LMFDB - Embedded newform 3024.2.cc.b.2897.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3024.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			2897.6
Root			$1.69547 + 0.354107i$ of defining polynomial
Character	$\chi$	$=$	3024.2897
Dual form			3024.2.cc.b.881.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.895175 + 1.55049i) q^{5} +(2.30191 - 1.30430i) q^{7} +O(q^{10})$	$q+(0.895175 + 1.55049i) q^{5} +(2.30191 - 1.30430i) q^{7} +(-2.07976 - 1.20075i) q^{11} +(-4.23601 + 2.44566i) q^{13} -3.66466 q^{17} -3.01701i q^{19} +(3.26178 - 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +(5.68202 + 3.28052i) q^{29} +(4.02408 - 2.32330i) q^{31} +(4.08292 + 2.40150i) q^{35} +9.36404 q^{37} +(4.04094 + 6.99911i) q^{41} +(3.48127 - 6.02973i) q^{43} +(2.56802 - 4.44794i) q^{47} +(3.59758 - 6.00478i) q^{49} -4.29953i q^{55} +(7.29501 + 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} +(-7.58394 - 4.37859i) q^{65} +(0.285115 + 0.493834i) q^{67} +5.96254i q^{71} -12.3814i q^{73} +(-6.35358 - 0.0513786i) q^{77} +(1.51831 - 2.62979i) q^{79} +(-7.00270 + 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} +3.74863 q^{89} +(-6.56103 + 11.1547i) q^{91} +(4.67784 - 2.70075i) q^{95} +(4.77256 + 2.75544i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{7}+O(q^{10}) $ 16 * q - 2 * q^7	$ 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) $ 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.895175	+	1.55049i	0.400334	+	0.693399i	0.993766	−	0.111485i	$-0.0355607\pi$
$5$	0.895175	+	1.55049i	0.400334	+	0.693399i	−0.593432	+	0.804884i	$0.702227\pi$
$6$		0			0
$7$	2.30191	−	1.30430i	0.870040	−	0.492981i
$7$	2.30191	−	1.30430i	0.870040	−	0.492981i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.07976	−	1.20075i	−0.627072	−	0.362040i	0.152545	−	0.988297i	$-0.451253\pi$
$11$	−2.07976	−	1.20075i	−0.627072	−	0.362040i	−0.779617	+	0.626256i	$0.784586\pi$
$12$		0			0
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.954820	−	0.297186i	$-0.903952\pi$
$13$	−4.23601	+	2.44566i	−1.17486	+	0.678305i	−0.220039	+	0.975491i	$0.570618\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.66466			−0.888812			−0.444406	−	0.895826i	$-0.646585\pi$
$17$	−3.66466			−0.888812			−0.444406	+	0.895826i	$0.646585\pi$
$18$		0			0
$19$		−	3.01701i		−	0.692150i	−0.938207	−	0.346075i	$-0.887514\pi$
$19$		−	3.01701i		−	0.692150i	0.938207	−	0.346075i	$-0.112486\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.26178	−	1.88319i	0.680129	−	0.392673i	−0.119775	−	0.992801i	$-0.538217\pi$
$23$	3.26178	−	1.88319i	0.680129	−	0.392673i	0.799904	+	0.600128i	$0.204884\pi$
$24$		0			0
$25$	0.897324	−	1.55421i	0.179465	−	0.310842i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.68202	+	3.28052i	1.05512	+	0.609176i	0.924080	−	0.382200i	$-0.124833\pi$
$29$	5.68202	+	3.28052i	1.05512	+	0.609176i	0.131045	+	0.991376i	$0.458167\pi$
$30$		0			0
$31$	4.02408	−	2.32330i	0.722746	−	0.417278i	−0.0930163	−	0.995665i	$-0.529651\pi$
$31$	4.02408	−	2.32330i	0.722746	−	0.417278i	0.815763	+	0.578387i	$0.196318\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.08292	+	2.40150i	0.690140	+	0.405928i
$36$		0			0
$37$	9.36404			1.53944			0.769719	−	0.638382i	$-0.220396\pi$
$37$	9.36404			1.53944			0.769719	+	0.638382i	$0.220396\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	4.04094	+	6.99911i	0.631088	+	1.09308i	0.987330	+	0.158683i	$0.0507248\pi$
$41$	4.04094	+	6.99911i	0.631088	+	1.09308i	−0.356241	+	0.934394i	$0.615942\pi$
$42$		0			0
$43$	3.48127	−	6.02973i	0.530888	−	0.919526i	−0.468462	−	0.883484i	$-0.655192\pi$
$43$	3.48127	−	6.02973i	0.530888	−	0.919526i	0.999350	−	0.0360419i	$-0.0114750\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.56802	−	4.44794i	0.374584	−	0.648799i	−0.615680	−	0.787996i	$-0.711119\pi$
$47$	2.56802	−	4.44794i	0.374584	−	0.648799i	0.990265	+	0.139197i	$0.0444520\pi$
$48$		0			0
$49$	3.59758	−	6.00478i	0.513940	−	0.857826i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$		0			0
$55$		−	4.29953i		−	0.579749i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	7.29501	+	12.6353i	0.949729	+	1.64498i	0.745994	+	0.665953i	$0.231975\pi$
$59$	7.29501	+	12.6353i	0.949729	+	1.64498i	0.203735	+	0.979026i	$0.434692\pi$
$60$		0			0
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.972317	−	0.233665i	$-0.0750718\pi$
$61$	9.81058	+	5.66414i	1.25612	+	0.725219i	0.283799	+	0.958884i	$0.408405\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−7.58394	−	4.37859i	−0.940672	−	0.543097i
$66$		0			0
$67$	0.285115	+	0.493834i	0.0348324	+	0.0603315i	0.882916	−	0.469531i	$-0.155577\pi$
$67$	0.285115	+	0.493834i	0.0348324	+	0.0603315i	−0.848084	+	0.529862i	$0.822244\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			5.96254i			0.707623i	0.935317	+	0.353811i	$0.115115\pi$
$71$			5.96254i			0.707623i	−0.935317	+	0.353811i	$0.884885\pi$
$72$		0			0
$73$		−	12.3814i		−	1.44913i	−0.689204	−	0.724567i	$-0.742040\pi$
$73$		−	12.3814i		−	1.44913i	0.689204	−	0.724567i	$-0.257960\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−6.35358	−	0.0513786i	−0.724057	−	0.00585514i
$78$		0			0
$79$	1.51831	−	2.62979i	0.170824	−	0.295875i	−0.767884	−	0.640588i	$-0.778691\pi$
$79$	1.51831	−	2.62979i	0.170824	−	0.295875i	0.938708	+	0.344713i	$0.112024\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.00270	+	12.1290i	−0.768646	+	1.33133i	0.169651	+	0.985504i	$0.445736\pi$
$83$	−7.00270	+	12.1290i	−0.768646	+	1.33133i	−0.938297	+	0.345830i	$0.887597\pi$
$84$		0			0
$85$	−3.28052	−	5.68202i	−0.355822	−	0.616302i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.74863			0.397354			0.198677	−	0.980065i	$-0.436336\pi$
$89$	3.74863			0.397354			0.198677	+	0.980065i	$0.436336\pi$
$90$		0			0
$91$	−6.56103	+	11.1547i	−0.687783	+	1.16934i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.67784	−	2.70075i	0.479936	−	0.277091i
$96$		0			0
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	0.722323	−	0.691556i	$-0.243074\pi$
