LMFDB - Embedded newform 504.2.ch.b.269.24

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			269.24
Character	$\chi$	$=$	504.269
Dual form			504.2.ch.b.341.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

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	−0.114983	−	0.993367i	$-0.536681\pi$
$5$	1.53798	−	0.887954i	0.687806	−	0.397105i	0.802790	+	0.596262i	$0.203348\pi$
$6$		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	−0.356330	−	0.934360i	$-0.615972\pi$
$11$	2.09284	−	3.62490i	0.631015	−	1.09295i	0.987345	−	0.158589i	$-0.0506945\pi$
$12$		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	0.433252	+	0.901273i	$0.357366\pi$
$17$	−2.32502	+	4.02705i	−0.563899	+	0.976702i	−0.997151	+	0.0754291i	$0.975967\pi$
$18$		0			0
$19$	−0.0315203	−	0.0545948i	−0.00723126	−	0.0125249i	0.862387	−	0.506249i	$-0.168968\pi$
$19$	−0.0315203	−	0.0545948i	−0.00723126	−	0.0125249i	−0.869618	+	0.493724i	$0.835635\pi$
$20$	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	$-0.828945\pi$
$23$	−4.05375	+	2.34043i	−0.845265	+	0.488014i	0.0137854	+	0.999905i	$0.495612\pi$
$24$		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	0.959254	−	0.282546i	$-0.0911790\pi$
$31$	6.64896	+	3.83878i	1.19419	+	0.689465i	0.234935	+	0.972011i	$0.424512\pi$
$32$	−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	−0.240772	−	0.970582i	$-0.577400\pi$
$37$	2.91602	−	1.68357i	0.479391	−	0.276777i	0.720163	+	0.693805i	$0.244067\pi$
$38$	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	$-0.725983\pi$
$43$		−	9.94628i		−	1.51679i	0.651793	−	0.758397i	$-0.274017\pi$
$44$	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	0.840259	−	0.542186i	$-0.182403\pi$
$47$	−0.338788	−	0.586799i	−0.0494174	−	0.0855934i	−0.889676	+	0.456592i	$0.849070\pi$
$48$		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	−0.981399	−	0.191979i	$-0.938509\pi$
$53$	−2.36197	+	4.09104i	−0.324441	+	0.561948i	0.656958	+	0.753927i	$0.271843\pi$
$54$		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	0.860789	−	0.508963i	$-0.169971\pi$
$59$	6.53211	+	3.77132i	0.850408	+	0.490983i	−0.0103803	+	0.999946i	$0.503304\pi$
$60$		0			0
$61$	7.23104	+	12.5245i	0.925840	+	1.60360i	0.790204	+	0.612844i	$0.209975\pi$
$61$	7.23104	+	12.5245i	0.925840	+	1.60360i	0.135636	+	0.990759i	$0.456692\pi$
$62$	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	$-0.464511\pi$
$67$	−5.67866	−	3.27857i	−0.693758	−	0.400542i	−0.805018	+	0.593250i	$0.797845\pi$
$68$	−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	$0.0979846\pi$
$71$			5.10606i			0.605978i	−0.952994	+	0.302989i	$0.902015\pi$
$72$		0			0
$73$	1.29332	+	0.746696i	0.151371	+	0.0873942i	0.573772	−	0.819015i	$-0.305479\pi$
$73$	1.29332	+	0.746696i	0.151371	+	0.0873942i	−0.422401	+	0.906409i	$0.638813\pi$
$74$	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	−0.976623	−	0.214961i	$-0.931038\pi$
$79$	−5.99485	−	10.3834i	−0.674473	−	1.16822i	0.302150	−	0.953260i	$-0.402296\pi$
$80$	−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	$-0.862085\pi$
$83$		−	7.64992i		−	0.839688i	0.907596	−	0.419844i	$-0.137915\pi$
$84$		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	−0.742499	−	0.669847i	$-0.766360\pi$
$89$	−8.97506	−	15.5453i	−0.951354	−	1.64779i	−0.208855	−	0.977947i	$-0.566974\pi$
$90$		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	$0.0691547\pi$
$97$			4.24586i			0.431102i	−0.976493	+	0.215551i	$0.930845\pi$
$98$	−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	0.669892	−	0.742459i	$-0.266341\pi$
