LMFDB - Embedded newform 2888.1.s.b.477.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(333,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 17]))

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

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

chi := DirichletCharacter("2888.333");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2888 = 2^{3} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2888.s (of order $18$, degree $6$, not 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:	$1.44129975648$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.152.1
Artin image:	$S_3\times C_{18}$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{54} - \cdots)$

Embedding invariants

Embedding label			477.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	2888.477
Dual form			2888.1.s.b.333.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 0.866025i) q^{12} +(0.766044 - 0.642788i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.173648 + 0.984808i) q^{17} +(-0.173648 + 0.984808i) q^{21} +(0.939693 + 0.342020i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(0.500000 + 0.866025i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(0.173648 + 0.984808i) q^{29} +(-0.766044 + 0.642788i) q^{32} +(-0.939693 - 0.342020i) q^{34} -2.00000 q^{37} +1.00000 q^{39} +(-0.939693 - 0.342020i) q^{42} +(-0.500000 + 0.866025i) q^{46} +(0.347296 + 1.96962i) q^{47} +(0.173648 + 0.984808i) q^{48} +(0.500000 + 0.866025i) q^{50} +(-0.766044 + 0.642788i) q^{51} +(-0.939693 + 0.342020i) q^{52} +(-0.939693 - 0.342020i) q^{53} +(0.766044 + 0.642788i) q^{54} +1.00000 q^{56} -1.00000 q^{58} +(0.173648 - 0.984808i) q^{59} +(-0.500000 - 0.866025i) q^{64} +(0.173648 + 0.984808i) q^{67} +(0.500000 - 0.866025i) q^{68} +(0.500000 + 0.866025i) q^{69} +(-0.766044 - 0.642788i) q^{73} +(0.347296 - 1.96962i) q^{74} +1.00000 q^{75} +(-0.173648 + 0.984808i) q^{78} +(0.939693 - 0.342020i) q^{81} +(0.500000 - 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{87} +(0.939693 + 0.342020i) q^{91} +(-0.766044 - 0.642788i) q^{92} -2.00000 q^{94} -1.00000 q^{96} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 + 3 * q^8	$ 6 q + 3 q^{7} + 3 q^{8} - 3 q^{12} + 3 q^{26} + 3 q^{27} - 12 q^{37} + 6 q^{39} - 3 q^{46} + 3 q^{50} + 6 q^{56} - 6 q^{58} - 3 q^{64} + 3 q^{68} + 3 q^{69} + 6 q^{75} + 3 q^{84} - 3 q^{87} - 12 q^{94} - 6 q^{96}+O(q^{100}) $ 6 * q + 3 * q^7 + 3 * q^8 - 3 * q^12 + 3 * q^26 + 3 * q^27 - 12 * q^37 + 6 * q^39 - 3 * q^46 + 3 * q^50 + 6 * q^56 - 6 * q^58 - 3 * q^64 + 3 * q^68 + 3 * q^69 + 6 * q^75 + 3 * q^84 - 3 * q^87 - 12 * q^94 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{18}\right)$

Coefficient data

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

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

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

$2$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$2$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$3$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$3$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$4$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$5$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$5$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$6$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$7$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$8$	0.500000	−	0.866025i	0.500000	−	0.866025i
$9$		0			0
$10$		0			0
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$13$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$13$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$14$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$15$		0			0
$16$	0.766044	+	0.642788i	0.766044	+	0.642788i
$17$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$17$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$18$		0			0
$19$		0			0
$19$		0			0
$20$		0			0
$21$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$22$		0			0
$23$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$23$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$24$	0.939693	−	0.342020i	0.939693	−	0.342020i
$25$	0.766044	−	0.642788i	0.766044	−	0.642788i
$26$	0.500000	+	0.866025i	0.500000	+	0.866025i
$27$	0.500000	−	0.866025i	0.500000	−	0.866025i
$28$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$29$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$29$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$33$		0			0
$34$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$35$		0			0
$36$		0			0
$37$	−2.00000			−2.00000			−1.00000			$\pi$
$37$	−2.00000			−2.00000			−1.00000			$\pi$
$38$		0			0
$39$	1.00000			1.00000
$40$		0			0
$41$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$41$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$42$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$43$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$43$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$44$		0			0
$45$		0			0
$46$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$47$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$47$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$48$	0.173648	+	0.984808i	0.173648	+	0.984808i
$49$		0			0
$50$	0.500000	+	0.866025i	0.500000	+	0.866025i
$51$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$52$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$53$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$53$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$54$	0.766044	+	0.642788i	0.766044	+	0.642788i
