LMFDB - Embedded newform 1116.1.x.a.955.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1116,1,Mod(811,1116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1116, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 4]))

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

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

chi := DirichletCharacter("1116.811");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1116 = 2^{2} \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1116.x (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:	$0.556956554098$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 124)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.15376.1

Embedding invariants

Embedding label			955.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1116.955
Dual form			1116.1.x.a.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +(0.866025 + 0.500000i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{14} +1.00000 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.866025 - 0.500000i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(0.866025 + 0.500000i) q^{26} +(0.866025 - 0.500000i) q^{28} +1.00000i q^{31} +1.00000i q^{32} +(-0.866025 + 0.500000i) q^{34} +1.00000i q^{35} +(-0.500000 - 0.866025i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-0.866025 - 0.500000i) q^{40} +(0.500000 - 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{43} +(-0.866025 - 0.500000i) q^{44} +(-0.500000 + 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(0.866025 - 0.500000i) q^{55} +(0.500000 + 0.866025i) q^{56} +(0.866025 - 0.500000i) q^{59} -1.00000 q^{62} -1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.866025 - 0.500000i) q^{67} +(-0.500000 - 0.866025i) q^{68} -1.00000 q^{70} +(-0.866025 - 0.500000i) q^{71} +(-0.500000 + 0.866025i) q^{73} +(0.866025 - 0.500000i) q^{74} +(-0.866025 + 0.500000i) q^{76} -1.00000 q^{77} +(-0.866025 + 0.500000i) q^{79} +(0.500000 - 0.866025i) q^{80} +(0.866025 + 0.500000i) q^{82} +(-0.866025 - 0.500000i) q^{83} +1.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(0.500000 - 0.866025i) q^{88} +1.00000i q^{91} -1.00000i q^{95} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{5}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^5	$ 4 q - 4 q^{4} + 2 q^{5} + 2 q^{13} - 2 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{20} - 2 q^{22} - 2 q^{37} + 2 q^{38} + 2 q^{41} - 2 q^{52} - 2 q^{53} + 2 q^{56} - 4 q^{62} - 4 q^{64} - 2 q^{65} - 2 q^{68} - 4 q^{70} - 2 q^{73} - 4 q^{77} + 2 q^{80} + 4 q^{85} + 2 q^{86} + 2 q^{88}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^5 + 2 * q^13 - 2 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^20 - 2 * q^22 - 2 * q^37 + 2 * q^38 + 2 * q^41 - 2 * q^52 - 2 * q^53 + 2 * q^56 - 4 * q^62 - 4 * q^64 - 2 * q^65 - 2 * q^68 - 4 * q^70 - 2 * q^73 - 4 * q^77 + 2 * q^80 + 4 * q^85 + 2 * q^86 + 2 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1116\mathbb{Z}\right)^\times$.

$n$	$497$	$559$	$685$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			1.00000i			1.00000i
$2$			1.00000i			1.00000i
$3$		0			0
$3$		0			0
$4$	−1.00000			−1.00000
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$6$		0			0
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$		−	1.00000i		−	1.00000i
$9$		0			0
$10$	0.866025	+	0.500000i	0.866025	+	0.500000i
$11$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$11$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$13$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$14$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$15$		0			0
$16$	1.00000			1.00000
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$19$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$20$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$21$		0			0
$22$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$		0			0
$25$		0			0
$26$	0.866025	+	0.500000i	0.866025	+	0.500000i
$27$		0			0
$28$	0.866025	−	0.500000i	0.866025	−	0.500000i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$			1.00000i			1.00000i
$31$			1.00000i			1.00000i
$32$			1.00000i			1.00000i
$33$		0			0
$34$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$35$			1.00000i			1.00000i
$36$		0			0
$37$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$37$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$38$	0.500000	+	0.866025i	0.500000	+	0.866025i
$39$		0			0
$40$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$42$		0			0
$43$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$43$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$44$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$45$		0			0
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$		0			0
$52$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$53$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$53$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$54$		0			0
$55$	0.866025	−	0.500000i	0.866025	−	0.500000i
$56$	0.500000	+	0.866025i	0.500000	+	0.866025i
$57$		0			0
$58$		0			0
$59$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$59$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$		0			0			−	1.00000i	$-0.5\pi$
$61$		0			0				1.00000i	$0.5\pi$
$62$	−1.00000			−1.00000
$63$		0			0
$64$	−1.00000			−1.00000
$65$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$66$		0			0
