LMFDB - Embedded newform 403.2.f.b.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (of order $3$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Character	$\chi$	$=$	403.373
Dual form			403.2.f.b.94.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21866 + 2.11078i) q^{2} +(0.165727 - 0.287048i) q^{3} +(-1.97025 - 3.41258i) q^{4} -0.0487430 q^{5} +(0.403929 + 0.699625i) q^{6} +(0.449852 + 0.779167i) q^{7} +4.72962 q^{8} +(1.44507 + 2.50293i) q^{9} +O(q^{10})$	\(q+(-1.21866 + 2.11078i) q^{2} +(0.165727 - 0.287048i) q^{3} +(-1.97025 - 3.41258i) q^{4} -0.0487430 q^{5} +(0.403929 + 0.699625i) q^{6} +(0.449852 + 0.779167i) q^{7} +4.72962 q^{8} +(1.44507 + 2.50293i) q^{9} +(0.0594010 - 0.102886i) q^{10} +(0.844123 - 1.46206i) q^{11} -1.30610 q^{12} +(3.17234 - 1.71356i) q^{13} -2.19286 q^{14} +(-0.00807803 + 0.0139916i) q^{15} +(-1.82329 + 3.15803i) q^{16} +(0.475554 + 0.823683i) q^{17} -7.04418 q^{18} +(3.28920 + 5.69706i) q^{19} +(0.0960360 + 0.166339i) q^{20} +0.298211 q^{21} +(2.05739 + 3.56351i) q^{22} +(-3.33552 + 5.77728i) q^{23} +(0.783826 - 1.35763i) q^{24} -4.99762 q^{25} +(-0.249048 + 8.78434i) q^{26} +1.95231 q^{27} +(1.77265 - 3.07031i) q^{28} +(-4.14065 + 7.17182i) q^{29} +(-0.0196887 - 0.0341018i) q^{30} -1.00000 q^{31} +(0.285699 + 0.494845i) q^{32} +(-0.279788 - 0.484607i) q^{33} -2.31815 q^{34} +(-0.0219271 - 0.0379789i) q^{35} +(5.69430 - 9.86282i) q^{36} +(3.18391 - 5.51469i) q^{37} -16.0336 q^{38} +(0.0338684 - 1.19459i) q^{39} -0.230536 q^{40} +(0.617932 - 1.07029i) q^{41} +(-0.363417 + 0.629456i) q^{42} +(1.26394 + 2.18921i) q^{43} -6.65254 q^{44} +(-0.0704370 - 0.122000i) q^{45} +(-8.12970 - 14.0811i) q^{46} +8.70641 q^{47} +(0.604336 + 1.04674i) q^{48} +(3.09527 - 5.36116i) q^{49} +(6.09039 - 10.5489i) q^{50} +0.315248 q^{51} +(-12.0980 - 7.44970i) q^{52} -7.18912 q^{53} +(-2.37920 + 4.12089i) q^{54} +(-0.0411451 + 0.0712653i) q^{55} +(2.12763 + 3.68517i) q^{56} +2.18044 q^{57} +(-10.0921 - 17.4800i) q^{58} +(3.11259 + 5.39116i) q^{59} +0.0636630 q^{60} +(4.30494 + 7.45637i) q^{61} +(1.21866 - 2.11078i) q^{62} +(-1.30014 + 2.25190i) q^{63} -8.68582 q^{64} +(-0.154629 + 0.0835240i) q^{65} +1.36386 q^{66} +(6.69862 - 11.6023i) q^{67} +(1.87392 - 3.24573i) q^{68} +(1.10557 + 1.91490i) q^{69} +0.106887 q^{70} +(5.34815 + 9.26327i) q^{71} +(6.83463 + 11.8379i) q^{72} -1.14523 q^{73} +(7.76018 + 13.4410i) q^{74} +(-0.828241 + 1.43456i) q^{75} +(12.9611 - 22.4493i) q^{76} +1.51892 q^{77} +(2.48025 + 1.52729i) q^{78} -3.73386 q^{79} +(0.0888724 - 0.153932i) q^{80} +(-4.01166 + 6.94839i) q^{81} +(1.50610 + 2.60863i) q^{82} -4.08465 q^{83} +(-0.587551 - 1.01767i) q^{84} +(-0.0231799 - 0.0401488i) q^{85} -6.16125 q^{86} +(1.37243 + 2.37713i) q^{87} +(3.99238 - 6.91501i) q^{88} +(1.62186 - 2.80914i) q^{89} +0.343354 q^{90} +(2.76223 + 1.70093i) q^{91} +26.2872 q^{92} +(-0.165727 + 0.287048i) q^{93} +(-10.6101 + 18.3773i) q^{94} +(-0.160325 - 0.277692i) q^{95} +0.189392 q^{96} +(-4.93165 - 8.54186i) q^{97} +(7.54414 + 13.0668i) q^{98} +4.87926 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) $ 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.21866	+	2.11078i	−0.861721	+	1.49254i	0.00854540	+	0.999963i	$0.497280\pi$
$2$	−1.21866	+	2.11078i	−0.861721	+	1.49254i	−0.870266	+	0.492581i	$0.836053\pi$
$3$	0.165727	−	0.287048i	0.0956825	−	0.165727i	−0.814211	−	0.580569i	$-0.802830\pi$
$3$	0.165727	−	0.287048i	0.0956825	−	0.165727i	0.909893	+	0.414842i	$0.136163\pi$
$4$	−1.97025	−	3.41258i	−0.985126	−	1.70629i
$5$	−0.0487430			−0.0217985			−0.0108993	−	0.999941i	$-0.503469\pi$
$5$	−0.0487430			−0.0217985			−0.0108993	+	0.999941i	$0.503469\pi$
$6$	0.403929	+	0.699625i	0.164903	+	0.285621i
$7$	0.449852	+	0.779167i	0.170028	+	0.294498i	0.938429	−	0.345471i	$-0.112281\pi$
$7$	0.449852	+	0.779167i	0.170028	+	0.294498i	−0.768401	+	0.639968i	$0.778947\pi$
$8$	4.72962			1.67217
$9$	1.44507	+	2.50293i	0.481690	+	0.834311i
$10$	0.0594010	−	0.102886i	0.0187842	−	0.0325353i
$11$	0.844123	−	1.46206i	0.254513	−	0.440829i	−0.710250	−	0.703949i	$-0.751418\pi$
$11$	0.844123	−	1.46206i	0.254513	−	0.440829i	0.964763	+	0.263120i	$0.0847516\pi$
$12$	−1.30610			−0.377038
$13$	3.17234	−	1.71356i	0.879848	−	0.475256i
$13$	3.17234	−	1.71356i	0.879848	−	0.475256i
$14$	−2.19286			−0.586068
$15$	−0.00807803	+	0.0139916i	−0.00208574	+	0.00361260i
$16$	−1.82329	+	3.15803i	−0.455822	+	0.789506i
$17$	0.475554	+	0.823683i	0.115339	+	0.199772i	0.917915	−	0.396777i	$-0.129871\pi$
$17$	0.475554	+	0.823683i	0.115339	+	0.199772i	−0.802576	+	0.596549i	$0.796538\pi$
$18$	−7.04418			−1.66033
$19$	3.28920	+	5.69706i	0.754595	+	1.30700i	0.945576	+	0.325402i	$0.105500\pi$
$19$	3.28920	+	5.69706i	0.754595	+	1.30700i	−0.190981	+	0.981594i	$0.561167\pi$
$20$	0.0960360	+	0.166339i	0.0214743	+	0.0371946i
$21$	0.298211			0.0650749
$22$	2.05739	+	3.56351i	0.438638	+	0.759743i
$23$	−3.33552	+	5.77728i	−0.695503	+	1.20465i	0.274508	+	0.961585i	$0.411485\pi$
$23$	−3.33552	+	5.77728i	−0.695503	+	1.20465i	−0.970011	+	0.243062i	$0.921848\pi$
$24$	0.783826	−	1.35763i	0.159998	−	0.277124i
$25$	−4.99762			−0.999525
$26$	−0.249048	+	8.78434i	−0.0488423	+	1.72275i
$27$	1.95231			0.375722
$28$	1.77265	−	3.07031i	0.334999	−	0.580235i
$29$	−4.14065	+	7.17182i	−0.768899	+	1.33177i	0.169261	+	0.985571i	$0.445862\pi$
$29$	−4.14065	+	7.17182i	−0.768899	+	1.33177i	−0.938160	+	0.346201i	$0.887471\pi$
$30$	−0.0196887	−	0.0341018i	−0.00359465	−	0.00622611i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	0.285699	+	0.494845i	0.0505049	+	0.0874770i
$33$	−0.279788	−	0.484607i	−0.0487048	−	0.0843592i
$34$	−2.31815			−0.397559
$35$	−0.0219271	−	0.0379789i	−0.00370636	−	0.00641961i
$36$	5.69430	−	9.86282i	0.949051	−	1.64380i
$37$	3.18391	−	5.51469i	0.523431	−	0.906609i	−0.476197	−	0.879338i	$-0.657985\pi$
$37$	3.18391	−	5.51469i	0.523431	−	0.906609i	0.999628	−	0.0272703i	$-0.00868149\pi$
$38$	−16.0336			−2.60100
$39$	0.0338684	−	1.19459i	0.00542328	−	0.191288i
$40$	−0.230536			−0.0364509
$41$	0.617932	−	1.07029i	0.0965048	−	0.167151i	−0.813731	−	0.581242i	$-0.802567\pi$
$41$	0.617932	−	1.07029i	0.0965048	−	0.167151i	0.910236	+	0.414091i	$0.135900\pi$
$42$	−0.363417	+	0.629456i	−0.0560764	+	0.0971272i
$43$	1.26394	+	2.18921i	0.192749	+	0.333851i	0.946160	−	0.323698i	$-0.104926\pi$
$43$	1.26394	+	2.18921i	0.192749	+	0.333851i	−0.753411	+	0.657550i	$0.771593\pi$
$44$	−6.65254			−1.00291
$45$	−0.0704370	−	0.122000i	−0.0105001	−	0.0181867i
$46$	−8.12970	−	14.0811i	−1.19866	−	2.07614i
$47$	8.70641			1.26996			0.634980	−	0.772528i	$-0.281008\pi$
$47$	8.70641			1.26996			0.634980	+	0.772528i	$0.281008\pi$
$48$	0.604336	+	1.04674i	0.0872284	+	0.151084i
$49$	3.09527	−	5.36116i	0.442181	−	0.765880i
$50$	6.09039	−	10.5489i	0.861312	−	1.49184i
$51$	0.315248			0.0441436
$52$	−12.0980	−	7.44970i	−1.67769	−	1.03309i
$53$	−7.18912			−0.987501			−0.493751	−	0.869604i	$-0.664374\pi$
$53$	−7.18912			−0.987501			−0.493751	+	0.869604i	$0.664374\pi$
$54$	−2.37920	+	4.12089i	−0.323768	+	0.560782i
$55$	−0.0411451	+	0.0712653i	−0.00554800	+	0.00960941i
$56$	2.12763	+	3.68517i	0.284317	+	0.492451i
$57$	2.18044			0.288806
$58$	−10.0921	−	17.4800i	−1.32515	−	2.29523i
$59$	3.11259	+	5.39116i	0.405224	+	0.701869i	0.994348	−	0.106174i	$-0.0338600\pi$
$59$	3.11259	+	5.39116i	0.405224	+	0.701869i	−0.589123	+	0.808043i	$0.700527\pi$
$60$	0.0636630			0.00821886
$61$	4.30494	+	7.45637i	0.551191	+	0.954690i	0.998189	+	0.0601553i	$0.0191596\pi$
$61$	4.30494	+	7.45637i	0.551191	+	0.954690i	−0.446998	+	0.894535i	$0.647507\pi$
$62$	1.21866	−	2.11078i	0.154770	−	0.268069i
$63$	−1.30014	+	2.25190i	−0.163802	+	0.283713i
$64$	−8.68582			−1.08573
$65$	−0.154629	+	0.0835240i	−0.0191794	+	0.0103599i
$66$	1.36386			0.167880
$67$	6.69862	−	11.6023i	0.818366	−	1.41745i	−0.0885193	−	0.996074i	$-0.528214\pi$
$67$	6.69862	−	11.6023i	0.818366	−	1.41745i	0.906885	−	0.421377i	$-0.138453\pi$
$68$	1.87392	−	3.24573i	0.227246	−	0.393602i
$69$	1.10557	+	1.91490i	0.133095	+	0.230527i
$70$	0.106887			0.0127754
$71$	5.34815	+	9.26327i	0.634709	+	1.09935i	0.986577	+	0.163298i	$0.0522132\pi$
$71$	5.34815	+	9.26327i	0.634709	+	1.09935i	−0.351868	+	0.936050i	$0.614453\pi$
$72$	6.83463	+	11.8379i	0.805469	+	1.39511i
$73$	−1.14523			−0.134039			−0.0670193	−	0.997752i	$-0.521349\pi$
$73$	−1.14523			−0.134039			−0.0670193	+	0.997752i	$0.521349\pi$
$74$	7.76018	+	13.4410i	0.902103	+	1.56249i
