LMFDB - Embedded newform 1152.2.p.a.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(191,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("1152.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1152.191
Dual form			1152.2.p.a.959.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 0.866025i) q^{3} +(-1.41421 - 2.44949i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.41421 - 2.44949i) q^{5} +(1.50000 + 2.59808i) q^{9} +(4.50000 + 2.59808i) q^{11} +(4.24264 - 2.44949i) q^{13} +4.89898i q^{15} +1.73205i q^{17} -3.00000 q^{19} +(4.24264 + 7.34847i) q^{23} +(-1.50000 + 2.59808i) q^{25} -5.19615i q^{27} +(2.82843 - 4.89898i) q^{29} +(-4.50000 - 7.79423i) q^{33} -4.89898i q^{37} -8.48528 q^{39} +(4.50000 - 2.59808i) q^{41} +(-4.50000 + 7.79423i) q^{43} +(4.24264 - 7.34847i) q^{45} +(4.24264 - 7.34847i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(1.50000 - 2.59808i) q^{51} +5.65685 q^{53} -14.6969i q^{55} +(4.50000 + 2.59808i) q^{57} +(4.50000 - 2.59808i) q^{59} +(-8.48528 - 4.89898i) q^{61} +(-12.0000 - 6.92820i) q^{65} +(1.50000 + 2.59808i) q^{67} -14.6969i q^{69} +8.48528 q^{71} +5.00000 q^{73} +(4.50000 - 2.59808i) q^{75} +(-12.7279 - 7.34847i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-9.00000 - 5.19615i) q^{83} +(4.24264 - 2.44949i) q^{85} +(-8.48528 + 4.89898i) q^{87} +13.8564i q^{89} +(4.24264 + 7.34847i) q^{95} +(0.500000 - 0.866025i) q^{97} +15.5885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 6 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 6 * q^9	$ 4 q - 6 q^{3} + 6 q^{9} + 18 q^{11} - 12 q^{19} - 6 q^{25} - 18 q^{33} + 18 q^{41} - 18 q^{43} - 14 q^{49} + 6 q^{51} + 18 q^{57} + 18 q^{59} - 48 q^{65} + 6 q^{67} + 20 q^{73} + 18 q^{75} - 18 q^{81} - 36 q^{83} + 2 q^{97}+O(q^{100}) $ 4 * q - 6 * q^3 + 6 * q^9 + 18 * q^11 - 12 * q^19 - 6 * q^25 - 18 * q^33 + 18 * q^41 - 18 * q^43 - 14 * q^49 + 6 * q^51 + 18 * q^57 + 18 * q^59 - 48 * q^65 + 6 * q^67 + 20 * q^73 + 18 * q^75 - 18 * q^81 - 36 * q^83 + 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$3$	−1.50000	−	0.866025i	−0.866025	−	0.500000i
$4$		0			0
$5$	−1.41421	−	2.44949i	−0.632456	−	1.09545i	−0.987048	−	0.160424i	$-0.948714\pi$
$5$	−1.41421	−	2.44949i	−0.632456	−	1.09545i	0.354593	−	0.935021i	$-0.384620\pi$
$6$		0			0
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$		0			0
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	4.50000	+	2.59808i	1.35680	+	0.783349i	0.989191	−	0.146631i	$-0.0468429\pi$
$11$	4.50000	+	2.59808i	1.35680	+	0.783349i	0.367610	+	0.929980i	$0.380176\pi$
$12$		0			0
$13$	4.24264	−	2.44949i	1.17670	−	0.679366i	0.221449	−	0.975172i	$-0.428921\pi$
$13$	4.24264	−	2.44949i	1.17670	−	0.679366i	0.955248	+	0.295806i	$0.0955881\pi$
$14$		0			0
$15$			4.89898i			1.26491i
$16$		0			0
$17$			1.73205i			0.420084i	0.977692	+	0.210042i	$0.0673601\pi$
$17$			1.73205i			0.420084i	−0.977692	+	0.210042i	$0.932640\pi$
$18$		0			0
$19$	−3.00000			−0.688247			−0.344124	−	0.938924i	$-0.611824\pi$
$19$	−3.00000			−0.688247			−0.344124	+	0.938924i	$0.611824\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.24264	+	7.34847i	0.884652	+	1.53226i	0.846112	+	0.533005i	$0.178937\pi$
$23$	4.24264	+	7.34847i	0.884652	+	1.53226i	0.0385394	+	0.999257i	$0.487729\pi$
$24$		0			0
$25$	−1.50000	+	2.59808i	−0.300000	+	0.519615i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	2.82843	−	4.89898i	0.525226	−	0.909718i	−0.474343	−	0.880340i	$-0.657314\pi$
$29$	2.82843	−	4.89898i	0.525226	−	0.909718i	0.999568	−	0.0293774i	$-0.00935245\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$		0			0
$33$	−4.50000	−	7.79423i	−0.783349	−	1.35680i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	4.89898i		−	0.805387i	−0.915335	−	0.402694i	$-0.868074\pi$
$37$		−	4.89898i		−	0.805387i	0.915335	−	0.402694i	$-0.131926\pi$
$38$		0			0
$39$	−8.48528			−1.35873
$40$		0			0
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$		0			0
$43$	−4.50000	+	7.79423i	−0.686244	+	1.18861i	0.286801	+	0.957990i	$0.407408\pi$
$43$	−4.50000	+	7.79423i	−0.686244	+	1.18861i	−0.973044	+	0.230618i	$0.925925\pi$
$44$		0			0
$45$	4.24264	−	7.34847i	0.632456	−	1.09545i
$46$		0			0
$47$	4.24264	−	7.34847i	0.618853	−	1.07188i	−0.370843	−	0.928696i	$-0.620931\pi$
$47$	4.24264	−	7.34847i	0.618853	−	1.07188i	0.989695	−	0.143189i	$-0.0457356\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$		0			0
$53$	5.65685			0.777029			0.388514	−	0.921443i	$-0.372988\pi$
$53$	5.65685			0.777029			0.388514	+	0.921443i	$0.372988\pi$
$54$		0			0
$55$		−	14.6969i		−	1.98173i
$56$		0			0
$57$	4.50000	+	2.59808i	0.596040	+	0.344124i
$58$		0			0
$59$	4.50000	−	2.59808i	0.585850	−	0.338241i	−0.177605	−	0.984102i	$-0.556835\pi$
$59$	4.50000	−	2.59808i	0.585850	−	0.338241i	0.763455	+	0.645861i	$0.223502\pi$
$60$		0			0
$61$	−8.48528	−	4.89898i	−1.08643	−	0.627250i	−0.153806	−	0.988101i	$-0.549153\pi$
$61$	−8.48528	−	4.89898i	−1.08643	−	0.627250i	−0.932623	+	0.360851i	$0.882486\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−12.0000	−	6.92820i	−1.48842	−	0.859338i
$66$		0			0
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$		0			0
$69$		−	14.6969i		−	1.76930i
$70$		0			0
$71$	8.48528			1.00702			0.503509	−	0.863990i	$-0.332042\pi$
$71$	8.48528			1.00702			0.503509	+	0.863990i	$0.332042\pi$
$72$		0			0
$73$	5.00000			0.585206			0.292603	−	0.956234i	$-0.405479\pi$
$73$	5.00000			0.585206			0.292603	+	0.956234i	$0.405479\pi$
$74$		0			0
$75$	4.50000	−	2.59808i	0.519615	−	0.300000i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−12.7279	−	7.34847i	−1.43200	−	0.826767i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	−12.7279	−	7.34847i	−1.43200	−	0.826767i	−0.997274	+	0.0737937i	$0.976489\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−9.00000	−	5.19615i	−0.987878	−	0.570352i	−0.0832389	−	0.996530i	$-0.526526\pi$
$83$	−9.00000	−	5.19615i	−0.987878	−	0.570352i	−0.904639	+	0.426178i	$0.859860\pi$
