LMFDB - Embedded newform 3024.2.df.d.1601.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(17,3024)]

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, 1]))

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

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

chi := DirichletCharacter("3024.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.df (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} - 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:	$\Z[a_1, \ldots, a_{19}]$
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			1601.2
Root			$-0.811340 + 1.53027i$ of defining polynomial
Character	$\chi$	$=$	3024.1601
Dual form			3024.2.df.d.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.74332 q^{5} +(-1.70417 - 2.02381i) q^{7} +O(q^{10})$	$q-2.74332 q^{5} +(-1.70417 - 2.02381i) q^{7} -0.418355i q^{11} +(-1.32512 + 0.765056i) q^{13} +(-1.95291 - 3.38253i) q^{17} +(5.11994 + 2.95600i) q^{19} -8.92450i q^{23} +2.52579 q^{25} +(-6.00378 - 3.46629i) q^{29} +(3.05626 + 1.76453i) q^{31} +(4.67507 + 5.55196i) q^{35} +(-4.54861 + 7.87842i) q^{37} +(1.06236 + 1.84006i) q^{41} +(5.77846 - 10.0086i) q^{43} +(-0.885373 - 1.53351i) q^{47} +(-1.19164 + 6.89783i) q^{49} +(-3.39526 + 1.96025i) q^{53} +1.14768i q^{55} +(-2.02728 + 3.51135i) q^{59} +(-1.61459 + 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(-6.38441 + 11.0581i) q^{67} +8.51021i q^{71} +(1.65059 - 0.952971i) q^{73} +(-0.846673 + 0.712947i) q^{77} +(-0.433633 - 0.751074i) q^{79} +(-3.45880 + 5.99082i) q^{83} +(5.35744 + 9.27936i) q^{85} +(-4.88864 + 8.46738i) q^{89} +(3.80655 + 1.37800i) q^{91} +(-14.0456 - 8.10924i) q^{95} +(-0.200411 - 0.115707i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{7}+O(q^{10}) $ 16 * q + q^7	$ 16 q + q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + 15 q^{35} + q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 13 q^{49} - 15 q^{59} + 3 q^{61} + 39 q^{65} + 7 q^{67} + 45 q^{77} + q^{79} + 6 q^{85} + 21 q^{89} - 9 q^{91} + 6 q^{95} + 3 q^{97}+O(q^{100}) $ 16 * q + q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + 15 * q^35 + q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 13 * q^49 - 15 * q^59 + 3 * q^61 + 39 * q^65 + 7 * q^67 + 45 * q^77 + q^79 + 6 * q^85 + 21 * q^89 - 9 * q^91 + 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−2.74332			−1.22685			−0.613425	−	0.789753i	$-0.710209\pi$
$5$	−2.74332			−1.22685			−0.613425	+	0.789753i	$0.710209\pi$
$6$		0			0
$7$	−1.70417	−	2.02381i	−0.644114	−	0.764929i
$7$	−1.70417	−	2.02381i	−0.644114	−	0.764929i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	0.418355i		−	0.126139i	−0.998009	−	0.0630695i	$-0.979911\pi$
$11$		−	0.418355i		−	0.126139i	0.998009	−	0.0630695i	$-0.0200890\pi$
$12$		0			0
$13$	−1.32512	+	0.765056i	−0.367521	+	0.212188i	−0.672375	−	0.740211i	$-0.734726\pi$
$13$	−1.32512	+	0.765056i	−0.367521	+	0.212188i	0.304854	+	0.952399i	$0.401392\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.95291	−	3.38253i	−0.473649	−	0.820385i	0.525896	−	0.850549i	$-0.323730\pi$
$17$	−1.95291	−	3.38253i	−0.473649	−	0.820385i	−0.999545	+	0.0301645i	$0.990397\pi$
$18$		0			0
$19$	5.11994	+	2.95600i	1.17459	+	0.678152i	0.954758	−	0.297385i	$-0.0961144\pi$
$19$	5.11994	+	2.95600i	1.17459	+	0.678152i	0.219836	+	0.975537i	$0.429448\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	8.92450i		−	1.86089i	−0.366436	−	0.930443i	$-0.619422\pi$
$23$		−	8.92450i		−	1.86089i	0.366436	−	0.930443i	$-0.380578\pi$
$24$		0			0
$25$	2.52579			0.505159
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.00378	−	3.46629i	−1.11487	−	0.643673i	−0.174787	−	0.984606i	$-0.555924\pi$
$29$	−6.00378	−	3.46629i	−1.11487	−	0.643673i	−0.940088	+	0.340933i	$0.889257\pi$
$30$		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	0.201095	+	0.979572i	$0.435550\pi$
$37$	−4.54861	+	7.87842i	−0.747787	+	1.29520i	−0.948881	+	0.315633i	$0.897783\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.06236	+	1.84006i	0.165913	+	0.287370i	0.936979	−	0.349385i	$-0.113610\pi$
$41$	1.06236	+	1.84006i	0.165913	+	0.287370i	−0.771066	+	0.636755i	$0.780276\pi$
$42$		0			0
$43$	5.77846	−	10.0086i	0.881208	−	1.52630i	0.0312079	−	0.999513i	$-0.490065\pi$
$43$	5.77846	−	10.0086i	0.881208	−	1.52630i	0.850000	−	0.526783i	$-0.176602\pi$
$44$		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
$49$	−1.19164	+	6.89783i	−0.170234	+	0.985404i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.39526	+	1.96025i	−0.466374	+	0.269261i	−0.714721	−	0.699410i	$-0.753446\pi$
$53$	−3.39526	+	1.96025i	−0.466374	+	0.269261i	0.248346	+	0.968671i	$0.420113\pi$
$54$		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	−0.599789	−	0.800158i	$-0.704749\pi$
$61$	−1.61459	+	0.932184i	−0.206727	+	0.119354i	0.393062	+	0.919512i	$0.371416\pi$
$62$		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	$0.451437\pi$
