LMFDB - Embedded newform 2268.2.t.a.1781.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2268,2,Mod(1781,2268)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2268, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("2268.1781");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.t (of order $6$, degree $2$, 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:	$18.1100711784$
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} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + 5x^14 - 17x^13 + 22x^12 - 31x^11 + 62x^10 - 52x^9 + 52x^8 - 156x^7 + 558x^6 - 837x^5 + 1782x^4 - 4131x^3 + 3645x^2 - 4374*x + 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			1781.2
Root			$-0.811340 + 1.53027i$ of defining polynomial
Character	$\chi$	$=$	2268.1781
Dual form			2268.2.t.a.2105.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37166 - 2.37578i) q^{5} +(0.900590 + 2.48776i) q^{7} +O(q^{10})$	$q+(-1.37166 - 2.37578i) q^{5} +(0.900590 + 2.48776i) q^{7} +(-0.362306 - 0.209178i) q^{11} +1.53011i q^{13} +(1.95291 - 3.38253i) q^{17} +(-5.11994 + 2.95600i) q^{19} +(7.72884 - 4.46225i) q^{23} +(-1.26290 + 2.18740i) q^{25} +6.93257i q^{29} +(3.05626 + 1.76453i) q^{31} +(4.67507 - 5.55196i) q^{35} +(-4.54861 - 7.87842i) q^{37} +2.12472 q^{41} +11.5569 q^{43} +(-0.885373 - 1.53351i) q^{47} +(-5.37787 + 4.48090i) q^{49} +(3.39526 + 1.96025i) q^{53} +1.14768i q^{55} +(-2.02728 + 3.51135i) q^{59} +(1.61459 - 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(6.38441 - 11.0581i) q^{67} -8.51021i q^{71} +(1.65059 + 0.952971i) q^{73} +(0.194094 - 1.08971i) q^{77} +(0.433633 + 0.751074i) q^{79} +6.91761 q^{83} -10.7149 q^{85} +(4.88864 + 8.46738i) q^{89} +(-3.80655 + 1.37800i) q^{91} +(14.0456 + 8.10924i) q^{95} -0.231415i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{7}+O(q^{10}) $ 16 * q + 2 * q^7	$ 16 q + 2 q^{7} - 6 q^{11} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{31} + 15 q^{35} + q^{37} - 12 q^{41} + 4 q^{43} - 18 q^{47} - 8 q^{49} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} + 48 q^{77} - q^{79} - 12 q^{85} - 21 q^{89} + 9 q^{91} - 6 q^{95}+O(q^{100}) $ 16 * q + 2 * q^7 - 6 * q^11 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^31 + 15 * q^35 + q^37 - 12 * q^41 + 4 * q^43 - 18 * q^47 - 8 * q^49 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 + 48 * q^77 - q^79 - 12 * q^85 - 21 * q^89 + 9 * q^91 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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
$5$	−1.37166	−	2.37578i	−0.613425	−	1.06248i	−0.990659	−	0.136365i	$-0.956458\pi$
$5$	−1.37166	−	2.37578i	−0.613425	−	1.06248i	0.377234	−	0.926118i	$-0.376875\pi$
$6$		0			0
$7$	0.900590	+	2.48776i	0.340391	+	0.940284i
$7$	0.900590	+	2.48776i	0.340391	+	0.940284i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.362306	−	0.209178i	−0.109240	−	0.0630695i	0.444385	−	0.895836i	$-0.353422\pi$
$11$	−0.362306	−	0.209178i	−0.109240	−	0.0630695i	−0.553624	+	0.832767i	$0.686756\pi$
$12$		0			0
$13$			1.53011i			0.424377i	0.977229	+	0.212188i	$0.0680590\pi$
$13$			1.53011i			0.424377i	−0.977229	+	0.212188i	$0.931941\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.95291	−	3.38253i	0.473649	−	0.820385i	−0.525896	−	0.850549i	$-0.676270\pi$
$17$	1.95291	−	3.38253i	0.473649	−	0.820385i	0.999545	+	0.0301645i	$0.00960312\pi$
$18$		0			0
$19$	−5.11994	+	2.95600i	−1.17459	+	0.678152i	−0.954758	−	0.297385i	$-0.903886\pi$
$19$	−5.11994	+	2.95600i	−1.17459	+	0.678152i	−0.219836	+	0.975537i	$0.570552\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.72884	−	4.46225i	1.61157	−	0.930443i	0.622569	−	0.782565i	$-0.286089\pi$
$23$	7.72884	−	4.46225i	1.61157	−	0.930443i	0.989006	−	0.147878i	$-0.0472444\pi$
$24$		0			0
$25$	−1.26290	+	2.18740i	−0.252579	+	0.437480i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			6.93257i			1.28735i	0.765301	+	0.643673i	$0.222590\pi$
$29$			6.93257i			1.28735i	−0.765301	+	0.643673i	$0.777410\pi$
$30$		0			0
$31$	3.05626	+	1.76453i	0.548921	+	0.316920i	0.748687	−	0.662924i	$-0.230685\pi$
$31$	3.05626	+	1.76453i	0.548921	+	0.316920i	−0.199766	+	0.979844i	$0.564018\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.67507	−	5.55196i	0.790231	−	0.938453i
$36$		0			0
$37$	−4.54861	−	7.87842i	−0.747787	−	1.29520i	−0.948881	−	0.315633i	$-0.897783\pi$
$37$	−4.54861	−	7.87842i	−0.747787	−	1.29520i	0.201095	−	0.979572i	$-0.435550\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.12472			0.331826			0.165913	−	0.986140i	$-0.446943\pi$
$41$	2.12472			0.331826			0.165913	+	0.986140i	$0.446943\pi$
$42$		0			0
$43$	11.5569			1.76242			0.881208	−	0.472730i	$-0.156731\pi$
$43$	11.5569			1.76242			0.881208	+	0.472730i	$0.156731\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.885373	−	1.53351i	−0.129145	−	0.223686i	0.794201	−	0.607656i	$-0.207890\pi$
$47$	−0.885373	−	1.53351i	−0.129145	−	0.223686i	−0.923346	+	0.383970i	$0.874557\pi$
$48$		0			0
$49$	−5.37787	+	4.48090i	−0.768268	+	0.640129i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.39526	+	1.96025i	0.466374	+	0.269261i	0.714721	−	0.699410i	$-0.246554\pi$
$53$	3.39526	+	1.96025i	0.466374	+	0.269261i	−0.248346	+	0.968671i	$0.579887\pi$
$54$		0			0
$55$			1.14768i			0.154753i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.02728	+	3.51135i	−0.263929	+	0.457139i	−0.967283	−	0.253702i	$-0.918352\pi$
$59$	−2.02728	+	3.51135i	−0.263929	+	0.457139i	0.703353	+	0.710840i	$0.251685\pi$
$60$		0			0
$61$	1.61459	−	0.932184i	0.206727	−	0.119354i	−0.393062	−	0.919512i	$-0.628584\pi$
$61$	1.61459	−	0.932184i	0.206727	−	0.119354i	0.599789	+	0.800158i	$0.295251\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.63521	−	2.09879i	0.450893	−	0.260323i
$66$		0			0
$67$	6.38441	−	11.0581i	0.779979	−	1.35096i	−0.151974	−	0.988385i	$-0.548563\pi$
$67$	6.38441	−	11.0581i	0.779979	−	1.35096i	0.931953	−	0.362579i	$-0.118104\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	8.51021i		−	1.00998i	−0.863126	−	0.504988i	$-0.831497\pi$
$71$		−	8.51021i		−	1.00998i	0.863126	−	0.504988i	$-0.168503\pi$
$72$		0			0
$73$	1.65059	+	0.952971i	0.193187	+	0.111537i	0.593474	−	0.804853i	$-0.297756\pi$
