LMFDB - Embedded newform 990.2.t.b.131.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.19
Character	$\chi$	$=$	990.131
Dual form			990.2.t.b.461.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50274 + 0.861268i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.00548788 + 1.73204i) q^{6} +(1.26719 - 0.731611i) q^{7} -1.00000 q^{8} +(1.51643 + 2.58852i) q^{9} -1.00000i q^{10} +(3.30189 + 0.312246i) q^{11} +(-1.49725 + 0.870774i) q^{12} +(0.354032 + 0.204400i) q^{13} +(1.26719 + 0.731611i) q^{14} +(-0.870774 - 1.49725i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.86818 q^{17} +(-1.48351 + 2.60753i) q^{18} +6.41008i q^{19} +(0.866025 - 0.500000i) q^{20} +(2.53436 - 0.00802999i) q^{21} +(1.38053 + 3.01565i) q^{22} +(7.54804 + 4.35786i) q^{23} +(-1.50274 - 0.861268i) q^{24} +(0.500000 + 0.866025i) q^{25} +0.408801i q^{26} +(0.0493903 + 5.19592i) q^{27} +1.46322i q^{28} +(-5.07036 - 8.78212i) q^{29} +(0.861268 - 1.50274i) q^{30} +(0.478423 - 0.828652i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.69295 + 3.31304i) q^{33} +(-1.43409 - 2.48391i) q^{34} -1.46322 q^{35} +(-2.99994 + 0.0190105i) q^{36} +8.03901 q^{37} +(-5.55129 + 3.20504i) q^{38} +(0.355973 + 0.612076i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-0.185968 + 0.322106i) q^{41} +(1.27414 + 2.19081i) q^{42} +(-7.17709 + 4.14369i) q^{43} +(-1.92136 + 2.70340i) q^{44} +(-0.0190105 - 2.99994i) q^{45} +8.71572i q^{46} +(-5.43736 + 3.13926i) q^{47} +(-0.00548788 - 1.73204i) q^{48} +(-2.42949 + 4.20800i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-4.31011 - 2.47027i) q^{51} +(-0.354032 + 0.204400i) q^{52} -6.52693i q^{53} +(-4.47510 + 2.64073i) q^{54} +(-2.70340 - 1.92136i) q^{55} +(-1.26719 + 0.731611i) q^{56} +(-5.52080 + 9.63265i) q^{57} +(5.07036 - 8.78212i) q^{58} +(3.76646 + 2.17457i) q^{59} +(1.73204 - 0.00548788i) q^{60} +(8.21542 - 4.74317i) q^{61} +0.956845 q^{62} +(3.81539 + 2.17070i) q^{63} +1.00000 q^{64} +(-0.204400 - 0.354032i) q^{65} +(-0.522702 + 5.72073i) q^{66} +(-0.265166 + 0.459281i) q^{67} +(1.43409 - 2.48391i) q^{68} +(7.58942 + 13.0496i) q^{69} +(-0.731611 - 1.26719i) q^{70} -5.71056i q^{71} +(-1.51643 - 2.58852i) q^{72} -3.68830i q^{73} +(4.01950 + 6.96198i) q^{74} +(0.00548788 + 1.73204i) q^{75} +(-5.55129 - 3.20504i) q^{76} +(4.41256 - 2.02003i) q^{77} +(-0.352087 + 0.614319i) q^{78} +(-3.20431 + 1.85001i) q^{79} +1.00000i q^{80} +(-4.40086 + 7.85063i) q^{81} -0.371936 q^{82} +(-6.46495 - 11.1976i) q^{83} +(-1.26023 + 2.19884i) q^{84} +(2.48391 + 1.43409i) q^{85} +(-7.17709 - 4.14369i) q^{86} +(-0.0556511 - 17.5642i) q^{87} +(-3.30189 - 0.312246i) q^{88} -7.53973i q^{89} +(2.58852 - 1.51643i) q^{90} +0.598166 q^{91} +(-7.54804 + 4.35786i) q^{92} +(1.43264 - 0.833196i) q^{93} +(-5.43736 - 3.13926i) q^{94} +(3.20504 - 5.55129i) q^{95} +(1.49725 - 0.870774i) q^{96} +(-9.30082 - 16.1095i) q^{97} -4.85898 q^{98} +(4.19885 + 9.02051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.50274	+	0.861268i	0.867605	+	0.497254i
$3$	1.50274	+	0.861268i	0.867605	+	0.497254i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	0.00548788	+	1.73204i	0.00224042	+	0.707103i
$7$	1.26719	−	0.731611i	0.478952	−	0.276523i	−0.241028	−	0.970518i	$-0.577484\pi$
$7$	1.26719	−	0.731611i	0.478952	−	0.276523i	0.719980	+	0.693995i	$0.244151\pi$
$8$	−1.00000			−0.353553
$9$	1.51643	+	2.58852i	0.505478	+	0.862840i
$10$		−	1.00000i		−	0.316228i
$11$	3.30189	+	0.312246i	0.995558	+	0.0941456i
$11$	3.30189	+	0.312246i	0.995558	+	0.0941456i
$12$	−1.49725	+	0.870774i	−0.432218	+	0.251371i
$13$	0.354032	+	0.204400i	0.0981907	+	0.0566904i	0.548291	−	0.836287i	$-0.315279\pi$
$13$	0.354032	+	0.204400i	0.0981907	+	0.0566904i	−0.450101	+	0.892978i	$0.648612\pi$
$14$	1.26719	+	0.731611i	0.338670	+	0.195531i
$15$	−0.870774	−	1.49725i	−0.224833	−	0.386588i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.86818			−0.695635			−0.347817	−	0.937562i	$-0.613077\pi$
$17$	−2.86818			−0.695635			−0.347817	+	0.937562i	$0.613077\pi$
$18$	−1.48351	+	2.60753i	−0.349666	+	0.614601i
$19$			6.41008i			1.47057i	0.677757	+	0.735286i	$0.262952\pi$
$19$			6.41008i			1.47057i	−0.677757	+	0.735286i	$0.737048\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	2.53436	−	0.00802999i	0.553043	−	0.00175229i
$22$	1.38053	+	3.01565i	0.294331	+	0.642938i
$23$	7.54804	+	4.35786i	1.57387	+	0.908677i	0.995687	+	0.0927729i	$0.0295731\pi$
$23$	7.54804	+	4.35786i	1.57387	+	0.908677i	0.578187	+	0.815904i	$0.303760\pi$
$24$	−1.50274	−	0.861268i	−0.306745	−	0.175806i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$			0.408801i			0.0801724i
$27$	0.0493903	+	5.19592i	0.00950516	+	0.999955i
$28$			1.46322i			0.276523i
$29$	−5.07036	−	8.78212i	−0.941543	−	1.63080i	−0.762530	−	0.646953i	$-0.776043\pi$
$29$	−5.07036	−	8.78212i	−0.941543	−	1.63080i	−0.179012	−	0.983847i	$-0.557290\pi$
$30$	0.861268	−	1.50274i	0.157245	−	0.274361i
$31$	0.478423	−	0.828652i	0.0859272	−	0.148830i	−0.819859	−	0.572566i	$-0.805948\pi$
$31$	0.478423	−	0.828652i	0.0859272	−	0.148830i	0.905786	+	0.423736i	$0.139281\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	4.69295	+	3.31304i	0.816938	+	0.576726i
$34$	−1.43409	−	2.48391i	−0.245944	−	0.425988i
$35$	−1.46322			−0.247330
$36$	−2.99994	+	0.0190105i	−0.499990	+	0.00316841i
$37$	8.03901			1.32160			0.660802	−	0.750560i	$-0.270216\pi$
$37$	8.03901			1.32160			0.660802	+	0.750560i	$0.270216\pi$
$38$	−5.55129	+	3.20504i	−0.900538	+	0.519926i
$39$	0.355973	+	0.612076i	0.0570013	+	0.0980106i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−0.185968	+	0.322106i	−0.0290433	+	0.0503045i	−0.880182	−	0.474637i	$-0.842579\pi$
$41$	−0.185968	+	0.322106i	−0.0290433	+	0.0503045i	0.851138	+	0.524941i	$0.175913\pi$
$42$	1.27414	+	2.19081i	0.196603	+	0.338049i
$43$	−7.17709	+	4.14369i	−1.09450	+	0.631907i	−0.934770	−	0.355254i	$-0.884394\pi$
$43$	−7.17709	+	4.14369i	−1.09450	+	0.631907i	−0.159726	+	0.987161i	$0.551061\pi$
$44$	−1.92136	+	2.70340i	−0.289656	+	0.407553i
$45$	−0.0190105	−	2.99994i	−0.00283392	−	0.447205i
$46$			8.71572i			1.28506i
$47$	−5.43736	+	3.13926i	−0.793120	+	0.457908i	−0.841060	−	0.540942i	$-0.818068\pi$
$47$	−5.43736	+	3.13926i	−0.793120	+	0.457908i	0.0479395	+	0.998850i	$0.484735\pi$
$48$	−0.00548788	−	1.73204i	−0.000792107	−	0.249999i
$49$	−2.42949	+	4.20800i	−0.347070	+	0.601143i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−4.31011	−	2.47027i	−0.603536	−	0.345907i
$52$	−0.354032	+	0.204400i	−0.0490954	+	0.0283452i
$53$		−	6.52693i		−	0.896543i	−0.893897	−	0.448272i	$-0.852040\pi$
$53$		−	6.52693i		−	0.896543i	0.893897	−	0.448272i	$-0.147960\pi$
$54$	−4.47510	+	2.64073i	−0.608984	+	0.359358i
$55$	−2.70340	−	1.92136i	−0.364527	−	0.259076i
$56$	−1.26719	+	0.731611i	−0.169335	+	0.0977656i
$57$	−5.52080	+	9.63265i	−0.731247	+	1.27588i
$58$	5.07036	−	8.78212i	0.665771	−	1.15315i
$59$	3.76646	+	2.17457i	0.490352	+	0.283105i	0.724720	−	0.689043i	$-0.241969\pi$
$59$	3.76646	+	2.17457i	0.490352	+	0.283105i	−0.234369	+	0.972148i	$0.575302\pi$
$60$	1.73204	−	0.00548788i	0.223606	−	0.000708482i
$61$	8.21542	−	4.74317i	1.05188	−	0.607301i	0.128702	−	0.991683i	$-0.458919\pi$
$61$	8.21542	−	4.74317i	1.05188	−	0.607301i	0.923174	+	0.384382i	$0.125586\pi$
$62$	0.956845			0.121519
$63$	3.81539	+	2.17070i	0.480694	+	0.273482i
$64$	1.00000			0.125000
$65$	−0.204400	−	0.354032i	−0.0253527	−	0.0439122i
$66$	−0.522702	+	5.72073i	−0.0643402	+	0.704174i
$67$	−0.265166	+	0.459281i	−0.0323952	+	0.0561101i	−0.881768	−	0.471683i	$-0.843647\pi$
$67$	−0.265166	+	0.459281i	−0.0323952	+	0.0561101i	0.849373	+	0.527793i	$0.176980\pi$
$68$	1.43409	−	2.48391i	0.173909	−	0.301219i
$69$	7.58942	+	13.0496i	0.913659	+	1.57099i
$70$	−0.731611	−	1.26719i	−0.0874442	−	0.151458i
$71$		−	5.71056i		−	0.677719i	−0.940837	−	0.338859i	$-0.889959\pi$
$71$		−	5.71056i		−	0.677719i	0.940837	−	0.338859i	$-0.110041\pi$
$72$	−1.51643	−	2.58852i	−0.178713	−	0.305060i
$73$		−	3.68830i		−	0.431682i	−0.976428	−	0.215841i	$-0.930751\pi$
$73$		−	3.68830i		−	0.431682i	0.976428	−	0.215841i	$-0.0692493\pi$
$74$	4.01950	+	6.96198i	0.467258	+	0.809314i
$75$	0.00548788	+	1.73204i	0.000633686	+	0.199999i
$76$	−5.55129	−	3.20504i	−0.636776	−	0.367643i
$77$	4.41256	−	2.02003i	0.502858	−	0.230204i
$78$	−0.352087	+	0.614319i	−0.0398660	+	0.0695580i
$79$	−3.20431	+	1.85001i	−0.360513	+	0.208142i	−0.669306	−	0.742987i	$-0.733408\pi$
$79$	−3.20431	+	1.85001i	−0.360513	+	0.208142i	0.308793	+	0.951129i	$0.400075\pi$
$80$			1.00000i			0.111803i
$81$	−4.40086	+	7.85063i	−0.488984	+	0.872293i
$82$	−0.371936			−0.0410735
$83$	−6.46495	−	11.1976i	−0.709620	−	1.22910i	−0.964998	−	0.262257i	$-0.915533\pi$
$83$	−6.46495	−	11.1976i	−0.709620	−	1.22910i	0.255378	−	0.966841i	$-0.417800\pi$
$84$	−1.26023	+	2.19884i	−0.137502	+	0.239913i
$85$	2.48391	+	1.43409i	0.269418	+	0.155549i
