LMFDB - Embedded newform 1224.1.cx.a.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1224,1,Mod(11,1224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1224, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([24, 24, 8, 21]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("1224.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1224 = 2^{3} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1224.cx (of order $48$, degree $16$, 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:	$0.610855575463$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{48}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{48} - \cdots)$

Embedding invariants

Embedding label			419.1
Root			$0.793353 - 0.608761i$ of defining polynomial
Character	$\chi$	$=$	1224.419
Dual form			1224.1.cx.a.371.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.991445 + 0.130526i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.965926 - 0.258819i) q^{4} +(0.991445 + 0.130526i) q^{6} +(-0.923880 + 0.382683i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.608761 + 0.206647i) q^{11} -1.00000 q^{12} +(0.866025 - 0.500000i) q^{16} +(0.130526 + 0.991445i) q^{17} +(-0.923880 - 0.382683i) q^{18} +(0.478235 + 0.198092i) q^{19} +(0.576581 - 0.284338i) q^{22} +(0.991445 - 0.130526i) q^{24} +(-0.608761 + 0.793353i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-0.793353 + 0.608761i) q^{32} +(0.641502 - 0.0420463i) q^{33} +(-0.258819 - 0.965926i) q^{34} +(0.965926 + 0.258819i) q^{36} +(-0.500000 - 0.133975i) q^{38} +(1.88981 - 0.123864i) q^{41} +(-0.207107 - 0.158919i) q^{43} +(-0.534534 + 0.357164i) q^{44} +(-0.965926 + 0.258819i) q^{48} +(0.608761 + 0.793353i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.130526 - 0.991445i) q^{51} +(0.793353 + 0.608761i) q^{54} +(-0.410670 - 0.315118i) q^{57} +(-0.158919 + 1.20711i) q^{59} +(0.707107 - 0.707107i) q^{64} +(-0.630526 + 0.125419i) q^{66} +(1.71723 + 0.991445i) q^{67} +(0.382683 + 0.923880i) q^{68} +(-0.991445 - 0.130526i) q^{72} +(1.25026 + 0.835400i) q^{73} +(0.793353 - 0.608761i) q^{75} +(0.513210 + 0.0675653i) q^{76} +(0.500000 + 0.866025i) q^{81} +(-1.85747 + 0.369474i) q^{82} +(0.241181 + 1.83195i) q^{83} +(0.226078 + 0.130526i) q^{86} +(0.483342 - 0.423880i) q^{88} +(0.541196 - 0.541196i) q^{89} +(0.923880 - 0.382683i) q^{96} +(-1.78990 - 0.117317i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-0.630526 - 0.125419i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{12} - 8 q^{38} + 8 q^{43} + 8 q^{50} - 8 q^{66} + 8 q^{81} + 8 q^{83} - 8 q^{99}+O(q^{100}) $ 16 * q - 16 * q^12 - 8 * q^38 + 8 * q^43 + 8 * q^50 - 8 * q^66 + 8 * q^81 + 8 * q^83 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1224\mathbb{Z}\right)^\times$.

$n$	$137$	$613$	$649$	$919$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$-1$

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 $

$2$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$2$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$3$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$3$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$4$	0.965926	−	0.258819i	0.965926	−	0.258819i
$5$		0			0		−0.442289	−	0.896873i	$-0.645833\pi$
$5$		0			0		0.442289	+	0.896873i	$0.354167\pi$
$6$	0.991445	+	0.130526i	0.991445	+	0.130526i
$7$		0			0		−0.896873	−	0.442289i	$-0.854167\pi$
$7$		0			0		0.896873	+	0.442289i	$0.145833\pi$
$8$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$9$	0.866025	+	0.500000i	0.866025	+	0.500000i
$10$		0			0
$11$	−0.608761	+	0.206647i	−0.608761	+	0.206647i	−0.608761	−	0.793353i	$-0.708333\pi$
$11$	−0.608761	+	0.206647i	−0.608761	+	0.206647i			1.00000i	$0.5\pi$
$12$	−1.00000			−1.00000
$13$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$13$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$14$		0			0
$15$		0			0
$16$	0.866025	−	0.500000i	0.866025	−	0.500000i
$17$	0.130526	+	0.991445i	0.130526	+	0.991445i
$17$	0.130526	+	0.991445i	0.130526	+	0.991445i
$18$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$19$	0.478235	+	0.198092i	0.478235	+	0.198092i	0.608761	−	0.793353i	$-0.291667\pi$
$19$	0.478235	+	0.198092i	0.478235	+	0.198092i	−0.130526	+	0.991445i	$0.541667\pi$
$20$		0			0
$21$		0			0
$22$	0.576581	−	0.284338i	0.576581	−	0.284338i
$23$		0			0		0.659346	−	0.751840i	$-0.270833\pi$
$23$		0			0		−0.659346	+	0.751840i	$0.729167\pi$
$24$	0.991445	−	0.130526i	0.991445	−	0.130526i
$25$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$28$		0			0
$29$		0			0		0.0654031	−	0.997859i	$-0.479167\pi$
$29$		0			0		−0.0654031	+	0.997859i	$0.520833\pi$
$30$		0			0
$31$		0			0		0.321439	−	0.946930i	$-0.395833\pi$
$31$		0			0		−0.321439	+	0.946930i	$0.604167\pi$
$32$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$33$	0.641502	−	0.0420463i	0.641502	−	0.0420463i
$34$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$35$		0			0
$36$	0.965926	+	0.258819i	0.965926	+	0.258819i
$37$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$37$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$38$	−0.500000	−	0.133975i	−0.500000	−	0.133975i
$39$		0			0
$40$		0			0
$41$	1.88981	−	0.123864i	1.88981	−	0.123864i	0.923880	−	0.382683i	$-0.125000\pi$
$41$	1.88981	−	0.123864i	1.88981	−	0.123864i	0.965926	+	0.258819i	$0.0833333\pi$
$42$		0			0
$43$	−0.207107	−	0.158919i	−0.207107	−	0.158919i	0.500000	−	0.866025i	$-0.333333\pi$
$43$	−0.207107	−	0.158919i	−0.207107	−	0.158919i	−0.707107	+	0.707107i	$0.750000\pi$
$44$	−0.534534	+	0.357164i	−0.534534	+	0.357164i
$45$		0			0
$46$		0			0
$47$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$47$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$48$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$49$	0.608761	+	0.793353i	0.608761	+	0.793353i
$50$	0.500000	−	0.866025i	0.500000	−	0.866025i
$51$	0.130526	−	0.991445i	0.130526	−	0.991445i
$52$		0			0
