LMFDB - Embedded newform 220.2.l.d.23.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(23,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.23"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$220 = 2^{2} \cdot 5 \cdot 11$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	220.l (of order $4$ , degree $2$ , minimal)

Newform invariants

comment:select newform

sage:traces = [28,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	220.23
Dual form			220.2.l.d.67.11

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15410 - 0.817343i) q^{2} +(-1.62701 + 1.62701i) q^{3} +(0.663900 - 1.88659i) q^{4} +(-0.0183109 + 2.23599i) q^{5} +(-0.547909 + 3.20756i) q^{6} +(1.77258 + 1.77258i) q^{7} +(-0.775788 - 2.71995i) q^{8} -2.29432i q^{9} +(1.80644 + 2.59553i) q^{10} +1.00000i q^{11} +(1.98934 + 4.14968i) q^{12} +(4.00489 + 4.00489i) q^{13} +(3.49453 + 0.596929i) q^{14} +(-3.60819 - 3.66777i) q^{15} +(-3.11847 - 2.50502i) q^{16} +(1.12489 - 1.12489i) q^{17} +(-1.87525 - 2.64788i) q^{18} -5.87411 q^{19} +(4.20625 + 1.51902i) q^{20} -5.76800 q^{21} +(0.817343 + 1.15410i) q^{22} +(6.73550 - 6.73550i) q^{23} +(5.68761 + 3.16318i) q^{24} +(-4.99933 - 0.0818860i) q^{25} +(7.89542 + 1.34868i) q^{26} +(-1.14814 - 1.14814i) q^{27} +(4.52094 - 2.16732i) q^{28} -6.21347i q^{29} +(-7.16205 - 1.28385i) q^{30} +0.425403i q^{31} +(-5.64650 - 0.342181i) q^{32} +(-1.62701 - 1.62701i) q^{33} +(0.378817 - 2.21767i) q^{34} +(-3.99592 + 3.93101i) q^{35} +(-4.32846 - 1.52320i) q^{36} +(-2.75120 + 2.75120i) q^{37} +(-6.77931 + 4.80116i) q^{38} -13.0320 q^{39} +(6.09600 - 1.68485i) q^{40} +0.275777 q^{41} +(-6.65685 + 4.71443i) q^{42} +(1.49540 - 1.49540i) q^{43} +(1.88659 + 0.663900i) q^{44} +(5.13009 + 0.0420111i) q^{45} +(2.26823 - 13.2787i) q^{46} +(0.621320 + 0.621320i) q^{47} +(9.14948 - 0.998099i) q^{48} -0.715953i q^{49} +(-5.83666 + 3.99166i) q^{50} +3.66043i q^{51} +(10.2145 - 4.89676i) q^{52} +(-0.0170182 - 0.0170182i) q^{53} +(-2.26350 - 0.386647i) q^{54} +(-2.23599 - 0.0183109i) q^{55} +(3.44618 - 6.19647i) q^{56} +(9.55723 - 9.55723i) q^{57} +(-5.07854 - 7.17097i) q^{58} +9.21240 q^{59} +(-9.31508 + 4.37216i) q^{60} +3.36500 q^{61} +(0.347700 + 0.490958i) q^{62} +(4.06686 - 4.06686i) q^{63} +(-6.79631 + 4.22021i) q^{64} +(-9.02825 + 8.88158i) q^{65} +(-3.20756 - 0.547909i) q^{66} +(7.30534 + 7.30534i) q^{67} +(-1.37540 - 2.86904i) q^{68} +21.9174i q^{69} +(-1.39872 + 7.80282i) q^{70} -6.52136i q^{71} +(-6.24045 + 1.77991i) q^{72} +(-4.43765 - 4.43765i) q^{73} +(-0.926489 + 5.42384i) q^{74} +(8.26719 - 8.00073i) q^{75} +(-3.89982 + 11.0821i) q^{76} +(-1.77258 + 1.77258i) q^{77} +(-15.0402 + 10.6516i) q^{78} -8.08617 q^{79} +(5.65831 - 6.92702i) q^{80} +10.6191 q^{81} +(0.318275 - 0.225405i) q^{82} +(4.93412 - 4.93412i) q^{83} +(-3.82937 + 10.8819i) q^{84} +(2.49466 + 2.53585i) q^{85} +(0.503588 - 2.94810i) q^{86} +(10.1094 + 10.1094i) q^{87} +(2.71995 - 0.775788i) q^{88} +0.427109i q^{89} +(5.95498 - 4.14456i) q^{90} +14.1979i q^{91} +(-8.23546 - 17.1788i) q^{92} +(-0.692135 - 0.692135i) q^{93} +(1.22490 + 0.209235i) q^{94} +(0.107560 - 13.1345i) q^{95} +(9.74364 - 8.63017i) q^{96} +(6.93455 - 6.93455i) q^{97} +(-0.585179 - 0.826282i) q^{98} +2.29432 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$28 q + 2 q^{2} + 4 q^{3} - 4 q^{4} + 2 q^{5} - 12 q^{6} + 2 q^{7} + 2 q^{8} - 6 q^{10} + 8 q^{12} + 6 q^{13} + 20 q^{14} - 8 q^{15} + 8 q^{16} - 14 q^{17} - 6 q^{18} - 4 q^{19} + 8 q^{20} - 16 q^{21} - 2 q^{22}+ \cdots + 20 q^{99}+O(q^{100})$ 28 * q + 2 * q^2 + 4 * q^3 - 4 * q^4 + 2 * q^5 - 12 * q^6 + 2 * q^7 + 2 * q^8 - 6 * q^10 + 8 * q^12 + 6 * q^13 + 20 * q^14 - 8 * q^15 + 8 * q^16 - 14 * q^17 - 6 * q^18 - 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 + 8 * q^23 - 28 * q^24 - 4 * q^25 + 4 * q^26 - 44 * q^27 + 8 * q^28 - 24 * q^30 - 38 * q^32 + 4 * q^33 + 52 * q^34 + 10 * q^35 - 4 * q^36 + 20 * q^37 - 48 * q^38 - 32 * q^39 + 46 * q^40 + 12 * q^41 + 32 * q^42 - 2 * q^43 - 10 * q^45 + 4 * q^46 + 44 * q^47 + 44 * q^48 - 18 * q^50 - 52 * q^52 - 28 * q^53 + 40 * q^54 + 2 * q^55 + 4 * q^56 - 8 * q^57 - 36 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 20 * q^62 + 10 * q^63 - 28 * q^64 - 30 * q^65 - 16 * q^67 + 68 * q^68 - 40 * q^70 - 38 * q^72 + 22 * q^73 + 20 * q^74 + 56 * q^75 + 4 * q^76 - 2 * q^77 - 40 * q^78 + 20 * q^79 + 12 * q^80 + 12 * q^81 + 12 * q^82 - 2 * q^83 - 120 * q^84 - 14 * q^85 - 20 * q^86 + 48 * q^87 + 14 * q^88 - 10 * q^90 + 4 * q^92 - 20 * q^93 + 20 * q^94 - 92 * q^95 + 40 * q^96 + 16 * q^97 - 82 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$ .

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	1.15410	−	0.817343i	0.816073	−	0.577949i
$2$	1.15410	−	0.817343i	0.816073	−	0.577949i
$3$	−1.62701	+	1.62701i	−0.939355	+	0.939355i	−0.998263	−	0.0589088i	$-0.981238\pi$
$3$	−1.62701	+	1.62701i	−0.939355	+	0.939355i	0.0589088	+	0.998263i	$0.481238\pi$
$4$	0.663900	−	1.88659i	0.331950	−	0.943297i
$5$	−0.0183109	+	2.23599i	−0.00818887	+	0.999966i
$5$	−0.0183109	+	2.23599i	−0.00818887	+	0.999966i
$6$	−0.547909	+	3.20756i	−0.223683	+	1.30948i
$7$	1.77258	+	1.77258i	0.669971	+	0.669971i	0.957709	−	0.287738i	$-0.0929034\pi$
$7$	1.77258	+	1.77258i	0.669971	+	0.669971i	−0.287738	+	0.957709i	$0.592903\pi$
$8$	−0.775788	−	2.71995i	−0.274282	−	0.961649i
$9$		−	2.29432i		−	0.764774i
$10$	1.80644	+	2.59553i	0.571247	+	0.820778i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	1.98934	+	4.14968i	0.574272	+	1.19791i
$13$	4.00489	+	4.00489i	1.11076	+	1.11076i	0.993048	+	0.117709i	$0.0375551\pi$
$13$	4.00489	+	4.00489i	1.11076	+	1.11076i	0.117709	+	0.993048i	$0.462445\pi$
$14$	3.49453	+	0.596929i	0.933954	+	0.159536i
$15$	−3.60819	−	3.66777i	−0.931631	−	0.947015i
$16$	−3.11847	−	2.50502i	−0.779619	−	0.626255i
$17$	1.12489	−	1.12489i	0.272827	−	0.272827i	−0.557410	−	0.830237i	$-0.688205\pi$
$17$	1.12489	−	1.12489i	0.272827	−	0.272827i	0.830237	+	0.557410i	$0.188205\pi$
$18$	−1.87525	−	2.64788i	−0.442000	−	0.624111i
$19$	−5.87411			−1.34761			−0.673806	−	0.738908i	$-0.735342\pi$
$19$	−5.87411			−1.34761			−0.673806	+	0.738908i	$0.735342\pi$
$20$	4.20625	+	1.51902i	0.940547	+	0.339663i
$21$	−5.76800			−1.25868
$22$	0.817343	+	1.15410i	0.174258	+	0.246055i
$23$	6.73550	−	6.73550i	1.40445	−	1.40445i	0.619272	−	0.785176i	$-0.287428\pi$
$23$	6.73550	−	6.73550i	1.40445	−	1.40445i	0.785176	−	0.619272i	$-0.212572\pi$
$24$	5.68761	+	3.16318i	1.16098	+	0.645681i
$25$	−4.99933	−	0.0818860i	−0.999866	−	0.0163772i
$26$	7.89542	+	1.34868i	1.54842	+	0.264498i
$27$	−1.14814	−	1.14814i	−0.220960	−	0.220960i
$28$	4.52094	−	2.16732i	0.854378	−	0.409585i
$29$		−	6.21347i		−	1.15381i	−0.816811	−	0.576906i	$-0.804260\pi$
$29$		−	6.21347i		−	1.15381i	0.816811	−	0.576906i	$-0.195740\pi$
$30$	−7.16205	−	1.28385i	−1.30761	−	0.234398i
$31$			0.425403i			0.0764046i	0.999270	+	0.0382023i	$0.0121631\pi$
$31$			0.425403i			0.0764046i	−0.999270	+	0.0382023i	$0.987837\pi$
$32$	−5.64650	−	0.342181i	−0.998169	−	0.0604895i
$33$	−1.62701	−	1.62701i	−0.283226	−	0.283226i
$34$	0.378817	−	2.21767i	0.0649666	−	0.380327i
$35$	−3.99592	+	3.93101i	−0.675434	+	0.664462i
$36$	−4.32846	−	1.52320i	−0.721409	−	0.253867i
$37$	−2.75120	+	2.75120i	−0.452295	+	0.452295i	−0.896116	−	0.443821i	$-0.853623\pi$
$37$	−2.75120	+	2.75120i	−0.452295	+	0.452295i	0.443821	+	0.896116i	$0.353623\pi$
$38$	−6.77931	+	4.80116i	−1.09975	+	0.778851i
$39$	−13.0320			−2.08679
$40$	6.09600	−	1.68485i	0.963863	−	0.266398i
$41$	0.275777			0.0430692			0.0215346	−	0.999768i	$-0.493145\pi$
$41$	0.275777			0.0430692			0.0215346	+	0.999768i	$0.493145\pi$
$42$	−6.65685	+	4.71443i	−1.02717	+	0.727453i
$43$	1.49540	−	1.49540i	0.228046	−	0.228046i	−0.583830	−	0.811876i	$-0.698446\pi$
$43$	1.49540	−	1.49540i	0.228046	−	0.228046i	0.811876	+	0.583830i	$0.198446\pi$
$44$	1.88659	+	0.663900i	0.284415	+	0.100087i
$45$	5.13009	+	0.0420111i	0.764749	+	0.00626264i
$46$	2.26823	−	13.2787i	0.334433	−	1.95783i
$47$	0.621320	+	0.621320i	0.0906289	+	0.0906289i	0.750968	−	0.660339i	$-0.229587\pi$
$47$	0.621320	+	0.621320i	0.0906289	+	0.0906289i	−0.660339	+	0.750968i	$0.729587\pi$
$48$	9.14948	−	0.998099i	1.32061	−	0.144063i
$49$		−	0.715953i		−	0.102279i
$50$	−5.83666	+	3.99166i	−0.825429	+	0.564507i
$51$			3.66043i			0.512563i
$52$	10.2145	−	4.89676i	1.41649	−	0.679058i
$53$	−0.0170182	−	0.0170182i	−0.00233763	−	0.00233763i	0.705937	−	0.708275i	$-0.250526\pi$
$53$	−0.0170182	−	0.0170182i	−0.00233763	−	0.00233763i	−0.708275	+	0.705937i	$0.750526\pi$
