LMFDB - Embedded newform 3024.2.cc.a.2897.6

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			2897.6
Root			$-1.82904 + 1.05600i$ of defining polynomial
Character	$\chi$	$=$	3024.2897
Dual form			3024.2.cc.a.881.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41899 + 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +O(q^{10})$	$q+(1.41899 + 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +(0.136673 + 0.0789082i) q^{11} +(3.41468 - 1.97146i) q^{13} +4.14487 q^{17} -6.33597i q^{19} +(0.472958 - 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +(-4.02704 - 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(6.98284 - 2.76016i) q^{35} -2.46050 q^{37} +(-1.99569 - 3.45664i) q^{41} +(-3.28434 + 5.68864i) q^{43} +(4.33370 - 7.50619i) q^{47} +(-6.69896 - 2.03076i) q^{49} -2.60234i q^{53} +0.447879i q^{55} +(-1.80686 - 3.12957i) q^{59} +(2.91472 + 1.68281i) q^{61} +(9.69076 + 5.59496i) q^{65} +(0.663715 + 1.14959i) q^{67} +0.409310i q^{71} -15.0124i q^{73} +(0.259540 - 0.327080i) q^{77} +(2.16372 - 3.74766i) q^{79} +(-3.22585 + 5.58733i) q^{83} +(5.88151 + 10.1871i) q^{85} +5.05368 q^{89} +(-3.83482 - 9.70160i) q^{91} +(15.5723 - 8.99066i) q^{95} +(2.18452 + 1.26123i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

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

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
$5$	1.41899	+	2.45776i	0.634590	+	1.09914i	0.986602	+	0.163146i	$0.0521643\pi$
$5$	1.41899	+	2.45776i	0.634590	+	1.09914i	−0.352012	+	0.935995i	$0.614502\pi$
$6$		0			0
$7$	0.387972	−	2.61715i	0.146640	−	0.989190i
$7$	0.387972	−	2.61715i	0.146640	−	0.989190i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.136673	+	0.0789082i	0.0412085	+	0.0237917i	0.520463	−	0.853884i	$-0.325759\pi$
$11$	0.136673	+	0.0789082i	0.0412085	+	0.0237917i	−0.479254	+	0.877676i	$0.659093\pi$
$12$		0			0
$13$	3.41468	−	1.97146i	0.947061	−	0.546786i	0.0548943	−	0.998492i	$-0.482518\pi$
$13$	3.41468	−	1.97146i	0.947061	−	0.546786i	0.892167	+	0.451706i	$0.149184\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.14487			1.00528			0.502640	−	0.864496i	$-0.332362\pi$
$17$	4.14487			1.00528			0.502640	+	0.864496i	$0.332362\pi$
$18$		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	−0.449880	−	0.893089i	$-0.648533\pi$
$23$	0.472958	−	0.273062i	0.0986185	−	0.0569374i	0.548498	+	0.836152i	$0.315200\pi$
$24$		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	0.0770966	−	0.997024i	$-0.475435\pi$
$29$	−4.02704	−	2.32501i	−0.747803	−	0.431744i	−0.824900	+	0.565279i	$0.808768\pi$
$30$		0			0
$31$	0.112086	−	0.0647129i	0.0201313	−	0.0116228i	−0.489901	−	0.871778i	$-0.662967\pi$
$31$	0.112086	−	0.0647129i	0.0201313	−	0.0116228i	0.510032	+	0.860156i	$0.329634\pi$
$32$		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	$-0.267557\pi$
$41$	−1.99569	−	3.45664i	−0.311675	−	0.539836i	−0.978725	+	0.205176i	$0.934223\pi$
$42$		0			0
$43$	−3.28434	+	5.68864i	−0.500857	+	0.867509i	0.499143	+	0.866520i	$0.333648\pi$
$43$	−3.28434	+	5.68864i	−0.500857	+	0.867509i	−1.00000		0.000989450i	$0.999685\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.33370	−	7.50619i	0.632135	−	1.09489i	−0.354979	−	0.934874i	$-0.615512\pi$
$47$	4.33370	−	7.50619i	0.632135	−	1.09489i	0.987114	−	0.160016i	$-0.0511547\pi$
$48$		0			0
$49$	−6.69896	−	2.03076i	−0.956994	−	0.290109i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	2.60234i		−	0.357459i	−0.983898	−	0.178730i	$-0.942801\pi$
$53$		−	2.60234i		−	0.357459i	0.983898	−	0.178730i	$-0.0571988\pi$
$54$		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	$-0.242252\pi$
$59$	−1.80686	−	3.12957i	−0.235233	−	0.407436i	−0.959340	+	0.282252i	$0.908919\pi$
$60$		0			0
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	0.674852	−	0.737953i	$-0.264208\pi$
$61$	2.91472	+	1.68281i	0.373191	+	0.215462i	−0.301660	+	0.953415i	$0.597541\pi$
$62$		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	0.903717	−	0.428131i	$-0.140828\pi$
$67$	0.663715	+	1.14959i	0.0810857	+	0.140445i	−0.822631	+	0.568576i	$0.807495\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.409310i			0.0485761i	0.999705	+	0.0242881i	$0.00773189\pi$
