LMFDB - Embedded newform 504.2.cj.d.37.5

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			37.5
Root			$0.264742 - 1.38921i$ of defining polynomial
Character	$\chi$	$=$	504.37
Dual form			504.2.cj.d.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.264742 + 1.38921i) q^{2} +(-1.85982 + 0.735566i) q^{4} +(-0.937379 - 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 - 2.38896i) q^{8} +O(q^{10})$	\(q+(0.264742 + 1.38921i) q^{2} +(-1.85982 + 0.735566i) q^{4} +(-0.937379 - 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 - 2.38896i) q^{8} +(0.503673 - 1.44550i) q^{10} +(4.52607 - 2.61313i) q^{11} -4.43692i q^{13} +(2.47529 - 2.80587i) q^{14} +(2.91789 - 2.73604i) q^{16} +(3.65568 + 6.33182i) q^{17} +(-2.42308 - 1.39897i) q^{19} +(2.14144 + 0.317025i) q^{20} +(4.82843 + 5.59587i) q^{22} +(1.51423 - 2.62272i) q^{23} +(-1.91421 - 3.31552i) q^{25} +(6.16383 - 1.17464i) q^{26} +(4.55327 + 2.69588i) q^{28} -3.06147i q^{29} +(3.20711 + 5.55487i) q^{31} +(4.57343 + 3.32922i) q^{32} +(-7.82843 + 6.75481i) q^{34} +(0.388275 + 2.83730i) q^{35} +(-7.85718 - 4.53635i) q^{37} +(1.30197 - 3.73654i) q^{38} +(0.126515 + 3.05885i) q^{40} -6.05692 q^{41} -10.7117i q^{43} +(-6.49556 + 8.18917i) q^{44} +(4.04440 + 1.40924i) q^{46} +(4.54269 - 7.86817i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(4.09918 - 3.53701i) q^{50} +(3.26365 + 8.25189i) q^{52} +(-1.71393 + 0.989538i) q^{53} -5.65685 q^{55} +(-2.53970 + 7.03917i) q^{56} +(4.25303 - 0.810499i) q^{58} +(6.01255 - 3.47135i) q^{59} +(6.85351 + 3.95687i) q^{61} +(-6.86784 + 5.92596i) q^{62} +(-3.41421 + 7.23486i) q^{64} +(-2.40125 + 4.15908i) q^{65} +(5.26190 - 3.03796i) q^{67} +(-11.4564 - 9.08707i) q^{68} +(-3.83882 + 1.29055i) q^{70} -5.53732 q^{71} +(1.50000 + 2.59808i) q^{73} +(4.22182 - 12.1163i) q^{74} +(5.53553 + 0.819496i) q^{76} +(-12.8017 - 5.22625i) q^{77} +(0.621320 - 1.07616i) q^{79} +(-4.21590 + 0.985562i) q^{80} +(-1.60352 - 8.41435i) q^{82} +12.1689i q^{83} -7.91375i q^{85} +(14.8808 - 2.83583i) q^{86} +(-13.0961 - 6.85570i) q^{88} +(-3.02846 + 5.24545i) q^{89} +(-9.27659 + 7.19367i) q^{91} +(-0.887016 + 5.99162i) q^{92} +(12.1332 + 4.22773i) q^{94} +(1.51423 + 2.62272i) q^{95} -4.82843 q^{97} +(-9.87968 - 0.626050i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.264742	+	1.38921i	0.187201	+	0.982322i
$2$	0.264742	+	1.38921i	0.187201	+	0.982322i
$3$		0			0
$3$		0			0
$4$	−1.85982	+	0.735566i	−0.929912	+	0.367783i
$5$	−0.937379	−	0.541196i	−0.419209	−	0.242030i	0.275530	−	0.961292i	$-0.411147\pi$
$5$	−0.937379	−	0.541196i	−0.419209	−	0.242030i	−0.694739	+	0.719262i	$0.744480\pi$
$6$		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
$10$	0.503673	−	1.44550i	0.159275	−	0.457106i
$11$	4.52607	−	2.61313i	1.36466	−	0.787887i	0.374420	−	0.927259i	$-0.377842\pi$
$11$	4.52607	−	2.61313i	1.36466	−	0.787887i	0.990240	+	0.139372i	$0.0445084\pi$
$12$		0			0
$13$		−	4.43692i		−	1.23058i	−0.788300	−	0.615291i	$-0.789039\pi$
$13$		−	4.43692i		−	1.23058i	0.788300	−	0.615291i	$-0.210961\pi$
$14$	2.47529	−	2.80587i	0.661550	−	0.749901i
$15$		0			0
$16$	2.91789	−	2.73604i	0.729472	−	0.684011i
$17$	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	0.195603	−	0.980683i	$-0.437334\pi$
$19$	−2.42308	−	1.39897i	−0.555893	−	0.320945i	−0.751495	+	0.659738i	$0.770667\pi$
$20$	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
$26$	6.16383	−	1.17464i	1.20883	−	0.230366i
$27$		0			0
$28$	4.55327	+	2.69588i	0.860487	+	0.509473i
$29$		−	3.06147i		−	0.568500i	−0.958750	−	0.284250i	$-0.908255\pi$
$29$		−	3.06147i		−	0.568500i	0.958750	−	0.284250i	$-0.0917446\pi$
$30$		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	$0.637941\pi$
$32$	4.57343	+	3.32922i	0.808477	+	0.588528i
$33$		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	−0.312755	−	0.949834i	$-0.601252\pi$
$37$	−7.85718	−	4.53635i	−1.29171	−	0.745771i	−0.978958	+	0.204063i	$0.934585\pi$
$38$	1.30197	−	3.73654i	0.211208	−	0.606147i
$39$		0			0
$40$	0.126515	+	3.05885i	0.0200037	+	0.483647i
$41$	−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	$-0.695769\pi$
$43$		−	10.7117i		−	1.63352i	0.576980	−	0.816758i	$-0.304231\pi$
$44$	−6.49556	+	8.18917i	−0.979242	+	1.23456i
$45$		0			0
$46$	4.04440	+	1.40924i	0.596314	+	0.207782i
$47$	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
$52$	3.26365	+	8.25189i	0.452587	+	1.14433i
$53$	−1.71393	+	0.989538i	−0.235426	+	0.135923i	−0.613073	−	0.790026i	$-0.710067\pi$
$53$	−1.71393	+	0.989538i	−0.235426	+	0.135923i	0.377647	+	0.925950i	$0.376733\pi$
$54$		0			0
$55$	−5.65685			−0.762770
$56$	−2.53970	+	7.03917i	−0.339382	+	0.940649i
$57$		0			0
$58$	4.25303	−	0.810499i	0.558450	−	0.106424i
$59$	6.01255	−	3.47135i	0.782767	−	0.451931i	−0.0546428	−	0.998506i	$-0.517402\pi$
$59$	6.01255	−	3.47135i	0.782767	−	0.451931i	0.837410	+	0.546575i	$0.184069\pi$
$60$		0			0
