LMFDB - Embedded newform 3024.2.cc.a.881.1

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			881.1
Root			$1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.a.2897.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41899 + 2.45776i) q^{5} +(2.07253 + 1.64457i) q^{7} +O(q^{10})$	$q+(-1.41899 + 2.45776i) q^{5} +(2.07253 + 1.64457i) q^{7} +(0.136673 - 0.0789082i) q^{11} +(-3.41468 - 1.97146i) q^{13} -4.14487 q^{17} -6.33597i q^{19} +(0.472958 + 0.273062i) q^{23} +(-1.52704 - 2.64491i) q^{25} +(-4.02704 + 2.32501i) q^{29} +(-0.112086 - 0.0647129i) q^{31} +(-6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +(1.99569 - 3.45664i) q^{41} +(-3.28434 - 5.68864i) q^{43} +(-4.33370 - 7.50619i) q^{47} +(1.59079 + 6.81685i) q^{49} +2.60234i q^{53} +0.447879i q^{55} +(1.80686 - 3.12957i) q^{59} +(-2.91472 + 1.68281i) q^{61} +(9.69076 - 5.59496i) q^{65} +(0.663715 - 1.14959i) q^{67} -0.409310i q^{71} -15.0124i q^{73} +(0.413030 + 0.0612283i) q^{77} +(2.16372 + 3.74766i) q^{79} +(3.22585 + 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} -5.05368 q^{89} +(-3.83482 - 9.70160i) q^{91} +(15.5723 + 8.99066i) q^{95} +(-2.18452 + 1.26123i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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
$5$	−1.41899	+	2.45776i	−0.634590	+	1.09914i	0.352012	+	0.935995i	$0.385498\pi$
$5$	−1.41899	+	2.45776i	−0.634590	+	1.09914i	−0.986602	+	0.163146i	$0.947836\pi$
$6$		0			0
$7$	2.07253	+	1.64457i	0.783344	+	0.621589i
$7$	2.07253	+	1.64457i	0.783344	+	0.621589i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.136673	−	0.0789082i	0.0412085	−	0.0237917i	−0.479254	−	0.877676i	$-0.659093\pi$
$11$	0.136673	−	0.0789082i	0.0412085	−	0.0237917i	0.520463	+	0.853884i	$0.325759\pi$
$12$		0			0
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.0548943	−	0.998492i	$-0.517482\pi$
$13$	−3.41468	−	1.97146i	−0.947061	−	0.546786i	−0.892167	+	0.451706i	$0.850816\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.14487			−1.00528			−0.502640	−	0.864496i	$-0.667638\pi$
$17$	−4.14487			−1.00528			−0.502640	+	0.864496i	$0.667638\pi$
$18$		0			0
$19$		−	6.33597i		−	1.45357i	−0.686864	−	0.726786i	$-0.741013\pi$
$19$		−	6.33597i		−	1.45357i	0.686864	−	0.726786i	$-0.258987\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.472958	+	0.273062i	0.0986185	+	0.0569374i	0.548498	−	0.836152i	$-0.315200\pi$
$23$	0.472958	+	0.273062i	0.0986185	+	0.0569374i	−0.449880	+	0.893089i	$0.648533\pi$
$24$		0			0
$25$	−1.52704	−	2.64491i	−0.305408	−	0.528983i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.02704	+	2.32501i	−0.747803	+	0.431744i	−0.824900	−	0.565279i	$-0.808768\pi$
$29$	−4.02704	+	2.32501i	−0.747803	+	0.431744i	0.0770966	+	0.997024i	$0.475435\pi$
$30$		0			0
$31$	−0.112086	−	0.0647129i	−0.0201313	−	0.0116228i	0.489901	−	0.871778i	$-0.337033\pi$
$31$	−0.112086	−	0.0647129i	−0.0201313	−	0.0116228i	−0.510032	+	0.860156i	$0.670366\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.98284	+	2.76016i	−1.18032	+	0.466552i
$36$		0			0
$37$	−2.46050			−0.404505			−0.202252	−	0.979333i	$-0.564826\pi$
$37$	−2.46050			−0.404505			−0.202252	+	0.979333i	$0.564826\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.99569	−	3.45664i	0.311675	−	0.539836i	−0.667050	−	0.745013i	$-0.732443\pi$
$41$	1.99569	−	3.45664i	0.311675	−	0.539836i	0.978725	+	0.205176i	$0.0657768\pi$
$42$		0			0
$43$	−3.28434	−	5.68864i	−0.500857	−	0.867509i	−1.00000		0.000989450i	$-0.999685\pi$
$43$	−3.28434	−	5.68864i	−0.500857	−	0.867509i	0.499143	−	0.866520i	$-0.333648\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.33370	−	7.50619i	−0.632135	−	1.09489i	−0.987114	−	0.160016i	$-0.948845\pi$
$47$	−4.33370	−	7.50619i	−0.632135	−	1.09489i	0.354979	−	0.934874i	$-0.384488\pi$
$48$		0			0
$49$	1.59079	+	6.81685i	0.227255	+	0.973835i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			2.60234i			0.357459i	0.983898	+	0.178730i	$0.0571988\pi$
$53$			2.60234i			0.357459i	−0.983898	+	0.178730i	$0.942801\pi$
$54$		0			0
$55$			0.447879i			0.0603920i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.80686	−	3.12957i	0.235233	−	0.407436i	−0.724107	−	0.689687i	$-0.757748\pi$
$59$	1.80686	−	3.12957i	0.235233	−	0.407436i	0.959340	+	0.282252i	$0.0910813\pi$
$60$		0			0
$61$	−2.91472	+	1.68281i	−0.373191	+	0.215462i	−0.674852	−	0.737953i	$-0.735792\pi$
$61$	−2.91472	+	1.68281i	−0.373191	+	0.215462i	0.301660	+	0.953415i	$0.402459\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.69076	−	5.59496i	1.20199	−	0.693970i
$66$		0			0
$67$	0.663715	−	1.14959i	0.0810857	−	0.140445i	−0.822631	−	0.568576i	$-0.807495\pi$
$67$	0.663715	−	1.14959i	0.0810857	−	0.140445i	0.903717	+	0.428131i	$0.140828\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	0.409310i		−	0.0485761i	−0.999705	−	0.0242881i	$-0.992268\pi$
$71$		−	0.409310i		−	0.0485761i	0.999705	−	0.0242881i	$-0.00773189\pi$
$72$		0			0
$73$		−	15.0124i		−	1.75707i	−0.477681	−	0.878533i	$-0.658522\pi$
$73$		−	15.0124i		−	1.75707i	0.477681	−	0.878533i	$-0.341478\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.413030	+	0.0612283i	0.0470691	+	0.00697762i
$78$		0			0
$79$	2.16372	+	3.74766i	0.243437	+	0.421645i	0.961691	−	0.274136i	$-0.0883918\pi$
$79$	2.16372	+	3.74766i	0.243437	+	0.421645i	−0.718254	+	0.695781i	$0.755058\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.22585	+	5.58733i	0.354083	+	0.613289i	0.986961	−	0.160963i	$-0.0514598\pi$
$83$	3.22585	+	5.58733i	0.354083	+	0.613289i	−0.632878	+	0.774252i	$0.718126\pi$
$84$		0			0
$85$	5.88151	−	10.1871i	0.637940	−	1.10494i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.05368			−0.535689			−0.267845	−	0.963462i	$-0.586311\pi$
$89$	−5.05368			−0.535689			−0.267845	+	0.963462i	$0.586311\pi$
$90$		0			0
$91$	−3.83482	−	9.70160i	−0.401999	−	1.01700i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	15.5723	+	8.99066i	1.59768	+	0.922422i
$96$		0			0
