783225i	0.842530	−	0.538650i	$-0.181065\pi$
$199$	−0.637900	−	1.10487i	−0.0452195	−	0.0783225i	−0.887749	+	0.460327i	$0.847732\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−5.75991	−	2.63797i	−0.406273	−	0.186068i
$202$			1.19597i			0.0841481i
$203$	−6.56416	−	11.3695i	−0.460714	−	0.797980i
$204$	10.0740	−	7.15734i	0.705323	−	0.501114i
$205$	−3.61128	+	2.08497i	−0.252223	+	0.145621i
$206$	−1.89833	−	1.09600i	−0.132263	−	0.0763620i
$207$	1.11971	+	5.87774i	0.0778252	+	0.408531i
$208$			1.84547i			0.127960i
$209$	3.40327	−	0.660958i	0.235409	−	0.0457194i
$210$	−5.30012	−	2.42739i	−0.365743	−	0.167506i
$211$	23.3524	+	13.4825i	1.60765	+	0.928177i	0.989895	+	0.141805i	$0.0452907\pi$
$211$	23.3524	+	13.4825i	1.60765	+	0.928177i	0.617754	+	0.786371i	$0.288043\pi$
$212$	−3.21210	+	5.56351i	−0.220608	+	0.382104i
$213$	−2.75924	+	0.260476i	−0.189060	+	0.0178475i
$214$	0.536127	−	0.928599i	0.0366489	−	0.0634777i
$215$	3.03766	−	1.75379i	0.207166	−	0.119608i
$216$	4.99038	−	1.44780i	0.339552	−	0.0985104i
$217$			27.8985i			1.89387i
$218$	0.897440	−	0.518137i	0.0607823	−	0.0350927i
$219$	−24.3296	+	2.29674i	−1.64404	+	0.155200i
$220$	−0.795353			−0.0536227
$221$	13.1669			0.885704
$222$	−0.591737	−	6.26833i	−0.0397148	−	0.420703i
$223$	19.3951	+	11.1978i	1.29879	+	0.749857i	0.980195	−	0.198034i	$-0.0634557\pi$
$223$	19.3951	+	11.1978i	1.29879	+	0.749857i	0.318595	+	0.947891i	$0.396789\pi$
$224$	1.68284	+	2.91477i	0.112440	+	0.194751i
$225$	−2.94700	+	0.561404i	−0.196467	+	0.0374269i
$226$	−5.85633	+	10.1435i	−0.389557	+	0.674733i
$227$	17.4096			1.15552			0.577758	−	0.816208i	$-0.303928\pi$
$227$	17.4096			1.15552			0.577758	+	0.816208i	$0.303928\pi$
$228$	−7.33763	−	1.77739i	−0.485947	−	0.117711i
$229$	1.93992			0.128193			0.0640966	−	0.997944i	$-0.479583\pi$
$229$	1.93992			0.128193			0.0640966	+	0.997944i	$0.479583\pi$
$230$	−0.997241	+	1.72727i	−0.0657561	+	0.113893i
$231$	−3.77971	+	2.68539i	−0.248687	+	0.176685i
$232$	1.95032	+	3.37805i	0.128045	+	0.221780i
$233$	−2.14005	−	1.23556i	−0.140199	−	0.0809440i	0.428260	−	0.903656i	$-0.359127\pi$
$233$	−2.14005	−	1.23556i	−0.140199	−	0.0809440i	−0.568459	+	0.822712i	$0.692460\pi$
$234$	5.22799	+	1.82205i	0.341765	+	0.119111i
$235$	−3.61507			−0.235821
$236$	8.80833			0.573373
$237$	−1.94571	−	20.6111i	−0.126388	−	1.33883i
$238$	20.7961	−	12.0067i	1.34801	−	0.778276i
$239$			13.1953i			0.853534i	0.904362	+	0.426767i	$0.140348\pi$
$239$			13.1953i			0.853534i	−0.904362	+	0.426767i	$0.859652\pi$
$240$	1.57475	+	0.721217i	0.101650	+	0.0465544i
$241$	23.5846	−	13.6166i	1.51922	−	0.877122i	0.519477	−	0.854485i	$-0.326127\pi$
$241$	23.5846	−	13.6166i	1.51922	−	0.877122i	0.999744	−	0.0226375i	$-0.00720636\pi$
$242$	5.18371	−	8.97844i	0.333221	−	0.577156i
$243$	0.825609	−	15.5666i	0.0529628	−	0.998596i
$244$	−3.34905	+	5.80073i	−0.214401	+	0.371354i
$245$	−3.74803	−	2.16392i	−0.239453	−	0.138248i
$246$	3.00744	−	6.56663i	0.191747	−	0.418673i
$247$	−5.27649	−	6.07190i	−0.335735	−	0.386345i
$248$		−	8.28909i		−	0.526358i
$249$	19.7579	−	14.0375i	1.25211	−	0.889591i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	18.6598	−	10.7733i	1.17780	−	0.680002i	0.222294	−	0.974980i	$-0.428646\pi$
$251$	18.6598	−	10.7733i	1.17780	−	0.680002i	0.955504	+	0.294978i	$0.0953123\pi$
$252$	9.91869	−	1.88951i	0.624819	−	0.119028i
$253$	0.793158	+	1.37379i	0.0498654	+	0.0863694i
$254$		−	3.80022i		−	0.238447i
$255$	5.14570	−	11.2355i	0.322236	−	0.703591i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.4617	−	25.0484i	−0.902096	−	1.56248i	−0.824768	−	0.565471i	$-0.808694\pi$
$257$	−14.4617	−	25.0484i	−0.902096	−	1.56248i	−0.0773283	−	0.997006i	$-0.524639\pi$
$258$	−2.52973	+	5.52357i	−0.157494	+	0.343883i
$259$		−	12.2346i		−	0.760224i
$260$	0.922734	+	1.59822i	0.0572255	+	0.0991175i
$261$	11.4952	−	2.18983i	0.711534	−	0.135547i
$262$	4.80319	−	2.77312i	0.296742	−	0.171324i
$263$	13.9401	+	8.04833i	0.859585	+	0.496281i	0.863873	−	0.503709i	$-0.168032\pi$
$263$	13.9401	+	8.04833i	0.859585	+	0.496281i	−0.00428849	+	0.999991i	$0.501365\pi$
$264$	1.12301	−	0.797872i	0.0691167	−	0.0491056i
$265$			6.42419i			0.394635i
$266$	−13.8706	−	4.77855i	−0.850463	−	0.292992i
$267$	−2.64948	+	5.78504i	−0.162145	+	0.354039i
$268$	3.16763	+	1.82883i	0.193494	+	0.111714i
$269$	−7.78283	+	13.4803i	−0.474528	+	0.821906i	−0.999575	−	0.0291674i	$-0.990714\pi$
$269$	−7.78283	+	13.4803i	−0.474528	+	0.821906i	0.525047	+	0.851073i	$0.324048\pi$
$270$	3.59789	−	3.74902i	0.218961	−	0.228158i
$271$	1.20476	−	2.08670i	0.0731839	−	0.126758i	−0.827111	−	0.562038i	$-0.810017\pi$
$271$	1.20476	−	2.08670i	0.0731839	−	0.126758i	0.900295	+	0.435280i	$0.143351\pi$
$272$	−6.17887	+	3.56737i	−0.374649	+	0.216304i
$273$	9.78121	+	4.47967i	0.591986	+	0.271122i
$274$			19.9319i			1.20413i
$275$	−0.688796	+	0.397676i	−0.0415359	+	0.0239808i
$276$	−0.324669	−	3.43925i	−0.0195428	−	0.207019i
$277$	30.7890			1.84993			0.924965	−	0.380052i	$-0.124094\pi$
$277$	30.7890			1.84993			0.924965	+	0.380052i	$0.124094\pi$
$278$	−10.3410			−0.620211
$279$	−23.4820	−	8.18391i	−1.40583	−	0.489958i
$280$	2.91477	+	1.68284i	0.174191	+	0.100569i
$281$	−12.6678	−	21.9413i	−0.755698	−	1.30891i	−0.945027	−	0.326993i	$-0.893965\pi$
$281$	−12.6678	−	21.9413i	−0.755698	−	1.30891i	0.189329	−	0.981914i	$-0.439369\pi$
$282$	5.10436	−	3.62652i	0.303960	−	0.215956i
$283$	4.10956	−	7.11797i	0.244288	−	0.423119i	−0.717643	−	0.696411i	$-0.754779\pi$
$283$	4.10956	−	7.11797i	0.244288	−	0.423119i	0.961931	+	0.273292i	$0.0881124\pi$
$284$	1.60013			0.0949504
$285$	−7.24327	+	2.12955i	−0.429055	+	0.126144i
$286$	1.46780			0.0867927
$287$	7.01736	−	12.1544i	0.414222	−	0.717453i
$288$	−2.94700	+	0.561404i	−0.173654	+	0.0330810i
$289$	16.9523	+	29.3622i	0.997192	+	1.72719i
$290$	3.37805	+	1.95032i	0.198366	+	0.114527i
$291$	−2.99514	−	31.7278i	−0.175578	−	1.85991i
$292$	14.1092			0.825676
$293$	−24.4468			−1.42820			−0.714099	−	0.700045i	$-0.753163\pi$
$293$	−24.4468			−1.42820			−0.714099	+	0.700045i	$0.753163\pi$
$294$	7.46288	−	0.704504i	0.435244	−	0.0410875i
$295$	7.62824	−	4.40416i	0.444133	−	0.256420i
$296$			3.63511i			0.211286i
$297$	−1.15151	−	3.96911i	−0.0668175	−	0.230311i
$298$	7.24356	−	4.18207i	0.419608	−	0.242261i
$299$	1.84038	−	3.18762i	0.106432	−	0.184345i
$300$	1.72438	−	0.162784i	0.0995574	−	0.00939833i
$301$	−5.90271	+	10.2238i	−0.340227	+	0.589290i
$302$	−19.3586	−	11.1767i	−1.11396	−	0.643147i
$303$	−1.88335	−	0.862553i	−0.108196	−	0.0495524i
$304$	4.12119	+	1.41979i	0.236366	+	0.0814303i
$305$			6.69811i			0.383532i
$306$	4.00547	+	21.0261i	0.228978	+	1.20198i
