LMFDB - Embedded newform 504.2.ch.b.341.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(269,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))

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

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

chi := DirichletCharacter("504.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.ch (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.15
Character	$\chi$	$=$	504.341
Dual form			504.2.ch.b.269.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.169197 - 1.40406i) q^{2} +(-1.94274 - 0.475124i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 + 2.64733i) q^{8} +O(q^{10})$	\(q+(0.169197 - 1.40406i) q^{2} +(-1.94274 - 0.475124i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 + 2.64733i) q^{8} +(1.50696 - 2.00917i) q^{10} +(2.09284 + 3.62490i) q^{11} -3.76443 q^{13} +(3.66352 - 0.760659i) q^{14} +(3.54851 + 1.84609i) q^{16} +(2.32502 + 4.02705i) q^{17} +(0.0315203 - 0.0545948i) q^{19} +(-2.56602 - 2.45580i) q^{20} +(5.44367 - 2.32514i) q^{22} +(4.05375 + 2.34043i) q^{23} +(-0.923074 - 1.59881i) q^{25} +(-0.636930 + 5.28547i) q^{26} +(-0.448151 - 5.27249i) q^{28} -6.47316 q^{29} +(6.64896 - 3.83878i) q^{31} +(3.19241 - 4.66996i) q^{32} +(6.04758 - 2.58309i) q^{34} +(-0.928631 + 4.60593i) q^{35} +(-2.91602 - 1.68357i) q^{37} +(-0.0713210 - 0.0534936i) q^{38} +(-3.88224 + 3.18732i) q^{40} +8.06290 q^{41} -9.94628i q^{43} +(-2.34357 - 8.03662i) q^{44} +(3.97198 - 5.29569i) q^{46} +(0.338788 - 0.586799i) q^{47} +(-5.57556 + 4.23240i) q^{49} +(-2.40100 + 1.02553i) q^{50} +(7.31332 + 1.78857i) q^{52} +(-2.36197 - 4.09104i) q^{53} +7.43338i q^{55} +(-7.47870 - 0.262861i) q^{56} +(-1.09524 + 9.08868i) q^{58} +(6.53211 - 3.77132i) q^{59} +(-7.23104 + 12.5245i) q^{61} +(-4.26487 - 9.98502i) q^{62} +(-6.01674 - 5.27247i) q^{64} +(-5.78962 - 3.34264i) q^{65} +(5.67866 - 3.27857i) q^{67} +(-2.60357 - 8.92819i) q^{68} +(6.30986 + 2.08316i) q^{70} +5.10606i q^{71} +(1.29332 - 0.746696i) q^{73} +(-2.85720 + 3.80940i) q^{74} +(-0.0871753 + 0.0910878i) q^{76} +(-7.32339 + 8.30706i) q^{77} +(-5.99485 + 10.3834i) q^{79} +(3.81831 + 5.99017i) q^{80} +(1.36422 - 11.3208i) q^{82} +7.64992i q^{83} +8.25803i q^{85} +(-13.9651 - 1.68288i) q^{86} +(-11.6804 + 1.93073i) q^{88} +(8.97506 - 15.5453i) q^{89} +(-3.17692 - 9.43947i) q^{91} +(-6.76340 - 6.47290i) q^{92} +(-0.766576 - 0.574962i) q^{94} +(0.0969554 - 0.0559773i) q^{95} -4.24586i q^{97} +(4.99915 + 8.54450i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) $ 56 * q - 8 * q^4 - 20 * q^7	$ 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) $ 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$-1$

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 $

$2$	0.169197	−	1.40406i	0.119640	−	0.992817i
$2$	0.169197	−	1.40406i	0.119640	−	0.992817i
$3$		0			0
$3$		0			0
$4$	−1.94274	−	0.475124i	−0.971372	−	0.237562i
$5$	1.53798	+	0.887954i	0.687806	+	0.397105i	0.802790	−	0.596262i	$-0.203348\pi$
$5$	1.53798	+	0.887954i	0.687806	+	0.397105i	−0.114983	+	0.993367i	$0.536681\pi$
$6$		0			0
$7$	0.843933	+	2.50754i	0.318977	+	0.947763i
$7$	0.843933	+	2.50754i	0.318977	+	0.947763i
$8$	−0.995807	+	2.64733i	−0.352071	+	0.935973i
$9$		0			0
$10$	1.50696	−	2.00917i	0.476542	−	0.635356i
$11$	2.09284	+	3.62490i	0.631015	+	1.09295i	0.987345	+	0.158589i	$0.0506945\pi$
$11$	2.09284	+	3.62490i	0.631015	+	1.09295i	−0.356330	+	0.934360i	$0.615972\pi$
$12$		0			0
$13$	−3.76443			−1.04406			−0.522032	−	0.852926i	$-0.674826\pi$
$13$	−3.76443			−1.04406			−0.522032	+	0.852926i	$0.674826\pi$
$14$	3.66352	−	0.760659i	0.979118	−	0.203295i
$15$		0			0
$16$	3.54851	+	1.84609i	0.887129	+	0.461522i
$17$	2.32502	+	4.02705i	0.563899	+	0.976702i	0.997151	+	0.0754291i	$0.0240327\pi$
$17$	2.32502	+	4.02705i	0.563899	+	0.976702i	−0.433252	+	0.901273i	$0.642634\pi$
$18$		0			0
$19$	0.0315203	−	0.0545948i	0.00723126	−	0.0125249i	−0.862387	−	0.506249i	$-0.831032\pi$
$19$	0.0315203	−	0.0545948i	0.00723126	−	0.0125249i	0.869618	+	0.493724i	$0.164365\pi$
$20$	−2.56602	−	2.45580i	−0.573779	−	0.549134i
$21$		0			0
$22$	5.44367	−	2.32514i	1.16059	−	0.495721i
$23$	4.05375	+	2.34043i	0.845265	+	0.488014i	0.859050	−	0.511891i	$-0.171055\pi$
$23$	4.05375	+	2.34043i	0.845265	+	0.488014i	−0.0137854	+	0.999905i	$0.504388\pi$
$24$		0			0
$25$	−0.923074	−	1.59881i	−0.184615	−	0.319762i
$26$	−0.636930	+	5.28547i	−0.124912	+	1.03657i
$27$		0			0
$28$	−0.448151	−	5.27249i	−0.0846926	−	0.996407i
$29$	−6.47316			−1.20204			−0.601018	−	0.799235i	$-0.705238\pi$
$29$	−6.47316			−1.20204			−0.601018	+	0.799235i	$0.705238\pi$
$30$		0			0
$31$	6.64896	−	3.83878i	1.19419	−	0.689465i	0.234935	−	0.972011i	$-0.424512\pi$
$31$	6.64896	−	3.83878i	1.19419	−	0.689465i	0.959254	+	0.282546i	$0.0911790\pi$
$32$	3.19241	−	4.66996i	0.564344	−	0.825540i
$33$		0			0
$34$	6.04758	−	2.58309i	1.03715	−	0.442996i
$35$	−0.928631	+	4.60593i	−0.156967	+	0.778544i
$36$		0			0
$37$	−2.91602	−	1.68357i	−0.479391	−	0.276777i	0.240772	−	0.970582i	$-0.422600\pi$
$37$	−2.91602	−	1.68357i	−0.479391	−	0.276777i	−0.720163	+	0.693805i	$0.755933\pi$
$38$	−0.0713210	−	0.0534936i	−0.0115698	−	0.00867781i
$39$		0			0
$40$	−3.88224	+	3.18732i	−0.613837	+	0.503959i
$41$	8.06290			1.25921			0.629606	−	0.776914i	$-0.283216\pi$
$41$	8.06290			1.25921			0.629606	+	0.776914i	$0.283216\pi$
$42$		0			0
$43$		−	9.94628i		−	1.51679i	−0.651793	−	0.758397i	$-0.725983\pi$
$43$		−	9.94628i		−	1.51679i	0.651793	−	0.758397i	$-0.274017\pi$
$44$	−2.34357	−	8.03662i	−0.353307	−	1.21157i
$45$		0			0
$46$	3.97198	−	5.29569i	0.585636	−	0.780807i
$47$	0.338788	−	0.586799i	0.0494174	−	0.0855934i	−0.840259	−	0.542186i	$-0.817597\pi$
$47$	0.338788	−	0.586799i	0.0494174	−	0.0855934i	0.889676	+	0.456592i	$0.150930\pi$
$48$		0			0
$49$	−5.57556	+	4.23240i	−0.796508	+	0.604628i
$50$	−2.40100	+	1.02553i	−0.339553	+	0.145032i
$51$		0			0
$52$	7.31332	+	1.78857i	1.01418	+	0.248030i
$53$	−2.36197	−	4.09104i	−0.324441	−	0.561948i	0.656958	−	0.753927i	$-0.271843\pi$
$53$	−2.36197	−	4.09104i	−0.324441	−	0.561948i	−0.981399	+	0.191979i	$0.938509\pi$
$54$		0			0
$55$			7.43338i			1.00232i
$56$	−7.47870	−	0.262861i	−0.999383	−	0.0351262i
$57$		0			0
$58$	−1.09524	+	9.08868i	−0.143812	+	1.19340i
$59$	6.53211	−	3.77132i	0.850408	−	0.490983i	−0.0103803	−	0.999946i	$-0.503304\pi$
$59$	6.53211	−	3.77132i	0.850408	−	0.490983i	0.860789	+	0.508963i	$0.169971\pi$
$60$		0			0
$61$	−7.23104	+	12.5245i	−0.925840	+	1.60360i	−0.135636	+	0.990759i	$0.543308\pi$
$61$	−7.23104	+	12.5245i	−0.925840	+	1.60360i	−0.790204	+	0.612844i	$0.790025\pi$
$62$	−4.26487	−	9.98502i	−0.541640	−	1.26810i
$63$		0			0
$64$	−6.01674	−	5.27247i	−0.752092	−	0.659058i
$65$	−5.78962	−	3.34264i	−0.718115	−	0.414604i
$66$		0			0
$67$	5.67866	−	3.27857i	0.693758	−	0.400542i	−0.111260	−	0.993791i	$-0.535489\pi$
$67$	5.67866	−	3.27857i	0.693758	−	0.400542i	0.805018	+	0.593250i	$0.202155\pi$
$68$	−2.60357	−	8.92819i	−0.315729	−	1.08270i
$69$		0			0
$70$	6.30986	+	2.08316i	0.754173	+	0.248985i
$71$			5.10606i			0.605978i	0.952994	+	0.302989i	$0.0979846\pi$
$71$			5.10606i			0.605978i	−0.952994	+	0.302989i	$0.902015\pi$
$72$		0			0
$73$	1.29332	−	0.746696i	0.151371	−	0.0873942i	−0.422401	−	0.906409i	$-0.638813\pi$
$73$	1.29332	−	0.746696i	0.151371	−	0.0873942i	0.573772	+	0.819015i	$0.305479\pi$
$74$	−2.85720	+	3.80940i	−0.332143	+	0.442834i
$75$		0			0
$76$	−0.0871753	+	0.0910878i	−0.00999969	+	0.0104485i
$77$	−7.32339	+	8.30706i	−0.834578	+	0.946677i
