LMFDB - Embedded newform 2888.1.u.b.99.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(99,2888)]

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([9, 9, 2]))

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

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

chi := DirichletCharacter("2888.99");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2888 = 2^{3} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2888.u (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:	$D_{9}$
Projective field:	Galois closure of 9.1.69564674215936.1

Embedding invariants

Embedding label			99.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	2888.99
Dual form			2888.1.u.b.1867.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.266044 + 1.50881i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.266044 - 1.50881i) q^{6} +(-0.500000 - 0.866025i) q^{8} +(-1.26604 + 0.460802i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.266044 + 1.50881i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.266044 - 1.50881i) q^{6} +(-0.500000 - 0.866025i) q^{8} +(-1.26604 + 0.460802i) q^{9} +(0.939693 + 1.62760i) q^{11} +(-0.766044 + 1.32683i) q^{12} +(0.173648 + 0.984808i) q^{16} +(0.939693 + 0.342020i) q^{17} +1.34730 q^{18} +(-0.326352 - 1.85083i) q^{22} +(1.17365 - 0.984808i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.266044 - 0.460802i) q^{27} +(0.173648 - 0.984808i) q^{32} +(-2.20574 + 1.85083i) q^{33} +(-0.766044 - 0.642788i) q^{34} +(-1.26604 - 0.460802i) q^{36} +(0.0603074 + 0.342020i) q^{41} +(-0.766044 + 0.642788i) q^{43} +(-0.326352 + 1.85083i) q^{44} +(-1.43969 + 0.524005i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.266044 + 1.50881i) q^{51} +(0.0923963 + 0.524005i) q^{54} +(1.76604 + 0.642788i) q^{59} +(-0.500000 + 0.866025i) q^{64} +(2.70574 - 0.984808i) q^{66} +(-0.326352 + 0.118782i) q^{67} +(0.500000 + 0.866025i) q^{68} +(1.03209 + 0.866025i) q^{72} +(-0.326352 - 1.85083i) q^{73} +1.53209 q^{75} +(-0.407604 + 0.342020i) q^{81} +(0.0603074 - 0.342020i) q^{82} +(-0.173648 + 0.300767i) q^{83} +(0.939693 - 0.342020i) q^{86} +(0.939693 - 1.62760i) q^{88} +(-0.173648 + 0.984808i) q^{89} +1.53209 q^{96} +(-0.326352 - 0.118782i) q^{97} +(0.173648 + 0.984808i) q^{98} +(-1.93969 - 1.62760i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{3} - 3 q^{6} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^3 - 3 * q^6 - 3 * q^8 - 3 * q^9	$ 6 q - 3 q^{3} - 3 q^{6} - 3 q^{8} - 3 q^{9} + 6 q^{18} - 3 q^{22} + 6 q^{24} + 3 q^{27} - 3 q^{33} - 3 q^{36} + 6 q^{41} - 3 q^{44} - 3 q^{48} - 3 q^{49} - 3 q^{50} + 3 q^{51} - 3 q^{54} + 6 q^{59} - 3 q^{64} + 6 q^{66} - 3 q^{67} + 3 q^{68} - 3 q^{72} - 3 q^{73} - 6 q^{81} + 6 q^{82} - 3 q^{97} - 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^3 - 3 * q^6 - 3 * q^8 - 3 * q^9 + 6 * q^18 - 3 * q^22 + 6 * q^24 + 3 * q^27 - 3 * q^33 - 3 * q^36 + 6 * q^41 - 3 * q^44 - 3 * q^48 - 3 * q^49 - 3 * q^50 + 3 * q^51 - 3 * q^54 + 6 * q^59 - 3 * q^64 + 6 * q^66 - 3 * q^67 + 3 * q^68 - 3 * q^72 - 3 * q^73 - 6 * q^81 + 6 * q^82 - 3 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$2$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$3$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$3$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	0.766044	+	0.642788i	0.766044	+	0.642788i
$5$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$5$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$6$	0.266044	−	1.50881i	0.266044	−	1.50881i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$9$	−1.26604	+	0.460802i	−1.26604	+	0.460802i
$10$		0			0
$11$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$11$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$12$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$13$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$13$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$14$		0			0
$15$		0			0
$16$	0.173648	+	0.984808i	0.173648	+	0.984808i
$17$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$17$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$18$	1.34730			1.34730
$19$		0			0
$19$		0			0
$20$		0			0
$21$		0			0
$22$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$23$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$23$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$24$	1.17365	−	0.984808i	1.17365	−	0.984808i
$25$	0.173648	−	0.984808i	0.173648	−	0.984808i
$26$		0			0
$27$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$28$		0			0
$29$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$29$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.173648	−	0.984808i	0.173648	−	0.984808i
$33$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$34$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$35$		0			0
$36$	−1.26604	−	0.460802i	−1.26604	−	0.460802i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	1.00000			$0$
$41$	0.0603074	+	0.342020i	0.0603074	+	0.342020i	−0.939693	+	0.342020i	$0.888889\pi$
$42$		0			0
$43$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	−0.939693	−	0.342020i	$-0.888889\pi$
$43$	−0.766044	+	0.642788i	−0.766044	+	0.642788i	0.173648	+	0.984808i	$0.444444\pi$
$44$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$45$		0			0
$46$		0			0
