LMFDB - Embedded newform 504.2.cj.d.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(37,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("504.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 $ x^16 + 4x^14 + 6x^12 + 8x^10 + 20x^8 + 32x^6 + 96x^4 + 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.1
Root			$-1.33546 - 0.465333i$ of defining polynomial
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.d.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33546 + 0.465333i) q^{2} +(1.56693 - 1.24287i) q^{4} +(0.937379 + 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 + 2.38896i) q^{8} +O(q^{10})$	\(q+(-1.33546 + 0.465333i) q^{2} +(1.56693 - 1.24287i) q^{4} +(0.937379 + 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 + 2.38896i) q^{8} +(-1.50367 - 0.286555i) q^{10} +(-4.52607 + 2.61313i) q^{11} +4.43692i q^{13} +(3.13812 + 2.03770i) q^{14} +(0.910541 - 3.89499i) q^{16} +(3.65568 + 6.33182i) q^{17} +(2.42308 + 1.39897i) q^{19} +(2.14144 - 0.317025i) q^{20} +(4.82843 - 5.59587i) q^{22} +(1.51423 - 2.62272i) q^{23} +(-1.91421 - 3.31552i) q^{25} +(-2.06465 - 5.92535i) q^{26} +(-5.13905 - 1.26100i) q^{28} +3.06147i q^{29} +(3.20711 + 5.55487i) q^{31} +(0.596471 + 5.62532i) q^{32} +(-7.82843 - 6.75481i) q^{34} +(-0.388275 - 2.83730i) q^{35} +(7.85718 + 4.53635i) q^{37} +(-3.88692 - 0.740730i) q^{38} +(-2.71230 + 1.41986i) q^{40} -6.05692 q^{41} +10.7117i q^{43} +(-3.84425 + 9.71991i) q^{44} +(-0.801760 + 4.20718i) q^{46} +(4.54269 - 7.86817i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(4.09918 + 3.53701i) q^{50} +(5.51453 + 6.95235i) q^{52} +(1.71393 - 0.989538i) q^{53} -5.65685 q^{55} +(7.44981 - 0.707354i) q^{56} +(-1.42460 - 4.08848i) q^{58} +(-6.01255 + 3.47135i) q^{59} +(-6.85351 - 3.95687i) q^{61} +(-6.86784 - 5.92596i) q^{62} +(-3.41421 - 7.23486i) q^{64} +(-2.40125 + 4.15908i) q^{65} +(-5.26190 + 3.03796i) q^{67} +(13.5978 + 5.37798i) q^{68} +(1.83882 + 3.60843i) q^{70} -5.53732 q^{71} +(1.50000 + 2.59808i) q^{73} +(-12.6039 - 2.40192i) q^{74} +(5.53553 - 0.819496i) q^{76} +(12.8017 + 5.22625i) q^{77} +(0.621320 - 1.07616i) q^{79} +(2.96147 - 3.15830i) q^{80} +(8.08880 - 2.81849i) q^{82} -12.1689i q^{83} +7.91375i q^{85} +(-4.98450 - 14.3051i) q^{86} +(0.610867 - 14.7694i) q^{88} +(-3.02846 + 5.24545i) q^{89} +(9.27659 - 7.19367i) q^{91} +(-0.887016 - 5.99162i) q^{92} +(-2.40528 + 12.6215i) q^{94} +(1.51423 + 2.62272i) q^{95} -4.82843 q^{97} +(-0.827545 - 9.86485i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 8 q^{7}+O(q^{10}) $ 16 * q - 8 * q^4 + 8 * q^7	$ 16 q - 8 q^{4} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 32 q^{22} - 8 q^{25} - 16 q^{28} + 40 q^{31} - 80 q^{34} - 32 q^{40} - 8 q^{46} + 40 q^{49} + 8 q^{52} - 32 q^{64} - 16 q^{70} + 24 q^{73} + 32 q^{76} - 24 q^{79} - 16 q^{82} - 32 q^{88} - 24 q^{94} - 32 q^{97}+O(q^{100}) $ 16 * q - 8 * q^4 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 32 * q^22 - 8 * q^25 - 16 * q^28 + 40 * q^31 - 80 * q^34 - 32 * q^40 - 8 * q^46 + 40 * q^49 + 8 * q^52 - 32 * q^64 - 16 * q^70 + 24 * q^73 + 32 * q^76 - 24 * q^79 - 16 * q^82 - 32 * q^88 - 24 * q^94 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.33546	+	0.465333i	−0.944316	+	0.329040i
$2$	−1.33546	+	0.465333i	−0.944316	+	0.329040i
$3$		0			0
$3$		0			0
$4$	1.56693	−	1.24287i	0.783465	−	0.621436i
$5$	0.937379	+	0.541196i	0.419209	+	0.242030i	0.694739	−	0.719262i	$-0.255520\pi$
$5$	0.937379	+	0.541196i	0.419209	+	0.242030i	−0.275530	+	0.961292i	$0.588853\pi$
$6$		0			0
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$7$	−1.62132	−	2.09077i	−0.612801	−	0.790237i
$8$	−1.51423	+	2.38896i	−0.535361	+	0.844623i
$9$		0			0
$10$	−1.50367	−	0.286555i	−0.475503	−	0.0906165i
$11$	−4.52607	+	2.61313i	−1.36466	+	0.787887i	−0.990240	−	0.139372i	$-0.955492\pi$
$11$	−4.52607	+	2.61313i	−1.36466	+	0.787887i	−0.374420	+	0.927259i	$0.622158\pi$
$12$		0			0
$13$			4.43692i			1.23058i	0.788300	+	0.615291i	$0.210961\pi$
$13$			4.43692i			1.23058i	−0.788300	+	0.615291i	$0.789039\pi$
$14$	3.13812	+	2.03770i	0.838698	+	0.544597i
$15$		0			0
$16$	0.910541	−	3.89499i	0.227635	−	0.973746i
$17$	3.65568	+	6.33182i	0.886631	+	1.53569i	0.843832	+	0.536607i	$0.180294\pi$
$17$	3.65568	+	6.33182i	0.886631	+	1.53569i	0.0427992	+	0.999084i	$0.486372\pi$
$18$		0			0
$19$	2.42308	+	1.39897i	0.555893	+	0.320945i	0.751495	−	0.659738i	$-0.229333\pi$
$19$	2.42308	+	1.39897i	0.555893	+	0.320945i	−0.195603	+	0.980683i	$0.562666\pi$
$20$	2.14144	−	0.317025i	0.478842	−	0.0708890i
$21$		0			0
$22$	4.82843	−	5.59587i	1.02942	−	1.19304i
$23$	1.51423	−	2.62272i	0.315739	−	0.546876i	−0.663855	−	0.747861i	$-0.731081\pi$
$23$	1.51423	−	2.62272i	0.315739	−	0.546876i	0.979594	+	0.200985i	$0.0644143\pi$
$24$		0			0
$25$	−1.91421	−	3.31552i	−0.382843	−	0.663103i
$26$	−2.06465	−	5.92535i	−0.404911	−	1.16206i
$27$		0			0
$28$	−5.13905	−	1.26100i	−0.971190	−	0.238306i
$29$			3.06147i			0.568500i	0.958750	+	0.284250i	$0.0917446\pi$
$29$			3.06147i			0.568500i	−0.958750	+	0.284250i	$0.908255\pi$
$30$		0			0
$31$	3.20711	+	5.55487i	0.576013	+	0.997684i	0.995931	+	0.0901221i	$0.0287257\pi$
$31$	3.20711	+	5.55487i	0.576013	+	0.997684i	−0.419917	+	0.907562i	$0.637941\pi$
$32$	0.596471	+	5.62532i	0.105442	+	0.994425i
$33$		0			0
$34$	−7.82843	−	6.75481i	−1.34256	−	1.15844i
$35$	−0.388275	−	2.83730i	−0.0656305	−	0.479591i
$36$		0			0
$37$	7.85718	+	4.53635i	1.29171	+	0.745771i	0.978958	−	0.204063i	$-0.0654149\pi$
$37$	7.85718	+	4.53635i	1.29171	+	0.745771i	0.312755	+	0.949834i	$0.398748\pi$
$38$	−3.88692	−	0.740730i	−0.630542	−	0.120162i
$39$		0			0
$40$	−2.71230	+	1.41986i	−0.428852	+	0.224500i
$41$	−6.05692			−0.945932			−0.472966	−	0.881081i	$-0.656817\pi$
$41$	−6.05692			−0.945932			−0.472966	+	0.881081i	$0.656817\pi$
$42$		0			0
$43$			10.7117i			1.63352i	0.576980	+	0.816758i	$0.304231\pi$
$43$			10.7117i			1.63352i	−0.576980	+	0.816758i	$0.695769\pi$
$44$	−3.84425	+	9.71991i	−0.579543	+	1.46533i
$45$		0			0
$46$	−0.801760	+	4.20718i	−0.118213	+	0.620314i
$47$	4.54269	−	7.86817i	0.662620	−	1.14769i	−0.317305	−	0.948323i	$-0.602778\pi$
$47$	4.54269	−	7.86817i	0.662620	−	1.14769i	0.979925	−	0.199367i	$-0.0638887\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$	4.09918	+	3.53701i	0.579712	+	0.500208i
$51$		0			0
$52$	5.51453	+	6.95235i	0.764727	+	0.964117i
$53$	1.71393	−	0.989538i	0.235426	−	0.135923i	−0.377647	−	0.925950i	$-0.623267\pi$
$53$	1.71393	−	0.989538i	0.235426	−	0.135923i	0.613073	+	0.790026i	$0.289933\pi$
$54$		0			0
$55$	−5.65685			−0.762770
$56$	7.44981	−	0.707354i	0.995523	−	0.0945242i
$57$		0			0
$58$	−1.42460	−	4.08848i	−0.187059	−	0.536844i
$59$	−6.01255	+	3.47135i	−0.782767	+	0.451931i	−0.837410	−	0.546575i	$-0.815931\pi$
$59$	−6.01255	+	3.47135i	−0.782767	+	0.451931i	0.0546428	+	0.998506i	$0.482598\pi$
$60$		0			0
$61$	−6.85351	−	3.95687i	−0.877502	−	0.506626i	−0.00766783	−	0.999971i	$-0.502441\pi$
$61$	−6.85351	−	3.95687i	−0.877502	−	0.506626i	−0.869834	+	0.493345i	$0.835774\pi$
$62$	−6.86784	−	5.92596i	−0.872217	−	0.752598i
$63$		0			0
$64$	−3.41421	−	7.23486i	−0.426777	−	0.904357i
$65$	−2.40125	+	4.15908i	−0.297838	+	0.515870i
$66$		0			0
$67$	−5.26190	+	3.03796i	−0.642843	+	0.371146i	−0.785709	−	0.618597i	$-0.787702\pi$
$67$	−5.26190	+	3.03796i	−0.642843	+	0.371146i	0.142866	+	0.989742i	$0.454368\pi$
$68$	13.5978	+	5.37798i	1.64898	+	0.652176i
$69$		0			0
$70$	1.83882	+	3.60843i	0.219781	+	0.431290i
$71$	−5.53732			−0.657159			−0.328579	−	0.944476i	$-0.606570\pi$
