LMFDB - Embedded newform 3024.2.ca.c.2033.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(2033,3024)] 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, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.2033"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,-2] 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:	$16$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2033.5
Root			$0.320287 + 1.70218i$ of defining polynomial
Character	$\chi$	$=$	3024.2033
Dual form			3024.2.ca.c.2609.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0338034 - 0.0585493i) q^{5} +(-1.19767 - 2.35915i) q^{7} +(-3.40282 + 1.96462i) q^{11} +(3.32589 - 1.92020i) q^{13} +(-0.775337 + 1.34292i) q^{17} +(-5.06375 + 2.92356i) q^{19} +(4.78687 + 2.76370i) q^{23} +(2.49771 + 4.32617i) q^{25} +(-1.20840 - 0.697671i) q^{29} -1.26595i q^{31} +(-0.178612 - 0.00962461i) q^{35} +(-4.35534 - 7.54368i) q^{37} +(5.17415 + 8.96188i) q^{41} +(-0.735847 + 1.27452i) q^{43} -3.54265 q^{47} +(-4.13117 + 5.65097i) q^{49} +(6.28910 + 3.63101i) q^{53} +0.265644i q^{55} +9.40086 q^{59} -0.0815124i q^{61} -0.259638i q^{65} +15.3451 q^{67} +4.30975i q^{71} +(6.12768 + 3.53782i) q^{73} +(8.71030 + 5.67480i) q^{77} +6.84639 q^{79} +(3.93194 - 6.81032i) q^{83} +(0.0524181 + 0.0907908i) q^{85} +(-5.84745 - 10.1281i) q^{89} +(-8.51336 - 5.54650i) q^{91} +0.395305i q^{95} +(-0.363295 - 0.209749i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7} + 12 q^{11} + 6 q^{13} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 6 q^{29} + 30 q^{35} - 2 q^{37} + 6 q^{41} + 2 q^{43} - 36 q^{47} - 8 q^{49} + 36 q^{53} + 60 q^{59} + 28 q^{67} + 42 q^{77} - 32 q^{79}+ \cdots + 6 q^{97}+O(q^{100}) $ 16 * q - 2 * q^7 + 12 * q^11 + 6 * q^13 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 6 * q^29 + 30 * q^35 - 2 * q^37 + 6 * q^41 + 2 * q^43 - 36 * q^47 - 8 * q^49 + 36 * q^53 + 60 * q^59 + 28 * q^67 + 42 * q^77 - 32 * q^79 - 12 * q^85 + 24 * q^89 + 12 * q^91 + 6 * q^97

Character values

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

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

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
$5$	0.0338034	−	0.0585493i	0.0151174	−	0.0261840i	−0.858368	−	0.513035i	$-0.828521\pi$
$5$	0.0338034	−	0.0585493i	0.0151174	−	0.0261840i	0.873485	+	0.486851i	$0.161854\pi$
$6$		0			0
$7$	−1.19767	−	2.35915i	−0.452677	−	0.891675i
$7$	−1.19767	−	2.35915i	−0.452677	−	0.891675i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.40282	+	1.96462i	−1.02599	+	0.592356i	−0.915833	−	0.401559i	$-0.868469\pi$
$11$	−3.40282	+	1.96462i	−1.02599	+	0.592356i	−0.110157	+	0.993914i	$0.535135\pi$
$12$		0			0
$13$	3.32589	−	1.92020i	0.922435	−	0.532568i	0.0380241	−	0.999277i	$-0.487894\pi$
$13$	3.32589	−	1.92020i	0.922435	−	0.532568i	0.884411	+	0.466709i	$0.154560\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.775337	+	1.34292i	−0.188047	+	0.325707i	−0.944599	−	0.328227i	$-0.893549\pi$
$17$	−0.775337	+	1.34292i	−0.188047	+	0.325707i	0.756552	+	0.653933i	$0.226882\pi$
$18$		0			0
$19$	−5.06375	+	2.92356i	−1.16170	+	0.670710i	−0.951712	−	0.306994i	$-0.900677\pi$
$19$	−5.06375	+	2.92356i	−1.16170	+	0.670710i	−0.209991	+	0.977703i	$0.567344\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.78687	+	2.76370i	0.998132	+	0.576272i	0.907695	−	0.419630i	$-0.137840\pi$
$23$	4.78687	+	2.76370i	0.998132	+	0.576272i	0.0904369	+	0.995902i	$0.471174\pi$
$24$		0			0
$25$	2.49771	+	4.32617i	0.499543	+	0.865234i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.20840	−	0.697671i	−0.224394	−	0.129554i	0.383589	−	0.923504i	$-0.374688\pi$
$29$	−1.20840	−	0.697671i	−0.224394	−	0.129554i	−0.607983	+	0.793950i	$0.708021\pi$
$30$		0			0
$31$		−	1.26595i		−	0.227372i	−0.993517	−	0.113686i	$-0.963734\pi$
$31$		−	1.26595i		−	0.227372i	0.993517	−	0.113686i	$-0.0362657\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.178612	−	0.00962461i	−0.0301909	−	0.00162686i
$36$		0			0
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	−0.962567	−	0.271044i	$-0.912631\pi$
$37$	−4.35534	−	7.54368i	−0.716014	−	1.24017i	0.246553	−	0.969129i	$-0.420702\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.17415	+	8.96188i	0.808066	+	1.39961i	0.914202	+	0.405260i	$0.132819\pi$
$41$	5.17415	+	8.96188i	0.808066	+	1.39961i	−0.106136	+	0.994352i	$0.533848\pi$
$42$		0			0
$43$	−0.735847	+	1.27452i	−0.112216	+	0.194363i	−0.916663	−	0.399660i	$-0.869128\pi$
$43$	−0.735847	+	1.27452i	−0.112216	+	0.194363i	0.804448	+	0.594023i	$0.202461\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.54265			−0.516748			−0.258374	−	0.966045i	$-0.583187\pi$
$47$	−3.54265			−0.516748			−0.258374	+	0.966045i	$0.583187\pi$
$48$		0			0
$49$	−4.13117	+	5.65097i	−0.590167	+	0.807281i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.28910	+	3.63101i	0.863874	+	0.498758i	0.865308	−	0.501241i	$-0.167123\pi$
$53$	6.28910	+	3.63101i	0.863874	+	0.498758i	−0.00143340	+	0.999999i	$0.500456\pi$
$54$		0			0
$55$			0.265644i			0.0358194i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	9.40086			1.22389			0.611944	−	0.790901i	$-0.290388\pi$
$59$	9.40086			1.22389			0.611944	+	0.790901i	$0.290388\pi$
$60$		0			0
$61$		−	0.0815124i		−	0.0104366i	−0.999986	−	0.00521830i	$-0.998339\pi$
$61$		−	0.0815124i		−	0.0104366i	0.999986	−	0.00521830i	$-0.00166104\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$		−	0.259638i		−	0.0322041i
$66$		0			0
$67$	15.3451			1.87471			0.937354	−	0.348379i	$-0.113268\pi$
$67$	15.3451			1.87471			0.937354	+	0.348379i	$0.113268\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			4.30975i			0.511474i	0.966746	+	0.255737i	$0.0823181\pi$
$71$			4.30975i			0.511474i	−0.966746	+	0.255737i	$0.917682\pi$
$72$		0			0
$73$	6.12768	+	3.53782i	0.717191	+	0.414070i	0.813718	−	0.581260i	$-0.197440\pi$
$73$	6.12768	+	3.53782i	0.717191	+	0.414070i	−0.0965271	+	0.995330i	$0.530773\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	8.71030	+	5.67480i	0.992630	+	0.646703i
$78$		0			0
$79$	6.84639			0.770279			0.385140	−	0.922858i	$-0.374153\pi$