$101$	3.63654	+	2.09956i	0.361849	+	0.208914i	−0.308042	+	0.951373i	$0.599674\pi$
$102$		0			0
$103$	−11.3144	+	6.53235i	−1.11484	+	0.643652i	−0.940078	−	0.340959i	$-0.889248\pi$
$103$	−11.3144	+	6.53235i	−1.11484	+	0.643652i	−0.174759	+	0.984611i	$0.555915\pi$
$104$	−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	−0.999961	−	0.00883827i	$-0.997187\pi$
$107$	−5.25101	−	9.09502i	−0.507635	−	0.879249i	0.492326	−	0.870411i	$-0.336147\pi$
$108$		0			0
$109$	2.19797	+	1.26900i	0.210528	+	0.121548i	0.601557	−	0.798830i	$-0.294547\pi$
$109$	2.19797	+	1.26900i	0.210528	+	0.121548i	−0.391029	+	0.920378i	$0.627881\pi$
$110$	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	$-0.931116\pi$
$113$		−	4.56501i		−	0.429440i	0.976676	−	0.214720i	$-0.0688838\pi$
$114$		0			0
$115$	−4.15639	+	7.19909i	−0.387586	+	0.671318i
$116$	−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	−0.242191	−	0.970229i	$-0.577866\pi$
$131$	5.45901	−	3.15176i	0.476956	−	0.275371i	0.719147	+	0.694858i	$0.244533\pi$
$132$		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	0.899061	−	0.437824i	$-0.144251\pi$
$137$	11.3468	+	6.55109i	0.969425	+	0.559698i	0.0703639	+	0.997521i	$0.477584\pi$
$138$		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	0.941793	−	0.336193i	$-0.109140\pi$
$149$	2.19406	+	3.80023i	0.179745	+	0.311327i	−0.762048	+	0.647520i	$0.775806\pi$
$150$		0			0
$151$	1.37428	−	2.38033i	0.111838	−	0.193708i	−0.804674	−	0.593717i	$-0.797660\pi$
$151$	1.37428	−	2.38033i	0.111838	−	0.193708i	0.916511	+	0.400009i	$0.130993\pi$
$152$	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	−0.838089	−	0.545534i	$-0.816327\pi$
$157$	0.669124	−	1.15896i	0.0534019	−	0.0924948i	0.891491	+	0.453039i	$0.149660\pi$
$158$	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	−0.623976	−	0.781444i	$-0.714484\pi$
$163$	−3.30942	+	1.91070i	−0.259214	+	0.149657i	0.364762	+	0.931101i	$0.381150\pi$
$164$	−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	−0.540166	−	0.841559i	$-0.681638\pi$
$173$	−1.07114	+	0.618425i	−0.0814375	+	0.0470180i	0.458728	+	0.888577i	$0.348305\pi$
$174$		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	0.323275	+	0.946305i	$0.395216\pi$
$179$	−8.80192	+	15.2454i	−0.657886	+	1.13949i	−0.981162	+	0.193188i	$0.938117\pi$
$180$		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	0.112038	−	0.993704i	$-0.464262\pi$
$191$	14.2159	−	8.20758i	1.02863	−	0.593880i	0.916592	+	0.399824i	$0.130929\pi$
$192$		0			0
$193$	−11.7627	+	20.3736i	−0.846696	+	1.46652i	0.0374435	+	0.999299i	$0.488079\pi$
$193$	−11.7627	+	20.3736i	−0.846696	+	1.46652i	−0.884140	+	0.467222i	$0.845255\pi$
$194$	−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	0.836151	−	0.548499i	$-0.184800\pi$
$199$	10.9922	+	6.34632i	0.779213	+	0.449879i	−0.0569382	+	0.998378i	$0.518134\pi$
$200$	−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	$-0.773345\pi$
$211$		−	18.9821i		−	1.30678i	0.757020	−	0.653392i	$-0.226655\pi$
$212$	−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	$0.0926036\pi$
$223$			8.56676i			0.573673i	−0.957980	+	0.286836i	$0.907396\pi$
$224$	−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	0.851159	−	0.524908i	$-0.175900\pi$
$227$	12.3870	+	7.15164i	0.822155	+	0.474671i	−0.0290044	+	0.999579i	$0.509234\pi$
$228$		0			0
$229$	−14.0246	−	24.2914i	−0.926774	−	1.60522i	−0.788683	−	0.614800i	$-0.789237\pi$
$229$	−14.0246	−	24.2914i	−0.926774	−	1.60522i	−0.138091	−	0.990420i	$-0.544097\pi$