$67$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$67$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$68$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$69$		0			0
$70$	−1.00000			−1.00000
$71$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$71$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$72$		0			0
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$74$	0.866025	−	0.500000i	0.866025	−	0.500000i
$75$		0			0
$76$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$77$	−1.00000			−1.00000
$78$		0			0
$79$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$79$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$80$	0.500000	−	0.866025i	0.500000	−	0.866025i
$81$		0			0
$82$	0.866025	+	0.500000i	0.866025	+	0.500000i
$83$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$83$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$84$		0			0
$85$	1.00000			1.00000
$86$	0.500000	+	0.866025i	0.500000	+	0.866025i
$87$		0			0
$88$	0.500000	−	0.866025i	0.500000	−	0.866025i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$			1.00000i			1.00000i
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	1.00000i		−	1.00000i
$96$		0			0
$97$		0			0			−	1.00000i	$-0.5\pi$
$97$		0			0				1.00000i	$0.5\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$104$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$105$		0			0
$106$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$107$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$107$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	0.500000	+	0.866025i	0.500000	+	0.866025i
$111$		0			0
$112$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$113$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$113$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.500000	+	0.866025i	0.500000	+	0.866025i
$119$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$120$		0			0
$121$		0			0
$122$		0			0
$123$		0			0
$124$		−	1.00000i		−	1.00000i
$125$	1.00000			1.00000
$126$		0			0
$127$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$127$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$128$		−	1.00000i		−	1.00000i
$129$		0			0
$130$	0.866025	−	0.500000i	0.866025	−	0.500000i
$131$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$131$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$132$		0			0
$133$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$134$	0.500000	−	0.866025i	0.500000	−	0.866025i
$135$		0			0
$136$	0.866025	−	0.500000i	0.866025	−	0.500000i
$137$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$137$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$138$		0			0
$139$		0			0		1.00000			$0$
$139$		0			0		−1.00000			$\pi$
$140$		−	1.00000i		−	1.00000i
$141$		0			0
$142$	0.500000	−	0.866025i	0.500000	−	0.866025i
$143$	0.866025	−	0.500000i	0.866025	−	0.500000i
$144$		0			0
$145$		0			0
$146$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$147$		0			0
$148$	0.500000	+	0.866025i	0.500000	+	0.866025i
$149$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$149$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$150$		0			0
$151$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$151$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$152$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$153$		0			0
$154$		−	1.00000i		−	1.00000i
$155$	0.866025	+	0.500000i	0.866025	+	0.500000i
$156$		0			0
$157$		0			0			−	1.00000i	$-0.5\pi$
$157$		0			0				1.00000i	$0.5\pi$
$158$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$159$		0			0
$160$	0.866025	+	0.500000i	0.866025	+	0.500000i
$161$		0			0
$162$		0			0
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$165$		0			0
$166$	0.500000	−	0.866025i	0.500000	−	0.866025i
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$168$		0			0
$169$		0			0
$170$			1.00000i			1.00000i
$171$		0			0
$172$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$173$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$173$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$174$		0			0
$175$		0			0
$176$	0.866025	+	0.500000i	0.866025	+	0.500000i
$177$		0			0
$178$		0			0
$179$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$179$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$180$		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			$\pi$
$182$	−1.00000			−1.00000
$183$		0			0
$184$		0			0
$185$	−1.00000			−1.00000
$186$		0			0
$187$			1.00000i			1.00000i
$188$		0			0
$189$		0			0
$190$	1.00000			1.00000
$191$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$191$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$193$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$197$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$198$		0			0
$199$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$199$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$206$	0.500000	−	0.866025i	0.500000	−	0.866025i
$207$		0			0
$208$	0.500000	−	0.866025i	0.500000	−	0.866025i
$209$	1.00000			1.00000
$210$		0			0
$211$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$211$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$212$	0.500000	−	0.866025i	0.500000	−	0.866025i
$213$		0			0
$214$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$215$		−	1.00000i		−	1.00000i
$216$		0			0
$217$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$218$		0			0
$219$		0			0
$220$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$221$	1.00000			1.00000
$222$		0			0
