LMFDB - Embedded newform 504.2.ch.b.341.24

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			341.24
Character	$\chi$	$=$	504.341
Dual form			504.2.ch.b.269.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.13135 - 0.848557i) q^{2} +(0.559903 - 1.92003i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 - 2.64733i) q^{8} +O(q^{10})$	\(q+(1.13135 - 0.848557i) q^{2} +(0.559903 - 1.92003i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 - 2.64733i) q^{8} +(2.49347 - 0.300478i) q^{10} +(2.09284 + 3.62490i) q^{11} +3.76443 q^{13} +(3.08258 + 2.12078i) q^{14} +(-3.37302 - 2.15006i) q^{16} +(-2.32502 - 4.02705i) q^{17} +(-0.0315203 + 0.0545948i) q^{19} +(2.56602 - 2.45580i) q^{20} +(5.44367 + 2.32514i) q^{22} +(-4.05375 - 2.34043i) q^{23} +(-0.923074 - 1.59881i) q^{25} +(4.25888 - 3.19433i) q^{26} +(5.28708 - 0.216393i) q^{28} -6.47316 q^{29} +(6.64896 - 3.83878i) q^{31} +(-5.64051 + 0.429729i) q^{32} +(-6.04758 - 2.58309i) q^{34} +(-0.928631 + 4.60593i) q^{35} +(2.91602 + 1.68357i) q^{37} +(0.0106663 + 0.0885126i) q^{38} +(0.819176 - 4.95578i) q^{40} -8.06290 q^{41} +9.94628i q^{43} +(8.13170 - 1.98872i) q^{44} +(-6.57220 + 0.791988i) q^{46} +(-0.338788 + 0.586799i) q^{47} +(-5.57556 + 4.23240i) q^{49} +(-2.40100 - 1.02553i) q^{50} +(2.10771 - 7.22781i) q^{52} +(-2.36197 - 4.09104i) q^{53} +7.43338i q^{55} +(5.79791 - 4.73120i) q^{56} +(-7.32341 + 5.49285i) q^{58} +(6.53211 - 3.77132i) q^{59} +(7.23104 - 12.5245i) q^{61} +(4.26487 - 9.98502i) q^{62} +(-6.01674 + 5.27247i) q^{64} +(5.78962 + 3.34264i) q^{65} +(-5.67866 + 3.27857i) q^{67} +(-9.03382 + 2.20934i) q^{68} +(2.85779 + 5.99891i) q^{70} -5.10606i q^{71} +(1.29332 - 0.746696i) q^{73} +(4.72764 - 0.569709i) q^{74} +(0.0871753 + 0.0910878i) q^{76} +(-7.32339 + 8.30706i) q^{77} +(-5.99485 + 10.3834i) q^{79} +(-3.27849 - 6.30184i) q^{80} +(-9.12195 + 6.84183i) q^{82} +7.64992i q^{83} -8.25803i q^{85} +(8.43998 + 11.2527i) q^{86} +(7.51226 - 9.15014i) q^{88} +(-8.97506 + 15.5453i) q^{89} +(3.17692 + 9.43947i) q^{91} +(-6.76340 + 6.47290i) q^{92} +(0.114644 + 0.951355i) q^{94} +(-0.0969554 + 0.0559773i) q^{95} -4.24586i q^{97} +(-2.71647 + 9.51949i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.13135	−	0.848557i	0.799985	−	0.600020i
$2$	1.13135	−	0.848557i	0.799985	−	0.600020i
$3$		0			0
$3$		0			0
$4$	0.559903	−	1.92003i	0.279951	−	0.960014i
$5$	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
$10$	2.49347	−	0.300478i	0.788506	−	0.0950196i
$11$	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	$-0.325174\pi$
$13$	3.76443			1.04406			0.522032	+	0.852926i	$0.325174\pi$
$14$	3.08258	+	2.12078i	0.823853	+	0.566803i
$15$		0			0
$16$	−3.37302	−	2.15006i	−0.843254	−	0.537515i
$17$	−2.32502	−	4.02705i	−0.563899	−	0.976702i	−0.997151	−	0.0754291i	$-0.975967\pi$
$17$	−2.32502	−	4.02705i	−0.563899	−	0.976702i	0.433252	−	0.901273i	$-0.357366\pi$
$18$		0			0
$19$	−0.0315203	+	0.0545948i	−0.00723126	+	0.0125249i	−0.869618	−	0.493724i	$-0.835635\pi$
$19$	−0.0315203	+	0.0545948i	−0.00723126	+	0.0125249i	0.862387	+	0.506249i	$0.168968\pi$
$20$	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	0.0137854	−	0.999905i	$-0.495612\pi$
$23$	−4.05375	−	2.34043i	−0.845265	−	0.488014i	−0.859050	+	0.511891i	$0.828945\pi$
$24$		0			0
$25$	−0.923074	−	1.59881i	−0.184615	−	0.319762i
$26$	4.25888	−	3.19433i	0.835236	−	0.626460i
$27$		0			0
$28$	5.28708	−	0.216393i	0.999163	−	0.0408945i
$29$	−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	$0.0911790\pi$
$32$	−5.64051	+	0.429729i	−0.997110	+	0.0759661i
$33$		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	0.720163	−	0.693805i	$-0.244067\pi$
$37$	2.91602	+	1.68357i	0.479391	+	0.276777i	−0.240772	+	0.970582i	$0.577400\pi$
$38$	0.0106663	+	0.0885126i	0.00173030	+	0.0143586i
$39$		0			0
$40$	0.819176	−	4.95578i	0.129523	−	0.783578i
$41$	−8.06290			−1.25921			−0.629606	−	0.776914i	$-0.716784\pi$
$41$	−8.06290			−1.25921			−0.629606	+	0.776914i	$0.716784\pi$
$42$		0			0
$43$			9.94628i			1.51679i	0.651793	+	0.758397i	$0.274017\pi$
$43$			9.94628i			1.51679i	−0.651793	+	0.758397i	$0.725983\pi$
$44$	8.13170	−	1.98872i	1.22590	−	0.299810i
$45$		0			0
$46$	−6.57220	+	0.791988i	−0.969017	+	0.116772i
$47$	−0.338788	+	0.586799i	−0.0494174	+	0.0855934i	−0.889676	−	0.456592i	$-0.849070\pi$
$47$	−0.338788	+	0.586799i	−0.0494174	+	0.0855934i	0.840259	+	0.542186i	$0.182403\pi$
$48$		0			0
$49$	−5.57556	+	4.23240i	−0.796508	+	0.604628i
$50$	−2.40100	−	1.02553i	−0.339553	−	0.145032i
$51$		0			0
$52$	2.10771	−	7.22781i	0.292287	−	1.00232i
$53$	−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
$56$	5.79791	−	4.73120i	0.774778	−	0.632233i
$57$		0			0
$58$	−7.32341	+	5.49285i	−0.961611	+	0.721246i
$59$	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	$-0.456692\pi$
$61$	7.23104	−	12.5245i	0.925840	−	1.60360i	0.790204	−	0.612844i	$-0.209975\pi$
$62$	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	−0.805018	−	0.593250i	$-0.797845\pi$
