LMFDB - Embedded newform 403.2.r.a.218.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(218,403)]

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([5, 0]))

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

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

chi := DirichletCharacter("403.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.r (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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			218.11
Character	$\chi$	$=$	403.218
Dual form			403.2.r.a.342.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.697346 + 0.402613i) q^{2} +(0.727281 + 1.25969i) q^{3} +(-0.675806 + 1.17053i) q^{4} -3.57617i q^{5} +(-1.01433 - 0.585626i) q^{6} +(-1.02623 - 0.592496i) q^{7} -2.69880i q^{8} +(0.442123 - 0.765780i) q^{9} +O(q^{10})$	\(q+(-0.697346 + 0.402613i) q^{2} +(0.727281 + 1.25969i) q^{3} +(-0.675806 + 1.17053i) q^{4} -3.57617i q^{5} +(-1.01433 - 0.585626i) q^{6} +(-1.02623 - 0.592496i) q^{7} -2.69880i q^{8} +(0.442123 - 0.765780i) q^{9} +(1.43981 + 2.49383i) q^{10} +(-0.406760 + 0.234843i) q^{11} -1.96600 q^{12} +(0.820069 - 3.51105i) q^{13} +0.954187 q^{14} +(4.50487 - 2.60089i) q^{15} +(-0.265037 - 0.459058i) q^{16} +(1.22695 - 2.12513i) q^{17} +0.712018i q^{18} +(-6.07528 - 3.50756i) q^{19} +(4.18602 + 2.41680i) q^{20} -1.72365i q^{21} +(0.189102 - 0.327534i) q^{22} +(1.02566 + 1.77649i) q^{23} +(3.39965 - 1.96279i) q^{24} -7.78903 q^{25} +(0.841723 + 2.77859i) q^{26} +5.64988 q^{27} +(1.38707 - 0.800825i) q^{28} +(3.03735 + 5.26085i) q^{29} +(-2.09430 + 3.62744i) q^{30} -1.00000i q^{31} +(5.04411 + 2.91222i) q^{32} +(-0.591658 - 0.341594i) q^{33} +1.97594i q^{34} +(-2.11887 + 3.66999i) q^{35} +(0.597579 + 1.03504i) q^{36} +(7.16745 - 4.13813i) q^{37} +5.64876 q^{38} +(5.01925 - 1.52049i) q^{39} -9.65140 q^{40} +(6.15746 - 3.55501i) q^{41} +(0.693963 + 1.20198i) q^{42} +(-5.82479 + 10.0888i) q^{43} -0.634833i q^{44} +(-2.73856 - 1.58111i) q^{45} +(-1.43048 - 0.825887i) q^{46} +1.03509i q^{47} +(0.385514 - 0.667729i) q^{48} +(-2.79790 - 4.84610i) q^{49} +(5.43165 - 3.13596i) q^{50} +3.56934 q^{51} +(3.55558 + 3.33270i) q^{52} -7.26836 q^{53} +(-3.93992 + 2.27472i) q^{54} +(0.839840 + 1.45465i) q^{55} +(-1.59903 + 2.76960i) q^{56} -10.2039i q^{57} +(-4.23617 - 2.44575i) q^{58} +(-8.80804 - 5.08532i) q^{59} +7.03077i q^{60} +(5.31712 - 9.20952i) q^{61} +(0.402613 + 0.697346i) q^{62} +(-0.907444 + 0.523913i) q^{63} -3.62984 q^{64} +(-12.5561 - 2.93271i) q^{65} +0.550121 q^{66} +(-0.577594 + 0.333474i) q^{67} +(1.65836 + 2.87236i) q^{68} +(-1.49188 + 2.58402i) q^{69} -3.41234i q^{70} +(0.851168 + 0.491422i) q^{71} +(-2.06669 - 1.19320i) q^{72} +0.578884i q^{73} +(-3.33213 + 5.77142i) q^{74} +(-5.66481 - 9.81175i) q^{75} +(8.21141 - 4.74086i) q^{76} +0.556575 q^{77} +(-2.88799 + 3.08113i) q^{78} +13.0561 q^{79} +(-1.64167 + 0.947820i) q^{80} +(2.78268 + 4.81975i) q^{81} +(-2.86259 + 4.95815i) q^{82} +8.23588i q^{83} +(2.01758 + 1.16485i) q^{84} +(-7.59985 - 4.38778i) q^{85} -9.38055i q^{86} +(-4.41802 + 7.65223i) q^{87} +(0.633796 + 1.09777i) q^{88} +(0.340557 - 0.196621i) q^{89} +2.54630 q^{90} +(-2.92187 + 3.11727i) q^{91} -2.77258 q^{92} +(1.25969 - 0.727281i) q^{93} +(-0.416742 - 0.721818i) q^{94} +(-12.5437 + 21.7262i) q^{95} +8.47201i q^{96} +(-5.76187 - 3.32662i) q^{97} +(3.90220 + 2.25294i) q^{98} +0.415319i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) $ 68 * q + 32 * q^4 - 34 * q^9	$ 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) $ 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.697346	+	0.402613i	−0.493098	+	0.284690i	−0.725859	−	0.687844i	$-0.758557\pi$
$2$	−0.697346	+	0.402613i	−0.493098	+	0.284690i	0.232761	+	0.972534i	$0.425224\pi$
$3$	0.727281	+	1.25969i	0.419896	+	0.727281i	0.995929	−	0.0901453i	$-0.0287332\pi$
$3$	0.727281	+	1.25969i	0.419896	+	0.727281i	−0.576032	+	0.817427i	$0.695400\pi$
$4$	−0.675806	+	1.17053i	−0.337903	+	0.585265i
$5$		−	3.57617i		−	1.59931i	−0.600457	−	0.799657i	$-0.705015\pi$
$5$		−	3.57617i		−	1.59931i	0.600457	−	0.799657i	$-0.294985\pi$
$6$	−1.01433	−	0.585626i	−0.414100	−	0.239081i
$7$	−1.02623	−	0.592496i	−0.387880	−	0.223943i	0.293361	−	0.956002i	$-0.405226\pi$
$7$	−1.02623	−	0.592496i	−0.387880	−	0.223943i	−0.681241	+	0.732059i	$0.738559\pi$
$8$		−	2.69880i		−	0.954171i
$9$	0.442123	−	0.765780i	0.147374	−	0.255260i
$10$	1.43981	+	2.49383i	0.455309	+	0.788619i
$11$	−0.406760	+	0.234843i	−0.122643	+	0.0708079i	−0.560066	−	0.828448i	$-0.689224\pi$
$11$	−0.406760	+	0.234843i	−0.122643	+	0.0708079i	0.437424	+	0.899256i	$0.355891\pi$
$12$	−1.96600			−0.567536
$13$	0.820069	−	3.51105i	0.227446	−	0.973791i
$13$	0.820069	−	3.51105i	0.227446	−	0.973791i
$14$	0.954187			0.255017
$15$	4.50487	−	2.60089i	1.16315	−	0.671546i
$16$	−0.265037	−	0.459058i	−0.0662593	−	0.114765i
$17$	1.22695	−	2.12513i	0.297578	−	0.515421i	−0.678003	−	0.735059i	$-0.737154\pi$
$17$	1.22695	−	2.12513i	0.297578	−	0.515421i	0.975581	+	0.219638i	$0.0704877\pi$
$18$			0.712018i			0.167824i
$19$	−6.07528	−	3.50756i	−1.39376	−	0.804690i	−0.400034	−	0.916500i	$-0.631002\pi$
$19$	−6.07528	−	3.50756i	−1.39376	−	0.804690i	−0.993730	+	0.111810i	$0.964335\pi$
$20$	4.18602	+	2.41680i	0.936022	+	0.540413i
$21$		−	1.72365i		−	0.376131i
$22$	0.189102	−	0.327534i	0.0403166	−	0.0698305i
$23$	1.02566	+	1.77649i	0.213865	+	0.370424i	0.952921	−	0.303220i	$-0.0980615\pi$
$23$	1.02566	+	1.77649i	0.213865	+	0.370424i	−0.739056	+	0.673644i	$0.764728\pi$
$24$	3.39965	−	1.96279i	0.693951	−	0.400653i
$25$	−7.78903			−1.55781
$26$	0.841723	+	2.77859i	0.165076	+	0.544926i
$27$	5.64988			1.08732
$28$	1.38707	−	0.800825i	0.262131	−	0.151342i
$29$	3.03735	+	5.26085i	0.564022	+	0.976915i	0.997140	+	0.0755775i	$0.0240800\pi$
$29$	3.03735	+	5.26085i	0.564022	+	0.976915i	−0.433118	+	0.901337i	$0.642587\pi$
$30$	−2.09430	+	3.62744i	−0.382365	+	0.662276i
$31$		−	1.00000i		−	0.179605i
$31$		−	1.00000i		−	0.179605i
$32$	5.04411	+	2.91222i	0.891681	+	0.514813i
$33$	−0.591658	−	0.341594i	−0.102995	−	0.0594639i
$34$			1.97594i			0.338871i
$35$	−2.11887	+	3.66999i	−0.358155	+	0.620342i
$36$	0.597579	+	1.03504i	0.0995965	+	0.172506i
$37$	7.16745	−	4.13813i	1.17832	−	0.680305i	0.222696	−	0.974888i	$-0.428514\pi$
$37$	7.16745	−	4.13813i	1.17832	−	0.680305i	0.955626	+	0.294583i	$0.0951808\pi$
$38$	5.64876			0.916350
$39$	5.01925	−	1.52049i	0.803724	−	0.243474i
$40$	−9.65140			−1.52602
$41$	6.15746	−	3.55501i	0.961634	−	0.555199i	0.0649582	−	0.997888i	$-0.479309\pi$
$41$	6.15746	−	3.55501i	0.961634	−	0.555199i	0.896675	+	0.442689i	$0.145975\pi$
$42$	0.693963	+	1.20198i	0.107081	+	0.185469i
$43$	−5.82479	+	10.0888i	−0.888272	+	1.53853i	−0.0463557	+	0.998925i	$0.514761\pi$
$43$	−5.82479	+	10.0888i	−0.888272	+	1.53853i	−0.841917	+	0.539608i	$0.818573\pi$
$44$		−	0.634833i		−	0.0957047i
$45$	−2.73856	−	1.58111i	−0.408241	−	0.235698i
$46$	−1.43048	−	0.825887i	−0.210912	−	0.121770i
$47$			1.03509i			0.150984i	0.997146	+	0.0754919i	$0.0240527\pi$
$47$			1.03509i			0.150984i	−0.997146	+	0.0754919i	$0.975947\pi$
$48$	0.385514	−	0.667729i	0.0556441	−	0.0963784i
$49$	−2.79790	−	4.84610i	−0.399699	−	0.692300i
$50$	5.43165	−	3.13596i	0.768151	−	0.443492i
$51$	3.56934			0.499808
$52$	3.55558	+	3.33270i	0.493071	+	0.462163i
$53$	−7.26836			−0.998386			−0.499193	−	0.866491i	$-0.666370\pi$
$53$	−7.26836			−0.998386			−0.499193	+	0.866491i	$0.666370\pi$
$54$	−3.93992	+	2.27472i	−0.536156	+	0.309550i
$55$	0.839840	+	1.45465i	0.113244	+	0.196144i
$56$	−1.59903	+	2.76960i	−0.213680	+	0.370104i
$57$		−	10.2039i		−	1.35154i
$58$	−4.23617	−	2.44575i	−0.556236	−	0.321143i
$59$	−8.80804	−	5.08532i	−1.14671	−	0.662053i	−0.198626	−	0.980075i	$-0.563648\pi$
$59$	−8.80804	−	5.08532i	−1.14671	−	0.662053i	−0.948083	+	0.318023i	$0.896981\pi$
$60$			7.03077i			0.907669i
$61$	5.31712	−	9.20952i	0.680787	−	1.17916i	−0.293954	−	0.955820i	$-0.594971\pi$
$61$	5.31712	−	9.20952i	0.680787	−	1.17916i	0.974741	−	0.223338i	$-0.0716954\pi$
$62$	0.402613	+	0.697346i	0.0511319	+	0.0885631i
$63$	−0.907444	+	0.523913i	−0.114327	+	0.0660068i
$64$	−3.62984			−0.453730
$65$	−12.5561	−	2.93271i	−1.55740	−	0.363758i
$66$	0.550121			0.0677152
$67$	−0.577594	+	0.333474i	−0.0705644	+	0.0407404i	−0.534867	−	0.844936i	$-0.679638\pi$
$67$	−0.577594	+	0.333474i	−0.0705644	+	0.0407404i	0.464303	+	0.885677i	$0.346305\pi$
$68$	1.65836	+	2.87236i	0.201105	+	0.348324i
$69$	−1.49188	+	2.58402i	−0.179602	+	0.311079i
$70$		−	3.41234i		−	0.407853i
$71$	0.851168	+	0.491422i	0.101015	+	0.0583211i	0.549656	−	0.835391i	$-0.314759\pi$
$71$	0.851168	+	0.491422i	0.101015	+	0.0583211i	−0.448641	+	0.893712i	$0.648092\pi$
$72$	−2.06669	−	1.19320i	−0.243562	−	0.140620i