$307$	−9.65029	−	5.57160i	−0.550771	−	0.317988i	0.198662	−	0.980068i	$-0.436340\pi$
$307$	−9.65029	−	5.57160i	−0.550771	−	0.317988i	−0.749433	+	0.662080i	$0.769674\pi$
$308$	2.31827	−	1.33845i	0.132096	−	0.0762655i
$309$	3.09504	−	2.19894i	0.176071	−	0.125094i
$310$	−4.14455	−	7.17856i	−0.235394	−	0.407715i
$311$		−	24.4400i		−	1.38587i	−0.721002	−	0.692933i	$-0.756318\pi$
$311$		−	24.4400i		−	1.38587i	0.721002	−	0.692933i	$-0.243682\pi$
$312$	−2.90616	−	1.33098i	−0.164529	−	0.0753521i
$313$	−1.06464	−	1.84401i	−0.0601771	−	0.104230i	0.834367	−	0.551209i	$-0.185833\pi$
$313$	−1.06464	−	1.84401i	−0.0601771	−	0.104230i	−0.894544	+	0.446979i	$0.852500\pi$
$314$	9.07185	+	15.7129i	0.511954	+	0.886731i
$315$	7.64508	−	6.59571i	0.430752	−	0.371626i
$316$			11.9527i			0.672394i
$317$	3.03351	+	5.25419i	0.170379	+	0.295105i	0.938552	−	0.345137i	$-0.112168\pi$
$317$	3.03351	+	5.25419i	0.170379	+	0.295105i	−0.768173	+	0.640242i	$0.778834\pi$
$318$	−6.44454	−	9.07076i	−0.361392	−	0.508663i
$319$	2.68674	−	1.55119i	0.150429	−	0.0868500i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	1.07565	+	1.51399i	0.0600369	+	0.0845026i
$322$		−	6.71280i		−	0.374090i
$323$	10.1298	−	29.4036i	0.563637	−	1.63606i
$324$	−1.31922	+	8.90279i	−0.0732899	+	0.494599i
$325$	1.59822	+	0.922734i	0.0886534	+	0.0511841i
$326$	−9.25852	+	16.0362i	−0.512782	+	0.888165i
$327$	0.168689	+	1.78694i	0.00932851	+	0.0988178i
$328$	−2.08497	+	3.61128i	−0.115123	+	0.199399i
$329$	10.5371	−	6.08359i	0.580929	−	0.335399i
$330$	0.573622	−	1.25248i	0.0315769	−	0.0689470i
$331$			7.63334i			0.419566i	0.977748	+	0.209783i	$0.0672758\pi$
$331$			7.63334i			0.419566i	−0.977748	+	0.209783i	$0.932724\pi$
$332$	−12.1185	+	6.99659i	−0.665087	+	0.383988i
$333$	10.2978	+	3.58898i	0.564318	+	0.196675i
$334$	19.8229			1.08466
$335$	3.65766			0.199839
$336$	−5.80374	+	0.547880i	−0.316620	+	0.0298893i
$337$	−4.98568	−	2.87848i	−0.271587	−	0.156801i	0.358022	−	0.933713i	$-0.383451\pi$
$337$	−4.98568	−	2.87848i	−0.271587	−	0.156801i	−0.629609	+	0.776912i	$0.716785\pi$
$338$	4.79712	+	8.30886i	0.260929	+	0.451942i
$339$	−11.7497	−	16.5379i	−0.638159	−	0.898215i
$340$	−3.56737	+	6.17887i	−0.193468	+	0.335096i
$341$	−6.59275			−0.357018
$342$	8.09098	−	10.2731i	0.437510	−	0.555504i
$343$	−8.99362			−0.485610
$344$	1.75379	−	3.03766i	0.0945581	−	0.163779i
$345$	−2.00080	−	2.81615i	−0.107719	−	0.151616i
$346$	−3.72918	−	6.45913i	−0.200482	−	0.347245i
$347$	16.8904	+	9.75166i	0.906723	+	0.523497i	0.879375	−	0.476129i	$-0.157961\pi$
$347$	16.8904	+	9.75166i	0.906723	+	0.523497i	0.0273475	+	0.999626i	$0.491294\pi$
$348$	−6.72620	+	0.634961i	−0.360562	+	0.0340375i
$349$	−0.423234			−0.0226552			−0.0113276	−	0.999936i	$-0.503606\pi$
$349$	−0.423234			−0.0226552			−0.0113276	+	0.999936i	$0.503606\pi$
$350$	3.36569			0.179904
$351$	−6.63980	+	6.91870i	−0.354406	+	0.369293i
$352$	−0.688796	+	0.397676i	−0.0367129	+	0.0211962i
$353$		−	24.0186i		−	1.27838i	−0.769049	−	0.639190i	$-0.779270\pi$
$353$		−	24.0186i		−	1.27838i	0.769049	−	0.639190i	$-0.220730\pi$
$354$	−6.35272	+	13.8709i	−0.337643	+	0.737232i
$355$	1.38576	−	0.800066i	0.0735483	−	0.0424631i
$356$	1.83681	−	3.18145i	0.0973507	−	0.168616i
$357$	3.90898	+	41.4082i	0.206885	+	2.19155i
$358$	0.153575	−	0.266000i	0.00811671	−	0.0140586i
$359$	9.83401	+	5.67767i	0.519019	+	0.299656i	0.736533	−	0.676401i	$-0.236461\pi$
$359$	9.83401	+	5.67767i	0.519019	+	0.299656i	−0.217514	+	0.976057i	$0.569795\pi$
$360$	−2.27148	+	1.95969i	−0.119717	+	0.103285i
$361$	−17.6188	+	7.11183i	−0.927305	+	0.374307i
$362$		−	13.4600i		−	0.707441i
$363$	10.4002	+	14.6385i	0.545872	+	0.768320i
$364$	−5.37912	−	3.10563i	−0.281942	−	0.162779i
$365$	12.2189	−	7.05458i	0.639566	−	0.369253i
$366$	−6.71932	−	9.45752i	−0.351225	−	0.494352i
$367$	−4.59216	−	7.95386i	−0.239709	−	0.415188i	0.720922	−	0.693016i	$-0.243719\pi$
$367$	−4.59216	−	7.95386i	−0.239709	−	0.415188i	−0.960631	+	0.277828i	$0.910385\pi$
$368$			1.99448i			0.103970i
$369$	8.17180	+	9.47193i	0.425407	+	0.493089i
$370$	1.81755	+	3.14810i	0.0944902	+	0.163662i
$371$	−10.8109	−	18.7250i	−0.561274	−	0.972156i
$372$	13.0533	+	5.97824i	0.676781	+	0.309957i
$373$		−	26.2996i		−	1.36174i	−0.732404	−	0.680870i	$-0.761602\pi$
$373$		−	26.2996i		−	1.36174i	0.732404	−	0.680870i	$-0.238398\pi$
$374$	2.83732	+	4.91438i	0.146714	+	0.254116i
$375$	1.41197	−	1.00317i	0.0729138	−	0.0518033i
$376$	−3.13074	+	1.80753i	−0.161456	+	0.0932164i
$377$	−6.23409	−	3.59925i	−0.321072	−	0.185371i
$378$	−4.17802	+	16.9822i	−0.214894	+	0.873472i
$379$			9.26609i			0.475967i	0.971269	+	0.237984i	$0.0764864\pi$
$379$			9.26609i			0.475967i	−0.971269	+	0.237984i	$0.923514\pi$
$380$	4.27895	−	0.831025i	0.219505	−	0.0426307i
$381$	5.98440	+	2.74078i	0.306590	+	0.140414i
$382$	17.5813	+	10.1505i	0.899535	+	0.519347i
$383$	−11.1774	+	19.3598i	−0.571137	+	0.989238i	0.425313	+	0.905046i	$0.360164\pi$
$383$	−11.1774	+	19.3598i	−0.571137	+	0.989238i	−0.996450	+	0.0841912i	$0.973169\pi$
$384$	1.72438	−	0.162784i	0.0879971	−	0.00830703i
$385$	1.33845	−	2.31827i	0.0682139	−	0.118150i
$386$	−4.00713	+	2.31352i	−0.203957	+	0.117755i
$387$	−6.87378	−	7.96739i	−0.349414	−	0.405005i
$388$			18.3995i			0.934092i
$389$	2.10271	−	1.21400i	0.106612	−	0.0615522i	−0.445746	−	0.895159i	$-0.647062\pi$
$389$	2.10271	−	1.21400i	0.106612	−	0.0615522i	0.552358	+	0.833607i	$0.313728\pi$
$390$	−3.18230	+	0.300413i	−0.161142	+	0.0152120i
$391$	14.2301			0.719647
$392$	−4.32785			−0.218589
$393$	0.902839	+	9.56386i	0.0455422	+	0.482433i
$394$	−15.1687	−	8.75764i	−0.764187	−	0.441203i
$395$	5.97636	+	10.3514i	0.300704	+	0.520834i
$396$	0.446514	+	2.34391i	0.0224382	+	0.117786i
$397$	−13.4569	+	23.3080i	−0.675383	+	1.16980i	0.300974	+	0.953632i	$0.402688\pi$
$397$	−13.4569	+	23.3080i	−0.675383	+	1.16980i	−0.976357	+	0.216165i	$0.930645\pi$
$398$	−1.27580			−0.0639500
$399$	17.5288	−	18.3964i	0.877537	−	0.920974i
$400$	−1.00000			−0.0500000
$401$	−5.27439	+	9.13551i	−0.263390	+	0.456206i	−0.967141	−	0.254242i	$-0.918174\pi$
$401$	−5.27439	+	9.13551i	−0.263390	+	0.456206i	0.703750	+	0.710447i	$0.251507\pi$
$402$	−5.16450	+	3.66925i	−0.257582	+	0.183005i
$403$	7.64863	+	13.2478i	0.381005	+	0.659921i
$404$	1.03574	+	0.597984i	0.0515300	+	0.0297508i
$405$	3.30892	+	8.36965i	0.164421	+	0.415891i
$406$	−13.1283			−0.651548
$407$	2.89119			0.143311
$408$	−1.16142	−	12.3030i	−0.0574989	−	0.609091i
$409$	15.0416	−	8.68429i	0.743761	−	0.429410i	−0.0796743	−	0.996821i	$-0.525388\pi$
$409$	15.0416	−	8.68429i	0.743761	−	0.429410i	0.823435	+	0.567410i	$0.192055\pi$
$410$			4.16994i			0.205939i