$55$		0			0
$56$	1.00000			1.00000
$57$		0			0
$58$	−1.00000			−1.00000
$59$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$59$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$60$		0			0
$61$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$61$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$62$		0			0
$63$		0			0
$64$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$65$		0			0
$66$		0			0
$67$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$67$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$68$	0.500000	−	0.866025i	0.500000	−	0.866025i
$69$	0.500000	+	0.866025i	0.500000	+	0.866025i
$70$		0			0
$71$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$71$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$72$		0			0
$73$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$73$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$74$	0.347296	−	1.96962i	0.347296	−	1.96962i
$75$	1.00000			1.00000
$76$		0			0
$77$		0			0
$78$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$79$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$79$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$80$		0			0
$81$	0.939693	−	0.342020i	0.939693	−	0.342020i
$82$		0			0
$83$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$83$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$84$	0.500000	−	0.866025i	0.500000	−	0.866025i
$85$		0			0
$86$		0			0
$87$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$88$		0			0
$89$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$89$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$90$		0			0
$91$	0.939693	+	0.342020i	0.939693	+	0.342020i
$92$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$93$		0			0
$94$	−2.00000			−2.00000
$95$		0			0
$96$	−1.00000			−1.00000
$97$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$97$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$98$		0			0
$99$		0			0
$100$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$101$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$101$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$102$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$103$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$103$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$104$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$105$		0			0
$106$	0.500000	−	0.866025i	0.500000	−	0.866025i
$107$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$107$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$108$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$109$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$109$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$110$		0			0
$111$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$112$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$		0			0
$116$	0.173648	−	0.984808i	0.173648	−	0.984808i
$117$		0			0
$118$	0.939693	+	0.342020i	0.939693	+	0.342020i
$119$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$127$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$128$	0.939693	−	0.342020i	0.939693	−	0.342020i
$129$		0			0
$130$		0			0
$131$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$131$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$132$		0			0
$133$		0			0
$134$	−1.00000			−1.00000
$135$		0			0
$136$	0.766044	+	0.642788i	0.766044	+	0.642788i
$137$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$137$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$138$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$139$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$139$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$140$		0			0
$141$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$	0.766044	−	0.642788i	0.766044	−	0.642788i
$147$		0			0
$148$	1.87939	+	0.684040i	1.87939	+	0.684040i
$149$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$149$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$150$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$157$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$157$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$158$		0			0
$159$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$160$		0			0
$161$	0.173648	+	0.984808i	0.173648	+	0.984808i
$162$	0.173648	+	0.984808i	0.173648	+	0.984808i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$167$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$168$	0.766044	+	0.642788i	0.766044	+	0.642788i
$169$		0			0
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$173$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$174$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$175$	0.939693	+	0.342020i	0.939693	+	0.342020i
$176$		0			0
$177$	0.766044	−	0.642788i	0.766044	−	0.642788i
$178$		0			0
$179$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$179$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$180$		0			0
$181$	−0.347296	−	1.96962i	−0.347296	−	1.96962i	−0.173648	−	0.984808i	$-0.555556\pi$
$181$	−0.347296	−	1.96962i	−0.347296	−	1.96962i	−0.173648	−	0.984808i	$-0.555556\pi$
$182$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$183$		0			0
$184$	0.766044	−	0.642788i	0.766044	−	0.642788i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.347296	−	1.96962i	0.347296	−	1.96962i
$189$	1.00000			1.00000
$190$		0			0