$79$	6.84639			0.770279			0.385140	+	0.922858i	$0.374153\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.93194	−	6.81032i	0.431587	−	0.747530i	−0.565423	−	0.824801i	$-0.691287\pi$
$83$	3.93194	−	6.81032i	0.431587	−	0.747530i	0.997010	+	0.0772707i	$0.0246206\pi$
$84$		0			0
$85$	0.0524181	+	0.0907908i	0.00568554	+	0.00984765i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.84745	−	10.1281i	−0.619828	−	1.07357i	−0.989517	−	0.144418i	$-0.953869\pi$
$89$	−5.84745	−	10.1281i	−0.619828	−	1.07357i	0.369688	−	0.929156i	$-0.379464\pi$
$90$		0			0
$91$	−8.51336	−	5.54650i	−0.892443	−	0.581431i
$92$		0			0
$93$		0			0
$94$		0			0
$95$			0.395305i			0.0405574i
$96$		0			0
$97$	−0.363295	−	0.209749i	−0.0368870	−	0.0212967i	0.481443	−	0.876477i	$-0.340113\pi$
$97$	−0.363295	−	0.209749i	−0.0368870	−	0.0212967i	−0.518330	+	0.855181i	$0.673446\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.69621	+	15.0623i	0.865305	+	1.49875i	0.866744	+	0.498753i	$0.166209\pi$
$101$	8.69621	+	15.0623i	0.865305	+	1.49875i	−0.00143888	+	0.999999i	$0.500458\pi$
$102$		0			0
$103$	−0.867010	−	0.500568i	−0.0854290	−	0.0493225i	0.456677	−	0.889633i	$-0.349040\pi$
$103$	−0.867010	−	0.500568i	−0.0854290	−	0.0493225i	−0.542106	+	0.840310i	$0.682373\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.02352	−	4.63238i	0.775663	−	0.447829i	−0.0592279	−	0.998244i	$-0.518864\pi$
$107$	8.02352	−	4.63238i	0.775663	−	0.447829i	0.834891	+	0.550415i	$0.185531\pi$
$108$		0			0
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	−0.823998	−	0.566593i	$-0.808261\pi$
$109$	0.821501	−	1.42288i	0.0786855	−	0.136287i	0.902683	+	0.430306i	$0.141594\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.6537	+	7.88296i	−1.28443	+	0.741567i	−0.977655	−	0.210215i	$-0.932584\pi$
$113$	−13.6537	+	7.88296i	−1.28443	+	0.741567i	−0.306776	+	0.951782i	$0.599250\pi$
$114$		0			0
$115$	0.323625	−	0.186845i	0.0301782	−	0.0174234i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.09675	+	0.220756i	0.375549	+	0.0202367i
$120$		0			0
$121$	2.21947	−	3.84424i	0.201770	−	0.349476i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.675760			0.0604418
$126$		0			0
$127$	19.0776			1.69286			0.846430	−	0.532501i	$-0.178748\pi$
$127$	19.0776			1.69286			0.846430	+	0.532501i	$0.178748\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−9.33404	+	16.1670i	−0.815519	+	1.41252i	0.0934359	+	0.995625i	$0.470215\pi$
$131$	−9.33404	+	16.1670i	−0.815519	+	1.41252i	−0.908955	+	0.416895i	$0.863118\pi$
$132$		0			0
$133$	12.9618	+	8.44468i	1.12393	+	0.732246i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.44329	+	3.14269i	−0.465052	+	0.268498i	−0.714166	−	0.699976i	$-0.753194\pi$
$137$	−5.44329	+	3.14269i	−0.465052	+	0.268498i	0.249114	+	0.968474i	$0.419861\pi$
$138$		0			0
$139$	−5.49596	+	3.17309i	−0.466161	+	0.269138i	−0.714631	−	0.699501i	$-0.753406\pi$
$139$	−5.49596	+	3.17309i	−0.466161	+	0.269138i	0.248470	+	0.968640i	$0.420072\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−7.54494	+	13.0682i	−0.630939	+	1.09282i
$144$		0			0
$145$	−0.0816962	+	0.0471673i	−0.00678450	+	0.00391703i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.21992	−	4.16842i	−0.591479	−	0.341491i	0.174203	−	0.984710i	$-0.444265\pi$
$149$	−7.21992	−	4.16842i	−0.591479	−	0.341491i	−0.765682	+	0.643219i	$0.777598\pi$
$150$		0			0
$151$	7.07721	+	12.2581i	0.575935	+	0.997548i	0.995939	+	0.0900264i	$0.0286951\pi$
$151$	7.07721	+	12.2581i	0.575935	+	0.997548i	−0.420005	+	0.907522i	$0.637972\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.0741205	−	0.0427935i	−0.00595350	−	0.00343726i
$156$		0			0
$157$		−	16.4593i		−	1.31360i	−0.754065	−	0.656799i	$-0.771910\pi$
$157$		−	16.4593i		−	1.31360i	0.754065	−	0.656799i	$-0.228090\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.786889	−	14.6030i	0.0620155	−	1.15087i
$162$		0			0
$163$	4.53345	+	7.85216i	0.355087	+	0.615029i	0.987133	−	0.159902i	$-0.0511179\pi$
$163$	4.53345	+	7.85216i	0.355087	+	0.615029i	−0.632046	+	0.774931i	$0.717785\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.64922	+	13.2488i	0.591914	+	1.02523i	0.993974	+	0.109612i	$0.0349608\pi$
$167$	7.64922	+	13.2488i	0.591914	+	1.02523i	−0.402060	+	0.915613i	$0.631706\pi$
$168$		0			0
$169$	0.874352	−	1.51442i	0.0672579	−	0.116494i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.30125			0.174961			0.0874804	−	0.996166i	$-0.472118\pi$
$173$	2.30125			0.174961			0.0874804	+	0.996166i	$0.472118\pi$
$174$		0			0
$175$	7.21464	−	11.0738i	0.545375	−	0.837101i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.8077	−	7.97186i	−1.03203	−	0.595845i	−0.114467	−	0.993427i	$-0.536516\pi$
$179$	−13.8077	−	7.97186i	−1.03203	−	0.595845i	−0.917567	+	0.397582i	$0.869849\pi$
$180$		0			0
$181$			18.4526i			1.37157i	0.727804	+	0.685785i	$0.240541\pi$
$181$			18.4526i			1.37157i	−0.727804	+	0.685785i	$0.759459\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.588903			−0.0432970
$186$		0			0
$187$		−	6.09297i		−	0.445562i
$188$		0			0
$189$		0			0
$190$		0			0
$191$			23.3437i			1.68909i	0.535484	+	0.844546i	$0.320129\pi$
$191$			23.3437i			1.68909i	−0.535484	+	0.844546i	$0.679871\pi$
$192$		0			0
$193$	21.2878			1.53233			0.766164	−	0.642646i	$-0.222163\pi$
$193$	21.2878			1.53233			0.766164	+	0.642646i	$0.222163\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.8467i		−	0.915288i	−0.889136	−	0.457644i	$-0.848693\pi$
$197$		−	12.8467i		−	0.915288i	0.889136	−	0.457644i	$-0.151307\pi$
$198$		0			0
$199$	3.24154	+	1.87150i	0.229787	+	0.132667i	0.610474	−	0.792037i	$-0.290979\pi$
$199$	3.24154	+	1.87150i	0.229787	+	0.132667i	−0.380687	+	0.924704i	$0.624312\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.198643	+	3.68638i	−0.0139420	+	0.258733i
$204$		0			0
$205$	0.699616			0.0488633
$206$		0			0
$207$		0			0
$208$		0			0
$209$	11.4874	−	19.8967i	0.794597	−	1.37628i
$210$		0			0
$211$	−4.69581	−	8.13339i	−0.323273	−	0.559925i	0.657888	−	0.753116i	$-0.271450\pi$
$211$	−4.69581	−	8.13339i	−0.323273	−	0.559925i	−0.981161	+	0.193190i	$0.938117\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0497483	+	0.0861666i	0.00339281	+	0.00587651i
$216$		0			0