$73$	1.65059	+	0.952971i	0.193187	+	0.111537i	−0.400286	+	0.916390i	$0.631089\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.194094	−	1.08971i	0.0221190	−	0.124184i
$78$		0			0
$79$	0.433633	+	0.751074i	0.0487875	+	0.0845024i	0.889388	−	0.457153i	$-0.151131\pi$
$79$	0.433633	+	0.751074i	0.0487875	+	0.0845024i	−0.840600	+	0.541656i	$0.817798\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.91761			0.759306			0.379653	−	0.925129i	$-0.376043\pi$
$83$	6.91761			0.759306			0.379653	+	0.925129i	$0.376043\pi$
$84$		0			0
$85$	−10.7149			−1.16219
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.88864	+	8.46738i	0.518195	+	0.897540i	0.999777	+	0.0211389i	$0.00672921\pi$
$89$	4.88864	+	8.46738i	0.518195	+	0.897540i	−0.481581	+	0.876401i	$0.659937\pi$
$90$		0			0
$91$	−3.80655	+	1.37800i	−0.399035	+	0.144454i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14.0456	+	8.10924i	1.44105	+	0.831990i
$96$		0			0
$97$		−	0.231415i		−	0.0234966i	−0.999931	−	0.0117483i	$-0.996260\pi$
$97$		−	0.231415i		−	0.0234966i	0.999931	−	0.0117483i	$-0.00373968\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.14031	−	12.3674i	0.710487	−	1.23060i	−0.254187	−	0.967155i	$-0.581808\pi$
$101$	7.14031	−	12.3674i	0.710487	−	1.23060i	0.964674	−	0.263445i	$-0.0848587\pi$
$102$		0			0
$103$	9.30617	−	5.37292i	0.916964	−	0.529410i	0.0342991	−	0.999412i	$-0.489080\pi$
$103$	9.30617	−	5.37292i	0.916964	−	0.529410i	0.882665	+	0.470002i	$0.155747\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.50534	−	3.17851i	0.532221	−	0.307278i	−0.209699	−	0.977766i	$-0.567249\pi$
$107$	5.50534	−	3.17851i	0.532221	−	0.307278i	0.741920	+	0.670488i	$0.233915\pi$
$108$		0			0
$109$	2.58036	−	4.46932i	0.247154	−	0.428083i	−0.715581	−	0.698530i	$-0.753838\pi$
$109$	2.58036	−	4.46932i	0.247154	−	0.428083i	0.962735	+	0.270447i	$0.0871714\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	10.6138i		−	0.998466i	−0.866468	−	0.499233i	$-0.833615\pi$
$113$		−	10.6138i		−	0.998466i	0.866468	−	0.499233i	$-0.166385\pi$
$114$		0			0
$115$	−21.2027	−	12.2414i	−1.97716	−	1.14151i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.1737	+	1.81208i	0.932620	+	0.166113i
$120$		0			0
$121$	−5.41249	−	9.37471i	−0.492044	−	0.852246i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.78753			−0.607096
$126$		0			0
$127$	10.2909			0.913169			0.456584	−	0.889680i	$-0.349073\pi$
$127$	10.2909			0.913169			0.456584	+	0.889680i	$0.349073\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.83048	−	17.0269i	−0.858893	−	1.48765i	−0.872986	−	0.487746i	$-0.837819\pi$
$131$	−9.83048	−	17.0269i	−0.858893	−	1.48765i	0.0140928	−	0.999901i	$-0.495514\pi$
$132$		0			0
$133$	−11.9648	−	10.0750i	−1.03748	−	0.873615i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.66411	−	2.69282i	−0.398481	−	0.230063i	0.287347	−	0.957827i	$-0.407227\pi$
$137$	−4.66411	−	2.69282i	−0.398481	−	0.230063i	−0.685829	+	0.727763i	$0.740560\pi$
$138$		0			0
$139$			17.0710i			1.44794i	0.689831	+	0.723971i	$0.257685\pi$
$139$			17.0710i			1.44794i	−0.689831	+	0.723971i	$0.742315\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.320065	−	0.554369i	0.0267652	−	0.0463587i
$144$		0			0
$145$	16.4703	−	9.50912i	1.36778	−	0.789690i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	9.31162	−	5.37607i	0.762838	−	0.440425i	−0.0674758	−	0.997721i	$-0.521495\pi$
$149$	9.31162	−	5.37607i	0.762838	−	0.440425i	0.830314	+	0.557296i	$0.188161\pi$
$150$		0			0
$151$	−3.78223	+	6.55102i	−0.307794	+	0.533115i	−0.977879	−	0.209169i	$-0.932924\pi$
$151$	−3.78223	+	6.55102i	−0.307794	+	0.533115i	0.670086	+	0.742284i	$0.266257\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	9.68135i		−	0.777625i
$156$		0			0
$157$	10.6317	+	6.13820i	0.848500	+	0.489882i	0.860144	−	0.510051i	$-0.170373\pi$
$157$	10.6317	+	6.13820i	0.848500	+	0.489882i	−0.0116445	+	0.999932i	$0.503707\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	18.0615	+	15.2088i	1.42345	+	1.19862i
$162$		0			0
$163$	5.91745	+	10.2493i	0.463490	+	0.802789i	0.999132	−	0.0416566i	$-0.0132635\pi$
$163$	5.91745	+	10.2493i	0.463490	+	0.802789i	−0.535642	+	0.844445i	$0.679930\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.5771			1.05063			0.525313	−	0.850909i	$-0.323948\pi$
$167$	13.5771			1.05063			0.525313	+	0.850909i	$0.323948\pi$
$168$		0			0
$169$	10.6588			0.819904
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.31085	−	14.3948i	−0.631862	−	1.09442i	−0.987171	−	0.159668i	$-0.948957\pi$
$173$	−8.31085	−	14.3948i	−0.631862	−	1.09442i	0.355308	−	0.934749i	$-0.384376\pi$
$174$		0			0
$175$	−6.57908	−	1.17183i	−0.497331	−	0.0885819i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.8080	−	8.54942i	−1.10680	−	0.639014i	−0.168805	−	0.985650i	$-0.553991\pi$
$179$	−14.8080	−	8.54942i	−1.10680	−	0.639014i	−0.938000	+	0.346636i	$0.887324\pi$
$180$		0			0
$181$			18.2171i			1.35407i	0.735952	+	0.677034i	$0.236735\pi$
$181$			18.2171i			1.35407i	−0.735952	+	0.677034i	$0.763265\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.4783	+	21.6130i	−0.917422	+	1.58902i
$186$		0			0
$187$	−1.41510	+	0.817009i	−0.103482	+	0.0597456i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	18.1860	−	10.4997i	1.31589	−	0.759730i	0.332826	−	0.942988i	$-0.391998\pi$
$191$	18.1860	−	10.4997i	1.31589	−	0.759730i	0.983065	+	0.183258i	$0.0586644\pi$
$192$		0			0
$193$	3.48741	−	6.04038i	0.251030	−	0.434796i	−0.712780	−	0.701388i	$-0.752564\pi$
$193$	3.48741	−	6.04038i	0.251030	−	0.434796i	0.963810	+	0.266592i	$0.0858975\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			16.0756i			1.14534i	0.819786	+	0.572670i	$0.194092\pi$
$197$			16.0756i			1.14534i	−0.819786	+	0.572670i	$0.805908\pi$
$198$		0			0
$199$	−5.44956	−	3.14630i	−0.386309	−	0.223036i	0.294251	−	0.955728i	$-0.404930\pi$
$199$	−5.44956	−	3.14630i	−0.386309	−	0.223036i	−0.680560	+	0.732693i	$0.738263\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−17.2466	+	6.24341i	−1.21047	+	0.438201i
$204$		0			0
$205$	−2.91440	−	5.04788i	−0.203550	−	0.352559i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.47331			0.171083
$210$		0			0