$73$			0.578884i			0.0677532i	0.999426	+	0.0338766i	$0.0107853\pi$
$73$			0.578884i			0.0677532i	−0.999426	+	0.0338766i	$0.989215\pi$
$74$	−3.33213	+	5.77142i	−0.387352	+	0.670914i
$75$	−5.66481	−	9.81175i	−0.654116	−	1.13296i
$76$	8.21141	−	4.74086i	0.941913	−	0.543814i
$77$	0.556575			0.0634276
$78$	−2.88799	+	3.08113i	−0.327000	+	0.348869i
$79$	13.0561			1.46893			0.734463	−	0.678648i	$-0.237434\pi$
$79$	13.0561			1.46893			0.734463	+	0.678648i	$0.237434\pi$
$80$	−1.64167	+	0.947820i	−0.183545	+	0.105970i
$81$	2.78268	+	4.81975i	0.309187	+	0.535528i
$82$	−2.86259	+	4.95815i	−0.316120	+	0.547536i
$83$			8.23588i			0.904005i	0.892017	+	0.452003i	$0.149290\pi$
$83$			8.23588i			0.904005i	−0.892017	+	0.452003i	$0.850710\pi$
$84$	2.01758	+	1.16485i	0.220136	+	0.127096i
$85$	−7.59985	−	4.38778i	−0.824320	−	0.475921i
$86$		−	9.38055i		−	1.01153i
$87$	−4.41802	+	7.65223i	−0.473661	+	0.820406i
$88$	0.633796	+	1.09777i	0.0675628	+	0.117022i
$89$	0.340557	−	0.196621i	0.0360989	−	0.0208417i	−0.481842	−	0.876258i	$-0.660032\pi$
$89$	0.340557	−	0.196621i	0.0360989	−	0.0208417i	0.517941	+	0.855416i	$0.326699\pi$
$90$	2.54630			0.268404
$91$	−2.92187	+	3.11727i	−0.306295	+	0.326779i
$92$	−2.77258			−0.289062
$93$	1.25969	−	0.727281i	0.130624	−	0.0754156i
$94$	−0.416742	−	0.721818i	−0.0429836	−	0.0744498i
$95$	−12.5437	+	21.7262i	−1.28695	+	2.22907i
$96$			8.47201i			0.864671i
$97$	−5.76187	−	3.32662i	−0.585029	−	0.337767i	0.178100	−	0.984012i	$-0.443005\pi$
$97$	−5.76187	−	3.32662i	−0.585029	−	0.337767i	−0.763130	+	0.646246i	$0.776338\pi$
$98$	3.90220	+	2.25294i	0.394182	+	0.227581i
$99$			0.415319i			0.0417411i
$100$	5.26387	−	9.11728i	0.526387	−	0.911728i
$101$	1.46834	+	2.54323i	0.146105	+	0.253061i	0.929785	−	0.368104i	$-0.119993\pi$
$101$	1.46834	+	2.54323i	0.146105	+	0.253061i	−0.783680	+	0.621165i	$0.786660\pi$
$102$	−2.48907	+	1.43706i	−0.246454	+	0.142291i
$103$	−11.0754			−1.09129			−0.545646	−	0.838016i	$-0.683716\pi$
$103$	−11.0754			−1.09129			−0.545646	+	0.838016i	$0.683716\pi$
$104$	−9.47564	−	2.21321i	−0.929163	−	0.217023i
$105$	−6.16406			−0.601551
$106$	5.06856	−	2.92633i	0.492302	−	0.284231i
$107$	0.0221431	+	0.0383529i	0.00214065	+	0.00370772i	0.867094	−	0.498145i	$-0.165985\pi$
$107$	0.0221431	+	0.0383529i	0.00214065	+	0.00370772i	−0.864953	+	0.501853i	$0.832652\pi$
$108$	−3.81822	+	6.61335i	−0.367408	+	0.636370i
$109$			14.4507i			1.38413i	0.721835	+	0.692065i	$0.243299\pi$
$109$			14.4507i			1.38413i	−0.721835	+	0.692065i	$0.756701\pi$
$110$	−1.17132	−	0.676261i	−0.111681	−	0.0644790i
$111$	10.4255	+	6.01917i	0.989546	+	0.571315i
$112$			0.628135i			0.0593532i
$113$	7.67830	−	13.2992i	0.722314	−	1.25108i	−0.237756	−	0.971325i	$-0.576412\pi$
$113$	7.67830	−	13.2992i	0.722314	−	1.25108i	0.960070	−	0.279760i	$-0.0902547\pi$
$114$	4.10824	+	7.11568i	0.384772	+	0.666444i
$115$	6.35305	−	3.66793i	0.592425	−	0.342037i
$116$	−8.21064			−0.762338
$117$	−2.32612	−	2.18031i	−0.215050	−	0.201570i
$118$	8.18967			0.753920
$119$	−2.51827	+	1.45392i	−0.230849	+	0.133281i
$120$	−7.01928	−	12.1578i	−0.640770	−	1.10985i
$121$	−5.38970	+	9.33523i	−0.489972	+	0.848657i
$122$			8.56296i			0.775254i
$123$	8.95641	+	5.17099i	0.807573	+	0.466252i
$124$	1.17053	+	0.675806i	0.105117	+	0.0606891i
$125$			9.97404i			0.892106i
$126$	0.421868	−	0.730697i	0.0375830	−	0.0650957i
$127$	−4.23836	−	7.34106i	−0.376094	−	0.651414i	0.614396	−	0.788998i	$-0.289400\pi$
$127$	−4.23836	−	7.34106i	−0.376094	−	0.651414i	−0.990490	+	0.137584i	$0.956066\pi$
$128$	−7.55697	+	4.36302i	−0.667948	+	0.385640i
$129$	−16.9451			−1.49193
$130$	9.93672	−	3.01015i	0.871508	−	0.264008i
$131$	13.9097			1.21530			0.607648	−	0.794206i	$-0.292113\pi$
$131$	13.9097			1.21530			0.607648	+	0.794206i	$0.292113\pi$
$132$	0.799692	−	0.461702i	0.0696043	−	0.0401860i
$133$	4.15644	+	7.19916i	0.360409	+	0.624246i
$134$	0.268522	−	0.465094i	0.0231968	−	0.0401780i
$135$		−	20.2050i		−	1.73897i
$136$	−5.73532	−	3.31129i	−0.491800	−	0.283941i
$137$	14.1476	+	8.16812i	1.20871	+	0.697849i	0.962478	−	0.271361i	$-0.0874738\pi$
$137$	14.1476	+	8.16812i	1.20871	+	0.697849i	0.246233	+	0.969211i	$0.420807\pi$
$138$		−	2.40261i		−	0.204524i
$139$	4.26543	−	7.38795i	0.361789	−	0.626638i	−0.626466	−	0.779449i	$-0.715499\pi$
$139$	4.26543	−	7.38795i	0.361789	−	0.626638i	0.988255	+	0.152811i	$0.0488326\pi$
$140$	−2.86389	−	4.96040i	−0.242043	−	0.419231i
$141$	−1.30389	+	0.752804i	−0.109808	+	0.0633975i
$142$	−0.791412			−0.0664138
$143$	0.490975	+	1.62074i	0.0410574	+	0.135533i
$144$	−0.468717			−0.0390597
$145$	18.8137	−	10.8621i	1.56239	−	0.902048i
$146$	−0.233066	−	0.403682i	−0.0192887	−	0.0334090i
$147$	4.06972	−	7.04895i	0.335664	−	0.581388i
$148$			11.1863i			0.919507i
$149$	16.6208	+	9.59600i	1.36163	+	0.786135i	0.989840	−	0.142184i	$-0.0454124\pi$
$149$	16.6208	+	9.59600i	1.36163	+	0.786135i	0.371785	+	0.928319i	$0.378746\pi$
$150$	7.90067	+	4.56146i	0.645087	+	0.372441i
$151$		−	0.948999i		−	0.0772284i	−0.999254	−	0.0386142i	$-0.987706\pi$
$151$		−	0.948999i		−	0.0772284i	0.999254	−	0.0386142i	$-0.0122943\pi$
$152$	−9.46622	+	16.3960i	−0.767812	+	1.32989i
$153$	−1.08492	−	1.87914i	−0.0877109	−	0.151920i
$154$	−0.388125	+	0.224084i	−0.0312760	+	0.0180572i
$155$	−3.57617			−0.287245
$156$	−1.61226	+	6.90274i	−0.129084	+	0.552662i
$157$	−6.42667			−0.512904			−0.256452	−	0.966557i	$-0.582554\pi$
$157$	−6.42667			−0.512904			−0.256452	+	0.966557i	$0.582554\pi$
$158$	−9.10463	+	5.25656i	−0.724325	+	0.418189i
$159$	−5.28614	−	9.15586i	−0.419218	−	0.726107i
$160$	10.4146	−	18.0386i	0.823347	−	1.42608i
$161$		−	2.43080i		−	0.191574i
$162$	−3.88099	−	2.24069i	−0.304919	−	0.176045i
$163$	−9.60691	−	5.54655i	−0.752471	−	0.434439i	0.0741149	−	0.997250i	$-0.476387\pi$
$163$	−9.60691	−	5.54655i	−0.752471	−	0.434439i	−0.826586	+	0.562810i	$0.809720\pi$
$164$			9.60999i			0.750414i
$165$	−1.22160	+	2.11587i	−0.0951015	+	0.164721i
$166$	−3.31587	−	5.74326i	−0.257362	−	0.445763i
$167$	−10.7372	+	6.19913i	−0.830870	+	0.479703i	−0.854151	−	0.520026i	$-0.825922\pi$
$167$	−10.7372	+	6.19913i	−0.830870	+	0.479703i	0.0232802	+	0.999729i	$0.492589\pi$
$168$	−4.65179			−0.358893
$169$	−11.6550	−	5.75861i	−0.896537	−	0.442970i
$170$	7.06631			0.541961
$171$	−5.37204	+	3.10155i	−0.410810	+	0.237181i
$172$	−7.87285	−	13.6362i	−0.600299	−	1.03975i
$173$	−5.79152	+	10.0312i	−0.440321	+	0.762659i	−0.997713	−	0.0675907i	$-0.978469\pi$
$173$	−5.79152	+	10.0312i	−0.440321	+	0.762659i	0.557392	+	0.830250i	$0.311802\pi$
$174$		−	7.11501i		−	0.539387i
$175$	7.99336	+	4.61497i	0.604241	+	0.348859i
$176$	0.215613	+	0.124484i	0.0162525	+	0.00938337i
$177$		−	14.7938i		−	1.11197i
$178$	−0.158324	+	0.274225i	−0.0118669	+	0.0205540i
$179$	8.35560	+	14.4723i	0.624527	+	1.08171i	0.988632	+	0.150355i	$0.0480415\pi$
$179$	8.35560	+	14.4723i	0.624527	+	1.08171i	−0.364105	+	0.931358i	$0.618625\pi$
$180$	3.70147	−	2.13705i	0.275891	−	0.159286i
$181$	21.5831			1.60426			0.802129	−	0.597150i	$-0.203700\pi$
$181$	21.5831			1.60426			0.802129	+	0.597150i	$0.203700\pi$
$182$	0.782499	−	3.35020i	0.0580027	−	0.248333i
$183$	15.4682			1.14344
$184$	4.79441	−	2.76805i	0.353448	−	0.204063i
$185$	−14.7987	−	25.6321i	−1.08802	−	1.88451i
$186$	−0.585626	+	1.01433i	−0.0429402	+	0.0743746i
$187$			1.15256i			0.0842836i
$188$	−1.21161	−	0.699521i	−0.0883655	−	0.0510178i
$189$	−5.79810	−	3.34753i	−0.421750	−	0.243497i
$190$		−	20.2010i		−	1.46553i
$191$	4.47344	−	7.74823i	0.323687	−	0.560643i	−0.657559	−	0.753403i	$-0.728411\pi$
$191$	4.47344	−	7.74823i	0.323687	−	0.560643i	0.981246	+	0.192761i	$0.0617442\pi$
$192$	−2.63992	−	4.57247i	−0.190519	−	0.329989i
$193$	10.2514	−	5.91862i	0.737909	−	0.426032i	−0.0833997	−	0.996516i	$-0.526578\pi$
$193$	10.2514	−	5.91862i	0.737909	−	0.426032i	0.821308	+	0.570484i	$0.193244\pi$
$194$	5.35736			0.384636
$195$	−5.43755	−	17.9497i	−0.389391	−	1.28541i
$196$	7.56333			0.540238
$197$	1.92430	−	1.11100i	0.137101	−	0.0791553i	−0.429881	−	0.902886i	$-0.641444\pi$
$197$	1.92430	−	1.11100i	0.137101	−	0.0791553i	0.566982	+	0.823730i	$0.308111\pi$
$198$	−0.167213	−	0.289621i	−0.0118833	−	0.0205825i
$199$	6.93640	−	12.0142i	0.491708	−	0.851664i	−0.508246	−	0.861212i	$-0.669706\pi$
$199$	6.93640	−	12.0142i	0.491708	−	0.851664i	0.999954	+	0.00954799i	$0.00303926\pi$
$200$			21.0211i			1.48641i
$201$	−0.840147	−	0.485059i	−0.0592594	−	0.0342134i
$202$	−2.04788	−	1.18234i	−0.144088	−	0.0831893i
$203$		−	7.19848i		−	0.505234i
$204$	−2.41218	+	4.17802i	−0.168887	+	0.292520i
$205$	−12.7133	−	22.0202i	−0.887938	−	1.53795i
$206$	7.72339	−	4.45910i	0.538114	−	0.310680i
$207$	1.81387			0.126073
$208$	−1.82913	+	0.554101i	−0.126827	+	0.0384200i
$209$	3.29491			0.227914
$210$	4.29849	−	2.48173i	0.296624	−	0.171256i
