LMFDB - Embedded newform 3024.2.t.j.1873.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(289,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.289"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,-4,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1873.6
Root			$-0.473632 + 1.66604i$ of defining polynomial
Character	$\chi$	$=$	3024.1873
Dual form			3024.2.t.j.289.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90301 q^{5} +(2.43415 - 1.03677i) q^{7} -3.06586 q^{11} +(1.13161 - 1.96000i) q^{13} +(0.713726 - 1.23621i) q^{17} +(-2.98444 - 5.16919i) q^{19} -7.15543 q^{23} -1.37856 q^{25} +(-0.468164 - 0.810884i) q^{29} +(-4.11065 - 7.11985i) q^{31} +(4.63221 - 1.97298i) q^{35} +(-1.41550 - 2.45171i) q^{37} +(5.31672 - 9.20883i) q^{41} +(-2.98444 - 5.16919i) q^{43} +(0.483340 - 0.837169i) q^{47} +(4.85021 - 5.04732i) q^{49} +(-5.45142 + 9.44213i) q^{53} -5.83436 q^{55} +(5.68180 + 9.84117i) q^{59} +(-0.449718 + 0.778935i) q^{61} +(2.15346 - 3.72990i) q^{65} +(0.813810 + 1.40956i) q^{67} -2.36378 q^{71} +(-0.996286 + 1.72562i) q^{73} +(-7.46279 + 3.17860i) q^{77} +(-4.16945 + 7.22169i) q^{79} +(-7.98203 - 13.8253i) q^{83} +(1.35822 - 2.35251i) q^{85} +(2.58992 + 4.48587i) q^{89} +(0.722433 - 5.94416i) q^{91} +(-5.67940 - 9.83701i) q^{95} +(0.922890 + 1.59849i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 4 q^{5} + 3 q^{7} - 4 q^{11} + 2 q^{13} - 2 q^{17} - 7 q^{19} - 22 q^{23} + 18 q^{25} - q^{29} + q^{31} - 19 q^{35} + 10 q^{37} + 33 q^{41} - 7 q^{43} - 3 q^{47} - 13 q^{49} + 15 q^{53} + 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) $ 14 * q - 4 * q^5 + 3 * q^7 - 4 * q^11 + 2 * q^13 - 2 * q^17 - 7 * q^19 - 22 * q^23 + 18 * q^25 - q^29 + q^31 - 19 * q^35 + 10 * q^37 + 33 * q^41 - 7 * q^43 - 3 * q^47 - 13 * q^49 + 15 * q^53 + 28 * q^55 - 14 * q^59 - 10 * q^61 - 15 * q^65 - 6 * q^67 + 2 * q^71 + 21 * q^73 - 19 * q^77 + 10 * q^79 - 25 * q^83 + 8 * q^85 + 6 * q^89 - 2 * q^91 - 28 * q^95 - 18 * q^97

Character values

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

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	1.90301			0.851051			0.425525	−	0.904947i	$-0.360089\pi$
$5$	1.90301			0.851051			0.425525	+	0.904947i	$0.360089\pi$
$6$		0			0
$7$	2.43415	−	1.03677i	0.920024	−	0.391863i
$7$	2.43415	−	1.03677i	0.920024	−	0.391863i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.06586			−0.924393			−0.462196	−	0.886778i	$-0.652938\pi$
$11$	−3.06586			−0.924393			−0.462196	+	0.886778i	$0.652938\pi$
$12$		0			0
$13$	1.13161	−	1.96000i	0.313851	−	0.543607i	−0.665341	−	0.746539i	$-0.731714\pi$
$13$	1.13161	−	1.96000i	0.313851	−	0.543607i	0.979193	+	0.202933i	$0.0650473\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.713726	−	1.23621i	0.173104	−	0.299825i	−0.766400	−	0.642364i	$-0.777954\pi$
$17$	0.713726	−	1.23621i	0.173104	−	0.299825i	0.939503	+	0.342539i	$0.111287\pi$
$18$		0			0
$19$	−2.98444	−	5.16919i	−0.684677	−	1.18589i	−0.973538	−	0.228524i	$-0.926610\pi$
$19$	−2.98444	−	5.16919i	−0.684677	−	1.18589i	0.288862	−	0.957371i	$-0.406723\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.15543			−1.49201			−0.746005	−	0.665940i	$-0.768031\pi$
$23$	−7.15543			−1.49201			−0.746005	+	0.665940i	$0.768031\pi$
$24$		0			0
$25$	−1.37856			−0.275713
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.468164	−	0.810884i	−0.0869359	−	0.150577i	0.819279	−	0.573396i	$-0.194374\pi$
$29$	−0.468164	−	0.810884i	−0.0869359	−	0.150577i	−0.906214	+	0.422818i	$0.861041\pi$
$30$		0			0
$31$	−4.11065	−	7.11985i	−0.738294	−	1.27876i	−0.953263	−	0.302142i	$-0.902298\pi$
$31$	−4.11065	−	7.11985i	−0.738294	−	1.27876i	0.214969	−	0.976621i	$-0.431035\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.63221	−	1.97298i	0.782987	−	0.333495i
$36$		0			0
$37$	−1.41550	−	2.45171i	−0.232706	−	0.403059i	0.725897	−	0.687803i	$-0.241425\pi$
$37$	−1.41550	−	2.45171i	−0.232706	−	0.403059i	−0.958604	+	0.284744i	$0.908091\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.31672	−	9.20883i	0.830332	−	1.43818i	−0.0674429	−	0.997723i	$-0.521484\pi$
$41$	5.31672	−	9.20883i	0.830332	−	1.43818i	0.897775	−	0.440454i	$-0.145183\pi$
$42$		0			0
$43$	−2.98444	−	5.16919i	−0.455122	−	0.788295i	0.543573	−	0.839362i	$-0.317071\pi$
$43$	−2.98444	−	5.16919i	−0.455122	−	0.788295i	−0.998695	+	0.0510671i	$0.983738\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.483340	−	0.837169i	0.0705023	−	0.122114i	−0.828619	−	0.559813i	$-0.810873\pi$
$47$	0.483340	−	0.837169i	0.0705023	−	0.122114i	0.899122	+	0.437699i	$0.144206\pi$
$48$		0			0
$49$	4.85021	−	5.04732i	0.692887	−	0.721046i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.45142	+	9.44213i	−0.748810	+	1.29698i	0.199583	+	0.979881i	$0.436041\pi$
$53$	−5.45142	+	9.44213i	−0.748810	+	1.29698i	−0.948393	+	0.317096i	$0.897292\pi$
$54$		0			0
$55$	−5.83436			−0.786705
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.68180	+	9.84117i	0.739708	+	1.28121i	0.952627	+	0.304142i	$0.0983697\pi$
$59$	5.68180	+	9.84117i	0.739708	+	1.28121i	−0.212919	+	0.977070i	$0.568297\pi$
$60$		0			0
$61$	−0.449718	+	0.778935i	−0.0575805	+	0.0997324i	−0.893379	−	0.449304i	$-0.851672\pi$
$61$	−0.449718	+	0.778935i	−0.0575805	+	0.0997324i	0.835798	+	0.549037i	$0.185005\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	2.15346	−	3.72990i	0.267104	−	0.462637i
$66$		0			0
$67$	0.813810	+	1.40956i	0.0994227	+	0.172205i	0.911446	−	0.411420i	$-0.134967\pi$
$67$	0.813810	+	1.40956i	0.0994227	+	0.172205i	−0.812023	+	0.583625i	$0.801634\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.36378			−0.280529			−0.140264	−	0.990114i	$-0.544795\pi$
$71$	−2.36378			−0.280529			−0.140264	+	0.990114i	$0.544795\pi$
$72$		0			0
$73$	−0.996286	+	1.72562i	−0.116606	+	0.201968i	−0.918421	−	0.395605i	$-0.870535\pi$
$73$	−0.996286	+	1.72562i	−0.116606	+	0.201968i	0.801814	+	0.597573i	$0.203868\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.46279	+	3.17860i	−0.850463	+	0.362235i
$78$		0			0
$79$	−4.16945	+	7.22169i	−0.469099	+	0.812504i	−0.999376	−	0.0353209i	$-0.988755\pi$