$61$	6.85351	+	3.95687i	0.877502	+	0.506626i	0.869834	−	0.493345i	$-0.164226\pi$
$61$	6.85351	+	3.95687i	0.877502	+	0.506626i	0.00766783	+	0.999971i	$0.497559\pi$
$62$	−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	−0.142866	−	0.989742i	$-0.545632\pi$
$67$	5.26190	−	3.03796i	0.642843	−	0.371146i	0.785709	+	0.618597i	$0.212298\pi$
$68$	−11.4564	−	9.08707i	−1.38929	−	1.10197i
$69$		0			0
$70$	−3.83882	+	1.29055i	−0.458826	+	0.154250i
$71$	−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	$0.777159\pi$
$74$	4.22182	−	12.1163i	0.490777	−	1.40849i
$75$		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	$0.144397\pi$
$80$	−4.21590	+	0.985562i	−0.471352	+	0.110189i
$81$		0			0
$82$	−1.60352	−	8.41435i	−0.177079	−	0.929210i
$83$			12.1689i			1.33572i	0.744289	+	0.667858i	$0.232789\pi$
$83$			12.1689i			1.33572i	−0.744289	+	0.667858i	$0.767211\pi$
$84$		0			0
$85$		−	7.91375i		−	0.858367i
$86$	14.8808	−	2.83583i	1.60464	−	0.305796i
$87$		0			0
$88$	−13.0961	−	6.85570i	−1.39605	−	0.730820i
$89$	−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
$94$	12.1332	+	4.22773i	1.25144	+	0.436057i
$95$	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	$0.578829\pi$
$98$	−9.87968	−	0.626050i	−0.997998	−	0.0632406i
$99$		0			0
$100$	5.99888	+	4.75824i	0.599888	+	0.475824i
$101$	−9.05213	+	5.22625i	−0.900721	+	0.520031i	−0.877434	−	0.479697i	$-0.840746\pi$
$101$	−9.05213	+	5.22625i	−0.900721	+	0.520031i	−0.0232869	+	0.999729i	$0.507413\pi$
$102$		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	0.790876	−	0.611976i	$-0.209625\pi$
$107$	6.78910	+	3.91969i	0.656327	+	0.378931i	−0.134549	+	0.990907i	$0.542959\pi$
$108$		0			0
$109$	3.01102	−	1.73841i	0.288403	−	0.166510i	−0.348818	−	0.937190i	$-0.613417\pi$
$109$	3.01102	−	1.73841i	0.288403	−	0.166510i	0.637222	+	0.770681i	$0.280084\pi$
$110$	−1.49761	−	7.85857i	−0.142791	−	0.749286i
$111$		0			0
$112$	−10.4513	−	1.66463i	−0.987552	−	0.157292i
$113$	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
$116$	2.25191	+	5.69379i	0.209085	+	0.528655i
$117$		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
$122$	−3.68253	+	10.5685i	−0.333401	+	0.956830i
$123$		0			0
$124$	−10.0506	−	7.97204i	−0.902573	−	0.715911i
$125$			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	$0.442188\pi$
$128$	−10.9546	−	2.82770i	−0.968262	−	0.249936i
$129$		0			0
$130$	−6.41356	−	2.23476i	−0.562506	−	0.196001i
$131$	−1.87476	−	1.08239i	−0.163798	−	0.0945690i	0.415860	−	0.909429i	$-0.363481\pi$
$131$	−1.87476	−	1.08239i	−0.163798	−	0.0945690i	−0.579658	+	0.814860i	$0.696814\pi$
$132$		0			0
$133$	1.00367	+	7.33428i	0.0870295	+	0.635963i
$134$	5.61341	+	6.50562i	0.484925	+	0.562000i
$135$		0			0
$136$	9.59089	−	18.3211i	0.822412	−	1.57102i
$137$	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	$-0.975165\pi$
$139$		−	1.83783i		−	0.155883i	0.996958	−	0.0779415i	$-0.0248347\pi$
$140$	−2.80914	−	4.99127i	−0.237416	−	0.421839i
$141$		0			0
$142$	−1.46596	−	7.69251i	−0.123021	−	0.645541i
$143$	−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	0.645660	−	0.763625i	$-0.276582\pi$
$149$	3.74952	+	2.16478i	0.307172	+	0.177346i	−0.338488	+	0.940971i	$0.609915\pi$
$150$		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	$0.874526\pi$
$152$	0.327034	+	7.90699i	0.0265260	+	0.641341i
$153$		0			0
$154$	3.87124	−	19.1678i	0.311954	−	1.54459i
$155$		−	6.94269i		−	0.557651i
$156$		0			0
$157$	−13.7070	+	7.91375i	−1.09394	+	0.631586i	−0.934622	−	0.355642i	$-0.884262\pi$
$157$	−13.7070	+	7.91375i	−1.09394	+	0.631586i	−0.159316	+	0.987228i	$0.550929\pi$
$158$	1.65950	+	0.578242i	0.132023	+	0.0460025i
$159$		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	0.384686	−	0.923047i	$-0.374310\pi$
$163$	−2.83882	−	1.63899i	−0.222353	−	0.128376i	−0.607039	+	0.794672i	$0.707643\pi$
$164$	11.2648	−	4.45526i	0.879633	−	0.347898i
$165$		0			0
$166$	−16.9053	+	3.22163i	−1.31210	+	0.250047i
$167$	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
$170$	10.9939	−	2.09510i	0.843192	−	0.160687i
$171$		0			0
$172$	7.87914	+	19.9218i	0.600779	+	1.51903i
$173$	−19.0416	−	10.9937i	−1.44771	−	0.835836i	−0.449365	−	0.893348i	$-0.648350\pi$
$173$	−19.0416	−	10.9937i	−1.44771	−	0.835836i	−0.998345	+	0.0575128i	$0.981683\pi$
$174$		0			0
$175$	−3.82843	+	9.37769i	−0.289402	+	0.708887i
$176$	6.05692	−	20.0083i	0.456558	−	1.50818i
$177$		0			0
$178$	−8.08880	−	2.81849i	−0.606281	−	0.211254i
$179$	5.23600	−	3.02301i	0.391357	−	0.225950i	−0.291391	−	0.956604i	$-0.594118\pi$
$179$	5.23600	−	3.02301i	0.391357	−	0.225950i	0.682748	+	0.730654i	$0.260785\pi$
$180$		0			0
$181$			14.6686i			1.09031i	0.838337	+	0.545153i	$0.183528\pi$
$181$			14.6686i			1.09031i	−0.838337	+	0.545153i	$0.816472\pi$
$182$	−12.4494	−	10.9827i	−0.922814	−	0.814091i
$183$		0			0
$184$	−8.55846	+	0.353979i	−0.630938	+	0.0260957i