$54$	−2.26350	−	0.386647i	−0.308024	−	0.0526160i
$55$	−2.23599	−	0.0183109i	−0.301501	−	0.00246904i
$56$	3.44618	−	6.19647i	0.460516	−	0.828038i
$57$	9.55723	−	9.55723i	1.26589	−	1.26589i
$58$	−5.07854	−	7.17097i	−0.666844	−	0.941594i
$59$	9.21240			1.19935			0.599676	−	0.800243i	$-0.295296\pi$
$59$	9.21240			1.19935			0.599676	+	0.800243i	$0.295296\pi$
$60$	−9.31508	+	4.37216i	−1.20257	+	0.564443i
$61$	3.36500			0.430844			0.215422	−	0.976521i	$-0.430887\pi$
$61$	3.36500			0.430844			0.215422	+	0.976521i	$0.430887\pi$
$62$	0.347700	+	0.490958i	0.0441580	+	0.0623517i
$63$	4.06686	−	4.06686i	0.512376	−	0.512376i
$64$	−6.79631	+	4.22021i	−0.849538	+	0.527527i
$65$	−9.02825	+	8.88158i	−1.11982	+	1.10162i
$66$	−3.20756	−	0.547909i	−0.394823	−	0.0674429i
$67$	7.30534	+	7.30534i	0.892489	+	0.892489i	0.994757	−	0.102268i	$-0.0326098\pi$
$67$	7.30534	+	7.30534i	0.892489	+	0.892489i	−0.102268	+	0.994757i	$0.532610\pi$
$68$	−1.37540	−	2.86904i	−0.166792	−	0.347922i
$69$			21.9174i			2.63855i
$70$	−1.39872	+	7.80282i	−0.167179	+	0.932616i
$71$		−	6.52136i		−	0.773944i	−0.922092	−	0.386972i	$-0.873521\pi$
$71$		−	6.52136i		−	0.773944i	0.922092	−	0.386972i	$-0.126479\pi$
$72$	−6.24045	+	1.77991i	−0.735444	+	0.209764i
$73$	−4.43765	−	4.43765i	−0.519387	−	0.519387i	0.397999	−	0.917386i	$-0.369705\pi$
$73$	−4.43765	−	4.43765i	−0.519387	−	0.519387i	−0.917386	+	0.397999i	$0.869705\pi$
$74$	−0.926489	+	5.42384i	−0.107702	+	0.630509i
$75$	8.26719	−	8.00073i	0.954613	−	0.923845i
$76$	−3.89982	+	11.0821i	−0.447340	+	1.27120i
$77$	−1.77258	+	1.77258i	−0.202004	+	0.202004i
$78$	−15.0402	+	10.6516i	−1.70297	+	1.20606i
$79$	−8.08617			−0.909765			−0.454883	−	0.890551i	$-0.650319\pi$
$79$	−8.08617			−0.909765			−0.454883	+	0.890551i	$0.650319\pi$
$80$	5.65831	−	6.92702i	0.632618	−	0.774464i
$81$	10.6191			1.17989
$82$	0.318275	−	0.225405i	0.0351476	−	0.0248918i
$83$	4.93412	−	4.93412i	0.541590	−	0.541590i	−0.382405	−	0.923995i	$-0.624904\pi$
$83$	4.93412	−	4.93412i	0.541590	−	0.541590i	0.923995	+	0.382405i	$0.124904\pi$
$84$	−3.82937	+	10.8819i	−0.417819	+	1.18731i
$85$	2.49466	+	2.53585i	0.270584	+	0.275052i
$86$	0.503588	−	2.94810i	0.0543033	−	0.317902i
$87$	10.1094	+	10.1094i	1.08384	+	1.08384i
$88$	2.71995	−	0.775788i	0.289948	−	0.0826992i
$89$			0.427109i			0.0452734i	0.999744	+	0.0226367i	$0.00720611\pi$
$89$			0.427109i			0.0452734i	−0.999744	+	0.0226367i	$0.992794\pi$
$90$	5.95498	−	4.14456i	0.627710	−	0.436875i
$91$			14.1979i			1.48835i
$92$	−8.23546	−	17.1788i	−0.858606	−	1.79102i
$93$	−0.692135	−	0.692135i	−0.0717710	−	0.0717710i
$94$	1.22490	+	0.209235i	0.126339	+	0.0215809i
$95$	0.107560	−	13.1345i	0.0110354	−	1.34757i
$96$	9.74364	−	8.63017i	0.994456	−	0.880813i
$97$	6.93455	−	6.93455i	0.704097	−	0.704097i	−0.261190	−	0.965287i	$-0.584115\pi$
$97$	6.93455	−	6.93455i	0.704097	−	0.704097i	0.965287	+	0.261190i	$0.0841150\pi$
$98$	−0.585179	−	0.826282i	−0.0591120	−	0.0834671i
$99$	2.29432			0.230588
$100$	−3.47354	+	9.37734i	−0.347354	+	0.937734i
$101$	−15.8215			−1.57430			−0.787149	−	0.616763i	$-0.788444\pi$
$101$	−15.8215			−1.57430			−0.787149	+	0.616763i	$0.788444\pi$
$102$	2.99183	+	4.22451i	0.296235	+	0.418288i
$103$	−6.15098	+	6.15098i	−0.606074	+	0.606074i	−0.941918	−	0.335844i	$-0.890979\pi$
$103$	−6.15098	+	6.15098i	−0.606074	+	0.606074i	0.335844	+	0.941918i	$0.390979\pi$
$104$	7.78618	−	14.0001i	0.763498	−	1.37282i
$105$	0.105617	−	12.8972i	0.0103072	−	1.25864i
$106$	−0.0335504	−	0.00573101i	−0.00325870	−	0.000556645i
$107$	5.85807	+	5.85807i	0.566321	+	0.566321i	0.931096	−	0.364775i	$-0.118854\pi$
$107$	5.85807	+	5.85807i	0.566321	+	0.566321i	−0.364775	+	0.931096i	$0.618854\pi$
$108$	−2.92833	+	1.40383i	−0.281779	+	0.135084i
$109$		−	3.38097i		−	0.323838i	−0.986804	−	0.161919i	$-0.948232\pi$
$109$		−	3.38097i		−	0.323838i	0.986804	−	0.161919i	$-0.0517683\pi$
$110$	−2.59553	+	1.80644i	−0.247474	+	0.172237i
$111$		−	8.95247i		−	0.849730i
$112$	−1.08740	−	9.96807i	−0.102749	−	0.941894i
$113$	2.58064	+	2.58064i	0.242766	+	0.242766i	0.817993	−	0.575228i	$-0.195086\pi$
$113$	2.58064	+	2.58064i	0.242766	+	0.242766i	−0.575228	+	0.817993i	$0.695086\pi$
$114$	3.21847	−	18.8415i	0.301438	−	1.76467i
$115$	14.9372	+	15.1839i	1.39290	+	1.41590i
$116$	−11.7223	−	4.12512i	−1.08839	−	0.383008i
$117$	9.18852	−	9.18852i	0.849479	−	0.849479i
$118$	10.6320	−	7.52969i	0.978759	−	0.693164i
$119$	3.98792			0.365572
$120$	−7.17699	+	12.6595i	−0.655167	+	1.15565i
$121$	−1.00000			−0.0909091
$122$	3.88355	−	2.75036i	0.351600	−	0.249006i
$123$	−0.448693	+	0.448693i	−0.0404572	+	0.0404572i
$124$	0.802563	+	0.282425i	0.0720723	+	0.0253625i
$125$	0.274639	−	11.1770i	0.0245644	−	0.999698i
$126$	1.36955	−	8.01759i	0.122009	−	0.714264i
$127$	6.56387	+	6.56387i	0.582449	+	0.582449i	0.935576	−	0.353127i	$-0.114882\pi$
$127$	6.56387	+	6.56387i	0.582449	+	0.582449i	−0.353127	+	0.935576i	$0.614882\pi$
$128$	−4.39426	+	10.4255i	−0.388402	+	0.921490i
$129$			4.86606i			0.428433i
$130$	−3.16021	+	17.6294i	−0.277169	+	1.54620i
$131$		−	7.65277i		−	0.668625i	−0.942462	−	0.334313i	$-0.891496\pi$
$131$		−	7.65277i		−	0.668625i	0.942462	−	0.334313i	$-0.108504\pi$
$132$	−4.14968	+	1.98934i	−0.361183	+	0.173149i
$133$	−10.4123	−	10.4123i	−0.902861	−	0.902861i
$134$	14.4021	+	2.46013i	1.24415	+	0.212523i
$135$	2.58827	−	2.54622i	0.222762	−	0.219144i
$136$	−3.93234	−	2.18698i	−0.337195	−	0.187532i
$137$	−10.4963	+	10.4963i	−0.896756	+	0.896756i	−0.995148	−	0.0983917i	$-0.968630\pi$
$137$	−10.4963	+	10.4963i	−0.896756	+	0.896756i	0.0983917	+	0.995148i	$0.468630\pi$
$138$	17.9141	+	25.2950i	1.52495	+	2.15325i
$139$	−7.51776			−0.637648			−0.318824	−	0.947814i	$-0.603288\pi$
$139$	−7.51776			−0.637648			−0.318824	+	0.947814i	$0.603288\pi$
$140$	4.76333	+	10.1485i	0.402574	+	0.857703i
$141$	−2.02179			−0.170265
$142$	−5.33019	−	7.52632i	−0.447300	−	0.631594i
$143$	−4.00489	+	4.00489i	−0.334906	+	0.334906i
$144$	−5.74732	+	7.15479i	−0.478943	+	0.596232i
$145$	13.8933	+	0.113774i	1.15377	+	0.00944842i
$146$	−8.74858	−	1.49441i	−0.724037	−	0.123678i
$147$	1.16486	+	1.16486i	0.0960762	+	0.0960762i
$148$	3.36388	+	7.01692i	0.276509	+	0.576788i
$149$		−	18.3664i		−	1.50463i	−0.658801	−	0.752317i	$-0.728936\pi$
$149$		−	18.3664i		−	1.50463i	0.658801	−	0.752317i	$-0.271064\pi$
$150$	3.00183	−	15.9908i	0.245098	−	1.30564i
$151$			10.7065i			0.871284i	0.900120	+	0.435642i	$0.143479\pi$
$151$			10.7065i			0.871284i	−0.900120	+	0.435642i	$0.856521\pi$
$152$	4.55706	+	15.9773i	0.369626	+	1.29593i
$153$	−2.58087	−	2.58087i	−0.208651	−	0.208651i
$154$	−0.596929	+	3.49453i	−0.0481019	+	0.281598i
$155$	−0.951198	−	0.00778950i	−0.0764021	−	0.000625668i
$156$	−8.65194	+	24.5861i	−0.692710	+	1.96846i
$157$	−16.1076	+	16.1076i	−1.28552	+	1.28552i	−0.348045	+	0.937478i	$0.613154\pi$
$157$	−16.1076	+	16.1076i	−1.28552	+	1.28552i	−0.937478	+	0.348045i	$0.886846\pi$
$158$	−9.33226	+	6.60918i	−0.742435	+	0.525798i
$159$	0.0553775			0.00439172
$160$	0.868506	−	12.6193i	0.0686614	−	0.997640i
$161$	23.8784			1.88188
$162$	12.2555	−	8.67941i	0.962880	−	0.681919i
$163$	−4.46640	+	4.46640i	−0.349835	+	0.349835i	−0.860048	−	0.510213i	$-0.829567\pi$
$163$	−4.46640	+	4.46640i	−0.349835	+	0.349835i	0.510213	+	0.860048i	$0.329567\pi$
$164$	0.183089	−	0.520280i	0.0142968	−	0.0406270i
$165$	3.66777	−	3.60819i	0.285536	−	0.280897i
$166$	1.66160	−	9.72734i	0.128965	−	0.754988i
$167$	−7.71540	−	7.71540i	−0.597035	−	0.597035i	0.342487	−	0.939523i	$-0.388731\pi$
$167$	−7.71540	−	7.71540i	−0.597035	−	0.597035i	−0.939523	+	0.342487i	$0.888731\pi$
$168$	4.47474	+	15.6887i	0.345234	+	1.21041i
$169$			19.0783i			1.46756i
$170$	4.95175	+	0.887640i	0.379782	+	0.0680789i
$171$			13.4771i			1.03062i
$172$	−1.82842	−	3.81401i	−0.139415	−	0.290815i
$173$	11.4713	+	11.4713i	0.872147	+	0.872147i	0.992706	−	0.120559i	$-0.0384687\pi$
$173$	11.4713	+	11.4713i	0.872147	+	0.872147i	−0.120559	+	0.992706i	$0.538469\pi$
$174$	19.9301	+	3.40441i	1.51089	+	0.258088i
$175$	−8.71654	−	9.00684i	−0.658908	−	0.680853i
$176$	2.50502	−	3.11847i	0.188823	−	0.235064i
$177$	−14.9887	+	14.9887i	−1.12662	+	1.12662i
$178$	0.349095	+	0.492927i	0.0261657	+	0.0369464i
$179$	−14.4543			−1.08037			−0.540184	−	0.841547i	$-0.681646\pi$
$179$	−14.4543			−1.08037			−0.540184	+	0.841547i	$0.681646\pi$
$180$	3.48512	−	9.65050i	0.259766	−	0.719306i
$181$	6.67264			0.495973			0.247987	−	0.968763i	$-0.420231\pi$