$211$	10.3459	+	17.9196i	0.712240	+	1.23364i	0.964014	+	0.265850i	$0.0856526\pi$
$211$	10.3459	+	17.9196i	0.712240	+	1.23364i	−0.251774	+	0.967786i	$0.581014\pi$
$212$	4.91200	−	8.50783i	0.337357	−	0.584320i
$213$			1.42961i			0.0979552i
$214$	−0.0308828	−	0.0178302i	−0.00211110	−	0.00121885i
$215$	36.0794	+	20.8305i	2.46060	+	1.42063i
$216$		−	15.2479i		−	1.03749i
$217$	−0.592496	+	1.02623i	−0.0402213	+	0.0696653i
$218$	−5.81806	−	10.0772i	−0.394049	−	0.682512i
$219$	−0.729213	+	0.421011i	−0.0492757	+	0.0284493i
$220$	−2.27027			−0.153062
$221$	−6.45528	−	6.05063i	−0.434229	−	0.407010i
$222$	−9.69359			−0.650591
$223$	1.34168	−	0.774618i	0.0898454	−	0.0518723i	−0.454404	−	0.890796i	$-0.650148\pi$
$223$	1.34168	−	0.774618i	0.0898454	−	0.0518723i	0.544250	+	0.838923i	$0.316814\pi$
$224$	−3.45096	−	5.97724i	−0.230577	−	0.399371i
$225$	−3.44371	+	5.96468i	−0.229581	+	0.397645i
$226$			12.3655i			0.822543i
$227$	8.60288	+	4.96687i	0.570993	+	0.329663i	0.757546	−	0.652782i	$-0.226398\pi$
$227$	8.60288	+	4.96687i	0.570993	+	0.329663i	−0.186553	+	0.982445i	$0.559732\pi$
$228$	11.9440	+	6.89588i	0.791012	+	0.456691i
$229$			26.9481i			1.78078i	0.455195	+	0.890392i	$0.349569\pi$
$229$			26.9481i			1.78078i	−0.455195	+	0.890392i	$0.650431\pi$
$230$	−2.95352	+	5.11564i	−0.194749	+	0.337315i
$231$	0.404787	+	0.701111i	0.0266330	+	0.0461297i
$232$	14.1980	−	8.19722i	0.932144	−	0.538174i
$233$	19.6331			1.28621			0.643104	−	0.765778i	$-0.277646\pi$
$233$	19.6331			1.28621			0.643104	+	0.765778i	$0.277646\pi$
$234$	2.49993	+	0.583904i	0.163426	+	0.0381710i
$235$	3.70167			0.241470
$236$	11.9050	−	6.87338i	0.774952	−	0.447419i
$237$	9.49546	+	16.4466i	0.616797	+	1.06832i
$238$	1.17074	−	2.02778i	0.0758876	−	0.131441i
$239$			10.4124i			0.673524i	0.941590	+	0.336762i	$0.109332\pi$
$239$			10.4124i			0.673524i	−0.941590	+	0.336762i	$0.890668\pi$
$240$	−2.38792	−	1.37866i	−0.154139	−	0.0889924i
$241$	6.00768	+	3.46853i	0.386988	+	0.223428i	0.680854	−	0.732419i	$-0.261609\pi$
$241$	6.00768	+	3.46853i	0.386988	+	0.223428i	−0.293866	+	0.955847i	$0.594942\pi$
$242$		−	8.67985i		−	0.557962i
$243$	4.42723	−	7.66819i	0.284007	−	0.491915i
$244$	7.18667	+	12.4477i	0.460080	+	0.796881i
$245$	−17.3305	+	10.0058i	−1.10720	+	0.639245i
$246$	−8.32763			−0.530950
$247$	−17.2974	+	18.4542i	−1.10061	+	1.17421i
$248$	−2.69880			−0.171374
$249$	−10.3746	+	5.98980i	−0.657466	+	0.379588i
$250$	−4.01568	−	6.95536i	−0.253974	−	0.439896i
$251$	8.91303	−	15.4378i	0.562585	−	0.974426i	−0.434685	−	0.900583i	$-0.643140\pi$
$251$	8.91303	−	15.4378i	0.562585	−	0.974426i	0.997270	−	0.0738434i	$-0.0235265\pi$
$252$		−	1.41625i		−	0.0892156i
$253$	−0.834394	−	0.481738i	−0.0524579	−	0.0302866i
$254$	5.91121	+	3.41284i	0.370903	+	0.214141i
$255$		−	12.7646i		−	0.799350i
$256$	7.14306	−	12.3721i	0.446441	−	0.773258i
$257$	−7.28162	−	12.6121i	−0.454215	−	0.786723i	0.544428	−	0.838808i	$-0.316747\pi$
$257$	−7.28162	−	12.6121i	−0.454215	−	0.786723i	−0.998643	+	0.0520845i	$0.983413\pi$
$258$	11.8166	−	6.82230i	0.735667	−	0.424738i
$259$	−9.80731			−0.609397
$260$	11.9183	−	12.7154i	0.739143	−	0.788575i
$261$	5.37154			0.332490
$262$	−9.69988	+	5.60023i	−0.599260	+	0.345983i
$263$	9.94368	+	17.2230i	0.613153	+	1.06201i	0.990705	+	0.136025i	$0.0434326\pi$
$263$	9.94368	+	17.2230i	0.613153	+	1.06201i	−0.377552	+	0.925988i	$0.623234\pi$
$264$	−0.921896	+	1.59677i	−0.0567388	+	0.0982744i
$265$			25.9929i			1.59673i
$266$	−5.79695	−	3.34687i	−0.355434	−	0.205210i
$267$	0.495361	+	0.285997i	0.0303156	+	0.0175027i
$268$		−	0.901455i		−	0.0550651i
$269$	−3.30899	+	5.73135i	−0.201753	+	0.349446i	−0.949093	−	0.314995i	$-0.897997\pi$
$269$	−3.30899	+	5.73135i	−0.201753	+	0.349446i	0.747340	+	0.664441i	$0.231330\pi$
$270$	8.13478	+	14.0899i	0.495067	+	0.857481i
$271$	12.8878	−	7.44078i	0.782878	−	0.451995i	−0.0545711	−	0.998510i	$-0.517379\pi$
$271$	12.8878	−	7.44078i	0.782878	−	0.451995i	0.837449	+	0.546515i	$0.184046\pi$
$272$	−1.30075			−0.0788694
$273$	−6.05181	−	1.41351i	−0.366272	−	0.0855494i
$274$	−13.1544			−0.794684
$275$	3.16827	−	1.82920i	0.191054	−	0.110305i
$276$	−2.01645	−	3.49259i	−0.121376	−	0.210229i
$277$	−2.81585	+	4.87719i	−0.169188	+	0.293042i	−0.938135	−	0.346271i	$-0.887448\pi$
$277$	−2.81585	+	4.87719i	−0.169188	+	0.293042i	0.768947	+	0.639313i	$0.220781\pi$
$278$			6.86928i			0.411992i
$279$	−0.765780	−	0.442123i	−0.0458461	−	0.0264692i
$280$	9.90459	+	5.71842i	0.591913	+	0.341741i
$281$		−	10.4667i		−	0.624394i	−0.950017	−	0.312197i	$-0.898935\pi$
$281$		−	10.4667i		−	0.624394i	0.950017	−	0.312197i	$-0.101065\pi$
$282$	0.606177	−	1.04993i	0.0360973	−	0.0625224i
$283$	−11.4426	−	19.8192i	−0.680192	−	1.17813i	−0.974922	−	0.222547i	$-0.928563\pi$
$283$	−11.4426	−	19.8192i	−0.680192	−	1.17813i	0.294729	−	0.955581i	$-0.404770\pi$
$284$	−1.15045	+	0.664212i	−0.0682665	+	0.0394137i
$285$	−36.4911			−2.16154
$286$	−0.994912	−	0.932547i	−0.0588304	−	0.0551426i
$287$	−8.42533			−0.497331
$288$	4.46024	−	2.57512i	0.262822	−	0.151740i
$289$	5.48920	+	9.50758i	0.322894	+	0.559269i
$290$	−8.74645	+	15.1493i	−0.513609	+	0.889597i
$291$		−	9.67755i		−	0.567308i
$292$	−0.677600	−	0.391213i	−0.0396536	−	0.0228940i
$293$	−9.89170	−	5.71097i	−0.577879	−	0.333639i	0.182411	−	0.983222i	$-0.441610\pi$
$293$	−9.89170	−	5.71097i	−0.577879	−	0.333639i	−0.760290	+	0.649584i	$0.774943\pi$
$294$			6.55408i			0.382242i
$295$	−18.1860	+	31.4991i	−1.05883	+	1.83395i
$296$	−11.1680	−	19.3436i	−0.649127	−	1.12432i
$297$	−2.29815	+	1.32684i	−0.133352	+	0.0769908i
$298$	−15.4539			−0.895220
$299$	7.07847	−	2.14429i	0.409358	−	0.124008i
$300$	15.3133			0.884111
$301$	11.9552	−	6.90234i	0.689086	−	0.397844i
$302$	0.382079	+	0.661781i	0.0219862	+	0.0380812i
$303$	−2.13579	+	3.69929i	−0.122698	+	0.212519i
$304$			3.71854i			0.213273i
$305$	−32.9348	−	19.0149i	−1.88584	−	1.08879i
$306$	1.51314	+	0.873609i	0.0865002	+	0.0499409i
$307$		−	28.5045i		−	1.62684i	−0.581680	−	0.813418i	$-0.697604\pi$
$307$		−	28.5045i		−	1.62684i	0.581680	−	0.813418i	$-0.302396\pi$
$308$	−0.376136	+	0.651487i	−0.0214324	+	0.0371219i
$309$	−8.05494	−	13.9516i	−0.458229	−	0.793677i
$310$	2.49383	−	1.43981i	0.141640	−	0.0817760i
$311$	12.0992			0.686085			0.343042	−	0.939320i	$-0.388543\pi$
$311$	12.0992			0.686085			0.343042	+	0.939320i	$0.388543\pi$
$312$	−4.10351	−	13.5460i	−0.232316	−	0.766890i
$313$	−14.4652			−0.817623			−0.408812	−	0.912619i	$-0.634057\pi$
$313$	−14.4652			−0.817623			−0.408812	+	0.912619i	$0.634057\pi$
$314$	4.48161	−	2.58746i	0.252912	−	0.146019i
$315$	1.87360	+	3.24518i	0.105566	+	0.182845i
$316$	−8.82339	+	15.2826i	−0.496354	+	0.859711i
$317$			31.9323i			1.79349i	0.442544	+	0.896747i	$0.354076\pi$
$317$			31.9323i			1.79349i	−0.442544	+	0.896747i	$0.645924\pi$
$318$	7.37254	+	4.25654i	0.413432	+	0.238695i
$319$	−2.47095	−	1.42660i	−0.138347	−	0.0798744i
$320$			12.9809i			0.725657i
$321$	−0.0322085	+	0.0557868i	−0.00179770	+	0.00311371i
$322$	0.978670	+	1.69511i	0.0545392	+	0.0944646i
$323$	−14.9081	+	8.60719i	−0.829508	+	0.478917i
$324$	−7.52221			−0.417901
$325$	−6.38754	+	27.3477i	−0.354317	+	1.51698i
$326$	8.93246			0.494723
$327$	−18.2034	+	10.5098i	−1.00665	+	0.581191i
$328$	−9.59428	−	16.6178i	−0.529755	−	0.917563i
$329$	0.613289	−	1.06225i	0.0338117	−	0.0585636i
$330$		−	1.96733i		−	0.108298i
$331$	−10.7860	−	6.22731i	−0.592853	−	0.342284i	0.173372	−	0.984856i	$-0.444534\pi$
$331$	−10.7860	−	6.22731i	−0.592853	−	0.342284i	−0.766225	+	0.642573i	$0.777867\pi$
$332$	−9.64034	−	5.56585i	−0.529082	−	0.305466i
$333$		−	7.31826i		−	0.401038i
$334$	4.99170	−	8.64588i	0.273134	−	0.473082i
$335$	1.19256	+	2.06558i	0.0651566	+	0.112855i
$336$	−0.791254	+	0.456831i	−0.0431665	+	0.0249222i
$337$	−10.2505			−0.558382			−0.279191	−	0.960236i	$-0.590066\pi$
$337$	−10.2505			−0.558382			−0.279191	+	0.960236i	$0.590066\pi$
$338$	10.4460	−	0.676701i	0.568190	−	0.0368077i
$339$	22.3371			1.21319
$340$	10.2720	−	5.93057i	0.557080	−	0.321630i
$341$	0.234843	+	0.406760i	0.0127175	+	0.0220273i
$342$	2.49745	−	4.32571i	0.135047	−	0.233907i
$343$			14.9259i			0.805924i
$344$	27.2278	+	15.7200i	1.46802	+	0.847564i
$345$	9.24091	+	5.33524i	0.497514	+	0.287240i
$346$		−	9.32697i		−	0.501421i
$347$	−1.80980	+	3.13466i	−0.0971550	+	0.168277i	−0.910506	−	0.413496i	$-0.864308\pi$
$347$	−1.80980	+	3.13466i	−0.0971550	+	0.168277i	0.813351	+	0.581773i	$0.197641\pi$
$348$	−5.97144	−	10.3428i	−0.320103	−	0.554435i
$349$	−21.5248	+	12.4273i	−1.15220	+	0.665220i	−0.949421	−	0.314005i	$-0.898329\pi$
$349$	−21.5248	+	12.4273i	−1.15220	+	0.665220i	−0.202774	+	0.979226i	$0.564996\pi$
$350$	−7.43219			−0.397267
$351$	4.63329	−	19.8370i	0.247307	−	1.05882i
$352$	−2.73566			−0.145811
