LMFDB - Embedded newform 990.2.z.a.431.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(161,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.161"); 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.z (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-8] 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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			431.7
Character	$\chi$	$=$	990.431
Dual form			990.2.z.a.611.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.951057 - 0.309017i) q^{5} +(0.0895822 - 0.123299i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.00000i q^{10} +(-3.00966 + 1.39353i) q^{11} +(-5.28073 - 1.71581i) q^{13} +(-0.0895822 - 0.123299i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.04130 - 6.28247i) q^{17} +(0.940078 + 1.29391i) q^{19} +(-0.951057 - 0.309017i) q^{20} +(0.395293 + 3.29298i) q^{22} -5.41177i q^{23} +(0.809017 - 0.587785i) q^{25} +(-3.26367 + 4.49206i) q^{26} +(-0.144947 + 0.0470961i) q^{28} +(-7.87592 - 5.72219i) q^{29} +(0.344004 - 1.05873i) q^{31} +1.00000 q^{32} -6.60578 q^{34} +(0.0470961 - 0.144947i) q^{35} +(2.04795 + 1.48792i) q^{37} +(1.52108 - 0.494228i) q^{38} +(-0.587785 + 0.809017i) q^{40} +(4.72024 - 3.42946i) q^{41} -2.61291i q^{43} +(3.25397 + 0.641642i) q^{44} +(-5.14690 - 1.67233i) q^{46} +(2.74273 + 3.77505i) q^{47} +(2.15594 + 6.63530i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(3.26367 + 4.49206i) q^{52} +(-2.33573 - 0.758925i) q^{53} +(-2.43173 + 2.25537i) q^{55} +0.152406i q^{56} +(-7.87592 + 5.72219i) q^{58} +(7.83490 - 10.7838i) q^{59} +(-8.25376 + 2.68181i) q^{61} +(-0.900614 - 0.654334i) q^{62} +(0.309017 - 0.951057i) q^{64} -5.55249 q^{65} -5.15651 q^{67} +(-2.04130 + 6.28247i) q^{68} +(-0.123299 - 0.0895822i) q^{70} +(-11.4955 + 3.73511i) q^{71} +(-5.67506 + 7.81104i) q^{73} +(2.04795 - 1.48792i) q^{74} -1.59936i q^{76} +(-0.0977902 + 0.495925i) q^{77} +(11.8575 + 3.85275i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-1.80297 - 5.54898i) q^{82} +(-4.00918 - 12.3390i) q^{83} +(-3.88278 - 5.34419i) q^{85} +(-2.48502 - 0.807432i) q^{86} +(1.61577 - 2.89643i) q^{88} +0.935139i q^{89} +(-0.684618 + 0.497404i) q^{91} +(-3.18096 + 4.37821i) q^{92} +(4.43783 - 1.44194i) q^{94} +(1.29391 + 0.940078i) q^{95} +(-2.38481 + 7.33969i) q^{97} +6.97677 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) $ 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

Character values

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

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.951057	−	0.309017i	0.425325	−	0.138197i
$5$	0.951057	−	0.309017i	0.425325	−	0.138197i
$6$		0			0
$7$	0.0895822	−	0.123299i	0.0338589	−	0.0466027i	−0.791752	−	0.610843i	$-0.790831\pi$
$7$	0.0895822	−	0.123299i	0.0338589	−	0.0466027i	0.825611	+	0.564240i	$0.190831\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$		0			0
$10$		−	1.00000i		−	0.316228i
$11$	−3.00966	+	1.39353i	−0.907447	+	0.420166i
$11$	−3.00966	+	1.39353i	−0.907447	+	0.420166i
$12$		0			0
$13$	−5.28073	−	1.71581i	−1.46461	−	0.475881i	−0.535136	−	0.844766i	$-0.679740\pi$
$13$	−5.28073	−	1.71581i	−1.46461	−	0.475881i	−0.929475	+	0.368885i	$0.879740\pi$
$14$	−0.0895822	−	0.123299i	−0.0239418	−	0.0329531i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.04130	−	6.28247i	−0.495088	−	1.52372i	−0.816820	−	0.576893i	$-0.804265\pi$
$17$	−2.04130	−	6.28247i	−0.495088	−	1.52372i	0.321732	−	0.946831i	$-0.395735\pi$
$18$		0			0
$19$	0.940078	+	1.29391i	0.215669	+	0.296842i	0.903120	−	0.429388i	$-0.141271\pi$
$19$	0.940078	+	1.29391i	0.215669	+	0.296842i	−0.687452	+	0.726230i	$0.741271\pi$
$20$	−0.951057	−	0.309017i	−0.212663	−	0.0690983i
$21$		0			0
$22$	0.395293	+	3.29298i	0.0842768	+	0.702067i
$23$		−	5.41177i		−	1.12843i	−0.825627	−	0.564216i	$-0.809178\pi$
$23$		−	5.41177i		−	1.12843i	0.825627	−	0.564216i	$-0.190822\pi$
$24$		0			0
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	−3.26367	+	4.49206i	−0.640059	+	0.880965i
$27$		0			0
$28$	−0.144947	+	0.0470961i	−0.0273924	+	0.00890033i
$29$	−7.87592	−	5.72219i	−1.46252	−	1.06258i	−0.982697	−	0.185219i	$-0.940701\pi$
$29$	−7.87592	−	5.72219i	−1.46252	−	1.06258i	−0.479824	−	0.877365i	$-0.659299\pi$
$30$		0			0
$31$	0.344004	−	1.05873i	0.0617849	−	0.190154i	−0.915400	−	0.402546i	$-0.868125\pi$
$31$	0.344004	−	1.05873i	0.0617849	−	0.190154i	0.977185	+	0.212392i	$0.0681253\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−6.60578			−1.13288
$35$	0.0470961	−	0.144947i	0.00796070	−	0.0245005i
$36$		0			0
$37$	2.04795	+	1.48792i	0.336681	+	0.244613i	0.743260	−	0.669002i	$-0.233278\pi$
$37$	2.04795	+	1.48792i	0.336681	+	0.244613i	−0.406579	+	0.913616i	$0.633278\pi$
$38$	1.52108	−	0.494228i	0.246751	−	0.0801744i
$39$		0			0
$40$	−0.587785	+	0.809017i	−0.0929370	+	0.127917i
$41$	4.72024	−	3.42946i	0.737178	−	0.535591i	−0.154648	−	0.987970i	$-0.549424\pi$
$41$	4.72024	−	3.42946i	0.737178	−	0.535591i	0.891826	+	0.452378i	$0.149424\pi$
$42$		0			0
$43$		−	2.61291i		−	0.398464i	−0.979952	−	0.199232i	$-0.936155\pi$
$43$		−	2.61291i		−	0.398464i	0.979952	−	0.199232i	$-0.0638448\pi$
$44$	3.25397	+	0.641642i	0.490554	+	0.0967311i
$45$		0			0
$46$	−5.14690	−	1.67233i	−0.758869	−	0.246571i
$47$	2.74273	+	3.77505i	0.400069	+	0.550647i	0.960761	−	0.277377i	$-0.0894650\pi$
$47$	2.74273	+	3.77505i	0.400069	+	0.550647i	−0.560693	+	0.828024i	$0.689465\pi$
$48$		0			0
$49$	2.15594	+	6.63530i	0.307992	+	0.947901i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$		0			0
$52$	3.26367	+	4.49206i	0.452590	+	0.622936i
$53$	−2.33573	−	0.758925i	−0.320837	−	0.104246i	0.144171	−	0.989553i	$-0.453949\pi$
$53$	−2.33573	−	0.758925i	−0.320837	−	0.104246i	−0.465008	+	0.885306i	$0.653949\pi$
$54$		0			0
$55$	−2.43173	+	2.25537i	−0.327895	+	0.304114i
$56$			0.152406i			0.0203661i
$57$		0			0
$58$	−7.87592	+	5.72219i	−1.03416	+	0.751360i
$59$	7.83490	−	10.7838i	1.02002	−	1.40393i	0.107825	−	0.994170i	$-0.465611\pi$
$59$	7.83490	−	10.7838i	1.02002	−	1.40393i	0.912192	−	0.409763i	$-0.134389\pi$
$60$		0			0
$61$	−8.25376	+	2.68181i	−1.05679	+	0.343371i	−0.785328	−	0.619080i	$-0.787506\pi$
$61$	−8.25376	+	2.68181i	−1.05679	+	0.343371i	−0.271458	+	0.962450i	$0.587506\pi$
$62$	−0.900614	−	0.654334i	−0.114378	−	0.0831005i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−5.55249			−0.688701
$66$		0			0
$67$	−5.15651			−0.629968			−0.314984	−	0.949097i	$-0.601999\pi$
$67$	−5.15651			−0.629968			−0.314984	+	0.949097i	$0.601999\pi$
$68$	−2.04130	+	6.28247i	−0.247544	+	0.761862i
$69$		0			0
$70$	−0.123299	−	0.0895822i	−0.0147371	−	0.0107071i
$71$	−11.4955	+	3.73511i	−1.36426	+	0.443275i	−0.897464	−	0.441088i	$-0.854592\pi$
$71$	−11.4955	+	3.73511i	−1.36426	+	0.443275i	−0.466798	+	0.884364i	$0.654592\pi$
$72$		0			0
$73$	−5.67506	+	7.81104i	−0.664215	+	0.914214i	−0.999612	−	0.0278634i	$-0.991130\pi$
$73$	−5.67506	+	7.81104i	−0.664215	+	0.914214i	0.335397	+	0.942077i	$0.391130\pi$
$74$	2.04795	−	1.48792i	0.238070	−	0.172968i
$75$		0			0
$76$		−	1.59936i		−	0.183459i
$77$	−0.0977902	+	0.495925i	−0.0111442	+	0.0565159i
$78$		0			0
$79$	11.8575	+	3.85275i	1.33408	+	0.433468i	0.887306	−	0.461180i	$-0.152574\pi$
$79$	11.8575	+	3.85275i	1.33408	+	0.433468i	0.446771	+	0.894648i	$0.352574\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$		0			0
$82$	−1.80297	−	5.54898i	−0.199105	−	0.612782i