$97$	−2.18452	+	1.26123i	−0.221805	+	0.128059i	−0.606786	−	0.794866i	$-0.707541\pi$
$97$	−2.18452	+	1.26123i	−0.221805	+	0.128059i	0.384981	+	0.922925i	$0.374208\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.49573	−	2.59068i	−0.148831	−	0.257782i	0.781965	−	0.623323i	$-0.214218\pi$
$101$	−1.49573	−	2.59068i	−0.148831	−	0.257782i	−0.930796	+	0.365540i	$0.880884\pi$
$102$		0			0
$103$	11.4286	+	6.59832i	1.12610	+	0.650152i	0.942950	−	0.332934i	$-0.108038\pi$
$103$	11.4286	+	6.59832i	1.12610	+	0.650152i	0.183146	+	0.983086i	$0.441372\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	19.5555i		−	1.89051i	−0.326339	−	0.945253i	$-0.605815\pi$
$107$		−	19.5555i		−	1.89051i	0.326339	−	0.945253i	$-0.394185\pi$
$108$		0			0
$109$	13.2484			1.26897			0.634485	−	0.772935i	$-0.281212\pi$
$109$	13.2484			1.26897			0.634485	+	0.772935i	$0.281212\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.72665	+	5.03834i	0.820935	+	0.473967i	0.850739	−	0.525589i	$-0.176155\pi$
$113$	8.72665	+	5.03834i	0.820935	+	0.473967i	−0.0298041	+	0.999556i	$0.509488\pi$
$114$		0			0
$115$	−1.34224	+	0.774943i	−0.125165	+	0.0722638i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.59038	−	6.81653i	−0.787479	−	0.624870i
$120$		0			0
$121$	−5.48755	+	9.50471i	−0.498868	+	0.864065i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−5.52245			−0.493943
$126$		0			0
$127$	12.4897			1.10828			0.554140	−	0.832423i	$-0.313047\pi$
$127$	12.4897			1.10828			0.554140	+	0.832423i	$0.313047\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.02249	+	8.69921i	−0.438817	+	0.760054i	−0.997599	−	0.0692612i	$-0.977936\pi$
$131$	−5.02249	+	8.69921i	−0.438817	+	0.760054i	0.558781	+	0.829315i	$0.311269\pi$
$132$		0			0
$133$	10.4199	−	13.1315i	0.903524	−	1.13865i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.96410	−	4.02073i	0.594984	−	0.343514i	−0.172082	−	0.985083i	$-0.555049\pi$
$137$	6.96410	−	4.02073i	0.594984	−	0.343514i	0.767066	+	0.641569i	$0.221716\pi$
$138$		0			0
$139$	−16.3702	−	9.45136i	−1.38850	−	0.801654i	−0.395358	−	0.918527i	$-0.629379\pi$
$139$	−16.3702	−	9.45136i	−1.38850	−	0.801654i	−0.993147	+	0.116873i	$0.962713\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.622259			−0.0520359
$144$		0			0
$145$		−	13.1966i		−	1.09592i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−16.8063	−	9.70313i	−1.37683	−	0.794912i	−0.385051	−	0.922895i	$-0.625816\pi$
$149$	−16.8063	−	9.70313i	−1.37683	−	0.794912i	−0.991776	+	0.127984i	$0.959149\pi$
$150$		0			0
$151$	−0.893968	−	1.54840i	−0.0727501	−	0.126007i	0.827356	−	0.561678i	$-0.189844\pi$
$151$	−0.893968	−	1.54840i	−0.0727501	−	0.126007i	−0.900106	+	0.435672i	$0.856511\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.318097	−	0.183653i	0.0255502	−	0.0147514i
$156$		0			0
$157$	3.80255	+	2.19540i	0.303477	+	0.175212i	0.644004	−	0.765022i	$-0.277272\pi$
$157$	3.80255	+	2.19540i	0.303477	+	0.175212i	−0.340527	+	0.940235i	$0.610605\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.531151	+	1.34374i	0.0418606	+	0.105902i
$162$		0			0
$163$	−5.43560			−0.425749			−0.212874	−	0.977080i	$-0.568283\pi$
$163$	−5.43560			−0.425749			−0.212874	+	0.977080i	$0.568283\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.25273	+	9.09799i	−0.406468	+	0.704024i	−0.994491	−	0.104821i	$-0.966573\pi$
$167$	−5.25273	+	9.09799i	−0.406468	+	0.704024i	0.588023	+	0.808844i	$0.299907\pi$
$168$		0			0
$169$	1.27335	+	2.20550i	0.0979497	+	0.169654i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.77949	−	15.2065i	−0.667492	−	1.15613i	−0.978603	−	0.205757i	$-0.934034\pi$
$173$	−8.77949	−	15.2065i	−0.667492	−	1.15613i	0.311111	−	0.950374i	$-0.399299\pi$
$174$		0			0
$175$	1.18490	−	7.99300i	0.0895699	−	0.604214i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	18.2033i		−	1.36058i	−0.732945	−	0.680288i	$-0.761855\pi$
$179$		−	18.2033i		−	1.36058i	0.732945	−	0.680288i	$-0.238145\pi$
$180$		0			0
$181$			6.60182i			0.490710i	0.969433	+	0.245355i	$0.0789045\pi$
$181$			6.60182i			0.490710i	−0.969433	+	0.245355i	$0.921096\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.49142	−	6.04732i	0.256694	−	0.444608i
$186$		0			0
$187$	−0.566492	+	0.327065i	−0.0414260	+	0.0239173i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.3063	+	7.10506i	−0.890454	+	0.514104i	−0.874091	−	0.485762i	$-0.838542\pi$
$191$	−12.3063	+	7.10506i	−0.890454	+	0.514104i	−0.0163630	+	0.999866i	$0.505209\pi$
$192$		0			0
$193$	5.00214	−	8.66395i	0.360062	−	0.623645i	−0.627909	−	0.778287i	$-0.716089\pi$
$193$	5.00214	−	8.66395i	0.360062	−	0.623645i	0.987971	+	0.154642i	$0.0494223\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	20.1017i		−	1.43218i	−0.698006	−	0.716092i	$-0.745929\pi$
$197$		−	20.1017i		−	1.43218i	0.698006	−	0.716092i	$-0.254071\pi$
$198$		0			0
$199$		−	12.9378i		−	0.917136i	−0.888659	−	0.458568i	$-0.848363\pi$
$199$		−	12.9378i		−	0.917136i	0.888659	−	0.458568i	$-0.151637\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−12.1698	−	1.80408i	−0.854154	−	0.126622i
$204$		0			0
$205$	5.66372	+	9.80984i	0.395571	+	0.685149i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.499960	−	0.865957i	−0.0345830	−	0.0598995i
$210$		0			0
$211$	4.50720	−	7.80669i	0.310288	−	0.537435i	−0.668136	−	0.744039i	$-0.732908\pi$
$211$	4.50720	−	7.80669i	0.310288	−	0.537435i	0.978425	+	0.206604i	$0.0662411\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	18.6417			1.27135
$216$		0			0
$217$	−0.125877	−	0.318453i	−0.00854510	−	0.0216180i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.1534	+	8.17147i	0.952061	+	0.549672i
$222$		0			0
$223$	1.95429	−	1.12831i	0.130869	−	0.0755571i	−0.433136	−	0.901328i	$-0.642593\pi$
$223$	1.95429	−	1.12831i	0.130869	−	0.0755571i	0.564005	+	0.825771i	$0.309260\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.32085	−	16.1442i	−0.618647	−	1.07153i	−0.989733	−	0.142929i	$-0.954348\pi$
$227$	−9.32085	−	16.1442i	−0.618647	−	1.07153i	0.371086	−	0.928598i	$-0.378985\pi$