$97$	4.77256	+	2.75544i	0.484580	+	0.279772i	−0.237743	+	0.971328i	$0.576408\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	0.125162	−	0.216787i	0.0124541	−	0.0215711i	−0.859731	−	0.510747i	$-0.829369\pi$
$101$	0.125162	−	0.216787i	0.0124541	−	0.0215711i	0.872185	+	0.489176i	$0.162702\pi$
$102$		0			0
$103$	−0.145433	+	0.0839657i	−0.0143299	+	0.00827339i	−0.507148	−	0.861859i	$-0.669300\pi$
$103$	−0.145433	+	0.0839657i	−0.0143299	+	0.00827339i	0.492818	+	0.870132i	$0.335967\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	7.99080i		−	0.772500i	−0.922394	−	0.386250i	$-0.873770\pi$
$107$		−	7.99080i		−	0.772500i	0.922394	−	0.386250i	$-0.126230\pi$
$108$		0			0
$109$	−18.9533			−1.81540			−0.907700	−	0.419619i	$-0.862164\pi$
$109$	−18.9533			−1.81540			−0.907700	+	0.419619i	$0.862164\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.00418	−	0.579764i	0.0944653	−	0.0545396i	−0.452023	−	0.892006i	$-0.649298\pi$
$113$	1.00418	−	0.579764i	0.0944653	−	0.0545396i	0.546488	+	0.837467i	$0.315964\pi$
$114$		0			0
$115$	5.83973	+	3.37157i	0.544558	+	0.314401i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.43573	+	4.77984i	−0.773302	+	0.438167i
$120$		0			0
$121$	−2.61639	−	4.53172i	−0.237854	−	0.411974i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	12.1648			1.08805
$126$		0			0
$127$	−1.40150			−0.124363			−0.0621817	−	0.998065i	$-0.519806\pi$
$127$	−1.40150			−0.124363			−0.0621817	+	0.998065i	$0.519806\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.24589	−	9.08614i	−0.458335	−	0.793860i	0.540538	−	0.841320i	$-0.318221\pi$
$131$	−5.24589	−	9.08614i	−0.458335	−	0.793860i	−0.998873	+	0.0474597i	$0.984887\pi$
$132$		0			0
$133$	−3.93510	−	6.94489i	−0.341216	−	0.602198i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.08812	+	2.36028i	0.349272	+	0.201652i	0.664365	−	0.747409i	$-0.268702\pi$
$137$	4.08812	+	2.36028i	0.349272	+	0.201652i	−0.315093	+	0.949061i	$0.602036\pi$
$138$		0			0
$139$	2.04707	−	1.18187i	0.173630	−	0.100245i	−0.410666	−	0.911786i	$-0.634704\pi$
$139$	2.04707	−	1.18187i	0.173630	−	0.100245i	0.584296	+	0.811540i	$0.301371\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	11.7465			0.982295
$144$		0			0
$145$			11.7465i			0.975497i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.0377	−	8.68202i	1.23194	−	0.711259i	0.264503	−	0.964385i	$-0.414792\pi$
$149$	15.0377	−	8.68202i	1.23194	−	0.711259i	0.967433	+	0.253126i	$0.0814587\pi$
$150$		0			0
$151$	−5.61639	+	9.72787i	−0.457055	+	0.791643i	−0.998804	−	0.0488977i	$-0.984429\pi$
$151$	−5.61639	+	9.72787i	−0.457055	+	0.791643i	0.541749	+	0.840541i	$0.317762\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	7.20451	+	4.15953i	0.578680	+	0.334101i
$156$		0			0
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.0616014	−	0.998101i	$-0.480379\pi$
$157$	11.9885	−	6.92154i	0.956783	−	0.552399i	0.895181	+	0.445702i	$0.147046\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.05208	−	8.58930i	0.398159	−	0.676931i
$162$		0			0
$163$	4.33577			0.339604			0.169802	−	0.985478i	$-0.445687\pi$
$163$	4.33577			0.339604			0.169802	+	0.985478i	$0.445687\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.20756	−	10.7518i	−0.480355	−	0.832000i	0.519391	−	0.854537i	$-0.326159\pi$
$167$	−6.20756	−	10.7518i	−0.480355	−	0.832000i	−0.999746	+	0.0225370i	$0.992826\pi$
$168$		0			0
$169$	5.46254	−	9.46139i	0.420195	−	0.727799i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.70908	+	15.0846i	−0.662139	+	1.14686i	0.317913	+	0.948120i	$0.397018\pi$
$173$	−8.70908	+	15.0846i	−0.662139	+	1.14686i	−0.980052	+	0.198739i	$0.936315\pi$
$174$		0			0
$175$	0.0383954	−	4.74804i	0.00290242	−	0.358918i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			13.1221i			0.980789i	0.871501	+	0.490395i	$0.163147\pi$
$179$			13.1221i			0.980789i	−0.871501	+	0.490395i	$0.836853\pi$
$180$		0			0
$181$			13.3577i			0.992873i	0.868073	+	0.496437i	$0.165359\pi$
$181$			13.3577i			0.992873i	−0.868073	+	0.496437i	$0.834641\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.38245	+	14.5188i	0.616290	+	1.06745i
$186$		0			0
$187$	7.62164	+	4.40035i	0.557349	+	0.321786i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.01361	−	4.62666i	−0.579845	−	0.334774i	0.181227	−	0.983441i	$-0.441993\pi$
$191$	−8.01361	−	4.62666i	−0.579845	−	0.334774i	−0.761072	+	0.648668i	$0.775326\pi$
$192$		0			0
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.846923	+	0.531716i	$0.178452\pi$
$193$	12.2801	+	21.2698i	0.883941	+	1.53103i	0.0370176	+	0.999315i	$0.488214\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			12.4861i			0.889598i	0.895630	+	0.444799i	$0.146725\pi$
$197$			12.4861i			0.889598i	−0.895630	+	0.444799i	$0.853275\pi$
$198$		0			0
$199$		−	0.179145i		−	0.0126993i	−0.999980	−	0.00634964i	$-0.997979\pi$
$199$		−	0.179145i		−	0.0126993i	0.999980	−	0.00634964i	$-0.00202117\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	17.3583	+	0.140369i	1.21831	+	0.00985198i
$204$		0			0
$205$	−7.23469	+	12.5309i	−0.505293	+	0.875193i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.62268	+	6.27467i	−0.250586	+	0.434028i
$210$		0			0
$211$	−7.56103	−	13.0961i	−0.520523	−	0.901572i	−0.999715	−	0.0238622i	$-0.992404\pi$
$211$	−7.56103	−	13.0961i	−0.520523	−	0.901572i	0.479192	−	0.877710i	$-0.340930\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	12.4654			0.850131
$216$		0			0
$217$	6.23278	−	10.5967i	0.423109	−	0.719348i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.5236	−	8.96254i	1.04423	−	0.602885i
$222$		0			0
$223$	7.27049	+	4.19762i	0.486868	+	0.281093i	0.723274	−	0.690561i	$-0.242636\pi$
$223$	7.27049	+	4.19762i	0.486868	+	0.281093i	−0.236406	+	0.971654i	$0.575970\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.21261	−	2.10030i	0.0804836	−	0.139402i	−0.822974	−	0.568079i	$-0.807687\pi$
$227$	1.21261	−	2.10030i	0.0804836	−	0.139402i	0.903458	+	0.428677i	$0.141020\pi$
$228$		0			0
