LMFDB - Embedded newform 1728.2.z.a.1583.22

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			1583.22
Character	$\chi$	$=$	1728.1583
Dual form			1728.2.z.a.143.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.81396 - 1.02195i) q^{5} +(-1.46715 - 2.54117i) q^{7} +O(q^{10})$	$q+(3.81396 - 1.02195i) q^{5} +(-1.46715 - 2.54117i) q^{7} +(-2.65006 - 0.710081i) q^{11} +(-2.34729 + 0.628955i) q^{13} -2.89808i q^{17} +(1.99906 - 1.99906i) q^{19} +(-2.07141 - 1.19593i) q^{23} +(9.17180 - 5.29534i) q^{25} +(-8.46218 - 2.26743i) q^{29} +(0.439075 + 0.253500i) q^{31} +(-8.19258 - 8.19258i) q^{35} +(1.36407 - 1.36407i) q^{37} +(-0.745739 + 1.29166i) q^{41} +(1.27136 - 4.74478i) q^{43} +(-3.25802 - 5.64306i) q^{47} +(-0.805035 + 1.39436i) q^{49} +(5.17979 + 5.17979i) q^{53} -10.8329 q^{55} +(0.664781 + 2.48100i) q^{59} +(2.99657 - 11.1833i) q^{61} +(-8.30972 + 4.79762i) q^{65} +(2.53505 + 9.46095i) q^{67} +4.65399i q^{71} +4.91897i q^{73} +(2.08358 + 7.77604i) q^{77} +(3.61263 - 2.08575i) q^{79} +(-3.37411 + 12.5924i) q^{83} +(-2.96169 - 11.0532i) q^{85} -7.33327 q^{89} +(5.04210 + 5.04210i) q^{91} +(5.58139 - 9.66725i) q^{95} +(2.50134 + 4.33245i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	3.81396	−	1.02195i	1.70566	−	0.457029i	0.731302	−	0.682053i	$-0.238913\pi$
$5$	3.81396	−	1.02195i	1.70566	−	0.457029i	0.974353	+	0.225024i	$0.0722462\pi$
$6$		0			0
$7$	−1.46715	−	2.54117i	−0.554529	−	0.960473i	−0.997940	−	0.0641541i	$-0.979565\pi$
$7$	−1.46715	−	2.54117i	−0.554529	−	0.960473i	0.443411	−	0.896318i	$-0.353768\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.65006	−	0.710081i	−0.799022	−	0.214097i	−0.163868	−	0.986482i	$-0.552397\pi$
$11$	−2.65006	−	0.710081i	−0.799022	−	0.214097i	−0.635155	+	0.772385i	$0.719064\pi$
$12$		0			0
$13$	−2.34729	+	0.628955i	−0.651021	+	0.174441i	−0.569191	−	0.822206i	$-0.692743\pi$
$13$	−2.34729	+	0.628955i	−0.651021	+	0.174441i	−0.0818307	+	0.996646i	$0.526077\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	2.89808i		−	0.702889i	−0.936209	−	0.351444i	$-0.885691\pi$
$17$		−	2.89808i		−	0.702889i	0.936209	−	0.351444i	$-0.114309\pi$
$18$		0			0
$19$	1.99906	−	1.99906i	0.458615	−	0.458615i	−0.439586	−	0.898201i	$-0.644875\pi$
$19$	1.99906	−	1.99906i	0.458615	−	0.458615i	0.898201	+	0.439586i	$0.144875\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.07141	−	1.19593i	−0.431918	−	0.249368i	0.268245	−	0.963351i	$-0.413556\pi$
$23$	−2.07141	−	1.19593i	−0.431918	−	0.249368i	−0.700163	+	0.713983i	$0.746890\pi$
$24$		0			0
$25$	9.17180	−	5.29534i	1.83436	−	1.05907i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−8.46218	−	2.26743i	−1.57139	−	0.421052i	−0.635141	−	0.772396i	$-0.719058\pi$
$29$	−8.46218	−	2.26743i	−1.57139	−	0.421052i	−0.936246	+	0.351344i	$0.885725\pi$
$30$		0			0
$31$	0.439075	+	0.253500i	0.0788602	+	0.0455300i	0.538912	−	0.842362i	$-0.318836\pi$
$31$	0.439075	+	0.253500i	0.0788602	+	0.0455300i	−0.460051	+	0.887892i	$0.652169\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−8.19258	−	8.19258i	−1.38480	−	1.38480i
$36$		0			0
$37$	1.36407	−	1.36407i	0.224251	−	0.224251i	−0.586035	−	0.810286i	$-0.699312\pi$
$37$	1.36407	−	1.36407i	0.224251	−	0.224251i	0.810286	+	0.586035i	$0.199312\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.745739	+	1.29166i	−0.116465	+	0.201723i	−0.918364	−	0.395736i	$-0.870490\pi$
$41$	−0.745739	+	1.29166i	−0.116465	+	0.201723i	0.801899	+	0.597459i	$0.203823\pi$
$42$		0			0
$43$	1.27136	−	4.74478i	0.193881	−	0.723572i	−0.798673	−	0.601765i	$-0.794464\pi$
$43$	1.27136	−	4.74478i	0.193881	−	0.723572i	0.992554	−	0.121807i	$-0.0388690\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.25802	−	5.64306i	−0.475231	−	0.823124i	0.524367	−	0.851493i	$-0.324302\pi$
$47$	−3.25802	−	5.64306i	−0.475231	−	0.823124i	−0.999598	+	0.0283684i	$0.990969\pi$
$48$		0			0
$49$	−0.805035	+	1.39436i	−0.115005	+	0.199195i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.17979	+	5.17979i	0.711499	+	0.711499i	0.966849	−	0.255349i	$-0.0821905\pi$
$53$	5.17979	+	5.17979i	0.711499	+	0.711499i	−0.255349	+	0.966849i	$0.582191\pi$
$54$		0			0
$55$	−10.8329			−1.46071
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.664781	+	2.48100i	0.0865472	+	0.322998i	0.995603	−	0.0936766i	$-0.0298620\pi$
$59$	0.664781	+	2.48100i	0.0865472	+	0.322998i	−0.909056	+	0.416675i	$0.863195\pi$
$60$		0			0
$61$	2.99657	−	11.1833i	0.383671	−	1.43188i	−0.456580	−	0.889682i	$-0.650926\pi$
$61$	2.99657	−	11.1833i	0.383671	−	1.43188i	0.840251	−	0.542198i	$-0.182408\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.30972	+	4.79762i	−1.03069	+	0.595071i
$66$		0			0
$67$	2.53505	+	9.46095i	0.309706	+	1.15584i	0.928818	+	0.370536i	$0.120826\pi$
$67$	2.53505	+	9.46095i	0.309706	+	1.15584i	−0.619112	+	0.785303i	$0.712507\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			4.65399i			0.552327i	0.961111	+	0.276164i	$0.0890632\pi$
$71$			4.65399i			0.552327i	−0.961111	+	0.276164i	$0.910937\pi$
$72$		0			0
$73$			4.91897i			0.575722i	0.957672	+	0.287861i	$0.0929441\pi$
$73$			4.91897i			0.575722i	−0.957672	+	0.287861i	$0.907056\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.08358	+	7.77604i	0.237446	+	0.886162i
$78$		0			0
$79$	3.61263	−	2.08575i	0.406453	−	0.234666i	−0.282812	−	0.959175i	$-0.591267\pi$
$79$	3.61263	−	2.08575i	0.406453	−	0.234666i	0.689264	+	0.724510i	$0.257934\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.37411	+	12.5924i	−0.370357	+	1.38219i	0.489654	+	0.871917i	$0.337123\pi$
$83$	−3.37411	+	12.5924i	−0.370357	+	1.38219i	−0.860011	+	0.510275i	$0.829544\pi$
$84$		0			0
$85$	−2.96169	−	11.0532i	−0.321241	−	1.19889i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.33327			−0.777325			−0.388662	−	0.921380i	$-0.627063\pi$
$89$	−7.33327			−0.777325			−0.388662	+	0.921380i	$0.627063\pi$
$90$		0			0
$91$	5.04210	+	5.04210i	0.528556	+	0.528556i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.58139	−	9.66725i	0.572639	−	0.991839i