$211$	2.59627			0.178735			0.0893674	−	0.995999i	$-0.471515\pi$
$211$	2.59627			0.178735			0.0893674	+	0.995999i	$0.471515\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.8522	−	27.4568i	−1.08111	−	1.87254i
$216$		0			0
$217$	−1.63729	+	9.19236i	−0.111147	+	0.624018i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	5.17565	+	2.98816i	0.348152	+	0.201006i
$222$		0			0
$223$			23.9272i			1.60228i	0.598476	+	0.801141i	$0.295773\pi$
$223$			23.9272i			1.60228i	−0.598476	+	0.801141i	$0.704227\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.86609	−	3.23216i	0.123857	−	0.214526i	−0.797429	−	0.603413i	$-0.793807\pi$
$227$	1.86609	−	3.23216i	0.123857	−	0.214526i	0.921285	+	0.388887i	$0.127140\pi$
$228$		0			0
$229$	−18.2455	+	10.5341i	−1.20570	+	0.696111i	−0.961817	−	0.273694i	$-0.911754\pi$
$229$	−18.2455	+	10.5341i	−1.20570	+	0.696111i	−0.243882	+	0.969805i	$0.578421\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.0542	−	6.38215i	0.724186	−	0.418109i	−0.0921057	−	0.995749i	$-0.529360\pi$
$233$	11.0542	−	6.38215i	0.724186	−	0.418109i	0.816291	+	0.577640i	$0.196026\pi$
$234$		0			0
$235$	−2.42886	+	4.20691i	−0.158441	+	0.274429i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	12.7618i		−	0.825494i	−0.910846	−	0.412747i	$-0.864569\pi$
$239$		−	12.7618i		−	0.825494i	0.910846	−	0.412747i	$-0.135431\pi$
$240$		0			0
$241$	2.63438	+	1.52096i	0.169695	+	0.0979737i	0.582442	−	0.812872i	$-0.302097\pi$
$241$	2.63438	+	1.52096i	0.169695	+	0.0979737i	−0.412747	+	0.910846i	$0.635431\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	18.0223	+	6.63039i	1.15140	+	0.423600i
$246$		0			0
$247$	−4.52301	−	7.83408i	−0.287792	−	0.498470i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.32067			0.398957			0.199478	−	0.979902i	$-0.436075\pi$
$251$	6.32067			0.398957			0.199478	+	0.979902i	$0.436075\pi$
$252$		0			0
$253$	−3.73361			−0.234730
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.2538	+	21.2242i	0.764372	+	1.32393i	0.940578	+	0.339577i	$0.110284\pi$
$257$	12.2538	+	21.2242i	0.764372	+	1.32393i	−0.176206	+	0.984353i	$0.556383\pi$
$258$		0			0
$259$	15.5032	−	18.4111i	0.963320	−	1.14401i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−21.1163	−	12.1915i	−1.30208	−	0.751759i	−0.321323	−	0.946970i	$-0.604128\pi$
$263$	−21.1163	−	12.1915i	−1.30208	−	0.751759i	−0.980761	+	0.195211i	$0.937461\pi$
$264$		0			0
$265$		−	10.7552i		−	0.660686i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.94525	+	8.56542i	−0.301517	+	0.522243i	−0.976480	−	0.215609i	$-0.930826\pi$
$269$	−4.94525	+	8.56542i	−0.301517	+	0.522243i	0.674963	+	0.737852i	$0.264160\pi$
$270$		0			0
$271$	−5.10505	+	2.94740i	−0.310110	+	0.179042i	−0.646976	−	0.762511i	$-0.723966\pi$
$271$	−5.10505	+	2.94740i	−0.310110	+	0.179042i	0.336866	+	0.941553i	$0.390633\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.915111	−	0.528340i	0.0551833	−	0.0318601i
$276$		0			0
$277$	−11.6469	+	20.1731i	−0.699796	+	1.21208i	0.268741	+	0.963213i	$0.413392\pi$
$277$	−11.6469	+	20.1731i	−0.699796	+	1.21208i	−0.968537	+	0.248870i	$0.919941\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			25.1680i			1.50140i	0.660644	+	0.750700i	$0.270283\pi$
$281$			25.1680i			1.50140i	−0.660644	+	0.750700i	$0.729717\pi$
$282$		0			0
$283$	8.62942	+	4.98220i	0.512966	+	0.296161i	0.734052	−	0.679093i	$-0.237627\pi$
$283$	8.62942	+	4.98220i	0.512966	+	0.296161i	−0.221086	+	0.975254i	$0.570960\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.91350	+	5.28579i	0.112951	+	0.312011i
$288$		0			0
$289$	0.872317	+	1.51090i	0.0513128	+	0.0888764i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−13.5813			−0.793429			−0.396714	−	0.917942i	$-0.629850\pi$
$293$	−13.5813			−0.793429			−0.396714	+	0.917942i	$0.629850\pi$
$294$		0			0
$295$	11.1229			0.647603
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.82774	+	11.8260i	0.394858	+	0.683915i
$300$		0			0
$301$	10.4081	+	28.7508i	0.599911	+	1.65717i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−4.42933	−	2.55728i	−0.253623	−	0.146429i
$306$		0			0
$307$		−	16.9849i		−	0.969381i	−0.874686	−	0.484691i	$-0.838932\pi$
$307$		−	16.9849i		−	0.969381i	0.874686	−	0.484691i	$-0.161068\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.00148940	−	0.00257972i	8.44563e−5	−	0.000146283i	−0.865983	−	0.500073i	$-0.833306\pi$
$311$	0.00148940	−	0.00257972i	8.44563e−5	−	0.000146283i	0.866068	+	0.499927i	$0.166640\pi$
$312$		0			0
$313$	10.6154	−	6.12878i	0.600015	−	0.346419i	−0.169032	−	0.985611i	$-0.554064\pi$
$313$	10.6154	−	6.12878i	0.600015	−	0.346419i	0.769048	+	0.639191i	$0.220731\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.0008	+	11.5475i	−1.12336	+	0.648571i	−0.942256	−	0.334894i	$-0.891300\pi$
$317$	−20.0008	+	11.5475i	−1.12336	+	0.648571i	−0.181102	+	0.983464i	$0.557966\pi$
$318$		0			0
$319$	1.45014	−	2.51172i	0.0811922	−	0.140629i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			23.0911i			1.28482i
$324$		0			0
$325$	−3.34697	−	1.93237i	−0.185656	−	0.107189i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.01765	−	3.58366i	0.166368	−	0.197574i
$330$		0			0
$331$	1.73106	+	2.99829i	0.0951479	+	0.164801i	0.909670	−	0.415331i	$-0.136334\pi$
$331$	1.73106	+	2.99829i	0.0951479	+	0.164801i	−0.814522	+	0.580132i	$0.803001\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−35.0289			−1.91383
$336$		0			0
$337$	18.2604			0.994705			0.497352	−	0.867549i	$-0.334306\pi$
$337$	18.2604			0.994705			0.497352	+	0.867549i	$0.334306\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.738202	−	1.27860i	−0.0399759	−	0.0692403i
$342$		0			0
$343$	−15.9907	−	9.34339i	−0.863414	−	0.504496i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.62386	+	2.66959i	0.248222	+	0.143311i	0.618950	−	0.785431i	$-0.287558\pi$
$347$	4.62386	+	2.66959i	0.248222	+	0.143311i	−0.370728	+	0.928741i	$0.620892\pi$
$348$		0			0
$349$			0.0157983i			0.000845662i	1.00000		0.000422831i	$0.000134591\pi$
$349$			0.0157983i			0.000845662i	−1.00000		0.000422831i	$0.999865\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.1543	+	29.7121i	−0.913029	+	1.58141i	−0.103268	+	0.994654i	$0.532930\pi$