$75$	−0.828241	+	1.43456i	−0.0956371	+	0.165648i
$76$	12.9611	−	22.4493i	1.48674	−	2.57511i
$77$	1.51892			0.173097
$78$	2.48025	+	1.52729i	0.280833	+	0.172932i
$79$	−3.73386			−0.420092			−0.210046	−	0.977691i	$-0.567361\pi$
$79$	−3.73386			−0.420092			−0.210046	+	0.977691i	$0.567361\pi$
$80$	0.0888724	−	0.153932i	0.00993624	−	0.0172101i
$81$	−4.01166	+	6.94839i	−0.445740	+	0.772044i
$82$	1.50610	+	2.60863i	0.166320	+	0.288075i
$83$	−4.08465			−0.448349			−0.224174	−	0.974549i	$-0.571968\pi$
$83$	−4.08465			−0.448349			−0.224174	+	0.974549i	$0.571968\pi$
$84$	−0.587551	−	1.01767i	−0.0641070	−	0.111037i
$85$	−0.0231799	−	0.0401488i	−0.00251421	−	0.00435474i
$86$	−6.16125			−0.664384
$87$	1.37243	+	2.37713i	0.147140	+	0.254855i
$88$	3.99238	−	6.91501i	0.425590	−	0.737143i
$89$	1.62186	−	2.80914i	0.171917	−	0.297768i	−0.767173	−	0.641440i	$-0.778337\pi$
$89$	1.62186	−	2.80914i	0.171917	−	0.297768i	0.939090	+	0.343672i	$0.111671\pi$
$90$	0.343354			0.0361927
$91$	2.76223	+	1.70093i	0.289561	+	0.178306i
$92$	26.2872			2.74063
$93$	−0.165727	+	0.287048i	−0.0171851	+	0.0297654i
$94$	−10.6101	+	18.3773i	−1.09435	+	1.89547i
$95$	−0.160325	−	0.277692i	−0.0164490	−	0.0284906i
$96$	0.189392			0.0193297
$97$	−4.93165	−	8.54186i	−0.500733	−	0.867295i	−1.00000		0.000846480i	$-0.999731\pi$
$97$	−4.93165	−	8.54186i	−0.500733	−	0.867295i	0.499267	−	0.866448i	$-0.333603\pi$
$98$	7.54414	+	13.0668i	0.762073	+	1.31995i
$99$	4.87926			0.490384
$100$	9.84658	+	17.0548i	0.984658	+	1.70548i
$101$	4.53556	−	7.85583i	0.451305	−	0.781684i	−0.547162	−	0.837027i	$-0.684292\pi$
$101$	4.53556	−	7.85583i	0.451305	−	0.781684i	0.998467	+	0.0553428i	$0.0176252\pi$
$102$	−0.384180	+	0.665419i	−0.0380395	+	0.0658863i
$103$	−2.47755			−0.244120			−0.122060	−	0.992523i	$-0.538950\pi$
$103$	−2.47755			−0.244120			−0.122060	+	0.992523i	$0.538950\pi$
$104$	15.0040	−	8.10450i	1.47126	−	0.794711i
$105$	−0.0145357			−0.00141854
$106$	8.76107	−	15.1746i	0.850951	−	1.47389i
$107$	−1.08766	+	1.88388i	−0.105148	+	0.182121i	−0.913799	−	0.406168i	$-0.866865\pi$
$107$	−1.08766	+	1.88388i	−0.105148	+	0.182121i	0.808651	+	0.588289i	$0.200198\pi$
$108$	−3.84654	−	6.66241i	−0.370134	−	0.641091i
$109$	12.1275			1.16160			0.580800	−	0.814046i	$-0.302740\pi$
$109$	12.1275			1.16160			0.580800	+	0.814046i	$0.302740\pi$
$110$	−0.100283	−	0.173696i	−0.00956165	−	0.0165613i
$111$	−1.05532	−	1.82786i	−0.100166	−	0.173493i
$112$	−3.28084			−0.310010
$113$	−6.15409	−	10.6592i	−0.578928	−	1.00273i	−0.995603	−	0.0936771i	$-0.970138\pi$
$113$	−6.15409	−	10.6592i	−0.578928	−	1.00273i	0.416675	−	0.909056i	$-0.363195\pi$
$114$	−2.65721	+	4.60242i	−0.248870	+	0.431056i
$115$	0.162583	−	0.281602i	0.0151609	−	0.0262595i
$116$	32.6325			3.02985
$117$	8.87317	+	5.46393i	0.820325	+	0.505141i
$118$	−15.1727			−1.39676
$119$	−0.427858	+	0.741072i	−0.0392217	+	0.0679339i
$120$	−0.0382060	+	0.0661748i	−0.00348772	+	0.00604090i
$121$	4.07491	+	7.05796i	0.370447	+	0.641633i
$122$	−20.9850			−1.89989
$123$	−0.204816	−	0.354752i	−0.0184676	−	0.0319869i
$124$	1.97025	+	3.41258i	0.176934	+	0.306459i
$125$	0.487314			0.0435867
$126$	−3.16884	−	5.48859i	−0.282303	−	0.488963i
$127$	4.97702	−	8.62044i	0.441639	−	0.764941i	−0.556173	−	0.831067i	$-0.687731\pi$
$127$	4.97702	−	8.62044i	0.441639	−	0.764941i	0.997811	+	0.0661261i	$0.0210640\pi$
$128$	10.0136	−	17.3441i	0.885090	−	1.53302i
$129$	0.837876			0.0737709
$130$	0.0121393	−	0.428175i	0.00106469	−	0.0375534i
$131$	16.4622			1.43831			0.719154	−	0.694851i	$-0.244530\pi$
$131$	16.4622			1.43831			0.719154	+	0.694851i	$0.244530\pi$
$132$	−1.10251	+	1.90960i	−0.0959608	+	0.166209i
$133$	−2.95931	+	5.12568i	−0.256605	+	0.444453i
$134$	16.3266	+	28.2786i	1.41041	+	2.44290i
$135$	−0.0951614			−0.00819019
$136$	2.24919	+	3.89571i	0.192866	+	0.334054i
$137$	−5.05259	−	8.75135i	−0.431672	−	0.747678i	0.565345	−	0.824854i	$-0.308743\pi$
$137$	−5.05259	−	8.75135i	−0.431672	−	0.747678i	−0.997017	+	0.0771761i	$0.975410\pi$
$138$	−5.38925			−0.458763
$139$	−5.61038	−	9.71746i	−0.475866	−	0.824224i	0.523752	−	0.851871i	$-0.324532\pi$
$139$	−5.61038	−	9.71746i	−0.475866	−	0.824224i	−0.999618	+	0.0276470i	$0.991199\pi$
$140$	−0.0864041	+	0.149656i	−0.00730248	+	0.0126483i
$141$	1.44289	−	2.49915i	0.121513	−	0.210467i
$142$	−26.0703			−2.18777
$143$	0.172507	−	6.08461i	0.0144258	−	0.508821i
$144$	−10.5391			−0.878259
$145$	0.201828	−	0.349576i	0.0167609	−	0.0290307i
$146$	1.39564	−	2.41732i	0.115504	−	0.200058i
$147$	−1.02594	−	1.77698i	−0.0846179	−	0.146563i
$148$	−25.0924			−2.06258
$149$	−5.40451	−	9.36088i	−0.442754	−	0.766873i	0.555138	−	0.831758i	$-0.312665\pi$
$149$	−5.40451	−	9.36088i	−0.442754	−	0.766873i	−0.997893	+	0.0648849i	$0.979332\pi$
$150$	−2.01868	−	3.49646i	−0.164825	−	0.285485i
$151$	−16.2140			−1.31947			−0.659736	−	0.751497i	$-0.729332\pi$
$151$	−16.2140			−1.31947			−0.659736	+	0.751497i	$0.729332\pi$
$152$	15.5567	+	26.9450i	1.26181	+	2.18553i
$153$	−1.37442	+	2.38056i	−0.111115	+	0.192457i
$154$	−1.85105	+	3.20611i	−0.149162	+	0.258355i
$155$	0.0487430			0.00391513
$156$	−4.14338	+	2.23807i	−0.331736	+	0.179189i
$157$	−10.3030			−0.822265			−0.411133	−	0.911576i	$-0.634867\pi$
$157$	−10.3030			−0.822265			−0.411133	+	0.911576i	$0.634867\pi$
$158$	4.55030	−	7.88135i	0.362003	−	0.627007i
$159$	−1.19143	+	2.06362i	−0.0944866	+	0.163656i
$160$	−0.0139258	−	0.0241202i	−0.00110093	−	0.00190687i
$161$	−6.00196			−0.473021
$162$	−9.77767	−	16.9354i	−0.768207	−	1.33057i
$163$	−0.859902	−	1.48939i	−0.0673527	−	0.116658i	0.830383	−	0.557194i	$-0.188122\pi$
$163$	−0.859902	−	1.48939i	−0.0673527	−	0.116658i	−0.897735	+	0.440535i	$0.854789\pi$
$164$	−4.86993			−0.380278
$165$	0.0136377	+	0.0236212i	0.00106169	+	0.00183891i
$166$	4.97779	−	8.62178i	0.386351	−	0.669180i
$167$	0.285033	−	0.493692i	0.0220565	−	0.0382030i	−0.854786	−	0.518980i	$-0.826312\pi$
$167$	0.285033	−	0.493692i	0.0220565	−	0.0382030i	0.876843	+	0.480777i	$0.159645\pi$
$168$	1.41042			0.108817
$169$	7.12742	−	10.8720i	0.548263	−	0.836306i
$170$	0.112993			0.00866620
$171$	−9.50625	+	16.4653i	−0.726961	+	1.25913i
$172$	4.98057	−	8.62659i	0.379765	−	0.657772i
$173$	−8.93709	−	15.4795i	−0.679474	−	1.17688i	−0.975139	−	0.221592i	$-0.928875\pi$
$173$	−8.93709	−	15.4795i	−0.679474	−	1.17688i	0.295665	−	0.955292i	$-0.404459\pi$
$174$	−6.69011			−0.507176
$175$	−2.24819	−	3.89399i	−0.169947	−	0.294358i
$176$	3.07816	+	5.33152i	0.232025	+	0.401879i
$177$	2.06336			0.155092
$178$	3.95298	+	6.84676i	0.296288	+	0.513186i
$179$	−9.00751	+	15.6015i	−0.673253	+	1.16611i	0.303724	+	0.952760i	$0.401770\pi$
$179$	−9.00751	+	15.6015i	−0.673253	+	1.16611i	−0.976976	+	0.213348i	$0.931563\pi$
$180$	−0.277557	+	0.480743i	−0.0206879	+	0.0358325i
$181$	15.6815			1.16560			0.582799	−	0.812616i	$-0.301957\pi$
$181$	15.6815			1.16560			0.582799	+	0.812616i	$0.301957\pi$
$182$	−6.95650	+	3.75760i	−0.515650	+	0.278532i
$183$	2.85378			0.210957
$184$	−15.7757	+	27.3244i	−1.16300	+	2.01438i
$185$	−0.155193	+	0.268802i	−0.0114100	+	0.0197627i
$186$	−0.403929	−	0.699625i	−0.0296175	−	0.0512990i
$187$	1.60570			0.117421
$188$	−17.1538	−	29.7113i	−1.25107	−	2.16692i
$189$	0.878251	+	1.52118i	0.0638834	+	0.110649i
$190$	0.781527			0.0566980
$191$	−5.67399	−	9.82764i	−0.410556	−	0.711103i	0.584395	−	0.811469i	$-0.301332\pi$
$191$	−5.67399	−	9.82764i	−0.410556	−	0.711103i	−0.994951	+	0.100366i	$0.967999\pi$
$192$	−1.43948	+	2.49324i	−0.103885	+	0.179934i
$193$	9.26470	−	16.0469i	0.666888	−	1.15508i	−0.311882	−	0.950121i	$-0.600959\pi$
$193$	9.26470	−	16.0469i	0.666888	−	1.15508i	0.978770	−	0.204963i	$-0.0657074\pi$
$194$	24.0400			1.72597
$195$	−0.00165085	+	0.0582281i	−0.000118220	+	0.00416980i
$196$	−24.3938			−1.74242
$197$	−10.0061	+	17.3310i	−0.712902	+	1.23478i	0.250861	+	0.968023i	$0.419286\pi$
$197$	−10.0061	+	17.3310i	−0.712902	+	1.23478i	−0.963763	+	0.266759i	$0.914047\pi$
$198$	−5.94615	+	10.2990i	−0.422575	+	0.731921i
$199$	3.27397	+	5.67068i	0.232085	+	0.401984i	0.958422	−	0.285356i	$-0.0921118\pi$
$199$	3.27397	+	5.67068i	0.232085	+	0.401984i	−0.726336	+	0.687340i	$0.758778\pi$
$200$	−23.6369			−1.67138
$201$	−2.22028	−	3.84564i	−0.156607	−	0.271251i
$202$	11.0546	+	19.1471i	0.777799	+	1.34719i
$203$	−7.45073			−0.522938
$204$	−0.621119	−	1.07581i	−0.0434870	−	0.0753217i
$205$	−0.0301199	+	0.0521691i	−0.00210366	+	0.00364365i
$206$	3.01928	−	5.22955i	0.210363	−	0.364360i
$207$	−19.2802			−1.34007