$67$	−6.38441	+	11.0581i	−0.779979	+	1.35096i	−0.931953	+	0.362579i	$0.881896\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			8.51021i			1.00998i	0.863126	+	0.504988i	$0.168503\pi$
$71$			8.51021i			1.00998i	−0.863126	+	0.504988i	$0.831497\pi$
$72$		0			0
$73$	1.65059	−	0.952971i	0.193187	−	0.111537i	−0.400286	−	0.916390i	$-0.631089\pi$
$73$	1.65059	−	0.952971i	0.193187	−	0.111537i	0.593474	+	0.804853i	$0.297756\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.846673	+	0.712947i	−0.0964874	+	0.0812479i
$78$		0			0
$79$	−0.433633	−	0.751074i	−0.0487875	−	0.0845024i	0.840600	−	0.541656i	$-0.182202\pi$
$79$	−0.433633	−	0.751074i	−0.0487875	−	0.0845024i	−0.889388	+	0.457153i	$0.848869\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.45880	+	5.99082i	−0.379653	+	0.657578i	−0.991012	−	0.133775i	$-0.957290\pi$
$83$	−3.45880	+	5.99082i	−0.379653	+	0.657578i	0.611359	+	0.791354i	$0.290623\pi$
$84$		0			0
$85$	5.35744	+	9.27936i	0.581096	+	1.00649i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.88864	+	8.46738i	−0.518195	+	0.897540i	0.481581	+	0.876401i	$0.340063\pi$
$89$	−4.88864	+	8.46738i	−0.518195	+	0.897540i	−0.999777	+	0.0211389i	$0.993271\pi$
$90$		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
$97$	−0.200411	−	0.115707i	−0.0203486	−	0.0117483i	0.489791	−	0.871840i	$-0.337073\pi$
$97$	−0.200411	−	0.115707i	−0.0203486	−	0.0117483i	−0.510140	+	0.860091i	$0.670406\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	14.2806			1.42097			0.710487	−	0.703710i	$-0.248475\pi$
$101$	14.2806			1.42097			0.710487	+	0.703710i	$0.248475\pi$
$102$		0			0
$103$			10.7458i			1.05882i	0.848366	+	0.529410i	$0.177587\pi$
$103$			10.7458i			1.05882i	−0.848366	+	0.529410i	$0.822413\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.50534	+	3.17851i	0.532221	+	0.307278i	0.741920	−	0.670488i	$-0.233915\pi$
$107$	5.50534	+	3.17851i	0.532221	+	0.307278i	−0.209699	+	0.977766i	$0.567249\pi$
$108$		0			0
$109$	2.58036	+	4.46932i	0.247154	+	0.428083i	0.962735	−	0.270447i	$-0.0871714\pi$
$109$	2.58036	+	4.46932i	0.247154	+	0.428083i	−0.715581	+	0.698530i	$0.753838\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.19186	+	5.30692i	−0.864697	+	0.499233i	−0.865582	−	0.500766i	$-0.833052\pi$
$113$	−9.19186	+	5.30692i	−0.864697	+	0.499233i	0.000885276		1.00000i	$0.499718\pi$
$114$		0			0
$115$			24.4827i			2.28303i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.51754	+	9.71671i	−0.322452	+	0.890730i
$120$		0			0
$121$	10.8250			0.984089
$122$		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	$-0.650927\pi$
$127$	−10.2909			−0.913169			−0.456584	+	0.889680i	$0.650927\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	19.6610			1.71779			0.858893	−	0.512155i	$-0.171153\pi$
$131$	19.6610			1.71779			0.858893	+	0.512155i	$0.171153\pi$
$132$		0			0
$133$	−2.74284	−	15.3993i	−0.237834	−	1.33529i
$134$		0			0
$135$		0			0
$136$		0			0
$137$			5.38565i			0.460127i	0.973176	+	0.230063i	$0.0738933\pi$
$137$			5.38565i			0.460127i	−0.973176	+	0.230063i	$0.926107\pi$
$138$		0			0
$139$	14.7839	−	8.53549i	1.25395	−	0.723971i	0.282062	−	0.959396i	$-0.408982\pi$
$139$	14.7839	−	8.53549i	1.25395	−	0.723971i	0.971892	+	0.235425i	$0.0756484\pi$
$140$		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
$149$			10.7521i			0.880849i	0.897790	+	0.440425i	$0.145172\pi$
$149$			10.7521i			0.880849i	−0.897790	+	0.440425i	$0.854828\pi$
$150$		0			0
$151$	−7.56447			−0.615588			−0.307794	−	0.951453i	$-0.599591\pi$
$151$	−7.56447			−0.615588			−0.307794	+	0.951453i	$0.599591\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−8.38430	−	4.84068i	−0.673443	−	0.388812i
$156$		0			0
$157$	−10.6317	−	6.13820i	−0.848500	−	0.489882i	0.0116445	−	0.999932i	$-0.496293\pi$
$157$	−10.6317	−	6.13820i	−0.848500	−	0.489882i	−0.860144	+	0.510051i	$0.829627\pi$
$158$		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	$-0.986736\pi$
$163$	−5.91745	+	10.2493i	−0.463490	+	0.802789i	0.535642	+	0.844445i	$0.320070\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.78854	−	11.7581i	−0.525313	−	0.909869i	−0.999565	−	0.0294798i	$-0.990615\pi$
$167$	−6.78854	−	11.7581i	−0.525313	−	0.909869i	0.474252	−	0.880389i	$-0.342718\pi$
$168$		0			0
$169$	−5.32938	+	9.23075i	−0.409952	+	0.710058i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.31085	+	14.3948i	0.631862	+	1.09442i	0.987171	+	0.159668i	$0.0510425\pi$
$173$	8.31085	+	14.3948i	0.631862	+	1.09442i	−0.355308	+	0.934749i	$0.615624\pi$
$174$		0			0
$175$	−4.30437	−	5.11173i	−0.325380	−	0.386411i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−14.8080	+	8.54942i	−1.10680	+	0.639014i	−0.938000	−	0.346636i	$-0.887324\pi$
$179$	−14.8080	+	8.54942i	−1.10680	+	0.639014i	−0.168805	+	0.985650i	$0.553991\pi$
$180$		0			0
$181$		−	18.2171i		−	1.35407i	−0.735952	−	0.677034i	$-0.763265\pi$
$181$		−	18.2171i		−	1.35407i	0.735952	−	0.677034i	$-0.236735\pi$
$182$		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	−0.983065	−	0.183258i	$-0.941336\pi$