$67$	−5.67866	+	3.27857i	−0.693758	+	0.400542i	0.111260	+	0.993791i	$0.464511\pi$
$68$	−9.03382	+	2.20934i	−1.09551	+	0.267922i
$69$		0			0
$70$	2.85779	+	5.99891i	0.341571	+	0.717007i
$71$		−	5.10606i		−	0.605978i	−0.952994	−	0.302989i	$-0.902015\pi$
$71$		−	5.10606i		−	0.605978i	0.952994	−	0.302989i	$-0.0979846\pi$
$72$		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	$0.305479\pi$
$74$	4.72764	−	0.569709i	0.549577	−	0.0662273i
$75$		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	$0.931038\pi$
$80$	−3.27849	−	6.30184i	−0.366546	−	0.704567i
$81$		0			0
$82$	−9.12195	+	6.84183i	−1.00735	+	0.755553i
$83$			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
$86$	8.43998	+	11.2527i	0.910107	+	1.21341i
$87$		0			0
$88$	7.51226	−	9.15014i	0.800809	−	0.975409i
$89$	−8.97506	+	15.5453i	−0.951354	+	1.64779i	−0.208855	+	0.977947i	$0.566974\pi$
$89$	−8.97506	+	15.5453i	−0.951354	+	1.64779i	−0.742499	+	0.669847i	$0.766360\pi$
$90$		0			0
$91$	3.17692	+	9.43947i	0.333032	+	0.989526i
$92$	−6.76340	+	6.47290i	−0.705133	+	0.674846i
$93$		0			0
$94$	0.114644	+	0.951355i	0.0118246	+	0.0981248i
$95$	−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	$-0.0691547\pi$
$98$	−2.71647	+	9.51949i	−0.274405	+	0.961614i
$99$		0			0
$100$	−3.58660	+	0.877150i	−0.358660	+	0.0877150i
$101$	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	−0.391029	−	0.920378i	$-0.627881\pi$
$109$	2.19797	−	1.26900i	0.210528	−	0.121548i	0.601557	+	0.798830i	$0.294547\pi$
$110$	6.30764	+	8.40975i	0.601410	+	0.801838i
$111$		0			0
$112$	2.54477	−	10.2725i	0.240458	−	0.970660i
$113$			4.56501i			0.429440i	0.976676	+	0.214720i	$0.0688838\pi$
$113$			4.56501i			0.429440i	−0.976676	+	0.214720i	$0.931116\pi$
$114$		0			0
$115$	−4.15639	−	7.19909i	−0.387586	−	0.671318i
$116$	−3.62434	+	12.4287i	−0.336512	+	1.15397i
$117$		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
$122$	−2.44694	−	20.3056i	−0.221536	−	1.83838i
$123$		0			0
$124$	−3.64779	−	14.9155i	−0.327581	−	1.33945i
$125$		−	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	$0.379020\pi$
$128$	−2.33304	+	11.0705i	−0.206214	+	0.978507i
$129$		0			0
$130$	9.38651	−	1.13113i	0.823251	−	0.0992066i
$131$	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
$136$	−8.34566	+	10.1652i	−0.715634	+	0.871663i
$137$	11.3468	−	6.55109i	0.969425	−	0.559698i	0.0703639	−	0.997521i	$-0.477584\pi$
$137$	11.3468	−	6.55109i	0.969425	−	0.559698i	0.899061	+	0.437824i	$0.144251\pi$
$138$		0			0
$139$	−19.1125			−1.62110			−0.810549	−	0.585671i	$-0.800831\pi$
$139$	−19.1125			−1.62110			−0.810549	+	0.585671i	$0.800831\pi$
$140$	8.32358	+	4.36187i	0.703471	+	0.368646i
$141$		0			0
$142$	−4.33278	−	5.77674i	−0.363599	−	0.484773i
$143$	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	$0.797660\pi$
$152$	0.175919	+	0.0290789i	0.0142689	+	0.00235861i
$153$		0			0
$154$	−1.23630	+	15.6125i	−0.0996239	+	1.25809i
$155$	13.6346			1.09516
$156$		0			0
$157$	0.669124	+	1.15896i	0.0534019	+	0.0924948i	0.891491	−	0.453039i	$-0.149660\pi$
$157$	0.669124	+	1.15896i	0.0534019	+	0.0924948i	−0.838089	+	0.545534i	$0.816327\pi$
$158$	2.02862	+	16.8342i	0.161388	+	1.33926i
$159$		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	0.364762	−	0.931101i	$-0.381150\pi$
$163$	−3.30942	−	1.91070i	−0.259214	−	0.149657i	−0.623976	+	0.781444i	$0.714484\pi$
$164$	−4.51444	+	15.4810i	−0.352518	+	1.20886i
$165$		0			0
$166$	6.49139	+	8.65473i	0.503830	+	0.671737i
$167$	−7.25804			−0.561644			−0.280822	−	0.959760i	$-0.590607\pi$
$167$	−7.25804			−0.561644			−0.280822	+	0.959760i	$0.590607\pi$
$168$		0			0
$169$	1.17093			0.0900713
$170$	−7.00741	−	9.34272i	−0.537444	−	0.716554i
$171$		0			0
$172$	19.0971	+	5.56895i	1.45614	+	0.424628i
$173$	−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
$178$	3.03711	+	25.2030i	0.227641	+	1.88904i
$179$	−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	$-0.290214\pi$
$181$	16.4773			1.22475			0.612376	+	0.790567i	$0.290214\pi$
$182$	11.6041	+	7.98354i	0.860156	+	0.591779i
$183$		0			0
$184$	−2.15915	+	13.0622i	−0.159175	+	0.962961i
$185$	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	0.916592	−	0.399824i	$-0.130929\pi$
$191$	14.2159	+	8.20758i	1.02863	+	0.593880i	0.112038	+	0.993704i	$0.464262\pi$
$192$		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	$-0.488079\pi$
$194$	−3.60285	−	4.80355i	−0.258670	−	0.344875i
$195$		0			0
$196$	5.00455	+	13.0750i	0.357468	+	0.933925i
$197$	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	$0.184800\pi$
$200$	−3.31338	+	4.03579i	−0.234291	+	0.285374i
$201$		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
$206$	−18.3436	+	2.21051i	−1.27806	+	0.154013i
$207$		0			0
$208$	−12.6975	−	8.09374i	−0.880412	−	0.561200i
$209$	−0.263868			−0.0182521
$210$		0			0
$211$			18.9821i			1.30678i	0.757020	+	0.653392i	$0.226655\pi$
$211$			18.9821i			1.30678i	−0.757020	+	0.653392i	$0.773345\pi$
$212$	−9.17739	+	2.24445i	−0.630306	+	0.154150i
$213$		0			0
