LMFDB - Embedded newform 504.2.bs.a.257.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(257,504)]

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, 0, 5, 5]))

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

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

chi := DirichletCharacter("504.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (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:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.12
Character	$\chi$	$=$	504.257
Dual form			504.2.bs.a.353.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0250939 - 1.73187i) q^{3} +(-1.42382 - 2.46612i) q^{5} +(1.38343 - 2.25524i) q^{7} +(-2.99874 - 0.0869188i) q^{9} +O(q^{10})$	\(q+(0.0250939 - 1.73187i) q^{3} +(-1.42382 - 2.46612i) q^{5} +(1.38343 - 2.25524i) q^{7} +(-2.99874 - 0.0869188i) q^{9} +(2.12201 + 1.22514i) q^{11} +(3.06053 + 1.76700i) q^{13} +(-4.30673 + 2.40398i) q^{15} +(-2.91986 - 5.05735i) q^{17} +(-2.90135 - 1.67510i) q^{19} +(-3.87107 - 2.45251i) q^{21} +(-6.94378 + 4.00899i) q^{23} +(-1.55450 + 2.69248i) q^{25} +(-0.225782 + 5.19124i) q^{27} +(-1.45334 + 0.839088i) q^{29} +3.98626i q^{31} +(2.17503 - 3.64429i) q^{33} +(-7.53145 - 0.200659i) q^{35} +(4.07975 - 7.06633i) q^{37} +(3.13701 - 5.25609i) q^{39} +(5.43807 - 9.41902i) q^{41} +(3.27732 + 5.67649i) q^{43} +(4.05530 + 7.51902i) q^{45} +6.62900 q^{47} +(-3.17224 - 6.23994i) q^{49} +(-8.83193 + 4.92991i) q^{51} +(-7.64443 + 4.41352i) q^{53} -6.97750i q^{55} +(-2.97386 + 4.98273i) q^{57} -0.356828 q^{59} +2.91251i q^{61} +(-4.34457 + 6.64264i) q^{63} -10.0635i q^{65} +14.2970 q^{67} +(6.76880 + 12.1263i) q^{69} -9.96779i q^{71} +(5.42680 - 3.13316i) q^{73} +(4.62402 + 2.75976i) q^{75} +(5.69864 - 3.09074i) q^{77} -11.5011 q^{79} +(8.98489 + 0.521294i) q^{81} +(-0.189004 - 0.327365i) q^{83} +(-8.31469 + 14.4015i) q^{85} +(1.41672 + 2.53806i) q^{87} +(7.05715 - 12.2233i) q^{89} +(8.21903 - 4.45771i) q^{91} +(6.90368 + 0.100031i) q^{93} +9.54013i q^{95} +(4.00681 - 2.31334i) q^{97} +(-6.25686 - 3.85832i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.0250939	−	1.73187i	0.0144880	−	0.999895i
$3$	0.0250939	−	1.73187i	0.0144880	−	0.999895i
$4$		0			0
$5$	−1.42382	−	2.46612i	−0.636750	−	1.10288i	−0.986141	−	0.165906i	$-0.946945\pi$
$5$	−1.42382	−	2.46612i	−0.636750	−	1.10288i	0.349392	−	0.936977i	$-0.386388\pi$
$6$		0			0
$7$	1.38343	−	2.25524i	0.522888	−	0.852402i
$7$	1.38343	−	2.25524i	0.522888	−	0.852402i
$8$		0			0
$9$	−2.99874	−	0.0869188i	−0.999580	−	0.0289729i
$10$		0			0
$11$	2.12201	+	1.22514i	0.639809	+	0.369394i	0.784541	−	0.620077i	$-0.212899\pi$
$11$	2.12201	+	1.22514i	0.639809	+	0.369394i	−0.144732	+	0.989471i	$0.546232\pi$
$12$		0			0
$13$	3.06053	+	1.76700i	0.848837	+	0.490076i	0.860258	−	0.509858i	$-0.170302\pi$
$13$	3.06053	+	1.76700i	0.848837	+	0.490076i	−0.0114212	+	0.999935i	$0.503636\pi$
$14$		0			0
$15$	−4.30673	+	2.40398i	−1.11199	+	0.620705i
$16$		0			0
$17$	−2.91986	−	5.05735i	−0.708170	−	1.22659i	−0.965535	−	0.260272i	$-0.916188\pi$
$17$	−2.91986	−	5.05735i	−0.708170	−	1.22659i	0.257365	−	0.966314i	$-0.417146\pi$
$18$		0			0
$19$	−2.90135	−	1.67510i	−0.665616	−	0.384294i	0.128797	−	0.991671i	$-0.458888\pi$
$19$	−2.90135	−	1.67510i	−0.665616	−	0.384294i	−0.794414	+	0.607377i	$0.792222\pi$
$20$		0			0
$21$	−3.87107	−	2.45251i	−0.844736	−	0.535182i
$22$		0			0
$23$	−6.94378	+	4.00899i	−1.44788	+	0.835932i	−0.998355	−	0.0573367i	$-0.981739\pi$
$23$	−6.94378	+	4.00899i	−1.44788	+	0.835932i	−0.449522	+	0.893269i	$0.648406\pi$
$24$		0			0
$25$	−1.55450	+	2.69248i	−0.310901	+	0.538496i
$26$		0			0
$27$	−0.225782	+	5.19124i	−0.0434518	+	0.999056i
$28$		0			0
$29$	−1.45334	+	0.839088i	−0.269879	+	0.155815i	−0.628833	−	0.777541i	$-0.716467\pi$
$29$	−1.45334	+	0.839088i	−0.269879	+	0.155815i	0.358954	+	0.933355i	$0.383134\pi$
$30$		0			0
$31$			3.98626i			0.715953i	0.933731	+	0.357977i	$0.116533\pi$
$31$			3.98626i			0.715953i	−0.933731	+	0.357977i	$0.883467\pi$
$32$		0			0
$33$	2.17503	−	3.64429i	0.378625	−	0.634390i
$34$		0			0
$35$	−7.53145	−	0.200659i	−1.27305	−	0.0339176i
$36$		0			0
$37$	4.07975	−	7.06633i	0.670706	−	1.16170i	−0.306998	−	0.951710i	$-0.599324\pi$
$37$	4.07975	−	7.06633i	0.670706	−	1.16170i	0.977704	−	0.209987i	$-0.0673422\pi$
$38$		0			0
$39$	3.13701	−	5.25609i	0.502323	−	0.841648i
$40$		0			0
$41$	5.43807	−	9.41902i	0.849284	−	1.47100i	−0.0325634	−	0.999470i	$-0.510367\pi$
$41$	5.43807	−	9.41902i	0.849284	−	1.47100i	0.881848	−	0.471534i	$-0.156300\pi$
$42$		0			0
$43$	3.27732	+	5.67649i	0.499787	+	0.865656i	1.00000		0.000246348i	$-7.84151e-5\pi$
$43$	3.27732	+	5.67649i	0.499787	+	0.865656i	−0.500213	+	0.865902i	$0.666745\pi$
$44$		0			0
$45$	4.05530	+	7.51902i	0.604529	+	1.12087i
$46$		0			0
$47$	6.62900			0.966940			0.483470	−	0.875361i	$-0.339376\pi$
$47$	6.62900			0.966940			0.483470	+	0.875361i	$0.339376\pi$
$48$		0			0
$49$	−3.17224	−	6.23994i	−0.453177	−	0.891421i
$50$		0			0
$51$	−8.83193	+	4.92991i	−1.23672	+	0.690325i
$52$		0			0
$53$	−7.64443	+	4.41352i	−1.05004	+	0.606243i	−0.922662	−	0.385611i	$-0.873991\pi$
$53$	−7.64443	+	4.41352i	−1.05004	+	0.606243i	−0.127382	+	0.991854i	$0.540657\pi$
$54$		0			0
$55$		−	6.97750i		−	0.940846i
$56$		0			0
$57$	−2.97386	+	4.98273i	−0.393897	+	0.659979i
$58$		0			0
$59$	−0.356828			−0.0464551			−0.0232276	−	0.999730i	$-0.507394\pi$
$59$	−0.356828			−0.0464551			−0.0232276	+	0.999730i	$0.507394\pi$
$60$		0			0
$61$			2.91251i			0.372909i	0.982464	+	0.186454i	$0.0596996\pi$
$61$			2.91251i			0.372909i	−0.982464	+	0.186454i	$0.940300\pi$
$62$		0			0
$63$	−4.34457	+	6.64264i	−0.547365	+	0.836894i
$64$		0			0
$65$		−	10.0635i		−	1.24822i
$66$		0			0
$67$	14.2970			1.74666			0.873329	−	0.487131i	$-0.161956\pi$
$67$	14.2970			1.74666			0.873329	+	0.487131i	$0.161956\pi$
$68$		0			0
$69$	6.76880	+	12.1263i	0.814868	+	1.45984i
$70$		0			0
$71$		−	9.96779i		−	1.18296i	−0.806320	−	0.591479i	$-0.798544\pi$
$71$		−	9.96779i		−	1.18296i	0.806320	−	0.591479i	$-0.201456\pi$
$72$		0			0
$73$	5.42680	−	3.13316i	0.635159	−	0.366709i	−0.147589	−	0.989049i	$-0.547151\pi$
$73$	5.42680	−	3.13316i	0.635159	−	0.366709i	0.782747	+	0.622340i	$0.213818\pi$
$74$		0			0
$75$	4.62402	+	2.75976i	0.533935	+	0.318670i
$76$		0			0
$77$	5.69864	−	3.09074i	0.649420	−	0.352223i
$78$		0			0
$79$	−11.5011			−1.29398			−0.646989	−	0.762499i	$-0.723972\pi$
$79$	−11.5011			−1.29398			−0.646989	+	0.762499i	$0.723972\pi$
$80$		0			0
$81$	8.98489	+	0.521294i	0.998321	+	0.0579215i
$82$		0			0