$71$	−5.53732			−0.657159			−0.328579	+	0.944476i	$0.606570\pi$
$72$		0			0
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	0.940356	−	0.340193i	$-0.110493\pi$
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	−0.764794	+	0.644275i	$0.777159\pi$
$74$	−12.6039	−	2.40192i	−1.46517	−	0.279218i
$75$		0			0
$76$	5.53553	−	0.819496i	0.634969	−	0.0940026i
$77$	12.8017	+	5.22625i	1.45888	+	0.595587i
$78$		0			0
$79$	0.621320	−	1.07616i	0.0699040	−	0.121077i	−0.828955	−	0.559316i	$-0.811064\pi$
$79$	0.621320	−	1.07616i	0.0699040	−	0.121077i	0.898859	+	0.438238i	$0.144397\pi$
$80$	2.96147	−	3.15830i	0.331103	−	0.353108i
$81$		0			0
$82$	8.08880	−	2.81849i	0.893259	−	0.311250i
$83$		−	12.1689i		−	1.33572i	−0.744289	−	0.667858i	$-0.767211\pi$
$83$		−	12.1689i		−	1.33572i	0.744289	−	0.667858i	$-0.232789\pi$
$84$		0			0
$85$			7.91375i			0.858367i
$86$	−4.98450	−	14.3051i	−0.537492	−	1.54256i
$87$		0			0
$88$	0.610867	−	14.7694i	0.0651186	−	1.57443i
$89$	−3.02846	+	5.24545i	−0.321016	+	0.556016i	−0.980698	−	0.195529i	$-0.937358\pi$
$89$	−3.02846	+	5.24545i	−0.321016	+	0.556016i	0.659682	+	0.751545i	$0.270691\pi$
$90$		0			0
$91$	9.27659	−	7.19367i	0.972451	−	0.754102i
$92$	−0.887016	−	5.99162i	−0.0924778	−	0.624669i
$93$		0			0
$94$	−2.40528	+	12.6215i	−0.248086	+	1.30181i
$95$	1.51423	+	2.62272i	0.155357	+	0.269086i
$96$		0			0
$97$	−4.82843			−0.490252			−0.245126	−	0.969491i	$-0.578829\pi$
$97$	−4.82843			−0.490252			−0.245126	+	0.969491i	$0.578829\pi$
$98$	−0.827545	−	9.86485i	−0.0835947	−	0.996500i
$99$		0			0
$100$	−7.12020	−	2.81606i	−0.712020	−	0.281606i
$101$	9.05213	−	5.22625i	0.900721	−	0.520031i	0.0232869	−	0.999729i	$-0.492587\pi$
$101$	9.05213	−	5.22625i	0.900721	−	0.520031i	0.877434	+	0.479697i	$0.159254\pi$
$102$		0			0
$103$	3.79289	−	6.56948i	0.373725	−	0.647310i	−0.616410	−	0.787425i	$-0.711414\pi$
$103$	3.79289	−	6.56948i	0.373725	−	0.647310i	0.990135	+	0.140115i	$0.0447471\pi$
$104$	−10.5996	−	6.71852i	−1.03938	−	0.658805i
$105$		0			0
$106$	−1.82843	+	2.11904i	−0.177593	+	0.205819i
$107$	−6.78910	−	3.91969i	−0.656327	−	0.378931i	0.134549	−	0.990907i	$-0.457041\pi$
$107$	−6.78910	−	3.91969i	−0.656327	−	0.378931i	−0.790876	+	0.611976i	$0.790375\pi$
$108$		0			0
$109$	−3.01102	+	1.73841i	−0.288403	+	0.166510i	−0.637222	−	0.770681i	$-0.719916\pi$
$109$	−3.01102	+	1.73841i	−0.288403	+	0.166510i	0.348818	+	0.937190i	$0.386583\pi$
$110$	7.55453	−	2.63232i	0.720296	−	0.250982i
$111$		0			0
$112$	−9.61980	+	4.41129i	−0.908986	+	0.416828i
$113$	1.25443			0.118007			0.0590034	−	0.998258i	$-0.481208\pi$
$113$	1.25443			0.118007			0.0590034	+	0.998258i	$0.481208\pi$
$114$		0			0
$115$	2.83882	−	1.63899i	0.264721	−	0.152837i
$116$	3.80501	+	4.79711i	0.353286	+	0.445400i
$117$		0			0
$118$	6.41421	−	7.43370i	0.590476	−	0.684327i
$119$	7.31135	−	17.9091i	0.670230	−	1.64172i
$120$		0			0
$121$	8.15685	−	14.1281i	0.741532	−	1.28437i
$122$	10.9939	+	2.09510i	0.995339	+	0.189682i
$123$		0			0
$124$	11.9293	+	4.71807i	1.07128	+	0.423696i
$125$		−	9.55582i		−	0.854699i
$126$		0			0
$127$	4.07107			0.361249			0.180624	−	0.983552i	$-0.442188\pi$
$127$	4.07107			0.361249			0.180624	+	0.983552i	$0.442188\pi$
$128$	7.92618	+	8.07315i	0.700582	+	0.713572i
$129$		0			0
$130$	1.27142	−	6.67168i	0.111511	−	0.585145i
$131$	1.87476	+	1.08239i	0.163798	+	0.0945690i	0.579658	−	0.814860i	$-0.303186\pi$
$131$	1.87476	+	1.08239i	0.163798	+	0.0945690i	−0.415860	+	0.909429i	$0.636519\pi$
$132$		0			0
$133$	−1.00367	−	7.33428i	−0.0870295	−	0.635963i
$134$	5.61341	−	6.50562i	0.484925	−	0.562000i
$135$		0			0
$136$	−20.6620	−	0.854582i	−1.77175	−	0.0732798i
$137$	6.05692	+	10.4909i	0.517478	+	0.896298i	0.999794	+	0.0203005i	$0.00646228\pi$
$137$	6.05692	+	10.4909i	0.517478	+	0.896298i	−0.482316	+	0.875997i	$0.660204\pi$
$138$		0			0
$139$			1.83783i			0.155883i	0.996958	+	0.0779415i	$0.0248347\pi$
$139$			1.83783i			0.155883i	−0.996958	+	0.0779415i	$0.975165\pi$
$140$	−4.13480	−	3.96327i	−0.349454	−	0.334957i
$141$		0			0
$142$	7.39489	−	2.57670i	0.620566	−	0.216232i
$143$	−11.5942	−	20.0818i	−0.969559	−	1.67933i
$144$		0			0
$145$	−1.65685	+	2.86976i	−0.137594	+	0.238320i
$146$	−3.21217	−	2.77164i	−0.265841	−	0.229382i
$147$		0			0
$148$	17.9497	−	2.65733i	1.47546	−	0.218431i
$149$	−3.74952	−	2.16478i	−0.307172	−	0.177346i	0.338488	−	0.940971i	$-0.390085\pi$
$149$	−3.74952	−	2.16478i	−0.307172	−	0.177346i	−0.645660	+	0.763625i	$0.723418\pi$
$150$		0			0
$151$	−1.58579	−	2.74666i	−0.129049	−	0.223520i	0.794259	−	0.607579i	$-0.207859\pi$
$151$	−1.58579	−	2.74666i	−0.129049	−	0.223520i	−0.923309	+	0.384059i	$0.874526\pi$
$152$	−7.01117	+	3.67027i	−0.568681	+	0.297699i
$153$		0			0
$154$	−19.5281	−	1.02244i	−1.57362	−	0.0823907i
$155$			6.94269i			0.557651i
$156$		0			0
$157$	13.7070	−	7.91375i	1.09394	−	0.631586i	0.159316	−	0.987228i	$-0.449071\pi$
$157$	13.7070	−	7.91375i	1.09394	−	0.631586i	0.934622	+	0.355642i	$0.115738\pi$
$158$	−0.328979	+	1.72629i	−0.0261722	+	0.137336i
$159$		0			0
$160$	−2.48528	+	5.59587i	−0.196479	+	0.442392i
$161$	−7.93857	+	1.08637i	−0.625647	+	0.0856178i
$162$		0			0
$163$	2.83882	+	1.63899i	0.222353	+	0.128376i	0.607039	−	0.794672i	$-0.292357\pi$
$163$	2.83882	+	1.63899i	0.222353	+	0.128376i	−0.384686	+	0.923047i	$0.625690\pi$
$164$	−9.49077	+	7.52797i	−0.741105	+	0.587836i
$165$		0			0
$166$	5.66261	+	16.2512i	0.439504	+	1.26134i
$167$	5.53732			0.428491			0.214245	−	0.976780i	$-0.431271\pi$
$167$	5.53732			0.428491			0.214245	+	0.976780i	$0.431271\pi$
$168$		0			0
$169$	−6.68629			−0.514330
$170$	−3.68253	−	10.5685i	−0.282437	−	0.810569i
$171$		0			0
$172$	13.3132	+	16.7845i	1.01513	+	1.27980i
$173$	19.0416	+	10.9937i	1.44771	+	0.835836i	0.998345	−	0.0575128i	$-0.0183170\pi$
$173$	19.0416	+	10.9937i	1.44771	+	0.835836i	0.449365	+	0.893348i	$0.351650\pi$
$174$		0			0
$175$	−3.82843	+	9.37769i	−0.289402	+	0.708887i
$176$	6.05692	+	20.0083i	0.456558	+	1.50818i
$177$		0			0
$178$	1.60352	−	8.41435i	0.120189	−	0.630682i
$179$	−5.23600	+	3.02301i	−0.391357	+	0.225950i	−0.682748	−	0.730654i	$-0.739215\pi$
$179$	−5.23600	+	3.02301i	−0.391357	+	0.225950i	0.291391	+	0.956604i	$0.405882\pi$
$180$		0			0
$181$		−	14.6686i		−	1.09031i	−0.838337	−	0.545153i	$-0.816472\pi$
$181$		−	14.6686i		−	1.09031i	0.838337	−	0.545153i	$-0.183528\pi$
$182$	−9.04110	+	13.9236i	−0.670171	+	1.03209i
$183$		0			0
$184$	3.97268	+	7.58884i	0.292870	+	0.559456i
$185$	4.91010	+	8.50455i	0.360998	+	0.625267i
$186$		0			0
$187$	−33.0917	−	19.1055i	−2.41990	−	1.39713i
$188$	−2.66105	−	17.9749i	−0.194077	−	1.31095i
$189$		0			0
$190$	−3.24264	−	2.79793i	−0.235246	−	0.202983i
$191$	−10.0800	+	17.4591i	−0.729364	+	1.26330i	0.227788	+	0.973711i	$0.426851\pi$
$191$	−10.0800	+	17.4591i	−0.729364	+	1.26330i	−0.957152	+	0.289585i	$0.906483\pi$
$192$		0			0
$193$	6.15685	+	10.6640i	0.443180	+	0.767610i	0.997923	−	0.0644111i	$-0.0205169\pi$
$193$	6.15685	+	10.6640i	0.443180	+	0.767610i	−0.554743	+	0.832022i	$0.687184\pi$
$194$	6.44819	−	2.24683i	0.462953	−	0.161313i
$195$		0			0
$196$	5.69560	+	12.7891i	0.406828	+	0.913505i
$197$		−	10.2668i		−	0.731479i	−0.930717	−	0.365739i	$-0.880816\pi$
$197$		−	10.2668i		−	0.731479i	0.930717	−	0.365739i	$-0.119184\pi$
$198$		0			0
$199$	−2.41421	−	4.18154i	−0.171139	−	0.296422i	0.767679	−	0.640834i	$-0.221411\pi$
$199$	−2.41421	−	4.18154i	−0.171139	−	0.296422i	−0.938818	+	0.344413i	$0.888078\pi$
$200$	10.8192	+	0.447483i	0.765031	+	0.0316418i
$201$		0			0
$202$	−9.65685	+	11.1917i	−0.679454	+	0.787447i
$203$	6.40083	−	4.96362i	0.449250	−	0.348378i
