LMFDB - Embedded newform 3024.2.cc.a.2897.5

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 $ x^12 - 7x^10 + 37x^8 - 78x^6 + 123x^4 - 36*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2897.5
Root			$0.474636 - 0.274031i$ of defining polynomial
Character	$\chi$	$=$	3024.2897
Dual form			3024.2.cc.a.881.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10552 + 1.91482i) q^{5} +(-2.60579 + 0.458109i) q^{7} +O(q^{10})$	$q+(1.10552 + 1.91482i) q^{5} +(-2.60579 + 0.458109i) q^{7} +(-2.93818 - 1.69636i) q^{11} +(1.56060 - 0.901012i) q^{13} -5.96901 q^{17} +1.64419i q^{19} +(2.05563 - 1.18682i) q^{23} +(0.0556321 - 0.0963576i) q^{25} +(-2.44437 - 1.41126i) q^{29} +(9.28558 - 5.36103i) q^{31} +(-3.75796 - 4.48318i) q^{35} +1.69963 q^{37} +(-0.455074 - 0.788211i) q^{41} +(1.96108 - 3.39669i) q^{43} +(-0.123005 + 0.213051i) q^{47} +(6.58027 - 2.38747i) q^{49} -7.87589i q^{53} -7.50146i q^{55} +(5.39093 + 9.33736i) q^{59} +(-1.22853 - 0.709292i) q^{61} +(3.45056 + 1.99218i) q^{65} +(-3.99381 - 6.91748i) q^{67} -12.1743i q^{71} +0.426103i q^{73} +(8.43339 + 3.07435i) q^{77} +(-2.49381 + 4.31941i) q^{79} +(4.28541 - 7.42254i) q^{83} +(-6.59888 - 11.4296i) q^{85} +10.5358 q^{89} +(-3.65383 + 3.06277i) q^{91} +(-3.14833 + 1.81769i) q^{95} +(6.30108 + 3.63793i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{7}+O(q^{10}) $ 12 * q + 2 * q^7	$ 12 q + 2 q^{7} + 24 q^{23} - 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 78 q^{65} - 12 q^{67} + 24 q^{77} + 6 q^{79} - 6 q^{85} + 24 q^{91} + 72 q^{95}+O(q^{100}) $ 12 * q + 2 * q^7 + 24 * q^23 - 30 * q^29 - 4 * q^37 + 10 * q^43 + 6 * q^49 + 78 * q^65 - 12 * q^67 + 24 * q^77 + 6 * q^79 - 6 * q^85 + 24 * q^91 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.10552	+	1.91482i	0.494405	+	0.856335i	0.999979	−	0.00644798i	$-0.00205247\pi$
$5$	1.10552	+	1.91482i	0.494405	+	0.856335i	−0.505574	+	0.862783i	$0.668719\pi$
$6$		0			0
$7$	−2.60579	+	0.458109i	−0.984896	+	0.173149i
$7$	−2.60579	+	0.458109i	−0.984896	+	0.173149i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.93818	−	1.69636i	−0.885894	−	0.511471i	−0.0132968	−	0.999912i	$-0.504233\pi$
$11$	−2.93818	−	1.69636i	−0.885894	−	0.511471i	−0.872597	+	0.488440i	$0.837566\pi$
$12$		0			0
$13$	1.56060	−	0.901012i	0.432832	−	0.249896i	−0.267720	−	0.963497i	$-0.586270\pi$
$13$	1.56060	−	0.901012i	0.432832	−	0.249896i	0.700552	+	0.713601i	$0.252937\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.96901			−1.44770			−0.723849	−	0.689959i	$-0.757629\pi$
$17$	−5.96901			−1.44770			−0.723849	+	0.689959i	$0.757629\pi$
$18$		0			0
$19$			1.64419i			0.377202i	0.982054	+	0.188601i	$0.0603953\pi$
$19$			1.64419i			0.377202i	−0.982054	+	0.188601i	$0.939605\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.05563	−	1.18682i	0.428629	−	0.247469i	−0.270133	−	0.962823i	$-0.587068\pi$
$23$	2.05563	−	1.18682i	0.428629	−	0.247469i	0.698762	+	0.715354i	$0.253734\pi$
$24$		0			0
$25$	0.0556321	−	0.0963576i	0.0111264	−	0.0192715i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.44437	−	1.41126i	−0.453908	−	0.262064i	0.255571	−	0.966790i	$-0.417736\pi$
$29$	−2.44437	−	1.41126i	−0.453908	−	0.262064i	−0.709479	+	0.704726i	$0.751070\pi$
$30$		0			0
$31$	9.28558	−	5.36103i	1.66774	−	0.962870i	0.698887	−	0.715232i	$-0.253679\pi$
$31$	9.28558	−	5.36103i	1.66774	−	0.962870i	0.968853	−	0.247638i	$-0.0796544\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.75796	−	4.48318i	−0.635211	−	0.757795i
$36$		0			0
$37$	1.69963			0.279417			0.139709	−	0.990193i	$-0.455383\pi$
$37$	1.69963			0.279417			0.139709	+	0.990193i	$0.455383\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.455074	−	0.788211i	−0.0710706	−	0.123098i	0.828300	−	0.560285i	$-0.189308\pi$
$41$	−0.455074	−	0.788211i	−0.0710706	−	0.123098i	−0.899371	+	0.437187i	$0.855975\pi$
$42$		0			0
$43$	1.96108	−	3.39669i	0.299062	−	0.517990i	−0.676860	−	0.736112i	$-0.736660\pi$
$43$	1.96108	−	3.39669i	0.299062	−	0.517990i	0.975922	+	0.218122i	$0.0699931\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.123005	+	0.213051i	−0.0179422	+	0.0310767i	−0.874857	−	0.484381i	$-0.839045\pi$
$47$	−0.123005	+	0.213051i	−0.0179422	+	0.0310767i	0.856915	+	0.515458i	$0.172378\pi$
$48$		0			0
$49$	6.58027	−	2.38747i	0.940039	−	0.341067i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	7.87589i		−	1.08184i	−0.841075	−	0.540919i	$-0.818077\pi$
$53$		−	7.87589i		−	1.08184i	0.841075	−	0.540919i	$-0.181923\pi$
$54$		0			0
$55$		−	7.50146i		−	1.01150i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.39093	+	9.33736i	0.701839	+	1.21562i	0.967820	+	0.251643i	$0.0809709\pi$
$59$	5.39093	+	9.33736i	0.701839	+	1.21562i	−0.265981	+	0.963978i	$0.585696\pi$
$60$		0			0
$61$	−1.22853	−	0.709292i	−0.157297	−	0.0908155i	0.419285	−	0.907855i	$-0.362281\pi$
$61$	−1.22853	−	0.709292i	−0.157297	−	0.0908155i	−0.576582	+	0.817039i	$0.695614\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.45056	+	1.99218i	0.427989	+	0.247100i
$66$		0			0
$67$	−3.99381	−	6.91748i	−0.487922	−	0.845105i	0.511982	−	0.858996i	$-0.328911\pi$
$67$	−3.99381	−	6.91748i	−0.487922	−	0.845105i	−0.999904	+	0.0138913i	$0.995578\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.1743i		−	1.44482i	−0.691463	−	0.722412i	$-0.743034\pi$
$71$		−	12.1743i		−	1.44482i	0.691463	−	0.722412i	$-0.256966\pi$
$72$		0			0
$73$			0.426103i			0.0498715i	0.999689	+	0.0249358i	$0.00793812\pi$
$73$			0.426103i			0.0498715i	−0.999689	+	0.0249358i	$0.992062\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.43339	+	3.07435i	0.961074	+	0.350354i
$78$		0			0
$79$	−2.49381	+	4.31941i	−0.280576	+	0.485971i	−0.971527	−	0.236930i	$-0.923859\pi$
$79$	−2.49381	+	4.31941i	−0.280576	+	0.485971i	0.690951	+	0.722902i	$0.257192\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.28541	−	7.42254i	0.470384	−	0.814730i	−0.529042	−	0.848596i	$-0.677449\pi$
$83$	4.28541	−	7.42254i	0.470384	−	0.814730i	0.999426	+	0.0338660i	$0.0107819\pi$
$84$		0			0
