LMFDB - Embedded newform 570.2.s.a.521.12

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			521.12
Character	$\chi$	$=$	570.521
Dual form			570.2.s.a.221.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.72438 + 0.162784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00317 + 1.41197i) q^{6} +3.36569 q^{7} +1.00000 q^{8} +(2.94700 + 0.561404i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72438 + 0.162784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00317 + 1.41197i) q^{6} +3.36569 q^{7} +1.00000 q^{8} +(2.94700 + 0.561404i) 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} +(1.41197 + 1.00317i) 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} +(5.80374 + 0.547880i) q^{21} +(0.688796 + 0.397676i) q^{22} +(-1.72727 + 0.997241i) q^{23} +(1.72438 + 0.162784i) 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} +(0.129471 - 1.37149i) q^{33} +(6.17887 - 3.56737i) q^{34} +(2.91477 + 1.68284i) q^{35} +(-0.987311 - 2.83288i) 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} +(-3.37635 + 4.75224i) 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} +(-1.00317 + 1.41197i) q^{48} +4.32785 q^{49} -1.00000 q^{50} +(-10.0740 - 7.15734i) q^{51} +(-1.59822 - 0.922734i) q^{52} +(3.21210 + 5.56351i) q^{53} +(-3.74902 + 3.59789i) q^{54} +(0.397676 - 0.688796i) q^{55} +3.36569 q^{56} +(-0.736463 - 7.51383i) q^{57} -3.90064 q^{58} +(4.40416 - 7.62824i) q^{59} +(0.162784 - 1.72438i) q^{60} +(-3.34905 - 5.80073i) q^{61} +(-7.17856 - 4.14455i) q^{62} +(9.91869 + 1.88951i) q^{63} +1.00000 q^{64} +1.84547 q^{65} +(1.12301 + 0.797872i) 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} +(2.94700 + 0.561404i) 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} +(-0.300413 + 3.18230i) q^{78} +(-10.3514 - 5.97636i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(8.36965 + 3.30892i) 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} +(-2.83288 + 0.987311i) q^{90} +(5.37912 - 3.10563i) q^{91} +(1.72727 + 0.997241i) q^{92} +(-1.34933 + 14.2936i) 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} +(0.446514 - 2.34391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 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} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 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} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * 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
$3$	1.72438	+	0.162784i	0.995574	+	0.0939833i
$3$	1.72438	+	0.162784i	0.995574	+	0.0939833i
$4$	−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
$6$	−1.00317	+	1.41197i	−0.409541	+	0.576434i
$7$	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
$9$	2.94700	+	0.561404i	0.982334	+	0.187135i
$10$	−0.866025	+	0.500000i	−0.273861	+	0.158114i
$11$		−	0.795353i		−	0.239808i	−0.992785	−	0.119904i	$-0.961741\pi$
$11$		−	0.795353i		−	0.239808i	0.992785	−	0.119904i	$-0.0382587\pi$
$12$	−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
$15$	1.41197	+	1.00317i	0.364569	+	0.259017i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−6.17887	−	3.56737i	−1.49860	−	0.865214i	−0.498597	−	0.866834i	$-0.666151\pi$
$17$	−6.17887	−	3.56737i	−1.49860	−	0.865214i	−0.999999	+	0.00161968i	$0.999484\pi$
$18$	−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
$21$	5.80374	+	0.547880i	1.26648	+	0.119557i
$22$	0.688796	+	0.397676i	0.146852	+	0.0847849i
$23$	−1.72727	+	0.997241i	−0.360161	+	0.207939i	−0.669151	−	0.743126i	$-0.733342\pi$
$23$	−1.72727	+	0.997241i	−0.360161	+	0.207939i	0.308990	+	0.951065i	$0.400009\pi$
$24$	1.72438	+	0.162784i	0.351988	+	0.0332281i
$25$	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	0.988317	−	0.152413i	$-0.0487043\pi$
$29$	1.95032	+	3.37805i	0.362165	+	0.627288i	−0.626152	+	0.779701i	$0.715371\pi$
$30$	−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
$33$	0.129471	−	1.37149i	0.0225379	−	0.238746i
$34$	6.17887	−	3.56737i	1.05967	−	0.611799i
$35$	2.91477	+	1.68284i	0.492686	+	0.284452i
$36$	−0.987311	−	2.83288i	−0.164552	−	0.472147i
$37$		−	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	−0.981637	−	0.190757i	$-0.938906\pi$
$41$	−2.08497	+	3.61128i	−0.325618	+	0.563987i	0.656019	+	0.754744i	$0.272239\pi$
$42$	−3.37635	+	4.75224i	−0.520982	+	0.733287i
$43$	−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	−0.710641	−	0.703555i	$-0.751595\pi$
$47$	−3.13074	+	1.80753i	−0.456665	+	0.263656i	0.253976	+	0.967211i	$0.418262\pi$
$48$	−1.00317	+	1.41197i	−0.144795	+	0.203800i
$49$	4.32785			0.618264
$50$	−1.00000			−0.141421
$51$	−10.0740	−	7.15734i	−1.41065	−	1.00223i
$52$	−1.59822	−	0.922734i	−0.221634	−	0.127960i
$53$	3.21210	+	5.56351i	0.441215	+	0.764207i	0.997780	−	0.0665970i	$-0.0212142\pi$
$53$	3.21210	+	5.56351i	0.441215	+	0.764207i	−0.556565	+	0.830804i	$0.687881\pi$
$54$	−3.74902	+	3.59789i	−0.510177	+	0.489611i
$55$	0.397676	−	0.688796i	0.0536227	−	0.0928772i
$56$	3.36569			0.449759
$57$	−0.736463	−	7.51383i	−0.0975469	−	0.995231i
$58$	−3.90064			−0.512179
$59$	4.40416	−	7.62824i	0.573373	−	0.993112i	−0.422843	−	0.906203i	$-0.638968\pi$
$59$	4.40416	−	7.62824i	0.573373	−	0.993112i	0.996216	−	0.0869089i	$-0.0276989\pi$
$60$	0.162784	−	1.72438i	0.0210153	−	0.222617i
$61$	−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
$63$	9.91869	+	1.88951i	1.24964	+	0.238056i
$64$	1.00000			0.125000
$65$	1.84547			0.228902
$66$	1.12301	+	0.797872i	0.138233	+	0.0982112i
