LMFDB - Embedded newform 2535.1.bc.a.2117.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2535,1,Mod(188,2535)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2535, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 5]))

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

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

chi := DirichletCharacter("2535.188");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2535 = 3 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2535.bc (of order $12$, degree $4$, 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:	$1.26512980702$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{8}$
Projective field:	Galois closure of 8.2.12049171875.1

Embedding invariants

Embedding label			2117.3
Root			$0.130526 - 0.991445i$ of defining polynomial
Character	$\chi$	$=$	2535.2117
Dual form			2535.1.bc.a.188.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.382683 + 0.662827i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.207107 - 0.358719i) q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.198092 - 0.739288i) q^{6} +1.08239 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.382683 + 0.662827i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.207107 - 0.358719i) q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.198092 - 0.739288i) q^{6} +1.08239 q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.0999004 - 0.758819i) q^{10} +(-0.478235 + 1.78480i) q^{11} +(-0.292893 + 0.292893i) q^{12} +(0.793353 + 0.608761i) q^{15} +(0.207107 + 0.358719i) q^{16} +0.765367i q^{18} +(-0.328618 + 0.252157i) q^{20} +(-1.36603 + 0.366025i) q^{22} +(-1.04551 - 0.280144i) q^{24} +(0.707107 + 0.707107i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-0.0999004 + 0.758819i) q^{30} +(0.382683 - 0.662827i) q^{32} +(0.923880 - 1.60021i) q^{33} +(0.358719 - 0.207107i) q^{36} +(-1.00000 - 0.414214i) q^{40} +(0.739288 + 0.198092i) q^{41} +(1.36603 - 0.366025i) q^{43} +(0.541196 + 0.541196i) q^{44} +(-0.608761 - 0.793353i) q^{45} +1.84776i q^{47} +(-0.107206 - 0.400100i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.198092 + 0.739288i) q^{50} +(0.198092 - 0.739288i) q^{54} +(1.12484 - 1.46593i) q^{55} +(0.198092 + 0.739288i) q^{59} +(0.382683 - 0.158513i) q^{60} +(0.707107 - 1.22474i) q^{61} +1.00000 q^{64} +1.41421 q^{66} +(0.198092 + 0.739288i) q^{71} +(0.937379 + 0.541196i) q^{72} +(-0.500000 - 0.866025i) q^{75} +1.41421i q^{79} +(-0.0540657 - 0.410670i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.151613 + 0.565826i) q^{82} -1.84776i q^{83} +(0.765367 + 0.765367i) q^{86} +(-0.517638 + 1.93185i) q^{88} +(1.78480 + 0.478235i) q^{89} +(0.292893 - 0.707107i) q^{90} +(-1.22474 + 0.707107i) q^{94} +(-0.541196 + 0.541196i) q^{96} +(-0.382683 + 0.662827i) q^{98} +(-1.30656 + 1.30656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4}+O(q^{10}) $ 16 * q - 8 * q^4	$ 16 q - 8 q^{4} - 16 q^{12} - 8 q^{16} - 8 q^{22} - 16 q^{40} + 8 q^{43} + 8 q^{48} + 8 q^{49} + 16 q^{64} - 8 q^{75} + 8 q^{81} + 8 q^{82} + 16 q^{90}+O(q^{100}) $ 16 * q - 8 * q^4 - 16 * q^12 - 8 * q^16 - 8 * q^22 - 16 * q^40 + 8 * q^43 + 8 * q^48 + 8 * q^49 + 16 * q^64 - 8 * q^75 + 8 * q^81 + 8 * q^82 + 16 * q^90

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2535\mathbb{Z}\right)^\times$.

$n$	$1522$	$1691$	$1861$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.382683	+	0.662827i	0.382683	+	0.662827i	0.991445	−	0.130526i	$-0.0416667\pi$
$2$	0.382683	+	0.662827i	0.382683	+	0.662827i	−0.608761	+	0.793353i	$0.708333\pi$
$3$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$3$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$4$	0.207107	−	0.358719i	0.207107	−	0.358719i
$5$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$5$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$6$	−0.198092	−	0.739288i	−0.198092	−	0.739288i
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	1.08239			1.08239
$9$	0.866025	+	0.500000i	0.866025	+	0.500000i
$10$	−0.0999004	−	0.758819i	−0.0999004	−	0.758819i
$11$	−0.478235	+	1.78480i	−0.478235	+	1.78480i	0.130526	+	0.991445i	$0.458333\pi$
$11$	−0.478235	+	1.78480i	−0.478235	+	1.78480i	−0.608761	+	0.793353i	$0.708333\pi$
$12$	−0.292893	+	0.292893i	−0.292893	+	0.292893i
$13$		0			0
$13$		0			0
$14$		0			0
$15$	0.793353	+	0.608761i	0.793353	+	0.608761i
$16$	0.207107	+	0.358719i	0.207107	+	0.358719i
$17$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$17$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$18$			0.765367i			0.765367i
$19$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$19$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$20$	−0.328618	+	0.252157i	−0.328618	+	0.252157i
$21$		0			0
$22$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$23$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$23$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$24$	−1.04551	−	0.280144i	−1.04551	−	0.280144i
$25$	0.707107	+	0.707107i	0.707107	+	0.707107i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$28$		0			0
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	−0.0999004	+	0.758819i	−0.0999004	+	0.758819i
$31$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$31$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$32$	0.382683	−	0.662827i	0.382683	−	0.662827i
$33$	0.923880	−	1.60021i	0.923880	−	1.60021i
$34$		0			0
$35$		0			0
$36$	0.358719	−	0.207107i	0.358719	−	0.207107i
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$		0			0
$40$	−1.00000	−	0.414214i	−1.00000	−	0.414214i
$41$	0.739288	+	0.198092i	0.739288	+	0.198092i	0.608761	−	0.793353i	$-0.291667\pi$
$41$	0.739288	+	0.198092i	0.739288	+	0.198092i	0.130526	+	0.991445i	$0.458333\pi$
