LMFDB - Embedded newform 570.2.s.a.221.7

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			221.7
Character	$\chi$	$=$	570.221
Dual form			570.2.s.a.521.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.362568 + 1.69368i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.28548 - 1.16083i) q^{6} -0.535070 q^{7} +1.00000 q^{8} +(-2.73709 + 1.22815i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.362568 + 1.69368i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.28548 - 1.16083i) q^{6} -0.535070 q^{7} +1.00000 q^{8} +(-2.73709 + 1.22815i) q^{9} +(-0.866025 - 0.500000i) q^{10} +5.20870i q^{11} +(-1.64805 - 0.532846i) q^{12} +(1.58889 + 0.917346i) q^{13} +(0.267535 + 0.463384i) q^{14} +(1.16083 + 1.28548i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93717 + 2.27312i) q^{17} +(2.43215 + 1.75631i) q^{18} +(-1.25777 - 4.17349i) q^{19} +1.00000i q^{20} +(-0.193999 - 0.906236i) q^{21} +(4.51086 - 2.60435i) q^{22} +(5.55808 + 3.20896i) q^{23} +(0.362568 + 1.69368i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.83469i q^{26} +(-3.07247 - 4.19046i) q^{27} +(0.267535 - 0.463384i) q^{28} +(-4.19776 + 7.27074i) q^{29} +(0.532846 - 1.64805i) q^{30} -4.17904i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-8.82185 + 1.88851i) q^{33} +(3.93717 + 2.27312i) q^{34} +(-0.463384 + 0.267535i) q^{35} +(0.304938 - 2.98446i) q^{36} +5.32678i q^{37} +(-2.98546 + 3.17601i) q^{38} +(-0.977607 + 3.02367i) q^{39} +(0.866025 - 0.500000i) q^{40} +(2.33917 + 4.05157i) q^{41} +(-0.687824 + 0.621126i) q^{42} +(4.21877 + 7.30712i) q^{43} +(-4.51086 - 2.60435i) q^{44} +(-1.75631 + 2.43215i) q^{45} -6.41792i q^{46} +(3.52343 + 2.03425i) q^{47} +(1.28548 - 1.16083i) q^{48} -6.71370 q^{49} -1.00000 q^{50} +(-5.27743 - 5.84413i) q^{51} +(-1.58889 + 0.917346i) q^{52} +(-3.26957 + 5.66307i) q^{53} +(-2.09281 + 4.75606i) q^{54} +(2.60435 + 4.51086i) q^{55} -0.535070 q^{56} +(6.61252 - 3.64344i) q^{57} +8.39553 q^{58} +(-3.47483 - 6.01858i) q^{59} +(-1.69368 + 0.362568i) q^{60} +(4.11360 - 7.12497i) q^{61} +(-3.61915 + 2.08952i) q^{62} +(1.46453 - 0.657144i) q^{63} +1.00000 q^{64} +1.83469 q^{65} +(6.04642 + 6.69569i) q^{66} +(-0.445224 - 0.257050i) q^{67} -4.54625i q^{68} +(-3.41976 + 10.5771i) q^{69} +(0.463384 + 0.267535i) q^{70} +(3.29907 + 5.71415i) q^{71} +(-2.73709 + 1.22815i) q^{72} +(3.05629 + 5.29365i) q^{73} +(4.61313 - 2.66339i) q^{74} +(1.64805 + 0.532846i) q^{75} +(4.24323 + 0.997481i) q^{76} -2.78702i q^{77} +(3.10738 - 0.665201i) q^{78} +(7.65758 - 4.42110i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(5.98331 - 6.72310i) q^{81} +(2.33917 - 4.05157i) q^{82} -13.2159i q^{83} +(0.881823 + 0.285110i) q^{84} +(-2.27312 + 3.93717i) q^{85} +(4.21877 - 7.30712i) q^{86} +(-13.8363 - 4.47352i) q^{87} +5.20870i q^{88} +(8.15273 - 14.1209i) q^{89} +(2.98446 + 0.304938i) q^{90} +(-0.850166 - 0.490844i) q^{91} +(-5.55808 + 3.20896i) q^{92} +(7.07794 - 1.51519i) q^{93} -4.06851i q^{94} +(-3.17601 - 2.98546i) q^{95} +(-1.64805 - 0.532846i) q^{96} +(0.567737 - 0.327783i) q^{97} +(3.35685 + 5.81424i) q^{98} +(-6.39704 - 14.2567i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	0.362568	+	1.69368i	0.209329	+	0.977845i
$3$	0.362568	+	1.69368i	0.209329	+	0.977845i
$4$	−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
$6$	1.28548	−	1.16083i	0.524797	−	0.473908i
$7$	−0.535070			−0.202237			−0.101119	−	0.994874i	$-0.532242\pi$
$7$	−0.535070			−0.202237			−0.101119	+	0.994874i	$0.532242\pi$
$8$	1.00000			0.353553
$9$	−2.73709	+	1.22815i	−0.912363	+	0.409382i
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$			5.20870i			1.57048i	0.619191	+	0.785240i	$0.287461\pi$
$11$			5.20870i			1.57048i	−0.619191	+	0.785240i	$0.712539\pi$
$12$	−1.64805	−	0.532846i	−0.475752	−	0.153819i
$13$	1.58889	+	0.917346i	0.440679	+	0.254426i	0.703885	−	0.710314i	$-0.251447\pi$
$13$	1.58889	+	0.917346i	0.440679	+	0.254426i	−0.263207	+	0.964739i	$0.584780\pi$
$14$	0.267535	+	0.463384i	0.0715017	+	0.123845i
$15$	1.16083	+	1.28548i	0.299726	+	0.331911i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.93717	+	2.27312i	−0.954903	+	0.551313i	−0.894601	−	0.446867i	$-0.852540\pi$
$17$	−3.93717	+	2.27312i	−0.954903	+	0.551313i	−0.0603023	+	0.998180i	$0.519206\pi$
$18$	2.43215	+	1.75631i	0.573263	+	0.413967i
$19$	−1.25777	−	4.17349i	−0.288553	−	0.957464i
$19$	−1.25777	−	4.17349i	−0.288553	−	0.957464i
$20$			1.00000i			0.223607i
$21$	−0.193999	−	0.906236i	−0.0423341	−	0.197757i
$22$	4.51086	−	2.60435i	0.961719	−	0.555249i
$23$	5.55808	+	3.20896i	1.15894	+	0.669114i	0.951050	−	0.309038i	$-0.100007\pi$
$23$	5.55808	+	3.20896i	1.15894	+	0.669114i	0.207890	+	0.978152i	$0.433340\pi$
$24$	0.362568	+	1.69368i	0.0740089	+	0.345721i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		−	1.83469i		−	0.359813i
$27$	−3.07247	−	4.19046i	−0.591296	−	0.806454i
$28$	0.267535	−	0.463384i	0.0505593	−	0.0875713i
$29$	−4.19776	+	7.27074i	−0.779505	+	1.35014i	0.152722	+	0.988269i	$0.451196\pi$
$29$	−4.19776	+	7.27074i	−0.779505	+	1.35014i	−0.932227	+	0.361873i	$0.882137\pi$
$30$	0.532846	−	1.64805i	0.0972839	−	0.300892i
$31$		−	4.17904i		−	0.750577i	−0.926908	−	0.375289i	$-0.877544\pi$
$31$		−	4.17904i		−	0.750577i	0.926908	−	0.375289i	$-0.122456\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−8.82185	+	1.88851i	−1.53569	+	0.328747i
$34$	3.93717	+	2.27312i	0.675218	+	0.389837i
$35$	−0.463384	+	0.267535i	−0.0783262	+	0.0452216i
$36$	0.304938	−	2.98446i	0.0508229	−	0.497410i
$37$			5.32678i			0.875718i	0.899044	+	0.437859i	$0.144263\pi$
$37$			5.32678i			0.875718i	−0.899044	+	0.437859i	$0.855737\pi$
$38$	−2.98546	+	3.17601i	−0.484306	+	0.515216i
$39$	−0.977607	+	3.02367i	−0.156542	+	0.484174i
$40$	0.866025	−	0.500000i	0.136931	−	0.0790569i
$41$	2.33917	+	4.05157i	0.365318	+	0.632749i	0.988827	−	0.149067i	$-0.0476271\pi$
$41$	2.33917	+	4.05157i	0.365318	+	0.632749i	−0.623509	+	0.781816i	$0.714294\pi$
$42$	−0.687824	+	0.621126i	−0.106133	+	0.0958418i
$43$	4.21877	+	7.30712i	0.643356	+	1.11433i	0.984679	+	0.174379i	$0.0557919\pi$
$43$	4.21877	+	7.30712i	0.643356	+	1.11433i	−0.341322	+	0.939946i	$0.610875\pi$
$44$	−4.51086	−	2.60435i	−0.680038	−	0.392620i
$45$	−1.75631	+	2.43215i	−0.261816	+	0.362564i
$46$		−	6.41792i		−	0.946271i
$47$	3.52343	+	2.03425i	0.513945	+	0.296726i	0.734454	−	0.678659i	$-0.237438\pi$
$47$	3.52343	+	2.03425i	0.513945	+	0.296726i	−0.220509	+	0.975385i	$0.570772\pi$
$48$	1.28548	−	1.16083i	0.185544	−	0.167552i
$49$	−6.71370			−0.959100
$50$	−1.00000			−0.141421
$51$	−5.27743	−	5.84413i	−0.738988	−	0.818341i
$52$	−1.58889	+	0.917346i	−0.220339	+	0.127213i
$53$	−3.26957	+	5.66307i	−0.449110	+	0.777882i	−0.998328	−	0.0577971i	$-0.981592\pi$
$53$	−3.26957	+	5.66307i	−0.449110	+	0.777882i	0.549218	+	0.835679i	$0.314926\pi$
$54$	−2.09281	+	4.75606i	−0.284795	+	0.647218i
$55$	2.60435	+	4.51086i	0.351170	+	0.608245i
$56$	−0.535070			−0.0715017
$57$	6.61252	−	3.64344i	0.875849	−	0.482585i
$58$	8.39553			1.10239
$59$	−3.47483	−	6.01858i	−0.452384	−	0.783552i	0.546149	−	0.837688i	$-0.316093\pi$
$59$	−3.47483	−	6.01858i	−0.452384	−	0.783552i	−0.998534	+	0.0541355i	$0.982760\pi$
$60$	−1.69368	+	0.362568i	−0.218653	+	0.0468073i
$61$	4.11360	−	7.12497i	0.526693	−	0.912259i	−0.472823	−	0.881157i	$-0.656765\pi$
$61$	4.11360	−	7.12497i	0.526693	−	0.912259i	0.999516	−	0.0311016i	$-0.00990154\pi$
$62$	−3.61915	+	2.08952i	−0.459633	+	0.265369i
$63$	1.46453	−	0.657144i	0.184514	−	0.0827924i
$64$	1.00000			0.125000
$65$	1.83469			0.227565
$66$	6.04642	+	6.69569i	0.744263	+	0.824183i
$67$	−0.445224	−	0.257050i	−0.0543927	−	0.0314037i	0.472557	−	0.881300i	$-0.343331\pi$
$67$	−0.445224	−	0.257050i	−0.0543927	−	0.0314037i	−0.526950	+	0.849896i	$0.676664\pi$
$68$		−	4.54625i		−	0.551313i
$69$	−3.41976	+	10.5771i	−0.411691	+	1.27333i
$70$	0.463384	+	0.267535i	0.0553850	+	0.0319765i
$71$	3.29907	+	5.71415i	0.391527	+	0.678145i	0.992651	−	0.121011i	$-0.0386135\pi$
$71$	3.29907	+	5.71415i	0.391527	+	0.678145i	−0.601124	+	0.799156i	$0.705280\pi$
$72$	−2.73709	+	1.22815i	−0.322569	+	0.144739i
$73$	3.05629	+	5.29365i	0.357712	+	0.619575i	0.987578	−	0.157128i	$-0.0502236\pi$
$73$	3.05629	+	5.29365i	0.357712	+	0.619575i	−0.629866	+	0.776704i	$0.716890\pi$
$74$	4.61313	−	2.66339i	0.536265	−	0.309613i
$75$	1.64805	+	0.532846i	0.190301	+	0.0615277i
$76$	4.24323	+	0.997481i	0.486732	+	0.114419i
$77$		−	2.78702i		−	0.317610i
$78$	3.10738	−	0.665201i	0.351841	−	0.0753191i
$79$	7.65758	−	4.42110i	0.861545	−	0.497413i	−0.00298455	−	0.999996i	$-0.500950\pi$
$79$	7.65758	−	4.42110i	0.861545	−	0.497413i	0.864529	+	0.502582i	$0.167617\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	5.98331	−	6.72310i	0.664812	−	0.747011i