$96$		0			0
$97$	2.50134	+	4.33245i	0.253973	+	0.439893i	0.964616	−	0.263659i	$-0.0849294\pi$
$97$	2.50134	+	4.33245i	0.253973	+	0.439893i	−0.710643	+	0.703552i	$0.751596\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.82933	−	10.5592i	0.281529	−	1.05068i	−0.669810	−	0.742533i	$-0.733624\pi$
$101$	2.82933	−	10.5592i	0.281529	−	1.05068i	0.951339	−	0.308147i	$-0.0997090\pi$
$102$		0			0
$103$	0.321949	−	0.557632i	0.0317226	−	0.0549451i	−0.849728	−	0.527221i	$-0.823234\pi$
$103$	0.321949	−	0.557632i	0.0317226	−	0.0549451i	0.881451	+	0.472276i	$0.156567\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.74155	−	3.74155i	0.361709	−	0.361709i	−0.502733	−	0.864442i	$-0.667672\pi$
$107$	3.74155	−	3.74155i	0.361709	−	0.361709i	0.864442	+	0.502733i	$0.167672\pi$
$108$		0			0
$109$	6.00859	+	6.00859i	0.575518	+	0.575518i	0.933665	−	0.358147i	$-0.116591\pi$
$109$	6.00859	+	6.00859i	0.575518	+	0.575518i	−0.358147	+	0.933665i	$0.616591\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−14.4387	−	8.33620i	−1.35828	−	0.784204i	−0.368889	−	0.929474i	$-0.620262\pi$
$113$	−14.4387	−	8.33620i	−1.35828	−	0.784204i	−0.989392	+	0.145270i	$0.953595\pi$
$114$		0			0
$115$	−9.12244	−	2.44435i	−0.850672	−	0.227937i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.36453	+	4.25191i	−0.675105	+	0.389772i
$120$		0			0
$121$	−3.00769	−	1.73649i	−0.273426	−	0.157863i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	15.6093	−	15.6093i	1.39613	−	1.39613i
$126$		0			0
$127$		−	17.9975i		−	1.59702i	−0.601983	−	0.798509i	$-0.705623\pi$
$127$		−	17.9975i		−	1.59702i	0.601983	−	0.798509i	$-0.294377\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	17.4121	−	4.66555i	1.52130	−	0.407631i	0.601131	−	0.799151i	$-0.294717\pi$
$131$	17.4121	−	4.66555i	1.52130	−	0.407631i	0.920170	+	0.391520i	$0.128051\pi$
$132$		0			0
$133$	−8.01285	−	2.14704i	−0.694802	−	0.186172i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.396155	+	0.686161i	0.0338458	+	0.0586227i	0.882452	−	0.470402i	$-0.155891\pi$
$137$	0.396155	+	0.686161i	0.0338458	+	0.0586227i	−0.848606	+	0.529025i	$0.822558\pi$
$138$		0			0
$139$	20.5134	−	5.49654i	1.73992	−	0.466211i	0.757492	−	0.652844i	$-0.226424\pi$
$139$	20.5134	−	5.49654i	1.73992	−	0.466211i	0.982430	+	0.186633i	$0.0597576\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.66706			0.557528
$144$		0			0
$145$	−34.5916			−2.87268
$146$		0			0
$147$		0			0
$148$		0			0
$149$	11.3030	−	3.02863i	0.925977	−	0.248115i	0.235839	−	0.971792i	$-0.424216\pi$
$149$	11.3030	−	3.02863i	0.925977	−	0.248115i	0.690139	+	0.723677i	$0.257550\pi$
$150$		0			0
$151$	4.24025	+	7.34432i	0.345066	+	0.597673i	0.985366	−	0.170453i	$-0.0545230\pi$
$151$	4.24025	+	7.34432i	0.345066	+	0.597673i	−0.640299	+	0.768125i	$0.721190\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.93368	+	0.518128i	0.155317	+	0.0416170i
$156$		0			0
$157$	3.53516	−	0.947242i	0.282136	−	0.0755981i	−0.114976	−	0.993368i	$-0.536679\pi$
$157$	3.53516	−	0.947242i	0.282136	−	0.0755981i	0.397112	+	0.917770i	$0.370012\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			7.01840i			0.553127i
$162$		0			0
$163$	3.86060	−	3.86060i	0.302385	−	0.302385i	−0.539561	−	0.841946i	$-0.681410\pi$
$163$	3.86060	−	3.86060i	0.302385	−	0.302385i	0.841946	+	0.539561i	$0.181410\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.98224	−	3.45385i	−0.462920	−	0.267267i	0.250351	−	0.968155i	$-0.419454\pi$
$167$	−5.98224	−	3.45385i	−0.462920	−	0.267267i	−0.713271	+	0.700888i	$0.752787\pi$
$168$		0			0
$169$	−6.14414	+	3.54732i	−0.472626	+	0.272871i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.86859	−	1.03659i	−0.294123	−	0.0788101i	0.108740	−	0.994070i	$-0.465318\pi$
$173$	−3.86859	−	1.03659i	−0.294123	−	0.0788101i	−0.402863	+	0.915260i	$0.631985\pi$
$174$		0			0
$175$	−26.9127	−	15.5381i	−2.03441	−	1.17457i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.0625	+	10.0625i	0.752109	+	0.752109i	0.974872	−	0.222764i	$-0.0715078\pi$
$179$	10.0625	+	10.0625i	0.752109	+	0.752109i	−0.222764	+	0.974872i	$0.571508\pi$
$180$		0			0
$181$	15.0346	−	15.0346i	1.11751	−	1.11751i	0.125405	−	0.992106i	$-0.459977\pi$
$181$	15.0346	−	15.0346i	1.11751	−	1.11751i	0.992106	−	0.125405i	$-0.0400229\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.80849	−	6.59651i	0.280006	−	0.484985i
$186$		0			0
$187$	−2.05787	+	7.68009i	−0.150487	+	0.561624i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−10.9007	−	18.8806i	−0.788749	−	1.36615i	−0.926734	−	0.375719i	$-0.877396\pi$
$191$	−10.9007	−	18.8806i	−0.788749	−	1.36615i	0.137984	−	0.990434i	$-0.455938\pi$
$192$		0			0
$193$	−2.34723	+	4.06553i	−0.168958	+	0.292643i	−0.938054	−	0.346490i	$-0.887373\pi$
$193$	−2.34723	+	4.06553i	−0.168958	+	0.292643i	0.769096	+	0.639133i	$0.220707\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.3226	−	14.3226i	−1.02044	−	1.02044i	−0.999787	−	0.0206566i	$-0.993424\pi$
$197$	−14.3226	−	14.3226i	−1.02044	−	1.02044i	−0.0206566	−	0.999787i	$-0.506576\pi$
$198$		0			0
$199$	14.4965			1.02763			0.513816	−	0.857901i	$-0.328232\pi$
$199$	14.4965			1.02763			0.513816	+	0.857901i	$0.328232\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	6.65332	+	24.8305i	0.466971	+	1.74276i
$204$		0			0
$205$	−1.52421	+	5.68844i	−0.106456	+	0.397298i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.71710	+	3.87812i	−0.464632	+	0.268255i
$210$		0			0
$211$	1.71268	+	6.39179i	0.117905	+	0.440029i	0.999488	−	0.0320010i	$-0.0101880\pi$
$211$	1.71268	+	6.39179i	0.117905	+	0.440029i	−0.881582	+	0.472030i	$0.843521\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	19.3957i		−	1.32277i
$216$		0			0
$217$		−	1.48769i		−	0.100991i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.82276	+	6.80265i	0.122612	+	0.457596i
$222$		0			0
$223$	−1.59599	+	0.921443i	−0.106875	+	0.0617044i	−0.552485	−	0.833523i	$-0.686320\pi$