$47$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$47$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$48$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$51$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$52$		0			0
$53$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$53$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$54$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$55$		0			0
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$59$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$60$		0			0
$61$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$61$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$62$		0			0
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$65$		0			0
$66$	2.70574	−	0.984808i	2.70574	−	0.984808i
$67$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$67$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$68$	0.500000	+	0.866025i	0.500000	+	0.866025i
$69$		0			0
$70$		0			0
$71$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$71$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$72$	1.03209	+	0.866025i	1.03209	+	0.866025i
$73$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$73$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$74$		0			0
$75$	1.53209			1.53209
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$79$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$80$		0			0
$81$	−0.407604	+	0.342020i	−0.407604	+	0.342020i
$82$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$83$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$83$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$84$		0			0
$85$		0			0
$86$	0.939693	−	0.342020i	0.939693	−	0.342020i
$87$		0			0
$88$	0.939693	−	1.62760i	0.939693	−	1.62760i
$89$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$89$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.53209			1.53209
$97$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$97$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$98$	0.173648	+	0.984808i	0.173648	+	0.984808i
$99$	−1.93969	−	1.62760i	−1.93969	−	1.62760i
$100$	0.766044	−	0.642788i	0.766044	−	0.642788i
$101$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$101$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$102$	0.766044	−	1.32683i	0.766044	−	1.32683i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$107$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$108$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$109$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$109$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$113$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$119$		0			0
$120$		0			0
$121$	−1.26604	+	2.19285i	−1.26604	+	2.19285i
$122$		0			0
$123$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$127$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$128$	0.766044	−	0.642788i	0.766044	−	0.642788i
$129$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$130$		0			0
$131$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$131$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$132$	−2.87939			−2.87939
$133$		0			0
$134$	0.347296			0.347296
$135$		0			0
$136$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$137$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$137$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$138$		0			0
$139$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	−0.939693	−	0.342020i	$-0.888889\pi$
$139$	0.0603074	−	0.342020i	0.0603074	−	0.342020i	1.00000			$0$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$145$		0			0
$146$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$147$	1.17365	−	0.984808i	1.17365	−	0.984808i
$148$		0			0
$149$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$149$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$150$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$		0			0
$153$	−1.34730			−1.34730
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$157$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.500000	−	0.181985i	0.500000	−	0.181985i
$163$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$163$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$164$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$165$		0			0
$166$	0.266044	−	0.223238i	0.266044	−	0.223238i
$167$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$167$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$168$		0			0
$169$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$170$		0			0
$171$		0			0
$172$	−1.00000			−1.00000
$173$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$173$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$174$		0			0
$175$		0			0
$176$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$177$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$178$	0.500000	−	0.866025i	0.500000	−	0.866025i
$179$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$179$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$180$		0			0
$181$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$181$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.326352	+	1.85083i	0.326352	+	1.85083i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$193$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$193$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$194$	0.266044	+	0.223238i	0.266044	+	0.223238i
$195$		0			0
$196$	0.173648	−	0.984808i	0.173648	−	0.984808i
