LMFDB - Embedded newform 1728.2.z.a.719.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(143,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("1728.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.z (of order $12$, degree $4$, not 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:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			719.8
Character	$\chi$	$=$	1728.719
Dual form			1728.2.z.a.1007.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.310357 - 1.15827i) q^{5} +(-0.356047 - 0.616691i) q^{7} +O(q^{10})$	$q+(-0.310357 - 1.15827i) q^{5} +(-0.356047 - 0.616691i) q^{7} +(-0.611314 + 2.28146i) q^{11} +(-1.31401 - 4.90394i) q^{13} -0.863180i q^{17} +(0.539682 + 0.539682i) q^{19} +(-0.689728 - 0.398215i) q^{23} +(3.08486 - 1.78104i) q^{25} +(-2.22809 + 8.31534i) q^{29} +(-4.18508 - 2.41626i) q^{31} +(-0.603793 + 0.603793i) q^{35} +(-6.95600 - 6.95600i) q^{37} +(-3.17027 + 5.49108i) q^{41} +(-12.0362 - 3.22509i) q^{43} +(-1.31575 - 2.27895i) q^{47} +(3.24646 - 5.62304i) q^{49} +(8.87081 - 8.87081i) q^{53} +2.83227 q^{55} +(-12.7025 + 3.40363i) q^{59} +(0.548319 + 0.146922i) q^{61} +(-5.27228 + 3.04395i) q^{65} +(6.89625 - 1.84784i) q^{67} -3.03550i q^{71} +11.6817i q^{73} +(1.62461 - 0.435313i) q^{77} +(-0.841919 + 0.486082i) q^{79} +(-11.1696 - 2.99289i) q^{83} +(-0.999796 + 0.267894i) q^{85} -4.35531 q^{89} +(-2.55637 + 2.55637i) q^{91} +(0.457603 - 0.792591i) q^{95} +(-2.89654 - 5.01695i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 6 * q^5 + 4 * q^7	$ 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85} - 20 q^{91} - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.310357	−	1.15827i	−0.138796	−	0.517994i	−0.999953	−	0.00965542i	$-0.996927\pi$
$5$	−0.310357	−	1.15827i	−0.138796	−	0.517994i	0.861157	−	0.508339i	$-0.169740\pi$
$6$		0			0
$7$	−0.356047	−	0.616691i	−0.134573	−	0.233087i	0.790861	−	0.611996i	$-0.209633\pi$
$7$	−0.356047	−	0.616691i	−0.134573	−	0.233087i	−0.925434	+	0.378908i	$0.876300\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.611314	+	2.28146i	−0.184318	+	0.687885i	0.810457	+	0.585798i	$0.199219\pi$
$11$	−0.611314	+	2.28146i	−0.184318	+	0.687885i	−0.994775	+	0.102087i	$0.967448\pi$
$12$		0			0
$13$	−1.31401	−	4.90394i	−0.364440	−	1.36011i	−0.868178	−	0.496253i	$-0.834709\pi$
$13$	−1.31401	−	4.90394i	−0.364440	−	1.36011i	0.503738	−	0.863857i	$-0.331958\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	0.863180i		−	0.209352i	−0.994506	−	0.104676i	$-0.966619\pi$
$17$		−	0.863180i		−	0.209352i	0.994506	−	0.104676i	$-0.0333806\pi$
$18$		0			0
$19$	0.539682	+	0.539682i	0.123811	+	0.123811i	0.766297	−	0.642486i	$-0.222097\pi$
$19$	0.539682	+	0.539682i	0.123811	+	0.123811i	−0.642486	+	0.766297i	$0.722097\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.689728	−	0.398215i	−0.143818	−	0.0830335i	0.426364	−	0.904552i	$-0.359794\pi$
$23$	−0.689728	−	0.398215i	−0.143818	−	0.0830335i	−0.570182	+	0.821518i	$0.693128\pi$
$24$		0			0
$25$	3.08486	−	1.78104i	0.616972	−	0.356209i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.22809	+	8.31534i	−0.413746	+	1.54412i	0.373589	+	0.927594i	$0.378127\pi$
$29$	−2.22809	+	8.31534i	−0.413746	+	1.54412i	−0.787335	+	0.616526i	$0.788540\pi$
$30$		0			0
$31$	−4.18508	−	2.41626i	−0.751663	−	0.433973i	0.0746314	−	0.997211i	$-0.476222\pi$
$31$	−4.18508	−	2.41626i	−0.751663	−	0.433973i	−0.826295	+	0.563238i	$0.809555\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.603793	+	0.603793i	−0.102060	+	0.102060i
$36$		0			0
$37$	−6.95600	−	6.95600i	−1.14356	−	1.14356i	−0.987794	−	0.155765i	$-0.950216\pi$
$37$	−6.95600	−	6.95600i	−1.14356	−	1.14356i	−0.155765	−	0.987794i	$-0.549784\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.17027	+	5.49108i	−0.495114	+	0.857562i	−0.999984	−	0.00563304i	$-0.998207\pi$
$41$	−3.17027	+	5.49108i	−0.495114	+	0.857562i	0.504870	+	0.863195i	$0.331540\pi$
$42$		0			0
$43$	−12.0362	−	3.22509i	−1.83550	−	0.491822i	−0.837035	−	0.547150i	$-0.815713\pi$
$43$	−12.0362	−	3.22509i	−1.83550	−	0.491822i	−0.998468	+	0.0553283i	$0.982379\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.31575	−	2.27895i	−0.191923	−	0.332420i	0.753965	−	0.656915i	$-0.228139\pi$
$47$	−1.31575	−	2.27895i	−0.191923	−	0.332420i	−0.945887	+	0.324495i	$0.894806\pi$
$48$		0			0
$49$	3.24646	−	5.62304i	0.463780	−	0.803291i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.87081	−	8.87081i	1.21850	−	1.21850i	0.250342	−	0.968157i	$-0.419457\pi$
$53$	8.87081	−	8.87081i	1.21850	−	1.21850i	0.968157	−	0.250342i	$-0.0805431\pi$
$54$		0			0
$55$	2.83227			0.381903
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−12.7025	+	3.40363i	−1.65373	+	0.443115i	−0.960654	−	0.277749i	$-0.910412\pi$
$59$	−12.7025	+	3.40363i	−1.65373	+	0.443115i	−0.693076	+	0.720865i	$0.743745\pi$
$60$		0			0
$61$	0.548319	+	0.146922i	0.0702051	+	0.0188114i	0.293751	−	0.955882i	$-0.405096\pi$
$61$	0.548319	+	0.146922i	0.0702051	+	0.0188114i	−0.223546	+	0.974693i	$0.571763\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.27228	+	3.04395i	−0.653946	+	0.377556i
$66$		0			0
$67$	6.89625	−	1.84784i	0.842511	−	0.225750i	0.188347	−	0.982103i	$-0.439687\pi$
$67$	6.89625	−	1.84784i	0.842511	−	0.225750i	0.654164	+	0.756352i	$0.273020\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.03550i		−	0.360248i	−0.983644	−	0.180124i	$-0.942350\pi$
$71$		−	3.03550i		−	0.360248i	0.983644	−	0.180124i	$-0.0576499\pi$
$72$		0			0
$73$			11.6817i			1.36724i	0.729839	+	0.683619i	$0.239595\pi$
$73$			11.6817i			1.36724i	−0.729839	+	0.683619i	$0.760405\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.62461	−	0.435313i	0.185142	−	0.0496085i
$78$		0			0
$79$	−0.841919	+	0.486082i	−0.0947233	+	0.0546885i	−0.546613	−	0.837385i	$-0.684083\pi$
$79$	−0.841919	+	0.486082i	−0.0947233	+	0.0546885i	0.451890	+	0.892074i	$0.350750\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.1696	−	2.99289i	−1.22602	−	0.328512i	−0.412994	−	0.910734i	$-0.635517\pi$