$42$		0			0
$43$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$43$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$44$	0.541196	+	0.541196i	0.541196	+	0.541196i
$45$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$46$		0			0
$47$			1.84776i			1.84776i	0.382683	+	0.923880i	$0.375000\pi$
$47$			1.84776i			1.84776i	−0.382683	+	0.923880i	$0.625000\pi$
$48$	−0.107206	−	0.400100i	−0.107206	−	0.400100i
$49$	0.500000	+	0.866025i	0.500000	+	0.866025i
$50$	−0.198092	+	0.739288i	−0.198092	+	0.739288i
$51$		0			0
$52$		0			0
$53$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$53$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$54$	0.198092	−	0.739288i	0.198092	−	0.739288i
$55$	1.12484	−	1.46593i	1.12484	−	1.46593i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.198092	+	0.739288i	0.198092	+	0.739288i	0.991445	+	0.130526i	$0.0416667\pi$
$59$	0.198092	+	0.739288i	0.198092	+	0.739288i	−0.793353	+	0.608761i	$0.791667\pi$
$60$	0.382683	−	0.158513i	0.382683	−	0.158513i
$61$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$61$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			1.00000
$65$		0			0
$66$	1.41421			1.41421
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.198092	+	0.739288i	0.198092	+	0.739288i	0.991445	+	0.130526i	$0.0416667\pi$
$71$	0.198092	+	0.739288i	0.198092	+	0.739288i	−0.793353	+	0.608761i	$0.791667\pi$
$72$	0.937379	+	0.541196i	0.937379	+	0.541196i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$76$		0			0
$77$		0			0
$78$		0			0
$79$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$79$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$80$	−0.0540657	−	0.410670i	−0.0540657	−	0.410670i
$81$	0.500000	+	0.866025i	0.500000	+	0.866025i
$82$	0.151613	+	0.565826i	0.151613	+	0.565826i
$83$		−	1.84776i		−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$83$		−	1.84776i		−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$84$		0			0
$85$		0			0
$86$	0.765367	+	0.765367i	0.765367	+	0.765367i
$87$		0			0
$88$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$89$	1.78480	+	0.478235i	1.78480	+	0.478235i	0.991445	−	0.130526i	$-0.0416667\pi$
$89$	1.78480	+	0.478235i	1.78480	+	0.478235i	0.793353	+	0.608761i	$0.208333\pi$
$90$	0.292893	−	0.707107i	0.292893	−	0.707107i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$95$		0			0
$96$	−0.541196	+	0.541196i	−0.541196	+	0.541196i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	−0.382683	+	0.662827i	−0.382683	+	0.662827i
$99$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$100$	0.400100	−	0.107206i	0.400100	−	0.107206i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$		0			0
$103$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$103$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$107$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$108$	−0.400100	+	0.107206i	−0.400100	+	0.107206i
$109$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$109$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$110$	1.40211	+	0.184592i	1.40211	+	0.184592i
$111$		0			0
$112$		0			0
$113$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$113$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.414214	+	0.414214i	−0.414214	+	0.414214i
$119$		0			0
$120$	0.858719	+	0.658919i	0.858719	+	0.658919i
$121$	−2.09077	−	1.20711i	−2.09077	−	1.20711i
$122$	1.08239			1.08239
$123$	−0.662827	−	0.382683i	−0.662827	−	0.382683i
$124$		0			0
$125$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$126$		0			0
$127$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$127$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$128$		0			0
$129$	−1.41421			−1.41421
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	−0.382683	−	0.662827i	−0.382683	−	0.662827i
$133$		0			0
$134$		0			0
$135$	0.382683	+	0.923880i	0.382683	+	0.923880i
$136$		0			0
$137$	0.662827	+	0.382683i	0.662827	+	0.382683i	0.793353	−	0.608761i	$-0.208333\pi$
$137$	0.662827	+	0.382683i	0.662827	+	0.382683i	−0.130526	+	0.991445i	$0.541667\pi$
$138$		0			0
$139$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$139$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$140$		0			0
$141$	0.478235	−	1.78480i	0.478235	−	1.78480i
$142$	−0.414214	+	0.414214i	−0.414214	+	0.414214i
$143$		0			0
$144$			0.414214i			0.414214i
$145$		0			0
$146$		0			0
$147$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$148$		0			0
$149$	−0.739288	+	0.198092i	−0.739288	+	0.198092i	−0.608761	−	0.793353i	$-0.708333\pi$
$149$	−0.739288	+	0.198092i	−0.739288	+	0.198092i	−0.130526	+	0.991445i	$0.541667\pi$
$150$	0.382683	−	0.662827i	0.382683	−	0.662827i
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$157$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$158$	−0.937379	+	0.541196i	−0.937379	+	0.541196i
$159$		0			0
$160$	−0.607206	+	0.465926i	−0.607206	+	0.465926i
$161$		0			0
$162$	−0.382683	+	0.662827i	−0.382683	+	0.662827i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	0.224171	−	0.224171i	0.224171	−	0.224171i
$165$	−1.46593	+	1.12484i	−1.46593	+	1.12484i
$166$	1.22474	−	0.707107i	1.22474	−	0.707107i
$167$	−0.662827	+	0.382683i	−0.662827	+	0.382683i	−0.793353	−	0.608761i	$-0.791667\pi$
$167$	−0.662827	+	0.382683i	−0.662827	+	0.382683i	0.130526	+	0.991445i	$0.458333\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$		0			0
$172$	0.151613	−	0.565826i	0.151613	−	0.565826i
$173$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$173$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$174$		0			0
$175$		0			0
$176$	−0.739288	+	0.198092i	−0.739288	+	0.198092i
$177$		−	0.765367i		−	0.765367i