$214$	1.77691	+	14.7454i	0.121467	+	1.00798i
$215$	−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
$220$	14.2723	+	4.16197i	0.962238	+	0.280600i
$221$	−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	$-0.0926036\pi$
$224$	−5.83777	−	13.7812i	−0.390053	−	0.920793i
$225$		0			0
$226$	3.87367	+	5.16462i	0.257673	+	0.343545i
$227$	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	$0.544097\pi$
$229$	−14.0246	+	24.2914i	−0.926774	+	1.60522i	−0.788683	+	0.614800i	$0.789237\pi$
$230$	−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	0.232718	−	0.972544i	$-0.425238\pi$
$233$	−7.52792	−	4.34625i	−0.493170	−	0.284732i	−0.725889	+	0.687812i	$0.758571\pi$
$234$		0			0
$235$	−1.04210	+	0.601657i	−0.0679792	+	0.0392478i
$236$	−3.58369	−	14.6534i	−0.233278	−	0.953856i
$237$		0			0
$238$	1.37345	−	17.3445i	0.0890278	−	1.12428i
$239$		−	12.4878i		−	0.807772i	−0.914809	−	0.403886i	$-0.867659\pi$
$239$		−	12.4878i		−	0.807772i	0.914809	−	0.403886i	$-0.132341\pi$
$240$		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	$0.0647117\pi$
$242$	1.10315	+	9.15429i	0.0709129	+	0.588460i
$243$		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
$248$	−16.7836	−	13.7793i	−1.06576	−	0.874988i
$249$		0			0
$250$	−10.3169	−	13.7551i	−0.652496	−	0.869949i
$251$			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
$254$	9.45990	−	7.09530i	0.593567	−	0.445199i
$255$		0			0
$256$	6.75450	+	14.5044i	0.422156	+	0.906523i
$257$	11.8457	−	20.5174i	0.738915	−	1.27984i	−0.214069	−	0.976819i	$-0.568672\pi$
$257$	11.8457	−	20.5174i	0.738915	−	1.27984i	0.952984	−	0.303020i	$-0.0979950\pi$
$258$		0			0
$259$	−1.76069	+	8.73287i	−0.109404	+	0.542634i
$260$	9.65959	−	9.24469i	0.599063	−	0.573331i
$261$		0			0
$262$	8.85049	−	1.06654i	0.546785	−	0.0658909i
$263$	13.5097	−	7.79983i	0.833044	−	0.480958i	−0.0218497	−	0.999761i	$-0.506956\pi$
$263$	13.5097	−	7.79983i	0.833044	−	0.480958i	0.854894	+	0.518803i	$0.173622\pi$
$264$		0			0
$265$		−	8.38927i		−	0.515349i
$266$	−0.212948	+	0.101445i	−0.0130567	+	0.00621999i
$267$		0			0
$268$	3.11546	+	12.7389i	0.190307	+	0.778150i
$269$	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	−0.993270	−	0.115825i	$-0.963049\pi$
$277$	−23.1275	+	13.3527i	−1.38960	+	0.802284i	−0.396327	+	0.918109i	$0.629715\pi$
$278$	−21.6229	+	16.2180i	−1.29685	+	0.972691i
$279$		0			0
$280$	13.1182	−	2.12822i	0.783961	−	0.127186i
$281$			26.1930i			1.56254i	0.624193	+	0.781271i	$0.285428\pi$
$281$			26.1930i			1.56254i	−0.624193	+	0.781271i	$0.714572\pi$
$282$		0			0
$283$	−2.62071	−	4.53920i	−0.155785	−	0.269827i	0.777560	−	0.628809i	$-0.216457\pi$
$283$	−2.62071	−	4.53920i	−0.155785	−	0.269827i	−0.933345	+	0.358982i	$0.883124\pi$
$284$	−9.80378	−	2.85890i	−0.581748	−	0.169644i
$285$		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
$290$	−16.1407	+	1.94505i	−0.947813	+	0.114217i
$291$		0			0
$292$	−0.709547	−	2.90128i	−0.0415231	−	0.169785i
$293$			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
$296$	1.55316	−	9.39619i	0.0902757	−	0.546142i
$297$		0			0
$298$	−0.742458	−	6.16117i	−0.0430094	−	0.356907i
$299$	−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
$304$	0.223701	−	0.116379i	0.0128301	−	0.00667478i
$305$	22.2424	−	12.8417i	1.27360	−	0.735312i
$306$		0			0
$307$	17.8873			1.02088			0.510442	−	0.859912i	$-0.329482\pi$
$307$	17.8873			1.02088			0.510442	+	0.859912i	$0.329482\pi$
$308$	11.8494	+	18.7123i	0.675182	+	1.06623i
$309$		0			0
$310$	15.4255	−	11.5698i	0.876112	−	0.657119i
$311$	−0.257495	−	0.445994i	−0.0146012	−	0.0252900i	0.858632	−	0.512592i	$-0.171315\pi$
$311$	−0.257495	−	0.445994i	−0.0146012	−	0.0252900i	−0.873234	+	0.487302i	$0.837981\pi$
$312$		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
$320$	−13.9353	+	2.76637i	−0.779009	+	0.154645i
$321$		0			0
$322$	−7.53244	−	15.8117i	−0.419766	−	0.881151i
$323$	0.293141			0.0163108
$324$		0			0
$325$	−3.47485	−	6.01861i	−0.192750	−	0.333853i
$326$	−5.36545	+	0.646568i	−0.297165	+	0.0358101i
$327$		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	0.258548	−	0.965998i	$-0.416756\pi$
$331$	−8.16441	−	4.71372i	−0.448756	−	0.259090i	−0.707305	+	0.706909i	$0.750089\pi$
$332$	14.6881	+	4.28321i	0.806112	+	0.235072i
$333$		0			0
$334$	−8.21138	+	6.15886i	−0.449307	+	0.336998i
$335$	−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	$0.632202\pi$
$338$	1.32473	−	0.993598i	0.0720557	−	0.0540446i
$339$		0			0
$340$	−15.8557	−	4.62370i	−0.859894	−	0.250755i
$341$	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
$346$	−1.73661	+	0.209271i	−0.0933605	+	0.0112505i
$347$	−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	$-0.115503\pi$
$349$	34.9301			1.86977			0.934884	+	0.354954i	$0.115503\pi$
$350$	0.545287	−	6.88610i	0.0291468	−	0.368077i
$351$		0			0
$352$	−13.3624	−	19.5469i	−0.712218	−	1.04186i
$353$	3.71324	+	6.43152i	0.197636	+	0.342315i	0.947761	−	0.318980i	$-0.103340\pi$
$353$	3.71324	+	6.43152i	0.197636	+	0.342315i	−0.750126	+	0.661295i	$0.770007\pi$
