LMFDB - Embedded newform 3024.2.df.c.1601.6

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} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
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			1601.6
Root			$1.58110 - 0.707199i$ of defining polynomial
Character	$\chi$	$=$	3024.1601
Dual form			3024.2.df.c.17.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.900258 q^{5} +(-1.05755 + 2.42520i) q^{7} +O(q^{10})$	$q+0.900258 q^{5} +(-1.05755 + 2.42520i) q^{7} -3.12809i q^{11} +(1.99033 - 1.14912i) q^{13} +(-2.57638 - 4.46242i) q^{17} +(-2.38111 - 1.37474i) q^{19} +1.71570i q^{23} -4.18954 q^{25} +(1.85590 + 1.07151i) q^{29} +(-8.66298 - 5.00158i) q^{31} +(-0.952070 + 2.18330i) q^{35} +(-4.73701 + 8.20475i) q^{37} +(1.22134 + 2.11542i) q^{41} +(0.273155 - 0.473119i) q^{43} +(3.93034 + 6.80755i) q^{47} +(-4.76317 - 5.12955i) q^{49} +(-12.0733 + 6.97054i) q^{53} -2.81608i q^{55} +(3.99222 - 6.91472i) q^{59} +(6.28224 - 3.62705i) q^{61} +(1.79181 - 1.03450i) q^{65} +(1.83525 - 3.17875i) q^{67} -14.1484i q^{71} +(-10.9190 + 6.30409i) q^{73} +(7.58623 + 3.30812i) q^{77} +(-3.27402 - 5.67077i) q^{79} +(-0.184437 + 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} +(6.00244 - 10.3965i) q^{89} +(0.681960 + 6.04220i) q^{91} +(-2.14361 - 1.23762i) q^{95} +(-8.86815 - 5.12003i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 6 q^{13} - 18 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 10 q^{49} - 36 q^{53} + 30 q^{59} - 60 q^{61} - 42 q^{65} - 14 q^{67} + 18 q^{77} + 16 q^{79} - 12 q^{85} - 24 q^{89} + 12 q^{91} - 66 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q - 2 * q^7 - 6 * q^13 - 18 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 10 * q^49 - 36 * q^53 + 30 * q^59 - 60 * q^61 - 42 * q^65 - 14 * q^67 + 18 * q^77 + 16 * q^79 - 12 * q^85 - 24 * q^89 + 12 * q^91 - 66 * q^95 - 6 * 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
$5$	0.900258			0.402608			0.201304	−	0.979529i	$-0.435482\pi$
$5$	0.900258			0.402608			0.201304	+	0.979529i	$0.435482\pi$
$6$		0			0
$7$	−1.05755	+	2.42520i	−0.399717	+	0.916638i
$7$	−1.05755	+	2.42520i	−0.399717	+	0.916638i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	3.12809i		−	0.943154i	−0.881825	−	0.471577i	$-0.843685\pi$
$11$		−	3.12809i		−	0.943154i	0.881825	−	0.471577i	$-0.156315\pi$
$12$		0			0
$13$	1.99033	−	1.14912i	0.552019	−	0.318708i	−0.197917	−	0.980219i	$-0.563418\pi$
$13$	1.99033	−	1.14912i	0.552019	−	0.318708i	0.749936	+	0.661511i	$0.230084\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.57638	−	4.46242i	−0.624863	−	1.08230i	−0.988567	−	0.150780i	$-0.951821\pi$
$17$	−2.57638	−	4.46242i	−0.624863	−	1.08230i	0.363704	−	0.931515i	$-0.381512\pi$
$18$		0			0
$19$	−2.38111	−	1.37474i	−0.546264	−	0.315386i	0.201350	−	0.979519i	$-0.435467\pi$
$19$	−2.38111	−	1.37474i	−0.546264	−	0.315386i	−0.747614	+	0.664134i	$0.768801\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$			1.71570i			0.357748i	0.983872	+	0.178874i	$0.0572455\pi$
$23$			1.71570i			0.357748i	−0.983872	+	0.178874i	$0.942755\pi$
$24$		0			0
$25$	−4.18954			−0.837907
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.85590	+	1.07151i	0.344633	+	0.198974i	0.662319	−	0.749222i	$-0.269572\pi$
$29$	1.85590	+	1.07151i	0.344633	+	0.198974i	−0.317686	+	0.948196i	$0.602906\pi$
$30$		0			0
$31$	−8.66298	−	5.00158i	−1.55592	−	0.898309i	−0.997640	−	0.0686548i	$-0.978129\pi$
$31$	−8.66298	−	5.00158i	−1.55592	−	0.898309i	−0.558277	−	0.829655i	$-0.688537\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.952070	+	2.18330i	−0.160929	+	0.369046i
$36$		0			0
$37$	−4.73701	+	8.20475i	−0.778760	+	1.34885i	0.153896	+	0.988087i	$0.450818\pi$
$37$	−4.73701	+	8.20475i	−0.778760	+	1.34885i	−0.932657	+	0.360766i	$0.882515\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.22134	+	2.11542i	0.190741	+	0.330373i	0.945496	−	0.325634i	$-0.105578\pi$
$41$	1.22134	+	2.11542i	0.190741	+	0.330373i	−0.754755	+	0.656007i	$0.772244\pi$
$42$		0			0
$43$	0.273155	−	0.473119i	0.0416558	−	0.0721499i	−0.844446	−	0.535641i	$-0.820070\pi$
$43$	0.273155	−	0.473119i	0.0416558	−	0.0721499i	0.886102	+	0.463491i	$0.153403\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.93034	+	6.80755i	0.573299	+	0.992983i	0.996224	+	0.0868184i	$0.0276700\pi$
$47$	3.93034	+	6.80755i	0.573299	+	0.992983i	−0.422925	+	0.906165i	$0.638997\pi$
$48$		0			0
$49$	−4.76317	−	5.12955i	−0.680452	−	0.732792i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−12.0733	+	6.97054i	−1.65840	+	0.957478i	−0.684947	+	0.728593i	$0.740175\pi$
$53$	−12.0733	+	6.97054i	−1.65840	+	0.957478i	−0.973454	+	0.228885i	$0.926492\pi$
$54$		0			0
$55$		−	2.81608i		−	0.379721i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.99222	−	6.91472i	0.519742	−	0.900220i	−0.479994	−	0.877272i	$-0.659361\pi$
$59$	3.99222	−	6.91472i	0.519742	−	0.900220i	0.999737	−	0.0229484i	$-0.00730534\pi$
$60$		0			0
$61$	6.28224	−	3.62705i	0.804359	−	0.464397i	−0.0406343	−	0.999174i	$-0.512938\pi$
$61$	6.28224	−	3.62705i	0.804359	−	0.464397i	0.844993	+	0.534777i	$0.179605\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.79181	−	1.03450i	0.222247	−	0.128314i
$66$		0			0
$67$	1.83525	−	3.17875i	0.224212	−	0.388346i	−0.731871	−	0.681443i	$-0.761353\pi$
$67$	1.83525	−	3.17875i	0.224212	−	0.388346i	0.956083	+	0.293097i	$0.0946859\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	14.1484i		−	1.67911i	−0.543275	−	0.839555i	$-0.682816\pi$
$71$		−	14.1484i		−	1.67911i	0.543275	−	0.839555i	$-0.317184\pi$
$72$		0			0
$73$	−10.9190	+	6.30409i	−1.27797	+	0.737838i	−0.976475	−	0.215629i	$-0.930820\pi$
$73$	−10.9190	+	6.30409i	−1.27797	+	0.737838i	−0.301498	+	0.953467i	$0.597487\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.58623	+	3.30812i	0.864531	+	0.376995i
$78$		0			0
$79$	−3.27402	−	5.67077i	−0.368356	−	0.638011i	0.620953	−	0.783848i	$-0.286746\pi$
$79$	−3.27402	−	5.67077i	−0.368356	−	0.638011i	−0.989309	+	0.145837i	$0.953413\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−0.184437	+	0.319454i	−0.0202446	+	0.0350646i	−0.875970	−	0.482365i	$-0.839778\pi$
