LMFDB - Embedded newform 990.2.n.k.91.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(91,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,2,0,-2,2,0,-3,2,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 14x^{6} - 12x^{5} + 121x^{4} + 120x^{3} + 1400x^{2} + 3000x + 10000 $ x^8 - 3x^7 + 14x^6 - 12x^5 + 121x^4 + 120x^3 + 1400x^2 + 3000*x + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.1
Root			$1.07734 + 3.31572i$ of defining polynomial
Character	$\chi$	$=$	990.91
Dual form			990.2.n.k.631.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-1.07734 + 3.31572i) q^{7} +(-0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(2.01151 + 2.63701i) q^{11} +(-4.06370 + 2.95245i) q^{13} +(1.07734 + 3.31572i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-3.05220 - 2.21755i) q^{17} +(1.66583 + 5.12691i) q^{19} +(0.809017 - 0.587785i) q^{20} +(3.17734 + 0.951057i) q^{22} +6.49515 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.55220 + 4.77717i) q^{26} +(2.82052 + 2.04923i) q^{28} +(-0.886361 + 2.72794i) q^{29} +(-7.55659 + 5.49018i) q^{31} -1.00000 q^{32} -3.77272 q^{34} +(-2.82052 + 2.04923i) q^{35} +(2.73607 - 8.42075i) q^{37} +(4.36121 + 3.16861i) q^{38} +(0.309017 - 0.951057i) q^{40} +(1.79098 + 5.51207i) q^{41} +3.93548 q^{43} +(3.12954 - 1.09817i) q^{44} +(5.25468 - 3.81775i) q^{46} +(-3.70688 - 11.4086i) q^{47} +(-4.17023 - 3.02985i) q^{49} +(0.809017 + 0.587785i) q^{50} +(1.55220 + 4.77717i) q^{52} +(3.41555 - 2.48154i) q^{53} +(0.0773437 + 3.31572i) q^{55} +3.48636 q^{56} +(0.886361 + 2.72794i) q^{58} +(-0.0224320 + 0.0690385i) q^{59} +(8.87711 + 6.44960i) q^{61} +(-2.88636 + 8.88330i) q^{62} +(-0.809017 + 0.587785i) q^{64} -5.02301 q^{65} +15.6783 q^{67} +(-3.05220 + 2.21755i) q^{68} +(-1.07734 + 3.31572i) q^{70} +(-3.48636 - 2.53299i) q^{71} +(-1.85410 + 5.70634i) q^{73} +(-2.73607 - 8.42075i) q^{74} +5.39076 q^{76} +(-10.9107 + 3.82862i) q^{77} +(8.67023 - 6.29929i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(4.68885 + 3.40665i) q^{82} +(-1.23607 - 0.898056i) q^{83} +(-1.16583 - 3.58807i) q^{85} +(3.18387 - 2.31322i) q^{86} +(1.88636 - 2.72794i) q^{88} -3.32360 q^{89} +(-5.41151 - 16.6549i) q^{91} +(2.00711 - 6.17725i) q^{92} +(-9.70475 - 7.05091i) q^{94} +(-1.66583 + 5.12691i) q^{95} +(-5.44913 + 3.95902i) q^{97} -5.15469 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} + 8 q^{10} + 3 q^{13} + 3 q^{14} - 2 q^{16} - 5 q^{17} + 4 q^{19} + 2 q^{20} - 16 q^{23} - 2 q^{25} + 7 q^{26} + 2 q^{28} + 3 q^{29} - 22 q^{31} - 8 q^{32}+ \cdots - 30 q^{98}+O(q^{100}) $ 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 + 8 * q^10 + 3 * q^13 + 3 * q^14 - 2 * q^16 - 5 * q^17 + 4 * q^19 + 2 * q^20 - 16 * q^23 - 2 * q^25 + 7 * q^26 + 2 * q^28 + 3 * q^29 - 22 * q^31 - 8 * q^32 - 10 * q^34 - 2 * q^35 + 4 * q^37 + 11 * q^38 - 2 * q^40 - q^41 - 2 * q^43 + 11 * q^46 + q^47 - 5 * q^49 + 2 * q^50 - 7 * q^52 + 30 * q^53 - 5 * q^55 - 2 * q^56 - 3 * q^58 + 8 * q^59 + 12 * q^61 - 13 * q^62 - 2 * q^64 - 8 * q^65 + 58 * q^67 - 5 * q^68 - 3 * q^70 + 2 * q^71 + 12 * q^73 - 4 * q^74 + 14 * q^76 - 22 * q^77 + 41 * q^79 + 2 * q^80 - 4 * q^82 + 8 * q^83 + 27 * q^86 + 5 * q^88 - 10 * q^89 - 47 * q^91 + 19 * q^92 - q^94 - 4 * q^95 - 40 * q^97 - 30 * q^98

Character values

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

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$		0			0
$7$	−1.07734	+	3.31572i	−0.407198	+	1.25323i	0.511849	+	0.859076i	$0.328961\pi$
$7$	−1.07734	+	3.31572i	−0.407198	+	1.25323i	−0.919046	+	0.394150i	$0.871039\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$		0			0
$10$	1.00000			0.316228
$11$	2.01151	+	2.63701i	0.606492	+	0.795090i
$11$	2.01151	+	2.63701i	0.606492	+	0.795090i
$12$		0			0
$13$	−4.06370	+	2.95245i	−1.12707	+	0.818863i	−0.985265	−	0.171032i	$-0.945290\pi$
$13$	−4.06370	+	2.95245i	−1.12707	+	0.818863i	−0.141802	+	0.989895i	$0.545290\pi$
$14$	1.07734	+	3.31572i	0.287932	+	0.886164i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−3.05220	−	2.21755i	−0.740266	−	0.537835i	0.152528	−	0.988299i	$-0.451258\pi$
$17$	−3.05220	−	2.21755i	−0.740266	−	0.537835i	−0.892794	+	0.450464i	$0.851258\pi$
$18$		0			0
$19$	1.66583	+	5.12691i	0.382169	+	1.17619i	0.938513	+	0.345243i	$0.112203\pi$
$19$	1.66583	+	5.12691i	0.382169	+	1.17619i	−0.556345	+	0.830952i	$0.687797\pi$
$20$	0.809017	−	0.587785i	0.180902	−	0.131433i
$21$		0			0
$22$	3.17734	+	0.951057i	0.677411	+	0.202766i
$23$	6.49515			1.35433			0.677166	−	0.735830i	$-0.263208\pi$
$23$	6.49515			1.35433			0.677166	+	0.735830i	$0.263208\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.55220	+	4.77717i	−0.304411	+	0.936880i
$27$		0			0
$28$	2.82052	+	2.04923i	0.533029	+	0.387268i
$29$	−0.886361	+	2.72794i	−0.164593	+	0.506565i	−0.999006	−	0.0445743i	$-0.985807\pi$
$29$	−0.886361	+	2.72794i	−0.164593	+	0.506565i	0.834413	+	0.551140i	$0.185807\pi$
$30$		0			0
$31$	−7.55659	+	5.49018i	−1.35720	+	0.986066i	−0.358586	+	0.933497i	$0.616741\pi$
$31$	−7.55659	+	5.49018i	−1.35720	+	0.986066i	−0.998617	+	0.0525697i	$0.983259\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−3.77272			−0.647016
$35$	−2.82052	+	2.04923i	−0.476755	+	0.346383i
$36$		0			0
$37$	2.73607	−	8.42075i	0.449807	−	1.38436i	−0.427318	−	0.904101i	$-0.640542\pi$
$37$	2.73607	−	8.42075i	0.449807	−	1.38436i	0.877125	−	0.480262i	$-0.159458\pi$
$38$	4.36121	+	3.16861i	0.707482	+	0.514016i
$39$		0			0
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	1.79098	+	5.51207i	0.279704	+	0.860840i	0.987936	+	0.154861i	$0.0494930\pi$
$41$	1.79098	+	5.51207i	0.279704	+	0.860840i	−0.708232	+	0.705980i	$0.750507\pi$
$42$		0			0
$43$	3.93548			0.600155			0.300078	−	0.953915i	$-0.402987\pi$
$43$	3.93548			0.600155			0.300078	+	0.953915i	$0.402987\pi$
$44$	3.12954	−	1.09817i	0.471796	−	0.165556i
$45$		0			0
$46$	5.25468	−	3.81775i	0.774761	−	0.562897i
$47$	−3.70688	−	11.4086i	−0.540704	−	1.66412i	−0.730990	−	0.682388i	$-0.760941\pi$
$47$	−3.70688	−	11.4086i	−0.540704	−	1.66412i	0.190285	−	0.981729i	$-0.439059\pi$
$48$		0			0
$49$	−4.17023	−	3.02985i	−0.595747	−	0.432836i
$50$	0.809017	+	0.587785i	0.114412	+	0.0831254i
$51$		0			0
$52$	1.55220	+	4.77717i	0.215251	+	0.662474i
$53$	3.41555	−	2.48154i	0.469161	−	0.340866i	−0.327953	−	0.944694i	$-0.606359\pi$
$53$	3.41555	−	2.48154i	0.469161	−	0.340866i	0.797114	+	0.603828i	$0.206359\pi$
$54$		0			0
$55$	0.0773437	+	3.31572i	0.0104290	+	0.447092i
$56$	3.48636			0.465884
$57$		0			0
$58$	0.886361	+	2.72794i	0.116385	+	0.358196i
$59$	−0.0224320	+	0.0690385i	−0.00292039	+	0.00898805i	−0.952506	−	0.304520i	$-0.901504\pi$
$59$	−0.0224320	+	0.0690385i	−0.00292039	+	0.00898805i	0.949586	+	0.313508i	$0.101504\pi$
$60$		0			0
$61$	8.87711	+	6.44960i	1.13660	+	0.825787i	0.986642	−	0.162906i	$-0.0520867\pi$
$61$	8.87711	+	6.44960i	1.13660	+	0.825787i	0.149956	+	0.988693i	$0.452087\pi$
$62$	−2.88636	+	8.88330i	−0.366568	+	1.12818i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−5.02301			−0.623028
$66$		0			0
$67$	15.6783			1.91541			0.957703	−	0.287758i	$-0.0929099\pi$
$67$	15.6783			1.91541			0.957703	+	0.287758i	$0.0929099\pi$
$68$	−3.05220	+	2.21755i	−0.370133	+	0.268917i
$69$		0			0
$70$	−1.07734	+	3.31572i	−0.128767	+	0.396305i
$71$	−3.48636	−	2.53299i	−0.413754	−	0.300610i	0.361366	−	0.932424i	$-0.382311\pi$
$71$	−3.48636	−	2.53299i	−0.413754	−	0.300610i	−0.775120	+	0.631814i	$0.782311\pi$
$72$		0			0