$83$	−0.189004	−	0.327365i	−0.0207459	−	0.0359329i	0.855466	−	0.517859i	$-0.173271\pi$
$83$	−0.189004	−	0.327365i	−0.0207459	−	0.0359329i	−0.876212	+	0.481926i	$0.839937\pi$
$84$		0			0
$85$	−8.31469	+	14.4015i	−0.901855	+	1.56206i
$86$		0			0
$87$	1.41672	+	2.53806i	0.151888	+	0.272108i
$88$		0			0
$89$	7.05715	−	12.2233i	0.748056	−	1.29567i	−0.200697	−	0.979653i	$-0.564321\pi$
$89$	7.05715	−	12.2233i	0.748056	−	1.29567i	0.948753	−	0.316018i	$-0.102346\pi$
$90$		0			0
$91$	8.21903	−	4.45771i	0.861588	−	0.467295i
$92$		0			0
$93$	6.90368	+	0.100031i	0.715878	+	0.0103727i
$94$		0			0
$95$			9.54013i			0.978796i
$96$		0			0
$97$	4.00681	−	2.31334i	0.406830	−	0.234884i	−0.282597	−	0.959239i	$-0.591196\pi$
$97$	4.00681	−	2.31334i	0.406830	−	0.234884i	0.689427	+	0.724355i	$0.257862\pi$
$98$		0			0
$99$	−6.25686	−	3.85832i	−0.628838	−	0.387776i
$100$		0			0
$101$	2.59307	−	4.49133i	0.258020	−	0.446904i	−0.707691	−	0.706522i	$-0.750263\pi$
$101$	2.59307	−	4.49133i	0.258020	−	0.446904i	0.965711	+	0.259618i	$0.0835966\pi$
$102$		0			0
$103$	1.33310	−	0.769667i	0.131355	−	0.0758376i	−0.432883	−	0.901450i	$-0.642504\pi$
$103$	1.33310	−	0.769667i	0.131355	−	0.0758376i	0.564237	+	0.825613i	$0.309170\pi$
$104$		0			0
$105$	−0.536509	+	13.0385i	−0.0523579	+	1.27242i
$106$		0			0
$107$	3.87110	+	2.23498i	0.374234	+	0.216064i	0.675306	−	0.737537i	$-0.264011\pi$
$107$	3.87110	+	2.23498i	0.374234	+	0.216064i	−0.301073	+	0.953601i	$0.597345\pi$
$108$		0			0
$109$	4.01087	+	6.94704i	0.384172	+	0.665405i	0.991654	−	0.128928i	$-0.0411536\pi$
$109$	4.01087	+	6.94704i	0.384172	+	0.665405i	−0.607482	+	0.794333i	$0.707820\pi$
$110$		0			0
$111$	−12.1356	−	7.24291i	−1.15186	−	0.687467i
$112$		0			0
$113$	5.38337	+	3.10809i	0.506425	+	0.292385i	0.731363	−	0.681988i	$-0.238885\pi$
$113$	5.38337	+	3.10809i	0.506425	+	0.292385i	−0.224938	+	0.974373i	$0.572218\pi$
$114$		0			0
$115$	19.7733	+	11.4161i	1.84387	+	1.06456i
$116$		0			0
$117$	−9.02414	−	5.56478i	−0.834282	−	0.514464i
$118$		0			0
$119$	−15.4450	−	0.411497i	−1.41584	−	0.0377219i
$120$		0			0
$121$	−2.49806	−	4.32677i	−0.227096	−	0.393342i
$122$		0			0
$123$	−16.1760	−	9.65439i	−1.45855	−	0.870507i
$124$		0			0
$125$	−5.38484			−0.481635
$126$		0			0
$127$	6.86154			0.608863			0.304432	−	0.952534i	$-0.401534\pi$
$127$	6.86154			0.608863			0.304432	+	0.952534i	$0.401534\pi$
$128$		0			0
$129$	9.91317	−	5.53344i	0.872806	−	0.487193i
$130$		0			0
$131$	1.30606	+	2.26216i	0.114111	+	0.197646i	0.917424	−	0.397911i	$-0.130265\pi$
$131$	1.30606	+	2.26216i	0.114111	+	0.197646i	−0.803313	+	0.595557i	$0.796931\pi$
$132$		0			0
$133$	−7.79158	+	4.22588i	−0.675615	+	0.366430i
$134$		0			0
$135$	13.1237	−	6.83457i	1.12951	−	0.588226i
$136$		0			0
$137$	6.29742	+	3.63582i	0.538025	+	0.310629i	0.744278	−	0.667870i	$-0.232794\pi$
$137$	6.29742	+	3.63582i	0.538025	+	0.310629i	−0.206253	+	0.978499i	$0.566127\pi$
$138$		0			0
$139$	12.0010	+	6.92876i	1.01791	+	0.587690i	0.913498	−	0.406844i	$-0.133371\pi$
$139$	12.0010	+	6.92876i	1.01791	+	0.587690i	0.104412	+	0.994534i	$0.466704\pi$
$140$		0			0
$141$	0.166348	−	11.4806i	0.0140090	−	0.966838i
$142$		0			0
$143$	4.32964	+	7.49915i	0.362062	+	0.627110i
$144$		0			0
$145$	4.13859	+	2.38941i	0.343691	+	0.198430i
$146$		0			0
$147$	−10.8864	+	5.33731i	−0.897893	+	0.440214i
$148$		0			0
$149$	−9.16356	+	5.29058i	−0.750708	+	0.433422i	−0.825950	−	0.563744i	$-0.809361\pi$
$149$	−9.16356	+	5.29058i	−0.750708	+	0.433422i	0.0752415	+	0.997165i	$0.476027\pi$
$150$		0			0
$151$	6.21804	−	10.7700i	0.506017	−	0.876447i	−0.493959	−	0.869485i	$-0.664451\pi$
$151$	6.21804	−	10.7700i	0.506017	−	0.876447i	0.999976	−	0.00696194i	$-0.00221607\pi$
$152$		0			0
$153$	8.31633	+	15.4195i	0.672335	+	1.24659i
$154$		0			0
$155$	9.83060	−	5.67570i	0.789613	−	0.455883i
$156$		0			0
$157$			14.4243i			1.15118i	0.817738	+	0.575591i	$0.195228\pi$
$157$			14.4243i			1.15118i	−0.817738	+	0.575591i	$0.804772\pi$
$158$		0			0
$159$	7.45180	+	13.3499i	0.590966	+	1.05872i
$160$		0			0
$161$	−0.564989	+	21.2061i	−0.0445274	+	1.67127i
$162$		0			0
$163$	9.88117	−	17.1147i	0.773953	−	1.34053i	−0.161429	−	0.986884i	$-0.551610\pi$
$163$	9.88117	−	17.1147i	0.773953	−	1.34053i	0.935381	−	0.353641i	$-0.115057\pi$
$164$		0			0
$165$	−12.0841	−	0.175093i	−0.940747	−	0.0136310i
$166$		0			0
$167$	−3.65608	+	6.33251i	−0.282916	+	0.490025i	−0.972102	−	0.234560i	$-0.924635\pi$
$167$	−3.65608	+	6.33251i	−0.282916	+	0.490025i	0.689186	+	0.724585i	$0.257968\pi$
$168$		0			0
$169$	−0.255454	−	0.442460i	−0.0196503	−	0.0340354i
$170$		0			0
$171$	8.55481	+	5.27537i	0.654203	+	0.403417i
$172$		0			0
$173$	−1.31984			−0.100345			−0.0501727	−	0.998741i	$-0.515977\pi$
$173$	−1.31984			−0.100345			−0.0501727	+	0.998741i	$0.515977\pi$
$174$		0			0
$175$	3.92165	+	7.23065i	0.296449	+	0.546586i
$176$		0			0
$177$	−0.00895422	+	0.617980i	−0.000673041	+	0.0464502i
$178$		0			0
$179$	2.75119	−	1.58840i	0.205634	−	0.118723i	−0.393647	−	0.919262i	$-0.628787\pi$
$179$	2.75119	−	1.58840i	0.205634	−	0.118723i	0.599281	+	0.800539i	$0.295453\pi$
$180$		0			0
$181$		−	15.6184i		−	1.16091i	−0.814293	−	0.580454i	$-0.802875\pi$
$181$		−	15.6184i		−	1.16091i	0.814293	−	0.580454i	$-0.197125\pi$
$182$		0			0
$183$	5.04409	+	0.0730863i	0.372870	+	0.00540269i
$184$		0			0
$185$	−23.2352			−1.70829
$186$		0			0
$187$		−	14.3090i		−	1.04637i
$188$		0			0
$189$	11.3952	+	7.69092i	0.828876	+	0.559432i
$190$		0			0
$191$		−	2.82082i		−	0.204107i	−0.994779	−	0.102054i	$-0.967459\pi$
$191$		−	2.82082i		−	0.204107i	0.994779	−	0.102054i	$-0.0325413\pi$
$192$		0			0
$193$	−18.8259			−1.35512			−0.677560	−	0.735467i	$-0.736963\pi$
$193$	−18.8259			−1.35512			−0.677560	+	0.735467i	$0.736963\pi$
$194$		0			0
$195$	−17.4287	−	0.252533i	−1.24809	−	0.0180842i
$196$		0			0
$197$			0.460422i			0.0328037i	0.999865	+	0.0164019i	$0.00522111\pi$
$197$			0.460422i			0.0328037i	−0.999865	+	0.0164019i	$0.994779\pi$
$198$		0			0
$199$	−18.2059	+	10.5112i	−1.29058	+	0.745116i	−0.978757	−	0.205024i	$-0.934273\pi$
$199$	−18.2059	+	10.5112i	−1.29058	+	0.745116i	−0.311822	+	0.950140i	$0.600939\pi$
$200$		0			0
$201$	0.358768	−	24.7606i	0.0253055	−	1.74647i
$202$		0			0
$203$	−0.118253	+	4.43846i	−0.00829974	+	0.311519i
$204$		0			0
$205$	−30.9713			−2.16313
$206$		0			0
$207$	21.1710	−	11.4184i	1.47149	−	0.793632i
$208$		0			0
$209$	−4.10446	−	7.10914i	−0.283912	−	0.491749i
$210$		0			0
$211$	−6.60494	+	11.4401i	−0.454703	+	0.787568i	−0.998671	−	0.0515374i	$-0.983588\pi$
$211$	−6.60494	+	11.4401i	−0.454703	+	0.787568i	0.543968	+	0.839106i	$0.316921\pi$
$212$		0			0