$78$		0			0
$79$	−5.99485	+	10.3834i	−0.674473	+	1.16822i	0.302150	+	0.953260i	$0.402296\pi$
$79$	−5.99485	+	10.3834i	−0.674473	+	1.16822i	−0.976623	+	0.214961i	$0.931038\pi$
$80$	3.81831	+	5.99017i	0.426900	+	0.669721i
$81$		0			0
$82$	1.36422	−	11.3208i	0.150653	−	1.25017i
$83$			7.64992i			0.839688i	0.907596	+	0.419844i	$0.137915\pi$
$83$			7.64992i			0.839688i	−0.907596	+	0.419844i	$0.862085\pi$
$84$		0			0
$85$			8.25803i			0.895709i
$86$	−13.9651	−	1.68288i	−1.50590	−	0.181470i
$87$		0			0
$88$	−11.6804	+	1.93073i	−1.24513	+	0.205817i
$89$	8.97506	−	15.5453i	0.951354	−	1.64779i	0.208855	−	0.977947i	$-0.433026\pi$
$89$	8.97506	−	15.5453i	0.951354	−	1.64779i	0.742499	−	0.669847i	$-0.233640\pi$
$90$		0			0
$91$	−3.17692	−	9.43947i	−0.333032	−	0.989526i
$92$	−6.76340	−	6.47290i	−0.705133	−	0.674846i
$93$		0			0
$94$	−0.766576	−	0.574962i	−0.0790663	−	0.0593028i
$95$	0.0969554	−	0.0559773i	0.00994742	−	0.00574315i
$96$		0			0
$97$		−	4.24586i		−	0.431102i	−0.976493	−	0.215551i	$-0.930845\pi$
$97$		−	4.24586i		−	0.431102i	0.976493	−	0.215551i	$-0.0691547\pi$
$98$	4.99915	+	8.54450i	0.504991	+	0.863125i
$99$		0			0
$100$	1.03366	+	3.54466i	0.103366	+	0.354466i
$101$	3.63654	−	2.09956i	0.361849	−	0.208914i	−0.308042	−	0.951373i	$-0.599674\pi$
$101$	3.63654	−	2.09956i	0.361849	−	0.208914i	0.669892	+	0.742459i	$0.266341\pi$
$102$		0			0
$103$	−11.3144	−	6.53235i	−1.11484	−	0.643652i	−0.174759	−	0.984611i	$-0.555915\pi$
$103$	−11.3144	−	6.53235i	−1.11484	−	0.643652i	−0.940078	+	0.340959i	$0.889248\pi$
$104$	3.74865	−	9.96569i	0.367585	−	0.977217i
$105$		0			0
$106$	−6.14369	+	2.62414i	−0.596728	+	0.254879i
$107$	−5.25101	+	9.09502i	−0.507635	+	0.879249i	0.492326	+	0.870411i	$0.336147\pi$
$107$	−5.25101	+	9.09502i	−0.507635	+	0.879249i	−0.999961	+	0.00883827i	$0.997187\pi$
$108$		0			0
$109$	−2.19797	+	1.26900i	−0.210528	+	0.121548i	−0.601557	−	0.798830i	$-0.705453\pi$
$109$	−2.19797	+	1.26900i	−0.210528	+	0.121548i	0.391029	+	0.920378i	$0.372119\pi$
$110$	10.4369	+	1.25771i	0.995117	+	0.119918i
$111$		0			0
$112$	−1.63444	+	10.4560i	−0.154440	+	0.988002i
$113$		−	4.56501i		−	0.429440i	−0.976676	−	0.214720i	$-0.931116\pi$
$113$		−	4.56501i		−	0.429440i	0.976676	−	0.214720i	$-0.0688838\pi$
$114$		0			0
$115$	4.15639	+	7.19909i	0.387586	+	0.671318i
$116$	12.5757	+	3.07556i	1.16763	+	0.285558i
$117$		0			0
$118$	−4.18992	−	9.80954i	−0.385714	−	0.903041i
$119$	−8.13584	+	9.22863i	−0.745811	+	0.845988i
$120$		0			0
$121$	−3.25995	+	5.64639i	−0.296359	+	0.513308i
$122$	16.3617	+	12.2719i	1.48132	+	1.11105i
$123$		0			0
$124$	−14.7411	+	4.29869i	−1.32379	+	0.386033i
$125$		−	12.1581i		−	1.08746i
$126$		0			0
$127$	8.36161			0.741973			0.370986	−	0.928638i	$-0.379020\pi$
$127$	8.36161			0.741973			0.370986	+	0.928638i	$0.379020\pi$
$128$	−8.42085	+	7.55575i	−0.744305	+	0.667840i
$129$		0			0
$130$	−5.67284	+	7.56339i	−0.497541	+	0.663353i
$131$	5.45901	+	3.15176i	0.476956	+	0.275371i	0.719147	−	0.694858i	$-0.244533\pi$
$131$	5.45901	+	3.15176i	0.476956	+	0.275371i	−0.242191	+	0.970229i	$0.577866\pi$
$132$		0			0
$133$	0.163500	+	0.0329643i	0.0141772	+	0.00285837i
$134$	−3.64249	−	8.52788i	−0.314663	−	0.736696i
$135$		0			0
$136$	−12.9762	+	2.14493i	−1.11270	+	0.183926i
$137$	−11.3468	+	6.55109i	−0.969425	+	0.559698i	−0.899061	−	0.437824i	$-0.855749\pi$
$137$	−11.3468	+	6.55109i	−0.969425	+	0.559698i	−0.0703639	+	0.997521i	$0.522416\pi$
$138$		0			0
$139$	19.1125			1.62110			0.810549	−	0.585671i	$-0.199169\pi$
$139$	19.1125			1.62110			0.810549	+	0.585671i	$0.199169\pi$
$140$	3.99248	−	8.50693i	0.337426	−	0.718967i
$141$		0			0
$142$	7.16920	+	0.863931i	0.601626	+	0.0724994i
$143$	−7.87834	−	13.6457i	−0.658820	−	1.14111i
$144$		0			0
$145$	−9.95561	−	5.74787i	−0.826768	−	0.477335i
$146$	−0.829578	−	1.94223i	−0.0686564	−	0.160740i
$147$		0			0
$148$	4.86518	+	4.65621i	0.399916	+	0.382738i
$149$	2.19406	−	3.80023i	0.179745	−	0.311327i	−0.762048	−	0.647520i	$-0.775806\pi$
$149$	2.19406	−	3.80023i	0.179745	−	0.311327i	0.941793	+	0.336193i	$0.109140\pi$
$150$		0			0
$151$	1.37428	+	2.38033i	0.111838	+	0.193708i	0.916511	−	0.400009i	$-0.130993\pi$
$151$	1.37428	+	2.38033i	0.111838	+	0.193708i	−0.804674	+	0.593717i	$0.797660\pi$
$152$	0.113142	+	0.137811i	0.00917707	+	0.0111779i
$153$		0			0
$154$	10.4245	+	11.6880i	0.840028	+	0.941844i
$155$	13.6346			1.09516
$156$		0			0
$157$	−0.669124	−	1.15896i	−0.0534019	−	0.0924948i	0.838089	−	0.545534i	$-0.183673\pi$
$157$	−0.669124	−	1.15896i	−0.0534019	−	0.0924948i	−0.891491	+	0.453039i	$0.850340\pi$
$158$	13.5645	+	10.1739i	1.07914	+	0.809395i
$159$		0			0
$160$	9.05658	−	4.34760i	0.715986	−	0.343708i
$161$	−2.44765	+	12.1401i	−0.192902	+	0.956776i
$162$		0			0
$163$	3.30942	+	1.91070i	0.259214	+	0.149657i	0.623976	−	0.781444i	$-0.285516\pi$
$163$	3.30942	+	1.91070i	0.259214	+	0.149657i	−0.364762	+	0.931101i	$0.618850\pi$
$164$	−15.6642	−	3.83088i	−1.22316	−	0.299141i
$165$		0			0
$166$	10.7409	+	1.29434i	0.833656	+	0.100461i
$167$	7.25804			0.561644			0.280822	−	0.959760i	$-0.409393\pi$
$167$	7.25804			0.561644			0.280822	+	0.959760i	$0.409393\pi$
$168$		0			0
$169$	1.17093			0.0900713
$170$	11.5947	+	1.39723i	0.889276	+	0.107163i
$171$		0			0
$172$	−4.72572	+	19.3231i	−0.360332	+	1.47337i
$173$	−1.07114	−	0.618425i	−0.0814375	−	0.0470180i	0.458728	−	0.888577i	$-0.348305\pi$
$173$	−1.07114	−	0.618425i	−0.0814375	−	0.0470180i	−0.540166	+	0.841559i	$0.681638\pi$
$174$		0			0
$175$	3.23008	−	3.66394i	0.244171	−	0.276968i
$176$	0.734572	+	16.7266i	0.0553705	+	1.26081i
$177$		0			0
$178$	−20.3078	−	15.2317i	−1.52214	−	1.14166i
$179$	−8.80192	−	15.2454i	−0.657886	−	1.13949i	−0.981162	−	0.193188i	$-0.938117\pi$
$179$	−8.80192	−	15.2454i	−0.657886	−	1.13949i	0.323275	−	0.946305i	$-0.395216\pi$
$180$		0			0
$181$	−16.4773			−1.22475			−0.612376	−	0.790567i	$-0.709786\pi$
$181$	−16.4773			−1.22475			−0.612376	+	0.790567i	$0.709786\pi$
$182$	−13.7911	+	2.86345i	−1.02226	+	0.212253i
$183$		0			0
$184$	−10.2327	+	8.40100i	−0.754361	+	0.619330i
$185$	−2.98986	−	5.17859i	−0.219819	−	0.380737i
$186$		0			0
$187$	−9.73176	+	16.8559i	−0.711657	+	1.23263i
$188$	−0.936981	+	0.979033i	−0.0683364	+	0.0714033i
$189$		0			0
$190$	−0.0621906	−	0.145602i	−0.00451178	−	0.0105631i
$191$	−14.2159	−	8.20758i	−1.02863	−	0.593880i	−0.112038	−	0.993704i	$-0.535738\pi$
$191$	−14.2159	−	8.20758i	−1.02863	−	0.593880i	−0.916592	+	0.399824i	$0.869071\pi$
$192$		0			0
$193$	−11.7627	−	20.3736i	−0.846696	−	1.46652i	−0.884140	−	0.467222i	$-0.845255\pi$
$193$	−11.7627	−	20.3736i	−0.846696	−	1.46652i	0.0374435	−	0.999299i	$-0.488079\pi$
$194$	−5.96142	−	0.718387i	−0.428005	−	0.0515772i
$195$		0			0
$196$	12.8428	−	5.57339i	0.917342	−	0.398099i
$197$	0.792724			0.0564792			0.0282396	−	0.999601i	$-0.491010\pi$
$197$	0.792724			0.0564792			0.0282396	+	0.999601i	$0.491010\pi$
$198$		0			0
$199$	10.9922	−	6.34632i	0.779213	−	0.449879i	−0.0569382	−	0.998378i	$-0.518134\pi$
$199$	10.9922	−	6.34632i	0.779213	−	0.449879i	0.836151	+	0.548499i	$0.184800\pi$
$200$	5.15179	−	0.851576i	0.364287	−	0.0602155i
$201$		0			0
$202$	−2.33260	−	5.46115i	−0.164121	−	0.384245i
$203$	−5.46292	−	16.2317i	−0.383421	−	1.13925i
$204$		0			0
$205$	12.4006	+	7.15948i	0.866095	+	0.500040i
$206$	−11.0861	+	14.7807i	−0.772408	+	1.02982i
$207$		0			0
$208$	−13.3581	−	6.94947i	−0.926220	−	0.481859i
$209$	0.263868			0.0182521
$210$		0			0
$211$		−	18.9821i		−	1.30678i	−0.757020	−	0.653392i	$-0.773345\pi$
