LMFDB - Embedded newform 3024.2.cc.b.881.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(881,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3024, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.cc (of order $6$, degree $2$, 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:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.8
Root			$1.62181 + 0.608059i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.b.2897.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.94556 - 3.36980i) q^{5} +(-2.09985 - 1.60954i) q^{7} +O(q^{10})$	$q+(1.94556 - 3.36980i) q^{5} +(-2.09985 - 1.60954i) q^{7} +(3.41614 - 1.97231i) q^{11} +(-2.46687 - 1.42425i) q^{13} +0.742117 q^{17} -1.78474i q^{19} +(-5.41535 - 3.12656i) q^{23} +(-5.07039 - 8.78217i) q^{25} +(2.50079 - 1.44383i) q^{29} +(3.04125 + 1.75587i) q^{31} +(-9.50923 + 3.94462i) q^{35} +3.00158 q^{37} +(-5.24705 + 9.08816i) q^{41} +(-0.471521 - 0.816699i) q^{43} +(-1.09263 - 1.89248i) q^{47} +(1.81873 + 6.75960i) q^{49} -15.3490i q^{55} +(-0.0105673 + 0.0183031i) q^{59} +(2.13832 - 1.23456i) q^{61} +(-9.59886 + 5.54191i) q^{65} +(6.72463 - 11.6474i) q^{67} -1.94304i q^{71} -4.85486i q^{73} +(-10.3479 - 1.35688i) q^{77} +(1.81806 + 3.14898i) q^{79} +(4.02998 + 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} -9.26646 q^{89} +(2.88766 + 6.96124i) q^{91} +(-6.01422 - 3.47231i) q^{95} +(-16.2983 + 9.40980i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.94556	−	3.36980i	0.870080	−	1.50702i	0.00816625	−	0.999967i	$-0.497401\pi$
$5$	1.94556	−	3.36980i	0.870080	−	1.50702i	0.861913	−	0.507056i	$-0.169266\pi$
$6$		0			0
$7$	−2.09985	−	1.60954i	−0.793668	−	0.608351i
$7$	−2.09985	−	1.60954i	−0.793668	−	0.608351i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.41614	−	1.97231i	1.03001	−	0.594674i	0.113019	−	0.993593i	$-0.463948\pi$
$11$	3.41614	−	1.97231i	1.03001	−	0.594674i	0.916986	+	0.398919i	$0.130615\pi$
$12$		0			0
$13$	−2.46687	−	1.42425i	−0.684186	−	0.395015i	0.117244	−	0.993103i	$-0.462594\pi$
$13$	−2.46687	−	1.42425i	−0.684186	−	0.395015i	−0.801430	+	0.598088i	$0.795927\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.742117			0.179990			0.0899949	−	0.995942i	$-0.471315\pi$
$17$	0.742117			0.179990			0.0899949	+	0.995942i	$0.471315\pi$
$18$		0			0
$19$		−	1.78474i		−	0.409447i	−0.978820	−	0.204723i	$-0.934370\pi$
$19$		−	1.78474i		−	0.409447i	0.978820	−	0.204723i	$-0.0656295\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.41535	−	3.12656i	−1.12918	−	0.651932i	−0.185451	−	0.982654i	$-0.559374\pi$
$23$	−5.41535	−	3.12656i	−1.12918	−	0.651932i	−0.943728	+	0.330722i	$0.892708\pi$
$24$		0			0
$25$	−5.07039	−	8.78217i	−1.01408	−	1.75643i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.50079	−	1.44383i	0.464385	−	0.268113i	−0.249501	−	0.968374i	$-0.580267\pi$
$29$	2.50079	−	1.44383i	0.464385	−	0.268113i	0.713886	+	0.700262i	$0.246933\pi$
$30$		0			0
$31$	3.04125	+	1.75587i	0.546225	+	0.315363i	0.747598	−	0.664152i	$-0.231207\pi$
$31$	3.04125	+	1.75587i	0.546225	+	0.315363i	−0.201373	+	0.979515i	$0.564540\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−9.50923	+	3.94462i	−1.60735	+	0.666762i
$36$		0			0
$37$	3.00158			0.493456			0.246728	−	0.969085i	$-0.420645\pi$
$37$	3.00158			0.493456			0.246728	+	0.969085i	$0.420645\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.24705	+	9.08816i	−0.819452	+	1.41933i	0.0866345	+	0.996240i	$0.472389\pi$
$41$	−5.24705	+	9.08816i	−0.819452	+	1.41933i	−0.906087	+	0.423092i	$0.860945\pi$
$42$		0			0
$43$	−0.471521	−	0.816699i	−0.0719063	−	0.124545i	0.827830	−	0.560978i	$-0.189575\pi$
$43$	−0.471521	−	0.816699i	−0.0719063	−	0.124545i	−0.899737	+	0.436433i	$0.856242\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.09263	−	1.89248i	−0.159376	−	0.276047i	0.775268	−	0.631633i	$-0.217615\pi$
$47$	−1.09263	−	1.89248i	−0.159376	−	0.276047i	−0.934644	+	0.355585i	$0.884282\pi$
$48$		0			0
$49$	1.81873	+	6.75960i	0.259819	+	0.965657i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		−	15.3490i		−	2.06965i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.0105673	+	0.0183031i	−0.00137575	+	0.00238286i	−0.866712	−	0.498808i	$-0.833771\pi$
$59$	−0.0105673	+	0.0183031i	−0.00137575	+	0.00238286i	0.865337	+	0.501191i	$0.167105\pi$
$60$		0			0
$61$	2.13832	−	1.23456i	0.273783	−	0.158069i	−0.356822	−	0.934172i	$-0.616140\pi$
$61$	2.13832	−	1.23456i	0.273783	−	0.158069i	0.630606	+	0.776103i	$0.282807\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.59886	+	5.54191i	−1.19059	+	0.687389i
$66$		0			0
$67$	6.72463	−	11.6474i	0.821544	−	1.42296i	−0.0829874	−	0.996551i	$-0.526446\pi$
$67$	6.72463	−	11.6474i	0.821544	−	1.42296i	0.904532	−	0.426406i	$-0.140221\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.94304i		−	0.230597i	−0.993331	−	0.115298i	$-0.963218\pi$
$71$		−	1.94304i		−	0.230597i	0.993331	−	0.115298i	$-0.0367824\pi$
$72$		0			0
$73$		−	4.85486i		−	0.568218i	−0.958792	−	0.284109i	$-0.908302\pi$
$73$		−	4.85486i		−	0.568218i	0.958792	−	0.284109i	$-0.0916978\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.3479	−	1.35688i	−1.17925	−	0.154630i
$78$		0			0
$79$	1.81806	+	3.14898i	0.204548	+	0.354288i	0.949989	−	0.312284i	$-0.101094\pi$
$79$	1.81806	+	3.14898i	0.204548	+	0.354288i	−0.745440	+	0.666572i	$0.767761\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.02998	+	6.98012i	0.442347	+	0.766168i	0.997863	−	0.0653378i	$-0.0208125\pi$
$83$	4.02998	+	6.98012i	0.442347	+	0.766168i	−0.555516	+	0.831506i	$0.687479\pi$
$84$		0			0
$85$	1.44383	−	2.50079i	0.156605	−	0.271249i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−9.26646			−0.982243			−0.491122	−	0.871091i	$-0.663413\pi$
$89$	−9.26646			−0.982243			−0.491122	+	0.871091i	$0.663413\pi$
$90$		0			0
$91$	2.88766	+	6.96124i	0.302709	+	0.729736i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.01422	−	3.47231i	−0.617046	−	0.356251i