$82$	2.33917	−	4.05157i	0.258319	−	0.447421i
$83$		−	13.2159i		−	1.45063i	−0.688416	−	0.725316i	$-0.741694\pi$
$83$		−	13.2159i		−	1.45063i	0.688416	−	0.725316i	$-0.258306\pi$
$84$	0.881823	+	0.285110i	0.0962148	+	0.0311080i
$85$	−2.27312	+	3.93717i	−0.246555	+	0.427046i
$86$	4.21877	−	7.30712i	0.454922	−	0.787947i
$87$	−13.8363	−	4.47352i	−1.48340	−	0.479612i
$88$			5.20870i			0.555249i
$89$	8.15273	−	14.1209i	0.864187	−	1.49682i	−0.00366426	−	0.999993i	$-0.501166\pi$
$89$	8.15273	−	14.1209i	0.864187	−	1.49682i	0.867852	−	0.496823i	$-0.165500\pi$
$90$	2.98446	+	0.304938i	0.314590	+	0.0321433i
$91$	−0.850166	−	0.490844i	−0.0891217	−	0.0514544i
$92$	−5.55808	+	3.20896i	−0.579470	+	0.334557i
$93$	7.07794	−	1.51519i	0.733948	−	0.157117i
$94$		−	4.06851i		−	0.419635i
$95$	−3.17601	−	2.98546i	−0.325851	−	0.306302i
$96$	−1.64805	−	0.532846i	−0.168204	−	0.0543833i
$97$	0.567737	−	0.327783i	0.0576449	−	0.0332813i	−0.470901	−	0.882186i	$-0.656071\pi$
$97$	0.567737	−	0.327783i	0.0576449	−	0.0332813i	0.528545	+	0.848905i	$0.322738\pi$
$98$	3.35685	+	5.81424i	0.339093	+	0.587326i
$99$	−6.39704	−	14.2567i	−0.642927	−	1.43285i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−10.5737	−	6.10474i	−1.05212	−	0.607444i	−0.128881	−	0.991660i	$-0.541139\pi$
$101$	−10.5737	−	6.10474i	−1.05212	−	0.607444i	−0.923243	+	0.384216i	$0.874472\pi$
$102$	−2.42245	+	7.49245i	−0.239858	+	0.741863i
$103$		−	10.0328i		−	0.988561i	−0.869303	−	0.494280i	$-0.835432\pi$
$103$		−	10.0328i		−	0.988561i	0.869303	−	0.494280i	$-0.164568\pi$
$104$	1.58889	+	0.917346i	0.155803	+	0.0899531i
$105$	−0.621126	−	0.687824i	−0.0606157	−	0.0671247i
$106$	6.53915			0.635138
$107$	19.9736			1.93092			0.965459	−	0.260554i	$-0.0839052\pi$
$107$	19.9736			1.93092			0.965459	+	0.260554i	$0.0839052\pi$
$108$	5.16528	−	0.565605i	0.497029	−	0.0544253i
$109$	−6.94887	+	4.01193i	−0.665581	+	0.384273i	−0.794400	−	0.607395i	$-0.792215\pi$
$109$	−6.94887	+	4.01193i	−0.665581	+	0.384273i	0.128819	+	0.991668i	$0.458881\pi$
$110$	2.60435	−	4.51086i	0.248315	−	0.430094i
$111$	−9.02185	+	1.93132i	−0.856317	+	0.183313i
$112$	0.267535	+	0.463384i	0.0252797	+	0.0437857i
$113$	16.8013			1.58054			0.790269	−	0.612760i	$-0.209941\pi$
$113$	16.8013			1.58054			0.790269	+	0.612760i	$0.209941\pi$
$114$	−6.46157	−	3.90489i	−0.605181	−	0.365726i
$115$	6.41792			0.598474
$116$	−4.19776	−	7.27074i	−0.389753	−	0.675071i
$117$	−5.47557	−	0.559466i	−0.506216	−	0.0517227i
$118$	−3.47483	+	6.01858i	−0.319884	+	0.554055i
$119$	2.10666	−	1.21628i	0.193117	−	0.111496i
$120$	1.16083	+	1.28548i	0.105969	+	0.117348i
$121$	−16.1305			−1.46641
$122$	−8.22721			−0.744856
$123$	−6.01394	+	5.43078i	−0.542259	+	0.489677i
$124$	3.61915	+	2.08952i	0.325009	+	0.187644i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.30137	−	0.939751i	−0.115935	−	0.0837197i
$127$	7.49011	+	4.32442i	0.664640	+	0.383730i	0.794043	−	0.607862i	$-0.207973\pi$
$127$	7.49011	+	4.32442i	0.664640	+	0.383730i	−0.129403	+	0.991592i	$0.541306\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−10.8463	+	9.79456i	−0.954965	+	0.862363i
$130$	−0.917346	−	1.58889i	−0.0804565	−	0.139355i
$131$	−16.6710	+	9.62499i	−1.45655	+	0.840939i	−0.998840	−	0.0481626i	$-0.984663\pi$
$131$	−16.6710	+	9.62499i	−1.45655	+	0.840939i	−0.457710	+	0.889102i	$0.651330\pi$
$132$	2.77543	−	8.58420i	0.241570	−	0.747159i
$133$	0.672996	+	2.23311i	0.0583562	+	0.193635i
$134$			0.514100i			0.0444115i
$135$	−4.75606	−	2.09281i	−0.409337	−	0.180120i
$136$	−3.93717	+	2.27312i	−0.337609	+	0.194919i
$137$	−1.62271	−	0.936869i	−0.138637	−	0.0800421i	0.429077	−	0.903268i	$-0.358839\pi$
$137$	−1.62271	−	0.936869i	−0.138637	−	0.0800421i	−0.567714	+	0.823226i	$0.692172\pi$
$138$	10.8699	−	2.32693i	0.925306	−	0.198082i
$139$	3.33569	−	5.77758i	0.282929	−	0.490048i	−0.689176	−	0.724594i	$-0.742027\pi$
$139$	3.33569	−	5.77758i	0.282929	−	0.490048i	0.972105	+	0.234546i	$0.0753604\pi$
$140$		−	0.535070i		−	0.0452216i
$141$	−2.16789	+	6.70511i	−0.182569	+	0.564672i
$142$	3.29907	−	5.71415i	0.276852	−	0.479521i
$143$	−4.77817	+	8.27604i	−0.399571	+	0.692077i
$144$	2.43215	+	1.75631i	0.202679	+	0.146360i
$145$			8.39553i			0.697211i
$146$	3.05629	−	5.29365i	0.252941	−	0.438106i
$147$	−2.43417	−	11.3708i	−0.200767	−	0.937851i
$148$	−4.61313	−	2.66339i	−0.379197	−	0.218929i
$149$	−3.13836	+	1.81193i	−0.257104	+	0.148439i	−0.623013	−	0.782211i	$-0.714092\pi$
$149$	−3.13836	+	1.81193i	−0.257104	+	0.148439i	0.365909	+	0.930651i	$0.380758\pi$
$150$	−0.362568	−	1.69368i	−0.0296036	−	0.138288i
$151$		−	19.7459i		−	1.60690i	−0.595371	−	0.803451i	$-0.702995\pi$
$151$		−	19.7459i		−	1.60690i	0.595371	−	0.803451i	$-0.297005\pi$
$152$	−1.25777	−	4.17349i	−0.102019	−	0.338515i
$153$	7.98464	−	11.0572i	0.645520	−	0.893918i
$154$	−2.41363	+	1.39351i	−0.194496	+	0.112292i
$155$	−2.08952	−	3.61915i	−0.167834	−	0.290697i
$156$	−2.12977	−	2.35847i	−0.170518	−	0.188828i
$157$	2.03388	+	3.52278i	0.162321	+	0.281149i	0.935701	−	0.352795i	$-0.114769\pi$
$157$	2.03388	+	3.52278i	0.162321	+	0.281149i	−0.773380	+	0.633943i	$0.781435\pi$
$158$	−7.65758	−	4.42110i	−0.609204	−	0.351724i
$159$	−10.7769	−	3.48436i	−0.854660	−	0.276327i
$160$			1.00000i			0.0790569i
$161$	−2.97396	−	1.71702i	−0.234381	−	0.135320i
$162$	−8.81403	−	1.82015i	−0.692495	−	0.143004i
$163$	6.73334			0.527396			0.263698	−	0.964605i	$-0.415058\pi$
$163$	6.73334			0.527396			0.263698	+	0.964605i	$0.415058\pi$
$164$	−4.67835			−0.365318
$165$	−6.69569	+	6.04642i	−0.521259	+	0.470713i
$166$	−11.4453	+	6.60794i	−0.888327	+	0.512876i
$167$	3.32598	−	5.76077i	0.257372	−	0.445782i	−0.708165	−	0.706047i	$-0.750477\pi$
$167$	3.32598	−	5.76077i	0.257372	−	0.445782i	0.965537	+	0.260265i	$0.0838101\pi$
$168$	−0.193999	−	0.906236i	−0.0149674	−	0.0699176i
$169$	−4.81695	−	8.34321i	−0.370535	−	0.641785i
$170$	4.54625			0.348681
$171$	8.56829	+	9.87848i	0.655234	+	0.755426i
$172$	−8.43754			−0.643356
$173$	1.61948	+	2.80502i	0.123127	+	0.213262i	0.920999	−	0.389565i	$-0.127374\pi$
$173$	1.61948	+	2.80502i	0.123127	+	0.213262i	−0.797872	+	0.602826i	$0.794041\pi$
$174$	3.04395	+	14.2193i	0.230761	+	1.07796i
$175$	−0.267535	+	0.463384i	−0.0202237	+	0.0350285i
$176$	4.51086	−	2.60435i	0.340019	−	0.196310i
$177$	8.93367	−	8.06738i	0.671496	−	0.606382i
$178$	−16.3055			−1.22215
$179$	13.4218			1.00319			0.501597	−	0.865101i	$-0.332746\pi$
$179$	13.4218			1.00319			0.501597	+	0.865101i	$0.332746\pi$
$180$	−1.22815	−	2.73709i	−0.0915407	−	0.204011i
$181$	−5.80040	−	3.34886i	−0.431140	−	0.248919i	0.268692	−	0.963226i	$-0.413409\pi$
$181$	−5.80040	−	3.34886i	−0.431140	−	0.248919i	−0.699832	+	0.714307i	$0.746742\pi$
$182$			0.981688i			0.0727675i
$183$	13.5589	+	4.38383i	1.00230	+	0.324062i
$184$	5.55808	+	3.20896i	0.409747	+	0.236568i
$185$	2.66339	+	4.61313i	0.195816	+	0.339164i
$186$	−4.85116	−	5.37208i	−0.355704	−	0.393900i
$187$	−11.8400	−	20.5075i	−0.865827	−	1.49966i
$188$	−3.52343	+	2.03425i	−0.256973	+	0.148363i
$189$	1.64398	+	2.24219i	0.119582	+	0.163095i
$190$	−0.997481	+	4.24323i	−0.0723649	+	0.307837i
$191$			9.59528i			0.694290i	0.937811	+	0.347145i	$0.112849\pi$
$191$			9.59528i			0.694290i	−0.937811	+	0.347145i	$0.887151\pi$
$192$	0.362568	+	1.69368i	0.0261661	+	0.122231i
$193$	8.36220	−	4.82792i	0.601924	−	0.347521i	−0.167874	−	0.985808i	$-0.553690\pi$
$193$	8.36220	−	4.82792i	0.601924	−	0.347521i	0.769798	+	0.638287i	$0.220357\pi$
$194$	−0.567737	−	0.327783i	−0.0407611	−	0.0235334i
$195$	0.665201	+	3.10738i	0.0476360	+	0.222524i
$196$	3.35685	−	5.81424i	0.239775	−	0.415303i
$197$		−	3.26552i		−	0.232659i	−0.993211	−	0.116329i	$-0.962887\pi$
$197$		−	3.26552i		−	0.232659i	0.993211	−	0.116329i	$-0.0371128\pi$
$198$	−9.14811	+	12.6683i	−0.650128	+	0.900299i
$199$	−0.305926	+	0.529880i	−0.0216865	+	0.0375622i	−0.876665	−	0.481101i	$-0.840237\pi$
$199$	−0.305926	+	0.529880i	−0.0216865	+	0.0375622i	0.854978	+	0.518663i	$0.173570\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	0.273936	−	0.847263i	0.0193220	−	0.0597614i
$202$			12.2095i			0.859056i
$203$	2.24610	−	3.89035i	0.157645	−	0.273049i
$204$	7.69988	−	1.64832i	0.539099	−	0.115406i
$205$	4.05157	+	2.33917i	0.282974	+	0.163375i
$206$	−8.68866	+	5.01640i	−0.605367	+	0.349509i
$207$	−19.1540	−	1.95707i	−1.33130	−	0.136025i
$208$		−	1.83469i		−	0.127213i
$209$	21.7384	−	6.55135i	1.50368	−	0.453167i
$210$	−0.285110	+	0.881823i	−0.0196744	+	0.0608516i
$211$	−4.21436	+	2.43316i	−0.290129	+	0.167506i	−0.638000	−	0.770037i	$-0.720238\pi$
$211$	−4.21436	+	2.43316i	−0.290129	+	0.167506i	0.347871	+	0.937542i	$0.386905\pi$
