LMFDB - Embedded newform 3024.2.cc.c.881.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 $ x^16 - 3x^14 - 9x^12 - 9x^10 + 225x^8 - 81x^6 - 729x^4 - 2187*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.5
Root			$-0.604587 - 1.62311i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.c.2897.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.266780 - 0.462077i) q^{5} +(1.89325 - 1.84814i) q^{7} +O(q^{10})$	$q+(0.266780 - 0.462077i) q^{5} +(1.89325 - 1.84814i) q^{7} +(-3.39936 + 1.96262i) q^{11} +(0.116911 + 0.0674987i) q^{13} +4.32533 q^{17} -2.22935i q^{19} +(-1.70375 - 0.983658i) q^{23} +(2.35766 + 4.08358i) q^{25} +(5.16548 - 2.98229i) q^{29} +(-0.800341 - 0.462077i) q^{31} +(-0.348901 - 1.36787i) q^{35} +7.79871 q^{37} +(-4.59027 + 7.95059i) q^{41} +(-3.24544 - 5.62127i) q^{43} +(3.04329 + 5.27114i) q^{47} +(0.168767 - 6.99797i) q^{49} -11.0167i q^{53} +2.09435i q^{55} +(1.89588 - 3.28377i) q^{59} +(9.35116 - 5.39889i) q^{61} +(0.0623791 - 0.0360146i) q^{65} +(5.75701 - 9.97144i) q^{67} -3.22884i q^{71} +0.381041i q^{73} +(-2.80863 + 9.99820i) q^{77} +(4.60310 + 7.97280i) q^{79} +(1.28020 + 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +17.1334 q^{89} +(0.346088 - 0.0882763i) q^{91} +(-1.03013 - 0.594746i) q^{95} +(-13.6747 + 7.89507i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7}+O(q^{10}) $ 16 * q + q^7	$ 16 q + q^{7} + 6 q^{11} + 6 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} - 4 q^{43} - 5 q^{49} + 24 q^{65} - 14 q^{67} + 21 q^{77} - 20 q^{79} + 6 q^{85} + 18 q^{91} - 60 q^{95}+O(q^{100}) $ 16 * q + q^7 + 6 * q^11 + 6 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 - 4 * q^43 - 5 * q^49 + 24 * q^65 - 14 * q^67 + 21 * q^77 - 20 * q^79 + 6 * q^85 + 18 * q^91 - 60 * 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
$5$	0.266780	−	0.462077i	0.119308	−	0.206647i	−0.800186	−	0.599752i	$-0.795266\pi$
$5$	0.266780	−	0.462077i	0.119308	−	0.206647i	0.919494	+	0.393105i	$0.128599\pi$
$6$		0			0
$7$	1.89325	−	1.84814i	0.715580	−	0.698531i
$7$	1.89325	−	1.84814i	0.715580	−	0.698531i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.39936	+	1.96262i	−1.02494	+	0.591752i	−0.915532	−	0.402245i	$-0.868230\pi$
$11$	−3.39936	+	1.96262i	−1.02494	+	0.591752i	−0.109412	+	0.993996i	$0.534897\pi$
$12$		0			0
$13$	0.116911	+	0.0674987i	0.0324253	+	0.0187208i	0.516125	−	0.856513i	$-0.327374\pi$
$13$	0.116911	+	0.0674987i	0.0324253	+	0.0187208i	−0.483700	+	0.875234i	$0.660707\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.32533			1.04905			0.524523	−	0.851396i	$-0.324244\pi$
$17$	4.32533			1.04905			0.524523	+	0.851396i	$0.324244\pi$
$18$		0			0
$19$		−	2.22935i		−	0.511448i	−0.966750	−	0.255724i	$-0.917686\pi$
$19$		−	2.22935i		−	0.511448i	0.966750	−	0.255724i	$-0.0823138\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.70375	−	0.983658i	−0.355255	−	0.205107i	0.311742	−	0.950167i	$-0.399088\pi$
$23$	−1.70375	−	0.983658i	−0.355255	−	0.205107i	−0.666998	+	0.745060i	$0.732421\pi$
$24$		0			0
$25$	2.35766	+	4.08358i	0.471531	+	0.816716i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.16548	−	2.98229i	0.959205	−	0.553798i	0.0632771	−	0.997996i	$-0.479845\pi$
$29$	5.16548	−	2.98229i	0.959205	−	0.553798i	0.895928	+	0.444198i	$0.146511\pi$
$30$		0			0
$31$	−0.800341	−	0.462077i	−0.143745	−	0.0829915i	0.426402	−	0.904534i	$-0.359781\pi$
$31$	−0.800341	−	0.462077i	−0.143745	−	0.0829915i	−0.570148	+	0.821542i	$0.693114\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.348901	−	1.36787i	−0.0589751	−	0.231213i
$36$		0			0
$37$	7.79871			1.28210			0.641050	−	0.767499i	$-0.278499\pi$
$37$	7.79871			1.28210			0.641050	+	0.767499i	$0.278499\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.59027	+	7.95059i	−0.716880	+	1.24167i	0.245349	+	0.969435i	$0.421097\pi$
$41$	−4.59027	+	7.95059i	−0.716880	+	1.24167i	−0.962230	+	0.272239i	$0.912236\pi$
$42$		0			0
$43$	−3.24544	−	5.62127i	−0.494926	−	0.857236i	0.505057	−	0.863086i	$-0.331471\pi$
$43$	−3.24544	−	5.62127i	−0.494926	−	0.857236i	−0.999983	+	0.00584958i	$0.998138\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.04329	+	5.27114i	0.443910	+	0.768874i	0.997976	−	0.0635985i	$-0.0202577\pi$
$47$	3.04329	+	5.27114i	0.443910	+	0.768874i	−0.554066	+	0.832473i	$0.686924\pi$
$48$		0			0
$49$	0.168767	−	6.99797i	0.0241096	−	0.999709i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	11.0167i		−	1.51326i	−0.653845	−	0.756628i	$-0.726845\pi$
$53$		−	11.0167i		−	1.51326i	0.653845	−	0.756628i	$-0.273155\pi$
$54$		0			0
$55$			2.09435i			0.282402i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.89588	−	3.28377i	0.246823	−	0.427510i	−0.715820	−	0.698285i	$-0.753947\pi$
$59$	1.89588	−	3.28377i	0.246823	−	0.427510i	0.962643	+	0.270775i	$0.0872801\pi$
$60$		0			0
$61$	9.35116	−	5.39889i	1.19729	−	0.691258i	0.237342	−	0.971426i	$-0.423724\pi$
$61$	9.35116	−	5.39889i	1.19729	−	0.691258i	0.959951	+	0.280168i	$0.0903903\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.0623791	−	0.0360146i	0.00773718	−	0.00446706i
$66$		0			0
$67$	5.75701	−	9.97144i	0.703331	−	1.21820i	−0.263960	−	0.964534i	$-0.585029\pi$
$67$	5.75701	−	9.97144i	0.703331	−	1.21820i	0.967291	−	0.253671i	$-0.0816381\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.22884i		−	0.383192i	−0.981474	−	0.191596i	$-0.938634\pi$
$71$		−	3.22884i		−	0.383192i	0.981474	−	0.191596i	$-0.0613664\pi$
$72$		0			0
$73$			0.381041i			0.0445975i	0.999751	+	0.0222988i	$0.00709850\pi$
$73$			0.381041i			0.0445975i	−0.999751	+	0.0222988i	$0.992901\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.80863	+	9.99820i	−0.320073	+	1.13940i
$78$		0			0
$79$	4.60310	+	7.97280i	0.517889	+	0.897011i	0.999784	+	0.0207814i	$0.00661541\pi$
$79$	4.60310	+	7.97280i	0.517889	+	0.897011i	−0.481895	+	0.876229i	$0.660051\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.28020	+	2.21737i	0.140520	+	0.243388i	0.927693	−	0.373345i	$-0.121789\pi$
$83$	1.28020	+	2.21737i	0.140520	+	0.243388i	−0.787172	+	0.616733i	$0.788456\pi$
$84$		0			0
