LMFDB - Embedded newform 580.1.bm.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [580,1,Mod(3,580)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(580, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 21, 5]))

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

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

chi := DirichletCharacter("580.3");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$580 = 2^{2} \cdot 5 \cdot 29$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	580.bm (of order $28$ , degree $12$ , 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:	$0.289457707327$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1$ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$D_{28}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{28} - \cdots)$

Embedding invariants

Embedding label			3.1
Root			$0.433884 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	580.3
Dual form			580.1.bm.a.387.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974928 + 0.222521i) q^{2} +(0.900969 - 0.433884i) q^{4} +(0.433884 - 0.900969i) q^{5} +(-0.781831 + 0.623490i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-0.222521 + 0.974928i) q^{10} +(0.0739590 + 0.656405i) q^{13} +(0.623490 - 0.781831i) q^{16} -1.94986i q^{17} +(-0.781831 - 0.623490i) q^{18} -1.00000i q^{20} +(-0.623490 - 0.781831i) q^{25} +(-0.218169 - 0.623490i) q^{26} +(0.781831 + 0.623490i) q^{29} +(-0.433884 + 0.900969i) q^{32} +(0.433884 + 1.90097i) q^{34} +(0.900969 + 0.433884i) q^{36} +(1.12349 + 1.40881i) q^{37} +(0.222521 + 0.974928i) q^{40} +(-1.33485 - 1.33485i) q^{41} +(0.974928 - 0.222521i) q^{45} +(0.781831 - 0.623490i) q^{49} +(0.781831 + 0.623490i) q^{50} +(0.351438 + 0.559311i) q^{52} +(-0.566116 + 0.900969i) q^{53} +(-0.900969 - 0.433884i) q^{58} +(-1.59842 + 0.559311i) q^{61} +(0.222521 - 0.974928i) q^{64} +(0.623490 + 0.218169i) q^{65} +(-0.846011 - 1.75676i) q^{68} +(-0.974928 - 0.222521i) q^{72} +(-0.433884 - 0.0990311i) q^{73} +(-1.40881 - 1.12349i) q^{74} +(-0.433884 - 0.900969i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(1.59842 + 1.00435i) q^{82} +(-1.75676 - 0.846011i) q^{85} +(-1.05737 + 1.68280i) q^{89} +(-0.900969 + 0.433884i) q^{90} +(-0.781831 + 0.376510i) q^{97} +(-0.623490 + 0.781831i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q + 2 q^{4} - 2 q^{9} - 2 q^{10} - 2 q^{13} - 2 q^{16} + 2 q^{25} - 12 q^{26} + 2 q^{36} + 4 q^{37} + 2 q^{40} - 2 q^{41} + 2 q^{52} - 12 q^{53} - 2 q^{58} + 2 q^{61} + 2 q^{64} - 2 q^{65} - 2 q^{81}+ \cdots + 2 q^{98}+O(q^{100})$ 12 * q + 2 * q^4 - 2 * q^9 - 2 * q^10 - 2 * q^13 - 2 * q^16 + 2 * q^25 - 12 * q^26 + 2 * q^36 + 4 * q^37 + 2 * q^40 - 2 * q^41 + 2 * q^52 - 12 * q^53 - 2 * q^58 + 2 * q^61 + 2 * q^64 - 2 * q^65 - 2 * q^81 - 2 * q^82 + 2 * q^89 - 2 * q^90 + 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/580\mathbb{Z}\right)^\times$ .

$n$	$117$	$291$	$321$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{28}\right)$

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

)

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

$2$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$2$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$3$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$3$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$4$	0.900969	−	0.433884i	0.900969	−	0.433884i
$5$	0.433884	−	0.900969i	0.433884	−	0.900969i
$5$	0.433884	−	0.900969i	0.433884	−	0.900969i
$6$		0			0
$7$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$7$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$8$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$9$	0.623490	+	0.781831i	0.623490	+	0.781831i
$10$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$11$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$11$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$12$		0			0
$13$	0.0739590	+	0.656405i	0.0739590	+	0.656405i	0.974928	+	0.222521i	$0.0714286\pi$
$13$	0.0739590	+	0.656405i	0.0739590	+	0.656405i	−0.900969	+	0.433884i	$0.857143\pi$
$14$		0			0
$15$		0			0
$16$	0.623490	−	0.781831i	0.623490	−	0.781831i
$17$		−	1.94986i		−	1.94986i	−0.222521	−	0.974928i	$-0.571429\pi$
$17$		−	1.94986i		−	1.94986i	0.222521	−	0.974928i	$-0.428571\pi$
$18$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$19$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$19$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$20$		−	1.00000i		−	1.00000i
$21$		0			0
$22$		0			0
$23$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$23$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$24$		0			0
$25$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$26$	−0.218169	−	0.623490i	−0.218169	−	0.623490i
$27$		0			0
$28$		0			0
$29$	0.781831	+	0.623490i	0.781831	+	0.623490i
$29$	0.781831	+	0.623490i	0.781831	+	0.623490i
$30$		0			0
$31$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$31$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$32$	−0.433884	+	0.900969i	−0.433884	+	0.900969i
$33$		0			0
$34$	0.433884	+	1.90097i	0.433884	+	1.90097i
$35$		0			0
$36$	0.900969	+	0.433884i	0.900969	+	0.433884i
$37$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.900969	+	0.433884i	$0.142857\pi$
$37$	1.12349	+	1.40881i	1.12349	+	1.40881i	0.222521	+	0.974928i	$0.428571\pi$
$38$		0			0
$39$		0			0
$40$	0.222521	+	0.974928i	0.222521	+	0.974928i
$41$	−1.33485	−	1.33485i	−1.33485	−	1.33485i	−0.900969	−	0.433884i	$-0.857143\pi$