$197$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$197$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$198$	1.26604	+	2.19285i	1.26604	+	2.19285i
$199$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$199$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$200$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$201$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$202$		0			0
$203$		0			0
$204$	−1.17365	+	0.984808i	−1.17365	+	0.984808i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$211$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$212$		0			0
$213$		0			0
$214$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$215$		0			0
$216$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$217$		0			0
$218$		0			0
$219$	2.70574	−	0.984808i	2.70574	−	0.984808i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$223$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$224$		0			0
$225$	0.233956	+	1.32683i	0.233956	+	1.32683i
$226$	1.76604	+	0.642788i	1.76604	+	0.642788i
$227$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$227$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$233$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$234$		0			0
$235$		0			0
$236$	0.939693	+	1.62760i	0.939693	+	1.62760i
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$		0			0
$241$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$241$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$242$	1.93969	−	1.62760i	1.93969	−	1.62760i
$243$	−1.03209	−	0.866025i	−1.03209	−	0.866025i
$244$		0			0
$245$		0			0
$246$	0.532089			0.532089
$247$		0			0
$248$		0			0
$249$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$250$		0			0
$251$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$251$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$257$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$257$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$258$	0.766044	+	1.32683i	0.766044	+	1.32683i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.17365	+	0.984808i	1.17365	+	0.984808i
$263$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$263$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$264$	2.70574	+	0.984808i	2.70574	+	0.984808i
$265$		0			0
$266$		0			0
$267$	−1.53209			−1.53209
$268$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$269$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$269$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$270$		0			0
$271$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$271$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$272$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$273$		0			0
$274$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$275$	1.76604	−	0.642788i	1.76604	−	0.642788i
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$279$		0			0
$280$		0			0
$281$	1.17365	+	0.984808i	1.17365	+	0.984808i	1.00000			$0$
$281$	1.17365	+	0.984808i	1.17365	+	0.984808i	0.173648	+	0.984808i	$0.444444\pi$
$282$		0			0
$283$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$283$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.233956	+	1.32683i	0.233956	+	1.32683i
$289$		0			0
$290$		0			0
$291$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$292$	0.939693	−	1.62760i	0.939693	−	1.62760i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$295$		0			0
$296$		0			0
$297$	0.500000	−	0.866025i	0.500000	−	0.866025i
$298$		0			0
$299$		0			0
$300$	1.17365	+	0.984808i	1.17365	+	0.984808i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	1.26604	+	0.460802i	1.26604	+	0.460802i
$307$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$307$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$311$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$312$		0			0
$313$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.939693	−	0.342020i	$-0.888889\pi$
$313$	−1.43969	+	0.524005i	−1.43969	+	0.524005i	−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$317$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.43969	+	0.524005i	1.43969	+	0.524005i
$322$		0			0
$323$		0			0
$324$	−0.532089			−0.532089
$325$		0			0
$326$	0.266044	+	1.50881i	0.266044	+	1.50881i
$327$		0			0
$328$	0.266044	−	0.223238i	0.266044	−	0.223238i
$329$		0			0
$330$		0			0
$331$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$331$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$332$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.17365	−	0.984808i	1.17365	−	0.984808i	0.173648	−	0.984808i	$-0.444444\pi$
$337$	1.17365	−	0.984808i	1.17365	−	0.984808i	1.00000			$0$
$338$	0.766044	+	0.642788i	0.766044	+	0.642788i
$339$	−0.500000	−	2.83564i	−0.500000	−	2.83564i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	0.939693	+	0.342020i	0.939693	+	0.342020i
$345$		0			0
$346$		0			0
$347$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$347$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$348$		0			0
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$		0			0
$351$		0			0
$352$	1.76604	−	0.642788i	1.76604	−	0.642788i
$353$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$353$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$354$	1.43969	−	2.49362i	1.43969	−	2.49362i
$355$		0			0
$356$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$357$		0			0
