LMFDB - Embedded newform 209.1.h.a.87.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,1,Mod(87,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("209.87");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$N$	$=$	$209 = 11 \cdot 19$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	209.h (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:	$0.104304587640$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{2} + 1$ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.43681.1
Artin image:	$\SL(2,3):C_2$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{16} - \cdots)$

Embedding invariants

Embedding label			87.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	209.87
Dual form			209.1.h.a.197.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(0.866025 - 0.500000i) q^{6} +1.00000i q^{8} +(0.866025 - 0.500000i) q^{10} +1.00000i q^{11} +(-0.866025 + 0.500000i) q^{13} +(-0.500000 - 0.866025i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{17} -1.00000i q^{19} +(0.500000 - 0.866025i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.866025 - 0.500000i) q^{24} +1.00000 q^{26} -1.00000 q^{27} +(0.866025 - 0.500000i) q^{29} +1.00000i q^{30} +(-0.866025 - 0.500000i) q^{33} +(-0.500000 - 0.866025i) q^{34} +(-0.500000 + 0.866025i) q^{38} -1.00000i q^{39} +(-0.866025 - 0.500000i) q^{40} +(-0.866025 - 0.500000i) q^{41} +(0.866025 + 0.500000i) q^{43} +1.00000i q^{46} +(-0.500000 - 0.866025i) q^{47} +(0.500000 + 0.866025i) q^{48} +1.00000 q^{49} +(-0.866025 + 0.500000i) q^{51} +(0.500000 + 0.866025i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.866025 - 0.500000i) q^{55} +(0.866025 + 0.500000i) q^{57} -1.00000 q^{58} +(-0.500000 + 0.866025i) q^{59} +(0.866025 - 0.500000i) q^{61} -1.00000 q^{64} -1.00000i q^{65} +(0.500000 + 0.866025i) q^{66} +(0.500000 + 0.866025i) q^{67} +1.00000 q^{69} +(0.500000 - 0.866025i) q^{71} +(0.866025 + 0.500000i) q^{73} +(-0.500000 + 0.866025i) q^{78} +(0.866025 + 0.500000i) q^{79} +(0.500000 + 0.866025i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +(-0.866025 + 0.500000i) q^{85} +(-0.500000 - 0.866025i) q^{86} +1.00000i q^{87} -1.00000 q^{88} +(0.500000 + 0.866025i) q^{89} +1.00000i q^{94} +(0.866025 + 0.500000i) q^{95} +(0.500000 - 0.866025i) q^{97} +(-0.866025 - 0.500000i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{3} - 2 q^{5} - 2 q^{15} + 2 q^{16} + 2 q^{22} - 2 q^{23} + 4 q^{26} - 4 q^{27} - 2 q^{34} - 2 q^{38} - 2 q^{47} + 2 q^{48} + 4 q^{49} + 2 q^{53} - 4 q^{58} - 2 q^{59} - 4 q^{64} + 2 q^{66} + 2 q^{67}+ \cdots + 2 q^{97}+O(q^{100})$ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^15 + 2 * q^16 + 2 * q^22 - 2 * q^23 + 4 * q^26 - 4 * q^27 - 2 * q^34 - 2 * q^38 - 2 * q^47 + 2 * q^48 + 4 * q^49 + 2 * q^53 - 4 * q^58 - 2 * q^59 - 4 * q^64 + 2 * q^66 + 2 * q^67 + 4 * q^69 + 2 * q^71 - 2 * q^78 + 2 * q^80 + 2 * q^81 + 2 * q^82 - 2 * q^86 - 4 * q^88 + 2 * q^89 + 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$ .

