LMFDB - Embedded newform 2535.1.bc.a.2108.4

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			2108.4
Root			$0.608761 + 0.793353i$ of defining polynomial
Character	$\chi$	$=$	2535.2108
Dual form			2535.1.bc.a.1502.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.923880 + 1.60021i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.20711 + 2.09077i) q^{4} +(0.382683 + 0.923880i) q^{5} +(-1.78480 + 0.478235i) q^{6} -2.61313 q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.923880 + 1.60021i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.20711 + 2.09077i) q^{4} +(0.382683 + 0.923880i) q^{5} +(-1.78480 + 0.478235i) q^{6} -2.61313 q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.12484 + 1.46593i) q^{10} +(0.739288 + 0.198092i) q^{11} +(-1.70711 - 1.70711i) q^{12} +(-0.991445 + 0.130526i) q^{15} +(-1.20711 - 2.09077i) q^{16} -1.84776i q^{18} +(-2.39356 - 0.315118i) q^{20} +(0.366025 + 1.36603i) q^{22} +(0.676327 - 2.52409i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.707107 - 0.707107i) q^{27} +(-1.12484 - 1.46593i) q^{30} +(0.923880 - 1.60021i) q^{32} +(-0.382683 + 0.662827i) q^{33} +(2.09077 - 1.20711i) q^{36} +(-1.00000 - 2.41421i) q^{40} +(0.478235 - 1.78480i) q^{41} +(-0.366025 - 1.36603i) q^{43} +(-1.30656 + 1.30656i) q^{44} +(0.130526 - 0.991445i) q^{45} +0.765367i q^{47} +(2.33195 - 0.624844i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.78480 - 0.478235i) q^{50} +(1.78480 + 0.478235i) q^{54} +(0.0999004 + 0.758819i) q^{55} +(1.78480 - 0.478235i) q^{59} +(0.923880 - 2.23044i) q^{60} +(-0.707107 + 1.22474i) q^{61} +1.00000 q^{64} -1.41421 q^{66} +(1.78480 - 0.478235i) q^{71} +(2.26303 + 1.30656i) q^{72} +(-0.500000 - 0.866025i) q^{75} +1.41421i q^{79} +(1.46968 - 1.91532i) q^{80} +(0.500000 + 0.866025i) q^{81} +(3.29788 - 0.883663i) q^{82} -0.765367i q^{83} +(1.84776 - 1.84776i) q^{86} +(-1.93185 - 0.517638i) q^{88} +(-0.198092 + 0.739288i) q^{89} +(1.70711 - 0.707107i) q^{90} +(-1.22474 + 0.707107i) q^{94} +(1.30656 + 1.30656i) q^{96} +(-0.923880 + 1.60021i) q^{98} +(-0.541196 - 0.541196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2535\mathbb{Z}\right)^\times$.

