LMFDB - Embedded newform 3024.2.cc.b.881.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			881.7
Root			$-1.40917 + 1.00709i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.b.2897.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17468 - 2.03460i) q^{5} +(2.63145 - 0.274725i) q^{7} +O(q^{10})$	$q+(1.17468 - 2.03460i) q^{5} +(2.63145 - 0.274725i) q^{7} +(-4.91614 + 2.83834i) q^{11} +(-1.48943 - 0.859925i) q^{13} -1.76883 q^{17} +1.13932i q^{19} +(-3.18272 - 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} +(-3.59886 + 2.07781i) q^{29} +(-7.24879 - 4.18509i) q^{31} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} +(3.99709 - 6.92317i) q^{41} +(-1.76053 - 3.04933i) q^{43} +(-5.90494 - 10.2277i) q^{47} +(6.84905 - 1.44585i) q^{49} +13.3365i q^{55} +(-1.11483 + 1.93094i) q^{59} +(-7.79396 + 4.49985i) q^{61} +(-3.49921 + 2.02027i) q^{65} +(5.43562 - 9.41477i) q^{67} -4.52106i q^{71} +5.34234i q^{73} +(-12.1568 + 8.81952i) q^{77} +(-6.51422 - 11.2830i) q^{79} +(6.27298 + 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} -1.16106 q^{89} +(-4.15561 - 1.85366i) q^{91} +(2.31806 + 1.33834i) q^{95} +(3.97536 - 2.29517i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.17468	−	2.03460i	0.525332	−	0.909902i	−0.474232	−	0.880400i	$-0.657274\pi$
$5$	1.17468	−	2.03460i	0.525332	−	0.909902i	0.999565	−	0.0295026i	$-0.00939234\pi$
$6$		0			0
$7$	2.63145	−	0.274725i	0.994594	−	0.103836i
$7$	2.63145	−	0.274725i	0.994594	−	0.103836i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.91614	+	2.83834i	−1.48227	+	0.855790i	−0.999798	−	0.0201197i	$-0.993595\pi$
$11$	−4.91614	+	2.83834i	−1.48227	+	0.855790i	−0.482475	+	0.875910i	$0.660262\pi$
$12$		0			0
$13$	−1.48943	−	0.859925i	−0.413094	−	0.238500i	0.279024	−	0.960284i	$-0.409989\pi$
$13$	−1.48943	−	0.859925i	−0.413094	−	0.238500i	−0.692118	+	0.721784i	$0.743322\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.76883			−0.429004			−0.214502	−	0.976724i	$-0.568813\pi$
$17$	−1.76883			−0.429004			−0.214502	+	0.976724i	$0.568813\pi$
$18$		0			0
$19$			1.13932i			0.261378i	0.991423	+	0.130689i	$0.0417189\pi$
$19$			1.13932i			0.261378i	−0.991423	+	0.130689i	$0.958281\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.18272	−	1.83755i	−0.663644	−	0.383155i	0.130020	−	0.991511i	$-0.458496\pi$
$23$	−3.18272	−	1.83755i	−0.663644	−	0.383155i	−0.793664	+	0.608356i	$0.791829\pi$
$24$		0			0
$25$	−0.259741	−	0.449885i	−0.0519482	−	0.0899769i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.59886	+	2.07781i	−0.668292	+	0.385839i	−0.795429	−	0.606046i	$-0.792755\pi$
$29$	−3.59886	+	2.07781i	−0.668292	+	0.385839i	0.127137	+	0.991885i	$0.459421\pi$
$30$		0			0
$31$	−7.24879	−	4.18509i	−1.30192	−	0.751665i	−0.321188	−	0.947015i	$-0.604082\pi$
$31$	−7.24879	−	4.18509i	−1.30192	−	0.751665i	−0.980734	+	0.195350i	$0.937416\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.53215	−	5.67667i	0.428012	−	0.959532i
$36$		0			0
$37$	−9.19773			−1.51210			−0.756049	−	0.654515i	$-0.772873\pi$
$37$	−9.19773			−1.51210			−0.756049	+	0.654515i	$0.772873\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.99709	−	6.92317i	0.624241	−	1.08122i	−0.364446	−	0.931225i	$-0.618742\pi$
$41$	3.99709	−	6.92317i	0.624241	−	1.08122i	0.988687	−	0.149993i	$-0.0479251\pi$
$42$		0			0
$43$	−1.76053	−	3.04933i	−0.268478	−	0.465018i	0.699991	−	0.714152i	$-0.253187\pi$
$43$	−1.76053	−	3.04933i	−0.268478	−	0.465018i	−0.968469	+	0.249134i	$0.919854\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.90494	−	10.2277i	−0.861324	−	1.49186i	−0.870651	−	0.491901i	$-0.836302\pi$
$47$	−5.90494	−	10.2277i	−0.861324	−	1.49186i	0.00932669	−	0.999957i	$-0.497031\pi$
$48$		0			0
$49$	6.84905	−	1.44585i	0.978436	−	0.206550i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$			13.3365i			1.79830i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.11483	+	1.93094i	−0.145139	+	0.251387i	−0.929425	−	0.369012i	$-0.879696\pi$
$59$	−1.11483	+	1.93094i	−0.145139	+	0.251387i	0.784286	+	0.620399i	$0.213029\pi$
$60$		0			0
$61$	−7.79396	+	4.49985i	−0.997915	+	0.576146i	−0.907631	−	0.419770i	$-0.862111\pi$
$61$	−7.79396	+	4.49985i	−0.997915	+	0.576146i	−0.0902842	+	0.995916i	$0.528778\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.49921	+	2.02027i	−0.434024	+	0.250584i
$66$		0			0
$67$	5.43562	−	9.41477i	0.664067	−	1.15020i	−0.315470	−	0.948935i	$-0.602162\pi$
$67$	5.43562	−	9.41477i	0.664067	−	1.15020i	0.979537	−	0.201262i	$-0.0645044\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	4.52106i		−	0.536551i	−0.963342	−	0.268276i	$-0.913546\pi$
$71$		−	4.52106i		−	0.536551i	0.963342	−	0.268276i	$-0.0864538\pi$
$72$		0			0
$73$			5.34234i			0.625274i	0.949873	+	0.312637i	$0.101212\pi$
$73$			5.34234i			0.625274i	−0.949873	+	0.312637i	$0.898788\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.1568	+	8.81952i	−1.38540	+	1.00508i
$78$		0			0
$79$	−6.51422	−	11.2830i	−0.732907	−	1.26943i	−0.955636	−	0.294551i	$-0.904830\pi$
$79$	−6.51422	−	11.2830i	−0.732907	−	1.26943i	0.222729	−	0.974880i	$-0.428503\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.27298	+	10.8651i	0.688549	+	1.19260i	0.972307	+	0.233707i	$0.0750855\pi$
$83$	6.27298	+	10.8651i	0.688549	+	1.19260i	−0.283758	+	0.958896i	$0.591581\pi$
$84$		0			0
$85$	−2.07781	+	3.59886i	−0.225370	+	0.390352i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.16106			−0.123072			−0.0615360	−	0.998105i	$-0.519600\pi$
$89$	−1.16106			−0.123072			−0.0615360	+	0.998105i	$0.519600\pi$
$90$		0			0
$91$	−4.15561	−	1.85366i	−0.435626	−	0.194317i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.31806	+	1.33834i	0.237828	+	0.137310i
$96$		0			0
$97$	3.97536	−	2.29517i	0.403636	−	0.233039i	−0.284416	−	0.958701i	$-0.591800\pi$