$191$	−18.1860	+	10.4997i	−1.31589	+	0.759730i	−0.332826	+	0.942988i	$0.608002\pi$
$192$		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	$-0.595070\pi$
$199$	5.44956	−	3.14630i	0.386309	−	0.223036i	0.680560	+	0.732693i	$0.261737\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	3.21633	+	18.0577i	0.225742	+	1.26740i
$204$		0			0
$205$	−2.91440	−	5.04788i	−0.203550	−	0.352559i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.23666	−	2.14195i	0.0855414	−	0.148162i
$210$		0			0
$211$	1.29814	+	2.24844i	0.0893674	+	0.154789i	0.907244	−	0.420605i	$-0.138182\pi$
$211$	1.29814	+	2.24844i	0.0893674	+	0.154789i	−0.817876	+	0.575394i	$0.804849\pi$
$212$		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
$223$	−20.7215	−	11.9636i	−1.38762	−	0.801141i	−0.394571	−	0.918866i	$-0.629107\pi$
$223$	−20.7215	−	11.9636i	−1.38762	−	0.801141i	−0.993046	+	0.117725i	$0.962440\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.73218			−0.247713			−0.123857	−	0.992300i	$-0.539526\pi$
$227$	−3.73218			−0.247713			−0.123857	+	0.992300i	$0.539526\pi$
$228$		0			0
$229$			21.0681i			1.39222i	0.717935	+	0.696111i	$0.245088\pi$
$229$			21.0681i			1.39222i	−0.717935	+	0.696111i	$0.754912\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.0542	−	6.38215i	−0.724186	−	0.418109i	0.0921057	−	0.995749i	$-0.470640\pi$
$233$	−11.0542	−	6.38215i	−0.724186	−	0.418109i	−0.816291	+	0.577640i	$0.803974\pi$
$234$		0			0
$235$	2.42886	+	4.20691i	0.158441	+	0.274429i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.0521	−	6.38091i	0.714899	−	0.412747i	−0.0979736	−	0.995189i	$-0.531236\pi$
$239$	11.0521	−	6.38091i	0.714899	−	0.412747i	0.812872	+	0.582442i	$0.197903\pi$
$240$		0			0
$241$			3.04192i			0.195947i	0.995189	+	0.0979737i	$0.0312361\pi$
$241$			3.04192i			0.195947i	−0.995189	+	0.0979737i	$0.968764\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.26904	−	18.9229i	0.208851	−	1.20894i
$246$		0			0
$247$	−9.04601			−0.575584
$248$		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
$257$	24.5076			1.52874			0.764372	−	0.644776i	$-0.223049\pi$
$257$	24.5076			1.52874			0.764372	+	0.644776i	$0.223049\pi$
$258$		0			0
$259$	23.6960	−	4.22061i	1.47240	−	0.262256i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	24.3830i		−	1.50352i	−0.659438	−	0.751759i	$-0.729206\pi$
$263$		−	24.3830i		−	1.50352i	0.659438	−	0.751759i	$-0.270794\pi$
$264$		0			0
$265$	9.31427	−	5.37760i	0.572171	−	0.330343i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.94525	+	8.56542i	0.301517	+	0.522243i	0.976480	−	0.215609i	$-0.0691737\pi$
$269$	4.94525	+	8.56542i	0.301517	+	0.522243i	−0.674963	+	0.737852i	$0.735840\pi$
$270$		0			0
$271$	5.10505	+	2.94740i	0.310110	+	0.179042i	0.646976	−	0.762511i	$-0.276034\pi$
$271$	5.10505	+	2.94740i	0.310110	+	0.179042i	−0.336866	+	0.941553i	$0.609367\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	1.05668i		−	0.0637202i
$276$		0			0
$277$	23.2939			1.39959			0.699796	−	0.714343i	$-0.253274\pi$
$277$	23.2939			1.39959			0.699796	+	0.714343i	$0.253274\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−21.7962	−	12.5840i	−1.30025	−	0.750700i	−0.319803	−	0.947484i	$-0.603617\pi$
$281$	−21.7962	−	12.5840i	−1.30025	−	0.750700i	−0.980447	+	0.196784i	$0.936950\pi$
$282$		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
$293$	−6.79065	−	11.7618i	−0.396714	−	0.687129i	0.596604	−	0.802536i	$-0.296516\pi$
$293$	−6.79065	−	11.7618i	−0.396714	−	0.687129i	−0.993318	+	0.115406i	$0.963183\pi$
$294$		0			0
$295$	5.56147	−	9.63275i	0.323801	−	0.560841i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.82774	+	11.8260i	0.394858	+	0.683915i
$300$		0			0
$301$	−30.1030	+	5.36177i	−1.73511	+	0.309048i
$302$		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	−0.769048	−	0.639191i	$-0.779269\pi$
$313$	−10.6154	+	6.12878i	−0.600015	+	0.346419i	0.169032	+	0.985611i	$0.445936\pi$
$314$		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
$329$	−1.59472	+	4.40519i	−0.0879196	+	0.242866i
$330$		0			0
$331$	−1.73106	−	2.99829i	−0.0951479	−	0.164801i	0.814522	−	0.580132i	$-0.196999\pi$
$331$	−1.73106	−	2.99829i	−0.0951479	−	0.164801i	−0.909670	+	0.415331i	$0.863666\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.5145	−	30.3359i	0.956917	−	1.65743i
$336$		0			0
$337$	−9.13018	−	15.8139i	−0.497352	−	0.861440i	0.502643	−	0.864494i	$-0.332361\pi$
$337$	−9.13018	−	15.8139i	−0.497352	−	0.861440i	−0.999995	+	0.00305455i	$0.999028\pi$
$338$		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	0.370728	−	0.928741i	$-0.379108\pi$
$347$	−4.62386	−	2.66959i	−0.248222	−	0.143311i	−0.618950	+	0.785431i	$0.712442\pi$
$348$		0			0
$349$	0.0136817	+	0.00789914i	0.000732365	+	0.000422831i	0.500366	−	0.865814i	$-0.333199\pi$
$349$	0.0136817	+	0.00789914i	0.000732365	+	0.000422831i	−0.499634	+	0.866237i	$0.666532\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−34.3085			−1.82606			−0.913029	−	0.407894i	$-0.866263\pi$