$185$	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	$0.687184\pi$
$194$	−1.27829	−	6.70771i	−0.0917757	−	0.481586i
$195$		0			0
$196$	−1.74585	−	13.8907i	−0.124703	−	0.992194i
$197$			10.2668i			0.731479i	0.930717	+	0.365739i	$0.119184\pi$
$197$			10.2668i			0.731479i	−0.930717	+	0.365739i	$0.880816\pi$
$198$		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	$0.888078\pi$
$200$	−5.02206	+	9.59342i	−0.355113	+	0.678357i
$201$		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
$206$	10.1305	+	3.52992i	0.705829	+	0.245941i
$207$		0			0
$208$	−12.1396	−	12.9464i	−0.841731	−	0.897674i
$209$	−14.6227			−1.01147
$210$		0			0
$211$			6.55596i			0.451331i	0.974205	+	0.225666i	$0.0724557\pi$
$211$			6.55596i			0.451331i	−0.974205	+	0.225666i	$0.927544\pi$
$212$	2.45974	−	3.10107i	0.168935	−	0.212983i
$213$		0			0
$214$	−3.64792	+	10.4692i	−0.249367	+	0.715660i
$215$	−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
$220$	10.5208	−	4.16099i	0.709309	−	0.280534i
$221$	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	$0.366732\pi$
$224$	−0.454369	−	14.9597i	−0.0303588	−	0.999539i
$225$		0			0
$226$	0.332100	+	1.74267i	0.0220910	+	0.115921i
$227$	20.7556	−	11.9832i	1.37760	−	0.795355i	0.385726	−	0.922613i	$-0.373951\pi$
$227$	20.7556	−	11.9832i	1.37760	−	0.795355i	0.991870	+	0.127258i	$0.0406176\pi$
$228$		0			0
$229$	21.5642	+	12.4501i	1.42500	+	0.822725i	0.996721	−	0.0809200i	$-0.0257858\pi$
$229$	21.5642	+	12.4501i	1.42500	+	0.822725i	0.428282	+	0.903645i	$0.359119\pi$
$230$	−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
$236$	−8.62888	+	10.8787i	−0.561692	+	0.708144i
$237$		0			0
$238$	26.8151	+	5.41574i	1.73817	+	0.351050i
$239$	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	$0.741557\pi$
$242$	21.7864	+	7.59131i	1.40048	+	0.487988i
$243$		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
$248$	8.41404	−	16.0730i	0.534292	−	1.02064i
$249$		0			0
$250$	−13.2751	+	2.52983i	−0.839589	+	0.160000i
$251$			17.3952i			1.09798i	0.835830	+	0.548988i	$0.184987\pi$
$251$			17.3952i			1.09798i	−0.835830	+	0.548988i	$0.815013\pi$
$252$		0			0
$253$		−	15.8275i		−	0.995066i
$254$	1.07778	+	5.65558i	0.0676261	+	0.354863i
$255$		0			0
$256$	1.02812	−	15.9669i	0.0642577	−	0.997933i
$257$	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
$262$	1.00735	−	2.89099i	0.0622340	−	0.178606i
$263$	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
$266$	−9.92316	+	3.33601i	−0.608428	+	0.204544i
$267$		0			0
$268$	−7.55158	+	9.52053i	−0.461286	+	0.581559i
$269$	−7.49903	+	4.32957i	−0.457224	+	0.263978i	−0.710876	−	0.703317i	$-0.751701\pi$
$269$	−7.49903	+	4.32957i	−0.457224	+	0.263978i	0.253652	+	0.967295i	$0.418368\pi$
$270$		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	0.220191	−	0.975457i	$-0.429332\pi$
$277$	19.5568	−	11.2912i	1.17506	−	0.678420i	0.954866	+	0.297037i	$0.0959985\pi$
$278$	2.55314	−	0.486552i	0.153127	−	0.0291814i
$279$		0			0
$280$	6.19024	−	5.22389i	0.369937	−	0.312187i
$281$	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	−0.880241	−	0.474527i	$-0.842619\pi$
$283$	−15.2986	+	8.83267i	−0.909409	+	0.525047i	−0.0291680	+	0.999575i	$0.509286\pi$
$284$	10.2984	−	4.07306i	0.611100	−	0.241692i
$285$		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
$290$	−4.42534	−	1.54198i	−0.259865	−	0.0905481i
$291$		0			0
$292$	−4.70079	−	3.72861i	−0.275093	−	0.218201i
$293$		−	26.1313i		−	1.52660i	−0.646042	−	0.763302i	$-0.723577\pi$
$293$		−	26.1313i		−	1.52660i	0.646042	−	0.763302i	$-0.276423\pi$
$294$		0			0
$295$	−7.51472			−0.437524
$296$	1.06045	+	25.6395i	0.0616377	+	1.49027i
$297$		0			0
$298$	−2.01469	+	5.78198i	−0.116708	+	0.334941i
$299$	−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
$304$	−10.8979	+	2.54763i	−0.625038	+	0.146117i
$305$	−4.28289	−	7.41818i	−0.245238	−	0.424764i
$306$		0			0
$307$		−	19.5855i		−	1.11781i	−0.829233	−	0.558903i	$-0.811223\pi$
$307$		−	19.5855i		−	1.11781i	0.829233	−	0.558903i	$-0.188777\pi$
$308$	27.6531	+	0.303452i	1.57568	+	0.0172908i
$309$		0			0
$310$	9.64488	−	1.83802i	0.547792	−	0.104393i
$311$	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	$0.0982827\pi$
$317$	30.1294	+	17.3952i	1.69223	+	0.977012i	0.739524	+	0.673130i	$0.235051\pi$
$318$		0			0
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$	7.11589	−	4.93404i	0.397790	−	0.275821i
$321$		0			0
$322$	−3.61087	−	10.7407i	−0.201226	−	0.598558i
$323$		−	20.4567i		−	1.13824i
$324$		0			0
$325$	−14.7107	+	8.49322i	−0.816002	+	0.471119i
$326$	1.52535	−	4.37763i	0.0844815	−	0.242454i
$327$		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	0.373274	−	0.927721i	$-0.378235\pi$
$331$	−4.43043	−	2.55791i	−0.243518	−	0.140595i	−0.616793	+	0.787126i	$0.711568\pi$
$332$	−8.95106	−	22.6321i	−0.491253	−	1.24210i
$333$		0			0
$334$	1.46596	+	7.69251i	0.0802138	+	0.420916i
