LMFDB - Embedded newform 728.1.bs.b.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,1,Mod(51,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 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("728.51");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	728.bs (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:	$0.363319329197$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of 9.1.13763268972544.1

Embedding invariants

Embedding label			51.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	728.51
Dual form			728.1.bs.b.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.766044 - 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.939693 + 1.62760i) q^{5} -1.53209 q^{6} +(-0.766044 - 0.642788i) q^{7} -1.00000 q^{8} +(-0.673648 + 1.16679i) q^{9} +(0.939693 + 1.62760i) q^{10} +(-0.766044 + 1.32683i) q^{12} -1.00000 q^{13} +(-0.939693 + 0.342020i) q^{14} +2.87939 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.173648 - 0.300767i) q^{17} +(0.673648 + 1.16679i) q^{18} +1.87939 q^{20} +(-0.266044 + 1.50881i) q^{21} +(0.766044 + 1.32683i) q^{24} +(-1.26604 - 2.19285i) q^{25} +(-0.500000 + 0.866025i) q^{26} +0.532089 q^{27} +(-0.173648 + 0.984808i) q^{28} +(1.43969 - 2.49362i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} -0.347296 q^{34} +(1.76604 - 0.642788i) q^{35} +1.34730 q^{36} +(0.766044 - 1.32683i) q^{37} +(0.766044 + 1.32683i) q^{39} +(0.939693 - 1.62760i) q^{40} +(1.17365 + 0.984808i) q^{42} -1.87939 q^{43} +(-1.26604 - 2.19285i) q^{45} +(0.173648 - 0.300767i) q^{47} +1.53209 q^{48} +(0.173648 + 0.984808i) q^{49} -2.53209 q^{50} +(-0.266044 + 0.460802i) q^{51} +(0.500000 + 0.866025i) q^{52} +(0.266044 - 0.460802i) q^{54} +(0.766044 + 0.642788i) q^{56} +(-1.43969 - 2.49362i) q^{60} -1.00000 q^{62} +(1.26604 - 0.460802i) q^{63} +1.00000 q^{64} +(0.939693 - 1.62760i) q^{65} +(-0.173648 + 0.300767i) q^{68} +(0.326352 - 1.85083i) q^{70} -0.347296 q^{71} +(0.673648 - 1.16679i) q^{72} +(-0.766044 - 1.32683i) q^{74} +(-1.93969 + 3.35965i) q^{75} +1.53209 q^{78} +(-0.939693 - 1.62760i) q^{80} +(0.266044 + 0.460802i) q^{81} +(1.43969 - 0.524005i) q^{84} +0.652704 q^{85} +(-0.939693 + 1.62760i) q^{86} -2.53209 q^{90} +(0.766044 + 0.642788i) q^{91} +(-0.766044 + 1.32683i) q^{93} +(-0.173648 - 0.300767i) q^{94} +(0.766044 - 1.32683i) q^{96} +(0.939693 + 0.342020i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} - 3 q^{9} - 6 q^{13} + 6 q^{15} - 3 q^{16} + 3 q^{18} + 3 q^{21} - 3 q^{25} - 3 q^{26} - 6 q^{27} + 3 q^{30} - 3 q^{31} + 3 q^{32} + 6 q^{35} + 6 q^{36} + 6 q^{42} - 3 q^{45}+ \cdots - 6 q^{90}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 - 3 * q^9 - 6 * q^13 + 6 * q^15 - 3 * q^16 + 3 * q^18 + 3 * q^21 - 3 * q^25 - 3 * q^26 - 6 * q^27 + 3 * q^30 - 3 * q^31 + 3 * q^32 + 6 * q^35 + 6 * q^36 + 6 * q^42 - 3 * q^45 - 6 * q^50 + 3 * q^51 + 3 * q^52 - 3 * q^54 - 3 * q^60 - 6 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^70 + 3 * q^72 - 6 * q^75 - 3 * q^81 + 3 * q^84 + 6 * q^85 - 6 * q^90

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	0.500000	−	0.866025i	0.500000	−	0.866025i
$2$	0.500000	−	0.866025i	0.500000	−	0.866025i
$3$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$3$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$5$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$6$	−1.53209			−1.53209
$7$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$7$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$8$	−1.00000			−1.00000
$9$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$10$	0.939693	+	1.62760i	0.939693	+	1.62760i
$11$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$11$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$12$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$13$	−1.00000			−1.00000
$13$	−1.00000			−1.00000
$14$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$15$	2.87939			2.87939
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$17$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$18$	0.673648	+	1.16679i	0.673648	+	1.16679i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	1.87939			1.87939
$21$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$22$		0			0
$23$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$23$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$24$	0.766044	+	1.32683i	0.766044	+	1.32683i
$25$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$26$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$27$	0.532089			0.532089
$28$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	1.43969	−	2.49362i	1.43969	−	2.49362i
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$31$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$32$	0.500000	+	0.866025i	0.500000	+	0.866025i
$33$		0			0
$34$	−0.347296			−0.347296
$35$	1.76604	−	0.642788i	1.76604	−	0.642788i
$36$	1.34730			1.34730
$37$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$37$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$38$		0			0
$39$	0.766044	+	1.32683i	0.766044	+	1.32683i
$40$	0.939693	−	1.62760i	0.939693	−	1.62760i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$	1.17365	+	0.984808i	1.17365	+	0.984808i