$83$	−4.00918	−	12.3390i	−0.440065	−	1.35438i	−0.887806	−	0.460217i	$-0.847772\pi$
$83$	−4.00918	−	12.3390i	−0.440065	−	1.35438i	0.447742	−	0.894163i	$-0.352228\pi$
$84$		0			0
$85$	−3.88278	−	5.34419i	−0.421147	−	0.579659i
$86$	−2.48502	−	0.807432i	−0.267967	−	0.0870677i
$87$		0			0
$88$	1.61577	−	2.89643i	0.172241	−	0.308760i
$89$			0.935139i			0.0991246i	0.998771	+	0.0495623i	$0.0157826\pi$
$89$			0.935139i			0.0991246i	−0.998771	+	0.0495623i	$0.984217\pi$
$90$		0			0
$91$	−0.684618	+	0.497404i	−0.0717674	+	0.0521421i
$92$	−3.18096	+	4.37821i	−0.331638	+	0.456460i
$93$		0			0
$94$	4.43783	−	1.44194i	0.457728	−	0.148725i
$95$	1.29391	+	0.940078i	0.132752	+	0.0964499i
$96$		0			0
$97$	−2.38481	+	7.33969i	−0.242141	+	0.745233i	0.753953	+	0.656929i	$0.228145\pi$
$97$	−2.38481	+	7.33969i	−0.242141	+	0.745233i	−0.996094	+	0.0883040i	$0.971855\pi$
$98$	6.97677			0.704760
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−5.07090	+	15.6066i	−0.504573	+	1.55292i	0.296914	+	0.954904i	$0.404043\pi$
$101$	−5.07090	+	15.6066i	−0.504573	+	1.55292i	−0.801487	+	0.598012i	$0.795957\pi$
$102$		0			0
$103$	3.89495	+	2.82985i	0.383781	+	0.278833i	0.762902	−	0.646514i	$-0.223774\pi$
$103$	3.89495	+	2.82985i	0.383781	+	0.278833i	−0.379121	+	0.925347i	$0.623774\pi$
$104$	5.28073	−	1.71581i	0.517818	−	0.168249i
$105$		0			0
$106$	−1.44356	+	1.98689i	−0.140211	+	0.192984i
$107$	16.0668	−	11.6732i	1.55324	−	1.12849i	0.611947	−	0.790899i	$-0.290387\pi$
$107$	16.0668	−	11.6732i	1.55324	−	1.12849i	0.941292	−	0.337594i	$-0.109613\pi$
$108$		0			0
$109$		−	6.93652i		−	0.664398i	−0.943209	−	0.332199i	$-0.892209\pi$
$109$		−	6.93652i		−	0.664398i	0.943209	−	0.332199i	$-0.107791\pi$
$110$	1.39353	+	3.00966i	0.132868	+	0.286960i
$111$		0			0
$112$	0.144947	+	0.0470961i	0.0136962	+	0.00445017i
$113$	5.29489	+	7.28779i	0.498101	+	0.685577i	0.981856	−	0.189626i	$-0.0607276\pi$
$113$	5.29489	+	7.28779i	0.498101	+	0.685577i	−0.483755	+	0.875203i	$0.660728\pi$
$114$		0			0
$115$	−1.67233	−	5.14690i	−0.155946	−	0.479951i
$116$	3.00833	+	9.25870i	0.279317	+	0.859648i
$117$		0			0
$118$	−7.83490	−	10.7838i	−0.721261	−	0.992731i
$119$	−0.957488	−	0.311107i	−0.0877728	−	0.0285191i
$120$		0			0
$121$	7.11612	−	8.38813i	0.646920	−	0.762558i
$122$			8.67852i			0.785716i
$123$		0			0
$124$	−0.900614	+	0.654334i	−0.0808775	+	0.0587609i
$125$	0.587785	−	0.809017i	0.0525731	−	0.0723607i
$126$		0			0
$127$	13.7362	−	4.46317i	1.21889	−	0.396042i	0.372213	−	0.928147i	$-0.378599\pi$
$127$	13.7362	−	4.46317i	1.21889	−	0.396042i	0.846678	+	0.532105i	$0.178599\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$		0			0
$130$	−1.71581	+	5.28073i	−0.150487	+	0.463151i
$131$	−13.5703			−1.18564			−0.592821	−	0.805335i	$-0.701986\pi$
$131$	−13.5703			−1.18564			−0.592821	+	0.805335i	$0.701986\pi$
$132$		0			0
$133$	0.243752			0.0211360
$134$	−1.59345	+	4.90413i	−0.137653	+	0.423653i
$135$		0			0
$136$	5.34419	+	3.88278i	0.458261	+	0.332946i
$137$	2.97795	−	0.967595i	0.254424	−	0.0826672i	−0.179028	−	0.983844i	$-0.557295\pi$
$137$	2.97795	−	0.967595i	0.254424	−	0.0826672i	0.433452	+	0.901177i	$0.357295\pi$
$138$		0			0
$139$	−4.01186	+	5.52185i	−0.340281	+	0.468357i	−0.944524	−	0.328444i	$-0.893476\pi$
$139$	−4.01186	+	5.52185i	−0.340281	+	0.468357i	0.604242	+	0.796801i	$0.293476\pi$
$140$	−0.123299	+	0.0895822i	−0.0104207	+	0.00757107i
$141$		0			0
$142$			12.0871i			1.01432i
$143$	18.2843	−	2.19486i	1.52901	−	0.183544i
$144$		0			0
$145$	−9.25870	−	3.00833i	−0.768893	−	0.249828i
$146$	5.67506	+	7.81104i	0.469671	+	0.646447i
$147$		0			0
$148$	−0.782248	−	2.40751i	−0.0643004	−	0.197896i
$149$	4.23188	+	13.0244i	0.346689	+	1.06700i	0.960673	+	0.277681i	$0.0895657\pi$
$149$	4.23188	+	13.0244i	0.346689	+	1.06700i	−0.613985	+	0.789318i	$0.710434\pi$
$150$		0			0
$151$	4.55787	+	6.27337i	0.370914	+	0.510520i	0.953149	−	0.302501i	$-0.0978215\pi$
$151$	4.55787	+	6.27337i	0.370914	+	0.510520i	−0.582235	+	0.813021i	$0.697822\pi$
$152$	−1.52108	−	0.494228i	−0.123376	−	0.0400872i
$153$		0			0
$154$	0.441434	+	0.246253i	0.0355717	+	0.0198437i
$155$		−	1.11322i		−	0.0894160i
$156$		0			0
$157$	15.1300	−	10.9926i	1.20751	−	0.877305i	0.212505	−	0.977160i	$-0.431838\pi$
$157$	15.1300	−	10.9926i	1.20751	−	0.877305i	0.995002	+	0.0998549i	$0.0318379\pi$
$158$	7.32836	−	10.0866i	0.583013	−	0.802449i
$159$		0			0
$160$	0.951057	−	0.309017i	0.0751876	−	0.0244299i
$161$	−0.667267	−	0.484798i	−0.0525880	−	0.0382074i
$162$		0			0
$163$	4.93985	−	15.2033i	0.386919	−	1.19081i	−0.548160	−	0.836374i	$-0.684671\pi$
$163$	4.93985	−	15.2033i	0.386919	−	1.19081i	0.935079	−	0.354440i	$-0.115329\pi$
$164$	−5.83454			−0.455601
$165$		0			0
$166$	−12.9740			−1.00698
$167$	7.56336	−	23.2776i	0.585271	−	1.80128i	−0.0129103	−	0.999917i	$-0.504110\pi$
$167$	7.56336	−	23.2776i	0.585271	−	1.80128i	0.598181	−	0.801361i	$-0.295890\pi$
$168$		0			0
$169$	14.4249	+	10.4803i	1.10961	+	0.806176i
$170$	−6.28247	+	2.04130i	−0.481844	+	0.156560i
$171$		0			0
$172$	−1.53583	+	2.11389i	−0.117106	+	0.161182i
$173$	−6.44905	+	4.68551i	−0.490312	+	0.356233i	−0.805304	−	0.592862i	$-0.797998\pi$
$173$	−6.44905	+	4.68551i	−0.490312	+	0.356233i	0.314992	+	0.949094i	$0.397998\pi$
$174$		0			0
$175$		−	0.152406i		−	0.0115208i
$176$	−2.25537	−	2.43173i	−0.170005	−	0.183299i
$177$		0			0
$178$	0.889370	+	0.288974i	0.0666611	+	0.0216595i
$179$	2.53469	+	3.48870i	0.189452	+	0.260758i	0.893168	−	0.449723i	$-0.148477\pi$
$179$	2.53469	+	3.48870i	0.189452	+	0.260758i	−0.703716	+	0.710481i	$0.748477\pi$
$180$		0			0
$181$	−5.94243	−	18.2889i	−0.441697	−	1.35940i	−0.886066	−	0.463560i	$-0.846572\pi$
$181$	−5.94243	−	18.2889i	−0.441697	−	1.35940i	0.444369	−	0.895844i	$-0.353428\pi$
$182$	0.261501	+	0.804817i	0.0193837	+	0.0596570i
$183$		0			0
$184$	3.18096	+	4.37821i	0.234503	+	0.322766i
$185$	2.40751	+	0.782248i	0.177004	+	0.0575120i
$186$		0			0
$187$	14.8985	+	16.0635i	1.08948	+	1.17468i
$188$		−	4.66622i		−	0.340319i
$189$		0			0
$190$	1.29391	−	0.940078i	0.0938698	−	0.0682004i
$191$	−9.78384	+	13.4663i	−0.707934	+	0.974387i	0.291905	+	0.956447i	$0.405711\pi$
$191$	−9.78384	+	13.4663i	−0.707934	+	0.974387i	−0.999839	+	0.0179401i	$0.994289\pi$
$192$		0			0
$193$	−1.28936	+	0.418938i	−0.0928100	+	0.0301558i	−0.355054	−	0.934846i	$-0.615538\pi$
$193$	−1.28936	+	0.418938i	−0.0928100	+	0.0301558i	0.262244	+	0.965002i	$0.415538\pi$
$194$	6.24351	+	4.53618i	0.448258	+	0.325679i
$195$		0			0
$196$	2.15594	−	6.63530i	0.153996	−	0.473950i
$197$	5.96944			0.425305			0.212653	−	0.977128i	$-0.431790\pi$
$197$	5.96944			0.425305			0.212653	+	0.977128i	$0.431790\pi$
$198$		0			0
$199$	−9.51803			−0.674715			−0.337358	−	0.941377i	$-0.609533\pi$
$199$	−9.51803			−0.674715			−0.337358	+	0.941377i	$0.609533\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$		0			0
$202$	13.2758	+	9.64542i	0.934081	+	0.678649i
$203$	−1.41108	+	0.458489i	−0.0990386	+	0.0321796i
$204$		0			0
$205$	3.42946	−	4.72024i	0.239524	−	0.329676i
$206$	3.89495	−	2.82985i	0.271374	−	0.197165i
$207$		0			0
$208$		−	5.55249i		−	0.384996i
$209$	−4.63242	−	2.58419i	−0.320431	−	0.178752i
$210$		0			0
$211$	8.98630	+	2.91983i	0.618643	+	0.201009i	0.601538	−	0.798845i	$-0.294555\pi$
$211$	8.98630	+	2.91983i	0.618643	+	0.201009i	0.0171051	+	0.999854i	$0.494555\pi$
$212$	1.44356	+	1.98689i	0.0991442	+	0.136460i