$73$	−1.85410	+	5.70634i	−0.217006	+	0.667876i	0.781999	+	0.623280i	$0.214200\pi$
$73$	−1.85410	+	5.70634i	−0.217006	+	0.667876i	−0.999005	+	0.0445966i	$0.985800\pi$
$74$	−2.73607	−	8.42075i	−0.318061	−	0.978892i
$75$		0			0
$76$	5.39076			0.618362
$77$	−10.9107	+	3.82862i	−1.24339	+	0.436312i
$78$		0			0
$79$	8.67023	−	6.29929i	0.975477	−	0.708726i	0.0187838	−	0.999824i	$-0.494021\pi$
$79$	8.67023	−	6.29929i	0.975477	−	0.708726i	0.956693	+	0.291098i	$0.0940206\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$		0			0
$82$	4.68885	+	3.40665i	0.517796	+	0.376201i
$83$	−1.23607	−	0.898056i	−0.135676	−	0.0985744i	0.517877	−	0.855455i	$-0.326722\pi$
$83$	−1.23607	−	0.898056i	−0.135676	−	0.0985744i	−0.653553	+	0.756881i	$0.726722\pi$
$84$		0			0
$85$	−1.16583	−	3.58807i	−0.126453	−	0.389181i
$86$	3.18387	−	2.31322i	0.343326	−	0.249441i
$87$		0			0
$88$	1.88636	−	2.72794i	0.201087	−	0.290799i
$89$	−3.32360			−0.352300			−0.176150	−	0.984363i	$-0.556364\pi$
$89$	−3.32360			−0.352300			−0.176150	+	0.984363i	$0.556364\pi$
$90$		0			0
$91$	−5.41151	−	16.6549i	−0.567280	−	1.74591i
$92$	2.00711	−	6.17725i	0.209256	−	0.644023i
$93$		0			0
$94$	−9.70475	−	7.05091i	−1.00097	−	0.727246i
$95$	−1.66583	+	5.12691i	−0.170911	+	0.526010i
$96$		0			0
$97$	−5.44913	+	3.95902i	−0.553275	+	0.401978i	−0.828991	−	0.559261i	$-0.811085\pi$
$97$	−5.44913	+	3.95902i	−0.553275	+	0.401978i	0.275717	+	0.961239i	$0.411085\pi$
$98$	−5.15469			−0.520702
$99$		0			0
$100$	1.00000			0.100000
$101$	0.183872	−	0.133591i	0.0182960	−	0.0132928i	−0.578600	−	0.815612i	$-0.696401\pi$
$101$	0.183872	−	0.133591i	0.0182960	−	0.0132928i	0.596896	+	0.802319i	$0.296401\pi$
$102$		0			0
$103$	2.90190	−	8.93114i	0.285933	−	0.880011i	−0.700184	−	0.713962i	$-0.746899\pi$
$103$	2.90190	−	8.93114i	0.285933	−	0.880011i	0.986117	−	0.166049i	$-0.0531011\pi$
$104$	4.06370	+	2.95245i	0.398479	+	0.289512i
$105$		0			0
$106$	1.30462	−	4.01521i	0.126716	−	0.389992i
$107$	−5.40498	−	16.6348i	−0.522519	−	1.60815i	−0.769171	−	0.639043i	$-0.779330\pi$
$107$	−5.40498	−	16.6348i	−0.522519	−	1.60815i	0.246652	−	0.969104i	$-0.420670\pi$
$108$		0			0
$109$	−5.52786			−0.529473			−0.264737	−	0.964321i	$-0.585285\pi$
$109$	−5.52786			−0.529473			−0.264737	+	0.964321i	$0.585285\pi$
$110$	2.01151	+	2.63701i	0.191790	+	0.251429i
$111$		0			0
$112$	2.82052	−	2.04923i	0.266514	−	0.193634i
$113$	5.04105	+	15.5148i	0.474222	+	1.45950i	0.847004	+	0.531586i	$0.178404\pi$
$113$	5.04105	+	15.5148i	0.474222	+	1.45950i	−0.372782	+	0.927919i	$0.621596\pi$
$114$		0			0
$115$	5.25468	+	3.81775i	0.490002	+	0.356007i
$116$	2.32052	+	1.68596i	0.215455	+	0.156537i
$117$		0			0
$118$	0.0224320	+	0.0690385i	0.00206503	+	0.00635551i
$119$	10.6410	−	7.73117i	0.975463	−	0.708715i
$120$		0			0
$121$	−2.90769	+	10.6087i	−0.264336	+	0.964431i
$122$	10.9727			0.993423
$123$		0			0
$124$	2.88636	+	8.88330i	0.259203	+	0.797744i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$		0			0
$127$	3.57427	+	2.59686i	0.317165	+	0.230434i	0.734965	−	0.678105i	$-0.237199\pi$
$127$	3.57427	+	2.59686i	0.317165	+	0.230434i	−0.417800	+	0.908539i	$0.637199\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$		0			0
$130$	−4.06370	+	2.95245i	−0.356410	+	0.258947i
$131$	1.31202			0.114631			0.0573157	−	0.998356i	$-0.481746\pi$
$131$	1.31202			0.114631			0.0573157	+	0.998356i	$0.481746\pi$
$132$		0			0
$133$	−18.7941			−1.62966
$134$	12.6840	−	9.21546i	1.09573	−	0.796094i
$135$		0			0
$136$	−1.16583	+	3.58807i	−0.0999695	+	0.307675i
$137$	1.33474	+	0.969748i	0.114035	+	0.0828512i	0.643341	−	0.765580i	$-0.277548\pi$
$137$	1.33474	+	0.969748i	0.114035	+	0.0828512i	−0.529306	+	0.848431i	$0.677548\pi$
$138$		0			0
$139$	−0.00403700	+	0.0124246i	−0.000342414	+	0.00105384i	−0.951228	−	0.308490i	$-0.900176\pi$
$139$	−0.00403700	+	0.0124246i	−0.000342414	+	0.00105384i	0.950885	+	0.309544i	$0.100176\pi$
$140$	1.07734	+	3.31572i	0.0910522	+	0.280230i
$141$		0			0
$142$	−4.30937			−0.361635
$143$	−15.9598	−	4.77717i	−1.33463	−	0.399487i
$144$		0			0
$145$	−2.32052	+	1.68596i	−0.192709	+	0.140011i
$146$	1.85410	+	5.70634i	0.153447	+	0.472260i
$147$		0			0
$148$	−7.16312	−	5.20431i	−0.588805	−	0.427792i
$149$	−6.65601	−	4.83587i	−0.545281	−	0.396170i	0.280761	−	0.959778i	$-0.409413\pi$
$149$	−6.65601	−	4.83587i	−0.545281	−	0.396170i	−0.826043	+	0.563607i	$0.809413\pi$
$150$		0			0
$151$	−0.0590853	−	0.181846i	−0.00480829	−	0.0147984i	0.948624	−	0.316407i	$-0.102476\pi$
$151$	−0.0590853	−	0.181846i	−0.00480829	−	0.0147984i	−0.953432	+	0.301608i	$0.902476\pi$
$152$	4.36121	−	3.16861i	0.353741	−	0.257008i
$153$		0			0
$154$	−6.57653	+	9.51057i	−0.529952	+	0.766383i
$155$	−9.34046			−0.750244
$156$		0			0
$157$	−5.92763	−	18.2434i	−0.473076	−	1.45598i	−0.848535	−	0.529140i	$-0.822515\pi$
$157$	−5.92763	−	18.2434i	−0.473076	−	1.45598i	0.375458	−	0.926839i	$-0.377485\pi$
$158$	3.31173	−	10.1925i	0.263467	−	0.810869i
$159$		0			0
$160$	−0.809017	−	0.587785i	−0.0639584	−	0.0464685i
$161$	−6.99750	+	21.5361i	−0.551481	+	1.69728i
$162$		0			0
$163$	−17.2971	+	12.5670i	−1.35481	+	0.984327i	−0.356054	+	0.934466i	$0.615878\pi$
$163$	−17.2971	+	12.5670i	−1.35481	+	0.984327i	−0.998756	+	0.0498614i	$0.984122\pi$
$164$	5.79573			0.452571
$165$		0			0
$166$	−1.52786			−0.118585
$167$	16.9408	−	12.3082i	1.31092	−	0.952439i	0.310922	−	0.950436i	$-0.399362\pi$
$167$	16.9408	−	12.3082i	1.31092	−	0.952439i	0.999998	−	0.00200319i	$-0.000637635\pi$
$168$		0			0
$169$	3.77947	−	11.6320i	0.290729	−	0.894771i
$170$	−3.05220	−	2.21755i	−0.234093	−	0.170078i
$171$		0			0
$172$	1.21613	−	3.74287i	0.0927291	−	0.285391i
$173$	−1.40901	−	4.33650i	−0.107125	−	0.329698i	0.883098	−	0.469188i	$-0.155453\pi$
$173$	−1.40901	−	4.33650i	−0.107125	−	0.329698i	−0.990223	+	0.139491i	$0.955453\pi$
$174$		0			0
$175$	−3.48636			−0.263544
$176$	−0.0773437	−	3.31572i	−0.00583000	−	0.249932i
$177$		0			0
$178$	−2.68885	+	1.95356i	−0.201538	+	0.146426i
$179$	2.80023	+	8.61821i	0.209299	+	0.644156i	0.999509	+	0.0313202i	$0.00997115\pi$
$179$	2.80023	+	8.61821i	0.209299	+	0.644156i	−0.790211	+	0.612835i	$0.790029\pi$
$180$		0			0
$181$	6.47214	+	4.70228i	0.481070	+	0.349518i	0.801740	−	0.597673i	$-0.203908\pi$
$181$	6.47214	+	4.70228i	0.481070	+	0.349518i	−0.320670	+	0.947191i	$0.603908\pi$
$182$	−14.1675	−	10.2933i	−1.05017	−	0.762990i
$183$		0			0
$184$	−2.00711	−	6.17725i	−0.147966	−	0.455393i
$185$	7.16312	−	5.20431i	0.526643	−	0.382629i
$186$		0			0
$187$	−0.291796	−	12.5093i	−0.0213382	−	0.914770i
$188$	−11.9957			−0.874878
$189$		0			0
$190$	1.66583	+	5.12691i	0.120852	+	0.371945i
$191$	2.19076	−	6.74247i	0.158518	−	0.487868i	−0.839982	−	0.542614i	$-0.817435\pi$
$191$	2.19076	−	6.74247i	0.158518	−	0.487868i	0.998500	+	0.0547455i	$0.0174348\pi$
$192$		0			0
$193$	−5.06024	−	3.67648i	−0.364244	−	0.264639i	0.390576	−	0.920571i	$-0.372276\pi$
$193$	−5.06024	−	3.67648i	−0.364244	−	0.264639i	−0.754820	+	0.655932i	$0.772276\pi$
$194$	−2.08138	+	6.40583i	−0.149434	+	0.459912i
$195$		0			0
$196$	−4.17023	+	3.02985i	−0.297874	+	0.216418i
$197$	15.6383			1.11418			0.557090	−	0.830452i	$-0.311918\pi$
$197$	15.6383			1.11418			0.557090	+	0.830452i	$0.311918\pi$
$198$		0			0
$199$	−11.9815			−0.849346			−0.424673	−	0.905347i	$-0.639611\pi$
$199$	−11.9815			−0.849346			−0.424673	+	0.905347i	$0.639611\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$		0			0
$202$	0.0702330	−	0.216155i	0.00494158	−	0.0152086i