$96$		0			0
$97$	−16.2983	+	9.40980i	−1.65484	+	0.955421i	−0.679794	+	0.733403i	$0.737931\pi$
$97$	−16.2983	+	9.40980i	−1.65484	+	0.955421i	−0.975043	+	0.222018i	$0.928736\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.14079	+	7.17206i	0.412024	+	0.713647i	0.995111	−	0.0987631i	$-0.0314886\pi$
$101$	4.14079	+	7.17206i	0.412024	+	0.713647i	−0.583087	+	0.812410i	$0.698155\pi$
$102$		0			0
$103$	−14.7646	−	8.52435i	−1.45480	−	0.839929i	−0.456051	−	0.889953i	$-0.650737\pi$
$103$	−14.7646	−	8.52435i	−1.45480	−	0.839929i	−0.998748	+	0.0500247i	$0.984070\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			14.3369i			1.38600i	0.720936	+	0.693001i	$0.243712\pi$
$107$			14.3369i			1.38600i	−0.720936	+	0.693001i	$0.756288\pi$
$108$		0			0
$109$	11.2800			1.08042			0.540212	−	0.841529i	$-0.318344\pi$
$109$	11.2800			1.08042			0.540212	+	0.841529i	$0.318344\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.51501	+	4.91614i	0.801024	+	0.462472i	0.843829	−	0.536612i	$-0.180296\pi$
$113$	8.51501	+	4.91614i	0.801024	+	0.462472i	−0.0428049	+	0.999083i	$0.513629\pi$
$114$		0			0
$115$	−21.0718	+	12.1658i	−1.96495	+	1.13447i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−1.55833	−	1.19447i	−0.142852	−	0.109497i
$120$		0			0
$121$	2.28001	−	3.94910i	0.207274	−	0.359009i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−20.0033			−1.78915
$126$		0			0
$127$	−2.94462			−0.261293			−0.130646	−	0.991429i	$-0.541705\pi$
$127$	−2.94462			−0.261293			−0.130646	+	0.991429i	$0.541705\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.53255	+	13.0468i	−0.658122	+	1.13990i	0.322979	+	0.946406i	$0.395316\pi$
$131$	−7.53255	+	13.0468i	−0.658122	+	1.13990i	−0.981101	+	0.193495i	$0.938018\pi$
$132$		0			0
$133$	−2.87261	+	3.74768i	−0.249087	+	0.324965i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.6139	−	7.85997i	1.16311	−	0.671523i	0.211064	−	0.977472i	$-0.432307\pi$
$137$	13.6139	−	7.85997i	1.16311	−	0.671523i	0.952048	+	0.305950i	$0.0989739\pi$
$138$		0			0
$139$	2.86373	+	1.65337i	0.242898	+	0.140237i	0.616508	−	0.787349i	$-0.288547\pi$
$139$	2.86373	+	1.65337i	0.242898	+	0.140237i	−0.373610	+	0.927586i	$0.621880\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−11.2362			−0.939620
$144$		0			0
$145$		−	11.2362i		−	0.933118i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.52765	−	5.50079i	−0.780535	−	0.450642i	0.0560848	−	0.998426i	$-0.482138\pi$
$149$	−9.52765	−	5.50079i	−0.780535	−	0.450642i	−0.836620	+	0.547784i	$0.815472\pi$
$150$		0			0
$151$	−0.719988	−	1.24706i	−0.0585918	−	0.101484i	0.835242	−	0.549883i	$-0.185328\pi$
$151$	−0.719988	−	1.24706i	−0.0585918	−	0.101484i	−0.893834	+	0.448399i	$0.851994\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.8339	−	6.83228i	0.950518	−	0.548782i
$156$		0			0
$157$	−14.3822	−	8.30354i	−1.14782	−	0.662695i	−0.199465	−	0.979905i	$-0.563921\pi$
$157$	−14.3822	−	8.30354i	−1.14782	−	0.662695i	−0.948355	+	0.317210i	$0.897254\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.33909	+	15.2815i	0.499591	+	1.20435i
$162$		0			0
$163$	12.3955			0.970887			0.485444	−	0.874268i	$-0.338658\pi$
$163$	12.3955			0.970887			0.485444	+	0.874268i	$0.338658\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.86087	−	10.1513i	0.453528	−	0.785534i	−0.545074	−	0.838388i	$-0.683498\pi$
$167$	5.86087	−	10.1513i	0.453528	−	0.785534i	0.998602	+	0.0528541i	$0.0168318\pi$
$168$		0			0
$169$	−2.44304	−	4.23147i	−0.187926	−	0.325498i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.38548	−	14.5241i	−0.637536	−	1.10425i	−0.985972	−	0.166913i	$-0.946620\pi$
$173$	−8.38548	−	14.5241i	−0.637536	−	1.10425i	0.348435	−	0.937333i	$-0.386713\pi$
$174$		0			0
$175$	−3.48824	+	26.6022i	−0.263686	+	2.01094i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	5.77532i		−	0.431668i	−0.976430	−	0.215834i	$-0.930753\pi$
$179$		−	5.77532i		−	0.431668i	0.976430	−	0.215834i	$-0.0692470\pi$
$180$		0			0
$181$		−	5.53310i		−	0.411272i	−0.978629	−	0.205636i	$-0.934074\pi$
$181$		−	5.53310i		−	0.411272i	0.978629	−	0.205636i	$-0.0659263\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.83974	−	10.1147i	0.429346	−	0.743649i
$186$		0			0
$187$	2.53518	−	1.46368i	0.185390	−	0.107035i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.38124	+	3.10686i	−0.389373	+	0.224805i	−0.681888	−	0.731456i	$-0.738841\pi$
$191$	−5.38124	+	3.10686i	−0.389373	+	0.224805i	0.292515	+	0.956261i	$0.405508\pi$
$192$		0			0
$193$	3.90271	−	6.75970i	0.280923	−	0.486574i	−0.690689	−	0.723152i	$-0.742693\pi$
$193$	3.90271	−	6.75970i	0.280923	−	0.486574i	0.971612	+	0.236578i	$0.0760260\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.7737i		−	0.910092i	−0.890468	−	0.455046i	$-0.849623\pi$
$197$		−	12.7737i		−	0.910092i	0.890468	−	0.455046i	$-0.150377\pi$
$198$		0			0
$199$			1.81201i			0.128450i	0.997935	+	0.0642250i	$0.0204575\pi$
$199$			1.81201i			0.128450i	−0.997935	+	0.0642250i	$0.979542\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.57519	−	0.993303i	−0.531674	−	0.0697162i
$204$		0			0
$205$	20.4169	+	35.3631i	1.42598	+	2.46986i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.52006	−	6.09692i	−0.243487	−	0.421732i
$210$		0			0
$211$	1.88766	−	3.26953i	0.129952	−	0.225083i	−0.793706	−	0.608302i	$-0.791851\pi$
$211$	1.88766	−	3.26953i	0.129952	−	0.225083i	0.923658	+	0.383218i	$0.125184\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.66949			−0.250257
$216$		0			0
$217$	−3.56002	−	8.58209i	−0.241670	−	0.582590i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.83070	−	1.05696i	−0.123146	−	0.0710987i
$222$		0			0
$223$	11.0662	−	6.38910i	0.741051	−	0.427846i	−0.0814006	−	0.996681i	$-0.525939\pi$
$223$	11.0662	−	6.38910i	0.741051	−	0.427846i	0.822451	+	0.568836i	$0.192606\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.99110	+	17.3051i	0.663133	+	1.14858i	0.979788	+	0.200039i	$0.0641068\pi$
