LMFDB - Embedded newform 3024.2.q.j.2305.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3024,2,Mod(2305,3024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))

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

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

chi := DirichletCharacter("3024.2305");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$14$
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			2305.2
Root			$-0.473632 - 1.66604i$ of defining polynomial
Character	$\chi$	$=$	3024.2305
Dual form			3024.2.q.j.2881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951504 - 1.64805i) q^{5} +(-2.11495 + 1.58965i) q^{7} +O(q^{10})$	$q+(-0.951504 - 1.64805i) q^{5} +(-2.11495 + 1.58965i) q^{7} +(1.53293 - 2.65512i) q^{11} +(1.13161 - 1.96000i) q^{13} +(0.713726 + 1.23621i) q^{17} +(-2.98444 + 5.16919i) q^{19} +(3.57771 + 6.19678i) q^{23} +(0.689282 - 1.19387i) q^{25} +(-0.468164 - 0.810884i) q^{29} +8.22129 q^{31} +(4.63221 + 1.97298i) q^{35} +(-1.41550 + 2.45171i) q^{37} +(5.31672 - 9.20883i) q^{41} +(-2.98444 - 5.16919i) q^{43} -0.966679 q^{47} +(1.94600 - 6.72407i) q^{49} +(-5.45142 - 9.44213i) q^{53} -5.83436 q^{55} -11.3636 q^{59} +0.899436 q^{61} -4.30692 q^{65} -1.62762 q^{67} -2.36378 q^{71} +(-0.996286 - 1.72562i) q^{73} +(0.978644 + 8.05226i) q^{77} +8.33889 q^{79} +(-7.98203 - 13.8253i) q^{83} +(1.35822 - 2.35251i) q^{85} +(2.58992 - 4.48587i) q^{89} +(0.722433 + 5.94416i) q^{91} +11.3588 q^{95} +(0.922890 + 1.59849i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 2 q^{5} - 6 q^{7}+O(q^{10}) $ 14 * q + 2 * q^5 - 6 * q^7	$ 14 q + 2 q^{5} - 6 q^{7} + 2 q^{11} + 2 q^{13} - 2 q^{17} - 7 q^{19} + 11 q^{23} - 9 q^{25} - q^{29} - 2 q^{31} - 19 q^{35} + 10 q^{37} + 33 q^{41} - 7 q^{43} + 6 q^{47} - 4 q^{49} + 15 q^{53} + 28 q^{55} + 28 q^{59} + 20 q^{61} + 30 q^{65} + 12 q^{67} + 2 q^{71} + 21 q^{73} + 47 q^{77} - 20 q^{79} - 25 q^{83} + 8 q^{85} + 6 q^{89} - 2 q^{91} + 56 q^{95} - 18 q^{97}+O(q^{100}) $ 14 * q + 2 * q^5 - 6 * q^7 + 2 * q^11 + 2 * q^13 - 2 * q^17 - 7 * q^19 + 11 * q^23 - 9 * q^25 - q^29 - 2 * q^31 - 19 * q^35 + 10 * q^37 + 33 * q^41 - 7 * q^43 + 6 * q^47 - 4 * q^49 + 15 * q^53 + 28 * q^55 + 28 * q^59 + 20 * q^61 + 30 * q^65 + 12 * q^67 + 2 * q^71 + 21 * q^73 + 47 * q^77 - 20 * q^79 - 25 * q^83 + 8 * q^85 + 6 * q^89 - 2 * q^91 + 56 * q^95 - 18 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.951504	−	1.64805i	−0.425525	−	0.737032i	0.570944	−	0.820989i	$-0.306577\pi$
$5$	−0.951504	−	1.64805i	−0.425525	−	0.737032i	−0.996469	+	0.0839575i	$0.973244\pi$
$6$		0			0
$7$	−2.11495	+	1.58965i	−0.799375	+	0.600833i
$7$	−2.11495	+	1.58965i	−0.799375	+	0.600833i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.53293	−	2.65512i	0.462196	−	0.800548i	−0.536874	−	0.843663i	$-0.680395\pi$
$11$	1.53293	−	2.65512i	0.462196	−	0.800548i	0.999070	+	0.0431149i	$0.0137282\pi$
$12$		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	0.939503	−	0.342539i	$-0.111287\pi$
$17$	0.713726	+	1.23621i	0.173104	+	0.299825i	−0.766400	+	0.642364i	$0.777954\pi$
$18$		0			0
$19$	−2.98444	+	5.16919i	−0.684677	+	1.18589i	0.288862	+	0.957371i	$0.406723\pi$
$19$	−2.98444	+	5.16919i	−0.684677	+	1.18589i	−0.973538	+	0.228524i	$0.926610\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.57771	+	6.19678i	0.746005	+	1.29212i	0.949724	+	0.313089i	$0.101364\pi$
$23$	3.57771	+	6.19678i	0.746005	+	1.29212i	−0.203719	+	0.979029i	$0.565303\pi$
$24$		0			0
$25$	0.689282	−	1.19387i	0.137856	−	0.238774i
$26$		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
$31$	8.22129			1.47659			0.738294	−	0.674479i	$-0.235632\pi$
$31$	8.22129			1.47659			0.738294	+	0.674479i	$0.235632\pi$
$32$		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	−0.958604	−	0.284744i	$-0.908091\pi$
$37$	−1.41550	+	2.45171i	−0.232706	+	0.403059i	0.725897	+	0.687803i	$0.241425\pi$
$38$		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
$47$	−0.966679			−0.141005			−0.0705023	−	0.997512i	$-0.522460\pi$
$47$	−0.966679			−0.141005			−0.0705023	+	0.997512i	$0.522460\pi$
$48$		0			0
$49$	1.94600	−	6.72407i	0.278001	−	0.960581i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−5.45142	−	9.44213i	−0.748810	−	1.29698i	−0.948393	−	0.317096i	$-0.897292\pi$