$223$	−1.59599	+	0.921443i	−0.106875	+	0.0617044i	0.445610	+	0.895227i	$0.352987\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−0.184084	+	0.687012i	−0.0122181	+	0.0455986i	−0.971766	−	0.235948i	$-0.924181\pi$
$227$	−0.184084	+	0.687012i	−0.0122181	+	0.0455986i	0.959548	+	0.281546i	$0.0908473\pi$
$228$		0			0
$229$	1.98433	+	7.40562i	0.131128	+	0.489377i	0.999984	−	0.00568843i	$-0.00181069\pi$
$229$	1.98433	+	7.40562i	0.131128	+	0.489377i	−0.868856	+	0.495066i	$0.835144\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.36925			−0.0897024			−0.0448512	−	0.998994i	$-0.514281\pi$
$233$	−1.36925			−0.0897024			−0.0448512	+	0.998994i	$0.514281\pi$
$234$		0			0
$235$	−18.1929	−	18.1929i	−1.18677	−	1.18677i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.773627	+	1.33996i	−0.0500418	+	0.0866749i	−0.889961	−	0.456036i	$-0.849269\pi$
$239$	−0.773627	+	1.33996i	−0.0500418	+	0.0866749i	0.839919	+	0.542711i	$0.182602\pi$
$240$		0			0
$241$	3.83660	+	6.64519i	0.247137	+	0.428054i	0.962730	−	0.270463i	$-0.0871769\pi$
$241$	3.83660	+	6.64519i	0.247137	+	0.428054i	−0.715593	+	0.698517i	$0.753844\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.64541	+	6.14075i	−0.105121	+	0.392318i
$246$		0			0
$247$	−3.43505	+	5.94968i	−0.218567	+	0.378569i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−5.46632	+	5.46632i	−0.345031	+	0.345031i	−0.858255	−	0.513224i	$-0.828451\pi$
$251$	−5.46632	+	5.46632i	−0.345031	+	0.345031i	0.513224	+	0.858255i	$0.328451\pi$
$252$		0			0
$253$	4.64014	+	4.64014i	0.291723	+	0.291723i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	20.5918	+	11.8887i	1.28448	+	0.741596i	0.977664	−	0.210172i	$-0.0674025\pi$
$257$	20.5918	+	11.8887i	1.28448	+	0.741596i	0.306818	+	0.951768i	$0.400736\pi$
$258$		0			0
$259$	−5.46761	−	1.46504i	−0.339741	−	0.0910333i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.13704	+	3.54322i	−0.378426	+	0.218484i	−0.677133	−	0.735860i	$-0.736778\pi$
$263$	−6.13704	+	3.54322i	−0.378426	+	0.218484i	0.298707	+	0.954345i	$0.403445\pi$
$264$		0			0
$265$	25.0490	+	14.4621i	1.53875	+	0.888397i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−20.6616	+	20.6616i	−1.25976	+	1.25976i	−0.308553	+	0.951207i	$0.599845\pi$
$269$	−20.6616	+	20.6616i	−1.25976	+	1.25976i	−0.951207	+	0.308553i	$0.900155\pi$
$270$		0			0
$271$			16.6901i			1.01385i	0.861989	+	0.506927i	$0.169218\pi$
$271$			16.6901i			1.01385i	−0.861989	+	0.506927i	$0.830782\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−28.0659	+	7.52024i	−1.69244	+	0.453487i
$276$		0			0
$277$	4.49217	+	1.20367i	0.269908	+	0.0723217i	0.391235	−	0.920291i	$-0.372048\pi$
$277$	4.49217	+	1.20367i	0.269908	+	0.0723217i	−0.121326	+	0.992613i	$0.538715\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	11.4153	+	19.7719i	0.680979	+	1.17949i	0.974682	+	0.223594i	$0.0717790\pi$
$281$	11.4153	+	19.7719i	0.680979	+	1.17949i	−0.293703	+	0.955897i	$0.594888\pi$
$282$		0			0
$283$	24.9438	−	6.68368i	1.48276	−	0.397303i	0.575472	−	0.817822i	$-0.304818\pi$
$283$	24.9438	−	6.68368i	1.48276	−	0.397303i	0.907284	+	0.420518i	$0.138152\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.37643			0.258333
$288$		0			0
$289$	8.60110			0.505947
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.76706	−	0.741431i	0.161653	−	0.0433149i	−0.177085	−	0.984196i	$-0.556667\pi$
$293$	2.76706	−	0.741431i	0.161653	−	0.0433149i	0.338738	+	0.940881i	$0.390000\pi$
$294$		0			0
$295$	5.07090	+	8.78306i	0.295239	+	0.511370i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.61438	+	1.50437i	0.324688	+	0.0869998i
$300$		0			0
$301$	−13.9226	+	3.73054i	−0.802484	+	0.215025i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	45.7152i		−	2.61764i
$306$		0			0
$307$	7.67329	−	7.67329i	0.437938	−	0.437938i	−0.453380	−	0.891317i	$-0.649782\pi$
$307$	7.67329	−	7.67329i	0.437938	−	0.437938i	0.891317	+	0.453380i	$0.149782\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.0777	+	8.70513i	0.854980	+	0.493623i	0.862328	−	0.506350i	$-0.169006\pi$
$311$	15.0777	+	8.70513i	0.854980	+	0.493623i	−0.00734815	+	0.999973i	$0.502339\pi$
$312$		0			0
$313$	−21.3027	+	12.2991i	−1.20410	+	0.695189i	−0.961465	−	0.274928i	$-0.911346\pi$
$313$	−21.3027	+	12.2991i	−1.20410	+	0.695189i	−0.242638	+	0.970117i	$0.578013\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.99342	+	2.14183i	0.448955	+	0.120297i	0.476211	−	0.879331i	$-0.342010\pi$
$317$	7.99342	+	2.14183i	0.448955	+	0.120297i	−0.0272552	+	0.999629i	$0.508677\pi$
$318$		0			0
$319$	20.8152	+	12.0177i	1.16543	+	0.672860i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.79343	−	5.79343i	−0.322355	−	0.322355i
$324$		0			0
$325$	−18.1983	+	18.1983i	−1.00946	+	1.00946i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−9.55998	+	16.5584i	−0.527059	+	0.912893i
$330$		0			0
$331$	−6.84245	+	25.5364i	−0.376095	+	1.40361i	0.475643	+	0.879639i	$0.342216\pi$
$331$	−6.84245	+	25.5364i	−0.376095	+	1.40361i	−0.851738	+	0.523968i	$0.824451\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	19.3372	+	33.4930i	1.05650	+	1.82992i
$336$		0			0
$337$	12.3368	−	21.3679i	0.672026	−	1.16398i	−0.305302	−	0.952256i	$-0.598757\pi$
$337$	12.3368	−	21.3679i	0.672026	−	1.16398i	0.977329	−	0.211728i	$-0.0679092\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.983569	−	0.983569i	−0.0532632	−	0.0532632i
$342$		0			0
$343$	−15.8156			−0.853964
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.16895	+	23.0228i	0.331166	+	1.23593i	0.907966	+	0.419044i	$0.137635\pi$
$347$	6.16895	+	23.0228i	0.331166	+	1.23593i	−0.576799	+	0.816886i	$0.695699\pi$
$348$		0			0
$349$	6.94337	−	25.9130i	0.371670	−	1.38709i	−0.486479	−	0.873692i	$-0.661719\pi$
$349$	6.94337	−	25.9130i	0.371670	−	1.38709i	0.858149	−	0.513400i	$-0.171614\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.54075	+	3.19895i	−0.294904	+	0.170263i	−0.640151	−	0.768249i	$-0.721128\pi$