$230$	−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	$-0.758571\pi$
$233$	−7.52792	+	4.34625i	−0.493170	+	0.284732i	0.232718	+	0.972544i	$0.425238\pi$
$234$		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	$0.132341\pi$
$239$			12.4878i			0.807772i	−0.914809	+	0.403886i	$0.867659\pi$
$240$		0			0
$241$	20.0923	+	11.6003i	1.29426	+	0.747240i	0.979406	−	0.201900i	$-0.0647117\pi$
$241$	20.0923	+	11.6003i	1.29426	+	0.747240i	0.314852	+	0.949141i	$0.398045\pi$
$242$	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	$-0.854665\pi$
$251$		−	13.9698i		−	0.881768i	0.897564	−	0.440884i	$-0.145335\pi$
$252$		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	0.952984	+	0.303020i	$0.0979950\pi$
$257$	11.8457	+	20.5174i	0.738915	+	1.27984i	−0.214069	+	0.976819i	$0.568672\pi$
$258$		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	0.854894	−	0.518803i	$-0.173622\pi$
$263$	13.5097	+	7.79983i	0.833044	+	0.480958i	−0.0218497	+	0.999761i	$0.506956\pi$
$264$		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	0.961635	+	0.274332i	$0.0884566\pi$
$269$	27.5546	+	15.9086i	1.68003	+	0.969966i	0.718396	+	0.695635i	$0.244877\pi$
$270$		0			0
$271$	8.16789	−	4.71573i	0.496164	−	0.286460i	−0.230964	−	0.972962i	$-0.574188\pi$
$271$	8.16789	−	4.71573i	0.496164	−	0.286460i	0.727128	+	0.686502i	$0.240855\pi$
$272$	−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	$-0.629715\pi$
$277$	−23.1275	−	13.3527i	−1.38960	−	0.802284i	−0.993270	+	0.115825i	$0.963049\pi$
$278$	−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	$-0.714572\pi$
$281$		−	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	$-0.883124\pi$
$283$	−2.62071	+	4.53920i	−0.155785	+	0.269827i	0.777560	+	0.628809i	$0.216457\pi$
$284$	−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	$-0.922105\pi$
$293$		−	8.29435i		−	0.484561i	0.970206	−	0.242280i	$-0.0778954\pi$
$294$		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	−0.873234	−	0.487302i	$-0.837981\pi$
$311$	−0.257495	+	0.445994i	−0.0146012	+	0.0252900i	0.858632	+	0.512592i	$0.171315\pi$
$312$		0			0
$313$	20.1970	−	11.6607i	1.14160	−	0.659104i	0.194775	−	0.980848i	$-0.437602\pi$
$313$	20.1970	−	11.6607i	1.14160	−	0.659104i	0.946827	+	0.321744i	$0.104269\pi$
$314$	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	−0.994322	−	0.106417i	$-0.966062\pi$
$317$	−10.4926	−	18.1736i	−0.589321	−	1.02073i	0.405001	−	0.914316i	$-0.367271\pi$
$318$		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	−0.707305	−	0.706909i	$-0.750089\pi$
$331$	−8.16441	+	4.71372i	−0.448756	+	0.259090i	0.258548	+	0.965998i	$0.416756\pi$
$332$	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	0.405830	+	0.913948i	$0.366982\pi$
$347$	−10.9642	+	18.9905i	−0.588587	+	1.01946i	−0.994418	+	0.105515i	$0.966351\pi$
$348$		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	−0.750126	−	0.661295i	$-0.770007\pi$
$353$	3.71324	−	6.43152i	0.197636	−	0.342315i	0.947761	+	0.318980i	$0.103340\pi$
$354$		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	$-0.600888\pi$
$359$	6.73364	−	3.88767i	0.355388	−	0.205183i	0.667056	+	0.745008i	$0.267554\pi$
$360$		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	0.306193	−	0.951970i	$-0.400945\pi$
$367$	−6.99509	−	4.03862i	−0.365141	−	0.210814i	−0.671333	+	0.741155i	$0.734278\pi$
$368$	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	0.280105	−	0.959969i	$-0.409631\pi$
$373$	24.1708	−	13.9550i	1.25152	−	0.722563i	0.971410	+	0.237407i	$0.0762974\pi$