$213$	−17.2629	−	0.250131i	−1.18283	−	0.0171387i
$214$		0			0
$215$	9.33260	−	16.1645i	0.636478	−	1.10241i
$216$		0			0
$217$	8.98998	+	5.51471i	0.610280	+	0.374363i
$218$		0			0
$219$	−5.29005	−	9.47713i	−0.357468	−	0.640405i
$220$		0			0
$221$		−	20.6375i		−	1.38823i
$222$		0			0
$223$	−14.0631	+	8.11932i	−0.941734	+	0.543710i	−0.890503	−	0.454977i	$-0.849648\pi$
$223$	−14.0631	+	8.11932i	−0.941734	+	0.543710i	−0.0512303	+	0.998687i	$0.516314\pi$
$224$		0			0
$225$	4.89558	−	7.93894i	0.326372	−	0.529263i
$226$		0			0
$227$	−9.72569	+	16.8454i	−0.645517	+	1.11807i	0.338665	+	0.940907i	$0.390025\pi$
$227$	−9.72569	+	16.8454i	−0.645517	+	1.11807i	−0.984182	+	0.177161i	$0.943309\pi$
$228$		0			0
$229$	20.6008	−	11.8939i	1.36134	−	0.785968i	0.371534	−	0.928419i	$-0.378832\pi$
$229$	20.6008	−	11.8939i	1.36134	−	0.785968i	0.989802	+	0.142451i	$0.0454985\pi$
$230$		0			0
$231$	−5.20976	−	9.94685i	−0.342777	−	0.654455i
$232$		0			0
$233$	−2.78781	−	1.60954i	−0.182635	−	0.105445i	0.405895	−	0.913920i	$-0.366960\pi$
$233$	−2.78781	−	1.60954i	−0.182635	−	0.105445i	−0.588530	+	0.808475i	$0.700293\pi$
$234$		0			0
$235$	−9.43848	−	16.3479i	−0.615699	−	1.06642i
$236$		0			0
$237$	−0.288609	+	19.9185i	−0.0187471	+	1.29384i
$238$		0			0
$239$	18.0756	+	10.4360i	1.16921	+	0.675047i	0.953495	−	0.301409i	$-0.0974568\pi$
$239$	18.0756	+	10.4360i	1.16921	+	0.675047i	0.215720	+	0.976455i	$0.430790\pi$
$240$		0			0
$241$	−24.3265	−	14.0449i	−1.56701	−	0.904711i	−0.996516	−	0.0834066i	$-0.973420\pi$
$241$	−24.3265	−	14.0449i	−1.56701	−	0.904711i	−0.570490	−	0.821305i	$-0.693247\pi$
$242$		0			0
$243$	1.12828	−	15.5476i	0.0723791	−	0.997377i
$244$		0			0
$245$	−10.8718	+	16.7077i	−0.694573	+	1.06741i
$246$		0			0
$247$	−5.91978	−	10.2534i	−0.376667	−	0.652406i
$248$		0			0
$249$	−0.571695	+	0.319115i	−0.0362297	+	0.0202231i
$250$		0			0
$251$	16.1314			1.01821			0.509104	−	0.860705i	$-0.329977\pi$
$251$	16.1314			1.01821			0.509104	+	0.860705i	$0.329977\pi$
$252$		0			0
$253$	−19.6463			−1.23515
$254$		0			0
$255$	24.7328	+	14.7613i	1.54883	+	0.924391i
$256$		0			0
$257$	4.19452	+	7.26512i	0.261647	+	0.453186i	0.966680	−	0.255989i	$-0.0824011\pi$
$257$	4.19452	+	7.26512i	0.261647	+	0.453186i	−0.705033	+	0.709175i	$0.749068\pi$
$258$		0			0
$259$	−10.2922	−	18.9766i	−0.639529	−	1.17915i
$260$		0			0
$261$	4.43113	−	2.38988i	0.274280	−	0.147930i
$262$		0			0
$263$	7.60764	+	4.39227i	0.469107	+	0.270839i	0.715866	−	0.698238i	$-0.246032\pi$
$263$	7.60764	+	4.39227i	0.469107	+	0.270839i	−0.246759	+	0.969077i	$0.579366\pi$
$264$		0			0
$265$	21.7685	+	12.5681i	1.33723	+	0.772050i
$266$		0			0
$267$	−20.9921	−	12.5288i	−1.28470	−	0.766749i
$268$		0			0
$269$	11.2556	+	19.4952i	0.686263	+	1.18864i	0.973038	+	0.230645i	$0.0740835\pi$
$269$	11.2556	+	19.4952i	0.686263	+	1.18864i	−0.286775	+	0.957998i	$0.592583\pi$
$270$		0			0
$271$	0.620567	+	0.358284i	0.0376967	+	0.0217642i	0.518730	−	0.854938i	$-0.326405\pi$
$271$	0.620567	+	0.358284i	0.0376967	+	0.0217642i	−0.481033	+	0.876702i	$0.659738\pi$
$272$		0			0
$273$	−7.51392	−	14.3461i	−0.454763	−	0.868268i
$274$		0			0
$275$	−6.59734	+	3.80897i	−0.397834	+	0.229690i
$276$		0			0
$277$	−12.5903	+	21.8070i	−0.756478	+	1.31026i	0.188158	+	0.982139i	$0.439748\pi$
$277$	−12.5903	+	21.8070i	−0.756478	+	1.31026i	−0.944636	+	0.328119i	$0.893585\pi$
$278$		0			0
$279$	0.346481	−	11.9538i	0.0207433	−	0.715653i
$280$		0			0
$281$	16.1227	−	9.30843i	0.961798	−	0.555294i	0.0650718	−	0.997881i	$-0.479272\pi$
$281$	16.1227	−	9.30843i	0.961798	−	0.555294i	0.896726	+	0.442586i	$0.145939\pi$
$282$		0			0
$283$		−	21.6976i		−	1.28979i	−0.764272	−	0.644894i	$-0.776902\pi$
$283$		−	21.6976i		−	1.28979i	0.764272	−	0.644894i	$-0.223098\pi$
$284$		0			0
$285$	16.5222	+	0.239399i	0.978694	+	0.0141808i
$286$		0			0
$287$	−13.7190	−	25.2947i	−0.809805	−	1.49310i
$288$		0			0
$289$	−8.55117	+	14.8111i	−0.503010	+	0.871239i
$290$		0			0
$291$	−3.90585	−	6.99733i	−0.228965	−	0.410191i
$292$		0			0
$293$	13.8196	−	23.9363i	0.807350	−	1.39837i	−0.107343	−	0.994222i	$-0.534234\pi$
$293$	13.8196	−	23.9363i	0.807350	−	1.39837i	0.914693	−	0.404150i	$-0.132433\pi$
$294$		0			0
$295$	0.508058	+	0.879982i	0.0295803	+	0.0512346i
$296$		0			0
$297$	−6.83912	+	10.7392i	−0.396846	+	0.623154i
$298$		0			0
$299$	−28.3355			−1.63868
$300$		0			0
$301$	17.3358	+	0.461874i	0.999219	+	0.0266220i
$302$		0			0
$303$	−7.71332	−	4.60356i	−0.443119	−	0.264468i
$304$		0			0
$305$	7.18261	−	4.14688i	0.411275	−	0.237450i
$306$		0			0
$307$			9.45086i			0.539389i	0.962946	+	0.269695i	$0.0869228\pi$
$307$			9.45086i			0.539389i	−0.962946	+	0.269695i	$0.913077\pi$
$308$		0			0
$309$	−1.29951	−	2.32807i	−0.0739266	−	0.132439i
$310$		0			0
$311$	11.8000			0.669116			0.334558	−	0.942375i	$-0.391413\pi$
$311$	11.8000			0.669116			0.334558	+	0.942375i	$0.391413\pi$
$312$		0			0
$313$			15.6571i			0.884992i	0.896770	+	0.442496i	$0.145907\pi$
$313$			15.6571i			0.884992i	−0.896770	+	0.442496i	$0.854093\pi$
$314$		0			0
$315$	22.5674	+	1.25635i	1.27153	+	0.0707872i
$316$		0			0
$317$			16.2138i			0.910656i	0.890324	+	0.455328i	$0.150478\pi$
$317$			16.2138i			0.910656i	−0.890324	+	0.455328i	$0.849522\pi$
$318$		0			0
$319$	−4.11200			−0.230228
$320$		0			0
$321$	3.96784	−	6.64816i	0.221463	−	0.371064i
$322$		0			0
$323$			19.5642i			1.08858i
$324$		0			0
$325$	−9.51521	+	5.49361i	−0.527809	+	0.304730i
$326$		0			0
$327$	12.1320	−	6.77198i	0.670901	−	0.374491i
$328$		0			0
$329$	9.17077	−	14.9500i	0.505601	−	0.824221i
$330$		0			0
$331$	−27.2548			−1.49806			−0.749029	−	0.662537i	$-0.769480\pi$
$331$	−27.2548			−1.49806			−0.749029	+	0.662537i	$0.769480\pi$
$332$		0			0
$333$	−12.8483	+	20.8355i	−0.704083	+	1.14178i
$334$		0			0
$335$	−20.3563	−	35.2582i	−1.11218	−	1.92636i
$336$		0			0
$337$	3.58953	−	6.21725i	0.195534	−	0.338675i	−0.751541	−	0.659686i	$-0.770689\pi$
$337$	3.58953	−	6.21725i	0.195534	−	0.338675i	0.947076	+	0.321011i	$0.104023\pi$
$338$		0			0
$339$	5.51790	−	9.24531i	0.299691	−	0.502136i
$340$		0			0
$341$	−4.88373	+	8.45887i	−0.264469	+	0.458073i
$342$		0			0
$343$	−18.4612	−	1.47837i	−0.996809	−	0.0798245i
$344$		0			0
$345$	20.2674	−	33.9583i	1.09116	−	1.82825i
$346$		0			0
$347$		−	2.61594i		−	0.140431i	−0.997532	−	0.0702156i	$-0.977631\pi$
$347$		−	2.61594i		−	0.140431i	0.997532	−	0.0702156i	$-0.0223687\pi$
$348$		0			0
$349$	16.8392	−	9.72212i	0.901382	−	0.520413i	0.0237334	−	0.999718i	$-0.492445\pi$
$349$	16.8392	−	9.72212i	0.901382	−	0.520413i	0.877648	+	0.479305i	$0.159111\pi$
$350$		0			0