$86$	−7.17709	−	4.14369i	−0.773925	−	0.446826i
$87$	−0.0556511	−	17.5642i	−0.00596642	−	1.88308i
$88$	−3.30189	−	0.312246i	−0.351983	−	0.0332855i
$89$		−	7.53973i		−	0.799209i	−0.916688	−	0.399605i	$-0.869147\pi$
$89$		−	7.53973i		−	0.799209i	0.916688	−	0.399605i	$-0.130853\pi$
$90$	2.58852	−	1.51643i	0.272854	−	0.159846i
$91$	0.598166			0.0627048
$92$	−7.54804	+	4.35786i	−0.786937	+	0.454338i
$93$	1.43264	−	0.833196i	0.148557	−	0.0863984i
$94$	−5.43736	−	3.13926i	−0.560821	−	0.323790i
$95$	3.20504	−	5.55129i	0.328830	−	0.569550i
$96$	1.49725	−	0.870774i	0.152812	−	0.0888730i
$97$	−9.30082	−	16.1095i	−0.944355	−	1.63567i	−0.757038	−	0.653371i	$-0.773354\pi$
$97$	−9.30082	−	16.1095i	−0.944355	−	1.63567i	−0.187317	−	0.982299i	$-0.559979\pi$
$98$	−4.85898			−0.490831
$99$	4.19885	+	9.02051i	0.422000	+	0.906596i
$100$	−1.00000			−0.100000
$101$	−2.62335	−	4.54377i	−0.261033	−	0.452122i	0.705484	−	0.708726i	$-0.250730\pi$
$101$	−2.62335	−	4.54377i	−0.261033	−	0.452122i	−0.966517	+	0.256604i	$0.917396\pi$
$102$	−0.0157402	−	4.96780i	−0.00155851	−	0.491886i
$103$	2.93353	−	5.08102i	0.289049	−	0.500647i	−0.684534	−	0.728981i	$-0.739994\pi$
$103$	2.93353	−	5.08102i	0.289049	−	0.500647i	0.973583	+	0.228334i	$0.0733277\pi$
$104$	−0.354032	−	0.204400i	−0.0347157	−	0.0200431i
$105$	−2.19884	−	1.26023i	−0.214584	−	0.122986i
$106$	5.65249	−	3.26347i	0.549018	−	0.316976i
$107$	4.60520			0.445202			0.222601	−	0.974910i	$-0.428545\pi$
$107$	4.60520			0.445202			0.222601	+	0.974910i	$0.428545\pi$
$108$	−4.52449	−	2.55519i	−0.435369	−	0.245873i
$109$			12.7899i			1.22505i	0.790452	+	0.612524i	$0.209846\pi$
$109$			12.7899i			1.22505i	−0.790452	+	0.612524i	$0.790154\pi$
$110$	0.312246	−	3.30189i	0.0297715	−	0.314823i
$111$	12.0805	+	6.92374i	1.14663	+	0.657172i
$112$	−1.26719	−	0.731611i	−0.119738	−	0.0691307i
$113$	−12.2279	−	7.05979i	−1.15031	−	0.664129i	−0.201344	−	0.979521i	$-0.564531\pi$
$113$	−12.2279	−	7.05979i	−1.15031	−	0.664129i	−0.948962	+	0.315391i	$0.897864\pi$
$114$	−11.1025	+	0.0351777i	−1.03985	+	0.00329470i
$115$	−4.35786	−	7.54804i	−0.406373	−	0.703858i
$116$	10.1407			0.941543
$117$	0.00777150	+	1.22638i	0.000718475	+	0.113379i
$118$			4.34914i			0.400371i
$119$	−3.63452	+	2.09839i	−0.333176	+	0.192359i
$120$	0.870774	+	1.49725i	0.0794904	+	0.136679i
$121$	10.8050	+	2.06200i	0.982273	+	0.187455i
$122$	8.21542	+	4.74317i	0.743789	+	0.429427i
$123$	−0.556881	+	0.323872i	−0.0502122	+	0.0292026i
$124$	0.478423	+	0.828652i	0.0429636	+	0.0744152i
$125$		−	1.00000i		−	0.0894427i
$126$	0.0278166	+	4.38958i	0.00247810	+	0.391055i
$127$			13.6254i			1.20906i	0.796582	+	0.604530i	$0.206639\pi$
$127$			13.6254i			1.20906i	−0.796582	+	0.604530i	$0.793361\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−14.3541	+	0.0454802i	−1.26381	+	0.00400431i
$130$	0.204400	−	0.354032i	0.0179271	−	0.0310506i
$131$	7.83507	−	13.5707i	0.684553	−	1.18568i	−0.289024	−	0.957322i	$-0.593331\pi$
$131$	7.83507	−	13.5707i	0.684553	−	1.18568i	0.973577	−	0.228359i	$-0.0733360\pi$
$132$	−5.21565	+	2.40769i	−0.453964	+	0.209563i
$133$	4.68968	+	8.12277i	0.406647	+	0.704333i
$134$	−0.530332			−0.0458137
$135$	2.55519	−	4.52449i	0.219915	−	0.389406i
$136$	2.86818			0.245944
$137$	14.7996	−	8.54454i	1.26441	−	0.730010i	0.290488	−	0.956879i	$-0.406182\pi$
$137$	14.7996	−	8.54454i	1.26441	−	0.730010i	0.973925	+	0.226869i	$0.0728489\pi$
$138$	−7.50658	+	13.0974i	−0.639002	+	1.11493i
$139$	0.984121	+	0.568183i	0.0834721	+	0.0481926i	0.541155	−	0.840923i	$-0.317987\pi$
$139$	0.984121	+	0.568183i	0.0834721	+	0.0481926i	−0.457683	+	0.889115i	$0.651321\pi$
$140$	0.731611	−	1.26719i	0.0618324	−	0.107097i
$141$	−10.8747	+	0.0344558i	−0.915812	+	0.00290170i
$142$	4.94549	−	2.85528i	0.415016	−	0.239610i
$143$	1.10515	+	0.785453i	0.0924174	+	0.0656829i
$144$	1.48351	−	2.60753i	0.123626	−	0.217294i
$145$			10.1407i			0.842141i
$146$	3.19416	−	1.84415i	0.264350	−	0.152623i
$147$	−7.27510	+	4.23107i	−0.600040	+	0.348973i
$148$	−4.01950	+	6.96198i	−0.330401	+	0.572271i
$149$	0.817421	−	1.41582i	0.0669658	−	0.115988i	−0.830599	−	0.556872i	$-0.812002\pi$
$149$	0.817421	−	1.41582i	0.0669658	−	0.115988i	0.897564	+	0.440884i	$0.145335\pi$
$150$	−1.49725	+	0.870774i	−0.122250	+	0.0710984i
$151$	18.5744	−	10.7239i	1.51156	−	0.872701i	0.511654	−	0.859192i	$-0.329033\pi$
$151$	18.5744	−	10.7239i	1.51156	−	0.872701i	0.999909	−	0.0135092i	$-0.00430023\pi$
$152$		−	6.41008i		−	0.519926i
$153$	−4.34940	−	7.42433i	−0.351628	−	0.600221i
$154$	3.95568	+	2.81138i	0.318757	+	0.226547i
$155$	−0.828652	+	0.478423i	−0.0665590	+	0.0384278i
$156$	−0.708060	+	0.00224345i	−0.0566902	+	0.000179620i
$157$	−5.03859	+	8.72709i	−0.402123	+	0.696497i	−0.993982	−	0.109544i	$-0.965061\pi$
$157$	−5.03859	+	8.72709i	−0.402123	+	0.696497i	0.591859	+	0.806042i	$0.298394\pi$
$158$	−3.20431	−	1.85001i	−0.254921	−	0.147179i
$159$	5.62144	−	9.80826i	0.445809	−	0.777846i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	12.7530			1.00508
$162$	−8.99928	+	0.114061i	−0.707050	+	0.00896145i
$163$	12.4779			0.977341			0.488670	−	0.872468i	$-0.337482\pi$
$163$	12.4779			0.977341			0.488670	+	0.872468i	$0.337482\pi$
$164$	−0.185968	−	0.322106i	−0.0145217	−	0.0251523i
$165$	−2.40769	−	5.21565i	−0.187439	−	0.406038i
$166$	6.46495	−	11.1976i	0.501777	−	0.869104i
$167$	−5.53040	+	9.57893i	−0.427955	+	0.741240i	−0.996691	−	0.0812799i	$-0.974099\pi$
$167$	−5.53040	+	9.57893i	−0.427955	+	0.741240i	0.568736	+	0.822520i	$0.307433\pi$
$168$	−2.53436	+	0.00802999i	−0.195530	+	0.000619527i
$169$	−6.41644	−	11.1136i	−0.493572	−	0.854892i
$170$			2.86818i			0.219979i
$171$	−16.5926	+	9.72045i	−1.26887	+	0.743342i
$172$		−	8.28739i		−	0.631907i
$173$	−0.545882	−	0.945495i	−0.0415026	−	0.0718846i	0.844528	−	0.535512i	$-0.179881\pi$
$173$	−0.545882	−	0.945495i	−0.0415026	−	0.0718846i	−0.886031	+	0.463627i	$0.846548\pi$
$174$	15.1832	−	8.83028i	1.15103	−	0.669421i
$175$	1.26719	+	0.731611i	0.0957904	+	0.0553046i
$176$	−1.38053	−	3.01565i	−0.104062	−	0.227313i
$177$	3.78712	+	6.51174i	0.284657	+	0.489452i
$178$	6.52959	−	3.76986i	0.489414	−	0.282563i
$179$			1.38374i			0.103426i	0.998662	+	0.0517129i	$0.0164681\pi$
$179$			1.38374i			0.103426i	−0.998662	+	0.0517129i	$0.983532\pi$
$180$	2.60753	+	1.48351i	0.194354	+	0.110574i
$181$	−7.10273			−0.527942			−0.263971	−	0.964531i	$-0.585032\pi$
$181$	−7.10273			−0.527942			−0.263971	+	0.964531i	$0.585032\pi$
$182$	0.299083	+	0.518027i	0.0221695	+	0.0383987i
$183$	16.4308	−	0.0520599i	1.21460	−	0.00384838i
$184$	−7.54804	−	4.35786i	−0.556449	−	0.321266i
$185$	−6.96198	−	4.01950i	−0.511855	−	0.295520i
$186$	1.43789	+	0.824101i	0.105431	+	0.0604260i
$187$	−9.47041	−	0.895576i	−0.692545	−	0.0654910i
$188$		−	6.27852i		−	0.457908i
$189$	3.86398	+	6.54807i	0.281063	+	0.476302i
$190$	6.41008			0.465036
$191$	3.37061	−	1.94602i	0.243889	−	0.140809i	−0.373074	−	0.927802i	$-0.621696\pi$
$191$	3.37061	−	1.94602i	0.243889	−	0.140809i	0.616963	+	0.786992i	$0.288363\pi$
$192$	1.50274	+	0.861268i	0.108451	+	0.0621567i
$193$	1.94393	+	1.12233i	0.139927	+	0.0807868i	0.568329	−	0.822801i	$-0.307590\pi$
$193$	1.94393	+	1.12233i	0.139927	+	0.0807868i	−0.428402	+	0.903588i	$0.640923\pi$
$194$	9.30082	−	16.1095i	0.667760	−	1.15659i
$195$	−0.00224345	−	0.708060i	−0.000160657	−	0.0507052i
$196$	−2.42949	−	4.20800i	−0.173535	−	0.300572i
$197$	−23.2128			−1.65385			−0.826923	−	0.562316i	$-0.809911\pi$
$197$	−23.2128			−1.65385			−0.826923	+	0.562316i	$0.809911\pi$
$198$	−5.71257	+	8.14657i	−0.405975	+	0.578951i
$199$	−4.10464			−0.290970			−0.145485	−	0.989360i	$-0.546474\pi$
$199$	−4.10464			−0.290970			−0.145485	+	0.989360i	$0.546474\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−0.794039	+	0.461799i	−0.0560072	+	0.0325728i
$202$	2.62335	−	4.54377i	0.184578	−	0.319699i
$203$	−12.8502	−	7.41906i	−0.901907	−	0.520716i
$204$	4.29437	−	2.49753i	0.300666	−	0.174862i
$205$	0.322106	−	0.185968i	0.0224969	−	0.0129886i
$206$	5.86705			0.408777
$207$	0.165690	+	26.1466i	0.0115163	+	1.81732i
$208$		−	0.408801i		−	0.0283452i
$209$	−2.00152	+	21.1654i	−0.138448	+	1.46404i
$210$	−0.00802999	−	2.53436i	−0.000554122	−	0.174888i
$211$	17.5793	+	10.1494i	1.21021	+	0.698715i	0.962805	−	0.270197i	$-0.0870889\pi$
$211$	17.5793	+	10.1494i	1.21021	+	0.698715i	0.247405	+	0.968912i	$0.420422\pi$
$212$	5.65249	+	3.26347i	0.388215	+	0.224136i
$213$	4.91832	−	8.58146i	0.336998	−	0.587992i
$214$	2.30260	+	3.98822i	0.157403	+	0.272629i
$215$	8.28739			0.565195
$216$	−0.0493903	−	5.19592i	−0.00336058	−	0.353537i
$217$		−	1.40008i		−	0.0950434i
$218$	−11.0764	+	6.39494i	−0.750186	+	0.433120i
$219$	3.17661	−	5.54254i	0.214656	−	0.374530i
$220$	3.01565	−	1.38053i	0.203315	−	0.0930756i
$221$	−1.01543	−	0.586256i	−0.0683049	−	0.0394358i
$222$	0.0441171	+	13.9239i	0.00296095	+	0.934511i