$83$	−0.184437	+	0.319454i	−0.0202446	+	0.0350646i	0.855726	+	0.517430i	$0.173111\pi$
$84$		0			0
$85$	−2.31940	−	4.01733i	−0.251575	−	0.435740i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	6.00244	−	10.3965i	0.636258	−	1.10203i	−0.349990	−	0.936754i	$-0.613815\pi$
$89$	6.00244	−	10.3965i	0.636258	−	1.10203i	0.986247	−	0.165277i	$-0.0528518\pi$
$90$		0			0
$91$	0.681960	+	6.04220i	0.0714888	+	0.633395i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.14361	−	1.23762i	−0.219930	−	0.126977i
$96$		0			0
$97$	−8.86815	−	5.12003i	−0.900424	−	0.519860i	−0.0230864	−	0.999733i	$-0.507349\pi$
$97$	−8.86815	−	5.12003i	−0.900424	−	0.519860i	−0.877338	+	0.479873i	$0.840683\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.71939			0.270589			0.135294	−	0.990805i	$-0.456802\pi$
$101$	2.71939			0.270589			0.135294	+	0.990805i	$0.456802\pi$
$102$		0			0
$103$		−	1.37248i		−	0.135235i	−0.997711	−	0.0676174i	$-0.978460\pi$
$103$		−	1.37248i		−	0.135235i	0.997711	−	0.0676174i	$-0.0215397\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−12.3585	−	7.13519i	−1.19474	−	0.689785i	−0.235364	−	0.971907i	$-0.575628\pi$
$107$	−12.3585	−	7.13519i	−1.19474	−	0.689785i	−0.959378	+	0.282122i	$0.908962\pi$
$108$		0			0
$109$	−2.64583	−	4.58271i	−0.253425	−	0.438944i	0.711042	−	0.703150i	$-0.248224\pi$
$109$	−2.64583	−	4.58271i	−0.253425	−	0.438944i	−0.964466	+	0.264206i	$0.914890\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.30371	−	1.33005i	0.216715	−	0.125121i	−0.387713	−	0.921780i	$-0.626735\pi$
$113$	2.30371	−	1.33005i	0.216715	−	0.125121i	0.604428	+	0.796659i	$0.293402\pi$
$114$		0			0
$115$			1.54457i			0.144032i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	13.5469	−	1.52898i	1.24184	−	0.140162i
$120$		0			0
$121$	1.21507			0.110461
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.27295			−0.739955
$126$		0			0
$127$	−6.10587			−0.541808			−0.270904	−	0.962606i	$-0.587323\pi$
$127$	−6.10587			−0.541808			−0.270904	+	0.962606i	$0.587323\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.95758			−0.695257			−0.347629	−	0.937632i	$-0.613013\pi$
$131$	−7.95758			−0.695257			−0.347629	+	0.937632i	$0.613013\pi$
$132$		0			0
$133$	5.85215	−	4.32081i	0.507446	−	0.374662i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	21.8400i		−	1.86591i	−0.359988	−	0.932957i	$-0.617219\pi$
$137$		−	21.8400i		−	1.86591i	0.359988	−	0.932957i	$-0.382781\pi$
$138$		0			0
$139$	−11.7109	+	6.76127i	−0.993302	+	0.573483i	−0.906260	−	0.422721i	$-0.861075\pi$
$139$	−11.7109	+	6.76127i	−0.993302	+	0.573483i	−0.0870425	+	0.996205i	$0.527742\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.59454	−	6.22593i	−0.300591	−	0.520639i
$144$		0			0
$145$	1.67079	+	0.964632i	0.138752	+	0.0801083i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	5.09444i		−	0.417353i	−0.977985	−	0.208676i	$-0.933084\pi$
$149$		−	5.09444i		−	0.417353i	0.977985	−	0.208676i	$-0.0669156\pi$
$150$		0			0
$151$	21.1755			1.72324			0.861618	−	0.507557i	$-0.169451\pi$
$151$	21.1755			1.72324			0.861618	+	0.507557i	$0.169451\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.79892	−	4.50271i	−0.626424	−	0.361666i
$156$		0			0
$157$	−0.311703	−	0.179962i	−0.0248766	−	0.0143625i	0.487510	−	0.873117i	$-0.337905\pi$
$157$	−0.311703	−	0.179962i	−0.0248766	−	0.0143625i	−0.512387	+	0.858755i	$0.671239\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.16091	−	1.81444i	−0.327926	−	0.142998i
$162$		0			0
$163$	−6.18640	+	10.7152i	−0.484557	+	0.839277i	−0.999843	−	0.0177416i	$-0.994352\pi$
$163$	−6.18640	+	10.7152i	−0.484557	+	0.839277i	0.515286	+	0.857018i	$0.327686\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.40866	+	12.8322i	0.573299	+	0.992984i	0.996224	+	0.0868188i	$0.0276701\pi$
$167$	7.40866	+	12.8322i	0.573299	+	0.992984i	−0.422925	+	0.906165i	$0.638997\pi$
$168$		0			0
$169$	−3.85905	+	6.68407i	−0.296850	+	0.514159i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.31772	−	4.01441i	−0.176213	−	0.305210i	0.764367	−	0.644781i	$-0.223051\pi$
$173$	−2.31772	−	4.01441i	−0.176213	−	0.305210i	−0.940580	+	0.339571i	$0.889718\pi$
$174$		0			0
$175$	4.43065	−	10.1605i	0.334926	−	0.768058i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.25855	−	3.03602i	0.393042	−	0.226923i	−0.290435	−	0.956895i	$-0.593800\pi$
$179$	5.25855	−	3.03602i	0.393042	−	0.226923i	0.683477	+	0.729972i	$0.260467\pi$
$180$		0			0
$181$		−	7.12701i		−	0.529746i	−0.964283	−	0.264873i	$-0.914670\pi$
$181$		−	7.12701i		−	0.529746i	0.964283	−	0.264873i	$-0.0853301\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.26453	+	7.38639i	−0.313535	+	0.543058i
$186$		0			0
$187$	−13.9588	+	8.05913i	−1.02077	+	0.589342i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−12.4713	+	7.20032i	−0.902394	+	0.520997i	−0.877976	−	0.478705i	$-0.841106\pi$
$191$	−12.4713	+	7.20032i	−0.902394	+	0.520997i	−0.0244176	+	0.999702i	$0.507773\pi$
$192$		0			0
$193$	−8.90573	+	15.4252i	−0.641048	+	1.11033i	0.344151	+	0.938914i	$0.388167\pi$
$193$	−8.90573	+	15.4252i	−0.641048	+	1.11033i	−0.985199	+	0.171414i	$0.945166\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	19.1025i		−	1.36100i	−0.732750	−	0.680498i	$-0.761764\pi$
$197$		−	19.1025i		−	1.36100i	0.732750	−	0.680498i	$-0.238236\pi$
$198$		0			0
$199$	−11.6008	+	6.69771i	−0.822357	+	0.474788i	−0.851229	−	0.524795i	$-0.824142\pi$
$199$	−11.6008	+	6.69771i	−0.822357	+	0.474788i	0.0288716	+	0.999583i	$0.490809\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.56133	+	3.36776i	−0.320143	+	0.236370i
$204$		0			0
$205$	1.09952	+	1.90442i	0.0767937	+	0.133011i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.30029	+	7.44832i	−0.297457	+	0.515211i
$210$		0			0
$211$	9.37193	+	16.2327i	0.645190	+	1.11750i	0.984258	+	0.176740i	$0.0565552\pi$
$211$	9.37193	+	16.2327i	0.645190	+	1.11750i	−0.339067	+	0.940762i	$0.610111\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.245910	−	0.425929i	0.0167709	−	0.0290481i
$216$		0			0
$217$	21.2914	−	15.7200i	1.44535	−	1.06714i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−10.2557	−	5.92113i	−0.689873	−	0.398298i