$223$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$223$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$224$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$225$		0			0
$226$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$227$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$227$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$228$		0			0
$229$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$229$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		0			0
$236$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$237$		0			0
$238$	0.500000	−	0.866025i	0.500000	−	0.866025i
$239$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$239$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$241$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		−	1.00000i		−	1.00000i
$248$	1.00000			1.00000
$249$		0			0
$250$			1.00000i			1.00000i
$251$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$251$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$	0.500000	+	0.866025i	0.500000	+	0.866025i
$255$		0			0
$256$	1.00000			1.00000
$257$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$257$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$258$		0			0
$259$	0.866025	+	0.500000i	0.866025	+	0.500000i
$260$	0.500000	+	0.866025i	0.500000	+	0.866025i
$261$		0			0
$262$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$		0			0
$265$	0.500000	+	0.866025i	0.500000	+	0.866025i
$266$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$267$		0			0
$268$	0.866025	+	0.500000i	0.866025	+	0.500000i
$269$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$269$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	0.500000	+	0.866025i	0.500000	+	0.866025i
$273$		0			0
$274$	0.866025	+	0.500000i	0.866025	+	0.500000i
$275$		0			0
$276$		0			0
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$		0			0
$279$		0			0
$280$	1.00000			1.00000
$281$	−2.00000			−2.00000			−1.00000			$\pi$
$281$	−2.00000			−2.00000			−1.00000			$\pi$
$282$		0			0
$283$		0			0		1.00000			$0$
$283$		0			0		−1.00000			$\pi$
$284$	0.866025	+	0.500000i	0.866025	+	0.500000i
$285$		0			0
$286$	0.500000	+	0.866025i	0.500000	+	0.866025i
$287$			1.00000i			1.00000i
$288$		0			0
$289$		0			0
$290$		0			0
$291$		0			0
$292$	0.500000	−	0.866025i	0.500000	−	0.866025i
$293$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$293$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$294$		0			0
$295$		−	1.00000i		−	1.00000i
$296$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$297$		0			0
$298$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$299$		0			0
$300$		0			0
$301$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$302$	2.00000			2.00000
$303$		0			0
$304$	0.866025	−	0.500000i	0.866025	−	0.500000i
$305$		0			0
$306$		0			0
$307$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$307$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$308$	1.00000			1.00000
$309$		0			0
$310$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$313$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$314$		0			0
$315$		0			0
$316$	0.866025	−	0.500000i	0.866025	−	0.500000i
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$318$		0			0
$319$		0			0
$320$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$321$		0			0
$322$		0			0
$323$	0.866025	+	0.500000i	0.866025	+	0.500000i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		0			0
$328$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$329$		0			0
$330$		0			0
$331$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$331$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$332$	0.866025	+	0.500000i	0.866025	+	0.500000i
$333$		0			0
$334$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$335$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$336$		0			0
$337$	−2.00000			−2.00000			−1.00000			$\pi$
$337$	−2.00000			−2.00000			−1.00000			$\pi$
$338$		0			0
$339$		0			0
$340$	−1.00000			−1.00000
$341$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$342$		0			0
$343$		−	1.00000i		−	1.00000i
$344$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$345$		0			0
$346$	0.866025	+	0.500000i	0.866025	+	0.500000i
$347$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$347$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$		0			0
$352$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$353$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$353$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$354$		0			0
$355$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$356$		0			0
$357$		0			0
$358$	0.500000	+	0.866025i	0.500000	+	0.866025i
$359$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$359$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$		0			0
$362$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$363$		0			0
$364$		−	1.00000i		−	1.00000i
$365$	0.500000	+	0.866025i	0.500000	+	0.866025i
$366$		0			0
$367$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$367$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$368$		0			0
$369$		0			0
$370$		−	1.00000i		−	1.00000i
$371$		−	1.00000i		−	1.00000i
$372$		0			0
$373$	−2.00000			−2.00000			−1.00000			$\pi$
$373$	−2.00000			−2.00000			−1.00000			$\pi$
$374$	−1.00000			−1.00000
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$379$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$380$			1.00000i			1.00000i
