LMFDB - Embedded newform 3024.2.cc.b.881.3

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			881.3
Root			$-1.69547 + 0.354107i$ of defining polynomial
Character	$\chi$	$=$	3024.881
Dual form			3024.2.cc.b.2897.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.895175 + 1.55049i) q^{5} +(-0.0213944 + 2.64566i) q^{7} +O(q^{10})$	$q+(-0.895175 + 1.55049i) q^{5} +(-0.0213944 + 2.64566i) q^{7} +(-2.07976 + 1.20075i) q^{11} +(4.23601 + 2.44566i) q^{13} +3.66466 q^{17} -3.01701i q^{19} +(3.26178 + 1.88319i) q^{23} +(0.897324 + 1.55421i) q^{25} +(5.68202 - 3.28052i) q^{29} +(-4.02408 - 2.32330i) q^{31} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +(-4.04094 + 6.99911i) q^{41} +(3.48127 + 6.02973i) q^{43} +(-2.56802 - 4.44794i) q^{47} +(-6.99908 - 0.113205i) q^{49} -4.29953i q^{55} +(-7.29501 + 12.6353i) q^{59} +(-9.81058 + 5.66414i) q^{61} +(-7.58394 + 4.37859i) q^{65} +(0.285115 - 0.493834i) q^{67} -5.96254i q^{71} -12.3814i q^{73} +(-3.13229 - 5.52805i) q^{77} +(1.51831 + 2.62979i) q^{79} +(7.00270 + 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} -3.74863 q^{89} +(-6.56103 + 11.1547i) q^{91} +(4.67784 + 2.70075i) q^{95} +(-4.77256 + 2.75544i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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	$-0.964439\pi$
$5$	−0.895175	+	1.55049i	−0.400334	+	0.693399i	0.593432	+	0.804884i	$0.297773\pi$
$6$		0			0
$7$	−0.0213944	+	2.64566i	−0.00808631	+	0.999967i
$7$	−0.0213944	+	2.64566i	−0.00808631	+	0.999967i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.07976	+	1.20075i	−0.627072	+	0.362040i	−0.779617	−	0.626256i	$-0.784586\pi$
$11$	−2.07976	+	1.20075i	−0.627072	+	0.362040i	0.152545	+	0.988297i	$0.451253\pi$
$12$		0			0
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.954820	−	0.297186i	$-0.0960482\pi$
$13$	4.23601	+	2.44566i	1.17486	+	0.678305i	0.220039	+	0.975491i	$0.429382\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.66466			0.888812			0.444406	−	0.895826i	$-0.353415\pi$
$17$	3.66466			0.888812			0.444406	+	0.895826i	$0.353415\pi$
$18$		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	0.799904	−	0.600128i	$-0.204884\pi$
$23$	3.26178	+	1.88319i	0.680129	+	0.392673i	−0.119775	+	0.992801i	$0.538217\pi$
$24$		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	0.131045	−	0.991376i	$-0.458167\pi$
$29$	5.68202	−	3.28052i	1.05512	−	0.609176i	0.924080	+	0.382200i	$0.124833\pi$
$30$		0			0
$31$	−4.02408	−	2.32330i	−0.722746	−	0.417278i	0.0930163	−	0.995665i	$-0.470349\pi$
$31$	−4.02408	−	2.32330i	−0.722746	−	0.417278i	−0.815763	+	0.578387i	$0.803682\pi$
$32$		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	0.356241	+	0.934394i	$0.384058\pi$
$41$	−4.04094	+	6.99911i	−0.631088	+	1.09308i	−0.987330	+	0.158683i	$0.949275\pi$
$42$		0			0
$43$	3.48127	+	6.02973i	0.530888	+	0.919526i	0.999350	+	0.0360419i	$0.0114750\pi$
$43$	3.48127	+	6.02973i	0.530888	+	0.919526i	−0.468462	+	0.883484i	$0.655192\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.56802	−	4.44794i	−0.374584	−	0.648799i	0.615680	−	0.787996i	$-0.288881\pi$
$47$	−2.56802	−	4.44794i	−0.374584	−	0.648799i	−0.990265	+	0.139197i	$0.955548\pi$
$48$		0			0
$49$	−6.99908	−	0.113205i	−0.999869	−	0.0161721i
$50$		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	−0.203735	+	0.979026i	$0.565308\pi$
$59$	−7.29501	+	12.6353i	−0.949729	+	1.64498i	−0.745994	+	0.665953i	$0.768025\pi$
$60$		0			0
$61$	−9.81058	+	5.66414i	−1.25612	+	0.725219i	−0.972317	−	0.233665i	$-0.924928\pi$
$61$	−9.81058	+	5.66414i	−1.25612	+	0.725219i	−0.283799	+	0.958884i	$0.591595\pi$
$62$		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	−0.848084	−	0.529862i	$-0.822244\pi$
$67$	0.285115	−	0.493834i	0.0348324	−	0.0603315i	0.882916	+	0.469531i	$0.155577\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	5.96254i		−	0.707623i	−0.935317	−	0.353811i	$-0.884885\pi$
$71$		−	5.96254i		−	0.707623i	0.935317	−	0.353811i	$-0.115115\pi$
$72$		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
$77$	−3.13229	−	5.52805i	−0.356958	−	0.629979i