$85$	−6.59888	−	11.4296i	−0.715750	−	1.23971i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	10.5358			1.11680			0.558399	−	0.829573i	$-0.311416\pi$
$89$	10.5358			1.11680			0.558399	+	0.829573i	$0.311416\pi$
$90$		0			0
$91$	−3.65383	+	3.06277i	−0.383025	+	0.321065i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.14833	+	1.81769i	−0.323012	+	0.186491i
$96$		0			0
$97$	6.30108	+	3.63793i	0.639777	+	0.369376i	0.784529	−	0.620092i	$-0.212905\pi$
$97$	6.30108	+	3.63793i	0.639777	+	0.369376i	−0.144751	+	0.989468i	$0.546238\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.33405	+	4.04270i	−0.232247	+	0.402264i	−0.958469	−	0.285197i	$-0.907941\pi$
$101$	−2.33405	+	4.04270i	−0.232247	+	0.402264i	0.726222	+	0.687460i	$0.241274\pi$
$102$		0			0
$103$	−5.40462	+	3.12036i	−0.532533	+	0.307458i	−0.742047	−	0.670348i	$-0.766145\pi$
$103$	−5.40462	+	3.12036i	−0.532533	+	0.307458i	0.209515	+	0.977806i	$0.432812\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			1.48939i			0.143985i	0.997405	+	0.0719925i	$0.0229358\pi$
$107$			1.48939i			0.143985i	−0.997405	+	0.0719925i	$0.977064\pi$
$108$		0			0
$109$	−4.38688			−0.420187			−0.210093	−	0.977681i	$-0.567377\pi$
$109$	−4.38688			−0.420187			−0.210093	+	0.977681i	$0.567377\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	14.8764	−	8.58887i	1.39945	−	0.807973i	0.405115	−	0.914266i	$-0.367231\pi$
$113$	14.8764	−	8.58887i	1.39945	−	0.807973i	0.994335	+	0.106293i	$0.0338981\pi$
$114$		0			0
$115$	4.54510	+	2.62412i	0.423833	+	0.244700i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	15.5540	−	2.73445i	1.42583	−	0.250667i
$120$		0			0
$121$	0.255260	+	0.442124i	0.0232055	+	0.0401931i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.3013			1.01081
$126$		0			0
$127$	−6.32141			−0.560935			−0.280467	−	0.959864i	$-0.590489\pi$
$127$	−6.32141			−0.560935			−0.280467	+	0.959864i	$0.590489\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	8.51213	+	14.7434i	0.743708	+	1.28814i	0.950796	+	0.309818i	$0.100268\pi$
$131$	8.51213	+	14.7434i	0.743708	+	1.28814i	−0.207088	+	0.978322i	$0.566399\pi$
$132$		0			0
$133$	−0.753215	−	4.28440i	−0.0653121	−	0.371505i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.42580	−	3.13259i	−0.463557	−	0.267635i	0.249982	−	0.968251i	$-0.419575\pi$
$137$	−5.42580	−	3.13259i	−0.463557	−	0.267635i	−0.713539	+	0.700616i	$0.752909\pi$
$138$		0			0
$139$	6.65488	−	3.84220i	0.564460	−	0.325891i	−0.190474	−	0.981692i	$-0.561002\pi$
$139$	6.65488	−	3.84220i	0.564460	−	0.325891i	0.754934	+	0.655801i	$0.227669\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.11375			−0.511258
$144$		0			0
$145$		−	6.24071i		−	0.518263i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−13.3695	+	7.71887i	−1.09527	+	0.632355i	−0.934975	−	0.354714i	$-0.884578\pi$
$149$	−13.3695	+	7.71887i	−1.09527	+	0.632355i	−0.160296	+	0.987069i	$0.551245\pi$
$150$		0			0
$151$	5.84362	−	10.1215i	0.475547	−	0.823672i	−0.524060	−	0.851681i	$-0.675583\pi$
$151$	5.84362	−	10.1215i	0.475547	−	0.823672i	0.999608	+	0.0280089i	$0.00891668\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	20.5309	+	11.8535i	1.64908	+	0.952096i
$156$		0			0
$157$	4.93586	−	2.84972i	0.393924	−	0.227432i	−0.289935	−	0.957046i	$-0.593634\pi$
$157$	4.93586	−	2.84972i	0.393924	−	0.227432i	0.683859	+	0.729614i	$0.260300\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.81285	+	4.03430i	−0.379306	+	0.317948i
$162$		0			0
$163$	10.2101			0.799721			0.399860	−	0.916576i	$-0.369059\pi$
$163$	10.2101			0.799721			0.399860	+	0.916576i	$0.369059\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.80661	−	3.12914i	−0.139800	−	0.242140i	0.787621	−	0.616160i	$-0.211312\pi$
$167$	−1.80661	−	3.12914i	−0.139800	−	0.242140i	−0.927421	+	0.374020i	$0.877979\pi$
$168$		0			0
$169$	−4.87636	+	8.44610i	−0.375104	+	0.649700i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.03957	−	15.6570i	0.687266	−	1.19038i	−0.285453	−	0.958393i	$-0.592144\pi$
$173$	9.03957	−	15.6570i	0.687266	−	1.19038i	0.972719	−	0.231987i	$-0.0745226\pi$
$174$		0			0
$175$	−0.100823	+	0.276573i	−0.00762152	+	0.0209070i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	5.03194i		−	0.376105i	−0.982159	−	0.188052i	$-0.939783\pi$
$179$		−	5.03194i		−	0.376105i	0.982159	−	0.188052i	$-0.0602175\pi$
$180$		0			0
$181$		−	13.5592i		−	1.00785i	−0.863747	−	0.503925i	$-0.831889\pi$
$181$		−	13.5592i		−	1.00785i	0.863747	−	0.503925i	$-0.168111\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.87898	+	3.25449i	0.138145	+	0.239275i
$186$		0			0
$187$	17.5380	+	10.1256i	1.28251	+	0.740455i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.86948	−	5.12080i	−0.641773	−	0.370528i	0.143524	−	0.989647i	$-0.454156\pi$
$191$	−8.86948	−	5.12080i	−0.641773	−	0.370528i	−0.785297	+	0.619119i	$0.787490\pi$
$192$		0			0
$193$	−8.06615	−	13.9710i	−0.580614	−	1.00565i	−0.995407	−	0.0957374i	$-0.969479\pi$
$193$	−8.06615	−	13.9710i	−0.580614	−	1.00565i	0.414792	−	0.909916i	$-0.363854\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			3.86303i			0.275230i	0.990486	+	0.137615i	$0.0439436\pi$
$197$			3.86303i			0.275230i	−0.990486	+	0.137615i	$0.956056\pi$
$198$		0			0
$199$			15.2034i			1.07774i	0.842388	+	0.538871i	$0.181149\pi$
$199$			15.2034i			1.07774i	−0.842388	+	0.538871i	$0.818851\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.01602	+	2.55765i	0.492428	+	0.179512i
$204$		0			0
$205$	1.00619	−	1.74277i	0.0702753	−	0.121720i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.78913	−	4.83091i	0.192928	−	0.334161i
$210$		0			0
$211$	−11.9523	−	20.7021i	−0.822833	−	1.42519i	−0.903564	−	0.428453i	$-0.859059\pi$
$211$	−11.9523	−	20.7021i	−0.822833	−	1.42519i	0.0807311	−	0.996736i	$-0.474274\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.67208			0.591431
$216$		0			0
$217$	−21.7403	+	18.2235i	−1.47583	+	1.23709i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−9.31522	+	5.37815i	−0.626610	+	0.361773i
$222$		0			0
$223$	−16.6198	−	9.59545i	−1.11294	−	0.642559i	−0.173354	−	0.984860i	$-0.555461\pi$