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	−0.441092	−	0.897462i	$-0.645409\pi$
$229$	1.74915	−	1.00987i	0.115587	−	0.0667344i	0.556679	+	0.830728i	$0.312075\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	12.7289i		−	0.833899i	−0.908930	−	0.416950i	$-0.863099\pi$
$233$		−	12.7289i		−	0.833899i	0.908930	−	0.416950i	$-0.136901\pi$
$234$		0			0
$235$	9.19531			0.599836
$236$		0			0
$237$		0			0
$238$		0			0
$239$	15.1117	−	8.72474i	0.977494	−	0.564356i	0.0759814	−	0.997109i	$-0.475791\pi$
$239$	15.1117	−	8.72474i	0.977494	−	0.564356i	0.901513	+	0.432753i	$0.142458\pi$
$240$		0			0
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	0.783769	−	0.621052i	$-0.213295\pi$
$241$	9.90142	+	5.71659i	0.637807	+	0.368238i	−0.145963	+	0.989290i	$0.546628\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.5308	+	0.202676i	0.800564	+	0.0129485i
$246$		0			0
$247$	7.37859	+	12.7801i	0.469489	+	0.813178i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−27.3560			−1.72669			−0.863347	−	0.504611i	$-0.831636\pi$
$251$	−27.3560			−1.72669			−0.863347	+	0.504611i	$0.831636\pi$
$252$		0			0
$253$	−9.04499			−0.568653
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.74837	−	3.02826i	−0.109060	−	0.188898i	0.806330	−	0.591466i	$-0.201451\pi$
$257$	−1.74837	−	3.02826i	−0.109060	−	0.188898i	−0.915390	+	0.402569i	$0.868117\pi$
$258$		0			0
$259$	21.5552	−	12.2136i	1.33937	−	0.758914i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.35150	−	4.82174i	−0.514976	−	0.297321i	0.219901	−	0.975522i	$-0.429427\pi$
$263$	−8.35150	−	4.82174i	−0.514976	−	0.297321i	−0.734877	+	0.678201i	$0.762760\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	6.91107			0.421376			0.210688	−	0.977553i	$-0.432430\pi$
$269$	6.91107			0.421376			0.210688	+	0.977553i	$0.432430\pi$
$270$		0			0
$271$		−	20.6312i		−	1.25326i	−0.779318	−	0.626629i	$-0.784434\pi$
$271$		−	20.6312i		−	1.25326i	0.779318	−	0.626629i	$-0.215566\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.73244	+	2.15493i	−0.225075	+	0.129947i
$276$		0			0
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	−0.533166	−	0.846011i	$-0.678998\pi$
$277$	7.75718	−	13.4358i	0.466084	−	0.807281i	0.999250	+	0.0387296i	$0.0123311\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.7759	−	6.79883i	−0.702492	−	0.405584i	0.105783	−	0.994389i	$-0.466265\pi$
$281$	−11.7759	−	6.79883i	−0.702492	−	0.405584i	−0.808275	+	0.588805i	$0.799599\pi$
$282$		0			0
$283$	4.71796	−	2.72392i	0.280454	−	0.161920i	−0.353175	−	0.935557i	$-0.614898\pi$
$283$	4.71796	−	2.72392i	0.280454	−	0.161920i	0.633629	+	0.773637i	$0.281565\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	18.4308	+	10.8407i	1.08794	+	0.639907i
$288$		0			0
$289$	−3.57023			−0.210014
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−12.2311	−	21.1849i	−0.714550	−	1.23764i	−0.963133	−	0.269026i	$-0.913298\pi$
$293$	−12.2311	−	21.1849i	−0.714550	−	1.23764i	0.248583	−	0.968610i	$-0.420035\pi$
$294$		0			0
$295$	−13.0606	+	22.6216i	−0.760418	+	1.31708i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.21130	+	15.9544i	−0.532703	+	0.922670i
$300$		0			0
$301$	0.148959	−	18.4205i	0.00858585	−	1.06174i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			20.2816i			1.16132i
$306$		0			0
$307$			31.2223i			1.78195i	0.454053	+	0.890975i	$0.349978\pi$
$307$			31.2223i			1.78195i	−0.454053	+	0.890975i	$0.650022\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.45501	−	9.44836i	−0.309325	−	0.535767i	0.668889	−	0.743362i	$-0.266770\pi$
$311$	−5.45501	−	9.44836i	−0.309325	−	0.535767i	−0.978215	+	0.207594i	$0.933437\pi$
$312$		0			0
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	0.581458	−	0.813576i	$-0.302482\pi$
$313$	2.96532	+	1.71203i	0.167610	+	0.0967694i	−0.413849	+	0.910346i	$0.635816\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.4953	−	9.52357i	−0.926468	−	0.534897i	−0.0407755	−	0.999168i	$-0.512983\pi$
$317$	−16.4953	−	9.52357i	−0.926468	−	0.534897i	−0.885693	+	0.464272i	$0.846316\pi$
$318$		0			0
$319$	−7.87817	−	13.6454i	−0.441093	−	0.763995i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			11.0563i			0.615191i
$324$		0			0
$325$			8.77821i			0.486927i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.109882	−	13.5882i	0.00605801	−	0.749144i
$330$		0			0
$331$	0.0366251	−	0.0634366i	0.00201310	−	0.00348679i	−0.865017	−	0.501742i	$-0.832693\pi$
$331$	0.0366251	−	0.0634366i	0.00201310	−	0.00348679i	0.867030	+	0.498256i	$0.166026\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.510456	+	0.884136i	−0.0278892	+	0.0483055i
$336$		0			0
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	0.894829	−	0.446408i	$-0.147297\pi$
$337$	1.11639	+	1.93364i	0.0608136	+	0.105332i	−0.834016	+	0.551741i	$0.813964\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−11.1589			−0.604286
$342$		0			0
$343$	0.449242	−	18.5148i	0.0242568	−	0.999706i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	27.5751	−	15.9205i	1.48031	−	0.854656i	0.480556	−	0.876964i	$-0.340435\pi$
$347$	27.5751	−	15.9205i	1.48031	−	0.854656i	0.999751	+	0.0223084i	$0.00710156\pi$
$348$		0			0
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	0.117925	−	0.993022i	$-0.462376\pi$
$349$	−12.7613	−	7.36772i	−0.683095	−	0.394385i	−0.801020	+	0.598637i	$0.795709\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.07979	−	1.87025i	0.0574713	−	0.0995431i	−0.835858	−	0.548945i	$-0.815030\pi$
$353$	1.07979	−	1.87025i	0.0574713	−	0.0995431i	0.893330	+	0.449402i	$0.148363\pi$
$354$		0			0
$355$	−9.24484	+	5.33751i	−0.490665	+	0.283286i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	32.6448i		−	1.72293i	−0.507820	−	0.861463i	$-0.669549\pi$
$359$		−	32.6448i		−	1.72293i	0.507820	−	0.861463i	$-0.330451\pi$
$360$		0			0
$361$	9.89765			0.520929
$362$		0			0
$363$		0			0
$364$		0			0
$365$	19.1972	−	11.0835i	1.00483	−	0.580138i
$366$		0			0
$367$	−25.7212	−	14.8501i	−1.34264	−	0.775171i	−0.355442	−	0.934698i	$-0.615670\pi$