$353$	−17.1543	+	29.7121i	−0.913029	+	1.58141i	−0.809761	+	0.586760i	$0.800403\pi$
$354$		0			0
$355$	−20.2184	+	11.6731i	−1.07308	+	0.619544i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.42754	−	3.13359i	0.286454	−	0.165385i	−0.349887	−	0.936792i	$-0.613780\pi$
$359$	5.42754	−	3.13359i	0.286454	−	0.165385i	0.636342	+	0.771407i	$0.280447\pi$
$360$		0			0
$361$	7.97583	−	13.8145i	0.419781	−	0.727081i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	5.22861i		−	0.273678i
$366$		0			0
$367$	−16.4888	−	9.51984i	−0.860711	−	0.496931i	0.00353959	−	0.999994i	$-0.498873\pi$
$367$	−16.4888	−	9.51984i	−0.860711	−	0.496931i	−0.864250	+	0.503062i	$0.832207\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.81890	+	10.2120i	−0.0944324	+	0.530179i
$372$		0			0
$373$	−5.41901	−	9.38600i	−0.280586	−	0.485989i	0.690943	−	0.722909i	$-0.257195\pi$
$373$	−5.41901	−	9.38600i	−0.280586	−	0.485989i	−0.971529	+	0.236920i	$0.923862\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−10.6076			−0.546320
$378$		0			0
$379$	0.700312			0.0359726			0.0179863	−	0.999838i	$-0.494274\pi$
$379$	0.700312			0.0359726			0.0179863	+	0.999838i	$0.494274\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−19.0235	−	32.9497i	−0.972056	−	1.68365i	−0.689327	−	0.724451i	$-0.742094\pi$
$383$	−19.0235	−	32.9497i	−0.972056	−	1.68365i	−0.282729	−	0.959200i	$-0.591240\pi$
$384$		0			0
$385$	−2.85515	+	1.03359i	−0.145512	+	0.0526767i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.6958	+	9.63934i	0.846512	+	0.488734i	0.859473	−	0.511182i	$-0.170792\pi$
$389$	16.6958	+	9.63934i	0.846512	+	0.488734i	−0.0129603	+	0.999916i	$0.504125\pi$
$390$		0			0
$391$		−	34.8574i		−	1.76281i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.18959	−	2.06044i	0.0598549	−	0.103672i
$396$		0			0
$397$	−17.3610	+	10.0234i	−0.871325	+	0.503059i	−0.867788	−	0.496934i	$-0.834459\pi$
$397$	−17.3610	+	10.0234i	−0.871325	+	0.503059i	−0.00353639	+	0.999994i	$0.501126\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	26.4232	−	15.2554i	1.31951	−	0.761820i	0.335861	−	0.941912i	$-0.390973\pi$
$401$	26.4232	−	15.2554i	1.31951	−	0.761820i	0.983650	+	0.180092i	$0.0576395\pi$
$402$		0			0
$403$	−2.69993	+	4.67642i	−0.134493	+	0.232949i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			3.80587i			0.188650i
$408$		0			0
$409$	0.150631	+	0.0869667i	0.00744821	+	0.00430023i	0.503719	−	0.863867i	$-0.331965\pi$
$409$	0.150631	+	0.0869667i	0.00744821	+	0.00430023i	−0.496271	+	0.868168i	$0.665298\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−10.5611	−	1.88109i	−0.519680	−	0.0925624i
$414$		0			0
$415$	−9.48860	−	16.4347i	−0.465777	−	0.806749i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−28.1380			−1.37463			−0.687316	−	0.726359i	$-0.741211\pi$
$419$	−28.1380			−1.37463			−0.687316	+	0.726359i	$0.741211\pi$
$420$		0			0
$421$	3.12259			0.152186			0.0760929	−	0.997101i	$-0.475755\pi$
$421$	3.12259			0.152186			0.0760929	+	0.997101i	$0.475755\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.93264	+	8.54358i	0.239268	+	0.414424i
$426$		0			0
$427$	3.77313	+	3.17719i	0.182595	+	0.153755i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.58876	−	4.95872i	−0.413706	−	0.238853i	0.278675	−	0.960385i	$-0.410105\pi$
$431$	−8.58876	−	4.95872i	−0.413706	−	0.238853i	−0.692381	+	0.721532i	$0.743438\pi$
$432$		0			0
$433$		−	17.1274i		−	0.823092i	−0.911389	−	0.411546i	$-0.864989\pi$
$433$		−	17.1274i		−	0.823092i	0.911389	−	0.411546i	$-0.135011\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−26.3808	+	45.6929i	−1.26196	+	2.18579i
$438$		0			0
$439$	18.5795	−	10.7269i	0.886750	−	0.511965i	0.0138721	−	0.999904i	$-0.495584\pi$
$439$	18.5795	−	10.7269i	0.886750	−	0.511965i	0.872878	+	0.487938i	$0.162251\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.84340	−	3.37369i	0.277628	−	0.160289i	−0.354721	−	0.934972i	$-0.615424\pi$
$443$	5.84340	−	3.37369i	0.277628	−	0.160289i	0.632349	+	0.774683i	$0.282091\pi$
$444$		0			0
$445$	13.4111	−	23.2287i	0.635747	−	1.10115i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			5.81624i			0.274485i	0.990537	+	0.137243i	$0.0438240\pi$
$449$			5.81624i			0.274485i	−0.990537	+	0.137243i	$0.956176\pi$
$450$		0			0
$451$	−0.769801	−	0.444445i	−0.0362485	−	0.0209281i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	8.49512	+	7.15338i	0.398258	+	0.335356i
$456$		0			0
$457$	16.6949	+	28.9164i	0.780954	+	1.35265i	0.931386	+	0.364032i	$0.118600\pi$
$457$	16.6949	+	28.9164i	0.780954	+	1.35265i	−0.150432	+	0.988620i	$0.548066\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−37.0308			−1.72469			−0.862347	−	0.506317i	$-0.831007\pi$
$461$	−37.0308			−1.72469			−0.862347	+	0.506317i	$0.831007\pi$
$462$		0			0
$463$	−21.1236			−0.981695			−0.490848	−	0.871245i	$-0.663313\pi$
$463$	−21.1236			−0.981695			−0.490848	+	0.871245i	$0.663313\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.30470	−	16.1162i	−0.430570	−	0.745770i	0.566352	−	0.824163i	$-0.308354\pi$
$467$	−9.30470	−	16.1162i	−0.430570	−	0.745770i	−0.996922	+	0.0783937i	$0.975021\pi$
$468$		0			0
$469$	33.2596	+	5.92402i	1.53579	+	0.273546i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−4.18715	−	2.41745i	−0.192525	−	0.111155i
$474$		0			0
$475$		−	14.9325i		−	0.685149i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.16703	+	12.4137i	−0.327470	+	0.567194i	−0.982009	−	0.188834i	$-0.939529\pi$
$479$	−7.16703	+	12.4137i	−0.327470	+	0.567194i	0.654539	+	0.756028i	$0.272863\pi$
$480$		0			0
$481$	12.0549	−	6.95988i	0.549655	−	0.317343i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.549791	+	0.317422i	−0.0249647	+	0.0144134i
$486$		0			0
$487$	−5.64829	+	9.78313i	−0.255949	+	0.443316i	−0.965153	−	0.261687i	$-0.915721\pi$
$487$	−5.64829	+	9.78313i	−0.255949	+	0.443316i	0.709204	+	0.705003i	$0.249054\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			10.2087i			0.460711i	0.973107	+	0.230356i	$0.0739889\pi$
$491$			10.2087i			0.460711i	−0.973107	+	0.230356i	$0.926011\pi$
$492$		0			0
$493$	23.4496	+	13.5387i	1.05612	+	0.609751i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.1713	−	7.66422i	0.949665	−	0.343787i