$41$	−1.33485	−	1.33485i	−1.33485	−	1.33485i	−0.433884	−	0.900969i	$-0.642857\pi$
$42$		0			0
$43$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$43$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$44$		0			0
$45$	0.974928	−	0.222521i	0.974928	−	0.222521i
$46$		0			0
$47$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$47$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$48$		0			0
$49$	0.781831	−	0.623490i	0.781831	−	0.623490i
$50$	0.781831	+	0.623490i	0.781831	+	0.623490i
$51$		0			0
$52$	0.351438	+	0.559311i	0.351438	+	0.559311i
$53$	−0.566116	+	0.900969i	−0.566116	+	0.900969i	0.433884	+	0.900969i	$0.357143\pi$
$53$	−0.566116	+	0.900969i	−0.566116	+	0.900969i	−1.00000			$\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	−1.59842	+	0.559311i	−1.59842	+	0.559311i	−0.974928	−	0.222521i	$-0.928571\pi$
$61$	−1.59842	+	0.559311i	−1.59842	+	0.559311i	−0.623490	+	0.781831i	$0.714286\pi$
$62$		0			0
$63$		0			0
$64$	0.222521	−	0.974928i	0.222521	−	0.974928i
$65$	0.623490	+	0.218169i	0.623490	+	0.218169i
$66$		0			0
$67$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$67$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$68$	−0.846011	−	1.75676i	−0.846011	−	1.75676i
$69$		0			0
$70$		0			0
$71$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$71$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$72$	−0.974928	−	0.222521i	−0.974928	−	0.222521i
$73$	−0.433884	−	0.0990311i	−0.433884	−	0.0990311i		−	1.00000i	$-0.5\pi$
$73$	−0.433884	−	0.0990311i	−0.433884	−	0.0990311i	−0.433884	+	0.900969i	$0.642857\pi$
$74$	−1.40881	−	1.12349i	−1.40881	−	1.12349i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$79$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$80$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$81$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$82$	1.59842	+	1.00435i	1.59842	+	1.00435i
$83$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$83$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$84$		0			0
$85$	−1.75676	−	0.846011i	−1.75676	−	0.846011i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.05737	+	1.68280i	−1.05737	+	1.68280i	−0.433884	+	0.900969i	$0.642857\pi$
$89$	−1.05737	+	1.68280i	−1.05737	+	1.68280i	−0.623490	+	0.781831i	$0.714286\pi$
$90$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.781831	+	0.376510i	−0.781831	+	0.376510i	−0.781831	−	0.623490i	$-0.785714\pi$
$97$	−0.781831	+	0.376510i	−0.781831	+	0.376510i			1.00000i	$0.5\pi$
$98$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$99$		0			0
$100$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$101$	0.119137	+	0.189606i	0.119137	+	0.189606i	0.900969	−	0.433884i	$-0.142857\pi$
$101$	0.119137	+	0.189606i	0.119137	+	0.189606i	−0.781831	+	0.623490i	$0.785714\pi$
$102$		0			0
$103$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$103$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$104$	−0.467085	−	0.467085i	−0.467085	−	0.467085i
$105$		0			0
$106$	0.351438	−	1.00435i	0.351438	−	1.00435i
$107$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$107$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$108$		0			0
$109$	−0.781831	−	0.376510i	−0.781831	−	0.376510i		−	1.00000i	$-0.5\pi$
$109$	−0.781831	−	0.376510i	−0.781831	−	0.376510i	−0.781831	+	0.623490i	$0.785714\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.541044	−	1.12349i	0.541044	−	1.12349i	−0.433884	−	0.900969i	$-0.642857\pi$
$113$	0.541044	−	1.12349i	0.541044	−	1.12349i	0.974928	−	0.222521i	$-0.0714286\pi$
$114$		0			0
$115$		0			0
$116$	0.974928	+	0.222521i	0.974928	+	0.222521i
$117$	−0.467085	+	0.467085i	−0.467085	+	0.467085i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$122$	1.43388	−	0.900969i	1.43388	−	0.900969i
$123$		0			0
$124$		0			0
$125$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$126$		0			0
$127$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$127$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$128$			1.00000i			1.00000i
$129$		0			0
$130$	−0.656405	−	0.0739590i	−0.656405	−	0.0739590i
$131$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$131$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	1.21572	+	1.52446i	1.21572	+	1.52446i
$137$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−0.222521	+	0.974928i	$0.571429\pi$
$137$	−1.22252	+	0.974928i	−1.22252	+	0.974928i	−1.00000			$\pi$
$138$		0			0
$139$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$139$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.00000			1.00000
$145$	0.900969	−	0.433884i	0.900969	−	0.433884i
$146$	0.445042			0.445042
$147$		0			0
$148$	1.62349	+	0.781831i	1.62349	+	0.781831i
$149$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$149$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$150$		0			0
$151$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$151$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$152$		0			0
$153$	1.52446	−	1.21572i	1.52446	−	1.21572i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	1.56366			1.56366			0.781831	−	0.623490i	$-0.214286\pi$
$157$	1.56366			1.56366			0.781831	+	0.623490i	$0.214286\pi$
$158$		0			0
$159$		0			0
$160$	0.623490	+	0.781831i	0.623490	+	0.781831i
$161$		0			0
$162$		−	1.00000i		−	1.00000i
$163$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$163$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$164$	−1.78183	−	0.623490i	−1.78183	−	0.623490i