$223$	5.60415	+	9.70667i	0.375282	+	0.650007i	0.990369	−	0.138452i	$-0.0442127\pi$
$223$	5.60415	+	9.70667i	0.375282	+	0.650007i	−0.615088	+	0.788459i	$0.710879\pi$
$224$		−	1.46322i		−	0.0977656i
$225$	−1.48351	+	2.60753i	−0.0989004	+	0.173835i
$226$		−	14.1196i		−	0.939221i
$227$	−4.37231	−	7.57307i	−0.290201	−	0.502642i	0.683656	−	0.729804i	$-0.260389\pi$
$227$	−4.37231	−	7.57307i	−0.290201	−	0.502642i	−0.973857	+	0.227162i	$0.927055\pi$
$228$	−5.58172	−	9.59748i	−0.369659	−	0.635608i
$229$	−9.66650	+	16.7429i	−0.638780	+	1.10640i	0.346920	+	0.937895i	$0.387227\pi$
$229$	−9.66650	+	16.7429i	−0.638780	+	1.10640i	−0.985701	+	0.168505i	$0.946106\pi$
$230$	4.35786	−	7.54804i	0.287349	−	0.497703i
$231$	8.37070	+	0.764829i	0.550752	+	0.0503221i
$232$	5.07036	+	8.78212i	0.332886	+	0.576575i
$233$	−7.40485			−0.485108			−0.242554	−	0.970138i	$-0.577985\pi$
$233$	−7.40485			−0.485108			−0.242554	+	0.970138i	$0.577985\pi$
$234$	−1.05819	+	0.619919i	−0.0691759	+	0.0405254i
$235$	6.27852			0.409566
$236$	−3.76646	+	2.17457i	−0.245176	+	0.141552i
$237$	−6.40858	+	0.0203052i	−0.416282	+	0.00131897i
$238$	−3.63452	−	2.09839i	−0.235591	−	0.136018i
$239$	10.9305	−	18.9321i	0.707033	−	1.22462i	−0.258919	−	0.965899i	$-0.583366\pi$
$239$	10.9305	−	18.9321i	0.707033	−	1.22462i	0.965953	−	0.258719i	$-0.0833003\pi$
$240$	−0.861268	+	1.50274i	−0.0555946	+	0.0970012i
$241$	8.84950	−	5.10926i	0.570047	−	0.329117i	−0.187121	−	0.982337i	$-0.559916\pi$
$241$	8.84950	−	5.10926i	0.570047	−	0.329117i	0.757168	+	0.653220i	$0.226582\pi$
$242$	3.61675	+	10.3884i	0.232494	+	0.667792i
$243$	−13.3748	+	8.00711i	−0.857996	+	0.513656i
$244$			9.48635i			0.607301i
$245$	4.20800	−	2.42949i	0.268839	−	0.155214i
$246$	−0.558922	−	0.320337i	−0.0356356	−	0.0204239i
$247$	−1.31022	+	2.26937i	−0.0833674	+	0.144397i
$248$	−0.478423	+	0.828652i	−0.0303799	+	0.0526195i
$249$	−0.0709577	−	22.3951i	−0.00449676	−	1.41923i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$		−	14.0042i		−	0.883936i	−0.897031	−	0.441968i	$-0.854281\pi$
$251$		−	14.0042i		−	0.883936i	0.897031	−	0.441968i	$-0.145719\pi$
$252$	−3.78758	+	2.21888i	−0.238595	+	0.139776i
$253$	23.5621	+	16.7460i	1.48134	+	1.05281i
$254$	−11.8000	+	6.81271i	−0.740395	+	0.427467i
$255$	2.49753	+	4.29437i	0.156402	+	0.268924i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−21.8400	−	12.6093i	−1.36234	−	0.786547i	−0.372405	−	0.928070i	$-0.621467\pi$
$257$	−21.8400	−	12.6093i	−1.36234	−	0.786547i	−0.989935	+	0.141523i	$0.954800\pi$
$258$	−7.21644	−	12.4083i	−0.449276	−	0.772505i
$259$	10.1869	−	5.88142i	0.632985	−	0.365454i
$260$	0.408801			0.0253527
$261$	15.0438	−	26.4422i	0.931190	−	1.63673i
$262$	15.6701			0.968104
$263$	−15.8988	−	27.5376i	−0.980364	−	1.69804i	−0.660961	−	0.750420i	$-0.729851\pi$
$263$	−15.8988	−	27.5376i	−0.980364	−	1.69804i	−0.319403	−	0.947619i	$-0.603482\pi$
$264$	−4.69295	−	3.31304i	−0.288831	−	0.203904i
$265$	−3.26347	+	5.65249i	−0.200473	+	0.347230i
$266$	−4.68968	+	8.12277i	−0.287543	+	0.498039i
$267$	6.49373	−	11.3302i	0.397410	−	0.693398i
$268$	−0.265166	−	0.459281i	−0.0161976	−	0.0280551i
$269$			23.7818i			1.45000i	0.688749	+	0.724999i	$0.258160\pi$
$269$			23.7818i			1.45000i	−0.688749	+	0.724999i	$0.741840\pi$
$270$	5.19592	−	0.0493903i	0.316213	−	0.00300580i
$271$		−	20.4696i		−	1.24344i	−0.783239	−	0.621721i	$-0.786434\pi$
$271$		−	20.4696i		−	1.24344i	0.783239	−	0.621721i	$-0.213566\pi$
$272$	1.43409	+	2.48391i	0.0869544	+	0.150609i
$273$	0.898886	+	0.515181i	0.0544030	+	0.0311802i
$274$	14.7996	+	8.54454i	0.894075	+	0.516195i
$275$	1.38053	+	3.01565i	0.0832493	+	0.181850i
$276$	−15.0960	+	0.0478308i	−0.908672	+	0.00287908i
$277$	20.6454	−	11.9196i	1.24046	−	0.716179i	0.271272	−	0.962503i	$-0.412556\pi$
$277$	20.6454	−	11.9196i	1.24046	−	0.716179i	0.969188	+	0.246323i	$0.0792225\pi$
$278$			1.13637i			0.0681547i
$279$	2.87048	−	0.0181901i	0.171851	−	0.00108901i
$280$	1.46322			0.0874442
$281$	14.6086	+	25.3028i	0.871474	+	1.50944i	0.860472	+	0.509498i	$0.170169\pi$
$281$	14.6086	+	25.3028i	0.871474	+	1.50944i	0.0110025	+	0.999939i	$0.496498\pi$
$282$	−5.46717	−	9.40051i	−0.325565	−	0.559792i
$283$	−21.3819	−	12.3448i	−1.27102	−	0.733825i	−0.295842	−	0.955237i	$-0.595600\pi$
$283$	−21.3819	−	12.3448i	−1.27102	−	0.733825i	−0.975180	+	0.221412i	$0.928934\pi$
$284$	4.94549	+	2.85528i	0.293461	+	0.169430i
$285$	9.59748	−	5.58172i	0.568505	−	0.330633i
$286$	−0.127646	+	1.34982i	−0.00754788	+	0.0798163i
$287$			0.544225i			0.0321246i
$288$	2.99994	−	0.0190105i	0.176773	−	0.00112020i
$289$	−8.77357			−0.516092
$290$	−8.78212	+	5.07036i	−0.515704	+	0.297742i
$291$	−0.102084	−	32.2188i	−0.00598424	−	1.88870i
$292$	3.19416	+	1.84415i	0.186924	+	0.107921i
$293$	8.84379	−	15.3179i	0.516660	−	0.894881i	−0.483153	−	0.875536i	$-0.660509\pi$
$293$	8.84379	−	15.3179i	0.516660	−	0.894881i	0.999813	−	0.0193451i	$-0.00615813\pi$
$294$	−7.30177	−	4.18489i	−0.425848	−	0.244068i
$295$	−2.17457	−	3.76646i	−0.126608	−	0.219292i
$296$	−8.03901			−0.467258
$297$	−1.45932	+	17.1718i	−0.0846784	+	0.996408i
$298$	1.63484			0.0947039
$299$	1.78150	+	3.08564i	0.103027	+	0.178447i
$300$	−1.50274	−	0.861268i	−0.0867605	−	0.0497254i
$301$	−6.06314	+	10.5017i	−0.349474	+	0.605306i
$302$	18.5744	+	10.7239i	1.06884	+	0.617093i
$303$	−0.0287933	−	9.08750i	−0.00165413	−	0.522063i
$304$	5.55129	−	3.20504i	0.318388	−	0.183822i
$305$	−9.48635			−0.543187
$306$	4.25496	−	7.47885i	0.243240	−	0.427538i
$307$			10.4138i			0.594348i	0.954823	+	0.297174i	$0.0960441\pi$
$307$			10.4138i			0.594348i	−0.954823	+	0.297174i	$0.903956\pi$
$308$	−0.456885	+	4.83140i	−0.0260334	+	0.275295i
$309$	8.78443	−	5.10887i	0.499729	−	0.290634i
$310$	−0.828652	−	0.478423i	−0.0470643	−	0.0271726i
$311$	−0.258357	−	0.149163i	−0.0146501	−	0.00845823i	0.492657	−	0.870224i	$-0.336026\pi$
$311$	−0.258357	−	0.149163i	−0.0146501	−	0.00845823i	−0.507307	+	0.861765i	$0.669359\pi$
$312$	−0.355973	−	0.612076i	−0.0201530	−	0.0346520i
$313$	6.60789	+	11.4452i	0.373500	+	0.646921i	0.990101	−	0.140355i	$-0.0448242\pi$
$313$	6.60789	+	11.4452i	0.373500	+	0.646921i	−0.616601	+	0.787276i	$0.711491\pi$
$314$	−10.0772			−0.568688
$315$	−2.21888	−	3.78758i	−0.125020	−	0.213406i
$316$		−	3.70001i		−	0.208142i
$317$	−26.8991	+	15.5302i	−1.51081	+	0.872265i	−0.510886	+	0.859648i	$0.670683\pi$
$317$	−26.8991	+	15.5302i	−1.51081	+	0.872265i	−0.999920	+	0.0126163i	$0.995984\pi$
$318$	11.3049	−	0.0358190i	0.633949	−	0.00200863i
$319$	−13.9996	−	30.5808i	−0.783828	−	1.71220i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	6.92041	+	3.96632i	0.386259	+	0.221378i
$322$	6.37652	+	11.0445i	0.355349	+	0.615483i
$323$		−	18.3852i		−	1.02298i
$324$	−4.59842	−	7.73657i	−0.255468	−	0.429810i
$325$			0.408801i			0.0226762i
$326$	6.23893	+	10.8061i	0.345542	+	0.598497i
$327$	−11.0155	+	19.2198i	−0.609160	+	1.06286i
$328$	0.185968	−	0.322106i	0.0102684	−	0.0177853i
$329$	−4.59344	+	7.95606i	−0.253244	+	0.438632i
$330$	3.31304	−	4.69295i	0.182377	−	0.258338i
$331$	−16.3056	−	28.2421i	−0.896235	−	1.55232i	−0.832269	−	0.554373i	$-0.812958\pi$
$331$	−16.3056	−	28.2421i	−0.896235	−	1.55232i	−0.0639665	−	0.997952i	$-0.520375\pi$
$332$	12.9299			0.709620
$333$	12.1906	+	20.8091i	0.668042	+	1.14033i
$334$	−11.0608			−0.605220
$335$	0.459281	−	0.265166i	0.0250932	−	0.0144876i
$336$	−1.27414	−	2.19081i	−0.0695098	−	0.119518i
$337$	−8.64557	−	4.99152i	−0.470954	−	0.271906i	0.245685	−	0.969350i	$-0.420987\pi$
$337$	−8.64557	−	4.99152i	−0.470954	−	0.271906i	−0.716639	+	0.697444i	$0.754321\pi$
$338$	6.41644	−	11.1136i	0.349008	−	0.604500i
$339$	−12.2950	−	21.1405i	−0.667771	−	1.14820i
$340$	−2.48391	+	1.43409i	−0.134709	+	0.0777743i
$341$	1.83844	−	2.58674i	0.0995573	−	0.140080i
$342$	−16.7145	−	9.50939i	−0.903814	−	0.514209i
$343$			17.3523i			0.936937i
$344$	7.17709	−	4.14369i	0.386963	−	0.223413i
$345$	−0.0478308	−	15.0960i	−0.00257513	−	0.812741i
$346$	0.545882	−	0.945495i	0.0293468	−	0.0508301i
$347$	−12.8574	+	22.2696i	−0.690219	+	1.19550i	0.281546	+	0.959548i	$0.409153\pi$
$347$	−12.8574	+	22.2696i	−0.690219	+	1.19550i	−0.971766	+	0.235948i	$0.924181\pi$
$348$	15.2388	+	8.73388i	0.816887	+	0.468185i
$349$	19.2655	−	11.1229i	1.03126	−	0.595397i	0.113913	−	0.993491i	$-0.463661\pi$
$349$	19.2655	−	11.1229i	1.03126	−	0.595397i	0.917345	+	0.398094i	$0.130328\pi$
$350$			1.46322i			0.0782125i
$351$	−1.04456	+	1.84961i	−0.0557546	+	0.0987251i
$352$	1.92136	−	2.70340i	0.102409	−	0.144092i
$353$	−12.7595	+	7.36672i	−0.679121	+	0.392091i	−0.799524	−	0.600634i	$-0.794915\pi$
$353$	−12.7595	+	7.36672i	−0.679121	+	0.392091i	0.120403	+	0.992725i	$0.461581\pi$
$354$	−3.74578	+	6.53561i	−0.199086	+	0.347364i
$355$	−2.85528	+	4.94549i	−0.151542	+	0.262479i
$356$	6.52959	+	3.76986i	0.346068	+	0.199802i
$357$	−7.26900	+	0.0230314i	−0.384716	+	0.00121895i