$85$	1.15391	−	1.99863i	0.125159	−	0.216782i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	17.1334			1.81614			0.908068	−	0.418822i	$-0.137557\pi$
$89$	17.1334			1.81614			0.908068	+	0.418822i	$0.137557\pi$
$90$		0			0
$91$	0.346088	−	0.0882763i	0.0362799	−	0.00925387i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.03013	−	0.594746i	−0.105689	−	0.0610197i
$96$		0			0
$97$	−13.6747	+	7.89507i	−1.38845	+	0.801622i	−0.993141	−	0.116925i	$-0.962696\pi$
$97$	−13.6747	+	7.89507i	−1.38845	+	0.801622i	−0.395310	+	0.918548i	$0.629363\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.36862	−	12.7628i	−0.733205	−	1.26995i	−0.955506	−	0.294970i	$-0.904690\pi$
$101$	−7.36862	−	12.7628i	−0.733205	−	1.26995i	0.222301	−	0.974978i	$-0.428643\pi$
$102$		0			0
$103$	−11.1442	−	6.43410i	−1.09807	−	0.633970i	−0.162356	−	0.986732i	$-0.551909\pi$
$103$	−11.1442	−	6.43410i	−1.09807	−	0.633970i	−0.935713	+	0.352762i	$0.885243\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	15.7824i		−	1.52574i	−0.646552	−	0.762870i	$-0.723790\pi$
$107$		−	15.7824i		−	1.52574i	0.646552	−	0.762870i	$-0.276210\pi$
$108$		0			0
$109$	−3.08340			−0.295336			−0.147668	−	0.989037i	$-0.547177\pi$
$109$	−3.08340			−0.295336			−0.147668	+	0.989037i	$0.547177\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.96173	−	4.59671i	−0.748977	−	0.432422i	0.0763472	−	0.997081i	$-0.475674\pi$
$113$	−7.96173	−	4.59671i	−0.748977	−	0.432422i	−0.825324	+	0.564659i	$0.809008\pi$
$114$		0			0
$115$	−0.909051	+	0.524841i	−0.0847694	+	0.0489417i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	8.18891	−	7.99380i	0.750676	−	0.732791i
$120$		0			0
$121$	2.20375	−	3.81700i	0.200340	−	0.347000i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	5.18371			0.463645
$126$		0			0
$127$	10.1065			0.896810			0.448405	−	0.893831i	$-0.351992\pi$
$127$	10.1065			0.896810			0.448405	+	0.893831i	$0.351992\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.81823	+	13.5416i	−0.683082	+	1.18313i	0.290954	+	0.956737i	$0.406027\pi$
$131$	−7.81823	+	13.5416i	−0.683082	+	1.18313i	−0.974036	+	0.226395i	$0.927306\pi$
$132$		0			0
$133$	−4.12015	−	4.22071i	−0.357262	−	0.365982i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.13891	+	1.23490i	−0.182739	+	0.105505i	−0.588579	−	0.808440i	$-0.700312\pi$
$137$	−2.13891	+	1.23490i	−0.182739	+	0.105505i	0.405840	+	0.913944i	$0.366979\pi$
$138$		0			0
$139$	16.8526	+	9.72984i	1.42942	+	0.825274i	0.997074	−	0.0764359i	$-0.0243540\pi$
$139$	16.8526	+	9.72984i	1.42942	+	0.825274i	0.432342	+	0.901710i	$0.357687\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.529897			−0.0443122
$144$		0			0
$145$		−	3.18247i		−	0.264289i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−13.7303	−	7.92720i	−1.12483	−	0.649422i	−0.182201	−	0.983261i	$-0.558322\pi$
$149$	−13.7303	−	7.92720i	−1.12483	−	0.649422i	−0.942630	+	0.333840i	$0.891656\pi$
$150$		0			0
$151$	4.16548	+	7.21482i	0.338982	+	0.587134i	0.984242	−	0.176829i	$-0.0565841\pi$
$151$	4.16548	+	7.21482i	0.338982	+	0.587134i	−0.645260	+	0.763963i	$0.723251\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.427030	+	0.246546i	−0.0342999	+	0.0198031i
$156$		0			0
$157$	7.73794	+	4.46750i	0.617555	+	0.356545i	0.775916	−	0.630836i	$-0.217288\pi$
$157$	7.73794	+	4.46750i	0.617555	+	0.356545i	−0.158362	+	0.987381i	$0.550621\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.04355	+	1.28645i	−0.397487	+	0.101386i
$162$		0			0
$163$	14.2062			1.11272			0.556358	−	0.830943i	$-0.312198\pi$
$163$	14.2062			1.11272			0.556358	+	0.830943i	$0.312198\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.27308	−	10.8653i	0.485425	−	0.840781i	−0.514434	−	0.857530i	$-0.671998\pi$
$167$	6.27308	−	10.8653i	0.485425	−	0.840781i	0.999860	+	0.0167485i	$0.00533145\pi$
$168$		0			0
$169$	−6.49089	−	11.2425i	−0.499299	−	0.864811i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−10.6787	−	18.4960i	−0.811886	−	1.40623i	−0.911543	−	0.411206i	$-0.865108\pi$
$173$	−10.6787	−	18.4960i	−0.811886	−	1.40623i	0.0996566	−	0.995022i	$-0.468226\pi$
$174$		0			0
$175$	12.0106	+	3.37395i	0.907920	+	0.255047i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	5.81113i		−	0.434344i	−0.976133	−	0.217172i	$-0.930317\pi$
$179$		−	5.81113i		−	0.434344i	0.976133	−	0.217172i	$-0.0696833\pi$
$180$		0			0
$181$			7.38877i			0.549203i	0.961558	+	0.274602i	$0.0885460\pi$
$181$			7.38877i			0.549203i	−0.961558	+	0.274602i	$0.911454\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.08054	−	3.60360i	0.152964	−	0.264942i
$186$		0			0
$187$	−14.7033	+	8.48897i	−1.07521	+	0.620775i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.86109	−	3.96125i	0.496451	−	0.286626i	−0.230796	−	0.973002i	$-0.574133\pi$
$191$	6.86109	−	3.96125i	0.496451	−	0.286626i	0.727247	+	0.686376i	$0.240800\pi$
$192$		0			0
$193$	3.16548	−	5.48277i	0.227856	−	0.394659i	−0.729316	−	0.684177i	$-0.760162\pi$
$193$	3.16548	−	5.48277i	0.227856	−	0.394659i	0.957173	+	0.289518i	$0.0934951\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			15.1580i			1.07996i	0.841677	+	0.539981i	$0.181569\pi$
$197$			15.1580i			1.07996i	−0.841677	+	0.539981i	$0.818431\pi$
$198$		0			0
$199$			8.55084i			0.606153i	0.952966	+	0.303076i	$0.0980137\pi$
$199$			8.55084i			0.606153i	−0.952966	+	0.303076i	$0.901986\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.26784	−	15.1927i	0.299544	−	1.06632i
$204$		0			0
$205$	2.44919	+	4.24212i	0.171059	+	0.296282i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.37536	+	7.57835i	0.302650	+	0.524205i
$210$		0			0
$211$	2.80782	−	4.86329i	0.193299	−	0.334803i	−0.753043	−	0.657971i	$-0.771415\pi$
$211$	2.80782	−	4.86329i	0.193299	−	0.334803i	0.946341	+	0.323169i	$0.104748\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.46328			−0.236194
$216$		0			0
$217$	−2.36922	+	0.604315i	−0.160833	+	0.0410236i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.505679	+	0.291954i	0.0340156	+	0.0196389i
$222$		0			0
$223$	−6.00510	+	3.46705i	−0.402131	+	0.232171i	−0.687403	−	0.726276i	$-0.741249\pi$