$228$		0			0
$229$	−12.3891	−	7.15283i	−0.818692	−	0.472672i	0.0312731	−	0.999511i	$-0.490044\pi$
$229$	−12.3891	−	7.15283i	−0.818692	−	0.472672i	−0.849965	+	0.526839i	$0.823377\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	17.0679i		−	1.11815i	−0.829116	−	0.559077i	$-0.811156\pi$
$233$		−	17.0679i		−	1.11815i	0.829116	−	0.559077i	$-0.188844\pi$
$234$		0			0
$235$	24.5979			1.60459
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.93560	+	1.11752i	0.125203	+	0.0722863i	0.561294	−	0.827617i	$-0.310304\pi$
$239$	1.93560	+	1.11752i	0.125203	+	0.0722863i	−0.436090	+	0.899903i	$0.643637\pi$
$240$		0			0
$241$	−3.91464	+	2.26012i	−0.252164	+	0.145587i	−0.620755	−	0.784005i	$-0.713174\pi$
$241$	−3.91464	+	2.26012i	−0.252164	+	0.145587i	0.368591	+	0.929592i	$0.379840\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−19.0114	−	5.76324i	−1.21460	−	0.368200i
$246$		0			0
$247$	−12.4911	+	21.6353i	−0.794793	+	1.37662i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−21.1727			−1.33641			−0.668205	−	0.743978i	$-0.732937\pi$
$251$	−21.1727			−1.33641			−0.668205	+	0.743978i	$0.732937\pi$
$252$		0			0
$253$	0.0861875			0.00541856
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−15.6502	+	27.1070i	−0.976236	+	1.69089i	−0.300440	+	0.953801i	$0.597134\pi$
$257$	−15.6502	+	27.1070i	−0.976236	+	1.69089i	−0.675796	+	0.737089i	$0.736200\pi$
$258$		0			0
$259$	−5.09948	−	4.04647i	−0.316866	−	0.251435i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.78220	+	3.33836i	−0.356546	+	0.205852i	−0.667564	−	0.744552i	$-0.732663\pi$
$263$	−5.78220	+	3.33836i	−0.356546	+	0.205852i	0.311019	+	0.950404i	$0.399330\pi$
$264$		0			0
$265$	−6.39593	−	3.69269i	−0.392899	−	0.226840i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.6589			0.649887			0.324944	−	0.945733i	$-0.394655\pi$
$269$	10.6589			0.649887			0.324944	+	0.945733i	$0.394655\pi$
$270$		0			0
$271$			7.44498i			0.452250i	0.974098	+	0.226125i	$0.0726058\pi$
$271$			7.44498i			0.452250i	−0.974098	+	0.226125i	$0.927394\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.417411	−	0.240992i	−0.0251708	−	0.0145324i
$276$		0			0
$277$	13.2793	+	23.0004i	0.797874	+	1.38196i	0.920998	+	0.389568i	$0.127376\pi$
$277$	13.2793	+	23.0004i	0.797874	+	1.38196i	−0.123124	+	0.992391i	$0.539291\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.0993	+	12.1817i	−1.25868	+	0.726699i	−0.972818	−	0.231572i	$-0.925613\pi$
$281$	−21.0993	+	12.1817i	−1.25868	+	0.726699i	−0.285862	+	0.958271i	$0.592280\pi$
$282$		0			0
$283$	−7.49302	−	4.32610i	−0.445414	−	0.257160i	0.260478	−	0.965480i	$-0.416120\pi$
$283$	−7.49302	−	4.32610i	−0.445414	−	0.257160i	−0.705891	+	0.708320i	$0.749453\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.82082	−	3.88195i	0.579704	−	0.229144i
$288$		0			0
$289$	0.179961			0.0105860
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.40023	+	7.62143i	−0.257064	+	0.445249i	−0.965454	−	0.260573i	$-0.916089\pi$
$293$	−4.40023	+	7.62143i	−0.257064	+	0.445249i	0.708390	+	0.705821i	$0.249422\pi$
$294$		0			0
$295$	5.12782	+	8.88164i	0.298553	+	0.517109i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.07667	−	1.86484i	−0.0622652	−	0.107846i
$300$		0			0
$301$	2.54846	−	17.1912i	0.146891	−	0.990885i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	9.55155i		−	0.546920i
$306$		0			0
$307$			11.1747i			0.637771i	0.947793	+	0.318886i	$0.103309\pi$
$307$			11.1747i			0.637771i	−0.947793	+	0.318886i	$0.896691\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.20279	−	14.2076i	0.465137	−	0.805641i	−0.534070	−	0.845440i	$-0.679338\pi$
$311$	8.20279	−	14.2076i	0.465137	−	0.805641i	0.999208	+	0.0397985i	$0.0126716\pi$
$312$		0			0
$313$	−7.10514	+	4.10216i	−0.401606	+	0.231868i	−0.687177	−	0.726490i	$-0.741150\pi$
$313$	−7.10514	+	4.10216i	−0.401606	+	0.231868i	0.285570	+	0.958358i	$0.407817\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−19.8427	+	11.4562i	−1.11448	+	0.643443i	−0.939985	−	0.341215i	$-0.889161\pi$
$317$	−19.8427	+	11.4562i	−1.11448	+	0.643443i	−0.174491	+	0.984659i	$0.555828\pi$
$318$		0			0
$319$	−0.366926	+	0.635534i	−0.0205439	+	0.0355831i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			26.2618i			1.46125i
$324$		0			0
$325$			12.0420i			0.667972i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.36271	−	22.6839i	0.185392	−	1.25060i
$330$		0			0
$331$	9.63161	+	16.6824i	0.529401	+	0.916950i	0.999412	+	0.0342892i	$0.0109167\pi$
$331$	9.63161	+	16.6824i	0.529401	+	0.916950i	−0.470011	+	0.882661i	$0.655750\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.88361	+	3.26250i	0.102912	+	0.178249i
$336$		0			0
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	−0.921170	−	0.389161i	$-0.872765\pi$
$337$	−2.26829	+	3.92878i	−0.123561	+	0.214015i	0.797608	+	0.603176i	$0.206098\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.0204255			−0.00110610
$342$		0			0
$343$	−7.91381	+	16.7443i	−0.427306	+	0.904107i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.56294	+	4.36646i	0.406000	+	0.234404i	0.689070	−	0.724695i	$-0.258019\pi$
$347$	7.56294	+	4.36646i	0.406000	+	0.234404i	−0.283070	+	0.959099i	$0.591353\pi$
$348$		0			0
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	−0.275597	−	0.961273i	$-0.588876\pi$
$349$	7.82927	−	4.52023i	0.419091	−	0.241963i	0.694689	+	0.719311i	$0.255542\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.607896	−	1.05291i	−0.0323550	−	0.0560406i	0.849394	−	0.527758i	$-0.176967\pi$
$353$	−0.607896	−	1.05291i	−0.0323550	−	0.0560406i	−0.881750	+	0.471718i	$0.843634\pi$
$354$		0			0
$355$	1.00598	+	0.580805i	0.0533920	+	0.0308259i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	17.3069i		−	0.913424i	−0.889615	−	0.456712i	$-0.849027\pi$
$359$		−	17.3069i		−	0.913424i	0.889615	−	0.456712i	$-0.150973\pi$
$360$		0			0
$361$	−21.1445			−1.11287
$362$		0			0
$363$		0			0
$364$		0			0
$365$	36.8968	+	21.3024i	1.93127	+	1.11502i