$353$	5.51851	−	3.18611i	0.293721	−	0.169580i	−0.345898	−	0.938272i	$-0.612426\pi$
$353$	5.51851	−	3.18611i	0.293721	−	0.169580i	0.639619	+	0.768692i	$0.279092\pi$
$354$	5.95620	+	10.3164i	0.316568	+	0.548312i
$355$	1.75741	−	3.04393i	0.0932737	−	0.161555i
$356$			0.531509i			0.0281699i
$357$	−3.66298	−	2.11482i	−0.193866	−	0.111928i
$358$	−11.6535	−	6.72815i	−0.615906	−	0.355594i
$359$			21.3325i			1.12589i	0.826496	+	0.562943i	$0.190331\pi$
$359$			21.3325i			1.12589i	−0.826496	+	0.562943i	$0.809669\pi$
$360$	−4.26711	+	7.39085i	−0.224896	+	0.389532i
$361$	15.1060	+	26.1643i	0.795052	+	1.37707i
$362$	−15.0509	+	8.68963i	−0.791057	+	0.456717i
$363$	−15.6793			−0.822950
$364$	−1.67425	−	5.52680i	−0.0877543	−	0.289683i
$365$	2.07019			0.108359
$366$	−10.7867	+	6.22768i	−0.563828	+	0.325526i
$367$	1.93301	+	3.34806i	0.100902	+	0.174768i	0.912057	−	0.410064i	$-0.134494\pi$
$367$	1.93301	+	3.34806i	0.100902	+	0.174768i	−0.811154	+	0.584832i	$0.801160\pi$
$368$	0.543676	−	0.941674i	0.0283411	−	0.0490881i
$369$		−	6.28701i		−	0.327289i
$370$	20.6396	+	11.9163i	1.07300	+	0.619498i
$371$	7.45903	+	4.30648i	0.387254	+	0.223581i
$372$			1.96600i			0.101933i
$373$	−17.3531	+	30.0565i	−0.898511	+	1.55627i	−0.0691120	+	0.997609i	$0.522017\pi$
$373$	−17.3531	+	30.0565i	−0.898511	+	1.55627i	−0.829399	+	0.558657i	$0.811317\pi$
$374$	−0.464036	−	0.803734i	−0.0239947	−	0.0415601i
$375$	−12.5642	+	7.25394i	−0.648812	+	0.374592i
$376$	2.79351			0.144064
$377$	20.9619	−	6.35004i	1.07960	−	0.327044i
$378$	5.39104			0.277285
$379$	18.0206	−	10.4042i	0.925654	−	0.534427i	0.0402199	−	0.999191i	$-0.487194\pi$
$379$	18.0206	−	10.4042i	0.925654	−	0.534427i	0.885435	+	0.464764i	$0.153861\pi$
$380$	−16.9541	−	29.3654i	−0.869729	−	1.50642i
$381$	6.16497	−	10.6780i	0.315841	−	0.547052i
$382$			7.20427i			0.368602i
$383$	−11.5392	−	6.66215i	−0.589624	−	0.340420i	0.175325	−	0.984511i	$-0.443903\pi$
$383$	−11.5392	−	6.66215i	−0.589624	−	0.340420i	−0.764949	+	0.644091i	$0.777236\pi$
$384$	−10.9921	−	6.34628i	−0.560938	−	0.323857i
$385$		−	1.99041i		−	0.101441i
$386$	−4.76583	+	8.25466i	−0.242574	+	0.420151i
$387$	5.15055	+	8.92102i	0.261817	+	0.453481i
$388$	7.78781	−	4.49629i	0.395366	−	0.228265i
$389$	7.71954			0.391396			0.195698	−	0.980664i	$-0.437303\pi$
$389$	7.71954			0.391396			0.195698	+	0.980664i	$0.437303\pi$
$390$	11.0186	+	10.3279i	0.557951	+	0.522976i
$391$	5.03372			0.254566
$392$	−13.0787	+	7.55097i	−0.660573	+	0.381382i
$393$	10.1163	+	17.5219i	0.510298	+	0.883862i
$394$	−0.894604	+	1.54950i	−0.0450695	+	0.0780626i
$395$		−	46.6909i		−	2.34927i
$396$	−0.486143	−	0.280675i	−0.0244296	−	0.0141044i
$397$	12.4273	+	7.17489i	0.623707	+	0.360097i	0.778311	−	0.627879i	$-0.216077\pi$
$397$	12.4273	+	7.17489i	0.623707	+	0.360097i	−0.154604	+	0.987977i	$0.549410\pi$
$398$			11.1707i			0.559939i
$399$	−6.04580	+	10.4716i	−0.302668	+	0.524237i
$400$	2.06438	+	3.57562i	0.103219	+	0.178781i
$401$	5.30042	−	3.06020i	0.264690	−	0.152819i	−0.361782	−	0.932263i	$-0.617831\pi$
$401$	5.30042	−	3.06020i	0.264690	−	0.152819i	0.626472	+	0.779444i	$0.284498\pi$
$402$	0.781165			0.0389610
$403$	−3.51105	−	0.820069i	−0.174898	−	0.0408505i
$404$	−3.96924			−0.197477
$405$	17.2363	−	9.95136i	0.856477	−	0.494487i
$406$	2.89820	+	5.01983i	0.143835	+	0.249130i
$407$	−1.94362	+	3.36645i	−0.0963418	+	0.166869i
$408$		−	9.63296i		−	0.476903i
$409$	−22.6416	−	13.0721i	−1.11956	−	0.646376i	−0.178268	−	0.983982i	$-0.557049\pi$
$409$	−22.6416	−	13.0721i	−1.11956	−	0.646376i	−0.941287	+	0.337606i	$0.890383\pi$
$410$	17.7312	+	10.2371i	0.875682	+	0.505575i
$411$			23.7621i			1.17210i
$412$	7.48482	−	12.9641i	0.368751	−	0.638695i
$413$	6.02607	+	10.4375i	0.296524	+	0.513594i
$414$	−1.26490	+	0.730288i	−0.0621662	+	0.0358917i
$415$	29.4529			1.44579
$416$	14.3615	−	15.3219i	0.704129	−	0.751219i
$417$	12.4087			0.607656
$418$	−2.29769	+	1.32657i	−0.112384	+	0.0648848i
$419$	−9.30041	−	16.1088i	−0.454355	−	0.786965i	0.544296	−	0.838893i	$-0.316797\pi$
$419$	−9.30041	−	16.1088i	−0.454355	−	0.786965i	−0.998651	+	0.0519277i	$0.983463\pi$
$420$	4.16571	−	7.21522i	0.203266	−	0.352067i
$421$		−	22.3459i		−	1.08907i	−0.838737	−	0.544537i	$-0.816705\pi$
$421$		−	22.3459i		−	1.08907i	0.838737	−	0.544537i	$-0.183295\pi$
$422$	−14.4293	−	8.33078i	−0.702409	−	0.405536i
$423$	0.792653	+	0.457639i	0.0385401	+	0.0222511i
$424$			19.6159i			0.952631i
$425$	−9.55672	+	16.5527i	−0.463569	+	0.802925i
$426$	−0.575579	−	0.996932i	−0.0278869	−	0.0483015i
$427$	−10.9132	+	6.30075i	−0.528127	+	0.304914i
$428$	−0.0598577			−0.00289333
$429$	−1.68456	+	1.79721i	−0.0813311	+	0.0867703i
$430$	−33.5465			−1.61775
$431$	34.9926	−	20.2030i	1.68553	−	0.973143i	0.727666	−	0.685932i	$-0.240605\pi$
$431$	34.9926	−	20.2030i	1.68553	−	0.973143i	0.957867	−	0.287211i	$-0.0927281\pi$
$432$	−1.49743	−	2.59362i	−0.0720451	−	0.124786i
$433$	−16.5531	+	28.6708i	−0.795490	+	1.37783i	0.127037	+	0.991898i	$0.459453\pi$
$433$	−16.5531	+	28.6708i	−0.795490	+	1.37783i	−0.922527	+	0.385932i	$0.873880\pi$
$434$		−	0.954187i		−	0.0458024i
$435$	27.3657	+	15.7996i	1.31209	+	0.757533i
$436$	−16.9150	−	9.76589i	−0.810083	−	0.467701i
$437$		−	14.3902i		−	0.688379i
$438$	0.339009	−	0.587181i	0.0161985	−	0.0280566i
$439$	−17.4705	−	30.2598i	−0.833823	−	1.44422i	−0.894985	−	0.446096i	$-0.852814\pi$
$439$	−17.4705	−	30.2598i	−0.833823	−	1.44422i	0.0611624	−	0.998128i	$-0.480519\pi$
$440$	3.92580	−	2.26656i	0.187155	−	0.108054i
$441$	−4.94806			−0.235622
$442$	6.93763	+	1.62041i	0.329989	+	0.0770749i
$443$	0.956806			0.0454592			0.0227296	−	0.999742i	$-0.492764\pi$
$443$	0.956806			0.0454592			0.0227296	+	0.999742i	$0.492764\pi$
$444$	−14.0912	+	8.13558i	−0.668741	+	0.386098i
$445$	−0.703149	−	1.21789i	−0.0333325	−	0.0577335i
$446$	−0.623743	+	1.08035i	−0.0295351	+	0.0511563i
$447$			27.9160i			1.32038i
$448$	3.72507	+	2.15067i	0.175993	+	0.101609i
$449$	−11.1849	−	6.45758i	−0.527846	−	0.304752i	0.212293	−	0.977206i	$-0.431907\pi$
$449$	−11.1849	−	6.45758i	−0.527846	−	0.304752i	−0.740139	+	0.672454i	$0.765240\pi$
$450$		−	5.54593i		−	0.261438i
$451$	−1.66974	+	2.89207i	−0.0786250	+	0.136182i
$452$	10.3781	+	17.9754i	0.488144	+	0.845490i
$453$	1.19544	−	0.690189i	0.0561668	−	0.0324279i
$454$	−7.99891			−0.375407
$455$	11.1479	+	10.4491i	0.522622	+	0.489862i
$456$	−27.5384			−1.28961
$457$	−11.3944	+	6.57856i	−0.533008	+	0.307732i	−0.742240	−	0.670134i	$-0.766237\pi$
$457$	−11.3944	+	6.57856i	−0.533008	+	0.307732i	0.209233	+	0.977866i	$0.432903\pi$
$458$	−10.8497	−	18.7922i	−0.506972	−	0.878101i
$459$	6.93211	−	12.0068i	0.323563	−	0.560428i
$460$			9.91524i			0.462300i
$461$	−6.27944	−	3.62544i	−0.292463	−	0.168853i	0.346589	−	0.938017i	$-0.387340\pi$
$461$	−6.27944	−	3.62544i	−0.292463	−	0.168853i	−0.639052	+	0.769164i	$0.720673\pi$
$462$	−0.564553	−	0.325945i	−0.0262654	−	0.0151643i
$463$		−	11.7830i		−	0.547601i	−0.961787	−	0.273800i	$-0.911719\pi$
$463$		−	11.7830i		−	0.547601i	0.961787	−	0.273800i	$-0.0882807\pi$
$464$	1.61002	−	2.78864i	0.0747435	−	0.129459i
$465$	−2.60089	−	4.50487i	−0.120613	−	0.208908i
$466$	−13.6911	+	7.90455i	−0.634227	+	0.366171i
$467$	19.5757			0.905856			0.452928	−	0.891547i	$-0.350380\pi$
$467$	19.5757			0.905856			0.452928	+	0.891547i	$0.350380\pi$
$468$	4.12412	−	1.24933i	0.190638	−	0.0577503i
$469$	0.790329			0.0364940
$470$	−2.58135	+	1.49034i	−0.119069	+	0.0687443i
$471$	−4.67400	−	8.09560i	−0.215366	−	0.373026i
$472$	−13.7243	+	23.7712i	−0.631712	+	1.09416i
$473$		−	5.47165i		−	0.251587i
$474$	−13.2433	−	7.64599i	−0.608283	−	0.351192i
$475$	47.3205	+	27.3205i	2.17121	+	1.25355i
$476$		−	3.93028i		−	0.180144i
$477$	−3.21351	+	5.56596i	−0.147137	+	0.254848i
$478$	−4.19218	−	7.26107i	−0.191746	−	0.332114i
$479$	18.3363	−	10.5865i	0.837808	−	0.483709i	−0.0187107	−	0.999825i	$-0.505956\pi$
$479$	18.3363	−	10.5865i	0.837808	−	0.483709i	0.856518	+	0.516116i	$0.172623\pi$
$480$	30.2974			1.38288
$481$	−8.65139	−	28.5589i	−0.394469	−	1.30217i
$482$	−5.58591			−0.254431
$483$	3.06205	−	1.76787i	0.139328	−	0.0804410i
$484$	−7.28477	−	12.6176i	−0.331126	−	0.573527i
$485$	−11.8966	+	20.6055i	−0.540195	+	0.935646i
$486$			7.12985i			0.323416i
$487$	19.4208	+	11.2126i	0.880041	+	0.508092i	0.870672	−	0.491864i	$-0.163684\pi$
$487$	19.4208	+	11.2126i	0.880041	+	0.508092i	0.00936905	+	0.999956i	$0.497018\pi$
$488$	−24.8547	−	14.3499i	−1.12512	−	0.649587i
$489$		−	16.1356i		−	0.729678i
$490$	8.05690	−	13.9550i	0.363974	−	0.630421i
$491$	13.1968	+	22.8575i	0.595561	+	1.03154i	0.993467	+	0.114116i	$0.0364037\pi$
$491$	13.1968	+	22.8575i	0.595561	+	1.03154i	−0.397906	+	0.917426i	$0.630263\pi$
$492$	−12.1056	+	6.98916i	−0.545762	+	0.315096i
$493$	14.9067			0.671363
