LMFDB - Embedded newform 504.1.bn.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,1,Mod(13,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 3]))

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

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

chi := DirichletCharacter("504.13");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	504.bn (of order $6$, degree $2$, 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:	$0.251528766367$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.4536.1
Artin image:	$C_3\times S_3$
Artin field:	Galois closure of 6.0.14224896.1

Embedding invariants

Embedding label			13.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	504.13
Dual form			504.1.bn.b.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +(-0.500000 + 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{18} -1.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{21} +(0.500000 - 0.866025i) q^{23} +1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -1.00000 q^{30} +(-0.500000 + 0.866025i) q^{32} -1.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.500000 + 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{45} -1.00000 q^{46} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.00000 - 1.73205i) q^{52} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{56} -1.00000 q^{57} +(-1.00000 + 1.73205i) q^{59} +(0.500000 + 0.866025i) q^{60} +(0.500000 + 0.866025i) q^{61} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(0.500000 - 0.866025i) q^{69} +(0.500000 + 0.866025i) q^{70} -1.00000 q^{71} +1.00000 q^{72} +(0.500000 - 0.866025i) q^{76} +2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} -1.00000 q^{80} +1.00000 q^{81} +(-1.00000 - 1.73205i) q^{83} +1.00000 q^{84} -1.00000 q^{90} +2.00000 q^{91} +(0.500000 + 0.866025i) q^{92} +(-0.500000 + 0.866025i) q^{95} +(-0.500000 + 0.866025i) q^{96} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} - q^{4} + q^{5} - q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 - q^4 + q^5 - q^6 - q^7 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} + 2 q^{3} - q^{4} + q^{5} - q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} - q^{12} - 2 q^{13} - q^{14} + q^{15} - q^{16} - q^{18} - 2 q^{19} + q^{20} - q^{21} + q^{23} + 2 q^{24} + 4 q^{26} + 2 q^{27} + 2 q^{28} - 2 q^{30} - q^{32} - 2 q^{35} - q^{36} + q^{38} - 2 q^{39} + q^{40} - q^{42} + q^{45} - 2 q^{46} - q^{48} - q^{49} - 2 q^{52} - q^{54} - q^{56} - 2 q^{57} - 2 q^{59} + q^{60} + q^{61} - q^{63} + 2 q^{64} + 2 q^{65} + q^{69} + q^{70} - 2 q^{71} + 2 q^{72} + q^{76} + 4 q^{78} + q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{83} + 2 q^{84} - 2 q^{90} + 4 q^{91} + q^{92} - q^{95} - q^{96} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 + 2 * q^3 - q^4 + q^5 - q^6 - q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 - q^12 - 2 * q^13 - q^14 + q^15 - q^16 - q^18 - 2 * q^19 + q^20 - q^21 + q^23 + 2 * q^24 + 4 * q^26 + 2 * q^27 + 2 * q^28 - 2 * q^30 - q^32 - 2 * q^35 - q^36 + q^38 - 2 * q^39 + q^40 - q^42 + q^45 - 2 * q^46 - q^48 - q^49 - 2 * q^52 - q^54 - q^56 - 2 * q^57 - 2 * q^59 + q^60 + q^61 - q^63 + 2 * q^64 + 2 * q^65 + q^69 + q^70 - 2 * q^71 + 2 * q^72 + q^76 + 4 * q^78 + q^79 - 2 * q^80 + 2 * q^81 - 2 * q^83 + 2 * q^84 - 2 * q^90 + 4 * q^91 + q^92 - q^95 - q^96 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$2$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$3$	1.00000			1.00000
$3$	1.00000			1.00000
$4$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$6$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$7$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$7$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$8$	1.00000			1.00000
$9$	1.00000			1.00000
$10$	−1.00000			−1.00000
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$13$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$13$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$14$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$15$	0.500000	−	0.866025i	0.500000	−	0.866025i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$19$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$20$	0.500000	+	0.866025i	0.500000	+	0.866025i
$21$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$22$		0			0
$23$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$23$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$24$	1.00000			1.00000
$25$		0			0
$26$	2.00000			2.00000
$27$	1.00000			1.00000
$28$	1.00000			1.00000
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	−1.00000			−1.00000
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$33$		0			0
$34$		0			0
$35$	−1.00000			−1.00000
$36$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$	0.500000	+	0.866025i	0.500000	+	0.866025i
$39$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$40$	0.500000	−	0.866025i	0.500000	−	0.866025i