$84$		0			0
$85$	4.24264	−	2.44949i	0.460179	−	0.265684i
$86$		0			0
$87$	−8.48528	+	4.89898i	−0.909718	+	0.525226i
$88$		0			0
$89$			13.8564i			1.46878i	0.678730	+	0.734388i	$0.262531\pi$
$89$			13.8564i			1.46878i	−0.678730	+	0.734388i	$0.737469\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.24264	+	7.34847i	0.435286	+	0.753937i
$96$		0			0
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	−0.839525	−	0.543321i	$-0.817167\pi$
$97$	0.500000	−	0.866025i	0.0507673	−	0.0879316i	0.890292	+	0.455389i	$0.150500\pi$
$98$		0			0
$99$			15.5885i			1.56670i
$100$		0			0
$101$	1.41421	−	2.44949i	0.140720	−	0.243733i	−0.787048	−	0.616891i	$-0.788392\pi$
$101$	1.41421	−	2.44949i	0.140720	−	0.243733i	0.927768	+	0.373158i	$0.121725\pi$
$102$		0			0
$103$	12.7279	−	7.34847i	1.25412	−	0.724066i	0.282194	−	0.959357i	$-0.408938\pi$
$103$	12.7279	−	7.34847i	1.25412	−	0.724066i	0.971925	+	0.235291i	$0.0756043\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			5.19615i			0.502331i	0.967944	+	0.251166i	$0.0808138\pi$
$107$			5.19615i			0.502331i	−0.967944	+	0.251166i	$0.919186\pi$
$108$		0			0
$109$			9.79796i			0.938474i	0.883072	+	0.469237i	$0.155471\pi$
$109$			9.79796i			0.938474i	−0.883072	+	0.469237i	$0.844529\pi$
$110$		0			0
$111$	−4.24264	+	7.34847i	−0.402694	+	0.697486i
$112$		0			0
$113$	12.0000	−	6.92820i	1.12887	−	0.651751i	0.185216	−	0.982698i	$-0.440702\pi$
$113$	12.0000	−	6.92820i	1.12887	−	0.651751i	0.943649	+	0.330947i	$0.107368\pi$
$114$		0			0
$115$	12.0000	−	20.7846i	1.11901	−	1.93817i
$116$		0			0
$117$	12.7279	+	7.34847i	1.17670	+	0.679366i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	8.00000	+	13.8564i	0.727273	+	1.25967i
$122$		0			0
$123$	−9.00000			−0.811503
$124$		0			0
$125$	−5.65685			−0.505964
$126$		0			0
$127$		−	14.6969i		−	1.30414i	−0.758158	−	0.652071i	$-0.773900\pi$
$127$		−	14.6969i		−	1.30414i	0.758158	−	0.652071i	$-0.226100\pi$
$128$		0			0
$129$	13.5000	−	7.79423i	1.18861	−	0.686244i
$130$		0			0
$131$	−9.00000	+	5.19615i	−0.786334	+	0.453990i	−0.838670	−	0.544640i	$-0.816666\pi$
$131$	−9.00000	+	5.19615i	−0.786334	+	0.453990i	0.0523366	+	0.998630i	$0.483333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−12.7279	+	7.34847i	−1.09545	+	0.632456i
$136$		0			0
$137$	7.50000	+	4.33013i	0.640768	+	0.369948i	0.784910	−	0.619609i	$-0.212709\pi$
$137$	7.50000	+	4.33013i	0.640768	+	0.369948i	−0.144142	+	0.989557i	$0.546042\pi$
$138$		0			0
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	0.609618	−	0.792695i	$-0.291323\pi$
$139$	−4.50000	−	7.79423i	−0.381685	−	0.661098i	−0.991303	+	0.131597i	$0.957989\pi$
$140$		0			0
$141$	−12.7279	+	7.34847i	−1.07188	+	0.618853i
$142$		0			0
$143$	25.4558			2.12872
$144$		0			0
$145$	−16.0000			−1.32873
$146$		0			0
$147$			12.1244i			1.00000i
$148$		0			0
$149$	−1.41421	−	2.44949i	−0.115857	−	0.200670i	0.802265	−	0.596968i	$-0.203628\pi$
$149$	−1.41421	−	2.44949i	−0.115857	−	0.200670i	−0.918122	+	0.396298i	$0.870295\pi$
$150$		0			0
$151$	−12.7279	−	7.34847i	−1.03578	−	0.598010i	−0.117147	−	0.993115i	$-0.537375\pi$
$151$	−12.7279	−	7.34847i	−1.03578	−	0.598010i	−0.918636	+	0.395105i	$0.870708\pi$
$152$		0			0
$153$	−4.50000	+	2.59808i	−0.363803	+	0.210042i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	16.9706	−	9.79796i	1.35440	−	0.781962i	0.365536	−	0.930797i	$-0.380886\pi$
$157$	16.9706	−	9.79796i	1.35440	−	0.781962i	0.988862	+	0.148835i	$0.0475523\pi$
$158$		0			0
$159$	−8.48528	−	4.89898i	−0.672927	−	0.388514i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	24.0000			1.87983			0.939913	−	0.341415i	$-0.110906\pi$
$163$	24.0000			1.87983			0.939913	+	0.341415i	$0.110906\pi$
$164$		0			0
$165$	−12.7279	+	22.0454i	−0.990867	+	1.71623i
$166$		0			0
$167$	4.24264	+	7.34847i	0.328305	+	0.568642i	0.982176	−	0.187965i	$-0.0601892\pi$
$167$	4.24264	+	7.34847i	0.328305	+	0.568642i	−0.653870	+	0.756607i	$0.726856\pi$
$168$		0			0
$169$	5.50000	−	9.52628i	0.423077	−	0.732791i
$170$		0			0
$171$	−4.50000	−	7.79423i	−0.344124	−	0.596040i
$172$		0			0
$173$	−2.82843	+	4.89898i	−0.215041	+	0.372463i	−0.953285	−	0.302071i	$-0.902322\pi$
$173$	−2.82843	+	4.89898i	−0.215041	+	0.372463i	0.738244	+	0.674534i	$0.235655\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.00000			−0.676481
$178$		0			0
$179$		−	10.3923i		−	0.776757i	−0.921500	−	0.388379i	$-0.873035\pi$
$179$		−	10.3923i		−	0.776757i	0.921500	−	0.388379i	$-0.126965\pi$
$180$		0			0
$181$			14.6969i			1.09241i	0.837650	+	0.546207i	$0.183929\pi$
$181$			14.6969i			1.09241i	−0.837650	+	0.546207i	$0.816071\pi$
$182$		0			0
$183$	8.48528	+	14.6969i	0.627250	+	1.08643i
$184$		0			0
$185$	−12.0000	+	6.92820i	−0.882258	+	0.509372i
$186$		0			0
$187$	−4.50000	+	7.79423i	−0.329073	+	0.569970i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.48528	+	14.6969i	−0.613973	+	1.06343i	0.376590	+	0.926380i	$0.377096\pi$
$191$	−8.48528	+	14.6969i	−0.613973	+	1.06343i	−0.990564	+	0.137053i	$0.956237\pi$
$192$		0			0
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	0.847469	−	0.530845i	$-0.178125\pi$
$193$	−0.500000	−	0.866025i	−0.0359908	−	0.0623379i	−0.883460	+	0.468507i	$0.844792\pi$
$194$		0			0
$195$	12.0000	+	20.7846i	0.859338	+	1.48842i
$196$		0			0
$197$	−11.3137			−0.806068			−0.403034	−	0.915185i	$-0.632044\pi$
$197$	−11.3137			−0.806068			−0.403034	+	0.915185i	$0.632044\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$		−	5.19615i		−	0.366508i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−12.7279	−	7.34847i	−0.888957	−	0.513239i
$206$		0			0
$207$	−12.7279	+	22.0454i	−0.884652	+	1.53226i
$208$		0			0
$209$	−13.5000	−	7.79423i	−0.933815	−	0.539138i
$210$		0			0
$211$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$211$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$212$		0			0
$213$	−12.7279	−	7.34847i	−0.872103	−	0.503509i
$214$		0			0