$208$	−0.372612	+	13.1426i	−0.0258360	+	0.911277i
$209$	11.1060			0.768215
$210$	0.0177140	−	0.0306816i	0.00122238	−	0.00211723i
$211$	−3.37369	+	5.84341i	−0.232255	+	0.402277i	−0.958471	−	0.285189i	$-0.907944\pi$
$211$	−3.37369	+	5.84341i	−0.232255	+	0.402277i	0.726217	+	0.687466i	$0.241277\pi$
$212$	14.1644	+	24.5334i	0.972814	+	1.68496i
$213$	3.54533			0.242922
$214$	−2.65096	−	4.59160i	−0.181216	−	0.313875i
$215$	−0.0616082	−	0.106709i	−0.00420165	−	0.00727747i
$216$	9.23369			0.628273
$217$	−0.449852	−	0.779167i	−0.0305380	−	0.0528933i
$218$	−14.7792	+	25.5984i	−1.00098	+	1.73374i
$219$	−0.189795	+	0.328734i	−0.0128251	+	0.0222138i
$220$	0.324265			0.0218619
$221$	2.92005	+	1.79811i	0.196424	+	0.120954i
$222$	5.14429			0.345262
$223$	−4.98104	+	8.62741i	−0.333555	+	0.577734i	−0.983206	−	0.182498i	$-0.941582\pi$
$223$	−4.98104	+	8.62741i	−0.333555	+	0.577734i	0.649651	+	0.760232i	$0.274915\pi$
$224$	−0.257045	+	0.445214i	−0.0171745	+	0.0297471i
$225$	−7.22191	−	12.5087i	−0.481461	−	0.833915i
$226$	29.9989			1.99550
$227$	4.86643	+	8.42890i	0.322996	+	0.559446i	0.981105	−	0.193477i	$-0.0619766\pi$
$227$	4.86643	+	8.42890i	0.322996	+	0.559446i	−0.658109	+	0.752923i	$0.728643\pi$
$228$	−4.29601	−	7.44091i	−0.284510	−	0.492787i
$229$	−18.3306			−1.21132			−0.605661	−	0.795723i	$-0.707091\pi$
$229$	−18.3306			−1.21132			−0.605661	+	0.795723i	$0.707091\pi$
$230$	0.396266	+	0.686353i	0.0261290	+	0.0452568i
$231$	0.251726	−	0.436003i	0.0165624	−	0.0286869i
$232$	−19.5837	+	33.9200i	−1.28573	+	2.22696i
$233$	−5.69286			−0.372952			−0.186476	−	0.982460i	$-0.559707\pi$
$233$	−5.69286			−0.372952			−0.186476	+	0.982460i	$0.559707\pi$
$234$	−22.3465	+	12.0706i	−1.46084	+	0.789081i
$235$	−0.424376			−0.0276833
$236$	12.2652	−	21.2439i	0.798395	−	1.38286i
$237$	−0.618802	+	1.07180i	−0.0401955	+	0.0696207i
$238$	−1.04282	−	1.80622i	−0.0675963	−	0.117080i
$239$	17.4134			1.12638			0.563188	−	0.826329i	$-0.309575\pi$
$239$	17.4134			1.12638			0.563188	+	0.826329i	$0.309575\pi$
$240$	−0.0294571	−	0.0510212i	−0.00190145	−	0.00329341i
$241$	−10.5565	−	18.2844i	−0.680006	−	1.17780i	−0.974979	−	0.222299i	$-0.928644\pi$
$241$	−10.5565	−	18.2844i	−0.680006	−	1.17780i	0.294973	−	0.955506i	$-0.404689\pi$
$242$	−19.8637			−1.27689
$243$	4.25814	+	7.37532i	0.273160	+	0.473127i
$244$	16.9636	−	29.3819i	1.08598	−	1.88098i
$245$	−0.150872	+	0.261319i	−0.00963889	+	0.0166950i
$246$	0.998403			0.0636558
$247$	20.1967	+	12.4368i	1.28509	+	0.791332i
$248$	−4.72962			−0.300331
$249$	−0.676937	+	1.17249i	−0.0428991	+	0.0743035i
$250$	−0.593869	+	1.02861i	−0.0375596	+	0.0650551i
$251$	−2.55711	−	4.42904i	−0.161403	−	0.279559i	0.773969	−	0.633224i	$-0.218269\pi$
$251$	−2.55711	−	4.42904i	−0.161403	−	0.279559i	−0.935372	+	0.353665i	$0.884935\pi$
$252$	10.2464			0.645462
$253$	5.63117	+	9.75347i	0.354029	+	0.613195i
$254$	12.1306	+	21.0107i	0.761139	+	1.31833i
$255$	−0.0153661			−0.000962265
$256$	15.7206	+	27.2289i	0.982537	+	1.70180i
$257$	10.1705	−	17.6159i	0.634421	−	1.09885i	−0.352217	−	0.935918i	$-0.614572\pi$
$257$	10.1705	−	17.6159i	0.634421	−	1.09885i	0.986638	−	0.162930i	$-0.0520946\pi$
$258$	−1.02108	+	1.76857i	−0.0635699	+	0.110106i
$259$	5.72915			0.355992
$260$	0.589691	+	0.363120i	0.0365711	+	0.0225198i
$261$	−23.9341			−1.48148
$262$	−20.0618	+	34.7480i	−1.23942	+	2.14674i
$263$	6.10241	−	10.5697i	0.376291	−	0.651754i	−0.614229	−	0.789128i	$-0.710533\pi$
$263$	6.10241	−	10.5697i	0.376291	−	0.651754i	0.990519	+	0.137374i	$0.0438661\pi$
$264$	−1.32329	−	2.29201i	−0.0814430	−	0.141063i
$265$	0.350419			0.0215261
$266$	−7.21277	−	12.4929i	−0.442243	−	0.765988i
$267$	−0.537571	−	0.931101i	−0.0328988	−	0.0569824i
$268$	−52.7919			−3.22478
$269$	−13.2430	−	22.9376i	−0.807442	−	1.39853i	−0.914630	−	0.404292i	$-0.867518\pi$
$269$	−13.2430	−	22.9376i	−0.807442	−	1.39853i	0.107188	−	0.994239i	$-0.465815\pi$
$270$	0.115969	−	0.200864i	0.00705766	−	0.0122242i
$271$	2.14874	−	3.72173i	0.130527	−	0.226079i	−0.793353	−	0.608762i	$-0.791667\pi$
$271$	2.14874	−	3.72173i	0.130527	−	0.226079i	0.923880	+	0.382683i	$0.125000\pi$
$272$	−3.46828			−0.210296
$273$	0.946025	−	0.511002i	0.0572560	−	0.0309272i
$274$	24.6295			1.48792
$275$	−4.21861	+	7.30684i	−0.254392	+	0.440619i
$276$	4.35650	−	7.54569i	0.262231	−	0.454197i
$277$	3.74597	+	6.48822i	0.225074	+	0.389839i	0.956342	−	0.292251i	$-0.0944043\pi$
$277$	3.74597	+	6.48822i	0.225074	+	0.389839i	−0.731268	+	0.682090i	$0.761071\pi$
$278$	27.3485			1.64025
$279$	−1.44507	−	2.50293i	−0.0865140	−	0.149847i
$280$	−0.103707	−	0.179626i	−0.00619769	−	0.0107347i
$281$	15.5014			0.924739			0.462369	−	0.886687i	$-0.346999\pi$
$281$	15.5014			0.924739			0.462369	+	0.886687i	$0.346999\pi$
$282$	3.51677	+	6.09123i	0.209421	+	0.362727i
$283$	8.19911	−	14.2013i	0.487386	−	0.844178i	−0.512508	−	0.858682i	$-0.671284\pi$
$283$	8.19911	−	14.2013i	0.487386	−	0.844178i	0.999895	+	0.0145041i	$0.00461697\pi$
$284$	21.0744	−	36.5020i	1.25054	−	2.16599i
$285$	−0.106281			−0.00629554
$286$	12.6330	+	7.77918i	0.747007	+	0.459993i
$287$	1.11191			0.0656342
$288$	−0.825709	+	1.43017i	−0.0486554	+	0.0842736i
$289$	8.04770	−	13.9390i	0.473394	−	0.819942i
$290$	0.491917	+	0.852026i	0.0288864	+	0.0500327i
$291$	−3.26923			−0.191646
$292$	2.25638	+	3.90817i	0.132045	+	0.228708i
$293$	−4.77535	−	8.27115i	−0.278979	−	0.483206i	0.692152	−	0.721751i	$-0.256663\pi$
$293$	−4.77535	−	8.27115i	−0.278979	−	0.483206i	−0.971131	+	0.238546i	$0.923329\pi$
$294$	5.00107			0.291668
$295$	−0.151717	−	0.262781i	−0.00883329	−	0.0152997i
$296$	15.0587	−	26.0824i	0.875268	−	1.51601i
$297$	1.64799	−	2.85440i	0.0956260	−	0.165629i
$298$	26.3450			1.52612
$299$	−0.681654	+	24.0431i	−0.0394211	+	1.39045i
$300$	6.52738			0.376858
$301$	−1.13717	+	1.96964i	−0.0655456	+	0.113528i
$302$	19.7593	−	34.2240i	1.13702	−	1.96937i
$303$	−1.50333	−	2.60385i	−0.0863641	−	0.149587i
$304$	−23.9886			−1.37584
$305$	−0.209835	−	0.363446i	−0.0120151	−	0.0208108i
$306$	−3.34988	−	5.80217i	−0.191500	−	0.331688i
$307$	12.5368			0.715512			0.357756	−	0.933815i	$-0.383542\pi$
$307$	12.5368			0.715512			0.357756	+	0.933815i	$0.383542\pi$
$308$	−2.99266	−	5.18344i	−0.170523	−	0.295354i
$309$	−0.410596	+	0.711173i	−0.0233580	+	0.0404572i
$310$	−0.0594010	+	0.102886i	−0.00337375	+	0.00584351i
$311$	9.97394			0.565570			0.282785	−	0.959183i	$-0.408742\pi$
$311$	9.97394			0.565570			0.282785	+	0.959183i	$0.408742\pi$
$312$	0.160185	−	5.64998i	0.00906867	−	0.319867i
$313$	−21.9564			−1.24105			−0.620526	−	0.784186i	$-0.713081\pi$
$313$	−21.9564			−1.24105			−0.620526	+	0.784186i	$0.713081\pi$
$314$	12.5558	−	21.7472i	0.708563	−	1.22727i
$315$	0.0633725	−	0.109764i	0.00357064	−	0.00618452i
$316$	7.35666	+	12.7421i	0.413844	+	0.716799i
$317$	−33.2694			−1.86860			−0.934299	−	0.356491i	$-0.883973\pi$
$317$	−33.2694			−1.86860			−0.934299	+	0.356491i	$0.883973\pi$
$318$	−2.90389	−	5.02969i	−0.162842	−	0.282051i
$319$	6.99043	+	12.1078i	0.391389	+	0.677906i
$320$	0.423373			0.0236673
$321$	0.360508	+	0.624418i	0.0201216	+	0.0348516i
$322$	7.31433	−	12.6688i	0.407612	−	0.706005i
$323$	−3.12838	+	5.41852i	−0.174068	+	0.301494i
$324$	31.6159			1.75644
$325$	−15.8541	+	8.56373i	−0.879429	+	0.475030i
$326$	4.19170			0.232157
$327$	2.00985	−	3.48116i	0.111145	−	0.192508i
$328$	2.92259	−	5.06207i	0.161373	−	0.279506i
$329$	3.91660	+	6.78375i	0.215929	+	0.374000i
$330$	−0.0664787			−0.00365953
$331$	14.4279	+	24.9899i	0.793030	+	1.37357i	0.924083	+	0.382193i	$0.124831\pi$
$331$	14.4279	+	24.9899i	0.793030	+	1.37357i	−0.131053	+	0.991375i	$0.541836\pi$
$332$	8.04779	+	13.9392i	0.441680	+	0.765012i
$333$	18.4039			1.00852
$334$	0.694716	+	1.20328i	0.0380132	+	0.0658407i
$335$	−0.326510	+	0.565533i	−0.0178392	+	0.0308984i
$336$	−0.543724	+	0.941757i	−0.0296626	+	0.0513771i
$337$	0.603321			0.0328650			0.0164325	−	0.999865i	$-0.494769\pi$
$337$	0.603321			0.0328650			0.0164325	+	0.999865i	$0.494769\pi$
$338$	14.2624	+	28.2936i	0.775773	+	1.53897i
$339$	−4.07960			−0.221573
$340$	−0.0913405	+	0.158206i	−0.00495363	+	0.00857995i
$341$	−0.844123	+	1.46206i	−0.0457118	+	0.0791752i
$342$	−23.1697	−	40.1311i	−1.25288	−	2.17004i
$343$	11.8676			0.640789
$344$	5.97797	+	10.3541i	0.322310	+	0.558258i
$345$	−0.0538888	−	0.0933381i	−0.00290127	−	0.00502515i
$346$	43.5650			2.34207
$347$	−15.9909	−	27.6971i	−0.858436	−	1.48686i	−0.873420	−	0.486968i	$-0.838103\pi$