$367$	−25.7212	−	14.8501i	−1.34264	−	0.775171i	−0.987194	+	0.159527i	$0.949003\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	0.890950	−	0.454102i	$-0.150040\pi$
$373$	1.00836	+	1.74653i	0.0522109	+	0.0904320i	−0.838739	+	0.544534i	$0.816707\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−32.0921			−1.65283
$378$		0			0
$379$	18.8709			0.969332			0.484666	−	0.874699i	$-0.338941\pi$
$379$	18.8709			0.969332			0.484666	+	0.874699i	$0.338941\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.418256	−	0.724440i	−0.0213719	−	0.0370172i	0.855142	−	0.518394i	$-0.173470\pi$
$383$	−0.418256	−	0.724440i	−0.0213719	−	0.0370172i	−0.876514	+	0.481377i	$0.840137\pi$
$384$		0			0
$385$	−5.60790	−	9.89714i	−0.285805	−	0.504405i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−21.4964	−	12.4109i	−1.08991	−	0.629260i	−0.156357	−	0.987701i	$-0.549975\pi$
$389$	−21.4964	−	12.4109i	−1.08991	−	0.629260i	−0.933552	+	0.358441i	$0.883308\pi$
$390$		0			0
$391$	−11.9533	+	6.90127i	−0.604507	+	0.349012i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.43662			0.273546
$396$		0			0
$397$		−	3.03390i		−	0.152267i	−0.997098	−	0.0761336i	$-0.975742\pi$
$397$		−	3.03390i		−	0.152267i	0.997098	−	0.0761336i	$-0.0242575\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−11.3251	+	6.53854i	−0.565548	+	0.326519i	−0.755369	−	0.655300i	$-0.772542\pi$
$401$	−11.3251	+	6.53854i	−0.565548	+	0.326519i	0.189822	+	0.981819i	$0.439209\pi$
$402$		0			0
$403$	−11.3640	+	19.6831i	−0.566083	+	0.980485i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−19.4750	−	11.2439i	−0.965339	−	0.557339i
$408$		0			0
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	−0.376044	−	0.926602i	$-0.622716\pi$
$409$	4.82124	−	2.78354i	0.238395	−	0.137637i	0.614439	+	0.788965i	$0.289382\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	33.2728	+	19.5705i	1.63725	+	0.963000i
$414$		0			0
$415$	−25.0746			−1.23086
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.19938	+	14.2017i	0.400566	+	0.693800i	0.993794	−	0.111234i	$-0.0354802\pi$
$419$	8.19938	+	14.2017i	0.400566	+	0.693800i	−0.593228	+	0.805034i	$0.702147\pi$
$420$		0			0
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	−0.990578	−	0.136952i	$-0.956269\pi$
$421$	−7.72892	+	13.3869i	−0.376684	+	0.652437i	0.613893	+	0.789389i	$0.289603\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.28839	+	5.69566i	−0.159510	+	0.276280i
$426$		0			0
$427$	29.9708	+	0.242361i	1.45039	+	0.0117287i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			25.0266i			1.20549i	0.797935	+	0.602744i	$0.205926\pi$
$431$			25.0266i			1.20549i	−0.797935	+	0.602744i	$0.794074\pi$
$432$		0			0
$433$		−	2.25168i		−	0.108209i	−0.998535	−	0.0541044i	$-0.982770\pi$
$433$		−	2.25168i		−	0.108209i	0.998535	−	0.0541044i	$-0.0172304\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−5.68161	−	9.84084i	−0.271788	−	0.470751i
$438$		0			0
$439$	−16.2293	−	9.37000i	−0.774583	−	0.447206i	0.0599239	−	0.998203i	$-0.480914\pi$
$439$	−16.2293	−	9.37000i	−0.774583	−	0.447206i	−0.834507	+	0.550997i	$0.814248\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.04314	−	0.602256i	−0.0495610	−	0.0286141i	0.475015	−	0.879978i	$-0.342443\pi$
$443$	−1.04314	−	0.602256i	−0.0495610	−	0.0286141i	−0.524576	+	0.851364i	$0.675776\pi$
$444$		0			0
$445$	3.35568	+	5.81221i	0.159074	+	0.275525i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			26.8022i			1.26487i	0.774612	+	0.632436i	$0.217945\pi$
$449$			26.8022i			1.26487i	−0.774612	+	0.632436i	$0.782055\pi$
$450$		0			0
$451$		−	19.4087i		−	0.913918i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−23.1686	−	0.187354i	−1.08616	−	0.00878331i
$456$		0			0
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	−0.981291	−	0.192529i	$-0.938331\pi$
$457$	−6.92442	+	11.9934i	−0.323911	+	0.561030i	0.657381	+	0.753559i	$0.271664\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.40241	+	4.16110i	−0.111892	+	0.193802i	−0.916533	−	0.399959i	$-0.869024\pi$
$461$	−2.40241	+	4.16110i	−0.111892	+	0.193802i	0.804641	+	0.593761i	$0.202358\pi$
$462$		0			0
$463$	−10.5194	−	18.2201i	−0.488877	−	0.846760i	0.511041	−	0.859556i	$-0.329260\pi$
$463$	−10.5194	−	18.2201i	−0.488877	−	0.846760i	−0.999918	+	0.0127960i	$0.995927\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.82302			0.269457			0.134729	−	0.990883i	$-0.456984\pi$
$467$	5.82302			0.269457			0.134729	+	0.990883i	$0.456984\pi$
$468$		0			0
$469$	1.30042	+	0.764885i	0.0600478	+	0.0353191i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−14.4804	+	8.36028i	−0.665811	+	0.384406i
$474$		0			0
$475$	−4.68907	−	2.70724i	−0.215149	−	0.124217i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.4781	−	23.3447i	0.615828	−	1.06665i	−0.374411	−	0.927263i	$-0.622155\pi$
$479$	13.4781	−	23.3447i	0.615828	−	1.06665i	0.990239	−	0.139382i	$-0.0445117\pi$
$480$		0			0
$481$	−39.6662	+	22.9013i	−1.80862	+	1.04421i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			9.86639i			0.448010i
$486$		0			0
$487$	13.6268			0.617487			0.308744	−	0.951145i	$-0.400091\pi$
$487$	13.6268			0.617487			0.308744	+	0.951145i	$0.400091\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−33.7430	+	19.4815i	−1.52280	+	0.879188i	−0.523162	+	0.852234i	$0.675248\pi$
$491$	−33.7430	+	19.4815i	−1.52280	+	0.879188i	−0.999637	+	0.0269544i	$0.991419\pi$
$492$		0			0
$493$	−20.8227	−	12.0220i	−0.937807	−	0.541443i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.77696	+	13.7252i	0.348844	+	0.615660i
$498$		0			0
$499$	13.0048	+	22.5250i	0.582176	+	1.00836i	0.995221	+	0.0976483i	$0.0311320\pi$
$499$	13.0048	+	22.5250i	0.582176	+	1.00836i	−0.413045	+	0.910711i	$0.635535\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	10.5271			0.469378			0.234689	−	0.972070i	$-0.424593\pi$
$503$	10.5271			0.469378			0.234689	+	0.972070i	$0.424593\pi$
$504$		0			0
$505$	0.448168			0.0199432