$191$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$191$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.173648	−	0.984808i	0.173648	−	0.984808i
$193$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$193$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$197$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$198$		0			0
$199$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$199$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$200$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$201$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$202$		0			0
$203$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$204$	0.939693	−	0.342020i	0.939693	−	0.342020i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	1.00000			1.00000
$209$		0			0
$210$		0			0
$211$	0.173648	−	0.984808i	0.173648	−	0.984808i	−0.766044	−	0.642788i	$-0.777778\pi$
$211$	0.173648	−	0.984808i	0.173648	−	0.984808i	0.939693	−	0.342020i	$-0.111111\pi$
$212$	0.766044	+	0.642788i	0.766044	+	0.642788i
$213$		0			0
$214$	0.939693	−	0.342020i	0.939693	−	0.342020i
$215$		0			0
$216$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$217$		0			0
$218$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$219$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$220$		0			0
$221$	0.500000	+	0.866025i	0.500000	+	0.866025i
$222$	1.53209	−	1.28558i	1.53209	−	1.28558i
$223$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$223$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$224$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$225$		0			0
$226$		0			0
$227$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$227$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$	0.939693	+	0.342020i	0.939693	+	0.342020i
$233$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$233$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$234$		0			0
$235$		0			0
$236$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$237$		0			0
$238$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$239$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$239$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$240$		0			0
$241$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$241$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$242$	0.939693	−	0.342020i	0.939693	−	0.342020i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$251$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.173648	+	0.984808i	0.173648	+	0.984808i
$257$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$257$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$258$		0			0
$259$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$263$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.173648	−	0.984808i	0.173648	−	0.984808i
$269$	−1.53209	−	1.28558i	−1.53209	−	1.28558i	−0.766044	−	0.642788i	$-0.777778\pi$
$269$	−1.53209	−	1.28558i	−1.53209	−	1.28558i	−0.766044	−	0.642788i	$-0.777778\pi$
$270$		0			0
$271$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$271$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$272$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$273$	0.500000	+	0.866025i	0.500000	+	0.866025i
$274$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$275$		0			0
$276$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$281$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$282$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$283$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$283$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$		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
$295$		0			0
$296$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$297$		0			0
$298$		0			0
$299$	0.939693	−	0.342020i	0.939693	−	0.342020i
$300$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.53209	−	1.28558i	−1.53209	−	1.28558i	−0.766044	−	0.642788i	$-0.777778\pi$
$307$	−1.53209	−	1.28558i	−1.53209	−	1.28558i	−0.766044	−	0.642788i	$-0.777778\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$311$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$312$	0.500000	−	0.866025i	0.500000	−	0.866025i
$313$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$313$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$317$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$318$	0.939693	−	0.342020i	0.939693	−	0.342020i
$319$		0			0
$320$		0			0
$321$	0.173648	−	0.984808i	0.173648	−	0.984808i
$322$	−1.00000			−1.00000
$323$		0			0
$324$	−1.00000			−1.00000
$325$	0.173648	−	0.984808i	0.173648	−	0.984808i
$326$		0			0
$327$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$328$		0			0
$329$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$330$		0			0
$331$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$331$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$337$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$337$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	1.00000			1.00000
$344$		0			0
$345$		0			0
$346$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$347$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$347$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$348$	0.766044	−	0.642788i	0.766044	−	0.642788i
$349$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$349$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$350$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$351$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$352$		0			0