$n$	$1522$	$1691$	$1861$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{12}\right)$

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 $

$2$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.793353	+	0.608761i	$0.208333\pi$
$2$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.130526	+	0.991445i	$0.458333\pi$
$3$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$3$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$4$	−1.20711	+	2.09077i	−1.20711	+	2.09077i
$5$	0.382683	+	0.923880i	0.382683	+	0.923880i
$5$	0.382683	+	0.923880i	0.382683	+	0.923880i
$6$	−1.78480	+	0.478235i	−1.78480	+	0.478235i
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$	−2.61313			−2.61313
$9$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$10$	−1.12484	+	1.46593i	−1.12484	+	1.46593i
$11$	0.739288	+	0.198092i	0.739288	+	0.198092i	0.608761	−	0.793353i	$-0.291667\pi$
$11$	0.739288	+	0.198092i	0.739288	+	0.198092i	0.130526	+	0.991445i	$0.458333\pi$
$12$	−1.70711	−	1.70711i	−1.70711	−	1.70711i
$13$		0			0
$13$		0			0
$14$		0			0
$15$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$16$	−1.20711	−	2.09077i	−1.20711	−	2.09077i
$17$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$17$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$18$		−	1.84776i		−	1.84776i
$19$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$19$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$20$	−2.39356	−	0.315118i	−2.39356	−	0.315118i
$21$		0			0
$22$	0.366025	+	1.36603i	0.366025	+	1.36603i
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$	0.676327	−	2.52409i	0.676327	−	2.52409i
$25$	−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	$0.833333\pi$
$30$	−1.12484	−	1.46593i	−1.12484	−	1.46593i
$31$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$31$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$32$	0.923880	−	1.60021i	0.923880	−	1.60021i
$33$	−0.382683	+	0.662827i	−0.382683	+	0.662827i
$34$		0			0
$35$		0			0
$36$	2.09077	−	1.20711i	2.09077	−	1.20711i
$37$		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	−	2.41421i	−1.00000	−	2.41421i
$41$	0.478235	−	1.78480i	0.478235	−	1.78480i	−0.130526	−	0.991445i	$-0.541667\pi$
$41$	0.478235	−	1.78480i	0.478235	−	1.78480i	0.608761	−	0.793353i	$-0.291667\pi$
$42$		0			0
$43$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$43$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$44$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$45$	0.130526	−	0.991445i	0.130526	−	0.991445i
$46$		0			0
$47$			0.765367i			0.765367i	0.923880	+	0.382683i	$0.125000\pi$
$47$			0.765367i			0.765367i	−0.923880	+	0.382683i	$0.875000\pi$
$48$	2.33195	−	0.624844i	2.33195	−	0.624844i
$49$	0.500000	+	0.866025i	0.500000	+	0.866025i
$50$	−1.78480	−	0.478235i	−1.78480	−	0.478235i
$51$		0			0
$52$		0			0
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$	1.78480	+	0.478235i	1.78480	+	0.478235i
$55$	0.0999004	+	0.758819i	0.0999004	+	0.758819i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.793353	−	0.608761i	$-0.208333\pi$
$59$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.991445	+	0.130526i	$0.0416667\pi$
$60$	0.923880	−	2.23044i	0.923880	−	2.23044i
$61$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$61$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$62$		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
$71$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.793353	−	0.608761i	$-0.208333\pi$
$71$	1.78480	−	0.478235i	1.78480	−	0.478235i	0.991445	+	0.130526i	$0.0416667\pi$
$72$	2.26303	+	1.30656i	2.26303	+	1.30656i
$73$		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	$0.750000\pi$
$80$	1.46968	−	1.91532i	1.46968	−	1.91532i
$81$	0.500000	+	0.866025i	0.500000	+	0.866025i
$82$	3.29788	−	0.883663i	3.29788	−	0.883663i
$83$		−	0.765367i		−	0.765367i	−0.923880	−	0.382683i	$-0.875000\pi$
$83$		−	0.765367i		−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$84$		0			0
$85$		0			0
$86$	1.84776	−	1.84776i	1.84776	−	1.84776i
$87$		0			0