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.469435	−	0.813086i	−0.0208074	−	0.0360394i	0.855434	−	0.517911i	$-0.173290\pi$
$509$	−0.469435	−	0.813086i	−0.0208074	−	0.0360394i	−0.876242	+	0.481872i	$0.839957\pi$
$510$		0			0
$511$	−16.1491	−	28.5009i	−0.714395	−	1.26081i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.260376	−	0.150328i	−0.0114735	−	0.00662424i
$516$		0			0
$517$	−10.6818	+	6.16711i	−0.469783	+	0.271229i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	39.5054			1.73076			0.865382	−	0.501112i	$-0.167076\pi$
$521$	39.5054			1.73076			0.865382	+	0.501112i	$0.167076\pi$
$522$		0			0
$523$			24.3292i			1.06384i	0.846794	+	0.531922i	$0.178530\pi$
$523$			24.3292i			1.06384i	−0.846794	+	0.531922i	$0.821470\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.7469	+	8.51413i	−0.642385	+	0.370881i
$528$		0			0
$529$	−4.40718	+	7.63346i	−0.191616	+	0.331889i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−34.2349	−	19.7655i	−1.48288	−	0.856141i
$534$		0			0
$535$	12.3896	−	7.15316i	0.535651	−	0.309258i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−14.6924	+	8.16873i	−0.632845	+	0.351852i
$540$		0			0
$541$	42.7281			1.83702			0.918512	−	0.395394i	$-0.129392\pi$
$541$	42.7281			1.83702			0.918512	+	0.395394i	$0.129392\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−16.9665	−	29.3869i	−0.726767	−	1.25880i
$546$		0			0
$547$	12.2477	−	21.2136i	0.523672	−	0.907026i	−0.475949	−	0.879473i	$-0.657895\pi$
$547$	12.2477	−	21.2136i	0.523672	−	0.907026i	0.999620	−	0.0275530i	$-0.00877149\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	9.89735	−	17.1427i	0.421641	−	0.730304i
$552$		0			0
$553$	0.0649667	−	8.03389i	0.00276266	−	0.341636i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	2.54431i		−	0.107806i	−0.998546	−	0.0539030i	$-0.982834\pi$
$557$		−	2.54431i		−	0.107806i	0.998546	−	0.0539030i	$-0.0171662\pi$
$558$		0			0
$559$			34.0560i			1.44042i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.90707	−	13.6954i	−0.333243	−	0.577194i	0.649902	−	0.760018i	$-0.274810\pi$
$563$	−7.90707	−	13.6954i	−0.333243	−	0.577194i	−0.983146	+	0.182823i	$0.941476\pi$
$564$		0			0
$565$	1.79783	+	1.03798i	0.0756354	+	0.0436681i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.52793	+	3.19155i	0.231743	+	0.133797i	0.611376	−	0.791340i	$-0.290616\pi$
$569$	5.52793	+	3.19155i	0.231743	+	0.133797i	−0.379633	+	0.925137i	$0.623950\pi$
$570$		0			0
$571$	−3.91188	−	6.77557i	−0.163707	−	0.283549i	0.772488	−	0.635029i	$-0.219012\pi$
$571$	−3.91188	−	6.77557i	−0.163707	−	0.283549i	−0.936195	+	0.351480i	$0.885678\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	6.75933i		−	0.281884i
$576$		0			0
$577$			14.3197i			0.596138i	0.954544	+	0.298069i	$0.0963425\pi$
$577$			14.3197i			0.596138i	−0.954544	+	0.298069i	$0.903657\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.299637	+	37.0536i	−0.0124310	+	1.53724i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.37575	+	4.11492i	−0.0980577	+	0.169841i	−0.910881	−	0.412670i	$-0.864596\pi$
$587$	−2.37575	+	4.11492i	−0.0980577	+	0.169841i	0.812823	+	0.582511i	$0.197930\pi$
$588$		0			0
$589$	−7.00943	−	12.1407i	−0.288819	−	0.500249i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.58070			−0.147042			−0.0735208	−	0.997294i	$-0.523424\pi$
$593$	−3.58070			−0.147042			−0.0735208	+	0.997294i	$0.523424\pi$
$594$		0			0
$595$	−14.9625	−	8.80071i	−0.613404	−	0.360794i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−13.0471	+	7.53277i	−0.533091	+	0.307780i	−0.742274	−	0.670096i	$-0.766253\pi$
$599$	−13.0471	+	7.53277i	−0.533091	+	0.307780i	0.209183	+	0.977877i	$0.432920\pi$
$600$		0			0
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	0.0366096	−	0.999330i	$-0.488344\pi$
$601$	−19.8704	−	11.4722i	−0.810530	−	0.467960i	−0.847140	+	0.531370i	$0.821678\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.68425	−	8.11336i	0.190442	−	0.329855i
$606$		0			0
$607$	−21.2030	+	12.2416i	−0.860605	+	0.496870i	−0.864215	−	0.503123i	$-0.832184\pi$
$607$	−21.2030	+	12.2416i	−0.860605	+	0.496870i	0.00360990	+	0.999993i	$0.498851\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			25.1221i			1.01633i
$612$		0			0
$613$	−0.880086			−0.0355463			−0.0177732	−	0.999842i	$-0.505658\pi$
$613$	−0.880086			−0.0355463			−0.0177732	+	0.999842i	$0.505658\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	11.7607	−	6.79005i	0.473468	−	0.273357i	−0.244222	−	0.969719i	$-0.578533\pi$
$617$	11.7607	−	6.79005i	0.473468	−	0.273357i	0.717690	+	0.696362i	$0.245199\pi$
$618$		0			0
$619$	30.7325	+	17.7434i	1.23524	+	0.713169i	0.968118	−	0.250493i	$-0.0805926\pi$
$619$	30.7325	+	17.7434i	1.23524	+	0.713169i	0.267126	+	0.963662i	$0.413926\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.62901	−	4.88936i	0.345714	−	0.195888i
$624$		0			0
$625$	6.40300	+	11.0903i	0.256120	+	0.443613i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−34.3161			−1.36827
$630$		0			0
$631$	−26.9822			−1.07415			−0.537073	−	0.843536i	$-0.680470\pi$
$631$	−26.9822			−1.07415			−0.537073	+	0.843536i	$0.680470\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.25459	−	2.17302i	−0.0497869	−	0.0862335i
$636$		0			0
$637$	−0.553721	+	34.2348i	−0.0219392	+	1.35643i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.932777	−	0.538539i	−0.0368425	−	0.0212710i	0.481466	−	0.876465i	$-0.340105\pi$
$641$	−0.932777	−	0.538539i	−0.0368425	−	0.0212710i	−0.518308	+	0.855194i	$0.673438\pi$
$642$		0			0
$643$	−33.3126	+	19.2330i	−1.31372	+	0.758477i	−0.982710	−	0.185150i	$-0.940723\pi$
$643$	−33.3126	+	19.2330i	−1.31372	+	0.758477i	−0.331010	+	0.943627i	$0.607389\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.95210			−0.351943			−0.175972	−	0.984395i	$-0.556307\pi$
$647$	−8.95210			−0.351943			−0.175972	+	0.984395i	$0.556307\pi$
$648$		0			0
$649$		−	35.0380i		−	1.37536i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.85934	−	5.69229i	0.385826	−	0.222757i	−0.294524	−	0.955644i	$-0.595161\pi$