$215$	25.4558			1.73607
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.50000	−	4.33013i	−0.506803	−	0.292603i
$220$		0			0
$221$	4.24264	+	7.34847i	0.285391	+	0.494312i
$222$		0			0
$223$	12.7279	+	7.34847i	0.852325	+	0.492090i	0.861435	−	0.507869i	$-0.169566\pi$
$223$	12.7279	+	7.34847i	0.852325	+	0.492090i	−0.00910984	+	0.999959i	$0.502900\pi$
$224$		0			0
$225$	−9.00000			−0.600000
$226$		0			0
$227$	−13.5000	−	7.79423i	−0.896026	−	0.517321i	−0.0201176	−	0.999798i	$-0.506404\pi$
$227$	−13.5000	−	7.79423i	−0.896026	−	0.517321i	−0.875909	+	0.482476i	$0.839737\pi$
$228$		0			0
$229$	−8.48528	+	4.89898i	−0.560723	+	0.323734i	−0.753436	−	0.657522i	$-0.771605\pi$
$229$	−8.48528	+	4.89898i	−0.560723	+	0.323734i	0.192713	+	0.981255i	$0.438272\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	22.5167i		−	1.47512i	−0.675284	−	0.737558i	$-0.735979\pi$
$233$		−	22.5167i		−	1.47512i	0.675284	−	0.737558i	$-0.264021\pi$
$234$		0			0
$235$	−24.0000			−1.56559
$236$		0			0
$237$	12.7279	+	22.0454i	0.826767	+	1.43200i
$238$		0			0
$239$	4.24264	+	7.34847i	0.274434	+	0.475333i	0.969992	−	0.243137i	$-0.0781763\pi$
$239$	4.24264	+	7.34847i	0.274434	+	0.475333i	−0.695558	+	0.718470i	$0.744843\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$		0			0
$243$	13.5000	−	7.79423i	0.866025	−	0.500000i
$244$		0			0
$245$	−9.89949	+	17.1464i	−0.632456	+	1.09545i
$246$		0			0
$247$	−12.7279	+	7.34847i	−0.809858	+	0.467572i
$248$		0			0
$249$	9.00000	+	15.5885i	0.570352	+	0.987878i
$250$		0			0
$251$		−	5.19615i		−	0.327978i	−0.986462	−	0.163989i	$-0.947564\pi$
$251$		−	5.19615i		−	0.327978i	0.986462	−	0.163989i	$-0.0524362\pi$
$252$		0			0
$253$			44.0908i			2.77197i
$254$		0			0
$255$	−8.48528			−0.531369
$256$		0			0
$257$	1.50000	−	0.866025i	0.0935674	−	0.0540212i	−0.452486	−	0.891771i	$-0.649463\pi$
$257$	1.50000	−	0.866025i	0.0935674	−	0.0540212i	0.546054	+	0.837750i	$0.316129\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	16.9706			1.05045
$262$		0			0
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$	−8.00000	−	13.8564i	−0.491436	−	0.851192i
$266$		0			0
$267$	12.0000	−	20.7846i	0.734388	−	1.27200i
$268$		0			0
$269$	11.3137			0.689809			0.344904	−	0.938638i	$-0.387911\pi$
$269$	11.3137			0.689809			0.344904	+	0.938638i	$0.387911\pi$
$270$		0			0
$271$		−	29.3939i		−	1.78555i	−0.450502	−	0.892775i	$-0.648755\pi$
$271$		−	29.3939i		−	1.78555i	0.450502	−	0.892775i	$-0.351245\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−13.5000	+	7.79423i	−0.814081	+	0.470010i
$276$		0			0
$277$	−12.7279	−	7.34847i	−0.764747	−	0.441527i	0.0662507	−	0.997803i	$-0.478896\pi$
$277$	−12.7279	−	7.34847i	−0.764747	−	0.441527i	−0.830997	+	0.556276i	$0.812230\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	0.813227	−	0.581947i	$-0.197709\pi$
$281$	12.0000	+	6.92820i	0.715860	+	0.413302i	−0.0973670	+	0.995249i	$0.531042\pi$
$282$		0			0
$283$	12.0000	+	20.7846i	0.713326	+	1.23552i	0.963602	+	0.267342i	$0.0861454\pi$
$283$	12.0000	+	20.7846i	0.713326	+	1.23552i	−0.250276	+	0.968175i	$0.580521\pi$
$284$		0			0
$285$		−	14.6969i		−	0.870572i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	14.0000			0.823529
$290$		0			0
$291$	−1.50000	+	0.866025i	−0.0879316	+	0.0507673i
$292$		0			0
$293$	14.1421	+	24.4949i	0.826192	+	1.43101i	0.901005	+	0.433810i	$0.142831\pi$
$293$	14.1421	+	24.4949i	0.826192	+	1.43101i	−0.0748122	+	0.997198i	$0.523836\pi$
$294$		0			0
$295$	−12.7279	−	7.34847i	−0.741048	−	0.427844i
$296$		0			0
$297$	13.5000	−	23.3827i	0.783349	−	1.35680i
$298$		0			0
$299$	36.0000	+	20.7846i	2.08193	+	1.20201i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4.24264	+	2.44949i	−0.243733	+	0.140720i
$304$		0			0
$305$			27.7128i			1.58683i
$306$		0			0
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$		0			0
$309$	−25.4558			−1.44813
$310$		0			0
$311$	−8.48528	−	14.6969i	−0.481156	−	0.833387i	0.518610	−	0.855011i	$-0.326450\pi$
$311$	−8.48528	−	14.6969i	−0.481156	−	0.833387i	−0.999766	+	0.0216240i	$0.993116\pi$
$312$		0			0
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	0.0863973	+	0.996261i	$0.472465\pi$
$313$	−14.5000	+	25.1147i	−0.819588	+	1.41957i	−0.905986	+	0.423308i	$0.860869\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.89949	+	17.1464i	−0.556011	+	0.963039i	0.441813	+	0.897107i	$0.354335\pi$
$317$	−9.89949	+	17.1464i	−0.556011	+	0.963039i	−0.997824	+	0.0659322i	$0.978998\pi$
$318$		0			0
$319$	25.4558	−	14.6969i	1.42525	−	0.822871i
$320$		0			0
$321$	4.50000	−	7.79423i	0.251166	−	0.435031i
$322$		0			0
$323$		−	5.19615i		−	0.289122i
$324$		0			0
$325$			14.6969i			0.815239i
$326$		0			0
$327$	8.48528	−	14.6969i	0.469237	−	0.812743i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−12.0000	+	20.7846i	−0.659580	+	1.14243i	0.321145	+	0.947030i	$0.395932\pi$
$331$	−12.0000	+	20.7846i	−0.659580	+	1.14243i	−0.980725	+	0.195395i	$0.937401\pi$
$332$		0			0
$333$	12.7279	−	7.34847i	0.697486	−	0.402694i
$334$		0			0
$335$	4.24264	−	7.34847i	0.231800	−	0.401490i
$336$		0			0
$337$	11.5000	+	19.9186i	0.626445	+	1.08503i	0.988260	+	0.152784i	$0.0488240\pi$
$337$	11.5000	+	19.9186i	0.626445	+	1.08503i	−0.361815	+	0.932250i	$0.617843\pi$
$338$		0			0
$339$	−24.0000			−1.30350
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−36.0000	+	20.7846i	−1.93817	+	1.11901i
$346$		0			0
$347$	31.5000	−	18.1865i	1.69101	−	0.976304i	0.737303	−	0.675562i	$-0.236099\pi$
$347$	31.5000	−	18.1865i	1.69101	−	0.976304i	0.953705	−	0.300742i	$-0.0972344\pi$
$348$		0			0
$349$	−25.4558	−	14.6969i	−1.36262	−	0.786709i	−0.372648	−	0.927973i	$-0.621550\pi$
$349$	−25.4558	−	14.6969i	−1.36262	−	0.786709i	−0.989972	+	0.141264i	$0.954883\pi$
$350$		0			0
$351$	−12.7279	−	22.0454i	−0.679366	−	1.17670i
$352$		0			0
$353$	22.5000	+	12.9904i	1.19755	+	0.691408i	0.960009	−	0.279968i	$-0.0903240\pi$
$353$	22.5000	+	12.9904i	1.19755	+	0.691408i	0.237545	+	0.971377i	$0.423657\pi$