$222$		0			0
$223$	2.21609	+	1.27946i	0.148400	+	0.0856789i	0.572362	−	0.820001i	$-0.306027\pi$
$223$	2.21609	+	1.27946i	0.148400	+	0.0856789i	−0.423961	+	0.905680i	$0.639361\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−8.72909			−0.579370			−0.289685	−	0.957122i	$-0.593551\pi$
$227$	−8.72909			−0.579370			−0.289685	+	0.957122i	$0.593551\pi$
$228$		0			0
$229$		−	3.93729i		−	0.260183i	−0.991502	−	0.130092i	$-0.958473\pi$
$229$		−	3.93729i		−	0.260183i	0.991502	−	0.130092i	$-0.0415272\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.92147	−	2.26406i	−0.256904	−	0.148324i	0.366018	−	0.930608i	$-0.380721\pi$
$233$	−3.92147	−	2.26406i	−0.256904	−	0.148324i	−0.622921	+	0.782284i	$0.714054\pi$
$234$		0			0
$235$	3.53832	+	6.12855i	0.230815	+	0.399782i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.55315	+	4.36081i	−0.488573	+	0.282078i	−0.723982	−	0.689819i	$-0.757690\pi$
$239$	−7.55315	+	4.36081i	−0.488573	+	0.282078i	0.235409	+	0.971896i	$0.424357\pi$
$240$		0			0
$241$			19.7816i			1.27424i	0.770763	+	0.637122i	$0.219875\pi$
$241$			19.7816i			1.27424i	−0.770763	+	0.637122i	$0.780125\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.28808	−	4.61791i	−0.273955	−	0.295028i
$246$		0			0
$247$	−6.31894			−0.402064
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.80791			−0.240353			−0.120176	−	0.992753i	$-0.538346\pi$
$251$	−3.80791			−0.240353			−0.120176	+	0.992753i	$0.538346\pi$
$252$		0			0
$253$	5.36686			0.337411
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.0754			0.940379			0.470189	−	0.882566i	$-0.344186\pi$
$257$	15.0754			0.940379			0.470189	+	0.882566i	$0.344186\pi$
$258$		0			0
$259$	−14.8885	−	20.1652i	−0.925126	−	1.25300i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	7.61931i		−	0.469827i	−0.972016	−	0.234913i	$-0.924519\pi$
$263$		−	7.61931i		−	0.469827i	0.972016	−	0.234913i	$-0.0754806\pi$
$264$		0			0
$265$	−10.8691	+	6.27529i	−0.667684	+	0.385488i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.32720	−	7.49493i	−0.263834	−	0.456974i	0.703424	−	0.710771i	$-0.251654\pi$
$269$	−4.32720	−	7.49493i	−0.263834	−	0.456974i	−0.967257	+	0.253797i	$0.918320\pi$
$270$		0			0
$271$	15.6611	+	9.04193i	0.951343	+	0.549258i	0.893498	−	0.449068i	$-0.148244\pi$
$271$	15.6611	+	9.04193i	0.951343	+	0.549258i	0.0578449	+	0.998326i	$0.481577\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			13.1052i			0.790275i
$276$		0			0
$277$	9.98145			0.599727			0.299864	−	0.953982i	$-0.403059\pi$
$277$	9.98145			0.599727			0.299864	+	0.953982i	$0.403059\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	13.0297	+	7.52272i	0.777289	+	0.448768i	0.835469	−	0.549538i	$-0.185196\pi$
$281$	13.0297	+	7.52272i	0.777289	+	0.448768i	−0.0581797	+	0.998306i	$0.518530\pi$
$282$		0			0
$283$	3.48950	+	2.01467i	0.207429	+	0.119759i	0.600116	−	0.799913i	$-0.295121\pi$
$283$	3.48950	+	2.01467i	0.207429	+	0.119759i	−0.392687	+	0.919672i	$0.628454\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.42194	+	0.724819i	−0.379075	+	0.0427847i
$288$		0			0
$289$	−4.77544	+	8.27131i	−0.280908	+	0.486548i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.59608	+	11.4248i	0.385347	+	0.667441i	0.991817	−	0.127665i	$-0.0407483\pi$
$293$	6.59608	+	11.4248i	0.385347	+	0.667441i	−0.606470	+	0.795106i	$0.707415\pi$
$294$		0			0
$295$	3.59402	−	6.22503i	0.209252	−	0.362435i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.97154	+	3.41481i	0.114017	+	0.197484i
$300$		0			0
$301$	0.858530	+	1.16280i	0.0494849	+	0.0670229i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	5.65564	−	3.26528i	0.323841	−	0.186970i
$306$		0			0
$307$		−	28.7690i		−	1.64194i	−0.570974	−	0.820968i	$-0.693434\pi$
$307$		−	28.7690i		−	1.64194i	0.570974	−	0.820968i	$-0.306566\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	15.4228	−	26.7132i	0.874550	−	1.51476i	0.0173077	−	0.999850i	$-0.494491\pi$
$311$	15.4228	−	26.7132i	0.874550	−	1.51476i	0.857242	−	0.514914i	$-0.172176\pi$
$312$		0			0
$313$	15.9055	−	9.18304i	0.899032	−	0.519056i	0.0221460	−	0.999755i	$-0.492950\pi$
$313$	15.9055	−	9.18304i	0.899032	−	0.519056i	0.876886	+	0.480698i	$0.159617\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.1173	+	8.72800i	−0.849074	+	0.490213i	−0.860338	−	0.509723i	$-0.829748\pi$
$317$	−15.1173	+	8.72800i	−0.849074	+	0.490213i	0.0112642	+	0.999937i	$0.496414\pi$
$318$		0			0
$319$	3.35176	−	5.80543i	0.187663	−	0.325042i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			14.1673i			0.788292i
$324$		0			0
$325$	−8.33857	+	4.81428i	−0.462541	+	0.267048i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−20.6662	+	2.33251i	−1.13936	+	0.128596i
$330$		0			0
$331$	5.21472	+	9.03216i	0.286627	+	0.496452i	0.973002	−	0.230795i	$-0.0741326\pi$
$331$	5.21472	+	9.03216i	0.286627	+	0.496452i	−0.686375	+	0.727247i	$0.740799\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.65220	−	2.86169i	0.0902693	−	0.156351i
$336$		0			0
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	−0.869626	−	0.493712i	$-0.835640\pi$
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	0.00724616	−	0.999974i	$-0.497693\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.6454	+	27.0986i	−0.847244	+	1.46747i
$342$		0			0
$343$	17.4775	−	6.12685i	0.943694	−	0.330819i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.8472	−	6.26261i	−0.582306	−	0.336195i	0.179743	−	0.983714i	$-0.442473\pi$
$347$	−10.8472	−	6.26261i	−0.582306	−	0.336195i	−0.762049	+	0.647519i	$0.775807\pi$
$348$		0			0
$349$	−12.2560	−	7.07599i	−0.656047	−	0.378769i	0.134722	−	0.990883i	$-0.456986\pi$
$349$	−12.2560	−	7.07599i	−0.656047	−	0.378769i	−0.790769	+	0.612115i	$0.790319\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.96535			0.264279			0.132139	−	0.991231i	$-0.457815\pi$
$353$	4.96535			0.264279			0.132139	+	0.991231i	$0.457815\pi$
$354$		0			0
$355$		−	12.7372i		−	0.676022i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−15.0013	−	8.66098i	−0.791736	−	0.457109i	0.0488375	−	0.998807i	$-0.484448\pi$