$203$	−8.09017	−	5.87785i	−0.567819	−	0.412544i
$204$		0			0
$205$	−1.79098	+	5.51207i	−0.125087	+	0.384980i
$206$	−2.90190	−	8.93114i	−0.202185	−	0.622262i
$207$		0			0
$208$	5.02301			0.348283
$209$	−10.1689	+	14.7056i	−0.703398	+	1.01721i
$210$		0			0
$211$	2.16891	−	1.57580i	0.149314	−	0.108483i	−0.510620	−	0.859806i	$-0.670584\pi$
$211$	2.16891	−	1.57580i	0.149314	−	0.108483i	0.659934	+	0.751323i	$0.270584\pi$
$212$	−1.30462	−	4.01521i	−0.0896018	−	0.275766i
$213$		0			0
$214$	−14.1504	−	10.2809i	−0.967302	−	0.702786i
$215$	3.18387	+	2.31322i	0.217138	+	0.157760i
$216$		0			0
$217$	−10.0629	−	30.9704i	−0.683113	−	2.10241i
$218$	−4.47214	+	3.24920i	−0.302891	+	0.220063i
$219$		0			0
$220$	3.17734	+	0.951057i	0.214216	+	0.0641202i
$221$	18.9504			1.27474
$222$		0			0
$223$	1.23203	+	3.79180i	0.0825029	+	0.253918i	0.983796	−	0.179292i	$-0.0573808\pi$
$223$	1.23203	+	3.79180i	0.0825029	+	0.253918i	−0.901293	+	0.433210i	$0.857381\pi$
$224$	1.07734	−	3.31572i	0.0719831	−	0.221541i
$225$		0			0
$226$	13.1976	+	9.58864i	0.877894	+	0.637827i
$227$	−0.418041	+	1.28660i	−0.0277463	+	0.0853944i	−0.963971	−	0.266008i	$-0.914295\pi$
$227$	−0.418041	+	1.28660i	−0.0277463	+	0.0853944i	0.936224	+	0.351403i	$0.114295\pi$
$228$		0			0
$229$	17.5412	−	12.7444i	1.15915	−	0.842174i	0.169482	−	0.985533i	$-0.445790\pi$
$229$	17.5412	−	12.7444i	1.15915	−	0.842174i	0.989671	+	0.143359i	$0.0457904\pi$
$230$	6.49515			0.428277
$231$		0			0
$232$	2.86832			0.188315
$233$	−15.4337	+	11.2132i	−1.01110	+	0.734604i	−0.964439	−	0.264307i	$-0.914857\pi$
$233$	−15.4337	+	11.2132i	−1.01110	+	0.734604i	−0.0466569	+	0.998911i	$0.514857\pi$
$234$		0			0
$235$	3.70688	−	11.4086i	0.241810	−	0.744216i
$236$	0.0587277	+	0.0426681i	0.00382284	+	0.00277746i
$237$		0			0
$238$	4.06452	−	12.5093i	0.263464	−	0.810857i
$239$	−7.76393	−	23.8949i	−0.502207	−	1.54563i	−0.805416	−	0.592710i	$-0.798058\pi$
$239$	−7.76393	−	23.8949i	−0.502207	−	1.54563i	0.303209	−	0.952924i	$-0.401942\pi$
$240$		0			0
$241$	−0.413051			−0.0266069			−0.0133035	−	0.999912i	$-0.504235\pi$
$241$	−0.413051			−0.0266069			−0.0133035	+	0.999912i	$0.504235\pi$
$242$	3.88329	+	10.2917i	0.249627	+	0.661579i
$243$		0			0
$244$	8.87711	−	6.44960i	0.568299	−	0.412893i
$245$	−1.59289	−	4.90240i	−0.101766	−	0.313203i
$246$		0			0
$247$	−21.9064	−	15.9159i	−1.39387	−	1.01271i
$248$	7.55659	+	5.49018i	0.479844	+	0.348627i
$249$		0			0
$250$	0.309017	+	0.951057i	0.0195440	+	0.0601501i
$251$	−9.66845	+	7.02454i	−0.610267	+	0.443385i	−0.849508	−	0.527575i	$-0.823101\pi$
$251$	−9.66845	+	7.02454i	−0.610267	+	0.443385i	0.239241	+	0.970960i	$0.423101\pi$
$252$		0			0
$253$	13.0650	+	17.1278i	0.821391	+	1.07682i
$254$	4.41804			0.277213
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	1.67376	−	5.15131i	0.104406	−	0.321330i	−0.885184	−	0.465241i	$-0.845968\pi$
$257$	1.67376	−	5.15131i	0.104406	−	0.321330i	0.989591	+	0.143911i	$0.0459678\pi$
$258$		0			0
$259$	24.9732	+	18.1441i	1.55176	+	1.12742i
$260$	−1.55220	+	4.77717i	−0.0962631	+	0.296267i
$261$		0			0
$262$	1.06144	−	0.771184i	0.0655762	−	0.0476439i
$263$	28.9799			1.78698			0.893488	−	0.449088i	$-0.148251\pi$
$263$	28.9799			1.78698			0.893488	+	0.449088i	$0.148251\pi$
$264$		0			0
$265$	4.22185			0.259346
$266$	−15.2047	+	11.0469i	−0.932263	+	0.677329i
$267$		0			0
$268$	4.84485	−	14.9109i	0.295947	−	0.910830i
$269$	−17.9201	−	13.0197i	−1.09261	−	0.793824i	−0.112768	−	0.993621i	$-0.535972\pi$
$269$	−17.9201	−	13.0197i	−1.09261	−	0.793824i	−0.979837	+	0.199797i	$0.935972\pi$
$270$		0			0
$271$	−0.0790223	+	0.243206i	−0.00480026	+	0.0147737i	−0.953428	−	0.301621i	$-0.902472\pi$
$271$	−0.0790223	+	0.243206i	−0.00480026	+	0.0147737i	0.948628	+	0.316395i	$0.102472\pi$
$272$	1.16583	+	3.58807i	0.0706891	+	0.217559i
$273$		0			0
$274$	1.64983			0.0996701
$275$	−1.88636	+	2.72794i	−0.113752	+	0.164501i
$276$		0			0
$277$	−17.4535	+	12.6807i	−1.04868	+	0.761911i	−0.971961	−	0.235142i	$-0.924445\pi$
$277$	−17.4535	+	12.6807i	−1.04868	+	0.761911i	−0.0767193	+	0.997053i	$0.524445\pi$
$278$	0.00403700	+	0.0124246i	0.000242123	+	0.000745179i
$279$		0			0
$280$	2.82052	+	2.04923i	0.168558	+	0.122465i
$281$	8.85410	+	6.43288i	0.528191	+	0.383754i	0.819681	−	0.572821i	$-0.194151\pi$
$281$	8.85410	+	6.43288i	0.528191	+	0.383754i	−0.291489	+	0.956574i	$0.594151\pi$
$282$		0			0
$283$	1.13122	+	3.48153i	0.0672439	+	0.206956i	0.979032	−	0.203705i	$-0.0652982\pi$
$283$	1.13122	+	3.48153i	0.0672439	+	0.206956i	−0.911788	+	0.410660i	$0.865298\pi$
$284$	−3.48636	+	2.53299i	−0.206877	+	0.150305i
$285$		0			0
$286$	−15.7197	+	5.51613i	−0.929526	+	0.326176i
$287$	−20.2060			−1.19272
$288$		0			0
$289$	−0.854918	−	2.63117i	−0.0502893	−	0.154775i
$290$	−0.886361	+	2.72794i	−0.0520489	+	0.160190i
$291$		0			0
$292$	4.85410	+	3.52671i	0.284065	+	0.206385i
$293$	3.40901	−	10.4919i	0.199157	−	0.612941i	−0.800746	−	0.599004i	$-0.795563\pi$
$293$	3.40901	−	10.4919i	0.199157	−	0.612941i	0.999903	−	0.0139375i	$-0.00443658\pi$
$294$		0			0
$295$	−0.0587277	+	0.0426681i	−0.00341926	+	0.00248424i
$296$	−8.85410			−0.514634
$297$		0			0
$298$	−8.22728			−0.476593
$299$	−26.3943	+	19.1766i	−1.52642	+	1.10901i
$300$		0			0
$301$	−4.23987	+	13.0490i	−0.244382	+	0.752130i
$302$	−0.154687	−	0.112387i	−0.00890125	−	0.00646714i
$303$		0			0
$304$	1.66583	−	5.12691i	0.0955422	−	0.294049i
$305$	3.39076	+	10.4357i	0.194154	+	0.597545i
$306$		0			0
$307$	−4.29560			−0.245163			−0.122581	−	0.992458i	$-0.539117\pi$
$307$	−4.29560			−0.245163			−0.122581	+	0.992458i	$0.539117\pi$
$308$	0.269648	+	11.5598i	0.0153646	+	0.658680i
$309$		0			0
$310$	−7.55659	+	5.49018i	−0.429185	+	0.311822i
$311$	6.78694	+	20.8881i	0.384852	+	1.18445i	0.936587	+	0.350434i	$0.113966\pi$
$311$	6.78694	+	20.8881i	0.384852	+	1.18445i	−0.551735	+	0.834019i	$0.686034\pi$
$312$		0			0
$313$	11.1504	+	8.10125i	0.630259	+	0.457910i	0.856490	−	0.516164i	$-0.172640\pi$
$313$	11.1504	+	8.10125i	0.630259	+	0.457910i	−0.226231	+	0.974074i	$0.572640\pi$
$314$	−15.5187	−	11.2750i	−0.875773	−	0.636286i
$315$		0			0
$316$	−3.31173	−	10.1925i	−0.186300	−	0.573371i
$317$	0.434519	−	0.315697i	0.0244050	−	0.0177313i	−0.575516	−	0.817791i	$-0.695199\pi$
$317$	0.434519	−	0.315697i	0.0244050	−	0.0177313i	0.599921	+	0.800059i	$0.295199\pi$
$318$		0			0
$319$	−8.97653	+	3.14991i	−0.502589	+	0.176361i
$320$	−1.00000			−0.0559017
$321$		0			0
$322$	6.99750	+	21.5361i	0.389956	+	1.20016i
$323$	6.28473	−	19.3424i	0.349692	−	1.07624i
$324$		0			0
$325$	−4.06370	−	2.95245i	−0.225414	−	0.163773i
$326$	−6.60689	+	20.3339i	−0.365922	+	1.12619i
$327$		0			0
$328$	4.68885	−	3.40665i	0.258898	−	0.188101i
$329$	41.8214			2.30569
$330$		0			0
$331$	31.5887			1.73627			0.868135	−	0.496328i	$-0.165319\pi$
$331$	31.5887			1.73627			0.868135	+	0.496328i	$0.165319\pi$
$332$	−1.23607	+	0.898056i	−0.0678380	+	0.0492872i
$333$		0			0
$334$	6.47081	−	19.9151i	0.354067	−	1.08971i
$335$	12.6840	+	9.21546i	0.693001	+	0.503494i
$336$		0			0
$337$	−3.66833	+	11.2900i	−0.199827	+	0.615003i	0.800060	+	0.599921i	$0.204801\pi$
$337$	−3.66833	+	11.2900i	−0.199827	+	0.615003i	−0.999886	+	0.0150827i	$0.995199\pi$
$338$	−3.77947	−	11.6320i	−0.205576	−	0.632699i
$339$		0			0
$340$	−3.77272			−0.204605
$341$	−29.6778	−	8.88330i	−1.60714	−	0.481058i
$342$		0			0
$343$	−5.20475	+	3.78147i	−0.281030	+	0.204180i
$344$	−1.21613	−	3.74287i	−0.0655694	−	0.201802i
