LMFDB - Embedded newform 2883.1.h.c.521.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2883,1,Mod(521,2883)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2883, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 1, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2883.521"); S:= CuspForms(chi, 1); N := Newforms(S);

Level:	$ N $	$=$	$ 2883 = 3 \cdot 31^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2883.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.43880443142$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.268119.1

Embedding invariants

Embedding label			521.3
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2883.521
Dual form			2883.1.h.c.1400.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.866025 + 0.500000i) q^{14} +(-0.707107 + 0.707107i) q^{15} -1.00000 q^{16} +(-1.22474 + 0.707107i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.965926 + 0.258819i) q^{21} +(-0.965926 - 0.258819i) q^{24} +(0.707107 - 0.707107i) q^{27} -1.41421i q^{29} +(-0.707107 - 0.707107i) q^{30} +(-0.707107 - 1.22474i) q^{34} +1.00000i q^{35} +(0.866025 - 0.500000i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(0.866025 + 0.500000i) q^{41} +(-0.258819 - 0.965926i) q^{42} +(0.707107 + 1.22474i) q^{43} +(-0.500000 - 0.866025i) q^{45} +(0.258819 - 0.965926i) q^{48} +(-0.366025 - 1.36603i) q^{51} +(0.707107 + 0.707107i) q^{54} +(-0.866025 + 0.500000i) q^{56} +(0.965926 - 0.258819i) q^{57} +1.41421 q^{58} +(-0.866025 + 0.500000i) q^{59} +1.41421 q^{61} -1.00000i q^{63} -1.00000 q^{64} -1.00000 q^{70} +(0.866025 + 0.500000i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-0.866025 - 0.500000i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(1.22474 + 0.707107i) q^{83} -1.41421 q^{85} +(-1.22474 + 0.707107i) q^{86} +(1.36603 + 0.366025i) q^{87} +(0.866025 - 0.500000i) q^{90} -1.00000i q^{95} -1.00000 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{7} - 4 q^{10} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 4 q^{40} - 4 q^{45} + 4 q^{51} - 8 q^{64} - 8 q^{70} + 4 q^{72} + 4 q^{81} - 4 q^{82} + 4 q^{87} - 8 q^{97}+O(q^{100}) $ 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 4 * q^40 - 4 * q^45 + 4 * q^51 - 8 * q^64 - 8 * q^70 + 4 * q^72 + 4 * q^81 - 4 * q^82 + 4 * q^87 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2883\mathbb{Z}\right)^\times$.

$n$	$962$	$964$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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	0.866025	+	0.500000i	$0.166667\pi$
$2$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$3$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$4$		0			0
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$5$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$6$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$8$			1.00000i			1.00000i
$9$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$10$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$15$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$16$	−1.00000			−1.00000
$17$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$17$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$18$	0.500000	−	0.866025i	0.500000	−	0.866025i
$19$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$19$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$20$		0			0
$21$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$25$		0			0
$26$		0			0
$27$	0.707107	−	0.707107i	0.707107	−	0.707107i
$28$		0			0
$29$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$29$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$30$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$31$		0			0
$31$		0			0
$32$		0			0
$33$		0			0
$34$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$35$			1.00000i			1.00000i
$36$		0			0
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	0.866025	−	0.500000i	0.866025	−	0.500000i
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$41$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$41$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$42$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$43$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$43$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$46$		0			0
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.258819	−	0.965926i	0.258819	−	0.965926i
$49$		0			0
$50$		0			0
$51$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$52$		0			0
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$	0.707107	+	0.707107i	0.707107	+	0.707107i
$55$		0			0
$56$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$57$	0.965926	−	0.258819i	0.965926	−	0.258819i
$58$	1.41421			1.41421
$59$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$59$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$60$		0			0
$61$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$61$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$62$		0			0
$63$		−	1.00000i		−	1.00000i
$64$	−1.00000			−1.00000
$65$		0			0
$66$		0			0
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$		0			0
$69$		0			0
$70$	−1.00000			−1.00000