$n$	$78$	$134$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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

)

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

$2$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$2$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$5$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$6$	0.866025	−	0.500000i	0.866025	−	0.500000i
$7$		0			0		1.00000			$0$
$7$		0			0		−1.00000			$\pi$
$8$			1.00000i			1.00000i
$9$		0			0
$10$	0.866025	−	0.500000i	0.866025	−	0.500000i
$11$			1.00000i			1.00000i
$11$			1.00000i			1.00000i
$12$		0			0
$13$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$13$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$14$		0			0
$15$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$17$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$18$		0			0
$19$		−	1.00000i		−	1.00000i
$19$		−	1.00000i		−	1.00000i
$20$		0			0
$21$		0			0
$22$	0.500000	−	0.866025i	0.500000	−	0.866025i
$23$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$23$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$24$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$25$		0			0
$26$	1.00000			1.00000
$27$	−1.00000			−1.00000
$28$		0			0
$29$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$29$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$30$			1.00000i			1.00000i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$		0			0
$33$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$34$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$35$		0			0
$36$		0			0
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$39$		−	1.00000i		−	1.00000i
$40$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$41$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$43$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$44$		0			0
$45$		0			0
$46$			1.00000i			1.00000i
$47$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$47$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$48$	0.500000	+	0.866025i	0.500000	+	0.866025i
$49$	1.00000			1.00000
$50$		0			0
$51$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$52$		0			0
$53$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$53$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$54$	0.866025	+	0.500000i	0.866025	+	0.500000i
$55$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$56$		0			0
$57$	0.866025	+	0.500000i	0.866025	+	0.500000i
$58$	−1.00000			−1.00000
$59$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$59$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$60$		0			0
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$62$		0			0
$63$		0			0
$64$	−1.00000			−1.00000
$65$		−	1.00000i		−	1.00000i
$66$	0.500000	+	0.866025i	0.500000	+	0.866025i
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$67$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$	1.00000			1.00000
$70$		0			0
$71$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$71$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$72$		0			0
$73$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$73$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$79$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$79$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$80$	0.500000	+	0.866025i	0.500000	+	0.866025i
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$	0.500000	+	0.866025i	0.500000	+	0.866025i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$86$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$87$			1.00000i			1.00000i
$88$	−1.00000			−1.00000
$89$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$89$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$			1.00000i			1.00000i
$95$	0.866025	+	0.500000i	0.866025	+	0.500000i
$96$		0			0
$97$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$97$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$98$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$99$		0			0
$100$		0			0
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$101$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$102$	1.00000			1.00000
$103$		0			0			−	1.00000i	$-0.5\pi$
$103$		0			0				1.00000i	$0.5\pi$
$104$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$105$		0			0
$106$		−	1.00000i		−	1.00000i
$107$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$107$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$108$		0			0
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$109$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$110$	0.500000	+	0.866025i	0.500000	+	0.866025i
$111$		0			0
$112$		0			0
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$115$	1.00000			1.00000
$116$		0			0
$117$		0			0
$118$	0.866025	−	0.500000i	0.866025	−	0.500000i
$119$		0			0
$120$	0.866025	−	0.500000i	0.866025	−	0.500000i
$121$	−1.00000			−1.00000
$122$	−1.00000			−1.00000
$123$	0.866025	−	0.500000i	0.866025	−	0.500000i
$124$		0			0
$125$	−1.00000			−1.00000
$126$		0			0
$127$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$127$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$128$	0.866025	+	0.500000i	0.866025	+	0.500000i
$129$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$130$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$		0			0
$134$		−	1.00000i		−	1.00000i
$135$	0.500000	−	0.866025i	0.500000	−	0.866025i
$136$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$137$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$137$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$138$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$139$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$139$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$140$		0			0