$83$	−11.1696	−	2.99289i	−1.22602	−	0.328512i	−0.813030	+	0.582221i	$0.802184\pi$
$84$		0			0
$85$	−0.999796	+	0.267894i	−0.108443	+	0.0290572i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.35531			−0.461662			−0.230831	−	0.972994i	$-0.574144\pi$
$89$	−4.35531			−0.461662			−0.230831	+	0.972994i	$0.574144\pi$
$90$		0			0
$91$	−2.55637	+	2.55637i	−0.267981	+	0.267981i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.457603	−	0.792591i	0.0469490	−	0.0813181i
$96$		0			0
$97$	−2.89654	−	5.01695i	−0.294099	−	0.509395i	0.680676	−	0.732585i	$-0.261686\pi$
$97$	−2.89654	−	5.01695i	−0.294099	−	0.509395i	−0.974775	+	0.223190i	$0.928353\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.01216	−	2.41480i	−0.896744	−	0.240282i	−0.219127	−	0.975696i	$-0.570321\pi$
$101$	−9.01216	−	2.41480i	−0.896744	−	0.240282i	−0.677617	+	0.735415i	$0.736987\pi$
$102$		0			0
$103$	2.02100	−	3.50047i	0.199135	−	0.344911i	−0.749113	−	0.662442i	$-0.769520\pi$
$103$	2.02100	−	3.50047i	0.199135	−	0.344911i	0.948248	+	0.317530i	$0.102854\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.91703	−	7.91703i	−0.765368	−	0.765368i	0.211919	−	0.977287i	$-0.432029\pi$
$107$	−7.91703	−	7.91703i	−0.765368	−	0.765368i	−0.977287	+	0.211919i	$0.932029\pi$
$108$		0			0
$109$	−8.25467	+	8.25467i	−0.790654	+	0.790654i	−0.981600	−	0.190946i	$-0.938844\pi$
$109$	−8.25467	+	8.25467i	−0.790654	+	0.790654i	0.190946	+	0.981600i	$0.438844\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.70455	+	3.87087i	0.630711	+	0.364141i	0.781027	−	0.624497i	$-0.214696\pi$
$113$	6.70455	+	3.87087i	0.630711	+	0.364141i	−0.150316	+	0.988638i	$0.548029\pi$
$114$		0			0
$115$	−0.247178	+	0.922480i	−0.0230494	+	0.0860217i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.532316	+	0.307333i	−0.0487973	+	0.0281731i
$120$		0			0
$121$	4.69494	+	2.71063i	0.426813	+	0.246421i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.25990	−	7.25990i	−0.649345	−	0.649345i
$126$		0			0
$127$		−	7.21656i		−	0.640366i	−0.947356	−	0.320183i	$-0.896256\pi$
$127$		−	7.21656i		−	0.640366i	0.947356	−	0.320183i	$-0.103744\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.56297	+	5.83309i	0.136558	+	0.509640i	0.999987	+	0.00516943i	$0.00164549\pi$
$131$	1.56297	+	5.83309i	0.136558	+	0.509640i	−0.863429	+	0.504470i	$0.831688\pi$
$132$		0			0
$133$	0.140665	−	0.524969i	0.0121972	−	0.0455206i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.72483	−	4.71954i	−0.232798	−	0.403217i	0.725833	−	0.687871i	$-0.241455\pi$
$137$	−2.72483	−	4.71954i	−0.232798	−	0.403217i	−0.958630	+	0.284654i	$0.908121\pi$
$138$		0			0
$139$	3.85291	+	14.3793i	0.326800	+	1.21963i	0.912490	+	0.409098i	$0.134157\pi$
$139$	3.85291	+	14.3793i	0.326800	+	1.21963i	−0.585691	+	0.810534i	$0.699177\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.9914			1.00277
$144$		0			0
$145$	10.3229			0.857271
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.98723	−	11.1485i	−0.244724	−	0.913321i	−0.973522	−	0.228593i	$-0.926588\pi$
$149$	−2.98723	−	11.1485i	−0.244724	−	0.913321i	0.728798	−	0.684728i	$-0.240079\pi$
$150$		0			0
$151$	−4.79677	−	8.30825i	−0.390355	−	0.676116i	0.602141	−	0.798390i	$-0.294315\pi$
$151$	−4.79677	−	8.30825i	−0.390355	−	0.676116i	−0.992496	+	0.122274i	$0.960981\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.49981	+	5.59736i	−0.120467	+	0.449591i
$156$		0			0
$157$	−2.82669	−	10.5494i	−0.225595	−	0.841931i	−0.982165	−	0.188019i	$-0.939793\pi$
$157$	−2.82669	−	10.5494i	−0.225595	−	0.841931i	0.756571	−	0.653912i	$-0.226873\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			0.567132i			0.0446963i
$162$		0			0
$163$	−10.4644	−	10.4644i	−0.819633	−	0.819633i	0.166422	−	0.986055i	$-0.446779\pi$
$163$	−10.4644	−	10.4644i	−0.819633	−	0.819633i	−0.986055	+	0.166422i	$0.946779\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.5061	+	6.64303i	0.890367	+	0.514053i	0.874062	−	0.485814i	$-0.161477\pi$
$167$	11.5061	+	6.64303i	0.890367	+	0.514053i	0.0163043	+	0.999867i	$0.494810\pi$
$168$		0			0
$169$	−11.0637	+	6.38764i	−0.851056	+	0.491357i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.95118	−	7.28191i	0.148346	−	0.553633i	−0.851238	−	0.524780i	$-0.824148\pi$
$173$	1.95118	−	7.28191i	0.148346	−	0.553633i	0.999584	−	0.0288536i	$-0.00918567\pi$
$174$		0			0
$175$	−2.19671	−	1.26827i	−0.166056	−	0.0958723i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	15.1045	−	15.1045i	1.12896	−	1.12896i	0.138617	−	0.990346i	$-0.455734\pi$
$179$	15.1045	−	15.1045i	1.12896	−	1.12896i	0.990346	−	0.138617i	$-0.0442657\pi$
$180$		0			0
$181$	−3.08895	−	3.08895i	−0.229600	−	0.229600i	0.582926	−	0.812525i	$-0.301908\pi$
$181$	−3.08895	−	3.08895i	−0.229600	−	0.229600i	−0.812525	+	0.582926i	$0.801908\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.89808	+	10.2158i	−0.433635	+	0.751078i
$186$		0			0
$187$	1.96931	+	0.527675i	0.144010	+	0.0385874i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.50481	+	4.33846i	0.181242	+	0.313920i	0.942304	−	0.334759i	$-0.108655\pi$
$191$	2.50481	+	4.33846i	0.181242	+	0.313920i	−0.761062	+	0.648679i	$0.775322\pi$
$192$		0			0
$193$	−2.87512	+	4.97985i	−0.206956	+	0.358457i	−0.950754	−	0.309946i	$-0.899689\pi$
$193$	−2.87512	+	4.97985i	−0.206956	+	0.358457i	0.743799	+	0.668404i	$0.233022\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.515447	−	0.515447i	0.0367240	−	0.0367240i	−0.688506	−	0.725230i	$-0.741733\pi$
$197$	0.515447	−	0.515447i	0.0367240	−	0.0367240i	0.725230	+	0.688506i	$0.241733\pi$
$198$		0			0
$199$	21.6583			1.53532			0.767659	−	0.640858i	$-0.221421\pi$
$199$	21.6583			1.53532			0.767659	+	0.640858i	$0.221421\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.92130	−	1.58661i	0.415594	−	0.111358i
$204$		0			0
$205$	7.34407	+	1.96784i	0.512932	+	0.137440i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.56118	+	0.901345i	−0.107989	+	0.0623473i
$210$		0			0
$211$	−2.24771	+	0.602272i	−0.154739	+	0.0414621i	−0.335357	−	0.942091i	$-0.608857\pi$
