LMFDB - Embedded newform 99.2.f.c.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(37,99)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			82.1
Root			$-0.476925 - 1.46782i$ of defining polynomial
Character	$\chi$	$=$	99.82
Dual form			99.2.f.c.64.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.476925 - 1.46782i) q^{2} +(-0.309017 + 0.224514i) q^{4} +(0.476925 - 1.46782i) q^{5} +(-0.190983 + 0.138757i) q^{7} +(-2.02029 - 1.46782i) q^{8} +O(q^{10})$	\(q+(-0.476925 - 1.46782i) q^{2} +(-0.309017 + 0.224514i) q^{4} +(0.476925 - 1.46782i) q^{5} +(-0.190983 + 0.138757i) q^{7} +(-2.02029 - 1.46782i) q^{8} -2.38197 q^{10} +(2.31504 + 2.37499i) q^{11} +(-1.30902 - 4.02874i) q^{13} +(0.294756 + 0.214153i) q^{14} +(-1.42705 + 4.39201i) q^{16} +(-1.83812 + 5.65714i) q^{17} +(3.73607 + 2.71441i) q^{19} +(0.182169 + 0.560659i) q^{20} +(2.38197 - 4.53077i) q^{22} +7.49164 q^{23} +(2.11803 + 1.53884i) q^{25} +(-5.28918 + 3.84281i) q^{26} +(0.0278640 - 0.0857567i) q^{28} +(-1.54336 + 1.12132i) q^{29} +(-0.736068 - 2.26538i) q^{31} +2.13287 q^{32} +9.18034 q^{34} +(0.112587 + 0.346506i) q^{35} +(-5.04508 + 3.66547i) q^{37} +(2.20246 - 6.77846i) q^{38} +(-3.11803 + 2.26538i) q^{40} +(-4.51750 - 3.28216i) q^{41} -10.7082 q^{43} +(-1.24861 - 0.214153i) q^{44} +(-3.57295 - 10.9964i) q^{46} +(-0.771681 - 0.560659i) q^{47} +(-2.14590 + 6.60440i) q^{49} +(1.24861 - 3.84281i) q^{50} +(1.30902 + 0.951057i) q^{52} +(-2.79197 - 8.59279i) q^{53} +(4.59017 - 2.26538i) q^{55} +0.589512 q^{56} +(2.38197 + 1.73060i) q^{58} +(6.83254 - 4.96413i) q^{59} +(1.33688 - 4.11450i) q^{61} +(-2.97414 + 2.16084i) q^{62} +(1.83688 + 5.65334i) q^{64} -6.53779 q^{65} +3.85410 q^{67} +(-0.702099 - 2.16084i) q^{68} +(0.454915 - 0.330515i) q^{70} +(-2.38463 + 7.33912i) q^{71} +(5.23607 - 3.80423i) q^{73} +(7.78639 + 5.65714i) q^{74} -1.76393 q^{76} +(-0.771681 - 0.132354i) q^{77} +(-0.163119 - 0.502029i) q^{79} +(5.76611 + 4.18932i) q^{80} +(-2.66312 + 8.19624i) q^{82} +(1.36119 - 4.18932i) q^{83} +(7.42705 + 5.39607i) q^{85} +(5.10701 + 15.7178i) q^{86} +(-1.19098 - 8.19624i) q^{88} -16.7518 q^{89} +(0.809017 + 0.587785i) q^{91} +(-2.31504 + 1.68198i) q^{92} +(-0.454915 + 1.40008i) q^{94} +(5.76611 - 4.18932i) q^{95} +(-3.95492 - 12.1720i) q^{97} +10.7175 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) $ 8 * q + 2 * q^4 - 6 * q^7	$ 8 q + 2 q^{4} - 6 q^{7} - 28 q^{10} - 6 q^{13} + 2 q^{16} + 12 q^{19} + 28 q^{22} + 8 q^{25} + 36 q^{28} + 12 q^{31} - 16 q^{34} - 18 q^{37} - 16 q^{40} - 32 q^{43} - 42 q^{46} - 44 q^{49} + 6 q^{52} - 8 q^{55} + 28 q^{58} + 42 q^{61} + 46 q^{64} + 4 q^{67} + 26 q^{70} + 24 q^{73} - 32 q^{76} + 30 q^{79} + 10 q^{82} + 46 q^{85} - 14 q^{88} + 2 q^{91} - 26 q^{94} - 54 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 - 6 * q^7 - 28 * q^10 - 6 * q^13 + 2 * q^16 + 12 * q^19 + 28 * q^22 + 8 * q^25 + 36 * q^28 + 12 * q^31 - 16 * q^34 - 18 * q^37 - 16 * q^40 - 32 * q^43 - 42 * q^46 - 44 * q^49 + 6 * q^52 - 8 * q^55 + 28 * q^58 + 42 * q^61 + 46 * q^64 + 4 * q^67 + 26 * q^70 + 24 * q^73 - 32 * q^76 + 30 * q^79 + 10 * q^82 + 46 * q^85 - 14 * q^88 + 2 * q^91 - 26 * q^94 - 54 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.476925	−	1.46782i	−0.337237	−	1.03791i	−0.965610	−	0.259996i	$-0.916279\pi$
$2$	−0.476925	−	1.46782i	−0.337237	−	1.03791i	0.628373	−	0.777912i	$-0.283721\pi$
$3$		0			0
$3$		0			0
$4$	−0.309017	+	0.224514i	−0.154508	+	0.112257i
$5$	0.476925	−	1.46782i	0.213287	−	0.656431i	−0.785983	−	0.618248i	$-0.787843\pi$
$5$	0.476925	−	1.46782i	0.213287	−	0.656431i	0.999271	−	0.0381834i	$-0.0121571\pi$
$6$		0			0
$7$	−0.190983	+	0.138757i	−0.0721848	+	0.0524453i	−0.623292	−	0.781989i	$-0.714205\pi$
$7$	−0.190983	+	0.138757i	−0.0721848	+	0.0524453i	0.551108	+	0.834434i	$0.314205\pi$
$8$	−2.02029	−	1.46782i	−0.714279	−	0.518954i
$9$		0			0
$10$	−2.38197			−0.753244
$11$	2.31504	+	2.37499i	0.698012	+	0.716086i
$11$	2.31504	+	2.37499i	0.698012	+	0.716086i
$12$		0			0
$13$	−1.30902	−	4.02874i	−0.363056	−	1.11737i	−0.951189	−	0.308608i	$-0.900137\pi$
$13$	−1.30902	−	4.02874i	−0.363056	−	1.11737i	0.588133	−	0.808764i	$-0.299863\pi$
$14$	0.294756	+	0.214153i	0.0787768	+	0.0572347i
$15$		0			0
$16$	−1.42705	+	4.39201i	−0.356763	+	1.09800i
$17$	−1.83812	+	5.65714i	−0.445809	+	1.37206i	0.435785	+	0.900051i	$0.356471\pi$
$17$	−1.83812	+	5.65714i	−0.445809	+	1.37206i	−0.881594	+	0.472008i	$0.843529\pi$
$18$		0			0
$19$	3.73607	+	2.71441i	0.857113	+	0.622729i	0.927098	−	0.374819i	$-0.122295\pi$
$19$	3.73607	+	2.71441i	0.857113	+	0.622729i	−0.0699852	+	0.997548i	$0.522295\pi$
$20$	0.182169	+	0.560659i	0.0407343	+	0.125367i
$21$		0			0
$22$	2.38197	−	4.53077i	0.507837	−	0.965963i
$23$	7.49164			1.56211			0.781057	−	0.624460i	$-0.214681\pi$
$23$	7.49164			1.56211			0.781057	+	0.624460i	$0.214681\pi$
$24$		0			0
$25$	2.11803	+	1.53884i	0.423607	+	0.307768i
$26$	−5.28918	+	3.84281i	−1.03729	+	0.753638i
$27$		0			0
$28$	0.0278640	−	0.0857567i	0.00526581	−	0.0162065i
$29$	−1.54336	+	1.12132i	−0.286595	+	0.208224i	−0.721789	−	0.692113i	$-0.756680\pi$
$29$	−1.54336	+	1.12132i	−0.286595	+	0.208224i	0.435194	+	0.900337i	$0.356680\pi$
$30$		0			0
$31$	−0.736068	−	2.26538i	−0.132202	−	0.406875i	0.862943	−	0.505302i	$-0.168619\pi$
$31$	−0.736068	−	2.26538i	−0.132202	−	0.406875i	−0.995144	+	0.0984270i	$0.968619\pi$
$32$	2.13287			0.377042
$33$		0			0
$34$	9.18034			1.57442
$35$	0.112587	+	0.346506i	0.0190306	+	0.0585703i
$36$		0			0
$37$	−5.04508	+	3.66547i	−0.829407	+	0.602599i	−0.919391	−	0.393344i	$-0.871318\pi$
$37$	−5.04508	+	3.66547i	−0.829407	+	0.602599i	0.0899846	+	0.995943i	$0.471318\pi$
$38$	2.20246	−	6.77846i	0.357286	−	1.09961i
$39$		0			0
$40$	−3.11803	+	2.26538i	−0.493004	+	0.358189i
$41$	−4.51750	−	3.28216i	−0.705515	−	0.512587i	0.176209	−	0.984353i	$-0.443617\pi$
$41$	−4.51750	−	3.28216i	−0.705515	−	0.512587i	−0.881724	+	0.471766i	$0.843617\pi$
$42$		0			0
$43$	−10.7082			−1.63299			−0.816493	−	0.577355i	$-0.804085\pi$
$43$	−10.7082			−1.63299			−0.816493	+	0.577355i	$0.804085\pi$
$44$	−1.24861	−	0.214153i	−0.188234	−	0.0322847i
$45$		0			0
$46$	−3.57295	−	10.9964i	−0.526803	−	1.62133i
$47$	−0.771681	−	0.560659i	−0.112561	−	0.0817805i	0.530081	−	0.847947i	$-0.322162\pi$
$47$	−0.771681	−	0.560659i	−0.112561	−	0.0817805i	−0.642642	+	0.766167i	$0.722162\pi$
$48$		0			0
$49$	−2.14590	+	6.60440i	−0.306557	+	0.943485i
$50$	1.24861	−	3.84281i	0.176580	−	0.543456i
$51$		0			0
$52$	1.30902	+	0.951057i	0.181528	+	0.131888i
$53$	−2.79197	−	8.59279i	−0.383506	−	1.18031i	−0.937558	−	0.347829i	$-0.886919\pi$
$53$	−2.79197	−	8.59279i	−0.383506	−	1.18031i	0.554052	−	0.832482i	$-0.313081\pi$
$54$		0			0
$55$	4.59017	−	2.26538i	0.618938	−	0.305464i
$56$	0.589512			0.0787768
$57$		0			0
$58$	2.38197	+	1.73060i	0.312767	+	0.227239i
$59$	6.83254	−	4.96413i	0.889521	−	0.646275i	−0.0462319	−	0.998931i	$-0.514721\pi$
$59$	6.83254	−	4.96413i	0.889521	−	0.646275i	0.935753	+	0.352656i	$0.114721\pi$
$60$		0			0
$61$	1.33688	−	4.11450i	0.171170	−	0.526807i	−0.828268	−	0.560332i	$-0.810673\pi$
$61$	1.33688	−	4.11450i	0.171170	−	0.526807i	0.999438	+	0.0335251i	$0.0106734\pi$
$62$	−2.97414	+	2.16084i	−0.377716	+	0.274427i
$63$		0			0
$64$	1.83688	+	5.65334i	0.229610	+	0.706667i
$65$	−6.53779			−0.810913
$66$		0			0
$67$	3.85410			0.470853			0.235427	−	0.971892i	$-0.424351\pi$
$67$	3.85410			0.470853			0.235427	+	0.971892i	$0.424351\pi$
$68$	−0.702099	−	2.16084i	−0.0851420	−	0.262040i
$69$		0			0
$70$	0.454915	−	0.330515i	0.0543727	−	0.0395041i