$71$			0.409310i			0.0485761i	−0.999705	+	0.0242881i	$0.992268\pi$
$72$		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
$77$	0.259540	−	0.327080i	0.0295773	−	0.0372742i
$78$		0			0
$79$	2.16372	−	3.74766i	0.243437	−	0.421645i	−0.718254	−	0.695781i	$-0.755058\pi$
$79$	2.16372	−	3.74766i	0.243437	−	0.421645i	0.961691	+	0.274136i	$0.0883918\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.22585	+	5.58733i	−0.354083	+	0.613289i	−0.986961	−	0.160963i	$-0.948540\pi$
$83$	−3.22585	+	5.58733i	−0.354083	+	0.613289i	0.632878	+	0.774252i	$0.281874\pi$
$84$		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	$-0.413689\pi$
$89$	5.05368			0.535689			0.267845	+	0.963462i	$0.413689\pi$
$90$		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	$-0.292459\pi$
$97$	2.18452	+	1.26123i	0.221805	+	0.128059i	−0.384981	+	0.922925i	$0.625792\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.49573	−	2.59068i	0.148831	−	0.257782i	−0.781965	−	0.623323i	$-0.785782\pi$
$101$	1.49573	−	2.59068i	0.148831	−	0.257782i	0.930796	+	0.365540i	$0.119116\pi$
$102$		0			0
$103$	−11.4286	+	6.59832i	−1.12610	+	0.650152i	−0.942950	−	0.332934i	$-0.891962\pi$
$103$	−11.4286	+	6.59832i	−1.12610	+	0.650152i	−0.183146	+	0.983086i	$0.558628\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			19.5555i			1.89051i	0.326339	+	0.945253i	$0.394185\pi$
$107$			19.5555i			1.89051i	−0.326339	+	0.945253i	$0.605815\pi$
$108$		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	−0.0298041	−	0.999556i	$-0.509488\pi$
$113$	8.72665	−	5.03834i	0.820935	−	0.473967i	0.850739	+	0.525589i	$0.176155\pi$
$114$		0			0
$115$	1.34224	+	0.774943i	0.125165	+	0.0722638i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.60809	−	10.8478i	0.147414	−	0.994412i
$120$		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	$-0.0220642\pi$
$131$	5.02249	+	8.69921i	0.438817	+	0.760054i	−0.558781	+	0.829315i	$0.688731\pi$
$132$		0			0
$133$	−16.5822	−	2.45818i	−1.43786	−	0.213151i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.96410	+	4.02073i	0.594984	+	0.343514i	0.767066	−	0.641569i	$-0.221716\pi$
$137$	6.96410	+	4.02073i	0.594984	+	0.343514i	−0.172082	+	0.985083i	$0.555049\pi$
$138$		0			0
$139$	16.3702	−	9.45136i	1.38850	−	0.801654i	0.395358	−	0.918527i	$-0.370621\pi$
$139$	16.3702	−	9.45136i	1.38850	−	0.801654i	0.993147	+	0.116873i	$0.0372872\pi$
$140$		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	−0.991776	−	0.127984i	$-0.959149\pi$
$149$	−16.8063	+	9.70313i	−1.37683	+	0.794912i	−0.385051	+	0.922895i	$0.625816\pi$
$150$		0			0
$151$	−0.893968	+	1.54840i	−0.0727501	+	0.126007i	−0.900106	−	0.435672i	$-0.856511\pi$
$151$	−0.893968	+	1.54840i	−0.0727501	+	0.126007i	0.827356	+	0.561678i	$0.189844\pi$
$152$		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	$-0.722728\pi$
$157$	−3.80255	+	2.19540i	−0.303477	+	0.175212i	0.340527	+	0.940235i	$0.389395\pi$
$158$		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	$-0.0334268\pi$
$167$	5.25273	+	9.09799i	0.406468	+	0.704024i	−0.588023	+	0.808844i	$0.700093\pi$
$168$		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	−0.311111	−	0.950374i	$-0.600701\pi$
$173$	8.77949	−	15.2065i	0.667492	−	1.15613i	0.978603	−	0.205757i	$-0.0659656\pi$
$174$		0			0
$175$	6.32969	+	5.02265i	0.478480	+	0.379677i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			18.2033i			1.36058i	0.732945	+	0.680288i	$0.238145\pi$
$179$			18.2033i			1.36058i	−0.732945	+	0.680288i	$0.761855\pi$
$180$		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	−0.0163630	−	0.999866i	$-0.505209\pi$
$191$	−12.3063	−	7.10506i	−0.890454	−	0.514104i	−0.874091	+	0.485762i	$0.838542\pi$
$192$		0			0
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	0.987971	−	0.154642i	$-0.0494223\pi$
$193$	5.00214	+	8.66395i	0.360062	+	0.623645i	−0.627909	+	0.778287i	$0.716089\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			20.1017i			1.43218i	0.698006	+	0.716092i	$0.254071\pi$
$197$			20.1017i			1.43218i	−0.698006	+	0.716092i	$0.745929\pi$