$211$	−2.24771	+	0.602272i	−0.154739	+	0.0414621i	0.180618	+	0.983553i	$0.442190\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			14.9421i			1.01904i
$216$		0			0
$217$			3.44121i			0.233604i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.23299	+	1.13423i	−0.284742	+	0.0762963i
$222$		0			0
$223$	16.3604	−	9.44569i	1.09557	−	0.632530i	0.160520	−	0.987033i	$-0.448683\pi$
$223$	16.3604	−	9.44569i	1.09557	−	0.632530i	0.935055	+	0.354502i	$0.115350\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.88169	+	2.11189i	0.523126	+	0.140171i	0.510712	−	0.859752i	$-0.329382\pi$
$227$	7.88169	+	2.11189i	0.523126	+	0.140171i	0.0124139	+	0.999923i	$0.496048\pi$
$228$		0			0
$229$	−7.31287	+	1.95948i	−0.483248	+	0.129486i	−0.492215	−	0.870474i	$-0.663813\pi$
$229$	−7.31287	+	1.95948i	−0.483248	+	0.129486i	0.00896646	+	0.999960i	$0.497146\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−6.77947			−0.444138			−0.222069	−	0.975031i	$-0.571281\pi$
$233$	−6.77947			−0.444138			−0.222069	+	0.975031i	$0.571281\pi$
$234$		0			0
$235$	−2.23129	+	2.23129i	−0.145553	+	0.145553i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.48431	−	16.4273i	0.613489	−	1.06259i	−0.377159	−	0.926149i	$-0.623099\pi$
$239$	9.48431	−	16.4273i	0.613489	−	1.06259i	0.990648	−	0.136445i	$-0.0435677\pi$
$240$		0			0
$241$	0.0512556	+	0.0887774i	0.00330167	+	0.00571865i	0.867672	−	0.497138i	$-0.165616\pi$
$241$	0.0512556	+	0.0887774i	0.00330167	+	0.00571865i	−0.864370	+	0.502857i	$0.832282\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.52056	−	2.01513i	−0.480471	−	0.128742i
$246$		0			0
$247$	1.93742	−	3.35571i	0.123275	−	0.213519i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.59142	−	6.59142i	−0.416047	−	0.416047i	0.467792	−	0.883839i	$-0.345050\pi$
$251$	−6.59142	−	6.59142i	−0.416047	−	0.416047i	−0.883839	+	0.467792i	$0.845050\pi$
$252$		0			0
$253$	1.33015	−	1.33015i	0.0836258	−	0.0836258i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	14.3072	+	8.26024i	0.892456	+	0.515260i	0.874745	−	0.484583i	$-0.161029\pi$
$257$	14.3072	+	8.26024i	0.892456	+	0.515260i	0.0177109	+	0.999843i	$0.494362\pi$
$258$		0			0
$259$	−1.81304	+	6.76637i	−0.112657	+	0.420442i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−22.2913	+	12.8699i	−1.37454	+	0.793593i	−0.991496	−	0.130136i	$-0.958458\pi$
$263$	−22.2913	+	12.8699i	−1.37454	+	0.793593i	−0.383047	+	0.923729i	$0.625125\pi$
$264$		0			0
$265$	−13.0279	−	7.52167i	−0.800298	−	0.462052i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.62506	+	4.62506i	0.281995	+	0.281995i	0.833904	−	0.551909i	$-0.186101\pi$
$269$	4.62506	+	4.62506i	0.281995	+	0.281995i	−0.551909	+	0.833904i	$0.686101\pi$
$270$		0			0
$271$			6.13012i			0.372378i	0.982514	+	0.186189i	$0.0596137\pi$
$271$			6.13012i			0.372378i	−0.982514	+	0.186189i	$0.940386\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.17756	+	8.12675i	0.131312	+	0.490062i
$276$		0			0
$277$	−0.185077	+	0.690716i	−0.0111202	+	0.0415011i	−0.971263	−	0.238009i	$-0.923505\pi$
$277$	−0.185077	+	0.690716i	−0.0111202	+	0.0415011i	0.960143	+	0.279510i	$0.0901720\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.17559	+	8.96438i	0.308750	+	0.534770i	0.978089	−	0.208187i	$-0.0667561\pi$
$281$	5.17559	+	8.96438i	0.308750	+	0.534770i	−0.669339	+	0.742957i	$0.733423\pi$
$282$		0			0
$283$	6.79689	+	25.3663i	0.404033	+	1.50787i	0.805832	+	0.592144i	$0.201718\pi$
$283$	6.79689	+	25.3663i	0.404033	+	1.50787i	−0.401799	+	0.915728i	$0.631615\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.51507			0.266516
$288$		0			0
$289$	16.2549			0.956172
$290$		0			0
$291$		0			0
$292$		0			0
$293$	5.21478	+	19.4618i	0.304651	+	1.13697i	0.933246	+	0.359239i	$0.116964\pi$
$293$	5.21478	+	19.4618i	0.304651	+	1.13697i	−0.628595	+	0.777733i	$0.716370\pi$
$294$		0			0
$295$	7.88465	+	13.6566i	0.459062	+	0.795119i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.04651	+	3.90564i	−0.0605215	+	0.225869i
$300$		0			0
$301$	2.29657	+	8.57090i	0.132372	+	0.494018i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	0.680700i		−	0.0389768i
$306$		0			0
$307$	5.92691	+	5.92691i	0.338267	+	0.338267i	0.855715	−	0.517448i	$-0.173118\pi$
$307$	5.92691	+	5.92691i	0.338267	+	0.338267i	−0.517448	+	0.855715i	$0.673118\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	22.5904	+	13.0426i	1.28098	+	0.739576i	0.977028	−	0.213110i	$-0.0683592\pi$
$311$	22.5904	+	13.0426i	1.28098	+	0.739576i	0.303956	+	0.952686i	$0.401692\pi$
$312$		0			0
$313$	0.538716	−	0.311028i	0.0304500	−	0.0175803i	−0.484698	−	0.874682i	$-0.661070\pi$
$313$	0.538716	−	0.311028i	0.0304500	−	0.0175803i	0.515148	+	0.857101i	$0.327737\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.67189	−	13.7037i	0.206234	−	0.769675i	−0.782836	−	0.622228i	$-0.786228\pi$
$317$	3.67189	−	13.7037i	0.206234	−	0.769675i	0.989070	−	0.147447i	$-0.0471056\pi$
$318$		0			0
$319$	−17.6090	−	10.1666i	−0.985916	−	0.569219i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.465843	−	0.465843i	0.0259202	−	0.0259202i
$324$		0			0
$325$	−12.7877	−	12.7877i	−0.709333	−	0.709333i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.936941	+	1.62283i	−0.0516552	+	0.0894694i
$330$		0			0
$331$	−10.3567	−	2.77508i	−0.569257	−	0.152532i	−0.0373014	−	0.999304i	$-0.511876\pi$
$331$	−10.3567	−	2.77508i	−0.569257	−	0.152532i	−0.531956	+	0.846772i	$0.678543\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−4.28061	−	7.41423i	−0.233874	−	0.405082i
$336$		0			0
$337$	−5.91237	+	10.2405i	−0.322067	+	0.557837i	−0.980914	−	0.194440i	$-0.937711\pi$
$337$	−5.91237	+	10.2405i	−0.322067	+	0.557837i	0.658847	+	0.752277i	$0.271044\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	8.07099	−	8.07099i	0.437069	−	0.437069i
$342$		0			0
$343$	−9.60823			−0.518795
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−0.332138	+	0.0889961i	−0.0178301	+	0.00477756i	−0.267723	−	0.963496i	$-0.586271\pi$
$347$	−0.332138	+	0.0889961i	−0.0178301	+	0.00477756i	0.249893	+	0.968273i	$0.419605\pi$
$348$		0			0