$347$	−15.9909	−	27.6971i	−0.858436	−	1.48686i	0.0149834	−	0.999888i	$-0.495230\pi$
$348$	5.40809	−	9.36708i	0.289904	−	0.502128i
$349$	0.755519	−	1.30860i	0.0404420	−	0.0700476i	−0.845096	−	0.534615i	$-0.820457\pi$
$349$	0.755519	−	1.30860i	0.0404420	−	0.0700476i	0.885538	+	0.464567i	$0.153790\pi$
$350$	10.9591			0.585789
$351$	6.19338	−	3.34540i	0.330578	−	0.178564i
$352$	0.964659			0.0514165
$353$	−4.37970	+	7.58586i	−0.233108	+	0.403754i	−0.958721	−	0.284348i	$-0.908223\pi$
$353$	−4.37970	+	7.58586i	−0.233108	+	0.403754i	0.725613	+	0.688103i	$0.241556\pi$
$354$	−2.51453	+	4.35529i	−0.133646	+	0.231481i
$355$	−0.260685	−	0.451519i	−0.0138357	−	0.0239642i
$356$	−12.7819			−0.677438
$357$	0.141815	+	0.245631i	0.00750566	+	0.0130002i
$358$	−21.9541	−	38.0257i	−1.16031	−	2.00972i
$359$	−15.5001			−0.818063			−0.409032	−	0.912520i	$-0.634133\pi$
$359$	−15.5001			−0.818063			−0.409032	+	0.912520i	$0.634133\pi$
$360$	−0.333140	−	0.577016i	−0.0175580	−	0.0304114i
$361$	−12.1377	+	21.0231i	−0.638826	+	1.10648i
$362$	−19.1104	+	33.1002i	−1.00442	+	1.73971i
$363$	2.70129			0.141781
$364$	0.362262	−	12.7776i	0.0189877	−	0.669728i
$365$	0.0558217			0.00292184
$366$	−3.47778	+	6.02368i	−0.181786	+	0.314863i
$367$	−9.88204	+	17.1162i	−0.515838	+	0.893458i	0.483993	+	0.875072i	$0.339186\pi$
$367$	−9.88204	+	17.1162i	−0.515838	+	0.893458i	−0.999831	+	0.0183859i	$0.994147\pi$
$368$	−12.1632	−	21.0673i	−0.634051	−	1.09821i
$369$	3.57182			0.185941
$370$	−0.378254	−	0.655156i	−0.0196645	−	0.0340599i
$371$	−3.23404	−	5.60153i	−0.167903	−	0.290817i
$372$	1.30610			0.0677179
$373$	2.07347	+	3.59135i	0.107360	+	0.185953i	0.914700	−	0.404134i	$-0.132427\pi$
$373$	2.07347	+	3.59135i	0.107360	+	0.185953i	−0.807340	+	0.590087i	$0.799094\pi$
$374$	−1.95680	+	3.38928i	−0.101184	+	0.175255i
$375$	0.0807611	−	0.139882i	0.00417048	−	0.00722349i
$376$	41.1781			2.12360
$377$	−0.846194	+	29.8467i	−0.0435812	+	1.53718i
$378$	−4.28115			−0.220199
$379$	0.473392	−	0.819939i	0.0243165	−	0.0421174i	−0.853611	−	0.520911i	$-0.825592\pi$
$379$	0.473392	−	0.819939i	0.0243165	−	0.0421174i	0.877928	+	0.478793i	$0.158926\pi$
$380$	−0.631763	+	1.09425i	−0.0324088	+	0.0561337i
$381$	−1.64965	−	2.85728i	−0.0845142	−	0.146383i
$382$	27.6586			1.41514
$383$	7.42511	+	12.8607i	0.379405	+	0.657149i	0.990976	−	0.134041i	$-0.0427953\pi$
$383$	7.42511	+	12.8607i	0.379405	+	0.657149i	−0.611570	+	0.791190i	$0.709462\pi$
$384$	−3.31906	−	5.74879i	−0.169375	−	0.293367i
$385$	−0.0740368			−0.00377327
$386$	22.5810	+	39.1115i	1.14934	+	1.99072i
$387$	−3.65296	+	6.32712i	−0.185691	+	0.321626i
$388$	−19.4332	+	33.6593i	−0.986570	+	1.70879i
$389$	−15.7314			−0.797612			−0.398806	−	0.917035i	$-0.630575\pi$
$389$	−15.7314			−0.797612			−0.398806	+	0.917035i	$0.630575\pi$
$390$	−0.120895	−	0.0744447i	−0.00612174	−	0.00376965i
$391$	−6.34487			−0.320874
$392$	14.6394	−	25.3563i	0.739404	−	1.28068i
$393$	2.72823	−	4.72543i	0.137621	−	0.238366i
$394$	−24.3879	−	42.2411i	−1.22865	−	2.12808i
$395$	0.182000			0.00915739
$396$	−9.61338	−	16.6509i	−0.483091	−	0.836737i
$397$	0.558120	+	0.966693i	0.0280113	+	0.0485169i	0.879691	−	0.475545i	$-0.157749\pi$
$397$	0.558120	+	0.966693i	0.0280113	+	0.0485169i	−0.851680	+	0.524062i	$0.824416\pi$
$398$	−15.9594			−0.799972
$399$	0.980875	+	1.69893i	0.0491052	+	0.0850527i
$400$	9.11210	−	15.7826i	0.455605	−	0.789131i
$401$	13.6442	−	23.6324i	0.681358	−	1.18015i	−0.293209	−	0.956048i	$-0.594723\pi$
$401$	13.6442	−	23.6324i	0.681358	−	1.18015i	0.974567	−	0.224098i	$-0.0719435\pi$
$402$	10.8231			0.539805
$403$	−3.17234	+	1.71356i	−0.158025	+	0.0853585i
$404$	−35.7448			−1.77837
$405$	0.195540	−	0.338685i	0.00971647	−	0.0168294i
$406$	9.07988	−	15.7268i	0.450627	−	0.780509i
$407$	−5.37521	−	9.31014i	−0.266439	−	0.461487i
$408$	1.49101			0.0738158
$409$	−2.13403	−	3.69624i	−0.105521	−	0.182767i	0.808430	−	0.588592i	$-0.200318\pi$
$409$	−2.13403	−	3.69624i	−0.105521	−	0.182767i	−0.913951	+	0.405825i	$0.866984\pi$
$410$	−0.0734116	−	0.127153i	−0.00362554	−	0.00627962i
$411$	−3.34940			−0.165214
$412$	4.88139	+	8.45482i	0.240489	+	0.416539i
$413$	−2.80041	+	4.85045i	−0.137799	+	0.238675i
$414$	23.4960	−	40.6962i	1.15476	−	2.00011i
$415$	0.199098			0.00977334
$416$	1.75428	+	1.08025i	0.0860106	+	0.0529637i
$417$	−3.71916			−0.182128
$418$	−13.5344	+	23.4422i	−0.661987	+	1.14660i
$419$	−16.3661	+	28.3469i	−0.799536	+	1.38484i	0.120382	+	0.992728i	$0.461588\pi$
$419$	−16.3661	+	28.3469i	−0.799536	+	1.38484i	−0.919919	+	0.392110i	$0.871745\pi$
$420$	0.0286390	+	0.0496041i	0.00139744	+	0.00242043i
$421$	24.5539			1.19669			0.598343	−	0.801240i	$-0.295826\pi$
$421$	24.5539			1.19669			0.598343	+	0.801240i	$0.295826\pi$
$422$	−8.22275	−	14.2422i	−0.400277	−	0.693301i
$423$	12.5814	+	21.7916i	0.611727	+	1.05954i
$424$	−34.0018			−1.65127
$425$	−2.37664	−	4.11646i	−0.115284	−	0.199678i
$426$	−4.32055	+	7.48340i	−0.209331	+	0.362572i
$427$	−3.87317	+	6.70853i	−0.187436	+	0.324649i
$428$	8.57183			0.414335
$429$	−1.71798	−	1.05790i	−0.0829450	−	0.0510760i
$430$	0.300317			0.0144826
$431$	6.94660	−	12.0319i	0.334606	−	0.579555i	−0.648803	−	0.760956i	$-0.724730\pi$
$431$	6.94660	−	12.0319i	0.334606	−	0.579555i	0.983409	+	0.181402i	$0.0580634\pi$
$432$	−3.55962	+	6.16544i	−0.171262	+	0.296635i
$433$	9.32059	+	16.1437i	0.447919	+	0.775819i	0.998250	−	0.0591276i	$-0.0188319\pi$
$433$	9.32059	+	16.1437i	0.447919	+	0.775819i	−0.550331	+	0.834946i	$0.685499\pi$
$434$	2.19286			0.105261
$435$	−0.0668966	−	0.115868i	−0.00320744	−	0.00555546i
$436$	−23.8942	−	41.3859i	−1.14432	−	1.98203i
$437$	−43.8847			−2.09929
$438$	−0.462590	−	0.801229i	−0.0221034	−	0.0382842i
$439$	−5.58955	+	9.68138i	−0.266775	+	0.462067i	−0.968027	−	0.250846i	$-0.919291\pi$
$439$	−5.58955	+	9.68138i	−0.266775	+	0.462067i	0.701252	+	0.712913i	$0.252625\pi$
$440$	−0.194601	+	0.337058i	−0.00927722	+	0.0160686i
$441$	17.8915			0.851976
$442$	−7.35394	+	3.97229i	−0.349791	+	0.188942i
$443$	20.7379			0.985289			0.492644	−	0.870231i	$-0.336030\pi$
$443$	20.7379			0.985289			0.492644	+	0.870231i	$0.336030\pi$
$444$	−4.15849	+	7.20271i	−0.197353	+	0.341826i
$445$	−0.0790542	+	0.136926i	−0.00374753	+	0.00649091i
$446$	−12.1404	−	21.0277i	−0.574863	−	0.995692i
$447$	−3.58269			−0.169455
$448$	−3.90734	−	6.76771i	−0.184604	−	0.319744i
$449$	0.196162	+	0.339763i	0.00925748	+	0.0160344i	0.870617	−	0.491961i	$-0.163720\pi$
$449$	0.196162	+	0.339763i	0.00925748	+	0.0160344i	−0.861360	+	0.507996i	$0.830387\pi$
$450$	35.2042			1.65954
$451$	−1.04322	−	1.80691i	−0.0491234	−	0.0850842i
$452$	−24.2502	+	42.0026i	−1.14063	+	1.97564i
$453$	−2.68709	+	4.65418i	−0.126250	+	0.218672i
$454$	−23.7220			−1.11333
$455$	−0.134639	−	0.0829084i	−0.00631199	−	0.00388681i
$456$	10.3127			0.482934
$457$	16.6898	−	28.9076i	0.780717	−	1.35224i	−0.150808	−	0.988563i	$-0.548188\pi$
$457$	16.6898	−	28.9076i	0.780717	−	1.35224i	0.931525	−	0.363678i	$-0.118479\pi$
$458$	22.3388	−	38.6919i	1.04382	−	1.80795i
$459$	0.928428	+	1.60808i	0.0433353	+	0.0750589i
$460$	−1.28132			−0.0597418
$461$	17.8948	+	30.9948i	0.833445	+	1.44357i	0.895290	+	0.445484i	$0.146968\pi$
$461$	17.8948	+	30.9948i	0.833445	+	1.44357i	−0.0618447	+	0.998086i	$0.519698\pi$
$462$	0.613537	+	1.06268i	0.0285443	+	0.0494402i
$463$	−28.7675			−1.33694			−0.668470	−	0.743739i	$-0.733051\pi$
$463$	−28.7675			−1.33694			−0.668470	+	0.743739i	$0.733051\pi$
$464$	−15.0992	−	26.1526i	−0.700962	−	1.21410i
$465$	0.00807803	−	0.0139916i	0.000374610	−	0.000648843i
$466$	6.93765	−	12.0164i	0.321380	−	0.556647i
$467$	−0.117071			−0.00541742			−0.00270871	−	0.999996i	$-0.500862\pi$
$467$	−0.117071			−0.00541742			−0.00270871	+	0.999996i	$0.500862\pi$
$468$	1.16370	−	41.0457i	0.0537921	−	1.89734i
$469$	12.0536			0.556581
$470$	0.517170	−	0.895764i	0.0238553	−	0.0413185i
$471$	−1.70748	+	2.95744i	−0.0786764	+	0.136272i
$472$	14.7214	+	25.4982i	0.677606	+	1.17365i
$473$	4.26768			0.196228
$474$	−1.50822	−	2.61231i	−0.0692746	−	0.119987i
$475$	−16.4382	−	28.4718i	−0.754236	−	1.30638i
$476$	3.37195			0.154553
$477$	−10.3888	−	17.9939i	−0.475669	−	0.823883i
$478$	−21.2209	+	36.7557i	−0.970622	+	1.68117i
$479$	−11.0543	+	19.1466i	−0.505082	+	0.874828i	0.494900	+	0.868950i	$0.335205\pi$
$479$	−11.0543	+	19.1466i	−0.505082	+	0.874828i	−0.999983	+	0.00587857i	$0.998129\pi$
$480$	−0.00923153			−0.000421360
$481$	0.650671	−	22.9502i	0.0296680	−	1.04644i
$482$	51.4592			2.34390