$43$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$43$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$44$		0			0
$45$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$46$		0			0
$47$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$47$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$48$	1.53209			1.53209
$49$	0.173648	+	0.984808i	0.173648	+	0.984808i
$50$	−2.53209			−2.53209
$51$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$52$	0.500000	+	0.866025i	0.500000	+	0.866025i
$53$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$53$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$54$	0.266044	−	0.460802i	0.266044	−	0.460802i
$55$		0			0
$56$	0.766044	+	0.642788i	0.766044	+	0.642788i
$57$		0			0
$58$		0			0
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$	−1.00000			−1.00000
$63$	1.26604	−	0.460802i	1.26604	−	0.460802i
$64$	1.00000			1.00000
$65$	0.939693	−	1.62760i	0.939693	−	1.62760i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$69$		0			0
$70$	0.326352	−	1.85083i	0.326352	−	1.85083i
$71$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$71$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$72$	0.673648	−	1.16679i	0.673648	−	1.16679i
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$75$	−1.93969	+	3.35965i	−1.93969	+	3.35965i
$76$		0			0
$77$		0			0
$78$	1.53209			1.53209
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$81$	0.266044	+	0.460802i	0.266044	+	0.460802i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	1.43969	−	0.524005i	1.43969	−	0.524005i
$85$	0.652704			0.652704
$86$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$87$		0			0
$88$		0			0
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$	−2.53209			−2.53209
$91$	0.766044	+	0.642788i	0.766044	+	0.642788i
$92$		0			0
$93$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$94$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$95$		0			0
$96$	0.766044	−	1.32683i	0.766044	−	1.32683i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	0.939693	+	0.342020i	0.939693	+	0.342020i
$99$		0			0
$100$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$	0.266044	+	0.460802i	0.266044	+	0.460802i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	1.00000			1.00000
$105$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$106$		0			0
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$108$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$109$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$109$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$110$		0			0
$111$	−2.34730			−2.34730
$112$	0.939693	−	0.342020i	0.939693	−	0.342020i
$113$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$113$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.673648	−	1.16679i	0.673648	−	1.16679i
$118$		0			0
$119$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$120$	−2.87939			−2.87939
$121$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$125$	2.87939			2.87939
$126$	0.233956	−	1.32683i	0.233956	−	1.32683i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	0.500000	−	0.866025i	0.500000	−	0.866025i
$129$	1.43969	+	2.49362i	1.43969	+	2.49362i
$130$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$131$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$131$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$136$	0.173648	+	0.300767i	0.173648	+	0.300767i
$137$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$137$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$138$		0			0
$139$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$139$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$140$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$141$	−0.532089			−0.532089
$142$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$143$		0			0
$144$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$145$		0			0
$146$		0			0
$147$	1.17365	−	0.984808i	1.17365	−	0.984808i
$148$	−1.53209			−1.53209
$149$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$149$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$150$	1.93969	+	3.35965i	1.93969	+	3.35965i
$151$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$151$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$152$		0			0
$153$	0.467911			0.467911
$154$		0			0
$155$	1.87939			1.87939
$156$	0.766044	−	1.32683i	0.766044	−	1.32683i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$		0			0
$159$		0			0
$160$	−1.87939			−1.87939
$161$		0			0
$162$	0.532089			0.532089
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$167$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$168$	0.266044	−	1.50881i	0.266044	−	1.50881i
$169$	1.00000			1.00000
$170$	0.326352	−	0.565258i	0.326352	−	0.565258i
$171$		0			0
$172$	0.939693	+	1.62760i	0.939693	+	1.62760i
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$		0			0
$175$	−0.439693	+	2.49362i	−0.439693	+	2.49362i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$179$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$180$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	0.939693	−	0.342020i	0.939693	−	0.342020i
$183$		0			0
$184$		0			0
$185$	1.43969	+	2.49362i	1.43969	+	2.49362i