$358$	−1.19836	+	0.691871i	−0.0633351	+	0.0365665i
$359$	9.73365			0.513722			0.256861	−	0.966448i	$-0.417312\pi$
$359$	9.73365			0.513722			0.256861	+	0.966448i	$0.417312\pi$
$360$	0.0190105	+	2.99994i	0.00100194	+	0.158111i
$361$	−22.0891			−1.16258
$362$	−3.55137	−	6.15114i	−0.186656	−	0.323297i
$363$	14.4611	+	12.4047i	0.759013	+	0.651076i
$364$	−0.299083	+	0.518027i	−0.0156762	+	0.0271520i
$365$	−1.84415	+	3.19416i	−0.0965271	+	0.167190i
$366$	8.26046	+	14.2034i	0.431781	+	0.742425i
$367$	0.747133	+	1.29407i	0.0390000	+	0.0675501i	0.884867	−	0.465845i	$-0.154249\pi$
$367$	0.747133	+	1.29407i	0.0390000	+	0.0675501i	−0.845867	+	0.533395i	$0.820916\pi$
$368$		−	8.71572i		−	0.454338i
$369$	−1.11579	+	0.00707068i	−0.0580855	+	0.000368085i
$370$		−	8.03901i		−	0.417928i
$371$	−4.77518	−	8.27085i	−0.247915	−	0.429401i
$372$	0.00525105	+	1.65730i	0.000272254	+	0.0859268i
$373$	6.08320	+	3.51214i	0.314976	+	0.181852i	0.649151	−	0.760660i	$-0.275124\pi$
$373$	6.08320	+	3.51214i	0.314976	+	0.181852i	−0.334175	+	0.942511i	$0.608458\pi$
$374$	−3.95961	−	8.64941i	−0.204747	−	0.447250i
$375$	0.861268	−	1.50274i	0.0444757	−	0.0776010i
$376$	5.43736	−	3.13926i	0.280410	−	0.161895i
$377$		−	4.14553i		−	0.213506i
$378$	−3.73880	+	6.62034i	−0.192303	+	0.340513i
$379$	0.0105305			0.000540913			0.000270457	−	1.00000i	$-0.499914\pi$
$379$	0.0105305			0.000540913			0.000270457		1.00000i	$0.499914\pi$
$380$	3.20504	+	5.55129i	0.164415	+	0.284775i
$381$	−11.7351	+	20.4754i	−0.601209	+	1.04899i
$382$	3.37061	+	1.94602i	0.172456	+	0.0995672i
$383$	11.8628	+	6.84898i	0.606160	+	0.349967i	0.771461	−	0.636276i	$-0.219526\pi$
$383$	11.8628	+	6.84898i	0.606160	+	0.349967i	−0.165301	+	0.986243i	$0.552860\pi$
$384$	0.00548788	+	1.73204i	0.000280052	+	0.0883879i
$385$	−4.83140	−	0.456885i	−0.246231	−	0.0232850i
$386$			2.24465i			0.114250i
$387$	−21.6096	−	12.2944i	−1.09848	−	0.624959i
$388$	18.6016			0.944355
$389$	28.5177	−	16.4647i	1.44590	−	0.834792i	0.447669	−	0.894200i	$-0.352254\pi$
$389$	28.5177	−	16.4647i	1.44590	−	0.834792i	0.998234	+	0.0594074i	$0.0189211\pi$
$390$	0.612076	−	0.355973i	0.0309937	−	0.0180254i
$391$	−21.6491	−	12.4991i	−1.09484	−	0.632107i
$392$	2.42949	−	4.20800i	0.122708	−	0.212536i
$393$	23.4621	−	13.6451i	1.18351	−	0.688306i
$394$	−11.6064	−	20.1029i	−0.584723	−	1.01277i
$395$	3.70001			0.186168
$396$	−9.91142	−	0.873948i	−0.498068	−	0.0439175i
$397$	−7.13376			−0.358033			−0.179017	−	0.983846i	$-0.557292\pi$
$397$	−7.13376			−0.358033			−0.179017	+	0.983846i	$0.557292\pi$
$398$	−2.05232	−	3.55472i	−0.102873	−	0.178182i
$399$	0.0514728	+	16.2454i	0.00257686	+	0.813290i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	14.5771	+	8.41611i	0.727947	+	0.420280i	0.817671	−	0.575686i	$-0.195265\pi$
$401$	14.5771	+	8.41611i	0.727947	+	0.420280i	−0.0897238	+	0.995967i	$0.528598\pi$
$402$	−0.796950	−	0.456758i	−0.0397482	−	0.0227810i
$403$	0.338754	−	0.195579i	0.0168745	−	0.00974251i
$404$	5.24670			0.261033
$405$	7.73657	−	4.59842i	0.384433	−	0.228497i
$406$		−	14.8381i		−	0.736404i
$407$	26.5439	+	2.51015i	1.31573	+	0.124423i
$408$	4.31011	+	2.47027i	0.213382	+	0.122297i
$409$	4.21460	+	2.43330i	0.208399	+	0.120319i	0.600567	−	0.799574i	$-0.294942\pi$
$409$	4.21460	+	2.43330i	0.208399	+	0.120319i	−0.392168	+	0.919893i	$0.628275\pi$
$410$	0.322106	+	0.185968i	0.0159077	+	0.00918431i
$411$	29.5990	−	0.0937829i	1.46001	−	0.00462597i
$412$	2.93353	+	5.08102i	0.144524	+	0.250324i
$413$	6.36375			0.313140
$414$	−22.5608	+	13.2168i	−1.10880	+	0.649571i
$415$			12.9299i			0.634704i
$416$	0.354032	−	0.204400i	0.0173578	−	0.0100215i
$417$	0.989517	+	1.70142i	0.0484569	+	0.0833190i
$418$	−19.3305	+	8.84933i	−0.945487	+	0.432835i
$419$	12.0105	+	6.93426i	0.586751	+	0.338761i	0.763812	−	0.645439i	$-0.223326\pi$
$419$	12.0105	+	6.93426i	0.586751	+	0.338761i	−0.177061	+	0.984200i	$0.556659\pi$
$420$	2.19081	−	1.27414i	0.106900	−	0.0621714i
$421$	−0.496307	−	0.859630i	−0.0241885	−	0.0418958i	0.853678	−	0.520802i	$-0.174367\pi$
$421$	−0.496307	−	0.859630i	−0.0241885	−	0.0418958i	−0.877866	+	0.478906i	$0.841034\pi$
$422$			20.2988i			0.988132i
$423$	−16.3714	−	9.31423i	−0.796006	−	0.452873i
$424$			6.52693i			0.316976i
$425$	−1.43409	−	2.48391i	−0.0695635	−	0.120487i
$426$	9.89093	−	0.0313389i	0.479217	−	0.00151837i
$427$	6.94031	−	12.0210i	0.335865	−	0.581736i
$428$	−2.30260	+	3.98822i	−0.111300	+	0.192778i
$429$	0.984266	+	2.13216i	0.0475208	+	0.102942i
$430$	4.14369	+	7.17709i	0.199827	+	0.346110i
$431$	−32.4527			−1.56319			−0.781596	−	0.623784i	$-0.785594\pi$
$431$	−32.4527			−1.56319			−0.781596	+	0.623784i	$0.785594\pi$
$432$	4.47510	−	2.64073i	0.215308	−	0.127052i
$433$	−21.2855			−1.02292			−0.511459	−	0.859308i	$-0.670895\pi$
$433$	−21.2855			−1.02292			−0.511459	+	0.859308i	$0.670895\pi$
$434$	1.21250	−	0.700038i	0.0582020	−	0.0336029i
$435$	−8.73388	+	15.2388i	−0.418758	+	0.730646i
$436$	−11.0764	−	6.39494i	−0.530462	−	0.306262i
$437$	−27.9342	+	48.3835i	−1.33627	+	2.31450i
$438$	6.38828	−	0.0202409i	0.305244	−	0.000967149i
$439$	−14.7741	+	8.52982i	−0.705128	+	0.407106i	−0.809255	−	0.587458i	$-0.800129\pi$
$439$	−14.7741	+	8.52982i	−0.705128	+	0.407106i	0.104126	+	0.994564i	$0.466795\pi$
$440$	2.70340	+	1.92136i	0.128880	+	0.0915972i
$441$	−14.5767	+	0.0923716i	−0.694126	+	0.00439865i
$442$		−	1.17251i		−	0.0557707i
$443$	−17.7337	+	10.2385i	−0.842552	+	0.486448i	−0.858131	−	0.513431i	$-0.828374\pi$
$443$	−17.7337	+	10.2385i	−0.842552	+	0.486448i	0.0155786	+	0.999879i	$0.495041\pi$
$444$	−12.0364	+	7.00015i	−0.571222	+	0.332213i
$445$	−3.76986	+	6.52959i	−0.178709	+	0.309532i
$446$	−5.60415	+	9.70667i	−0.265364	+	0.459624i
$447$	2.44777	−	1.42358i	0.115775	−	0.0673329i
$448$	1.26719	−	0.731611i	0.0598690	−	0.0345654i
$449$			1.96862i			0.0929049i	0.998921	+	0.0464524i	$0.0147916\pi$
$449$			1.96862i			0.0929049i	−0.998921	+	0.0464524i	$0.985208\pi$
$450$	−2.99994	+	0.0190105i	−0.141419	+	0.000896163i
$451$	−0.714623	+	1.00549i	−0.0336503	+	0.0473468i
$452$	12.2279	−	7.05979i	0.575153	−	0.332065i
$453$	37.1486	−	0.117703i	1.74539	−	0.00553018i
$454$	4.37231	−	7.57307i	0.205203	−	0.355422i
$455$	−0.518027	−	0.299083i	−0.0242855	−	0.0140212i
$456$	5.52080	−	9.63265i	0.258535	−	0.451090i
$457$	−21.4429	+	12.3801i	−1.00306	+	0.579115i	−0.909151	−	0.416466i	$-0.863268\pi$
$457$	−21.4429	+	12.3801i	−1.00306	+	0.579115i	−0.0939051	+	0.995581i	$0.529935\pi$
$458$	−19.3330			−0.903372
$459$	−0.141660	−	14.9028i	−0.00661212	−	0.695603i
$460$	8.71572			0.406373
$461$	9.80315	+	16.9796i	0.456578	+	0.790817i	0.998777	−	0.0494331i	$-0.0157415\pi$
$461$	9.80315	+	16.9796i	0.456578	+	0.790817i	−0.542199	+	0.840250i	$0.682408\pi$
$462$	3.52299	+	7.63165i	0.163904	+	0.355057i
$463$	−0.812232	+	1.40683i	−0.0377476	+	0.0653808i	−0.884282	−	0.466953i	$-0.845352\pi$
$463$	−0.812232	+	1.40683i	−0.0377476	+	0.0653808i	0.846534	+	0.532334i	$0.178685\pi$
$464$	−5.07036	+	8.78212i	−0.235386	+	0.407700i
$465$	−1.65730	+	0.00525105i	−0.0768553	+	0.000243512i
$466$	−3.70242	−	6.41278i	−0.171511	−	0.297067i
$467$			6.10089i			0.282315i	0.989987	+	0.141158i	$0.0450825\pi$
$467$			6.10089i			0.282315i	−0.989987	+	0.141158i	$0.954918\pi$
$468$	−1.06596	−	0.606458i	−0.0492740	−	0.0280335i
$469$			0.775994i			0.0358321i
$470$	3.13926	+	5.43736i	0.144803	+	0.250807i
$471$	−15.0880	+	8.77494i	−0.695220	+	0.404328i
$472$	−3.76646	−	2.17457i	−0.173366	−	0.100093i
$473$	−24.9918	+	11.4410i	−1.14913	+	0.526059i
$474$	−3.22187	−	5.53984i	−0.147986	−	0.254453i
$475$	−5.55129	+	3.20504i	−0.254711	+	0.147057i
$476$		−	4.19678i		−	0.192359i
$477$	16.8951	−	9.89766i	0.773573	−	0.453183i
$478$	21.8609			0.999896
$479$	4.09864	+	7.09906i	0.187272	+	0.324364i	0.944340	−	0.328972i	$-0.106702\pi$
$479$	4.09864	+	7.09906i	0.187272	+	0.324364i	−0.757068	+	0.653336i	$0.773369\pi$
$480$	−1.73204	+	0.00548788i	−0.0790565	+	0.000250486i
$481$	2.84606	+	1.64317i	0.129769	+	0.0749223i
$482$	8.84950	+	5.10926i	0.403084	+	0.232721i
$483$	19.1645	+	10.9838i	0.872013	+	0.499780i
$484$	−7.18825	+	8.32641i	−0.326739	+	0.378473i
$485$			18.6016i			0.844657i
$486$	−13.6218	−	7.57939i	−0.617896	−	0.343808i
$487$	7.11175			0.322264			0.161132	−	0.986933i	$-0.448486\pi$
$487$	7.11175			0.322264			0.161132	+	0.986933i	$0.448486\pi$
$488$	−8.21542	+	4.74317i	−0.371894	+	0.214713i
$489$	18.7509	+	10.7468i	0.847946	+	0.485986i
$490$	4.20800	+	2.42949i	0.190098	+	0.109753i
$491$	−7.99583	+	13.8492i	−0.360847	+	0.625005i	−0.988100	−	0.153810i	$-0.950846\pi$
$491$	−7.99583	+	13.8492i	−0.360847	+	0.625005i	0.627254	+	0.778815i	$0.284179\pi$
$492$	−0.00204114	−	0.644209i	−9.20217e−5	−	0.0290432i
$493$	14.5427	+	25.1887i	0.654970	+	1.13444i
$494$	−2.62044			−0.117899
$495$	0.873948	−	9.91142i	0.0392810	−	0.445485i
$496$	−0.956845			−0.0429636
$497$	−4.17791	−	7.23635i	−0.187405	−	0.324595i