$165$		0			0
$166$		0			0
$167$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$167$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$168$		0			0
$169$	0.549531	−	0.125427i	0.549531	−	0.125427i
$170$	1.90097	+	0.433884i	1.90097	+	0.433884i
$171$		0			0
$172$		0			0
$173$	−1.19745	+	1.19745i	−1.19745	+	1.19745i	−0.222521	+	0.974928i	$0.571429\pi$
$173$	−1.19745	+	1.19745i	−1.19745	+	1.19745i	−0.974928	+	0.222521i	$0.928571\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.656405	−	1.87590i	0.656405	−	1.87590i
$179$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$179$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$180$	0.781831	−	0.623490i	0.781831	−	0.623490i
$181$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$181$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.75676	−	0.400969i	1.75676	−	0.400969i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$191$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$192$		0			0
$193$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.222521	−	0.974928i	$-0.428571\pi$
$193$	1.12349	−	0.541044i	1.12349	−	0.541044i	0.900969	+	0.433884i	$0.142857\pi$
$194$	0.678448	−	0.541044i	0.678448	−	0.541044i
$195$		0			0
$196$	0.433884	−	0.900969i	0.433884	−	0.900969i
$197$	0.119137	+	0.189606i	0.119137	+	0.189606i	0.900969	−	0.433884i	$-0.142857\pi$
$197$	0.119137	+	0.189606i	0.119137	+	0.189606i	−0.781831	+	0.623490i	$0.785714\pi$
$198$		0			0
$199$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$199$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$200$	0.974928	+	0.222521i	0.974928	+	0.222521i
$201$		0			0
$202$	−0.158342	−	0.158342i	−0.158342	−	0.158342i
$203$		0			0
$204$		0			0
$205$	−1.78183	+	0.623490i	−1.78183	+	0.623490i
$206$		0			0
$207$		0			0
$208$	0.559311	+	0.351438i	0.559311	+	0.351438i
$209$		0			0
$210$		0			0
$211$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$211$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$212$	−0.119137	+	1.05737i	−0.119137	+	1.05737i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.846011	+	0.193096i	0.846011	+	0.193096i
$219$		0			0
$220$		0			0
$221$	1.27989	−	0.144209i	1.27989	−	0.144209i
$222$		0			0
$223$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$223$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$224$		0			0
$225$	0.222521	−	0.974928i	0.222521	−	0.974928i
$226$	−0.277479	+	1.21572i	−0.277479	+	1.21572i
$227$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$227$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$228$		0			0
$229$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.781831	−	0.623490i	$-0.785714\pi$
$229$	−1.00435	+	0.351438i	−1.00435	+	0.351438i	−0.222521	+	0.974928i	$0.571429\pi$
$230$		0			0
$231$		0			0
$232$	−1.00000			−1.00000
$233$	1.40532	+	1.40532i	1.40532	+	1.40532i	0.781831	+	0.623490i	$0.214286\pi$
$233$	1.40532	+	1.40532i	1.40532	+	1.40532i	0.623490	+	0.781831i	$0.285714\pi$
$234$	0.351438	−	0.559311i	0.351438	−	0.559311i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$239$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$240$		0			0
$241$	−0.347948	+	0.277479i	−0.347948	+	0.277479i	−0.781831	−	0.623490i	$-0.785714\pi$
$241$	−0.347948	+	0.277479i	−0.347948	+	0.277479i	0.433884	+	0.900969i	$0.357143\pi$
$242$	0.900969	−	0.433884i	0.900969	−	0.433884i
$243$		0			0
$244$	−1.19745	+	1.19745i	−1.19745	+	1.19745i
$245$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	0.900969	−	0.433884i	0.900969	−	0.433884i
$251$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$251$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$257$	0.623490	−	1.78183i	0.623490	−	1.78183i		−	1.00000i	$-0.5\pi$
$257$	0.623490	−	1.78183i	0.623490	−	1.78183i	0.623490	−	0.781831i	$-0.285714\pi$
$258$		0			0
$259$		0			0
$260$	0.656405	−	0.0739590i	0.656405	−	0.0739590i
$261$			1.00000i			1.00000i
$262$		0			0
$263$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$263$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$264$		0			0
$265$	0.566116	+	0.900969i	0.566116	+	0.900969i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.97493	+	0.222521i	1.97493	+	0.222521i	1.00000			$0$
$269$	1.97493	+	0.222521i	1.97493	+	0.222521i	0.974928	+	0.222521i	$0.0714286\pi$
$270$		0			0
$271$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$271$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$272$	−1.52446	−	1.21572i	−1.52446	−	1.21572i
$273$		0			0
$274$	0.974928	−	1.22252i	0.974928	−	1.22252i
$275$		0			0
$276$		0			0
$277$	−0.189606	−	1.68280i	−0.189606	−	1.68280i	−0.623490	−	0.781831i	$-0.714286\pi$
$277$	−0.189606	−	1.68280i	−0.189606	−	1.68280i	0.433884	−	0.900969i	$-0.357143\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.541044	+	0.678448i	0.541044	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$281$	0.541044	+	0.678448i	0.541044	+	0.678448i	−0.433884	+	0.900969i	$0.642857\pi$
$282$		0			0
$283$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$283$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.974928	+	0.222521i	−0.974928	+	0.222521i
$289$	−2.80194			−2.80194
$290$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$291$		0			0
$292$	−0.433884	+	0.0990311i	−0.433884	+	0.0990311i
$293$	0.781831	+	0.376510i	0.781831	+	0.376510i	0.781831	−	0.623490i	$-0.214286\pi$
$293$	0.781831	+	0.376510i	0.781831	+	0.376510i			1.00000i	$0.5\pi$
$294$		0			0
$295$		0			0
$296$	−1.75676	−	0.400969i	−1.75676	−	0.400969i