$71$	−2.38463	+	7.33912i	−0.283003	+	0.870994i	0.703987	+	0.710213i	$0.251401\pi$
$71$	−2.38463	+	7.33912i	−0.283003	+	0.870994i	−0.986990	+	0.160781i	$0.948599\pi$
$72$		0			0
$73$	5.23607	−	3.80423i	0.612835	−	0.445251i	−0.237576	−	0.971369i	$-0.576353\pi$
$73$	5.23607	−	3.80423i	0.612835	−	0.445251i	0.850412	+	0.526118i	$0.176353\pi$
$74$	7.78639	+	5.65714i	0.905150	+	0.657630i
$75$		0			0
$76$	−1.76393			−0.202337
$77$	−0.771681	−	0.132354i	−0.0879412	−	0.0150831i
$78$		0			0
$79$	−0.163119	−	0.502029i	−0.0183523	−	0.0564826i	0.941461	−	0.337122i	$-0.109453\pi$
$79$	−0.163119	−	0.502029i	−0.0183523	−	0.0564826i	−0.959813	+	0.280639i	$0.909453\pi$
$80$	5.76611	+	4.18932i	0.644670	+	0.468380i
$81$		0			0
$82$	−2.66312	+	8.19624i	−0.294092	+	0.905123i
$83$	1.36119	−	4.18932i	0.149410	−	0.459838i	−0.848141	−	0.529770i	$-0.822278\pi$
$83$	1.36119	−	4.18932i	0.149410	−	0.459838i	0.997552	+	0.0699322i	$0.0222783\pi$
$84$		0			0
$85$	7.42705	+	5.39607i	0.805577	+	0.585286i
$86$	5.10701	+	15.7178i	0.550703	+	1.69489i
$87$		0			0
$88$	−1.19098	−	8.19624i	−0.126959	−	0.873722i
$89$	−16.7518			−1.77569			−0.887844	−	0.460145i	$-0.847798\pi$
$89$	−16.7518			−1.77569			−0.887844	+	0.460145i	$0.847798\pi$
$90$		0			0
$91$	0.809017	+	0.587785i	0.0848080	+	0.0616166i
$92$	−2.31504	+	1.68198i	−0.241360	+	0.175358i
$93$		0			0
$94$	−0.454915	+	1.40008i	−0.0469209	+	0.144408i
$95$	5.76611	−	4.18932i	0.591590	−	0.429815i
$96$		0			0
$97$	−3.95492	−	12.1720i	−0.401561	−	1.23588i	−0.923733	−	0.383037i	$-0.874878\pi$
$97$	−3.95492	−	12.1720i	−0.401561	−	1.23588i	0.522172	−	0.852840i	$-0.325122\pi$
$98$	10.7175			1.08263
$99$		0			0
$100$	−1.00000			−0.100000
$101$	3.26889	+	10.0606i	0.325267	+	1.00107i	0.971320	+	0.237776i	$0.0764185\pi$
$101$	3.26889	+	10.0606i	0.325267	+	1.00107i	−0.646053	+	0.763293i	$0.723581\pi$
$102$		0			0
$103$	−5.61803	+	4.08174i	−0.553561	+	0.402186i	−0.829097	−	0.559105i	$-0.811145\pi$
$103$	−5.61803	+	4.08174i	−0.553561	+	0.402186i	0.275535	+	0.961291i	$0.411145\pi$
$104$	−3.26889	+	10.0606i	−0.320541	+	0.986525i
$105$		0			0
$106$	−11.2812	+	8.19624i	−1.09572	+	0.796089i
$107$	7.60422	+	5.52479i	0.735128	+	0.534102i	0.891182	−	0.453647i	$-0.149877\pi$
$107$	7.60422	+	5.52479i	0.735128	+	0.534102i	−0.156054	+	0.987749i	$0.549877\pi$
$108$		0			0
$109$	−0.291796			−0.0279490			−0.0139745	−	0.999902i	$-0.504448\pi$
$109$	−0.291796			−0.0279490			−0.0139745	+	0.999902i	$0.504448\pi$
$110$	−5.51435	−	5.65714i	−0.525773	−	0.539388i
$111$		0			0
$112$	−0.336881	−	1.03681i	−0.0318323	−	0.0979696i
$113$	−9.14758	−	6.64611i	−0.860532	−	0.625213i	0.0674974	−	0.997719i	$-0.478499\pi$
$113$	−9.14758	−	6.64611i	−0.860532	−	0.625213i	−0.928030	+	0.372506i	$0.878499\pi$
$114$		0			0
$115$	3.57295	−	10.9964i	0.333179	−	1.02542i
$116$	0.225173	−	0.693013i	0.0209068	−	0.0643446i
$117$		0			0
$118$	−10.5451	−	7.66145i	−0.970754	−	0.705294i
$119$	−0.433921	−	1.33547i	−0.0397775	−	0.122422i
$120$		0			0
$121$	−0.281153	+	10.9964i	−0.0255594	+	0.999673i
$122$	−6.67695			−0.604503
$123$		0			0
$124$	0.736068	+	0.534785i	0.0661009	+	0.0480251i
$125$	9.51192	−	6.91082i	0.850772	−	0.618122i
$126$		0			0
$127$	−2.23607	+	6.88191i	−0.198419	+	0.610671i	0.801501	+	0.597994i	$0.204035\pi$
$127$	−2.23607	+	6.88191i	−0.198419	+	0.610671i	−0.999920	+	0.0126769i	$0.995965\pi$
$128$	10.8731	−	7.89978i	0.961057	−	0.698249i
$129$		0			0
$130$	3.11803	+	9.59632i	0.273470	+	0.841653i
$131$	−12.1217			−1.05908			−0.529540	−	0.848285i	$-0.677635\pi$
$131$	−12.1217			−1.05908			−0.529540	+	0.848285i	$0.677635\pi$
$132$		0			0
$133$	−1.09017			−0.0945297
$134$	−1.83812	−	5.65714i	−0.158789	−	0.488703i
$135$		0			0
$136$	12.0172	−	8.73102i	1.03047	−	0.748679i
$137$	−3.26889	+	10.0606i	−0.279280	+	0.859537i	0.708775	+	0.705435i	$0.249248\pi$
$137$	−3.26889	+	10.0606i	−0.279280	+	0.859537i	−0.988055	+	0.154102i	$0.950752\pi$
$138$		0			0
$139$	11.0172	−	8.00448i	0.934468	−	0.678931i	−0.0126143	−	0.999920i	$-0.504015\pi$
$139$	11.0172	−	8.00448i	0.934468	−	0.678931i	0.947083	+	0.320989i	$0.104015\pi$
$140$	−0.112587	−	0.0817991i	−0.00951532	−	0.00691328i
$141$		0			0
$142$	11.9098			0.999451
$143$	6.53779	−	12.4356i	0.546717	−	1.03992i
$144$		0			0
$145$	0.909830	+	2.80017i	0.0755573	+	0.232541i
$146$	−8.08115	−	5.87130i	−0.668801	−	0.485912i
$147$		0			0
$148$	0.736068	−	2.26538i	0.0605044	−	0.186213i
$149$	4.22274	−	12.9963i	0.345941	−	1.06470i	−0.615138	−	0.788420i	$-0.710900\pi$
$149$	4.22274	−	12.9963i	0.345941	−	1.06470i	0.961078	−	0.276276i	$-0.0891004\pi$
$150$		0			0
$151$	7.09017	+	5.15131i	0.576990	+	0.419208i	0.837638	−	0.546226i	$-0.183936\pi$
$151$	7.09017	+	5.15131i	0.576990	+	0.419208i	−0.260648	+	0.965434i	$0.583936\pi$
$152$	−3.56365	−	10.9678i	−0.289050	−	0.889605i
$153$		0			0
$154$	0.173762	+	1.19581i	0.0140021	+	0.0963615i
$155$	−3.67624			−0.295282
$156$		0			0
$157$	−8.61803	−	6.26137i	−0.687794	−	0.499712i	0.188140	−	0.982142i	$-0.439754\pi$
$157$	−8.61803	−	6.26137i	−0.687794	−	0.499712i	−0.875934	+	0.482431i	$0.839754\pi$
$158$	−0.659094	+	0.478860i	−0.0524347	+	0.0380961i
$159$		0			0
$160$	1.01722	−	3.13068i	0.0804184	−	0.247502i
$161$	−1.43078	+	1.03952i	−0.112761	+	0.0819256i
$162$		0			0
$163$	1.11803	+	3.44095i	0.0875712	+	0.269516i	0.985247	−	0.171141i	$-0.0547454\pi$
$163$	1.11803	+	3.44095i	0.0875712	+	0.269516i	−0.897675	+	0.440657i	$0.854745\pi$
$164$	2.13287			0.166549
$165$		0			0
$166$	−6.79837			−0.527656
$167$	2.38463	+	7.33912i	0.184528	+	0.567918i	0.999940	−	0.0109626i	$-0.00348959\pi$
$167$	2.38463	+	7.33912i	0.184528	+	0.567918i	−0.815412	+	0.578881i	$0.803490\pi$
$168$		0			0
$169$	−4.00000	+	2.90617i	−0.307692	+	0.223552i
$170$	4.37833	−	13.4751i	0.335803	−	1.03350i
$171$		0			0
$172$	3.30902	−	2.40414i	0.252310	−	0.183314i
$173$	−2.20246	−	1.60018i	−0.167450	−	0.121659i	0.500904	−	0.865503i	$-0.333001\pi$
$173$	−2.20246	−	1.60018i	−0.167450	−	0.121659i	−0.668354	+	0.743843i	$0.733001\pi$
$174$		0			0
$175$	−0.618034			−0.0467190
$176$	−13.7347	+	6.77846i	−1.03529	+	0.510946i
$177$		0			0
$178$	7.98936	+	24.5887i	0.598828	+	1.84300i
$179$	15.0959	+	10.9678i	1.12832	+	0.819771i	0.985449	−	0.169971i	$-0.0543674\pi$
$179$	15.0959	+	10.9678i	1.12832	+	0.819771i	0.142868	+	0.989742i	$0.454367\pi$
$180$		0			0
$181$	2.39919	−	7.38394i	0.178330	−	0.548844i	−0.821440	−	0.570295i	$-0.806829\pi$
$181$	2.39919	−	7.38394i	0.178330	−	0.548844i	0.999770	+	0.0214515i	$0.00682876\pi$
$182$	0.476925	−	1.46782i	0.0353520	−	0.108802i
$183$		0			0
$184$	−15.1353	−	10.9964i	−1.11579	−	0.810666i
$185$	2.97414	+	9.15345i	0.218663	+	0.672975i
$186$		0			0
$187$	−17.6910	+	8.73102i	−1.29369	+	0.638476i
$188$	0.364338			0.0265721
$189$		0			0
$190$	−8.89919	−	6.46564i	−0.645615	−	0.469067i
$191$	−2.97414	+	2.16084i	−0.215201	+	0.156353i	−0.690164	−	0.723653i	$-0.742462\pi$
$191$	−2.97414	+	2.16084i	−0.215201	+	0.156353i	0.474963	+	0.880006i	$0.342462\pi$
$192$		0			0
$193$	2.97214	−	9.14729i	0.213939	−	0.658437i	−0.785288	−	0.619130i	$-0.787485\pi$
$193$	2.97214	−	9.14729i	0.213939	−	0.658437i	0.999227	−	0.0393062i	$-0.0125148\pi$
$194$	−15.9801	+	11.6102i	−1.14731	+	0.833567i
$195$		0			0
$196$	−0.819660	−	2.52265i	−0.0585472	−	0.180190i
$197$	12.1217			0.863637			0.431818	−	0.901961i	$-0.357872\pi$
$197$	12.1217			0.863637			0.431818	+	0.901961i	$0.357872\pi$
$198$		0			0
$199$	−26.4164			−1.87261			−0.936305	−	0.351189i	$-0.885778\pi$
$199$	−26.4164			−1.87261			−0.936305	+	0.351189i	$0.885778\pi$
$200$	−2.02029	−	6.21780i	−0.142856	−	0.439665i
$201$		0			0