$359$	−15.0013	−	8.66098i	−0.791736	−	0.457109i	−0.840573	+	0.541698i	$0.817782\pi$
$360$		0			0
$361$	−5.72021	−	9.90769i	−0.301063	−	0.521457i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.82992	+	5.67531i	−0.514522	+	0.297059i
$366$		0			0
$367$			1.37177i			0.0716057i	0.999359	+	0.0358029i	$0.0113988\pi$
$367$			1.37177i			0.0716057i	−0.999359	+	0.0358029i	$0.988601\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.13676	−	36.6519i	−0.214770	−	1.90287i
$372$		0			0
$373$	−4.80975			−0.249040			−0.124520	−	0.992217i	$-0.539739\pi$
$373$	−4.80975			−0.249040			−0.124520	+	0.992217i	$0.539739\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.92515			0.253658
$378$		0			0
$379$	−19.5669			−1.00508			−0.502542	−	0.864553i	$-0.667602\pi$
$379$	−19.5669			−1.00508			−0.502542	+	0.864553i	$0.667602\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	31.4697			1.60803			0.804014	−	0.594610i	$-0.202694\pi$
$383$	31.4697			1.60803			0.804014	+	0.594610i	$0.202694\pi$
$384$		0			0
$385$	6.82956	+	2.97816i	0.348067	+	0.151781i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	4.06605i		−	0.206157i	−0.994673	−	0.103078i	$-0.967131\pi$
$389$		−	4.06605i		−	0.206157i	0.994673	−	0.103078i	$-0.0328693\pi$
$390$		0			0
$391$	7.65617	−	4.42029i	0.387189	−	0.223544i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.94746	−	5.10515i	−0.148303	−	0.256868i
$396$		0			0
$397$	−3.81692	−	2.20370i	−0.191566	−	0.110601i	0.401150	−	0.916013i	$-0.368611\pi$
$397$	−3.81692	−	2.20370i	−0.191566	−	0.110601i	−0.592715	+	0.805412i	$0.701944\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			18.5428i			0.925985i	0.886362	+	0.462992i	$0.153224\pi$
$401$			18.5428i			0.925985i	−0.886362	+	0.462992i	$0.846776\pi$
$402$		0			0
$403$	−22.9896			−1.14519
$404$		0			0
$405$		0			0
$406$		0			0
$407$	25.6652	+	14.8178i	1.27218	+	0.734491i
$408$		0			0
$409$	21.5555	+	12.4451i	1.06585	+	0.615370i	0.927045	−	0.374949i	$-0.122340\pi$
$409$	21.5555	+	12.4451i	1.06585	+	0.615370i	0.138807	+	0.990319i	$0.455673\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	12.5476	+	16.9946i	0.617426	+	0.836249i
$414$		0			0
$415$	−0.166041	+	0.287591i	−0.00815062	+	0.0141173i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.57422	+	4.45869i	0.125759	+	0.217821i	0.922029	−	0.387120i	$-0.126530\pi$
$419$	2.57422	+	4.45869i	0.125759	+	0.217821i	−0.796270	+	0.604941i	$0.793197\pi$
$420$		0			0
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	0.323063	+	0.946377i	$0.395287\pi$
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	−0.981119	+	0.193408i	$0.938046\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	10.7938	+	18.6955i	0.523577	+	0.906863i
$426$		0			0
$427$	2.15252	+	19.0715i	0.104168	+	0.922933i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.10874	−	4.68159i	0.390584	−	0.225504i	−0.291829	−	0.956471i	$-0.594264\pi$
$431$	8.10874	−	4.68159i	0.390584	−	0.225504i	0.682413	+	0.730966i	$0.260930\pi$
$432$		0			0
$433$			21.0373i			1.01099i	0.862830	+	0.505494i	$0.168690\pi$
$433$			21.0373i			1.01099i	−0.862830	+	0.505494i	$0.831310\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.35863	−	4.08527i	0.112829	−	0.195425i
$438$		0			0
$439$	17.6867	−	10.2114i	0.844141	−	0.487365i	−0.0145289	−	0.999894i	$-0.504625\pi$
$439$	17.6867	−	10.2114i	0.844141	−	0.487365i	0.858670	+	0.512530i	$0.171292\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	28.0288	−	16.1825i	1.33169	−	0.768852i	0.346131	−	0.938186i	$-0.387495\pi$
$443$	28.0288	−	16.1825i	1.33169	−	0.768852i	0.985559	+	0.169334i	$0.0541618\pi$
$444$		0			0
$445$	5.40375	−	9.35956i	0.256162	−	0.443686i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	21.5693i		−	1.01792i	−0.860791	−	0.508958i	$-0.830031\pi$
$449$		−	21.5693i		−	1.01792i	0.860791	−	0.508958i	$-0.169969\pi$
$450$		0			0
$451$	6.61721	−	3.82045i	0.311592	−	0.179898i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.613939	+	5.43954i	0.0287819	+	0.255010i
$456$		0			0
$457$	−10.5350	−	18.2471i	−0.492806	−	0.853564i	0.507160	−	0.861852i	$-0.330695\pi$
$457$	−10.5350	−	18.2471i	−0.492806	−	0.853564i	−0.999966	+	0.00828760i	$0.997362\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	15.8412	−	27.4378i	0.737800	−	1.27791i	−0.215684	−	0.976463i	$-0.569198\pi$
$461$	15.8412	−	27.4378i	0.737800	−	1.27791i	0.953484	−	0.301444i	$-0.0974687\pi$
$462$		0			0
$463$	−4.40058	−	7.62202i	−0.204512	−	0.354225i	0.745465	−	0.666545i	$-0.232227\pi$
$463$	−4.40058	−	7.62202i	−0.204512	−	0.354225i	−0.949977	+	0.312319i	$0.898894\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.49444	+	16.4449i	−0.439350	+	0.760977i	−0.997639	−	0.0686693i	$-0.978125\pi$
$467$	−9.49444	+	16.4449i	−0.439350	+	0.760977i	0.558289	+	0.829646i	$0.311458\pi$
$468$		0			0
$469$	5.76822	+	7.81254i	0.266352	+	0.360750i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.47996	−	0.854453i	−0.0680485	−	0.0392878i
$474$		0			0
$475$	9.97575	+	5.75950i	0.457719	+	0.264264i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	24.1401			1.10299			0.551495	−	0.834178i	$-0.314058\pi$
$479$	24.1401			1.10299			0.551495	+	0.834178i	$0.314058\pi$
$480$		0			0
$481$			21.7736i			0.992790i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.98362	−	4.60935i	−0.362518	−	0.209300i
$486$		0			0
$487$	−7.05542	−	12.2204i	−0.319712	−	0.553757i	0.660716	−	0.750636i	$-0.270253\pi$
$487$	−7.05542	−	12.2204i	−0.319712	−	0.553757i	−0.980428	+	0.196879i	$0.936919\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−18.8344	+	10.8740i	−0.849982	+	0.490738i	−0.860645	−	0.509206i	$-0.829939\pi$
$491$	−18.8344	+	10.8740i	−0.849982	+	0.490738i	0.0106626	+	0.999943i	$0.496606\pi$
$492$		0			0
$493$		−	11.0424i		−	0.497326i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	34.3127	+	14.9627i	1.53914	+	0.671169i
$498$		0			0
$499$	8.42465			0.377139			0.188570	−	0.982060i	$-0.439615\pi$
$499$	8.42465			0.377139			0.188570	+	0.982060i	$0.439615\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8.71316			0.388501			0.194250	−	0.980952i	$-0.437773\pi$