$354$		0			0
$355$	−12.0000	−	20.7846i	−0.636894	−	1.10313i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−16.9706			−0.895672			−0.447836	−	0.894116i	$-0.647805\pi$
$359$	−16.9706			−0.895672			−0.447836	+	0.894116i	$0.647805\pi$
$360$		0			0
$361$	−10.0000			−0.526316
$362$		0			0
$363$		−	27.7128i		−	1.45455i
$364$		0			0
$365$	−7.07107	−	12.2474i	−0.370117	−	0.641061i
$366$		0			0
$367$	−12.7279	−	7.34847i	−0.664392	−	0.383587i	0.129556	−	0.991572i	$-0.458645\pi$
$367$	−12.7279	−	7.34847i	−0.664392	−	0.383587i	−0.793948	+	0.607985i	$0.791978\pi$
$368$		0			0
$369$	13.5000	+	7.79423i	0.702782	+	0.405751i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	12.7279	−	7.34847i	0.659027	−	0.380489i	−0.132879	−	0.991132i	$-0.542422\pi$
$373$	12.7279	−	7.34847i	0.659027	−	0.380489i	0.791906	+	0.610643i	$0.209089\pi$
$374$		0			0
$375$	8.48528	+	4.89898i	0.438178	+	0.252982i
$376$		0			0
$377$		−	27.7128i		−	1.42728i
$378$		0			0
$379$	−15.0000			−0.770498			−0.385249	−	0.922813i	$-0.625884\pi$
$379$	−15.0000			−0.770498			−0.385249	+	0.922813i	$0.625884\pi$
$380$		0			0
$381$	−12.7279	+	22.0454i	−0.652071	+	1.12942i
$382$		0			0
$383$	4.24264	+	7.34847i	0.216789	+	0.375489i	0.953824	−	0.300365i	$-0.0971084\pi$
$383$	4.24264	+	7.34847i	0.216789	+	0.375489i	−0.737036	+	0.675854i	$0.763775\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−27.0000			−1.37249
$388$		0			0
$389$	11.3137	−	19.5959i	0.573628	−	0.993552i	−0.422561	−	0.906334i	$-0.638869\pi$
$389$	11.3137	−	19.5959i	0.573628	−	0.993552i	0.996189	−	0.0872182i	$-0.0277977\pi$
$390$		0			0
$391$	−12.7279	+	7.34847i	−0.643679	+	0.371628i
$392$		0			0
$393$	18.0000			0.907980
$394$		0			0
$395$			41.5692i			2.09157i
$396$		0			0
$397$		−	4.89898i		−	0.245873i	−0.992415	−	0.122936i	$-0.960769\pi$
$397$		−	4.89898i		−	0.245873i	0.992415	−	0.122936i	$-0.0392311\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.5000	+	6.06218i	−0.524345	+	0.302731i	−0.738711	−	0.674023i	$-0.764565\pi$
$401$	−10.5000	+	6.06218i	−0.524345	+	0.302731i	0.214366	+	0.976753i	$0.431232\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	25.4558			1.26491
$406$		0			0
$407$	12.7279	−	22.0454i	0.630900	−	1.09275i
$408$		0			0
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$410$		0			0
$411$	−7.50000	−	12.9904i	−0.369948	−	0.640768i
$412$		0			0
$413$		0			0
$414$		0			0
$415$			29.3939i			1.44289i
$416$		0			0
$417$			15.5885i			0.763370i
$418$		0			0
$419$	9.00000	−	5.19615i	0.439679	−	0.253849i	−0.263783	−	0.964582i	$-0.584970\pi$
$419$	9.00000	−	5.19615i	0.439679	−	0.253849i	0.703461	+	0.710734i	$0.251637\pi$
$420$		0			0
$421$	4.24264	+	2.44949i	0.206774	+	0.119381i	0.599811	−	0.800142i	$-0.295242\pi$
$421$	4.24264	+	2.44949i	0.206774	+	0.119381i	−0.393037	+	0.919522i	$0.628576\pi$
$422$		0			0
$423$	25.4558			1.23771
$424$		0			0
$425$	−4.50000	−	2.59808i	−0.218282	−	0.126025i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−38.1838	−	22.0454i	−1.84353	−	1.06436i
$430$		0			0
$431$	−16.9706			−0.817443			−0.408722	−	0.912659i	$-0.634025\pi$
$431$	−16.9706			−0.817443			−0.408722	+	0.912659i	$0.634025\pi$
$432$		0			0
$433$	31.0000			1.48976			0.744882	−	0.667196i	$-0.232506\pi$
$433$	31.0000			1.48976			0.744882	+	0.667196i	$0.232506\pi$
$434$		0			0
$435$	24.0000	+	13.8564i	1.15071	+	0.664364i
$436$		0			0
$437$	−12.7279	−	22.0454i	−0.608859	−	1.05457i
$438$		0			0
$439$	25.4558	+	14.6969i	1.21494	+	0.701447i	0.963832	−	0.266512i	$-0.0858712\pi$
$439$	25.4558	+	14.6969i	1.21494	+	0.701447i	0.251110	+	0.967959i	$0.419205\pi$
$440$		0			0
$441$	10.5000	−	18.1865i	0.500000	−	0.866025i
$442$		0			0
$443$	4.50000	+	2.59808i	0.213801	+	0.123438i	0.603077	−	0.797683i	$-0.293941\pi$
$443$	4.50000	+	2.59808i	0.213801	+	0.123438i	−0.389275	+	0.921121i	$0.627275\pi$
$444$		0			0
$445$	33.9411	−	19.5959i	1.60896	−	0.928936i
$446$		0			0
$447$			4.89898i			0.231714i
$448$		0			0
$449$		−	15.5885i		−	0.735665i	−0.929892	−	0.367832i	$-0.880100\pi$
$449$		−	15.5885i		−	0.735665i	0.929892	−	0.367832i	$-0.119900\pi$
$450$		0			0
$451$	27.0000			1.27138
$452$		0			0
$453$	12.7279	+	22.0454i	0.598010	+	1.03578i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	14.5000	−	25.1147i	0.678281	−	1.17482i	−0.297217	−	0.954810i	$-0.596058\pi$
$457$	14.5000	−	25.1147i	0.678281	−	1.17482i	0.975498	−	0.220008i	$-0.0706083\pi$
$458$		0			0
$459$	9.00000			0.420084
$460$		0			0
$461$	1.41421	−	2.44949i	0.0658665	−	0.114084i	−0.831212	−	0.555956i	$-0.812352\pi$
$461$	1.41421	−	2.44949i	0.0658665	−	0.114084i	0.897078	+	0.441872i	$0.145686\pi$
$462$		0			0
$463$	−12.7279	+	7.34847i	−0.591517	+	0.341512i	−0.765697	−	0.643201i	$-0.777606\pi$
$463$	−12.7279	+	7.34847i	−0.591517	+	0.341512i	0.174180	+	0.984714i	$0.444272\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			15.5885i			0.721348i	0.932692	+	0.360674i	$0.117453\pi$
$467$			15.5885i			0.721348i	−0.932692	+	0.360674i	$0.882547\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−33.9411			−1.56392
$472$		0			0
$473$	−40.5000	+	23.3827i	−1.86219	+	1.07514i
$474$		0			0
$475$	4.50000	−	7.79423i	0.206474	−	0.357624i
$476$		0			0
$477$	8.48528	+	14.6969i	0.388514	+	0.672927i
$478$		0			0
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−12.0000	−	20.7846i	−0.547153	−	0.947697i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.82843			−0.128432
$486$		0			0
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$		0			0
$489$	−36.0000	−	20.7846i	−1.62798	−	0.939913i
$490$		0			0
$491$	4.50000	−	2.59808i	0.203082	−	0.117250i	−0.395010	−	0.918677i	$-0.629259\pi$
$491$	4.50000	−	2.59808i	0.203082	−	0.117250i	0.598092	+	0.801427i	$0.295926\pi$
$492$		0			0
$493$	8.48528	+	4.89898i	0.382158	+	0.220639i
$494$		0			0
$495$	38.1838	−	22.0454i	1.71623	−	0.990867i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.50000	−	2.59808i	−0.0671492	−	0.116306i	0.830496	−	0.557024i	$-0.188057\pi$