$366$		0			0
$367$	24.4297	−	14.1045i	1.27522	−	0.736250i	0.299256	−	0.954173i	$-0.403262\pi$
$367$	24.4297	−	14.1045i	1.27522	−	0.736250i	0.975966	+	0.217923i	$0.0699282\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.27973	+	5.39344i	−0.222193	+	0.280014i
$372$		0			0
$373$	−14.1264	+	24.4676i	−0.731435	+	1.26688i	0.224835	+	0.974397i	$0.427816\pi$
$373$	−14.1264	+	24.4676i	−0.731435	+	1.26688i	−0.956270	+	0.292486i	$0.905518\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	18.3347			0.944287
$378$		0			0
$379$	−14.6447			−0.752250			−0.376125	−	0.926569i	$-0.622744\pi$
$379$	−14.6447			−0.752250			−0.376125	+	0.926569i	$0.622744\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.3932	−	21.4657i	0.633264	−	1.09684i	−0.353617	−	0.935390i	$-0.615048\pi$
$383$	12.3932	−	21.4657i	0.633264	−	1.09684i	0.986880	−	0.161454i	$-0.0516184\pi$
$384$		0			0
$385$	−0.736567	+	0.928244i	−0.0375390	+	0.0473077i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.43706	+	2.56174i	−0.224968	+	0.129885i	−0.608248	−	0.793747i	$-0.708128\pi$
$389$	−4.43706	+	2.56174i	−0.224968	+	0.129885i	0.383281	+	0.923632i	$0.374794\pi$
$390$		0			0
$391$	−1.96035	−	1.13181i	−0.0991391	−	0.0572380i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−12.2811			−0.617930
$396$		0			0
$397$			1.92094i			0.0964093i	0.998837	+	0.0482046i	$0.0153500\pi$
$397$			1.92094i			0.0964093i	−0.998837	+	0.0482046i	$0.984650\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.4612	+	7.19446i	0.622282	+	0.359274i	0.777757	−	0.628565i	$-0.216358\pi$
$401$	12.4612	+	7.19446i	0.622282	+	0.359274i	−0.155475	+	0.987840i	$0.549691\pi$
$402$		0			0
$403$	0.255158	+	0.441947i	0.0127103	+	0.0220150i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.336285	+	0.194154i	−0.0166690	+	0.00962386i
$408$		0			0
$409$	8.42281	+	4.86291i	0.416481	+	0.240455i	0.693571	−	0.720389i	$-0.256037\pi$
$409$	8.42281	+	4.86291i	0.416481	+	0.240455i	−0.277090	+	0.960844i	$0.589370\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.89158	−	3.51464i	0.437526	−	0.172944i
$414$		0			0
$415$	−18.3097			−0.898789
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−14.9512	+	25.8963i	−0.730416	+	1.26512i	0.226289	+	0.974060i	$0.427340\pi$
$419$	−14.9512	+	25.8963i	−0.730416	+	1.26512i	−0.956706	+	0.291058i	$0.905993\pi$
$420$		0			0
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	−0.991002	−	0.133848i	$-0.957266\pi$
$421$	−12.5452	−	21.7290i	−0.611417	−	1.05901i	0.379585	−	0.925157i	$-0.376067\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.32939	+	10.9628i	0.307021	+	0.531775i
$426$		0			0
$427$	−8.80835	−	1.30577i	−0.426266	−	0.0631905i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	6.39061i		−	0.307825i	−0.988084	−	0.153913i	$-0.950813\pi$
$431$		−	6.39061i		−	0.307825i	0.988084	−	0.153913i	$-0.0491874\pi$
$432$		0			0
$433$			33.1771i			1.59439i	0.603721	+	0.797196i	$0.293684\pi$
$433$			33.1771i			1.59439i	−0.603721	+	0.797196i	$0.706316\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.73012	−	2.99665i	0.0827627	−	0.143349i
$438$		0			0
$439$	−7.32931	+	4.23158i	−0.349809	+	0.201962i	−0.664601	−	0.747198i	$-0.731399\pi$
$439$	−7.32931	+	4.23158i	−0.349809	+	0.201962i	0.314792	+	0.949161i	$0.398065\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.1082	−	9.30006i	0.765322	−	0.441859i	−0.0658812	−	0.997827i	$-0.520986\pi$
$443$	16.1082	−	9.30006i	0.765322	−	0.441859i	0.831203	+	0.555969i	$0.187652\pi$
$444$		0			0
$445$	7.17111	−	12.4207i	0.339943	−	0.588799i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			20.3100i			0.958489i	0.877681	+	0.479245i	$0.159089\pi$
$449$			20.3100i			0.958489i	−0.877681	+	0.479245i	$0.840911\pi$
$450$		0			0
$451$		−	0.629906i		−	0.0296611i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	29.2857	+	4.34137i	1.37294	+	0.203527i
$456$		0			0
$457$	−5.67830	−	9.83511i	−0.265620	−	0.460067i	0.702106	−	0.712072i	$-0.252243\pi$
$457$	−5.67830	−	9.83511i	−0.265620	−	0.460067i	−0.967726	+	0.252005i	$0.918910\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	19.4984	+	33.7721i	0.908129	+	1.57293i	0.816661	+	0.577117i	$0.195822\pi$
$461$	19.4984	+	33.7721i	0.908129	+	1.57293i	0.0914676	+	0.995808i	$0.470844\pi$
$462$		0			0
$463$	5.03443	−	8.71990i	0.233970	−	0.405248i	−0.725003	−	0.688746i	$-0.758162\pi$
$463$	5.03443	−	8.71990i	0.233970	−	0.405248i	0.958973	+	0.283498i	$0.0914949\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.59330			0.166278			0.0831389	−	0.996538i	$-0.473505\pi$
$467$	3.59330			0.166278			0.0831389	+	0.996538i	$0.473505\pi$
$468$		0			0
$469$	3.26615	−	1.29103i	0.150817	−	0.0596145i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.897761	−	0.518322i	−0.0412791	−	0.0238325i
$474$		0			0
$475$	−16.7581	+	9.67530i	−0.768915	+	0.443933i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.811090	+	1.40485i	0.0370597	+	0.0641892i	0.883960	−	0.467562i	$-0.154868\pi$
$479$	0.811090	+	1.40485i	0.0370597	+	0.0641892i	−0.846901	+	0.531751i	$0.821534\pi$
$480$		0			0
$481$	8.40183	+	4.85080i	0.383090	+	0.221177i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	7.15869i		−	0.325060i
$486$		0			0
$487$	−7.99573			−0.362321			−0.181161	−	0.983454i	$-0.557985\pi$
$487$	−7.99573			−0.362321			−0.181161	+	0.983454i	$0.557985\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	9.30632	+	5.37300i	0.419988	+	0.242480i	0.695072	−	0.718940i	$-0.255372\pi$
$491$	9.30632	+	5.37300i	0.419988	+	0.242480i	−0.275084	+	0.961420i	$0.588706\pi$
$492$		0			0
$493$	16.6916	−	9.63688i	0.751751	−	0.434023i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.673138	−	0.848308i	0.0301944	−	0.0380518i
$498$		0			0
$499$	8.46050	−	14.6540i	0.378744	−	0.656004i	−0.612136	−	0.790753i	$-0.709689\pi$
$499$	8.46050	−	14.6540i	0.378744	−	0.656004i	0.990880	+	0.134749i	$0.0430227\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	33.9226			1.51253			0.756267	−	0.654263i	$-0.227021\pi$