$349$	23.9142	+	6.40780i	1.28010	+	0.343001i	0.833892	−	0.551928i	$-0.186108\pi$
$349$	23.9142	+	6.40780i	1.28010	+	0.343001i	0.446207	+	0.894930i	$0.352774\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.76381	−	3.32774i	0.306776	−	0.177117i	−0.338707	−	0.940892i	$-0.609989\pi$
$353$	5.76381	−	3.32774i	0.306776	−	0.177117i	0.645483	+	0.763775i	$0.276656\pi$
$354$		0			0
$355$	−3.51593	+	0.942090i	−0.186606	+	0.0500010i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	25.7733i		−	1.36026i	−0.733091	−	0.680130i	$-0.761923\pi$
$359$		−	25.7733i		−	1.36026i	0.733091	−	0.680130i	$-0.238077\pi$
$360$		0			0
$361$		−	18.4175i		−	0.969341i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	13.5305	−	3.62550i	0.708221	−	0.189767i
$366$		0			0
$367$	10.6689	−	6.15969i	0.556912	−	0.321533i	−0.194993	−	0.980805i	$-0.562468\pi$
$367$	10.6689	−	6.15969i	0.556912	−	0.321533i	0.751905	+	0.659271i	$0.229135\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.62898	−	2.31213i	−0.447994	−	0.120040i
$372$		0			0
$373$	26.8045	−	7.18223i	1.38788	−	0.371882i	0.513904	−	0.857848i	$-0.328199\pi$
$373$	26.8045	−	7.18223i	1.38788	−	0.371882i	0.873978	+	0.485966i	$0.161532\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	43.7057			2.25096
$378$		0			0
$379$	20.2758	−	20.2758i	1.04150	−	1.04150i	0.0423953	−	0.999101i	$-0.486501\pi$
$379$	20.2758	−	20.2758i	1.04150	−	1.04150i	0.999101	−	0.0423953i	$-0.0134989\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.9618	+	22.4505i	−0.662317	+	1.14717i	0.317689	+	0.948195i	$0.397093\pi$
$383$	−12.9618	+	22.4505i	−0.662317	+	1.14717i	−0.980005	+	0.198971i	$0.936240\pi$
$384$		0			0
$385$	−1.00842	−	1.74663i	−0.0513938	−	0.0890167i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.90667	−	1.85064i	−0.350182	−	0.0938310i	0.0794404	−	0.996840i	$-0.474687\pi$
$389$	−6.90667	−	1.85064i	−0.350182	−	0.0938310i	−0.429622	+	0.903009i	$0.641353\pi$
$390$		0			0
$391$	−0.343731	+	0.595360i	−0.0173832	+	0.0301086i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.824310	+	0.824310i	0.0414756	+	0.0414756i
$396$		0			0
$397$	−14.8178	+	14.8178i	−0.743683	+	0.743683i	−0.973285	−	0.229602i	$-0.926258\pi$
$397$	−14.8178	+	14.8178i	−0.743683	+	0.743683i	0.229602	+	0.973285i	$0.426258\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.39082	+	2.53504i	0.219267	+	0.126594i	0.605611	−	0.795761i	$-0.292929\pi$
$401$	4.39082	+	2.53504i	0.219267	+	0.126594i	−0.386344	+	0.922355i	$0.626262\pi$
$402$		0			0
$403$	−6.34997	+	23.6984i	−0.316314	+	1.18050i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	20.1221	−	11.6175i	0.997416	−	0.575858i
$408$		0			0
$409$	20.8923	+	12.0622i	1.03306	+	0.596436i	0.917859	−	0.396906i	$-0.129916\pi$
$409$	20.8923	+	12.0622i	1.03306	+	0.596436i	0.115199	+	0.993342i	$0.463250\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.62169	+	6.62169i	0.325832	+	0.325832i
$414$		0			0
$415$			13.8663i			0.680670i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.15499	+	19.2387i	0.251838	+	0.939871i	0.969822	+	0.243812i	$0.0783981\pi$
$419$	5.15499	+	19.2387i	0.251838	+	0.939871i	−0.717985	+	0.696059i	$0.754935\pi$
$420$		0			0
$421$	−8.46180	+	31.5799i	−0.412403	+	1.53911i	0.377578	+	0.925978i	$0.376757\pi$
$421$	−8.46180	+	31.5799i	−0.412403	+	1.53911i	−0.789981	+	0.613131i	$0.789910\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.53736	−	2.66279i	−0.0745731	−	0.129164i
$426$		0			0
$427$	−0.104622	−	0.390455i	−0.00506302	−	0.0188954i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.5413			−0.555923			−0.277962	−	0.960592i	$-0.589659\pi$
$431$	−11.5413			−0.555923			−0.277962	+	0.960592i	$0.589659\pi$
$432$		0			0
$433$	24.2215			1.16401			0.582006	−	0.813184i	$-0.302268\pi$
$433$	24.2215			1.16401			0.582006	+	0.813184i	$0.302268\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.157324	−	0.587143i	−0.00752585	−	0.0280868i
$438$		0			0
$439$	4.47756	+	7.75537i	0.213702	+	0.370143i	0.952870	−	0.303378i	$-0.0981144\pi$
$439$	4.47756	+	7.75537i	0.213702	+	0.370143i	−0.739168	+	0.673521i	$0.764781\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.29309	−	19.7541i	0.251482	−	0.938545i	−0.718531	−	0.695495i	$-0.755185\pi$
$443$	5.29309	−	19.7541i	0.251482	−	0.938545i	0.970014	−	0.243051i	$-0.0781481\pi$
$444$		0			0
$445$	1.35170	+	5.04462i	0.0640768	+	0.239138i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			2.34595i			0.110712i	0.998467	+	0.0553561i	$0.0176294\pi$
$449$			2.34595i			0.110712i	−0.998467	+	0.0553561i	$0.982371\pi$
$450$		0			0
$451$	−10.5896	−	10.5896i	−0.498646	−	0.498646i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.75436	+	2.16758i	0.176007	+	0.101618i
$456$		0			0
$457$	24.1000	−	13.9141i	1.12735	−	0.650876i	0.184084	−	0.982911i	$-0.441068\pi$
$457$	24.1000	−	13.9141i	1.12735	−	0.650876i	0.943267	+	0.332034i	$0.107735\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.15168	+	19.2263i	−0.239937	+	0.895459i	0.735923	+	0.677065i	$0.236748\pi$
$461$	−5.15168	+	19.2263i	−0.239937	+	0.895459i	−0.975861	+	0.218394i	$0.929918\pi$
$462$		0			0
$463$	−21.3818	−	12.3448i	−0.993699	−	0.573712i	−0.0873209	−	0.996180i	$-0.527831\pi$
$463$	−21.3818	−	12.3448i	−0.993699	−	0.573712i	−0.906378	+	0.422468i	$0.861164\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.0708	+	14.0708i	−0.651120	+	0.651120i	−0.953263	−	0.302143i	$-0.902298\pi$
$467$	−14.0708	+	14.0708i	−0.651120	+	0.651120i	0.302143	+	0.953263i	$0.402298\pi$
$468$		0			0
$469$	−3.59494	−	3.59494i	−0.165999	−	0.165999i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	14.7158	−	25.4885i	0.676633	−	1.17196i
$474$		0			0
$475$	2.62604	+	0.703645i	0.120491	+	0.0322855i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−12.8097	−	22.1870i	−0.585288	−	1.01375i	−0.994839	−	0.101462i	$-0.967648\pi$
$479$	−12.8097	−	22.1870i	−0.585288	−	1.01375i	0.409551	−	0.912287i	$-0.365685\pi$
$480$		0			0
$481$	−24.9716	+	43.2521i	−1.13861	+	1.97212i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.91202	+	4.91202i	−0.223043	+	0.223043i