$411$	−31.3879	−	14.3753i	−1.54825	−	0.709079i
$412$	−1.89833	+	1.09600i	−0.0935240	+	0.0539961i
$413$	−14.8230	+	25.6743i	−0.729394	+	1.26335i
$414$	5.65013	+	1.96917i	0.277689	+	0.0967796i
$415$	−6.99659	+	12.1185i	−0.343449	+	0.594872i
$416$	1.59822	+	0.922734i	0.0783593	+	0.0452408i
$417$	7.45810	−	16.2845i	0.365225	−	0.797455i
$418$	1.12923	−	3.27780i	0.0552325	−	0.160322i
$419$			29.5663i			1.44441i	0.691680	+	0.722204i	$0.256871\pi$
$419$			29.5663i			1.44441i	−0.691680	+	0.722204i	$0.743129\pi$
$420$	−4.75224	+	3.37635i	−0.231886	+	0.164749i
$421$	2.75755	+	1.59207i	0.134395	+	0.0775930i	0.565690	−	0.824618i	$-0.308610\pi$
$421$	2.75755	+	1.59207i	0.134395	+	0.0775930i	−0.431295	+	0.902211i	$0.641943\pi$
$422$	23.3524	−	13.4825i	1.13678	−	0.656320i
$423$	2.02951	+	10.6536i	0.0986783	+	0.517996i
$424$	3.21210	+	5.56351i	0.155993	+	0.270188i
$425$			7.13474i			0.346086i
$426$	−1.15404	+	2.51981i	−0.0559136	+	0.122085i
$427$	−11.2719	−	19.5234i	−0.545484	−	0.944806i
$428$	−0.536127	−	0.928599i	−0.0259147	−	0.0448855i
$429$	−1.05860	+	2.31142i	−0.0511098	+	0.111596i
$430$		−	3.50758i		−	0.169151i
$431$	12.6847	+	21.9705i	0.611000	+	1.05828i	0.991072	+	0.133326i	$0.0425656\pi$
$431$	12.6847	+	21.9705i	0.611000	+	1.05828i	−0.380073	+	0.924957i	$0.624101\pi$
$432$	1.24136	−	5.04569i	0.0597248	−	0.242761i
$433$	−34.0276	+	19.6459i	−1.63526	+	0.944120i	−0.652832	+	0.757503i	$0.726419\pi$
$433$	−34.0276	+	19.6459i	−1.63526	+	0.944120i	−0.982433	+	0.186617i	$0.940248\pi$
$434$	24.1608	+	13.9492i	1.15976	+	0.669585i
$435$	−5.50758	+	3.91299i	−0.264068	+	0.187614i
$436$		−	1.03627i		−	0.0496285i
$437$	−5.70255	−	6.56217i	−0.272790	−	0.313911i
$438$	−10.1758	+	22.2184i	−0.486217	+	1.06164i
$439$	9.49324	+	5.48093i	0.453088	+	0.261590i	0.709133	−	0.705074i	$-0.249086\pi$
$439$	9.49324	+	5.48093i	0.453088	+	0.261590i	−0.256046	+	0.966665i	$0.582420\pi$
$440$	−0.397676	+	0.688796i	−0.0189585	+	0.0328370i
$441$	−4.27293	+	12.2603i	−0.203473	+	0.583823i
$442$	6.58347	−	11.4029i	0.313144	−	0.542381i
$443$	28.0730	−	16.2079i	1.33379	−	0.770062i	0.347909	−	0.937528i	$-0.386892\pi$
$443$	28.0730	−	16.2079i	1.33379	−	0.770062i	0.985878	+	0.167466i	$0.0535584\pi$
$444$	−5.72440	−	2.62170i	−0.271668	−	0.124421i
$445$		−	3.67362i		−	0.174146i
$446$	19.3951	−	11.1978i	0.918383	−	0.530229i
$447$	1.36155	+	14.4230i	0.0643990	+	0.682184i
$448$	3.36569			0.159014
$449$	−1.66858			−0.0787453			−0.0393727	−	0.999225i	$-0.512536\pi$
$449$	−1.66858			−0.0787453			−0.0393727	+	0.999225i	$0.512536\pi$
$450$	−0.987311	+	2.83288i	−0.0465423	+	0.133543i
$451$	2.87224	+	1.65829i	0.135248	+	0.0780857i
$452$	5.85633	+	10.1435i	0.275458	+	0.477108i
$453$	31.5623	−	22.4242i	1.48293	−	1.05358i
$454$	8.70480	−	15.0772i	0.408536	−	0.707606i
$455$	−6.21127			−0.291189
$456$	−5.20808	+	5.46588i	−0.243891	+	0.255963i
$457$	−14.4764			−0.677179			−0.338589	−	0.940934i	$-0.609950\pi$
$457$	−14.4764			−0.677179			−0.338589	+	0.940934i	$0.609950\pi$
$458$	0.969958	−	1.68002i	0.0453232	−	0.0785020i
$459$	−35.9997	−	8.85676i	−1.68032	−	0.413398i
$460$	0.997241	+	1.72727i	0.0464966	+	0.0805344i
$461$	−25.3943	−	14.6614i	−1.18273	−	0.682851i	−0.226087	−	0.974107i	$-0.572593\pi$
$461$	−25.3943	−	14.6614i	−1.18273	−	0.682851i	−0.956645	+	0.291256i	$0.905927\pi$
$462$	0.435758	+	4.61602i	0.0202733	+	0.214757i
$463$	41.3040			1.91956			0.959781	−	0.280751i	$-0.0905836\pi$
$463$	41.3040			1.91956			0.959781	+	0.280751i	$0.0905836\pi$
$464$	3.90064			0.181083
$465$	14.2936	−	1.34933i	0.662849	−	0.0625737i
$466$	−2.14005	+	1.23556i	−0.0991358	+	0.0572361i
$467$			13.2112i			0.611341i	0.952137	+	0.305671i	$0.0988806\pi$
$467$			13.2112i			0.611341i	−0.952137	+	0.305671i	$0.901119\pi$
$468$	4.19194	−	3.61655i	0.193772	−	0.167175i
$469$	−10.6612	+	6.15527i	−0.492291	+	0.284224i
$470$	−1.80753	+	3.13074i	−0.0833753	+	0.144410i
$471$	−31.2867	+	2.95350i	−1.44162	+	0.136090i
$472$	4.40416	−	7.62824i	0.202718	−	0.351118i
$473$	−2.41601	−	1.39488i	−0.111088	−	0.0641368i
$474$	−18.8226	−	8.62051i	−0.864550	−	0.395953i
$475$	3.29017	−	2.85916i	0.150963	−	0.131187i
$476$		−	24.0133i		−	1.10065i
$477$	18.9321	−	3.60657i	0.866842	−	0.165133i
$478$	11.4275	+	6.59766i	0.522681	+	0.301770i
$479$	−29.9827	+	17.3105i	−1.36995	+	0.790939i	−0.990921	−	0.134448i	$-0.957074\pi$
$479$	−29.9827	+	17.3105i	−1.36995	+	0.790939i	−0.379025	+	0.925386i	$0.623741\pi$
$480$	1.41197	−	1.00317i	0.0644473	−	0.0457881i
$481$	−3.35424	−	5.80971i	−0.152940	−	0.264900i
$482$		−	27.2332i		−	1.24044i
$483$	10.5710	+	4.84139i	0.480997	+	0.220291i
$484$	−5.18371	−	8.97844i	−0.235623	−	0.408111i
$485$	9.19973	+	15.9344i	0.417738	+	0.723544i
$486$	−13.0682	−	8.49829i	−0.592788	−	0.385490i
$487$			20.7783i			0.941554i	0.882252	+	0.470777i	$0.156026\pi$
$487$			20.7783i			0.941554i	−0.882252	+	0.470777i	$0.843974\pi$
$488$	3.34905	+	5.80073i	0.151605	+	0.262587i
$489$	−18.5757	−	26.1455i	−0.840022	−	1.18234i
$490$	−3.74803	+	2.16392i	−0.169319	+	0.0977562i
$491$	−3.62316	−	2.09183i	−0.163511	−	0.0944030i	0.416012	−	0.909359i	$-0.363428\pi$
$491$	−3.62316	−	2.09183i	−0.163511	−	0.0944030i	−0.579522	+	0.814956i	$0.696761\pi$
$492$	−4.18315	−	5.88783i	−0.188591	−	0.265444i
$493$		−	27.8300i		−	1.25340i
$494$	−7.89666	+	1.53363i	−0.355288	+	0.0690013i
$495$	1.55865	+	1.80663i	0.0700559	+	0.0812018i
$496$	−7.17856	−	4.14455i	−0.322327	−	0.186096i
$497$	−2.69277	+	4.66402i	−0.120787	+	0.209210i
$498$	−2.27787	−	24.1296i	−0.102074	−	1.08127i
$499$	2.93329	−	5.08061i	0.131312	−	0.227439i	−0.792871	−	0.609390i	$-0.791414\pi$
$499$	2.93329	−	5.08061i	0.131312	−	0.227439i	0.924183	+	0.381951i	$0.124748\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−14.2966	+	31.2162i	−0.638726	+	1.39464i
$502$		−	21.5465i		−	0.961668i
$503$	9.79822	−	5.65701i	0.436881	−	0.252233i	−0.265393	−	0.964140i	$-0.585502\pi$
$503$	9.79822	−	5.65701i	0.436881	−	0.252233i	0.702274	+	0.711907i	$0.252168\pi$
$504$	3.32298	−	9.53459i	0.148017	−	0.424704i
$505$	1.19597			0.0532199
$506$	1.58632			0.0705204
$507$	−16.5442	+	1.56179i	−0.734752	+	0.0693615i
$508$	−3.29108	−	1.90011i	−0.146018	−	0.0843036i
$509$	−10.8249	−	18.7493i	−0.479806	−	0.831048i	0.519926	−	0.854211i	$-0.325960\pi$
$509$	−10.8249	−	18.7493i	−0.479806	−	0.831048i	−0.999732	+	0.0231634i	$0.992626\pi$
$510$	−7.15734	−	10.0740i	−0.316932	−	0.446086i
$511$	−23.7435	+	41.1249i	−1.05035	+	1.81926i
$512$	−1.00000			−0.0441942
$513$	10.3422	+	20.1504i	0.456619	+	0.889662i
$514$	−28.9234			−1.27576
$515$	−1.09600	+	1.89833i	−0.0482956	+	0.0836504i
$516$	3.51869	+	4.95260i	0.154902	+	0.218026i
