LMFDB - Embedded newform 1728.2.z.a.1007.8

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			1007.8
Character	$\chi$	$=$	1728.1007
Dual form			1728.2.z.a.719.8

$q$-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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.310357	+	1.15827i	−0.138796	+	0.517994i	0.861157	+	0.508339i	$0.169740\pi$
$5$	−0.310357	+	1.15827i	−0.138796	+	0.517994i	−0.999953	+	0.00965542i	$0.996927\pi$
$6$		0			0
$7$	−0.356047	+	0.616691i	−0.134573	+	0.233087i	−0.925434	−	0.378908i	$-0.876300\pi$
$7$	−0.356047	+	0.616691i	−0.134573	+	0.233087i	0.790861	+	0.611996i	$0.209633\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.611314	−	2.28146i	−0.184318	−	0.687885i	−0.994775	−	0.102087i	$-0.967448\pi$
$11$	−0.611314	−	2.28146i	−0.184318	−	0.687885i	0.810457	−	0.585798i	$-0.199219\pi$
$12$		0			0
$13$	−1.31401	+	4.90394i	−0.364440	+	1.36011i	0.503738	+	0.863857i	$0.331958\pi$
$13$	−1.31401	+	4.90394i	−0.364440	+	1.36011i	−0.868178	+	0.496253i	$0.834709\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			0.863180i			0.209352i	0.994506	+	0.104676i	$0.0333806\pi$
$17$			0.863180i			0.209352i	−0.994506	+	0.104676i	$0.966619\pi$
$18$		0			0
$19$	0.539682	−	0.539682i	0.123811	−	0.123811i	−0.642486	−	0.766297i	$-0.722097\pi$
$19$	0.539682	−	0.539682i	0.123811	−	0.123811i	0.766297	+	0.642486i	$0.222097\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.689728	+	0.398215i	−0.143818	+	0.0830335i	−0.570182	−	0.821518i	$-0.693128\pi$
$23$	−0.689728	+	0.398215i	−0.143818	+	0.0830335i	0.426364	+	0.904552i	$0.359794\pi$
$24$		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	−0.787335	−	0.616526i	$-0.788540\pi$
$29$	−2.22809	−	8.31534i	−0.413746	−	1.54412i	0.373589	−	0.927594i	$-0.378127\pi$
$30$		0			0
$31$	−4.18508	+	2.41626i	−0.751663	+	0.433973i	−0.826295	−	0.563238i	$-0.809555\pi$
$31$	−4.18508	+	2.41626i	−0.751663	+	0.433973i	0.0746314	+	0.997211i	$0.476222\pi$
$32$		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	−0.155765	+	0.987794i	$0.549784\pi$
$37$	−6.95600	+	6.95600i	−1.14356	+	1.14356i	−0.987794	+	0.155765i	$0.950216\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.17027	−	5.49108i	−0.495114	−	0.857562i	0.504870	−	0.863195i	$-0.331540\pi$
$41$	−3.17027	−	5.49108i	−0.495114	−	0.857562i	−0.999984	+	0.00563304i	$0.998207\pi$
$42$		0			0
$43$	−12.0362	+	3.22509i	−1.83550	+	0.491822i	−0.998468	−	0.0553283i	$-0.982379\pi$
$43$	−12.0362	+	3.22509i	−1.83550	+	0.491822i	−0.837035	+	0.547150i	$0.815713\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.31575	+	2.27895i	−0.191923	+	0.332420i	−0.945887	−	0.324495i	$-0.894806\pi$
$47$	−1.31575	+	2.27895i	−0.191923	+	0.332420i	0.753965	+	0.656915i	$0.228139\pi$
$48$		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	0.968157	+	0.250342i	$0.0805431\pi$
$53$	8.87081	+	8.87081i	1.21850	+	1.21850i	0.250342	+	0.968157i	$0.419457\pi$
$54$		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	−0.693076	−	0.720865i	$-0.743745\pi$
$59$	−12.7025	−	3.40363i	−1.65373	−	0.443115i	−0.960654	+	0.277749i	$0.910412\pi$
$60$		0			0
$61$	0.548319	−	0.146922i	0.0702051	−	0.0188114i	−0.223546	−	0.974693i	$-0.571763\pi$
$61$	0.548319	−	0.146922i	0.0702051	−	0.0188114i	0.293751	+	0.955882i	$0.405096\pi$
$62$		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	0.654164	−	0.756352i	$-0.273020\pi$
$67$	6.89625	+	1.84784i	0.842511	+	0.225750i	0.188347	+	0.982103i	$0.439687\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			3.03550i			0.360248i	0.983644	+	0.180124i	$0.0576499\pi$
$71$			3.03550i			0.360248i	−0.983644	+	0.180124i	$0.942350\pi$
$72$		0			0
$73$		−	11.6817i		−	1.36724i	−0.729839	−	0.683619i	$-0.760405\pi$