$212$	−3.26957	−	5.66307i	−0.224555	−	0.388941i
$213$	−8.48180	+	7.65933i	−0.581163	+	0.524808i
$214$	−9.98679	−	17.2976i	−0.682683	−	1.18244i
$215$	7.30712	+	4.21877i	0.498342	+	0.287718i
$216$	−3.07247	−	4.19046i	−0.209055	−	0.285125i
$217$			2.23608i			0.151795i
$218$	6.94887	+	4.01193i	0.470637	+	0.271722i
$219$	−7.85763	+	7.09569i	−0.530969	+	0.479482i
$220$	−5.20870			−0.351170
$221$	−8.34096			−0.561074
$222$	6.18350	+	6.84749i	0.415009	+	0.459574i
$223$	4.74349	−	2.73866i	0.317648	−	0.183394i	−0.332696	−	0.943034i	$-0.607958\pi$
$223$	4.74349	−	2.73866i	0.317648	−	0.183394i	0.650344	+	0.759640i	$0.274625\pi$
$224$	0.267535	−	0.463384i	0.0178754	−	0.0309611i
$225$	−0.304938	+	2.98446i	−0.0203292	+	0.198964i
$226$	−8.40067	−	14.5504i	−0.558805	−	0.967878i
$227$	12.2736			0.814630			0.407315	−	0.913288i	$-0.366465\pi$
$227$	12.2736			0.814630			0.407315	+	0.913288i	$0.366465\pi$
$228$	−0.150951	+	7.54833i	−0.00999696	+	0.499900i
$229$	25.2326			1.66742			0.833708	−	0.552205i	$-0.186214\pi$
$229$	25.2326			1.66742			0.833708	+	0.552205i	$0.186214\pi$
$230$	−3.20896	−	5.55808i	−0.211593	−	0.366489i
$231$	4.72031	−	1.01048i	0.310573	−	0.0664849i
$232$	−4.19776	+	7.27074i	−0.275597	+	0.477347i
$233$	−15.1283	+	8.73433i	−0.991088	+	0.572205i	−0.905599	−	0.424134i	$-0.860578\pi$
$233$	−15.1283	+	8.73433i	−0.991088	+	0.572205i	−0.0854886	+	0.996339i	$0.527245\pi$
$234$	2.25327	+	5.02171i	0.147301	+	0.328280i
$235$	4.06851			0.265400
$236$	6.94966			0.452384
$237$	10.2643	+	11.3665i	0.666739	+	0.738335i
$238$	−2.10666	−	1.21628i	−0.136554	−	0.0788397i
$239$		−	27.8911i		−	1.80413i	−0.431603	−	0.902063i	$-0.642052\pi$
$239$		−	27.8911i		−	1.80413i	0.431603	−	0.902063i	$-0.357948\pi$
$240$	0.532846	−	1.64805i	0.0343950	−	0.106381i
$241$	21.8025	+	12.5877i	1.40442	+	0.810843i	0.994842	−	0.101432i	$-0.0323424\pi$
$241$	21.8025	+	12.5877i	1.40442	+	0.810843i	0.409579	+	0.912275i	$0.365676\pi$
$242$	8.06525	+	13.9694i	0.518454	+	0.897989i
$243$	13.5561	+	7.69622i	0.869625	+	0.493713i
$244$	4.11360	+	7.12497i	0.263346	+	0.456129i
$245$	−5.81424	+	3.35685i	−0.371458	+	0.214461i
$246$	7.71016	+	2.49284i	0.491582	+	0.158938i
$247$	1.83007	−	7.78502i	0.116445	−	0.495349i
$248$		−	4.17904i		−	0.265369i
$249$	22.3834	−	4.79166i	1.41849	−	0.303659i
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$	−15.5790	−	8.99456i	−0.983340	−	0.567732i	−0.0800634	−	0.996790i	$-0.525512\pi$
$251$	−15.5790	−	8.99456i	−0.983340	−	0.567732i	−0.903277	+	0.429058i	$0.858846\pi$
$252$	−0.163163	+	1.59690i	−0.0102783	+	0.100595i
$253$	−16.7145	+	28.9504i	−1.05083	+	1.82009i
$254$		−	8.64884i		−	0.542676i
$255$	−7.49245	−	2.42245i	−0.469196	−	0.151700i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.62204	−	13.2018i	0.475450	−	0.823503i	−0.524155	−	0.851623i	$-0.675619\pi$
$257$	7.62204	−	13.2018i	0.475450	−	0.823503i	0.999605	+	0.0281201i	$0.00895207\pi$
$258$	13.9055	+	4.49591i	0.865719	+	0.279903i
$259$		−	2.85020i		−	0.177103i
$260$	−0.917346	+	1.58889i	−0.0568914	+	0.0985387i
$261$	2.56011	−	25.0561i	0.158467	−	1.55094i
$262$	16.6710	+	9.62499i	1.02994	+	0.594634i
$263$	−19.9274	+	11.5051i	−1.22878	+	0.709436i	−0.966774	−	0.255631i	$-0.917717\pi$
$263$	−19.9274	+	11.5051i	−1.22878	+	0.709436i	−0.262004	+	0.965067i	$0.584383\pi$
$264$	−8.82185	+	1.88851i	−0.542947	+	0.116230i
$265$			6.53915i			0.401697i
$266$	1.59743	−	1.69939i	0.0979447	−	0.104196i
$267$	26.8722	+	8.68829i	1.64455	+	0.531715i
$268$	0.445224	−	0.257050i	0.0271964	−	0.0157018i
$269$	11.9188	+	20.6440i	0.726702	+	1.25868i	0.958270	+	0.285866i	$0.0922813\pi$
$269$	11.9188	+	20.6440i	0.726702	+	1.25868i	−0.231567	+	0.972819i	$0.574385\pi$
$270$	0.565605	+	5.16528i	0.0344216	+	0.314349i
$271$	10.8992	+	18.8780i	0.662082	+	1.14676i	0.980068	+	0.198664i	$0.0636602\pi$
$271$	10.8992	+	18.8780i	0.662082	+	1.14676i	−0.317986	+	0.948095i	$0.603006\pi$
$272$	3.93717	+	2.27312i	0.238726	+	0.137828i
$273$	0.523088	−	1.61787i	0.0316587	−	0.0979181i
$274$			1.87374i			0.113197i
$275$	4.51086	+	2.60435i	0.272015	+	0.157048i
$276$	−7.45013	−	8.25013i	−0.448445	−	0.496600i
$277$	−6.33971			−0.380916			−0.190458	−	0.981695i	$-0.560997\pi$
$277$	−6.33971			−0.380916			−0.190458	+	0.981695i	$0.560997\pi$
$278$	−6.67138			−0.400123
$279$	5.13247	+	11.4384i	0.307273	+	0.684799i
$280$	−0.463384	+	0.267535i	−0.0276925	+	0.0159883i
$281$	−11.6032	+	20.0973i	−0.692188	+	1.19890i	0.278932	+	0.960311i	$0.410020\pi$
$281$	−11.6032	+	20.0973i	−0.692188	+	1.19890i	−0.971120	+	0.238594i	$0.923314\pi$
$282$	6.89074	−	1.47511i	0.410338	−	0.0878416i
$283$	8.02179	+	13.8941i	0.476846	+	0.825921i	0.999648	−	0.0265330i	$-0.00844670\pi$
$283$	8.02179	+	13.8941i	0.476846	+	0.825921i	−0.522802	+	0.852454i	$0.675113\pi$
$284$	−6.59813			−0.391527
$285$	3.90489	−	6.46157i	0.231306	−	0.382750i
$286$	9.55635			0.565079
$287$	−1.25162	−	2.16787i	−0.0738809	−	0.127965i
$288$	0.304938	−	2.98446i	0.0179686	−	0.175861i
$289$	1.83418	−	3.17689i	0.107893	−	0.186876i
$290$	7.27074	−	4.19776i	0.426953	−	0.246501i
$291$	0.761002	+	0.842719i	0.0446107	+	0.0494011i
$292$	−6.11259			−0.357712
$293$	−20.9324			−1.22288			−0.611441	−	0.791290i	$-0.709410\pi$
$293$	−20.9324			−1.22288			−0.611441	+	0.791290i	$0.709410\pi$
$294$	−8.63035	+	7.79348i	−0.503332	+	0.454525i
$295$	−6.01858	−	3.47483i	−0.350415	−	0.202312i
$296$			5.32678i			0.309613i
$297$	21.8268	−	16.0035i	1.26652	−	0.928620i
$298$	3.13836	+	1.81193i	0.181800	+	0.104962i
$299$	5.88745	+	10.1974i	0.340480	+	0.589729i
$300$	−1.28548	+	1.16083i	−0.0742174	+	0.0670207i
$301$	−2.25734	−	3.90982i	−0.130111	−	0.225358i
$302$	−17.1005	+	9.87297i	−0.984022	+	0.568126i
$303$	6.50577	−	20.1219i	0.373747	−	1.15597i
$304$	−2.98546	+	3.17601i	−0.171228	+	0.182157i
$305$		−	8.22721i		−	0.471088i
$306$	−13.5681	−	1.38632i	−0.775637	−	0.0792508i
$307$	−9.83298	+	5.67707i	−0.561198	+	0.324008i	−0.753626	−	0.657303i	$-0.771697\pi$
$307$	−9.83298	+	5.67707i	−0.561198	+	0.324008i	0.192428	+	0.981311i	$0.438364\pi$
$308$	2.41363	+	1.39351i	0.137529	+	0.0794025i
$309$	16.9923	−	3.63757i	0.966660	−	0.206934i
$310$	−2.08952	+	3.61915i	−0.118677	+	0.205554i
$311$			6.21309i			0.352312i	0.984362	+	0.176156i	$0.0563663\pi$
$311$			6.21309i			0.352312i	−0.984362	+	0.176156i	$0.943634\pi$
$312$	−0.977607	+	3.02367i	−0.0553461	+	0.171181i
$313$	−5.11268	+	8.85542i	−0.288986	+	0.500538i	−0.973568	−	0.228398i	$-0.926651\pi$
$313$	−5.11268	+	8.85542i	−0.288986	+	0.500538i	0.684582	+	0.728936i	$0.259985\pi$
$314$	2.03388	−	3.52278i	0.114778	−	0.198802i
$315$	0.939751	−	1.30137i	0.0529490	−	0.0733239i
$316$			8.84221i			0.497413i
$317$	−5.46022	+	9.45738i	−0.306677	+	0.531179i	−0.977633	−	0.210317i	$-0.932550\pi$
$317$	−5.46022	+	9.45738i	−0.306677	+	0.531179i	0.670957	+	0.741497i	$0.265884\pi$
$318$	2.37089	+	11.0752i	0.132953	+	0.621067i
$319$	−37.8711	−	21.8649i	−2.12037	−	1.22420i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	7.24178	+	33.8288i	0.404197	+	1.88814i
$322$			3.43403i			0.191371i
$323$	14.4389	+	13.5726i	0.803403	+	0.755202i
$324$	2.83072	+	8.54325i	0.157262	+	0.474625i
$325$	1.58889	−	0.917346i	0.0881357	−	0.0508852i
$326$	−3.36667	−	5.83124i	−0.186463	−	0.322963i
$327$	−9.31435	−	10.3145i	−0.515085	−	0.570396i
$328$	2.33917	+	4.05157i	0.129159	+	0.223710i
$329$	−1.88528	−	1.08847i	−0.103939	−	0.0600092i
$330$	8.58420	+	2.77543i	0.472545	+	0.152782i
$331$		−	5.24791i		−	0.288451i	−0.989545	−	0.144226i	$-0.953931\pi$
$331$		−	5.24791i		−	0.288451i	0.989545	−	0.144226i	$-0.0460691\pi$
$332$	11.4453	+	6.60794i	0.628142	+	0.362658i
$333$	−6.54207	−	14.5799i	−0.358503	−	0.798972i
$334$	−6.65196			−0.363979
$335$	−0.514100			−0.0280883
$336$	−0.687824	+	0.621126i	−0.0375239	+	0.0338852i
$337$	10.1877	−	5.88185i	0.554957	−	0.320405i	−0.196162	−	0.980572i	$-0.562848\pi$
$337$	10.1877	−	5.88185i	0.554957	−	0.320405i	0.751119	+	0.660167i	$0.229514\pi$
$338$	−4.81695	+	8.34321i	−0.262008	+	0.453811i
$339$	6.09163	+	28.4561i	0.330852	+	1.54552i
$340$	−2.27312	−	3.93717i	−0.123277	−	0.213523i
$341$	21.7673			1.17877
$342$	4.27087	−	12.3596i	0.230942	−	0.668331i
$343$	7.33779			0.396203
$344$	4.21877	+	7.30712i	0.227461	+	0.393974i
$345$	2.32693	+	10.8699i	0.125278	+	0.585215i
$346$	1.61948	−	2.80502i	0.0870638	−	0.150799i
$347$	−18.1066	+	10.4539i	−0.972015	+	0.561193i	−0.899850	−	0.436200i	$-0.856324\pi$
$347$	−18.1066	+	10.4539i	−0.972015	+	0.561193i	−0.0721651	+	0.997393i	$0.522991\pi$
$348$	10.7923	−	9.74580i	0.578529	−	0.522430i
$349$	3.49912			0.187304			0.0936518	−	0.995605i	$-0.470146\pi$
$349$	3.49912			0.187304			0.0936518	+	0.995605i	$0.470146\pi$