$503$	8.71316			0.388501			0.194250	+	0.980952i	$0.437773\pi$
$504$		0			0
$505$	2.44815			0.108941
$506$		0			0
$507$		0			0
$508$		0			0
$509$	29.8354			1.32243			0.661214	−	0.750197i	$-0.270041\pi$
$509$	29.8354			1.32243			0.661214	+	0.750197i	$0.270041\pi$
$510$		0			0
$511$	−3.74125	−	33.1477i	−0.165503	−	1.46637i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	1.23559i		−	0.0544465i
$516$		0			0
$517$	21.2946	−	12.2944i	0.936536	−	0.540709i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.89004	−	17.1301i	−0.433291	−	0.750482i	0.563864	−	0.825868i	$-0.309314\pi$
$521$	−9.89004	−	17.1301i	−0.433291	−	0.750482i	−0.997154	+	0.0753863i	$0.975981\pi$
$522$		0			0
$523$	10.5932	+	6.11597i	0.463207	+	0.267433i	0.713392	−	0.700766i	$-0.247158\pi$
$523$	10.5932	+	6.11597i	0.463207	+	0.267433i	−0.250185	+	0.968198i	$0.580491\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			51.5438i			2.24528i
$528$		0			0
$529$	20.0564			0.872016
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.86174	+	2.80693i	0.210585	+	0.121581i
$534$		0			0
$535$	−11.1258	−	6.42351i	−0.481012	−	0.277713i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−16.0457	+	14.8996i	−0.691136	+	0.641771i
$540$		0			0
$541$	−0.348944	+	0.604389i	−0.0150023	+	0.0259847i	−0.873429	−	0.486951i	$-0.838109\pi$
$541$	−0.348944	+	0.604389i	−0.0150023	+	0.0259847i	0.858427	+	0.512936i	$0.171442\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−2.38193	−	4.12562i	−0.102031	−	0.176722i
$546$		0			0
$547$	−21.0049	+	36.3815i	−0.898103	+	1.55556i	−0.0681854	+	0.997673i	$0.521721\pi$
$547$	−21.0049	+	36.3815i	−0.898103	+	1.55556i	−0.829917	+	0.557887i	$0.811612\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.94608	−	5.10275i	−0.125507	−	0.217385i
$552$		0			0
$553$	17.2152	−	1.94301i	0.732064	−	0.0826251i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.85612	−	2.80368i	0.205760	−	0.118796i	−0.393579	−	0.919291i	$-0.628763\pi$
$557$	4.85612	−	2.80368i	0.205760	−	0.118796i	0.599340	+	0.800495i	$0.295430\pi$
$558$		0			0
$559$		−	1.25555i		−	0.0531042i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.5948	+	30.4751i	−0.741532	+	1.28437i	0.210266	+	0.977644i	$0.432567\pi$
$563$	−17.5948	+	30.4751i	−0.741532	+	1.28437i	−0.951798	+	0.306727i	$0.900766\pi$
$564$		0			0
$565$	2.07394	−	1.19739i	0.0872512	−	0.0503745i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.63608	+	4.40869i	−0.320121	+	0.184822i	−0.651447	−	0.758695i	$-0.725838\pi$
$569$	−7.63608	+	4.40869i	−0.320121	+	0.184822i	0.331325	+	0.943517i	$0.392504\pi$
$570$		0			0
$571$	−5.94140	+	10.2908i	−0.248640	+	0.430657i	−0.963149	−	0.268970i	$-0.913317\pi$
$571$	−5.94140	+	10.2908i	−0.248640	+	0.430657i	0.714509	+	0.699626i	$0.246650\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	7.18799i		−	0.299760i
$576$		0			0
$577$	15.8314	−	9.14028i	0.659071	−	0.380515i	−0.132852	−	0.991136i	$-0.542413\pi$
$577$	15.8314	−	9.14028i	0.659071	−	0.380515i	0.791923	+	0.610621i	$0.209080\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.579687	−	0.785135i	−0.0240495	−	0.0325729i
$582$		0			0
$583$	21.8045	+	37.7664i	0.903049	+	1.56413i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.75389	−	3.03782i	0.0723907	−	0.125384i	−0.827558	−	0.561380i	$-0.810270\pi$
$587$	1.75389	−	3.03782i	0.0723907	−	0.125384i	0.899949	+	0.435996i	$0.143604\pi$
$588$		0			0
$589$	13.7517	+	23.8186i	0.566628	+	0.981429i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−24.2336	+	41.9738i	−0.995155	+	1.72366i	−0.412428	+	0.910990i	$0.635319\pi$
$593$	−24.2336	+	41.9738i	−0.995155	+	1.72366i	−0.582727	+	0.812668i	$0.698014\pi$
$594$		0			0
$595$	12.1957	−	1.37648i	0.499975	−	0.0564302i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	21.7773	+	12.5731i	0.889796	+	0.513724i	0.873876	−	0.486149i	$-0.161599\pi$
$599$	21.7773	+	12.5731i	0.889796	+	0.513724i	0.0159203	+	0.999873i	$0.494932\pi$
$600$		0			0
$601$	−11.2731	−	6.50854i	−0.459840	−	0.265489i	0.252137	−	0.967692i	$-0.418867\pi$
$601$	−11.2731	−	6.50854i	−0.459840	−	0.265489i	−0.711977	+	0.702203i	$0.752200\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.09388			0.0444726
$606$		0			0
$607$			8.20468i			0.333018i	0.986040	+	0.166509i	$0.0532494\pi$
$607$			8.20468i			0.333018i	−0.986040	+	0.166509i	$0.946751\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15.6454	+	9.03286i	0.632944	+	0.365430i
$612$		0			0
$613$	2.35051	+	4.07120i	0.0949361	+	0.164434i	0.909582	−	0.415525i	$-0.136402\pi$
$613$	2.35051	+	4.07120i	0.0949361	+	0.164434i	−0.814646	+	0.579959i	$0.803069\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−17.0178	+	9.82521i	−0.685109	+	0.395548i	−0.801777	−	0.597623i	$-0.796112\pi$
$617$	−17.0178	+	9.82521i	−0.685109	+	0.395548i	0.116668	+	0.993171i	$0.462779\pi$
$618$		0			0
$619$			34.7087i			1.39506i	0.716555	+	0.697531i	$0.245718\pi$
$619$			34.7087i			1.39506i	−0.716555	+	0.697531i	$0.754282\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	18.8658	+	25.5520i	0.755840	+	1.02372i
$624$		0			0
$625$	13.4999			0.539996
$626$		0			0
$627$		0			0
$628$		0			0
$629$	48.8174			1.94648
$630$		0			0
$631$	−22.9139			−0.912188			−0.456094	−	0.889932i	$-0.650752\pi$
$631$	−22.9139			−0.912188			−0.456094	+	0.889932i	$0.650752\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.49685			−0.218136
$636$		0			0
$637$	−15.3747	−	4.73606i	−0.609170	−	0.187650i
$638$		0			0
$639$		0			0
$640$		0			0
$641$		−	13.8527i		−	0.547148i	−0.961851	−	0.273574i	$-0.911794\pi$
$641$		−	13.8527i		−	0.547148i	0.961851	−	0.273574i	$-0.0882059\pi$
$642$		0			0
$643$	−27.9684	+	16.1476i	−1.10297	+	0.636797i	−0.936998	−	0.349334i	$-0.886408\pi$
$643$	−27.9684	+	16.1476i	−1.10297	+	0.636797i	−0.165967	+	0.986131i	$0.553075\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.96715	+	15.5316i	0.352535	+	0.610609i	0.986693	−	0.162595i	$-0.0519864\pi$
$647$	8.96715	+	15.5316i	0.352535	+	0.610609i	−0.634158	+	0.773204i	$0.718653\pi$
$648$		0			0
$649$	−21.6298	−	12.4880i	−0.849046	−	0.490197i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			7.49493i			0.293299i	0.989188	+	0.146650i	$0.0468490\pi$