$483$	−0.994687	+	1.72285i	−0.0452598	+	0.0783923i
$484$	16.0572	−	27.8119i	0.729874	−	1.26418i
$485$	0.240383	+	0.416356i	0.0109152	+	0.0189057i
$486$	−20.7569			−0.941551
$487$	−0.683495	−	1.18385i	−0.0309721	−	0.0536453i	0.850124	−	0.526583i	$-0.176527\pi$
$487$	−0.683495	−	1.18385i	−0.0309721	−	0.0536453i	−0.881096	+	0.472937i	$0.843194\pi$
$488$	20.3607	+	35.2658i	0.921687	+	1.59641i
$489$	−0.570036			−0.0257779
$490$	−0.367724	−	0.636916i	−0.0166121	−	0.0287729i
$491$	4.13934	−	7.16955i	0.186806	−	0.323557i	−0.757378	−	0.652977i	$-0.773520\pi$
$491$	4.13934	−	7.16955i	0.186806	−	0.323557i	0.944184	+	0.329420i	$0.106853\pi$
$492$	−0.807079	+	1.39790i	−0.0363859	+	0.0630223i
$493$	−7.87640			−0.354735
$494$	−50.8641	+	27.4746i	−2.28848	+	1.23614i
$495$	−0.237830			−0.0106897
$496$	1.82329	−	3.15803i	0.0818680	−	0.141800i
$497$	−4.81176	+	8.33421i	−0.215837	+	0.373840i
$498$	−1.64991	−	2.85772i	−0.0739342	−	0.128058i
$499$	15.1295			0.677288			0.338644	−	0.940915i	$-0.390032\pi$
$499$	15.1295			0.677288			0.338644	+	0.940915i	$0.390032\pi$
$500$	−0.960132	−	1.66300i	−0.0429384	−	0.0743715i
$501$	−0.0944754	−	0.163636i	−0.00422085	−	0.00731073i
$502$	12.4650			0.556338
$503$	−8.66816	−	15.0137i	−0.386494	−	0.669427i	0.605481	−	0.795860i	$-0.292981\pi$
$503$	−8.66816	−	15.0137i	−0.386494	−	0.669427i	−0.991975	+	0.126432i	$0.959647\pi$
$504$	−6.14915	+	10.6506i	−0.273905	+	0.474418i
$505$	−0.221077	+	0.382916i	−0.00983779	+	0.0170396i
$506$	−27.4499			−1.22030
$507$	−1.93957	−	3.84769i	−0.0861392	−	0.170882i
$508$	−39.2239			−1.74028
$509$	14.6010	−	25.2896i	0.647176	−	1.12094i	−0.336618	−	0.941641i	$-0.609283\pi$
$509$	14.6010	−	25.2896i	0.647176	−	1.12094i	0.983794	−	0.179301i	$-0.0573835\pi$
$510$	0.0187261	−	0.0324345i	0.000829204	−	0.00143622i
$511$	−0.515183	−	0.892322i	−0.0227903	−	0.0394740i
$512$	−36.5775			−1.61651
$513$	6.42154	+	11.1224i	0.283518	+	0.491067i
$514$	24.7888	+	42.9355i	1.09339	+	1.89380i
$515$	0.120763			0.00532145
$516$	−1.65083	−	2.85932i	−0.0726737	−	0.125874i
$517$	7.34928	−	12.7293i	0.323221	−	0.559835i
$518$	−6.98187	+	12.0930i	−0.306766	+	0.531334i
$519$	−5.92447			−0.260055
$520$	−0.731337	+	0.395037i	−0.0320713	+	0.0173235i
$521$	−9.79007			−0.428911			−0.214455	−	0.976734i	$-0.568798\pi$
$521$	−9.79007			−0.428911			−0.214455	+	0.976734i	$0.568798\pi$
$522$	29.1675	−	50.5195i	1.27663	−	2.21118i
$523$	−20.5580	+	35.6076i	−0.898940	+	1.55701i	−0.0700891	+	0.997541i	$0.522328\pi$
$523$	−20.5580	+	35.6076i	−0.898940	+	1.55701i	−0.828851	+	0.559469i	$0.811005\pi$
$524$	−32.4347	−	56.1785i	−1.41692	−	2.45417i
$525$	−1.49035			−0.0650440
$526$	14.8735	+	25.7616i	0.648515	+	1.12326i
$527$	−0.475554	−	0.823683i	−0.0207154	−	0.0358802i
$528$	2.04053			0.0888029
$529$	−10.7513	−	18.6219i	−0.467449	−	0.809646i
$530$	−0.427041	+	0.739656i	−0.0185495	+	0.0321286i
$531$	−8.99581	+	15.5812i	−0.390385	+	0.676167i
$532$	23.3224			1.01115
$533$	0.126282	−	4.45418i	0.00546989	−	0.192932i
$534$	2.62046			0.113398
$535$	0.0530156	−	0.0918257i	0.00229206	−	0.00396997i
$536$	31.6819	−	54.8747i	1.36845	−	2.37023i
$537$	2.98557	+	5.17117i	0.128837	+	0.223152i
$538$	64.5549			2.78316
$539$	−5.22557	−	9.05095i	−0.225081	−	0.389852i
$540$	0.187492	+	0.324746i	0.00806837	+	0.0139748i
$541$	−19.5243			−0.839415			−0.419708	−	0.907659i	$-0.637867\pi$
$541$	−19.5243			−0.839415			−0.419708	+	0.907659i	$0.637867\pi$
$542$	5.23716	+	9.07102i	0.224955	+	0.389634i
$543$	2.59885	−	4.50134i	0.111527	−	0.193171i
$544$	−0.271730	+	0.470650i	−0.0116503	+	0.0201790i
$545$	−0.591129			−0.0253212
$546$	−0.0742688	+	2.61958i	−0.00317841	+	0.112108i
$547$	23.0264			0.984538			0.492269	−	0.870443i	$-0.336168\pi$
$547$	23.0264			0.984538			0.492269	+	0.870443i	$0.336168\pi$
$548$	−19.9098	+	34.4847i	−0.850504	+	1.47312i
$549$	−12.4419	+	21.5499i	−0.531006	+	0.919729i
$550$	−10.2821	−	17.8091i	−0.438429	−	0.759382i
$551$	−54.4777			−2.32083
$552$	5.22893	+	9.05677i	0.222558	+	0.385482i
$553$	−1.67969	−	2.90930i	−0.0714276	−	0.123716i
$554$	−18.2602			−0.775803
$555$	0.0514393	+	0.0890956i	0.00218348	+	0.00378190i
$556$	−22.1077	+	38.2917i	−0.937576	+	1.62393i
$557$	0.390375	−	0.676149i	0.0165407	−	0.0286494i	−0.857637	−	0.514256i	$-0.828068\pi$
$557$	0.390375	−	0.676149i	0.0165407	−	0.0286494i	0.874177	+	0.485607i	$0.161401\pi$
$558$	7.04418			0.298204
$559$	7.76099	+	4.77907i	0.328255	+	0.202133i
$560$	0.159918			0.00675777
$561$	0.266108	−	0.460913i	0.0112351	−	0.0194598i
$562$	−18.8910	+	32.7201i	−0.796867	+	1.38021i
$563$	13.7712	+	23.8525i	0.580389	+	1.00526i	0.995433	+	0.0954617i	$0.0304328\pi$
$563$	13.7712	+	23.8525i	0.580389	+	1.00526i	−0.415044	+	0.909801i	$0.636234\pi$
$564$	−11.3714			−0.478823
$565$	0.299969	+	0.519561i	0.0126198	+	0.0218581i
$566$	19.9838	+	34.6130i	0.839982	+	1.45489i
$567$	−7.21861			−0.303153
$568$	25.2947	+	43.8118i	1.06134	+	1.83830i
$569$	−3.53812	+	6.12820i	−0.148326	+	0.256907i	−0.930609	−	0.366016i	$-0.880722\pi$
$569$	−3.53812	+	6.12820i	−0.148326	+	0.256907i	0.782283	+	0.622923i	$0.214055\pi$
$570$	0.129520	−	0.224336i	0.00542500	−	0.00939638i
$571$	37.4320			1.56648			0.783240	−	0.621719i	$-0.213566\pi$
$571$	37.4320			1.56648			0.783240	+	0.621719i	$0.213566\pi$
$572$	−21.1041	+	11.3995i	−0.882406	+	0.476638i
$573$	−3.76133			−0.157132
$574$	−1.35504	+	2.34700i	−0.0565584	+	0.0979619i
$575$	16.6697	−	28.8727i	0.695173	−	1.20407i
$576$	−12.5516	−	21.7400i	−0.522984	−	0.905835i
$577$	44.6828			1.86017			0.930085	−	0.367345i	$-0.119733\pi$
$577$	44.6828			1.86017			0.930085	+	0.367345i	$0.119733\pi$
$578$	19.6148	+	33.9738i	0.815867	+	1.41312i
$579$	−3.07082	−	5.31882i	−0.127619	−	0.221043i
$580$	−1.59061			−0.0660463
$581$	−1.83749	−	3.18263i	−0.0762319	−	0.132038i
$582$	3.98407	−	6.90061i	0.165145	−	0.286040i
$583$	−6.06850	+	10.5109i	−0.251331	+	0.435319i
$584$	−5.41649			−0.224136
$585$	−0.432505	−	0.266328i	−0.0178819	−	0.0110113i
$586$	23.2781			0.961608
$587$	17.2417	−	29.8635i	0.711642	−	1.23260i	−0.252598	−	0.967571i	$-0.581285\pi$
$587$	17.2417	−	29.8635i	0.711642	−	1.23260i	0.964240	−	0.265029i	$-0.0853816\pi$
$588$	−4.04271	+	7.00219i	−0.166719	+	0.288765i
$589$	−3.28920	−	5.69706i	−0.135529	−	0.234743i
$590$	0.739563			0.0304473
$591$	3.31655	+	5.74443i	0.136425	+	0.236294i
$592$	11.6103	+	20.1097i	0.477182	+	0.826504i
$593$	22.9831			0.943804			0.471902	−	0.881651i	$-0.343568\pi$
$593$	22.9831			0.943804			0.471902	+	0.881651i	$0.343568\pi$
$594$	4.01667	+	6.95707i	0.164806	+	0.285452i
$595$	0.0208551	−	0.0361220i	0.000854974	−	0.00148086i
$596$	−21.2965	+	36.8866i	−0.872338	+	1.51093i
$597$	2.17034			0.0888261
$598$	−49.9189	−	30.7391i	−2.04134	−	1.25702i
$599$	8.62966			0.352598			0.176299	−	0.984337i	$-0.443587\pi$
$599$	8.62966			0.352598			0.176299	+	0.984337i	$0.443587\pi$
$600$	−3.91727	+	6.78491i	−0.159922	+	0.276993i
$601$	3.27015	−	5.66406i	0.133392	−	0.231042i	−0.791590	−	0.611053i	$-0.790746\pi$
$601$	3.27015	−	5.66406i	0.133392	−	0.231042i	0.924982	+	0.380011i	$0.124080\pi$
$602$	−2.77165	−	4.80064i	−0.112964	−	0.195660i
$603$	38.7198			1.57679
$604$	31.9456	+	55.3314i	1.29985	+	2.25140i
$605$	−0.198623	−	0.344026i	−0.00807519	−	0.0139866i
$606$	7.32818			0.297687
$607$	17.5393	+	30.3789i	0.711896	+	1.23304i	0.964144	+	0.265378i	$0.0854967\pi$
$607$	17.5393	+	30.3789i	0.711896	+	1.23304i	−0.252248	+	0.967663i	$0.581170\pi$
$608$	−1.87944	+	3.25529i	−0.0762214	+	0.132019i
$609$	−1.23479	+	2.13871i	−0.0500361	+	0.0866650i
$610$	1.02287			0.0414148
$611$	27.6197	−	14.9190i	1.11737	−	0.603556i
$612$	10.8318			0.437849
$613$	23.4335	−	40.5880i	0.946470	−	1.63933i	0.193690	−	0.981063i	$-0.437954\pi$
$613$	23.4335	−	40.5880i	0.946470	−	1.63933i	0.752780	−	0.658272i	$-0.228712\pi$
$614$	−15.2780	+	26.4624i	−0.616572	+	1.06793i
$615$	0.00998335	+	0.0172917i	0.000402567	+	0.000697267i
$616$	7.18393			0.289449
$617$	1.15451	+	1.99967i	0.0464789	+	0.0805038i	0.888329	−	0.459208i	$-0.151867\pi$
$617$	1.15451	+	1.99967i	0.0464789	+	0.0805038i	−0.841850	+	0.539712i	$0.818533\pi$
$618$	−1.00075	−	1.73335i	−0.0402562	−	0.0697257i
$619$	−33.0883			−1.32993			−0.664966	−	0.746873i	$-0.731554\pi$
$619$	−33.0883			−1.32993			−0.664966	+	0.746873i	$0.731554\pi$
$620$	−0.0960360	−	0.166339i	−0.00385690	−	0.00668034i
$621$	−6.51196	+	11.2790i	−0.261316	+	0.452613i
$622$	−12.1548	+	21.0528i	−0.487364	+	0.844139i
$623$	2.91839			0.116923