$358$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$359$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$359$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	−3.64543	−	1.32683i	−3.64543	−	1.32683i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$367$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$368$		0			0
$369$	−0.233956	−	0.405223i	−0.233956	−	0.405223i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$	0.326352	−	1.85083i	0.326352	−	1.85083i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	2.00000			2.00000			1.00000			$0$
$379$	2.00000			2.00000			1.00000			$0$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$383$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$384$	1.17365	+	0.984808i	1.17365	+	0.984808i
$385$		0			0
$386$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$387$	0.673648	−	1.16679i	0.673648	−	1.16679i
$388$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$389$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$389$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$390$		0			0
$391$		0			0
$392$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$393$	0.407604	−	2.31164i	0.407604	−	2.31164i
$394$		0			0
$395$		0			0
$396$	−0.439693	−	2.49362i	−0.439693	−	2.49362i
$397$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$397$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$398$		0			0
$399$		0			0
$400$	1.00000			1.00000
$401$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$401$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$402$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	1.43969	−	0.524005i	1.43969	−	0.524005i
$409$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$409$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$410$		0			0
$411$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.532089			0.532089
$418$		0			0
$419$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$419$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$420$		0			0
$421$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$421$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$422$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$423$		0			0
$424$		0			0
$425$	0.500000	−	0.866025i	0.500000	−	0.866025i
$426$		0			0
$427$		0			0
$428$	0.939693	−	0.342020i	0.939693	−	0.342020i
$429$		0			0
$430$		0			0
$431$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$431$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$432$	0.407604	−	0.342020i	0.407604	−	0.342020i
$433$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$433$	1.53209	+	1.28558i	1.53209	+	1.28558i	0.766044	+	0.642788i	$0.222222\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−2.87939			−2.87939
$439$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$439$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$440$		0			0
$441$	1.03209	+	0.866025i	1.03209	+	0.866025i
$442$		0			0
$443$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$443$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$449$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$450$	0.233956	−	1.32683i	0.233956	−	1.32683i
$451$	−0.500000	+	0.419550i	−0.500000	+	0.419550i
$452$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$453$		0			0
$454$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$455$		0			0
$456$		0			0
$457$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$457$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$458$		0			0
$459$	−0.0923963	−	0.524005i	−0.0923963	−	0.524005i
$460$		0			0
$461$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$461$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$462$		0			0
$463$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$463$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$464$		0			0
$465$		0			0
$466$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$467$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$473$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$479$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$480$		0			0
$481$		0			0
$482$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$483$		0			0
$484$	−2.37939	+	0.866025i	−2.37939	+	0.866025i
$485$		0			0
$486$	0.673648	+	1.16679i	0.673648	+	1.16679i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$		0			0
$489$	1.79813	−	1.50881i	1.79813	−	1.50881i
$490$		0			0
$491$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	−0.939693	−	0.342020i	$-0.888889\pi$
$491$	−0.173648	−	0.984808i	−0.173648	−	0.984808i	0.766044	−	0.642788i	$-0.222222\pi$
$492$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.407604	+	0.342020i	0.407604	+	0.342020i
$499$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$499$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$500$		0			0
$501$		0			0
$502$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$503$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$503$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.266044	−	1.50881i	0.266044	−	1.50881i
$508$		0			0
$509$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$509$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			1.00000
$513$		0			0
$514$	1.53209			1.53209
$515$		0			0
$516$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$521$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$522$		0			0
$523$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$523$	−1.87939	+	0.684040i	−1.87939	+	0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$524$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−2.20574	−	1.85083i	−2.20574	−	1.85083i
