LMFDB - Embedded newform 644.2.bc.a.493.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,2,Mod(5,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 3]))

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

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

chi := DirichletCharacter("644.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	644.bc (of order $66$, degree $20$, 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:	$5.14236589017$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.14
Character	$\chi$	$=$	644.493
Dual form			644.2.bc.a.145.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.07703 + 2.08915i) q^{3} +(-1.91113 + 0.182491i) q^{5} +(-1.59718 - 2.10927i) q^{7} +(-1.46438 + 2.05643i) q^{9} +O(q^{10})$	\(q+(1.07703 + 2.08915i) q^{3} +(-1.91113 + 0.182491i) q^{5} +(-1.59718 - 2.10927i) q^{7} +(-1.46438 + 2.05643i) q^{9} +(-4.49309 + 1.55507i) q^{11} +(0.745327 + 2.53835i) q^{13} +(-2.43960 - 3.79609i) q^{15} +(-5.84573 - 2.34028i) q^{17} +(-0.322718 + 0.129197i) q^{19} +(2.68637 - 5.60850i) q^{21} +(-4.23139 + 2.25728i) q^{23} +(-1.29052 + 0.248728i) q^{25} +(1.10615 + 0.159040i) q^{27} +(1.32351 + 9.20518i) q^{29} +(1.67513 - 0.0797961i) q^{31} +(-8.08798 - 7.71187i) q^{33} +(3.43734 + 3.73962i) q^{35} +(-2.79728 - 1.99193i) q^{37} +(-4.50025 + 4.29098i) q^{39} +(-5.04246 - 2.30282i) q^{41} +(6.29938 - 9.80202i) q^{43} +(2.42334 - 4.19735i) q^{45} +(10.3462 - 5.97339i) q^{47} +(-1.89805 + 6.73776i) q^{49} +(-1.40685 - 14.7332i) q^{51} +(5.62487 + 5.89919i) q^{53} +(8.30310 - 3.79190i) q^{55} +(-0.617489 - 0.535058i) q^{57} +(-12.5129 - 3.03561i) q^{59} +(5.30756 + 2.73624i) q^{61} +(6.67645 - 0.195716i) q^{63} +(-1.88764 - 4.71510i) q^{65} +(1.42074 + 7.37151i) q^{67} +(-9.27314 - 6.40885i) q^{69} +(2.28796 + 2.64045i) q^{71} +(-3.04438 + 3.87124i) q^{73} +(-1.90957 - 2.42821i) q^{75} +(10.4563 + 6.99341i) q^{77} +(-3.95083 + 4.14351i) q^{79} +(3.33619 + 9.63930i) q^{81} +(-1.09746 - 2.40310i) q^{83} +(11.5990 + 3.40578i) q^{85} +(-17.8055 + 12.6793i) q^{87} +(0.0201083 - 0.422126i) q^{89} +(4.16365 - 5.62629i) q^{91} +(1.97087 + 3.41365i) q^{93} +(0.593180 - 0.305805i) q^{95} +(-5.36173 + 11.7406i) q^{97} +(3.38168 - 11.5170i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 20 q^{9}+O(q^{10}) $ 320 * q - 20 * q^9	$ 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) $ 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.07703	+	2.08915i	0.621825	+	1.20617i	0.963841	+	0.266478i	$0.0858598\pi$
$3$	1.07703	+	2.08915i	0.621825	+	1.20617i	−0.342017	+	0.939694i	$0.611110\pi$
$4$		0			0
$5$	−1.91113	+	0.182491i	−0.854684	+	0.0816124i	−0.513194	−	0.858273i	$-0.671538\pi$
$5$	−1.91113	+	0.182491i	−0.854684	+	0.0816124i	−0.341490	+	0.939885i	$0.610932\pi$
$6$		0			0
$7$	−1.59718	−	2.10927i	−0.603676	−	0.797229i
$7$	−1.59718	−	2.10927i	−0.603676	−	0.797229i
$8$		0			0
$9$	−1.46438	+	2.05643i	−0.488127	+	0.685478i
$10$		0			0
$11$	−4.49309	+	1.55507i	−1.35472	+	0.468872i	−0.905423	−	0.424512i	$-0.860446\pi$
$11$	−4.49309	+	1.55507i	−1.35472	+	0.468872i	−0.449295	+	0.893384i	$0.648325\pi$
$12$		0			0
$13$	0.745327	+	2.53835i	0.206716	+	0.704011i	0.995949	+	0.0899174i	$0.0286603\pi$
$13$	0.745327	+	2.53835i	0.206716	+	0.704011i	−0.789233	+	0.614094i	$0.789522\pi$
$14$		0			0
$15$	−2.43960	−	3.79609i	−0.629902	−	0.980147i
$16$		0			0
$17$	−5.84573	−	2.34028i	−1.41780	−	0.567600i	−0.468918	−	0.883242i	$-0.655356\pi$
$17$	−5.84573	−	2.34028i	−1.41780	−	0.567600i	−0.948879	+	0.315641i	$0.897780\pi$
$18$		0			0
$19$	−0.322718	+	0.129197i	−0.0740366	+	0.0296398i	−0.408385	−	0.912810i	$-0.633908\pi$
$19$	−0.322718	+	0.129197i	−0.0740366	+	0.0296398i	0.334349	+	0.942449i	$0.391484\pi$
$20$		0			0
$21$	2.68637	−	5.60850i	0.586215	−	1.22387i
$22$		0			0
$23$	−4.23139	+	2.25728i	−0.882306	+	0.470676i
$23$	−4.23139	+	2.25728i	−0.882306	+	0.470676i
$24$		0			0
$25$	−1.29052	+	0.248728i	−0.258105	+	0.0497456i
$26$		0			0
$27$	1.10615	+	0.159040i	0.212878	+	0.0306073i
$28$		0			0
$29$	1.32351	+	9.20518i	0.245769	+	1.70936i	0.622153	+	0.782896i	$0.286258\pi$
$29$	1.32351	+	9.20518i	0.245769	+	1.70936i	−0.376384	+	0.926464i	$0.622833\pi$
$30$		0			0
$31$	1.67513	−	0.0797961i	0.300862	−	0.0143318i	0.103392	−	0.994641i	$-0.467031\pi$
$31$	1.67513	−	0.0797961i	0.300862	−	0.0143318i	0.197470	+	0.980309i	$0.436727\pi$
$32$		0			0
$33$	−8.08798	−	7.71187i	−1.40794	−	1.34246i
$34$		0			0
$35$	3.43734	+	3.73962i	0.581016	+	0.632112i
$36$		0			0
$37$	−2.79728	−	1.99193i	−0.459869	−	0.327471i	0.326533	−	0.945186i	$-0.394119\pi$
$37$	−2.79728	−	1.99193i	−0.459869	−	0.327471i	−0.786403	+	0.617714i	$0.788059\pi$
$38$		0			0
$39$	−4.50025	+	4.29098i	−0.720617	+	0.687107i
$40$		0			0
$41$	−5.04246	−	2.30282i	−0.787500	−	0.359639i	−0.0192712	−	0.999814i	$-0.506135\pi$
$41$	−5.04246	−	2.30282i	−0.787500	−	0.359639i	−0.768229	+	0.640175i	$0.778862\pi$
$42$		0			0
$43$	6.29938	−	9.80202i	0.960646	−	1.49479i	0.0941816	−	0.995555i	$-0.469977\pi$
$43$	6.29938	−	9.80202i	0.960646	−	1.49479i	0.866464	−	0.499239i	$-0.166387\pi$
$44$		0			0
$45$	2.42334	−	4.19735i	0.361251	−	0.625704i
$46$		0			0
$47$	10.3462	−	5.97339i	1.50915	−	0.871308i	0.509207	−	0.860644i	$-0.329939\pi$
$47$	10.3462	−	5.97339i	1.50915	−	0.871308i	0.999943	−	0.0106642i	$-0.00339458\pi$
$48$		0			0
$49$	−1.89805	+	6.73776i	−0.271150	+	0.962537i
$50$		0			0
$51$	−1.40685	−	14.7332i	−0.196998	−	2.06305i
$52$		0			0
$53$	5.62487	+	5.89919i	0.772635	+	0.810316i	0.986016	−	0.166653i	$-0.0532959\pi$
$53$	5.62487	+	5.89919i	0.772635	+	0.810316i	−0.213381	+	0.976969i	$0.568447\pi$
$54$		0			0
$55$	8.30310	−	3.79190i	1.11959	−	0.511299i
$56$		0			0
$57$	−0.617489	−	0.535058i	−0.0817885	−	0.0708701i
$58$		0			0
$59$	−12.5129	−	3.03561i	−1.62905	−	0.395202i	−0.685931	−	0.727667i	$-0.740605\pi$
$59$	−12.5129	−	3.03561i	−1.62905	−	0.395202i	−0.943116	+	0.332464i	$0.892120\pi$
$60$		0			0
$61$	5.30756	+	2.73624i	0.679564	+	0.350339i	0.763205	−	0.646156i	$-0.223625\pi$
$61$	5.30756	+	2.73624i	0.679564	+	0.350339i	−0.0836412	+	0.996496i	$0.526655\pi$
$62$		0			0
$63$	6.67645	−	0.195716i	0.841154	−	0.0246579i
$64$		0			0
$65$	−1.88764	−	4.71510i	−0.234133	−	0.584837i
$66$		0			0
$67$	1.42074	+	7.37151i	0.173571	+	0.900573i	0.959383	+	0.282107i	$0.0910334\pi$
$67$	1.42074	+	7.37151i	0.173571	+	0.900573i	−0.785812	+	0.618466i	$0.787754\pi$
$68$		0			0
$69$	−9.27314	−	6.40885i	−1.11636	−	0.771535i
$70$		0			0
$71$	2.28796	+	2.64045i	0.271531	+	0.313364i	0.875095	−	0.483951i	$-0.160799\pi$
$71$	2.28796	+	2.64045i	0.271531	+	0.313364i	−0.603564	+	0.797315i	$0.706253\pi$
$72$		0			0
$73$	−3.04438	+	3.87124i	−0.356318	+	0.453095i	−0.930858	−	0.365382i	$-0.880939\pi$
$73$	−3.04438	+	3.87124i	−0.356318	+	0.453095i	0.574540	+	0.818476i	$0.305181\pi$
$74$		0			0
$75$	−1.90957	−	2.42821i	−0.220498	−	0.280385i
$76$		0			0
$77$	10.4563	+	6.99341i	1.19161	+	0.796973i
$78$		0			0