$202$	13.2082	−	9.59632i	0.929326	−	0.675195i
$203$	0.139165	−	0.428305i	0.00976746	−	0.0300611i
$204$		0			0
$205$	−6.97214	+	5.06555i	−0.486955	+	0.353794i
$206$	8.67066	+	6.29960i	0.604113	+	0.438914i
$207$		0			0
$208$	19.5623			1.35640
$209$	2.20246	+	15.1571i	0.152347	+	1.04844i
$210$		0			0
$211$	3.40983	+	10.4944i	0.234742	+	0.722463i	0.997155	+	0.0753721i	$0.0240145\pi$
$211$	3.40983	+	10.4944i	0.234742	+	0.722463i	−0.762413	+	0.647091i	$0.775986\pi$
$212$	2.79197	+	2.02848i	0.191753	+	0.139317i
$213$		0			0
$214$	4.48278	−	13.7966i	0.306436	−	0.943114i
$215$	−5.10701	+	15.7178i	−0.348295	+	1.07194i
$216$		0			0
$217$	0.454915	+	0.330515i	0.0308816	+	0.0224368i
$218$	0.139165	+	0.428305i	0.00942543	+	0.0290085i
$219$		0			0
$220$	−0.909830	+	1.73060i	−0.0613407	+	0.116677i
$221$	25.1973			1.69495
$222$		0			0
$223$	15.5172	+	11.2739i	1.03911	+	0.754958i	0.970112	−	0.242659i	$-0.0780197\pi$
$223$	15.5172	+	11.2739i	1.03911	+	0.754958i	0.0689984	+	0.997617i	$0.478020\pi$
$224$	−0.407343	+	0.295952i	−0.0272167	+	0.0197741i
$225$		0			0
$226$	−5.39261	+	16.5967i	−0.358711	+	1.10400i
$227$	−7.60422	+	5.52479i	−0.504710	+	0.366693i	−0.810813	−	0.585305i	$-0.800975\pi$
$227$	−7.60422	+	5.52479i	−0.504710	+	0.366693i	0.306103	+	0.951998i	$0.400975\pi$
$228$		0			0
$229$	−2.94427	−	9.06154i	−0.194563	−	0.598803i	−0.999981	−	0.00609663i	$-0.998059\pi$
$229$	−2.94427	−	9.06154i	−0.194563	−	0.598803i	0.805418	−	0.592707i	$-0.201941\pi$
$230$	−17.8448			−1.17665
$231$		0			0
$232$	4.76393			0.312767
$233$	1.29161	+	3.97517i	0.0846162	+	0.260422i	0.984409	−	0.175896i	$-0.0562823\pi$
$233$	1.29161	+	3.97517i	0.0846162	+	0.260422i	−0.899793	+	0.436318i	$0.856282\pi$
$234$		0			0
$235$	−1.19098	+	0.865300i	−0.0776912	+	0.0564459i
$236$	−0.996854	+	3.06800i	−0.0648897	+	0.199710i
$237$		0			0
$238$	−1.75329	+	1.27384i	−0.113649	+	0.0825707i
$239$	−12.8934	−	9.36761i	−0.834005	−	0.605940i	0.0866846	−	0.996236i	$-0.472373\pi$
$239$	−12.8934	−	9.36761i	−0.834005	−	0.605940i	−0.920690	+	0.390296i	$0.872373\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$	16.2749	−	4.83178i	1.04619	−	0.310598i
$243$		0			0
$244$	0.510643	+	1.57160i	0.0326906	+	0.100611i
$245$	8.67066	+	6.29960i	0.553948	+	0.402467i
$246$		0			0
$247$	6.04508	−	18.6049i	0.384640	−	1.18380i
$248$	−1.83812	+	5.65714i	−0.116721	+	0.359229i
$249$		0			0
$250$	−14.6803	−	10.6659i	−0.928466	−	0.674570i
$251$	−4.56050	−	14.0358i	−0.287856	−	0.885931i	−0.985528	−	0.169513i	$-0.945780\pi$
$251$	−4.56050	−	14.0358i	−0.287856	−	0.885931i	0.697672	−	0.716418i	$-0.254220\pi$
$252$		0			0
$253$	17.3435	+	17.7926i	1.09037	+	1.11861i
$254$	11.1679			0.700735
$255$		0			0
$256$	−7.16312	−	5.20431i	−0.447695	−	0.325269i
$257$	−12.7808	+	9.28581i	−0.797245	+	0.579233i	−0.910105	−	0.414378i	$-0.863999\pi$
$257$	−12.7808	+	9.28581i	−0.797245	+	0.579233i	0.112859	+	0.993611i	$0.463999\pi$
$258$		0			0
$259$	0.454915	−	1.40008i	0.0282670	−	0.0869970i
$260$	2.02029	−	1.46782i	0.125293	−	0.0910306i
$261$		0			0
$262$	5.78115	+	17.7926i	0.357161	+	1.09923i
$263$	4.63009			0.285503			0.142752	−	0.989759i	$-0.454405\pi$
$263$	4.63009			0.285503			0.142752	+	0.989759i	$0.454405\pi$
$264$		0			0
$265$	−13.9443			−0.856590
$266$	0.519929	+	1.60018i	0.0318789	+	0.0981132i
$267$		0			0
$268$	−1.19098	+	0.865300i	−0.0727509	+	0.0528566i
$269$	8.30632	−	25.5642i	0.506445	−	1.55868i	−0.291882	−	0.956454i	$-0.594281\pi$
$269$	8.30632	−	25.5642i	0.506445	−	1.55868i	0.798327	−	0.602224i	$-0.205719\pi$
$270$		0			0
$271$	24.2984	−	17.6538i	1.47602	−	1.07239i	0.497209	−	0.867631i	$-0.334358\pi$
$271$	24.2984	−	17.6538i	1.47602	−	1.07239i	0.978812	−	0.204761i	$-0.0656418\pi$
$272$	−22.2232	−	16.1461i	−1.34748	−	0.978999i
$273$		0			0
$274$	16.3262			0.986304
$275$	1.24861	+	8.59279i	0.0752938	+	0.518165i
$276$		0			0
$277$	6.68034	+	20.5600i	0.401383	+	1.23533i	0.923878	+	0.382687i	$0.125001\pi$
$277$	6.68034	+	20.5600i	0.401383	+	1.23533i	−0.522495	+	0.852642i	$0.674999\pi$
$278$	−17.0036	−	12.3538i	−1.01981	−	0.740932i
$279$		0			0
$280$	0.281153	−	0.865300i	0.0168021	−	0.0517116i
$281$	−2.72239	+	8.37864i	−0.162404	+	0.499828i	−0.998836	−	0.0482433i	$-0.984638\pi$
$281$	−2.72239	+	8.37864i	−0.162404	+	0.499828i	0.836432	+	0.548071i	$0.184638\pi$
$282$		0			0
$283$	−5.61803	−	4.08174i	−0.333957	−	0.242634i	0.408151	−	0.912915i	$-0.366174\pi$
$283$	−5.61803	−	4.08174i	−0.333957	−	0.242634i	−0.742108	+	0.670280i	$0.766174\pi$
$284$	−0.910846	−	2.80330i	−0.0540488	−	0.166345i
$285$		0			0
$286$	−21.3713	−	3.66547i	−1.26371	−	0.216744i
$287$	1.31819			0.0778102
$288$		0			0
$289$	−14.8713	−	10.8046i	−0.874784	−	0.635568i
$290$	3.67624	−	2.67094i	0.215876	−	0.156843i
$291$		0			0
$292$	−0.763932	+	2.35114i	−0.0447057	+	0.137590i
$293$	16.6392	−	12.0891i	0.972074	−	0.706253i	0.0161504	−	0.999870i	$-0.494859\pi$
$293$	16.6392	−	12.0891i	0.972074	−	0.706253i	0.955923	+	0.293617i	$0.0948589\pi$
$294$		0			0
$295$	−4.02786	−	12.3965i	−0.234511	−	0.721752i
$296$	15.5728			0.905150
$297$		0			0
$298$	−21.0902			−1.22172
$299$	−9.80668	−	30.1819i	−0.567135	−	1.74546i
$300$		0			0
$301$	2.04508	−	1.48584i	0.117877	−	0.0856425i
$302$	4.17974	−	12.8639i	0.240517	−	0.740235i
$303$		0			0
$304$	−17.2533	+	12.5352i	−0.989544	+	0.718946i
$305$	−5.40177	−	3.92461i	−0.309304	−	0.224723i
$306$		0			0
$307$	−16.2705			−0.928607			−0.464304	−	0.885676i	$-0.653695\pi$
$307$	−16.2705			−0.928607			−0.464304	+	0.885676i	$0.653695\pi$
$308$	0.268178	−	0.132354i	0.0152808	−	0.00754155i
$309$		0			0
$310$	1.75329	+	5.39607i	0.0995801	+	0.306476i
$311$	−19.5008	−	14.1681i	−1.10579	−	0.803401i	−0.123792	−	0.992308i	$-0.539506\pi$
$311$	−19.5008	−	14.1681i	−1.10579	−	0.803401i	−0.981995	+	0.188907i	$0.939506\pi$
$312$		0			0
$313$	0.107391	−	0.330515i	0.00607009	−	0.0186818i	−0.947976	−	0.318343i	$-0.896874\pi$
$313$	0.107391	−	0.330515i	0.00607009	−	0.0186818i	0.954046	+	0.299661i	$0.0968736\pi$
$314$	−5.08043	+	15.6360i	−0.286705	+	0.882389i
$315$		0			0
$316$	0.163119	+	0.118513i	0.00917616	+	0.00666687i
$317$	3.26889	+	10.0606i	0.183599	+	0.565061i	0.999921	−	0.0125363i	$-0.00399055\pi$
$317$	3.26889	+	10.0606i	0.183599	+	0.565061i	−0.816322	+	0.577597i	$0.803991\pi$
$318$		0			0
$319$	−6.23607	−	1.06957i	−0.349153	−	0.0598844i
$320$	9.17416			0.512851
$321$		0			0
$322$	2.20820	+	1.60435i	0.123058	+	0.0894072i
$323$	−22.2232	+	16.1461i	−1.23653	+	0.898391i
$324$		0			0
$325$	3.42705	−	10.5474i	0.190099	−	0.585063i
$326$	4.51750	−	3.28216i	0.250201	−	0.181782i
$327$		0			0
$328$	4.30902	+	13.2618i	0.237926	+	0.732260i
$329$	0.225173			0.0124142
$330$		0			0
$331$	20.7082			1.13823			0.569113	−	0.822259i	$-0.307287\pi$
$331$	20.7082			1.13823			0.569113	+	0.822259i	$0.307287\pi$
$332$	0.519929	+	1.60018i	0.0285348	+	0.0878212i
$333$		0			0
$334$	9.63525	−	7.00042i	0.527218	−	0.383046i
$335$	1.83812	−	5.65714i	0.100427	−	0.309083i
$336$		0			0
$337$	−3.76393	+	2.73466i	−0.205034	+	0.148966i	−0.685564	−	0.728012i	$-0.740444\pi$
$337$	−3.76393	+	2.73466i	−0.205034	+	0.148966i	0.480530	+	0.876978i	$0.340444\pi$
$338$	6.17345	+	4.48527i	0.335791	+	0.243967i
$339$		0			0
$340$	−3.50658			−0.190171
$341$	3.67624	−	6.99262i	0.199079	−	0.378671i
$342$		0			0
$343$	−1.01722	−	3.13068i	−0.0549248	−	0.169041i
$344$	21.6336	+	15.7178i	1.16641	+	0.847445i
$345$		0			0
$346$	−1.29837	+	3.99598i	−0.0698010	+	0.214825i
$347$	0.814685	−	2.50734i	0.0437346	−	0.134601i	−0.926805	−	0.375543i	$-0.877456\pi$
$347$	0.814685	−	2.50734i	0.0437346	−	0.134601i	0.970540	+	0.240942i	$0.0774563\pi$