$67$	−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	−0.814637	−	0.579970i	$-0.803064\pi$
$71$	0.800066	−	1.38576i	0.0949504	−	0.164459i	0.909588	+	0.415512i	$0.136397\pi$
$72$	2.94700	+	0.561404i	0.347308	+	0.0661621i
$73$	−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
$78$	−0.300413	+	3.18230i	−0.0340150	+	0.360324i
$79$	−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
$81$	8.36965	+	3.30892i	0.929961	+	0.367658i
$82$	−2.08497	−	3.61128i	−0.230247	−	0.398799i
$83$			13.9932i			1.53595i	0.640479	+	0.767976i	$0.278736\pi$
$83$			13.9932i			1.53595i	−0.640479	+	0.767976i	$0.721264\pi$
$84$	−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	0.752101	−	0.659048i	$-0.229040\pi$
$89$	−1.83681	−	3.18145i	−0.194701	−	0.337233i	−0.946803	+	0.321815i	$0.895707\pi$
$90$	−2.83288	+	0.987311i	−0.298612	+	0.104072i
$91$	5.37912	−	3.10563i	0.563885	−	0.325559i
$92$	1.72727	+	0.997241i	0.180080	+	0.103970i
$93$	−1.34933	+	14.2936i	−0.139919	+	1.48218i
$94$		−	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
$99$	0.446514	−	2.34391i	0.0448764	−	0.235572i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	1.03574	−	0.597984i	0.103060	−	0.0595017i	−0.447584	−	0.894242i	$-0.647716\pi$
$101$	1.03574	−	0.597984i	0.103060	−	0.0595017i	0.550644	+	0.834740i	$0.314382\pi$
$102$	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
$105$	4.75224	+	3.37635i	0.463772	+	0.329498i
$106$	−6.42419			−0.623973
$107$	−1.07225			−0.103659			−0.0518293	−	0.998656i	$-0.516505\pi$
$107$	−1.07225			−0.103659			−0.0518293	+	0.998656i	$0.516505\pi$
$108$	−1.24136	−	5.04569i	−0.119450	−	0.485522i
$109$	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
$111$	0.591737	−	6.26833i	0.0561652	−	0.594963i
$112$	−1.68284	+	2.91477i	−0.159014	+	0.275420i
$113$	11.7127			1.10183			0.550917	−	0.834560i	$-0.314278\pi$
$113$	11.7127			1.10183			0.550917	+	0.834560i	$0.314278\pi$
$114$	6.87540	+	3.11912i	0.643940	+	0.292132i
$115$	−1.99448			−0.185986
$116$	1.95032	−	3.37805i	0.181083	−	0.313644i
$117$	5.22799	−	1.82205i	0.483328	−	0.168449i
$118$	4.40416	+	7.62824i	0.405436	+	0.702236i
$119$	−20.7961	−	12.0067i	−1.90638	−	1.10065i
$120$	1.41197	+	1.00317i	0.128895	+	0.0915762i
$121$	10.3674			0.942492
$122$	6.69811			0.606418
$123$	−4.18315	+	5.88783i	−0.377182	+	0.530888i
$124$	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
$129$	−3.51869	+	4.95260i	−0.309803	+	0.436052i
$130$	−0.922734	+	1.59822i	−0.0809291	+	0.140173i
$131$	−4.80319	−	2.77312i	−0.419656	−	0.242289i	0.275274	−	0.961366i	$-0.411231\pi$
$131$	−4.80319	−	2.77312i	−0.419656	−	0.242289i	−0.694930	+	0.719077i	$0.744565\pi$
$132$	−1.25248	+	0.573622i	−0.109015	+	0.0499274i
$133$	−2.79697	−	14.4016i	−0.242528	−	1.24878i
$134$		−	3.65766i		−	0.315974i
$135$	3.59789	+	3.74902i	0.309657	+	0.322664i
$136$	−6.17887	−	3.56737i	−0.529833	−	0.305899i
$137$	17.2616	−	9.96597i	1.47475	−	0.851450i	0.475159	−	0.879900i	$-0.342390\pi$
$137$	17.2616	−	9.96597i	1.47475	−	0.851450i	0.999595	+	0.0284500i	$0.00905713\pi$
$138$	0.324669	−	3.43925i	0.0276377	−	0.292769i
$139$	−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
$147$	7.46288	+	0.704504i	0.615528	+	0.0581065i
$148$	−3.14810	+	1.81755i	−0.258772	+	0.149402i
$149$	−7.24356	−	4.18207i	−0.593415	−	0.342608i	0.173031	−	0.984916i	$-0.444644\pi$
$149$	−7.24356	−	4.18207i	−0.593415	−	0.342608i	−0.766447	+	0.642308i	$0.777977\pi$
$150$	−1.72438	−	0.162784i	−0.140795	−	0.0132912i
$151$		−	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
$156$	−2.60574	−	1.85131i	−0.208626	−	0.148224i
$157$	−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
$162$	−7.05043	+	5.59387i	−0.553934	+	0.439496i
$163$	−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
$165$	0.797872	−	1.12301i	0.0621142	−	0.0874265i
$166$	−12.1185	−	6.99659i	−0.940575	−	0.543041i
$167$	−9.91145	−	17.1671i	−0.766971	−	1.32843i	−0.939198	−	0.343376i	$-0.888430\pi$
$167$	−9.91145	−	17.1671i	−0.766971	−	1.32843i	0.172227	−	0.985057i	$-0.444904\pi$
$168$	5.80374	+	0.547880i	0.447768	+	0.0422698i
$169$	−4.79712	+	8.30886i	−0.369009	+	0.639143i
$170$	7.13474			0.547210
$171$	−0.0468143	−	13.0766i	−0.00357998	−	0.999994i
$172$	3.50758			0.267451
$173$	−3.72918	+	6.45913i	−0.283524	+	0.491079i	−0.972250	−	0.233943i	$-0.924837\pi$
$173$	−3.72918	+	6.45913i	−0.283524	+	0.491079i	0.688726	+	0.725022i	$0.258170\pi$
$174$	−6.72620	−	0.634961i	−0.509912	−	0.0481363i
$175$	1.68284	+	2.91477i	0.127211	+	0.220336i
$176$	0.688796	+	0.397676i	0.0519199	+	0.0299760i
$177$	8.83623	−	12.4371i	0.664172	−	0.934829i
$178$	3.67362			0.275349
$179$	−0.307151			−0.0229575			−0.0114788	−	0.999934i	$-0.503654\pi$
$179$	−0.307151			−0.0229575			−0.0114788	+	0.999934i	$0.503654\pi$
$180$	0.561404	−	2.94700i	0.0418446	−	0.219657i
$181$	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
$186$	−11.7039	−	8.31535i	−0.858174	−	0.609711i
$187$	−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	$-0.737432\pi$
$191$		−	20.3011i		−	1.46893i	0.678644	−	0.734467i	$-0.262568\pi$
$192$	1.72438	+	0.162784i	0.124447	+	0.0117479i
$193$	−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
$195$	3.18230	+	0.300413i	0.227889	+	0.0215130i
$196$	−2.16392	−	3.74803i	−0.154566	−	0.267716i
$197$			17.5153i			1.24791i	0.781460	+	0.623956i	$0.214476\pi$
$197$			17.5153i			1.24791i	−0.781460	+	0.623956i	$0.785524\pi$
$198$	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
$204$	−1.16142	+	12.3030i	−0.0813157	+	0.861385i
$205$	−3.61128	+	2.08497i	−0.252223	+	0.145621i