$213$		0			0
$214$	−6.13698	−	18.8877i	−0.419515	−	1.29114i
$215$	−0.807432	−	2.48502i	−0.0550664	−	0.169477i
$216$		0			0
$217$	−0.0997246	−	0.137259i	−0.00676975	−	0.00931776i
$218$	−6.59702	−	2.14350i	−0.446807	−	0.145176i
$219$		0			0
$220$	3.29298	−	0.395293i	0.222013	−	0.0266507i
$221$			36.6785i			2.46727i
$222$		0			0
$223$	3.28441	−	2.38627i	0.219941	−	0.159796i	−0.472359	−	0.881406i	$-0.656598\pi$
$223$	3.28441	−	2.38627i	0.219941	−	0.159796i	0.692300	+	0.721610i	$0.256598\pi$
$224$	0.0895822	−	0.123299i	0.00598546	−	0.00823828i
$225$		0			0
$226$	8.56731	−	2.78369i	0.569889	−	0.185168i
$227$	1.03359	+	0.750948i	0.0686019	+	0.0498422i	0.621558	−	0.783368i	$-0.286500\pi$
$227$	1.03359	+	0.750948i	0.0686019	+	0.0498422i	−0.552956	+	0.833211i	$0.686500\pi$
$228$		0			0
$229$	5.69723	−	17.5343i	0.376483	−	1.15870i	−0.565989	−	0.824413i	$-0.691505\pi$
$229$	5.69723	−	17.5343i	0.376483	−	1.15870i	0.942472	−	0.334284i	$-0.108495\pi$
$230$	−5.41177			−0.356842
$231$		0			0
$232$	9.73517			0.639145
$233$	−2.56554	+	7.89593i	−0.168074	+	0.517279i	−0.999250	−	0.0387310i	$-0.987668\pi$
$233$	−2.56554	+	7.89593i	−0.168074	+	0.517279i	0.831175	+	0.556010i	$0.187668\pi$
$234$		0			0
$235$	3.77505	+	2.74273i	0.246257	+	0.178916i
$236$	−12.6771	+	4.11905i	−0.825211	+	0.268127i
$237$		0			0
$238$	−0.591760	+	0.814488i	−0.0383581	+	0.0527954i
$239$	14.2272	−	10.3367i	0.920280	−	0.668622i	−0.0233138	−	0.999728i	$-0.507422\pi$
$239$	14.2272	−	10.3367i	0.920280	−	0.668622i	0.943594	+	0.331106i	$0.107422\pi$
$240$		0			0
$241$		−	11.7908i		−	0.759514i	−0.925086	−	0.379757i	$-0.876008\pi$
$241$		−	11.7908i		−	0.759514i	0.925086	−	0.379757i	$-0.123992\pi$
$242$	−5.77858	−	9.35991i	−0.371461	−	0.601678i
$243$		0			0
$244$	8.25376	+	2.68181i	0.528393	+	0.171685i
$245$	4.10084	+	5.64433i	0.261993	+	0.360603i
$246$		0			0
$247$	−2.74420	−	8.44577i	−0.174609	−	0.537391i
$248$	0.344004	+	1.05873i	0.0218443	+	0.0672297i
$249$		0			0
$250$	−0.587785	−	0.809017i	−0.0371748	−	0.0511667i
$251$	2.51653	+	0.817672i	0.158842	+	0.0516110i	0.387359	−	0.921929i	$-0.373387\pi$
$251$	2.51653	+	0.817672i	0.158842	+	0.0516110i	−0.228516	+	0.973540i	$0.573387\pi$
$252$		0			0
$253$	7.54149	+	16.2876i	0.474129	+	1.02399i
$254$		−	14.4431i		−	0.906241i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	12.5168	−	17.2279i	0.780778	−	1.07465i	−0.214417	−	0.976742i	$-0.568785\pi$
$257$	12.5168	−	17.2279i	0.780778	−	1.07465i	0.995196	−	0.0979069i	$-0.0312148\pi$
$258$		0			0
$259$	0.366920	−	0.119219i	0.0227993	−	0.00740794i
$260$	4.49206	+	3.26367i	0.278586	+	0.202404i
$261$		0			0
$262$	−4.19345	+	12.9061i	−0.259072	+	0.797342i
$263$	−9.65974			−0.595645			−0.297822	−	0.954621i	$-0.596260\pi$
$263$	−9.65974			−0.595645			−0.297822	+	0.954621i	$0.596260\pi$
$264$		0			0
$265$	−2.45593			−0.150867
$266$	0.0753235	−	0.231822i	0.00461838	−	0.0142139i
$267$		0			0
$268$	4.17171	+	3.03092i	0.254827	+	0.185143i
$269$	−9.17955	+	2.98262i	−0.559687	+	0.181853i	−0.575180	−	0.818027i	$-0.695068\pi$
$269$	−9.17955	+	2.98262i	−0.559687	+	0.181853i	0.0154934	+	0.999880i	$0.495068\pi$
$270$		0			0
$271$	1.14450	−	1.57527i	0.0695234	−	0.0956907i	−0.772839	−	0.634602i	$-0.781164\pi$
$271$	1.14450	−	1.57527i	0.0695234	−	0.0956907i	0.842363	+	0.538911i	$0.181164\pi$
$272$	5.34419	−	3.88278i	0.324039	−	0.235428i
$273$		0			0
$274$		−	3.13120i		−	0.189163i
$275$	−1.61577	+	2.89643i	−0.0974345	+	0.174661i
$276$		0			0
$277$	−17.2145	−	5.59331i	−1.03432	−	0.336070i	−0.257821	−	0.966193i	$-0.583004\pi$
$277$	−17.2145	−	5.59331i	−1.03432	−	0.336070i	−0.776495	+	0.630123i	$0.783004\pi$
$278$	4.01186	+	5.52185i	0.240615	+	0.331178i
$279$		0			0
$280$	0.0470961	+	0.144947i	0.00281453	+	0.00866224i
$281$	−7.17964	−	22.0966i	−0.428301	−	1.31818i	−0.899798	−	0.436307i	$-0.856286\pi$
$281$	−7.17964	−	22.0966i	−0.428301	−	1.31818i	0.471497	−	0.881868i	$-0.343714\pi$
$282$		0			0
$283$	13.4332	+	18.4892i	0.798520	+	1.09907i	0.992995	+	0.118160i	$0.0376997\pi$
$283$	13.4332	+	18.4892i	0.798520	+	1.09907i	−0.194475	+	0.980907i	$0.562300\pi$
$284$	11.4955	+	3.73511i	0.682131	+	0.221638i
$285$		0			0
$286$	3.56271	−	18.0676i	0.210667	−	1.06836i
$287$		−	0.889221i		−	0.0524891i
$288$		0			0
$289$	−21.5493	+	15.6565i	−1.26760	+	0.920968i
$290$	−5.72219	+	7.87592i	−0.336018	+	0.462490i
$291$		0			0
$292$	9.18243	−	2.98355i	0.537361	−	0.174599i
$293$	−22.5322	−	16.3706i	−1.31635	−	0.956382i	−0.999970	−	0.00774809i	$-0.997534\pi$
$293$	−22.5322	−	16.3706i	−1.31635	−	0.956382i	−0.316377	−	0.948634i	$-0.602466\pi$
$294$		0			0
$295$	4.11905	−	12.6771i	0.239820	−	0.738091i
$296$	−2.53141			−0.147135
$297$		0			0
$298$	13.6946			0.793309
$299$	−9.28559	+	28.5781i	−0.536999	+	1.65271i
$300$		0			0
$301$	−0.322169	−	0.234070i	−0.0185695	−	0.0134916i
$302$	7.37479	−	2.39622i	0.424372	−	0.137887i
$303$		0			0
$304$	−0.940078	+	1.29391i	−0.0539171	+	0.0742106i
$305$	−7.02107	+	5.10111i	−0.402025	+	0.292089i
$306$		0			0
$307$		−	25.3291i		−	1.44561i	−0.691054	−	0.722803i	$-0.742853\pi$
$307$		−	25.3291i		−	1.44561i	0.691054	−	0.722803i	$-0.257147\pi$
$308$	0.370611	−	0.343732i	0.0211175	−	0.0195859i
$309$		0			0
$310$	−1.05873	−	0.344004i	−0.0601321	−	0.0195381i
$311$	7.22756	+	9.94788i	0.409837	+	0.564092i	0.963179	−	0.268862i	$-0.0866476\pi$
$311$	7.22756	+	9.94788i	0.409837	+	0.564092i	−0.553342	+	0.832954i	$0.686648\pi$
$312$		0			0
$313$	−3.26566	−	10.0507i	−0.184586	−	0.568097i	0.815355	−	0.578961i	$-0.196542\pi$
$313$	−3.26566	−	10.0507i	−0.184586	−	0.568097i	−0.999941	+	0.0108643i	$0.996542\pi$
$314$	−5.77915	−	17.7864i	−0.326136	−	1.00374i
$315$		0			0
$316$	−7.32836	−	10.0866i	−0.412253	−	0.567417i
$317$	0.647860	+	0.210502i	0.0363874	+	0.0118230i	0.327154	−	0.944971i	$-0.393910\pi$
$317$	0.647860	+	0.210502i	0.0363874	+	0.0118230i	−0.290767	+	0.956794i	$0.593910\pi$
$318$		0			0
$319$	31.6779	+	6.24649i	1.77362	+	0.349736i
$320$		−	1.00000i		−	0.0559017i
$321$		0			0
$322$	−0.667267	+	0.484798i	−0.0371854	+	0.0270167i
$323$	6.20995	−	8.54726i	0.345531	−	0.475582i
$324$		0			0
$325$	−5.28073	+	1.71581i	−0.292922	+	0.0951762i
$326$	−12.9327	−	9.39615i	−0.716276	−	0.520405i
$327$		0			0
$328$	−1.80297	+	5.54898i	−0.0995525	+	0.306391i
$329$	0.711161			0.0392076
$330$		0			0
$331$	−10.5021			−0.577246			−0.288623	−	0.957443i	$-0.593197\pi$
$331$	−10.5021			−0.577246			−0.288623	+	0.957443i	$0.593197\pi$
$332$	−4.00918	+	12.3390i	−0.220032	+	0.677190i
$333$		0			0
$334$	−19.8011	−	14.3864i	−1.08347	−	0.787187i
$335$	−4.90413	+	1.59345i	−0.267941	+	0.0870595i
$336$		0			0
$337$	−1.47591	+	2.03141i	−0.0803978	+	0.110658i	−0.847322	−	0.531080i	$-0.821786\pi$
$337$	−1.47591	+	2.03141i	−0.0803978	+	0.110658i	0.766924	+	0.641738i	$0.221786\pi$
$338$	14.4249	−	10.4803i	0.784610	−	0.570053i
$339$		0			0
$340$			6.60578i			0.358249i
$341$	0.440048	+	3.66581i	0.0238299	+	0.198515i
$342$		0			0
$343$	2.02589	+	0.658252i	0.109388	+	0.0355423i
$344$	1.53583	+	2.11389i	0.0828063	+	0.113973i
$345$		0			0
$346$	2.46332	+	7.58131i	0.132429	+	0.407574i
$347$	−3.75461	−	11.5555i	−0.201558	−	0.620331i	−0.999837	−	0.0180439i	$-0.994256\pi$
$347$	−3.75461	−	11.5555i	−0.201558	−	0.620331i	0.798279	−	0.602287i	$-0.205744\pi$
$348$		0			0
$349$	11.2628	+	15.5019i	0.602885	+	0.829799i	0.995969	−	0.0897032i	$-0.0285918\pi$