$97$	3.97536	−	2.29517i	0.403636	−	0.233039i	0.688052	+	0.725662i	$0.258466\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.31155	+	5.73577i	0.329511	+	0.570730i	0.982415	−	0.186711i	$-0.0597827\pi$
$101$	3.31155	+	5.73577i	0.329511	+	0.570730i	−0.652904	+	0.757441i	$0.726449\pi$
$102$		0			0
$103$	−5.07471	−	2.92989i	−0.500026	−	0.288690i	0.228698	−	0.973497i	$-0.426553\pi$
$103$	−5.07471	−	2.92989i	−0.500026	−	0.288690i	−0.728724	+	0.684807i	$0.759886\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			4.71563i			0.455878i	0.973675	+	0.227939i	$0.0731986\pi$
$107$			4.71563i			0.455878i	−0.973675	+	0.227939i	$0.926801\pi$
$108$		0			0
$109$	4.23669			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$109$	4.23669			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.91693	−	3.41614i	−0.556618	−	0.321363i	0.195169	−	0.980770i	$-0.437474\pi$
$113$	−5.91693	−	3.41614i	−0.556618	−	0.321363i	−0.751787	+	0.659406i	$0.770808\pi$
$114$		0			0
$115$	−7.47736	+	4.31705i	−0.697267	+	0.402567i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.65458	+	0.485942i	−0.426685	+	0.0445462i
$120$		0			0
$121$	10.6123	−	18.3810i	0.964754	−	1.67100i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.5263			0.941504
$126$		0			0
$127$	6.67667			0.592459			0.296229	−	0.955117i	$-0.404271\pi$
$127$	6.67667			0.592459			0.296229	+	0.955117i	$0.404271\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.73653	+	6.47185i	−0.326462	+	0.565448i	−0.981807	−	0.189881i	$-0.939190\pi$
$131$	−3.73653	+	6.47185i	−0.326462	+	0.565448i	0.655345	+	0.755329i	$0.272523\pi$
$132$		0			0
$133$	0.313000	+	2.99806i	0.0271406	+	0.259965i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.91772	+	3.99395i	−0.591021	+	0.341226i	−0.765501	−	0.643435i	$-0.777509\pi$
$137$	−6.91772	+	3.99395i	−0.591021	+	0.341226i	0.174480	+	0.984661i	$0.444175\pi$
$138$		0			0
$139$	17.9792	+	10.3803i	1.52498	+	0.880446i	0.999562	+	0.0295993i	$0.00942312\pi$
$139$	17.9792	+	10.3803i	1.52498	+	0.880446i	0.525415	+	0.850846i	$0.323910\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.76302			0.816425
$144$		0			0
$145$			9.76302i			0.810774i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.03726	+	0.598865i	0.0849760	+	0.0490609i	0.541886	−	0.840452i	$-0.317710\pi$
$149$	1.03726	+	0.598865i	0.0849760	+	0.0490609i	−0.456910	+	0.889513i	$0.651044\pi$
$150$		0			0
$151$	7.61229	+	13.1849i	0.619480	+	1.07297i	0.989581	+	0.143979i	$0.0459897\pi$
$151$	7.61229	+	13.1849i	0.619480	+	1.07297i	−0.370101	+	0.928991i	$0.620677\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−17.0300	+	9.83228i	−1.36788	+	0.789748i
$156$		0			0
$157$	−8.68358	−	5.01347i	−0.693025	−	0.400118i	0.111719	−	0.993740i	$-0.464364\pi$
$157$	−8.68358	−	5.01347i	−0.693025	−	0.400118i	−0.804744	+	0.593621i	$0.797698\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.88000	−	3.96104i	−0.699842	−	0.312173i
$162$		0			0
$163$	−12.0032			−0.940160			−0.470080	−	0.882624i	$-0.655775\pi$
$163$	−12.0032			−0.940160			−0.470080	+	0.882624i	$0.655775\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.57472	+	14.8518i	−0.663532	+	1.14927i	0.316150	+	0.948709i	$0.397610\pi$
$167$	−8.57472	+	14.8518i	−0.663532	+	1.14927i	−0.979681	+	0.200561i	$0.935723\pi$
$168$		0			0
$169$	−5.02106	−	8.69673i	−0.386235	−	0.668979i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.993738	+	1.72121i	0.0755525	+	0.130861i	0.901326	−	0.433140i	$-0.142595\pi$
$173$	0.993738	+	1.72121i	0.0755525	+	0.130861i	−0.825774	+	0.564001i	$0.809261\pi$
$174$		0			0
$175$	−0.807090	−	1.11249i	−0.0610103	−	0.0840964i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			8.31122i			0.621210i	0.950539	+	0.310605i	$0.100532\pi$
$179$			8.31122i			0.621210i	−0.950539	+	0.310605i	$0.899468\pi$
$180$		0			0
$181$		−	15.4541i		−	1.14870i	−0.818611	−	0.574348i	$-0.805256\pi$
$181$		−	15.4541i		−	1.14870i	0.818611	−	0.574348i	$-0.194744\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.8044	+	18.7137i	−0.794354	+	1.37586i
$186$		0			0
$187$	8.69581	−	5.02053i	0.635901	−	0.367137i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.6851	−	6.16904i	0.773146	−	0.446376i	−0.0608498	−	0.998147i	$-0.519381\pi$
$191$	10.6851	−	6.16904i	0.773146	−	0.446376i	0.833996	+	0.551771i	$0.186048\pi$
$192$		0			0
$193$	−2.19694	+	3.80521i	−0.158139	+	0.273905i	−0.934198	−	0.356756i	$-0.883883\pi$
$193$	−2.19694	+	3.80521i	−0.158139	+	0.273905i	0.776058	+	0.630661i	$0.217216\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	10.8865i		−	0.775632i	−0.921737	−	0.387816i	$-0.873230\pi$
$197$		−	10.8865i		−	0.775632i	0.921737	−	0.387816i	$-0.126770\pi$
$198$		0			0
$199$		−	27.5665i		−	1.95414i	−0.212926	−	0.977068i	$-0.568299\pi$
$199$		−	27.5665i		−	1.95414i	0.212926	−	0.977068i	$-0.431701\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.89940	+	6.45634i	−0.624616	+	0.453146i
$204$		0			0
$205$	−9.39060	−	16.2650i	−0.655868	−	1.13600i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.23377	−	5.60106i	−0.223685	−	0.387433i
$210$		0			0
$211$	−5.15561	+	8.92978i	−0.354927	+	0.614751i	−0.987105	−	0.160071i	$-0.948828\pi$
$211$	−5.15561	+	8.92978i	−0.354927	+	0.614751i	0.632179	+	0.774823i	$0.282161\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.27223			−0.564161
$216$		0			0
$217$	−20.2246	−	9.02143i	−1.37293	−	0.612415i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.63455	+	1.52106i	0.177219	+	0.102318i
$222$		0			0
$223$	−6.24329	+	3.60456i	−0.418081	+	0.241379i	−0.694256	−	0.719728i	$-0.744267\pi$
$223$	−6.24329	+	3.60456i	−0.418081	+	0.241379i	0.276175	+	0.961107i	$0.410933\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.37800	−	11.0470i	−0.423323	−	0.733217i	0.572939	−	0.819598i	$-0.305803\pi$
$227$	−6.37800	−	11.0470i	−0.423323	−	0.733217i	−0.996262	+	0.0863812i	$0.972470\pi$
$228$		0			0
$229$	−3.89208	−	2.24709i	−0.257196	−	0.148492i	0.365859	−	0.930670i	$-0.380775\pi$