$653$	9.85934	−	5.69229i	0.385826	−	0.222757i	0.680350	+	0.732887i	$0.261828\pi$
$654$		0			0
$655$	9.39197	−	16.2674i	0.366975	−	0.635619i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	31.4373	+	18.1503i	1.22462	+	0.707036i	0.965900	−	0.258915i	$-0.0833650\pi$
$659$	31.4373	+	18.1503i	1.22462	+	0.707036i	0.258723	+	0.965952i	$0.416698\pi$
$660$		0			0
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.963886	−	0.266315i	$-0.914194\pi$
$661$	−31.2425	+	18.0379i	−1.21519	+	0.701593i	−0.251308	+	0.967907i	$0.580861\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.24536	−	12.3182i	0.280963	−	0.477680i
$666$		0			0
$667$	24.7114			0.956828
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−13.6025	−	23.5602i	−0.525117	−	0.909530i
$672$		0			0
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	−0.758939	−	0.651161i	$-0.774282\pi$
$673$	4.78512	−	8.28806i	0.184453	−	0.319481i	0.943392	+	0.331680i	$0.107615\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.81408	+	13.5344i	−0.300320	+	0.520169i	−0.976208	−	0.216835i	$-0.930427\pi$
$677$	−7.81408	+	13.5344i	−0.300320	+	0.520169i	0.675889	+	0.737004i	$0.263760\pi$
$678$		0			0
$679$	14.5799	+	0.117902i	0.559526	+	0.00452465i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	11.1313i		−	0.425926i	−0.977060	−	0.212963i	$-0.931689\pi$
$683$		−	11.1313i		−	0.425926i	0.977060	−	0.212963i	$-0.0683114\pi$
$684$		0			0
$685$			8.45145i			0.322913i
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−2.61903	−	1.51210i	−0.0996324	−	0.0575228i	0.449356	−	0.893353i	$-0.351654\pi$
$691$	−2.61903	−	1.51210i	−0.0996324	−	0.0575228i	−0.548988	+	0.835830i	$0.684987\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.66497	+	2.11597i	0.139020	+	0.0802633i
$696$		0			0
$697$	−14.8087	−	25.6494i	−0.560919	−	0.971540i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			50.1486i			1.89409i	0.321103	+	0.947044i	$0.395946\pi$
$701$			50.1486i			1.89409i	−0.321103	+	0.947044i	$0.604054\pi$
$702$		0			0
$703$		−	28.2514i		−	1.06552i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.00535553	−	0.662274i	0.000201415	−	0.0249074i
$708$		0			0
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	−0.830163	−	0.557520i	$-0.811753\pi$
$709$	1.80385	−	3.12436i	0.0677449	−	0.117338i	0.897908	+	0.440183i	$0.145086\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	8.75046	−	15.1562i	0.327707	−	0.567605i
$714$		0			0
$715$	10.5152	+	18.2129i	0.393246	+	0.681123i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−34.3161			−1.27977			−0.639887	−	0.768469i	$-0.721019\pi$
$719$	−34.3161			−1.27977			−0.639887	+	0.768469i	$0.721019\pi$
$720$		0			0
$721$	−0.225257	+	0.382970i	−0.00838899	+	0.0142626i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.1972	−	5.88737i	0.378716	−	0.218651i
$726$		0			0
$727$	−19.4757	−	11.2443i	−0.722315	−	0.417029i	0.0932892	−	0.995639i	$-0.470262\pi$
$727$	−19.4757	−	11.2443i	−0.722315	−	0.417029i	−0.815604	+	0.578610i	$0.803595\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.7577	+	22.0970i	−0.471860	+	0.817285i
$732$		0			0
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.0899987	−	0.995942i	$-0.471314\pi$
$733$	27.0065	−	15.5922i	0.997509	−	0.575912i	0.907510	+	0.420030i	$0.137980\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	1.36941i		−	0.0504429i
$738$		0			0
$739$	−4.08628			−0.150316			−0.0751581	−	0.997172i	$-0.523946\pi$
$739$	−4.08628			−0.150316			−0.0751581	+	0.997172i	$0.523946\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.78246	+	1.02910i	−0.0653921	+	0.0377542i	−0.532340	−	0.846531i	$-0.678687\pi$
$743$	−1.78246	+	1.02910i	−0.0653921	+	0.0377542i	0.466947	+	0.884285i	$0.345354\pi$
$744$		0			0
$745$	26.9227	+	15.5439i	0.986373	+	0.569483i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−10.4224	−	18.3941i	−0.380828	−	0.672106i
$750$		0			0
$751$	11.9053	+	20.6205i	0.434429	+	0.752454i	0.997249	−	0.0741262i	$-0.0236168\pi$
$751$	11.9053	+	20.6205i	0.434429	+	0.752454i	−0.562820	+	0.826580i	$0.690283\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−20.1106			−0.731900
$756$		0			0
$757$	10.0754			0.366197			0.183098	−	0.983095i	$-0.441387\pi$
$757$	10.0754			0.366197			0.183098	+	0.983095i	$0.441387\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.9368	−	24.1392i	−0.505207	−	0.875044i	−0.999982	−	0.00602283i	$-0.998083\pi$
$761$	−13.9368	−	24.1392i	−0.505207	−	0.875044i	0.494775	−	0.869021i	$-0.335250\pi$
$762$		0			0
$763$	−43.6289	+	24.7209i	−1.57947	+	0.894957i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−61.8035	−	35.6823i	−2.23159	−	1.28841i
$768$		0			0
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	−0.607800	−	0.794090i	$-0.707948\pi$
$769$	−6.21166	+	3.58631i	−0.223998	+	0.129326i	0.383802	+	0.923415i	$0.374615\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.14153			0.0770255			0.0385128	−	0.999258i	$-0.487738\pi$
$773$	2.14153			0.0770255			0.0385128	+	0.999258i	$0.487738\pi$
$774$		0			0
$775$		−	8.33903i		−	0.299547i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	21.1164	−	12.1916i	0.756573	−	0.436808i
$780$		0			0
$781$	7.15953	−	12.4007i	0.256188	−	0.443731i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	21.4635	+	12.3920i	0.766066	+	0.442288i
$786$		0			0
$787$	−15.8961	+	9.17759i	−0.566633	+	0.327146i	−0.755804	−	0.654798i	$-0.772753\pi$
$787$	−15.8961	+	9.17759i	−0.566633	+	0.327146i	0.189170	+	0.981944i	$0.439420\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.55534	−	2.64432i	0.0553017	−	0.0940212i
$792$		0			0
$793$	−55.4103			−1.96768
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.4226	−	21.5166i	−0.440031	−	0.762156i	0.557660	−	0.830069i	$-0.311699\pi$
$797$	−12.4226	−	21.5166i	−0.440031	−	0.762156i	−0.997691	+	0.0679130i	$0.978366\pi$
$798$		0			0
$799$	−9.41094	+	16.3002i	−0.332935	+	0.576660i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−14.8670	+	25.7504i	−0.524645	+	0.908712i