$73$		−	11.6817i		−	1.36724i	0.729839	−	0.683619i	$-0.239595\pi$
$74$		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	0.451890	−	0.892074i	$-0.350750\pi$
$79$	−0.841919	−	0.486082i	−0.0947233	−	0.0546885i	−0.546613	+	0.837385i	$0.684083\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.1696	+	2.99289i	−1.22602	+	0.328512i	−0.813030	−	0.582221i	$-0.802184\pi$
$83$	−11.1696	+	2.99289i	−1.22602	+	0.328512i	−0.412994	+	0.910734i	$0.635517\pi$
$84$		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	−0.974775	−	0.223190i	$-0.928353\pi$
$97$	−2.89654	+	5.01695i	−0.294099	+	0.509395i	0.680676	+	0.732585i	$0.261686\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−9.01216	+	2.41480i	−0.896744	+	0.240282i	−0.677617	−	0.735415i	$-0.736987\pi$
$101$	−9.01216	+	2.41480i	−0.896744	+	0.240282i	−0.219127	+	0.975696i	$0.570321\pi$
$102$		0			0
$103$	2.02100	+	3.50047i	0.199135	+	0.344911i	0.948248	−	0.317530i	$-0.102854\pi$
$103$	2.02100	+	3.50047i	0.199135	+	0.344911i	−0.749113	+	0.662442i	$0.769520\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.91703	+	7.91703i	−0.765368	+	0.765368i	−0.977287	−	0.211919i	$-0.932029\pi$
$107$	−7.91703	+	7.91703i	−0.765368	+	0.765368i	0.211919	+	0.977287i	$0.432029\pi$
$108$		0			0
$109$	−8.25467	−	8.25467i	−0.790654	−	0.790654i	0.190946	−	0.981600i	$-0.438844\pi$
$109$	−8.25467	−	8.25467i	−0.790654	−	0.790654i	−0.981600	+	0.190946i	$0.938844\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.70455	−	3.87087i	0.630711	−	0.364141i	−0.150316	−	0.988638i	$-0.548029\pi$
$113$	6.70455	−	3.87087i	0.630711	−	0.364141i	0.781027	+	0.624497i	$0.214696\pi$
$114$		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	$0.103744\pi$
$127$			7.21656i			0.640366i	−0.947356	+	0.320183i	$0.896256\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.56297	−	5.83309i	0.136558	−	0.509640i	−0.863429	−	0.504470i	$-0.831688\pi$
$131$	1.56297	−	5.83309i	0.136558	−	0.509640i	0.999987	−	0.00516943i	$-0.00164549\pi$
$132$		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	−0.958630	−	0.284654i	$-0.908121\pi$
$137$	−2.72483	+	4.71954i	−0.232798	+	0.403217i	0.725833	+	0.687871i	$0.241455\pi$
$138$		0			0
$139$	3.85291	−	14.3793i	0.326800	−	1.21963i	−0.585691	−	0.810534i	$-0.699177\pi$
$139$	3.85291	−	14.3793i	0.326800	−	1.21963i	0.912490	−	0.409098i	$-0.134157\pi$
$140$		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	0.728798	+	0.684728i	$0.240079\pi$
$149$	−2.98723	+	11.1485i	−0.244724	+	0.913321i	−0.973522	+	0.228593i	$0.926588\pi$
$150$		0			0
$151$	−4.79677	+	8.30825i	−0.390355	+	0.676116i	−0.992496	−	0.122274i	$-0.960981\pi$
$151$	−4.79677	+	8.30825i	−0.390355	+	0.676116i	0.602141	+	0.798390i	$0.294315\pi$
$152$		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	0.756571	+	0.653912i	$0.226873\pi$
$157$	−2.82669	+	10.5494i	−0.225595	+	0.841931i	−0.982165	+	0.188019i	$0.939793\pi$
$158$		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	−0.986055	−	0.166422i	$-0.946779\pi$
$163$	−10.4644	+	10.4644i	−0.819633	+	0.819633i	0.166422	+	0.986055i	$0.446779\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.5061	−	6.64303i	0.890367	−	0.514053i	0.0163043	−	0.999867i	$-0.494810\pi$
$167$	11.5061	−	6.64303i	0.890367	−	0.514053i	0.874062	+	0.485814i	$0.161477\pi$
$168$		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	0.999584	+	0.0288536i	$0.00918567\pi$
$173$	1.95118	+	7.28191i	0.148346	+	0.553633i	−0.851238	+	0.524780i	$0.824148\pi$
$174$		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	0.990346	+	0.138617i	$0.0442657\pi$
$179$	15.1045	+	15.1045i	1.12896	+	1.12896i	0.138617	+	0.990346i	$0.455734\pi$
$180$		0			0
$181$	−3.08895	+	3.08895i	−0.229600	+	0.229600i	−0.812525	−	0.582926i	$-0.801908\pi$
