LMFDB - Embedded newform 702.2.bb.a.89.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [702,2,Mod(71,702)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(702, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([10, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("702.71"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 702 = 2 \cdot 3^{3} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	702.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.60549822189$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 234)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			89.1
Character	$\chi$	$=$	702.89
Dual form			702.2.bb.a.71.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-3.04921 - 0.817032i) q^{5} +(2.84235 + 0.761606i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.73384 - 1.57838i) q^{10} +(0.616853 + 0.616853i) q^{11} +(-3.08613 - 1.86435i) q^{13} +(-2.54838 + 1.47131i) q^{14} -1.00000 q^{16} +(1.80087 - 3.11920i) q^{17} +(-4.90132 + 1.31331i) q^{19} +(-0.817032 + 3.04921i) q^{20} -0.872362 q^{22} +(-1.86758 + 3.23474i) q^{23} +(4.29998 + 2.48260i) q^{25} +(3.50052 - 0.863928i) q^{26} +(0.761606 - 2.84235i) q^{28} -8.59946i q^{29} +(1.33067 - 4.96612i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.932200 + 3.47902i) q^{34} +(-8.04466 - 4.64459i) q^{35} +(-5.77159 - 1.54649i) q^{37} +(2.53711 - 4.39440i) q^{38} +(-1.57838 - 2.73384i) q^{40} +(-2.82738 - 10.5519i) q^{41} +(5.48696 - 3.16790i) q^{43} +(0.616853 - 0.616853i) q^{44} +(-0.966728 - 3.60788i) q^{46} +(-6.10838 + 1.63674i) q^{47} +(1.43675 + 0.829510i) q^{49} +(-4.79601 + 1.28509i) q^{50} +(-1.86435 + 3.08613i) q^{52} -6.73100i q^{53} +(-1.37692 - 2.38490i) q^{55} +(1.47131 + 2.54838i) q^{56} +(6.08073 + 6.08073i) q^{58} +(3.89902 + 3.89902i) q^{59} +(-3.18449 - 5.51569i) q^{61} +(2.57066 + 4.45251i) q^{62} +1.00000i q^{64} +(7.88701 + 8.20625i) q^{65} +(-7.99294 + 2.14170i) q^{67} +(-3.11920 - 1.80087i) q^{68} +(8.97266 - 2.40422i) q^{70} +(1.65986 + 6.19468i) q^{71} +(10.6419 - 10.6419i) q^{73} +(5.17467 - 2.98760i) q^{74} +(1.31331 + 4.90132i) q^{76} +(1.28351 + 2.22311i) q^{77} +(-1.30671 + 2.26329i) q^{79} +(3.04921 + 0.817032i) q^{80} +(9.46058 + 5.46207i) q^{82} +(-2.96889 - 11.0800i) q^{83} +(-8.03972 + 8.03972i) q^{85} +(-1.63983 + 6.11991i) q^{86} +0.872362i q^{88} +(-2.10194 + 7.84455i) q^{89} +(-7.35197 - 7.64956i) q^{91} +(3.23474 + 1.86758i) q^{92} +(3.16193 - 5.47662i) q^{94} +16.0181 q^{95} +(-4.37811 + 16.3393i) q^{97} +(-1.60249 + 0.429386i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) $ 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/702\mathbb{Z}\right)^\times$.

$n$	$379$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−3.04921	−	0.817032i	−1.36365	−	0.365388i	−0.498492	−	0.866894i	$-0.666113\pi$
$5$	−3.04921	−	0.817032i	−1.36365	−	0.365388i	−0.865154	+	0.501506i	$0.832779\pi$
$6$		0			0
$7$	2.84235	+	0.761606i	1.07431	+	0.287860i	0.752262	−	0.658864i	$-0.228963\pi$
$7$	2.84235	+	0.761606i	1.07431	+	0.287860i	0.322046	+	0.946724i	$0.395629\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	2.73384	−	1.57838i	0.864517	−	0.499129i
$11$	0.616853	+	0.616853i	0.185988	+	0.185988i	0.793959	−	0.607971i	$-0.208016\pi$
$11$	0.616853	+	0.616853i	0.185988	+	0.185988i	−0.607971	+	0.793959i	$0.708016\pi$
$12$		0			0
$13$	−3.08613	−	1.86435i	−0.855938	−	0.517078i
$13$	−3.08613	−	1.86435i	−0.855938	−	0.517078i
$14$	−2.54838	+	1.47131i	−0.681084	+	0.393224i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.80087	−	3.11920i	0.436776	−	0.756518i	−0.560663	−	0.828044i	$-0.689454\pi$
$17$	1.80087	−	3.11920i	0.436776	−	0.756518i	0.997439	+	0.0715262i	$0.0227870\pi$
$18$		0			0
$19$	−4.90132	+	1.31331i	−1.12444	+	0.301293i	−0.772679	−	0.634797i	$-0.781084\pi$
$19$	−4.90132	+	1.31331i	−1.12444	+	0.301293i	−0.351761	+	0.936090i	$0.614417\pi$
$20$	−0.817032	+	3.04921i	−0.182694	+	0.681823i
$21$		0			0
$22$	−0.872362			−0.185988
$23$	−1.86758	+	3.23474i	−0.389416	+	0.674489i	−0.992371	−	0.123286i	$-0.960657\pi$
$23$	−1.86758	+	3.23474i	−0.389416	+	0.674489i	0.602955	+	0.797775i	$0.293990\pi$
$24$		0			0
$25$	4.29998	+	2.48260i	0.859997	+	0.496519i
$26$	3.50052	−	0.863928i	0.686508	−	0.169430i
$27$		0			0
$28$	0.761606	−	2.84235i	0.143930	−	0.537154i
$29$		−	8.59946i		−	1.59688i	−0.602075	−	0.798439i	$-0.705659\pi$
$29$		−	8.59946i		−	1.59688i	0.602075	−	0.798439i	$-0.294341\pi$
$30$		0			0
$31$	1.33067	−	4.96612i	0.238995	−	0.891942i	−0.737312	−	0.675553i	$-0.763905\pi$
$31$	1.33067	−	4.96612i	0.238995	−	0.891942i	0.976307	−	0.216390i	$-0.0694282\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$	0.932200	+	3.47902i	0.159871	+	0.596647i
$35$	−8.04466	−	4.64459i	−1.35980	−	0.785079i
$36$		0			0
$37$	−5.77159	−	1.54649i	−0.948844	−	0.254242i	−0.248972	−	0.968511i	$-0.580093\pi$
$37$	−5.77159	−	1.54649i	−0.948844	−	0.254242i	−0.699872	+	0.714269i	$0.746760\pi$
$38$	2.53711	−	4.39440i	0.411574	−	0.712867i
$39$		0			0
$40$	−1.57838	−	2.73384i	−0.249565	−	0.432258i
$41$	−2.82738	−	10.5519i	−0.441562	−	1.64793i	−0.724858	−	0.688899i	$-0.758094\pi$
$41$	−2.82738	−	10.5519i	−0.441562	−	1.64793i	0.283296	−	0.959033i	$-0.408572\pi$
$42$		0			0
$43$	5.48696	−	3.16790i	0.836754	−	0.483100i	−0.0194056	−	0.999812i	$-0.506177\pi$
$43$	5.48696	−	3.16790i	0.836754	−	0.483100i	0.856159	+	0.516712i	$0.172844\pi$
$44$	0.616853	−	0.616853i	0.0929941	−	0.0929941i
$45$		0			0
$46$	−0.966728	−	3.60788i	−0.142536	−	0.531953i
$47$	−6.10838	+	1.63674i	−0.890999	+	0.238742i	−0.675146	−	0.737684i	$-0.735920\pi$
$47$	−6.10838	+	1.63674i	−0.890999	+	0.238742i	−0.215852	+	0.976426i	$0.569253\pi$
$48$		0			0
$49$	1.43675	+	0.829510i	0.205251	+	0.118501i
$50$	−4.79601	+	1.28509i	−0.678258	+	0.181739i
$51$		0			0
$52$	−1.86435	+	3.08613i	−0.258539	+	0.427969i
$53$		−	6.73100i		−	0.924574i	−0.886730	−	0.462287i	$-0.847029\pi$
$53$		−	6.73100i		−	0.924574i	0.886730	−	0.462287i	$-0.152971\pi$
$54$		0			0
$55$	−1.37692	−	2.38490i	−0.185664	−	0.321580i
$56$	1.47131	+	2.54838i	0.196612	+	0.340542i
$57$		0			0
$58$	6.08073	+	6.08073i	0.798439	+	0.798439i
$59$	3.89902	+	3.89902i	0.507609	+	0.507609i	0.913792	−	0.406183i	$-0.133140\pi$
$59$	3.89902	+	3.89902i	0.507609	+	0.507609i	−0.406183	+	0.913792i	$0.633140\pi$
$60$		0			0
$61$	−3.18449	−	5.51569i	−0.407732	−	0.706212i	0.586903	−	0.809657i	$-0.300347\pi$
$61$	−3.18449	−	5.51569i	−0.407732	−	0.706212i	−0.994635	+	0.103445i	$0.967014\pi$
$62$	2.57066	+	4.45251i	0.326474	+	0.565469i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	7.88701	+	8.20625i	0.978263	+	1.01786i
$66$		0			0
$67$	−7.99294	+	2.14170i	−0.976493	+	0.261650i	−0.711567	−	0.702618i	$-0.752014\pi$
$67$	−7.99294	+	2.14170i	−0.976493	+	0.261650i	−0.264926	+	0.964269i	$0.585347\pi$
$68$	−3.11920	−	1.80087i	−0.378259	−	0.218388i
$69$		0			0
$70$	8.97266	−	2.40422i	1.07244	−	0.287359i
$71$	1.65986	+	6.19468i	0.196989	+	0.735174i	0.991743	+	0.128242i	$0.0409333\pi$
$71$	1.65986	+	6.19468i	0.196989	+	0.735174i	−0.794754	+	0.606932i	$0.792400\pi$
$72$		0			0
$73$	10.6419	−	10.6419i	1.24555	−	1.24555i	0.287878	−	0.957667i	$-0.407050\pi$
$73$	10.6419	−	10.6419i	1.24555	−	1.24555i	0.957667	−	0.287878i	$-0.0929498\pi$
$74$	5.17467	−	2.98760i	0.601543	−	0.347301i
$75$		0			0
$76$	1.31331	+	4.90132i	0.150646	+	0.562220i
$77$	1.28351	+	2.22311i	0.146270	+	0.253347i
$78$		0			0
$79$	−1.30671	+	2.26329i	−0.147016	+	0.254640i	−0.930123	−	0.367247i	$-0.880300\pi$