$653$			7.49493i			0.293299i	−0.989188	+	0.146650i	$0.953151\pi$
$654$		0			0
$655$	−7.16388			−0.279916
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.32497	−	5.38377i	−0.363249	−	0.209722i	0.307256	−	0.951627i	$-0.400589\pi$
$659$	−9.32497	−	5.38377i	−0.363249	−	0.209722i	−0.670505	+	0.741905i	$0.733923\pi$
$660$		0			0
$661$	−10.0813	−	5.82044i	−0.392117	−	0.226389i	0.290960	−	0.956735i	$-0.406025\pi$
$661$	−10.0813	−	5.82044i	−0.392117	−	0.226389i	−0.683077	+	0.730346i	$0.739359\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.26845	−	3.88984i	0.204302	−	0.150842i
$666$		0			0
$667$	−1.83838	+	3.18417i	−0.0711825	+	0.123292i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−11.3457	−	19.6514i	−0.437997	−	0.758634i
$672$		0			0
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	−0.876449	−	0.481496i	$-0.840094\pi$
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	0.855212	+	0.518279i	$0.173427\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.61618	+	9.72751i	0.215847	+	0.373859i	0.953534	−	0.301284i	$-0.0974153\pi$
$677$	5.61618	+	9.72751i	0.215847	+	0.373859i	−0.737687	+	0.675143i	$0.764082\pi$
$678$		0			0
$679$	21.7956	−	16.0923i	0.836439	−	0.617566i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−37.6792	+	21.7541i	−1.44175	+	0.832396i	−0.997967	−	0.0637365i	$-0.979698\pi$
$683$	−37.6792	+	21.7541i	−1.44175	+	0.832396i	−0.443786	+	0.896133i	$0.646365\pi$
$684$		0			0
$685$		−	19.6616i		−	0.751231i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−16.0200	+	27.7474i	−0.610312	+	1.05709i
$690$		0			0
$691$	27.9085	−	16.1130i	1.06169	−	0.612967i	0.135791	−	0.990738i	$-0.456642\pi$
$691$	27.9085	−	16.1130i	1.06169	−	0.612967i	0.925899	+	0.377770i	$0.123309\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−10.5428	+	6.08689i	−0.399911	+	0.230889i
$696$		0			0
$697$	6.29326	−	10.9002i	0.238374	−	0.412876i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			21.8995i			0.827133i	0.910474	+	0.413566i	$0.135717\pi$
$701$			21.8995i			0.827133i	−0.910474	+	0.413566i	$0.864283\pi$
$702$		0			0
$703$	22.5587	−	13.0243i	0.850818	−	0.491220i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.87589	+	6.59505i	−0.108159	+	0.248032i
$708$		0			0
$709$	9.02351	+	15.6292i	0.338885	+	0.586966i	0.984223	−	0.176931i	$-0.0566168\pi$
$709$	9.02351	+	15.6292i	0.338885	+	0.586966i	−0.645338	+	0.763897i	$0.723284\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.58120	−	14.8631i	0.321369	−	0.556627i
$714$		0			0
$715$	−3.23602	−	5.60494i	−0.121020	−	0.209613i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.65944	−	8.07039i	0.173768	−	0.300975i	−0.765966	−	0.642881i	$-0.777739\pi$
$719$	4.65944	−	8.07039i	0.173768	−	0.300975i	0.939734	+	0.341906i	$0.111072\pi$
$720$		0			0
$721$	3.32854	+	1.45147i	0.123961	+	0.0540557i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.77537	−	4.48911i	−0.288770	−	0.166722i
$726$		0			0
$727$	−6.73516	−	3.88855i	−0.249793	−	0.144218i	0.369876	−	0.929081i	$-0.379400\pi$
$727$	−6.73516	−	3.88855i	−0.249793	−	0.144218i	−0.619670	+	0.784863i	$0.712733\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.81500			−0.104117
$732$		0			0
$733$			36.1238i			1.33426i	0.744941	+	0.667131i	$0.232478\pi$
$733$			36.1238i			1.33426i	−0.744941	+	0.667131i	$0.767522\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.94341	−	5.74083i	−0.366270	−	0.211466i
$738$		0			0
$739$	−12.0693	−	20.9046i	−0.443975	−	0.768987i	0.554005	−	0.832513i	$-0.313099\pi$
$739$	−12.0693	−	20.9046i	−0.443975	−	0.768987i	−0.997980	+	0.0635263i	$0.979765\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.5762	−	6.10618i	0.388003	−	0.224014i	−0.293291	−	0.956023i	$-0.594751\pi$
$743$	10.5762	−	6.10618i	0.388003	−	0.224014i	0.681295	+	0.732009i	$0.261417\pi$
$744$		0			0
$745$		−	4.58631i		−	0.168029i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	30.3740	−	22.4260i	1.10984	−	0.819428i
$750$		0			0
$751$	23.4381			0.855268			0.427634	−	0.903952i	$-0.359347\pi$
$751$	23.4381			0.855268			0.427634	+	0.903952i	$0.359347\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	19.0634			0.693788
$756$		0			0
$757$	3.52341			0.128060			0.0640302	−	0.997948i	$-0.479605\pi$
$757$	3.52341			0.128060			0.0640302	+	0.997948i	$0.479605\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.4042			−0.775900			−0.387950	−	0.921680i	$-0.626817\pi$
$761$	−21.4042			−0.775900			−0.387950	+	0.921680i	$0.626817\pi$
$762$		0			0
$763$	13.9121	−	1.57020i	0.503651	−	0.0568451i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	18.3501i		−	0.662585i
$768$		0			0
$769$	23.4043	−	13.5125i	0.843982	−	0.487273i	−0.0146339	−	0.999893i	$-0.504658\pi$
$769$	23.4043	−	13.5125i	0.843982	−	0.487273i	0.858616	+	0.512620i	$0.171325\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.10280	+	14.0345i	0.291437	+	0.504784i	0.974150	−	0.225903i	$-0.0725332\pi$
$773$	8.10280	+	14.0345i	0.291437	+	0.504784i	−0.682712	+	0.730687i	$0.739200\pi$
$774$		0			0
$775$	36.2939	+	20.9543i	1.30371	+	0.752700i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	6.71607i		−	0.240628i
$780$		0			0
$781$	−44.2575			−1.58366
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.280613	−	0.162012i	−0.0100155	−	0.00578246i
$786$		0			0
$787$	33.1317	+	19.1286i	1.18102	+	0.681860i	0.956249	−	0.292553i	$-0.0945047\pi$
$787$	33.1317	+	19.1286i	1.18102	+	0.681860i	0.224767	+	0.974413i	$0.427838\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.789335	+	6.99356i	0.0280655	+	0.248662i
$792$		0			0
$793$	8.33583	−	14.4381i	0.296014	−	0.512712i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.38709	+	7.59866i	0.155399	+	0.269158i	0.933204	−	0.359347i	$-0.117000\pi$
$797$	4.38709	+	7.59866i	0.155399	+	0.269158i	−0.777805	+	0.628505i	$0.783667\pi$
$798$		0			0
$799$	20.2521	−	35.0776i	0.716467	−	1.24096i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	19.7197	+	34.1556i	0.695895	+	1.20532i
$804$		0			0