$486$		0			0
$487$	−24.8039			−1.12397			−0.561986	−	0.827147i	$-0.689962\pi$
$487$	−24.8039			−1.12397			−0.561986	+	0.827147i	$0.689962\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	36.3890	−	9.75039i	1.64221	−	0.440029i	0.684793	−	0.728737i	$-0.259892\pi$
$491$	36.3890	−	9.75039i	1.64221	−	0.440029i	0.957417	+	0.288708i	$0.0932257\pi$
$492$		0			0
$493$	7.17764	+	1.92324i	0.323265	+	0.0866185i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.87197	+	1.08078i	−0.0839692	+	0.0484796i
$498$		0			0
$499$	20.1205	−	5.39127i	0.900717	−	0.241346i	0.221393	−	0.975185i	$-0.428940\pi$
$499$	20.1205	−	5.39127i	0.900717	−	0.241346i	0.679324	+	0.733838i	$0.262273\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	4.55397i		−	0.203051i	−0.994833	−	0.101526i	$-0.967628\pi$
$503$		−	4.55397i		−	0.203051i	0.994833	−	0.101526i	$-0.0323724\pi$
$504$		0			0
$505$			11.1880i			0.497858i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.44927	−	1.99603i	0.330183	−	0.0884723i	−0.0899191	−	0.995949i	$-0.528661\pi$
$509$	7.44927	−	1.99603i	0.330183	−	0.0884723i	0.420102	+	0.907477i	$0.361994\pi$
$510$		0			0
$511$	7.20399	−	4.15923i	0.318686	−	0.183993i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.68172	−	1.25446i	−0.206301	−	0.0552782i
$516$		0			0
$517$	6.00367	−	1.60868i	0.264041	−	0.0707496i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−41.5553			−1.82057			−0.910286	−	0.413980i	$-0.864138\pi$
$521$	−41.5553			−1.82057			−0.910286	+	0.413980i	$0.864138\pi$
$522$		0			0
$523$	−7.94661	+	7.94661i	−0.347481	+	0.347481i	−0.859171	−	0.511689i	$-0.829020\pi$
$523$	−7.94661	+	7.94661i	−0.347481	+	0.347481i	0.511689	+	0.859171i	$0.329020\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.08567	+	3.61248i	−0.0908531	+	0.157362i
$528$		0			0
$529$	−11.1829	−	19.3693i	−0.486211	−	0.842142i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	31.0937	+	8.33153i	1.34682	+	0.360879i
$534$		0			0
$535$	−6.71295	+	11.6272i	−0.290226	+	0.502686i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.8441	+	10.8441i	0.467089	+	0.467089i
$540$		0			0
$541$	23.7454	−	23.7454i	1.02090	−	1.02090i	0.0211185	−	0.999777i	$-0.493277\pi$
$541$	23.7454	−	23.7454i	1.02090	−	1.02090i	0.999777	−	0.0211185i	$-0.00672274\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	12.1230	+	6.99924i	0.519294	+	0.299814i
$546$		0			0
$547$	0.183171	−	0.683605i	0.00783185	−	0.0292288i	−0.961899	−	0.273404i	$-0.911850\pi$
$547$	0.183171	−	0.683605i	0.00783185	−	0.0292288i	0.969731	+	0.244175i	$0.0785171\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.69010	+	3.28518i	−0.242406	+	0.139953i
$552$		0			0
$553$	0.599525	+	0.346136i	0.0254944	+	0.0147192i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.0432	+	11.0432i	0.467916	+	0.467916i	0.901239	−	0.433322i	$-0.142659\pi$
$557$	11.0432	+	11.0432i	0.467916	+	0.467916i	−0.433322	+	0.901239i	$0.642659\pi$
$558$		0			0
$559$			63.2626i			2.67572i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.6019	−	43.2988i	−0.488961	−	1.82483i	−0.561522	−	0.827462i	$-0.689784\pi$
$563$	−11.6019	−	43.2988i	−0.488961	−	1.82483i	0.0725616	−	0.997364i	$-0.476883\pi$
$564$		0			0
$565$	2.40271	−	8.96703i	0.101083	−	0.377246i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−12.4715	−	21.6013i	−0.522833	−	0.905574i	−0.999647	−	0.0265695i	$-0.991542\pi$
$569$	−12.4715	−	21.6013i	−0.522833	−	0.905574i	0.476814	−	0.879004i	$-0.341792\pi$
$570$		0			0
$571$	−9.27714	−	34.6227i	−0.388236	−	1.44892i	−0.833002	−	0.553270i	$-0.813380\pi$
$571$	−9.27714	−	34.6227i	−0.388236	−	1.44892i	0.444766	−	0.895647i	$-0.353287\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.83695			−0.118309
$576$		0			0
$577$	−20.2125			−0.841457			−0.420729	−	0.907187i	$-0.638226\pi$
$577$	−20.2125			−0.841457			−0.420729	+	0.907187i	$0.638226\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.13122	+	7.95381i	0.0884178	+	0.329980i
$582$		0			0
$583$	14.8155	+	25.6612i	0.613596	+	1.06278i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.425823	−	1.58919i	0.0175756	−	0.0655930i	−0.956581	−	0.291466i	$-0.905857\pi$
$587$	0.425823	−	1.58919i	0.0175756	−	0.0655930i	0.974157	+	0.225873i	$0.0725235\pi$
$588$		0			0
$589$	−0.954602	−	3.56262i	−0.0393337	−	0.146795i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	35.7642i		−	1.46866i	−0.678793	−	0.734329i	$-0.737497\pi$
$593$		−	35.7642i		−	1.46866i	0.678793	−	0.734329i	$-0.262503\pi$
$594$		0			0
$595$	0.521182	+	0.521182i	0.0213664	+	0.0213664i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.2410	−	13.9955i	−0.990460	−	0.571842i	−0.0850481	−	0.996377i	$-0.527104\pi$
$599$	−24.2410	−	13.9955i	−0.990460	−	0.571842i	−0.905412	+	0.424535i	$0.860438\pi$
$600$		0			0
$601$	−9.43704	+	5.44848i	−0.384945	+	0.222248i	−0.679968	−	0.733242i	$-0.738006\pi$
$601$	−9.43704	+	5.44848i	−0.384945	+	0.222248i	0.295023	+	0.955490i	$0.404673\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.68253	−	6.27927i	0.0684044	−	0.255289i
$606$		0			0
$607$	36.6954	+	21.1861i	1.48942	+	0.859916i	0.999927	−	0.0120914i	$-0.00384892\pi$
$607$	36.6954	+	21.1861i	1.48942	+	0.859916i	0.489492	+	0.872008i	$0.337182\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.44695	+	9.44695i	−0.382183	+	0.382183i
$612$		0			0
$613$	11.5060	+	11.5060i	0.464722	+	0.464722i	0.900200	−	0.435477i	$-0.143420\pi$
$613$	11.5060	+	11.5060i	0.464722	+	0.464722i	−0.435477	+	0.900200i	$0.643420\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.520100	−	0.900840i	0.0209384	−	0.0362665i	−0.855366	−	0.518024i	$-0.826668\pi$
$617$	0.520100	−	0.900840i	0.0209384	−	0.0362665i	0.876305	+	0.481757i	$0.160001\pi$
$618$		0			0
$619$	17.6575	+	4.73131i	0.709714	+	0.190167i	0.595578	−	0.803298i	$-0.296923\pi$
$619$	17.6575	+	4.73131i	0.709714	+	0.190167i	0.114136	+	0.993465i	$0.463590\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.55069	+	2.68588i	0.0621272	+	0.107608i
$624$		0			0