$88$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$89$	−0.198092	+	0.739288i	−0.198092	+	0.739288i	0.793353	+	0.608761i	$0.208333\pi$
$89$	−0.198092	+	0.739288i	−0.198092	+	0.739288i	−0.991445	+	0.130526i	$0.958333\pi$
$90$	1.70711	−	0.707107i	1.70711	−	0.707107i
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$95$		0			0
$96$	1.30656	+	1.30656i	1.30656	+	1.30656i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	−0.923880	+	1.60021i	−0.923880	+	1.60021i
$99$	−0.541196	−	0.541196i	−0.541196	−	0.541196i
$100$	−0.624844	−	2.33195i	−0.624844	−	2.33195i
$101$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$107$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$108$	0.624844	+	2.33195i	0.624844	+	2.33195i
$109$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$109$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$110$	−1.12197	+	0.860919i	−1.12197	+	0.860919i
$111$		0			0
$112$		0			0
$113$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$113$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	2.41421	+	2.41421i	2.41421	+	2.41421i
$119$		0			0
$120$	2.59077	−	0.341081i	2.59077	−	0.341081i
$121$	−0.358719	−	0.207107i	−0.358719	−	0.207107i
$122$	−2.61313			−2.61313
$123$	1.60021	+	0.923880i	1.60021	+	0.923880i
$124$		0			0
$125$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$126$		0			0
$127$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$127$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$128$		0			0
$129$	1.41421			1.41421
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	−0.923880	−	1.60021i	−0.923880	−	1.60021i
$133$		0			0
$134$		0			0
$135$	0.923880	+	0.382683i	0.923880	+	0.382683i
$136$		0			0
$137$	−1.60021	−	0.923880i	−1.60021	−	0.923880i	−0.991445	−	0.130526i	$-0.958333\pi$
$137$	−1.60021	−	0.923880i	−1.60021	−	0.923880i	−0.608761	−	0.793353i	$-0.708333\pi$
$138$		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
$141$	−0.739288	−	0.198092i	−0.739288	−	0.198092i
$142$	2.41421	+	2.41421i	2.41421	+	2.41421i
$143$		0			0
$144$			2.41421i			2.41421i
$145$		0			0
$146$		0			0
$147$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$148$		0			0
$149$	−0.478235	−	1.78480i	−0.478235	−	1.78480i	−0.608761	−	0.793353i	$-0.708333\pi$
$149$	−0.478235	−	1.78480i	−0.478235	−	1.78480i	0.130526	−	0.991445i	$-0.458333\pi$
$150$	0.923880	−	1.60021i	0.923880	−	1.60021i
$151$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$151$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$152$		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			$\pi$
$158$	−2.26303	+	1.30656i	−2.26303	+	1.30656i
$159$		0			0
$160$	1.83195	+	0.241181i	1.83195	+	0.241181i
$161$		0			0
$162$	−0.923880	+	1.60021i	−0.923880	+	1.60021i
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$	3.15432	+	3.15432i	3.15432	+	3.15432i
$165$	−0.758819	−	0.0999004i	−0.758819	−	0.0999004i
$166$	1.22474	−	0.707107i	1.22474	−	0.707107i
$167$	1.60021	−	0.923880i	1.60021	−	0.923880i	0.608761	−	0.793353i	$-0.291667\pi$
$167$	1.60021	−	0.923880i	1.60021	−	0.923880i	0.991445	−	0.130526i	$-0.0416667\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$		0			0
$172$	3.29788	+	0.883663i	3.29788	+	0.883663i
$173$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$173$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$174$		0			0
$175$		0			0
$176$	−0.478235	−	1.78480i	−0.478235	−	1.78480i
$177$			1.84776i			1.84776i
$178$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$	1.91532	+	1.46968i	1.91532	+	1.46968i
$181$		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
$188$	−1.60021	−	0.923880i	−1.60021	−	0.923880i
$189$		0			0
$190$		0			0
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$193$		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
$196$	−2.41421			−2.41421
$197$	0.382683	+	0.662827i	0.382683	+	0.662827i	0.991445	−	0.130526i	$-0.0416667\pi$
$197$	0.382683	+	0.662827i	0.382683	+	0.662827i	−0.608761	+	0.793353i	$0.708333\pi$
$198$	0.366025	−	1.36603i	0.366025	−	1.36603i