$229$	−3.89208	−	2.24709i	−0.257196	−	0.148492i	−0.623055	+	0.782178i	$0.714109\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	2.15403i		−	0.141115i	−0.997508	−	0.0705577i	$-0.977522\pi$
$233$		−	2.15403i		−	0.141115i	0.997508	−	0.0705577i	$-0.0224779\pi$
$234$		0			0
$235$	−27.7456			−1.80993
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−8.78317	−	5.07096i	−0.568136	−	0.328013i	0.188269	−	0.982118i	$-0.439712\pi$
$239$	−8.78317	−	5.07096i	−0.568136	−	0.328013i	−0.756404	+	0.654104i	$0.773046\pi$
$240$		0			0
$241$	−9.13490	+	5.27404i	−0.588431	+	0.339731i	−0.764477	−	0.644651i	$-0.777003\pi$
$241$	−9.13490	+	5.27404i	−0.588431	+	0.339731i	0.176046	+	0.984382i	$0.443669\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.10370	−	15.6335i	0.326064	−	0.998789i
$246$		0			0
$247$	0.979729	−	1.69694i	0.0623387	−	0.107974i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	29.3005			1.84943			0.924714	−	0.380662i	$-0.124304\pi$
$251$	29.3005			1.84943			0.924714	+	0.380662i	$0.124304\pi$
$252$		0			0
$253$	20.8623			1.31160
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−3.81430	+	6.60656i	−0.237930	+	0.412106i	−0.960120	−	0.279588i	$-0.909802\pi$
$257$	−3.81430	+	6.60656i	−0.237930	+	0.412106i	0.722190	+	0.691694i	$0.243135\pi$
$258$		0			0
$259$	−24.2034	+	2.52685i	−1.50392	+	0.157011i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.5531	+	6.09281i	−0.650729	+	0.375699i	−0.788736	−	0.614733i	$-0.789264\pi$
$263$	−10.5531	+	6.09281i	−0.650729	+	0.375699i	0.138006	+	0.990431i	$0.455931\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	2.77433			0.169154			0.0845771	−	0.996417i	$-0.473046\pi$
$269$	2.77433			0.169154			0.0845771	+	0.996417i	$0.473046\pi$
$270$		0			0
$271$			3.20793i			0.194868i	0.995242	+	0.0974338i	$0.0310634\pi$
$271$			3.20793i			0.194868i	−0.995242	+	0.0974338i	$0.968937\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.55385	+	1.47446i	0.154003	+	0.0889135i
$276$		0			0
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	0.673925	−	0.738800i	$-0.264607\pi$
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	−0.976782	+	0.214236i	$0.931274\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.21999	+	2.43641i	−0.251743	+	0.145344i	−0.620562	−	0.784157i	$-0.713096\pi$
$281$	−4.21999	+	2.43641i	−0.251743	+	0.145344i	0.368819	+	0.929501i	$0.379762\pi$
$282$		0			0
$283$	−2.44030	−	1.40891i	−0.145061	−	0.0837508i	0.425713	−	0.904858i	$-0.360023\pi$
$283$	−2.44030	−	1.40891i	−0.145061	−	0.0837508i	−0.570774	+	0.821107i	$0.693357\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.61618	−	19.3161i	0.508597	−	1.14019i
$288$		0			0
$289$	−13.8712			−0.815956
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.05694	+	7.02683i	−0.237009	+	0.410512i	−0.959855	−	0.280498i	$-0.909500\pi$
$293$	−4.05694	+	7.02683i	−0.237009	+	0.410512i	0.722846	+	0.691010i	$0.242834\pi$
$294$		0			0
$295$	2.61914	+	4.53648i	0.152492	+	0.264124i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.16030	+	5.47381i	0.182765	+	0.316558i
$300$		0			0
$301$	−5.47047	−	7.54049i	−0.315313	−	0.434626i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			21.1435i			1.21067i
$306$		0			0
$307$		−	10.8996i		−	0.622074i	−0.950398	−	0.311037i	$-0.899324\pi$
$307$		−	10.8996i		−	0.622074i	0.950398	−	0.311037i	$-0.100676\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.11819	+	7.13291i	−0.233521	+	0.404470i	−0.958842	−	0.283941i	$-0.908358\pi$
$311$	−4.11819	+	7.13291i	−0.233521	+	0.404470i	0.725321	+	0.688411i	$0.241691\pi$
$312$		0			0
$313$	29.2736	−	16.9011i	1.65464	−	0.955308i	0.679516	−	0.733661i	$-0.262190\pi$
$313$	29.2736	−	16.9011i	1.65464	−	0.955308i	0.975127	−	0.221648i	$-0.0711435\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.82913	+	3.36545i	−0.327396	+	0.189022i	−0.654685	−	0.755902i	$-0.727199\pi$
$317$	−5.82913	+	3.36545i	−0.327396	+	0.189022i	0.327288	+	0.944925i	$0.393865\pi$
$318$		0			0
$319$	11.7950	−	20.4296i	0.660394	−	1.14384i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	2.01526i		−	0.112132i
$324$		0			0
$325$			0.893431i			0.0495586i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−18.3484	−	25.2913i	−1.01158	−	1.39436i
$330$		0			0
$331$	−16.0284	−	27.7621i	−0.881002	−	1.52594i	−0.850228	−	0.526415i	$-0.823536\pi$
$331$	−16.0284	−	27.7621i	−0.881002	−	1.52594i	−0.0307744	−	0.999526i	$-0.509797\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−12.7702	−	22.1187i	−0.697712	−	1.20847i
$336$		0			0
$337$	−12.1123	+	20.9791i	−0.659799	+	1.14280i	0.320869	+	0.947124i	$0.396025\pi$
$337$	−12.1123	+	20.9791i	−0.659799	+	1.14280i	−0.980668	+	0.195681i	$0.937308\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	47.5148			2.57307
$342$		0			0
$343$	17.6257	−	5.68629i	0.951700	−	0.307031i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	19.7453	+	11.3999i	1.05998	+	0.611981i	0.925427	−	0.378926i	$-0.123706\pi$
$347$	19.7453	+	11.3999i	1.05998	+	0.611981i	0.134554	+	0.990906i	$0.457040\pi$
$348$		0			0
$349$	2.46389	−	1.42253i	0.131889	−	0.0761461i	−0.432604	−	0.901584i	$-0.642405\pi$
$349$	2.46389	−	1.42253i	0.131889	−	0.0761461i	0.564493	+	0.825438i	$0.309072\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.57212	−	6.18709i	−0.190125	−	0.329306i	0.755167	−	0.655533i	$-0.227556\pi$
$353$	−3.57212	−	6.18709i	−0.190125	−	0.329306i	−0.945291	+	0.326227i	$0.894223\pi$
$354$		0			0
$355$	−9.19856	−	5.31079i	−0.488209	−	0.281868i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			11.6037i			0.612421i	0.951964	+	0.306210i	$0.0990611\pi$
$359$			11.6037i			0.612421i	−0.951964	+	0.306210i	$0.900939\pi$
$360$		0			0
$361$	17.7019			0.931682
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.8695	+	6.27554i	0.568938	+	0.328477i
$366$		0			0
$367$	6.78525	−	3.91747i	0.354187	−	0.204490i	−0.312341	−	0.949970i	$-0.601113\pi$