$498$		0			0
$499$	9.56672	+	16.5701i	0.428265	+	0.741777i	0.996719	−	0.0809379i	$-0.0257915\pi$
$499$	9.56672	+	16.5701i	0.428265	+	0.741777i	−0.568454	+	0.822715i	$0.692458\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−0.268917			−0.0119904			−0.00599520	−	0.999982i	$-0.501908\pi$
$503$	−0.268917			−0.0119904			−0.00599520	+	0.999982i	$0.501908\pi$
$504$		0			0
$505$	−39.1763			−1.74332
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−10.9439	−	18.9553i	−0.485079	−	0.840181i	0.514774	−	0.857326i	$-0.327876\pi$
$509$	−10.9439	−	18.9553i	−0.485079	−	0.840181i	−0.999853	+	0.0171449i	$0.994542\pi$
$510$		0			0
$511$	−0.884252	+	4.96452i	−0.0391170	+	0.219617i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−25.5298	−	14.7396i	−1.12498	−	0.649506i
$516$		0			0
$517$			0.740802i			0.0325804i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.856074	+	1.48276i	−0.0375053	+	0.0649610i	−0.884169	−	0.467168i	$-0.845274\pi$
$521$	−0.856074	+	1.48276i	−0.0375053	+	0.0649610i	0.846663	+	0.532129i	$0.178608\pi$
$522$		0			0
$523$	7.16320	−	4.13568i	0.313225	−	0.180841i	−0.335144	−	0.942167i	$-0.608785\pi$
$523$	7.16320	−	4.13568i	0.313225	−	0.180841i	0.648369	+	0.761326i	$0.275452\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11.9372	−	6.89193i	0.519992	−	0.300217i
$528$		0			0
$529$	28.3233	−	49.0574i	1.23145	−	2.13293i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			3.25106i			0.140819i
$534$		0			0
$535$	−15.1029	−	8.71966i	−0.652955	−	0.376984i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.88574	−	0.498528i	0.124298	−	0.0214731i
$540$		0			0
$541$	−10.1997	−	17.6664i	−0.438518	−	0.759536i	0.559057	−	0.829129i	$-0.311163\pi$
$541$	−10.1997	−	17.6664i	−0.438518	−	0.759536i	−0.997575	+	0.0695932i	$0.977830\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−14.1575			−0.606441
$546$		0			0
$547$	−37.9261			−1.62160			−0.810801	−	0.585322i	$-0.800968\pi$
$547$	−37.9261			−1.62160			−0.810801	+	0.585322i	$0.800968\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−20.4927	−	35.4943i	−0.873017	−	1.51211i
$552$		0			0
$553$	−1.47796	+	1.75518i	−0.0628494	+	0.0746380i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.5919	−	8.42463i	−0.618278	−	0.356963i	0.157920	−	0.987452i	$-0.449521\pi$
$557$	−14.5919	−	8.42463i	−0.618278	−	0.356963i	−0.776198	+	0.630489i	$0.782854\pi$
$558$		0			0
$559$			17.6834i			0.747928i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.28035	+	14.3420i	−0.348975	+	0.604443i	−0.986068	−	0.166345i	$-0.946804\pi$
$563$	−8.28035	+	14.3420i	−0.348975	+	0.604443i	0.637093	+	0.770787i	$0.280137\pi$
$564$		0			0
$565$	−25.2162	+	14.5586i	−1.06085	+	0.612484i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.49856	−	3.17460i	0.230512	−	0.133086i	−0.380296	−	0.924865i	$-0.624178\pi$
$569$	5.49856	−	3.17460i	0.230512	−	0.133086i	0.610808	+	0.791779i	$0.290845\pi$
$570$		0			0
$571$	−22.8703	+	39.6125i	−0.957092	+	1.65773i	−0.227585	+	0.973758i	$0.573083\pi$
$571$	−22.8703	+	39.6125i	−0.957092	+	1.65773i	−0.729507	+	0.683973i	$0.760250\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			22.5414i			0.940043i
$576$		0			0
$577$	15.3719	+	8.87497i	0.639940	+	0.369470i	0.784592	−	0.620013i	$-0.212873\pi$
$577$	15.3719	+	8.87497i	0.639940	+	0.369470i	−0.144651	+	0.989483i	$0.546206\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.22993	+	17.2093i	0.258461	+	0.713963i
$582$		0			0
$583$	−0.820082	−	1.42042i	−0.0339643	−	0.0588280i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.82297			0.364163			0.182081	−	0.983283i	$-0.441717\pi$
$587$	8.82297			0.364163			0.182081	+	0.983283i	$0.441717\pi$
$588$		0			0
$589$	−20.8638			−0.859679
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.24849	−	7.35860i	−0.174465	−	0.302181i	0.765511	−	0.643422i	$-0.222486\pi$
$593$	−4.24849	−	7.35860i	−0.174465	−	0.302181i	−0.939976	+	0.341241i	$0.889153\pi$
$594$		0			0
$595$	−9.64972	−	26.6560i	−0.395600	−	1.09279i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.21158	+	1.85421i	0.131222	+	0.0757609i	0.564174	−	0.825656i	$-0.309195\pi$
$599$	3.21158	+	1.85421i	0.131222	+	0.0757609i	−0.432952	+	0.901417i	$0.642528\pi$
$600$		0			0
$601$		−	7.09036i		−	0.289222i	−0.989489	−	0.144611i	$-0.953807\pi$
$601$		−	7.09036i		−	0.289222i	0.989489	−	0.144611i	$-0.0461930\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−14.8482	+	25.7178i	−0.603664	+	1.04558i
$606$		0			0
$607$	29.4396	−	16.9970i	1.19492	−	0.689886i	0.235500	−	0.971874i	$-0.424327\pi$
$607$	29.4396	−	16.9970i	1.19492	−	0.689886i	0.959418	+	0.281988i	$0.0909939\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.34644	−	1.35472i	0.0949270	−	0.0548061i
$612$		0			0
$613$	−11.6761	+	20.2237i	−0.471595	+	0.816827i	−0.999472	−	0.0324944i	$-0.989655\pi$
$613$	−11.6761	+	20.2237i	−0.471595	+	0.816827i	0.527877	+	0.849321i	$0.322988\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			45.1277i			1.81677i	0.418133	+	0.908386i	$0.362684\pi$
$617$			45.1277i			1.81677i	−0.418133	+	0.908386i	$0.637316\pi$
$618$		0			0
$619$	7.97914	+	4.60676i	0.320709	+	0.185161i	0.651708	−	0.758470i	$-0.274053\pi$
$619$	7.97914	+	4.60676i	0.320709	+	0.185161i	−0.331000	+	0.943631i	$0.607386\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.6621	+	19.7874i	−0.667554	+	0.792765i
$624$		0			0
$625$	15.6247	+	27.0627i	0.624987	+	1.08251i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−35.5320			−1.41675
$630$		0			0
$631$	17.6136			0.701188			0.350594	−	0.936528i	$-0.385980\pi$
$631$	17.6136			0.701188			0.350594	+	0.936528i	$0.385980\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−14.1156	−	24.4489i	−0.560160	−	0.970226i
$636$		0			0
$637$	−6.85628	−	8.22875i	−0.271656	−	0.326035i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	16.5759	+	9.57009i	0.654708	+	0.377996i	0.790258	−	0.612775i	$-0.209947\pi$
$641$	16.5759	+	9.57009i	0.654708	+	0.377996i	−0.135550	+	0.990771i	$0.543280\pi$
$642$		0			0
$643$		−	2.32244i		−	0.0915882i	−0.998951	−	0.0457941i	$-0.985418\pi$
$643$		−	2.32244i		−	0.0915882i	0.998951	−	0.0457941i	$-0.0145818\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.9310	+	22.3971i	−0.508370	+	0.880522i	0.491583	+	0.870831i	$0.336418\pi$