$198$		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
$203$	−7.64729	+	9.63734i	−0.536735	+	0.676408i
$204$		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	0.978425	−	0.206604i	$-0.0662411\pi$
$211$	4.50720	+	7.80669i	0.310288	+	0.537435i	−0.668136	+	0.744039i	$0.732908\pi$
$212$		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	$-0.357407\pi$
$223$	−1.95429	−	1.12831i	−0.130869	−	0.0755571i	−0.564005	+	0.825771i	$0.690740\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.32085	−	16.1442i	0.618647	−	1.07153i	−0.371086	−	0.928598i	$-0.621015\pi$
$227$	9.32085	−	16.1442i	0.618647	−	1.07153i	0.989733	−	0.142929i	$-0.0456522\pi$
$228$		0			0
$229$	12.3891	−	7.15283i	0.818692	−	0.472672i	−0.0312731	−	0.999511i	$-0.509956\pi$
$229$	12.3891	−	7.15283i	0.818692	−	0.472672i	0.849965	+	0.526839i	$0.176623\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			17.0679i			1.11815i	0.829116	+	0.559077i	$0.188844\pi$
$233$			17.0679i			1.11815i	−0.829116	+	0.559077i	$0.811156\pi$
$234$		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	−0.436090	−	0.899903i	$-0.643637\pi$
$239$	1.93560	−	1.11752i	0.125203	−	0.0722863i	0.561294	+	0.827617i	$0.310304\pi$
$240$		0			0
$241$	3.91464	+	2.26012i	0.252164	+	0.145587i	0.620755	−	0.784005i	$-0.286826\pi$
$241$	3.91464	+	2.26012i	0.252164	+	0.145587i	−0.368591	+	0.929592i	$0.620160\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.51461	−	19.3460i	−0.288428	−	1.23597i
$246$		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	$-0.267063\pi$
$251$	21.1727			1.33641			0.668205	+	0.743978i	$0.267063\pi$
$252$		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	0.675796	+	0.737089i	$0.263800\pi$
$257$	15.6502	+	27.1070i	0.976236	+	1.69089i	0.300440	+	0.953801i	$0.402866\pi$
$258$		0			0
$259$	−0.954606	+	6.43951i	−0.0593163	+	0.400132i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−5.78220	−	3.33836i	−0.356546	−	0.205852i	0.311019	−	0.950404i	$-0.399330\pi$
$263$	−5.78220	−	3.33836i	−0.356546	−	0.205852i	−0.667564	+	0.744552i	$0.732663\pi$
$264$		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	$-0.605345\pi$
$269$	−10.6589			−0.649887			−0.324944	+	0.945733i	$0.605345\pi$
$270$		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	−0.123124	−	0.992391i	$-0.539291\pi$
$277$	13.2793	−	23.0004i	0.797874	−	1.38196i	0.920998	−	0.389568i	$-0.127376\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.0993	−	12.1817i	−1.25868	−	0.726699i	−0.285862	−	0.958271i	$-0.592280\pi$
$281$	−21.0993	−	12.1817i	−1.25868	−	0.726699i	−0.972818	+	0.231572i	$0.925613\pi$
$282$		0			0
$283$	7.49302	−	4.32610i	0.445414	−	0.257160i	−0.260478	−	0.965480i	$-0.583880\pi$
$283$	7.49302	−	4.32610i	0.445414	−	0.257160i	0.705891	+	0.708320i	$0.250547\pi$
$284$		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	$-0.0839114\pi$
$293$	4.40023	+	7.62143i	0.257064	+	0.445249i	−0.708390	+	0.705821i	$0.750578\pi$
$294$		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
$301$	13.6138	+	10.8026i	0.784686	+	0.622654i
$302$		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	$-0.320662\pi$
$311$	−8.20279	−	14.2076i	−0.465137	−	0.805641i	−0.999208	+	0.0397985i	$0.987328\pi$
$312$		0			0
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	0.687177	−	0.726490i	$-0.258850\pi$
$313$	7.10514	+	4.10216i	0.401606	+	0.231868i	−0.285570	+	0.958358i	$0.592183\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−19.8427	−	11.4562i	−1.11448	−	0.643443i	−0.174491	−	0.984659i	$-0.555828\pi$
$317$	−19.8427	−	11.4562i	−1.11448	−	0.643443i	−0.939985	+	0.341215i	$0.889161\pi$
$318$		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
$329$	−17.9635	−	14.2541i	−0.990359	−	0.785856i
$330$		0			0
$331$	9.63161	−	16.6824i	0.529401	−	0.916950i	−0.470011	−	0.882661i	$-0.655750\pi$
$331$	9.63161	−	16.6824i	0.529401	−	0.916950i	0.999412	−	0.0342892i	$-0.0109167\pi$
$332$		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	0.797608	−	0.603176i	$-0.206098\pi$
$337$	−2.26829	−	3.92878i	−0.123561	−	0.214015i	−0.921170	+	0.389161i	$0.872765\pi$