$199$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$199$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$200$	1.84776	−	1.84776i	1.84776	−	1.84776i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	1.83195	−	0.241181i	1.83195	−	0.241181i
$206$	−2.52409	−	0.676327i	−2.52409	−	0.676327i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$211$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$212$		0			0
$213$			1.84776i			1.84776i
$214$		0			0
$215$	1.12197	−	0.860919i	1.12197	−	0.860919i
$216$	−1.84776	+	1.84776i	−1.84776	+	1.84776i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−1.70711	−	0.707107i	−1.70711	−	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
$225$	0.965926	−	0.258819i	0.965926	−	0.258819i
$226$		0			0
$227$	−0.923880	+	1.60021i	−0.923880	+	1.60021i	−0.130526	+	0.991445i	$0.541667\pi$
$227$	−0.923880	+	1.60021i	−0.923880	+	1.60021i	−0.793353	+	0.608761i	$0.791667\pi$
$228$		0			0
$229$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$229$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$233$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$234$		0			0
$235$	−0.707107	+	0.292893i	−0.707107	+	0.292893i
$236$	−1.15456	+	4.30888i	−1.15456	+	4.30888i
$237$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$238$		0			0
$239$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$239$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.923880	−	0.382683i	$-0.125000\pi$
$240$	1.46968	+	1.91532i	1.46968	+	1.91532i
$241$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$241$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$242$		−	0.765367i		−	0.765367i
$243$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$244$	−1.70711	−	2.95680i	−1.70711	−	2.95680i
$245$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$246$			3.41421i			3.41421i
$247$		0			0
$248$		0			0
$249$	0.739288	+	0.198092i	0.739288	+	0.198092i
$250$	−0.241181	−	1.83195i	−0.241181	−	1.83195i
$251$		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		0.258819	−	0.965926i	$-0.416667\pi$
$257$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$258$	1.30656	+	2.26303i	1.30656	+	2.26303i
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$263$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$264$	1.00000	−	1.73205i	1.00000	−	1.73205i
$265$		0			0
$266$		0			0
$267$	−0.662827	−	0.382683i	−0.662827	−	0.382683i
$268$		0			0
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$	0.241181	+	1.83195i	0.241181	+	1.83195i
$271$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$271$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$272$		0			0
$273$		0			0
$274$		−	3.41421i		−	3.41421i
$275$	−0.662827	+	0.382683i	−0.662827	+	0.382683i
$276$		0			0
$277$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$277$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	−0.923880	−	0.382683i	$-0.875000\pi$
$281$	−0.541196	+	0.541196i	−0.541196	+	0.541196i	0.382683	+	0.923880i	$0.375000\pi$
$282$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$283$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$283$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$284$	−1.15456	+	4.30888i	−1.15456	+	4.30888i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.60021	+	0.923880i	−1.60021	+	0.923880i
$289$	0.866025	−	0.500000i	0.866025	−	0.500000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.923880	+	1.60021i	−0.923880	+	1.60021i	−0.130526	+	0.991445i	$0.541667\pi$
$293$	−0.923880	+	1.60021i	−0.923880	+	1.60021i	−0.793353	+	0.608761i	$0.791667\pi$
$294$	−1.30656	−	1.30656i	−1.30656	−	1.30656i
$295$	1.12484	+	1.46593i	1.12484	+	1.46593i
$296$		0			0
$297$	0.662827	−	0.382683i	0.662827	−	0.382683i
$298$	2.41421	−	2.41421i	2.41421	−	2.41421i
$299$		0			0
$300$	2.41421			2.41421
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.40211	−	0.184592i	−1.40211	−	0.184592i
$306$		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	$-0.250000\pi$
$313$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$314$	−2.52409	−	0.676327i	−2.52409	−	0.676327i