$647$	−12.9310	+	22.3971i	−0.508370	+	0.880522i	−0.999953	+	0.00969167i	$0.996915\pi$
$648$		0			0
$649$	1.46899	−	0.848123i	0.0576630	−	0.0332918i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−20.1140	+	11.6128i	−0.787123	+	0.454446i	−0.838949	−	0.544211i	$-0.816829\pi$
$653$	−20.1140	+	11.6128i	−0.787123	+	0.454446i	0.0518258	+	0.998656i	$0.483496\pi$
$654$		0			0
$655$	−26.9681	+	46.7102i	−1.05373	+	1.82512i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			15.8196i			0.616245i	0.951347	+	0.308122i	$0.0997006\pi$
$659$			15.8196i			0.616245i	−0.951347	+	0.308122i	$0.900299\pi$
$660$		0			0
$661$	15.8006	+	9.12248i	0.614572	+	0.354823i	0.774753	−	0.632264i	$-0.217874\pi$
$661$	15.8006	+	9.12248i	0.614572	+	0.354823i	−0.160181	+	0.987088i	$0.551208\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−7.52447	+	42.2452i	−0.291787	+	1.63820i
$666$		0			0
$667$	30.9349	+	53.5807i	1.19780	+	2.07465i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.779968			−0.0301103
$672$		0			0
$673$	−28.8367			−1.11157			−0.555787	−	0.831325i	$-0.687583\pi$
$673$	−28.8367			−1.11157			−0.555787	+	0.831325i	$0.687583\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−16.7668	−	29.0409i	−0.644400	−	1.11613i	−0.984440	−	0.175722i	$-0.943774\pi$
$677$	−16.7668	−	29.0409i	−0.644400	−	1.11613i	0.340040	−	0.940411i	$-0.389559\pi$
$678$		0			0
$679$	0.575703	−	0.208410i	0.0220935	−	0.00799803i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.0943	+	11.0241i	0.730621	+	0.421824i	0.818649	−	0.574294i	$-0.194723\pi$
$683$	19.0943	+	11.0241i	0.730621	+	0.421824i	−0.0880282	+	0.996118i	$0.528057\pi$
$684$		0			0
$685$			14.7745i			0.564506i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.99941	+	5.19512i	−0.114268	+	0.197918i
$690$		0			0
$691$	22.8662	−	13.2018i	0.869869	−	0.502219i	0.00256453	−	0.999997i	$-0.499184\pi$
$691$	22.8662	−	13.2018i	0.869869	−	0.502219i	0.867305	+	0.497777i	$0.165850\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	40.5569	−	23.4156i	1.53841	−	0.888203i
$696$		0			0
$697$	4.14938	−	7.18694i	0.157169	−	0.272225i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	20.5140i		−	0.774804i	−0.921911	−	0.387402i	$-0.873373\pi$
$701$		−	20.5140i		−	0.774804i	0.921911	−	0.387402i	$-0.126627\pi$
$702$		0			0
$703$	46.5772	+	26.8913i	1.75669	+	1.01423i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	37.1975	+	6.62541i	1.39896	+	0.249174i
$708$		0			0
$709$	3.13054	+	5.42226i	0.117570	+	0.203637i	0.918804	−	0.394714i	$-0.129156\pi$
$709$	3.13054	+	5.42226i	0.117570	+	0.203637i	−0.801234	+	0.598351i	$0.795823\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	31.4951			1.17950
$714$		0			0
$715$	−1.75608			−0.0656737
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.6111	+	20.1111i	0.433023	+	0.750017i	0.997132	−	0.0756828i	$-0.0241136\pi$
$719$	11.6111	+	20.1111i	0.433023	+	0.750017i	−0.564109	+	0.825700i	$0.690780\pi$
$720$		0			0
$721$	21.7476	+	18.3127i	0.809922	+	0.682001i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−15.1643	−	8.75512i	−0.563189	−	0.325157i
$726$		0			0
$727$		−	2.89828i		−	0.107491i	−0.998555	−	0.0537457i	$-0.982884\pi$
$727$		−	2.89828i		−	0.107491i	0.998555	−	0.0537457i	$-0.0171160\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	22.5696	−	39.0917i	0.834767	−	1.44586i
$732$		0			0
$733$	−10.2963	+	5.94457i	−0.380302	+	0.219568i	−0.677950	−	0.735108i	$-0.737131\pi$
$733$	−10.2963	+	5.94457i	−0.380302	+	0.219568i	0.297647	+	0.954676i	$0.403798\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.62622	+	2.67095i	−0.170409	+	0.0983858i
$738$		0			0
$739$	17.2254	−	29.8354i	0.633648	−	1.09751i	−0.353151	−	0.935566i	$-0.614890\pi$
$739$	17.2254	−	29.8354i	0.633648	−	1.09751i	0.986800	−	0.161945i	$-0.0517767\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			2.81826i			0.103392i	0.998663	+	0.0516960i	$0.0164627\pi$
$743$			2.81826i			0.103392i	−0.998663	+	0.0516960i	$0.983537\pi$
$744$		0			0
$745$	−25.5447	−	14.7483i	−0.935887	−	0.540335i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	12.8654	+	10.8334i	0.470092	+	0.395844i
$750$		0			0
$751$	−3.86045	−	6.68649i	−0.140870	−	0.243993i	0.786955	−	0.617011i	$-0.211657\pi$
$751$	−3.86045	−	6.68649i	−0.140870	−	0.243993i	−0.927824	+	0.373017i	$0.878323\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	20.7517			0.755233
$756$		0			0
$757$	1.17924			0.0428603			0.0214302	−	0.999770i	$-0.493178\pi$
$757$	1.17924			0.0428603			0.0214302	+	0.999770i	$0.493178\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.56644	+	2.71316i	0.0567835	+	0.0983520i	0.893020	−	0.450017i	$-0.148582\pi$
$761$	1.56644	+	2.71316i	0.0567835	+	0.0983520i	−0.836236	+	0.548369i	$0.815249\pi$
$762$		0			0
$763$	13.4424	+	2.39429i	0.486648	+	0.0866791i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.37276	−	3.10196i	−0.193999	−	0.112005i
$768$		0			0
$769$			6.39124i			0.230474i	0.993338	+	0.115237i	$0.0367627\pi$
$769$			6.39124i			0.230474i	−0.993338	+	0.115237i	$0.963237\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−23.9779	+	41.5309i	−0.862425	+	1.49376i	0.00715621	+	0.999974i	$0.497722\pi$
$773$	−23.9779	+	41.5309i	−0.862425	+	1.49376i	−0.869581	+	0.493790i	$0.835611\pi$
$774$		0			0
$775$	−7.71948	+	4.45685i	−0.277292	+	0.160095i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−10.8784	+	6.28067i	−0.389761	+	0.225028i
$780$		0			0
$781$	−1.78015	+	3.08331i	−0.0636987	+	0.110329i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	33.6781i		−	1.20202i
$786$		0			0
$787$	−5.23136	−	3.02033i	−0.186478	−	0.107663i	0.403855	−	0.914823i	$-0.367670\pi$
$787$	−5.23136	−	3.02033i	−0.186478	−	0.107663i	−0.590333	+	0.807160i	$0.701003\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	26.4047	−	9.55872i	0.938842	−	0.339869i
$792$		0			0
$793$	1.42635	+	2.47050i	0.0506510	+	0.0877301i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.56500			0.0554352			0.0277176	−	0.999616i	$-0.491176\pi$
$797$	1.56500			0.0554352			0.0277176	+	0.999616i	$0.491176\pi$
$798$		0			0