$223$	−16.6198	−	9.59545i	−1.11294	−	0.642559i	−0.939591	+	0.342300i	$0.888794\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−4.33604	+	7.51024i	−0.287793	+	0.498472i	−0.973283	−	0.229610i	$-0.926255\pi$
$227$	−4.33604	+	7.51024i	−0.287793	+	0.498472i	0.685490	+	0.728082i	$0.259588\pi$
$228$		0			0
$229$	−12.4437	+	7.18439i	−0.822304	+	0.474758i	−0.851211	−	0.524824i	$-0.824131\pi$
$229$	−12.4437	+	7.18439i	−0.822304	+	0.474758i	0.0289060	+	0.999582i	$0.490798\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	29.7160i		−	1.94676i	−0.229194	−	0.973381i	$-0.573609\pi$
$233$		−	29.7160i		−	1.94676i	0.229194	−	0.973381i	$-0.426391\pi$
$234$		0			0
$235$	−0.543941			−0.0354828
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.7101	+	7.91556i	−0.886836	+	0.512015i	−0.872906	−	0.487888i	$-0.837767\pi$
$239$	−13.7101	+	7.91556i	−0.886836	+	0.512015i	−0.0139296	+	0.999903i	$0.504434\pi$
$240$		0			0
$241$	4.34973	+	2.51132i	0.280190	+	0.161768i	0.633510	−	0.773735i	$-0.281614\pi$
$241$	4.34973	+	2.51132i	0.280190	+	0.161768i	−0.353319	+	0.935503i	$0.614947\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.8462	+	9.96066i	0.756828	+	0.636363i
$246$		0			0
$247$	1.48143	+	2.56591i	0.0942612	+	0.163265i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.29728			0.460600			0.230300	−	0.973120i	$-0.426029\pi$
$251$	7.29728			0.460600			0.230300	+	0.973120i	$0.426029\pi$
$252$		0			0
$253$	−8.05308			−0.506293
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.00397	−	6.93508i	−0.249761	−	0.432598i	0.713699	−	0.700453i	$-0.247019\pi$
$257$	−4.00397	−	6.93508i	−0.249761	−	0.432598i	−0.963459	+	0.267855i	$0.913685\pi$
$258$		0			0
$259$	−4.42887	+	0.778614i	−0.275197	+	0.0483807i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.6051	−	7.85489i	−0.838925	−	0.484353i	0.0179738	−	0.999838i	$-0.494278\pi$
$263$	−13.6051	−	7.85489i	−0.838925	−	0.484353i	−0.856899	+	0.515485i	$0.827612\pi$
$264$		0			0
$265$	15.0810	−	8.70699i	0.926416	−	0.534866i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.4924			0.639731			0.319866	−	0.947463i	$-0.396362\pi$
$269$	10.4924			0.639731			0.319866	+	0.947463i	$0.396362\pi$
$270$		0			0
$271$		−	22.2537i		−	1.35181i	−0.736987	−	0.675907i	$-0.763752\pi$
$271$		−	22.2537i		−	1.35181i	0.736987	−	0.675907i	$-0.236248\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.326914	+	0.188744i	−0.0197137	+	0.0113817i
$276$		0			0
$277$	11.4251	−	19.7889i	0.686468	−	1.18900i	−0.286505	−	0.958079i	$-0.592493\pi$
$277$	11.4251	−	19.7889i	0.686468	−	1.18900i	0.972973	−	0.230919i	$-0.0741733\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.796041	−	0.459595i	−0.0474878	−	0.0274171i	0.476068	−	0.879408i	$-0.342062\pi$
$281$	−0.796041	−	0.459595i	−0.0474878	−	0.0274171i	−0.523556	+	0.851991i	$0.675395\pi$
$282$		0			0
$283$	−19.1573	+	11.0605i	−1.13878	+	0.657477i	−0.946129	−	0.323790i	$-0.895043\pi$
$283$	−19.1573	+	11.0605i	−1.13878	+	0.657477i	−0.192654	+	0.981267i	$0.561710\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.54691	+	1.84544i	0.0913113	+	0.108933i
$288$		0			0
$289$	18.6291			1.09583
$290$		0			0
$291$		0			0
$292$		0			0
$293$	14.6259	+	25.3328i	0.854453	+	1.47996i	0.877152	+	0.480214i	$0.159441\pi$
$293$	14.6259	+	25.3328i	0.854453	+	1.47996i	−0.0226986	+	0.999742i	$0.507226\pi$
$294$		0			0
$295$	−11.9196	+	20.6454i	−0.693986	+	1.20202i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.13868	−	3.70430i	0.123683	−	0.214225i
$300$		0			0
$301$	−3.55410	+	9.74944i	−0.204855	+	0.561948i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	3.13656i		−	0.179599i
$306$		0			0
$307$		−	14.8451i		−	0.847254i	−0.905837	−	0.423627i	$-0.860757\pi$
$307$		−	14.8451i		−	0.847254i	0.905837	−	0.423627i	$-0.139243\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.69002	−	16.7836i	−0.549471	−	0.951711i	−0.998311	−	0.0580991i	$-0.981496\pi$
$311$	−9.69002	−	16.7836i	−0.549471	−	0.951711i	0.448840	−	0.893612i	$-0.351837\pi$
$312$		0			0
$313$	−12.6608	−	7.30974i	−0.715633	−	0.413171i	0.0975102	−	0.995235i	$-0.468912\pi$
$313$	−12.6608	−	7.30974i	−0.715633	−	0.413171i	−0.813143	+	0.582064i	$0.802245\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.7046	+	8.48973i	0.825895	+	0.476831i	0.852445	−	0.522817i	$-0.175119\pi$
$317$	14.7046	+	8.48973i	0.825895	+	0.476831i	−0.0265499	+	0.999647i	$0.508452\pi$
$318$		0			0
$319$	4.78799	+	8.29305i	0.268076	+	0.464321i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	9.81416i		−	0.546074i
$324$		0			0
$325$		−	0.200501i		−	0.0111218i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.222925	−	0.611517i	0.0122903	−	0.0337140i
$330$		0			0
$331$	9.94801	−	17.2305i	0.546792	−	0.947072i	−0.451700	−	0.892170i	$-0.649182\pi$
$331$	9.94801	−	17.2305i	0.546792	−	0.947072i	0.998492	−	0.0549016i	$-0.0174845\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.83051	−	15.2949i	0.482462	−	0.835649i
$336$		0			0
$337$	0.490168	+	0.848996i	0.0267012	+	0.0462478i	0.879067	−	0.476698i	$-0.158166\pi$
$337$	0.490168	+	0.848996i	0.0267012	+	0.0462478i	−0.852366	+	0.522946i	$0.824833\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−36.3769			−1.96992
$342$		0			0
$343$	−16.0531	+	9.23572i	−0.866785	+	0.498682i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	18.3702	−	10.6060i	0.986162	−	0.569361i	0.0820373	−	0.996629i	$-0.473857\pi$
$347$	18.3702	−	10.6060i	0.986162	−	0.569361i	0.904125	+	0.427268i	$0.140524\pi$
$348$		0			0
$349$	−8.69945	−	5.02263i	−0.465671	−	0.268855i	0.248755	−	0.968566i	$-0.419979\pi$
$349$	−8.69945	−	5.02263i	−0.465671	−	0.268855i	−0.714426	+	0.699711i	$0.753312\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.37327	−	2.37858i	0.0730920	−	0.126599i	−0.827163	−	0.561962i	$-0.810047\pi$
$353$	1.37327	−	2.37858i	0.0730920	−	0.126599i	0.900255	+	0.435363i	$0.143380\pi$
$354$		0			0
$355$	23.3116	−	13.4590i	1.23725	−	0.714329i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	10.0013i		−	0.527849i	−0.964543	−	0.263925i	$-0.914983\pi$
$359$		−	10.0013i		−	0.527849i	0.964543	−	0.263925i	$-0.0850170\pi$