$79$	−1.30671	+	2.26329i	−0.147016	+	0.254640i	0.783107	+	0.621887i	$0.213634\pi$
$80$	3.04921	+	0.817032i	0.340912	+	0.0913470i
$81$		0			0
$82$	9.46058	+	5.46207i	1.04475	+	0.603185i
$83$	−2.96889	−	11.0800i	−0.325878	−	1.21619i	−0.913426	−	0.407004i	$-0.866573\pi$
$83$	−2.96889	−	11.0800i	−0.325878	−	1.21619i	0.587548	−	0.809189i	$-0.300093\pi$
$84$		0			0
$85$	−8.03972	+	8.03972i	−0.872030	+	0.872030i
$86$	−1.63983	+	6.11991i	−0.176827	+	0.659927i
$87$		0			0
$88$			0.872362i			0.0929941i
$89$	−2.10194	+	7.84455i	−0.222805	+	0.831521i	0.760467	+	0.649377i	$0.224970\pi$
$89$	−2.10194	+	7.84455i	−0.222805	+	0.831521i	−0.983272	+	0.182144i	$0.941696\pi$
$90$		0			0
$91$	−7.35197	−	7.64956i	−0.770696	−	0.801892i
$92$	3.23474	+	1.86758i	0.337244	+	0.194708i
$93$		0			0
$94$	3.16193	−	5.47662i	0.326128	−	0.564871i
$95$	16.0181			1.64343
$96$		0			0
$97$	−4.37811	+	16.3393i	−0.444530	+	1.65901i	0.272644	+	0.962115i	$0.412102\pi$
$97$	−4.37811	+	16.3393i	−0.444530	+	1.65901i	−0.717174	+	0.696894i	$0.754565\pi$
$98$	−1.60249	+	0.429386i	−0.161876	+	0.0433745i
$99$		0			0
$100$	2.48260	−	4.29998i	0.248260	−	0.429998i
$101$	−5.16265			−0.513703			−0.256851	−	0.966451i	$-0.582685\pi$
$101$	−5.16265			−0.513703			−0.256851	+	0.966451i	$0.582685\pi$
$102$		0			0
$103$	−7.99184	+	4.61409i	−0.787459	+	0.454640i	−0.839067	−	0.544028i	$-0.816899\pi$
$103$	−7.99184	+	4.61409i	−0.787459	+	0.454640i	0.0516081	+	0.998667i	$0.483565\pi$
$104$	−0.863928	−	3.50052i	−0.0847151	−	0.343254i
$105$		0			0
$106$	4.75954	+	4.75954i	0.462287	+	0.462287i
$107$	−0.210437	+	0.121496i	−0.0203437	+	0.0117454i	−0.510137	−	0.860093i	$-0.670405\pi$
$107$	−0.210437	+	0.121496i	−0.0203437	+	0.0117454i	0.489794	+	0.871838i	$0.337072\pi$
$108$		0			0
$109$	2.87971	+	2.87971i	0.275827	+	0.275827i	0.831440	−	0.555614i	$-0.187517\pi$
$109$	2.87971	+	2.87971i	0.275827	+	0.275827i	−0.555614	+	0.831440i	$0.687517\pi$
$110$	2.66001	+	0.712747i	0.253622	+	0.0679578i
$111$		0			0
$112$	−2.84235	−	0.761606i	−0.268577	−	0.0719650i
$113$			3.05691i			0.287570i	0.989609	+	0.143785i	$0.0459274\pi$
$113$			3.05691i			0.287570i	−0.989609	+	0.143785i	$0.954073\pi$
$114$		0			0
$115$	8.33750	−	8.33750i	0.777476	−	0.777476i
$116$	−8.59946			−0.798439
$117$		0			0
$118$	−5.51405			−0.507609
$119$	7.49432	−	7.49432i	0.687004	−	0.687004i
$120$		0			0
$121$		−	10.2390i		−	0.930817i
$122$	6.15196	+	1.64841i	0.556972	+	0.149240i
$123$		0			0
$124$	−4.96612	−	1.33067i	−0.445971	−	0.119498i
$125$	0.0776933	+	0.0776933i	0.00694910	+	0.00694910i
$126$		0			0
$127$	16.5577	−	9.55958i	1.46926	−	0.848276i	0.469851	−	0.882746i	$-0.344308\pi$
$127$	16.5577	−	9.55958i	1.46926	−	0.848276i	0.999406	+	0.0344705i	$0.0109745\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−11.3797	−	0.225741i	−0.998062	−	0.0197988i
$131$	10.6970	−	6.17593i	0.934603	−	0.539593i	0.0463386	−	0.998926i	$-0.485245\pi$
$131$	10.6970	−	6.17593i	0.934603	−	0.539593i	0.888264	+	0.459332i	$0.151911\pi$
$132$		0			0
$133$	−14.9315			−1.29473
$134$	4.13745	−	7.16627i	0.357421	−	0.619072i
$135$		0			0
$136$	3.47902	−	0.932200i	0.298323	−	0.0799355i
$137$	−1.79956	+	6.71605i	−0.153747	+	0.573791i	0.845463	+	0.534035i	$0.179325\pi$
$137$	−1.79956	+	6.71605i	−0.153747	+	0.573791i	−0.999209	+	0.0397562i	$0.987342\pi$
$138$		0			0
$139$	−5.68120			−0.481873			−0.240937	−	0.970541i	$-0.577455\pi$
$139$	−5.68120			−0.481873			−0.240937	+	0.970541i	$0.577455\pi$
$140$	−4.64459	+	8.04466i	−0.392539	+	0.679898i
$141$		0			0
$142$	−5.55400	−	3.20660i	−0.466081	−	0.269092i
$143$	−0.753658	−	3.05372i	−0.0630240	−	0.255365i
$144$		0			0
$145$	−7.02603	+	26.2215i	−0.583480	+	2.17758i
$146$			15.0500i			1.24555i
$147$		0			0
$148$	−1.54649	+	5.77159i	−0.127121	+	0.474422i
$149$	−14.6958	+	14.6958i	−1.20393	+	1.20393i	−0.230964	+	0.972962i	$0.574188\pi$
$149$	−14.6958	+	14.6958i	−1.20393	+	1.20393i	−0.972962	+	0.230964i	$0.925812\pi$
$150$		0			0
$151$	−1.90772	−	7.11970i	−0.155248	−	0.579393i	−0.999084	−	0.0427921i	$-0.986375\pi$
$151$	−1.90772	−	7.11970i	−0.155248	−	0.579393i	0.843836	−	0.536601i	$-0.180292\pi$
$152$	−4.39440	−	2.53711i	−0.356433	−	0.205787i
$153$		0			0
$154$	−2.47956	−	0.664396i	−0.199809	−	0.0535386i
$155$	−8.11497	+	14.0555i	−0.651810	+	1.12897i
$156$		0			0
$157$	−5.21020	−	9.02434i	−0.415819	−	0.720220i	0.579695	−	0.814834i	$-0.303172\pi$
$157$	−5.21020	−	9.02434i	−0.415819	−	0.720220i	−0.995514	+	0.0946134i	$0.969838\pi$
$158$	−0.676403	−	2.52437i	−0.0538118	−	0.200828i
$159$		0			0
$160$	−2.73384	+	1.57838i	−0.216129	+	0.124782i
$161$	−7.77191	+	7.77191i	−0.612512	+	0.612512i
$162$		0			0
$163$	1.76529	+	6.58816i	0.138268	+	0.516025i	0.999963	+	0.00859756i	$0.00273672\pi$
$163$	1.76529	+	6.58816i	0.138268	+	0.516025i	−0.861695	+	0.507427i	$0.830597\pi$
$164$	−10.5519	+	2.82738i	−0.823966	+	0.220781i
$165$		0			0
$166$	9.93410	+	5.73546i	0.771036	+	0.445158i
$167$	13.2930	−	3.56186i	1.02865	−	0.275625i	0.295245	−	0.955422i	$-0.404599\pi$
$167$	13.2930	−	3.56186i	1.02865	−	0.275625i	0.733400	+	0.679797i	$0.237932\pi$
$168$		0			0
$169$	6.04839	+	11.5073i	0.465261	+	0.885174i
$170$		−	11.3699i		−	0.872030i
$171$		0			0
$172$	−3.16790	−	5.48696i	−0.241550	−	0.418377i
$173$	−2.03004	−	3.51613i	−0.154341	−	0.267326i	0.778478	−	0.627672i	$-0.215992\pi$
$173$	−2.03004	−	3.51613i	−0.154341	−	0.267326i	−0.932819	+	0.360346i	$0.882659\pi$
$174$		0			0
$175$	10.3313	+	10.3313i	0.780974	+	0.780974i
$176$	−0.616853	−	0.616853i	−0.0464970	−	0.0464970i
$177$		0			0
$178$	−4.06064	−	7.03323i	−0.304358	−	0.527163i
$179$	9.70640	+	16.8120i	0.725490	+	1.25659i	0.958772	+	0.284177i	$0.0917203\pi$
$179$	9.70640	+	16.8120i	0.725490	+	1.25659i	−0.233282	+	0.972409i	$0.574946\pi$
$180$		0			0
$181$		−	0.0982851i		−	0.00730547i	−0.999993	−	0.00365274i	$-0.998837\pi$
$181$		−	0.0982851i		−	0.00730547i	0.999993	−	0.00365274i	$-0.00116270\pi$
$182$	10.6077	+	0.210427i	0.786294	+	0.0155979i
$183$		0			0
$184$	−3.60788	+	0.966728i	−0.265976	+	0.0712681i
$185$	16.3352	+	9.43115i	1.20099	+	0.693392i
$186$		0			0
$187$	3.03496	−	0.813216i	0.221938	−	0.0594682i
$188$	1.63674	+	6.10838i	0.119371	+	0.445499i
$189$		0			0
$190$	−11.3265	+	11.3265i	−0.821714	+	0.821714i
$191$	−10.9961	+	6.34858i	−0.795648	+	0.459367i	−0.841947	−	0.539560i	$-0.818591\pi$
$191$	−10.9961	+	6.34858i	−0.795648	+	0.459367i	0.0462993	+	0.998928i	$0.485257\pi$
$192$		0			0
$193$	6.14134	+	22.9198i	0.442063	+	1.64980i	0.723576	+	0.690244i	$0.242497\pi$
$193$	6.14134	+	22.9198i	0.442063	+	1.64980i	−0.281513	+	0.959557i	$0.590836\pi$
$194$	−8.45787	−	14.6495i	−0.607240	−	1.05177i
$195$		0			0
$196$	0.829510	−	1.43675i	0.0592507	−	0.102625i
$197$	5.16169	+	1.38307i	0.367755	+	0.0985397i	0.437964	−	0.898993i	$-0.355700\pi$
$197$	5.16169	+	1.38307i	0.367755	+	0.0985397i	−0.0702085	+	0.997532i	$0.522366\pi$
$198$		0			0
$199$	−7.44445	−	4.29806i	−0.527723	−	0.304681i	0.212366	−	0.977190i	$-0.431883\pi$
$199$	−7.44445	−	4.29806i	−0.527723	−	0.304681i	−0.740089	+	0.672509i	$0.765217\pi$
$200$	1.28509	+	4.79601i	0.0908694	+	0.339129i
$201$		0			0
$202$	3.65055	−	3.65055i	0.256851	−	0.256851i
$203$	6.54940	−	24.4427i	0.459678	−	1.71554i
$204$		0			0
$205$			34.4850i			2.40854i
$206$	2.38843	−	8.91374i	0.166410	−	0.621050i
$207$		0			0
$208$	3.08613	+	1.86435i	0.213985	+	0.129269i
$209$	−3.83351	−	2.21328i	−0.265169	−	0.153096i
$210$		0			0