$499$	−1.50000	−	2.59808i	−0.0671492	−	0.116306i	−0.897645	+	0.440719i	$0.854724\pi$
$500$		0			0
$501$		−	14.6969i		−	0.656611i
$502$		0			0
$503$	−33.9411			−1.51336			−0.756680	−	0.653785i	$-0.773180\pi$
$503$	−33.9411			−1.51336			−0.756680	+	0.653785i	$0.773180\pi$
$504$		0			0
$505$	−8.00000			−0.355995
$506$		0			0
$507$	−16.5000	+	9.52628i	−0.732791	+	0.423077i
$508$		0			0
$509$	−5.65685	−	9.79796i	−0.250736	−	0.434287i	0.712993	−	0.701171i	$-0.247339\pi$
$509$	−5.65685	−	9.79796i	−0.250736	−	0.434287i	−0.963729	+	0.266884i	$0.914006\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$			15.5885i			0.688247i
$514$		0			0
$515$	−36.0000	−	20.7846i	−1.58635	−	0.915879i
$516$		0			0
$517$	38.1838	−	22.0454i	1.67932	−	0.969556i
$518$		0			0
$519$	8.48528	−	4.89898i	0.372463	−	0.215041i
$520$		0			0
$521$		−	36.3731i		−	1.59353i	−0.604287	−	0.796766i	$-0.706542\pi$
$521$		−	36.3731i		−	1.59353i	0.604287	−	0.796766i	$-0.293458\pi$
$522$		0			0
$523$	−24.0000			−1.04945			−0.524723	−	0.851273i	$-0.675831\pi$
$523$	−24.0000			−1.04945			−0.524723	+	0.851273i	$0.675831\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−24.5000	+	42.4352i	−1.06522	+	1.84501i
$530$		0			0
$531$	13.5000	+	7.79423i	0.585850	+	0.338241i
$532$		0			0
$533$	12.7279	−	22.0454i	0.551308	−	0.954893i
$534$		0			0
$535$	12.7279	−	7.34847i	0.550276	−	0.317702i
$536$		0			0
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$		0			0
$539$		−	36.3731i		−	1.56670i
$540$		0			0
$541$			4.89898i			0.210624i	0.994439	+	0.105312i	$0.0335841\pi$
$541$			4.89898i			0.210624i	−0.994439	+	0.105312i	$0.966416\pi$
$542$		0			0
$543$	12.7279	−	22.0454i	0.546207	−	0.946059i
$544$		0			0
$545$	24.0000	−	13.8564i	1.02805	−	0.593543i
$546$		0			0
$547$	1.50000	−	2.59808i	0.0641354	−	0.111086i	−0.832175	−	0.554513i	$-0.812904\pi$
$547$	1.50000	−	2.59808i	0.0641354	−	0.111086i	0.896310	+	0.443428i	$0.146238\pi$
$548$		0			0
$549$		−	29.3939i		−	1.25450i
$550$		0			0
$551$	−8.48528	+	14.6969i	−0.361485	+	0.626111i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	24.0000			1.01874
$556$		0			0
$557$	−11.3137			−0.479377			−0.239689	−	0.970850i	$-0.577045\pi$
$557$	−11.3137			−0.479377			−0.239689	+	0.970850i	$0.577045\pi$
$558$		0			0
$559$			44.0908i			1.86484i
$560$		0			0
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$		0			0
$563$	−22.5000	+	12.9904i	−0.948262	+	0.547479i	−0.892541	−	0.450967i	$-0.851079\pi$
$563$	−22.5000	+	12.9904i	−0.948262	+	0.547479i	−0.0557214	+	0.998446i	$0.517746\pi$
$564$		0			0
$565$	−33.9411	−	19.5959i	−1.42791	−	0.824406i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	28.5000	+	16.4545i	1.19478	+	0.689808i	0.959387	−	0.282092i	$-0.0910284\pi$
$569$	28.5000	+	16.4545i	1.19478	+	0.689808i	0.235395	+	0.971900i	$0.424362\pi$
$570$		0			0
$571$	16.5000	+	28.5788i	0.690504	+	1.19599i	0.971673	+	0.236329i	$0.0759443\pi$
$571$	16.5000	+	28.5788i	0.690504	+	1.19599i	−0.281170	+	0.959658i	$0.590722\pi$
$572$		0			0
$573$	25.4558	−	14.6969i	1.06343	−	0.613973i
$574$		0			0
$575$	−25.4558			−1.06158
$576$		0			0
$577$	−31.0000			−1.29055			−0.645273	−	0.763952i	$-0.723257\pi$
$577$	−31.0000			−1.29055			−0.645273	+	0.763952i	$0.723257\pi$
$578$		0			0
$579$			1.73205i			0.0719816i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	25.4558	+	14.6969i	1.05427	+	0.608685i
$584$		0			0
$585$		−	41.5692i		−	1.71868i
$586$		0			0
$587$	−4.50000	−	2.59808i	−0.185735	−	0.107234i	0.404249	−	0.914649i	$-0.367533\pi$
$587$	−4.50000	−	2.59808i	−0.185735	−	0.107234i	−0.589984	+	0.807415i	$0.700866\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	16.9706	+	9.79796i	0.698076	+	0.403034i
$592$		0			0
$593$			27.7128i			1.13803i	0.822328	+	0.569014i	$0.192675\pi$
$593$			27.7128i			1.13803i	−0.822328	+	0.569014i	$0.807325\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$	4.24264	+	7.34847i	0.173350	+	0.300250i	0.939589	−	0.342305i	$-0.111208\pi$
$599$	4.24264	+	7.34847i	0.173350	+	0.300250i	−0.766239	+	0.642555i	$0.777874\pi$
$600$		0			0
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	−0.731774	−	0.681547i	$-0.761308\pi$
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	0.956124	+	0.292962i	$0.0946409\pi$
$602$		0			0
$603$	−4.50000	+	7.79423i	−0.183254	+	0.317406i
$604$		0			0
$605$	22.6274	−	39.1918i	0.919935	−	1.59337i
$606$		0			0
$607$	−25.4558	+	14.6969i	−1.03322	+	0.596530i	−0.917906	−	0.396799i	$-0.870121\pi$
$607$	−25.4558	+	14.6969i	−1.03322	+	0.596530i	−0.115315	+	0.993329i	$0.536788\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	41.5692i		−	1.68171i
$612$		0			0
$613$			14.6969i			0.593604i	0.954939	+	0.296802i	$0.0959201\pi$
$613$			14.6969i			0.593604i	−0.954939	+	0.296802i	$0.904080\pi$
$614$		0			0
$615$	12.7279	+	22.0454i	0.513239	+	0.888957i
$616$		0			0
$617$	−19.5000	+	11.2583i	−0.785040	+	0.453243i	−0.838214	−	0.545342i	$-0.816400\pi$
$617$	−19.5000	+	11.2583i	−0.785040	+	0.453243i	0.0531732	+	0.998585i	$0.483066\pi$
$618$		0			0
$619$	4.50000	−	7.79423i	0.180870	−	0.313276i	−0.761307	−	0.648392i	$-0.775442\pi$
$619$	4.50000	−	7.79423i	0.180870	−	0.313276i	0.942177	+	0.335115i	$0.108775\pi$
$620$		0			0
$621$	38.1838	−	22.0454i	1.53226	−	0.884652i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$		0			0
$627$	13.5000	+	23.3827i	0.539138	+	0.933815i
$628$		0			0
$629$	8.48528			0.338330
$630$		0			0
$631$			44.0908i			1.75523i	0.479368	+	0.877614i	$0.340866\pi$
$631$			44.0908i			1.75523i	−0.479368	+	0.877614i	$0.659134\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−36.0000	+	20.7846i	−1.42862	+	0.824812i
$636$		0			0
$637$	−29.6985	−	17.1464i	−1.17670	−	0.679366i
$638$		0			0
$639$	12.7279	+	22.0454i	0.503509	+	0.872103i
$640$		0			0
$641$	1.50000	+	0.866025i	0.0592464	+	0.0342059i	0.529331	−	0.848416i	$-0.322443\pi$