$204$		0			0
$205$	−5.67763	−	3.27798i	−0.396543	−	0.228944i
$206$	−2.00828	+	10.5383i	−0.139923	+	0.734236i
$207$		0			0
$208$	17.2818	+	4.04000i	1.19827	+	0.280124i
$209$	−14.6227			−1.01147
$210$		0			0
$211$		−	6.55596i		−	0.451331i	−0.974205	−	0.225666i	$-0.927544\pi$
$211$		−	6.55596i		−	0.451331i	0.974205	−	0.225666i	$-0.0724557\pi$
$212$	1.45574	−	3.68073i	0.0999806	−	0.252794i
$213$		0			0
$214$	10.8906	+	2.07541i	0.744464	+	0.141872i
$215$	−5.79712	+	10.0409i	−0.395360	+	0.684784i
$216$		0			0
$217$	6.41421	−	15.7116i	0.435425	−	1.06657i
$218$	3.21217	−	3.72271i	0.217555	−	0.252134i
$219$		0			0
$220$	−8.86390	+	7.03074i	−0.597604	+	0.474013i
$221$	−28.0938	+	16.2200i	−1.88979	+	1.09107i
$222$		0			0
$223$	12.1421			0.813098			0.406549	−	0.913629i	$-0.366732\pi$
$223$	12.1421			0.813098			0.406549	+	0.913629i	$0.366732\pi$
$224$	10.7942	−	10.3675i	0.721217	−	0.692710i
$225$		0			0
$226$	−1.67525	+	0.583728i	−0.111436	+	0.0388290i
$227$	−20.7556	+	11.9832i	−1.37760	+	0.795355i	−0.991870	−	0.127258i	$-0.959382\pi$
$227$	−20.7556	+	11.9832i	−1.37760	+	0.795355i	−0.385726	+	0.922613i	$0.626049\pi$
$228$		0			0
$229$	−21.5642	−	12.4501i	−1.42500	−	0.822725i	−0.428282	−	0.903645i	$-0.640881\pi$
$229$	−21.5642	−	12.4501i	−1.42500	−	0.822725i	−0.996721	+	0.0809200i	$0.974214\pi$
$230$	−3.02846	+	3.50981i	−0.199691	+	0.231430i
$231$		0			0
$232$	−7.31371	−	4.63577i	−0.480168	−	0.304353i
$233$	7.93857	−	13.7500i	0.520073	−	0.900792i	−0.479655	−	0.877457i	$-0.659238\pi$
$233$	7.93857	−	13.7500i	0.520073	−	0.900792i	0.999728	−	0.0233352i	$-0.00742849\pi$
$234$		0			0
$235$	8.51645	−	4.91697i	0.555552	−	0.320748i
$236$	−5.10681	+	12.9122i	−0.332425	+	0.840512i
$237$		0			0
$238$	−1.43036	+	27.3191i	−0.0927166	+	1.77084i
$239$	20.6796			1.33765			0.668827	−	0.743418i	$-0.266797\pi$
$239$	20.6796			1.33765			0.668827	+	0.743418i	$0.266797\pi$
$240$		0			0
$241$	4.41421	+	7.64564i	0.284344	+	0.492499i	0.972450	−	0.233112i	$-0.0748907\pi$
$241$	4.41421	+	7.64564i	0.284344	+	0.492499i	−0.688106	+	0.725611i	$0.741557\pi$
$242$	−4.31892	+	22.6632i	−0.277631	+	1.45685i
$243$		0			0
$244$	−15.6569	+	2.31788i	−1.00233	+	0.148387i
$245$	−5.30262	+	5.41196i	−0.338772	+	0.345758i
$246$		0			0
$247$	−6.20711	+	10.7510i	−0.394949	+	0.684071i
$248$	−18.1266	−	0.749721i	−1.15104	−	0.0476073i
$249$		0			0
$250$	4.44664	+	12.7615i	0.281230	+	0.807105i
$251$		−	17.3952i		−	1.09798i	−0.835830	−	0.548988i	$-0.815013\pi$
$251$		−	17.3952i		−	1.09798i	0.835830	−	0.548988i	$-0.184987\pi$
$252$		0			0
$253$			15.8275i			0.995066i
$254$	−5.43677	+	1.89440i	−0.341133	+	0.118865i
$255$		0			0
$256$	−14.3418	−	7.09309i	−0.896364	−	0.443318i
$257$	9.71260	−	16.8227i	0.605855	−	1.04937i	−0.386061	−	0.922473i	$-0.626164\pi$
$257$	9.71260	−	16.8227i	0.605855	−	1.04937i	0.991916	−	0.126898i	$-0.0405022\pi$
$258$		0			0
$259$	−3.25455	−	23.7824i	−0.202228	−	1.47777i
$260$	1.40662	+	9.50143i	0.0872347	+	0.589254i
$261$		0			0
$262$	−3.00735	−	0.573109i	−0.185794	−	0.0354068i
$263$	4.28289	+	7.41818i	0.264094	+	0.457425i	0.967326	−	0.253536i	$-0.0815936\pi$
$263$	4.28289	+	7.41818i	0.264094	+	0.457425i	−0.703232	+	0.710961i	$0.748260\pi$
$264$		0			0
$265$	2.14214			0.131590
$266$	4.75325	+	9.32762i	0.291441	+	0.571913i
$267$		0			0
$268$	−4.46923	+	11.3001i	−0.273002	+	0.690265i
$269$	7.49903	−	4.32957i	0.457224	−	0.263978i	−0.253652	−	0.967295i	$-0.581632\pi$
$269$	7.49903	−	4.32957i	0.457224	−	0.263978i	0.710876	+	0.703317i	$0.248299\pi$
$270$		0			0
$271$	−2.07107	+	3.58719i	−0.125808	+	0.217907i	−0.922049	−	0.387074i	$-0.873486\pi$
$271$	−2.07107	+	3.58719i	−0.125808	+	0.217907i	0.796240	+	0.604981i	$0.206819\pi$
$272$	27.9910	−	8.47343i	1.69720	−	0.513777i
$273$		0			0
$274$	−12.9706	−	11.1917i	−0.783580	−	0.676117i
$275$	17.3277	+	10.0042i	1.04490	+	0.603274i
$276$		0			0
$277$	−19.5568	+	11.2912i	−1.17506	+	0.678420i	−0.954866	−	0.297037i	$-0.904001\pi$
$277$	−19.5568	+	11.2912i	−1.17506	+	0.678420i	−0.220191	+	0.975457i	$0.570668\pi$
$278$	−0.855205	−	2.45436i	−0.0512918	−	0.147203i
$279$		0			0
$280$	7.36611	+	3.36875i	0.440209	+	0.201321i
$281$	21.9341			1.30848			0.654238	−	0.756289i	$-0.272990\pi$
$281$	21.9341			1.30848			0.654238	+	0.756289i	$0.272990\pi$
$282$		0			0
$283$	15.2986	−	8.83267i	0.909409	−	0.525047i	0.0291680	−	0.999575i	$-0.490714\pi$
$283$	15.2986	−	8.83267i	0.909409	−	0.525047i	0.880241	+	0.474527i	$0.157381\pi$
$284$	−8.67659	+	6.88218i	−0.514861	+	0.408382i
$285$		0			0
$286$	24.8284	+	21.4234i	1.46814	+	1.26679i
$287$	9.82021	+	12.6636i	0.579669	+	0.747510i
$288$		0			0
$289$	−18.2279	+	31.5717i	−1.07223	+	1.85716i
$290$	0.877278	−	4.60345i	0.0515155	−	0.270324i
$291$		0			0
$292$	5.57947	+	2.20670i	0.326514	+	0.129137i
$293$			26.1313i			1.52660i	0.646042	+	0.763302i	$0.276423\pi$
$293$			26.1313i			1.52660i	−0.646042	+	0.763302i	$0.723577\pi$
$294$		0			0
$295$	−7.51472			−0.437524
$296$	−22.7347	+	11.9014i	−1.32143	+	0.691754i
$297$		0			0
$298$	6.01469	+	1.14622i	0.348422	+	0.0663986i
$299$	11.6368	+	6.71852i	0.672975	+	0.388542i
$300$		0			0
$301$	22.3957	−	17.3671i	1.29086	−	1.00102i
$302$	3.39587	+	2.93015i	0.195411	+	0.168611i
$303$		0			0
$304$	7.65527	−	8.16405i	0.439060	−	0.468240i
$305$	−4.28289	−	7.41818i	−0.245238	−	0.424764i
$306$		0			0
$307$			19.5855i			1.11781i	0.829233	+	0.558903i	$0.188777\pi$
$307$			19.5855i			1.11781i	−0.829233	+	0.558903i	$0.811223\pi$
$308$	26.5549	−	7.72163i	1.51310	−	0.439981i
$309$		0			0
$310$	−3.23067	−	9.27172i	−0.183489	−	0.526598i
$311$	4.80249	+	8.31816i	0.272324	+	0.471680i	0.969457	−	0.245263i	$-0.0788743\pi$
$311$	4.80249	+	8.31816i	0.272324	+	0.471680i	−0.697132	+	0.716943i	$0.745541\pi$
$312$		0			0
$313$	13.9853	−	24.2232i	0.790495	−	1.36918i	−0.135166	−	0.990823i	$-0.543157\pi$
$313$	13.9853	−	24.2232i	0.790495	−	1.36918i	0.925661	−	0.378354i	$-0.123510\pi$
$314$	−14.6227	+	16.9469i	−0.825207	+	0.956366i
$315$		0			0
$316$	−0.363961	−	2.45849i	−0.0204744	−	0.138301i
$317$	−30.1294	−	17.3952i	−1.69223	−	0.977012i	−0.952710	−	0.303882i	$-0.901717\pi$
$317$	−30.1294	−	17.3952i	−1.69223	−	0.977012i	−0.739524	−	0.673130i	$-0.764949\pi$
$318$		0			0
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$	0.715063	−	8.62956i	0.0399733	−	0.482407i
$321$		0			0
$322$	10.0961	−	5.14488i	0.562636	−	0.286713i
$323$			20.4567i			1.13824i
$324$		0			0
$325$	14.7107	−	8.49322i	0.816002	−	0.471119i
$326$	−4.55381	−	0.867819i	−0.252212	−	0.0480641i
$327$		0			0
$328$	9.17157	−	14.4697i	0.506415	−	0.798956i
$329$	−23.8157	+	3.25910i	−1.31300	+	0.179680i
$330$		0			0
$331$	4.43043	+	2.55791i	0.243518	+	0.140595i	0.616793	−	0.787126i	$-0.288432\pi$
$331$	4.43043	+	2.55791i	0.243518	+	0.140595i	−0.373274	+	0.927721i	$0.621765\pi$
$332$	−15.1244	−	19.0679i	−0.830061	−	1.04649i
$333$		0			0
$334$	−7.39489	+	2.57670i	−0.404631	+	0.140991i
$335$	−6.57652			−0.359314
$336$		0			0
$337$	1.34315			0.0731658			0.0365829	−	0.999331i	$-0.488353\pi$
$337$	1.34315			0.0731658			0.0365829	+	0.999331i	$0.488353\pi$
$338$	8.92930	−	3.11135i	0.485690	−	0.169235i
$339$		0			0
$340$	9.83577	+	12.4003i	0.533420	+	0.672500i
$341$	−29.0312	−	16.7611i	−1.57213	−	0.907667i
$342$		0			0
$343$	17.0000	−	7.34847i	0.917914	−	0.396780i
$344$	−25.5897	−	16.2200i	−1.37971	−	0.874521i
$345$		0			0
$346$	−30.5452	−	5.82099i	−1.64212	−	0.312938i
$347$	23.3403	−	13.4755i	1.25297	−	0.723403i	0.281273	−	0.959628i	$-0.409243\pi$
$347$	23.3403	−	13.4755i	1.25297	−	0.723403i	0.971698	+	0.236225i	$0.0759101\pi$