$178$	0.366025	+	1.36603i	0.366025	+	1.36603i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	−0.410670	+	0.0540657i	−0.410670	+	0.0540657i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.662827	+	0.382683i	0.662827	+	0.382683i
$189$		0			0
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$		0			0
$196$	0.414214			0.414214
$197$	−0.923880	−	1.60021i	−0.923880	−	1.60021i	−0.793353	−	0.608761i	$-0.791667\pi$
$197$	−0.923880	−	1.60021i	−0.923880	−	1.60021i	−0.130526	−	0.991445i	$-0.541667\pi$
$198$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$199$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$199$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$200$	0.765367	+	0.765367i	0.765367	+	0.765367i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.607206	−	0.465926i	−0.607206	−	0.465926i
$206$	0.280144	−	1.04551i	0.280144	−	1.04551i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$211$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$212$		0			0
$213$		−	0.765367i		−	0.765367i
$214$		0			0
$215$	−1.40211	−	0.184592i	−1.40211	−	0.184592i
$216$	−0.765367	−	0.765367i	−0.765367	−	0.765367i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$221$		0			0
$222$		0			0
$223$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$223$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$224$		0			0
$225$	0.258819	+	0.965926i	0.258819	+	0.965926i
$226$		0			0
$227$	−0.382683	+	0.662827i	−0.382683	+	0.662827i	−0.991445	−	0.130526i	$-0.958333\pi$
$227$	−0.382683	+	0.662827i	−0.382683	+	0.662827i	0.608761	+	0.793353i	$0.291667\pi$
$228$		0			0
$229$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$229$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$233$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$234$		0			0
$235$	0.707107	−	1.70711i	0.707107	−	1.70711i
$236$	0.306223	+	0.0820522i	0.306223	+	0.0820522i
$237$	0.366025	−	1.36603i	0.366025	−	1.36603i
$238$		0			0
$239$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	0.382683	−	0.923880i	$-0.375000\pi$
$239$	−0.541196	−	0.541196i	−0.541196	−	0.541196i	−0.923880	+	0.382683i	$0.875000\pi$
$240$	−0.0540657	+	0.410670i	−0.0540657	+	0.410670i
$241$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$241$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$242$		−	1.84776i		−	1.84776i
$243$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$244$	−0.292893	−	0.507306i	−0.292893	−	0.507306i
$245$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$246$		−	0.585786i		−	0.585786i
$247$		0			0
$248$		0			0
$249$	−0.478235	+	1.78480i	−0.478235	+	1.78480i
$250$	0.465926	−	0.607206i	0.465926	−	0.607206i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.500000	−	0.866025i	0.500000	−	0.866025i
$257$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$257$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$258$	−0.541196	−	0.937379i	−0.541196	−	0.937379i
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$263$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$264$	1.00000	−	1.73205i	1.00000	−	1.73205i
$265$		0			0
$266$		0			0
$267$	−1.60021	−	0.923880i	−1.60021	−	0.923880i
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	−0.465926	+	0.607206i	−0.465926	+	0.607206i
$271$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$271$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$272$		0			0
$273$		0			0
$274$			0.585786i			0.585786i
$275$	−1.60021	+	0.923880i	−1.60021	+	0.923880i
$276$		0			0
$277$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$277$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.30656	−	1.30656i	−1.30656	−	1.30656i	−0.923880	−	0.382683i	$-0.875000\pi$
$281$	−1.30656	−	1.30656i	−1.30656	−	1.30656i	−0.382683	−	0.923880i	$-0.625000\pi$
$282$	1.36603	−	0.366025i	1.36603	−	0.366025i
$283$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$283$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$284$	0.306223	+	0.0820522i	0.306223	+	0.0820522i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.662827	−	0.382683i	0.662827	−	0.382683i
$289$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.382683	+	0.662827i	−0.382683	+	0.662827i	−0.991445	−	0.130526i	$-0.958333\pi$
$293$	−0.382683	+	0.662827i	−0.382683	+	0.662827i	0.608761	+	0.793353i	$0.291667\pi$
$294$	0.541196	−	0.541196i	0.541196	−	0.541196i
$295$	0.0999004	−	0.758819i	0.0999004	−	0.758819i
$296$		0			0
$297$	1.60021	−	0.923880i	1.60021	−	0.923880i
$298$	−0.414214	−	0.414214i	−0.414214	−	0.414214i
$299$		0			0
$300$	−0.414214			−0.414214
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.12197	+	0.860919i	−1.12197	+	0.860919i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	0.707107	+	1.22474i	0.707107	+	1.22474i
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$313$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$314$	0.280144	−	1.04551i	0.280144	−	1.04551i
$315$		0			0
$316$	0.507306	+	0.292893i	0.507306	+	0.292893i
$317$	−1.84776			−1.84776			−0.923880	−	0.382683i	$-0.875000\pi$
$317$	−1.84776			−1.84776			−0.923880	+	0.382683i	$0.875000\pi$
$318$		0			0
$319$		0			0
$320$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.414214			0.414214
$325$		0			0
$326$		0			0
$327$		0			0
$328$	0.800199	+	0.214413i	0.800199	+	0.214413i
$329$		0			0
$330$	−1.30656	−	0.541196i	−1.30656	−	0.541196i
$331$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$331$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$332$	−0.662827	−	0.382683i	−0.662827	−	0.382683i
$333$		0			0
$334$	−0.507306	−	0.292893i	−0.507306	−	0.292893i
$335$		0			0
$336$		0			0
$337$	1.41421	−	1.41421i	1.41421	−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$337$	1.41421	−	1.41421i	1.41421	−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	1.47858	−	0.396183i	1.47858	−	0.396183i