$186$	0.766044	+	1.32683i	0.766044	+	1.32683i
$187$		0			0
$188$	−0.347296			−0.347296
$189$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$	−2.87939			−2.87939
$196$	0.766044	−	0.642788i	0.766044	−	0.642788i
$197$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$197$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	1.26604	+	2.19285i	1.26604	+	2.19285i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.532089			0.532089
$205$		0			0
$206$		0			0
$207$		0			0
$208$	0.500000	−	0.866025i	0.500000	−	0.866025i
$209$		0			0
$210$	−2.70574	+	0.984808i	−2.70574	+	0.984808i
$211$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$211$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$212$		0			0
$213$	0.266044	+	0.460802i	0.266044	+	0.460802i
$214$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$215$	1.76604	−	3.05888i	1.76604	−	3.05888i
$216$	−0.532089			−0.532089
$217$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$218$	−1.87939			−1.87939
$219$		0			0
$220$		0			0
$221$	0.173648	+	0.300767i	0.173648	+	0.300767i
$222$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$223$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$223$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$224$	0.173648	−	0.984808i	0.173648	−	0.984808i
$225$	3.41147			3.41147
$226$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$		0			0
$229$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$229$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$233$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$234$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$235$	0.326352	+	0.565258i	0.326352	+	0.565258i
$236$		0			0
$237$		0			0
$238$	0.266044	+	0.223238i	0.266044	+	0.223238i
$239$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$239$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$240$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$241$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$241$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$242$	0.500000	+	0.866025i	0.500000	+	0.866025i
$243$	0.673648	−	1.16679i	0.673648	−	1.16679i
$244$		0			0
$245$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$246$		0			0
$247$		0			0
$248$	0.500000	+	0.866025i	0.500000	+	0.866025i
$249$		0			0
$250$	1.43969	−	2.49362i	1.43969	−	2.49362i
$251$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$251$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$252$	−1.03209	−	0.866025i	−1.03209	−	0.866025i
$253$		0			0
$254$		0			0
$255$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$257$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$258$	2.87939			2.87939
$259$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$260$	−1.87939			−1.87939
$261$		0			0
$262$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$269$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$270$	0.500000	+	0.866025i	0.500000	+	0.866025i
$271$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$271$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$272$	0.347296			0.347296
$273$	0.266044	−	1.50881i	0.266044	−	1.50881i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$	0.173648	−	0.300767i	0.173648	−	0.300767i
$279$	1.34730			1.34730
$280$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$283$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$283$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$284$	0.173648	+	0.300767i	0.173648	+	0.300767i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.34730			−1.34730
$289$	0.439693	−	0.761570i	0.439693	−	0.761570i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$293$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$294$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$295$		0			0
$296$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$297$		0			0
$298$	0.500000	+	0.866025i	0.500000	+	0.866025i
$299$		0			0
$300$	3.87939			3.87939
$301$	1.43969	+	1.20805i	1.43969	+	1.20805i
$302$	0.347296			0.347296
$303$		0			0
$304$		0			0
$305$		0			0
$306$	0.233956	−	0.405223i	0.233956	−	0.405223i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	0.939693	−	1.62760i	0.939693	−	1.62760i
$311$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$311$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$312$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$313$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$313$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$314$		0			0
$315$	−0.439693	+	2.49362i	−0.439693	+	2.49362i
$316$		0			0
$317$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$317$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$321$	−1.53209			−1.53209
$322$		0			0
$323$		0			0
$324$	0.266044	−	0.460802i	0.266044	−	0.460802i
$325$	1.26604	+	2.19285i	1.26604	+	2.19285i
$326$		0			0
$327$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$328$		0			0
$329$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	1.03209	+	1.78763i	1.03209	+	1.78763i
$334$	0.500000	−	0.866025i	0.500000	−	0.866025i
$335$		0			0
$336$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$337$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$337$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$338$	0.500000	−	0.866025i	0.500000	−	0.866025i