$141$	1.00000			1.00000
$142$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$143$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$144$		0			0
$145$			1.00000i			1.00000i
$146$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$147$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$148$		0			0
$149$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$149$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$150$		0			0
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	1.00000			1.00000
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$158$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$159$	−1.00000			−1.00000
$160$		0			0
$161$		0			0
$162$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$		0			0
$165$	0.866025	−	0.500000i	0.866025	−	0.500000i
$166$		0			0
$167$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$167$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$		0			0
$170$	1.00000			1.00000
$171$		0			0
$172$		0			0
$173$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$173$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$174$	0.500000	−	0.866025i	0.500000	−	0.866025i
$175$		0			0
$176$	0.866025	+	0.500000i	0.866025	+	0.500000i
$177$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$178$		−	1.00000i		−	1.00000i
$179$	2.00000			2.00000			1.00000			$0$
$179$	2.00000			2.00000			1.00000			$0$
$180$		0			0
$181$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$181$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$182$		0			0
$183$			1.00000i			1.00000i
$184$	0.866025	−	0.500000i	0.866025	−	0.500000i
$185$		0			0
$186$		0			0
$187$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$188$		0			0
$189$		0			0
$190$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$	0.500000	−	0.866025i	0.500000	−	0.866025i
$193$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$193$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$194$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$195$	0.866025	+	0.500000i	0.866025	+	0.500000i
$196$		0			0
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$		0			0
$199$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$199$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$200$		0			0
$201$	−1.00000			−1.00000
$202$	1.00000			1.00000
$203$		0			0
$204$		0			0
$205$	0.866025	−	0.500000i	0.866025	−	0.500000i
$206$		0			0
$207$		0			0
$208$			1.00000i			1.00000i
$209$	1.00000			1.00000
$210$		0			0
$211$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$211$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$212$		0			0
$213$	0.500000	+	0.866025i	0.500000	+	0.866025i
$214$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$215$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$216$		−	1.00000i		−	1.00000i
$217$		0			0
$218$	0.500000	+	0.866025i	0.500000	+	0.866025i
$219$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$220$		0			0
$221$	−1.00000			−1.00000
$222$		0			0
$223$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$223$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		0			0		1.00000			$0$
$227$		0			0		−1.00000			$\pi$
$228$		0			0
$229$	−2.00000			−2.00000			−1.00000			$\pi$
$229$	−2.00000			−2.00000			−1.00000			$\pi$
$230$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$231$		0			0
$232$	0.500000	+	0.866025i	0.500000	+	0.866025i
$233$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$233$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$234$		0			0
$235$	1.00000			1.00000
$236$		0			0
$237$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−1.00000			−1.00000
$241$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$241$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$242$	0.866025	+	0.500000i	0.866025	+	0.500000i
$243$		0			0
$244$		0			0
$245$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$246$	−1.00000			−1.00000
$247$	0.500000	+	0.866025i	0.500000	+	0.866025i
$248$		0			0
$249$		0			0
$250$	0.866025	+	0.500000i	0.866025	+	0.500000i
$251$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$251$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$252$		0			0
$253$	0.866025	−	0.500000i	0.866025	−	0.500000i
$254$	1.00000			1.00000
$255$		−	1.00000i		−	1.00000i
$256$		0			0
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$258$	1.00000			1.00000
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.500000	+	0.866025i	0.500000	+	0.866025i
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$263$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$264$	0.500000	−	0.866025i	0.500000	−	0.866025i
$265$	−1.00000			−1.00000
$266$		0			0
$267$	−1.00000			−1.00000
$268$		0			0
$269$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$270$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$271$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$271$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$272$	0.866025	−	0.500000i	0.866025	−	0.500000i
$273$		0			0
$274$			1.00000i			1.00000i
$275$		0			0
$276$		0			0
$277$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$277$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$278$	1.00000			1.00000
$279$		0			0
$280$		0			0
$281$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$281$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$282$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$283$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$283$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$286$			1.00000i			1.00000i
$287$		0			0
$288$		0			0
$289$		0			0