$345$		0			0
$346$	−3.68885	−	2.68010i	−0.198314	−	0.144083i
$347$	−6.10323	−	4.43426i	−0.327639	−	0.238043i	0.411789	−	0.911279i	$-0.364904\pi$
$347$	−6.10323	−	4.43426i	−0.327639	−	0.238043i	−0.739428	+	0.673236i	$0.764904\pi$
$348$		0			0
$349$	6.08753	+	18.7355i	0.325858	+	1.00289i	0.971052	+	0.238869i	$0.0767766\pi$
$349$	6.08753	+	18.7355i	0.325858	+	1.00289i	−0.645194	+	0.764019i	$0.723223\pi$
$350$	−2.82052	+	2.04923i	−0.150763	+	0.109536i
$351$		0			0
$352$	−2.01151	−	2.63701i	−0.107214	−	0.140553i
$353$	−3.55539			−0.189234			−0.0946171	−	0.995514i	$-0.530163\pi$
$353$	−3.55539			−0.189234			−0.0946171	+	0.995514i	$0.530163\pi$
$354$		0			0
$355$	−1.33167	−	4.09846i	−0.0706777	−	0.217524i
$356$	−1.02705	+	3.16093i	−0.0544334	+	0.167529i
$357$		0			0
$358$	7.33109	+	5.32635i	0.387460	+	0.281506i
$359$	7.97271	−	24.5375i	0.420784	−	1.29504i	−0.486190	−	0.873853i	$-0.661614\pi$
$359$	7.97271	−	24.5375i	0.420784	−	1.29504i	0.906974	−	0.421186i	$-0.138386\pi$
$360$		0			0
$361$	−8.13891	+	5.91326i	−0.428364	+	0.311224i
$362$	8.00000			0.420471
$363$		0			0
$364$	−17.5120			−0.917879
$365$	−4.85410	+	3.52671i	−0.254075	+	0.184597i
$366$		0			0
$367$	1.48093	−	4.55782i	0.0773037	−	0.237916i	−0.904936	−	0.425548i	$-0.860081\pi$
$367$	1.48093	−	4.55782i	0.0773037	−	0.237916i	0.982239	+	0.187632i	$0.0600813\pi$
$368$	−5.25468	−	3.81775i	−0.273919	−	0.199014i
$369$		0			0
$370$	2.73607	−	8.42075i	0.142241	−	0.437774i
$371$	4.54838	+	13.9985i	0.236140	+	0.726765i
$372$		0			0
$373$	20.7350			1.07362			0.536809	−	0.843704i	$-0.319630\pi$
$373$	20.7350			1.07362			0.536809	+	0.843704i	$0.319630\pi$
$374$	−7.58885	−	9.94872i	−0.392410	−	0.514436i
$375$		0			0
$376$	−9.70475	+	7.05091i	−0.500484	+	0.363623i
$377$	−4.45220	−	13.7025i	−0.229300	−	0.705713i
$378$		0			0
$379$	20.3026	+	14.7507i	1.04287	+	0.757693i	0.970845	−	0.239710i	$-0.0770522\pi$
$379$	20.3026	+	14.7507i	1.04287	+	0.757693i	0.0720301	+	0.997402i	$0.477052\pi$
$380$	4.36121	+	3.16861i	0.223725	+	0.162546i
$381$		0			0
$382$	−2.19076	−	6.74247i	−0.112089	−	0.344975i
$383$	13.8777	−	10.0827i	0.709117	−	0.515204i	−0.173772	−	0.984786i	$-0.555596\pi$
$383$	13.8777	−	10.0827i	0.709117	−	0.515204i	0.882889	+	0.469582i	$0.155596\pi$
$384$		0			0
$385$	−11.0773	−	3.31572i	−0.564554	−	0.168985i
$386$	−6.25480			−0.318361
$387$		0			0
$388$	2.08138	+	6.40583i	0.105666	+	0.325207i
$389$	−6.18006	+	19.0203i	−0.313341	+	0.964365i	0.663091	+	0.748539i	$0.269244\pi$
$389$	−6.18006	+	19.0203i	−0.313341	+	0.964365i	−0.976432	+	0.215826i	$0.930756\pi$
$390$		0			0
$391$	−19.8245	−	14.4033i	−1.00257	−	0.728407i
$392$	−1.59289	+	4.90240i	−0.0804529	+	0.247609i
$393$		0			0
$394$	12.6516	−	9.19194i	0.637379	−	0.463083i
$395$	10.7170			0.539230
$396$		0			0
$397$	−9.22209			−0.462843			−0.231422	−	0.972854i	$-0.574338\pi$
$397$	−9.22209			−0.462843			−0.231422	+	0.972854i	$0.574338\pi$
$398$	−9.69324	+	7.04255i	−0.485878	+	0.353011i
$399$		0			0
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	4.47983	+	3.25478i	0.223712	+	0.162536i	0.693996	−	0.719979i	$-0.255849\pi$
$401$	4.47983	+	3.25478i	0.223712	+	0.162536i	−0.470284	+	0.882515i	$0.655849\pi$
$402$		0			0
$403$	14.4982	−	44.6209i	0.722208	−	2.22273i
$404$	−0.0702330	−	0.216155i	−0.00349422	−	0.0107541i
$405$		0			0
$406$	−10.0000			−0.496292
$407$	27.7093	−	9.72333i	1.37350	−	0.481968i
$408$		0			0
$409$	10.8806	−	7.90520i	0.538010	−	0.390887i	−0.285336	−	0.958428i	$-0.592105\pi$
$409$	10.8806	−	7.90520i	0.538010	−	0.390887i	0.823345	+	0.567541i	$0.192105\pi$
$410$	1.79098	+	5.51207i	0.0884502	+	0.272222i
$411$		0			0
$412$	−7.59728	−	5.51975i	−0.374291	−	0.271938i
$413$	−0.204746	−	0.148756i	−0.0100749	−	0.00731982i
$414$		0			0
$415$	−0.472136	−	1.45309i	−0.0231762	−	0.0713291i
$416$	4.06370	−	2.95245i	0.199239	−	0.144756i
$417$		0			0
$418$	0.416941	+	17.8743i	0.0203932	+	0.874258i
$419$	22.3274			1.09076			0.545382	−	0.838187i	$-0.316384\pi$
$419$	22.3274			1.09076			0.545382	+	0.838187i	$0.316384\pi$
$420$		0			0
$421$	−5.94091	−	18.2843i	−0.289542	−	0.891120i	−0.985000	−	0.172553i	$-0.944798\pi$
$421$	−5.94091	−	18.2843i	−0.289542	−	0.891120i	0.695458	−	0.718567i	$-0.255202\pi$
$422$	0.828449	−	2.54971i	0.0403283	−	0.124118i
$423$		0			0
$424$	−3.41555	−	2.48154i	−0.165874	−	0.120514i
$425$	1.16583	−	3.58807i	0.0565513	−	0.174047i
$426$		0			0
$427$	−30.9488	+	22.4856i	−1.49772	+	1.08815i
$428$	−17.4909			−0.845453
$429$		0			0
$430$	3.93548			0.189786
$431$	6.99573	−	5.08269i	0.336972	−	0.244825i	−0.406411	−	0.913690i	$-0.633220\pi$
$431$	6.99573	−	5.08269i	0.336972	−	0.244825i	0.743383	+	0.668866i	$0.233220\pi$
$432$		0			0
$433$	5.27258	−	16.2273i	0.253384	−	0.779837i	−0.740759	−	0.671770i	$-0.765534\pi$
$433$	5.27258	−	16.2273i	0.253384	−	0.779837i	0.994144	−	0.108066i	$-0.0344658\pi$
$434$	−26.3450	−	19.1407i	−1.26460	−	0.918785i
$435$		0			0
$436$	−1.70820	+	5.25731i	−0.0818081	+	0.251780i
$437$	10.8198	+	33.3001i	0.517583	+	1.59296i
$438$		0			0
$439$	27.4202			1.30870			0.654348	−	0.756194i	$-0.272943\pi$
$439$	27.4202			1.30870			0.654348	+	0.756194i	$0.272943\pi$
$440$	3.12954	−	1.09817i	0.149195	−	0.0523533i
$441$		0			0
$442$	15.3312	−	11.1388i	0.729231	−	0.529818i
$443$	5.81803	+	17.9060i	0.276423	+	0.850742i	0.988839	+	0.148985i	$0.0476007\pi$
$443$	5.81803	+	17.9060i	0.276423	+	0.850742i	−0.712417	+	0.701757i	$0.752399\pi$
$444$		0			0
$445$	−2.68885	−	1.95356i	−0.127464	−	0.0926077i
$446$	3.22550	+	2.34346i	0.152732	+	0.110966i
$447$		0			0
$448$	−1.07734	−	3.31572i	−0.0508997	−	0.156653i
$449$	−7.92779	+	5.75988i	−0.374136	+	0.271825i	−0.758924	−	0.651179i	$-0.774275\pi$
$449$	−7.92779	+	5.75988i	−0.374136	+	0.271825i	0.384788	+	0.923005i	$0.374275\pi$
$450$		0			0
$451$	−10.9328	+	15.8104i	−0.514807	+	0.744482i
$452$	16.3132			0.767307
$453$		0			0
$454$	0.418041	+	1.28660i	0.0196196	+	0.0603830i
$455$	5.41151	−	16.6549i	0.253695	−	0.780794i
$456$		0			0
$457$	17.1132	+	12.4335i	0.800521	+	0.581612i	0.911067	−	0.412259i	$-0.135260\pi$
$457$	17.1132	+	12.4335i	0.800521	+	0.581612i	−0.110546	+	0.993871i	$0.535260\pi$
$458$	6.70013	−	20.6209i	0.313077	−	0.963550i
$459$		0			0
$460$	5.25468	−	3.81775i	0.245001	−	0.178004i
$461$	0.345449			0.0160892			0.00804459	−	0.999968i	$-0.497439\pi$
$461$	0.345449			0.0160892			0.00804459	+	0.999968i	$0.497439\pi$
$462$		0			0
$463$	14.3198			0.665496			0.332748	−	0.943016i	$-0.392024\pi$
$463$	14.3198			0.665496			0.332748	+	0.943016i	$0.392024\pi$
$464$	2.32052	−	1.68596i	0.107728	−	0.0782686i
$465$		0			0
$466$	−5.89515	+	18.1434i	−0.273088	+	0.840477i
$467$	−30.3592	−	22.0572i	−1.40486	−	1.02069i	−0.994045	−	0.108967i	$-0.965246\pi$
$467$	−30.3592	−	22.0572i	−1.40486	−	1.02069i	−0.410811	−	0.911721i	$-0.634754\pi$
$468$		0			0
$469$	−16.8909	+	51.9848i	−0.779949	+	2.40044i
$470$	−3.70688	−	11.4086i	−0.170986	−	0.526240i
$471$		0			0
$472$	0.0725914			0.00334129
$473$	7.91624	+	10.3779i	0.363989	+	0.477178i
$474$		0			0
$475$	−4.36121	+	3.16861i	−0.200106	+	0.145386i
$476$	−4.06452	−	12.5093i	−0.186297	−	0.573363i
$477$		0			0
$478$	−20.3262	−	14.7679i	−0.929700	−	0.675467i
$479$	33.4997	+	24.3389i	1.53064	+	1.11207i	0.955883	+	0.293749i	$0.0949031\pi$
$479$	33.4997	+	24.3389i	1.53064	+	1.11207i	0.574756	+	0.818325i	$0.305097\pi$
$480$		0			0
$481$	13.7433	+	42.2975i	0.626640	+	1.92860i
$482$	−0.334165	+	0.242785i	−0.0152208	+	0.0110586i
$483$		0			0