$53$	−5.45142	−	9.44213i	−0.748810	−	1.29698i	0.199583	−	0.979881i	$-0.436041\pi$
$54$		0			0
$55$	−5.83436			−0.786705
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−11.3636			−1.47942			−0.739708	−	0.672928i	$-0.765036\pi$
$59$	−11.3636			−1.47942			−0.739708	+	0.672928i	$0.765036\pi$
$60$		0			0
$61$	0.899436			0.115161			0.0575805	−	0.998341i	$-0.481661\pi$
$61$	0.899436			0.115161			0.0575805	+	0.998341i	$0.481661\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.30692			−0.534207
$66$		0			0
$67$	−1.62762			−0.198845			−0.0994227	−	0.995045i	$-0.531700\pi$
$67$	−1.62762			−0.198845			−0.0994227	+	0.995045i	$0.531700\pi$
$68$		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	0.801814	−	0.597573i	$-0.203868\pi$
$73$	−0.996286	−	1.72562i	−0.116606	−	0.201968i	−0.918421	+	0.395605i	$0.870535\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.978644	+	8.05226i	0.111527	+	0.917640i
$78$		0			0
$79$	8.33889			0.938198			0.469099	−	0.883145i	$-0.344579\pi$
$79$	8.33889			0.938198			0.469099	+	0.883145i	$0.344579\pi$
$80$		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	−0.695486	−	0.718540i	$-0.744811\pi$
$89$	2.58992	−	4.48587i	0.274531	−	0.475501i	0.970017	+	0.243039i	$0.0781442\pi$
$90$		0			0
$91$	0.722433	+	5.94416i	0.0757316	+	0.623118i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	11.3588			1.16539
$96$		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
$101$	−4.03175	+	6.98320i	−0.401174	+	0.694854i	−0.993868	−	0.110574i	$-0.964731\pi$
$101$	−4.03175	+	6.98320i	−0.401174	+	0.694854i	0.592694	+	0.805428i	$0.298064\pi$
$102$		0			0
$103$	−8.89931	−	15.4141i	−0.876875	−	1.51879i	−0.854752	−	0.519037i	$-0.826291\pi$
$103$	−8.89931	−	15.4141i	−0.876875	−	1.51879i	−0.0221235	−	0.999755i	$-0.507043\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.76005	−	15.1729i	0.846866	−	1.46682i	−0.0371245	−	0.999311i	$-0.511820\pi$
$107$	8.76005	−	15.1729i	0.846866	−	1.46682i	0.883991	−	0.467505i	$-0.154847\pi$
$108$		0			0
$109$	1.11441	+	1.93021i	0.106741	+	0.184881i	0.914448	−	0.404703i	$-0.132625\pi$
$109$	1.11441	+	1.93021i	0.106741	+	0.184881i	−0.807707	+	0.589584i	$0.799292\pi$
$110$		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
$115$	6.80842	−	11.7925i	0.634888	−	1.09966i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.47464	−	1.47994i	−0.318519	−	0.135666i
$120$		0			0
$121$	0.800238	+	1.38605i	0.0727489	+	0.126005i
$122$		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
$131$	−1.19177	−	2.06420i	−0.104125	−	0.180350i	0.809255	−	0.587457i	$-0.199871\pi$
$131$	−1.19177	−	2.06420i	−0.104125	−	0.180350i	−0.913380	+	0.407107i	$0.866538\pi$
$132$		0			0
$133$	−1.90530	−	15.6768i	−0.165211	−	1.35935i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.49099	−	9.51068i	0.469127	−	0.812552i	−0.530250	−	0.847841i	$-0.677902\pi$
$137$	5.49099	−	9.51068i	0.469127	−	0.812552i	0.999377	+	0.0352893i	$0.0112353\pi$
$138$		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
$149$	8.81197	+	15.2628i	0.721904	+	1.25038i	0.960236	+	0.279191i	$0.0900664\pi$
$149$	8.81197	+	15.2628i	0.721904	+	1.25038i	−0.238331	+	0.971184i	$0.576600\pi$
$150$		0			0
$151$	−10.1832	+	17.6378i	−0.828697	+	1.43535i	0.0703634	+	0.997521i	$0.477584\pi$
$151$	−10.1832	+	17.6378i	−0.828697	+	1.43535i	−0.899061	+	0.437824i	$0.855749\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−7.82259	−	13.5491i	−0.628326	−	1.08829i
$156$		0			0
$157$	9.28235			0.740812			0.370406	−	0.928870i	$-0.379218\pi$
$157$	9.28235			0.740812			0.370406	+	0.928870i	$0.379218\pi$
$158$		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	0.153803	−	0.988101i	$-0.450848\pi$
$163$	11.9069	−	20.6234i	0.932623	−	1.61535i	0.778819	−	0.627248i	$-0.215819\pi$
$164$		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
$173$	−0.360099			−0.0273778			−0.0136889	−	0.999906i	$-0.504357\pi$
$173$	−0.360099			−0.0273778			−0.0136889	+	0.999906i	$0.504357\pi$
$174$		0			0
$175$	0.440047	+	3.62069i	0.0332644	+	0.273699i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.57701	−	6.19556i	−0.267358	−	0.463078i	0.700821	−	0.713337i	$-0.252817\pi$