$351$	−9.86392	+	15.4890i	−0.526497	+	0.826741i
$352$		0			0
$353$	−3.62158	+	6.27275i	−0.192757	+	0.333865i	−0.946163	−	0.323691i	$-0.895076\pi$
$353$	−3.62158	+	6.27275i	−0.192757	+	0.333865i	0.753406	+	0.657556i	$0.228410\pi$
$354$		0			0
$355$	−24.5818	+	14.1923i	−1.30467	+	0.753249i
$356$		0			0
$357$	−1.10023	+	26.7383i	−0.0582306	+	1.41514i
$358$		0			0
$359$	20.9106	+	12.0727i	1.10362	+	0.637174i	0.937169	−	0.348875i	$-0.113436\pi$
$359$	20.9106	+	12.0727i	1.10362	+	0.637174i	0.166449	+	0.986050i	$0.446770\pi$
$360$		0			0
$361$	−3.88809	−	6.73438i	−0.204637	−	0.354441i
$362$		0			0
$363$	−7.55608	+	4.21774i	−0.396591	+	0.221374i
$364$		0			0
$365$	−15.4535	−	8.92210i	−0.808874	−	0.467004i
$366$		0			0
$367$	−15.6944	−	9.06117i	−0.819242	−	0.472989i	0.0309133	−	0.999522i	$-0.490158\pi$
$367$	−15.6944	−	9.06117i	−0.819242	−	0.472989i	−0.850155	+	0.526533i	$0.823492\pi$
$368$		0			0
$369$	−17.1261	+	27.7725i	−0.891547	+	1.44578i
$370$		0			0
$371$	−0.621999	+	23.3458i	−0.0322926	+	1.21206i
$372$		0			0
$373$	1.48379	+	2.57000i	0.0768277	+	0.133069i	0.901880	−	0.431987i	$-0.142188\pi$
$373$	1.48379	+	2.57000i	0.0768277	+	0.133069i	−0.825052	+	0.565057i	$0.808854\pi$
$374$		0			0
$375$	−0.135127	+	9.32585i	−0.00697792	+	0.481585i
$376$		0			0
$377$	−5.93066			−0.305444
$378$		0			0
$379$	18.5393			0.952302			0.476151	−	0.879363i	$-0.342032\pi$
$379$	18.5393			0.952302			0.476151	+	0.879363i	$0.342032\pi$
$380$		0			0
$381$	0.172183	−	11.8833i	0.00882119	−	0.608799i
$382$		0			0
$383$	10.2522	+	17.7574i	0.523865	+	0.907361i	0.999614	+	0.0277798i	$0.00884372\pi$
$383$	10.2522	+	17.7574i	0.523865	+	0.907361i	−0.475749	+	0.879581i	$0.657823\pi$
$384$		0			0
$385$	−15.7360	−	9.65289i	−0.801979	−	0.491957i
$386$		0			0
$387$	−9.33444	−	17.3072i	−0.474496	−	0.879773i
$388$		0			0
$389$	17.9067	+	10.3384i	0.907906	+	0.524180i	0.879757	−	0.475424i	$-0.157705\pi$
$389$	17.9067	+	10.3384i	0.907906	+	0.524180i	0.0281490	+	0.999604i	$0.491039\pi$
$390$		0			0
$391$	40.5497	+	23.4114i	2.05069	+	1.18396i
$392$		0			0
$393$	3.95055	−	2.20516i	0.199279	−	0.111236i
$394$		0			0
$395$	16.3755	+	28.3632i	0.823941	+	1.42711i
$396$		0			0
$397$	−16.3016	−	9.41174i	−0.818154	−	0.472362i	0.0316252	−	0.999500i	$-0.489932\pi$
$397$	−16.3016	−	9.41174i	−0.818154	−	0.472362i	−0.849780	+	0.527138i	$0.823265\pi$
$398$		0			0
$399$	7.12314	+	13.6000i	0.356603	+	0.680853i
$400$		0			0
$401$	−18.0225	+	10.4053i	−0.899999	+	0.519615i	−0.877200	−	0.480125i	$-0.840591\pi$
$401$	−18.0225	+	10.4053i	−0.899999	+	0.519615i	−0.0227993	+	0.999740i	$0.507258\pi$
$402$		0			0
$403$	−7.04370	+	12.2000i	−0.350872	+	0.607728i
$404$		0			0
$405$	−11.5073	−	22.9001i	−0.571800	−	1.13791i
$406$		0			0
$407$	17.3145	−	9.99653i	0.858248	−	0.495510i
$408$		0			0
$409$		−	20.4860i		−	1.01297i	−0.862249	−	0.506484i	$-0.830945\pi$
$409$		−	20.4860i		−	1.01297i	0.862249	−	0.506484i	$-0.169055\pi$
$410$		0			0
$411$	6.45479	−	10.8151i	0.318391	−	0.533468i
$412$		0			0
$413$	−0.493648	+	0.804735i	−0.0242908	+	0.0395984i
$414$		0			0
$415$	−0.538214	+	0.932214i	−0.0264199	+	0.0457606i
$416$		0			0
$417$	12.3009	−	20.6102i	0.602376	−	1.00929i
$418$		0			0
$419$	−4.73143	+	8.19508i	−0.231146	+	0.400356i	−0.958146	−	0.286282i	$-0.907581\pi$
$419$	−4.73143	+	8.19508i	−0.231146	+	0.400356i	0.727000	+	0.686638i	$0.240914\pi$
$420$		0			0
$421$	10.7720	+	18.6576i	0.524994	+	0.909316i	0.999576	+	0.0291051i	$0.00926576\pi$
$421$	10.7720	+	18.6576i	0.524994	+	0.909316i	−0.474582	+	0.880211i	$0.657401\pi$
$422$		0			0
$423$	−19.8787	−	0.576185i	−0.966534	−	0.0280151i
$424$		0			0
$425$	18.1557			0.880683
$426$		0			0
$427$	6.56842	+	4.02926i	0.317868	+	0.194989i
$428$		0			0
$429$	13.0962	−	7.31018i	0.632290	−	0.352939i
$430$		0			0
$431$	−11.0859	+	6.40047i	−0.533991	+	0.308300i	−0.742640	−	0.669691i	$-0.766427\pi$
$431$	−11.0859	+	6.40047i	−0.533991	+	0.308300i	0.208649	+	0.977991i	$0.433093\pi$
$432$		0			0
$433$			2.02304i			0.0972210i	0.998818	+	0.0486105i	$0.0154793\pi$
$433$			2.02304i			0.0972210i	−0.998818	+	0.0486105i	$0.984521\pi$
$434$		0			0
$435$	4.24201	−	7.10753i	0.203389	−	0.340780i
$436$		0			0
$437$	26.8618			1.28497
$438$		0			0
$439$			15.1798i			0.724492i	0.932083	+	0.362246i	$0.117990\pi$
$439$			15.1798i			0.724492i	−0.932083	+	0.362246i	$0.882010\pi$
$440$		0			0
$441$	8.97035	+	18.9877i	0.427159	+	0.904176i
$442$		0			0
$443$			33.6081i			1.59677i	0.602148	+	0.798385i	$0.294312\pi$
$443$			33.6081i			1.59677i	−0.602148	+	0.798385i	$0.705688\pi$
$444$		0			0
$445$	−40.1923			−1.90530
$446$		0			0
$447$	8.93265	+	16.0029i	0.422500	+	0.756909i
$448$		0			0
$449$			27.9231i			1.31777i	0.752242	+	0.658887i	$0.228973\pi$
$449$			27.9231i			1.31777i	−0.752242	+	0.658887i	$0.771027\pi$
$450$		0			0
$451$	23.0793	−	13.3248i	1.08676	−	0.627441i
$452$		0			0
$453$	−18.4961	−	11.0391i	−0.869024	−	0.518662i
$454$		0			0
$455$	−22.6956	−	13.9222i	−1.06399	−	0.652681i
$456$		0			0
$457$	36.7644			1.71977			0.859883	−	0.510490i	$-0.170536\pi$
$457$	36.7644			1.71977			0.859883	+	0.510490i	$0.170536\pi$
$458$		0			0
$459$	26.9132	−	14.0159i	1.25620	−	0.654204i
$460$		0			0
$461$	8.88310	+	15.3860i	0.413727	+	0.716597i	0.995294	−	0.0969021i	$-0.0308934\pi$
$461$	8.88310	+	15.3860i	0.413727	+	0.716597i	−0.581567	+	0.813499i	$0.697560\pi$
$462$		0			0
$463$	−14.6989	+	25.4592i	−0.683114	+	1.18319i	0.290911	+	0.956750i	$0.406042\pi$
$463$	−14.6989	+	25.4592i	−0.683114	+	1.18319i	−0.974025	+	0.226439i	$0.927292\pi$
$464$		0			0
$465$	−9.58288	−	17.1677i	−0.444395	−	0.796135i
$466$		0			0
$467$	5.55677	−	9.62460i	0.257137	−	0.445373i	−0.708337	−	0.705874i	$-0.750554\pi$
$467$	5.55677	−	9.62460i	0.257137	−	0.445373i	0.965474	+	0.260501i	$0.0838877\pi$
$468$		0			0
$469$	19.7789	−	32.2432i	0.913306	−	1.48885i
$470$		0			0
$471$	24.9809	+	0.361961i	1.15106	+	0.0166783i
$472$		0			0
$473$			16.0607i			0.738472i
$474$		0			0
$475$	9.02034	−	5.20790i	0.413882	−	0.238955i
$476$		0			0
$477$	23.3073	−	12.5705i	1.06717	−	0.575566i
$478$		0			0
$479$	0.424408	−	0.735096i	0.0193917	−	0.0335874i	−0.856167	−	0.516700i	$-0.827160\pi$
$479$	0.424408	−	0.735096i	0.0193917	−	0.0335874i	0.875558	+	0.483112i	$0.160494\pi$
$480$		0			0
$481$	24.9723	−	14.4178i	1.13864	−	0.657395i
$482$		0			0
$483$	36.7119	+	1.51063i	1.67045	+	0.0687360i
$484$		0			0
$485$	−11.4099	−	6.58753i	−0.518098	−	0.299124i
$486$		0			0
$487$	15.4308	+	26.7270i	0.699238	+	1.21112i	0.968731	+	0.248113i	$0.0798106\pi$
$487$	15.4308	+	26.7270i	0.699238	+	1.21112i	−0.269493	+	0.963002i	$0.586856\pi$