$79$	−3.95083	+	4.14351i	−0.444503	+	0.466182i	−0.907423	−	0.420219i	$-0.861953\pi$
$79$	−3.95083	+	4.14351i	−0.444503	+	0.466182i	0.462920	+	0.886400i	$0.346802\pi$
$80$		0			0
$81$	3.33619	+	9.63930i	0.370688	+	1.07103i
$82$		0			0
$83$	−1.09746	−	2.40310i	−0.120462	−	0.263774i	0.839789	−	0.542913i	$-0.182679\pi$
$83$	−1.09746	−	2.40310i	−0.120462	−	0.263774i	−0.960251	+	0.279138i	$0.909951\pi$
$84$		0			0
$85$	11.5990	+	3.40578i	1.25809	+	0.369409i
$86$		0			0
$87$	−17.8055	+	12.6793i	−1.90896	+	1.35936i
$88$		0			0
$89$	0.0201083	−	0.422126i	0.00213148	−	0.0447453i	−0.997551	−	0.0699426i	$-0.977718\pi$
$89$	0.0201083	−	0.422126i	0.00213148	−	0.0447453i	0.999682	+	0.0251973i	$0.00802141\pi$
$90$		0			0
$91$	4.16365	−	5.62629i	0.436469	−	0.589796i
$92$		0			0
$93$	1.97087	+	3.41365i	0.204370	+	0.353979i
$94$		0			0
$95$	0.593180	−	0.305805i	0.0608589	−	0.0313750i
$96$		0			0
$97$	−5.36173	+	11.7406i	−0.544401	+	1.19207i	0.414947	+	0.909846i	$0.363800\pi$
$97$	−5.36173	+	11.7406i	−0.544401	+	1.19207i	−0.959348	+	0.282227i	$0.908927\pi$
$98$		0			0
$99$	3.38168	−	11.5170i	0.339872	−	1.15750i
$100$		0			0
$101$	0.890774	−	9.32860i	0.0886353	−	0.928231i	−0.836342	−	0.548208i	$-0.815310\pi$
$101$	0.890774	−	9.32860i	0.0886353	−	0.928231i	0.924977	−	0.380023i	$-0.124084\pi$
$102$		0			0
$103$	5.45257	+	1.05090i	0.537258	+	0.103548i	0.450661	−	0.892695i	$-0.351188\pi$
$103$	5.45257	+	1.05090i	0.537258	+	0.103548i	0.0865974	+	0.996243i	$0.472401\pi$
$104$		0			0
$105$	−4.11051	+	11.2088i	−0.401145	+	1.09387i
$106$		0			0
$107$	−4.45703	+	8.64543i	−0.430877	+	0.835785i	0.569032	+	0.822315i	$0.307318\pi$
$107$	−4.45703	+	8.64543i	−0.430877	+	0.835785i	−0.999909	+	0.0134700i	$0.995712\pi$
$108$		0			0
$109$	−4.03871	+	10.0882i	−0.386838	+	0.966274i	0.599327	+	0.800505i	$0.295435\pi$
$109$	−4.03871	+	10.0882i	−0.386838	+	0.966274i	−0.986164	+	0.165770i	$0.946989\pi$
$110$		0			0
$111$	1.14869	−	7.98930i	0.109029	−	0.758311i
$112$		0			0
$113$	−3.62691	+	3.14274i	−0.341191	+	0.295644i	−0.808554	−	0.588422i	$-0.799749\pi$
$113$	−3.62691	+	3.14274i	−0.341191	+	0.295644i	0.467363	+	0.884065i	$0.345204\pi$
$114$		0			0
$115$	7.67481	−	5.08615i	0.715680	−	0.474286i
$116$		0			0
$117$	−6.31139	−	2.18439i	−0.583488	−	0.201947i
$118$		0			0
$119$	4.40039	+	16.0681i	0.403383	+	1.47296i
$120$		0			0
$121$	9.12301	−	7.17441i	0.829364	−	0.652219i
$122$		0			0
$123$	−0.619965	−	13.0147i	−0.0559004	−	1.17349i
$124$		0			0
$125$	11.6313	−	3.41525i	1.04033	−	0.305469i
$126$		0			0
$127$	−13.2110	+	15.2463i	−1.17228	+	1.35289i	−0.249121	+	0.968472i	$0.580142\pi$
$127$	−13.2110	+	15.2463i	−1.17228	+	1.35289i	−0.923161	+	0.384414i	$0.874404\pi$
$128$		0			0
$129$	27.2625	+	2.60326i	2.40033	+	0.229204i
$130$		0			0
$131$	−17.5306	+	4.25288i	−1.53166	+	0.371576i	−0.910967	−	0.412480i	$-0.864663\pi$
$131$	−17.5306	+	4.25288i	−1.53166	+	0.371576i	−0.620690	+	0.784056i	$0.713148\pi$
$132$		0			0
$133$	0.787950	+	0.474350i	0.0683239	+	0.0411313i
$134$		0			0
$135$	−2.14302	−	0.102085i	−0.184442	−	0.00878604i
$136$		0			0
$137$	−3.27808	−	1.89260i	−0.280065	−	0.161696i	0.353388	−	0.935477i	$-0.385030\pi$
$137$	−3.27808	−	1.89260i	−0.280065	−	0.161696i	−0.633453	+	0.773781i	$0.718363\pi$
$138$		0			0
$139$		−	20.3100i		−	1.72267i	−0.508034	−	0.861337i	$-0.669628\pi$
$139$		−	20.3100i		−	1.72267i	0.508034	−	0.861337i	$-0.330372\pi$
$140$		0			0
$141$	23.6225	+	15.1813i	1.98937	+	1.27849i
$142$		0			0
$143$	−7.29614	−	10.2460i	−0.610134	−	0.856813i
$144$		0			0
$145$	−4.20925	−	17.3508i	−0.349560	−	1.44090i
$146$		0			0
$147$	−16.1205	+	3.29148i	−1.32959	+	0.271476i
$148$		0			0
$149$	−2.30100	+	11.9387i	−0.188506	+	0.978060i	0.757236	+	0.653141i	$0.226549\pi$
$149$	−2.30100	+	11.9387i	−0.188506	+	0.978060i	−0.945742	+	0.324919i	$0.894663\pi$
$150$		0			0
$151$	4.19767	−	17.3030i	0.341601	−	1.40810i	−0.499074	−	0.866560i	$-0.666326\pi$
$151$	4.19767	−	17.3030i	0.341601	−	1.40810i	0.840675	−	0.541540i	$-0.182159\pi$
$152$		0			0
$153$	13.3730	−	8.59430i	1.08114	−	0.694808i
$154$		0			0
$155$	−3.18683	+	0.458196i	−0.255972	+	0.0368032i
$156$		0			0
$157$	−0.0946881	−	0.0744635i	−0.00755693	−	0.00594284i	0.614373	−	0.789015i	$-0.289409\pi$
$157$	−0.0946881	−	0.0744635i	−0.00755693	−	0.00594284i	−0.621930	+	0.783073i	$0.713651\pi$
$158$		0			0
$159$	−6.26614	+	18.1048i	−0.496937	+	1.43580i
$160$		0			0
$161$	11.5195	+	5.31987i	0.907864	+	0.419265i
$162$		0			0
$163$	1.74191	−	5.03291i	0.136437	−	0.394208i	−0.855998	−	0.516978i	$-0.827057\pi$
$163$	1.74191	−	5.03291i	0.136437	−	0.394208i	0.992435	+	0.122771i	$0.0391779\pi$
$164$		0			0
$165$	16.8645	+	13.2624i	1.31290	+	1.03248i
$166$		0			0
$167$	3.82446	−	0.549875i	0.295946	−	0.0425506i	0.00725732	−	0.999974i	$-0.497690\pi$
$167$	3.82446	−	0.549875i	0.295946	−	0.0425506i	0.288688	+	0.957423i	$0.406781\pi$
$168$		0			0
$169$	5.04859	−	3.24453i	0.388353	−	0.249579i
$170$		0			0
$171$	0.206897	−	0.852842i	0.0158218	−	0.0652185i
$172$		0			0
$173$	−3.43411	+	17.8179i	−0.261091	+	1.35467i	0.580372	+	0.814352i	$0.302907\pi$
$173$	−3.43411	+	17.8179i	−0.261091	+	1.35467i	−0.841462	+	0.540316i	$0.818305\pi$
$174$		0			0
$175$	2.58583	+	2.32480i	0.195470	+	0.175738i
$176$		0			0
$177$	−7.13500	−	29.4109i	−0.536299	−	2.21066i
$178$		0			0
$179$	8.81521	+	12.3792i	0.658880	+	0.925267i	0.999891	−	0.0147924i	$-0.00470873\pi$
$179$	8.81521	+	12.3792i	0.658880	+	0.925267i	−0.341011	+	0.940059i	$0.610769\pi$
$180$		0			0
$181$	−1.10326	−	0.709024i	−0.0820049	−	0.0527014i	0.498996	−	0.866604i	$-0.333702\pi$
$181$	−1.10326	−	0.709024i	−0.0820049	−	0.0527014i	−0.581001	+	0.813903i	$0.697339\pi$
$182$		0			0
$183$			14.0353i			1.03752i
$184$		0			0
$185$	5.70947	+	3.29636i	0.419769	+	0.242353i
$186$		0			0
$187$	29.9047	+	1.42453i	2.18685	+	0.104172i
$188$		0			0
$189$	−1.43126	−	2.58718i	−0.104109	−	0.188190i
$190$		0			0
$191$	5.26890	−	1.27822i	0.381244	−	0.0924888i	−0.0405569	−	0.999177i	$-0.512913\pi$
$191$	5.26890	−	1.27822i	0.381244	−	0.0924888i	0.421801	+	0.906688i	$0.361398\pi$
$192$		0			0
$193$	2.78531	+	0.265964i	0.200491	+	0.0191445i	0.194818	−	0.980839i	$-0.437588\pi$
$193$	2.78531	+	0.265964i	0.200491	+	0.0191445i	0.00567248	+	0.999984i	$0.498194\pi$
$194$		0			0
$195$	7.81751	−	9.02189i	0.559823	−	0.646071i
$196$		0			0
$197$	9.46901	−	2.78035i	0.674639	−	0.198092i	0.0735711	−	0.997290i	$-0.476560\pi$
$197$	9.46901	−	2.78035i	0.674639	−	0.198092i	0.601068	+	0.799198i	$0.294742\pi$
$198$		0			0
$199$	−0.454057	−	9.53183i	−0.0321872	−	0.675693i	−0.956091	−	0.293069i	$-0.905323\pi$
$199$	−0.454057	−	9.53183i	−0.0321872	−	0.675693i	0.923904	−	0.382624i	$-0.124980\pi$
$200$		0			0
$201$	−13.8700	+	10.9075i	−0.978315	+	0.769355i
$202$		0			0
$203$	17.3023	−	17.4939i	1.21439	−	1.22783i
$204$		0			0
$205$	10.0571	+	3.48078i	0.702415	+	0.243108i
$206$		0			0
$207$	1.55442	−	12.0071i	0.108040	−	0.834551i
$208$		0			0
$209$	1.24909	−	1.08234i	0.0864014	−	0.0748673i