$350$	0.535070			0.0286007
$351$	−1.03771	−	9.47669i	−0.0553888	−	0.505828i
$352$	−4.51086	−	2.60435i	−0.240430	−	0.138812i
$353$		−	0.0613213i		−	0.00326380i	−0.999999	−	0.00163190i	$-0.999481\pi$
$353$		−	0.0613213i		−	0.00326380i	0.999999	−	0.00163190i	$-0.000519451\pi$
$354$	−11.4534	−	3.70309i	−0.608741	−	0.196817i
$355$	5.71415	+	3.29907i	0.303276	+	0.175096i
$356$	8.15273	+	14.1209i	0.432094	+	0.748408i
$357$	2.82379	+	3.12702i	0.149451	+	0.165499i
$358$	−6.71091	−	11.6236i	−0.354683	−	0.614328i
$359$	15.0843	−	8.70894i	0.796120	−	0.459640i	−0.0459927	−	0.998942i	$-0.514645\pi$
$359$	15.0843	−	8.70894i	0.796120	−	0.459640i	0.842113	+	0.539302i	$0.181312\pi$
$360$	−1.75631	+	2.43215i	−0.0925659	+	0.128186i
$361$	−15.8360	+	10.4986i	−0.833475	+	0.552558i
$362$			6.69773i			0.352025i
$363$	−5.84841	−	27.3199i	−0.306962	−	1.43392i
$364$	0.850166	−	0.490844i	0.0445608	−	0.0257272i
$365$	5.29365	+	3.05629i	0.277083	+	0.159974i
$366$	−2.98292	−	13.9342i	−0.155920	−	0.728354i
$367$	−1.34926	+	2.33699i	−0.0704309	+	0.121990i	−0.899090	−	0.437763i	$-0.855771\pi$
$367$	−1.34926	+	2.33699i	−0.0704309	+	0.121990i	0.828659	+	0.559753i	$0.189104\pi$
$368$		−	6.41792i		−	0.334557i
$369$	−11.3784	−	8.21665i	−0.592338	−	0.427742i
$370$	2.66339	−	4.61313i	0.138463	−	0.239825i
$371$	1.74945	−	3.03014i	0.0908269	−	0.157317i
$372$	−2.22678	+	6.88727i	−0.115453	+	0.357088i
$373$		−	10.4311i		−	0.540101i	−0.962846	−	0.270051i	$-0.912960\pi$
$373$		−	10.4311i		−	0.540101i	0.962846	−	0.270051i	$-0.0870405\pi$
$374$	−11.8400	+	20.5075i	−0.612232	+	1.06042i
$375$	1.69368	−	0.362568i	0.0874611	−	0.0187229i
$376$	3.52343	+	2.03425i	0.181707	+	0.104909i
$377$	−13.3396	+	7.70160i	−0.687022	+	0.396653i
$378$	1.11980	−	2.54483i	0.0575963	−	0.130892i
$379$			9.19756i			0.472447i	0.971699	+	0.236223i	$0.0759097\pi$
$379$			9.19756i			0.472447i	−0.971699	+	0.236223i	$0.924090\pi$
$380$	4.17349	−	1.25777i	0.214095	−	0.0645224i
$381$	−4.60850	+	14.2537i	−0.236100	+	0.730241i
$382$	8.30976	−	4.79764i	0.425164	−	0.245469i
$383$	−5.34538	−	9.25846i	−0.273136	−	0.473085i	0.696527	−	0.717530i	$-0.254728\pi$
$383$	−5.34538	−	9.25846i	−0.273136	−	0.473085i	−0.969663	+	0.244445i	$0.921394\pi$
$384$	1.28548	−	1.16083i	0.0655996	−	0.0592385i
$385$	−1.39351	−	2.41363i	−0.0710197	−	0.123010i
$386$	−8.36220	−	4.82792i	−0.425625	−	0.245735i
$387$	−20.5214	−	14.8190i	−1.04316	−	0.753291i
$388$			0.655566i			0.0332813i
$389$	20.5861	+	11.8854i	1.04376	+	0.602614i	0.920895	−	0.389810i	$-0.127459\pi$
$389$	20.5861	+	11.8854i	1.04376	+	0.602614i	0.122863	+	0.992424i	$0.460793\pi$
$390$	2.35847	−	2.12977i	0.119426	−	0.107845i
$391$	−29.1774			−1.47557
$392$	−6.71370			−0.339093
$393$	−22.3460	−	24.7455i	−1.12721	−	1.24825i
$394$	−2.82802	+	1.63276i	−0.142474	+	0.0822572i
$395$	4.42110	−	7.65758i	0.222450	−	0.385295i
$396$	15.5452	+	1.58833i	0.781173	+	0.0798165i
$397$	11.0077	+	19.0660i	0.552463	+	0.956893i	0.998096	+	0.0616779i	$0.0196452\pi$
$397$	11.0077	+	19.0660i	0.552463	+	0.956893i	−0.445633	+	0.895216i	$0.647022\pi$
$398$	0.611852			0.0306694
$399$	−3.53816	+	1.94949i	−0.177129	+	0.0975967i
$400$	−1.00000			−0.0500000
$401$	−2.08815	−	3.61678i	−0.104277	−	0.180614i	0.809165	−	0.587581i	$-0.199920\pi$
$401$	−2.08815	−	3.61678i	−0.104277	−	0.180614i	−0.913443	+	0.406967i	$0.866586\pi$
$402$	−0.870720	+	0.186396i	−0.0434276	+	0.00929660i
$403$	3.83362	−	6.64003i	0.190966	−	0.330763i
$404$	10.5737	−	6.10474i	0.526062	−	0.303722i
$405$	1.82015	−	8.81403i	0.0904440	−	0.437972i
$406$	−4.49219			−0.222944
$407$	−27.7456			−1.37530
$408$	−5.27743	−	5.84413i	−0.261272	−	0.289327i
$409$	5.63570	+	3.25377i	0.278667	+	0.160889i	0.632820	−	0.774299i	$-0.281897\pi$
$409$	5.63570	+	3.25377i	0.278667	+	0.160889i	−0.354153	+	0.935188i	$0.615231\pi$
$410$		−	4.67835i		−	0.231047i
$411$	0.998413	−	3.08802i	0.0492481	−	0.152321i
$412$	8.68866	+	5.01640i	0.428059	+	0.247140i
$413$	1.85928	+	3.22036i	0.0914890	+	0.158464i
$414$	7.88215	+	17.5664i	0.387387	+	0.863342i
$415$	−6.60794	−	11.4453i	−0.324371	−	0.561827i
$416$	−1.58889	+	0.917346i	−0.0779017	+	0.0449766i
$417$	10.9948	+	3.55481i	0.538417	+	0.174080i
$418$	−16.5429	−	15.5504i	−0.809137	−	0.760593i
$419$		−	32.4656i		−	1.58605i	−0.609189	−	0.793025i	$-0.708505\pi$
$419$		−	32.4656i		−	1.58605i	0.609189	−	0.793025i	$-0.291495\pi$
$420$	0.906236	−	0.193999i	0.0442198	−	0.00946619i
$421$	22.1581	−	12.7930i	1.07992	−	0.623491i	0.149044	−	0.988831i	$-0.452380\pi$
$421$	22.1581	−	12.7930i	1.07992	−	0.623491i	0.930874	+	0.365339i	$0.119047\pi$
$422$	4.21436	+	2.43316i	0.205152	+	0.118444i
$423$	−12.1423	−	1.24064i	−0.590379	−	0.0603220i
$424$	−3.26957	+	5.66307i	−0.158785	+	0.275023i
$425$			4.54625i			0.220525i
$426$	10.8741	+	3.51579i	0.526850	+	0.170340i
$427$	−2.20106	+	3.81236i	−0.106517	+	0.184493i
$428$	−9.98679	+	17.2976i	−0.482730	+	0.836112i
$429$	−15.7494	−	5.09206i	−0.760386	−	0.245847i
$430$		−	8.43754i		−	0.406894i
$431$	−4.97293	+	8.61337i	−0.239538	+	0.414892i	−0.960582	−	0.277998i	$-0.910329\pi$
$431$	−4.97293	+	8.61337i	−0.239538	+	0.414892i	0.721044	+	0.692889i	$0.243663\pi$
$432$	−2.09281	+	4.75606i	−0.100690	+	0.228826i
$433$	−21.0832	−	12.1724i	−1.01319	−	0.584968i	−0.101069	−	0.994879i	$-0.532226\pi$
$433$	−21.0832	−	12.1724i	−1.01319	−	0.584968i	−0.912125	+	0.409911i	$0.865560\pi$
$434$	1.93650	−	1.11804i	0.0929549	−	0.0536675i
$435$	−14.2193	+	3.04395i	−0.681764	+	0.145946i
$436$		−	8.02386i		−	0.384273i
$437$	6.40176	−	27.2327i	0.306237	−	1.30272i
$438$	10.0739	+	3.25706i	0.481348	+	0.155629i
$439$	−32.3043	+	18.6509i	−1.54180	+	0.890159i	−0.543075	+	0.839684i	$0.682740\pi$
$439$	−32.3043	+	18.6509i	−1.54180	+	0.890159i	−0.998725	+	0.0504744i	$0.983927\pi$
$440$	2.60435	+	4.51086i	0.124157	+	0.215047i
$441$	18.3760	−	8.24541i	0.875047	−	0.392639i
$442$	4.17048	+	7.22348i	0.198369	+	0.343586i
$443$	14.9279	+	8.61861i	0.709244	+	0.409482i	0.810781	−	0.585349i	$-0.199043\pi$
$443$	14.9279	+	8.61861i	0.709244	+	0.409482i	−0.101537	+	0.994832i	$0.532376\pi$
$444$	2.83835	−	8.77882i	0.134702	−	0.416624i
$445$		−	16.3055i		−	0.772953i
$446$	−4.74349	−	2.73866i	−0.224611	−	0.129679i
$447$	−4.20670	−	4.65842i	−0.198970	−	0.220336i
$448$	−0.535070			−0.0252797
$449$	14.5905			0.688568			0.344284	−	0.938865i	$-0.388122\pi$
$449$	14.5905			0.688568			0.344284	+	0.938865i	$0.388122\pi$
$450$	2.73709	−	1.22815i	0.129028	−	0.0578954i
$451$	−21.1034	+	12.1840i	−0.993719	+	0.573724i
$452$	−8.40067	+	14.5504i	−0.395134	+	0.684393i
$453$	33.4433	−	7.15925i	1.57130	−	0.336371i
$454$	−6.13682	−	10.6293i	−0.288015	−	0.498857i
$455$	−0.981688			−0.0460222
$456$	6.61252	−	3.64344i	0.309659	−	0.170619i
$457$	−35.8465			−1.67683			−0.838414	−	0.545034i	$-0.816517\pi$
$457$	−35.8465			−1.67683			−0.838414	+	0.545034i	$0.816517\pi$
$458$	−12.6163	−	21.8521i	−0.589521	−	1.02108i
$459$	21.6222	+	9.51443i	1.00924	+	0.444096i
$460$	−3.20896	+	5.55808i	−0.149619	+	0.259147i
$461$	−12.6225	+	7.28761i	−0.587889	+	0.339418i	−0.764262	−	0.644905i	$-0.776897\pi$
$461$	−12.6225	+	7.28761i	−0.587889	+	0.339418i	0.176373	+	0.984323i	$0.443563\pi$
$462$	−3.23526	−	3.58266i	−0.150518	−	0.166681i
$463$	20.1328			0.935649			0.467825	−	0.883821i	$-0.345038\pi$
$463$	20.1328			0.935649			0.467825	+	0.883821i	$0.345038\pi$
$464$	8.39553			0.389753
$465$	5.37208	−	4.85116i	0.249124	−	0.224967i
$466$	15.1283	+	8.73433i	0.700805	+	0.404610i
$467$		−	0.535926i		−	0.0247997i	−0.999923	−	0.0123999i	$-0.996053\pi$
$467$		−	0.535926i		−	0.0247997i	0.999923	−	0.0123999i	$-0.00394710\pi$
$468$	3.22229	−	4.46225i	0.148951	−	0.206267i
$469$	0.238226	+	0.137540i	0.0110002	+	0.00635099i
$470$	−2.03425	−	3.52343i	−0.0938331	−	0.162524i
$471$	−5.22904	+	4.72198i	−0.240941	+	0.217578i
$472$	−3.47483	−	6.01858i	−0.159942	−	0.277028i
$473$	−38.0606	+	21.9743i	−1.75003	+	1.01038i
$474$	4.71153	−	14.5724i	0.216408	−	0.669333i
$475$	−4.24323	−	0.997481i	−0.194693	−	0.0457676i
$476$			2.43256i			0.111496i
$477$	1.99403	−	19.5158i	0.0913005	−	0.893569i
$478$	−24.1544	+	13.9456i	−1.10480	+	0.637855i
$479$	−21.8777	−	12.6311i	−0.999618	−	0.577130i	−0.0914830	−	0.995807i	$-0.529161\pi$
$479$	−21.8777	−	12.6311i	−0.999618	−	0.577130i	−0.908135	+	0.418677i	$0.862494\pi$
$480$	−1.69368	+	0.362568i	−0.0773055	+	0.0165489i
$481$	−4.88650	+	8.46367i	−0.222805	+	0.385910i
$482$		−	25.1753i		−	1.14670i
$483$	1.82981	−	5.65947i	0.0832593	−	0.257515i
$484$	8.06525	−	13.9694i	0.366602	−	0.634974i
$485$	0.327783	−	0.567737i	0.0148839	−	0.0257796i
$486$	−0.112938	−	15.5880i	−0.00512296	−	0.707088i
$487$		−	27.4924i		−	1.24580i	−0.782302	−	0.622899i	$-0.785955\pi$