$517$	1.43763	+	2.49004i	0.0632268	+	0.109512i
$518$	−10.5955	−	6.11732i	−0.465540	−	0.268780i
$519$	12.8611	−	1.21410i	0.564539	−	0.0532931i
$520$	1.84547			0.0809291
$521$	−31.4041			−1.37584			−0.687920	−	0.725787i	$-0.741476\pi$
$521$	−31.4041			−1.37584			−0.687920	+	0.725787i	$0.741476\pi$
$522$	3.85114	−	11.0500i	0.168560	−	0.483647i
$523$	9.94201	−	5.74002i	0.434734	−	0.250994i	−0.266627	−	0.963800i	$-0.585909\pi$
$523$	9.94201	−	5.74002i	0.434734	−	0.250994i	0.701361	+	0.712806i	$0.252576\pi$
$524$		−	5.54624i		−	0.242289i
$525$	−2.42739	+	5.30012i	−0.105940	+	0.231316i
$526$	13.9401	−	8.04833i	0.607818	−	0.350924i
$527$	−29.5703	+	51.2172i	−1.28810	+	2.23106i
$528$	−0.129471	−	1.37149i	−0.00563449	−	0.0596866i
$529$	−9.51102	+	16.4736i	−0.413523	+	0.716242i
$530$	5.56351	+	3.21210i	0.241664	+	0.139525i
$531$	−17.2616	−	20.0079i	−0.749090	−	0.868270i
$532$	−11.0737	+	9.62305i	−0.480104	+	0.417212i
$533$		−	7.69550i		−	0.333329i
$534$	3.68525	+	5.18703i	0.159476	+	0.224465i
$535$	−0.928599	−	0.536127i	−0.0401468	−	0.0231788i
$536$	3.16763	−	1.82883i	0.136821	−	0.0789935i
$537$	0.308123	+	0.433687i	0.0132965	+	0.0187150i
$538$	7.78283	+	13.4803i	0.335542	+	0.581175i
$539$			3.44217i			0.148265i
$540$	−1.44780	−	4.99038i	−0.0623034	−	0.214752i
$541$	15.6183	+	27.0516i	0.671482	+	1.16304i	0.977484	+	0.211010i	$0.0676752\pi$
$541$	15.6183	+	27.0516i	0.671482	+	1.16304i	−0.306002	+	0.952031i	$0.598991\pi$
$542$	−1.20476	−	2.08670i	−0.0517488	−	0.0896316i
$543$	21.1962	+	9.70757i	0.909614	+	0.416592i
$544$			7.13474i			0.305899i
$545$	−0.518137	−	0.897440i	−0.0221946	−	0.0384421i
$546$	8.77012	−	6.23094i	0.375326	−	0.266660i
$547$	−6.49439	+	3.74954i	−0.277680	+	0.160319i	−0.632373	−	0.774664i	$-0.717919\pi$
$547$	−6.49439	+	3.74954i	−0.277680	+	0.160319i	0.354693	+	0.934983i	$0.384586\pi$
$548$	17.2616	+	9.96597i	0.737377	+	0.425725i
$549$	19.7393	−	3.76034i	0.842454	−	0.160488i
$550$			0.795353i			0.0339140i
$551$	−12.8337	+	11.1526i	−0.546736	+	0.475115i
$552$	−3.14081	−	1.43845i	−0.133682	−	0.0612247i
$553$	−34.8395	−	20.1146i	−1.48152	−	0.855359i
$554$	15.3945	−	26.6640i	0.654049	−	1.13285i
$555$	−6.26833	+	0.591737i	−0.266076	+	0.0251178i
$556$	−5.17049	+	8.95556i	−0.219278	+	0.379800i
$557$	9.64943	−	5.57110i	0.408860	−	0.236055i	−0.281440	−	0.959579i	$-0.590812\pi$
$557$	9.64943	−	5.57110i	0.408860	−	0.236055i	0.690300	+	0.723524i	$0.257479\pi$
$558$	−18.8285	+	16.2441i	−0.797073	+	0.687666i
$559$			6.47313i			0.273784i
$560$	2.91477	−	1.68284i	0.123172	−	0.0711131i
$561$	−9.78525	+	0.923739i	−0.413134	+	0.0390003i
$562$	−25.3356			−1.06872
$563$	25.6386			1.08054			0.540269	−	0.841492i	$-0.318323\pi$
$563$	25.6386			1.08054			0.540269	+	0.841492i	$0.318323\pi$
$564$	−0.588475	−	6.23377i	−0.0247793	−	0.262489i
$565$	10.1435	+	5.85633i	0.426738	+	0.246378i
$566$	−4.10956	−	7.11797i	−0.172738	−	0.299191i
$567$	−23.7296	−	18.8272i	−0.996547	−	0.790669i
$568$	0.800066	−	1.38576i	0.0335700	−	0.0581450i
$569$	−36.2410			−1.51930			−0.759651	−	0.650331i	$-0.774630\pi$
$569$	−36.2410			−1.51930			−0.759651	+	0.650331i	$0.774630\pi$
$570$	−1.77739	+	7.33763i	−0.0744468	+	0.307340i
$571$	6.61731			0.276926			0.138463	−	0.990368i	$-0.455784\pi$
$571$	6.61731			0.276926			0.138463	+	0.990368i	$0.455784\pi$
$572$	0.733899	−	1.27115i	0.0306859	−	0.0531495i
$573$	−28.6645	+	20.3654i	−1.19748	+	0.850776i
$574$	−7.01736	−	12.1544i	−0.292899	−	0.507316i
$575$	1.72727	+	0.997241i	0.0720322	+	0.0415878i
$576$	−0.987311	+	2.83288i	−0.0411380	+	0.118037i
$577$	36.0337			1.50010			0.750051	−	0.661380i	$-0.230029\pi$
$577$	36.0337			1.50010			0.750051	+	0.661380i	$0.230029\pi$
$578$	33.9045			1.41024
$579$	−0.753206	−	7.97878i	−0.0313022	−	0.331587i
$580$	3.37805	−	1.95032i	0.140266	−	0.0809826i
$581$		−	47.0967i		−	1.95390i
$582$	−28.9746	−	13.2700i	−1.20104	−	0.550060i
$583$	4.42496	−	2.55475i	0.183263	−	0.105807i
$584$	7.05458	−	12.2189i	0.291920	−	0.505621i
$585$	1.82205	−	5.22799i	0.0753326	−	0.216151i
$586$	−12.2234	+	21.1716i	−0.504944	+	0.874589i
$587$	−24.1606	−	13.9491i	−0.997214	−	0.575742i	−0.0897909	−	0.995961i	$-0.528620\pi$
$587$	−24.1606	−	13.9491i	−0.997214	−	0.575742i	−0.907423	+	0.420219i	$0.861953\pi$
$588$	3.12132	−	6.81529i	0.128721	−	0.281058i
$589$	35.4686	−	6.88844i	1.46146	−	0.283833i
$590$		−	8.80833i		−	0.362633i
$591$	24.7310	−	17.5707i	1.01730	−	0.722764i
$592$	3.14810	+	1.81755i	0.129386	+	0.0747010i
$593$	12.3343	−	7.12119i	0.506508	−	0.292432i	−0.224889	−	0.974384i	$-0.572202\pi$
$593$	12.3343	−	7.12119i	0.506508	−	0.292432i	0.731397	+	0.681952i	$0.238869\pi$
$594$	−4.01311	−	0.987317i	−0.164660	−	0.0405101i
$595$	−12.0067	−	20.7961i	−0.492225	−	0.852558i
$596$		−	8.36414i		−	0.342608i
$597$	0.920128	−	2.00907i	0.0376583	−	0.0822257i
$598$	−1.84038	−	3.18762i	−0.0752586	−	0.130352i
$599$	9.64054	+	16.6979i	0.393902	+	0.682258i	0.992960	−	0.118447i	$-0.0377917\pi$
$599$	9.64054	+	16.6979i	0.393902	+	0.682258i	−0.599059	+	0.800705i	$0.704458\pi$
$600$	0.721217	−	1.57475i	0.0294436	−	0.0642890i
$601$		−	41.5244i		−	1.69382i	−0.531740	−	0.846908i	$-0.678462\pi$
$601$		−	41.5244i		−	1.69382i	0.531740	−	0.846908i	$-0.321538\pi$
$602$	5.90271	+	10.2238i	0.240577	+	0.416691i
$603$	−2.05343	−	10.7791i	−0.0836220	−	0.438961i
$604$	−19.3586	+	11.1767i	−0.787691	+	0.454773i
$605$	−8.97844	−	5.18371i	−0.365026	−	0.210748i
$606$	−1.68867	+	1.19976i	−0.0685976	+	0.0487368i
$607$		−	24.8694i		−	1.00942i	−0.863290	−	0.504709i	$-0.831600\pi$
$607$		−	24.8694i		−	1.00942i	0.863290	−	0.504709i	$-0.168400\pi$
$608$	3.29017	−	2.85916i	0.133434	−	0.115954i
$609$	9.46837	−	20.6739i	0.383678	−	0.837747i
$610$	5.80073	+	3.34905i	0.234865	+	0.135599i
$611$	3.33575	−	5.77768i	0.134950	−	0.233740i
$612$	20.2119	+	7.04421i	0.817017	+	0.284745i
$613$	3.40073	−	5.89023i	0.137354	−	0.237904i	−0.789140	−	0.614213i	$-0.789474\pi$
$613$	3.40073	−	5.89023i	0.137354	−	0.237904i	0.926494	+	0.376309i	$0.122807\pi$
$614$	−9.65029	+	5.57160i	−0.389454	+	0.224851i
$615$	−6.56663	−	3.00744i	−0.264792	−	0.121271i
$616$		−	2.67691i		−	0.107856i
$617$	−4.62048	+	2.66763i	−0.186013	+	0.107395i	−0.590115	−	0.807319i	$-0.700918\pi$
$617$	−4.62048	+	2.66763i	−0.186013	+	0.107395i	0.404101	+	0.914714i	$0.367584\pi$
$618$	−0.356823	−	3.77985i	−0.0143535	−	0.152048i
$619$	9.41765			0.378528			0.189264	−	0.981926i	$-0.439390\pi$
$619$	9.41765			0.378528			0.189264	+	0.981926i	$0.439390\pi$
$620$	−8.28909			−0.332898
$621$	−7.17593	+	7.47735i	−0.287960	+	0.300056i
$622$	−21.1657	−	12.2200i	−0.848666	−	0.489977i
$623$	6.18212	+	10.7078i	0.247682	+	0.428997i