$71$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$71$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$72$	0.500000	−	0.866025i	0.500000	−	0.866025i
$73$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$73$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$81$	0.500000	+	0.866025i	0.500000	+	0.866025i
$82$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$83$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$83$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$84$		0			0
$85$	−1.41421			−1.41421
$86$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$87$	1.36603	+	0.366025i	1.36603	+	0.366025i
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	0.866025	−	0.500000i	0.866025	−	0.500000i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		−	1.00000i		−	1.00000i
$96$		0			0
$97$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$97$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$101$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$102$	1.36603	−	0.366025i	1.36603	−	0.366025i
$103$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$103$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$104$		0			0
$105$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$106$		0			0
$107$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$107$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$108$		0			0
$109$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$109$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$110$		0			0
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$113$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$113$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$114$	0.258819	+	0.965926i	0.258819	+	0.965926i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$119$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$120$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$			1.41421i			1.41421i
$123$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$124$		0			0
$125$		−	1.00000i		−	1.00000i
$126$	1.00000			1.00000
$127$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$127$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$128$		−	1.00000i		−	1.00000i
$129$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$130$		0			0
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$		0			0
$133$	0.500000	−	0.866025i	0.500000	−	0.866025i
$134$		0			0
$135$	0.965926	−	0.258819i	0.965926	−	0.258819i
$136$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$		0			0
$142$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$143$		0			0
$144$	0.866025	+	0.500000i	0.866025	+	0.500000i
$145$	0.707107	−	1.22474i	0.707107	−	1.22474i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$151$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$152$	0.866025	−	0.500000i	0.866025	−	0.500000i
$153$	1.41421			1.41421
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$157$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$163$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$163$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$164$		0			0
$165$		0			0
$166$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$167$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$167$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$168$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$169$	0.500000	+	0.866025i	0.500000	+	0.866025i
$170$		−	1.41421i		−	1.41421i
$171$			1.00000i			1.00000i
$172$		0			0
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$175$		0			0
$176$		0			0
$177$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$178$		0			0
$179$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$179$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$180$		0			0
$181$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$181$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$182$		0			0
$183$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	0.965926	+	0.258819i	0.965926	+	0.258819i
$190$	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	$0.833333\pi$
$192$	0.258819	−	0.965926i	0.258819	−	0.965926i
$193$	−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			$\pi$
$194$		−	1.00000i		−	1.00000i
$195$		0			0
$196$		0			0
$197$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$197$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$198$		0			0
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$		0			0
$201$		0			0
$202$	1.00000			1.00000
$203$	1.22474	−	0.707107i	1.22474	−	0.707107i
$204$		0			0
$205$	0.500000	+	0.866025i	0.500000	+	0.866025i
$206$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$207$		0			0
$208$		0			0
$209$		0			0
$210$	0.258819	−	0.965926i	0.258819	−	0.965926i
$211$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$211$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$212$		0			0
$213$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$214$	0.500000	+	0.866025i	0.500000	+	0.866025i
$215$			1.41421i			1.41421i
$216$	0.707107	+	0.707107i	0.707107	+	0.707107i
$217$		0			0
$218$			1.00000i			1.00000i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$223$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$224$		0			0
$225$		0			0