$354$		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	0.667056	−	0.745008i	$-0.267554\pi$
$359$	6.73364	+	3.88767i	0.355388	+	0.205183i	−0.311668	+	0.950191i	$0.600888\pi$
$360$		0			0
$361$	9.49801	+	16.4510i	0.499895	+	0.865844i
$362$	18.6416	−	13.9820i	0.979783	−	0.734876i
$363$		0			0
$364$	19.9028	−	0.814598i	1.04319	−	0.0426965i
$365$	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	$0.400945\pi$
$368$	8.64130	+	16.6101i	0.450459	+	0.865862i
$369$		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	0.971410	−	0.237407i	$-0.0762974\pi$
$373$	24.1708	+	13.9550i	1.25152	+	0.722563i	0.280105	+	0.959969i	$0.409631\pi$
$374$	−3.29317	−	27.3279i	−0.170286	−	1.41309i
$375$		0			0
$376$	1.89082	+	0.312547i	0.0975115	+	0.0161184i
$377$	−24.3678			−1.25500
$378$		0			0
$379$		−	29.0460i		−	1.49199i	−0.665949	−	0.745997i	$-0.731973\pi$
$379$		−	29.0460i		−	1.49199i	0.665949	−	0.745997i	$-0.268027\pi$
$380$	0.0531923	+	0.217499i	0.00272871	+	0.0111575i
$381$		0			0
$382$	23.0478	−	2.77740i	1.17923	−	0.142104i
$383$	−5.63040	+	9.75214i	−0.287700	+	0.498311i	−0.973260	−	0.229705i	$-0.926224\pi$
$383$	−5.63040	+	9.75214i	−0.287700	+	0.498311i	0.685560	+	0.728016i	$0.259557\pi$
$384$		0			0
$385$	−18.6395	+	6.27327i	−0.949958	+	0.319716i
$386$	−30.5958	−	13.0683i	−1.55729	−	0.665160i
$387$		0			0
$388$	−8.15217	−	2.37727i	−0.413864	−	0.120688i
$389$	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
$392$	16.7567	+	10.5457i	0.846343	+	0.532638i
$393$		0			0
$394$	0.896848	−	0.672671i	0.0451825	−	0.0338887i
$395$	−18.4399	+	10.6463i	−0.927814	+	0.535674i
$396$		0			0
$397$	−13.8771	+	24.0358i	−0.696471	+	1.20632i	0.273211	+	0.961954i	$0.411914\pi$
$397$	−13.8771	+	24.0358i	−0.696471	+	1.20632i	−0.969682	+	0.244369i	$0.921419\pi$
$398$	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	0.589624	−	0.807678i	$-0.299276\pi$
$401$	3.70394	+	2.13847i	0.184966	+	0.106790i	−0.404658	+	0.914468i	$0.632609\pi$
$402$		0			0
$403$	25.0295	−	14.4508i	1.24681	−	0.719846i
$404$	−1.99510	−	8.15781i	−0.0992600	−	0.405866i
$405$		0			0
$406$	−19.9540	−	13.7282i	−0.990302	−	0.681318i
$407$			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	$0.206320\pi$
$410$	−20.1046	+	2.42273i	−0.992897	+	0.119650i
$411$		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
$416$	−21.2333	+	1.61769i	−1.04105	+	0.0793136i
$417$		0			0
$418$	−0.298527	+	0.223907i	−0.0146014	+	0.0109516i
$419$			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	$-0.874609\pi$
$421$		−	15.7506i		−	0.767635i	0.923409	−	0.383818i	$-0.125391\pi$
$422$	16.1074	+	21.4754i	0.784097	+	1.04541i
$423$		0			0
$424$	−8.47829	+	10.3268i	−0.411742	+	0.501514i
$425$	−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
$430$	2.98864	+	24.8008i	0.144125	+	1.19600i
$431$	−6.36898	+	3.67713i	−0.306783	+	0.177121i	−0.645486	−	0.763772i	$-0.723345\pi$
$431$	−6.36898	+	3.67713i	−0.306783	+	0.177121i	0.338703	+	0.940893i	$0.390012\pi$
$432$		0			0
$433$			8.06468i			0.387564i	0.981045	+	0.193782i	$0.0620754\pi$
$433$			8.06468i			0.387564i	−0.981045	+	0.193782i	$0.937925\pi$
$434$	28.6371	+	2.26768i	1.37463	+	0.108852i
$435$		0			0
$436$	−1.20587	−	4.93069i	−0.0577505	−	0.236137i
$437$	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
$446$	−7.26938	−	9.69200i	−0.344215	−	0.458930i
$447$		0			0
$448$	−18.2987	−	10.6376i	−0.864530	−	0.502581i
$449$		−	34.7839i		−	1.64155i	−0.571250	−	0.820776i	$-0.693541\pi$
$449$		−	34.7839i		−	1.64155i	0.571250	−	0.820776i	$-0.306459\pi$
$450$		0			0
$451$	−16.8743	−	29.2272i	−0.794582	−	1.37626i
$452$	8.76494	+	2.55596i	0.412268	+	0.120222i
$453$		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	$0.247785\pi$
$458$	4.74585	+	39.3827i	0.221759	+	1.84023i
$459$		0			0
$460$	−16.1496	+	3.94961i	−0.752980	+	0.184151i
$461$			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	$0.717879\pi$
$464$	21.8341	+	13.9177i	1.01362	+	0.646112i
$465$		0			0
$466$	−12.2047	+	1.47074i	−0.565374	+	0.0681309i
$467$	−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
$472$	−16.4886	−	13.5372i	−0.758952	−	0.623098i
$473$	−36.0543	+	20.8160i	−1.65778	+	0.957118i
$474$		0			0
$475$	0.116382			0.00533999
$476$	−13.1640	−	20.7882i	−0.603369	−	0.952825i
$477$		0			0
$478$	−10.5966	−	14.1281i	−0.484679	−	0.646205i
$479$	−0.640883	−	1.11004i	−0.0292827	−	0.0507191i	0.851013	−	0.525145i	$-0.175989\pi$
$479$	−0.640883	−	1.11004i	−0.0292827	−	0.0507191i	−0.880295	+	0.474426i	$0.842656\pi$
$480$		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	$-0.341680\pi$
$488$	−40.3573	−	6.67095i	−1.82689	−	0.301980i
$489$		0			0
$490$	−12.6308	+	12.2287i	−0.570600	+	0.552437i
$491$	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
$494$	0.0401525	+	0.333200i	0.00180655	+	0.0149914i
$495$		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	0.610914	−	0.791697i	$-0.290802\pi$
$499$	5.15436	+	2.97587i	0.230741	+	0.133218i	−0.380173	+	0.924915i	$0.624135\pi$