$487$		−	27.4924i		−	1.24580i	0.782302	−	0.622899i	$-0.214045\pi$
$488$	4.11360	−	7.12497i	0.186214	−	0.322532i
$489$	2.44129	+	11.4041i	0.110399	+	0.515711i
$490$	5.81424	+	3.35685i	0.262660	+	0.151647i
$491$	9.52214	−	5.49761i	0.429728	−	0.248104i	−0.269503	−	0.963000i	$-0.586859\pi$
$491$	9.52214	−	5.49761i	0.429728	−	0.248104i	0.699231	+	0.714896i	$0.253526\pi$
$492$	−1.69622	−	7.92361i	−0.0764715	−	0.357224i
$493$		−	38.1681i		−	1.71901i
$494$	−7.65706	+	2.30762i	−0.344508	+	0.103825i
$495$	−12.6683	−	9.14811i	−0.569399	−	0.411177i
$496$	−3.61915	+	2.08952i	−0.162505	+	0.0938221i
$497$	−1.76523	−	3.05747i	−0.0791814	−	0.137146i
$498$	−15.3414	−	16.9888i	−0.687465	−	0.761286i
$499$	7.16095	+	12.4031i	0.320568	+	0.555241i	0.980605	−	0.195992i	$-0.0627928\pi$
$499$	7.16095	+	12.4031i	0.320568	+	0.555241i	−0.660037	+	0.751233i	$0.729459\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	10.9628	+	3.54447i	0.489781	+	0.158355i
$502$			17.9891i			0.802894i
$503$	0.853524	+	0.492782i	0.0380567	+	0.0219721i	0.518908	−	0.854830i	$-0.326339\pi$
$503$	0.853524	+	0.492782i	0.0380567	+	0.0219721i	−0.480851	+	0.876802i	$0.659672\pi$
$504$	1.46453	−	0.657144i	0.0652355	−	0.0292715i
$505$	−12.2095			−0.543315
$506$	33.4290			1.48610
$507$	12.3842	−	11.1834i	0.550003	−	0.496670i
$508$	−7.49011	+	4.32442i	−0.332320	+	0.191865i
$509$	−9.01611	+	15.6164i	−0.399632	+	0.692183i	−0.993680	−	0.112246i	$-0.964195\pi$
$509$	−9.01611	+	15.6164i	−0.399632	+	0.692183i	0.594048	+	0.804429i	$0.297529\pi$
$510$	1.64832	+	7.69988i	0.0729890	+	0.340956i
$511$	−1.63533	−	2.83247i	−0.0723427	−	0.125301i
$512$	1.00000			0.0441942
$513$	−13.6244	+	18.0935i	−0.601531	+	0.798850i
$514$	−15.2441			−0.672387
$515$	−5.01640	−	8.68866i	−0.221049	−	0.382868i
$516$	−3.05918	−	14.2905i	−0.134673	−	0.629103i
$517$	−10.5958	+	18.3525i	−0.466003	+	0.807141i
$518$	−2.46835	+	1.42510i	−0.108453	+	0.0626153i
$519$	−4.16363	+	3.75989i	−0.182763	+	0.165041i
$520$	1.83469			0.0804565
$521$	31.2308			1.36825			0.684124	−	0.729366i	$-0.260185\pi$
$521$	31.2308			1.36825			0.684124	+	0.729366i	$0.260185\pi$
$522$	−22.9793	+	10.3109i	−1.00578	+	0.451298i
$523$	30.0065	+	17.3243i	1.31209	+	0.757538i	0.982443	−	0.186565i	$-0.0597355\pi$
$523$	30.0065	+	17.3243i	1.31209	+	0.757538i	0.329651	+	0.944103i	$0.393069\pi$
$524$		−	19.2500i		−	0.840939i
$525$	−0.881823	−	0.285110i	−0.0384859	−	0.0124432i
$526$	19.9274	+	11.5051i	0.868878	+	0.501647i
$527$	9.49947	+	16.4536i	0.413803	+	0.716728i
$528$	6.04642	+	6.69569i	0.263137	+	0.291393i
$529$	9.09485	+	15.7527i	0.395428	+	0.684902i
$530$	5.66307	−	3.26957i	0.245988	−	0.142021i
$531$	16.9026	+	12.2058i	0.733511	+	0.529686i
$532$	−2.27043	−	0.533722i	−0.0984354	−	0.0231398i
$533$			8.58332i			0.371785i
$534$	−5.91184	−	27.6162i	−0.255830	−	1.19507i
$535$	17.2976	−	9.98679i	0.747842	−	0.431767i
$536$	−0.445224	−	0.257050i	−0.0192307	−	0.0111029i
$537$	4.86633	+	22.7322i	0.209997	+	0.980969i
$538$	11.9188	−	20.6440i	0.513856	−	0.890025i
$539$		−	34.9696i		−	1.50625i
$540$	4.19046	−	3.07247i	0.180329	−	0.132218i
$541$	−18.2442	+	31.5999i	−0.784379	+	1.35858i	0.144990	+	0.989433i	$0.453685\pi$
$541$	−18.2442	+	31.5999i	−0.784379	+	1.35858i	−0.929369	+	0.369151i	$0.879648\pi$
$542$	10.8992	−	18.8780i	0.468163	−	0.810881i
$543$	3.56885	−	11.0382i	0.153154	−	0.473694i
$544$		−	4.54625i		−	0.194919i
$545$	−4.01193	+	6.94887i	−0.171852	+	0.297657i
$546$	−1.66266	+	0.355929i	−0.0711554	+	0.0152323i
$547$	32.3959	+	18.7038i	1.38515	+	0.799716i	0.992764	−	0.120085i	$-0.0383167\pi$
$547$	32.3959	+	18.7038i	1.38515	+	0.799716i	0.392385	+	0.919801i	$0.371650\pi$
$548$	1.62271	−	0.936869i	0.0693185	−	0.0400211i
$549$	−2.50879	+	24.5538i	−0.107072	+	1.04793i
$550$		−	5.20870i		−	0.222100i
$551$	35.6242	+	8.37438i	1.51764	+	0.356761i
$552$	−3.41976	+	10.5771i	−0.145555	+	0.450190i
$553$	−4.09734	+	2.36560i	−0.174237	+	0.100596i
$554$	3.16986	+	5.49035i	0.134674	+	0.233263i
$555$	−6.84749	+	6.18350i	−0.290660	+	0.262475i
$556$	3.33569	+	5.77758i	0.141465	+	0.245024i
$557$	−17.6536	−	10.1923i	−0.748005	−	0.431861i	0.0769675	−	0.997034i	$-0.475476\pi$
$557$	−17.6536	−	10.1923i	−0.748005	−	0.431861i	−0.824973	+	0.565173i	$0.808810\pi$
$558$	7.33970	−	10.1640i	0.310714	−	0.430278i
$559$			15.4803i			0.654746i
$560$	0.463384	+	0.267535i	0.0195815	+	0.0113054i
$561$	30.4403	−	27.4885i	1.28519	−	1.16057i
$562$	23.2064			0.978901
$563$	−4.90484			−0.206714			−0.103357	−	0.994644i	$-0.532958\pi$
$563$	−4.90484			−0.206714			−0.103357	+	0.994644i	$0.532958\pi$
$564$	−4.72285	−	5.23000i	−0.198868	−	0.220223i
$565$	14.5504	−	8.40067i	0.612140	−	0.353419i
$566$	8.02179	−	13.8941i	0.337181	−	0.584014i
$567$	−3.20149	+	3.59733i	−0.134450	+	0.151073i
$568$	3.29907	+	5.71415i	0.138426	+	0.239760i
$569$	−16.9616			−0.711068			−0.355534	−	0.934663i	$-0.615701\pi$
$569$	−16.9616			−0.711068			−0.355534	+	0.934663i	$0.615701\pi$
$570$	−7.54833	−	0.150951i	−0.316165	−	0.00632263i
$571$	−13.9462			−0.583632			−0.291816	−	0.956474i	$-0.594260\pi$
$571$	−13.9462			−0.583632			−0.291816	+	0.956474i	$0.594260\pi$
$572$	−4.77817	−	8.27604i	−0.199785	−	0.346039i
$573$	−16.2513	+	3.47894i	−0.678908	+	0.145335i
$574$	−1.25162	+	2.16787i	−0.0522417	+	0.0904852i
$575$	5.55808	−	3.20896i	0.231788	−	0.133823i
$576$	−2.73709	+	1.22815i	−0.114045	+	0.0511728i
$577$	−4.90123			−0.204041			−0.102020	−	0.994782i	$-0.532531\pi$
$577$	−4.90123			−0.204041			−0.102020	+	0.994782i	$0.532531\pi$
$578$	−3.66836			−0.152584
$579$	11.2088	+	12.4124i	0.465822	+	0.515843i
$580$	−7.27074	−	4.19776i	−0.301901	−	0.174303i
$581$			7.07142i			0.293372i
$582$	0.349315	−	1.08041i	0.0144796	−	0.0447843i
$583$	−29.4972	−	17.0302i	−1.22165	−	0.705319i
$584$	3.05629	+	5.29365i	0.126470	+	0.219053i
$585$	−5.02171	+	2.25327i	−0.207622	+	0.0931613i
$586$	10.4662	+	18.1280i	0.432354	+	0.748859i
$587$	39.6685	−	22.9026i	1.63730	−	0.945293i	0.655537	−	0.755163i	$-0.272442\pi$
$587$	39.6685	−	22.9026i	1.63730	−	0.945293i	0.981759	−	0.190130i	$-0.0608910\pi$
$588$	11.0645	+	3.57737i	0.456293	+	0.147528i
$589$	−17.4412	+	5.25628i	−0.718651	+	0.216581i
$590$			6.94966i			0.286113i
$591$	5.53074	−	1.18397i	0.227504	−	0.0487021i
$592$	4.61313	−	2.66339i	0.189598	−	0.109465i
$593$	−23.0106	−	13.2852i	−0.944933	−	0.545557i	−0.0534296	−	0.998572i	$-0.517015\pi$
$593$	−23.0106	−	13.2852i	−0.944933	−	0.545557i	−0.891503	+	0.453014i	$0.850349\pi$
$594$	−24.7729	−	10.9008i	−1.01644	−	0.447266i
$595$	1.21628	−	2.10666i	0.0498626	−	0.0863646i
$596$		−	3.62387i		−	0.148439i
$597$	−1.00836	−	0.326023i	−0.0412696	−	0.0133432i
$598$	5.88745	−	10.1974i	0.240756	−	0.417001i
$599$	18.2454	−	31.6020i	0.745488	−	1.29122i	−0.204479	−	0.978871i	$-0.565550\pi$
$599$	18.2454	−	31.6020i	0.745488	−	1.29122i	0.949967	−	0.312352i	$-0.101117\pi$
$600$	1.64805	+	0.532846i	0.0672814	+	0.0217533i
$601$		−	5.57468i		−	0.227396i	−0.993515	−	0.113698i	$-0.963730\pi$
$601$		−	5.57468i		−	0.227396i	0.993515	−	0.113698i	$-0.0362696\pi$
$602$	−2.25734	+	3.90982i	−0.0920021	+	0.159352i
$603$	1.53431	+	0.156768i	0.0624820	+	0.00638411i
$604$	17.1005	+	9.87297i	0.695809	+	0.401725i
$605$	−13.9694	+	8.06525i	−0.567938	+	0.327899i
$606$	−20.6789	+	4.42677i	−0.840024	+	0.179825i
$607$			7.25553i			0.294493i	0.989100	+	0.147246i	$0.0470410\pi$
$607$			7.25553i			0.294493i	−0.989100	+	0.147246i	$0.952959\pi$
$608$	4.24323	+	0.997481i	0.172086	+	0.0404532i
$609$	7.40337	+	2.39365i	0.300000	+	0.0969954i
$610$	−7.12497	+	4.11360i	−0.288482	+	0.166555i
$611$	3.73223	+	6.46441i	0.150990	+	0.261522i
$612$	5.58346	+	12.4435i	0.225698	+	0.502998i
$613$	−3.18359	−	5.51414i	−0.128584	−	0.222714i	0.794544	−	0.607206i	$-0.207710\pi$
$613$	−3.18359	−	5.51414i	−0.128584	−	0.222714i	−0.923128	+	0.384492i	$0.874377\pi$
$614$	9.83298	+	5.67707i	0.396827	+	0.229108i
$615$	−2.49284	+	7.71016i	−0.100521	+	0.310904i
$616$		−	2.78702i		−	0.112292i
$617$	7.70794	+	4.45018i	0.310310	+	0.179158i	0.647065	−	0.762435i	$-0.275996\pi$
$617$	7.70794	+	4.45018i	0.310310	+	0.179158i	−0.336755	+	0.941592i	$0.609329\pi$
$618$	−11.6464	−	12.8970i	−0.468487	−	0.518793i
$619$	−9.83923			−0.395472			−0.197736	−	0.980255i	$-0.563359\pi$
$619$	−9.83923			−0.395472			−0.197736	+	0.980255i	$0.563359\pi$
$620$	4.17904			0.167834
$621$	−3.63001	−	33.1503i	−0.145667	−	1.33028i
$622$	5.38070	−	3.10655i	0.215746	−	0.124561i
$623$	−4.36228	+	7.55569i	−0.174771	+	0.302712i
$624$	3.10738	−	0.665201i	0.124395	−	0.0266293i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.2254			0.408688
$627$	18.9775	+	34.4426i	0.757890	+	1.37550i
$628$	−4.06776			−0.162321
$629$	−12.1084	−	20.9724i	−0.482795	−	0.836225i