$488$		0			0
$489$	−29.3924	−	17.5424i	−1.32917	−	0.793293i
$490$		0			0
$491$	−1.44754	−	0.835738i	−0.0653266	−	0.0377163i	0.466981	−	0.884267i	$-0.345342\pi$
$491$	−1.44754	−	0.835738i	−0.0653266	−	0.0377163i	−0.532308	+	0.846551i	$0.678675\pi$
$492$		0			0
$493$	8.48712	+	4.90004i	0.382241	+	0.220687i
$494$		0			0
$495$	−0.606476	+	20.9237i	−0.0272591	+	0.940451i
$496$		0			0
$497$	−22.4798	−	13.7897i	−1.00836	−	0.618555i
$498$		0			0
$499$	−15.3185	−	26.5325i	−0.685752	−	1.18776i	−0.973200	−	0.229961i	$-0.926140\pi$
$499$	−15.3185	−	26.5325i	−0.685752	−	1.18776i	0.287448	−	0.957796i	$-0.407193\pi$
$500$		0			0
$501$	10.8753	+	6.49076i	0.485874	+	0.289986i
$502$		0			0
$503$	−23.1480			−1.03212			−0.516059	−	0.856553i	$-0.672601\pi$
$503$	−23.1480			−1.03212			−0.516059	+	0.856553i	$0.672601\pi$
$504$		0			0
$505$	−14.7682			−0.657177
$506$		0			0
$507$	−0.772693	+	0.431311i	−0.0343165	+	0.0191552i
$508$		0			0
$509$	14.2933	+	24.7567i	0.633540	+	1.09732i	0.986822	+	0.161807i	$0.0517321\pi$
$509$	14.2933	+	24.7567i	0.633540	+	1.09732i	−0.353282	+	0.935517i	$0.614935\pi$
$510$		0			0
$511$	0.441558	−	16.5733i	0.0195334	−	0.733158i
$512$		0			0
$513$	9.35092	−	14.6834i	0.412853	−	0.648290i
$514$		0			0
$515$	−3.79619	−	2.19173i	−0.167280	−	0.0965792i
$516$		0			0
$517$	14.0668	+	8.12146i	0.618657	+	0.357182i
$518$		0			0
$519$	−0.0331199	+	2.28578i	−0.00145380	+	0.100335i
$520$		0			0
$521$	−15.2580	−	26.4276i	−0.668464	−	1.15781i	−0.978334	−	0.207034i	$-0.933619\pi$
$521$	−15.2580	−	26.4276i	−0.668464	−	1.15781i	0.309870	−	0.950779i	$-0.399714\pi$
$522$		0			0
$523$	−4.95092	−	2.85841i	−0.216488	−	0.124990i	0.387835	−	0.921729i	$-0.373223\pi$
$523$	−4.95092	−	2.85841i	−0.216488	−	0.124990i	−0.604323	+	0.796739i	$0.706556\pi$
$524$		0			0
$525$	12.6209	−	6.61034i	0.550823	−	0.288499i
$526$		0			0
$527$	20.1599	−	11.6393i	0.878179	−	0.507017i
$528$		0			0
$529$	20.6440	−	35.7565i	0.897566	−	1.55463i
$530$		0			0
$531$	1.07004	+	0.0310151i	0.0464356	+	0.00134594i
$532$		0			0
$533$	33.2867	−	19.2181i	1.44181	−	0.832428i
$534$		0			0
$535$		−	12.7288i		−	0.550315i
$536$		0			0
$537$	−2.68186	−	4.80456i	−0.115731	−	0.207332i
$538$		0			0
$539$	0.913305	−	17.1276i	0.0393388	−	0.737740i
$540$		0			0
$541$	−0.746219	+	1.29249i	−0.0320825	+	0.0555684i	−0.881621	−	0.471958i	$-0.843547\pi$
$541$	−0.746219	+	1.29249i	−0.0320825	+	0.0555684i	0.849538	+	0.527527i	$0.176881\pi$
$542$		0			0
$543$	−27.0491	−	0.391927i	−1.16079	−	0.0168192i
$544$		0			0
$545$	11.4215	−	19.7826i	0.489243	−	0.847394i
$546$		0			0
$547$	12.8119	+	22.1909i	0.547798	+	0.948814i	0.998425	+	0.0561019i	$0.0178672\pi$
$547$	12.8119	+	22.1909i	0.547798	+	0.948814i	−0.450627	+	0.892712i	$0.648799\pi$
$548$		0			0
$549$	0.253152	−	8.73386i	0.0108043	−	0.372752i
$550$		0			0
$551$	5.62222			0.239515
$552$		0			0
$553$	−15.9110	+	25.9378i	−0.676606	+	1.10299i
$554$		0			0
$555$	−0.583063	+	40.2404i	−0.0247497	+	1.70811i
$556$		0			0
$557$	2.59567	−	1.49861i	0.109982	−	0.0634983i	−0.444000	−	0.896027i	$-0.646441\pi$
$557$	2.59567	−	1.49861i	0.109982	−	0.0634983i	0.553982	+	0.832529i	$0.313108\pi$
$558$		0			0
$559$			23.1640i			0.979734i
$560$		0			0
$561$	−24.7812	−	0.359068i	−1.04626	−	0.0151599i
$562$		0			0
$563$	16.4782			0.694473			0.347237	−	0.937778i	$-0.387120\pi$
$563$	16.4782			0.694473			0.347237	+	0.937778i	$0.387120\pi$
$564$		0			0
$565$		−	17.7014i		−	0.744704i
$566$		0			0
$567$	13.6056	−	19.5419i	0.571382	−	0.820684i
$568$		0			0
$569$			27.6019i			1.15713i	0.815636	+	0.578565i	$0.196387\pi$
$569$			27.6019i			1.15713i	−0.815636	+	0.578565i	$0.803613\pi$
$570$		0			0
$571$	−4.80141			−0.200933			−0.100466	−	0.994940i	$-0.532033\pi$
$571$	−4.80141			−0.200933			−0.100466	+	0.994940i	$0.532033\pi$
$572$		0			0
$573$	−4.88528	−	0.0707853i	−0.204086	−	0.00295710i
$574$		0			0
$575$		−	24.9280i		−	1.03957i
$576$		0			0
$577$	21.7405	−	12.5519i	0.905068	−	0.522541i	0.0262269	−	0.999656i	$-0.491651\pi$
$577$	21.7405	−	12.5519i	0.905068	−	0.522541i	0.878841	+	0.477115i	$0.158317\pi$
$578$		0			0
$579$	−0.472416	+	32.6041i	−0.0196330	+	1.35498i
$580$		0			0
$581$	−0.999760	−	0.0266364i	−0.0414770	−	0.00110506i
$582$		0			0
$583$	−21.6287			−0.895770
$584$		0			0
$585$	−0.874707	+	30.1778i	−0.0361647	+	1.24770i
$586$		0			0
$587$	−4.88189	−	8.45567i	−0.201497	−	0.349003i	0.747514	−	0.664246i	$-0.231247\pi$
$587$	−4.88189	−	8.45567i	−0.201497	−	0.349003i	−0.949011	+	0.315243i	$0.897914\pi$
$588$		0			0
$589$	6.67737	−	11.5656i	0.275136	−	0.476550i
$590$		0			0
$591$	0.797391	+	0.0115538i	0.0328003	+	0.000475260i
$592$		0			0
$593$	−18.7627	+	32.4980i	−0.770492	+	1.33453i	0.166802	+	0.985990i	$0.446656\pi$
$593$	−18.7627	+	32.4980i	−0.770492	+	1.33453i	−0.937294	+	0.348541i	$0.886677\pi$
$594$		0			0
$595$	20.9760	+	38.6751i	0.859932	+	1.58552i
$596$		0			0
$597$	17.7471	+	31.7939i	0.726340	+	1.30124i
$598$		0			0
$599$		−	34.4907i		−	1.40925i	−0.709580	−	0.704625i	$-0.751115\pi$
$599$		−	34.4907i		−	1.40925i	0.709580	−	0.704625i	$-0.248885\pi$
$600$		0			0
$601$	−11.9095	+	6.87593i	−0.485797	+	0.280475i	−0.722829	−	0.691027i	$-0.757159\pi$
$601$	−11.9095	+	6.87593i	−0.485797	+	0.280475i	0.237032	+	0.971502i	$0.423825\pi$
$602$		0			0
$603$	−42.8730	−	1.24268i	−1.74592	−	0.0506058i
$604$		0			0
$605$	−7.11356	+	12.3210i	−0.289207	+	0.500922i
$606$		0			0
$607$	−19.1826	+	11.0751i	−0.778599	+	0.449524i	−0.835934	−	0.548831i	$-0.815073\pi$
$607$	−19.1826	+	11.0751i	−0.778599	+	0.449524i	0.0573346	+	0.998355i	$0.481740\pi$
$608$		0			0
$609$	7.68387	+	0.316177i	0.311366	+	0.0128121i
$610$		0			0
$611$	20.2882	+	11.7134i	0.820774	+	0.473874i
$612$		0			0
$613$	15.2060	+	26.3376i	0.614166	+	1.06377i	0.990530	+	0.137295i	$0.0438409\pi$
$613$	15.2060	+	26.3376i	0.614166	+	1.06377i	−0.376364	+	0.926472i	$0.622826\pi$
$614$		0			0
$615$	−0.777190	+	53.6382i	−0.0313393	+	2.16290i
$616$		0			0
$617$	−1.80935	−	1.04463i	−0.0728418	−	0.0420553i	0.463137	−	0.886287i	$-0.346724\pi$
$617$	−1.80935	−	1.04463i	−0.0728418	−	0.0420553i	−0.535979	+	0.844232i	$0.680057\pi$
$618$		0			0
$619$	3.27077	+	1.88838i	0.131463	+	0.0759003i	0.564289	−	0.825577i	$-0.309150\pi$
$619$	3.27077	+	1.88838i	0.131463	+	0.0759003i	−0.432826	+	0.901477i	$0.642484\pi$
$620$		0			0
$621$	−19.2439	−	36.9520i	−0.772230	−	1.48283i
$622$		0			0
$623$	−17.8035	−	32.8257i	−0.713283	−	1.31513i
$624$		0			0
$625$	15.4396	+	26.7421i	0.617582	+	1.06968i
$626$		0			0
$627$	−12.4151	+	6.92999i	−0.495811	+	0.276757i
$628$		0			0