$181$	6.67264			0.495973			0.247987	+	0.968763i	$0.420231\pi$
$182$	11.6046	+	16.3859i	0.860190	+	1.21460i
$183$	−5.47488	+	5.47488i	−0.404715	+	0.404715i
$184$	−23.5456	−	13.0949i	−1.73580	−	0.965371i
$185$	−6.10129	−	6.20204i	−0.448576	−	0.455983i
$186$	−1.36451	−	0.233082i	−0.100050	−	0.0170904i
$187$	1.12489	+	1.12489i	0.0822604	+	0.0822604i
$188$	1.58467	−	0.759685i	0.115574	−	0.0554057i
$189$		−	4.07034i		−	0.296074i
$190$	−10.6112	−	15.2464i	−0.769819	−	1.10609i
$191$		−	9.15027i		−	0.662090i	−0.943615	−	0.331045i	$-0.892599\pi$
$191$		−	9.15027i		−	0.662090i	0.943615	−	0.331045i	$-0.107401\pi$
$192$	4.19133	−	17.9240i	0.302483	−	1.29355i
$193$	−5.13425	−	5.13425i	−0.369572	−	0.369572i	0.497749	−	0.867321i	$-0.334160\pi$
$193$	−5.13425	−	5.13425i	−0.369572	−	0.369572i	−0.867321	+	0.497749i	$0.834160\pi$
$194$	2.33527	−	13.6711i	0.167662	−	0.981527i
$195$	0.238627	−	29.1395i	0.0170885	−	2.08672i
$196$	−1.35071	−	0.475321i	−0.0964794	−	0.0339515i
$197$	−1.80697	+	1.80697i	−0.128742	+	0.128742i	−0.768542	−	0.639800i	$-0.779017\pi$
$197$	−1.80697	+	1.80697i	−0.128742	+	0.128742i	0.639800	+	0.768542i	$0.279017\pi$
$198$	2.64788	−	1.87525i	0.188177	−	0.133268i
$199$	−22.1787			−1.57221			−0.786103	−	0.618095i	$-0.787905\pi$
$199$	−22.1787			−1.57221			−0.786103	+	0.618095i	$0.787905\pi$
$200$	3.65569	+	13.6615i	0.258496	+	0.966012i
$201$	−23.7717			−1.67673
$202$	−18.2596	+	12.9316i	−1.28474	+	0.909864i
$203$	11.0138	−	11.0138i	0.773020	−	0.773020i
$204$	6.90574	+	2.43016i	0.483499	+	0.170145i
$205$	−0.00504973	+	0.616636i	−0.000352688	+	0.0430677i
$206$	−2.07139	+	12.1263i	−0.144321	+	0.844880i
$207$	−15.4534	−	15.4534i	−1.07409	−	1.07409i
$208$	−2.45683	−	22.5215i	−0.170350	−	1.56158i
$209$		−	5.87411i		−	0.406320i
$210$	−10.4195	−	14.9710i	−0.719017	−	1.03310i
$211$			3.53342i			0.243251i	0.992576	+	0.121625i	$0.0388106\pi$
$211$			3.53342i			0.243251i	−0.992576	+	0.121625i	$0.961189\pi$
$212$	−0.0434048	+	0.0208080i	−0.00298105	+	0.00142910i
$213$	10.6103	+	10.6103i	0.727008	+	0.727008i
$214$	11.5489	+	1.97275i	0.789464	+	0.134855i
$215$	3.31632	+	3.37109i	0.226171	+	0.229906i
$216$	−2.23218	+	4.01362i	−0.151881	+	0.273092i
$217$	−0.754059	+	0.754059i	−0.0511889	+	0.0511889i
$218$	−2.76341	−	3.90198i	−0.187162	−	0.264275i
$219$	14.4402			0.975778
$220$	−1.51902	+	4.20625i	−0.102412	+	0.283586i
$221$	9.01016			0.606089
$222$	−7.31724	−	10.3321i	−0.491101	−	0.693442i
$223$	15.5960	−	15.5960i	1.04438	−	1.04438i	0.0454164	−	0.998968i	$-0.485539\pi$
$223$	15.5960	−	15.5960i	1.04438	−	1.04438i	0.998968	−	0.0454164i	$-0.0144615\pi$
$224$	−9.40230	−	10.6154i	−0.628217	−	0.709270i
$225$	−0.187873	+	11.4701i	−0.0125249	+	0.764672i
$226$	5.08758	+	0.869050i	0.338421	+	0.0578084i
$227$	−9.85837	−	9.85837i	−0.654323	−	0.654323i	0.299708	−	0.954031i	$-0.403111\pi$
$227$	−9.85837	−	9.85837i	−0.654323	−	0.654323i	−0.954031	+	0.299708i	$0.903111\pi$
$228$	−11.6856	−	24.3757i	−0.773896	−	1.61432i
$229$		−	9.89151i		−	0.653649i	−0.945085	−	0.326825i	$-0.894021\pi$
$229$		−	9.89151i		−	0.653649i	0.945085	−	0.326825i	$-0.105979\pi$
$230$	29.6495	+	5.31490i	1.95503	+	0.350454i
$231$		−	5.76800i		−	0.379506i
$232$	−16.9003	+	4.82033i	−1.10956	+	0.316470i
$233$	−1.71713	−	1.71713i	−0.112493	−	0.112493i	0.648620	−	0.761113i	$-0.275347\pi$
$233$	−1.71713	−	1.71713i	−0.112493	−	0.112493i	−0.761113	+	0.648620i	$0.775347\pi$
$234$	3.09431	−	18.1147i	0.202281	−	1.18419i
$235$	−1.40064	+	1.37789i	−0.0913680	+	0.0898837i
$236$	6.11611	−	17.3801i	0.398125	−	1.13135i
$237$	13.1563	−	13.1563i	0.854592	−	0.854592i
$238$	4.60246	−	3.25950i	0.298333	−	0.211282i
$239$	6.86079			0.443787			0.221894	−	0.975071i	$-0.428776\pi$
$239$	6.86079			0.443787			0.221894	+	0.975071i	$0.428776\pi$
$240$	2.06421	+	20.4764i	0.133244	+	1.32175i
$241$	14.9776			0.964791			0.482395	−	0.875954i	$-0.339767\pi$
$241$	14.9776			0.964791			0.482395	+	0.875954i	$0.339767\pi$
$242$	−1.15410	+	0.817343i	−0.0741884	+	0.0525408i
$243$	−13.8329	+	13.8329i	−0.887379	+	0.887379i
$244$	2.23402	−	6.34838i	0.143018	−	0.406413i
$245$	1.60087	+	0.0131097i	0.102276	+	0.000837550i
$246$	−0.151101	+	0.884573i	−0.00963383	+	0.0563983i
$247$	−23.5252	−	23.5252i	−1.49687	−	1.49687i
$248$	1.15708	−	0.330022i	0.0734745	−	0.0209564i
$249$			16.0557i			1.01749i
$250$	−8.81846	−	13.1238i	−0.557728	−	0.830024i
$251$			20.2090i			1.27558i	0.770211	+	0.637789i	$0.220151\pi$
$251$			20.2090i			1.27558i	−0.770211	+	0.637789i	$0.779849\pi$
$252$	−4.97253	−	10.3725i	−0.313240	−	0.653406i
$253$	6.73550	+	6.73550i	0.423457	+	0.423457i
$254$	12.9403	+	2.21043i	0.811947	+	0.138695i
$255$	−8.18469	−	0.0670257i	−0.512545	−	0.00419731i
$256$	3.44977	+	15.6237i	0.215610	+	0.976479i
$257$	−8.60820	+	8.60820i	−0.536965	+	0.536965i	−0.922636	−	0.385671i	$-0.873970\pi$
$257$	−8.60820	+	8.60820i	−0.536965	+	0.536965i	0.385671	+	0.922636i	$0.373970\pi$
$258$	3.97724	+	5.61593i	0.247612	+	0.349632i
$259$	−9.75343			−0.606048
$260$	10.7621	+	22.9291i	0.667436	+	1.42200i
$261$	−14.2557			−0.882405
$262$	−6.25494	−	8.83207i	−0.386431	−	0.545647i
$263$	−19.7503	+	19.7503i	−1.21785	+	1.21785i	−0.249471	+	0.968382i	$0.580257\pi$
$263$	−19.7503	+	19.7503i	−1.21785	+	1.21785i	−0.968382	+	0.249471i	$0.919743\pi$
$264$	−3.16318	+	5.68761i	−0.194680	+	0.350048i
$265$	0.0383642	−	0.0377409i	0.00235669	−	0.00231841i
$266$	−20.5273	−	3.50642i	−1.25861	−	0.214993i
$267$	−0.694910	−	0.694910i	−0.0425278	−	0.0425278i
$268$	18.6322	−	8.93220i	1.13814	−	0.545621i
$269$			2.99875i			0.182837i	0.995813	+	0.0914186i	$0.0291401\pi$
$269$			2.99875i			0.182837i	−0.995813	+	0.0914186i	$0.970860\pi$
$270$	0.905986	−	5.05410i	0.0551366	−	0.307583i
$271$		−	9.28573i		−	0.564068i	−0.959404	−	0.282034i	$-0.908991\pi$
$271$		−	9.28573i		−	0.564068i	0.959404	−	0.282034i	$-0.0910091\pi$
$272$	−6.32584	+	0.690073i	−0.383560	+	0.0418418i
$273$	−23.1002	−	23.1002i	−1.39809	−	1.39809i
$274$	−3.53470	+	20.6928i	−0.213539	+	1.25010i
$275$	0.0818860	−	4.99933i	0.00493791	−	0.301471i
$276$	41.3493	+	14.5510i	2.48894	+	0.875866i
$277$	−3.19990	+	3.19990i	−0.192263	+	0.192263i	−0.796673	−	0.604410i	$-0.793409\pi$
$277$	−3.19990	+	3.19990i	−0.192263	+	0.192263i	0.604410	+	0.796673i	$0.293409\pi$
$278$	−8.67625	+	6.14459i	−0.520367	+	0.368528i
$279$	0.976012			0.0584323
$280$	13.7922	+	7.81910i	0.824239	+	0.467281i
$281$	6.44616			0.384546			0.192273	−	0.981342i	$-0.438414\pi$
$281$	6.44616			0.384546			0.192273	+	0.981342i	$0.438414\pi$
$282$	−2.33335	+	1.65250i	−0.138949	+	0.0984047i
$283$	−17.0966	+	17.0966i	−1.01629	+	1.01629i	−0.0164227	+	0.999865i	$0.505228\pi$
$283$	−17.0966	+	17.0966i	−1.01629	+	1.01629i	−0.999865	+	0.0164227i	$0.994772\pi$
$284$	−12.3032	−	4.32953i	−0.730059	−	0.256910i
$285$	21.1949	+	21.5449i	1.25548	+	1.27621i
$286$	−1.34868	+	7.89542i	−0.0797491	+	0.466866i
$287$	0.488836	+	0.488836i	0.0288551	+	0.0288551i
$288$	−0.785073	+	12.9549i	−0.0462608	+	0.763374i
$289$			14.4692i			0.851131i
$290$	16.1272	−	11.2243i	0.947024	−	0.659111i
$291$			22.5652i			1.32279i
$292$	−11.3182	+	5.42589i	−0.662347	+	0.317526i
$293$	−17.7803	−	17.7803i	−1.03874	−	1.03874i	−0.999219	−	0.0395185i	$-0.987418\pi$
$293$	−17.7803	−	17.7803i	−1.03874	−	1.03874i	−0.0395185	−	0.999219i	$-0.512582\pi$
$294$	2.29646	+	0.392277i	0.133932	+	0.0228780i
$295$	−0.168687	+	20.5989i	−0.00982134	+	1.19931i
$296$	9.61749	+	5.34880i	0.559005	+	0.310892i
$297$	1.14814	−	1.14814i	0.0666221	−	0.0666221i
$298$	−15.0117	−	21.1967i	−0.869602	−	1.22789i
$299$	53.9499			3.12000
$300$	−9.60555	−	20.9085i	−0.554576	−	1.20715i
$301$	5.30142			0.305569
$302$	8.75090	+	12.3564i	0.503558	+	0.711031i
$303$	25.7417	−	25.7417i	1.47882	−	1.47882i
$304$	18.3182	+	14.7147i	1.05062	+	0.843948i
$305$	−0.0616160	+	7.52411i	−0.00352812	+	0.430829i
$306$	−5.08804	−	0.869129i	−0.290864	−	0.0496848i
$307$	2.87766	+	2.87766i	0.164237	+	0.164237i	0.784441	−	0.620204i	$-0.212950\pi$
$307$	2.87766	+	2.87766i	0.164237	+	0.164237i	−0.620204	+	0.784441i	$0.712950\pi$
$308$	2.16732	+	4.52094i	0.123494	+	0.257605i
$309$		−	20.0154i		−	1.13864i
$310$	−1.10415	+	0.768466i	−0.0627113	+	0.0436459i
$311$			5.05802i			0.286814i	0.989664	+	0.143407i	$0.0458058\pi$
$311$			5.05802i			0.286814i	−0.989664	+	0.143407i	$0.954194\pi$
$312$	10.1101	+	35.4465i	0.572370	+	2.00676i
$313$	8.12286	+	8.12286i	0.459131	+	0.459131i	0.898370	−	0.439239i	$-0.144752\pi$
$313$	8.12286	+	8.12286i	0.459131	+	0.459131i	−0.439239	+	0.898370i	$0.644752\pi$