$181$	−3.08895	+	3.08895i	−0.229600	+	0.229600i	0.582926	+	0.812525i	$0.301908\pi$
$182$		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	−0.761062	−	0.648679i	$-0.775322\pi$
$191$	2.50481	−	4.33846i	0.181242	−	0.313920i	0.942304	+	0.334759i	$0.108655\pi$
$192$		0			0
$193$	−2.87512	−	4.97985i	−0.206956	−	0.358457i	0.743799	−	0.668404i	$-0.233022\pi$
$193$	−2.87512	−	4.97985i	−0.206956	−	0.358457i	−0.950754	+	0.309946i	$0.899689\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.515447	+	0.515447i	0.0367240	+	0.0367240i	0.725230	−	0.688506i	$-0.241733\pi$
$197$	0.515447	+	0.515447i	0.0367240	+	0.0367240i	−0.688506	+	0.725230i	$0.741733\pi$
$198$		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	0.180618	−	0.983553i	$-0.442190\pi$
$211$	−2.24771	−	0.602272i	−0.154739	−	0.0414621i	−0.335357	+	0.942091i	$0.608857\pi$
$212$		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	0.935055	−	0.354502i	$-0.115350\pi$
$223$	16.3604	+	9.44569i	1.09557	+	0.632530i	0.160520	+	0.987033i	$0.448683\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.88169	−	2.11189i	0.523126	−	0.140171i	0.0124139	−	0.999923i	$-0.496048\pi$
$227$	7.88169	−	2.11189i	0.523126	−	0.140171i	0.510712	+	0.859752i	$0.329382\pi$
$228$		0			0
$229$	−7.31287	−	1.95948i	−0.483248	−	0.129486i	0.00896646	−	0.999960i	$-0.497146\pi$
$229$	−7.31287	−	1.95948i	−0.483248	−	0.129486i	−0.492215	+	0.870474i	$0.663813\pi$
$230$		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	0.990648	+	0.136445i	$0.0435677\pi$
$239$	9.48431	+	16.4273i	0.613489	+	1.06259i	−0.377159	+	0.926149i	$0.623099\pi$
$240$		0			0
$241$	0.0512556	−	0.0887774i	0.00330167	−	0.00571865i	−0.864370	−	0.502857i	$-0.832282\pi$
$241$	0.0512556	−	0.0887774i	0.00330167	−	0.00571865i	0.867672	+	0.497138i	$0.165616\pi$
$242$		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	−0.883839	−	0.467792i	$-0.845050\pi$
$251$	−6.59142	+	6.59142i	−0.416047	+	0.416047i	0.467792	+	0.883839i	$0.345050\pi$
$252$		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	0.0177109	−	0.999843i	$-0.494362\pi$
$257$	14.3072	−	8.26024i	0.892456	−	0.515260i	0.874745	+	0.484583i	$0.161029\pi$
$258$		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	−0.383047	−	0.923729i	$-0.625125\pi$
$263$	−22.2913	−	12.8699i	−1.37454	−	0.793593i	−0.991496	+	0.130136i	$0.958458\pi$
$264$		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	−0.551909	−	0.833904i	$-0.686101\pi$
$269$	4.62506	−	4.62506i	0.281995	−	0.281995i	0.833904	+	0.551909i	$0.186101\pi$
$270$		0			0
$271$		−	6.13012i		−	0.372378i	−0.982514	−	0.186189i	$-0.940386\pi$
$271$		−	6.13012i		−	0.372378i	0.982514	−	0.186189i	$-0.0596137\pi$
$272$		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	0.960143	−	0.279510i	$-0.0901720\pi$
$277$	−0.185077	−	0.690716i	−0.0111202	−	0.0415011i	−0.971263	+	0.238009i	$0.923505\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.17559	−	8.96438i	0.308750	−	0.534770i	−0.669339	−	0.742957i	$-0.733423\pi$
$281$	5.17559	−	8.96438i	0.308750	−	0.534770i	0.978089	+	0.208187i	$0.0667561\pi$
$282$		0			0
$283$	6.79689	−	25.3663i	0.404033	−	1.50787i	−0.401799	−	0.915728i	$-0.631615\pi$
$283$	6.79689	−	25.3663i	0.404033	−	1.50787i	0.805832	−	0.592144i	$-0.201718\pi$
$284$		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	−0.628595	−	0.777733i	$-0.716370\pi$
$293$	5.21478	−	19.4618i	0.304651	−	1.13697i	0.933246	−	0.359239i	$-0.116964\pi$
$294$		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	−0.517448	−	0.855715i	$-0.673118\pi$
$307$	5.92691	−	5.92691i	0.338267	−	0.338267i	0.855715	+	0.517448i	$0.173118\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	22.5904	−	13.0426i	1.28098	−	0.739576i	0.303956	−	0.952686i	$-0.401692\pi$