$529$	0.173648	+	0.984808i	0.173648	+	0.984808i
$530$		0			0
$531$	−2.53209			−2.53209
$532$		0			0
$533$		0			0
$534$	1.43969	+	0.524005i	1.43969	+	0.524005i
$535$		0			0
$536$	0.266044	+	0.223238i	0.266044	+	0.223238i
$537$	0.407604	−	0.342020i	0.407604	−	0.342020i
$538$		0			0
$539$	0.939693	−	1.62760i	0.939693	−	1.62760i
$540$		0			0
$541$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$541$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$542$		0			0
$543$		0			0
$544$	0.500000	−	0.866025i	0.500000	−	0.866025i
$545$		0			0
$546$		0			0
$547$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	0.173648	−	0.984808i	$-0.444444\pi$
$547$	−0.766044	−	0.642788i	−0.766044	−	0.642788i	−0.939693	+	0.342020i	$0.888889\pi$
$548$	0.266044	+	1.50881i	0.266044	+	1.50881i
$549$		0			0
$550$	−1.87939			−1.87939
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.266044	−	0.223238i	0.266044	−	0.223238i
$557$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$557$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−2.70574	+	0.984808i	−2.70574	+	0.984808i
$562$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$563$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$563$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$564$		0			0
$565$		0			0
$566$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$567$		0			0
$568$		0			0
$569$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$569$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$571$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.233956	−	1.32683i	0.233956	−	1.32683i
$577$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$577$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$578$		0			0
$579$	1.43969	−	0.524005i	1.43969	−	0.524005i
$580$		0			0
$581$		0			0
$582$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$583$		0			0
$584$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$585$		0			0
$586$		0			0
$587$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.766044	−	0.642788i	$-0.222222\pi$
$587$	0.939693	+	0.342020i	0.939693	+	0.342020i	0.173648	+	0.984808i	$0.444444\pi$
$588$	1.53209			1.53209
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$593$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$594$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$599$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$600$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$601$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.173648	−	0.984808i	$-0.444444\pi$
$601$	0.939693	−	1.62760i	0.939693	−	1.62760i	0.766044	−	0.642788i	$-0.222222\pi$
$602$		0			0
$603$	0.358441	−	0.300767i	0.358441	−	0.300767i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.03209	−	0.866025i	−1.03209	−	0.866025i
$613$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$613$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$614$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$615$		0			0
$616$		0			0
$617$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$617$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$618$		0			0
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$619$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$626$	1.53209			1.53209
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$631$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$632$		0			0
$633$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.266044	−	0.223238i	0.266044	−	0.223238i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	0.266044	−	0.223238i	0.266044	−	0.223238i	0.766044	+	0.642788i	$0.222222\pi$
$642$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$643$	0.266044	+	1.50881i	0.266044	+	1.50881i	0.766044	+	0.642788i	$0.222222\pi$
$643$	0.266044	+	1.50881i	0.266044	+	1.50881i	−0.500000	+	0.866025i	$0.666667\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	0.500000	+	0.181985i	0.500000	+	0.181985i
$649$	0.613341	+	3.47843i	0.613341	+	3.47843i
$650$		0			0
$651$		0			0
$652$	0.266044	−	1.50881i	0.266044	−	1.50881i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$		0			0
$656$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$657$	1.26604	+	2.19285i	1.26604	+	2.19285i
$658$		0			0
$659$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	0.766044	+	0.642788i	$0.222222\pi$
$659$	−0.173648	+	0.984808i	−0.173648	+	0.984808i	−0.939693	+	0.342020i	$0.888889\pi$
$660$		0			0
$661$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$661$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$662$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$663$		0			0
$664$	0.347296			0.347296
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$674$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$675$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$676$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$679$		0			0
$680$		0			0
$681$	0.0923963	+	0.524005i	0.0923963	+	0.524005i
$682$		0			0
$683$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$683$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$689$		0			0
$690$		0			0
$691$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$691$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$692$		0			0
$693$		0			0