$360$		0			0
$361$	16.2967			0.857719
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.815912	+	0.471067i	−0.0427068	+	0.0246568i
$366$		0			0
$367$	−5.03560	−	2.90731i	−0.262856	−	0.151760i	0.362781	−	0.931875i	$-0.381827\pi$
$367$	−5.03560	−	2.90731i	−0.262856	−	0.151760i	−0.625637	+	0.780114i	$0.715161\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.60801	+	20.5229i	0.187319	+	1.06550i
$372$		0			0
$373$	7.75959	+	13.4400i	0.401776	+	0.695897i	0.993940	−	0.109920i	$-0.0350596\pi$
$373$	7.75959	+	13.4400i	0.401776	+	0.695897i	−0.592164	+	0.805817i	$0.701726\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.08623			−0.261954
$378$		0			0
$379$	−2.79714			−0.143679			−0.0718396	−	0.997416i	$-0.522887\pi$
$379$	−2.79714			−0.143679			−0.0718396	+	0.997416i	$0.522887\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.74229	+	3.01773i	0.0890268	+	0.154199i	0.907100	−	0.420915i	$-0.138291\pi$
$383$	1.74229	+	3.01773i	0.0890268	+	0.154199i	−0.818073	+	0.575114i	$0.804958\pi$
$384$		0			0
$385$	3.43648	+	19.5472i	0.175139	+	0.996219i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.37017	+	3.67782i	0.322980	+	0.186473i	0.652720	−	0.757599i	$-0.273628\pi$
$389$	6.37017	+	3.67782i	0.322980	+	0.186473i	−0.329740	+	0.944072i	$0.606961\pi$
$390$		0			0
$391$	−12.2701	+	7.08414i	−0.620525	+	0.358260i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−11.0279			−0.554872
$396$		0			0
$397$		−	19.2838i		−	0.967825i	−0.875116	−	0.483912i	$-0.839215\pi$
$397$		−	19.2838i		−	0.967825i	0.875116	−	0.483912i	$-0.160785\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.60576	+	5.54589i	−0.479689	+	0.276949i	−0.720287	−	0.693676i	$-0.755990\pi$
$401$	−9.60576	+	5.54589i	−0.479689	+	0.276949i	0.240598	+	0.970625i	$0.422656\pi$
$402$		0			0
$403$	9.66071	−	16.7328i	0.481234	−	0.833522i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.99381	−	2.88318i	−0.247534	−	0.142914i
$408$		0			0
$409$	−17.5597	+	10.1381i	−0.868274	+	0.501298i	−0.866774	−	0.498701i	$-0.833811\pi$
$409$	−17.5597	+	10.1381i	−0.868274	+	0.501298i	−0.00149954	+	0.999999i	$0.500477\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−18.3252	−	21.8616i	−0.901722	−	1.07574i
$414$		0			0
$415$	18.9505			0.930243
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.54936	+	9.61177i	0.271104	+	0.469566i	0.969145	−	0.246492i	$-0.0792779\pi$
$419$	5.54936	+	9.61177i	0.271104	+	0.469566i	−0.698041	+	0.716058i	$0.745945\pi$
$420$		0			0
$421$	4.59269	−	7.95478i	0.223834	−	0.387692i	−0.732135	−	0.681160i	$-0.761476\pi$
$421$	4.59269	−	7.95478i	0.223834	−	0.387692i	0.955969	+	0.293467i	$0.0948092\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.332068	+	0.575159i	−0.0161077	+	0.0278993i
$426$		0			0
$427$	3.52622	+	1.28547i	0.170646	+	0.0622080i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			15.1102i			0.727833i	0.931432	+	0.363916i	$0.118561\pi$
$431$			15.1102i			0.727833i	−0.931432	+	0.363916i	$0.881439\pi$
$432$		0			0
$433$			3.33578i			0.160307i	0.996783	+	0.0801537i	$0.0255411\pi$
$433$			3.33578i			0.160307i	−0.996783	+	0.0801537i	$0.974459\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.95135	+	3.37984i	0.0933458	+	0.161680i
$438$		0			0
$439$	5.91032	+	3.41233i	0.282084	+	0.162861i	0.634367	−	0.773032i	$-0.281261\pi$
$439$	5.91032	+	3.41233i	0.282084	+	0.162861i	−0.352282	+	0.935894i	$0.614594\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.77747	+	5.64503i	0.464542	+	0.268203i	0.713952	−	0.700195i	$-0.246903\pi$
$443$	9.77747	+	5.64503i	0.464542	+	0.268203i	−0.249410	+	0.968398i	$0.580237\pi$
$444$		0			0
$445$	11.6476	+	20.1743i	0.552151	+	0.956354i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			24.8554i			1.17300i	0.809950	+	0.586498i	$0.199494\pi$
$449$			24.8554i			1.17300i	−0.809950	+	0.586498i	$0.800506\pi$
$450$		0			0
$451$			3.08787i			0.145402i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.90406	−	3.61047i	−0.464310	−	0.169262i
$456$		0			0
$457$	6.30470	−	10.9201i	0.294922	−	0.510819i	−0.680045	−	0.733170i	$-0.738040\pi$
$457$	6.30470	−	10.9201i	0.294922	−	0.510819i	0.974967	+	0.222351i	$0.0713732\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.4031	−	24.9470i	0.670821	−	1.16190i	−0.306851	−	0.951758i	$-0.599275\pi$
$461$	14.4031	−	24.9470i	0.670821	−	1.16190i	0.977672	−	0.210138i	$-0.0673913\pi$
$462$		0			0
$463$	12.5858	+	21.7993i	0.584912	+	1.01310i	0.994886	+	0.101001i	$0.0322045\pi$
$463$	12.5858	+	21.7993i	0.584912	+	1.01310i	−0.409974	+	0.912097i	$0.634462\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−25.5951			−1.18440			−0.592199	−	0.805792i	$-0.701740\pi$
$467$	−25.5951			−1.18440			−0.592199	+	0.805792i	$0.701740\pi$
$468$		0			0
$469$	13.5760	+	16.1959i	0.626881	+	0.747857i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.5240	+	6.65338i	−0.529874	+	0.305923i
$474$		0			0
$475$	0.158430	+	0.0914695i	0.00726926	+	0.00419691i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.267749	−	0.463755i	0.0122338	−	0.0211895i	−0.859844	−	0.510557i	$-0.829439\pi$
$479$	0.267749	−	0.463755i	0.0122338	−	0.0211895i	0.872077	+	0.489368i	$0.162772\pi$
$480$		0			0
$481$	2.65244	−	1.53138i	0.120941	−	0.0698251i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			16.0873i			0.730485i
$486$		0			0
$487$	−34.1323			−1.54668			−0.773341	−	0.633990i	$-0.781416\pi$
$487$	−34.1323			−1.54668			−0.773341	+	0.633990i	$0.781416\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.86948	−	3.38874i	0.264886	−	0.152932i	−0.361675	−	0.932304i	$-0.617795\pi$
$491$	5.86948	−	3.38874i	0.264886	−	0.152932i	0.626561	+	0.779372i	$0.284462\pi$
$492$		0			0
$493$	14.5905	+	8.42380i	0.657121	+	0.379389i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.57715	+	31.7237i	0.250169	+	1.42300i
$498$		0			0
$499$	4.30037	+	7.44846i	0.192511	+	0.333439i	0.946082	−	0.323928i	$-0.105004\pi$
$499$	4.30037	+	7.44846i	0.192511	+	0.333439i	−0.753571	+	0.657367i	$0.771670\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	2.96518			0.132211			0.0661055	−	0.997813i	$-0.478943\pi$