$339$	0.766044	+	1.32683i	0.766044	+	1.32683i
$340$	−0.326352	−	0.565258i	−0.326352	−	0.565258i
$341$		0			0
$342$		0			0
$343$	0.500000	−	0.866025i	0.500000	−	0.866025i
$344$	1.87939			1.87939
$345$		0			0
$346$		0			0
$347$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$347$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$348$		0			0
$349$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$349$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$350$	1.93969	+	1.62760i	1.93969	+	1.62760i
$351$	−0.532089			−0.532089
$352$		0			0
$353$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$353$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$354$		0			0
$355$	0.326352	−	0.565258i	0.326352	−	0.565258i
$356$		0			0
$357$	0.500000	−	0.181985i	0.500000	−	0.181985i
$358$	1.87939			1.87939
$359$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$359$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$360$	1.26604	+	2.19285i	1.26604	+	2.19285i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	1.53209			1.53209
$364$	0.173648	−	0.984808i	0.173648	−	0.984808i
$365$		0			0
$366$		0			0
$367$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$367$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$368$		0			0
$369$		0			0
$370$	2.87939			2.87939
$371$		0			0
$372$	1.53209			1.53209
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−2.20574	−	3.82045i	−2.20574	−	3.82045i
$376$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$377$		0			0
$378$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$383$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$384$	−1.53209			−1.53209
$385$		0			0
$386$		0			0
$387$	1.26604	−	2.19285i	1.26604	−	2.19285i
$388$		0			0
$389$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$389$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$390$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$391$		0			0
$392$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$393$	−2.87939			−2.87939
$394$	0.939693	−	1.62760i	0.939693	−	1.62760i
$395$		0			0
$396$		0			0
$397$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$397$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	2.53209			2.53209
$401$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$401$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$	0.500000	+	0.866025i	0.500000	+	0.866025i
$404$		0			0
$405$	−1.00000			−1.00000
$406$		0			0
$407$		0			0
$408$	0.266044	−	0.460802i	0.266044	−	0.460802i
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$417$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$418$		0			0
$419$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$419$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$420$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$421$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$421$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$422$	0.173648	−	0.300767i	0.173648	−	0.300767i
$423$	0.233956	+	0.405223i	0.233956	+	0.405223i
$424$		0			0
$425$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$426$	0.532089			0.532089
$427$		0			0
$428$	−1.00000			−1.00000
$429$		0			0
$430$	−1.76604	−	3.05888i	−1.76604	−	3.05888i
$431$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$431$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$432$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$433$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$433$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$434$	0.766044	+	0.642788i	0.766044	+	0.642788i
$435$		0			0
$436$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$442$	0.347296			0.347296
$443$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$443$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$444$	1.17365	+	2.03282i	1.17365	+	2.03282i
$445$		0			0
$446$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$447$	1.53209			1.53209
$448$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	1.70574	−	2.95442i	1.70574	−	2.95442i
$451$		0			0
$452$	0.500000	+	0.866025i	0.500000	+	0.866025i
$453$	0.266044	−	0.460802i	0.266044	−	0.460802i
$454$		0			0
$455$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$459$	−0.0923963	−	0.160035i	−0.0923963	−	0.160035i
$460$		0			0
$461$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$461$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$462$		0			0
$463$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$463$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$464$		0			0
$465$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$466$	0.766044	+	1.32683i	0.766044	+	1.32683i
$467$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$467$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$468$	−1.34730			−1.34730
$469$		0			0
$470$	0.652704			0.652704
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	0.326352	−	0.118782i	0.326352	−	0.118782i
$477$		0			0
$478$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$479$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$479$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$480$	1.43969	+	2.49362i	1.43969	+	2.49362i