$694$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$695$		0			0
$696$		0			0
$697$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$698$		0			0
$699$	1.79813	+	1.50881i	1.79813	+	1.50881i
$700$		0			0
$701$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$701$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$702$		0			0
$703$		0			0
$704$	−1.87939			−1.87939
$705$		0			0
$706$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$707$		0			0
$708$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$709$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$709$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$710$		0			0
$711$		0			0
$712$	0.939693	−	0.342020i	0.939693	−	0.342020i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$717$		0			0
$718$		0			0
$719$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$719$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	2.34730			2.34730
$724$		0			0
$725$		0			0
$726$	2.97178	+	2.49362i	2.97178	+	2.49362i
$727$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$727$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$728$		0			0
$729$	0.766044	−	1.32683i	0.766044	−	1.32683i
$730$		0			0
$731$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$732$		0			0
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$738$	0.0812519	+	0.460802i	0.0812519	+	0.460802i
$739$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	0.173648	−	0.984808i	$-0.444444\pi$
$739$	−0.326352	−	0.118782i	−0.326352	−	0.118782i	−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$743$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0812519	−	0.460802i	0.0812519	−	0.460802i
$748$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$749$		0			0
$750$		0			0
$751$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$751$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$752$		0			0
$753$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$757$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$758$	−1.87939	−	0.684040i	−1.87939	−	0.684040i
$759$		0			0
$760$		0			0
$761$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$761$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$769$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.173648	−	0.984808i	$-0.444444\pi$
$769$	0.939693	−	0.342020i	0.939693	−	0.342020i	0.766044	+	0.642788i	$0.222222\pi$
$770$		0			0
$771$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$772$	0.500000	−	0.866025i	0.500000	−	0.866025i
$773$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$773$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$774$	−1.03209	+	0.866025i	−1.03209	+	0.866025i
$775$		0			0
$776$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.766044	−	0.642788i	0.766044	−	0.642788i
$785$		0			0
$786$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$787$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$787$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.439693	+	2.49362i	−0.439693	+	2.49362i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$801$	−0.233956	−	1.32683i	−0.233956	−	1.32683i
$802$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$803$	2.70574	−	2.27038i	2.70574	−	2.27038i
$804$	0.0923963	−	0.524005i	0.0923963	−	0.524005i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$809$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$810$		0			0
$811$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$811$	0.347296	−	1.96962i	0.347296	−	1.96962i	0.173648	−	0.984808i	$-0.444444\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.53209			−1.53209
$817$		0			0
$818$	−1.87939			−1.87939
$819$		0			0
$820$		0			0
$821$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$821$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$822$	1.79813	−	1.50881i	1.79813	−	1.50881i
$823$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$823$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$824$		0			0
$825$	1.43969	+	2.49362i	1.43969	+	2.49362i
$826$		0			0
$827$	1.76604	−	0.642788i	1.76604	−	0.642788i	0.766044	−	0.642788i	$-0.222222\pi$
$827$	1.76604	−	0.642788i	1.76604	−	0.642788i	1.00000			$0$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$834$	−0.500000	−	0.181985i	−0.500000	−	0.181985i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.939693	+	0.342020i	0.939693	+	0.342020i
$839$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$839$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$840$		0			0
$841$	0.766044	−	0.642788i	0.766044	−	0.642788i
$842$		0			0
$843$	−1.17365	+	2.03282i	−1.17365	+	2.03282i
$844$	0.500000	+	0.866025i	0.500000	+	0.866025i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$850$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$851$		0			0
$852$		0			0
$853$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$853$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$854$		0			0
$855$		0			0
$856$	−1.00000			−1.00000
$857$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$857$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$858$		0			0
$859$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.939693	−	0.342020i	$-0.888889\pi$
$859$	−1.43969	−	1.20805i	−1.43969	−	1.20805i	−0.500000	−	0.866025i	$-0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$863$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$864$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$865$		0			0