$349$	11.2628	+	15.5019i	0.602885	+	0.829799i	−0.393084	+	0.919503i	$0.628592\pi$
$350$	−0.144947	−	0.0470961i	−0.00774774	−	0.00251739i
$351$		0			0
$352$	−3.00966	+	1.39353i	−0.160415	+	0.0742756i
$353$			15.8425i			0.843214i	0.906779	+	0.421607i	$0.138534\pi$
$353$			15.8425i			0.843214i	−0.906779	+	0.421607i	$0.861466\pi$
$354$		0			0
$355$	−9.77863	+	7.10459i	−0.518996	+	0.377073i
$356$	0.549661	−	0.756544i	0.0291320	−	0.0400967i
$357$		0			0
$358$	4.10122	−	1.33257i	0.216756	−	0.0704283i
$359$	−12.3838	−	8.99737i	−0.653593	−	0.474863i	0.210900	−	0.977508i	$-0.432360\pi$
$359$	−12.3838	−	8.99737i	−0.653593	−	0.474863i	−0.864493	+	0.502645i	$0.832360\pi$
$360$		0			0
$361$	5.08088	−	15.6373i	0.267415	−	0.823017i
$362$	−19.2301			−1.01071
$363$		0			0
$364$	0.846234			0.0443547
$365$	−2.98355	+	9.18243i	−0.156166	+	0.480631i
$366$		0			0
$367$	−5.62988	−	4.09035i	−0.293878	−	0.213515i	0.431070	−	0.902318i	$-0.358136\pi$
$367$	−5.62988	−	4.09035i	−0.293878	−	0.213515i	−0.724948	+	0.688804i	$0.758136\pi$
$368$	5.14690	−	1.67233i	0.268301	−	0.0871762i
$369$		0			0
$370$	1.48792	−	2.04795i	0.0773535	−	0.106468i
$371$	−0.302815	+	0.220008i	−0.0157214	+	0.0114222i
$372$		0			0
$373$		−	20.1218i		−	1.04187i	−0.853597	−	0.520933i	$-0.825584\pi$
$373$		−	20.1218i		−	1.04187i	0.853597	−	0.520933i	$-0.174416\pi$
$374$	19.8812	−	9.20538i	1.02803	−	0.475999i
$375$		0			0
$376$	−4.43783	−	1.44194i	−0.228864	−	0.0743624i
$377$	31.7724	+	43.7309i	1.63636	+	2.25226i
$378$		0			0
$379$	6.18964	+	19.0498i	0.317941	+	0.978520i	0.974527	+	0.224270i	$0.0719996\pi$
$379$	6.18964	+	19.0498i	0.317941	+	0.978520i	−0.656587	+	0.754251i	$0.728000\pi$
$380$	−0.494228	−	1.52108i	−0.0253534	−	0.0780296i
$381$		0			0
$382$	9.78384	+	13.4663i	0.500585	+	0.688996i
$383$	35.9330	+	11.6753i	1.83609	+	0.596582i	0.998755	+	0.0498930i	$0.0158880\pi$
$383$	35.9330	+	11.6753i	1.83609	+	0.596582i	0.837336	+	0.546689i	$0.184112\pi$
$384$		0			0
$385$	0.0602452	+	0.501871i	0.00307038	+	0.0255777i
$386$			1.35571i			0.0690039i
$387$		0			0
$388$	6.24351	−	4.53618i	0.316966	−	0.230290i
$389$	−2.95903	+	4.07275i	−0.150029	+	0.206497i	−0.877416	−	0.479731i	$-0.840734\pi$
$389$	−2.95903	+	4.07275i	−0.150029	+	0.206497i	0.727387	+	0.686227i	$0.240734\pi$
$390$		0			0
$391$	−33.9993	+	11.0470i	−1.71942	+	0.558673i
$392$	−5.64433	−	4.10084i	−0.285082	−	0.207124i
$393$		0			0
$394$	1.84466	−	5.67728i	0.0929326	−	0.286017i
$395$	12.4678			0.627321
$396$		0			0
$397$	4.46058			0.223870			0.111935	−	0.993716i	$-0.464295\pi$
$397$	4.46058			0.223870			0.111935	+	0.993716i	$0.464295\pi$
$398$	−2.94123	+	9.05218i	−0.147431	+	0.453745i
$399$		0			0
$400$	0.809017	+	0.587785i	0.0404508	+	0.0293893i
$401$	8.52629	−	2.77036i	0.425782	−	0.138345i	−0.0882842	−	0.996095i	$-0.528138\pi$
$401$	8.52629	−	2.77036i	0.425782	−	0.138345i	0.514067	+	0.857750i	$0.328138\pi$
$402$		0			0
$403$	−3.63318	+	5.00065i	−0.180982	+	0.249100i
$404$	13.2758	−	9.64542i	0.660495	−	0.479878i
$405$		0			0
$406$			1.48370i			0.0736348i
$407$	−8.23711	−	1.62426i	−0.408299	−	0.0805114i
$408$		0			0
$409$	−11.2169	−	3.64459i	−0.554639	−	0.180213i	0.0182683	−	0.999833i	$-0.494185\pi$
$409$	−11.2169	−	3.64459i	−0.554639	−	0.180213i	−0.572908	+	0.819620i	$0.694185\pi$
$410$	−3.42946	−	4.72024i	−0.169369	−	0.233116i
$411$		0			0
$412$	−1.48774	−	4.57879i	−0.0732956	−	0.225581i
$413$	−0.627769	−	1.93208i	−0.0308905	−	0.0950712i
$414$		0			0
$415$	−7.62592	−	10.4962i	−0.374341	−	0.515237i
$416$	−5.28073	−	1.71581i	−0.258909	−	0.0841247i
$417$		0			0
$418$	−3.88920	+	3.60713i	−0.190227	+	0.176431i
$419$		−	2.74738i		−	0.134218i	−0.997746	−	0.0671092i	$-0.978622\pi$
$419$		−	2.74738i		−	0.134218i	0.997746	−	0.0671092i	$-0.0213776\pi$
$420$		0			0
$421$	−31.6239	+	22.9761i	−1.54126	+	1.11979i	−0.591715	+	0.806148i	$0.701549\pi$
$421$	−31.6239	+	22.9761i	−1.54126	+	1.11979i	−0.949542	+	0.313641i	$0.898451\pi$
$422$	5.55384	−	7.64421i	0.270357	−	0.372114i
$423$		0			0
$424$	2.33573	−	0.758925i	0.113433	−	0.0368567i
$425$	−5.34419	−	3.88278i	−0.259231	−	0.188343i
$426$		0			0
$427$	−0.408725	+	1.25793i	−0.0197796	+	0.0608753i
$428$	−19.8597			−0.959954
$429$		0			0
$430$	−2.61291			−0.126006
$431$	6.58603	−	20.2697i	0.317238	−	0.976358i	−0.657586	−	0.753380i	$-0.728422\pi$
$431$	6.58603	−	20.2697i	0.317238	−	0.976358i	0.974823	−	0.222978i	$-0.0715778\pi$
$432$		0			0
$433$	1.57276	+	1.14268i	0.0755822	+	0.0549137i	0.624935	−	0.780677i	$-0.285126\pi$
$433$	1.57276	+	1.14268i	0.0755822	+	0.0549137i	−0.549353	+	0.835591i	$0.685126\pi$
$434$	−0.161358	+	0.0524283i	−0.00774542	+	0.00251664i
$435$		0			0
$436$	−4.07718	+	5.61176i	−0.195262	+	0.268755i
$437$	7.00232	−	5.08748i	0.334966	−	0.243367i
$438$		0			0
$439$			16.9345i			0.808238i	0.914706	+	0.404119i	$0.132422\pi$
$439$			16.9345i			0.808238i	−0.914706	+	0.404119i	$0.867578\pi$
$440$	0.641642	−	3.25397i	0.0305891	−	0.155127i
$441$		0			0
$442$	34.8834	+	11.3343i	1.65923	+	0.539117i
$443$	−5.33419	−	7.34189i	−0.253435	−	0.348824i	0.663275	−	0.748375i	$-0.269166\pi$
$443$	−5.33419	−	7.34189i	−0.253435	−	0.348824i	−0.916711	+	0.399552i	$0.869166\pi$
$444$		0			0
$445$	0.288974	+	0.889370i	0.0136987	+	0.0421602i
$446$	−1.25453	−	3.86106i	−0.0594039	−	0.182826i
$447$		0			0
$448$	−0.0895822	−	0.123299i	−0.00423236	−	0.00582534i
$449$	5.42830	+	1.76376i	0.256178	+	0.0832371i	0.434290	−	0.900773i	$-0.356999\pi$
$449$	5.42830	+	1.76376i	0.256178	+	0.0832371i	−0.178113	+	0.984010i	$0.556999\pi$
$450$		0			0
$451$	−9.42727	+	16.8993i	−0.443913	+	0.795758i
$452$		−	9.00820i		−	0.423710i
$453$		0			0
$454$	1.03359	−	0.750948i	0.0485089	−	0.0352438i
$455$	−0.497404	+	0.684618i	−0.0233187	+	0.0320954i
$456$		0			0
$457$	−21.9767	+	7.14067i	−1.02803	+	0.334026i	−0.774010	−	0.633173i	$-0.781752\pi$
$457$	−21.9767	+	7.14067i	−1.02803	+	0.334026i	−0.254018	+	0.967200i	$0.581752\pi$
$458$	−14.9155	−	10.8368i	−0.696957	−	0.506369i
$459$		0			0
$460$	−1.67233	+	5.14690i	−0.0779728	+	0.239975i
$461$	−32.2987			−1.50430			−0.752151	−	0.658991i	$-0.770984\pi$
$461$	−32.2987			−1.50430			−0.752151	+	0.658991i	$0.770984\pi$
$462$		0			0
$463$	−4.19877			−0.195134			−0.0975668	−	0.995229i	$-0.531106\pi$
$463$	−4.19877			−0.195134			−0.0975668	+	0.995229i	$0.531106\pi$
$464$	3.00833	−	9.25870i	0.139658	−	0.429824i
$465$		0			0
$466$	6.71668	+	4.87995i	0.311144	+	0.226059i
$467$	15.2751	−	4.96319i	0.706848	−	0.229669i	0.0665364	−	0.997784i	$-0.478805\pi$
$467$	15.2751	−	4.96319i	0.706848	−	0.229669i	0.640312	+	0.768115i	$0.278805\pi$
$468$		0			0
$469$	−0.461931	+	0.635794i	−0.0213300	+	0.0293582i
$470$	3.77505	−	2.74273i	0.174130	−	0.126513i
$471$		0			0
$472$			13.3295i			0.613541i
$473$	3.64117	+	7.86396i	0.167421	+	0.361585i
$474$		0			0
$475$	1.52108	+	0.494228i	0.0697918	+	0.0226767i
$476$	0.591760	+	0.814488i	0.0271233	+	0.0373320i
$477$		0			0
$478$	−5.43430	−	16.7251i	−0.248559	−	0.764986i
$479$	−5.37815	−	16.5522i	−0.245734	−	0.756291i	−0.995515	−	0.0946049i	$-0.969841\pi$
$479$	−5.37815	−	16.5522i	−0.245734	−	0.756291i	0.749781	−	0.661686i	$-0.230159\pi$
$480$		0			0
$481$	−8.26168	−	11.3712i	−0.376700	−	0.518483i
$482$	−11.2137	−	3.64357i	−0.510772	−	0.165960i
$483$		0			0
$484$	−10.6875	+	2.60339i	−0.485795	+	0.118336i
$485$			7.71741i			0.350429i
$486$		0			0
$487$	−30.2542	+	21.9809i	−1.37095	+	0.996051i	−0.373285	+	0.927717i	$0.621769\pi$