$629$	−47.6492			−1.89990
$630$		0			0
$631$	−33.9356			−1.35095			−0.675477	−	0.737381i	$-0.736062\pi$
$631$	−33.9356			−1.35095			−0.675477	+	0.737381i	$0.736062\pi$
$632$		0			0
$633$	19.6470	+	11.7260i	0.780898	+	0.466065i
$634$		0			0
$635$	−9.76957	−	16.9214i	−0.387693	−	0.671505i
$636$		0			0
$637$	1.31724	−	24.7028i	0.0521910	−	0.978762i
$638$		0			0
$639$	−0.866388	+	29.8908i	−0.0342738	+	1.18246i
$640$		0			0
$641$	27.2653	+	15.7416i	1.07692	+	0.621758i	0.930063	−	0.367401i	$-0.119752\pi$
$641$	27.2653	+	15.7416i	1.07692	+	0.621758i	0.146853	+	0.989158i	$0.453086\pi$
$642$		0			0
$643$	−18.8249	−	10.8686i	−0.742382	−	0.428614i	0.0805529	−	0.996750i	$-0.474331\pi$
$643$	−18.8249	−	10.8686i	−0.742382	−	0.428614i	−0.822935	+	0.568136i	$0.807665\pi$
$644$		0			0
$645$	−27.7607	−	16.5685i	−1.09308	−	0.652383i
$646$		0			0
$647$	−11.9562	−	20.7088i	−0.470047	−	0.814146i	0.529366	−	0.848393i	$-0.322430\pi$
$647$	−11.9562	−	20.7088i	−0.470047	−	0.814146i	−0.999413	+	0.0342478i	$0.989096\pi$
$648$		0			0
$649$	−0.757192	−	0.437165i	−0.0297224	−	0.0171602i
$650$		0			0
$651$	9.77636	−	15.4311i	0.383166	−	0.604792i
$652$		0			0
$653$	−1.75971	+	1.01597i	−0.0688627	+	0.0397579i	−0.534036	−	0.845462i	$-0.679325\pi$
$653$	−1.75971	+	1.01597i	−0.0688627	+	0.0397579i	0.465173	+	0.885220i	$0.345992\pi$
$654$		0			0
$655$	3.71918	−	6.44181i	0.145320	−	0.251702i
$656$		0			0
$657$	−16.5459	+	8.92385i	−0.645517	+	0.348153i
$658$		0			0
$659$	−23.9579	+	13.8321i	−0.933269	+	0.538823i	−0.887844	−	0.460145i	$-0.847798\pi$
$659$	−23.9579	+	13.8321i	−0.933269	+	0.538823i	−0.0454251	+	0.998968i	$0.514464\pi$
$660$		0			0
$661$		−	32.0370i		−	1.24609i	−0.782184	−	0.623047i	$-0.785894\pi$
$661$		−	32.0370i		−	1.24609i	0.782184	−	0.623047i	$-0.214106\pi$
$662$		0			0
$663$	−35.7415	−	0.517876i	−1.38808	−	0.0201126i
$664$		0			0
$665$	21.5153	+	13.1981i	0.834327	+	0.511801i
$666$		0			0
$667$	6.72779	−	11.6529i	0.260501	−	0.451201i
$668$		0			0
$669$	13.7087	+	24.5592i	0.530009	+	0.949512i
$670$		0			0
$671$	−3.56823	+	6.18036i	−0.137750	+	0.238590i
$672$		0			0
$673$	16.4796	+	28.5435i	0.635242	+	1.10027i	0.986464	+	0.163979i	$0.0524330\pi$
$673$	16.4796	+	28.5435i	0.635242	+	1.10027i	−0.351222	+	0.936292i	$0.614234\pi$
$674$		0			0
$675$	−13.6264	−	8.67773i	−0.524479	−	0.334006i
$676$		0			0
$677$	−17.3583			−0.667135			−0.333567	−	0.942726i	$-0.608252\pi$
$677$	−17.3583			−0.667135			−0.333567	+	0.942726i	$0.608252\pi$
$678$		0			0
$679$	0.326019	−	12.2367i	0.0125115	−	0.469601i
$680$		0			0
$681$	28.9299	+	17.2663i	1.10860	+	0.661647i
$682$		0			0
$683$	28.1068	−	16.2275i	1.07548	−	0.620927i	0.145804	−	0.989313i	$-0.453423\pi$
$683$	28.1068	−	16.2275i	1.07548	−	0.620927i	0.929673	+	0.368387i	$0.120090\pi$
$684$		0			0
$685$		−	20.7069i		−	0.791171i
$686$		0			0
$687$	−20.0816	−	35.9763i	−0.766162	−	1.37258i
$688$		0			0
$689$	−31.1946			−1.18842
$690$		0			0
$691$			41.0315i			1.56091i	0.625211	+	0.780455i	$0.285013\pi$
$691$			41.0315i			1.56091i	−0.625211	+	0.780455i	$0.714987\pi$
$692$		0			0
$693$	−17.3574	+	8.77301i	−0.659352	+	0.333259i
$694$		0			0
$695$		−	39.4612i		−	1.49685i
$696$		0			0
$697$	−63.5137			−2.40575
$698$		0			0
$699$	−2.85747	+	4.78773i	−0.108079	+	0.181088i
$700$		0			0
$701$		−	42.3994i		−	1.60140i	−0.599064	−	0.800701i	$-0.704460\pi$
$701$		−	42.3994i		−	1.60140i	0.599064	−	0.800701i	$-0.295540\pi$
$702$		0			0
$703$	−23.6736	+	13.6680i	−0.892866	+	0.515497i
$704$		0			0
$705$	−28.5493	+	15.9360i	−1.07523	+	0.600184i
$706$		0			0
$707$	−6.54170	−	12.0614i	−0.246026	−	0.453617i
$708$		0			0
$709$	22.1166			0.830607			0.415304	−	0.909683i	$-0.363675\pi$
$709$	22.1166			0.830607			0.415304	+	0.909683i	$0.363675\pi$
$710$		0			0
$711$	34.4889	+	0.999664i	1.29344	+	0.0374903i
$712$		0			0
$713$	−15.9809	−	27.6797i	−0.598489	−	1.03661i
$714$		0			0
$715$	12.3292	−	21.3548i	0.461086	−	0.798625i
$716$		0			0
$717$	18.5273	−	31.0427i	0.691915	−	1.15931i
$718$		0			0
$719$	1.91881	−	3.32348i	0.0715597	−	0.123945i	−0.828025	−	0.560691i	$-0.810536\pi$
$719$	1.91881	−	3.32348i	0.0715597	−	0.123945i	0.899585	+	0.436746i	$0.143869\pi$
$720$		0			0
$721$	0.108470	−	4.07125i	0.00403962	−	0.151621i
$722$		0			0
$723$	−24.9344	+	41.7778i	−0.927319	+	1.55373i
$724$		0			0
$725$		−	5.21747i		−	0.193772i
$726$		0			0
$727$	7.45945	−	4.30671i	0.276656	−	0.159727i	−0.355253	−	0.934770i	$-0.615605\pi$
$727$	7.45945	−	4.30671i	0.276656	−	0.159727i	0.631908	+	0.775043i	$0.282272\pi$
$728$		0			0
$729$	−26.8980	−	2.34418i	−0.996224	−	0.0868215i
$730$		0			0
$731$	19.1386	−	33.1491i	0.707868	−	1.22606i
$732$		0			0
$733$	−10.1047	+	5.83398i	−0.373227	+	0.215483i	−0.674867	−	0.737939i	$-0.735799\pi$
$733$	−10.1047	+	5.83398i	−0.373227	+	0.215483i	0.301640	+	0.953422i	$0.402466\pi$
$734$		0			0
$735$	28.6627	+	19.2478i	1.05724	+	0.709964i
$736$		0			0
$737$	30.3383	+	17.5159i	1.11753	+	0.645205i
$738$		0			0
$739$	8.95318	+	15.5074i	0.329348	+	0.570447i	0.982383	−	0.186881i	$-0.0598377\pi$
$739$	8.95318	+	15.5074i	0.329348	+	0.570447i	−0.653035	+	0.757328i	$0.726504\pi$
$740$		0			0
$741$	−17.9060	+	9.99499i	−0.657794	+	0.367175i
$742$		0			0
$743$	28.1621	+	16.2594i	1.03317	+	0.596500i	0.917890	−	0.396834i	$-0.129891\pi$
$743$	28.1621	+	16.2594i	1.03317	+	0.596500i	0.115277	+	0.993333i	$0.463224\pi$
$744$		0			0
$745$	26.0945	+	15.0656i	0.956027	+	0.551962i
$746$		0			0
$747$	0.538320	+	0.998109i	0.0196961	+	0.0365189i
$748$		0			0
$749$	10.3958	−	5.63833i	0.379855	−	0.206020i
$750$		0			0
$751$	2.65685	+	4.60180i	0.0969499	+	0.167922i	0.910421	−	0.413684i	$-0.135758\pi$
$751$	2.65685	+	4.60180i	0.0969499	+	0.167922i	−0.813471	+	0.581606i	$0.802425\pi$
$752$		0			0
$753$	0.404801	−	27.9375i	0.0147518	−	1.01810i
$754$		0			0
$755$	−35.4134			−1.28883
$756$		0			0
$757$	8.07735			0.293576			0.146788	−	0.989168i	$-0.453106\pi$
$757$	8.07735			0.293576			0.146788	+	0.989168i	$0.453106\pi$
$758$		0			0
$759$	−0.493003	+	34.0248i	−0.0178949	+	1.23502i
$760$		0			0
$761$	−7.36098	−	12.7496i	−0.266835	−	0.462172i	0.701208	−	0.712957i	$-0.252645\pi$
$761$	−7.36098	−	12.7496i	−0.266835	−	0.462172i	−0.968043	+	0.250785i	$0.919311\pi$
$762$		0			0
$763$	21.2160	+	0.565254i	0.768071	+	0.0204636i
$764$		0			0
$765$	26.1854	−	42.4635i	0.946733	−	1.53527i
$766$		0			0
$767$	−1.09208	−	0.630514i	−0.0394328	−	0.0227665i
$768$		0			0
$769$	19.8651	+	11.4691i	0.716355	+	0.413588i	0.813410	−	0.581691i	$-0.197609\pi$
$769$	19.8651	+	11.4691i	0.716355	+	0.413588i	−0.0970545	+	0.995279i	$0.530942\pi$
$770$		0			0