$348$		0			0
$349$	10.6631	+	7.74721i	0.570784	+	0.414699i	0.835390	−	0.549658i	$-0.185242\pi$
$349$	10.6631	+	7.74721i	0.570784	+	0.414699i	−0.264606	+	0.964357i	$0.585242\pi$
$350$	0.294756	+	0.907165i	0.0157554	+	0.0484900i
$351$		0			0
$352$	4.93769	+	5.06555i	0.263180	+	0.269995i
$353$	3.53707			0.188259			0.0941296	−	0.995560i	$-0.469993\pi$
$353$	3.53707			0.188259			0.0941296	+	0.995560i	$0.469993\pi$
$354$		0			0
$355$	9.63525	+	7.00042i	0.511386	+	0.371544i
$356$	5.17659	−	3.76102i	0.274359	−	0.199333i
$357$		0			0
$358$	8.89919	−	27.3889i	0.470337	−	1.44755i
$359$	−21.1567	+	15.3713i	−1.11661	+	0.811264i	−0.983692	−	0.179863i	$-0.942434\pi$
$359$	−21.1567	+	15.3713i	−1.11661	+	0.811264i	−0.132917	+	0.991127i	$0.542434\pi$
$360$		0			0
$361$	0.718847	+	2.21238i	0.0378341	+	0.116441i
$362$	−11.9826			−0.629789
$363$		0			0
$364$	−0.381966			−0.0200205
$365$	−3.08672	−	9.49996i	−0.161567	−	0.497251i
$366$		0			0
$367$	4.88197	−	3.54696i	0.254837	−	0.185150i	−0.453031	−	0.891495i	$-0.649657\pi$
$367$	4.88197	−	3.54696i	0.254837	−	0.185150i	0.707868	+	0.706345i	$0.249657\pi$
$368$	−10.6909	+	32.9034i	−0.557304	+	1.71521i
$369$		0			0
$370$	12.0172	−	8.73102i	0.624746	−	0.453904i
$371$	1.72553	+	1.25367i	0.0895851	+	0.0650874i
$372$		0			0
$373$	12.4164			0.642897			0.321449	−	0.946927i	$-0.395830\pi$
$373$	12.4164			0.642897			0.321449	+	0.946927i	$0.395830\pi$
$374$	21.2529	+	21.8032i	1.09896	+	1.12742i
$375$		0			0
$376$	0.736068	+	2.26538i	0.0379598	+	0.116828i
$377$	6.53779	+	4.74998i	0.336713	+	0.244636i
$378$		0			0
$379$	0.545085	−	1.67760i	0.0279991	−	0.0861725i	−0.936080	−	0.351786i	$-0.885574\pi$
$379$	0.545085	−	1.67760i	0.0279991	−	0.0861725i	0.964080	+	0.265613i	$0.0855745\pi$
$380$	−0.841263	+	2.58914i	−0.0431559	+	0.132820i
$381$		0			0
$382$	4.59017	+	3.33495i	0.234854	+	0.170631i
$383$	4.36191	+	13.4246i	0.222883	+	0.685964i	0.998500	+	0.0547592i	$0.0174391\pi$
$383$	4.36191	+	13.4246i	0.222883	+	0.685964i	−0.775617	+	0.631204i	$0.782561\pi$
$384$		0			0
$385$	−0.562306	+	1.06957i	−0.0286578	+	0.0545103i
$386$	−14.8441			−0.755545
$387$		0			0
$388$	3.95492	+	2.87341i	0.200780	+	0.145875i
$389$	15.7550	−	11.4466i	0.798808	−	0.580368i	−0.111756	−	0.993736i	$-0.535648\pi$
$389$	15.7550	−	11.4466i	0.798808	−	0.580368i	0.910564	+	0.413368i	$0.135648\pi$
$390$		0			0
$391$	−13.7705	+	42.3813i	−0.696405	+	2.14331i
$392$	14.0294	−	10.1930i	0.708593	−	0.514823i
$393$		0			0
$394$	−5.78115	−	17.7926i	−0.291250	−	0.896376i
$395$	−0.814685			−0.0409913
$396$		0			0
$397$	−2.41641			−0.121276			−0.0606380	−	0.998160i	$-0.519314\pi$
$397$	−2.41641			−0.121276			−0.0606380	+	0.998160i	$0.519314\pi$
$398$	12.5986	+	38.7746i	0.631513	+	1.94360i
$399$		0			0
$400$	−9.78115	+	7.10642i	−0.489058	+	0.355321i
$401$	1.02343	−	3.14980i	0.0511078	−	0.157294i	−0.922245	−	0.386605i	$-0.873648\pi$
$401$	1.02343	−	3.14980i	0.0511078	−	0.157294i	0.973353	+	0.229312i	$0.0736475\pi$
$402$		0			0
$403$	−8.16312	+	5.93085i	−0.406634	+	0.295437i
$404$	−3.26889	−	2.37499i	−0.162634	−	0.118160i
$405$		0			0
$406$	−0.695048			−0.0344947
$407$	−20.3850	−	3.49631i	−1.01045	−	0.173306i
$408$		0			0
$409$	−7.09017	−	21.8213i	−0.350586	−	1.07899i	−0.958525	−	0.285010i	$-0.908003\pi$
$409$	−7.09017	−	21.8213i	−0.350586	−	1.07899i	0.607938	−	0.793984i	$-0.291997\pi$
$410$	10.7605	+	7.81798i	0.531425	+	0.386103i
$411$		0			0
$412$	0.819660	−	2.52265i	0.0403818	−	0.124282i
$413$	−0.616090	+	1.89613i	−0.0303158	+	0.0933024i
$414$		0			0
$415$	−5.50000	−	3.99598i	−0.269984	−	0.196155i
$416$	−2.79197	−	8.59279i	−0.136887	−	0.421296i
$417$		0			0
$418$	21.1976	−	10.4616i	1.03681	−	0.511695i
$419$	−16.0763			−0.785378			−0.392689	−	0.919671i	$-0.628455\pi$
$419$	−16.0763			−0.785378			−0.392689	+	0.919671i	$0.628455\pi$
$420$		0			0
$421$	−17.9721	−	13.0575i	−0.875908	−	0.636385i	0.0562575	−	0.998416i	$-0.482083\pi$
$421$	−17.9721	−	13.0575i	−0.875908	−	0.636385i	−0.932166	+	0.362032i	$0.882083\pi$
$422$	13.7777	−	10.0101i	0.670687	−	0.487282i
$423$		0			0
$424$	−6.97214	+	21.4580i	−0.338597	+	1.04209i
$425$	−12.5986	+	9.15345i	−0.611124	+	0.444008i
$426$		0			0
$427$	0.315595	+	0.971301i	0.0152727	+	0.0470045i
$428$	−3.59023			−0.173540
$429$		0			0
$430$	25.5066			1.23004
$431$	−1.69895	−	5.22884i	−0.0818357	−	0.251864i	0.901764	−	0.432228i	$-0.142272\pi$
$431$	−1.69895	−	5.22884i	−0.0818357	−	0.251864i	−0.983600	+	0.180364i	$0.942272\pi$
$432$		0			0
$433$	−23.1803	+	16.8415i	−1.11398	+	0.809351i	−0.983285	−	0.182072i	$-0.941720\pi$
$433$	−23.1803	+	16.8415i	−1.11398	+	0.809351i	−0.130691	+	0.991423i	$0.541720\pi$
$434$	0.268178	−	0.825366i	0.0128729	−	0.0396189i
$435$		0			0
$436$	0.0901699	−	0.0655123i	0.00431836	−	0.00313747i
$437$	27.9893	+	20.3354i	1.33891	+	0.972774i
$438$		0			0
$439$	−25.0000			−1.19318			−0.596592	−	0.802544i	$-0.703479\pi$
$439$	−25.0000			−1.19318			−0.596592	+	0.802544i	$0.703479\pi$
$440$	−12.5986	−	2.16084i	−0.600617	−	0.103014i
$441$		0			0
$442$	−12.0172	−	36.9852i	−0.571601	−	1.75921i
$443$	−15.2084	−	11.0496i	−0.722575	−	0.524982i	0.164631	−	0.986355i	$-0.447357\pi$
$443$	−15.2084	−	11.0496i	−0.722575	−	0.524982i	−0.887206	+	0.461374i	$0.847357\pi$
$444$		0			0
$445$	−7.98936	+	24.5887i	−0.378732	+	1.16562i
$446$	9.14758	−	28.1534i	0.433151	−	1.33310i
$447$		0			0
$448$	−1.13525	−	0.824811i	−0.0536358	−	0.0389687i
$449$	−0.139165	−	0.428305i	−0.00656760	−	0.0202130i	0.947719	−	0.319106i	$-0.103383\pi$
$449$	−0.139165	−	0.428305i	−0.00656760	−	0.0202130i	−0.954287	+	0.298893i	$0.903383\pi$
$450$		0			0
$451$	−2.66312	−	18.3273i	−0.125401	−	0.863001i
$452$	4.31890			0.203144
$453$		0			0
$454$	11.7361	+	8.52675i	0.550801	+	0.400180i
$455$	1.24861	−	0.907165i	0.0585356	−	0.0425286i
$456$		0			0
$457$	7.38854	−	22.7396i	0.345622	−	1.06371i	−0.615629	−	0.788036i	$-0.711098\pi$
$457$	7.38854	−	22.7396i	0.345622	−	1.06371i	0.961250	−	0.275677i	$-0.0889021\pi$
$458$	−11.8965	+	8.64335i	−0.555889	+	0.403877i
$459$		0			0
$460$	1.36475	+	4.20025i	0.0636316	+	0.195838i
$461$	19.6134			0.913485			0.456743	−	0.889599i	$-0.349016\pi$
$461$	19.6134			0.913485			0.456743	+	0.889599i	$0.349016\pi$
$462$		0			0
$463$	−1.43769			−0.0668153			−0.0334077	−	0.999442i	$-0.510636\pi$
$463$	−1.43769			−0.0668153			−0.0334077	+	0.999442i	$0.510636\pi$
$464$	−2.72239	−	8.37864i	−0.126384	−	0.388969i
$465$		0			0
$466$	5.21885	−	3.79171i	0.241758	−	0.175648i
$467$	−1.50036	+	4.61763i	−0.0694283	+	0.213678i	−0.979751	−	0.200222i	$-0.935834\pi$
$467$	−1.50036	+	4.61763i	−0.0694283	+	0.213678i	0.910322	+	0.413900i	$0.135834\pi$
$468$		0			0
$469$	−0.736068	+	0.534785i	−0.0339885	+	0.0246941i
$470$	1.83812	+	1.33547i	0.0847861	+	0.0616007i
$471$		0			0
$472$	−21.0902			−0.970754
$473$	−24.7900	−	25.4319i	−1.13984	−	1.16936i
$474$		0			0
$475$	3.73607	+	11.4984i	0.171423	+	0.527584i
$476$	0.433921	+	0.315262i	0.0198887	+	0.0144500i
$477$		0			0
$478$	−7.60081	+	23.3929i	−0.347653	+	1.06997i
$479$	11.3766	−	35.0136i	0.519811	−	1.59981i	−0.254543	−	0.967061i	$-0.581925\pi$
$479$	11.3766	−	35.0136i	0.519811	−	1.59981i	0.774354	−	0.632752i	$-0.218075\pi$
$480$		0			0
$481$	21.3713	+	15.5272i	0.974448	+	0.707978i
$482$	−6.67695	−	20.5495i	−0.304127	−	0.936006i
$483$		0			0
$484$	−2.38197	−	3.46120i	−0.108271	−	0.157327i
$485$	−19.7525			−0.896916
$486$		0			0
$487$	13.6631	+	9.92684i	0.619135	+	0.449828i	0.852619	−	0.522533i	$-0.175013\pi$
$487$	13.6631	+	9.92684i	0.619135	+	0.449828i	−0.233484	+	0.972361i	$0.575013\pi$