$217$	−2.98657	+	1.51619i	−0.202741	+	0.102926i
$218$		0			0
$219$		0			0
$220$		0			0
$221$			5.95522i			0.400591i
$222$		0			0
$223$	17.7695	+	10.2592i	1.18993	+	0.687008i	0.958291	−	0.285793i	$-0.0922570\pi$
$223$	17.7695	+	10.2592i	1.18993	+	0.687008i	0.231642	+	0.972801i	$0.425590\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.38828	−	16.2610i	−0.623122	−	1.07928i	−0.988901	−	0.148577i	$-0.952531\pi$
$227$	−9.38828	−	16.2610i	−0.623122	−	1.07928i	0.365779	−	0.930702i	$-0.380803\pi$
$228$		0			0
$229$	−4.31740	−	2.49265i	−0.285302	−	0.164719i	0.350519	−	0.936556i	$-0.386005\pi$
$229$	−4.31740	−	2.49265i	−0.285302	−	0.164719i	−0.635821	+	0.771836i	$0.719338\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.7747	+	7.37548i	−0.836899	+	0.483184i	−0.856209	−	0.516630i	$-0.827186\pi$
$233$	−12.7747	+	7.37548i	−0.836899	+	0.483184i	0.0193101	+	0.999814i	$0.493853\pi$
$234$		0			0
$235$	−0.119754	+	0.207419i	−0.00781186	+	0.0135305i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−0.155388	+	0.0897132i	−0.0100512	+	0.00580307i	−0.505017	−	0.863109i	$-0.668514\pi$
$239$	−0.155388	+	0.0897132i	−0.0100512	+	0.00580307i	0.494966	+	0.868912i	$0.335181\pi$
$240$		0			0
$241$	5.31183	−	3.06679i	0.342165	−	0.197549i	−0.319064	−	0.947733i	$-0.603368\pi$
$241$	5.31183	−	3.06679i	0.342165	−	0.197549i	0.661229	+	0.750184i	$0.270035\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.191212	+	0.432899i	0.0122161	+	0.0276569i
$246$		0			0
$247$	−11.2276	+	19.4468i	−0.714397	+	1.23737i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.11296			−0.0702495			−0.0351247	−	0.999383i	$-0.511183\pi$
$251$	−1.11296			−0.0702495			−0.0351247	+	0.999383i	$0.511183\pi$
$252$		0			0
$253$	−21.7185			−1.36543
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.37366	+	4.11130i	−0.148065	+	0.256456i	−0.930512	−	0.366261i	$-0.880638\pi$
$257$	−2.37366	+	4.11130i	−0.148065	+	0.256456i	0.782447	+	0.622717i	$0.213971\pi$
$258$		0			0
$259$	−12.5804	+	19.3098i	−0.781708	+	1.19985i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	3.65146	−	2.10817i	0.225159	−	0.129995i	−0.383178	−	0.923675i	$-0.625170\pi$
$263$	3.65146	−	2.10817i	0.225159	−	0.129995i	0.608337	+	0.793679i	$0.291837\pi$
$264$		0			0
$265$	0.425186	−	0.245482i	0.0261190	−	0.0150798i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.97265	+	13.8090i	−0.486101	+	0.841952i	−0.999872	−	0.0159753i	$-0.994915\pi$
$269$	−7.97265	+	13.8090i	−0.486101	+	0.841952i	0.513771	+	0.857927i	$0.328248\pi$
$270$		0			0
$271$	−14.1913	+	8.19335i	−0.862060	+	0.497710i	−0.864702	−	0.502286i	$-0.832492\pi$
$271$	−14.1913	+	8.19335i	−0.862060	+	0.497710i	0.00264173	+	0.999997i	$0.499159\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−16.9986	−	9.81413i	−1.02505	−	0.591814i
$276$		0			0
$277$	0.928004	+	1.60735i	0.0557583	+	0.0965763i	0.892557	−	0.450934i	$-0.148909\pi$
$277$	0.928004	+	1.60735i	0.0557583	+	0.0965763i	−0.836799	+	0.547510i	$0.815576\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.628441	+	0.362830i	0.0374896	+	0.0216446i	0.518628	−	0.855000i	$-0.326443\pi$
$281$	0.628441	+	0.362830i	0.0374896	+	0.0216446i	−0.481138	+	0.876645i	$0.659776\pi$
$282$		0			0
$283$		−	11.6276i		−	0.691192i	−0.938383	−	0.345596i	$-0.887677\pi$
$283$		−	11.6276i		−	0.691192i	0.938383	−	0.345596i	$-0.112323\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	14.9455	−	22.9400i	0.882205	−	1.35410i
$288$		0			0
$289$	7.29770	+	12.6400i	0.429277	+	0.743529i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.45034	+	11.1723i	0.376833	+	0.652694i	0.990600	−	0.136794i	$-0.0436797\pi$
$293$	6.45034	+	11.1723i	0.376833	+	0.652694i	−0.613766	+	0.789488i	$0.710346\pi$
$294$		0			0
$295$	0.317781	−	0.550413i	0.0185019	−	0.0320463i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	21.2275			1.22762
$300$		0			0
$301$	3.88809	+	0.209512i	0.224106	+	0.0120761i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.00477249	−	0.00275540i	−0.000273272	−	0.000157774i
$306$		0			0
$307$		−	20.5111i		−	1.17063i	−0.810806	−	0.585315i	$-0.800971\pi$
$307$		−	20.5111i		−	1.17063i	0.810806	−	0.585315i	$-0.199029\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−15.0288			−0.852206			−0.426103	−	0.904675i	$-0.640114\pi$
$311$	−15.0288			−0.852206			−0.426103	+	0.904675i	$0.640114\pi$
$312$		0			0
$313$			1.11536i			0.0630438i	0.999503	+	0.0315219i	$0.0100354\pi$
$313$			1.11536i			0.0630438i	−0.999503	+	0.0315219i	$0.989965\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			1.23344i			0.0692768i	0.999400	+	0.0346384i	$0.0110280\pi$
$317$			1.23344i			0.0692768i	−0.999400	+	0.0346384i	$0.988972\pi$
$318$		0			0
$319$	5.48263			0.306969
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	9.06696i		−	0.504499i
$324$		0			0
$325$	16.6142	+	9.59223i	0.921592	+	0.532081i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.24292	+	8.35763i	0.233920	+	0.460771i
$330$		0			0
$331$	5.02462			0.276178			0.138089	−	0.990420i	$-0.455904\pi$
$331$	5.02462			0.276178			0.138089	+	0.990420i	$0.455904\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	0.518719	−	0.898447i	0.0283406	−	0.0490874i
$336$		0			0
$337$	10.6356	+	18.4213i	0.579356	+	1.00347i	0.995553	+	0.0941995i	$0.0300292\pi$
$337$	10.6356	+	18.4213i	0.579356	+	1.00347i	−0.416198	+	0.909274i	$0.636638\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.48712	+	4.30781i	0.134685	+	0.233281i
$342$		0			0
$343$	18.2793	+	2.97805i	0.986987	+	0.160799i
$344$		0			0
$345$		0			0
$346$		0			0
$347$			21.5735i			1.15813i	0.815282	+	0.579063i	$0.196582\pi$
$347$			21.5735i			1.15813i	−0.815282	+	0.579063i	$0.803418\pi$
$348$		0			0
$349$	−24.1105	−	13.9202i	−1.29061	−	0.745132i	−0.311845	−	0.950133i	$-0.600947\pi$
$349$	−24.1105	−	13.9202i	−1.29061	−	0.745132i	−0.978762	+	0.205001i	$0.934280\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.85124	−	4.93850i	−0.151756	−	0.262850i	0.780117	−	0.625634i	$-0.215160\pi$
$353$	−2.85124	−	4.93850i	−0.151756	−	0.262850i	−0.931873	+	0.362784i	$0.881826\pi$
$354$		0			0