$503$	33.9226			1.51253			0.756267	+	0.654263i	$0.227021\pi$
$504$		0			0
$505$	8.48968			0.377786
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.06805	−	8.77812i	0.224637	−	0.389083i	−0.731573	−	0.681763i	$-0.761214\pi$
$509$	5.06805	−	8.77812i	0.224637	−	0.389083i	0.956211	+	0.292680i	$0.0945469\pi$
$510$		0			0
$511$	24.6889	−	31.1137i	1.09217	−	1.37639i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−32.4341	+	18.7259i	−1.42922	+	0.825160i
$516$		0			0
$517$	−1.18460	−	0.683930i	−0.0520987	−	0.0300792i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−31.6986			−1.38874			−0.694370	−	0.719618i	$-0.744317\pi$
$521$	−31.6986			−1.38874			−0.694370	+	0.719618i	$0.744317\pi$
$522$		0			0
$523$		−	8.09911i		−	0.354149i	−0.984197	−	0.177075i	$-0.943337\pi$
$523$		−	8.09911i		−	0.354149i	0.984197	−	0.177075i	$-0.0566634\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.464582	+	0.268227i	0.0202375	+	0.0116841i
$528$		0			0
$529$	−11.3509	−	19.6603i	−0.493516	−	0.854795i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−13.6293	+	7.86887i	−0.590350	+	0.340839i
$534$		0			0
$535$	48.0628	+	27.7490i	2.07793	+	1.19970i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.755323	+	0.806153i	0.0325341	+	0.0347235i
$540$		0			0
$541$	1.21634			0.0522944			0.0261472	−	0.999658i	$-0.491676\pi$
$541$	1.21634			0.0522944			0.0261472	+	0.999658i	$0.491676\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−18.7994	+	32.5614i	−0.805276	+	1.39478i
$546$		0			0
$547$	−13.1278	−	22.7380i	−0.561305	−	0.972209i	−0.997383	−	0.0722999i	$-0.976966\pi$
$547$	−13.1278	−	22.7380i	−0.561305	−	0.972209i	0.436078	−	0.899909i	$-0.356367\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	14.7312	+	25.5152i	0.627571	+	1.08699i
$552$		0			0
$553$	−1.67892	+	11.3255i	−0.0713950	+	0.481611i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	27.2172i		−	1.15323i	−0.817016	−	0.576615i	$-0.804373\pi$
$557$		−	27.2172i		−	1.15323i	0.817016	−	0.576615i	$-0.195627\pi$
$558$		0			0
$559$			25.8998i			1.09545i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.68017	+	8.10630i	−0.197246	+	0.341640i	−0.947634	−	0.319357i	$-0.896533\pi$
$563$	−4.68017	+	8.10630i	−0.197246	+	0.341640i	0.750389	+	0.660997i	$0.229866\pi$
$564$		0			0
$565$	−24.7660	+	14.2987i	−1.04191	+	0.601549i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	30.2424	−	17.4605i	1.26783	−	0.731980i	0.293251	−	0.956036i	$-0.405263\pi$
$569$	30.2424	−	17.4605i	1.26783	−	0.731980i	0.974576	+	0.224055i	$0.0719296\pi$
$570$		0			0
$571$	−0.735987	+	1.27477i	−0.0308001	+	0.0533473i	−0.881015	−	0.473089i	$-0.843139\pi$
$571$	−0.735987	+	1.27477i	−0.0308001	+	0.0533473i	0.850214	+	0.526436i	$0.176472\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	1.66791i		−	0.0695567i
$576$		0			0
$577$		−	18.6196i		−	0.775146i	−0.921839	−	0.387573i	$-0.873314\pi$
$577$		−	18.6196i		−	0.775146i	0.921839	−	0.387573i	$-0.126686\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.50307	+	16.8851i	−0.103845	+	0.700510i
$582$		0			0
$583$	0.205346	+	0.355670i	0.00850458	+	0.0147304i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.28551	+	16.0830i	0.383254	+	0.663816i	0.991525	−	0.129914i	$-0.0414700\pi$
$587$	9.28551	+	16.0830i	0.383254	+	0.663816i	−0.608271	+	0.793729i	$0.708137\pi$
$588$		0			0
$589$	−0.410019	+	0.710174i	−0.0168945	+	0.0292622i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	30.9228			1.26985			0.634924	−	0.772574i	$-0.281031\pi$
$593$	30.9228			1.26985			0.634924	+	0.772574i	$0.281031\pi$
$594$		0			0
$595$	28.9430	−	11.4405i	1.18655	−	0.469015i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	11.8741	+	6.85553i	0.485164	+	0.280109i	0.722566	−	0.691302i	$-0.242963\pi$
$599$	11.8741	+	6.85553i	0.485164	+	0.280109i	−0.237402	+	0.971411i	$0.576296\pi$
$600$		0			0
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	−0.806523	−	0.591203i	$-0.798653\pi$
$601$	−17.1065	+	9.87644i	−0.697788	+	0.402868i	0.108735	+	0.994071i	$0.465320\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−15.5735	−	26.9741i	−0.633153	−	1.09665i
$606$		0			0
$607$	15.5219	+	8.96157i	0.630014	+	0.363739i	0.780757	−	0.624834i	$-0.214833\pi$
$607$	15.5219	+	8.96157i	0.630014	+	0.363739i	−0.150744	+	0.988573i	$0.548167\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			34.1750i			1.38257i
$612$		0			0
$613$	−41.4327			−1.67345			−0.836725	−	0.547623i	$-0.815533\pi$
$613$	−41.4327			−1.67345			−0.836725	+	0.547623i	$0.815533\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−19.9686	−	11.5289i	−0.803904	−	0.464134i	0.0409302	−	0.999162i	$-0.486968\pi$
$617$	−19.9686	−	11.5289i	−0.803904	−	0.464134i	−0.844835	+	0.535028i	$0.820301\pi$
$618$		0			0
$619$	−1.67850	+	0.969082i	−0.0674646	+	0.0389507i	−0.533353	−	0.845893i	$-0.679068\pi$
$619$	−1.67850	+	0.969082i	−0.0674646	+	0.0389507i	0.465888	+	0.884844i	$0.345735\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−10.4739	−	8.31113i	−0.419629	−	0.332978i
$624$		0			0
$625$	15.4715	−	26.7974i	0.618860	−	1.07190i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	10.1985			0.406640
$630$		0			0
$631$	−23.5831			−0.938827			−0.469414	−	0.882978i	$-0.655535\pi$
$631$	−23.5831			−0.938827			−0.469414	+	0.882978i	$0.655535\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−17.7227	+	30.6966i	−0.703303	+	1.21816i
$636$		0			0
$637$	8.00715	−	26.4135i	0.317255	−	1.04654i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.5093	+	12.4184i	−0.849568	+	0.490498i	−0.860505	−	0.509442i	$-0.829852\pi$
$641$	−21.5093	+	12.4184i	−0.849568	+	0.490498i	0.0109373	+	0.999940i	$0.496518\pi$
$642$		0			0
$643$	−37.9247	−	21.8959i	−1.49561	−	0.863489i	−0.495619	−	0.868540i	$-0.665059\pi$
$643$	−37.9247	−	21.8959i	−1.49561	−	0.863489i	−0.999987	+	0.00505169i	$0.998392\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	29.3713			1.15471			0.577353	−	0.816494i	$-0.304086\pi$