$494$	4.63237	−	19.8331i	0.208420	−	0.892333i
$495$	1.48525			0.0667571
$496$	−0.459058	+	0.265037i	−0.0206123	+	0.0119005i
$497$	−0.582332	−	1.00863i	−0.0261211	−	0.0452432i
$498$	4.82314	−	8.35393i	0.216130	−	0.374349i
$499$		−	17.6676i		−	0.790908i	−0.918486	−	0.395454i	$-0.870587\pi$
$499$		−	17.6676i		−	0.790908i	0.918486	−	0.395454i	$-0.129413\pi$
$500$	−11.6749	−	6.74051i	−0.522118	−	0.301445i
$501$	−15.6179	−	9.01703i	−0.697759	−	0.402851i
$502$			14.3540i			0.640650i
$503$	−15.5491	+	26.9318i	−0.693298	+	1.20083i	0.277453	+	0.960739i	$0.410510\pi$
$503$	−15.5491	+	26.9318i	−0.693298	+	1.20083i	−0.970751	+	0.240089i	$0.922823\pi$
$504$	1.41394	+	2.44901i	0.0629818	+	0.109088i
$505$	9.09504	−	5.25103i	0.404724	−	0.233668i
$506$	0.775815			0.0344892
$507$	−1.22240	−	18.8698i	−0.0542885	−	0.838036i
$508$	11.4572			0.508333
$509$	−20.7284	+	11.9676i	−0.918771	+	0.530453i	−0.883243	−	0.468916i	$-0.844645\pi$
$509$	−20.7284	+	11.9676i	−0.918771	+	0.530453i	−0.0355281	+	0.999369i	$0.511311\pi$
$510$	5.13919	+	8.90134i	0.227567	+	0.394158i
$511$	0.342987	−	0.594070i	0.0151728	−	0.0262801i
$512$		−	5.94852i		−	0.262890i
$513$	−34.3246	−	19.8173i	−1.51547	−	0.874955i
$514$	10.1556	+	5.86335i	0.447945	+	0.258621i
$515$			39.6076i			1.74532i
$516$	11.4516	−	19.8347i	0.504127	−	0.873173i
$517$	−0.243084	−	0.421035i	−0.0106908	−	0.0185171i
$518$	6.83909	−	3.94855i	0.300492	−	0.173489i
$519$	−16.8483			−0.739557
$520$	−7.91481	+	33.8866i	−0.347087	+	1.48602i
$521$	21.9259			0.960593			0.480297	−	0.877106i	$-0.340529\pi$
$521$	21.9259			0.960593			0.480297	+	0.877106i	$0.340529\pi$
$522$	−3.74582	+	2.16265i	−0.163950	+	0.0946566i
$523$	−5.25910	−	9.10903i	−0.229964	−	0.398310i	0.727833	−	0.685755i	$-0.240528\pi$
$523$	−5.25910	−	9.10903i	−0.229964	−	0.398310i	−0.957797	+	0.287444i	$0.907194\pi$
$524$	−9.40025	+	16.2817i	−0.410652	+	0.711270i
$525$			13.4255i			0.585938i
$526$	−13.8684	−	8.00691i	−0.604690	−	0.349118i
$527$	−2.12513	−	1.22695i	−0.0925723	−	0.0534467i
$528$			0.362141i			0.0157602i
$529$	9.39605	−	16.2744i	0.408524	−	0.707584i
$530$	−10.4651	−	18.1261i	−0.454574	−	0.787346i
$531$	−7.78848	+	4.49668i	−0.337991	+	0.195139i
$532$	−11.2358			−0.487132
$533$	−7.43229	−	24.5345i	−0.321928	−	1.06271i
$534$	−0.460584			−0.0199314
$535$	0.137157	−	0.0791875i	0.00592981	−	0.00342357i
$536$	0.899982	+	1.55881i	0.0388733	+	0.0673305i
$537$	−12.1537	+	21.0509i	−0.524473	+	0.908414i
$538$		−	5.32898i		−	0.229748i
$539$	2.27615	+	1.31413i	0.0980405	+	0.0566037i
$540$	23.6505	+	13.6546i	1.01776	+	0.587602i
$541$		−	1.11774i		−	0.0480555i	−0.999711	−	0.0240277i	$-0.992351\pi$
$541$		−	1.11774i		−	0.0480555i	0.999711	−	0.0240277i	$-0.00764900\pi$
$542$	−5.99151	+	10.3776i	−0.257357	+	0.445756i
$543$	15.6970	+	27.1880i	0.673622	+	1.16675i
$544$	12.3777	−	7.14628i	0.530690	−	0.306394i
$545$	51.6784			2.21366
$546$	4.78931	−	1.45083i	0.204963	−	0.0620900i
$547$	22.0802			0.944081			0.472041	−	0.881577i	$-0.343518\pi$
$547$	22.0802			0.944081			0.472041	+	0.881577i	$0.343518\pi$
$548$	−19.1220	+	11.0401i	−0.816853	+	0.471611i
$549$	−4.70164	−	8.14348i	−0.200661	−	0.347555i
$550$	−1.47292	+	2.55117i	−0.0628055	+	0.108782i
$551$		−	42.6148i		−	1.81545i
$552$	6.97377	+	4.02631i	0.296823	+	0.171371i
$553$	−13.3986	−	7.73570i	−0.569767	−	0.328955i
$554$		−	4.53479i		−	0.192665i
$555$	21.5256	−	37.2835i	0.913711	−	1.58259i
$556$	5.76521	+	9.98563i	0.244499	+	0.423485i
$557$	26.7122	−	15.4223i	1.13183	−	0.653463i	0.187436	−	0.982277i	$-0.439982\pi$
$557$	26.7122	−	15.4223i	1.13183	−	0.653463i	0.944395	+	0.328814i	$0.106649\pi$
$558$	0.712018			0.0301421
$559$	30.6457	+	28.7247i	1.29617	+	1.21492i
$560$	2.24632			0.0949244
$561$	−1.45187	+	0.838236i	−0.0612979	+	0.0353903i
$562$	4.21405	+	7.29895i	0.177759	+	0.307887i
$563$	3.98259	−	6.89804i	0.167846	−	0.290718i	−0.769816	−	0.638266i	$-0.779652\pi$
$563$	3.98259	−	6.89804i	0.167846	−	0.290718i	0.937662	+	0.347548i	$0.112986\pi$
$564$		−	2.03500i		−	0.0856888i
$565$	−47.5603	−	27.4589i	−2.00088	−	1.15521i
$566$	15.9589	+	9.21389i	0.670803	+	0.387289i
$567$		−	6.59492i		−	0.276961i
$568$	1.32625	−	2.29714i	0.0556483	−	0.0963857i
$569$	−0.258639	−	0.447976i	−0.0108427	−	0.0187801i	0.860553	−	0.509361i	$-0.170118\pi$
$569$	−0.258639	−	0.447976i	−0.0108427	−	0.0187801i	−0.871396	+	0.490581i	$0.836785\pi$
$570$	25.4469	−	14.6918i	1.06585	−	0.615371i
$571$	−26.5949			−1.11296			−0.556481	−	0.830860i	$-0.687849\pi$
$571$	−26.5949			−1.11296			−0.556481	+	0.830860i	$0.687849\pi$
$572$	−2.22893	−	0.520607i	−0.0931963	−	0.0217677i
$573$	13.0138			0.543660
$574$	5.87537	−	3.39215i	0.245233	−	0.141585i
$575$	−7.98888	−	13.8371i	−0.333159	−	0.577049i
$576$	−1.60484	+	2.77966i	−0.0668682	+	0.115819i
$577$			21.6385i			0.900823i	0.892821	+	0.450412i	$0.148723\pi$
$577$			21.6385i			0.900823i	−0.892821	+	0.450412i	$0.851277\pi$
$578$	−7.65575	−	4.42005i	−0.318437	−	0.183850i
$579$	14.9112	+	8.60901i	0.619690	+	0.357778i
$580$			29.3627i			1.21922i
$581$	4.87973	−	8.45194i	0.202445	−	0.350646i
$582$	3.89631	+	6.74860i	0.161507	+	0.279739i
$583$	2.95648	−	1.70692i	0.122445	−	0.0706936i
$584$	1.56229			0.0646482
$585$	−7.79717	+	8.31862i	−0.322373	+	0.343933i
$586$	9.19725			0.379935
$587$	−8.37078	+	4.83287i	−0.345499	+	0.199474i	−0.662701	−	0.748884i	$-0.730590\pi$
$587$	−8.37078	+	4.83287i	−0.345499	+	0.199474i	0.317202	+	0.948358i	$0.397257\pi$
$588$	5.50067	+	9.52744i	0.226844	+	0.392905i
$589$	−3.50756	+	6.07528i	−0.144527	+	0.250327i
$590$		−	29.2877i		−	1.20576i
$591$	2.79902	+	1.61602i	0.115136	+	0.0664740i
$592$	−3.79929	−	2.19352i	−0.156150	−	0.0901531i
$593$		−	8.29806i		−	0.340761i	−0.985378	−	0.170380i	$-0.945500\pi$
$593$		−	8.29806i		−	0.340761i	0.985378	−	0.170380i	$-0.0544996\pi$
$594$	1.06840	−	1.85053i	0.0438371	−	0.0759281i
$595$	5.19949	+	9.00577i	0.213158	+	0.369201i
$596$	−22.4648	+	12.9701i	−0.920194	+	0.531274i
$597$	20.1789			0.825866
$598$	−4.07282	+	4.34520i	−0.166550	+	0.177688i
$599$	−8.99445			−0.367503			−0.183752	−	0.982973i	$-0.558824\pi$
$599$	−8.99445			−0.367503			−0.183752	+	0.982973i	$0.558824\pi$
$600$	−26.4800	+	15.2882i	−1.08104	+	0.624139i
$601$	10.3062	+	17.8508i	0.420398	+	0.728150i	0.995978	−	0.0895948i	$-0.0285572\pi$
$601$	10.3062	+	17.8508i	0.420398	+	0.728150i	−0.575581	+	0.817745i	$0.695224\pi$
$602$	−5.55794	+	9.62664i	−0.226525	+	0.392352i
$603$			0.589747i			0.0240164i
$604$	1.11083	+	0.641339i	0.0451991	+	0.0260957i
$605$	33.3844	+	19.2745i	1.35727	+	0.783620i
$606$		−	3.43958i		−	0.139723i
$607$	−3.41368	+	5.91266i	−0.138557	+	0.239988i	−0.926951	−	0.375183i	$-0.877580\pi$
$607$	−3.41368	+	5.91266i	−0.138557	+	0.239988i	0.788394	+	0.615171i	$0.210913\pi$
$608$	−20.4296	−	35.3851i	−0.828529	−	1.43505i
$609$	9.06784	−	5.23532i	0.367448	−	0.212146i
$610$	30.6226			1.23987
$611$	3.63426	+	0.848847i	0.147027	+	0.0343407i
$612$	2.93279			0.118551
$613$	−16.6415	+	9.60795i	−0.672142	+	0.388062i	−0.796888	−	0.604127i	$-0.793522\pi$
$613$	−16.6415	+	9.60795i	−0.672142	+	0.388062i	0.124746	+	0.992189i	$0.460189\pi$
$614$	11.4763	+	19.8775i	0.463144	+	0.802190i
$615$	18.4924	−	32.0297i	0.745684	−	1.29156i
$616$		−	1.50209i		−	0.0605208i
$617$	−27.1174	−	15.6562i	−1.09170	−	0.630296i	−0.157674	−	0.987491i	$-0.550400\pi$
$617$	−27.1174	−	15.6562i	−1.09170	−	0.630296i	−0.934030	+	0.357196i	$0.883733\pi$
$618$	11.2342	+	6.48605i	0.451904	+	0.260907i
$619$		−	26.3880i		−	1.06062i	−0.847803	−	0.530312i	$-0.822075\pi$
$619$		−	26.3880i		−	1.06062i	0.847803	−	0.530312i	$-0.177925\pi$
$620$	2.41680	−	4.18602i	0.0970610	−	0.168115i
$621$	5.79485	+	10.0370i	0.232539	+	0.402770i
$622$	−8.43736	+	4.87131i	−0.338307	+	0.195322i
$623$	−0.465988			−0.0186694
$624$	−2.02828	−	1.90114i	−0.0811963	−	0.0761066i
$625$	−3.27621			−0.131048
$626$	10.0873	−	5.82389i	0.403168	−	0.232769i
$627$	2.39633	+	4.15056i	0.0957000	+	0.165757i
$628$	4.34318	−	7.52260i	0.173312	−	0.300185i
$629$		−	20.3091i		−	0.809776i
$630$	−2.61310	−	1.50868i	−0.104108	−	0.0601071i
$631$	−30.0976	−	17.3768i	−1.19816	−	0.691761i	−0.238019	−	0.971260i	$-0.576498\pi$
$631$	−30.0976	−	17.3768i	−1.19816	−	0.691761i	−0.960146	+	0.279500i	$0.909831\pi$
$632$		−	35.2359i		−	1.40161i
$633$	−15.0487	+	26.0652i	−0.598134	+	1.03600i
$634$	−12.8563	−	22.2678i	−0.510590	−	0.884369i
$635$	−26.2529	+	15.1571i	−1.04182	+	0.601492i
$636$	14.2896			0.566620
$637$	−19.3094	+	5.84943i	−0.765065	+	0.231763i
$638$	2.29747			0.0909579
$639$	0.752642	−	0.434538i	0.0297741	−	0.0171901i
$640$	15.6029	+	27.0250i	0.616759	+	1.06826i
$641$	22.8257	−	39.5353i	0.901561	−	1.56155i	0.0760936	−	0.997101i	$-0.475755\pi$
$641$	22.8257	−	39.5353i	0.901561	−	1.56155i	0.825468	−	0.564449i	$-0.190911\pi$