$311$	22.5904	−	13.0426i	1.28098	−	0.739576i	0.977028	+	0.213110i	$0.0683592\pi$
$312$		0			0
$313$	0.538716	+	0.311028i	0.0304500	+	0.0175803i	0.515148	−	0.857101i	$-0.327737\pi$
$313$	0.538716	+	0.311028i	0.0304500	+	0.0175803i	−0.484698	+	0.874682i	$0.661070\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.67189	+	13.7037i	0.206234	+	0.769675i	0.989070	+	0.147447i	$0.0471056\pi$
$317$	3.67189	+	13.7037i	0.206234	+	0.769675i	−0.782836	+	0.622228i	$0.786228\pi$
$318$		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	−0.531956	−	0.846772i	$-0.678543\pi$
$331$	−10.3567	+	2.77508i	−0.569257	+	0.152532i	−0.0373014	+	0.999304i	$0.511876\pi$
$332$		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	0.658847	−	0.752277i	$-0.271044\pi$
$337$	−5.91237	−	10.2405i	−0.322067	−	0.557837i	−0.980914	+	0.194440i	$0.937711\pi$
$338$		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	0.249893	−	0.968273i	$-0.419605\pi$
$347$	−0.332138	−	0.0889961i	−0.0178301	−	0.00477756i	−0.267723	+	0.963496i	$0.586271\pi$
$348$		0			0
$349$	23.9142	−	6.40780i	1.28010	−	0.343001i	0.446207	−	0.894930i	$-0.352774\pi$
$349$	23.9142	−	6.40780i	1.28010	−	0.343001i	0.833892	+	0.551928i	$0.186108\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.76381	+	3.32774i	0.306776	+	0.177117i	0.645483	−	0.763775i	$-0.276656\pi$
$353$	5.76381	+	3.32774i	0.306776	+	0.177117i	−0.338707	+	0.940892i	$0.609989\pi$
$354$		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	$0.238077\pi$
$359$			25.7733i			1.36026i	−0.733091	+	0.680130i	$0.761923\pi$
$360$		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	0.751905	−	0.659271i	$-0.229135\pi$
$367$	10.6689	+	6.15969i	0.556912	+	0.321533i	−0.194993	+	0.980805i	$0.562468\pi$
$368$		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	0.873978	−	0.485966i	$-0.161532\pi$
$373$	26.8045	+	7.18223i	1.38788	+	0.371882i	0.513904	+	0.857848i	$0.328199\pi$
$374$		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	0.999101	+	0.0423953i	$0.0134989\pi$
$379$	20.2758	+	20.2758i	1.04150	+	1.04150i	0.0423953	+	0.999101i	$0.486501\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.9618	−	22.4505i	−0.662317	−	1.14717i	−0.980005	−	0.198971i	$-0.936240\pi$
$383$	−12.9618	−	22.4505i	−0.662317	−	1.14717i	0.317689	−	0.948195i	$-0.397093\pi$
$384$		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	−0.429622	−	0.903009i	$-0.641353\pi$
$389$	−6.90667	+	1.85064i	−0.350182	+	0.0938310i	0.0794404	+	0.996840i	$0.474687\pi$
$390$		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	0.229602	−	0.973285i	$-0.426258\pi$
$397$	−14.8178	−	14.8178i	−0.743683	−	0.743683i	−0.973285	+	0.229602i	$0.926258\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.39082	−	2.53504i	0.219267	−	0.126594i	−0.386344	−	0.922355i	$-0.626262\pi$
$401$	4.39082	−	2.53504i	0.219267	−	0.126594i	0.605611	+	0.795761i	$0.292929\pi$
$402$		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	0.115199	−	0.993342i	$-0.463250\pi$
$409$	20.8923	−	12.0622i	1.03306	−	0.596436i	0.917859	+	0.396906i	$0.129916\pi$
$410$		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	−0.717985	−	0.696059i	$-0.754935\pi$
$419$	5.15499	−	19.2387i	0.251838	−	0.939871i	0.969822	−	0.243812i	$-0.0783981\pi$
$420$		0			0
$421$	−8.46180	−	31.5799i	−0.412403	−	1.53911i	−0.789981	−	0.613131i	$-0.789910\pi$
$421$	−8.46180	−	31.5799i	−0.412403	−	1.53911i	0.377578	−	0.925978i	$-0.376757\pi$
$422$		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	−0.739168	−	0.673521i	$-0.764781\pi$
$439$	4.47756	−	7.75537i	0.213702	−	0.370143i	0.952870	+	0.303378i	$0.0981144\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.29309	+	19.7541i	0.251482	+	0.938545i	0.970014	+	0.243051i	$0.0781481\pi$