$345$		0			0
$346$		0			0
$347$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$347$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$348$		0			0
$349$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$349$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$350$		0			0
$351$		0			0
$352$	1.00000	+	1.00000i	1.00000	+	1.00000i
$353$	−0.662827	+	0.382683i	−0.662827	+	0.382683i	−0.793353	−	0.608761i	$-0.791667\pi$
$353$	−0.662827	+	0.382683i	−0.662827	+	0.382683i	0.130526	+	0.991445i	$0.458333\pi$
$354$	0.507306	−	0.292893i	0.507306	−	0.292893i
$355$	0.0999004	−	0.758819i	0.0999004	−	0.758819i
$356$	0.541196	−	0.541196i	0.541196	−	0.541196i
$357$		0			0
$358$		0			0
$359$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$359$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.923880	−	0.382683i	$-0.125000\pi$
$360$	−0.658919	−	0.858719i	−0.658919	−	0.858719i
$361$	0.866025	−	0.500000i	0.866025	−	0.500000i
$362$		0			0
$363$	1.70711	+	1.70711i	1.70711	+	1.70711i
$364$		0			0
$365$		0			0
$366$	−1.04551	−	0.280144i	−1.04551	−	0.280144i
$367$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$367$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$368$		0			0
$369$	0.541196	+	0.541196i	0.541196	+	0.541196i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$373$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$374$		0			0
$375$	0.130526	+	0.991445i	0.130526	+	0.991445i
$376$			2.00000i			2.00000i
$377$		0			0
$378$		0			0
$379$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$379$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.60021	+	0.923880i	1.60021	+	0.923880i	0.991445	+	0.130526i	$0.0416667\pi$
$383$	1.60021	+	0.923880i	1.60021	+	0.923880i	0.608761	+	0.793353i	$0.291667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.36603	+	0.366025i	1.36603	+	0.366025i
$388$		0			0
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	0.541196	+	0.937379i	0.541196	+	0.937379i
$393$		0			0
$394$	0.707107	−	1.22474i	0.707107	−	1.22474i
$395$	0.541196	−	1.30656i	0.541196	−	1.30656i
$396$	0.198092	+	0.739288i	0.198092	+	0.739288i
$397$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$397$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$398$	−1.08239			−1.08239
$399$		0			0
$400$	−0.107206	+	0.400100i	−0.107206	+	0.400100i
$401$	0.198092	−	0.739288i	0.198092	−	0.739288i	−0.793353	−	0.608761i	$-0.791667\pi$
$401$	0.198092	−	0.739288i	0.198092	−	0.739288i	0.991445	−	0.130526i	$-0.0416667\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$409$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$410$	0.0764605	−	0.580775i	0.0764605	−	0.580775i
$411$	−0.541196	−	0.541196i	−0.541196	−	0.541196i
$412$	−0.565826	+	0.151613i	−0.565826	+	0.151613i
$413$		0			0
$414$		0			0
$415$	−0.707107	+	1.70711i	−0.707107	+	1.70711i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$419$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$420$		0			0
$421$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$421$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$422$	−0.541196	+	0.937379i	−0.541196	+	0.937379i
$423$	−0.923880	+	1.60021i	−0.923880	+	1.60021i
$424$		0			0
$425$		0			0
$426$	0.507306	−	0.292893i	0.507306	−	0.292893i
$427$		0			0
$428$		0			0
$429$		0			0
$430$	−0.414214	−	1.00000i	−0.414214	−	1.00000i
$431$	−1.78480	−	0.478235i	−1.78480	−	0.478235i	−0.793353	−	0.608761i	$-0.791667\pi$
$431$	−1.78480	−	0.478235i	−1.78480	−	0.478235i	−0.991445	+	0.130526i	$0.958333\pi$
$432$	0.107206	−	0.400100i	0.107206	−	0.400100i
$433$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$433$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	1.21752	−	1.58671i	1.21752	−	1.58671i
$441$			1.00000i			1.00000i
$442$		0			0
$443$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$443$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$444$		0			0
$445$	−1.46593	−	1.12484i	−1.46593	−	1.12484i
$446$		0			0
$447$	0.765367			0.765367
$448$		0			0
$449$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	−0.991445	−	0.130526i	$-0.958333\pi$
$449$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	0.793353	−	0.608761i	$-0.208333\pi$
$450$	−0.541196	+	0.541196i	−0.541196	+	0.541196i
$451$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$452$		0			0
$453$		0			0
$454$	−0.585786			−0.585786
$455$		0			0
$456$		0			0
$457$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$457$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.478235	−	1.78480i	−0.478235	−	1.78480i	−0.608761	−	0.793353i	$-0.708333\pi$
$461$	−0.478235	−	1.78480i	−0.478235	−	1.78480i	0.130526	−	0.991445i	$-0.458333\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$467$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$468$		0			0
$469$		0			0
$470$	1.40211	−	0.184592i	1.40211	−	0.184592i
$471$	0.707107	+	1.22474i	0.707107	+	1.22474i
$472$	0.214413	+	0.800199i	0.214413	+	0.800199i
$473$			2.61313i			2.61313i
$474$	1.04551	−	0.280144i	1.04551	−	0.280144i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	0.151613	−	0.565826i	0.151613	−	0.565826i
$479$	−1.78480	−	0.478235i	−1.78480	−	0.478235i	−0.793353	−	0.608761i	$-0.791667\pi$
$479$	−1.78480	−	0.478235i	−1.78480	−	0.478235i	−0.991445	+	0.130526i	$0.958333\pi$
$480$	0.707107	−	0.292893i	0.707107	−	0.292893i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$485$		0			0
$486$	0.541196	−	0.541196i	0.541196	−	0.541196i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	0.765367	−	1.32565i	0.765367	−	1.32565i
$489$		0			0