$79$	−4.16945	+	7.22169i	−0.469099	+	0.812504i	0.530277	+	0.847825i	$0.322088\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.98203	−	13.8253i	−0.876141	−	1.51752i	−0.855542	−	0.517734i	$-0.826776\pi$
$83$	−7.98203	−	13.8253i	−0.876141	−	1.51752i	−0.0205995	−	0.999788i	$-0.506557\pi$
$84$		0			0
$85$	1.35822	−	2.35251i	0.147320	−	0.255166i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.58992	+	4.48587i	0.274531	+	0.475501i	0.970017	−	0.243039i	$-0.0781442\pi$
$89$	2.58992	+	4.48587i	0.274531	+	0.475501i	−0.695486	+	0.718540i	$0.744811\pi$
$90$		0			0
$91$	0.722433	−	5.94416i	0.0757316	−	0.623118i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5.67940	−	9.83701i	−0.582694	−	1.00926i
$96$		0			0
$97$	0.922890	+	1.59849i	0.0937053	+	0.162302i	0.909068	−	0.416649i	$-0.136796\pi$
$97$	0.922890	+	1.59849i	0.0937053	+	0.162302i	−0.815362	+	0.578951i	$0.803462\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.06350			0.802349			0.401174	−	0.916002i	$-0.368602\pi$
$101$	8.06350			0.802349			0.401174	+	0.916002i	$0.368602\pi$
$102$		0			0
$103$	17.7986			1.75375			0.876875	−	0.480718i	$-0.159624\pi$
$103$	17.7986			1.75375			0.876875	+	0.480718i	$0.159624\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.76005	+	15.1729i	0.846866	+	1.46682i	0.883991	+	0.467505i	$0.154847\pi$
$107$	8.76005	+	15.1729i	0.846866	+	1.46682i	−0.0371245	+	0.999311i	$0.511820\pi$
$108$		0			0
$109$	1.11441	−	1.93021i	0.106741	−	0.184881i	−0.807707	−	0.589584i	$-0.799292\pi$
$109$	1.11441	−	1.93021i	0.106741	−	0.184881i	0.914448	+	0.404703i	$0.132625\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	7.59999	−	13.1636i	0.714947	−	1.23832i	−0.248033	−	0.968751i	$-0.579784\pi$
$113$	7.59999	−	13.1636i	0.714947	−	1.23832i	0.962980	−	0.269573i	$-0.0868824\pi$
$114$		0			0
$115$	−13.6168			−1.26978
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.455652	−	3.74909i	0.0417695	−	0.343679i
$120$		0			0
$121$	−1.60048			−0.145498
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−12.1385			−1.08570
$126$		0			0
$127$	16.9303			1.50232			0.751161	−	0.660119i	$-0.229494\pi$
$127$	16.9303			1.50232			0.751161	+	0.660119i	$0.229494\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.38354			0.208251			0.104125	−	0.994564i	$-0.466796\pi$
$131$	2.38354			0.208251			0.104125	+	0.994564i	$0.466796\pi$
$132$		0			0
$133$	−12.6238	−	9.48844i	−1.09463	−	0.822752i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.9820			−0.938254			−0.469127	−	0.883131i	$-0.655431\pi$
$137$	−10.9820			−0.938254			−0.469127	+	0.883131i	$0.655431\pi$
$138$		0			0
$139$	3.70422	−	6.41590i	0.314188	−	0.544190i	−0.665076	−	0.746775i	$-0.731601\pi$
$139$	3.70422	−	6.41590i	0.314188	−	0.544190i	0.979265	+	0.202585i	$0.0649344\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.46936	+	6.00910i	−0.290122	+	0.502506i
$144$		0			0
$145$	−0.890919	−	1.54312i	−0.0739868	−	0.128149i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−17.6239			−1.44381			−0.721904	−	0.691993i	$-0.756733\pi$
$149$	−17.6239			−1.44381			−0.721904	+	0.691993i	$0.756733\pi$
$150$		0			0
$151$	20.3664			1.65739			0.828697	−	0.559697i	$-0.189083\pi$
$151$	20.3664			1.65739			0.828697	+	0.559697i	$0.189083\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.82259	−	13.5491i	−0.628326	−	1.08829i
$156$		0			0
$157$	−4.64118	−	8.03875i	−0.370406	−	0.641562i	0.619222	−	0.785216i	$-0.287448\pi$
$157$	−4.64118	−	8.03875i	−0.370406	−	0.641562i	−0.989628	+	0.143654i	$0.954115\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−17.4174	+	7.41854i	−1.37268	+	0.584663i
$162$		0			0
$163$	11.9069	+	20.6234i	0.932623	+	1.61535i	0.778819	+	0.627248i	$0.215819\pi$
$163$	11.9069	+	20.6234i	0.932623	+	1.61535i	0.153803	+	0.988101i	$0.450848\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.883505	+	1.53028i	−0.0683676	+	0.118416i	−0.898183	−	0.439622i	$-0.855112\pi$
$167$	−0.883505	+	1.53028i	−0.0683676	+	0.118416i	0.829815	+	0.558038i	$0.188446\pi$
$168$		0			0
$169$	3.93893	+	6.82242i	0.302994	+	0.524802i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.180049	−	0.311855i	0.0136889	−	0.0237099i	−0.859100	−	0.511808i	$-0.828976\pi$
$173$	0.180049	−	0.311855i	0.0136889	−	0.0237099i	0.872789	+	0.488098i	$0.162309\pi$
$174$		0			0
$175$	−3.35564	+	1.42926i	−0.253662	+	0.108042i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.57701	+	6.19556i	−0.267358	+	0.463078i	−0.968179	−	0.250260i	$-0.919484\pi$
$179$	−3.57701	+	6.19556i	−0.267358	+	0.463078i	0.700821	+	0.713337i	$0.252817\pi$
$180$		0			0
$181$	11.0542			0.821650			0.410825	−	0.911714i	$-0.365241\pi$
$181$	11.0542			0.821650			0.410825	+	0.911714i	$0.365241\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.69370	−	4.66563i	−0.198045	−	0.343024i
$186$		0			0
$187$	−2.18819	+	3.79005i	−0.160016	+	0.277156i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.35083	−	7.53586i	0.314815	−	0.545276i	−0.664583	−	0.747214i	$-0.731391\pi$
$191$	4.35083	−	7.53586i	0.314815	−	0.545276i	0.979398	+	0.201939i	$0.0647241\pi$
$192$		0			0
$193$	0.709644	+	1.22914i	0.0510813	+	0.0884754i	0.890435	−	0.455110i	$-0.150400\pi$
$193$	0.709644	+	1.22914i	0.0510813	+	0.0884754i	−0.839354	+	0.543585i	$0.817067\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.69424			−0.405698			−0.202849	−	0.979210i	$-0.565020\pi$
$197$	−5.69424			−0.405698			−0.202849	+	0.979210i	$0.565020\pi$
$198$		0			0
$199$	−2.61327	+	4.52631i	−0.185250	+	0.320862i	−0.943661	−	0.330915i	$-0.892643\pi$
$199$	−2.61327	+	4.52631i	−0.185250	+	0.320862i	0.758411	+	0.651777i	$0.225976\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.98028	−	1.48844i	−0.138989	−	0.104468i
$204$		0			0
$205$	10.1178	−	17.5245i	0.706655	−	1.22396i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	9.14987	+	15.8480i	0.632910	+	1.09623i
$210$		0			0
$211$	5.93079	−	10.2724i	0.408293	−	0.707183i	−0.586406	−	0.810017i	$-0.699458\pi$
$211$	5.93079	−	10.2724i	0.408293	−	0.707183i	0.994699	+	0.102834i	$0.0327910\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.67940	−	9.83701i	−0.387332	−	0.670879i