$226$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$229$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$230$		0			0
$231$		0			0
$232$	1.41421			1.41421
$233$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$233$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	0.707107	−	1.22474i	0.707107	−	1.22474i
$239$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$239$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$240$	0.707107	−	0.707107i	0.707107	−	0.707107i
$241$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$241$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$242$	0.866025	−	0.500000i	0.866025	−	0.500000i
$243$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$244$		0			0
$245$		0			0
$246$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$247$		0			0
$248$		0			0
$249$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$250$	1.00000			1.00000
$251$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$251$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	0.366025	−	1.36603i	0.366025	−	1.36603i
$256$		0			0
$257$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$257$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$258$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$259$		0			0
$260$		0			0
$261$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$262$		0			0
$263$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$263$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$264$		0			0
$265$		0			0
$266$	0.866025	+	0.500000i	0.866025	+	0.500000i
$267$		0			0
$268$		0			0
$269$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$269$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$270$	0.258819	+	0.965926i	0.258819	+	0.965926i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	1.22474	−	0.707107i	1.22474	−	0.707107i
$273$		0			0
$274$		0			0
$275$		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
$281$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$281$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$282$		0			0
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$		0			0
$285$	0.965926	+	0.258819i	0.965926	+	0.258819i
$286$		0			0
$287$			1.00000i			1.00000i
$288$		0			0
$289$	0.500000	−	0.866025i	0.500000	−	0.866025i
$290$	1.22474	+	0.707107i	1.22474	+	0.707107i
$291$	0.258819	−	0.965926i	0.258819	−	0.965926i
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$		0			0
$295$	−1.00000			−1.00000
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$302$		−	1.41421i		−	1.41421i
$303$	0.965926	+	0.258819i	0.965926	+	0.258819i
$304$	0.500000	+	0.866025i	0.500000	+	0.866025i
$305$	1.22474	+	0.707107i	1.22474	+	0.707107i
$306$			1.41421i			1.41421i
$307$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$307$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$308$		0			0
$309$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$310$		0			0
$311$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$311$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$313$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$314$		−	1.00000i		−	1.00000i
$315$	0.500000	−	0.866025i	0.500000	−	0.866025i
$316$		0			0
$317$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$317$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$318$		0			0
$319$		0			0
$320$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$321$	0.258819	+	0.965926i	0.258819	+	0.965926i
$322$		0			0
$323$	1.22474	+	0.707107i	1.22474	+	0.707107i
$324$		0			0
$325$		0			0
$326$			1.00000i			1.00000i
$327$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$328$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$329$		0			0
$330$		0			0
$331$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$331$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$332$		0			0
$333$		0			0
$334$	0.707107	+	1.22474i	0.707107	+	1.22474i
$335$		0			0
$336$	0.965926	−	0.258819i	0.965926	−	0.258819i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$339$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$340$		0			0
$341$		0			0
$342$	−1.00000			−1.00000
$343$	1.00000			1.00000
$344$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$345$		0			0
$346$		0			0
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$		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			0
$353$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$353$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$354$	0.965926	−	0.258819i	0.965926	−	0.258819i
$355$	0.500000	+	0.866025i	0.500000	+	0.866025i
$356$		0			0
$357$	1.00000	−	1.00000i	1.00000	−	1.00000i
$358$	0.707107	+	1.22474i	0.707107	+	1.22474i
$359$	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	$0.5\pi$
$360$	0.866025	−	0.500000i	0.866025	−	0.500000i
$361$		0			0
$362$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$363$	0.965926	−	0.258819i	0.965926	−	0.258819i
$364$		0			0
$365$		0			0
$366$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$367$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$367$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$368$		0			0
$369$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$373$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	0.965926	+	0.258819i	0.965926	+	0.258819i