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$354$	0.500000	+	0.866025i	0.500000	+	0.866025i
$355$		0			0
$356$		0			0
$357$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$358$	1.53209	+	1.28558i	1.53209	+	1.28558i
$359$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$359$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$360$		0			0
$361$		0			0
$362$	2.00000			2.00000
$363$	0.173648	−	0.984808i	0.173648	−	0.984808i
$364$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$365$		0			0
$366$		0			0
$367$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$367$	1.53209	−	1.28558i	1.53209	−	1.28558i	0.766044	−	0.642788i	$-0.222222\pi$
$368$	0.500000	+	0.866025i	0.500000	+	0.866025i
$369$		0			0
$370$		0			0
$371$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$372$		0			0
$373$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$373$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$374$		0			0
$375$		0			0
$376$	1.87939	+	0.684040i	1.87939	+	0.684040i
$377$	0.766044	+	0.642788i	0.766044	+	0.642788i
$378$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$379$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$379$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$380$		0			0
$381$		0			0
$382$	0.173648	−	0.984808i	0.173648	−	0.984808i
$383$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$383$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$384$	0.939693	+	0.342020i	0.939693	+	0.342020i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$389$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$390$		0			0
$391$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$397$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$398$	1.00000			1.00000
$399$		0			0
$400$	1.00000			1.00000
$401$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$401$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$402$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$407$		0			0
$408$	0.173648	+	0.984808i	0.173648	+	0.984808i
$409$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$409$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$410$		0			0
$411$	0.500000	+	0.866025i	0.500000	+	0.866025i
$412$		0			0
$413$	0.939693	−	0.342020i	0.939693	−	0.342020i
$414$		0			0
$415$		0			0
$416$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$417$		0			0
$418$		0			0
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$421$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$422$	0.939693	+	0.342020i	0.939693	+	0.342020i
$423$		0			0
$424$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$425$	0.500000	+	0.866025i	0.500000	+	0.866025i
$426$		0			0
$427$		0			0
$428$	0.173648	+	0.984808i	0.173648	+	0.984808i
$429$		0			0
$430$		0			0
$431$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$431$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$432$	0.939693	−	0.342020i	0.939693	−	0.342020i
$433$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$433$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$434$		0			0
$435$		0			0
$436$	1.00000			1.00000
$437$		0			0
$438$	1.00000			1.00000
$439$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$439$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$440$		0			0
$441$		0			0
$442$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$443$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$443$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$444$	1.00000	+	1.73205i	1.00000	+	1.73205i
$445$		0			0
$446$		0			0
$447$		0			0
$448$	0.500000	−	0.866025i	0.500000	−	0.866025i
$449$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$449$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$455$		0			0
$456$		0			0
$457$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$457$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$	0.766044	+	0.642788i	0.766044	+	0.642788i
$460$		0			0
$461$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$461$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$462$		0			0
$463$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$463$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$464$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$465$		0			0
$466$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$467$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$467$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$468$		0			0
$469$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$470$		0			0
$471$		0			0
$472$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$473$		0			0
$474$		0			0
$475$		0			0
$476$	1.00000			1.00000
$477$		0			0
$478$	0.766044	+	0.642788i	0.766044	+	0.642788i
$479$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$479$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$480$		0			0
$481$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$482$		0			0
$483$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$484$	0.173648	+	0.984808i	0.173648	+	0.984808i
$485$		0			0
$486$		0			0
$487$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$487$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$491$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$492$		0			0
$493$	−1.00000			−1.00000
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$499$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$503$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.87939	+	0.684040i	1.87939	+	0.684040i	0.939693	+	0.342020i	$0.111111\pi$