$206$	1.89833	+	1.09600i	0.132263	+	0.0763620i
$207$	−5.65013	+	1.96917i	−0.392711	+	0.136867i
$208$			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
$213$	1.60520	−	2.25934i	0.109987	−	0.154807i
$214$	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
$219$	−14.1538	+	19.9217i	−0.956428	+	1.34618i
$220$	−0.795353			−0.0536227
$221$	−13.1669			−0.885704
$222$	5.13266	+	3.64662i	0.344482	+	0.244745i
$223$	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
$225$	0.987311	+	2.83288i	0.0658208	+	0.188859i
$226$	−5.85633	+	10.1435i	−0.389557	+	0.674733i
$227$	−17.4096			−1.15552			−0.577758	−	0.816208i	$-0.696072\pi$
$227$	−17.4096			−1.15552			−0.577758	+	0.816208i	$0.696072\pi$
$228$	−6.13894	+	4.39471i	−0.406561	+	0.291047i
$229$	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
$231$	0.435758	−	4.61602i	0.0286707	−	0.303712i
$232$	1.95032	+	3.37805i	0.128045	+	0.221780i
$233$	2.14005	+	1.23556i	0.140199	+	0.0809440i	0.568459	−	0.822712i	$-0.307540\pi$
$233$	2.14005	+	1.23556i	0.140199	+	0.0809440i	−0.428260	+	0.903656i	$0.640873\pi$
$234$	−1.03605	+	5.43860i	−0.0677289	+	0.355532i
$235$	−3.61507			−0.235821
$236$	−8.80833			−0.573373
$237$	−16.8769	−	11.9906i	−1.09627	−	0.778872i
$238$	20.7961	−	12.0067i	1.34801	−	0.778276i
$239$		−	13.1953i		−	0.853534i	−0.904362	−	0.426767i	$-0.859652\pi$
$239$		−	13.1953i		−	0.853534i	0.904362	−	0.426767i	$-0.140348\pi$
$240$	−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
$243$	13.8939	+	7.06829i	0.891291	+	0.453431i
$244$	−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
$249$	−2.27787	+	24.1296i	−0.144354	+	1.52915i
$250$	−0.866025	−	0.500000i	−0.0547723	−	0.0316228i
$251$	−18.6598	+	10.7733i	−1.17780	+	0.680002i	−0.955504	−	0.294978i	$-0.904688\pi$
$251$	−18.6598	+	10.7733i	−1.17780	+	0.680002i	−0.222294	+	0.974980i	$0.571354\pi$
$252$	−3.32298	−	9.53459i	−0.209328	−	0.600623i
$253$	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	$0.191306\pi$
$257$	14.4617	+	25.0484i	0.902096	+	1.56248i	0.0773283	+	0.997006i	$0.475361\pi$
$258$	−2.52973	−	5.52357i	−0.157494	−	0.343883i
$259$		−	12.2346i		−	0.760224i
$260$	−0.922734	−	1.59822i	−0.0572255	−	0.0991175i
$261$	3.85114	+	11.0500i	0.238380	+	0.683980i
$262$	4.80319	−	2.77312i	0.296742	−	0.171324i
$263$	−13.9401	−	8.04833i	−0.859585	−	0.496281i	0.00428849	−	0.999991i	$-0.498635\pi$
$263$	−13.9401	−	8.04833i	−0.859585	−	0.496281i	−0.863873	+	0.503709i	$0.831968\pi$
$264$	0.129471	−	1.37149i	0.00796837	−	0.0844096i
$265$			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	−0.525047	−	0.851073i	$-0.675952\pi$
$269$	7.78283	−	13.4803i	0.474528	−	0.821906i	0.999575	+	0.0291674i	$0.00928560\pi$
$270$	−5.04569	+	1.24136i	−0.307071	+	0.0755466i
$271$	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
$276$	2.81615	+	2.00080i	0.169512	+	0.120434i
$277$	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
$279$	−4.65353	+	24.4280i	−0.278600	+	1.46246i
$280$	2.91477	+	1.68284i	0.174191	+	0.100569i
$281$	12.6678	+	21.9413i	0.755698	+	1.30891i	0.945027	+	0.326993i	$0.106035\pi$
$281$	12.6678	+	21.9413i	0.755698	+	1.30891i	−0.189329	+	0.981914i	$0.560631\pi$
$282$	0.588475	−	6.23377i	0.0350432	−	0.371215i
$283$	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
$285$	3.11912	−	6.87540i	0.184761	−	0.407263i
$286$	1.46780			0.0867927
$287$	−7.01736	+	12.1544i	−0.414222	+	0.717453i
$288$	−0.987311	−	2.83288i	−0.0581779	−	0.166929i
$289$	16.9523	+	29.3622i	0.997192	+	1.72719i
$290$	−3.37805	−	1.95032i	−0.198366	−	0.114527i
$291$	−25.9795	−	18.4577i	−1.52294	−	1.08201i
$292$	14.1092			0.825676
$293$	24.4468			1.42820			0.714099	−	0.700045i	$-0.246837\pi$
$293$	24.4468			1.42820			0.714099	+	0.700045i	$0.246837\pi$
$294$	−4.34156	+	6.11079i	−0.253205	+	0.356388i
$295$	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
$300$	1.00317	−	1.41197i	0.0579179	−	0.0815201i
$301$	−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
$306$	20.2119	−	7.04421i	1.15544	−	0.402691i
$307$	−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
$309$	0.356823	−	3.77985i	0.0202989	−	0.215028i
$310$	−4.14455	−	7.17856i	−0.235394	−	0.407715i
$311$			24.4400i			1.38587i	0.721002	+	0.692933i	$0.243682\pi$
$311$			24.4400i			1.38587i	−0.721002	+	0.692933i	$0.756318\pi$
$312$	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	0.768173	−	0.640242i	$-0.221166\pi$
$317$	−3.03351	−	5.25419i	−0.170379	−	0.295105i	−0.938552	+	0.345137i	$0.887832\pi$
$318$	−11.0778	−	1.04575i	−0.621211	−	0.0586430i
$319$	2.68674	−	1.55119i	0.150429	−	0.0868500i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−1.84898	−	0.174546i	−0.103200	−	0.00974219i
$322$		−	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
$327$	1.46319	+	1.03956i	0.0809144	+	0.0574876i
$328$	−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
$333$	2.04077	−	10.7127i	0.111833	−	0.587051i
$334$	19.8229			1.08466
$335$	−3.65766			−0.199839
$336$	−3.37635	+	4.75224i	−0.184195	+	0.259256i
$337$	−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
$339$	20.1971	+	1.90663i	1.09696	+	0.103554i
$340$	−3.56737	+	6.17887i	−0.193468	+	0.335096i
$341$	6.59275			0.357018
$342$	11.3481	+	6.49776i	0.613634	+	0.351359i
$343$	−8.99362			−0.485610
$344$	−1.75379	+	3.03766i	−0.0945581	+	0.163779i
$345$	−3.43925	−	0.324669i	−0.185163	−	0.0174796i
$346$	−3.72918	−	6.45913i	−0.200482	−	0.347245i
$347$	−16.8904	−	9.75166i	−0.906723	−	0.523497i	−0.0273475	−	0.999626i	$-0.508706\pi$