$211$		−	18.9821i		−	1.30678i	0.757020	−	0.653392i	$-0.226655\pi$
$212$	2.64494	+	9.07008i	0.181655	+	0.622936i
$213$		0			0
$214$	11.8815	+	8.91157i	0.812200	+	0.609182i
$215$	8.83184	−	15.2972i	0.602326	−	1.04326i
$216$		0			0
$217$	15.2372	+	13.4329i	1.03437	+	0.911884i
$218$	1.40986	+	3.30079i	0.0954876	+	0.223558i
$219$		0			0
$220$	3.53178	−	14.4412i	0.238112	−	0.973623i
$221$	−8.75236	−	15.1595i	−0.588747	−	1.01974i
$222$		0			0
$223$		−	8.56676i		−	0.573673i	−0.957980	−	0.286836i	$-0.907396\pi$
$223$		−	8.56676i		−	0.573673i	0.957980	−	0.286836i	$-0.0926036\pi$
$224$	14.4043	+	4.06398i	0.962428	+	0.271536i
$225$		0			0
$226$	−6.40952	−	0.772386i	−0.426355	−	0.0513783i
$227$	12.3870	−	7.15164i	0.822155	−	0.474671i	−0.0290044	−	0.999579i	$-0.509234\pi$
$227$	12.3870	−	7.15164i	0.822155	−	0.474671i	0.851159	+	0.524908i	$0.175900\pi$
$228$		0			0
$229$	14.0246	−	24.2914i	0.926774	−	1.60522i	0.138091	−	0.990420i	$-0.455903\pi$
$229$	14.0246	−	24.2914i	0.926774	−	1.60522i	0.788683	−	0.614800i	$-0.210763\pi$
$230$	10.8112	−	4.61775i	0.712867	−	0.304485i
$231$		0			0
$232$	6.44602	−	17.1366i	0.423202	−	1.12507i
$233$	7.52792	+	4.34625i	0.493170	+	0.284732i	0.725889	−	0.687812i	$-0.241429\pi$
$233$	7.52792	+	4.34625i	0.493170	+	0.284732i	−0.232718	+	0.972544i	$0.574762\pi$
$234$		0			0
$235$	1.04210	−	0.601657i	0.0679792	−	0.0392478i
$236$	−14.4821	+	4.22314i	−0.942702	+	0.274903i
$237$		0			0
$238$	11.5810	+	12.9846i	0.750682	+	0.841668i
$239$			12.4878i			0.807772i	0.914809	+	0.403886i	$0.132341\pi$
$239$			12.4878i			0.807772i	−0.914809	+	0.403886i	$0.867659\pi$
$240$		0			0
$241$	20.0923	−	11.6003i	1.29426	−	0.747240i	0.314852	−	0.949141i	$-0.398045\pi$
$241$	20.0923	−	11.6003i	1.29426	−	0.747240i	0.979406	+	0.201900i	$0.0647117\pi$
$242$	7.37628	+	5.53250i	0.474165	+	0.355642i
$243$		0			0
$244$	19.9988	−	20.8963i	1.28029	−	1.33775i
$245$	−12.3333	+	1.55851i	−0.787944	+	0.0995697i
$246$		0			0
$247$	−0.118656	+	0.205518i	−0.00754991	+	0.0130768i
$248$	3.54144	+	21.4247i	0.224882	+	1.36047i
$249$		0			0
$250$	−17.0707	−	2.05712i	−1.07965	−	0.130104i
$251$			13.9698i			0.881768i	0.897564	+	0.440884i	$0.145335\pi$
$251$			13.9698i			0.881768i	−0.897564	+	0.440884i	$0.854665\pi$
$252$		0			0
$253$			19.5926i			1.23178i
$254$	1.41476	−	11.7402i	0.0887699	−	0.736643i
$255$		0			0
$256$	9.18391	+	13.1018i	0.573994	+	0.818859i
$257$	−11.8457	+	20.5174i	−0.738915	+	1.27984i	0.214069	+	0.976819i	$0.431328\pi$
$257$	−11.8457	+	20.5174i	−0.738915	+	1.27984i	−0.952984	+	0.303020i	$0.902005\pi$
$258$		0			0
$259$	1.76069	−	8.73287i	0.109404	−	0.542634i
$260$	9.65959	+	9.24469i	0.599063	+	0.573331i
$261$		0			0
$262$	5.34890	−	7.13148i	0.330456	−	0.440585i
$263$	−13.5097	+	7.79983i	−0.833044	+	0.480958i	−0.854894	−	0.518803i	$-0.826378\pi$
$263$	−13.5097	+	7.79983i	−0.833044	+	0.480958i	0.0218497	+	0.999761i	$0.493044\pi$
$264$		0			0
$265$		−	8.38927i		−	0.515349i
$266$	0.0739474	−	0.223986i	0.00453401	−	0.0137334i
$267$		0			0
$268$	−12.5899	+	3.67137i	−0.769051	+	0.224264i
$269$	27.5546	−	15.9086i	1.68003	−	0.969966i	0.718396	−	0.695635i	$-0.244877\pi$
$269$	27.5546	−	15.9086i	1.68003	−	0.969966i	0.961635	−	0.274332i	$-0.0884566\pi$
$270$		0			0
$271$	8.16789	+	4.71573i	0.496164	+	0.286460i	0.727128	−	0.686502i	$-0.240855\pi$
$271$	8.16789	+	4.71573i	0.496164	+	0.286460i	−0.230964	+	0.972962i	$0.574188\pi$
$272$	0.816065	+	18.5822i	0.0494812	+	1.12671i
$273$		0			0
$274$	7.27825	+	17.0400i	0.439695	+	1.02942i
$275$	3.86369	−	6.69211i	0.232989	−	0.403549i
$276$		0			0
$277$	23.1275	−	13.3527i	1.38960	−	0.802284i	0.396327	−	0.918109i	$-0.370285\pi$
$277$	23.1275	−	13.3527i	1.38960	−	0.802284i	0.993270	+	0.115825i	$0.0369513\pi$
$278$	3.23377	−	26.8349i	0.193949	−	1.60945i
$279$		0			0
$280$	−11.2687	−	7.04502i	−0.673433	−	0.421020i
$281$		−	26.1930i		−	1.56254i	−0.624193	−	0.781271i	$-0.714572\pi$
$281$		−	26.1930i		−	1.56254i	0.624193	−	0.781271i	$-0.285428\pi$
$282$		0			0
$283$	2.62071	+	4.53920i	0.155785	+	0.269827i	0.933345	−	0.358982i	$-0.116876\pi$
$283$	2.62071	+	4.53920i	0.155785	+	0.269827i	−0.777560	+	0.628809i	$0.783543\pi$
$284$	2.42601	−	9.91978i	0.143957	−	0.588630i
$285$		0			0
$286$	−20.4923	+	8.75282i	−1.21174	+	0.517565i
$287$	6.80454	+	20.2181i	0.401659	+	1.19343i
$288$		0			0
$289$	−2.31140	+	4.00346i	−0.135964	+	0.235497i
$290$	−9.75480	+	13.0057i	−0.572821	+	0.763721i
$291$		0			0
$292$	−2.86736	+	0.836155i	−0.167799	+	0.0489323i
$293$			8.29435i			0.484561i	0.970206	+	0.242280i	$0.0778954\pi$
$293$			8.29435i			0.484561i	−0.970206	+	0.242280i	$0.922105\pi$
$294$		0			0
$295$	13.3950			0.779888
$296$	7.36075	−	6.04317i	0.427835	−	0.351252i
$297$		0			0
$298$	−4.96450	−	3.72357i	−0.287586	−	0.215701i
$299$	−15.2600	−	8.81039i	−0.882511	−	0.509518i
$300$		0			0
$301$	24.9407	−	8.39399i	1.43756	−	0.483821i
$302$	3.57464	−	1.52683i	0.205697	−	0.0878589i
$303$		0			0
$304$	0.212637	−	0.135541i	0.0121956	−	0.00777382i
$305$	−22.2424	+	12.8417i	−1.27360	+	0.735312i
$306$		0			0
$307$	−17.8873			−1.02088			−0.510442	−	0.859912i	$-0.670518\pi$
$307$	−17.8873			−1.02088			−0.510442	+	0.859912i	$0.670518\pi$
$308$	18.1744	−	12.6590i	1.03558	−	0.721312i
$309$		0			0
$310$	2.30694	−	19.1438i	0.131025	−	1.08729i
$311$	0.257495	+	0.445994i	0.0146012	+	0.0252900i	0.873234	−	0.487302i	$-0.162019\pi$
$311$	0.257495	+	0.445994i	0.0146012	+	0.0252900i	−0.858632	+	0.512592i	$0.828685\pi$
$312$		0			0
$313$	20.1970	+	11.6607i	1.14160	+	0.659104i	0.946827	−	0.321744i	$-0.104269\pi$
$313$	20.1970	+	11.6607i	1.14160	+	0.659104i	0.194775	+	0.980848i	$0.437602\pi$
$314$	−1.74045	+	0.743395i	−0.0982195	+	0.0419522i
$315$		0			0
$316$	16.5799	−	17.3240i	0.932689	−	0.974549i
$317$	−10.4926	+	18.1736i	−0.589321	+	1.02073i	0.405001	+	0.914316i	$0.367271\pi$
$317$	−10.4926	+	18.1736i	−0.589321	+	1.02073i	−0.994322	+	0.106417i	$0.966062\pi$
$318$		0			0
$319$	−13.5473	−	23.4646i	−0.758503	−	1.31376i
$320$	−4.57192	−	13.4515i	−0.255578	−	0.751964i
$321$		0			0
$322$	16.6313	+	5.49071i	0.926824	+	0.305985i
$323$	0.293141			0.0163108
$324$		0			0
$325$	3.47485	+	6.01861i	0.192750	+	0.333853i
$326$	3.24267	−	4.32333i	0.179595	−	0.239447i
$327$		0			0
$328$	−8.02909	+	21.3452i	−0.443332	+	1.17859i
$329$	1.75734	+	0.354308i	0.0968852	+	0.0195336i
$330$		0			0
$331$	8.16441	+	4.71372i	0.448756	+	0.259090i	0.707305	−	0.706909i	$-0.249911\pi$
$331$	8.16441	+	4.71372i	0.448756	+	0.259090i	−0.258548	+	0.965998i	$0.583244\pi$
$332$	3.63466	−	14.8618i	0.199478	−	0.815649i
$333$		0			0
$334$	1.22804	−	10.1907i	0.0671953	−	0.557610i
$335$	11.6449			0.636229
$336$		0			0
$337$	−14.8141			−0.806977			−0.403488	−	0.914985i	$-0.632202\pi$
$337$	−14.8141			−0.806977			−0.403488	+	0.914985i	$0.632202\pi$
$338$	0.198117	−	1.64405i	0.0107762	−	0.0894244i
$339$		0			0
$340$	3.92359	−	16.0432i	0.212787	−	0.870067i
$341$	27.8304	+	16.0679i	1.50710	+	0.870125i
$342$		0			0
$343$	−15.3183	−	10.4091i	−0.827111	−	0.562038i
$344$	26.3311	+	9.90457i	1.41968	+	0.534019i
$345$		0			0
$346$	−1.04954	+	1.39931i	−0.0564235	+	0.0752274i
$347$	−10.9642	−	18.9905i	−0.588587	−	1.01946i	−0.994418	−	0.105515i	$-0.966351\pi$
$347$	−10.9642	−	18.9905i	−0.588587	−	1.01946i	0.405830	−	0.913948i	$-0.366982\pi$
$348$		0			0
$349$	−34.9301			−1.86977			−0.934884	−	0.354954i	$-0.884497\pi$
$349$	−34.9301			−1.86977			−0.934884	+	0.354954i	$0.884497\pi$
$350$	−4.59785	−	5.15514i	−0.245766	−	0.275554i