$315$		0			0
$316$	−2.95680	−	1.70711i	−2.95680	−	1.70711i
$317$	0.765367			0.765367			0.382683	−	0.923880i	$-0.375000\pi$
$317$	0.765367			0.765367			0.382683	+	0.923880i	$0.375000\pi$
$318$		0			0
$319$		0			0
$320$	0.382683	+	0.923880i	0.382683	+	0.923880i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−2.41421			−2.41421
$325$		0			0
$326$		0			0
$327$		0			0
$328$	−1.24969	+	4.66390i	−1.24969	+	4.66390i
$329$		0			0
$330$	−0.541196	−	1.30656i	−0.541196	−	1.30656i
$331$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$331$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$332$	1.60021	+	0.923880i	1.60021	+	0.923880i
$333$		0			0
$334$	2.95680	+	1.70711i	2.95680	+	1.70711i
$335$		0			0
$336$		0			0
$337$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$337$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$		0			0
$344$	0.956470	+	3.56960i	0.956470	+	3.56960i
$345$		0			0
$346$		0			0
$347$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$347$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$348$		0			0
$349$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$349$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$350$		0			0
$351$		0			0
$352$	1.00000	−	1.00000i	1.00000	−	1.00000i
$353$	1.60021	−	0.923880i	1.60021	−	0.923880i	0.608761	−	0.793353i	$-0.291667\pi$
$353$	1.60021	−	0.923880i	1.60021	−	0.923880i	0.991445	−	0.130526i	$-0.0416667\pi$
$354$	−2.95680	+	1.70711i	−2.95680	+	1.70711i
$355$	1.12484	+	1.46593i	1.12484	+	1.46593i
$356$	−1.30656	−	1.30656i	−1.30656	−	1.30656i
$357$		0			0
$358$		0			0
$359$	0.541196	+	0.541196i	0.541196	+	0.541196i	0.923880	−	0.382683i	$-0.125000\pi$
$359$	0.541196	+	0.541196i	0.541196	+	0.541196i	−0.382683	+	0.923880i	$0.625000\pi$
$360$	−0.341081	+	2.59077i	−0.341081	+	2.59077i
$361$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$362$		0			0
$363$	0.292893	−	0.292893i	0.292893	−	0.292893i
$364$		0			0
$365$		0			0
$366$	0.676327	−	2.52409i	0.676327	−	2.52409i
$367$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$367$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$368$		0			0
$369$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$373$	1.93185	−	0.517638i	1.93185	−	0.517638i	0.965926	−	0.258819i	$-0.0833333\pi$
$374$		0			0
$375$	0.608761	−	0.793353i	0.608761	−	0.793353i
$376$		−	2.00000i		−	2.00000i
$377$		0			0
$378$		0			0
$379$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$379$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.662827	+	0.382683i	0.662827	+	0.382683i	0.793353	−	0.608761i	$-0.208333\pi$
$383$	0.662827	+	0.382683i	0.662827	+	0.382683i	−0.130526	+	0.991445i	$0.541667\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$388$		0			0
$389$		0			0		1.00000			$0$
$389$		0			0		−1.00000			$\pi$
$390$		0			0
$391$		0			0
$392$	−1.30656	−	2.26303i	−1.30656	−	2.26303i
$393$		0			0
$394$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$395$	−1.30656	+	0.541196i	−1.30656	+	0.541196i
$396$	1.78480	−	0.478235i	1.78480	−	0.478235i
$397$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$397$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$398$	2.61313			2.61313
$399$		0			0
$400$	2.33195	+	0.624844i	2.33195	+	0.624844i
$401$	1.78480	+	0.478235i	1.78480	+	0.478235i	0.991445	−	0.130526i	$-0.0416667\pi$
$401$	1.78480	+	0.478235i	1.78480	+	0.478235i	0.793353	+	0.608761i	$0.208333\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$409$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$410$	2.07844	+	2.70868i	2.07844	+	2.70868i
$411$	1.30656	−	1.30656i	1.30656	−	1.30656i
$412$	−0.883663	−	3.29788i	−0.883663	−	3.29788i
$413$		0			0
$414$		0			0
$415$	0.707107	−	0.292893i	0.707107	−	0.292893i
$416$		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	$-0.750000\pi$
$421$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$422$	1.30656	−	2.26303i	1.30656	−	2.26303i
$423$	0.382683	−	0.662827i	0.382683	−	0.662827i
$424$		0			0
$425$		0			0