$381$		0			0
$382$	0.500000	−	0.866025i	0.500000	−	0.866025i
$383$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$383$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$384$		0			0
$385$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$386$	0.866025	−	0.500000i	0.866025	−	0.500000i
$387$		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			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$395$			1.00000i			1.00000i
$396$		0			0
$397$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$397$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$398$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$399$		0			0
$400$		0			0
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$	0.866025	+	0.500000i	0.866025	+	0.500000i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.00000i		−	1.00000i
$408$		0			0
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$410$	0.866025	−	0.500000i	0.866025	−	0.500000i
$411$		0			0
$412$	0.866025	+	0.500000i	0.866025	+	0.500000i
$413$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$414$		0			0
$415$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$416$	0.866025	+	0.500000i	0.866025	+	0.500000i
$417$		0			0
$418$			1.00000i			1.00000i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$421$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$422$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$423$		0			0
$424$	0.866025	+	0.500000i	0.866025	+	0.500000i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.866025	−	0.500000i	0.866025	−	0.500000i
$429$		0			0
$430$	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			0
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$	0.866025	−	0.500000i	0.866025	−	0.500000i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$439$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$440$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$441$		0			0
$442$			1.00000i			1.00000i
$443$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$443$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$444$		0			0
$445$		0			0
$446$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$447$		0			0
$448$	0.866025	−	0.500000i	0.866025	−	0.500000i
$449$	2.00000			2.00000			1.00000			$0$
$449$	2.00000			2.00000			1.00000			$0$
$450$		0			0
$451$	0.866025	−	0.500000i	0.866025	−	0.500000i
$452$	0.500000	−	0.866025i	0.500000	−	0.866025i
$453$		0			0
$454$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$455$	0.866025	+	0.500000i	0.866025	+	0.500000i
$456$		0			0
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$459$		0			0
$460$		0			0
$461$		0			0			−	1.00000i	$-0.5\pi$
$461$		0			0				1.00000i	$0.5\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$	1.00000			1.00000
$470$		0			0
$471$		0			0
$472$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$473$	1.00000			1.00000
$474$		0			0
$475$		0			0
$476$	0.866025	+	0.500000i	0.866025	+	0.500000i
$477$		0			0
$478$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$479$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$479$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−1.00000			−1.00000
$482$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$487$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$491$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$492$		0			0
$493$		0			0
$494$	1.00000			1.00000
$495$		0			0
$496$			1.00000i			1.00000i
$497$	1.00000			1.00000
$498$		0			0
$499$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$499$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$500$	−1.00000			−1.00000
$501$		0			0
$502$	0.500000	+	0.866025i	0.500000	+	0.866025i
$503$	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
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$509$	−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			0
$511$		−	1.00000i		−	1.00000i
$512$			1.00000i			1.00000i
$513$		0			0
$514$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$515$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$516$		0			0
$517$		0			0
$518$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$519$		0			0
$520$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	0.866025	−	0.500000i	0.866025	−	0.500000i
$525$		0			0
$526$		0			0
$527$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$528$		0			0
$529$	1.00000			1.00000
$530$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$531$		0			0
$532$	0.500000	−	0.866025i	0.500000	−	0.866025i
$533$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$534$		0			0
$535$			1.00000i			1.00000i
$536$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$537$		0			0
$538$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$539$		0			0
$540$		0			0
$541$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$541$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$542$		0			0
$543$		0			0
$544$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$545$		0			0
$546$		0			0
$547$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$547$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$548$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.500000	−	0.866025i	0.500000	−	0.866025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		−	1.00000i		−	1.00000i
$560$			1.00000i			1.00000i
$561$		0			0
$562$		−	2.00000i		−	2.00000i
$563$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$563$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$	0.500000	+	0.866025i	0.500000	+	0.866025i