$53$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$53$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$54$	0.793353	+	0.608761i	0.793353	+	0.608761i
$55$		0			0
$56$		0			0
$57$	−0.410670	−	0.315118i	−0.410670	−	0.315118i
$58$		0			0
$59$	−0.158919	+	1.20711i	−0.158919	+	1.20711i	0.707107	+	0.707107i	$0.250000\pi$
$59$	−0.158919	+	1.20711i	−0.158919	+	1.20711i	−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$		0			0		0.442289	−	0.896873i	$-0.354167\pi$
$61$		0			0		−0.442289	+	0.896873i	$0.645833\pi$
$62$		0			0
$63$		0			0
$64$	0.707107	−	0.707107i	0.707107	−	0.707107i
$65$		0			0
$66$	−0.630526	+	0.125419i	−0.630526	+	0.125419i
$67$	1.71723	+	0.991445i	1.71723	+	0.991445i	0.923880	+	0.382683i	$0.125000\pi$
$67$	1.71723	+	0.991445i	1.71723	+	0.991445i	0.793353	+	0.608761i	$0.208333\pi$
$68$	0.382683	+	0.923880i	0.382683	+	0.923880i
$69$		0			0
$70$		0			0
$71$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$71$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$72$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$73$	1.25026	+	0.835400i	1.25026	+	0.835400i	0.991445	−	0.130526i	$-0.0416667\pi$
$73$	1.25026	+	0.835400i	1.25026	+	0.835400i	0.258819	+	0.965926i	$0.416667\pi$
$74$		0			0
$75$	0.793353	−	0.608761i	0.793353	−	0.608761i
$76$	0.513210	+	0.0675653i	0.513210	+	0.0675653i
$77$		0			0
$78$		0			0
$79$		0			0		−0.321439	−	0.946930i	$-0.604167\pi$
$79$		0			0		0.321439	+	0.946930i	$0.395833\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.500000	+	0.866025i
$82$	−1.85747	+	0.369474i	−1.85747	+	0.369474i
$83$	0.241181	+	1.83195i	0.241181	+	1.83195i	0.500000	+	0.866025i	$0.333333\pi$
$83$	0.241181	+	1.83195i	0.241181	+	1.83195i	−0.258819	+	0.965926i	$0.583333\pi$
$84$		0			0
$85$		0			0
$86$	0.226078	+	0.130526i	0.226078	+	0.130526i
$87$		0			0
$88$	0.483342	−	0.423880i	0.483342	−	0.423880i
$89$	0.541196	−	0.541196i	0.541196	−	0.541196i	−0.382683	−	0.923880i	$-0.625000\pi$
$89$	0.541196	−	0.541196i	0.541196	−	0.541196i	0.923880	+	0.382683i	$0.125000\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.923880	−	0.382683i	0.923880	−	0.382683i
$97$	−1.78990	−	0.117317i	−1.78990	−	0.117317i	−0.866025	−	0.500000i	$-0.833333\pi$
$97$	−1.78990	−	0.117317i	−1.78990	−	0.117317i	−0.923880	+	0.382683i	$0.875000\pi$
$98$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$99$	−0.630526	−	0.125419i	−0.630526	−	0.125419i
$100$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$			1.00000i			1.00000i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.491445	−	0.735499i	0.491445	−	0.735499i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	0.491445	−	0.735499i	0.491445	−	0.735499i	0.991445	+	0.130526i	$0.0416667\pi$
$108$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$109$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$109$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.835400	−	0.732626i	−0.835400	−	0.732626i	0.130526	−	0.991445i	$-0.458333\pi$
$113$	−0.835400	−	0.732626i	−0.835400	−	0.732626i	−0.965926	+	0.258819i	$0.916667\pi$
$114$	0.448288	+	0.258819i	0.448288	+	0.258819i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		−	1.21752i		−	1.21752i
$119$		0			0
$120$		0			0
$121$	−0.465466	+	0.357164i	−0.465466	+	0.357164i
$122$		0			0
$123$	−1.85747	−	0.369474i	−1.85747	−	0.369474i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$127$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$128$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$129$	0.158919	+	0.207107i	0.158919	+	0.207107i
$130$		0			0
$131$	0.349942	−	0.172572i	0.349942	−	0.172572i	−0.258819	−	0.965926i	$-0.583333\pi$
$131$	0.349942	−	0.172572i	0.349942	−	0.172572i	0.608761	+	0.793353i	$0.291667\pi$
$132$	0.608761	−	0.206647i	0.608761	−	0.206647i
$133$		0			0
$134$	−1.83195	−	0.758819i	−1.83195	−	0.758819i
$135$		0			0
$136$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$137$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$137$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$138$		0			0
$139$	−0.123864	−	0.0420463i	−0.123864	−	0.0420463i	0.258819	−	0.965926i	$-0.416667\pi$
$139$	−0.123864	−	0.0420463i	−0.123864	−	0.0420463i	−0.382683	+	0.923880i	$0.625000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.00000			1.00000
$145$		0			0
$146$	−1.34861	−	0.665060i	−1.34861	−	0.665060i
$147$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$148$		0			0
$149$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$149$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$150$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$151$		0			0		0.991445	−	0.130526i	$-0.0416667\pi$
$151$		0			0		−0.991445	+	0.130526i	$0.958333\pi$
$152$	−0.517638			−0.517638
$153$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$157$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$163$	−0.923880	−	1.38268i	−0.923880	−	1.38268i	−0.923880	−	0.382683i	$-0.875000\pi$
$163$	−0.923880	−	1.38268i	−0.923880	−	1.38268i		−	1.00000i	$-0.5\pi$
$164$	1.79335	−	0.608761i	1.79335	−	0.608761i
$165$		0			0
$166$	−0.478235	−	1.78480i	−0.478235	−	1.78480i
$167$		0			0		−0.946930	−	0.321439i	$-0.895833\pi$
$167$		0			0		0.946930	+	0.321439i	$0.104167\pi$
$168$		0			0
$169$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$170$		0			0
$171$	0.315118	+	0.410670i	0.315118	+	0.410670i
$172$	−0.241181	−	0.0999004i	−0.241181	−	0.0999004i
$173$		0			0		−0.659346	−	0.751840i	$-0.729167\pi$
$173$		0			0		0.659346	+	0.751840i	$0.270833\pi$
$174$		0			0
$175$		0			0
$176$	−0.423880	+	0.483342i	−0.423880	+	0.483342i
$177$	0.465926	−	1.12484i	0.465926	−	1.12484i
$178$	−0.465926	+	0.607206i	−0.465926	+	0.607206i
$179$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	−0.923880	−	0.382683i	$-0.875000\pi$
$179$	−0.541196	−	1.30656i	−0.541196	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$180$		0			0