$216$		0			0
$217$	−17.3876	−	13.0690i	−1.18035	−	0.887182i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.61531	−	2.79781i	−0.108658	−	0.188201i
$222$		0			0
$223$	−12.2950	−	21.2955i	−0.823333	−	1.42605i	−0.903187	−	0.429248i	$-0.858779\pi$
$223$	−12.2950	−	21.2955i	−0.823333	−	1.42605i	0.0798535	−	0.996807i	$-0.474555\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.3180			1.01669			0.508344	−	0.861154i	$-0.330258\pi$
$227$	15.3180			1.01669			0.508344	+	0.861154i	$0.330258\pi$
$228$		0			0
$229$	17.0459			1.12643			0.563214	−	0.826311i	$-0.309565\pi$
$229$	17.0459			1.12643			0.563214	+	0.826311i	$0.309565\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.88255	−	17.1171i	−0.647427	−	1.12138i	−0.983735	−	0.179625i	$-0.942512\pi$
$233$	−9.88255	−	17.1171i	−0.647427	−	1.12138i	0.336308	−	0.941752i	$-0.390822\pi$
$234$		0			0
$235$	0.919799	−	1.59314i	0.0600011	−	0.103925i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.35041	−	14.4633i	0.540143	−	0.935555i	−0.458752	−	0.888564i	$-0.651703\pi$
$239$	8.35041	−	14.4633i	0.540143	−	0.935555i	0.998895	−	0.0469909i	$-0.0149632\pi$
$240$		0			0
$241$	6.39995			0.412257			0.206129	−	0.978525i	$-0.433914\pi$
$241$	6.39995			0.412257			0.206129	+	0.978525i	$0.433914\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.22999	−	9.60509i	0.589682	−	0.613647i
$246$		0			0
$247$	−13.5088			−0.859547
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−26.8346			−1.69378			−0.846891	−	0.531766i	$-0.821529\pi$
$251$	−26.8346			−1.69378			−0.846891	+	0.531766i	$0.821529\pi$
$252$		0			0
$253$	21.9376			1.37920
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.17597			−0.447625			−0.223812	−	0.974632i	$-0.571850\pi$
$257$	−7.17597			−0.447625			−0.223812	+	0.974632i	$0.571850\pi$
$258$		0			0
$259$	−5.98741	−	4.50030i	−0.372039	−	0.279635i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.4137			1.25876			0.629382	−	0.777096i	$-0.283308\pi$
$263$	20.4137			1.25876			0.629382	+	0.777096i	$0.283308\pi$
$264$		0			0
$265$	−10.3741	+	17.9685i	−0.637275	+	1.10379i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.37251	−	5.84136i	0.205626	−	0.356154i	−0.744706	−	0.667392i	$-0.767410\pi$
$269$	3.37251	−	5.84136i	0.205626	−	0.356154i	0.950332	+	0.311238i	$0.100744\pi$
$270$		0			0
$271$	1.04632	+	1.81228i	0.0635596	+	0.110088i	0.896054	−	0.443945i	$-0.146421\pi$
$271$	1.04632	+	1.81228i	0.0635596	+	0.110088i	−0.832495	+	0.554033i	$0.813088\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.22649			0.254867
$276$		0			0
$277$	−23.5410			−1.41444			−0.707221	−	0.706992i	$-0.750052\pi$
$277$	−23.5410			−1.41444			−0.707221	+	0.706992i	$0.750052\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−9.66048	−	16.7324i	−0.576296	−	0.998173i	−0.995900	−	0.0904661i	$-0.971164\pi$
$281$	−9.66048	−	16.7324i	−0.576296	−	0.998173i	0.419604	−	0.907707i	$-0.362169\pi$
$282$		0			0
$283$	−2.22658	−	3.85655i	−0.132356	−	0.229248i	0.792228	−	0.610225i	$-0.208921\pi$
$283$	−2.22658	−	3.85655i	−0.132356	−	0.229248i	−0.924584	+	0.380977i	$0.875588\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.39426	−	27.9279i	0.200357	−	1.64853i
$288$		0			0
$289$	7.48119	+	12.9578i	0.440070	+	0.762224i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	11.7314	−	20.3193i	0.685354	−	1.18707i	−0.287972	−	0.957639i	$-0.592981\pi$
$293$	11.7314	−	20.3193i	0.685354	−	1.18707i	0.973325	−	0.229429i	$-0.0736858\pi$
$294$		0			0
$295$	10.8125	+	18.7278i	0.629529	+	1.09038i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.09714	+	14.0247i	−0.468270	+	0.811067i
$300$		0			0
$301$	−12.6238	−	9.48844i	−0.727627	−	0.546904i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.855817	+	1.48232i	−0.0490039	+	0.0848773i
$306$		0			0
$307$	−7.79955			−0.445144			−0.222572	−	0.974916i	$-0.571445\pi$
$307$	−7.79955			−0.445144			−0.222572	+	0.974916i	$0.571445\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−7.49449	−	12.9808i	−0.424974	−	0.736076i	0.571444	−	0.820641i	$-0.306383\pi$
$311$	−7.49449	−	12.9808i	−0.424974	−	0.736076i	−0.996418	+	0.0845650i	$0.973050\pi$
$312$		0			0
$313$	−3.46332	+	5.99864i	−0.195758	+	0.339063i	−0.947149	−	0.320794i	$-0.896050\pi$
$313$	−3.46332	+	5.99864i	−0.195758	+	0.339063i	0.751391	+	0.659858i	$0.229383\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.42872	−	9.40282i	0.304907	−	0.528115i	−0.672333	−	0.740249i	$-0.734708\pi$
$317$	5.42872	−	9.40282i	0.304907	−	0.528115i	0.977241	+	0.212133i	$0.0680412\pi$
$318$		0			0
$319$	1.43533	+	2.48606i	0.0803629	+	0.139193i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.52027			−0.474081
$324$		0			0
$325$	−1.55999	+	2.70199i	−0.0865328	+	0.149879i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.308570	−	2.53891i	0.0170120	−	0.139975i
$330$		0			0
$331$	−4.02584	+	6.97297i	−0.221280	+	0.383269i	−0.955197	−	0.295971i	$-0.904357\pi$
$331$	−4.02584	+	6.97297i	−0.221280	+	0.383269i	0.733917	+	0.679240i	$0.237690\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.54869	+	2.68240i	0.0846138	+	0.146555i
$336$		0			0
$337$	11.4293	−	19.7961i	0.622594	−	1.07836i	−0.366407	−	0.930455i	$-0.619412\pi$
$337$	11.4293	−	19.7961i	0.622594	−	1.07836i	0.989001	−	0.147909i	$-0.0472543\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.6027	+	21.8285i	0.682474	+	1.18208i
$342$		0			0
$343$	6.57324	−	17.3145i	0.354922	−	0.934896i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−12.8892	−	22.3247i	−0.691928	−	1.19845i	−0.971205	−	0.238244i	$-0.923428\pi$
$347$	−12.8892	−	22.3247i	−0.691928	−	1.19845i	0.279278	−	0.960210i	$-0.409905\pi$
$348$		0			0
$349$	6.90108	+	11.9530i	0.369406	+	0.639830i	0.989473	−	0.144719i	$-0.0462277\pi$
$349$	6.90108	+	11.9530i	0.369406	+	0.639830i	−0.620067	+	0.784549i	$0.712894\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	24.9028			1.32544			0.662721	−	0.748866i	$-0.269402\pi$
$353$	24.9028			1.32544			0.662721	+	0.748866i	$0.269402\pi$
$354$		0			0
$355$	−4.49829			−0.238744