$353$	−5.54075	+	3.19895i	−0.294904	+	0.170263i	0.345247	+	0.938512i	$0.387795\pi$
$354$		0			0
$355$	4.75614	+	17.7502i	0.252430	+	0.942080i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	17.2363i		−	0.909697i	−0.890569	−	0.454849i	$-0.849693\pi$
$359$		−	17.2363i		−	0.909697i	0.890569	−	0.454849i	$-0.150307\pi$
$360$		0			0
$361$			11.0076i			0.579345i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.02693	+	18.7608i	0.263121	+	0.981983i
$366$		0			0
$367$	1.26366	−	0.729575i	0.0659625	−	0.0380835i	−0.466656	−	0.884439i	$-0.654541\pi$
$367$	1.26366	−	0.729575i	0.0659625	−	0.0380835i	0.532619	+	0.846355i	$0.321208\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	5.56323	−	20.7623i	0.288829	−	1.07792i
$372$		0			0
$373$	−2.08247	−	7.77189i	−0.107826	−	0.402413i	0.890824	−	0.454348i	$-0.150128\pi$
$373$	−2.08247	−	7.77189i	−0.107826	−	0.402413i	−0.998650	+	0.0519349i	$0.983461\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	21.2893			1.09646
$378$		0			0
$379$	16.4748	+	16.4748i	0.846255	+	0.846255i	0.989664	−	0.143409i	$-0.0458063\pi$
$379$	16.4748	+	16.4748i	0.846255	+	0.846255i	−0.143409	+	0.989664i	$0.545806\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.19654	+	9.00067i	−0.265531	+	0.459913i	−0.967703	−	0.252095i	$-0.918881\pi$
$383$	−5.19654	+	9.00067i	−0.265531	+	0.459913i	0.702172	+	0.712008i	$0.252214\pi$
$384$		0			0
$385$	15.8934	+	27.5282i	0.810004	+	1.40297i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.24292	+	23.2989i	−0.316529	+	1.18130i	0.606029	+	0.795442i	$0.292761\pi$
$389$	−6.24292	+	23.2989i	−0.316529	+	1.18130i	−0.922558	+	0.385859i	$0.873905\pi$
$390$		0			0
$391$	−3.46590	+	6.00311i	−0.175278	+	0.303590i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	11.6469	−	11.6469i	0.586019	−	0.586019i
$396$		0			0
$397$	8.37131	+	8.37131i	0.420144	+	0.420144i	0.885253	−	0.465109i	$-0.153985\pi$
$397$	8.37131	+	8.37131i	0.420144	+	0.420144i	−0.465109	+	0.885253i	$0.653985\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.16266	+	1.82596i	0.157936	+	0.0911842i	0.576885	−	0.816825i	$-0.304268\pi$
$401$	3.16266	+	1.82596i	0.157936	+	0.0911842i	−0.418949	+	0.908010i	$0.637601\pi$
$402$		0			0
$403$	−1.19008	−	0.318880i	−0.0592820	−	0.0158846i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.58345	+	2.64626i	−0.227193	+	0.131170i
$408$		0			0
$409$	−12.1263	−	7.00113i	−0.599607	−	0.346184i	0.169280	−	0.985568i	$-0.445856\pi$
$409$	−12.1263	−	7.00113i	−0.599607	−	0.346184i	−0.768887	+	0.639385i	$0.779189\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.32931	−	5.32931i	0.262238	−	0.262238i
$414$		0			0
$415$			51.4750i			2.52681i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.601258	−	0.161107i	0.0293734	−	0.00787057i	−0.244102	−	0.969749i	$-0.578493\pi$
$419$	0.601258	−	0.161107i	0.0293734	−	0.00787057i	0.273476	+	0.961879i	$0.411827\pi$
$420$		0			0
$421$	17.3705	+	4.65440i	0.846585	+	0.226842i	0.655936	−	0.754816i	$-0.272274\pi$
$421$	17.3705	+	4.65440i	0.846585	+	0.226842i	0.190649	+	0.981658i	$0.438941\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−15.3463	−	26.5806i	−0.744407	−	1.28935i
$426$		0			0
$427$	−32.8152	+	8.79280i	−1.58804	+	0.425514i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	6.34380			0.305570			0.152785	−	0.988259i	$-0.451176\pi$
$431$	6.34380			0.305570			0.152785	+	0.988259i	$0.451176\pi$
$432$		0			0
$433$	26.7319			1.28465			0.642327	−	0.766430i	$-0.277969\pi$
$433$	26.7319			1.28465			0.642327	+	0.766430i	$0.277969\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.53158	+	1.75013i	−0.312448	+	0.0837202i
$438$		0			0
$439$	−0.347800	−	0.602407i	−0.0165996	−	0.0287513i	0.857606	−	0.514307i	$-0.171951\pi$
$439$	−0.347800	−	0.602407i	−0.0165996	−	0.0287513i	−0.874206	+	0.485555i	$0.838617\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−15.8656	−	4.25119i	−0.753800	−	0.201980i	−0.138597	−	0.990349i	$-0.544259\pi$
$443$	−15.8656	−	4.25119i	−0.753800	−	0.201980i	−0.615203	+	0.788369i	$0.710926\pi$
$444$		0			0
$445$	−27.9688	+	7.49422i	−1.32585	+	0.355260i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			12.0759i			0.569896i	0.958543	+	0.284948i	$0.0919763\pi$
$449$			12.0759i			0.569896i	−0.958543	+	0.284948i	$0.908024\pi$
$450$		0			0
$451$	2.89343	−	2.89343i	0.136247	−	0.136247i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	24.3831	+	14.0776i	1.14310	+	0.659969i
$456$		0			0
$457$	−10.6069	+	6.12391i	−0.496171	+	0.286464i	−0.727131	−	0.686499i	$-0.759147\pi$
$457$	−10.6069	+	6.12391i	−0.496171	+	0.286464i	0.230960	+	0.972963i	$0.425813\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	30.3154	+	8.12298i	1.41193	+	0.378325i	0.882613	−	0.470101i	$-0.155783\pi$
$461$	30.3154	+	8.12298i	1.41193	+	0.378325i	0.529314	+	0.848426i	$0.322449\pi$
$462$		0			0
$463$	−30.9163	−	17.8495i	−1.43680	−	0.829538i	−0.439176	−	0.898401i	$-0.644729\pi$
$463$	−30.9163	−	17.8495i	−1.43680	−	0.829538i	−0.997626	+	0.0688633i	$0.978063\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−7.64586	−	7.64586i	−0.353808	−	0.353808i	0.507716	−	0.861524i	$-0.330490\pi$
$467$	−7.64586	−	7.64586i	−0.353808	−	0.353808i	−0.861524	+	0.507716i	$0.830490\pi$
$468$		0			0
$469$	20.3226	−	20.3226i	0.938411	−	0.938411i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.73836	+	11.6712i	−0.309830	+	0.536641i
$474$		0			0
$475$	7.74926	−	28.9206i	0.355560	−	1.32697i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.03628	−	5.25898i	−0.138731	−	0.240289i	0.788286	−	0.615310i	$-0.210969\pi$
$479$	−3.03628	−	5.25898i	−0.138731	−	0.240289i	−0.927017	+	0.375020i	$0.877636\pi$
$480$		0			0
$481$	−2.34393	+	4.05980i	−0.106874	+	0.185111i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	13.9675	+	13.9675i	0.634234	+	0.634234i
$486$		0			0
$487$	7.15811			0.324365			0.162183	−	0.986761i	$-0.448147\pi$