$335$	−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	$0.488353\pi$
$338$	−1.77014	−	9.28868i	−0.0962830	−	0.505238i
$339$		0			0
$340$	5.82108	+	14.7182i	0.315692	+	0.798205i
$341$	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
$346$	10.2315	−	29.3634i	0.550047	−	1.57859i
$347$	−23.3403	+	13.4755i	−1.25297	+	0.723403i	−0.971698	−	0.236225i	$-0.924090\pi$
$347$	−23.3403	+	13.4755i	−1.25297	+	0.723403i	−0.281273	+	0.959628i	$0.590757\pi$
$348$		0			0
$349$		−	1.35778i		−	0.0726805i	−0.999339	−	0.0363403i	$-0.988430\pi$
$349$		−	1.35778i		−	0.0726805i	0.999339	−	0.0363403i	$-0.0115700\pi$
$350$	−14.0412	−	2.83583i	−0.750531	−	0.151582i
$351$		0			0
$352$	29.3993	+	3.11731i	1.56699	+	0.166153i
$353$	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
$362$	−20.3777	+	3.88338i	−1.07103	+	0.204106i
$363$		0			0
$364$	11.9614	−	20.2025i	0.626948	−	1.05890i
$365$		−	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	$0.878218\pi$
$368$	−2.75754	−	11.7958i	−0.143747	−	0.614899i
$369$		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	0.374091	−	0.927392i	$-0.377955\pi$
$373$	−4.67396	−	2.69851i	−0.242008	−	0.139724i	−0.616099	+	0.787668i	$0.711288\pi$
$374$	−17.7808	+	51.0294i	−0.919424	+	2.63867i
$375$		0			0
$376$	−25.6754	+	1.06194i	−1.32411	+	0.0547653i
$377$	−13.5835			−0.699586
$378$		0			0
$379$		−	30.7773i		−	1.58092i	−0.612513	−	0.790461i	$-0.709841\pi$
$379$		−	30.7773i		−	1.58092i	0.612513	−	0.790461i	$-0.290159\pi$
$380$	−4.74539	−	3.76399i	−0.243433	−	0.193088i
$381$		0			0
$382$	−26.9230	−	9.38112i	−1.37750	−	0.479980i
$383$	−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
$388$	8.98002	−	3.55162i	0.455892	−	0.180306i
$389$	−12.6408	+	7.29818i	−0.640915	+	0.370033i	−0.784967	−	0.619538i	$-0.787320\pi$
$389$	−12.6408	+	7.29818i	−0.640915	+	0.370033i	0.144052	+	0.989570i	$0.453987\pi$
$390$		0			0
$391$	22.1421			1.11978
$392$	18.8350	−	6.10281i	0.951309	−	0.308238i
$393$		0			0
$394$	−14.2628	+	2.71805i	−0.718548	+	0.136933i
$395$	−1.16483	+	0.672512i	−0.0586087	+	0.0338378i
$396$		0			0
$397$	5.01836	+	2.89735i	0.251864	+	0.145414i	0.620618	−	0.784113i	$-0.286882\pi$
$397$	5.01836	+	2.89735i	0.251864	+	0.145414i	−0.368753	+	0.929527i	$0.620215\pi$
$398$	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
$404$	12.9911	−	16.3783i	0.646332	−	0.814853i
$405$		0			0
$406$	−8.59009	−	7.57803i	−0.426319	−	0.376091i
$407$	−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	$-0.579522\pi$
$410$	−3.05071	+	8.75526i	−0.150664	+	0.432391i
$411$		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
$416$	14.7715	−	20.2920i	0.724232	−	0.994896i
$417$		0			0
$418$	−3.87124	−	20.3140i	−0.189349	−	0.993592i
$419$			13.8854i			0.678346i	0.940724	+	0.339173i	$0.110147\pi$
$419$			13.8854i			0.678346i	−0.940724	+	0.339173i	$0.889853\pi$
$420$		0			0
$421$		−	6.75481i		−	0.329209i	−0.986360	−	0.164605i	$-0.947365\pi$
$421$		−	6.75481i		−	0.329209i	0.986360	−	0.164605i	$-0.0526348\pi$
$422$	−9.10763	+	1.73564i	−0.443352	+	0.0844896i
$423$		0			0
$424$	4.95924	+	2.59611i	0.240842	+	0.126078i
$425$	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
$430$	−15.4837	−	5.39518i	−0.746690	−	0.260179i
$431$	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	$0.552236\pi$
$434$	23.5248	+	4.75120i	1.12923	+	0.228065i
$435$		0			0
$436$	−4.32125	+	5.44794i	−0.206950	+	0.260909i
$437$	−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	−0.284115	−	0.958790i	$-0.591700\pi$
$443$	−26.4465	−	15.2689i	−1.25651	−	0.725446i	−0.972394	+	0.233344i	$0.925033\pi$
$444$		0			0
$445$	5.67763	−	3.27798i	0.269146	−	0.155391i
$446$	3.21453	+	16.8680i	0.152213	+	0.798723i
$447$		0			0
$448$	20.6620	−	4.59168i	0.976186	−	0.216937i
$449$	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
$452$	−2.33302	+	0.922715i	−0.109736	+	0.0434009i
$453$		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	$0.103295\pi$
$458$	−11.5869	+	33.2533i	−0.541419	+	1.55383i
$459$		0			0
$460$	4.07411	−	5.13637i	0.189956	−	0.239484i
$461$			20.5336i			0.956345i	0.878266	+	0.478172i	$0.158701\pi$
$461$			20.5336i			0.956345i	−0.878266	+	0.478172i	$0.841299\pi$
$462$		0			0
$463$	−24.2132			−1.12528			−0.562641	−	0.826701i	$-0.690215\pi$
$463$	−24.2132			−1.12528			−0.562641	+	0.826701i	$0.690215\pi$
$464$	−8.37631	−	8.93301i	−0.388860	−	0.414705i
$465$		0			0
$466$	21.2033	+	7.38815i	0.982226	+	0.342250i
$467$	−6.46744	−	3.73398i	−0.299278	−	0.172788i	0.342841	−	0.939394i	$-0.388611\pi$
$467$	−6.46744	−	3.73398i	−0.299278	−	0.172788i	−0.642118	+	0.766606i	$0.721944\pi$
$468$		0			0
$469$	−14.8829	−	6.07591i	−0.687228	−	0.280560i
$470$	−9.08538	−	10.5294i	−0.419077	−	0.485686i
$471$		0			0
$472$	−17.3973	−	9.10729i	−0.800775	−	0.419197i
$473$	−27.9910	−	48.4818i	−1.28703	−	2.22919i
$474$		0			0
$475$			10.7117i			0.491486i
$476$	−0.424519	+	38.6857i	−0.0194578	+	1.77316i
$477$		0			0