$347$	−16.8904	−	9.75166i	−0.906723	−	0.523497i	−0.879375	+	0.476129i	$0.842039\pi$
$348$	3.91299	−	5.50758i	0.209758	−	0.295237i
$349$	−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
$351$	9.31167	−	2.29088i	0.497020	−	0.122278i
$352$	−0.688796	+	0.397676i	−0.0367129	+	0.0211962i
$353$			24.0186i			1.27838i	0.769049	+	0.639190i	$0.220730\pi$
$353$			24.0186i			1.27838i	−0.769049	+	0.639190i	$0.779270\pi$
$354$	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
$357$	−33.9060	−	24.0894i	−1.79450	−	1.27494i
$358$	0.153575	−	0.266000i	0.00811671	−	0.0140586i
$359$	−9.83401	−	5.67767i	−0.519019	−	0.299656i	0.217514	−	0.976057i	$-0.430205\pi$
$359$	−9.83401	−	5.67767i	−0.519019	−	0.299656i	−0.736533	+	0.676401i	$0.763539\pi$
$360$	2.27148	+	1.95969i	0.119717	+	0.103285i
$361$	−17.6188	+	7.11183i	−0.927305	+	0.374307i
$362$			13.4600i			0.707441i
$363$	17.8774	+	1.68765i	0.938320	+	0.0885785i
$364$	−5.37912	−	3.10563i	−0.281942	−	0.162779i
$365$	−12.2189	+	7.05458i	−0.639566	+	0.369253i
$366$	11.5501	+	1.09034i	0.603734	+	0.0569932i
$367$	−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
$375$	−0.162784	+	1.72438i	−0.00840612	+	0.0890468i
$376$	−3.13074	+	1.80753i	−0.161456	+	0.0932164i
$377$	6.23409	+	3.59925i	0.321072	+	0.185371i
$378$	−12.6180	+	12.1094i	−0.649002	+	0.622840i
$379$			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	$-0.639836\pi$
$383$	11.1774	−	19.3598i	0.571137	−	0.989238i	0.996450	−	0.0841912i	$-0.0268307\pi$
$384$	−1.00317	+	1.41197i	−0.0511927	+	0.0720542i
$385$	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	−0.552358	−	0.833607i	$-0.686272\pi$
$389$	−2.10271	+	1.21400i	−0.106612	+	0.0615522i	0.445746	+	0.895159i	$0.352938\pi$
$390$	−1.85131	+	2.60574i	−0.0937449	+	0.131947i
$391$	14.2301			0.719647
$392$	4.32785			0.218589
$393$	−7.83112	−	5.56381i	−0.395028	−	0.280657i
$394$	−15.1687	−	8.75764i	−0.764187	−	0.441203i
$395$	−5.97636	−	10.3514i	−0.300704	−	0.520834i
$396$	−2.25314	+	0.785261i	−0.113225	+	0.0394608i
$397$	−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
$399$	−2.47870	−	25.2892i	−0.124090	−	1.26604i
$400$	−1.00000			−0.0500000
$401$	5.27439	−	9.13551i	0.263390	−	0.456206i	−0.703750	−	0.710447i	$-0.748493\pi$
$401$	5.27439	−	9.13551i	0.263390	−	0.456206i	0.967141	+	0.254242i	$0.0818259\pi$
$402$	0.595408	−	6.30722i	0.0296963	−	0.314575i
$403$	7.64863	+	13.2478i	0.381005	+	0.659921i
$404$	−1.03574	−	0.597984i	−0.0515300	−	0.0297508i
$405$	5.59387	+	7.05043i	0.277962	+	0.350339i
$406$	−13.1283			−0.651548
$407$	−2.89119			−0.143311
$408$	−10.0740	−	7.15734i	−0.498739	−	0.354341i
$409$	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
$414$	1.11971	−	5.87774i	0.0550307	−	0.288875i
$415$	−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	$-0.743129\pi$
$419$		−	29.5663i		−	1.44441i	0.691680	−	0.722204i	$-0.256871\pi$
$420$	0.547880	−	5.80374i	0.0267338	−	0.283193i
$421$	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
$423$	−10.2411	+	3.56920i	−0.497937	+	0.173540i
$424$	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	$-0.957434\pi$
$431$	−12.6847	−	21.9705i	−0.611000	−	1.05828i	0.380073	−	0.924957i	$-0.375899\pi$
$432$	−3.74902	+	3.59789i	−0.180375	+	0.173104i
$433$	−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
$435$	−0.634961	+	6.72620i	−0.0304440	+	0.322496i
$436$		−	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
$441$	12.7542	+	2.42967i	0.607342	+	0.115699i
$442$	6.58347	−	11.4029i	0.313144	−	0.542381i
$443$	−28.0730	+	16.2079i	−1.33379	+	0.770062i	−0.985878	−	0.167466i	$-0.946442\pi$
$443$	−28.0730	+	16.2079i	−1.33379	+	0.770062i	−0.347909	+	0.937528i	$0.613108\pi$
$444$	−5.72440	+	2.62170i	−0.271668	+	0.124421i
$445$		−	3.67362i		−	0.174146i
$446$	−19.3951	+	11.1978i	−0.918383	+	0.530229i
$447$	−11.8099	−	8.39063i	−0.558589	−	0.396863i
$448$	3.36569			0.159014
$449$	1.66858			0.0787453			0.0393727	−	0.999225i	$-0.487464\pi$
$449$	1.66858			0.0787453			0.0393727	+	0.999225i	$0.487464\pi$
$450$	−2.94700	−	0.561404i	−0.138923	−	0.0264648i
$451$	2.87224	+	1.65829i	0.135248	+	0.0780857i
$452$	−5.85633	−	10.1435i	−0.275458	−	0.477108i
$453$	3.63877	−	38.5459i	0.170964	−	1.81104i
$454$	8.70480	−	15.0772i	0.408536	−	0.707606i
$455$	6.21127			0.291189
$456$	−0.736463	−	7.51383i	−0.0344880	−	0.351867i
$457$	−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
$459$	−25.6700	−	26.7483i	−1.19817	−	1.24850i
$460$	0.997241	+	1.72727i	0.0464966	+	0.0805344i
$461$	25.3943	+	14.6614i	1.18273	+	0.682851i	0.956645	−	0.291256i	$-0.0940732\pi$
$461$	25.3943	+	14.6614i	1.18273	+	0.682851i	0.226087	+	0.974107i	$0.427407\pi$
$462$	3.77971	+	2.68539i	0.175848	+	0.124936i
$463$	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
$465$	−8.31535	+	11.7039i	−0.385615	+	0.542757i
$466$	−2.14005	+	1.23556i	−0.0991358	+	0.0572361i
$467$		−	13.2112i		−	0.611341i	−0.952137	−	0.305671i	$-0.901119\pi$
$467$		−	13.2112i		−	0.611341i	0.952137	−	0.305671i	$-0.0988806\pi$
$468$	−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
$471$	−18.2012	+	25.6183i	−0.838666	+	1.18043i
$472$	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
$477$	6.34268	+	18.1990i	0.290411	+	0.833274i
$478$	11.4275	+	6.59766i	0.522681	+	0.301770i
$479$	29.9827	−	17.3105i	1.36995	−	0.790939i	0.379025	−	0.925386i	$-0.376259\pi$
$479$	29.9827	−	17.3105i	1.36995	−	0.790939i	0.990921	+	0.134448i	$0.0429261\pi$
$480$	0.162784	−	1.72438i	0.00743003	−	0.0787070i