$227$	9.99110	+	17.3051i	0.663133	+	1.14858i	−0.316655	+	0.948541i	$0.602560\pi$
$228$		0			0
$229$	−8.77402	−	5.06568i	−0.579804	−	0.334750i	0.181252	−	0.983437i	$-0.441985\pi$
$229$	−8.77402	−	5.06568i	−0.579804	−	0.334750i	−0.761055	+	0.648687i	$0.775318\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	7.31007i		−	0.478898i	−0.970909	−	0.239449i	$-0.923033\pi$
$233$		−	7.31007i		−	0.478898i	0.970909	−	0.239449i	$-0.0769669\pi$
$234$		0			0
$235$	−8.50307			−0.554679
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.28317	+	4.20494i	0.471109	+	0.271995i	0.716704	−	0.697378i	$-0.245650\pi$
$239$	7.28317	+	4.20494i	0.471109	+	0.271995i	−0.245595	+	0.969373i	$0.578983\pi$
$240$		0			0
$241$	7.75277	−	4.47607i	0.499400	−	0.288329i	−0.229066	−	0.973411i	$-0.573567\pi$
$241$	7.75277	−	4.47607i	0.499400	−	0.288329i	0.728466	+	0.685082i	$0.240234\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	26.3170	+	7.02242i	1.68133	+	0.448646i
$246$		0			0
$247$	−2.54191	+	4.40271i	−0.161738	+	0.280138i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−12.6432			−0.798033			−0.399017	−	0.916944i	$-0.630648\pi$
$251$	−12.6432			−0.798033			−0.399017	+	0.916944i	$0.630648\pi$
$252$		0			0
$253$	−24.6661			−1.55075
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.15329	+	14.1219i	−0.508588	+	0.880900i	0.491362	+	0.870955i	$0.336499\pi$
$257$	−8.15329	+	14.1219i	−0.508588	+	0.880900i	−0.999951	+	0.00994523i	$0.996834\pi$
$258$		0			0
$259$	−6.30286	−	4.83117i	−0.391641	−	0.300194i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.5434	−	11.8608i	1.26676	−	0.731366i	0.292389	−	0.956300i	$-0.405550\pi$
$263$	20.5434	−	11.8608i	1.26676	−	0.731366i	0.974374	+	0.224934i	$0.0722166\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.28288			0.444045			0.222022	−	0.975042i	$-0.428734\pi$
$269$	7.28288			0.444045			0.222022	+	0.975042i	$0.428734\pi$
$270$		0			0
$271$			22.6879i			1.37819i	0.724669	+	0.689097i	$0.241993\pi$
$271$			22.6879i			1.37819i	−0.724669	+	0.689097i	$0.758007\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−34.6423	−	20.0007i	−2.08901	−	1.20609i
$276$		0			0
$277$	−12.0838	−	20.9298i	−0.726046	−	1.25755i	−0.958542	−	0.284951i	$-0.908023\pi$
$277$	−12.0838	−	20.9298i	−0.726046	−	1.25755i	0.232496	−	0.972597i	$-0.425311\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4.11229	−	2.37423i	0.245319	−	0.141635i	−0.372300	−	0.928112i	$-0.621431\pi$
$281$	4.11229	−	2.37423i	0.245319	−	0.141635i	0.617619	+	0.786478i	$0.288097\pi$
$282$		0			0
$283$	−25.4484	−	14.6926i	−1.51275	−	0.873387i	−0.999889	−	0.0149153i	$-0.995252\pi$
$283$	−25.4484	−	14.6926i	−1.51275	−	0.873387i	−0.512861	−	0.858471i	$-0.671415\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	25.6458	−	10.6384i	1.51382	−	0.627965i
$288$		0			0
$289$	−16.4493			−0.967604
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.31206	−	5.73666i	0.193493	−	0.335139i	−0.752913	−	0.658121i	$-0.771352\pi$
$293$	3.31206	−	5.73666i	0.193493	−	0.335139i	0.946405	+	0.322981i	$0.104685\pi$
$294$		0			0
$295$	0.0411186	+	0.0712195i	0.00239402	+	0.00414656i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.90597	+	15.4256i	0.515046	+	0.892085i
$300$		0			0
$301$	−0.324389	+	2.47388i	−0.0186975	+	0.142592i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	9.60761i		−	0.550130i
$306$		0			0
$307$		−	21.7242i		−	1.23987i	−0.784655	−	0.619933i	$-0.787160\pi$
$307$		−	21.7242i		−	1.23987i	0.784655	−	0.619933i	$-0.212840\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.14900	+	5.45422i	−0.178563	+	0.309281i	−0.941389	−	0.337324i	$-0.890478\pi$
$311$	−3.14900	+	5.45422i	−0.178563	+	0.309281i	0.762825	+	0.646605i	$0.223812\pi$
$312$		0			0
$313$	19.2423	−	11.1095i	1.08764	−	0.627948i	0.154691	−	0.987963i	$-0.450562\pi$
$313$	19.2423	−	11.1095i	1.08764	−	0.627948i	0.932946	+	0.360015i	$0.117229\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−13.5632	+	7.83070i	−0.761784	+	0.439816i	−0.829936	−	0.557859i	$-0.811623\pi$
$317$	−13.5632	+	7.83070i	−0.761784	+	0.439816i	0.0681519	+	0.997675i	$0.478290\pi$
$318$		0			0
$319$	5.69536	−	9.86466i	0.318879	−	0.552315i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.32448i		−	0.0736963i
$324$		0			0
$325$			28.8859i			1.60230i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.751687	+	5.73256i	−0.0414418	+	0.316046i
$330$		0			0
$331$	0.636129	+	1.10181i	0.0349648	+	0.0605608i	0.882978	−	0.469414i	$-0.155535\pi$
$331$	0.636129	+	1.10181i	0.0349648	+	0.0605608i	−0.848013	+	0.529975i	$0.822201\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−26.1663	−	45.3214i	−1.42962	−	2.47617i
$336$		0			0
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	−0.950422	−	0.310962i	$-0.899349\pi$
$337$	−3.78001	+	6.54717i	−0.205910	+	0.356647i	0.744512	+	0.667609i	$0.232682\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	13.8525			0.750153
$342$		0			0
$343$	7.06081	−	17.1215i	0.381248	−	0.924473i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.1470	+	11.0545i	1.02787	+	0.593439i	0.916373	−	0.400326i	$-0.131103\pi$
$347$	19.1470	+	11.0545i	1.02787	+	0.593439i	0.111494	+	0.993765i	$0.464436\pi$
$348$		0			0
$349$	12.7682	−	7.37173i	0.683467	−	0.394600i	−0.117693	−	0.993050i	$-0.537550\pi$
$349$	12.7682	−	7.37173i	0.683467	−	0.394600i	0.801160	+	0.598450i	$0.204217\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	8.63881	+	14.9629i	0.459798	+	0.796393i	0.998950	−	0.0458154i	$-0.0145886\pi$
$353$	8.63881	+	14.9629i	0.459798	+	0.796393i	−0.539152	+	0.842208i	$0.681255\pi$
$354$		0			0
$355$	−6.54767	−	3.78030i	−0.347514	−	0.200638i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			10.9129i			0.575963i	0.957636	+	0.287982i	$0.0929842\pi$
$359$			10.9129i			0.575963i	−0.957636	+	0.287982i	$0.907016\pi$
$360$		0			0
$361$	15.8147			0.832353