$478$	5.47476	+	28.7284i	0.250410	+	1.31401i
$479$	−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	$0.533075\pi$
$488$	−0.924993	−	22.3643i	−0.0418725	−	1.01239i
$489$		0			0
$490$	8.92219	+	5.93369i	0.403063	+	0.268057i
$491$			3.06147i			0.138162i	0.997611	+	0.0690810i	$0.0220067\pi$
$491$			3.06147i			0.138162i	−0.997611	+	0.0690810i	$0.977993\pi$
$492$		0			0
$493$	19.3846	−	11.1917i	0.873041	−	0.504050i
$494$	−16.5787	−	5.77674i	−0.745913	−	0.259908i
$495$		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	0.225695	−	0.974198i	$-0.427535\pi$
$499$	−11.2839	−	6.51478i	−0.505138	−	0.291642i	−0.730833	+	0.682556i	$0.760868\pi$
$500$	−7.02893	−	17.7721i	−0.314343	−	0.794794i
$501$		0			0
$502$	−24.1656	+	4.60524i	−1.07856	+	0.205542i
$503$	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
$506$	21.9878	−	4.19020i	0.977475	−	0.186277i
$507$		0			0
$508$	−7.57147	+	2.99454i	−0.335930	+	0.132861i
$509$	15.2921	+	8.82892i	0.677812	+	0.391335i	0.799030	−	0.601291i	$-0.205347\pi$
$509$	15.2921	+	8.82892i	0.677812	+	0.391335i	−0.121218	+	0.992626i	$0.538680\pi$
$510$		0			0
$511$	3.00000	−	7.34847i	0.132712	−	0.325077i
$512$	22.4537	−	2.79884i	0.992321	−	0.123692i
$513$		0			0
$514$	25.9417	+	9.03918i	1.14424	+	0.398701i
$515$	−7.11076	+	4.10540i	−0.313337	+	0.180905i
$516$		0			0
$517$		−	47.4825i		−	2.08828i
$518$	−32.1772	+	10.8175i	−1.41379	+	0.475292i
$519$		0			0
$520$	13.5719	−	0.561336i	0.595167	−	0.0246162i
$521$	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	0.419246	−	0.907873i	$-0.362294\pi$
$523$	−3.59896	−	2.07786i	−0.157371	−	0.0908584i	−0.576618	+	0.817014i	$0.695628\pi$
$524$	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
$530$	0.567113	+	2.97588i	0.0246338	+	0.129264i
$531$		0			0
$532$	−7.26150	−	12.9022i	−0.314826	−	0.559381i
$533$			26.8741i			1.16405i
$534$		0			0
$535$	−4.24264	−	7.34847i	−0.183425	−	0.317702i
$536$	−15.2253	−	7.97027i	−0.657631	−	0.344263i
$537$		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	−0.0555806	−	0.998454i	$-0.517701\pi$
$541$	−22.0513	−	12.7313i	−0.948058	−	0.547361i	−0.892477	+	0.451093i	$0.851034\pi$
$542$	−5.53167	−	1.92747i	−0.237606	−	0.0827920i
$543$		0			0
$544$	−4.36101	+	41.1287i	−0.186977	+	1.76338i
$545$	−3.76329			−0.161202
$546$		0			0
$547$		−	31.6550i		−	1.35347i	−0.736227	−	0.676735i	$-0.763394\pi$
$547$		−	31.6550i		−	1.35347i	0.736227	−	0.676735i	$-0.236606\pi$
$548$	−18.9815	−	15.0559i	−0.810851	−	0.643158i
$549$		0			0
$550$	9.31054	−	26.7204i	0.397003	−	1.13936i
$551$	−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
$556$	1.35185	+	3.41805i	0.0573311	+	0.144957i
$557$	10.1503	−	5.86030i	0.430084	−	0.248309i	−0.269299	−	0.963057i	$-0.586792\pi$
$557$	10.1503	−	5.86030i	0.430084	−	0.248309i	0.699382	+	0.714748i	$0.253459\pi$
$558$		0			0
$559$	−47.5269			−2.01017
$560$	8.89591	+	7.21657i	0.375921	+	0.304956i
$561$		0			0
$562$	5.80686	+	30.4711i	0.244948	+	1.28534i
$563$	−19.2691	+	11.1250i	−0.812095	+	0.468864i	−0.847683	−	0.530503i	$-0.822003\pi$
$563$	−19.2691	+	11.1250i	−0.812095	+	0.468864i	0.0355876	+	0.999367i	$0.488670\pi$
$564$		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	−0.484010	−	0.875062i	$-0.660820\pi$
$571$	0.760141	−	0.438868i	0.0318109	−	0.0183660i	0.515821	+	0.856696i	$0.327487\pi$
$572$	36.3347	+	28.8203i	1.51923	+	1.20504i
$573$		0			0
$574$	−14.9927	+	16.9950i	−0.625781	+	0.709356i
$575$	−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	$0.629891\pi$
$578$	−48.6855	−	16.9641i	−2.02505	−	0.705614i
$579$		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
$584$	3.93534	−	7.51752i	0.162846	−	0.311077i
$585$		0			0
$586$	36.3019	−	6.91804i	1.49962	−	0.285782i
$587$		−	39.1200i		−	1.61465i	−0.590104	−	0.807327i	$-0.700913\pi$
$587$		−	39.1200i		−	1.61465i	0.590104	−	0.807327i	$-0.299087\pi$
$588$		0			0
$589$		−	17.9465i		−	0.739474i
$590$	−1.98946	−	10.4395i	−0.0819048	−	0.429789i
$591$		0			0
$592$	−35.3380	+	8.26105i	−1.45238	+	0.339527i
$593$	−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
$598$	6.25270	−	17.9447i	0.255692	−	0.733813i
$599$	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	$0.315931\pi$
$602$	−30.0556	−	26.5145i	−1.22498	−	1.08065i
$603$		0			0
$604$	4.96963	+	3.94186i	0.202212	+	0.160392i
$605$	−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	−0.854000	−	0.520272i	$-0.825830\pi$
$613$	−20.5605	+	11.8706i	−0.830432	+	0.479450i	0.0235688	+	0.999722i	$0.492497\pi$
$614$	27.2085	−	5.18511i	1.09804	−	0.209254i
$615$		0			0
$616$	6.89936	+	38.4963i	0.277983	+	1.55106i
$617$	−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	0.0618958	−	0.998083i	$-0.480285\pi$
$619$	23.8151	−	13.7496i	0.957209	−	0.552645i	0.895313	+	0.445438i	$0.146952\pi$
$620$	5.10681	+	12.9122i	0.205094	+	0.518566i
$621$		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