$625$	2.74947	−	4.76221i	0.109979	−	0.190489i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−6.00428	+	6.00428i	−0.239406	+	0.239406i
$630$		0			0
$631$	−18.9729			−0.755301			−0.377650	−	0.925948i	$-0.623268\pi$
$631$	−18.9729			−0.755301			−0.377650	+	0.925948i	$0.623268\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−8.35872	+	2.23971i	−0.331706	+	0.0888803i
$636$		0			0
$637$	−31.8409	−	8.53175i	−1.26158	−	0.338040i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.62975	+	3.82769i	−0.261859	+	0.151185i	−0.625182	−	0.780479i	$-0.714975\pi$
$641$	−6.62975	+	3.82769i	−0.261859	+	0.151185i	0.363323	+	0.931663i	$0.381642\pi$
$642$		0			0
$643$	18.3287	−	4.91116i	0.722813	−	0.193677i	0.121387	−	0.992605i	$-0.461266\pi$
$643$	18.3287	−	4.91116i	0.722813	−	0.193677i	0.601427	+	0.798928i	$0.294599\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	1.59451i		−	0.0626865i	−0.999509	−	0.0313432i	$-0.990022\pi$
$647$		−	1.59451i		−	0.0626865i	0.999509	−	0.0313432i	$-0.00997849\pi$
$648$		0			0
$649$		−	31.0610i		−	1.21925i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.34296	−	0.359845i	0.0525540	−	0.0140818i	−0.232446	−	0.972609i	$-0.574673\pi$
$653$	1.34296	−	0.359845i	0.0525540	−	0.0140818i	0.285000	+	0.958527i	$0.408006\pi$
$654$		0			0
$655$	6.27121	−	3.62069i	0.245037	−	0.141472i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.0586	+	7.51827i	1.09301	+	0.292870i	0.759914	−	0.650024i	$-0.225241\pi$
$659$	28.0586	+	7.51827i	1.09301	+	0.292870i	0.333093	+	0.942894i	$0.391908\pi$
$660$		0			0
$661$	−0.302749	+	0.0811214i	−0.0117756	+	0.00315526i	−0.264702	−	0.964330i	$-0.585274\pi$
$661$	−0.302749	+	0.0811214i	−0.0117756	+	0.00315526i	0.252926	+	0.967486i	$0.418607\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.651712			−0.0252723
$666$		0			0
$667$	4.84807	−	4.84807i	0.187718	−	0.187718i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.670391	+	1.16115i	−0.0258802	+	0.0448257i
$672$		0			0
$673$	−14.6918	−	25.4470i	−0.566329	−	0.980911i	−0.996925	−	0.0783659i	$-0.975030\pi$
$673$	−14.6918	−	25.4470i	−0.566329	−	0.980911i	0.430595	−	0.902545i	$-0.358304\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.06366	+	1.89270i	0.271478	+	0.0727424i	0.391990	−	0.919969i	$-0.371787\pi$
$677$	7.06366	+	1.89270i	0.271478	+	0.0727424i	−0.120511	+	0.992712i	$0.538453\pi$
$678$		0			0
$679$	−2.06261	+	3.57254i	−0.0791556	+	0.137102i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	20.6264	+	20.6264i	0.789247	+	0.789247i	0.981371	−	0.192123i	$-0.0615374\pi$
$683$	20.6264	+	20.6264i	0.789247	+	0.789247i	−0.192123	+	0.981371i	$0.561537\pi$
$684$		0			0
$685$	−4.62083	+	4.62083i	−0.176553	+	0.176553i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−55.1583	−	31.8456i	−2.10136	−	1.21322i
$690$		0			0
$691$	0.467582	−	1.74504i	0.0177876	−	0.0663844i	−0.956462	−	0.291858i	$-0.905726\pi$
$691$	0.467582	−	1.74504i	0.0177876	−	0.0663844i	0.974249	+	0.225474i	$0.0723931\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	15.4593	−	8.92542i	0.586404	−	0.338560i
$696$		0			0
$697$	4.73979	+	2.73652i	0.179532	+	0.103653i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−31.2193	−	31.2193i	−1.17914	−	1.17914i	−0.979964	−	0.199174i	$-0.936174\pi$
$701$	−31.2193	−	31.2193i	−1.17914	−	1.17914i	−0.199174	−	0.979964i	$-0.563826\pi$
$702$		0			0
$703$		−	7.50805i		−	0.283171i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.71957	+	6.41751i	0.0646709	+	0.241355i
$708$		0			0
$709$	−5.00387	+	18.6747i	−0.187924	+	0.701344i	0.806061	+	0.591832i	$0.201595\pi$
$709$	−5.00387	+	18.6747i	−0.187924	+	0.701344i	−0.993986	+	0.109511i	$0.965071\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.92438	+	3.33312i	0.0720686	+	0.124826i
$714$		0			0
$715$	−3.72162	−	13.8893i	−0.139181	−	0.519430i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	5.23889			0.195378			0.0976889	−	0.995217i	$-0.468855\pi$
$719$	5.23889			0.195378			0.0976889	+	0.995217i	$0.468855\pi$
$720$		0			0
$721$	−2.87828			−0.107193
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.93665	+	29.6200i	0.294760	+	1.10006i
$726$		0			0
$727$	−20.0812	−	34.7817i	−0.744772	−	1.28998i	−0.950301	−	0.311332i	$-0.899225\pi$
$727$	−20.0812	−	34.7817i	−0.744772	−	1.28998i	0.205530	−	0.978651i	$-0.434108\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.78383	+	10.3894i	−0.102964	+	0.384266i
$732$		0			0
$733$	−12.3274	−	46.0065i	−0.455324	−	1.69929i	−0.687135	−	0.726530i	$-0.741132\pi$
$733$	−12.3274	−	46.0065i	−0.455324	−	1.69929i	0.231811	−	0.972761i	$-0.425535\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			16.8631i			0.621161i
$738$		0			0
$739$	−9.18363	−	9.18363i	−0.337825	−	0.337825i	0.517723	−	0.855548i	$-0.326780\pi$
$739$	−9.18363	−	9.18363i	−0.337825	−	0.337825i	−0.855548	+	0.517723i	$0.826780\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−42.0760	−	24.2926i	−1.54362	−	0.891208i	−0.998606	−	0.0527792i	$-0.983192\pi$
$743$	−42.0760	−	24.2926i	−1.54362	−	0.891208i	−0.545011	−	0.838429i	$-0.683475\pi$
$744$		0			0
$745$	−11.9859	+	6.92004i	−0.439128	+	0.253531i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.06353	+	7.70120i	−0.0753998	+	0.281396i
$750$		0			0
$751$	−25.5639	−	14.7593i	−0.932839	−	0.538575i	−0.0451310	−	0.998981i	$-0.514371\pi$
$751$	−25.5639	−	14.7593i	−0.932839	−	0.538575i	−0.887708	+	0.460406i	$0.847704\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.13448	+	8.13448i	−0.296044	+	0.296044i
$756$		0			0
$757$	30.3982	+	30.3982i	1.10484	+	1.10484i	0.993818	+	0.111022i	$0.0354123\pi$
$757$	30.3982	+	30.3982i	1.10484	+	1.10484i	0.111022	+	0.993818i	$0.464588\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.97086	−	5.14568i	0.107694	−	0.186531i	−0.807142	−	0.590357i	$-0.798987\pi$
$761$	2.97086	−	5.14568i	0.107694	−	0.186531i	0.914836	+	0.403827i	$0.132320\pi$
$762$		0			0
$763$	8.02963	+	2.15153i	0.290692	+	0.0778907i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	33.3825	+	57.8201i	1.20537	+	2.08776i