$647$	29.3713			1.15471			0.577353	+	0.816494i	$0.304086\pi$
$648$		0			0
$649$		−	0.570305i		−	0.0223864i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	28.0816	+	16.2129i	1.09892	+	0.634461i	0.935937	−	0.352168i	$-0.114556\pi$
$653$	28.0816	+	16.2129i	1.09892	+	0.634461i	0.162981	+	0.986629i	$0.447889\pi$
$654$		0			0
$655$	−14.2537	−	24.6881i	−0.556938	−	0.964645i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.203016	+	0.117211i	−0.00790837	+	0.00456590i	−0.503949	−	0.863733i	$-0.668120\pi$
$659$	−0.203016	+	0.117211i	−0.00790837	+	0.00456590i	0.496041	+	0.868299i	$0.334787\pi$
$660$		0			0
$661$	−3.05138	−	1.76171i	−0.118685	−	0.0685227i	0.439482	−	0.898251i	$-0.355162\pi$
$661$	−3.05138	−	1.76171i	−0.118685	−	0.0685227i	−0.558167	+	0.829728i	$0.688495\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	17.4883	+	44.2431i	0.678167	+	1.71567i
$666$		0			0
$667$	−2.53950			−0.0983296
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.265576	+	0.459990i	−0.0102524	+	0.0177577i
$672$		0			0
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	0.986829	−	0.161770i	$-0.0517202\pi$
$673$	9.16585	+	15.8757i	0.353318	+	0.611964i	−0.633511	+	0.773734i	$0.718387\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.9260	+	29.3166i	0.650517	+	1.12673i	0.982998	+	0.183619i	$0.0587812\pi$
$677$	16.9260	+	29.3166i	0.650517	+	1.12673i	−0.332480	+	0.943110i	$0.607885\pi$
$678$		0			0
$679$	−6.60168	−	0.978646i	−0.253349	−	0.0375570i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	28.0284i		−	1.07248i	−0.844066	−	0.536239i	$-0.819844\pi$
$683$		−	28.0284i		−	1.07248i	0.844066	−	0.536239i	$-0.180156\pi$
$684$		0			0
$685$			22.8214i			0.871962i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	5.13043	−	8.88616i	0.195454	−	0.338536i
$690$		0			0
$691$	−42.7393	+	24.6756i	−1.62588	+	0.938703i	−0.640577	+	0.767894i	$0.721305\pi$
$691$	−42.7393	+	24.6756i	−1.62588	+	0.938703i	−0.985304	+	0.170809i	$0.945362\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	46.4583	−	26.8227i	1.76226	−	1.01744i
$696$		0			0
$697$	−8.27188	+	14.3273i	−0.313320	+	0.542686i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	26.3889i		−	0.996696i	−0.866977	−	0.498348i	$-0.833940\pi$
$701$		−	26.3889i		−	0.996696i	0.866977	−	0.498348i	$-0.166060\pi$
$702$		0			0
$703$			15.5897i			0.587976i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.16060	−	7.82911i	0.0436489	−	0.294444i
$708$		0			0
$709$	5.35661	+	9.27792i	0.201172	+	0.348440i	0.948906	−	0.315558i	$-0.102192\pi$
$709$	5.35661	+	9.27792i	0.201172	+	0.348440i	−0.747735	+	0.663998i	$0.768858\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.0353413	−	0.0612130i	−0.00132354	−	0.00229244i
$714$		0			0
$715$	0.882977	−	1.52936i	0.0330215	−	0.0571949i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17.5794			−0.655601			−0.327801	−	0.944747i	$-0.606307\pi$
$719$	−17.5794			−0.655601			−0.327801	+	0.944747i	$0.606307\pi$
$720$		0			0
$721$	12.8348	+	32.4704i	0.477994	+	1.20926i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	12.2989	+	7.10079i	0.456771	+	0.263717i
$726$		0			0
$727$	−43.4695	+	25.0971i	−1.61220	+	0.930802i	−0.623336	+	0.781954i	$0.714223\pi$
$727$	−43.4695	+	25.0971i	−1.61220	+	0.930802i	−0.988860	+	0.148847i	$0.952444\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	13.6132	+	23.5787i	0.503501	+	0.872089i
$732$		0			0
$733$	34.5617	+	19.9542i	1.27656	+	0.737025i	0.976215	−	0.216804i	$-0.0695633\pi$
$733$	34.5617	+	19.9542i	1.27656	+	0.737025i	0.300350	+	0.953829i	$0.402897\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	0.209490i		−	0.00771668i
$738$		0			0
$739$	−30.3432			−1.11619			−0.558096	−	0.829777i	$-0.688468\pi$
$739$	−30.3432			−1.11619			−0.558096	+	0.829777i	$0.688468\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−39.5861	−	22.8550i	−1.45227	−	0.838470i	−0.453662	−	0.891174i	$-0.649883\pi$
$743$	−39.5861	−	22.8550i	−1.45227	−	0.838470i	−0.998610	+	0.0527041i	$0.983216\pi$
$744$		0			0
$745$	47.6959	−	27.5372i	1.74744	−	1.00889i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	32.1604	−	40.5295i	1.17512	−	1.48092i
$750$		0			0
$751$	6.07753	−	10.5266i	0.221772	−	0.384121i	−0.733574	−	0.679610i	$-0.762149\pi$
$751$	6.07753	−	10.5266i	0.221772	−	0.384121i	0.955346	+	0.295489i	$0.0954826\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.07411			0.184666
$756$		0			0
$757$	−9.71614			−0.353139			−0.176570	−	0.984288i	$-0.556500\pi$
$757$	−9.71614			−0.353139			−0.176570	+	0.984288i	$0.556500\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	19.4175	−	33.6320i	0.703882	−	1.21916i	−0.263211	−	0.964738i	$-0.584782\pi$
$761$	19.4175	−	33.6320i	0.703882	−	1.21916i	0.967093	−	0.254422i	$-0.0818851\pi$
$762$		0			0
$763$	27.4578	+	21.7880i	0.994040	+	0.788777i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.3397	+	7.12432i	−0.445560	+	0.257244i
$768$		0			0
$769$	−9.42879	−	5.44371i	−0.340011	−	0.196305i	0.320266	−	0.947328i	$-0.396228\pi$
$769$	−9.42879	−	5.44371i	−0.340011	−	0.196305i	−0.660277	+	0.751022i	$0.729561\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	37.3337			1.34280			0.671400	−	0.741096i	$-0.265693\pi$
$773$	37.3337			1.34280			0.671400	+	0.741096i	$0.265693\pi$
$774$		0			0
$775$			0.395277i			0.0141988i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−21.9012	−	12.6446i	−0.784691	−	0.453041i
$780$		0			0
$781$	−0.0322979	−	0.0559416i	−0.00115571	−	0.00200175i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−10.7915	+	6.23049i	−0.385166	+	0.222376i
$786$		0			0
$787$	15.4554	+	8.92315i	0.550924	+	0.318076i	0.749495	−	0.662011i	$-0.230297\pi$
$787$	15.4554	+	8.92315i	0.550924	+	0.318076i	−0.198571	+	0.980087i	$0.563630\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	9.80039	+	24.7937i	0.348462	+	0.881562i
$792$		0			0
$793$	13.2704			0.471246