$355$	0.252333	+	0.145685i	0.0133924	+	0.00773213i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.5815	+	10.7280i	−0.980693	+	0.566203i	−0.902479	−	0.430733i	$-0.858255\pi$
$359$	−18.5815	+	10.7280i	−0.980693	+	0.566203i	−0.0782137	+	0.996937i	$0.524922\pi$
$360$		0			0
$361$	7.59435	−	13.1538i	0.399703	−	0.692305i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.414273	−	0.239181i	0.0216841	−	0.0125193i
$366$		0			0
$367$	7.97484	−	4.60428i	0.416283	−	0.240341i	−0.277203	−	0.960811i	$-0.589407\pi$
$367$	7.97484	−	4.60428i	0.416283	−	0.240341i	0.693486	+	0.720470i	$0.256074\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.03383	−	19.1857i	0.0536739	−	0.996071i
$372$		0			0
$373$	−14.1000	+	24.4219i	−0.730071	+	1.26452i	0.226782	+	0.973946i	$0.427180\pi$
$373$	−14.1000	+	24.4219i	−0.730071	+	1.26452i	−0.956852	+	0.290574i	$0.906154\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.35867			−0.275986
$378$		0			0
$379$	4.72569			0.242742			0.121371	−	0.992607i	$-0.461271\pi$
$379$	4.72569			0.242742			0.121371	+	0.992607i	$0.461271\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	17.1174	−	29.6483i	0.874660	−	1.51496i	0.0175357	−	0.999846i	$-0.494418\pi$
$383$	17.1174	−	29.6483i	0.874660	−	1.51496i	0.857124	−	0.515110i	$-0.172249\pi$
$384$		0			0
$385$	0.626693	−	0.318154i	0.0319392	−	0.0162146i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	16.0167	−	9.24726i	0.812080	−	0.468855i	−0.0355974	−	0.999366i	$-0.511333\pi$
$389$	16.0167	−	9.24726i	0.812080	−	0.468855i	0.847678	+	0.530511i	$0.178000\pi$
$390$		0			0
$391$	−7.42288	+	4.28560i	−0.375391	+	0.216732i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.231432	−	0.400851i	0.0116446	−	0.0201690i
$396$		0			0
$397$	−1.76126	+	1.01687i	−0.0883952	+	0.0510350i	−0.543546	−	0.839379i	$-0.682919\pi$
$397$	−1.76126	+	1.01687i	−0.0883952	+	0.0510350i	0.455151	+	0.890414i	$0.349585\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	27.2137	+	15.7118i	1.35899	+	0.784611i	0.989487	−	0.144620i	$-0.0461961\pi$
$401$	27.2137	+	15.7118i	1.35899	+	0.784611i	0.369499	+	0.929231i	$0.379529\pi$
$402$		0			0
$403$	−2.43088	−	4.21041i	−0.121091	−	0.209736i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	29.6409	+	17.1132i	1.46925	+	0.848270i
$408$		0			0
$409$		−	0.550583i		−	0.0272246i	−0.999907	−	0.0136123i	$-0.995667\pi$
$409$		−	0.550583i		−	0.0272246i	0.999907	−	0.0136123i	$-0.00433306\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−11.2591	−	22.1780i	−0.554026	−	1.09131i
$414$		0			0
$415$	−0.265826	−	0.460425i	−0.0130489	−	0.0226014i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.5649	+	20.0310i	0.564984	+	0.978580i	0.997051	+	0.0767392i	$0.0244509\pi$
$419$	11.5649	+	20.0310i	0.564984	+	0.978580i	−0.432068	+	0.901841i	$0.642216\pi$
$420$		0			0
$421$	5.49773	−	9.52235i	0.267943	−	0.464091i	−0.700387	−	0.713763i	$-0.746989\pi$
$421$	5.49773	−	9.52235i	0.267943	−	0.464091i	0.968330	+	0.249672i	$0.0803228\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.74628			−0.375750
$426$		0			0
$427$	−0.192300	+	0.0976251i	−0.00930605	+	0.00472441i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.19720	−	4.15530i	−0.346677	−	0.200154i	0.316544	−	0.948578i	$-0.397478\pi$
$431$	−7.19720	−	4.15530i	−0.346677	−	0.200154i	−0.663221	+	0.748424i	$0.730811\pi$
$432$		0			0
$433$		−	26.1051i		−	1.25453i	−0.778806	−	0.627265i	$-0.784174\pi$
$433$		−	26.1051i		−	1.25453i	0.778806	−	0.627265i	$-0.215826\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−32.3193			−1.54604
$438$		0			0
$439$		−	40.8308i		−	1.94875i	−0.224940	−	0.974373i	$-0.572218\pi$
$439$		−	40.8308i		−	1.94875i	0.224940	−	0.974373i	$-0.427782\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		−	18.2565i		−	0.867391i	−0.901059	−	0.433696i	$-0.857209\pi$
$443$		−	18.2565i		−	0.867391i	0.901059	−	0.433696i	$-0.142791\pi$
$444$		0			0
$445$	−0.790656			−0.0374807
$446$		0			0
$447$		0			0
$448$		0			0
$449$			26.0881i			1.23117i	0.788070	+	0.615586i	$0.211081\pi$
$449$			26.0881i			1.23117i	−0.788070	+	0.615586i	$0.788919\pi$
$450$		0			0
$451$	−35.2134	−	20.3305i	−1.65813	−	0.957325i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.612524	+	0.310960i	−0.0287156	+	0.0145781i
$456$		0			0
$457$	−6.39973			−0.299367			−0.149683	−	0.988734i	$-0.547825\pi$
$457$	−6.39973			−0.299367			−0.149683	+	0.988734i	$0.547825\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.04099	+	1.80304i	−0.0484836	+	0.0839761i	−0.889249	−	0.457424i	$-0.848772\pi$
$461$	−1.04099	+	1.80304i	−0.0484836	+	0.0839761i	0.840765	+	0.541400i	$0.182106\pi$
$462$		0			0
$463$	0.959084	+	1.66118i	0.0445724	+	0.0772017i	0.887451	−	0.460902i	$-0.152474\pi$
$463$	0.959084	+	1.66118i	0.0445724	+	0.0772017i	−0.842879	+	0.538104i	$0.819141\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.1178	−	29.6488i	−0.792116	−	1.37199i	−0.924654	−	0.380807i	$-0.875646\pi$
$467$	−17.1178	−	29.6488i	−0.792116	−	1.37199i	0.132539	−	0.991178i	$-0.457687\pi$
$468$		0			0
$469$	−18.3784	−	36.2015i	−0.848637	−	1.67163i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	5.78264i		−	0.265886i
$474$		0			0
$475$	−25.2956	−	14.6044i	−1.16064	−	0.670096i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.29123	+	9.16468i	0.241763	+	0.418745i	0.961216	−	0.275795i	$-0.0889411\pi$
$479$	5.29123	+	9.16468i	0.241763	+	0.418745i	−0.719454	+	0.694540i	$0.755608\pi$
$480$		0			0
$481$	−28.9708	−	16.7263i	−1.32095	−	0.762653i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.0245613	+	0.0141804i	−0.00111527	+	0.000643901i
$486$		0			0
$487$	−5.95804	+	10.3196i	−0.269985	+	0.467627i	−0.968858	−	0.247619i	$-0.920352\pi$
$487$	−5.95804	+	10.3196i	−0.269985	+	0.467627i	0.698873	+	0.715246i	$0.253685\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−14.9826	+	8.65023i	−0.676157	+	0.390379i	−0.798406	−	0.602120i	$-0.794323\pi$
$491$	−14.9826	+	8.65023i	−0.676157	+	0.390379i	0.122248	+	0.992500i	$0.460990\pi$
$492$		0			0
$493$	1.87384	−	1.08186i	0.0843933	−	0.0487245i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.1674	−	5.16167i	0.456068	−	0.231532i
$498$		0			0
$499$	−6.41484	+	11.1108i	−0.287168	+	0.497389i	−0.973133	−	0.230246i	$-0.926047\pi$