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.6980	+	18.5295i	0.564620	+	0.977951i	0.997085	+	0.0763002i	$0.0243107\pi$
$359$	10.6980	+	18.5295i	0.564620	+	0.977951i	−0.432465	+	0.901651i	$0.642356\pi$
$360$		0			0
$361$	−8.31371	+	14.3998i	−0.437564	+	0.757883i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.89594	+	3.28386i	−0.0992380	+	0.171885i
$366$		0			0
$367$	11.5158			0.601121			0.300560	−	0.953763i	$-0.402826\pi$
$367$	11.5158			0.601121			0.300560	+	0.953763i	$0.402826\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.48026	+	28.6355i	−0.180686	+	1.48668i
$372$		0			0
$373$	−1.69398			−0.0877109			−0.0438555	−	0.999038i	$-0.513964\pi$
$373$	−1.69398			−0.0877109			−0.0438555	+	0.999038i	$0.513964\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.11911			−0.109140
$378$		0			0
$379$	−8.50319			−0.436780			−0.218390	−	0.975862i	$-0.570080\pi$
$379$	−8.50319			−0.436780			−0.218390	+	0.975862i	$0.570080\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−12.7819			−0.653124			−0.326562	−	0.945176i	$-0.605890\pi$
$383$	−12.7819			−0.653124			−0.326562	+	0.945176i	$0.605890\pi$
$384$		0			0
$385$	−14.2017	+	6.04890i	−0.723787	+	0.308280i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.55959			−0.180479			−0.0902393	−	0.995920i	$-0.528763\pi$
$389$	−3.55959			−0.180479			−0.0902393	+	0.995920i	$0.528763\pi$
$390$		0			0
$391$	−5.10701	+	8.84560i	−0.258273	+	0.447341i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.93448	+	13.7429i	−0.399227	+	0.691482i
$396$		0			0
$397$	11.0411	+	19.1238i	0.554138	+	0.959795i	0.997970	+	0.0636848i	$0.0202852\pi$
$397$	11.0411	+	19.1238i	0.554138	+	0.959795i	−0.443832	+	0.896110i	$0.646381\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.59853			−0.129765			−0.0648823	−	0.997893i	$-0.520667\pi$
$401$	−2.59853			−0.129765			−0.0648823	+	0.997893i	$0.520667\pi$
$402$		0			0
$403$	−18.6066			−0.926859
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.33973	+	7.51662i	0.215112	+	0.372585i
$408$		0			0
$409$	−1.51604	−	2.62585i	−0.0749632	−	0.129840i	0.826107	−	0.563513i	$-0.190551\pi$
$409$	−1.51604	−	2.62585i	−0.0749632	−	0.129840i	−0.901070	+	0.433673i	$0.857217\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	24.0334	+	18.0642i	1.18261	+	0.888881i
$414$		0			0
$415$	−15.1899	−	26.3096i	−0.745641	−	1.29149i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−17.4979	+	30.3073i	−0.854829	+	1.48061i	0.0219749	+	0.999759i	$0.493005\pi$
$419$	−17.4979	+	30.3073i	−0.854829	+	1.48061i	−0.876804	+	0.480848i	$0.840329\pi$
$420$		0			0
$421$	13.3264	+	23.0820i	0.649488	+	1.12495i	0.983245	+	0.182288i	$0.0583502\pi$
$421$	13.3264	+	23.0820i	0.649488	+	1.12495i	−0.333757	+	0.942659i	$0.608316\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.983916	+	1.70419i	−0.0477269	+	0.0826655i
$426$		0			0
$427$	−0.287106	+	2.36230i	−0.0138940	+	0.114320i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.77241	+	15.1943i	−0.422552	+	0.731882i	−0.996188	−	0.0872286i	$-0.972199\pi$
$431$	−8.77241	+	15.1943i	−0.422552	+	0.731882i	0.573636	+	0.819110i	$0.305532\pi$
$432$		0			0
$433$	−18.0202			−0.865997			−0.432998	−	0.901395i	$-0.642544\pi$
$433$	−18.0202			−0.865997			−0.432998	+	0.901395i	$0.642544\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	21.3549	+	36.9878i	1.02154	+	1.76937i
$438$		0			0
$439$	18.7159	−	32.4169i	0.893263	−	1.54718i	0.0573222	−	0.998356i	$-0.481744\pi$
$439$	18.7159	−	32.4169i	0.893263	−	1.54718i	0.835940	−	0.548820i	$-0.184923\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.67162	+	6.35944i	−0.174444	+	0.302146i	−0.939969	−	0.341261i	$-0.889146\pi$
$443$	−3.67162	+	6.35944i	−0.174444	+	0.302146i	0.765525	+	0.643407i	$0.222479\pi$
$444$		0			0
$445$	4.92863	+	8.53664i	0.233639	+	0.404675i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	40.3618			1.90479			0.952395	−	0.304866i	$-0.0986115\pi$
$449$	40.3618			1.90479			0.952395	+	0.304866i	$0.0986115\pi$
$450$		0			0
$451$	−16.3003	+	28.2330i	−0.767553	+	1.32944i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.37480	−	11.3118i	0.0644514	−	0.530305i
$456$		0			0
$457$	13.7360	−	23.7914i	0.642543	−	1.11292i	−0.342321	−	0.939583i	$-0.611213\pi$
$457$	13.7360	−	23.7914i	0.642543	−	1.11292i	0.984863	−	0.173333i	$-0.0554538\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.36325	+	5.82532i	0.156642	+	0.271312i	0.933656	−	0.358172i	$-0.116600\pi$
$461$	3.36325	+	5.82532i	0.156642	+	0.271312i	−0.777014	+	0.629484i	$0.783266\pi$
$462$		0			0
$463$	−1.89569	+	3.28344i	−0.0881004	+	0.152594i	−0.906708	−	0.421759i	$-0.861413\pi$
$463$	−1.89569	+	3.28344i	−0.0881004	+	0.152594i	0.818608	+	0.574353i	$0.194746\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.2166	+	17.6957i	0.472769	+	0.818860i	0.999514	−	0.0311635i	$-0.00992126\pi$
$467$	10.2166	+	17.6957i	0.472769	+	0.818860i	−0.526746	+	0.850023i	$0.676588\pi$
$468$		0			0
$469$	3.44233	+	2.58735i	0.158952	+	0.119473i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	9.14987	+	15.8480i	0.420712	+	0.728694i
$474$		0			0
$475$	4.11423	+	7.12606i	0.188774	+	0.326966i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	27.9079			1.27514			0.637572	−	0.770391i	$-0.279939\pi$
$479$	27.9079			1.27514			0.637572	+	0.770391i	$0.279939\pi$
$480$		0			0
$481$	−6.40715			−0.292141
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.75627	+	3.04194i	0.0797480	+	0.138128i
$486$		0			0
$487$	5.89480	−	10.2101i	0.267119	−	0.462663i	−0.700998	−	0.713163i	$-0.747262\pi$
$487$	5.89480	−	10.2101i	0.267119	−	0.462663i	0.968117	+	0.250500i	$0.0805951\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	13.2596	−	22.9662i	0.598396	−	1.03645i	−0.394662	−	0.918826i	$-0.629138\pi$
$491$	13.2596	−	22.9662i	0.598396	−	1.03645i	0.993058	−	0.117626i	$-0.0375283\pi$
$492$		0			0
$493$	−1.33656			−0.0601957
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.75380	+	2.45070i	−0.258093	+	0.109929i
$498$		0			0
$499$	−42.3329			−1.89508			−0.947540	−	0.319637i	$-0.896439\pi$
$499$	−42.3329			−1.89508			−0.947540	+	0.319637i	$0.896439\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.0768			0.493890			0.246945	−	0.969029i	$-0.420573\pi$