$223$	−6.00510	+	3.46705i	−0.402131	+	0.232171i	0.285272	+	0.958447i	$0.407916\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.28833	−	12.6238i	−0.483743	−	0.837868i	0.516082	−	0.856539i	$-0.327390\pi$
$227$	−7.28833	−	12.6238i	−0.483743	−	0.837868i	−0.999826	+	0.0186708i	$0.994057\pi$
$228$		0			0
$229$	21.2722	+	12.2815i	1.40571	+	0.811586i	0.994971	−	0.100167i	$-0.0319377\pi$
$229$	21.2722	+	12.2815i	1.40571	+	0.811586i	0.410738	+	0.911753i	$0.365271\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	10.5142i		−	0.688808i	−0.938822	−	0.344404i	$-0.888081\pi$
$233$		−	10.5142i		−	0.688808i	0.938822	−	0.344404i	$-0.111919\pi$
$234$		0			0
$235$	3.24756			0.211848
$236$		0			0
$237$		0			0
$238$		0			0
$239$	16.9075	+	9.76154i	1.09365	+	0.631422i	0.934547	−	0.355839i	$-0.115805\pi$
$239$	16.9075	+	9.76154i	1.09365	+	0.631422i	0.159108	+	0.987261i	$0.449138\pi$
$240$		0			0
$241$	11.3780	−	6.56909i	0.732922	−	0.423152i	−0.0865685	−	0.996246i	$-0.527590\pi$
$241$	11.3780	−	6.56909i	0.732922	−	0.423152i	0.819490	+	0.573093i	$0.194257\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.18857	−	1.94490i	−0.203711	−	0.124255i
$246$		0			0
$247$	0.150478	−	0.260636i	0.00957469	−	0.0165838i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	22.6864			1.43195			0.715977	−	0.698124i	$-0.245981\pi$
$251$	22.6864			1.43195			0.715977	+	0.698124i	$0.245981\pi$
$252$		0			0
$253$	7.72218			0.485489
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.80481	−	11.7863i	0.424472	−	0.735207i	−0.571899	−	0.820324i	$-0.693793\pi$
$257$	6.80481	−	11.7863i	0.424472	−	0.735207i	0.996371	+	0.0851169i	$0.0271264\pi$
$258$		0			0
$259$	14.7649	−	14.4131i	0.917445	−	0.895586i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	19.7930	−	11.4275i	1.22049	−	0.704651i	0.255468	−	0.966817i	$-0.417770\pi$
$263$	19.7930	−	11.4275i	1.22049	−	0.704651i	0.965023	+	0.262167i	$0.0844371\pi$
$264$		0			0
$265$	−5.09055	−	2.93903i	−0.312710	−	0.180543i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	10.6775			0.651018			0.325509	−	0.945539i	$-0.394464\pi$
$269$	10.6775			0.651018			0.325509	+	0.945539i	$0.394464\pi$
$270$		0			0
$271$			4.51473i			0.274251i	0.990554	+	0.137125i	$0.0437863\pi$
$271$			4.51473i			0.274251i	−0.990554	+	0.137125i	$0.956214\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−16.0290	−	9.25436i	−0.966587	−	0.558059i
$276$		0			0
$277$	3.34952	+	5.80154i	0.201253	+	0.348581i	0.948932	−	0.315479i	$-0.102165\pi$
$277$	3.34952	+	5.80154i	0.201253	+	0.348581i	−0.747679	+	0.664060i	$0.768832\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.1414	−	8.74187i	0.903258	−	0.521496i	0.0250023	−	0.999687i	$-0.492041\pi$
$281$	15.1414	−	8.74187i	0.903258	−	0.521496i	0.878256	+	0.478191i	$0.158707\pi$
$282$		0			0
$283$	−7.42049	−	4.28422i	−0.441102	−	0.254670i	0.262963	−	0.964806i	$-0.415300\pi$
$283$	−7.42049	−	4.28422i	−0.441102	−	0.254670i	−0.704065	+	0.710135i	$0.748634\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.00327	+	23.5359i	0.354362	+	1.38928i
$288$		0			0
$289$	1.70845			0.100497
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.1436	+	21.0333i	−0.709434	+	1.22878i	0.255633	+	0.966774i	$0.417716\pi$
$293$	−12.1436	+	21.0333i	−0.709434	+	1.22878i	−0.965067	+	0.262002i	$0.915617\pi$
$294$		0			0
$295$	−1.01157	−	1.75209i	−0.0588958	−	0.102010i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.132791	−	0.230001i	−0.00767951	−	0.0133013i
$300$		0			0
$301$	−16.5333	−	4.64443i	−0.952965	−	0.267700i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	5.76127i		−	0.329890i
$306$		0			0
$307$			12.4777i			0.712139i	0.934460	+	0.356069i	$0.115883\pi$
$307$			12.4777i			0.712139i	−0.934460	+	0.356069i	$0.884117\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.07984	+	15.7267i	−0.514871	+	0.891782i	0.484980	+	0.874525i	$0.338827\pi$
$311$	−9.07984	+	15.7267i	−0.514871	+	0.891782i	−0.999851	+	0.0172571i	$0.994507\pi$
$312$		0			0
$313$	2.76700	−	1.59753i	0.156400	−	0.0902977i	−0.419757	−	0.907636i	$-0.637885\pi$
$313$	2.76700	−	1.59753i	0.156400	−	0.0902977i	0.576157	+	0.817339i	$0.304551\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	22.5893	−	13.0419i	1.26874	−	0.732508i	0.293991	−	0.955808i	$-0.405016\pi$
$317$	22.5893	−	13.0419i	1.26874	−	0.732508i	0.974750	+	0.223300i	$0.0716831\pi$
$318$		0			0
$319$	−11.7062	+	20.2757i	−0.655421	+	1.13522i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	9.64266i		−	0.536532i
$324$		0			0
$325$			0.636555i			0.0353097i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	15.5035	+	4.35514i	0.854736	+	0.240107i
$330$		0			0
$331$	−8.06484	−	13.9687i	−0.443283	−	0.767789i	0.554647	−	0.832085i	$-0.312853\pi$
$331$	−8.06484	−	13.9687i	−0.443283	−	0.767789i	−0.997931	+	0.0642960i	$0.979520\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.07171	−	5.32036i	−0.167826	−	0.290683i
$336$		0			0
$337$	−4.16548	+	7.21482i	−0.226908	+	0.393016i	−0.956890	−	0.290450i	$-0.906195\pi$
$337$	−4.16548	+	7.21482i	−0.226908	+	0.393016i	0.729982	+	0.683466i	$0.239528\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.62752			0.196441
$342$		0			0
$343$	−12.6137	−	13.5608i	−0.681075	−	0.732213i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−30.1403	−	17.4015i	−1.61801	−	0.934161i	−0.987433	−	0.158037i	$-0.949483\pi$
$347$	−30.1403	−	17.4015i	−1.61801	−	0.934161i	−0.630581	−	0.776124i	$-0.717183\pi$
$348$		0			0
$349$	−19.6825	+	11.3637i	−1.05358	+	0.608283i	−0.923649	−	0.383240i	$-0.874808\pi$
$349$	−19.6825	+	11.3637i	−1.05358	+	0.608283i	−0.129929	+	0.991523i	$0.541475\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.02829	−	6.97721i	−0.214404	−	0.371359i	0.738684	−	0.674052i	$-0.235448\pi$
$353$	−4.02829	−	6.97721i	−0.214404	−	0.371359i	−0.953088	+	0.302693i	$0.902114\pi$
$354$		0			0
$355$	−1.49197	−	0.861390i	−0.0791856	−	0.0457178i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			17.8217i			0.940594i	0.882508	+	0.470297i	$0.155853\pi$
$359$			17.8217i			0.940594i	−0.882508	+	0.470297i	$0.844147\pi$
$360$		0			0
$361$	14.0300			0.738421