$866$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.467911			0.467911
$874$		0			0
$875$		0			0
$876$	2.70574	+	0.984808i	2.70574	+	0.984808i
$877$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$877$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$881$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$882$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$883$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	−0.500000	−	0.866025i	$-0.666667\pi$
$883$	−0.326352	+	0.118782i	−0.326352	+	0.118782i	0.173648	+	0.984808i	$0.444444\pi$
$884$		0			0
$885$		0			0
$886$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$887$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$887$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.17365	−	0.984808i	1.17365	−	0.984808i
$899$		0			0
$900$	−0.673648	+	1.16679i	−0.673648	+	1.16679i
$901$		0			0
$902$	0.613341	−	0.223238i	0.613341	−	0.223238i
$903$		0			0
$904$	0.939693	+	1.62760i	0.939693	+	1.62760i
$905$		0			0
$906$		0			0
$907$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.500000	+	0.866025i	$0.666667\pi$
$907$	−1.43969	+	1.20805i	−1.43969	+	1.20805i	−0.939693	+	0.342020i	$0.888889\pi$
$908$	0.266044	+	0.223238i	0.266044	+	0.223238i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	−0.652704			−0.652704
$914$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.0923963	+	0.524005i	−0.0923963	+	0.524005i
$919$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$919$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$920$		0			0
$921$	2.70574	−	0.984808i	2.70574	−	0.984808i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.76604	+	0.642788i	1.76604	+	0.642788i	1.00000			$0$
$929$	1.76604	+	0.642788i	1.76604	+	0.642788i	0.766044	+	0.642788i	$0.222222\pi$
$930$		0			0
$931$		0			0
$932$	1.53209			1.53209
$933$		0			0
$934$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$935$		0			0
$936$		0			0
$937$	0.266044	−	1.50881i	0.266044	−	1.50881i	−0.500000	−	0.866025i	$-0.666667\pi$
$937$	0.266044	−	1.50881i	0.266044	−	1.50881i	0.766044	−	0.642788i	$-0.222222\pi$
$938$		0			0
$939$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$940$		0			0
$941$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$941$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$942$		0			0
$943$		0			0
$944$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$945$		0			0
$946$	1.43969	+	1.20805i	1.43969	+	1.20805i
$947$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$947$	0.347296	+	1.96962i	0.347296	+	1.96962i	0.173648	+	0.984808i	$0.444444\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	−0.500000	−	0.866025i	$-0.666667\pi$
$953$	−0.326352	−	1.85083i	−0.326352	−	1.85083i	0.173648	−	0.984808i	$-0.444444\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$	−0.233956	+	1.32683i	−0.233956	+	1.32683i
$964$	1.17365	−	0.984808i	1.17365	−	0.984808i
$965$		0			0
$966$		0			0
$967$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$967$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$968$	2.53209			2.53209
$969$		0			0
$970$		0			0
$971$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	−1.43969	−	0.524005i	−1.43969	−	0.524005i	−0.939693	+	0.342020i	$0.888889\pi$
$972$	−0.233956	−	1.32683i	−0.233956	−	1.32683i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$977$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$978$	−2.20574	+	0.802823i	−2.20574	+	0.802823i
$979$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$980$		0			0
$981$		0			0
$982$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$983$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$983$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$984$	0.407604	+	0.342020i	0.407604	+	0.342020i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$991$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$992$		0			0
$993$	−2.20574	+	1.85083i	−2.20574	+	1.85083i
$994$		0			0
$995$		0			0
$996$	−0.266044	−	0.460802i	−0.266044	−	0.460802i
$997$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$997$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$998$	1.76604	−	0.642788i	1.76604	−	0.642788i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.u.b.99.1		6
8.3	odd	2	CM	2888.1.u.b.99.1		6
19.2	odd	18		2888.1.u.e.1859.1		6
19.3	odd	18		2888.1.u.a.2411.1		6
19.4	even	9		2888.1.k.b.2819.1		6
19.5	even	9	inner	2888.1.u.b.1867.1		6
19.6	even	9		2888.1.k.b.2595.1		6
19.7	even	3		152.1.u.a.139.1	yes	6
19.8	odd	6		2888.1.u.a.2555.1		6
19.9	even	9		2888.1.f.d.723.3		3
19.10	odd	18		2888.1.f.c.723.1		3
19.11	even	3		2888.1.u.g.2555.1		6
19.12	odd	6		2888.1.u.e.595.1		6
19.13	odd	18		2888.1.k.c.2595.3		6
19.14	odd	18		2888.1.u.f.1867.1		6
19.15	odd	18		2888.1.k.c.2819.3		6
19.16	even	9		2888.1.u.g.2411.1		6
19.17	even	9		152.1.u.a.35.1	✓	6
19.18	odd	2		2888.1.u.f.99.1		6
57.17	odd	18		1368.1.eh.a.1099.1		6
57.26	odd	6		1368.1.eh.a.595.1		6
76.7	odd	6		608.1.bg.a.367.1		6
76.55	odd	18		608.1.bg.a.111.1		6
95.7	odd	12		3800.1.cq.b.899.2		12
95.17	odd	36		3800.1.cq.b.1099.1		12
95.64	even	6		3800.1.cv.c.1051.1		6
95.74	even	18		3800.1.cv.c.1251.1		6
95.83	odd	12		3800.1.cq.b.899.1		12
95.93	odd	36		3800.1.cq.b.1099.2		12
152.3	even	18		2888.1.u.a.2411.1		6
152.11	odd	6		2888.1.u.g.2555.1		6
152.27	even	6		2888.1.u.a.2555.1		6
152.35	odd	18		2888.1.u.g.2411.1		6