$443$	5.29309	+	19.7541i	0.251482	+	0.938545i	−0.718531	+	0.695495i	$0.755185\pi$
$444$		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	$-0.982371\pi$
$449$		−	2.34595i		−	0.110712i	0.998467	−	0.0553561i	$-0.0176294\pi$
$450$		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	0.943267	−	0.332034i	$-0.107735\pi$
$457$	24.1000	+	13.9141i	1.12735	+	0.650876i	0.184084	+	0.982911i	$0.441068\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−5.15168	−	19.2263i	−0.239937	−	0.895459i	−0.975861	−	0.218394i	$-0.929918\pi$
$461$	−5.15168	−	19.2263i	−0.239937	−	0.895459i	0.735923	−	0.677065i	$-0.236748\pi$
$462$		0			0
$463$	−21.3818	+	12.3448i	−0.993699	+	0.573712i	−0.906378	−	0.422468i	$-0.861164\pi$
$463$	−21.3818	+	12.3448i	−0.993699	+	0.573712i	−0.0873209	+	0.996180i	$0.527831\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−14.0708	−	14.0708i	−0.651120	−	0.651120i	0.302143	−	0.953263i	$-0.402298\pi$
$467$	−14.0708	−	14.0708i	−0.651120	−	0.651120i	−0.953263	+	0.302143i	$0.902298\pi$
$468$		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	0.409551	+	0.912287i	$0.365685\pi$
$479$	−12.8097	+	22.1870i	−0.585288	+	1.01375i	−0.994839	+	0.101462i	$0.967648\pi$
$480$		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	0.957417	−	0.288708i	$-0.0932257\pi$
$491$	36.3890	+	9.75039i	1.64221	+	0.440029i	0.684793	+	0.728737i	$0.259892\pi$
$492$		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	0.679324	−	0.733838i	$-0.262273\pi$
$499$	20.1205	+	5.39127i	0.900717	+	0.241346i	0.221393	+	0.975185i	$0.428940\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			4.55397i			0.203051i	0.994833	+	0.101526i	$0.0323724\pi$
$503$			4.55397i			0.203051i	−0.994833	+	0.101526i	$0.967628\pi$
$504$		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	0.420102	−	0.907477i	$-0.361994\pi$
$509$	7.44927	+	1.99603i	0.330183	+	0.0884723i	−0.0899191	+	0.995949i	$0.528661\pi$
$510$		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	0.511689	−	0.859171i	$-0.329020\pi$
$523$	−7.94661	−	7.94661i	−0.347481	−	0.347481i	−0.859171	+	0.511689i	$0.829020\pi$
$524$		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	0.999777	+	0.0211185i	$0.00672274\pi$
$541$	23.7454	+	23.7454i	1.02090	+	1.02090i	0.0211185	+	0.999777i	$0.493277\pi$
$542$		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	0.969731	−	0.244175i	$-0.0785171\pi$
$547$	0.183171	+	0.683605i	0.00783185	+	0.0292288i	−0.961899	+	0.273404i	$0.911850\pi$
$548$		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	−0.433322	−	0.901239i	$-0.642659\pi$
$557$	11.0432	−	11.0432i	0.467916	−	0.467916i	0.901239	+	0.433322i	$0.142659\pi$
$558$		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	0.0725616	+	0.997364i	$0.476883\pi$
$563$	−11.6019	+	43.2988i	−0.488961	+	1.82483i	−0.561522	+	0.827462i	$0.689784\pi$
$564$		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	0.476814	+	0.879004i	$0.341792\pi$
$569$	−12.4715	+	21.6013i	−0.522833	+	0.905574i	−0.999647	+	0.0265695i	$0.991542\pi$
$570$		0			0
$571$	−9.27714	+	34.6227i	−0.388236	+	1.44892i	0.444766	+	0.895647i	$0.353287\pi$
$571$	−9.27714	+	34.6227i	−0.388236	+	1.44892i	−0.833002	+	0.553270i	$0.813380\pi$
$572$		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	0.974157	−	0.225873i	$-0.0725235\pi$
$587$	0.425823	+	1.58919i	0.0175756	+	0.0655930i	−0.956581	+	0.291466i	$0.905857\pi$
$588$		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	$0.262503\pi$
$593$			35.7642i			1.46866i	−0.678793	+	0.734329i	$0.737497\pi$
$594$		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	−0.905412	−	0.424535i	$-0.860438\pi$
$599$	−24.2410	+	13.9955i	−0.990460	+	0.571842i	−0.0850481	+	0.996377i	$0.527104\pi$
$600$		0			0