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.176070	+	0.101654i	0.00921594	+	0.00532083i
$366$		0			0
$367$	20.5888	−	11.8870i	1.07473	−	0.620494i	0.145258	−	0.989394i	$-0.453599\pi$
$367$	20.5888	−	11.8870i	1.07473	−	0.620494i	0.929469	+	0.368900i	$0.120266\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−20.3603	−	20.8573i	−1.05706	−	1.08286i
$372$		0			0
$373$	−5.26858	+	9.12545i	−0.272797	+	0.472498i	−0.969577	−	0.244787i	$-0.921282\pi$
$373$	−5.26858	+	9.12545i	−0.272797	+	0.472498i	0.696780	+	0.717285i	$0.254615\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.805203			0.0414700
$378$		0			0
$379$	−24.0049			−1.23305			−0.616525	−	0.787336i	$-0.711460\pi$
$379$	−24.0049			−1.23305			−0.616525	+	0.787336i	$0.711460\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−18.0980	+	31.3466i	−0.924764	+	1.60174i	−0.132823	+	0.991140i	$0.542404\pi$
$383$	−18.0980	+	31.3466i	−0.924764	+	1.60174i	−0.791941	+	0.610598i	$0.790929\pi$
$384$		0			0
$385$	3.87065	+	3.96512i	0.197267	+	0.202081i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−18.6031	+	10.7405i	−0.943215	+	0.544565i	−0.890967	−	0.454069i	$-0.849972\pi$
$389$	−18.6031	+	10.7405i	−0.943215	+	0.544565i	−0.0522481	+	0.998634i	$0.516639\pi$
$390$		0			0
$391$	−7.36925	−	4.25464i	−0.372679	−	0.215166i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.91207			0.247153
$396$		0			0
$397$			21.3049i			1.06926i	0.845086	+	0.534630i	$0.179549\pi$
$397$			21.3049i			1.06926i	−0.845086	+	0.534630i	$0.820451\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.6821	−	9.05406i	−0.783126	−	0.452138i	0.0544110	−	0.998519i	$-0.482672\pi$
$401$	−15.6821	−	9.05406i	−0.783126	−	0.452138i	−0.837537	+	0.546381i	$0.816005\pi$
$402$		0			0
$403$	−0.0623791	−	0.108044i	−0.00310733	−	0.00538205i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−26.5106	+	15.3059i	−1.31408	+	0.758685i
$408$		0			0
$409$	−17.6807	−	10.2080i	−0.874254	−	0.504751i	−0.00549461	−	0.999985i	$-0.501749\pi$
$409$	−17.6807	−	10.2080i	−0.874254	−	0.504751i	−0.868760	+	0.495234i	$0.835082\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.47948	−	9.72083i	−0.122007	−	0.478331i
$414$		0			0
$415$	1.36613			0.0670607
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−12.6789	+	21.9606i	−0.619407	+	1.07284i	0.370187	+	0.928957i	$0.379294\pi$
$419$	−12.6789	+	21.9606i	−0.619407	+	1.07284i	−0.989594	+	0.143887i	$0.954040\pi$
$420$		0			0
$421$	−3.21875	−	5.57503i	−0.156872	−	0.271710i	0.776867	−	0.629665i	$-0.216808\pi$
$421$	−3.21875	−	5.57503i	−0.156872	−	0.271710i	−0.933739	+	0.357954i	$0.883474\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.1976	+	17.6628i	0.494658	+	0.856773i
$426$		0			0
$427$	7.72615	−	27.5037i	0.373895	−	1.33100i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			15.1392i			0.729230i	0.931158	+	0.364615i	$0.118799\pi$
$431$			15.1392i			0.729230i	−0.931158	+	0.364615i	$0.881201\pi$
$432$		0			0
$433$			8.44792i			0.405981i	0.979181	+	0.202991i	$0.0650661\pi$
$433$			8.44792i			0.405981i	−0.979181	+	0.202991i	$0.934934\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.19292	+	3.79824i	−0.104901	+	0.181695i
$438$		0			0
$439$	−23.6831	+	13.6734i	−1.13033	+	0.652598i	−0.944018	−	0.329893i	$-0.892987\pi$
$439$	−23.6831	+	13.6734i	−1.13033	+	0.652598i	−0.186314	+	0.982490i	$0.559654\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.6520	+	8.45931i	−0.696135	+	0.401914i	−0.805906	−	0.592043i	$-0.798322\pi$
$443$	−14.6520	+	8.45931i	−0.696135	+	0.401914i	0.109771	+	0.993957i	$0.464988\pi$
$444$		0			0
$445$	4.57085	−	7.91695i	0.216679	−	0.375299i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			22.5985i			1.06649i	0.845962	+	0.533244i	$0.179027\pi$
$449$			22.5985i			1.06649i	−0.845962	+	0.533244i	$0.820973\pi$
$450$		0			0
$451$		−	36.0358i		−	1.69686i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0515391	−	0.183470i	0.00241619	−	0.00860120i
$456$		0			0
$457$	17.4018	+	30.1408i	0.814022	+	1.40993i	0.910028	+	0.414547i	$0.136060\pi$
$457$	17.4018	+	30.1408i	0.814022	+	1.40993i	−0.0960053	+	0.995381i	$0.530607\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.8264	+	23.9479i	0.643958	+	1.11537i	0.984541	+	0.175153i	$0.0560420\pi$
$461$	13.8264	+	23.9479i	0.643958	+	1.11537i	−0.340584	+	0.940214i	$0.610625\pi$
$462$		0			0
$463$	−10.6272	+	18.4069i	−0.493889	+	0.855440i	−0.999975	−	0.00704260i	$-0.997758\pi$
$463$	−10.6272	+	18.4069i	−0.493889	+	0.855440i	0.506087	+	0.862483i	$0.331092\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.80757			0.407566			0.203783	−	0.979016i	$-0.434676\pi$
$467$	8.80757			0.407566			0.203783	+	0.979016i	$0.434676\pi$
$468$		0			0
$469$	−7.52915	−	29.5181i	−0.347664	−	1.36302i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	22.0648	+	12.7391i	1.01454	+	0.585746i
$474$		0			0
$475$	9.10373	−	5.25604i	0.417708	−	0.241164i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.83139	−	11.8323i	−0.312134	−	0.540633i	0.666690	−	0.745335i	$-0.267711\pi$
$479$	−6.83139	−	11.8323i	−0.312134	−	0.540633i	−0.978824	+	0.204703i	$0.934377\pi$
$480$		0			0
$481$	0.911756	+	0.526403i	0.0415725	+	0.0240019i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			8.42499i			0.382559i
$486$		0			0
$487$	−16.6206			−0.753149			−0.376575	−	0.926386i	$-0.622898\pi$
$487$	−16.6206			−0.753149			−0.376575	+	0.926386i	$0.622898\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	17.8129	+	10.2843i	0.803883	+	0.464122i	0.844827	−	0.535039i	$-0.179703\pi$
$491$	17.8129	+	10.2843i	0.803883	+	0.464122i	−0.0409440	+	0.999161i	$0.513037\pi$
$492$		0			0
$493$	22.3424	−	12.8994i	1.00625	−	0.580959i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.96734	−	6.11299i	−0.267672	−	0.274205i
$498$		0			0
$499$	−1.34609	+	2.33149i	−0.0602592	+	0.104372i	−0.894581	−	0.446905i	$-0.852526\pi$
$499$	−1.34609	+	2.33149i	−0.0602592	+	0.104372i	0.834322	+	0.551277i	$0.185859\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	27.3871			1.22113			0.610566	−	0.791965i	$-0.290942\pi$
$503$	27.3871			1.22113			0.610566	+	0.791965i	$0.290942\pi$