$314$	−5.42435	+	31.7552i	−0.306114	+	1.79205i
$315$	9.01900	+	9.16794i	0.508163	+	0.516555i
$316$	−5.36841	+	15.2553i	−0.301996	+	0.858179i
$317$	13.6243	−	13.6243i	0.765216	−	0.765216i	−0.212044	−	0.977260i	$-0.568012\pi$
$317$	13.6243	−	13.6243i	0.765216	−	0.765216i	0.977260	+	0.212044i	$0.0680120\pi$
$318$	0.0639112	−	0.0452624i	0.00358396	−	0.00253819i
$319$	6.21347			0.347887
$320$	−9.31192	−	15.2738i	−0.520552	−	0.853830i
$321$	−19.0623			−1.06395
$322$	27.5580	−	19.5168i	1.53575	−	1.08763i
$323$	−6.60775	+	6.60775i	−0.367665	+	0.367665i
$324$	7.04998	−	20.0338i	0.391666	−	1.11299i
$325$	−19.6938	−	20.3497i	−1.09242	−	1.12880i
$326$	−1.50410	+	8.80526i	−0.0833041	+	0.487678i
$327$	5.50086	+	5.50086i	0.304199	+	0.304199i
$328$	−0.213945	−	0.750102i	−0.0118131	−	0.0414175i
$329$			2.20267i			0.121437i
$330$	1.28385	−	7.16205i	0.0706738	−	0.394258i
$331$			6.14562i			0.337794i	0.985634	+	0.168897i	$0.0540205\pi$
$331$			6.14562i			0.337794i	−0.985634	+	0.168897i	$0.945980\pi$
$332$	−6.03292	−	12.5844i	−0.331099	−	0.690660i
$333$	6.31214	+	6.31214i	0.345903	+	0.345903i
$334$	−15.2105	−	2.59822i	−0.832280	−	0.142168i
$335$	−16.4685	+	16.2009i	−0.899768	+	0.885151i
$336$	17.9873	+	14.4489i	0.981290	+	0.788254i
$337$	23.2405	−	23.2405i	1.26599	−	1.26599i	0.317852	−	0.948140i	$-0.397038\pi$
$337$	23.2405	−	23.2405i	1.26599	−	1.26599i	0.948140	−	0.317852i	$-0.102962\pi$
$338$	15.5936	+	22.0183i	0.848177	+	1.19764i
$339$	−8.39744			−0.456087
$340$	6.44033	−	3.02285i	0.349276	−	0.163937i
$341$	−0.425403			−0.0230369
$342$	11.0154	+	15.5539i	0.595645	+	0.841060i
$343$	13.6771	−	13.6771i	0.738494	−	0.738494i
$344$	−5.22753	−	2.90731i	−0.281850	−	0.156751i
$345$	−49.0073	−	0.401328i	−2.63846	−	0.0216068i
$346$	22.6150	+	3.86305i	1.21579	+	0.207679i
$347$	−25.2993	−	25.2993i	−1.35814	−	1.35814i	−0.876214	−	0.481922i	$-0.839939\pi$
$347$	−25.2993	−	25.2993i	−1.35814	−	1.35814i	−0.481922	−	0.876214i	$-0.660061\pi$
$348$	25.7839	−	12.3607i	1.38216	−	0.662602i
$349$		−	26.5419i		−	1.42075i	−0.703822	−	0.710377i	$-0.748525\pi$
$349$		−	26.5419i		−	1.42075i	0.703822	−	0.710377i	$-0.251475\pi$
$350$	−17.4214	−	3.27040i	−0.931216	−	0.174810i
$351$		−	9.19639i		−	0.490867i
$352$	0.342181	−	5.64650i	0.0182383	−	0.300959i
$353$	16.4475	+	16.4475i	0.875414	+	0.875414i	0.993056	−	0.117642i	$-0.0375334\pi$
$353$	16.4475	+	16.4475i	0.875414	+	0.875414i	−0.117642	+	0.993056i	$0.537533\pi$
$354$	−5.04755	+	29.5493i	−0.268274	+	1.57053i
$355$	14.5817	+	0.119412i	0.773918	+	0.00633773i
$356$	0.805781	+	0.283557i	0.0427063	+	0.0150285i
$357$	−6.48839	+	6.48839i	−0.343402	+	0.343402i
$358$	−16.6818	+	11.8142i	−0.881660	+	0.624398i
$359$	10.3559			0.546562			0.273281	−	0.961934i	$-0.411891\pi$
$359$	10.3559			0.546562			0.273281	+	0.961934i	$0.411891\pi$
$360$	−3.86559	−	13.9862i	−0.203735	−	0.737138i
$361$	15.5051			0.816059
$362$	7.70090	−	5.45384i	0.404750	−	0.286647i
$363$	1.62701	−	1.62701i	0.0853959	−	0.0853959i
$364$	26.7858	+	9.42601i	1.40396	+	0.494057i
$365$	10.0038	−	9.84129i	0.523623	−	0.515117i
$366$	−1.84371	+	10.7934i	−0.0963723	+	0.564181i
$367$	22.4190	+	22.4190i	1.17026	+	1.17026i	0.982147	+	0.188118i	$0.0602386\pi$
$367$	22.4190	+	22.4190i	1.17026	+	1.17026i	0.188118	+	0.982147i	$0.439761\pi$
$368$	−37.8770	+	4.13193i	−1.97448	+	0.215392i
$369$		−	0.632722i		−	0.0329382i
$370$	−12.1107	−	2.17094i	−0.629606	−	0.112862i
$371$		−	0.0603320i		−	0.00313228i
$372$	−1.76529	+	0.846269i	−0.0915258	+	0.0438770i
$373$	5.80065	+	5.80065i	0.300346	+	0.300346i	0.841149	−	0.540803i	$-0.181880\pi$
$373$	5.80065	+	5.80065i	0.300346	+	0.300346i	−0.540803	+	0.841149i	$0.681880\pi$
$374$	2.21767	+	0.378817i	0.114673	+	0.0195882i
$375$	17.7382	+	18.6319i	0.915996	+	0.962146i
$376$	1.20795	−	2.17198i	0.0622953	−	0.112011i
$377$	24.8843	−	24.8843i	1.28161	−	1.28161i
$378$	−3.32687	−	4.69759i	−0.171116	−	0.241618i
$379$	−1.88316			−0.0967313			−0.0483657	−	0.998830i	$-0.515401\pi$
$379$	−1.88316			−0.0967313			−0.0483657	+	0.998830i	$0.515401\pi$
$380$	−24.7080	−	8.92289i	−1.26749	−	0.457734i
$381$	−21.3590			−1.09425
$382$	−7.47891	−	10.5603i	−0.382654	−	0.540314i
$383$	−18.7808	+	18.7808i	−0.959654	+	0.959654i	−0.999217	−	0.0395628i	$-0.987403\pi$
$383$	−18.7808	+	18.7808i	−0.959654	+	0.959654i	0.0395628	+	0.999217i	$0.487403\pi$
$384$	−9.81284	−	24.1119i	−0.500759	−	1.23045i
$385$	−3.93101	−	3.99592i	−0.200343	−	0.203651i
$386$	−10.1219	−	1.72900i	−0.515191	−	0.0880038i
$387$	−3.43093	−	3.43093i	−0.174404	−	0.174404i
$388$	−8.47884	−	17.6865i	−0.430448	−	0.897898i
$389$		−	21.3613i		−	1.08306i	−0.840681	−	0.541531i	$-0.817845\pi$
$389$		−	21.3613i		−	1.08306i	0.840681	−	0.541531i	$-0.182155\pi$
$390$	−23.5415	−	33.8249i	−1.19207	−	1.71279i
$391$		−	15.1534i		−	0.766343i
$392$	−1.94736	+	0.555427i	−0.0983565	+	0.0280533i
$393$	12.4511	+	12.4511i	0.628076	+	0.628076i
$394$	−0.608513	+	3.56235i	−0.0306564	+	0.179469i
$395$	0.148065	−	18.0806i	0.00744996	−	0.909735i
$396$	1.52320	−	4.32846i	0.0765437	−	0.217513i
$397$	−8.49533	+	8.49533i	−0.426369	+	0.426369i	−0.887389	−	0.461021i	$-0.847483\pi$
$397$	−8.49533	+	8.49533i	−0.426369	+	0.426369i	0.461021	+	0.887389i	$0.347483\pi$
$398$	−25.5965	+	18.1276i	−1.28304	+	0.908655i
$399$	33.8818			1.69621
$400$	15.3852	+	12.7788i	0.769258	+	0.638939i
$401$	7.08319			0.353718			0.176859	−	0.984236i	$-0.443406\pi$
$401$	7.08319			0.353718			0.176859	+	0.984236i	$0.443406\pi$
$402$	−27.4350	+	19.4297i	−1.36833	+	0.969063i
$403$	−1.70369	+	1.70369i	−0.0848670	+	0.0848670i
$404$	−10.5039	+	29.8487i	−0.522588	+	1.48503i
$405$	−0.194444	+	23.7441i	−0.00966201	+	1.17986i
$406$	3.70900	−	21.7132i	0.184074	−	1.07761i
$407$	−2.75120	−	2.75120i	−0.136372	−	0.136372i
$408$	9.95620	−	2.83972i	0.492905	−	0.140587i
$409$			20.2812i			1.00284i	0.865203	+	0.501421i	$0.167189\pi$
$409$			20.2812i			1.00284i	−0.865203	+	0.501421i	$0.832811\pi$
$410$	0.498176	+	0.715788i	0.0246031	+	0.0353503i
$411$		−	34.1550i		−	1.68474i
$412$	7.52076	+	15.6880i	0.370521	+	0.772894i
$413$	16.3297	+	16.3297i	0.803531	+	0.803531i
$414$	−30.4655	−	5.20406i	−1.49730	−	0.255765i
$415$	10.9423	+	11.1230i	0.537136	+	0.546006i
$416$	−21.2432	−	23.9840i	−1.04153	−	1.17591i
$417$	12.2315	−	12.2315i	0.598977	−	0.598977i
$418$	−4.80116	−	6.77931i	−0.234832	−	0.331587i
$419$	−0.336904			−0.0164588			−0.00822942	−	0.999966i	$-0.502620\pi$
$419$	−0.336904			−0.0164588			−0.00822942	+	0.999966i	$0.502620\pi$
$420$	−24.2617	−	8.76170i	−1.18385	−	0.427527i
$421$	27.7172			1.35085			0.675427	−	0.737427i	$-0.263959\pi$
$421$	27.7172			1.35085			0.675427	+	0.737427i	$0.263959\pi$
$422$	2.88802	+	4.07792i	0.140586	+	0.198510i
$423$	1.42551	−	1.42551i	0.0693106	−	0.0693106i
$424$	−0.0330862	+	0.0594912i	−0.00160681	+	0.00288915i
$425$	−5.71583	+	5.53160i	−0.277259	+	0.268322i
$426$	20.9177	+	3.57311i	1.01346	+	0.173118i
$427$	5.96471	+	5.96471i	0.288652	+	0.288652i
$428$	14.9410	−	7.16263i	0.722199	−	0.346219i
$429$		−	13.0320i		−	0.629191i
$430$	6.58271	+	1.18000i	0.317446	+	0.0569047i
$431$			6.75663i			0.325456i	0.986671	+	0.162728i	$0.0520292\pi$
$431$			6.75663i			0.325456i	−0.986671	+	0.162728i	$0.947971\pi$
$432$	0.704336	+	6.45658i	0.0338874	+	0.310642i
$433$	15.4077	+	15.4077i	0.740448	+	0.740448i	0.972664	−	0.232216i	$-0.0745976\pi$
$433$	15.4077	+	15.4077i	0.740448	+	0.740448i	−0.232216	+	0.972664i	$0.574598\pi$
$434$	−0.253935	+	1.48659i	−0.0121893	+	0.0713584i
$435$	−22.7896	+	22.4194i	−1.09268	+	1.07493i
$436$	−6.37851	−	2.24462i	−0.305475	−	0.107498i
$437$	−39.5650	+	39.5650i	−1.89265	+	1.89265i
$438$	16.6654	−	11.8026i	0.796306	−	0.563950i
$439$	−2.32635			−0.111030			−0.0555152	−	0.998458i	$-0.517680\pi$
$439$	−2.32635			−0.111030			−0.0555152	+	0.998458i	$0.517680\pi$
$440$	1.68485	+	6.09600i	0.0803221	+	0.290616i
$441$	−1.64263			−0.0782203
$442$	10.3986	−	7.36440i	0.494613	−	0.350289i
$443$	19.6942	−	19.6942i	0.935702	−	0.935702i	−0.0623522	−	0.998054i	$-0.519860\pi$
$443$	19.6942	−	19.6942i	0.935702	−	0.935702i	0.998054	+	0.0623522i	$0.0198602\pi$
$444$	−16.8897	−	5.94354i	−0.801548	−	0.282068i
$445$	−0.955012	−	0.00782074i	−0.0452719	−	0.000370739i
$446$	5.25207	−	30.7466i	0.248693	−	1.45589i
$447$	29.8823	+	29.8823i	1.41339	+	1.41339i
$448$	−19.5276	−	4.56632i	−0.922593	−	0.215738i
$449$			7.06056i			0.333208i	0.986024	+	0.166604i	$0.0532802\pi$
$449$			7.06056i			0.333208i	−0.986024	+	0.166604i	$0.946720\pi$
$450$	9.15816	+	13.3912i	0.431720	+	0.631266i