152.43	odd	18	inner	2888.1.u.b.1867.1		6
152.45	even	6		608.1.bg.a.367.1		6
152.51	even	18		2888.1.k.c.2595.3		6
152.59	even	18		2888.1.u.e.1859.1		6
152.67	even	18		2888.1.f.c.723.1		3
152.75	even	2		2888.1.u.f.99.1		6
152.83	odd	6		152.1.u.a.139.1	yes	6
152.91	even	18		2888.1.k.c.2819.3		6
152.93	even	18		608.1.bg.a.111.1		6
152.99	odd	18		2888.1.k.b.2819.1		6
152.107	even	6		2888.1.u.e.595.1		6
152.123	odd	18		2888.1.f.d.723.3		3
152.131	odd	18		152.1.u.a.35.1	✓	6
152.139	odd	18		2888.1.k.b.2595.1		6
152.147	even	18		2888.1.u.f.1867.1		6
456.83	even	6		1368.1.eh.a.595.1		6
456.131	even	18		1368.1.eh.a.1099.1		6
760.83	even	12		3800.1.cq.b.899.1		12
760.283	even	36		3800.1.cq.b.1099.2		12
760.387	even	12		3800.1.cq.b.899.2		12
760.539	odd	6		3800.1.cv.c.1051.1		6
760.587	even	36		3800.1.cq.b.1099.1		12
760.739	odd	18		3800.1.cv.c.1251.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.1.u.a.35.1	✓	6	19.17	even	9
152.1.u.a.35.1	✓	6	152.131	odd	18
152.1.u.a.139.1	yes	6	19.7	even	3
152.1.u.a.139.1	yes	6	152.83	odd	6
608.1.bg.a.111.1		6	76.55	odd	18
608.1.bg.a.111.1		6	152.93	even	18
608.1.bg.a.367.1		6	76.7	odd	6
608.1.bg.a.367.1		6	152.45	even	6
1368.1.eh.a.595.1		6	57.26	odd	6
1368.1.eh.a.595.1		6	456.83	even	6
1368.1.eh.a.1099.1		6	57.17	odd	18
1368.1.eh.a.1099.1		6	456.131	even	18
2888.1.f.c.723.1		3	19.10	odd	18
2888.1.f.c.723.1		3	152.67	even	18
2888.1.f.d.723.3		3	19.9	even	9
2888.1.f.d.723.3		3	152.123	odd	18
2888.1.k.b.2595.1		6	19.6	even	9
2888.1.k.b.2595.1		6	152.139	odd	18
2888.1.k.b.2819.1		6	19.4	even	9
2888.1.k.b.2819.1		6	152.99	odd	18
2888.1.k.c.2595.3		6	19.13	odd	18
2888.1.k.c.2595.3		6	152.51	even	18
2888.1.k.c.2819.3		6	19.15	odd	18
2888.1.k.c.2819.3		6	152.91	even	18
2888.1.u.a.2411.1		6	19.3	odd	18
2888.1.u.a.2411.1		6	152.3	even	18
2888.1.u.a.2555.1		6	19.8	odd	6
2888.1.u.a.2555.1		6	152.27	even	6
2888.1.u.b.99.1		6	1.1	even	1	trivial
2888.1.u.b.99.1		6	8.3	odd	2	CM
2888.1.u.b.1867.1		6	19.5	even	9	inner
2888.1.u.b.1867.1		6	152.43	odd	18	inner
2888.1.u.e.595.1		6	19.12	odd	6
2888.1.u.e.595.1		6	152.107	even	6
2888.1.u.e.1859.1		6	19.2	odd	18
2888.1.u.e.1859.1		6	152.59	even	18
2888.1.u.f.99.1		6	19.18	odd	2
2888.1.u.f.99.1		6	152.75	even	2
2888.1.u.f.1867.1		6	19.14	odd	18
2888.1.u.f.1867.1		6	152.147	even	18
2888.1.u.g.2411.1		6	19.16	even	9
2888.1.u.g.2411.1		6	152.35	odd	18
2888.1.u.g.2555.1		6	19.11	even	3
2888.1.u.g.2555.1		6	152.11	odd	6
3800.1.cq.b.899.1		12	95.83	odd	12
3800.1.cq.b.899.1		12	760.83	even	12
3800.1.cq.b.899.2		12	95.7	odd	12
3800.1.cq.b.899.2		12	760.387	even	12
3800.1.cq.b.1099.1		12	95.17	odd	36
3800.1.cq.b.1099.1		12	760.587	even	36
3800.1.cq.b.1099.2		12	95.93	odd	36
3800.1.cq.b.1099.2		12	760.283	even	36
3800.1.cv.c.1051.1		6	95.64	even	6
3800.1.cv.c.1051.1		6	760.539	odd	6
3800.1.cv.c.1251.1		6	95.74	even	18
3800.1.cv.c.1251.1		6	760.739	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.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.266044 + 1.50881i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.266044 - 1.50881i) q^{6} +(-0.500000 - 0.866025i) q^{8} +(-1.26604 + 0.460802i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.266044 + 1.50881i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.266044 - 1.50881i) q^{6} +(-0.500000 - 0.866025i) q^{8} +(-1.26604 + 0.460802i) q^{9} +(0.939693 + 1.62760i) q^{11} +(-0.766044 + 1.32683i) q^{12} +(0.173648 + 0.984808i) q^{16} +(0.939693 + 0.342020i) q^{17} +1.34730 q^{18} +(-0.326352 - 1.85083i) q^{22} +(1.17365 - 0.984808i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.266044 - 0.460802i) q^{27} +(0.173648 - 0.984808i) q^{32} +(-2.20574 + 1.85083i) q^{33} +(-0.766044 - 0.642788i) q^{34} +(-1.26604 - 0.460802i) q^{36} +(0.0603074 + 0.342020i) q^{41} +(-0.766044 + 0.642788i) q^{43} +(-0.326352 + 1.85083i) q^{44} +(-1.43969 + 0.524005i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.266044 + 1.50881i) q^{51} +(0.0923963 + 0.524005i) q^{54} +(1.76604 + 0.642788i) q^{59} +(-0.500000 + 0.866025i) q^{64} +(2.70574 - 0.984808i) q^{66} +(-0.326352 + 0.118782i) q^{67} +(0.500000 + 0.866025i) q^{68} +(1.03209 + 0.866025i) q^{72} +(-0.326352 - 1.85083i) q^{73} +1.53209 q^{75} +(-0.407604 + 0.342020i) q^{81} +(0.0603074 - 0.342020i) q^{82} +(-0.173648 + 0.300767i) q^{83} +(0.939693 - 0.342020i) q^{86} +(0.939693 - 1.62760i) q^{88} +(-0.173648 + 0.984808i) q^{89} +1.53209 q^{96} +(-0.326352 - 0.118782i) q^{97} +(0.173648 + 0.984808i) q^{98} +(-1.93969 - 1.62760i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{3} - 3 q^{6} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^3 - 3 * q^6 - 3 * q^8 - 3 * q^9	\( 6 q - 3 q^{3} - 3 q^{6} - 3 q^{8} - 3 q^{9} + 6 q^{18} - 3 q^{22} + 6 q^{24} + 3 q^{27} - 3 q^{33} - 3 q^{36} + 6 q^{41} - 3 q^{44} - 3 q^{48} - 3 q^{49} - 3 q^{50} + 3 q^{51} - 3 q^{54} + 6 q^{59} - 3 q^{64} + 6 q^{66} - 3 q^{67} + 3 q^{68} - 3 q^{72} - 3 q^{73} - 6 q^{81} + 6 q^{82} - 3 q^{97} - 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^3 - 3 * q^6 - 3 * q^8 - 3 * q^9 + 6 * q^18 - 3 * q^22 + 6 * q^24 + 3 * q^27 - 3 * q^33 - 3 * q^36 + 6 * q^41 - 3 * q^44 - 3 * q^48 - 3 * q^49 - 3 * q^50 + 3 * q^51 - 3 * q^54 + 6 * q^59 - 3 * q^64 + 6 * q^66 - 3 * q^67 + 3 * q^68 - 3 * q^72 - 3 * q^73 - 6 * q^81 + 6 * q^82 - 3 * q^97 - 6 * q^99

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