$642$		−	0.0518702i		−	0.00204716i
$643$	12.5626	+	7.25304i	0.495422	+	0.286032i	0.726821	−	0.686827i	$-0.240997\pi$
$643$	12.5626	+	7.25304i	0.495422	+	0.286032i	−0.231399	+	0.972859i	$0.574330\pi$
$644$	2.84532	+	1.64275i	0.112121	+	0.0647332i
$645$			60.5985i			2.38606i
$646$	6.93073	−	12.0044i	0.272686	−	0.472306i
$647$	16.0642	+	27.8240i	0.631548	+	1.09387i	0.987235	+	0.159268i	$0.0509134\pi$
$647$	16.0642	+	27.8240i	0.631548	+	1.09387i	−0.355688	+	0.934605i	$0.615753\pi$
$648$	13.0076	−	7.50992i	0.510985	−	0.295018i
$649$	4.77701			0.187514
$650$	−6.55621	−	21.6425i	−0.257156	−	0.848889i
$651$	−1.72365			−0.0675550
$652$	12.9848	−	7.49678i	0.508524	−	0.293597i
$653$	−0.566768	−	0.981672i	−0.0221794	−	0.0384158i	0.854723	−	0.519085i	$-0.173727\pi$
$653$	−0.566768	−	0.981672i	−0.0221794	−	0.0384158i	−0.876902	+	0.480669i	$0.840394\pi$
$654$	8.46273	−	14.6579i	0.330919	−	0.573168i
$655$		−	49.7435i		−	1.94364i
$656$	−3.26391	−	1.88442i	−0.127434	−	0.0735743i
$657$	0.443298	+	0.255938i	0.0172947	+	0.00998509i
$658$			0.987672i			0.0385035i
$659$	−1.98484	+	3.43784i	−0.0773183	+	0.133919i	−0.902092	−	0.431544i	$-0.857969\pi$
$659$	−1.98484	+	3.43784i	−0.0773183	+	0.133919i	0.824774	+	0.565463i	$0.191302\pi$
$660$	−1.65113	−	2.85984i	−0.0642701	−	0.111319i
$661$	17.9456	−	10.3609i	0.698002	−	0.402992i	−0.108601	−	0.994085i	$-0.534637\pi$
$661$	17.9456	−	10.3609i	0.698002	−	0.402992i	0.806603	+	0.591094i	$0.201304\pi$
$662$	10.0288			0.389780
$663$	2.92711	−	12.5322i	0.113679	−	0.486708i
$664$	22.2270			0.862576
$665$	25.7454	−	14.8641i	0.998366	−	0.576407i
$666$	2.94643	+	5.10336i	0.114172	+	0.197751i
$667$	−6.23057	+	10.7917i	−0.241249	+	0.417855i
$668$		−	16.7576i		−	0.648372i
$669$	1.95156	+	1.12673i	0.0754515	+	0.0435619i
$670$	−1.66326	−	0.960282i	−0.0642572	−	0.0370989i
$671$			4.99475i			0.192820i
$672$	5.01964	−	8.69427i	0.193637	−	0.335389i
$673$	16.2713	+	28.1828i	0.627214	+	1.08637i	0.988108	+	0.153760i	$0.0491384\pi$
$673$	16.2713	+	28.1828i	0.627214	+	1.08637i	−0.360894	+	0.932607i	$0.617528\pi$
$674$	7.14816	−	4.12699i	0.275337	−	0.158966i
$675$	−44.0071			−1.69383
$676$	14.6171	−	9.75079i	0.562197	−	0.375030i
$677$	5.02148			0.192991			0.0964957	−	0.995333i	$-0.469237\pi$
$677$	5.02148			0.192991			0.0964957	+	0.995333i	$0.469237\pi$
$678$	−15.5767	+	8.99323i	−0.598220	+	0.345383i
$679$	3.94202	+	6.82778i	0.151281	+	0.262026i
$680$	−11.8418	+	20.5105i	−0.454111	+	0.786542i
$681$			14.4493i			0.553697i
$682$	−0.327534	−	0.189102i	−0.0125419	−	0.00724108i
$683$	−37.8427	−	21.8485i	−1.44801	−	0.836010i	−0.449648	−	0.893206i	$-0.648451\pi$
$683$	−37.8427	−	21.8485i	−1.44801	−	0.836010i	−0.998363	+	0.0571959i	$0.981784\pi$
$684$		−	8.38418i		−	0.320577i
$685$	29.2106	−	50.5943i	1.11608	−	1.93311i
$686$	−6.00937	−	10.4085i	−0.229439	−	0.397400i
$687$	−33.9463	+	19.5989i	−1.29513	+	0.747744i
$688$	6.17515			0.235425
$689$	−5.96055	+	25.5196i	−0.227079	+	0.972219i
$690$	−8.59215			−0.327098
$691$	2.78418	−	1.60745i	0.105915	−	0.0611501i	−0.446107	−	0.894980i	$-0.647190\pi$
$691$	2.78418	−	1.60745i	0.105915	−	0.0611501i	0.552022	+	0.833830i	$0.313856\pi$
$692$	−7.82789	−	13.5583i	−0.297572	−	0.515409i
$693$	0.246075	−	0.426214i	0.00934761	−	0.0161905i
$694$		−	2.91459i		−	0.110636i
$695$	−26.4206	−	15.2539i	−1.00219	−	0.578615i
$696$	20.6519	+	11.9234i	0.782808	+	0.451954i
$697$		−	17.4472i		−	0.660861i
$698$	10.0068	−	17.3323i	0.378764	−	0.656038i
$699$	14.2788	+	24.7316i	0.540074	+	0.935436i
$700$	−10.8039	+	6.23765i	−0.408350	+	0.235761i
$701$	−29.8039			−1.12568			−0.562840	−	0.826566i	$-0.690291\pi$
$701$	−29.8039			−1.12568			−0.562840	+	0.826566i	$0.690291\pi$
$702$	4.75564	+	15.6987i	0.179490	+	0.592509i
$703$	−58.0590			−2.18974
$704$	1.47647	−	0.852443i	0.0556467	−	0.0321277i
$705$	2.69216	+	4.66295i	0.101393	+	0.175617i
$706$	−2.56554	+	4.44365i	−0.0965554	+	0.167239i
$707$		−	3.47994i		−	0.130876i
$708$	17.3166	+	9.99777i	0.650799	+	0.375739i
$709$	−17.2603	−	9.96521i	−0.648222	−	0.374251i	0.139552	−	0.990215i	$-0.455434\pi$
$709$	−17.2603	−	9.96521i	−0.648222	−	0.374251i	−0.787775	+	0.615963i	$0.788767\pi$
$710$			2.83023i			0.106217i
$711$	5.77241	−	9.99811i	0.216482	−	0.374958i
$712$	−0.530640	−	0.919096i	−0.0198866	−	0.0344446i
$713$	1.77649	−	1.02566i	0.0665302	−	0.0384112i
$714$	3.40582			0.127460
$715$	5.79606	−	1.75581i	0.216760	−	0.0656637i
$716$	−22.5870			−0.844118
$717$	−13.1164	+	7.57277i	−0.489842	+	0.282810i
$718$	−8.58874	−	14.8761i	−0.320529	−	0.555173i
$719$	0.758477	−	1.31372i	0.0282864	−	0.0489935i	−0.851536	−	0.524297i	$-0.824328\pi$
$719$	0.758477	−	1.31372i	0.0282864	−	0.0489935i	0.879822	+	0.475303i	$0.157662\pi$
$720$			1.67621i			0.0624688i
$721$	11.3660	+	6.56214i	0.423291	+	0.244387i
$722$	−21.0682	−	12.1637i	−0.784077	−	0.452687i
$723$			10.0904i			0.375266i
$724$	−14.5860	+	25.2636i	−0.542083	+	0.938916i
$725$	−23.6580	−	40.9769i	−0.878636	−	1.52184i
$726$	10.9339	−	6.31269i	0.405795	−	0.234286i
$727$	11.1550			0.413717			0.206858	−	0.978371i	$-0.433676\pi$
$727$	11.1550			0.413717			0.206858	+	0.978371i	$0.433676\pi$
$728$	8.41291	+	7.88555i	0.311803	+	0.292258i
$729$	29.5755			1.09539
$730$	−1.44364	+	0.833485i	−0.0534315	+	0.0308487i
$731$	14.2934	+	24.7569i	0.528661	+	0.915668i
$732$	−10.4535	+	18.1059i	−0.386371	+	0.669215i
$733$			7.80414i			0.288252i	0.989559	+	0.144126i	$0.0460371\pi$
$733$			7.80414i			0.288252i	−0.989559	+	0.144126i	$0.953963\pi$
$734$	−2.69595	−	1.55651i	−0.0995093	−	0.0574517i
$735$	−25.2083	−	14.5540i	−0.929822	−	0.536833i
$736$			11.9478i			0.440401i
$737$	0.156628	−	0.271288i	0.00576948	−	0.00999303i
$738$	2.53123	+	4.38422i	0.0931760	+	0.161386i
$739$	−31.7993	+	18.3594i	−1.16976	+	0.675360i	−0.953623	−	0.301004i	$-0.902678\pi$
$739$	−31.7993	+	18.3594i	−1.16976	+	0.675360i	−0.216134	+	0.976364i	$0.569345\pi$
$740$	40.0041			1.47058
$741$	−35.8266	−	8.36793i	−1.31612	−	0.307404i
$742$	−6.93537			−0.254606
$743$	33.3891	−	19.2772i	1.22493	−	0.707213i	0.258964	−	0.965887i	$-0.416619\pi$
$743$	33.3891	−	19.2772i	1.22493	−	0.707213i	0.965965	+	0.258674i	$0.0832856\pi$
$744$	−1.96279	−	3.39965i	−0.0719594	−	0.124637i
$745$	34.3170	−	59.4387i	1.25728	−	2.17767i
$746$		−	27.9464i		−	1.02319i
$747$	6.30687	+	3.64127i	0.230756	+	0.133227i
$748$	−1.34911	−	0.778907i	−0.0493282	−	0.0284797i
$749$		−	0.0524788i		−	0.00191753i
$750$	5.84106	−	10.1170i	0.213285	−	0.369421i
$751$	−6.89394	−	11.9407i	−0.251564	−	0.435721i	0.712393	−	0.701781i	$-0.247611\pi$
$751$	−6.89394	−	11.9407i	−0.251564	−	0.435721i	−0.963956	+	0.266060i	$0.914278\pi$
$752$	0.475168	−	0.274338i	0.0173276	−	0.0100041i
$753$	25.9291			0.944909
$754$	−12.0611	+	12.8677i	−0.439240	+	0.468615i
$755$	−3.39379			−0.123512
$756$	7.83678	−	4.52457i	0.285021	−	0.164557i
$757$	−20.0897	−	34.7964i	−0.730173	−	1.26470i	−0.956809	−	0.290717i	$-0.906106\pi$
$757$	−20.0897	−	34.7964i	−0.730173	−	1.26470i	0.226636	−	0.973980i	$-0.427227\pi$
$758$	−8.37772	+	14.5106i	−0.304292	+	0.527050i
$759$		−	1.40144i		−	0.0508689i
$760$	58.6349	+	33.8529i	2.12691	+	1.22797i
$761$	−7.82011	−	4.51494i	−0.283479	−	0.163667i	0.351518	−	0.936181i	$-0.385665\pi$
$761$	−7.82011	−	4.51494i	−0.283479	−	0.163667i	−0.634997	+	0.772514i	$0.718999\pi$
$762$			9.92839i			0.359667i
$763$	8.56201	−	14.8298i	0.309966	−	0.536876i
$764$	6.04636	+	10.4726i	0.218750	+	0.378885i
$765$	−6.72014	+	3.87988i	−0.242967	+	0.140277i
$766$	10.7291			0.387657
$767$	−25.0780	+	26.7552i	−0.905515	+	0.966073i
$768$	20.7800			0.749835
$769$	21.5852	−	12.4622i	0.778383	−	0.449399i	−0.0574742	−	0.998347i	$-0.518305\pi$
$769$	21.5852	−	12.4622i	0.778383	−	0.449399i	0.835857	+	0.548948i	$0.184971\pi$
$770$	0.801365	+	1.38800i	0.0288792	+	0.0500202i
$771$	10.5916	−	18.3451i	0.381446	−	0.660684i
$772$			15.9994i			0.575829i
$773$	−2.82343	−	1.63011i	−0.101552	−	0.0586310i	0.448364	−	0.893851i	$-0.352007\pi$
$773$	−2.82343	−	1.63011i	−0.101552	−	0.0586310i	−0.549916	+	0.835220i	$0.685340\pi$
$774$	−7.18343	−	4.14736i	−0.258203	−	0.149074i
$775$			7.78903i			0.279790i
$776$	−8.97789	+	15.5502i	−0.322287	+	0.558218i
$777$	−7.13268	−	12.3542i	−0.255883	−	0.443203i
$778$	−5.38319	+	3.10799i	−0.192997	+	0.111427i
$779$	−49.8777			−1.78705
$780$	24.6854	+	5.76572i	0.883879	+	0.206446i
$781$	−0.461628			−0.0165184
$782$	−3.51024	+	2.02664i	−0.125526	+	0.0724725i
$783$	17.1607	+	29.7232i	0.613273	+	1.06222i
$784$	−1.48309	+	2.56879i	−0.0529676	+	0.0917427i
$785$			22.9829i			0.820294i
$786$	−14.1091	−	8.14588i	−0.503254	−	0.290554i
$787$	−27.6680	−	15.9741i	−0.986259	−	0.569417i	−0.0821049	−	0.996624i	$-0.526164\pi$
$787$	−27.6680	−	15.9741i	−0.986259	−	0.569417i	−0.904154	+	0.427207i	$0.859498\pi$