$488$	−8.74024	+	6.35016i	−0.395652	+	0.287458i
$489$		0			0
$490$	5.11146	−	15.7314i	0.230912	−	0.710674i
$491$	25.0151	−	18.1746i	1.12892	−	0.820206i	0.143380	−	0.989668i	$-0.454203\pi$
$491$	25.0151	−	18.1746i	1.12892	−	0.820206i	0.985537	+	0.169462i	$0.0542029\pi$
$492$		0			0
$493$	−3.50658	−	10.7921i	−0.157928	−	0.486053i
$494$	−30.1917			−1.35839
$495$		0			0
$496$	11.0000			0.493915
$497$	−0.562934	−	1.73253i	−0.0252510	−	0.0777147i
$498$		0			0
$499$	7.88197	−	5.72658i	0.352845	−	0.256357i	−0.397216	−	0.917725i	$-0.630024\pi$
$499$	7.88197	−	5.72658i	0.352845	−	0.256357i	0.750062	+	0.661368i	$0.230024\pi$
$500$	−1.38777	+	4.27112i	−0.0620630	+	0.191010i
$501$		0			0
$502$	−18.4271	+	13.3880i	−0.822440	+	0.597537i
$503$	9.03500	+	6.56431i	0.402851	+	0.292688i	0.770701	−	0.637197i	$-0.219906\pi$
$503$	9.03500	+	6.56431i	0.402851	+	0.292688i	−0.367850	+	0.929885i	$0.619906\pi$
$504$		0			0
$505$	16.3262			0.726508
$506$	17.8448	−	33.9429i	0.793299	−	1.50894i
$507$		0			0
$508$	−0.854102	−	2.62866i	−0.0378946	−	0.116628i
$509$	6.71996	+	4.88233i	0.297857	+	0.216406i	0.726669	−	0.686988i	$-0.241068\pi$
$509$	6.71996	+	4.88233i	0.297857	+	0.216406i	−0.428812	+	0.903394i	$0.641068\pi$
$510$		0			0
$511$	−0.472136	+	1.45309i	−0.0208861	+	0.0642807i
$512$	4.08358	−	12.5680i	0.180470	−	0.555431i
$513$		0			0
$514$	19.7254	+	14.3314i	0.870051	+	0.632129i
$515$	3.31190	+	10.1930i	0.145940	+	0.449156i
$516$		0			0
$517$	−0.454915	−	3.13068i	−0.0200071	−	0.137687i
$518$	−2.27204			−0.0998276
$519$		0			0
$520$	13.2082	+	9.59632i	0.579218	+	0.420827i
$521$	−4.40491	+	3.20036i	−0.192983	+	0.140210i	−0.680081	−	0.733137i	$-0.738055\pi$
$521$	−4.40491	+	3.20036i	−0.192983	+	0.140210i	0.487098	+	0.873347i	$0.338055\pi$
$522$		0			0
$523$	5.70163	−	17.5478i	0.249315	−	0.767312i	−0.745582	−	0.666414i	$-0.767828\pi$
$523$	5.70163	−	17.5478i	0.249315	−	0.767312i	0.994897	−	0.100898i	$-0.0321716\pi$
$524$	3.74582	−	2.72150i	0.163637	−	0.118889i
$525$		0			0
$526$	−2.20820	−	6.79615i	−0.0962823	−	0.296326i
$527$	14.1686			0.617193
$528$		0			0
$529$	33.1246			1.44020
$530$	6.65037	+	20.4677i	0.288874	+	0.889062i
$531$		0			0
$532$	0.336881	−	0.244758i	0.0146056	−	0.0106116i
$533$	−7.30947	+	22.4962i	−0.316608	+	0.974420i
$534$		0			0
$535$	11.7361	−	8.52675i	0.507394	−	0.368644i
$536$	−7.78639	−	5.65714i	−0.336321	−	0.244351i
$537$		0			0
$538$	−41.4853			−1.78856
$539$	−20.6532	+	10.1930i	−0.889597	+	0.439042i
$540$		0			0
$541$	−12.2467	−	37.6915i	−0.526527	−	1.62048i	−0.761276	−	0.648428i	$-0.775427\pi$
$541$	−12.2467	−	37.6915i	−0.526527	−	1.62048i	0.234749	−	0.972056i	$-0.424573\pi$
$542$	−37.5012	−	27.2462i	−1.61081	−	1.17032i
$543$		0			0
$544$	−3.92047	+	12.0660i	−0.168089	+	0.517324i
$545$	−0.139165	+	0.428305i	−0.00596117	+	0.0183466i
$546$		0			0
$547$	7.30902	+	5.31031i	0.312511	+	0.227053i	0.732973	−	0.680258i	$-0.238132\pi$
$547$	7.30902	+	5.31031i	0.312511	+	0.227053i	−0.420462	+	0.907310i	$0.638132\pi$
$548$	−1.24861	−	3.84281i	−0.0533378	−	0.164157i
$549$		0			0
$550$	12.0172	−	5.93085i	0.512416	−	0.252892i
$551$	−8.80982			−0.375311
$552$		0			0
$553$	0.100813	+	0.0732450i	0.00428701	+	0.00311469i
$554$	26.9924	−	19.6111i	1.14680	−	0.833197i
$555$		0			0
$556$	−1.60739	+	4.94704i	−0.0681686	+	0.209801i
$557$	14.3242	−	10.4071i	0.606935	−	0.440964i	−0.241399	−	0.970426i	$-0.577606\pi$
$557$	14.3242	−	10.4071i	0.606935	−	0.440964i	0.848334	+	0.529462i	$0.177606\pi$
$558$		0			0
$559$	14.0172	+	43.1406i	0.592865	+	1.82465i
$560$	−1.68253			−0.0710997
$561$		0			0
$562$	13.5967			0.573544
$563$	12.5291	+	38.5605i	0.528037	+	1.62513i	0.758231	+	0.651986i	$0.226064\pi$
$563$	12.5291	+	38.5605i	0.528037	+	1.62513i	−0.230194	+	0.973145i	$0.573936\pi$
$564$		0			0
$565$	−14.1180	+	10.2574i	−0.593950	+	0.431530i
$566$	−3.31190	+	10.1930i	−0.139209	+	0.428443i
$567$		0			0
$568$	15.5902	−	11.3269i	0.654149	−	0.475267i
$569$	24.0183	+	17.4503i	1.00690	+	0.731554i	0.963556	−	0.267506i	$-0.0861995\pi$
$569$	24.0183	+	17.4503i	1.00690	+	0.731554i	0.0433420	+	0.999060i	$0.486199\pi$
$570$		0			0
$571$	−34.9787			−1.46381			−0.731907	−	0.681405i	$-0.761369\pi$
$571$	−34.9787			−1.46381			−0.731907	+	0.681405i	$0.761369\pi$
$572$	0.771681	+	5.31064i	0.0322656	+	0.222049i
$573$		0			0
$574$	−0.628677	−	1.93487i	−0.0262405	−	0.0807599i
$575$	15.8675	+	11.5284i	0.661722	+	0.480769i
$576$		0			0
$577$	−10.0902	+	31.0543i	−0.420059	+	1.29281i	0.487587	+	0.873074i	$0.337877\pi$
$577$	−10.0902	+	31.0543i	−0.420059	+	1.29281i	−0.907647	+	0.419735i	$0.862123\pi$
$578$	−8.76682	+	26.9815i	−0.364652	+	1.12228i
$579$		0			0
$580$	−0.909830	−	0.661030i	−0.0377786	−	0.0274478i
$581$	0.321334	+	0.988964i	0.0133312	+	0.0410292i
$582$		0			0
$583$	13.9443	−	26.5236i	0.577513	−	1.09849i
$584$	−16.1623			−0.668801
$585$		0			0
$586$	−25.6803	−	18.6579i	−1.06085	−	0.770749i
$587$	7.37905	−	5.36119i	0.304566	−	0.221280i	−0.424995	−	0.905196i	$-0.639724\pi$
$587$	7.37905	−	5.36119i	0.304566	−	0.221280i	0.729561	+	0.683915i	$0.239724\pi$
$588$		0			0
$589$	3.39919	−	10.4616i	0.140061	−	0.431064i
$590$	−16.2749	+	11.8244i	−0.670026	+	0.486803i
$591$		0			0
$592$	−8.89919	−	27.3889i	−0.365754	−	1.12568i
$593$	1.09301			0.0448847			0.0224424	−	0.999748i	$-0.492856\pi$
$593$	1.09301			0.0448847			0.0224424	+	0.999748i	$0.492856\pi$
$594$		0			0
$595$	−2.16718			−0.0888459
$596$	1.61294	+	4.96413i	0.0660688	+	0.203339i
$597$		0			0
$598$	−39.6246	+	28.7890i	−1.62037	+	1.17727i
$599$	−3.81540	+	11.7426i	−0.155893	+	0.479789i	−0.998250	−	0.0591301i	$-0.981167\pi$
$599$	−3.81540	+	11.7426i	−0.155893	+	0.479789i	0.842357	+	0.538920i	$0.181167\pi$
$600$		0			0
$601$	−28.6074	+	20.7845i	−1.16692	+	0.847817i	−0.990637	−	0.136523i	$-0.956407\pi$
$601$	−28.6074	+	20.7845i	−1.16692	+	0.847817i	−0.176283	+	0.984340i	$0.556407\pi$
$602$	−3.15631	−	2.29319i	−0.128641	−	0.0934635i
$603$		0			0
$604$	−3.34752			−0.136209
$605$	16.0067	+	5.65714i	0.650765	+	0.229996i
$606$		0			0
$607$	−8.15248	−	25.0907i	−0.330899	−	1.01840i	−0.968707	−	0.248207i	$-0.920159\pi$
$607$	−8.15248	−	25.0907i	−0.330899	−	1.01840i	0.637808	−	0.770195i	$-0.279841\pi$
$608$	7.96856	+	5.78950i	0.323168	+	0.234795i
$609$		0			0
$610$	−3.18441	+	9.80059i	−0.128933	+	0.396814i
$611$	−1.24861	+	3.84281i	−0.0505132	+	0.155464i
$612$		0			0
$613$	−34.7426	−	25.2420i	−1.40324	−	1.01952i	−0.994262	−	0.106972i	$-0.965885\pi$
$613$	−34.7426	−	25.2420i	−1.40324	−	1.01952i	−0.408980	−	0.912543i	$-0.634115\pi$
$614$	7.75981	+	23.8823i	0.313161	+	0.963809i
$615$		0			0
$616$	1.36475	+	1.40008i	0.0549871	+	0.0564110i
$617$	−1.76854			−0.0711986			−0.0355993	−	0.999366i	$-0.511334\pi$
$617$	−1.76854			−0.0711986			−0.0355993	+	0.999366i	$0.511334\pi$
$618$		0			0
$619$	23.3713	+	16.9803i	0.939373	+	0.682494i	0.948270	−	0.317466i	$-0.102832\pi$
$619$	23.3713	+	16.9803i	0.939373	+	0.682494i	−0.00889683	+	0.999960i	$0.502832\pi$
$620$	1.13602	−	0.825366i	0.0456236	−	0.0331475i
$621$		0			0
$622$	−11.4959	+	35.3808i	−0.460945	+	1.41864i
$623$	3.19931	−	2.32444i	0.128178	−	0.0931265i
$624$		0			0
$625$	−1.56231	−	4.80828i	−0.0624922	−	0.192331i
$626$	−0.536356			−0.0214371
$627$		0			0
$628$	4.06888			0.162366
$629$	−11.4626	−	35.2783i	−0.457045	−	1.40664i
$630$		0			0
$631$	15.8713	−	11.5312i	0.631827	−	0.459049i	−0.225205	−	0.974311i	$-0.572305\pi$
$631$	15.8713	−	11.5312i	0.631827	−	0.459049i	0.857033	+	0.515262i	$0.172305\pi$
$632$	−0.407343	+	1.25367i	−0.0162032	+	0.0498684i
$633$		0			0
$634$	13.2082	−	9.59632i	0.524565	−	0.381119i