$348$		0			0
$349$			1.35778i			0.0726805i	0.999339	+	0.0363403i	$0.0115700\pi$
$349$			1.35778i			0.0726805i	−0.999339	+	0.0363403i	$0.988430\pi$
$350$	0.748977	−	14.3051i	0.0400345	−	0.764638i
$351$		0			0
$352$	−17.3993	−	23.9019i	−0.927388	−	1.27398i
$353$	7.93857	+	13.7500i	0.422527	+	0.731839i	0.996186	−	0.0872559i	$-0.0278098\pi$
$353$	7.93857	+	13.7500i	0.422527	+	0.731839i	−0.573659	+	0.819094i	$0.694476\pi$
$354$		0			0
$355$	−5.19057	−	2.99678i	−0.275487	−	0.159052i
$356$	1.77403	+	11.9832i	0.0940235	+	0.635110i
$357$		0			0
$358$	5.58579	−	6.47360i	0.295218	−	0.342140i
$359$	−7.31135	+	12.6636i	−0.385878	+	0.668361i	−0.991891	−	0.127094i	$-0.959435\pi$
$359$	−7.31135	+	12.6636i	−0.385878	+	0.668361i	0.606012	+	0.795455i	$0.292768\pi$
$360$		0			0
$361$	−5.58579	−	9.67487i	−0.293989	−	0.509203i
$362$	6.82576	+	19.5893i	0.358754	+	1.02959i
$363$		0			0
$364$	5.59495	−	22.8016i	0.293255	−	1.19513i
$365$			3.24718i			0.169965i
$366$		0			0
$367$	−2.69239	−	4.66335i	−0.140542	−	0.243425i	0.787159	−	0.616750i	$-0.211551\pi$
$367$	−2.69239	−	4.66335i	−0.140542	−	0.243425i	−0.927701	+	0.373325i	$0.878218\pi$
$368$	−8.83670	−	8.28600i	−0.460645	−	0.431938i
$369$		0			0
$370$	−10.5147	−	9.07269i	−0.546634	−	0.471667i
$371$	−4.84772	−	1.97908i	−0.251681	−	0.102748i
$372$		0			0
$373$	4.67396	+	2.69851i	0.242008	+	0.139724i	0.616099	−	0.787668i	$-0.288712\pi$
$373$	4.67396	+	2.69851i	0.242008	+	0.139724i	−0.374091	+	0.927392i	$0.622045\pi$
$374$	53.0831	+	10.1160i	2.74486	+	0.523088i
$375$		0			0
$376$	11.9180	+	22.7665i	0.614625	+	1.17409i
$377$	−13.5835			−0.699586
$378$		0			0
$379$			30.7773i			1.58092i	0.612513	+	0.790461i	$0.290159\pi$
$379$			30.7773i			1.58092i	−0.612513	+	0.790461i	$0.709841\pi$
$380$	5.63240	+	2.22763i	0.288936	+	0.114275i
$381$		0			0
$382$	5.33720	−	28.0066i	0.273075	−	1.43294i
$383$	−3.28826	+	5.69544i	−0.168022	+	0.291023i	−0.937724	−	0.347380i	$-0.887071\pi$
$383$	−3.28826	+	5.69544i	−0.168022	+	0.291023i	0.769702	+	0.638403i	$0.220405\pi$
$384$		0			0
$385$	9.17157	+	11.8272i	0.467427	+	0.602769i
$386$	−13.1846	−	11.3764i	−0.671077	−	0.579043i
$387$		0			0
$388$	−7.56581	+	6.00111i	−0.384096	+	0.304660i
$389$	12.6408	−	7.29818i	0.640915	−	0.370033i	−0.144052	−	0.989570i	$-0.546013\pi$
$389$	12.6408	−	7.29818i	0.640915	−	0.370033i	0.784967	+	0.619538i	$0.212680\pi$
$390$		0			0
$391$	22.1421			1.11978
$392$	−13.5574	−	14.4290i	−0.684754	−	0.728774i
$393$		0			0
$394$	4.77748	+	13.7109i	0.240686	+	0.690747i
$395$	1.16483	−	0.672512i	0.0586087	−	0.0338378i
$396$		0			0
$397$	−5.01836	−	2.89735i	−0.251864	−	0.145414i	0.368753	−	0.929527i	$-0.379785\pi$
$397$	−5.01836	−	2.89735i	−0.251864	−	0.145414i	−0.620618	+	0.784113i	$0.713118\pi$
$398$	5.16991	+	4.46088i	0.259144	+	0.223604i
$399$		0			0
$400$	−14.6569	+	4.43692i	−0.732843	+	0.221846i
$401$	17.0239	−	29.4863i	0.850135	−	1.47248i	−0.0309504	−	0.999521i	$-0.509853\pi$
$401$	17.0239	−	29.4863i	0.850135	−	1.47248i	0.881086	−	0.472957i	$-0.156813\pi$
$402$		0			0
$403$	−24.6465	+	14.2297i	−1.22773	+	0.708831i
$404$	7.68850	−	19.4398i	0.382517	−	0.967167i
$405$		0			0
$406$	−6.23834	+	9.60725i	−0.309603	+	0.476800i
$407$	−47.4162			−2.35033
$408$		0			0
$409$	−19.4706	−	33.7240i	−0.962757	−	1.66754i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	−19.4706	−	33.7240i	−0.962757	−	1.66754i	−0.247234	−	0.968956i	$-0.579522\pi$
$410$	9.10763	+	1.73564i	0.449794	+	0.0857171i
$411$		0			0
$412$	−2.22183	−	15.0080i	−0.109461	−	0.739391i
$413$	17.0061	+	6.94269i	0.836813	+	0.341628i
$414$		0			0
$415$	6.58579	−	11.4069i	0.323284	−	0.559944i
$416$	−24.9591	+	2.64650i	−1.22372	+	0.129755i
$417$		0			0
$418$	19.5281	−	6.80443i	0.955150	−	0.332815i
$419$		−	13.8854i		−	0.678346i	−0.940724	−	0.339173i	$-0.889853\pi$
$419$		−	13.8854i		−	0.678346i	0.940724	−	0.339173i	$-0.110147\pi$
$420$		0			0
$421$			6.75481i			0.329209i	0.986360	+	0.164605i	$0.0526348\pi$
$421$			6.75481i			0.329209i	−0.986360	+	0.164605i	$0.947365\pi$
$422$	3.05071	+	8.75526i	0.148506	+	0.426199i
$423$		0			0
$424$	−0.231323	+	5.59289i	−0.0112340	+	0.271615i
$425$	13.9955	−	24.2409i	0.678881	−	1.17586i
$426$		0			0
$427$	2.83882	+	20.7445i	0.137380	+	1.00390i
$428$	−15.5097	+	2.29610i	−0.749690	+	0.110986i
$429$		0			0
$430$	3.06948	−	16.1069i	0.148024	−	0.776742i
$431$	5.79712	+	10.0409i	0.279237	+	0.483653i	0.971195	−	0.238284i	$-0.0765850\pi$
$431$	5.79712	+	10.0409i	0.279237	+	0.483653i	−0.691958	+	0.721938i	$0.743252\pi$
$432$		0			0
$433$	−6.79899			−0.326739			−0.163369	−	0.986565i	$-0.552236\pi$
$433$	−6.79899			−0.326739			−0.163369	+	0.986565i	$0.552236\pi$
$434$	−1.25485	+	23.9670i	−0.0602347	+	1.15045i
$435$		0			0
$436$	−2.55743	+	6.46628i	−0.122479	+	0.309679i
$437$	7.33820	−	4.23671i	0.351034	−	0.202670i
$438$		0			0
$439$	−9.24264	+	16.0087i	−0.441127	+	0.764055i	−0.997773	−	0.0666950i	$-0.978755\pi$
$439$	−9.24264	+	16.0087i	−0.441127	+	0.764055i	0.556646	+	0.830750i	$0.312088\pi$
$440$	8.56578	−	13.5140i	0.408358	−	0.644253i
$441$		0			0
$442$	29.9706	−	34.7341i	1.42555	−	1.65213i
$443$	26.4465	+	15.2689i	1.25651	+	0.725446i	0.972394	−	0.233344i	$-0.0749668\pi$
$443$	26.4465	+	15.2689i	1.25651	+	0.725446i	0.284115	+	0.958790i	$0.408300\pi$
$444$		0			0
$445$	−5.67763	+	3.27798i	−0.269146	+	0.155391i
$446$	−16.2154	+	5.65014i	−0.767821	+	0.267542i
$447$		0			0
$448$	−9.59089	+	18.8684i	−0.453127	+	0.891446i
$449$	7.31135			0.345044			0.172522	−	0.985006i	$-0.444808\pi$
$449$	7.31135			0.345044			0.172522	+	0.985006i	$0.444808\pi$
$450$		0			0
$451$	27.4140	−	15.8275i	1.29088	−	0.745288i
$452$	1.96560	−	1.55909i	0.0924542	−	0.0733336i
$453$		0			0
$454$	22.1421	−	25.6614i	1.03918	−	1.20435i
$455$	12.5889	−	1.72275i	0.590175	−	0.0807636i
$456$		0			0
$457$	4.22792	−	7.32298i	0.197774	−	0.342554i	−0.750032	−	0.661401i	$-0.769962\pi$
$457$	4.22792	−	7.32298i	0.197774	−	0.342554i	0.947806	+	0.318847i	$0.103295\pi$
$458$	34.5917	+	6.59212i	1.61636	+	0.308030i
$459$		0			0
$460$	2.41117	−	6.09647i	0.112421	−	0.284249i
$461$		−	20.5336i		−	0.956345i	−0.878266	−	0.478172i	$-0.841299\pi$
$461$		−	20.5336i		−	0.956345i	0.878266	−	0.478172i	$-0.158701\pi$
$462$		0			0
$463$	−24.2132			−1.12528			−0.562641	−	0.826701i	$-0.690215\pi$
$463$	−24.2132			−1.12528			−0.562641	+	0.826701i	$0.690215\pi$
$464$	11.9244	+	2.78759i	0.553575	+	0.129411i
$465$		0			0
$466$	−4.20334	+	22.0567i	−0.194716	+	1.02176i
$467$	6.46744	+	3.73398i	0.299278	+	0.172788i	0.642118	−	0.766606i	$-0.278056\pi$
$467$	6.46744	+	3.73398i	0.299278	+	0.172788i	−0.342841	+	0.939394i	$0.611389\pi$
$468$		0			0
$469$	14.8829	+	6.07591i	0.687228	+	0.280560i
$470$	−9.08538	+	10.5294i	−0.419077	+	0.485686i
$471$		0			0
$472$	0.811492	−	19.6201i	0.0373519	−	0.903090i
$473$	−27.9910	−	48.4818i	−1.28703	−	2.22919i
$474$		0			0
$475$		−	10.7117i		−	0.491486i
$476$	−10.8023	−	37.1493i	−0.495123	−	1.70274i
$477$		0			0
$478$	−27.6169	+	9.62291i	−1.26317	+	0.440142i
$479$	−14.3629	−	24.8773i	−0.656258	−	1.13667i	−0.981577	−	0.191067i	$-0.938805\pi$
$479$	−14.3629	−	24.8773i	−0.656258	−	1.13667i	0.325319	−	0.945604i	$-0.394528\pi$
$480$		0			0
$481$	−20.1274	+	34.8617i	−0.917731	+	1.58956i
$482$	−9.45280	−	8.15640i	−0.430563	−	0.371514i
$483$		0			0
$484$	−4.77817	−	32.2756i	−0.217190	−	1.46707i
$485$	−4.52607	−	2.61313i	−0.205518	−	0.118656i
$486$		0			0
$487$	17.8640	+	30.9413i	0.809493	+	1.40208i	0.913215	+	0.407477i	$0.133591\pi$
$487$	17.8640	+	30.9413i	0.809493	+	1.40208i	−0.103722	+	0.994606i	$0.533075\pi$