$351$		0			0
$352$	23.6093	+	1.79871i	1.25838	+	0.0958715i
$353$	−3.71324	−	6.43152i	−0.197636	−	0.342315i	0.750126	−	0.661295i	$-0.229993\pi$
$353$	−3.71324	−	6.43152i	−0.197636	−	0.342315i	−0.947761	+	0.318980i	$0.896660\pi$
$354$		0			0
$355$	−4.53395	+	7.85303i	−0.240637	+	0.416796i
$356$	−24.8222	+	25.9362i	−1.31557	+	1.37462i
$357$		0			0
$358$	−22.8946	+	9.77891i	−1.21002	+	0.516832i
$359$	−6.73364	−	3.88767i	−0.355388	−	0.205183i	0.311668	−	0.950191i	$-0.399112\pi$
$359$	−6.73364	−	3.88767i	−0.355388	−	0.205183i	−0.667056	+	0.745008i	$0.732446\pi$
$360$		0			0
$361$	9.49801	+	16.4510i	0.499895	+	0.865844i
$362$	−2.78792	+	23.1351i	−0.146530	+	1.21595i
$363$		0			0
$364$	1.68703	+	19.8479i	0.0884246	+	1.04031i
$365$	2.65213			0.138819
$366$		0			0
$367$	−6.99509	+	4.03862i	−0.365141	+	0.210814i	−0.671333	−	0.741155i	$-0.734278\pi$
$367$	−6.99509	+	4.03862i	−0.365141	+	0.210814i	0.306193	+	0.951970i	$0.400945\pi$
$368$	10.0641	+	15.7886i	0.524629	+	0.823040i
$369$		0			0
$370$	−7.77690	+	3.32173i	−0.404302	+	0.172688i
$371$	8.26513	−	9.37530i	0.429104	−	0.486741i
$372$		0			0
$373$	−24.1708	−	13.9550i	−1.25152	−	0.722563i	−0.280105	−	0.959969i	$-0.590369\pi$
$373$	−24.1708	−	13.9550i	−1.25152	−	0.722563i	−0.971410	+	0.237407i	$0.923703\pi$
$374$	22.0201	+	16.5159i	1.13863	+	0.854017i
$375$		0			0
$376$	1.21608	+	1.48122i	0.0627147	+	0.0763883i
$377$	24.3678			1.25500
$378$		0			0
$379$			29.0460i			1.49199i	0.665949	+	0.745997i	$0.268027\pi$
$379$			29.0460i			1.49199i	−0.665949	+	0.745997i	$0.731973\pi$
$380$	−0.214956	+	0.0626836i	−0.0110270	+	0.00321560i
$381$		0			0
$382$	−13.9292	+	18.5713i	−0.712679	+	0.950189i
$383$	5.63040	−	9.75214i	0.287700	−	0.498311i	−0.685560	−	0.728016i	$-0.740443\pi$
$383$	5.63040	−	9.75214i	0.287700	−	0.498311i	0.973260	+	0.229705i	$0.0737760\pi$
$384$		0			0
$385$	−18.6395	+	6.27327i	−0.949958	+	0.319716i
$386$	−30.5958	+	13.0683i	−1.55729	+	0.665160i
$387$		0			0
$388$	−2.01731	+	8.24862i	−0.102413	+	0.418760i
$389$	2.51811	+	4.36149i	0.127673	+	0.221136i	0.922775	−	0.385340i	$-0.125916\pi$
$389$	2.51811	+	4.36149i	0.127673	+	0.221136i	−0.795102	+	0.606476i	$0.792583\pi$
$390$		0			0
$391$			21.7662i			1.10076i
$392$	−5.65238	−	18.9750i	−0.285488	−	0.958382i
$393$		0			0
$394$	0.134127	−	1.11303i	0.00675720	−	0.0560736i
$395$	−18.4399	+	10.6463i	−0.927814	+	0.535674i
$396$		0			0
$397$	13.8771	−	24.0358i	0.696471	−	1.20632i	−0.273211	−	0.961954i	$-0.588086\pi$
$397$	13.8771	−	24.0358i	0.696471	−	1.20632i	0.969682	−	0.244369i	$-0.0785808\pi$
$398$	−7.05075	−	16.5074i	−0.353422	−	0.827440i
$399$		0			0
$400$	−0.323993	−	7.37748i	−0.0161996	−	0.368874i
$401$	−3.70394	−	2.13847i	−0.184966	−	0.106790i	0.404658	−	0.914468i	$-0.367391\pi$
$401$	−3.70394	−	2.13847i	−0.184966	−	0.106790i	−0.589624	+	0.807678i	$0.700724\pi$
$402$		0			0
$403$	−25.0295	+	14.4508i	−1.24681	+	0.719846i
$404$	−8.06242	+	2.35110i	−0.401121	+	0.116971i
$405$		0			0
$406$	−23.7146	+	4.92387i	−1.17694	+	0.244368i
$407$		−	14.0937i		−	0.698600i
$408$		0			0
$409$	13.6093	−	7.85734i	0.672937	−	0.388521i	−0.124251	−	0.992251i	$-0.539653\pi$
$409$	13.6093	−	7.85734i	0.672937	−	0.388521i	0.797189	+	0.603730i	$0.206320\pi$
$410$	12.1505	−	16.1998i	0.600068	−	0.800049i
$411$		0			0
$412$	18.8772	+	18.0664i	0.930015	+	0.890069i
$413$	14.9694	+	13.1968i	0.736596	+	0.649373i
$414$		0			0
$415$	−6.79278	+	11.7654i	−0.333444	+	0.577543i
$416$	−12.0176	+	17.5797i	−0.589211	+	0.861917i
$417$		0			0
$418$	0.0446457	−	0.370485i	0.00218369	−	0.0181210i
$419$			38.0838i			1.86052i	0.366904	+	0.930259i	$0.380418\pi$
$419$			38.0838i			1.86052i	−0.366904	+	0.930259i	$0.619582\pi$
$420$		0			0
$421$			15.7506i			0.767635i	0.923409	+	0.383818i	$0.125391\pi$
$421$			15.7506i			0.767635i	−0.923409	+	0.383818i	$0.874609\pi$
$422$	−26.6520	−	3.21172i	−1.29740	−	0.156344i
$423$		0			0
$424$	13.1824	−	2.17902i	0.640195	−	0.105822i
$425$	4.29232	−	7.43452i	0.208208	−	0.360627i
$426$		0			0
$427$	−37.5083	−	7.56230i	−1.81516	−	0.365965i
$428$	14.5226	−	15.1744i	0.701978	−	0.733483i
$429$		0			0
$430$	−19.9838	−	14.9886i	−0.963704	−	0.722816i
$431$	6.36898	−	3.67713i	0.306783	−	0.177121i	−0.338703	−	0.940893i	$-0.609988\pi$
$431$	6.36898	−	3.67713i	0.306783	−	0.177121i	0.645486	+	0.763772i	$0.276655\pi$
$432$		0			0
$433$			8.06468i			0.387564i	0.981045	+	0.193782i	$0.0620754\pi$
$433$			8.06468i			0.387564i	−0.981045	+	0.193782i	$0.937925\pi$
$434$	21.4386	−	19.1210i	1.02909	−	0.917840i
$435$		0			0
$436$	4.87303	−	1.42103i	0.233376	−	0.0680552i
$437$	0.255551	−	0.147542i	0.0122247	−	0.00705791i
$438$		0			0
$439$	−5.02415	−	2.90069i	−0.239790	−	0.138443i	0.375290	−	0.926907i	$-0.377543\pi$
$439$	−5.02415	−	2.90069i	−0.239790	−	0.138443i	−0.615080	+	0.788465i	$0.710876\pi$
$440$	−19.6786	−	7.40221i	−0.938142	−	0.352887i
$441$		0			0
$442$	−22.7657	+	9.72385i	−1.08285	+	0.462516i
$443$	−7.82446	+	13.5524i	−0.371751	+	0.643892i	−0.989835	−	0.142220i	$-0.954576\pi$
$443$	−7.82446	+	13.5524i	−0.371751	+	0.643892i	0.618084	+	0.786112i	$0.287909\pi$
$444$		0			0
$445$	27.6069	−	15.9389i	1.30869	−	0.755575i
$446$	−12.0282	−	1.44947i	−0.569552	−	0.0686344i
$447$		0			0
$448$	8.14322	−	19.5368i	0.384731	−	0.923029i
$449$			34.7839i			1.64155i	0.571250	+	0.820776i	$0.306459\pi$
$449$			34.7839i			1.64155i	−0.571250	+	0.820776i	$0.693541\pi$
$450$		0			0
$451$	16.8743	+	29.2272i	0.794582	+	1.37626i
$452$	−2.16894	+	8.86864i	−0.102019	+	0.417146i
$453$		0			0
$454$	−7.94546	−	18.6021i	−0.372899	−	0.873039i
$455$	3.49577	−	17.3387i	0.163884	−	0.812851i
$456$		0			0
$457$	−5.38911	+	9.33422i	−0.252092	+	0.436636i	−0.964102	−	0.265533i	$-0.914452\pi$
$457$	−5.38911	+	9.33422i	−0.252092	+	0.436636i	0.712010	+	0.702170i	$0.247785\pi$
$458$	−31.7335	−	23.8014i	−1.48281	−	1.11217i
$459$		0			0
$460$	−4.65435	−	15.9608i	−0.217010	−	0.744176i
$461$			19.5062i			0.908494i	0.890876	+	0.454247i	$0.150092\pi$
$461$			19.5062i			0.908494i	−0.890876	+	0.454247i	$0.849908\pi$
$462$		0			0
$463$	−27.2099			−1.26455			−0.632275	−	0.774744i	$-0.717879\pi$
$463$	−27.2099			−1.26455			−0.632275	+	0.774744i	$0.717879\pi$
$464$	−22.9701	−	11.9500i	−1.06636	−	0.554767i
$465$		0			0
$466$	7.37607	−	9.83425i	0.341690	−	0.455563i
$467$	−29.3243	−	16.9304i	−1.35697	−	0.783445i	−0.367752	−	0.929924i	$-0.619872\pi$
$467$	−29.3243	−	16.9304i	−1.35697	−	0.783445i	−0.989214	+	0.146479i	$0.953206\pi$
$468$		0			0
$469$	13.0136	+	11.4726i	0.600911	+	0.529755i
$470$	−0.668440	−	1.56497i	−0.0308328	−	0.0721865i
$471$		0			0
$472$	3.47920	+	21.0482i	0.160143	+	0.968820i
$473$	36.0543	−	20.8160i	1.65778	−	0.957118i
$474$		0			0
$475$	−0.116382			−0.00533999
$476$	20.1906	−	14.0633i	0.925435	−	0.644593i
$477$		0			0
$478$	17.5336	+	2.11291i	0.801970	+	0.0966421i
$479$	0.640883	+	1.11004i	0.0292827	+	0.0507191i	0.880295	−	0.474426i	$-0.157344\pi$
$479$	0.640883	+	1.11004i	0.0292827	+	0.0507191i	−0.851013	+	0.525145i	$0.824011\pi$
$480$		0			0
$481$	10.9772	+	6.33766i	0.500515	+	0.288973i
$482$	−12.8879	−	30.1734i	−0.587028	−	1.37436i
$483$		0			0
$484$	9.01598	−	9.42062i	0.409817	−	0.428210i
$485$	3.77013	−	6.53005i	0.171193	−	0.296515i
$486$		0			0
$487$	−11.5313	−	19.9728i	−0.522534	−	0.905055i	−0.999656	−	0.0262185i	$-0.991653\pi$
$487$	−11.5313	−	19.9728i	−0.522534	−	0.905055i	0.477122	−	0.878837i	$-0.341680\pi$
$488$	−25.9559	−	31.6150i	−1.17497	−	1.43114i
$489$		0			0
$490$	0.101483	+	17.5803i	0.00458454	+	0.794197i