$500$	−23.3440	−	6.80737i	−1.04397	−	0.304435i
$501$		0			0
$502$	11.8542	+	15.8048i	0.529079	+	0.705401i
$503$	−1.41791			−0.0632214			−0.0316107	−	0.999500i	$-0.510064\pi$
$503$	−1.41791			−0.0632214			−0.0316107	+	0.999500i	$0.510064\pi$
$504$		0			0
$505$	7.45725			0.331843
$506$	−16.6254	−	22.1661i	−0.739090	−	0.985402i
$507$		0			0
$508$	4.68169	−	16.0545i	0.207716	−	0.712304i
$509$	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
$514$	−4.00852	−	33.2641i	−0.176808	−	1.46722i
$515$	−11.6009	−	20.0933i	−0.511195	−	0.885416i
$516$		0			0
$517$	−2.83612			−0.124732
$518$	5.41838	+	11.3740i	0.238070	+	0.499744i
$519$		0			0
$520$	3.08373	−	18.6557i	0.135231	−	0.818106i
$521$	11.7714	+	20.3887i	0.515715	+	0.893244i	0.999834	+	0.0182421i	$0.00580695\pi$
$521$	11.7714	+	20.3887i	0.515715	+	0.893244i	−0.484119	+	0.875002i	$0.660860\pi$
$522$		0			0
$523$	14.4448	−	25.0191i	0.631626	−	1.09401i	−0.355593	−	0.934641i	$-0.615721\pi$
$523$	14.4448	−	25.0191i	0.631626	−	1.09401i	0.987219	−	0.159368i	$-0.0509456\pi$
$524$	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
$530$	−7.11877	−	9.49119i	−0.309220	−	0.412271i
$531$		0			0
$532$	−0.154837	+	0.295468i	−0.00671301	+	0.0128102i
$533$	−30.3522			−1.31470
$534$		0			0
$535$	−16.1519	+	9.32532i	−0.698309	+	0.403169i
$536$	14.3343	+	11.7685i	0.619148	+	0.508320i
$537$		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	0.537896	−	0.843011i	$-0.319219\pi$
$541$	1.78575	+	1.03100i	0.0767754	+	0.0443263i	−0.461121	+	0.887337i	$0.652553\pi$
$542$	13.2423	−	1.59578i	0.568806	−	0.0685445i
$543$		0			0
$544$	14.8448	+	21.7155i	0.636466	+	0.931042i
$545$	4.50726			0.193070
$546$		0			0
$547$			35.7819i			1.52992i	0.644076	+	0.764962i	$0.277242\pi$
$547$			35.7819i			1.52992i	−0.644076	+	0.764962i	$0.722758\pi$
$548$	−6.22516	−	25.4542i	−0.265926	−	1.08735i
$549$		0			0
$550$	−1.30745	−	10.8497i	−0.0557499	−	0.462632i
$551$	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
$556$	−10.7011	+	36.6965i	−0.453828	+	1.55628i
$557$	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
$560$	13.0353	−	13.5393i	0.550843	−	0.572139i
$561$		0			0
$562$	22.2262	+	29.6334i	0.937556	+	1.25001i
$563$	−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	0.139812	−	0.990178i	$-0.455350\pi$
$569$	−15.4525	−	8.92150i	−0.647802	−	0.374009i	−0.787614	+	0.616169i	$0.788684\pi$
$570$		0			0
$571$	−15.9523	+	9.21009i	−0.667585	+	0.385430i	−0.795161	−	0.606398i	$-0.792614\pi$
$571$	−15.9523	+	9.21009i	−0.667585	+	0.385430i	0.127576	+	0.991829i	$0.459280\pi$
$572$	30.6112	−	7.48638i	1.27992	−	0.313021i
$573$		0			0
$574$	−24.8545	−	17.0997i	−1.03741	−	0.713726i
$575$			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	$0.471930\pi$
$578$	0.782163	+	6.49066i	0.0325337	+	0.269976i
$579$		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
$584$	−3.26465	−	2.68027i	−0.135092	−	0.110910i
$585$		0			0
$586$	7.03822	+	9.38380i	0.290746	+	0.387641i
$587$			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
$590$	15.1545	−	11.3664i	0.623899	−	0.467949i
$591$		0			0
$592$	−6.21603	−	11.9483i	−0.255477	−	0.491073i
$593$	10.4731	−	18.1399i	0.430078	−	0.744918i	−0.566801	−	0.823855i	$-0.691819\pi$
$593$	10.4731	−	18.1399i	0.430078	−	0.744918i	0.996880	+	0.0789370i	$0.0251526\pi$
$594$		0			0
$595$	20.7074	−	6.96922i	0.848920	−	0.285710i
$596$	−6.06808	−	6.34042i	−0.248558	−	0.259714i
$597$		0			0
$598$	−24.7406	+	2.98138i	−1.01172	+	0.121918i
$599$	1.58346	−	0.914209i	0.0646983	−	0.0373536i	−0.467302	−	0.884098i	$-0.654774\pi$
$599$	1.58346	−	0.914209i	0.0646983	−	0.0373536i	0.532000	+	0.846744i	$0.321441\pi$
$600$		0			0
$601$			29.7207i			1.21233i	0.795338	+	0.606166i	$0.207293\pi$
$601$			29.7207i			1.21233i	−0.795338	+	0.606166i	$0.792707\pi$
$602$	−21.0939	+	30.6602i	−0.859723	+	1.24961i
$603$		0			0
$604$	5.33976	−	1.30591i	0.217272	−	0.0531367i
$605$	−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	−0.355985	−	0.934492i	$-0.615855\pi$
$613$	6.81649	−	3.93550i	0.275316	−	0.158954i	0.631301	+	0.775538i	$0.282521\pi$
$614$	20.2368	−	15.1784i	0.816692	−	0.612551i
$615$		0			0
$616$	29.2842	+	11.1152i	1.17990	+	0.447845i
$617$			8.93676i			0.359781i	0.983687	+	0.179890i	$0.0575743\pi$
$617$			8.93676i			0.359781i	−0.983687	+	0.179890i	$0.942426\pi$
$618$		0			0
$619$	3.80163	+	6.58462i	0.152801	+	0.264658i	0.932256	−	0.361799i	$-0.117837\pi$
$619$	3.80163	+	6.58462i	0.152801	+	0.264658i	−0.779455	+	0.626458i	$0.784504\pi$
$620$	7.63407	−	26.1789i	0.306592	−	1.05137i
$621$		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
$626$	32.7447	−	3.94593i	1.30874	−	0.157711i
$627$		0			0
$628$	2.59987	−	0.635834i	0.103746	−	0.0253725i
$629$		−	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	$0.0316769\pi$
$632$	33.4580	+	5.53051i	1.33089	+	0.219992i
$633$		0			0
$634$	3.55062	+	29.4643i	0.141013	+	1.17018i
$635$	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
$640$	−13.4183	+	14.9547i	−0.530405	+	0.591135i