$504$		0			0
$505$	−7.86321			−0.349908
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.96117	+	5.12890i	−0.131252	+	0.227334i	−0.924159	−	0.382007i	$-0.875233\pi$
$509$	−2.96117	+	5.12890i	−0.131252	+	0.227334i	0.792908	+	0.609342i	$0.208566\pi$
$510$		0			0
$511$	0.704217	+	0.721405i	0.0311527	+	0.0319131i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.94609	+	3.43298i	−0.262016	+	0.151275i
$516$		0			0
$517$	−20.6905	−	11.9456i	−0.909966	−	0.525369i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−39.1886			−1.71688			−0.858442	−	0.512911i	$-0.828567\pi$
$521$	−39.1886			−1.71688			−0.858442	+	0.512911i	$0.828567\pi$
$522$		0			0
$523$			23.0358i			1.00728i	0.863912	+	0.503642i	$0.168007\pi$
$523$			23.0358i			1.00728i	−0.863912	+	0.503642i	$0.831993\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.46173	−	1.99863i	−0.150796	−	0.0870618i
$528$		0			0
$529$	−9.56484	−	16.5668i	−0.415862	−	0.720295i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.07331	+	0.619675i	−0.0464901	+	0.0268411i
$534$		0			0
$535$	−7.29267	−	4.21043i	−0.315290	−	0.182033i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	13.1606	+	24.1198i	0.566869	+	1.03891i
$540$		0			0
$541$	−3.32605			−0.142998			−0.0714990	−	0.997441i	$-0.522778\pi$
$541$	−3.32605			−0.142998			−0.0714990	+	0.997441i	$0.522778\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.822590	+	1.42477i	−0.0352359	+	0.0610303i
$546$		0			0
$547$	−13.8937	−	24.0646i	−0.594051	−	1.02893i	−0.993680	−	0.112249i	$-0.964195\pi$
$547$	−13.8937	−	24.0646i	−0.594051	−	1.02893i	0.399629	−	0.916677i	$-0.369139\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.64857	−	11.5157i	−0.283238	−	0.490583i
$552$		0			0
$553$	23.4497	+	6.58732i	0.997181	+	0.280121i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			3.61667i			0.153243i	0.997060	+	0.0766216i	$0.0244133\pi$
$557$			3.61667i			0.153243i	−0.997060	+	0.0766216i	$0.975587\pi$
$558$		0			0
$559$		−	0.876252i		−	0.0370615i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.75452	+	8.23506i	−0.200379	+	0.347067i	−0.948651	−	0.316326i	$-0.897551\pi$
$563$	−4.75452	+	8.23506i	−0.200379	+	0.347067i	0.748272	+	0.663393i	$0.230884\pi$
$564$		0			0
$565$	−4.24807	+	2.45262i	−0.178718	+	0.103183i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.09742	+	5.25240i	−0.381384	+	0.220192i	−0.678420	−	0.734674i	$-0.737335\pi$
$569$	−9.09742	+	5.25240i	−0.381384	+	0.220192i	0.297036	+	0.954866i	$0.404002\pi$
$570$		0			0
$571$	2.24201	−	3.88328i	0.0938252	−	0.162510i	−0.815292	−	0.579049i	$-0.803424\pi$
$571$	2.24201	−	3.88328i	0.0938252	−	0.162510i	0.909118	+	0.416539i	$0.136757\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	9.27651i		−	0.386857i
$576$		0			0
$577$		−	47.1812i		−	1.96418i	−0.188410	−	0.982090i	$-0.560333\pi$
$577$		−	47.1812i		−	1.96418i	0.188410	−	0.982090i	$-0.439667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.52175	+	1.83205i	0.270568	+	0.0760061i
$582$		0			0
$583$	21.6215	+	37.4496i	0.895473	+	1.55100i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.65373	+	9.79255i	0.233354	+	0.404182i	0.958793	−	0.284105i	$-0.0916964\pi$
$587$	5.65373	+	9.79255i	0.233354	+	0.404182i	−0.725439	+	0.688287i	$0.758363\pi$
$588$		0			0
$589$	−1.03013	+	1.78424i	−0.0424458	+	0.0735183i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.44980			−0.388057			−0.194028	−	0.980996i	$-0.562155\pi$
$593$	−9.44980			−0.388057			−0.194028	+	0.980996i	$0.562155\pi$
$594$		0			0
$595$	−1.50911	−	5.91649i	−0.0618676	−	0.242553i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	31.6406	+	18.2677i	1.29280	+	0.746398i	0.979150	−	0.203140i	$-0.0651147\pi$
$599$	31.6406	+	18.2677i	1.29280	+	0.746398i	0.313650	+	0.949539i	$0.398448\pi$
$600$		0			0
$601$	1.92247	−	1.10994i	0.0784193	−	0.0452754i	−0.460278	−	0.887775i	$-0.652250\pi$
$601$	1.92247	−	1.10994i	0.0784193	−	0.0452754i	0.538697	+	0.842500i	$0.318917\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.17583	−	2.03660i	−0.0478043	−	0.0827995i
$606$		0			0
$607$	−1.71759	−	0.991653i	−0.0697149	−	0.0402499i	0.464737	−	0.885449i	$-0.346149\pi$
$607$	−1.71759	−	0.991653i	−0.0697149	−	0.0402499i	−0.534452	+	0.845199i	$0.679482\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			0.821673i			0.0332413i
$612$		0			0
$613$	−23.1365			−0.934476			−0.467238	−	0.884132i	$-0.654751\pi$
$613$	−23.1365			−0.934476			−0.467238	+	0.884132i	$0.654751\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.19807	+	0.691704i	0.0482323	+	0.0278470i	0.523922	−	0.851766i	$-0.324468\pi$
$617$	1.19807	+	0.691704i	0.0482323	+	0.0278470i	−0.475690	+	0.879613i	$0.657802\pi$
$618$		0			0
$619$	−5.22550	+	3.01694i	−0.210031	+	0.121261i	−0.601326	−	0.799004i	$-0.705361\pi$
$619$	−5.22550	+	3.01694i	−0.210031	+	0.121261i	0.391295	+	0.920265i	$0.372027\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	32.4378	−	31.6649i	1.29959	−	1.26863i
$624$		0			0
$625$	−10.4054	+	18.0226i	−0.416215	+	0.720905i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	33.7320			1.34498
$630$		0			0
$631$	20.4727			0.815004			0.407502	−	0.913204i	$-0.366400\pi$
$631$	20.4727			0.815004			0.407502	+	0.913204i	$0.366400\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.69622	−	4.67000i	0.106996	−	0.185323i
$636$		0			0
$637$	0.492084	−	0.806748i	0.0194971	−	0.0319645i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−40.2246	+	23.2237i	−1.58878	+	0.917281i	−0.595269	+	0.803527i	$0.702954\pi$
$641$	−40.2246	+	23.2237i	−1.58878	+	0.917281i	−0.993509	+	0.113754i	$0.963712\pi$
$642$		0			0
$643$	−9.74133	−	5.62416i	−0.384161	−	0.221795i	0.295466	−	0.955353i	$-0.404525\pi$
$643$	−9.74133	−	5.62416i	−0.384161	−	0.221795i	−0.679627	+	0.733558i	$0.737858\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.65015			−0.182816			−0.0914081	−	0.995814i	$-0.529137\pi$
$647$	−4.65015			−0.182816			−0.0914081	+	0.995814i	$0.529137\pi$
$648$		0			0
$649$			14.8836i			0.584232i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.99966	−	1.73186i	−0.117386	−	0.0677727i	0.440157	−	0.897921i	$-0.354923\pi$