$481$	−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
$489$	−31.9305	−	3.01428i	−1.44395	−	0.136310i
$490$	−3.74803	+	2.16392i	−0.169319	+	0.0977562i
$491$	3.62316	+	2.09183i	0.163511	+	0.0944030i	0.579522	−	0.814956i	$-0.303239\pi$
$491$	3.62316	+	2.09183i	0.163511	+	0.0944030i	−0.416012	+	0.909359i	$0.636572\pi$
$492$	7.19059	+	0.678800i	0.324177	+	0.0306027i
$493$		−	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
$498$	−19.7579	−	14.0375i	−0.885375	−	0.629036i
$499$	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	−0.702274	−	0.711907i	$-0.747832\pi$
$503$	−9.79822	+	5.65701i	−0.436881	+	0.252233i	0.265393	+	0.964140i	$0.414498\pi$
$504$	9.91869	+	1.88951i	0.441814	+	0.0841655i
$505$	1.19597			0.0532199
$506$	−1.58632			−0.0705204
$507$	−9.62463	+	13.5468i	−0.427445	+	0.601633i
$508$	−3.29108	−	1.90011i	−0.146018	−	0.0843036i
$509$	10.8249	+	18.7493i	0.479806	+	0.831048i	0.999732	−	0.0231634i	$-0.00737381\pi$
$509$	10.8249	+	18.7493i	0.479806	+	0.831048i	−0.519926	+	0.854211i	$0.674040\pi$
$510$	12.3030	+	1.16142i	0.544788	+	0.0514286i
$511$	−23.7435	+	41.1249i	−1.05035	+	1.81926i
$512$	1.00000			0.0441942
$513$	2.04794	−	22.5567i	0.0904186	−	0.995904i
$514$	−28.9234			−1.27576
$515$	1.09600	−	1.89833i	0.0482956	−	0.0836504i
$516$	6.04842	+	0.570978i	0.266267	+	0.0251359i
$517$	1.43763	+	2.49004i	0.0632268	+	0.109512i
$518$	10.5955	+	6.11732i	0.465540	+	0.268780i
$519$	−7.48198	+	10.5310i	−0.328423	+	0.462259i
$520$	1.84547			0.0809291
$521$	31.4041			1.37584			0.687920	−	0.725787i	$-0.258524\pi$
$521$	31.4041			1.37584			0.687920	+	0.725787i	$0.258524\pi$
$522$	−11.4952	−	2.18983i	−0.503131	−	0.0958464i
$523$	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
$528$	1.12301	+	0.797872i	0.0488729	+	0.0347229i
$529$	−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
$534$	6.33473	+	0.598006i	0.274131	+	0.0258782i
$535$	−0.928599	−	0.536127i	−0.0401468	−	0.0231788i
$536$	−3.16763	+	1.82883i	−0.136821	+	0.0789935i
$537$	−0.529646	−	0.0499992i	−0.0228559	−	0.00215762i
$538$	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
$546$	−1.01109	+	10.7106i	−0.0432708	+	0.458372i
$547$	−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
$549$	−6.61312	−	18.9749i	−0.282241	−	0.809831i
$550$			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
$555$	3.64662	−	5.13266i	0.154791	−	0.217869i
$556$	−5.17049	+	8.95556i	−0.219278	+	0.379800i
$557$	−9.64943	+	5.57110i	−0.408860	+	0.236055i	−0.690300	−	0.723524i	$-0.742521\pi$
$557$	−9.64943	+	5.57110i	−0.408860	+	0.236055i	0.281440	+	0.959579i	$0.409188\pi$
$558$	−18.8285	−	16.2441i	−0.797073	−	0.687666i
$559$			6.47313i			0.273784i
$560$	−2.91477	+	1.68284i	−0.123172	+	0.0711131i
$561$	−5.69261	+	8.01241i	−0.240342	+	0.338284i
$562$	−25.3356			−1.06872
$563$	−25.6386			−1.08054			−0.540269	−	0.841492i	$-0.681677\pi$
$563$	−25.6386			−1.08054			−0.540269	+	0.841492i	$0.681677\pi$
$564$	5.10436	+	3.62652i	0.214932	+	0.152704i
$565$	10.1435	+	5.85633i	0.426738	+	0.246378i
$566$	4.10956	+	7.11797i	0.172738	+	0.299191i
$567$	28.1696	+	11.1368i	1.18301	+	0.467701i
$568$	0.800066	−	1.38576i	0.0335700	−	0.0581450i
$569$	36.2410			1.51930			0.759651	−	0.650331i	$-0.225370\pi$
$569$	36.2410			1.51930			0.759651	+	0.650331i	$0.225370\pi$
$570$	4.39471	+	6.13894i	0.184074	+	0.257132i
$571$	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
$573$	3.30469	−	35.0069i	0.138055	−	1.46243i
$574$	−7.01736	−	12.1544i	−0.292899	−	0.507316i
$575$	−1.72727	−	0.997241i	−0.0720322	−	0.0415878i
$576$	2.94700	+	0.561404i	0.122792	+	0.0233918i
$577$	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
$579$	−6.53323	−	4.64169i	−0.271512	−	0.192902i
$580$	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
$585$	5.43860	+	1.03605i	0.224858	+	0.0428355i
$586$	−12.2234	+	21.1716i	−0.504944	+	0.874589i
$587$	24.1606	+	13.9491i	0.997214	+	0.575742i	0.907423	−	0.420219i	$-0.138047\pi$
$587$	24.1606	+	13.9491i	0.997214	+	0.575742i	0.0897909	+	0.995961i	$0.471380\pi$
$588$	−3.12132	−	6.81529i	−0.128721	−	0.281058i
$589$	35.4686	−	6.88844i	1.46146	−	0.283833i
$590$			8.80833i			0.362633i
$591$	−2.85120	+	30.2031i	−0.117283	+	1.24239i
$592$	3.14810	+	1.81755i	0.129386	+	0.0747010i
$593$	−12.3343	+	7.12119i	−0.506508	+	0.292432i	−0.731397	−	0.681952i	$-0.761131\pi$
$593$	−12.3343	+	7.12119i	−0.506508	+	0.292432i	0.224889	+	0.974384i	$0.427798\pi$
$594$	2.86159	+	2.98179i	0.117413	+	0.122345i
$595$	−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	0.599059	−	0.800705i	$-0.295542\pi$
$599$	−9.64054	−	16.6979i	−0.393902	−	0.682258i	−0.992960	+	0.118447i	$0.962208\pi$
$600$	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
$603$	−10.3617	+	3.61125i	−0.421962	+	0.147062i
$604$	−19.3586	+	11.1767i	−0.787691	+	0.454773i
$605$	8.97844	+	5.18371i	0.365026	+	0.210748i
$606$	−0.194684	+	2.06231i	−0.00790852	+	0.0837756i
$607$		−	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
$612$	−4.00547	+	21.0261i	−0.161912	+	0.849930i
$613$	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	−0.404101	−	0.914714i	$-0.632416\pi$
$617$	4.62048	−	2.66763i	0.186013	−	0.107395i	0.590115	+	0.807319i	$0.299082\pi$
$618$	3.09504	+	2.19894i	0.124501	+	0.0884545i
$619$	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
$621$	−10.0635	+	2.47586i	−0.403836	+	0.0993529i
$622$	−21.1657	−	12.2200i	−0.848666	−	0.489977i
$623$	−6.18212	−	10.7078i	−0.247682	−	0.428997i