$41$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$41$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$42$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$43$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$43$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$44$		0			0
$45$	0.500000	−	0.866025i	0.500000	−	0.866025i
$46$	−1.00000			−1.00000
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$49$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$50$		0			0
$51$		0			0
$52$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$55$		0			0
$56$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$57$	−1.00000			−1.00000
$58$		0			0
$59$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$59$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$60$	0.500000	+	0.866025i	0.500000	+	0.866025i
$61$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$61$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$64$	1.00000			1.00000
$65$	1.00000	+	1.73205i	1.00000	+	1.73205i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	0.500000	−	0.866025i	0.500000	−	0.866025i
$70$	0.500000	+	0.866025i	0.500000	+	0.866025i
$71$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$71$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$72$	1.00000			1.00000
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$		0			0
$76$	0.500000	−	0.866025i	0.500000	−	0.866025i
$77$		0			0
$78$	2.00000			2.00000
$79$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$79$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$80$	−1.00000			−1.00000
$81$	1.00000			1.00000
$82$		0			0
$83$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$84$	1.00000			1.00000
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−1.00000			−1.00000
$91$	2.00000			2.00000
$92$	0.500000	+	0.866025i	0.500000	+	0.866025i
$93$		0			0
$94$		0			0
$95$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$96$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$	1.00000			1.00000
$99$		0			0
$100$		0			0
$101$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$101$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$105$	−1.00000			−1.00000
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$		0			0
$111$		0			0
$112$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$114$	0.500000	+	0.866025i	0.500000	+	0.866025i
$115$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$116$		0			0
$117$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$118$	2.00000			2.00000
$119$		0			0
$120$	0.500000	−	0.866025i	0.500000	−	0.866025i
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$	0.500000	−	0.866025i	0.500000	−	0.866025i
$123$		0			0
$124$		0			0
$125$	1.00000			1.00000
$126$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$127$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$127$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$128$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$129$		0			0
$130$	1.00000	−	1.73205i	1.00000	−	1.73205i
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$132$		0			0
$133$	0.500000	+	0.866025i	0.500000	+	0.866025i
$134$		0			0
$135$	0.500000	−	0.866025i	0.500000	−	0.866025i
$136$		0			0
$137$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$137$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$138$	−1.00000			−1.00000
$139$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$139$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$140$	0.500000	−	0.866025i	0.500000	−	0.866025i
$141$		0			0
$142$	0.500000	+	0.866025i	0.500000	+	0.866025i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$145$		0			0
$146$		0			0
$147$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$148$		0			0
$149$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$149$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$150$		0			0
$151$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$151$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$152$	−1.00000			−1.00000
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$158$	0.500000	−	0.866025i	0.500000	−	0.866025i
$159$		0			0
$160$	0.500000	+	0.866025i	0.500000	+	0.866025i
$161$	−1.00000			−1.00000
$162$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$167$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$167$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$168$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$169$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$170$		0			0
$171$	−1.00000			−1.00000
$172$		0			0
$173$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$173$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	0.500000	+	0.866025i	0.500000	+	0.866025i
$181$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$181$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$182$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$183$	0.500000	+	0.866025i	0.500000	+	0.866025i
$184$	0.500000	−	0.866025i	0.500000	−	0.866025i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$190$	1.00000			1.00000
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	1.00000			1.00000