$771$	12.6875	−	7.08205i	0.456929	−	0.255054i
$772$		0			0
$773$	−26.1369	−	45.2705i	−0.940081	−	1.62827i	−0.765314	−	0.643657i	$-0.777416\pi$
$773$	−26.1369	−	45.2705i	−0.940081	−	1.62827i	−0.174767	−	0.984610i	$-0.555917\pi$
$774$		0			0
$775$	−10.7329	−	6.19666i	−0.385538	−	0.222591i
$776$		0			0
$777$	−33.1233	+	17.3486i	−1.18829	+	0.622378i
$778$		0			0
$779$	−31.5556	+	18.2186i	−1.13060	+	0.652750i
$780$		0			0
$781$	12.2119	−	21.1517i	0.436978	−	0.756868i
$782$		0			0
$783$	−4.02777	−	7.73411i	−0.143941	−	0.276395i
$784$		0			0
$785$	35.5720	−	20.5375i	1.26962	−	0.733015i
$786$		0			0
$787$		−	46.2318i		−	1.64798i	−0.566601	−	0.823992i	$-0.691742\pi$
$787$		−	46.2318i		−	1.64798i	0.566601	−	0.823992i	$-0.308258\pi$
$788$		0			0
$789$	7.79775	−	13.0652i	0.277607	−	0.465134i
$790$		0			0
$791$	14.4570	−	7.84098i	0.514033	−	0.278793i
$792$		0			0
$793$	−5.14639	+	8.91381i	−0.182754	+	0.316539i
$794$		0			0
$795$	22.3125	−	37.3849i	0.791343	−	1.32590i
$796$		0			0
$797$	−14.6716	+	25.4120i	−0.519695	+	0.900139i	0.480042	+	0.877245i	$0.340621\pi$
$797$	−14.6716	+	25.4120i	−0.519695	+	0.900139i	−0.999738	+	0.0228937i	$0.992712\pi$
$798$		0			0
$799$	−19.3558	−	33.5252i	−0.684758	−	1.18604i
$800$		0			0
$801$	−22.2250	+	36.0412i	−0.785281	+	1.27345i
$802$		0			0
$803$	15.3543			0.541840
$804$		0			0
$805$	53.1012	−	28.8002i	1.87157	−	1.01507i
$806$		0			0
$807$	34.0456	−	19.0039i	1.19846	−	0.668970i
$808$		0			0
$809$	−2.07638	+	1.19880i	−0.0730016	+	0.0421475i	−0.536057	−	0.844182i	$-0.680087\pi$
$809$	−2.07638	+	1.19880i	−0.0730016	+	0.0421475i	0.463055	+	0.886330i	$0.346753\pi$
$810$		0			0
$811$		−	46.6726i		−	1.63890i	−0.573153	−	0.819449i	$-0.694280\pi$
$811$		−	46.6726i		−	1.63890i	0.573153	−	0.819449i	$-0.305720\pi$
$812$		0			0
$813$	0.636074	−	1.06575i	0.0223081	−	0.0373775i
$814$		0			0
$815$	−56.2759			−1.97126
$816$		0			0
$817$		−	21.9593i		−	0.768260i
$818$		0			0
$819$	−25.0342	+	12.6531i	−0.874766	+	0.442136i
$820$		0			0
$821$			3.79814i			0.132556i	0.997801	+	0.0662781i	$0.0211124\pi$
$821$			3.79814i			0.132556i	−0.997801	+	0.0662781i	$0.978888\pi$
$822$		0			0
$823$	−7.85990			−0.273979			−0.136990	−	0.990572i	$-0.543743\pi$
$823$	−7.85990			−0.273979			−0.136990	+	0.990572i	$0.543743\pi$
$824$		0			0
$825$	6.43109	+	11.5213i	0.223902	+	0.401120i
$826$		0			0
$827$		−	4.21235i		−	0.146478i	−0.997314	−	0.0732389i	$-0.976666\pi$
$827$		−	4.21235i		−	0.146478i	0.997314	−	0.0732389i	$-0.0233335\pi$
$828$		0			0
$829$	−34.8209	+	20.1039i	−1.20938	+	0.698237i	−0.962624	−	0.270841i	$-0.912698\pi$
$829$	−34.8209	+	20.1039i	−1.20938	+	0.698237i	−0.246757	+	0.969077i	$0.579365\pi$
$830$		0			0
$831$	37.4510	+	22.3520i	1.29916	+	0.775381i
$832$		0			0
$833$	−22.2951	+	34.2629i	−0.772479	+	1.18714i
$834$		0			0
$835$	20.8223			0.720587
$836$		0			0
$837$	−20.6936	−	0.900026i	−0.715277	−	0.0311094i
$838$		0			0
$839$	−10.7834	−	18.6774i	−0.372285	−	0.644816i	0.617632	−	0.786467i	$-0.288092\pi$
$839$	−10.7834	−	18.6774i	−0.372285	−	0.644816i	−0.989917	+	0.141651i	$0.954759\pi$
$840$		0			0
$841$	−13.0919	+	22.6758i	−0.451444	+	0.781923i
$842$		0			0
$843$	−15.7164	−	28.1559i	−0.541301	−	0.969742i
$844$		0			0
$845$	−0.727440	+	1.25996i	−0.0250247	+	0.0433441i
$846$		0			0
$847$	−13.2138	−	0.352053i	−0.454032	−	0.0120967i
$848$		0			0
$849$	−37.5774	−	0.544477i	−1.28965	−	0.0186864i
$850$		0			0
$851$			65.4227i			2.24266i
$852$		0			0
$853$	14.3748	−	8.29930i	0.492184	−	0.284163i	−0.233296	−	0.972406i	$-0.574951\pi$
$853$	14.3748	−	8.29930i	0.492184	−	0.284163i	0.725480	+	0.688243i	$0.241618\pi$
$854$		0			0
$855$	0.829216	−	28.6084i	0.0283586	−	0.978385i
$856$		0			0
$857$	−1.35961	+	2.35491i	−0.0464434	+	0.0804423i	−0.888313	−	0.459239i	$-0.848122\pi$
$857$	−1.35961	+	2.35491i	−0.0464434	+	0.0804423i	0.841869	+	0.539682i	$0.181455\pi$
$858$		0			0
$859$	−9.51017	+	5.49070i	−0.324483	+	0.187340i	−0.653389	−	0.757022i	$-0.726653\pi$
$859$	−9.51017	+	5.49070i	−0.324483	+	0.187340i	0.328906	+	0.944363i	$0.393320\pi$
$860$		0			0
$861$	−44.1514	+	23.1247i	−1.50468	+	0.788088i
$862$		0			0
$863$	−3.07641	−	1.77617i	−0.104722	−	0.0604615i	0.446724	−	0.894672i	$-0.352591\pi$
$863$	−3.07641	−	1.77617i	−0.104722	−	0.0604615i	−0.551446	+	0.834210i	$0.685924\pi$
$864$		0			0
$865$	1.87920	+	3.25488i	0.0638949	+	0.110669i
$866$		0			0
$867$	25.4362	+	15.1812i	0.863860	+	0.515580i
$868$		0			0
$869$	−24.4055	−	14.0905i	−0.827899	−	0.477988i
$870$		0			0
$871$	43.7564	+	25.2628i	1.48263	+	0.855996i
$872$		0			0
$873$	−12.2165	+	6.58882i	−0.413465	+	0.222998i
$874$		0			0
$875$	−7.44956	+	12.1441i	−0.251841	+	0.410547i
$876$		0			0
$877$	3.94711	+	6.83659i	0.133284	+	0.230855i	0.924941	−	0.380111i	$-0.124114\pi$
$877$	3.94711	+	6.83659i	0.133284	+	0.230855i	−0.791656	+	0.610967i	$0.790781\pi$
$878$		0			0
$879$	−41.1077	−	24.5344i	−1.38653	−	0.827525i
$880$		0			0
$881$	34.5647			1.16451			0.582257	−	0.813005i	$-0.302170\pi$
$881$	34.5647			1.16451			0.582257	+	0.813005i	$0.302170\pi$
$882$		0			0
$883$	−3.82772			−0.128813			−0.0644065	−	0.997924i	$-0.520515\pi$
$883$	−3.82772			−0.128813			−0.0644065	+	0.997924i	$0.520515\pi$
$884$		0			0
$885$	1.53676	−	0.857808i	0.0516577	−	0.0288349i
$886$		0			0
$887$	−14.8679	−	25.7519i	−0.499214	−	0.864664i	0.500785	−	0.865571i	$-0.333045\pi$
$887$	−14.8679	−	25.7519i	−0.499214	−	0.864664i	−1.00000		0.000907200i	$0.999711\pi$
$888$		0			0
$889$	9.49246	−	15.4744i	0.318367	−	0.518996i
$890$		0			0
$891$	18.4273	+	12.1139i	0.617339	+	0.405832i
$892$		0			0
$893$	−19.2331	−	11.1042i	−0.643611	−	0.371589i
$894$		0			0
$895$	−7.83438	−	4.52318i	−0.261874	−	0.151193i
$896$		0			0
$897$	−0.711048	+	49.0733i	−0.0237412	+	1.63851i
$898$		0			0
$899$	−3.34482	−	5.79340i	−0.111556	−	0.193221i
$900$		0			0
$901$	44.6414	+	25.7737i	1.48722	+	0.858646i
$902$		0			0
$903$	1.23493	−	30.0117i	0.0410958	−	0.998728i
$904$		0			0
$905$	−38.5169	+	22.2378i	−1.28035	+	0.739208i
$906$		0			0
$907$	8.49436	−	14.7127i	0.282051	−	0.488526i	−0.689839	−	0.723963i	$-0.742319\pi$
$907$	8.49436	−	14.7127i	0.282051	−	0.488526i	0.971890	+	0.235437i	$0.0756520\pi$
$908$		0			0
$909$	−8.16632	+	13.2429i	−0.270860	+	0.439240i
$910$		0			0
$911$	−28.9782	+	16.7306i	−0.960090	+	0.554308i	−0.896201	−	0.443649i	$-0.853684\pi$
$911$	−28.9782	+	16.7306i	−0.960090	+	0.554308i	−0.0638890	+	0.997957i	$0.520350\pi$
$912$		0			0
$913$		−	0.926226i		−	0.0306536i
$914$		0			0
$915$	−7.00161	−	12.5434i	−0.231466	−	0.414672i
$916$		0			0
$917$	6.90857	+	0.184064i	0.228141	+	0.00607832i