$509$	1.87939	+	0.684040i	1.87939	+	0.684040i	0.939693	+	0.342020i	$0.111111\pi$
$510$		0			0
$511$	0.173648	−	0.984808i	0.173648	−	0.984808i
$512$	−1.00000			−1.00000
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	1.87939	−	0.684040i	1.87939	−	0.684040i
$519$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$520$		0			0
$521$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$521$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$523$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$524$		0			0
$525$	0.500000	+	0.866025i	0.500000	+	0.866025i
$526$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	0.939693	+	0.342020i	0.939693	+	0.342020i
$537$	1.87939	−	0.684040i	1.87939	−	0.684040i
$538$	1.53209	−	1.28558i	1.53209	−	1.28558i
$539$		0			0
$540$		0			0
$541$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$541$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$542$	0.173648	+	0.984808i	0.173648	+	0.984808i
$543$	1.00000	−	1.73205i	1.00000	−	1.73205i
$544$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$545$		0			0
$546$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$547$	1.87939	+	0.684040i	1.87939	+	0.684040i	0.939693	+	0.342020i	$0.111111\pi$
$547$	1.87939	+	0.684040i	1.87939	+	0.684040i	0.939693	+	0.342020i	$0.111111\pi$
$548$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$549$		0			0
$550$		0			0
$551$		0			0
$552$	1.00000			1.00000
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$557$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$563$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$564$	1.53209	−	1.28558i	1.53209	−	1.28558i
$565$		0			0
$566$		0			0
$567$	0.766044	+	0.642788i	0.766044	+	0.642788i
$568$		0			0
$569$		0			0		1.00000			$0$
$569$		0			0		−1.00000			$\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$574$		0			0
$575$	0.939693	−	0.342020i	0.939693	−	0.342020i
$576$		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
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$585$		0			0
$586$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$587$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$587$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$593$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$593$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.500000	−	0.866025i	0.500000	−	0.866025i
$598$	0.173648	+	0.984808i	0.173648	+	0.984808i
$599$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$599$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$600$	0.500000	−	0.866025i	0.500000	−	0.866025i
$601$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$601$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$	−1.00000			−1.00000
$610$		0			0
$611$	1.53209	+	1.28558i	1.53209	+	1.28558i
$612$		0			0
$613$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$613$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$614$	1.53209	−	1.28558i	1.53209	−	1.28558i
$615$		0			0
$616$		0			0
$617$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$617$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$	0.766044	−	0.642788i	0.766044	−	0.642788i
$622$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$623$		0			0
$624$	0.766044	+	0.642788i	0.766044	+	0.642788i
$625$	0.173648	−	0.984808i	0.173648	−	0.984808i
$626$	1.00000			1.00000
$627$		0			0
$628$		0			0
$629$	0.347296	−	1.96962i	0.347296	−	1.96962i
$630$		0			0
$631$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$631$	−1.87939	−	0.684040i	−1.87939	−	0.684040i	−0.939693	−	0.342020i	$-0.888889\pi$
$632$		0			0
$633$	0.766044	−	0.642788i	0.766044	−	0.642788i
$634$	0.500000	+	0.866025i	0.500000	+	0.866025i
$635$		0			0
$636$	0.173648	+	0.984808i	0.173648	+	0.984808i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$641$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$642$	0.939693	+	0.342020i	0.939693	+	0.342020i
$643$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$643$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$644$	0.173648	−	0.984808i	0.173648	−	0.984808i
$645$		0			0
$646$		0			0
$647$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$647$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$648$	0.173648	−	0.984808i	0.173648	−	0.984808i
$649$		0			0
$650$	0.939693	+	0.342020i	0.939693	+	0.342020i
$651$		0			0
$652$		0			0
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$	0.500000	−	0.866025i	0.500000	−	0.866025i
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$659$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$659$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$660$		0			0
$661$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.173648	−	0.984808i	$-0.555556\pi$
$661$	−0.939693	−	0.342020i	−0.939693	−	0.342020i	−0.766044	+	0.642788i	$0.777778\pi$
$662$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$663$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$673$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$673$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$676$		0			0
$677$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$677$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.766044	+	0.642788i	0.766044	+	0.642788i
$682$		0			0
$683$	−2.00000			−2.00000			−1.00000			$\pi$
$683$	−2.00000			−2.00000			−1.00000			$\pi$
$684$		0			0
$685$		0			0
$686$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$687$		0			0