$353$	−34.3085			−1.82606			−0.913029	+	0.407894i	$0.866263\pi$
$354$		0			0
$355$		−	23.3462i		−	1.23909i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.42754	+	3.13359i	0.286454	+	0.165385i	0.636342	−	0.771407i	$-0.280447\pi$
$359$	5.42754	+	3.13359i	0.286454	+	0.165385i	−0.349887	+	0.936792i	$0.613780\pi$
$360$		0			0
$361$	7.97583	+	13.8145i	0.419781	+	0.727081i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.52811	+	2.61430i	−0.237012	+	0.136839i
$366$		0			0
$367$			19.0397i			0.993863i	0.867790	+	0.496931i	$0.165540\pi$
$367$			19.0397i			0.993863i	−0.867790	+	0.496931i	$0.834460\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	9.75326	+	3.53077i	0.506364	+	0.183308i
$372$		0			0
$373$	10.8380			0.561172			0.280586	−	0.959829i	$-0.409471\pi$
$373$	10.8380			0.561172			0.280586	+	0.959829i	$0.409471\pi$
$374$		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	$-0.505726\pi$
$379$	−0.700312			−0.0359726			−0.0179863	+	0.999838i	$0.505726\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	38.0470			1.94411			0.972056	−	0.234749i	$-0.0754269\pi$
$383$	38.0470			1.94411			0.972056	+	0.234749i	$0.0754269\pi$
$384$		0			0
$385$	2.32269	−	1.95584i	0.118375	−	0.0996789i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	19.2787i		−	0.977468i	−0.872433	−	0.488734i	$-0.837459\pi$
$389$		−	19.2787i		−	0.977468i	0.872433	−	0.488734i	$-0.162541\pi$
$390$		0			0
$391$	−30.1874	+	17.4287i	−1.52664	+	0.881407i
$392$		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	−0.00353639	−	0.999994i	$-0.501126\pi$
$397$	−17.3610	−	10.0234i	−0.871325	−	0.503059i	−0.867788	+	0.496934i	$0.834459\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			30.5109i			1.52364i	0.647789	+	0.761820i	$0.275694\pi$
$401$			30.5109i			1.52364i	−0.647789	+	0.761820i	$0.724306\pi$
$402$		0			0
$403$	−5.39987			−0.268987
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.29598	+	1.90294i	0.163376	+	0.0943250i
$408$		0			0
$409$	−0.150631	−	0.0869667i	−0.00744821	−	0.00430023i	0.496271	−	0.868168i	$-0.334702\pi$
$409$	−0.150631	−	0.0869667i	−0.00744821	−	0.00430023i	−0.503719	+	0.863867i	$0.668035\pi$
$410$		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
$419$	14.0690	+	24.3682i	0.687316	+	1.19047i	0.972703	+	0.232054i	$0.0745445\pi$
$419$	14.0690	+	24.3682i	0.687316	+	1.19047i	−0.285387	+	0.958412i	$0.592122\pi$
$420$		0			0
$421$	−1.56130	+	2.70424i	−0.0760929	+	0.131797i	−0.901561	−	0.432652i	$-0.857578\pi$
$421$	−1.56130	+	2.70424i	−0.0760929	+	0.131797i	0.825468	+	0.564449i	$0.190911\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.93264	−	8.54358i	−0.239268	−	0.414424i
$426$		0			0
$427$	4.63809	+	1.67903i	0.224453	+	0.0812540i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.58876	+	4.95872i	−0.413706	+	0.238853i	−0.692381	−	0.721532i	$-0.743438\pi$
$431$	−8.58876	+	4.95872i	−0.413706	+	0.238853i	0.278675	+	0.960385i	$0.410105\pi$
$432$		0			0
$433$			17.1274i			0.823092i	0.911389	+	0.411546i	$0.135011\pi$
$433$			17.1274i			0.823092i	−0.911389	+	0.411546i	$0.864989\pi$
$434$		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	−0.632349	−	0.774683i	$-0.717909\pi$
$443$	−5.84340	+	3.37369i	−0.277628	+	0.160289i	0.354721	+	0.934972i	$0.384576\pi$
$444$		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
$455$	−10.4426	−	3.78030i	−0.489555	−	0.177223i
$456$		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
$461$	−18.5154	+	32.0696i	−0.862347	+	1.49363i	0.00730959	+	0.999973i	$0.497673\pi$
$461$	−18.5154	+	32.0696i	−0.862347	+	1.49363i	−0.869657	+	0.493656i	$0.835660\pi$
$462$		0			0
$463$	−10.5618	−	18.2935i	−0.490848	−	0.850173i	0.509097	−	0.860709i	$-0.329980\pi$
$463$	−10.5618	−	18.2935i	−0.490848	−	0.850173i	−0.999944	+	0.0105362i	$0.996646\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.30470	+	16.1162i	−0.430570	+	0.745770i	−0.996922	−	0.0783937i	$-0.975021\pi$
$467$	−9.30470	+	16.1162i	−0.430570	+	0.745770i	0.566352	+	0.824163i	$0.308354\pi$
$468$		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
$475$	12.9319	+	7.46624i	0.593356	+	0.342574i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.3341			0.654940			0.327470	−	0.944862i	$-0.393804\pi$
$479$	14.3341			0.654940			0.327470	+	0.944862i	$0.393804\pi$
$480$		0			0
$481$		−	13.9198i		−	0.634687i
$482$		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	$-0.0842789\pi$
$487$	5.64829	+	9.78313i	0.255949	+	0.443316i	−0.709204	+	0.705003i	$0.750946\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.84097	+	5.10434i	−0.398988	+	0.230356i	−0.686047	−	0.727557i	$-0.740656\pi$
$491$	−8.84097	+	5.10434i	−0.398988	+	0.230356i	0.287059	+	0.957913i	$0.407322\pi$
$492$		0			0
$493$			27.0773i			1.21950i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	17.2231	−	14.5028i	0.772561	−	0.650540i
$498$		0			0
$499$	19.1334			0.856531			0.428265	−	0.903653i	$-0.359125\pi$
$499$	19.1334			0.856531			0.428265	+	0.903653i	$0.359125\pi$