$805$	−3.74589	−	1.63347i	−0.132025	−	0.0575721i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	26.6053	−	15.3606i	0.935394	−	0.540050i	0.0468805	−	0.998901i	$-0.485072\pi$
$809$	26.6053	−	15.3606i	0.935394	−	0.540050i	0.888513	+	0.458851i	$0.151739\pi$
$810$		0			0
$811$		−	8.70634i		−	0.305721i	−0.988248	−	0.152861i	$-0.951151\pi$
$811$		−	8.70634i		−	0.305721i	0.988248	−	0.152861i	$-0.0488485\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.56936	+	9.64641i	−0.195086	+	0.337899i
$816$		0			0
$817$	−1.30083	+	0.751032i	−0.0455101	+	0.0262753i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−45.4098	+	26.2173i	−1.58481	+	0.914992i	−0.590670	+	0.806914i	$0.701136\pi$
$821$	−45.4098	+	26.2173i	−1.58481	+	0.914992i	−0.994142	+	0.108078i	$0.965530\pi$
$822$		0			0
$823$	4.18199	−	7.24342i	0.145775	−	0.252490i	−0.783887	−	0.620904i	$-0.786766\pi$
$823$	4.18199	−	7.24342i	0.145775	−	0.252490i	0.929662	+	0.368414i	$0.120099\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	26.4934i		−	0.921267i	−0.887590	−	0.460634i	$-0.847622\pi$
$827$		−	26.4934i		−	0.921267i	0.887590	−	0.460634i	$-0.152378\pi$
$828$		0			0
$829$	−5.14134	+	2.96835i	−0.178566	+	0.103095i	−0.586619	−	0.809863i	$-0.699541\pi$
$829$	−5.14134	+	2.96835i	−0.178566	+	0.103095i	0.408053	+	0.912958i	$0.366208\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−10.6185	+	34.4709i	−0.367908	+	1.19435i
$834$		0			0
$835$	6.66970	+	11.5523i	0.230815	+	0.399783i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	3.80537	−	6.59110i	0.131376	−	0.227550i	−0.792831	−	0.609441i	$-0.791394\pi$
$839$	3.80537	−	6.59110i	0.131376	−	0.227550i	0.924207	+	0.381891i	$0.124727\pi$
$840$		0			0
$841$	−12.2037	−	21.1375i	−0.420819	−	0.728880i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.47414	+	6.01739i	−0.119514	+	0.207004i
$846$		0			0
$847$	−1.28500	+	2.94680i	−0.0441533	+	0.101253i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−14.0769	−	8.12730i	−0.482550	−	0.278600i
$852$		0			0
$853$	24.8764	+	14.3624i	0.851751	+	0.491759i	0.861241	−	0.508196i	$-0.169688\pi$
$853$	24.8764	+	14.3624i	0.851751	+	0.491759i	−0.00949029	+	0.999955i	$0.503021\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	40.2396			1.37456			0.687280	−	0.726393i	$-0.258805\pi$
$857$	40.2396			1.37456			0.687280	+	0.726393i	$0.258805\pi$
$858$		0			0
$859$			15.3871i			0.525001i	0.964932	+	0.262501i	$0.0845472\pi$
$859$			15.3871i			0.525001i	−0.964932	+	0.262501i	$0.915453\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−16.6494	−	9.61252i	−0.566751	−	0.327214i	0.189099	−	0.981958i	$-0.439443\pi$
$863$	−16.6494	−	9.61252i	−0.566751	−	0.327214i	−0.755851	+	0.654744i	$0.772776\pi$
$864$		0			0
$865$	−2.08655	−	3.61400i	−0.0709447	−	0.122880i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−17.7386	+	10.2414i	−0.601742	+	0.347416i
$870$		0			0
$871$		−	8.43569i		−	0.285833i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.74908	−	20.0635i	0.295773	−	0.678271i
$876$		0			0
$877$	−10.7807			−0.364038			−0.182019	−	0.983295i	$-0.558263\pi$
$877$	−10.7807			−0.364038			−0.182019	+	0.983295i	$0.558263\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−44.2875			−1.49208			−0.746041	−	0.665900i	$-0.768048\pi$
$881$	−44.2875			−1.49208			−0.746041	+	0.665900i	$0.768048\pi$
$882$		0			0
$883$	47.6098			1.60220			0.801098	−	0.598533i	$-0.204249\pi$
$883$	47.6098			1.60220			0.801098	+	0.598533i	$0.204249\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.97993			0.0664795			0.0332398	−	0.999447i	$-0.489418\pi$
$887$	1.97993			0.0664795			0.0332398	+	0.999447i	$0.489418\pi$
$888$		0			0
$889$	6.45727	−	14.8079i	0.216570	−	0.496642i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	21.6127i		−	0.723242i
$894$		0			0
$895$	4.73405	−	2.73320i	0.158242	−	0.0913609i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−10.7184	−	18.5649i	−0.357480	−	0.619173i
$900$		0			0
$901$	62.2109	+	35.9175i	2.07255	+	1.19659i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	6.41615i		−	0.213280i
$906$		0			0
$907$	−34.0505			−1.13063			−0.565314	−	0.824876i	$-0.691245\pi$
$907$	−34.0505			−1.13063			−0.565314	+	0.824876i	$0.691245\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−6.58371	−	3.80111i	−0.218128	−	0.125936i	0.386955	−	0.922099i	$-0.373527\pi$
$911$	−6.58371	−	3.80111i	−0.218128	−	0.125936i	−0.605083	+	0.796162i	$0.706860\pi$
$912$		0			0
$913$	0.999280	+	0.576934i	0.0330713	+	0.0190937i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	8.41556	−	19.2987i	0.277906	−	0.637300i
$918$		0			0
$919$	4.11136	−	7.12109i	0.135621	−	0.234903i	−0.790213	−	0.612832i	$-0.790030\pi$
$919$	4.11136	−	7.12109i	0.135621	−	0.234903i	0.925835	+	0.377929i	$0.123364\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−16.2582	−	28.1601i	−0.535146	−	0.926900i
$924$		0			0
$925$	19.8459	−	34.3741i	0.652529	−	1.13021i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.53982	−	4.39909i	−0.0833287	−	0.144329i	0.821349	−	0.570426i	$-0.193222\pi$
$929$	−2.53982	−	4.39909i	−0.0833287	−	0.144329i	−0.904678	+	0.426096i	$0.859888\pi$
$930$		0			0
$931$	4.28986	+	18.7621i	0.140594	+	0.614903i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−12.5665	+	7.25530i	−0.410970	+	0.237274i
$936$		0			0
$937$		−	10.8127i		−	0.353236i	−0.984280	−	0.176618i	$-0.943484\pi$
$937$		−	10.8127i		−	0.353236i	0.984280	−	0.176618i	$-0.0565157\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.58193	−	16.5964i	0.312362	−	0.541027i	−0.666511	−	0.745495i	$-0.732213\pi$
$941$	9.58193	−	16.5964i	0.312362	−	0.541027i	0.978873	+	0.204468i	$0.0655464\pi$
$942$		0			0
$943$	−3.62942	+	2.09545i	−0.118190	+	0.0682372i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.9930	+	12.6977i	−0.714676	+	0.412618i	−0.812790	−	0.582557i	$-0.802052\pi$
$947$	−21.9930	+	12.6977i	−0.714676	+	0.412618i	0.0981139	+	0.995175i	$0.468719\pi$
$948$		0			0
$949$	−14.4883	+	25.0945i	−0.470310	+	0.814601i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	18.4818i		−	0.598686i	−0.954146	−	0.299343i	$-0.903233\pi$
$953$		−	18.4818i		−	0.598686i	0.954146	−	0.299343i	$-0.0967674\pi$