$484$	9.19098	+	6.04366i	0.417772	+	0.274712i
$485$	−6.73549			−0.305843
$486$		0			0
$487$	11.8994	+	36.6226i	0.539214	+	1.65953i	0.734364	+	0.678756i	$0.237480\pi$
$487$	11.8994	+	36.6226i	0.539214	+	1.65953i	−0.195151	+	0.980773i	$0.562520\pi$
$488$	3.39076	−	10.4357i	0.153492	−	0.472401i
$489$		0			0
$490$	−4.17023	−	3.02985i	−0.188392	−	0.136875i
$491$	−6.71567	+	20.6687i	−0.303074	+	0.932766i	0.677315	+	0.735693i	$0.263144\pi$
$491$	−6.71567	+	20.6687i	−0.303074	+	0.932766i	−0.980389	+	0.197073i	$0.936856\pi$
$492$		0			0
$493$	8.75468	−	6.36065i	0.394291	−	0.286469i
$494$	−27.0778			−1.21829
$495$		0			0
$496$	9.34046			0.419399
$497$	12.1547	−	8.83090i	0.545212	−	0.396120i
$498$		0			0
$499$	−7.37630	+	22.7019i	−0.330208	+	1.01628i	0.638826	+	0.769351i	$0.279420\pi$
$499$	−7.37630	+	22.7019i	−0.330208	+	1.01628i	−0.969034	+	0.246926i	$0.920580\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$		0			0
$502$	−3.69302	+	11.3659i	−0.164828	+	0.507287i
$503$	4.40630	+	13.5612i	0.196467	+	0.604664i	0.999956	+	0.00934428i	$0.00297442\pi$
$503$	4.40630	+	13.5612i	0.196467	+	0.604664i	−0.803489	+	0.595319i	$0.797026\pi$
$504$		0			0
$505$	0.227279			0.0101138
$506$	20.6373	+	6.17725i	0.917439	+	0.274612i
$507$		0			0
$508$	3.57427	−	2.59686i	0.158583	−	0.115217i
$509$	−5.70439	−	17.5563i	−0.252843	−	0.778169i	−0.994247	−	0.107111i	$-0.965840\pi$
$509$	−5.70439	−	17.5563i	−0.252843	−	0.778169i	0.741405	−	0.671058i	$-0.234160\pi$
$510$		0			0
$511$	−16.9231	−	12.2954i	−0.748635	−	0.543915i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$		0			0
$514$	−1.67376	−	5.15131i	−0.0738265	−	0.227215i
$515$	7.59728	−	5.51975i	0.334776	−	0.243229i
$516$		0			0
$517$	22.6283	−	32.7236i	0.995190	−	1.43918i
$518$	30.8686			1.35629
$519$		0			0
$520$	1.55220	+	4.77717i	0.0680683	+	0.209493i
$521$	6.44010	−	19.8206i	0.282146	−	0.868356i	−0.705094	−	0.709114i	$-0.749095\pi$
$521$	6.44010	−	19.8206i	0.282146	−	0.868356i	0.987240	−	0.159242i	$-0.0509049\pi$
$522$		0			0
$523$	1.21493	+	0.882698i	0.0531252	+	0.0385977i	0.614031	−	0.789282i	$-0.289547\pi$
$523$	1.21493	+	0.882698i	0.0531252	+	0.0385977i	−0.560906	+	0.827880i	$0.689547\pi$
$524$	0.405435	−	1.24780i	0.0177115	−	0.0545105i
$525$		0			0
$526$	23.4452	−	17.0339i	1.02226	−	0.742715i
$527$	35.2389			1.53503
$528$		0			0
$529$	19.1869			0.834214
$530$	3.41555	−	2.48154i	0.148362	−	0.107791i
$531$		0			0
$532$	−5.80770	+	17.8743i	−0.251796	+	0.774947i
$533$	−23.5521	−	17.1116i	−1.02016	−	0.741186i
$534$		0			0
$535$	5.40498	−	16.6348i	0.233678	−	0.719185i
$536$	−4.84485	−	14.9109i	−0.209266	−	0.644054i
$537$		0			0
$538$	−22.1504			−0.954972
$539$	−0.398682	−	17.0915i	−0.0171725	−	0.736184i
$540$		0			0
$541$	12.6510	−	9.19148i	0.543909	−	0.395173i	−0.281626	−	0.959524i	$-0.590874\pi$
$541$	12.6510	−	9.19148i	0.543909	−	0.395173i	0.825535	+	0.564352i	$0.190874\pi$
$542$	0.0790223	+	0.243206i	0.00339430	+	0.0104466i
$543$		0			0
$544$	3.05220	+	2.21755i	0.130862	+	0.0950767i
$545$	−4.47214	−	3.24920i	−0.191565	−	0.139180i
$546$		0			0
$547$	−14.3082	−	44.0361i	−0.611774	−	1.88285i	−0.440902	−	0.897555i	$-0.645342\pi$
$547$	−14.3082	−	44.0361i	−0.611774	−	1.88285i	−0.170872	−	0.985293i	$-0.554658\pi$
$548$	1.33474	−	0.969748i	0.0570174	−	0.0414256i
$549$		0			0
$550$	0.0773437	+	3.31572i	0.00329794	+	0.141383i
$551$	−15.4624			−0.658722
$552$		0			0
$553$	11.5459	+	35.5346i	0.490981	+	1.51108i
$554$	−6.66665	+	20.5178i	−0.283239	+	0.871720i
$555$		0			0
$556$	0.0105690	+	0.00767884i	0.000448226	+	0.000325655i
$557$	−10.0965	+	31.0737i	−0.427801	+	1.31664i	0.472486	+	0.881338i	$0.343357\pi$
$557$	−10.0965	+	31.0737i	−0.427801	+	1.31664i	−0.900287	+	0.435298i	$0.856643\pi$
$558$		0			0
$559$	−15.9926	+	11.6193i	−0.676416	+	0.491445i
$560$	3.48636			0.147325
$561$		0			0
$562$	10.9443			0.461656
$563$	−3.93548	+	2.85930i	−0.165861	+	0.120505i	−0.667619	−	0.744503i	$-0.732687\pi$
$563$	−3.93548	+	2.85930i	−0.165861	+	0.120505i	0.501759	+	0.865008i	$0.332687\pi$
$564$		0			0
$565$	−5.04105	+	15.5148i	−0.212078	+	0.652710i
$566$	2.96157	+	2.15170i	0.124484	+	0.0904429i
$567$		0			0
$568$	−1.33167	+	4.09846i	−0.0558756	+	0.171968i
$569$	−1.91387	−	5.89028i	−0.0802335	−	0.246933i	0.902891	−	0.429869i	$-0.141440\pi$
$569$	−1.91387	−	5.89028i	−0.0802335	−	0.246933i	−0.983125	+	0.182935i	$0.941440\pi$
$570$		0			0
$571$	−1.17841			−0.0493151			−0.0246575	−	0.999696i	$-0.507850\pi$
$571$	−1.17841			−0.0493151			−0.0246575	+	0.999696i	$0.507850\pi$
$572$	−9.47521	+	13.7025i	−0.396178	+	0.572929i
$573$		0			0
$574$	−16.3470	+	11.8768i	−0.682310	+	0.495727i
$575$	2.00711	+	6.17725i	0.0837023	+	0.257609i
$576$		0			0
$577$	−6.75850	−	4.91034i	−0.281360	−	0.204420i	0.438150	−	0.898902i	$-0.355634\pi$
$577$	−6.75850	−	4.91034i	−0.281360	−	0.204420i	−0.719510	+	0.694482i	$0.755634\pi$
$578$	−2.23821	−	1.62615i	−0.0930971	−	0.0676390i
$579$		0			0
$580$	0.886361	+	2.72794i	0.0368041	+	0.113271i
$581$	4.30937	−	3.13094i	0.178783	−	0.129893i
$582$		0			0
$583$	13.4142	+	4.01521i	0.555561	+	0.166293i
$584$	6.00000			0.248282
$585$		0			0
$586$	−3.40901	−	10.4919i	−0.140825	−	0.433415i
$587$	6.78623	−	20.8859i	0.280098	−	0.862052i	−0.707728	−	0.706485i	$-0.750280\pi$
$587$	6.78623	−	20.8859i	0.280098	−	0.862052i	0.987825	−	0.155567i	$-0.0497203\pi$
$588$		0			0
$589$	−40.7357	−	29.5962i	−1.67849	−	1.21949i
$590$	−0.0224320	+	0.0690385i	−0.000923510	+	0.00284227i
$591$		0			0
$592$	−7.16312	+	5.20431i	−0.294402	+	0.213896i
$593$	10.3677			0.425752			0.212876	−	0.977079i	$-0.431717\pi$
$593$	10.3677			0.425752			0.212876	+	0.977079i	$0.431717\pi$
$594$		0			0
$595$	13.1531			0.539223
$596$	−6.65601	+	4.83587i	−0.272641	+	0.198085i
$597$		0			0
$598$	−10.0817	+	31.0284i	−0.412273	+	1.26885i
$599$	16.6740	+	12.1144i	0.681281	+	0.494980i	0.873782	−	0.486317i	$-0.161660\pi$
$599$	16.6740	+	12.1144i	0.681281	+	0.494980i	−0.192501	+	0.981297i	$0.561660\pi$
$600$		0			0
$601$	−12.5937	+	38.7594i	−0.513707	+	1.58103i	0.271915	+	0.962321i	$0.412343\pi$
$601$	−12.5937	+	38.7594i	−0.513707	+	1.58103i	−0.785622	+	0.618707i	$0.787657\pi$
$602$	4.23987	+	13.0490i	0.172804	+	0.531836i
$603$		0			0
$604$	−0.191204			−0.00777998
$605$	−8.58803	+	6.87355i	−0.349153	+	0.279450i
$606$		0			0
$607$	4.24486	−	3.08407i	0.172293	−	0.125179i	−0.498297	−	0.867007i	$-0.666041\pi$
$607$	4.24486	−	3.08407i	0.172293	−	0.125179i	0.670590	+	0.741828i	$0.266041\pi$
$608$	−1.66583	−	5.12691i	−0.0675585	−	0.207924i
$609$		0			0
$610$	8.87711	+	6.44960i	0.359424	+	0.261137i
$611$	48.7470	+	35.4168i	1.97209	+	1.43281i
$612$		0			0
$613$	−12.1919	−	37.5229i	−0.492427	−	1.51553i	−0.820929	−	0.571031i	$-0.806544\pi$
$613$	−12.1919	−	37.5229i	−0.492427	−	1.51553i	0.328502	−	0.944503i	$-0.393456\pi$
$614$	−3.47521	+	2.52489i	−0.140248	+	0.101896i
$615$		0			0
$616$	7.01283	+	9.19358i	0.282555	+	0.370420i
$617$	−23.2275			−0.935105			−0.467552	−	0.883965i	$-0.654864\pi$
$617$	−23.2275			−0.935105			−0.467552	+	0.883965i	$0.654864\pi$
$618$		0			0
$619$	−6.28723	−	19.3501i	−0.252705	−	0.777746i	−0.994273	−	0.106868i	$-0.965918\pi$
$619$	−6.28723	−	19.3501i	−0.252705	−	0.777746i	0.741568	−	0.670877i	$-0.234082\pi$
$620$	−2.88636	+	8.88330i	−0.115919	+	0.356762i
$621$		0			0
$622$	17.7684	+	12.9095i	0.712450	+	0.517625i
$623$	3.58066	−	11.0201i	0.143456	−	0.441512i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	13.7827			0.550866