$376$		0			0
$377$		0			0
$378$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$379$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$379$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$380$		0			0
$381$		0			0
$382$	0.500000	−	0.866025i	0.500000	−	0.866025i
$383$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$383$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$384$	0.965926	+	0.258819i	0.965926	+	0.258819i
$385$		0			0
$386$	0.866025	−	0.500000i	0.866025	−	0.500000i
$387$		−	1.41421i		−	1.41421i
$388$		0			0
$389$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$389$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	0.707107	−	1.22474i	0.707107	−	1.22474i
$395$		0			0
$396$		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			0
$399$	0.707107	+	0.707107i	0.707107	+	0.707107i
$400$		0			0
$401$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$401$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$			1.00000i			1.00000i
$406$	0.707107	+	1.22474i	0.707107	+	1.22474i
$407$		0			0
$408$	1.36603	−	0.366025i	1.36603	−	0.366025i
$409$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$409$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$410$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$411$		0			0
$412$		0			0
$413$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$414$		0			0
$415$	0.707107	+	1.22474i	0.707107	+	1.22474i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$419$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$420$		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			$\pi$
$422$	0.866025	−	0.500000i	0.866025	−	0.500000i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$427$	0.707107	+	1.22474i	0.707107	+	1.22474i
$428$		0			0
$429$		0			0
$430$	−1.41421			−1.41421
$431$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$431$	1.73205	−	1.00000i	1.73205	−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$432$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$433$		0			0			−	1.00000i	$-0.5\pi$
$433$		0			0				1.00000i	$0.5\pi$
$434$		0			0
$435$	1.00000	+	1.00000i	1.00000	+	1.00000i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$443$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$		0			0
$446$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$447$		0			0
$448$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	0.366025	−	1.36603i	0.366025	−	1.36603i
$454$		0			0
$455$		0			0
$456$	0.258819	+	0.965926i	0.258819	+	0.965926i
$457$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$457$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$458$		0			0
$459$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$460$		0			0
$461$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$461$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$462$		0			0
$463$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$463$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$464$			1.41421i			1.41421i
$465$		0			0
$466$	1.00000			1.00000
$467$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$467$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.258819	−	0.965926i	0.258819	−	0.965926i
$472$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$473$		0			0
$474$		0			0
$475$		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
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$486$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$487$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$487$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$488$			1.41421i			1.41421i
$489$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$490$		0			0
$491$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$491$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$492$		0			0
$493$	1.00000	+	1.73205i	1.00000	+	1.73205i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			1.00000i			1.00000i
$498$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$499$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$499$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$500$		0			0
$501$	0.366025	+	1.36603i	0.366025	+	1.36603i
$502$	0.707107	+	1.22474i	0.707107	+	1.22474i
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$504$	1.00000			1.00000
$505$	0.500000	−	0.866025i	0.500000	−	0.866025i
$506$		0			0
$507$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$508$		0			0
$509$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$509$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$510$	1.36603	+	0.366025i	1.36603	+	0.366025i
$511$		0			0
$512$		−	1.00000i		−	1.00000i
$513$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$514$	0.500000	−	0.866025i	0.500000	−	0.866025i
$515$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$521$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$522$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$		0			0
$525$		0			0
$526$	−1.41421			−1.41421
$527$		0			0
$528$		0			0
$529$	1.00000			1.00000
$530$		0			0
$531$	1.00000			1.00000
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.00000			1.00000
$536$		0			0