$635$	9.03500	+	6.56431i	0.358543	+	0.260497i
$636$		0			0
$637$	29.4164			1.16552
$638$	1.40420	+	9.66356i	0.0555927	+	0.382584i
$639$		0			0
$640$	−6.40983	−	19.7274i	−0.253371	−	0.779795i
$641$	9.91927	+	7.20677i	0.391787	+	0.284650i	0.766188	−	0.642617i	$-0.222151\pi$
$641$	9.91927	+	7.20677i	0.391787	+	0.284650i	−0.374400	+	0.927267i	$0.622151\pi$
$642$		0			0
$643$	8.70163	−	26.7809i	0.343159	−	1.05613i	−0.619404	−	0.785073i	$-0.712626\pi$
$643$	8.70163	−	26.7809i	0.343159	−	1.05613i	0.962562	−	0.271061i	$-0.0873745\pi$
$644$	0.208747	−	0.642458i	0.00822580	−	0.0253164i
$645$		0			0
$646$	34.2984	+	24.9192i	1.34945	+	0.980434i
$647$	12.1913	+	37.5210i	0.479290	+	1.47510i	0.840084	+	0.542456i	$0.182506\pi$
$647$	12.1913	+	37.5210i	0.479290	+	1.47510i	−0.360794	+	0.932645i	$0.617494\pi$
$648$		0			0
$649$	27.6074	+	4.73504i	1.08368	+	0.185867i
$650$	−17.1161			−0.671350
$651$		0			0
$652$	−1.11803	−	0.812299i	−0.0437856	−	0.0318121i
$653$	−33.8249	+	24.5753i	−1.32367	+	0.961704i	−0.323794	+	0.946128i	$0.604958\pi$
$653$	−33.8249	+	24.5753i	−1.32367	+	0.961704i	−0.999879	+	0.0155768i	$0.995042\pi$
$654$		0			0
$655$	−5.78115	+	17.7926i	−0.225888	+	0.695213i
$656$	20.8620	−	15.1571i	0.814523	−	0.591785i
$657$		0			0
$658$	−0.107391	−	0.330515i	−0.00418653	−	0.0128848i
$659$	3.53707			0.137785			0.0688924	−	0.997624i	$-0.478053\pi$
$659$	3.53707			0.137785			0.0688924	+	0.997624i	$0.478053\pi$
$660$		0			0
$661$	22.5623			0.877572			0.438786	−	0.898592i	$-0.355409\pi$
$661$	22.5623			0.877572			0.438786	+	0.898592i	$0.355409\pi$
$662$	−9.87626	−	30.3960i	−0.383852	−	1.18137i
$663$		0			0
$664$	−8.89919	+	6.46564i	−0.345355	+	0.250915i
$665$	−0.519929	+	1.60018i	−0.0201620	+	0.0620522i
$666$		0			0
$667$	−11.5623	+	8.40051i	−0.447694	+	0.325269i
$668$	−2.38463	−	1.73253i	−0.0922639	−	0.0670337i
$669$		0			0
$670$	−9.18034			−0.354667
$671$	12.8668	−	6.35016i	0.496718	−	0.245145i
$672$		0			0
$673$	4.25329	+	13.0903i	0.163952	+	0.504593i	0.998958	−	0.0456488i	$-0.0145355\pi$
$673$	4.25329	+	13.0903i	0.163952	+	0.504593i	−0.835005	+	0.550242i	$0.814536\pi$
$674$	5.80911	+	4.22056i	0.223759	+	0.162570i
$675$		0			0
$676$	0.583592	−	1.79611i	0.0224459	−	0.0690812i
$677$	1.90770	−	5.87130i	0.0733189	−	0.225652i	−0.907681	−	0.419661i	$-0.862149\pi$
$677$	1.90770	−	5.87130i	0.0733189	−	0.225652i	0.981000	+	0.194009i	$0.0621490\pi$
$678$		0			0
$679$	2.44427	+	1.77587i	0.0938025	+	0.0681515i
$680$	−7.08429	−	21.8032i	−0.271670	−	0.836115i
$681$		0			0
$682$	−12.0172	−	2.06111i	−0.460163	−	0.0789242i
$683$	31.7351			1.21431			0.607155	−	0.794584i	$-0.292311\pi$
$683$	31.7351			1.21431			0.607155	+	0.794584i	$0.292311\pi$
$684$		0			0
$685$	13.2082	+	9.59632i	0.504660	+	0.366657i
$686$	−4.11016	+	2.98620i	−0.156927	+	0.114014i
$687$		0			0
$688$	15.2812	−	47.0306i	0.582588	−	1.79302i
$689$	−30.9634	+	22.4962i	−1.17961	+	0.857038i
$690$		0			0
$691$	−3.81966	−	11.7557i	−0.145307	−	0.447208i	0.851744	−	0.523959i	$-0.175545\pi$
$691$	−3.81966	−	11.7557i	−0.145307	−	0.447208i	−0.997050	+	0.0767507i	$0.975545\pi$
$692$	1.03986			0.0395295
$693$		0			0
$694$	−4.06888			−0.154453
$695$	−6.49478	−	19.9889i	−0.246361	−	0.758222i
$696$		0			0
$697$	26.8713	−	19.5232i	1.01782	−	0.739492i
$698$	6.28603	−	19.3464i	0.237930	−	0.732273i
$699$		0			0
$700$	0.190983	−	0.138757i	0.00721848	−	0.00524453i
$701$	−31.0760	−	22.5780i	−1.17372	−	0.852760i	−0.182274	−	0.983248i	$-0.558346\pi$
$701$	−31.0760	−	22.5780i	−1.17372	−	0.852760i	−0.991450	+	0.130488i	$0.958346\pi$
$702$		0			0
$703$	−28.7984			−1.08615
$704$	−9.17416	+	17.4503i	−0.345764	+	0.657683i
$705$		0			0
$706$	−1.68692	−	5.19180i	−0.0634880	−	0.195396i
$707$	−2.02029	−	1.46782i	−0.0759807	−	0.0552032i
$708$		0			0
$709$	−12.2984	+	37.8505i	−0.461875	+	1.42151i	0.400995	+	0.916080i	$0.368664\pi$
$709$	−12.2984	+	37.8505i	−0.461875	+	1.42151i	−0.862870	+	0.505425i	$0.831336\pi$
$710$	5.68010	−	17.4815i	0.213170	−	0.656070i
$711$		0			0
$712$	33.8435	+	24.5887i	1.26834	+	0.921501i
$713$	−5.51435	−	16.9714i	−0.206514	−	0.635585i
$714$		0			0
$715$	−15.1353	−	15.5272i	−0.566026	−	0.580683i
$716$	−7.12730			−0.266360
$717$		0			0
$718$	32.6525	+	23.7234i	1.21858	+	0.885350i
$719$	28.7609	−	20.8960i	1.07260	−	0.779291i	0.0962240	−	0.995360i	$-0.469323\pi$
$719$	28.7609	−	20.8960i	1.07260	−	0.779291i	0.976378	+	0.216069i	$0.0693235\pi$
$720$		0			0
$721$	0.506578	−	1.55909i	0.0188659	−	0.0580634i
$722$	2.90455	−	2.11028i	0.108096	−	0.0785366i
$723$		0			0
$724$	0.916408	+	2.82041i	0.0340580	+	0.104820i
$725$	−4.99442			−0.185488
$726$		0			0
$727$	−0.562306			−0.0208548			−0.0104274	−	0.999946i	$-0.503319\pi$
$727$	−0.562306			−0.0208548			−0.0104274	+	0.999946i	$0.503319\pi$
$728$	−0.771681	−	2.37499i	−0.0286004	−	0.0880230i
$729$		0			0
$730$	−12.4721	+	9.06154i	−0.461614	+	0.335383i
$731$	19.6829	−	60.5779i	0.728000	−	2.24055i
$732$		0			0
$733$	−13.4721	+	9.78808i	−0.497605	+	0.361531i	−0.808101	−	0.589044i	$-0.799505\pi$
$733$	−13.4721	+	9.78808i	−0.497605	+	0.361531i	0.310497	+	0.950574i	$0.399505\pi$
$734$	−7.53464	−	5.47424i	−0.278109	−	0.202058i
$735$		0			0
$736$	15.9787			0.588983
$737$	8.92241	+	9.15345i	0.328661	+	0.337172i
$738$		0			0
$739$	4.25329	+	13.0903i	0.156460	+	0.481534i	0.998306	−	0.0581840i	$-0.0185310\pi$
$739$	4.25329	+	13.0903i	0.156460	+	0.481534i	−0.841846	+	0.539718i	$0.818531\pi$
$740$	−2.97414	−	2.16084i	−0.109331	−	0.0794340i
$741$		0			0
$742$	1.01722	−	3.13068i	0.0373434	−	0.114931i
$743$	−13.6221	+	41.9244i	−0.499746	+	1.53806i	0.309683	+	0.950840i	$0.399777\pi$
$743$	−13.6221	+	41.9244i	−0.499746	+	1.53806i	−0.809428	+	0.587219i	$0.800223\pi$
$744$		0			0
$745$	−17.0623	−	12.3965i	−0.625115	−	0.454172i
$746$	−5.92170	−	18.2251i	−0.216809	−	0.667269i
$747$		0			0
$748$	3.50658	−	6.66991i	0.128213	−	0.243876i
$749$	−2.21888			−0.0810762
$750$		0			0
$751$	−29.5344	−	21.4580i	−1.07773	−	0.783015i	−0.100442	−	0.994943i	$-0.532026\pi$
$751$	−29.5344	−	21.4580i	−1.07773	−	0.783015i	−0.977285	+	0.211928i	$0.932026\pi$
$752$	3.56365	−	2.58914i	0.129953	−	0.0944163i
$753$		0			0
$754$	3.85410	−	11.8617i	0.140358	−	0.431978i
$755$	10.9427	−	7.95034i	0.398246	−	0.289342i
$756$		0			0
$757$	−1.57953	−	4.86128i	−0.0574089	−	0.176686i	0.918240	−	0.396024i	$-0.129610\pi$
$757$	−1.57953	−	4.86128i	−0.0574089	−	0.176686i	−0.975649	+	0.219338i	$0.929610\pi$
$758$	−2.72239			−0.0988815
$759$		0			0
$760$	−17.7984			−0.645615
$761$	2.17588	+	6.69666i	0.0788755	+	0.242754i	0.982717	−	0.185113i	$-0.0592652\pi$
$761$	2.17588	+	6.69666i	0.0788755	+	0.242754i	−0.903842	+	0.427867i	$0.859265\pi$
$762$		0			0
$763$	0.0557281	−	0.0404888i	0.00201749	−	0.00146579i
$764$	0.433921	−	1.33547i	0.0156987	−	0.0483156i
$765$		0			0
$766$	17.6246	−	12.8050i	0.636803	−	0.462665i
$767$	−28.9431	−	21.0284i	−1.04508	−	0.759292i
$768$		0			0
$769$	11.2705			0.406425			0.203212	−	0.979135i	$-0.434862\pi$
$769$	11.2705			0.406425			0.203212	+	0.979135i	$0.434862\pi$
$770$	1.83812	+	0.315262i	0.0662412	+	0.0113612i
$771$		0			0
$772$	1.13525	+	3.49396i	0.0408587	+	0.125750i
$773$	−39.1141	−	28.4181i	−1.40684	−	1.02213i	−0.993773	−	0.111426i	$-0.964458\pi$
$773$	−39.1141	−	28.4181i	−1.40684	−	1.02213i	−0.413065	−	0.910702i	$-0.635542\pi$
$774$		0			0
$775$	1.92705	−	5.93085i	0.0692217	−	0.213043i
$776$	−9.87626	+	30.3960i	−0.354537	+	1.09115i
$777$		0			0
$778$	−24.3156	−	17.6663i	−0.871756	−	0.633368i
$779$	−7.96856	−	24.5247i	−0.285503	−	0.878689i
$780$		0			0
$781$	−22.9508	+	11.3269i	−0.821246	+	0.405309i