$503$	11.0768			0.493890			0.246945	+	0.969029i	$0.420573\pi$
$504$		0			0
$505$	15.3449			0.682839
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−24.7262			−1.09597			−0.547984	−	0.836489i	$-0.684605\pi$
$509$	−24.7262			−1.09597			−0.547984	+	0.836489i	$0.684605\pi$
$510$		0			0
$511$	−0.636042	+	5.23334i	−0.0281368	+	0.231509i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	33.8709			1.49253
$516$		0			0
$517$	−1.48185	+	2.56665i	−0.0651719	+	0.112881i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.42298	+	11.1249i	−0.281396	+	0.487392i	−0.971729	−	0.236100i	$-0.924131\pi$
$521$	−6.42298	+	11.1249i	−0.281396	+	0.487392i	0.690333	+	0.723492i	$0.257464\pi$
$522$		0			0
$523$	1.70453	+	2.95234i	0.0745340	+	0.129097i	0.900884	−	0.434061i	$-0.142920\pi$
$523$	1.70453	+	2.95234i	0.0745340	+	0.129097i	−0.826350	+	0.563158i	$0.809586\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.7355			−0.511206
$528$		0			0
$529$	28.2002			1.22609
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.0329	−	20.8416i	−0.521202	−	0.902748i
$534$		0			0
$535$	16.6704	+	28.8741i	0.720726	+	1.24833i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−14.8701	+	15.4744i	−0.640500	+	0.666530i
$540$		0			0
$541$	−22.9553	−	39.7598i	−0.986926	−	1.70941i	−0.633043	−	0.774117i	$-0.718194\pi$
$541$	−22.9553	−	39.7598i	−0.986926	−	1.70941i	−0.353884	−	0.935289i	$-0.615139\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.12073	−	3.67321i	0.0908421	−	0.157343i
$546$		0			0
$547$	12.5502	+	21.7376i	0.536608	+	0.929432i	0.999084	+	0.0428004i	$0.0136280\pi$
$547$	12.5502	+	21.7376i	0.536608	+	0.929432i	−0.462476	+	0.886632i	$0.653039\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.79441	+	4.84006i	−0.119046	+	0.206194i
$552$		0			0
$553$	−2.66183	+	21.9015i	−0.113192	+	0.931345i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.836144	+	1.44824i	−0.0354285	+	0.0613640i	−0.883196	−	0.469004i	$-0.844613\pi$
$557$	−0.836144	+	1.44824i	−0.0354285	+	0.0613640i	0.847767	+	0.530368i	$0.177946\pi$
$558$		0			0
$559$	−13.5088			−0.571363
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.3764	+	19.7046i	0.479460	+	0.830449i	0.999722	−	0.0235574i	$-0.00749926\pi$
$563$	11.3764	+	19.7046i	0.479460	+	0.830449i	−0.520263	+	0.854006i	$0.674166\pi$
$564$		0			0
$565$	14.4628	−	25.0504i	0.608456	−	1.05388i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−13.0292	+	22.5673i	−0.546214	+	0.946071i	0.452315	+	0.891858i	$0.350598\pi$
$569$	−13.0292	+	22.5673i	−0.546214	+	0.946071i	−0.998529	+	0.0542125i	$0.982735\pi$
$570$		0			0
$571$	6.24174	+	10.8110i	0.261209	+	0.452427i	0.966563	−	0.256428i	$-0.0825455\pi$
$571$	6.24174	+	10.8110i	0.261209	+	0.452427i	−0.705355	+	0.708855i	$0.749212\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	9.86421			0.411366
$576$		0			0
$577$	−10.3756	+	17.9710i	−0.431941	+	0.748143i	−0.997040	−	0.0768793i	$-0.975504\pi$
$577$	−10.3756	+	17.9710i	−0.431941	+	0.748143i	0.565100	+	0.825023i	$0.308838\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−33.7631	−	25.3773i	−1.40073	−	1.05283i
$582$		0			0
$583$	16.7133	−	28.9483i	0.692195	−	1.19892i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	8.67294	+	15.0220i	0.357971	+	0.620023i	0.987622	−	0.156855i	$-0.0501355\pi$
$587$	8.67294	+	15.0220i	0.357971	+	0.620023i	−0.629651	+	0.776878i	$0.716802\pi$
$588$		0			0
$589$	−24.5359	+	42.4975i	−1.01099	+	1.75108i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	14.0203	+	24.2839i	0.575745	+	0.997220i	0.995960	+	0.0897956i	$0.0286214\pi$
$593$	14.0203	+	24.2839i	0.575745	+	0.997220i	−0.420215	+	0.907425i	$0.638045\pi$
$594$		0			0
$595$	0.867109	−	7.13455i	0.0355480	−	0.292488i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−11.6047	−	20.0999i	−0.474155	−	0.821260i	0.525407	−	0.850851i	$-0.323913\pi$
$599$	−11.6047	−	20.0999i	−0.474155	−	0.821260i	−0.999562	+	0.0295906i	$0.990580\pi$
$600$		0			0
$601$	−0.348014	−	0.602779i	−0.0141958	−	0.0245878i	0.858840	−	0.512244i	$-0.171185\pi$
$601$	−0.348014	−	0.602779i	−0.0141958	−	0.0245878i	−0.873036	+	0.487656i	$0.837852\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.04572			−0.123826
$606$		0			0
$607$	1.71065			0.0694333			0.0347166	−	0.999397i	$-0.488947\pi$
$607$	1.71065			0.0694333			0.0347166	+	0.999397i	$0.488947\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.09390	−	1.89469i	−0.0442545	−	0.0766511i
$612$		0			0
$613$	1.77253	−	3.07010i	0.0715916	−	0.124000i	−0.828007	−	0.560717i	$-0.810525\pi$
$613$	1.77253	−	3.07010i	0.0715916	−	0.124000i	0.899599	+	0.436717i	$0.143859\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.58526	+	9.67395i	−0.224854	+	0.389458i	−0.956276	−	0.292467i	$-0.905524\pi$
$617$	−5.58526	+	9.67395i	−0.224854	+	0.389458i	0.731422	+	0.681925i	$0.238857\pi$
$618$		0			0
$619$	−19.2172			−0.772403			−0.386201	−	0.922415i	$-0.626213\pi$
$619$	−19.2172			−0.772403			−0.386201	+	0.922415i	$0.626213\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	10.9551	+	8.23414i	0.438906	+	0.329894i
$624$		0			0
$625$	−16.2067			−0.648270
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.04111			−0.161130
$630$		0			0
$631$	23.1101			0.920000			0.460000	−	0.887919i	$-0.347849\pi$
$631$	23.1101			0.920000			0.460000	+	0.887919i	$0.347849\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	32.2185			1.27855
$636$		0			0
$637$	−4.40423	−	15.2180i	−0.174502	−	0.602960i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	20.3938			0.805506			0.402753	−	0.915309i	$-0.368053\pi$
$641$	20.3938			0.805506			0.402753	+	0.915309i	$0.368053\pi$
$642$		0			0
$643$	1.31644	−	2.28015i	0.0519154	−	0.0899202i	−0.838900	−	0.544286i	$-0.816801\pi$
$643$	1.31644	−	2.28015i	0.0519154	−	0.0899202i	0.890815	+	0.454366i	$0.150134\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.63856	−	6.30217i	0.143047	−	0.247764i	−0.785596	−	0.618740i	$-0.787643\pi$
$647$	3.63856	−	6.30217i	0.143047	−	0.247764i	0.928642	+	0.370976i	$0.120977\pi$