$210$		0			0
$211$	2.48551	−	17.2871i	0.171109	−	1.19009i	−0.705436	−	0.708774i	$-0.749249\pi$
$211$	2.48551	−	17.2871i	0.171109	−	1.19009i	0.876546	−	0.481319i	$-0.159842\pi$
$212$		0			0
$213$	−3.05209	+	7.62375i	−0.209126	+	0.522371i
$214$		0			0
$215$	−10.2502	+	19.8825i	−0.699055	+	1.35598i
$216$		0			0
$217$	−2.84379	−	3.40585i	−0.193049	−	0.231204i
$218$		0			0
$219$	−11.3665	−	2.19071i	−0.768077	−	0.148035i
$220$		0			0
$221$	1.58346	−	16.5828i	0.106515	−	1.11548i
$222$		0			0
$223$	2.75868	−	9.39520i	0.184735	−	0.629149i	−0.814092	−	0.580735i	$-0.802765\pi$
$223$	2.75868	−	9.39520i	0.184735	−	0.629149i	0.998827	−	0.0484141i	$-0.0154167\pi$
$224$		0			0
$225$	1.37832	−	3.01811i	0.0918883	−	0.201207i
$226$		0			0
$227$	−7.54245	+	3.88840i	−0.500610	+	0.258082i	−0.689987	−	0.723822i	$-0.742384\pi$
$227$	−7.54245	+	3.88840i	−0.500610	+	0.258082i	0.189377	+	0.981905i	$0.439353\pi$
$228$		0			0
$229$	−0.273976	−	0.474540i	−0.0181048	−	0.0313585i	0.856831	−	0.515597i	$-0.172430\pi$
$229$	−0.273976	−	0.474540i	−0.0181048	−	0.0313585i	−0.874936	+	0.484239i	$0.839097\pi$
$230$		0			0
$231$	−3.34849	+	29.3770i	−0.220314	+	1.93286i
$232$		0			0
$233$	−0.713124	+	14.9703i	−0.0467183	+	0.980738i	0.846856	+	0.531823i	$0.178493\pi$
$233$	−0.713124	+	14.9703i	−0.0467183	+	0.980738i	−0.893574	+	0.448916i	$0.851810\pi$
$234$		0			0
$235$	−18.6829	+	13.3040i	−1.21874	+	0.867859i
$236$		0			0
$237$	−12.9116	−	3.79119i	−0.838698	−	0.246264i
$238$		0			0
$239$	−7.85179	−	17.1930i	−0.507890	−	1.11212i	−0.973824	−	0.227304i	$-0.927009\pi$
$239$	−7.85179	−	17.1930i	−0.507890	−	1.11212i	0.465934	−	0.884820i	$-0.345719\pi$
$240$		0			0
$241$	−5.97526	−	17.2644i	−0.384900	−	1.11210i	−0.956542	−	0.291593i	$-0.905815\pi$
$241$	−5.97526	−	17.2644i	−0.384900	−	1.11210i	0.571642	−	0.820503i	$-0.306306\pi$
$242$		0			0
$243$	−14.2312	+	14.9253i	−0.912933	+	0.957456i
$244$		0			0
$245$	2.39784	−	13.2231i	0.153192	−	0.844794i
$246$		0			0
$247$	−0.568477	−	0.722878i	−0.0361713	−	0.0459956i
$248$		0			0
$249$	3.83844	−	4.88097i	0.243251	−	0.309319i
$250$		0			0
$251$	−6.30123	−	7.27201i	−0.397730	−	0.459005i	0.521195	−	0.853438i	$-0.325487\pi$
$251$	−6.30123	−	7.27201i	−0.397730	−	0.459005i	−0.918925	+	0.394433i	$0.870941\pi$
$252$		0			0
$253$	15.5018	−	16.7223i	0.974589	−	1.05132i
$254$		0			0
$255$	5.37733	+	27.9003i	0.336742	+	1.74718i
$256$		0			0
$257$	−1.35644	−	3.38823i	−0.0846126	−	0.211352i	0.880027	−	0.474923i	$-0.157524\pi$
$257$	−1.35644	−	3.38823i	−0.0846126	−	0.211352i	−0.964640	+	0.263571i	$0.915100\pi$
$258$		0			0
$259$	0.266224	+	9.08168i	0.0165424	+	0.564308i
$260$		0			0
$261$	−20.8680	−	10.7582i	−1.29169	−	0.665915i
$262$		0			0
$263$	−22.1325	−	5.36928i	−1.36475	−	0.331084i	−0.514511	−	0.857484i	$-0.672026\pi$
$263$	−22.1325	−	5.36928i	−1.36475	−	0.331084i	−0.850237	+	0.526400i	$0.823542\pi$
$264$		0			0
$265$	−11.8264	−	10.2476i	−0.726491	−	0.629508i
$266$		0			0
$267$	0.903542	−	0.412634i	0.0552959	−	0.0252528i
$268$		0			0
$269$	−0.240835	−	0.252581i	−0.0146840	−	0.0154001i	0.716351	−	0.697740i	$-0.245811\pi$
$269$	−0.240835	−	0.252581i	−0.0146840	−	0.0154001i	−0.731035	+	0.682340i	$0.760962\pi$
$270$		0			0
$271$	0.301525	+	3.15771i	0.0183163	+	0.191817i	0.999999	+	0.00129476i	$0.000412136\pi$
$271$	0.301525	+	3.15771i	0.0183163	+	0.191817i	−0.981683	+	0.190522i	$0.938982\pi$
$272$		0			0
$273$	16.2385	+	2.63879i	0.982802	+	0.159707i
$274$		0			0
$275$	5.41165	−	3.12442i	0.326335	−	0.188409i
$276$		0			0
$277$	6.23781	−	10.8042i	0.374794	−	0.649162i	−0.615502	−	0.788135i	$-0.711047\pi$
$277$	6.23781	−	10.8042i	0.374794	−	0.649162i	0.990296	+	0.138973i	$0.0443802\pi$
$278$		0			0
$279$	−2.28893	+	3.56164i	−0.137035	+	0.213230i
$280$		0			0
$281$	−3.05460	−	1.39499i	−0.182222	−	0.0832181i	0.322215	−	0.946667i	$-0.395573\pi$
$281$	−3.05460	−	1.39499i	−0.182222	−	0.0832181i	−0.504437	+	0.863449i	$0.668300\pi$
$282$		0			0
$283$	15.1052	−	14.4027i	0.897908	−	0.856154i	−0.0923030	−	0.995731i	$-0.529423\pi$
$283$	15.1052	−	14.4027i	0.897908	−	0.856154i	0.990211	+	0.139577i	$0.0445744\pi$
$284$		0			0
$285$	1.27775	+	0.909879i	0.0756872	+	0.0538966i
$286$		0			0
$287$	3.19645	+	14.3139i	0.188680	+	0.844924i
$288$		0			0
$289$	16.3921	+	15.6299i	0.964244	+	0.919405i
$290$		0			0
$291$	−30.3025	+	1.44349i	−1.77637	+	0.0846187i
$292$		0			0
$293$	1.95922	+	13.6267i	0.114459	+	0.796080i	0.963491	+	0.267739i	$0.0862765\pi$
$293$	1.95922	+	13.6267i	0.114459	+	0.796080i	−0.849032	+	0.528341i	$0.822814\pi$
$294$		0			0
$295$	24.4679	+	3.51795i	1.42457	+	0.204823i
$296$		0			0
$297$	−5.21734	+	1.00556i	−0.302741	+	0.0583485i
$298$		0			0
$299$	−8.88354	−	9.05834i	−0.513748	−	0.523857i
$300$		0			0
$301$	−30.7363	+	2.36848i	−1.77161	+	0.136517i
$302$		0			0
$303$	20.4482	−	8.18624i	1.17472	−	0.470287i
$304$		0			0
$305$	−10.6428	−	4.26073i	−0.609404	−	0.243969i
$306$		0			0
$307$	3.29330	+	5.12447i	0.187958	+	0.292469i	0.922425	−	0.386175i	$-0.126204\pi$
$307$	3.29330	+	5.12447i	0.187958	+	0.292469i	−0.734467	+	0.678645i	$0.762568\pi$
$308$		0			0
$309$	3.67711	+	12.5231i	0.209184	+	0.712414i
$310$		0			0
$311$	−9.17603	+	3.17586i	−0.520325	+	0.180086i	−0.574592	−	0.818440i	$-0.694839\pi$
$311$	−9.17603	+	3.17586i	−0.520325	+	0.180086i	0.0542666	+	0.998526i	$0.482718\pi$
$312$		0			0
$313$	−17.9668	+	25.2309i	−1.01554	+	1.42613i	−0.113982	+	0.993483i	$0.536361\pi$
$313$	−17.9668	+	25.2309i	−1.01554	+	1.42613i	−0.901562	+	0.432649i	$0.857579\pi$
$314$		0			0
$315$	−12.7239	+	1.59243i	−0.716908	+	0.0897234i
$316$		0			0
$317$	−6.56292	+	0.626683i	−0.368611	+	0.0351980i	−0.277718	−	0.960663i	$-0.589578\pi$
$317$	−6.56292	+	0.626683i	−0.368611	+	0.0351980i	−0.0908926	+	0.995861i	$0.528972\pi$
$318$		0			0
$319$	−20.2614	−	39.3015i	−1.13442	−	2.20046i
$320$		0			0
$321$	−22.8620			−1.27603
$322$		0			0
$323$	2.18888			0.121792
$324$		0			0
$325$	−1.59322	−	3.09042i	−0.0883760	−	0.171425i
$326$		0			0
$327$	−25.4256	+	2.42785i	−1.40604	+	0.134260i
$328$		0			0
$329$	−29.1242	−	12.2824i	−1.60567	−	0.677151i
$330$		0			0
$331$	−3.49569	+	4.90901i	−0.192141	+	0.269824i	−0.899396	−	0.437134i	$-0.855994\pi$
$331$	−3.49569	+	4.90901i	−0.192141	+	0.269824i	0.707256	+	0.706958i	$0.249933\pi$
$332$		0			0
$333$	8.19255	−	2.83547i	0.448949	−	0.155383i
$334$		0			0
$335$	−4.06046	−	13.8286i	−0.221846	−	0.755540i
$336$		0			0
$337$	10.4283	+	16.2268i	0.568067	+	0.883929i	0.999837	−	0.0180546i	$-0.00574727\pi$
$337$	10.4283	+	16.2268i	0.568067	+	0.883929i	−0.431770	+	0.901984i	$0.642111\pi$
$338$		0			0
$339$	−10.4719	−	4.19233i	−0.568758	−	0.227696i
$340$		0			0
$341$	−7.40240	+	2.96348i	−0.400863	+	0.160481i
$342$		0			0
$343$	17.2433	−	6.75790i	0.931050	−	0.364893i
$344$		0			0
$345$	18.8918	+	10.5559i	1.01710	+	0.568310i
$346$		0			0
$347$	−7.18492	+	1.38478i	−0.385707	+	0.0743389i	−0.378419	−	0.925635i	$-0.623532\pi$