$488$	19.8306	−	10.3811i	0.897688	−	0.469930i
$489$		0			0
$490$	4.56309	−	9.69496i	0.206139	−	0.437974i
$491$		−	3.06147i		−	0.138162i	−0.997611	−	0.0690810i	$-0.977993\pi$
$491$		−	3.06147i		−	0.138162i	0.997611	−	0.0690810i	$-0.0220067\pi$
$492$		0			0
$493$	−19.3846	+	11.1917i	−0.873041	+	0.504050i
$494$	3.28656	−	17.2460i	0.147869	−	0.775933i
$495$		0			0
$496$	24.5563	−	7.43370i	1.10261	−	0.333783i
$497$	8.97777	+	11.5773i	0.402708	+	0.519311i
$498$		0			0
$499$	11.2839	+	6.51478i	0.505138	+	0.291642i	0.730833	−	0.682556i	$-0.239132\pi$
$499$	11.2839	+	6.51478i	0.505138	+	0.291642i	−0.225695	+	0.974198i	$0.572465\pi$
$500$	−11.8767	−	14.9733i	−0.531140	−	0.669627i
$501$		0			0
$502$	8.09456	+	23.2307i	0.361278	+	1.03684i
$503$	31.7543			1.41585			0.707926	−	0.706286i	$-0.249631\pi$
$503$	31.7543			1.41585			0.707926	+	0.706286i	$0.249631\pi$
$504$		0			0
$505$	11.3137			0.503453
$506$	−7.36506	−	21.1371i	−0.327417	−	0.939657i
$507$		0			0
$508$	6.37908	−	5.05981i	0.283026	−	0.224493i
$509$	−15.2921	−	8.82892i	−0.677812	−	0.391335i	0.121218	−	0.992626i	$-0.461320\pi$
$509$	−15.2921	−	8.82892i	−0.677812	−	0.391335i	−0.799030	+	0.601291i	$0.794653\pi$
$510$		0			0
$511$	3.00000	−	7.34847i	0.132712	−	0.325077i
$512$	22.4537	+	2.79884i	0.992321	+	0.123692i
$513$		0			0
$514$	−5.14266	+	26.9857i	−0.226833	+	1.19029i
$515$	7.11076	−	4.10540i	0.313337	−	0.180905i
$516$		0			0
$517$			47.4825i			2.08828i
$518$	15.4131	+	30.2461i	0.677212	+	1.32894i
$519$		0			0
$520$	−6.29982	−	12.0343i	−0.276265	−	0.527738i
$521$	5.53732	+	9.59092i	0.242594	+	0.420186i	0.961453	−	0.274971i	$-0.0886683\pi$
$521$	5.53732	+	9.59092i	0.242594	+	0.420186i	−0.718858	+	0.695157i	$0.755335\pi$
$522$		0			0
$523$	3.59896	+	2.07786i	0.157371	+	0.0908584i	0.576618	−	0.817014i	$-0.304372\pi$
$523$	3.59896	+	2.07786i	0.157371	+	0.0908584i	−0.419246	+	0.907873i	$0.637706\pi$
$524$	4.28289	−	0.634051i	0.187099	−	0.0276986i
$525$		0			0
$526$	−9.17157	−	7.91375i	−0.399900	−	0.345056i
$527$	−23.4483	+	40.6136i	−1.02142	+	1.76916i
$528$		0			0
$529$	6.91421	+	11.9758i	0.300618	+	0.520686i
$530$	−2.86075	+	0.996807i	−0.124263	+	0.0432985i
$531$		0			0
$532$	−10.6883	−	10.2449i	−0.463394	−	0.444171i
$533$		−	26.8741i		−	1.16405i
$534$		0			0
$535$	−4.24264	−	7.34847i	−0.183425	−	0.317702i
$536$	0.710179	−	17.1706i	0.0306751	−	0.741657i
$537$		0			0
$538$	−8.00000	+	9.27153i	−0.344904	+	0.399724i
$539$	−9.82868	−	35.2387i	−0.423351	−	1.51784i
$540$		0			0
$541$	22.0513	+	12.7313i	0.948058	+	0.547361i	0.892477	−	0.451093i	$-0.148966\pi$
$541$	22.0513	+	12.7313i	0.948058	+	0.547361i	0.0555806	+	0.998454i	$0.482299\pi$
$542$	1.09660	−	5.75431i	0.0471029	−	0.247169i
$543$		0			0
$544$	−33.4380	+	24.3411i	−1.43364	+	1.04362i
$545$	−3.76329			−0.161202
$546$		0			0
$547$			31.6550i			1.35347i	0.736227	+	0.676735i	$0.236606\pi$
$547$			31.6550i			1.35347i	−0.736227	+	0.676735i	$0.763394\pi$
$548$	22.5296	+	8.91053i	0.962417	+	0.380639i
$549$		0			0
$550$	−27.7958	−	5.29704i	−1.18522	−	0.225867i
$551$	−4.28289	+	7.41818i	−0.182457	+	0.316025i
$552$		0			0
$553$	−3.25736	+	0.445759i	−0.138517	+	0.0189556i
$554$	20.8633	−	24.1794i	0.886398	−	1.02728i
$555$		0			0
$556$	2.28419	+	2.87976i	0.0968713	+	0.122129i
$557$	−10.1503	+	5.86030i	−0.430084	+	0.248309i	−0.699382	−	0.714748i	$-0.746541\pi$
$557$	−10.1503	+	5.86030i	−0.430084	+	0.248309i	0.269299	+	0.963057i	$0.413208\pi$
$558$		0			0
$559$	−47.5269			−2.01017
$560$	−11.4048	−	1.07115i	−0.481940	−	0.0452643i
$561$		0			0
$562$	−29.2921	+	10.2066i	−1.23561	+	0.430541i
$563$	19.2691	−	11.1250i	0.812095	−	0.468864i	−0.0355876	−	0.999367i	$-0.511330\pi$
$563$	19.2691	−	11.1250i	0.812095	−	0.468864i	0.847683	+	0.530503i	$0.177997\pi$
$564$		0			0
$565$	1.17588	+	0.678892i	0.0494695	+	0.0285612i
$566$	−16.3206	+	18.9147i	−0.686008	+	0.795043i
$567$		0			0
$568$	8.38478	−	13.2284i	0.351817	−	0.555052i
$569$	5.53732	−	9.59092i	0.232137	−	0.402072i	−0.726300	−	0.687378i	$-0.758762\pi$
$569$	5.53732	−	9.59092i	0.232137	−	0.402072i	0.958437	+	0.285306i	$0.0920951\pi$
$570$		0			0
$571$	−0.760141	+	0.438868i	−0.0318109	+	0.0183660i	−0.515821	−	0.856696i	$-0.672513\pi$
$571$	−0.760141	+	0.438868i	−0.0318109	+	0.0183660i	0.484010	+	0.875062i	$0.339180\pi$
$572$	−43.1265	−	17.0566i	−1.80321	−	0.713174i
$573$		0			0
$574$	−19.0073	−	12.3422i	−0.793351	−	0.515152i
$575$	−11.5942			−0.483513
$576$		0			0
$577$	14.3284	+	24.8176i	0.596500	+	1.03317i	0.993333	+	0.115278i	$0.0367759\pi$
$577$	14.3284	+	24.8176i	0.596500	+	1.03317i	−0.396833	+	0.917891i	$0.629891\pi$
$578$	9.65139	−	50.6449i	0.401445	−	2.10655i
$579$		0			0
$580$	0.970563	+	6.55596i	0.0403004	+	0.272222i
$581$	−25.4425	+	19.7298i	−1.05553	+	0.818528i
$582$		0			0
$583$	−5.17157	+	8.95743i	−0.214185	+	0.370979i
$584$	−8.47803	−	0.350653i	−0.350823	−	0.0145101i
$585$		0			0
$586$	−12.1597	−	34.8974i	−0.502314	−	1.44160i
$587$			39.1200i			1.61465i	0.590104	+	0.807327i	$0.299087\pi$
$587$			39.1200i			1.61465i	−0.590104	+	0.807327i	$0.700913\pi$
$588$		0			0
$589$			17.9465i			0.739474i
$590$	10.0356	−	3.49685i	0.413161	−	0.143963i
$591$		0			0
$592$	24.8233	−	26.4731i	1.02023	−	1.08804i
$593$	−9.08538	+	15.7363i	−0.373092	+	0.646214i	−0.990039	−	0.140790i	$-0.955036\pi$
$593$	−9.08538	+	15.7363i	−0.373092	+	0.646214i	0.616948	+	0.787004i	$0.288369\pi$
$594$		0			0
$595$	16.5458	−	12.8307i	0.678313	−	0.526008i
$596$	−8.56578	+	1.26810i	−0.350868	+	0.0519435i
$597$		0			0
$598$	−18.6669	−	3.55735i	−0.763347	−	0.145471i
$599$	17.6512	+	30.5727i	0.721207	+	1.24917i	0.960516	+	0.278224i	$0.0897456\pi$
$599$	17.6512	+	30.5727i	0.721207	+	1.24917i	−0.239309	+	0.970943i	$0.576921\pi$
$600$		0			0
$601$	26.7990			1.09315			0.546577	−	0.837409i	$-0.315931\pi$
$601$	26.7990			1.09315			0.546577	+	0.837409i	$0.315931\pi$
$602$	−21.8271	+	33.6145i	−0.889608	+	1.37003i
$603$		0			0
$604$	−5.89857	−	2.33290i	−0.240009	−	0.0949244i
$605$	15.2921	−	8.82892i	0.621713	−	0.358946i
$606$		0			0
$607$	13.0355	−	22.5782i	0.529096	−	0.916421i	−0.470328	−	0.882492i	$-0.655864\pi$
$607$	13.0355	−	22.5782i	0.529096	−	0.916421i	0.999424	−	0.0339296i	$-0.0108022\pi$
$608$	−6.42433	+	14.4650i	−0.260541	+	0.586635i
$609$		0			0
$610$	9.17157	+	7.91375i	0.371346	+	0.320418i
$611$	34.9105	+	20.1556i	1.41233	+	0.815407i
$612$		0			0
$613$	20.5605	−	11.8706i	0.830432	−	0.479450i	−0.0235688	−	0.999722i	$-0.507503\pi$
$613$	20.5605	−	11.8706i	0.830432	−	0.479450i	0.854000	+	0.520272i	$0.174170\pi$
$614$	−9.11379	−	26.1558i	−0.367803	−	1.05556i
$615$		0			0
$616$	−31.8699	+	22.6688i	−1.28408	+	0.913353i
$617$	−14.6227			−0.588688			−0.294344	−	0.955700i	$-0.595101\pi$
$617$	−14.6227			−0.588688			−0.294344	+	0.955700i	$0.595101\pi$
$618$		0			0
$619$	−23.8151	+	13.7496i	−0.957209	+	0.552645i	−0.895313	−	0.445438i	$-0.853048\pi$
$619$	−23.8151	+	13.7496i	−0.957209	+	0.552645i	−0.0618958	+	0.998083i	$0.519715\pi$
$620$	8.62888	+	10.8787i	0.346544	+	0.436900i
$621$		0			0
$622$	−10.2843	−	8.87385i	−0.412362	−	0.355809i
$623$	15.8771	−	2.17274i	0.636104	−	0.0870488i
$624$		0			0
$625$	−4.39949	+	7.62015i	−0.175980	+	0.304806i
$626$	−7.40498	+	38.8571i	−0.295963	+	1.55304i
$627$		0			0
$628$	11.6422	−	29.4364i	0.464573	−	1.17464i
$629$			66.3336i			2.64489i
$630$		0			0
$631$	0.828427			0.0329792			0.0164896	−	0.999864i	$-0.494751\pi$
$631$	0.828427			0.0329792			0.0164896	+	0.999864i	$0.494751\pi$
$632$	1.63007	+	3.11386i	0.0648408	+	0.123863i
$633$		0			0
$634$	48.3313	+	9.21048i	1.91948	+	0.365795i