$297$		0			0
$298$	0.347948	−	0.277479i	0.347948	−	0.277479i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.189606	+	1.68280i	−0.189606	+	1.68280i
$306$	−1.21572	+	1.52446i	−1.21572	+	1.52446i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.993712	−	0.111964i	$-0.964286\pi$
$311$		0			0		0.993712	+	0.111964i	$0.0357143\pi$
$312$		0			0
$313$	1.43388	−	0.900969i	1.43388	−	0.900969i	0.433884	−	0.900969i	$-0.357143\pi$
$313$	1.43388	−	0.900969i	1.43388	−	0.900969i	1.00000			$0$
$314$	−1.52446	+	0.347948i	−1.52446	+	0.347948i
$315$		0			0
$316$		0			0
$317$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$317$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$318$		0			0
$319$		0			0
$320$	−0.781831	−	0.623490i	−0.781831	−	0.623490i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.222521	+	0.974928i	0.222521	+	0.974928i
$325$	0.467085	−	0.467085i	0.467085	−	0.467085i
$326$		0			0
$327$		0			0
$328$	1.87590	+	0.211363i	1.87590	+	0.211363i
$329$		0			0
$330$		0			0
$331$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$331$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$332$		0			0
$333$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.541044	−	0.678448i	0.541044	−	0.678448i	−0.433884	−	0.900969i	$-0.642857\pi$
$337$	0.541044	−	0.678448i	0.541044	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$338$	−0.507843	+	0.244564i	−0.507843	+	0.244564i
$339$		0			0
$340$	−1.94986			−1.94986
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	0.900969	−	1.43388i	0.900969	−	1.43388i
$347$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$347$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$348$		0			0
$349$		−	0.445042i		−	0.445042i	−0.974928	−	0.222521i	$-0.928571\pi$
$349$		−	0.445042i		−	0.445042i	0.974928	−	0.222521i	$-0.0714286\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.59842	−	1.00435i	−1.59842	−	1.00435i	−0.974928	−	0.222521i	$-0.928571\pi$
$353$	−1.59842	−	1.00435i	−1.59842	−	1.00435i	−0.623490	−	0.781831i	$-0.714286\pi$
$354$		0			0
$355$		0			0
$356$	−0.222521	+	1.97493i	−0.222521	+	1.97493i
$357$		0			0
$358$		0			0
$359$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$359$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$360$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$361$	0.781831	+	0.623490i	0.781831	+	0.623490i
$362$	1.21572	+	0.277479i	1.21572	+	0.277479i
$363$		0			0
$364$		0			0
$365$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$366$		0			0
$367$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$367$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$368$		0			0
$369$	0.211363	−	1.87590i	0.211363	−	1.87590i
$370$	−1.62349	+	0.781831i	−1.62349	+	0.781831i
$371$		0			0
$372$		0			0
$373$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.974928	−	0.222521i	$-0.928571\pi$
$373$	−1.87590	−	0.656405i	−1.87590	−	0.656405i	−0.900969	−	0.433884i	$-0.857143\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.351438	+	0.559311i	−0.351438	+	0.559311i
$378$		0			0
$379$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$379$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$383$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$384$		0			0
$385$		0			0
$386$	−0.974928	+	0.777479i	−0.974928	+	0.777479i
$387$		0			0
$388$	−0.541044	+	0.678448i	−0.541044	+	0.678448i
$389$	1.19745	−	1.19745i	1.19745	−	1.19745i	0.222521	−	0.974928i	$-0.428571\pi$
$389$	1.19745	−	1.19745i	1.19745	−	1.19745i	0.974928	−	0.222521i	$-0.0714286\pi$
$390$		0			0
$391$		0			0
$392$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$393$		0			0
$394$	−0.158342	−	0.158342i	−0.158342	−	0.158342i
$395$		0			0
$396$		0			0
$397$	−1.05737	−	0.119137i	−1.05737	−	0.119137i	−0.433884	−	0.900969i	$-0.642857\pi$
$397$	−1.05737	−	0.119137i	−1.05737	−	0.119137i	−0.623490	+	0.781831i	$0.714286\pi$
$398$		0			0
$399$		0			0
$400$	−1.00000			−1.00000
$401$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$401$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$402$		0			0
$403$		0			0
$404$	0.189606	+	0.119137i	0.189606	+	0.119137i
$405$	0.781831	+	0.623490i	0.781831	+	0.623490i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.656405	−	1.87590i	−0.656405	−	1.87590i	−0.433884	−	0.900969i	$-0.642857\pi$
$409$	−0.656405	−	1.87590i	−0.656405	−	1.87590i	−0.222521	−	0.974928i	$-0.571429\pi$
$410$	1.59842	−	1.00435i	1.59842	−	1.00435i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.623490	−	0.218169i	−0.623490	−	0.218169i
$417$		0			0
$418$		0			0
$419$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$419$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$420$		0			0
$421$	1.19745	−	0.752407i	1.19745	−	0.752407i	0.222521	−	0.974928i	$-0.428571\pi$
$421$	1.19745	−	0.752407i	1.19745	−	0.752407i	0.974928	+	0.222521i	$0.0714286\pi$
$422$		0			0
$423$		0			0
$424$	−0.119137	−	1.05737i	−0.119137	−	1.05737i
$425$	−1.52446	+	1.21572i	−1.52446	+	1.21572i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$431$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$432$		0			0
$433$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$433$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$434$		0			0
$435$		0			0
$436$	−0.867767			−0.867767
$437$		0			0
$438$		0			0
$439$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$439$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$440$		0			0