$211$	4.87073	−	8.43636i	0.335315	−	0.580783i	−0.648230	−	0.761444i	$-0.724491\pi$
$211$	4.87073	−	8.43636i	0.335315	−	0.580783i	0.983545	+	0.180662i	$0.0578239\pi$
$212$	−6.73100			−0.462287
$213$		0			0
$214$	0.0628908	−	0.234711i	0.00429912	−	0.0160445i
$215$	−19.3191	+	5.17655i	−1.31755	+	0.353038i
$216$		0			0
$217$	7.56446	−	13.1020i	0.513509	−	0.889424i
$218$	−4.07253			−0.275827
$219$		0			0
$220$	−2.38490	+	1.37692i	−0.160790	+	0.0928321i
$221$	−11.3730	+	6.26881i	−0.765032	+	0.421686i
$222$		0			0
$223$	13.4223	+	13.4223i	0.898824	+	0.898824i	0.995332	−	0.0965083i	$-0.0307674\pi$
$223$	13.4223	+	13.4223i	0.898824	+	0.898824i	−0.0965083	+	0.995332i	$0.530767\pi$
$224$	2.54838	−	1.47131i	0.170271	−	0.0983061i
$225$		0			0
$226$	−2.16156	−	2.16156i	−0.143785	−	0.143785i
$227$	14.9418	+	4.00365i	0.991723	+	0.265731i	0.717974	−	0.696070i	$-0.245070\pi$
$227$	14.9418	+	4.00365i	0.991723	+	0.265731i	0.273749	+	0.961801i	$0.411736\pi$
$228$		0			0
$229$	−14.6426	−	3.92348i	−0.967612	−	0.259271i	−0.259792	−	0.965664i	$-0.583654\pi$
$229$	−14.6426	−	3.92348i	−0.967612	−	0.259271i	−0.707819	+	0.706394i	$0.750321\pi$
$230$			11.7910i			0.777476i
$231$		0			0
$232$	6.08073	−	6.08073i	0.399220	−	0.399220i
$233$	11.5129			0.754237			0.377118	−	0.926165i	$-0.376915\pi$
$233$	11.5129			0.754237			0.377118	+	0.926165i	$0.376915\pi$
$234$		0			0
$235$	19.9630			1.30224
$236$	3.89902	−	3.89902i	0.253805	−	0.253805i
$237$		0			0
$238$			10.5986i			0.687004i
$239$	−3.89177	−	1.04280i	−0.251737	−	0.0674528i	0.130743	−	0.991416i	$-0.458264\pi$
$239$	−3.89177	−	1.04280i	−0.251737	−	0.0674528i	−0.382481	+	0.923963i	$0.624930\pi$
$240$		0			0
$241$	−14.3057	−	3.83319i	−0.921509	−	0.246918i	−0.233279	−	0.972410i	$-0.574945\pi$
$241$	−14.3057	−	3.83319i	−0.921509	−	0.246918i	−0.688230	+	0.725492i	$0.741612\pi$
$242$	7.24006	+	7.24006i	0.465408	+	0.465408i
$243$		0			0
$244$	−5.51569	+	3.18449i	−0.353106	+	0.203866i
$245$	−3.70322	−	3.70322i	−0.236590	−	0.236590i
$246$		0			0
$247$	17.5746	+	5.08475i	1.11824	+	0.323535i
$248$	4.45251	−	2.57066i	0.282734	−	0.163237i
$249$		0			0
$250$	−0.109875			−0.00694910
$251$	−1.98281	+	3.43432i	−0.125154	+	0.216772i	−0.921793	−	0.387682i	$-0.873276\pi$
$251$	−1.98281	+	3.43432i	−0.125154	+	0.216772i	0.796639	+	0.604455i	$0.206609\pi$
$252$		0			0
$253$	−3.14737	+	0.843337i	−0.197874	+	0.0530201i
$254$	−4.94840	+	18.4677i	−0.310490	+	1.15877i
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.92795	−	11.9996i	0.432153	−	0.748512i	−0.564905	−	0.825156i	$-0.691087\pi$
$257$	6.92795	−	11.9996i	0.432153	−	0.748512i	0.997059	+	0.0766441i	$0.0244205\pi$
$258$		0			0
$259$	−15.2271	−	8.79137i	−0.946165	−	0.546269i
$260$	8.20625	−	7.88701i	0.508930	−	0.489132i
$261$		0			0
$262$	−3.19690	+	11.9310i	−0.197505	+	0.737098i
$263$		−	16.0207i		−	0.987880i	−0.869496	−	0.493940i	$-0.835556\pi$
$263$		−	16.0207i		−	0.987880i	0.869496	−	0.493940i	$-0.164444\pi$
$264$		0			0
$265$	−5.49945	+	20.5242i	−0.337828	+	1.26079i
$266$	10.5582	−	10.5582i	0.647363	−	0.647363i
$267$		0			0
$268$	2.14170	+	7.99294i	0.130825	+	0.488246i
$269$	−1.90561	−	1.10021i	−0.116187	−	0.0670808i	0.440780	−	0.897615i	$-0.354702\pi$
$269$	−1.90561	−	1.10021i	−0.116187	−	0.0670808i	−0.556967	+	0.830534i	$0.688035\pi$
$270$		0			0
$271$	−5.96826	−	1.59919i	−0.362546	−	0.0971439i	0.0729474	−	0.997336i	$-0.476759\pi$
$271$	−5.96826	−	1.59919i	−0.362546	−	0.0971439i	−0.435494	+	0.900192i	$0.643426\pi$
$272$	−1.80087	+	3.11920i	−0.109194	+	0.189129i
$273$		0			0
$274$	−3.47648	−	6.02145i	−0.210022	−	0.363769i
$275$	1.12106	+	4.18385i	0.0676025	+	0.252296i
$276$		0			0
$277$	17.6848	−	10.2103i	1.06258	−	0.613479i	0.136433	−	0.990649i	$-0.456436\pi$
$277$	17.6848	−	10.2103i	1.06258	−	0.613479i	0.926144	+	0.377170i	$0.123103\pi$
$278$	4.01721	−	4.01721i	0.240937	−	0.240937i
$279$		0			0
$280$	−2.40422	−	8.97266i	−0.143679	−	0.536219i
$281$	−20.0659	+	5.37665i	−1.19703	+	0.320744i	−0.801662	−	0.597777i	$-0.796051\pi$
$281$	−20.0659	+	5.37665i	−1.19703	+	0.320744i	−0.395372	+	0.918521i	$0.629384\pi$
$282$		0			0
$283$	−20.8752	−	12.0523i	−1.24090	−	0.716436i	−0.271626	−	0.962403i	$-0.587561\pi$
$283$	−20.8752	−	12.0523i	−1.24090	−	0.716436i	−0.969278	+	0.245966i	$0.920895\pi$
$284$	6.19468	−	1.65986i	0.367587	−	0.0984946i
$285$		0			0
$286$	2.69222	+	1.62639i	0.159194	+	0.0961703i
$287$		−	32.1456i		−	1.89750i
$288$		0			0
$289$	2.01371	+	3.48785i	0.118454	+	0.205168i
$290$	−13.5733	−	23.5096i	−0.797049	−	1.38053i
$291$		0			0
$292$	−10.6419	−	10.6419i	−0.622773	−	0.622773i
$293$	−1.83330	−	1.83330i	−0.107103	−	0.107103i	0.651525	−	0.758627i	$-0.274130\pi$
$293$	−1.83330	−	1.83330i	−0.107103	−	0.107103i	−0.758627	+	0.651525i	$0.774130\pi$
$294$		0			0
$295$	−8.70329	−	15.0745i	−0.506725	−	0.877674i
$296$	−2.98760	−	5.17467i	−0.173651	−	0.300772i
$297$		0			0
$298$		−	20.7830i		−	1.20393i
$299$	11.7943	−	6.50100i	0.682080	−	0.375962i
$300$		0			0
$301$	18.0086	−	4.82538i	1.03800	−	0.278131i
$302$	6.38335	+	3.68543i	0.367321	+	0.212073i
$303$		0			0
$304$	4.90132	−	1.31331i	0.281110	−	0.0753232i
$305$	5.20366	+	19.4203i	0.297961	+	1.11200i
$306$		0			0
$307$	0.409589	−	0.409589i	0.0233765	−	0.0233765i	−0.695322	−	0.718698i	$-0.744738\pi$
$307$	0.409589	−	0.409589i	0.0233765	−	0.0233765i	0.718698	+	0.695322i	$0.244738\pi$
$308$	2.22311	−	1.28351i	0.126674	−	0.0731350i
$309$		0			0
$310$	−4.20062	−	15.6769i	−0.238579	−	0.890389i
$311$	−8.67641	−	15.0280i	−0.491994	−	0.852159i	0.507963	−	0.861379i	$-0.330398\pi$
$311$	−8.67641	−	15.0280i	−0.491994	−	0.852159i	−0.999957	+	0.00921998i	$0.997065\pi$
$312$		0			0
$313$	12.3328	−	21.3610i	0.697089	−	1.20739i	−0.272382	−	0.962189i	$-0.587812\pi$
$313$	12.3328	−	21.3610i	0.697089	−	1.20739i	0.969471	−	0.245205i	$-0.0788552\pi$
$314$	10.0653	+	2.69700i	0.568020	+	0.152200i
$315$		0			0
$316$	2.26329	+	1.30671i	0.127320	+	0.0735082i
$317$	−6.46561	−	24.1300i	−0.363145	−	1.35528i	−0.869918	−	0.493196i	$-0.835828\pi$
$317$	−6.46561	−	24.1300i	−0.363145	−	1.35528i	0.506773	−	0.862080i	$-0.330838\pi$
$318$		0			0
$319$	5.30460	−	5.30460i	0.297000	−	0.297000i
$320$	0.817032	−	3.04921i	0.0456735	−	0.170456i
$321$		0			0
$322$		−	10.9911i		−	0.612512i
$323$	−4.73019	+	17.6533i	−0.263195	+	0.982257i
$324$		0			0
$325$	−8.64188	−	15.6783i	−0.479365	−	0.869675i
$326$	−5.90679	−	3.41028i	−0.327147	−	0.188878i
$327$		0			0
$328$	5.46207	−	9.46058i	0.301592	−	0.522373i
$329$	−18.6087			−1.02593
$330$		0			0
$331$	8.32961	−	31.0865i	0.457837	−	1.70867i	−0.221775	−	0.975098i	$-0.571185\pi$
$331$	8.32961	−	31.0865i	0.457837	−	1.70867i	0.679612	−	0.733572i	$-0.262148\pi$
$332$	−11.0800	+	2.96889i	−0.608097	+	0.162939i
$333$		0			0
$334$	−6.88098	+	11.9182i	−0.376510	+	0.652135i
$335$	26.1219			1.42719
$336$		0			0
$337$	25.7601	−	14.8726i	1.40324	−	0.810161i	0.408516	−	0.912751i	$-0.366046\pi$
$337$	25.7601	−	14.8726i	1.40324	−	0.810161i	0.994724	+	0.102590i	$0.0327131\pi$
$338$	−12.4137	−	3.86000i	−0.675217	−	0.209956i
$339$		0			0
$340$	8.03972	+	8.03972i	0.436015	+	0.436015i
$341$	3.88419	−	2.24254i	0.210341	−	0.121440i
$342$		0			0
$343$	−11.1132	−	11.1132i	−0.600058	−	0.600058i
$344$	6.11991	+	1.63983i	0.329963	+	0.0884134i
$345$		0			0
$346$	3.92173	+	1.05082i	0.210833	+	0.0564927i
$347$			33.9806i			1.82418i	0.409995	+	0.912088i	$0.365531\pi$
$347$			33.9806i			1.82418i	−0.409995	+	0.912088i	$0.634469\pi$
$348$		0			0