$290$	0.500000	−	0.866025i	0.500000	−	0.866025i
$291$	0.500000	+	0.866025i	0.500000	+	0.866025i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	0.866025	−	0.500000i	0.866025	−	0.500000i
$295$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$296$		0			0
$297$		−	1.00000i		−	1.00000i
$298$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$299$	0.866025	+	0.500000i	0.866025	+	0.500000i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		−	1.00000i		−	1.00000i
$304$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$305$			1.00000i			1.00000i
$306$		0			0
$307$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$307$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	1.00000			1.00000
$313$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$313$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$314$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$315$		0			0
$316$		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			$\pi$
$318$	0.866025	+	0.500000i	0.866025	+	0.500000i
$319$	0.500000	+	0.866025i	0.500000	+	0.866025i
$320$	0.500000	−	0.866025i	0.500000	−	0.866025i
$321$	1.73205	+	1.00000i	1.73205	+	1.00000i
$322$		0			0
$323$	0.500000	−	0.866025i	0.500000	−	0.866025i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.866025	−	0.500000i	0.866025	−	0.500000i
$328$	0.500000	−	0.866025i	0.500000	−	0.866025i
$329$		0			0
$330$	−1.00000			−1.00000
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		0			0
$333$		0			0
$334$	−1.00000			−1.00000
$335$	−1.00000			−1.00000
$336$		0			0
$337$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$337$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$345$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$346$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$347$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$347$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$348$		0			0
$349$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$349$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$350$		0			0
$351$	0.866025	−	0.500000i	0.866025	−	0.500000i
$352$		0			0
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$			1.00000i			1.00000i
$355$	0.500000	+	0.866025i	0.500000	+	0.866025i
$356$		0			0
$357$		0			0
$358$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$359$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$359$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$360$		0			0
$361$	−1.00000			−1.00000
$362$			1.00000i			1.00000i
$363$	0.500000	−	0.866025i	0.500000	−	0.866025i
$364$		0			0
$365$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$366$	0.500000	−	0.866025i	0.500000	−	0.866025i
$367$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$367$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$368$	−1.00000			−1.00000
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		1.00000			$0$
$373$		0			0		−1.00000			$\pi$
$374$	0.866025	−	0.500000i	0.866025	−	0.500000i
$375$	0.500000	−	0.866025i	0.500000	−	0.866025i
$376$	0.866025	−	0.500000i	0.866025	−	0.500000i
$377$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$378$		0			0
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$		0			0
$381$		−	1.00000i		−	1.00000i
$382$		0			0
$383$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$383$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$384$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$385$		0			0
$386$	0.500000	+	0.866025i	0.500000	+	0.866025i
$387$		0			0
$388$		0			0
$389$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$389$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$390$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$391$		−	1.00000i		−	1.00000i
$392$			1.00000i			1.00000i
$393$	0.866025	−	0.500000i	0.866025	−	0.500000i
$394$		0			0
$395$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$396$		0			0
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$398$		−	1.00000i		−	1.00000i
$399$		0			0
$400$		0			0
$401$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$401$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$402$	0.866025	+	0.500000i	0.866025	+	0.500000i
$403$		0			0
$404$		0			0
$405$	0.500000	+	0.866025i	0.500000	+	0.866025i
$406$		0			0
$407$		0			0
$408$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$409$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$409$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$410$	−1.00000			−1.00000
$411$	1.00000			1.00000
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	1.00000i		−	1.00000i
$418$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$421$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$422$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$423$		0			0
$424$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$425$		0			0
$426$		−	1.00000i		−	1.00000i
$427$		0			0
$428$		0			0
$429$	1.00000			1.00000
$430$	1.00000			1.00000
$431$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$431$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$432$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$433$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$433$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$434$		0			0
$435$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$436$		0			0
$437$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$438$	1.00000			1.00000
$439$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$439$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$440$	0.500000	−	0.866025i	0.500000	−	0.866025i
$441$		0			0
$442$	0.866025	+	0.500000i	0.866025	+	0.500000i