$490$	0.607206	−	0.465926i	0.607206	−	0.465926i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	−0.274552	+	0.158513i	−0.274552	+	0.158513i
$493$		0			0
$494$		0			0
$495$	1.70711	−	0.707107i	1.70711	−	0.707107i
$496$		0			0
$497$		0			0
$498$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$499$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$499$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$500$	−0.410670	−	0.0540657i	−0.410670	−	0.0540657i
$501$	0.739288	−	0.198092i	0.739288	−	0.198092i
$502$		0			0
$503$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$503$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	0.478235	−	1.78480i	0.478235	−	1.78480i	−0.130526	−	0.991445i	$-0.541667\pi$
$509$	0.478235	−	1.78480i	0.478235	−	1.78480i	0.608761	−	0.793353i	$-0.291667\pi$
$510$		0			0
$511$		0			0
$512$	0.765367			0.765367
$513$		0			0
$514$		0			0
$515$	0.541196	+	1.30656i	0.541196	+	1.30656i
$516$	−0.292893	+	0.507306i	−0.292893	+	0.507306i
$517$	−3.29788	−	0.883663i	−3.29788	−	0.883663i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$523$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.765367			0.765367
$529$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$530$		0			0
$531$	−0.198092	+	0.739288i	−0.198092	+	0.739288i
$532$		0			0
$533$		0			0
$534$		−	1.41421i		−	1.41421i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.78480	+	0.478235i	−1.78480	+	0.478235i
$540$	0.410670	+	0.0540657i	0.410670	+	0.0540657i
$541$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$541$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$547$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$548$	0.274552	−	0.158513i	0.274552	−	0.158513i
$549$	1.22474	−	0.707107i	1.22474	−	0.707107i
$550$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.765367	+	0.765367i	−0.765367	+	0.765367i
$555$		0			0
$556$		0			0
$557$	0.662827	−	0.382683i	0.662827	−	0.382683i	−0.130526	−	0.991445i	$-0.541667\pi$
$557$	0.662827	−	0.382683i	0.662827	−	0.382683i	0.793353	+	0.608761i	$0.208333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.366025	−	1.36603i	0.366025	−	1.36603i
$563$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$563$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$564$	−0.541196	−	0.541196i	−0.541196	−	0.541196i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	0.214413	+	0.800199i	0.214413	+	0.800199i
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$571$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.866025	+	0.500000i	0.866025	+	0.500000i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−0.662827	−	0.382683i	−0.662827	−	0.382683i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.585786			−0.585786
$587$	0.382683	+	0.662827i	0.382683	+	0.662827i	0.991445	−	0.130526i	$-0.0416667\pi$
$587$	0.382683	+	0.662827i	0.382683	+	0.662827i	−0.608761	+	0.793353i	$0.708333\pi$
$588$	−0.400100	−	0.107206i	−0.400100	−	0.107206i
$589$		0			0
$590$	0.541196	−	0.224171i	0.541196	−	0.224171i
$591$	0.478235	+	1.78480i	0.478235	+	1.78480i
$592$		0			0
$593$	−1.84776			−1.84776			−0.923880	−	0.382683i	$-0.875000\pi$
$593$	−1.84776			−1.84776			−0.923880	+	0.382683i	$0.875000\pi$
$594$	1.22474	+	0.707107i	1.22474	+	0.707107i
$595$		0			0
$596$	−0.0820522	+	0.306223i	−0.0820522	+	0.306223i
$597$	1.00000	−	1.00000i	1.00000	−	1.00000i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	−0.541196	−	0.937379i	−0.541196	−	0.937379i
$601$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$601$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.46968	+	1.91532i	1.46968	+	1.91532i
$606$		0			0
$607$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$608$		0			0
$609$		0			0
$610$	−1.00000	−	0.414214i	−1.00000	−	0.414214i
$611$		0			0
$612$		0			0
$613$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$613$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$614$		0			0
$615$	0.465926	+	0.607206i	0.465926	+	0.607206i
$616$		0			0
$617$	0.923880	−	1.60021i	0.923880	−	1.60021i	0.130526	−	0.991445i	$-0.458333\pi$
$617$	0.923880	−	1.60021i	0.923880	−	1.60021i	0.793353	−	0.608761i	$-0.208333\pi$
$618$	−0.541196	+	0.937379i	−0.541196	+	0.937379i
$619$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$619$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$			1.00000i			1.00000i
$626$		0			0
$627$		0			0
$628$	−0.565826	+	0.151613i	−0.565826	+	0.151613i
$629$		0			0
$630$		0			0
$631$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$631$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$632$			1.53073i			1.53073i
$633$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$634$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−0.198092	+	0.739288i	−0.198092	+	0.739288i
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$643$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$644$		0			0
$645$	1.30656	+	0.541196i	1.30656	+	0.541196i
$646$		0			0
$647$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$647$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$648$	0.541196	+	0.937379i	0.541196	+	0.937379i
$649$	−1.41421			−1.41421
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$653$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$654$		0			0
$655$		0			0
$656$	0.0820522	+	0.306223i	0.0820522	+	0.306223i
$657$		0			0
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$	0.0999004	+	0.758819i	0.0999004	+	0.758819i
$661$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$661$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$662$		0			0
$663$		0			0
$664$		−	2.00000i		−	2.00000i
$665$		0			0
$666$		0			0
$667$		0			0
$668$			0.317025i			0.317025i
$669$		0			0
$670$		0			0
$671$	1.84776	+	1.84776i	1.84776	+	1.84776i
$672$		0			0