$441$	0.974928	+	0.222521i	0.974928	+	0.222521i
$442$	−1.21572	+	0.425397i	−1.21572	+	0.425397i
$443$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$443$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$444$		0			0
$445$	1.05737	+	1.68280i	1.05737	+	1.68280i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.900969	+	0.566116i	−0.900969	+	0.566116i	−0.900969	−	0.433884i	$-0.857143\pi$
$449$	−0.900969	+	0.566116i	−0.900969	+	0.566116i			1.00000i	$0.5\pi$
$450$			1.00000i			1.00000i
$451$		0			0
$452$		−	1.24698i		−	1.24698i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.0739590	+	0.211363i	0.0739590	+	0.211363i	0.974928	−	0.222521i	$-0.0714286\pi$
$457$	0.0739590	+	0.211363i	0.0739590	+	0.211363i	−0.900969	+	0.433884i	$0.857143\pi$
$458$	0.900969	−	0.566116i	0.900969	−	0.566116i
$459$		0			0
$460$		0			0
$461$	0.467085	+	1.33485i	0.467085	+	1.33485i	0.900969	+	0.433884i	$0.142857\pi$
$461$	0.467085	+	1.33485i	0.467085	+	1.33485i	−0.433884	+	0.900969i	$0.642857\pi$
$462$		0			0
$463$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$463$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$464$	0.974928	−	0.222521i	0.974928	−	0.222521i
$465$		0			0
$466$	−1.68280	−	1.05737i	−1.68280	−	1.05737i
$467$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$467$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$468$	−0.218169	+	0.623490i	−0.218169	+	0.623490i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−1.05737	+	0.119137i	−1.05737	+	0.119137i
$478$		0			0
$479$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$479$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$480$		0			0
$481$	−0.841658	+	0.841658i	−0.841658	+	0.841658i
$482$	0.277479	−	0.347948i	0.277479	−	0.347948i
$483$		0			0
$484$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$485$			0.867767i			0.867767i
$486$		0			0
$487$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$487$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$488$	0.900969	−	1.43388i	0.900969	−	1.43388i
$489$		0			0
$490$	0.433884	+	0.900969i	0.433884	+	0.900969i
$491$		0			0		0.532032	−	0.846724i	$-0.321429\pi$
$491$		0			0		−0.532032	+	0.846724i	$0.678571\pi$
$492$		0			0
$493$	1.21572	−	1.52446i	1.21572	−	1.52446i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$499$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$500$	−0.781831	+	0.623490i	−0.781831	+	0.623490i
$501$		0			0
$502$		0			0
$503$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$503$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$504$		0			0
$505$	0.222521	−	0.0250721i	0.222521	−	0.0250721i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.974928	+	0.222521i	$0.0714286\pi$
$509$	1.40881	+	1.12349i	1.40881	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$510$		0			0
$511$		0			0
$512$	0.433884	+	0.900969i	0.433884	+	0.900969i
$513$		0			0
$514$	−0.211363	+	1.87590i	−0.211363	+	1.87590i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−0.623490	+	0.218169i	−0.623490	+	0.218169i
$521$		−	1.24698i		−	1.24698i	−0.781831	−	0.623490i	$-0.785714\pi$
$521$		−	1.24698i		−	1.24698i	0.781831	−	0.623490i	$-0.214286\pi$
$522$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$523$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$523$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	0.433884	−	0.900969i	0.433884	−	0.900969i
$530$	−0.752407	−	0.752407i	−0.752407	−	0.752407i
$531$		0			0
$532$		0			0
$533$	0.777479	−	0.974928i	0.777479	−	0.974928i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.97493	+	0.222521i	−1.97493	+	0.222521i
$539$		0			0
$540$		0			0
$541$	0.623490	−	1.78183i	0.623490	−	1.78183i		−	1.00000i	$-0.5\pi$
$541$	0.623490	−	1.78183i	0.623490	−	1.78183i	0.623490	−	0.781831i	$-0.285714\pi$
$542$		0			0
$543$		0			0
$544$	1.75676	+	0.846011i	1.75676	+	0.846011i
$545$	−0.678448	+	0.541044i	−0.678448	+	0.541044i
$546$		0			0
$547$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$547$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$548$	−0.678448	+	1.40881i	−0.678448	+	1.40881i
$549$	−1.43388	−	0.900969i	−1.43388	−	0.900969i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.559311	+	1.59842i	0.559311	+	1.59842i
$555$		0			0
$556$		0			0
$557$	1.59842	−	1.00435i	1.59842	−	1.00435i	0.623490	−	0.781831i	$-0.285714\pi$
$557$	1.59842	−	1.00435i	1.59842	−	1.00435i	0.974928	−	0.222521i	$-0.0714286\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−0.678448	−	0.541044i	−0.678448	−	0.541044i
$563$		0			0			−	1.00000i	$-0.5\pi$
$563$		0			0				1.00000i	$0.5\pi$
$564$		0			0
$565$	−0.777479	−	0.974928i	−0.777479	−	0.974928i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.211363	+	1.87590i	0.211363	+	1.87590i	0.433884	+	0.900969i	$0.357143\pi$
$569$	0.211363	+	1.87590i	0.211363	+	1.87590i	−0.222521	+	0.974928i	$0.571429\pi$
$570$		0			0
$571$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$571$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.900969	−	0.433884i	0.900969	−	0.433884i
$577$	1.62349	+	0.781831i	1.62349	+	0.781831i	1.00000			$0$
$577$	1.62349	+	0.781831i	1.62349	+	0.781831i	0.623490	+	0.781831i	$0.285714\pi$
$578$	2.73169	−	0.623490i	2.73169	−	0.623490i
$579$		0			0
$580$	0.623490	−	0.781831i	0.623490	−	0.781831i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.400969	−	0.193096i	0.400969	−	0.193096i
$585$	0.218169	+	0.623490i	0.218169	+	0.623490i
$586$	−0.846011	−	0.193096i	−0.846011	−	0.193096i