$491$	33.6759			1.51977			0.759886	−	0.650057i	$-0.225255\pi$
$491$	33.6759			1.51977			0.759886	+	0.650057i	$0.225255\pi$
$492$		0			0
$493$	−15.0502	−	26.0677i	−0.677827	−	1.17403i
$494$	0.268483	+	0.201373i	0.0120796	+	0.00906019i
$495$		0			0
$496$	30.6807	−	1.34739i	1.37760	−	0.0604994i
$497$	−12.8037	+	4.30917i	−0.574323	+	0.193293i
$498$		0			0
$499$	−5.15436	−	2.97587i	−0.230741	−	0.133218i	0.380173	−	0.924915i	$-0.375865\pi$
$499$	−5.15436	−	2.97587i	−0.230741	−	0.133218i	−0.610914	+	0.791697i	$0.709198\pi$
$500$	−5.77662	+	23.6202i	−0.258338	+	1.05633i
$501$		0			0
$502$	19.6144	+	2.36365i	0.875435	+	0.105495i
$503$	1.41791			0.0632214			0.0316107	−	0.999500i	$-0.489936\pi$
$503$	1.41791			0.0632214			0.0316107	+	0.999500i	$0.489936\pi$
$504$		0			0
$505$	7.45725			0.331843
$506$	27.5091	+	3.31501i	1.22293	+	0.147370i
$507$		0			0
$508$	−16.2445	−	3.97280i	−0.720732	−	0.176265i
$509$	7.25269	+	4.18734i	0.321470	+	0.185601i	0.652048	−	0.758178i	$-0.273910\pi$
$509$	7.25269	+	4.18734i	0.321470	+	0.185601i	−0.330578	+	0.943779i	$0.607244\pi$
$510$		0			0
$511$	2.96385	+	2.61289i	0.131113	+	0.115587i
$512$	19.9495	−	10.6779i	0.881651	−	0.471903i
$513$		0			0
$514$	26.8033	+	20.1035i	1.18224	+	0.886728i
$515$	−11.6009	−	20.0933i	−0.511195	−	0.885416i
$516$		0			0
$517$	2.83612			0.124732
$518$	−11.9635	−	3.94968i	−0.525647	−	0.173539i
$519$		0			0
$520$	14.6144	−	11.9984i	0.640885	−	0.526166i
$521$	−11.7714	−	20.3887i	−0.515715	−	0.893244i	−0.999834	−	0.0182421i	$-0.994193\pi$
$521$	−11.7714	−	20.3887i	−0.515715	−	0.893244i	0.484119	−	0.875002i	$-0.339140\pi$
$522$		0			0
$523$	−14.4448	+	25.0191i	−0.631626	+	1.09401i	0.355593	+	0.934641i	$0.384279\pi$
$523$	−14.4448	+	25.0191i	−0.631626	+	1.09401i	−0.987219	+	0.159368i	$0.949054\pi$
$524$	−9.10798	−	8.71677i	−0.397884	−	0.380794i
$525$		0			0
$526$	8.66560	+	20.2881i	0.377838	+	0.884603i
$527$	30.9179	+	17.8504i	1.34680	+	0.777577i
$528$		0			0
$529$	−0.544750	−	0.943535i	−0.0236848	−	0.0410233i
$530$	−11.7790	−	1.41944i	−0.511647	−	0.0616565i
$531$		0			0
$532$	−0.301977	−	0.141724i	−0.0130923	−	0.00614451i
$533$	−30.3522			−1.31470
$534$		0			0
$535$	−16.1519	+	9.32532i	−0.698309	+	0.403169i
$536$	3.02463	+	18.2981i	0.130644	+	0.790358i
$537$		0			0
$538$	−17.6745	−	41.3798i	−0.762000	−	1.78401i
$539$	−27.0108	−	11.3531i	−1.16344	−	0.489014i
$540$		0			0
$541$	−1.78575	−	1.03100i	−0.0767754	−	0.0443263i	0.461121	−	0.887337i	$-0.347447\pi$
$541$	−1.78575	−	1.03100i	−0.0767754	−	0.0443263i	−0.537896	+	0.843011i	$0.680781\pi$
$542$	8.00314	−	10.6703i	0.343764	−	0.458328i
$543$		0			0
$544$	26.2285	+	1.99825i	1.12454	+	0.0856745i
$545$	−4.50726			−0.193070
$546$		0			0
$547$		−	35.7819i		−	1.52992i	−0.644076	−	0.764962i	$-0.722758\pi$
$547$		−	35.7819i		−	1.52992i	0.644076	−	0.764962i	$-0.277242\pi$
$548$	25.1566	−	7.33595i	1.07464	−	0.313376i
$549$		0			0
$550$	−8.74237	−	6.55712i	−0.372776	−	0.279597i
$551$	−0.204036	+	0.353401i	−0.00869224	+	0.0150554i
$552$		0			0
$553$	−31.0960	−	6.26947i	−1.32234	−	0.266605i
$554$	−14.8348	−	34.7315i	−0.630270	−	1.47560i
$555$		0			0
$556$	−37.1306	−	9.08079i	−1.57469	−	0.385111i
$557$	11.9748	+	20.7409i	0.507388	+	0.878821i	0.999963	+	0.00855174i	$0.00272214\pi$
$557$	11.9748	+	20.7409i	0.507388	+	0.878821i	−0.492576	+	0.870270i	$0.663945\pi$
$558$		0			0
$559$			37.4421i			1.58363i
$560$	−11.7982	+	14.6299i	−0.498566	+	0.618225i
$561$		0			0
$562$	−36.7764	−	4.43177i	−1.55132	−	0.186943i
$563$	−22.4987	+	12.9896i	−0.948206	+	0.547447i	−0.892523	−	0.451001i	$-0.851067\pi$
$563$	−22.4987	+	12.9896i	−0.948206	+	0.547447i	−0.0556830	+	0.998448i	$0.517734\pi$
$564$		0			0
$565$	4.05352	−	7.02090i	0.170533	−	0.295371i
$566$	6.81671	−	2.91160i	0.286528	−	0.122384i
$567$		0			0
$568$	−13.5174	−	5.08465i	−0.567179	−	0.213347i
$569$	15.4525	+	8.92150i	0.647802	+	0.374009i	0.787614	−	0.616169i	$-0.211316\pi$
$569$	15.4525	+	8.92150i	0.647802	+	0.374009i	−0.139812	+	0.990178i	$0.544650\pi$
$570$		0			0
$571$	15.9523	−	9.21009i	0.667585	−	0.385430i	−0.127576	−	0.991829i	$-0.540720\pi$
$571$	15.9523	−	9.21009i	0.667585	−	0.385430i	0.795161	+	0.606398i	$0.207386\pi$
$572$	8.82221	+	30.2533i	0.368875	+	1.26495i
$573$		0			0
$574$	29.5386	−	6.13312i	1.23292	−	0.255991i
$575$		−	8.64157i		−	0.360378i
$576$		0			0
$577$	−17.5485	+	10.1317i	−0.730556	+	0.421786i	−0.818625	−	0.574328i	$-0.805263\pi$
$577$	−17.5485	+	10.1317i	−0.730556	+	0.421786i	0.0880698	+	0.996114i	$0.471930\pi$
$578$	5.22999	+	3.92270i	0.217539	+	0.163163i
$579$		0			0
$580$	16.6103	+	15.8968i	0.689703	+	0.660079i
$581$	−19.1825	+	6.45602i	−0.795825	+	0.267841i
$582$		0			0
$583$	9.88642	−	17.1238i	0.409454	−	0.709195i
$584$	0.688860	+	4.16740i	0.0285052	+	0.172448i
$585$		0			0
$586$	11.6457	+	1.40338i	0.481080	+	0.0579730i
$587$			3.63501i			0.150033i	0.997182	+	0.0750164i	$0.0239009\pi$
$587$			3.63501i			0.150033i	−0.997182	+	0.0750164i	$0.976099\pi$
$588$		0			0
$589$		−	0.483999i		−	0.0199428i
$590$	2.26640	−	18.8074i	0.0933061	−	0.774287i
$591$		0			0
$592$	−7.23953	−	11.3574i	−0.297543	−	0.466786i
$593$	−10.4731	+	18.1399i	−0.430078	+	0.744918i	−0.996880	−	0.0789370i	$-0.974847\pi$
$593$	−10.4731	+	18.1399i	−0.430078	+	0.744918i	0.566801	+	0.823855i	$0.308181\pi$
$594$		0			0
$595$	−20.7074	+	6.96922i	−0.848920	+	0.285710i
$596$	−6.06808	+	6.34042i	−0.248558	+	0.259714i
$597$		0			0
$598$	−14.9522	+	19.9353i	−0.611442	+	0.815214i
$599$	−1.58346	+	0.914209i	−0.0646983	+	0.0373536i	−0.532000	−	0.846744i	$-0.678559\pi$
$599$	−1.58346	+	0.914209i	−0.0646983	+	0.0373536i	0.467302	+	0.884098i	$0.345226\pi$
$600$		0			0
$601$			29.7207i			1.21233i	0.795338	+	0.606166i	$0.207293\pi$
$601$			29.7207i			1.21233i	−0.795338	+	0.606166i	$0.792707\pi$
$602$	−7.56573	−	36.4384i	−0.308356	−	1.48512i
$603$		0			0
$604$	−1.53893	−	5.27733i	−0.0626182	−	0.214731i
$605$	−10.0275	+	5.78937i	−0.407675	+	0.235371i
$606$		0			0
$607$	−5.04013	−	2.90992i	−0.204573	−	0.118110i	0.394214	−	0.919019i	$-0.371017\pi$
$607$	−5.04013	−	2.90992i	−0.204573	−	0.118110i	−0.598787	+	0.800909i	$0.704350\pi$
$608$	−0.154330	−	0.321488i	−0.00625890	−	0.0130381i
$609$		0			0
$610$	14.2671	+	33.4024i	0.577657	+	1.35242i
$611$	−1.27534	+	2.20896i	−0.0515949	+	0.0893650i
$612$		0			0
$613$	−6.81649	+	3.93550i	−0.275316	+	0.158954i	−0.631301	−	0.775538i	$-0.717479\pi$
$613$	−6.81649	+	3.93550i	−0.275316	+	0.158954i	0.355985	+	0.934492i	$0.384145\pi$
$614$	−3.02648	+	25.1148i	−0.122139	+	1.01355i
$615$		0			0
$616$	−14.6989	−	27.6597i	−0.592234	−	1.11444i
$617$		−	8.93676i		−	0.359781i	−0.983687	−	0.179890i	$-0.942426\pi$
$617$		−	8.93676i		−	0.359781i	0.983687	−	0.179890i	$-0.0575743\pi$
$618$		0			0
$619$	−3.80163	−	6.58462i	−0.152801	−	0.264658i	0.779455	−	0.626458i	$-0.215496\pi$
$619$	−3.80163	−	6.58462i	−0.152801	−	0.264658i	−0.932256	+	0.361799i	$0.882163\pi$
$620$	−26.4886	−	6.47815i	−1.06381	−	0.260169i
$621$		0			0
$622$	0.669768	−	0.286076i	0.0268552	−	0.0114706i
$623$	46.5547	+	9.38620i	1.86518	+	0.376050i
$624$		0			0
$625$	6.18050	−	10.7049i	0.247220	−	0.428197i
$626$	19.7896	−	26.3848i	0.790952	−	1.05455i
$627$		0			0
$628$	0.749289	+	2.56947i	0.0298999	+	0.102533i
$629$		−	15.6573i		−	0.624296i
$630$		0			0
$631$	49.9909			1.99010			0.995052	−	0.0993517i	$-0.0316769\pi$
$631$	49.9909			1.99010			0.995052	+	0.0993517i	$0.0316769\pi$
$632$	−21.5185	−	26.2102i	−0.855962	−	1.04259i
$633$		0			0
$634$	23.7415	+	17.8071i	0.942895	+	0.707209i