$799$	−6.91620			−0.244678
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.398681	−	0.690535i	−0.0140691	−	0.0243685i
$804$		0			0
$805$	11.3586	−	63.7716i	0.400339	−	2.24765i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	15.3445	+	8.85918i	0.539485	+	0.311472i	0.744870	−	0.667209i	$-0.232511\pi$
$809$	15.3445	+	8.85918i	0.539485	+	0.311472i	−0.205385	+	0.978681i	$0.565845\pi$
$810$		0			0
$811$		−	27.5261i		−	0.966571i	−0.875463	−	0.483285i	$-0.839443\pi$
$811$		−	27.5261i		−	0.966571i	0.875463	−	0.483285i	$-0.160557\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	16.2334	−	28.1171i	0.568633	−	0.984901i
$816$		0			0
$817$	−59.1707	+	34.1622i	−2.07012	+	1.19519i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.0343	+	13.2989i	−0.803903	+	0.464134i	−0.844834	−	0.535028i	$-0.820301\pi$
$821$	−23.0343	+	13.2989i	−0.803903	+	0.464134i	0.0409311	+	0.999162i	$0.486968\pi$
$822$		0			0
$823$	−12.0797	+	20.9227i	−0.421073	+	0.729319i	−0.996045	−	0.0888537i	$-0.971680\pi$
$823$	−12.0797	+	20.9227i	−0.421073	+	0.729319i	0.574972	+	0.818173i	$0.305013\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	9.64923i		−	0.335537i	−0.985826	−	0.167768i	$-0.946344\pi$
$827$		−	9.64923i		−	0.335537i	0.985826	−	0.167768i	$-0.0536561\pi$
$828$		0			0
$829$	−25.1481	−	14.5193i	−0.873430	−	0.504275i	−0.00494329	−	0.999988i	$-0.501574\pi$
$829$	−25.1481	−	14.5193i	−0.873430	−	0.504275i	−0.868486	+	0.495713i	$0.834907\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.65431	+	26.9416i	0.161262	+	0.933471i
$834$		0			0
$835$	−18.6231	−	32.2562i	−0.644480	−	1.11627i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	13.6877			0.472550			0.236275	−	0.971686i	$-0.424073\pi$
$839$	13.6877			0.472550			0.236275	+	0.971686i	$0.424073\pi$
$840$		0			0
$841$	−19.0605			−0.657260
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−14.6202	−	25.3229i	−0.502949	−	0.871134i
$846$		0			0
$847$	18.4476	−	21.9077i	0.633866	−	0.752759i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−70.3110	−	40.5941i	−2.41023	−	1.39155i
$852$		0			0
$853$		−	46.7866i		−	1.60194i	−0.598702	−	0.800972i	$-0.704317\pi$
$853$		−	46.7866i		−	1.60194i	0.598702	−	0.800972i	$-0.295683\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−15.8980	+	27.5361i	−0.543065	+	0.940616i	0.455661	+	0.890153i	$0.349403\pi$
$857$	−15.8980	+	27.5361i	−0.543065	+	0.940616i	−0.998726	+	0.0504623i	$0.983931\pi$
$858$		0			0
$859$	−21.9005	+	12.6442i	−0.747235	+	0.431416i	−0.824694	−	0.565579i	$-0.808653\pi$
$859$	−21.9005	+	12.6442i	−0.747235	+	0.431416i	0.0774592	+	0.996996i	$0.475319\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.9513	+	9.20946i	−0.542987	+	0.313494i	−0.746289	−	0.665622i	$-0.768166\pi$
$863$	−15.9513	+	9.20946i	−0.542987	+	0.313494i	0.203302	+	0.979116i	$0.434833\pi$
$864$		0			0
$865$	−22.7993	+	39.4896i	−0.775200	+	1.34269i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	0.362825i		−	0.0123080i
$870$		0			0
$871$	16.9202	+	9.76886i	0.573318	+	0.331005i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.11279	−	16.8857i	−0.206650	−	0.570842i
$876$		0			0
$877$	4.44695	+	7.70234i	0.150163	+	0.260089i	0.931287	−	0.364286i	$-0.118687\pi$
$877$	4.44695	+	7.70234i	0.150163	+	0.260089i	−0.781124	+	0.624375i	$0.785354\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−13.1721			−0.443780			−0.221890	−	0.975072i	$-0.571223\pi$
$881$	−13.1721			−0.443780			−0.221890	+	0.975072i	$0.571223\pi$
$882$		0			0
$883$	12.6729			0.426477			0.213239	−	0.977000i	$-0.431599\pi$
$883$	12.6729			0.426477			0.213239	+	0.977000i	$0.431599\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	16.6991	+	28.9238i	0.560703	+	0.971165i	0.997435	+	0.0715740i	$0.0228022\pi$
$887$	16.6991	+	28.9238i	0.560703	+	0.971165i	−0.436733	+	0.899591i	$0.643864\pi$
$888$		0			0
$889$	9.26788	+	25.6012i	0.310835	+	0.858638i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.06611	+	5.23432i	0.303386	+	0.175160i
$894$		0			0
$895$			46.9076i			1.56795i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.2328	+	21.1877i	−0.407985	+	0.706651i
$900$		0			0
$901$	13.2612	−	7.65638i	0.441796	−	0.255071i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	43.2799	−	24.9877i	1.43867	−	0.830618i
$906$		0			0
$907$	14.6563	−	25.3855i	0.486655	−	0.842912i	−0.513227	−	0.858253i	$-0.671550\pi$
$907$	14.6563	−	25.3855i	0.486655	−	0.842912i	0.999882	+	0.0153411i	$0.00488340\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			1.99249i			0.0660142i	0.999455	+	0.0330071i	$0.0105084\pi$
$911$			1.99249i			0.0660142i	−0.999455	+	0.0330071i	$0.989492\pi$
$912$		0			0
$913$	−2.50629	−	1.44701i	−0.0829462	−	0.0478890i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	33.5055	−	39.7901i	1.10645	−	1.31398i
$918$		0			0
$919$	−0.897678	−	1.55482i	−0.0296117	−	0.0512889i	0.850840	−	0.525425i	$-0.176094\pi$
$919$	−0.897678	−	1.55482i	−0.0296117	−	0.0512889i	−0.880451	+	0.474136i	$0.842760\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	13.0216			0.428611
$924$		0			0
$925$	22.9777			0.755502
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−12.4178	−	21.5083i	−0.407415	−	0.705664i	0.587184	−	0.809453i	$-0.300237\pi$
$929$	−12.4178	−	21.5083i	−0.407415	−	0.705664i	−0.994599	+	0.103789i	$0.966903\pi$
$930$		0			0
$931$	14.2888	−	38.8389i	0.468298	−	1.27289i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	3.88207	+	2.24132i	0.126957	+	0.0732988i
$936$		0			0
$937$		−	27.9046i		−	0.911605i	−0.890081	−	0.455802i	$-0.849352\pi$
$937$		−	27.9046i		−	0.911605i	0.890081	−	0.455802i	$-0.150648\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	26.2537	−	45.4728i	0.855847	−	1.48237i	−0.0200094	−	0.999800i	$-0.506370\pi$
$941$	26.2537	−	45.4728i	0.855847	−	1.48237i	0.875857	−	0.482571i	$-0.160297\pi$
$942$		0			0
$943$	16.4216	−	9.48104i	0.534762	−	0.308745i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	37.3591	−	21.5693i	1.21401	−	0.700907i	0.250377	−	0.968148i	$-0.419445\pi$
$947$	37.3591	−	21.5693i	1.21401	−	0.700907i	0.963630	+	0.267241i	$0.0861121\pi$
$948$		0			0