$537$	0.366025	+	1.36603i	0.366025	+	1.36603i
$538$	0.707107	−	1.22474i	0.707107	−	1.22474i
$539$		0			0
$540$		0			0
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$544$		0			0
$545$	0.866025	+	0.500000i	0.866025	+	0.500000i
$546$		0			0
$547$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$547$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$548$		0			0
$549$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$550$		0			0
$551$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$557$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$558$		0			0
$559$		0			0
$560$		−	1.00000i		−	1.00000i
$561$		0			0
$562$	1.00000			1.00000
$563$	−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
$567$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$568$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$571$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$571$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$572$		0			0
$573$	0.707107	−	0.707107i	0.707107	−	0.707107i
$574$	−1.00000			−1.00000
$575$		0			0
$576$	0.866025	+	0.500000i	0.866025	+	0.500000i
$577$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$577$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$578$	0.866025	+	0.500000i	0.866025	+	0.500000i
$579$	0.965926	−	0.258819i	0.965926	−	0.258819i
$580$		0			0
$581$			1.41421i			1.41421i
$582$	0.965926	+	0.258819i	0.965926	+	0.258819i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$		−	1.00000i		−	1.00000i
$591$	1.00000	−	1.00000i	1.00000	−	1.00000i
$592$		0			0
$593$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$593$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$596$		0			0
$597$		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
$601$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$601$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$602$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$603$		0			0
$604$		0			0
$605$		−	1.00000i		−	1.00000i
$606$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$607$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$608$		0			0
$609$	0.366025	+	1.36603i	0.366025	+	1.36603i
$610$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$611$		0			0
$612$		0			0
$613$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$613$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$614$	0.866025	−	0.500000i	0.866025	−	0.500000i
$615$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$616$		0			0
$617$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$617$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$618$	0.707107	−	0.707107i	0.707107	−	0.707107i
$619$		0			0			−	1.00000i	$-0.5\pi$
$619$		0			0				1.00000i	$0.5\pi$
$620$		0			0
$621$		0			0
$622$	−1.00000			−1.00000
$623$		0			0
$624$		0			0
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$	1.22474	−	0.707107i	1.22474	−	0.707107i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	0.866025	+	0.500000i	0.866025	+	0.500000i
$631$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$631$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$632$		0			0
$633$	0.965926	−	0.258819i	0.965926	−	0.258819i
$634$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$640$	0.500000	−	0.866025i	0.500000	−	0.866025i
$641$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$641$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$642$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$643$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$643$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$644$		0			0
$645$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$646$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$647$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$647$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$648$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$653$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$654$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$655$		0			0
$656$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$657$		0			0
$658$		0			0
$659$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$659$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$660$		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			$0$
$662$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$663$		0			0
$664$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$665$	0.866025	−	0.500000i	0.866025	−	0.500000i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$673$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$679$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$680$		−	1.41421i		−	1.41421i
$681$		0			0
$682$		0			0
$683$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$683$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$684$		0			0
$685$		0			0
$686$			1.00000i			1.00000i
$687$		0			0
$688$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$689$		0			0
$690$		0			0
$691$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$691$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$697$	−1.41421			−1.41421
$698$		0			0
$699$	0.965926	+	0.258819i	0.965926	+	0.258819i