$78$		0			0
$79$	1.51831	+	2.62979i	0.170824	+	0.295875i	0.938708	−	0.344713i	$-0.112024\pi$
$79$	1.51831	+	2.62979i	0.170824	+	0.295875i	−0.767884	+	0.640588i	$0.778691\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.00270	+	12.1290i	0.768646	+	1.33133i	0.938297	+	0.345830i	$0.112403\pi$
$83$	7.00270	+	12.1290i	0.768646	+	1.33133i	−0.169651	+	0.985504i	$0.554264\pi$
$84$		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	$-0.563664\pi$
$89$	−3.74863			−0.397354			−0.198677	+	0.980065i	$0.563664\pi$
$90$		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	$-0.756926\pi$
$97$	−4.77256	+	2.75544i	−0.484580	+	0.279772i	0.237743	+	0.971328i	$0.423592\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.125162	−	0.216787i	−0.0124541	−	0.0215711i	0.859731	−	0.510747i	$-0.170631\pi$
$101$	−0.125162	−	0.216787i	−0.0124541	−	0.0215711i	−0.872185	+	0.489176i	$0.837298\pi$
$102$		0			0
$103$	0.145433	+	0.0839657i	0.0143299	+	0.00827339i	0.507148	−	0.861859i	$-0.330700\pi$
$103$	0.145433	+	0.0839657i	0.0143299	+	0.00827339i	−0.492818	+	0.870132i	$0.664033\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			7.99080i			0.772500i	0.922394	+	0.386250i	$0.126230\pi$
$107$			7.99080i			0.772500i	−0.922394	+	0.386250i	$0.873770\pi$
$108$		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	0.546488	−	0.837467i	$-0.315964\pi$
$113$	1.00418	+	0.579764i	0.0944653	+	0.0545396i	−0.452023	+	0.892006i	$0.649298\pi$
$114$		0			0
$115$	−5.83973	+	3.37157i	−0.544558	+	0.314401i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.0784032	+	9.69548i	−0.00718721	+	0.888783i
$120$		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	$-0.681779\pi$
$131$	5.24589	−	9.08614i	0.458335	−	0.793860i	0.998873	+	0.0474597i	$0.0151126\pi$
$132$		0			0
$133$	7.98200	+	0.0645470i	0.692127	+	0.00559694i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.08812	−	2.36028i	0.349272	−	0.201652i	−0.315093	−	0.949061i	$-0.602036\pi$
$137$	4.08812	−	2.36028i	0.349272	−	0.201652i	0.664365	+	0.747409i	$0.268702\pi$
$138$		0			0
$139$	−2.04707	−	1.18187i	−0.173630	−	0.100245i	0.410666	−	0.911786i	$-0.365296\pi$
$139$	−2.04707	−	1.18187i	−0.173630	−	0.100245i	−0.584296	+	0.811540i	$0.698629\pi$
$140$		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	0.967433	−	0.253126i	$-0.0814587\pi$
$149$	15.0377	+	8.68202i	1.23194	+	0.711259i	0.264503	+	0.964385i	$0.414792\pi$
$150$		0			0
$151$	−5.61639	−	9.72787i	−0.457055	−	0.791643i	0.541749	−	0.840541i	$-0.317762\pi$
$151$	−5.61639	−	9.72787i	−0.457055	−	0.791643i	−0.998804	+	0.0488977i	$0.984429\pi$
$152$		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	$-0.519621\pi$
$157$	−11.9885	−	6.92154i	−0.956783	−	0.552399i	−0.895181	+	0.445702i	$0.852954\pi$
$158$		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	$-0.673841\pi$
$167$	6.20756	−	10.7518i	0.480355	−	0.832000i	0.999746	+	0.0225370i	$0.00717435\pi$
$168$		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	0.980052	+	0.198739i	$0.0636846\pi$
$173$	8.70908	+	15.0846i	0.662139	+	1.14686i	−0.317913	+	0.948120i	$0.602982\pi$
$174$		0			0
$175$	−4.13112	+	2.34077i	−0.312283	+	0.176945i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	13.1221i		−	0.980789i	−0.871501	−	0.490395i	$-0.836853\pi$
$179$		−	13.1221i		−	0.980789i	0.871501	−	0.490395i	$-0.163147\pi$
$180$		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	−0.761072	−	0.648668i	$-0.775326\pi$
$191$	−8.01361	+	4.62666i	−0.579845	+	0.334774i	0.181227	+	0.983441i	$0.441993\pi$
$192$		0			0
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.0370176	−	0.999315i	$-0.488214\pi$
$193$	12.2801	−	21.2698i	0.883941	−	1.53103i	0.846923	−	0.531716i	$-0.178452\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	12.4861i		−	0.889598i	−0.895630	−	0.444799i	$-0.853275\pi$
$197$		−	12.4861i		−	0.889598i	0.895630	−	0.444799i	$-0.146725\pi$
$198$		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
$203$	8.55758	+	15.1029i	0.600625	+	1.06002i
$204$		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	0.479192	+	0.877710i	$0.340930\pi$