$498$	19.3593	−	11.2590i	0.867510	−	0.504528i
$499$	−7.76994	+	13.4579i	−0.347830	+	0.602460i	−0.985864	−	0.167549i	$-0.946415\pi$
$499$	−7.76994	+	13.4579i	−0.347830	+	0.602460i	0.638033	+	0.770009i	$0.279748\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−16.5608	+	9.63145i	−0.739880	+	0.430302i
$502$	12.1280	−	7.00209i	0.541298	−	0.312519i
$503$	2.30304			0.102687			0.0513437	−	0.998681i	$-0.483650\pi$
$503$	2.30304			0.102687			0.0513437	+	0.998681i	$0.483650\pi$
$504$	−3.81539	−	2.17070i	−0.169951	−	0.0966906i
$505$			5.24670i			0.233475i
$506$	−2.72145	+	28.7784i	−0.120983	+	1.27936i
$507$	−0.0704253	−	22.2271i	−0.00312770	−	0.987140i
$508$	−11.8000	−	6.81271i	−0.523538	−	0.302265i
$509$	−19.9168	−	11.4990i	−0.882797	−	0.509683i	−0.0112177	−	0.999937i	$-0.503571\pi$
$509$	−19.9168	−	11.4990i	−0.882797	−	0.509683i	−0.871580	+	0.490254i	$0.836904\pi$
$510$	−2.47027	+	4.31011i	−0.109385	+	0.190855i
$511$	−2.69840	−	4.67376i	−0.119370	−	0.206755i
$512$	−1.00000			−0.0441942
$513$	−33.3062	+	0.316595i	−1.47051	+	0.0139780i
$514$		−	25.2186i		−	1.11235i
$515$	−5.08102	+	2.93353i	−0.223896	+	0.129267i
$516$	7.13766	−	12.4538i	0.314218	−	0.548246i
$517$	−18.9338	+	8.66771i	−0.832708	+	0.381206i
$518$	10.1869	+	5.88142i	0.447588	+	0.258415i
$519$	−0.00599147	−	1.89098i	−0.000262996	−	0.0830048i
$520$	0.204400	+	0.354032i	0.00896355	+	0.0155253i
$521$		−	10.3842i		−	0.454939i	−0.973785	−	0.227470i	$-0.926955\pi$
$521$		−	10.3842i		−	0.454939i	0.973785	−	0.227470i	$-0.0730453\pi$
$522$	30.4216	−	0.192780i	1.33152	−	0.00843775i
$523$			15.3047i			0.669229i	0.942355	+	0.334614i	$0.108606\pi$
$523$			15.3047i			0.669229i	−0.942355	+	0.334614i	$0.891394\pi$
$524$	7.83507	+	13.5707i	0.342277	+	0.592840i
$525$	1.27414	+	2.19081i	0.0556078	+	0.0956146i
$526$	15.8988	−	27.5376i	0.693222	−	1.20070i
$527$	−1.37220	+	2.37672i	−0.0597740	+	0.103532i
$528$	0.522702	−	5.72073i	0.0227477	−	0.248963i
$529$	26.4819	+	45.8680i	1.15139	+	1.99426i
$530$	−6.52693			−0.283512
$531$	0.0826792	+	13.0472i	0.00358797	+	0.566198i
$532$	−9.37936			−0.406647
$533$	−0.131677	+	0.0760238i	−0.00570357	+	0.00329296i
$534$	13.0591	−	0.0413771i	0.565124	−	0.00179056i
$535$	−3.98822	−	2.30260i	−0.172426	−	0.0995501i
$536$	0.265166	−	0.459281i	0.0114534	−	0.0198379i
$537$	−1.19177	+	2.07940i	−0.0514288	+	0.0897328i
$538$	−20.5956	+	11.8909i	−0.887939	+	0.512652i
$539$	−9.33585	+	13.1358i	−0.402124	+	0.565798i
$540$	2.64073	+	4.47510i	0.113639	+	0.192578i
$541$			23.4462i			1.00803i	0.863695	+	0.504015i	$0.168144\pi$
$541$			23.4462i			1.00803i	−0.863695	+	0.504015i	$0.831856\pi$
$542$	17.7272	−	10.2348i	0.761450	−	0.439623i
$543$	−10.6735	−	6.11736i	−0.458045	−	0.262521i
$544$	−1.43409	+	2.48391i	−0.0614860	+	0.106497i
$545$	6.39494	−	11.0764i	0.273929	−	0.474459i
$546$	0.00328266	+	1.03605i	0.000140485	+	0.0443388i
$547$	−15.1712	+	8.75911i	−0.648675	+	0.374513i	−0.787948	−	0.615741i	$-0.788857\pi$
$547$	−15.1712	+	8.75911i	−0.648675	+	0.374513i	0.139273	+	0.990254i	$0.455523\pi$
$548$			17.0891i			0.730010i
$549$	24.7359	+	14.0731i	1.05570	+	0.600623i
$550$	−1.92136	+	2.70340i	−0.0819270	+	0.115273i
$551$	56.2941	−	32.5014i	2.39821	−	1.38461i
$552$	−7.58942	−	13.0496i	−0.323027	−	0.555428i
$553$	−2.70697	+	4.68861i	−0.115112	+	0.199380i
$554$	20.6454	+	11.9196i	0.877137	+	0.506415i
$555$	−7.00015	−	12.0364i	−0.297140	−	0.510916i
$556$	−0.984121	+	0.568183i	−0.0417360	+	0.0240963i
$557$	26.5254			1.12392			0.561958	−	0.827166i	$-0.310048\pi$
$557$	26.5254			1.12392			0.561958	+	0.827166i	$0.310048\pi$
$558$	1.45099	+	2.47681i	0.0614254	+	0.104852i
$559$	−3.38789			−0.143292
$560$	0.731611	+	1.26719i	0.0309162	+	0.0535484i
$561$	−13.4602	−	9.50238i	−0.568290	−	0.401191i
$562$	−14.6086	+	25.3028i	−0.616225	+	1.06733i
$563$	−4.88964	+	8.46911i	−0.206074	+	0.356930i	−0.950474	−	0.310803i	$-0.899402\pi$
$563$	−4.88964	+	8.46911i	−0.206074	+	0.356930i	0.744400	+	0.667733i	$0.232735\pi$
$564$	5.40749	−	9.43496i	0.227697	−	0.397284i
$565$	7.05979	+	12.2279i	0.297008	+	0.514432i
$566$		−	24.6897i		−	1.03779i
$567$	0.166896	+	13.1679i	0.00700897	+	0.553001i
$568$			5.71056i			0.239610i
$569$	−7.06816	−	12.2424i	−0.296313	−	0.513229i	0.678977	−	0.734160i	$-0.262424\pi$
$569$	−7.06816	−	12.2424i	−0.296313	−	0.513229i	−0.975289	+	0.220931i	$0.929090\pi$
$570$	9.63265	+	5.52080i	0.403467	+	0.231241i
$571$	7.96470	+	4.59842i	0.333312	+	0.192438i	0.657311	−	0.753620i	$-0.271694\pi$
$571$	7.96470	+	4.59842i	0.333312	+	0.192438i	−0.323998	+	0.946058i	$0.605027\pi$
$572$	−1.23280	+	0.564363i	−0.0515459	+	0.0235972i
$573$	6.74119	−	0.0213591i	0.281617	−	0.000892289i
$574$	−0.471313	+	0.272112i	−0.0196722	+	0.0113578i
$575$			8.71572i			0.363471i
$576$	1.51643	+	2.58852i	0.0631847	+	0.107855i
$577$	−15.6154			−0.650078			−0.325039	−	0.945701i	$-0.605377\pi$
$577$	−15.6154			−0.650078			−0.325039	+	0.945701i	$0.605377\pi$
$578$	−4.38678	−	7.59813i	−0.182466	−	0.316041i
$579$	1.95458	+	3.36080i	0.0812297	+	0.139670i
$580$	−8.78212	−	5.07036i	−0.364658	−	0.210535i
$581$	−16.3846	−	9.45965i	−0.679748	−	0.392453i
$582$	27.8513	−	16.1978i	1.15447	−	0.671421i
$583$	2.03801	−	21.5512i	0.0844056	−	0.892561i
$584$			3.68830i			0.152623i
$585$	0.606458	−	1.06596i	0.0250740	−	0.0440720i
$586$	17.6876			0.730667
$587$	17.4235	−	10.0594i	0.719143	−	0.415197i	−0.0952943	−	0.995449i	$-0.530379\pi$
$587$	17.4235	−	10.0594i	0.719143	−	0.415197i	0.814437	+	0.580252i	$0.197046\pi$
$588$	−0.0266655	−	8.41596i	−0.00109967	−	0.347068i
$589$	5.31172	+	3.06673i	0.218866	+	0.126362i
$590$	2.17457	−	3.76646i	0.0895256	−	0.155063i
$591$	−34.8828	−	19.9925i	−1.43488	−	0.822380i
$592$	−4.01950	−	6.96198i	−0.165201	−	0.286136i
$593$	−13.8771			−0.569865			−0.284933	−	0.958548i	$-0.591971\pi$
$593$	−13.8771			−0.569865			−0.284933	+	0.958548i	$0.591971\pi$
$594$	−15.6009	+	7.32209i	−0.640111	+	0.300429i
$595$	4.19678			0.172051
$596$	0.817421	+	1.41582i	0.0334829	+	0.0579941i
$597$	−6.16819	−	3.53519i	−0.252447	−	0.144686i
$598$	−1.78150	+	3.08564i	−0.0728508	+	0.126181i
$599$	20.0579	+	11.5804i	0.819545	+	0.473164i	0.850259	−	0.526364i	$-0.176445\pi$
$599$	20.0579	+	11.5804i	0.819545	+	0.473164i	−0.0307148	+	0.999528i	$0.509778\pi$
$600$	−0.00548788	−	1.73204i	−0.000224042	−	0.0707103i
$601$	5.48392	−	3.16615i	0.223694	−	0.129150i	−0.383966	−	0.923347i	$-0.625442\pi$
$601$	5.48392	−	3.16615i	0.223694	−	0.129150i	0.607660	+	0.794198i	$0.292109\pi$
$602$	−12.1263			−0.494230
$603$	−1.59096	+	0.0100819i	−0.0647891	+	0.000410566i
$604$			21.4479i			0.872701i
$605$	−8.32641	−	7.18825i	−0.338517	−	0.292244i
$606$	7.85561	−	4.56869i	0.319112	−	0.185590i
$607$	−14.6550	−	8.46104i	−0.594826	−	0.343423i	0.172177	−	0.985066i	$-0.444920\pi$
$607$	−14.6550	−	8.46104i	−0.594826	−	0.343423i	−0.767004	+	0.641643i	$0.778253\pi$
$608$	5.55129	+	3.20504i	0.225134	+	0.129981i
$609$	−12.9207	−	22.2164i	−0.523571	−	0.900253i
$610$	−4.74317	−	8.21542i	−0.192045	−	0.332633i
$611$	−2.56666			−0.103836
$612$	8.60436	−	0.0545254i	0.347810	−	0.00220406i
$613$		−	27.0260i		−	1.09157i	−0.837926	−	0.545784i	$-0.816232\pi$
$613$		−	27.0260i		−	1.09157i	0.837926	−	0.545784i	$-0.183768\pi$
$614$	−9.01863	+	5.20691i	−0.363962	+	0.210134i
$615$	0.644209	−	0.00204114i	0.0259770	−	8.23067e-5i
$616$	−4.41256	+	2.02003i	−0.177787	+	0.0813892i
$617$	2.04849	+	1.18270i	0.0824693	+	0.0476137i	0.540668	−	0.841236i	$-0.318172\pi$
$617$	2.04849	+	1.18270i	0.0824693	+	0.0476137i	−0.458198	+	0.888850i	$0.651505\pi$
$618$	8.81663	+	5.05311i	0.354657	+	0.203266i
$619$	−13.1543	−	22.7840i	−0.528717	−	0.915765i	−0.999439	−	0.0334835i	$-0.989340\pi$
$619$	−13.1543	−	22.7840i	−0.528717	−	0.915765i	0.470722	−	0.882282i	$-0.343993\pi$
$620$		−	0.956845i		−	0.0384278i
$621$	−22.2703	+	39.4342i	−0.893676	+	1.58244i
$622$		−	0.298325i		−	0.0119617i
$623$	−5.51615	−	9.55425i	−0.221000	−	0.382783i
$624$	0.352087	−	0.614319i	0.0140948	−	0.0245925i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.60789	+	11.4452i	−0.264104	+	0.457442i
$627$	−21.2368	+	30.0822i	−0.848117	+	1.20137i
$628$	−5.03859	−	8.72709i	−0.201061	−	0.348249i
$629$	−23.0573			−0.919354
$630$	2.17070	−	3.81539i	0.0864827	−	0.152009i
$631$	−3.15671			−0.125667			−0.0628333	−	0.998024i	$-0.520014\pi$
$631$	−3.15671			−0.125667			−0.0628333	+	0.998024i	$0.520014\pi$
$632$	3.20431	−	1.85001i	0.127460	−	0.0735893i
$633$	17.6757	+	30.3924i	0.702546	+	1.20799i
$634$	−26.8991	−	15.5302i	−1.06830	−	0.616784i
$635$	6.81271	−	11.8000i	0.270354	−	0.468267i
$636$	5.68348	+	9.77244i	0.225365	+	0.387502i
$637$	−1.72023	+	0.993177i	−0.0681581	+	0.0393511i
$638$	19.4840	−	27.4144i	0.771378	−	1.08535i
$639$	14.7819	−	8.65968i	0.584762	−	0.342572i
$640$		−	1.00000i		−	0.0395285i
$641$	0.682071	−	0.393794i	0.0269402	−	0.0155539i	−0.486469	−	0.873698i	$-0.661715\pi$