$673$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$674$	1.47858	+	0.396183i	1.47858	+	0.396183i
$675$		−	1.00000i		−	1.00000i
$676$		0			0
$677$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$677$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.541196	−	0.541196i	0.541196	−	0.541196i
$682$		0			0
$683$	0.382683	−	0.662827i	0.382683	−	0.662827i	−0.608761	−	0.793353i	$-0.708333\pi$
$683$	0.382683	−	0.662827i	0.382683	−	0.662827i	0.991445	+	0.130526i	$0.0416667\pi$
$684$		0			0
$685$	−0.465926	−	0.607206i	−0.465926	−	0.607206i
$686$		0			0
$687$		0			0
$688$	0.414214	+	0.414214i	0.414214	+	0.414214i
$689$		0			0
$690$		0			0
$691$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$691$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$		0			0
$704$	−0.478235	+	1.78480i	−0.478235	+	1.78480i
$705$	−1.12484	+	1.46593i	−1.12484	+	1.46593i
$706$	−0.507306	−	0.292893i	−0.507306	−	0.292893i
$707$		0			0
$708$	−0.274552	−	0.158513i	−0.274552	−	0.158513i
$709$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$709$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$710$	0.541196	−	0.224171i	0.541196	−	0.224171i
$711$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$712$	1.93185	+	0.517638i	1.93185	+	0.517638i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.382683	+	0.662827i	0.382683	+	0.662827i
$718$	1.36603	+	0.366025i	1.36603	+	0.366025i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	0.158513	−	0.382683i	0.158513	−	0.382683i
$721$		0			0
$722$	0.662827	+	0.382683i	0.662827	+	0.382683i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	−0.478235	+	1.78480i	−0.478235	+	1.78480i
$727$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$727$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$728$		0			0
$729$			1.00000i			1.00000i
$730$		0			0
$731$		0			0
$732$	0.151613	+	0.565826i	0.151613	+	0.565826i
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$	−1.04551	+	0.280144i	−1.04551	+	0.280144i
$735$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$736$		0			0
$737$		0			0
$738$	−0.151613	+	0.565826i	−0.151613	+	0.565826i
$739$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$739$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.60021	−	0.923880i	1.60021	−	0.923880i	0.608761	−	0.793353i	$-0.291667\pi$
$743$	1.60021	−	0.923880i	1.60021	−	0.923880i	0.991445	−	0.130526i	$-0.0416667\pi$
$744$		0			0
$745$	0.758819	+	0.0999004i	0.758819	+	0.0999004i
$746$	−1.08239	+	1.08239i	−1.08239	+	1.08239i
$747$	0.923880	−	1.60021i	0.923880	−	1.60021i
$748$		0			0
$749$		0			0
$750$	−0.607206	+	0.465926i	−0.607206	+	0.465926i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−0.662827	+	0.382683i	−0.662827	+	0.382683i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.517638	+	1.93185i	−0.517638	+	1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$757$	−0.517638	+	1.93185i	−0.517638	+	1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.793353	−	0.608761i	$-0.208333\pi$
$761$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.991445	+	0.130526i	$0.0416667\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$			1.41421i			1.41421i
$767$		0			0
$768$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$769$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$769$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.60021	−	0.923880i	−1.60021	−	0.923880i	−0.991445	−	0.130526i	$-0.958333\pi$
$773$	−1.60021	−	0.923880i	−1.60021	−	0.923880i	−0.608761	−	0.793353i	$-0.708333\pi$
$774$	0.280144	+	1.04551i	0.280144	+	1.04551i
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−1.41421			−1.41421
$782$		0			0
$783$		0			0
$784$	−0.207107	+	0.358719i	−0.207107	+	0.358719i
$785$	0.541196	+	1.30656i	0.541196	+	1.30656i
$786$		0			0
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	−0.765367			−0.765367
$789$		0			0
$790$	1.07313	−	0.141281i	1.07313	−	0.141281i
$791$		0			0
$792$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.292893	+	0.507306i	0.292893	+	0.507306i
$797$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$797$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$798$		0			0
$799$		0			0
$800$	0.739288	−	0.198092i	0.739288	−	0.198092i
$801$	1.30656	+	1.30656i	1.30656	+	1.30656i
$802$	0.565826	−	0.151613i	0.565826	−	0.151613i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$809$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$810$	0.607206	−	0.465926i	0.607206	−	0.465926i
$811$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$811$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−0.292893	+	0.121320i	−0.292893	+	0.121320i
$821$	1.78480	+	0.478235i	1.78480	+	0.478235i	0.991445	−	0.130526i	$-0.0416667\pi$
$821$	1.78480	+	0.478235i	1.78480	+	0.478235i	0.793353	+	0.608761i	$0.208333\pi$
$822$	0.151613	−	0.565826i	0.151613	−	0.565826i
$823$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$823$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$824$	−1.08239	−	1.08239i	−1.08239	−	1.08239i
$825$	1.78480	−	0.478235i	1.78480	−	0.478235i
$826$		0			0
$827$		−	1.84776i		−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$827$		−	1.84776i		−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$828$		0			0
$829$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$829$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$830$	−1.40211	+	0.184592i	−1.40211	+	0.184592i
$831$		−	1.41421i		−	1.41421i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.758819	−	0.0999004i	0.758819	−	0.0999004i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.478235	−	1.78480i	−0.478235	−	1.78480i	−0.608761	−	0.793353i	$-0.708333\pi$