$338$		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	−0.283070	−	0.959099i	$-0.591353\pi$
$347$	7.56294	−	4.36646i	0.406000	−	0.234404i	0.689070	+	0.724695i	$0.258019\pi$
$348$		0			0
$349$	−7.82927	−	4.52023i	−0.419091	−	0.241963i	0.275597	−	0.961273i	$-0.411124\pi$
$349$	−7.82927	−	4.52023i	−0.419091	−	0.241963i	−0.694689	+	0.719311i	$0.744458\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.607896	−	1.05291i	0.0323550	−	0.0560406i	−0.849394	−	0.527758i	$-0.823033\pi$
$353$	0.607896	−	1.05291i	0.0323550	−	0.0560406i	0.881750	+	0.471718i	$0.156366\pi$
$354$		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	$0.150973\pi$
$359$			17.3069i			0.913424i	−0.889615	+	0.456712i	$0.849027\pi$
$360$		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	$-0.596738\pi$
$367$	−24.4297	−	14.1045i	−1.27522	−	0.736250i	−0.975966	+	0.217923i	$0.930072\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.81073	−	1.00964i	−0.353595	−	0.0524177i
$372$		0			0
$373$	−14.1264	−	24.4676i	−0.731435	−	1.26688i	−0.956270	−	0.292486i	$-0.905518\pi$
$373$	−14.1264	−	24.4676i	−0.731435	−	1.26688i	0.224835	−	0.974397i	$-0.427816\pi$
$374$		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	−0.986880	−	0.161454i	$-0.948382\pi$
$383$	−12.3932	−	21.4657i	−0.633264	−	1.09684i	0.353617	−	0.935390i	$-0.384952\pi$
$384$		0			0
$385$	1.17217	+	0.173764i	0.0597391	+	0.00885585i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.43706	−	2.56174i	−0.224968	−	0.129885i	0.383281	−	0.923632i	$-0.374794\pi$
$389$	−4.43706	−	2.56174i	−0.224968	−	0.129885i	−0.608248	+	0.793747i	$0.708128\pi$
$390$		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	−0.155475	−	0.987840i	$-0.549691\pi$
$401$	12.4612	−	7.19446i	0.622282	−	0.359274i	0.777757	+	0.628565i	$0.216358\pi$
$402$		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	$-0.743963\pi$
$409$	−8.42281	+	4.86291i	−0.416481	+	0.240455i	0.277090	+	0.960844i	$0.410630\pi$
$410$		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	0.956706	+	0.291058i	$0.0940072\pi$
$419$	14.9512	+	25.8963i	0.730416	+	1.26512i	−0.226289	+	0.974060i	$0.572660\pi$
$420$		0			0
$421$	−12.5452	+	21.7290i	−0.611417	+	1.05901i	0.379585	+	0.925157i	$0.376067\pi$
$421$	−12.5452	+	21.7290i	−0.611417	+	1.05901i	−0.991002	+	0.133848i	$0.957266\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.32939	+	10.9628i	−0.307021	+	0.531775i
$426$		0			0
$427$	5.53500	−	6.97537i	0.267857	−	0.337562i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			6.39061i			0.307825i	0.988084	+	0.153913i	$0.0491874\pi$
$431$			6.39061i			0.307825i	−0.988084	+	0.153913i	$0.950813\pi$
$432$		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	$-0.268601\pi$
$439$	7.32931	+	4.23158i	0.349809	+	0.201962i	−0.314792	+	0.949161i	$0.601935\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.1082	+	9.30006i	0.765322	+	0.441859i	0.831203	−	0.555969i	$-0.187652\pi$
$443$	16.1082	+	9.30006i	0.765322	+	0.441859i	−0.0658812	+	0.997827i	$0.520986\pi$
$444$		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	$-0.840911\pi$
$449$		−	20.3100i		−	0.958489i	0.877681	−	0.479245i	$-0.159089\pi$
$450$		0			0
$451$		−	0.629906i		−	0.0296611i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	18.4026	−	23.1915i	0.862727	−	1.08723i
$456$		0			0
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	−0.967726	−	0.252005i	$-0.918910\pi$
$457$	−5.67830	+	9.83511i	−0.265620	+	0.460067i	0.702106	+	0.712072i	$0.252243\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−19.4984	+	33.7721i	−0.908129	+	1.57293i	−0.0914676	+	0.995808i	$0.529156\pi$
$461$	−19.4984	+	33.7721i	−0.908129	+	1.57293i	−0.816661	+	0.577117i	$0.804178\pi$
$462$		0			0
$463$	5.03443	+	8.71990i	0.233970	+	0.405248i	0.958973	−	0.283498i	$-0.0914949\pi$
$463$	5.03443	+	8.71990i	0.233970	+	0.405248i	−0.725003	+	0.688746i	$0.758162\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.59330			−0.166278			−0.0831389	−	0.996538i	$-0.526495\pi$
$467$	−3.59330			−0.166278			−0.0831389	+	0.996538i	$0.526495\pi$