$443$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$443$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$444$		0			0
$445$	−1.00000			−1.00000
$446$	0.866025	−	0.500000i	0.866025	−	0.500000i
$447$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	0.500000	−	0.866025i	0.500000	−	0.866025i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$457$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$457$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$458$	1.73205	+	1.00000i	1.73205	+	1.00000i
$459$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$460$		0			0
$461$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$461$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$		−	1.00000i		−	1.00000i
$465$		0			0
$466$	0.500000	+	0.866025i	0.500000	+	0.866025i
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$		0			0
$470$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$471$	0.500000	+	0.866025i	0.500000	+	0.866025i
$472$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$473$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$474$	1.00000			1.00000
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$479$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$480$		0			0
$481$		0			0
$482$	−1.00000			−1.00000
$483$		0			0
$484$		0			0
$485$	0.500000	+	0.866025i	0.500000	+	0.866025i
$486$		0			0
$487$		0			0			−	1.00000i	$-0.5\pi$
$487$		0			0				1.00000i	$0.5\pi$
$488$	0.500000	+	0.866025i	0.500000	+	0.866025i
$489$		0			0
$490$	0.866025	−	0.500000i	0.866025	−	0.500000i
$491$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$491$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$	1.00000			1.00000
$494$		−	1.00000i		−	1.00000i
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$500$		0			0
$501$			1.00000i			1.00000i
$502$		−	1.00000i		−	1.00000i
$503$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$503$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$504$		0			0
$505$		−	1.00000i		−	1.00000i
$506$	−1.00000			−1.00000
$507$		0			0
$508$		0			0
$509$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$509$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$510$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$			1.00000i			1.00000i
$514$		−	1.00000i		−	1.00000i
$515$		0			0
$516$		0			0
$517$	0.866025	−	0.500000i	0.866025	−	0.500000i
$518$		0			0
$519$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$520$	1.00000			1.00000
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$523$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$524$		0			0
$525$		0			0
$526$	0.500000	+	0.866025i	0.500000	+	0.866025i
$527$		0			0
$528$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$529$		0			0
$530$	0.866025	+	0.500000i	0.866025	+	0.500000i
$531$		0			0
$532$		0			0
$533$	1.00000			1.00000
$534$	0.866025	+	0.500000i	0.866025	+	0.500000i
$535$	1.73205	+	1.00000i	1.73205	+	1.00000i
$536$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$537$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$538$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$539$			1.00000i			1.00000i
$540$		0			0
$541$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$541$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$542$	0.500000	+	0.866025i	0.500000	+	0.866025i
$543$	1.00000			1.00000
$544$		0			0
$545$	0.866025	−	0.500000i	0.866025	−	0.500000i
$546$		0			0
$547$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$547$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$552$			1.00000i			1.00000i
$553$		0			0
$554$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$555$		0			0
$556$		0			0
$557$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$557$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$558$		0			0
$559$	−1.00000			−1.00000
$560$		0			0
$561$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$562$	1.00000			1.00000
$563$		0			0		1.00000			$0$
$563$		0			0		−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$	0.500000	+	0.866025i	0.500000	+	0.866025i
$567$		0			0
$568$	0.866025	+	0.500000i	0.866025	+	0.500000i
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$	1.00000			1.00000
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$		0			0			−	1.00000i	$-0.5\pi$
$577$		0			0				1.00000i	$0.5\pi$
$578$		0			0
$579$	0.866025	−	0.500000i	0.866025	−	0.500000i
$580$		0			0
$581$		0			0
$582$		−	1.00000i		−	1.00000i
$583$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$584$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$585$		0			0
$586$		0			0
$587$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$587$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$			1.00000i			1.00000i
$591$		0			0
$592$		0			0
$593$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$593$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$594$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$595$		0			0
$596$		0			0
$597$	−1.00000			−1.00000
$598$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$599$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$599$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$600$		0			0
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.500000	−	0.866025i	0.500000	−	0.866025i
$606$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$	0.500000	−	0.866025i	0.500000	−	0.866025i
$611$	0.866025	+	0.500000i	0.866025	+	0.500000i
$612$		0			0
$613$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$613$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$614$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$615$			1.00000i			1.00000i
$616$		0			0