$626$	37.3537	+	13.0156i	1.49295	+	0.520209i
$627$		0			0
$628$	19.6715	−	24.8006i	0.784980	−	0.989651i
$629$		−	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	$0.494751\pi$
$632$	−3.51172	+	0.145245i	−0.139689	+	0.00577754i
$633$		0			0
$634$	−16.1891	+	46.4613i	−0.642952	+	1.84522i
$635$	−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
$640$	8.73831	+	8.57923i	0.345412	+	0.339124i
$641$	−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	$-0.996987\pi$
$643$		−	0.480049i		−	0.0189313i	0.999955	−	0.00946565i	$-0.00301305\pi$
$644$	13.9652	−	7.85979i	0.550307	−	0.309719i
$645$		0			0
$646$	28.4187	−	5.41574i	1.11812	−	0.213079i
$647$	−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	0.882351	−	0.470592i	$-0.155960\pi$
$653$	23.4069	+	13.5140i	0.915982	+	0.528843i	0.0336311	+	0.999434i	$0.489293\pi$
$654$		0			0
$655$	1.17157	+	2.02922i	0.0457771	+	0.0792883i
$656$	−17.6734	+	16.5720i	−0.690031	+	0.647028i
$657$		0			0
$658$	−10.8326	−	32.2222i	−0.422299	−	1.25615i
$659$			24.7862i			0.965535i	0.875749	+	0.482767i	$0.160368\pi$
$659$			24.7862i			0.965535i	−0.875749	+	0.482767i	$0.839632\pi$
$660$		0			0
$661$	−25.2345	+	14.5691i	−0.981508	+	0.566674i	−0.902725	−	0.430218i	$-0.858437\pi$
$661$	−25.2345	+	14.5691i	−0.981508	+	0.566674i	−0.0787826	+	0.996892i	$0.525103\pi$
$662$	2.38056	−	6.83199i	0.0925230	−	0.265533i
$663$		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
$668$	−10.2984	+	4.07306i	−0.398458	+	0.157591i
$669$		0			0
$670$	−1.74108	−	9.13619i	−0.0672638	−	0.352962i
$671$	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	$0.758260\pi$
$674$	0.355587	+	1.86592i	0.0136967	+	0.0718724i
$675$		0			0
$676$	12.4353	−	4.91821i	0.478282	−	0.189162i
$677$	10.9269	+	6.30864i	0.419955	+	0.242461i	0.695058	−	0.718954i	$-0.255379\pi$
$677$	10.9269	+	6.30864i	0.419955	+	0.242461i	−0.275103	+	0.961415i	$0.588712\pi$
$678$		0			0
$679$	7.82843	+	10.0951i	0.300427	+	0.387416i
$680$	−18.9056	+	11.9832i	−0.724996	+	0.459536i
$681$		0			0
$682$	−15.5990	+	44.7678i	−0.597318	+	1.71425i
$683$	−2.58469	+	1.49227i	−0.0989005	+	0.0571002i	−0.548634	−	0.836062i	$-0.684852\pi$
$683$	−2.58469	+	1.49227i	−0.0989005	+	0.0571002i	0.449734	+	0.893163i	$0.351519\pi$
$684$		0			0
$685$		−	13.1119i		−	0.500981i
$686$	14.7092	+	21.6712i	0.561600	+	0.827409i
$687$		0			0
$688$	−29.3076	−	31.2555i	−1.11734	−	1.19160i
$689$	4.39050	+	7.60457i	0.167265	+	0.289711i
$690$		0			0
$691$	7.61365	+	4.39574i	0.289637	+	0.167222i	0.637778	−	0.770220i	$-0.279854\pi$
$691$	7.61365	+	4.39574i	0.289637	+	0.167222i	−0.348141	+	0.937442i	$0.613187\pi$
$692$	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
$698$	1.88625	−	0.359462i	0.0713957	−	0.0136059i
$699$		0			0
$700$	0.222290	−	20.2569i	0.00840178	−	0.765639i
$701$			3.24718i			0.122644i	0.998118	+	0.0613221i	$0.0195317\pi$
$701$			3.24718i			0.122644i	−0.998118	+	0.0613221i	$0.980468\pi$
$702$		0			0
$703$	12.6924	+	21.9839i	0.478702	+	0.829137i
$704$	3.45263	+	41.6672i	0.130126	+	1.57039i
$705$		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	0.716498	−	0.697589i	$-0.245744\pi$
$709$	12.5311	+	7.23486i	0.470617	+	0.271711i	−0.245881	+	0.969300i	$0.579077\pi$
$710$	−2.78900	+	8.00417i	−0.104669	+	0.300391i
$711$		0			0
$712$	17.1169	−	0.707959i	0.641484	−	0.0265319i
$713$	19.4252			0.727479
$714$		0			0
$715$			25.0990i			0.938651i
$716$	−7.51442	+	9.47368i	−0.280827	+	0.354048i
$717$		0			0
$718$	−19.5281	−	6.80443i	−0.728782	−	0.253939i
$719$	−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
$724$	−10.7897	−	27.2809i	−0.400995	−	1.01389i
$725$	−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	$0.552773\pi$
$728$	31.2323	+	11.2685i	1.15754	+	0.417637i
$729$		0			0
$730$	4.51102	−	0.859664i	0.166960	−	0.0318176i
$731$	67.8244	−	39.1584i	2.50858	−	1.44833i
$732$		0			0
$733$	16.3736	+	9.45332i	0.604774	+	0.349166i	0.770917	−	0.636935i	$-0.219798\pi$
$733$	16.3736	+	9.45332i	0.604774	+	0.349166i	−0.166144	+	0.986102i	$0.553132\pi$
$734$	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	0.0358930	−	0.999356i	$-0.488572\pi$
$739$	24.9909	−	14.4285i	0.919307	−	0.530762i	0.883414	+	0.468594i	$0.155239\pi$
$740$	−15.3876	−	12.2053i	−0.565659	−	0.448674i
$741$		0			0
$742$	−1.46596	+	7.25846i	−0.0538171	+	0.266467i
$743$	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
$746$	2.51141	−	7.20753i	0.0919494	−	0.263886i
$747$		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	$0.118441\pi$
$752$	−8.27261	−	35.3874i	−0.301671	−	1.29045i
$753$		0			0
$754$	−3.59612	−	18.8704i	−0.130963	−	0.687218i
$755$			3.43289i			0.124936i
$756$		0			0
$757$		−	1.35778i		−	0.0493495i	−0.999696	−	0.0246748i	$-0.992145\pi$
$757$		−	1.35778i		−	0.0493495i	0.999696	−	0.0246748i	$-0.00785502\pi$
$758$	42.7562	−	8.14803i	1.55297	−	0.295950i
$759$		0			0
$760$	3.97268	−	7.58884i	0.144104	−	0.275276i