$566$		0			0
$567$		0			0
$568$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$569$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$570$		0			0
$571$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$571$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$572$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$573$		0			0
$574$	−1.00000			−1.00000
$575$		0			0
$576$		0			0
$577$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$577$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.00000			1.00000
$582$		0			0
$583$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$584$	0.866025	+	0.500000i	0.866025	+	0.500000i
$585$		0			0
$586$	0.866025	−	0.500000i	0.866025	−	0.500000i
$587$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$587$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$588$		0			0
$589$	0.500000	+	0.866025i	0.500000	+	0.866025i
$590$	1.00000			1.00000
$591$		0			0
$592$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$593$	−2.00000			−2.00000			−1.00000			$\pi$
$593$	−2.00000			−2.00000			−1.00000			$\pi$
$594$		0			0
$595$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$596$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$597$		0			0
$598$		0			0
$599$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$599$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$601$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$602$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$603$		0			0
$604$			2.00000i			2.00000i
$605$		0			0
$606$		0			0
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$608$	0.500000	+	0.866025i	0.500000	+	0.866025i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$613$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$614$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$615$		0			0
$616$			1.00000i			1.00000i
$617$	−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
$619$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$619$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$620$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$	0.866025	−	0.500000i	0.866025	−	0.500000i
$627$		0			0
$628$		0			0
$629$	0.500000	−	0.866025i	0.500000	−	0.866025i
$630$		0			0
$631$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$631$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$632$	0.500000	+	0.866025i	0.500000	+	0.866025i
$633$		0			0
$634$	0.866025	−	0.500000i	0.866025	−	0.500000i
$635$		−	1.00000i		−	1.00000i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$647$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$647$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$648$		0			0
$649$	1.00000			1.00000
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0			−	1.00000i	$-0.5\pi$
$653$		0			0				1.00000i	$0.5\pi$
$654$		0			0
$655$			1.00000i			1.00000i
$656$	0.500000	−	0.866025i	0.500000	−	0.866025i
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$662$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$663$		0			0
$664$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$665$	0.500000	+	0.866025i	0.500000	+	0.866025i
$666$		0			0
$667$		0			0
$668$	0.866025	−	0.500000i	0.866025	−	0.500000i
$669$		0			0
$670$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$671$		0			0
$672$		0			0
$673$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$674$		−	2.00000i		−	2.00000i
$675$		0			0
$676$		0			0
$677$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$677$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$678$		0			0
$679$		0			0
$680$		−	1.00000i		−	1.00000i
$681$		0			0
$682$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$686$	1.00000			1.00000
$687$		0			0
$688$	0.866025	−	0.500000i	0.866025	−	0.500000i
$689$	0.500000	+	0.866025i	0.500000	+	0.866025i
$690$		0			0
$691$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$691$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$692$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$693$		0			0
$694$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$695$		0			0
$696$		0			0
$697$	1.00000			1.00000
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$701$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$702$		0			0
$703$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$704$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$705$		0			0
$706$	0.866025	−	0.500000i	0.866025	−	0.500000i
$707$		0			0
$708$		0			0
$709$	2.00000			2.00000			1.00000			$0$
$709$	2.00000			2.00000			1.00000			$0$
$710$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$711$		0			0
$712$		0			0
$713$		0			0
$714$		0			0
$715$		−	1.00000i		−	1.00000i
$716$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$717$		0			0
$718$	0.500000	−	0.866025i	0.500000	−	0.866025i
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$720$		0			0
$721$	1.00000			1.00000
$722$		0			0
$723$		0			0
$724$	0.500000	−	0.866025i	0.500000	−	0.866025i
$725$		0			0
$726$		0			0
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$728$	1.00000			1.00000
$729$		0			0
$730$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$731$	0.866025	+	0.500000i	0.866025	+	0.500000i
$732$		0			0
$733$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$733$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$734$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$735$		0			0