$641$	34.4319	−	19.8793i	1.35998	−	0.785184i	0.370358	−	0.928889i	$-0.379235\pi$
$641$	34.4319	−	19.8793i	1.35998	−	0.785184i	0.989621	+	0.143705i	$0.0459016\pi$
$642$		0			0
$643$	−28.7989			−1.13572			−0.567858	−	0.823126i	$-0.692228\pi$
$643$	−28.7989			−1.13572			−0.567858	+	0.823126i	$0.692228\pi$
$644$	−21.9389	−	11.4968i	−0.864515	−	0.453039i
$645$		0			0
$646$	0.331645	−	0.248747i	0.0130484	−	0.00978682i
$647$	13.1134	+	22.7130i	0.515540	+	0.892941i	0.999837	+	0.0180376i	$0.00574185\pi$
$647$	13.1134	+	22.7130i	0.515540	+	0.892941i	−0.484298	+	0.874903i	$0.660925\pi$
$648$		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
$656$	27.1963	+	17.3357i	1.06184	+	0.676845i
$657$		0			0
$658$	−2.28881	+	1.09035i	−0.0892273	+	0.0425064i
$659$	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	0.642085	−	0.766633i	$-0.278069\pi$
$661$	−8.81544	−	15.2688i	−0.342881	−	0.593887i	−0.984966	+	0.172746i	$0.944736\pi$
$662$	−13.2367	+	1.59510i	−0.514457	+	0.0619951i
$663$		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
$668$	−4.06380	+	13.9357i	−0.157233	+	0.539186i
$669$		0			0
$670$	−13.1744	+	9.88136i	−0.508973	+	0.381750i
$671$	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	$0.711756\pi$
$674$	−16.7599	+	12.5706i	−0.645569	+	0.484202i
$675$		0			0
$676$	0.655605	−	2.24821i	0.0252156	−	0.0864697i
$677$	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
$682$	45.1204	−	5.43728i	1.72775	−	0.208204i
$683$	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
$686$	−26.1631	+	1.22214i	−0.998911	+	0.0466615i
$687$		0			0
$688$	21.3851	−	33.5490i	0.815299	−	1.27904i
$689$	−8.89145	−	15.4004i	−0.338737	−	0.586710i
$690$		0			0
$691$	20.3501	−	35.2473i	0.774153	−	1.34087i	−0.161116	−	0.986935i	$-0.551509\pi$
$691$	20.3501	−	35.2473i	0.774153	−	1.34087i	0.935269	−	0.353937i	$-0.115157\pi$
$692$	−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
$698$	39.5182	−	29.6402i	1.49579	−	1.12190i
$699$		0			0
$700$	−5.22634	−	8.25329i	−0.197537	−	0.311945i
$701$	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
$704$	−31.7042	−	10.7757i	−1.19490	−	0.406123i
$705$		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	0.605467	−	0.795871i	$-0.292987\pi$
$709$	5.83014	+	3.36604i	0.218956	+	0.126414i	−0.386511	+	0.922285i	$0.626320\pi$
$710$	−1.53426	−	12.7318i	−0.0575798	−	0.477817i
$711$		0			0
$712$	50.0909	+	8.27988i	1.87723	+	0.310302i
$713$	−35.9376			−1.34587
$714$		0			0
$715$			27.9824i			1.04648i
$716$	−34.1998	+	8.36401i	−1.27811	+	0.312578i
$717$		0			0
$718$	10.9170	−	1.31556i	0.407419	−	0.0490964i
$719$	−1.45947	+	2.52788i	−0.0544291	+	0.0942739i	−0.891956	−	0.452122i	$-0.850667\pi$
$719$	−1.45947	+	2.52788i	−0.0544291	+	0.0942739i	0.837527	+	0.546396i	$0.184001\pi$
$720$		0			0
$721$	6.83160	−	33.8841i	0.254422	−	1.26191i
$722$	24.7052	+	10.5523i	0.919433	+	0.392715i
$723$		0			0
$724$	9.22571	−	31.6370i	0.342871	−	1.17578i
$725$	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	$-0.0184702\pi$
$728$	21.8258	−	17.8103i	0.808919	−	0.660093i
$729$		0			0
$730$	3.00048	−	2.25048i	0.111053	−	0.0832941i
$731$	40.0541	−	23.1252i	1.48145	−	0.855318i
$732$		0			0
$733$	−3.93077	+	6.80830i	−0.145186	+	0.251470i	−0.929442	−	0.368967i	$-0.879712\pi$
$733$	−3.93077	+	6.80830i	−0.145186	+	0.251470i	0.784256	+	0.620437i	$0.213045\pi$
$734$	−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	−0.481274	−	0.876570i	$-0.659826\pi$
$739$	1.01186	−	0.584195i	0.0372217	−	0.0214900i	0.518495	+	0.855080i	$0.326492\pi$
$740$	11.6171	−	2.84111i	0.427052	−	0.104441i
$741$		0			0
$742$	1.39528	−	17.6202i	0.0512224	−	0.646857i
$743$			6.12199i			0.224594i	0.993675	+	0.112297i	$0.0358208\pi$
$743$			6.12199i			0.224594i	−0.993675	+	0.112297i	$0.964179\pi$
$744$		0			0
$745$	6.74886	−	3.89645i	0.247259	−	0.142755i
$746$	39.1872	−	4.72229i	1.43475	−	0.172895i
$747$		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	$-0.108415\pi$
$752$	2.40439	−	1.25087i	0.0876791	−	0.0456144i
$753$		0			0
$754$	−27.5685	+	20.6774i	−1.00398	+	0.753028i
$755$			4.88120i			0.177645i
$756$		0			0
$757$		−	35.8599i		−	1.30335i	−0.758498	−	0.651676i	$-0.774066\pi$
$757$		−	35.8599i		−	1.30335i	0.758498	−	0.651676i	$-0.225934\pi$
$758$	−24.6472	−	32.8612i	−0.895227	−	1.19357i
$759$		0			0
$760$	0.244739	+	0.200931i	0.00887763	+	0.00728852i
$761$	−4.88971	+	8.46923i	−0.177252	+	0.307009i	−0.940938	−	0.338578i	$-0.890054\pi$
$761$	−4.88971	+	8.46923i	−0.177252	+	0.307009i	0.763686	+	0.645587i	$0.223387\pi$
$762$		0			0
$763$	5.03702	+	4.44056i	0.182352	+	0.160759i
$764$	23.7183	−	22.6996i	0.858099	−	0.821241i
$765$		0			0
$766$	1.90529	+	15.8108i	0.0688411	+	0.571267i
$767$	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	$-0.432566\pi$
$770$	−15.7646	+	22.9140i	−0.568116	+	0.825762i
$771$		0			0
$772$	−45.7038	+	11.1775i	−1.64491	+	0.402286i
$773$	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
$782$	18.4698	+	24.6251i	0.660480	+	0.880593i