$624$	−2.60574	+	1.85131i	−0.104313	+	0.0741118i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−2.12928			−0.0851033
$627$	4.34730	+	4.14226i	0.173615	+	0.165426i
$628$	18.1437			0.724013
$629$	12.9678	−	22.4609i	0.517059	−	0.895573i
$630$	−1.88951	−	9.91869i	−0.0752799	−	0.395170i
$631$	14.1067	+	24.4335i	0.561578	+	0.972682i	0.997359	+	0.0726292i	$0.0231390\pi$
$631$	14.1067	+	24.4335i	0.561578	+	0.972682i	−0.435781	+	0.900053i	$0.643528\pi$
$632$	10.3514	+	5.97636i	0.411755	+	0.237727i
$633$	4.38948	+	46.4982i	0.174466	+	1.84814i
$634$	6.06702			0.240952
$635$	−3.80022			−0.150807
$636$	−11.0778	+	1.04575i	−0.439262	+	0.0414669i
$637$	6.91687	−	3.99345i	0.274056	−	0.158226i
$638$		−	3.10238i		−	0.122825i
$639$	−3.13577	−	3.63467i	−0.124049	−	0.143785i
$640$	−0.866025	+	0.500000i	−0.0342327	+	0.0197642i
$641$	−4.02668	+	6.97441i	−0.159044	+	0.275473i	−0.934524	−	0.355899i	$-0.884175\pi$
$641$	−4.02668	+	6.97441i	−0.159044	+	0.275473i	0.775480	+	0.631372i	$0.217508\pi$
$642$	1.84898	−	0.174546i	0.0729733	−	0.00688877i
$643$	−11.4346	+	19.8053i	−0.450936	+	0.781044i	−0.998444	−	0.0557564i	$-0.982243\pi$
$643$	−11.4346	+	19.8053i	−0.450936	+	0.781044i	0.547509	+	0.836800i	$0.315576\pi$
$644$	−5.81345	−	3.35640i	−0.229082	−	0.132261i
$645$	5.52357	+	2.52973i	0.217491	+	0.0996080i
$646$	−20.3994	−	23.4745i	−0.802603	−	0.923591i
$647$		−	12.1854i		−	0.479056i	−0.970889	−	0.239528i	$-0.923007\pi$
$647$		−	12.1854i		−	0.479056i	0.970889	−	0.239528i	$-0.0769926\pi$
$648$	7.05043	+	5.59387i	0.276967	+	0.219748i
$649$	−6.06714	−	3.50286i	−0.238156	−	0.137499i
$650$	1.59822	−	0.922734i	0.0626874	−	0.0361926i
$651$	−39.3918	+	27.9869i	−1.54389	+	1.09689i
$652$	9.25852	+	16.0362i	0.362592	+	0.628027i
$653$			46.1577i			1.80629i	0.429335	+	0.903145i	$0.358748\pi$
$653$			46.1577i			1.80629i	−0.429335	+	0.903145i	$0.641252\pi$
$654$	1.63188	+	0.747379i	0.0638114	+	0.0292248i
$655$	−2.77312	−	4.80319i	−0.108355	−	0.187676i
$656$	2.08497	+	3.61128i	0.0814045	+	0.140997i
$657$	−27.6496	−	32.0486i	−1.07871	−	1.25034i
$658$		−	12.1672i		−	0.474326i
$659$	−7.15219	−	12.3880i	−0.278610	−	0.482567i	0.692430	−	0.721485i	$-0.256540\pi$
$659$	−7.15219	−	12.3880i	−0.278610	−	0.482567i	−0.971040	+	0.238919i	$0.923207\pi$
$660$	−0.797872	−	1.12301i	−0.0310571	−	0.0437132i
$661$	−10.1413	+	5.85511i	−0.394452	+	0.227737i	−0.684088	−	0.729400i	$-0.739799\pi$
$661$	−10.1413	+	5.85511i	−0.394452	+	0.227737i	0.289635	+	0.957137i	$0.406466\pi$
$662$	6.61066	+	3.81667i	0.256931	+	0.148339i
$663$	13.2086	+	18.5913i	0.512981	+	0.722026i
$664$			13.9932i			0.543041i
$665$	−4.77855	+	13.8706i	−0.185304	+	0.537880i
$666$	8.25707	−	7.12369i	0.319955	−	0.276038i
$667$	−6.73746	−	3.88987i	−0.260875	−	0.150617i
$668$	9.91145	−	17.1671i	0.383486	−	0.664217i
$669$	3.64563	+	38.6185i	0.140948	+	1.49308i
$670$	1.82883	−	3.16763i	0.0706539	−	0.122376i
$671$	4.61363	−	2.66368i	0.178107	−	0.102830i
$672$	−2.42739	+	5.30012i	−0.0936387	+	0.204457i
$673$			0.722505i			0.0278505i	0.999903	+	0.0139253i	$0.00443269\pi$
$673$			0.722505i			0.0278505i	−0.999903	+	0.0139253i	$0.995567\pi$
$674$	−4.98568	+	2.87848i	−0.192041	+	0.110875i
$675$	−3.74902	−	3.59789i	−0.144300	−	0.138483i
$676$	9.59425			0.369009
$677$	13.7283			0.527620			0.263810	−	0.964575i	$-0.415021\pi$
$677$	13.7283			0.527620			0.263810	+	0.964575i	$0.415021\pi$
$678$	−20.1971	+	1.90663i	−0.775666	+	0.0732237i
$679$	−53.6302	−	30.9634i	−2.05814	−	1.18827i
$680$	3.56737	+	6.17887i	0.136802	+	0.236949i
$681$	17.4647	+	24.5818i	0.669250	+	0.941977i
$682$	−3.29638	+	5.70949i	−0.126225	+	0.218628i
$683$	−27.2992			−1.04457			−0.522287	−	0.852770i	$-0.674921\pi$
$683$	−27.2992			−1.04457			−0.522287	+	0.852770i	$0.674921\pi$
$684$	−4.85125	−	12.1435i	−0.185492	−	0.464320i
$685$	19.9319			0.761560
$686$	−4.49681	+	7.78871i	−0.171689	+	0.297374i
$687$	1.94606	+	2.73910i	0.0742468	+	0.104503i
$688$	−1.75379	−	3.03766i	−0.0668627	−	0.115810i
$689$	−10.2673	−	5.92782i	−0.391152	−	0.225832i
$690$	−3.43925	+	0.324669i	−0.130930	+	0.0123600i
$691$	−7.97929			−0.303546			−0.151773	−	0.988415i	$-0.548498\pi$
$691$	−7.97929			−0.303546			−0.151773	+	0.988415i	$0.548498\pi$
$692$	−7.45836			−0.283524
$693$	−7.58336	−	2.64294i	−0.288068	−	0.100397i
$694$	16.8904	−	9.75166i	0.641150	−	0.370168i
$695$			10.3410i			0.392256i
$696$	−2.81321	+	6.14254i	−0.106634	+	0.232832i
$697$	25.7655	−	14.8757i	0.975939	−	0.563459i
$698$	−0.211617	+	0.366531i	−0.00800982	+	0.0138734i
$699$	−0.402257	−	4.26115i	−0.0152148	−	0.161171i
$700$	1.68284	−	2.91477i	0.0636055	−	0.110168i
$701$	34.6741	+	20.0191i	1.30962	+	0.756111i	0.982033	−	0.188710i	$-0.0604306\pi$
$701$	34.6741	+	20.0191i	1.30962	+	0.756111i	0.327589	+	0.944820i	$0.393764\pi$
$702$	2.67187	+	9.20958i	0.100843	+	0.347593i
$703$	−15.5544	+	3.02087i	−0.586647	+	0.113934i
$704$			0.795353i			0.0299760i
$705$	−3.62652	−	5.10436i	−0.136583	−	0.192241i
$706$	−20.8007	−	12.0093i	−0.782845	−	0.451976i
$707$	−3.48597	+	2.01263i	−0.131104	+	0.0756927i
$708$	8.83623	+	12.4371i	0.332086	+	0.467414i
$709$	−7.94313	−	13.7579i	−0.298310	−	0.516689i	0.677439	−	0.735579i	$-0.263090\pi$
$709$	−7.94313	−	13.7579i	−0.298310	−	0.516689i	−0.975750	+	0.218890i	$0.929756\pi$
$710$		−	1.60013i		−	0.0600519i
$711$	27.1504	−	23.4237i	1.01822	−	0.878456i
$712$	−1.83681	−	3.18145i	−0.0688373	−	0.119230i
$713$	8.26622	+	14.3175i	0.309572	+	0.536195i
$714$	37.8150	+	17.3188i	1.41519	+	0.648140i
$715$		−	1.46780i		−	0.0548925i
$716$	−0.153575	−	0.266000i	−0.00573938	−	0.00994090i
$717$	−18.6314	+	13.2371i	−0.695801	+	0.494349i
$718$	9.83401	−	5.67767i	0.367002	−	0.211889i
$719$	10.7413	+	6.20149i	0.400583	+	0.231276i	0.686735	−	0.726908i	$-0.259043\pi$
$719$	10.7413	+	6.20149i	0.400583	+	0.231276i	−0.286153	+	0.958184i	$0.592376\pi$
$720$	0.561404	+	2.94700i	0.0209223	+	0.109828i
$721$		−	7.37759i		−	0.274756i
$722$	−2.65038	+	18.8142i	−0.0986368	+	0.700193i
$723$	42.8855	+	19.6411i	1.59493	+	0.730459i
$724$	−11.6567	−	6.72999i	−0.433218	−	0.250118i
$725$	1.95032	−	3.37805i	0.0724330	−	0.125458i
$726$	17.8774	−	1.68765i	0.663493	−	0.0626345i
$727$	10.0726	−	17.4462i	0.373571	−	0.647044i	−0.616541	−	0.787323i	$-0.711467\pi$
$727$	10.0726	−	17.4462i	0.373571	−	0.647044i	0.990112	+	0.140279i	$0.0447999\pi$
$728$	−5.37912	+	3.10563i	−0.199363	+	0.115102i
$729$	22.8077	−	14.4501i	0.844731	−	0.535191i
$730$		−	14.1092i		−	0.522203i
$731$	−21.6729	+	12.5128i	−0.801601	+	0.462804i
$732$	−11.5501	+	1.09034i	−0.426904	+	0.0403003i
$733$	−50.0396			−1.84826			−0.924128	−	0.382084i	$-0.875207\pi$