$481$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$482$		0			0
$483$		0			0
$484$	1.00000			1.00000
$485$		0			0
$486$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$487$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$487$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$491$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$491$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.00000			1.00000
$497$	0.266044	+	0.223238i	0.266044	+	0.223238i
$498$		0			0
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$501$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$502$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$503$		0			0		1.00000			$0$
$503$		0			0		−1.00000			$\pi$
$504$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$505$		0			0
$506$		0			0
$507$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$508$		0			0
$509$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$509$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$510$	−1.00000			−1.00000
$511$		0			0
$512$	−1.00000			−1.00000
$513$		0			0
$514$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$515$		0			0
$516$	1.43969	−	2.49362i	1.43969	−	2.49362i
$517$		0			0
$518$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$519$		0			0
$520$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$521$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$521$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$522$		0			0
$523$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$523$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$524$	−1.87939			−1.87939
$525$	3.64543	−	1.32683i	3.64543	−	1.32683i
$526$		0			0
$527$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$528$		0			0
$529$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.939693	+	1.62760i	0.939693	+	1.62760i
$536$		0			0
$537$	1.43969	−	2.49362i	1.43969	−	2.49362i
$538$		0			0
$539$		0			0
$540$	1.00000			1.00000
$541$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$541$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$542$	0.939693	+	1.62760i	0.939693	+	1.62760i
$543$		0			0
$544$	0.173648	−	0.300767i	0.173648	−	0.300767i
$545$	3.53209			3.53209
$546$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$547$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$547$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	2.20574	−	3.82045i	2.20574	−	3.82045i
$556$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$557$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$557$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$558$	0.673648	−	1.16679i	0.673648	−	1.16679i
$559$	1.87939			1.87939
$560$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$561$		0			0
$562$		0			0
$563$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$563$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$564$	0.266044	+	0.460802i	0.266044	+	0.460802i
$565$	0.939693	−	1.62760i	0.939693	−	1.62760i
$566$	−2.00000			−2.00000
$567$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$568$	0.347296			0.347296
$569$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$569$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$570$		0			0
$571$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$571$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$577$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$577$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$578$	−0.439693	−	0.761570i	−0.439693	−	0.761570i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	1.26604	+	2.19285i	1.26604	+	2.19285i
$586$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$589$		0			0
$590$		0			0
$591$	−1.43969	−	2.49362i	−1.43969	−	2.49362i
$592$	0.766044	+	1.32683i	0.766044	+	1.32683i
$593$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$593$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$594$		0			0
$595$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$596$	1.00000			1.00000
$597$		0			0
$598$		0			0
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$	1.93969	−	3.35965i	1.93969	−	3.35965i
$601$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$601$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$602$	1.76604	−	0.642788i	1.76604	−	0.642788i
$603$		0			0
$604$	0.173648	−	0.300767i	0.173648	−	0.300767i
$605$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$606$		0			0
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$612$	−0.233956	−	0.405223i	−0.233956	−	0.405223i
$613$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$613$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$		0			0
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	−1.53209			−1.53209
$625$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$626$	0.173648	+	0.300767i	0.173648	+	0.300767i
$627$		0			0
$628$		0			0
$629$	−0.532089			−0.532089
$630$	1.93969	+	1.62760i	1.93969	+	1.62760i
$631$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$631$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$632$		0			0
$633$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$634$	0.500000	+	0.866025i	0.500000	+	0.866025i
$635$		0			0
$636$		0			0
$637$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$638$		0			0