$503$	2.96518			0.132211			0.0661055	+	0.997813i	$0.478943\pi$
$504$		0			0
$505$	−10.3214			−0.459297
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.04882	−	5.28072i	−0.135137	−	0.234064i	0.790513	−	0.612445i	$-0.209814\pi$
$509$	−3.04882	−	5.28072i	−0.135137	−	0.234064i	−0.925650	+	0.378382i	$0.876481\pi$
$510$		0			0
$511$	−0.195201	−	1.11033i	−0.00863519	−	0.0491183i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.9499	−	6.89926i	−0.526574	−	0.304018i
$516$		0			0
$517$	0.722823	−	0.417322i	0.0317897	−	0.0183538i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−32.6929			−1.43230			−0.716150	−	0.697946i	$-0.754097\pi$
$521$	−32.6929			−1.43230			−0.716150	+	0.697946i	$0.754097\pi$
$522$		0			0
$523$			2.00252i			0.0875643i	0.999041	+	0.0437821i	$0.0139407\pi$
$523$			2.00252i			0.0875643i	−0.999041	+	0.0437821i	$0.986059\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−55.4257	+	32.0001i	−2.41438	+	1.39394i
$528$		0			0
$529$	−8.68292	+	15.0393i	−0.377518	+	0.653881i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.42037	−	0.820053i	−0.0615232	−	0.0355204i
$534$		0			0
$535$	−2.85192	+	1.64656i	−0.123299	+	0.0711870i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−23.3840	−	4.14769i	−1.00722	−	0.178654i
$540$		0			0
$541$	−11.4451			−0.492061			−0.246031	−	0.969262i	$-0.579126\pi$
$541$	−11.4451			−0.492061			−0.246031	+	0.969262i	$0.579126\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.84980	−	8.40010i	−0.207743	−	0.359821i
$546$		0			0
$547$	3.91961	−	6.78896i	0.167590	−	0.290275i	−0.769982	−	0.638066i	$-0.779735\pi$
$547$	3.91961	−	6.78896i	0.167590	−	0.290275i	0.937572	+	0.347791i	$0.113068\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.32037	−	4.01899i	0.0988510	−	0.171215i
$552$		0			0
$553$	4.51959	−	12.3979i	0.192192	−	0.527212i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			0.0134996i			0.000571997i	1.00000		0.000285998i	$9.10361e-5\pi$
$557$			0.0134996i			0.000571997i	−1.00000		0.000285998i	$0.999909\pi$
$558$		0			0
$559$		−	7.06782i		−	0.298937i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.54528	+	16.5329i	0.402286	+	0.696779i	0.994001	−	0.109368i	$-0.0348826\pi$
$563$	9.54528	+	16.5329i	0.402286	+	0.696779i	−0.591716	+	0.806147i	$0.701549\pi$
$564$		0			0
$565$	32.8923	+	18.9904i	1.38379	+	0.798932i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−32.3406	−	18.6719i	−1.35579	−	0.782765i	−0.366735	−	0.930325i	$-0.619525\pi$
$569$	−32.3406	−	18.6719i	−1.35579	−	0.782765i	−0.989053	+	0.147561i	$0.952858\pi$
$570$		0			0
$571$	22.6421	+	39.2173i	0.947544	+	1.64119i	0.750576	+	0.660784i	$0.229776\pi$
$571$	22.6421	+	39.2173i	0.947544	+	1.64119i	0.196968	+	0.980410i	$0.436890\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	0.264101i		−	0.0110138i
$576$		0			0
$577$			37.0988i			1.54444i	0.635354	+	0.772221i	$0.280854\pi$
$577$			37.0988i			1.54444i	−0.635354	+	0.772221i	$0.719146\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.76653	+	21.3048i	−0.322210	+	0.883870i
$582$		0			0
$583$	−13.3603	+	23.1408i	−0.553329	+	0.958393i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.0612	−	29.5509i	0.704191	−	1.21969i	−0.262792	−	0.964853i	$-0.584643\pi$
$587$	17.0612	−	29.5509i	0.704191	−	1.21969i	0.966983	−	0.254842i	$-0.0820235\pi$
$588$		0			0
$589$	8.81453	+	15.2672i	0.363197	+	0.629075i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	19.6999			0.808980			0.404490	−	0.914542i	$-0.367449\pi$
$593$	19.6999			0.808980			0.404490	+	0.914542i	$0.367449\pi$
$594$		0			0
$595$	22.4313	+	26.7601i	0.919594	+	1.09706i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.74033	+	5.62358i	−0.397979	+	0.229773i	−0.685612	−	0.727967i	$-0.740465\pi$
$599$	−9.74033	+	5.62358i	−0.397979	+	0.229773i	0.287632	+	0.957741i	$0.407132\pi$
$600$		0			0
$601$	−29.7646	−	17.1846i	−1.21412	−	0.700975i	−0.250469	−	0.968125i	$-0.580585\pi$
$601$	−29.7646	−	17.1846i	−1.21412	−	0.700975i	−0.963655	+	0.267150i	$0.913918\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.564393	+	0.977557i	−0.0229458	+	0.0397433i
$606$		0			0
$607$	−33.7888	+	19.5080i	−1.37145	+	0.791804i	−0.991110	−	0.133044i	$-0.957525\pi$
$607$	−33.7888	+	19.5080i	−1.37145	+	0.791804i	−0.380335	+	0.924849i	$0.624191\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			0.443317i			0.0179347i
$612$		0			0
$613$	−16.1099			−0.650672			−0.325336	−	0.945598i	$-0.605477\pi$
$613$	−16.1099			−0.650672			−0.325336	+	0.945598i	$0.605477\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.03569	+	4.06205i	−0.283246	+	0.163532i	−0.634892	−	0.772601i	$-0.718955\pi$
$617$	−7.03569	+	4.06205i	−0.283246	+	0.163532i	0.351646	+	0.936133i	$0.385622\pi$
$618$		0			0
$619$	32.4018	+	18.7072i	1.30234	+	0.751906i	0.980805	−	0.194991i	$-0.0624678\pi$
$619$	32.4018	+	18.7072i	1.30234	+	0.751906i	0.321535	+	0.946898i	$0.395801\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−27.4542	+	4.82656i	−1.09993	+	0.193372i
$624$		0			0
$625$	12.2156	+	21.1581i	0.488626	+	0.846325i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−10.1451			−0.404511
$630$		0			0
$631$	19.8268			0.789294			0.394647	−	0.918833i	$-0.370867\pi$
$631$	19.8268			0.789294			0.394647	+	0.918833i	$0.370867\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.98848	−	12.1044i	−0.277329	−	0.480348i
$636$		0			0
$637$	8.11802	−	9.65478i	0.321648	−	0.382536i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.01849	+	4.62948i	0.316711	+	0.182853i	0.649926	−	0.759998i	$-0.274800\pi$
$641$	8.01849	+	4.62948i	0.316711	+	0.182853i	−0.333214	+	0.942851i	$0.608133\pi$
$642$		0			0
$643$	36.3456	−	20.9841i	1.43333	−	0.827534i	0.435958	−	0.899967i	$-0.356410\pi$
$643$	36.3456	−	20.9841i	1.43333	−	0.827534i	0.997373	+	0.0724332i	$0.0230764\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.28587			−0.247123			−0.123561	−	0.992337i	$-0.539432\pi$
$647$	−6.28587			−0.247123			−0.123561	+	0.992337i	$0.539432\pi$
$648$		0			0