$587$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$587$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.80194			1.80194
$593$	0.119137	+	1.05737i	0.119137	+	1.05737i	0.900969	+	0.433884i	$0.142857\pi$
$593$	0.119137	+	1.05737i	0.119137	+	1.05737i	−0.781831	+	0.623490i	$0.785714\pi$
$594$		0			0
$595$		0			0
$596$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$597$		0			0
$598$		0			0
$599$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$599$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$600$		0			0
$601$	1.40532	+	0.158342i	1.40532	+	0.158342i	0.781831	−	0.623490i	$-0.214286\pi$
$601$	1.40532	+	0.158342i	1.40532	+	0.158342i	0.623490	+	0.781831i	$0.285714\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$606$		0			0
$607$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$607$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$608$		0			0
$609$		0			0
$610$	−0.189606	−	1.68280i	−0.189606	−	1.68280i
$611$		0			0
$612$	0.846011	−	1.75676i	0.846011	−	1.75676i
$613$	−0.623490	+	1.78183i	−0.623490	+	1.78183i			1.00000i	$0.5\pi$
$613$	−0.623490	+	1.78183i	−0.623490	+	1.78183i	−0.623490	+	0.781831i	$0.714286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.974928	−	1.22252i	−0.974928	−	1.22252i	−0.974928	−	0.222521i	$-0.928571\pi$
$617$	−0.974928	−	1.22252i	−0.974928	−	1.22252i		−	1.00000i	$-0.5\pi$
$618$		0			0
$619$		0			0		0.330279	−	0.943883i	$-0.392857\pi$
$619$		0			0		−0.330279	+	0.943883i	$0.607143\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$626$	−1.19745	+	1.19745i	−1.19745	+	1.19745i
$627$		0			0
$628$	1.40881	−	0.678448i	1.40881	−	0.678448i
$629$	2.74698	−	2.19064i	2.74698	−	2.19064i
$630$		0			0
$631$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$631$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$632$		0			0
$633$		0			0
$634$	−0.193096	−	0.400969i	−0.193096	−	0.400969i
$635$		0			0
$636$		0			0
$637$	0.467085	+	0.467085i	0.467085	+	0.467085i
$638$		0			0
$639$		0			0
$640$	0.900969	+	0.433884i	0.900969	+	0.433884i
$641$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.433884	−	0.900969i	$-0.357143\pi$
$641$	1.33485	−	0.467085i	1.33485	−	0.467085i	0.900969	+	0.433884i	$0.142857\pi$
$642$		0			0
$643$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$643$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$647$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$648$	−0.433884	−	0.900969i	−0.433884	−	0.900969i
$649$		0			0
$650$	−0.351438	+	0.559311i	−0.351438	+	0.559311i
$651$		0			0
$652$		0			0
$653$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.781831	−	0.623490i	$-0.785714\pi$
$653$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$654$		0			0
$655$		0			0
$656$	−1.87590	+	0.211363i	−1.87590	+	0.211363i
$657$	−0.193096	−	0.400969i	−0.193096	−	0.400969i
$658$		0			0
$659$		0			0		0.111964	−	0.993712i	$-0.464286\pi$
$659$		0			0		−0.111964	+	0.993712i	$0.535714\pi$
$660$		0			0
$661$	0.400969	−	1.75676i	0.400969	−	1.75676i	−0.222521	−	0.974928i	$-0.571429\pi$
$661$	0.400969	−	1.75676i	0.400969	−	1.75676i	0.623490	−	0.781831i	$-0.285714\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$		−	1.80194i		−	1.80194i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.119137	+	0.189606i	0.119137	+	0.189606i	0.900969	−	0.433884i	$-0.142857\pi$
$673$	0.119137	+	0.189606i	0.119137	+	0.189606i	−0.781831	+	0.623490i	$0.785714\pi$
$674$	−0.376510	+	0.781831i	−0.376510	+	0.781831i
$675$		0			0
$676$	0.440689	−	0.351438i	0.440689	−	0.351438i
$677$	1.40881	−	0.678448i	1.40881	−	0.678448i	0.433884	−	0.900969i	$-0.357143\pi$
$677$	1.40881	−	0.678448i	1.40881	−	0.678448i	0.974928	+	0.222521i	$0.0714286\pi$
$678$		0			0
$679$		0			0
$680$	1.90097	−	0.433884i	1.90097	−	0.433884i
$681$		0			0
$682$		0			0
$683$		0			0		0.993712	−	0.111964i	$-0.0357143\pi$
$683$		0			0		−0.993712	+	0.111964i	$0.964286\pi$
$684$		0			0
$685$	0.347948	+	1.52446i	0.347948	+	1.52446i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.633270	−	0.304967i	−0.633270	−	0.304967i
$690$		0			0
$691$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$691$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$692$	−0.559311	+	1.59842i	−0.559311	+	1.59842i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−2.60277	+	2.60277i	−2.60277	+	2.60277i
$698$	0.0990311	+	0.433884i	0.0990311	+	0.433884i
$699$		0			0
$700$		0			0
$701$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$701$	−1.90097	+	0.433884i	−1.90097	+	0.433884i	−1.00000			$\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.78183	+	0.623490i	1.78183	+	0.623490i
$707$		0			0
$708$		0			0
$709$	−0.974928	+	1.22252i	−0.974928	+	1.22252i			1.00000i	$0.5\pi$
$709$	−0.974928	+	1.22252i	−0.974928	+	1.22252i	−0.974928	+	0.222521i	$0.928571\pi$
$710$		0			0
$711$		0			0
$712$	−0.222521	−	1.97493i	−0.222521	−	1.97493i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.974928	−	0.222521i	$-0.928571\pi$
$719$		0			0		0.974928	+	0.222521i	$0.0714286\pi$
$720$	0.433884	−	0.900969i	0.433884	−	0.900969i
$721$		0			0
$722$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$723$		0			0
$724$	−1.24698			−1.24698
$725$		−	1.00000i		−	1.00000i
$726$		0			0
$727$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$727$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$728$		0			0
$729$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$730$	0.193096	−	0.400969i	0.193096	−	0.400969i