$639$	0.233956	−	0.405223i	0.233956	−	0.405223i
$640$	0.939693	+	1.62760i	0.939693	+	1.62760i
$641$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$641$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$	−5.41147			−5.41147
$646$		0			0
$647$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$647$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$648$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$649$		0			0
$650$	2.53209			2.53209
$651$	1.43969	−	0.524005i	1.43969	−	0.524005i
$652$		0			0
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$	1.43969	+	2.49362i	1.43969	+	2.49362i
$655$	1.76604	+	3.05888i	1.76604	+	3.05888i
$656$		0			0
$657$		0			0
$658$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$659$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$659$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$661$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$662$		0			0
$663$	0.266044	−	0.460802i	0.266044	−	0.460802i
$664$		0			0
$665$		0			0
$666$	2.06418			2.06418
$667$		0			0
$668$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$669$	1.17365	+	2.03282i	1.17365	+	2.03282i
$670$		0			0
$671$		0			0
$672$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$673$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$673$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$674$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$675$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	1.53209			1.53209
$679$		0			0
$680$	−0.652704			−0.652704
$681$		0			0
$682$		0			0
$683$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$683$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$684$		0			0
$685$		0			0
$686$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$687$	−2.34730			−2.34730
$688$	0.939693	−	1.62760i	0.939693	−	1.62760i
$689$		0			0
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$		0			0
$694$	−0.347296			−0.347296
$695$	−0.326352	+	0.565258i	−0.326352	+	0.565258i
$696$		0			0
$697$		0			0
$698$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$699$	2.34730			2.34730
$700$	2.37939	−	0.866025i	2.37939	−	0.866025i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$703$		0			0
$704$		0			0
$705$	0.500000	−	0.866025i	0.500000	−	0.866025i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$709$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$710$	−0.326352	−	0.565258i	−0.326352	−	0.565258i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$715$		0			0
$716$	0.939693	−	1.62760i	0.939693	−	1.62760i
$717$	1.17365	+	2.03282i	1.17365	+	2.03282i
$718$	0.500000	+	0.866025i	0.500000	+	0.866025i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	2.53209			2.53209
$721$		0			0
$722$	−1.00000			−1.00000
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.766044	−	1.32683i	0.766044	−	1.32683i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$729$	−1.53209			−1.53209
$730$		0			0
$731$	0.326352	+	0.565258i	0.326352	+	0.565258i
$732$		0			0
$733$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$733$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$734$		0			0
$735$	0.500000	+	2.83564i	0.500000	+	2.83564i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	1.43969	−	2.49362i	1.43969	−	2.49362i
$741$		0			0
$742$		0			0
$743$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$743$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$744$	0.766044	−	1.32683i	0.766044	−	1.32683i
$745$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$750$	−4.41147			−4.41147
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	0.173648	+	0.300767i	0.173648	+	0.300767i
$753$	0.766044	+	1.32683i	0.766044	+	1.32683i
$754$		0			0
$755$	−0.652704			−0.652704
$756$	−0.0923963	+	0.524005i	−0.0923963	+	0.524005i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$761$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$762$		0			0
$763$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$764$		0			0
$765$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$766$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$767$		0			0
$768$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$769$		0			0		1.00000			$0$
$769$		0			0		−1.00000			$\pi$
$770$		0			0
$771$	−2.87939			−2.87939
$772$		0			0
$773$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$773$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$774$	−1.26604	−	2.19285i	−1.26604	−	2.19285i
$775$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$776$		0			0
$777$	1.79813	+	1.50881i	1.79813	+	1.50881i
$778$		0			0
$779$		0			0
$780$	1.43969	+	2.49362i	1.43969	+	2.49362i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$785$		0			0
$786$	−1.43969	+	2.49362i	−1.43969	+	2.49362i
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$789$		0			0
$790$		0			0
$791$	0.766044	+	0.642788i	0.766044	+	0.642788i
$792$		0			0
$793$		0			0
$794$	0.500000	+	0.866025i	0.500000	+	0.866025i
$795$		0			0
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$	−0.120615			−0.120615
$800$	1.26604	−	2.19285i	1.26604	−	2.19285i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	1.00000			1.00000
$807$		0			0
$808$		0			0