$804$		0			0
$805$	17.8401	+	0.144265i	0.628781	+	0.00508468i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	37.7861i		−	1.32849i	−0.747516	−	0.664244i	$-0.768754\pi$
$809$		−	37.7861i		−	1.32849i	0.747516	−	0.664244i	$-0.231246\pi$
$810$		0			0
$811$			36.5165i			1.28227i	0.767429	+	0.641134i	$0.221536\pi$
$811$			36.5165i			1.28227i	−0.767429	+	0.641134i	$0.778464\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.88128	+	6.72257i	0.135955	+	0.235481i
$816$		0			0
$817$	−18.1918	−	10.5030i	−0.636449	−	0.367454i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.52142	+	3.18779i	0.192699	+	0.111255i	0.593245	−	0.805022i	$-0.297846\pi$
$821$	5.52142	+	3.18779i	0.192699	+	0.111255i	−0.400547	+	0.916276i	$0.631180\pi$
$822$		0			0
$823$	14.0293	+	24.2995i	0.489032	+	0.847028i	0.999920	−	0.0126187i	$-0.00401678\pi$
$823$	14.0293	+	24.2995i	0.489032	+	0.847028i	−0.510888	+	0.859647i	$0.670683\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			0.581579i			0.0202235i	0.999949	+	0.0101117i	$0.00321872\pi$
$827$			0.581579i			0.0202235i	−0.999949	+	0.0101117i	$0.996781\pi$
$828$		0			0
$829$		−	51.9246i		−	1.80342i	−0.432346	−	0.901708i	$-0.642314\pi$
$829$		−	51.9246i		−	1.80342i	0.432346	−	0.901708i	$-0.357686\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−13.1839	+	22.0055i	−0.456796	+	0.762446i
$834$		0			0
$835$	11.1137	−	19.2495i	0.384606	−	0.666156i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.33038	+	5.76838i	−0.114977	+	0.199147i	−0.917771	−	0.397111i	$-0.870013\pi$
$839$	−3.33038	+	5.76838i	−0.114977	+	0.199147i	0.802793	+	0.596257i	$0.203346\pi$
$840$		0			0
$841$	7.02357	+	12.1652i	0.242192	+	0.419489i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	19.5597			0.672874
$846$		0			0
$847$	−11.9334	−	7.01904i	−0.410038	−	0.241177i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	30.5435	−	17.6343i	1.04702	−	0.604495i
$852$		0			0
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	0.133281	−	0.991078i	$-0.457449\pi$
$853$	−19.2287	−	11.1017i	−0.658378	−	0.380115i	−0.791659	+	0.610964i	$0.790782\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.64830	−	13.2472i	0.261261	−	0.452517i	−0.705316	−	0.708893i	$-0.749195\pi$
$857$	7.64830	−	13.2472i	0.261261	−	0.452517i	0.966577	+	0.256375i	$0.0825283\pi$
$858$		0			0
$859$	−3.68620	+	2.12823i	−0.125772	+	0.0726143i	−0.561566	−	0.827432i	$-0.689801\pi$
$859$	−3.68620	+	2.12823i	−0.125772	+	0.0726143i	0.435794	+	0.900046i	$0.356468\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			23.6624i			0.805476i	0.915315	+	0.402738i	$0.131941\pi$
$863$			23.6624i			0.805476i	−0.915315	+	0.402738i	$0.868059\pi$
$864$		0			0
$865$	−31.1846			−1.06031
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.31546	+	3.64623i	−0.214237	+	0.123690i
$870$		0			0
$871$	−2.41551	−	1.39459i	−0.0818463	−	0.0472540i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	28.0023	−	15.8666i	0.946649	−	0.536389i
$876$		0			0
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	0.985226	−	0.171258i	$-0.0547831\pi$
$877$	10.1962	+	17.6603i	0.344300	+	0.596344i	−0.640927	+	0.767602i	$0.721450\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−32.4586			−1.09356			−0.546780	−	0.837276i	$-0.684147\pi$
$881$	−32.4586			−1.09356			−0.546780	+	0.837276i	$0.684147\pi$
$882$		0			0
$883$	24.8311			0.835632			0.417816	−	0.908532i	$-0.362796\pi$
$883$	24.8311			0.835632			0.417816	+	0.908532i	$0.362796\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−4.86059	−	8.41879i	−0.163203	−	0.282675i	0.772813	−	0.634634i	$-0.218849\pi$
$887$	−4.86059	−	8.41879i	−0.163203	−	0.282675i	−0.936016	+	0.351959i	$0.885516\pi$
$888$		0			0
$889$	−3.22614	+	1.82799i	−0.108201	+	0.0613088i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−13.4195	−	7.74775i	−0.449066	−	0.259269i
$894$		0			0
$895$	−20.3456	+	11.7465i	−0.680079	+	0.392644i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	30.4865			1.01678
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−20.7110	+	11.9575i	−0.688458	+	0.397481i
$906$		0			0
$907$	−8.04314	+	13.9311i	−0.267068	+	0.462575i	−0.968103	−	0.250551i	$-0.919388\pi$
$907$	−8.04314	+	13.9311i	−0.267068	+	0.462575i	0.701035	+	0.713127i	$0.252722\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	27.0087	+	15.5935i	0.894838	+	0.516635i	0.875522	−	0.483179i	$-0.160518\pi$
$911$	27.0087	+	15.5935i	0.894838	+	0.516635i	0.0193161	+	0.999813i	$0.493851\pi$
$912$		0			0
$913$	29.1279	−	16.8170i	0.963993	−	0.556562i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−23.9267	−	14.0733i	−0.790128	−	0.464740i
$918$		0			0
$919$	−25.7664			−0.849955			−0.424977	−	0.905204i	$-0.639718\pi$
$919$	−25.7664			−0.849955			−0.424977	+	0.905204i	$0.639718\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.5824	−	25.2574i	−0.479984	−	0.831357i
$924$		0			0
$925$	8.40258	−	14.5537i	0.276275	−	0.478522i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	27.3744	−	47.4138i	0.898124	−	1.55560i	0.0682329	−	0.997669i	$-0.478264\pi$
$929$	27.3744	−	47.4138i	0.898124	−	1.55560i	0.829891	−	0.557926i	$-0.188403\pi$
$930$		0			0
$931$	−18.1165	−	10.8539i	−0.593744	−	0.355723i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			15.7563i			0.515288i
$936$		0			0
$937$			58.2065i			1.90152i	0.309924	+	0.950761i	$0.399696\pi$
$937$			58.2065i			1.90152i	−0.309924	+	0.950761i	$0.600304\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−16.6658	−	28.8660i	−0.543289	−	0.941005i	−0.998712	−	0.0507297i	$-0.983845\pi$
$941$	−16.6658	−	28.8660i	−0.543289	−	0.941005i	0.455423	−	0.890275i	$-0.349488\pi$
$942$		0			0
$943$	26.3613	+	15.2197i	0.858443	+	0.495622i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.59497	−	3.80761i	−0.214308	−	0.123731i	0.389004	−	0.921236i	$-0.372819\pi$
$947$	−6.59497	−	3.80761i	−0.214308	−	0.123731i	−0.603312	+	0.797505i	$0.706153\pi$
$948$		0			0