$768$		0			0
$769$	−6.00863	+	10.4073i	−0.216677	+	0.375295i	−0.953790	−	0.300474i	$-0.902855\pi$
$769$	−6.00863	+	10.4073i	−0.216677	+	0.375295i	0.737113	+	0.675769i	$0.236188\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−22.2746	+	22.2746i	−0.801163	+	0.801163i	−0.983277	−	0.182114i	$-0.941706\pi$
$773$	−22.2746	+	22.2746i	−0.801163	+	0.801163i	0.182114	+	0.983277i	$0.441706\pi$
$774$		0			0
$775$	−17.2139			−0.618340
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.67437	+	1.25249i	−0.167477	+	0.0448753i
$780$		0			0
$781$	6.92536	+	1.85565i	0.247809	+	0.0664002i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−11.3417	+	6.54815i	−0.404803	+	0.233713i
$786$		0			0
$787$	5.98650	−	1.60408i	0.213396	−	0.0571792i	−0.150537	−	0.988604i	$-0.548100\pi$
$787$	5.98650	−	1.60408i	0.213396	−	0.0571792i	0.363933	+	0.931425i	$0.381434\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	5.51285i		−	0.196014i
$792$		0			0
$793$		−	2.88198i		−	0.102342i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−33.1217	+	8.87494i	−1.17323	+	0.314367i	−0.792239	−	0.610211i	$-0.791085\pi$
$797$	−33.1217	+	8.87494i	−1.17323	+	0.314367i	−0.380993	+	0.924578i	$0.624418\pi$
$798$		0			0
$799$	−1.96715	+	1.13573i	−0.0695927	+	0.0401794i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−26.6513	−	7.14118i	−0.940503	−	0.252007i
$804$		0			0
$805$	0.656892	−	0.176014i	0.0231524	−	0.00620367i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	12.8401			0.451432			0.225716	−	0.974193i	$-0.427528\pi$
$809$	12.8401			0.451432			0.225716	+	0.974193i	$0.427528\pi$
$810$		0			0
$811$	37.1183	−	37.1183i	1.30340	−	1.30340i	0.377314	−	0.926086i	$-0.376848\pi$
$811$	37.1183	−	37.1183i	1.30340	−	1.30340i	0.926086	−	0.377314i	$-0.123152\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.87287	+	15.3683i	−0.310803	+	0.538327i
$816$		0			0
$817$	−4.75519	−	8.23624i	−0.166363	−	0.288149i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−27.1312	−	7.26977i	−0.946884	−	0.253717i	−0.247844	−	0.968800i	$-0.579722\pi$
$821$	−27.1312	−	7.26977i	−0.946884	−	0.253717i	−0.699040	+	0.715083i	$0.746389\pi$
$822$		0			0
$823$	−9.61847	+	16.6597i	−0.335279	+	0.580720i	−0.983538	−	0.180700i	$-0.942164\pi$
$823$	−9.61847	+	16.6597i	−0.335279	+	0.580720i	0.648260	+	0.761419i	$0.275497\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.7848	+	28.7848i	1.00095	+	1.00095i	1.00000		0.000945916i	$0.000301094\pi$
$827$	28.7848	+	28.7848i	1.00095	+	1.00095i	0.000945916		1.00000i	$0.499699\pi$
$828$		0			0
$829$	−23.5696	+	23.5696i	−0.818606	+	0.818606i	−0.985906	−	0.167300i	$-0.946495\pi$
$829$	−23.5696	+	23.5696i	−0.818606	+	0.818606i	0.167300	+	0.985906i	$0.446495\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.85369	−	2.80228i	−0.168171	−	0.0970933i
$834$		0			0
$835$	4.12343	−	15.3889i	0.142697	−	0.532553i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.76796	−	3.33013i	0.199132	−	0.114969i	−0.397119	−	0.917767i	$-0.629990\pi$
$839$	5.76796	−	3.33013i	0.199132	−	0.114969i	0.596251	+	0.802798i	$0.296656\pi$
$840$		0			0
$841$	−39.0658	−	22.5546i	−1.34710	−	0.777747i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	10.8323	+	10.8323i	0.372643	+	0.372643i
$846$		0			0
$847$		−	3.86044i		−	0.132646i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.02777	+	7.56773i	0.0695109	+	0.259418i
$852$		0			0
$853$	−2.94440	+	10.9887i	−0.100814	+	0.376245i	−0.997837	−	0.0657407i	$-0.979059\pi$
$853$	−2.94440	+	10.9887i	−0.100814	+	0.376245i	0.897022	+	0.441985i	$0.145726\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.7885	+	27.3465i	0.539326	+	0.934140i	0.998940	+	0.0460211i	$0.0146542\pi$
$857$	15.7885	+	27.3465i	0.539326	+	0.934140i	−0.459615	+	0.888118i	$0.652013\pi$
$858$		0			0
$859$	−7.30262	−	27.2537i	−0.249162	−	0.929886i	−0.971246	−	0.238080i	$-0.923482\pi$
$859$	−7.30262	−	27.2537i	−0.249162	−	0.929886i	0.722084	−	0.691806i	$-0.243185\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−29.1288			−0.991557			−0.495779	−	0.868449i	$-0.665117\pi$
$863$	−29.1288			−0.991557			−0.495779	+	0.868449i	$0.665117\pi$
$864$		0			0
$865$	−9.03998			−0.307369
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.594298	−	2.21795i	−0.0201602	−	0.0752388i
$870$		0			0
$871$	−18.1235	−	31.3907i	−0.614090	−	1.06363i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.89225	+	7.06198i	−0.0639698	+	0.238739i
$876$		0			0
$877$	8.63165	+	32.2138i	0.291470	+	1.08778i	0.943980	+	0.330001i	$0.107049\pi$
$877$	8.63165	+	32.2138i	0.291470	+	1.08778i	−0.652510	+	0.757780i	$0.726284\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	10.4223i		−	0.351136i	−0.984467	−	0.175568i	$-0.943824\pi$
$881$		−	10.4223i		−	0.351136i	0.984467	−	0.175568i	$-0.0561763\pi$
$882$		0			0
$883$	−7.73247	−	7.73247i	−0.260218	−	0.260218i	0.564924	−	0.825143i	$-0.308905\pi$
$883$	−7.73247	−	7.73247i	−0.260218	−	0.260218i	−0.825143	+	0.564924i	$0.808905\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.0565	−	12.7343i	−0.740584	−	0.427577i	0.0816974	−	0.996657i	$-0.473966\pi$
$887$	−22.0565	−	12.7343i	−0.740584	−	0.427577i	−0.822282	+	0.569081i	$0.807299\pi$
$888$		0			0
$889$	−4.45039	+	2.56943i	−0.149261	+	0.0861761i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.519821	−	1.94000i	0.0173951	−	0.0649196i
$894$		0			0
$895$	−22.1829	−	12.8073i	−0.741492	−	0.428100i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	29.4168	−	29.4168i	0.981104	−	0.981104i
$900$		0			0
$901$	−7.65711	−	7.65711i	−0.255095	−	0.255095i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.61915	+	4.53651i	−0.0870637	+	0.150799i
$906$		0			0
$907$	−35.2550	−	9.44656i	−1.17062	−	0.313668i	−0.379423	−	0.925223i	$-0.623877\pi$
$907$	−35.2550	−	9.44656i	−1.17062	−	0.313668i	−0.791202	+	0.611555i	$0.790544\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.86150	−	8.42037i	−0.161069	−	0.278979i	0.774183	−	0.632961i	$-0.218161\pi$
$911$	−4.86150	−	8.42037i	−0.161069	−	0.278979i	−0.935252	+	0.353982i	$0.884827\pi$