$211$	−7.56103	+	13.0961i	−0.520523	+	0.901572i	−0.999715	+	0.0238622i	$0.992404\pi$
$212$		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	$-0.757364\pi$
$223$	−7.27049	+	4.19762i	−0.486868	+	0.281093i	0.236406	+	0.971654i	$0.424030\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.21261	−	2.10030i	−0.0804836	−	0.139402i	0.822974	−	0.568079i	$-0.192313\pi$
$227$	−1.21261	−	2.10030i	−0.0804836	−	0.139402i	−0.903458	+	0.428677i	$0.858980\pi$
$228$		0			0
$229$	−1.74915	−	1.00987i	−0.115587	−	0.0667344i	0.441092	−	0.897462i	$-0.354591\pi$
$229$	−1.74915	−	1.00987i	−0.115587	−	0.0667344i	−0.556679	+	0.830728i	$0.687925\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			12.7289i			0.833899i	0.908930	+	0.416950i	$0.136901\pi$
$233$			12.7289i			0.833899i	−0.908930	+	0.416950i	$0.863099\pi$
$234$		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	0.901513	−	0.432753i	$-0.142458\pi$
$239$	15.1117	+	8.72474i	0.977494	+	0.564356i	0.0759814	+	0.997109i	$0.475791\pi$
$240$		0			0
$241$	−9.90142	+	5.71659i	−0.637807	+	0.368238i	−0.783769	−	0.621052i	$-0.786705\pi$
$241$	−9.90142	+	5.71659i	−0.637807	+	0.368238i	0.145963	+	0.989290i	$0.453372\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.44093	−	10.7507i	0.411496	−	0.686835i
$246$		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	$-0.168364\pi$
$251$	27.3560			1.72669			0.863347	+	0.504611i	$0.168364\pi$
$252$		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	$-0.798549\pi$
$257$	1.74837	−	3.02826i	0.109060	−	0.188898i	0.915390	+	0.402569i	$0.131883\pi$
$258$		0			0
$259$	−0.200338	+	24.7741i	−0.0124484	+	1.53939i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.35150	+	4.82174i	−0.514976	+	0.297321i	−0.734877	−	0.678201i	$-0.762760\pi$
$263$	−8.35150	+	4.82174i	−0.514976	+	0.297321i	0.219901	+	0.975522i	$0.429427\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.91107			−0.421376			−0.210688	−	0.977553i	$-0.567570\pi$
$269$	−6.91107			−0.421376			−0.210688	+	0.977553i	$0.567570\pi$
$270$		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	0.999250	−	0.0387296i	$-0.0123311\pi$
$277$	7.75718	+	13.4358i	0.466084	+	0.807281i	−0.533166	+	0.846011i	$0.678998\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−11.7759	+	6.79883i	−0.702492	+	0.405584i	−0.808275	−	0.588805i	$-0.799599\pi$
$281$	−11.7759	+	6.79883i	−0.702492	+	0.405584i	0.105783	+	0.994389i	$0.466265\pi$
$282$		0			0
$283$	−4.71796	−	2.72392i	−0.280454	−	0.161920i	0.353175	−	0.935557i	$-0.385102\pi$
$283$	−4.71796	−	2.72392i	−0.280454	−	0.161920i	−0.633629	+	0.773637i	$0.718435\pi$
$284$		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	−0.248583	−	0.968610i	$-0.579965\pi$
$293$	12.2311	−	21.1849i	0.714550	−	1.23764i	0.963133	−	0.269026i	$-0.0867017\pi$
$294$		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
$301$	−16.0271	+	9.08127i	−0.923788	+	0.523435i
$302$		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	$-0.733230\pi$
$311$	5.45501	−	9.44836i	0.309325	−	0.535767i	0.978215	+	0.207594i	$0.0665634\pi$
$312$		0			0
$313$	−2.96532	+	1.71203i	−0.167610	+	0.0967694i	−0.581458	−	0.813576i	$-0.697518\pi$
$313$	−2.96532	+	1.71203i	−0.167610	+	0.0967694i	0.413849	+	0.910346i	$0.364184\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.4953	+	9.52357i	−0.926468	+	0.534897i	−0.885693	−	0.464272i	$-0.846316\pi$
$317$	−16.4953	+	9.52357i	−0.926468	+	0.534897i	−0.0407755	+	0.999168i	$0.512983\pi$
$318$		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
$329$	11.8227	−	6.69896i	0.651807	−	0.369326i
$330$		0			0
$331$	0.0366251	+	0.0634366i	0.00201310	+	0.00348679i	0.867030	−	0.498256i	$-0.166026\pi$
$331$	0.0366251	+	0.0634366i	0.00201310	+	0.00348679i	−0.865017	+	0.501742i	$0.832693\pi$
$332$		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	−0.834016	−	0.551741i	$-0.813964\pi$
$337$	1.11639	−	1.93364i	0.0608136	−	0.105332i	0.894829	+	0.446408i	$0.147297\pi$
$338$		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	0.999751	−	0.0223084i	$-0.00710156\pi$