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$617$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$618$		0			0
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$	0.500000	+	0.866025i	0.500000	+	0.866025i
$622$		0			0
$623$		0			0
$624$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$		−	1.00000i		−	1.00000i
$627$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$631$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$632$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$633$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$634$			1.00000i			1.00000i
$635$		−	1.00000i		−	1.00000i
$636$		0			0
$637$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$638$		−	1.00000i		−	1.00000i
$639$		0			0
$640$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$641$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$642$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$643$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$644$		0			0
$645$		−	1.00000i		−	1.00000i
$646$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	0.866025	+	0.500000i	0.866025	+	0.500000i
$649$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.00000			2.00000			1.00000			$0$
$653$	2.00000			2.00000			1.00000			$0$
$654$	−1.00000			−1.00000
$655$	0.866025	−	0.500000i	0.866025	−	0.500000i
$656$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$657$		0			0
$658$		0			0
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$660$		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
$663$	0.500000	−	0.866025i	0.500000	−	0.866025i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$668$		0			0
$669$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$670$	0.866025	+	0.500000i	0.866025	+	0.500000i
$671$	0.500000	+	0.866025i	0.500000	+	0.866025i
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$	0.500000	+	0.866025i	0.500000	+	0.866025i
$675$		0			0
$676$		0			0
$677$		0			0		1.00000			$0$
$677$		0			0		−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$	1.00000			1.00000
$686$		0			0
$687$	1.00000	−	1.73205i	1.00000	−	1.73205i
$688$	0.866025	−	0.500000i	0.866025	−	0.500000i
$689$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$690$	0.866025	−	0.500000i	0.866025	−	0.500000i
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$		0			0
$693$		0			0
$694$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$695$		−	1.00000i		−	1.00000i
$696$	−1.00000			−1.00000
$697$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$698$	1.00000	−	1.73205i	1.00000	−	1.73205i
$699$	0.866025	−	0.500000i	0.866025	−	0.500000i
$700$		0			0
$701$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$701$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$702$	−1.00000			−1.00000
$703$		0			0
$704$		−	1.00000i		−	1.00000i
$705$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$709$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$710$		−	1.00000i		−	1.00000i
$711$		0			0
$712$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$713$		0			0
$714$		0			0
$715$	1.00000			1.00000
$716$		0			0
$717$		0			0
$718$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$719$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$719$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$720$		0			0
$721$		0			0
$722$	0.866025	+	0.500000i	0.866025	+	0.500000i
$723$			1.00000i			1.00000i
$724$		0			0
$725$		0			0
$726$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$727$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$727$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$728$		0			0
$729$	1.00000			1.00000
$730$	1.00000			1.00000
$731$	0.500000	+	0.866025i	0.500000	+	0.866025i
$732$		0			0
$733$		0			0		1.00000			$0$
$733$		0			0		−1.00000			$\pi$
$734$			1.00000i			1.00000i
$735$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$736$		0			0
$737$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$738$		0			0
$739$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$739$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$740$		0			0
$741$	−1.00000			−1.00000
$742$		0			0
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$752$	−1.00000			−1.00000
$753$	−1.00000			−1.00000
$754$	0.866025	−	0.500000i	0.866025	−	0.500000i
$755$		0			0
$756$		0			0
$757$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$757$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$758$		0			0
$759$			1.00000i			1.00000i
$760$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$767$		−	1.00000i		−	1.00000i
$768$		0			0
$769$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$769$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$770$		0			0
$771$	−1.00000			−1.00000
$772$		0			0
$773$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$773$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$774$		0			0
$775$		0			0
$776$	0.866025	+	0.500000i	0.866025	+	0.500000i
$777$		0			0
$778$			1.00000i			1.00000i
$779$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$780$		0			0
$781$	0.866025	+	0.500000i	0.866025	+	0.500000i
$782$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$783$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$784$	0.500000	−	0.866025i	0.500000	−	0.866025i
$785$	0.500000	+	0.866025i	0.500000	+	0.866025i
$786$	−1.00000			−1.00000
$787$		0			0		1.00000			$0$
$787$		0			0		−1.00000			$\pi$
$788$		0			0
$789$	0.866025	−	0.500000i	0.866025	−	0.500000i
$790$	1.00000			1.00000
$791$		0			0
$792$		0			0
$793$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$794$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$795$	0.500000	−	0.866025i	0.500000	−	0.866025i