$451$			0.275777i			0.0129859i
$452$	6.58190	−	3.15533i	0.309586	−	0.148414i
$453$	−17.4196	−	17.4196i	−0.818445	−	0.818445i
$454$	−19.4352	−	3.31989i	−0.912141	−	0.155810i
$455$	−31.7465	−	0.259977i	−1.48830	−	0.0121879i
$456$	−33.4096	−	18.5808i	−1.56455	−	0.870128i
$457$	−15.2962	+	15.2962i	−0.715528	+	0.715528i	−0.967686	−	0.252158i	$-0.918860\pi$
$457$	−15.2962	+	15.2962i	−0.715528	+	0.715528i	0.252158	+	0.967686i	$0.418860\pi$
$458$	−8.08476	−	11.4158i	−0.377776	−	0.533425i
$459$	−2.58308			−0.120568
$460$	38.5626	−	18.0999i	1.79799	−	0.843911i
$461$	−37.1744			−1.73138			−0.865692	−	0.500578i	$-0.833121\pi$
$461$	−37.1744			−1.73138			−0.865692	+	0.500578i	$0.833121\pi$
$462$	−4.71443	−	6.65685i	−0.219335	−	0.309705i
$463$	20.6001	−	20.6001i	0.957368	−	0.957368i	−0.0417601	−	0.999128i	$-0.513297\pi$
$463$	20.6001	−	20.6001i	0.957368	−	0.957368i	0.999128	+	0.0417601i	$0.0132965\pi$
$464$	−15.5648	+	19.3765i	−0.722580	+	0.899533i
$465$	1.56028	−	1.53494i	0.0723564	−	0.0711809i
$466$	−3.38522	−	0.578257i	−0.156817	−	0.0267872i
$467$	8.96863	+	8.96863i	0.415019	+	0.415019i	0.883483	−	0.468464i	$-0.155192\pi$
$467$	8.96863	+	8.96863i	0.415019	+	0.415019i	−0.468464	+	0.883483i	$0.655192\pi$
$468$	−11.2347	−	23.4353i	−0.519326	−	1.08329i
$469$			25.8985i			1.19588i
$470$	−0.490276	+	2.73503i	−0.0226147	+	0.126158i
$471$		−	52.4143i		−	2.41512i
$472$	−7.14687	−	25.0573i	−0.328961	−	1.15336i
$473$	1.49540	+	1.49540i	0.0687586	+	0.0687586i
$474$	4.43048	−	25.9369i	0.203499	−	1.19132i
$475$	29.3666	+	0.481007i	1.34743	+	0.0220701i
$476$	2.64758	−	7.52359i	0.121352	−	0.344843i
$477$	−0.0390452	+	0.0390452i	−0.00178776	+	0.00178776i
$478$	7.91804	−	5.60762i	0.362163	−	0.256486i
$479$	16.2974			0.744649			0.372325	−	0.928103i	$-0.378561\pi$
$479$	16.2974			0.744649			0.372325	+	0.928103i	$0.378561\pi$
$480$	19.1186	+	21.9447i	0.872640	+	1.00164i
$481$	−22.0365			−1.00478
$482$	17.2856	−	12.2418i	0.787339	−	0.557600i
$483$	−38.8503	+	38.8503i	−1.76775	+	1.76775i
$484$	−0.663900	+	1.88659i	−0.0301773	+	0.0857543i
$485$	15.3786	+	15.6326i	0.698308	+	0.709839i
$486$	−4.65833	+	27.2707i	−0.211306	+	1.23703i
$487$	−8.11368	−	8.11368i	−0.367666	−	0.367666i	0.498959	−	0.866625i	$-0.333716\pi$
$487$	−8.11368	−	8.11368i	−0.367666	−	0.367666i	−0.866625	+	0.498959i	$0.833716\pi$
$488$	−2.61052	−	9.15264i	−0.118173	−	0.414320i
$489$		−	14.5338i		−	0.657239i
$490$	1.85828	−	1.29333i	0.0839484	−	0.0584265i
$491$		−	1.13849i		−	0.0513792i	−0.999670	−	0.0256896i	$-0.991822\pi$
$491$		−	1.13849i		−	0.0513792i	0.999670	−	0.0256896i	$-0.00817815\pi$
$492$	0.548614	+	1.14439i	0.0247334	+	0.0515930i
$493$	−6.98949	−	6.98949i	−0.314791	−	0.314791i
$494$	−46.3786	−	7.92229i	−2.08667	−	0.356441i
$495$	−0.0420111	+	5.13009i	−0.00188826	+	0.230580i
$496$	1.06564	−	1.32661i	0.0478488	−	0.0595665i
$497$	11.5596	−	11.5596i	0.518519	−	0.518519i
$498$	13.1230	+	18.5299i	0.588057	+	0.830345i
$499$	30.3735			1.35971			0.679853	−	0.733349i	$-0.262044\pi$
$499$	30.3735			1.35971			0.679853	+	0.733349i	$0.262044\pi$
$500$	−20.9041	−	7.93852i	−0.934858	−	0.355021i
$501$	25.1061			1.12166
$502$	16.5177	+	23.3232i	0.737219	+	1.04096i
$503$	15.9790	−	15.9790i	0.712470	−	0.712470i	−0.254582	−	0.967051i	$-0.581938\pi$
$503$	15.9790	−	15.9790i	0.712470	−	0.712470i	0.967051	+	0.254582i	$0.0819377\pi$
$504$	−14.2167	−	7.90665i	−0.633262	−	0.352190i
$505$	0.289705	−	35.3767i	0.0128917	−	1.57424i
$506$	13.2787	+	2.26823i	0.590309	+	0.100835i
$507$	−31.0406	−	31.0406i	−1.37856	−	1.37856i
$508$	16.7411	−	8.02560i	0.742766	−	0.356079i
$509$			19.6290i			0.870038i	0.900421	+	0.435019i	$0.143258\pi$
$509$			19.6290i			0.870038i	−0.900421	+	0.435019i	$0.856742\pi$
$510$	−9.50075	+	6.61235i	−0.420700	+	0.292800i
$511$		−	15.7321i		−	0.695948i
$512$	16.7513	+	15.2117i	0.740309	+	0.672267i
$513$	6.74432	+	6.74432i	0.297769	+	0.297769i
$514$	−2.89888	+	16.9706i	−0.127864	+	0.748541i
$515$	−13.6409	−	13.8662i	−0.601090	−	0.611016i
$516$	9.18028	+	3.23058i	0.404139	+	0.142218i
$517$	−0.621320	+	0.621320i	−0.0273256	+	0.0273256i
$518$	−11.2564	+	7.97190i	−0.494580	+	0.350265i
$519$	−37.3278			−1.63851
$520$	31.1615	+	17.6662i	1.36652	+	0.774714i
$521$	−3.15224			−0.138102			−0.0690510	−	0.997613i	$-0.521997\pi$
$521$	−3.15224			−0.138102			−0.0690510	+	0.997613i	$0.521997\pi$
$522$	−16.4525	+	11.6518i	−0.720107	+	0.509985i
$523$	−8.51987	+	8.51987i	−0.372548	+	0.372548i	−0.868405	−	0.495856i	$-0.834854\pi$
$523$	−8.51987	+	8.51987i	−0.372548	+	0.372548i	0.495856	+	0.868405i	$0.334854\pi$
$524$	−14.4377	−	5.08067i	−0.630712	−	0.221950i
$525$	28.8361	+	0.472318i	1.25851	+	0.0206137i
$526$	−6.65106	+	38.9366i	−0.290000	+	1.69771i
$527$	0.478533	+	0.478533i	0.0208452	+	0.0208452i
$528$	0.998099	+	9.14948i	0.0434367	+	0.398180i
$529$		−	67.7339i		−	2.94495i
$530$	0.0134288	−	0.0749135i	0.000583311	−	0.00325404i
$531$		−	21.1362i		−	0.917234i
$532$	−26.5565	+	12.7311i	−1.15137	+	0.551961i
$533$	1.10446	+	1.10446i	0.0478394	+	0.0478394i
$534$	−1.36998	−	0.234017i	−0.0592847	−	0.0101269i
$535$	−13.2059	+	12.9913i	−0.570940	+	0.561665i
$536$	14.2028	−	25.5376i	0.613468	−	1.10306i
$537$	23.5174	−	23.5174i	1.01485	−	1.01485i
$538$	2.45101	+	3.46087i	0.105671	+	0.149209i
$539$	0.715953			0.0308383
$540$	−3.08533	−	6.57344i	−0.132772	−	0.282876i
$541$	−25.9759			−1.11679			−0.558395	−	0.829575i	$-0.688583\pi$
$541$	−25.9759			−1.11679			−0.558395	+	0.829575i	$0.688583\pi$
$542$	−7.58963	−	10.7167i	−0.326002	−	0.460320i
$543$	−10.8565	+	10.8565i	−0.465895	+	0.465895i
$544$	−6.73663	+	5.96679i	−0.288831	+	0.255824i
$545$	7.55982	+	0.0619085i	0.323827	+	0.00265187i
$546$	−45.5408	−	7.77918i	−1.94897	−	0.332918i
$547$	−17.6483	−	17.6483i	−0.754587	−	0.754587i	0.220745	−	0.975332i	$-0.429151\pi$
$547$	−17.6483	−	17.6483i	−0.754587	−	0.754587i	−0.975332	+	0.220745i	$0.929151\pi$
$548$	12.8337	+	26.7706i	0.548229	+	1.14359i
$549$		−	7.72039i		−	0.329498i
$550$	−3.99166	−	5.83666i	−0.170205	−	0.248876i
$551$			36.4986i			1.55489i
$552$	59.6145	−	17.0033i	2.53736	−	0.723708i
$553$	−14.3334	−	14.3334i	−0.609516	−	0.609516i
$554$	−1.07759	+	6.30843i	−0.0457825	+	0.268019i
$555$	20.0176	+	0.163928i	0.849702	+	0.00695834i
$556$	−4.99104	+	14.1830i	−0.211667	+	0.601491i
$557$	−20.4176	+	20.4176i	−0.865123	+	0.865123i	−0.991928	−	0.126805i	$-0.959528\pi$
$557$	−20.4176	+	20.4176i	−0.865123	+	0.865123i	0.126805	+	0.991928i	$0.459528\pi$
$558$	1.12642	−	0.797737i	0.0476850	−	0.0337709i
$559$	11.9778			0.506608
$560$	22.3084	−	2.24889i	0.942703	−	0.0950329i
$561$	−3.66043			−0.154543
$562$	7.43952	−	5.26873i	0.313817	−	0.222248i
$563$	−15.8100	+	15.8100i	−0.666312	+	0.666312i	−0.956860	−	0.290549i	$-0.906162\pi$
$563$	−15.8100	+	15.8100i	−0.666312	+	0.666312i	0.290549	+	0.956860i	$0.406162\pi$
$564$	−1.34226	+	3.81429i	−0.0565195	+	0.160611i
$565$	−5.81754	+	5.72303i	−0.244746	+	0.240770i
$566$	−5.75742	+	33.7050i	−0.242002	+	1.41673i
$567$	18.8231	+	18.8231i	0.790495	+	0.790495i
$568$	−17.7378	+	5.05919i	−0.744262	+	0.212279i
$569$		−	1.45636i		−	0.0610538i	−0.999534	−	0.0305269i	$-0.990281\pi$
$569$		−	1.45636i		−	0.0610538i	0.999534	−	0.0305269i	$-0.00971853\pi$
$570$	42.0706	+	7.54149i	1.76215	+	0.315878i
$571$		−	19.8610i		−	0.831159i	−0.909557	−	0.415579i	$-0.863579\pi$
$571$		−	19.8610i		−	0.831159i	0.909557	−	0.415579i	$-0.136421\pi$
$572$	4.89676	+	10.2145i	0.204744	+	0.427088i
$573$	14.8876	+	14.8876i	0.621937	+	0.621937i
$574$	0.963714	+	0.164619i	0.0402246	+	0.00687108i
$575$	−34.2245	+	33.1214i	−1.42726	+	1.38126i
$576$	9.68253	+	15.5929i	0.403439	+	0.649705i
$577$	−10.5669	+	10.5669i	−0.439907	+	0.439907i	−0.891981	−	0.452073i	$-0.850685\pi$
$577$	−10.5669	+	10.5669i	−0.439907	+	0.439907i	0.452073	+	0.891981i	$0.350685\pi$
$578$	11.8263	+	16.6990i	0.491910	+	0.694585i
$579$	16.7070			0.694318
$580$	9.43838	−	26.1354i	0.391907	−	1.08521i
$581$	17.4922			0.725698
$582$	18.4435	+	26.0425i	0.764507	+	1.07950i
$583$	0.0170182	−	0.0170182i	0.000704821	−	0.000704821i
$584$	−8.62753	+	15.5129i	−0.357010	+	0.641927i
$585$	20.3772	+	20.7137i	0.842494	+	0.856406i
$586$	−35.0529	−	5.98766i	−1.44802	−	0.247348i
$587$	8.38164	+	8.38164i	0.345947	+	0.345947i	0.858598	−	0.512650i	$-0.171336\pi$
$587$	8.38164	+	8.38164i	0.345947	+	0.345947i	−0.512650	+	0.858598i	$0.671336\pi$
$588$	2.97097	−	1.42427i	0.122521	−	0.0587359i
$589$		−	2.49886i		−	0.102964i
$590$	16.6417	+	23.9110i	0.685126	+	0.984402i
$591$		−	5.87993i		−	0.241868i