$653$	−2.99966	−	1.73186i	−0.117386	−	0.0677727i	−0.557543	+	0.830148i	$0.688256\pi$
$654$		0			0
$655$	4.17150	+	7.22524i	0.162994	+	0.282314i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.59819	+	0.922715i	−0.0622566	+	0.0359439i	−0.530805	−	0.847494i	$-0.678110\pi$
$659$	−1.59819	+	0.922715i	−0.0622566	+	0.0359439i	0.468549	+	0.883438i	$0.344777\pi$
$660$		0			0
$661$	17.5196	+	10.1149i	0.681433	+	0.393426i	0.800395	−	0.599473i	$-0.204623\pi$
$661$	17.5196	+	10.1149i	0.681433	+	0.393426i	−0.118962	+	0.992899i	$0.537957\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.04947	+	0.777823i	−0.118253	+	0.0301627i
$666$		0			0
$667$	−11.7342			−0.454351
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−21.1919	+	36.7055i	−0.818106	+	1.41700i
$672$		0			0
$673$	−7.31596	−	12.6716i	−0.282009	−	0.488455i	0.689870	−	0.723933i	$-0.257668\pi$
$673$	−7.31596	−	12.6716i	−0.282009	−	0.488455i	−0.971880	+	0.235478i	$0.924334\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.71449	−	13.3619i	−0.296492	−	0.513539i	0.678839	−	0.734287i	$-0.262483\pi$
$677$	−7.71449	−	13.3619i	−0.296492	−	0.513539i	−0.975331	+	0.220748i	$0.929150\pi$
$678$		0			0
$679$	−11.2983	+	40.2200i	−0.433590	+	1.54350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			15.7197i			0.601499i	0.953703	+	0.300750i	$0.0972368\pi$
$683$			15.7197i			0.601499i	−0.953703	+	0.300750i	$0.902763\pi$
$684$		0			0
$685$			1.31779i			0.0503501i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.743611	−	1.28797i	0.0283293	−	0.0490678i
$690$		0			0
$691$	41.5878	−	24.0107i	1.58207	−	0.913411i	0.587517	−	0.809212i	$-0.300106\pi$
$691$	41.5878	−	24.0107i	1.58207	−	0.913411i	0.994556	−	0.104199i	$-0.0332278\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.99187	−	5.19146i	0.341081	−	0.196923i
$696$		0			0
$697$	−19.8544	+	34.3889i	−0.752040	+	1.30257i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			24.7005i			0.932923i	0.884541	+	0.466462i	$0.154471\pi$
$701$			24.7005i			0.932923i	−0.884541	+	0.466462i	$0.845529\pi$
$702$		0			0
$703$		−	17.3860i		−	0.655727i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−37.5381	−	10.5449i	−1.41176	−	0.396583i
$708$		0			0
$709$	−17.0432	−	29.5196i	−0.640070	−	1.10863i	−0.985417	−	0.170159i	$-0.945572\pi$
$709$	−17.0432	−	29.5196i	−0.640070	−	1.10863i	0.345347	−	0.938475i	$-0.387761\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.909051	+	1.57452i	0.0340442	+	0.0589663i
$714$		0			0
$715$	−0.141366	+	0.244853i	−0.00528679	+	0.00915698i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	18.4758			0.689032			0.344516	−	0.938780i	$-0.388043\pi$
$719$	18.4758			0.689032			0.344516	+	0.938780i	$0.388043\pi$
$720$		0			0
$721$	−32.9898	+	8.41466i	−1.22860	+	0.313378i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	24.3569	+	14.0624i	0.904591	+	0.522266i
$726$		0			0
$727$	−39.2911	+	22.6847i	−1.45723	+	0.841330i	−0.998874	−	0.0474398i	$-0.984894\pi$
$727$	−39.2911	+	22.6847i	−1.45723	+	0.841330i	−0.458353	+	0.888770i	$0.651560\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−14.0376	−	24.3138i	−0.519200	−	0.899280i
$732$		0			0
$733$	−43.3683	−	25.0387i	−1.60184	−	0.924825i	−0.991119	−	0.132981i	$-0.957545\pi$
$733$	−43.3683	−	25.0387i	−1.60184	−	0.924825i	−0.610724	−	0.791843i	$-0.709122\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			45.1953i			1.66479i
$738$		0			0
$739$	16.9404			0.623163			0.311582	−	0.950219i	$-0.399141\pi$
$739$	16.9404			0.623163			0.311582	+	0.950219i	$0.399141\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	34.4723	+	19.9026i	1.26467	+	0.730156i	0.973974	−	0.226661i	$-0.0727808\pi$
$743$	34.4723	+	19.9026i	1.26467	+	0.730156i	0.290693	+	0.956816i	$0.406114\pi$
$744$		0			0
$745$	−7.32595	+	4.22964i	−0.268402	+	0.154962i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−29.1680	−	29.8799i	−1.06578	−	1.09179i
$750$		0			0
$751$	−14.7028	+	25.4659i	−0.536512	+	0.929265i	0.462577	+	0.886579i	$0.346925\pi$
$751$	−14.7028	+	25.4659i	−0.536512	+	0.929265i	−0.999089	+	0.0426862i	$0.986408\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.44507			0.161773
$756$		0			0
$757$	−27.4010			−0.995908			−0.497954	−	0.867203i	$-0.665915\pi$
$757$	−27.4010			−0.995908			−0.497954	+	0.867203i	$0.665915\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−6.11067	+	10.5840i	−0.221511	+	0.383669i	−0.955267	−	0.295744i	$-0.904432\pi$
$761$	−6.11067	+	10.5840i	−0.221511	+	0.383669i	0.733756	+	0.679413i	$0.237766\pi$
$762$		0			0
$763$	−5.83763	+	5.69855i	−0.211337	+	0.206301i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.443300	−	0.255939i	0.0160066	−	0.00924143i
$768$		0			0
$769$	29.4039	+	16.9764i	1.06033	+	0.612184i	0.925524	−	0.378688i	$-0.123625\pi$
$769$	29.4039	+	16.9764i	1.06033	+	0.612184i	0.134809	+	0.990872i	$0.456958\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	30.2094			1.08656			0.543279	−	0.839552i	$-0.317183\pi$
$773$	30.2094			1.08656			0.543279	+	0.839552i	$0.317183\pi$
$774$		0			0
$775$		−	4.35767i		−	0.156532i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.7246	+	10.2333i	0.635051	+	0.366647i
$780$		0			0
$781$	6.33698	+	10.9760i	0.226755	+	0.392751i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.12866	−	2.38368i	0.147358	−	0.0850772i
$786$		0			0
$787$	33.3310	+	19.2436i	1.18812	+	0.685962i	0.957879	−	0.287172i	$-0.0927151\pi$
$787$	33.3310	+	19.2436i	1.18812	+	0.685962i	0.230241	+	0.973134i	$0.426048\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−23.5689	+	6.01168i	−0.838013	+	0.213751i
$792$		0			0
$793$	1.45767			0.0517635
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−6.72949	+	11.6558i	−0.238371	+	0.412870i	−0.960247	−	0.279152i	$-0.909947\pi$
$797$	−6.72949	+	11.6558i	−0.238371	+	0.412870i	0.721876	+	0.692022i	$0.243280\pi$
$798$		0			0
$799$	13.1632	+	22.7994i	0.465682	+	0.806584i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.747839	−	1.29529i	−0.0263907	−	0.0457100i
$804$		0			0