$624$	3.71081	+	2.28505i	0.148551	+	0.0914750i
$625$	24.9644			0.998575
$626$	26.7574	−	46.3452i	1.06944	−	1.85233i
$627$	1.84056	−	3.18794i	0.0735048	−	0.127314i
$628$	20.2994	+	35.1596i	0.810035	+	1.40302i
$629$	6.05647			0.241487
$630$	0.154459	+	0.267530i	0.00615378	+	0.0106587i
$631$	9.33990	+	16.1772i	0.371816	+	0.644004i	0.989845	−	0.142151i	$-0.0454020\pi$
$631$	9.33990	+	16.1772i	0.371816	+	0.644004i	−0.618029	+	0.786155i	$0.712069\pi$
$632$	−17.6598			−0.702468
$633$	1.11822	+	1.93682i	0.0444454	+	0.0769817i
$634$	40.5440	−	70.2243i	1.61021	−	2.78896i
$635$	−0.242595	+	0.420186i	−0.00962707	+	0.0166746i
$636$	9.38968			0.372325
$637$	0.632556	−	22.3113i	0.0250628	−	0.884006i
$638$	−34.0758			−1.34907
$639$	−15.4569	+	26.7721i	−0.611465	+	1.05909i
$640$	−0.488095	+	0.845405i	−0.0192937	+	0.0334176i
$641$	22.7092	+	39.3335i	0.896961	+	1.55358i	0.831359	+	0.555736i	$0.187563\pi$
$641$	22.7092	+	39.3335i	0.896961	+	1.55358i	0.0656020	+	0.997846i	$0.479103\pi$
$642$	−1.75734			−0.0693568
$643$	−0.541666	−	0.938194i	−0.0213612	−	0.0369987i	0.855147	−	0.518385i	$-0.173467\pi$
$643$	−0.541666	−	0.938194i	−0.0213612	−	0.0369987i	−0.876508	+	0.481387i	$0.840133\pi$
$644$	11.8254	+	20.4822i	0.465985	+	0.807110i
$645$	−0.0408406			−0.00160810
$646$	−7.62486	−	13.2066i	−0.299996	−	0.519608i
$647$	7.08000	−	12.2629i	0.278344	−	0.482105i	−0.692630	−	0.721293i	$-0.743548\pi$
$647$	7.08000	−	12.2629i	0.278344	−	0.482105i	0.970973	+	0.239188i	$0.0768813\pi$
$648$	−18.9736	+	32.8633i	−0.745355	+	1.29099i
$649$	10.5096			0.412539
$650$	1.24465	−	43.9008i	0.0488191	−	1.72193i
$651$	−0.298211			−0.0116878
$652$	−3.38845	+	5.86896i	−0.132702	+	0.229846i
$653$	−24.2127	+	41.9376i	−0.947517	+	1.64115i	−0.196884	+	0.980427i	$0.563082\pi$
$653$	−24.2127	+	41.9376i	−0.947517	+	1.64115i	−0.750632	+	0.660720i	$0.770251\pi$
$654$	4.89863	+	8.48468i	0.191552	+	0.331777i
$655$	−0.802416			−0.0313530
$656$	2.25334	+	3.90289i	0.0879780	+	0.152382i
$657$	−1.65493	−	2.86642i	−0.0645650	−	0.111830i
$658$	−19.0920			−0.744283
$659$	−10.5264	−	18.2322i	−0.410049	−	0.710226i	0.584845	−	0.811145i	$-0.301155\pi$
$659$	−10.5264	−	18.2322i	−0.410049	−	0.710226i	−0.994895	+	0.100918i	$0.967822\pi$
$660$	0.0537394	−	0.0930794i	0.00209180	−	0.00362311i
$661$	−9.27614	+	16.0667i	−0.360800	+	0.624924i	−0.988093	−	0.153860i	$-0.950830\pi$
$661$	−9.27614	+	16.0667i	−0.360800	+	0.624924i	0.627293	+	0.778783i	$0.284163\pi$
$662$	−70.3308			−2.73348
$663$	1.00007	−	0.540197i	0.0388396	−	0.0209795i
$664$	−19.3189			−0.749717
$665$	0.144246	−	0.249841i	0.00559360	−	0.00968841i
$666$	−22.4280	+	38.8464i	−0.869067	+	1.50527i
$667$	−27.6224	−	47.8434i	−1.06954	−	1.85250i
$668$	−2.24635			−0.0869139
$669$	1.65099	+	2.85959i	0.0638308	+	0.110558i
$670$	−0.795809	−	1.37838i	−0.0307448	−	0.0532515i
$671$	14.5356			0.561140
$672$	0.0851985	+	0.147568i	0.00328660	+	0.00569256i
$673$	3.92318	−	6.79516i	0.151228	−	0.261934i	−0.780451	−	0.625216i	$-0.785011\pi$
$673$	3.92318	−	6.79516i	0.151228	−	0.261934i	0.931679	+	0.363282i	$0.118344\pi$
$674$	−0.735241	+	1.27348i	−0.0283204	+	0.0490524i
$675$	−9.75691			−0.375544
$676$	−51.1443	−	2.90235i	−1.96709	−	0.111629i
$677$	−24.5015			−0.941667			−0.470834	−	0.882222i	$-0.656047\pi$
$677$	−24.5015			−0.941667			−0.470834	+	0.882222i	$0.656047\pi$
$678$	4.97163	−	8.61112i	0.190934	−	0.330708i
$679$	4.43703	−	7.68516i	0.170277	−	0.294929i
$680$	−0.109632	−	0.189889i	−0.00420420	−	0.00728189i
$681$	3.22599			0.123620
$682$	−2.05739	−	3.56351i	−0.0787817	−	0.136454i
$683$	−11.1171	−	19.2554i	−0.425383	−	0.736786i	0.571073	−	0.820899i	$-0.306527\pi$
$683$	−11.1171	−	19.2554i	−0.425383	−	0.736786i	−0.996456	+	0.0841139i	$0.973194\pi$
$684$	74.9188			2.86459
$685$	0.246278	+	0.426567i	0.00940982	+	0.0162983i
$686$	−14.4625	+	25.0498i	−0.552182	+	0.956407i
$687$	−3.03788	+	5.26176i	−0.115902	+	0.200749i
$688$	−9.21811			−0.351437
$689$	−22.8063	+	12.3190i	−0.868851	+	0.469316i
$690$	0.262688			0.0100004
$691$	−24.3794	+	42.2264i	−0.927437	+	1.60637i	−0.139844	+	0.990174i	$0.544660\pi$
$691$	−24.3794	+	42.2264i	−0.927437	+	1.60637i	−0.787593	+	0.616195i	$0.788673\pi$
$692$	−35.2166	+	60.9970i	−1.33874	+	2.31876i
$693$	2.19495	+	3.80176i	0.0833792	+	0.144417i
$694$	77.9497			2.95893
$695$	0.273466	+	0.473658i	0.0103732	+	0.0179669i
$696$	6.49110	+	11.2429i	0.246045	+	0.426162i
$697$	1.17544			0.0445229
$698$	1.84144	+	3.18946i	0.0696995	+	0.120723i
$699$	−0.943461	+	1.63412i	−0.0356850	+	0.0618082i
$700$	−8.85902	+	15.3443i	−0.334839	+	0.579959i
$701$	−8.75488			−0.330667			−0.165334	−	0.986238i	$-0.552870\pi$
$701$	−8.75488			−0.330667			−0.165334	+	0.986238i	$0.552870\pi$
$702$	−0.486219	+	17.1497i	−0.0183511	+	0.647275i
$703$	41.8900			1.57991
$704$	−7.33190	+	12.6992i	−0.276331	+	0.478620i
$705$	−0.0703306	+	0.121816i	−0.00264880	+	0.00458786i
$706$	−10.6747	−	18.4891i	−0.401748	−	0.695847i
$707$	8.16134			0.306939
$708$	−4.06534	−	7.04138i	−0.152785	−	0.264631i
$709$	16.7907	+	29.0823i	0.630586	+	1.09221i	0.987432	+	0.158044i	$0.0505189\pi$
$709$	16.7907	+	29.0823i	0.630586	+	1.09221i	−0.356846	+	0.934163i	$0.616148\pi$
$710$	1.27074			0.0476901
$711$	−5.39569	−	9.34561i	−0.202354	−	0.350488i
$712$	7.67078	−	13.2862i	0.287475	−	0.497921i
$713$	3.33552	−	5.77728i	0.124916	−	0.216361i
$714$	−0.691297			−0.0258711
$715$	−0.00840851	+	0.296582i	−0.000314460	+	0.0110915i
$716$	70.9883			2.65296
$717$	2.88586	−	4.99846i	0.107775	−	0.186671i
$718$	18.8893	−	32.7172i	0.704942	−	1.22100i
$719$	−20.2430	−	35.0619i	−0.754936	−	1.30759i	−0.945406	−	0.325894i	$-0.894335\pi$
$719$	−20.2430	−	35.0619i	−0.754936	−	1.30759i	0.190471	−	0.981693i	$-0.438999\pi$
$720$	0.513707			0.0191447
$721$	−1.11453	−	1.93042i	−0.0415073	−	0.0718927i
$722$	−29.5834	−	51.2399i	−1.10098	−	1.90695i
$723$	−6.99800			−0.260259
$724$	−30.8966	−	53.5144i	−1.14826	−	1.98885i
$725$	20.6934	−	35.8420i	0.768534	−	1.33114i
$726$	−3.29195	+	5.70183i	−0.122176	+	0.211615i
$727$	−36.8726			−1.36753			−0.683765	−	0.729703i	$-0.739658\pi$
$727$	−36.8726			−1.36753			−0.683765	+	0.729703i	$0.739658\pi$
$728$	13.0643	+	8.04476i	0.484196	+	0.298159i
$729$	−21.2472			−0.786933
$730$	−0.0680275	+	0.117827i	−0.00251781	+	0.00436098i
$731$	−1.20214	+	2.08217i	−0.0444629	+	0.0770120i
$732$	−5.62266	−	9.73873i	−0.207820	−	0.359954i
$733$	−49.6304			−1.83314			−0.916571	−	0.399872i	$-0.869055\pi$
$733$	−49.6304			−1.83314			−0.916571	+	0.399872i	$0.869055\pi$
$734$	−24.0856	−	41.7175i	−0.889017	−	1.53982i
$735$	0.0500073	+	0.0866151i	0.00184455	+	0.00319485i
$736$	−3.81181			−0.140505
$737$	−11.3089	−	19.5876i	−0.416569	−	0.721519i
$738$	−4.35283	+	7.53931i	−0.160230	+	0.277526i
$739$	23.2346	−	40.2436i	0.854700	−	1.48038i	−0.0222234	−	0.999753i	$-0.507075\pi$
$739$	23.2346	−	40.2436i	0.854700	−	1.48038i	0.876923	−	0.480630i	$-0.159592\pi$
$740$	1.22308			0.0449612
$741$	6.91708	−	3.73631i	0.254105	−	0.137257i
$742$	15.7648			0.578743
$743$	13.3068	−	23.0481i	0.488180	−	0.845553i	−0.511727	−	0.859148i	$-0.670994\pi$
$743$	13.3068	−	23.0481i	0.488180	−	0.845553i	0.999908	+	0.0135948i	$0.00432749\pi$
$744$	−0.783826	+	1.35763i	−0.0287365	+	0.0497730i
$745$	0.263432	+	0.456277i	0.00965139	+	0.0167167i
$746$	−10.1074			−0.370058
$747$	−5.90260	−	10.2236i	−0.215965	−	0.374062i
$748$	−3.16364	−	5.47958i	−0.115674	−	0.200353i
$749$	−1.95714			−0.0715123
$750$	0.196840	+	0.340937i	0.00718759	+	0.0124493i
$751$	2.27698	−	3.94384i	0.0830880	−	0.143913i	−0.821487	−	0.570227i	$-0.806855\pi$
$751$	2.27698	−	3.94384i	0.0830880	−	0.143913i	0.904575	+	0.426315i	$0.140188\pi$
$752$	−15.8743	+	27.4951i	−0.578876	+	1.00264i
$753$	−1.69513			−0.0617739
$754$	−61.9684	−	38.1590i	−2.25676	−	1.38967i
$755$	0.790316			0.0287626
$756$	3.46075	−	5.99420i	0.125866	−	0.218007i
$757$	−7.10637	+	12.3086i	−0.258285	+	0.447363i	−0.965783	−	0.259353i	$-0.916491\pi$
$757$	−7.10637	+	12.3086i	−0.258285	+	0.447363i	0.707497	+	0.706716i	$0.249824\pi$
$758$	1.15381	+	1.99845i	0.0419081	+	0.0725870i
$759$	3.73295			0.135497
$760$	−0.758279	−	1.31338i	−0.0275057	−	0.0476412i
$761$	−23.8019	−	41.2261i	−0.862819	−	1.49445i	−0.869197	−	0.494466i	$-0.835364\pi$
$761$	−23.8019	−	41.2261i	−0.862819	−	1.49445i	0.00637822	−	0.999980i	$-0.497970\pi$
$762$	8.04144			0.291311
$763$	5.45557	+	9.44932i	0.197505	+	0.342088i
$764$	−22.3584	+	38.7259i	−0.808898	+	1.40105i
$765$	0.0669931	−	0.116035i	0.00242214	−	0.00419527i