$181$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$181$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.284338	−	0.576581i	−0.284338	−	0.576581i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$191$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$192$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$193$	−1.50046	−	1.31587i	−1.50046	−	1.31587i	−0.793353	−	0.608761i	$-0.791667\pi$
$193$	−1.50046	−	1.31587i	−1.50046	−	1.31587i	−0.707107	−	0.707107i	$-0.750000\pi$
$194$	1.78990	−	0.117317i	1.78990	−	0.117317i
$195$		0			0
$196$	0.793353	+	0.608761i	0.793353	+	0.608761i
$197$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$197$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$198$	0.641502	+	0.0420463i	0.641502	+	0.0420463i
$199$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$199$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$200$	0.258819	−	0.965926i	0.258819	−	0.965926i
$201$	−1.40211	−	1.40211i	−1.40211	−	1.40211i
$202$		0			0
$203$		0			0
$204$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.332066	−	0.0217648i	−0.332066	−	0.0217648i
$210$		0			0
$211$	0.0255190	+	0.389345i	0.0255190	+	0.389345i	0.991445	+	0.130526i	$0.0416667\pi$
$211$	0.0255190	+	0.389345i	0.0255190	+	0.389345i	−0.965926	+	0.258819i	$0.916667\pi$
$212$		0			0
$213$		0			0
$214$	−0.391239	+	0.793353i	−0.391239	+	0.793353i
$215$		0			0
$216$	0.923880	+	0.382683i	0.923880	+	0.382683i
$217$		0			0
$218$		0			0
$219$	−0.991445	−	1.13053i	−0.991445	−	1.13053i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.130526	−	0.991445i	$-0.541667\pi$
$223$		0			0		0.130526	+	0.991445i	$0.458333\pi$
$224$		0			0
$225$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$226$	0.923880	+	0.617317i	0.923880	+	0.617317i
$227$	0.641502	+	1.88981i	0.641502	+	1.88981i	0.382683	+	0.923880i	$0.375000\pi$
$227$	0.641502	+	1.88981i	0.641502	+	1.88981i	0.258819	+	0.965926i	$0.416667\pi$
$228$	−0.478235	−	0.198092i	−0.478235	−	0.198092i
$229$		0			0		−0.991445	−	0.130526i	$-0.958333\pi$
$229$		0			0		0.991445	+	0.130526i	$0.0416667\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.108761	+	0.0726721i	0.108761	+	0.0726721i	0.608761	−	0.793353i	$-0.291667\pi$
$233$	0.108761	+	0.0726721i	0.108761	+	0.0726721i	−0.500000	+	0.866025i	$0.666667\pi$
$234$		0			0
$235$		0			0
$236$	0.158919	+	1.20711i	0.158919	+	1.20711i
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$	−0.991445	+	0.869474i	−0.991445	+	0.869474i	−0.991445	−	0.130526i	$-0.958333\pi$
$241$	−0.991445	+	0.869474i	−0.991445	+	0.869474i			1.00000i	$0.5\pi$
$242$	0.414864	−	0.414864i	0.414864	−	0.414864i
$243$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$244$		0			0
$245$		0			0
$246$	1.88981	+	0.123864i	1.88981	+	0.123864i
$247$		0			0
$248$		0			0
$249$	0.241181	−	1.83195i	0.241181	−	1.83195i
$250$		0			0
$251$	−1.12197	−	1.12197i	−1.12197	−	1.12197i	−0.991445	−	0.130526i	$-0.958333\pi$
$251$	−1.12197	−	1.12197i	−1.12197	−	1.12197i	−0.130526	−	0.991445i	$-0.541667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.500000	−	0.866025i	0.500000	−	0.866025i
$257$	−0.965926	−	1.25882i	−0.965926	−	1.25882i	−0.965926	−	0.258819i	$-0.916667\pi$
$257$	−0.965926	−	1.25882i	−0.965926	−	1.25882i		−	1.00000i	$-0.5\pi$
$258$	−0.184592	−	0.184592i	−0.184592	−	0.184592i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.324423	+	0.216773i	−0.324423	+	0.216773i
$263$		0			0		−0.793353	−	0.608761i	$-0.791667\pi$
$263$		0			0		0.793353	+	0.608761i	$0.208333\pi$
$264$	−0.576581	+	0.284338i	−0.576581	+	0.284338i
$265$		0			0
$266$		0			0
$267$	−0.662827	+	0.382683i	−0.662827	+	0.382683i
$268$	1.91532	+	0.513210i	1.91532	+	0.513210i
$269$		0			0		−0.195090	−	0.980785i	$-0.562500\pi$
$269$		0			0		0.195090	+	0.980785i	$0.437500\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	0.608761	+	0.793353i	0.608761	+	0.793353i
$273$		0			0
$274$	−1.53264	+	1.17604i	−1.53264	+	1.17604i
$275$	0.206647	−	0.608761i	0.206647	−	0.608761i
$276$		0			0
$277$		0			0		0.0654031	−	0.997859i	$-0.479167\pi$
$277$		0			0		−0.0654031	+	0.997859i	$0.520833\pi$
$278$	0.128293	+	0.0255190i	0.128293	+	0.0255190i
$279$		0			0
$280$		0			0
$281$	0.860919	−	1.12197i	0.860919	−	1.12197i	−0.130526	−	0.991445i	$-0.541667\pi$
$281$	0.860919	−	1.12197i	0.860919	−	1.12197i	0.991445	−	0.130526i	$-0.0416667\pi$
$282$		0			0
$283$	−1.29335	+	1.47479i	−1.29335	+	1.47479i	−0.500000	+	0.866025i	$0.666667\pi$
$283$	−1.29335	+	1.47479i	−1.29335	+	1.47479i	−0.793353	+	0.608761i	$0.791667\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$289$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$290$		0			0
$291$	1.69855	+	0.576581i	1.69855	+	0.576581i
$292$	1.42388	+	0.483342i	1.42388	+	0.483342i
$293$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$293$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$294$	0.500000	+	0.866025i	0.500000	+	0.866025i
$295$		0			0
$296$		0			0
$297$	0.576581	+	0.284338i	0.576581	+	0.284338i
$298$		0			0
$299$		0			0
$300$	0.608761	−	0.793353i	0.608761	−	0.793353i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.513210	−	0.0675653i	0.513210	−	0.0675653i
$305$		0			0
$306$	0.258819	−	0.965926i	0.258819	−	0.965926i
$307$	1.73205			1.73205			0.866025	−	0.500000i	$-0.166667\pi$
$307$	1.73205			1.73205			0.866025	+	0.500000i	$0.166667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.442289	−	0.896873i	$-0.645833\pi$
$311$		0			0		0.442289	+	0.896873i	$0.354167\pi$
$312$		0			0
$313$	−0.793353	−	0.391239i	−0.793353	−	0.391239i		−	1.00000i	$-0.5\pi$
$313$	−0.793353	−	0.391239i	−0.793353	−	0.391239i	−0.793353	+	0.608761i	$0.791667\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.946930	−	0.321439i	$-0.104167\pi$
$317$		0			0		−0.946930	+	0.321439i	$0.895833\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.665060	+	0.583242i	−0.665060	+	0.583242i
$322$		0			0