$649$		−	36.5798i		−	1.43588i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.1668	+	11.6433i	−0.789189	+	0.455638i	−0.839677	−	0.543086i	$-0.817256\pi$
$653$	−20.1668	+	11.6433i	−0.789189	+	0.455638i	0.0504882	+	0.998725i	$0.483922\pi$
$654$		0			0
$655$	−18.8207	+	32.5985i	−0.735387	+	1.27373i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	25.8880	+	14.9464i	1.00845	+	0.582230i	0.910738	−	0.412984i	$-0.135514\pi$
$659$	25.8880	+	14.9464i	1.00845	+	0.582230i	0.0977141	+	0.995215i	$0.468847\pi$
$660$		0			0
$661$	−17.6184	+	10.1720i	−0.685278	+	0.395645i	−0.801841	−	0.597538i	$-0.796146\pi$
$661$	−17.6184	+	10.1720i	−0.685278	+	0.395645i	0.116563	+	0.993183i	$0.462812\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.37118	−	6.17878i	0.285842	−	0.239603i
$666$		0			0
$667$	−6.69963			−0.259411
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.40643	+	4.16805i	0.0928990	+	0.160906i
$672$		0			0
$673$	−8.55996	+	14.8263i	−0.329962	+	0.571511i	−0.982504	−	0.186241i	$-0.940369\pi$
$673$	−8.55996	+	14.8263i	−0.329962	+	0.571511i	0.652542	+	0.757753i	$0.273703\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.2078	−	24.6085i	0.546048	−	0.945783i	−0.452492	−	0.891769i	$-0.649465\pi$
$677$	14.2078	−	24.6085i	0.546048	−	0.945783i	0.998540	−	0.0540148i	$-0.0172018\pi$
$678$		0			0
$679$	−18.0858	−	6.59310i	−0.694071	−	0.253020i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			20.9274i			0.800764i	0.916348	+	0.400382i	$0.131123\pi$
$683$			20.9274i			0.800764i	−0.916348	+	0.400382i	$0.868877\pi$
$684$		0			0
$685$		−	13.8526i		−	0.529281i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.09627	−	12.2911i	−0.270346	−	0.468254i
$690$		0			0
$691$	−20.7918	−	12.0041i	−0.790957	−	0.456659i	0.0493424	−	0.998782i	$-0.484287\pi$
$691$	−20.7918	−	12.0041i	−0.790957	−	0.456659i	−0.840299	+	0.542123i	$0.817621\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	14.7143	+	8.49529i	0.558144	+	0.322245i
$696$		0			0
$697$	2.71634	+	4.70484i	0.102889	+	0.178208i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	42.0117i		−	1.58676i	−0.608728	−	0.793379i	$-0.708320\pi$
$701$		−	42.0117i		−	1.58676i	0.608728	−	0.793379i	$-0.291680\pi$
$702$		0			0
$703$			2.79450i			0.105397i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.23006	−	11.6037i	0.159088	−	0.436401i
$708$		0			0
$709$	−18.6094	+	32.2324i	−0.698891	+	1.21051i	0.269960	+	0.962871i	$0.412989\pi$
$709$	−18.6094	+	32.2324i	−0.698891	+	1.21051i	−0.968851	+	0.247643i	$0.920344\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	12.7252	−	22.0406i	0.476561	−	0.825428i
$714$		0			0
$715$	−6.75890	−	11.7068i	−0.252769	−	0.437808i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.2978			−0.682392			−0.341196	−	0.939992i	$-0.610832\pi$
$719$	−18.2978			−0.682392			−0.341196	+	0.939992i	$0.610832\pi$
$720$		0			0
$721$	12.6538	−	10.6069i	0.471253	−	0.395021i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.271971	+	0.157022i	−0.0101007	+	0.00583166i
$726$		0			0
$727$	−28.3214	−	16.3514i	−1.05038	−	0.606439i	−0.127626	−	0.991822i	$-0.540736\pi$
$727$	−28.3214	−	16.3514i	−1.05038	−	0.606439i	−0.922756	+	0.385384i	$0.874069\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−11.7057	+	20.2749i	−0.432951	+	0.749893i
$732$		0			0
$733$	−0.431812	+	0.249307i	−0.0159494	+	0.00920836i	−0.507953	−	0.861385i	$-0.669598\pi$
$733$	−0.431812	+	0.249307i	−0.0159494	+	0.00920836i	0.492004	+	0.870593i	$0.336264\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			27.0997i			0.998231i
$738$		0			0
$739$	47.7046			1.75484			0.877421	−	0.479722i	$-0.159263\pi$
$739$	47.7046			1.75484			0.877421	+	0.479722i	$0.159263\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	9.20534	−	5.31470i	0.337711	−	0.194978i	−0.321548	−	0.946893i	$-0.604203\pi$
$743$	9.20534	−	5.31470i	0.337711	−	0.194978i	0.659259	+	0.751916i	$0.270870\pi$
$744$		0			0
$745$	−29.5606	−	17.0668i	−1.08302	−	0.625279i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.682303	−	3.88104i	−0.0249308	−	0.141810i
$750$		0			0
$751$	9.55927	+	16.5571i	0.348823	+	0.604179i	0.986041	−	0.166505i	$-0.0532482\pi$
$751$	9.55927	+	16.5571i	0.348823	+	0.604179i	−0.637218	+	0.770684i	$0.719915\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	25.8411			0.940453
$756$		0			0
$757$	28.5388			1.03726			0.518631	−	0.854998i	$-0.326442\pi$
$757$	28.5388			1.03726			0.518631	+	0.854998i	$0.326442\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.6650	+	37.5249i	0.785355	+	1.36028i	0.928787	+	0.370615i	$0.120853\pi$
$761$	21.6650	+	37.5249i	0.785355	+	1.36028i	−0.143431	+	0.989660i	$0.545814\pi$
$762$		0			0
$763$	11.4313	−	2.00967i	0.413840	−	0.0727548i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	16.8261	+	9.71458i	0.607557	+	0.350773i
$768$		0			0
$769$	−5.75189	+	3.32086i	−0.207419	+	0.119753i	−0.600111	−	0.799917i	$-0.704877\pi$
$769$	−5.75189	+	3.32086i	−0.207419	+	0.119753i	0.392693	+	0.919670i	$0.371544\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−44.4831			−1.59995			−0.799973	−	0.600036i	$-0.795153\pi$
$773$	−44.4831			−1.59995			−0.799973	+	0.600036i	$0.795153\pi$
$774$		0			0
$775$		−	1.19298i		−	0.0428532i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.29596	−	0.748226i	0.0464328	−	0.0268080i
$780$		0			0
$781$	−20.6520	+	35.7703i	−0.738986	+	1.27996i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	10.9134	+	6.30087i	0.389517	+	0.224888i
$786$		0			0
$787$	−19.0399	+	10.9927i	−0.678700	+	0.391848i	−0.799365	−	0.600846i	$-0.794831\pi$
$787$	−19.0399	+	10.9927i	−0.678700	+	0.391848i	0.120665	+	0.992693i	$0.461497\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−34.8300	+	29.1958i	−1.23841	+	1.03808i
$792$		0			0
$793$	−2.55632			−0.0907776
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−9.71892	−	16.8337i	−0.344262	−	0.596279i	0.640958	−	0.767576i	$-0.278537\pi$
$797$	−9.71892	−	16.8337i	−0.344262	−	0.596279i	−0.985219	+	0.171297i	$0.945204\pi$
$798$		0			0