$700$		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	$0.166667\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$707$	0.866025	−	0.500000i	0.866025	−	0.500000i
$708$		0			0
$709$		0			0			−	1.00000i	$-0.5\pi$
$709$		0			0				1.00000i	$0.5\pi$
$710$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	1.00000	+	1.00000i	1.00000	+	1.00000i
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$719$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$719$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$720$	0.500000	+	0.866025i	0.500000	+	0.866025i
$721$	−1.00000			−1.00000
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.258819	+	0.965926i	0.258819	+	0.965926i
$727$	−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
$729$		−	1.00000i		−	1.00000i
$730$		0			0
$731$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$732$		0			0
$733$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$733$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$734$	1.22474	+	0.707107i	1.22474	+	0.707107i
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.866025	−	0.500000i	0.866025	−	0.500000i
$739$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$739$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$743$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$744$		0			0
$745$		0			0
$746$		−	1.00000i		−	1.00000i
$747$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$748$		0			0
$749$	0.866025	+	0.500000i	0.866025	+	0.500000i
$750$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$751$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$	0.366025	+	1.36603i	0.366025	+	1.36603i
$754$		0			0
$755$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$756$		0			0
$757$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$757$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$758$		0			0
$759$		0			0
$760$	1.00000			1.00000
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$		0			0
$763$	0.500000	+	0.866025i	0.500000	+	0.866025i
$764$		0			0
$765$	1.22474	+	0.707107i	1.22474	+	0.707107i
$766$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$767$		0			0
$768$		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			0
$771$	0.707107	−	0.707107i	0.707107	−	0.707107i
$772$		0			0
$773$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$773$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$774$	1.41421			1.41421
$775$		0			0
$776$		−	1.00000i		−	1.00000i
$777$		0			0
$778$	0.707107	+	1.22474i	0.707107	+	1.22474i
$779$		−	1.00000i		−	1.00000i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$784$		0			0
$785$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$786$		0			0
$787$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$787$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$788$		0			0
$789$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$790$		0			0
$791$			1.00000i			1.00000i
$792$		0			0
$793$		0			0
$794$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$795$		0			0
$796$		0			0
$797$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$797$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$798$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	1.41421			1.41421
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.00000	−	1.00000i	1.00000	−	1.00000i
$808$	1.00000			1.00000
$809$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$809$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$810$	−1.00000			−1.00000
$811$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$811$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.866025	+	0.500000i	0.866025	+	0.500000i
$816$	0.366025	+	1.36603i	0.366025	+	1.36603i
$817$	0.707107	−	1.22474i	0.707107	−	1.22474i
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		1.00000			$0$
$821$		0			0		−1.00000			$\pi$
$822$		0			0
$823$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$823$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$824$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$825$		0			0
$826$	0.500000	−	0.866025i	0.500000	−	0.866025i
$827$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$827$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$828$		0			0
$829$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$829$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$830$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.41421			1.41421
$836$		0			0
$837$		0			0
$838$	−1.00000			−1.00000
$839$		0			0		1.00000			$0$
$839$		0			0		−1.00000			$\pi$
$840$	0.258819	−	0.965926i	0.258819	−	0.965926i
$841$	−1.00000			−1.00000
$842$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$843$	0.965926	+	0.258819i	0.965926	+	0.258819i
$844$		0			0
$845$			1.00000i			1.00000i
$846$		0			0
$847$	0.500000	−	0.866025i	0.500000	−	0.866025i
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$855$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$856$	0.500000	+	0.866025i	0.500000	+	0.866025i
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$		0			0
$859$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$859$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$860$		0			0
$861$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$862$	1.00000	+	1.73205i	1.00000	+	1.73205i