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−16.3599	−	9.44541i	−0.856318	−	0.494395i
$366$		0			0
$367$	30.9407	−	17.8636i	1.61509	−	0.932472i	0.626923	−	0.779081i	$-0.284314\pi$
$367$	30.9407	−	17.8636i	1.61509	−	0.932472i	0.988166	−	0.153391i	$-0.0490194\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	16.0300	−	27.7648i	0.830003	−	1.43761i	−0.0680328	−	0.997683i	$-0.521672\pi$
$373$	16.0300	−	27.7648i	0.830003	−	1.43761i	0.898035	−	0.439923i	$-0.144994\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−8.22549			−0.423634
$378$		0			0
$379$	−34.8891			−1.79214			−0.896068	−	0.443918i	$-0.853588\pi$
$379$	−34.8891			−1.79214			−0.896068	+	0.443918i	$0.853588\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.76711	−	15.1851i	0.447978	−	0.775921i	−0.550276	−	0.834983i	$-0.685477\pi$
$383$	8.76711	−	15.1851i	0.447978	−	0.775921i	0.998254	+	0.0590616i	$0.0188108\pi$
$384$		0			0
$385$	−24.7048	+	32.2305i	−1.25908	+	1.64262i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.60060	−	3.81086i	0.334664	−	0.193218i	−0.323246	−	0.946315i	$-0.604774\pi$
$389$	6.60060	−	3.81086i	0.334664	−	0.193218i	0.657910	+	0.753097i	$0.271441\pi$
$390$		0			0
$391$	−4.01882	−	2.32027i	−0.203241	−	0.117341i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	14.1486			0.711893
$396$		0			0
$397$			37.6469i			1.88944i	0.327873	+	0.944722i	$0.393668\pi$
$397$			37.6469i			1.88944i	−0.327873	+	0.944722i	$0.606332\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−18.5689	−	10.7207i	−0.927284	−	0.535368i	−0.0413326	−	0.999145i	$-0.513160\pi$
$401$	−18.5689	−	10.7207i	−0.927284	−	0.535368i	−0.885952	+	0.463778i	$0.846494\pi$
$402$		0			0
$403$	−5.00158	−	8.66299i	−0.249146	−	0.431534i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	10.2538	−	5.92004i	0.508262	−	0.293445i
$408$		0			0
$409$	25.6086	+	14.7851i	1.26627	+	0.731079i	0.974279	−	0.225344i	$-0.0723506\pi$
$409$	25.6086	+	14.7851i	1.26627	+	0.731079i	0.291986	+	0.956423i	$0.405684\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.0516494	−	0.0214252i	0.00254150	−	0.00105427i
$414$		0			0
$415$	31.3622			1.53951
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.56481	+	6.17443i	−0.174152	+	0.301641i	−0.939868	−	0.341539i	$-0.889052\pi$
$419$	−3.56481	+	6.17443i	−0.174152	+	0.301641i	0.765715	+	0.643180i	$0.222385\pi$
$420$		0			0
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	0.804226	−	0.594323i	$-0.202580\pi$
$421$	−2.31007	−	4.00115i	−0.112586	−	0.195004i	−0.916812	+	0.399319i	$0.869247\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.76282	−	6.51739i	−0.182524	−	0.316140i
$426$		0			0
$427$	−6.47721	−	0.849330i	−0.313454	−	0.0411020i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	4.00771i		−	0.193045i	−0.995331	−	0.0965223i	$-0.969228\pi$
$431$		−	4.00771i		−	0.193045i	0.995331	−	0.0965223i	$-0.0307719\pi$
$432$		0			0
$433$		−	29.4125i		−	1.41348i	−0.707475	−	0.706738i	$-0.750166\pi$
$433$		−	29.4125i		−	1.41348i	0.707475	−	0.706738i	$-0.249834\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.58008	+	9.66498i	−0.266931	+	0.462339i
$438$		0			0
$439$	18.5130	−	10.6885i	0.883575	−	0.510133i	0.0117398	−	0.999931i	$-0.496263\pi$
$439$	18.5130	−	10.6885i	0.883575	−	0.510133i	0.871836	+	0.489799i	$0.162930\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.05227	−	2.91693i	0.240041	−	0.138587i	−0.375155	−	0.926962i	$-0.622410\pi$
$443$	5.05227	−	2.91693i	0.240041	−	0.138587i	0.615195	+	0.788375i	$0.289077\pi$
$444$		0			0
$445$	−18.0284	+	31.2262i	−0.854630	+	1.48026i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			22.5823i			1.06573i	0.846202	+	0.532863i	$0.178884\pi$
$449$			22.5823i			1.06573i	−0.846202	+	0.532863i	$0.821116\pi$
$450$		0			0
$451$			41.3953i			1.94923i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	29.0761	+	3.81263i	1.36311	+	0.178739i
$456$		0			0
$457$	−19.9311	−	34.5218i	−0.932340	−	1.61486i	−0.779310	−	0.626638i	$-0.784430\pi$
$457$	−19.9311	−	34.5218i	−0.932340	−	1.61486i	−0.153029	−	0.988222i	$-0.548903\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.68254	+	6.37834i	0.171513	+	0.297069i	0.938949	−	0.344056i	$-0.111801\pi$
$461$	3.68254	+	6.37834i	0.171513	+	0.297069i	−0.767436	+	0.641125i	$0.778468\pi$
$462$		0			0
$463$	14.3457	−	24.8475i	0.666702	−	1.15476i	−0.312119	−	0.950043i	$-0.601039\pi$
$463$	14.3457	−	24.8475i	0.666702	−	1.15476i	0.978821	−	0.204718i	$-0.0656278\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.6704			−0.632590			−0.316295	−	0.948661i	$-0.602439\pi$
$467$	−13.6704			−0.632590			−0.316295	+	0.948661i	$0.602439\pi$
$468$		0			0
$469$	−32.8677	+	13.6342i	−1.51769	+	0.629569i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.22157	−	1.85997i	−0.148128	−	0.0855216i
$474$		0			0
$475$	−15.6739	+	9.04931i	−0.719166	+	0.415211i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.20537	+	9.01596i	0.237839	+	0.411950i	0.960094	−	0.279677i	$-0.0902275\pi$
$479$	5.20537	+	9.01596i	0.237839	+	0.411950i	−0.722255	+	0.691627i	$0.756894\pi$
$480$		0			0
$481$	−7.40449	−	4.27499i	−0.337616	−	0.194923i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			73.2292i			3.32517i
$486$		0			0
$487$	−2.33850			−0.105968			−0.0529838	−	0.998595i	$-0.516873\pi$
$487$	−2.33850			−0.105968			−0.0529838	+	0.998595i	$0.516873\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−29.3448	−	16.9422i	−1.32431	−	0.764591i	−0.339898	−	0.940462i	$-0.610392\pi$
$491$	−29.3448	−	16.9422i	−1.32431	−	0.764591i	−0.984413	+	0.175871i	$0.943726\pi$
$492$		0			0
$493$	1.85588	−	1.07149i	0.0835845	−	0.0482575i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.12741	+	4.08010i	−0.140284	+	0.183017i
$498$		0			0
$499$	−8.30223	+	14.3799i	−0.371659	+	0.643732i	−0.989821	−	0.142319i	$-0.954544\pi$
$499$	−8.30223	+	14.3799i	−0.371659	+	0.643732i	0.618162	+	0.786051i	$0.287877\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−35.3661			−1.57690			−0.788449	−	0.615100i	$-0.789115\pi$