$179$	−3.57701	−	6.19556i	−0.267358	−	0.463078i	−0.968179	+	0.250260i	$0.919484\pi$
$180$		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
$185$	5.38741			0.396090
$186$		0			0
$187$	4.37637			0.320032
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.70167			−0.629630			−0.314815	−	0.949153i	$-0.601943\pi$
$191$	−8.70167			−0.629630			−0.314815	+	0.949153i	$0.601943\pi$
$192$		0			0
$193$	−1.41929			−0.102163			−0.0510813	−	0.998694i	$-0.516267\pi$
$193$	−1.41929			−0.102163			−0.0510813	+	0.998694i	$0.516267\pi$
$194$		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	0.758411	−	0.651777i	$-0.225976\pi$
$199$	−2.61327	−	4.52631i	−0.185250	−	0.320862i	−0.943661	+	0.330915i	$0.892643\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.27917	+	0.970758i	0.159966	+	0.0681339i
$204$		0			0
$205$	−20.2355			−1.41331
$206$		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
$221$	3.23063			0.217316
$222$		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
$227$	−7.65898	+	13.2657i	−0.508344	+	0.880478i	0.491609	+	0.870816i	$0.336409\pi$
$227$	−7.65898	+	13.2657i	−0.508344	+	0.880478i	−0.999953	+	0.00966216i	$0.996924\pi$
$228$		0			0
$229$	−8.52297	−	14.7622i	−0.563214	−	0.975515i	−0.997213	−	0.0746016i	$-0.976231\pi$
$229$	−8.52297	−	14.7622i	−0.563214	−	0.975515i	0.434000	−	0.900913i	$-0.357102\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−9.88255	+	17.1171i	−0.647427	+	1.12138i	0.336308	+	0.941752i	$0.390822\pi$
$233$	−9.88255	+	17.1171i	−0.647427	+	1.12138i	−0.983735	+	0.179625i	$0.942512\pi$
$234$		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
$241$	−3.19998	+	5.54252i	−0.206129	+	0.357025i	−0.950492	−	0.310750i	$-0.899420\pi$
$241$	−3.19998	+	5.54252i	−0.206129	+	0.357025i	0.744363	+	0.667775i	$0.232753\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−12.9332	+	3.19086i	−0.826275	+	0.203856i
$246$		0			0
$247$	6.75442	+	11.6990i	0.429774	+	0.744390i
$248$		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
$257$	3.58798	+	6.21457i	0.223812	+	0.387654i	0.955962	−	0.293489i	$-0.0948164\pi$
$257$	3.58798	+	6.21457i	0.223812	+	0.387654i	−0.732150	+	0.681143i	$0.761483\pi$
$258$		0			0
$259$	−0.903673	−	7.43540i	−0.0561515	−	0.462013i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−10.2069	+	17.6788i	−0.629382	+	1.09012i	0.358294	+	0.933609i	$0.383359\pi$
$263$	−10.2069	+	17.6788i	−0.629382	+	1.09012i	−0.987676	+	0.156513i	$0.949975\pi$
$264$		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	0.950332	−	0.311238i	$-0.100744\pi$
$269$	3.37251	+	5.84136i	0.205626	+	0.356154i	−0.744706	+	0.667392i	$0.767410\pi$
$270$		0			0
$271$	1.04632	−	1.81228i	0.0635596	−	0.110088i	−0.832495	−	0.554033i	$-0.813088\pi$
$271$	1.04632	−	1.81228i	0.0635596	−	0.110088i	0.896054	+	0.443945i	$0.146421\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.11324	−	3.66025i	−0.127433	−	0.220721i
$276$		0			0
$277$	11.7705	−	20.3871i	0.707221	−	1.22494i	−0.258662	−	0.965968i	$-0.583282\pi$
$277$	11.7705	−	20.3871i	0.707221	−	1.22494i	0.965884	−	0.258976i	$-0.0833850\pi$
$278$		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
$283$	4.45316			0.264713			0.132356	−	0.991202i	$-0.457746\pi$
$283$	4.45316			0.264713			0.132356	+	0.991202i	$0.457746\pi$
$284$		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
$299$	16.1943			0.936539
$300$		0			0
$301$	14.5292	+	6.18836i	0.837446	+	0.356691i
$302$		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
$311$	14.9890			0.849947			0.424974	−	0.905206i	$-0.360283\pi$
$311$	14.9890			0.849947			0.424974	+	0.905206i	$0.360283\pi$
$312$		0			0
$313$	6.92663			0.391517			0.195758	−	0.980652i	$-0.437283\pi$
$313$	6.92663			0.391517			0.195758	+	0.980652i	$0.437283\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.8574			−0.609815			−0.304907	−	0.952382i	$-0.598626\pi$
$317$	−10.8574			−0.609815			−0.304907	+	0.952382i	$0.598626\pi$
$318$		0			0
$319$	−2.87065			−0.160726
$320$		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
$329$	2.04448	−	1.53668i	0.112716	−	0.0847202i
$330$		0			0
$331$	8.05169			0.442561			0.221280	−	0.975210i	$-0.428976\pi$
$331$	8.05169			0.442561			0.221280	+	0.975210i	$0.428976\pi$
$332$		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