$347$	−7.18492	+	1.38478i	−0.385707	+	0.0743389i	−0.00728817	+	0.999973i	$0.502320\pi$
$348$		0			0
$349$	−25.8069	−	3.71046i	−1.38141	−	0.198617i	−0.588766	−	0.808303i	$-0.700386\pi$
$349$	−25.8069	−	3.71046i	−1.38141	−	0.198617i	−0.792643	+	0.609687i	$0.791295\pi$
$350$		0			0
$351$	0.420743	+	2.92633i	0.0224576	+	0.156196i
$352$		0			0
$353$	18.6594	−	0.888855i	0.993137	−	0.0473090i	0.455283	−	0.890347i	$-0.349538\pi$
$353$	18.6594	−	0.888855i	0.993137	−	0.0473090i	0.537854	+	0.843038i	$0.319235\pi$
$354$		0			0
$355$	−4.85446	−	4.62872i	−0.257648	−	0.245667i
$356$		0			0
$357$	−28.8292	+	26.4989i	−1.52580	+	1.40247i
$358$		0			0
$359$	7.79253	+	5.54903i	0.411274	+	0.292867i	0.766906	−	0.641759i	$-0.221795\pi$
$359$	7.79253	+	5.54903i	0.411274	+	0.292867i	−0.355632	+	0.934626i	$0.615734\pi$
$360$		0			0
$361$	−13.6635	+	13.0281i	−0.719131	+	0.685690i
$362$		0			0
$363$	24.8142	+	11.3323i	1.30241	+	0.594789i
$364$		0			0
$365$	5.11174	−	7.95403i	0.267561	−	0.416333i
$366$		0			0
$367$	−8.91845	+	15.4472i	−0.465539	+	0.806338i	−0.999226	−	0.0393447i	$-0.987473\pi$
$367$	−8.91845	+	15.4472i	−0.465539	+	0.806338i	0.533686	+	0.845683i	$0.320806\pi$
$368$		0			0
$369$	12.1197	−	6.99730i	0.630925	−	0.364265i
$370$		0			0
$371$	3.45908	−	21.2864i	0.179586	−	1.10514i
$372$		0			0
$373$	3.23369	+	33.8648i	0.167434	+	1.75345i	0.555221	+	0.831703i	$0.312634\pi$
$373$	3.23369	+	33.8648i	0.167434	+	1.75345i	−0.387787	+	0.921749i	$0.626760\pi$
$374$		0			0
$375$	19.6622	+	20.6211i	1.01535	+	1.06487i
$376$		0			0
$377$	−22.3795	+	10.2204i	−1.15260	+	0.526377i
$378$		0			0
$379$	19.7351	+	17.1006i	1.01373	+	0.878399i	0.992606	−	0.121378i	$-0.0387313\pi$
$379$	19.7351	+	17.1006i	1.01373	+	0.878399i	0.0211200	+	0.999777i	$0.493277\pi$
$380$		0			0
$381$	−46.0803	−	11.1790i	−2.36077	−	0.572716i
$382$		0			0
$383$	−20.0633	−	10.3434i	−1.02519	−	0.528521i	−0.138243	−	0.990398i	$-0.544146\pi$
$383$	−20.0633	−	10.3434i	−1.02519	−	0.528521i	−0.886944	+	0.461878i	$0.847176\pi$
$384$		0			0
$385$	−21.2597	−	11.4571i	−1.08349	−	0.583910i
$386$		0			0
$387$	10.9325	+	27.3081i	0.555732	+	1.38815i
$388$		0			0
$389$	2.43716	+	12.6452i	0.123569	+	0.641137i	0.989912	+	0.141687i	$0.0452525\pi$
$389$	2.43716	+	12.6452i	0.123569	+	0.641137i	−0.866343	+	0.499450i	$0.833535\pi$
$390$		0			0
$391$	30.0182	−	3.29282i	1.51809	−	0.166525i
$392$		0			0
$393$	−27.7659	−	32.0436i	−1.40061	−	1.61639i
$394$		0			0
$395$	6.79440	−	8.63979i	0.341864	−	0.434715i
$396$		0			0
$397$	−7.32784	−	9.31810i	−0.367774	−	0.467662i	0.566581	−	0.824006i	$-0.308266\pi$
$397$	−7.32784	−	9.31810i	−0.367774	−	0.467662i	−0.934355	+	0.356344i	$0.884023\pi$
$398$		0			0
$399$	−0.142341	+	2.15703i	−0.00712597	+	0.107987i
$400$		0			0
$401$	2.01960	−	2.11810i	0.100854	−	0.105773i	−0.671372	−	0.741120i	$-0.734295\pi$
$401$	2.01960	−	2.11810i	0.100854	−	0.105773i	0.772226	+	0.635348i	$0.219143\pi$
$402$		0			0
$403$	1.45107	+	4.19258i	0.0722828	+	0.208847i
$404$		0			0
$405$	−8.13499	−	17.8131i	−0.404231	−	0.885142i
$406$		0			0
$407$	15.6660	+	4.59995i	0.776535	+	0.228011i
$408$		0			0
$409$	0.726045	−	0.517014i	0.0359006	−	0.0255647i	−0.561966	−	0.827160i	$-0.689955\pi$
$409$	0.726045	−	0.517014i	0.0359006	−	0.0255647i	0.597866	+	0.801596i	$0.296015\pi$
$410$		0			0
$411$	0.423330	−	8.88679i	0.0208813	−	0.438353i
$412$		0			0
$413$	13.5825	+	31.2416i	0.668350	+	1.53730i
$414$		0			0
$415$	2.53593	+	4.39236i	0.124484	+	0.215612i
$416$		0			0
$417$	42.4307	−	21.8745i	2.07784	−	1.07120i
$418$		0			0
$419$	0.507565	−	1.11141i	0.0247962	−	0.0542960i	−0.896829	−	0.442378i	$-0.854135\pi$
$419$	0.507565	−	1.11141i	0.0247962	−	0.0542960i	0.921625	+	0.388082i	$0.126862\pi$
$420$		0			0
$421$	10.0468	−	34.2164i	0.489652	−	1.66760i	−0.229939	−	0.973205i	$-0.573853\pi$
$421$	10.0468	−	34.2164i	0.489652	−	1.66760i	0.719591	−	0.694398i	$-0.244329\pi$
$422$		0			0
$423$	−2.86691	+	30.0236i	−0.139394	+	1.45980i
$424$		0			0
$425$	8.12614	+	1.56618i	0.394176	+	0.0759711i
$426$		0			0
$427$	−2.70565	−	15.5653i	−0.130936	−	0.753260i
$428$		0			0
$429$	13.5472	−	26.2780i	0.654067	−	1.26871i
$430$		0			0
$431$	11.6185	−	29.0217i	0.559645	−	1.39793i	−0.331174	−	0.943570i	$-0.607445\pi$
$431$	11.6185	−	29.0217i	0.559645	−	1.39793i	0.890820	−	0.454357i	$-0.150131\pi$
$432$		0			0
$433$	2.38188	−	16.5663i	0.114466	−	0.796127i	−0.849019	−	0.528363i	$-0.822806\pi$
$433$	2.38188	−	16.5663i	0.114466	−	0.796127i	0.963484	−	0.267764i	$-0.0862849\pi$
$434$		0			0
$435$	31.7149	−	27.4811i	1.52061	−	1.31762i
$436$		0			0
$437$	1.07391	−	1.27515i	0.0513723	−	0.0609986i
$438$		0			0
$439$	3.63309	+	1.25743i	0.173398	+	0.0600137i	0.412388	−	0.911008i	$-0.364695\pi$
$439$	3.63309	+	1.25743i	0.173398	+	0.0600137i	−0.238989	+	0.971022i	$0.576816\pi$
$440$		0			0
$441$	−11.0763	−	13.7699i	−0.527443	−	0.655707i
$442$		0			0
$443$	15.5773	−	12.2501i	0.740098	−	0.582020i	−0.175326	−	0.984510i	$-0.556098\pi$
$443$	15.5773	−	12.2501i	0.740098	−	0.582020i	0.915424	+	0.402491i	$0.131855\pi$
$444$		0			0
$445$	0.0386045	+	0.810408i	0.00183003	+	0.0384170i
$446$		0			0
$447$	−27.4201	+	8.05126i	−1.29693	+	0.380812i
$448$		0			0
$449$	−23.5515	+	27.1799i	−1.11146	+	1.28270i	−0.155947	+	0.987765i	$0.549843\pi$
$449$	−23.5515	+	27.1799i	−1.11146	+	1.28270i	−0.955518	+	0.294933i	$0.904703\pi$
$450$		0			0
$451$	26.2373	+	2.50536i	1.23547	+	0.117973i
$452$		0			0
$453$	40.6696	−	9.86634i	1.91083	−	0.463561i
$454$		0			0
$455$	−6.93053	+	11.5124i	−0.324908	+	0.539710i
$456$		0			0
$457$	−9.49691	−	0.452394i	−0.444247	−	0.0211621i	−0.175733	−	0.984438i	$-0.556230\pi$
$457$	−9.49691	−	0.452394i	−0.444247	−	0.0211621i	−0.268514	+	0.963276i	$0.586533\pi$
$458$		0			0
$459$	−6.09404	−	3.51840i	−0.284446	−	0.164225i
$460$		0			0
$461$		−	38.3528i		−	1.78627i	−0.449792	−	0.893133i	$-0.648502\pi$
$461$		−	38.3528i		−	1.78627i	0.449792	−	0.893133i	$-0.351498\pi$
$462$		0			0
$463$	−3.71651	−	2.38846i	−0.172721	−	0.111001i	0.451424	−	0.892310i	$-0.350916\pi$
$463$	−3.71651	−	2.38846i	−0.172721	−	0.111001i	−0.624145	+	0.781309i	$0.714553\pi$
$464$		0			0
$465$	−4.38955	−	6.16427i	−0.203561	−	0.285861i
$466$		0			0
$467$	−2.21939	−	9.14845i	−0.102701	−	0.423340i	0.897129	−	0.441769i	$-0.145649\pi$
$467$	−2.21939	−	9.14845i	−0.102701	−	0.423340i	−0.999830	+	0.0184288i	$0.994134\pi$
$468$		0			0
$469$	13.2793	−	14.7703i	0.613183	−	0.682031i
$470$		0			0
$471$	0.0535834	−	0.278017i	0.00246899	−	0.0128104i
$472$		0			0
$473$	−13.0608	+	53.8373i	−0.600536	+	2.47544i
$474$		0			0
$475$	0.384341	−	0.247001i	0.0176348	−	0.0113332i
$476$		0			0
$477$	−20.3682	+	2.92851i	−0.932598	+	0.134087i
$478$		0			0
$479$	−18.0454	−	14.1911i	−0.824515	−	0.648406i	0.114063	−	0.993474i	$-0.463614\pi$
$479$	−18.0454	−	14.1911i	−0.824515	−	0.648406i	−0.938578	+	0.345068i	$0.887856\pi$
$480$		0			0
$481$	2.97133	−	8.58510i	0.135481	−	0.391447i
$482$		0			0
$483$	1.29285	+	29.7956i	0.0588268	+	1.35575i