$374$	−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	$0.268027\pi$
$379$			29.0460i			1.49199i	−0.665949	+	0.745997i	$0.731973\pi$
$380$	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	0.685560	−	0.728016i	$-0.259557\pi$
$383$	−5.63040	−	9.75214i	−0.287700	−	0.498311i	−0.973260	+	0.229705i	$0.926224\pi$
$384$		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	−0.795102	−	0.606476i	$-0.792583\pi$
$389$	2.51811	−	4.36149i	0.127673	−	0.221136i	0.922775	+	0.385340i	$0.125916\pi$
$390$		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	−0.969682	−	0.244369i	$-0.921419\pi$
$397$	−13.8771	−	24.0358i	−0.696471	−	1.20632i	0.273211	−	0.961954i	$-0.411914\pi$
$398$	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	$-0.632609\pi$
$401$	3.70394	−	2.13847i	0.184966	−	0.106790i	0.589624	+	0.807678i	$0.299276\pi$
$402$		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	0.797189	−	0.603730i	$-0.206320\pi$
$409$	13.6093	+	7.85734i	0.672937	+	0.388521i	−0.124251	+	0.992251i	$0.539653\pi$
$410$	−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	$-0.619582\pi$
$419$		−	38.0838i		−	1.86052i	0.366904	−	0.930259i	$-0.380418\pi$
$420$		0			0
$421$			15.7506i			0.767635i	0.923409	+	0.383818i	$0.125391\pi$
$421$			15.7506i			0.767635i	−0.923409	+	0.383818i	$0.874609\pi$
$422$	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	0.338703	−	0.940893i	$-0.390012\pi$
$431$	−6.36898	−	3.67713i	−0.306783	−	0.177121i	−0.645486	+	0.763772i	$0.723345\pi$
$432$		0			0
$433$		−	8.06468i		−	0.387564i	−0.981045	−	0.193782i	$-0.937925\pi$
$433$		−	8.06468i		−	0.387564i	0.981045	−	0.193782i	$-0.0620754\pi$
$434$	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	−0.615080	−	0.788465i	$-0.710876\pi$
$439$	−5.02415	+	2.90069i	−0.239790	+	0.138443i	0.375290	+	0.926907i	$0.377543\pi$
$440$	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	0.618084	−	0.786112i	$-0.287909\pi$
$443$	−7.82446	−	13.5524i	−0.371751	−	0.643892i	−0.989835	+	0.142220i	$0.954576\pi$
$444$		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	$0.306459\pi$
$449$			34.7839i			1.64155i	−0.571250	+	0.820776i	$0.693541\pi$
$450$		0			0
$451$	−16.8743	+	29.2272i	−0.794582	+	1.37626i
$452$	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	0.712010	−	0.702170i	$-0.247785\pi$
$457$	−5.38911	−	9.33422i	−0.252092	−	0.436636i	−0.964102	+	0.265533i	$0.914452\pi$
$458$	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	$-0.849908\pi$
$461$		−	19.5062i		−	0.908494i	0.890876	−	0.454247i	$-0.150092\pi$
$462$		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	−0.989214	−	0.146479i	$-0.953206\pi$
$467$	−29.3243	+	16.9304i	−1.35697	+	0.783445i	−0.367752	+	0.929924i	$0.619872\pi$
$468$		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	−0.880295	−	0.474426i	$-0.842656\pi$
$479$	−0.640883	+	1.11004i	−0.0292827	+	0.0507191i	0.851013	+	0.525145i	$0.175989\pi$
$480$		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	0.477122	+	0.878837i	$0.341680\pi$
$487$	−11.5313	+	19.9728i	−0.522534	+	0.905055i	−0.999656	+	0.0262185i	$0.991653\pi$
$488$	−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	−0.380173	−	0.924915i	$-0.624135\pi$
$499$	5.15436	−	2.97587i	0.230741	−	0.133218i	0.610914	+	0.791697i	$0.290802\pi$
$500$	−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	−0.330578	−	0.943779i	$-0.607244\pi$
$509$	7.25269	−	4.18734i	0.321470	−	0.185601i	0.652048	+	0.758178i	$0.273910\pi$