$635$	12.8600	+	7.42473i	0.510334	+	0.294641i
$636$		0			0
$637$	20.9888	−	15.9326i	0.831606	−	0.631271i
$638$	−35.2378	+	15.0510i	−1.39508	+	0.595875i
$639$		0			0
$640$	−19.6603	+	4.14327i	−0.777140	+	0.163777i
$641$	−34.4319	+	19.8793i	−1.35998	+	0.785184i	−0.989621	−	0.143705i	$-0.954098\pi$
$641$	−34.4319	+	19.8793i	−1.35998	+	0.785184i	−0.370358	+	0.928889i	$0.620765\pi$
$642$		0			0
$643$	28.7989			1.13572			0.567858	−	0.823126i	$-0.307772\pi$
$643$	28.7989			1.13572			0.567858	+	0.823126i	$0.307772\pi$
$644$	10.5232	−	22.4222i	0.414673	−	0.883559i
$645$		0			0
$646$	0.0495986	−	0.411587i	0.00195143	−	0.0161937i
$647$	−13.1134	−	22.7130i	−0.515540	−	0.892941i	−0.999837	−	0.0180376i	$-0.994258\pi$
$647$	−13.1134	−	22.7130i	−0.515540	−	0.892941i	0.484298	−	0.874903i	$-0.339075\pi$
$648$		0			0
$649$	27.3413	+	15.7855i	1.07324	+	0.619635i
$650$	9.03840	−	3.86055i	0.354515	−	0.151423i
$651$		0			0
$652$	−5.52155	−	5.28438i	−0.216240	−	0.206952i
$653$	−3.12639	+	5.41506i	−0.122345	+	0.211908i	−0.920692	−	0.390290i	$-0.872375\pi$
$653$	−3.12639	+	5.41506i	−0.122345	+	0.211908i	0.798347	+	0.602198i	$0.205708\pi$
$654$		0			0
$655$	5.59724	+	9.69470i	0.218702	+	0.378803i
$656$	28.6113	+	14.8848i	1.11708	+	0.581155i
$657$		0			0
$658$	0.794805	−	2.40745i	0.0309847	−	0.0938523i
$659$	32.2081			1.25465			0.627326	−	0.778757i	$-0.284150\pi$
$659$	32.2081			1.25465			0.627326	+	0.778757i	$0.284150\pi$
$660$		0			0
$661$	8.81544	+	15.2688i	0.342881	+	0.593887i	0.984966	−	0.172746i	$-0.0552639\pi$
$661$	8.81544	+	15.2688i	0.342881	+	0.593887i	−0.642085	+	0.766633i	$0.721931\pi$
$662$	7.99972	−	10.6657i	0.310918	−	0.414535i
$663$		0			0
$664$	−20.2519	−	7.61784i	−0.785925	−	0.295630i
$665$	0.222189	+	0.195879i	0.00861613	+	0.00759586i
$666$		0			0
$667$	−26.2406	−	15.1500i	−1.01604	−	0.586611i
$668$	−14.1005	−	3.44847i	−0.545566	−	0.133425i
$669$		0			0
$670$	1.97028	−	16.3501i	0.0761186	−	0.631659i
$671$	−60.5336			−2.33687
$672$		0			0
$673$	−32.0260			−1.23451			−0.617256	−	0.786762i	$-0.711756\pi$
$673$	−32.0260			−1.23451			−0.617256	+	0.786762i	$0.711756\pi$
$674$	−2.50651	+	20.7999i	−0.0965470	+	0.801180i
$675$		0			0
$676$	−2.27481	−	0.556336i	−0.0874928	−	0.0213975i
$677$	20.5345	+	11.8556i	0.789205	+	0.455648i	0.839683	−	0.543077i	$-0.182741\pi$
$677$	20.5345	+	11.8556i	0.789205	+	0.455648i	−0.0504774	+	0.998725i	$0.516074\pi$
$678$		0			0
$679$	10.6467	−	3.58322i	0.408582	−	0.137511i
$680$	−21.8618	−	8.22341i	−0.838360	−	0.315353i
$681$		0			0
$682$	27.2690	−	36.3568i	1.04419	−	1.39217i
$683$	9.16325	+	15.8712i	0.350622	+	0.607295i	0.986359	−	0.164611i	$-0.0526369\pi$
$683$	9.16325	+	15.8712i	0.350622	+	0.607295i	−0.635737	+	0.771906i	$0.719304\pi$
$684$		0			0
$685$	−23.2683			−0.889035
$686$	−17.2068	+	19.7466i	−0.656957	+	0.753928i
$687$		0			0
$688$	18.3617	−	35.2945i	0.700034	−	1.34559i
$689$	8.89145	+	15.4004i	0.338737	+	0.586710i
$690$		0			0
$691$	−20.3501	+	35.2473i	−0.774153	+	1.34087i	0.161116	+	0.986935i	$0.448491\pi$
$691$	−20.3501	+	35.2473i	−0.774153	+	1.34087i	−0.935269	+	0.353937i	$0.884843\pi$
$692$	1.78713	+	1.71037i	0.0679365	+	0.0650184i
$693$		0			0
$694$	−28.5188	+	12.1812i	−1.08256	+	0.462391i
$695$	29.3946	+	16.9710i	1.11500	+	0.643746i
$696$		0			0
$697$	18.7464	+	32.4697i	0.710069	+	1.22988i
$698$	−5.91008	+	49.0439i	−0.223700	+	1.85634i
$699$		0			0
$700$	−8.01604	+	5.58341i	−0.302978	+	0.211033i
$701$	12.2653			0.463255			0.231628	−	0.972805i	$-0.425595\pi$
$701$	12.2653			0.463255			0.231628	+	0.972805i	$0.425595\pi$
$702$		0			0
$703$	−0.183828	+	0.106133i	−0.00693321	+	0.00400289i
$704$	6.52012	−	32.8445i	0.245736	−	1.23787i
$705$		0			0
$706$	−9.65848	+	4.12540i	−0.363502	+	0.155262i
$707$	8.33373	+	7.34690i	0.313422	+	0.276309i
$708$		0			0
$709$	−5.83014	−	3.36604i	−0.218956	−	0.126414i	0.386511	−	0.922285i	$-0.373680\pi$
$709$	−5.83014	−	3.36604i	−0.218956	−	0.126414i	−0.605467	+	0.795871i	$0.707013\pi$
$710$	10.2590	+	7.69463i	0.385012	+	0.288774i
$711$		0			0
$712$	32.2160	+	39.2400i	1.20735	+	1.47058i
$713$	35.9376			1.34587
$714$		0			0
$715$		−	27.9824i		−	1.04648i
$716$	9.85644	+	33.7999i	0.368352	+	1.26316i
$717$		0			0
$718$	−6.59782	+	8.79663i	−0.246228	+	0.328287i
$719$	1.45947	−	2.52788i	0.0544291	−	0.0942739i	−0.837527	−	0.546396i	$-0.815999\pi$
$719$	1.45947	−	2.52788i	0.0544291	−	0.0942739i	0.891956	+	0.452122i	$0.149333\pi$
$720$		0			0
$721$	6.83160	−	33.8841i	0.254422	−	1.26191i
$722$	24.7052	−	10.5523i	0.919433	−	0.392715i
$723$		0			0
$724$	32.0113	+	7.82878i	1.18969	+	0.290954i
$725$	5.97521	+	10.3494i	0.221914	+	0.384366i
$726$		0			0
$727$		−	3.12734i		−	0.115987i	−0.998317	−	0.0579933i	$-0.981530\pi$
$727$		−	3.12734i		−	0.115987i	0.998317	−	0.0579933i	$-0.0184702\pi$
$728$	28.1530	+	0.989520i	1.04342	+	0.0366741i
$729$		0			0
$730$	0.448732	−	3.72374i	0.0166083	−	0.137822i
$731$	40.0541	−	23.1252i	1.48145	−	0.855318i
$732$		0			0
$733$	3.93077	−	6.80830i	0.145186	−	0.251470i	−0.784256	−	0.620437i	$-0.786955\pi$
$733$	3.93077	−	6.80830i	0.145186	−	0.251470i	0.929442	+	0.368967i	$0.120288\pi$
$734$	4.48689	+	10.5048i	0.165614	+	0.387740i
$735$		0			0
$736$	23.8710	−	11.4592i	0.879895	−	0.422392i
$737$	23.7690	+	13.7231i	0.875543	+	0.505495i
$738$		0			0
$739$	−1.01186	+	0.584195i	−0.0372217	+	0.0214900i	−0.518495	−	0.855080i	$-0.673508\pi$
$739$	−1.01186	+	0.584195i	−0.0372217	+	0.0214900i	0.481274	+	0.876570i	$0.340174\pi$
$740$	3.34806	+	11.4812i	0.123077	+	0.422058i
$741$		0			0
$742$	−11.7650	−	13.1910i	−0.431907	−	0.484256i
$743$		−	6.12199i		−	0.224594i	−0.993675	−	0.112297i	$-0.964179\pi$
$743$		−	6.12199i		−	0.224594i	0.993675	−	0.112297i	$-0.0358208\pi$
$744$		0			0
$745$	6.74886	−	3.89645i	0.247259	−	0.142755i
$746$	−23.6832	+	31.5760i	−0.867104	+	1.15608i
$747$		0			0
$748$	26.9150	−	28.1229i	0.984109	−	1.02828i
$749$	−27.2377	−	5.49156i	−0.995243	−	0.200657i
$750$		0			0
$751$	20.8430	−	36.1012i	0.760573	−	1.31735i	−0.181983	−	0.983302i	$-0.558252\pi$
$751$	20.8430	−	36.1012i	0.760573	−	1.31735i	0.942556	−	0.334049i	$-0.108415\pi$
$752$	2.28548	−	1.45683i	0.0833428	−	0.0531251i
$753$		0			0
$754$	4.12295	−	34.2137i	0.150149	−	1.24599i
$755$			4.88120i			0.177645i
$756$		0			0
$757$			35.8599i			1.30335i	0.758498	+	0.651676i	$0.225934\pi$
$757$			35.8599i			1.30335i	−0.758498	+	0.651676i	$0.774066\pi$
$758$	40.7822	+	4.91450i	1.48128	+	0.178503i
$759$		0			0
$760$	0.0516414	+	0.312416i	0.00187323	+	0.0113325i
$761$	4.88971	−	8.46923i	0.177252	−	0.307009i	−0.763686	−	0.645587i	$-0.776613\pi$
$761$	4.88971	−	8.46923i	0.177252	−	0.307009i	0.940938	+	0.338578i	$0.109946\pi$
$762$		0			0
$763$	−5.03702	−	4.44056i	−0.182352	−	0.160759i
$764$	23.7183	+	22.6996i	0.858099	+	0.821241i
$765$		0			0
$766$	−12.7399	−	9.55543i	−0.460311	−	0.345252i
$767$	−24.5897	+	14.1968i	−0.887881	+	0.512619i
$768$		0			0
$769$		−	54.2218i		−	1.95529i	−0.210269	−	0.977644i	$-0.567434\pi$
$769$		−	54.2218i		−	1.95529i	0.210269	−	0.977644i	$-0.432566\pi$
$770$	5.65427	+	27.2324i	0.203766	+	0.981386i
$771$		0			0
$772$	13.1719	+	45.1694i	0.474068	+	1.62568i
$773$	20.8017	−	12.0099i	0.748185	−	0.431965i	−0.0768527	−	0.997042i	$-0.524487\pi$
$773$	20.8017	−	12.0099i	0.748185	−	0.431965i	0.825038	+	0.565078i	$0.191154\pi$
$774$		0			0
$775$	−12.2750	−	7.08696i	−0.440930	−	0.254571i
$776$	11.2402	+	4.22806i	0.403500	+	0.151778i
$777$		0			0
$778$	6.54983	−	2.79761i	0.234823	−	0.100299i