$347$	25.7784			1.38386			0.691928	−	0.721967i	$-0.256762\pi$
$347$	25.7784			1.38386			0.691928	+	0.721967i	$0.256762\pi$
$348$		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
$353$	−12.4514	+	21.5665i	−0.662721	+	1.14787i	0.317177	+	0.948366i	$0.397265\pi$
$353$	−12.4514	+	21.5665i	−0.662721	+	1.14787i	−0.979898	+	0.199500i	$0.936068\pi$
$354$		0			0
$355$	2.24914	+	3.89563i	0.119372	+	0.206759i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.6980	−	18.5295i	0.564620	−	0.977951i	−0.432465	−	0.901651i	$-0.642356\pi$
$359$	10.6980	−	18.5295i	0.564620	−	0.977951i	0.997085	−	0.0763002i	$-0.0243107\pi$
$360$		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
$367$	−5.75791	+	9.97299i	−0.300560	+	0.520586i	−0.976263	−	0.216589i	$-0.930507\pi$
$367$	−5.75791	+	9.97299i	−0.300560	+	0.520586i	0.675703	+	0.737174i	$0.263840\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	26.5392	+	11.3038i	1.37785	+	0.586861i
$372$		0			0
$373$	0.846990	+	1.46703i	0.0438555	+	0.0759599i	0.887120	−	0.461539i	$-0.152703\pi$
$373$	0.846990	+	1.46703i	0.0438555	+	0.0759599i	−0.843264	+	0.537499i	$0.819369\pi$
$374$		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
$383$	6.39094	+	11.0694i	0.326562	+	0.565622i	0.981827	−	0.189777i	$-0.0607765\pi$
$383$	6.39094	+	11.0694i	0.326562	+	0.565622i	−0.655265	+	0.755399i	$0.727443\pi$
$384$		0			0
$385$	12.3394	−	9.27461i	0.628872	−	0.472678i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.77980	−	3.08270i	0.0902393	−	0.156299i	−0.817372	−	0.576110i	$-0.804570\pi$
$389$	1.77980	−	3.08270i	0.0902393	−	0.156299i	0.907612	+	0.419811i	$0.137903\pi$
$390$		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	−0.443832	−	0.896110i	$-0.646381\pi$
$397$	11.0411	−	19.1238i	0.554138	−	0.959795i	0.997970	−	0.0636848i	$-0.0202852\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.29927	+	2.25040i	0.0648823	+	0.112379i	0.896642	−	0.442757i	$-0.145999\pi$
$401$	1.29927	+	2.25040i	0.0648823	+	0.112379i	−0.831759	+	0.555136i	$0.812666\pi$
$402$		0			0
$403$	9.30328	−	16.1138i	0.463429	−	0.802683i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.33973	+	7.51662i	0.215112	+	0.372585i
$408$		0			0
$409$	3.03208			0.149926			0.0749632	−	0.997186i	$-0.476116\pi$
$409$	3.03208			0.149926			0.0749632	+	0.997186i	$0.476116\pi$
$410$		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
$425$	1.96783			0.0954539
$426$		0			0
$427$	−1.90226	+	1.42979i	−0.0920568	+	0.0691925i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.77241	−	15.1943i	−0.422552	−	0.731882i	0.573636	−	0.819110i	$-0.305532\pi$
$431$	−8.77241	−	15.1943i	−0.422552	−	0.731882i	−0.996188	+	0.0872286i	$0.972199\pi$
$432$		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
$437$	−42.7098			−2.04309
$438$		0			0
$439$	−37.4319			−1.78653			−0.893263	−	0.449535i	$-0.851590\pi$
$439$	−37.4319			−1.78653			−0.893263	+	0.449535i	$0.851590\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.34324			0.348888			0.174444	−	0.984667i	$-0.444187\pi$
$443$	7.34324			0.348888			0.174444	+	0.984667i	$0.444187\pi$
$444$		0			0
$445$	−9.85726			−0.467279
$446$		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
$455$	9.10890	−	6.84650i	0.427032	−	0.320969i
$456$		0			0
$457$	−27.4720			−1.28509			−0.642543	−	0.766250i	$-0.722120\pi$
$457$	−27.4720			−1.28509			−0.642543	+	0.766250i	$0.722120\pi$
$458$		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	−0.526746	−	0.850023i	$-0.676588\pi$
$467$	10.2166	−	17.6957i	0.472769	−	0.818860i	0.999514	+	0.0311635i	$0.00992126\pi$
$468$		0			0
$469$	3.44233	−	2.58735i	0.158952	−	0.119473i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−18.2997			−0.841423
$474$		0			0
$475$	4.11423	+	7.12606i	0.188774	+	0.326966i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−13.9539	+	24.1689i	−0.637572	+	1.10431i	0.348392	+	0.937349i	$0.386728\pi$
$479$	−13.9539	+	24.1689i	−0.637572	+	1.10431i	−0.985964	+	0.166958i	$0.946606\pi$
$480$		0			0
$481$	3.20358	+	5.54876i	0.146071	+	0.253002i
$482$		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	0.968117	−	0.250500i	$-0.0805951\pi$
$487$	5.89480	+	10.2101i	0.267119	+	0.462663i	−0.700998	+	0.713163i	$0.747262\pi$