$347$	27.5751	+	15.9205i	1.48031	+	0.854656i	0.480556	+	0.876964i	$0.340435\pi$
$348$		0			0
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	−0.117925	−	0.993022i	$-0.537624\pi$
$349$	12.7613	−	7.36772i	0.683095	−	0.394385i	0.801020	+	0.598637i	$0.204291\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.07979	−	1.87025i	−0.0574713	−	0.0995431i	0.835858	−	0.548945i	$-0.184970\pi$
$353$	−1.07979	−	1.87025i	−0.0574713	−	0.0995431i	−0.893330	+	0.449402i	$0.851637\pi$
$354$		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	$0.330451\pi$
$359$			32.6448i			1.72293i	−0.507820	+	0.861463i	$0.669549\pi$
$360$		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	$-0.384330\pi$
$367$	25.7212	−	14.8501i	1.34264	−	0.775171i	0.987194	+	0.159527i	$0.0509969\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.00836	−	1.74653i	0.0522109	−	0.0904320i	−0.838739	−	0.544534i	$-0.816707\pi$
$373$	1.00836	−	1.74653i	0.0522109	−	0.0904320i	0.890950	+	0.454102i	$0.150040\pi$
$374$		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	$-0.826530\pi$
$383$	0.418256	−	0.724440i	0.0213719	−	0.0370172i	0.876514	+	0.481377i	$0.159863\pi$
$384$		0			0
$385$	11.3751	+	0.0919857i	0.579730	+	0.00468803i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−21.4964	+	12.4109i	−1.08991	+	0.629260i	−0.933552	−	0.358441i	$-0.883308\pi$
$389$	−21.4964	+	12.4109i	−1.08991	+	0.629260i	−0.156357	+	0.987701i	$0.549975\pi$
$390$		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	0.189822	−	0.981819i	$-0.439209\pi$
$401$	−11.3251	−	6.53854i	−0.565548	−	0.326519i	−0.755369	+	0.655300i	$0.772542\pi$
$402$		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	$-0.377284\pi$
$409$	−4.82124	−	2.78354i	−0.238395	−	0.137637i	−0.614439	+	0.788965i	$0.710618\pi$
$410$		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	$-0.964520\pi$
$419$	−8.19938	+	14.2017i	−0.400566	+	0.693800i	0.593228	+	0.805034i	$0.297853\pi$
$420$		0			0
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	0.613893	−	0.789389i	$-0.289603\pi$
$421$	−7.72892	−	13.3869i	−0.376684	−	0.652437i	−0.990578	+	0.136952i	$0.956269\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.28839	+	5.69566i	0.159510	+	0.276280i
$426$		0			0
$427$	−14.7755	−	26.0767i	−0.715038	−	1.26194i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	25.0266i		−	1.20549i	−0.797935	−	0.602744i	$-0.794074\pi$
$431$		−	25.0266i		−	1.20549i	0.797935	−	0.602744i	$-0.205926\pi$
$432$		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	$-0.519086\pi$
$439$	16.2293	−	9.37000i	0.774583	−	0.447206i	0.834507	+	0.550997i	$0.185752\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.04314	+	0.602256i	−0.0495610	+	0.0286141i	−0.524576	−	0.851364i	$-0.675776\pi$
$443$	−1.04314	+	0.602256i	−0.0495610	+	0.0286141i	0.475015	+	0.879978i	$0.342443\pi$
$444$		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	$-0.782055\pi$
$449$		−	26.8022i		−	1.26487i	0.774612	−	0.632436i	$-0.217945\pi$
$450$		0			0
$451$		−	19.4087i		−	0.913918i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−11.4220	−	20.1583i	−0.535473	−	0.945033i
$456$		0			0
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	0.657381	−	0.753559i	$-0.271664\pi$
$457$	−6.92442	−	11.9934i	−0.323911	−	0.561030i	−0.981291	+	0.192529i	$0.938331\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.40241	+	4.16110i	0.111892	+	0.193802i	0.916533	−	0.399959i	$-0.130976\pi$
$461$	2.40241	+	4.16110i	0.111892	+	0.193802i	−0.804641	+	0.593761i	$0.797642\pi$
$462$		0			0
$463$	−10.5194	+	18.2201i	−0.488877	+	0.846760i	−0.999918	−	0.0127960i	$-0.995927\pi$
$463$	−10.5194	+	18.2201i	−0.488877	+	0.846760i	0.511041	+	0.859556i	$0.329260\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.82302			−0.269457			−0.134729	−	0.990883i	$-0.543016\pi$
$467$	−5.82302			−0.269457			−0.134729	+	0.990883i	$0.543016\pi$
$468$		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	−0.990239	−	0.139382i	$-0.955488\pi$
$479$	−13.4781	−	23.3447i	−0.615828	−	1.06665i	0.374411	−	0.927263i	$-0.377845\pi$