$510$		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	−0.484119	−	0.875002i	$-0.660860\pi$
$521$	11.7714	−	20.3887i	0.515715	−	0.893244i	0.999834	−	0.0182421i	$-0.00580695\pi$
$522$		0			0
$523$	14.4448	+	25.0191i	0.631626	+	1.09401i	0.987219	+	0.159368i	$0.0509456\pi$
$523$	14.4448	+	25.0191i	0.631626	+	1.09401i	−0.355593	+	0.934641i	$0.615721\pi$
$524$	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	−0.461121	−	0.887337i	$-0.652553\pi$
$541$	1.78575	−	1.03100i	0.0767754	−	0.0443263i	0.537896	+	0.843011i	$0.319219\pi$
$542$	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	$-0.722758\pi$
$547$		−	35.7819i		−	1.52992i	0.644076	−	0.764962i	$-0.277242\pi$
$548$	−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	−0.492576	−	0.870270i	$-0.663945\pi$
$557$	11.9748	−	20.7409i	0.507388	−	0.878821i	0.999963	−	0.00855174i	$-0.00272214\pi$
$558$		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	−0.0556830	−	0.998448i	$-0.517734\pi$
$563$	−22.4987	−	12.9896i	−0.948206	−	0.547447i	−0.892523	+	0.451001i	$0.851067\pi$
$564$		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	$-0.788684\pi$
$569$	−15.4525	+	8.92150i	−0.647802	+	0.374009i	0.139812	+	0.990178i	$0.455350\pi$
$570$		0			0
$571$	−15.9523	−	9.21009i	−0.667585	−	0.385430i	0.127576	−	0.991829i	$-0.459280\pi$
$571$	−15.9523	−	9.21009i	−0.667585	−	0.385430i	−0.795161	+	0.606398i	$0.792614\pi$
$572$	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	0.0880698	−	0.996114i	$-0.471930\pi$
$577$	−17.5485	−	10.1317i	−0.730556	−	0.421786i	−0.818625	+	0.574328i	$0.805263\pi$
$578$	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	$-0.976099\pi$
$587$		−	3.63501i		−	0.150033i	0.997182	−	0.0750164i	$-0.0239009\pi$
$588$		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	0.996880	−	0.0789370i	$-0.0251526\pi$
$593$	10.4731	+	18.1399i	0.430078	+	0.744918i	−0.566801	+	0.823855i	$0.691819\pi$
$594$		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	0.532000	−	0.846744i	$-0.321441\pi$
$599$	1.58346	+	0.914209i	0.0646983	+	0.0373536i	−0.467302	+	0.884098i	$0.654774\pi$
$600$		0			0
$601$		−	29.7207i		−	1.21233i	−0.795338	−	0.606166i	$-0.792707\pi$
$601$		−	29.7207i		−	1.21233i	0.795338	−	0.606166i	$-0.207293\pi$
$602$	−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	−0.598787	−	0.800909i	$-0.704350\pi$
$607$	−5.04013	+	2.90992i	−0.204573	+	0.118110i	0.394214	+	0.919019i	$0.371017\pi$
$608$	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	$-0.282521\pi$
$613$	6.81649	+	3.93550i	0.275316	+	0.158954i	−0.355985	+	0.934492i	$0.615855\pi$
$614$	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	$-0.942426\pi$
$617$		−	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	$-0.784504\pi$
$619$	3.80163	−	6.58462i	0.152801	−	0.264658i	0.932256	+	0.361799i	$0.117837\pi$
$620$	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	0.989621	−	0.143705i	$-0.0459016\pi$
$641$	34.4319	+	19.8793i	1.35998	+	0.785184i	0.370358	+	0.928889i	$0.379235\pi$
$642$		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	−0.484298	−	0.874903i	$-0.660925\pi$
$647$	13.1134	−	22.7130i	0.515540	−	0.892941i	0.999837	−	0.0180376i	$-0.00574185\pi$
$648$		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	0.798347	−	0.602198i	$-0.205708\pi$
$653$	−3.12639	−	5.41506i	−0.122345	−	0.211908i	−0.920692	+	0.390290i	$0.872375\pi$
$654$		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	−0.984966	−	0.172746i	$-0.944736\pi$
$661$	−8.81544	+	15.2688i	−0.342881	+	0.593887i	0.642085	+	0.766633i	$0.278069\pi$