$912$		0			0
$913$	13.6563	−	23.6534i	0.451957	−	0.782813i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.04073	−	3.04073i	0.100414	−	0.100414i
$918$		0			0
$919$	26.5741			0.876599			0.438300	−	0.898829i	$-0.355581\pi$
$919$	26.5741			0.876599			0.438300	+	0.898829i	$0.355581\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.8859	+	3.98867i	−0.489976	+	0.131289i
$924$		0			0
$925$	−33.8472	−	9.06934i	−1.11289	−	0.298198i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−20.9365	+	12.0877i	−0.686904	+	0.396584i	−0.802451	−	0.596718i	$-0.796471\pi$
$929$	−20.9365	+	12.0877i	−0.686904	+	0.396584i	0.115547	+	0.993302i	$0.463138\pi$
$930$		0			0
$931$	4.78670	−	1.28259i	0.156878	−	0.0420353i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	2.44476i		−	0.0799521i
$936$		0			0
$937$		−	1.33551i		−	0.0436291i	−0.999762	−	0.0218146i	$-0.993056\pi$
$937$		−	1.33551i		−	0.0436291i	0.999762	−	0.0218146i	$-0.00694434\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−21.3261	+	5.71431i	−0.695211	+	0.186281i	−0.589085	−	0.808071i	$-0.700512\pi$
$941$	−21.3261	+	5.71431i	−0.695211	+	0.186281i	−0.106126	+	0.994353i	$0.533845\pi$
$942$		0			0
$943$	4.37325	−	2.52490i	0.142413	−	0.0822220i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.4634	+	6.28700i	0.762458	+	0.204300i	0.619037	−	0.785362i	$-0.287523\pi$
$947$	23.4634	+	6.28700i	0.762458	+	0.204300i	0.143421	+	0.989662i	$0.454190\pi$
$948$		0			0
$949$	57.2863	−	15.3498i	1.85959	−	0.498277i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	15.2157			0.492885			0.246442	−	0.969157i	$-0.420738\pi$
$953$	15.2157			0.492885			0.246442	+	0.969157i	$0.420738\pi$
$954$		0			0
$955$	4.24772	−	4.24772i	0.137453	−	0.137453i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.94033	+	3.36075i	−0.0626566	+	0.108524i
$960$		0			0
$961$	−3.82339	−	6.62230i	−0.123335	−	0.213623i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.66032	+	1.78463i	0.214403	+	0.0574492i
$966$		0			0
$967$	16.3260	−	28.2775i	0.525010	−	0.909344i	−0.474566	−	0.880220i	$-0.657395\pi$
$967$	16.3260	−	28.2775i	0.525010	−	0.909344i	0.999576	−	0.0291241i	$-0.00927179\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.6028	−	23.6028i	−0.757449	−	0.757449i	0.218408	−	0.975858i	$-0.429914\pi$
$971$	−23.6028	−	23.6028i	−0.757449	−	0.757449i	−0.975858	+	0.218408i	$0.929914\pi$
$972$		0			0
$973$	7.49574	−	7.49574i	0.240303	−	0.240303i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−30.2605	−	17.4709i	−0.968119	−	0.558944i	−0.0694570	−	0.997585i	$-0.522127\pi$
$977$	−30.2605	−	17.4709i	−0.968119	−	0.558944i	−0.898662	+	0.438641i	$0.855460\pi$
$978$		0			0
$979$	2.66246	−	9.93644i	0.0850926	−	0.317570i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−28.8301	+	16.6450i	−0.919536	+	0.530895i	−0.883487	−	0.468455i	$-0.844811\pi$
$983$	−28.8301	+	16.6450i	−0.919536	+	0.530895i	−0.0360492	+	0.999350i	$0.511477\pi$
$984$		0			0
$985$	−0.756999	−	0.437053i	−0.0241200	−	0.0139257i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.01742	+	7.01742i	0.223141	+	0.223141i
$990$		0			0
$991$		−	10.4637i		−	0.332390i	−0.986093	−	0.166195i	$-0.946852\pi$
$991$		−	10.4637i		−	0.332390i	0.986093	−	0.166195i	$-0.0531482\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−6.72182	−	25.0862i	−0.213096	−	0.795286i
$996$		0			0
$997$	7.47474	−	27.8961i	0.236727	−	0.883479i	−0.740635	−	0.671907i	$-0.765475\pi$
$997$	7.47474	−	27.8961i	0.236727	−	0.883479i	0.977363	−	0.211571i	$-0.0678580\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.z.a.719.8		88
3.2	odd	2		576.2.y.a.527.4		88
4.3	odd	2		432.2.v.a.395.16		88
9.2	odd	6	inner	1728.2.z.a.143.8		88
9.7	even	3		576.2.y.a.335.8		88
12.11	even	2		144.2.u.a.59.7	yes	88
16.3	odd	4	inner	1728.2.z.a.1583.8		88
16.13	even	4		432.2.v.a.179.22		88
36.7	odd	6		144.2.u.a.11.1	✓	88
36.11	even	6		432.2.v.a.251.22		88
48.29	odd	4		144.2.u.a.131.1	yes	88
48.35	even	4		576.2.y.a.239.8		88
144.29	odd	12		432.2.v.a.35.16		88
144.61	even	12		144.2.u.a.83.7	yes	88
144.83	even	12	inner	1728.2.z.a.1007.8		88
144.115	odd	12		576.2.y.a.47.4		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.1	✓	88	36.7	odd	6
144.2.u.a.59.7	yes	88	12.11	even	2
144.2.u.a.83.7	yes	88	144.61	even	12
144.2.u.a.131.1	yes	88	48.29	odd	4
432.2.v.a.35.16		88	144.29	odd	12
432.2.v.a.179.22		88	16.13	even	4
432.2.v.a.251.22		88	36.11	even	6
432.2.v.a.395.16		88	4.3	odd	2
576.2.y.a.47.4		88	144.115	odd	12
576.2.y.a.239.8		88	48.35	even	4
576.2.y.a.335.8		88	9.7	even	3
576.2.y.a.527.4		88	3.2	odd	2
1728.2.z.a.143.8		88	9.2	odd	6	inner
1728.2.z.a.719.8		88	1.1	even	1	trivial
1728.2.z.a.1007.8		88	144.83	even	12	inner
1728.2.z.a.1583.8		88	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.310357 - 1.15827i) q^{5} +(-0.356047 - 0.616691i) q^{7} +O(q^{10})\)	\(q+(-0.310357 - 1.15827i) q^{5} +(-0.356047 - 0.616691i) q^{7} +(-0.611314 + 2.28146i) q^{11} +(-1.31401 - 4.90394i) q^{13} -0.863180i q^{17} +(0.539682 + 0.539682i) q^{19} +(-0.689728 - 0.398215i) q^{23} +(3.08486 - 1.78104i) q^{25} +(-2.22809 + 8.31534i) q^{29} +(-4.18508 - 2.41626i) q^{31} +(-0.603793 + 0.603793i) q^{35} +(-6.95600 - 6.95600i) q^{37} +(-3.17027 + 5.49108i) q^{41} +(-12.0362 - 3.22509i) q^{43} +(-1.31575 - 2.27895i) q^{47} +(3.24646 - 5.62304i) q^{49} +(8.87081 - 8.87081i) q^{53} +2.83227 q^{55} +(-12.7025 + 3.40363i) q^{59} +(0.548319 + 0.146922i) q^{61} +(-5.27228 + 3.04395i) q^{65} +(6.89625 - 1.84784i) q^{67} -3.03550i q^{71} +11.6817i q^{73} +(1.62461 - 0.435313i) q^{77} +(-0.841919 + 0.486082i) q^{79} +(-11.1696 - 2.99289i) q^{83} +(-0.999796 + 0.267894i) q^{85} -4.35531 q^{89} +(-2.55637 + 2.55637i) q^{91} +(0.457603 - 0.792591i) q^{95} +(-2.89654 - 5.01695i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 6 * q^5 + 4 * q^7	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85} - 20 q^{91} - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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