$193$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$193$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$194$		0			0
$195$	1.00000	+	1.73205i	1.00000	+	1.73205i
$196$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		0			0
$201$		0			0
$202$	0.500000	−	0.866025i	0.500000	−	0.866025i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.500000	−	0.866025i	0.500000	−	0.866025i
$208$	2.00000			2.00000
$209$		0			0
$210$	0.500000	+	0.866025i	0.500000	+	0.866025i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$	−1.00000			−1.00000
$214$		0			0
$215$		0			0
$216$	1.00000			1.00000
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$223$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$224$	1.00000			1.00000
$225$		0			0
$226$	−1.00000			−1.00000
$227$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$227$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$228$	0.500000	−	0.866025i	0.500000	−	0.866025i
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$230$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$231$		0			0
$232$		0			0
$233$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$233$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$234$	2.00000			2.00000
$235$		0			0
$236$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$237$	0.500000	+	0.866025i	0.500000	+	0.866025i
$238$		0			0
$239$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$239$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$240$	−1.00000			−1.00000
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$	1.00000			1.00000
$243$	1.00000			1.00000
$244$	−1.00000			−1.00000
$245$	0.500000	+	0.866025i	0.500000	+	0.866025i
$246$		0			0
$247$	1.00000	−	1.73205i	1.00000	−	1.73205i
$248$		0			0
$249$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$250$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$251$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$251$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$252$	1.00000			1.00000
$253$		0			0
$254$	0.500000	+	0.866025i	0.500000	+	0.866025i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$		0			0
$260$	−2.00000			−2.00000
$261$		0			0
$262$	−1.00000			−1.00000
$263$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$263$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		0			0
$266$	0.500000	−	0.866025i	0.500000	−	0.866025i
$267$		0			0
$268$		0			0
$269$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$269$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$270$	−1.00000			−1.00000
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	2.00000			2.00000
$274$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$275$		0			0
$276$	0.500000	+	0.866025i	0.500000	+	0.866025i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$	−1.00000			−1.00000
$279$		0			0
$280$	−1.00000			−1.00000
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$281$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$283$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$284$	0.500000	−	0.866025i	0.500000	−	0.866025i
$285$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$286$		0			0
$287$		0			0
$288$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$289$	1.00000			1.00000
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$293$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$294$	1.00000			1.00000
$295$	1.00000	+	1.73205i	1.00000	+	1.73205i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.00000	+	1.73205i	1.00000	+	1.73205i
$300$		0			0
$301$		0			0
$302$	0.500000	−	0.866025i	0.500000	−	0.866025i
$303$	0.500000	+	0.866025i	0.500000	+	0.866025i
$304$	0.500000	+	0.866025i	0.500000	+	0.866025i
$305$	1.00000			1.00000
$306$		0			0
$307$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$307$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	−1.00000			−1.00000
$315$	−1.00000			−1.00000
$316$	−1.00000			−1.00000
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$		0			0
$319$		0			0
$320$	0.500000	−	0.866025i	0.500000	−	0.866025i
$321$		0			0
$322$	0.500000	+	0.866025i	0.500000	+	0.866025i
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$	2.00000			2.00000
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$337$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$337$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$338$	−1.50000	+	2.59808i	−1.50000	+	2.59808i
$339$	0.500000	−	0.866025i	0.500000	−	0.866025i
$340$		0			0
$341$		0			0
$342$	0.500000	+	0.866025i	0.500000	+	0.866025i
$343$	1.00000			1.00000
$344$		0			0
$345$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$346$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$347$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$347$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$348$		0			0
$349$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$350$		0			0
$351$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$352$		0			0
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$	2.00000			2.00000