$736$		0			0
$737$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$738$		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	$0.833333\pi$
$740$	1.00000			1.00000
$741$		0			0
$742$	1.00000			1.00000
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$	1.00000			1.00000
$746$		−	2.00000i		−	2.00000i
$747$		0			0
$748$		−	1.00000i		−	1.00000i
$749$	0.500000	−	0.866025i	0.500000	−	0.866025i
$750$		0			0
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$756$		0			0
$757$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$757$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$758$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$759$		0			0
$760$	−1.00000			−1.00000
$761$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$761$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$762$		0			0
$763$		0			0
$764$	0.866025	+	0.500000i	0.866025	+	0.500000i
$765$		0			0
$766$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$767$		−	1.00000i		−	1.00000i
$768$		0			0
$769$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$769$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$770$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$771$		0			0
$772$	0.500000	+	0.866025i	0.500000	+	0.866025i
$773$	2.00000			2.00000			1.00000			$0$
$773$	2.00000			2.00000			1.00000			$0$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	0.866025	−	0.500000i	0.866025	−	0.500000i
$779$		−	1.00000i		−	1.00000i
$780$		0			0
$781$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$787$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$788$	0.500000	−	0.866025i	0.500000	−	0.866025i
$789$		0			0
$790$	−1.00000			−1.00000
$791$		−	1.00000i		−	1.00000i
$792$		0			0
$793$		0			0
$794$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$795$		0			0
$796$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$797$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$797$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$804$		0			0
$805$		0			0
$806$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$807$		0			0
$808$		0			0
$809$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$809$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$810$		0			0
$811$	−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	$0.833333\pi$
$812$		0			0
$813$		0			0
$814$	1.00000			1.00000
$815$		0			0
$816$		0			0
$817$	0.500000	−	0.866025i	0.500000	−	0.866025i
$818$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$819$		0			0
$820$	0.500000	+	0.866025i	0.500000	+	0.866025i
$821$		0			0			−	1.00000i	$-0.5\pi$
$821$		0			0				1.00000i	$0.5\pi$
$822$		0			0
$823$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$823$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$824$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$825$		0			0
$826$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$827$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$827$	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	$0.5\pi$
$830$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$831$		0			0
$832$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$833$		0			0
$834$		0			0
$835$			1.00000i			1.00000i
$836$	−1.00000			−1.00000
$837$		0			0
$838$		0			0
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$		0			0
$841$	−1.00000			−1.00000
$842$	0.866025	+	0.500000i	0.866025	+	0.500000i
$843$		0			0
$844$	0.866025	−	0.500000i	0.866025	−	0.500000i
$845$		0			0
$846$		0			0
$847$		0			0
$848$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$		0			0
$855$		0			0
$856$	0.500000	+	0.866025i	0.500000	+	0.866025i
$857$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$857$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$858$		0			0
$859$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$859$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$860$			1.00000i			1.00000i
$861$		0			0
$862$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$863$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$863$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$864$		0			0
$865$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$866$		0			0
$867$		0			0
$868$	0.500000	+	0.866025i	0.500000	+	0.866025i
$869$	−1.00000			−1.00000
$870$		0			0
$871$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$876$		0			0
$877$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$877$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$878$	0.500000	−	0.866025i	0.500000	−	0.866025i
$879$		0			0
$880$	0.866025	−	0.500000i	0.866025	−	0.500000i
$881$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$881$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$882$		0			0
$883$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$883$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$884$	−1.00000			−1.00000
$885$		0			0
$886$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$887$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$887$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$890$		0			0
$891$		0			0
$892$	0.866025	−	0.500000i	0.866025	−	0.500000i
$893$		0			0
$894$		0			0
$895$		−	1.00000i		−	1.00000i
$896$	0.500000	+	0.866025i	0.500000	+	0.866025i
$897$		0			0
$898$			2.00000i			2.00000i
$899$		0			0
$900$		0			0
$901$	−1.00000			−1.00000
$902$	0.500000	+	0.866025i	0.500000	+	0.866025i
$903$		0			0