$487$	7.15811			0.324365			0.162183	+	0.986761i	$0.448147\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−7.24226	−	27.0285i	−0.326838	−	1.21978i	−0.912451	−	0.409187i	$-0.865813\pi$
$491$	−7.24226	−	27.0285i	−0.326838	−	1.21978i	0.585612	−	0.810591i	$-0.300854\pi$
$492$		0			0
$493$	−6.57122	+	24.5241i	−0.295953	+	1.10451i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	11.8266	−	6.82809i	0.530495	−	0.306282i
$498$		0			0
$499$	−11.4708	−	42.8097i	−0.513505	−	1.91643i	−0.378568	−	0.925573i	$-0.623584\pi$
$499$	−11.4708	−	42.8097i	−0.513505	−	1.91643i	−0.134937	−	0.990854i	$-0.543083\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			3.93000i			0.175230i	0.996154	+	0.0876151i	$0.0279245\pi$
$503$			3.93000i			0.175230i	−0.996154	+	0.0876151i	$0.972075\pi$
$504$		0			0
$505$		−	43.1638i		−	1.92077i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.8415	−	40.4609i	−0.480539	−	1.79340i	−0.599358	−	0.800481i	$-0.704577\pi$
$509$	−10.8415	−	40.4609i	−0.480539	−	1.79340i	0.118819	−	0.992916i	$-0.462089\pi$
$510$		0			0
$511$	12.4999	−	7.21684i	0.552965	−	0.319254i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.658030	−	2.45580i	0.0289963	−	0.108216i
$516$		0			0
$517$	4.62691	+	17.2679i	0.203491	+	0.759441i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	26.1826			1.14708			0.573540	−	0.819178i	$-0.305570\pi$
$521$	26.1826			1.14708			0.573540	+	0.819178i	$0.305570\pi$
$522$		0			0
$523$	−7.29036	−	7.29036i	−0.318785	−	0.318785i	0.529515	−	0.848300i	$-0.322374\pi$
$523$	−7.29036	−	7.29036i	−0.318785	−	0.318785i	−0.848300	+	0.529515i	$0.822374\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.734665	−	1.27248i	0.0320025	−	0.0554300i
$528$		0			0
$529$	−8.63952	−	14.9641i	−0.375631	−	0.650612i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.938073	−	3.50093i	0.0406324	−	0.151642i
$534$		0			0
$535$	10.4465	−	18.0938i	0.451640	−	0.782263i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.12350	−	3.12350i	0.134539	−	0.134539i
$540$		0			0
$541$	13.6906	+	13.6906i	0.588607	+	0.588607i	0.937254	−	0.348647i	$-0.113359\pi$
$541$	13.6906	+	13.6906i	0.588607	+	0.588607i	−0.348647	+	0.937254i	$0.613359\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	29.0570	+	16.7761i	1.24466	+	0.718607i
$546$		0			0
$547$	−29.0133	−	7.77408i	−1.24052	−	0.332396i	−0.421851	−	0.906665i	$-0.638620\pi$
$547$	−29.0133	−	7.77408i	−1.24052	−	0.332396i	−0.818666	+	0.574269i	$0.805286\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−21.4491	+	12.3836i	−0.913762	+	0.527561i
$552$		0			0
$553$	−10.6005	−	6.12021i	−0.450780	−	0.260258i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.85284	−	1.85284i	0.0785074	−	0.0785074i	−0.666763	−	0.745270i	$-0.732321\pi$
$557$	1.85284	−	1.85284i	0.0785074	−	0.0785074i	0.745270	+	0.666763i	$0.232321\pi$
$558$		0			0
$559$			11.9370i			0.504882i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	26.1400	−	7.00420i	1.10167	−	0.295192i	0.338226	−	0.941065i	$-0.390173\pi$
$563$	26.1400	−	7.00420i	1.10167	−	0.295192i	0.763445	+	0.645873i	$0.223506\pi$
$564$		0			0
$565$	−63.5879	−	17.0383i	−2.67516	−	0.716808i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.84691	−	10.1271i	−0.245115	−	0.424552i	0.717049	−	0.697023i	$-0.245492\pi$
$569$	−5.84691	−	10.1271i	−0.245115	−	0.424552i	−0.962164	+	0.272471i	$0.912159\pi$
$570$		0			0
$571$	−44.1127	+	11.8200i	−1.84606	+	0.494650i	−0.999303	−	0.0373319i	$-0.988114\pi$
$571$	−44.1127	+	11.8200i	−1.84606	+	0.494650i	−0.846756	+	0.531982i	$0.821447\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−25.3314			−1.05639
$576$		0			0
$577$	−32.6884			−1.36083			−0.680417	−	0.732825i	$-0.738202\pi$
$577$	−32.6884			−1.36083			−0.680417	+	0.732825i	$0.738202\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	36.9497	−	9.90064i	1.53293	−	0.410748i
$582$		0			0
$583$	−10.0487	−	17.4048i	−0.416174	−	0.720834i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	28.3101	+	7.58567i	1.16848	+	0.313094i	0.790349	−	0.612657i	$-0.209899\pi$
$587$	28.3101	+	7.58567i	1.16848	+	0.313094i	0.378134	+	0.925751i	$0.376566\pi$
$588$		0			0
$589$	1.38450	−	0.370975i	0.0570472	−	0.0152858i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			43.9681i			1.80555i	0.430111	+	0.902776i	$0.358474\pi$
$593$			43.9681i			1.80555i	−0.430111	+	0.902776i	$0.641526\pi$
$594$		0			0
$595$	−23.7428	+	23.7428i	−0.973360	+	0.973360i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.81411	+	1.62473i	0.114982	+	0.0663846i	0.556388	−	0.830923i	$-0.312187\pi$
$599$	2.81411	+	1.62473i	0.114982	+	0.0663846i	−0.441406	+	0.897307i	$0.645520\pi$
$600$		0			0
$601$	12.6206	−	7.28651i	0.514806	−	0.297223i	−0.220001	−	0.975500i	$-0.570606\pi$
$601$	12.6206	−	7.28651i	0.514806	−	0.297223i	0.734807	+	0.678276i	$0.237273\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−13.2458	−	3.54920i	−0.538519	−	0.144296i
$606$		0			0
$607$	−32.0317	−	18.4935i	−1.30013	−	0.750629i	−0.319702	−	0.947518i	$-0.603583\pi$
$607$	−32.0317	−	18.4935i	−1.30013	−	0.750629i	−0.980426	+	0.196889i	$0.936916\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	11.1967	+	11.1967i	0.452972	+	0.452972i
$612$		0			0
$613$	3.34985	−	3.34985i	0.135299	−	0.135299i	−0.636214	−	0.771513i	$-0.719500\pi$
$613$	3.34985	−	3.34985i	0.135299	−	0.135299i	0.771513	+	0.636214i	$0.219500\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.04358	−	7.00369i	0.162789	−	0.281958i	−0.773079	−	0.634309i	$-0.781285\pi$
$617$	4.04358	−	7.00369i	0.162789	−	0.281958i	0.935868	+	0.352352i	$0.114618\pi$
$618$		0			0
$619$	−11.6692	+	43.5499i	−0.469023	+	1.75042i	0.174171	+	0.984715i	$0.444275\pi$
$619$	−11.6692	+	43.5499i	−0.469023	+	1.75042i	−0.643194	+	0.765703i	$0.722391\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.7590	+	18.6351i	0.431049	+	0.746599i
$624$		0			0
$625$	17.1046	−	29.6260i	0.684182	−	1.18504i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.95318	−	3.95318i	−0.157624	−	0.157624i