$733$	−50.0396			−1.84826			−0.924128	+	0.382084i	$0.875207\pi$
$734$	−9.18432			−0.339000
$735$	−0.704504	−	7.46288i	−0.0259860	−	0.275272i
$736$	1.72727	+	0.997241i	0.0636681	+	0.0367588i
$737$	−1.45457	−	2.51938i	−0.0535796	−	0.0928026i
$738$	12.2888	−	2.34102i	0.452358	−	0.0861742i
$739$	−6.80780	+	11.7914i	−0.250429	+	0.433755i	−0.963644	−	0.267190i	$-0.913905\pi$
$739$	−6.80780	+	11.7914i	−0.250429	+	0.433755i	0.713215	+	0.700945i	$0.247238\pi$
$740$	3.63511			0.133629
$741$	3.28012	−	13.5414i	0.120498	−	0.497455i
$742$	−21.6218			−0.793762
$743$	−9.67139	+	16.7513i	−0.354809	+	0.614547i	−0.987085	−	0.160196i	$-0.948787\pi$
$743$	−9.67139	+	16.7513i	−0.354809	+	0.614547i	0.632276	+	0.774743i	$0.282121\pi$
$744$	11.7039	−	8.31535i	0.429087	−	0.304855i
$745$	−4.18207	−	7.24356i	−0.153219	−	0.265383i
$746$	−22.7761	−	13.1498i	−0.833892	−	0.481448i
$747$	39.6410	+	13.8156i	1.45039	+	0.505488i
$748$	5.67464			0.207485
$749$	3.60887			0.131865
$750$	−0.162784	−	1.72438i	−0.00594403	−	0.0629656i
$751$	11.2415	−	6.49028i	0.410208	−	0.236834i	−0.280671	−	0.959804i	$-0.590557\pi$
$751$	11.2415	−	6.49028i	0.410208	−	0.236834i	0.690879	+	0.722970i	$0.257224\pi$
$752$			3.61507i			0.131828i
$753$	33.9304	+	15.5397i	1.23649	+	0.566299i
$754$	−6.23409	+	3.59925i	−0.227032	+	0.131077i
$755$	−11.1767	+	19.3586i	−0.406762	+	0.704532i
$756$	12.6180	+	12.1094i	0.458913	+	0.440414i
$757$	−18.4177	+	31.9004i	−0.669403	+	1.15944i	0.308668	+	0.951170i	$0.400117\pi$
$757$	−18.4177	+	31.9004i	−0.669403	+	1.15944i	−0.978071	+	0.208270i	$0.933217\pi$
$758$	8.02467	+	4.63305i	0.291469	+	0.168280i
$759$	−1.14408	+	2.49806i	−0.0415274	+	0.0906737i
$760$	1.41979	−	4.12119i	0.0515010	−	0.149491i
$761$		−	24.0894i		−	0.873241i	−0.899646	−	0.436621i	$-0.856175\pi$
$761$		−	24.0894i		−	0.873241i	0.899646	−	0.436621i	$-0.143825\pi$
$762$	5.36578	−	3.81225i	0.194382	−	0.138103i
$763$	3.02050	+	1.74389i	0.109350	+	0.0631330i
$764$	17.5813	−	10.1505i	0.636067	−	0.367234i
$765$	21.0261	−	4.00547i	0.760200	−	0.144818i
$766$	11.1774	+	19.3598i	0.403855	+	0.699497i
$767$			16.2555i			0.586952i
$768$	0.721217	−	1.57475i	0.0260247	−	0.0568240i
$769$	1.39798	+	2.42138i	0.0504126	+	0.0873172i	0.890131	−	0.455706i	$-0.150613\pi$
$769$	1.39798	+	2.42138i	0.0504126	+	0.0873172i	−0.839718	+	0.543023i	$0.817280\pi$
$770$	−1.33845	−	2.31827i	−0.0482345	−	0.0835447i
$771$	20.8601	−	45.5472i	0.751257	−	1.64034i
$772$			4.62703i			0.166531i
$773$	−4.17275	−	7.22742i	−0.150084	−	0.259952i	0.781174	−	0.624313i	$-0.214621\pi$
$773$	−4.17275	−	7.22742i	−0.150084	−	0.259952i	−0.931258	+	0.364361i	$0.881288\pi$
$774$	−10.3369	+	1.96917i	−0.371551	+	0.0707804i
$775$	−7.17856	+	4.14455i	−0.257862	+	0.148876i
$776$	15.9344	+	9.19973i	0.572012	+	0.330251i
$777$	17.2749	−	12.2734i	0.619735	−	0.440305i
$778$		−	2.42800i		−	0.0870480i
$779$	−17.1851	−	5.92042i	−0.615721	−	0.212121i
$780$	−1.33098	+	2.90616i	−0.0476569	+	0.104057i
$781$	−1.10216	−	0.636335i	−0.0394386	−	0.0227699i
$782$	7.11505	−	12.3236i	0.254434	−	0.440692i
$783$	14.6236	+	14.0341i	0.522604	+	0.501537i
$784$	−2.16392	+	3.74803i	−0.0772830	+	0.133858i
$785$	15.7129	−	9.07185i	0.560818	−	0.323788i
$786$	8.73396	+	4.00005i	0.311530	+	0.142677i
$787$			34.0004i			1.21198i	0.795471	+	0.605992i	$0.207224\pi$
$787$			34.0004i			1.21198i	−0.795471	+	0.605992i	$0.792776\pi$
$788$	−15.1687	+	8.75764i	−0.540362	+	0.311978i
$789$	2.62028	+	27.7568i	0.0932844	+	0.988170i
$790$	11.9527			0.425259
$791$	−39.4211			−1.40165
$792$	2.25314	+	0.785261i	0.0800618	+	0.0279030i
$793$	−10.7051	−	6.18057i	−0.380148	−	0.219479i
$794$	13.4569	+	23.3080i	0.477568	+	0.827172i
$795$	−9.07076	+	6.44454i	−0.321707	+	0.228564i
$796$	−0.637900	+	1.10487i	−0.0226097	+	0.0391612i
$797$	−0.634867			−0.0224881			−0.0112441	−	0.999937i	$-0.503579\pi$
$797$	−0.634867			−0.0224881			−0.0112441	+	0.999937i	$0.503579\pi$
$798$	−7.16740	−	24.3786i	−0.253723	−	0.862993i
$799$	25.7926			0.912475
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−10.8262	+	2.06238i	−0.382524	+	0.0728708i
$802$	5.27439	+	9.13551i	0.186245	+	0.322586i
$803$	−9.71833	−	5.61088i	−0.342952	−	0.198004i
$804$	0.595408	+	6.30722i	0.0209984	+	0.222438i
$805$	−6.71280			−0.236595
$806$	15.2973			0.538823
$807$	−26.8412	+	2.53384i	−0.944854	+	0.0891953i
$808$	1.03574	−	0.597984i	0.0364372	−	0.0210370i
$809$			47.4357i			1.66775i	0.551953	+	0.833875i	$0.313883\pi$
$809$			47.4357i			1.66775i	−0.551953	+	0.833875i	$0.686117\pi$
$810$	8.90279	+	1.31922i	0.312812	+	0.0463526i
$811$	−30.2251	+	17.4505i	−1.06135	+	0.612770i	−0.925805	−	0.378002i	$-0.876611\pi$
$811$	−30.2251	+	17.4505i	−1.06135	+	0.612770i	−0.135544	+	0.990771i	$0.543278\pi$
$812$	−6.56416	+	11.3695i	−0.230357	+	0.398990i
$813$	4.15493	−	0.392231i	0.145720	−	0.0137561i
$814$	1.44560	−	2.50385i	0.0506682	−	0.0877598i
$815$	16.0362	+	9.25852i	0.561725	+	0.324312i
$816$	−11.2355	−	5.14570i	−0.393319	−	0.180135i
$817$	14.4554	+	4.98001i	0.505731	+	0.174229i
$818$		−	17.3686i		−	0.607278i
$819$	3.48703	+	18.3046i	0.121847	+	0.639615i
$820$	3.61128	+	2.08497i	0.126111	+	0.0728104i
$821$	−15.1395	+	8.74082i	−0.528373	+	0.305057i	−0.740354	−	0.672217i	$-0.765342\pi$
$821$	−15.1395	+	8.74082i	−0.528373	+	0.305057i	0.211980	+	0.977274i	$0.432009\pi$
$822$	−28.1433	+	19.9951i	−0.981609	+	0.697408i
$823$	−4.16579	−	7.21536i	−0.145210	−	0.251512i	0.784241	−	0.620456i	$-0.213053\pi$
$823$	−4.16579	−	7.21536i	−0.145210	−	0.251512i	−0.929451	+	0.368945i	$0.879719\pi$
$824$			2.19200i			0.0763620i
$825$	−1.25248	−	0.573622i	−0.0436059	−	0.0199710i
$826$	14.8230	+	25.6743i	0.515760	+	0.893322i
$827$	−26.3348	−	45.6132i	−0.915751	−	1.58613i	−0.805797	−	0.592191i	$-0.798263\pi$
$827$	−26.3348	−	45.6132i	−0.915751	−	1.58613i	−0.109954	−	0.993937i	$-0.535070\pi$
$828$	4.53042	−	3.90857i	0.157443	−	0.135832i
$829$		−	26.7190i		−	0.927990i	−0.885838	−	0.463995i	$-0.846416\pi$
$829$		−	26.7190i		−	0.927990i	0.885838	−	0.463995i	$-0.153584\pi$
$830$	6.99659	+	12.1185i	0.242855	+	0.420638i
$831$	30.8865	+	43.4731i	1.07144	+	1.50806i
$832$	1.59822	−	0.922734i	0.0554084	−	0.0319901i
$833$	26.7412	+	15.4390i	0.926528	+	0.534931i
$834$	−10.3737	−	14.6011i	−0.359213	−	0.505596i
$835$		−	19.8229i		−	0.686000i
$836$	−2.27404	−	2.61684i	−0.0786494	−	0.0905054i
$837$	−12.0010	−	41.3657i	−0.414814	−	1.42981i
$838$	25.6052	+	14.7832i	0.884516	+	0.510676i
$839$	19.4936	−	33.7640i	0.672996	−	1.16566i	−0.304055	−	0.952655i	$-0.598341\pi$
$839$	19.4936	−	33.7640i	0.672996	−	1.16566i	0.977050	−	0.213008i	$-0.0683260\pi$
$840$	0.547880	+	5.80374i	0.0189036	+	0.200248i