$809$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$809$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$810$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	2.87939			2.87939
$814$		0			0
$815$		0			0
$816$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$817$		0			0
$818$		0			0
$819$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$820$		0			0
$821$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$821$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$822$		0			0
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$829$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$830$		0			0
$831$		0			0
$832$	−1.00000			−1.00000
$833$	0.266044	−	0.223238i	0.266044	−	0.223238i
$834$	−0.532089			−0.532089
$835$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$836$		0			0
$837$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$838$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$839$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$839$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$840$	2.20574	+	1.85083i	2.20574	+	1.85083i
$841$	1.00000			1.00000
$842$	0.939693	−	1.62760i	0.939693	−	1.62760i
$843$		0			0
$844$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$845$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$846$	0.467911			0.467911
$847$	0.939693	−	0.342020i	0.939693	−	0.342020i
$848$		0			0
$849$	−1.53209	+	2.65366i	−1.53209	+	2.65366i
$850$	0.439693	+	0.761570i	0.439693	+	0.761570i
$851$		0			0
$852$	0.266044	−	0.460802i	0.266044	−	0.460802i
$853$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$853$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$854$		0			0
$855$		0			0
$856$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$857$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$857$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$858$		0			0
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$860$	−3.53209			−3.53209
$861$		0			0
$862$	−1.87939			−1.87939
$863$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$863$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$864$	0.266044	+	0.460802i	0.266044	+	0.460802i
$865$		0			0
$866$	0.766044	−	1.32683i	0.766044	−	1.32683i
$867$	−1.34730			−1.34730
$868$	0.939693	−	0.342020i	0.939693	−	0.342020i
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.939693	+	1.62760i	0.939693	+	1.62760i
$873$		0			0
$874$		0			0
$875$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$876$		0			0
$877$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$877$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$878$		0			0
$879$	1.17365	+	2.03282i	1.17365	+	2.03282i
$880$		0			0
$881$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$881$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$882$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$883$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$883$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$884$	0.173648	−	0.300767i	0.173648	−	0.300767i
$885$		0			0
$886$	0.766044	+	1.32683i	0.766044	+	1.32683i
$887$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$887$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$888$	2.34730			2.34730
$889$		0			0
$890$		0			0
$891$		0			0
$892$	0.766044	+	1.32683i	0.766044	+	1.32683i
$893$		0			0
$894$	0.766044	−	1.32683i	0.766044	−	1.32683i
$895$	−3.53209			−3.53209
$896$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−1.70574	−	2.95442i	−1.70574	−	2.95442i
$901$		0			0
$902$		0			0
$903$	0.500000	−	2.83564i	0.500000	−	2.83564i
$904$	1.00000			1.00000
$905$		0			0
$906$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$907$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$907$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$908$		0			0
$909$		0			0
$910$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.53209			−1.53209
$917$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$918$	−0.184793			−0.184793
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$		0			0
$922$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$923$	0.347296			0.347296
$924$		0			0
$925$	−3.87939			−3.87939
$926$	0.500000	−	0.866025i	0.500000	−	0.866025i
$927$		0			0
$928$		0			0
$929$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$929$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$930$	−2.87939			−2.87939
$931$		0			0
$932$	1.53209			1.53209
$933$		0			0
$934$	1.00000	+	1.73205i	1.00000	+	1.73205i
$935$		0			0
$936$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$937$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$937$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$	0.532089			0.532089
$940$	0.326352	−	0.565258i	0.326352	−	0.565258i
$941$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$941$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	0.939693	−	0.342020i	0.939693	−	0.342020i
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	1.53209			1.53209
$952$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$953$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$953$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$954$		0			0
$955$		0			0
$956$	0.766044	+	1.32683i	0.766044	+	1.32683i
$957$		0			0