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.707107	+	0.707107i	0.707107	+	0.707107i
$868$		0			0
$869$		0			0
$870$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$871$		0			0
$872$			1.00000i			1.00000i
$873$	0.866025	+	0.500000i	0.866025	+	0.500000i
$874$		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			$0$
$878$	0.866025	+	0.500000i	0.866025	+	0.500000i
$879$		0			0
$880$		0			0
$881$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$881$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$	0.258819	−	0.965926i	0.258819	−	0.965926i
$886$	0.500000	−	0.866025i	0.500000	−	0.866025i
$887$	−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			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	1.41421			1.41421
$896$	0.866025	−	0.500000i	0.866025	−	0.500000i
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$904$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$905$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$906$	1.36603	+	0.366025i	1.36603	+	0.366025i
$907$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$907$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$910$		0			0
$911$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$911$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$912$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$913$		0			0
$914$			1.41421i			1.41421i
$915$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$916$		0			0
$917$		0			0
$918$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$		0			0
$921$	0.965926	−	0.258819i	0.965926	−	0.258819i
$922$	−1.41421			−1.41421
$923$		0			0
$924$		0			0
$925$		0			0
$926$		−	1.41421i		−	1.41421i
$927$	0.866025	−	0.500000i	0.866025	−	0.500000i
$928$		0			0
$929$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$929$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$934$	−1.00000			−1.00000
$935$		0			0
$936$		0			0
$937$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$937$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$938$		0			0
$939$	1.36603	−	0.366025i	1.36603	−	0.366025i
$940$		0			0
$941$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$941$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$942$	0.965926	+	0.258819i	0.965926	+	0.258819i
$943$		0			0
$944$	0.866025	−	0.500000i	0.866025	−	0.500000i
$945$	0.707107	+	0.707107i	0.707107	+	0.707107i
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$952$	0.707107	−	1.22474i	0.707107	−	1.22474i
$953$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$953$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$954$		0			0
$955$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$956$		0			0
$957$		0			0
$958$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$959$		0			0
$960$	0.707107	−	0.707107i	0.707107	−	0.707107i
$961$		0			0
$962$		0			0
$963$	−1.00000			−1.00000
$964$		0			0
$965$		−	1.00000i		−	1.00000i
$966$		0			0
$967$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$967$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$968$	0.866025	−	0.500000i	0.866025	−	0.500000i
$969$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$970$	0.500000	−	0.866025i	0.500000	−	0.866025i
$971$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$971$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.41421			−1.41421
$977$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$977$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$978$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$979$		0			0
$980$		0			0
$981$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$982$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$985$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$986$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$991$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$992$		0			0
$993$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$994$	−1.00000			−1.00000
$995$		0			0
$996$		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			$\pi$
$998$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2883.1.h.c.521.3		8
3.2	odd	2	inner	2883.1.h.c.521.2		8
31.2	even	5		2883.1.o.e.1805.2		32
31.3	odd	30		2883.1.l.d.1589.3		16
31.4	even	5		2883.1.o.e.338.2		32
31.5	even	3	inner	2883.1.h.c.1400.4		8
31.6	odd	6		2883.1.b.c.962.4	yes	4
31.7	even	15		2883.1.l.d.1349.2		16
31.8	even	5		2883.1.o.e.2654.3		32
31.9	even	15		2883.1.o.e.2738.3		32
31.10	even	15		2883.1.o.e.1508.2		32
31.11	odd	30		2883.1.o.e.1196.2		32
31.12	odd	30		2883.1.l.d.2453.2		16
31.13	odd	30		2883.1.o.e.2768.3		32
31.14	even	15		2883.1.l.d.374.4		16
31.15	odd	10		2883.1.o.e.1409.4		32
31.16	even	5		2883.1.o.e.1409.3		32
31.17	odd	30		2883.1.l.d.374.3		16
31.18	even	15		2883.1.o.e.2768.4		32
31.19	even	15		2883.1.l.d.2453.1		16
31.20	even	15		2883.1.o.e.1196.1		32
31.21	odd	30		2883.1.o.e.1508.1		32
31.22	odd	30		2883.1.o.e.2738.4		32
31.23	odd	10		2883.1.o.e.2654.4		32
31.24	odd	30		2883.1.l.d.1349.1		16
31.25	even	3		2883.1.b.c.962.3	yes	4
31.26	odd	6	inner	2883.1.h.c.1400.3		8
31.27	odd	10		2883.1.o.e.338.1		32
31.28	even	15		2883.1.l.d.1589.4		16
31.29	odd	10		2883.1.o.e.1805.1		32