$761$	−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
$766$	−8.78271	−	3.06027i	−0.317332	−	0.110572i
$767$	−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	$0.371238\pi$
$770$	−14.0024	+	15.8724i	−0.504610	+	0.572002i
$771$		0			0
$772$	−19.2947	−	15.3044i	−0.694432	−	0.550816i
$773$	−32.3258	+	18.6633i	−1.16268	+	0.671272i	−0.951944	−	0.306271i	$-0.900919\pi$
$773$	−32.3258	+	18.6633i	−1.16268	+	0.671272i	−0.210733	+	0.977544i	$0.567585\pi$
$774$		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
$782$	5.86195	+	30.7601i	0.209623	+	1.09998i
$783$		0			0
$784$	13.4645	+	24.5501i	0.480875	+	0.876789i
$785$	17.1316			0.611452
$786$		0			0
$787$	2.83882	−	1.63899i	0.101193	−	0.0584237i	−0.448550	−	0.893758i	$-0.648059\pi$
$787$	2.83882	−	1.63899i	0.101193	−	0.0584237i	0.549742	+	0.835334i	$0.314726\pi$
$788$	−7.55190	−	19.0944i	−0.269025	−	0.680211i
$789$		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
$794$	−2.69647	+	7.73863i	−0.0956941	+	0.274634i
$795$		0			0
$796$	7.56581	+	6.00111i	0.268163	+	0.212704i
$797$		−	11.0096i		−	0.389981i	−0.980805	−	0.194991i	$-0.937532\pi$
$797$		−	11.0096i		−	0.389981i	0.980805	−	0.194991i	$-0.0624676\pi$
$798$		0			0
$799$	66.4264			2.35000
$800$	2.28355	−	21.5361i	0.0807356	−	0.761417i
$801$		0			0
$802$	45.4697	+	15.8436i	1.60559	+	0.559457i
$803$	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
$808$	26.1923	+	13.7114i	0.921442	+	0.482365i
$809$	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	$0.187580\pi$
$811$			31.6550i			1.11156i	−0.831330	+	0.555779i	$0.812420\pi$
$812$	8.25334	−	13.9397i	0.289635	−	0.489187i
$813$		0			0
$814$	−12.5530	−	65.8711i	−0.439984	−	2.30878i
$815$	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	0.0884301	−	0.996082i	$-0.471815\pi$
$821$	−20.9164	−	12.0761i	−0.729988	−	0.421459i	−0.818418	+	0.574624i	$0.805148\pi$
$822$		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	$0.981784\pi$
$824$	−21.4375	+	0.886659i	−0.746811	+	0.0308882i
$825$		0			0
$826$	5.14266	−	25.4631i	0.178936	−	0.885973i
$827$		−	39.1969i		−	1.36301i	−0.731814	−	0.681505i	$-0.761326\pi$
$827$		−	39.1969i		−	1.36301i	0.731814	−	0.681505i	$-0.238674\pi$
$828$		0			0
$829$	−1.49074	+	0.860677i	−0.0517754	+	0.0298926i	−0.525664	−	0.850692i	$-0.676183\pi$
$829$	−1.49074	+	0.860677i	−0.0517754	+	0.0298926i	0.473889	+	0.880585i	$0.342850\pi$
$830$	17.5902	+	6.12917i	0.610564	+	0.212747i
$831$		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
$836$	27.1956	−	10.7560i	0.940581	−	0.372003i
$837$		0			0
$838$	−19.2898	+	3.67604i	−0.666354	+	0.126987i
$839$	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
$842$	9.38386	−	1.78828i	0.323389	−	0.0616282i
$843$		0			0
$844$	−4.82234	−	12.1929i	−0.165992	−	0.419698i
$845$	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
$850$	37.3809	+	13.0251i	1.28216	+	0.446758i
$851$	−23.7952	+	13.7381i	−0.815688	+	0.470937i
$852$		0			0
$853$			37.0520i			1.26864i	0.773072	+	0.634318i	$0.218719\pi$
$853$			37.0520i			1.26864i	−0.773072	+	0.634318i	$0.781281\pi$
$854$	28.0669	−	9.43565i	0.960430	−	0.322881i
$855$		0			0
$856$	−0.916300	−	22.1542i	−0.0313185	−	0.757214i
$857$	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	0.247590	−	0.968865i	$-0.420362\pi$
$859$	−13.7070	−	7.91375i	−0.467677	−	0.270014i	−0.715267	+	0.698851i	$0.753695\pi$
$860$	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
$866$	−1.79998	−	9.44524i	−0.0611657	−	0.320962i
$867$		0			0
$868$	−0.372429	+	33.9388i	−0.0126411	+	1.15196i
$869$		−	6.49435i		−	0.220306i
$870$		0			0
$871$	−13.4792	−	23.3466i	−0.456725	−	0.791070i
$872$	−8.71237	−	4.56083i	−0.295038	−	0.154449i
$873$		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	0.930280	−	0.366849i	$-0.119564\pi$
$877$	31.9158	+	18.4266i	1.07772	+	0.622222i	0.147439	+	0.989071i	$0.452897\pi$
$878$	−24.6864	−	8.60181i	−0.833127	−	0.290297i
$879$		0			0
$880$	−16.5061	+	15.4774i	−0.556419	+	0.521743i
$881$	−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	$0.225662\pi$
$883$			38.6910i			1.30206i	−0.759054	+	0.651028i	$0.774338\pi$
$884$	−40.3186	+	50.8311i	−1.35606	+	1.70963i
$885$		0			0
$886$	14.2102	−	40.7821i	0.477402	−	1.37010i
$887$	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
$892$	−22.5822	+	8.93134i	−0.756109	+	0.299043i
$893$	−22.0146	+	12.7101i	−0.736691	+	0.425329i
$894$		0			0
$895$	−6.54416			−0.218747
$896$	11.8489	+	27.4882i	0.395844	+	0.918318i
$897$		0			0
$898$	1.93562	+	10.1570i	0.0645925	+	0.338944i
$899$	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	−0.866968	−	0.498364i	$-0.833934\pi$
$907$	−26.1668	+	15.1074i	−0.868855	+	0.501634i	−0.00188752	+	0.999998i	$0.500601\pi$
$908$	−29.7872	+	37.5538i	−0.988525	+	1.24627i
$909$		0			0
$910$	5.72606	+	17.0325i	0.189817	+	0.564623i
$911$	−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