$904$	0.866025	+	0.500000i	0.866025	+	0.500000i
$905$	0.500000	+	0.866025i	0.500000	+	0.866025i
$906$		0			0
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$909$		0			0
$910$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$911$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$911$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$914$		0			0
$915$		0			0
$916$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$917$	0.500000	−	0.866025i	0.500000	−	0.866025i
$918$		0			0
$919$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$919$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.866025	+	0.500000i	0.866025	+	0.500000i
$936$		0			0
$937$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$937$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$938$			1.00000i			1.00000i
$939$		0			0
$940$		0			0
$941$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$941$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$942$		0			0
$943$		0			0
$944$	0.866025	−	0.500000i	0.866025	−	0.500000i
$945$		0			0
$946$			1.00000i			1.00000i
$947$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$947$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$948$		0			0
$949$	0.500000	+	0.866025i	0.500000	+	0.866025i
$950$		0			0
$951$		0			0
$952$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$956$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$957$		0			0
$958$	0.500000	+	0.866025i	0.500000	+	0.866025i
$959$			1.00000i			1.00000i
$960$		0			0
$961$	−1.00000			−1.00000
$962$		−	1.00000i		−	1.00000i
$963$		0			0
$964$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$965$	−1.00000			−1.00000
$966$		0			0
$967$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$967$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$971$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$972$		0			0
$973$		0			0
$974$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$975$		0			0
$976$		0			0
$977$		0			0			−	1.00000i	$-0.5\pi$
$977$		0			0				1.00000i	$0.5\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$983$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$983$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$984$		0			0
$985$	0.500000	+	0.866025i	0.500000	+	0.866025i
$986$		0			0
$987$		0			0
$988$			1.00000i			1.00000i
$989$		0			0
$990$		0			0
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$991$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$992$	−1.00000			−1.00000
$993$		0			0
$994$			1.00000i			1.00000i
$995$	0.866025	−	0.500000i	0.866025	−	0.500000i
$996$		0			0
$997$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$997$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$998$	0.500000	+	0.866025i	0.500000	+	0.866025i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1116.1.x.a.955.2		4
3.2	odd	2		124.1.i.a.87.1	yes	4
4.3	odd	2	inner	1116.1.x.a.955.1		4
12.11	even	2		124.1.i.a.87.2	yes	4
15.2	even	4		3100.1.t.b.1699.1		4
15.8	even	4		3100.1.t.a.1699.1		4
15.14	odd	2		3100.1.z.a.1451.2		4
24.5	odd	2		1984.1.s.a.831.1		4
24.11	even	2		1984.1.s.a.831.2		4
31.5	even	3	inner	1116.1.x.a.811.2		4
60.23	odd	4		3100.1.t.b.1699.2		4
60.47	odd	4		3100.1.t.a.1699.2		4
60.59	even	2		3100.1.z.a.1451.1		4
93.2	odd	10		3844.1.n.e.3727.2		16
93.5	odd	6		124.1.i.a.67.1	✓	4
93.8	odd	10		3844.1.n.e.3615.1		16
93.11	even	30		3844.1.n.f.235.2		16
93.14	odd	30		3844.1.l.d.1335.1		8
93.17	even	30		3844.1.l.c.1335.1		8
93.20	odd	30		3844.1.n.e.235.2		16
93.23	even	10		3844.1.n.f.3615.1		16
93.26	even	6		3844.1.i.d.439.1		4
93.29	even	10		3844.1.n.f.3727.2		16
93.35	odd	10		3844.1.n.e.1299.2		16
93.38	odd	30		3844.1.l.d.3271.2		8
93.41	odd	30		3844.1.n.e.547.2		16
93.44	even	30		3844.1.n.f.1807.1		16
93.47	odd	10		3844.1.n.e.3331.1		16
93.50	odd	30		3844.1.l.d.531.2		8
93.53	even	30		3844.1.n.f.3699.1		16
93.56	odd	6		3844.1.b.d.1923.1		2
93.59	odd	30		3844.1.l.d.3511.1		8
93.65	even	30		3844.1.l.c.3511.1		8
93.68	even	6		3844.1.b.c.1923.1		2
93.71	odd	30		3844.1.n.e.3699.1		16
93.74	even	30		3844.1.l.c.531.2		8
93.77	even	10		3844.1.n.f.3331.1		16
93.80	odd	30		3844.1.n.e.1807.1		16
93.83	even	30		3844.1.n.f.547.2		16
93.86	even	30		3844.1.l.c.3271.2		8
93.89	even	10		3844.1.n.f.1299.2		16
93.92	even	2		3844.1.i.d.2443.1		4
124.67	odd	6	inner	1116.1.x.a.811.1		4
372.11	odd	30		3844.1.n.f.235.1		16
372.23	odd	10		3844.1.n.f.3615.2		16
372.35	even	10		3844.1.n.e.1299.1		16
372.47	even	10		3844.1.n.e.3331.2		16
372.59	even	30		3844.1.l.d.3511.2		8
372.71	even	30		3844.1.n.e.3699.2		16
372.83	odd	30		3844.1.n.f.547.1		16
372.95	even	10		3844.1.n.e.3727.1		16
372.107	even	30		3844.1.l.d.1335.2		8
372.119	odd	6		3844.1.i.d.439.2		4
372.131	even	30		3844.1.l.d.3271.1		8
372.143	even	30		3844.1.l.d.531.1		8
372.167	odd	30		3844.1.l.c.531.1		8
372.179	odd	30		3844.1.l.c.3271.1		8
372.191	even	6		124.1.i.a.67.2	yes	4
372.203	odd	30		3844.1.l.c.1335.2		8
372.215	odd	10		3844.1.n.f.3727.1		16
372.227	even	30		3844.1.n.e.547.1		16
372.239	odd	30		3844.1.n.f.3699.2		16
372.251	odd	30		3844.1.l.c.3511.2		8
372.263	odd	10		3844.1.n.f.3331.2		16
372.275	odd	10		3844.1.n.f.1299.1		16
372.287	even	10		3844.1.n.e.3615.2		16
372.299	even	30		3844.1.n.e.235.1		16
372.323	odd	30		3844.1.n.f.1807.2		16
372.335	even	6		3844.1.b.d.1923.2		2
372.347	odd	6		3844.1.b.c.1923.2		2
372.359	even	30		3844.1.n.e.1807.2		16
372.371	odd	2		3844.1.i.d.2443.2		4
465.98	even	12		3100.1.t.a.2299.2		4