$641$	0.682071	−	0.393794i	0.0269402	−	0.0155539i	0.513410	+	0.858144i	$0.328382\pi$
$642$	0.0252728	+	7.97640i	0.000997438	+	0.314804i
$643$	−22.0915	+	38.2635i	−0.871202	+	1.50897i	−0.0104479	+	0.999945i	$0.503326\pi$
$643$	−22.0915	+	38.2635i	−0.871202	+	1.50897i	−0.860754	+	0.509021i	$0.830008\pi$
$644$	−6.37652	+	11.0445i	−0.251270	+	0.435212i
$645$	12.4538	+	7.13766i	0.490366	+	0.281045i
$646$	15.9221	−	9.19261i	0.626445	−	0.361678i
$647$		−	32.5409i		−	1.27932i	−0.768660	−	0.639658i	$-0.779076\pi$
$647$		−	32.5409i		−	1.27932i	0.768660	−	0.639658i	$-0.220924\pi$
$648$	4.40086	−	7.85063i	0.172882	−	0.308402i
$649$	11.7575	+	8.35626i	0.461521	+	0.328012i
$650$	−0.354032	+	0.204400i	−0.0138863	+	0.00801724i
$651$	1.20584	−	2.10395i	0.0472607	−	0.0824602i
$652$	−6.23893	+	10.8061i	−0.244335	+	0.423201i
$653$	−6.74882	−	3.89643i	−0.264102	−	0.152479i	0.362103	−	0.932138i	$-0.382059\pi$
$653$	−6.74882	−	3.89643i	−0.264102	−	0.152479i	−0.626204	+	0.779659i	$0.715392\pi$
$654$	−22.1526	+	0.0701893i	−0.866236	+	0.00274462i
$655$	−13.5707	+	7.83507i	−0.530253	+	0.306141i
$656$	0.371936			0.0145217
$657$	9.54722	−	5.59305i	0.372473	−	0.218206i
$658$	−9.18687			−0.358142
$659$	13.9665	+	24.1907i	0.544058	+	0.942337i	0.998666	+	0.0516447i	$0.0164463\pi$
$659$	13.9665	+	24.1907i	0.544058	+	0.942337i	−0.454607	+	0.890692i	$0.650220\pi$
$660$	5.72073	+	0.522702i	0.222679	+	0.0203462i
$661$	−19.0092	+	32.9249i	−0.739372	+	1.28063i	0.213407	+	0.976963i	$0.431544\pi$
$661$	−19.0092	+	32.9249i	−0.739372	+	1.28063i	−0.952778	+	0.303666i	$0.901789\pi$
$662$	16.3056	−	28.2421i	0.633734	−	1.09766i
$663$	−1.02099	−	1.75554i	−0.0396521	−	0.0681796i
$664$	6.46495	+	11.1976i	0.250889	+	0.434552i
$665$		−	9.37936i		−	0.363716i
$666$	−11.9259	+	20.9619i	−0.462120	+	0.812259i
$667$		−	88.3837i		−	3.42223i
$668$	−5.53040	−	9.57893i	−0.213978	−	0.370620i
$669$	0.0615098	+	19.4132i	0.00237811	+	0.750559i
$670$	0.459281	+	0.265166i	0.0177436	+	0.0102443i
$671$	28.6075	−	13.0962i	1.10438	−	0.505574i
$672$	1.26023	−	2.19884i	0.0486143	−	0.0848220i
$673$	−15.5254	+	8.96360i	−0.598460	+	0.345521i	−0.768436	−	0.639927i	$-0.778965\pi$
$673$	−15.5254	+	8.96360i	−0.598460	+	0.345521i	0.169975	+	0.985448i	$0.445631\pi$
$674$		−	9.98305i		−	0.384533i
$675$	−4.47510	+	2.64073i	−0.172247	+	0.101642i
$676$	12.8329			0.493572
$677$	22.3964	+	38.7917i	0.860763	+	1.49088i	0.871194	+	0.490939i	$0.163346\pi$
$677$	22.3964	+	38.7917i	0.860763	+	1.49088i	−0.0104315	+	0.999946i	$0.503321\pi$
$678$	12.1608	−	21.2180i	0.467031	−	0.814873i
$679$	−23.5718	−	13.6092i	−0.904601	−	0.522272i
$680$	−2.48391	−	1.43409i	−0.0952537	−	0.0549948i
$681$	−0.0479895	−	15.1461i	−0.00183896	−	0.580398i
$682$	3.15940	+	0.298771i	0.120980	+	0.0114405i
$683$			20.5416i			0.786004i	0.919538	+	0.393002i	$0.128563\pi$
$683$			20.5416i			0.786004i	−0.919538	+	0.393002i	$0.871437\pi$
$684$	−0.121859	−	19.2298i	−0.00465938	−	0.735271i
$685$	−17.0891			−0.652940
$686$	−15.0276	+	8.67616i	−0.573755	+	0.331257i
$687$	−28.9463	+	16.8347i	−1.10437	+	0.642283i
$688$	7.17709	+	4.14369i	0.273624	+	0.157977i
$689$	1.33411	−	2.31074i	0.0508254	−	0.0880322i
$690$	13.0496	−	7.58942i	0.496790	−	0.288924i
$691$	7.19339	+	12.4593i	0.273649	+	0.473974i	0.969793	−	0.243928i	$-0.0784359\pi$
$691$	7.19339	+	12.4593i	0.273649	+	0.473974i	−0.696144	+	0.717902i	$0.745103\pi$
$692$	1.09176			0.0415026
$693$	11.9202	+	8.35876i	0.452812	+	0.317523i
$694$	−25.7147			−0.976118
$695$	−0.568183	−	0.984121i	−0.0215524	−	0.0373298i
$696$	0.0556511	+	17.5642i	0.00210945	+	0.665768i
$697$	0.533389	−	0.923857i	0.0202036	−	0.0349936i
$698$	19.2655	+	11.1229i	0.729210	+	0.421009i
$699$	−11.1275	−	6.37756i	−0.420882	−	0.241221i
$700$	−1.26719	+	0.731611i	−0.0478952	+	0.0276523i
$701$	46.7089			1.76417			0.882085	−	0.471090i	$-0.156139\pi$
$701$	46.7089			1.76417			0.882085	+	0.471090i	$0.156139\pi$
$702$	−2.12409	+	0.0201908i	−0.0801688	+	0.000762051i
$703$			51.5306i			1.94351i
$704$	3.30189	+	0.312246i	0.124445	+	0.0117682i
$705$	9.43496	+	5.40749i	0.355341	+	0.203658i
$706$	−12.7595	−	7.36672i	−0.480211	−	0.277250i
$707$	−6.64855	−	3.83854i	−0.250044	−	0.144363i
$708$	−7.53289	+	0.0238676i	−0.283103	+	0.000896998i
$709$	−17.1659	−	29.7323i	−0.644680	−	1.11662i	−0.984375	−	0.176083i	$-0.943657\pi$
$709$	−17.1659	−	29.7323i	−0.644680	−	1.11662i	0.339695	−	0.940536i	$-0.389676\pi$
$710$	−5.71056			−0.214313
$711$	−9.64789	−	5.48899i	−0.361824	−	0.205853i
$712$			7.53973i			0.282563i
$713$	7.22230	−	4.16980i	0.270477	−	0.156160i
$714$	−3.65444	−	6.28362i	−0.136764	−	0.235159i
$715$	−0.564363	−	1.23280i	−0.0211060	−	0.0461040i
$716$	−1.19836	−	0.691871i	−0.0447847	−	0.0258564i
$717$	32.7313	−	19.0359i	1.22237	−	0.710910i
$718$	4.86682	+	8.42959i	0.181628	+	0.314589i
$719$			33.4924i			1.24906i	0.781002	+	0.624528i	$0.214709\pi$
$719$			33.4924i			1.24906i	−0.781002	+	0.624528i	$0.785291\pi$
$720$	−2.58852	+	1.51643i	−0.0964684	+	0.0565141i
$721$		−	8.58480i		−	0.319715i
$722$	−11.0445	−	19.1297i	−0.411035	−	0.711933i
$723$	17.6989	−	0.0560781i	0.658230	−	0.00208557i
$724$	3.55137	−	6.15114i	0.131985	−	0.228605i
$725$	5.07036	−	8.78212i	0.188309	−	0.326160i
$726$	−3.51218	+	18.7260i	−0.130349	+	0.694989i
$727$	−19.3784	−	33.5643i	−0.718704	−	1.24483i	−0.961514	−	0.274757i	$-0.911402\pi$
$727$	−19.3784	−	33.5643i	−0.718704	−	1.24483i	0.242810	−	0.970074i	$-0.421931\pi$
$728$	−0.598166			−0.0221695
$729$	−26.9951	+	0.513256i	−0.999819	+	0.0190095i
$730$	−3.68830			−0.136510
$731$	20.5851	−	11.8848i	0.761369	−	0.439577i
$732$	−8.17029	+	14.2555i	−0.301983	+	0.526898i
$733$	−12.7756	−	7.37599i	−0.471877	−	0.272438i	0.245148	−	0.969486i	$-0.421163\pi$
$733$	−12.7756	−	7.37599i	−0.471877	−	0.272438i	−0.717025	+	0.697047i	$0.754497\pi$
$734$	−0.747133	+	1.29407i	−0.0275772	+	0.0477651i
$735$	8.41596	−	0.0266655i	0.310427	−	0.000983572i
$736$	7.54804	−	4.35786i	0.278224	−	0.160633i
$737$	−1.01896	+	1.43370i	−0.0375338	+	0.0528110i
$738$	−0.564016	−	0.962764i	−0.0207617	−	0.0354398i
$739$		−	12.4999i		−	0.459815i	−0.973212	−	0.229908i	$-0.926158\pi$
$739$		−	12.4999i		−	0.459815i	0.973212	−	0.229908i	$-0.0738424\pi$
$740$	6.96198	−	4.01950i	0.255928	−	0.147760i
$741$	−3.92345	+	2.28181i	−0.144132	+	0.0838245i
$742$	4.77518	−	8.27085i	0.175302	−	0.303632i
$743$	−18.4678	+	31.9872i	−0.677518	+	1.17349i	0.298209	+	0.954501i	$0.403611\pi$
$743$	−18.4678	+	31.9872i	−0.677518	+	1.17349i	−0.975726	+	0.218994i	$0.929722\pi$
$744$	−1.43264	+	0.833196i	−0.0525230	+	0.0305464i
$745$	−1.41582	+	0.817421i	−0.0518715	+	0.0299480i
$746$			7.02427i			0.257177i
$747$	19.1816	−	33.7151i	0.701817	−	1.23357i
$748$	5.51080	−	7.75383i	0.201495	−	0.283508i
$749$	5.83565	−	3.36922i	0.213230	−	0.123108i
$750$	1.73204	−	0.00548788i	0.0632452	−	0.000200389i
$751$	20.1184	−	34.8461i	0.734131	−	1.27155i	−0.220972	−	0.975280i	$-0.570923\pi$
$751$	20.1184	−	34.8461i	0.734131	−	1.27155i	0.955103	−	0.296273i	$-0.0957438\pi$
$752$	5.43736	+	3.13926i	0.198280	+	0.114477i
$753$	12.0614	−	21.0446i	0.439540	−	0.766907i
$754$	3.59014	−	2.07277i	0.130745	−	0.0754857i
$755$	−21.4479			−0.780567
$756$	−7.60278	+	0.0722689i	−0.276510	+	0.00262840i
$757$	30.6089			1.11250			0.556250	−	0.831015i	$-0.312240\pi$
$757$	30.6089			1.11250			0.556250	+	0.831015i	$0.312240\pi$
$758$	0.00526523	+	0.00911964i	0.000191242	+	0.000331240i
$759$	20.9848	+	45.4582i	0.761699	+	1.65003i
$760$	−3.20504	+	5.55129i	−0.116259	+	0.201366i
$761$	−23.5229	+	40.7428i	−0.852703	+	1.47692i	0.0260566	+	0.999660i	$0.491705\pi$
$761$	−23.5229	+	40.7428i	−0.852703	+	1.47692i	−0.878760	+	0.477265i	$0.841628\pi$
$762$	−23.5998	+	0.0747747i	−0.854930	+	0.00270880i
$763$	9.35722	+	16.2072i	0.338754	+	0.586739i
$764$			3.89205i			0.140809i
$765$	0.0545254	+	8.60436i	0.00197137	+	0.311091i
$766$			13.6980i			0.494928i
$767$	0.888965	+	1.53973i	0.0320987	+	0.0555965i
$768$	−1.49725	+	0.870774i	−0.0540273	+	0.0314213i
$769$	11.4047	+	6.58448i	0.411262	+	0.237442i	0.691332	−	0.722537i	$-0.257024\pi$
$769$	11.4047	+	6.58448i	0.411262	+	0.237442i	−0.280070	+	0.959980i	$0.590358\pi$
$770$	−2.02003	−	4.41256i	−0.0727967	−	0.159018i
$771$	−21.9597	−	37.7585i	−0.790860	−	1.35984i
$772$	−1.94393	+	1.12233i	−0.0699634	+	0.0403934i
$773$			39.4631i			1.41939i	0.704510	+	0.709694i	$0.251167\pi$
$773$			39.4631i			1.41939i	−0.704510	+	0.709694i	$0.748833\pi$
$774$	−0.157547	−	24.8617i	−0.00566292	−	0.893634i
$775$	0.956845			0.0343709
$776$	9.30082	+	16.1095i	0.333880	+	0.578297i
$777$	20.3737	−	0.0645531i	0.730904	−	0.00231583i
$778$	28.5177	+	16.4647i	1.02241	+	0.590287i
$779$	−2.06472	−	1.19207i	−0.0739764	−	0.0427103i
$780$	0.614319	+	0.352087i	0.0219962	+	0.0126067i
$781$	1.78310	−	18.8557i	0.0638042	−	0.674708i
$782$		−	24.9982i		−	0.893935i
$783$	45.3808	−	26.7789i	1.62178	−	0.957001i