$841$	6.89251	−	11.9382i	0.237673	−	0.411662i
$842$	2.75755	−	1.59207i	0.0950316	−	0.0548665i
$843$	18.2725	−	39.8973i	0.629337	−	1.37414i
$844$		−	26.9651i		−	0.928177i
$845$	8.30886	−	4.79712i	0.285834	−	0.165026i
$846$	10.2411	+	3.56920i	0.352095	+	0.122712i
$847$	34.8935			1.19895
$848$	6.42419			0.220608
$849$	14.1729	−	1.33794i	0.486414	−	0.0459180i
$850$	6.17887	+	3.56737i	0.211933	+	0.122360i
$851$	−3.62508	−	6.27882i	−0.124266	−	0.215235i
$852$	1.60520	+	2.25934i	0.0549933	+	0.0774036i
$853$	3.28239	−	5.68527i	0.112387	−	0.194660i	−0.804345	−	0.594162i	$-0.797484\pi$
$853$	3.28239	−	5.68527i	0.112387	−	0.194660i	0.916732	+	0.399502i	$0.130817\pi$
$854$	−22.5437			−0.771431
$855$	−10.2731	−	8.09098i	−0.351332	−	0.276706i
$856$	−1.07225			−0.0366489
$857$	−0.771649	+	1.33654i	−0.0263590	+	0.0456552i	−0.878904	−	0.476999i	$-0.841725\pi$
$857$	−0.771649	+	1.33654i	−0.0263590	+	0.0456552i	0.852545	+	0.522654i	$0.175058\pi$
$858$	1.47245	+	2.07249i	0.0502685	+	0.0707535i
$859$	2.26168	+	3.91734i	0.0771674	+	0.133658i	0.902027	−	0.431680i	$-0.142079\pi$
$859$	2.26168	+	3.91734i	0.0771674	+	0.133658i	−0.824859	+	0.565338i	$0.808746\pi$
$860$	−3.03766	−	1.75379i	−0.103583	−	0.0598038i
$861$	24.2013	−	2.28463i	0.824777	−	0.0778599i
$862$	25.3694			0.864084
$863$	−11.5515			−0.393217			−0.196608	−	0.980482i	$-0.562993\pi$
$863$	−11.5515			−0.393217			−0.196608	+	0.980482i	$0.562993\pi$
$864$	−3.74902	−	3.59789i	−0.127544	−	0.122403i
$865$	−6.45913	+	3.72918i	−0.219617	+	0.126796i
$866$			39.2917i			1.33519i
$867$	−24.4525	+	53.3912i	−0.830451	+	1.81326i
$868$	24.1608	−	13.9492i	0.820071	−	0.473468i
$869$	4.75332	−	8.23299i	0.161245	−	0.279285i
$870$	0.634961	+	6.72620i	0.0215272	+	0.228039i
$871$	−3.37505	+	5.84576i	−0.114359	+	0.198076i
$872$	−0.897440	−	0.518137i	−0.0303912	−	0.0175463i
$873$	41.7940	−	36.0573i	1.41451	−	1.22035i
$874$	−8.53428	+	1.65746i	−0.288676	+	0.0560645i
$875$		−	3.36569i		−	0.113781i
$876$	14.1538	+	19.9217i	0.478214	+	0.673091i
$877$	44.7475	+	25.8350i	1.51102	+	0.872386i	0.999917	+	0.0128639i	$0.00409481\pi$
$877$	44.7475	+	25.8350i	1.51102	+	0.872386i	0.511099	+	0.859522i	$0.329239\pi$
$878$	9.49324	−	5.48093i	0.320381	−	0.184972i
$879$	−24.5242	−	34.5181i	−0.827182	−	1.16427i
$880$	0.397676	+	0.688796i	0.0134057	+	0.0232193i
$881$		−	8.64964i		−	0.291414i	−0.989328	−	0.145707i	$-0.953454\pi$
$881$		−	8.64964i		−	0.291414i	0.989328	−	0.145707i	$-0.0465457\pi$
$882$	8.48125	+	9.83061i	0.285579	+	0.331014i
$883$	27.8076	+	48.1641i	0.935799	+	1.62085i	0.773202	+	0.634160i	$0.218654\pi$
$883$	27.8076	+	48.1641i	0.935799	+	1.62085i	0.162597	+	0.986692i	$0.448013\pi$
$884$	−6.58347	−	11.4029i	−0.221426	−	0.383521i
$885$	13.8709	+	6.35272i	0.466267	+	0.213544i
$886$		−	32.4159i		−	1.08903i
$887$	−15.4908	−	26.8308i	−0.520129	−	0.900890i	−0.999726	−	0.0234014i	$-0.992550\pi$
$887$	−15.4908	−	26.8308i	−0.520129	−	0.900890i	0.479597	−	0.877489i	$-0.340783\pi$
$888$	−5.13266	+	3.64662i	−0.172241	+	0.122373i
$889$	11.0768	−	6.39517i	0.371502	−	0.214487i
$890$	−3.18145	−	1.83681i	−0.106642	−	0.0615700i
$891$	4.44910	−	5.60758i	0.149051	−	0.187861i
$892$		−	22.3955i		−	0.749857i
$893$	−10.3361	−	11.8942i	−0.345883	−	0.398023i
$894$	13.1714	+	6.03236i	0.440519	+	0.201752i
$895$	−0.266000	−	0.153575i	−0.00889141	−	0.00513346i
$896$	1.68284	−	2.91477i	0.0562199	−	0.0973756i
$897$	6.34703	−	0.599167i	0.211921	−	0.0200056i
$898$	−0.834292	+	1.44504i	−0.0278407	+	0.0482215i
$899$	28.0010	−	16.1664i	0.933885	−	0.539179i
$900$	1.95969	+	2.27148i	0.0653231	+	0.0757159i
$901$		−	45.8349i		−	1.52698i
$902$	2.87224	−	1.65829i	0.0956351	−	0.0552150i
$903$	−20.3571	+	1.92173i	−0.677441	+	0.0639513i
$904$	11.7127			0.389557
$905$	−13.4600			−0.447425
$906$	−3.63877	−	38.5459i	−0.120890	−	1.28060i
$907$	−19.5392	−	11.2809i	−0.648788	−	0.374578i	0.139204	−	0.990264i	$-0.455546\pi$
$907$	−19.5392	−	11.2809i	−0.648788	−	0.374578i	−0.787992	+	0.615686i	$0.788879\pi$
$908$	−8.70480	−	15.0772i	−0.288879	−	0.500353i
$909$	−0.671422	−	3.52452i	−0.0222697	−	0.116901i
$910$	−3.10563	+	5.37912i	−0.102951	+	0.178316i
$911$	33.0252			1.09417			0.547086	−	0.837076i	$-0.315737\pi$
$911$	33.0252			1.09417			0.547086	+	0.837076i	$0.315737\pi$
$912$	2.12955	+	7.24327i	0.0705165	+	0.239849i
$913$	11.1295			0.368333
$914$	−7.23822	+	12.5370i	−0.239419	+	0.414686i
$915$	−9.45752	+	6.71932i	−0.312656	+	0.222134i
$916$	−0.969958	−	1.68002i	−0.0320483	−	0.0555093i
$917$	16.1660	+	9.33346i	0.533849	+	0.308218i
$918$	−25.6700	+	26.7483i	−0.847238	+	0.882825i
$919$	2.71554			0.0895776			0.0447888	−	0.998996i	$-0.485739\pi$
$919$	2.71554			0.0895776			0.0447888	+	0.998996i	$0.485739\pi$
$920$	1.99448			0.0657561
$921$	−1.81393	−	19.2152i	−0.0597711	−	0.633161i
$922$	−25.3943	+	14.6614i	−0.836318	+	0.482848i
$923$			2.95299i			0.0971990i
$924$	4.21547	+	1.93063i	0.138679	+	0.0635131i
$925$	3.14810	−	1.81755i	0.103509	−	0.0597608i
$926$	20.6520	−	35.7703i	0.678667	−	1.17549i
$927$	6.20968	+	2.16419i	0.203953	+	0.0710812i
$928$	1.95032	−	3.37805i	0.0640223	−	0.110890i
$929$	45.5906	+	26.3217i	1.49578	+	0.863588i	0.999988	−	0.00485418i	$-0.00154514\pi$
$929$	45.5906	+	26.3217i	1.49578	+	0.863588i	0.495790	+	0.868442i	$0.334878\pi$
$930$	5.97824	−	13.0533i	0.196034	−	0.428034i
$931$	−3.59655	−	18.5186i	−0.117872	−	0.606924i
$932$			2.47111i			0.0809440i
$933$	34.5085	−	24.5174i	1.12976	−	0.802664i
$934$	11.4412	+	6.60560i	0.374369	+	0.216142i
$935$	4.91438	−	2.83732i	0.160717	−	0.0927902i
$936$	−1.03605	−	5.43860i	−0.0338645	−	0.177766i
$937$	1.99845	+	3.46141i	0.0652865	+	0.113079i	0.896821	−	0.442394i	$-0.145871\pi$
$937$	1.99845	+	3.46141i	0.0652865	+	0.113079i	−0.831535	+	0.555473i	$0.812537\pi$
$938$			12.3105i			0.401954i
$939$	1.53568	−	3.35310i	0.0501149	−	0.109424i
$940$	1.80753	+	3.13074i	0.0589552	+	0.102113i
$941$	10.2092	+	17.6829i	0.332811	+	0.576446i	0.983062	−	0.183274i	$-0.0586695\pi$
$941$	10.2092	+	17.6829i	0.332811	+	0.576446i	−0.650251	+	0.759720i	$0.725336\pi$
$942$	−13.0856	+	28.5718i	−0.426350	+	0.930921i
$943$		−	8.31687i		−	0.270835i
$944$	−4.40416	−	7.62824i	−0.143343	−	0.248278i
$945$	16.9822	+	4.17802i	0.552432	+	0.135911i
$946$	−2.41601	+	1.39488i	−0.0785512	+	0.0453515i
$947$	−28.8707	−	16.6685i	−0.938171	−	0.541654i	−0.0487848	−	0.998809i	$-0.515535\pi$
$947$	−28.8707	−	16.6685i	−0.938171	−	0.541654i	−0.889387	+	0.457156i	$0.848868\pi$
$948$	−16.8769	+	11.9906i	−0.548136	+	0.389436i
$949$			26.0380i			0.845229i
$950$	−0.831025	−	4.27895i	−0.0269620	−	0.138827i
$951$	−4.37564	+	9.55406i	−0.141890	+	0.309811i
$952$	−20.7961	−	12.0067i	−0.674007	−	0.389138i