$500$		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
$509$	−21.8877			−0.970157			−0.485079	−	0.874471i	$-0.661209\pi$
$509$	−21.8877			−0.970157			−0.485079	+	0.874471i	$0.661209\pi$
$510$		0			0
$511$	−4.74152	−	1.71647i	−0.209753	−	0.0759323i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	29.4793i		−	1.29901i
$516$		0			0
$517$	−0.641553	+	0.370401i	−0.0282155	+	0.0162902i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.856074	+	1.48276i	0.0375053	+	0.0649610i	0.884169	−	0.467168i	$-0.154726\pi$
$521$	0.856074	+	1.48276i	0.0375053	+	0.0649610i	−0.846663	+	0.532129i	$0.821392\pi$
$522$		0			0
$523$	−7.16320	−	4.13568i	−0.313225	−	0.180841i	0.335144	−	0.942167i	$-0.391215\pi$
$523$	−7.16320	−	4.13568i	−0.313225	−	0.180841i	−0.648369	+	0.761326i	$0.724548\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		−	13.7839i		−	0.600435i
$528$		0			0
$529$	−56.6466			−2.46290
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.81550	−	1.62553i	−0.121953	−	0.0704096i
$534$		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	−0.997575	−	0.0695932i	$-0.977830\pi$
$541$	−10.1997	+	17.6664i	−0.438518	+	0.759536i	0.559057	+	0.829129i	$0.311163\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.07875	−	12.2608i	−0.303220	−	0.525193i
$546$		0			0
$547$	−18.9630	+	32.8449i	−0.810801	+	1.40435i	0.101503	+	0.994835i	$0.467635\pi$
$547$	−18.9630	+	32.8449i	−0.810801	+	1.40435i	−0.912304	+	0.409513i	$0.865699\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−20.4927	−	35.4943i	−0.873017	−	1.51211i
$552$		0			0
$553$	−0.781051	+	2.15755i	−0.0332137	+	0.0917482i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	14.5919	−	8.42463i	0.618278	−	0.356963i	−0.157920	−	0.987452i	$-0.550479\pi$
$557$	14.5919	−	8.42463i	0.618278	−	0.356963i	0.776198	+	0.630489i	$0.217146\pi$
$558$		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	$-0.426917\pi$
$571$	22.8703	−	39.6125i	0.957092	−	1.65773i	0.729507	−	0.683973i	$-0.239750\pi$
$572$		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	−0.144651	−	0.989483i	$-0.546206\pi$
$577$	15.3719	−	8.87497i	0.639940	−	0.369470i	0.784592	+	0.620013i	$0.212873\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.0187	−	3.20939i	0.747541	−	0.133148i
$582$		0			0
$583$	0.820082	+	1.42042i	0.0339643	+	0.0588280i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.41148	+	7.64091i	−0.182081	+	0.315374i	−0.942589	−	0.333955i	$-0.891617\pi$
$587$	−4.41148	+	7.64091i	−0.182081	+	0.315374i	0.760508	+	0.649329i	$0.224950\pi$
$588$		0			0
$589$	10.4319	+	18.0686i	0.429839	+	0.744503i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.24849	−	7.35860i	0.174465	−	0.302181i	−0.765511	−	0.643422i	$-0.777514\pi$
$593$	4.24849	−	7.35860i	0.174465	−	0.302181i	0.939976	+	0.341241i	$0.110847\pi$
$594$		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	0.432952	−	0.901417i	$-0.357472\pi$
$599$	−3.21158	−	1.85421i	−0.131222	−	0.0757609i	−0.564174	+	0.825656i	$0.690805\pi$
$600$		0			0
$601$	−6.14043	−	3.54518i	−0.250473	−	0.144611i	0.369508	−	0.929228i	$-0.379526\pi$
$601$	−6.14043	−	3.54518i	−0.250473	−	0.144611i	−0.619981	+	0.784617i	$0.712860\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−29.6964			−1.20733
$606$		0			0
$607$			33.9940i			1.37977i	0.723918	+	0.689886i	$0.242339\pi$
$607$			33.9940i			1.37977i	−0.723918	+	0.689886i	$0.757661\pi$
$608$		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	0.527877	−	0.849321i	$-0.322988\pi$
$613$	−11.6761	−	20.2237i	−0.471595	−	0.816827i	−0.999472	+	0.0324944i	$0.989655\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.0817	−	22.5638i	1.57337	−	0.908386i	0.577618	−	0.816307i	$-0.303982\pi$
$617$	39.0817	−	22.5638i	1.57337	−	0.908386i	0.995752	−	0.0920787i	$-0.0293511\pi$
$618$		0			0
$619$		−	9.21352i		−	0.370323i	−0.982708	−	0.185161i	$-0.940719\pi$
$619$		−	9.21352i		−	0.370323i	0.982708	−	0.185161i	$-0.0592808\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	25.4674	−	4.53612i	1.02033	−	0.181736i
$624$		0			0
$625$	−31.2493			−1.24997
$626$		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	$-0.614020\pi$
$631$	−17.6136			−0.701188			−0.350594	+	0.936528i	$0.614020\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	28.2312			1.12032
$636$		0			0
$637$	−3.69817	−	10.0521i	−0.146527	−	0.398278i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	19.1402i		−	0.755991i	−0.925807	−	0.377996i	$-0.876613\pi$
$641$		−	19.1402i		−	0.755991i	0.925807	−	0.377996i	$-0.123387\pi$
$642$		0			0
$643$	−2.01129	+	1.16122i	−0.0793177	+	0.0457941i	−0.539134	−	0.842220i	$-0.681248\pi$
$643$	−2.01129	+	1.16122i	−0.0793177	+	0.0457941i	0.459817	+	0.888014i	$0.347915\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.9310	−	22.3971i	−0.508370	−	0.880522i	−0.999953	−	0.00969167i	$-0.996915\pi$
$647$	−12.9310	−	22.3971i	−0.508370	−	0.880522i	0.491583	−	0.870831i	$-0.336418\pi$
$648$		0			0