$592$	15.4714	−	1.68774i	0.635869	−	0.0693658i
$593$	−25.4497	−	25.4497i	−1.04509	−	1.04509i	−0.998934	−	0.0461586i	$-0.985302\pi$
$593$	−25.4497	−	25.4497i	−1.04509	−	1.04509i	−0.0461586	−	0.998934i	$-0.514698\pi$
$594$	0.386647	−	2.26350i	0.0158643	−	0.0928726i
$595$	−0.0730223	+	8.91696i	−0.00299362	+	0.365560i
$596$	−34.6499	−	12.1934i	−1.41932	−	0.499463i
$597$	36.0850	−	36.0850i	1.47686	−	1.47686i
$598$	62.2637	−	44.0956i	2.54615	−	1.80320i
$599$	−45.0702			−1.84152			−0.920760	−	0.390130i	$-0.872430\pi$
$599$	−45.0702			−1.84152			−0.920760	+	0.390130i	$0.872430\pi$
$600$	−28.1752	−	16.2795i	−1.15025	−	0.664608i
$601$	−44.4859			−1.81462			−0.907309	−	0.420464i	$-0.861867\pi$
$601$	−44.4859			−1.81462			−0.907309	+	0.420464i	$0.861867\pi$
$602$	6.11837	−	4.33308i	0.249366	−	0.176603i
$603$	16.7608	−	16.7608i	0.682553	−	0.682553i
$604$	20.1989	+	7.10805i	0.821880	+	0.289223i
$605$	0.0183109	−	2.23599i	0.000744443	−	0.0909060i
$606$	8.66873	−	50.7484i	0.352143	−	2.06151i
$607$	−6.38595	−	6.38595i	−0.259198	−	0.259198i	0.565530	−	0.824728i	$-0.308672\pi$
$607$	−6.38595	−	6.38595i	−0.259198	−	0.259198i	−0.824728	+	0.565530i	$0.808672\pi$
$608$	33.1681	+	2.01000i	1.34514	+	0.0815165i
$609$			35.8392i			1.45228i
$610$	6.07867	+	8.73394i	0.246118	+	0.353627i
$611$			4.97664i			0.201333i
$612$	−6.58249	+	3.15562i	−0.266082	+	0.127558i
$613$	−13.1245	−	13.1245i	−0.530095	−	0.530095i	0.390505	−	0.920601i	$-0.372300\pi$
$613$	−13.1245	−	13.1245i	−0.530095	−	0.530095i	−0.920601	+	0.390505i	$0.872300\pi$
$614$	5.67314	+	0.969074i	0.228949	+	0.0391087i
$615$	−0.995057	−	1.01149i	−0.0401246	−	0.0407872i
$616$	6.19647	+	3.44618i	0.249663	+	0.138851i
$617$	−20.1520	+	20.1520i	−0.811290	+	0.811290i	−0.984827	−	0.173537i	$-0.944480\pi$
$617$	−20.1520	+	20.1520i	−0.811290	+	0.811290i	0.173537	+	0.984827i	$0.444480\pi$
$618$	−16.3595	−	23.0998i	−0.658074	−	0.929210i
$619$	−36.1170			−1.45167			−0.725833	−	0.687871i	$-0.758546\pi$
$619$	−36.1170			−1.45167			−0.725833	+	0.687871i	$0.758546\pi$
$620$	−0.646196	+	1.78935i	−0.0259518	+	0.0718622i
$621$	−15.4666			−0.620655
$622$	4.13414	+	5.83747i	0.165764	+	0.234061i
$623$	−0.757083	+	0.757083i	−0.0303319	+	0.0303319i
$624$	40.6400	+	32.6454i	1.62690	+	1.30686i
$625$	24.9866	+	0.818750i	0.999464	+	0.0327500i
$626$	16.0138	+	2.73544i	0.640039	+	0.109330i
$627$	9.55723	+	9.55723i	0.381679	+	0.381679i
$628$	19.6946	+	41.0822i	0.785901	+	1.63936i
$629$			6.18962i			0.246796i
$630$	17.9022	+	3.20911i	0.713241	+	0.127854i
$631$			1.96566i			0.0782519i	0.999234	+	0.0391259i	$0.0124574\pi$
$631$			1.96566i			0.0782519i	−0.999234	+	0.0391259i	$0.987543\pi$
$632$	6.27315	+	21.9940i	0.249533	+	0.874875i
$633$	−5.74891	−	5.74891i	−0.228499	−	0.228499i
$634$	4.58809	−	26.8595i	0.182216	−	1.06673i
$635$	−14.7970	+	14.5566i	−0.587199	+	0.577660i
$636$	0.0367651	−	0.104475i	0.00145783	−	0.00414270i
$637$	2.86731	−	2.86731i	0.113607	−	0.113607i
$638$	7.17097	−	5.07854i	0.283901	−	0.201061i
$639$	−14.9621			−0.591892
$640$	−23.2308	−	10.0164i	−0.918279	−	0.395935i
$641$	23.2614			0.918769			0.459385	−	0.888237i	$-0.348070\pi$
$641$	23.2614			0.918769			0.459385	+	0.888237i	$0.348070\pi$
$642$	−21.9998	+	15.5804i	−0.868263	+	0.614910i
$643$	7.71067	−	7.71067i	0.304079	−	0.304079i	−0.538528	−	0.842607i	$-0.681020\pi$
$643$	7.71067	−	7.71067i	0.304079	−	0.304079i	0.842607	+	0.538528i	$0.181020\pi$
$644$	15.8528	−	45.0488i	0.624689	−	1.77517i
$645$	−10.8805	−	0.0891019i	−0.428418	−	0.00350838i
$646$	−2.22521	+	13.0268i	−0.0875498	+	0.512533i
$647$	25.7319	+	25.7319i	1.01162	+	1.01162i	0.999932	+	0.0116920i	$0.00372177\pi$
$647$	25.7319	+	25.7319i	1.01162	+	1.01162i	0.0116920	+	0.999932i	$0.496278\pi$
$648$	−8.23813	−	28.8833i	−0.323624	−	1.13464i
$649$			9.21240i			0.361618i
$650$	−39.3614	−	7.38902i	−1.54388	−	0.289821i
$651$		−	2.45372i		−	0.0961690i
$652$	5.46104	+	11.3915i	0.213871	+	0.446127i
$653$	−21.6712	−	21.6712i	−0.848061	−	0.848061i	0.141830	−	0.989891i	$-0.454701\pi$
$653$	−21.6712	−	21.6712i	−0.848061	−	0.848061i	−0.989891	+	0.141830i	$0.954701\pi$
$654$	10.8447	+	1.85246i	0.424059	+	0.0724369i
$655$	17.1115	+	0.140129i	0.668603	+	0.00547529i
$656$	−0.860005	−	0.690827i	−0.0335775	−	0.0269723i
$657$	−10.1814	+	10.1814i	−0.397214	+	0.397214i
$658$	1.80034	+	2.54211i	0.0701846	+	0.0991017i
$659$	18.2003			0.708982			0.354491	−	0.935059i	$-0.384654\pi$
$659$	18.2003			0.708982			0.354491	+	0.935059i	$0.384654\pi$
$660$	−4.37216	−	9.31508i	−0.170186	−	0.362589i
$661$	13.3582			0.519575			0.259787	−	0.965666i	$-0.416348\pi$
$661$	13.3582			0.519575			0.259787	+	0.965666i	$0.416348\pi$
$662$	5.02308	+	7.09267i	0.195228	+	0.275664i
$663$	−14.6596	+	14.6596i	−0.569333	+	0.569333i
$664$	−17.2484	−	9.59275i	−0.669368	−	0.372271i
$665$	23.4725	−	23.0912i	0.910224	−	0.895437i
$666$	12.4440	+	2.12566i	0.482197	+	0.0823678i
$667$	−41.8508	−	41.8508i	−1.62047	−	1.62047i
$668$	−19.6781	+	9.43357i	−0.761368	+	0.364996i
$669$			50.7497i			1.96209i
$670$	−5.76455	+	32.1579i	−0.222704	+	1.24237i
$671$			3.36500i			0.129904i
$672$	32.5690	+	1.97370i	1.25637	+	0.0761370i
$673$	14.7081	+	14.7081i	0.566956	+	0.566956i	0.931274	−	0.364319i	$-0.118698\pi$
$673$	14.7081	+	14.7081i	0.566956	+	0.566956i	−0.364319	+	0.931274i	$0.618698\pi$
$674$	7.82643	−	45.8174i	0.301463	−	1.76482i
$675$	5.64593	+	5.83397i	0.217312	+	0.224550i
$676$	35.9931	+	12.6661i	1.38435	+	0.487158i
$677$	−4.49751	+	4.49751i	−0.172853	+	0.172853i	−0.788232	−	0.615378i	$-0.789003\pi$
$677$	−4.49751	+	4.49751i	−0.172853	+	0.172853i	0.615378	+	0.788232i	$0.289003\pi$
$678$	−9.69150	+	6.86360i	−0.372200	+	0.263595i
$679$	24.5840			0.943449
$680$	4.96208	−	8.75264i	0.190287	−	0.335648i
$681$	32.0793			1.22928
$682$	−0.490958	+	0.347700i	−0.0187998	+	0.0133141i
$683$	26.4086	−	26.4086i	1.01050	−	1.01050i	0.0105541	−	0.999944i	$-0.496640\pi$
$683$	26.4086	−	26.4086i	1.01050	−	1.01050i	0.999944	−	0.0105541i	$-0.00335955\pi$
$684$	25.4258	+	8.94744i	0.972180	+	0.342114i
$685$	−23.2774	−	23.6618i	−0.889383	−	0.904069i
$686$	4.60587	−	26.9637i	0.175853	−	1.02948i
$687$	16.0936	+	16.0936i	0.614008	+	0.614008i
$688$	−8.40937	+	0.917362i	−0.320604	+	0.0349741i
$689$		−	0.136312i		−	0.00519307i
$690$	−56.8874	+	39.5926i	−2.16566	+	1.50726i
$691$		−	0.468687i		−	0.0178297i	−0.999960	−	0.00891485i	$-0.997162\pi$
$691$		−	0.468687i		−	0.0178297i	0.999960	−	0.00891485i	$-0.00283772\pi$
$692$	29.2575	−	14.0259i	1.11220	−	0.533185i
$693$	4.06686	+	4.06686i	0.154487	+	0.154487i
$694$	−49.8761	−	8.51973i	−1.89327	−	0.323405i
$695$	0.137657	−	16.8097i	0.00522162	−	0.637626i
$696$	19.6543	−	35.3398i	0.744995	−	1.33955i
$697$	0.310220	−	0.310220i	0.0117504	−	0.0117504i
$698$	−21.6938	−	30.6320i	−0.821123	−	1.15944i
$699$	5.58757			0.211341
$700$	−22.7792	+	10.4649i	−0.860971	+	0.395537i
$701$	−9.01098			−0.340340			−0.170170	−	0.985415i	$-0.554432\pi$
$701$	−9.01098			−0.340340			−0.170170	+	0.985415i	$0.554432\pi$
$702$	−7.51661	−	10.6136i	−0.283696	−	0.400583i
$703$	16.1609	−	16.1609i	0.609518	−	0.609518i
$704$	−4.22021	−	6.79631i	−0.159055	−	0.256145i
$705$	0.0370207	−	4.52070i	0.00139428	−	0.170260i
$706$	32.4254	+	5.53884i	1.22035	+	0.208457i
$707$	−28.0448	−	28.0448i	−1.05473	−	1.05473i
$708$	18.3266	+	38.2285i	0.688754	+	1.43671i
$709$			46.0950i			1.73113i	0.500794	+	0.865566i	$0.333041\pi$
$709$			46.0950i			1.73113i	−0.500794	+	0.865566i	$0.666959\pi$
$710$	16.9264	−	11.7805i	0.635236	−	0.442113i
$711$			18.5523i			0.695765i
$712$	1.16172	−	0.331346i	0.0435372	−	0.0124177i
$713$	2.86530	+	2.86530i	0.107306	+	0.107306i
$714$	−2.18502	+	12.7915i	−0.0817721	+	0.478710i
$715$	−8.88158	−	9.02825i	−0.332152	−	0.337637i
$716$	−9.59624	+	27.2695i	−0.358628	+	1.01911i
$717$	−11.1626	+	11.1626i	−0.416874	+	0.416874i
$718$	11.9517	−	8.46430i	0.446034	−	0.315885i
$719$	−9.19998			−0.343101			−0.171551	−	0.985175i	$-0.554878\pi$
$719$	−9.19998			−0.343101			−0.171551	+	0.985175i	$0.554878\pi$
$720$	−15.8928	−	12.9820i	−0.592290	−	0.483810i
$721$	−21.8061			−0.812103
$722$	17.8945	−	12.6730i	0.665964	−	0.471641i
$723$	−24.3687	+	24.3687i	−0.906281	+	0.906281i
$724$	4.42996	−	12.5886i	0.164638	−	0.467850i
$725$	−0.508796	+	31.0632i	−0.0188962	+	1.15366i
$726$	0.547909	−	3.20756i	0.0203348	−	0.119044i
$727$	5.12247	+	5.12247i	0.189982	+	0.189982i	0.795688	−	0.605706i	$-0.207109\pi$
$727$	5.12247	+	5.12247i	0.189982	+	0.189982i	−0.605706	+	0.795688i	$0.707109\pi$
$728$	38.6178	−	11.0146i	1.43127	−	0.408228i