$783$		0			0
$784$	27.9063	−	2.28818i	0.996655	−	0.0817206i
$785$			2.37661i			0.0848247i
$786$		0			0
$787$	−13.5019	−	23.3859i	−0.481290	−	0.833619i	0.518479	−	0.855090i	$-0.326498\pi$
$787$	−13.5019	−	23.3859i	−0.481290	−	0.833619i	−0.999769	+	0.0214714i	$0.993165\pi$
$788$	0.443848	−	1.52205i	0.0158114	−	0.0542209i
$789$		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
$794$	4.69592	+	38.9684i	0.166652	+	1.38294i
$795$		0			0
$796$	−6.03058	−	24.6586i	−0.213748	−	0.874000i
$797$		−	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
$800$	5.89366	+	8.62144i	0.208372	+	0.304814i
$801$		0			0
$802$	6.00506	−	0.723645i	0.212046	−	0.0255528i
$803$	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
$808$	−9.17952	−	7.53638i	−0.322934	−	0.265129i
$809$	−10.5996	+	6.11967i	−0.372661	+	0.215156i	−0.674620	−	0.738165i	$-0.735693\pi$
$809$	−10.5996	+	6.11967i	−0.372661	+	0.215156i	0.301959	+	0.953321i	$0.402359\pi$
$810$		0			0
$811$	−51.5601			−1.81052			−0.905260	−	0.424858i	$-0.860324\pi$
$811$	−51.5601			−1.81052			−0.905260	+	0.424858i	$0.860324\pi$
$812$	−34.2241	+	1.40075i	−1.20103	+	0.0491567i
$813$		0			0
$814$	11.9593	+	15.9449i	0.419174	+	0.558869i
$815$	−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	$0.732774\pi$
$824$	−6.02638	+	36.4578i	−0.209939	+	1.27007i
$825$		0			0
$826$	28.1339	+	2.22783i	0.978903	+	0.0775160i
$827$	−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	0.960294	−	0.278990i	$-0.0899997\pi$
$829$	6.86797	+	11.8957i	0.238534	+	0.413154i	−0.721760	+	0.692144i	$0.756666\pi$
$830$	2.29864	+	19.0749i	0.0797868	+	0.662099i
$831$		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
$836$	−0.147740	+	0.506634i	−0.00510971	+	0.0175223i
$837$		0			0
$838$	32.3163	+	43.0861i	1.11635	+	1.48839i
$839$	−18.7998			−0.649040			−0.324520	−	0.945879i	$-0.605203\pi$
$839$	−18.7998			−0.649040			−0.324520	+	0.945879i	$0.605203\pi$
$840$		0			0
$841$	12.9019			0.444892
$842$	−13.3652	−	17.8194i	−0.460597	−	0.614097i
$843$		0			0
$844$	36.4462	+	10.6281i	1.25453	+	0.365836i
$845$	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
$850$	1.45250	+	12.0533i	0.0498202	+	0.413426i
$851$	−7.88055	−	13.6495i	−0.270142	−	0.467899i
$852$		0			0
$853$	4.23719			0.145079			0.0725393	−	0.997366i	$-0.476890\pi$
$853$	4.23719			0.145079			0.0725393	+	0.997366i	$0.476890\pi$
$854$	48.8521	−	23.2724i	1.67168	−	0.796364i
$855$		0			0
$856$	29.3065	+	4.84429i	1.00168	+	0.165574i
$857$	6.78696	+	11.7554i	0.231838	+	0.401556i	0.958349	−	0.285599i	$-0.0921927\pi$
$857$	6.78696	+	11.7554i	0.231838	+	0.401556i	−0.726511	+	0.687155i	$0.758859\pi$
$858$		0			0
$859$	−14.8653	+	25.7475i	−0.507198	+	0.878494i	0.492767	+	0.870161i	$0.335986\pi$
$859$	−14.8653	+	25.7475i	−0.507198	+	0.878494i	−0.999965	+	0.00833211i	$0.997348\pi$
$860$	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	0.880130	−	0.474732i	$-0.157455\pi$
$863$	26.7055	+	15.4184i	0.909066	+	0.524849i	0.0289352	+	0.999581i	$0.490788\pi$
$864$		0			0
$865$	−1.09827	−	1.90225i	−0.0373422	−	0.0646785i
$866$	6.84334	+	9.12397i	0.232546	+	0.310045i
$867$		0			0
$868$	34.3229	−	21.7347i	1.16499	−	0.737724i
$869$	−50.1850			−1.70241
$870$		0			0
$871$	−21.3769	+	12.3420i	−0.724329	+	0.418191i
$872$	−5.54822	−	4.55509i	−0.187887	−	0.154255i
$873$		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	0.660461	−	0.750860i	$-0.270361\pi$
$877$	10.0815	+	5.82055i	0.340428	+	0.196546i	−0.320033	+	0.947406i	$0.603694\pi$
$878$	−8.14547	+	0.981578i	−0.274896	+	0.0331266i
$879$		0			0
$880$	15.9822	−	25.0729i	0.538760	−	0.845208i
$881$	23.5879			0.794698			0.397349	−	0.917668i	$-0.369930\pi$
$881$	23.5879			0.794698			0.397349	+	0.917668i	$0.369930\pi$
$882$		0			0
$883$			39.4950i			1.32911i	0.747239	+	0.664556i	$0.231379\pi$
$883$			39.4950i			1.32911i	−0.747239	+	0.664556i	$0.768621\pi$
$884$	−34.0072	+	8.31691i	−1.14379	+	0.279728i
$885$		0			0
$886$	2.64775	+	21.9720i	0.0889529	+	0.738162i
$887$	27.3283	−	47.3340i	0.917595	−	1.58932i	0.114537	−	0.993419i	$-0.463462\pi$
$887$	27.3283	−	47.3340i	0.917595	−	1.58932i	0.803058	−	0.595901i	$-0.203205\pi$
$888$		0			0
$889$	7.05664	+	20.9671i	0.236672	+	0.703214i
$890$	−17.7081	+	41.4585i	−0.593576	+	1.38969i
$891$		0			0
$892$	−16.4484	−	4.79655i	−0.550734	−	0.160601i
$893$	−0.0213575	−	0.0369922i	−0.000714700	−	0.00123790i
$894$		0			0
$895$		−	31.2628i		−	1.04500i
$896$	−29.7288	+	3.49258i	−0.993170	+	0.116679i
$897$		0			0
$898$	−29.5161	−	39.3527i	−0.984964	−	1.31322i
$899$	−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	−0.623907	−	0.781498i	$-0.714456\pi$
$907$	−7.80208	+	4.50453i	−0.259064	+	0.149571i	0.364844	+	0.931069i	$0.381122\pi$
$908$	−6.79583	−	27.7876i	−0.225528	−	0.922165i
$909$		0			0
$910$	10.7579	+	22.5825i	0.356622	+	0.748602i
$911$		−	35.3463i		−	1.17107i	−0.810646	−	0.585537i	$-0.800884\pi$
$911$		−	35.3463i		−	1.17107i	0.810646	−	0.585537i	$-0.199116\pi$
$912$		0			0