$662$	−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	−0.0504774	−	0.998725i	$-0.516074\pi$
$677$	20.5345	−	11.8556i	0.789205	−	0.455648i	0.839683	+	0.543077i	$0.182741\pi$
$678$		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	−0.635737	−	0.771906i	$-0.719304\pi$
$683$	9.16325	−	15.8712i	0.350622	−	0.607295i	0.986359	+	0.164611i	$0.0526369\pi$
$684$		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	0.935269	+	0.353937i	$0.115157\pi$
$691$	20.3501	+	35.2473i	0.774153	+	1.34087i	−0.161116	+	0.986935i	$0.551509\pi$
$692$	−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	−0.386511	−	0.922285i	$-0.626320\pi$
$709$	5.83014	−	3.36604i	0.218956	−	0.126414i	0.605467	+	0.795871i	$0.292987\pi$
$710$	−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	0.837527	−	0.546396i	$-0.184001\pi$
$719$	−1.45947	−	2.52788i	−0.0544291	−	0.0942739i	−0.891956	+	0.452122i	$0.850667\pi$
$720$		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	$0.0184702\pi$
$727$			3.12734i			0.115987i	−0.998317	+	0.0579933i	$0.981530\pi$
$728$	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	0.784256	−	0.620437i	$-0.213045\pi$
$733$	−3.93077	−	6.80830i	−0.145186	−	0.251470i	−0.929442	+	0.368967i	$0.879712\pi$
$734$	−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	$-0.326492\pi$
$739$	1.01186	+	0.584195i	0.0372217	+	0.0214900i	−0.481274	+	0.876570i	$0.659826\pi$
$740$	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	$-0.964179\pi$
$743$		−	6.12199i		−	0.224594i	0.993675	−	0.112297i	$-0.0358208\pi$
$744$		0			0
$745$	6.74886	+	3.89645i	0.247259	+	0.142755i
$746$	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	0.942556	+	0.334049i	$0.108415\pi$
$751$	20.8430	+	36.1012i	0.760573	+	1.31735i	−0.181983	+	0.983302i	$0.558252\pi$
$752$	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	$0.225934\pi$
$757$			35.8599i			1.30335i	−0.758498	+	0.651676i	$0.774066\pi$
$758$	−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	0.763686	−	0.645587i	$-0.223387\pi$
$761$	−4.88971	−	8.46923i	−0.177252	−	0.307009i	−0.940938	+	0.338578i	$0.890054\pi$
$762$		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	$0.432566\pi$
$769$			54.2218i			1.95529i	−0.210269	+	0.977644i	$0.567434\pi$
$770$	−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	0.825038	−	0.565078i	$-0.191154\pi$
$773$	20.8017	+	12.0099i	0.748185	+	0.431965i	−0.0768527	+	0.997042i	$0.524487\pi$
$774$		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	−0.999769	−	0.0214714i	$-0.993165\pi$
$787$	−13.5019	+	23.3859i	−0.481290	+	0.833619i	0.518479	+	0.855090i	$0.326498\pi$
$788$	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	$0.182651\pi$
$797$			30.6501i			1.08568i	−0.839835	+	0.542841i	$0.817349\pi$
$798$		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	0.301959	−	0.953321i	$-0.402359\pi$
$809$	−10.5996	−	6.11967i	−0.372661	−	0.215156i	−0.674620	+	0.738165i	$0.735693\pi$
$810$		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	0.931976	+	0.362520i	$0.118084\pi$
$821$	22.3477	+	38.7073i	0.779940	+	1.35090i	−0.152036	+	0.988375i	$0.548583\pi$
$822$		0			0
$823$	8.91299	−	15.4378i	0.310687	−	0.538126i	−0.667824	−	0.744319i	$-0.732774\pi$
$823$	8.91299	−	15.4378i	0.310687	−	0.538126i	0.978511	+	0.206193i	$0.0661075\pi$
$824$	−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	−0.721760	−	0.692144i	$-0.756666\pi$
$829$	6.86797	−	11.8957i	0.238534	−	0.413154i	0.960294	+	0.278990i	$0.0899997\pi$