$487$	−30.2542	+	21.9809i	−1.37095	+	0.996051i	−0.997662	+	0.0683345i	$0.978231\pi$
$488$	5.10111	−	7.02107i	0.230916	−	0.317829i
$489$		0			0
$490$	6.63530	−	2.15594i	0.299753	−	0.0973955i
$491$	9.58642	+	6.96494i	0.432629	+	0.314323i	0.782699	−	0.622400i	$-0.213842\pi$
$491$	9.58642	+	6.96494i	0.432629	+	0.314323i	−0.350070	+	0.936723i	$0.613842\pi$
$492$		0			0
$493$	−19.8724	+	61.1609i	−0.895007	+	2.75455i
$494$	−8.88040			−0.399548
$495$		0			0
$496$	1.11322			0.0499850
$497$	−0.569254	+	1.75198i	−0.0255345	+	0.0785871i
$498$		0			0
$499$	−16.3465	−	11.8764i	−0.731768	−	0.531660i	0.158354	−	0.987382i	$-0.449381\pi$
$499$	−16.3465	−	11.8764i	−0.731768	−	0.531660i	−0.890122	+	0.455722i	$0.849381\pi$
$500$	−0.951057	+	0.309017i	−0.0425325	+	0.0138197i
$501$		0			0
$502$	1.55530	−	2.14069i	0.0694166	−	0.0955438i
$503$	4.87978	−	3.54537i	0.217579	−	0.158080i	−0.473657	−	0.880709i	$-0.657066\pi$
$503$	4.87978	−	3.54537i	0.217579	−	0.158080i	0.691236	+	0.722629i	$0.257066\pi$
$504$		0			0
$505$			16.4098i			0.730225i
$506$	17.8209	−	2.13924i	0.792235	−	0.0951007i
$507$		0			0
$508$	−13.7362	−	4.46317i	−0.609446	−	0.198021i
$509$	21.6510	+	29.8001i	0.959665	+	1.32087i	0.947098	+	0.320944i	$0.104000\pi$
$509$	21.6510	+	29.8001i	0.959665	+	1.32087i	0.0125669	+	0.999921i	$0.496000\pi$
$510$		0			0
$511$	0.454712	+	1.39946i	0.0201153	+	0.0619085i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$		0			0
$514$	−12.5168	−	17.2279i	−0.552094	−	0.759892i
$515$	4.57879	+	1.48774i	0.201766	+	0.0655576i
$516$		0			0
$517$	−13.5154	−	7.53952i	−0.594405	−	0.331588i
$518$		−	0.385802i		−	0.0169512i
$519$		0			0
$520$	4.49206	−	3.26367i	0.196990	−	0.143121i
$521$	−16.0407	+	22.0781i	−0.702756	+	0.967261i	0.297166	+	0.954826i	$0.403958\pi$
$521$	−16.0407	+	22.0781i	−0.702756	+	0.967261i	−0.999923	+	0.0124353i	$0.996042\pi$
$522$		0			0
$523$	9.53302	−	3.09747i	0.416850	−	0.135443i	−0.0930801	−	0.995659i	$-0.529671\pi$
$523$	9.53302	−	3.09747i	0.416850	−	0.135443i	0.509930	+	0.860216i	$0.329671\pi$
$524$	10.9786	+	7.97641i	0.479602	+	0.348451i
$525$		0			0
$526$	−2.98502	+	9.18696i	−0.130153	+	0.400570i
$527$	−7.35369			−0.320332
$528$		0			0
$529$	−6.28727			−0.273359
$530$	−0.758925	+	2.33573i	−0.0329656	+	0.101458i
$531$		0			0
$532$	−0.197199	−	0.143274i	−0.00854968	−	0.00621170i
$533$	−30.8106	+	10.0110i	−1.33456	+	0.433624i
$534$		0			0
$535$	11.6732	−	16.0668i	0.504678	−	0.694629i
$536$	4.17171	−	3.03092i	0.180190	−	0.130916i
$537$		0			0
$538$			9.65195i			0.416125i
$539$	−15.7352	−	16.9656i	−0.677762	−	0.730762i
$540$		0			0
$541$	−27.7079	−	9.00283i	−1.19125	−	0.387062i	−0.354718	−	0.934973i	$-0.615423\pi$
$541$	−27.7079	−	9.00283i	−1.19125	−	0.387062i	−0.836536	+	0.547911i	$0.815423\pi$
$542$	−1.14450	−	1.57527i	−0.0491605	−	0.0676636i
$543$		0			0
$544$	−2.04130	−	6.28247i	−0.0875200	−	0.269359i
$545$	−2.14350	−	6.59702i	−0.0918176	−	0.282585i
$546$		0			0
$547$	4.47249	+	6.15585i	0.191230	+	0.263205i	0.893856	−	0.448354i	$-0.147989\pi$
$547$	4.47249	+	6.15585i	0.191230	+	0.263205i	−0.702626	+	0.711559i	$0.747989\pi$
$548$	−2.97795	−	0.967595i	−0.127212	−	0.0413336i
$549$		0			0
$550$	2.25537	+	2.43173i	0.0961691	+	0.103689i
$551$		−	15.5700i		−	0.663304i
$552$		0			0
$553$	1.53727	−	1.11689i	0.0653712	−	0.0474949i
$554$	−10.6391	+	14.6435i	−0.452013	+	0.622142i
$555$		0			0
$556$	6.49132	−	2.10916i	0.275293	−	0.0894482i
$557$	−15.2894	−	11.1084i	−0.647831	−	0.470677i	0.214700	−	0.976680i	$-0.431123\pi$
$557$	−15.2894	−	11.1084i	−0.647831	−	0.470677i	−0.862532	+	0.506003i	$0.831123\pi$
$558$		0			0
$559$	−4.48326	+	13.7981i	−0.189622	+	0.583596i
$560$	0.152406			0.00644034
$561$		0			0
$562$	−23.2338			−0.980058
$563$	−9.70359	+	29.8646i	−0.408958	+	1.25864i	0.508588	+	0.861010i	$0.330168\pi$
$563$	−9.70359	+	29.8646i	−0.408958	+	1.25864i	−0.917545	+	0.397632i	$0.869832\pi$
$564$		0			0
$565$	7.28779	+	5.29489i	0.306599	+	0.222758i
$566$	21.7353	−	7.06224i	0.913605	−	0.296848i
$567$		0			0
$568$	7.10459	−	9.77863i	0.298102	−	0.410302i
$569$	−1.56100	+	1.13414i	−0.0654407	+	0.0475454i	−0.620025	−	0.784582i	$-0.712877\pi$
$569$	−1.56100	+	1.13414i	−0.0654407	+	0.0475454i	0.554584	+	0.832128i	$0.312877\pi$
$570$		0			0
$571$		−	19.3196i		−	0.808500i	−0.914649	−	0.404250i	$-0.867533\pi$
$571$		−	19.3196i		−	0.808500i	0.914649	−	0.404250i	$-0.132467\pi$
$572$	−16.0824	−	8.97154i	−0.672438	−	0.375119i
$573$		0			0
$574$	−0.845699	−	0.274784i	−0.0352988	−	0.0114693i
$575$	−3.18096	−	4.37821i	−0.132655	−	0.182584i
$576$		0			0
$577$	−7.88433	−	24.2655i	−0.328229	−	1.01018i	−0.969962	−	0.243256i	$-0.921784\pi$
$577$	−7.88433	−	24.2655i	−0.328229	−	1.01018i	0.641733	−	0.766928i	$-0.278216\pi$
$578$	8.23109	+	25.3327i	0.342368	+	1.05370i
$579$		0			0
$580$	5.72219	+	7.87592i	0.237601	+	0.327030i
$581$	−1.88054	−	0.611024i	−0.0780179	−	0.0253496i
$582$		0			0
$583$	8.08735	−	0.970814i	0.334944	−	0.0402070i
$584$		−	9.65498i		−	0.399526i
$585$		0			0
$586$	−22.5322	+	16.3706i	−0.930798	+	0.676264i
$587$	27.4017	−	37.7152i	1.13099	−	1.55667i	0.344812	−	0.938672i	$-0.387943\pi$
$587$	27.4017	−	37.7152i	1.13099	−	1.55667i	0.786177	−	0.618001i	$-0.212057\pi$
$588$		0			0
$589$	1.69329	−	0.550184i	0.0697709	−	0.0226700i
$590$	−10.7838	−	7.83490i	−0.443963	−	0.322558i
$591$		0			0
$592$	−0.782248	+	2.40751i	−0.0321502	+	0.0989481i
$593$	−5.28272			−0.216935			−0.108468	−	0.994100i	$-0.534594\pi$
$593$	−5.28272			−0.216935			−0.108468	+	0.994100i	$0.534594\pi$
$594$		0			0
$595$	−1.00676			−0.0412733
$596$	4.23188	−	13.0244i	0.173344	−	0.533499i
$597$		0			0
$598$	24.3100	+	17.6622i	0.994109	+	0.722263i
$599$	−22.0596	+	7.16760i	−0.901331	+	0.292860i	−0.722786	−	0.691072i	$-0.757139\pi$
$599$	−22.0596	+	7.16760i	−0.901331	+	0.292860i	−0.178544	+	0.983932i	$0.557139\pi$
$600$		0			0
$601$	8.42912	−	11.6017i	0.343831	−	0.473243i	−0.601724	−	0.798704i	$-0.705519\pi$
$601$	8.42912	−	11.6017i	0.343831	−	0.473243i	0.945555	+	0.325461i	$0.105519\pi$
$602$	−0.322169	+	0.234070i	−0.0131306	+	0.00953997i
$603$		0			0
$604$		−	7.75432i		−	0.315519i
$605$	4.17576	−	10.1766i	0.169769	−	0.413737i
$606$		0			0
$607$	−2.40028	−	0.779897i	−0.0974242	−	0.0316550i	0.259899	−	0.965636i	$-0.416311\pi$
$607$	−2.40028	−	0.779897i	−0.0974242	−	0.0316550i	−0.357324	+	0.933981i	$0.616311\pi$
$608$	0.940078	+	1.29391i	0.0381252	+	0.0524748i
$609$		0			0
$610$	2.68181	+	8.25376i	0.108583	+	0.334185i
$611$	−8.00636	−	24.6410i	−0.323902	−	0.996869i
$612$		0			0
$613$	16.3068	+	22.4444i	0.658625	+	0.906520i	0.999435	−	0.0336127i	$-0.0107013\pi$
$613$	16.3068	+	22.4444i	0.658625	+	0.906520i	−0.340810	+	0.940132i	$0.610701\pi$
$614$	−24.0894	−	7.82711i	−0.972168	−	0.315877i
$615$		0			0
$616$	−0.212383	−	0.458691i	−0.00855717	−	0.0184812i
$617$		−	18.5712i		−	0.747649i	−0.927500	−	0.373824i	$-0.878046\pi$
$617$		−	18.5712i		−	0.747649i	0.927500	−	0.373824i	$-0.121954\pi$
$618$		0			0
$619$	17.0712	−	12.4029i	0.686148	−	0.498516i	−0.189243	−	0.981930i	$-0.560603\pi$
$619$	17.0712	−	12.4029i	0.686148	−	0.498516i	0.875392	+	0.483414i	$0.160603\pi$
$620$	−0.654334	+	0.900614i	−0.0262787	+	0.0361695i
$621$		0			0
$622$	11.6944	−	3.79975i	0.468904	−	0.152356i
$623$	0.115302	+	0.0837718i	0.00461948	+	0.00335625i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−10.5679			−0.422378
$627$		0			0