$349$	−5.80406	+	5.80406i	−0.310684	+	0.310684i	−0.845175	−	0.534490i	$-0.820504\pi$
$349$	−5.80406	+	5.80406i	−0.310684	+	0.310684i	0.534490	+	0.845175i	$0.320504\pi$
$350$	−14.6107			−0.780974
$351$		0			0
$352$	0.872362			0.0464970
$353$	11.0972	−	11.0972i	0.590646	−	0.590646i	−0.347160	−	0.937806i	$-0.612854\pi$
$353$	11.0972	−	11.0972i	0.590646	−	0.590646i	0.937806	+	0.347160i	$0.112854\pi$
$354$		0			0
$355$		−	20.2450i		−	1.07449i
$356$	7.84455	+	2.10194i	0.415760	+	0.111403i
$357$		0			0
$358$	−18.7513	−	5.02440i	−0.991038	−	0.265548i
$359$	12.5155	+	12.5155i	0.660544	+	0.660544i	0.955508	−	0.294964i	$-0.0953077\pi$
$359$	12.5155	+	12.5155i	0.660544	+	0.660544i	−0.294964	+	0.955508i	$0.595308\pi$
$360$		0			0
$361$	5.84370	−	3.37386i	0.307563	−	0.177572i
$362$	0.0694981	+	0.0694981i	0.00365274	+	0.00365274i
$363$		0			0
$364$	−7.64956	+	7.35197i	−0.400946	+	0.385348i
$365$	−41.1443	+	23.7547i	−2.15359	+	1.24338i
$366$		0			0
$367$	26.4242			1.37933			0.689666	−	0.724128i	$-0.257757\pi$
$367$	26.4242			1.37933			0.689666	+	0.724128i	$0.257757\pi$
$368$	1.86758	−	3.23474i	0.0973541	−	0.168622i
$369$		0			0
$370$	−18.2196	+	4.88192i	−0.947191	+	0.253799i
$371$	5.12638	−	19.1319i	0.266148	−	0.993278i
$372$		0			0
$373$	22.6990			1.17531			0.587656	−	0.809111i	$-0.300051\pi$
$373$	22.6990			1.17531			0.587656	+	0.809111i	$0.300051\pi$
$374$	−1.57101	+	2.72107i	−0.0812351	+	0.140703i
$375$		0			0
$376$	−5.47662	−	3.16193i	−0.282435	−	0.163064i
$377$	−16.0324	+	26.5390i	−0.825711	+	1.36683i
$378$		0			0
$379$	−2.62959	+	9.81377i	−0.135073	+	0.504100i	0.864924	+	0.501902i	$0.167366\pi$
$379$	−2.62959	+	9.81377i	−0.135073	+	0.504100i	−0.999998	+	0.00219770i	$0.999300\pi$
$380$		−	16.0181i		−	0.821714i
$381$		0			0
$382$	3.28627	−	12.2645i	0.168140	−	0.627508i
$383$	13.2359	−	13.2359i	0.676323	−	0.676323i	−0.282843	−	0.959166i	$-0.591278\pi$
$383$	13.2359	−	13.2359i	0.676323	−	0.676323i	0.959166	+	0.282843i	$0.0912777\pi$
$384$		0			0
$385$	−2.09735	−	7.82740i	−0.106891	−	0.398921i
$386$	−20.5493	−	11.8641i	−1.04593	−	0.603869i
$387$		0			0
$388$	16.3393	+	4.37811i	0.829505	+	0.222265i
$389$	−10.9802	+	19.0182i	−0.556716	+	0.964261i	0.441051	+	0.897482i	$0.354606\pi$
$389$	−10.9802	+	19.0182i	−0.556716	+	0.964261i	−0.997768	+	0.0667792i	$0.978728\pi$
$390$		0			0
$391$	6.72653	+	11.6507i	0.340175	+	0.589201i
$392$	0.429386	+	1.60249i	0.0216873	+	0.0809380i
$393$		0			0
$394$	−4.62785	+	2.67189i	−0.233148	+	0.134608i
$395$	5.83361	−	5.83361i	0.293521	−	0.293521i
$396$		0			0
$397$	0.908301	+	3.38983i	0.0455863	+	0.170130i	0.984966	−	0.172748i	$-0.0552647\pi$
$397$	0.908301	+	3.38983i	0.0455863	+	0.170130i	−0.939380	+	0.342879i	$0.888598\pi$
$398$	8.30321	−	2.22484i	0.416202	−	0.111521i
$399$		0			0
$400$	−4.29998	−	2.48260i	−0.214999	−	0.124130i
$401$	2.43364	−	0.652092i	0.121530	−	0.0325639i	−0.197541	−	0.980295i	$-0.563296\pi$
$401$	2.43364	−	0.652092i	0.121530	−	0.0325639i	0.319071	+	0.947731i	$0.396629\pi$
$402$		0			0
$403$	−13.3652	+	12.8453i	−0.665769	+	0.639868i
$404$			5.16265i			0.256851i
$405$		0			0
$406$	12.6525	+	21.9147i	0.627932	+	1.08761i
$407$	−2.60626	−	4.51418i	−0.129188	−	0.223760i
$408$		0			0
$409$	12.1955	+	12.1955i	0.603027	+	0.603027i	0.941115	−	0.338087i	$-0.109780\pi$
$409$	12.1955	+	12.1955i	0.603027	+	0.603027i	−0.338087	+	0.941115i	$0.609780\pi$
$410$	−24.3846	−	24.3846i	−1.20427	−	1.20427i
$411$		0			0
$412$	4.61409	+	7.99184i	0.227320	+	0.393730i
$413$	8.11288	+	14.0519i	0.399209	+	0.691450i
$414$		0			0
$415$			36.2110i			1.77753i
$416$	−3.50052	+	0.863928i	−0.171627	+	0.0423576i
$417$		0			0
$418$	4.27572	−	1.14568i	0.209133	−	0.0560369i
$419$	16.2513	+	9.38271i	0.793929	+	0.458375i	0.841344	−	0.540500i	$-0.181765\pi$
$419$	16.2513	+	9.38271i	0.793929	+	0.458375i	−0.0474148	+	0.998875i	$0.515098\pi$
$420$		0			0
$421$	−23.1335	+	6.19861i	−1.12746	+	0.302102i	−0.773898	−	0.633310i	$-0.781696\pi$
$421$	−23.1335	+	6.19861i	−1.12746	+	0.302102i	−0.353560	+	0.935412i	$0.615029\pi$
$422$	2.52128	+	9.40954i	0.122734	+	0.458049i
$423$		0			0
$424$	4.75954	−	4.75954i	0.231144	−	0.231144i
$425$	15.4874	−	8.94168i	0.751252	−	0.433735i
$426$		0			0
$427$	−4.85065	−	18.1029i	−0.234740	−	0.876060i
$428$	0.121496	+	0.210437i	0.00587271	+	0.0101718i
$429$		0			0
$430$	10.0003	−	17.3211i	0.482259	−	0.835296i
$431$	0.739992	+	0.198280i	0.0356441	+	0.00955082i	0.276597	−	0.960986i	$-0.410793\pi$
$431$	0.739992	+	0.198280i	0.0356441	+	0.00955082i	−0.240953	+	0.970537i	$0.577460\pi$
$432$		0			0
$433$	12.3652	+	7.13904i	0.594233	+	0.343080i	0.766769	−	0.641923i	$-0.221863\pi$
$433$	12.3652	+	7.13904i	0.594233	+	0.343080i	−0.172537	+	0.985003i	$0.555196\pi$
$434$	3.91565	+	14.6134i	0.187957	+	0.701467i
$435$		0			0
$436$	2.87971	−	2.87971i	0.137913	−	0.137913i
$437$	4.90539	−	18.3072i	0.234657	−	0.875751i
$438$		0			0
$439$			12.6884i			0.605584i	0.953057	+	0.302792i	$0.0979187\pi$
$439$			12.6884i			0.605584i	−0.953057	+	0.302792i	$0.902081\pi$
$440$	0.712747	−	2.66001i	0.0339789	−	0.126811i
$441$		0			0
$442$	3.60922	−	12.4747i	0.171673	−	0.593359i
$443$	−9.00475	−	5.19889i	−0.427828	−	0.247007i	0.270593	−	0.962694i	$-0.412780\pi$
$443$	−9.00475	−	5.19889i	−0.427828	−	0.247007i	−0.698421	+	0.715687i	$0.746114\pi$
$444$		0			0
$445$	12.8185	−	22.2023i	0.607655	−	1.05249i
$446$	−18.9820			−0.898824
$447$		0			0
$448$	−0.761606	+	2.84235i	−0.0359825	+	0.134289i
$449$	8.91529	−	2.38885i	0.420739	−	0.112737i	−0.0422369	−	0.999108i	$-0.513448\pi$
$449$	8.91529	−	2.38885i	0.420739	−	0.112737i	0.462976	+	0.886371i	$0.346782\pi$
$450$		0			0
$451$	4.76490	−	8.25305i	0.224370	−	0.388621i
$452$	3.05691			0.143785
$453$		0			0
$454$	−13.3965	+	7.73445i	−0.628727	+	0.362996i
$455$	16.1677	+	29.3319i	0.757955	+	1.37510i
$456$		0			0
$457$	−6.15569	−	6.15569i	−0.287951	−	0.287951i	0.548319	−	0.836270i	$-0.315268\pi$
$457$	−6.15569	−	6.15569i	−0.287951	−	0.287951i	−0.836270	+	0.548319i	$0.815268\pi$
$458$	13.1282	−	7.57958i	0.613441	−	0.354170i
$459$		0			0
$460$	−8.33750	−	8.33750i	−0.388738	−	0.388738i
$461$	−10.0949	−	2.70491i	−0.470165	−	0.125980i	0.0159546	−	0.999873i	$-0.494921\pi$
$461$	−10.0949	−	2.70491i	−0.470165	−	0.125980i	−0.486119	+	0.873892i	$0.661588\pi$
$462$		0			0
$463$	5.41897	+	1.45201i	0.251841	+	0.0674806i	0.382531	−	0.923943i	$-0.375053\pi$
$463$	5.41897	+	1.45201i	0.251841	+	0.0674806i	−0.130690	+	0.991423i	$0.541719\pi$
$464$			8.59946i			0.399220i
$465$		0			0
$466$	−8.14087	+	8.14087i	−0.377118	+	0.377118i
$467$	−11.8737			−0.549447			−0.274724	−	0.961523i	$-0.588586\pi$
$467$	−11.8737			−0.549447			−0.274724	+	0.961523i	$0.588586\pi$
$468$		0			0
$469$	−24.3499			−1.12437
$470$	−14.1159	+	14.1159i	−0.651120	+	0.651120i
$471$		0			0
$472$			5.51405i			0.253805i
$473$	5.33877	+	1.43052i	0.245477	+	0.0657754i
$474$		0			0
$475$	−24.3360	−	6.52081i	−1.11661	−	0.299195i
$476$	−7.49432	−	7.49432i	−0.343502	−	0.343502i
$477$		0			0
$478$	3.48926	−	2.01453i	0.159595	−	0.0921423i
$479$	−22.2164	−	22.2164i	−1.01509	−	1.01509i	−0.999884	−	0.0152087i	$-0.995159\pi$
$479$	−22.2164	−	22.2164i	−1.01509	−	1.01509i	−0.0152087	−	0.999884i	$-0.504841\pi$
$480$		0			0
$481$	14.9287	+	15.5330i	0.680689	+	0.708242i
$482$	12.8261	−	7.40516i	0.584213	−	0.337296i
$483$		0			0
$484$	−10.2390			−0.465408
$485$	26.6995	−	46.2450i	1.21236	−	2.09988i
$486$		0			0
$487$	−25.9413	+	6.95096i	−1.17551	+	0.314978i	−0.793145	−	0.609032i	$-0.791558\pi$