$688$		0			0
$689$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$690$		0			0
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$	1.00000	−	1.73205i	1.00000	−	1.73205i
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.500000	+	0.866025i	0.500000	+	0.866025i
$697$		0			0
$698$		0			0
$699$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$700$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$701$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$701$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$702$	1.00000			1.00000
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.766044	+	0.642788i	0.766044	+	0.642788i
$707$		0			0
$708$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$709$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$709$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		0			0
$714$	0.500000	−	0.866025i	0.500000	−	0.866025i
$715$		0			0
$716$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$717$	0.939693	−	0.342020i	0.939693	−	0.342020i
$718$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$719$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$719$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−0.347296	+	1.96962i	−0.347296	+	1.96962i
$725$	0.766044	+	0.642788i	0.766044	+	0.642788i
$726$	0.939693	+	0.342020i	0.939693	+	0.342020i
$727$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$727$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$728$	0.766044	−	0.642788i	0.766044	−	0.642788i
$729$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$	1.00000	+	1.73205i	1.00000	+	1.73205i
$735$		0			0
$736$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$737$		0			0
$738$		0			0
$739$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$739$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$740$		0			0
$741$		0			0
$742$	1.00000			1.00000
$743$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$743$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$744$		0			0
$745$		0			0
$746$	0.939693	−	0.342020i	0.939693	−	0.342020i
$747$		0			0
$748$		0			0
$749$	0.500000	−	0.866025i	0.500000	−	0.866025i
$750$		0			0
$751$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$751$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$752$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$753$		0			0
$754$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$755$		0			0
$756$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$757$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$757$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$758$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$759$		0			0
$760$		0			0
$761$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$761$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$762$		0			0
$763$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$764$	0.939693	+	0.342020i	0.939693	+	0.342020i
$765$		0			0
$766$		0			0
$767$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$768$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$769$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$769$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$773$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.347296	−	1.96962i	0.347296	−	1.96962i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$783$	0.939693	+	0.342020i	0.939693	+	0.342020i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$787$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$788$		0			0
$789$	0.347296	+	1.96962i	0.347296	+	1.96962i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$797$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$797$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$798$		0			0
$799$	−2.00000			−2.00000
$800$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	0.766044	−	0.642788i	0.766044	−	0.642788i
$805$		0			0
$806$		0			0
$807$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$808$		0			0
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$809$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$810$		0			0
$811$	0.766044	−	0.642788i	0.766044	−	0.642788i	−0.173648	−	0.984808i	$-0.555556\pi$
$811$	0.766044	−	0.642788i	0.766044	−	0.642788i	0.939693	+	0.342020i	$0.111111\pi$
$812$	0.939693	−	0.342020i	0.939693	−	0.342020i
$813$	0.939693	+	0.342020i	0.939693	+	0.342020i
$814$		0			0
$815$		0			0
$816$	−1.00000			−1.00000
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$821$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$822$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$823$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$823$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$824$		0			0
$825$		0			0
$826$	0.173648	+	0.984808i	0.173648	+	0.984808i
$827$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$827$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$828$		0			0
$829$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$829$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$839$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$840$		0			0
$841$		0			0
$842$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$843$		0			0
$844$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$845$		0			0
$846$		0			0
$847$	0.500000	−	0.866025i	0.500000	−	0.866025i
$848$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$849$		0			0