$323$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$324$	0.707107	+	0.707107i	0.707107	+	0.707107i
$325$		0			0
$326$	1.09645	+	1.25026i	1.09645	+	1.25026i
$327$		0			0
$328$	−1.69855	+	0.837633i	−1.69855	+	0.837633i
$329$		0			0
$330$		0			0
$331$	0.465926	−	0.607206i	0.465926	−	0.607206i	−0.500000	−	0.866025i	$-0.666667\pi$
$331$	0.465926	−	0.607206i	0.465926	−	0.607206i	0.965926	+	0.258819i	$0.0833333\pi$
$332$	0.707107	+	1.70711i	0.707107	+	1.70711i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0420463	−	0.123864i	0.0420463	−	0.123864i	−0.923880	−	0.382683i	$-0.875000\pi$
$337$	0.0420463	−	0.123864i	0.0420463	−	0.123864i	0.965926	+	0.258819i	$0.0833333\pi$
$338$	0.793353	−	0.608761i	0.793353	−	0.608761i
$339$	0.617317	+	0.923880i	0.617317	+	0.923880i
$340$		0			0
$341$		0			0
$342$	−0.366025	−	0.366025i	−0.366025	−	0.366025i
$343$		0			0
$344$	0.252157	+	0.0675653i	0.252157	+	0.0675653i
$345$		0			0
$346$		0			0
$347$	1.50046	−	0.0983454i	1.50046	−	0.0983454i	0.707107	−	0.707107i	$-0.250000\pi$
$347$	1.50046	−	0.0983454i	1.50046	−	0.0983454i	0.793353	+	0.608761i	$0.208333\pi$
$348$		0			0
$349$		0			0		−0.793353	−	0.608761i	$-0.791667\pi$
$349$		0			0		0.793353	+	0.608761i	$0.208333\pi$
$350$		0			0
$351$		0			0
$352$	0.357164	−	0.534534i	0.357164	−	0.534534i
$353$	−0.513210	+	1.91532i	−0.513210	+	1.91532i	−0.130526	+	0.991445i	$0.541667\pi$
$353$	−0.513210	+	1.91532i	−0.513210	+	1.91532i	−0.382683	+	0.923880i	$0.625000\pi$
$354$	−0.315118	+	1.17604i	−0.315118	+	1.17604i
$355$		0			0
$356$	0.382683	−	0.662827i	0.382683	−	0.662827i
$357$		0			0
$358$	0.707107	+	1.22474i	0.707107	+	1.22474i
$359$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$359$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$360$		0			0
$361$	−0.517638	−	0.517638i	−0.517638	−	0.517638i
$362$		0			0
$363$	0.542046	−	0.224523i	0.542046	−	0.224523i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.442289	−	0.896873i	$-0.354167\pi$
$367$		0			0		−0.442289	+	0.896873i	$0.645833\pi$
$368$		0			0
$369$	1.69855	+	0.837633i	1.69855	+	0.837633i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$	0.357164	+	0.534534i	0.357164	+	0.534534i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.09645	+	0.732626i	1.09645	+	0.732626i	0.965926	−	0.258819i	$-0.0833333\pi$
$379$	1.09645	+	0.732626i	1.09645	+	0.732626i	0.130526	+	0.991445i	$0.458333\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.991445	−	0.130526i	$-0.958333\pi$
$383$		0			0		0.991445	+	0.130526i	$0.0416667\pi$
$384$	0.793353	−	0.608761i	0.793353	−	0.608761i
$385$		0			0
$386$	1.65938	+	1.10876i	1.65938	+	1.10876i
$387$	−0.0999004	−	0.241181i	−0.0999004	−	0.241181i
$388$	−1.75928	+	0.349942i	−1.75928	+	0.349942i
$389$		0			0		−0.130526	−	0.991445i	$-0.541667\pi$
$389$		0			0		0.130526	+	0.991445i	$0.458333\pi$
$390$		0			0
$391$		0			0
$392$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$393$	−0.382683	+	0.0761205i	−0.382683	+	0.0761205i
$394$		0			0
$395$		0			0
$396$	−0.641502	+	0.0420463i	−0.641502	+	0.0420463i
$397$		0			0		0.195090	−	0.980785i	$-0.437500\pi$
$397$		0			0		−0.195090	+	0.980785i	$0.562500\pi$
$398$		0			0
$399$		0			0
$400$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$401$	−0.117317	−	1.78990i	−0.117317	−	1.78990i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	−0.117317	−	1.78990i	−0.117317	−	1.78990i	0.382683	−	0.923880i	$-0.375000\pi$
$402$	1.57313	+	1.20711i	1.57313	+	1.20711i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.258819	+	0.965926i	0.258819	+	0.965926i
$409$	−0.608761	+	1.05441i	−0.608761	+	1.05441i	0.382683	+	0.923880i	$0.375000\pi$
$409$	−0.608761	+	1.05441i	−0.608761	+	1.05441i	−0.991445	+	0.130526i	$0.958333\pi$
$410$		0			0
$411$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.108761	+	0.0726721i	0.108761	+	0.0726721i
$418$	0.332066	−	0.0217648i	0.332066	−	0.0217648i
$419$	0.835400	+	0.732626i	0.835400	+	0.732626i	0.965926	−	0.258819i	$-0.0833333\pi$
$419$	0.835400	+	0.732626i	0.835400	+	0.732626i	−0.130526	+	0.991445i	$0.541667\pi$
$420$		0			0
$421$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$421$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$422$	−0.0761205	−	0.382683i	−0.0761205	−	0.382683i
$423$		0			0
$424$		0			0
$425$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$426$		0			0
$427$		0			0
$428$	0.284338	−	0.837633i	0.284338	−	0.837633i
$429$		0			0
$430$		0			0
$431$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$431$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$432$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$433$	−0.739288	−	1.78480i	−0.739288	−	1.78480i	−0.608761	−	0.793353i	$-0.708333\pi$
$433$	−0.739288	−	1.78480i	−0.739288	−	1.78480i	−0.130526	−	0.991445i	$-0.541667\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.13053	+	0.991445i	1.13053	+	0.991445i
$439$		0			0		−0.659346	−	0.751840i	$-0.729167\pi$
$439$		0			0		0.659346	+	0.751840i	$0.270833\pi$
$440$		0			0
$441$	0.130526	+	0.991445i	0.130526	+	0.991445i
$442$		0			0
$443$	−1.71723	+	0.991445i	−1.71723	+	0.991445i	−0.793353	+	0.608761i	$0.791667\pi$
$443$	−1.71723	+	0.991445i	−1.71723	+	0.991445i	−0.923880	+	0.382683i	$0.875000\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.491445	−	0.735499i	−0.491445	−	0.735499i	0.500000	−	0.866025i	$-0.333333\pi$
$449$	−0.491445	−	0.735499i	−0.491445	−	0.735499i	−0.991445	+	0.130526i	$0.958333\pi$
$450$	0.866025	−	0.500000i	0.866025	−	0.500000i
$451$	−1.12484	+	0.465926i	−1.12484	+	0.465926i
$452$	−0.996552	−	0.491445i	−0.996552	−	0.491445i
$453$		0			0
$454$	−0.882683	−	1.78990i	−0.882683	−	1.78990i
$455$		0			0
$456$	0.500000	+	0.133975i	0.500000	+	0.133975i
$457$	1.91532	−	0.252157i	1.91532	−	0.252157i	0.923880	−	0.382683i	$-0.125000\pi$
$457$	1.91532	−	0.252157i	1.91532	−	0.252157i	0.991445	+	0.130526i	$0.0416667\pi$
$458$		0			0
$459$	0.608761	−	0.793353i	0.608761	−	0.793353i