$782$	68.7758			2.45942
$783$		0			0
$784$	−25.9443	−	18.8496i	−0.926581	−	0.673201i
$785$	−13.3007	+	9.66356i	−0.474724	+	0.344907i
$786$		0			0
$787$	−13.5279	+	41.6345i	−0.482216	+	1.48411i	0.353756	+	0.935338i	$0.384904\pi$
$787$	−13.5279	+	41.6345i	−0.482216	+	1.48411i	−0.835972	+	0.548771i	$0.815096\pi$
$788$	−3.74582	+	2.72150i	−0.133439	+	0.0969493i
$789$		0			0
$790$	0.388544	+	1.19581i	0.0138238	+	0.0425452i
$791$	2.66923			0.0949069
$792$		0			0
$793$	−18.3262			−0.650784
$794$	1.15245	+	3.54686i	0.0408988	+	0.125873i
$795$		0			0
$796$	8.16312	−	5.93085i	0.289334	−	0.210214i
$797$	−0.953850	+	2.93565i	−0.0337871	+	0.103986i	−0.966528	−	0.256562i	$-0.917410\pi$
$797$	−0.953850	+	2.93565i	−0.0337871	+	0.103986i	0.932741	+	0.360548i	$0.117410\pi$
$798$		0			0
$799$	4.59017	−	3.33495i	0.162389	−	0.117982i
$800$	4.51750	+	3.28216i	0.159718	+	0.116042i
$801$		0			0
$802$	−5.11146			−0.180492
$803$	21.1567	+	3.62866i	0.746604	+	0.128053i
$804$		0			0
$805$	0.843459	+	2.59590i	0.0297280	+	0.0914934i
$806$	12.5986	+	9.15345i	0.443768	+	0.322417i
$807$		0			0
$808$	8.16312	−	25.1235i	0.287178	−	0.883842i
$809$	7.96856	−	24.5247i	0.280160	−	0.862243i	−0.707648	−	0.706565i	$-0.750244\pi$
$809$	7.96856	−	24.5247i	0.280160	−	0.862243i	0.987808	−	0.155678i	$-0.0497562\pi$
$810$		0			0
$811$	−5.83688	−	4.24074i	−0.204961	−	0.148913i	0.480570	−	0.876956i	$-0.340430\pi$
$811$	−5.83688	−	4.24074i	−0.204961	−	0.148913i	−0.685531	+	0.728044i	$0.740430\pi$
$812$	0.0531562	+	0.163598i	0.00186542	+	0.00574117i
$813$		0			0
$814$	4.59017	+	31.5891i	0.160885	+	1.10720i
$815$	5.58394			0.195597
$816$		0			0
$817$	−40.0066	−	29.0665i	−1.39965	−	1.01691i
$818$	−28.6484	+	20.8142i	−1.00167	+	0.727753i
$819$		0			0
$820$	1.01722	−	3.13068i	0.0355229	−	0.109328i
$821$	−24.3560	+	17.6957i	−0.850031	+	0.617584i	−0.925155	−	0.379590i	$-0.876065\pi$
$821$	−24.3560	+	17.6957i	−0.850031	+	0.617584i	0.0751234	+	0.997174i	$0.476065\pi$
$822$		0			0
$823$	16.9615	+	52.2021i	0.591240	+	1.81965i	0.572615	+	0.819825i	$0.305929\pi$
$823$	16.9615	+	52.2021i	0.591240	+	1.81965i	0.0186257	+	0.999827i	$0.494071\pi$
$824$	17.3413			0.604113
$825$		0			0
$826$	3.07701			0.107063
$827$	10.2140	+	31.4355i	0.355176	+	1.09312i	0.955907	+	0.293669i	$0.0948763\pi$
$827$	10.2140	+	31.4355i	0.355176	+	1.09312i	−0.600731	+	0.799451i	$0.705124\pi$
$828$		0			0
$829$	7.30902	−	5.31031i	0.253853	−	0.184435i	−0.453580	−	0.891216i	$-0.649853\pi$
$829$	7.30902	−	5.31031i	0.253853	−	0.184435i	0.707433	+	0.706781i	$0.249853\pi$
$830$	−3.24231	+	9.97882i	−0.112542	+	0.346370i
$831$		0			0
$832$	20.3713	−	14.8006i	0.706249	−	0.513120i
$833$	−33.4176	−	24.2793i	−1.15785	−	0.841228i
$834$		0			0
$835$	11.9098			0.412157
$836$	−4.08358	−	4.18932i	−0.141234	−	0.144891i
$837$		0			0
$838$	7.66718	+	23.5972i	0.264858	+	0.815151i
$839$	39.3393	+	28.5817i	1.35814	+	0.986749i	0.998561	+	0.0536359i	$0.0170810\pi$
$839$	39.3393	+	28.5817i	1.35814	+	0.986749i	0.359583	+	0.933113i	$0.382919\pi$
$840$		0			0
$841$	−7.83688	+	24.1194i	−0.270237	+	0.831705i
$842$	−10.5948	+	32.6074i	−0.365120	+	1.12373i
$843$		0			0
$844$	−3.40983	−	2.47739i	−0.117371	−	0.0852752i
$845$	2.35805	+	7.25732i	0.0811193	+	0.249660i
$846$		0			0
$847$	−1.47214	−	2.13914i	−0.0505832	−	0.0735017i
$848$	41.7239			1.43281
$849$		0			0
$850$	19.4443	+	14.1271i	0.666933	+	0.484555i
$851$	−37.7959	+	27.4604i	−1.29563	+	0.941329i
$852$		0			0
$853$	6.54508	−	20.1437i	0.224099	−	0.689707i	−0.774282	−	0.632840i	$-0.781889\pi$
$853$	6.54508	−	20.1437i	0.224099	−	0.689707i	0.998382	−	0.0568668i	$-0.0181110\pi$
$854$	1.27518	−	0.926476i	0.0436359	−	0.0317033i
$855$		0			0
$856$	−7.25329	−	22.3233i	−0.247912	−	0.762996i
$857$	−40.9953			−1.40037			−0.700186	−	0.713961i	$-0.746899\pi$
$857$	−40.9953			−1.40037			−0.700186	+	0.713961i	$0.746899\pi$
$858$		0			0
$859$	15.5836			0.531705			0.265853	−	0.964014i	$-0.414347\pi$
$859$	15.5836			0.531705			0.265853	+	0.964014i	$0.414347\pi$
$860$	−1.95070	−	6.00365i	−0.0665185	−	0.204723i
$861$		0			0
$862$	−6.86475	+	4.98753i	−0.233814	+	0.169876i
$863$	7.63080	−	23.4852i	0.259755	−	0.799445i	−0.733100	−	0.680121i	$-0.761927\pi$
$863$	7.63080	−	23.4852i	0.259755	−	0.799445i	0.992855	−	0.119324i	$-0.0380728\pi$
$864$		0			0
$865$	−3.39919	+	2.46965i	−0.115576	+	0.0839708i
$866$	35.7757	+	25.9925i	1.21571	+	0.883262i
$867$		0			0
$868$	−0.214782			−0.00729017
$869$	0.814685	−	1.54962i	0.0276363	−	0.0525674i
$870$		0			0
$871$	−5.04508	−	15.5272i	−0.170946	−	0.526118i
$872$	0.589512	+	0.428305i	0.0199634	+	0.0145043i
$873$		0			0
$874$	16.5000	−	50.7818i	0.558121	−	1.71772i
$875$	−0.857690	+	2.63970i	−0.0289952	+	0.0892380i
$876$		0			0
$877$	−2.04508	−	1.48584i	−0.0690576	−	0.0501733i	0.552721	−	0.833366i	$-0.313590\pi$
$877$	−2.04508	−	1.48584i	−0.0690576	−	0.0501733i	−0.621778	+	0.783193i	$0.713590\pi$
$878$	11.9231	+	36.6956i	0.402386	+	1.23842i
$879$		0			0
$880$	3.39919	+	23.3929i	0.114587	+	0.788574i
$881$	47.8114			1.61081			0.805403	−	0.592728i	$-0.201949\pi$
$881$	47.8114			1.61081			0.805403	+	0.592728i	$0.201949\pi$
$882$		0			0
$883$	40.3607	+	29.3238i	1.35825	+	0.986823i	0.998554	+	0.0537512i	$0.0171178\pi$
$883$	40.3607	+	29.3238i	1.35825	+	0.986823i	0.359691	+	0.933072i	$0.382882\pi$
$884$	−7.78639	+	5.65714i	−0.261885	+	0.190270i
$885$		0			0
$886$	−8.96556	+	27.5932i	−0.301204	+	0.927010i
$887$	−13.3273	+	9.68287i	−0.447488	+	0.325119i	−0.788603	−	0.614903i	$-0.789195\pi$
$887$	−13.3273	+	9.68287i	−0.447488	+	0.325119i	0.341115	+	0.940021i	$0.389195\pi$
$888$		0			0
$889$	−0.527864	−	1.62460i	−0.0177040	−	0.0544873i
$890$	39.9022			1.33753
$891$		0			0
$892$	−7.32624			−0.245301
$893$	−1.36119	−	4.18932i	−0.0455506	−	0.140190i
$894$		0			0
$895$	23.2984	−	16.9273i	0.778779	−	0.565816i
$896$	−0.980428	+	3.01745i	−0.0327538	+	0.100806i
$897$		0			0
$898$	−0.562306	+	0.408539i	−0.0187644	+	0.0136331i
$899$	3.67624	+	2.67094i	0.122609	+	0.0890809i
$900$		0			0
$901$	53.7426			1.79043
$902$	−25.6312	+	12.6498i	−0.853426	+	0.421191i
$903$		0			0
$904$	8.72542	+	26.8541i	0.290203	+	0.893154i
$905$	−9.69409	−	7.04317i	−0.322243	−	0.234123i
$906$		0			0
$907$	14.4828	−	44.5734i	0.480893	−	1.48004i	−0.356950	−	0.934124i	$-0.616183\pi$
$907$	14.4828	−	44.5734i	0.480893	−	1.48004i	0.837842	−	0.545912i	$-0.183817\pi$
$908$	1.10944	−	3.41451i	0.0368181	−	0.113314i
$909$		0			0
$910$	−1.92705	−	1.40008i	−0.0638811	−	0.0464123i
$911$	−11.7144	−	36.0532i	−0.388115	−	1.19449i	−0.934195	−	0.356762i	$-0.883881\pi$
$911$	−11.7144	−	36.0532i	−0.388115	−	1.19449i	0.546081	−	0.837733i	$-0.316119\pi$
$912$		0			0
$913$	13.1008	−	6.46564i	0.433574	−	0.213981i
$914$	−36.9015			−1.22059
$915$		0			0
$916$	2.94427	+	2.13914i	0.0972815	+	0.0706791i
$917$	2.31504	−	1.68198i	0.0764495	−	0.0555438i
$918$		0			0
$919$	−0.871323	+	2.68166i	−0.0287423	+	0.0884597i	−0.964399	−	0.264453i	$-0.914809\pi$
$919$	−0.871323	+	2.68166i	−0.0287423	+	0.0884597i	0.935656	+	0.352912i	$0.114809\pi$
$920$	−23.3592	+	16.9714i	−0.770129	+	0.559532i
$921$		0			0
$922$	−9.35410	−	28.7890i	−0.308061	−	0.948114i
$923$	32.6889			1.07597
$924$		0			0
$925$	−16.3262			−0.536803
$926$	0.685672	+	2.11028i	0.0225326	+	0.0693482i
$927$		0			0
$928$	−3.29180	+	2.39163i	−0.108058	+	0.0785091i
$929$	0.268178	−	0.825366i	0.00879863	−	0.0270794i	−0.946561	−	0.322525i	$-0.895468\pi$
$929$	0.268178	−	0.825366i	0.00879863	−	0.0270794i	0.955359	+	0.295446i	$0.0954682\pi$
$930$		0			0
$931$	−25.9443	+	18.8496i	−0.850289	+	0.617771i