$480$		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	−0.999637	−	0.0269544i	$-0.991419\pi$
$491$	−33.7430	−	19.4815i	−1.52280	−	0.879188i	−0.523162	−	0.852234i	$-0.675248\pi$
$492$		0			0
$493$	20.8227	−	12.0220i	0.937807	−	0.541443i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	15.7749	+	0.127565i	0.707600	+	0.00572206i
$498$		0			0
$499$	13.0048	−	22.5250i	0.582176	−	1.00836i	−0.413045	−	0.910711i	$-0.635535\pi$
$499$	13.0048	−	22.5250i	0.582176	−	1.00836i	0.995221	−	0.0976483i	$-0.0311320\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−10.5271			−0.469378			−0.234689	−	0.972070i	$-0.575407\pi$
$503$	−10.5271			−0.469378			−0.234689	+	0.972070i	$0.575407\pi$
$504$		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	$-0.826710\pi$
$509$	0.469435	−	0.813086i	0.0208074	−	0.0360394i	0.876242	+	0.481872i	$0.160043\pi$
$510$		0			0
$511$	32.7571	+	0.264892i	1.44909	+	0.0117181i
$512$		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	$-0.832924\pi$
$521$	−39.5054			−1.73076			−0.865382	+	0.501112i	$0.832924\pi$
$522$		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	0.999620	+	0.0275530i	$0.00877149\pi$
$547$	12.2477	+	21.2136i	0.523672	+	0.907026i	−0.475949	+	0.879473i	$0.657895\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−9.89735	−	17.1427i	−0.421641	−	0.730304i
$552$		0			0
$553$	−6.99004	+	3.96068i	−0.297247	+	0.168425i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			2.54431i			0.107806i	0.998546	+	0.0539030i	$0.0171662\pi$
$557$			2.54431i			0.107806i	−0.998546	+	0.0539030i	$0.982834\pi$
$558$		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	$-0.725190\pi$
$563$	7.90707	−	13.6954i	0.333243	−	0.577194i	0.983146	+	0.182823i	$0.0585236\pi$
$564$		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	−0.379633	−	0.925137i	$-0.623950\pi$
$569$	5.52793	−	3.19155i	0.231743	−	0.133797i	0.611376	+	0.791340i	$0.290616\pi$
$570$		0			0
$571$	−3.91188	+	6.77557i	−0.163707	+	0.283549i	−0.936195	−	0.351480i	$-0.885678\pi$
$571$	−3.91188	+	6.77557i	−0.163707	+	0.283549i	0.772488	+	0.635029i	$0.219012\pi$
$572$		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
$581$	−32.2392	+	18.2673i	−1.33751	+	0.757855i
$582$		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	$-0.135404\pi$
$587$	2.37575	+	4.11492i	0.0980577	+	0.169841i	−0.812823	+	0.582511i	$0.802070\pi$
$588$		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	$-0.476576\pi$
$593$	3.58070			0.147042			0.0735208	+	0.997294i	$0.476576\pi$
$594$		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	0.209183	−	0.977877i	$-0.432920\pi$
$599$	−13.0471	−	7.53277i	−0.533091	−	0.307780i	−0.742274	+	0.670096i	$0.766253\pi$
$600$		0			0
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	−0.0366096	−	0.999330i	$-0.511656\pi$
$601$	19.8704	−	11.4722i	0.810530	−	0.467960i	0.847140	+	0.531370i	$0.178322\pi$
$602$		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	$-0.167816\pi$
$607$	21.2030	+	12.2416i	0.860605	+	0.496870i	−0.00360990	+	0.999993i	$0.501149\pi$
$608$		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	0.717690	−	0.696362i	$-0.245199\pi$
$617$	11.7607	+	6.79005i	0.473468	+	0.273357i	−0.244222	+	0.969719i	$0.578533\pi$
$618$		0			0
$619$	−30.7325	+	17.7434i	−1.23524	+	0.713169i	−0.968118	−	0.250493i	$-0.919407\pi$
$619$	−30.7325	+	17.7434i	−1.23524	+	0.713169i	−0.267126	+	0.963662i	$0.586074\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.0801996	−	9.91762i	0.00321313	−	0.397341i
$624$		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
$637$	−29.3714	−	17.5969i	−1.16374	−	0.697216i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.932777	+	0.538539i	−0.0368425	+	0.0212710i	−0.518308	−	0.855194i	$-0.673438\pi$
$641$	−0.932777	+	0.538539i	−0.0368425	+	0.0212710i	0.481466	+	0.876465i	$0.340105\pi$
$642$		0			0
$643$	33.3126	+	19.2330i	1.31372	+	0.758477i	0.982710	−	0.185150i	$-0.0592773\pi$
$643$	33.3126	+	19.2330i	1.31372	+	0.758477i	0.331010	+	0.943627i	$0.392611\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.95210			0.351943			0.175972	−	0.984395i	$-0.443693\pi$