$624$	−0.300413	+	3.18230i	−0.0120261	+	0.127394i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.12928			0.0851033
$627$	−5.97614	+	0.585748i	−0.238664	+	0.0233925i
$628$	18.1437			0.724013
$629$	−12.9678	+	22.4609i	−0.517059	+	0.895573i
$630$	−9.53459	+	3.32298i	−0.379867	+	0.132391i
$631$	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
$633$	38.0739	+	27.0505i	1.51330	+	1.07516i
$634$	6.06702			0.240952
$635$	3.80022			0.150807
$636$	6.44454	−	9.07076i	0.255543	−	0.359679i
$637$	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	−0.775480	−	0.631372i	$-0.782492\pi$
$641$	4.02668	−	6.97441i	0.159044	−	0.275473i	0.934524	+	0.355899i	$0.115825\pi$
$642$	1.07565	−	1.51399i	0.0424525	−	0.0597524i
$643$	−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	$0.0769926\pi$
$647$			12.1854i			0.479056i	−0.970889	+	0.239528i	$0.923007\pi$
$648$	8.36965	+	3.30892i	0.328791	+	0.129987i
$649$	−6.06714	−	3.50286i	−0.238156	−	0.137499i
$650$	−1.59822	+	0.922734i	−0.0626874	+	0.0361926i
$651$	−4.54142	+	48.1077i	−0.177992	+	1.88549i
$652$	9.25852	+	16.0362i	0.362592	+	0.628027i
$653$		−	46.1577i		−	1.80629i	−0.429335	−	0.903145i	$-0.641252\pi$
$653$		−	46.1577i		−	1.80629i	0.429335	−	0.903145i	$-0.358748\pi$
$654$	−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	0.971040	−	0.238919i	$-0.0767930\pi$
$659$	7.15219	+	12.3880i	0.278610	+	0.482567i	−0.692430	+	0.721485i	$0.743460\pi$
$660$	−1.37149	−	0.129471i	−0.0533853	−	0.00503964i
$661$	−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
$663$	−22.7049	−	2.14337i	−0.881784	−	0.0832414i
$664$			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
$669$	31.6217	+	22.4664i	1.22257	+	0.868602i
$670$	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
$675$	1.24136	+	5.04569i	0.0477798	+	0.194209i
$676$	9.59425			0.369009
$677$	−13.7283			−0.527620			−0.263810	−	0.964575i	$-0.584979\pi$
$677$	−13.7283			−0.527620			−0.263810	+	0.964575i	$0.584979\pi$
$678$	−11.7497	+	16.5379i	−0.451246	+	0.635134i
$679$	−53.6302	−	30.9634i	−2.05814	−	1.18827i
$680$	−3.56737	−	6.17887i	−0.136802	−	0.236949i
$681$	−30.0208	−	2.83400i	−1.15040	−	0.108599i
$682$	−3.29638	+	5.70949i	−0.126225	+	0.218628i
$683$	27.2992			1.04457			0.522287	−	0.852770i	$-0.325079\pi$
$683$	27.2992			1.04457			0.522287	+	0.852770i	$0.325079\pi$
$684$	−11.3013	+	6.57885i	−0.432115	+	0.251549i
$685$	19.9319			0.761560
$686$	4.49681	−	7.78871i	0.171689	−	0.297374i
$687$	3.34516	+	0.315787i	0.127626	+	0.0120480i
$688$	−1.75379	−	3.03766i	−0.0668627	−	0.115810i
$689$	10.2673	+	5.92782i	0.391152	+	0.225832i
$690$	2.00080	−	2.81615i	0.0761691	−	0.107209i
$691$	−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
$693$	1.50283	−	7.88886i	0.0570877	−	0.299673i
$694$	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
$699$	3.48914	+	2.47894i	0.131971	+	0.0937621i
$700$	1.68284	−	2.91477i	0.0636055	−	0.110168i
$701$	−34.6741	−	20.0191i	−1.30962	−	0.756111i	−0.327589	−	0.944820i	$-0.606236\pi$
$701$	−34.6741	−	20.0191i	−1.30962	−	0.756111i	−0.982033	+	0.188710i	$0.939569\pi$
$702$	−2.67187	+	9.20958i	−0.100843	+	0.347593i
$703$	−15.5544	+	3.02087i	−0.586647	+	0.113934i
$704$		−	0.795353i		−	0.0299760i
$705$	−6.23377	−	0.588475i	−0.234777	−	0.0221632i
$706$	−20.8007	−	12.0093i	−0.782845	−	0.451976i
$707$	3.48597	−	2.01263i	0.131104	−	0.0756927i
$708$	−15.1889	−	1.43385i	−0.570836	−	0.0538875i
$709$	−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
$717$	2.14799	−	22.7538i	0.0802180	−	0.849756i
$718$	9.83401	−	5.67767i	0.367002	−	0.211889i
$719$	−10.7413	−	6.20149i	−0.400583	−	0.231276i	0.286153	−	0.958184i	$-0.407624\pi$
$719$	−10.7413	−	6.20149i	−0.400583	−	0.231276i	−0.686735	+	0.726908i	$0.740957\pi$
$720$	−2.83288	+	0.987311i	−0.105575	+	0.0367949i
$721$		−	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
$726$	−10.4002	+	14.6385i	−0.385989	+	0.543284i
$727$	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
$732$	−6.71932	+	9.45752i	−0.248353	+	0.349560i
$733$	−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
$735$	6.11079	+	4.34156i	0.225400	+	0.160141i
$736$	1.72727	+	0.997241i	0.0636681	+	0.0367588i
$737$	1.45457	+	2.51938i	0.0535796	+	0.0928026i
$738$	−4.11703	−	11.8130i	−0.151550	−	0.434841i
$739$	−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
$741$	−8.11030	−	11.3292i	−0.297939	−	0.416189i
$742$	−21.6218			−0.793762
$743$	9.67139	−	16.7513i	0.354809	−	0.614547i	−0.632276	−	0.774743i	$-0.717879\pi$
$743$	9.67139	−	16.7513i	0.354809	−	0.614547i	0.987085	+	0.160196i	$0.0512126\pi$
$744$	−1.34933	+	14.2936i	−0.0494689	+	0.524028i
$745$	−4.18207	−	7.24356i	−0.153219	−	0.265383i
$746$	22.7761	+	13.1498i	0.833892	+	0.481448i
$747$	−7.85583	+	41.2380i	−0.287430	+	1.50882i
$748$	5.67464			0.207485
$749$	−3.60887			−0.131865
$750$	−1.41197	−	1.00317i	−0.0515578	−	0.0366305i
$751$	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
$756$	−4.17802	−	16.9822i	−0.151953	−	0.617638i
$757$	−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	$0.143825\pi$
$761$			24.0894i			0.873241i	−0.899646	+	0.436621i	$0.856175\pi$
$762$	−0.618614	+	6.55303i	−0.0224100	+	0.237391i
$763$	3.02050	+	1.74389i	0.109350	+	0.0631330i
$764$	−17.5813	+	10.1505i	−0.636067	+	0.367234i
$765$	−7.04421	−	20.2119i	−0.254684	−	0.730762i
$766$	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	0.931258	−	0.364361i	$-0.118712\pi$
$773$	4.17275	+	7.22742i	0.150084	+	0.259952i	−0.781174	+	0.624313i	$0.785379\pi$