$630$		0			0
$631$	3.49919			0.139300			0.0696502	−	0.997571i	$-0.477812\pi$
$631$	3.49919			0.139300			0.0696502	+	0.997571i	$0.477812\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−18.3925	−	68.6417i	−0.729883	−	2.72396i
$636$		0			0
$637$	1.01266	−	3.77930i	0.0401231	−	0.149741i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.01739	+	2.31944i	−0.158677	+	0.0916125i	−0.577236	−	0.816577i	$-0.695869\pi$
$641$	−4.01739	+	2.31944i	−0.158677	+	0.0916125i	0.418559	+	0.908190i	$0.362535\pi$
$642$		0			0
$643$	10.6535	+	39.7595i	0.420134	+	1.56796i	0.774324	+	0.632789i	$0.218090\pi$
$643$	10.6535	+	39.7595i	0.420134	+	1.56796i	−0.354190	+	0.935173i	$0.615243\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			2.08960i			0.0821505i	0.999156	+	0.0410752i	$0.0130783\pi$
$647$			2.08960i			0.0821505i	−0.999156	+	0.0410752i	$0.986922\pi$
$648$		0			0
$649$		−	7.04684i		−	0.276613i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.75454	−	17.7442i	−0.186059	−	0.694383i	−0.994401	−	0.105670i	$-0.966301\pi$
$653$	−4.75454	−	17.7442i	−0.186059	−	0.694383i	0.808342	−	0.588713i	$-0.200365\pi$
$654$		0			0
$655$	61.6410	−	35.5885i	2.40851	−	1.39056i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−7.84088	+	29.2626i	−0.305437	+	1.13991i	0.627131	+	0.778914i	$0.284229\pi$
$659$	−7.84088	+	29.2626i	−0.305437	+	1.13991i	−0.932568	+	0.360994i	$0.882438\pi$
$660$		0			0
$661$	12.5011	+	46.6546i	0.486235	+	1.81465i	0.574434	+	0.818551i	$0.305222\pi$
$661$	12.5011	+	46.6546i	0.486235	+	1.81465i	−0.0881985	+	0.996103i	$0.528111\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−32.7549			−1.27018
$666$		0			0
$667$	14.8169	+	14.8169i	0.573714	+	0.573714i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15.8822	+	27.5087i	−0.613124	+	1.06196i
$672$		0			0
$673$	8.92590	+	15.4601i	0.344068	+	0.595944i	0.985184	−	0.171500i	$-0.0548615\pi$
$673$	8.92590	+	15.4601i	0.344068	+	0.595944i	−0.641116	+	0.767444i	$0.721528\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−0.575049	+	2.14611i	−0.0221009	+	0.0824818i	−0.976095	−	0.217342i	$-0.930261\pi$
$677$	−0.575049	+	2.14611i	−0.0221009	+	0.0824818i	0.953995	+	0.299824i	$0.0969279\pi$
$678$		0			0
$679$	7.33966	−	12.7127i	0.281670	−	0.487867i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.857818	−	0.857818i	0.0328235	−	0.0328235i	−0.690505	−	0.723328i	$-0.742611\pi$
$683$	0.857818	−	0.857818i	0.0328235	−	0.0328235i	0.723328	+	0.690505i	$0.242611\pi$
$684$		0			0
$685$	2.21214	+	2.21214i	0.0845216	+	0.0845216i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−15.4163	−	8.90063i	−0.587316	−	0.339087i
$690$		0			0
$691$	37.8791	+	10.1497i	1.44099	+	0.386112i	0.892880	−	0.450295i	$-0.148681\pi$
$691$	37.8791	+	10.1497i	1.44099	+	0.386112i	0.548109	+	0.836407i	$0.315348\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	72.6201	−	41.9272i	2.75464	−	1.59039i
$696$		0			0
$697$	3.74334	+	2.16122i	0.141789	+	0.0818619i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	14.3403	−	14.3403i	0.541627	−	0.541627i	−0.382379	−	0.924006i	$-0.624895\pi$
$701$	14.3403	−	14.3403i	0.541627	−	0.541627i	0.924006	+	0.382379i	$0.124895\pi$
$702$		0			0
$703$		−	5.45369i		−	0.205690i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−30.9838	+	8.30208i	−1.16527	+	0.312232i
$708$		0			0
$709$	−4.26177	−	1.14194i	−0.160054	−	0.0428864i	0.177902	−	0.984048i	$-0.443069\pi$
$709$	−4.26177	−	1.14194i	−0.160054	−	0.0428864i	−0.337956	+	0.941162i	$0.609736\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.606335	−	1.05020i	−0.0227074	−	0.0393304i
$714$		0			0
$715$	25.4279	−	6.81339i	0.950951	−	0.254806i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−49.2509			−1.83675			−0.918374	−	0.395714i	$-0.870497\pi$
$719$	−49.2509			−1.83675			−0.918374	+	0.395714i	$0.870497\pi$
$720$		0			0
$721$	−1.88938			−0.0703644
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−89.6203	+	24.0137i	−3.32841	+	0.891846i
$726$		0			0
$727$	2.18154	+	3.77855i	0.0809090	+	0.140139i	0.903641	−	0.428291i	$-0.140884\pi$
$727$	2.18154	+	3.77855i	0.0809090	+	0.140139i	−0.822732	+	0.568430i	$0.807551\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−13.7508	−	3.68451i	−0.508591	−	0.136277i
$732$		0			0
$733$	30.7314	−	8.23445i	1.13509	−	0.304146i	0.358114	−	0.933678i	$-0.383420\pi$
$733$	30.7314	−	8.23445i	1.13509	−	0.304146i	0.776975	+	0.629532i	$0.216753\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	26.8722i		−	0.989849i
$738$		0			0
$739$	32.4463	−	32.4463i	1.19356	−	1.19356i	0.217495	−	0.976061i	$-0.430211\pi$
$739$	32.4463	−	32.4463i	1.19356	−	1.19356i	0.976061	−	0.217495i	$-0.0697887\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.8406	−	6.25880i	−0.397702	−	0.229613i	0.287790	−	0.957693i	$-0.407079\pi$
$743$	−10.8406	−	6.25880i	−0.397702	−	0.229613i	−0.685492	+	0.728080i	$0.740413\pi$
$744$		0			0
$745$	40.0141	−	23.1021i	1.46600	−	0.846397i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−14.9973	−	4.01852i	−0.547990	−	0.146834i
$750$		0			0
$751$	34.0479	+	19.6575i	1.24242	+	0.717314i	0.969587	−	0.244747i	$-0.0787047\pi$
$751$	34.0479	+	19.6575i	1.24242	+	0.717314i	0.272837	+	0.962060i	$0.412038\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	23.6777	+	23.6777i	0.861718	+	0.861718i
$756$		0			0
$757$	−25.3026	+	25.3026i	−0.919640	+	0.919640i	−0.997003	−	0.0773631i	$-0.975350\pi$
$757$	−25.3026	+	25.3026i	−0.919640	+	0.919640i	0.0773631	+	0.997003i	$0.475350\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−11.0907	+	19.2097i	−0.402039	+	0.696352i	−0.993972	−	0.109635i	$-0.965032\pi$
$761$	−11.0907	+	19.2097i	−0.402039	+	0.696352i	0.591933	+	0.805987i	$0.298365\pi$
$762$		0			0
$763$	6.45338	−	24.0843i	0.233628	−	0.871911i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.12087	−	5.40551i	−0.112688	−	0.195182i
$768$		0			0
$769$	0.792978	−	1.37348i	0.0285955	−	0.0495289i	−0.851374	−	0.524560i	$-0.824230\pi$