$484$		0			0
$485$	8.10443	−	23.4162i	0.368003	−	1.06327i
$486$		0			0
$487$	9.98437	+	7.85180i	0.452435	+	0.355799i	0.818225	−	0.574899i	$-0.194959\pi$
$487$	9.98437	+	7.85180i	0.452435	+	0.355799i	−0.365790	+	0.930698i	$0.619201\pi$
$488$		0			0
$489$	12.3906	−	1.78150i	0.560322	−	0.0805621i
$490$		0			0
$491$	−4.41399	+	2.83670i	−0.199200	+	0.128018i	−0.636438	−	0.771327i	$-0.719593\pi$
$491$	−4.41399	+	2.83670i	−0.199200	+	0.128018i	0.437238	+	0.899346i	$0.355957\pi$
$492$		0			0
$493$	13.8058	−	56.9083i	0.621783	−	2.56302i
$494$		0			0
$495$	−4.36110	+	22.6276i	−0.196017	+	1.01703i
$496$		0			0
$497$	1.91514	−	9.04321i	0.0859059	−	0.405643i
$498$		0			0
$499$	5.63910	+	23.2447i	0.252441	+	1.04058i	0.947024	+	0.321163i	$0.104074\pi$
$499$	5.63910	+	23.2447i	0.252441	+	1.04058i	−0.694583	+	0.719413i	$0.744411\pi$
$500$		0			0
$501$	5.26784	+	7.39764i	0.235350	+	0.330502i
$502$		0			0
$503$	30.6615	+	19.7049i	1.36713	+	0.878600i	0.998696	−	0.0510552i	$-0.0162584\pi$
$503$	30.6615	+	19.7049i	1.36713	+	0.878600i	0.368432	+	0.929655i	$0.379895\pi$
$504$		0			0
$505$			17.9907i			0.800578i
$506$		0			0
$507$	12.2158	+	7.05280i	0.542523	+	0.313226i
$508$		0			0
$509$	9.92210	+	0.472648i	0.439789	+	0.0209498i	0.266309	−	0.963888i	$-0.414196\pi$
$509$	9.92210	+	0.472648i	0.439789	+	0.0209498i	0.173480	+	0.984837i	$0.444499\pi$
$510$		0			0
$511$	13.0279	+	0.238358i	0.576321	+	0.0105443i
$512$		0			0
$513$	−0.377522	+	0.0915858i	−0.0166680	+	0.00404361i
$514$		0			0
$515$	−10.6124	−	1.01336i	−0.467637	−	0.0446539i
$516$		0			0
$517$	−37.1974	+	42.9281i	−1.63594	+	1.88797i
$518$		0			0
$519$	−40.9229	+	12.0160i	−1.79631	+	0.527445i
$520$		0			0
$521$	0.322878	+	6.77805i	0.0141456	+	0.296952i	0.994843	+	0.101423i	$0.0323394\pi$
$521$	0.322878	+	6.77805i	0.0141456	+	0.296952i	−0.980698	+	0.195529i	$0.937358\pi$
$522$		0			0
$523$	0.419323	−	0.329759i	0.0183357	−	0.0144194i	−0.608949	−	0.793209i	$-0.708409\pi$
$523$	0.419323	−	0.329759i	0.0183357	−	0.0144194i	0.627285	+	0.778790i	$0.284166\pi$
$524$		0			0
$525$	−2.07184	+	7.90607i	−0.0904224	+	0.345049i
$526$		0			0
$527$	−9.97908	−	3.45379i	−0.434695	−	0.150450i
$528$		0			0
$529$	12.8094	−	19.1029i	0.556929	−	0.830560i
$530$		0			0
$531$	24.5662	−	21.2868i	1.06608	−	0.923767i
$532$		0			0
$533$	2.08707	−	14.5159i	0.0904010	−	0.628753i
$534$		0			0
$535$	6.94026	−	17.3359i	0.300053	−	0.749497i
$536$		0			0
$537$	−16.3678	+	31.7491i	−0.706323	+	1.37008i
$538$		0			0
$539$	−1.94961	−	33.2250i	−0.0839759	−	1.43110i
$540$		0			0
$541$	−24.8654	−	4.79241i	−1.06905	−	0.206042i	−0.375769	−	0.926713i	$-0.622621\pi$
$541$	−24.8654	−	4.79241i	−1.06905	−	0.206042i	−0.693277	+	0.720672i	$0.743834\pi$
$542$		0			0
$543$	0.293009	−	3.06853i	0.0125742	−	0.131683i
$544$		0			0
$545$	5.87749	−	20.0169i	0.251764	−	0.857430i
$546$		0			0
$547$	9.48409	−	20.7673i	0.405510	−	0.887944i	−0.591171	−	0.806546i	$-0.701334\pi$
$547$	9.48409	−	20.7673i	0.405510	−	0.887944i	0.996682	−	0.0813979i	$-0.0259385\pi$
$548$		0			0
$549$	−13.3992	+	6.90776i	−0.571863	+	0.294816i
$550$		0			0
$551$	−1.61640	−	2.79969i	−0.0688610	−	0.119271i
$552$		0			0
$553$	15.0500	+	1.71545i	0.639990	+	0.0729483i
$554$		0			0
$555$	−0.737319	+	15.4782i	−0.0312974	+	0.657014i
$556$		0			0
$557$	13.5166	−	9.62511i	0.572715	−	0.407829i	−0.256675	−	0.966498i	$-0.582627\pi$
$557$	13.5166	−	9.62511i	0.572715	−	0.407829i	0.829391	+	0.558669i	$0.188688\pi$
$558$		0			0
$559$	29.5760	+	8.68431i	1.25093	+	0.367307i
$560$		0			0
$561$	29.2322	+	64.0096i	1.23418	+	2.70249i
$562$		0			0
$563$	8.39166	+	24.2461i	0.353666	+	1.02185i	0.971806	+	0.235783i	$0.0757655\pi$
$563$	8.39166	+	24.2461i	0.353666	+	1.02185i	−0.618139	+	0.786068i	$0.712113\pi$
$564$		0			0
$565$	6.35798	−	6.66806i	0.267482	−	0.280527i
$566$		0			0
$567$	15.0034	−	22.4326i	0.630083	−	0.942081i
$568$		0			0
$569$	−23.7990	−	30.2629i	−0.997706	−	1.26869i	−0.963060	−	0.269287i	$-0.913212\pi$
$569$	−23.7990	−	30.2629i	−0.997706	−	1.26869i	−0.0346461	−	0.999400i	$-0.511030\pi$
$570$		0			0
$571$	−28.7761	+	36.5918i	−1.20424	+	1.53132i	−0.424229	+	0.905555i	$0.639455\pi$
$571$	−28.7761	+	36.5918i	−1.20424	+	1.53132i	−0.780013	+	0.625763i	$0.784788\pi$
$572$		0			0
$573$	8.34517	+	9.63084i	0.348624	+	0.402334i
$574$		0			0
$575$	4.89926	−	3.96554i	0.204313	−	0.165374i
$576$		0			0
$577$	−0.879750	−	4.56458i	−0.0366245	−	0.190026i	0.959009	−	0.283376i	$-0.0914545\pi$
$577$	−0.879750	−	4.56458i	−0.0366245	−	0.190026i	−0.995633	+	0.0933503i	$0.970242\pi$
$578$		0			0
$579$	2.44422	+	6.10537i	0.101578	+	0.253731i
$580$		0			0
$581$	−3.31595	+	6.15301i	−0.137569	+	0.255270i
$582$		0			0
$583$	−34.4467	−	17.7585i	−1.42664	−	0.735482i
$584$		0			0
$585$	12.4605	+	3.02289i	0.515180	+	0.124981i
$586$		0			0
$587$	13.5889	+	11.7748i	0.560873	+	0.485999i	0.888543	−	0.458793i	$-0.151718\pi$
$587$	13.5889	+	11.7748i	0.560873	+	0.485999i	−0.327670	+	0.944792i	$0.606264\pi$
$588$		0			0
$589$	−0.530285	+	0.242173i	−0.0218500	+	0.00997856i
$590$		0			0
$591$	16.0070	+	16.7876i	0.658440	+	0.690552i
$592$		0			0
$593$	−0.678123	−	7.10162i	−0.0278472	−	0.291629i	−0.998658	−	0.0517836i	$-0.983509\pi$
$593$	−0.678123	−	7.10162i	−0.0278472	−	0.291629i	0.970811	−	0.239845i	$-0.0770967\pi$
$594$		0			0
$595$	−11.3420	−	29.9051i	−0.464976	−	1.22599i
$596$		0			0
$597$	19.4244	−	11.2147i	0.794987	−	0.458986i
$598$		0			0
$599$	−11.0655	+	19.1660i	−0.452125	+	0.783103i	−0.998518	−	0.0544257i	$-0.982667\pi$
$599$	−11.0655	+	19.1660i	−0.452125	+	0.783103i	0.546393	+	0.837529i	$0.316001\pi$
$600$		0			0
$601$	−10.1004	+	15.7166i	−0.412006	+	0.641093i	−0.983793	−	0.179309i	$-0.942614\pi$
$601$	−10.1004	+	15.7166i	−0.412006	+	0.641093i	0.571787	+	0.820402i	$0.306250\pi$
$602$		0			0
$603$	−17.2395	−	7.87303i	−0.702048	−	0.320615i
$604$		0			0
$605$	−16.1260	+	15.3761i	−0.655615	+	0.625128i
$606$		0			0
$607$	34.1569	+	24.3230i	1.38639	+	0.987242i	0.997832	+	0.0658162i	$0.0209651\pi$
$607$	34.1569	+	24.3230i	1.38639	+	0.987242i	0.388555	+	0.921425i	$0.372974\pi$
$608$		0			0
$609$	55.1827	+	17.3057i	2.23611	+	0.701261i
$610$		0			0
$611$	22.8739	+	21.8102i	0.925377	+	0.882345i
$612$		0			0
$613$	−26.2366	+	1.24981i	−1.05969	+	0.0504792i	−0.570180	−	0.821520i	$-0.693127\pi$
$613$	−26.2366	+	1.24981i	−1.05969	+	0.0504792i	−0.489508	+	0.871999i	$0.662824\pi$
$614$		0			0
$615$	3.55989	+	24.7596i	0.143549	+	0.998404i
$616$		0			0
$617$	14.7000	+	2.11355i	0.591801	+	0.0850882i	0.431707	−	0.902014i	$-0.357911\pi$
$617$	14.7000	+	2.11355i	0.591801	+	0.0850882i	0.160094	+	0.987102i	$0.448820\pi$
$618$		0			0
$619$	−41.3287	+	7.96546i	−1.66114	+	0.320159i	−0.931520	−	0.363691i	$-0.881516\pi$
$619$	−41.3287	+	7.96546i	−1.66114	+	0.320159i	−0.729623	+	0.683850i	$0.760304\pi$
$620$		0			0
$621$	−5.03955	+	1.82393i	−0.202230	+	0.0731917i
$622$		0			0
$623$	−0.922495	+	0.631796i	−0.0369590	+	0.0253124i
$624$		0			0
$625$	−15.5050	+	6.20725i	−0.620199	+	0.248290i