$488$		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
$493$	0.668281	−	1.15750i	0.0300979	−	0.0521310i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.99927	−	3.75759i	0.224248	−	0.168551i
$498$		0			0
$499$	21.1664	+	36.6614i	0.947540	+	1.64119i	0.750584	+	0.660776i	$0.229773\pi$
$499$	21.1664	+	36.6614i	0.947540	+	1.64119i	0.196957	+	0.980412i	$0.436894\pi$
$500$		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
$509$	12.3631	+	21.4135i	0.547984	+	0.949136i	0.998413	+	0.0563236i	$0.0179379\pi$
$509$	12.3631	+	21.4135i	0.547984	+	0.949136i	−0.450429	+	0.892812i	$0.648729\pi$
$510$		0			0
$511$	4.85023	+	2.06584i	0.214561	+	0.0913875i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−16.9355	+	29.3331i	−0.746265	+	1.29257i
$516$		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	0.690333	−	0.723492i	$-0.257464\pi$
$521$	−6.42298	−	11.1249i	−0.281396	−	0.487392i	−0.971729	+	0.236100i	$0.924131\pi$
$522$		0			0
$523$	1.70453	−	2.95234i	0.0745340	−	0.129097i	−0.826350	−	0.563158i	$-0.809586\pi$
$523$	1.70453	−	2.95234i	0.0745340	−	0.129097i	0.900884	+	0.434061i	$0.142920\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.86775	+	10.1632i	0.255603	+	0.442718i
$528$		0			0
$529$	−14.1001	+	24.4221i	−0.613047	+	1.06183i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−12.0329	−	20.8416i	−0.521202	−	0.902748i
$534$		0			0
$535$	−33.3409			−1.44145
$536$		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	−0.353884	+	0.935289i	$0.615139\pi$
$541$	−22.9553	+	39.7598i	−0.986926	+	1.70941i	−0.633043	+	0.774117i	$0.718194\pi$
$542$		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
$551$	5.58882			0.238092
$552$		0			0
$553$	−17.6363	+	13.2559i	−0.749972	+	0.563700i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.836144	−	1.44824i	−0.0354285	−	0.0613640i	0.847767	−	0.530368i	$-0.177946\pi$
$557$	−0.836144	−	1.44824i	−0.0354285	−	0.0613640i	−0.883196	+	0.469004i	$0.844613\pi$
$558$		0			0
$559$	−13.5088			−0.571363
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−22.7529			−0.958920			−0.479460	−	0.877564i	$-0.659167\pi$
$563$	−22.7529			−0.958920			−0.479460	+	0.877564i	$0.659167\pi$
$564$		0			0
$565$	−28.9257			−1.21691
$566$		0			0
$567$		0			0
$568$		0			0
$569$	26.0585			1.09243			0.546214	−	0.837646i	$-0.316068\pi$
$569$	26.0585			1.09243			0.546214	+	0.837646i	$0.316068\pi$
$570$		0			0
$571$	−12.4835			−0.522418			−0.261209	−	0.965282i	$-0.584121\pi$
$571$	−12.4835			−0.522418			−0.261209	+	0.965282i	$0.584121\pi$
$572$		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	0.565100	−	0.825023i	$-0.308838\pi$
$577$	−10.3756	−	17.9710i	−0.431941	−	0.748143i	−0.997040	+	0.0768793i	$0.975504\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	38.8590	+	16.5511i	1.61214	+	0.686654i
$582$		0			0
$583$	−33.4266			−1.38439
$584$		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	−0.420215	−	0.907425i	$-0.638045\pi$
$593$	14.0203	−	24.2839i	0.575745	−	0.997220i	0.995960	−	0.0897956i	$-0.0286214\pi$
$594$		0			0
$595$	0.867109	+	7.13455i	0.0355480	+	0.292488i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	23.2094			0.948310			0.474155	−	0.880441i	$-0.342754\pi$
$599$	23.2094			0.948310			0.474155	+	0.880441i	$0.342754\pi$
$600$		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
$605$	1.52286	−	2.63767i	0.0619130	−	0.107237i
$606$		0			0
$607$	−0.855327	−	1.48147i	−0.0347166	−	0.0601310i	0.848145	−	0.529764i	$-0.177720\pi$
$607$	−0.855327	−	1.48147i	−0.0347166	−	0.0601310i	−0.882862	+	0.469633i	$0.844386\pi$
$608$		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	0.899599	−	0.436717i	$-0.143859\pi$
$613$	1.77253	+	3.07010i	0.0715916	+	0.124000i	−0.828007	+	0.560717i	$0.810525\pi$
$614$		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
$619$	9.60858	−	16.6425i	0.386201	−	0.668920i	−0.605734	−	0.795667i	$-0.707120\pi$
$619$	9.60858	−	16.6425i	0.386201	−	0.668920i	0.991935	+	0.126747i	$0.0404537\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.65344	+	13.6044i	0.0662436	+	0.545051i
$624$		0			0
$625$	8.10337	+	14.0355i	0.324135	+	0.561418i
$626$		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