$628$	−18.7017			−0.746280
$629$	5.16736	−	15.9035i	0.206036	−	0.634114i
$630$		0			0
$631$	32.3436	+	23.4990i	1.28758	+	0.935479i	0.999753	−	0.0222041i	$-0.00706836\pi$
$631$	32.3436	+	23.4990i	1.28758	+	0.935479i	0.287823	+	0.957683i	$0.407068\pi$
$632$	−11.8575	+	3.85275i	−0.471668	+	0.153254i
$633$		0			0
$634$	0.400399	−	0.551103i	0.0159019	−	0.0218871i
$635$	11.6847	−	8.48945i	0.463694	−	0.336893i
$636$		0			0
$637$		−	38.7384i		−	1.53487i
$638$	15.7298	−	28.1972i	0.622748	−	1.11634i
$639$		0			0
$640$	−0.951057	−	0.309017i	−0.0375938	−	0.0122150i
$641$	18.1622	+	24.9981i	0.717362	+	0.987364i	0.999607	+	0.0280221i	$0.00892087\pi$
$641$	18.1622	+	24.9981i	0.717362	+	0.987364i	−0.282245	+	0.959342i	$0.591079\pi$
$642$		0			0
$643$	−3.38171	−	10.4078i	−0.133362	−	0.410445i	0.861970	−	0.506960i	$-0.169231\pi$
$643$	−3.38171	−	10.4078i	−0.133362	−	0.410445i	−0.995332	+	0.0965143i	$0.969231\pi$
$644$	0.254873	+	0.784420i	0.0100434	+	0.0309105i
$645$		0			0
$646$	−6.20995	−	8.54726i	−0.244327	−	0.336287i
$647$	12.9007	+	4.19169i	0.507178	+	0.164792i	0.551419	−	0.834229i	$-0.314087\pi$
$647$	12.9007	+	4.19169i	0.507178	+	0.164792i	−0.0442403	+	0.999021i	$0.514087\pi$
$648$		0			0
$649$	−8.55278	+	43.3738i	−0.335726	+	1.70257i
$650$			5.55249i			0.217787i
$651$		0			0
$652$	−12.9327	+	9.39615i	−0.506483	+	0.367982i
$653$	−18.4874	+	25.4457i	−0.723468	+	0.995768i	0.275933	+	0.961177i	$0.411013\pi$
$653$	−18.4874	+	25.4457i	−0.723468	+	0.995768i	−0.999402	+	0.0345916i	$0.988987\pi$
$654$		0			0
$655$	−12.9061	+	4.19345i	−0.504283	+	0.163852i
$656$	4.72024	+	3.42946i	0.184295	+	0.133898i
$657$		0			0
$658$	0.219761	−	0.676354i	0.00856716	−	0.0263670i
$659$	−29.4398			−1.14681			−0.573406	−	0.819271i	$-0.694378\pi$
$659$	−29.4398			−1.14681			−0.573406	+	0.819271i	$0.694378\pi$
$660$		0			0
$661$	6.45084			0.250908			0.125454	−	0.992099i	$-0.459961\pi$
$661$	6.45084			0.250908			0.125454	+	0.992099i	$0.459961\pi$
$662$	−3.24532	+	9.98806i	−0.126133	+	0.388197i
$663$		0			0
$664$	10.4962	+	7.62592i	0.407331	+	0.295943i
$665$	0.231822	−	0.0753235i	0.00898966	−	0.00292092i
$666$		0			0
$667$	−30.9672	+	42.6227i	−1.19905	+	1.65036i
$668$	−19.8011	+	14.3864i	−0.766129	+	0.556625i
$669$		0			0
$670$			5.15651i			0.199213i
$671$	21.1038	−	19.5732i	0.814705	−	0.755617i
$672$		0			0
$673$	−9.10081	−	2.95703i	−0.350810	−	0.113985i	0.128311	−	0.991734i	$-0.459045\pi$
$673$	−9.10081	−	2.95703i	−0.350810	−	0.113985i	−0.479121	+	0.877749i	$0.659045\pi$
$674$	1.47591	+	2.03141i	0.0568498	+	0.0782471i
$675$		0			0
$676$	−5.50981	−	16.9575i	−0.211916	−	0.652210i
$677$	0.0262757	+	0.0808683i	0.00100986	+	0.00310802i	0.951560	−	0.307463i	$-0.0994799\pi$
$677$	0.0262757	+	0.0808683i	0.00100986	+	0.00310802i	−0.950550	+	0.310571i	$0.899480\pi$
$678$		0			0
$679$	0.691342	+	0.951551i	0.0265313	+	0.0365172i
$680$	6.28247	+	2.04130i	0.240922	+	0.0782802i
$681$		0			0
$682$	3.62238	+	0.714288i	0.138708	+	0.0273515i
$683$			39.5811i			1.51453i	0.653108	+	0.757265i	$0.273465\pi$
$683$			39.5811i			1.51453i	−0.653108	+	0.757265i	$0.726535\pi$
$684$		0			0
$685$	2.53320	−	1.84048i	0.0967885	−	0.0703210i
$686$	1.25207	−	1.72333i	0.0478042	−	0.0657969i
$687$		0			0
$688$	2.48502	−	0.807432i	0.0947406	−	0.0307831i
$689$	11.0322	+	8.01536i	0.420293	+	0.305361i
$690$		0			0
$691$	10.8812	−	33.4890i	0.413942	−	1.27398i	−0.499252	−	0.866457i	$-0.666392\pi$
$691$	10.8812	−	33.4890i	0.413942	−	1.27398i	0.913194	−	0.407525i	$-0.133608\pi$
$692$	7.97146			0.303029
$693$		0			0
$694$	−12.1502			−0.461214
$695$	−2.10916	+	6.49132i	−0.0800049	+	0.246230i
$696$		0			0
$697$	−31.1809	−	22.6543i	−1.18106	−	0.858091i
$698$	18.2236	−	5.92121i	0.689774	−	0.224121i
$699$		0			0
$700$	−0.0895822	+	0.123299i	−0.00338589	+	0.00466027i
$701$	16.1575	−	11.7391i	0.610260	−	0.443380i	−0.239246	−	0.970959i	$-0.576900\pi$
$701$	16.1575	−	11.7391i	0.610260	−	0.443380i	0.849506	+	0.527579i	$0.176900\pi$
$702$		0			0
$703$			4.04862i			0.152697i
$704$	0.395293	+	3.29298i	0.0148982	+	0.124109i
$705$		0			0
$706$	15.0672	+	4.89562i	0.567060	+	0.184249i
$707$	1.47002	+	2.02331i	0.0552859	+	0.0760945i
$708$		0			0
$709$	−6.85765	−	21.1057i	−0.257545	−	0.792641i	−0.993318	−	0.115413i	$-0.963181\pi$
$709$	−6.85765	−	21.1057i	−0.257545	−	0.792641i	0.735773	−	0.677228i	$-0.236819\pi$
$710$	3.73511	+	11.4955i	0.140176	+	0.431417i
$711$		0			0
$712$	−0.549661	−	0.756544i	−0.0205994	−	0.0283527i
$713$	−5.72963	−	1.86167i	−0.214576	−	0.0697201i
$714$		0			0
$715$	16.7111	−	7.73758i	0.624960	−	0.289369i
$716$		−	4.31227i		−	0.161157i
$717$		0			0
$718$	−12.3838	+	8.99737i	−0.462160	+	0.335779i
$719$	23.3892	−	32.1925i	0.872271	−	1.20058i	−0.106231	−	0.994341i	$-0.533878\pi$
$719$	23.3892	−	32.1925i	0.872271	−	1.20058i	0.978502	−	0.206237i	$-0.0661217\pi$
$720$		0			0
$721$	0.697836	−	0.226741i	0.0259888	−	0.00844427i
$722$	−13.3019	−	9.66440i	−0.495046	−	0.359672i
$723$		0			0
$724$	−5.94243	+	18.2889i	−0.220849	+	0.679702i
$725$	−9.73517			−0.361555
$726$		0			0
$727$	−2.80594			−0.104066			−0.0520332	−	0.998645i	$-0.516570\pi$
$727$	−2.80594			−0.104066			−0.0520332	+	0.998645i	$0.516570\pi$
$728$	0.261501	−	0.804817i	0.00969186	−	0.0298285i
$729$		0			0
$730$	7.81104	+	5.67506i	0.289100	+	0.210043i
$731$	−16.4155	+	5.33372i	−0.607150	+	0.197275i
$732$		0			0
$733$	12.6587	−	17.4232i	0.467561	−	0.643542i	−0.508494	−	0.861065i	$-0.669798\pi$
$733$	12.6587	−	17.4232i	0.467561	−	0.643542i	0.976055	+	0.217523i	$0.0697977\pi$
$734$	−5.62988	+	4.09035i	−0.207803	+	0.150978i
$735$		0			0
$736$		−	5.41177i		−	0.199481i
$737$	15.5194	−	7.18578i	0.571663	−	0.264691i
$738$		0			0
$739$	12.9939	+	4.22198i	0.477989	+	0.155308i	0.538095	−	0.842884i	$-0.319144\pi$
$739$	12.9939	+	4.22198i	0.477989	+	0.155308i	−0.0601064	+	0.998192i	$0.519144\pi$
$740$	−1.48792	−	2.04795i	−0.0546972	−	0.0752842i
$741$		0			0
$742$	0.115665	+	0.355980i	0.00424619	+	0.0130684i
$743$	−0.729233	−	2.24435i	−0.0267529	−	0.0823371i	0.936789	−	0.349896i	$-0.113783\pi$
$743$	−0.729233	−	2.24435i	−0.0267529	−	0.0823371i	−0.963542	+	0.267559i	$0.913783\pi$
$744$		0			0
$745$	8.04951	+	11.0792i	0.294911	+	0.405910i
$746$	−19.1370	−	6.21797i	−0.700654	−	0.227656i
$747$		0			0
$748$	−2.61122	−	21.7527i	−0.0954757	−	0.795359i
$749$		−	3.02674i		−	0.110595i
$750$		0			0
$751$	−27.8725	+	20.2506i	−1.01708	+	0.738954i	−0.965683	−	0.259724i	$-0.916369\pi$
$751$	−27.8725	+	20.2506i	−1.01708	+	0.738954i	−0.0514006	+	0.998678i	$0.516369\pi$
$752$	−2.74273	+	3.77505i	−0.100017	+	0.137662i
$753$		0			0
$754$	51.4088	−	16.7037i	1.87220	−	0.608314i
$755$	6.27337	+	4.55787i	0.228311	+	0.165878i
$756$		0			0
$757$	11.5933	−	35.6806i	0.421367	−	1.29683i	−0.485064	−	0.874478i	$-0.661204\pi$
$757$	11.5933	−	35.6806i	0.421367	−	1.29683i	0.906431	−	0.422354i	$-0.138796\pi$
$758$	20.0301			0.727526
$759$		0			0
$760$	−1.59936			−0.0580147
$761$	14.2773	−	43.9409i	0.517551	−	1.59286i	−0.261041	−	0.965328i	$-0.584066\pi$
$761$	14.2773	−	43.9409i	0.517551	−	1.59286i	0.778592	−	0.627530i	$-0.215934\pi$
$762$		0			0
$763$	−0.855268	−	0.621388i	−0.0309628	−	0.0224958i
$764$	15.8306	−	5.14367i	0.572731	−	0.186091i
$765$		0			0
$766$	22.2078	−	30.5664i	0.802401	−	1.10441i
$767$	−59.8770	+	43.5032i	−2.16203	+	1.57081i
$768$		0			0
$769$		−	21.8773i		−	0.788916i	−0.918914	−	0.394458i	$-0.870932\pi$