$769$	0.792978	−	1.37348i	0.0285955	−	0.0495289i	0.879969	+	0.475031i	$0.157563\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.198602	+	0.198602i	0.00714323	+	0.00714323i	0.710669	−	0.703526i	$-0.248392\pi$
$773$	0.198602	+	0.198602i	0.00714323	+	0.00714323i	−0.703526	+	0.710669i	$0.748392\pi$
$774$		0			0
$775$	5.36948			0.192877
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.09132	+	4.07287i	0.0391007	+	0.145926i
$780$		0			0
$781$	3.30471	−	12.3334i	0.118252	−	0.441322i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.5149	−	7.22549i	0.446676	−	0.257889i
$786$		0			0
$787$	3.76684	+	14.0581i	0.134274	+	0.501116i	1.00000		0.000597888i	$0.000190314\pi$
$787$	3.76684	+	14.0581i	0.134274	+	0.501116i	−0.865726	+	0.500518i	$0.833143\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			48.9217i			1.73946i
$792$		0			0
$793$			28.1353i			0.999112i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.12214	+	11.6520i	0.110592	+	0.412734i	0.998919	−	0.0464762i	$-0.0147992\pi$
$797$	3.12214	+	11.6520i	0.110592	+	0.412734i	−0.888328	+	0.459210i	$0.848132\pi$
$798$		0			0
$799$	−16.3541	+	9.44202i	−0.578565	+	0.334035i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.49286	−	13.0355i	0.123261	−	0.460015i
$804$		0			0
$805$	7.17244	+	26.7679i	0.252795	+	0.943445i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.40097			0.189888			0.0949441	−	0.995483i	$-0.469733\pi$
$809$	5.40097			0.189888			0.0949441	+	0.995483i	$0.469733\pi$
$810$		0			0
$811$	−19.4041	−	19.4041i	−0.681371	−	0.681371i	0.278938	−	0.960309i	$-0.410018\pi$
$811$	−19.4041	−	19.4041i	−0.681371	−	0.681371i	−0.960309	+	0.278938i	$0.910018\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.7788	−	18.6695i	0.377566	−	0.653964i
$816$		0			0
$817$	−6.94356	−	12.0266i	−0.242924	−	0.420758i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.53178	−	20.6449i	0.193061	−	0.720512i	−0.799700	−	0.600400i	$-0.795008\pi$
$821$	5.53178	−	20.6449i	0.193061	−	0.720512i	0.992760	−	0.120112i	$-0.0383253\pi$
$822$		0			0
$823$	15.8047	−	27.3746i	0.550918	−	0.954217i	−0.447291	−	0.894389i	$-0.647611\pi$
$823$	15.8047	−	27.3746i	0.550918	−	0.954217i	0.998209	−	0.0598289i	$-0.0190555\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−11.4058	+	11.4058i	−0.396617	+	0.396617i	−0.877038	−	0.480421i	$-0.840484\pi$
$827$	−11.4058	+	11.4058i	−0.396617	+	0.396617i	0.480421	+	0.877038i	$0.340484\pi$
$828$		0			0
$829$	−15.8083	−	15.8083i	−0.549043	−	0.549043i	0.377121	−	0.926164i	$-0.376914\pi$
$829$	−15.8083	−	15.8083i	−0.549043	−	0.549043i	−0.926164	+	0.377121i	$0.876914\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.04098	+	2.33306i	0.140012	+	0.0808357i
$834$		0			0
$835$	−26.3457	−	7.05931i	−0.911730	−	0.244297i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−28.2922	+	16.3345i	−0.976755	+	0.563930i	−0.901289	−	0.433219i	$-0.857378\pi$
$839$	−28.2922	+	16.3345i	−0.976755	+	0.563930i	−0.0754662	+	0.997148i	$0.524044\pi$
$840$		0			0
$841$	41.3525	+	23.8749i	1.42595	+	0.823272i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−19.8083	+	19.8083i	−0.681428	+	0.681428i
$846$		0			0
$847$			10.1907i			0.350158i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.45686	+	1.19421i	−0.152779	+	0.0409371i
$852$		0			0
$853$	38.7224	+	10.3756i	1.32583	+	0.355255i	0.851159	−	0.524907i	$-0.175900\pi$
$853$	38.7224	+	10.3756i	1.32583	+	0.355255i	0.474672	+	0.880163i	$0.342567\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.0140657	+	0.0243624i	0.000480474	+	0.000832205i	0.866266	−	0.499584i	$-0.166514\pi$
$857$	0.0140657	+	0.0243624i	0.000480474	+	0.000832205i	−0.865785	+	0.500416i	$0.833180\pi$
$858$		0			0
$859$	−11.7598	+	3.15104i	−0.401240	+	0.107512i	−0.453795	−	0.891106i	$-0.649930\pi$
$859$	−11.7598	+	3.15104i	−0.401240	+	0.107512i	0.0525549	+	0.998618i	$0.483264\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	40.1140			1.36550			0.682748	−	0.730654i	$-0.260785\pi$
$863$	40.1140			1.36550			0.682748	+	0.730654i	$0.260785\pi$
$864$		0			0
$865$	−15.8140			−0.537692
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−11.0547	+	2.96211i	−0.375006	+	0.100483i
$870$		0			0
$871$	−11.9010	−	20.6132i	−0.403251	−	0.698451i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−62.5669	−	16.7647i	−2.11515	−	0.566752i
$876$		0			0
$877$	−45.8849	+	12.2948i	−1.54942	+	0.415167i	−0.929297	−	0.369334i	$-0.879586\pi$
$877$	−45.8849	+	12.2948i	−1.54942	+	0.415167i	−0.620127	+	0.784501i	$0.712919\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			20.6694i			0.696371i	0.937426	+	0.348186i	$0.113202\pi$
$881$			20.6694i			0.696371i	−0.937426	+	0.348186i	$0.886798\pi$
$882$		0			0
$883$	37.7611	−	37.7611i	1.27076	−	1.27076i	0.325075	−	0.945688i	$-0.394610\pi$
$883$	37.7611	−	37.7611i	1.27076	−	1.27076i	0.945688	−	0.325075i	$-0.105390\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.4908	−	14.1398i	−0.822322	−	0.474768i	0.0288948	−	0.999582i	$-0.490801\pi$
$887$	−24.4908	−	14.1398i	−0.822322	−	0.474768i	−0.851216	+	0.524815i	$0.824135\pi$
$888$		0			0
$889$	−45.7347	+	26.4049i	−1.53389	+	0.885593i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−17.7937	−	4.76782i	−0.595445	−	0.159549i
$894$		0			0
$895$	48.6615	+	28.0947i	1.62657	+	0.939103i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.14074	−	3.14074i	−0.104750	−	0.104750i
$900$		0			0
$901$	15.0115	−	15.0115i	0.500105	−	0.500105i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	41.9767	−	72.7058i	1.39535	−	2.41682i
$906$		0			0
$907$	9.12179	−	34.0430i	0.302884	−	1.13038i	−0.631867	−	0.775077i	$-0.717711\pi$
$907$	9.12179	−	34.0430i	0.302884	−	1.13038i	0.934751	−	0.355302i	$-0.115622\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.81619	−	15.2701i	−0.292093	−	0.505921i	0.682211	−	0.731155i	$-0.261018\pi$
$911$	−8.81619	−	15.2701i	−0.292093	−	0.505921i	−0.974305	+	0.225235i	$0.927685\pi$