$649$	1.46899	+	0.848123i	0.0576630	+	0.0332918i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	23.2257i		−	0.908891i	−0.890774	−	0.454446i	$-0.849837\pi$
$653$		−	23.2257i		−	0.908891i	0.890774	−	0.454446i	$-0.150163\pi$
$654$		0			0
$655$	−53.9363			−2.10746
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.7002	+	7.90981i	0.533684	+	0.308122i	0.742515	−	0.669829i	$-0.233633\pi$
$659$	13.7002	+	7.90981i	0.533684	+	0.308122i	−0.208832	+	0.977952i	$0.566966\pi$
$660$		0			0
$661$	−15.8006	−	9.12248i	−0.614572	−	0.354823i	0.160181	−	0.987088i	$-0.448792\pi$
$661$	−15.8006	−	9.12248i	−0.614572	−	0.354823i	−0.774753	+	0.632264i	$0.782126\pi$
$662$		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
$671$	0.389984	+	0.675472i	0.0150552	+	0.0260763i
$672$		0			0
$673$	14.4184	−	24.9733i	0.555787	−	0.962651i	−0.442055	−	0.896988i	$-0.645750\pi$
$673$	14.4184	−	24.9733i	0.555787	−	0.962651i	0.997842	−	0.0656633i	$-0.0209163\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	16.7668	+	29.0409i	0.644400	+	1.11613i	0.984440	+	0.175722i	$0.0562261\pi$
$677$	16.7668	+	29.0409i	0.644400	+	1.11613i	−0.340040	+	0.940411i	$0.610441\pi$
$678$		0			0
$679$	0.107364	+	0.602779i	0.00412023	+	0.0231325i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	19.0943	−	11.0241i	0.730621	−	0.421824i	−0.0880282	−	0.996118i	$-0.528057\pi$
$683$	19.0943	−	11.0241i	0.730621	−	0.421824i	0.818649	+	0.574294i	$0.194723\pi$
$684$		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
$707$	−24.3365	−	28.9013i	−0.915270	−	1.08695i
$708$		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
$713$	15.7476	−	27.2756i	0.589751	−	1.02148i
$714$		0			0
$715$	−0.878041	−	1.52081i	−0.0328369	−	0.0568751i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	11.6111	−	20.1111i	0.433023	−	0.750017i	−0.564109	−	0.825700i	$-0.690780\pi$
$719$	11.6111	−	20.1111i	0.433023	−	0.750017i	0.997132	+	0.0756828i	$0.0241136\pi$
$720$		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
$727$	2.50999	+	1.44914i	0.0930903	+	0.0537457i	0.545822	−	0.837901i	$-0.316217\pi$
$727$	2.50999	+	1.44914i	0.0930903	+	0.0537457i	−0.452732	+	0.891647i	$0.649551\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−45.1392			−1.66953
$732$		0			0
$733$			11.8891i			0.439135i	0.975597	+	0.219568i	$0.0704647\pi$
$733$			11.8891i			0.439135i	−0.975597	+	0.219568i	$0.929535\pi$
$734$		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	−0.986800	−	0.161945i	$-0.948223\pi$
$739$	−17.2254	−	29.8354i	−0.633648	−	1.09751i	0.353151	−	0.935566i	$-0.385110\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.44069	+	1.40913i	−0.0895401	+	0.0516960i	−0.544101	−	0.839019i	$-0.683129\pi$
$743$	−2.44069	+	1.40913i	−0.0895401	+	0.0516960i	0.454561	+	0.890715i	$0.349796\pi$
$744$		0			0
$745$		−	29.4965i		−	1.08067i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.94930	−	16.5585i	−0.107765	−	0.605034i
$750$		0			0
$751$	−7.72089			−0.281739			−0.140870	−	0.990028i	$-0.544990\pi$
$751$	−7.72089			−0.281739			−0.140870	+	0.990028i	$0.544990\pi$
$752$		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
$761$	3.13289			0.113567			0.0567835	−	0.998387i	$-0.481916\pi$
$761$	3.13289			0.113567			0.0567835	+	0.998387i	$0.481916\pi$
$762$		0			0
$763$	4.64770	−	12.8386i	0.168258	−	0.464790i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	6.20393i		−	0.224011i
$768$		0			0
$769$	−5.53497	+	3.19562i	−0.199596	+	0.115237i	−0.596467	−	0.802637i	$-0.703429\pi$
$769$	−5.53497	+	3.19562i	−0.199596	+	0.115237i	0.396871	+	0.917874i	$0.370096\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	23.9779	+	41.5309i	0.862425	+	1.49376i	0.869581	+	0.493790i	$0.164389\pi$
$773$	23.9779	+	41.5309i	0.862425	+	1.49376i	−0.00715621	+	0.999974i	$0.502278\pi$
$774$		0			0
$775$	7.71948	+	4.45685i	0.277292	+	0.160095i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			12.5613i			0.450057i
$780$		0			0
$781$	3.56029			0.127397
$782$		0			0
$783$		0			0
$784$		0			0
$785$	29.1661	+	16.8390i	1.04098	+	0.601011i
$786$		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
$797$	0.782501	+	1.35533i	0.0277176	+	0.0480083i	0.879551	−	0.475804i	$-0.157843\pi$
$797$	0.782501	+	1.35533i	0.0277176	+	0.0480083i	−0.851834	+	0.523812i	$0.824509\pi$
$798$		0			0
$799$	−3.45810	+	5.98961i	−0.122339	+	0.211897i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.398681	−	0.690535i	−0.0140691	−	0.0243685i
$804$		0			0
$805$	49.5485	−	41.7226i	1.74635	−	1.47053i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−15.3445	+	8.85918i	−0.539485	+	0.311472i	−0.744870	−	0.667209i	$-0.767489\pi$
$809$	−15.3445	+	8.85918i	−0.539485	+	0.311472i	0.205385	+	0.978681i	$0.434155\pi$
$810$		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	−0.574972	−	0.818173i	$-0.694987\pi$
$823$	12.0797	−	20.9227i	0.421073	−	0.729319i	0.996045	+	0.0888537i	$0.0283204\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			9.64923i			0.335537i	0.985826	+	0.167768i	$0.0536561\pi$