$850$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$851$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$852$		0			0
$853$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$853$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$854$		0			0
$855$		0			0
$856$	−1.00000			−1.00000
$857$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$857$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$858$		0			0
$859$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$859$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$	0.173648	+	0.984808i	0.173648	+	0.984808i
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	0.766044	+	0.642788i	0.766044	+	0.642788i
$872$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$877$	0.766044	+	0.642788i	0.766044	+	0.642788i	0.939693	−	0.342020i	$-0.111111\pi$
$877$	0.766044	+	0.642788i	0.766044	+	0.642788i	−0.173648	+	0.984808i	$0.555556\pi$
$878$		0			0
$879$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$880$		0			0
$881$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$882$		0			0
$883$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$883$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$884$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$885$		0			0
$886$		0			0
$887$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$887$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$888$	−1.87939	+	0.684040i	−1.87939	+	0.684040i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.766044	+	0.642788i	0.766044	+	0.642788i
$897$	0.939693	+	0.342020i	0.939693	+	0.342020i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.500000	−	0.866025i	0.500000	−	0.866025i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.766044	−	0.642788i	$-0.777778\pi$
$907$	−0.939693	+	0.342020i	−0.939693	+	0.342020i	−0.173648	+	0.984808i	$0.555556\pi$
$908$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	0.173648	−	0.984808i	0.173648	−	0.984808i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$919$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$919$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	−0.347296	−	1.96962i	−0.347296	−	1.96962i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−1.53209	+	1.28558i	−1.53209	+	1.28558i
$926$	1.87939	−	0.684040i	1.87939	−	0.684040i
$927$		0			0
$928$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$929$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$929$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$930$		0			0
$931$		0			0
$932$	2.00000			2.00000
$933$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$937$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$938$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$939$	0.500000	−	0.866025i	0.500000	−	0.866025i
$940$		0			0
$941$	0.173648	+	0.984808i	0.173648	+	0.984808i	0.939693	+	0.342020i	$0.111111\pi$
$941$	0.173648	+	0.984808i	0.173648	+	0.984808i	−0.766044	+	0.642788i	$0.777778\pi$
$942$		0			0
$943$		0			0
$944$	0.766044	−	0.642788i	0.766044	−	0.642788i
$945$		0			0
$946$		0			0
$947$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$947$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$948$		0			0
$949$	−1.00000			−1.00000
$950$		0			0
$951$	1.00000			1.00000
$952$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$953$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$953$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$954$		0			0
$955$		0			0
$956$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$957$		0			0
$958$	1.00000	−	1.73205i	1.00000	−	1.73205i
$959$	0.173648	+	0.984808i	0.173648	+	0.984808i
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$963$		0			0
$964$		0			0
$965$		0			0
$966$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$967$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$967$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$		0			0
$971$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$971$	−0.347296	+	1.96962i	−0.347296	+	1.96962i	−0.173648	+	0.984808i	$0.555556\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	0.766044	−	0.642788i	0.766044	−	0.642788i
$976$		0			0
$977$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$977$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$		0			0
$983$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$983$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$984$		0			0
$985$		0			0
$986$	0.173648	−	0.984808i	0.173648	−	0.984808i
$987$	−2.00000			−2.00000
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$991$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$992$		0			0
$993$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$997$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$998$		0			0
$999$	−1.00000	+	1.73205i	−1.00000	+	1.73205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.s.b.477.1		6
8.5	even	2		2888.1.s.a.477.1		6
19.2	odd	18		2888.1.l.a.293.1		2
19.3	odd	18		152.1.g.b.37.1	yes	1
19.4	even	9	inner	2888.1.s.b.2293.1		6
19.5	even	9		2888.1.l.b.69.1		2
19.6	even	9	inner	2888.1.s.b.2789.1		6
19.7	even	3	inner	2888.1.s.b.1029.1		6
19.8	odd	6		2888.1.s.a.1021.1		6
19.9	even	9	inner	2888.1.s.b.333.1		6
19.10	odd	18		2888.1.s.a.333.1		6
19.11	even	3	inner	2888.1.s.b.1021.1		6
19.12	odd	6		2888.1.s.a.1029.1		6
19.13	odd	18		2888.1.s.a.2789.1		6
19.14	odd	18		2888.1.l.a.69.1		2
19.15	odd	18		2888.1.s.a.2293.1		6
19.16	even	9		152.1.g.a.37.1	✓	1
19.17	even	9		2888.1.l.b.293.1		2
19.18	odd	2		2888.1.s.a.477.1		6