$601$	−9.43704	−	5.44848i	−0.384945	−	0.222248i	0.295023	−	0.955490i	$-0.404673\pi$
$601$	−9.43704	−	5.44848i	−0.384945	−	0.222248i	−0.679968	+	0.733242i	$0.738006\pi$
$602$		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	0.489492	−	0.872008i	$-0.337182\pi$
$607$	36.6954	−	21.1861i	1.48942	−	0.859916i	0.999927	+	0.0120914i	$0.00384892\pi$
$608$		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	−0.435477	−	0.900200i	$-0.643420\pi$
$613$	11.5060	−	11.5060i	0.464722	−	0.464722i	0.900200	+	0.435477i	$0.143420\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.520100	+	0.900840i	0.0209384	+	0.0362665i	0.876305	−	0.481757i	$-0.160001\pi$
$617$	0.520100	+	0.900840i	0.0209384	+	0.0362665i	−0.855366	+	0.518024i	$0.826668\pi$
$618$		0			0
$619$	17.6575	−	4.73131i	0.709714	−	0.190167i	0.114136	−	0.993465i	$-0.463590\pi$
$619$	17.6575	−	4.73131i	0.709714	−	0.190167i	0.595578	+	0.803298i	$0.296923\pi$
$620$		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	0.363323	−	0.931663i	$-0.381642\pi$
$641$	−6.62975	−	3.82769i	−0.261859	−	0.151185i	−0.625182	+	0.780479i	$0.714975\pi$
$642$		0			0
$643$	18.3287	+	4.91116i	0.722813	+	0.193677i	0.601427	−	0.798928i	$-0.294599\pi$
$643$	18.3287	+	4.91116i	0.722813	+	0.193677i	0.121387	+	0.992605i	$0.461266\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1.59451i			0.0626865i	0.999509	+	0.0313432i	$0.00997849\pi$
$647$			1.59451i			0.0626865i	−0.999509	+	0.0313432i	$0.990022\pi$
$648$		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	0.285000	−	0.958527i	$-0.408006\pi$
$653$	1.34296	+	0.359845i	0.0525540	+	0.0140818i	−0.232446	+	0.972609i	$0.574673\pi$
$654$		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	0.333093	−	0.942894i	$-0.391908\pi$
$659$	28.0586	−	7.51827i	1.09301	−	0.292870i	0.759914	+	0.650024i	$0.225241\pi$
$660$		0			0
$661$	−0.302749	−	0.0811214i	−0.0117756	−	0.00315526i	0.252926	−	0.967486i	$-0.418607\pi$
$661$	−0.302749	−	0.0811214i	−0.0117756	−	0.00315526i	−0.264702	+	0.964330i	$0.585274\pi$
$662$		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	0.430595	+	0.902545i	$0.358304\pi$
$673$	−14.6918	+	25.4470i	−0.566329	+	0.980911i	−0.996925	+	0.0783659i	$0.975030\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.06366	−	1.89270i	0.271478	−	0.0727424i	−0.120511	−	0.992712i	$-0.538453\pi$
$677$	7.06366	−	1.89270i	0.271478	−	0.0727424i	0.391990	+	0.919969i	$0.371787\pi$
$678$		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	−0.192123	−	0.981371i	$-0.561537\pi$
$683$	20.6264	−	20.6264i	0.789247	−	0.789247i	0.981371	+	0.192123i	$0.0615374\pi$
$684$		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	0.974249	−	0.225474i	$-0.0723931\pi$
$691$	0.467582	+	1.74504i	0.0177876	+	0.0663844i	−0.956462	+	0.291858i	$0.905726\pi$
$692$		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	−0.199174	+	0.979964i	$0.563826\pi$
$701$	−31.2193	+	31.2193i	−1.17914	+	1.17914i	−0.979964	+	0.199174i	$0.936174\pi$
$702$		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	−0.993986	−	0.109511i	$-0.965071\pi$
$709$	−5.00387	−	18.6747i	−0.187924	−	0.701344i	0.806061	−	0.591832i	$-0.201595\pi$
$710$		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	0.205530	+	0.978651i	$0.434108\pi$
$727$	−20.0812	+	34.7817i	−0.744772	+	1.28998i	−0.950301	+	0.311332i	$0.899225\pi$
$728$		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	0.231811	+	0.972761i	$0.425535\pi$
$733$	−12.3274	+	46.0065i	−0.455324	+	1.69929i	−0.687135	+	0.726530i	$0.741132\pi$
$734$		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	−0.855548	−	0.517723i	$-0.826780\pi$
$739$	−9.18363	+	9.18363i	−0.337825	+	0.337825i	0.517723	+	0.855548i	$0.326780\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−42.0760	+	24.2926i	−1.54362	+	0.891208i	−0.545011	+	0.838429i	$0.683475\pi$