$503$	−35.3661			−1.57690			−0.788449	+	0.615100i	$0.789115\pi$
$504$		0			0
$505$	32.2246			1.43398
$506$		0			0
$507$		0			0
$508$		0			0
$509$	18.5291	−	32.0933i	0.821287	−	1.42251i	−0.0834371	−	0.996513i	$-0.526590\pi$
$509$	18.5291	−	32.0933i	0.821287	−	1.42251i	0.904724	−	0.425998i	$-0.140077\pi$
$510$		0			0
$511$	−7.81411	+	10.1945i	−0.345676	+	0.450977i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−57.4507	+	33.1692i	−2.53158	+	1.46161i
$516$		0			0
$517$	−7.46513	−	4.30999i	−0.328316	−	0.189553i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.78309			−0.0781187			−0.0390594	−	0.999237i	$-0.512436\pi$
$521$	−1.78309			−0.0781187			−0.0390594	+	0.999237i	$0.512436\pi$
$522$		0			0
$523$			24.0538i			1.05180i	0.850546	+	0.525901i	$0.176272\pi$
$523$			24.0538i			1.05180i	−0.850546	+	0.525901i	$0.823728\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.25696	+	1.30306i	0.0983149	+	0.0567621i
$528$		0			0
$529$	8.05069	+	13.9442i	0.350030	+	0.606270i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	25.8876	−	14.9462i	1.12132	−	0.647392i
$534$		0			0
$535$	48.3126	+	27.8933i	2.08874	+	1.20593i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	19.5451	+	19.5046i	0.841866	+	0.840124i
$540$		0			0
$541$	30.0032			1.28994			0.644968	−	0.764209i	$-0.276871\pi$
$541$	30.0032			1.28994			0.644968	+	0.764209i	$0.276871\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	21.9458	−	38.0113i	0.940056	−	1.62822i
$546$		0			0
$547$	10.7816	+	18.6743i	0.460987	+	0.798454i	0.999010	−	0.0444765i	$-0.0141620\pi$
$547$	10.7816	+	18.6743i	0.460987	+	0.798454i	−0.538023	+	0.842930i	$0.680829\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.57686	−	4.46325i	−0.109778	−	0.190141i
$552$		0			0
$553$	1.25076	−	9.53864i	0.0531878	−	0.405624i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			36.9477i			1.56552i	0.622321	+	0.782762i	$0.286190\pi$
$557$			36.9477i			1.56552i	−0.622321	+	0.782762i	$0.713810\pi$
$558$		0			0
$559$			2.68625i			0.113616i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.58422	−	13.1363i	0.319637	−	0.553627i	−0.660776	−	0.750584i	$-0.729772\pi$
$563$	7.58422	−	13.1363i	0.319637	−	0.553627i	0.980412	+	0.196957i	$0.0631058\pi$
$564$		0			0
$565$	33.1329	−	19.1293i	1.39391	−	0.804774i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	31.8084	−	18.3646i	1.33348	−	0.769885i	0.347648	−	0.937625i	$-0.386980\pi$
$569$	31.8084	−	18.3646i	1.33348	−	0.769885i	0.985831	+	0.167740i	$0.0536470\pi$
$570$		0			0
$571$	5.61387	−	9.72351i	0.234933	−	0.406916i	−0.724320	−	0.689464i	$-0.757846\pi$
$571$	5.61387	−	9.72351i	0.234933	−	0.406916i	0.959253	+	0.282548i	$0.0911795\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			63.4114i			2.64444i
$576$		0			0
$577$			36.5515i			1.52166i	0.648952	+	0.760829i	$0.275208\pi$
$577$			36.5515i			1.52166i	−0.648952	+	0.760829i	$0.724792\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.77248	−	21.1436i	0.115022	−	0.877186i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.99738	+	8.65571i	0.206264	+	0.357259i	0.950535	−	0.310619i	$-0.100536\pi$
$587$	4.99738	+	8.65571i	0.206264	+	0.357259i	−0.744271	+	0.667878i	$0.767203\pi$
$588$		0			0
$589$	3.13376	−	5.42784i	0.129124	−	0.223650i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−7.78223			−0.319578			−0.159789	−	0.987151i	$-0.551081\pi$
$593$	−7.78223			−0.319578			−0.159789	+	0.987151i	$0.551081\pi$
$594$		0			0
$595$	−7.05696	+	2.92737i	−0.289307	+	0.120010i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	21.6614	+	12.5062i	0.885061	+	0.510990i	0.872324	−	0.488929i	$-0.162612\pi$
$599$	21.6614	+	12.5062i	0.885061	+	0.510990i	0.0127373	+	0.999919i	$0.495945\pi$
$600$		0			0
$601$	25.9925	−	15.0068i	1.06026	−	0.612139i	0.134753	−	0.990879i	$-0.456976\pi$
$601$	25.9925	−	15.0068i	1.06026	−	0.612139i	0.925503	+	0.378740i	$0.123643\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.87179	−	15.3664i	−0.360689	−	0.624732i
$606$		0			0
$607$	−3.96882	−	2.29140i	−0.161089	−	0.0930050i	0.417288	−	0.908774i	$-0.362981\pi$
$607$	−3.96882	−	2.29140i	−0.161089	−	0.0930050i	−0.578378	+	0.815769i	$0.696314\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			6.22468i			0.251823i
$612$		0			0
$613$	30.5522			1.23399			0.616996	−	0.786966i	$-0.288349\pi$
$613$	30.5522			1.23399			0.616996	+	0.786966i	$0.288349\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	28.2484	+	16.3092i	1.13724	+	0.656585i	0.945745	−	0.324909i	$-0.105334\pi$
$617$	28.2484	+	16.3092i	1.13724	+	0.656585i	0.191493	+	0.981494i	$0.438667\pi$
$618$		0			0
$619$	17.3244	−	10.0023i	0.696327	−	0.402024i	−0.109651	−	0.993970i	$-0.534973\pi$
$619$	17.3244	−	10.0023i	0.696327	−	0.402024i	0.805978	+	0.591946i	$0.201640\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	19.4582	+	14.9148i	0.779575	+	0.597548i
$624$		0			0
$625$	−13.5657	+	23.4965i	−0.542628	+	0.939859i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.22752			0.0888171
$630$		0			0
$631$	−6.09634			−0.242692			−0.121346	−	0.992610i	$-0.538721\pi$
$631$	−6.09634			−0.242692			−0.121346	+	0.992610i	$0.538721\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.72893	+	9.92279i	−0.227345	+	0.393774i
$636$		0			0
$637$	5.14076	−	19.2654i	0.203685	−	0.763322i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−28.9612	+	16.7207i	−1.14390	+	0.660429i	−0.947393	−	0.320074i	$-0.896292\pi$
$641$	−28.9612	+	16.7207i	−1.14390	+	0.660429i	−0.196504	+	0.980503i	$0.562959\pi$
$642$		0			0
$643$	16.6022	+	9.58527i	0.654726	+	0.378006i	0.790264	−	0.612766i	$-0.209943\pi$
$643$	16.6022	+	9.58527i	0.654726	+	0.378006i	−0.135539	+	0.990772i	$0.543276\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	44.6049			1.75360			0.876800	−	0.480854i	$-0.159673\pi$
$647$	44.6049			1.75360			0.876800	+	0.480854i	$0.159673\pi$