$487$	−25.9413	+	6.95096i	−1.17551	+	0.314978i	−0.382368	+	0.924010i	$0.624891\pi$
$488$	1.64841	−	6.15196i	0.0746201	−	0.278486i
$489$		0			0
$490$	5.23714			0.236590
$491$	−1.33729	+	2.31626i	−0.0603512	+	0.104531i	−0.894622	−	0.446823i	$-0.852555\pi$
$491$	−1.33729	+	2.31626i	−0.0603512	+	0.104531i	0.834271	+	0.551354i	$0.185889\pi$
$492$		0			0
$493$	−26.8235	−	15.4865i	−1.20807	−	0.697478i
$494$	−16.0226	+	8.83164i	−0.720889	+	0.397354i
$495$		0			0
$496$	−1.33067	+	4.96612i	−0.0597488	+	0.222986i
$497$			18.8716i			0.846509i
$498$		0			0
$499$	−1.15780	+	4.32098i	−0.0518304	+	0.193434i	−0.986987	−	0.160802i	$-0.948592\pi$
$499$	−1.15780	+	4.32098i	−0.0518304	+	0.193434i	0.935156	+	0.354235i	$0.115259\pi$
$500$	0.0776933	−	0.0776933i	0.00347455	−	0.00347455i
$501$		0			0
$502$	−1.02638	−	3.83049i	−0.0458094	−	0.170963i
$503$	−35.5709	−	20.5369i	−1.58603	−	0.915694i	−0.993952	−	0.109812i	$-0.964975\pi$
$503$	−35.5709	−	20.5369i	−1.58603	−	0.915694i	−0.592076	−	0.805882i	$-0.701692\pi$
$504$		0			0
$505$	15.7420	+	4.21805i	0.700509	+	0.187701i
$506$	1.62920	−	2.82186i	0.0724268	−	0.125447i
$507$		0			0
$508$	−9.55958	−	16.5577i	−0.424138	−	0.734628i
$509$	2.46519	+	9.20021i	0.109268	+	0.407792i	0.998794	−	0.0490909i	$-0.0156324\pi$
$509$	2.46519	+	9.20021i	0.109268	+	0.407792i	−0.889527	+	0.456883i	$0.848966\pi$
$510$		0			0
$511$	38.3531	−	22.1432i	1.69664	−	0.979557i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	3.58617	+	13.3838i	0.158179	+	0.590333i
$515$	28.1386	−	7.53972i	1.23994	−	0.332240i
$516$		0			0
$517$	−4.77760	−	2.75835i	−0.210118	−	0.121312i
$518$	16.9836	−	4.55075i	0.746217	−	0.199948i
$519$		0			0
$520$	−0.225741	+	11.3797i	−0.00989939	+	0.499031i
$521$		−	8.13120i		−	0.356234i	−0.984009	−	0.178117i	$-0.942999\pi$
$521$		−	8.13120i		−	0.356234i	0.984009	−	0.178117i	$-0.0570006\pi$
$522$		0			0
$523$	18.9364	+	32.7988i	0.828031	+	1.43419i	0.899580	+	0.436755i	$0.143872\pi$
$523$	18.9364	+	32.7988i	0.828031	+	1.43419i	−0.0715491	+	0.997437i	$0.522794\pi$
$524$	−6.17593	−	10.6970i	−0.269797	−	0.467302i
$525$		0			0
$526$	11.3284	+	11.3284i	0.493940	+	0.493940i
$527$	−13.0940	−	13.0940i	−0.570383	−	0.570383i
$528$		0			0
$529$	4.52432	+	7.83636i	0.196710	+	0.340711i
$530$	−10.6241	−	18.4015i	−0.461482	−	0.799310i
$531$		0			0
$532$			14.9315i			0.647363i
$533$	−10.9468	+	37.8358i	−0.474159	+	1.63885i
$534$		0			0
$535$	0.740930	−	0.198532i	0.0320332	−	0.00858327i
$536$	−7.16627	−	4.13745i	−0.309536	−	0.178711i
$537$		0			0
$538$	2.12544	−	0.569509i	0.0916341	−	0.0245533i
$539$	0.374580	+	1.39795i	0.0161343	+	0.0602140i
$540$		0			0
$541$	−9.80824	+	9.80824i	−0.421689	+	0.421689i	−0.885785	−	0.464096i	$-0.846379\pi$
$541$	−9.80824	+	9.80824i	−0.421689	+	0.421689i	0.464096	+	0.885785i	$0.346379\pi$
$542$	5.35100	−	3.08940i	0.229845	−	0.132701i
$543$		0			0
$544$	−0.932200	−	3.47902i	−0.0399678	−	0.149162i
$545$	−6.42802	−	11.1337i	−0.275346	−	0.476914i
$546$		0			0
$547$	−18.8226	+	32.6018i	−0.804798	+	1.39395i	0.111629	+	0.993750i	$0.464393\pi$
$547$	−18.8226	+	32.6018i	−0.804798	+	1.39395i	−0.916427	+	0.400201i	$0.868940\pi$
$548$	6.71605	+	1.79956i	0.286895	+	0.0768734i
$549$		0			0
$550$	−3.75114	−	2.16572i	−0.159949	−	0.0923467i
$551$	11.2937	+	42.1487i	0.481128	+	1.79559i
$552$		0			0
$553$	−5.43787	+	5.43787i	−0.231242	+	0.231242i
$554$	−5.28525	+	19.7248i	−0.224549	+	0.838028i
$555$		0			0
$556$			5.68120i			0.240937i
$557$	8.83844	−	32.9855i	0.374497	−	1.39764i	−0.479582	−	0.877497i	$-0.659212\pi$
$557$	8.83844	−	32.9855i	0.374497	−	1.39764i	0.854079	−	0.520143i	$-0.174122\pi$
$558$		0			0
$559$	−22.8396	−	0.453073i	−0.966010	−	0.0191630i
$560$	8.04466	+	4.64459i	0.339949	+	0.196270i
$561$		0			0
$562$	10.3869	−	17.9906i	0.438145	−	0.758889i
$563$	29.5035			1.24343			0.621713	−	0.783245i	$-0.286437\pi$
$563$	29.5035			1.24343			0.621713	+	0.783245i	$0.286437\pi$
$564$		0			0
$565$	2.49759	−	9.32115i	0.105075	−	0.392144i
$566$	23.2833	−	6.23874i	0.978670	−	0.262234i
$567$		0			0
$568$	−3.20660	+	5.55400i	−0.134546	+	0.233041i
$569$	−14.7196			−0.617076			−0.308538	−	0.951212i	$-0.599840\pi$
$569$	−14.7196			−0.617076			−0.308538	+	0.951212i	$0.599840\pi$
$570$		0			0
$571$	16.5923	−	9.57956i	0.694365	−	0.400892i	−0.110880	−	0.993834i	$-0.535367\pi$
$571$	16.5923	−	9.57956i	0.694365	−	0.400892i	0.805245	+	0.592942i	$0.202034\pi$
$572$	−3.05372	+	0.753658i	−0.127682	+	0.0315120i
$573$		0			0
$574$	22.7304	+	22.7304i	0.948748	+	0.948748i
$575$	−16.0611	+	9.27287i	−0.669794	+	0.386706i
$576$		0			0
$577$	0.887796	+	0.887796i	0.0369594	+	0.0369594i	0.725345	−	0.688386i	$-0.241680\pi$
$577$	0.887796	+	0.887796i	0.0369594	+	0.0369594i	−0.688386	+	0.725345i	$0.741680\pi$
$578$	−3.89020	−	1.04237i	−0.161811	−	0.0433571i
$579$		0			0
$580$	26.2215	+	7.02603i	1.08879	+	0.291740i
$581$		−	33.7545i		−	1.40037i
$582$		0			0
$583$	4.15204	−	4.15204i	0.171960	−	0.171960i
$584$	15.0500			0.622773
$585$		0			0
$586$	2.59268			0.107103
$587$	7.08404	−	7.08404i	0.292390	−	0.292390i	−0.545634	−	0.838024i	$-0.683711\pi$
$587$	7.08404	−	7.08404i	0.292390	−	0.292390i	0.838024	+	0.545634i	$0.183711\pi$
$588$		0			0
$589$			26.0881i			1.07494i
$590$	16.8135	+	4.50515i	0.692199	+	0.185474i
$591$		0			0
$592$	5.77159	+	1.54649i	0.237211	+	0.0635605i
$593$	−26.1095	−	26.1095i	−1.07219	−	1.07219i	−0.997183	−	0.0750069i	$-0.976102\pi$
$593$	−26.1095	−	26.1095i	−1.07219	−	1.07219i	−0.0750069	−	0.997183i	$-0.523898\pi$
$594$		0			0
$595$	−28.9748	+	16.7286i	−1.18785	+	0.685807i
$596$	14.6958	+	14.6958i	0.601963	+	0.601963i
$597$		0			0
$598$	−3.74290	+	12.9367i	−0.153059	+	0.529021i
$599$	−6.17074	+	3.56268i	−0.252130	+	0.145567i	−0.620739	−	0.784017i	$-0.713167\pi$
$599$	−6.17074	+	3.56268i	−0.252130	+	0.145567i	0.368609	+	0.929584i	$0.379834\pi$
$600$		0			0
$601$	−3.21196			−0.131018			−0.0655092	−	0.997852i	$-0.520867\pi$
$601$	−3.21196			−0.131018			−0.0655092	+	0.997852i	$0.520867\pi$
$602$	−9.32193	+	16.1461i	−0.379933	+	0.658064i
$603$		0			0
$604$	−7.11970	+	1.90772i	−0.289697	+	0.0776240i
$605$	−8.36558	+	31.2208i	−0.340109	+	1.26930i
$606$		0			0
$607$	−41.3322			−1.67762			−0.838812	−	0.544421i	$-0.816749\pi$
$607$	−41.3322			−1.67762			−0.838812	+	0.544421i	$0.816749\pi$
$608$	−2.53711	+	4.39440i	−0.102893	+	0.178217i
$609$		0			0
$610$	−17.4118	−	10.0527i	−0.704982	−	0.407022i
$611$	21.9027	+	6.33698i	0.886088	+	0.256367i
$612$		0			0
$613$	5.73651	−	21.4090i	0.231695	−	0.864699i	−0.747915	−	0.663794i	$-0.768945\pi$
$613$	5.73651	−	21.4090i	0.231695	−	0.864699i	0.979611	−	0.200905i	$-0.0643883\pi$
$614$			0.579246i			0.0233765i
$615$		0			0
$616$	−0.664396	+	2.47956i	−0.0267693	+	0.0999043i
$617$	15.7837	−	15.7837i	0.635428	−	0.635428i	−0.313997	−	0.949424i	$-0.601668\pi$
$617$	15.7837	−	15.7837i	0.635428	−	0.635428i	0.949424	+	0.313997i	$0.101668\pi$
$618$		0			0
$619$	−4.30594	−	16.0700i	−0.173070	−	0.645907i	−0.996872	−	0.0790293i	$-0.974818\pi$
$619$	−4.30594	−	16.0700i	−0.173070	−	0.645907i	0.823802	−	0.566878i	$-0.191849\pi$
$620$	14.0555	+	8.11497i	0.564484	+	0.325905i
$621$		0			0
$622$	16.7615	+	4.49124i	0.672076	+	0.180082i
$623$	−11.9489	+	20.6961i	−0.478723	+	0.829173i
$624$		0			0
$625$	−12.5864	−	21.8003i	−0.503456	−	0.872012i
$626$	6.38391	+	23.8251i	0.255152	+	0.952241i
$627$		0			0
$628$	−9.02434	+	5.21020i	−0.360110	+	0.207910i
$629$	−15.2177	+	15.2177i	−0.606771	+	0.606771i
$630$		0			0