$367$	6.78525	−	3.91747i	0.354187	−	0.204490i	0.666528	+	0.745480i	$0.267780\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	0.314905	+	0.949123i	$0.398027\pi$
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	−0.979417	+	0.201845i	$0.935306\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	7.14702			0.368091
$378$		0			0
$379$	15.1045			0.775868			0.387934	−	0.921687i	$-0.373189\pi$
$379$	15.1045			0.775868			0.387934	+	0.921687i	$0.373189\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.763322	+	1.32211i	−0.0390040	+	0.0675568i	−0.884868	−	0.465841i	$-0.845752\pi$
$383$	−0.763322	+	1.32211i	−0.0390040	+	0.0675568i	0.845864	+	0.533398i	$0.179085\pi$
$384$		0			0
$385$	3.66388	+	35.0944i	0.186729	+	1.78858i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.8948	+	7.44483i	−0.653794	+	0.377468i	−0.789908	−	0.613225i	$-0.789872\pi$
$389$	−12.8948	+	7.44483i	−0.653794	+	0.377468i	0.136115	+	0.990693i	$0.456538\pi$
$390$		0			0
$391$	5.62969	+	3.25030i	0.284706	+	0.164375i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−30.6085			−1.54008
$396$		0			0
$397$			28.7869i			1.44478i	0.691488	+	0.722388i	$0.256955\pi$
$397$			28.7869i			1.44478i	−0.691488	+	0.722388i	$0.743045\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	33.0592	+	19.0868i	1.65090	+	0.953147i	0.976703	+	0.214595i	$0.0688431\pi$
$401$	33.0592	+	19.0868i	1.65090	+	0.953147i	0.674196	+	0.738552i	$0.264490\pi$
$402$		0			0
$403$	7.19773	+	12.4668i	0.358544	+	0.621017i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	45.2173	−	26.1062i	2.24134	−	1.29404i
$408$		0			0
$409$	−6.03355	−	3.48347i	−0.298340	−	0.172247i	0.343357	−	0.939205i	$-0.388436\pi$
$409$	−6.03355	−	3.48347i	−0.298340	−	0.172247i	−0.641697	+	0.766958i	$0.721769\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.40314	+	5.38745i	−0.118251	+	0.265099i
$414$		0			0
$415$	29.4750			1.44687
$416$		0			0
$417$		0			0
$418$		0			0
$419$	17.4232	−	30.1778i	0.851177	−	1.47428i	−0.0289690	−	0.999580i	$-0.509222\pi$
$419$	17.4232	−	30.1778i	0.851177	−	1.47428i	0.880146	−	0.474702i	$-0.157444\pi$
$420$		0			0
$421$	2.84597	+	4.92936i	0.138704	+	0.240242i	0.927006	−	0.375046i	$-0.122373\pi$
$421$	2.84597	+	4.92936i	0.138704	+	0.240242i	−0.788302	+	0.615288i	$0.789040\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.459437	+	0.795769i	0.0222860	+	0.0386005i
$426$		0			0
$427$	−19.2732	+	13.9823i	−0.932696	+	0.676652i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	30.2936i		−	1.45919i	−0.683880	−	0.729595i	$-0.739709\pi$
$431$		−	30.2936i		−	1.45919i	0.683880	−	0.729595i	$-0.260291\pi$
$432$		0			0
$433$			23.6094i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$433$			23.6094i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.09355	−	3.62614i	0.100148	−	0.173462i
$438$		0			0
$439$	21.6681	−	12.5101i	1.03416	−	0.597075i	0.115989	−	0.993250i	$-0.462996\pi$
$439$	21.6681	−	12.5101i	1.03416	−	0.597075i	0.918175	+	0.396175i	$0.129663\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−19.9446	+	11.5150i	−0.947595	+	0.547094i	−0.892333	−	0.451377i	$-0.850933\pi$
$443$	−19.9446	+	11.5150i	−0.947595	+	0.547094i	−0.0552622	+	0.998472i	$0.517599\pi$
$444$		0			0
$445$	−1.36387	+	2.36229i	−0.0646537	+	0.111983i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	15.9028i		−	0.750501i	−0.926923	−	0.375251i	$-0.877557\pi$
$449$		−	15.9028i		−	0.750501i	0.926923	−	0.375251i	$-0.122443\pi$
$450$		0			0
$451$			45.3804i			2.13688i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.65298	+	6.27756i	−0.405658	+	0.294297i
$456$		0			0
$457$	2.83307	+	4.90702i	0.132525	+	0.229541i	0.924649	−	0.380819i	$-0.124358\pi$
$457$	2.83307	+	4.90702i	0.132525	+	0.229541i	−0.792124	+	0.610360i	$0.791025\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−15.7292	−	27.2438i	−0.732582	−	1.26887i	−0.955776	−	0.294095i	$-0.904982\pi$
$461$	−15.7292	−	27.2438i	−0.732582	−	1.26887i	0.223194	−	0.974774i	$-0.428352\pi$
$462$		0			0
$463$	−4.55148	+	7.88340i	−0.211525	+	0.366373i	−0.952192	−	0.305500i	$-0.901176\pi$
$463$	−4.55148	+	7.88340i	−0.211525	+	0.366373i	0.740667	+	0.671873i	$0.234510\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	30.3032			1.40226			0.701132	−	0.713032i	$-0.252678\pi$
$467$	30.3032			1.40226			0.701132	+	0.713032i	$0.252678\pi$
$468$		0			0
$469$	11.7171	−	26.2678i	0.541045	−	1.21293i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	17.3100	+	9.99395i	0.795916	+	0.459522i
$474$		0			0
$475$	0.512563	−	0.295928i	0.0235180	−	0.0135781i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.33143	+	4.03816i	0.106526	+	0.184508i	0.914361	−	0.404901i	$-0.132694\pi$
$479$	2.33143	+	4.03816i	0.106526	+	0.184508i	−0.807835	+	0.589409i	$0.799361\pi$
$480$		0			0
$481$	13.6994	+	7.90935i	0.624639	+	0.360636i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	10.7844i		−	0.489693i
$486$		0			0
$487$	19.4821			0.882818			0.441409	−	0.897306i	$-0.354479\pi$
$487$	19.4821			0.882818			0.441409	+	0.897306i	$0.354479\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.7437	−	10.2443i	−0.800762	−	0.462320i	0.0429758	−	0.999076i	$-0.486316\pi$
$491$	−17.7437	−	10.2443i	−0.800762	−	0.462320i	−0.843737	+	0.536756i	$0.819649\pi$
$492$		0			0
$493$	6.36577	−	3.67528i	0.286700	−	0.165526i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.24205	−	11.8969i	−0.0557135	−	0.533651i
$498$		0			0
$499$	−5.12598	+	8.87845i	−0.229470	+	0.397454i	−0.957651	−	0.287931i	$-0.907033\pi$
$499$	−5.12598	+	8.87845i	−0.229470	+	0.397454i	0.728181	+	0.685385i	$0.240366\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.5521			0.648845			0.324422	−	0.945912i	$-0.394830\pi$
$503$	14.5521			0.648845			0.324422	+	0.945912i	$0.394830\pi$
$504$		0			0
$505$	15.5600			0.692412