$729$		−	13.1553i		−	0.487232i
$730$	3.50169	−	19.5344i	0.129603	−	0.723000i
$731$		−	3.36433i		−	0.124434i
$732$	6.69411	+	13.9637i	0.247421	+	0.516111i
$733$	−10.6647	−	10.6647i	−0.393909	−	0.393909i	0.482169	−	0.876078i	$-0.339849\pi$
$733$	−10.6647	−	10.6647i	−0.393909	−	0.393909i	−0.876078	+	0.482169i	$0.839849\pi$
$734$	44.1979	+	7.54979i	1.63137	+	0.278668i
$735$	−2.62595	+	2.58329i	−0.0968598	+	0.0952862i
$736$	−40.3367	+	35.7272i	−1.48683	+	1.31692i
$737$	−7.30534	+	7.30534i	−0.269096	+	0.269096i
$738$	−0.517151	−	0.730226i	−0.0190366	−	0.0268800i
$739$	−17.8426			−0.656352			−0.328176	−	0.944617i	$-0.606434\pi$
$739$	−17.8426			−0.656352			−0.328176	+	0.944617i	$0.606434\pi$
$740$	−15.7514	+	7.39312i	−0.579032	+	0.271777i
$741$	76.5514			2.81218
$742$	−0.0493120	−	0.0696293i	−0.00181030	−	0.00255617i
$743$	−26.7447	+	26.7447i	−0.981167	+	0.981167i	−0.999826	−	0.0186586i	$-0.994060\pi$
$743$	−26.7447	+	26.7447i	−0.981167	+	0.981167i	0.0186586	+	0.999826i	$0.494060\pi$
$744$	−1.34563	+	2.41953i	−0.0493330	+	0.0887041i
$745$	41.0671	+	0.336305i	1.50458	+	0.0123213i
$746$	11.4357	+	1.95342i	0.418690	+	0.0715197i
$747$	−11.3205	−	11.3205i	−0.414194	−	0.414194i
$748$	2.86904	−	1.37540i	0.104902	−	0.0502897i
$749$			20.7677i			0.758837i
$750$	35.7003	+	7.00487i	1.30359	+	0.255782i
$751$		−	9.76020i		−	0.356155i	−0.984016	−	0.178077i	$-0.943012\pi$
$751$		−	9.76020i		−	0.356155i	0.984016	−	0.178077i	$-0.0569877\pi$
$752$	−0.381153	−	3.49399i	−0.0138992	−	0.127413i
$753$	−32.8802	−	32.8802i	−1.19822	−	1.19822i
$754$	8.37998	−	49.0580i	0.305181	−	1.78659i
$755$	−23.9397	−	0.196046i	−0.871255	−	0.00713484i
$756$	−7.67909	−	2.70230i	−0.279286	−	0.0982817i
$757$	−16.7093	+	16.7093i	−0.607310	+	0.607310i	−0.942242	−	0.334932i	$-0.891287\pi$
$757$	−16.7093	+	16.7093i	−0.607310	+	0.607310i	0.334932	+	0.942242i	$0.391287\pi$
$758$	−2.17335	+	1.53919i	−0.0789398	+	0.0559058i
$759$	−21.9174			−0.795553
$760$	−35.8086	+	9.89699i	−1.29891	+	0.359002i
$761$	12.3322			0.447041			0.223521	−	0.974699i	$-0.428245\pi$
$761$	12.3322			0.447041			0.223521	+	0.974699i	$0.428245\pi$
$762$	−24.6504	+	17.4576i	−0.892990	+	0.632422i
$763$	5.99302	−	5.99302i	0.216962	−	0.216962i
$764$	−17.2628	−	6.07486i	−0.624548	−	0.219781i
$765$	5.81807	−	5.72355i	0.210353	−	0.206935i
$766$	−6.32459	+	37.0253i	−0.228517	+	1.33778i
$767$	36.8947	+	36.8947i	1.33219	+	1.33219i
$768$	−31.0327	−	19.8071i	−1.11980	−	0.714726i
$769$			9.35663i			0.337409i	0.985667	+	0.168704i	$0.0539583\pi$
$769$			9.35663i			0.337409i	−0.985667	+	0.168704i	$0.946042\pi$
$770$	−7.80282	−	1.39872i	−0.281194	−	0.0504063i
$771$		−	28.0113i		−	1.00880i
$772$	−13.0949	+	6.27762i	−0.471295	+	0.225937i
$773$	−1.32034	−	1.32034i	−0.0474893	−	0.0474893i	0.682963	−	0.730453i	$-0.260691\pi$
$773$	−1.32034	−	1.32034i	−0.0474893	−	0.0474893i	−0.730453	+	0.682963i	$0.760691\pi$
$774$	−6.76389	−	1.15539i	−0.243123	−	0.0415297i
$775$	0.0348345	−	2.12673i	0.00125129	−	0.0763944i
$776$	−24.2414	−	13.4819i	−0.870216	−	0.483973i
$777$	15.8689	−	15.8689i	0.569294	−	0.569294i
$778$	−17.4595	−	24.6531i	−0.625954	−	0.883857i
$779$	−1.61995			−0.0580406
$780$	−54.8159	−	19.7959i	−1.96272	−	0.708806i
$781$	6.52136			0.233353
$782$	−12.3856	−	17.4886i	−0.442907	−	0.625392i
$783$	−7.13396	+	7.13396i	−0.254947	+	0.254947i
$784$	−1.79347	+	2.23268i	−0.0640527	+	0.0797386i
$785$	−35.7214	−	36.3113i	−1.27495	−	1.29601i
$786$	24.5467	+	4.19302i	0.875552	+	0.149560i
$787$	5.38946	+	5.38946i	0.192113	+	0.192113i	0.796609	−	0.604495i	$-0.206625\pi$
$787$	5.38946	+	5.38946i	0.192113	+	0.192113i	−0.604495	+	0.796609i	$0.706625\pi$
$788$	2.20938	+	4.60868i	0.0787058	+	0.164177i
$789$		−	64.2677i		−	2.28799i
$790$	−14.6072	−	20.9879i	−0.519701	−	0.746716i
$791$			9.14875i			0.325292i
$792$	−1.77991	−	6.24045i	−0.0632462	−	0.221745i
$793$	13.4764	+	13.4764i	0.478563	+	0.478563i
$794$	−2.86087	+	16.7481i	−0.101529	+	0.594367i
$795$	−0.00101401	+	0.123824i	−3.59633e−5	+	0.00439157i
$796$	−14.7244	+	41.8422i	−0.521894	+	1.48306i
$797$	35.3081	−	35.3081i	1.25068	−	1.25068i	0.295259	−	0.955417i	$-0.404594\pi$
$797$	35.3081	−	35.3081i	1.25068	−	1.25068i	0.955417	−	0.295259i	$-0.0954059\pi$
$798$	39.1030	−	27.6931i	1.38423	−	0.980324i
$799$	1.39784			0.0494520
$800$	28.2007	+	2.17304i	0.997044	+	0.0768286i
$801$	0.979925			0.0346240
$802$	8.17472	−	5.78940i	0.288659	−	0.204431i
$803$	4.43765	−	4.43765i	0.156601	−	0.156601i
$804$	−15.7820	+	44.8476i	−0.556590	+	1.58165i
$805$	−0.437234	+	53.3918i	−0.0154105	+	1.88182i
$806$	−0.573732	+	3.35874i	−0.0202089	+	0.118306i
$807$	−4.87900	−	4.87900i	−0.171749	−	0.171749i
$808$	12.2741	+	43.0337i	0.431802	+	1.51392i
$809$			25.5115i			0.896936i	0.893799	+	0.448468i	$0.148030\pi$
$809$			25.5115i			0.896936i	−0.893799	+	0.448468i	$0.851970\pi$
$810$	19.1827	+	27.5621i	0.674011	+	0.968432i
$811$		−	40.3812i		−	1.41798i	−0.705221	−	0.708988i	$-0.749152\pi$
$811$		−	40.3812i		−	1.41798i	0.705221	−	0.708988i	$-0.250848\pi$
$812$	−13.4666	−	28.0907i	−0.472584	−	0.985791i
$813$	15.1080	+	15.1080i	0.529860	+	0.529860i
$814$	−5.42384	−	0.926489i	−0.190106	−	0.0324734i
$815$	−9.90505	−	10.0686i	−0.346959	−	0.352688i
$816$	9.16944	−	11.4150i	0.320995	−	0.399603i
$817$	−8.78414	+	8.78414i	−0.307318	+	0.307318i
$818$	16.5767	+	23.4066i	0.579592	+	0.818393i
$819$	32.5747			1.13825
$820$	1.15999	+	0.418911i	0.0405086	+	0.0146290i
$821$	−11.5294			−0.402378			−0.201189	−	0.979552i	$-0.564481\pi$
$821$	−11.5294			−0.402378			−0.201189	+	0.979552i	$0.564481\pi$
$822$	−27.9164	−	39.4184i	−0.973696	−	1.37487i
$823$	12.4682	−	12.4682i	0.434613	−	0.434613i	−0.455581	−	0.890194i	$-0.650569\pi$
$823$	12.4682	−	12.4682i	0.434613	−	0.434613i	0.890194	+	0.455581i	$0.150569\pi$
$824$	21.5022	+	11.9585i	0.749066	+	0.416595i
$825$	8.00073	+	8.26719i	0.278550	+	0.287827i
$826$	32.1930	+	5.49915i	1.12014	+	0.191340i
$827$	−11.1145	−	11.1145i	−0.386490	−	0.386490i	0.486943	−	0.873434i	$-0.338112\pi$
$827$	−11.1145	−	11.1145i	−0.386490	−	0.386490i	−0.873434	+	0.486943i	$0.838112\pi$
$828$	−39.4138	+	18.8948i	−1.36972	+	0.656639i
$829$		−	1.62148i		−	0.0563164i	−0.999603	−	0.0281582i	$-0.991036\pi$
$829$		−	1.62148i		−	0.0563164i	0.999603	−	0.0281582i	$-0.00896421\pi$
$830$	21.7198	+	3.89345i	0.753906	+	0.135144i
$831$		−	10.4125i		−	0.361207i
$832$	−44.1200	−	10.3170i	−1.52959	−	0.357677i
$833$	−0.805371	−	0.805371i	−0.0279045	−	0.0279045i
$834$	4.11904	−	24.1137i	0.142631	−	0.834988i
$835$	17.3929	−	17.1103i	0.601904	−	0.592126i
$836$	−11.0821	−	3.89982i	−0.383281	−	0.134878i
$837$	0.488424	−	0.488424i	0.0168824	−	0.0168824i
$838$	−0.388821	+	0.275366i	−0.0134316	+	0.00951237i
$839$	31.8604			1.09994			0.549972	−	0.835183i	$-0.314639\pi$
$839$	31.8604			1.09994			0.549972	+	0.835183i	$0.314639\pi$
$840$	−35.1617	+	9.71821i	−1.21319	+	0.335310i
$841$	−9.60717			−0.331282
$842$	31.9885	−	22.6545i	1.10240	−	0.780725i
$843$	−10.4880	+	10.4880i	−0.361225	+	0.361225i
$844$	6.66613	+	2.34584i	0.229458	+	0.0807470i
$845$	−42.6590	−	0.349341i	−1.46752	−	0.0120177i
$846$	0.480051	−	2.81031i	0.0165045	−	0.0966205i
$847$	−1.77258	−	1.77258i	−0.0609064	−	0.0609064i
$848$	0.0104399	+	0.0957016i	0.000358508	+	0.00328641i
$849$		−	55.6327i		−	1.90931i
$850$	−2.07543	+	11.0558i	−0.0711866	+	0.379212i
$851$			37.0614i			1.27045i
$852$	27.0616	−	12.9732i	0.927114	−	0.444454i
$853$	7.85271	+	7.85271i	0.268872	+	0.268872i	0.828645	−	0.559774i	$-0.189112\pi$
$853$	7.85271	+	7.85271i	0.268872	+	0.268872i	−0.559774	+	0.828645i	$0.689112\pi$
$854$	11.7591	+	2.00866i	0.402388	+	0.0687350i
$855$	−30.1347	−	0.246777i	−1.03058	−	0.00843961i
$856$	11.3891	−	20.4783i	0.389270	−	0.699934i
$857$	23.9645	−	23.9645i	0.818611	−	0.818611i	−0.167296	−	0.985907i	$-0.553503\pi$
$857$	23.9645	−	23.9645i	0.818611	−	0.818611i	0.985907	+	0.167296i	$0.0535034\pi$
$858$	−10.6516	−	15.0402i	−0.363640	−	0.513466i
$859$	15.9534			0.544322			0.272161	−	0.962252i	$-0.412262\pi$
$859$	15.9534			0.544322			0.272161	+	0.962252i	$0.412262\pi$
$860$	8.56158	−	4.01849i	0.291947	−	0.137029i
$861$	−1.59068			−0.0542103
$862$	5.52249	+	7.79784i	0.188097	+	0.265595i
$863$	24.6273	−	24.6273i	0.838322	−	0.838322i	−0.150316	−	0.988638i	$-0.548029\pi$
$863$	24.6273	−	24.6273i	0.838322	−	0.838322i	0.988638	+	0.150316i	$0.0480292\pi$
$864$	6.09012	+	6.87586i	0.207190	+	0.233922i
$865$	−25.8598	+	25.4397i	−0.879260	+	0.864976i
$866$	30.3755	+	5.18868i	1.03220	+	0.176318i