$630$	−1.59690	−	0.163163i	−0.0636218	−	0.00650057i
$631$	8.42353	−	14.5900i	0.335335	−	0.580818i	−0.648214	−	0.761458i	$-0.724484\pi$
$631$	8.42353	−	14.5900i	0.335335	−	0.580818i	0.983549	+	0.180641i	$0.0578171\pi$
$632$	7.65758	−	4.42110i	0.304602	−	0.175862i
$633$	−5.64898	−	6.25558i	−0.224527	−	0.248637i
$634$	10.9204			0.433706
$635$	8.64884			0.343219
$636$	8.40597	−	7.59085i	0.333318	−	0.300997i
$637$	−10.6673	−	6.15878i	−0.422655	−	0.244020i
$638$			43.7297i			1.73128i
$639$	−16.0477	−	11.5884i	−0.634836	−	0.458430i
$640$	−0.866025	−	0.500000i	−0.0342327	−	0.0197642i
$641$	−18.3162	−	31.7246i	−0.723446	−	1.25305i	−0.959610	−	0.281333i	$-0.909224\pi$
$641$	−18.3162	−	31.7246i	−0.723446	−	1.25305i	0.236164	−	0.971713i	$-0.424110\pi$
$642$	25.6757	−	23.1860i	1.01334	−	0.915077i
$643$	−16.7131	−	28.9479i	−0.659099	−	1.14159i	−0.980849	−	0.194769i	$-0.937604\pi$
$643$	−16.7131	−	28.9479i	−0.659099	−	1.14159i	0.321750	−	0.946825i	$-0.395729\pi$
$644$	2.97396	−	1.71702i	0.117190	−	0.0676600i
$645$	−4.49591	+	13.9055i	−0.177026	+	0.547529i
$646$	4.53480	−	19.2908i	0.178419	−	0.758986i
$647$			23.6956i			0.931570i	0.884898	+	0.465785i	$0.154228\pi$
$647$			23.6956i			0.931570i	−0.884898	+	0.465785i	$0.845772\pi$
$648$	5.98331	−	6.72310i	0.235047	−	0.264108i
$649$	31.3489	−	18.0993i	1.23055	−	0.710461i
$650$	−1.58889	−	0.917346i	−0.0623214	−	0.0359813i
$651$	−3.78719	+	0.810730i	−0.148432	+	0.0317750i
$652$	−3.36667	+	5.83124i	−0.131849	+	0.228369i
$653$		−	35.0646i		−	1.37218i	−0.727515	−	0.686092i	$-0.759325\pi$
$653$		−	35.0646i		−	1.37218i	0.727515	−	0.686092i	$-0.240675\pi$
$654$	−4.27548	+	13.2237i	−0.167184	+	0.517089i
$655$	−9.62499	+	16.6710i	−0.376079	+	0.651389i
$656$	2.33917	−	4.05157i	0.0913294	−	0.158187i
$657$	−14.8667	−	10.7356i	−0.580006	−	0.418837i
$658$			2.17694i			0.0848658i
$659$	−7.25327	+	12.5630i	−0.282547	+	0.489386i	−0.972011	−	0.234934i	$-0.924513\pi$
$659$	−7.25327	+	12.5630i	−0.282547	+	0.489386i	0.689464	+	0.724320i	$0.257846\pi$
$660$	−1.88851	−	8.82185i	−0.0735100	−	0.343390i
$661$	40.0197	+	23.1054i	1.55658	+	0.898695i	0.997580	+	0.0695304i	$0.0221501\pi$
$661$	40.0197	+	23.1054i	1.55658	+	0.898695i	0.559005	+	0.829164i	$0.311183\pi$
$662$	−4.54482	+	2.62396i	−0.176640	+	0.101983i
$663$	−3.02417	−	14.1269i	−0.117449	−	0.548643i
$664$		−	13.2159i		−	0.512876i
$665$	1.69939	+	1.59743i	0.0658993	+	0.0619457i
$666$	−9.35551	+	12.9555i	−0.362519	+	0.502017i
$667$	−46.6630	+	26.9409i	−1.80680	+	1.04316i
$668$	3.32598	+	5.76077i	0.128686	+	0.222891i
$669$	6.35824	+	7.04100i	0.245824	+	0.272221i
$670$	0.257050	+	0.445224i	0.00993071	+	0.0172005i
$671$	37.1118	+	21.4265i	1.43268	+	0.827161i
$672$	0.881823	+	0.285110i	0.0340171	+	0.0109983i
$673$		−	16.5098i		−	0.636405i	−0.948023	−	0.318202i	$-0.896921\pi$
$673$		−	16.5098i		−	0.636405i	0.948023	−	0.318202i	$-0.103079\pi$
$674$	−10.1877	−	5.88185i	−0.392414	−	0.226560i
$675$	−5.16528	+	0.565605i	−0.198812	+	0.0217701i
$676$	9.63391			0.370535
$677$	−35.1622			−1.35139			−0.675696	−	0.737181i	$-0.736157\pi$
$677$	−35.1622			−1.35139			−0.675696	+	0.737181i	$0.736157\pi$
$678$	21.5979	−	19.5035i	0.829461	−	0.749029i
$679$	−0.303779	+	0.175387i	−0.0116580	+	0.00673072i
$680$	−2.27312	+	3.93717i	−0.0871703	+	0.150983i
$681$	4.45003	+	20.7876i	0.170525	+	0.796582i
$682$	−10.8837	−	18.8511i	−0.416757	−	0.721844i
$683$	37.8100			1.44676			0.723380	−	0.690450i	$-0.242587\pi$
$683$	37.8100			1.44676			0.723380	+	0.690450i	$0.242587\pi$
$684$	−12.8392	+	2.48112i	−0.490918	+	0.0948680i
$685$	−1.87374			−0.0715919
$686$	−3.66889	−	6.35471i	−0.140079	−	0.242624i
$687$	9.14853	+	42.7359i	0.349038	+	1.63048i
$688$	4.21877	−	7.30712i	0.160839	−	0.278581i
$689$	−10.3900	+	5.99866i	−0.395827	+	0.228531i
$690$	8.25013	−	7.45013i	0.314077	−	0.283622i
$691$	32.1235			1.22203			0.611017	−	0.791617i	$-0.290761\pi$
$691$	32.1235			1.22203			0.611017	+	0.791617i	$0.290761\pi$
$692$	−3.23896			−0.123127
$693$	3.42286	+	7.62831i	0.130024	+	0.289775i
$694$	18.1066	+	10.4539i	0.687318	+	0.396823i
$695$		−	6.67138i		−	0.253060i
$696$	−13.8363	−	4.47352i	−0.524462	−	0.169568i
$697$	−18.4194	−	10.6345i	−0.697686	−	0.402809i
$698$	−1.74956	−	3.03033i	−0.0662218	−	0.114700i
$699$	−20.2782	−	22.4557i	−0.766991	−	0.849352i
$700$	−0.267535	−	0.463384i	−0.0101119	−	0.0175143i
$701$	−23.8066	+	13.7447i	−0.899161	+	0.519131i	−0.876928	−	0.480622i	$-0.840411\pi$
$701$	−23.8066	+	13.7447i	−0.899161	+	0.519131i	−0.0222334	+	0.999753i	$0.507078\pi$
$702$	−7.68820	+	5.63703i	−0.290172	+	0.212756i
$703$	22.2313	−	6.69988i	0.838468	−	0.252691i
$704$			5.20870i			0.196310i
$705$	1.47511	+	6.89074i	0.0555559	+	0.259520i
$706$	−0.0531058	+	0.0306607i	−0.00199866	+	0.00115393i
$707$	5.65768	+	3.26646i	0.212779	+	0.122848i
$708$	2.51972	+	11.7705i	0.0946970	+	0.442362i
$709$	2.73932	−	4.74464i	0.102877	−	0.178189i	−0.809992	−	0.586441i	$-0.800528\pi$
$709$	2.73932	−	4.74464i	0.102877	−	0.178189i	0.912869	+	0.408253i	$0.133862\pi$
$710$		−	6.59813i		−	0.247624i
$711$	−15.5297	+	21.5056i	−0.582409	+	0.806522i
$712$	8.15273	−	14.1209i	0.305536	−	0.529205i
$713$	13.4104	−	23.2274i	0.502222	−	0.869874i
$714$	1.29618	−	4.00898i	0.0485083	−	0.150032i
$715$			9.55635i			0.357387i
$716$	−6.71091	+	11.6236i	−0.250799	+	0.434396i
$717$	47.2386	−	10.1124i	1.76416	−	0.377656i
$718$	−15.0843	−	8.70894i	−0.562942	−	0.325015i
$719$	−39.6746	+	22.9061i	−1.47961	+	0.854254i	−0.999734	−	0.0230807i	$-0.992653\pi$
$719$	−39.6746	+	22.9061i	−1.47961	+	0.854254i	−0.479878	+	0.877335i	$0.659319\pi$
$720$	2.98446	+	0.304938i	0.111224	+	0.0113644i
$721$			5.36825i			0.199924i
$722$	17.0101	+	8.46509i	0.633049	+	0.315038i
$723$	−13.4146	+	41.4903i	−0.498893	+	1.54304i
$724$	5.80040	−	3.34886i	0.215570	−	0.124459i
$725$	4.19776	+	7.27074i	0.155901	+	0.270028i
$726$	−20.7355	+	18.7248i	−0.769567	+	0.694943i
$727$	4.46581	+	7.73500i	0.165628	+	0.286875i	0.936878	−	0.349657i	$-0.113702\pi$
$727$	4.46581	+	7.73500i	0.165628	+	0.286875i	−0.771250	+	0.636532i	$0.780368\pi$
$728$	−0.850166	−	0.490844i	−0.0315093	−	0.0181919i
$729$	−8.11990	+	25.7501i	−0.300737	+	0.953707i
$730$		−	6.11259i		−	0.226237i
$731$	−33.2200	−	19.1796i	−1.22869	−	0.709382i
$732$	−10.5759	+	9.55040i	−0.390898	+	0.352993i
$733$	−9.80467			−0.362144			−0.181072	−	0.983470i	$-0.557957\pi$
$733$	−9.80467			−0.362144			−0.181072	+	0.983470i	$0.557957\pi$
$734$	2.69852			0.0996043
$735$	−7.79348	−	8.63035i	−0.287467	−	0.318335i
$736$	−5.55808	+	3.20896i	−0.204874	+	0.118284i
$737$	1.33890	−	2.31903i	0.0493188	−	0.0854227i
$738$	−1.42660	+	13.9624i	−0.0525140	+	0.513961i
$739$	21.8672	+	37.8751i	0.804397	+	1.39326i	0.916697	+	0.399582i	$0.130845\pi$
$739$	21.8672	+	37.8751i	0.804397	+	1.39326i	−0.112300	+	0.993674i	$0.535822\pi$
$740$	−5.32678			−0.195816
$741$	13.8488	+	0.276948i	0.508750	+	0.0101739i
$742$	−3.49890			−0.128449
$743$	16.1731	+	28.0126i	0.593332	+	1.02768i	0.993780	+	0.111361i	$0.0355211\pi$
$743$	16.1731	+	28.0126i	0.593332	+	1.02768i	−0.400448	+	0.916319i	$0.631146\pi$
$744$	7.07794	−	1.51519i	0.259490	−	0.0555494i
$745$	−1.81193	+	3.13836i	−0.0663841	+	0.114981i
$746$	−9.03359	+	5.21555i	−0.330743	+	0.190955i
$747$	16.2310	+	36.1730i	0.593863	+	1.32350i
$748$	23.6800			0.865827
$749$	−10.6873			−0.390504
$750$	−1.16083	−	1.28548i	−0.0423876	−	0.0469392i
$751$	−9.87219	−	5.69971i	−0.360241	−	0.207985i	0.308945	−	0.951080i	$-0.400024\pi$
$751$	−9.87219	−	5.69971i	−0.360241	−	0.207985i	−0.669187	+	0.743094i	$0.733357\pi$
$752$		−	4.06851i		−	0.148363i
$753$	9.58543	−	29.6470i	0.349312	−	1.08040i
$754$	13.3396	+	7.70160i	0.485798	+	0.280476i
$755$	−9.87297	−	17.1005i	−0.359314	−	0.622350i
$756$	−2.76378	+	0.302638i	−0.100518	+	0.0110068i
$757$	−8.74057	−	15.1391i	−0.317682	−	0.550241i	0.662322	−	0.749219i	$-0.269571\pi$
$757$	−8.74057	−	15.1391i	−0.317682	−	0.550241i	−0.980004	+	0.198978i	$0.936238\pi$
$758$	7.96532	−	4.59878i	0.289313	−	0.167035i
$759$	−55.0927	−	17.8125i	−1.99974	−	0.646552i
$760$	−3.17601	−	2.98546i	−0.115206	−	0.108294i
$761$		−	34.6889i		−	1.25747i	−0.777620	−	0.628735i	$-0.783573\pi$
$761$		−	34.6889i		−	1.25747i	0.777620	−	0.628735i	$-0.216427\pi$
$762$	14.6483	−	3.13579i	0.530653	−	0.113598i
$763$	3.71813	−	2.14666i	0.134605	−	0.0777144i
$764$	−8.30976	−	4.79764i	−0.300636	−	0.173573i
$765$	1.38632	−	13.5681i	0.0501226	−	0.490556i
$766$	−5.34538	+	9.25846i	−0.193136	+	0.334522i
$767$		−	12.7505i		−	0.460393i
$768$	−1.64805	−	0.532846i	−0.0594690	−	0.0192274i
$769$	27.5176	−	47.6619i	0.992310	−	1.71873i	0.388958	−	0.921256i	$-0.372835\pi$