31.30	odd	2	inner	2883.1.h.c.521.4		8
93.2	odd	10		2883.1.o.e.1805.4		32
93.5	odd	6	inner	2883.1.h.c.1400.1		8
93.8	odd	10		2883.1.o.e.2654.1		32
93.11	even	30		2883.1.o.e.1196.4		32
93.14	odd	30		2883.1.l.d.374.2		16
93.17	even	30		2883.1.l.d.374.1		16
93.20	odd	30		2883.1.o.e.1196.3		32
93.23	even	10		2883.1.o.e.2654.2		32
93.26	even	6	inner	2883.1.h.c.1400.2		8
93.29	even	10		2883.1.o.e.1805.3		32
93.35	odd	10		2883.1.o.e.338.3		32
93.38	odd	30		2883.1.l.d.1349.4		16
93.41	odd	30		2883.1.o.e.1508.3		32
93.44	even	30		2883.1.o.e.2768.1		32
93.47	odd	10		2883.1.o.e.1409.2		32
93.50	odd	30		2883.1.l.d.2453.4		16
93.53	even	30		2883.1.o.e.2738.1		32
93.56	odd	6		2883.1.b.c.962.1	✓	4
93.59	odd	30		2883.1.l.d.1589.1		16
93.65	even	30		2883.1.l.d.1589.2		16
93.68	even	6		2883.1.b.c.962.2	yes	4
93.71	odd	30		2883.1.o.e.2738.2		32
93.74	even	30		2883.1.l.d.2453.3		16
93.77	even	10		2883.1.o.e.1409.1		32
93.80	odd	30		2883.1.o.e.2768.2		32
93.83	even	30		2883.1.o.e.1508.4		32
93.86	even	30		2883.1.l.d.1349.3		16
93.89	even	10		2883.1.o.e.338.4		32
93.92	even	2	inner	2883.1.h.c.521.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2883.1.b.c.962.1	✓	4	93.56	odd	6
2883.1.b.c.962.2	yes	4	93.68	even	6
2883.1.b.c.962.3	yes	4	31.25	even	3
2883.1.b.c.962.4	yes	4	31.6	odd	6
2883.1.h.c.521.1		8	93.92	even	2	inner
2883.1.h.c.521.2		8	3.2	odd	2	inner
2883.1.h.c.521.3		8	1.1	even	1	trivial
2883.1.h.c.521.4		8	31.30	odd	2	inner
2883.1.h.c.1400.1		8	93.5	odd	6	inner
2883.1.h.c.1400.2		8	93.26	even	6	inner
2883.1.h.c.1400.3		8	31.26	odd	6	inner
2883.1.h.c.1400.4		8	31.5	even	3	inner
2883.1.l.d.374.1		16	93.17	even	30
2883.1.l.d.374.2		16	93.14	odd	30
2883.1.l.d.374.3		16	31.17	odd	30
2883.1.l.d.374.4		16	31.14	even	15
2883.1.l.d.1349.1		16	31.24	odd	30
2883.1.l.d.1349.2		16	31.7	even	15
2883.1.l.d.1349.3		16	93.86	even	30
2883.1.l.d.1349.4		16	93.38	odd	30
2883.1.l.d.1589.1		16	93.59	odd	30
2883.1.l.d.1589.2		16	93.65	even	30
2883.1.l.d.1589.3		16	31.3	odd	30
2883.1.l.d.1589.4		16	31.28	even	15
2883.1.l.d.2453.1		16	31.19	even	15
2883.1.l.d.2453.2		16	31.12	odd	30
2883.1.l.d.2453.3		16	93.74	even	30
2883.1.l.d.2453.4		16	93.50	odd	30
2883.1.o.e.338.1		32	31.27	odd	10
2883.1.o.e.338.2		32	31.4	even	5
2883.1.o.e.338.3		32	93.35	odd	10
2883.1.o.e.338.4		32	93.89	even	10
2883.1.o.e.1196.1		32	31.20	even	15
2883.1.o.e.1196.2		32	31.11	odd	30
2883.1.o.e.1196.3		32	93.20	odd	30
2883.1.o.e.1196.4		32	93.11	even	30
2883.1.o.e.1409.1		32	93.77	even	10
2883.1.o.e.1409.2		32	93.47	odd	10
2883.1.o.e.1409.3		32	31.16	even	5
2883.1.o.e.1409.4		32	31.15	odd	10
2883.1.o.e.1508.1		32	31.21	odd	30
2883.1.o.e.1508.2		32	31.10	even	15
2883.1.o.e.1508.3		32	93.41	odd	30
2883.1.o.e.1508.4		32	93.83	even	30
2883.1.o.e.1805.1		32	31.29	odd	10
2883.1.o.e.1805.2		32	31.2	even	5
2883.1.o.e.1805.3		32	93.29	even	10
2883.1.o.e.1805.4		32	93.2	odd	10
2883.1.o.e.2654.1		32	93.8	odd	10
2883.1.o.e.2654.2		32	93.23	even	10
2883.1.o.e.2654.3		32	31.8	even	5
2883.1.o.e.2654.4		32	31.23	odd	10
2883.1.o.e.2738.1		32	93.53	even	30
2883.1.o.e.2738.2		32	93.71	odd	30
2883.1.o.e.2738.3		32	31.9	even	15
2883.1.o.e.2738.4		32	31.22	odd	30
2883.1.o.e.2768.1		32	93.44	even	30
2883.1.o.e.2768.2		32	93.80	odd	30
2883.1.o.e.2768.3		32	31.13	odd	30
2883.1.o.e.2768.4		32	31.18	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2883 = 3 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2883.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.258819 + 0.965926i) q^{3} +(0.866025 + 0.500000i) q^{5} +(-0.965926 - 0.258819i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-0.866025 + 0.500000i) q^{14} +(-0.707107 + 0.707107i) q^{15} -1.00000 q^{16} +(-1.22474 + 0.707107i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-0.965926 + 0.258819i) q^{21} +(-0.965926 - 0.258819i) q^{24} +(0.707107 - 0.707107i) q^{27} -1.41421i q^{29} +(-0.707107 - 0.707107i) q^{30} +(-0.707107 - 1.22474i) q^{34} +1.00000i q^{35} +(0.866025 - 0.500000i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(0.866025 + 0.500000i) q^{41} +(-0.258819 - 0.965926i) q^{42} +(0.707107 + 1.22474i) q^{43} +(-0.500000 - 0.866025i) q^{45} +(0.258819 - 0.965926i) q^{48} +(-0.366025 - 1.36603i) q^{51} +(0.707107 + 0.707107i) q^{54} +(-0.866025 + 0.500000i) q^{56} +(0.965926 - 0.258819i) q^{57} +1.41421 q^{58} +(-0.866025 + 0.500000i) q^{59} +1.41421 q^{61} -1.00000i q^{63} -1.00000 q^{64} -1.00000 q^{70} +(0.866025 + 0.500000i) q^{71} +(0.500000 - 0.866025i) q^{72} +(-0.866025 - 0.500000i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +(1.22474 + 0.707107i) q^{83} -1.41421 q^{85} +(-1.22474 + 0.707107i) q^{86} +(1.36603 + 0.366025i) q^{87} +(0.866025 - 0.500000i) q^{90} -1.00000i q^{95} -1.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{7} - 4 q^{10} - 8 q^{16} + 4 q^{18} - 4 q^{19} - 4 q^{40} - 4 q^{45} + 4 q^{51} - 8 q^{64} - 8 q^{70} + 4 q^{72} + 4 q^{81} - 4 q^{82} + 4 q^{87} - 8 q^{97}+O(q^{100}) \) 8 * q + 4 * q^7 - 4 * q^10 - 8 * q^16 + 4 * q^18 - 4 * q^19 - 4 * q^40 - 4 * q^45 + 4 * q^51 - 8 * q^64 - 8 * q^70 + 4 * q^72 + 4 * q^81 - 4 * q^82 + 4 * q^87 - 8 * q^97

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