$932$	−1.29161	−	0.938410i	−0.0423081	−	0.0307386i
$933$		0			0
$934$	7.49342			0.245192
$935$	4.37833	+	30.1313i	0.143187	+	0.985399i
$936$		0			0
$937$	10.2533	+	31.5564i	0.334960	+	1.03090i	0.966742	+	0.255755i	$0.0823241\pi$
$937$	10.2533	+	31.5564i	0.334960	+	1.03090i	−0.631781	+	0.775147i	$0.717676\pi$
$938$	1.13602	+	0.825366i	0.0370923	+	0.0269492i
$939$		0			0
$940$	0.173762	−	0.534785i	0.00566749	−	0.0174428i
$941$	−13.9598	+	42.9640i	−0.455078	+	1.40059i	0.415966	+	0.909380i	$0.363443\pi$
$941$	−13.9598	+	42.9640i	−0.455078	+	1.40059i	−0.871044	+	0.491205i	$0.836557\pi$
$942$		0			0
$943$	−33.8435	−	24.5887i	−1.10209	−	0.800719i
$944$	12.0521	+	37.0927i	0.392264	+	1.20726i
$945$		0			0
$946$	−25.5066	+	48.5164i	−0.829290	+	1.57740i
$947$	−25.3365			−0.823324			−0.411662	−	0.911337i	$-0.635052\pi$
$947$	−25.3365			−0.823324			−0.411662	+	0.911337i	$0.635052\pi$
$948$		0			0
$949$	−22.1803	−	16.1150i	−0.720004	−	0.523114i
$950$	15.0959	−	10.9678i	0.489774	−	0.355842i
$951$		0			0
$952$	−1.08359	+	3.33495i	−0.0351194	+	0.108086i
$953$	37.6834	−	27.3786i	1.22068	−	0.886879i	0.224527	−	0.974468i	$-0.427916\pi$
$953$	37.6834	−	27.3786i	1.22068	−	0.886879i	0.996157	+	0.0875894i	$0.0279163\pi$
$954$		0			0
$955$	1.75329	+	5.39607i	0.0567351	+	0.174613i
$956$	6.08744			0.196882
$957$		0			0
$958$	−56.8197			−1.83576
$959$	−0.771681	−	2.37499i	−0.0249189	−	0.0766924i
$960$		0			0
$961$	20.4894	−	14.8864i	0.660947	−	0.480206i
$962$	12.5986	−	38.7746i	0.406197	−	1.25014i
$963$		0			0
$964$	−4.32624	+	3.14320i	−0.139339	+	0.101236i
$965$	−12.0091	−	8.72515i	−0.386588	−	0.280872i
$966$		0			0
$967$	42.6869			1.37272			0.686359	−	0.727263i	$-0.259208\pi$
$967$	42.6869			1.37272			0.686359	+	0.727263i	$0.259208\pi$
$968$	16.7088	−	21.8032i	0.537041	−	0.700782i
$969$		0			0
$970$	9.42047	+	28.9932i	0.302473	+	0.930917i
$971$	−10.5784	−	7.68563i	−0.339476	−	0.246644i	0.404965	−	0.914332i	$-0.367284\pi$
$971$	−10.5784	−	7.68563i	−0.339476	−	0.246644i	−0.744441	+	0.667689i	$0.767284\pi$
$972$		0			0
$973$	−0.993422	+	3.05744i	−0.0318477	+	0.0980170i
$974$	8.05457	−	24.7894i	0.258085	−	0.794304i
$975$		0			0
$976$	16.1631	+	11.7432i	0.517369	+	0.375890i
$977$	−8.85283	−	27.2462i	−0.283227	−	0.871683i	−0.986924	−	0.161184i	$-0.948469\pi$
$977$	−8.85283	−	27.2462i	−0.283227	−	0.871683i	0.703697	−	0.710500i	$-0.251531\pi$
$978$		0			0
$979$	−38.7812	−	39.7854i	−1.23945	−	1.27155i
$980$	−4.09373			−0.130769
$981$		0			0
$982$	−38.6074	−	28.0499i	−1.23201	−	0.895109i
$983$	31.9603	−	23.2205i	1.01937	−	0.740618i	0.0532194	−	0.998583i	$-0.483052\pi$
$983$	31.9603	−	23.2205i	1.01937	−	0.740618i	0.966154	+	0.257964i	$0.0830517\pi$
$984$		0			0
$985$	5.78115	−	17.7926i	0.184203	−	0.566918i
$986$	−14.1686	+	10.2941i	−0.451220	+	0.327830i
$987$		0			0
$988$	2.30902	+	7.10642i	0.0734596	+	0.226085i
$989$	−80.2220			−2.55091
$990$		0			0
$991$	−24.7295			−0.785558			−0.392779	−	0.919633i	$-0.628486\pi$
$991$	−24.7295			−0.785558			−0.392779	+	0.919633i	$0.628486\pi$
$992$	−1.56994	−	4.83178i	−0.0498456	−	0.153409i
$993$		0			0
$994$	−2.27458	+	1.65258i	−0.0721451	+	0.0524165i
$995$	−12.5986	+	38.7746i	−0.399404	+	1.22924i
$996$		0			0
$997$	3.02786	−	2.19987i	0.0958934	−	0.0696706i	−0.538805	−	0.842430i	$-0.681124\pi$
$997$	3.02786	−	2.19987i	0.0958934	−	0.0696706i	0.634699	+	0.772760i	$0.281124\pi$
$998$	−12.1647	−	8.83819i	−0.385068	−	0.279768i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.f.c.82.1	yes	8
3.2	odd	2	inner	99.2.f.c.82.2	yes	8
9.2	odd	6		891.2.n.e.676.2		16
9.4	even	3		891.2.n.e.379.2		16
9.5	odd	6		891.2.n.e.379.1		16
9.7	even	3		891.2.n.e.676.1		16
11.3	even	5		1089.2.a.v.1.2		4
11.8	odd	10		1089.2.a.w.1.3		4
11.9	even	5	inner	99.2.f.c.64.1	✓	8
33.8	even	10		1089.2.a.w.1.2		4
33.14	odd	10		1089.2.a.v.1.3		4
33.20	odd	10	inner	99.2.f.c.64.2	yes	8
99.20	odd	30		891.2.n.e.757.1		16
99.31	even	15		891.2.n.e.460.1		16
99.86	odd	30		891.2.n.e.460.2		16
99.97	even	15		891.2.n.e.757.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.f.c.64.1	✓	8	11.9	even	5	inner
99.2.f.c.64.2	yes	8	33.20	odd	10	inner
99.2.f.c.82.1	yes	8	1.1	even	1	trivial
99.2.f.c.82.2	yes	8	3.2	odd	2	inner
891.2.n.e.379.1		16	9.5	odd	6
891.2.n.e.379.2		16	9.4	even	3
891.2.n.e.460.1		16	99.31	even	15
891.2.n.e.460.2		16	99.86	odd	30
891.2.n.e.676.1		16	9.7	even	3
891.2.n.e.676.2		16	9.2	odd	6
891.2.n.e.757.1		16	99.20	odd	30
891.2.n.e.757.2		16	99.97	even	15
1089.2.a.v.1.2		4	11.3	even	5
1089.2.a.v.1.3		4	33.14	odd	10
1089.2.a.w.1.2		4	33.8	even	10
1089.2.a.w.1.3		4	11.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.476925 - 1.46782i) q^{2} +(-0.309017 + 0.224514i) q^{4} +(0.476925 - 1.46782i) q^{5} +(-0.190983 + 0.138757i) q^{7} +(-2.02029 - 1.46782i) q^{8} +O(q^{10})\)	\(q+(-0.476925 - 1.46782i) q^{2} +(-0.309017 + 0.224514i) q^{4} +(0.476925 - 1.46782i) q^{5} +(-0.190983 + 0.138757i) q^{7} +(-2.02029 - 1.46782i) q^{8} -2.38197 q^{10} +(2.31504 + 2.37499i) q^{11} +(-1.30902 - 4.02874i) q^{13} +(0.294756 + 0.214153i) q^{14} +(-1.42705 + 4.39201i) q^{16} +(-1.83812 + 5.65714i) q^{17} +(3.73607 + 2.71441i) q^{19} +(0.182169 + 0.560659i) q^{20} +(2.38197 - 4.53077i) q^{22} +7.49164 q^{23} +(2.11803 + 1.53884i) q^{25} +(-5.28918 + 3.84281i) q^{26} +(0.0278640 - 0.0857567i) q^{28} +(-1.54336 + 1.12132i) q^{29} +(-0.736068 - 2.26538i) q^{31} +2.13287 q^{32} +9.18034 q^{34} +(0.112587 + 0.346506i) q^{35} +(-5.04508 + 3.66547i) q^{37} +(2.20246 - 6.77846i) q^{38} +(-3.11803 + 2.26538i) q^{40} +(-4.51750 - 3.28216i) q^{41} -10.7082 q^{43} +(-1.24861 - 0.214153i) q^{44} +(-3.57295 - 10.9964i) q^{46} +(-0.771681 - 0.560659i) q^{47} +(-2.14590 + 6.60440i) q^{49} +(1.24861 - 3.84281i) q^{50} +(1.30902 + 0.951057i) q^{52} +(-2.79197 - 8.59279i) q^{53} +(4.59017 - 2.26538i) q^{55} +0.589512 q^{56} +(2.38197 + 1.73060i) q^{58} +(6.83254 - 4.96413i) q^{59} +(1.33688 - 4.11450i) q^{61} +(-2.97414 + 2.16084i) q^{62} +(1.83688 + 5.65334i) q^{64} -6.53779 q^{65} +3.85410 q^{67} +(-0.702099 - 2.16084i) q^{68} +(0.454915 - 0.330515i) q^{70} +(-2.38463 + 7.33912i) q^{71} +(5.23607 - 3.80423i) q^{73} +(7.78639 + 5.65714i) q^{74} -1.76393 q^{76} +(-0.771681 - 0.132354i) q^{77} +(-0.163119 - 0.502029i) q^{79} +(5.76611 + 4.18932i) q^{80} +(-2.66312 + 8.19624i) q^{82} +(1.36119 - 4.18932i) q^{83} +(7.42705 + 5.39607i) q^{85} +(5.10701 + 15.7178i) q^{86} +(-1.19098 - 8.19624i) q^{88} -16.7518 q^{89} +(0.809017 + 0.587785i) q^{91} +(-2.31504 + 1.68198i) q^{92} +(-0.454915 + 1.40008i) q^{94} +(5.76611 - 4.18932i) q^{95} +(-3.95492 - 12.1720i) q^{97} +10.7175 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} - 6 q^{7}+O(q^{10}) \) 8 * q + 2 * q^4 - 6 * q^7	\( 8 q + 2 q^{4} - 6 q^{7} - 28 q^{10} - 6 q^{13} + 2 q^{16} + 12 q^{19} + 28 q^{22} + 8 q^{25} + 36 q^{28} + 12 q^{31} - 16 q^{34} - 18 q^{37} - 16 q^{40} - 32 q^{43} - 42 q^{46} - 44 q^{49} + 6 q^{52} - 8 q^{55} + 28 q^{58} + 42 q^{61} + 46 q^{64} + 4 q^{67} + 26 q^{70} + 24 q^{73} - 32 q^{76} + 30 q^{79} + 10 q^{82} + 46 q^{85} - 14 q^{88} + 2 q^{91} - 26 q^{94} - 54 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 - 6 * q^7 - 28 * q^10 - 6 * q^13 + 2 * q^16 + 12 * q^19 + 28 * q^22 + 8 * q^25 + 36 * q^28 + 12 * q^31 - 16 * q^34 - 18 * q^37 - 16 * q^40 - 32 * q^43 - 42 * q^46 - 44 * q^49 + 6 * q^52 - 8 * q^55 + 28 * q^58 + 42 * q^61 + 46 * q^64 + 4 * q^67 + 26 * q^70 + 24 * q^73 - 32 * q^76 + 30 * q^79 + 10 * q^82 + 46 * q^85 - 14 * q^88 + 2 * q^91 - 26 * q^94 - 54 * q^97

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