$912$		0			0
$913$	17.8832	−	30.9746i	0.591847	−	1.02511i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−37.4020	−	37.4020i	−1.23512	−	1.23512i
$918$		0			0
$919$	−40.6483			−1.34086			−0.670431	−	0.741972i	$-0.733891\pi$
$919$	−40.6483			−1.34086			−0.670431	+	0.741972i	$0.733891\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.92715	−	10.9243i	−0.0963483	−	0.359577i
$924$		0			0
$925$	5.28775	−	19.7341i	0.173860	−	0.648855i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	46.7331	−	26.9814i	1.53326	−	0.885230i	0.534055	−	0.845450i	$-0.320667\pi$
$929$	46.7331	−	26.9814i	1.53326	−	0.885230i	0.999208	−	0.0397807i	$-0.0126659\pi$
$930$		0			0
$931$	1.17810	+	4.39672i	0.0386106	+	0.144097i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			31.3946i			1.02671i
$936$		0			0
$937$		−	47.0464i		−	1.53694i	−0.639886	−	0.768470i	$-0.721018\pi$
$937$		−	47.0464i		−	1.53694i	0.639886	−	0.768470i	$-0.278982\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.645083	−	2.40748i	−0.0210291	−	0.0784816i	0.954614	−	0.297846i	$-0.0962683\pi$
$941$	−0.645083	−	2.40748i	−0.0210291	−	0.0784816i	−0.975643	+	0.219365i	$0.929602\pi$
$942$		0			0
$943$	3.08946	−	1.78370i	0.100607	−	0.0580853i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.4692	−	50.2676i	0.437689	−	1.63348i	−0.296859	−	0.954921i	$-0.595939\pi$
$947$	13.4692	−	50.2676i	0.437689	−	1.63348i	0.734548	−	0.678557i	$-0.237394\pi$
$948$		0			0
$949$	−3.09381	−	11.5462i	−0.100429	−	0.374807i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−61.2734			−1.98484			−0.992420	−	0.122896i	$-0.960782\pi$
$953$	−61.2734			−1.98484			−0.992420	+	0.122896i	$0.960782\pi$
$954$		0			0
$955$	−60.8700	−	60.8700i	−1.96971	−	1.96971i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.16244	−	2.01340i	0.0375370	−	0.0650160i
$960$		0			0
$961$	−15.3715	−	26.6242i	−0.495854	−	0.858844i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.79750	+	17.9045i	−0.154437	+	0.576367i
$966$		0			0
$967$	3.75805	−	6.50913i	0.120851	−	0.209319i	−0.799253	−	0.600995i	$-0.794771\pi$
$967$	3.75805	−	6.50913i	0.120851	−	0.209319i	0.920103	+	0.391676i	$0.128104\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−20.5494	+	20.5494i	−0.659461	+	0.659461i	−0.955253	−	0.295791i	$-0.904417\pi$
$971$	−20.5494	+	20.5494i	−0.659461	+	0.659461i	0.295791	+	0.955253i	$0.404417\pi$
$972$		0			0
$973$	−44.0638	−	44.0638i	−1.41262	−	1.41262i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−48.8661	−	28.2129i	−1.56337	−	0.902610i	−0.996913	−	0.0785154i	$-0.974982\pi$
$977$	−48.8661	−	28.2129i	−1.56337	−	0.902610i	−0.566453	−	0.824094i	$-0.691685\pi$
$978$		0			0
$979$	19.4336	+	5.20721i	0.621100	+	0.166423i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	5.17882	−	2.98999i	0.165179	−	0.0953660i	−0.415132	−	0.909761i	$-0.636265\pi$
$983$	5.17882	−	2.98999i	0.165179	−	0.0953660i	0.580311	+	0.814395i	$0.302931\pi$
$984$		0			0
$985$	−69.2628	−	39.9889i	−2.20690	−	1.27415i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.30792	+	8.30792i	−0.264176	+	0.264176i
$990$		0			0
$991$		−	20.2358i		−	0.642812i	−0.946942	−	0.321406i	$-0.895845\pi$
$991$		−	20.2358i		−	0.642812i	0.946942	−	0.321406i	$-0.104155\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	55.2892	−	14.8147i	1.75278	−	0.469657i
$996$		0			0
$997$	0.647795	+	0.173576i	0.0205159	+	0.00549721i	0.269062	−	0.963123i	$-0.413286\pi$
$997$	0.647795	+	0.173576i	0.0205159	+	0.00549721i	−0.248547	+	0.968620i	$0.579953\pi$
$998$		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.1583.22		88
3.2	odd	2		576.2.y.a.239.3		88
4.3	odd	2		432.2.v.a.179.3		88
9.2	odd	6	inner	1728.2.z.a.1007.22		88
9.7	even	3		576.2.y.a.47.9		88
12.11	even	2		144.2.u.a.131.20	yes	88
16.5	even	4		432.2.v.a.395.5		88
16.11	odd	4	inner	1728.2.z.a.719.22		88
36.7	odd	6		144.2.u.a.83.18	yes	88
36.11	even	6		432.2.v.a.35.5		88
48.5	odd	4		144.2.u.a.59.18	yes	88
48.11	even	4		576.2.y.a.527.9		88
144.11	even	12	inner	1728.2.z.a.143.22		88
144.43	odd	12		576.2.y.a.335.3		88
144.101	odd	12		432.2.v.a.251.3		88
144.133	even	12		144.2.u.a.11.20	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.20	✓	88	144.133	even	12
144.2.u.a.59.18	yes	88	48.5	odd	4
144.2.u.a.83.18	yes	88	36.7	odd	6
144.2.u.a.131.20	yes	88	12.11	even	2
432.2.v.a.35.5		88	36.11	even	6
432.2.v.a.179.3		88	4.3	odd	2
432.2.v.a.251.3		88	144.101	odd	12
432.2.v.a.395.5		88	16.5	even	4
576.2.y.a.47.9		88	9.7	even	3
576.2.y.a.239.3		88	3.2	odd	2
576.2.y.a.335.3		88	144.43	odd	12
576.2.y.a.527.9		88	48.11	even	4
1728.2.z.a.143.22		88	144.11	even	12	inner
1728.2.z.a.719.22		88	16.11	odd	4	inner
1728.2.z.a.1007.22		88	9.2	odd	6	inner
1728.2.z.a.1583.22		88	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(3.81396 - 1.02195i) q^{5} +(-1.46715 - 2.54117i) q^{7} +O(q^{10})\)	\(q+(3.81396 - 1.02195i) q^{5} +(-1.46715 - 2.54117i) q^{7} +(-2.65006 - 0.710081i) q^{11} +(-2.34729 + 0.628955i) q^{13} -2.89808i q^{17} +(1.99906 - 1.99906i) q^{19} +(-2.07141 - 1.19593i) q^{23} +(9.17180 - 5.29534i) q^{25} +(-8.46218 - 2.26743i) q^{29} +(0.439075 + 0.253500i) q^{31} +(-8.19258 - 8.19258i) q^{35} +(1.36407 - 1.36407i) q^{37} +(-0.745739 + 1.29166i) q^{41} +(1.27136 - 4.74478i) q^{43} +(-3.25802 - 5.64306i) q^{47} +(-0.805035 + 1.39436i) q^{49} +(5.17979 + 5.17979i) q^{53} -10.8329 q^{55} +(0.664781 + 2.48100i) q^{59} +(2.99657 - 11.1833i) q^{61} +(-8.30972 + 4.79762i) q^{65} +(2.53505 + 9.46095i) q^{67} +4.65399i q^{71} +4.91897i q^{73} +(2.08358 + 7.77604i) q^{77} +(3.61263 - 2.08575i) q^{79} +(-3.37411 + 12.5924i) q^{83} +(-2.96169 - 11.0532i) q^{85} -7.33327 q^{89} +(5.04210 + 5.04210i) q^{91} +(5.58139 - 9.66725i) q^{95} +(2.50134 + 4.33245i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7}+O(q^{10}) \) 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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