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$		−	1.00000i		−	1.00000i
$800$		0			0
$801$		0			0
$802$	0.866025	−	0.500000i	0.866025	−	0.500000i
$803$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.500000	+	0.866025i	0.500000	+	0.866025i
$808$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		−	1.00000i		−	1.00000i
$811$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$811$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$812$		0			0
$813$	0.866025	−	0.500000i	0.866025	−	0.500000i
$814$		0			0
$815$		0			0
$816$			1.00000i			1.00000i
$817$	0.500000	−	0.866025i	0.500000	−	0.866025i
$818$	−1.00000			−1.00000
$819$		0			0
$820$		0			0
$821$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$821$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$822$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$823$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$823$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$827$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$828$		0			0
$829$		0			0			−	1.00000i	$-0.5\pi$
$829$		0			0				1.00000i	$0.5\pi$
$830$		0			0
$831$	1.73205	+	1.00000i	1.73205	+	1.00000i
$832$	0.866025	−	0.500000i	0.866025	−	0.500000i
$833$	0.866025	+	0.500000i	0.866025	+	0.500000i
$834$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$835$			1.00000i			1.00000i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$839$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$840$		0			0
$841$		0			0
$842$	0.866025	−	0.500000i	0.866025	−	0.500000i
$843$		−	1.00000i		−	1.00000i
$844$		0			0
$845$		0			0
$846$		0			0
$847$		0			0
$848$	1.00000			1.00000
$849$	0.866025	−	0.500000i	0.866025	−	0.500000i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$853$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$854$		0			0
$855$		0			0
$856$	2.00000			2.00000
$857$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$857$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$858$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$859$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	1.00000			1.00000
$863$		0			0			−	1.00000i	$-0.5\pi$
$863$		0			0				1.00000i	$0.5\pi$
$864$		0			0
$865$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$866$			1.00000i			1.00000i
$867$		0			0
$868$		0			0
$869$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$870$	0.500000	+	0.866025i	0.500000	+	0.866025i
$871$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$872$	0.500000	−	0.866025i	0.500000	−	0.866025i
$873$		0			0
$874$	1.00000			1.00000
$875$		0			0
$876$		0			0
$877$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$877$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$878$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$879$		0			0
$880$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$883$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$884$		0			0
$885$	1.00000			1.00000
$886$			1.00000i			1.00000i
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$		0			0
$889$		0			0
$890$	0.866025	+	0.500000i	0.866025	+	0.500000i
$891$	0.866025	+	0.500000i	0.866025	+	0.500000i
$892$		0			0
$893$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$894$	1.00000			1.00000
$895$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$896$		0			0
$897$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$898$		0			0
$899$		0			0
$900$		0			0
$901$			1.00000i			1.00000i
$902$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$903$		0			0
$904$		0			0
$905$	1.00000			1.00000
$906$		0			0
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	0.866025	−	0.500000i	0.866025	−	0.500000i
$913$		0			0
$914$	1.00000	−	1.73205i	1.00000	−	1.73205i
$915$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$916$		0			0
$917$		0			0
$918$	0.500000	+	0.866025i	0.500000	+	0.866025i
$919$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$919$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$920$			1.00000i			1.00000i
$921$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$922$	0.500000	+	0.866025i	0.500000	+	0.866025i
$923$			1.00000i			1.00000i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$929$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$930$		0			0
$931$		−	1.00000i		−	1.00000i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$936$		0			0
$937$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$937$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$938$		0			0
$939$	−1.00000			−1.00000
$940$		0			0
$941$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$941$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$942$		−	1.00000i		−	1.00000i
$943$			1.00000i			1.00000i
$944$	0.500000	+	0.866025i	0.500000	+	0.866025i
$945$		0			0
$946$	0.866025	−	0.500000i	0.866025	−	0.500000i
$947$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$947$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$948$		0			0
$949$	−1.00000			−1.00000
$950$		0			0
$951$	1.00000			1.00000
$952$		0			0
$953$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$953$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−1.00000			−1.00000
$958$	1.00000			1.00000
$959$		0			0
$960$	0.500000	+	0.866025i	0.500000	+	0.866025i
$961$	−1.00000			−1.00000
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.866025	−	0.500000i	0.866025	−	0.500000i
$966$		0			0
$967$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$967$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$968$		−	1.00000i		−	1.00000i
$969$	0.500000	+	0.866025i	0.500000	+	0.866025i
$970$		−	1.00000i		−	1.00000i
$971$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$971$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		−	1.00000i		−	1.00000i