465.284	odd	6		3100.1.z.a.2051.2		4
465.377	even	12		3100.1.t.b.2299.2		4
744.5	odd	6		1984.1.s.a.191.2		4
744.563	even	6		1984.1.s.a.191.1		4
1860.563	odd	12		3100.1.t.b.2299.1		4
1860.1307	odd	12		3100.1.t.a.2299.1		4
1860.1679	even	6		3100.1.z.a.2051.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.1.i.a.67.1	✓	4	93.5	odd	6
124.1.i.a.67.2	yes	4	372.191	even	6
124.1.i.a.87.1	yes	4	3.2	odd	2
124.1.i.a.87.2	yes	4	12.11	even	2
1116.1.x.a.811.1		4	124.67	odd	6	inner
1116.1.x.a.811.2		4	31.5	even	3	inner
1116.1.x.a.955.1		4	4.3	odd	2	inner
1116.1.x.a.955.2		4	1.1	even	1	trivial
1984.1.s.a.191.1		4	744.563	even	6
1984.1.s.a.191.2		4	744.5	odd	6
1984.1.s.a.831.1		4	24.5	odd	2
1984.1.s.a.831.2		4	24.11	even	2
3100.1.t.a.1699.1		4	15.8	even	4
3100.1.t.a.1699.2		4	60.47	odd	4
3100.1.t.a.2299.1		4	1860.1307	odd	12
3100.1.t.a.2299.2		4	465.98	even	12
3100.1.t.b.1699.1		4	15.2	even	4
3100.1.t.b.1699.2		4	60.23	odd	4
3100.1.t.b.2299.1		4	1860.563	odd	12
3100.1.t.b.2299.2		4	465.377	even	12
3100.1.z.a.1451.1		4	60.59	even	2
3100.1.z.a.1451.2		4	15.14	odd	2
3100.1.z.a.2051.1		4	1860.1679	even	6
3100.1.z.a.2051.2		4	465.284	odd	6
3844.1.b.c.1923.1		2	93.68	even	6
3844.1.b.c.1923.2		2	372.347	odd	6
3844.1.b.d.1923.1		2	93.56	odd	6
3844.1.b.d.1923.2		2	372.335	even	6
3844.1.i.d.439.1		4	93.26	even	6
3844.1.i.d.439.2		4	372.119	odd	6
3844.1.i.d.2443.1		4	93.92	even	2
3844.1.i.d.2443.2		4	372.371	odd	2
3844.1.l.c.531.1		8	372.167	odd	30
3844.1.l.c.531.2		8	93.74	even	30
3844.1.l.c.1335.1		8	93.17	even	30
3844.1.l.c.1335.2		8	372.203	odd	30
3844.1.l.c.3271.1		8	372.179	odd	30
3844.1.l.c.3271.2		8	93.86	even	30
3844.1.l.c.3511.1		8	93.65	even	30
3844.1.l.c.3511.2		8	372.251	odd	30
3844.1.l.d.531.1		8	372.143	even	30
3844.1.l.d.531.2		8	93.50	odd	30
3844.1.l.d.1335.1		8	93.14	odd	30
3844.1.l.d.1335.2		8	372.107	even	30
3844.1.l.d.3271.1		8	372.131	even	30
3844.1.l.d.3271.2		8	93.38	odd	30
3844.1.l.d.3511.1		8	93.59	odd	30
3844.1.l.d.3511.2		8	372.59	even	30
3844.1.n.e.235.1		16	372.299	even	30
3844.1.n.e.235.2		16	93.20	odd	30
3844.1.n.e.547.1		16	372.227	even	30
3844.1.n.e.547.2		16	93.41	odd	30
3844.1.n.e.1299.1		16	372.35	even	10
3844.1.n.e.1299.2		16	93.35	odd	10
3844.1.n.e.1807.1		16	93.80	odd	30
3844.1.n.e.1807.2		16	372.359	even	30
3844.1.n.e.3331.1		16	93.47	odd	10
3844.1.n.e.3331.2		16	372.47	even	10
3844.1.n.e.3615.1		16	93.8	odd	10
3844.1.n.e.3615.2		16	372.287	even	10
3844.1.n.e.3699.1		16	93.71	odd	30
3844.1.n.e.3699.2		16	372.71	even	30
3844.1.n.e.3727.1		16	372.95	even	10
3844.1.n.e.3727.2		16	93.2	odd	10
3844.1.n.f.235.1		16	372.11	odd	30
3844.1.n.f.235.2		16	93.11	even	30
3844.1.n.f.547.1		16	372.83	odd	30
3844.1.n.f.547.2		16	93.83	even	30
3844.1.n.f.1299.1		16	372.275	odd	10
3844.1.n.f.1299.2		16	93.89	even	10
3844.1.n.f.1807.1		16	93.44	even	30
3844.1.n.f.1807.2		16	372.323	odd	30
3844.1.n.f.3331.1		16	93.77	even	10
3844.1.n.f.3331.2		16	372.263	odd	10
3844.1.n.f.3615.1		16	93.23	even	10
3844.1.n.f.3615.2		16	372.23	odd	10
3844.1.n.f.3699.1		16	93.53	even	30
3844.1.n.f.3699.2		16	372.239	odd	30
3844.1.n.f.3727.1		16	372.215	odd	10
3844.1.n.f.3727.2		16	93.29	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1116.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(0.866025 + 0.500000i) q^{10} +(0.866025 + 0.500000i) q^{11} +(0.500000 - 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{14} +1.00000 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.866025 - 0.500000i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-0.500000 + 0.866025i) q^{22} +(0.866025 + 0.500000i) q^{26} +(0.866025 - 0.500000i) q^{28} +1.00000i q^{31} +1.00000i q^{32} +(-0.866025 + 0.500000i) q^{34} +1.00000i q^{35} +(-0.500000 - 0.866025i) q^{37} +(0.500000 + 0.866025i) q^{38} +(-0.866025 - 0.500000i) q^{40} +(0.500000 - 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{43} +(-0.866025 - 0.500000i) q^{44} +(-0.500000 + 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(0.866025 - 0.500000i) q^{55} +(0.500000 + 0.866025i) q^{56} +(0.866025 - 0.500000i) q^{59} -1.00000 q^{62} -1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(-0.866025 - 0.500000i) q^{67} +(-0.500000 - 0.866025i) q^{68} -1.00000 q^{70} +(-0.866025 - 0.500000i) q^{71} +(-0.500000 + 0.866025i) q^{73} +(0.866025 - 0.500000i) q^{74} +(-0.866025 + 0.500000i) q^{76} -1.00000 q^{77} +(-0.866025 + 0.500000i) q^{79} +(0.500000 - 0.866025i) q^{80} +(0.866025 + 0.500000i) q^{82} +(-0.866025 - 0.500000i) q^{83} +1.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(0.500000 - 0.866025i) q^{88} +1.00000i q^{91} -1.00000i q^{95} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{5}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^5	\( 4 q - 4 q^{4} + 2 q^{5} + 2 q^{13} - 2 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{20} - 2 q^{22} - 2 q^{37} + 2 q^{38} + 2 q^{41} - 2 q^{52} - 2 q^{53} + 2 q^{56} - 4 q^{62} - 4 q^{64} - 2 q^{65} - 2 q^{68} - 4 q^{70} - 2 q^{73} - 4 q^{77} + 2 q^{80} + 4 q^{85} + 2 q^{86} + 2 q^{88}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^5 + 2 * q^13 - 2 * q^14 + 4 * q^16 + 2 * q^17 - 2 * q^20 - 2 * q^22 - 2 * q^37 + 2 * q^38 + 2 * q^41 - 2 * q^52 - 2 * q^53 + 2 * q^56 - 4 * q^62 - 4 * q^64 - 2 * q^65 - 2 * q^68 - 4 * q^70 - 2 * q^73 - 4 * q^77 + 2 * q^80 + 4 * q^85 + 2 * q^86 + 2 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more