$626$		0			0
$627$	3.60649	+	1.44382i	0.144029	+	0.0576606i
$628$		0			0
$629$	11.6904	+	18.1907i	0.466128	+	0.725310i
$630$		0			0
$631$	4.94996	+	16.8580i	0.197055	+	0.671107i	0.997433	+	0.0716111i	$0.0228141\pi$
$631$	4.94996	+	16.8580i	0.197055	+	0.671107i	−0.800378	+	0.599496i	$0.795368\pi$
$632$		0			0
$633$	38.7923	−	13.4261i	1.54186	−	0.533641i
$634$		0			0
$635$	22.4656	−	31.5485i	0.891519	−	1.25196i
$636$		0			0
$637$	−18.5175	+	0.203925i	−0.733688	+	0.00807980i
$638$		0			0
$639$	−8.78037	+	0.838423i	−0.347346	+	0.0331675i
$640$		0			0
$641$	17.4019	+	33.7550i	0.687334	+	1.33324i	0.931583	+	0.363530i	$0.118428\pi$
$641$	17.4019	+	33.7550i	0.687334	+	1.33324i	−0.244248	+	0.969713i	$0.578541\pi$
$642$		0			0
$643$	19.6796			0.776088			0.388044	−	0.921641i	$-0.373151\pi$
$643$	19.6796			0.776088			0.388044	+	0.921641i	$0.373151\pi$
$644$		0			0
$645$	−52.5773			−2.07023
$646$		0			0
$647$	15.7094	+	30.4720i	0.617600	+	1.19798i	0.965490	+	0.260441i	$0.0838680\pi$
$647$	15.7094	+	30.4720i	0.617600	+	1.19798i	−0.347890	+	0.937535i	$0.613102\pi$
$648$		0			0
$649$	60.9424	−	5.81929i	2.39220	−	0.228427i
$650$		0			0
$651$	4.05248	−	9.60930i	0.158829	−	0.376618i
$652$		0			0
$653$	3.39534	−	4.76808i	0.132870	−	0.186590i	−0.742781	−	0.669535i	$-0.766494\pi$
$653$	3.39534	−	4.76808i	0.132870	−	0.186590i	0.875651	+	0.482945i	$0.160433\pi$
$654$		0			0
$655$	32.7272	−	11.3270i	1.27876	−	0.442582i
$656$		0			0
$657$	−3.50283	−	11.9295i	−0.136658	−	0.465416i
$658$		0			0
$659$	−14.9121	−	23.2036i	−0.580892	−	0.903886i	0.419100	−	0.907940i	$-0.362346\pi$
$659$	−14.9121	−	23.2036i	−0.580892	−	0.903886i	−0.999992	+	0.00405459i	$0.998709\pi$
$660$		0			0
$661$	9.16417	+	3.66878i	0.356445	+	0.142699i	0.542972	−	0.839751i	$-0.317299\pi$
$661$	9.16417	+	3.66878i	0.356445	+	0.142699i	−0.186527	+	0.982450i	$0.559723\pi$
$662$		0			0
$663$	36.3493	−	14.5521i	1.41169	−	0.565156i
$664$		0			0
$665$	−1.59244	−	0.762751i	−0.0617522	−	0.0295782i
$666$		0			0
$667$	−26.3790	−	35.9632i	−1.02140	−	1.39250i
$668$		0			0
$669$	22.5992	−	4.35564i	0.873735	−	0.168399i
$670$		0			0
$671$	−28.1024	−	4.04052i	−1.08488	−	0.155982i
$672$		0			0
$673$	−5.27350	−	36.6780i	−0.203279	−	1.41383i	−0.794471	−	0.607303i	$-0.792252\pi$
$673$	−5.27350	−	36.6780i	−0.203279	−	1.41383i	0.591192	−	0.806531i	$-0.298658\pi$
$674$		0			0
$675$	−1.46707	+	0.0698851i	−0.0564675	+	0.00268988i
$676$		0			0
$677$	−8.42686	−	8.03499i	−0.323870	−	0.308810i	0.510648	−	0.859790i	$-0.329406\pi$
$677$	−8.42686	−	8.03499i	−0.323870	−	0.308810i	−0.834518	+	0.550980i	$0.814254\pi$
$678$		0			0
$679$	33.3276	−	7.44240i	1.27900	−	0.285613i
$680$		0			0
$681$	−16.2469	−	11.5694i	−0.622583	−	0.443340i
$682$		0			0
$683$	−17.0242	+	16.2325i	−0.651412	+	0.621120i	−0.941954	−	0.335742i	$-0.891013\pi$
$683$	−17.0242	+	16.2325i	−0.651412	+	0.621120i	0.290542	+	0.956862i	$0.406164\pi$
$684$		0			0
$685$	6.61022	+	3.01879i	0.252564	+	0.115342i
$686$		0			0
$687$	0.696305	−	1.08347i	0.0265657	−	0.0413370i
$688$		0			0
$689$	−10.7818	+	18.6747i	−0.410756	+	0.711450i
$690$		0			0
$691$	−21.2844	+	12.2886i	−0.809698	+	0.467479i	−0.846851	−	0.531831i	$-0.821504\pi$
$691$	−21.2844	+	12.2886i	−0.809698	+	0.467479i	0.0371533	+	0.999310i	$0.488171\pi$
$692$		0			0
$693$	−29.6935	+	11.2617i	−1.12796	+	0.427798i
$694$		0			0
$695$	3.70639	+	38.8151i	0.140592	+	1.47234i
$696$		0			0
$697$	24.0876	+	25.2624i	0.912384	+	0.956881i
$698$		0			0
$699$	−32.0433	+	14.6337i	−1.21199	+	0.553497i
$700$		0			0
$701$	8.03965	+	6.96639i	0.303653	+	0.263117i	0.793337	−	0.608783i	$-0.208342\pi$
$701$	8.03965	+	6.96639i	0.303653	+	0.263117i	−0.489683	+	0.871900i	$0.662888\pi$
$702$		0			0
$703$	1.16008	+	0.281433i	0.0437534	+	0.0106144i
$704$		0			0
$705$	−47.9162	−	24.7025i	−1.80463	−	0.930350i
$706$		0			0
$707$	−21.0993	+	13.0206i	−0.793520	+	0.489688i
$708$		0			0
$709$	7.20808	+	18.0049i	0.270705	+	0.676188i	0.999968	−	0.00804555i	$-0.00256101\pi$
$709$	7.20808	+	18.0049i	0.270705	+	0.676188i	−0.729263	+	0.684234i	$0.760137\pi$
$710$		0			0
$711$	−2.73534	−	14.1923i	−0.102583	−	0.532253i
$712$		0			0
$713$	−6.90800	+	4.11888i	−0.258707	+	0.154253i
$714$		0			0
$715$	15.8137	+	18.2500i	0.591398	+	0.682510i
$716$		0			0
$717$	27.4622	−	34.9210i	1.02559	−	1.30415i
$718$		0			0
$719$	−2.35925	−	3.00003i	−0.0879853	−	0.111882i	0.740067	−	0.672533i	$-0.234794\pi$
$719$	−2.35925	−	3.00003i	−0.0879853	−	0.111882i	−0.828053	+	0.560650i	$0.810551\pi$
$720$		0			0
$721$	−6.49210	−	13.1794i	−0.241778	−	0.490827i
$722$		0			0
$723$	29.6323	−	31.0775i	1.10204	−	1.15578i
$724$		0			0
$725$	−3.99760	−	11.5503i	−0.148467	−	0.428968i
$726$		0			0
$727$	10.0370	+	21.9780i	0.372253	+	0.815121i	0.999345	+	0.0361757i	$0.0115176\pi$
$727$	10.0370	+	21.9780i	0.372253	+	0.815121i	−0.627092	+	0.778945i	$0.715755\pi$
$728$		0			0
$729$	−17.1472	−	5.03488i	−0.635083	−	0.186477i
$730$		0			0
$731$	−59.7639	+	42.5577i	−2.21045	+	1.57405i
$732$		0			0
$733$	−1.22841	+	25.7875i	−0.0453724	+	0.952484i	0.855340	+	0.518067i	$0.173348\pi$
$733$	−1.22841	+	25.7875i	−0.0453724	+	0.952484i	−0.900712	+	0.434416i	$0.856955\pi$
$734$		0			0
$735$	30.2076	−	9.23228i	1.11423	−	0.340538i
$736$		0			0
$737$	−17.8468	−	30.9115i	−0.657394	−	1.13864i
$738$		0			0
$739$	9.12547	−	4.70451i	0.335686	−	0.173058i	−0.282140	−	0.959373i	$-0.591044\pi$
$739$	9.12547	−	4.70451i	0.335686	−	0.173058i	0.617825	+	0.786315i	$0.288014\pi$
$740$		0			0
$741$	0.897932	−	1.96620i	0.0329864	−	0.0722300i
$742$		0			0
$743$	−4.55781	+	15.5225i	−0.167210	+	0.569465i	0.832667	+	0.553774i	$0.186813\pi$
$743$	−4.55781	+	15.5225i	−0.167210	+	0.569465i	−0.999877	+	0.0156906i	$0.995005\pi$
$744$		0			0
$745$	2.21881	−	23.2364i	0.0812909	−	0.851316i
$746$		0			0
$747$	6.54891	+	1.26220i	0.239612	+	0.0461815i
$748$		0			0
$749$	25.3542	−	4.40721i	0.926423	−	0.161036i
$750$		0			0
$751$	−1.36519	+	2.64811i	−0.0498166	+	0.0966308i	−0.912430	−	0.409234i	$-0.865796\pi$
$751$	−1.36519	+	2.64811i	−0.0498166	+	0.0966308i	0.862613	+	0.505864i	$0.168826\pi$
$752$		0			0
$753$	8.40569	−	20.9964i	0.306320	−	0.765151i
$754$		0			0
$755$	−4.86465	+	33.8344i	−0.177043	+	1.23136i
$756$		0			0
$757$	−10.9477	+	9.48624i	−0.397901	+	0.344783i	−0.830713	−	0.556701i	$-0.812067\pi$
$757$	−10.9477	+	9.48624i	−0.397901	+	0.344783i	0.432812	+	0.901484i	$0.357521\pi$
$758$		0			0
$759$	51.6313	+	14.3751i	1.87410	+	0.521784i
$760$		0			0
$761$	39.9592	+	13.8300i	1.44852	+	0.501338i	0.934352	−	0.356351i	$-0.115979\pi$
$761$	39.9592	+	13.8300i	1.44852	+	0.501338i	0.514169	+	0.857689i	$0.328100\pi$
$762$		0			0
$763$	27.7293	−	7.59392i	1.00387	−	0.274918i
$764$		0			0
$765$	−23.9892	+	18.8653i	−0.867330	+	0.682076i
$766$		0			0
$767$	−1.62080	−	34.0248i	−0.0585236	−	1.22856i
$768$		0			0
$769$	13.4950	−	3.96249i	0.486643	−	0.142891i	−0.0292016	−	0.999574i	$-0.509296\pi$