$827$			9.64923i			0.335537i	−0.985826	+	0.167768i	$0.946344\pi$
$828$		0			0
$829$	−25.1481	+	14.5193i	−0.873430	+	0.504275i	−0.868486	−	0.495713i	$-0.834907\pi$
$829$	−25.1481	+	14.5193i	−0.873430	+	0.504275i	−0.00494329	+	0.999988i	$0.501574\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	25.6593	−	9.44005i	0.889041	−	0.327078i
$834$		0			0
$835$	18.6231	+	32.2562i	0.644480	+	1.11627i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−6.84383	+	11.8539i	−0.236275	+	0.409241i	−0.959642	−	0.281223i	$-0.909260\pi$
$839$	−6.84383	+	11.8539i	−0.236275	+	0.409241i	0.723367	+	0.690463i	$0.242593\pi$
$840$		0			0
$841$	9.53027	+	16.5069i	0.328630	+	0.569204i
$842$		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
$853$	−40.5184	−	23.3933i	−1.38732	−	0.800972i	−0.394310	−	0.918977i	$-0.629017\pi$
$853$	−40.5184	−	23.3933i	−1.38732	−	0.800972i	−0.993013	+	0.118006i	$0.962350\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−31.7960			−1.08613			−0.543065	−	0.839691i	$-0.682736\pi$
$857$	−31.7960			−1.08613			−0.543065	+	0.839691i	$0.682736\pi$
$858$		0			0
$859$		−	25.2885i		−	0.862832i	−0.902153	−	0.431416i	$-0.858014\pi$
$859$		−	25.2885i		−	0.862832i	0.902153	−	0.431416i	$-0.141986\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−15.9513	−	9.20946i	−0.542987	−	0.313494i	0.203302	−	0.979116i	$-0.434833\pi$
$863$	−15.9513	−	9.20946i	−0.542987	−	0.313494i	−0.746289	+	0.665622i	$0.768166\pi$
$864$		0			0
$865$	−22.7993	−	39.4896i	−0.775200	−	1.34269i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.314216	+	0.181413i	−0.0106590	+	0.00615400i
$870$		0			0
$871$		−	19.5377i		−	0.662010i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−11.5671	−	13.7367i	−0.391039	−	0.464385i
$876$		0			0
$877$	−8.89389			−0.300325			−0.150163	−	0.988661i	$-0.547980\pi$
$877$	−8.89389			−0.300325			−0.150163	+	0.988661i	$0.547980\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	13.1721			0.443780			0.221890	−	0.975072i	$-0.428777\pi$
$881$	13.1721			0.443780			0.221890	+	0.975072i	$0.428777\pi$
$882$		0			0
$883$	−12.6729			−0.426477			−0.213239	−	0.977000i	$-0.568401\pi$
$883$	−12.6729			−0.426477			−0.213239	+	0.977000i	$0.568401\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−33.3983			−1.12141			−0.560703	−	0.828017i	$-0.689469\pi$
$887$	−33.3983			−1.12141			−0.560703	+	0.828017i	$0.689469\pi$
$888$		0			0
$889$	17.5374	+	20.8268i	0.588185	+	0.698510i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	10.4686i		−	0.350320i
$894$		0			0
$895$	40.6231	−	23.4538i	1.35788	−	0.783974i
$896$		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
$905$			49.9753i			1.66124i
$906$		0			0
$907$	29.3127			0.973311			0.486655	−	0.873594i	$-0.338217\pi$
$907$	29.3127			0.973311			0.486655	+	0.873594i	$0.338217\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.72555	+	0.996246i	0.0571700	+	0.0330071i	0.528313	−	0.849050i	$-0.322825\pi$
$911$	1.72555	+	0.996246i	0.0571700	+	0.0330071i	−0.471143	+	0.882057i	$0.656158\pi$
$912$		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	$-0.823906\pi$
$919$	0.897678	−	1.55482i	0.0296117	−	0.0512889i	0.880451	+	0.474136i	$0.157240\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.51079	−	11.2770i	−0.214305	−	0.371188i
$924$		0			0
$925$	−11.4889	+	19.8993i	−0.377751	+	0.654284i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	12.4178	+	21.5083i	0.407415	+	0.705664i	0.994599	−	0.103789i	$-0.0330968\pi$
$929$	12.4178	+	21.5083i	0.407415	+	0.705664i	−0.587184	+	0.809453i	$0.699763\pi$
$930$		0			0
$931$	−26.4911	+	31.7940i	−0.868209	+	1.04200i
$932$		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	$0.150648\pi$
$937$			27.9046i			0.911605i	−0.890081	+	0.455802i	$0.849352\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−26.2537	+	45.4728i	−0.855847	+	1.48237i	0.0200094	+	0.999800i	$0.493630\pi$
$941$	−26.2537	+	45.4728i	−0.855847	+	1.48237i	−0.875857	+	0.482571i	$0.839703\pi$
$942$		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	−0.963630	−	0.267241i	$-0.913888\pi$
$947$	−37.3591	+	21.5693i	−1.21401	+	0.700907i	−0.250377	+	0.968148i	$0.580555\pi$
$948$		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
$959$	10.8995	−	9.17803i	0.351964	−	0.296374i
$960$		0			0
$961$	−9.27285	−	16.0610i	−0.299124	−	0.518098i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.56709	+	16.5707i	−0.307975	+	0.533429i
$966$		0			0
$967$	26.6398	+	46.1414i	0.856677	+	1.48381i	0.875080	+	0.483978i	$0.160809\pi$
$967$	26.6398	+	46.1414i	0.856677	+	1.48381i	−0.0184029	+	0.999831i	$0.505858\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−28.1556	+	48.7669i	−0.903555	+	1.56500i	−0.0807100	+	0.996738i	$0.525719\pi$
$971$	−28.1556	+	48.7669i	−0.903555	+	1.56500i	−0.822845	+	0.568266i	$0.807615\pi$
$972$		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
$979$	3.54237	+	2.04519i	0.113215	+	0.0653646i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	38.0505			1.21362			0.606811	−	0.794846i	$-0.292449\pi$