$839$	−0.478235	−	1.78480i	−0.478235	−	1.78480i	0.130526	−	0.991445i	$-0.458333\pi$
$840$		0			0
$841$	0.500000	−	0.866025i	0.500000	−	0.866025i
$842$		0			0
$843$	0.923880	+	1.60021i	0.923880	+	1.60021i
$844$	0.585786			0.585786
$845$		0			0
$846$	−1.41421			−1.41421
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.274552	−	0.158513i	−0.274552	−	0.158513i
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$857$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$858$		0			0
$859$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$859$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$860$	−0.356604	+	0.464736i	−0.356604	+	0.464736i
$861$		0			0
$862$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$863$			0.765367i			0.765367i	0.923880	+	0.382683i	$0.125000\pi$
$863$			0.765367i			0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$864$	−0.739288	+	0.198092i	−0.739288	+	0.198092i
$865$		0			0
$866$	1.08239	+	1.08239i	1.08239	+	1.08239i
$867$	0.965926	−	0.258819i	0.965926	−	0.258819i
$868$		0			0
$869$	−2.52409	−	0.676327i	−2.52409	−	0.676327i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$	0.541196	−	0.541196i	0.541196	−	0.541196i
$880$	0.758819	+	0.0999004i	0.758819	+	0.0999004i
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$	−0.662827	+	0.382683i	−0.662827	+	0.382683i
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$		0			0
$885$	−0.292893	+	0.707107i	−0.292893	+	0.707107i
$886$		0			0
$887$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$887$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$888$		0			0
$889$		0			0
$890$	0.184592	−	1.40211i	0.184592	−	1.40211i
$891$	−1.78480	+	0.478235i	−1.78480	+	0.478235i
$892$		0			0
$893$		0			0
$894$	0.292893	+	0.507306i	0.292893	+	0.507306i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.414214	−	0.414214i	0.414214	−	0.414214i
$899$		0			0
$900$	0.400100	+	0.107206i	0.400100	+	0.107206i
$901$		0			0
$902$	−1.08239			−1.08239
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$907$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$908$	0.158513	+	0.274552i	0.158513	+	0.274552i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	3.29788	+	0.883663i	3.29788	+	0.883663i
$914$		0			0
$915$	1.30656	−	0.541196i	1.30656	−	0.541196i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$919$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$920$		0			0
$921$		0			0
$922$	1.00000	−	1.00000i	1.00000	−	1.00000i
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$928$		0			0
$929$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.793353	−	0.608761i	$-0.208333\pi$
$929$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.991445	+	0.130526i	$0.0416667\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$937$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$938$		0			0
$939$		0			0
$940$	−0.465926	−	0.607206i	−0.465926	−	0.607206i
$941$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	−0.923880	−	0.382683i	$-0.875000\pi$
$941$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	0.382683	+	0.923880i	$0.375000\pi$
$942$	−0.541196	+	0.937379i	−0.541196	+	0.937379i
$943$		0			0
$944$	−0.224171	+	0.224171i	−0.224171	+	0.224171i
$945$		0			0
$946$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$947$	−1.60021	+	0.923880i	−1.60021	+	0.923880i	−0.608761	+	0.793353i	$0.708333\pi$
$947$	−1.60021	+	0.923880i	−1.60021	+	0.923880i	−0.991445	+	0.130526i	$0.958333\pi$
$948$	−0.414214	−	0.414214i	−0.414214	−	0.414214i
$949$		0			0
$950$		0			0
$951$	1.78480	+	0.478235i	1.78480	+	0.478235i
$952$		0			0
$953$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$953$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$954$		0			0
$955$		0			0
$956$	−0.306223	+	0.0820522i	−0.306223	+	0.0820522i
$957$		0			0
$958$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$959$		0			0
$960$	0.793353	+	0.608761i	0.793353	+	0.608761i
$961$		−	1.00000i		−	1.00000i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−2.26303	−	1.30656i	−2.26303	−	1.30656i
$969$		0			0
$970$		0			0
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$	−0.400100	−	0.107206i	−0.400100	−	0.107206i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.585786			0.585786
$977$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.793353	+	0.608761i	$0.208333\pi$
$977$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.130526	+	0.991445i	$0.458333\pi$
$978$		0			0
$979$	−1.70711	+	2.95680i	−1.70711	+	2.95680i
$980$	−0.382683	−	0.158513i	−0.382683	−	0.158513i
$981$		0			0
$982$		0			0
$983$	0.765367			0.765367			0.382683	−	0.923880i	$-0.375000\pi$
$983$	0.765367			0.765367			0.382683	+	0.923880i	$0.375000\pi$
$984$	−0.717439	−	0.414214i	−0.717439	−	0.414214i
$985$	0.241181	+	1.83195i	0.241181	+	1.83195i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	1.12197	+	0.860919i	1.12197	+	0.860919i
$991$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.12197	−	0.860919i	1.12197	−	0.860919i
$996$	0.541196	+	0.541196i	0.541196	+	0.541196i
$997$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$997$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2535.1.bc.a.2117.3		16
3.2	odd	2	inner	2535.1.bc.a.2117.2		16
5.3	odd	4		2535.1.bn.a.1103.3		16
13.2	odd	12		2535.1.j.a.2267.3	yes	8
13.3	even	3		2535.1.u.a.437.2	yes	8
13.4	even	6	inner	2535.1.bc.a.1502.2		16
13.5	odd	4		2535.1.bn.a.587.3		16
13.6	odd	12		2535.1.bn.a.1202.2		16
13.7	odd	12		2535.1.bn.a.1202.3		16
13.8	odd	4		2535.1.bn.a.587.2		16
13.9	even	3	inner	2535.1.bc.a.1502.3		16
13.10	even	6		2535.1.u.a.437.3	yes	8
13.11	odd	12		2535.1.j.a.2267.2	yes	8
13.12	even	2	inner	2535.1.bc.a.2117.2		16
15.8	even	4		2535.1.bn.a.1103.2		16