$355$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$359$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$360$	0.500000	−	0.866025i	0.500000	−	0.866025i
$361$		0			0
$362$	0.500000	+	0.866025i	0.500000	+	0.866025i
$363$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$364$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$365$		0			0
$366$	0.500000	−	0.866025i	0.500000	−	0.866025i
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$	−1.00000			−1.00000
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	1.00000			1.00000
$376$		0			0
$377$		0			0
$378$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$381$	−1.00000			−1.00000
$382$	0.500000	−	0.866025i	0.500000	−	0.866025i
$383$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$383$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$384$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$385$		0			0
$386$	−1.00000			−1.00000
$387$		0			0
$388$		0			0
$389$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$389$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$390$	1.00000	−	1.73205i	1.00000	−	1.73205i
$391$		0			0
$392$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$393$	0.500000	−	0.866025i	0.500000	−	0.866025i
$394$		0			0
$395$	1.00000			1.00000
$396$		0			0
$397$	2.00000			2.00000			1.00000			$0$
$397$	2.00000			2.00000			1.00000			$0$
$398$		0			0
$399$	0.500000	+	0.866025i	0.500000	+	0.866025i
$400$		0			0
$401$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$402$		0			0
$403$		0			0
$404$	−1.00000			−1.00000
$405$	0.500000	−	0.866025i	0.500000	−	0.866025i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$409$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$412$		0			0
$413$	2.00000			2.00000
$414$	−1.00000			−1.00000
$415$	−2.00000			−2.00000
$416$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$417$	0.500000	−	0.866025i	0.500000	−	0.866025i
$418$		0			0
$419$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$419$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$420$	0.500000	−	0.866025i	0.500000	−	0.866025i
$421$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$421$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	0.500000	+	0.866025i	0.500000	+	0.866025i
$427$	0.500000	−	0.866025i	0.500000	−	0.866025i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.00000			2.00000			1.00000			$0$
$431$	2.00000			2.00000			1.00000			$0$
$432$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$442$		0			0
$443$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$443$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$449$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$450$		0			0
$451$		0			0
$452$	0.500000	+	0.866025i	0.500000	+	0.866025i
$453$	0.500000	+	0.866025i	0.500000	+	0.866025i
$454$	0.500000	−	0.866025i	0.500000	−	0.866025i
$455$	1.00000	−	1.73205i	1.00000	−	1.73205i
$456$	−1.00000			−1.00000
$457$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$457$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$458$	−1.00000			−1.00000
$459$		0			0
$460$	1.00000			1.00000
$461$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$461$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$463$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$464$		0			0
$465$		0			0
$466$	0.500000	+	0.866025i	0.500000	+	0.866025i
$467$	2.00000			2.00000			1.00000			$0$
$467$	2.00000			2.00000			1.00000			$0$
$468$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$469$		0			0
$470$		0			0
$471$	0.500000	−	0.866025i	0.500000	−	0.866025i
$472$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$473$		0			0
$474$	0.500000	−	0.866025i	0.500000	−	0.866025i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.00000			−1.00000
$479$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$479$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$480$	0.500000	+	0.866025i	0.500000	+	0.866025i
$481$		0			0
$482$		0			0
$483$	−1.00000			−1.00000
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$487$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$487$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$488$	0.500000	+	0.866025i	0.500000	+	0.866025i
$489$		0			0
$490$	0.500000	−	0.866025i	0.500000	−	0.866025i
$491$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$491$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$492$		0			0
$493$		0			0
$494$	−2.00000			−2.00000
$495$		0			0
$496$		0			0
$497$	0.500000	+	0.866025i	0.500000	+	0.866025i
$498$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$501$		0			0
$502$	0.500000	+	0.866025i	0.500000	+	0.866025i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$505$	1.00000			1.00000
$506$		0			0
$507$	−1.50000	−	2.59808i	−1.50000	−	2.59808i
$508$	0.500000	−	0.866025i	0.500000	−	0.866025i
$509$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$509$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			1.00000
$513$	−1.00000			−1.00000
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$520$	1.00000	+	1.73205i	1.00000	+	1.73205i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$523$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$524$	0.500000	+	0.866025i	0.500000	+	0.866025i