$784$	4.85898			0.173535
$785$	8.72709	−	5.03859i	0.311483	−	0.179835i
$786$	23.5481	+	13.4962i	0.839932	+	0.481393i
$787$	14.6316	+	8.44756i	0.521561	+	0.301123i	0.737573	−	0.675267i	$-0.235972\pi$
$787$	14.6316	+	8.44756i	0.521561	+	0.301123i	−0.216012	+	0.976391i	$0.569305\pi$
$788$	11.6064	−	20.1029i	0.413461	−	0.716136i
$789$	−0.174502	−	55.0749i	−0.00621243	−	1.96072i
$790$	1.85001	+	3.20431i	0.0658203	+	0.114004i
$791$	−20.6601			−0.734588
$792$	−4.19885	−	9.02051i	−0.149200	−	0.320530i
$793$	3.87802			0.137713
$794$	−3.56688	−	6.17802i	−0.126584	−	0.219250i
$795$	−9.77244	+	5.68348i	−0.346593	+	0.201572i
$796$	2.05232	−	3.55472i	0.0727425	−	0.125994i
$797$	−18.9139	−	10.9200i	−0.669966	−	0.386805i	0.126098	−	0.992018i	$-0.459755\pi$
$797$	−18.9139	−	10.9200i	−0.669966	−	0.386805i	−0.796064	+	0.605213i	$0.793088\pi$
$798$	−14.0432	+	8.16730i	−0.497125	+	0.289119i
$799$	15.5953	−	9.00395i	0.551722	−	0.318537i
$800$	1.00000			0.0353553
$801$	19.5167	−	11.4335i	0.689589	−	0.403983i
$802$			16.8322i			0.594366i
$803$	1.15165	−	12.1784i	0.0406410	−	0.429765i
$804$	−0.00291040	−	0.918558i	−0.000102642	−	0.0323950i
$805$	−11.0445	−	6.37652i	−0.389266	−	0.224743i
$806$	0.338754	+	0.195579i	0.0119321	+	0.00688899i
$807$	−20.4825	+	35.7377i	−0.721017	+	1.25803i
$808$	2.62335	+	4.54377i	0.0922891	+	0.159849i
$809$	50.4245			1.77283			0.886415	−	0.462892i	$-0.153188\pi$
$809$	50.4245			1.77283			0.886415	+	0.462892i	$0.153188\pi$
$810$	7.85063	+	4.40086i	0.275843	+	0.154630i
$811$		−	28.8565i		−	1.01329i	−0.862155	−	0.506645i	$-0.830886\pi$
$811$		−	28.8565i		−	1.01329i	0.862155	−	0.506645i	$-0.169114\pi$
$812$	12.8502	−	7.41906i	0.450953	−	0.260358i
$813$	17.6299	−	30.7605i	0.618306	−	1.07882i
$814$	11.0981	+	24.2428i	0.388989	+	0.849710i
$815$	−10.8061	−	6.23893i	−0.378523	−	0.218540i
$816$	0.0157402	+	4.96780i	0.000551017	+	0.173908i
$817$	−26.5614	−	46.0057i	−0.929265	−	1.60953i
$818$			4.86660i			0.170157i
$819$	0.907079	+	1.54836i	0.0316959	+	0.0541042i
$820$			0.371936i			0.0129886i
$821$	−8.57640	−	14.8548i	−0.299319	−	0.518435i	0.676662	−	0.736294i	$-0.263426\pi$
$821$	−8.57640	−	14.8548i	−0.299319	−	0.518435i	−0.975980	+	0.217859i	$0.930093\pi$
$822$	14.8807	+	25.5866i	0.519025	+	0.892435i
$823$	9.45293	−	16.3730i	0.329509	−	0.570726i	−0.652906	−	0.757439i	$-0.726450\pi$
$823$	9.45293	−	16.3730i	0.329509	−	0.570726i	0.982414	+	0.186713i	$0.0597836\pi$
$824$	−2.93353	+	5.08102i	−0.102194	+	0.177006i
$825$	−0.522702	+	5.72073i	−0.0181982	+	0.199170i
$826$	3.18188	+	5.51117i	0.110712	+	0.191758i
$827$	39.7322			1.38162			0.690812	−	0.723034i	$-0.257253\pi$
$827$	39.7322			1.38162			0.690812	+	0.723034i	$0.257253\pi$
$828$	−22.7265	−	12.9298i	−0.789801	−	0.449343i
$829$	13.6747			0.474942			0.237471	−	0.971395i	$-0.423681\pi$
$829$	13.6747			0.474942			0.237471	+	0.971395i	$0.423681\pi$
$830$	−11.1976	+	6.46495i	−0.388675	+	0.224402i
$831$	41.2905	−	0.130827i	1.43235	−	0.00453833i
$832$	0.354032	+	0.204400i	0.0122738	+	0.00708630i
$833$	6.96821	−	12.0693i	0.241434	−	0.418176i
$834$	−0.978716	+	1.70766i	−0.0338902	+	0.0591314i
$835$	9.57893	−	5.53040i	0.331493	−	0.191387i
$836$	−17.3290	−	12.3161i	−0.599336	−	0.425960i
$837$	4.32924	+	2.44492i	0.149640	+	0.0845087i
$838$			13.8685i			0.479080i
$839$	1.79292	−	1.03514i	0.0618984	−	0.0357371i	−0.468731	−	0.883341i	$-0.655289\pi$
$839$	1.79292	−	1.03514i	0.0618984	−	0.0357371i	0.530630	+	0.847604i	$0.321955\pi$
$840$	2.19884	+	1.26023i	0.0758671	+	0.0434820i
$841$	−36.9171	+	63.9424i	−1.27300	+	2.20491i
$842$	0.496307	−	0.859630i	0.0171039	−	0.0296248i
$843$	0.160340	+	50.6053i	0.00552241	+	1.74294i
$844$	−17.5793	+	10.1494i	−0.605105	+	0.349357i
$845$			12.8329i			0.441465i
$846$	−0.119358	−	18.8352i	−0.00410360	−	0.647567i
$847$	15.2006	−	5.29211i	0.522297	−	0.181839i
$848$	−5.65249	+	3.26347i	−0.194107	+	0.112068i
$849$	−21.4991	−	36.9666i	−0.737849	−	1.26869i
$850$	1.43409	−	2.48391i	0.0491888	−	0.0851975i
$851$	60.6787	+	35.0329i	2.08004	+	1.20091i
$852$	4.97260	+	8.55013i	0.170359	+	0.292922i
$853$	−25.0714	+	14.4750i	−0.858429	+	0.495614i	−0.863486	−	0.504373i	$-0.831724\pi$
$853$	−25.0714	+	14.4750i	−0.858429	+	0.495614i	0.00505717	+	0.999987i	$0.498390\pi$
$854$	13.8806			0.474985
$855$	19.2298	−	0.121859i	0.657647	−	0.00416748i
$856$	−4.60520			−0.157403
$857$	−16.2842	−	28.2051i	−0.556259	−	0.963469i	−0.997804	−	0.0662300i	$-0.978903\pi$
$857$	−16.2842	−	28.2051i	−0.556259	−	0.963469i	0.441545	−	0.897239i	$-0.354430\pi$
$858$	−1.35437	+	1.91848i	−0.0462375	+	0.0654958i
$859$	18.4352	−	31.9307i	0.629001	−	1.08946i	−0.358751	−	0.933433i	$-0.616797\pi$
$859$	18.4352	−	31.9307i	0.629001	−	1.08946i	0.987752	−	0.156029i	$-0.0498693\pi$
$860$	−4.14369	+	7.17709i	−0.141299	+	0.244737i
$861$	−0.468724	+	0.817827i	−0.0159741	+	0.0278715i
$862$	−16.2264	−	28.1049i	−0.552672	−	0.957256i
$863$			4.56993i			0.155562i	0.996970	+	0.0777810i	$0.0247835\pi$
$863$			4.56993i			0.155562i	−0.996970	+	0.0777810i	$0.975216\pi$
$864$	4.52449	+	2.55519i	0.153926	+	0.0869292i
$865$			1.09176i			0.0371211i
$866$	−10.6428	−	18.4338i	−0.361656	−	0.626407i
$867$	−13.1844	−	7.55640i	−0.447764	−	0.256629i
$868$	1.21250	+	0.700038i	0.0411550	+	0.0237609i
$869$	−11.1579	+	5.10799i	−0.378507	+	0.173277i
$870$	−17.5642	+	0.0556511i	−0.595481	+	0.00188675i
$871$	−0.187754	+	0.108400i	−0.00636182	+	0.00367300i
$872$		−	12.7899i		−	0.433120i
$873$	27.5956	−	48.5043i	0.933971	−	1.64162i
$874$	−55.8684			−1.88978
$875$	−0.731611	−	1.26719i	−0.0247330	−	0.0428387i
$876$	3.21167	+	5.52229i	0.108512	+	0.186581i
$877$	17.0398	+	9.83791i	0.575392	+	0.332203i	0.759300	−	0.650741i	$-0.225542\pi$
$877$	17.0398	+	9.83791i	0.575392	+	0.332203i	−0.183908	+	0.982943i	$0.558875\pi$
$878$	−14.7741	−	8.52982i	−0.498601	−	0.287867i
$879$	26.4827	−	15.4019i	0.893240	−	0.519493i
$880$	−0.312246	+	3.30189i	−0.0105258	+	0.111307i
$881$			8.71014i			0.293452i	0.989177	+	0.146726i	$0.0468736\pi$
$881$			8.71014i			0.293452i	−0.989177	+	0.146726i	$0.953126\pi$
$882$	−7.36832	−	12.5776i	−0.248104	−	0.423509i
$883$	2.01439			0.0677898			0.0338949	−	0.999425i	$-0.489209\pi$
$883$	2.01439			0.0677898			0.0338949	+	0.999425i	$0.489209\pi$
$884$	1.01543	−	0.586256i	0.0341524	−	0.0197179i
$885$	−0.0238676	−	7.53289i	−0.000802299	−	0.253215i
$886$	−17.7337	−	10.2385i	−0.595774	−	0.343971i
$887$	10.9218	−	18.9171i	0.366718	−	0.635174i	−0.622332	−	0.782753i	$-0.713815\pi$
$887$	10.9218	−	18.9171i	0.366718	−	0.635174i	0.989050	+	0.147579i	$0.0471480\pi$
$888$	−12.0805	−	6.92374i	−0.405395	−	0.232346i
$889$	9.96850	+	17.2660i	0.334333	+	0.579081i
$890$	−7.53973			−0.252732
$891$	−16.9825	+	24.5478i	−0.568935	+	0.822382i
$892$	−11.2083			−0.375282
$893$	−20.1229	−	34.8539i	−0.673387	−	1.16634i
$894$	2.45674	+	1.40804i	0.0821656	+	0.0470919i
$895$	0.691871	−	1.19836i	0.0231267	−	0.0400566i
$896$	1.26719	+	0.731611i	0.0423338	+	0.0244414i
$897$	0.0195533	+	6.17125i	0.000652865	+	0.206052i
$898$	−1.70487	+	0.984309i	−0.0568924	+	0.0328468i
$899$	−9.70310			−0.323617
$900$	−1.51643	−	2.58852i	−0.0505478	−	0.0862840i
$901$			18.7204i			0.623667i
$902$	−1.22809	−	0.116135i	−0.0408910	−	0.00386689i
$903$	−18.1561	+	10.5592i	−0.604196	+	0.351390i
$904$	12.2279	+	7.05979i	0.406695	+	0.234805i
$905$	6.15114	+	3.55137i	0.204471	+	0.118051i
$906$	18.6762	+	32.1128i	0.620476	+	1.06688i
$907$	−0.563770	−	0.976478i	−0.0187197	−	0.0324234i	0.856514	−	0.516124i	$-0.172626\pi$
$907$	−0.563770	−	0.976478i	−0.0187197	−	0.0324234i	−0.875233	+	0.483701i	$0.839292\pi$
$908$	8.74462			0.290201
$909$	7.78351	−	13.6809i	0.258163	−	0.453767i
$910$		−	0.598166i		−	0.0198290i
$911$	24.9307	−	14.3937i	0.825990	−	0.476885i	−0.0264878	−	0.999649i	$-0.508432\pi$
$911$	24.9307	−	14.3937i	0.825990	−	0.476885i	0.852478	+	0.522764i	$0.175099\pi$
$912$	11.1025	−	0.0351777i	0.367641	−	0.00116485i
$913$	−17.8502	−	38.9920i	−0.590754	−	1.29045i
$914$	−21.4429	−	12.3801i	−0.709268	−	0.409496i
$915$	−14.2555	−	8.17029i	−0.471272	−	0.270101i
$916$	−9.66650	−	16.7429i	−0.319390	−	0.553200i
$917$		−	22.9289i		−	0.757179i
$918$	12.8354	−	7.57408i	0.423631	−	0.249982i
$919$		−	32.9443i		−	1.08673i	−0.839496	−	0.543366i	$-0.817150\pi$
$919$		−	32.9443i		−	1.08673i	0.839496	−	0.543366i	$-0.182850\pi$
$920$	4.35786	+	7.54804i	0.143674	+	0.248851i
$921$	−8.96909	+	15.6492i	−0.295542	+	0.515659i
$922$	−9.80315	+	16.9796i	−0.322850	+	0.559192i
$923$	1.16724	−	2.02172i	0.0384202	−	0.0665457i
$924$	−4.84771	+	6.86683i	−0.159478	+	0.225902i
$925$	4.01950	+	6.96198i	0.132160	+	0.228909i
$926$	−1.62446			−0.0533832
$927$	17.6008	−	0.111535i	0.578086	−	0.00366331i
$928$	−10.1407			−0.332886
$929$	49.2616	−	28.4412i	1.61622	−	0.933126i	0.628336	−	0.777942i	$-0.283736\pi$
$929$	49.2616	−	28.4412i	1.61622	−	0.933126i	0.987886	−	0.155184i	$-0.0495969\pi$