$766$	−36.1947			−1.30777
$767$	19.1123	+	11.7690i	0.690103	+	0.424953i
$768$	10.4213			0.376047
$769$	10.2169	−	17.6962i	0.368431	−	0.638142i	−0.620889	−	0.783898i	$-0.713228\pi$
$769$	10.2169	−	17.6962i	0.368431	−	0.638142i	0.989321	+	0.145756i	$0.0465616\pi$
$770$	0.0902255	−	0.156275i	0.00325150	−	0.00563177i
$771$	−3.37106	−	5.83885i	−0.121406	−	0.210281i
$772$	−73.0152			−2.62788
$773$	14.5685	+	25.2334i	0.523993	+	0.907582i	0.999610	+	0.0279296i	$0.00889143\pi$
$773$	14.5685	+	25.2334i	0.523993	+	0.907582i	−0.475617	+	0.879652i	$0.657775\pi$
$774$	−8.90342	−	15.4212i	−0.320027	−	0.554303i
$775$	4.99762			0.179520
$776$	−23.3248	−	40.3998i	−0.837313	−	1.45027i
$777$	0.949475	−	1.64454i	0.0340622	−	0.0589975i
$778$	19.1712	−	33.2054i	0.687319	−	1.19047i
$779$	8.13002			0.291288
$780$	0.201960	−	0.109090i	0.00723134	−	0.00390606i
$781$	18.0580			0.646165
$782$	7.73222	−	13.3926i	0.276504	−	0.478918i
$783$	−8.08383	+	14.0016i	−0.288893	+	0.500377i
$784$	11.2871	+	19.5499i	0.403111	+	0.698209i
$785$	0.502197			0.0179242
$786$	6.64955	+	11.5174i	0.237182	+	0.410811i
$787$	−8.85632	−	15.3396i	−0.315694	−	0.546797i	0.663891	−	0.747829i	$-0.268904\pi$
$787$	−8.85632	−	15.3396i	−0.315694	−	0.546797i	−0.979585	+	0.201032i	$0.935571\pi$
$788$	78.8578			2.80919
$789$	−2.02267	−	3.50336i	−0.0720089	−	0.124723i
$790$	−0.221795	+	0.384161i	−0.00789112	+	0.0136678i
$791$	5.53687	−	9.59013i	0.196868	−	0.340986i
$792$	23.0771			0.820008
$793$	26.4336	+	16.2773i	0.938686	+	0.578025i
$794$	−2.72063			−0.0965516
$795$	0.0580739	−	0.100587i	0.00205967	−	0.00356745i
$796$	12.9011	−	22.3453i	0.457267	−	0.792010i
$797$	−26.8089	−	46.4343i	−0.949619	−	1.64479i	−0.746228	−	0.665690i	$-0.768137\pi$
$797$	−26.8089	−	46.4343i	−0.949619	−	1.64479i	−0.203390	−	0.979098i	$-0.565196\pi$
$798$	−4.78140			−0.169260
$799$	4.14036	+	7.17132i	0.146476	+	0.253703i
$800$	−1.42782	−	2.47305i	−0.0504809	−	0.0874355i
$801$	9.37479			0.331242
$802$	33.2552	+	57.5996i	1.17428	+	2.03391i
$803$	−0.966711	+	1.67439i	−0.0341145	+	0.0590880i
$804$	−8.74904	+	15.1538i	−0.308555	+	0.534432i
$805$	0.292553			0.0103112
$806$	0.249048	−	8.78434i	0.00877234	−	0.309415i
$807$	−8.77891			−0.309032
$808$	21.4515	−	37.1551i	0.754662	−	1.30711i
$809$	16.9377	−	29.3370i	0.595500	−	1.03144i	−0.397977	−	0.917396i	$-0.630287\pi$
$809$	16.9377	−	29.3370i	0.595500	−	1.03144i	0.993476	−	0.114040i	$-0.0363792\pi$
$810$	0.476593	+	0.825483i	0.0167458	+	0.0290045i
$811$	−26.0448			−0.914555			−0.457277	−	0.889324i	$-0.651175\pi$
$811$	−26.0448			−0.914555			−0.457277	+	0.889324i	$0.651175\pi$
$812$	14.6798	+	25.4262i	0.515160	+	0.892284i
$813$	−0.712208	−	1.23358i	−0.0249782	−	0.0432636i
$814$	26.2022			0.918386
$815$	0.0419142	+	0.0725975i	0.00146819	+	0.00254298i
$816$	−0.574788	+	0.995562i	−0.0201216	+	0.0348516i
$817$	−8.31471	+	14.4015i	−0.290895	+	0.503845i
$818$	10.4026			0.363718
$819$	−0.265699	+	9.37165i	−0.00928427	+	0.327472i
$820$	0.237375			0.00828949
$821$	13.4635	−	23.3195i	0.469880	−	0.813855i	−0.529527	−	0.848293i	$-0.677631\pi$
$821$	13.4635	−	23.3195i	0.469880	−	0.813855i	0.999407	+	0.0344376i	$0.0109640\pi$
$822$	4.08178	−	7.06985i	0.142368	−	0.246589i
$823$	20.8480	+	36.1099i	0.726717	+	1.25871i	0.958263	+	0.285886i	$0.0922880\pi$
$823$	20.8480	+	36.1099i	0.726717	+	1.25871i	−0.231547	+	0.972824i	$0.574379\pi$
$824$	−11.7179			−0.408211
$825$	1.39827	+	2.42188i	0.0486817	+	0.0843191i
$826$	−6.82548	−	11.8221i	−0.237489	−	0.411343i
$827$	−28.2054			−0.980799			−0.490400	−	0.871498i	$-0.663149\pi$
$827$	−28.2054			−0.980799			−0.490400	+	0.871498i	$0.663149\pi$
$828$	37.9869	+	65.7952i	1.32014	+	2.28654i
$829$	−18.4519	+	31.9597i	−0.640862	+	1.11001i	0.344378	+	0.938831i	$0.388090\pi$
$829$	−18.4519	+	31.9597i	−0.640862	+	1.11001i	−0.985241	+	0.171175i	$0.945244\pi$
$830$	−0.242632	+	0.420251i	−0.00842189	+	0.0145871i
$831$	2.48324			0.0861425
$832$	−27.5543	+	14.8837i	−0.955275	+	0.515999i
$833$	5.88786			0.204002
$834$	4.53239	−	7.85032i	0.156944	−	0.271834i
$835$	−0.0138934	+	0.0240640i	−0.000480800	+	0.000832770i
$836$	−21.8815	−	37.9000i	−0.756789	−	1.31080i
$837$	−1.95231			−0.0674817
$838$	−39.8893	−	69.0904i	−1.37795	−	2.38669i
$839$	28.6941	+	49.6997i	0.990631	+	1.71582i	0.613583	+	0.789630i	$0.289728\pi$
$839$	28.6941	+	49.6997i	0.990631	+	1.71582i	0.377048	+	0.926194i	$0.376939\pi$
$840$	−0.0687483			−0.00237204
$841$	−19.7900	−	34.2772i	−0.682412	−	1.18197i
$842$	−29.9229	+	51.8279i	−1.03121	+	1.78611i
$843$	2.56901	−	4.44965i	0.0884813	−	0.153254i
$844$	26.5881			0.915200
$845$	−0.347412	+	0.529932i	−0.0119513	+	0.0182302i
$846$	−61.3295			−2.10855
$847$	−3.66622	+	6.35008i	−0.125973	+	0.218191i
$848$	13.1078	−	22.7034i	0.450125	−	0.779639i
$849$	−2.71763	−	4.70707i	−0.0932687	−	0.161546i
$850$	11.5852			0.397370
$851$	21.2399	+	36.7886i	0.728096	+	1.26110i
$852$	−6.98520	−	12.0987i	−0.239309	−	0.414495i
$853$	5.54919			0.190001			0.0950003	−	0.995477i	$-0.469715\pi$
$853$	5.54919			0.190001			0.0950003	+	0.995477i	$0.469715\pi$
$854$	−9.44014	−	16.3508i	−0.323035	−	0.559513i
$855$	0.463363	−	0.802568i	0.0158467	−	0.0274472i
$856$	−5.14421	+	8.91003i	−0.175825	+	0.304538i
$857$	8.76743			0.299490			0.149745	−	0.988725i	$-0.452155\pi$
$857$	8.76743			0.299490			0.149745	+	0.988725i	$0.452155\pi$
$858$	4.32663	−	2.33706i	0.147709	−	0.0797859i
$859$	−45.2067			−1.54243			−0.771216	−	0.636573i	$-0.780351\pi$
$859$	−45.2067			−1.54243			−0.771216	+	0.636573i	$0.780351\pi$
$860$	−0.242768	+	0.420486i	−0.00827831	+	0.0143384i
$861$	0.184274	−	0.319172i	0.00628004	−	0.0108774i
$862$	16.9311	+	29.3255i	0.576674	+	0.998829i
$863$	−10.2601			−0.349257			−0.174629	−	0.984634i	$-0.555872\pi$
$863$	−10.2601			−0.349257			−0.174629	+	0.984634i	$0.555872\pi$
$864$	0.557773	+	0.966090i	0.0189758	+	0.0328671i
$865$	0.435620	+	0.754516i	0.0148115	+	0.0256543i
$866$	−45.4345			−1.54393
$867$	−2.66744	−	4.62014i	−0.0905911	−	0.156908i
$868$	−1.77265	+	3.07031i	−0.0601675	+	0.104213i
$869$	−3.15184	+	5.45915i	−0.106919	+	0.185189i
$870$	0.326096			0.0110557
$871$	1.36895	−	48.2850i	0.0463850	−	1.63607i
$872$	57.3583			1.94240
$873$	14.2531	−	24.6872i	0.482396	−	0.835534i
$874$	53.4805	−	92.6309i	1.80900	−	3.13329i
$875$	0.219219	+	0.379699i	0.00741097	+	0.0128362i
$876$	1.49577			0.0505375
$877$	21.9933	+	38.0935i	0.742662	+	1.28633i	0.951279	+	0.308330i	$0.0997702\pi$
$877$	21.9933	+	38.0935i	0.742662	+	1.28633i	−0.208618	+	0.977997i	$0.566896\pi$
$878$	−13.6235	−	23.5966i	−0.459770	−	0.796346i
$879$	−3.16562			−0.106774
$880$	−0.150038	−	0.259874i	−0.00505780	−	0.00876036i
$881$	−6.94275	+	12.0252i	−0.233907	+	0.405139i	−0.958955	−	0.283560i	$-0.908485\pi$
$881$	−6.94275	+	12.0252i	−0.233907	+	0.405139i	0.725047	+	0.688699i	$0.241818\pi$
$882$	−21.8036	+	37.7649i	−0.734165	+	1.27161i
$883$	−27.5994			−0.928792			−0.464396	−	0.885628i	$-0.653729\pi$
$883$	−27.5994			−0.928792			−0.464396	+	0.885628i	$0.653729\pi$
$884$	0.382959	−	13.5076i	0.0128803	−	0.454310i
$885$	−0.100574			−0.00338077
$886$	−25.2724	+	43.7731i	−0.849044	+	1.47059i
$887$	11.1077	−	19.2390i	0.372959	−	0.645984i	−0.617060	−	0.786916i	$-0.711677\pi$
$887$	11.1077	−	19.2390i	0.372959	−	0.645984i	0.990019	+	0.140932i	$0.0450099\pi$
$888$	−4.99126	−	8.64511i	−0.167496	−	0.290111i
$889$	8.95569			0.300364
$890$	−0.192680	−	0.333731i	−0.00645865	−	0.0111867i
$891$	6.77266	+	11.7306i	0.226893	+	0.392990i
$892$	39.2556			1.31438
$893$	28.6371	+	49.6010i	0.958305	+	1.65983i
$894$	4.36607	−	7.56226i	0.146023	−	0.252920i
$895$	0.439053	−	0.760462i	0.0146759	−	0.0254194i
$896$	18.0187			0.601961
$897$	6.78854	+	4.18026i	0.226663	+	0.139575i
$898$	−0.956220			−0.0319095
$899$	4.14065	−	7.17182i	0.138098	−	0.239193i
$900$	−28.4580	+	49.2907i	−0.948600	+	1.64302i
$901$	−3.41881	−	5.92155i	−0.113897	−	0.197276i
$902$	5.08532			0.169323
$903$	0.376921	+	0.652846i	0.0125431	+	0.0217254i
$904$	−29.1065	−	50.4140i	−0.968069	−	1.67674i
$905$	−0.764364			−0.0254083
$906$	−6.54928	−	11.3437i	−0.217585	−	0.376869i
$907$	26.3192	−	45.5861i	0.873914	−	1.51366i	0.0159979	−	0.999872i	$-0.494907\pi$
$907$	26.3192	−	45.5861i	0.873914	−	1.51366i	0.857916	−	0.513791i	$-0.171759\pi$
$908$	19.1762	−	33.2141i	0.636384	−	1.10225i
$909$	26.2168			0.869557
$910$	0.339081	−	0.183157i	0.0112404	−	0.00607159i
$911$	−2.71762			−0.0900389			−0.0450195	−	0.998986i	$-0.514335\pi$