$949$	30.2808	+	52.4478i	0.982955	+	1.70253i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	55.7861i		−	1.80709i	−0.428495	−	0.903544i	$-0.640956\pi$
$953$		−	55.7861i		−	1.80709i	0.428495	−	0.903544i	$-0.359044\pi$
$954$		0			0
$955$		−	16.5667i		−	0.536085i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	12.4890	+	0.100993i	0.403291	+	0.00326125i
$960$		0			0
$961$	−4.70451	+	8.14845i	−0.151758	+	0.262853i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−21.9857	+	38.0803i	−0.707744	+	1.22585i
$966$		0			0
$967$	13.3369	+	23.1003i	0.428887	+	0.742855i	0.996775	−	0.0802517i	$-0.0255724\pi$
$967$	13.3369	+	23.1003i	0.428887	+	0.742855i	−0.567887	+	0.823106i	$0.692239\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.59942			−0.275968			−0.137984	−	0.990434i	$-0.544062\pi$
$971$	−8.59942			−0.275968			−0.137984	+	0.990434i	$0.544062\pi$
$972$		0			0
$973$	3.17064	−	5.39057i	0.101646	−	0.172814i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.7973	−	7.38854i	0.409423	−	0.236380i	−0.281119	−	0.959673i	$-0.590705\pi$
$977$	12.7973	−	7.38854i	0.409423	−	0.236380i	0.690542	+	0.723293i	$0.257372\pi$
$978$		0			0
$979$	−7.79627	−	4.50118i	−0.249170	−	0.143858i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.2568	−	17.7652i	0.327140	−	0.566623i	−0.654803	−	0.755800i	$-0.727248\pi$
$983$	10.2568	−	17.7652i	0.327140	−	0.566623i	0.981943	+	0.189176i	$0.0605818\pi$
$984$		0			0
$985$	−19.3596	+	11.1772i	−0.616847	+	0.356137i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	26.2236i		−	0.833861i
$990$		0			0
$991$	9.29294			0.295200			0.147600	−	0.989047i	$-0.452845\pi$
$991$	9.29294			0.295200			0.147600	+	0.989047i	$0.452845\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.277763	−	0.160366i	0.00880567	−	0.00508396i
$996$		0			0
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	0.499726	−	0.866183i	$-0.333434\pi$
$997$	−0.0172917	−	0.00998339i	−0.000547635	−	0.000316177i	−0.500274	+	0.865867i	$0.666767\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cc.b.2897.6		16
3.2	odd	2		1008.2.cc.b.209.1		16
4.3	odd	2		378.2.m.a.251.4		16
7.6	odd	2	inner	3024.2.cc.b.2897.3		16
9.4	even	3		1008.2.cc.b.545.8		16
9.5	odd	6	inner	3024.2.cc.b.881.3		16
12.11	even	2		126.2.m.a.83.8	yes	16
21.20	even	2		1008.2.cc.b.209.8		16
28.3	even	6		2646.2.t.a.1979.8		16
28.11	odd	6		2646.2.t.a.1979.5		16
28.19	even	6		2646.2.l.b.521.5		16
28.23	odd	6		2646.2.l.b.521.8		16
28.27	even	2		378.2.m.a.251.1		16
36.7	odd	6		1134.2.d.a.1133.11		16
36.11	even	6		1134.2.d.a.1133.6		16
36.23	even	6		378.2.m.a.125.1		16
36.31	odd	6		126.2.m.a.41.5	✓	16
63.13	odd	6		1008.2.cc.b.545.1		16
63.41	even	6	inner	3024.2.cc.b.881.6		16
84.11	even	6		882.2.t.b.803.2		16
84.23	even	6		882.2.l.a.227.2		16
84.47	odd	6		882.2.l.a.227.3		16
84.59	odd	6		882.2.t.b.803.3		16
84.83	odd	2		126.2.m.a.83.5	yes	16
252.23	even	6		2646.2.t.a.2285.8		16
252.31	even	6		882.2.l.a.509.6		16
252.59	odd	6		2646.2.l.b.1097.4		16
252.67	odd	6		882.2.l.a.509.7		16
252.83	odd	6		1134.2.d.a.1133.3		16
252.95	even	6		2646.2.l.b.1097.1		16
252.103	even	6		882.2.t.b.815.2		16
252.131	odd	6		2646.2.t.a.2285.5		16
252.139	even	6		126.2.m.a.41.8	yes	16
252.167	odd	6		378.2.m.a.125.4		16
252.223	even	6		1134.2.d.a.1133.14		16
252.247	odd	6		882.2.t.b.815.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	36.31	odd	6
126.2.m.a.41.8	yes	16	252.139	even	6
126.2.m.a.83.5	yes	16	84.83	odd	2
126.2.m.a.83.8	yes	16	12.11	even	2
378.2.m.a.125.1		16	36.23	even	6
378.2.m.a.125.4		16	252.167	odd	6
378.2.m.a.251.1		16	28.27	even	2
378.2.m.a.251.4		16	4.3	odd	2
882.2.l.a.227.2		16	84.23	even	6
882.2.l.a.227.3		16	84.47	odd	6
882.2.l.a.509.6		16	252.31	even	6
882.2.l.a.509.7		16	252.67	odd	6
882.2.t.b.803.2		16	84.11	even	6
882.2.t.b.803.3		16	84.59	odd	6
882.2.t.b.815.2		16	252.103	even	6
882.2.t.b.815.3		16	252.247	odd	6
1008.2.cc.b.209.1		16	3.2	odd	2
1008.2.cc.b.209.8		16	21.20	even	2
1008.2.cc.b.545.1		16	63.13	odd	6
1008.2.cc.b.545.8		16	9.4	even	3
1134.2.d.a.1133.3		16	252.83	odd	6
1134.2.d.a.1133.6		16	36.11	even	6
1134.2.d.a.1133.11		16	36.7	odd	6
1134.2.d.a.1133.14		16	252.223	even	6
2646.2.l.b.521.5		16	28.19	even	6
2646.2.l.b.521.8		16	28.23	odd	6
2646.2.l.b.1097.1		16	252.95	even	6
2646.2.l.b.1097.4		16	252.59	odd	6
2646.2.t.a.1979.5		16	28.11	odd	6
2646.2.t.a.1979.8		16	28.3	even	6
2646.2.t.a.2285.5		16	252.131	odd	6
2646.2.t.a.2285.8		16	252.23	even	6
3024.2.cc.b.881.3		16	9.5	odd	6	inner
3024.2.cc.b.881.6		16	63.41	even	6	inner
3024.2.cc.b.2897.3		16	7.6	odd	2	inner
3024.2.cc.b.2897.6		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.895175 + 1.55049i) q^{5} +(2.30191 - 1.30430i) q^{7} +O(q^{10})\)	\(q+(0.895175 + 1.55049i) q^{5} +(2.30191 - 1.30430i) q^{7} +(-2.07976 - 1.20075i) q^{11} +(-4.23601 + 2.44566i) q^{13} -3.66466 q^{17} -3.01701i q^{19} +(3.26178 - 1.88319i) q^{23} +(0.897324 - 1.55421i) q^{25} +(5.68202 + 3.28052i) q^{29} +(4.02408 - 2.32330i) q^{31} +(4.08292 + 2.40150i) q^{35} +9.36404 q^{37} +(4.04094 + 6.99911i) q^{41} +(3.48127 - 6.02973i) q^{43} +(2.56802 - 4.44794i) q^{47} +(3.59758 - 6.00478i) q^{49} -4.29953i q^{55} +(7.29501 + 12.6353i) q^{59} +(9.81058 + 5.66414i) q^{61} +(-7.58394 - 4.37859i) q^{65} +(0.285115 + 0.493834i) q^{67} +5.96254i q^{71} -12.3814i q^{73} +(-6.35358 - 0.0513786i) q^{77} +(1.51831 - 2.62979i) q^{79} +(-7.00270 + 12.1290i) q^{83} +(-3.28052 - 5.68202i) q^{85} +3.74863 q^{89} +(-6.56103 + 11.1547i) q^{91} +(4.67784 - 2.70075i) q^{95} +(4.77256 + 2.75544i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 16 * q - 2 * q^7	\( 16 q - 2 q^{7} - 12 q^{11} - 48 q^{23} - 8 q^{25} + 12 q^{29} - 8 q^{37} - 4 q^{43} - 8 q^{49} - 84 q^{65} + 28 q^{67} - 78 q^{77} + 4 q^{79} - 12 q^{85} - 24 q^{91} + 12 q^{95}+O(q^{100}) \) 16 * q - 2 * q^7 - 12 * q^11 - 48 * q^23 - 8 * q^25 + 12 * q^29 - 8 * q^37 - 4 * q^43 - 8 * q^49 - 84 * q^65 + 28 * q^67 - 78 * q^77 + 4 * q^79 - 12 * q^85 - 24 * q^91 + 12 * q^95

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