$743$	−42.0760	+	24.2926i	−1.54362	+	0.891208i	−0.998606	+	0.0527792i	$0.983192\pi$
$744$		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	−0.887708	−	0.460406i	$-0.847704\pi$
$751$	−25.5639	+	14.7593i	−0.932839	+	0.538575i	−0.0451310	+	0.998981i	$0.514371\pi$
$752$		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	0.111022	−	0.993818i	$-0.464588\pi$
$757$	30.3982	−	30.3982i	1.10484	−	1.10484i	0.993818	−	0.111022i	$-0.0354123\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.97086	+	5.14568i	0.107694	+	0.186531i	0.914836	−	0.403827i	$-0.132320\pi$
$761$	2.97086	+	5.14568i	0.107694	+	0.186531i	−0.807142	+	0.590357i	$0.798987\pi$
$762$		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	0.737113	−	0.675769i	$-0.236188\pi$
$769$	−6.00863	−	10.4073i	−0.216677	−	0.375295i	−0.953790	+	0.300474i	$0.902855\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−22.2746	−	22.2746i	−0.801163	−	0.801163i	0.182114	−	0.983277i	$-0.441706\pi$
$773$	−22.2746	−	22.2746i	−0.801163	−	0.801163i	−0.983277	+	0.182114i	$0.941706\pi$
$774$		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	0.363933	−	0.931425i	$-0.381434\pi$
$787$	5.98650	+	1.60408i	0.213396	+	0.0571792i	−0.150537	+	0.988604i	$0.548100\pi$
$788$		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	−0.380993	−	0.924578i	$-0.624418\pi$
$797$	−33.1217	−	8.87494i	−1.17323	−	0.314367i	−0.792239	+	0.610211i	$0.791085\pi$
$798$		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	0.926086	+	0.377314i	$0.123152\pi$
$811$	37.1183	+	37.1183i	1.30340	+	1.30340i	0.377314	+	0.926086i	$0.376848\pi$
$812$		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	−0.699040	−	0.715083i	$-0.746389\pi$
$821$	−27.1312	+	7.26977i	−0.946884	+	0.253717i	−0.247844	+	0.968800i	$0.579722\pi$
$822$		0			0
$823$	−9.61847	−	16.6597i	−0.335279	−	0.580720i	0.648260	−	0.761419i	$-0.275497\pi$
$823$	−9.61847	−	16.6597i	−0.335279	−	0.580720i	−0.983538	+	0.180700i	$0.942164\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.7848	−	28.7848i	1.00095	−	1.00095i	0.000945916	−	1.00000i	$-0.499699\pi$
$827$	28.7848	−	28.7848i	1.00095	−	1.00095i	1.00000		0.000945916i	$-0.000301094\pi$
$828$		0			0
$829$	−23.5696	−	23.5696i	−0.818606	−	0.818606i	0.167300	−	0.985906i	$-0.446495\pi$
$829$	−23.5696	−	23.5696i	−0.818606	−	0.818606i	−0.985906	+	0.167300i	$0.946495\pi$
$830$		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	0.596251	−	0.802798i	$-0.296656\pi$
$839$	5.76796	+	3.33013i	0.199132	+	0.114969i	−0.397119	+	0.917767i	$0.629990\pi$
$840$		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	0.897022	−	0.441985i	$-0.145726\pi$
$853$	−2.94440	−	10.9887i	−0.100814	−	0.376245i	−0.997837	+	0.0657407i	$0.979059\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	15.7885	−	27.3465i	0.539326	−	0.934140i	−0.459615	−	0.888118i	$-0.652013\pi$
$857$	15.7885	−	27.3465i	0.539326	−	0.934140i	0.998940	−	0.0460211i	$-0.0146542\pi$
$858$		0			0
$859$	−7.30262	+	27.2537i	−0.249162	+	0.929886i	0.722084	+	0.691806i	$0.243185\pi$
$859$	−7.30262	+	27.2537i	−0.249162	+	0.929886i	−0.971246	+	0.238080i	$0.923482\pi$
$860$		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	−0.652510	−	0.757780i	$-0.726284\pi$
$877$	8.63165	−	32.2138i	0.291470	−	1.08778i	0.943980	−	0.330001i	$-0.107049\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			10.4223i			0.351136i	0.984467	+	0.175568i	$0.0561763\pi$
$881$			10.4223i			0.351136i	−0.984467	+	0.175568i	$0.943824\pi$
$882$		0			0
$883$	−7.73247	+	7.73247i	−0.260218	+	0.260218i	−0.825143	−	0.564924i	$-0.808905\pi$