$918$		0			0
$919$	22.5522	−	39.0616i	0.743929	−	1.28852i	−0.206764	−	0.978391i	$-0.566293\pi$
$919$	22.5522	−	39.0616i	0.743929	−	1.28852i	0.950693	−	0.310132i	$-0.100373\pi$
$920$		0			0
$921$	16.3677	+	0.237159i	0.539333	+	0.00781466i
$922$		0			0
$923$	17.6130	−	30.5067i	0.579740	−	1.00414i
$924$		0			0
$925$	12.6840	+	21.9693i	0.417047	+	0.722346i
$926$		0			0
$927$	−4.06453	+	2.19216i	−0.133497	+	0.0720000i
$928$		0			0
$929$	−51.6815			−1.69562			−0.847808	−	0.530303i	$-0.822078\pi$
$929$	−51.6815			−1.69562			−0.847808	+	0.530303i	$0.822078\pi$
$930$		0			0
$931$	−1.24873	+	23.4181i	−0.0409256	+	0.767497i
$932$		0			0
$933$	0.296108	−	20.4360i	0.00969414	−	0.669046i
$934$		0			0
$935$	−35.2876	+	20.3733i	−1.15403	+	0.666279i
$936$		0			0
$937$			8.33138i			0.272174i	0.990697	+	0.136087i	$0.0434527\pi$
$937$			8.33138i			0.272174i	−0.990697	+	0.136087i	$0.956547\pi$
$938$		0			0
$939$	27.1161	+	0.392898i	0.884899	+	0.0128217i
$940$		0			0
$941$	24.7192			0.805824			0.402912	−	0.915239i	$-0.367998\pi$
$941$	24.7192			0.805824			0.402912	+	0.915239i	$0.367998\pi$
$942$		0			0
$943$			87.2048i			2.83978i
$944$		0			0
$945$	2.74214	−	39.0523i	0.0892017	−	1.27037i
$946$		0			0
$947$			12.1613i			0.395190i	0.980284	+	0.197595i	$0.0633130\pi$
$947$			12.1613i			0.395190i	−0.980284	+	0.197595i	$0.936687\pi$
$948$		0			0
$949$	22.1451			0.718862
$950$		0			0
$951$	28.0801	+	0.406867i	0.910560	+	0.0131936i
$952$		0			0
$953$		−	52.1520i		−	1.68937i	−0.535265	−	0.844684i	$-0.679788\pi$
$953$		−	52.1520i		−	1.68937i	0.535265	−	0.844684i	$-0.320212\pi$
$954$		0			0
$955$	−6.95647	+	4.01632i	−0.225106	+	0.129965i
$956$		0			0
$957$	−0.103186	+	7.12145i	−0.00333554	+	0.230204i
$958$		0			0
$959$	16.9117	−	9.17231i	0.546107	−	0.296189i
$960$		0			0
$961$	15.1097			0.487411
$962$		0			0
$963$	−11.4142	−	7.03860i	−0.367816	−	0.226816i
$964$		0			0
$965$	26.8047	+	46.4271i	0.862873	+	1.49454i
$966$		0			0
$967$	−2.82962	+	4.90104i	−0.0909943	+	0.157607i	−0.907930	−	0.419122i	$-0.862338\pi$
$967$	−2.82962	+	4.90104i	−0.0909943	+	0.157607i	0.816935	+	0.576729i	$0.195671\pi$
$968$		0			0
$969$	33.8826	+	0.490943i	1.08847	+	0.0157713i
$970$		0			0
$971$	4.02185	−	6.96605i	0.129067	−	0.223551i	−0.794248	−	0.607593i	$-0.792135\pi$
$971$	4.02185	−	6.96605i	0.129067	−	0.223551i	0.923315	+	0.384042i	$0.125468\pi$
$972$		0			0
$973$	32.2286	−	17.4796i	1.03320	−	0.560371i
$974$		0			0
$975$	9.27543	+	16.6169i	0.297052	+	0.532168i
$976$		0			0
$977$			31.1959i			0.998045i	0.866589	+	0.499022i	$0.166307\pi$
$977$			31.1959i			0.998045i	−0.866589	+	0.499022i	$0.833693\pi$
$978$		0			0
$979$	29.9506	−	17.2920i	0.957226	−	0.552655i
$980$		0			0
$981$	−11.4237	−	21.1810i	−0.364732	−	0.676257i
$982$		0			0
$983$	13.0016	−	22.5195i	0.414688	−	0.718261i	−0.580708	−	0.814112i	$-0.697224\pi$
$983$	13.0016	−	22.5195i	0.414688	−	0.718261i	0.995396	+	0.0958515i	$0.0305574\pi$
$984$		0			0
$985$	1.13546	−	0.655557i	0.0361787	−	0.0208878i
$986$		0			0
$987$	−25.6613	−	16.2577i	−0.816809	−	0.517489i
$988$		0			0
$989$	−45.5140	−	26.2775i	−1.44726	−	0.835576i
$990$		0			0
$991$	8.39386	+	14.5386i	0.266640	+	0.461834i	0.967992	−	0.250981i	$-0.0807533\pi$
$991$	8.39386	+	14.5386i	0.266640	+	0.461834i	−0.701352	+	0.712815i	$0.747420\pi$
$992$		0			0
$993$	−0.683929	+	47.2017i	−0.0217038	+	1.49790i
$994$		0			0
$995$	51.8436	+	29.9319i	1.64355	+	0.948905i
$996$		0			0
$997$	−17.2490	−	9.95871i	−0.546281	−	0.315396i	0.201339	−	0.979522i	$-0.435471\pi$
$997$	−17.2490	−	9.95871i	−0.546281	−	0.315396i	−0.747621	+	0.664126i	$0.768804\pi$
$998$		0			0
$999$	35.7619	+	22.7744i	1.13146	+	0.720551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.257.12	✓	48
3.2	odd	2		1512.2.bs.a.1097.21		48
4.3	odd	2		1008.2.ca.e.257.13		48
7.3	odd	6		504.2.cx.a.185.20	yes	48
9.2	odd	6		504.2.cx.a.425.20	yes	48
9.7	even	3		1512.2.cx.a.89.21		48
12.11	even	2		3024.2.ca.e.2609.21		48
21.17	even	6		1512.2.cx.a.17.21		48
28.3	even	6		1008.2.df.e.689.5		48
36.7	odd	6		3024.2.df.e.1601.21		48
36.11	even	6		1008.2.df.e.929.5		48
63.38	even	6	inner	504.2.bs.a.353.12	yes	48
63.52	odd	6		1512.2.bs.a.521.21		48
84.59	odd	6		3024.2.df.e.17.21		48
252.115	even	6		3024.2.ca.e.2033.21		48
252.227	odd	6		1008.2.ca.e.353.13		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.12	✓	48	1.1	even	1	trivial
504.2.bs.a.353.12	yes	48	63.38	even	6	inner
504.2.cx.a.185.20	yes	48	7.3	odd	6
504.2.cx.a.425.20	yes	48	9.2	odd	6
1008.2.ca.e.257.13		48	4.3	odd	2
1008.2.ca.e.353.13		48	252.227	odd	6
1008.2.df.e.689.5		48	28.3	even	6
1008.2.df.e.929.5		48	36.11	even	6
1512.2.bs.a.521.21		48	63.52	odd	6
1512.2.bs.a.1097.21		48	3.2	odd	2
1512.2.cx.a.17.21		48	21.17	even	6
1512.2.cx.a.89.21		48	9.7	even	3
3024.2.ca.e.2033.21		48	252.115	even	6
3024.2.ca.e.2609.21		48	12.11	even	2
3024.2.df.e.17.21		48	84.59	odd	6
3024.2.df.e.1601.21		48	36.7	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.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0250939 - 1.73187i) q^{3} +(-1.42382 - 2.46612i) q^{5} +(1.38343 - 2.25524i) q^{7} +(-2.99874 - 0.0869188i) q^{9} +O(q^{10})\)	\(q+(0.0250939 - 1.73187i) q^{3} +(-1.42382 - 2.46612i) q^{5} +(1.38343 - 2.25524i) q^{7} +(-2.99874 - 0.0869188i) q^{9} +(2.12201 + 1.22514i) q^{11} +(3.06053 + 1.76700i) q^{13} +(-4.30673 + 2.40398i) q^{15} +(-2.91986 - 5.05735i) q^{17} +(-2.90135 - 1.67510i) q^{19} +(-3.87107 - 2.45251i) q^{21} +(-6.94378 + 4.00899i) q^{23} +(-1.55450 + 2.69248i) q^{25} +(-0.225782 + 5.19124i) q^{27} +(-1.45334 + 0.839088i) q^{29} +3.98626i q^{31} +(2.17503 - 3.64429i) q^{33} +(-7.53145 - 0.200659i) q^{35} +(4.07975 - 7.06633i) q^{37} +(3.13701 - 5.25609i) q^{39} +(5.43807 - 9.41902i) q^{41} +(3.27732 + 5.67649i) q^{43} +(4.05530 + 7.51902i) q^{45} +6.62900 q^{47} +(-3.17224 - 6.23994i) q^{49} +(-8.83193 + 4.92991i) q^{51} +(-7.64443 + 4.41352i) q^{53} -6.97750i q^{55} +(-2.97386 + 4.98273i) q^{57} -0.356828 q^{59} +2.91251i q^{61} +(-4.34457 + 6.64264i) q^{63} -10.0635i q^{65} +14.2970 q^{67} +(6.76880 + 12.1263i) q^{69} -9.96779i q^{71} +(5.42680 - 3.13316i) q^{73} +(4.62402 + 2.75976i) q^{75} +(5.69864 - 3.09074i) q^{77} -11.5011 q^{79} +(8.98489 + 0.521294i) q^{81} +(-0.189004 - 0.327365i) q^{83} +(-8.31469 + 14.4015i) q^{85} +(1.41672 + 2.53806i) q^{87} +(7.05715 - 12.2233i) q^{89} +(8.21903 - 4.45771i) q^{91} +(6.90368 + 0.100031i) q^{93} +9.54013i q^{95} +(4.00681 - 2.31334i) q^{97} +(-6.25686 - 3.85832i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

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