$648$		0			0
$649$	−17.4196	−	30.1717i	−0.683781	−	1.18434i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−22.8671			−0.894858			−0.447429	−	0.894319i	$-0.647660\pi$
$653$	−22.8671			−0.894858			−0.447429	+	0.894319i	$0.647660\pi$
$654$		0			0
$655$	4.53589			0.177232
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−3.59545	−	6.22750i	−0.140059	−	0.242589i	0.787460	−	0.616366i	$-0.211396\pi$
$659$	−3.59545	−	6.22750i	−0.140059	−	0.242589i	−0.927519	+	0.373777i	$0.878062\pi$
$660$		0			0
$661$	17.2064	+	29.8023i	0.669250	+	1.15918i	0.978114	+	0.208069i	$0.0667179\pi$
$661$	17.2064	+	29.8023i	0.669250	+	1.15918i	−0.308864	+	0.951106i	$0.599949\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−24.0233	−	18.0566i	−0.931583	−	0.700204i
$666$		0			0
$667$	3.34991	+	5.80222i	0.129709	+	0.224663i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.37877	−	2.38811i	0.0532270	−	0.0921919i
$672$		0			0
$673$	3.46705	+	6.00511i	0.133645	+	0.231480i	0.925079	−	0.379775i	$-0.123998\pi$
$673$	3.46705	+	6.00511i	0.133645	+	0.231480i	−0.791434	+	0.611255i	$0.790665\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.3014	−	29.9668i	0.664945	−	1.15172i	−0.314355	−	0.949306i	$-0.601788\pi$
$677$	17.3014	−	29.9668i	0.664945	−	1.15172i	0.979300	−	0.202413i	$-0.0648784\pi$
$678$		0			0
$679$	3.90373	+	2.93415i	0.149811	+	0.112602i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.1618	+	33.1892i	−0.733206	+	1.26995i	0.222300	+	0.974978i	$0.428643\pi$
$683$	−19.1618	+	33.1892i	−0.733206	+	1.26995i	−0.955506	+	0.294971i	$0.904690\pi$
$684$		0			0
$685$	−20.8988			−0.798502
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.3377	+	21.3696i	0.470030	+	0.814116i
$690$		0			0
$691$	−3.94953	+	6.84079i	−0.150247	+	0.260236i	−0.931318	−	0.364206i	$-0.881340\pi$
$691$	−3.94953	+	6.84079i	−0.150247	+	0.260236i	0.781071	+	0.624442i	$0.214674\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	7.04916	−	12.2095i	0.267390	−	0.463133i
$696$		0			0
$697$	−7.58936	−	13.1452i	−0.287467	−	0.497908i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	25.9291			0.979329			0.489664	−	0.871911i	$-0.337119\pi$
$701$	25.9291			0.979329			0.489664	+	0.871911i	$0.337119\pi$
$702$		0			0
$703$	−8.44893	+	14.6340i	−0.318657	+	0.551931i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	19.6278	−	8.36001i	0.738180	−	0.314410i
$708$		0			0
$709$	−14.0523	+	24.3394i	−0.527746	+	0.914084i	0.471731	+	0.881743i	$0.343630\pi$
$709$	−14.0523	+	24.3394i	−0.527746	+	0.914084i	−0.999477	+	0.0323408i	$0.989704\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	29.4134	+	50.9456i	1.10154	+	1.90793i
$714$		0			0
$715$	−6.60221	+	11.4354i	−0.246909	+	0.427658i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−5.89461	−	10.2098i	−0.219832	−	0.380760i	0.734924	−	0.678149i	$-0.237218\pi$
$719$	−5.89461	−	10.2098i	−0.219832	−	0.380760i	−0.954756	+	0.297389i	$0.903884\pi$
$720$		0			0
$721$	43.3246	−	18.4531i	1.61349	−	0.687229i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.645394	+	1.11785i	0.0239693	+	0.0415161i
$726$		0			0
$727$	24.5207	+	42.4711i	0.909423	+	1.57517i	0.814868	+	0.579647i	$0.196809\pi$
$727$	24.5207	+	42.4711i	0.909423	+	1.57517i	0.0945549	+	0.995520i	$0.469857\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.52027			−0.315134
$732$		0			0
$733$	15.0927			0.557461			0.278731	−	0.960369i	$-0.410086\pi$
$733$	15.0927			0.557461			0.278731	+	0.960369i	$0.410086\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.49503	−	4.32152i	−0.0919056	−	0.159185i
$738$		0			0
$739$	−15.9556	+	27.6359i	−0.586937	+	1.01660i	0.407694	+	0.913119i	$0.366333\pi$
$739$	−15.9556	+	27.6359i	−0.586937	+	1.01660i	−0.994631	+	0.103486i	$0.967000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	12.1582	−	21.0586i	0.446041	−	0.772565i	−0.552083	−	0.833789i	$-0.686167\pi$
$743$	12.1582	−	21.0586i	0.446041	−	0.772565i	0.998124	+	0.0612238i	$0.0195003\pi$
$744$		0			0
$745$	−33.5385			−1.22875
$746$		0			0
$747$		0			0
$748$		0			0
$749$	37.0541	+	27.8509i	1.35393	+	1.01765i
$750$		0			0
$751$	33.4463			1.22047			0.610237	−	0.792219i	$-0.291074\pi$
$751$	33.4463			1.22047			0.610237	+	0.792219i	$0.291074\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	38.7574			1.41053
$756$		0			0
$757$	−32.1248			−1.16759			−0.583797	−	0.811899i	$-0.698434\pi$
$757$	−32.1248			−1.16759			−0.583797	+	0.811899i	$0.698434\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−33.7957			−1.22509			−0.612547	−	0.790435i	$-0.709855\pi$
$761$	−33.7957			−1.22509			−0.612547	+	0.790435i	$0.709855\pi$
$762$		0			0
$763$	0.711454	−	5.85382i	0.0257563	−	0.211923i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	25.7183			0.928634
$768$		0			0
$769$	16.8957	−	29.2643i	0.609276	−	1.05530i	−0.382084	−	0.924128i	$-0.624793\pi$
$769$	16.8957	−	29.2643i	0.609276	−	1.05530i	0.991360	−	0.131170i	$-0.0418733\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	12.0231	−	20.8247i	0.432443	−	0.749012i	−0.564640	−	0.825337i	$-0.690985\pi$
$773$	12.0231	−	20.8247i	0.432443	−	0.749012i	0.997083	+	0.0763245i	$0.0243185\pi$
$774$		0			0
$775$	5.66679	+	9.81516i	0.203557	+	0.352571i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−63.4696			−2.27404
$780$		0			0
$781$	7.24703			0.259319
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.83219	−	15.2978i	−0.315234	−	0.546002i
$786$		0			0
$787$	−3.22897	−	5.59274i	−0.115100	−	0.199360i	0.802719	−	0.596357i	$-0.203386\pi$
$787$	−3.22897	−	5.59274i	−0.115100	−	0.199360i	−0.917820	+	0.396997i	$0.870052\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.85193	−	39.9216i	0.172515	−	1.41945i
$792$		0			0
$793$	1.01781	+	1.76290i	0.0361435	+	0.0626023i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−18.6987	+	32.3871i	−0.662341	+	1.14721i	0.317658	+	0.948205i	$0.397104\pi$
$797$	−18.6987	+	32.3871i	−0.662341	+	1.14721i	−0.979999	+	0.199003i	$0.936230\pi$
$798$		0			0
$799$	−0.689944	−	1.19502i	−0.0244085	−	0.0422767i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.05448	−	5.29051i	0.107790	−	0.186698i