$635$	−16.1093	−	27.9020i	−0.639276	−	1.10726i
$636$		0			0
$637$	−10.9771	−	11.4232i	−0.434927	−	0.452603i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.1969	+	17.6615i	−0.402753	+	0.697589i	−0.994057	−	0.108860i	$-0.965280\pi$
$641$	−10.1969	+	17.6615i	−0.402753	+	0.697589i	0.591304	+	0.806449i	$0.298613\pi$
$642$		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	0.928642	−	0.370976i	$-0.120977\pi$
$647$	3.63856	+	6.30217i	0.143047	+	0.247764i	−0.785596	+	0.618740i	$0.787643\pi$
$648$		0			0
$649$	−17.4196	+	30.1717i	−0.683781	+	1.18434i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	11.4335	+	19.8035i	0.447429	+	0.774970i	0.998218	−	0.0596747i	$-0.0190063\pi$
$653$	11.4335	+	19.8035i	0.447429	+	0.774970i	−0.550789	+	0.834645i	$0.685673\pi$
$654$		0			0
$655$	−2.26794	+	3.92819i	−0.0886159	+	0.153487i
$656$		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
$661$	−34.4127			−1.33850			−0.669250	−	0.743037i	$-0.733385\pi$
$661$	−34.4127			−1.33850			−0.669250	+	0.743037i	$0.733385\pi$
$662$		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
$677$	−34.6027			−1.32989			−0.664945	−	0.746892i	$-0.731545\pi$
$677$	−34.6027			−1.32989			−0.664945	+	0.746892i	$0.731545\pi$
$678$		0			0
$679$	−4.49291	−	1.91365i	−0.172422	−	0.0734392i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−19.1618	−	33.1892i	−0.733206	−	1.26995i	−0.955506	−	0.294971i	$-0.904690\pi$
$683$	−19.1618	−	33.1892i	−0.733206	−	1.26995i	0.222300	−	0.974978i	$-0.428643\pi$
$684$		0			0
$685$	−20.8988			−0.798502
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−24.6755			−0.940061
$690$		0			0
$691$	7.89906			0.300495			0.150247	−	0.988648i	$-0.451993\pi$
$691$	7.89906			0.300495			0.150247	+	0.988648i	$0.451993\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−14.0983			−0.534780
$696$		0			0
$697$	15.1787			0.574935
$698$		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
$707$	−2.57392	−	21.1782i	−0.0968023	−	0.796488i
$708$		0			0
$709$	28.1047			1.05549			0.527746	−	0.849402i	$-0.323037\pi$
$709$	28.1047			1.05549			0.527746	+	0.849402i	$0.323037\pi$
$710$		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	−0.954756	−	0.297389i	$-0.903884\pi$
$719$	−5.89461	+	10.2098i	−0.219832	+	0.380760i	0.734924	+	0.678149i	$0.237218\pi$
$720$		0			0
$721$	43.3246	+	18.4531i	1.61349	+	0.687229i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.29079			−0.0479386
$726$		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
$731$	4.26014	−	7.37877i	0.157567	−	0.272914i
$732$		0			0
$733$	−7.54634	−	13.0706i	−0.278731	−	0.482775i	0.692339	−	0.721572i	$-0.256580\pi$
$733$	−7.54634	−	13.0706i	−0.278731	−	0.482775i	−0.971070	+	0.238797i	$0.923247\pi$
$734$		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	−0.994631	−	0.103486i	$-0.967000\pi$
$739$	−15.9556	−	27.6359i	−0.586937	−	1.01660i	0.407694	−	0.913119i	$-0.366333\pi$
$740$		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
$745$	16.7692	−	29.0452i	0.614377	−	1.06413i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	5.59253	+	46.0152i	0.204347	+	1.68136i
$750$		0			0
$751$	−16.7232	−	28.9654i	−0.610237	−	1.05696i	−0.991200	−	0.132371i	$-0.957741\pi$
$751$	−16.7232	−	28.9654i	−0.610237	−	1.05696i	0.380963	−	0.924590i	$-0.375592\pi$
$752$		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
$761$	16.8978	+	29.2679i	0.612547	+	1.06096i	0.990810	+	0.135264i	$0.0431881\pi$
$761$	16.8978	+	29.2679i	0.612547	+	1.06096i	−0.378263	+	0.925698i	$0.623479\pi$
$762$		0			0
$763$	−5.42529	−	2.31078i	−0.196409	−	0.0836557i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.8591	+	22.2727i	−0.464317	+	0.804221i
$768$		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	0.997083	−	0.0763245i	$-0.0243185\pi$
$773$	12.0231	+	20.8247i	0.432443	+	0.749012i	−0.564640	+	0.825337i	$0.690985\pi$
$774$		0			0
$775$	5.66679	−	9.81516i	0.203557	−	0.352571i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	31.7348	+	54.9663i	1.13702	+	1.96937i
$780$		0			0
$781$	−3.62351	+	6.27611i	−0.129659	+	0.224577i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.83219	−	15.2978i	−0.315234	−	0.546002i
$786$		0			0
$787$	6.45794			0.230201			0.115100	−	0.993354i	$-0.463281\pi$