$460$		0			0
$461$		0			0		0.991445	−	0.130526i	$-0.0416667\pi$
$461$		0			0		−0.991445	+	0.130526i	$0.958333\pi$
$462$		0			0
$463$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$463$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$464$		0			0
$465$		0			0
$466$	−0.117317	−	0.0578541i	−0.117317	−	0.0578541i
$467$	1.78480	−	0.739288i	1.78480	−	0.739288i	0.793353	−	0.608761i	$-0.208333\pi$
$467$	1.78480	−	0.739288i	1.78480	−	0.739288i	0.991445	−	0.130526i	$-0.0416667\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.315118	−	1.17604i	−0.315118	−	1.17604i
$473$	0.158919	+	0.0539456i	0.158919	+	0.0539456i
$474$		0			0
$475$	−0.448288	+	0.258819i	−0.448288	+	0.258819i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.659346	−	0.751840i	$-0.729167\pi$
$479$		0			0		0.659346	+	0.751840i	$0.270833\pi$
$480$		0			0
$481$		0			0
$482$	0.869474	−	0.991445i	0.869474	−	0.991445i
$483$		0			0
$484$	−0.357164	+	0.465466i	−0.357164	+	0.465466i
$485$		0			0
$486$	0.382683	+	0.923880i	0.382683	+	0.923880i
$487$		0			0		−0.980785	−	0.195090i	$-0.937500\pi$
$487$		0			0		0.980785	+	0.195090i	$0.0625000\pi$
$488$		0			0
$489$	0.534534	+	1.57469i	0.534534	+	1.57469i
$490$		0			0
$491$	−1.53264	+	1.17604i	−1.53264	+	1.17604i	−0.608761	+	0.793353i	$0.708333\pi$
$491$	−1.53264	+	1.17604i	−1.53264	+	1.17604i	−0.923880	+	0.382683i	$0.875000\pi$
$492$	−1.88981	+	0.123864i	−1.88981	+	0.123864i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$			1.84776i			1.84776i
$499$	0.991445	+	0.869474i	0.991445	+	0.869474i	0.991445	−	0.130526i	$-0.0416667\pi$
$499$	0.991445	+	0.869474i	0.991445	+	0.869474i			1.00000i	$0.5\pi$
$500$		0			0
$501$		0			0
$502$	1.25882	+	0.965926i	1.25882	+	0.965926i
$503$		0			0		0.831470	−	0.555570i	$-0.187500\pi$
$503$		0			0		−0.831470	+	0.555570i	$0.812500\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.965926	−	0.258819i	0.965926	−	0.258819i
$508$		0			0
$509$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$509$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$513$	−0.198092	−	0.478235i	−0.198092	−	0.478235i
$514$	1.12197	+	1.12197i	1.12197	+	1.12197i
$515$		0			0
$516$	0.207107	+	0.158919i	0.207107	+	0.158919i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.257264	+	1.29335i	−0.257264	+	1.29335i	0.608761	+	0.793353i	$0.291667\pi$
$521$	−0.257264	+	1.29335i	−0.257264	+	1.29335i	−0.866025	+	0.500000i	$0.833333\pi$
$522$		0			0
$523$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$523$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.923880	−	0.382683i	$-0.125000\pi$
$524$	0.293353	−	0.257264i	0.293353	−	0.257264i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.534534	−	0.357164i	0.534534	−	0.357164i
$529$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$530$		0			0
$531$	−0.741181	+	0.965926i	−0.741181	+	0.965926i
$532$		0			0
$533$		0			0
$534$	0.607206	−	0.465926i	0.607206	−	0.465926i
$535$		0			0
$536$	−1.96593	−	0.258819i	−1.96593	−	0.258819i
$537$	0.184592	+	1.40211i	0.184592	+	1.40211i
$538$		0			0
$539$	−0.534534	−	0.357164i	−0.534534	−	0.357164i
$540$		0			0
$541$		0			0		0.980785	−	0.195090i	$-0.0625000\pi$
$541$		0			0		−0.980785	+	0.195090i	$0.937500\pi$
$542$		0			0
$543$		0			0
$544$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$545$		0			0
$546$		0			0
$547$	1.34861	−	1.18270i	1.34861	−	1.18270i	0.382683	−	0.923880i	$-0.375000\pi$
$547$	1.34861	−	1.18270i	1.34861	−	1.18270i	0.965926	−	0.258819i	$-0.0833333\pi$
$548$	1.36603	−	1.36603i	1.36603	−	1.36603i
$549$		0			0
$550$	−0.125419	+	0.630526i	−0.125419	+	0.630526i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.130526	−	0.00855514i	−0.130526	−	0.00855514i
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.125419	+	0.630526i	0.125419	+	0.630526i
$562$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$563$	0.158919	+	0.207107i	0.158919	+	0.207107i	0.866025	−	0.500000i	$-0.166667\pi$
$563$	0.158919	+	0.207107i	0.158919	+	0.207107i	−0.707107	+	0.707107i	$0.750000\pi$
$564$		0			0
$565$		0			0
$566$	1.08979	−	1.63099i	1.08979	−	1.63099i
$567$		0			0
$568$		0			0
$569$	−0.207107	−	0.158919i	−0.207107	−	0.158919i	0.500000	−	0.866025i	$-0.333333\pi$
$569$	−0.207107	−	0.158919i	−0.207107	−	0.158919i	−0.707107	+	0.707107i	$0.750000\pi$
$570$		0			0
$571$	−1.88981	+	0.123864i	−1.88981	+	0.123864i	−0.965926	−	0.258819i	$-0.916667\pi$
$571$	−1.88981	+	0.123864i	−1.88981	+	0.123864i	−0.923880	+	0.382683i	$0.875000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.965926	−	0.258819i	0.965926	−	0.258819i
$577$			1.73205i			1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$577$			1.73205i			1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$578$	0.923880	−	0.382683i	0.923880	−	0.382683i
$579$	1.10876	+	1.65938i	1.10876	+	1.65938i
$580$		0			0
$581$		0			0
$582$	−1.75928	−	0.349942i	−1.75928	−	0.349942i
$583$		0			0
$584$	−1.47479	−	0.293353i	−1.47479	−	0.293353i
$585$		0			0
$586$		0			0
$587$	1.05441	−	1.37413i	1.05441	−	1.37413i	0.130526	−	0.991445i	$-0.458333\pi$
$587$	1.05441	−	1.37413i	1.05441	−	1.37413i	0.923880	−	0.382683i	$-0.125000\pi$
$588$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.70711	+	0.707107i	1.70711	+	0.707107i	1.00000			$0$
$593$	1.70711	+	0.707107i	1.70711	+	0.707107i	0.707107	+	0.707107i	$0.250000\pi$
$594$	−0.608761	−	0.206647i	−0.608761	−	0.206647i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$599$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$600$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$601$	0.837633	−	0.284338i	0.837633	−	0.284338i	0.130526	−	0.991445i	$-0.458333\pi$
$601$	0.837633	−	0.284338i	0.837633	−	0.284338i	0.707107	+	0.707107i	$0.250000\pi$
$602$		0			0
$603$	0.991445	+	1.71723i	0.991445	+	1.71723i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.442289	−	0.896873i	$-0.645833\pi$