$804$		0			0
$805$	−33.1455	+	14.1175i	−1.16822	+	0.497578i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	20.0048	−	34.6493i	0.703331	−	1.21821i	−0.263959	−	0.964534i	$-0.585028\pi$
$809$	20.0048	−	34.6493i	0.703331	−	1.21821i	0.967290	−	0.253672i	$-0.0816383\pi$
$810$		0			0
$811$	27.6946			0.972489			0.486245	−	0.873823i	$-0.338366\pi$
$811$	27.6946			0.972489			0.486245	+	0.873823i	$0.338366\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	22.6590	+	39.2465i	0.793709	+	1.37474i
$816$		0			0
$817$	−17.8137	+	30.8543i	−0.623223	+	1.07945i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.188732	+	0.326893i	−0.00658679	+	0.0114087i	−0.869300	−	0.494285i	$-0.835430\pi$
$821$	−0.188732	+	0.326893i	−0.00658679	+	0.0114087i	0.862713	+	0.505693i	$0.168763\pi$
$822$		0			0
$823$	5.50313	+	9.53170i	0.191827	+	0.332254i	0.945856	−	0.324587i	$-0.105225\pi$
$823$	5.50313	+	9.53170i	0.191827	+	0.332254i	−0.754029	+	0.656841i	$0.771892\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	28.2473			0.982254			0.491127	−	0.871088i	$-0.336585\pi$
$827$	28.2473			0.982254			0.491127	+	0.871088i	$0.336585\pi$
$828$		0			0
$829$	−14.7833	+	25.6054i	−0.513445	+	0.889313i	0.486433	+	0.873718i	$0.338298\pi$
$829$	−14.7833	+	25.6054i	−0.513445	+	0.889313i	−0.999878	+	0.0155953i	$0.995036\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.77783	−	9.59828i	−0.0962460	−	0.332561i
$834$		0			0
$835$	−1.68132	+	2.91212i	−0.0581843	+	0.100778i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	6.91508	+	11.9773i	0.238735	+	0.413501i	0.960352	−	0.278792i	$-0.0899339\pi$
$839$	6.91508	+	11.9773i	0.238735	+	0.413501i	−0.721617	+	0.692293i	$0.756601\pi$
$840$		0			0
$841$	14.0616	−	24.3555i	0.484884	−	0.839844i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.49581	+	12.9831i	0.257864	+	0.446633i
$846$		0			0
$847$	−3.89581	+	1.65933i	−0.133861	+	0.0570152i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.1285	+	17.5431i	0.347200	+	0.601369i
$852$		0			0
$853$	4.59367	+	7.95647i	0.157284	+	0.272424i	0.933888	−	0.357565i	$-0.116393\pi$
$853$	4.59367	+	7.95647i	0.157284	+	0.272424i	−0.776604	+	0.629989i	$0.783059\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−40.4460			−1.38161			−0.690805	−	0.723041i	$-0.742744\pi$
$857$	−40.4460			−1.38161			−0.690805	+	0.723041i	$0.742744\pi$
$858$		0			0
$859$	12.5128			0.426933			0.213466	−	0.976950i	$-0.431525\pi$
$859$	12.5128			0.426933			0.213466	+	0.976950i	$0.431525\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11.8005	−	20.4391i	−0.401694	−	0.695755i	0.592236	−	0.805764i	$-0.298245\pi$
$863$	−11.8005	−	20.4391i	−0.401694	−	0.695755i	−0.993931	+	0.110010i	$0.964912\pi$
$864$		0			0
$865$	0.342635	−	0.593462i	0.0116499	−	0.0201783i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.7830	−	22.1407i	0.433632	−	0.751073i
$870$		0			0
$871$	3.68365			0.124816
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−29.5469	+	12.5848i	−0.998866	+	0.425444i
$876$		0			0
$877$	−27.5467			−0.930185			−0.465092	−	0.885262i	$-0.653979\pi$
$877$	−27.5467			−0.930185			−0.465092	+	0.885262i	$0.653979\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−42.0894			−1.41803			−0.709014	−	0.705194i	$-0.750860\pi$
$881$	−42.0894			−1.41803			−0.709014	+	0.705194i	$0.750860\pi$
$882$		0			0
$883$	−8.58158			−0.288793			−0.144397	−	0.989520i	$-0.546124\pi$
$883$	−8.58158			−0.288793			−0.144397	+	0.989520i	$0.546124\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.51907			0.118159			0.0590795	−	0.998253i	$-0.481183\pi$
$887$	3.51907			0.118159			0.0590795	+	0.998253i	$0.481183\pi$
$888$		0			0
$889$	41.2110	−	17.5529i	1.38217	−	0.588704i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.76998			−0.193085
$894$		0			0
$895$	−6.80707	+	11.7902i	−0.227535	+	0.394103i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.84891	+	6.66651i	−0.128368	+	0.222341i
$900$		0			0
$901$	7.78163	+	13.4782i	0.259244	+	0.449023i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	21.0362			0.699266
$906$		0			0
$907$	−37.2826			−1.23795			−0.618974	−	0.785412i	$-0.712451\pi$
$907$	−37.2826			−1.23795			−0.618974	+	0.785412i	$0.712451\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−10.6458	−	18.4391i	−0.352711	−	0.610914i	0.634012	−	0.773323i	$-0.281407\pi$
$911$	−10.6458	−	18.4391i	−0.352711	−	0.610914i	−0.986723	+	0.162409i	$0.948074\pi$
$912$		0			0
$913$	24.4718	+	42.3864i	0.809899	+	1.40279i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.80190	−	2.47118i	0.191595	−	0.0816056i
$918$		0			0
$919$	−6.00453	−	10.4001i	−0.198071	−	0.343069i	0.749832	−	0.661628i	$-0.230134\pi$
$919$	−6.00453	−	10.4001i	−0.198071	−	0.343069i	−0.947903	+	0.318559i	$0.896801\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.67487	+	4.63301i	−0.0880444	+	0.152497i
$924$		0			0
$925$	1.95135	+	3.37984i	0.0641601	+	0.111129i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.2602	−	17.7712i	0.336626	−	0.583054i	−0.647170	−	0.762346i	$-0.724047\pi$
$929$	10.2602	−	17.7712i	0.336626	−	0.583054i	0.983796	+	0.179292i	$0.0573807\pi$
$930$		0			0
$931$	−40.5657	−	10.0083i	−1.32949	−	0.328008i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.16413	+	7.21249i	−0.136182	+	0.235874i
$936$		0			0
$937$	−10.9040			−0.356217			−0.178109	−	0.984011i	$-0.556998\pi$
$937$	−10.9040			−0.356217			−0.178109	+	0.984011i	$0.556998\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.4807	−	26.8134i	−0.504656	−	0.874090i	−0.999986	−	0.00538505i	$-0.998286\pi$
$941$	−15.4807	−	26.8134i	−0.504656	−	0.874090i	0.495329	−	0.868705i	$-0.335047\pi$
$942$		0			0
$943$	−38.0434	+	65.8931i	−1.23886	+	2.14578i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	16.0909	−	27.8702i	0.522884	−	0.905661i	−0.476762	−	0.879032i	$-0.658190\pi$
$947$	16.0909	−	27.8702i	0.522884	−	0.905661i	0.999645	−	0.0266283i	$-0.00847707\pi$
$948$		0			0
$949$	2.25481	+	3.90545i	0.0731942	+	0.126776i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−39.0934			−1.26636			−0.633179	−	0.774005i	$-0.718250\pi$