57.35	odd	18		1368.1.i.b.37.1		1
57.41	even	18		1368.1.i.a.37.1		1
76.3	even	18		608.1.g.b.113.1		1
76.35	odd	18		608.1.g.a.113.1		1
95.3	even	36		3800.1.b.b.949.1		2
95.22	even	36		3800.1.b.b.949.2		2
95.54	even	18		3800.1.o.b.1101.1		1
95.73	odd	36		3800.1.b.a.949.2		2
95.79	odd	18		3800.1.o.a.1101.1		1
95.92	odd	36		3800.1.b.a.949.1		2
152.3	even	18		608.1.g.a.113.1		1
152.5	even	18		2888.1.l.a.69.1		2
152.13	odd	18	inner	2888.1.s.b.2789.1		6
152.21	odd	18		2888.1.l.b.293.1		2
152.29	odd	18	inner	2888.1.s.b.333.1		6
152.35	odd	18		608.1.g.b.113.1		1
152.37	odd	2	CM	2888.1.s.b.477.1		6
152.45	even	6		2888.1.s.a.1029.1		6
152.53	odd	18	inner	2888.1.s.b.2293.1		6
152.61	even	18		2888.1.s.a.2293.1		6
152.69	odd	6	inner	2888.1.s.b.1029.1		6
152.85	even	18		2888.1.s.a.333.1		6
152.93	even	18		2888.1.l.a.293.1		2
152.101	even	18		2888.1.s.a.2789.1		6
152.109	odd	18		2888.1.l.b.69.1		2
152.117	odd	18		152.1.g.a.37.1	✓	1
152.125	even	6		2888.1.s.a.1021.1		6
152.141	odd	6	inner	2888.1.s.b.1021.1		6
152.149	even	18		152.1.g.b.37.1	yes	1
456.149	odd	18		1368.1.i.a.37.1		1
456.269	even	18		1368.1.i.b.37.1		1
760.117	even	36		3800.1.b.a.949.1		2
760.149	even	18		3800.1.o.a.1101.1		1
760.269	odd	18		3800.1.o.b.1101.1		1
760.453	odd	36		3800.1.b.b.949.1		2
760.573	even	36		3800.1.b.a.949.2		2
760.757	odd	36		3800.1.b.b.949.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.1.g.a.37.1	✓	1	19.16	even	9
152.1.g.a.37.1	✓	1	152.117	odd	18
152.1.g.b.37.1	yes	1	19.3	odd	18
152.1.g.b.37.1	yes	1	152.149	even	18
608.1.g.a.113.1		1	76.35	odd	18
608.1.g.a.113.1		1	152.3	even	18
608.1.g.b.113.1		1	76.3	even	18
608.1.g.b.113.1		1	152.35	odd	18
1368.1.i.a.37.1		1	57.41	even	18
1368.1.i.a.37.1		1	456.149	odd	18
1368.1.i.b.37.1		1	57.35	odd	18
1368.1.i.b.37.1		1	456.269	even	18
2888.1.l.a.69.1		2	19.14	odd	18
2888.1.l.a.69.1		2	152.5	even	18
2888.1.l.a.293.1		2	19.2	odd	18
2888.1.l.a.293.1		2	152.93	even	18
2888.1.l.b.69.1		2	19.5	even	9
2888.1.l.b.69.1		2	152.109	odd	18
2888.1.l.b.293.1		2	19.17	even	9
2888.1.l.b.293.1		2	152.21	odd	18
2888.1.s.a.333.1		6	19.10	odd	18
2888.1.s.a.333.1		6	152.85	even	18
2888.1.s.a.477.1		6	8.5	even	2
2888.1.s.a.477.1		6	19.18	odd	2
2888.1.s.a.1021.1		6	19.8	odd	6
2888.1.s.a.1021.1		6	152.125	even	6
2888.1.s.a.1029.1		6	19.12	odd	6
2888.1.s.a.1029.1		6	152.45	even	6
2888.1.s.a.2293.1		6	19.15	odd	18
2888.1.s.a.2293.1		6	152.61	even	18
2888.1.s.a.2789.1		6	19.13	odd	18
2888.1.s.a.2789.1		6	152.101	even	18
2888.1.s.b.333.1		6	19.9	even	9	inner
2888.1.s.b.333.1		6	152.29	odd	18	inner
2888.1.s.b.477.1		6	1.1	even	1	trivial
2888.1.s.b.477.1		6	152.37	odd	2	CM
2888.1.s.b.1021.1		6	19.11	even	3	inner
2888.1.s.b.1021.1		6	152.141	odd	6	inner
2888.1.s.b.1029.1		6	19.7	even	3	inner
2888.1.s.b.1029.1		6	152.69	odd	6	inner
2888.1.s.b.2293.1		6	19.4	even	9	inner
2888.1.s.b.2293.1		6	152.53	odd	18	inner
2888.1.s.b.2789.1		6	19.6	even	9	inner
2888.1.s.b.2789.1		6	152.13	odd	18	inner
3800.1.b.a.949.1		2	95.92	odd	36
3800.1.b.a.949.1		2	760.117	even	36
3800.1.b.a.949.2		2	95.73	odd	36
3800.1.b.a.949.2		2	760.573	even	36
3800.1.b.b.949.1		2	95.3	even	36
3800.1.b.b.949.1		2	760.453	odd	36
3800.1.b.b.949.2		2	95.22	even	36
3800.1.b.b.949.2		2	760.757	odd	36
3800.1.o.a.1101.1		1	95.79	odd	18
3800.1.o.a.1101.1		1	760.149	even	18
3800.1.o.b.1101.1		1	95.54	even	18
3800.1.o.b.1101.1		1	760.269	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.s (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(0.766044 + 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-0.500000 - 0.866025i) q^{12} +(0.766044 - 0.642788i) q^{13} +(-0.939693 + 0.342020i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-0.173648 + 0.984808i) q^{17} +(-0.173648 + 0.984808i) q^{21} +(0.939693 + 0.342020i) q^{23} +(0.939693 - 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(0.500000 + 0.866025i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.173648 - 0.984808i) q^{28} +(0.173648 + 0.984808i) q^{29} +(-0.766044 + 0.642788i) q^{32} +(-0.939693 - 0.342020i) q^{34} -2.00000 q^{37} +1.00000 q^{39} +(-0.939693 - 0.342020i) q^{42} +(-0.500000 + 0.866025i) q^{46} +(0.347296 + 1.96962i) q^{47} +(0.173648 + 0.984808i) q^{48} +(0.500000 + 0.866025i) q^{50} +(-0.766044 + 0.642788i) q^{51} +(-0.939693 + 0.342020i) q^{52} +(-0.939693 - 0.342020i) q^{53} +(0.766044 + 0.642788i) q^{54} +1.00000 q^{56} -1.00000 q^{58} +(0.173648 - 0.984808i) q^{59} +(-0.500000 - 0.866025i) q^{64} +(0.173648 + 0.984808i) q^{67} +(0.500000 - 0.866025i) q^{68} +(0.500000 + 0.866025i) q^{69} +(-0.766044 - 0.642788i) q^{73} +(0.347296 - 1.96962i) q^{74} +1.00000 q^{75} +(-0.173648 + 0.984808i) q^{78} +(0.939693 - 0.342020i) q^{81} +(0.500000 - 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{87} +(0.939693 + 0.342020i) q^{91} +(-0.766044 - 0.642788i) q^{92} -2.00000 q^{94} -1.00000 q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 + 3 * q^8	\( 6 q + 3 q^{7} + 3 q^{8} - 3 q^{12} + 3 q^{26} + 3 q^{27} - 12 q^{37} + 6 q^{39} - 3 q^{46} + 3 q^{50} + 6 q^{56} - 6 q^{58} - 3 q^{64} + 3 q^{68} + 3 q^{69} + 6 q^{75} + 3 q^{84} - 3 q^{87} - 12 q^{94} - 6 q^{96}+O(q^{100}) \) 6 * q + 3 * q^7 + 3 * q^8 - 3 * q^12 + 3 * q^26 + 3 * q^27 - 12 * q^37 + 6 * q^39 - 3 * q^46 + 3 * q^50 + 6 * q^56 - 6 * q^58 - 3 * q^64 + 3 * q^68 + 3 * q^69 + 6 * q^75 + 3 * q^84 - 3 * q^87 - 12 * q^94 - 6 * q^96

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