$647$	8.95210			0.351943			0.175972	+	0.984395i	$0.443693\pi$
$648$		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	0.680350	−	0.732887i	$-0.261828\pi$
$653$	9.85934	+	5.69229i	0.385826	+	0.222757i	−0.294524	+	0.955644i	$0.595161\pi$
$654$		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	0.258723	−	0.965952i	$-0.416698\pi$
$659$	31.4373	−	18.1503i	1.22462	−	0.707036i	0.965900	+	0.258915i	$0.0833650\pi$
$660$		0			0
$661$	31.2425	+	18.0379i	1.21519	+	0.701593i	0.963886	−	0.266315i	$-0.0858060\pi$
$661$	31.2425	+	18.0379i	1.21519	+	0.701593i	0.251308	+	0.967907i	$0.419139\pi$
$662$		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	0.943392	−	0.331680i	$-0.107615\pi$
$673$	4.78512	+	8.28806i	0.184453	+	0.319481i	−0.758939	+	0.651161i	$0.774282\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.81408	+	13.5344i	0.300320	+	0.520169i	0.976208	−	0.216835i	$-0.0695733\pi$
$677$	7.81408	+	13.5344i	0.300320	+	0.520169i	−0.675889	+	0.737004i	$0.736240\pi$
$678$		0			0
$679$	−7.18786	−	12.6855i	−0.275845	−	0.486826i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			11.1313i			0.425926i	0.977060	+	0.212963i	$0.0683114\pi$
$683$			11.1313i			0.425926i	−0.977060	+	0.212963i	$0.931689\pi$
$684$		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	$-0.648346\pi$
$691$	2.61903	−	1.51210i	0.0996324	−	0.0575228i	0.548988	+	0.835830i	$0.315013\pi$
$692$		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	$-0.604054\pi$
$701$		−	50.1486i		−	1.89409i	0.321103	−	0.947044i	$-0.395946\pi$
$702$		0			0
$703$		−	28.2514i		−	1.06552i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.576224	−	0.326499i	0.0216711	−	0.0122793i
$708$		0			0
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	0.897908	−	0.440183i	$-0.145086\pi$
$709$	1.80385	+	3.12436i	0.0677449	+	0.117338i	−0.830163	+	0.557520i	$0.811753\pi$
$710$		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	$-0.278981\pi$
$719$	34.3161			1.27977			0.639887	+	0.768469i	$0.278981\pi$
$720$		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	$-0.529738\pi$
$727$	19.4757	−	11.2443i	0.722315	−	0.417029i	0.815604	+	0.578610i	$0.196405\pi$
$728$		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	$-0.528686\pi$
$733$	−27.0065	−	15.5922i	−0.997509	−	0.575912i	−0.907510	+	0.420030i	$0.862020\pi$
$734$		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	0.466947	−	0.884285i	$-0.345354\pi$
$743$	−1.78246	−	1.02910i	−0.0653921	−	0.0377542i	−0.532340	+	0.846531i	$0.678687\pi$
$744$		0			0
$745$	−26.9227	+	15.5439i	−0.986373	+	0.569483i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−21.1410	−	0.170958i	−0.772475	−	0.00624667i
$750$		0			0
$751$	11.9053	−	20.6205i	0.434429	−	0.752454i	−0.562820	−	0.826580i	$-0.690283\pi$
$751$	11.9053	−	20.6205i	0.434429	−	0.752454i	0.997249	+	0.0741262i	$0.0236168\pi$
$752$		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	−0.494775	−	0.869021i	$-0.664750\pi$
$761$	13.9368	−	24.1392i	0.505207	−	0.875044i	0.999982	−	0.00602283i	$-0.00191714\pi$
$762$		0			0
$763$	0.405495	−	50.1442i	0.0146799	−	1.81534i
$764$		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	$-0.292052\pi$
$769$	6.21166	+	3.58631i	0.223998	+	0.129326i	−0.383802	+	0.923415i	$0.625385\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.14153			−0.0770255			−0.0385128	−	0.999258i	$-0.512262\pi$
$773$	−2.14153			−0.0770255			−0.0385128	+	0.999258i	$0.512262\pi$
$774$		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	$-0.227247\pi$
$787$	15.8961	+	9.17759i	0.566633	+	0.327146i	−0.189170	+	0.981944i	$0.560580\pi$
$788$		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	$-0.688301\pi$
$797$	12.4226	−	21.5166i	0.440031	−	0.762156i	0.997691	+	0.0679130i	$0.0216340\pi$
$798$		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
$805$	−8.79511	−	15.5221i	−0.309987	−	0.547082i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			37.7861i			1.32849i	0.747516	+	0.664244i	$0.231246\pi$
$809$			37.7861i			1.32849i	−0.747516	+	0.664244i	$0.768754\pi$