$914$	11.2925	+	3.93478i	0.373522	+	0.130151i
$915$		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	$0.234148\pi$
$920$	8.21410	+	4.29999i	0.270811	+	0.141767i
$921$		0			0
$922$	−28.5255	+	5.43610i	−0.939438	+	0.179028i
$923$			24.5687i			0.808687i
$924$		0			0
$925$			34.7341i			1.14205i
$926$	−6.41025	−	33.6373i	−0.210654	−	1.10539i
$927$		0			0
$928$	10.1923	−	14.0014i	0.334579	−	0.459619i
$929$	−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
$934$	3.47509	−	9.97319i	0.113708	−	0.326333i
$935$	−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	$0.686350\pi$
$938$	4.50061	−	22.2840i	0.146950	−	0.727600i
$939$		0			0
$940$	12.2223	−	15.4091i	0.398649	−	0.502590i
$941$	−1.71393	+	0.989538i	−0.0558725	+	0.0322580i	−0.527676	−	0.849446i	$-0.676936\pi$
$941$	−1.71393	+	0.989538i	−0.0558725	+	0.0322580i	0.471804	+	0.881704i	$0.343603\pi$
$942$		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	0.646451	−	0.762956i	$-0.276253\pi$
$947$	9.50703	+	5.48888i	0.308937	+	0.178365i	−0.337514	+	0.941321i	$0.609586\pi$
$948$		0			0
$949$	11.5275	−	6.65539i	0.374197	−	0.216043i
$950$	−14.8808	+	2.83583i	−0.482797	+	0.0920065i
$951$		0			0
$952$	−53.8551	+	9.65198i	−1.74545	+	0.312822i
$953$	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
$956$	−38.4604	+	15.2112i	−1.24390	+	0.491966i
$957$		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
$962$	−53.7589	−	18.7319i	−1.73326	−	0.603941i
$963$		0			0
$964$	−13.8335	−	10.9726i	−0.445548	−	0.353404i
$965$		−	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	$0.553553\pi$
$968$	−46.1027	+	1.90682i	−1.48180	+	0.0612874i
$969$		0			0
$970$	−2.43195	+	6.97947i	−0.0780851	+	0.224097i
$971$	31.2942	+	18.0677i	1.00428	+	0.579820i	0.909511	−	0.415679i	$-0.136456\pi$
$971$	31.2942	+	18.0677i	1.00428	+	0.579820i	0.0947671	+	0.995499i	$0.469789\pi$
$972$		0			0
$973$	−3.84249	+	2.97972i	−0.123185	+	0.0955254i
$974$	−38.2547	+	33.0083i	−1.22576	+	1.05765i
$975$		0			0
$976$	30.8239	−	7.20579i	0.986650	−	0.230652i
$977$	−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
$980$	−5.88108	+	13.9657i	−0.187864	+	0.446118i
$981$		0			0
$982$	−4.25303	+	0.810499i	−0.135720	+	0.0258641i
$983$	−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	$0.764408\pi$
$992$	−3.82589	+	36.0820i	−0.121472	+	1.14560i
$993$		0			0
$994$	−13.7065	+	15.5370i	−0.434743	+	0.492804i
$995$			5.22625i			0.165683i
$996$		0			0
$997$	47.8023	−	27.5987i	1.51392	−	0.874060i	0.514048	−	0.857761i	$-0.328145\pi$
$997$	47.8023	−	27.5987i	1.51392	−	0.874060i	0.999867	−	0.0162984i	$-0.00518816\pi$
$998$	6.06309	−	17.4005i	0.191924	−	0.550804i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.264742 + 1.38921i) q^{2} +(-1.85982 + 0.735566i) q^{4} +(-0.937379 - 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 - 2.38896i) q^{8} +O(q^{10})\)	\(q+(0.264742 + 1.38921i) q^{2} +(-1.85982 + 0.735566i) q^{4} +(-0.937379 - 0.541196i) q^{5} +(-1.62132 - 2.09077i) q^{7} +(-1.51423 - 2.38896i) q^{8} +(0.503673 - 1.44550i) q^{10} +(4.52607 - 2.61313i) q^{11} -4.43692i q^{13} +(2.47529 - 2.80587i) q^{14} +(2.91789 - 2.73604i) q^{16} +(3.65568 + 6.33182i) q^{17} +(-2.42308 - 1.39897i) q^{19} +(2.14144 + 0.317025i) q^{20} +(4.82843 + 5.59587i) q^{22} +(1.51423 - 2.62272i) q^{23} +(-1.91421 - 3.31552i) q^{25} +(6.16383 - 1.17464i) q^{26} +(4.55327 + 2.69588i) q^{28} -3.06147i q^{29} +(3.20711 + 5.55487i) q^{31} +(4.57343 + 3.32922i) q^{32} +(-7.82843 + 6.75481i) q^{34} +(0.388275 + 2.83730i) q^{35} +(-7.85718 - 4.53635i) q^{37} +(1.30197 - 3.73654i) q^{38} +(0.126515 + 3.05885i) q^{40} -6.05692 q^{41} -10.7117i q^{43} +(-6.49556 + 8.18917i) q^{44} +(4.04440 + 1.40924i) q^{46} +(4.54269 - 7.86817i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(4.09918 - 3.53701i) q^{50} +(3.26365 + 8.25189i) q^{52} +(-1.71393 + 0.989538i) q^{53} -5.65685 q^{55} +(-2.53970 + 7.03917i) q^{56} +(4.25303 - 0.810499i) q^{58} +(6.01255 - 3.47135i) q^{59} +(6.85351 + 3.95687i) q^{61} +(-6.86784 + 5.92596i) q^{62} +(-3.41421 + 7.23486i) q^{64} +(-2.40125 + 4.15908i) q^{65} +(5.26190 - 3.03796i) q^{67} +(-11.4564 - 9.08707i) q^{68} +(-3.83882 + 1.29055i) q^{70} -5.53732 q^{71} +(1.50000 + 2.59808i) q^{73} +(4.22182 - 12.1163i) q^{74} +(5.53553 + 0.819496i) q^{76} +(-12.8017 - 5.22625i) q^{77} +(0.621320 - 1.07616i) q^{79} +(-4.21590 + 0.985562i) q^{80} +(-1.60352 - 8.41435i) q^{82} +12.1689i q^{83} -7.91375i q^{85} +(14.8808 - 2.83583i) q^{86} +(-13.0961 - 6.85570i) q^{88} +(-3.02846 + 5.24545i) q^{89} +(-9.27659 + 7.19367i) q^{91} +(-0.887016 + 5.99162i) q^{92} +(12.1332 + 4.22773i) q^{94} +(1.51423 + 2.62272i) q^{95} -4.82843 q^{97} +(-9.87968 - 0.626050i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 8 q^{7}+O(q^{10}) \) 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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