$769$		−	21.8773i		−	0.788916i	0.918914	−	0.394458i	$-0.129068\pi$
$770$	0.495925	+	0.0977902i	0.0178719	+	0.00352412i
$771$		0			0
$772$	1.28936	+	0.418938i	0.0464050	+	0.0150779i
$773$	−18.7119	−	25.7547i	−0.673021	−	0.926333i	0.326803	−	0.945092i	$-0.394028\pi$
$773$	−18.7119	−	25.7547i	−0.673021	−	0.926333i	−0.999824	+	0.0187590i	$0.994028\pi$
$774$		0			0
$775$	−0.344004	−	1.05873i	−0.0123570	−	0.0380309i
$776$	−2.38481	−	7.33969i	−0.0856097	−	0.263480i
$777$		0			0
$778$	2.95903	+	4.07275i	0.106086	+	0.146015i
$779$	8.87479	+	2.88359i	0.317972	+	0.103315i
$780$		0			0
$781$	29.3925	−	27.2607i	1.05175	−	0.975466i
$782$			35.7490i			1.27838i
$783$		0			0
$784$	−5.64433	+	4.10084i	−0.201583	+	0.146459i
$785$	10.9926	−	15.1300i	0.392343	−	0.540013i
$786$		0			0
$787$	49.8997	−	16.2134i	1.77873	−	0.577946i	0.779885	−	0.625923i	$-0.215278\pi$
$787$	49.8997	−	16.2134i	1.77873	−	0.577946i	0.998848	+	0.0479773i	$0.0152775\pi$
$788$	−4.82938	−	3.50875i	−0.172040	−	0.124994i
$789$		0			0
$790$	3.85275	−	11.8575i	0.137075	−	0.421872i
$791$	1.37291			0.0488149
$792$		0			0
$793$	48.1874			1.71118
$794$	1.37840	−	4.24226i	0.0489174	−	0.150552i
$795$		0			0
$796$	7.70025	+	5.59456i	0.272928	+	0.198294i
$797$	−39.9840	+	12.9916i	−1.41631	+	0.460186i	−0.914426	−	0.404752i	$-0.867358\pi$
$797$	−39.9840	+	12.9916i	−1.41631	+	0.460186i	−0.501879	+	0.864938i	$0.667358\pi$
$798$		0			0
$799$	18.1179	−	24.9371i	0.640965	−	0.882213i
$800$	0.809017	−	0.587785i	0.0286031	−	0.0207813i
$801$		0			0
$802$		−	8.96507i		−	0.316568i
$803$	6.19504	−	31.4170i	0.218618	−	1.10868i
$804$		0			0
$805$	−0.784420	−	0.254873i	−0.0276472	−	0.00898311i
$806$	3.63318	+	5.00065i	0.127973	+	0.176140i
$807$		0			0
$808$	−5.07090	−	15.6066i	−0.178394	−	0.549039i
$809$	3.49199	+	10.7472i	0.122772	+	0.377853i	0.993489	−	0.113932i	$-0.0363447\pi$
$809$	3.49199	+	10.7472i	0.122772	+	0.377853i	−0.870717	+	0.491785i	$0.836345\pi$
$810$		0			0
$811$	21.1821	+	29.1547i	0.743805	+	1.02376i	0.998391	+	0.0567099i	$0.0180610\pi$
$811$	21.1821	+	29.1547i	0.743805	+	1.02376i	−0.254585	+	0.967050i	$0.581939\pi$
$812$	1.41108	+	0.458489i	0.0495193	+	0.0160898i
$813$		0			0
$814$	−4.09017	+	7.33204i	−0.143360	+	0.256988i
$815$		−	15.9857i		−	0.559954i
$816$		0			0
$817$	3.38085	−	2.45633i	0.118281	−	0.0859363i
$818$	−6.93242	+	9.54166i	−0.242386	+	0.333616i
$819$		0			0
$820$	−5.54898	+	1.80297i	−0.193779	+	0.0629625i
$821$	46.0430	+	33.4522i	1.60691	+	1.16749i	0.872257	+	0.489047i	$0.162655\pi$
$821$	46.0430	+	33.4522i	1.60691	+	1.16749i	0.734654	+	0.678442i	$0.237345\pi$
$822$		0			0
$823$	4.57501	−	14.0804i	0.159475	−	0.490813i	−0.839112	−	0.543959i	$-0.816925\pi$
$823$	4.57501	−	14.0804i	0.159475	−	0.490813i	0.998587	+	0.0531457i	$0.0169248\pi$
$824$	−4.81442			−0.167718
$825$		0			0
$826$	−2.03150			−0.0706851
$827$	−13.2411	+	40.7520i	−0.460439	+	1.41709i	0.404189	+	0.914675i	$0.367554\pi$
$827$	−13.2411	+	40.7520i	−0.460439	+	1.41709i	−0.864629	+	0.502411i	$0.832446\pi$
$828$		0			0
$829$	−18.3791	−	13.3532i	−0.638332	−	0.463775i	0.220945	−	0.975286i	$-0.429086\pi$
$829$	−18.3791	−	13.3532i	−0.638332	−	0.463775i	−0.859277	+	0.511511i	$0.829086\pi$
$830$	−12.3390	+	4.00918i	−0.428293	+	0.139161i
$831$		0			0
$832$	−3.26367	+	4.49206i	−0.113147	+	0.155734i
$833$	37.2852	−	27.0893i	1.29186	−	0.938588i
$834$		0			0
$835$		−	24.4756i		−	0.847012i
$836$	2.22876	+	4.81352i	0.0770832	+	0.166479i
$837$		0			0
$838$	−2.61291	−	0.848987i	−0.0902616	−	0.0293278i
$839$	13.1041	+	18.0362i	0.452403	+	0.622679i	0.972912	−	0.231177i	$-0.0742578\pi$
$839$	13.1041	+	18.0362i	0.452403	+	0.622679i	−0.520509	+	0.853856i	$0.674258\pi$
$840$		0			0
$841$	20.3251	+	62.5543i	0.700867	+	2.15705i
$842$	12.0793	+	37.1762i	0.416279	+	1.28118i
$843$		0			0
$844$	−5.55384	−	7.64421i	−0.191171	−	0.263124i
$845$	16.9575	+	5.50981i	0.583354	+	0.189543i
$846$		0			0
$847$	−0.396773	−	1.62884i	−0.0136333	−	0.0559676i
$848$		−	2.45593i		−	0.0843371i
$849$		0			0
$850$	−5.34419	+	3.88278i	−0.183304	+	0.133178i
$851$	8.05230	−	11.0830i	0.276029	−	0.379922i
$852$		0			0
$853$	−43.8232	+	14.2390i	−1.50048	+	0.487535i	−0.940157	−	0.340741i	$-0.889322\pi$
$853$	−43.8232	+	14.2390i	−1.50048	+	0.487535i	−0.560321	+	0.828276i	$0.689322\pi$
$854$	1.07006	+	0.777441i	0.0366165	+	0.0266035i
$855$		0			0
$856$	−6.13698	+	18.8877i	−0.209758	+	0.645568i
$857$	8.32137			0.284252			0.142126	−	0.989849i	$-0.454606\pi$
$857$	8.32137			0.284252			0.142126	+	0.989849i	$0.454606\pi$
$858$		0			0
$859$	10.6760			0.364259			0.182130	−	0.983275i	$-0.441701\pi$
$859$	10.6760			0.364259			0.182130	+	0.983275i	$0.441701\pi$
$860$	−0.807432	+	2.48502i	−0.0275332	+	0.0847385i
$861$		0			0
$862$	−17.2425	−	12.5274i	−0.587280	−	0.426684i
$863$	−52.7438	+	17.1375i	−1.79542	+	0.583367i	−0.999750	−	0.0223639i	$-0.992881\pi$
$863$	−52.7438	+	17.1375i	−1.79542	+	0.583367i	−0.795669	+	0.605731i	$0.792881\pi$
$864$		0			0
$865$	−4.68551	+	6.44905i	−0.159312	+	0.219274i
$866$	1.57276	−	1.14268i	0.0534447	−	0.0388298i
$867$		0			0
$868$			0.169662i			0.00575869i
$869$	−41.0561	+	4.92842i	−1.39273	+	0.167185i
$870$		0			0
$871$	27.2301	+	8.84761i	0.922658	+	0.299790i
$872$	4.07718	+	5.61176i	0.138071	+	0.190038i
$873$		0			0
$874$	−2.67465	−	8.23172i	−0.0904714	−	0.278442i
$875$	−0.0470961	−	0.144947i	−0.00159214	−	0.00490010i
$876$		0			0
$877$	−15.5665	−	21.4255i	−0.525644	−	0.723487i	0.460815	−	0.887496i	$-0.347557\pi$
$877$	−15.5665	−	21.4255i	−0.525644	−	0.723487i	−0.986459	+	0.164010i	$0.947557\pi$
$878$	16.1056	+	5.23304i	0.543539	+	0.176606i
$879$		0			0
$880$	−2.89643	−	1.61577i	−0.0976386	−	0.0544675i
$881$		−	10.0938i		−	0.340070i	−0.985438	−	0.170035i	$-0.945612\pi$
$881$		−	10.0938i		−	0.340070i	0.985438	−	0.170035i	$-0.0543881\pi$
$882$		0			0
$883$	39.7352	−	28.8693i	1.33720	−	0.971530i	0.337655	−	0.941270i	$-0.390366\pi$
$883$	39.7352	−	28.8693i	1.33720	−	0.971530i	0.999542	−	0.0302605i	$-0.00963370\pi$
$884$	21.5591	−	29.6736i	0.725111	−	0.998030i
$885$		0			0
$886$	−8.63091	+	2.80435i	−0.289961	+	0.0942140i
$887$	−3.03117	−	2.20228i	−0.101777	−	0.0739452i	0.535733	−	0.844388i	$-0.320035\pi$
$887$	−3.03117	−	2.20228i	−0.101777	−	0.0739452i	−0.637510	+	0.770442i	$0.720035\pi$
$888$		0			0
$889$	0.680214	−	2.09348i	0.0228137	−	0.0702132i
$890$	0.935139			0.0313459
$891$		0			0
$892$	−4.05976			−0.135931
$893$	−2.30617	+	7.09768i	−0.0771732	+	0.237515i
$894$		0			0
$895$	3.48870	+	2.53469i	0.116614	+	0.0847254i
$896$	−0.144947	+	0.0470961i	−0.00484234	+	0.00157337i
$897$		0			0
$898$	3.35488	−	4.61759i	0.111954	−	0.154091i
$899$	−8.76763	+	6.37005i	−0.292417	+	0.212453i
$900$		0			0
$901$			16.2234i			0.540478i
$902$	13.1590	+	14.1880i	0.438148	+	0.472410i
$903$		0			0
$904$	−8.56731	−	2.78369i	−0.284944	−	0.0925840i
$905$	−11.3032	−	15.5575i	−0.375730	−	0.517148i
$906$		0			0
$907$	12.2014	+	37.5522i	0.405142	+	1.24690i	0.920776	+	0.390091i	$0.127556\pi$
$907$	12.2014	+	37.5522i	0.405142	+	1.24690i	−0.515634	+	0.856809i	$0.672444\pi$
$908$	−0.394797	−	1.21506i	−0.0131018	−	0.0403232i
$909$		0			0
$910$	0.497404	+	0.684618i	0.0164888	+	0.0226949i
$911$	−2.86149	−	0.929754i	−0.0948053	−	0.0308041i	0.261230	−	0.965277i	$-0.415872\pi$
$911$	−2.86149	−	0.929754i	−0.0948053	−	0.0308041i	−0.356036	+	0.934472i	$0.615872\pi$
$912$		0			0
$913$	29.2611	+	31.5493i	0.968401	+	1.04413i