$805$	−0.751079	+	2.67371i	−0.0264721	+	0.0942357i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	51.7842i		−	1.82064i	−0.413909	−	0.910318i	$-0.635837\pi$
$809$		−	51.7842i		−	1.82064i	0.413909	−	0.910318i	$-0.364163\pi$
$810$		0			0
$811$			27.2471i			0.956775i	0.878149	+	0.478387i	$0.158779\pi$
$811$			27.2471i			0.956775i	−0.878149	+	0.478387i	$0.841221\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.78993	−	6.56436i	0.132756	−	0.229939i
$816$		0			0
$817$	−12.5318	+	7.23523i	−0.438432	+	0.253129i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−22.3465	+	12.9017i	−0.779897	+	0.450274i	−0.836394	−	0.548129i	$-0.815340\pi$
$821$	−22.3465	+	12.9017i	−0.779897	+	0.450274i	0.0564968	+	0.998403i	$0.482007\pi$
$822$		0			0
$823$	−0.570514	+	0.988159i	−0.0198869	+	0.0344451i	−0.875798	−	0.482679i	$-0.839664\pi$
$823$	−0.570514	+	0.988159i	−0.0198869	+	0.0344451i	0.855911	+	0.517124i	$0.172997\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	23.1713i		−	0.805746i	−0.915256	−	0.402873i	$-0.868012\pi$
$827$		−	23.1713i		−	0.805746i	0.915256	−	0.402873i	$-0.131988\pi$
$828$		0			0
$829$			9.60364i			0.333548i	0.985995	+	0.166774i	$0.0533351\pi$
$829$			9.60364i			0.333548i	−0.985995	+	0.166774i	$0.946665\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.729974	−	30.2685i	0.0252921	−	1.04874i
$834$		0			0
$835$	−3.34707	−	5.79729i	−0.115830	−	0.200623i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.7821	+	27.3354i	0.544859	+	0.943723i	0.998616	+	0.0525978i	$0.0167501\pi$
$839$	15.7821	+	27.3354i	0.544859	+	0.943723i	−0.453757	+	0.891126i	$0.649917\pi$
$840$		0			0
$841$	3.28812	−	5.69519i	0.113383	−	0.196386i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.92656			−0.238281
$846$		0			0
$847$	−2.88211	−	11.2993i	−0.0990304	−	0.388250i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−13.2870	−	7.67126i	−0.455473	−	0.262967i
$852$		0			0
$853$	−7.50412	+	4.33250i	−0.256936	+	0.148342i	−0.622936	−	0.782273i	$-0.714060\pi$
$853$	−7.50412	+	4.33250i	−0.256936	+	0.148342i	0.366000	+	0.930615i	$0.380727\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.4439	−	19.8214i	−0.390917	−	0.677088i	0.601654	−	0.798757i	$-0.294509\pi$
$857$	−11.4439	−	19.8214i	−0.390917	−	0.677088i	−0.992571	+	0.121669i	$0.961175\pi$
$858$		0			0
$859$	−11.4922	−	6.63503i	−0.392109	−	0.226384i	0.290964	−	0.956734i	$-0.406024\pi$
$859$	−11.4922	−	6.63503i	−0.392109	−	0.226384i	−0.683074	+	0.730350i	$0.739357\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			0.746752i			0.0254197i	0.999919	+	0.0127099i	$0.00404579\pi$
$863$			0.746752i			0.0254197i	−0.999919	+	0.0127099i	$0.995954\pi$
$864$		0			0
$865$	−11.3955			−0.387457
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−31.2951	−	18.0683i	−1.06162	−	0.612924i
$870$		0			0
$871$	1.34612	−	0.777181i	0.0456114	−	0.0263338i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	9.81404	−	9.58021i	0.331775	−	0.323870i
$876$		0			0
$877$	−2.18959	+	3.79249i	−0.0739373	+	0.128063i	−0.900624	−	0.434600i	$-0.856890\pi$
$877$	−2.18959	+	3.79249i	−0.0739373	+	0.128063i	0.826686	+	0.562663i	$0.190223\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−14.1505			−0.476742			−0.238371	−	0.971174i	$-0.576613\pi$
$881$	−14.1505			−0.476742			−0.238371	+	0.971174i	$0.576613\pi$
$882$		0			0
$883$	−23.0261			−0.774890			−0.387445	−	0.921893i	$-0.626642\pi$
$883$	−23.0261			−0.774890			−0.387445	+	0.921893i	$0.626642\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.1812	−	45.3471i	0.879077	−	1.52261i	0.0267221	−	0.999643i	$-0.491493\pi$
$887$	26.1812	−	45.3471i	0.879077	−	1.52261i	0.852355	−	0.522963i	$-0.175174\pi$
$888$		0			0
$889$	19.1342	−	18.6783i	0.641739	−	0.626449i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11.7512	−	6.78456i	0.393239	−	0.227037i
$894$		0			0
$895$	−2.68519	−	1.55029i	−0.0897560	−	0.0518206i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.51219			−0.183842
$900$		0			0
$901$		−	47.6507i		−	1.58748i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.41418	+	1.97118i	0.113491	+	0.0655242i
$906$		0			0
$907$	−12.1902	−	21.1141i	−0.404770	−	0.701082i	0.589525	−	0.807750i	$-0.299315\pi$
$907$	−12.1902	−	21.1141i	−0.404770	−	0.701082i	−0.994295	+	0.106669i	$0.965982\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−46.8606	+	27.0550i	−1.55256	+	0.896372i	−0.554629	+	0.832098i	$0.687140\pi$
$911$	−46.8606	+	27.0550i	−1.55256	+	0.896372i	−0.997932	+	0.0642741i	$0.979527\pi$
$912$		0			0
$913$	−8.70372	−	5.02509i	−0.288051	−	0.166306i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	10.2249	+	40.0867i	0.337655	+	1.32378i
$918$		0			0
$919$	−6.51894			−0.215040			−0.107520	−	0.994203i	$-0.534291\pi$
$919$	−6.51894			−0.215040			−0.107520	+	0.994203i	$0.534291\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	0.217942	−	0.377487i	0.00717365	−	0.0124251i
$924$		0			0
$925$	18.3867	+	31.8467i	0.604550	+	1.04711i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	13.9048	+	24.0838i	0.456202	+	0.790165i	0.998756	−	0.0498555i	$-0.0158761\pi$
$929$	13.9048	+	24.0838i	0.456202	+	0.790165i	−0.542554	+	0.840021i	$0.682543\pi$
$930$		0			0
$931$	−15.6009	−	0.376242i	−0.511299	−	0.0123308i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			9.05875i			0.296253i
$936$		0			0
$937$			54.8174i			1.79081i	0.445256	+	0.895403i	$0.353113\pi$
$937$			54.8174i			1.79081i	−0.445256	+	0.895403i	$0.646887\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.56526	−	4.44317i	0.0836252	−	0.144843i	−0.821179	−	0.570670i	$-0.806683\pi$
$941$	2.56526	−	4.44317i	0.0836252	−	0.144843i	0.904805	+	0.425827i	$0.140017\pi$
$942$		0			0
$943$	15.6413	−	9.03052i	0.509351	−	0.294074i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.606033	+	0.349893i	−0.0196934	+	0.0113700i	−0.509814	−	0.860284i	$-0.670286\pi$
$947$	−0.606033	+	0.349893i	−0.0196934	+	0.0113700i	0.490121	+	0.871654i	$0.336953\pi$
$948$		0			0
$949$	−0.0257198	+	0.0445480i	−0.000834899	+	0.00144609i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			0.162845i			0.00527506i	0.999997	+	0.00263753i	$0.000839552\pi$