$635$	3.81613	+	2.20325i	0.151439	+	0.0874332i
$636$		0			0
$637$	−30.0806	−	7.73196i	−1.19184	−	0.306352i
$638$	17.1316	+	14.7821i	0.678245	+	0.585228i
$639$		0			0
$640$	3.06068	+	11.8572i	0.120984	+	0.468698i
$641$	−3.65568	−	6.33182i	−0.144390	−	0.250092i	0.784755	−	0.619806i	$-0.212789\pi$
$641$	−3.65568	−	6.33182i	−0.144390	−	0.250092i	−0.929145	+	0.369715i	$0.879455\pi$
$642$		0			0
$643$			0.480049i			0.0189313i	0.999955	+	0.00946565i	$0.00301305\pi$
$643$			0.480049i			0.0189313i	−0.999955	+	0.00946565i	$0.996987\pi$
$644$	−11.0890	+	11.5689i	−0.436966	+	0.455878i
$645$		0			0
$646$	−9.51916	−	27.3191i	−0.374526	−	1.07486i
$647$	−17.6512	−	30.5727i	−0.693939	−	1.20194i	−0.970537	−	0.240952i	$-0.922541\pi$
$647$	−17.6512	−	30.5727i	−0.693939	−	1.20194i	0.276598	−	0.960986i	$-0.410793\pi$
$648$		0			0
$649$	18.1421	−	31.4231i	0.712141	−	1.23346i
$650$	−15.6934	+	18.1878i	−0.615547	+	0.713383i
$651$		0			0
$652$	6.48528	−	0.960099i	0.253983	−	0.0376004i
$653$	−23.4069	−	13.5140i	−0.915982	−	0.528843i	−0.0336311	−	0.999434i	$-0.510707\pi$
$653$	−23.4069	−	13.5140i	−0.915982	−	0.528843i	−0.882351	+	0.470592i	$0.844040\pi$
$654$		0			0
$655$	1.17157	+	2.02922i	0.0457771	+	0.0792883i
$656$	−5.51507	+	23.5916i	−0.215327	+	0.921098i
$657$		0			0
$658$	30.2884	−	15.4346i	1.18077	−	0.601705i
$659$		−	24.7862i		−	0.965535i	−0.875749	−	0.482767i	$-0.839632\pi$
$659$		−	24.7862i		−	0.965535i	0.875749	−	0.482767i	$-0.160368\pi$
$660$		0			0
$661$	25.2345	−	14.5691i	0.981508	−	0.566674i	0.0787826	−	0.996892i	$-0.474897\pi$
$661$	25.2345	−	14.5691i	0.981508	−	0.566674i	0.902725	+	0.430218i	$0.141563\pi$
$662$	−7.10696	−	1.35437i	−0.276220	−	0.0526391i
$663$		0			0
$664$	29.0711	+	18.4266i	1.12818	+	0.715090i
$665$	3.02846	−	7.41818i	0.117439	−	0.287665i
$666$		0			0
$667$	8.02938	+	4.63577i	0.310899	+	0.179498i
$668$	8.67659	−	6.88218i	0.335707	−	0.266279i
$669$		0			0
$670$	8.78271	−	3.06027i	0.339306	−	0.118229i
$671$	41.3592			1.59666
$672$		0			0
$673$	−37.6274			−1.45043			−0.725215	−	0.688522i	$-0.758260\pi$
$673$	−37.6274			−1.45043			−0.725215	+	0.688522i	$0.758260\pi$
$674$	−1.79372	+	0.625010i	−0.0690916	+	0.0240745i
$675$		0			0
$676$	−10.4770	+	8.31020i	−0.402960	+	0.319623i
$677$	−10.9269	−	6.30864i	−0.419955	−	0.242461i	0.275103	−	0.961415i	$-0.411288\pi$
$677$	−10.9269	−	6.30864i	−0.419955	−	0.242461i	−0.695058	+	0.718954i	$0.744621\pi$
$678$		0			0
$679$	7.82843	+	10.0951i	0.300427	+	0.387416i
$680$	−18.9056	−	11.9832i	−0.724996	−	0.459536i
$681$		0			0
$682$	46.5696	+	8.87476i	1.78324	+	0.339832i
$683$	2.58469	−	1.49227i	0.0989005	−	0.0571002i	−0.449734	−	0.893163i	$-0.648481\pi$
$683$	2.58469	−	1.49227i	0.0989005	−	0.0571002i	0.548634	+	0.836062i	$0.315148\pi$
$684$		0			0
$685$			13.1119i			0.500981i
$686$	−19.2834	+	17.7243i	−0.736244	+	0.676716i
$687$		0			0
$688$	41.7218	+	9.75342i	1.59063	+	0.371846i
$689$	4.39050	+	7.60457i	0.167265	+	0.289711i
$690$		0			0
$691$	−7.61365	−	4.39574i	−0.289637	−	0.167222i	0.348141	−	0.937442i	$-0.386813\pi$
$691$	−7.61365	−	4.39574i	−0.289637	−	0.167222i	−0.637778	+	0.770220i	$0.720146\pi$
$692$	43.5007	−	6.43996i	1.65365	−	0.244811i
$693$		0			0
$694$	−24.8995	+	28.8571i	−0.945172	+	1.09540i
$695$	−0.994629	+	1.72275i	−0.0377284	+	0.0653475i
$696$		0			0
$697$	−22.1421	−	38.3513i	−0.838693	−	1.45266i
$698$	−0.631822	−	1.81327i	−0.0239148	−	0.0686334i
$699$		0			0
$700$	5.65639	+	19.4524i	0.213791	+	0.735233i
$701$		−	3.24718i		−	0.122644i	−0.998118	−	0.0613221i	$-0.980468\pi$
$701$		−	3.24718i		−	0.122644i	0.998118	−	0.0613221i	$-0.0195317\pi$
$702$		0			0
$703$	12.6924	+	21.9839i	0.478702	+	0.829137i
$704$	34.3585	+	23.8237i	1.29494	+	0.897888i
$705$		0			0
$706$	−17.0000	−	14.6686i	−0.639803	−	0.552058i
$707$	−25.6033	−	10.4525i	−0.962911	−	0.393107i
$708$		0			0
$709$	−12.5311	−	7.23486i	−0.470617	−	0.271711i	0.245881	−	0.969300i	$-0.420923\pi$
$709$	−12.5311	−	7.23486i	−0.470617	−	0.271711i	−0.716498	+	0.697589i	$0.754256\pi$
$710$	8.32632	+	1.58674i	0.312481	+	0.0595494i
$711$		0			0
$712$	−7.94535	−	15.1777i	−0.297765	−	0.568807i
$713$	19.4252			0.727479
$714$		0			0
$715$		−	25.0990i		−	0.938651i
$716$	−4.44724	+	11.2445i	−0.166201	+	0.420227i
$717$		0			0
$718$	3.87124	−	20.3140i	0.144473	−	0.758113i
$719$	−11.5942	+	20.0818i	−0.432392	+	0.748925i	−0.997079	−	0.0763802i	$-0.975664\pi$
$719$	−11.5942	+	20.0818i	−0.432392	+	0.748925i	0.564687	+	0.825305i	$0.308997\pi$
$720$		0			0
$721$	−19.8848	+	2.72117i	−0.740548	+	0.101342i
$722$	11.9617	+	10.3212i	0.445167	+	0.384115i
$723$		0			0
$724$	−18.2311	−	22.9846i	−0.677555	−	0.854216i
$725$	10.1503	−	5.86030i	0.376974	−	0.217646i
$726$		0			0
$727$	−8.89949			−0.330064			−0.165032	−	0.986288i	$-0.552773\pi$
$727$	−8.89949			−0.330064			−0.165032	+	0.986288i	$0.552773\pi$
$728$	3.13848	+	33.0542i	0.116320	+	1.22507i
$729$		0			0
$730$	−1.51102	−	4.33649i	−0.0559253	−	0.160501i
$731$	−67.8244	+	39.1584i	−2.50858	+	1.44833i
$732$		0			0
$733$	−16.3736	−	9.45332i	−0.604774	−	0.349166i	0.166144	−	0.986102i	$-0.446868\pi$
$733$	−16.3736	−	9.45332i	−0.604774	−	0.349166i	−0.770917	+	0.636935i	$0.780202\pi$
$734$	5.76560	+	4.97488i	0.212812	+	0.183626i
$735$		0			0
$736$	15.6569	+	6.95365i	0.577119	+	0.256315i
$737$	15.8771	−	27.5000i	0.584842	−	1.01298i
$738$		0			0
$739$	−24.9909	+	14.4285i	−0.919307	+	0.530762i	−0.883414	−	0.468594i	$-0.844761\pi$
$739$	−24.9909	+	14.4285i	−0.919307	+	0.530762i	−0.0358930	+	0.999356i	$0.511428\pi$
$740$	18.2639	+	7.22341i	0.671393	+	0.265538i
$741$		0			0
$742$	7.39489	+	0.387178i	0.271475	+	0.0142137i
$743$	3.54806			0.130166			0.0650829	−	0.997880i	$-0.479269\pi$
$743$	3.54806			0.130166			0.0650829	+	0.997880i	$0.479269\pi$
$744$		0			0
$745$	−2.34315	−	4.05845i	−0.0858462	−	0.148690i
$746$	−7.49761	−	1.42882i	−0.274507	−	0.0523127i
$747$		0			0
$748$	−75.5980	+	11.1917i	−2.76414	+	0.409210i
$749$	2.81214	+	20.5495i	0.102753	+	0.750863i
$750$		0			0
$751$	4.13604	−	7.16383i	0.150926	−	0.261412i	−0.780642	−	0.624978i	$-0.785108\pi$
$751$	4.13604	−	7.16383i	0.150926	−	0.261412i	0.931568	+	0.363567i	$0.118441\pi$
$752$	−26.5101	−	24.8580i	−0.966724	−	0.906478i
$753$		0			0
$754$	18.1403	−	6.32085i	0.660630	−	0.230192i
$755$		−	3.43289i		−	0.124936i
$756$		0			0
$757$			1.35778i			0.0493495i	0.999696	+	0.0246748i	$0.00785502\pi$
$757$			1.35778i			0.0493495i	−0.999696	+	0.0246748i	$0.992145\pi$
$758$	−14.3217	−	41.1019i	−0.520187	−	1.49289i
$759$		0			0
$760$	−8.55846	−	0.353979i	−0.310448	−	0.0128402i
$761$	−18.2784	+	31.6591i	−0.662591	+	1.14764i	0.317342	+	0.948311i	$0.397210\pi$
$761$	−18.2784	+	31.6591i	−0.662591	+	1.14764i	−0.979933	+	0.199329i	$0.936124\pi$
$762$		0			0
$763$	8.51645	+	3.47682i	0.308316	+	0.125870i
$764$	5.90473	+	39.8853i	0.213626	+	1.44300i
$765$		0			0
$766$	1.74108	−	9.13619i	0.0629078	−	0.330104i
$767$	−15.4021	−	26.6772i	−0.556138	−	0.963259i
$768$		0			0
$769$	21.8284			0.787153			0.393577	−	0.919292i	$-0.371238\pi$
$769$	21.8284			0.787153			0.393577	+	0.919292i	$0.371238\pi$
$770$	−17.7519	−	11.5269i	−0.639734	−	0.415402i
$771$		0			0
$772$	22.9013	+	9.05754i	0.824237	+	0.325988i
$773$	32.3258	−	18.6633i	1.16268	−	0.671272i	0.210733	−	0.977544i	$-0.432415\pi$
$773$	32.3258	−	18.6633i	1.16268	−	0.671272i	0.951944	+	0.306271i	$0.0990815\pi$
$774$		0			0
$775$	12.2782	−	21.2664i	0.441045	−	0.763912i
$776$	7.31135	−	11.5349i	0.262462	−	0.414079i
$777$		0			0
$778$	−13.4853	+	15.6287i	−0.483471	+	0.560314i
$779$	−14.6764	−	8.47343i	−0.525837	−	0.303592i
$780$		0			0