$914$			23.1077i			0.764335i
$915$		0			0
$916$	−14.9155	+	10.8368i	−0.492823	+	0.358057i
$917$	−1.21566	+	1.67321i	−0.0401445	+	0.0552541i
$918$		0			0
$919$	−41.1363	+	13.3660i	−1.35696	+	0.440903i	−0.895027	−	0.446012i	$-0.852844\pi$
$919$	−41.1363	+	13.3660i	−1.35696	+	0.440903i	−0.461933	+	0.886915i	$0.652844\pi$
$920$	4.37821	+	3.18096i	0.144345	+	0.104873i
$921$		0			0
$922$	−9.98086	+	30.7179i	−0.328702	+	1.01164i
$923$	67.1132			2.20906
$924$		0			0
$925$	2.53141			0.0832322
$926$	−1.29749	+	3.99327i	−0.0426382	+	0.131227i
$927$		0			0
$928$	−7.87592	−	5.72219i	−0.258540	−	0.187840i
$929$	−11.8206	+	3.84075i	−0.387822	+	0.126011i	−0.496437	−	0.868073i	$-0.665359\pi$
$929$	−11.8206	+	3.84075i	−0.387822	+	0.126011i	0.108615	+	0.994084i	$0.465359\pi$
$930$		0			0
$931$	−6.55871	+	9.02729i	−0.214953	+	0.295857i
$932$	6.71668	−	4.87995i	0.220012	−	0.159848i
$933$		0			0
$934$		−	16.0612i		−	0.525539i
$935$	19.1332	+	10.6734i	0.625722	+	0.349058i
$936$		0			0
$937$	49.9695	+	16.2361i	1.63243	+	0.530410i	0.974829	−	0.222954i	$-0.0715699\pi$
$937$	49.9695	+	16.2361i	1.63243	+	0.530410i	0.657604	+	0.753364i	$0.271570\pi$
$938$	0.461931	+	0.635794i	0.0150826	+	0.0207594i
$939$		0			0
$940$	−1.44194	−	4.43783i	−0.0470309	−	0.144746i
$941$	−13.3965	−	41.2300i	−0.436712	−	1.34406i	−0.891322	−	0.453370i	$-0.850221\pi$
$941$	−13.3965	−	41.2300i	−0.436712	−	1.34406i	0.454610	−	0.890690i	$-0.349779\pi$
$942$		0			0
$943$	−18.5594	−	25.5449i	−0.604379	−	0.831856i
$944$	12.6771	+	4.11905i	0.412606	+	0.134064i
$945$		0			0
$946$	8.60426	−	1.03286i	0.279749	−	0.0335813i
$947$			22.6591i			0.736323i	0.929762	+	0.368162i	$0.120013\pi$
$947$			22.6591i			0.736323i	−0.929762	+	0.368162i	$0.879987\pi$
$948$		0			0
$949$	43.3707	−	31.5107i	1.40787	−	1.02288i
$950$	0.940078	−	1.29391i	0.0305001	−	0.0419798i
$951$		0			0
$952$	0.957488	−	0.311107i	0.0310324	−	0.0100830i
$953$	−4.55992	−	3.31297i	−0.147710	−	0.107318i	0.511476	−	0.859298i	$-0.329099\pi$
$953$	−4.55992	−	3.31297i	−0.147710	−	0.107318i	−0.659186	+	0.751980i	$0.729099\pi$
$954$		0			0
$955$	−5.14367	+	15.8306i	−0.166445	+	0.512266i
$956$	−17.5858			−0.568764
$957$		0			0
$958$	−17.4040			−0.562299
$959$	0.147468	−	0.453859i	0.00476198	−	0.0146559i
$960$		0			0
$961$	24.0769	+	17.4929i	0.776676	+	0.564288i
$962$	−13.3677	+	4.34342i	−0.430991	+	0.140038i
$963$		0			0
$964$	−6.93048	+	9.53898i	−0.223216	+	0.307230i
$965$	−1.09679	+	0.796867i	−0.0353070	+	0.0256521i
$966$		0			0
$967$		−	40.7386i		−	1.31006i	−0.755601	−	0.655032i	$-0.772655\pi$
$967$		−	40.7386i		−	1.31006i	0.755601	−	0.655032i	$-0.227345\pi$
$968$	−0.826645	+	10.9689i	−0.0265694	+	0.352554i
$969$		0			0
$970$	7.33969	+	2.38481i	0.235663	+	0.0765716i
$971$	3.51697	+	4.84070i	0.112865	+	0.155345i	0.861712	−	0.507397i	$-0.169392\pi$
$971$	3.51697	+	4.84070i	0.112865	+	0.155345i	−0.748847	+	0.662743i	$0.769392\pi$
$972$		0			0
$973$	0.321449	+	0.989318i	0.0103052	+	0.0317161i
$974$	11.5561	+	35.5659i	0.370280	+	1.13961i
$975$		0			0
$976$	−5.10111	−	7.02107i	−0.163282	−	0.224739i
$977$	−34.1828	−	11.1067i	−1.09360	−	0.355333i	−0.293966	−	0.955816i	$-0.594975\pi$
$977$	−34.1828	−	11.1067i	−1.09360	−	0.355333i	−0.799638	+	0.600483i	$0.794975\pi$
$978$		0			0
$979$	−1.30315	−	2.81445i	−0.0416488	−	0.0899503i
$980$		−	6.97677i		−	0.222865i
$981$		0			0
$982$	9.58642	−	6.96494i	0.305915	−	0.222260i
$983$	14.7163	−	20.2553i	0.469378	−	0.646044i	−0.507042	−	0.861921i	$-0.669261\pi$
$983$	14.7163	−	20.2553i	0.469378	−	0.646044i	0.976420	+	0.215878i	$0.0692612\pi$
$984$		0			0
$985$	5.67728	−	1.84466i	0.180893	−	0.0587757i
$986$	52.0266	+	37.7995i	1.65686	+	1.20378i
$987$		0			0
$988$	−2.74420	+	8.44577i	−0.0873045	+	0.268696i
$989$	−14.1405			−0.449640
$990$		0			0
$991$	43.2366			1.37346			0.686728	−	0.726914i	$-0.259046\pi$
$991$	43.2366			1.37346			0.686728	+	0.726914i	$0.259046\pi$
$992$	0.344004	−	1.05873i	0.0109221	−	0.0336149i
$993$		0			0
$994$	1.49033	+	1.08278i	0.0472702	+	0.0343438i
$995$	−9.05218	+	2.94123i	−0.286973	+	0.0932433i
$996$		0			0
$997$	7.12656	−	9.80887i	0.225701	−	0.310650i	−0.681116	−	0.732175i	$-0.738505\pi$
$997$	7.12656	−	9.80887i	0.225701	−	0.310650i	0.906817	+	0.421525i	$0.138505\pi$
$998$	−16.3465	+	11.8764i	−0.517438	+	0.375941i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.z.a.431.7	✓	32
3.2	odd	2		990.2.z.b.431.3	yes	32
11.6	odd	10		990.2.z.b.611.3	yes	32
33.17	even	10	inner	990.2.z.a.611.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.z.a.431.7	✓	32	1.1	even	1	trivial
990.2.z.a.611.7	yes	32	33.17	even	10	inner
990.2.z.b.431.3	yes	32	3.2	odd	2
990.2.z.b.611.3	yes	32	11.6	odd	10

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.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.951057 - 0.309017i) q^{5} +(0.0895822 - 0.123299i) q^{7} +(-0.809017 + 0.587785i) q^{8} -1.00000i q^{10} +(-3.00966 + 1.39353i) q^{11} +(-5.28073 - 1.71581i) q^{13} +(-0.0895822 - 0.123299i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-2.04130 - 6.28247i) q^{17} +(0.940078 + 1.29391i) q^{19} +(-0.951057 - 0.309017i) q^{20} +(0.395293 + 3.29298i) q^{22} -5.41177i q^{23} +(0.809017 - 0.587785i) q^{25} +(-3.26367 + 4.49206i) q^{26} +(-0.144947 + 0.0470961i) q^{28} +(-7.87592 - 5.72219i) q^{29} +(0.344004 - 1.05873i) q^{31} +1.00000 q^{32} -6.60578 q^{34} +(0.0470961 - 0.144947i) q^{35} +(2.04795 + 1.48792i) q^{37} +(1.52108 - 0.494228i) q^{38} +(-0.587785 + 0.809017i) q^{40} +(4.72024 - 3.42946i) q^{41} -2.61291i q^{43} +(3.25397 + 0.641642i) q^{44} +(-5.14690 - 1.67233i) q^{46} +(2.74273 + 3.77505i) q^{47} +(2.15594 + 6.63530i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(3.26367 + 4.49206i) q^{52} +(-2.33573 - 0.758925i) q^{53} +(-2.43173 + 2.25537i) q^{55} +0.152406i q^{56} +(-7.87592 + 5.72219i) q^{58} +(7.83490 - 10.7838i) q^{59} +(-8.25376 + 2.68181i) q^{61} +(-0.900614 - 0.654334i) q^{62} +(0.309017 - 0.951057i) q^{64} -5.55249 q^{65} -5.15651 q^{67} +(-2.04130 + 6.28247i) q^{68} +(-0.123299 - 0.0895822i) q^{70} +(-11.4955 + 3.73511i) q^{71} +(-5.67506 + 7.81104i) q^{73} +(2.04795 - 1.48792i) q^{74} -1.59936i q^{76} +(-0.0977902 + 0.495925i) q^{77} +(11.8575 + 3.85275i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-1.80297 - 5.54898i) q^{82} +(-4.00918 - 12.3390i) q^{83} +(-3.88278 - 5.34419i) q^{85} +(-2.48502 - 0.807432i) q^{86} +(1.61577 - 2.89643i) q^{88} +0.935139i q^{89} +(-0.684618 + 0.497404i) q^{91} +(-3.18096 + 4.37821i) q^{92} +(4.43783 - 1.44194i) q^{94} +(1.29391 + 0.940078i) q^{95} +(-2.38481 + 7.33969i) q^{97} +6.97677 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{2} - 8 q^{4} - 8 q^{8} - 8 q^{16} + 4 q^{17} + 8 q^{25} - 8 q^{29} + 32 q^{31} + 32 q^{32} + 24 q^{34} + 16 q^{37} + 32 q^{41} - 20 q^{46} - 20 q^{47} + 16 q^{49} + 8 q^{50} - 40 q^{53} + 8 q^{55}+ \cdots + 16 q^{98}+O(q^{100}) \) 32 * q - 8 * q^2 - 8 * q^4 - 8 * q^8 - 8 * q^16 + 4 * q^17 + 8 * q^25 - 8 * q^29 + 32 * q^31 + 32 * q^32 + 24 * q^34 + 16 * q^37 + 32 * q^41 - 20 * q^46 - 20 * q^47 + 16 * q^49 + 8 * q^50 - 40 * q^53 + 8 * q^55 - 8 * q^58 + 40 * q^59 - 28 * q^62 - 8 * q^64 + 8 * q^65 + 4 * q^68 - 40 * q^71 + 40 * q^73 + 16 * q^74 - 28 * q^77 + 20 * q^79 - 8 * q^82 - 24 * q^83 - 24 * q^91 + 20 * q^94 + 16 * q^95 + 48 * q^97 + 16 * q^98

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