$731$		0			0
$732$		0			0
$733$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$733$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.211363	+	1.87590i	0.211363	+	1.87590i
$739$		0			0		0.846724	−	0.532032i	$-0.178571\pi$
$739$		0			0		−0.846724	+	0.532032i	$0.821429\pi$
$740$	1.40881	−	1.12349i	1.40881	−	1.12349i
$741$		0			0
$742$		0			0
$743$		0			0		−0.781831	−	0.623490i	$-0.785714\pi$
$743$		0			0		0.781831	+	0.623490i	$0.214286\pi$
$744$		0			0
$745$			0.445042i			0.445042i
$746$	1.97493	+	0.222521i	1.97493	+	0.222521i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.330279	−	0.943883i	$-0.607143\pi$
$751$		0			0		0.330279	+	0.943883i	$0.392857\pi$
$752$		0			0
$753$		0			0
$754$	0.218169	−	0.623490i	0.218169	−	0.623490i
$755$		0			0
$756$		0			0
$757$	−0.541044	+	1.12349i	−0.541044	+	1.12349i	0.433884	+	0.900969i	$0.357143\pi$
$757$	−0.541044	+	1.12349i	−0.541044	+	1.12349i	−0.974928	+	0.222521i	$0.928571\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.974928	−	0.222521i	$-0.0714286\pi$
$761$	1.40881	+	0.678448i	1.40881	+	0.678448i	0.433884	+	0.900969i	$0.357143\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.433884	−	1.90097i	−0.433884	−	1.90097i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.119137	+	0.189606i	0.119137	+	0.189606i	0.900969	−	0.433884i	$-0.142857\pi$
$769$	0.119137	+	0.189606i	0.119137	+	0.189606i	−0.781831	+	0.623490i	$0.785714\pi$
$770$		0			0
$771$		0			0
$772$	0.777479	−	0.974928i	0.777479	−	0.974928i
$773$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.900969	−	0.433884i	$-0.857143\pi$
$773$	−1.12349	+	0.541044i	−1.12349	+	0.541044i	−0.222521	+	0.974928i	$0.571429\pi$
$774$		0			0
$775$		0			0
$776$	0.376510	−	0.781831i	0.376510	−	0.781831i
$777$		0			0
$778$	−0.900969	+	1.43388i	−0.900969	+	1.43388i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		−	1.00000i		−	1.00000i
$785$	0.678448	−	1.40881i	0.678448	−	1.40881i
$786$		0			0
$787$		0			0		−0.943883	−	0.330279i	$-0.892857\pi$
$787$		0			0		0.943883	+	0.330279i	$0.107143\pi$
$788$	0.189606	+	0.119137i	0.189606	+	0.119137i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−0.485352	−	1.00784i	−0.485352	−	1.00784i
$794$	1.05737	−	0.119137i	1.05737	−	0.119137i
$795$		0			0
$796$		0			0
$797$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.781831	−	0.623490i	$-0.785714\pi$
$797$	−1.75676	−	0.400969i	−1.75676	−	0.400969i	−0.974928	+	0.222521i	$0.928571\pi$
$798$		0			0
$799$		0			0
$800$	0.974928	−	0.222521i	0.974928	−	0.222521i
$801$	−1.97493	+	0.222521i	−1.97493	+	0.222521i
$802$	0.781831	+	1.62349i	0.781831	+	1.62349i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.211363	−	0.0739590i	−0.211363	−	0.0739590i
$809$	−0.623490	+	0.218169i	−0.623490	+	0.218169i	−0.623490	−	0.781831i	$-0.714286\pi$
$809$	−0.623490	+	0.218169i	−0.623490	+	0.218169i			1.00000i	$0.5\pi$
$810$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.05737	+	1.68280i	1.05737	+	1.68280i
$819$		0			0
$820$	−1.33485	+	1.33485i	−1.33485	+	1.33485i
$821$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.623490	−	0.781831i	$-0.285714\pi$
$821$	1.52446	−	1.21572i	1.52446	−	1.21572i	0.900969	−	0.433884i	$-0.142857\pi$
$822$		0			0
$823$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$823$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$827$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$828$		0			0
$829$	0.467085	+	0.467085i	0.467085	+	0.467085i	0.900969	−	0.433884i	$-0.142857\pi$
$829$	0.467085	+	0.467085i	0.467085	+	0.467085i	−0.433884	+	0.900969i	$0.642857\pi$
$830$		0			0
$831$		0			0
$832$	0.656405	+	0.0739590i	0.656405	+	0.0739590i
$833$	−1.21572	−	1.52446i	−1.21572	−	1.52446i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.846724	−	0.532032i	$-0.821429\pi$
$839$		0			0		0.846724	+	0.532032i	$0.178571\pi$
$840$		0			0
$841$	0.222521	+	0.974928i	0.222521	+	0.974928i
$842$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$843$		0			0
$844$		0			0
$845$	0.125427	−	0.549531i	0.125427	−	0.549531i
$846$		0			0
$847$		0			0
$848$	0.351438	+	1.00435i	0.351438	+	1.00435i
$849$		0			0
$850$	1.21572	−	1.52446i	1.21572	−	1.52446i
$851$		0			0
$852$		0			0
$853$		−	1.56366i		−	1.56366i	−0.623490	−	0.781831i	$-0.714286\pi$
$853$		−	1.56366i		−	1.56366i	0.623490	−	0.781831i	$-0.285714\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.158342	+	1.40532i	0.158342	+	1.40532i	0.781831	+	0.623490i	$0.214286\pi$
$857$	0.158342	+	1.40532i	0.158342	+	1.40532i	−0.623490	+	0.781831i	$0.714286\pi$
$858$		0			0
$859$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$859$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.943883	−	0.330279i	$-0.107143\pi$
$863$		0			0		−0.943883	+	0.330279i	$0.892857\pi$
$864$		0			0
$865$	0.559311	+	1.59842i	0.559311	+	1.59842i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.846011	−	0.193096i	0.846011	−	0.193096i
$873$	−0.781831	−	0.376510i	−0.781831	−	0.376510i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.33485	+	0.467085i	−1.33485	+	0.467085i	−0.900969	−	0.433884i	$-0.857143\pi$
$877$	−1.33485	+	0.467085i	−1.33485	+	0.467085i	−0.433884	+	0.900969i	$0.642857\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.119137	+	1.05737i	0.119137	+	1.05737i	0.900969	+	0.433884i	$0.142857\pi$
$881$	0.119137	+	1.05737i	0.119137	+	1.05737i	−0.781831	+	0.623490i	$0.785714\pi$
$882$	−1.00000			−1.00000
$883$		0			0		−0.111964	−	0.993712i	$-0.535714\pi$