$953$			0.162845i			0.00527506i	−0.999997	+	0.00263753i	$0.999160\pi$
$954$		0			0
$955$		−	4.22714i		−	0.136787i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.76722	+	6.29097i	−0.0570664	+	0.203146i
$960$		0			0
$961$	−15.0730	−	26.1071i	−0.486225	−	0.842166i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.68897	−	2.92539i	−0.0543700	−	0.0941716i
$966$		0			0
$967$	15.6968	−	27.1876i	0.504773	−	0.874293i	−0.495211	−	0.868773i	$-0.664909\pi$
$967$	15.6968	−	27.1876i	0.504773	−	0.874293i	0.999985	−	0.00552073i	$-0.00175731\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.92239			0.0937841			0.0468920	−	0.998900i	$-0.485068\pi$
$971$	2.92239			0.0937841			0.0468920	+	0.998900i	$0.485068\pi$
$972$		0			0
$973$	49.8882	−	12.7249i	1.59934	−	0.407942i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	24.7013	+	14.2613i	0.790264	+	0.456259i	0.840056	−	0.542500i	$-0.182522\pi$
$977$	24.7013	+	14.2613i	0.790264	+	0.456259i	−0.0497913	+	0.998760i	$0.515856\pi$
$978$		0			0
$979$	−58.2425	+	33.6263i	−1.86144	+	1.07470i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.62897	−	9.74967i	−0.179536	−	0.310966i	0.762185	−	0.647359i	$-0.224126\pi$
$983$	−5.62897	−	9.74967i	−0.179536	−	0.310966i	−0.941722	+	0.336393i	$0.890793\pi$
$984$		0			0
$985$	7.00416	+	4.04386i	0.223171	+	0.128848i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			12.7696i			0.406050i
$990$		0			0
$991$	−21.1622			−0.672240			−0.336120	−	0.941819i	$-0.609115\pi$
$991$	−21.1622			−0.672240			−0.336120	+	0.941819i	$0.609115\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	3.95114	+	2.28119i	0.125260	+	0.0723187i
$996$		0			0
$997$	−14.6576	+	8.46256i	−0.464210	+	0.268012i	−0.713813	−	0.700336i	$-0.753033\pi$
$997$	−14.6576	+	8.46256i	−0.464210	+	0.268012i	0.249603	+	0.968348i	$0.419700\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.c.881.5		16
3.2	odd	2		1008.2.cc.c.545.6		16
4.3	odd	2		756.2.x.a.125.5		16
7.6	odd	2	inner	3024.2.cc.c.881.4		16
9.2	odd	6	inner	3024.2.cc.c.2897.4		16
9.7	even	3		1008.2.cc.c.209.3		16
12.11	even	2		252.2.x.a.41.3	✓	16
21.20	even	2		1008.2.cc.c.545.3		16
28.3	even	6		5292.2.w.a.1097.4		16
28.11	odd	6		5292.2.w.a.1097.5		16
28.19	even	6		5292.2.bm.b.2285.5		16
28.23	odd	6		5292.2.bm.b.2285.4		16
28.27	even	2		756.2.x.a.125.4		16
36.7	odd	6		252.2.x.a.209.6	yes	16
36.11	even	6		756.2.x.a.629.4		16
36.23	even	6		2268.2.f.b.1133.9		16
36.31	odd	6		2268.2.f.b.1133.7		16
63.20	even	6	inner	3024.2.cc.c.2897.5		16
63.34	odd	6		1008.2.cc.c.209.6		16
84.11	even	6		1764.2.w.a.509.8		16
84.23	even	6		1764.2.bm.b.1697.4		16
84.47	odd	6		1764.2.bm.b.1697.5		16
84.59	odd	6		1764.2.w.a.509.1		16
84.83	odd	2		252.2.x.a.41.6	yes	16
252.11	even	6		5292.2.bm.b.4625.5		16
252.47	odd	6		5292.2.w.a.521.5		16
252.79	odd	6		1764.2.w.a.1109.1		16
252.83	odd	6		756.2.x.a.629.5		16
252.115	even	6		1764.2.bm.b.1685.4		16
252.139	even	6		2268.2.f.b.1133.10		16
252.151	odd	6		1764.2.bm.b.1685.5		16
252.167	odd	6		2268.2.f.b.1133.8		16
252.187	even	6		1764.2.w.a.1109.8		16
252.191	even	6		5292.2.w.a.521.4		16
252.223	even	6		252.2.x.a.209.3	yes	16
252.227	odd	6		5292.2.bm.b.4625.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.x.a.41.3	✓	16	12.11	even	2
252.2.x.a.41.6	yes	16	84.83	odd	2
252.2.x.a.209.3	yes	16	252.223	even	6
252.2.x.a.209.6	yes	16	36.7	odd	6
756.2.x.a.125.4		16	28.27	even	2
756.2.x.a.125.5		16	4.3	odd	2
756.2.x.a.629.4		16	36.11	even	6
756.2.x.a.629.5		16	252.83	odd	6
1008.2.cc.c.209.3		16	9.7	even	3
1008.2.cc.c.209.6		16	63.34	odd	6
1008.2.cc.c.545.3		16	21.20	even	2
1008.2.cc.c.545.6		16	3.2	odd	2
1764.2.w.a.509.1		16	84.59	odd	6
1764.2.w.a.509.8		16	84.11	even	6
1764.2.w.a.1109.1		16	252.79	odd	6
1764.2.w.a.1109.8		16	252.187	even	6
1764.2.bm.b.1685.4		16	252.115	even	6
1764.2.bm.b.1685.5		16	252.151	odd	6
1764.2.bm.b.1697.4		16	84.23	even	6
1764.2.bm.b.1697.5		16	84.47	odd	6
2268.2.f.b.1133.7		16	36.31	odd	6
2268.2.f.b.1133.8		16	252.167	odd	6
2268.2.f.b.1133.9		16	36.23	even	6
2268.2.f.b.1133.10		16	252.139	even	6
3024.2.cc.c.881.4		16	7.6	odd	2	inner
3024.2.cc.c.881.5		16	1.1	even	1	trivial
3024.2.cc.c.2897.4		16	9.2	odd	6	inner
3024.2.cc.c.2897.5		16	63.20	even	6	inner
5292.2.w.a.521.4		16	252.191	even	6
5292.2.w.a.521.5		16	252.47	odd	6
5292.2.w.a.1097.4		16	28.3	even	6
5292.2.w.a.1097.5		16	28.11	odd	6
5292.2.bm.b.2285.4		16	28.23	odd	6
5292.2.bm.b.2285.5		16	28.19	even	6
5292.2.bm.b.4625.4		16	252.227	odd	6
5292.2.bm.b.4625.5		16	252.11	even	6

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)

\(f(q)\)	\(=\)	\(q+(0.266780 - 0.462077i) q^{5} +(1.89325 - 1.84814i) q^{7} +O(q^{10})\)	\(q+(0.266780 - 0.462077i) q^{5} +(1.89325 - 1.84814i) q^{7} +(-3.39936 + 1.96262i) q^{11} +(0.116911 + 0.0674987i) q^{13} +4.32533 q^{17} -2.22935i q^{19} +(-1.70375 - 0.983658i) q^{23} +(2.35766 + 4.08358i) q^{25} +(5.16548 - 2.98229i) q^{29} +(-0.800341 - 0.462077i) q^{31} +(-0.348901 - 1.36787i) q^{35} +7.79871 q^{37} +(-4.59027 + 7.95059i) q^{41} +(-3.24544 - 5.62127i) q^{43} +(3.04329 + 5.27114i) q^{47} +(0.168767 - 6.99797i) q^{49} -11.0167i q^{53} +2.09435i q^{55} +(1.89588 - 3.28377i) q^{59} +(9.35116 - 5.39889i) q^{61} +(0.0623791 - 0.0360146i) q^{65} +(5.75701 - 9.97144i) q^{67} -3.22884i q^{71} +0.381041i q^{73} +(-2.80863 + 9.99820i) q^{77} +(4.60310 + 7.97280i) q^{79} +(1.28020 + 2.21737i) q^{83} +(1.15391 - 1.99863i) q^{85} +17.1334 q^{89} +(0.346088 - 0.0882763i) q^{91} +(-1.03013 - 0.594746i) q^{95} +(-13.6747 + 7.89507i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7}+O(q^{10}) \) 16 * q + q^7	\( 16 q + q^{7} + 6 q^{11} + 6 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} - 4 q^{43} - 5 q^{49} + 24 q^{65} - 14 q^{67} + 21 q^{77} - 20 q^{79} + 6 q^{85} + 18 q^{91} - 60 q^{95}+O(q^{100}) \) 16 * q + q^7 + 6 * q^11 + 6 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 - 4 * q^43 - 5 * q^49 + 24 * q^65 - 14 * q^67 + 21 * q^77 - 20 * q^79 + 6 * q^85 + 18 * q^91 - 60 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more