$830$	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	−0.726511	−	0.687155i	$-0.758859\pi$
$857$	6.78696	−	11.7554i	0.231838	−	0.401556i	0.958349	+	0.285599i	$0.0921927\pi$
$858$		0			0
$859$	−14.8653	−	25.7475i	−0.507198	−	0.878494i	−0.999965	−	0.00833211i	$-0.997348\pi$
$859$	−14.8653	−	25.7475i	−0.507198	−	0.878494i	0.492767	−	0.870161i	$-0.335986\pi$
$860$	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	$-0.490788\pi$
$863$	26.7055	−	15.4184i	0.909066	−	0.524849i	0.880130	+	0.474732i	$0.157455\pi$
$864$		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	−0.320033	−	0.947406i	$-0.603694\pi$
$877$	10.0815	−	5.82055i	0.340428	−	0.196546i	0.660461	+	0.750860i	$0.270361\pi$
$878$	−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	$-0.768621\pi$
$883$		−	39.4950i		−	1.32911i	0.747239	−	0.664556i	$-0.231379\pi$
$884$	−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	0.803058	+	0.595901i	$0.203205\pi$
$887$	27.3283	+	47.3340i	0.917595	+	1.58932i	0.114537	+	0.993419i	$0.463462\pi$
$888$		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	0.364844	−	0.931069i	$-0.381122\pi$
$907$	−7.80208	−	4.50453i	−0.259064	−	0.149571i	−0.623907	+	0.781498i	$0.714456\pi$
$908$	−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	$0.199116\pi$
$911$			35.3463i			1.17107i	−0.810646	+	0.585537i	$0.800884\pi$
$912$		0			0
$913$	−27.7302	−	16.0100i	−0.917736	−	0.529855i
$914$	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	0.627184	−	0.778871i	$-0.284208\pi$
$919$	−10.9416	−	18.9514i	−0.360931	−	0.625150i	−0.988114	+	0.153721i	$0.950874\pi$
$920$	−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	0.932383	−	0.361472i	$-0.117726\pi$
$929$	4.66786	+	8.08497i	0.153148	+	0.265259i	−0.779235	+	0.626731i	$0.784392\pi$
$930$		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	$-0.926211\pi$
$937$		−	14.0652i		−	0.459492i	0.973251	−	0.229746i	$-0.0737895\pi$
$938$	−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	0.942725	−	0.333571i	$-0.108254\pi$
$941$	34.5165	+	19.9281i	1.12521	+	0.649638i	0.182481	+	0.983209i	$0.441587\pi$
$942$		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	0.983525	−	0.180773i	$-0.0578600\pi$
$947$	10.3155	+	17.8669i	0.335208	+	0.580598i	−0.648317	+	0.761371i	$0.724527\pi$
$948$		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	$-0.797939\pi$
$953$		−	36.6133i		−	1.18602i	0.805194	−	0.593011i	$-0.202061\pi$
$954$		0			0
$955$	14.5759	−	25.2462i	0.471665	−	0.816948i
$956$	−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	−0.543653	−	0.839310i	$-0.682959\pi$
$971$	−2.76132	+	1.59425i	−0.0886149	+	0.0511618i	0.455038	+	0.890472i	$0.349626\pi$
$972$		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	0.556520	−	0.830834i	$-0.312136\pi$
$977$	3.60255	+	2.07994i	0.115256	+	0.0665430i	−0.441264	+	0.897377i	$0.645470\pi$
$978$		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	−0.983080	−	0.183179i	$-0.941361\pi$
$983$	−10.4374	+	18.0782i	−0.332902	+	0.576604i	0.650177	+	0.759783i	$0.274695\pi$
$984$		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	−0.748214	−	0.663457i	$-0.769088\pi$
$991$	6.31063	−	10.9303i	0.200464	−	0.347213i	0.948678	+	0.316244i	$0.102422\pi$
$992$	−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	−0.974427	−	0.224705i	$-0.927858\pi$
$997$	−9.23934	+	16.0030i	−0.292613	+	0.506820i	0.681814	+	0.731526i	$0.261191\pi$
$998$	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.269.24	yes	56
3.2	odd	2	inner	504.2.ch.b.269.5	✓	56