$627$		0			0
$628$	−19.1822			−0.765454
$629$	−27.0245	+	19.6344i	−1.07754	+	0.782875i
$630$		0			0
$631$	−0.816411	+	2.51266i	−0.0325008	+	0.100027i	−0.965991	−	0.258576i	$-0.916747\pi$
$631$	−0.816411	+	2.51266i	−0.0325008	+	0.100027i	0.933490	+	0.358603i	$0.116747\pi$
$632$	−8.67023	−	6.29929i	−0.344883	−	0.250572i
$633$		0			0
$634$	0.165972	−	0.510808i	0.00659157	−	0.0202868i
$635$	1.36525	+	4.20181i	0.0541783	+	0.166744i
$636$		0			0
$637$	25.8920			1.02588
$638$	−5.41069	+	7.82461i	−0.214211	+	0.309779i
$639$		0			0
$640$	−0.809017	+	0.587785i	−0.0319792	+	0.0232343i
$641$	−10.0079	−	30.8012i	−0.395289	−	1.21658i	−0.928736	−	0.370742i	$-0.879103\pi$
$641$	−10.0079	−	30.8012i	−0.395289	−	1.21658i	0.533447	−	0.845834i	$-0.320897\pi$
$642$		0			0
$643$	14.1163	+	10.2561i	0.556691	+	0.404459i	0.830246	−	0.557397i	$-0.188200\pi$
$643$	14.1163	+	10.2561i	0.556691	+	0.404459i	−0.273556	+	0.961856i	$0.588200\pi$
$644$	18.3197	+	13.3100i	0.721898	+	0.524489i
$645$		0			0
$646$	−6.28473	−	19.3424i	−0.247269	−	0.761017i
$647$	−10.7305	+	7.79614i	−0.421858	+	0.306498i	−0.778385	−	0.627787i	$-0.783961\pi$
$647$	−10.7305	+	7.79614i	−0.421858	+	0.306498i	0.356527	+	0.934285i	$0.383961\pi$
$648$		0			0
$649$	−0.227178	+	0.0797179i	−0.00891750	+	0.00312920i
$650$	−5.02301			−0.197019
$651$		0			0
$652$	6.60689	+	20.3339i	0.258746	+	0.796337i
$653$	−11.6490	+	35.8518i	−0.455859	+	1.40299i	0.414264	+	0.910157i	$0.364039\pi$
$653$	−11.6490	+	35.8518i	−0.455859	+	1.40299i	−0.870123	+	0.492834i	$0.835961\pi$
$654$		0			0
$655$	1.06144	+	0.771184i	0.0414740	+	0.0301327i
$656$	1.79098	−	5.51207i	0.0699260	−	0.215210i
$657$		0			0
$658$	33.8342	−	24.5820i	1.31899	−	0.958306i
$659$	−5.81331			−0.226454			−0.113227	−	0.993569i	$-0.536119\pi$
$659$	−5.81331			−0.226454			−0.113227	+	0.993569i	$0.536119\pi$
$660$		0			0
$661$	14.9727			0.582371			0.291186	−	0.956667i	$-0.405950\pi$
$661$	14.9727			0.582371			0.291186	+	0.956667i	$0.405950\pi$
$662$	25.5558	−	18.5674i	0.993253	−	0.721641i
$663$		0			0
$664$	−0.472136	+	1.45309i	−0.0183224	+	0.0563906i
$665$	−15.2047	−	11.0469i	−0.589615	−	0.428380i
$666$		0			0
$667$	−5.75704	+	17.7184i	−0.222914	+	0.686057i
$668$	−6.47081	−	19.9151i	−0.250363	−	0.770539i
$669$		0			0
$670$	15.6783			0.605705
$671$	0.848670	+	36.3825i	0.0327625	+	1.40453i
$672$		0			0
$673$	−8.81687	+	6.40583i	−0.339865	+	0.246927i	−0.744605	−	0.667505i	$-0.767362\pi$
$673$	−8.81687	+	6.40583i	−0.339865	+	0.246927i	0.404740	+	0.914432i	$0.367362\pi$
$674$	3.66833	+	11.2900i	0.141299	+	0.434873i
$675$		0			0
$676$	−9.89479	−	7.18899i	−0.380569	−	0.276500i
$677$	−17.7324	−	12.8833i	−0.681510	−	0.495146i	0.192348	−	0.981327i	$-0.438390\pi$
$677$	−17.7324	−	12.8833i	−0.681510	−	0.495146i	−0.873858	+	0.486180i	$0.838390\pi$
$678$		0			0
$679$	−7.25644	−	22.3330i	−0.278476	−	0.857062i
$680$	−3.05220	+	2.21755i	−0.117046	+	0.0850392i
$681$		0			0
$682$	−29.2313	+	10.2574i	−1.11933	+	0.392778i
$683$	31.7105			1.21337			0.606685	−	0.794943i	$-0.292499\pi$
$683$	31.7105			1.21337			0.606685	+	0.794943i	$0.292499\pi$
$684$		0			0
$685$	0.509827	+	1.56909i	0.0194795	+	0.0599517i
$686$	−1.98804	+	6.11855i	−0.0759036	+	0.233607i
$687$		0			0
$688$	−3.18387	−	2.31322i	−0.121384	−	0.0881906i
$689$	−6.55313	+	20.1685i	−0.249654	+	0.768357i
$690$		0			0
$691$	37.3662	−	27.1481i	1.42148	−	1.03276i	0.429952	−	0.902852i	$-0.358531\pi$
$691$	37.3662	−	27.1481i	1.42148	−	1.03276i	0.991526	−	0.129912i	$-0.0414695\pi$
$692$	−4.55966			−0.173332
$693$		0			0
$694$	−7.54401			−0.286367
$695$	−0.0105690	+	0.00767884i	−0.000400905	+	0.000291275i
$696$		0			0
$697$	6.75687	−	20.7955i	0.255935	−	0.787686i
$698$	15.9374	+	11.5792i	0.603238	+	0.438278i
$699$		0			0
$700$	−1.07734	+	3.31572i	−0.0407198	+	0.125323i
$701$	−13.6624	−	42.0486i	−0.516023	−	1.58815i	−0.781414	−	0.624013i	$-0.785501\pi$
$701$	−13.6624	−	42.0486i	−0.516023	−	1.58815i	0.265391	−	0.964141i	$-0.414499\pi$
$702$		0			0
$703$	47.7303			1.80018
$704$	−3.17734	−	0.951057i	−0.119751	−	0.0358443i
$705$		0			0
$706$	−2.87637	+	2.08981i	−0.108254	+	0.0786509i
$707$	0.244857	+	0.753593i	0.00920881	+	0.0283418i
$708$		0			0
$709$	4.75850	+	3.45725i	0.178709	+	0.129840i	0.673544	−	0.739147i	$-0.264771\pi$
$709$	4.75850	+	3.45725i	0.178709	+	0.129840i	−0.494834	+	0.868987i	$0.664771\pi$
$710$	−3.48636	−	2.53299i	−0.130841	−	0.0950613i
$711$		0			0
$712$	1.02705	+	3.16093i	0.0384902	+	0.118461i
$713$	−49.0812	+	35.6596i	−1.83810	+	1.33546i
$714$		0			0
$715$	−10.1038	−	13.2458i	−0.377861	−	0.495363i
$716$	9.06173			0.338653
$717$		0			0
$718$	−7.97271	−	24.5375i	−0.297539	−	0.915731i
$719$	6.46670	−	19.9025i	0.241167	−	0.742237i	−0.755076	−	0.655637i	$-0.772400\pi$
$719$	6.46670	−	19.9025i	0.241167	−	0.742237i	0.996243	−	0.0865994i	$-0.0276000\pi$
$720$		0			0
$721$	26.4868	+	19.2438i	0.986421	+	0.716677i
$722$	−3.10879	+	9.56786i	−0.115697	+	0.356079i
$723$		0			0
$724$	6.47214	−	4.70228i	0.240535	−	0.174759i
$725$	−2.86832			−0.106527
$726$		0			0
$727$	23.2667			0.862915			0.431457	−	0.902133i	$-0.358000\pi$
$727$	23.2667			0.862915			0.431457	+	0.902133i	$0.358000\pi$
$728$	−14.1675	+	10.2933i	−0.525083	+	0.381495i
$729$		0			0
$730$	−1.85410	+	5.70634i	−0.0686234	+	0.211201i
$731$	−12.0119	−	8.72713i	−0.444275	−	0.322785i
$732$		0			0
$733$	−15.2173	+	46.8340i	−0.562063	+	1.72985i	0.114456	+	0.993428i	$0.463488\pi$
$733$	−15.2173	+	46.8340i	−0.562063	+	1.72985i	−0.676519	+	0.736425i	$0.736512\pi$
$734$	−1.48093	−	4.55782i	−0.0546619	−	0.168232i
$735$		0			0
$736$	−6.49515			−0.239414
$737$	31.5369	+	41.3438i	1.16168	+	1.52292i
$738$		0			0
$739$	6.67890	−	4.85250i	0.245687	−	0.178502i	−0.458126	−	0.888887i	$-0.651479\pi$
$739$	6.67890	−	4.85250i	0.245687	−	0.178502i	0.703813	+	0.710385i	$0.251479\pi$
$740$	−2.73607	−	8.42075i	−0.100580	−	0.309553i
$741$		0			0
$742$	11.9078	+	8.65153i	0.437150	+	0.317608i
$743$	−4.28267	−	3.11154i	−0.157116	−	0.114151i	0.506450	−	0.862270i	$-0.330958\pi$
$743$	−4.28267	−	3.11154i	−0.157116	−	0.114151i	−0.663566	+	0.748118i	$0.730958\pi$
$744$		0			0
$745$	−2.54237	−	7.82461i	−0.0931452	−	0.286671i
$746$	16.7750	−	12.1877i	0.614176	−	0.446225i
$747$		0			0
$748$	−11.9872	−	3.58807i	−0.438296	−	0.131193i
$749$	60.9794			2.22814
$750$		0			0
$751$	−4.29751	−	13.2264i	−0.156818	−	0.482637i	0.841522	−	0.540223i	$-0.181660\pi$
$751$	−4.29751	−	13.2264i	−0.156818	−	0.482637i	−0.998341	+	0.0575851i	$0.981660\pi$
$752$	−3.70688	+	11.4086i	−0.135176	+	0.416029i
$753$		0			0
$754$	−11.6560	−	8.46859i	−0.424487	−	0.308408i
$755$	0.0590853	−	0.181846i	0.00215033	−	0.00661805i
$756$		0			0
$757$	2.37308	−	1.72414i	0.0862509	−	0.0626649i	−0.543824	−	0.839199i	$-0.683024\pi$
$757$	2.37308	−	1.72414i	0.0862509	−	0.0626649i	0.630075	+	0.776534i	$0.283024\pi$
$758$	25.0954			0.911506
$759$		0			0
$760$	5.39076			0.195543
$761$	−6.77964	+	4.92570i	−0.245762	+	0.178556i	−0.703846	−	0.710352i	$-0.748536\pi$
$761$	−6.77964	+	4.92570i	−0.245762	+	0.178556i	0.458085	+	0.888909i	$0.348536\pi$
$762$		0			0
$763$	5.95541	−	18.3289i	0.215600	−	0.663549i
$764$	−5.73549	−	4.16708i	−0.207503	−	0.150760i
$765$		0			0
$766$	5.30081	−	16.3142i	0.191526	−	0.589456i
$767$	−0.112676	−	0.346781i	−0.00406850	−	0.0125215i
$768$		0			0
$769$	7.26935			0.262140			0.131070	−	0.991373i	$-0.458159\pi$
$769$	7.26935			0.262140			0.131070	+	0.991373i	$0.458159\pi$
$770$	−10.9107	+	3.82862i	−0.393194	+	0.137974i