$631$	−3.53536	−	13.1942i	−0.140741	−	0.525251i	−0.999908	−	0.0135565i	$-0.995685\pi$
$631$	−3.53536	−	13.1942i	−0.140741	−	0.525251i	0.859168	−	0.511694i	$-0.170982\pi$
$632$	−2.52437	+	0.676403i	−0.100414	+	0.0269059i
$633$		0			0
$634$	21.6344	+	12.4906i	0.859211	+	0.496065i
$635$	−58.2982	+	15.6210i	−2.31350	+	0.619899i
$636$		0			0
$637$	−2.88751	−	5.23859i	−0.114407	−	0.207560i
$638$			7.50184i			0.297000i
$639$		0			0
$640$	1.57838	+	2.73384i	0.0623911	+	0.108065i
$641$	11.0893	+	19.2072i	0.438000	+	0.758638i	0.997535	−	0.0701685i	$-0.0223537\pi$
$641$	11.0893	+	19.2072i	0.438000	+	0.758638i	−0.559535	+	0.828807i	$0.689020\pi$
$642$		0			0
$643$	6.53919	+	6.53919i	0.257881	+	0.257881i	0.824192	−	0.566311i	$-0.191630\pi$
$643$	6.53919	+	6.53919i	0.257881	+	0.257881i	−0.566311	+	0.824192i	$0.691630\pi$
$644$	7.77191	+	7.77191i	0.306256	+	0.306256i
$645$		0			0
$646$	−9.13803	−	15.8275i	−0.359531	−	0.622726i
$647$	8.23841	+	14.2694i	0.323886	+	0.560986i	0.981286	−	0.192555i	$-0.0616774\pi$
$647$	8.23841	+	14.2694i	0.323886	+	0.560986i	−0.657401	+	0.753541i	$0.728344\pi$
$648$		0			0
$649$			4.81024i			0.188819i
$650$	17.1970	+	4.97550i	0.674520	+	0.195155i
$651$		0			0
$652$	6.58816	−	1.76529i	0.258012	−	0.0691342i
$653$	−29.3351	−	16.9366i	−1.14797	−	0.662781i	−0.199579	−	0.979882i	$-0.563957\pi$
$653$	−29.3351	−	16.9366i	−1.14797	−	0.662781i	−0.948392	+	0.317101i	$0.897291\pi$
$654$		0			0
$655$	−37.6633	+	10.0919i	−1.47163	+	0.394322i
$656$	2.82738	+	10.5519i	0.110390	+	0.411983i
$657$		0			0
$658$	13.1584	−	13.1584i	0.512966	−	0.512966i
$659$	−8.33425	+	4.81178i	−0.324656	+	0.187440i	−0.653466	−	0.756956i	$-0.726686\pi$
$659$	−8.33425	+	4.81178i	−0.324656	+	0.187440i	0.328810	+	0.944396i	$0.393352\pi$
$660$		0			0
$661$	6.81782	+	25.4445i	0.265182	+	0.989675i	0.962139	+	0.272561i	$0.0878706\pi$
$661$	6.81782	+	25.4445i	0.265182	+	0.989675i	−0.696956	+	0.717114i	$0.745463\pi$
$662$	16.0916	+	27.8714i	0.625417	+	1.08325i
$663$		0			0
$664$	5.73546	−	9.93410i	0.222579	−	0.385518i
$665$	45.5292	+	12.1995i	1.76555	+	0.473077i
$666$		0			0
$667$	27.8170	+	16.0601i	1.07708	+	0.621851i
$668$	−3.56186	−	13.2930i	−0.137812	−	0.514323i
$669$		0			0
$670$	−18.4710	+	18.4710i	−0.713597	+	0.713597i
$671$	1.43801	−	5.36673i	0.0555138	−	0.207180i
$672$		0			0
$673$		−	5.36459i		−	0.206790i	−0.994640	−	0.103395i	$-0.967029\pi$
$673$		−	5.36459i		−	0.206790i	0.994640	−	0.103395i	$-0.0329706\pi$
$674$	−7.69861	+	28.7316i	−0.296539	+	1.10670i
$675$		0			0
$676$	11.5073	−	6.04839i	0.442587	−	0.232631i
$677$	6.42329	+	3.70849i	0.246867	+	0.142529i	0.618329	−	0.785919i	$-0.287810\pi$
$677$	6.42329	+	3.70849i	0.246867	+	0.142529i	−0.371462	+	0.928448i	$0.621143\pi$
$678$		0			0
$679$	−24.8883	+	43.1078i	−0.955125	+	1.65433i
$680$	−11.3699			−0.436015
$681$		0			0
$682$	−1.16082	+	4.33226i	−0.0444503	+	0.165891i
$683$	−17.3967	+	4.66144i	−0.665668	+	0.178365i	−0.575803	−	0.817589i	$-0.695310\pi$
$683$	−17.3967	+	4.66144i	−0.665668	+	0.178365i	−0.0898653	+	0.995954i	$0.528644\pi$
$684$		0			0
$685$	10.9745	−	19.0083i	0.419312	−	0.726270i
$686$	15.7165			0.600058
$687$		0			0
$688$	−5.48696	+	3.16790i	−0.209188	+	0.120775i
$689$	−12.5489	+	20.7727i	−0.478077	+	0.791379i
$690$		0			0
$691$	11.2660	+	11.2660i	0.428581	+	0.428581i	0.888145	−	0.459564i	$-0.151994\pi$
$691$	11.2660	+	11.2660i	0.428581	+	0.428581i	−0.459564	+	0.888145i	$0.651994\pi$
$692$	−3.51613	+	2.03004i	−0.133663	+	0.0771704i
$693$		0			0
$694$	−24.0279	−	24.0279i	−0.912088	−	0.912088i
$695$	17.3231	+	4.64172i	0.657104	+	0.176071i
$696$		0			0
$697$	−38.0053	−	10.1835i	−1.43955	−	0.385727i
$698$		−	8.20818i		−	0.310684i
$699$		0			0
$700$	10.3313	−	10.3313i	0.390487	−	0.390487i
$701$	10.3675			0.391576			0.195788	−	0.980646i	$-0.437274\pi$
$701$	10.3675			0.391576			0.195788	+	0.980646i	$0.437274\pi$
$702$		0			0
$703$	30.3195			1.14352
$704$	−0.616853	+	0.616853i	−0.0232485	+	0.0232485i
$705$		0			0
$706$			15.6939i			0.590646i
$707$	−14.6741	−	3.93191i	−0.551876	−	0.147875i
$708$		0			0
$709$	22.1814	+	5.94348i	0.833038	+	0.223212i	0.650039	−	0.759901i	$-0.274753\pi$
$709$	22.1814	+	5.94348i	0.833038	+	0.223212i	0.182999	+	0.983113i	$0.441419\pi$
$710$	14.3154	+	14.3154i	0.537247	+	0.537247i
$711$		0			0
$712$	−7.03323	+	4.06064i	−0.263582	+	0.152179i
$713$	13.5790	+	13.5790i	0.508537	+	0.508537i
$714$		0			0
$715$	−0.196928	+	9.92717i	−0.00736467	+	0.371255i
$716$	16.8120	−	9.70640i	0.628293	−	0.362745i
$717$		0			0
$718$	−17.6996			−0.660544
$719$	25.3323	−	43.8768i	0.944735	−	1.63633i	0.188454	−	0.982082i	$-0.439652\pi$
$719$	25.3323	−	43.8768i	0.944735	−	1.63633i	0.756281	−	0.654247i	$-0.227014\pi$
$720$		0			0
$721$	−26.2298	+	7.02824i	−0.976847	+	0.261745i
$722$	−1.74644	+	6.51780i	−0.0649957	+	0.242567i
$723$		0			0
$724$	−0.0982851			−0.00365274
$725$	21.3490	−	36.9775i	0.792881	−	1.37331i
$726$		0			0
$727$	−26.9809	−	15.5774i	−1.00067	−	0.577734i	−0.0922201	−	0.995739i	$-0.529396\pi$
$727$	−26.9809	−	15.5774i	−1.00067	−	0.577734i	−0.908445	+	0.418004i	$0.862730\pi$
$728$	0.210427	−	10.6077i	0.00779894	−	0.393147i
$729$		0			0
$730$	12.2963	−	45.8905i	0.455107	−	1.69848i
$731$		−	22.8199i		−	0.844026i
$732$		0			0
$733$	1.99422	−	7.44254i	0.0736583	−	0.274896i	−0.919267	−	0.393634i	$-0.871218\pi$
$733$	1.99422	−	7.44254i	0.0736583	−	0.274896i	0.992926	+	0.118737i	$0.0378846\pi$
$734$	−18.6847	+	18.6847i	−0.689666	+	0.689666i
$735$		0			0
$736$	0.966728	+	3.60788i	0.0356341	+	0.132988i
$737$	−6.25158	−	3.60935i	−0.230280	−	0.132952i
$738$		0			0
$739$	9.13725	+	2.44832i	0.336119	+	0.0900629i	0.422931	−	0.906162i	$-0.361001\pi$
$739$	9.13725	+	2.44832i	0.336119	+	0.0900629i	−0.0868119	+	0.996225i	$0.527668\pi$
$740$	9.43115	−	16.3352i	0.346696	−	0.600495i
$741$		0			0
$742$	9.90340	+	17.1532i	0.363565	+	0.629713i
$743$	1.36869	+	5.10804i	0.0502125	+	0.187396i	0.986477	−	0.163901i	$-0.0524076\pi$
$743$	1.36869	+	5.10804i	0.0502125	+	0.187396i	−0.936264	+	0.351296i	$0.885741\pi$
$744$		0			0
$745$	56.8174	−	32.8036i	2.08163	−	1.20183i
$746$	−16.0506	+	16.0506i	−0.587656	+	0.587656i
$747$		0			0
$748$	−0.813216	−	3.03496i	−0.0297341	−	0.110969i
$749$	−0.690667	+	0.185064i	−0.0252364	+	0.00676208i
$750$		0			0
$751$	−13.5277	−	7.81023i	−0.493633	−	0.284999i	0.232447	−	0.972609i	$-0.425327\pi$
$751$	−13.5277	−	7.81023i	−0.493633	−	0.284999i	−0.726081	+	0.687610i	$0.758660\pi$
$752$	6.10838	−	1.63674i	0.222750	−	0.0596856i
$753$		0			0
$754$	−7.42931	−	30.1026i	−0.270560	−	1.09627i
$755$			23.2681i			0.846813i
$756$		0			0
$757$	−2.81998	−	4.88435i	−0.102494	−	0.177525i	0.810218	−	0.586129i	$-0.199349\pi$
$757$	−2.81998	−	4.88435i	−0.102494	−	0.177525i	−0.912712	+	0.408604i	$0.866016\pi$
$758$	−5.07998	−	8.79879i	−0.184513	−	0.319586i
$759$		0			0
$760$	11.3265	+	11.3265i	0.410857	+	0.410857i
$761$	12.9764	+	12.9764i	0.470394	+	0.470394i	0.902042	−	0.431648i	$-0.142068\pi$
$761$	12.9764	+	12.9764i	0.470394	+	0.470394i	−0.431648	+	0.902042i	$0.642068\pi$
$762$		0			0
$763$	5.99196	+	10.3784i	0.216923	+	0.375722i
$764$	6.34858	+	10.9961i	0.229684	+	0.397824i
$765$		0			0
$766$			18.7184i			0.676323i
$767$	−4.76374	−	19.3020i	−0.172009	−	0.696956i
$768$		0			0
$769$	−19.4642	+	5.21542i	−0.701897	+	0.188073i	−0.592080	−	0.805879i	$-0.701693\pi$
$769$	−19.4642	+	5.21542i	−0.701897	+	0.188073i	−0.109817	+	0.993952i	$0.535026\pi$
$770$	7.01786	+	4.05176i	0.252906	+	0.146015i
$771$		0			0