$468$		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	$-0.845132\pi$
$479$	−0.811090	+	1.40485i	−0.0370597	+	0.0641892i	0.846901	+	0.531751i	$0.178466\pi$
$480$		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	−0.275084	−	0.961420i	$-0.588706\pi$
$491$	9.30632	−	5.37300i	0.419988	−	0.242480i	0.695072	+	0.718940i	$0.255372\pi$
$492$		0			0
$493$	−16.6916	−	9.63688i	−0.751751	−	0.434023i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.07122	+	0.158801i	0.0480510	+	0.00712318i
$498$		0			0
$499$	8.46050	+	14.6540i	0.378744	+	0.656004i	0.990880	−	0.134749i	$-0.0430227\pi$
$499$	8.46050	+	14.6540i	0.378744	+	0.656004i	−0.612136	+	0.790753i	$0.709689\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−33.9226			−1.51253			−0.756267	−	0.654263i	$-0.772979\pi$
$503$	−33.9226			−1.51253			−0.756267	+	0.654263i	$0.772979\pi$
$504$		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	$-0.238786\pi$
$509$	−5.06805	−	8.77812i	−0.224637	−	0.389083i	−0.956211	+	0.292680i	$0.905453\pi$
$510$		0			0
$511$	−39.2897	−	5.82438i	−1.73807	−	0.257655i
$512$		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	$-0.255683\pi$
$521$	31.6986			1.38874			0.694370	+	0.719618i	$0.255683\pi$
$522$		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	0.436078	+	0.899909i	$0.356367\pi$
$547$	−13.1278	+	22.7380i	−0.561305	+	0.972209i	−0.997383	+	0.0722999i	$0.976966\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−14.7312	+	25.5152i	−0.627571	+	1.08699i
$552$		0			0
$553$	−8.96874	−	7.11676i	−0.381390	−	0.302635i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			27.2172i			1.15323i	0.817016	+	0.576615i	$0.195627\pi$
$557$			27.2172i			1.15323i	−0.817016	+	0.576615i	$0.804373\pi$
$558$		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	$-0.103467\pi$
$563$	4.68017	+	8.10630i	0.197246	+	0.341640i	−0.750389	+	0.660997i	$0.770134\pi$
$564$		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	0.974576	−	0.224055i	$-0.0719296\pi$
$569$	30.2424	+	17.4605i	1.26783	+	0.731980i	0.293251	+	0.956036i	$0.405263\pi$
$570$		0			0
$571$	−0.735987	−	1.27477i	−0.0308001	−	0.0533473i	0.850214	−	0.526436i	$-0.176472\pi$
$571$	−0.735987	−	1.27477i	−0.0308001	−	0.0533473i	−0.881015	+	0.473089i	$0.843139\pi$
$572$		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
$581$	13.3713	+	10.6103i	0.554737	+	0.440187i
$582$		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	$-0.958530\pi$
$587$	−9.28551	+	16.0830i	−0.383254	+	0.663816i	0.608271	+	0.793729i	$0.291863\pi$
$588$		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	$-0.718969\pi$
$593$	−30.9228			−1.26985			−0.634924	+	0.772574i	$0.718969\pi$
$594$		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	−0.237402	−	0.971411i	$-0.576296\pi$
$599$	11.8741	−	6.85553i	0.485164	−	0.280109i	0.722566	+	0.691302i	$0.242963\pi$
$600$		0			0
$601$	17.1065	+	9.87644i	0.697788	+	0.402868i	0.806523	−	0.591203i	$-0.201347\pi$
$601$	17.1065	+	9.87644i	0.697788	+	0.402868i	−0.108735	+	0.994071i	$0.534680\pi$
$602$		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	$-0.785167\pi$
$607$	−15.5219	+	8.96157i	−0.630014	+	0.363739i	0.150744	+	0.988573i	$0.451833\pi$
$608$		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	−0.844835	−	0.535028i	$-0.820301\pi$
$617$	−19.9686	+	11.5289i	−0.803904	+	0.464134i	0.0409302	+	0.999162i	$0.486968\pi$
$618$		0			0
$619$	1.67850	+	0.969082i	0.0674646	+	0.0389507i	0.533353	−	0.845893i	$-0.320932\pi$
$619$	1.67850	+	0.969082i	0.0674646	+	0.0389507i	−0.465888	+	0.884844i	$0.654265\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.96069	−	13.2263i	0.0785532	−	0.529899i
$624$		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
$637$	−26.8783	+	6.27236i	−1.06496	+	0.248520i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−21.5093	−	12.4184i	−0.849568	−	0.490498i	0.0109373	−	0.999940i	$-0.496518\pi$
$641$	−21.5093	−	12.4184i	−0.849568	−	0.490498i	−0.860505	+	0.509442i	$0.829852\pi$
$642$		0			0
$643$	37.9247	−	21.8959i	1.49561	−	0.863489i	0.495619	−	0.868540i	$-0.334941\pi$