$769$	27.5176	−	47.6619i	0.992310	−	1.71873i	0.603352	−	0.797475i	$-0.293831\pi$
$770$	−1.39351	+	2.41363i	−0.0502185	+	0.0869810i
$771$	25.1230	+	8.12274i	0.904784	+	0.292533i
$772$			9.65584i			0.347521i
$773$	−17.5536	+	30.4038i	−0.631360	+	1.09355i	0.355914	+	0.934519i	$0.384170\pi$
$773$	−17.5536	+	30.4038i	−0.631360	+	1.09355i	−0.987274	+	0.159029i	$0.949164\pi$
$774$	−2.57292	+	25.1815i	−0.0924818	+	0.905131i
$775$	−3.61915	−	2.08952i	−0.130004	−	0.0750577i
$776$	0.567737	−	0.327783i	0.0203806	−	0.0117667i
$777$	4.82732	−	1.03339i	0.173179	−	0.0370727i
$778$		−	23.7708i		−	0.852225i
$779$	13.9670	−	14.8585i	0.500421	−	0.532360i
$780$	−3.02367	−	0.977607i	−0.108265	−	0.0350040i
$781$	−29.7633	+	17.1838i	−1.06501	+	0.614886i
$782$	14.5887	+	25.2684i	0.521692	+	0.903597i
$783$	43.3652	−	4.74855i	1.54975	−	0.169699i
$784$	3.35685	+	5.81424i	0.119888	+	0.207651i
$785$	3.52278	+	2.03388i	0.125733	+	0.0725923i
$786$	−10.2573	+	31.7250i	−0.365865	+	1.13159i
$787$		−	10.2958i		−	0.367007i	−0.983019	−	0.183504i	$-0.941256\pi$
$787$		−	10.2958i		−	0.367007i	0.983019	−	0.183504i	$-0.0587439\pi$
$788$	2.82802	+	1.63276i	0.100744	+	0.0581646i
$789$	−26.7110	−	29.5793i	−0.950937	−	1.05305i
$790$	−8.84221			−0.314592
$791$	−8.98989			−0.319644
$792$	−6.39704	−	14.2567i	−0.227309	−	0.506588i
$793$	13.0721	−	7.54719i	0.464205	−	0.268009i
$794$	11.0077	−	19.0660i	0.390650	−	0.676626i
$795$	−11.0752	+	2.37089i	−0.392797	+	0.0840867i
$796$	−0.305926	−	0.529880i	−0.0108433	−	0.0187811i
$797$	0.450354			0.0159524			0.00797618	−	0.999968i	$-0.497461\pi$
$797$	0.450354			0.0159524			0.00797618	+	0.999968i	$0.497461\pi$
$798$	3.45739	+	2.08939i	0.122390	+	0.0739635i
$799$	−18.4964			−0.654357
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	−4.97215	+	48.6630i	−0.175682	+	1.71942i
$802$	−2.08815	+	3.61678i	−0.0737352	+	0.127713i
$803$	−27.5730	+	15.9193i	−0.973031	+	0.561780i
$804$	0.596784	+	0.660867i	0.0210469	+	0.0233070i
$805$	−3.43403			−0.121034
$806$	−7.66724			−0.270067
$807$	−30.6429	+	27.6715i	−1.07868	+	0.974081i
$808$	−10.5737	−	6.10474i	−0.371982	−	0.214764i
$809$		−	14.3150i		−	0.503289i	−0.967820	−	0.251644i	$-0.919029\pi$
$809$		−	14.3150i		−	0.503289i	0.967820	−	0.251644i	$-0.0809713\pi$
$810$	−8.54325	+	2.83072i	−0.300179	+	0.0994613i
$811$	16.6190	+	9.59499i	0.583572	+	0.336926i	0.762552	−	0.646927i	$-0.223946\pi$
$811$	16.6190	+	9.59499i	0.583572	+	0.336926i	−0.178980	+	0.983853i	$0.557280\pi$
$812$	2.24610	+	3.89035i	0.0788225	+	0.136525i
$813$	−28.0216	+	25.3044i	−0.982760	+	0.887463i
$814$	13.8728	+	24.0284i	0.486241	+	0.842195i
$815$	5.83124	−	3.36667i	0.204260	−	0.117929i
$816$	−2.42245	+	7.49245i	−0.0848026	+	0.262288i
$817$	25.1899	−	26.7977i	0.881284	−	0.937532i
$818$		−	6.50754i		−	0.227531i
$819$	2.92981	+	0.299354i	0.102376	+	0.0104603i
$820$	−4.05157	+	2.33917i	−0.141487	+	0.0816875i
$821$	−24.1859	−	13.9638i	−0.844095	−	0.487338i	0.0145591	−	0.999894i	$-0.495366\pi$
$821$	−24.1859	−	13.9638i	−0.844095	−	0.487338i	−0.858654	+	0.512556i	$0.828699\pi$
$822$	−3.17351	+	0.679358i	−0.110689	+	0.0236953i
$823$	−23.4718	+	40.6544i	−0.818176	+	1.41712i	0.0888479	+	0.996045i	$0.471681\pi$
$823$	−23.4718	+	40.6544i	−0.818176	+	1.41712i	−0.907024	+	0.421078i	$0.861652\pi$
$824$		−	10.0328i		−	0.349509i
$825$	−2.77543	+	8.58420i	−0.0966281	+	0.298864i
$826$	1.85928	−	3.22036i	0.0646925	−	0.112051i
$827$	−25.4082	+	44.0083i	−0.883531	+	1.53032i	−0.0361424	+	0.999347i	$0.511507\pi$
$827$	−25.4082	+	44.0083i	−0.883531	+	1.53032i	−0.847388	+	0.530974i	$0.821826\pi$
$828$	11.2719	−	15.6094i	0.391725	−	0.542462i
$829$			30.6365i			1.06405i	0.846729	+	0.532024i	$0.178569\pi$
$829$			30.6365i			1.06405i	−0.846729	+	0.532024i	$0.821431\pi$
$830$	−6.60794	+	11.4453i	−0.229365	+	0.397272i
$831$	−2.29858	−	10.7374i	−0.0797368	−	0.372477i
$832$	1.58889	+	0.917346i	0.0550848	+	0.0318032i
$833$	26.4329	−	15.2611i	0.915847	−	0.528765i
$834$	−2.41883	−	11.2992i	−0.0837572	−	0.391258i
$835$		−	6.65196i		−	0.230201i
$836$	−5.19558	+	22.1017i	−0.179693	+	0.764404i
$837$	−17.5121	+	12.8400i	−0.605306	+	0.443814i
$838$	−28.1161	+	16.2328i	−0.971254	+	0.560754i
$839$	−3.32523	−	5.75947i	−0.114800	−	0.198839i	0.802900	−	0.596114i	$-0.203289\pi$
$839$	−3.32523	−	5.75947i	−0.114800	−	0.198839i	−0.917700	+	0.397275i	$0.869956\pi$
$840$	−0.621126	−	0.687824i	−0.0214309	−	0.0237322i
$841$	−20.7424	−	35.9270i	−0.715256	−	1.23886i
$842$	−22.1581	−	12.7930i	−0.763618	−	0.440875i
$843$	−38.2453	−	12.3654i	−1.31724	−	0.425887i
$844$		−	4.86632i		−	0.167506i
$845$	−8.34321	−	4.81695i	−0.287015	−	0.165708i
$846$	4.99673	+	11.1359i	0.171791	+	0.382859i
$847$	8.63095			0.296563
$848$	6.53915			0.224555
$849$	−20.6238	+	18.6239i	−0.707805	+	0.639170i
$850$	3.93717	−	2.27312i	0.135044	−	0.0779675i
$851$	−17.0934	+	29.6067i	−0.585955	+	1.01490i
$852$	−2.39227	−	11.1751i	−0.0819579	−	0.382853i
$853$	−6.96853	−	12.0699i	−0.238598	−	0.413264i	0.721714	−	0.692191i	$-0.243354\pi$
$853$	−6.96853	−	12.0699i	−0.238598	−	0.413264i	−0.960312	+	0.278927i	$0.910021\pi$
$854$	4.40213			0.150638
$855$	12.3596	+	4.27087i	0.422689	+	0.146061i
$856$	19.9736			0.682683
$857$	8.48584	+	14.6979i	0.289871	+	0.502071i	0.973779	−	0.227498i	$-0.0730544\pi$
$857$	8.48584	+	14.6979i	0.289871	+	0.502071i	−0.683908	+	0.729568i	$0.739721\pi$
$858$	3.46483	+	16.1854i	0.118287	+	0.552559i
$859$	5.96482	−	10.3314i	0.203517	−	0.352502i	−0.746142	−	0.665787i	$-0.768096\pi$
$859$	5.96482	−	10.3314i	0.203517	−	0.352502i	0.949659	+	0.313285i	$0.101429\pi$
$860$	−7.30712	+	4.21877i	−0.249171	+	0.143859i
$861$	3.21788	−	2.90584i	0.109665	−	0.0990309i
$862$	9.94587			0.338758
$863$	−8.15086			−0.277458			−0.138729	−	0.990330i	$-0.544302\pi$
$863$	−8.15086			−0.277458			−0.138729	+	0.990330i	$0.544302\pi$
$864$	5.16528	−	0.565605i	0.175726	−	0.0192423i
$865$	2.80502	+	1.61948i	0.0953736	+	0.0550640i
$866$			24.3448i			0.827270i
$867$	6.04565	+	1.95467i	0.205321	+	0.0663841i
$868$	−1.93650	−	1.11804i	−0.0657291	−	0.0379487i
$869$	23.0282	+	39.8860i	0.781178	+	1.35304i
$870$	9.74580	+	10.7923i	0.330413	+	0.365894i
$871$	−0.471607	−	0.816848i	−0.0159798	−	0.0276778i
$872$	−6.94887	+	4.01193i	−0.235318	+	0.135861i
$873$	−1.15138	+	1.59444i	−0.0389683	+	0.0539635i
$874$	−26.7851	+	8.07228i	−0.906020	+	0.273049i
$875$			0.535070i			0.0180887i
$876$	−2.21623	−	10.3528i	−0.0748794	−	0.349787i
$877$	43.0842	−	24.8746i	1.45485	−	0.839957i	0.456098	−	0.889930i	$-0.349247\pi$
$877$	43.0842	−	24.8746i	1.45485	−	0.839957i	0.998751	+	0.0499723i	$0.0159133\pi$
$878$	32.3043	+	18.6509i	1.09022	+	0.629437i
$879$	−7.58941	−	35.4527i	−0.255984	−	1.19579i
$880$	2.60435	−	4.51086i	0.0877925	−	0.152061i
$881$		−	25.2877i		−	0.851964i	−0.904732	−	0.425982i	$-0.859929\pi$
$881$		−	25.2877i		−	0.851964i	0.904732	−	0.425982i	$-0.140071\pi$
$882$	−16.3287	−	11.7914i	−0.549817	−	0.397036i
$883$	15.1793	−	26.2913i	0.510823	−	0.884772i	−0.489098	−	0.872229i	$-0.662674\pi$
$883$	15.1793	−	26.2913i	0.510823	−	0.884772i	0.999921	−	0.0125430i	$-0.00399266\pi$
$884$	4.17048	−	7.22348i	0.140268	−	0.242952i
$885$	3.70309	−	11.4534i	0.124478	−	0.385002i
$886$		−	17.2372i		−	0.579095i
$887$	20.5824	−	35.6497i	0.691089	−	1.19700i	−0.280393	−	0.959885i	$-0.590465\pi$
$887$	20.5824	−	35.6497i	0.691089	−	1.19700i	0.971481	−	0.237116i	$-0.0762020\pi$
$888$	−9.02185	+	1.93132i	−0.302754	+	0.0648109i
$889$	−4.00773	−	2.31387i	−0.134415	−	0.0776046i
$890$	−14.1209	+	8.15273i	−0.473335	+	0.273280i
$891$	35.0186	+	31.1652i	1.17317	+	1.04407i
$892$			5.47731i			0.183394i
$893$	4.05826	−	17.2636i	0.135805	−	0.577705i
$894$	−1.93096	+	5.97232i	−0.0645810	+	0.199744i
$895$	11.6236	−	6.71091i	0.388535	−	0.224321i
$896$	0.267535	+	0.463384i	0.00893771	+	0.0154806i
$897$	−15.1364	+	13.6687i	−0.505391	+	0.456384i
$898$	−7.29525	−	12.6357i	−0.243446	−	0.421660i
$899$	30.3847	+	17.5426i	1.01339	+	0.585079i
$900$	−2.43215	−	1.75631i	−0.0810717	−	0.0585438i
$901$		−	29.7286i		−	0.990402i
$902$	21.1034	+	12.1840i	0.702666	+	0.405684i
$903$	5.80354	−	5.24078i	0.193130	−	0.174402i
$904$	16.8013			0.558805
$905$	−6.69773			−0.222640
$906$	−22.9217	−	25.3831i	−0.761523	−	0.843297i
$907$	51.4695	−	29.7159i	1.70902	−	0.986701i	0.773236	−	0.634118i	$-0.218637\pi$
$907$	51.4695	−	29.7159i	1.70902	−	0.986701i	0.935780	−	0.352583i	$-0.114697\pi$
$908$	−6.13682	+	10.6293i	−0.203657	+	0.352745i
$909$	36.4387	+	3.72313i	1.20860	+	0.123488i
$910$	0.490844	+	0.850166i	0.0162713	+	0.0281827i
$911$	36.4247			1.20680			0.603402	−	0.797437i	$-0.293811\pi$
$911$	36.4247			1.20680			0.603402	+	0.797437i	$0.293811\pi$
$912$	−6.46157	−	3.90489i	−0.213964	−	0.129304i
$913$	68.8375			2.27819