$607$		0			0		0.442289	+	0.896873i	$0.354167\pi$
$608$	−0.500000	+	0.133975i	−0.500000	+	0.133975i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	−1.71723	+	0.226078i	−1.71723	+	0.226078i
$615$		0			0
$616$		0			0
$617$	−0.665060	−	1.34861i	−0.665060	−	1.34861i	−0.923880	−	0.382683i	$-0.875000\pi$
$617$	−0.665060	−	1.34861i	−0.665060	−	1.34861i	0.258819	−	0.965926i	$-0.416667\pi$
$618$		0			0
$619$	−1.60876	−	0.793353i	−1.60876	−	0.793353i	−0.608761	−	0.793353i	$-0.708333\pi$
$619$	−1.60876	−	0.793353i	−1.60876	−	0.793353i	−1.00000			$\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$626$	0.837633	+	0.284338i	0.837633	+	0.284338i
$627$	0.315118	+	0.106968i	0.315118	+	0.106968i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$631$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$632$		0			0
$633$	0.0761205	−	0.382683i	0.0761205	−	0.382683i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.0862466	−	1.31587i	0.0862466	−	1.31587i	−0.707107	−	0.707107i	$-0.750000\pi$
$641$	0.0862466	−	1.31587i	0.0862466	−	1.31587i	0.793353	−	0.608761i	$-0.208333\pi$
$642$	0.583242	−	0.665060i	0.583242	−	0.665060i
$643$	0.483342	−	1.42388i	0.483342	−	1.42388i	−0.382683	−	0.923880i	$-0.625000\pi$
$643$	0.483342	−	1.42388i	0.483342	−	1.42388i	0.866025	−	0.500000i	$-0.166667\pi$
$644$		0			0
$645$		0			0
$646$	0.0675653	−	0.513210i	0.0675653	−	0.513210i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−0.793353	−	0.608761i	−0.793353	−	0.608761i
$649$	−0.152701	−	0.767680i	−0.152701	−	0.767680i
$650$		0			0
$651$		0			0
$652$	−1.25026	−	1.09645i	−1.25026	−	1.09645i
$653$		0			0		0.997859	−	0.0654031i	$-0.0208333\pi$
$653$		0			0		−0.997859	+	0.0654031i	$0.979167\pi$
$654$		0			0
$655$		0			0
$656$	1.57469	−	1.05217i	1.57469	−	1.05217i
$657$	0.665060	+	1.34861i	0.665060	+	1.34861i
$658$		0			0
$659$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$659$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$660$		0			0
$661$		0			0		−0.608761	−	0.793353i	$-0.708333\pi$
$661$		0			0		0.608761	+	0.793353i	$0.291667\pi$
$662$	−0.382683	+	0.662827i	−0.382683	+	0.662827i
$663$		0			0
$664$	−0.923880	−	1.60021i	−0.923880	−	1.60021i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.867580	−	1.75928i	0.867580	−	1.75928i	0.258819	−	0.965926i	$-0.416667\pi$
$673$	0.867580	−	1.75928i	0.867580	−	1.75928i	0.608761	−	0.793353i	$-0.291667\pi$
$674$	−0.0255190	+	0.128293i	−0.0255190	+	0.128293i
$675$	0.991445	−	0.130526i	0.991445	−	0.130526i
$676$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$677$		0			0		0.751840	−	0.659346i	$-0.229167\pi$
$677$		0			0		−0.751840	+	0.659346i	$0.770833\pi$
$678$	−0.732626	−	0.835400i	−0.732626	−	0.835400i
$679$		0			0
$680$		0			0
$681$	−0.130526	−	1.99144i	−0.130526	−	1.99144i
$682$		0			0
$683$	−1.47479	+	0.293353i	−1.47479	+	0.293353i	−0.866025	−	0.500000i	$-0.833333\pi$
$683$	−1.47479	+	0.293353i	−1.47479	+	0.293353i	−0.608761	+	0.793353i	$0.708333\pi$
$684$	0.410670	+	0.315118i	0.410670	+	0.315118i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.258819	−	0.0340742i	−0.258819	−	0.0340742i
$689$		0			0
$690$		0			0
$691$	0.630526	+	1.85747i	0.630526	+	1.85747i	0.500000	+	0.866025i	$0.333333\pi$
$691$	0.630526	+	1.85747i	0.630526	+	1.85747i	0.130526	+	0.991445i	$0.458333\pi$
$692$		0			0
$693$		0			0
$694$	−1.47479	+	0.293353i	−1.47479	+	0.293353i
$695$		0			0
$696$		0			0
$697$	0.369474	+	1.85747i	0.369474	+	1.85747i
$698$		0			0
$699$	−0.0862466	−	0.0983454i	−0.0862466	−	0.0983454i
$700$		0			0
$701$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$701$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$702$		0			0
$703$		0			0
$704$	−0.284338	+	0.576581i	−0.284338	+	0.576581i
$705$		0			0
$706$	0.258819	−	1.96593i	0.258819	−	1.96593i
$707$		0			0
$708$	0.158919	−	1.20711i	0.158919	−	1.20711i
$709$		0			0		−0.997859	−	0.0654031i	$-0.979167\pi$
$709$		0			0		0.997859	+	0.0654031i	$0.0208333\pi$
$710$		0			0
$711$		0			0
$712$	−0.292893	+	0.707107i	−0.292893	+	0.707107i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.860919	−	1.12197i	−0.860919	−	1.12197i
$717$		0			0
$718$		0			0
$719$		0			0		0.555570	−	0.831470i	$-0.312500\pi$
$719$		0			0		−0.555570	+	0.831470i	$0.687500\pi$
$720$		0			0
$721$		0			0
$722$	0.580775	+	0.445644i	0.580775	+	0.445644i
$723$	1.18270	−	0.583242i	1.18270	−	0.583242i
$724$		0			0
$725$		0			0
$726$	−0.508103	+	0.293353i	−0.508103	+	0.293353i
$727$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$727$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$728$		0			0
$729$			1.00000i			1.00000i
$730$		0			0
$731$	0.130526	−	0.226078i	0.130526	−	0.226078i
$732$		0			0
$733$		0			0		0.793353	−	0.608761i	$-0.208333\pi$
$733$		0			0		−0.793353	+	0.608761i	$0.791667\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.25026	−	0.248693i	−1.25026	−	0.248693i
$738$	−1.79335	−	0.608761i	−1.79335	−	0.608761i
$739$	−0.662827	−	1.60021i	−0.662827	−	1.60021i	−0.793353	−	0.608761i	$-0.791667\pi$
$739$	−0.662827	−	1.60021i	−0.662827	−	1.60021i	0.130526	−	0.991445i	$-0.458333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.896873	−	0.442289i	$-0.145833\pi$
$743$		0			0		−0.896873	+	0.442289i	$0.854167\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.707107	+	1.70711i	−0.707107	+	1.70711i
$748$	−0.423880	−	0.483342i	−0.423880	−	0.483342i
$749$		0			0
$750$		0			0
$751$		0			0		−0.946930	−	0.321439i	$-0.895833\pi$
$751$		0			0		0.946930	+	0.321439i	$0.104167\pi$
$752$		0			0
$753$	0.793353	+	1.37413i	0.793353	+	1.37413i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$757$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$758$	−1.18270	−	0.583242i	−1.18270	−	0.583242i
$759$		0			0
$760$		0			0
$761$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$761$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$769$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$769$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$	0.607206	+	1.46593i	0.607206	+	1.46593i