$977$		0			0			−	1.00000i	$-0.5\pi$
$977$		0			0				1.00000i	$0.5\pi$
$978$		0			0
$979$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$980$		0			0
$981$		0			0
$982$	0.500000	+	0.866025i	0.500000	+	0.866025i
$983$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$983$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$984$	0.500000	+	0.866025i	0.500000	+	0.866025i
$985$		0			0
$986$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$987$		0			0
$988$		0			0
$989$		−	1.00000i		−	1.00000i
$990$		0			0
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$991$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.00000			−1.00000
$996$		0			0
$997$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$997$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$998$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$999$		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	209.1.h.a.87.1	✓	4
3.2	odd	2		1881.1.bc.a.505.2		4
4.3	odd	2		3344.1.bb.a.2177.1		4
11.2	odd	10		2299.1.w.a.524.1		16
11.3	even	5		2299.1.w.a.1322.1		16
11.4	even	5		2299.1.w.a.2272.2		16
11.5	even	5		2299.1.w.a.239.2		16
11.6	odd	10		2299.1.w.a.239.1		16
11.7	odd	10		2299.1.w.a.2272.1		16
11.8	odd	10		2299.1.w.a.1322.2		16
11.9	even	5		2299.1.w.a.524.2		16
11.10	odd	2	inner	209.1.h.a.87.2	yes	4
19.2	odd	18		3971.1.q.d.956.1		12
19.3	odd	18		3971.1.q.d.2265.1		12
19.4	even	9		3971.1.q.e.1506.1		12
19.5	even	9		3971.1.q.e.3277.1		12
19.6	even	9		3971.1.q.e.54.1		12
19.7	even	3	inner	209.1.h.a.197.2	yes	4
19.8	odd	6		3971.1.c.b.362.1		2
19.9	even	9		3971.1.q.e.967.2		12
19.10	odd	18		3971.1.q.d.967.1		12
19.11	even	3		3971.1.c.e.362.2		2
19.12	odd	6		3971.1.h.d.3541.1		4
19.13	odd	18		3971.1.q.d.54.2		12
19.14	odd	18		3971.1.q.d.3277.2		12
19.15	odd	18		3971.1.q.d.1506.2		12
19.16	even	9		3971.1.q.e.2265.2		12
19.17	even	9		3971.1.q.e.956.2		12
19.18	odd	2		3971.1.h.d.2595.2		4
33.32	even	2		1881.1.bc.a.505.1		4
44.43	even	2		3344.1.bb.a.2177.2		4
57.26	odd	6		1881.1.bc.a.406.1		4
76.7	odd	6		3344.1.bb.a.2705.1		4
209.7	odd	30		2299.1.w.a.1546.1		16
209.10	even	18		3971.1.q.d.967.2		12
209.21	even	18		3971.1.q.d.956.2		12
209.26	even	15		2299.1.w.a.1546.2		16
209.32	even	18		3971.1.q.d.54.1		12
209.43	odd	18		3971.1.q.e.3277.2		12
209.54	odd	18		3971.1.q.e.2265.1		12
209.64	even	15		2299.1.w.a.2097.1		16
209.65	even	6		3971.1.c.b.362.2		2
209.83	odd	30		2299.1.w.a.1812.2		16
209.87	odd	6		3971.1.c.e.362.1		2
209.98	even	18		3971.1.q.d.2265.2		12
209.102	even	15		2299.1.w.a.596.1		16
209.109	even	18		3971.1.q.d.3277.1		12
209.120	odd	18		3971.1.q.e.54.2		12
209.131	odd	18		3971.1.q.e.956.1		12
209.140	odd	30		2299.1.w.a.596.2		16
209.142	odd	18		3971.1.q.e.967.1		12
209.159	even	15		2299.1.w.a.1812.1		16
209.164	even	6		3971.1.h.d.3541.2		4
209.175	odd	18		3971.1.q.e.1506.2		12
209.178	odd	30		2299.1.w.a.2097.2		16
209.186	even	18		3971.1.q.d.1506.1		12
209.197	odd	6	inner	209.1.h.a.197.1	yes	4
209.208	even	2		3971.1.h.d.2595.1		4
627.197	even	6		1881.1.bc.a.406.2		4
836.615	even	6		3344.1.bb.a.2705.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.1.h.a.87.1	✓	4	1.1	even	1	trivial
209.1.h.a.87.2	yes	4	11.10	odd	2	inner
209.1.h.a.197.1	yes	4	209.197	odd	6	inner
209.1.h.a.197.2	yes	4	19.7	even	3	inner
1881.1.bc.a.406.1		4	57.26	odd	6
1881.1.bc.a.406.2		4	627.197	even	6
1881.1.bc.a.505.1		4	33.32	even	2
1881.1.bc.a.505.2		4	3.2	odd	2
2299.1.w.a.239.1		16	11.6	odd	10
2299.1.w.a.239.2		16	11.5	even	5
2299.1.w.a.524.1		16	11.2	odd	10
2299.1.w.a.524.2		16	11.9	even	5
2299.1.w.a.596.1		16	209.102	even	15
2299.1.w.a.596.2		16	209.140	odd	30
2299.1.w.a.1322.1		16	11.3	even	5
2299.1.w.a.1322.2		16	11.8	odd	10
2299.1.w.a.1546.1		16	209.7	odd	30
2299.1.w.a.1546.2		16	209.26	even	15
2299.1.w.a.1812.1		16	209.159	even	15
2299.1.w.a.1812.2		16	209.83	odd	30
2299.1.w.a.2097.1		16	209.64	even	15
2299.1.w.a.2097.2		16	209.178	odd	30
2299.1.w.a.2272.1		16	11.7	odd	10
2299.1.w.a.2272.2		16	11.4	even	5
3344.1.bb.a.2177.1		4	4.3	odd	2
3344.1.bb.a.2177.2		4	44.43	even	2
3344.1.bb.a.2705.1		4	76.7	odd	6
3344.1.bb.a.2705.2		4	836.615	even	6
3971.1.c.b.362.1		2	19.8	odd	6
3971.1.c.b.362.2		2	209.65	even	6
3971.1.c.e.362.1		2	209.87	odd	6
3971.1.c.e.362.2		2	19.11	even	3
3971.1.h.d.2595.1		4	209.208	even	2
3971.1.h.d.2595.2		4	19.18	odd	2
3971.1.h.d.3541.1		4	19.12	odd	6
3971.1.h.d.3541.2		4	209.164	even	6
3971.1.q.d.54.1		12	209.32	even	18
3971.1.q.d.54.2		12	19.13	odd	18
3971.1.q.d.956.1		12	19.2	odd	18
3971.1.q.d.956.2		12	209.21	even	18
3971.1.q.d.967.1		12	19.10	odd	18
3971.1.q.d.967.2		12	209.10	even	18
3971.1.q.d.1506.1		12	209.186	even	18
3971.1.q.d.1506.2		12	19.15	odd	18
3971.1.q.d.2265.1		12	19.3	odd	18
3971.1.q.d.2265.2		12	209.98	even	18
3971.1.q.d.3277.1		12	209.109	even	18
3971.1.q.d.3277.2		12	19.14	odd	18
3971.1.q.e.54.1		12	19.6	even	9
3971.1.q.e.54.2		12	209.120	odd	18
3971.1.q.e.956.1		12	209.131	odd	18
3971.1.q.e.956.2		12	19.17	even	9
3971.1.q.e.967.1		12	209.142	odd	18
3971.1.q.e.967.2		12	19.9	even	9
3971.1.q.e.1506.1		12	19.4	even	9
3971.1.q.e.1506.2		12	209.175	odd	18
3971.1.q.e.2265.1		12	209.54	odd	18
3971.1.q.e.2265.2		12	19.16	even	9
3971.1.q.e.3277.1		12	19.5	even	9
3971.1.q.e.3277.2		12	209.43	odd	18

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

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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	209.1.h.a.87.1

Level	$209$
Weight	$1$
Character	209.87
Analytic conductor	$0.104$
Analytic rank	$0$
Dimension	$4$
Projective image	$A_{4}$
CM/RM	no
Inner twists	$4$