$499$	−6.41484	+	11.1108i	−0.287168	+	0.497389i	0.685965	+	0.727635i	$0.259380\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.9868			−0.489878			−0.244939	−	0.969539i	$-0.578768\pi$
$503$	−10.9868			−0.489878			−0.244939	+	0.969539i	$0.578768\pi$
$504$		0			0
$505$	1.17585			0.0523245
$506$		0			0
$507$		0			0
$508$		0			0
$509$	14.4838	−	25.0868i	0.641985	−	1.11195i	−0.343004	−	0.939334i	$-0.611444\pi$
$509$	14.4838	−	25.0868i	0.641985	−	1.11195i	0.984989	−	0.172617i	$-0.0552223\pi$
$510$		0			0
$511$	1.00730	−	18.6933i	0.0445602	−	0.826941i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.0586158	+	0.0338419i	−0.00258292	+	0.00149125i
$516$		0			0
$517$	12.0550	−	6.95996i	0.530178	−	0.306099i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.72133	−	9.90963i	0.250656	−	0.434149i	−0.713051	−	0.701113i	$-0.752687\pi$
$521$	5.72133	−	9.90963i	0.250656	−	0.434149i	0.963707	+	0.266964i	$0.0860204\pi$
$522$		0			0
$523$	−14.1536	+	8.17161i	−0.618896	+	0.357320i	−0.776439	−	0.630192i	$-0.782976\pi$
$523$	−14.1536	+	8.17161i	−0.618896	+	0.357320i	0.157543	+	0.987512i	$0.449643\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.70008	+	0.981539i	0.0740565	+	0.0427565i
$528$		0			0
$529$	3.77610	+	6.54039i	0.164178	+	0.284365i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	34.4173	+	19.8708i	1.49078	+	0.860700i
$534$		0			0
$535$		−	0.626362i		−	0.0270800i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.95563	−	27.3454i	0.127308	−	1.17785i
$540$		0			0
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	0.972858	+	0.231403i	$0.0743314\pi$
$541$	15.9752	+	27.6699i	0.686830	+	1.18962i	−0.286029	+	0.958221i	$0.592335\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.0555391	−	0.0961966i	−0.00237903	−	0.00412061i
$546$		0			0
$547$	−15.4351	+	26.7344i	−0.659958	+	1.14308i	0.320668	+	0.947192i	$0.396092\pi$
$547$	−15.4351	+	26.7344i	−0.659958	+	1.14308i	−0.980626	+	0.195889i	$0.937241\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.15871			0.347573
$552$		0			0
$553$	−8.19972	−	16.1517i	−0.348688	−	0.686839i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−12.2398	−	7.06667i	−0.518618	−	0.299424i	0.217751	−	0.976004i	$-0.430128\pi$
$557$	−12.2398	−	7.06667i	−0.518618	−	0.299424i	−0.736369	+	0.676580i	$0.763461\pi$
$558$		0			0
$559$			5.65190i			0.239050i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.11436			−0.215544			−0.107772	−	0.994176i	$-0.534372\pi$
$563$	−5.11436			−0.215544			−0.107772	+	0.994176i	$0.534372\pi$
$564$		0			0
$565$			1.06588i			0.0448421i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	37.2203i		−	1.56035i	−0.625559	−	0.780177i	$-0.715129\pi$
$569$		−	37.2203i		−	1.56035i	0.625559	−	0.780177i	$-0.284871\pi$
$570$		0			0
$571$	−5.27738			−0.220851			−0.110426	−	0.993884i	$-0.535221\pi$
$571$	−5.27738			−0.220851			−0.110426	+	0.993884i	$0.535221\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			27.6118i			1.15149i
$576$		0			0
$577$	−9.72172	−	5.61284i	−0.404721	−	0.233666i	0.283798	−	0.958884i	$-0.408405\pi$
$577$	−9.72172	−	5.61284i	−0.404721	−	0.233666i	−0.688519	+	0.725218i	$0.741739\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−20.7757	−	1.11951i	−0.861923	−	0.0464452i
$582$		0			0
$583$	−28.5343			−1.18177
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.4037	−	21.4838i	0.511955	−	0.886732i	−0.487949	−	0.872872i	$-0.662255\pi$
$587$	12.4037	−	21.4838i	0.511955	−	0.886732i	0.999904	−	0.0138602i	$-0.00441196\pi$
$588$		0			0
$589$	3.70108	+	6.41046i	0.152500	+	0.264138i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.47382	+	11.2130i	0.265848	+	0.460462i	0.967785	−	0.251777i	$-0.0810148\pi$
$593$	6.47382	+	11.2130i	0.265848	+	0.460462i	−0.701938	+	0.712238i	$0.747681\pi$
$594$		0			0
$595$	0.151410	−	0.232400i	0.00620718	−	0.00952746i
$596$		0			0
$597$		0			0
$598$		0			0
$599$			24.1574i			0.987043i	0.869734	+	0.493522i	$0.164291\pi$
$599$			24.1574i			0.987043i	−0.869734	+	0.493522i	$0.835709\pi$
$600$		0			0
$601$	−15.3377	−	8.85525i	−0.625640	−	0.361213i	0.153422	−	0.988161i	$-0.450971\pi$
$601$	−15.3377	−	8.85525i	−0.625640	−	0.361213i	−0.779061	+	0.626948i	$0.784304\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.150052	−	0.259897i	−0.00610046	−	0.0105663i
$606$		0			0
$607$	5.27200	+	3.04379i	0.213984	+	0.123544i	0.603162	−	0.797619i	$-0.293907\pi$
$607$	5.27200	+	3.04379i	0.213984	+	0.123544i	−0.389178	+	0.921163i	$0.627241\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.7824	+	6.80260i	−0.476667	+	0.275204i
$612$		0			0
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	−0.312332	−	0.949973i	$-0.601110\pi$
$613$	16.5026	−	28.5834i	0.666535	−	1.15447i	0.978867	−	0.204499i	$-0.0655566\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.36942	−	4.83209i	0.336940	−	0.194533i	−0.321978	−	0.946747i	$-0.604348\pi$
$617$	8.36942	−	4.83209i	0.336940	−	0.194533i	0.658918	+	0.752215i	$0.271014\pi$
$618$		0			0
$619$	−15.6756	+	9.05034i	−0.630057	+	0.363764i	−0.780774	−	0.624813i	$-0.785175\pi$
$619$	−15.6756	+	9.05034i	−0.630057	+	0.363764i	0.150717	+	0.988577i	$0.451842\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.8903	+	25.9251i	−0.676697	+	1.03867i
$624$		0			0
$625$	−12.4657	+	21.5913i	−0.498629	+	0.863651i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	13.5074			0.538577
$630$		0			0
$631$	5.07079			0.201865			0.100932	−	0.994893i	$-0.467817\pi$
$631$	5.07079			0.201865			0.100932	+	0.994893i	$0.467817\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	0.644887	−	1.11698i	0.0255916	−	0.0443259i
$636$		0			0
$637$	−2.88881	+	26.7272i	−0.114459	+	1.05897i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	7.62707	−	4.40349i	0.301251	−	0.173927i	−0.341754	−	0.939790i	$-0.611021\pi$
$641$	7.62707	−	4.40349i	0.301251	−	0.173927i	0.643005	+	0.765862i	$0.277688\pi$
$642$		0			0
$643$	2.52364	−	1.45702i	0.0995227	−	0.0574594i	−0.449413	−	0.893324i	$-0.648367\pi$
$643$	2.52364	−	1.45702i	0.0995227	−	0.0574594i	0.548935	+	0.835865i	$0.315033\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.15173	+	8.92306i	−0.202535	+	0.350802i	−0.949345	−	0.314237i	$-0.898251\pi$