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.74854	+	9.95676i	−0.203624	+	0.352687i	−0.949693	−	0.313181i	$-0.898605\pi$
$797$	−5.74854	+	9.95676i	−0.203624	+	0.352687i	0.746070	+	0.665868i	$0.231939\pi$
$798$		0			0
$799$	17.9626	+	31.1122i	0.635473	+	1.10067i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.18460	−	2.05179i	−0.0418037	−	0.0724061i
$804$		0			0
$805$	−4.05629	−	0.601312i	−0.142965	−	0.0211935i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			13.1945i			0.463893i	0.972729	+	0.231946i	$0.0745094\pi$
$809$			13.1945i			0.463893i	−0.972729	+	0.231946i	$0.925491\pi$
$810$		0			0
$811$			46.5800i			1.63565i	0.575469	+	0.817823i	$0.304819\pi$
$811$			46.5800i			1.63565i	−0.575469	+	0.817823i	$0.695181\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	7.71304	−	13.3594i	0.270176	−	0.467958i
$816$		0			0
$817$	−36.0431	+	20.8095i	−1.26099	+	0.728031i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−34.3623	+	19.8391i	−1.19925	+	0.692390i	−0.960389	−	0.278663i	$-0.910109\pi$
$821$	−34.3623	+	19.8391i	−1.19925	+	0.692390i	−0.238865	+	0.971053i	$0.576775\pi$
$822$		0			0
$823$	−19.6156	+	33.9751i	−0.683755	+	1.18430i	0.290071	+	0.957005i	$0.406321\pi$
$823$	−19.6156	+	33.9751i	−0.683755	+	1.18430i	−0.973826	+	0.227294i	$0.927012\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	21.0827i		−	0.733118i	−0.930395	−	0.366559i	$-0.880536\pi$
$827$		−	21.0827i		−	0.733118i	0.930395	−	0.366559i	$-0.119464\pi$
$828$		0			0
$829$			13.3261i			0.462834i	0.972855	+	0.231417i	$0.0743361\pi$
$829$			13.3261i			0.462834i	−0.972855	+	0.231417i	$0.925664\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−6.59361	−	28.2550i	−0.228455	−	0.978976i
$834$		0			0
$835$	−14.9071	−	25.8198i	−0.515881	−	0.893533i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.39768	+	14.5452i	0.289920	+	0.502156i	0.973790	−	0.227447i	$-0.0730379\pi$
$839$	8.39768	+	14.5452i	0.289920	+	0.502156i	−0.683870	+	0.729604i	$0.739705\pi$
$840$		0			0
$841$	−3.68862	+	6.38888i	−0.127194	+	0.220306i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−7.22744			−0.248632
$846$		0			0
$847$	−27.0043	+	10.6742i	−0.927878	+	0.366769i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.16372	−	0.671871i	−0.0398916	−	0.0230315i
$852$		0			0
$853$	−35.5011	+	20.4966i	−1.21554	+	0.701790i	−0.963960	−	0.266048i	$-0.914282\pi$
$853$	−35.5011	+	20.4966i	−1.21554	+	0.701790i	−0.251576	+	0.967838i	$0.580949\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−20.8718	−	36.1510i	−0.712967	−	1.23489i	−0.963739	−	0.266848i	$-0.914018\pi$
$857$	−20.8718	−	36.1510i	−0.712967	−	1.23489i	0.250772	−	0.968046i	$-0.419316\pi$
$858$		0			0
$859$	−24.0479	−	13.8841i	−0.820505	−	0.473719i	0.0300858	−	0.999547i	$-0.490422\pi$
$859$	−24.0479	−	13.8841i	−0.820505	−	0.473719i	−0.850590	+	0.525829i	$0.823755\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			45.6090i			1.55255i	0.630396	+	0.776274i	$0.282893\pi$
$863$			45.6090i			1.55255i	−0.630396	+	0.776274i	$0.717107\pi$
$864$		0			0
$865$	49.8319			1.69434
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.591443	+	0.341470i	0.0200633	+	0.0115836i
$870$		0			0
$871$	−4.53275	+	2.61698i	−0.153586	+	0.0886731i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.4455	−	9.08206i	−0.386927	−	0.307030i
$876$		0			0
$877$	−8.84368	+	15.3177i	−0.298630	+	0.517242i	−0.975823	−	0.218564i	$-0.929863\pi$
$877$	−8.84368	+	15.3177i	−0.298630	+	0.517242i	0.677193	+	0.735805i	$0.263196\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	11.6169			0.391384			0.195692	−	0.980665i	$-0.437305\pi$
$881$	11.6169			0.391384			0.195692	+	0.980665i	$0.437305\pi$
$882$		0			0
$883$	35.5480			1.19629			0.598143	−	0.801389i	$-0.295905\pi$
$883$	35.5480			1.19629			0.598143	+	0.801389i	$0.295905\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.2751	−	21.2610i	0.412156	−	0.713876i	−0.582969	−	0.812494i	$-0.698109\pi$
$887$	12.2751	−	21.2610i	0.412156	−	0.713876i	0.995125	+	0.0986188i	$0.0314424\pi$
$888$		0			0
$889$	25.8853	+	20.5401i	0.868165	+	0.688894i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−47.5590	+	27.4582i	−1.59150	+	0.918854i
$894$		0			0
$895$	44.7392	+	25.8302i	1.49547	+	0.863408i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.601834			0.0200723
$900$		0			0
$901$		−	10.7864i		−	0.359346i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−16.2257	−	9.36790i	−0.539360	−	0.311399i
$906$		0			0
$907$	18.4502	+	31.9567i	0.612628	+	1.06110i	0.990796	+	0.135366i	$0.0432211\pi$
$907$	18.4502	+	31.9567i	0.612628	+	1.06110i	−0.378167	+	0.925737i	$0.623446\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−34.4774	+	19.9056i	−1.14229	+	0.659500i	−0.946996	−	0.321245i	$-0.895899\pi$
$911$	−34.4774	+	19.9056i	−1.14229	+	0.659500i	−0.195292	+	0.980745i	$0.562565\pi$
$912$		0			0
$913$	0.881773	+	0.509092i	0.0291824	+	0.0168485i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.7157	+	9.76957i	−0.816186	+	0.322620i
$918$		0			0
$919$	56.8725			1.87605			0.938026	−	0.346565i	$-0.112652\pi$
$919$	56.8725			1.87605			0.938026	+	0.346565i	$0.112652\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.806939	+	1.39766i	−0.0265607	+	0.0460045i
$924$		0			0
$925$	3.75729	+	6.50783i	0.123539	+	0.213976i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	22.8885	+	39.6440i	0.750946	+	1.30068i	0.947365	+	0.320156i	$0.103735\pi$
$929$	22.8885	+	39.6440i	0.750946	+	1.30068i	−0.196419	+	0.980520i	$0.562931\pi$
$930$		0			0
$931$	43.1913	−	10.0792i	1.41554	−	0.330332i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	1.85640i		−	0.0607108i
$936$		0			0
$937$		−	24.0003i		−	0.784054i	−0.919954	−	0.392027i	$-0.871774\pi$
$937$		−	24.0003i		−	0.784054i	0.919954	−	0.392027i	$-0.128226\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.64316	+	2.84603i	−0.0535654	+	0.0927780i	−0.891565	−	0.452893i	$-0.850392\pi$
$941$	−1.64316	+	2.84603i	−0.0535654	+	0.0927780i	0.837999	+	0.545671i	$0.183725\pi$