$883$		0			0		0.111964	+	0.993712i	$0.464286\pi$
$884$	1.09057	−	0.685254i	1.09057	−	0.685254i
$885$		0			0
$886$		0			0
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$		0			0
$889$		0			0
$890$	−1.40532	−	1.40532i	−1.40532	−	1.40532i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.752407	−	0.752407i	0.752407	−	0.752407i
$899$		0			0
$900$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$901$	1.75676	+	1.10385i	1.75676	+	1.10385i
$902$		0			0
$903$		0			0
$904$	0.277479	+	1.21572i	0.277479	+	1.21572i
$905$	−0.974928	+	0.777479i	−0.974928	+	0.777479i
$906$		0			0
$907$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$907$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$908$		0			0
$909$	−0.0739590	+	0.211363i	−0.0739590	+	0.211363i
$910$		0			0
$911$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$911$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$912$		0			0
$913$		0			0
$914$	−0.119137	−	0.189606i	−0.119137	−	0.189606i
$915$		0			0
$916$	−0.752407	+	0.752407i	−0.752407	+	0.752407i
$917$		0			0
$918$		0			0
$919$		0			0		0.781831	−	0.623490i	$-0.214286\pi$
$919$		0			0		−0.781831	+	0.623490i	$0.785714\pi$
$920$		0			0
$921$		0			0
$922$	−0.752407	−	1.19745i	−0.752407	−	1.19745i
$923$		0			0
$924$		0			0
$925$	0.400969	−	1.75676i	0.400969	−	1.75676i
$926$		0			0
$927$		0			0
$928$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$929$			0.867767i			0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$929$			0.867767i			0.867767i	−0.900969	+	0.433884i	$0.857143\pi$
$930$		0			0
$931$		0			0
$932$	1.87590	+	0.656405i	1.87590	+	0.656405i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.0739590	−	0.656405i	0.0739590	−	0.656405i
$937$	−0.0250721	+	0.222521i	−0.0250721	+	0.222521i	0.974928	+	0.222521i	$0.0714286\pi$
$937$	−0.0250721	+	0.222521i	−0.0250721	+	0.222521i	−1.00000			$\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$941$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		−0.433884	−	0.900969i	$-0.642857\pi$
$947$		0			0		0.433884	+	0.900969i	$0.357143\pi$
$948$		0			0
$949$	0.0329149	−	0.292128i	0.0329149	−	0.292128i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.78183	−	0.623490i	−1.78183	−	0.623490i	−0.781831	−	0.623490i	$-0.785714\pi$
$953$	−1.78183	−	0.623490i	−1.78183	−	0.623490i	−1.00000			$\pi$
$954$	1.00435	−	0.351438i	1.00435	−	0.351438i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.433884	+	0.900969i	0.433884	+	0.900969i
$962$	0.633270	−	1.00784i	0.633270	−	1.00784i
$963$		0			0
$964$	−0.193096	+	0.400969i	−0.193096	+	0.400969i
$965$		−	1.24698i		−	1.24698i
$966$		0			0
$967$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$967$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$968$	0.623490	−	0.781831i	0.623490	−	0.781831i
$969$		0			0
$970$	−0.193096	−	0.846011i	−0.193096	−	0.846011i
$971$		0			0		−0.532032	−	0.846724i	$-0.678571\pi$
$971$		0			0		0.532032	+	0.846724i	$0.321429\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−0.559311	+	1.59842i	−0.559311	+	1.59842i
$977$	−1.97493	−	0.222521i	−1.97493	−	0.222521i	−0.974928	−	0.222521i	$-0.928571\pi$
$977$	−1.97493	−	0.222521i	−1.97493	−	0.222521i	−1.00000			$\pi$
$978$		0			0
$979$		0			0
$980$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$981$	−0.193096	−	0.846011i	−0.193096	−	0.846011i
$982$		0			0
$983$		0			0		0.433884	−	0.900969i	$-0.357143\pi$
$983$		0			0		−0.433884	+	0.900969i	$0.642857\pi$
$984$		0			0
$985$	0.222521	−	0.0250721i	0.222521	−	0.0250721i
$986$	−0.846011	+	1.75676i	−0.846011	+	1.75676i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.974928	−	0.222521i	$-0.0714286\pi$
$991$		0			0		−0.974928	+	0.222521i	$0.928571\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.974928	+	0.777479i	0.974928	+	0.777479i	0.974928	−	0.222521i	$-0.0714286\pi$
$997$	0.974928	+	0.777479i	0.974928	+	0.777479i			1.00000i	$0.5\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.1.bm.a.3.1	yes	12
4.3	odd	2	CM	580.1.bm.a.3.1	yes	12
5.2	odd	4		580.1.bd.a.467.1	✓	12
5.3	odd	4		2900.1.bx.c.2207.1		12
5.4	even	2		2900.1.cg.b.1743.1		12
20.3	even	4		2900.1.bx.c.2207.1		12
20.7	even	4		580.1.bd.a.467.1	✓	12
20.19	odd	2		2900.1.cg.b.1743.1		12
29.10	odd	28		580.1.bd.a.503.1	yes	12
116.39	even	28		580.1.bd.a.503.1	yes	12
145.39	odd	28		2900.1.bx.c.2243.1		12
145.68	even	28		2900.1.cg.b.2707.1		12
145.97	even	28	inner	580.1.bm.a.387.1	yes	12
580.39	even	28		2900.1.bx.c.2243.1		12
580.387	odd	28	inner	580.1.bm.a.387.1	yes	12
580.503	odd	28		2900.1.cg.b.2707.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.1.bd.a.467.1	✓	12	5.2	odd	4
580.1.bd.a.467.1	✓	12	20.7	even	4
580.1.bd.a.503.1	yes	12	29.10	odd	28
580.1.bd.a.503.1	yes	12	116.39	even	28
580.1.bm.a.3.1	yes	12	1.1	even	1	trivial
580.1.bm.a.3.1	yes	12	4.3	odd	2	CM
580.1.bm.a.387.1	yes	12	145.97	even	28	inner
580.1.bm.a.387.1	yes	12	580.387	odd	28	inner
2900.1.bx.c.2207.1		12	5.3	odd	4
2900.1.bx.c.2207.1		12	20.3	even	4
2900.1.bx.c.2243.1		12	145.39	odd	28
2900.1.bx.c.2243.1		12	580.39	even	28
2900.1.cg.b.1743.1		12	5.4	even	2
2900.1.cg.b.1743.1		12	20.19	odd	2
2900.1.cg.b.2707.1		12	145.68	even	28
2900.1.cg.b.2707.1		12	580.503	odd	28

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	580.1.bm.a.3.1

Level	$580$
Weight	$1$
Character	580.3
Analytic conductor	$0.289$
Analytic rank	$0$
Dimension	$12$
Projective image	$D_{28}$
CM discriminant	-4
Inner twists	$4$