$799$	0.734219	−	1.27171i	0.0259748	−	0.0449897i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	0.722823	−	1.25197i	0.0255079	−	0.0441809i
$804$		0			0
$805$	−13.0457	−	4.75574i	−0.459801	−	0.167618i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			21.0058i			0.738526i	0.929325	+	0.369263i	$0.120390\pi$
$809$			21.0058i			0.738526i	−0.929325	+	0.369263i	$0.879610\pi$
$810$		0			0
$811$			37.3291i			1.31080i	0.755281	+	0.655401i	$0.227500\pi$
$811$			37.3291i			1.31080i	−0.755281	+	0.655401i	$0.772500\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.2876	+	19.5506i	0.395386	+	0.684829i
$816$		0			0
$817$	5.58478	+	3.22438i	0.195387	+	0.112807i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.9017	+	6.29412i	0.380473	+	0.219666i	0.678024	−	0.735040i	$-0.262837\pi$
$821$	10.9017	+	6.29412i	0.380473	+	0.219666i	−0.297551	+	0.954706i	$0.596170\pi$
$822$		0			0
$823$	−22.4189	−	38.8307i	−0.781474	−	1.35355i	−0.931083	−	0.364808i	$-0.881135\pi$
$823$	−22.4189	−	38.8307i	−0.781474	−	1.35355i	0.149608	−	0.988745i	$-0.452199\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			25.7293i			0.894695i	0.894360	+	0.447347i	$0.147631\pi$
$827$			25.7293i			0.894695i	−0.894360	+	0.447347i	$0.852369\pi$
$828$		0			0
$829$			16.9628i			0.589142i	0.955630	+	0.294571i	$0.0951767\pi$
$829$			16.9628i			0.589142i	−0.955630	+	0.294571i	$0.904823\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−39.2777	+	14.2508i	−1.36089	+	0.493762i
$834$		0			0
$835$	3.99450	−	6.91867i	0.138235	−	0.239431i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	13.3539	−	23.1296i	0.461027	−	0.798522i	−0.537986	−	0.842954i	$-0.680815\pi$
$839$	13.3539	−	23.1296i	0.461027	−	0.798522i	0.999012	+	0.0444321i	$0.0141478\pi$
$840$		0			0
$841$	−10.5167	−	18.2155i	−0.362645	−	0.628120i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−21.5637			−0.741815
$846$		0			0
$847$	−0.867695	−	1.03514i	−0.0298144	−	0.0355680i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.49381	−	2.01715i	0.119766	−	0.0691471i
$852$		0			0
$853$	−37.6287	−	21.7249i	−1.28838	−	0.743848i	−0.310017	−	0.950731i	$-0.600335\pi$
$853$	−37.6287	−	21.7249i	−1.28838	−	0.743848i	−0.978366	+	0.206883i	$0.933668\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.83430	+	13.5694i	−0.267615	+	0.463522i	−0.968245	−	0.250002i	$-0.919569\pi$
$857$	−7.83430	+	13.5694i	−0.267615	+	0.463522i	0.700631	+	0.713524i	$0.252902\pi$
$858$		0			0
$859$	−17.3578	+	10.0216i	−0.592242	+	0.341931i	−0.765984	−	0.642860i	$-0.777748\pi$
$859$	−17.3578	+	10.0216i	−0.592242	+	0.341931i	0.173742	+	0.984791i	$0.444414\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	40.0219i		−	1.36236i	−0.732115	−	0.681181i	$-0.761467\pi$
$863$		−	40.0219i		−	1.36236i	0.732115	−	0.681181i	$-0.238533\pi$
$864$		0			0
$865$	39.9739			1.35915
$866$		0			0
$867$		0			0
$868$		0			0
$869$	14.6545	−	8.46079i	0.497120	−	0.287013i
$870$		0			0
$871$	−12.4655	−	7.19694i	−0.422376	−	0.243859i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−29.4487	+	5.17720i	−0.995547	+	0.175021i
$876$		0			0
$877$	−22.6353	−	39.2054i	−0.764338	−	1.32387i	−0.940596	−	0.339529i	$-0.889732\pi$
$877$	−22.6353	−	39.2054i	−0.764338	−	1.32387i	0.176257	−	0.984344i	$-0.443601\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	45.3385			1.52749			0.763746	−	0.645517i	$-0.223358\pi$
$881$	45.3385			1.52749			0.763746	+	0.645517i	$0.223358\pi$
$882$		0			0
$883$	−12.5650			−0.422845			−0.211423	−	0.977395i	$-0.567810\pi$
$883$	−12.5650			−0.422845			−0.211423	+	0.977395i	$0.567810\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−17.8620	−	30.9379i	−0.599748	−	1.03879i	−0.992858	−	0.119303i	$-0.961934\pi$
$887$	−17.8620	−	30.9379i	−0.599748	−	1.03879i	0.393110	−	0.919492i	$-0.371399\pi$
$888$		0			0
$889$	16.4723	−	2.89589i	0.552462	−	0.0971251i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.350296	−	0.202243i	−0.0117222	−	0.00676782i
$894$		0			0
$895$	9.63528	−	5.56293i	0.322072	−	0.185948i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.2632			−1.00933
$900$		0			0
$901$			47.0113i			1.56617i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	25.9635	−	14.9901i	0.863058	−	0.498287i
$906$		0			0
$907$	−4.52104	+	7.83067i	−0.150119	+	0.260013i	−0.931271	−	0.364327i	$-0.881299\pi$
$907$	−4.52104	+	7.83067i	−0.150119	+	0.260013i	0.781152	+	0.624341i	$0.214632\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−35.5171	−	20.5058i	−1.17673	−	0.679388i	−0.221478	−	0.975165i	$-0.571088\pi$
$911$	−35.5171	−	20.5058i	−1.17673	−	0.679388i	−0.955257	+	0.295777i	$0.904421\pi$
$912$		0			0
$913$	−25.1826	+	14.5392i	−0.833421	+	0.481176i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−28.9349	−	34.5188i	−0.955515	−	1.13991i
$918$		0			0
$919$	−10.2326			−0.337541			−0.168771	−	0.985655i	$-0.553980\pi$
$919$	−10.2326			−0.337541			−0.168771	+	0.985655i	$0.553980\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−10.9692	−	18.9992i	−0.361055	−	0.625366i
$924$		0			0
$925$	0.0945538	−	0.163772i	0.00310891	−	0.00538479i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.8330	+	22.2273i	−0.421036	+	0.729255i	−0.996041	−	0.0888945i	$-0.971667\pi$
$929$	−12.8330	+	22.2273i	−0.421036	+	0.729255i	0.575005	+	0.818150i	$0.305000\pi$
$930$		0			0
$931$	3.92544	+	10.8192i	0.128651	+	0.354585i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			44.7763i			1.46434i
$936$		0			0
$937$		−	15.9276i		−	0.520333i	−0.965564	−	0.260167i	$-0.916223\pi$
$937$		−	15.9276i		−	0.520333i	0.965564	−	0.260167i	$-0.0837775\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	19.6767	+	34.0810i	0.641442	+	1.11101i	0.985111	+	0.171919i	$0.0549967\pi$
$941$	19.6767	+	34.0810i	0.641442	+	1.11101i	−0.343669	+	0.939091i	$0.611670\pi$
$942$		0			0
$943$	−1.87093	−	1.08018i	−0.0609258	−	0.0351755i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.9086	+	16.6904i	0.939403	+	0.542365i	0.889773	−	0.456403i	$-0.150862\pi$
$947$	28.9086	+	16.6904i	0.939403	+	0.542365i	0.0496302	+	0.998768i	$0.484196\pi$
$948$		0			0