$426$	−2.95680	+	1.70711i	−2.95680	+	1.70711i
$427$		0			0
$428$		0			0
$429$		0			0
$430$	2.41421	+	1.00000i	2.41421	+	1.00000i
$431$	0.198092	−	0.739288i	0.198092	−	0.739288i	−0.793353	−	0.608761i	$-0.791667\pi$
$431$	0.198092	−	0.739288i	0.198092	−	0.739288i	0.991445	−	0.130526i	$-0.0416667\pi$
$432$	−2.33195	−	0.624844i	−2.33195	−	0.624844i
$433$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$433$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$434$		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	$0.833333\pi$
$440$	−0.261052	−	1.98289i	−0.261052	−	1.98289i
$441$		−	1.00000i		−	1.00000i
$442$		0			0
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	−0.758819	+	0.0999004i	−0.758819	+	0.0999004i
$446$		0			0
$447$	1.84776			1.84776
$448$		0			0
$449$	−1.78480	+	0.478235i	−1.78480	+	0.478235i	−0.991445	−	0.130526i	$-0.958333\pi$
$449$	−1.78480	+	0.478235i	−1.78480	+	0.478235i	−0.793353	+	0.608761i	$0.791667\pi$
$450$	1.30656	+	1.30656i	1.30656	+	1.30656i
$451$	0.707107	−	1.22474i	0.707107	−	1.22474i
$452$		0			0
$453$		0			0
$454$	−3.41421			−3.41421
$455$		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
$461$	0.739288	−	0.198092i	0.739288	−	0.198092i	0.130526	−	0.991445i	$-0.458333\pi$
$461$	0.739288	−	0.198092i	0.739288	−	0.198092i	0.608761	+	0.793353i	$0.291667\pi$
$462$		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	$-0.750000\pi$
$467$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$468$		0			0
$469$		0			0
$470$	−1.12197	−	0.860919i	−1.12197	−	0.860919i
$471$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$472$	−4.66390	+	1.24969i	−4.66390	+	1.24969i
$473$		−	1.08239i		−	1.08239i
$474$	−0.676327	−	2.52409i	−0.676327	−	2.52409i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	3.29788	+	0.883663i	3.29788	+	0.883663i
$479$	0.198092	−	0.739288i	0.198092	−	0.739288i	−0.793353	−	0.608761i	$-0.791667\pi$
$479$	0.198092	−	0.739288i	0.198092	−	0.739288i	0.991445	−	0.130526i	$-0.0416667\pi$
$480$	−0.707107	+	1.70711i	−0.707107	+	1.70711i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	0.866025	−	0.500000i	0.866025	−	0.500000i
$485$		0			0
$486$	−1.30656	−	1.30656i	−1.30656	−	1.30656i
$487$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$487$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$488$	1.84776	−	3.20041i	1.84776	−	3.20041i
$489$		0			0
$490$	−1.83195	−	0.241181i	−1.83195	−	0.241181i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$	−3.86324	+	2.23044i	−3.86324	+	2.23044i
$493$		0			0
$494$		0			0
$495$	0.292893	−	0.707107i	0.292893	−	0.707107i
$496$		0			0
$497$		0			0
$498$	0.366025	+	1.36603i	0.366025	+	1.36603i
$499$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$499$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$500$	1.91532	−	1.46968i	1.91532	−	1.46968i
$501$	0.478235	+	1.78480i	0.478235	+	1.78480i
$502$		0			0
$503$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$503$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.739288	−	0.198092i	−0.739288	−	0.198092i	−0.130526	−	0.991445i	$-0.541667\pi$
$509$	−0.739288	−	0.198092i	−0.739288	−	0.198092i	−0.608761	+	0.793353i	$0.708333\pi$
$510$		0			0
$511$		0			0
$512$	1.84776			1.84776
$513$		0			0
$514$		0			0
$515$	−1.30656	−	0.541196i	−1.30656	−	0.541196i
$516$	−1.70711	+	2.95680i	−1.70711	+	2.95680i
$517$	−0.151613	+	0.565826i	−0.151613	+	0.565826i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$		0			0
$523$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$523$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.84776			1.84776
$529$	0.866025	+	0.500000i	0.866025	+	0.500000i
$530$		0			0
$531$	−1.78480	−	0.478235i	−1.78480	−	0.478235i
$532$		0			0
$533$		0			0
$534$		−	1.41421i		−	1.41421i
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.198092	+	0.739288i	0.198092	+	0.739288i
$540$	−1.91532	+	1.46968i	−1.91532	+	1.46968i
$541$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$541$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$547$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$548$	3.86324	−	2.23044i	3.86324	−	2.23044i