$953$	−39.0934			−1.26636			−0.633179	+	0.774005i	$0.718250\pi$
$954$		0			0
$955$	8.27967	−	14.3408i	0.267924	−	0.464057i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−26.7318	+	11.3858i	−0.863216	+	0.367667i
$960$		0			0
$961$	−18.2948	+	31.6876i	−0.590156	+	1.02218i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.35046	+	2.33906i	0.0434728	+	0.0752971i
$966$		0			0
$967$	12.7235	−	22.0377i	0.409159	−	0.708684i	−0.585637	−	0.810574i	$-0.699155\pi$
$967$	12.7235	−	22.0377i	0.409159	−	0.708684i	0.994796	+	0.101889i	$0.0324888\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.81455	+	15.2673i	0.282872	+	0.489949i	0.972091	−	0.234604i	$-0.0753794\pi$
$971$	8.81455	+	15.2673i	0.282872	+	0.489949i	−0.689219	+	0.724553i	$0.742046\pi$
$972$		0			0
$973$	2.36482	−	19.4577i	0.0758128	−	0.623786i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	13.6269	+	23.6025i	0.435963	+	0.755109i	0.997374	−	0.0724277i	$-0.0230747\pi$
$977$	13.6269	+	23.6025i	0.435963	+	0.755109i	−0.561411	+	0.827537i	$0.689741\pi$
$978$		0			0
$979$	−7.94033	−	13.7531i	−0.253774	−	0.439550i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−20.6741			−0.659402			−0.329701	−	0.944085i	$-0.606948\pi$
$983$	−20.6741			−0.659402			−0.329701	+	0.944085i	$0.606948\pi$
$984$		0			0
$985$	−10.8362			−0.345269
$986$		0			0
$987$		0			0
$988$		0			0
$989$	21.3549	+	36.9878i	0.679047	+	1.17614i
$990$		0			0
$991$	26.0081	−	45.0474i	0.826175	−	1.43098i	−0.0748425	−	0.997195i	$-0.523845\pi$
$991$	26.0081	−	45.0474i	0.826175	−	1.43098i	0.901018	−	0.433782i	$-0.142821\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.97307	+	8.61361i	−0.157657	+	0.273070i
$996$		0			0
$997$	−9.28538			−0.294071			−0.147035	−	0.989131i	$-0.546973\pi$
$997$	−9.28538			−0.294071			−0.147035	+	0.989131i	$0.546973\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.t.j.1873.6		14
3.2	odd	2		1008.2.t.j.193.4		14
4.3	odd	2		756.2.l.b.361.6		14
7.2	even	3		3024.2.q.j.2305.2		14
9.2	odd	6		1008.2.q.j.529.6		14
9.7	even	3		3024.2.q.j.2881.2		14
12.11	even	2		252.2.l.b.193.4	yes	14
21.2	odd	6		1008.2.q.j.625.6		14
28.3	even	6		5292.2.j.g.1765.6		14
28.11	odd	6		5292.2.j.h.1765.2		14
28.19	even	6		5292.2.i.i.1549.6		14
28.23	odd	6		756.2.i.b.37.2		14
28.27	even	2		5292.2.l.i.361.2		14
36.7	odd	6		756.2.i.b.613.2		14
36.11	even	6		252.2.i.b.25.2	✓	14
36.23	even	6		2268.2.k.e.1621.6		14
36.31	odd	6		2268.2.k.f.1621.2		14
63.2	odd	6		1008.2.t.j.961.4		14
63.16	even	3	inner	3024.2.t.j.289.6		14
84.11	even	6		1764.2.j.g.589.7		14
84.23	even	6		252.2.i.b.121.2	yes	14
84.47	odd	6		1764.2.i.i.373.6		14
84.59	odd	6		1764.2.j.h.589.1		14
84.83	odd	2		1764.2.l.i.949.4		14
252.11	even	6		1764.2.j.g.1177.7		14
252.23	even	6		2268.2.k.e.1297.6		14
252.47	odd	6		1764.2.l.i.961.4		14
252.79	odd	6		756.2.l.b.289.6		14
252.83	odd	6		1764.2.i.i.1537.6		14
252.115	even	6		5292.2.j.g.3529.6		14
252.151	odd	6		5292.2.j.h.3529.2		14
252.187	even	6		5292.2.l.i.3313.2		14
252.191	even	6		252.2.l.b.205.4	yes	14
252.223	even	6		5292.2.i.i.2125.6		14
252.227	odd	6		1764.2.j.h.1177.1		14
252.247	odd	6		2268.2.k.f.1297.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.2	✓	14	36.11	even	6
252.2.i.b.121.2	yes	14	84.23	even	6
252.2.l.b.193.4	yes	14	12.11	even	2
252.2.l.b.205.4	yes	14	252.191	even	6
756.2.i.b.37.2		14	28.23	odd	6
756.2.i.b.613.2		14	36.7	odd	6
756.2.l.b.289.6		14	252.79	odd	6
756.2.l.b.361.6		14	4.3	odd	2
1008.2.q.j.529.6		14	9.2	odd	6
1008.2.q.j.625.6		14	21.2	odd	6
1008.2.t.j.193.4		14	3.2	odd	2
1008.2.t.j.961.4		14	63.2	odd	6
1764.2.i.i.373.6		14	84.47	odd	6
1764.2.i.i.1537.6		14	252.83	odd	6
1764.2.j.g.589.7		14	84.11	even	6
1764.2.j.g.1177.7		14	252.11	even	6
1764.2.j.h.589.1		14	84.59	odd	6
1764.2.j.h.1177.1		14	252.227	odd	6
1764.2.l.i.949.4		14	84.83	odd	2
1764.2.l.i.961.4		14	252.47	odd	6
2268.2.k.e.1297.6		14	252.23	even	6
2268.2.k.e.1621.6		14	36.23	even	6
2268.2.k.f.1297.2		14	252.247	odd	6
2268.2.k.f.1621.2		14	36.31	odd	6
3024.2.q.j.2305.2		14	7.2	even	3
3024.2.q.j.2881.2		14	9.7	even	3
3024.2.t.j.289.6		14	63.16	even	3	inner
3024.2.t.j.1873.6		14	1.1	even	1	trivial
5292.2.i.i.1549.6		14	28.19	even	6
5292.2.i.i.2125.6		14	252.223	even	6
5292.2.j.g.1765.6		14	28.3	even	6
5292.2.j.g.3529.6		14	252.115	even	6
5292.2.j.h.1765.2		14	28.11	odd	6
5292.2.j.h.3529.2		14	252.151	odd	6
5292.2.l.i.361.2		14	28.27	even	2
5292.2.l.i.3313.2		14	252.187	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.90301 q^{5} +(2.43415 - 1.03677i) q^{7} -3.06586 q^{11} +(1.13161 - 1.96000i) q^{13} +(0.713726 - 1.23621i) q^{17} +(-2.98444 - 5.16919i) q^{19} -7.15543 q^{23} -1.37856 q^{25} +(-0.468164 - 0.810884i) q^{29} +(-4.11065 - 7.11985i) q^{31} +(4.63221 - 1.97298i) q^{35} +(-1.41550 - 2.45171i) q^{37} +(5.31672 - 9.20883i) q^{41} +(-2.98444 - 5.16919i) q^{43} +(0.483340 - 0.837169i) q^{47} +(4.85021 - 5.04732i) q^{49} +(-5.45142 + 9.44213i) q^{53} -5.83436 q^{55} +(5.68180 + 9.84117i) q^{59} +(-0.449718 + 0.778935i) q^{61} +(2.15346 - 3.72990i) q^{65} +(0.813810 + 1.40956i) q^{67} -2.36378 q^{71} +(-0.996286 + 1.72562i) q^{73} +(-7.46279 + 3.17860i) q^{77} +(-4.16945 + 7.22169i) q^{79} +(-7.98203 - 13.8253i) q^{83} +(1.35822 - 2.35251i) q^{85} +(2.58992 + 4.48587i) q^{89} +(0.722433 - 5.94416i) q^{91} +(-5.67940 - 9.83701i) q^{95} +(0.922890 + 1.59849i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 4 q^{5} + 3 q^{7} - 4 q^{11} + 2 q^{13} - 2 q^{17} - 7 q^{19} - 22 q^{23} + 18 q^{25} - q^{29} + q^{31} - 19 q^{35} + 10 q^{37} + 33 q^{41} - 7 q^{43} - 3 q^{47} - 13 q^{49} + 15 q^{53} + 28 q^{55}+ \cdots - 18 q^{97}+O(q^{100}) \) 14 * q - 4 * q^5 + 3 * q^7 - 4 * q^11 + 2 * q^13 - 2 * q^17 - 7 * q^19 - 22 * q^23 + 18 * q^25 - q^29 + q^31 - 19 * q^35 + 10 * q^37 + 33 * q^41 - 7 * q^43 - 3 * q^47 - 13 * q^49 + 15 * q^53 + 28 * q^55 - 14 * q^59 - 10 * q^61 - 15 * q^65 - 6 * q^67 + 2 * q^71 + 21 * q^73 - 19 * q^77 + 10 * q^79 - 25 * q^83 + 8 * q^85 + 6 * q^89 - 2 * q^91 - 28 * q^95 - 18 * q^97

Introduction

L-functions

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