$641$	1.50000	+	0.866025i	0.0592464	+	0.0342059i	−0.470084	+	0.882622i	$0.655776\pi$
$642$		0			0
$643$	1.50000	+	2.59808i	0.0591542	+	0.102458i	0.894086	−	0.447895i	$-0.147826\pi$
$643$	1.50000	+	2.59808i	0.0591542	+	0.102458i	−0.834932	+	0.550353i	$0.814493\pi$
$644$		0			0
$645$	−38.1838	−	22.0454i	−1.50348	−	0.868037i
$646$		0			0
$647$	−16.9706			−0.667182			−0.333591	−	0.942718i	$-0.608260\pi$
$647$	−16.9706			−0.667182			−0.333591	+	0.942718i	$0.608260\pi$
$648$		0			0
$649$	27.0000			1.05984
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.65685	+	9.79796i	0.221370	+	0.383424i	0.955224	−	0.295883i	$-0.0956139\pi$
$653$	5.65685	+	9.79796i	0.221370	+	0.383424i	−0.733854	+	0.679307i	$0.762281\pi$
$654$		0			0
$655$	25.4558	+	14.6969i	0.994642	+	0.574257i
$656$		0			0
$657$	7.50000	+	12.9904i	0.292603	+	0.506803i
$658$		0			0
$659$	9.00000	+	5.19615i	0.350590	+	0.202413i	0.664945	−	0.746892i	$-0.268455\pi$
$659$	9.00000	+	5.19615i	0.350590	+	0.202413i	−0.314355	+	0.949306i	$0.601788\pi$
$660$		0			0
$661$	21.2132	−	12.2474i	0.825098	−	0.476371i	−0.0270733	−	0.999633i	$-0.508619\pi$
$661$	21.2132	−	12.2474i	0.825098	−	0.476371i	0.852171	+	0.523263i	$0.175285\pi$
$662$		0			0
$663$		−	14.6969i		−	0.570782i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	48.0000			1.85857
$668$		0			0
$669$	−12.7279	−	22.0454i	−0.492090	−	0.852325i
$670$		0			0
$671$	−25.4558	−	44.0908i	−0.982712	−	1.70211i
$672$		0			0
$673$	19.0000	−	32.9090i	0.732396	−	1.26855i	−0.223460	−	0.974713i	$-0.571735\pi$
$673$	19.0000	−	32.9090i	0.732396	−	1.26855i	0.955856	−	0.293834i	$-0.0949314\pi$
$674$		0			0
$675$	13.5000	+	7.79423i	0.519615	+	0.300000i
$676$		0			0
$677$	−14.1421	+	24.4949i	−0.543526	+	0.941415i	0.455172	+	0.890404i	$0.349578\pi$
$677$	−14.1421	+	24.4949i	−0.543526	+	0.941415i	−0.998698	+	0.0510117i	$0.983755\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	13.5000	+	23.3827i	0.517321	+	0.896026i
$682$		0			0
$683$		−	5.19615i		−	0.198825i	−0.995046	−	0.0994126i	$-0.968304\pi$
$683$		−	5.19615i		−	0.198825i	0.995046	−	0.0994126i	$-0.0316964\pi$
$684$		0			0
$685$		−	24.4949i		−	0.935902i
$686$		0			0
$687$	16.9706			0.647467
$688$		0			0
$689$	24.0000	−	13.8564i	0.914327	−	0.527887i
$690$		0			0
$691$	12.0000	−	20.7846i	0.456502	−	0.790684i	−0.542272	−	0.840203i	$-0.682436\pi$
$691$	12.0000	−	20.7846i	0.456502	−	0.790684i	0.998773	+	0.0495194i	$0.0157690\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−12.7279	+	22.0454i	−0.482798	+	0.836230i
$696$		0			0
$697$	4.50000	+	7.79423i	0.170450	+	0.295227i
$698$		0			0
$699$	−19.5000	+	33.7750i	−0.737558	+	1.27749i
$700$		0			0
$701$	36.7696			1.38877			0.694383	−	0.719605i	$-0.255677\pi$
$701$	36.7696			1.38877			0.694383	+	0.719605i	$0.255677\pi$
$702$		0			0
$703$			14.6969i			0.554306i
$704$		0			0
$705$	36.0000	+	20.7846i	1.35584	+	0.782794i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−42.4264	−	24.4949i	−1.59336	−	0.919925i	−0.992726	−	0.120399i	$-0.961583\pi$
$709$	−42.4264	−	24.4949i	−1.59336	−	0.919925i	−0.600632	−	0.799526i	$-0.705084\pi$
$710$		0			0
$711$		−	44.0908i		−	1.65353i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−36.0000	−	62.3538i	−1.34632	−	2.33190i
$716$		0			0
$717$		−	14.6969i		−	0.548867i
$718$		0			0
$719$	−25.4558			−0.949343			−0.474671	−	0.880163i	$-0.657433\pi$
$719$	−25.4558			−0.949343			−0.474671	+	0.880163i	$0.657433\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−10.5000	+	6.06218i	−0.390499	+	0.225455i
$724$		0			0
$725$	8.48528	+	14.6969i	0.315135	+	0.545831i
$726$		0			0
$727$	−12.7279	−	7.34847i	−0.472052	−	0.272540i	0.245046	−	0.969511i	$-0.421197\pi$
$727$	−12.7279	−	7.34847i	−0.472052	−	0.272540i	−0.717099	+	0.696972i	$0.754530\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−13.5000	−	7.79423i	−0.499316	−	0.288280i
$732$		0			0
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$	29.6985	−	17.1464i	1.09545	−	0.632456i
$736$		0			0
$737$			15.5885i			0.574208i
$738$		0			0
$739$	27.0000			0.993211			0.496606	−	0.867976i	$-0.334580\pi$
$739$	27.0000			0.993211			0.496606	+	0.867976i	$0.334580\pi$
$740$		0			0
$741$	25.4558			0.935144
$742$		0			0
$743$	−8.48528	−	14.6969i	−0.311295	−	0.539178i	0.667348	−	0.744746i	$-0.267429\pi$
$743$	−8.48528	−	14.6969i	−0.311295	−	0.539178i	−0.978643	+	0.205568i	$0.934096\pi$
$744$		0			0
$745$	−4.00000	+	6.92820i	−0.146549	+	0.253830i
$746$		0			0
$747$		−	31.1769i		−	1.14070i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−12.7279	+	7.34847i	−0.464448	+	0.268149i	−0.713913	−	0.700235i	$-0.753079\pi$
$751$	−12.7279	+	7.34847i	−0.464448	+	0.268149i	0.249464	+	0.968384i	$0.419745\pi$
$752$		0			0
$753$	−4.50000	+	7.79423i	−0.163989	+	0.284037i
$754$		0			0
$755$			41.5692i			1.51286i
$756$		0			0
$757$			29.3939i			1.06834i	0.845378	+	0.534169i	$0.179376\pi$
$757$			29.3939i			1.06834i	−0.845378	+	0.534169i	$0.820624\pi$
$758$		0			0
$759$	38.1838	−	66.1362i	1.38598	−	2.40059i
$760$		0			0
$761$	−12.0000	+	6.92820i	−0.435000	+	0.251147i	−0.701474	−	0.712695i	$-0.747474\pi$
$761$	−12.0000	+	6.92820i	−0.435000	+	0.251147i	0.266475	+	0.963842i	$0.414141\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	12.7279	+	7.34847i	0.460179	+	0.265684i
$766$		0			0
$767$	12.7279	−	22.0454i	0.459579	−	0.796014i
$768$		0			0
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	0.999364	−	0.0356685i	$-0.0113561\pi$
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	−0.530572	+	0.847640i	$0.678023\pi$
$770$		0			0
$771$	−3.00000			−0.108042
$772$		0			0
$773$	14.1421			0.508657			0.254329	−	0.967118i	$-0.418146\pi$
$773$	14.1421			0.508657			0.254329	+	0.967118i	$0.418146\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−13.5000	+	7.79423i	−0.483688	+	0.279257i
$780$		0			0
$781$	38.1838	+	22.0454i	1.36632	+	0.788847i
$782$		0			0
$783$	−25.4558	−	14.6969i	−0.909718	−	0.525226i
$784$		0			0