$771$		0			0
$772$	−5.06024	+	3.67648i	−0.182122	+	0.132319i
$773$	−4.34185	−	13.3629i	−0.156166	−	0.480628i	0.842111	−	0.539303i	$-0.181312\pi$
$773$	−4.34185	−	13.3629i	−0.156166	−	0.480628i	−0.998277	+	0.0586750i	$0.981312\pi$
$774$		0			0
$775$	−7.55659	−	5.49018i	−0.271441	−	0.197213i
$776$	5.44913	+	3.95902i	0.195612	+	0.142121i
$777$		0			0
$778$	6.18006	+	19.0203i	0.221566	+	0.681909i
$779$	−25.2764	+	18.3644i	−0.905622	+	0.657973i
$780$		0			0
$781$	−0.333303	−	14.2887i	−0.0119265	−	0.511290i
$782$	−24.5044			−0.876275
$783$		0			0
$784$	1.59289	+	4.90240i	0.0568888	+	0.175086i
$785$	5.92763	−	18.2434i	0.211566	−	0.651134i
$786$		0			0
$787$	−20.0778	−	14.5874i	−0.715698	−	0.519985i	0.169309	−	0.985563i	$-0.445846\pi$
$787$	−20.0778	−	14.5874i	−0.715698	−	0.519985i	−0.885007	+	0.465578i	$0.845846\pi$
$788$	4.83249	−	14.8729i	0.172150	−	0.529824i
$789$		0			0
$790$	8.67023	−	6.29929i	0.308473	−	0.224119i
$791$	−56.8736			−2.02219
$792$		0			0
$793$	−55.1161			−1.95723
$794$	−7.46082	+	5.42061i	−0.264775	+	0.192370i
$795$		0			0
$796$	−3.70249	+	11.3951i	−0.131231	+	0.403888i
$797$	−11.7159	−	8.51209i	−0.414998	−	0.301514i	0.360624	−	0.932711i	$-0.382564\pi$
$797$	−11.7159	−	8.51209i	−0.414998	−	0.301514i	−0.775622	+	0.631197i	$0.782564\pi$
$798$		0			0
$799$	−13.9850	+	43.0415i	−0.494755	+	1.52270i
$800$	−0.309017	−	0.951057i	−0.0109254	−	0.0336249i
$801$		0			0
$802$	5.53737			0.195531
$803$	−18.7772	+	6.58904i	−0.662634	+	0.232522i
$804$		0			0
$805$	−18.3197	+	13.3100i	−0.645685	+	0.469117i
$806$	−14.4982	−	44.6209i	−0.510678	−	1.57171i
$807$		0			0
$808$	−0.183872	−	0.133591i	−0.00646861	−	0.00469972i
$809$	−21.1869	−	15.3932i	−0.744891	−	0.541195i	0.149348	−	0.988785i	$-0.452282\pi$
$809$	−21.1869	−	15.3932i	−0.744891	−	0.541195i	−0.894239	+	0.447590i	$0.852282\pi$
$810$		0			0
$811$	1.04554	+	3.21785i	0.0367140	+	0.112994i	0.967734	−	0.251974i	$-0.0810798\pi$
$811$	1.04554	+	3.21785i	0.0367140	+	0.112994i	−0.931020	+	0.364968i	$0.881080\pi$
$812$	−8.09017	+	5.87785i	−0.283909	+	0.206272i
$813$		0			0
$814$	16.7020	−	24.1534i	0.585406	−	0.846578i
$815$	−21.3803			−0.748920
$816$		0			0
$817$	6.55586	+	20.1769i	0.229361	+	0.705900i
$818$	4.15601	−	12.7909i	0.145311	−	0.447223i
$819$		0			0
$820$	4.68885	+	3.40665i	0.163742	+	0.118965i
$821$	1.13447	−	3.49153i	0.0395932	−	0.121855i	−0.929306	−	0.369310i	$-0.879594\pi$
$821$	1.13447	−	3.49153i	0.0395932	−	0.121855i	0.968899	+	0.247455i	$0.0795941\pi$
$822$		0			0
$823$	14.6061	−	10.6119i	0.509136	−	0.369909i	−0.303360	−	0.952876i	$-0.598108\pi$
$823$	14.6061	−	10.6119i	0.509136	−	0.369909i	0.812496	+	0.582967i	$0.198108\pi$
$824$	−9.39076			−0.327142
$825$		0			0
$826$	−0.253079			−0.00880576
$827$	−40.7818	+	29.6297i	−1.41812	+	1.03032i	−0.426042	+	0.904703i	$0.640092\pi$
$827$	−40.7818	+	29.6297i	−1.41812	+	1.03032i	−0.992078	+	0.125621i	$0.959908\pi$
$828$		0			0
$829$	5.47493	−	16.8501i	0.190152	−	0.585228i	−0.809847	−	0.586641i	$-0.800450\pi$
$829$	5.47493	−	16.8501i	0.190152	−	0.585228i	0.999999	+	0.00141339i	$0.000449897\pi$
$830$	−1.23607	−	0.898056i	−0.0429045	−	0.0311720i
$831$		0			0
$832$	1.55220	−	4.77717i	0.0538127	−	0.165618i
$833$	6.00951	+	18.4954i	0.208217	+	0.640827i
$834$		0			0
$835$	20.9400			0.724658
$836$	10.8435	+	14.2155i	0.375031	+	0.491653i
$837$		0			0
$838$	18.0632	−	13.1237i	0.623984	−	0.453351i
$839$	10.0072	+	30.7989i	0.345485	+	1.06329i	0.961323	+	0.275422i	$0.0888176\pi$
$839$	10.0072	+	30.7989i	0.345485	+	1.06329i	−0.615838	+	0.787873i	$0.711182\pi$
$840$		0			0
$841$	16.8055	+	12.2099i	0.579499	+	0.421031i
$842$	−15.5535	−	11.3003i	−0.536010	−	0.389434i
$843$		0			0
$844$	−0.828449	−	2.54971i	−0.0285164	−	0.0877645i
$845$	9.89479	−	7.18899i	0.340391	−	0.247309i
$846$		0			0
$847$	−32.0431	−	21.0704i	−1.10101	−	0.723986i
$848$	−4.22185			−0.144979
$849$		0			0
$850$	−1.16583	−	3.58807i	−0.0399878	−	0.123070i
$851$	17.7712	−	54.6940i	0.609188	−	1.87489i
$852$		0			0
$853$	−32.4104	−	23.5475i	−1.10971	−	0.806251i	−0.127092	−	0.991891i	$-0.540564\pi$
$853$	−32.4104	−	23.5475i	−1.10971	−	0.806251i	−0.982618	+	0.185640i	$0.940564\pi$
$854$	−11.8214	+	36.3825i	−0.404519	+	1.24498i
$855$		0			0
$856$	−14.1504	+	10.2809i	−0.483651	+	0.351393i
$857$	−31.8187			−1.08691			−0.543454	−	0.839439i	$-0.682884\pi$
$857$	−31.8187			−1.08691			−0.543454	+	0.839439i	$0.682884\pi$
$858$		0			0
$859$	−37.5377			−1.28077			−0.640384	−	0.768055i	$-0.721225\pi$
$859$	−37.5377			−1.28077			−0.640384	+	0.768055i	$0.721225\pi$
$860$	3.18387	−	2.31322i	0.108569	−	0.0788801i
$861$		0			0
$862$	2.67213	−	8.22397i	0.0910131	−	0.280109i
$863$	−37.5795	−	27.3031i	−1.27922	−	0.929409i	−0.279693	−	0.960090i	$-0.590233\pi$
$863$	−37.5795	−	27.3031i	−1.27922	−	0.929409i	−0.999529	+	0.0306804i	$0.990233\pi$
$864$		0			0
$865$	1.40901	−	4.33650i	0.0479079	−	0.147445i
$866$	−5.27258	−	16.2273i	−0.179170	−	0.551428i
$867$		0			0
$868$	−32.5642			−1.10530
$869$	34.0515	+	10.1925i	1.15512	+	0.345756i
$870$		0			0
$871$	−63.7118	+	46.2894i	−2.15879	+	1.56845i
$872$	1.70820	+	5.25731i	0.0578471	+	0.178035i
$873$		0			0
$874$	28.3267	+	20.5806i	0.958165	+	0.696148i
$875$	−2.82052	−	2.04923i	−0.0953511	−	0.0692766i
$876$		0			0
$877$	17.0182	+	52.3765i	0.574662	+	1.76863i	0.637326	+	0.770594i	$0.280040\pi$
$877$	17.0182	+	52.3765i	0.574662	+	1.76863i	−0.0626639	+	0.998035i	$0.519960\pi$
$878$	22.1834	−	16.1172i	0.748654	−	0.543929i
$879$		0			0
$880$	1.88636	−	2.72794i	0.0635892	−	0.0919588i
$881$	43.4494			1.46385			0.731923	−	0.681387i	$-0.238623\pi$
$881$	43.4494			1.46385			0.731923	+	0.681387i	$0.238623\pi$
$882$		0			0
$883$	−14.3834	−	44.2676i	−0.484040	−	1.48972i	−0.833366	−	0.552721i	$-0.813589\pi$
$883$	−14.3834	−	44.2676i	−0.484040	−	1.48972i	0.349326	−	0.937001i	$-0.386411\pi$
$884$	5.85600	−	18.0229i	0.196959	−	0.606176i
$885$		0			0
$886$	15.2318	+	11.0665i	0.511722	+	0.371788i
$887$	−6.60213	+	20.3193i	−0.221678	+	0.682255i	0.776934	+	0.629582i	$0.216774\pi$
$887$	−6.60213	+	20.3193i	−0.221678	+	0.682255i	−0.998612	+	0.0526724i	$0.983226\pi$
$888$		0			0
$889$	−12.4612	+	9.05358i	−0.417935	+	0.303647i
$890$	−3.32360			−0.111407
$891$		0			0
$892$	3.98694			0.133492
$893$	52.3159	−	38.0097i	1.75069	−	1.27195i
$894$		0			0
$895$	−2.80023	+	8.61821i	−0.0936013	+	0.288075i
$896$	−2.82052	−	2.04923i	−0.0942270	−	0.0684599i
$897$		0			0
$898$	−3.02815	+	9.31968i	−0.101051	+	0.311002i
$899$	−8.27902	−	25.4802i	−0.276121	−	0.849812i
$900$		0			0
$901$	−15.9279			−0.530634
$902$	0.448263	+	19.2170i	0.0149255	+	0.639857i
$903$		0			0
$904$	13.1976	−	9.58864i	0.438947	−	0.318914i
$905$	2.47214	+	7.60845i	0.0821766	+	0.252914i
$906$		0			0
$907$	−13.5058	−	9.81256i	−0.448454	−	0.325821i	0.340531	−	0.940233i	$-0.389393\pi$
$907$	−13.5058	−	9.81256i	−0.448454	−	0.325821i	−0.788985	+	0.614412i	$0.789393\pi$
$908$	1.09444	+	0.795161i	0.0363204	+	0.0263883i
$909$		0			0
$910$	−5.41151	−	16.6549i	−0.179390	−	0.552105i
$911$	−8.60381	+	6.25104i	−0.285057	+	0.207106i	−0.721120	−	0.692810i	$-0.756372\pi$
$911$	−8.60381	+	6.25104i	−0.285057	+	0.207106i	0.436063	+	0.899916i	$0.356372\pi$
$912$		0			0
$913$	−0.118171	−	5.06597i	−0.00391088	−	0.167659i
$914$	21.1531			0.699681
$915$		0			0
$916$	−6.70013	−	20.6209i	−0.221379	−	0.681333i
$917$	−1.41349	+	4.35028i	−0.0466776	+	0.143659i
$918$		0			0
$919$	−41.3557	−	30.0466i	−1.36420	−	0.991147i	−0.998165	−	0.0605452i	$-0.980716\pi$