$810$		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	−0.400547	−	0.916276i	$-0.631180\pi$
$821$	5.52142	−	3.18779i	0.192699	−	0.111255i	0.593245	+	0.805022i	$0.297846\pi$
$822$		0			0
$823$	14.0293	−	24.2995i	0.489032	−	0.847028i	−0.510888	−	0.859647i	$-0.670683\pi$
$823$	14.0293	−	24.2995i	0.489032	−	0.847028i	0.999920	+	0.0126187i	$0.00401678\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	0.581579i		−	0.0202235i	−0.999949	−	0.0101117i	$-0.996781\pi$
$827$		−	0.581579i		−	0.0202235i	0.999949	−	0.0101117i	$-0.00321872\pi$
$828$		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
$833$	−25.6493	−	0.414857i	−0.888696	−	0.0143739i
$834$		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	$-0.129987\pi$
$839$	3.33038	+	5.76838i	0.114977	+	0.199147i	−0.802793	+	0.596257i	$0.796654\pi$
$840$		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	$-0.542551\pi$
$853$	19.2287	−	11.1017i	0.658378	−	0.380115i	0.791659	+	0.610964i	$0.209218\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.64830	−	13.2472i	−0.261261	−	0.452517i	0.705316	−	0.708893i	$-0.250805\pi$
$857$	−7.64830	−	13.2472i	−0.261261	−	0.452517i	−0.966577	+	0.256375i	$0.917472\pi$
$858$		0			0
$859$	3.68620	+	2.12823i	0.125772	+	0.0726143i	0.561566	−	0.827432i	$-0.310199\pi$
$859$	3.68620	+	2.12823i	0.125772	+	0.0726143i	−0.435794	+	0.900046i	$0.643532\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	23.6624i		−	0.805476i	−0.915315	−	0.402738i	$-0.868059\pi$
$863$		−	23.6624i		−	0.805476i	0.915315	−	0.402738i	$-0.131941\pi$
$864$		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
$875$	0.260258	−	32.1840i	0.00879833	−	1.08802i
$876$		0			0
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	−0.640927	−	0.767602i	$-0.721450\pi$
$877$	10.1962	−	17.6603i	0.344300	−	0.596344i	0.985226	+	0.171258i	$0.0547831\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	32.4586			1.09356			0.546780	−	0.837276i	$-0.315853\pi$
$881$	32.4586			1.09356			0.546780	+	0.837276i	$0.315853\pi$
$882$		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	$-0.781151\pi$
$887$	4.86059	−	8.41879i	0.163203	−	0.282675i	0.936016	+	0.351959i	$0.114484\pi$
$888$		0			0
$889$	0.0299843	−	3.70791i	0.00100564	−	0.124359i
$890$		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	0.701035	−	0.713127i	$-0.252722\pi$
$907$	−8.04314	−	13.9311i	−0.267068	−	0.462575i	−0.968103	+	0.250551i	$0.919388\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	27.0087	−	15.5935i	0.894838	−	0.516635i	0.0193161	−	0.999813i	$-0.493851\pi$
$911$	27.0087	−	15.5935i	0.894838	−	0.516635i	0.875522	+	0.483179i	$0.160518\pi$
$912$		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	−0.829891	−	0.557926i	$-0.811597\pi$
$929$	−27.3744	−	47.4138i	−0.898124	−	1.55560i	−0.0682329	−	0.997669i	$-0.521736\pi$
$930$		0			0
$931$	−0.341540	+	21.1163i	−0.0111935	+	0.692059i
$932$		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	−0.455423	−	0.890275i	$-0.650512\pi$
$941$	16.6658	−	28.8660i	0.543289	−	0.941005i	0.998712	−	0.0507297i	$-0.0161547\pi$
$942$		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	−0.603312	−	0.797505i	$-0.706153\pi$
$947$	−6.59497	+	3.80761i	−0.214308	+	0.123731i	0.389004	+	0.921236i	$0.372819\pi$
$948$		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	$0.359044\pi$
$953$			55.7861i			1.80709i	−0.428495	+	0.903544i	$0.640956\pi$
$954$		0			0
$955$		−	16.5667i		−	0.536085i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.15705	+	10.8663i	0.198821	+	0.350891i
$960$		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	−0.567887	−	0.823106i	$-0.692239\pi$
$967$	13.3369	−	23.1003i	0.428887	−	0.742855i	0.996775	+	0.0802517i	$0.0255724\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.59942			0.275968			0.137984	−	0.990434i	$-0.455938\pi$
$971$	8.59942			0.275968			0.137984	+	0.990434i	$0.455938\pi$
$972$		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	0.690542	−	0.723293i	$-0.257372\pi$
$977$	12.7973	+	7.38854i	0.409423	+	0.236380i	−0.281119	+	0.959673i	$0.590705\pi$