$647$	−5.15173	+	8.92306i	−0.202535	+	0.350802i	0.746809	+	0.665038i	$0.231585\pi$
$648$		0			0
$649$	−31.9895	+	18.4691i	−1.25570	+	0.724976i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.3666	−	8.87194i	−0.601343	−	0.347186i	0.168227	−	0.985748i	$-0.446196\pi$
$653$	−15.3666	−	8.87194i	−0.601343	−	0.347186i	−0.769570	+	0.638563i	$0.779529\pi$
$654$		0			0
$655$	0.631045	+	1.09300i	0.0246570	+	0.0427071i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.08467	−	2.35828i	−0.159116	−	0.0918657i	0.418328	−	0.908296i	$-0.362616\pi$
$659$	−4.08467	−	2.35828i	−0.159116	−	0.0918657i	−0.577444	+	0.816430i	$0.695950\pi$
$660$		0			0
$661$			9.42879i			0.366737i	0.983044	+	0.183369i	$0.0587002\pi$
$661$			9.42879i			0.366737i	−0.983044	+	0.183369i	$0.941300\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.932583	−	0.473445i	0.0361640	−	0.0183594i
$666$		0			0
$667$	−3.85631	−	6.67932i	−0.149317	−	0.258624i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.160141	+	0.277372i	0.00618218	+	0.0107078i
$672$		0			0
$673$	−6.42728	+	11.1324i	−0.247753	+	0.429122i	−0.962902	−	0.269851i	$-0.913026\pi$
$673$	−6.42728	+	11.1324i	−0.247753	+	0.429122i	0.715149	+	0.698972i	$0.246359\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−49.1893			−1.89050			−0.945248	−	0.326352i	$-0.894181\pi$
$677$	−49.1893			−1.89050			−0.945248	+	0.326352i	$0.894181\pi$
$678$		0			0
$679$	−0.0597202	+	1.10828i	−0.00229185	+	0.0425318i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	36.2732	+	20.9424i	1.38796	+	0.801337i	0.993085	−	0.117399i	$-0.0374556\pi$
$683$	36.2732	+	20.9424i	1.38796	+	0.801337i	0.394872	+	0.918736i	$0.370789\pi$
$684$		0			0
$685$			0.424934i			0.0162359i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	27.8891			1.06249
$690$		0			0
$691$		−	6.42914i		−	0.244576i	−0.992495	−	0.122288i	$-0.960977\pi$
$691$		−	6.42914i		−	0.244576i	0.992495	−	0.122288i	$-0.0390231\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			0.429046i			0.0162746i
$696$		0			0
$697$	−16.0468			−0.607817
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	33.7907i		−	1.27626i	−0.769930	−	0.638129i	$-0.779709\pi$
$701$		−	33.7907i		−	1.27626i	0.769930	−	0.638129i	$-0.220291\pi$
$702$		0			0
$703$	44.1087	+	25.4662i	1.66359	+	0.960475i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	25.1190	−	38.5553i	0.944696	−	1.45002i
$708$		0			0
$709$	−29.6833			−1.11478			−0.557390	−	0.830251i	$-0.688197\pi$
$709$	−29.6833			−1.11478			−0.557390	+	0.830251i	$0.688197\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.49871	−	6.05995i	0.131028	−	0.226947i
$714$		0			0
$715$	0.510090	+	0.883501i	0.0190763	+	0.0330411i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.1588	−	31.4519i	−0.677207	−	1.17296i	−0.975818	−	0.218583i	$-0.929857\pi$
$719$	−18.1588	−	31.4519i	−0.677207	−	1.17296i	0.298611	−	0.954375i	$-0.403477\pi$
$720$		0			0
$721$	−0.142523	+	2.64492i	−0.00530784	+	0.0985020i
$722$		0			0
$723$		0			0
$724$		0			0
$725$		−	6.97033i		−	0.258872i
$726$		0			0
$727$	−14.9225	−	8.61552i	−0.553446	−	0.319532i	0.197065	−	0.980390i	$-0.436859\pi$
$727$	−14.9225	−	8.61552i	−0.553446	−	0.319532i	−0.750511	+	0.660858i	$0.770192\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.14106	−	1.97637i	−0.0422036	−	0.0730987i
$732$		0			0
$733$	−37.2907	−	21.5298i	−1.37736	−	0.795222i	−0.385523	−	0.922698i	$-0.625979\pi$
$733$	−37.2907	−	21.5298i	−1.37736	−	0.795222i	−0.991842	+	0.127477i	$0.959312\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−52.2168	+	30.1474i	−1.92343	+	1.11049i
$738$		0			0
$739$	1.87511	−	3.24778i	0.0689770	−	0.119472i	−0.829474	−	0.558545i	$-0.811360\pi$
$739$	1.87511	−	3.24778i	0.0689770	−	0.119472i	0.898451	+	0.439073i	$0.144693\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.9862	+	13.8484i	−0.879967	+	0.508049i	−0.870648	−	0.491907i	$-0.836300\pi$
$743$	−23.9862	+	13.8484i	−0.879967	+	0.508049i	−0.00931965	+	0.999957i	$0.502967\pi$
$744$		0			0
$745$	−0.488116	+	0.281814i	−0.0178832	+	0.0103249i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−20.5380	−	13.3806i	−0.750443	−	0.488917i
$750$		0			0
$751$	−2.08856	+	3.61750i	−0.0762127	+	0.132004i	−0.901613	−	0.432544i	$-0.857616\pi$
$751$	−2.08856	+	3.61750i	−0.0762127	+	0.132004i	0.825400	+	0.564548i	$0.190949\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.956936			0.0348264
$756$		0			0
$757$	35.9359			1.30611			0.653057	−	0.757309i	$-0.273486\pi$
$757$	35.9359			1.30611			0.653057	+	0.757309i	$0.273486\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	14.5715	−	25.2385i	0.528216	−	0.914896i	−0.471243	−	0.882003i	$-0.656195\pi$
$761$	14.5715	−	25.2385i	0.528216	−	0.914896i	0.999459	−	0.0328930i	$-0.0104720\pi$
$762$		0			0
$763$	−4.34068	−	0.233900i	−0.157143	−	0.00846775i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	31.2662	−	18.0515i	1.12896	−	0.651804i
$768$		0			0
$769$	0.795911	−	0.459519i	0.0287013	−	0.0165707i	−0.485581	−	0.874192i	$-0.661392\pi$
$769$	0.795911	−	0.459519i	0.0287013	−	0.0165707i	0.514282	+	0.857621i	$0.328058\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.69708	−	8.13558i	0.168942	−	0.292616i	−0.769106	−	0.639121i	$-0.779298\pi$
$773$	4.69708	−	8.13558i	0.168942	−	0.292616i	0.938048	+	0.346505i	$0.112632\pi$
$774$		0			0
$775$	5.47672	−	3.16199i	0.196730	−	0.113582i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−52.4011	−	30.2538i	−1.87747	−	1.08396i
$780$		0			0
$781$	−8.46703	−	14.6653i	−0.302974	−	0.524767i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−0.963683	−	0.556383i	−0.0343953	−	0.0198581i
$786$		0			0
$787$			30.5960i			1.09063i	0.838231	+	0.545315i	$0.183590\pi$
$787$			30.5960i			1.09063i	−0.838231	+	0.545315i	$0.816410\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	34.9497	+	22.7699i	1.24267	+	0.809604i
$792$		0			0
$793$	−0.156520	−	0.271101i	−0.00555820	−	0.00962709i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.64717	+	2.85299i	0.0583459	+	0.101058i	0.893723	−	0.448619i	$-0.148084\pi$
$797$	1.64717	+	2.85299i	0.0583459	+	0.101058i	−0.835377	+	0.549677i	$0.814751\pi$