$525$		0			0
$526$	0.500000	−	0.866025i	0.500000	−	0.866025i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$532$	−1.00000			−1.00000
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	0.500000	+	0.866025i	0.500000	+	0.866025i
$539$		0			0
$540$	0.500000	+	0.866025i	0.500000	+	0.866025i
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	−1.00000			−1.00000
$544$		0			0
$545$		0			0
$546$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$547$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$547$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$548$	2.00000			2.00000
$549$	0.500000	+	0.866025i	0.500000	+	0.866025i
$550$		0			0
$551$		0			0
$552$	0.500000	−	0.866025i	0.500000	−	0.866025i
$553$	0.500000	−	0.866025i	0.500000	−	0.866025i
$554$		0			0
$555$		0			0
$556$	0.500000	+	0.866025i	0.500000	+	0.866025i
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$	0.500000	+	0.866025i	0.500000	+	0.866025i
$561$		0			0
$562$	0.500000	−	0.866025i	0.500000	−	0.866025i
$563$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$563$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$564$		0			0
$565$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$566$	−1.00000			−1.00000
$567$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$568$	−1.00000			−1.00000
$569$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$570$	1.00000			1.00000
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	0.500000	+	0.866025i	0.500000	+	0.866025i
$574$		0			0
$575$		0			0
$576$	1.00000			1.00000
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$579$	0.500000	−	0.866025i	0.500000	−	0.866025i
$580$		0			0
$581$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.00000	+	1.73205i	1.00000	+	1.73205i
$586$	−1.00000			−1.00000
$587$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$587$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$588$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$589$		0			0
$590$	1.00000	−	1.73205i	1.00000	−	1.73205i
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	1.00000	−	1.73205i	1.00000	−	1.73205i
$599$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$599$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$600$		0			0
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$	−1.00000			−1.00000
$605$	0.500000	+	0.866025i	0.500000	+	0.866025i
$606$	0.500000	−	0.866025i	0.500000	−	0.866025i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$	0.500000	−	0.866025i	0.500000	−	0.866025i
$609$		0			0
$610$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	0.500000	+	0.866025i	0.500000	+	0.866025i
$615$		0			0
$616$		0			0
$617$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$617$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	0.500000	−	0.866025i	0.500000	−	0.866025i
$622$		0			0
$623$		0			0
$624$	2.00000			2.00000
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		0			0
$627$		0			0
$628$	0.500000	+	0.866025i	0.500000	+	0.866025i
$629$		0			0
$630$	0.500000	+	0.866025i	0.500000	+	0.866025i
$631$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$631$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$632$	0.500000	+	0.866025i	0.500000	+	0.866025i
$633$		0			0
$634$		0			0
$635$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$636$		0			0
$637$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$638$		0			0
$639$	−1.00000			−1.00000
$640$	−1.00000			−1.00000
$641$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$641$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$642$		0			0
$643$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$643$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$644$	0.500000	−	0.866025i	0.500000	−	0.866025i
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	1.00000			1.00000
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$659$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$660$		0			0
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$662$		0			0
$663$		0			0
$664$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$665$	1.00000			1.00000
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	1.00000			1.00000
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$674$	2.00000			2.00000
$675$		0			0
$676$	3.00000			3.00000
$677$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$677$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$678$	−1.00000			−1.00000
$679$		0			0
$680$		0			0
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$		0			0
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$	0.500000	−	0.866025i	0.500000	−	0.866025i
$685$	−2.00000			−2.00000
$686$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$687$	0.500000	−	0.866025i	0.500000	−	0.866025i
$688$		0			0
$689$		0			0
$690$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$691$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$691$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$692$	2.00000			2.00000