$643$	37.9247	−	21.8959i	1.49561	−	0.863489i	0.999987	+	0.00505169i	$0.00160801\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−29.3713			−1.15471			−0.577353	−	0.816494i	$-0.695914\pi$
$647$	−29.3713			−1.15471			−0.577353	+	0.816494i	$0.695914\pi$
$648$		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	0.162981	−	0.986629i	$-0.447889\pi$
$653$	28.0816	−	16.2129i	1.09892	−	0.634461i	0.935937	+	0.352168i	$0.114556\pi$
$654$		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	0.496041	−	0.868299i	$-0.334787\pi$
$659$	−0.203016	−	0.117211i	−0.00790837	−	0.00456590i	−0.503949	+	0.863733i	$0.668120\pi$
$660$		0			0
$661$	3.05138	−	1.76171i	0.118685	−	0.0685227i	−0.439482	−	0.898251i	$-0.644838\pi$
$661$	3.05138	−	1.76171i	0.118685	−	0.0685227i	0.558167	+	0.829728i	$0.311505\pi$
$662$		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	−0.633511	−	0.773734i	$-0.718387\pi$
$673$	9.16585	−	15.8757i	0.353318	−	0.611964i	0.986829	+	0.161770i	$0.0517202\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.9260	+	29.3166i	−0.650517	+	1.12673i	0.332480	+	0.943110i	$0.392115\pi$
$677$	−16.9260	+	29.3166i	−0.650517	+	1.12673i	−0.982998	+	0.183619i	$0.941219\pi$
$678$		0			0
$679$	4.14837	−	5.22790i	0.159200	−	0.200628i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			28.0284i			1.07248i	0.844066	+	0.536239i	$0.180156\pi$
$683$			28.0284i			1.07248i	−0.844066	+	0.536239i	$0.819844\pi$
$684$		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	0.985304	+	0.170809i	$0.0546381\pi$
$691$	42.7393	+	24.6756i	1.62588	+	0.938703i	0.640577	+	0.767894i	$0.278695\pi$
$692$		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	$0.166060\pi$
$701$			26.3889i			0.996696i	−0.866977	+	0.498348i	$0.833940\pi$
$702$		0			0
$703$			15.5897i			0.587976i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.19990	−	4.91966i	−0.233171	−	0.185023i
$708$		0			0
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	−0.747735	−	0.663998i	$-0.768858\pi$
$709$	5.35661	−	9.27792i	0.201172	−	0.348440i	0.948906	+	0.315558i	$0.102192\pi$
$710$		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	$-0.393693\pi$
$719$	17.5794			0.655601			0.327801	+	0.944747i	$0.393693\pi$
$720$		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	0.988860	+	0.148847i	$0.0475563\pi$
$727$	43.4695	+	25.0971i	1.61220	+	0.930802i	0.623336	+	0.781954i	$0.285777\pi$
$728$		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	$-0.930437\pi$
$733$	−34.5617	+	19.9542i	−1.27656	+	0.737025i	−0.300350	+	0.953829i	$0.597103\pi$
$734$		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	−0.998610	−	0.0527041i	$-0.983216\pi$
$743$	−39.5861	+	22.8550i	−1.45227	+	0.838470i	−0.453662	+	0.891174i	$0.649883\pi$
$744$		0			0
$745$	−47.6959	−	27.5372i	−1.74744	−	1.00889i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	51.1798	+	7.58700i	1.87007	+	0.277223i
$750$		0			0
$751$	6.07753	+	10.5266i	0.221772	+	0.384121i	0.955346	−	0.295489i	$-0.0954826\pi$
$751$	6.07753	+	10.5266i	0.221772	+	0.384121i	−0.733574	+	0.679610i	$0.762149\pi$
$752$		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	−0.967093	−	0.254422i	$-0.918115\pi$
$761$	−19.4175	−	33.6320i	−0.703882	−	1.21916i	0.263211	−	0.964738i	$-0.415218\pi$
$762$		0			0
$763$	5.14002	−	34.6732i	0.186081	−	1.25525i
$764$		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	$-0.603772\pi$
$769$	9.42879	−	5.44371i	0.340011	−	0.196305i	0.660277	+	0.751022i	$0.270439\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−37.3337			−1.34280			−0.671400	−	0.741096i	$-0.734307\pi$
$773$	−37.3337			−1.34280			−0.671400	+	0.741096i	$0.734307\pi$
$774$		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	$-0.769703\pi$
$787$	−15.4554	+	8.92315i	−0.550924	+	0.318076i	0.198571	+	0.980087i	$0.436370\pi$
$788$		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	$-0.101395\pi$
$797$	5.74854	+	9.95676i	0.203624	+	0.352687i	−0.746070	+	0.665868i	$0.768061\pi$
$798$		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
$805$	2.54890	−	3.21219i	0.0898367	−	0.113215i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	13.1945i		−	0.463893i	−0.972729	−	0.231946i	$-0.925491\pi$