$798$		0			0
$799$	2.74674	−	4.75750i	0.0971728	−	0.168308i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−27.8019			−0.981107
$804$		0			0
$805$	−0.828393	−	0.539702i	−0.0291970	−	0.0190220i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−19.7833	−	11.4219i	−0.695542	−	0.401572i	0.110143	−	0.993916i	$-0.464869\pi$
$809$	−19.7833	−	11.4219i	−0.695542	−	0.401572i	−0.805685	+	0.592344i	$0.798203\pi$
$810$		0			0
$811$		−	23.9412i		−	0.840691i	−0.907364	−	0.420345i	$-0.861909\pi$
$811$		−	23.9412i		−	0.840691i	0.907364	−	0.420345i	$-0.138091\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.612985			0.0214719
$816$		0			0
$817$		−	8.60515i		−	0.301056i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		−	2.28557i		−	0.0797669i	−0.999204	−	0.0398834i	$-0.987301\pi$
$821$		−	2.28557i		−	0.0797669i	0.999204	−	0.0398834i	$-0.0126987\pi$
$822$		0			0
$823$	22.9703			0.800694			0.400347	−	0.916364i	$-0.368890\pi$
$823$	22.9703			0.800694			0.400347	+	0.916364i	$0.368890\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	15.1679i		−	0.527438i	−0.964600	−	0.263719i	$-0.915051\pi$
$827$		−	15.1679i		−	0.527438i	0.964600	−	0.263719i	$-0.0849492\pi$
$828$		0			0
$829$	−5.73806	−	3.31287i	−0.199291	−	0.115061i	0.397034	−	0.917804i	$-0.370040\pi$
$829$	−5.73806	−	3.31287i	−0.199291	−	0.115061i	−0.596325	+	0.802743i	$0.703373\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.38577	−	9.92925i	−0.151958	−	0.344028i
$834$		0			0
$835$	1.03428			0.0357927
$836$		0			0
$837$		0			0
$838$		0			0
$839$	23.8462	−	41.3029i	0.823264	−	1.42593i	−0.0799756	−	0.996797i	$-0.525484\pi$
$839$	23.8462	−	41.3029i	0.823264	−	1.42593i	0.903239	−	0.429138i	$-0.141182\pi$
$840$		0			0
$841$	−13.5265	−	23.4286i	−0.466431	−	0.807883i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.0591122	−	0.102385i	−0.00203352	−	0.00352216i
$846$		0			0
$847$	−11.7273	−	0.631934i	−0.402956	−	0.0217135i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		−	48.1475i		−	1.65048i
$852$		0			0
$853$	22.0983	+	12.7585i	0.756632	+	0.436842i	0.828085	−	0.560602i	$-0.189430\pi$
$853$	22.0983	+	12.7585i	0.756632	+	0.436842i	−0.0714529	+	0.997444i	$0.522764\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.19043	+	5.52598i	0.108983	+	0.188764i	0.915358	−	0.402640i	$-0.131907\pi$
$857$	3.19043	+	5.52598i	0.108983	+	0.188764i	−0.806376	+	0.591404i	$0.798574\pi$
$858$		0			0
$859$	−29.7468	−	17.1743i	−1.01495	−	0.585980i	−0.102310	−	0.994753i	$-0.532624\pi$
$859$	−29.7468	−	17.1743i	−1.01495	−	0.585980i	−0.912636	+	0.408773i	$0.865957\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−31.3380	+	18.0930i	−1.06676	+	0.615893i	−0.927294	−	0.374334i	$-0.877871\pi$
$863$	−31.3380	+	18.0930i	−1.06676	+	0.615893i	−0.139464	+	0.990227i	$0.544538\pi$
$864$		0			0
$865$	0.0777901	−	0.134736i	0.00264494	−	0.00458118i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−23.2971	+	13.4506i	−0.790299	+	0.456279i
$870$		0			0
$871$	51.0362	−	29.4658i	1.72930	−	0.998410i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.809338	−	1.59422i	−0.0273606	−	0.0538944i
$876$		0			0
$877$	−17.0155	+	29.4716i	−0.574571	+	0.995186i	0.421517	+	0.906820i	$0.361498\pi$
$877$	−17.0155	+	29.4716i	−0.574571	+	0.995186i	−0.996088	+	0.0883657i	$0.971836\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−26.6961			−0.899416			−0.449708	−	0.893176i	$-0.648472\pi$
$881$	−26.6961			−0.899416			−0.449708	+	0.893176i	$0.648472\pi$
$882$		0			0
$883$	−11.2126			−0.377333			−0.188667	−	0.982041i	$-0.560417\pi$
$883$	−11.2126			−0.377333			−0.188667	+	0.982041i	$0.560417\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.09353	−	8.82225i	0.171024	−	0.296222i	−0.767754	−	0.640745i	$-0.778626\pi$
$887$	5.09353	−	8.82225i	0.171024	−	0.296222i	0.938778	+	0.344522i	$0.111959\pi$
$888$		0			0
$889$	−22.8486	−	45.0068i	−0.766318	−	1.50948i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	17.9391	−	10.3571i	0.600308	−	0.346588i
$894$		0			0
$895$	−0.933494	+	0.538953i	−0.0312033	+	0.0180152i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.883217	+	1.52978i	−0.0294569	+	0.0510209i
$900$		0			0
$901$	−9.75235	+	5.63052i	−0.324898	+	0.187580i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.08039	+	0.623761i	0.0359132	+	0.0207345i
$906$		0			0
$907$	−7.57428	−	13.1190i	−0.251500	−	0.435611i	0.712439	−	0.701734i	$-0.247591\pi$
$907$	−7.57428	−	13.1190i	−0.251500	−	0.435611i	−0.963939	+	0.266123i	$0.914257\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.43020	−	4.86718i	−0.279305	−	0.161257i	0.353804	−	0.935320i	$-0.384888\pi$
$911$	−8.43020	−	4.86718i	−0.279305	−	0.161257i	−0.633109	+	0.774063i	$0.718221\pi$
$912$		0			0
$913$			30.8991i			1.02261i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	49.3195	+	2.65761i	1.62867	+	0.0877621i
$918$		0			0
$919$	4.01638	+	6.95658i	0.132488	+	0.229476i	0.924635	−	0.380854i	$-0.124370\pi$
$919$	4.01638	+	6.95658i	0.132488	+	0.229476i	−0.792147	+	0.610330i	$0.791037\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	8.27560	+	14.3338i	0.272395	+	0.471801i
$924$		0			0
$925$	21.7568	−	37.6839i	0.715360	−	1.23904i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	26.2128			0.860014			0.430007	−	0.902826i	$-0.358511\pi$
$929$	26.2128			0.860014			0.430007	+	0.902826i	$0.358511\pi$
$930$		0			0
$931$	4.39828	−	40.6928i	0.144148	−	1.33365i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.356739	−	0.205963i	−0.0116666	−	0.00673573i
$936$		0			0
$937$			37.5797i			1.22768i	0.789432	+	0.613838i	$0.210375\pi$
$937$			37.5797i			1.22768i	−0.789432	+	0.613838i	$0.789625\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−9.27309			−0.302294			−0.151147	−	0.988511i	$-0.548297\pi$
$941$	−9.27309			−0.302294			−0.151147	+	0.988511i	$0.548297\pi$
$942$		0			0
$943$			57.1992i			1.86266i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	13.8586i		−	0.450343i	−0.974319	−	0.225171i	$-0.927706\pi$
$947$		−	13.8586i		−	0.450343i	0.974319	−	0.225171i	$-0.0722942\pi$
$948$		0			0
$949$	27.1733			0.882083