$774$	−3.46308	−	9.93656i	−0.124478	−	0.357162i
$775$	−7.17856	+	4.14455i	−0.257862	+	0.148876i
$776$	−15.9344	−	9.19973i	−0.572012	−	0.330251i
$777$	1.99160	−	21.0972i	0.0714483	−	0.756859i
$778$		−	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
$783$	4.84208	+	19.6814i	0.173042	+	0.703357i
$784$	−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
$789$	−22.7280	−	16.1476i	−0.809138	−	0.574871i
$790$	11.9527			0.425259
$791$	39.4211			1.40165
$792$	0.446514	−	2.34391i	0.0158662	−	0.0832871i
$793$	−10.7051	−	6.18057i	−0.380148	−	0.219479i
$794$	−13.4569	−	23.3080i	−0.477568	−	0.827172i
$795$	−1.04575	+	11.0778i	−0.0370891	+	0.392888i
$796$	−0.637900	+	1.10487i	−0.0226097	+	0.0391612i
$797$	0.634867			0.0224881			0.0112441	−	0.999937i	$-0.496421\pi$
$797$	0.634867			0.0224881			0.0112441	+	0.999937i	$0.496421\pi$
$798$	23.1404	+	10.4980i	0.819163	+	0.371624i
$799$	25.7926			0.912475
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.62700	−	10.4069i	−0.128154	−	0.367711i
$802$	5.27439	+	9.13551i	0.186245	+	0.322586i
$803$	9.71833	+	5.61088i	0.342952	+	0.198004i
$804$	5.16450	+	3.66925i	0.182138	+	0.129404i
$805$	−6.71280			−0.236595
$806$	−15.2973			−0.538823
$807$	15.6150	−	21.9782i	0.549673	−	0.773670i
$808$	1.03574	−	0.597984i	0.0364372	−	0.0210370i
$809$		−	47.4357i		−	1.66775i	−0.551953	−	0.833875i	$-0.686117\pi$
$809$		−	47.4357i		−	1.66775i	0.551953	−	0.833875i	$-0.313883\pi$
$810$	−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
$813$	2.41715	−	3.40216i	0.0847731	−	0.119319i
$814$	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
$819$	17.5958	−	6.13246i	0.614847	−	0.214285i
$820$	3.61128	+	2.08497i	0.126111	+	0.0728104i
$821$	15.1395	−	8.74082i	0.528373	−	0.305057i	−0.211980	−	0.977274i	$-0.567991\pi$
$821$	15.1395	−	8.74082i	0.528373	−	0.305057i	0.740354	+	0.672217i	$0.234658\pi$
$822$	−3.24460	+	34.3703i	−0.113168	+	1.19880i
$823$	−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	$0.201737\pi$
$827$	26.3348	+	45.6132i	0.915751	+	1.58613i	0.109954	+	0.993937i	$0.464930\pi$
$828$	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
$831$	53.0920	+	5.01195i	1.84174	+	0.173863i
$832$	1.59822	−	0.922734i	0.0554084	−	0.0319901i
$833$	−26.7412	−	15.4390i	−0.926528	−	0.534931i
$834$	17.8318	+	1.68335i	0.617466	+	0.0582895i
$835$		−	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	$0.401659\pi$
$839$	−19.4936	+	33.7640i	−0.672996	+	1.16566i	−0.977050	+	0.213008i	$0.931674\pi$
$840$	4.75224	+	3.37635i	0.163968	+	0.116495i
$841$	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
$846$	2.02951	−	10.6536i	0.0697761	−	0.366279i
$847$	34.8935			1.19895
$848$	−6.42419			−0.220608
$849$	8.24515	−	11.6051i	0.282973	−	0.398288i
$850$	6.17887	+	3.56737i	0.211933	+	0.122360i
$851$	3.62508	+	6.27882i	0.124266	+	0.215235i
$852$	−2.75924	−	0.260476i	−0.0945301	−	0.00892376i
$853$	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
$855$	6.49776	−	11.3481i	0.222219	−	0.388096i
$856$	−1.07225			−0.0366489
$857$	0.771649	−	1.33654i	0.0263590	−	0.0456552i	−0.852545	−	0.522654i	$-0.824942\pi$
$857$	0.771649	−	1.33654i	0.0263590	−	0.0456552i	0.878904	+	0.476999i	$0.158275\pi$
$858$	2.53105	+	0.238934i	0.0864086	+	0.00815707i
$859$	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
$861$	−14.0792	+	19.8166i	−0.479817	+	0.675348i
$862$	25.3694			0.864084
$863$	11.5515			0.393217			0.196608	−	0.980482i	$-0.437007\pi$
$863$	11.5515			0.393217			0.196608	+	0.980482i	$0.437007\pi$
$864$	−1.24136	−	5.04569i	−0.0422318	−	0.171658i
$865$	−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
$870$	−5.50758	−	3.91299i	−0.186724	−	0.132663i
$871$	−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
$876$	24.3296	+	2.29674i	0.822021	+	0.0775998i
$877$	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
$879$	42.1557	+	3.97955i	1.42188	+	0.134227i
$880$	0.397676	+	0.688796i	0.0134057	+	0.0232193i
$881$			8.64964i			0.291414i	0.989328	+	0.145707i	$0.0465457\pi$
$881$			8.64964i			0.291414i	−0.989328	+	0.145707i	$0.953454\pi$
$882$	−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	$0.00744958\pi$
$887$	15.4908	+	26.8308i	0.520129	+	0.900890i	−0.479597	+	0.877489i	$0.659217\pi$
$888$	0.591737	−	6.26833i	0.0198574	−	0.210351i
$889$	11.0768	−	6.39517i	0.371502	−	0.214487i
$890$	3.18145	+	1.83681i	0.106642	+	0.0615700i
$891$	2.63176	−	6.65683i	0.0881672	−	0.223012i
$892$		−	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
$897$	−3.69241	+	5.19711i	−0.123286	+	0.173526i
$898$	−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
$903$	−11.8428	+	16.6689i	−0.394104	+	0.554706i
$904$	11.7127			0.389557
$905$	13.4600			0.447425
$906$	31.5623	+	22.4242i	1.04859	+	0.744994i
$907$	−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
$909$	3.38804	−	1.18079i	0.112374	−	0.0391644i
$910$	−3.10563	+	5.37912i	−0.102951	+	0.178316i
$911$	−33.0252			−1.09417			−0.547086	−	0.837076i	$-0.684263\pi$
$911$	−33.0252			−1.09417			−0.547086	+	0.837076i	$0.684263\pi$
$912$	6.87540	+	3.11912i	0.227667	+	0.103284i
$913$	11.1295			0.368333
$914$	7.23822	−	12.5370i	0.239419	−	0.414686i
$915$	1.09034	−	11.5501i	0.0360457	−	0.381835i
$916$	−0.969958	−	1.68002i	−0.0320483	−	0.0555093i
$917$	−16.1660	−	9.33346i	−0.533849	−	0.308218i
$918$	35.9997	−	8.85676i	1.18817	−	0.292317i
$919$	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
$921$	−15.7338	−	11.1785i	−0.518448	−	0.368344i
$922$	−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