$769$	13.4950	−	3.96249i	0.486643	−	0.142891i	0.515844	+	0.856682i	$0.327478\pi$
$770$		0			0
$771$	5.61759	−	6.48305i	0.202313	−	0.233481i
$772$		0			0
$773$	10.3711	+	0.990316i	0.373021	+	0.0356192i	0.279883	−	0.960034i	$-0.409704\pi$
$773$	10.3711	+	0.990316i	0.373021	+	0.0356192i	0.0931377	+	0.995653i	$0.470310\pi$
$774$		0			0
$775$	−2.14194	+	0.519630i	−0.0769409	+	0.0186657i
$776$		0			0
$777$	−18.6863	+	10.3374i	−0.670366	+	0.370854i
$778$		0			0
$779$	1.92481	+	0.0916901i	0.0689635	+	0.00328514i
$780$		0			0
$781$	−14.3861	−	8.30583i	−0.514776	−	0.297206i
$782$		0			0
$783$			10.3928i			0.371408i
$784$		0			0
$785$	0.194550	+	0.125030i	0.00694380	+	0.00446251i
$786$		0			0
$787$	−31.5800	−	44.3480i	−1.12571	−	1.58083i	−0.759767	−	0.650195i	$-0.774687\pi$
$787$	−31.5800	−	44.3480i	−1.12571	−	1.58083i	−0.365940	−	0.930639i	$-0.619252\pi$
$788$		0			0
$789$	−12.6202	−	52.0210i	−0.449289	−	1.85200i
$790$		0			0
$791$	12.4217	+	2.63063i	0.441665	+	0.0935344i
$792$		0			0
$793$	−2.98966	+	15.5118i	−0.106166	+	0.550842i
$794$		0			0
$795$	8.67144	−	35.7442i	0.307544	−	1.26772i
$796$		0			0
$797$	4.73347	−	3.04201i	0.167668	−	0.107754i	−0.454116	−	0.890943i	$-0.650045\pi$
$797$	4.73347	−	3.04201i	0.167668	−	0.107754i	0.621784	+	0.783189i	$0.286408\pi$
$798$		0			0
$799$	−74.4605	+	10.7058i	−2.63422	+	0.378744i
$800$		0			0
$801$	0.838628	+	0.659505i	0.0296315	+	0.0233024i
$802$		0			0
$803$	7.65860	−	22.1281i	0.270266	−	0.780883i
$804$		0			0
$805$	−22.9861	−	8.06477i	−0.810154	−	0.284246i
$806$		0			0
$807$	0.268292	−	0.775178i	0.00944432	−	0.0272876i
$808$		0			0
$809$	−34.7507	−	27.3283i	−1.22177	−	0.960811i	−0.221873	−	0.975076i	$-0.571217\pi$
$809$	−34.7507	−	27.3283i	−1.22177	−	0.960811i	−0.999898	+	0.0142644i	$0.995459\pi$
$810$		0			0
$811$	7.35846	−	1.05799i	0.258390	−	0.0371509i	−0.0119021	−	0.999929i	$-0.503789\pi$
$811$	7.35846	−	1.05799i	0.258390	−	0.0371509i	0.270293	+	0.962778i	$0.412880\pi$
$812$		0			0
$813$	−6.27218	+	4.03088i	−0.219975	+	0.141369i
$814$		0			0
$815$	−2.41055	+	9.93643i	−0.0844380	+	0.348058i
$816$		0			0
$817$	−0.766533	+	3.97715i	−0.0268176	+	0.139143i
$818$		0			0
$819$	5.47293	+	16.8013i	0.191240	+	0.587085i
$820$		0			0
$821$	1.00372	+	4.13739i	0.0350301	+	0.144396i	0.986641	−	0.162909i	$-0.0520878\pi$
$821$	1.00372	+	4.13739i	0.0350301	+	0.144396i	−0.951611	+	0.307305i	$0.900573\pi$
$822$		0			0
$823$	24.1051	+	33.8509i	0.840252	+	1.17997i	0.981778	+	0.190034i	$0.0608597\pi$
$823$	24.1051	+	33.8509i	0.840252	+	1.17997i	−0.141526	+	0.989935i	$0.545201\pi$
$824$		0			0
$825$	12.3559	+	7.94065i	0.430177	+	0.276458i
$826$		0			0
$827$			14.9635i			0.520332i	0.965564	+	0.260166i	$0.0837773\pi$
$827$			14.9635i			0.520332i	−0.965564	+	0.260166i	$0.916223\pi$
$828$		0			0
$829$	−7.72484	−	4.45994i	−0.268295	−	0.154900i	0.359818	−	0.933023i	$-0.382839\pi$
$829$	−7.72484	−	4.45994i	−0.268295	−	0.154900i	−0.628112	+	0.778123i	$0.716172\pi$
$830$		0			0
$831$	29.2899	+	1.39525i	1.01606	+	0.0484007i
$832$		0			0
$833$	26.8637	−	34.9451i	0.930771	−	1.21078i
$834$		0			0
$835$	−7.20870	+	1.74881i	−0.249467	+	0.0605201i
$836$		0			0
$837$	1.86563	+	0.178146i	0.0644856	+	0.00615763i
$838$		0			0
$839$	22.1710	−	25.5867i	0.765427	−	0.883350i	−0.230541	−	0.973063i	$-0.574049\pi$
$839$	22.1710	−	25.5867i	0.765427	−	0.883350i	0.995968	+	0.0897128i	$0.0285949\pi$
$840$		0			0
$841$	−55.1584	+	16.1960i	−1.90201	+	0.558482i
$842$		0			0
$843$	−0.375560	−	7.88396i	−0.0129350	−	0.271538i
$844$		0			0
$845$	−9.05642	+	7.12205i	−0.311550	+	0.245006i
$846$		0			0
$847$	−29.7038	−	7.78408i	−1.02064	−	0.267464i
$848$		0			0
$849$	46.3582	+	16.0447i	1.59101	+	0.550654i
$850$		0			0
$851$	16.3327	+	2.11440i	0.559878	+	0.0724809i
$852$		0			0
$853$	−9.18202	+	7.95626i	−0.314386	+	0.272417i	−0.797732	−	0.603012i	$-0.793967\pi$
$853$	−9.18202	+	7.95626i	−0.314386	+	0.272417i	0.483346	+	0.875430i	$0.339421\pi$
$854$		0			0
$855$	−0.239772	+	1.66765i	−0.00820003	+	0.0570324i
$856$		0			0
$857$	20.7137	−	51.7404i	0.707568	−	1.76742i	0.0693102	−	0.997595i	$-0.477920\pi$
$857$	20.7137	−	51.7404i	0.707568	−	1.76742i	0.638257	−	0.769823i	$-0.279656\pi$
$858$		0			0
$859$	11.4172	−	22.1462i	0.389549	−	0.755619i	−0.609768	−	0.792580i	$-0.708737\pi$
$859$	11.4172	−	22.1462i	0.389549	−	0.755619i	0.999317	+	0.0369611i	$0.0117678\pi$
$860$		0			0
$861$	−26.4613	+	22.0944i	−0.901798	+	0.752976i
$862$		0			0
$863$	−31.2428	−	6.02155i	−1.06352	−	0.204976i	−0.372660	−	0.927968i	$-0.621554\pi$
$863$	−31.2428	−	6.02155i	−1.06352	−	0.204976i	−0.690856	+	0.722992i	$0.742766\pi$
$864$		0			0
$865$	3.31144	−	34.6790i	0.112592	−	1.17912i
$866$		0			0
$867$	−14.9983	+	51.0795i	−0.509369	+	1.73475i
$868$		0			0
$869$	11.3080	−	24.7610i	0.383597	−	0.839959i
$870$		0			0
$871$	−17.6525	+	9.10052i	−0.598134	+	0.308359i
$872$		0			0
$873$	−16.2921	−	28.2187i	−0.551403	−	0.955058i
$874$		0			0
$875$	−25.7809	−	19.0787i	−0.871552	−	0.644979i
$876$		0			0
$877$	0.666487	−	13.9913i	0.0225057	−	0.472452i	−0.959280	−	0.282458i	$-0.908850\pi$
$877$	0.666487	−	13.9913i	0.0225057	−	0.472452i	0.981785	−	0.189994i	$-0.0608468\pi$
$878$		0			0
$879$	−26.3581	+	18.7695i	−0.889035	+	0.633079i
$880$		0			0
$881$	−8.00067	−	2.34921i	−0.269549	−	0.0791469i	0.144165	−	0.989554i	$-0.453951\pi$
$881$	−8.00067	−	2.34921i	−0.269549	−	0.0791469i	−0.413714	+	0.910407i	$0.635769\pi$
$882$		0			0
$883$	23.2412	+	50.8912i	0.782130	+	1.71263i	0.697918	+	0.716178i	$0.254110\pi$
$883$	23.2412	+	50.8912i	0.782130	+	1.71263i	0.0842125	+	0.996448i	$0.473163\pi$
$884$		0			0
$885$	19.0031	+	54.9060i	0.638784	+	1.84564i
$886$		0			0
$887$	7.06085	−	7.40521i	0.237080	−	0.248642i	−0.594436	−	0.804143i	$-0.702625\pi$
$887$	7.06085	−	7.40521i	0.237080	−	0.248642i	0.831516	+	0.555500i	$0.187473\pi$
$888$		0			0
$889$	53.2587	+	3.51451i	1.78624	+	0.117873i
$890$		0			0
$891$	−29.9796	−	38.1222i	−1.00436	−	1.27714i
$892$		0			0
$893$	−2.56717	+	3.26442i	−0.0859070	+	0.109240i
$894$		0			0
$895$	−19.1061	−	22.0496i	−0.638647	−	0.737038i
$896$		0			0
$897$	9.35638	−	28.3152i	0.312401	−	0.945416i
$898$		0			0
$899$	2.95158	+	15.3142i	0.0984406	+	0.510758i
$900$		0			0
$901$	−19.0757	−	47.6488i	−0.635504	−	1.58741i
$902$		0			0
$903$	−38.0521	−	61.6619i	−1.26630	−	2.05198i
$904$		0			0
$905$	2.23787	+	1.15370i	0.0743894	+	0.0383504i
$906$		0			0
$907$	34.5685	+	8.38623i	1.14783	+	0.278460i	0.764170	−	0.645015i	$-0.223149\pi$
$907$	34.5685	+	8.38623i	1.14783	+	0.278460i	0.383658	+	0.923475i	$0.374664\pi$
$908$		0			0
$909$	17.8792	+	15.4924i	0.593017	+	0.513852i
$910$		0			0
$911$	−37.3696	+	17.0661i	−1.23811	+	0.565427i	−0.923429	−	0.383770i	$-0.874625\pi$
$911$	−37.3696	+	17.0661i	−1.23811	+	0.565427i	−0.314683	+	0.949197i	$0.601898\pi$
$912$		0			0
$913$	8.66797	+	9.09071i	0.286868	+	0.300858i
$914$		0			0
$915$	−2.56132	−	26.8233i	−0.0846745	−	0.886752i
$916$		0			0
$917$	36.9700	+	30.1842i	1.22086	+	0.996771i
$918$		0			0