$809$		−	13.1945i		−	0.463893i	0.972729	−	0.231946i	$-0.0745094\pi$
$810$		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	−0.238865	−	0.971053i	$-0.576775\pi$
$821$	−34.3623	−	19.8391i	−1.19925	−	0.692390i	−0.960389	+	0.278663i	$0.910109\pi$
$822$		0			0
$823$	−19.6156	−	33.9751i	−0.683755	−	1.18430i	−0.973826	−	0.227294i	$-0.927012\pi$
$823$	−19.6156	−	33.9751i	−0.683755	−	1.18430i	0.290071	−	0.957005i	$-0.406321\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			21.0827i			0.733118i	0.930395	+	0.366559i	$0.119464\pi$
$827$			21.0827i			0.733118i	−0.930395	+	0.366559i	$0.880536\pi$
$828$		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
$833$	−27.7663	−	8.41724i	−0.962046	−	0.291640i
$834$		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	$-0.926962\pi$
$839$	−8.39768	+	14.5452i	−0.289920	+	0.502156i	0.683870	+	0.729604i	$0.260295\pi$
$840$		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	$-0.0857179\pi$
$853$	35.5011	+	20.4966i	1.21554	+	0.701790i	0.251576	+	0.967838i	$0.419051\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	20.8718	−	36.1510i	0.712967	−	1.23489i	−0.250772	−	0.968046i	$-0.580684\pi$
$857$	20.8718	−	36.1510i	0.712967	−	1.23489i	0.963739	−	0.266848i	$-0.0859822\pi$
$858$		0			0
$859$	24.0479	−	13.8841i	0.820505	−	0.473719i	−0.0300858	−	0.999547i	$-0.509578\pi$
$859$	24.0479	−	13.8841i	0.820505	−	0.473719i	0.850590	+	0.525829i	$0.176245\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	45.6090i		−	1.55255i	−0.630396	−	0.776274i	$-0.717107\pi$
$863$		−	45.6090i		−	1.55255i	0.630396	−	0.776274i	$-0.282893\pi$
$864$		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
$875$	2.14256	−	14.4531i	0.0724316	−	0.488604i
$876$		0			0
$877$	−8.84368	−	15.3177i	−0.298630	−	0.517242i	0.677193	−	0.735805i	$-0.263196\pi$
$877$	−8.84368	−	15.3177i	−0.298630	−	0.517242i	−0.975823	+	0.218564i	$0.929863\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−11.6169			−0.391384			−0.195692	−	0.980665i	$-0.562695\pi$
$881$	−11.6169			−0.391384			−0.195692	+	0.980665i	$0.562695\pi$
$882$		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	$-0.301891\pi$
$887$	−12.2751	−	21.2610i	−0.412156	−	0.713876i	−0.995125	+	0.0986188i	$0.968558\pi$
$888$		0			0
$889$	4.84564	−	32.6874i	0.162518	−	1.09630i
$890$		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	−0.378167	−	0.925737i	$-0.623446\pi$
$907$	18.4502	−	31.9567i	0.612628	−	1.06110i	0.990796	−	0.135366i	$-0.0432211\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−34.4774	−	19.9056i	−1.14229	−	0.659500i	−0.195292	−	0.980745i	$-0.562565\pi$
$911$	−34.4774	−	19.9056i	−1.14229	−	0.659500i	−0.946996	+	0.321245i	$0.895899\pi$
$912$		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	0.196419	+	0.980520i	$0.437069\pi$
$929$	−22.8885	+	39.6440i	−0.750946	+	1.30068i	−0.947365	+	0.320156i	$0.896265\pi$
$930$		0			0
$931$	−12.8668	+	42.4444i	−0.421694	+	1.39106i
$932$		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	$-0.149608\pi$
$941$	1.64316	+	2.84603i	0.0535654	+	0.0927780i	−0.837999	+	0.545671i	$0.816275\pi$
$942$		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	0.0152815	−	0.999883i	$-0.495136\pi$
$947$	−25.9420	−	14.9776i	−0.843002	−	0.486707i	−0.858284	+	0.513176i	$0.828469\pi$
$948$		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	$0.0837504\pi$
$953$			16.0580i			0.520169i	−0.965586	+	0.260084i	$0.916250\pi$
$954$		0			0
$955$		−	40.3279i		−	1.30498i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	13.2247	−	16.6662i	0.427049	−	0.538179i
$960$		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	−0.916405	−	0.400252i	$-0.868923\pi$
$967$	−25.0275	−	43.3489i	−0.804831	−	1.39401i	0.111574	−	0.993756i	$-0.464411\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.04188			0.0334354			0.0167177	−	0.999860i	$-0.494678\pi$
$971$	1.04188			0.0334354			0.0167177	+	0.999860i	$0.494678\pi$
$972$		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	−0.798910	−	0.601450i	$-0.794590\pi$