$788$			3.00327i			0.106987i
$789$	−14.4637	+	25.0519i	−0.514922	+	0.891870i
$790$	18.7984	+	32.5597i	0.668816	+	1.15842i
$791$	−15.7595	+	9.09873i	−0.560342	+	0.323514i
$792$	1.12086			0.0398281
$793$	−27.9747	−	26.2211i	−0.993410	−	0.931139i
$794$	−11.5548			−0.410065
$795$	−32.7430	+	18.9042i	−1.16127	+	0.670462i
$796$	9.37532	+	16.2385i	0.332299	+	0.575559i
$797$	12.9742	−	22.4720i	0.459570	−	0.795998i	−0.539369	−	0.842070i	$-0.681337\pi$
$797$	12.9742	−	22.4720i	0.459570	−	0.795998i	0.998938	+	0.0460720i	$0.0146704\pi$
$798$		−	9.73647i		−	0.344667i
$799$	2.19971	+	1.27000i	0.0778202	+	0.0449295i
$800$	−39.2887	−	22.6834i	−1.38907	−	0.801978i
$801$		−	0.347722i		−	0.0122862i
$802$	−2.46415	+	4.26804i	−0.0870123	+	0.150710i
$803$	−0.135947	−	0.235467i	−0.00479746	−	0.00830945i
$804$	1.13555	−	0.655612i	0.0400479	−	0.0231216i
$805$	−8.69295			−0.306386
$806$	2.77859	−	0.841723i	0.0978716	−	0.0296484i
$807$	−9.62628			−0.338861
$808$	6.86369	−	3.96275i	0.241464	−	0.139409i
$809$	−3.93041	−	6.80766i	−0.138186	−	0.239345i	0.788624	−	0.614876i	$-0.210794\pi$
$809$	−3.93041	−	6.80766i	−0.138186	−	0.239345i	−0.926810	+	0.375531i	$0.877460\pi$
$810$	−8.01310	+	13.8791i	−0.281552	+	0.487662i
$811$			26.9463i			0.946211i	0.881006	+	0.473106i	$0.156867\pi$
$811$			26.9463i			0.946211i	−0.881006	+	0.473106i	$0.843133\pi$
$812$	8.42603	+	4.86477i	0.295696	+	0.170720i
$813$	18.7461	+	10.8231i	0.657455	+	0.379582i
$814$		−	3.13011i		−	0.109710i
$815$	−19.8354	+	34.3560i	−0.694805	+	1.20344i
$816$	−0.946010	−	1.63854i	−0.0331170	−	0.0573603i
$817$	70.7744	−	40.8616i	2.47608	−	1.42957i
$818$	21.0520			0.736068
$819$	1.09532	+	3.61573i	0.0382736	+	0.126344i
$820$	34.3670			1.20015
$821$	7.63106	−	4.40579i	0.266326	−	0.153763i	−0.360891	−	0.932608i	$-0.617527\pi$
$821$	7.63106	−	4.40579i	0.266326	−	0.153763i	0.627217	+	0.778845i	$0.284194\pi$
$822$	−9.56692	−	16.5704i	−0.333685	−	0.577959i
$823$	11.0646	−	19.1645i	0.385688	−	0.668032i	−0.606176	−	0.795331i	$-0.707297\pi$
$823$	11.0646	−	19.1645i	0.385688	−	0.668032i	0.991864	+	0.127299i	$0.0406306\pi$
$824$			29.8904i			1.04128i
$825$	4.60844	+	2.66069i	0.160445	+	0.0926332i
$826$	−8.40452	−	4.85235i	−0.292431	−	0.168835i
$827$			39.6385i			1.37837i	0.724587	+	0.689183i	$0.242031\pi$
$827$			39.6385i			1.37837i	−0.724587	+	0.689183i	$0.757969\pi$
$828$	−1.22582	+	2.12319i	−0.0426003	+	0.0737859i
$829$	23.2877	+	40.3356i	0.808817	+	1.40091i	0.913684	+	0.406426i	$0.133225\pi$
$829$	23.2877	+	40.3356i	0.808817	+	1.40091i	−0.104867	+	0.994486i	$0.533442\pi$
$830$	−20.5389	+	11.8581i	−0.712916	+	0.411602i
$831$	−8.19166			−0.284165
$832$	−2.97672	+	12.7446i	−0.103199	+	0.441838i
$833$	−13.7315			−0.475768
$834$	−8.65315	+	4.99590i	−0.299634	+	0.172994i
$835$	22.1692	+	38.3981i	0.767196	+	1.32882i
$836$	−2.22672	+	3.85679i	−0.0770126	+	0.133390i
$837$		−	5.64988i		−	0.195288i
$838$	12.9712	+	7.48893i	0.448083	+	0.258701i
$839$	28.6977	+	16.5686i	0.990754	+	0.572012i	0.905500	−	0.424347i	$-0.139496\pi$
$839$	28.6977	+	16.5686i	0.990754	+	0.572012i	0.0852547	+	0.996359i	$0.472830\pi$
$840$			16.6356i			0.573983i
$841$	−3.95101	+	6.84335i	−0.136242	+	0.235978i
$842$	8.99677	+	15.5829i	0.310049	+	0.537021i
$843$	13.1848	−	7.61227i	0.454110	−	0.262181i
$844$	−27.9672			−0.962672
$845$	−20.5938	+	41.6802i	−0.708448	+	1.43384i
$846$	−0.737005			−0.0253388
$847$	11.0622	−	6.38675i	0.380101	−	0.219451i
$848$	1.92639	+	3.33660i	0.0661524	+	0.114579i
$849$	16.6440	−	28.8282i	0.571220	−	0.989383i
$850$		−	15.3906i		−	0.527895i
$851$	14.7027	+	8.48862i	0.504003	+	0.290986i
$852$	−1.67340	−	0.966138i	−0.0573297	−	0.0330993i
$853$			21.7594i			0.745026i	0.928027	+	0.372513i	$0.121504\pi$
$853$			21.7594i			0.745026i	−0.928027	+	0.372513i	$0.878496\pi$
$854$	5.07352	−	8.78760i	0.173612	−	0.300706i
$855$	11.0917	+	19.2114i	0.379328	+	0.657015i
$856$	0.103507	−	0.0597598i	0.00353780	−	0.00204255i
$857$	−33.6394			−1.14910			−0.574551	−	0.818469i	$-0.694823\pi$
$857$	−33.6394			−1.14910			−0.574551	+	0.818469i	$0.694823\pi$
$858$	0.451137	−	1.93150i	0.0154016	−	0.0659404i
$859$	−28.2138			−0.962642			−0.481321	−	0.876544i	$-0.659843\pi$
$859$	−28.2138			−0.962642			−0.481321	+	0.876544i	$0.659843\pi$
$860$	−48.7654	+	28.1547i	−1.66289	+	0.960067i
$861$	−6.12758	−	10.6133i	−0.208828	−	0.361700i
$862$	−16.2680	+	28.1769i	−0.554089	+	0.959710i
$863$		−	33.1339i		−	1.12789i	−0.825812	−	0.563946i	$-0.809283\pi$
$863$		−	33.1339i		−	1.12789i	0.825812	−	0.563946i	$-0.190717\pi$
$864$	28.4986	+	16.4537i	0.969543	+	0.559766i
$865$	35.8734	+	20.7115i	1.21973	+	0.704212i
$866$		−	26.6579i		−	0.905874i
$867$	−7.98439	+	13.8294i	−0.271164	+	0.469670i
$868$	−0.800825	−	1.38707i	−0.0271818	−	0.0470802i
$869$	−5.31070	+	3.06614i	−0.180153	+	0.104012i
$870$	−25.4445			−0.862650
$871$	0.697178	+	2.30144i	0.0236230	+	0.0779812i
$872$	38.9997			1.32070
$873$	−5.09491	+	2.94155i	−0.172437	+	0.0995564i
$874$	5.79370	+	10.0350i	0.195975	+	0.339438i
$875$	5.90959	−	10.2357i	0.199780	−	0.346030i
$876$		−	1.13809i		−	0.0384524i
$877$	41.5595	+	23.9944i	1.40337	+	0.810234i	0.994736	−	0.102467i	$-0.0326735\pi$
$877$	41.5595	+	23.9944i	1.40337	+	0.810234i	0.408629	+	0.912700i	$0.366007\pi$
$878$	24.3660	+	14.0677i	0.822313	+	0.474763i
$879$		−	16.6139i		−	0.560374i
$880$	0.445178	−	0.771071i	0.0150069	−	0.0259928i
$881$	20.6513	+	35.7692i	0.695761	+	1.20509i	0.969923	+	0.243411i	$0.0782662\pi$
$881$	20.6513	+	35.7692i	0.695761	+	1.20509i	−0.274162	+	0.961684i	$0.588400\pi$
$882$	3.45051	−	1.99215i	0.116185	−	0.0670793i
$883$	−18.5224			−0.623327			−0.311664	−	0.950193i	$-0.600886\pi$
$883$	−18.5224			−0.623327			−0.311664	+	0.950193i	$0.600886\pi$
$884$	11.4450	−	3.46704i	0.384936	−	0.116609i
$885$	−52.9054			−1.77840
$886$	−0.667225	+	0.385222i	−0.0224159	+	0.0129418i
$887$	−6.23015	−	10.7909i	−0.209188	−	0.362324i	0.742271	−	0.670100i	$-0.233749\pi$
$887$	−6.23015	−	10.7909i	−0.209188	−	0.362324i	−0.951459	+	0.307775i	$0.900415\pi$
$888$	16.2446	−	28.1364i	0.545132	−	0.944196i
$889$			10.0449i			0.336894i
$890$	0.980677	+	0.566194i	0.0328724	+	0.0189789i
$891$	−2.26377	−	1.30699i	−0.0758392	−	0.0437858i
$892$			2.09397i			0.0701112i
$893$	3.63065	−	6.28847i	0.121495	−	0.210436i
$894$	−11.2393	−	19.4671i	−0.375900	−	0.651077i
$895$	51.7556	−	29.8811i	1.73000	−	0.998815i
$896$	10.3403			0.345445
$897$	7.84918	+	7.35716i	0.262077	+	0.245648i
$898$	10.3996			0.347040
$899$	5.26085	−	3.03735i	0.175459	−	0.101301i
$900$	−4.65456	−	8.06193i	−0.155152	−	0.268731i
$901$	−8.91789	+	15.4462i	−0.297098	+	0.514589i
$902$		−	2.68904i		−	0.0895351i
$903$	17.3896	+	10.0399i	0.578689	+	0.334106i
$904$	−35.8920	−	20.7222i	−1.19375	−	0.689211i
$905$		−	77.1849i		−	2.56571i
$906$	−0.555758	+	0.962602i	−0.0184638	+	0.0319803i
$907$	−5.56858	−	9.64507i	−0.184902	−	0.320259i	0.758642	−	0.651508i	$-0.225863\pi$
$907$	−5.56858	−	9.64507i	−0.184902	−	0.320259i	−0.943543	+	0.331249i	$0.892530\pi$
$908$	−11.6277	+	6.71328i	−0.385880	+	0.222788i
$909$	2.59674			0.0861285
$910$	−11.9809	−	2.79835i	−0.397163	−	0.0927645i
$911$	6.78703			0.224864			0.112432	−	0.993659i	$-0.464136\pi$
$911$	6.78703			0.224864			0.112432	+	0.993659i	$0.464136\pi$
$912$	−4.68420	+	2.70443i	−0.155109	+	0.0895525i
$913$	−1.93414	−	3.35003i	−0.0640107	−	0.110870i
$914$	5.29723	−	9.17507i	0.175217	−	0.303484i
$915$		−	55.3168i		−	1.82872i
$916$	−31.5436	−	18.2117i	−1.04223	−	0.601732i
$917$	−14.2746	−	8.24145i	−0.471389	−	0.272157i
$918$			11.1638i			0.368461i
$919$	13.3694	−	23.1564i	0.441014	−	0.763859i	−0.556751	−	0.830680i	$-0.687952\pi$
$919$	13.3694	−	23.1564i	0.441014	−	0.763859i	0.997765	+	0.0668204i	$0.0212855\pi$
$920$	−9.89904	−	17.1456i	−0.326362	−	0.565275i
$921$	35.9067	−	20.7308i	1.18317	−	0.683102i
$922$	5.83859			0.192284
$923$	2.42342	−	2.58550i	0.0797680	−	0.0851026i
$924$	−1.09423			−0.0359975
$925$	−55.8275	+	32.2320i	−1.83560	+	1.05978i
$926$	4.74397	+	8.21680i	0.155897	+	0.270021i
$927$	−4.89670	+	8.48133i	−0.160829	+	0.278563i
$928$			35.3817i			1.16146i
$929$	−25.4757	−	14.7084i	−0.835832	−	0.482568i	0.0200134	−	0.999800i	$-0.493629\pi$
$929$	−25.4757	−	14.7084i	−0.835832	−	0.482568i	−0.855845	+	0.517232i	$0.826962\pi$
$930$	3.62744	+	2.09430i	0.118948	+	0.0686748i
$931$			39.2552i			1.28654i
$932$	−13.2682	+	22.9812i	−0.434614	+	0.752773i
$933$	8.79955	+	15.2413i	0.288084	+	0.498977i
$934$	−13.6510	+	7.88143i	−0.446676	+	0.257888i
$935$	4.12176			0.134796
$936$	−5.88423	+	6.27775i	−0.192332	+	0.205195i
$937$	21.4432			0.700518			0.350259	−	0.936653i	$-0.386094\pi$
$937$	21.4432			0.700518			0.350259	+	0.936653i	$0.386094\pi$
$938$	−0.551133	+	0.318197i	−0.0179951	+	0.0103895i
$939$	−10.5203	−	18.2217i	−0.343317	−	0.594642i