$911$	−2.71762			−0.0900389			−0.0450195	+	0.998986i	$0.514335\pi$
$912$	−3.97556	+	6.88588i	−0.131644	+	0.228014i
$913$	−3.44795	+	5.97202i	−0.114110	+	0.197645i
$914$	40.6783	+	70.4570i	1.34552	+	2.33051i
$915$	−0.139102			−0.00459856
$916$	36.1160	+	62.5547i	1.19331	+	2.06687i
$917$	7.40556	+	12.8268i	0.244553	+	0.423578i
$918$	−4.52574			−0.149372
$919$	−0.738881	−	1.27978i	−0.0243734	−	0.0422160i	0.853581	−	0.520959i	$-0.174426\pi$
$919$	−0.738881	−	1.27978i	−0.0243734	−	0.0422160i	−0.877955	+	0.478743i	$0.841092\pi$
$920$	0.768956	−	1.33187i	0.0253517	−	0.0439105i
$921$	2.07768	−	3.59865i	0.0684620	−	0.118580i
$922$	−87.2307			−2.87279
$923$	32.8393	+	20.2218i	1.08092	+	0.665609i
$924$	−1.98386			−0.0652642
$925$	−15.9120	+	27.5603i	−0.523182	+	0.906178i
$926$	35.0578	−	60.7218i	1.15207	−	1.99544i
$927$	−3.58022	−	6.20113i	−0.117590	−	0.203672i
$928$	−4.73191			−0.155333
$929$	4.12628	+	7.14693i	0.135379	+	0.234483i	0.925742	−	0.378155i	$-0.123441\pi$
$929$	4.12628	+	7.14693i	0.135379	+	0.234483i	−0.790363	+	0.612639i	$0.790108\pi$
$930$	0.0196887	+	0.0341018i	0.000645618	+	0.00111824i
$931$	40.7238			1.33467
$932$	11.2164	+	19.4273i	0.367405	+	0.636364i
$933$	1.65295	−	2.86300i	0.0541152	−	0.0937303i
$934$	0.142670	−	0.247112i	0.00466830	−	0.00808574i
$935$	−0.0782667			−0.00255959
$936$	41.9668	+	25.8423i	1.37173	+	0.844683i
$937$	29.9258			0.977635			0.488817	−	0.872386i	$-0.337428\pi$
$937$	29.9258			0.977635			0.488817	+	0.872386i	$0.337428\pi$
$938$	−14.6892	+	25.4424i	−0.479618	+	0.830723i
$939$	−3.63878	+	6.30254i	−0.118747	+	0.205676i
$940$	0.836129	+	1.44822i	0.0272715	+	0.0472357i
$941$	19.7675			0.644402			0.322201	−	0.946671i	$-0.395577\pi$
$941$	19.7675			0.644402			0.322201	+	0.946671i	$0.395577\pi$
$942$	−4.16166	−	7.20821i	−0.135594	−	0.234856i
$943$	4.12225	+	7.13994i	0.134239	+	0.232508i
$944$	−22.7006			−0.738841
$945$	−0.0428086	−	0.0741466i	−0.00139256	−	0.00241199i
$946$	−5.20085	+	9.00813i	−0.169094	+	0.292880i
$947$	3.59548	−	6.22755i	0.116837	−	0.202368i	−0.801675	−	0.597760i	$-0.796058\pi$
$947$	3.59548	−	6.22755i	0.116837	−	0.202368i	0.918513	+	0.395392i	$0.129391\pi$
$948$	4.87679			0.158391
$949$	−3.63304	+	1.96241i	−0.117933	+	0.0637026i
$950$	80.1301			2.59976
$951$	−5.51364	+	9.54991i	−0.178792	+	0.309677i
$952$	−2.02361	+	3.50499i	−0.0655855	+	0.113597i
$953$	−5.93694	−	10.2831i	−0.192316	−	0.333102i	0.753701	−	0.657217i	$-0.228267\pi$
$953$	−5.93694	−	10.2831i	−0.192316	−	0.333102i	−0.946017	+	0.324116i	$0.894933\pi$
$954$	50.6414			1.63958
$955$	0.276567	+	0.479029i	0.00894951	+	0.0155010i
$956$	−34.3087	−	59.4244i	−1.10962	−	1.92192i
$957$	4.63401			0.149796
$958$	−26.9427	−	46.6662i	−0.870480	−	1.50772i
$959$	4.54584	−	7.87363i	0.146793	−	0.254253i
$960$	0.0701643	−	0.121528i	0.00226454	−	0.00392230i
$961$	1.00000			0.0322581
$962$	47.6499	+	29.3419i	1.53629	+	0.946021i
$963$	−6.28695			−0.202594
$964$	−41.5980	+	72.0499i	−1.33978	+	2.32057i
$965$	−0.451589	+	0.782176i	−0.0145372	+	0.0251791i
$966$	−2.42437	−	4.19912i	−0.0780027	−	0.135105i
$967$	−11.7075			−0.376486			−0.188243	−	0.982122i	$-0.560279\pi$
$967$	−11.7075			−0.376486			−0.188243	+	0.982122i	$0.560279\pi$
$968$	19.2728	+	33.3815i	0.619452	+	1.07292i
$969$	1.03691	+	1.79599i	0.0333105	+	0.0576955i
$970$	−1.17178			−0.0376236
$971$	−11.5808	−	20.0586i	−0.371647	−	0.643711i	0.618172	−	0.786043i	$-0.287873\pi$
$971$	−11.5808	−	20.0586i	−0.371647	−	0.643711i	−0.989819	+	0.142332i	$0.954540\pi$
$972$	16.7792	−	29.0625i	0.538194	−	0.932180i
$973$	5.04768	−	8.74284i	0.161821	−	0.280283i
$974$	3.33179			0.106757
$975$	−0.169261	+	5.97013i	−0.00542070	+	0.191197i
$976$	−31.3965			−1.00498
$977$	−7.62768	+	13.2115i	−0.244031	+	0.422674i	−0.961859	−	0.273547i	$-0.911803\pi$
$977$	−7.62768	+	13.2115i	−0.244031	+	0.422674i	0.717828	+	0.696221i	$0.245137\pi$
$978$	0.694678	−	1.20322i	0.0222134	−	0.0384747i
$979$	−2.73809	−	4.74252i	−0.0875099	−	0.151572i
$980$	1.18903			0.0379821
$981$	17.5250	+	30.3542i	0.559531	+	0.969136i
$982$	10.0889	+	17.4744i	0.321949	+	0.557632i
$983$	60.4366			1.92763			0.963814	−	0.266577i	$-0.0858928\pi$
$983$	60.4366			1.92763			0.963814	+	0.266577i	$0.0858928\pi$
$984$	−0.968703	−	1.67784i	−0.0308811	−	0.0534877i
$985$	0.487725	−	0.844764i	0.0155402	−	0.0269164i
$986$	9.59864	−	16.6253i	0.305683	−	0.529458i
$987$	2.59635			0.0826426
$988$	2.64877	−	93.4264i	0.0842685	−	2.97229i
$989$	−16.8636			−0.536231
$990$	0.289833	−	0.502006i	0.00921150	−	0.0159548i
$991$	−8.34254	+	14.4497i	−0.265010	+	0.459010i	−0.967566	−	0.252618i	$-0.918708\pi$
$991$	−8.34254	+	14.4497i	−0.265010	+	0.459010i	0.702557	+	0.711628i	$0.252042\pi$
$992$	−0.285699	−	0.494845i	−0.00907095	−	0.0157113i
$993$	9.56438			0.303516
$994$	−11.7278	−	20.3131i	−0.371982	−	0.644292i
$995$	−0.159583	−	0.276406i	−0.00505912	−	0.00876265i
$996$	5.33495			0.169044
$997$	−7.90466	−	13.6913i	−0.250343	−	0.433607i	0.713277	−	0.700882i	$-0.247210\pi$
$997$	−7.90466	−	13.6913i	−0.250343	−	0.433607i	−0.963620	+	0.267275i	$0.913877\pi$
$998$	−18.4376	+	31.9349i	−0.583633	+	1.01088i
$999$	6.21597	−	10.7664i	0.196665	−	0.340633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.b.373.2	yes	34
13.3	even	3	inner	403.2.f.b.94.2	✓	34
13.4	even	6		5239.2.a.n.1.2		17
13.9	even	3		5239.2.a.m.1.16		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.2	✓	34	13.3	even	3	inner
403.2.f.b.373.2	yes	34	1.1	even	1	trivial
5239.2.a.m.1.16		17	13.9	even	3
5239.2.a.n.1.2		17	13.4	even	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21866 + 2.11078i) q^{2} +(0.165727 - 0.287048i) q^{3} +(-1.97025 - 3.41258i) q^{4} -0.0487430 q^{5} +(0.403929 + 0.699625i) q^{6} +(0.449852 + 0.779167i) q^{7} +4.72962 q^{8} +(1.44507 + 2.50293i) q^{9} +O(q^{10})\)	\(q+(-1.21866 + 2.11078i) q^{2} +(0.165727 - 0.287048i) q^{3} +(-1.97025 - 3.41258i) q^{4} -0.0487430 q^{5} +(0.403929 + 0.699625i) q^{6} +(0.449852 + 0.779167i) q^{7} +4.72962 q^{8} +(1.44507 + 2.50293i) q^{9} +(0.0594010 - 0.102886i) q^{10} +(0.844123 - 1.46206i) q^{11} -1.30610 q^{12} +(3.17234 - 1.71356i) q^{13} -2.19286 q^{14} +(-0.00807803 + 0.0139916i) q^{15} +(-1.82329 + 3.15803i) q^{16} +(0.475554 + 0.823683i) q^{17} -7.04418 q^{18} +(3.28920 + 5.69706i) q^{19} +(0.0960360 + 0.166339i) q^{20} +0.298211 q^{21} +(2.05739 + 3.56351i) q^{22} +(-3.33552 + 5.77728i) q^{23} +(0.783826 - 1.35763i) q^{24} -4.99762 q^{25} +(-0.249048 + 8.78434i) q^{26} +1.95231 q^{27} +(1.77265 - 3.07031i) q^{28} +(-4.14065 + 7.17182i) q^{29} +(-0.0196887 - 0.0341018i) q^{30} -1.00000 q^{31} +(0.285699 + 0.494845i) q^{32} +(-0.279788 - 0.484607i) q^{33} -2.31815 q^{34} +(-0.0219271 - 0.0379789i) q^{35} +(5.69430 - 9.86282i) q^{36} +(3.18391 - 5.51469i) q^{37} -16.0336 q^{38} +(0.0338684 - 1.19459i) q^{39} -0.230536 q^{40} +(0.617932 - 1.07029i) q^{41} +(-0.363417 + 0.629456i) q^{42} +(1.26394 + 2.18921i) q^{43} -6.65254 q^{44} +(-0.0704370 - 0.122000i) q^{45} +(-8.12970 - 14.0811i) q^{46} +8.70641 q^{47} +(0.604336 + 1.04674i) q^{48} +(3.09527 - 5.36116i) q^{49} +(6.09039 - 10.5489i) q^{50} +0.315248 q^{51} +(-12.0980 - 7.44970i) q^{52} -7.18912 q^{53} +(-2.37920 + 4.12089i) q^{54} +(-0.0411451 + 0.0712653i) q^{55} +(2.12763 + 3.68517i) q^{56} +2.18044 q^{57} +(-10.0921 - 17.4800i) q^{58} +(3.11259 + 5.39116i) q^{59} +0.0636630 q^{60} +(4.30494 + 7.45637i) q^{61} +(1.21866 - 2.11078i) q^{62} +(-1.30014 + 2.25190i) q^{63} -8.68582 q^{64} +(-0.154629 + 0.0835240i) q^{65} +1.36386 q^{66} +(6.69862 - 11.6023i) q^{67} +(1.87392 - 3.24573i) q^{68} +(1.10557 + 1.91490i) q^{69} +0.106887 q^{70} +(5.34815 + 9.26327i) q^{71} +(6.83463 + 11.8379i) q^{72} -1.14523 q^{73} +(7.76018 + 13.4410i) q^{74} +(-0.828241 + 1.43456i) q^{75} +(12.9611 - 22.4493i) q^{76} +1.51892 q^{77} +(2.48025 + 1.52729i) q^{78} -3.73386 q^{79} +(0.0888724 - 0.153932i) q^{80} +(-4.01166 + 6.94839i) q^{81} +(1.50610 + 2.60863i) q^{82} -4.08465 q^{83} +(-0.587551 - 1.01767i) q^{84} +(-0.0231799 - 0.0401488i) q^{85} -6.16125 q^{86} +(1.37243 + 2.37713i) q^{87} +(3.99238 - 6.91501i) q^{88} +(1.62186 - 2.80914i) q^{89} +0.343354 q^{90} +(2.76223 + 1.70093i) q^{91} +26.2872 q^{92} +(-0.165727 + 0.287048i) q^{93} +(-10.6101 + 18.3773i) q^{94} +(-0.160325 - 0.277692i) q^{95} +0.189392 q^{96} +(-4.93165 - 8.54186i) q^{97} +(7.54414 + 13.0668i) q^{98} +4.87926 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

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