$914$	17.9232	+	31.0440i	0.592848	+	1.02684i
$915$	13.9342	−	2.98292i	0.460652	−	0.0986124i
$916$	−12.6163	+	21.8521i	−0.416854	+	0.722012i
$917$	8.92013	−	5.15004i	0.294569	−	0.170069i
$918$	−2.57138	−	23.4826i	−0.0848681	−	0.775042i
$919$	−8.83052			−0.291292			−0.145646	−	0.989337i	$-0.546526\pi$
$919$	−8.83052			−0.291292			−0.145646	+	0.989337i	$0.546526\pi$
$920$	6.41792			0.211593
$921$	−13.1803	−	14.5956i	−0.434304	−	0.480940i
$922$	12.6225	+	7.28761i	0.415700	+	0.240005i
$923$			12.1055i			0.398459i
$924$	−1.48505	+	4.59315i	−0.0488545	+	0.151103i
$925$	4.61313	+	2.66339i	0.151679	+	0.0875718i
$926$	−10.0664	−	17.4355i	−0.330802	−	0.572966i
$927$	12.3218	+	27.4607i	0.404699	+	0.901926i
$928$	−4.19776	−	7.27074i	−0.137798	−	0.238674i
$929$	−4.83299	+	2.79033i	−0.158565	+	0.0915477i	−0.577183	−	0.816615i	$-0.695848\pi$
$929$	−4.83299	+	2.79033i	−0.158565	+	0.0915477i	0.418618	+	0.908163i	$0.362515\pi$
$930$	−6.88727	−	2.22678i	−0.225842	−	0.0730190i
$931$	8.44431	+	28.0196i	0.276751	+	0.918304i
$932$		−	17.4687i		−	0.572205i
$933$	−10.5230	+	2.25267i	−0.344507	+	0.0737491i
$934$	−0.464126	+	0.267963i	−0.0151867	+	0.00876802i
$935$	−20.5075	−	11.8400i	−0.670667	−	0.387210i
$936$	−5.47557	−	0.559466i	−0.178974	−	0.0182867i
$937$	−27.7201	+	48.0126i	−0.905576	+	1.56850i	−0.0854328	+	0.996344i	$0.527227\pi$
$937$	−27.7201	+	48.0126i	−0.905576	+	1.56850i	−0.820143	+	0.572159i	$0.806106\pi$
$938$		−	0.275079i		−	0.00898166i
$939$	−16.8519	−	5.44854i	−0.549942	−	0.177806i
$940$	−2.03425	+	3.52343i	−0.0663500	+	0.114922i
$941$	−17.5976	+	30.4799i	−0.573665	+	0.993616i	0.422521	+	0.906353i	$0.361145\pi$
$941$	−17.5976	+	30.4799i	−0.573665	+	0.993616i	−0.996185	+	0.0872631i	$0.972188\pi$
$942$	6.70388	+	2.16749i	0.218424	+	0.0706206i
$943$			30.0253i			0.977757i
$944$	−3.47483	+	6.01858i	−0.113096	+	0.195888i
$945$	2.54483	+	1.11980i	0.0827832	+	0.0364271i
$946$	38.0606	+	21.9743i	1.23746	+	0.714446i
$947$	1.44559	−	0.834610i	0.0469753	−	0.0271212i	−0.476328	−	0.879267i	$-0.658033\pi$
$947$	1.44559	−	0.834610i	0.0469753	−	0.0271212i	0.523304	+	0.852146i	$0.324699\pi$
$948$	−14.9759	+	3.20590i	−0.486393	+	0.104123i
$949$			11.2147i			0.364045i
$950$	1.25777	+	4.17349i	0.0408075	+	0.135406i
$951$	−17.9975	−	5.81891i	−0.583607	−	0.188691i
$952$	2.10666	−	1.21628i	0.0682772	−	0.0394198i
$953$	−18.5367	−	32.1065i	−0.600462	−	1.04003i	−0.992751	−	0.120189i	$-0.961650\pi$
$953$	−18.5367	−	32.1065i	−0.600462	−	1.04003i	0.392289	−	0.919842i	$-0.371683\pi$
$954$	−17.8982	+	8.03103i	−0.579476	+	0.260014i
$955$	4.79764	+	8.30976i	0.155248	+	0.268897i
$956$	24.1544	+	13.9456i	0.781210	+	0.451032i
$957$	23.3012	−	72.0689i	0.753221	−	2.32966i
$958$			25.2622i			0.816185i
$959$	0.868260	+	0.501290i	0.0280376	+	0.0161875i
$960$	1.16083	+	1.28548i	0.0374657	+	0.0414888i
$961$	13.5357			0.436634
$962$	9.77300			0.315094
$963$	−54.6695	+	24.5305i	−1.76170	+	0.790484i
$964$	−21.8025	+	12.5877i	−0.702211	+	0.405421i
$965$	4.82792	−	8.36220i	0.155416	−	0.269189i
$966$	−5.81615	+	1.24507i	−0.187132	+	0.0400595i
$967$	−6.19162	−	10.7242i	−0.199109	−	0.344867i	0.749131	−	0.662422i	$-0.230471\pi$
$967$	−6.19162	−	10.7242i	−0.199109	−	0.344867i	−0.948240	+	0.317555i	$0.897138\pi$
$968$	−16.1305			−0.518454
$969$	−17.7526	+	29.3759i	−0.570295	+	0.943689i
$970$	−0.655566			−0.0210490
$971$	−12.0657	−	20.8984i	−0.387207	−	0.670662i	0.604866	−	0.796327i	$-0.293227\pi$
$971$	−12.0657	−	20.8984i	−0.387207	−	0.670662i	−0.992073	+	0.125666i	$0.959893\pi$
$972$	−13.4432	+	7.89183i	−0.431190	+	0.253131i
$973$	−1.78483	+	3.09141i	−0.0572189	+	0.0991060i
$974$	−23.8091	+	13.7462i	−0.762893	+	0.440456i
$975$	2.12977	+	2.35847i	0.0682072	+	0.0755314i
$976$	−8.22721			−0.263346
$977$	10.4531			0.334423			0.167212	−	0.985921i	$-0.446524\pi$
$977$	10.4531			0.334423			0.167212	+	0.985921i	$0.446524\pi$
$978$	8.65560	−	7.81628i	0.276776	−	0.249937i
$979$	73.5517	+	42.4651i	2.35072	+	1.35719i
$980$		−	6.71370i		−	0.214461i
$981$	14.0924	−	19.5152i	0.449936	−	0.623074i
$982$	−9.52214	−	5.49761i	−0.303864	−	0.175436i
$983$	0.0140700	+	0.0243700i	0.000448764	+	0.000777282i	0.866250	−	0.499611i	$-0.166524\pi$
$983$	0.0140700	+	0.0243700i	0.000448764	+	0.000777282i	−0.865801	+	0.500389i	$0.833190\pi$
$984$	−6.01394	+	5.43078i	−0.191717	+	0.173127i
$985$	−1.63276	−	2.82802i	−0.0520240	−	0.0901083i
$986$	−33.0546	+	19.0841i	−1.05267	+	0.607761i
$987$	1.15997	−	3.58770i	0.0369223	−	0.114198i
$988$	5.82699	+	5.47740i	0.185381	+	0.174259i
$989$			54.1514i			1.72192i
$990$	−1.58833	+	15.5452i	−0.0504804	+	0.494057i
$991$	−44.6814	+	25.7968i	−1.41935	+	0.819462i	−0.996242	−	0.0866170i	$-0.972394\pi$
$991$	−44.6814	+	25.7968i	−1.41935	+	0.819462i	−0.423108	+	0.906079i	$0.639061\pi$
$992$	3.61915	+	2.08952i	0.114908	+	0.0663423i
$993$	8.88827	−	1.90273i	0.282061	−	0.0603812i
$994$	−1.76523	+	3.05747i	−0.0559897	+	0.0969771i
$995$			0.611852i			0.0193970i
$996$	−7.04202	+	21.7805i	−0.223135	+	0.690140i
$997$	30.5747	−	52.9569i	0.968311	−	1.67716i	0.267866	−	0.963456i	$-0.413682\pi$
$997$	30.5747	−	52.9569i	0.968311	−	1.67716i	0.700445	−	0.713707i	$-0.252985\pi$
$998$	7.16095	−	12.4031i	0.226676	−	0.392614i
$999$	22.3217	−	16.3664i	0.706226	−	0.517809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.a.221.7	✓	24
3.2	odd	2		570.2.s.b.221.4	yes	24
19.8	odd	6		570.2.s.b.521.4	yes	24
57.8	even	6	inner	570.2.s.a.521.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.7	✓	24	1.1	even	1	trivial
570.2.s.a.521.7	yes	24	57.8	even	6	inner
570.2.s.b.221.4	yes	24	3.2	odd	2
570.2.s.b.521.4	yes	24	19.8	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.362568 + 1.69368i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.28548 - 1.16083i) q^{6} -0.535070 q^{7} +1.00000 q^{8} +(-2.73709 + 1.22815i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.362568 + 1.69368i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(1.28548 - 1.16083i) q^{6} -0.535070 q^{7} +1.00000 q^{8} +(-2.73709 + 1.22815i) q^{9} +(-0.866025 - 0.500000i) q^{10} +5.20870i q^{11} +(-1.64805 - 0.532846i) q^{12} +(1.58889 + 0.917346i) q^{13} +(0.267535 + 0.463384i) q^{14} +(1.16083 + 1.28548i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.93717 + 2.27312i) q^{17} +(2.43215 + 1.75631i) q^{18} +(-1.25777 - 4.17349i) q^{19} +1.00000i q^{20} +(-0.193999 - 0.906236i) q^{21} +(4.51086 - 2.60435i) q^{22} +(5.55808 + 3.20896i) q^{23} +(0.362568 + 1.69368i) q^{24} +(0.500000 - 0.866025i) q^{25} -1.83469i q^{26} +(-3.07247 - 4.19046i) q^{27} +(0.267535 - 0.463384i) q^{28} +(-4.19776 + 7.27074i) q^{29} +(0.532846 - 1.64805i) q^{30} -4.17904i q^{31} +(-0.500000 + 0.866025i) q^{32} +(-8.82185 + 1.88851i) q^{33} +(3.93717 + 2.27312i) q^{34} +(-0.463384 + 0.267535i) q^{35} +(0.304938 - 2.98446i) q^{36} +5.32678i q^{37} +(-2.98546 + 3.17601i) q^{38} +(-0.977607 + 3.02367i) q^{39} +(0.866025 - 0.500000i) q^{40} +(2.33917 + 4.05157i) q^{41} +(-0.687824 + 0.621126i) q^{42} +(4.21877 + 7.30712i) q^{43} +(-4.51086 - 2.60435i) q^{44} +(-1.75631 + 2.43215i) q^{45} -6.41792i q^{46} +(3.52343 + 2.03425i) q^{47} +(1.28548 - 1.16083i) q^{48} -6.71370 q^{49} -1.00000 q^{50} +(-5.27743 - 5.84413i) q^{51} +(-1.58889 + 0.917346i) q^{52} +(-3.26957 + 5.66307i) q^{53} +(-2.09281 + 4.75606i) q^{54} +(2.60435 + 4.51086i) q^{55} -0.535070 q^{56} +(6.61252 - 3.64344i) q^{57} +8.39553 q^{58} +(-3.47483 - 6.01858i) q^{59} +(-1.69368 + 0.362568i) q^{60} +(4.11360 - 7.12497i) q^{61} +(-3.61915 + 2.08952i) q^{62} +(1.46453 - 0.657144i) q^{63} +1.00000 q^{64} +1.83469 q^{65} +(6.04642 + 6.69569i) q^{66} +(-0.445224 - 0.257050i) q^{67} -4.54625i q^{68} +(-3.41976 + 10.5771i) q^{69} +(0.463384 + 0.267535i) q^{70} +(3.29907 + 5.71415i) q^{71} +(-2.73709 + 1.22815i) q^{72} +(3.05629 + 5.29365i) q^{73} +(4.61313 - 2.66339i) q^{74} +(1.64805 + 0.532846i) q^{75} +(4.24323 + 0.997481i) q^{76} -2.78702i q^{77} +(3.10738 - 0.665201i) q^{78} +(7.65758 - 4.42110i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(5.98331 - 6.72310i) q^{81} +(2.33917 - 4.05157i) q^{82} -13.2159i q^{83} +(0.881823 + 0.285110i) q^{84} +(-2.27312 + 3.93717i) q^{85} +(4.21877 - 7.30712i) q^{86} +(-13.8363 - 4.47352i) q^{87} +5.20870i q^{88} +(8.15273 - 14.1209i) q^{89} +(2.98446 + 0.304938i) q^{90} +(-0.850166 - 0.490844i) q^{91} +(-5.55808 + 3.20896i) q^{92} +(7.07794 - 1.51519i) q^{93} -4.06851i q^{94} +(-3.17601 - 2.98546i) q^{95} +(-1.64805 - 0.532846i) q^{96} +(0.567737 - 0.327783i) q^{97} +(3.35685 + 5.81424i) q^{98} +(-6.39704 - 14.2567i) 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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