$648$		0			0
$649$			0.0833680i			0.00327248i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.564755	+	0.326061i	0.0221006	+	0.0127598i	0.511010	−	0.859575i	$-0.329272\pi$
$653$	0.564755	+	0.326061i	0.0221006	+	0.0127598i	−0.488909	+	0.872335i	$0.662605\pi$
$654$		0			0
$655$	29.3100	+	50.7664i	1.14524	+	1.98361i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	26.2738	−	15.1692i	1.02348	−	0.590908i	0.108372	−	0.994110i	$-0.465436\pi$
$659$	26.2738	−	15.1692i	1.02348	−	0.590908i	0.915111	+	0.403202i	$0.132103\pi$
$660$		0			0
$661$	11.1004	+	6.40881i	0.431755	+	0.249274i	0.700094	−	0.714051i	$-0.253141\pi$
$661$	11.1004	+	6.40881i	0.431755	+	0.249274i	−0.268339	+	0.963325i	$0.586475\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.04011	+	16.9715i	0.273004	+	0.658126i
$666$		0			0
$667$	−18.0569			−0.699165
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.86986	−	8.43484i	0.187999	−	0.325623i
$672$		0			0
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	0.997103	−	0.0760644i	$-0.0242355\pi$
$673$	11.2246	+	19.4416i	0.432678	+	0.749420i	−0.564425	+	0.825484i	$0.690902\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	25.5903	+	44.3237i	0.983516	+	1.70350i	0.648353	+	0.761340i	$0.275458\pi$
$677$	25.5903	+	44.3237i	0.983516	+	1.70350i	0.335163	+	0.942160i	$0.391209\pi$
$678$		0			0
$679$	49.3694	+	6.47360i	1.89462	+	0.248434i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	14.5616i		−	0.557184i	−0.960410	−	0.278592i	$-0.910132\pi$
$683$		−	14.5616i		−	0.557184i	0.960410	−	0.278592i	$-0.0898677\pi$
$684$		0			0
$685$		−	61.1681i		−	2.33711i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−21.1757	+	12.2258i	−0.805560	+	0.465090i	−0.845412	−	0.534115i	$-0.820645\pi$
$691$	−21.1757	+	12.2258i	−0.805560	+	0.465090i	0.0398517	+	0.999206i	$0.487311\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	11.1431	−	6.43347i	0.422682	−	0.244035i
$696$		0			0
$697$	−3.89393	+	6.74448i	−0.147493	+	0.255465i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			2.21697i			0.0837337i	0.999123	+	0.0418669i	$0.0133305\pi$
$701$			2.21697i			0.0837337i	−0.999123	+	0.0418669i	$0.986669\pi$
$702$		0			0
$703$		−	5.35703i		−	0.202044i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.84871	−	21.7250i	0.107137	−	0.817054i
$708$		0			0
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	0.998857	−	0.0477959i	$-0.0152197\pi$
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	−0.540821	+	0.841138i	$0.681886\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.9796	−	19.0173i	−0.411190	−	0.712203i
$714$		0			0
$715$	−21.8607	+	37.8639i	−0.817544	+	1.41603i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	2.22752			0.0830725			0.0415363	−	0.999137i	$-0.486775\pi$
$719$	2.22752			0.0830725			0.0415363	+	0.999137i	$0.486775\pi$
$720$		0			0
$721$	17.2831	+	41.6641i	0.643657	+	1.55165i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−25.3599	−	14.6416i	−0.941844	−	0.543774i
$726$		0			0
$727$	10.4880	−	6.05523i	0.388977	−	0.224576i	−0.292740	−	0.956192i	$-0.594567\pi$
$727$	10.4880	−	6.05523i	0.388977	−	0.224576i	0.681717	+	0.731616i	$0.261234\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.349924	−	0.606086i	−0.0129424	−	0.0224169i
$732$		0			0
$733$	−13.5673	−	7.83306i	−0.501118	−	0.289321i	0.228057	−	0.973648i	$-0.426763\pi$
$733$	−13.5673	−	7.83306i	−0.501118	−	0.289321i	−0.729175	+	0.684327i	$0.760096\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	53.0522i		−	1.95420i
$738$		0			0
$739$	8.10454			0.298130			0.149065	−	0.988827i	$-0.452374\pi$
$739$	8.10454			0.298130			0.149065	+	0.988827i	$0.452374\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.5429	−	6.08697i	−0.386783	−	0.223309i	0.293982	−	0.955811i	$-0.405019\pi$
$743$	−10.5429	−	6.08697i	−0.386783	−	0.223309i	−0.680765	+	0.732502i	$0.738353\pi$
$744$		0			0
$745$	−37.0732	+	21.4042i	−1.35826	+	0.784189i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	23.0759	−	30.1054i	0.843176	−	1.10003i
$750$		0			0
$751$	17.3062	−	29.9752i	0.631511	−	1.09381i	−0.355732	−	0.934588i	$-0.615768\pi$
$751$	17.3062	−	29.9752i	0.631511	−	1.09381i	0.987243	−	0.159221i	$-0.0508983\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.60311			−0.203918
$756$		0			0
$757$	−39.0553			−1.41949			−0.709744	−	0.704459i	$-0.751190\pi$
$757$	−39.0553			−1.41949			−0.709744	+	0.704459i	$0.751190\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.11262	−	8.85532i	0.185332	−	0.321005i	−0.758356	−	0.651840i	$-0.773997\pi$
$761$	5.11262	−	8.85532i	0.185332	−	0.321005i	0.943688	+	0.330835i	$0.107330\pi$
$762$		0			0
$763$	−23.6862	−	18.1556i	−0.857499	−	0.657277i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.0521363	−	0.0301009i	0.00188253	−	0.00108688i
$768$		0			0
$769$	26.6746	+	15.4006i	0.961910	+	0.555359i	0.896760	−	0.442517i	$-0.145914\pi$
$769$	26.6746	+	15.4006i	0.961910	+	0.555359i	0.0651494	+	0.997876i	$0.479248\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−35.7833			−1.28704			−0.643518	−	0.765431i	$-0.722526\pi$
$773$	−35.7833			−1.28704			−0.643518	+	0.765431i	$0.722526\pi$
$774$		0			0
$775$		−	35.6117i		−	1.27921i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	16.2200	+	9.36461i	0.581141	+	0.335522i
$780$		0			0
$781$	−3.83228	−	6.63771i	−0.137130	−	0.237516i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−55.9626	+	32.3100i	−1.99739	+	1.15319i
$786$		0			0
$787$	13.2859	+	7.67064i	0.473592	+	0.273429i	0.717742	−	0.696309i	$-0.245176\pi$
$787$	13.2859	+	7.67064i	0.473592	+	0.273429i	−0.244150	+	0.969737i	$0.578509\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.96748	−	24.0284i	−0.354403	−	0.854353i
$792$		0			0
$793$	−7.03326			−0.249758
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.5200	+	30.3455i	−0.620590	+	1.07489i	0.368786	+	0.929514i	$0.379774\pi$