$693$		0			0
$694$		0			0
$695$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$696$		0			0
$697$		0			0
$698$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$699$	−1.00000			−1.00000
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	2.00000			2.00000
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.500000	−	0.866025i	0.500000	−	0.866025i
$708$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$709$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$709$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$710$	1.00000			1.00000
$711$	0.500000	+	0.866025i	0.500000	+	0.866025i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.500000	−	0.866025i	0.500000	−	0.866025i
$718$	0.500000	+	0.866025i	0.500000	+	0.866025i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$	−1.00000			−1.00000
$721$		0			0
$722$		0			0
$723$		0			0
$724$	0.500000	−	0.866025i	0.500000	−	0.866025i
$725$		0			0
$726$	1.00000			1.00000
$727$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$727$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$728$	2.00000			2.00000
$729$	1.00000			1.00000
$730$		0			0
$731$		0			0
$732$	−1.00000			−1.00000
$733$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$733$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$734$		0			0
$735$	0.500000	+	0.866025i	0.500000	+	0.866025i
$736$	0.500000	+	0.866025i	0.500000	+	0.866025i
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$	1.00000	−	1.73205i	1.00000	−	1.73205i
$742$		0			0
$743$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$743$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$748$		0			0
$749$		0			0
$750$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$752$		0			0
$753$	−1.00000			−1.00000
$754$		0			0
$755$	1.00000			1.00000
$756$	1.00000			1.00000
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$761$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$761$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$762$	0.500000	+	0.866025i	0.500000	+	0.866025i
$763$		0			0
$764$	−1.00000			−1.00000
$765$		0			0
$766$		0			0
$767$	−2.00000	−	3.46410i	−2.00000	−	3.46410i
$768$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$769$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$769$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$		0			0
$772$	0.500000	+	0.866025i	0.500000	+	0.866025i
$773$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$773$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−2.00000			−2.00000
$781$		0			0
$782$		0			0
$783$		0			0
$784$	1.00000			1.00000
$785$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$786$	−1.00000			−1.00000
$787$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$787$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$	0.500000	+	0.866025i	0.500000	+	0.866025i
$790$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$791$	−1.00000			−1.00000
$792$		0			0
$793$	−2.00000			−2.00000
$794$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$795$		0			0
$796$		0			0
$797$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$797$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$798$	0.500000	−	0.866025i	0.500000	−	0.866025i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	−1.00000			−1.00000
$803$		0			0
$804$		0			0
$805$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$806$		0			0
$807$	−1.00000			−1.00000
$808$	0.500000	+	0.866025i	0.500000	+	0.866025i
$809$	2.00000			2.00000			1.00000			$0$
$809$	2.00000			2.00000			1.00000			$0$
$810$	−1.00000			−1.00000
$811$	2.00000			2.00000			1.00000			$0$
$811$	2.00000			2.00000			1.00000			$0$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	2.00000			2.00000
$820$		0			0
$821$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$821$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$822$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$823$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$823$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	0.500000	+	0.866025i	0.500000	+	0.866025i
$829$	2.00000			2.00000			1.00000			$0$
$829$	2.00000			2.00000			1.00000			$0$
$830$	1.00000	+	1.73205i	1.00000	+	1.73205i
$831$		0			0
$832$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$833$		0			0
$834$	−1.00000			−1.00000
$835$		0			0
$836$		0			0
$837$		0			0
$838$	−1.00000			−1.00000
$839$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$839$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$840$	−1.00000			−1.00000
$841$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$842$		0			0
$843$	0.500000	+	0.866025i	0.500000	+	0.866025i
$844$		0			0
$845$	−3.00000			−3.00000
$846$		0			0
$847$	1.00000			1.00000
$848$		0			0
$849$	0.500000	−	0.866025i	0.500000	−	0.866025i
$850$		0			0
$851$		0			0
$852$	0.500000	−	0.866025i	0.500000	−	0.866025i
$853$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$853$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$854$	−1.00000			−1.00000