$927$	1.23060	−	6.45983i	0.0404182	−	0.212169i
$928$	1.95032	−	3.37805i	0.0640223	−	0.110890i
$929$	−45.5906	−	26.3217i	−1.49578	−	0.863588i	−0.495790	−	0.868442i	$-0.665122\pi$
$929$	−45.5906	−	26.3217i	−1.49578	−	0.863588i	−0.999988	+	0.00485418i	$0.998455\pi$
$930$	−5.97824	−	13.0533i	−0.196034	−	0.428034i
$931$	−3.59655	−	18.5186i	−0.117872	−	0.606924i
$932$		−	2.47111i		−	0.0809440i
$933$	−3.97844	+	42.1440i	−0.130248	+	1.37973i
$934$	11.4412	+	6.60560i	0.374369	+	0.216142i
$935$	−4.91438	+	2.83732i	−0.160717	+	0.0927902i
$936$	5.22799	−	1.82205i	0.170882	−	0.0595556i
$937$	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	0.650251	−	0.759720i	$-0.274664\pi$
$941$	−10.2092	−	17.6829i	−0.332811	−	0.576446i	−0.983062	+	0.183274i	$0.941331\pi$
$942$	−13.0856	−	28.5718i	−0.426350	−	0.930921i
$943$		−	8.31687i		−	0.270835i
$944$	4.40416	+	7.62824i	0.143343	+	0.248278i
$945$	12.1094	+	12.6180i	0.393918	+	0.410465i
$946$	−2.41601	+	1.39488i	−0.0785512	+	0.0453515i
$947$	28.8707	+	16.6685i	0.938171	+	0.541654i	0.889387	−	0.457156i	$-0.151132\pi$
$947$	28.8707	+	16.6685i	0.938171	+	0.541654i	0.0487848	+	0.998809i	$0.484465\pi$
$948$	−1.94571	+	20.6111i	−0.0631938	+	0.669417i
$949$			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	−0.938681	−	0.344786i	$-0.887951\pi$
$953$	−5.27108	+	9.12979i	−0.170747	+	0.295743i	0.767934	+	0.640529i	$0.221285\pi$
$954$	−18.9321	−	3.60657i	−0.612950	−	0.116767i
$955$	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
$960$	1.41197	+	1.00317i	0.0455711	+	0.0323771i
$961$	−37.7091			−1.21642
$962$	6.70848			0.216290
$963$	−3.15993	−	0.601968i	−0.101827	−	0.0193981i
$964$	−23.5846	−	13.6166i	−0.759610	−	0.438561i
$965$	−2.31352	−	4.00713i	−0.0744747	−	0.128994i
$966$	1.09274	−	11.5754i	0.0351582	−	0.372434i
$967$	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
$969$	−22.2541	+	49.0542i	−0.714905	+	1.57585i
$970$	18.3995			0.590771
$971$	−20.9023	+	36.2039i	−0.670787	+	1.16184i	0.306894	+	0.951744i	$0.400710\pi$
$971$	−20.9023	+	36.2039i	−0.670787	+	1.16184i	−0.977681	+	0.210094i	$0.932623\pi$
$972$	−0.825609	−	15.5666i	−0.0264814	−	0.499298i
$973$	−17.4023	−	30.1416i	−0.557891	−	0.966295i
$974$	−17.9945	−	10.3891i	−0.576582	−	0.332890i
$975$	2.60574	+	1.85131i	0.0834506	+	0.0592895i
$976$	6.69811			0.214401
$977$	−15.3174			−0.490046			−0.245023	−	0.969517i	$-0.578795\pi$
$977$	−15.3174			−0.490046			−0.245023	+	0.969517i	$0.578795\pi$
$978$	18.5757	−	26.1455i	0.593985	−	0.836041i
$979$	−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	−0.837909	−	0.545810i	$-0.816222\pi$
$983$	1.68463	−	2.91786i	0.0537313	−	0.0930654i	0.891640	+	0.452745i	$0.149555\pi$
$984$	−4.18315	+	5.88783i	−0.133354	+	0.187697i
$985$	−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
$990$	0.785261	+	2.25314i	0.0249572	+	0.0716095i
$991$	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
$993$	−1.24258	+	13.1628i	−0.0394322	+	0.417709i
$994$	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.a.521.12	yes	24
3.2	odd	2		570.2.s.b.521.9	yes	24
19.12	odd	6		570.2.s.b.221.9	yes	24
57.50	even	6	inner	570.2.s.a.221.12	✓	24

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

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72438 + 0.162784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00317 + 1.41197i) q^{6} +3.36569 q^{7} +1.00000 q^{8} +(2.94700 + 0.561404i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.72438 + 0.162784i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-1.00317 + 1.41197i) q^{6} +3.36569 q^{7} +1.00000 q^{8} +(2.94700 + 0.561404i) 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} +(1.41197 + 1.00317i) 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} +(5.80374 + 0.547880i) q^{21} +(0.688796 + 0.397676i) q^{22} +(-1.72727 + 0.997241i) q^{23} +(1.72438 + 0.162784i) 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} +(0.129471 - 1.37149i) q^{33} +(6.17887 - 3.56737i) q^{34} +(2.91477 + 1.68284i) q^{35} +(-0.987311 - 2.83288i) 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} +(-3.37635 + 4.75224i) 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} +(-1.00317 + 1.41197i) q^{48} +4.32785 q^{49} -1.00000 q^{50} +(-10.0740 - 7.15734i) q^{51} +(-1.59822 - 0.922734i) q^{52} +(3.21210 + 5.56351i) q^{53} +(-3.74902 + 3.59789i) q^{54} +(0.397676 - 0.688796i) q^{55} +3.36569 q^{56} +(-0.736463 - 7.51383i) q^{57} -3.90064 q^{58} +(4.40416 - 7.62824i) q^{59} +(0.162784 - 1.72438i) q^{60} +(-3.34905 - 5.80073i) q^{61} +(-7.17856 - 4.14455i) q^{62} +(9.91869 + 1.88951i) q^{63} +1.00000 q^{64} +1.84547 q^{65} +(1.12301 + 0.797872i) 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} +(2.94700 + 0.561404i) 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} +(-0.300413 + 3.18230i) q^{78} +(-10.3514 - 5.97636i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(8.36965 + 3.30892i) 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} +(-2.83288 + 0.987311i) q^{90} +(5.37912 - 3.10563i) q^{91} +(1.72727 + 0.997241i) q^{92} +(-1.34933 + 14.2936i) 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} +(0.446514 - 2.34391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * 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 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * 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 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

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