$787$	6.45794			0.230201			0.115100	+	0.993354i	$0.463281\pi$
$788$		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
$803$	−6.10896			−0.215580
$804$		0			0
$805$	4.34658	+	35.7636i	0.153197	+	1.26050i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	20.0048	+	34.6493i	0.703331	+	1.21821i	0.967290	+	0.253672i	$0.0816383\pi$
$809$	20.0048	+	34.6493i	0.703331	+	1.21821i	−0.263959	+	0.964534i	$0.585028\pi$
$810$		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
$815$	−45.3179			−1.58742
$816$		0			0
$817$	35.6274			1.24645
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.377464			0.0131736			0.00658679	−	0.999978i	$-0.497903\pi$
$821$	0.377464			0.0131736			0.00658679	+	0.999978i	$0.497903\pi$
$822$		0			0
$823$	−11.0063			−0.383654			−0.191827	−	0.981429i	$-0.561441\pi$
$823$	−11.0063			−0.383654			−0.191827	+	0.981429i	$0.561441\pi$
$824$		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	−0.999878	−	0.0155953i	$-0.995036\pi$
$829$	−14.7833	−	25.6054i	−0.513445	−	0.889313i	0.486433	−	0.873718i	$-0.338298\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.70126	−	2.39347i	0.336129	−	0.0829288i
$834$		0			0
$835$	3.36263			0.116369
$836$		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
$851$	−20.2570			−0.694401
$852$		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
$857$	20.2230	−	35.0273i	0.690805	−	1.19651i	−0.280770	−	0.959775i	$-0.590590\pi$
$857$	20.2230	−	35.0273i	0.690805	−	1.19651i	0.971575	−	0.236734i	$-0.0760769\pi$
$858$		0			0
$859$	−6.25642	−	10.8364i	−0.213466	−	0.369735i	0.739331	−	0.673343i	$-0.235142\pi$
$859$	−6.25642	−	10.8364i	−0.213466	−	0.369735i	−0.952797	+	0.303608i	$0.901809\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−11.8005	+	20.4391i	−0.401694	+	0.695755i	−0.993931	−	0.110010i	$-0.964912\pi$
$863$	−11.8005	+	20.4391i	−0.401694	+	0.695755i	0.592236	+	0.805764i	$0.298245\pi$
$864$		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
$871$	−1.84183	+	3.19014i	−0.0624079	+	0.108094i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	25.6722	−	19.2959i	0.867878	−	0.652322i
$876$		0			0
$877$	13.7733	+	23.8561i	0.465092	+	0.805564i	0.999206	−	0.0398493i	$-0.0126878\pi$
$877$	13.7733	+	23.8561i	0.465092	+	0.805564i	−0.534113	+	0.845413i	$0.679354\pi$
$878$		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
$887$	−1.75954	−	3.04761i	−0.0590795	−	0.102329i	0.834973	−	0.550291i	$-0.185483\pi$
$887$	−1.75954	−	3.04761i	−0.0590795	−	0.102329i	−0.894052	+	0.447962i	$0.852150\pi$
$888$		0			0
$889$	−35.8067	+	26.9133i	−1.20092	+	0.902644i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	2.88499	−	4.99695i	0.0965426	−	0.167217i
$894$		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
$905$	−10.5181	−	18.2178i	−0.349633	−	0.605582i
$906$		0			0
$907$	18.6413	−	32.2876i	0.618974	−	1.07209i	−0.370700	−	0.928753i	$-0.620882\pi$
$907$	18.6413	−	32.2876i	0.618974	−	1.07209i	0.989673	−	0.143341i	$-0.0457846\pi$
$908$		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
$913$	−48.9436			−1.61980
$914$		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	−0.947903	−	0.318559i	$-0.896801\pi$
$919$	−6.00453	+	10.4001i	−0.198071	+	0.343069i	0.749832	+	0.661628i	$0.230134\pi$
$920$		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
$929$	−20.5204			−0.673253			−0.336626	−	0.941638i	$-0.609286\pi$
$929$	−20.5204			−0.673253			−0.336626	+	0.941638i	$0.609286\pi$
$930$		0			0
$931$	28.9503	+	30.1268i	0.948807	+	0.987367i
$932$		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
$941$	30.9614			1.00931			0.504656	−	0.863320i	$-0.331619\pi$
$941$	30.9614			1.00931			0.504656	+	0.863320i	$0.331619\pi$
$942$		0			0
$943$	76.0868			2.47773
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.1818			−1.04577			−0.522884	−	0.852404i	$-0.675144\pi$
$947$	−32.1818			−1.04577			−0.522884	+	0.852404i	$0.675144\pi$
$948$		0			0
$949$	−4.50962			−0.146388
$950$		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
$959$	3.50552	+	28.8434i	0.113199	+	0.931400i
$960$		0			0
$961$	36.5897			1.18031
$962$		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	−0.689219	−	0.724553i	$-0.742046\pi$
$971$	8.81455	−	15.2673i	0.282872	−	0.489949i	0.972091	+	0.234604i	$0.0753794\pi$