$953$	5.27108	−	9.12979i	0.170747	−	0.295743i	−0.767934	−	0.640529i	$-0.778715\pi$
$953$	5.27108	−	9.12979i	0.170747	−	0.295743i	0.938681	+	0.344786i	$0.112049\pi$
$954$	6.34268	−	18.1990i	0.205352	−	0.589213i
$955$	10.1505	−	17.5813i	0.328464	−	0.568916i
$956$	11.4275	−	6.59766i	0.369591	−	0.213384i
$957$	4.88549	+	2.23749i	0.157925	+	0.0723278i
$958$			34.6211i			1.11856i
$959$	−58.0970	+	33.5423i	−1.87605	+	1.08314i
$960$	−0.162784	−	1.72438i	−0.00525383	−	0.0556543i
$961$	−37.7091			−1.21642
$962$	−6.70848			−0.216290
$963$	−1.05865	+	3.03757i	−0.0341145	+	0.0978843i
$964$	−23.5846	−	13.6166i	−0.759610	−	0.438561i
$965$	2.31352	+	4.00713i	0.0744747	+	0.128994i
$966$	9.47826	−	6.73406i	0.304958	−	0.216665i
$967$	28.1558	−	48.7673i	0.905431	−	1.56825i	0.0850923	−	0.996373i	$-0.472881\pi$
$967$	28.1558	−	48.7673i	0.905431	−	1.56825i	0.820338	−	0.571879i	$-0.193785\pi$
$968$	−10.3674			−0.333221
$969$	51.6789	−	15.1938i	1.66016	−	0.488095i
$970$	18.3995			0.590771
$971$	20.9023	−	36.2039i	0.670787	−	1.16184i	−0.306894	−	0.951744i	$-0.599290\pi$
$971$	20.9023	−	36.2039i	0.670787	−	1.16184i	0.977681	−	0.210094i	$-0.0673771\pi$
$972$	−13.8939	+	7.06829i	−0.445646	+	0.226716i
$973$	−17.4023	−	30.1416i	−0.557891	−	0.966295i
$974$	17.9945	+	10.3891i	0.576582	+	0.332890i
$975$	0.300413	+	3.18230i	0.00962090	+	0.101915i
$976$	6.69811			0.214401
$977$	15.3174			0.490046			0.245023	−	0.969517i	$-0.421205\pi$
$977$	15.3174			0.490046			0.245023	+	0.969517i	$0.421205\pi$
$978$	−31.9305	+	3.01428i	−1.02102	+	0.0963859i
$979$	−2.53037	+	1.46091i	−0.0808711	+	0.0466909i
$980$			4.32785i			0.138248i
$981$	−2.35387	+	2.03078i	−0.0751534	+	0.0648378i
$982$	−3.62316	+	2.09183i	−0.115620	+	0.0667530i
$983$	−1.68463	+	2.91786i	−0.0537313	+	0.0930654i	−0.891640	−	0.452745i	$-0.850445\pi$
$983$	−1.68463	+	2.91786i	−0.0537313	+	0.0930654i	0.837909	+	0.545810i	$0.183778\pi$
$984$	−7.19059	+	0.678800i	−0.229227	+	0.0216393i
$985$	−8.75764	+	15.1687i	−0.279042	+	0.483314i
$986$	−24.1015	−	13.9150i	−0.767549	−	0.443144i
$987$	19.1603	+	8.77518i	0.609879	+	0.279317i
$988$	−2.62017	+	7.60553i	−0.0833587	+	0.241964i
$989$			6.99581i			0.222454i
$990$	2.34391	−	0.446514i	0.0744943	−	0.0141912i
$991$	38.7708	+	22.3843i	1.23159	+	0.711061i	0.967362	−	0.253398i	$-0.0815483\pi$
$991$	38.7708	+	22.3843i	1.23159	+	0.711061i	0.264232	+	0.964459i	$0.414882\pi$
$992$	−7.17856	+	4.14455i	−0.227920	+	0.131589i
$993$	−10.7780	+	7.65751i	−0.342031	+	0.243004i
$994$	2.69277	+	4.66402i	0.0854096	+	0.147934i
$995$			1.27580i			0.0404455i
$996$	−22.0358	−	10.0921i	−0.698231	−	0.319781i
$997$	−1.88035	−	3.25686i	−0.0595512	−	0.103146i	0.834713	−	0.550685i	$-0.185634\pi$
$997$	−1.88035	−	3.25686i	−0.0595512	−	0.103146i	−0.894264	+	0.447540i	$0.852300\pi$
$998$	−2.93329	−	5.08061i	−0.0928516	−	0.160824i
$999$	5.26291	+	18.1406i	0.166511	+	0.573942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.b.521.9	yes	24
3.2	odd	2		570.2.s.a.521.12	yes	24
19.12	odd	6		570.2.s.a.221.12	✓	24
57.50	even	6	inner	570.2.s.b.221.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.12	✓	24	19.12	odd	6
570.2.s.a.521.12	yes	24	3.2	odd	2
570.2.s.b.221.9	yes	24	57.50	even	6	inner
570.2.s.b.521.9	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.00317 + 1.41197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.72438 - 0.162784i) q^{6} +3.36569 q^{7} -1.00000 q^{8} +(-0.987311 + 2.83288i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.00317 + 1.41197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.72438 - 0.162784i) q^{6} +3.36569 q^{7} -1.00000 q^{8} +(-0.987311 + 2.83288i) q^{9} +(-0.866025 + 0.500000i) q^{10} +0.795353i q^{11} +(0.721217 - 1.57475i) q^{12} +(1.59822 - 0.922734i) q^{13} +(1.68284 - 2.91477i) q^{14} +(-0.162784 - 1.72438i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.17887 + 3.56737i) q^{17} +(1.95969 + 2.27148i) q^{18} +(-0.831025 - 4.27895i) q^{19} +1.00000i q^{20} +(3.37635 + 4.75224i) q^{21} +(0.688796 + 0.397676i) q^{22} +(1.72727 - 0.997241i) q^{23} +(-1.00317 - 1.41197i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.84547i q^{26} +(-4.99038 + 1.44780i) q^{27} +(-1.68284 - 2.91477i) q^{28} +(-1.95032 - 3.37805i) q^{29} +(-1.57475 - 0.721217i) q^{30} +8.28909i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.12301 + 0.797872i) q^{33} +(6.17887 - 3.56737i) q^{34} +(-2.91477 - 1.68284i) q^{35} +(2.94700 - 0.561404i) q^{36} -3.63511i q^{37} +(-4.12119 - 1.41979i) q^{38} +(2.90616 + 1.33098i) q^{39} +(0.866025 + 0.500000i) q^{40} +(2.08497 - 3.61128i) q^{41} +(5.80374 - 0.547880i) q^{42} +(-1.75379 + 3.03766i) q^{43} +(0.688796 - 0.397676i) q^{44} +(2.27148 - 1.95969i) q^{45} -1.99448i q^{46} +(3.13074 - 1.80753i) q^{47} +(-1.72438 + 0.162784i) q^{48} +4.32785 q^{49} +1.00000 q^{50} +(1.16142 + 12.3030i) q^{51} +(-1.59822 - 0.922734i) q^{52} +(-3.21210 - 5.56351i) q^{53} +(-1.24136 + 5.04569i) q^{54} +(0.397676 - 0.688796i) q^{55} -3.36569 q^{56} +(5.20808 - 5.46588i) q^{57} -3.90064 q^{58} +(-4.40416 + 7.62824i) q^{59} +(-1.41197 + 1.00317i) q^{60} +(-3.34905 - 5.80073i) q^{61} +(7.17856 + 4.14455i) q^{62} +(-3.32298 + 9.53459i) q^{63} +1.00000 q^{64} -1.84547 q^{65} +(0.129471 + 1.37149i) q^{66} +(-3.16763 + 1.82883i) q^{67} -7.13474i q^{68} +(3.14081 + 1.43845i) q^{69} +(-2.91477 + 1.68284i) q^{70} +(-0.800066 + 1.38576i) q^{71} +(0.987311 - 2.83288i) q^{72} +(-7.05458 + 12.2189i) q^{73} +(-3.14810 - 1.81755i) q^{74} +(-0.721217 + 1.57475i) q^{75} +(-3.29017 + 2.85916i) q^{76} +2.67691i q^{77} +(2.60574 - 1.85131i) q^{78} +(-10.3514 - 5.97636i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-7.05043 - 5.59387i) q^{81} +(-2.08497 - 3.61128i) q^{82} -13.9932i q^{83} +(2.42739 - 5.30012i) q^{84} +(-3.56737 - 6.17887i) q^{85} +(1.75379 + 3.03766i) q^{86} +(2.81321 - 6.14254i) q^{87} -0.795353i q^{88} +(1.83681 + 3.18145i) q^{89} +(-0.561404 - 2.94700i) q^{90} +(5.37912 - 3.10563i) q^{91} +(-1.72727 - 0.997241i) q^{92} +(-11.7039 + 8.31535i) q^{93} -3.61507i q^{94} +(-1.41979 + 4.12119i) q^{95} +(-0.721217 + 1.57475i) q^{96} +(-15.9344 - 9.19973i) q^{97} +(2.16392 - 3.74803i) q^{98} +(-2.25314 - 0.785261i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9 + 2 * q^12 + 18 * q^13 - 6 * q^14 - 12 * q^16 - 12 * q^17 - 2 * q^18 + 6 * q^19 + 6 * q^21 + 18 * q^22 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * q^36 - 6 * q^38 + 40 * q^39 - 6 * q^41 - 6 * q^42 - 22 * q^43 + 18 * q^44 + 8 * q^45 - 12 * q^47 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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