$942$		0			0
$943$	1.88776	−	1.08990i	0.0614738	−	0.0354919i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−25.9420	+	14.9776i	−0.843002	+	0.486707i	−0.858284	−	0.513176i	$-0.828469\pi$
$947$	−25.9420	+	14.9776i	−0.843002	+	0.486707i	0.0152815	+	0.999883i	$0.495136\pi$
$948$		0			0
$949$	−29.5964	+	51.2624i	−0.960739	+	1.66405i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	16.0580i		−	0.520169i	−0.965586	−	0.260084i	$-0.916250\pi$
$953$		−	16.0580i		−	0.520169i	0.965586	−	0.260084i	$-0.0837504\pi$
$954$		0			0
$955$		−	40.3279i		−	1.30498i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	21.0457	+	3.11986i	0.679601	+	0.100745i
$960$		0			0
$961$	−15.4916	−	26.8323i	−0.499730	−	0.865557i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	14.1959	+	24.5881i	0.456983	+	0.791518i
$966$		0			0
$967$	−25.0275	+	43.3489i	−0.804831	+	1.39401i	0.111574	+	0.993756i	$0.464411\pi$
$967$	−25.0275	+	43.3489i	−0.804831	+	1.39401i	−0.916405	+	0.400252i	$0.868923\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.04188			−0.0334354			−0.0167177	−	0.999860i	$-0.505322\pi$
$971$	−1.04188			−0.0334354			−0.0167177	+	0.999860i	$0.505322\pi$
$972$		0			0
$973$	−18.3844	−	46.5102i	−0.589378	−	1.49105i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−21.1765	−	12.2262i	−0.677495	−	0.391152i	0.121416	−	0.992602i	$-0.461257\pi$
$977$	−21.1765	−	12.2262i	−0.677495	−	0.391152i	−0.798910	+	0.601450i	$0.794590\pi$
$978$		0			0
$979$	−0.690703	+	0.398777i	−0.0220750	+	0.0127450i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−28.0788	−	48.6339i	−0.895575	−	1.55118i	−0.833092	−	0.553135i	$-0.813431\pi$
$983$	−28.0788	−	48.6339i	−0.895575	−	1.55118i	−0.0624829	−	0.998046i	$-0.519902\pi$
$984$		0			0
$985$	49.4050	+	28.5240i	1.57417	+	0.908850i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	3.58731i		−	0.114070i
$990$		0			0
$991$	−18.2278			−0.579025			−0.289513	−	0.957174i	$-0.593493\pi$
$991$	−18.2278			−0.579025			−0.289513	+	0.957174i	$0.593493\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	31.7979	+	18.3586i	1.00806	+	0.582005i
$996$		0			0
$997$	−29.8197	+	17.2164i	−0.944399	+	0.545249i	−0.891337	−	0.453342i	$-0.850232\pi$
$997$	−29.8197	+	17.2164i	−0.944399	+	0.545249i	−0.0530623	+	0.998591i	$0.516898\pi$
$998$		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.881.1		12
3.2	odd	2		1008.2.cc.a.545.4		12
4.3	odd	2		189.2.o.a.125.1		12
7.6	odd	2	inner	3024.2.cc.a.881.6		12
9.2	odd	6	inner	3024.2.cc.a.2897.6		12
9.7	even	3		1008.2.cc.a.209.3		12
12.11	even	2		63.2.o.a.41.5	yes	12
21.20	even	2		1008.2.cc.a.545.3		12
28.3	even	6		1323.2.i.c.1097.2		12
28.11	odd	6		1323.2.i.c.1097.1		12
28.19	even	6		1323.2.s.c.962.5		12
28.23	odd	6		1323.2.s.c.962.6		12
28.27	even	2		189.2.o.a.125.2		12
36.7	odd	6		63.2.o.a.20.6	yes	12
36.11	even	6		189.2.o.a.62.2		12
36.23	even	6		567.2.c.c.566.9		12
36.31	odd	6		567.2.c.c.566.4		12
63.20	even	6	inner	3024.2.cc.a.2897.1		12
63.34	odd	6		1008.2.cc.a.209.4		12
84.11	even	6		441.2.i.c.68.6		12
84.23	even	6		441.2.s.c.374.1		12
84.47	odd	6		441.2.s.c.374.2		12
84.59	odd	6		441.2.i.c.68.5		12
84.83	odd	2		63.2.o.a.41.6	yes	12
252.11	even	6		1323.2.s.c.656.5		12
252.47	odd	6		1323.2.i.c.521.5		12
252.79	odd	6		441.2.i.c.227.1		12
252.83	odd	6		189.2.o.a.62.1		12
252.115	even	6		441.2.s.c.362.1		12
252.139	even	6		567.2.c.c.566.3		12
252.151	odd	6		441.2.s.c.362.2		12
252.167	odd	6		567.2.c.c.566.10		12
252.187	even	6		441.2.i.c.227.2		12
252.191	even	6		1323.2.i.c.521.6		12
252.223	even	6		63.2.o.a.20.5	✓	12
252.227	odd	6		1323.2.s.c.656.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	252.223	even	6
63.2.o.a.20.6	yes	12	36.7	odd	6
63.2.o.a.41.5	yes	12	12.11	even	2
63.2.o.a.41.6	yes	12	84.83	odd	2
189.2.o.a.62.1		12	252.83	odd	6
189.2.o.a.62.2		12	36.11	even	6
189.2.o.a.125.1		12	4.3	odd	2
189.2.o.a.125.2		12	28.27	even	2
441.2.i.c.68.5		12	84.59	odd	6
441.2.i.c.68.6		12	84.11	even	6
441.2.i.c.227.1		12	252.79	odd	6
441.2.i.c.227.2		12	252.187	even	6
441.2.s.c.362.1		12	252.115	even	6
441.2.s.c.362.2		12	252.151	odd	6
441.2.s.c.374.1		12	84.23	even	6
441.2.s.c.374.2		12	84.47	odd	6
567.2.c.c.566.3		12	252.139	even	6
567.2.c.c.566.4		12	36.31	odd	6
567.2.c.c.566.9		12	36.23	even	6
567.2.c.c.566.10		12	252.167	odd	6
1008.2.cc.a.209.3		12	9.7	even	3
1008.2.cc.a.209.4		12	63.34	odd	6
1008.2.cc.a.545.3		12	21.20	even	2
1008.2.cc.a.545.4		12	3.2	odd	2
1323.2.i.c.521.5		12	252.47	odd	6
1323.2.i.c.521.6		12	252.191	even	6
1323.2.i.c.1097.1		12	28.11	odd	6
1323.2.i.c.1097.2		12	28.3	even	6
1323.2.s.c.656.5		12	252.11	even	6
1323.2.s.c.656.6		12	252.227	odd	6
1323.2.s.c.962.5		12	28.19	even	6
1323.2.s.c.962.6		12	28.23	odd	6
3024.2.cc.a.881.1		12	1.1	even	1	trivial
3024.2.cc.a.881.6		12	7.6	odd	2	inner
3024.2.cc.a.2897.1		12	63.20	even	6	inner
3024.2.cc.a.2897.6		12	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.41899 + 2.45776i) q^{5} +(2.07253 + 1.64457i) q^{7} +O(q^{10})\)	\(q+(-1.41899 + 2.45776i) q^{5} +(2.07253 + 1.64457i) q^{7} +(0.136673 - 0.0789082i) q^{11} +(-3.41468 - 1.97146i) q^{13} -4.14487 q^{17} -6.33597i q^{19} +(0.472958 + 0.273062i) q^{23} +(-1.52704 - 2.64491i) q^{25} +(-4.02704 + 2.32501i) q^{29} +(-0.112086 - 0.0647129i) q^{31} +(-6.98284 + 2.76016i) q^{35} -2.46050 q^{37} +(1.99569 - 3.45664i) q^{41} +(-3.28434 - 5.68864i) q^{43} +(-4.33370 - 7.50619i) q^{47} +(1.59079 + 6.81685i) q^{49} +2.60234i q^{53} +0.447879i q^{55} +(1.80686 - 3.12957i) q^{59} +(-2.91472 + 1.68281i) q^{61} +(9.69076 - 5.59496i) q^{65} +(0.663715 - 1.14959i) q^{67} -0.409310i q^{71} -15.0124i q^{73} +(0.413030 + 0.0612283i) q^{77} +(2.16372 + 3.74766i) q^{79} +(3.22585 + 5.58733i) q^{83} +(5.88151 - 10.1871i) q^{85} -5.05368 q^{89} +(-3.83482 - 9.70160i) q^{91} +(15.5723 + 8.99066i) q^{95} +(-2.18452 + 1.26123i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 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