$978$		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	$-0.272752\pi$
$983$	−10.2568	−	17.7652i	−0.327140	−	0.566623i	−0.981943	+	0.189176i	$0.939418\pi$
$984$		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	$-0.666566\pi$
$997$	0.0172917	−	0.00998339i	0.000547635	−	0.000316177i	0.500274	+	0.865867i	$0.333233\pi$
$998$		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.881.3		16
3.2	odd	2		1008.2.cc.b.545.8		16
4.3	odd	2		378.2.m.a.125.1		16
7.6	odd	2	inner	3024.2.cc.b.881.6		16
9.2	odd	6	inner	3024.2.cc.b.2897.6		16
9.7	even	3		1008.2.cc.b.209.1		16
12.11	even	2		126.2.m.a.41.5	✓	16
21.20	even	2		1008.2.cc.b.545.1		16
28.3	even	6		2646.2.l.b.1097.4		16
28.11	odd	6		2646.2.l.b.1097.1		16
28.19	even	6		2646.2.t.a.2285.5		16
28.23	odd	6		2646.2.t.a.2285.8		16
28.27	even	2		378.2.m.a.125.4		16
36.7	odd	6		126.2.m.a.83.8	yes	16
36.11	even	6		378.2.m.a.251.4		16
36.23	even	6		1134.2.d.a.1133.11		16
36.31	odd	6		1134.2.d.a.1133.6		16
63.20	even	6	inner	3024.2.cc.b.2897.3		16
63.34	odd	6		1008.2.cc.b.209.8		16
84.11	even	6		882.2.l.a.509.7		16
84.23	even	6		882.2.t.b.815.3		16
84.47	odd	6		882.2.t.b.815.2		16
84.59	odd	6		882.2.l.a.509.6		16
84.83	odd	2		126.2.m.a.41.8	yes	16
252.11	even	6		2646.2.t.a.1979.5		16
252.47	odd	6		2646.2.l.b.521.5		16
252.79	odd	6		882.2.l.a.227.2		16
252.83	odd	6		378.2.m.a.251.1		16
252.115	even	6		882.2.t.b.803.3		16
252.139	even	6		1134.2.d.a.1133.3		16
252.151	odd	6		882.2.t.b.803.2		16
252.167	odd	6		1134.2.d.a.1133.14		16
252.187	even	6		882.2.l.a.227.3		16
252.191	even	6		2646.2.l.b.521.8		16
252.223	even	6		126.2.m.a.83.5	yes	16
252.227	odd	6		2646.2.t.a.1979.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.5	✓	16	12.11	even	2
126.2.m.a.41.8	yes	16	84.83	odd	2
126.2.m.a.83.5	yes	16	252.223	even	6
126.2.m.a.83.8	yes	16	36.7	odd	6
378.2.m.a.125.1		16	4.3	odd	2
378.2.m.a.125.4		16	28.27	even	2
378.2.m.a.251.1		16	252.83	odd	6
378.2.m.a.251.4		16	36.11	even	6
882.2.l.a.227.2		16	252.79	odd	6
882.2.l.a.227.3		16	252.187	even	6
882.2.l.a.509.6		16	84.59	odd	6
882.2.l.a.509.7		16	84.11	even	6
882.2.t.b.803.2		16	252.151	odd	6
882.2.t.b.803.3		16	252.115	even	6
882.2.t.b.815.2		16	84.47	odd	6
882.2.t.b.815.3		16	84.23	even	6
1008.2.cc.b.209.1		16	9.7	even	3
1008.2.cc.b.209.8		16	63.34	odd	6
1008.2.cc.b.545.1		16	21.20	even	2
1008.2.cc.b.545.8		16	3.2	odd	2
1134.2.d.a.1133.3		16	252.139	even	6
1134.2.d.a.1133.6		16	36.31	odd	6
1134.2.d.a.1133.11		16	36.23	even	6
1134.2.d.a.1133.14		16	252.167	odd	6
2646.2.l.b.521.5		16	252.47	odd	6
2646.2.l.b.521.8		16	252.191	even	6
2646.2.l.b.1097.1		16	28.11	odd	6
2646.2.l.b.1097.4		16	28.3	even	6
2646.2.t.a.1979.5		16	252.11	even	6
2646.2.t.a.1979.8		16	252.227	odd	6
2646.2.t.a.2285.5		16	28.19	even	6
2646.2.t.a.2285.8		16	28.23	odd	6
3024.2.cc.b.881.3		16	1.1	even	1	trivial
3024.2.cc.b.881.6		16	7.6	odd	2	inner
3024.2.cc.b.2897.3		16	63.20	even	6	inner
3024.2.cc.b.2897.6		16	9.2	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.895175 + 1.55049i) q^{5} +(-0.0213944 + 2.64566i) q^{7} +O(q^{10})\)	\(q+(-0.895175 + 1.55049i) q^{5} +(-0.0213944 + 2.64566i) q^{7} +(-2.07976 + 1.20075i) q^{11} +(4.23601 + 2.44566i) q^{13} +3.66466 q^{17} -3.01701i q^{19} +(3.26178 + 1.88319i) q^{23} +(0.897324 + 1.55421i) q^{25} +(5.68202 - 3.28052i) q^{29} +(-4.02408 - 2.32330i) q^{31} +(-4.08292 - 2.40150i) q^{35} +9.36404 q^{37} +(-4.04094 + 6.99911i) q^{41} +(3.48127 + 6.02973i) q^{43} +(-2.56802 - 4.44794i) q^{47} +(-6.99908 - 0.113205i) q^{49} -4.29953i q^{55} +(-7.29501 + 12.6353i) q^{59} +(-9.81058 + 5.66414i) q^{61} +(-7.58394 + 4.37859i) q^{65} +(0.285115 - 0.493834i) q^{67} -5.96254i q^{71} -12.3814i q^{73} +(-3.13229 - 5.52805i) q^{77} +(1.51831 + 2.62979i) q^{79} +(7.00270 + 12.1290i) q^{83} +(-3.28052 + 5.68202i) q^{85} -3.74863 q^{89} +(-6.56103 + 11.1547i) q^{91} +(4.67784 + 2.70075i) q^{95} +(-4.77256 + 2.75544i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{7}+O(q^{10}) \) 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

Introduction

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