$977$	−21.1765	+	12.2262i	−0.677495	+	0.391152i	0.121416	+	0.992602i	$0.461257\pi$
$978$		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	0.0624829	−	0.998046i	$-0.480098\pi$
$983$	28.0788	−	48.6339i	0.895575	−	1.55118i	0.833092	−	0.553135i	$-0.186569\pi$
$984$		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	$-0.149768\pi$
$997$	29.8197	+	17.2164i	0.944399	+	0.545249i	0.0530623	+	0.998591i	$0.483102\pi$
$998$		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.2897.6		12
3.2	odd	2		1008.2.cc.a.209.3		12
4.3	odd	2		189.2.o.a.62.2		12
7.6	odd	2	inner	3024.2.cc.a.2897.1		12
9.4	even	3		1008.2.cc.a.545.4		12
9.5	odd	6	inner	3024.2.cc.a.881.1		12
12.11	even	2		63.2.o.a.20.6	yes	12
21.20	even	2		1008.2.cc.a.209.4		12
28.3	even	6		1323.2.s.c.656.6		12
28.11	odd	6		1323.2.s.c.656.5		12
28.19	even	6		1323.2.i.c.521.5		12
28.23	odd	6		1323.2.i.c.521.6		12
28.27	even	2		189.2.o.a.62.1		12
36.7	odd	6		567.2.c.c.566.9		12
36.11	even	6		567.2.c.c.566.4		12
36.23	even	6		189.2.o.a.125.1		12
36.31	odd	6		63.2.o.a.41.5	yes	12
63.13	odd	6		1008.2.cc.a.545.3		12
63.41	even	6	inner	3024.2.cc.a.881.6		12
84.11	even	6		441.2.s.c.362.2		12
84.23	even	6		441.2.i.c.227.1		12
84.47	odd	6		441.2.i.c.227.2		12
84.59	odd	6		441.2.s.c.362.1		12
84.83	odd	2		63.2.o.a.20.5	✓	12
252.23	even	6		1323.2.s.c.962.6		12
252.31	even	6		441.2.i.c.68.5		12
252.59	odd	6		1323.2.i.c.1097.2		12
252.67	odd	6		441.2.i.c.68.6		12
252.83	odd	6		567.2.c.c.566.3		12
252.95	even	6		1323.2.i.c.1097.1		12
252.103	even	6		441.2.s.c.374.2		12
252.131	odd	6		1323.2.s.c.962.5		12
252.139	even	6		63.2.o.a.41.6	yes	12
252.167	odd	6		189.2.o.a.125.2		12
252.223	even	6		567.2.c.c.566.10		12
252.247	odd	6		441.2.s.c.374.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.o.a.20.5	✓	12	84.83	odd	2
63.2.o.a.20.6	yes	12	12.11	even	2
63.2.o.a.41.5	yes	12	36.31	odd	6
63.2.o.a.41.6	yes	12	252.139	even	6
189.2.o.a.62.1		12	28.27	even	2
189.2.o.a.62.2		12	4.3	odd	2
189.2.o.a.125.1		12	36.23	even	6
189.2.o.a.125.2		12	252.167	odd	6
441.2.i.c.68.5		12	252.31	even	6
441.2.i.c.68.6		12	252.67	odd	6
441.2.i.c.227.1		12	84.23	even	6
441.2.i.c.227.2		12	84.47	odd	6
441.2.s.c.362.1		12	84.59	odd	6
441.2.s.c.362.2		12	84.11	even	6
441.2.s.c.374.1		12	252.247	odd	6
441.2.s.c.374.2		12	252.103	even	6
567.2.c.c.566.3		12	252.83	odd	6
567.2.c.c.566.4		12	36.11	even	6
567.2.c.c.566.9		12	36.7	odd	6
567.2.c.c.566.10		12	252.223	even	6
1008.2.cc.a.209.3		12	3.2	odd	2
1008.2.cc.a.209.4		12	21.20	even	2
1008.2.cc.a.545.3		12	63.13	odd	6
1008.2.cc.a.545.4		12	9.4	even	3
1323.2.i.c.521.5		12	28.19	even	6
1323.2.i.c.521.6		12	28.23	odd	6
1323.2.i.c.1097.1		12	252.95	even	6
1323.2.i.c.1097.2		12	252.59	odd	6
1323.2.s.c.656.5		12	28.11	odd	6
1323.2.s.c.656.6		12	28.3	even	6
1323.2.s.c.962.5		12	252.131	odd	6
1323.2.s.c.962.6		12	252.23	even	6
3024.2.cc.a.881.1		12	9.5	odd	6	inner
3024.2.cc.a.881.6		12	63.41	even	6	inner
3024.2.cc.a.2897.1		12	7.6	odd	2	inner
3024.2.cc.a.2897.6		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)

\(f(q)\)	\(=\)	\(q+(1.41899 + 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +O(q^{10})\)	\(q+(1.41899 + 2.45776i) q^{5} +(0.387972 - 2.61715i) q^{7} +(0.136673 + 0.0789082i) q^{11} +(3.41468 - 1.97146i) q^{13} +4.14487 q^{17} -6.33597i q^{19} +(0.472958 - 0.273062i) q^{23} +(-1.52704 + 2.64491i) q^{25} +(-4.02704 - 2.32501i) q^{29} +(0.112086 - 0.0647129i) q^{31} +(6.98284 - 2.76016i) q^{35} -2.46050 q^{37} +(-1.99569 - 3.45664i) q^{41} +(-3.28434 + 5.68864i) q^{43} +(4.33370 - 7.50619i) q^{47} +(-6.69896 - 2.03076i) q^{49} -2.60234i q^{53} +0.447879i q^{55} +(-1.80686 - 3.12957i) q^{59} +(2.91472 + 1.68281i) q^{61} +(9.69076 + 5.59496i) q^{65} +(0.663715 + 1.14959i) q^{67} +0.409310i q^{71} -15.0124i q^{73} +(0.259540 - 0.327080i) q^{77} +(2.16372 - 3.74766i) q^{79} +(-3.22585 + 5.58733i) q^{83} +(5.88151 + 10.1871i) q^{85} +5.05368 q^{89} +(-3.83482 - 9.70160i) q^{91} +(15.5723 - 8.99066i) q^{95} +(2.18452 + 1.26123i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{7}+O(q^{10}) \) 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