39.2	even	12		2535.1.j.a.2267.2	yes	8
39.5	even	4		2535.1.bn.a.587.2		16
39.8	even	4		2535.1.bn.a.587.3		16
39.11	even	12		2535.1.j.a.2267.3	yes	8
39.17	odd	6	inner	2535.1.bc.a.1502.3		16
39.20	even	12		2535.1.bn.a.1202.2		16
39.23	odd	6		2535.1.u.a.437.2	yes	8
39.29	odd	6		2535.1.u.a.437.3	yes	8
39.32	even	12		2535.1.bn.a.1202.3		16
39.35	odd	6	inner	2535.1.bc.a.1502.2		16
39.38	odd	2	CM	2535.1.bc.a.2117.3		16
65.3	odd	12		2535.1.j.a.1958.3	yes	8
65.8	even	4	inner	2535.1.bc.a.2108.3		16
65.18	even	4	inner	2535.1.bc.a.2108.2		16
65.23	odd	12		2535.1.j.a.1958.2	✓	8
65.28	even	12		2535.1.u.a.1253.3	yes	8
65.33	even	12	inner	2535.1.bc.a.188.3		16
65.38	odd	4		2535.1.bn.a.1103.2		16
65.43	odd	12		2535.1.bn.a.488.3		16
65.48	odd	12		2535.1.bn.a.488.2		16
65.58	even	12	inner	2535.1.bc.a.188.2		16
65.63	even	12		2535.1.u.a.1253.2	yes	8
195.8	odd	4	inner	2535.1.bc.a.2108.2		16
195.23	even	12		2535.1.j.a.1958.3	yes	8
195.38	even	4		2535.1.bn.a.1103.3		16
195.68	even	12		2535.1.j.a.1958.2	✓	8
195.83	odd	4	inner	2535.1.bc.a.2108.3		16
195.98	odd	12	inner	2535.1.bc.a.188.2		16
195.113	even	12		2535.1.bn.a.488.3		16
195.128	odd	12		2535.1.u.a.1253.3	yes	8
195.158	odd	12		2535.1.u.a.1253.2	yes	8
195.173	even	12		2535.1.bn.a.488.2		16
195.188	odd	12	inner	2535.1.bc.a.188.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.1.j.a.1958.2	✓	8	65.23	odd	12
2535.1.j.a.1958.2	✓	8	195.68	even	12
2535.1.j.a.1958.3	yes	8	65.3	odd	12
2535.1.j.a.1958.3	yes	8	195.23	even	12
2535.1.j.a.2267.2	yes	8	13.11	odd	12
2535.1.j.a.2267.2	yes	8	39.2	even	12
2535.1.j.a.2267.3	yes	8	13.2	odd	12
2535.1.j.a.2267.3	yes	8	39.11	even	12
2535.1.u.a.437.2	yes	8	13.3	even	3
2535.1.u.a.437.2	yes	8	39.23	odd	6
2535.1.u.a.437.3	yes	8	13.10	even	6
2535.1.u.a.437.3	yes	8	39.29	odd	6
2535.1.u.a.1253.2	yes	8	65.63	even	12
2535.1.u.a.1253.2	yes	8	195.158	odd	12
2535.1.u.a.1253.3	yes	8	65.28	even	12
2535.1.u.a.1253.3	yes	8	195.128	odd	12
2535.1.bc.a.188.2		16	65.58	even	12	inner
2535.1.bc.a.188.2		16	195.98	odd	12	inner
2535.1.bc.a.188.3		16	65.33	even	12	inner
2535.1.bc.a.188.3		16	195.188	odd	12	inner
2535.1.bc.a.1502.2		16	13.4	even	6	inner
2535.1.bc.a.1502.2		16	39.35	odd	6	inner
2535.1.bc.a.1502.3		16	13.9	even	3	inner
2535.1.bc.a.1502.3		16	39.17	odd	6	inner
2535.1.bc.a.2108.2		16	65.18	even	4	inner
2535.1.bc.a.2108.2		16	195.8	odd	4	inner
2535.1.bc.a.2108.3		16	65.8	even	4	inner
2535.1.bc.a.2108.3		16	195.83	odd	4	inner
2535.1.bc.a.2117.2		16	3.2	odd	2	inner
2535.1.bc.a.2117.2		16	13.12	even	2	inner
2535.1.bc.a.2117.3		16	1.1	even	1	trivial
2535.1.bc.a.2117.3		16	39.38	odd	2	CM
2535.1.bn.a.488.2		16	65.48	odd	12
2535.1.bn.a.488.2		16	195.173	even	12
2535.1.bn.a.488.3		16	65.43	odd	12
2535.1.bn.a.488.3		16	195.113	even	12
2535.1.bn.a.587.2		16	13.8	odd	4
2535.1.bn.a.587.2		16	39.5	even	4
2535.1.bn.a.587.3		16	13.5	odd	4
2535.1.bn.a.587.3		16	39.8	even	4
2535.1.bn.a.1103.2		16	15.8	even	4
2535.1.bn.a.1103.2		16	65.38	odd	4
2535.1.bn.a.1103.3		16	5.3	odd	4
2535.1.bn.a.1103.3		16	195.38	even	4
2535.1.bn.a.1202.2		16	13.6	odd	12
2535.1.bn.a.1202.2		16	39.20	even	12
2535.1.bn.a.1202.3		16	13.7	odd	12
2535.1.bn.a.1202.3		16	39.32	even	12

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:	\( N \)	\(=\)	\( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2535.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.382683 + 0.662827i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.207107 - 0.358719i) q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.198092 - 0.739288i) q^{6} +1.08239 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.382683 + 0.662827i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.207107 - 0.358719i) q^{4} +(-0.923880 - 0.382683i) q^{5} +(-0.198092 - 0.739288i) q^{6} +1.08239 q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.0999004 - 0.758819i) q^{10} +(-0.478235 + 1.78480i) q^{11} +(-0.292893 + 0.292893i) q^{12} +(0.793353 + 0.608761i) q^{15} +(0.207107 + 0.358719i) q^{16} +0.765367i q^{18} +(-0.328618 + 0.252157i) q^{20} +(-1.36603 + 0.366025i) q^{22} +(-1.04551 - 0.280144i) q^{24} +(0.707107 + 0.707107i) q^{25} +(-0.707107 - 0.707107i) q^{27} +(-0.0999004 + 0.758819i) q^{30} +(0.382683 - 0.662827i) q^{32} +(0.923880 - 1.60021i) q^{33} +(0.358719 - 0.207107i) q^{36} +(-1.00000 - 0.414214i) q^{40} +(0.739288 + 0.198092i) q^{41} +(1.36603 - 0.366025i) q^{43} +(0.541196 + 0.541196i) q^{44} +(-0.608761 - 0.793353i) q^{45} +1.84776i q^{47} +(-0.107206 - 0.400100i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.198092 + 0.739288i) q^{50} +(0.198092 - 0.739288i) q^{54} +(1.12484 - 1.46593i) q^{55} +(0.198092 + 0.739288i) q^{59} +(0.382683 - 0.158513i) q^{60} +(0.707107 - 1.22474i) q^{61} +1.00000 q^{64} +1.41421 q^{66} +(0.198092 + 0.739288i) q^{71} +(0.937379 + 0.541196i) q^{72} +(-0.500000 - 0.866025i) q^{75} +1.41421i q^{79} +(-0.0540657 - 0.410670i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.151613 + 0.565826i) q^{82} -1.84776i q^{83} +(0.765367 + 0.765367i) q^{86} +(-0.517638 + 1.93185i) q^{88} +(1.78480 + 0.478235i) q^{89} +(0.292893 - 0.707107i) q^{90} +(-1.22474 + 0.707107i) q^{94} +(-0.541196 + 0.541196i) q^{96} +(-0.382683 + 0.662827i) q^{98} +(-1.30656 + 1.30656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4}+O(q^{10}) \) 16 * q - 8 * q^4	\( 16 q - 8 q^{4} - 16 q^{12} - 8 q^{16} - 8 q^{22} - 16 q^{40} + 8 q^{43} + 8 q^{48} + 8 q^{49} + 16 q^{64} - 8 q^{75} + 8 q^{81} + 8 q^{82} + 16 q^{90}+O(q^{100}) \) 16 * q - 8 * q^4 - 16 * q^12 - 8 * q^16 - 8 * q^22 - 16 * q^40 + 8 * q^43 + 8 * q^48 + 8 * q^49 + 16 * q^64 - 8 * q^75 + 8 * q^81 + 8 * q^82 + 16 * q^90

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