$883$	−7.73247	+	7.73247i	−0.260218	+	0.260218i	0.564924	+	0.825143i	$0.308905\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.0565	+	12.7343i	−0.740584	+	0.427577i	−0.822282	−	0.569081i	$-0.807299\pi$
$887$	−22.0565	+	12.7343i	−0.740584	+	0.427577i	0.0816974	+	0.996657i	$0.473966\pi$
$888$		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	−0.791202	−	0.611555i	$-0.790544\pi$
$907$	−35.2550	+	9.44656i	−1.17062	+	0.313668i	−0.379423	+	0.925223i	$0.623877\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−4.86150	+	8.42037i	−0.161069	+	0.278979i	−0.935252	−	0.353982i	$-0.884827\pi$
$911$	−4.86150	+	8.42037i	−0.161069	+	0.278979i	0.774183	+	0.632961i	$0.218161\pi$
$912$		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	0.115547	−	0.993302i	$-0.463138\pi$
$929$	−20.9365	−	12.0877i	−0.686904	−	0.396584i	−0.802451	+	0.596718i	$0.796471\pi$
$930$		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	$0.00694434\pi$
$937$			1.33551i			0.0436291i	−0.999762	+	0.0218146i	$0.993056\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−21.3261	−	5.71431i	−0.695211	−	0.186281i	−0.106126	−	0.994353i	$-0.533845\pi$
$941$	−21.3261	−	5.71431i	−0.695211	−	0.186281i	−0.589085	+	0.808071i	$0.700512\pi$
$942$		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	0.143421	−	0.989662i	$-0.454190\pi$
$947$	23.4634	−	6.28700i	0.762458	−	0.204300i	0.619037	+	0.785362i	$0.287523\pi$
$948$		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	0.999576	+	0.0291241i	$0.00927179\pi$
$967$	16.3260	+	28.2775i	0.525010	+	0.909344i	−0.474566	+	0.880220i	$0.657395\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−23.6028	+	23.6028i	−0.757449	+	0.757449i	−0.975858	−	0.218408i	$-0.929914\pi$
$971$	−23.6028	+	23.6028i	−0.757449	+	0.757449i	0.218408	+	0.975858i	$0.429914\pi$
$972$		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	−0.898662	−	0.438641i	$-0.855460\pi$
$977$	−30.2605	+	17.4709i	−0.968119	+	0.558944i	−0.0694570	+	0.997585i	$0.522127\pi$
$978$		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	−0.0360492	−	0.999350i	$-0.511477\pi$
$983$	−28.8301	−	16.6450i	−0.919536	−	0.530895i	−0.883487	+	0.468455i	$0.844811\pi$
$984$		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	$0.0531482\pi$
$991$			10.4637i			0.332390i	−0.986093	+	0.166195i	$0.946852\pi$
$992$		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	0.977363	+	0.211571i	$0.0678580\pi$
$997$	7.47474	+	27.8961i	0.236727	+	0.883479i	−0.740635	+	0.671907i	$0.765475\pi$
$998$		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.1007.8		88
3.2	odd	2		576.2.y.a.47.4		88
4.3	odd	2		432.2.v.a.35.16		88
9.4	even	3		576.2.y.a.239.8		88
9.5	odd	6	inner	1728.2.z.a.1583.8		88
12.11	even	2		144.2.u.a.83.7	yes	88
16.5	even	4		432.2.v.a.251.22		88
16.11	odd	4	inner	1728.2.z.a.143.8		88
36.23	even	6		432.2.v.a.179.22		88
36.31	odd	6		144.2.u.a.131.1	yes	88
48.5	odd	4		144.2.u.a.11.1	✓	88
48.11	even	4		576.2.y.a.335.8		88
144.5	odd	12		432.2.v.a.395.16		88
144.59	even	12	inner	1728.2.z.a.719.8		88
144.85	even	12		144.2.u.a.59.7	yes	88
144.139	odd	12		576.2.y.a.527.4		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.1	✓	88	48.5	odd	4
144.2.u.a.59.7	yes	88	144.85	even	12
144.2.u.a.83.7	yes	88	12.11	even	2
144.2.u.a.131.1	yes	88	36.31	odd	6
432.2.v.a.35.16		88	4.3	odd	2
432.2.v.a.179.22		88	36.23	even	6
432.2.v.a.251.22		88	16.5	even	4
432.2.v.a.395.16		88	144.5	odd	12
576.2.y.a.47.4		88	3.2	odd	2
576.2.y.a.239.8		88	9.4	even	3
576.2.y.a.335.8		88	48.11	even	4
576.2.y.a.527.4		88	144.139	odd	12
1728.2.z.a.143.8		88	16.11	odd	4	inner
1728.2.z.a.719.8		88	144.59	even	12	inner
1728.2.z.a.1007.8		88	1.1	even	1	trivial
1728.2.z.a.1583.8		88	9.5	odd	6	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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