$781$	25.0623	−	14.4697i	0.896799	−	0.517767i
$782$	−29.5700	+	10.3035i	−1.05742	+	0.368451i
$783$		0			0
$784$	24.8198	+	12.9607i	0.886420	+	0.462881i
$785$	17.1316			0.611452
$786$		0			0
$787$	−2.83882	+	1.63899i	−0.101193	+	0.0584237i	−0.549742	−	0.835334i	$-0.685274\pi$
$787$	−2.83882	+	1.63899i	−0.101193	+	0.0584237i	0.448550	+	0.893758i	$0.351941\pi$
$788$	−12.7603	−	16.0874i	−0.454567	−	0.573088i
$789$		0			0
$790$	−1.24264	+	1.44015i	−0.0442112	+	0.0512382i
$791$	−2.03383	−	2.62272i	−0.0723147	−	0.0932533i
$792$		0			0
$793$	17.5563	−	30.4085i	0.623444	−	1.07984i
$794$	8.05008	+	1.53410i	0.285687	+	0.0544432i
$795$		0			0
$796$	−8.98002	−	3.55162i	−0.318288	−	0.125884i
$797$			11.0096i			0.389981i	0.980805	+	0.194991i	$0.0624676\pi$
$797$			11.0096i			0.389981i	−0.980805	+	0.194991i	$0.937532\pi$
$798$		0			0
$799$	66.4264			2.35000
$800$	17.5091	−	12.7457i	0.619039	−	0.450628i
$801$		0			0
$802$	−9.01390	+	47.2998i	−0.318292	+	1.67021i
$803$	−13.5782	−	7.83938i	−0.479164	−	0.276646i
$804$		0			0
$805$	−8.02938	−	3.27798i	−0.282999	−	0.115534i
$806$	26.2930	−	30.4721i	0.926133	−	1.07333i
$807$		0			0
$808$	−1.22173	+	29.5389i	−0.0429804	+	1.03917i
$809$	22.5613	+	39.0773i	0.793212	+	1.37388i	0.923968	+	0.382469i	$0.124926\pi$
$809$	22.5613	+	39.0773i	0.793212	+	1.37388i	−0.130757	+	0.991415i	$0.541741\pi$
$810$		0			0
$811$		−	31.6550i		−	1.11156i	−0.831330	−	0.555779i	$-0.812420\pi$
$811$		−	31.6550i		−	1.11156i	0.831330	−	0.555779i	$-0.187580\pi$
$812$	3.86051	−	15.7330i	0.135477	−	0.552122i
$813$		0			0
$814$	63.3226	−	22.0643i	2.21946	−	0.773354i
$815$	1.77403	+	3.07271i	0.0621416	+	0.107632i
$816$		0			0
$817$	−14.9853	+	25.9553i	−0.524269	+	0.908060i
$818$	41.6951	+	35.9769i	1.45784	+	1.25790i
$819$		0			0
$820$	−12.9706	+	1.92020i	−0.452952	+	0.0670562i
$821$	20.9164	+	12.0761i	0.729988	+	0.421459i	0.818418	−	0.574624i	$-0.194852\pi$
$821$	20.9164	+	12.0761i	0.729988	+	0.421459i	−0.0884301	+	0.996082i	$0.528185\pi$
$822$		0			0
$823$	−12.8995	−	22.3426i	−0.449648	−	0.778813i	0.548715	−	0.836010i	$-0.315117\pi$
$823$	−12.8995	−	22.3426i	−0.449648	−	0.778813i	−0.998363	+	0.0571962i	$0.981784\pi$
$824$	9.95089	+	19.0088i	0.346656	+	0.662202i
$825$		0			0
$826$	−25.9417	−	1.35824i	−0.902626	−	0.0472592i
$827$			39.1969i			1.36301i	0.731814	+	0.681505i	$0.238674\pi$
$827$			39.1969i			1.36301i	−0.731814	+	0.681505i	$0.761326\pi$
$828$		0			0
$829$	1.49074	−	0.860677i	0.0517754	−	0.0298926i	−0.473889	−	0.880585i	$-0.657150\pi$
$829$	1.49074	−	0.860677i	0.0517754	−	0.0298926i	0.525664	+	0.850692i	$0.323817\pi$
$830$	−3.48707	+	18.2981i	−0.121038	+	0.635137i
$831$		0			0
$832$	32.1005	−	15.1486i	1.11288	−	0.525183i
$833$	−49.2978	+	13.7500i	−1.70807	+	0.476409i
$834$		0			0
$835$	5.19057	+	2.99678i	0.179627	+	0.103708i
$836$	−22.9128	+	18.1741i	−0.792454	+	0.628566i
$837$		0			0
$838$	6.46133	+	18.5434i	0.223203	+	0.640573i
$839$	18.1708			0.627324			0.313662	−	0.949535i	$-0.398444\pi$
$839$	18.1708			0.627324			0.313662	+	0.949535i	$0.398444\pi$
$840$		0			0
$841$	19.6274			0.676807
$842$	−3.14324	−	9.02080i	−0.108323	−	0.310877i
$843$		0			0
$844$	−8.14822	−	10.2727i	−0.280473	−	0.353602i
$845$	−6.26759	−	3.61859i	−0.215612	−	0.124483i
$846$		0			0
$847$	−42.7635	+	5.85204i	−1.46937	+	0.201079i
$848$	−2.29363	−	7.57675i	−0.0787637	−	0.260187i
$849$		0			0
$850$	−7.41038	+	38.8854i	−0.254174	+	1.33376i
$851$	23.7952	−	13.7381i	0.815688	−	0.470937i
$852$		0			0
$853$		−	37.0520i		−	1.26864i	−0.773072	−	0.634318i	$-0.781281\pi$
$853$		−	37.0520i		−	1.26864i	0.773072	−	0.634318i	$-0.218719\pi$
$854$	−13.4442	−	26.3825i	−0.460052	−	0.902791i
$855$		0			0
$856$	19.6442	−	10.2835i	0.671426	−	0.351484i
$857$	27.9910	+	48.4818i	0.956153	+	1.65611i	0.731706	+	0.681620i	$0.238724\pi$
$857$	27.9910	+	48.4818i	0.956153	+	1.65611i	0.224447	+	0.974486i	$0.427942\pi$
$858$		0			0
$859$	13.7070	+	7.91375i	0.467677	+	0.270014i	0.715267	−	0.698851i	$-0.246305\pi$
$859$	13.7070	+	7.91375i	0.467677	+	0.270014i	−0.247590	+	0.968865i	$0.579638\pi$
$860$	3.39587	+	22.9385i	0.115798	+	0.782196i
$861$		0			0
$862$	−12.4142	−	10.7117i	−0.422830	−	0.364841i
$863$	22.4537	−	38.8909i	0.764331	−	1.32386i	−0.176268	−	0.984342i	$-0.556403\pi$
$863$	22.4537	−	38.8909i	0.764331	−	1.32386i	0.940599	−	0.339518i	$-0.110264\pi$
$864$		0			0
$865$	11.8995	+	20.6105i	0.404595	+	0.700779i
$866$	9.07981	−	3.16379i	0.308544	−	0.107510i
$867$		0			0
$868$	−9.47681	−	32.5909i	−0.321664	−	1.10621i
$869$			6.49435i			0.220306i
$870$		0			0
$871$	−13.4792	−	23.3466i	−0.456725	−	0.791070i
$872$	0.406386	−	9.82555i	0.0137620	−	0.332735i
$873$		0			0
$874$	−7.82843	+	9.07269i	−0.264800	+	0.306888i
$875$	−19.9790	+	15.4930i	−0.675414	+	0.523761i
$876$		0			0
$877$	−31.9158	−	18.4266i	−1.07772	−	0.622222i	−0.147439	−	0.989071i	$-0.547103\pi$
$877$	−31.9158	−	18.4266i	−1.07772	−	0.622222i	−0.930280	+	0.366849i	$0.880436\pi$
$878$	4.89383	−	25.6800i	0.165159	−	0.866658i
$879$		0			0
$880$	−5.15080	+	22.0334i	−0.173633	+	0.742745i
$881$	−24.4429			−0.823503			−0.411751	−	0.911296i	$-0.635083\pi$
$881$	−24.4429			−0.823503			−0.411751	+	0.911296i	$0.635083\pi$
$882$		0			0
$883$		−	38.6910i		−	1.30206i	−0.759054	−	0.651028i	$-0.774338\pi$
$883$		−	38.6910i		−	1.30206i	0.759054	−	0.651028i	$-0.225662\pi$
$884$	−23.8617	+	60.3325i	−0.802555	+	2.02920i
$885$		0			0
$886$	−42.4234	−	8.08462i	−1.42524	−	0.271608i
$887$	1.25443	−	2.17274i	0.0421196	−	0.0729533i	−0.844197	−	0.536033i	$-0.819922\pi$
$887$	1.25443	−	2.17274i	0.0421196	−	0.0729533i	0.886317	+	0.463080i	$0.153256\pi$
$888$		0			0
$889$	−6.60051	−	8.51167i	−0.221374	−	0.285472i
$890$	6.05692	−	7.01962i	0.203028	−	0.235298i
$891$		0			0
$892$	19.0259	−	15.0911i	0.637034	−	0.505288i
$893$	22.0146	−	12.7101i	0.736691	−	0.425329i
$894$		0			0
$895$	−6.54416			−0.218747
$896$	4.02822	−	29.6610i	0.134573	−	0.990904i
$897$		0			0
$898$	−9.76405	+	3.40221i	−0.325831	+	0.113533i
$899$	−17.0061	+	9.81845i	−0.567184	+	0.327464i
$900$		0			0
$901$	12.5311	+	7.23486i	0.417473	+	0.241028i
$902$	−29.2454	+	33.8937i	−0.973765	+	1.12854i
$903$		0			0
$904$	−1.89949	+	2.99678i	−0.0631763	+	0.0996713i
$905$	7.93857	−	13.7500i	0.263887	−	0.457065i
$906$		0			0
$907$	26.1668	−	15.1074i	0.868855	−	0.501634i	0.00188752	−	0.999998i	$-0.499399\pi$
$907$	26.1668	−	15.1074i	0.868855	−	0.501634i	0.866968	+	0.498364i	$0.166066\pi$
$908$	−17.6289	+	44.5734i	−0.585036	+	1.47922i
$909$		0			0
$910$	−16.0103	+	8.15868i	−0.530737	+	0.270458i
$911$	−28.7258			−0.951728			−0.475864	−	0.879519i	$-0.657865\pi$
$911$	−28.7258			−0.951728			−0.475864	+	0.879519i	$0.657865\pi$
$912$		0			0
$913$	31.7990	+	55.0775i	1.05239	+	1.82280i
$914$	−2.23862	+	11.7470i	−0.0740468	+	0.388555i
$915$		0			0
$916$	−49.2635	+	7.29310i	−1.62771	+	0.240971i
$917$	−0.776550	−	5.67459i	−0.0256440	−	0.187392i
$918$		0			0
$919$	−6.37868	+	11.0482i	−0.210413	+	0.364446i	−0.951844	−	0.306583i	$-0.900814\pi$
$919$	−6.37868	+	11.0482i	−0.210413	+	0.364446i	0.741431	+	0.671029i	$0.234148\pi$
$920$	−0.383145	+	9.26361i	−0.0126319	+	0.305412i
$921$		0			0
$922$	9.55496	+	27.4219i	0.314676	+	0.903091i
$923$		−	24.5687i		−	0.808687i
$924$		0			0
$925$		−	34.7341i		−	1.14205i
$926$	32.3359	−	11.2672i	1.06262	−	0.370263i
$927$		0			0
$928$	−17.2217	+	1.82608i	−0.565331	+	0.0599439i
$929$	−4.17528	+	7.23179i	−0.136986	+	0.237267i	−0.926355	−	0.376653i	$-0.877075\pi$
$929$	−4.17528	+	7.23179i	−0.136986	+	0.237267i	0.789368	+	0.613920i	$0.210408\pi$
$930$		0			0