$785$	−48.0000	−	27.7128i	−1.71319	−	0.989113i
$786$		0			0
$787$	12.0000	+	20.7846i	0.427754	+	0.740891i	0.996673	−	0.0815020i	$-0.0259717\pi$
$787$	12.0000	+	20.7846i	0.427754	+	0.740891i	−0.568919	+	0.822393i	$0.692638\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−48.0000			−1.70453
$794$		0			0
$795$			27.7128i			0.982872i
$796$		0			0
$797$	1.41421	+	2.44949i	0.0500940	+	0.0867654i	0.889985	−	0.455990i	$-0.150715\pi$
$797$	1.41421	+	2.44949i	0.0500940	+	0.0867654i	−0.839891	+	0.542755i	$0.817381\pi$
$798$		0			0
$799$	12.7279	+	7.34847i	0.450282	+	0.259970i
$800$		0			0
$801$	−36.0000	+	20.7846i	−1.27200	+	0.734388i
$802$		0			0
$803$	22.5000	+	12.9904i	0.794008	+	0.458421i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−16.9706	−	9.79796i	−0.597392	−	0.344904i
$808$		0			0
$809$		−	8.66025i		−	0.304478i	−0.988344	−	0.152239i	$-0.951352\pi$
$809$		−	8.66025i		−	0.304478i	0.988344	−	0.152239i	$-0.0486484\pi$
$810$		0			0
$811$	−33.0000			−1.15879			−0.579393	−	0.815048i	$-0.696710\pi$
$811$	−33.0000			−1.15879			−0.579393	+	0.815048i	$0.696710\pi$
$812$		0			0
$813$	−25.4558	+	44.0908i	−0.892775	+	1.54633i
$814$		0			0
$815$	−33.9411	−	58.7878i	−1.18891	−	2.05925i
$816$		0			0
$817$	13.5000	−	23.3827i	0.472305	−	0.818057i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.82843	+	4.89898i	−0.0987128	+	0.170976i	−0.911152	−	0.412070i	$-0.864806\pi$
$821$	−2.82843	+	4.89898i	−0.0987128	+	0.170976i	0.812439	+	0.583046i	$0.198139\pi$
$822$		0			0
$823$	12.7279	−	7.34847i	0.443667	−	0.256152i	−0.261485	−	0.965208i	$-0.584212\pi$
$823$	12.7279	−	7.34847i	0.443667	−	0.256152i	0.705152	+	0.709056i	$0.250879\pi$
$824$		0			0
$825$	27.0000			0.940019
$826$		0			0
$827$		−	10.3923i		−	0.361376i	−0.983540	−	0.180688i	$-0.942168\pi$
$827$		−	10.3923i		−	0.361376i	0.983540	−	0.180688i	$-0.0578324\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$	12.7279	+	22.0454i	0.441527	+	0.764747i
$832$		0			0
$833$	10.5000	−	6.06218i	0.363803	−	0.210042i
$834$		0			0
$835$	12.0000	−	20.7846i	0.415277	−	0.719281i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−8.48528	+	14.6969i	−0.292944	+	0.507395i	−0.974505	−	0.224367i	$-0.927968\pi$
$839$	−8.48528	+	14.6969i	−0.292944	+	0.507395i	0.681560	+	0.731762i	$0.261302\pi$
$840$		0			0
$841$	−1.50000	−	2.59808i	−0.0517241	−	0.0895888i
$842$		0			0
$843$	−12.0000	−	20.7846i	−0.413302	−	0.715860i
$844$		0			0
$845$	−31.1127			−1.07031
$846$		0			0
$847$		0			0
$848$		0			0
$849$		−	41.5692i		−	1.42665i
$850$		0			0
$851$	36.0000	−	20.7846i	1.23406	−	0.712487i
$852$		0			0
$853$	12.7279	+	7.34847i	0.435796	+	0.251607i	0.701813	−	0.712362i	$-0.252374\pi$
$853$	12.7279	+	7.34847i	0.435796	+	0.251607i	−0.266017	+	0.963968i	$0.585708\pi$
$854$		0			0
$855$	−12.7279	+	22.0454i	−0.435286	+	0.753937i
$856$		0			0
$857$	12.0000	+	6.92820i	0.409912	+	0.236663i	0.690752	−	0.723092i	$-0.257280\pi$
$857$	12.0000	+	6.92820i	0.409912	+	0.236663i	−0.280840	+	0.959755i	$0.590613\pi$
$858$		0			0
$859$	7.50000	+	12.9904i	0.255897	+	0.443226i	0.965139	−	0.261739i	$-0.0842960\pi$
$859$	7.50000	+	12.9904i	0.255897	+	0.443226i	−0.709242	+	0.704965i	$0.750963\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−8.48528			−0.288842			−0.144421	−	0.989516i	$-0.546132\pi$
$863$	−8.48528			−0.288842			−0.144421	+	0.989516i	$0.546132\pi$
$864$		0			0
$865$	16.0000			0.544016
$866$		0			0
$867$	−21.0000	−	12.1244i	−0.713197	−	0.411765i
$868$		0			0
$869$	−38.1838	−	66.1362i	−1.29530	−	2.24352i
$870$		0			0
$871$	12.7279	+	7.34847i	0.431269	+	0.248993i
$872$		0			0
$873$	3.00000			0.101535
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.9706	+	9.79796i	−0.573055	+	0.330854i	−0.758369	−	0.651826i	$-0.774003\pi$
$877$	−16.9706	+	9.79796i	−0.573055	+	0.330854i	0.185313	+	0.982679i	$0.440670\pi$
$878$		0			0
$879$		−	48.9898i		−	1.65238i
$880$		0			0
$881$			41.5692i			1.40050i	0.713896	+	0.700251i	$0.246929\pi$
$881$			41.5692i			1.40050i	−0.713896	+	0.700251i	$0.753071\pi$
$882$		0			0
$883$	−45.0000			−1.51437			−0.757185	−	0.653200i	$-0.773426\pi$
$883$	−45.0000			−1.51437			−0.757185	+	0.653200i	$0.773426\pi$
$884$		0			0
$885$	12.7279	+	22.0454i	0.427844	+	0.741048i
$886$		0			0
$887$	−12.7279	−	22.0454i	−0.427362	−	0.740212i	0.569276	−	0.822147i	$-0.307224\pi$
$887$	−12.7279	−	22.0454i	−0.427362	−	0.740212i	−0.996638	+	0.0819342i	$0.973890\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−40.5000	+	23.3827i	−1.35680	+	0.783349i
$892$		0			0
$893$	−12.7279	+	22.0454i	−0.425924	+	0.737721i
$894$		0			0
$895$	−25.4558	+	14.6969i	−0.850895	+	0.491264i
$896$		0			0
$897$	−36.0000	−	62.3538i	−1.20201	−	2.08193i
$898$		0			0
$899$		0			0
$900$		0			0
$901$			9.79796i			0.326417i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	36.0000	−	20.7846i	1.19668	−	0.690904i
$906$		0			0
$907$	−7.50000	+	12.9904i	−0.249033	+	0.431339i	−0.963258	−	0.268578i	$-0.913446\pi$
$907$	−7.50000	+	12.9904i	−0.249033	+	0.431339i	0.714224	+	0.699917i	$0.246780\pi$
$908$		0			0
$909$	8.48528			0.281439
$910$		0			0
$911$	−16.9706	+	29.3939i	−0.562260	+	0.973863i	0.435039	+	0.900412i	$0.356735\pi$
$911$	−16.9706	+	29.3939i	−0.562260	+	0.973863i	−0.997299	+	0.0734510i	$0.976599\pi$
$912$		0			0
$913$	−27.0000	−	46.7654i	−0.893570	−	1.54771i
$914$		0			0
$915$	24.0000	−	41.5692i	0.793416	−	1.37424i
$916$		0			0
$917$		0			0
$918$		0			0
$919$			14.6969i			0.484807i	0.970175	+	0.242404i	$0.0779358\pi$
$919$			14.6969i			0.484807i	−0.970175	+	0.242404i	$0.922064\pi$
$920$		0			0
$921$	4.50000	+	2.59808i	0.148280	+	0.0856095i
$922$		0			0
$923$	36.0000	−	20.7846i	1.18495	−	0.684134i
$924$		0			0
$925$	12.7279	+	7.34847i	0.418491	+	0.241616i
$926$		0			0
$927$	38.1838	+	22.0454i	1.25412	+	0.724066i
$928$		0			0
$929$	−24.0000	−	13.8564i	−0.787414	−	0.454614i	0.0516371	−	0.998666i	$-0.483556\pi$
$929$	−24.0000	−	13.8564i	−0.787414	−	0.454614i	−0.839052	+	0.544052i	$0.816889\pi$