$772$	−1.78990	−	0.882683i	−1.78990	−	0.882683i
$773$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$773$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$774$	0.130526	+	0.226078i	0.130526	+	0.226078i
$775$		0			0
$776$	1.69855	−	0.576581i	1.69855	−	0.576581i
$777$		0			0
$778$		0			0
$779$	0.928308	+	0.315118i	0.928308	+	0.315118i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.923880	+	0.382683i	0.923880	+	0.382683i
$785$		0			0
$786$	0.369474	−	0.125419i	0.369474	−	0.125419i
$787$	0.996552	−	0.491445i	0.996552	−	0.491445i	0.130526	−	0.991445i	$-0.458333\pi$
$787$	0.996552	−	0.491445i	0.996552	−	0.491445i	0.866025	+	0.500000i	$0.166667\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.630526	−	0.125419i	0.630526	−	0.125419i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.793353	−	0.608761i	$-0.208333\pi$
$797$		0			0		−0.793353	+	0.608761i	$0.791667\pi$
$798$		0			0
$799$		0			0
$800$		−	1.00000i		−	1.00000i
$801$	0.739288	−	0.198092i	0.739288	−	0.198092i
$802$	0.349942	+	1.75928i	0.349942	+	1.75928i
$803$	−0.933745	−	0.250196i	−0.933745	−	0.250196i
$804$	−1.71723	−	0.991445i	−1.71723	−	0.991445i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.108761	+	0.0726721i	−0.108761	+	0.0726721i	−0.608761	−	0.793353i	$-0.708333\pi$
$809$	−0.108761	+	0.0726721i	−0.108761	+	0.0726721i	0.500000	+	0.866025i	$0.333333\pi$
$810$		0			0
$811$	−0.491445	+	0.735499i	−0.491445	+	0.735499i	−0.991445	−	0.130526i	$-0.958333\pi$
$811$	−0.491445	+	0.735499i	−0.491445	+	0.735499i	0.500000	+	0.866025i	$0.333333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$817$	−0.0675653	−	0.117027i	−0.0675653	−	0.117027i
$818$	0.465926	−	1.12484i	0.465926	−	1.12484i
$819$		0			0
$820$		0			0
$821$		0			0		−0.997859	−	0.0654031i	$-0.979167\pi$
$821$		0			0		0.997859	+	0.0654031i	$0.0208333\pi$
$822$	1.78480	−	0.739288i	1.78480	−	0.739288i
$823$		0			0		−0.0654031	−	0.997859i	$-0.520833\pi$
$823$		0			0		0.0654031	+	0.997859i	$0.479167\pi$
$824$		0			0
$825$	−0.357164	+	0.534534i	−0.357164	+	0.534534i
$826$		0			0
$827$	−0.324423	+	1.63099i	−0.324423	+	1.63099i	0.382683	+	0.923880i	$0.375000\pi$
$827$	−0.324423	+	1.63099i	−0.324423	+	1.63099i	−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$829$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$834$	−0.117317	−	0.0578541i	−0.117317	−	0.0578541i
$835$		0			0
$836$	−0.326384	+	0.0649219i	−0.326384	+	0.0649219i
$837$		0			0
$838$	−0.923880	−	0.617317i	−0.923880	−	0.617317i
$839$		0			0		−0.321439	−	0.946930i	$-0.604167\pi$
$839$		0			0		0.321439	+	0.946930i	$0.395833\pi$
$840$		0			0
$841$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$842$		0			0
$843$	−1.12197	+	0.860919i	−1.12197	+	0.860919i
$844$	0.125419	+	0.369474i	0.125419	+	0.369474i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.63099	−	1.08979i	1.63099	−	1.08979i
$850$	0.923880	+	0.382683i	0.923880	+	0.382683i
$851$		0			0
$852$		0			0
$853$		0			0		0.751840	−	0.659346i	$-0.229167\pi$
$853$		0			0		−0.751840	+	0.659346i	$0.770833\pi$
$854$		0			0
$855$		0			0
$856$	−0.172572	+	0.867580i	−0.172572	+	0.867580i
$857$	0.867580	−	1.75928i	0.867580	−	1.75928i	0.258819	−	0.965926i	$-0.416667\pi$
$857$	0.867580	−	1.75928i	0.867580	−	1.75928i	0.608761	−	0.793353i	$-0.291667\pi$
$858$		0			0
$859$	0.207107	−	1.57313i	0.207107	−	1.57313i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.207107	−	1.57313i	0.207107	−	1.57313i	0.707107	−	0.707107i	$-0.250000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$863$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$864$	0.991445	+	0.130526i	0.991445	+	0.130526i
$865$		0			0
$866$	0.965926	+	1.67303i	0.965926	+	1.67303i
$867$	1.00000			1.00000
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.49144	−	0.996552i	−1.49144	−	0.996552i
$874$		0			0
$875$		0			0
$876$	−1.25026	−	0.835400i	−1.25026	−	0.835400i
$877$		0			0		0.997859	−	0.0654031i	$-0.0208333\pi$
$877$		0			0		−0.997859	+	0.0654031i	$0.979167\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.382683	+	1.92388i	0.382683	+	1.92388i	0.382683	+	0.923880i	$0.375000\pi$
$881$	0.382683	+	1.92388i	0.382683	+	1.92388i			1.00000i	$0.5\pi$
$882$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$883$			1.58671i			1.58671i	0.608761	+	0.793353i	$0.291667\pi$
$883$			1.58671i			1.58671i	−0.608761	+	0.793353i	$0.708333\pi$
$884$		0			0
$885$		0			0
$886$	1.57313	−	1.20711i	1.57313	−	1.20711i
$887$		0			0		0.321439	−	0.946930i	$-0.395833\pi$
$887$		0			0		−0.321439	+	0.946930i	$0.604167\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.483342	−	0.423880i	−0.483342	−	0.423880i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.583242	+	0.665060i	0.583242	+	0.665060i
$899$		0			0
$900$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$901$		0			0
$902$	1.05441	−	0.608761i	1.05441	−	0.608761i
$903$		0			0
$904$	1.05217	+	0.357164i	1.05217	+	0.357164i
$905$		0			0
$906$		0			0
$907$	1.79335	−	0.608761i	1.79335	−	0.608761i	0.793353	−	0.608761i	$-0.208333\pi$
$907$	1.79335	−	0.608761i	1.79335	−	0.608761i	1.00000			$0$
$908$	1.10876	+	1.65938i	1.10876	+	1.65938i
$909$		0			0
$910$		0			0
$911$		0			0		−0.896873	−	0.442289i	$-0.854167\pi$
$911$		0			0		0.896873	+	0.442289i	$0.145833\pi$
$912$	−0.513210	−	0.0675653i	−0.513210	−	0.0675653i
$913$	−0.525388	−	1.06538i	−0.525388	−	1.06538i
$914$	−1.86603	+	0.500000i	−1.86603	+	0.500000i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−1.67303	−	0.448288i	−1.67303	−	0.448288i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.57469	+	0.534534i	−1.57469	+	0.534534i	−0.965926	−	0.258819i	$-0.916667\pi$
$929$	−1.57469	+	0.534534i	−1.57469	+	0.534534i	−0.608761	+	0.793353i	$0.708333\pi$
$930$		0			0
$931$	0.133975	+	0.500000i	0.133975	+	0.500000i