$930$	−0.833196	−	1.43264i	−0.0273216	−	0.0469780i
$931$	−26.9736	−	15.5732i	−0.884024	−	0.510392i
$932$	3.70242	−	6.41278i	0.121277	−	0.210058i
$933$	−0.259774	−	0.446667i	−0.00850461	−	0.0146232i
$934$	−5.28352	+	3.05044i	−0.172882	+	0.0998136i
$935$	7.75383	+	5.51080i	0.253577	+	0.180222i
$936$	−0.00777150	−	1.22638i	−0.000254019	−	0.0400854i
$937$			17.6228i			0.575713i	0.957674	+	0.287856i	$0.0929426\pi$
$937$			17.6228i			0.575713i	−0.957674	+	0.287856i	$0.907057\pi$
$938$	−0.672030	+	0.387997i	−0.0219426	+	0.0126685i
$939$	0.0725266	+	22.8903i	0.00236682	+	0.746996i
$940$	−3.13926	+	5.43736i	−0.102391	+	0.177347i
$941$	−19.4993	+	33.7738i	−0.635659	+	1.10099i	0.350716	+	0.936482i	$0.385938\pi$
$941$	−19.4993	+	33.7738i	−0.635659	+	1.10099i	−0.986375	+	0.164512i	$0.947395\pi$
$942$	−15.1433	−	8.67915i	−0.493396	−	0.282782i
$943$	−2.80739	+	1.62085i	−0.0914211	+	0.0527820i
$944$		−	4.34914i		−	0.141552i
$945$	−0.0722689	−	7.60278i	−0.00235091	−	0.247318i
$946$	−22.4041	−	15.9230i	−0.728421	−	0.517703i
$947$	−7.93143	+	4.57921i	−0.257737	+	0.148804i	−0.623302	−	0.781981i	$-0.714209\pi$
$947$	−7.93143	+	4.57921i	−0.257737	+	0.148804i	0.365565	+	0.930786i	$0.380876\pi$
$948$	3.18670	−	5.56014i	0.103499	−	0.180585i
$949$	0.753889	−	1.30577i	0.0244723	−	0.0423872i
$950$	−5.55129	−	3.20504i	−0.180108	−	0.103985i
$951$	−53.7980	+	0.170456i	−1.74452	+	0.00552742i
$952$	3.63452	−	2.09839i	0.117795	−	0.0680092i
$953$	48.7898			1.58046			0.790229	−	0.612812i	$-0.209962\pi$
$953$	48.7898			1.58046			0.790229	+	0.612812i	$0.209962\pi$
$954$	17.0192	+	9.68275i	0.551016	+	0.313490i
$955$	−3.89205			−0.125944
$956$	10.9305	+	18.9321i	0.353517	+	0.612309i
$957$	5.30058	−	58.0124i	0.171343	−	1.87527i
$958$	−4.09864	+	7.09906i	−0.132421	+	0.229360i
$959$	12.5026	−	21.6551i	0.403729	−	0.699279i
$960$	−0.870774	−	1.49725i	−0.0281041	−	0.0483235i
$961$	15.0422	+	26.0539i	0.485233	+	0.840448i
$962$			3.28635i			0.105956i
$963$	6.98348	+	11.9207i	0.225040	+	0.384138i
$964$			10.2185i			0.329117i
$965$	−1.12233	−	1.94393i	−0.0361289	−	0.0625772i
$966$	0.0699871	+	22.0888i	0.00225180	+	0.710695i
$967$	0.754349	+	0.435524i	0.0242582	+	0.0140055i	0.512080	−	0.858938i	$-0.328875\pi$
$967$	0.754349	+	0.435524i	0.0242582	+	0.0140055i	−0.487822	+	0.872943i	$0.662208\pi$
$968$	−10.8050	−	2.06200i	−0.347286	−	0.0662753i
$969$	15.8346	−	27.6281i	0.508681	−	0.887544i
$970$	−16.1095	+	9.30082i	−0.517244	+	0.298631i
$971$			44.1711i			1.41752i	0.705450	+	0.708760i	$0.250745\pi$
$971$			44.1711i			1.41752i	−0.705450	+	0.708760i	$0.749255\pi$
$972$	−0.246945	−	15.5865i	−0.00792076	−	0.499937i
$973$	1.66275			0.0533055
$974$	3.55587	+	6.15895i	0.113938	+	0.197346i
$975$	−0.352087	+	0.614319i	−0.0112758	+	0.0196740i
$976$	−8.21542	−	4.74317i	−0.262969	−	0.151825i
$977$	0.390201	+	0.225283i	0.0124836	+	0.00720743i	0.506229	−	0.862399i	$-0.331039\pi$
$977$	0.390201	+	0.225283i	0.0124836	+	0.00720743i	−0.493745	+	0.869607i	$0.664372\pi$
$978$	0.0684770	+	21.6122i	0.00218965	+	0.691081i
$979$	2.35425	−	24.8954i	0.0752421	−	0.795660i
$980$			4.85898i			0.155214i
$981$	−33.1068	+	19.3950i	−1.05702	+	0.619235i
$982$	−15.9917			−0.510315
$983$	−31.0951	+	17.9528i	−0.991781	+	0.572605i	−0.905806	−	0.423693i	$-0.860734\pi$
$983$	−31.0951	+	17.9528i	−0.991781	+	0.572605i	−0.0859745	+	0.996297i	$0.527400\pi$
$984$	0.556881	−	0.323872i	0.0177527	−	0.0103247i
$985$	20.1029	+	11.6064i	0.640531	+	0.369811i
$986$	−14.5427	+	25.1887i	−0.463134	+	0.802171i
$987$	−13.7550	+	7.99969i	−0.437827	+	0.254633i
$988$	−1.31022	−	2.26937i	−0.0416837	−	0.0721983i
$989$	−72.2306			−2.29680
$990$	9.02051	−	4.19885i	0.286691	−	0.133448i
$991$	8.10243			0.257382			0.128691	−	0.991685i	$-0.458922\pi$
$991$	8.10243			0.257382			0.128691	+	0.991685i	$0.458922\pi$
$992$	−0.478423	−	0.828652i	−0.0151899	−	0.0263097i
$993$	−0.178966	−	56.4839i	−0.00567932	−	1.79246i
$994$	4.17791	−	7.23635i	0.132515	−	0.229523i
$995$	3.55472	+	2.05232i	0.112692	+	0.0650629i
$996$	19.4302	+	11.1361i	0.615670	+	0.352861i
$997$	34.1931	−	19.7414i	1.08291	−	0.625216i	0.151227	−	0.988499i	$-0.451678\pi$
$997$	34.1931	−	19.7414i	1.08291	−	0.625216i	0.931679	+	0.363283i	$0.118344\pi$
$998$	−15.5399			−0.491906
$999$	0.397049	+	41.7700i	0.0125621	+	1.32154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.b.131.19	yes	48
3.2	odd	2		2970.2.t.a.2771.17		48
9.2	odd	6		990.2.t.a.461.19	yes	48
9.7	even	3		2970.2.t.b.791.17		48
11.10	odd	2		990.2.t.a.131.19	✓	48
33.32	even	2		2970.2.t.b.2771.17		48
99.43	odd	6		2970.2.t.a.791.17		48
99.65	even	6	inner	990.2.t.b.461.19	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.19	✓	48	11.10	odd	2
990.2.t.a.461.19	yes	48	9.2	odd	6
990.2.t.b.131.19	yes	48	1.1	even	1	trivial
990.2.t.b.461.19	yes	48	99.65	even	6	inner
2970.2.t.a.791.17		48	99.43	odd	6
2970.2.t.a.2771.17		48	3.2	odd	2
2970.2.t.b.791.17		48	9.7	even	3
2970.2.t.b.2771.17		48	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50274 + 0.861268i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(0.00548788 + 1.73204i) q^{6} +(1.26719 - 0.731611i) q^{7} -1.00000 q^{8} +(1.51643 + 2.58852i) q^{9} -1.00000i q^{10} +(3.30189 + 0.312246i) q^{11} +(-1.49725 + 0.870774i) q^{12} +(0.354032 + 0.204400i) q^{13} +(1.26719 + 0.731611i) q^{14} +(-0.870774 - 1.49725i) q^{15} +(-0.500000 - 0.866025i) q^{16} -2.86818 q^{17} +(-1.48351 + 2.60753i) q^{18} +6.41008i q^{19} +(0.866025 - 0.500000i) q^{20} +(2.53436 - 0.00802999i) q^{21} +(1.38053 + 3.01565i) q^{22} +(7.54804 + 4.35786i) q^{23} +(-1.50274 - 0.861268i) q^{24} +(0.500000 + 0.866025i) q^{25} +0.408801i q^{26} +(0.0493903 + 5.19592i) q^{27} +1.46322i q^{28} +(-5.07036 - 8.78212i) q^{29} +(0.861268 - 1.50274i) q^{30} +(0.478423 - 0.828652i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.69295 + 3.31304i) q^{33} +(-1.43409 - 2.48391i) q^{34} -1.46322 q^{35} +(-2.99994 + 0.0190105i) q^{36} +8.03901 q^{37} +(-5.55129 + 3.20504i) q^{38} +(0.355973 + 0.612076i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-0.185968 + 0.322106i) q^{41} +(1.27414 + 2.19081i) q^{42} +(-7.17709 + 4.14369i) q^{43} +(-1.92136 + 2.70340i) q^{44} +(-0.0190105 - 2.99994i) q^{45} +8.71572i q^{46} +(-5.43736 + 3.13926i) q^{47} +(-0.00548788 - 1.73204i) q^{48} +(-2.42949 + 4.20800i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-4.31011 - 2.47027i) q^{51} +(-0.354032 + 0.204400i) q^{52} -6.52693i q^{53} +(-4.47510 + 2.64073i) q^{54} +(-2.70340 - 1.92136i) q^{55} +(-1.26719 + 0.731611i) q^{56} +(-5.52080 + 9.63265i) q^{57} +(5.07036 - 8.78212i) q^{58} +(3.76646 + 2.17457i) q^{59} +(1.73204 - 0.00548788i) q^{60} +(8.21542 - 4.74317i) q^{61} +0.956845 q^{62} +(3.81539 + 2.17070i) q^{63} +1.00000 q^{64} +(-0.204400 - 0.354032i) q^{65} +(-0.522702 + 5.72073i) q^{66} +(-0.265166 + 0.459281i) q^{67} +(1.43409 - 2.48391i) q^{68} +(7.58942 + 13.0496i) q^{69} +(-0.731611 - 1.26719i) q^{70} -5.71056i q^{71} +(-1.51643 - 2.58852i) q^{72} -3.68830i q^{73} +(4.01950 + 6.96198i) q^{74} +(0.00548788 + 1.73204i) q^{75} +(-5.55129 - 3.20504i) q^{76} +(4.41256 - 2.02003i) q^{77} +(-0.352087 + 0.614319i) q^{78} +(-3.20431 + 1.85001i) q^{79} +1.00000i q^{80} +(-4.40086 + 7.85063i) q^{81} -0.371936 q^{82} +(-6.46495 - 11.1976i) q^{83} +(-1.26023 + 2.19884i) q^{84} +(2.48391 + 1.43409i) q^{85} +(-7.17709 - 4.14369i) q^{86} +(-0.0556511 - 17.5642i) q^{87} +(-3.30189 - 0.312246i) q^{88} -7.53973i q^{89} +(2.58852 - 1.51643i) q^{90} +0.598166 q^{91} +(-7.54804 + 4.35786i) q^{92} +(1.43264 - 0.833196i) q^{93} +(-5.43736 - 3.13926i) q^{94} +(3.20504 - 5.55129i) q^{95} +(1.49725 - 0.870774i) q^{96} +(-9.30082 - 16.1095i) q^{97} -4.85898 q^{98} +(4.19885 + 9.02051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 2 q^{3} - 24 q^{4} + 2 q^{6} - 48 q^{8} + 10 q^{9} - 12 q^{11} + 4 q^{12} - 24 q^{13} - 4 q^{15} - 24 q^{16} + 12 q^{17} + 8 q^{18} + 16 q^{21} - 6 q^{22} + 36 q^{23} + 2 q^{24} + 24 q^{25}+ \cdots - 44 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 2 * q^3 - 24 * q^4 + 2 * q^6 - 48 * q^8 + 10 * q^9 - 12 * q^11 + 4 * q^12 - 24 * q^13 - 4 * q^15 - 24 * q^16 + 12 * q^17 + 8 * q^18 + 16 * q^21 - 6 * q^22 + 36 * q^23 + 2 * q^24 + 24 * q^25 - 8 * q^27 - 8 * q^30 + 24 * q^32 + 12 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 + 40 * q^39 + 6 * q^41 + 8 * q^42 - 30 * q^43 + 6 * q^44 - 2 * q^48 + 24 * q^49 - 24 * q^50 - 22 * q^51 + 24 * q^52 - 22 * q^54 - 40 * q^57 - 54 * q^59 - 4 * q^60 + 38 * q^63 + 48 * q^64 - 12 * q^66 - 6 * q^67 - 6 * q^68 + 76 * q^69 - 10 * q^72 + 2 * q^75 - 6 * q^76 - 18 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 - 36 * q^83 - 8 * q^84 - 30 * q^86 + 44 * q^87 + 12 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 - 4 * q^96 + 6 * q^97 + 48 * q^98 - 44 * q^99

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