$855$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$856$		0			0
$857$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$857$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$859$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$863$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$863$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$864$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$865$	−2.00000			−2.00000
$866$		0			0
$867$	1.00000			1.00000
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	1.00000			1.00000
$875$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$	0.500000	−	0.866025i	0.500000	−	0.866025i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	1.00000			1.00000
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$	1.00000	+	1.73205i	1.00000	+	1.73205i
$886$		0			0
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$		0			0
$889$	0.500000	+	0.866025i	0.500000	+	0.866025i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$897$	1.00000	+	1.73205i	1.00000	+	1.73205i
$898$	0.500000	+	0.866025i	0.500000	+	0.866025i
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$		0			0
$904$	0.500000	−	0.866025i	0.500000	−	0.866025i
$905$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$906$	0.500000	−	0.866025i	0.500000	−	0.866025i
$907$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$907$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$908$	−1.00000			−1.00000
$909$	0.500000	+	0.866025i	0.500000	+	0.866025i
$910$	−2.00000			−2.00000
$911$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$911$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$912$	0.500000	+	0.866025i	0.500000	+	0.866025i
$913$		0			0
$914$	0.500000	−	0.866025i	0.500000	−	0.866025i
$915$	1.00000			1.00000
$916$	0.500000	+	0.866025i	0.500000	+	0.866025i
$917$	−1.00000			−1.00000
$918$		0			0
$919$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$919$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$920$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$921$	−1.00000			−1.00000
$922$	0.500000	−	0.866025i	0.500000	−	0.866025i
$923$	1.00000	−	1.73205i	1.00000	−	1.73205i
$924$		0			0
$925$		0			0
$926$	−1.00000			−1.00000
$927$		0			0
$928$		0			0
$929$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$929$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$930$		0			0
$931$	0.500000	−	0.866025i	0.500000	−	0.866025i
$932$	0.500000	−	0.866025i	0.500000	−	0.866025i
$933$		0			0
$934$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$935$		0			0
$936$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$941$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$942$	−1.00000			−1.00000
$943$		0			0
$944$	2.00000			2.00000
$945$	−1.00000			−1.00000
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$	−1.00000			−1.00000
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	2.00000			2.00000			1.00000			$0$
$953$	2.00000			2.00000			1.00000			$0$
$954$		0			0
$955$	1.00000			1.00000
$956$	0.500000	+	0.866025i	0.500000	+	0.866025i
$957$		0			0
$958$		0			0
$959$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$960$	0.500000	−	0.866025i	0.500000	−	0.866025i
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$966$	0.500000	+	0.866025i	0.500000	+	0.866025i
$967$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$967$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$968$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$969$		0			0
$970$		0			0
$971$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$972$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$973$	−1.00000			−1.00000
$974$	0.500000	+	0.866025i	0.500000	+	0.866025i
$975$		0			0
$976$	0.500000	−	0.866025i	0.500000	−	0.866025i
$977$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$977$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$	−1.00000			−1.00000
$981$		0			0
$982$		0			0
$983$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$983$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	1.00000	+	1.73205i	1.00000	+	1.73205i
$989$		0			0
$990$		0			0
$991$	2.00000			2.00000			1.00000			$0$
$991$	2.00000			2.00000			1.00000			$0$
$992$		0			0
$993$		0			0
$994$	0.500000	−	0.866025i	0.500000	−	0.866025i
$995$		0			0
$996$	2.00000			2.00000
$997$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$997$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.1.bn.b.13.1	yes	2
3.2	odd	2		1512.1.bn.a.685.1		2
4.3	odd	2		2016.1.bv.a.1777.1		2
7.2	even	3		3528.1.cw.a.2677.1		2
7.3	odd	6		3528.1.bp.b.3253.1		2
7.4	even	3		3528.1.bp.a.3253.1		2
7.5	odd	6		3528.1.cw.b.2677.1		2
7.6	odd	2		504.1.bn.a.13.1	✓	2
8.3	odd	2		2016.1.bv.b.1777.1		2
8.5	even	2		504.1.bn.a.13.1	✓	2
9.2	odd	6		1512.1.bn.a.181.1		2
9.7	even	3	inner	504.1.bn.b.349.1	yes	2
21.20	even	2		1512.1.bn.b.685.1		2
24.5	odd	2		1512.1.bn.b.685.1		2
28.27	even	2		2016.1.bv.b.1777.1		2
36.7	odd	6		2016.1.bv.a.1105.1		2
56.5	odd	6		3528.1.cw.a.2677.1		2
56.13	odd	2	CM	504.1.bn.b.13.1	yes	2