$797$	−17.5200	+	30.3455i	−0.620590	+	1.07489i	−0.989376	+	0.145379i	$0.953560\pi$
$798$		0			0
$799$	−0.810856	−	1.40444i	−0.0286860	−	0.0496857i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−9.57529	−	16.5849i	−0.337905	−	0.585268i
$804$		0			0
$805$	63.8289	+	8.36961i	2.24967	+	0.294990i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	27.2925i		−	0.959553i	−0.877391	−	0.479777i	$-0.840718\pi$
$809$		−	27.2925i		−	0.959553i	0.877391	−	0.479777i	$-0.159282\pi$
$810$		0			0
$811$		−	27.7628i		−	0.974883i	−0.873156	−	0.487442i	$-0.837930\pi$
$811$		−	27.7628i		−	0.974883i	0.873156	−	0.487442i	$-0.162070\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	24.1161	−	41.7703i	0.844749	−	1.46315i
$816$		0			0
$817$	−1.45759	+	0.841542i	−0.0509947	+	0.0294418i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	38.4968	−	22.2262i	1.34355	−	0.775698i	0.356223	−	0.934401i	$-0.384064\pi$
$821$	38.4968	−	22.2262i	1.34355	−	0.775698i	0.987326	+	0.158703i	$0.0507311\pi$
$822$		0			0
$823$	−25.5577	+	44.2672i	−0.890884	+	1.54306i	−0.0520663	+	0.998644i	$0.516581\pi$
$823$	−25.5577	+	44.2672i	−0.890884	+	1.54306i	−0.838818	+	0.544413i	$0.816753\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	14.5414i		−	0.505653i	−0.967512	−	0.252826i	$-0.918640\pi$
$827$		−	14.5414i		−	0.505653i	0.967512	−	0.252826i	$-0.0813601\pi$
$828$		0			0
$829$		−	27.9681i		−	0.971373i	−0.874133	−	0.485686i	$-0.838570\pi$
$829$		−	27.9681i		−	0.971373i	0.874133	−	0.485686i	$-0.161430\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.34971	+	5.01641i	0.0467648	+	0.173808i
$834$		0			0
$835$	−22.8053	−	39.5000i	−0.789211	−	1.36695i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.499354	+	0.864906i	0.0172396	+	0.0298599i	0.874517	−	0.484996i	$-0.161179\pi$
$839$	0.499354	+	0.864906i	0.0172396	+	0.0298599i	−0.857277	+	0.514856i	$0.827846\pi$
$840$		0			0
$841$	−10.3307	+	17.8933i	−0.356231	+	0.617011i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−19.0123			−0.654044
$846$		0			0
$847$	−11.1439	+	4.62273i	−0.382910	+	0.158839i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.2546	−	9.38460i	−0.557200	−	0.321700i
$852$		0			0
$853$	−8.48739	+	4.90020i	−0.290603	+	0.167780i	−0.638214	−	0.769859i	$-0.720326\pi$
$853$	−8.48739	+	4.90020i	−0.290603	+	0.167780i	0.347611	+	0.937639i	$0.386993\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.85002	+	6.66842i	0.131514	+	0.227789i	0.924260	−	0.381763i	$-0.124683\pi$
$857$	3.85002	+	6.66842i	0.131514	+	0.227789i	−0.792746	+	0.609552i	$0.791349\pi$
$858$		0			0
$859$	−16.4022	−	9.46979i	−0.559634	−	0.323105i	0.193364	−	0.981127i	$-0.438060\pi$
$859$	−16.4022	−	9.46979i	−0.559634	−	0.323105i	−0.752999	+	0.658022i	$0.771393\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			17.4540i			0.594141i	0.954856	+	0.297070i	$0.0960096\pi$
$863$			17.4540i			0.594141i	−0.954856	+	0.297070i	$0.903990\pi$
$864$		0			0
$865$	−65.2578			−2.21883
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.4215	+	7.17157i	0.421371	+	0.243279i
$870$		0			0
$871$	−33.1776	+	19.1551i	−1.12418	+	0.649045i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	42.0040	+	32.1963i	1.41999	+	1.08843i
$876$		0			0
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	−0.869318	−	0.494253i	$-0.835442\pi$
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	0.862695	+	0.505725i	$0.168775\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	37.0259			1.24744			0.623718	−	0.781650i	$-0.285622\pi$
$881$	37.0259			1.24744			0.623718	+	0.781650i	$0.285622\pi$
$882$		0			0
$883$	29.9586			1.00819			0.504094	−	0.863649i	$-0.331826\pi$
$883$	29.9586			1.00819			0.504094	+	0.863649i	$0.331826\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.4930	−	25.1026i	0.486626	−	0.842861i	−0.513256	−	0.858236i	$-0.671561\pi$
$887$	14.4930	−	25.1026i	0.486626	−	0.842861i	0.999882	+	0.0153745i	$0.00489405\pi$
$888$		0			0
$889$	6.18326	+	4.73950i	0.207380	+	0.158958i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.37759	+	1.95005i	−0.113027	+	0.0652560i
$894$		0			0
$895$	−19.4617	−	11.2362i	−0.650533	−	0.375586i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.1407			0.338211
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−18.6455	−	10.7650i	−0.619796	−	0.357839i
$906$		0			0
$907$	−1.94773	−	3.37357i	−0.0646733	−	0.112017i	0.831876	−	0.554962i	$-0.187267\pi$
$907$	−1.94773	−	3.37357i	−0.0646733	−	0.112017i	−0.896549	+	0.442945i	$0.853934\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.32768	−	0.766538i	0.0439881	−	0.0253966i	−0.477845	−	0.878444i	$-0.658582\pi$
$911$	1.32768	−	0.766538i	0.0439881	−	0.0253966i	0.521833	+	0.853048i	$0.325248\pi$
$912$		0			0
$913$	27.5339	+	15.8967i	0.911240	+	0.526105i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	36.8166	−	15.2723i	1.21579	−	0.504334i
$918$		0			0
$919$	−28.2531			−0.931984			−0.465992	−	0.884789i	$-0.654302\pi$
$919$	−28.2531			−0.931984			−0.465992	+	0.884789i	$0.654302\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.76737	+	4.79323i	−0.0910892	+	0.157771i
$924$		0			0
$925$	−15.2192	−	26.3603i	−0.500403	−	0.866723i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.64363	+	2.84685i	0.0539257	+	0.0934021i	0.891728	−	0.452571i	$-0.149493\pi$
$929$	1.64363	+	2.84685i	0.0539257	+	0.0934021i	−0.837802	+	0.545974i	$0.816160\pi$
$930$		0			0
$931$	12.0641	−	3.24596i	0.395385	−	0.106382i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	11.3907i		−	0.372517i
$936$		0			0
$937$		−	35.5084i		−	1.16001i	−0.814613	−	0.580005i	$-0.803051\pi$
$937$		−	35.5084i		−	1.16001i	0.814613	−	0.580005i	$-0.196949\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	6.24941	−	10.8243i	0.203725	−	0.352862i	−0.746001	−	0.665945i	$-0.768028\pi$
$941$	6.24941	−	10.8243i	0.203725	−	0.352862i	0.949726	+	0.313083i	$0.101362\pi$
$942$		0			0