$913$	−27.7302	+	16.0100i	−0.917736	+	0.529855i
$914$	1.82364	+	15.1332i	0.0603208	+	0.500563i
$915$		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	$0.284208\pi$
$920$	−14.9194	+	18.1723i	−0.491878	+	0.599122i
$921$		0			0
$922$	16.5521	+	22.0683i	0.545115	+	0.726782i
$923$		−	19.2214i		−	0.632680i
$924$		0			0
$925$		−	6.21623i		−	0.204388i
$926$	−30.7839	+	23.0891i	−1.01162	+	0.758756i
$927$		0			0
$928$	36.5119	−	2.78171i	1.19856	−	0.0913141i
$929$	4.66786	−	8.08497i	0.153148	−	0.265259i	−0.779235	−	0.626731i	$-0.784392\pi$
$929$	4.66786	−	8.08497i	0.153148	−	0.265259i	0.932383	+	0.361472i	$0.117726\pi$
$930$		0			0
$931$	−0.0553236	−	0.437803i	−0.00181316	−	0.0143484i
$932$	−12.5598	+	12.0203i	−0.411411	+	0.393739i
$933$		0			0
$934$	−47.5424	+	5.72914i	−1.55563	+	0.187463i
$935$	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	$0.926211\pi$
$938$	−24.4580	−	1.93675i	−0.798583	−	0.0632371i
$939$		0			0
$940$	0.571724	+	2.33773i	0.0186476	+	0.0762484i
$941$	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
$950$	0.131669	−	0.0987571i	0.00427191	−	0.00320410i
$951$		0			0
$952$	−32.5330	−	12.3483i	−1.05440	−	0.400211i
$953$			36.6133i			1.18602i	0.805194	+	0.593011i	$0.202061\pi$
$953$			36.6133i			1.18602i	−0.805194	+	0.593011i	$0.797939\pi$
$954$		0			0
$955$	14.5759	+	25.2462i	0.471665	+	0.816948i
$956$	−23.9770	−	6.99198i	−0.775472	−	0.226137i
$957$		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
$962$	17.7969	−	2.14463i	0.573794	−	0.0691456i
$963$		0			0
$964$	−11.0232	−	45.0728i	−0.355032	−	1.45170i
$965$		−	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	$0.551764\pi$
$968$	18.1942	+	3.00744i	0.584782	+	0.0966628i
$969$		0			0
$970$	−1.27579	−	10.5869i	−0.0409631	−	0.339926i
$971$	−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
$976$	−51.3189	+	26.6983i	−1.64268	+	0.854592i
$977$	3.60255	−	2.07994i	0.115256	−	0.0665430i	−0.441264	−	0.897377i	$-0.645470\pi$
$977$	3.60255	−	2.07994i	0.115256	−	0.0665430i	0.556520	+	0.830834i	$0.312136\pi$
$978$		0			0
$979$	−75.1334			−2.40127
$980$	−3.91305	+	24.5529i	−0.124998	+	0.784312i
$981$		0			0
$982$	38.0992	−	28.5759i	1.21579	−	0.911894i
$983$	−10.4374	−	18.0782i	−0.332902	−	0.576604i	0.650177	−	0.759783i	$-0.274695\pi$
$983$	−10.4374	−	18.0782i	−0.332902	−	0.576604i	−0.983080	+	0.183179i	$0.941361\pi$
$984$		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	$0.769088\pi$
$992$	−35.8539	+	24.5099i	−1.13836	+	0.778191i
$993$		0			0
$994$	10.8289	−	15.7398i	0.343470	−	0.499237i
$995$	22.5410			0.714597
$996$		0			0
$997$	−9.23934	−	16.0030i	−0.292613	−	0.506820i	0.681814	−	0.731526i	$-0.261191\pi$
$997$	−9.23934	−	16.0030i	−0.292613	−	0.506820i	−0.974427	+	0.224705i	$0.927858\pi$
$998$	8.35659	−	1.00702i	0.264523	−	0.0318766i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.13135 - 0.848557i) q^{2} +(0.559903 - 1.92003i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 - 2.64733i) q^{8} +O(q^{10})\)	\(q+(1.13135 - 0.848557i) q^{2} +(0.559903 - 1.92003i) q^{4} +(1.53798 + 0.887954i) q^{5} +(0.843933 + 2.50754i) q^{7} +(-0.995807 - 2.64733i) q^{8} +(2.49347 - 0.300478i) q^{10} +(2.09284 + 3.62490i) q^{11} +3.76443 q^{13} +(3.08258 + 2.12078i) q^{14} +(-3.37302 - 2.15006i) q^{16} +(-2.32502 - 4.02705i) q^{17} +(-0.0315203 + 0.0545948i) q^{19} +(2.56602 - 2.45580i) q^{20} +(5.44367 + 2.32514i) q^{22} +(-4.05375 - 2.34043i) q^{23} +(-0.923074 - 1.59881i) q^{25} +(4.25888 - 3.19433i) q^{26} +(5.28708 - 0.216393i) q^{28} -6.47316 q^{29} +(6.64896 - 3.83878i) q^{31} +(-5.64051 + 0.429729i) q^{32} +(-6.04758 - 2.58309i) q^{34} +(-0.928631 + 4.60593i) q^{35} +(2.91602 + 1.68357i) q^{37} +(0.0106663 + 0.0885126i) q^{38} +(0.819176 - 4.95578i) q^{40} -8.06290 q^{41} +9.94628i q^{43} +(8.13170 - 1.98872i) q^{44} +(-6.57220 + 0.791988i) q^{46} +(-0.338788 + 0.586799i) q^{47} +(-5.57556 + 4.23240i) q^{49} +(-2.40100 - 1.02553i) q^{50} +(2.10771 - 7.22781i) q^{52} +(-2.36197 - 4.09104i) q^{53} +7.43338i q^{55} +(5.79791 - 4.73120i) q^{56} +(-7.32341 + 5.49285i) q^{58} +(6.53211 - 3.77132i) q^{59} +(7.23104 - 12.5245i) q^{61} +(4.26487 - 9.98502i) q^{62} +(-6.01674 + 5.27247i) q^{64} +(5.78962 + 3.34264i) q^{65} +(-5.67866 + 3.27857i) q^{67} +(-9.03382 + 2.20934i) q^{68} +(2.85779 + 5.99891i) q^{70} -5.10606i q^{71} +(1.29332 - 0.746696i) q^{73} +(4.72764 - 0.569709i) q^{74} +(0.0871753 + 0.0910878i) q^{76} +(-7.32339 + 8.30706i) q^{77} +(-5.99485 + 10.3834i) q^{79} +(-3.27849 - 6.30184i) q^{80} +(-9.12195 + 6.84183i) q^{82} +7.64992i q^{83} -8.25803i q^{85} +(8.43998 + 11.2527i) q^{86} +(7.51226 - 9.15014i) q^{88} +(-8.97506 + 15.5453i) q^{89} +(3.17692 + 9.43947i) q^{91} +(-6.76340 + 6.47290i) q^{92} +(0.114644 + 0.951355i) q^{94} +(-0.0969554 + 0.0559773i) q^{95} -4.24586i q^{97} +(-2.71647 + 9.51949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7}+O(q^{10}) \) 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

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