$930$		0			0
$931$	10.5000	+	18.1865i	0.344124	+	0.596040i
$932$		0			0
$933$			29.3939i			0.962312i
$934$		0			0
$935$	25.4558			0.832495
$936$		0			0
$937$	−14.0000			−0.457360			−0.228680	−	0.973502i	$-0.573441\pi$
$937$	−14.0000			−0.457360			−0.228680	+	0.973502i	$0.573441\pi$
$938$		0			0
$939$	43.5000	−	25.1147i	1.41957	−	0.819588i
$940$		0			0
$941$	14.1421	+	24.4949i	0.461020	+	0.798511i	0.999012	−	0.0444393i	$-0.0141501\pi$
$941$	14.1421	+	24.4949i	0.461020	+	0.798511i	−0.537992	+	0.842950i	$0.680817\pi$
$942$		0			0
$943$	38.1838	+	22.0454i	1.24343	+	0.717897i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.5000	+	7.79423i	0.438691	+	0.253278i	0.703042	−	0.711148i	$-0.251824\pi$
$947$	13.5000	+	7.79423i	0.438691	+	0.253278i	−0.264351	+	0.964426i	$0.585158\pi$
$948$		0			0
$949$	21.2132	−	12.2474i	0.688610	−	0.397569i
$950$		0			0
$951$	29.6985	−	17.1464i	0.963039	−	0.556011i
$952$		0			0
$953$		−	19.0526i		−	0.617173i	−0.951196	−	0.308586i	$-0.900144\pi$
$953$		−	19.0526i		−	0.617173i	0.951196	−	0.308586i	$-0.0998559\pi$
$954$		0			0
$955$	48.0000			1.55324
$956$		0			0
$957$	−50.9117			−1.64574
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−15.5000	+	26.8468i	−0.500000	+	0.866025i
$962$		0			0
$963$	−13.5000	+	7.79423i	−0.435031	+	0.251166i
$964$		0			0
$965$	−1.41421	+	2.44949i	−0.0455251	+	0.0788519i
$966$		0			0
$967$	−25.4558	+	14.6969i	−0.818605	+	0.472622i	−0.849935	−	0.526887i	$-0.823359\pi$
$967$	−25.4558	+	14.6969i	−0.818605	+	0.472622i	0.0313303	+	0.999509i	$0.490026\pi$
$968$		0			0
$969$	−4.50000	+	7.79423i	−0.144561	+	0.250387i
$970$		0			0
$971$			51.9615i			1.66752i	0.552124	+	0.833762i	$0.313818\pi$
$971$			51.9615i			1.66752i	−0.552124	+	0.833762i	$0.686182\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	12.7279	−	22.0454i	0.407620	−	0.706018i
$976$		0			0
$977$	13.5000	−	7.79423i	0.431903	−	0.249359i	−0.268254	−	0.963348i	$-0.586447\pi$
$977$	13.5000	−	7.79423i	0.431903	−	0.249359i	0.700157	+	0.713989i	$0.253113\pi$
$978$		0			0
$979$	−36.0000	+	62.3538i	−1.15056	+	1.99284i
$980$		0			0
$981$	−25.4558	+	14.6969i	−0.812743	+	0.469237i
$982$		0			0
$983$	−12.7279	+	22.0454i	−0.405958	+	0.703139i	−0.994432	−	0.105376i	$-0.966395\pi$
$983$	−12.7279	+	22.0454i	−0.405958	+	0.703139i	0.588475	+	0.808516i	$0.299729\pi$
$984$		0			0
$985$	16.0000	+	27.7128i	0.509802	+	0.883004i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−76.3675			−2.42835
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$	36.0000	−	20.7846i	1.14243	−	0.659580i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	8.48528	+	4.89898i	0.268732	+	0.155152i	0.628311	−	0.777962i	$-0.283747\pi$
$997$	8.48528	+	4.89898i	0.268732	+	0.155152i	−0.359580	+	0.933114i	$0.617080\pi$
$998$		0			0
$999$	−25.4558			−0.805387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.p.a.191.1	✓	4
3.2	odd	2		3456.2.p.a.575.2		4
4.3	odd	2		1152.2.p.b.191.1	yes	4
8.3	odd	2	inner	1152.2.p.a.191.2	yes	4
8.5	even	2		1152.2.p.b.191.2	yes	4
9.4	even	3		3456.2.p.a.2879.1		4
9.5	odd	6	inner	1152.2.p.a.959.2	yes	4
12.11	even	2		3456.2.p.b.575.2		4
24.5	odd	2		3456.2.p.b.575.1		4
24.11	even	2		3456.2.p.a.575.1		4
36.23	even	6		1152.2.p.b.959.2	yes	4
36.31	odd	6		3456.2.p.b.2879.1		4
72.5	odd	6		1152.2.p.b.959.1	yes	4
72.13	even	6		3456.2.p.b.2879.2		4
72.59	even	6	inner	1152.2.p.a.959.1	yes	4
72.67	odd	6		3456.2.p.a.2879.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.p.a.191.1	✓	4	1.1	even	1	trivial
1152.2.p.a.191.2	yes	4	8.3	odd	2	inner
1152.2.p.a.959.1	yes	4	72.59	even	6	inner
1152.2.p.a.959.2	yes	4	9.5	odd	6	inner
1152.2.p.b.191.1	yes	4	4.3	odd	2
1152.2.p.b.191.2	yes	4	8.5	even	2
1152.2.p.b.959.1	yes	4	72.5	odd	6
1152.2.p.b.959.2	yes	4	36.23	even	6
3456.2.p.a.575.1		4	24.11	even	2
3456.2.p.a.575.2		4	3.2	odd	2
3456.2.p.a.2879.1		4	9.4	even	3
3456.2.p.a.2879.2		4	72.67	odd	6
3456.2.p.b.575.1		4	24.5	odd	2
3456.2.p.b.575.2		4	12.11	even	2
3456.2.p.b.2879.1		4	36.31	odd	6
3456.2.p.b.2879.2		4	72.13	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.41421 - 2.44949i) q^{5} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 0.866025i) q^{3} +(-1.41421 - 2.44949i) q^{5} +(1.50000 + 2.59808i) q^{9} +(4.50000 + 2.59808i) q^{11} +(4.24264 - 2.44949i) q^{13} +4.89898i q^{15} +1.73205i q^{17} -3.00000 q^{19} +(4.24264 + 7.34847i) q^{23} +(-1.50000 + 2.59808i) q^{25} -5.19615i q^{27} +(2.82843 - 4.89898i) q^{29} +(-4.50000 - 7.79423i) q^{33} -4.89898i q^{37} -8.48528 q^{39} +(4.50000 - 2.59808i) q^{41} +(-4.50000 + 7.79423i) q^{43} +(4.24264 - 7.34847i) q^{45} +(4.24264 - 7.34847i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(1.50000 - 2.59808i) q^{51} +5.65685 q^{53} -14.6969i q^{55} +(4.50000 + 2.59808i) q^{57} +(4.50000 - 2.59808i) q^{59} +(-8.48528 - 4.89898i) q^{61} +(-12.0000 - 6.92820i) q^{65} +(1.50000 + 2.59808i) q^{67} -14.6969i q^{69} +8.48528 q^{71} +5.00000 q^{73} +(4.50000 - 2.59808i) q^{75} +(-12.7279 - 7.34847i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-9.00000 - 5.19615i) q^{83} +(4.24264 - 2.44949i) q^{85} +(-8.48528 + 4.89898i) q^{87} +13.8564i q^{89} +(4.24264 + 7.34847i) q^{95} +(0.500000 - 0.866025i) q^{97} +15.5885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 6 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 6 * q^9	\( 4 q - 6 q^{3} + 6 q^{9} + 18 q^{11} - 12 q^{19} - 6 q^{25} - 18 q^{33} + 18 q^{41} - 18 q^{43} - 14 q^{49} + 6 q^{51} + 18 q^{57} + 18 q^{59} - 48 q^{65} + 6 q^{67} + 20 q^{73} + 18 q^{75} - 18 q^{81} - 36 q^{83} + 2 q^{97}+O(q^{100}) \) 4 * q - 6 * q^3 + 6 * q^9 + 18 * q^11 - 12 * q^19 - 6 * q^25 - 18 * q^33 + 18 * q^41 - 18 * q^43 - 14 * q^49 + 6 * q^51 + 18 * q^57 + 18 * q^59 - 48 * q^65 + 6 * q^67 + 20 * q^73 + 18 * q^75 - 18 * q^81 - 36 * q^83 + 2 * q^97

Introduction

L-functions

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