$772$	22.9198	−	6.14134i	0.824901	−	0.221031i
$773$	−5.89523	−	22.0013i	−0.212037	−	0.791331i	−0.987189	−	0.159557i	$-0.948994\pi$
$773$	−5.89523	−	22.0013i	−0.212037	−	0.791331i	0.775152	−	0.631774i	$-0.217673\pi$
$774$		0			0
$775$	18.0507	−	18.0507i	0.648402	−	0.648402i
$776$	−14.6495	+	8.45787i	−0.525885	+	0.303620i
$777$		0			0
$778$	−5.68375	−	21.2120i	−0.203772	−	0.760489i
$779$	27.7158	+	48.0051i	0.993020	+	1.71996i
$780$		0			0
$781$	−2.79732	+	4.84510i	−0.100096	+	0.173371i
$782$	−12.9947	−	3.48191i	−0.464688	−	0.124513i
$783$		0			0
$784$	−1.43675	−	0.829510i	−0.0513126	−	0.0296254i
$785$	8.51380	+	31.7740i	0.303871	+	1.13406i
$786$		0			0
$787$	39.3475	−	39.3475i	1.40259	−	1.40259i	0.610802	−	0.791784i	$-0.290847\pi$
$787$	39.3475	−	39.3475i	1.40259	−	1.40259i	0.791784	−	0.610802i	$-0.209153\pi$
$788$	1.38307	−	5.16169i	0.0492699	−	0.183878i
$789$		0			0
$790$			8.24997i			0.293521i
$791$	−2.32816	+	8.68882i	−0.0827799	+	0.308939i
$792$		0			0
$793$	−0.455446	+	22.9592i	−0.0161734	+	0.815303i
$794$	−3.03923	−	1.75470i	−0.107858	−	0.0622721i
$795$		0			0
$796$	−4.29806	+	7.44445i	−0.152341	+	0.263862i
$797$	13.2860			0.470613			0.235306	−	0.971921i	$-0.424391\pi$
$797$	13.2860			0.470613			0.235306	+	0.971921i	$0.424391\pi$
$798$		0			0
$799$	−5.89510	+	22.0008i	−0.208554	+	0.778333i
$800$	4.79601	−	1.28509i	0.169565	−	0.0454347i
$801$		0			0
$802$	−1.25974	+	2.18194i	−0.0444831	+	0.0770470i
$803$	13.1290			0.463313
$804$		0			0
$805$	30.0480	−	17.3482i	1.05905	−	0.611445i
$806$	0.367655	−	18.5336i	0.0129501	−	0.652819i
$807$		0			0
$808$	−3.65055	−	3.65055i	−0.128426	−	0.128426i
$809$	−27.6216	+	15.9473i	−0.971122	+	0.560678i	−0.899578	−	0.436760i	$-0.856126\pi$
$809$	−27.6216	+	15.9473i	−0.971122	+	0.560678i	−0.0715440	+	0.997437i	$0.522793\pi$
$810$		0			0
$811$	−3.25912	−	3.25912i	−0.114443	−	0.114443i	0.647566	−	0.762009i	$-0.275787\pi$
$811$	−3.25912	−	3.25912i	−0.114443	−	0.114443i	−0.762009	+	0.647566i	$0.775787\pi$
$812$	−24.4427	−	6.54940i	−0.857771	−	0.229839i
$813$		0			0
$814$	5.03492	+	1.34910i	0.176474	+	0.0472860i
$815$		−	21.5310i		−	0.754197i
$816$		0			0
$817$	−22.7329	+	22.7329i	−0.795325	+	0.795325i
$818$	−17.2470			−0.603027
$819$		0			0
$820$	34.4850			1.20427
$821$	32.7511	−	32.7511i	1.14302	−	1.14302i	0.155128	−	0.987894i	$-0.450421\pi$
$821$	32.7511	−	32.7511i	1.14302	−	1.14302i	0.987894	−	0.155128i	$-0.0495789\pi$
$822$		0			0
$823$			9.92250i			0.345877i	0.984933	+	0.172938i	$0.0553261\pi$
$823$			9.92250i			0.345877i	−0.984933	+	0.172938i	$0.944674\pi$
$824$	−8.91374	−	2.38843i	−0.310525	−	0.0832049i
$825$		0			0
$826$	−15.6729	−	4.19953i	−0.545329	−	0.146120i
$827$	−16.5758	−	16.5758i	−0.576398	−	0.576398i	0.357511	−	0.933909i	$-0.383625\pi$
$827$	−16.5758	−	16.5758i	−0.576398	−	0.576398i	−0.933909	+	0.357511i	$0.883625\pi$
$828$		0			0
$829$	−29.4031	+	16.9759i	−1.02121	+	0.589598i	−0.914455	−	0.404687i	$-0.867380\pi$
$829$	−29.4031	+	16.9759i	−1.02121	+	0.589598i	−0.106758	+	0.994285i	$0.534047\pi$
$830$	−25.6051	−	25.6051i	−0.888765	−	0.888765i
$831$		0			0
$832$	1.86435	−	3.08613i	0.0646347	−	0.106992i
$833$	5.17482	−	2.98768i	0.179297	−	0.103517i
$834$		0			0
$835$	−43.4433			−1.50342
$836$	−2.21328	+	3.83351i	−0.0765478	+	0.132585i
$837$		0			0
$838$	−18.1260	+	4.85685i	−0.626152	+	0.167777i
$839$	0.559089	−	2.08655i	0.0193019	−	0.0720357i	−0.955603	−	0.294657i	$-0.904795\pi$
$839$	0.559089	−	2.08655i	0.0193019	−	0.0720357i	0.974905	+	0.222621i	$0.0714613\pi$
$840$		0			0
$841$	−44.9507			−1.55002
$842$	11.9748	−	20.7409i	0.412678	−	0.714780i
$843$		0			0
$844$	−8.43636	−	4.87073i	−0.290391	−	0.167658i
$845$	−9.04100	−	40.0297i	−0.311020	−	1.37706i
$846$		0			0
$847$	7.79808	−	29.1028i	0.267945	−	0.999985i
$848$			6.73100i			0.231144i
$849$		0			0
$850$	−4.62856	+	17.2740i	−0.158758	+	0.592493i
$851$	15.7814	−	15.7814i	0.540979	−	0.540979i
$852$		0			0
$853$	10.0355	+	37.4530i	0.343609	+	1.28237i	0.894229	+	0.447611i	$0.147725\pi$
$853$	10.0355	+	37.4530i	0.343609	+	1.28237i	−0.550619	+	0.834756i	$0.685608\pi$
$854$	16.2306	+	9.37074i	0.555400	+	0.320660i
$855$		0			0
$856$	−0.234711	−	0.0628908i	−0.00802227	−	0.00214956i
$857$	−9.92497	+	17.1906i	−0.339031	+	0.587218i	−0.984251	−	0.176779i	$-0.943432\pi$
$857$	−9.92497	+	17.1906i	−0.339031	+	0.587218i	0.645220	+	0.763997i	$0.276766\pi$
$858$		0			0
$859$	−6.14228	−	10.6387i	−0.209572	−	0.362989i	0.742008	−	0.670391i	$-0.233874\pi$
$859$	−6.14228	−	10.6387i	−0.209572	−	0.362989i	−0.951580	+	0.307402i	$0.900540\pi$
$860$	5.17655	+	19.3191i	0.176519	+	0.658777i
$861$		0			0
$862$	−0.663458	+	0.383048i	−0.0225975	+	0.0130467i
$863$	30.8583	−	30.8583i	1.05043	−	1.05043i	0.0517694	−	0.998659i	$-0.483514\pi$
$863$	30.8583	−	30.8583i	1.05043	−	1.05043i	0.998659	−	0.0517694i	$-0.0164861\pi$
$864$		0			0
$865$	3.31721	+	12.3800i	0.112789	+	0.420932i
$866$	−13.7916	+	3.69544i	−0.468656	+	0.125576i
$867$		0			0
$868$	−13.1020	−	7.56446i	−0.444712	−	0.256755i
$869$	−2.20216	+	0.590068i	−0.0747033	+	0.0200167i
$870$		0			0
$871$	28.6601	+	8.29207i	0.971111	+	0.280966i
$872$			4.07253i			0.137913i
$873$		0			0
$874$	9.47649	+	16.4138i	0.320547	+	0.555204i
$875$	0.161660	+	0.280004i	0.00546511	+	0.00946585i
$876$		0			0
$877$	22.6846	+	22.6846i	0.766004	+	0.766004i	0.977400	−	0.211396i	$-0.0678011\pi$
$877$	22.6846	+	22.6846i	0.766004	+	0.766004i	−0.211396	+	0.977400i	$0.567801\pi$
$878$	−8.97204	−	8.97204i	−0.302792	−	0.302792i
$879$		0			0
$880$	1.37692	+	2.38490i	0.0464160	+	0.0803949i
$881$	7.71084	+	13.3556i	0.259785	+	0.449960i	0.966184	−	0.257853i	$-0.0830151\pi$
$881$	7.71084	+	13.3556i	0.259785	+	0.449960i	−0.706399	+	0.707813i	$0.749682\pi$
$882$		0			0
$883$		−	37.0096i		−	1.24547i	−0.782432	−	0.622736i	$-0.786021\pi$
$883$		−	37.0096i		−	1.24547i	0.782432	−	0.622736i	$-0.213979\pi$
$884$	6.26881	+	11.3730i	0.210843	+	0.382516i
$885$		0			0
$886$	10.0435	−	2.69114i	0.337418	−	0.0904108i
$887$	7.62537	+	4.40251i	0.256035	+	0.147822i	0.622524	−	0.782600i	$-0.286107\pi$
$887$	7.62537	+	4.40251i	0.256035	+	0.147822i	−0.366490	+	0.930422i	$0.619440\pi$
$888$		0			0
$889$	54.3434	−	14.5613i	1.82262	−	0.488369i
$890$	6.63534	+	24.7634i	0.222417	+	0.830072i
$891$		0			0
$892$	13.4223	−	13.4223i	0.449412	−	0.449412i
$893$	27.7896	−	16.0443i	0.929943	−	0.536903i
$894$		0			0
$895$	−15.8609	−	59.1936i	−0.530171	−	1.97862i
$896$	−1.47131	−	2.54838i	−0.0491530	−	0.0851356i
$897$		0			0
$898$	−4.61489	+	7.99323i	−0.154001	+	0.266738i
$899$	−42.7060	−	11.4430i	−1.42432	−	0.381646i
$900$		0			0
$901$	−20.9954	−	12.1217i	−0.699457	−	0.403832i
$902$	2.46649	+	9.20508i	0.0821253	+	0.306496i
$903$		0			0
$904$	−2.16156	+	2.16156i	−0.0718925	+	0.0718925i
$905$	−0.0803021	+	0.299691i	−0.00266933	+	0.00996208i
$906$		0			0
$907$			35.2836i			1.17157i	0.810465	+	0.585787i	$0.199215\pi$
$907$			35.2836i			1.17157i	−0.810465	+	0.585787i	$0.800785\pi$
$908$	4.00365	−	14.9418i	0.132866	−	0.495861i
$909$		0			0
$910$	−32.1731	−	9.30845i	−1.06653	−	0.308572i
$911$	−28.0830	−	16.2137i	−0.930431	−	0.537185i	−0.0434832	−	0.999054i	$-0.513845\pi$
$911$	−28.0830	−	16.2137i	−0.930431	−	0.537185i	−0.886948	+	0.461870i	$0.847179\pi$
$912$		0			0
$913$	5.00339	−	8.66613i	0.165588	−	0.286807i
$914$	8.70546			0.287951
$915$		0			0
$916$	−3.92348	+	14.6426i	−0.129635	+	0.483806i
$917$	35.1083	−	9.40725i	1.15938	−	0.310655i
$918$		0			0
$919$	−14.7996	+	25.6336i	−0.488193	+	0.845575i	−0.999908	−	0.0135801i	$-0.995677\pi$