4.3	odd	2		2016.2.cp.b.17.22		56
7.5	odd	6	inner	504.2.ch.b.341.15	yes	56
8.3	odd	2		2016.2.cp.b.17.7		56
8.5	even	2	inner	504.2.ch.b.269.14	yes	56
12.11	even	2		2016.2.cp.b.17.8		56
21.5	even	6	inner	504.2.ch.b.341.14	yes	56
24.5	odd	2	inner	504.2.ch.b.269.15	yes	56
24.11	even	2		2016.2.cp.b.17.21		56
28.19	even	6		2016.2.cp.b.593.21		56
56.5	odd	6	inner	504.2.ch.b.341.5	yes	56
56.19	even	6		2016.2.cp.b.593.8		56
84.47	odd	6		2016.2.cp.b.593.7		56
168.5	even	6	inner	504.2.ch.b.341.24	yes	56
168.131	odd	6		2016.2.cp.b.593.22		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.ch.b.269.5	✓	56	3.2	odd	2	inner
504.2.ch.b.269.14	yes	56	8.5	even	2	inner
504.2.ch.b.269.15	yes	56	24.5	odd	2	inner
504.2.ch.b.269.24	yes	56	1.1	even	1	trivial
504.2.ch.b.341.5	yes	56	56.5	odd	6	inner
504.2.ch.b.341.14	yes	56	21.5	even	6	inner
504.2.ch.b.341.15	yes	56	7.5	odd	6	inner
504.2.ch.b.341.24	yes	56	168.5	even	6	inner
2016.2.cp.b.17.7		56	8.3	odd	2
2016.2.cp.b.17.8		56	12.11	even	2
2016.2.cp.b.17.21		56	24.11	even	2
2016.2.cp.b.17.22		56	4.3	odd	2
2016.2.cp.b.593.7		56	84.47	odd	6
2016.2.cp.b.593.8		56	56.19	even	6
2016.2.cp.b.593.21		56	28.19	even	6
2016.2.cp.b.593.22		56	168.131	odd	6

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)

\(f(q)\)	\(=\)	\(q+(1.13135 + 0.848557i) q^{2} +(0.559903 + 1.92003i) q^{4} +(1.53798 - 0.887954i) q^{5} +(0.843933 - 2.50754i) q^{7} +(-0.995807 + 2.64733i) q^{8} +(2.49347 + 0.300478i) q^{10} +(2.09284 - 3.62490i) q^{11} +3.76443 q^{13} +(3.08258 - 2.12078i) q^{14} +(-3.37302 + 2.15006i) q^{16} +(-2.32502 + 4.02705i) q^{17} +(-0.0315203 - 0.0545948i) q^{19} +(2.56602 + 2.45580i) q^{20} +(5.44367 - 2.32514i) q^{22} +(-4.05375 + 2.34043i) q^{23} +(-0.923074 + 1.59881i) q^{25} +(4.25888 + 3.19433i) q^{26} +(5.28708 + 0.216393i) q^{28} -6.47316 q^{29} +(6.64896 + 3.83878i) q^{31} +(-5.64051 - 0.429729i) q^{32} +(-6.04758 + 2.58309i) q^{34} +(-0.928631 - 4.60593i) q^{35} +(2.91602 - 1.68357i) q^{37} +(0.0106663 - 0.0885126i) q^{38} +(0.819176 + 4.95578i) q^{40} -8.06290 q^{41} -9.94628i q^{43} +(8.13170 + 1.98872i) q^{44} +(-6.57220 - 0.791988i) q^{46} +(-0.338788 - 0.586799i) q^{47} +(-5.57556 - 4.23240i) q^{49} +(-2.40100 + 1.02553i) q^{50} +(2.10771 + 7.22781i) q^{52} +(-2.36197 + 4.09104i) q^{53} -7.43338i q^{55} +(5.79791 + 4.73120i) q^{56} +(-7.32341 - 5.49285i) q^{58} +(6.53211 + 3.77132i) q^{59} +(7.23104 + 12.5245i) q^{61} +(4.26487 + 9.98502i) q^{62} +(-6.01674 - 5.27247i) q^{64} +(5.78962 - 3.34264i) q^{65} +(-5.67866 - 3.27857i) q^{67} +(-9.03382 - 2.20934i) q^{68} +(2.85779 - 5.99891i) q^{70} +5.10606i q^{71} +(1.29332 + 0.746696i) q^{73} +(4.72764 + 0.569709i) q^{74} +(0.0871753 - 0.0910878i) q^{76} +(-7.32339 - 8.30706i) q^{77} +(-5.99485 - 10.3834i) q^{79} +(-3.27849 + 6.30184i) q^{80} +(-9.12195 - 6.84183i) q^{82} -7.64992i q^{83} +8.25803i q^{85} +(8.43998 - 11.2527i) q^{86} +(7.51226 + 9.15014i) q^{88} +(-8.97506 - 15.5453i) q^{89} +(3.17692 - 9.43947i) q^{91} +(-6.76340 - 6.47290i) q^{92} +(0.114644 - 0.951355i) q^{94} +(-0.0969554 - 0.0559773i) q^{95} +4.24586i q^{97} +(-2.71647 - 9.51949i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{4} - 20 q^{7} + 20 q^{16} - 16 q^{22} + 8 q^{25} + 36 q^{28} - 36 q^{31} + 60 q^{40} - 8 q^{46} - 28 q^{49} + 36 q^{52} - 44 q^{58} + 40 q^{64} - 60 q^{70} + 72 q^{73} - 12 q^{79} - 36 q^{82}+ \cdots - 180 q^{94}+O(q^{100}) \) 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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