$779$	0.254145	−	0.440193i	0.00910570	−	0.0157715i
$780$		0			0
$781$	−18.5090	+	10.6862i	−0.662303	+	0.382381i
$782$	30.5609	+	3.68277i	1.09286	+	0.131696i
$783$		0			0
$784$	−27.5983	+	4.72575i	−0.985654	+	0.168777i
$785$		−	2.37661i		−	0.0848247i
$786$		0			0
$787$	13.5019	+	23.3859i	0.481290	+	0.833619i	0.999769	−	0.0214714i	$-0.00683508\pi$
$787$	13.5019	+	23.3859i	0.481290	+	0.833619i	−0.518479	+	0.855090i	$0.673502\pi$
$788$	−1.54006	−	0.376642i	−0.0548624	−	0.0134173i
$789$		0			0
$790$	11.8280	+	27.6920i	0.420822	+	0.985238i
$791$	11.4470	−	3.85256i	0.407007	−	0.136981i
$792$		0			0
$793$	27.2208	−	47.1477i	0.966637	−	1.67426i
$794$	−31.3997	−	23.5510i	−1.11433	−	0.835793i
$795$		0			0
$796$	−24.3702	+	7.10665i	−0.863780	+	0.251888i
$797$		−	30.6501i		−	1.08568i	−0.839835	−	0.542841i	$-0.817349\pi$
$797$		−	30.6501i		−	1.08568i	0.839835	−	0.542841i	$-0.182651\pi$
$798$		0			0
$799$	3.15075			0.111466
$800$	−10.4132	−	0.793344i	−0.368163	−	0.0280490i
$801$		0			0
$802$	−3.62923	+	4.83871i	−0.128152	+	0.170861i
$803$	5.41340	+	3.12543i	0.191035	+	0.110294i
$804$		0			0
$805$	−14.5443	+	16.4979i	−0.512620	+	0.581474i
$806$	16.0548	+	37.5879i	0.565507	+	1.32398i
$807$		0			0
$808$	1.93693	+	11.7179i	0.0681411	+	0.412234i
$809$	10.5996	−	6.11967i	0.372661	−	0.215156i	−0.301959	−	0.953321i	$-0.597641\pi$
$809$	10.5996	−	6.11967i	0.372661	−	0.215156i	0.674620	+	0.738165i	$0.264307\pi$
$810$		0			0
$811$	51.5601			1.81052			0.905260	−	0.424858i	$-0.139676\pi$
$811$	51.5601			1.81052			0.905260	+	0.424858i	$0.139676\pi$
$812$	2.90096	+	34.1297i	0.101804	+	1.19772i
$813$		0			0
$814$	−19.7884	−	2.38462i	−0.693582	−	0.0835808i
$815$	3.39322	+	5.87723i	0.118859	+	0.205870i
$816$		0			0
$817$	−0.543015	−	0.313510i	−0.0189977	−	0.0109683i
$818$	−8.72949	−	20.4377i	−0.305219	−	0.714587i
$819$		0			0
$820$	−20.6895	−	19.8009i	−0.722510	−	0.691476i
$821$	22.3477	−	38.7073i	0.779940	−	1.35090i	−0.152036	−	0.988375i	$-0.548583\pi$
$821$	22.3477	−	38.7073i	0.779940	−	1.35090i	0.931976	−	0.362520i	$-0.118084\pi$
$822$		0			0
$823$	8.91299	+	15.4378i	0.310687	+	0.538126i	0.978511	−	0.206193i	$-0.0661075\pi$
$823$	8.91299	+	15.4378i	0.310687	+	0.538126i	−0.667824	+	0.744319i	$0.732774\pi$
$824$	28.5602	−	23.4479i	0.994943	−	0.816847i
$825$		0			0
$826$	21.0618	−	18.7850i	0.732835	−	0.653614i
$827$	−44.4781			−1.54665			−0.773327	−	0.634007i	$-0.781409\pi$
$827$	−44.4781			−1.54665			−0.773327	+	0.634007i	$0.781409\pi$
$828$		0			0
$829$	−6.86797	−	11.8957i	−0.238534	−	0.413154i	0.721760	−	0.692144i	$-0.243334\pi$
$829$	−6.86797	−	11.8957i	−0.238534	−	0.413154i	−0.960294	+	0.278990i	$0.910000\pi$
$830$	15.3700	+	11.5281i	0.533501	+	0.400147i
$831$		0			0
$832$	22.6496	+	19.8478i	0.785233	+	0.688099i
$833$	−30.0073	−	12.6126i	−1.03969	−	0.437002i
$834$		0			0
$835$	11.1627	+	6.44481i	0.386303	+	0.223032i
$836$	−0.512628	−	0.125370i	−0.0177296	−	0.00433601i
$837$		0			0
$838$	53.4718	+	6.44367i	1.84715	+	0.222593i
$839$	18.7998			0.649040			0.324520	−	0.945879i	$-0.394797\pi$
$839$	18.7998			0.649040			0.324520	+	0.945879i	$0.394797\pi$
$840$		0			0
$841$	12.9019			0.444892
$842$	22.1147	+	2.66495i	0.762122	+	0.0918402i
$843$		0			0
$844$	−9.01887	+	36.8774i	−0.310442	+	1.26937i
$845$	1.80086	+	1.03973i	0.0619516	+	0.0357678i
$846$		0			0
$847$	−16.9098	−	3.40928i	−0.581026	−	0.117144i
$848$	−0.829034	−	18.8775i	−0.0284691	−	0.648257i
$849$		0			0
$850$	−9.71224	−	7.28456i	−0.333127	−	0.249858i
$851$	−7.88055	−	13.6495i	−0.270142	−	0.467899i
$852$		0			0
$853$	−4.23719			−0.145079			−0.0725393	−	0.997366i	$-0.523110\pi$
$853$	−4.23719			−0.145079			−0.0725393	+	0.997366i	$0.523110\pi$
$854$	−16.9642	+	51.3843i	−0.580503	+	1.75833i
$855$		0			0
$856$	−18.8485	−	22.9581i	−0.644230	−	0.784691i
$857$	−6.78696	−	11.7554i	−0.231838	−	0.401556i	0.726511	−	0.687155i	$-0.241141\pi$
$857$	−6.78696	−	11.7554i	−0.231838	−	0.401556i	−0.958349	+	0.285599i	$0.907807\pi$
$858$		0			0
$859$	14.8653	−	25.7475i	0.507198	−	0.878494i	−0.492767	−	0.870161i	$-0.664014\pi$
$859$	14.8653	−	25.7475i	0.507198	−	0.878494i	0.999965	−	0.00833211i	$-0.00265222\pi$
$860$	−24.4261	+	25.5223i	−0.832922	+	0.870304i
$861$		0			0
$862$	−4.08528	−	9.56456i	−0.139145	−	0.325770i
$863$	−26.7055	−	15.4184i	−0.909066	−	0.524849i	−0.0289352	−	0.999581i	$-0.509212\pi$
$863$	−26.7055	−	15.4184i	−0.909066	−	0.524849i	−0.880130	+	0.474732i	$0.842545\pi$
$864$		0			0
$865$	−1.09827	−	1.90225i	−0.0373422	−	0.0646785i
$866$	11.3233	+	1.36452i	0.384780	+	0.0463683i
$867$		0			0
$868$	−23.2197	−	33.3362i	−0.788127	−	1.13151i
$869$	−50.1850			−1.70241
$870$		0			0
$871$	−21.3769	+	12.3420i	−0.724329	+	0.418191i
$872$	−1.17071	−	7.08245i	−0.0396452	−	0.239842i
$873$		0			0
$874$	−0.163919	−	0.383772i	−0.00554466	−	0.0129813i
$875$	30.4871	−	10.2606i	1.03065	−	0.346873i
$876$		0			0
$877$	−10.0815	−	5.82055i	−0.340428	−	0.196546i	0.320033	−	0.947406i	$-0.396306\pi$
$877$	−10.0815	−	5.82055i	−0.340428	−	0.196546i	−0.660461	+	0.750860i	$0.729639\pi$
$878$	−4.92281	+	6.56340i	−0.166137	+	0.221504i
$879$		0			0
$880$	−13.7227	+	26.3775i	−0.462592	+	0.889184i
$881$	−23.5879			−0.794698			−0.397349	−	0.917668i	$-0.630070\pi$
$881$	−23.5879			−0.794698			−0.397349	+	0.917668i	$0.630070\pi$
$882$		0			0
$883$		−	39.4950i		−	1.32911i	−0.747239	−	0.664556i	$-0.768621\pi$
$883$		−	39.4950i		−	1.32911i	0.747239	−	0.664556i	$-0.231379\pi$
$884$	9.80094	+	33.6095i	0.329641	+	1.13041i
$885$		0			0
$886$	17.7044	+	13.2790i	0.594791	+	0.446117i
$887$	−27.3283	+	47.3340i	−0.917595	+	1.58932i	−0.114537	+	0.993419i	$0.536538\pi$
$887$	−27.3283	+	47.3340i	−0.917595	+	1.58932i	−0.803058	+	0.595901i	$0.796795\pi$
$888$		0			0
$889$	7.05664	+	20.9671i	0.236672	+	0.703214i
$890$	−17.7081	−	41.4585i	−0.593576	−	1.38969i
$891$		0			0
$892$	−4.07027	+	16.6430i	−0.136283	+	0.557250i
$893$	−0.0213575	−	0.0369922i	−0.000714700	−	0.00123790i
$894$		0			0
$895$		−	31.2628i		−	1.04500i
$896$	−26.0530	−	14.7391i	−0.870370	−	0.492399i
$897$		0			0
$898$	48.8385	+	5.88533i	1.62976	+	0.196396i
$899$	−43.0398	+	24.8490i	−1.43546	+	0.828762i
$900$		0			0
$901$	10.9832	−	19.0235i	0.365904	−	0.633764i
$902$	43.8917	−	18.7474i	1.46143	−	0.624219i
$903$		0			0
$904$	12.0851	+	4.54587i	0.401944	+	0.151193i
$905$	−25.3419	−	14.6311i	−0.842392	−	0.486355i
$906$		0			0
$907$	7.80208	−	4.50453i	0.259064	−	0.149571i	−0.364844	−	0.931069i	$-0.618878\pi$
$907$	7.80208	−	4.50453i	0.259064	−	0.149571i	0.623907	+	0.781498i	$0.285544\pi$
$908$	−27.4627	+	8.00845i	−0.911382	+	0.265770i
$909$		0			0
$910$	−23.7530	−	7.84191i	−0.787405	−	0.259957i
$911$			35.3463i			1.17107i	0.810646	+	0.585537i	$0.199116\pi$
$911$			35.3463i			1.17107i	−0.810646	+	0.585537i	$0.800884\pi$
$912$		0			0
$913$	−27.7302	+	16.0100i	−0.917736	+	0.529855i
$914$	12.1939	+	9.14594i	0.403340	+	0.302521i
$915$		0			0
$916$	−38.7877	+	40.5285i	−1.28158	+	1.33910i
$917$	−3.29614	+	16.3486i	−0.108848	+	0.539878i
$918$		0			0
$919$	−10.9416	+	18.9514i	−0.360931	+	0.625150i	−0.988114	−	0.153721i	$-0.950874\pi$
$919$	−10.9416	+	18.9514i	−0.360931	+	0.625150i	0.627184	+	0.778871i	$0.284208\pi$
$920$	−23.1973	+	3.83445i	−0.764794	+	0.126418i
$921$		0			0
$922$	27.3878	+	3.30039i	0.901969	+	0.108693i
$923$		−	19.2214i		−	0.632680i
$924$		0			0
$925$			6.21623i			0.204388i
$926$	−4.60383	+	38.2042i	−0.151291	+	1.25547i
$927$		0			0
$928$	−20.6650	+	30.2294i	−0.678362	+	0.992329i
$929$	−4.66786	+	8.08497i	−0.153148	+	0.265259i	−0.932383	−	0.361472i	$-0.882274\pi$