$949$	−1.45815	+	2.52559i	−0.0473336	+	0.0819843i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	59.9829i		−	1.94304i	−0.236965	−	0.971518i	$-0.576153\pi$
$953$		−	59.9829i		−	1.94304i	0.236965	−	0.971518i	$-0.423847\pi$
$954$		0			0
$955$	−49.8899	−	28.8040i	−1.61440	−	0.932074i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.49864	−	14.0283i	0.0806853	−	0.452997i
$960$		0			0
$961$	−9.27285	−	16.0610i	−0.299124	−	0.518098i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−19.1342			−0.615951
$966$		0			0
$967$	53.2795			1.71335			0.856677	−	0.515853i	$-0.172525\pi$
$967$	53.2795			1.71335			0.856677	+	0.515853i	$0.172525\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.1556	−	48.7669i	−0.903555	−	1.56500i	−0.822845	−	0.568266i	$-0.807615\pi$
$971$	−28.1556	−	48.7669i	−0.903555	−	1.56500i	−0.0807100	−	0.996738i	$-0.525719\pi$
$972$		0			0
$973$	−42.4685	+	15.3740i	−1.36148	+	0.492867i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	22.5755	+	13.0340i	0.722254	+	0.416994i	0.815582	−	0.578642i	$-0.196417\pi$
$977$	22.5755	+	13.0340i	0.722254	+	0.416994i	−0.0933275	+	0.995635i	$0.529750\pi$
$978$		0			0
$979$		−	4.09038i		−	0.130729i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.0252	+	32.9527i	−0.606811	+	1.05103i	0.384952	+	0.922937i	$0.374218\pi$
$983$	−19.0252	+	32.9527i	−0.606811	+	1.05103i	−0.991763	+	0.128090i	$0.959115\pi$
$984$		0			0
$985$	38.1922	−	22.0503i	1.21690	−	0.702580i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	89.3217	−	51.5699i	2.84026	−	1.63983i
$990$		0			0
$991$	−5.68758	+	9.85118i	−0.180672	+	0.312933i	−0.942110	−	0.335305i	$-0.891161\pi$
$991$	−5.68758	+	9.85118i	−0.180672	+	0.312933i	0.761438	+	0.648238i	$0.224494\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			17.2626i			0.547262i
$996$		0			0
$997$	44.1590	+	25.4952i	1.39853	+	0.807441i	0.994239	−	0.107189i	$-0.0341851\pi$
$997$	44.1590	+	25.4952i	1.39853	+	0.807441i	0.404290	+	0.914631i	$0.367518\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.t.a.1781.2		16
3.2	odd	2		2268.2.t.b.1781.7		16
7.5	odd	6		2268.2.t.b.2105.7		16
9.2	odd	6		756.2.bm.a.17.2		16
9.4	even	3		756.2.w.a.521.2		16
9.5	odd	6		252.2.w.a.101.7	yes	16
9.7	even	3		252.2.bm.a.185.5	yes	16
21.5	even	6	inner	2268.2.t.a.2105.2		16
36.7	odd	6		1008.2.df.d.689.4		16
36.11	even	6		3024.2.df.d.17.2		16
36.23	even	6		1008.2.ca.d.353.2		16
36.31	odd	6		3024.2.ca.d.2033.2		16
63.2	odd	6		5292.2.w.b.1097.7		16
63.4	even	3		5292.2.x.a.4409.2		16
63.5	even	6		252.2.bm.a.173.5	yes	16
63.11	odd	6		5292.2.x.b.881.7		16
63.13	odd	6		5292.2.w.b.521.7		16
63.16	even	3		1764.2.w.b.509.2		16
63.20	even	6		5292.2.bm.a.2285.7		16
63.23	odd	6		1764.2.bm.a.1685.4		16
63.25	even	3		1764.2.x.b.293.7		16
63.31	odd	6		5292.2.x.b.4409.7		16
63.32	odd	6		1764.2.x.a.1469.2		16
63.34	odd	6		1764.2.bm.a.1697.4		16
63.38	even	6		5292.2.x.a.881.2		16
63.40	odd	6		756.2.bm.a.89.2		16
63.41	even	6		1764.2.w.b.1109.2		16
63.47	even	6		756.2.w.a.341.2		16
63.52	odd	6		1764.2.x.a.293.2		16
63.58	even	3		5292.2.bm.a.4625.7		16
63.59	even	6		1764.2.x.b.1469.7		16
63.61	odd	6		252.2.w.a.5.7	✓	16
252.47	odd	6		3024.2.ca.d.2609.2		16
252.103	even	6		3024.2.df.d.1601.2		16
252.131	odd	6		1008.2.df.d.929.4		16
252.187	even	6		1008.2.ca.d.257.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	63.61	odd	6
252.2.w.a.101.7	yes	16	9.5	odd	6
252.2.bm.a.173.5	yes	16	63.5	even	6
252.2.bm.a.185.5	yes	16	9.7	even	3
756.2.w.a.341.2		16	63.47	even	6
756.2.w.a.521.2		16	9.4	even	3
756.2.bm.a.17.2		16	9.2	odd	6
756.2.bm.a.89.2		16	63.40	odd	6
1008.2.ca.d.257.2		16	252.187	even	6
1008.2.ca.d.353.2		16	36.23	even	6
1008.2.df.d.689.4		16	36.7	odd	6
1008.2.df.d.929.4		16	252.131	odd	6
1764.2.w.b.509.2		16	63.16	even	3
1764.2.w.b.1109.2		16	63.41	even	6
1764.2.x.a.293.2		16	63.52	odd	6
1764.2.x.a.1469.2		16	63.32	odd	6
1764.2.x.b.293.7		16	63.25	even	3
1764.2.x.b.1469.7		16	63.59	even	6
1764.2.bm.a.1685.4		16	63.23	odd	6
1764.2.bm.a.1697.4		16	63.34	odd	6
2268.2.t.a.1781.2		16	1.1	even	1	trivial
2268.2.t.a.2105.2		16	21.5	even	6	inner
2268.2.t.b.1781.7		16	3.2	odd	2
2268.2.t.b.2105.7		16	7.5	odd	6
3024.2.ca.d.2033.2		16	36.31	odd	6
3024.2.ca.d.2609.2		16	252.47	odd	6
3024.2.df.d.17.2		16	36.11	even	6
3024.2.df.d.1601.2		16	252.103	even	6
5292.2.w.b.521.7		16	63.13	odd	6
5292.2.w.b.1097.7		16	63.2	odd	6
5292.2.x.a.881.2		16	63.38	even	6
5292.2.x.a.4409.2		16	63.4	even	3
5292.2.x.b.881.7		16	63.11	odd	6
5292.2.x.b.4409.7		16	63.31	odd	6
5292.2.bm.a.2285.7		16	63.20	even	6
5292.2.bm.a.4625.7		16	63.58	even	3

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37166 - 2.37578i) q^{5} +(0.900590 + 2.48776i) q^{7} +O(q^{10})\)	\(q+(-1.37166 - 2.37578i) q^{5} +(0.900590 + 2.48776i) q^{7} +(-0.362306 - 0.209178i) q^{11} +1.53011i q^{13} +(1.95291 - 3.38253i) q^{17} +(-5.11994 + 2.95600i) q^{19} +(7.72884 - 4.46225i) q^{23} +(-1.26290 + 2.18740i) q^{25} +6.93257i q^{29} +(3.05626 + 1.76453i) q^{31} +(4.67507 - 5.55196i) q^{35} +(-4.54861 - 7.87842i) q^{37} +2.12472 q^{41} +11.5569 q^{43} +(-0.885373 - 1.53351i) q^{47} +(-5.37787 + 4.48090i) q^{49} +(3.39526 + 1.96025i) q^{53} +1.14768i q^{55} +(-2.02728 + 3.51135i) q^{59} +(1.61459 - 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(6.38441 - 11.0581i) q^{67} -8.51021i q^{71} +(1.65059 + 0.952971i) q^{73} +(0.194094 - 1.08971i) q^{77} +(0.433633 + 0.751074i) q^{79} +6.91761 q^{83} -10.7149 q^{85} +(4.88864 + 8.46738i) q^{89} +(-3.80655 + 1.37800i) q^{91} +(14.0456 + 8.10924i) q^{95} -0.231415i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{7}+O(q^{10}) \) 16 * q + 2 * q^7	\( 16 q + 2 q^{7} - 6 q^{11} - 9 q^{17} + 21 q^{23} - 8 q^{25} - 6 q^{31} + 15 q^{35} + q^{37} - 12 q^{41} + 4 q^{43} - 18 q^{47} - 8 q^{49} - 15 q^{59} - 3 q^{61} + 39 q^{65} - 7 q^{67} + 48 q^{77} - q^{79} - 12 q^{85} - 21 q^{89} + 9 q^{91} - 6 q^{95}+O(q^{100}) \) 16 * q + 2 * q^7 - 6 * q^11 - 9 * q^17 + 21 * q^23 - 8 * q^25 - 6 * q^31 + 15 * q^35 + q^37 - 12 * q^41 + 4 * q^43 - 18 * q^47 - 8 * q^49 - 15 * q^59 - 3 * q^61 + 39 * q^65 - 7 * q^67 + 48 * q^77 - q^79 - 12 * q^85 - 21 * q^89 + 9 * q^91 - 6 * q^95

Introduction

L-functions

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