$954$		0			0
$955$	−11.2274	+	6.48215i	−0.363310	+	0.209757i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	52.9662	+	23.0969i	1.71037	+	0.745838i
$960$		0			0
$961$	34.5315	+	59.8103i	1.11392	+	1.92937i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.01745	+	13.8866i	−0.258091	+	0.447026i
$966$		0			0
$967$	9.64551	+	16.7065i	0.310179	+	0.537245i	0.978401	−	0.206717i	$-0.0662778\pi$
$967$	9.64551	+	16.7065i	0.310179	+	0.537245i	−0.668222	+	0.743962i	$0.732944\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.975444	−	1.68952i	0.0313035	−	0.0542192i	−0.849949	−	0.526865i	$-0.823367\pi$
$971$	0.975444	−	1.68952i	0.0313035	−	0.0542192i	0.881253	+	0.472645i	$0.156701\pi$
$972$		0			0
$973$	−4.01256	−	35.5515i	−0.128637	−	1.13973i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.4856	+	8.36326i	0.463435	+	0.267564i	0.713488	−	0.700668i	$-0.247115\pi$
$977$	14.4856	+	8.36326i	0.463435	+	0.267564i	−0.250052	+	0.968232i	$0.580448\pi$
$978$		0			0
$979$	−32.5213	−	18.7762i	−1.03938	−	0.600089i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−32.2916			−1.02994			−0.514970	−	0.857208i	$-0.672197\pi$
$983$	−32.2916			−1.02994			−0.514970	+	0.857208i	$0.672197\pi$
$984$		0			0
$985$		−	17.1972i		−	0.547947i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.811730	+	0.468652i	0.0258115	+	0.0149023i
$990$		0			0
$991$	−4.25134	−	7.36353i	−0.135048	−	0.233910i	0.790568	−	0.612375i	$-0.209786\pi$
$991$	−4.25134	−	7.36353i	−0.135048	−	0.233910i	−0.925616	+	0.378464i	$0.876452\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.4437	+	6.02967i	−0.331087	+	0.191153i
$996$		0			0
$997$		−	11.2975i		−	0.357797i	−0.983868	−	0.178898i	$-0.942747\pi$
$997$		−	11.2975i		−	0.357797i	0.983868	−	0.178898i	$-0.0572533\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.df.c.1601.6		16
3.2	odd	2		1008.2.df.c.929.4		16
4.3	odd	2		378.2.t.a.89.7		16
7.3	odd	6		3024.2.ca.c.2033.6		16
9.4	even	3		1008.2.ca.c.257.1		16
9.5	odd	6		3024.2.ca.c.2609.6		16
12.11	even	2		126.2.t.a.47.3	yes	16
21.17	even	6		1008.2.ca.c.353.1		16
28.3	even	6		378.2.l.a.143.7		16
28.11	odd	6		2646.2.l.a.521.6		16
28.19	even	6		2646.2.m.b.1763.3		16
28.23	odd	6		2646.2.m.a.1763.2		16
28.27	even	2		2646.2.t.b.1979.6		16
36.7	odd	6		1134.2.k.a.971.2		16
36.11	even	6		1134.2.k.b.971.7		16
36.23	even	6		378.2.l.a.341.3		16
36.31	odd	6		126.2.l.a.5.8	✓	16
63.31	odd	6		1008.2.df.c.689.4		16
63.59	even	6	inner	3024.2.df.c.17.6		16
84.11	even	6		882.2.l.b.227.1		16
84.23	even	6		882.2.m.a.587.8		16
84.47	odd	6		882.2.m.b.587.5		16
84.59	odd	6		126.2.l.a.101.4	yes	16
84.83	odd	2		882.2.t.a.803.2		16
252.23	even	6		2646.2.m.b.881.3		16
252.31	even	6		126.2.t.a.59.3	yes	16
252.59	odd	6		378.2.t.a.17.7		16
252.67	odd	6		882.2.t.a.815.2		16
252.95	even	6		2646.2.t.b.2285.6		16
252.103	even	6		882.2.m.a.293.8		16
252.115	even	6		1134.2.k.b.647.7		16
252.131	odd	6		2646.2.m.a.881.2		16
252.139	even	6		882.2.l.b.509.5		16
252.167	odd	6		2646.2.l.a.1097.2		16
252.227	odd	6		1134.2.k.a.647.2		16
252.247	odd	6		882.2.m.b.293.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.8	✓	16	36.31	odd	6
126.2.l.a.101.4	yes	16	84.59	odd	6
126.2.t.a.47.3	yes	16	12.11	even	2
126.2.t.a.59.3	yes	16	252.31	even	6
378.2.l.a.143.7		16	28.3	even	6
378.2.l.a.341.3		16	36.23	even	6
378.2.t.a.17.7		16	252.59	odd	6
378.2.t.a.89.7		16	4.3	odd	2
882.2.l.b.227.1		16	84.11	even	6
882.2.l.b.509.5		16	252.139	even	6
882.2.m.a.293.8		16	252.103	even	6
882.2.m.a.587.8		16	84.23	even	6
882.2.m.b.293.5		16	252.247	odd	6
882.2.m.b.587.5		16	84.47	odd	6
882.2.t.a.803.2		16	84.83	odd	2
882.2.t.a.815.2		16	252.67	odd	6
1008.2.ca.c.257.1		16	9.4	even	3
1008.2.ca.c.353.1		16	21.17	even	6
1008.2.df.c.689.4		16	63.31	odd	6
1008.2.df.c.929.4		16	3.2	odd	2
1134.2.k.a.647.2		16	252.227	odd	6
1134.2.k.a.971.2		16	36.7	odd	6
1134.2.k.b.647.7		16	252.115	even	6
1134.2.k.b.971.7		16	36.11	even	6
2646.2.l.a.521.6		16	28.11	odd	6
2646.2.l.a.1097.2		16	252.167	odd	6
2646.2.m.a.881.2		16	252.131	odd	6
2646.2.m.a.1763.2		16	28.23	odd	6
2646.2.m.b.881.3		16	252.23	even	6
2646.2.m.b.1763.3		16	28.19	even	6
2646.2.t.b.1979.6		16	28.27	even	2
2646.2.t.b.2285.6		16	252.95	even	6
3024.2.ca.c.2033.6		16	7.3	odd	6
3024.2.ca.c.2609.6		16	9.5	odd	6
3024.2.df.c.17.6		16	63.59	even	6	inner
3024.2.df.c.1601.6		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.900258 q^{5} +(-1.05755 + 2.42520i) q^{7} +O(q^{10})\)	\(q+0.900258 q^{5} +(-1.05755 + 2.42520i) q^{7} -3.12809i q^{11} +(1.99033 - 1.14912i) q^{13} +(-2.57638 - 4.46242i) q^{17} +(-2.38111 - 1.37474i) q^{19} +1.71570i q^{23} -4.18954 q^{25} +(1.85590 + 1.07151i) q^{29} +(-8.66298 - 5.00158i) q^{31} +(-0.952070 + 2.18330i) q^{35} +(-4.73701 + 8.20475i) q^{37} +(1.22134 + 2.11542i) q^{41} +(0.273155 - 0.473119i) q^{43} +(3.93034 + 6.80755i) q^{47} +(-4.76317 - 5.12955i) q^{49} +(-12.0733 + 6.97054i) q^{53} -2.81608i q^{55} +(3.99222 - 6.91472i) q^{59} +(6.28224 - 3.62705i) q^{61} +(1.79181 - 1.03450i) q^{65} +(1.83525 - 3.17875i) q^{67} -14.1484i q^{71} +(-10.9190 + 6.30409i) q^{73} +(7.58623 + 3.30812i) q^{77} +(-3.27402 - 5.67077i) q^{79} +(-0.184437 + 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} +(6.00244 - 10.3965i) q^{89} +(0.681960 + 6.04220i) q^{91} +(-2.14361 - 1.23762i) q^{95} +(-8.86815 - 5.12003i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 6 q^{13} - 18 q^{17} + 16 q^{25} - 6 q^{29} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 6 q^{41} + 2 q^{43} - 18 q^{47} + 10 q^{49} - 36 q^{53} + 30 q^{59} - 60 q^{61} - 42 q^{65} - 14 q^{67} + 18 q^{77} + 16 q^{79} - 12 q^{85} - 24 q^{89} + 12 q^{91} - 66 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q - 2 * q^7 - 6 * q^13 - 18 * q^17 + 16 * q^25 - 6 * q^29 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 6 * q^41 + 2 * q^43 - 18 * q^47 + 10 * q^49 - 36 * q^53 + 30 * q^59 - 60 * q^61 - 42 * q^65 - 14 * q^67 + 18 * q^77 + 16 * q^79 - 12 * q^85 - 24 * q^89 + 12 * q^91 - 66 * q^95 - 6 * q^97

Introduction

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