$949$	0.383923	+	0.664975i	0.0124627	+	0.0215860i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			44.4622i			1.44027i	0.693832	+	0.720137i	$0.255921\pi$
$953$			44.4622i			1.44027i	−0.693832	+	0.720137i	$0.744079\pi$
$954$		0			0
$955$		−	22.6447i		−	0.732764i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	15.5736	+	5.67725i	0.502896	+	0.183328i
$960$		0			0
$961$	41.9814	−	72.7138i	1.35424	−	2.34561i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	17.8347	−	30.8905i	0.574118	−	0.994401i
$966$		0			0
$967$	20.0556	+	34.7372i	0.644943	+	1.11707i	0.984315	+	0.176422i	$0.0564523\pi$
$967$	20.0556	+	34.7372i	0.644943	+	1.11707i	−0.339371	+	0.940652i	$0.610214\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	46.0026			1.47629			0.738147	−	0.674640i	$-0.235701\pi$
$971$	46.0026			1.47629			0.738147	+	0.674640i	$0.235701\pi$
$972$		0			0
$973$	−15.5811	+	13.0606i	−0.499506	+	0.418704i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	46.8323	−	27.0386i	1.49830	−	0.865042i	0.498299	−	0.867005i	$-0.333958\pi$
$977$	46.8323	−	27.0386i	1.49830	−	0.865042i	0.999998	+	0.00196335i	$0.000624955\pi$
$978$		0			0
$979$	−30.9562	−	17.8726i	−0.989365	−	0.571210i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.97890	−	12.0878i	0.222592	−	0.385541i	−0.733002	−	0.680226i	$-0.761881\pi$
$983$	6.97890	−	12.0878i	0.222592	−	0.385541i	0.955594	+	0.294685i	$0.0952148\pi$
$984$		0			0
$985$	−7.39703	+	4.27068i	−0.235689	+	0.136075i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	9.30979i		−	0.296034i
$990$		0			0
$991$	37.0297			1.17629			0.588144	−	0.808756i	$-0.299859\pi$
$991$	37.0297			1.17629			0.588144	+	0.808756i	$0.299859\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−29.1119	+	16.8077i	−0.922909	+	0.532841i
$996$		0			0
$997$	43.4282	+	25.0733i	1.37538	+	0.794079i	0.991600	−	0.129344i	$-0.0412871\pi$
$997$	43.4282	+	25.0733i	1.37538	+	0.794079i	0.383785	+	0.923422i	$0.374620\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.a.2897.5		12
3.2	odd	2		1008.2.cc.a.209.6		12
4.3	odd	2		189.2.o.a.62.4		12
7.6	odd	2	inner	3024.2.cc.a.2897.2		12
9.4	even	3		1008.2.cc.a.545.1		12
9.5	odd	6	inner	3024.2.cc.a.881.2		12
12.11	even	2		63.2.o.a.20.3	✓	12
21.20	even	2		1008.2.cc.a.209.1		12
28.3	even	6		1323.2.s.c.656.4		12
28.11	odd	6		1323.2.s.c.656.3		12
28.19	even	6		1323.2.i.c.521.3		12
28.23	odd	6		1323.2.i.c.521.4		12
28.27	even	2		189.2.o.a.62.3		12
36.7	odd	6		567.2.c.c.566.5		12
36.11	even	6		567.2.c.c.566.8		12
36.23	even	6		189.2.o.a.125.3		12
36.31	odd	6		63.2.o.a.41.4	yes	12
63.13	odd	6		1008.2.cc.a.545.6		12
63.41	even	6	inner	3024.2.cc.a.881.5		12
84.11	even	6		441.2.s.c.362.4		12
84.23	even	6		441.2.i.c.227.4		12
84.47	odd	6		441.2.i.c.227.3		12
84.59	odd	6		441.2.s.c.362.3		12
84.83	odd	2		63.2.o.a.20.4	yes	12
252.23	even	6		1323.2.s.c.962.4		12
252.31	even	6		441.2.i.c.68.4		12
252.59	odd	6		1323.2.i.c.1097.4		12
252.67	odd	6		441.2.i.c.68.3		12
252.83	odd	6		567.2.c.c.566.7		12
252.95	even	6		1323.2.i.c.1097.3		12
252.103	even	6		441.2.s.c.374.4		12
252.131	odd	6		1323.2.s.c.962.3		12
252.139	even	6		63.2.o.a.41.3	yes	12
252.167	odd	6		189.2.o.a.125.4		12
252.223	even	6		567.2.c.c.566.6		12
252.247	odd	6		441.2.s.c.374.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.3	✓	12	12.11	even	2
63.2.o.a.20.4	yes	12	84.83	odd	2
63.2.o.a.41.3	yes	12	252.139	even	6
63.2.o.a.41.4	yes	12	36.31	odd	6
189.2.o.a.62.3		12	28.27	even	2
189.2.o.a.62.4		12	4.3	odd	2
189.2.o.a.125.3		12	36.23	even	6
189.2.o.a.125.4		12	252.167	odd	6
441.2.i.c.68.3		12	252.67	odd	6
441.2.i.c.68.4		12	252.31	even	6
441.2.i.c.227.3		12	84.47	odd	6
441.2.i.c.227.4		12	84.23	even	6
441.2.s.c.362.3		12	84.59	odd	6
441.2.s.c.362.4		12	84.11	even	6
441.2.s.c.374.3		12	252.247	odd	6
441.2.s.c.374.4		12	252.103	even	6
567.2.c.c.566.5		12	36.7	odd	6
567.2.c.c.566.6		12	252.223	even	6
567.2.c.c.566.7		12	252.83	odd	6
567.2.c.c.566.8		12	36.11	even	6
1008.2.cc.a.209.1		12	21.20	even	2
1008.2.cc.a.209.6		12	3.2	odd	2
1008.2.cc.a.545.1		12	9.4	even	3
1008.2.cc.a.545.6		12	63.13	odd	6
1323.2.i.c.521.3		12	28.19	even	6
1323.2.i.c.521.4		12	28.23	odd	6
1323.2.i.c.1097.3		12	252.95	even	6
1323.2.i.c.1097.4		12	252.59	odd	6
1323.2.s.c.656.3		12	28.11	odd	6
1323.2.s.c.656.4		12	28.3	even	6
1323.2.s.c.962.3		12	252.131	odd	6
1323.2.s.c.962.4		12	252.23	even	6
3024.2.cc.a.881.2		12	9.5	odd	6	inner
3024.2.cc.a.881.5		12	63.41	even	6	inner
3024.2.cc.a.2897.2		12	7.6	odd	2	inner
3024.2.cc.a.2897.5		12	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:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.cc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.10552 + 1.91482i) q^{5} +(-2.60579 + 0.458109i) q^{7} +O(q^{10})\)	\(q+(1.10552 + 1.91482i) q^{5} +(-2.60579 + 0.458109i) q^{7} +(-2.93818 - 1.69636i) q^{11} +(1.56060 - 0.901012i) q^{13} -5.96901 q^{17} +1.64419i q^{19} +(2.05563 - 1.18682i) q^{23} +(0.0556321 - 0.0963576i) q^{25} +(-2.44437 - 1.41126i) q^{29} +(9.28558 - 5.36103i) q^{31} +(-3.75796 - 4.48318i) q^{35} +1.69963 q^{37} +(-0.455074 - 0.788211i) q^{41} +(1.96108 - 3.39669i) q^{43} +(-0.123005 + 0.213051i) q^{47} +(6.58027 - 2.38747i) q^{49} -7.87589i q^{53} -7.50146i q^{55} +(5.39093 + 9.33736i) q^{59} +(-1.22853 - 0.709292i) q^{61} +(3.45056 + 1.99218i) q^{65} +(-3.99381 - 6.91748i) q^{67} -12.1743i q^{71} +0.426103i q^{73} +(8.43339 + 3.07435i) q^{77} +(-2.49381 + 4.31941i) q^{79} +(4.28541 - 7.42254i) q^{83} +(-6.59888 - 11.4296i) q^{85} +10.5358 q^{89} +(-3.65383 + 3.06277i) q^{91} +(-3.14833 + 1.81769i) q^{95} +(6.30108 + 3.63793i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 12 * q + 2 * q^7	\( 12 q + 2 q^{7} + 24 q^{23} - 30 q^{29} - 4 q^{37} + 10 q^{43} + 6 q^{49} + 78 q^{65} - 12 q^{67} + 24 q^{77} + 6 q^{79} - 6 q^{85} + 24 q^{91} + 72 q^{95}+O(q^{100}) \) 12 * q + 2 * q^7 + 24 * q^23 - 30 * q^29 - 4 * q^37 + 10 * q^43 + 6 * q^49 + 78 * q^65 - 12 * q^67 + 24 * q^77 + 6 * q^79 - 6 * q^85 + 24 * q^91 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more