56.27	even	2		2016.1.bv.a.1777.1		2
56.37	even	6		3528.1.cw.b.2677.1		2
56.45	odd	6		3528.1.bp.a.3253.1		2
56.53	even	6		3528.1.bp.b.3253.1		2
63.16	even	3		3528.1.bp.a.1501.1		2
63.20	even	6		1512.1.bn.b.181.1		2
63.25	even	3		3528.1.cw.a.2077.1		2
63.34	odd	6		504.1.bn.a.349.1	yes	2
63.52	odd	6		3528.1.cw.b.2077.1		2
63.61	odd	6		3528.1.bp.b.1501.1		2
72.29	odd	6		1512.1.bn.b.181.1		2
72.43	odd	6		2016.1.bv.b.1105.1		2
72.61	even	6		504.1.bn.a.349.1	yes	2
168.125	even	2		1512.1.bn.a.685.1		2
252.223	even	6		2016.1.bv.b.1105.1		2
504.61	odd	6		3528.1.bp.a.1501.1		2
504.205	even	6		3528.1.bp.b.1501.1		2
504.277	even	6		3528.1.cw.b.2077.1		2
504.349	odd	6	inner	504.1.bn.b.349.1	yes	2
504.461	even	6		1512.1.bn.a.181.1		2
504.475	even	6		2016.1.bv.a.1105.1		2
504.493	odd	6		3528.1.cw.a.2077.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.1.bn.a.13.1	✓	2	7.6	odd	2
504.1.bn.a.13.1	✓	2	8.5	even	2
504.1.bn.a.349.1	yes	2	63.34	odd	6
504.1.bn.a.349.1	yes	2	72.61	even	6
504.1.bn.b.13.1	yes	2	1.1	even	1	trivial
504.1.bn.b.13.1	yes	2	56.13	odd	2	CM
504.1.bn.b.349.1	yes	2	9.7	even	3	inner
504.1.bn.b.349.1	yes	2	504.349	odd	6	inner
1512.1.bn.a.181.1		2	9.2	odd	6
1512.1.bn.a.181.1		2	504.461	even	6
1512.1.bn.a.685.1		2	3.2	odd	2
1512.1.bn.a.685.1		2	168.125	even	2
1512.1.bn.b.181.1		2	63.20	even	6
1512.1.bn.b.181.1		2	72.29	odd	6
1512.1.bn.b.685.1		2	21.20	even	2
1512.1.bn.b.685.1		2	24.5	odd	2
2016.1.bv.a.1105.1		2	36.7	odd	6
2016.1.bv.a.1105.1		2	504.475	even	6
2016.1.bv.a.1777.1		2	4.3	odd	2
2016.1.bv.a.1777.1		2	56.27	even	2
2016.1.bv.b.1105.1		2	72.43	odd	6
2016.1.bv.b.1105.1		2	252.223	even	6
2016.1.bv.b.1777.1		2	8.3	odd	2
2016.1.bv.b.1777.1		2	28.27	even	2
3528.1.bp.a.1501.1		2	63.16	even	3
3528.1.bp.a.1501.1		2	504.61	odd	6
3528.1.bp.a.3253.1		2	7.4	even	3
3528.1.bp.a.3253.1		2	56.45	odd	6
3528.1.bp.b.1501.1		2	63.61	odd	6
3528.1.bp.b.1501.1		2	504.205	even	6
3528.1.bp.b.3253.1		2	7.3	odd	6
3528.1.bp.b.3253.1		2	56.53	even	6
3528.1.cw.a.2077.1		2	63.25	even	3
3528.1.cw.a.2077.1		2	504.493	odd	6
3528.1.cw.a.2677.1		2	7.2	even	3
3528.1.cw.a.2677.1		2	56.5	odd	6
3528.1.cw.b.2077.1		2	63.52	odd	6
3528.1.cw.b.2077.1		2	504.277	even	6
3528.1.cw.b.2677.1		2	7.5	odd	6
3528.1.cw.b.2677.1		2	56.37	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	504.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +(-0.500000 + 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 - 0.866025i) q^{18} -1.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{21} +(0.500000 - 0.866025i) q^{23} +1.00000 q^{24} +2.00000 q^{26} +1.00000 q^{27} +1.00000 q^{28} -1.00000 q^{30} +(-0.500000 + 0.866025i) q^{32} -1.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.500000 + 0.866025i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-0.500000 + 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{45} -1.00000 q^{46} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.00000 - 1.73205i) q^{52} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 - 0.866025i) q^{56} -1.00000 q^{57} +(-1.00000 + 1.73205i) q^{59} +(0.500000 + 0.866025i) q^{60} +(0.500000 + 0.866025i) q^{61} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(0.500000 - 0.866025i) q^{69} +(0.500000 + 0.866025i) q^{70} -1.00000 q^{71} +1.00000 q^{72} +(0.500000 - 0.866025i) q^{76} +2.00000 q^{78} +(0.500000 + 0.866025i) q^{79} -1.00000 q^{80} +1.00000 q^{81} +(-1.00000 - 1.73205i) q^{83} +1.00000 q^{84} -1.00000 q^{90} +2.00000 q^{91} +(0.500000 + 0.866025i) q^{92} +(-0.500000 + 0.866025i) q^{95} +(-0.500000 + 0.866025i) q^{96} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} - q^{4} + q^{5} - q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 - q^4 + q^5 - q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} + 2 q^{3} - q^{4} + q^{5} - q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} - q^{12} - 2 q^{13} - q^{14} + q^{15} - q^{16} - q^{18} - 2 q^{19} + q^{20} - q^{21} + q^{23} + 2 q^{24} + 4 q^{26} + 2 q^{27} + 2 q^{28} - 2 q^{30} - q^{32} - 2 q^{35} - q^{36} + q^{38} - 2 q^{39} + q^{40} - q^{42} + q^{45} - 2 q^{46} - q^{48} - q^{49} - 2 q^{52} - q^{54} - q^{56} - 2 q^{57} - 2 q^{59} + q^{60} + q^{61} - q^{63} + 2 q^{64} + 2 q^{65} + q^{69} + q^{70} - 2 q^{71} + 2 q^{72} + q^{76} + 4 q^{78} + q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{83} + 2 q^{84} - 2 q^{90} + 4 q^{91} + q^{92} - q^{95} - q^{96} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 - q^4 + q^5 - q^6 - q^7 + 2 * q^8 + 2 * q^9 - 2 * q^10 - q^12 - 2 * q^13 - q^14 + q^15 - q^16 - q^18 - 2 * q^19 + q^20 - q^21 + q^23 + 2 * q^24 + 4 * q^26 + 2 * q^27 + 2 * q^28 - 2 * q^30 - q^32 - 2 * q^35 - q^36 + q^38 - 2 * q^39 + q^40 - q^42 + q^45 - 2 * q^46 - q^48 - q^49 - 2 * q^52 - q^54 - q^56 - 2 * q^57 - 2 * q^59 + q^60 + q^61 - q^63 + 2 * q^64 + 2 * q^65 + q^69 + q^70 - 2 * q^71 + 2 * q^72 + q^76 + 4 * q^78 + q^79 - 2 * q^80 + 2 * q^81 - 2 * q^83 + 2 * q^84 - 2 * q^90 + 4 * q^91 + q^92 - q^95 - q^96 + 2 * q^98

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