$943$	56.8293	−	32.8104i	1.85062	−	1.06845i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	31.2769	−	18.0577i	1.01636	−	0.586796i	0.103313	−	0.994649i	$-0.467056\pi$
$947$	31.2769	−	18.0577i	1.01636	−	0.586796i	0.913048	+	0.407852i	$0.133722\pi$
$948$		0			0
$949$	−6.91452	+	11.9763i	−0.224455	+	0.388767i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	45.2925i		−	1.46717i	−0.679599	−	0.733584i	$-0.737846\pi$
$953$		−	45.2925i		−	1.46717i	0.679599	−	0.733584i	$-0.262154\pi$
$954$		0			0
$955$			24.1783i			0.782392i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−41.2380	−	5.40737i	−1.33165	−	0.174613i
$960$		0			0
$961$	−9.33386	−	16.1667i	−0.301092	−	0.521507i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−15.1859	−	26.3028i	−0.488851	−	0.846716i
$966$		0			0
$967$	−12.0000	+	20.7845i	−0.385893	+	0.668385i	−0.991893	−	0.127079i	$-0.959440\pi$
$967$	−12.0000	+	20.7845i	−0.385893	+	0.668385i	0.606000	+	0.795465i	$0.292773\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	33.3626			1.07066			0.535328	−	0.844644i	$-0.320188\pi$
$971$	33.3626			1.07066			0.535328	+	0.844644i	$0.320188\pi$
$972$		0			0
$973$	−3.35222	−	8.08113i	−0.107467	−	0.259069i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	29.8846	+	17.2539i	0.956091	+	0.552000i	0.894968	−	0.446131i	$-0.147198\pi$
$977$	29.8846	+	17.2539i	0.956091	+	0.552000i	0.0611236	+	0.998130i	$0.480532\pi$
$978$		0			0
$979$	−31.6555	+	18.2763i	−1.01172	+	0.584114i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.20651	+	2.08973i	0.0384817	+	0.0666522i	0.884625	−	0.466304i	$-0.154415\pi$
$983$	1.20651	+	2.08973i	0.0384817	+	0.0666522i	−0.846143	+	0.532956i	$0.821081\pi$
$984$		0			0
$985$	−43.0450	−	24.8521i	−1.37153	−	0.791852i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			5.89695i			0.187512i
$990$		0			0
$991$	−48.5982			−1.54377			−0.771887	−	0.635760i	$-0.780687\pi$
$991$	−48.5982			−1.54377			−0.771887	+	0.635760i	$0.780687\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.10612	+	3.52537i	0.193577	+	0.111762i
$996$		0			0
$997$	−38.8449	+	22.4271i	−1.23023	+	0.710274i	−0.967078	−	0.254481i	$-0.918095\pi$
$997$	−38.8449	+	22.4271i	−1.23023	+	0.710274i	−0.263152	+	0.964754i	$0.584762\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.b.881.8		16
3.2	odd	2		1008.2.cc.b.545.2		16
4.3	odd	2		378.2.m.a.125.8		16
7.6	odd	2	inner	3024.2.cc.b.881.1		16
9.2	odd	6	inner	3024.2.cc.b.2897.1		16
9.7	even	3		1008.2.cc.b.209.7		16
12.11	even	2		126.2.m.a.41.4	yes	16
21.20	even	2		1008.2.cc.b.545.7		16
28.3	even	6		2646.2.l.b.1097.5		16
28.11	odd	6		2646.2.l.b.1097.8		16
28.19	even	6		2646.2.t.a.2285.4		16
28.23	odd	6		2646.2.t.a.2285.1		16
28.27	even	2		378.2.m.a.125.5		16
36.7	odd	6		126.2.m.a.83.1	yes	16
36.11	even	6		378.2.m.a.251.5		16
36.23	even	6		1134.2.d.a.1133.8		16
36.31	odd	6		1134.2.d.a.1133.9		16
63.20	even	6	inner	3024.2.cc.b.2897.8		16
63.34	odd	6		1008.2.cc.b.209.2		16
84.11	even	6		882.2.l.a.509.1		16
84.23	even	6		882.2.t.b.815.6		16
84.47	odd	6		882.2.t.b.815.7		16
84.59	odd	6		882.2.l.a.509.4		16
84.83	odd	2		126.2.m.a.41.1	✓	16
252.11	even	6		2646.2.t.a.1979.4		16
252.47	odd	6		2646.2.l.b.521.4		16
252.79	odd	6		882.2.l.a.227.8		16
252.83	odd	6		378.2.m.a.251.8		16
252.115	even	6		882.2.t.b.803.6		16
252.139	even	6		1134.2.d.a.1133.16		16
252.151	odd	6		882.2.t.b.803.7		16
252.167	odd	6		1134.2.d.a.1133.1		16
252.187	even	6		882.2.l.a.227.5		16
252.191	even	6		2646.2.l.b.521.1		16
252.223	even	6		126.2.m.a.83.4	yes	16
252.227	odd	6		2646.2.t.a.1979.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.1	✓	16	84.83	odd	2
126.2.m.a.41.4	yes	16	12.11	even	2
126.2.m.a.83.1	yes	16	36.7	odd	6
126.2.m.a.83.4	yes	16	252.223	even	6
378.2.m.a.125.5		16	28.27	even	2
378.2.m.a.125.8		16	4.3	odd	2
378.2.m.a.251.5		16	36.11	even	6
378.2.m.a.251.8		16	252.83	odd	6
882.2.l.a.227.5		16	252.187	even	6
882.2.l.a.227.8		16	252.79	odd	6
882.2.l.a.509.1		16	84.11	even	6
882.2.l.a.509.4		16	84.59	odd	6
882.2.t.b.803.6		16	252.115	even	6
882.2.t.b.803.7		16	252.151	odd	6
882.2.t.b.815.6		16	84.23	even	6
882.2.t.b.815.7		16	84.47	odd	6
1008.2.cc.b.209.2		16	63.34	odd	6
1008.2.cc.b.209.7		16	9.7	even	3
1008.2.cc.b.545.2		16	3.2	odd	2
1008.2.cc.b.545.7		16	21.20	even	2
1134.2.d.a.1133.1		16	252.167	odd	6
1134.2.d.a.1133.8		16	36.23	even	6
1134.2.d.a.1133.9		16	36.31	odd	6
1134.2.d.a.1133.16		16	252.139	even	6
2646.2.l.b.521.1		16	252.191	even	6
2646.2.l.b.521.4		16	252.47	odd	6
2646.2.l.b.1097.5		16	28.3	even	6
2646.2.l.b.1097.8		16	28.11	odd	6
2646.2.t.a.1979.1		16	252.227	odd	6
2646.2.t.a.1979.4		16	252.11	even	6
2646.2.t.a.2285.1		16	28.23	odd	6
2646.2.t.a.2285.4		16	28.19	even	6
3024.2.cc.b.881.1		16	7.6	odd	2	inner
3024.2.cc.b.881.8		16	1.1	even	1	trivial
3024.2.cc.b.2897.1		16	9.2	odd	6	inner
3024.2.cc.b.2897.8		16	63.20	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.94556 - 3.36980i) q^{5} +(-2.09985 - 1.60954i) q^{7} +O(q^{10})\)	\(q+(1.94556 - 3.36980i) q^{5} +(-2.09985 - 1.60954i) q^{7} +(3.41614 - 1.97231i) q^{11} +(-2.46687 - 1.42425i) q^{13} +0.742117 q^{17} -1.78474i q^{19} +(-5.41535 - 3.12656i) q^{23} +(-5.07039 - 8.78217i) q^{25} +(2.50079 - 1.44383i) q^{29} +(3.04125 + 1.75587i) q^{31} +(-9.50923 + 3.94462i) q^{35} +3.00158 q^{37} +(-5.24705 + 9.08816i) q^{41} +(-0.471521 - 0.816699i) q^{43} +(-1.09263 - 1.89248i) q^{47} +(1.81873 + 6.75960i) q^{49} -15.3490i q^{55} +(-0.0105673 + 0.0183031i) q^{59} +(2.13832 - 1.23456i) q^{61} +(-9.59886 + 5.54191i) q^{65} +(6.72463 - 11.6474i) q^{67} -1.94304i q^{71} -4.85486i q^{73} +(-10.3479 - 1.35688i) q^{77} +(1.81806 + 3.14898i) q^{79} +(4.02998 + 6.98012i) q^{83} +(1.44383 - 2.50079i) q^{85} -9.26646 q^{89} +(2.88766 + 6.96124i) q^{91} +(-6.01422 - 3.47231i) q^{95} +(-16.2983 + 9.40980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

Introduction

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