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.6617	+	28.8589i	−0.738517	+	1.27915i	0.214646	+	0.976692i	$0.431140\pi$
$509$	−16.6617	+	28.8589i	−0.738517	+	1.27915i	−0.953163	+	0.302457i	$0.902193\pi$
$510$		0			0
$511$	1.46768	+	14.0581i	0.0649262	+	0.621894i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−11.9223	+	6.88335i	−0.525360	+	0.303317i
$516$		0			0
$517$	58.0591	+	33.5204i	2.55343	+	1.47423i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.53925			−0.286490			−0.143245	−	0.989687i	$-0.545754\pi$
$521$	−6.53925			−0.286490			−0.143245	+	0.989687i	$0.545754\pi$
$522$		0			0
$523$			0.786858i			0.0344069i	0.999852	+	0.0172034i	$0.00547630\pi$
$523$			0.786858i			0.0344069i	−0.999852	+	0.0172034i	$0.994524\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	12.8219	+	7.40271i	0.558530	+	0.322467i
$528$		0			0
$529$	−4.74685	−	8.22178i	−0.206385	−	0.357469i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−11.9068	+	6.87440i	−0.515741	+	0.297763i
$534$		0			0
$535$	9.59445	+	5.53936i	0.414804	+	0.239487i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−29.5671	+	26.5479i	−1.27354	+	1.14350i
$540$		0			0
$541$	5.60454			0.240958			0.120479	−	0.992716i	$-0.461557\pi$
$541$	5.60454			0.240958			0.120479	+	0.992716i	$0.461557\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.97675	−	8.61999i	0.213181	−	0.369240i
$546$		0			0
$547$	6.91456	+	11.9764i	0.295645	+	0.512073i	0.975135	−	0.221612i	$-0.0711320\pi$
$547$	6.91456	+	11.9764i	0.295645	+	0.512073i	−0.679489	+	0.733685i	$0.737799\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.36729	−	4.10026i	−0.100850	−	0.174677i
$552$		0			0
$553$	−20.2415	−	27.9009i	−0.860758	−	1.18647i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	27.8233i		−	1.17891i	−0.807800	−	0.589456i	$-0.799342\pi$
$557$		−	27.8233i		−	1.17891i	0.807800	−	0.589456i	$-0.200658\pi$
$558$		0			0
$559$			6.05569i			0.256128i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−12.2650	+	21.2436i	−0.516909	+	0.895312i	0.482898	+	0.875676i	$0.339584\pi$
$563$	−12.2650	+	21.2436i	−0.516909	+	0.895312i	−0.999807	+	0.0196359i	$0.993749\pi$
$564$		0			0
$565$	−13.9010	+	8.02574i	−0.584819	+	0.337645i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	23.4762	−	13.5540i	0.984172	−	0.568212i	0.0806449	−	0.996743i	$-0.474302\pi$
$569$	23.4762	−	13.5540i	0.984172	−	0.568212i	0.903527	+	0.428531i	$0.140969\pi$
$570$		0			0
$571$	−14.9177	+	25.8382i	−0.624287	+	1.08130i	0.364391	+	0.931246i	$0.381277\pi$
$571$	−14.9177	+	25.8382i	−0.624287	+	1.08130i	−0.988678	+	0.150051i	$0.952056\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			1.90915i			0.0796169i
$576$		0			0
$577$		−	28.1666i		−	1.17259i	−0.810097	−	0.586296i	$-0.800585\pi$
$577$		−	28.1666i		−	1.17259i	0.810097	−	0.586296i	$-0.199415\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	19.4920	+	26.8677i	0.808663	+	1.11466i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.95928	−	8.58973i	−0.204692	−	0.354536i	0.745343	−	0.666681i	$-0.232286\pi$
$587$	−4.95928	−	8.58973i	−0.204692	−	0.354536i	−0.950034	+	0.312145i	$0.898952\pi$
$588$		0			0
$589$	4.76816	−	8.25870i	0.196469	−	0.340294i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−4.69872			−0.192953			−0.0964766	−	0.995335i	$-0.530757\pi$
$593$	−4.69872			−0.192953			−0.0964766	+	0.995335i	$0.530757\pi$
$594$		0			0
$595$	−4.47894	+	10.0411i	−0.183619	+	0.411643i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	12.7309	+	7.35019i	0.520170	+	0.300320i	0.737004	−	0.675888i	$-0.236240\pi$
$599$	12.7309	+	7.35019i	0.520170	+	0.300320i	−0.216834	+	0.976208i	$0.569573\pi$
$600$		0			0
$601$	−16.2923	+	9.40634i	−0.664575	+	0.383693i	−0.794018	−	0.607894i	$-0.792014\pi$
$601$	−16.2923	+	9.40634i	−0.664575	+	0.383693i	0.129443	+	0.991587i	$0.458681\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−24.9321	−	43.1836i	−1.01363	−	1.75566i
$606$		0			0
$607$	10.9051	+	6.29608i	0.442625	+	0.255550i	0.704711	−	0.709495i	$-0.251077\pi$
$607$	10.9051	+	6.29608i	0.442625	+	0.255550i	−0.262085	+	0.965045i	$0.584410\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			20.3112i			0.821704i
$612$		0			0
$613$	−9.82017			−0.396633			−0.198317	−	0.980138i	$-0.563547\pi$
$613$	−9.82017			−0.396633			−0.198317	+	0.980138i	$0.563547\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.25158	+	1.87730i	0.130904	+	0.0755772i	0.564022	−	0.825760i	$-0.309253\pi$
$617$	3.25158	+	1.87730i	0.130904	+	0.0755772i	−0.433118	+	0.901337i	$0.642587\pi$
$618$		0			0
$619$	9.56902	−	5.52468i	0.384611	−	0.222055i	−0.295211	−	0.955432i	$-0.595390\pi$
$619$	9.56902	−	5.52468i	0.384611	−	0.222055i	0.679823	+	0.733376i	$0.262057\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.05527	+	0.318972i	−0.122407	+	0.0127794i
$624$		0			0
$625$	13.6638	−	23.6664i	0.546551	−	0.946654i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	16.2692			0.648696
$630$		0			0
$631$	−19.4921			−0.775969			−0.387984	−	0.921666i	$-0.626829\pi$
$631$	−19.4921			−0.775969			−0.387984	+	0.921666i	$0.626829\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.84294	−	13.5844i	0.311238	−	0.539080i
$636$		0			0
$637$	−11.4445	−	3.73617i	−0.453449	−	0.148032i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	22.6669	−	13.0868i	0.895290	−	0.516896i	0.0196208	−	0.999807i	$-0.493754\pi$
$641$	22.6669	−	13.0868i	0.895290	−	0.516896i	0.875669	+	0.482912i	$0.160421\pi$
$642$		0			0
$643$	9.50955	+	5.49034i	0.375020	+	0.216518i	0.675649	−	0.737223i	$-0.263863\pi$
$643$	9.50955	+	5.49034i	0.375020	+	0.216518i	−0.300629	+	0.953741i	$0.597197\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−32.0126			−1.25855			−0.629273	−	0.777185i	$-0.716647\pi$
$647$	−32.0126			−1.25855			−0.629273	+	0.777185i	$0.716647\pi$
$648$		0			0