$929$	−4.66786	+	8.08497i	−0.153148	+	0.265259i	0.779235	+	0.626731i	$0.215608\pi$
$930$		0			0
$931$	0.0553236	+	0.437803i	0.00181316	+	0.0143484i
$932$	−12.5598	−	12.0203i	−0.411411	−	0.393739i
$933$		0			0
$934$	−28.7328	+	38.3084i	−0.940165	+	1.25349i
$935$	−29.9346	+	17.2827i	−0.978965	+	0.565206i
$936$		0			0
$937$			14.0652i			0.459492i	0.973251	+	0.229746i	$0.0737895\pi$
$937$			14.0652i			0.459492i	−0.973251	+	0.229746i	$0.926211\pi$
$938$	18.3100	−	16.3307i	0.597843	−	0.533215i
$939$		0			0
$940$	−2.31040	+	0.673739i	−0.0753569	+	0.0219749i
$941$	34.5165	−	19.9281i	1.12521	−	0.649638i	0.182481	−	0.983209i	$-0.441587\pi$
$941$	34.5165	−	19.9281i	1.12521	−	0.649638i	0.942725	+	0.333571i	$0.108254\pi$
$942$		0			0
$943$	32.6850	+	18.8707i	1.06437	+	0.614513i
$944$	30.1415	−	1.32371i	0.981021	−	0.0430830i
$945$		0			0
$946$	−23.1265	−	54.1442i	−0.751907	−	1.76038i
$947$	10.3155	−	17.8669i	0.335208	−	0.580598i	−0.648317	−	0.761371i	$-0.724527\pi$
$947$	10.3155	−	17.8669i	0.335208	−	0.580598i	0.983525	+	0.180773i	$0.0578600\pi$
$948$		0			0
$949$	−4.86860	+	2.81088i	−0.158041	+	0.0912452i
$950$	−0.0196916	+	0.163407i	−0.000638879	+	0.00530164i
$951$		0			0
$952$	−16.3295	−	30.7282i	−0.529243	−	0.995907i
$953$		−	36.6133i		−	1.18602i	−0.805194	−	0.593011i	$-0.797939\pi$
$953$		−	36.6133i		−	1.18602i	0.805194	−	0.593011i	$-0.202061\pi$
$954$		0			0
$955$	−14.5759	−	25.2462i	−0.471665	−	0.816948i
$956$	5.93328	−	24.2607i	0.191896	−	0.784647i
$957$		0			0
$958$	1.66700	−	0.712019i	0.0538582	−	0.0230043i
$959$	−26.0031	−	22.9240i	−0.839684	−	0.740254i
$960$		0			0
$961$	13.9724	−	24.2010i	0.450724	−	0.780677i
$962$	10.7557	−	14.3402i	0.346779	−	0.462347i
$963$		0			0
$964$	−44.5458	+	12.9901i	−1.43472	+	0.418382i
$965$		−	41.7789i		−	1.34491i
$966$		0			0
$967$	−10.0693			−0.323808			−0.161904	−	0.986806i	$-0.551764\pi$
$967$	−10.0693			−0.323808			−0.161904	+	0.986806i	$0.551764\pi$
$968$	−11.7016	−	14.2529i	−0.376104	−	0.458105i
$969$		0			0
$970$	−8.53067	−	6.39834i	−0.273903	−	0.205438i
$971$	−2.76132	−	1.59425i	−0.0886149	−	0.0511618i	0.455038	−	0.890472i	$-0.349626\pi$
$971$	−2.76132	−	1.59425i	−0.0886149	−	0.0511618i	−0.543653	+	0.839310i	$0.682959\pi$
$972$		0			0
$973$	16.1296	+	47.9253i	0.517092	+	1.53642i
$974$	−29.9940	+	12.8113i	−0.961071	+	0.410500i
$975$		0			0
$976$	−48.7809	+	31.0943i	−1.56144	+	0.995306i
$977$	−3.60255	+	2.07994i	−0.115256	+	0.0665430i	−0.556520	−	0.830834i	$-0.687864\pi$
$977$	−3.60255	+	2.07994i	−0.115256	+	0.0665430i	0.441264	+	0.897377i	$0.354530\pi$
$978$		0			0
$979$	75.1334			2.40127
$980$	24.7009	+	2.83205i	0.789041	+	0.0904664i
$981$		0			0
$982$	5.69786	−	47.2828i	0.181826	−	1.50886i
$983$	10.4374	+	18.0782i	0.332902	+	0.576604i	0.983080	−	0.183179i	$-0.0586387\pi$
$983$	10.4374	+	18.0782i	0.332902	+	0.576604i	−0.650177	+	0.759783i	$0.725305\pi$
$984$		0			0
$985$	1.21919	+	0.703903i	0.0388468	+	0.0224282i
$986$	−39.1470	+	16.7208i	−1.24669	+	0.532497i
$987$		0			0
$988$	0.328165	−	0.342893i	0.0104403	−	0.0109089i
$989$	23.2786	−	40.3197i	0.740216	−	1.28209i
$990$		0			0
$991$	6.31063	+	10.9303i	0.200464	+	0.347213i	0.948678	−	0.316244i	$-0.102422\pi$
$991$	6.31063	+	10.9303i	0.200464	+	0.347213i	−0.748214	+	0.663457i	$0.769088\pi$
$992$	3.29927	−	43.3053i	0.104752	−	1.37495i
$993$		0			0
$994$	3.88397	+	18.7062i	0.123192	+	0.593324i
$995$	22.5410			0.714597
$996$		0			0
$997$	9.23934	+	16.0030i	0.292613	+	0.506820i	0.974427	−	0.224705i	$-0.0721420\pi$
$997$	9.23934	+	16.0030i	0.292613	+	0.506820i	−0.681814	+	0.731526i	$0.738809\pi$
$998$	−5.05040	+	6.73351i	−0.159867	+	0.213145i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.ch.b.341.15	yes	56
3.2	odd	2	inner	504.2.ch.b.341.14	yes	56
4.3	odd	2		2016.2.cp.b.593.21		56
7.3	odd	6	inner	504.2.ch.b.269.24	yes	56
8.3	odd	2		2016.2.cp.b.593.8		56
8.5	even	2	inner	504.2.ch.b.341.5	yes	56
12.11	even	2		2016.2.cp.b.593.7		56
21.17	even	6	inner	504.2.ch.b.269.5	✓	56
24.5	odd	2	inner	504.2.ch.b.341.24	yes	56
24.11	even	2		2016.2.cp.b.593.22		56
28.3	even	6		2016.2.cp.b.17.22		56
56.3	even	6		2016.2.cp.b.17.7		56
56.45	odd	6	inner	504.2.ch.b.269.14	yes	56
84.59	odd	6		2016.2.cp.b.17.8		56
168.59	odd	6		2016.2.cp.b.17.21		56
168.101	even	6	inner	504.2.ch.b.269.15	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.5	✓	56	21.17	even	6	inner
504.2.ch.b.269.14	yes	56	56.45	odd	6	inner
504.2.ch.b.269.15	yes	56	168.101	even	6	inner
504.2.ch.b.269.24	yes	56	7.3	odd	6	inner
504.2.ch.b.341.5	yes	56	8.5	even	2	inner
504.2.ch.b.341.14	yes	56	3.2	odd	2	inner
504.2.ch.b.341.15	yes	56	1.1	even	1	trivial
504.2.ch.b.341.24	yes	56	24.5	odd	2	inner
2016.2.cp.b.17.7		56	56.3	even	6
2016.2.cp.b.17.8		56	84.59	odd	6
2016.2.cp.b.17.21		56	168.59	odd	6
2016.2.cp.b.17.22		56	28.3	even	6
2016.2.cp.b.593.7		56	12.11	even	2
2016.2.cp.b.593.8		56	8.3	odd	2
2016.2.cp.b.593.21		56	4.3	odd	2
2016.2.cp.b.593.22		56	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.ch (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.169197 - 1.40406i) q^{2} +(-1.94274 - 0.475124i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 + 2.64733i) q^{8} +O(q^{10})\)	\(q+(0.169197 - 1.40406i) q^{2} +(-1.94274 - 0.475124i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 + 2.64733i) q^{8} +(1.50696 - 2.00917i) q^{10} +(2.09284 + 3.62490i) q^{11} -3.76443 q^{13} +(3.66352 - 0.760659i) q^{14} +(3.54851 + 1.84609i) q^{16} +(2.32502 + 4.02705i) q^{17} +(0.0315203 - 0.0545948i) q^{19} +(-2.56602 - 2.45580i) q^{20} +(5.44367 - 2.32514i) q^{22} +(4.05375 + 2.34043i) q^{23} +(-0.923074 - 1.59881i) q^{25} +(-0.636930 + 5.28547i) q^{26} +(-0.448151 - 5.27249i) q^{28} -6.47316 q^{29} +(6.64896 - 3.83878i) q^{31} +(3.19241 - 4.66996i) q^{32} +(6.04758 - 2.58309i) q^{34} +(-0.928631 + 4.60593i) q^{35} +(-2.91602 - 1.68357i) q^{37} +(-0.0713210 - 0.0534936i) q^{38} +(-3.88224 + 3.18732i) q^{40} +8.06290 q^{41} -9.94628i q^{43} +(-2.34357 - 8.03662i) q^{44} +(3.97198 - 5.29569i) q^{46} +(0.338788 - 0.586799i) q^{47} +(-5.57556 + 4.23240i) q^{49} +(-2.40100 + 1.02553i) q^{50} +(7.31332 + 1.78857i) q^{52} +(-2.36197 - 4.09104i) q^{53} +7.43338i q^{55} +(-7.47870 - 0.262861i) q^{56} +(-1.09524 + 9.08868i) q^{58} +(6.53211 - 3.77132i) q^{59} +(-7.23104 + 12.5245i) q^{61} +(-4.26487 - 9.98502i) q^{62} +(-6.01674 - 5.27247i) q^{64} +(-5.78962 - 3.34264i) q^{65} +(5.67866 - 3.27857i) q^{67} +(-2.60357 - 8.92819i) q^{68} +(6.30986 + 2.08316i) q^{70} +5.10606i q^{71} +(1.29332 - 0.746696i) q^{73} +(-2.85720 + 3.80940i) q^{74} +(-0.0871753 + 0.0910878i) q^{76} +(-7.32339 + 8.30706i) q^{77} +(-5.99485 + 10.3834i) q^{79} +(3.81831 + 5.99017i) q^{80} +(1.36422 - 11.3208i) q^{82} +7.64992i q^{83} +8.25803i q^{85} +(-13.9651 - 1.68288i) q^{86} +(-11.6804 + 1.93073i) q^{88} +(8.97506 - 15.5453i) q^{89} +(-3.17692 - 9.43947i) q^{91} +(-6.76340 - 6.47290i) q^{92} +(-0.766576 - 0.574962i) q^{94} +(0.0969554 - 0.0559773i) q^{95} -4.24586i q^{97} +(4.99915 + 8.54450i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 56 * q - 8 * q^4 - 20 * q^7	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82} + 4 q^{88} - 180 q^{94}+O(q^{100}) \) 56 * q - 8 * q^4 - 20 * q^7 + 20 * q^16 - 16 * q^22 + 8 * q^25 + 36 * q^28 - 36 * q^31 + 60 * q^40 - 8 * q^46 - 28 * q^49 + 36 * q^52 - 44 * q^58 + 40 * q^64 - 60 * q^70 + 72 * q^73 - 12 * q^79 - 36 * q^82 + 4 * q^88 - 180 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more