$919$	−41.3557	−	30.0466i	−1.36420	−	0.991147i	−0.366032	−	0.930602i	$-0.619284\pi$
$920$	2.00711	−	6.17725i	0.0661725	−	0.203658i
$921$		0			0
$922$	0.279474	−	0.203050i	0.00920400	−	0.00668710i
$923$	21.6460			0.712488
$924$		0			0
$925$	8.85410			0.291121
$926$	11.5849	−	8.41695i	0.380704	−	0.276598i
$927$		0			0
$928$	0.886361	−	2.72794i	0.0290962	−	0.0895489i
$929$	28.1114	+	20.4241i	0.922305	+	0.670094i	0.944097	−	0.329669i	$-0.106937\pi$
$929$	28.1114	+	20.4241i	0.922305	+	0.670094i	−0.0217916	+	0.999763i	$0.506937\pi$
$930$		0			0
$931$	8.58686	−	26.4276i	0.281423	−	0.866131i
$932$	5.89515	+	18.1434i	0.193102	+	0.594307i
$933$		0			0
$934$	−37.5260			−1.22789
$935$	7.11671	−	10.2917i	0.232741	−	0.336576i
$936$		0			0
$937$	7.38648	−	5.36659i	0.241306	−	0.175319i	−0.460559	−	0.887629i	$-0.652351\pi$
$937$	7.38648	−	5.36659i	0.241306	−	0.175319i	0.701865	+	0.712310i	$0.252351\pi$
$938$	16.8909	+	51.9848i	0.551507	+	1.69736i
$939$		0			0
$940$	−9.70475	−	7.05091i	−0.316534	−	0.229975i
$941$	−23.6555	−	17.1868i	−0.771149	−	0.560272i	0.131161	−	0.991361i	$-0.458130\pi$
$941$	−23.6555	−	17.1868i	−0.771149	−	0.560272i	−0.902310	+	0.431089i	$0.858130\pi$
$942$		0			0
$943$	11.6327	+	35.8017i	0.378812	+	1.16586i
$944$	0.0587277	−	0.0426681i	0.00191142	−	0.00138873i
$945$		0			0
$946$	12.5044	+	3.74287i	0.406552	+	0.121691i
$947$	1.45043			0.0471327			0.0235663	−	0.999722i	$-0.492498\pi$
$947$	1.45043			0.0471327			0.0235663	+	0.999722i	$0.492498\pi$
$948$		0			0
$949$	−9.31317	−	28.6630i	−0.302318	−	0.930440i
$950$	−1.66583	+	5.12691i	−0.0540468	+	0.166339i
$951$		0			0
$952$	−10.6410	−	7.73117i	−0.344878	−	0.250569i
$953$	1.79738	−	5.53175i	0.0582227	−	0.179191i	−0.917716	−	0.397238i	$-0.869969\pi$
$953$	1.79738	−	5.53175i	0.0582227	−	0.179191i	0.975938	+	0.218047i	$0.0699687\pi$
$954$		0			0
$955$	5.73549	−	4.16708i	0.185596	−	0.134843i
$956$	−25.1246			−0.812588
$957$		0			0
$958$	41.4079			1.33783
$959$	−4.65339	+	3.38089i	−0.150266	+	0.109175i
$960$		0			0
$961$	17.3804	−	53.4914i	0.560658	−	1.72553i
$962$	35.9804	+	26.1413i	1.16006	+	0.842830i
$963$		0			0
$964$	−0.127640	+	0.392835i	−0.00411100	+	0.0126523i
$965$	−1.93284	−	5.94867i	−0.0622203	−	0.191495i
$966$		0			0
$967$	36.1447			1.16234			0.581168	−	0.813784i	$-0.302596\pi$
$967$	36.1447			1.16234			0.581168	+	0.813784i	$0.302596\pi$
$968$	10.9880	−	0.512900i	0.353169	−	0.0164852i
$969$		0			0
$970$	−5.44913	+	3.95902i	−0.174961	+	0.127117i
$971$	−12.1680	−	37.4491i	−0.390488	−	1.20180i	−0.932420	−	0.361377i	$-0.882307\pi$
$971$	−12.1680	−	37.4491i	−0.390488	−	1.20180i	0.541932	−	0.840423i	$-0.317693\pi$
$972$		0			0
$973$	−0.0368473	−	0.0267712i	−0.00118127	−	0.000858244i
$974$	31.1531	+	22.6340i	0.998208	+	0.725241i
$975$		0			0
$976$	−3.39076	−	10.4357i	−0.108535	−	0.334038i
$977$	18.7995	−	13.6587i	0.601450	−	0.436979i	−0.244943	−	0.969537i	$-0.578769\pi$
$977$	18.7995	−	13.6587i	0.601450	−	0.436979i	0.846393	+	0.532558i	$0.178769\pi$
$978$		0			0
$979$	−6.68543	−	8.76437i	−0.213667	−	0.280111i
$980$	−5.15469			−0.164660
$981$		0			0
$982$	6.71567	+	20.6687i	0.214306	+	0.659565i
$983$	−2.03411	+	6.26035i	−0.0648781	+	0.199674i	−0.978241	−	0.207472i	$-0.933476\pi$
$983$	−2.03411	+	6.26035i	−0.0648781	+	0.199674i	0.913363	+	0.407147i	$0.133476\pi$
$984$		0			0
$985$	12.6516	+	9.19194i	0.403114	+	0.292879i
$986$	3.34399	−	10.2917i	0.106494	−	0.327756i
$987$		0			0
$988$	−21.9064	+	15.9159i	−0.696936	+	0.506354i
$989$	25.5615			0.812810
$990$		0			0
$991$	−36.1457			−1.14821			−0.574103	−	0.818783i	$-0.694649\pi$
$991$	−36.1457			−1.14821			−0.574103	+	0.818783i	$0.694649\pi$
$992$	7.55659	−	5.49018i	0.239922	−	0.174314i
$993$		0			0
$994$	4.64268	−	14.2887i	0.147257	−	0.453210i
$995$	−9.69324	−	7.04255i	−0.307296	−	0.223264i
$996$		0			0
$997$	12.0278	−	37.0178i	0.380925	−	1.17237i	−0.558469	−	0.829525i	$-0.688611\pi$
$997$	12.0278	−	37.0178i	0.380925	−	1.17237i	0.939394	−	0.342840i	$-0.111389\pi$
$998$	7.37630	+	22.7019i	0.233493	+	0.718616i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.k.91.1		8
3.2	odd	2		330.2.m.e.91.1	✓	8
11.4	even	5	inner	990.2.n.k.631.1		8
33.2	even	10		3630.2.a.br.1.4		4
33.20	odd	10		3630.2.a.bt.1.1		4
33.26	odd	10		330.2.m.e.301.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.e.91.1	✓	8	3.2	odd	2
330.2.m.e.301.1	yes	8	33.26	odd	10
990.2.n.k.91.1		8	1.1	even	1	trivial
990.2.n.k.631.1		8	11.4	even	5	inner
3630.2.a.br.1.4		4	33.2	even	10
3630.2.a.bt.1.1		4	33.20	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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.809017 + 0.587785i) q^{5} +(-1.07734 + 3.31572i) q^{7} +(-0.309017 - 0.951057i) q^{8} +1.00000 q^{10} +(2.01151 + 2.63701i) q^{11} +(-4.06370 + 2.95245i) q^{13} +(1.07734 + 3.31572i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-3.05220 - 2.21755i) q^{17} +(1.66583 + 5.12691i) q^{19} +(0.809017 - 0.587785i) q^{20} +(3.17734 + 0.951057i) q^{22} +6.49515 q^{23} +(0.309017 + 0.951057i) q^{25} +(-1.55220 + 4.77717i) q^{26} +(2.82052 + 2.04923i) q^{28} +(-0.886361 + 2.72794i) q^{29} +(-7.55659 + 5.49018i) q^{31} -1.00000 q^{32} -3.77272 q^{34} +(-2.82052 + 2.04923i) q^{35} +(2.73607 - 8.42075i) q^{37} +(4.36121 + 3.16861i) q^{38} +(0.309017 - 0.951057i) q^{40} +(1.79098 + 5.51207i) q^{41} +3.93548 q^{43} +(3.12954 - 1.09817i) q^{44} +(5.25468 - 3.81775i) q^{46} +(-3.70688 - 11.4086i) q^{47} +(-4.17023 - 3.02985i) q^{49} +(0.809017 + 0.587785i) q^{50} +(1.55220 + 4.77717i) q^{52} +(3.41555 - 2.48154i) q^{53} +(0.0773437 + 3.31572i) q^{55} +3.48636 q^{56} +(0.886361 + 2.72794i) q^{58} +(-0.0224320 + 0.0690385i) q^{59} +(8.87711 + 6.44960i) q^{61} +(-2.88636 + 8.88330i) q^{62} +(-0.809017 + 0.587785i) q^{64} -5.02301 q^{65} +15.6783 q^{67} +(-3.05220 + 2.21755i) q^{68} +(-1.07734 + 3.31572i) q^{70} +(-3.48636 - 2.53299i) q^{71} +(-1.85410 + 5.70634i) q^{73} +(-2.73607 - 8.42075i) q^{74} +5.39076 q^{76} +(-10.9107 + 3.82862i) q^{77} +(8.67023 - 6.29929i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(4.68885 + 3.40665i) q^{82} +(-1.23607 - 0.898056i) q^{83} +(-1.16583 - 3.58807i) q^{85} +(3.18387 - 2.31322i) q^{86} +(1.88636 - 2.72794i) q^{88} -3.32360 q^{89} +(-5.41151 - 16.6549i) q^{91} +(2.00711 - 6.17725i) q^{92} +(-9.70475 - 7.05091i) q^{94} +(-1.66583 + 5.12691i) q^{95} +(-5.44913 + 3.95902i) q^{97} -5.15469 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 3 q^{7} + 2 q^{8} + 8 q^{10} + 3 q^{13} + 3 q^{14} - 2 q^{16} - 5 q^{17} + 4 q^{19} + 2 q^{20} - 16 q^{23} - 2 q^{25} + 7 q^{26} + 2 q^{28} + 3 q^{29} - 22 q^{31} - 8 q^{32}+ \cdots - 30 q^{98}+O(q^{100}) \) 8 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 3 * q^7 + 2 * q^8 + 8 * q^10 + 3 * q^13 + 3 * q^14 - 2 * q^16 - 5 * q^17 + 4 * q^19 + 2 * q^20 - 16 * q^23 - 2 * q^25 + 7 * q^26 + 2 * q^28 + 3 * q^29 - 22 * q^31 - 8 * q^32 - 10 * q^34 - 2 * q^35 + 4 * q^37 + 11 * q^38 - 2 * q^40 - q^41 - 2 * q^43 + 11 * q^46 + q^47 - 5 * q^49 + 2 * q^50 - 7 * q^52 + 30 * q^53 - 5 * q^55 - 2 * q^56 - 3 * q^58 + 8 * q^59 + 12 * q^61 - 13 * q^62 - 2 * q^64 - 8 * q^65 + 58 * q^67 - 5 * q^68 - 3 * q^70 + 2 * q^71 + 12 * q^73 - 4 * q^74 + 14 * q^76 - 22 * q^77 + 41 * q^79 + 2 * q^80 - 4 * q^82 + 8 * q^83 + 27 * q^86 + 5 * q^88 - 10 * q^89 - 47 * q^91 + 19 * q^92 - q^94 - 4 * q^95 - 40 * q^97 - 30 * q^98

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