$649$		−	12.6570i		−	0.496833i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.3686	−	11.1825i	−0.757952	−	0.437604i	0.0706080	−	0.997504i	$-0.477506\pi$
$653$	−19.3686	−	11.1825i	−0.757952	−	0.437604i	−0.828560	+	0.559900i	$0.810839\pi$
$654$		0			0
$655$	8.77843	+	15.2047i	0.343002	+	0.594097i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−19.2546	+	11.1166i	−0.750053	+	0.433043i	−0.825713	−	0.564091i	$-0.809227\pi$
$659$	−19.2546	+	11.1166i	−0.750053	+	0.433043i	0.0756603	+	0.997134i	$0.475894\pi$
$660$		0			0
$661$	9.13646	+	5.27494i	0.355367	+	0.205171i	0.667047	−	0.745016i	$-0.267558\pi$
$661$	9.13646	+	5.27494i	0.355367	+	0.205171i	−0.311679	+	0.950187i	$0.600892\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	6.46754	+	2.88493i	0.250801	+	0.111873i
$666$		0			0
$667$	15.2723			0.591344
$668$		0			0
$669$		0			0
$670$		0			0
$671$	25.5442	−	44.2438i	0.986121	−	1.70801i
$672$		0			0
$673$	9.93562	+	17.2090i	0.382990	+	0.663358i	0.991488	−	0.130197i	$-0.0415610\pi$
$673$	9.93562	+	17.2090i	0.382990	+	0.663358i	−0.608498	+	0.793555i	$0.708228\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.96449	−	13.7949i	−0.306100	−	0.530181i	0.671405	−	0.741090i	$-0.265691\pi$
$677$	−7.96449	−	13.7949i	−0.306100	−	0.530181i	−0.977506	+	0.210909i	$0.932358\pi$
$678$		0			0
$679$	9.83041	−	7.13176i	0.377256	−	0.273692i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	19.0269i		−	0.728042i	−0.931391	−	0.364021i	$-0.881404\pi$
$683$		−	19.0269i		−	0.728042i	0.931391	−	0.364021i	$-0.118596\pi$
$684$		0			0
$685$			18.7664i			0.717028i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.139477	−	0.0805273i	0.00530597	−	0.00306340i	−0.497345	−	0.867553i	$-0.665692\pi$
$691$	0.139477	−	0.0805273i	0.00530597	−	0.00306340i	0.502651	+	0.864490i	$0.332358\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	42.2396	−	24.3870i	1.60224	−	0.925053i
$696$		0			0
$697$	−7.07017	+	12.2459i	−0.267802	+	0.463847i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	9.98234i		−	0.377028i	−0.982071	−	0.188514i	$-0.939633\pi$
$701$		−	9.98234i		−	0.377028i	0.982071	−	0.188514i	$-0.0603670\pi$
$702$		0			0
$703$		−	10.4792i		−	0.395229i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	10.2899	+	14.1836i	0.386993	+	0.533430i
$708$		0			0
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	0.998857	−	0.0477959i	$-0.0152197\pi$
$709$	12.1962	+	21.1244i	0.458036	+	0.793342i	−0.540821	+	0.841138i	$0.681886\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	15.3806	+	26.6400i	0.576008	+	0.997676i
$714$		0			0
$715$	11.4684	−	19.8639i	0.428894	−	0.742867i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	16.2692			0.606739			0.303370	−	0.952873i	$-0.401888\pi$
$719$	16.2692			0.606739			0.303370	+	0.952873i	$0.401888\pi$
$720$		0			0
$721$	−14.1588	−	6.31570i	−0.527300	−	0.235209i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.86955	+	1.07938i	0.0694332	+	0.0400873i
$726$		0			0
$727$	20.6626	−	11.9296i	0.766335	−	0.442444i	−0.0652306	−	0.997870i	$-0.520778\pi$
$727$	20.6626	−	11.9296i	0.766335	−	0.442444i	0.831566	+	0.555427i	$0.187445\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.11408	+	5.39374i	0.115178	+	0.199495i
$732$		0			0
$733$	−10.6259	−	6.13486i	−0.392476	−	0.226596i	0.290756	−	0.956797i	$-0.406093\pi$
$733$	−10.6259	−	6.13486i	−0.392476	−	0.226596i	−0.683233	+	0.730201i	$0.739426\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			61.7125i			2.27321i
$738$		0			0
$739$	−41.8891			−1.54092			−0.770459	−	0.637490i	$-0.779973\pi$
$739$	−41.8891			−1.54092			−0.770459	+	0.637490i	$0.779973\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	43.9160	+	25.3549i	1.61112	+	0.930182i	0.989111	+	0.147173i	$0.0470176\pi$
$743$	43.9160	+	25.3549i	1.61112	+	0.930182i	0.622011	+	0.783008i	$0.286316\pi$
$744$		0			0
$745$	2.43690	−	1.40695i	0.0892813	−	0.0515466i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.29550	+	12.4090i	0.0473367	+	0.453413i
$750$		0			0
$751$	−16.3683	+	28.3508i	−0.597289	+	1.03454i	0.395930	+	0.918281i	$0.370422\pi$
$751$	−16.3683	+	28.3508i	−0.597289	+	1.03454i	−0.993219	+	0.116255i	$0.962911\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	35.7680			1.30173
$756$		0			0
$757$	−17.9255			−0.651512			−0.325756	−	0.945454i	$-0.605619\pi$
$757$	−17.9255			−0.651512			−0.325756	+	0.945454i	$0.605619\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.8509	−	37.8469i	0.792096	−	1.37195i	−0.132571	−	0.991174i	$-0.542323\pi$
$761$	21.8509	−	37.8469i	0.792096	−	1.37195i	0.924667	−	0.380777i	$-0.124343\pi$
$762$		0			0
$763$	11.1486	−	1.16393i	0.403608	−	0.0421370i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.32093	−	1.91734i	0.119912	−	0.0692311i
$768$		0			0
$769$	37.0864	+	21.4118i	1.33737	+	0.772131i	0.986417	−	0.164262i	$-0.0525242\pi$
$769$	37.0864	+	21.4118i	1.33737	+	0.772131i	0.350953	+	0.936393i	$0.385858\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−21.6051			−0.777080			−0.388540	−	0.921432i	$-0.627020\pi$
$773$	−21.6051			−0.777080			−0.388540	+	0.921432i	$0.627020\pi$
$774$		0			0
$775$			4.34816i			0.156191i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	7.88771	+	4.55397i	0.282606	+	0.163163i
$780$		0			0
$781$	12.8323	+	22.2262i	0.459175	+	0.795315i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−20.4008	+	11.7784i	−0.728137	+	0.420390i
$786$		0			0
$787$	−44.4307	−	25.6521i	−1.58378	−	0.914398i	−0.994300	−	0.106618i	$-0.965998\pi$
$787$	−44.4307	−	25.6521i	−1.58378	−	0.914398i	−0.589484	−	0.807780i	$-0.700669\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−16.5086	−	7.36387i	−0.586978	−	0.261829i
$792$		0			0
$793$	15.4781			0.549644
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−0.899094	+	1.55728i	−0.0318476	+	0.0551616i	−0.881510	−	0.472166i	$-0.843472\pi$
$797$	−0.899094	+	1.55728i	−0.0318476	+	0.0551616i	0.849662	+	0.527327i	$0.176806\pi$