$983$	38.0505			1.21362			0.606811	+	0.794846i	$0.292449\pi$
$984$		0			0
$985$		−	44.1005i		−	1.40516i
$986$		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	$-0.108839\pi$
$991$	5.68758	+	9.85118i	0.180672	+	0.312933i	−0.761438	+	0.648238i	$0.775506\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−14.9499	+	8.63131i	−0.473943	+	0.273631i
$996$		0			0
$997$			50.9904i			1.61488i	0.589948	+	0.807441i	$0.299148\pi$
$997$			50.9904i			1.61488i	−0.589948	+	0.807441i	$0.700852\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.d.1601.2		16
3.2	odd	2		1008.2.df.d.929.4		16
4.3	odd	2		756.2.bm.a.89.2		16
7.3	odd	6		3024.2.ca.d.2033.2		16
9.4	even	3		1008.2.ca.d.257.2		16
9.5	odd	6		3024.2.ca.d.2609.2		16
12.11	even	2		252.2.bm.a.173.5	yes	16
21.17	even	6		1008.2.ca.d.353.2		16
28.3	even	6		756.2.w.a.521.2		16
28.11	odd	6		5292.2.w.b.521.7		16
28.19	even	6		5292.2.x.a.4409.2		16
28.23	odd	6		5292.2.x.b.4409.7		16
28.27	even	2		5292.2.bm.a.4625.7		16
36.7	odd	6		2268.2.t.b.2105.7		16
36.11	even	6		2268.2.t.a.2105.2		16
36.23	even	6		756.2.w.a.341.2		16
36.31	odd	6		252.2.w.a.5.7	✓	16
63.31	odd	6		1008.2.df.d.689.4		16
63.59	even	6	inner	3024.2.df.d.17.2		16
84.11	even	6		1764.2.w.b.1109.2		16
84.23	even	6		1764.2.x.b.1469.7		16
84.47	odd	6		1764.2.x.a.1469.2		16
84.59	odd	6		252.2.w.a.101.7	yes	16
84.83	odd	2		1764.2.bm.a.1685.4		16
252.23	even	6		5292.2.x.a.881.2		16
252.31	even	6		252.2.bm.a.185.5	yes	16
252.59	odd	6		756.2.bm.a.17.2		16
252.67	odd	6		1764.2.bm.a.1697.4		16
252.95	even	6		5292.2.bm.a.2285.7		16
252.103	even	6		1764.2.x.b.293.7		16
252.115	even	6		2268.2.t.a.1781.2		16
252.131	odd	6		5292.2.x.b.881.7		16
252.139	even	6		1764.2.w.b.509.2		16
252.167	odd	6		5292.2.w.b.1097.7		16
252.227	odd	6		2268.2.t.b.1781.7		16
252.247	odd	6		1764.2.x.a.293.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.w.a.5.7	✓	16	36.31	odd	6
252.2.w.a.101.7	yes	16	84.59	odd	6
252.2.bm.a.173.5	yes	16	12.11	even	2
252.2.bm.a.185.5	yes	16	252.31	even	6
756.2.w.a.341.2		16	36.23	even	6
756.2.w.a.521.2		16	28.3	even	6
756.2.bm.a.17.2		16	252.59	odd	6
756.2.bm.a.89.2		16	4.3	odd	2
1008.2.ca.d.257.2		16	9.4	even	3
1008.2.ca.d.353.2		16	21.17	even	6
1008.2.df.d.689.4		16	63.31	odd	6
1008.2.df.d.929.4		16	3.2	odd	2
1764.2.w.b.509.2		16	252.139	even	6
1764.2.w.b.1109.2		16	84.11	even	6
1764.2.x.a.293.2		16	252.247	odd	6
1764.2.x.a.1469.2		16	84.47	odd	6
1764.2.x.b.293.7		16	252.103	even	6
1764.2.x.b.1469.7		16	84.23	even	6
1764.2.bm.a.1685.4		16	84.83	odd	2
1764.2.bm.a.1697.4		16	252.67	odd	6
2268.2.t.a.1781.2		16	252.115	even	6
2268.2.t.a.2105.2		16	36.11	even	6
2268.2.t.b.1781.7		16	252.227	odd	6
2268.2.t.b.2105.7		16	36.7	odd	6
3024.2.ca.d.2033.2		16	7.3	odd	6
3024.2.ca.d.2609.2		16	9.5	odd	6
3024.2.df.d.17.2		16	63.59	even	6	inner
3024.2.df.d.1601.2		16	1.1	even	1	trivial
5292.2.w.b.521.7		16	28.11	odd	6
5292.2.w.b.1097.7		16	252.167	odd	6
5292.2.x.a.881.2		16	252.23	even	6
5292.2.x.a.4409.2		16	28.19	even	6
5292.2.x.b.881.7		16	252.131	odd	6
5292.2.x.b.4409.7		16	28.23	odd	6
5292.2.bm.a.2285.7		16	252.95	even	6
5292.2.bm.a.4625.7		16	28.27	even	2

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.df (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.74332 q^{5} +(-1.70417 - 2.02381i) q^{7} +O(q^{10})\)	\(q-2.74332 q^{5} +(-1.70417 - 2.02381i) q^{7} -0.418355i q^{11} +(-1.32512 + 0.765056i) q^{13} +(-1.95291 - 3.38253i) q^{17} +(5.11994 + 2.95600i) q^{19} -8.92450i q^{23} +2.52579 q^{25} +(-6.00378 - 3.46629i) q^{29} +(3.05626 + 1.76453i) q^{31} +(4.67507 + 5.55196i) q^{35} +(-4.54861 + 7.87842i) q^{37} +(1.06236 + 1.84006i) q^{41} +(5.77846 - 10.0086i) q^{43} +(-0.885373 - 1.53351i) q^{47} +(-1.19164 + 6.89783i) q^{49} +(-3.39526 + 1.96025i) q^{53} +1.14768i q^{55} +(-2.02728 + 3.51135i) q^{59} +(-1.61459 + 0.932184i) q^{61} +(3.63521 - 2.09879i) q^{65} +(-6.38441 + 11.0581i) q^{67} +8.51021i q^{71} +(1.65059 - 0.952971i) q^{73} +(-0.846673 + 0.712947i) q^{77} +(-0.433633 - 0.751074i) q^{79} +(-3.45880 + 5.99082i) q^{83} +(5.35744 + 9.27936i) q^{85} +(-4.88864 + 8.46738i) q^{89} +(3.80655 + 1.37800i) q^{91} +(-14.0456 - 8.10924i) q^{95} +(-0.200411 - 0.115707i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{7}+O(q^{10}) \) 16 * q + q^7	\( 16 q + q^{7} + 3 q^{13} + 9 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} + 15 q^{35} + q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 13 q^{49} - 15 q^{59} + 3 q^{61} + 39 q^{65} + 7 q^{67} + 45 q^{77} + q^{79} + 6 q^{85} + 21 q^{89} - 9 q^{91} + 6 q^{95} + 3 q^{97}+O(q^{100}) \) 16 * q + q^7 + 3 * q^13 + 9 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 + 15 * q^35 + q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 13 * q^49 - 15 * q^59 + 3 * q^61 + 39 * q^65 + 7 * q^67 + 45 * q^77 + q^79 + 6 * q^85 + 21 * q^89 - 9 * q^91 + 6 * q^95 + 3 * q^97

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