$932$	0.123864	+	0.0420463i	0.123864	+	0.0420463i
$933$		0			0
$934$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$935$		0			0
$936$		0			0
$937$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$937$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$938$		0			0
$939$	0.665060	+	0.583242i	0.665060	+	0.583242i
$940$		0			0
$941$		0			0		0.659346	−	0.751840i	$-0.270833\pi$
$941$		0			0		−0.659346	+	0.751840i	$0.729167\pi$
$942$		0			0
$943$		0			0
$944$	0.465926	+	1.12484i	0.465926	+	1.12484i
$945$		0			0
$946$	−0.164600	−	0.0327410i	−0.164600	−	0.0327410i
$947$	0.117317	−	1.78990i	0.117317	−	1.78990i	−0.382683	−	0.923880i	$-0.625000\pi$
$947$	0.117317	−	1.78990i	0.117317	−	1.78990i	0.500000	−	0.866025i	$-0.333333\pi$
$948$		0			0
$949$		0			0
$950$	0.410670	−	0.315118i	0.410670	−	0.315118i
$951$		0			0
$952$		0			0
$953$		−	1.21752i		−	1.21752i	−0.793353	−	0.608761i	$-0.791667\pi$
$953$		−	1.21752i		−	1.21752i	0.793353	−	0.608761i	$-0.208333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.793353	−	0.608761i	−0.793353	−	0.608761i
$962$		0			0
$963$	0.793353	−	0.391239i	0.793353	−	0.391239i
$964$	−0.732626	+	1.09645i	−0.732626	+	1.09645i
$965$		0			0
$966$		0			0
$967$		0			0		−0.608761	−	0.793353i	$-0.708333\pi$
$967$		0			0		0.608761	+	0.793353i	$0.291667\pi$
$968$	0.293353	−	0.508103i	0.293353	−	0.508103i
$969$	0.258819	−	0.448288i	0.258819	−	0.448288i
$970$		0			0
$971$	0.292893	−	0.707107i	0.292893	−	0.707107i	−0.707107	−	0.707107i	$-0.750000\pi$
$971$	0.292893	−	0.707107i	0.292893	−	0.707107i	1.00000			$0$
$972$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.258819	+	1.96593i	−0.258819	+	1.96593i			1.00000i	$0.5\pi$
$977$	−0.258819	+	1.96593i	−0.258819	+	1.96593i	−0.258819	+	0.965926i	$0.583333\pi$
$978$	−0.735499	−	1.49144i	−0.735499	−	1.49144i
$979$	−0.217623	+	0.441296i	−0.217623	+	0.441296i
$980$		0			0
$981$		0			0
$982$	1.36603	−	1.36603i	1.36603	−	1.36603i
$983$		0			0		0.751840	−	0.659346i	$-0.229167\pi$
$983$		0			0		−0.751840	+	0.659346i	$0.770833\pi$
$984$	1.85747	−	0.369474i	1.85747	−	0.369474i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.831470	−	0.555570i	$-0.812500\pi$
$991$		0			0		0.831470	+	0.555570i	$0.187500\pi$
$992$		0			0
$993$	−0.607206	+	0.465926i	−0.607206	+	0.465926i
$994$		0			0
$995$		0			0
$996$	−0.241181	−	1.83195i	−0.241181	−	1.83195i
$997$		0			0		−0.321439	−	0.946930i	$-0.604167\pi$
$997$		0			0		0.321439	+	0.946930i	$0.395833\pi$
$998$	−1.09645	−	0.732626i	−1.09645	−	0.732626i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1224.1.cx.a.419.1	yes	16
3.2	odd	2		3672.1.dv.a.827.1		16
8.3	odd	2	CM	1224.1.cx.a.419.1	yes	16
9.2	odd	6		1224.1.cx.b.11.1	yes	16
9.7	even	3		3672.1.dv.b.3275.1		16
17.14	odd	16		1224.1.cx.b.779.1	yes	16
24.11	even	2		3672.1.dv.a.827.1		16
51.14	even	16		3672.1.dv.b.3635.1		16
72.11	even	6		1224.1.cx.b.11.1	yes	16
72.43	odd	6		3672.1.dv.b.3275.1		16
136.99	even	16		1224.1.cx.b.779.1	yes	16
153.65	even	48	inner	1224.1.cx.a.371.1	✓	16
153.133	odd	48		3672.1.dv.a.2411.1		16
408.371	odd	16		3672.1.dv.b.3635.1		16
1224.371	odd	48	inner	1224.1.cx.a.371.1	✓	16
1224.1051	even	48		3672.1.dv.a.2411.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1224.1.cx.a.371.1	✓	16	153.65	even	48	inner
1224.1.cx.a.371.1	✓	16	1224.371	odd	48	inner
1224.1.cx.a.419.1	yes	16	1.1	even	1	trivial
1224.1.cx.a.419.1	yes	16	8.3	odd	2	CM
1224.1.cx.b.11.1	yes	16	9.2	odd	6
1224.1.cx.b.11.1	yes	16	72.11	even	6
1224.1.cx.b.779.1	yes	16	17.14	odd	16
1224.1.cx.b.779.1	yes	16	136.99	even	16
3672.1.dv.a.827.1		16	3.2	odd	2
3672.1.dv.a.827.1		16	24.11	even	2
3672.1.dv.a.2411.1		16	153.133	odd	48
3672.1.dv.a.2411.1		16	1224.1051	even	48
3672.1.dv.b.3275.1		16	9.7	even	3
3672.1.dv.b.3275.1		16	72.43	odd	6
3672.1.dv.b.3635.1		16	51.14	even	16
3672.1.dv.b.3635.1		16	408.371	odd	16

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:	\( N \)	\(=\)	\( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1224.cx (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.991445 + 0.130526i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.965926 - 0.258819i) q^{4} +(0.991445 + 0.130526i) q^{6} +(-0.923880 + 0.382683i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.608761 + 0.206647i) q^{11} -1.00000 q^{12} +(0.866025 - 0.500000i) q^{16} +(0.130526 + 0.991445i) q^{17} +(-0.923880 - 0.382683i) q^{18} +(0.478235 + 0.198092i) q^{19} +(0.576581 - 0.284338i) q^{22} +(0.991445 - 0.130526i) q^{24} +(-0.608761 + 0.793353i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-0.793353 + 0.608761i) q^{32} +(0.641502 - 0.0420463i) q^{33} +(-0.258819 - 0.965926i) q^{34} +(0.965926 + 0.258819i) q^{36} +(-0.500000 - 0.133975i) q^{38} +(1.88981 - 0.123864i) q^{41} +(-0.207107 - 0.158919i) q^{43} +(-0.534534 + 0.357164i) q^{44} +(-0.965926 + 0.258819i) q^{48} +(0.608761 + 0.793353i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.130526 - 0.991445i) q^{51} +(0.793353 + 0.608761i) q^{54} +(-0.410670 - 0.315118i) q^{57} +(-0.158919 + 1.20711i) q^{59} +(0.707107 - 0.707107i) q^{64} +(-0.630526 + 0.125419i) q^{66} +(1.71723 + 0.991445i) q^{67} +(0.382683 + 0.923880i) q^{68} +(-0.991445 - 0.130526i) q^{72} +(1.25026 + 0.835400i) q^{73} +(0.793353 - 0.608761i) q^{75} +(0.513210 + 0.0675653i) q^{76} +(0.500000 + 0.866025i) q^{81} +(-1.85747 + 0.369474i) q^{82} +(0.241181 + 1.83195i) q^{83} +(0.226078 + 0.130526i) q^{86} +(0.483342 - 0.423880i) q^{88} +(0.541196 - 0.541196i) q^{89} +(0.923880 - 0.382683i) q^{96} +(-1.78990 - 0.117317i) q^{97} +(-0.707107 - 0.707107i) q^{98} +(-0.630526 - 0.125419i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{12} - 8 q^{38} + 8 q^{43} + 8 q^{50} - 8 q^{66} + 8 q^{81} + 8 q^{83} - 8 q^{99}+O(q^{100}) \) 16 * q - 16 * q^12 - 8 * q^38 + 8 * q^43 + 8 * q^50 - 8 * q^66 + 8 * q^81 + 8 * q^83 - 8 * q^99

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