$931$	−13.7070	+	13.9897i	−0.449229	+	0.458493i
$932$	−4.65030	−	31.4119i	−0.152326	−	1.02893i
$933$		0			0
$934$	−10.3746	−	1.97708i	−0.339467	−	0.0646921i
$935$	−20.6796	−	35.8182i	−0.676296	−	1.17138i
$936$		0			0
$937$	−33.8284			−1.10513			−0.552563	−	0.833471i	$-0.686350\pi$
$937$	−33.8284			−1.10513			−0.552563	+	0.833471i	$0.686350\pi$
$938$	−22.7029	−	1.18867i	−0.741276	−	0.0388113i
$939$		0			0
$940$	7.23351	−	18.2894i	0.235931	−	0.596535i
$941$	1.71393	−	0.989538i	0.0558725	−	0.0322580i	−0.471804	−	0.881704i	$-0.656397\pi$
$941$	1.71393	−	0.989538i	0.0558725	−	0.0322580i	0.527676	+	0.849446i	$0.323064\pi$
$942$		0			0
$943$	−9.17157	+	15.8856i	−0.298668	+	0.517307i
$944$	8.04618	+	26.5796i	0.261881	+	0.865092i
$945$		0			0
$946$	59.9411	+	51.7206i	1.94885	+	1.68158i
$947$	−9.50703	−	5.48888i	−0.308937	−	0.178365i	0.337514	−	0.941321i	$-0.390414\pi$
$947$	−9.50703	−	5.48888i	−0.308937	−	0.178365i	−0.646451	+	0.762956i	$0.723747\pi$
$948$		0			0
$949$	−11.5275	+	6.65539i	−0.374197	+	0.216043i
$950$	4.98450	+	14.3051i	0.161719	+	0.464118i
$951$		0			0
$952$	31.7129	+	44.5850i	1.02782	+	1.44501i
$953$	20.8948			0.676851			0.338425	−	0.940993i	$-0.390106\pi$
$953$	20.8948			0.676851			0.338425	+	0.940993i	$0.390106\pi$
$954$		0			0
$955$	−18.8976	+	10.9105i	−0.611511	+	0.353056i
$956$	32.4035	−	25.7021i	1.04800	−	0.831266i
$957$		0			0
$958$	30.7574	+	26.5392i	0.993725	+	0.857442i
$959$	12.1138	−	29.6727i	0.391176	−	0.958182i
$960$		0			0
$961$	−5.07107	+	8.78335i	−0.163583	+	0.283334i
$962$	10.6571	−	55.9225i	0.343600	−	1.80301i
$963$		0			0
$964$	16.4193	+	6.49389i	0.528831	+	0.209154i
$965$			13.3283i			0.429052i
$966$		0			0
$967$	−10.4142			−0.334899			−0.167449	−	0.985881i	$-0.553553\pi$
$967$	−10.4142			−0.334899			−0.167449	+	0.985881i	$0.553553\pi$
$968$	21.4000	+	40.8795i	0.687822	+	1.31392i
$969$		0			0
$970$	7.26038	+	1.38361i	0.233117	+	0.0444250i
$971$	−31.2942	−	18.0677i	−1.00428	−	0.579820i	−0.0947671	−	0.995499i	$-0.530211\pi$
$971$	−31.2942	−	18.0677i	−1.00428	−	0.579820i	−0.909511	+	0.415679i	$0.863544\pi$
$972$		0			0
$973$	3.84249	−	2.97972i	0.123185	−	0.0955254i
$974$	−38.2547	−	33.0083i	−1.22576	−	1.05765i
$975$		0			0
$976$	−21.6524	+	23.0914i	−0.693075	+	0.739138i
$977$	−8.56578	−	14.8364i	−0.274044	−	0.474657i	0.695850	−	0.718187i	$-0.255028\pi$
$977$	−8.56578	−	14.8364i	−0.274044	−	0.474657i	−0.969893	+	0.243530i	$0.921695\pi$
$978$		0			0
$979$		−	31.6550i		−	1.01170i
$980$	−1.58246	+	15.0706i	−0.0505498	+	0.481414i
$981$		0			0
$982$	1.42460	+	4.08848i	0.0454609	+	0.130469i
$983$	−20.4198	−	35.3682i	−0.651291	−	1.12807i	−0.982810	−	0.184621i	$-0.940894\pi$
$983$	−20.4198	−	35.3682i	−0.651291	−	1.12807i	0.331519	−	0.943449i	$-0.392439\pi$
$984$		0			0
$985$	5.55635	−	9.62388i	0.177040	−	0.306642i
$986$	20.6796	−	23.9665i	0.658573	−	0.763248i
$987$		0			0
$988$	3.63604	+	24.5607i	0.115678	+	0.781381i
$989$	28.0938	+	16.2200i	0.893330	+	0.515764i
$990$		0			0
$991$	6.76346	+	11.7146i	0.214848	+	0.372128i	0.953226	−	0.302260i	$-0.0977410\pi$
$991$	6.76346	+	11.7146i	0.214848	+	0.372128i	−0.738377	+	0.674388i	$0.764408\pi$
$992$	−29.3350	+	21.3543i	−0.931387	+	0.678000i
$993$		0			0
$994$	−17.3768	−	11.2834i	−0.551158	−	0.357887i
$995$		−	5.22625i		−	0.165683i
$996$		0			0
$997$	−47.8023	+	27.5987i	−1.51392	+	0.874060i	−0.514048	+	0.857761i	$0.671855\pi$
$997$	−47.8023	+	27.5987i	−1.51392	+	0.874060i	−0.999867	+	0.0162984i	$0.994812\pi$
$998$	−18.1008	−	3.44947i	−0.572972	−	0.109191i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cj.d.37.1	✓	16
3.2	odd	2	inner	504.2.cj.d.37.8	yes	16
4.3	odd	2		2016.2.cr.d.1297.6		16
7.4	even	3	inner	504.2.cj.d.109.5	yes	16
8.3	odd	2		2016.2.cr.d.1297.3		16
8.5	even	2	inner	504.2.cj.d.37.5	yes	16
12.11	even	2		2016.2.cr.d.1297.4		16
21.11	odd	6	inner	504.2.cj.d.109.4	yes	16
24.5	odd	2	inner	504.2.cj.d.37.4	yes	16
24.11	even	2		2016.2.cr.d.1297.5		16
28.11	odd	6		2016.2.cr.d.1873.4		16
56.11	odd	6		2016.2.cr.d.1873.5		16
56.53	even	6	inner	504.2.cj.d.109.1	yes	16
84.11	even	6		2016.2.cr.d.1873.6		16
168.11	even	6		2016.2.cr.d.1873.3		16
168.53	odd	6	inner	504.2.cj.d.109.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cj.d.37.1	✓	16	1.1	even	1	trivial
504.2.cj.d.37.4	yes	16	24.5	odd	2	inner
504.2.cj.d.37.5	yes	16	8.5	even	2	inner
504.2.cj.d.37.8	yes	16	3.2	odd	2	inner
504.2.cj.d.109.1	yes	16	56.53	even	6	inner
504.2.cj.d.109.4	yes	16	21.11	odd	6	inner
504.2.cj.d.109.5	yes	16	7.4	even	3	inner
504.2.cj.d.109.8	yes	16	168.53	odd	6	inner
2016.2.cr.d.1297.3		16	8.3	odd	2
2016.2.cr.d.1297.4		16	12.11	even	2
2016.2.cr.d.1297.5		16	24.11	even	2
2016.2.cr.d.1297.6		16	4.3	odd	2
2016.2.cr.d.1873.3		16	168.11	even	6
2016.2.cr.d.1873.4		16	28.11	odd	6
2016.2.cr.d.1873.5		16	56.11	odd	6
2016.2.cr.d.1873.6		16	84.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33546 + 0.465333i) q^{2} +(1.56693 - 1.24287i) q^{4} +(0.937379 + 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 + 2.38896i) q^{8} +O(q^{10})\)	\(q+(-1.33546 + 0.465333i) q^{2} +(1.56693 - 1.24287i) q^{4} +(0.937379 + 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 + 2.38896i) q^{8} +(-1.50367 - 0.286555i) q^{10} +(-4.52607 + 2.61313i) q^{11} +4.43692i q^{13} +(3.13812 + 2.03770i) q^{14} +(0.910541 - 3.89499i) q^{16} +(3.65568 + 6.33182i) q^{17} +(2.42308 + 1.39897i) q^{19} +(2.14144 - 0.317025i) q^{20} +(4.82843 - 5.59587i) q^{22} +(1.51423 - 2.62272i) q^{23} +(-1.91421 - 3.31552i) q^{25} +(-2.06465 - 5.92535i) q^{26} +(-5.13905 - 1.26100i) q^{28} +3.06147i q^{29} +(3.20711 + 5.55487i) q^{31} +(0.596471 + 5.62532i) q^{32} +(-7.82843 - 6.75481i) q^{34} +(-0.388275 - 2.83730i) q^{35} +(7.85718 + 4.53635i) q^{37} +(-3.88692 - 0.740730i) q^{38} +(-2.71230 + 1.41986i) q^{40} -6.05692 q^{41} +10.7117i q^{43} +(-3.84425 + 9.71991i) q^{44} +(-0.801760 + 4.20718i) q^{46} +(4.54269 - 7.86817i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(4.09918 + 3.53701i) q^{50} +(5.51453 + 6.95235i) q^{52} +(1.71393 - 0.989538i) q^{53} -5.65685 q^{55} +(7.44981 - 0.707354i) q^{56} +(-1.42460 - 4.08848i) q^{58} +(-6.01255 + 3.47135i) q^{59} +(-6.85351 - 3.95687i) q^{61} +(-6.86784 - 5.92596i) q^{62} +(-3.41421 - 7.23486i) q^{64} +(-2.40125 + 4.15908i) q^{65} +(-5.26190 + 3.03796i) q^{67} +(13.5978 + 5.37798i) q^{68} +(1.83882 + 3.60843i) q^{70} -5.53732 q^{71} +(1.50000 + 2.59808i) q^{73} +(-12.6039 - 2.40192i) q^{74} +(5.53553 - 0.819496i) q^{76} +(12.8017 + 5.22625i) q^{77} +(0.621320 - 1.07616i) q^{79} +(2.96147 - 3.15830i) q^{80} +(8.08880 - 2.81849i) q^{82} -12.1689i q^{83} +7.91375i q^{85} +(-4.98450 - 14.3051i) q^{86} +(0.610867 - 14.7694i) q^{88} +(-3.02846 + 5.24545i) q^{89} +(9.27659 - 7.19367i) q^{91} +(-0.887016 - 5.99162i) q^{92} +(-2.40528 + 12.6215i) q^{94} +(1.51423 + 2.62272i) q^{95} -4.82843 q^{97} +(-0.827545 - 9.86485i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 8 q^{7}+O(q^{10}) \) 16 * q - 8 * q^4 + 8 * q^7	\( 16 q - 8 q^{4} + 8 q^{7} - 8 q^{10} + 8 q^{16} + 32 q^{22} - 8 q^{25} - 16 q^{28} + 40 q^{31} - 80 q^{34} - 32 q^{40} - 8 q^{46} + 40 q^{49} + 8 q^{52} - 32 q^{64} - 16 q^{70} + 24 q^{73} + 32 q^{76} - 24 q^{79} - 16 q^{82} - 32 q^{88} - 24 q^{94} - 32 q^{97}+O(q^{100}) \) 16 * q - 8 * q^4 + 8 * q^7 - 8 * q^10 + 8 * q^16 + 32 * q^22 - 8 * q^25 - 16 * q^28 + 40 * q^31 - 80 * q^34 - 32 * q^40 - 8 * q^46 + 40 * q^49 + 8 * q^52 - 32 * q^64 - 16 * q^70 + 24 * q^73 + 32 * q^76 - 24 * q^79 - 16 * q^82 - 32 * q^88 - 24 * q^94 - 32 * q^97

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