$798$		0			0
$799$	10.4448	+	18.0910i	0.369512	+	0.640013i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−15.1634	−	26.2637i	−0.535103	−	0.926826i
$804$		0			0
$805$	−18.4903	+	13.4143i	−0.651697	+	0.472793i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	40.6883i		−	1.43052i	−0.698857	−	0.715262i	$-0.746308\pi$
$809$		−	40.6883i		−	1.43052i	0.698857	−	0.715262i	$-0.253692\pi$
$810$		0			0
$811$			0.378710i			0.0132983i	0.999978	+	0.00664916i	$0.00211651\pi$
$811$			0.378710i			0.0132983i	−0.999978	+	0.00664916i	$0.997883\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−14.0999	+	24.4217i	−0.493896	+	0.855453i
$816$		0			0
$817$	3.47416	−	2.00581i	0.121545	−	0.0701743i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.4968	+	6.63771i	−0.401243	+	0.231658i	−0.687020	−	0.726638i	$-0.741082\pi$
$821$	−11.4968	+	6.63771i	−0.401243	+	0.231658i	0.285777	+	0.958296i	$0.407748\pi$
$822$		0			0
$823$	13.8711	−	24.0255i	0.483517	−	0.837476i	−0.516304	−	0.856405i	$-0.672692\pi$
$823$	13.8711	−	24.0255i	0.483517	−	0.837476i	0.999821	+	0.0189295i	$0.00602582\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			27.7183i			0.963859i	0.876210	+	0.481929i	$0.160064\pi$
$827$			27.7183i			0.963859i	−0.876210	+	0.481929i	$0.839936\pi$
$828$		0			0
$829$		−	42.7361i		−	1.48429i	−0.670242	−	0.742143i	$-0.733810\pi$
$829$		−	42.7361i		−	1.48429i	0.670242	−	0.742143i	$-0.266190\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−12.1148	+	2.55746i	−0.419753	+	0.0886109i
$834$		0			0
$835$	20.1451	+	34.8923i	0.697149	+	1.20750i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.92438	+	3.33313i	0.0664370	+	0.115072i	0.897331	−	0.441359i	$-0.145504\pi$
$839$	1.92438	+	3.33313i	0.0664370	+	0.115072i	−0.830894	+	0.556431i	$0.812170\pi$
$840$		0			0
$841$	−5.86545	+	10.1593i	−0.202257	+	0.350319i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−23.5925			−0.811608
$846$		0			0
$847$	22.8760	−	51.2842i	0.786028	−	1.76215i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	29.2738	+	16.9013i	1.00349	+	0.579368i
$852$		0			0
$853$	26.3470	−	15.2114i	0.902103	−	0.520830i	0.0242213	−	0.999707i	$-0.492289\pi$
$853$	26.3470	−	15.2114i	0.902103	−	0.520830i	0.877882	+	0.478877i	$0.158956\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	19.4657	+	33.7156i	0.664937	+	1.15170i	0.979303	+	0.202402i	$0.0648748\pi$
$857$	19.4657	+	33.7156i	0.664937	+	1.15170i	−0.314366	+	0.949302i	$0.601792\pi$
$858$		0			0
$859$	11.5922	+	6.69275i	0.395520	+	0.228354i	0.684549	−	0.728967i	$-0.259999\pi$
$859$	11.5922	+	6.69275i	0.395520	+	0.228354i	−0.289029	+	0.957320i	$0.593332\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	21.7219i		−	0.739424i	−0.929146	−	0.369712i	$-0.879456\pi$
$863$		−	21.7219i		−	0.739424i	0.929146	−	0.369712i	$-0.120544\pi$
$864$		0			0
$865$	4.66929			0.158761
$866$		0			0
$867$		0			0
$868$		0			0
$869$	64.0496	+	36.9791i	2.17273	+	1.25443i
$870$		0			0
$871$	−16.1920	+	9.34845i	−0.548645	+	0.316760i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	27.6995	−	2.89185i	0.936415	−	0.0977625i
$876$		0			0
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	−0.869318	−	0.494253i	$-0.835442\pi$
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	0.862695	+	0.505725i	$0.168775\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	43.3363			1.46004			0.730018	−	0.683427i	$-0.239511\pi$
$881$	43.3363			1.46004			0.730018	+	0.683427i	$0.239511\pi$
$882$		0			0
$883$	−2.17403			−0.0731618			−0.0365809	−	0.999331i	$-0.511647\pi$
$883$	−2.17403			−0.0731618			−0.0365809	+	0.999331i	$0.511647\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.72215	−	9.91105i	0.192131	−	0.332781i	−0.753825	−	0.657075i	$-0.771793\pi$
$887$	5.72215	−	9.91105i	0.192131	−	0.332781i	0.945956	+	0.324294i	$0.105127\pi$
$888$		0			0
$889$	17.5693	−	1.83425i	0.589256	−	0.0615188i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	11.6526	−	6.72762i	0.389939	−	0.225131i
$894$		0			0
$895$	16.9100	+	9.76302i	0.565240	+	0.326342i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	34.7832			1.16009
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−31.4430	−	18.1536i	−1.04520	−	0.603447i
$906$		0			0
$907$	−26.9446	−	46.6694i	−0.894680	−	1.54963i	−0.834200	−	0.551462i	$-0.814070\pi$
$907$	−26.9446	−	46.6694i	−0.894680	−	1.54963i	−0.0604797	−	0.998169i	$-0.519263\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.00460	+	4.04411i	−0.232073	+	0.133987i	−0.611528	−	0.791223i	$-0.709445\pi$
$911$	−7.00460	+	4.04411i	−0.232073	+	0.133987i	0.379455	+	0.925210i	$0.376111\pi$
$912$		0			0
$913$	−61.6777	−	35.6097i	−2.04124	−	1.17851i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.05450	+	18.0569i	−0.265983	+	0.596290i
$918$		0			0
$919$	−25.6751			−0.846943			−0.423472	−	0.905909i	$-0.639189\pi$
$919$	−25.6751			−0.846943			−0.423472	+	0.905909i	$0.639189\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.88777	+	6.73382i	−0.127968	+	0.221646i
$924$		0			0
$925$	2.38903	+	4.13792i	0.0785507	+	0.136054i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.42618	+	9.39842i	0.178027	+	0.308352i	0.941205	−	0.337837i	$-0.109695\pi$
$929$	5.42618	+	9.39842i	0.178027	+	0.308352i	−0.763177	+	0.646189i	$0.776362\pi$
$930$		0			0
$931$	1.64729	+	7.80326i	0.0539877	+	0.255742i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	23.5900i		−	0.771477i
$936$		0			0
$937$		−	0.458120i		−	0.0149661i	−0.999972	−	0.00748306i	$-0.997618\pi$
$937$		−	0.458120i		−	0.0149661i	0.999972	−	0.00748306i	$-0.00238195\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.68890	+	6.38937i	−0.120255	+	0.208287i	−0.919868	−	0.392228i	$-0.871704\pi$
$941$	−3.68890	+	6.38937i	−0.120255	+	0.208287i	0.799613	+	0.600515i	$0.205038\pi$
$942$		0			0