$972$		0			0
$973$	2.36482	+	19.4577i	0.0758128	+	0.623786i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.2538			−0.871925			−0.435963	−	0.899965i	$-0.643592\pi$
$977$	−27.2538			−0.871925			−0.435963	+	0.899965i	$0.643592\pi$
$978$		0			0
$979$	−7.94033	−	13.7531i	−0.253774	−	0.439550i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.3371	−	17.9043i	0.329701	−	0.571059i	−0.652751	−	0.757572i	$-0.726385\pi$
$983$	10.3371	−	17.9043i	0.329701	−	0.571059i	0.982452	+	0.186513i	$0.0597187\pi$
$984$		0			0
$985$	5.41809	+	9.38440i	0.172635	+	0.299012i
$986$		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	0.901018	+	0.433782i	$0.142821\pi$
$991$	26.0081	+	45.0474i	0.826175	+	1.43098i	−0.0748425	+	0.997195i	$0.523845\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−4.97307	+	8.61361i	−0.157657	+	0.273070i
$996$		0			0
$997$	4.64269	−	8.04137i	0.147035	−	0.254673i	−0.783095	−	0.621902i	$-0.786360\pi$
$997$	4.64269	−	8.04137i	0.147035	−	0.254673i	0.930130	+	0.367229i	$0.119694\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.2	✓	14	252.11	even	6
252.2.i.b.121.2	yes	14	12.11	even	2
252.2.l.b.193.4	yes	14	84.11	even	6
252.2.l.b.205.4	yes	14	36.11	even	6
756.2.i.b.37.2		14	4.3	odd	2
756.2.i.b.613.2		14	252.151	odd	6
756.2.l.b.289.6		14	36.7	odd	6
756.2.l.b.361.6		14	28.11	odd	6
1008.2.q.j.529.6		14	63.11	odd	6
1008.2.q.j.625.6		14	3.2	odd	2
1008.2.t.j.193.4		14	21.11	odd	6
1008.2.t.j.961.4		14	9.2	odd	6
1764.2.i.i.373.6		14	84.83	odd	2
1764.2.i.i.1537.6		14	252.227	odd	6
1764.2.j.g.589.7		14	84.23	even	6
1764.2.j.g.1177.7		14	252.191	even	6
1764.2.j.h.589.1		14	84.47	odd	6
1764.2.j.h.1177.1		14	252.47	odd	6
1764.2.l.i.949.4		14	84.59	odd	6
1764.2.l.i.961.4		14	252.83	odd	6
2268.2.k.e.1297.6		14	36.23	even	6
2268.2.k.e.1621.6		14	252.95	even	6
2268.2.k.f.1297.2		14	36.31	odd	6
2268.2.k.f.1621.2		14	252.67	odd	6
3024.2.q.j.2305.2		14	1.1	even	1	trivial
3024.2.q.j.2881.2		14	63.25	even	3	inner
3024.2.t.j.289.6		14	9.7	even	3
3024.2.t.j.1873.6		14	7.4	even	3
5292.2.i.i.1549.6		14	28.27	even	2
5292.2.i.i.2125.6		14	252.115	even	6
5292.2.j.g.1765.6		14	28.19	even	6
5292.2.j.g.3529.6		14	252.187	even	6
5292.2.j.h.1765.2		14	28.23	odd	6
5292.2.j.h.3529.2		14	252.79	odd	6
5292.2.l.i.361.2		14	28.3	even	6
5292.2.l.i.3313.2		14	252.223	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.951504 - 1.64805i) q^{5} +(-2.11495 + 1.58965i) q^{7} +O(q^{10})\)	\(q+(-0.951504 - 1.64805i) q^{5} +(-2.11495 + 1.58965i) q^{7} +(1.53293 - 2.65512i) q^{11} +(1.13161 - 1.96000i) q^{13} +(0.713726 + 1.23621i) q^{17} +(-2.98444 + 5.16919i) q^{19} +(3.57771 + 6.19678i) q^{23} +(0.689282 - 1.19387i) q^{25} +(-0.468164 - 0.810884i) q^{29} +8.22129 q^{31} +(4.63221 + 1.97298i) q^{35} +(-1.41550 + 2.45171i) q^{37} +(5.31672 - 9.20883i) q^{41} +(-2.98444 - 5.16919i) q^{43} -0.966679 q^{47} +(1.94600 - 6.72407i) q^{49} +(-5.45142 - 9.44213i) q^{53} -5.83436 q^{55} -11.3636 q^{59} +0.899436 q^{61} -4.30692 q^{65} -1.62762 q^{67} -2.36378 q^{71} +(-0.996286 - 1.72562i) q^{73} +(0.978644 + 8.05226i) q^{77} +8.33889 q^{79} +(-7.98203 - 13.8253i) q^{83} +(1.35822 - 2.35251i) q^{85} +(2.58992 - 4.48587i) q^{89} +(0.722433 + 5.94416i) q^{91} +11.3588 q^{95} +(0.922890 + 1.59849i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 2 q^{5} - 6 q^{7}+O(q^{10}) \) 14 * q + 2 * q^5 - 6 * q^7	\( 14 q + 2 q^{5} - 6 q^{7} + 2 q^{11} + 2 q^{13} - 2 q^{17} - 7 q^{19} + 11 q^{23} - 9 q^{25} - q^{29} - 2 q^{31} - 19 q^{35} + 10 q^{37} + 33 q^{41} - 7 q^{43} + 6 q^{47} - 4 q^{49} + 15 q^{53} + 28 q^{55} + 28 q^{59} + 20 q^{61} + 30 q^{65} + 12 q^{67} + 2 q^{71} + 21 q^{73} + 47 q^{77} - 20 q^{79} - 25 q^{83} + 8 q^{85} + 6 q^{89} - 2 q^{91} + 56 q^{95} - 18 q^{97}+O(q^{100}) \) 14 * q + 2 * q^5 - 6 * q^7 + 2 * q^11 + 2 * q^13 - 2 * q^17 - 7 * q^19 + 11 * q^23 - 9 * q^25 - q^29 - 2 * q^31 - 19 * q^35 + 10 * q^37 + 33 * q^41 - 7 * q^43 + 6 * q^47 - 4 * q^49 + 15 * q^53 + 28 * q^55 + 28 * q^59 + 20 * q^61 + 30 * q^65 + 12 * q^67 + 2 * q^71 + 21 * q^73 + 47 * q^77 - 20 * q^79 - 25 * q^83 + 8 * q^85 + 6 * q^89 - 2 * q^91 + 56 * q^95 - 18 * q^97

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