$958$	1.53209			1.53209
$959$		0			0
$960$	2.87939			2.87939
$961$		0			0
$962$	0.766044	+	1.32683i	0.766044	+	1.32683i
$963$	0.673648	+	1.16679i	0.673648	+	1.16679i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$967$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$968$	0.500000	−	0.866025i	0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$971$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$972$	−1.34730			−1.34730
$973$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$974$	−1.00000			−1.00000
$975$	1.93969	−	3.35965i	1.93969	−	3.35965i
$976$		0			0
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$		0			0
$980$	0.326352	+	1.85083i	0.326352	+	1.85083i
$981$	2.53209			2.53209
$982$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$983$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$983$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$984$		0			0
$985$	−1.76604	+	3.05888i	−1.76604	+	3.05888i
$986$		0			0
$987$	0.407604	+	0.342020i	0.407604	+	0.342020i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$	0.500000	−	0.866025i	0.500000	−	0.866025i
$993$		0			0
$994$	0.326352	−	0.118782i	0.326352	−	0.118782i
$995$		0			0
$996$		0			0
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$	0.407604	−	0.705990i	0.407604	−	0.705990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.1.bs.b.51.1	yes	6
4.3	odd	2		2912.1.ci.a.1871.3		6
7.4	even	3	inner	728.1.bs.b.571.1	yes	6
8.3	odd	2		728.1.bs.a.51.1	✓	6
8.5	even	2		2912.1.ci.b.1871.3		6
13.12	even	2		728.1.bs.a.51.1	✓	6
28.11	odd	6		2912.1.ci.a.207.3		6
52.51	odd	2		2912.1.ci.b.1871.3		6
56.11	odd	6		728.1.bs.a.571.1	yes	6
56.53	even	6		2912.1.ci.b.207.3		6
91.25	even	6		728.1.bs.a.571.1	yes	6
104.51	odd	2	CM	728.1.bs.b.51.1	yes	6
104.77	even	2		2912.1.ci.a.1871.3		6
364.207	odd	6		2912.1.ci.b.207.3		6
728.389	even	6		2912.1.ci.a.207.3		6
728.571	odd	6	inner	728.1.bs.b.571.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.1.bs.a.51.1	✓	6	8.3	odd	2
728.1.bs.a.51.1	✓	6	13.12	even	2
728.1.bs.a.571.1	yes	6	56.11	odd	6
728.1.bs.a.571.1	yes	6	91.25	even	6
728.1.bs.b.51.1	yes	6	1.1	even	1	trivial
728.1.bs.b.51.1	yes	6	104.51	odd	2	CM
728.1.bs.b.571.1	yes	6	7.4	even	3	inner
728.1.bs.b.571.1	yes	6	728.571	odd	6	inner
2912.1.ci.a.207.3		6	28.11	odd	6
2912.1.ci.a.207.3		6	728.389	even	6
2912.1.ci.a.1871.3		6	4.3	odd	2
2912.1.ci.a.1871.3		6	104.77	even	2
2912.1.ci.b.207.3		6	56.53	even	6
2912.1.ci.b.207.3		6	364.207	odd	6
2912.1.ci.b.1871.3		6	8.5	even	2
2912.1.ci.b.1871.3		6	52.51	odd	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	728.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.766044 - 1.32683i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.939693 + 1.62760i) q^{5} -1.53209 q^{6} +(-0.766044 - 0.642788i) q^{7} -1.00000 q^{8} +(-0.673648 + 1.16679i) q^{9} +(0.939693 + 1.62760i) q^{10} +(-0.766044 + 1.32683i) q^{12} -1.00000 q^{13} +(-0.939693 + 0.342020i) q^{14} +2.87939 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.173648 - 0.300767i) q^{17} +(0.673648 + 1.16679i) q^{18} +1.87939 q^{20} +(-0.266044 + 1.50881i) q^{21} +(0.766044 + 1.32683i) q^{24} +(-1.26604 - 2.19285i) q^{25} +(-0.500000 + 0.866025i) q^{26} +0.532089 q^{27} +(-0.173648 + 0.984808i) q^{28} +(1.43969 - 2.49362i) q^{30} +(-0.500000 - 0.866025i) q^{31} +(0.500000 + 0.866025i) q^{32} -0.347296 q^{34} +(1.76604 - 0.642788i) q^{35} +1.34730 q^{36} +(0.766044 - 1.32683i) q^{37} +(0.766044 + 1.32683i) q^{39} +(0.939693 - 1.62760i) q^{40} +(1.17365 + 0.984808i) q^{42} -1.87939 q^{43} +(-1.26604 - 2.19285i) q^{45} +(0.173648 - 0.300767i) q^{47} +1.53209 q^{48} +(0.173648 + 0.984808i) q^{49} -2.53209 q^{50} +(-0.266044 + 0.460802i) q^{51} +(0.500000 + 0.866025i) q^{52} +(0.266044 - 0.460802i) q^{54} +(0.766044 + 0.642788i) q^{56} +(-1.43969 - 2.49362i) q^{60} -1.00000 q^{62} +(1.26604 - 0.460802i) q^{63} +1.00000 q^{64} +(0.939693 - 1.62760i) q^{65} +(-0.173648 + 0.300767i) q^{68} +(0.326352 - 1.85083i) q^{70} -0.347296 q^{71} +(0.673648 - 1.16679i) q^{72} +(-0.766044 - 1.32683i) q^{74} +(-1.93969 + 3.35965i) q^{75} +1.53209 q^{78} +(-0.939693 - 1.62760i) q^{80} +(0.266044 + 0.460802i) q^{81} +(1.43969 - 0.524005i) q^{84} +0.652704 q^{85} +(-0.939693 + 1.62760i) q^{86} -2.53209 q^{90} +(0.766044 + 0.642788i) q^{91} +(-0.766044 + 1.32683i) q^{93} +(-0.173648 - 0.300767i) q^{94} +(0.766044 - 1.32683i) q^{96} +(0.939693 + 0.342020i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} - 6 q^{8} - 3 q^{9} - 6 q^{13} + 6 q^{15} - 3 q^{16} + 3 q^{18} + 3 q^{21} - 3 q^{25} - 3 q^{26} - 6 q^{27} + 3 q^{30} - 3 q^{31} + 3 q^{32} + 6 q^{35} + 6 q^{36} + 6 q^{42} - 3 q^{45}+ \cdots - 6 q^{90}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 - 6 * q^8 - 3 * q^9 - 6 * q^13 + 6 * q^15 - 3 * q^16 + 3 * q^18 + 3 * q^21 - 3 * q^25 - 3 * q^26 - 6 * q^27 + 3 * q^30 - 3 * q^31 + 3 * q^32 + 6 * q^35 + 6 * q^36 + 6 * q^42 - 3 * q^45 - 6 * q^50 + 3 * q^51 + 3 * q^52 - 3 * q^54 - 3 * q^60 - 6 * q^62 + 3 * q^63 + 6 * q^64 + 3 * q^70 + 3 * q^72 - 6 * q^75 - 3 * q^81 + 3 * q^84 + 6 * q^85 - 6 * q^90

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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