$943$	−25.4433	+	14.6897i	−0.828548	+	0.478362i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−10.3846	+	5.99552i	−0.337453	+	0.194828i	−0.659145	−	0.752016i	$-0.729082\pi$
$947$	−10.3846	+	5.99552i	−0.337453	+	0.194828i	0.321692	+	0.946844i	$0.395748\pi$
$948$		0			0
$949$	4.59401	−	7.95706i	0.149128	−	0.258297i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	58.6883i		−	1.90110i	−0.310572	−	0.950550i	$-0.600521\pi$
$953$		−	58.6883i		−	1.90110i	0.310572	−	0.950550i	$-0.399479\pi$
$954$		0			0
$955$		−	28.9866i		−	0.937983i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.1064	+	12.4103i	−0.552394	+	0.400751i
$960$		0			0
$961$	19.5300	+	33.8270i	0.630000	+	1.09119i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	5.16140	+	8.93981i	0.166151	+	0.287783i
$966$		0			0
$967$	3.37560	−	5.84671i	0.108552	−	0.188018i	−0.806632	−	0.591054i	$-0.798712\pi$
$967$	3.37560	−	5.84671i	0.108552	−	0.188018i	0.915184	+	0.403037i	$0.132045\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	6.40724			0.205618			0.102809	−	0.994701i	$-0.467217\pi$
$971$	6.40724			0.205618			0.102809	+	0.994701i	$0.467217\pi$
$972$		0			0
$973$	50.1631	+	22.3759i	1.60816	+	0.717338i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.7769	−	6.79937i	−0.376775	−	0.217531i	0.299639	−	0.954053i	$-0.403134\pi$
$977$	−11.7769	−	6.79937i	−0.376775	−	0.217531i	−0.676414	+	0.736521i	$0.736467\pi$
$978$		0			0
$979$	5.70793	−	3.29547i	0.182426	−	0.105324i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−11.3849	−	19.7192i	−0.363122	−	0.628946i	0.625351	−	0.780344i	$-0.284956\pi$
$983$	−11.3849	−	19.7192i	−0.363122	−	0.628946i	−0.988473	+	0.151398i	$0.951623\pi$
$984$		0			0
$985$	−22.1497	−	12.7882i	−0.705749	−	0.407464i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			12.9402i			0.411475i
$990$		0			0
$991$	26.9905			0.857383			0.428691	−	0.903451i	$-0.358975\pi$
$991$	26.9905			0.857383			0.428691	+	0.903451i	$0.358975\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−56.0869	−	32.3818i	−1.77807	−	1.02657i
$996$		0			0
$997$	16.7263	−	9.65694i	0.529728	−	0.305838i	−0.211178	−	0.977448i	$-0.567730\pi$
$997$	16.7263	−	9.65694i	0.529728	−	0.305838i	0.740906	+	0.671609i	$0.234397\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.b.881.7		16
3.2	odd	2		1008.2.cc.b.545.6		16
4.3	odd	2		378.2.m.a.125.7		16
7.6	odd	2	inner	3024.2.cc.b.881.2		16
9.2	odd	6	inner	3024.2.cc.b.2897.2		16
9.7	even	3		1008.2.cc.b.209.3		16
12.11	even	2		126.2.m.a.41.2	✓	16
21.20	even	2		1008.2.cc.b.545.3		16
28.3	even	6		2646.2.l.b.1097.6		16
28.11	odd	6		2646.2.l.b.1097.7		16
28.19	even	6		2646.2.t.a.2285.3		16
28.23	odd	6		2646.2.t.a.2285.2		16
28.27	even	2		378.2.m.a.125.6		16
36.7	odd	6		126.2.m.a.83.3	yes	16
36.11	even	6		378.2.m.a.251.6		16
36.23	even	6		1134.2.d.a.1133.7		16
36.31	odd	6		1134.2.d.a.1133.10		16
63.20	even	6	inner	3024.2.cc.b.2897.7		16
63.34	odd	6		1008.2.cc.b.209.6		16
84.11	even	6		882.2.l.a.509.2		16
84.23	even	6		882.2.t.b.815.8		16
84.47	odd	6		882.2.t.b.815.5		16
84.59	odd	6		882.2.l.a.509.3		16
84.83	odd	2		126.2.m.a.41.3	yes	16
252.11	even	6		2646.2.t.a.1979.3		16
252.47	odd	6		2646.2.l.b.521.3		16
252.79	odd	6		882.2.l.a.227.7		16
252.83	odd	6		378.2.m.a.251.7		16
252.115	even	6		882.2.t.b.803.8		16
252.139	even	6		1134.2.d.a.1133.15		16
252.151	odd	6		882.2.t.b.803.5		16
252.167	odd	6		1134.2.d.a.1133.2		16
252.187	even	6		882.2.l.a.227.6		16
252.191	even	6		2646.2.l.b.521.2		16
252.223	even	6		126.2.m.a.83.2	yes	16
252.227	odd	6		2646.2.t.a.1979.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	12.11	even	2
126.2.m.a.41.3	yes	16	84.83	odd	2
126.2.m.a.83.2	yes	16	252.223	even	6
126.2.m.a.83.3	yes	16	36.7	odd	6
378.2.m.a.125.6		16	28.27	even	2
378.2.m.a.125.7		16	4.3	odd	2
378.2.m.a.251.6		16	36.11	even	6
378.2.m.a.251.7		16	252.83	odd	6
882.2.l.a.227.6		16	252.187	even	6
882.2.l.a.227.7		16	252.79	odd	6
882.2.l.a.509.2		16	84.11	even	6
882.2.l.a.509.3		16	84.59	odd	6
882.2.t.b.803.5		16	252.151	odd	6
882.2.t.b.803.8		16	252.115	even	6
882.2.t.b.815.5		16	84.47	odd	6
882.2.t.b.815.8		16	84.23	even	6
1008.2.cc.b.209.3		16	9.7	even	3
1008.2.cc.b.209.6		16	63.34	odd	6
1008.2.cc.b.545.3		16	21.20	even	2
1008.2.cc.b.545.6		16	3.2	odd	2
1134.2.d.a.1133.2		16	252.167	odd	6
1134.2.d.a.1133.7		16	36.23	even	6
1134.2.d.a.1133.10		16	36.31	odd	6
1134.2.d.a.1133.15		16	252.139	even	6
2646.2.l.b.521.2		16	252.191	even	6
2646.2.l.b.521.3		16	252.47	odd	6
2646.2.l.b.1097.6		16	28.3	even	6
2646.2.l.b.1097.7		16	28.11	odd	6
2646.2.t.a.1979.2		16	252.227	odd	6
2646.2.t.a.1979.3		16	252.11	even	6
2646.2.t.a.2285.2		16	28.23	odd	6
2646.2.t.a.2285.3		16	28.19	even	6
3024.2.cc.b.881.2		16	7.6	odd	2	inner
3024.2.cc.b.881.7		16	1.1	even	1	trivial
3024.2.cc.b.2897.2		16	9.2	odd	6	inner
3024.2.cc.b.2897.7		16	63.20	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.17468 - 2.03460i) q^{5} +(2.63145 - 0.274725i) q^{7} +O(q^{10})\)	\(q+(1.17468 - 2.03460i) q^{5} +(2.63145 - 0.274725i) q^{7} +(-4.91614 + 2.83834i) q^{11} +(-1.48943 - 0.859925i) q^{13} -1.76883 q^{17} +1.13932i q^{19} +(-3.18272 - 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} +(-3.59886 + 2.07781i) q^{29} +(-7.24879 - 4.18509i) q^{31} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} +(3.99709 - 6.92317i) q^{41} +(-1.76053 - 3.04933i) q^{43} +(-5.90494 - 10.2277i) q^{47} +(6.84905 - 1.44585i) q^{49} +13.3365i q^{55} +(-1.11483 + 1.93094i) q^{59} +(-7.79396 + 4.49985i) q^{61} +(-3.49921 + 2.02027i) q^{65} +(5.43562 - 9.41477i) q^{67} -4.52106i q^{71} +5.34234i q^{73} +(-12.1568 + 8.81952i) q^{77} +(-6.51422 - 11.2830i) q^{79} +(6.27298 + 10.8651i) q^{83} +(-2.07781 + 3.59886i) q^{85} -1.16106 q^{89} +(-4.15561 - 1.85366i) q^{91} +(2.31806 + 1.33834i) q^{95} +(3.97536 - 2.29517i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

Introduction

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