$919$	−26.1693	+	15.1088i	−0.863244	+	0.498394i	−0.865097	−	0.501604i	$-0.832743\pi$
$919$	−26.1693	+	15.1088i	−0.863244	+	0.498394i	0.00185322	+	0.999998i	$0.499410\pi$
$920$		0			0
$921$	−7.15880	+	12.3994i	−0.235891	+	0.408575i
$922$		0			0
$923$	−4.99711	+	7.77565i	−0.164482	+	0.255939i
$924$		0			0
$925$	4.10540	+	1.87487i	0.134985	+	0.0616454i
$926$		0			0
$927$	−10.1457	+	9.67395i	−0.333230	+	0.317734i
$928$		0			0
$929$	8.16374	+	5.81337i	0.267843	+	0.190730i	0.706086	−	0.708126i	$-0.250459\pi$
$929$	8.16374	+	5.81337i	0.267843	+	0.190730i	−0.438242	+	0.898857i	$0.644399\pi$
$930$		0			0
$931$	−0.257963	−	2.41962i	−0.00845440	−	0.0792998i
$932$		0			0
$933$	−16.5177	−	15.7496i	−0.540766	−	0.515619i
$934$		0			0
$935$	−57.4117	+	2.73486i	−1.87756	+	0.0894394i
$936$		0			0
$937$	6.83190	+	47.5169i	0.223188	+	1.55231i	0.725867	+	0.687835i	$0.241439\pi$
$937$	6.83190	+	47.5169i	0.223188	+	1.55231i	−0.502678	+	0.864474i	$0.667652\pi$
$938$		0			0
$939$	−72.0619	−	10.3609i	−2.35165	−	0.338116i
$940$		0			0
$941$	47.5165	−	9.15805i	1.54899	−	0.298544i	0.658162	−	0.752877i	$-0.271334\pi$
$941$	47.5165	−	9.15805i	1.54899	−	0.298544i	0.890832	+	0.454333i	$0.150122\pi$
$942$		0			0
$943$	26.5347	−	1.63814i	0.864090	−	0.0533451i
$944$		0			0
$945$	3.20746	+	4.68325i	0.104339	+	0.152346i
$946$		0			0
$947$	44.6521	−	17.8760i	1.45100	−	0.580892i	0.493607	−	0.869685i	$-0.335678\pi$
$947$	44.6521	−	17.8760i	1.45100	−	0.580892i	0.957392	+	0.288793i	$0.0932540\pi$
$948$		0			0
$949$	−12.0956	−	4.84236i	−0.392641	−	0.157190i
$950$		0			0
$951$	−8.37771	−	13.0360i	−0.271666	−	0.422721i
$952$		0			0
$953$	2.36212	+	8.04464i	0.0765165	+	0.260591i	0.988863	−	0.148827i	$-0.0475498\pi$
$953$	2.36212	+	8.04464i	0.0765165	+	0.260591i	−0.912347	+	0.409418i	$0.865732\pi$
$954$		0			0
$955$	−9.83629	+	3.40437i	−0.318295	+	0.110163i
$956$		0			0
$957$	60.2847	−	84.6580i	1.94873	−	2.73661i
$958$		0			0
$959$	1.24367	+	9.93718i	0.0401602	+	0.320888i
$960$		0			0
$961$	−28.0599	+	2.67940i	−0.905160	+	0.0864323i
$962$		0			0
$963$	−11.2520	−	21.8258i	−0.362590	−	0.703326i
$964$		0			0
$965$	−5.37162			−0.172919
$966$		0			0
$967$	−40.0273			−1.28719			−0.643596	−	0.765365i	$-0.722558\pi$
$967$	−40.0273			−1.28719			−0.643596	+	0.765365i	$0.722558\pi$
$968$		0			0
$969$	2.35749	+	4.57290i	0.0757335	+	0.146903i
$970$		0			0
$971$	35.8771	−	3.42585i	1.15135	−	0.109941i	0.498126	−	0.867104i	$-0.334022\pi$
$971$	35.8771	−	3.42585i	1.15135	−	0.109941i	0.653225	+	0.757164i	$0.273415\pi$
$972$		0			0
$973$	−42.8393	+	32.4387i	−1.37337	+	1.03994i
$974$		0			0
$975$	4.74039	−	6.65695i	0.151814	−	0.213193i
$976$		0			0
$977$	−38.8224	+	13.4366i	−1.24204	+	0.429874i	−0.867547	−	0.497356i	$-0.834304\pi$
$977$	−38.8224	+	13.4366i	−1.24204	+	0.429874i	−0.374493	+	0.927230i	$0.622183\pi$
$978$		0			0
$979$	0.566088	+	1.92792i	0.0180923	+	0.0616166i
$980$		0			0
$981$	−14.8315	−	23.0783i	−0.473534	−	0.736833i
$982$		0			0
$983$	33.1905	+	13.2875i	1.05861	+	0.423805i	0.834643	−	0.550792i	$-0.185674\pi$
$983$	33.1905	+	13.2875i	1.05861	+	0.423805i	0.223970	+	0.974596i	$0.428098\pi$
$984$		0			0
$985$	−17.5891	+	7.04162i	−0.560436	+	0.224365i
$986$		0			0
$987$	−5.70794	−	74.0734i	−0.181686	−	2.35778i
$988$		0			0
$989$	−4.52922	+	55.6957i	−0.144021	+	1.77102i
$990$		0			0
$991$	11.4930	−	2.21509i	0.365087	−	0.0703647i	−0.00340882	−	0.999994i	$-0.501085\pi$
$991$	11.4930	−	2.21509i	0.365087	−	0.0703647i	0.368496	+	0.929629i	$0.379873\pi$
$992$		0			0
$993$	−14.0206	−	2.01586i	−0.444932	−	0.0639715i
$994$		0			0
$995$	2.60723	+	18.1337i	0.0826549	+	0.574877i
$996$		0			0
$997$	25.7927	−	1.22866i	0.816864	−	0.0389120i	0.365010	−	0.931004i	$-0.381066\pi$
$997$	25.7927	−	1.22866i	0.816864	−	0.0389120i	0.451854	+	0.892092i	$0.350763\pi$
$998$		0			0
$999$	−2.77741	−	2.64825i	−0.0878732	−	0.0837869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.2.bc.a.493.14	yes	320
7.5	odd	6	inner	644.2.bc.a.33.14	✓	320
23.7	odd	22	inner	644.2.bc.a.605.14	yes	320
161.145	even	66	inner	644.2.bc.a.145.14	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.2.bc.a.33.14	✓	320	7.5	odd	6	inner
644.2.bc.a.145.14	yes	320	161.145	even	66	inner
644.2.bc.a.493.14	yes	320	1.1	even	1	trivial
644.2.bc.a.605.14	yes	320	23.7	odd	22	inner

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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	644.bc (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(1.07703 + 2.08915i) q^{3} +(-1.91113 + 0.182491i) q^{5} +(-1.59718 - 2.10927i) q^{7} +(-1.46438 + 2.05643i) q^{9} +O(q^{10})\)	\(q+(1.07703 + 2.08915i) q^{3} +(-1.91113 + 0.182491i) q^{5} +(-1.59718 - 2.10927i) q^{7} +(-1.46438 + 2.05643i) q^{9} +(-4.49309 + 1.55507i) q^{11} +(0.745327 + 2.53835i) q^{13} +(-2.43960 - 3.79609i) q^{15} +(-5.84573 - 2.34028i) q^{17} +(-0.322718 + 0.129197i) q^{19} +(2.68637 - 5.60850i) q^{21} +(-4.23139 + 2.25728i) q^{23} +(-1.29052 + 0.248728i) q^{25} +(1.10615 + 0.159040i) q^{27} +(1.32351 + 9.20518i) q^{29} +(1.67513 - 0.0797961i) q^{31} +(-8.08798 - 7.71187i) q^{33} +(3.43734 + 3.73962i) q^{35} +(-2.79728 - 1.99193i) q^{37} +(-4.50025 + 4.29098i) q^{39} +(-5.04246 - 2.30282i) q^{41} +(6.29938 - 9.80202i) q^{43} +(2.42334 - 4.19735i) q^{45} +(10.3462 - 5.97339i) q^{47} +(-1.89805 + 6.73776i) q^{49} +(-1.40685 - 14.7332i) q^{51} +(5.62487 + 5.89919i) q^{53} +(8.30310 - 3.79190i) q^{55} +(-0.617489 - 0.535058i) q^{57} +(-12.5129 - 3.03561i) q^{59} +(5.30756 + 2.73624i) q^{61} +(6.67645 - 0.195716i) q^{63} +(-1.88764 - 4.71510i) q^{65} +(1.42074 + 7.37151i) q^{67} +(-9.27314 - 6.40885i) q^{69} +(2.28796 + 2.64045i) q^{71} +(-3.04438 + 3.87124i) q^{73} +(-1.90957 - 2.42821i) q^{75} +(10.4563 + 6.99341i) q^{77} +(-3.95083 + 4.14351i) q^{79} +(3.33619 + 9.63930i) q^{81} +(-1.09746 - 2.40310i) q^{83} +(11.5990 + 3.40578i) q^{85} +(-17.8055 + 12.6793i) q^{87} +(0.0201083 - 0.422126i) q^{89} +(4.16365 - 5.62629i) q^{91} +(1.97087 + 3.41365i) q^{93} +(0.593180 - 0.305805i) q^{95} +(-5.36173 + 11.7406i) q^{97} +(3.38168 - 11.5170i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 20 q^{9}+O(q^{10}) \) 320 * q - 20 * q^9	\( 320 q - 20 q^{9} + 66 q^{21} + 21 q^{23} - 8 q^{25} - 12 q^{29} - 6 q^{31} - 38 q^{35} + 44 q^{37} - 20 q^{39} - 88 q^{43} - 42 q^{47} - 74 q^{49} + 44 q^{51} - 88 q^{57} + 55 q^{63} + 77 q^{65} - 32 q^{71} - 36 q^{73} + 24 q^{75} + 105 q^{77} + 44 q^{79} - 36 q^{81} + 60 q^{85} - 96 q^{87} - 20 q^{93} - 31 q^{95} + 242 q^{99}+O(q^{100}) \) 320 * q - 20 * q^9 + 66 * q^21 + 21 * q^23 - 8 * q^25 - 12 * q^29 - 6 * q^31 - 38 * q^35 + 44 * q^37 - 20 * q^39 - 88 * q^43 - 42 * q^47 - 74 * q^49 + 44 * q^51 - 88 * q^57 + 55 * q^63 + 77 * q^65 - 32 * q^71 - 36 * q^73 + 24 * q^75 + 105 * q^77 + 44 * q^79 - 36 * q^81 + 60 * q^85 - 96 * q^87 - 20 * q^93 - 31 * q^95 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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