$940$	−2.50161	+	4.33292i	−0.0815935	+	0.141324i
$941$			26.9191i			0.877539i	0.898600	+	0.438769i	$0.144585\pi$
$941$			26.9191i			0.877539i	−0.898600	+	0.438769i	$0.855415\pi$
$942$	6.51879	+	3.76362i	0.212394	+	0.122625i
$943$	12.6309	+	7.29245i	0.411319	+	0.237475i
$944$			5.39120i			0.175469i
$945$	−11.9714	+	20.7350i	−0.389429	+	0.674510i
$946$	2.20296	+	3.81563i	0.0716243	+	0.124057i
$947$	−45.4228	+	26.2249i	−1.47604	+	0.852194i	−0.999635	−	0.0270297i	$-0.991395\pi$
$947$	−45.4228	+	26.2249i	−1.47604	+	0.852194i	−0.476409	+	0.879224i	$0.658062\pi$
$948$	−25.6683			−0.833669
$949$	2.03249	+	0.474724i	0.0659774	+	0.0154102i
$950$	−43.9983			−1.42749
$951$	−40.2247	+	23.2237i	−1.30437	+	0.753081i
$952$	3.92386	+	6.79632i	0.127173	+	0.220270i
$953$	24.2441	−	41.9920i	0.785344	−	1.36026i	−0.143450	−	0.989658i	$-0.545819\pi$
$953$	24.2441	−	41.9920i	0.785344	−	1.36026i	0.928793	−	0.370598i	$-0.120847\pi$
$954$		−	5.17520i		−	0.167553i
$955$	−27.7090	−	15.9978i	−0.896643	−	0.517677i
$956$	−12.1881	−	7.03678i	−0.394190	−	0.227586i
$957$		−	4.15017i		−	0.134156i
$958$	−8.52451	+	14.7649i	−0.275414	+	0.477032i
$959$	−9.67916	−	16.7648i	−0.312556	−	0.541364i
$960$	−16.3519	+	9.44080i	−0.527757	+	0.304700i
$961$	−1.00000			−0.0322581
$962$	17.5312	+	16.4322i	0.565228	+	0.529797i
$963$	0.0391599			0.00126191
$964$	−8.12004	+	4.68811i	−0.261529	+	0.150994i
$965$	−21.1660	−	36.6606i	−0.681359	−	1.18015i
$966$	−1.42354	+	2.46564i	−0.0458016	+	0.0793306i
$967$			12.1101i			0.389436i	0.980859	+	0.194718i	$0.0623791\pi$
$967$			12.1101i			0.389436i	−0.980859	+	0.194718i	$0.937621\pi$
$968$	25.1940	+	14.5457i	0.809765	+	0.467518i
$969$	−21.6847	−	12.5197i	−0.696614	−	0.402191i
$970$		−	19.1588i		−	0.615153i
$971$	−11.2097	+	19.4159i	−0.359738	+	0.623084i	−0.987917	−	0.154985i	$-0.950467\pi$
$971$	−11.2097	+	19.4159i	−0.359738	+	0.623084i	0.628179	+	0.778069i	$0.283801\pi$
$972$	5.98390	+	10.3644i	0.191934	+	0.332439i
$973$	−8.75467	+	5.05451i	−0.280662	+	0.162040i
$974$	−18.0574			−0.578595
$975$	−39.0951	+	11.8432i	−1.25204	+	0.379284i
$976$	−5.63694			−0.180434
$977$	2.48614	−	1.43537i	0.0795387	−	0.0459217i	−0.459703	−	0.888073i	$-0.652044\pi$
$977$	2.48614	−	1.43537i	0.0795387	−	0.0459217i	0.539242	+	0.842151i	$0.318711\pi$
$978$	6.49641	+	11.2521i	0.207732	+	0.359803i
$979$	−0.0923500	+	0.159955i	−0.00295152	+	0.00511218i
$980$		−	27.0478i		−	0.864010i
$981$	11.0661	+	6.38901i	0.353313	+	0.203985i
$982$	−18.4054	−	10.6264i	−0.587340	−	0.339101i
$983$			2.26162i			0.0721346i	0.999349	+	0.0360673i	$0.0114831\pi$
$983$			2.26162i			0.0721346i	−0.999349	+	0.0360673i	$0.988517\pi$
$984$	13.9555	−	24.1716i	0.444885	−	0.770563i
$985$	−3.97312	−	6.88165i	−0.126594	−	0.219267i
$986$	−10.3951	+	6.00162i	−0.331048	+	0.191131i
$987$	1.78413			0.0567896
$988$	−9.91148	−	32.7185i	−0.315326	−	1.04091i
$989$	−23.8970			−0.759880
$990$	−1.03573	+	0.597982i	−0.0329178	+	0.0190051i
$991$	17.9427	+	31.0777i	0.569968	+	0.987214i	0.996568	+	0.0827737i	$0.0263779\pi$
$991$	17.9427	+	31.0777i	0.569968	+	0.987214i	−0.426600	+	0.904440i	$0.640289\pi$
$992$	2.91222	−	5.04411i	0.0924631	−	0.160151i
$993$		−	18.1160i		−	0.574895i
$994$	0.812174	+	0.468909i	0.0257606	+	0.0148729i
$995$	−42.9649	−	24.8058i	−1.36208	−	0.786396i
$996$		−	16.1918i		−	0.513056i
$997$	1.95002	−	3.37753i	0.0617577	−	0.106967i	−0.833493	−	0.552529i	$-0.813663\pi$
$997$	1.95002	−	3.37753i	0.0617577	−	0.106967i	0.895251	+	0.445562i	$0.146996\pi$
$998$	7.11319	+	12.3204i	0.225164	+	0.389995i
$999$	40.4953	−	23.3800i	1.28121	−	0.739709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.r.a.218.11	✓	68
13.2	odd	12		5239.2.a.r.1.11		34
13.4	even	6	inner	403.2.r.a.342.11	yes	68
13.11	odd	12		5239.2.a.q.1.24		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.r.a.218.11	✓	68	1.1	even	1	trivial
403.2.r.a.342.11	yes	68	13.4	even	6	inner
5239.2.a.q.1.24		34	13.11	odd	12
5239.2.a.r.1.11		34	13.2	odd	12

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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.697346 + 0.402613i) q^{2} +(0.727281 + 1.25969i) q^{3} +(-0.675806 + 1.17053i) q^{4} -3.57617i q^{5} +(-1.01433 - 0.585626i) q^{6} +(-1.02623 - 0.592496i) q^{7} -2.69880i q^{8} +(0.442123 - 0.765780i) q^{9} +O(q^{10})\)	\(q+(-0.697346 + 0.402613i) q^{2} +(0.727281 + 1.25969i) q^{3} +(-0.675806 + 1.17053i) q^{4} -3.57617i q^{5} +(-1.01433 - 0.585626i) q^{6} +(-1.02623 - 0.592496i) q^{7} -2.69880i q^{8} +(0.442123 - 0.765780i) q^{9} +(1.43981 + 2.49383i) q^{10} +(-0.406760 + 0.234843i) q^{11} -1.96600 q^{12} +(0.820069 - 3.51105i) q^{13} +0.954187 q^{14} +(4.50487 - 2.60089i) q^{15} +(-0.265037 - 0.459058i) q^{16} +(1.22695 - 2.12513i) q^{17} +0.712018i q^{18} +(-6.07528 - 3.50756i) q^{19} +(4.18602 + 2.41680i) q^{20} -1.72365i q^{21} +(0.189102 - 0.327534i) q^{22} +(1.02566 + 1.77649i) q^{23} +(3.39965 - 1.96279i) q^{24} -7.78903 q^{25} +(0.841723 + 2.77859i) q^{26} +5.64988 q^{27} +(1.38707 - 0.800825i) q^{28} +(3.03735 + 5.26085i) q^{29} +(-2.09430 + 3.62744i) q^{30} -1.00000i q^{31} +(5.04411 + 2.91222i) q^{32} +(-0.591658 - 0.341594i) q^{33} +1.97594i q^{34} +(-2.11887 + 3.66999i) q^{35} +(0.597579 + 1.03504i) q^{36} +(7.16745 - 4.13813i) q^{37} +5.64876 q^{38} +(5.01925 - 1.52049i) q^{39} -9.65140 q^{40} +(6.15746 - 3.55501i) q^{41} +(0.693963 + 1.20198i) q^{42} +(-5.82479 + 10.0888i) q^{43} -0.634833i q^{44} +(-2.73856 - 1.58111i) q^{45} +(-1.43048 - 0.825887i) q^{46} +1.03509i q^{47} +(0.385514 - 0.667729i) q^{48} +(-2.79790 - 4.84610i) q^{49} +(5.43165 - 3.13596i) q^{50} +3.56934 q^{51} +(3.55558 + 3.33270i) q^{52} -7.26836 q^{53} +(-3.93992 + 2.27472i) q^{54} +(0.839840 + 1.45465i) q^{55} +(-1.59903 + 2.76960i) q^{56} -10.2039i q^{57} +(-4.23617 - 2.44575i) q^{58} +(-8.80804 - 5.08532i) q^{59} +7.03077i q^{60} +(5.31712 - 9.20952i) q^{61} +(0.402613 + 0.697346i) q^{62} +(-0.907444 + 0.523913i) q^{63} -3.62984 q^{64} +(-12.5561 - 2.93271i) q^{65} +0.550121 q^{66} +(-0.577594 + 0.333474i) q^{67} +(1.65836 + 2.87236i) q^{68} +(-1.49188 + 2.58402i) q^{69} -3.41234i q^{70} +(0.851168 + 0.491422i) q^{71} +(-2.06669 - 1.19320i) q^{72} +0.578884i q^{73} +(-3.33213 + 5.77142i) q^{74} +(-5.66481 - 9.81175i) q^{75} +(8.21141 - 4.74086i) q^{76} +0.556575 q^{77} +(-2.88799 + 3.08113i) q^{78} +13.0561 q^{79} +(-1.64167 + 0.947820i) q^{80} +(2.78268 + 4.81975i) q^{81} +(-2.86259 + 4.95815i) q^{82} +8.23588i q^{83} +(2.01758 + 1.16485i) q^{84} +(-7.59985 - 4.38778i) q^{85} -9.38055i q^{86} +(-4.41802 + 7.65223i) q^{87} +(0.633796 + 1.09777i) q^{88} +(0.340557 - 0.196621i) q^{89} +2.54630 q^{90} +(-2.92187 + 3.11727i) q^{91} -2.77258 q^{92} +(1.25969 - 0.727281i) q^{93} +(-0.416742 - 0.721818i) q^{94} +(-12.5437 + 21.7262i) q^{95} +8.47201i q^{96} +(-5.76187 - 3.32662i) q^{97} +(3.90220 + 2.25294i) q^{98} +0.415319i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 32 q^{4} - 34 q^{9}+O(q^{10}) \) 68 * q + 32 * q^4 - 34 * q^9	\( 68 q + 32 q^{4} - 34 q^{9} + 8 q^{10} - 12 q^{11} - 16 q^{12} + 6 q^{13} - 8 q^{14} - 36 q^{16} - 6 q^{17} + 12 q^{19} - 12 q^{20} - 20 q^{22} - 8 q^{23} + 48 q^{24} - 72 q^{25} - 12 q^{27} - 6 q^{28} + 32 q^{30} + 6 q^{33} + 30 q^{35} + 40 q^{36} - 42 q^{37} - 36 q^{38} - 14 q^{39} + 8 q^{40} + 18 q^{41} - 16 q^{42} + 12 q^{43} + 60 q^{45} + 30 q^{46} - 46 q^{48} + 22 q^{49} + 56 q^{51} + 20 q^{53} - 114 q^{54} - 6 q^{55} - 2 q^{56} - 12 q^{58} + 6 q^{59} + 6 q^{61} - 8 q^{62} - 30 q^{63} + 24 q^{64} + 24 q^{65} + 8 q^{66} - 48 q^{67} + 58 q^{68} - 28 q^{69} - 30 q^{71} + 72 q^{72} + 8 q^{74} - 4 q^{75} - 12 q^{76} - 20 q^{77} + 26 q^{78} + 16 q^{79} + 42 q^{80} - 58 q^{81} - 42 q^{82} - 72 q^{84} + 30 q^{85} - 20 q^{87} + 64 q^{88} + 18 q^{89} + 52 q^{90} - 22 q^{91} + 48 q^{92} + 8 q^{94} - 32 q^{95} - 168 q^{98}+O(q^{100}) \) 68 * q + 32 * q^4 - 34 * q^9 + 8 * q^10 - 12 * q^11 - 16 * q^12 + 6 * q^13 - 8 * q^14 - 36 * q^16 - 6 * q^17 + 12 * q^19 - 12 * q^20 - 20 * q^22 - 8 * q^23 + 48 * q^24 - 72 * q^25 - 12 * q^27 - 6 * q^28 + 32 * q^30 + 6 * q^33 + 30 * q^35 + 40 * q^36 - 42 * q^37 - 36 * q^38 - 14 * q^39 + 8 * q^40 + 18 * q^41 - 16 * q^42 + 12 * q^43 + 60 * q^45 + 30 * q^46 - 46 * q^48 + 22 * q^49 + 56 * q^51 + 20 * q^53 - 114 * q^54 - 6 * q^55 - 2 * q^56 - 12 * q^58 + 6 * q^59 + 6 * q^61 - 8 * q^62 - 30 * q^63 + 24 * q^64 + 24 * q^65 + 8 * q^66 - 48 * q^67 + 58 * q^68 - 28 * q^69 - 30 * q^71 + 72 * q^72 + 8 * q^74 - 4 * q^75 - 12 * q^76 - 20 * q^77 + 26 * q^78 + 16 * q^79 + 42 * q^80 - 58 * q^81 - 42 * q^82 - 72 * q^84 + 30 * q^85 - 20 * q^87 + 64 * q^88 + 18 * q^89 + 52 * q^90 - 22 * q^91 + 48 * q^92 + 8 * q^94 - 32 * q^95 - 168 * q^98

Introduction

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