$919$	−14.7996	+	25.6336i	−0.488193	+	0.845575i	0.511715	+	0.859155i	$0.329011\pi$
$920$	11.7910			0.388738
$921$		0			0
$922$	9.05081	−	5.22549i	0.298072	−	0.172092i
$923$	6.42652	−	22.2122i	0.211531	−	0.731122i
$924$		0			0
$925$	−20.9784	−	20.9784i	−0.689767	−	0.689767i
$926$	−4.85852	+	2.80507i	−0.159661	+	0.0921802i
$927$		0			0
$928$	−6.08073	−	6.08073i	−0.199610	−	0.199610i
$929$	−22.5602	−	6.04499i	−0.740177	−	0.198330i	−0.131020	−	0.991380i	$-0.541825\pi$
$929$	−22.5602	−	6.04499i	−0.740177	−	0.198330i	−0.609157	+	0.793050i	$0.708492\pi$
$930$		0			0
$931$	−8.13139	−	2.17880i	−0.266496	−	0.0714073i
$932$		−	11.5129i		−	0.377118i
$933$		0			0
$934$	8.39594	−	8.39594i	0.274724	−	0.274724i
$935$	−9.91865			−0.324374
$936$		0			0
$937$	13.0003			0.424700			0.212350	−	0.977194i	$-0.431888\pi$
$937$	13.0003			0.424700			0.212350	+	0.977194i	$0.431888\pi$
$938$	17.2180	−	17.2180i	0.562187	−	0.562187i
$939$		0			0
$940$		−	19.9630i		−	0.651120i
$941$	−29.9063	−	8.01337i	−0.974918	−	0.261229i	−0.264015	−	0.964519i	$-0.585047\pi$
$941$	−29.9063	−	8.01337i	−0.974918	−	0.261229i	−0.710903	+	0.703290i	$0.751714\pi$
$942$		0			0
$943$	39.4130	+	10.5607i	1.28346	+	0.343903i
$944$	−3.89902	−	3.89902i	−0.126902	−	0.126902i
$945$		0			0
$946$	−4.78661	+	2.76355i	−0.155626	+	0.0898509i
$947$	−14.5173	−	14.5173i	−0.471747	−	0.471747i	0.430732	−	0.902480i	$-0.358255\pi$
$947$	−14.5173	−	14.5173i	−0.471747	−	0.471747i	−0.902480	+	0.430732i	$0.858255\pi$
$948$		0			0
$949$	−52.6827	+	13.0021i	−1.71015	+	0.422066i
$950$	21.8191	−	12.5972i	0.707904	−	0.408709i
$951$		0			0
$952$	10.5986			0.343502
$953$	−17.8354	+	30.8919i	−0.577747	+	1.00069i	0.417990	+	0.908451i	$0.362735\pi$
$953$	−17.8354	+	30.8919i	−0.577747	+	1.00069i	−0.995737	+	0.0922353i	$0.970599\pi$
$954$		0			0
$955$	38.7163	−	10.3740i	1.25283	−	0.335695i
$956$	−1.04280	+	3.89177i	−0.0337264	+	0.125869i
$957$		0			0
$958$	31.4187			1.01509
$959$	−10.2300	+	17.7188i	−0.330343	+	0.572171i
$960$		0			0
$961$	3.95508	+	2.28347i	0.127583	+	0.0736602i
$962$	−21.5396	−	0.427286i	−0.694466	−	0.0137763i
$963$		0			0
$964$	−3.83319	+	14.3057i	−0.123459	+	0.460754i
$965$		−	74.9048i		−	2.41127i
$966$		0			0
$967$	−9.51213	+	35.4997i	−0.305889	+	1.14159i	0.626288	+	0.779592i	$0.284574\pi$
$967$	−9.51213	+	35.4997i	−0.305889	+	1.14159i	−0.932177	+	0.362003i	$0.882093\pi$
$968$	7.24006	−	7.24006i	0.232704	−	0.232704i
$969$		0			0
$970$	13.8207	+	51.5796i	0.443756	+	1.65612i
$971$	2.23727	+	1.29169i	0.0717976	+	0.0414523i	0.535469	−	0.844555i	$-0.320135\pi$
$971$	2.23727	+	1.29169i	0.0717976	+	0.0414523i	−0.463671	+	0.886007i	$0.653468\pi$
$972$		0			0
$973$	−16.1480	−	4.32684i	−0.517680	−	0.138712i
$974$	13.4282	−	23.2584i	0.430268	−	0.745246i
$975$		0			0
$976$	3.18449	+	5.51569i	0.101933	+	0.176553i
$977$	8.15477	+	30.4340i	0.260894	+	0.973671i	0.964716	+	0.263294i	$0.0848089\pi$
$977$	8.15477	+	30.4340i	0.260894	+	0.973671i	−0.703821	+	0.710377i	$0.748524\pi$
$978$		0			0
$979$	−6.13552	+	3.54235i	−0.196092	+	0.113214i
$980$	−3.70322	+	3.70322i	−0.118295	+	0.118295i
$981$		0			0
$982$	−0.692234	−	2.58345i	−0.0220901	−	0.0824413i
$983$	−25.7225	+	6.89232i	−0.820420	+	0.219831i	−0.644530	−	0.764579i	$-0.722947\pi$
$983$	−25.7225	+	6.89232i	−0.820420	+	0.219831i	−0.175890	+	0.984410i	$0.556280\pi$
$984$		0			0
$985$	−14.6090	−	8.43454i	−0.465483	−	0.268747i
$986$	29.9177	−	8.01642i	0.952773	−	0.255295i
$987$		0			0
$988$	5.08475	−	17.5746i	0.161767	−	0.559122i
$989$			23.6652i			0.752508i
$990$		0			0
$991$	−12.7440	−	22.0732i	−0.404826	−	0.701179i	0.589475	−	0.807787i	$-0.299335\pi$
$991$	−12.7440	−	22.0732i	−0.404826	−	0.701179i	−0.994301	+	0.106607i	$0.966001\pi$
$992$	−2.57066	−	4.45251i	−0.0816184	−	0.141367i
$993$		0			0
$994$	−13.3443	−	13.3443i	−0.423254	−	0.423254i
$995$	19.1880	+	19.1880i	0.608301	+	0.608301i
$996$		0			0
$997$	−3.21008	−	5.56002i	−0.101664	−	0.176087i	0.810706	−	0.585453i	$-0.199083\pi$
$997$	−3.21008	−	5.56002i	−0.101664	−	0.176087i	−0.912370	+	0.409366i	$0.865750\pi$
$998$	−2.23670	−	3.87408i	−0.0708016	−	0.122632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	702.2.bb.a.89.1		56
3.2	odd	2		234.2.y.a.11.11	✓	56
9.4	even	3		234.2.z.a.167.2	yes	56
9.5	odd	6		702.2.bc.a.557.8		56
13.6	odd	12		702.2.bc.a.305.8		56
39.32	even	12		234.2.z.a.227.2	yes	56
117.32	even	12	inner	702.2.bb.a.71.1		56
117.58	odd	12		234.2.y.a.149.11	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
234.2.y.a.11.11	✓	56	3.2	odd	2
234.2.y.a.149.11	yes	56	117.58	odd	12
234.2.z.a.167.2	yes	56	9.4	even	3
234.2.z.a.227.2	yes	56	39.32	even	12
702.2.bb.a.71.1		56	117.32	even	12	inner
702.2.bb.a.89.1		56	1.1	even	1	trivial
702.2.bc.a.305.8		56	13.6	odd	12
702.2.bc.a.557.8		56	9.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 702 = 2 \cdot 3^{3} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	702.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-3.04921 - 0.817032i) q^{5} +(2.84235 + 0.761606i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.73384 - 1.57838i) q^{10} +(0.616853 + 0.616853i) q^{11} +(-3.08613 - 1.86435i) q^{13} +(-2.54838 + 1.47131i) q^{14} -1.00000 q^{16} +(1.80087 - 3.11920i) q^{17} +(-4.90132 + 1.31331i) q^{19} +(-0.817032 + 3.04921i) q^{20} -0.872362 q^{22} +(-1.86758 + 3.23474i) q^{23} +(4.29998 + 2.48260i) q^{25} +(3.50052 - 0.863928i) q^{26} +(0.761606 - 2.84235i) q^{28} -8.59946i q^{29} +(1.33067 - 4.96612i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.932200 + 3.47902i) q^{34} +(-8.04466 - 4.64459i) q^{35} +(-5.77159 - 1.54649i) q^{37} +(2.53711 - 4.39440i) q^{38} +(-1.57838 - 2.73384i) q^{40} +(-2.82738 - 10.5519i) q^{41} +(5.48696 - 3.16790i) q^{43} +(0.616853 - 0.616853i) q^{44} +(-0.966728 - 3.60788i) q^{46} +(-6.10838 + 1.63674i) q^{47} +(1.43675 + 0.829510i) q^{49} +(-4.79601 + 1.28509i) q^{50} +(-1.86435 + 3.08613i) q^{52} -6.73100i q^{53} +(-1.37692 - 2.38490i) q^{55} +(1.47131 + 2.54838i) q^{56} +(6.08073 + 6.08073i) q^{58} +(3.89902 + 3.89902i) q^{59} +(-3.18449 - 5.51569i) q^{61} +(2.57066 + 4.45251i) q^{62} +1.00000i q^{64} +(7.88701 + 8.20625i) q^{65} +(-7.99294 + 2.14170i) q^{67} +(-3.11920 - 1.80087i) q^{68} +(8.97266 - 2.40422i) q^{70} +(1.65986 + 6.19468i) q^{71} +(10.6419 - 10.6419i) q^{73} +(5.17467 - 2.98760i) q^{74} +(1.31331 + 4.90132i) q^{76} +(1.28351 + 2.22311i) q^{77} +(-1.30671 + 2.26329i) q^{79} +(3.04921 + 0.817032i) q^{80} +(9.46058 + 5.46207i) q^{82} +(-2.96889 - 11.0800i) q^{83} +(-8.03972 + 8.03972i) q^{85} +(-1.63983 + 6.11991i) q^{86} +0.872362i q^{88} +(-2.10194 + 7.84455i) q^{89} +(-7.35197 - 7.64956i) q^{91} +(3.23474 + 1.86758i) q^{92} +(3.16193 - 5.47662i) q^{94} +16.0181 q^{95} +(-4.37811 + 16.3393i) q^{97} +(-1.60249 + 0.429386i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 4 q^{7} - 56 q^{16} - 8 q^{19} - 4 q^{28} + 8 q^{31} - 24 q^{35} - 4 q^{37} + 36 q^{38} + 48 q^{41} + 12 q^{43} - 60 q^{47} + 24 q^{50} - 4 q^{52} + 120 q^{65} - 56 q^{67} - 24 q^{71} + 28 q^{73}+ \cdots + 48 q^{98}+O(q^{100}) \) 56 * q + 4 * q^7 - 56 * q^16 - 8 * q^19 - 4 * q^28 + 8 * q^31 - 24 * q^35 - 4 * q^37 + 36 * q^38 + 48 * q^41 + 12 * q^43 - 60 * q^47 + 24 * q^50 - 4 * q^52 + 120 * q^65 - 56 * q^67 - 24 * q^71 + 28 * q^73 - 48 * q^74 + 4 * q^76 + 24 * q^77 - 24 * q^79 + 60 * q^83 - 48 * q^86 + 4 * q^91 + 24 * q^92 + 20 * q^97 + 48 * q^98

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