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	2.65523i		−	0.0860115i	−0.999075	−	0.0430057i	$-0.986307\pi$
$953$		−	2.65523i		−	0.0860115i	0.999075	−	0.0430057i	$-0.0136934\pi$
$954$		0			0
$955$	1.36676	+	0.789097i	0.0442272	+	0.0255346i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	13.9333	+	9.07763i	0.449931	+	0.293132i
$960$		0			0
$961$	29.3974			0.948302
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.719600	−	1.24638i	0.0231647	−	0.0401225i
$966$		0			0
$967$	−7.14946	−	12.3832i	−0.229911	−	0.398218i	0.727870	−	0.685715i	$-0.240510\pi$
$967$	−7.14946	−	12.3832i	−0.229911	−	0.398218i	−0.957782	+	0.287497i	$0.907177\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.130666	+	0.226320i	0.00419326	+	0.00726295i	0.868114	−	0.496364i	$-0.165332\pi$
$971$	0.130666	+	0.226320i	0.00419326	+	0.00726295i	−0.863921	+	0.503627i	$0.831999\pi$
$972$		0			0
$973$	14.0681	+	9.16546i	0.451004	+	0.293831i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			39.1574i			1.25276i	0.779519	+	0.626378i	$0.215464\pi$
$977$			39.1574i			1.25276i	−0.779519	+	0.626378i	$0.784536\pi$
$978$		0			0
$979$	39.7957	+	22.9760i	1.27188	+	0.734318i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.1844	+	22.8361i	0.420517	+	0.728357i	0.995990	−	0.0894636i	$-0.0285153\pi$
$983$	13.1844	+	22.8361i	0.420517	+	0.728357i	−0.575473	+	0.817821i	$0.695182\pi$
$984$		0			0
$985$	−0.752163	−	0.434262i	−0.0239659	−	0.0138367i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.04481	+	4.06732i	−0.224012	+	0.129333i
$990$		0			0
$991$	22.9516	−	39.7534i	0.729082	−	1.26281i	−0.228189	−	0.973617i	$-0.573280\pi$
$991$	22.9516	−	39.7534i	0.729082	−	1.26281i	0.957271	−	0.289191i	$-0.0933862\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.219150	−	0.126526i	0.00694753	−	0.00401116i
$996$		0			0
$997$	−18.5929	+	10.7346i	−0.588844	+	0.339969i	−0.764640	−	0.644457i	$-0.777083\pi$
$997$	−18.5929	+	10.7346i	−0.588844	+	0.339969i	0.175796	+	0.984427i	$0.443750\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.ca.c.2033.5		16
3.2	odd	2		1008.2.ca.c.353.4		16
4.3	odd	2		378.2.l.a.143.3		16
7.5	odd	6		3024.2.df.c.1601.5		16
9.4	even	3		1008.2.df.c.689.2		16
9.5	odd	6		3024.2.df.c.17.5		16
12.11	even	2		126.2.l.a.101.6	yes	16
21.5	even	6		1008.2.df.c.929.2		16
28.3	even	6		2646.2.m.a.1763.6		16
28.11	odd	6		2646.2.m.b.1763.7		16
28.19	even	6		378.2.t.a.89.3		16
28.23	odd	6		2646.2.t.b.1979.2		16
28.27	even	2		2646.2.l.a.521.2		16
36.7	odd	6		1134.2.k.b.647.3		16
36.11	even	6		1134.2.k.a.647.6		16
36.23	even	6		378.2.t.a.17.3		16
36.31	odd	6		126.2.t.a.59.7	yes	16
63.5	even	6	inner	3024.2.ca.c.2609.5		16
63.40	odd	6		1008.2.ca.c.257.4		16
84.11	even	6		882.2.m.b.587.4		16
84.23	even	6		882.2.t.a.803.6		16
84.47	odd	6		126.2.t.a.47.7	yes	16
84.59	odd	6		882.2.m.a.587.1		16
84.83	odd	2		882.2.l.b.227.7		16
252.23	even	6		2646.2.l.a.1097.6		16
252.31	even	6		882.2.m.b.293.4		16
252.47	odd	6		1134.2.k.b.971.3		16
252.59	odd	6		2646.2.m.b.881.7		16
252.67	odd	6		882.2.m.a.293.1		16
252.95	even	6		2646.2.m.a.881.6		16
252.103	even	6		126.2.l.a.5.2	✓	16
252.131	odd	6		378.2.l.a.341.7		16
252.139	even	6		882.2.t.a.815.6		16
252.167	odd	6		2646.2.t.b.2285.2		16
252.187	even	6		1134.2.k.a.971.6		16
252.247	odd	6		882.2.l.b.509.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.2	✓	16	252.103	even	6
126.2.l.a.101.6	yes	16	12.11	even	2
126.2.t.a.47.7	yes	16	84.47	odd	6
126.2.t.a.59.7	yes	16	36.31	odd	6
378.2.l.a.143.3		16	4.3	odd	2
378.2.l.a.341.7		16	252.131	odd	6
378.2.t.a.17.3		16	36.23	even	6
378.2.t.a.89.3		16	28.19	even	6
882.2.l.b.227.7		16	84.83	odd	2
882.2.l.b.509.3		16	252.247	odd	6
882.2.m.a.293.1		16	252.67	odd	6
882.2.m.a.587.1		16	84.59	odd	6
882.2.m.b.293.4		16	252.31	even	6
882.2.m.b.587.4		16	84.11	even	6
882.2.t.a.803.6		16	84.23	even	6
882.2.t.a.815.6		16	252.139	even	6
1008.2.ca.c.257.4		16	63.40	odd	6
1008.2.ca.c.353.4		16	3.2	odd	2
1008.2.df.c.689.2		16	9.4	even	3
1008.2.df.c.929.2		16	21.5	even	6
1134.2.k.a.647.6		16	36.11	even	6
1134.2.k.a.971.6		16	252.187	even	6
1134.2.k.b.647.3		16	36.7	odd	6
1134.2.k.b.971.3		16	252.47	odd	6
2646.2.l.a.521.2		16	28.27	even	2
2646.2.l.a.1097.6		16	252.23	even	6
2646.2.m.a.881.6		16	252.95	even	6
2646.2.m.a.1763.6		16	28.3	even	6
2646.2.m.b.881.7		16	252.59	odd	6
2646.2.m.b.1763.7		16	28.11	odd	6
2646.2.t.b.1979.2		16	28.23	odd	6
2646.2.t.b.2285.2		16	252.167	odd	6
3024.2.ca.c.2033.5		16	1.1	even	1	trivial
3024.2.ca.c.2609.5		16	63.5	even	6	inner
3024.2.df.c.17.5		16	9.5	odd	6
3024.2.df.c.1601.5		16	7.5	odd	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.ca (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0338034 - 0.0585493i) q^{5} +(-1.19767 - 2.35915i) q^{7} +(-3.40282 + 1.96462i) q^{11} +(3.32589 - 1.92020i) q^{13} +(-0.775337 + 1.34292i) q^{17} +(-5.06375 + 2.92356i) q^{19} +(4.78687 + 2.76370i) q^{23} +(2.49771 + 4.32617i) q^{25} +(-1.20840 - 0.697671i) q^{29} -1.26595i q^{31} +(-0.178612 - 0.00962461i) q^{35} +(-4.35534 - 7.54368i) q^{37} +(5.17415 + 8.96188i) q^{41} +(-0.735847 + 1.27452i) q^{43} -3.54265 q^{47} +(-4.13117 + 5.65097i) q^{49} +(6.28910 + 3.63101i) q^{53} +0.265644i q^{55} +9.40086 q^{59} -0.0815124i q^{61} -0.259638i q^{65} +15.3451 q^{67} +4.30975i q^{71} +(6.12768 + 3.53782i) q^{73} +(8.71030 + 5.67480i) q^{77} +6.84639 q^{79} +(3.93194 - 6.81032i) q^{83} +(0.0524181 + 0.0907908i) q^{85} +(-5.84745 - 10.1281i) q^{89} +(-8.51336 - 5.54650i) q^{91} +0.395305i q^{95} +(-0.363295 - 0.209749i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7} + 12 q^{11} + 6 q^{13} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 6 q^{29} + 30 q^{35} - 2 q^{37} + 6 q^{41} + 2 q^{43} - 36 q^{47} - 8 q^{49} + 36 q^{53} + 60 q^{59} + 28 q^{67} + 42 q^{77} - 32 q^{79}+ \cdots + 6 q^{97}+O(q^{100}) \) 16 * q - 2 * q^7 + 12 * q^11 + 6 * q^13 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 6 * q^29 + 30 * q^35 - 2 * q^37 + 6 * q^41 + 2 * q^43 - 36 * q^47 - 8 * q^49 + 36 * q^53 + 60 * q^59 + 28 * q^67 + 42 * q^77 - 32 * q^79 - 12 * q^85 + 24 * q^89 + 12 * q^91 + 6 * q^97

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