$867$	−23.5416	−	23.5416i	−0.799514	−	0.799514i
$868$	0.921984	+	1.92322i	0.0312942	+	0.0652784i
$869$		−	8.08617i		−	0.274305i
$870$	−7.97718	+	44.5012i	−0.270452	+	1.50873i
$871$			58.5142i			1.98268i
$872$	−9.19607	+	2.62291i	−0.311418	+	0.0888230i
$873$	−15.9101	−	15.9101i	−0.538475	−	0.538475i
$874$	−13.3238	+	78.0003i	−0.450686	+	2.63840i
$875$	20.2988	−	19.3252i	0.686226	−	0.653311i
$876$	9.58684	−	27.2428i	0.323909	−	0.920448i
$877$	16.9440	−	16.9440i	0.572158	−	0.572158i	−0.360573	−	0.932731i	$-0.617419\pi$
$877$	16.9440	−	16.9440i	0.572158	−	0.572158i	0.932731	+	0.360573i	$0.117419\pi$
$878$	−2.68484	+	1.90142i	−0.0906089	+	0.0641699i
$879$	57.8575			1.95149
$880$	6.92702	+	5.65831i	0.233510	+	0.190741i
$881$	−33.1741			−1.11766			−0.558832	−	0.829281i	$-0.688750\pi$
$881$	−33.1741			−1.11766			−0.558832	+	0.829281i	$0.688750\pi$
$882$	−1.89576	+	1.34259i	−0.0638335	+	0.0452074i
$883$	−39.1299	+	39.1299i	−1.31682	+	1.31682i	−0.400550	+	0.916275i	$0.631181\pi$
$883$	−39.1299	+	39.1299i	−1.31682	+	1.31682i	−0.916275	+	0.400550i	$0.868819\pi$
$884$	5.98184	−	16.9985i	0.201191	−	0.571722i
$885$	−33.2401	−	33.7890i	−1.11735	−	1.13580i
$886$	6.63220	−	38.8261i	0.222813	−	1.30439i
$887$	−5.56472	−	5.56472i	−0.186845	−	0.186845i	0.607486	−	0.794331i	$-0.292178\pi$
$887$	−5.56472	−	5.56472i	−0.186845	−	0.186845i	−0.794331	+	0.607486i	$0.792178\pi$
$888$	−24.3503	+	6.94521i	−0.817143	+	0.233066i
$889$			23.2699i			0.780447i
$890$	−1.10857	+	0.771547i	−0.0371595	+	0.0258623i
$891$			10.6191i			0.355752i
$892$	−19.0691	−	39.7775i	−0.638482	−	1.33185i
$893$	−3.64970	−	3.64970i	−0.122133	−	0.122133i
$894$	58.9113	+	10.0631i	1.97029	+	0.336561i
$895$	0.264672	−	32.3198i	0.00884700	−	1.08033i
$896$	−26.2691	+	10.6908i	−0.877589	+	0.357154i
$897$	−87.7770	+	87.7770i	−2.93079	+	2.93079i
$898$	5.77090	+	8.14860i	0.192577	+	0.271922i
$899$	2.64323			0.0881566
$900$	21.5146	+	7.96942i	0.717155	+	0.265647i
$901$	−0.0382873			−0.00127554
$902$	0.225405	+	0.318275i	0.00750516	+	0.0105974i
$903$	−8.62546	+	8.62546i	−0.287037	+	0.287037i
$904$	5.01719	−	9.02124i	0.166869	−	0.300042i
$905$	−0.122182	+	14.9200i	−0.00406146	+	0.495957i
$906$	−34.3418	−	5.86619i	−1.14093	−	0.194891i
$907$	19.9115	+	19.9115i	0.661150	+	0.661150i	0.955651	−	0.294501i	$-0.0951535\pi$
$907$	19.9115	+	19.9115i	0.661150	+	0.661150i	−0.294501	+	0.955651i	$0.595153\pi$
$908$	−25.1437	+	12.0538i	−0.834424	+	0.400019i
$909$			36.2996i			1.20398i
$910$	−36.8512	+	25.6478i	−1.22160	+	0.850215i
$911$			14.3711i			0.476136i	0.971249	+	0.238068i	$0.0765141\pi$
$911$			14.3711i			0.476136i	−0.971249	+	0.238068i	$0.923486\pi$
$912$	−53.7450	+	5.86294i	−1.77968	+	0.194141i
$913$	4.93412	+	4.93412i	0.163295	+	0.163295i
$914$	−5.15113	+	30.1557i	−0.170384	+	0.997462i
$915$	−12.1415	−	12.3420i	−0.401387	−	0.408015i
$916$	−18.6613	−	6.56697i	−0.616585	−	0.216979i
$917$	13.5651	−	13.5651i	0.447959	−	0.447959i
$918$	−2.98114	+	2.11126i	−0.0983922	+	0.0696821i
$919$	−16.5363			−0.545484			−0.272742	−	0.962087i	$-0.587930\pi$
$919$	−16.5363			−0.545484			−0.272742	+	0.962087i	$0.587930\pi$
$920$	29.7113	−	52.4079i	0.979553	−	1.72784i
$921$	−9.36396			−0.308553
$922$	−42.9030	+	30.3842i	−1.41293	+	1.00065i
$923$	26.1174	−	26.1174i	0.859664	−	0.859664i
$924$	−10.8819	−	3.82937i	−0.357987	−	0.125977i
$925$	13.9794	−	13.5289i	0.459641	−	0.444827i
$926$	6.93725	−	40.6119i	0.227972	−	1.33459i
$927$	14.1123	+	14.1123i	0.463510	+	0.463510i
$928$	−2.12613	+	35.0843i	−0.0697936	+	1.15170i
$929$		−	12.1761i		−	0.399485i	−0.979848	−	0.199743i	$-0.935989\pi$
$929$		−	12.1761i		−	0.399485i	0.979848	−	0.199743i	$-0.0640106\pi$
$930$	0.546155	−	3.04676i	0.0179091	−	0.0999071i
$931$			4.20558i			0.137832i
$932$	−4.37952	+	2.09952i	−0.143456	+	0.0687722i
$933$	−8.22945	−	8.22945i	−0.269420	−	0.269420i
$934$	17.6812	+	3.02026i	0.578545	+	0.0988258i
$935$	−2.53585	+	2.49466i	−0.0829313	+	0.0815840i
$936$	−32.1207	−	17.8640i	−1.04990	−	0.583903i
$937$	9.30942	−	9.30942i	0.304125	−	0.304125i	−0.538500	−	0.842625i	$-0.681009\pi$
$937$	9.30942	−	9.30942i	0.304125	−	0.304125i	0.842625	+	0.538500i	$0.181009\pi$
$938$	21.1680	+	29.8895i	0.691159	+	0.975928i
$939$	−26.4319			−0.862574
$940$	1.66963	+	3.55723i	0.0544574	+	0.116024i
$941$	31.8841			1.03939			0.519696	−	0.854351i	$-0.326045\pi$
$941$	31.8841			1.03939			0.519696	+	0.854351i	$0.326045\pi$
$942$	−42.8405	−	60.4914i	−1.39582	−	1.97092i
$943$	1.85750	−	1.85750i	0.0604885	−	0.0604885i
$944$	−28.7286	−	23.0772i	−0.935037	−	0.751100i
$945$	9.10126	+	0.0745316i	0.296064	+	0.00242451i
$946$	2.94810	+	0.503588i	0.0958509	+	0.0163731i
$947$	13.3196	+	13.3196i	0.432830	+	0.432830i	0.889590	−	0.456760i	$-0.150990\pi$
$947$	13.3196	+	13.3196i	0.432830	+	0.432830i	−0.456760	+	0.889590i	$0.650990\pi$
$948$	−16.0861	−	33.5550i	−0.522453	−	1.08982i
$949$		−	35.5446i		−	1.15383i
$950$	34.2852	−	23.4475i	1.11236	−	0.760736i
$951$			44.3337i			1.43762i
$952$	−3.09378	−	10.8470i	−0.100270	−	0.351552i
$953$	20.6180	+	20.6180i	0.667882	+	0.667882i	0.957225	−	0.289343i	$-0.0934369\pi$
$953$	20.6180	+	20.6180i	0.667882	+	0.667882i	−0.289343	+	0.957225i	$0.593437\pi$
$954$	−0.0131488	+	0.0769755i	−0.000425708	+	0.00249217i
$955$	20.4599	+	0.167549i	0.662068	+	0.00542177i
$956$	4.55487	−	12.9435i	0.147315	−	0.418623i
$957$	−10.1094	+	10.1094i	−0.326790	+	0.326790i
$958$	18.8089	−	13.3206i	0.607688	−	0.430369i
$959$	−37.2108			−1.20160
$960$	40.0012	+	9.69998i	1.29103	+	0.313066i
$961$	30.8190			0.994162
$962$	−25.4324	+	18.0114i	−0.819973	+	0.580711i
$963$	13.4403	−	13.4403i	0.433108	−	0.433108i
$964$	9.94361	−	28.2566i	0.320262	−	0.910084i
$965$	11.5742	−	11.3861i	0.372586	−	0.366533i
$966$	−13.0832	+	76.5913i	−0.420944	+	2.46428i
$967$	−8.89205	−	8.89205i	−0.285949	−	0.285949i	0.549527	−	0.835476i	$-0.314808\pi$
$967$	−8.89205	−	8.89205i	−0.285949	−	0.285949i	−0.835476	+	0.549527i	$0.814808\pi$
$968$	0.775788	+	2.71995i	0.0249348	+	0.0874227i
$969$		−	21.5017i		−	0.690736i
$970$	30.5257	+	5.47197i	0.980121	+	0.175694i
$971$			28.9060i			0.927639i	0.885930	+	0.463819i	$0.153521\pi$
$971$			28.9060i			0.927639i	−0.885930	+	0.463819i	$0.846479\pi$
$972$	16.9134	+	35.2806i	0.542497	+	1.13163i
$973$	−13.3258	−	13.3258i	−0.427205	−	0.427205i
$974$	−15.9957	−	2.73235i	−0.512535	−	0.0875501i
$975$	65.1513	+	1.06714i	2.08651	+	0.0341758i
$976$	−10.4937	−	8.42938i	−0.335894	−	0.269818i
$977$	13.6201	−	13.6201i	0.435745	−	0.435745i	−0.454832	−	0.890577i	$-0.650301\pi$
$977$	13.6201	−	13.6201i	0.435745	−	0.435745i	0.890577	+	0.454832i	$0.150301\pi$
$978$	−11.8791	−	16.7734i	−0.379851	−	0.536355i
$979$	−0.427109			−0.0136505
$980$	1.08755	−	3.01148i	0.0347404	−	0.0961982i
$981$	−7.75703			−0.247663
$982$	−0.930535	−	1.31393i	−0.0296946	−	0.0419292i
$983$	21.4322	−	21.4322i	0.683582	−	0.683582i	−0.277223	−	0.960805i	$-0.589414\pi$
$983$	21.4322	−	21.4322i	0.683582	−	0.683582i	0.960805	+	0.277223i	$0.0894142\pi$
$984$	1.56851	+	0.872333i	0.0500024	+	0.0278090i
$985$	−4.00730	−	4.07347i	−0.127683	−	0.129792i
$986$	−13.7794	−	2.35377i	−0.438825	−	0.0749592i
$987$	−3.58377	−	3.58377i	−0.114073	−	0.114073i
$988$	−60.0008	+	28.7641i	−1.90888	+	0.915108i
$989$		−	20.1445i		−	0.640559i
$990$	4.14456	+	5.95498i	0.131723	+	0.189262i
$991$		−	31.5991i		−	1.00378i	−0.864932	−	0.501889i	$-0.832639\pi$
$991$		−	31.5991i		−	1.00378i	0.864932	−	0.501889i	$-0.167361\pi$
$992$	0.145565	−	2.40204i	0.00462168	−	0.0762647i
$993$	−9.99898	−	9.99898i	−0.317308	−	0.317308i
$994$	3.89279	−	22.7891i	0.123472	−	0.722827i
$995$	0.406112	−	49.5914i	0.0128746	−	1.57215i
$996$	30.2906	+	10.6594i	0.959795	+	0.337755i
$997$	29.1186	−	29.1186i	0.922197	−	0.922197i	−0.0749879	−	0.997184i	$-0.523892\pi$
$997$	29.1186	−	29.1186i	0.922197	−	0.922197i	0.997184	+	0.0749879i	$0.0238918\pi$
$998$	35.0541	−	24.8256i	1.10962	−	0.785840i
$999$	6.31755			0.199879

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.d.23.11	yes	28
4.3	odd	2		220.2.l.c.23.11	✓	28
5.2	odd	4		220.2.l.c.67.11	yes	28
20.7	even	4	inner	220.2.l.d.67.11	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.11	✓	28	4.3	odd	2
220.2.l.c.67.11	yes	28	5.2	odd	4
220.2.l.d.23.11	yes	28	1.1	even	1	trivial
220.2.l.d.67.11	yes	28	20.7	even	4	inner

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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.2.l.d.23.11

Level	$220$
Weight	$2$
Character	220.23
Analytic conductor	$1.757$
Analytic rank	$0$
Dimension	$28$
Inner twists	$2$