$549$	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
$554$	−1.84776	−	1.84776i	−1.84776	−	1.84776i
$555$		0			0
$556$		0			0
$557$	−1.60021	+	0.923880i	−1.60021	+	0.923880i	−0.608761	+	0.793353i	$0.708333\pi$
$557$	−1.60021	+	0.923880i	−1.60021	+	0.923880i	−0.991445	+	0.130526i	$0.958333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$	1.30656	−	1.30656i	1.30656	−	1.30656i
$565$		0			0
$566$		0			0
$567$		0			0
$568$	−4.66390	+	1.24969i	−4.66390	+	1.24969i
$569$		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			$\pi$
$578$	1.60021	+	0.923880i	1.60021	+	0.923880i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−3.41421			−3.41421
$587$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.793353	+	0.608761i	$0.208333\pi$
$587$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.130526	+	0.991445i	$0.458333\pi$
$588$	0.624844	−	2.33195i	0.624844	−	2.33195i
$589$		0			0
$590$	−1.30656	+	3.15432i	−1.30656	+	3.15432i
$591$	−0.739288	+	0.198092i	−0.739288	+	0.198092i
$592$		0			0
$593$	0.765367			0.765367			0.382683	−	0.923880i	$-0.375000\pi$
$593$	0.765367			0.765367			0.382683	+	0.923880i	$0.375000\pi$
$594$	1.22474	+	0.707107i	1.22474	+	0.707107i
$595$		0			0
$596$	4.30888	+	1.15456i	4.30888	+	1.15456i
$597$	1.00000	+	1.00000i	1.00000	+	1.00000i
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$	1.30656	+	2.26303i	1.30656	+	2.26303i
$601$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$601$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.0540657	−	0.410670i	0.0540657	−	0.410670i
$606$		0			0
$607$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$607$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$608$		0			0
$609$		0			0
$610$	−1.00000	−	2.41421i	−1.00000	−	2.41421i
$611$		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
$615$	−0.241181	+	1.83195i	−0.241181	+	1.83195i
$616$		0			0
$617$	−0.382683	+	0.662827i	−0.382683	+	0.662827i	−0.991445	−	0.130526i	$-0.958333\pi$
$617$	−0.382683	+	0.662827i	−0.382683	+	0.662827i	0.608761	+	0.793353i	$0.291667\pi$
$618$	1.30656	−	2.26303i	1.30656	−	2.26303i
$619$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$619$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$620$		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
$628$	−0.883663	−	3.29788i	−0.883663	−	3.29788i
$629$		0			0
$630$		0			0
$631$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$631$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$632$		−	3.69552i		−	3.69552i
$633$	1.36603	−	0.366025i	1.36603	−	0.366025i
$634$	0.707107	+	1.22474i	0.707107	+	1.22474i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−1.78480	−	0.478235i	−1.78480	−	0.478235i
$640$		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
$645$	0.541196	+	1.30656i	0.541196	+	1.30656i
$646$		0			0
$647$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$647$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$648$	−1.30656	−	2.26303i	−1.30656	−	2.26303i
$649$	1.41421			1.41421
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$653$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$654$		0			0
$655$		0			0
$656$	−4.30888	+	1.15456i	−4.30888	+	1.15456i
$657$		0			0
$658$		0			0
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$	1.12484	−	1.46593i	1.12484	−	1.46593i
$661$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$661$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$662$		0			0
$663$		0			0
$664$			2.00000i			2.00000i
$665$		0			0
$666$		0			0
$667$		0			0
$668$			4.46088i			4.46088i
$669$		0			0
$670$		0			0
$671$	−0.765367	+	0.765367i	−0.765367	+	0.765367i
$672$		0			0
$673$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$674$	0.956470	−	3.56960i	0.956470	−	3.56960i
$675$			1.00000i			1.00000i
$676$		0			0
$677$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$677$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−1.30656	−	1.30656i	−1.30656	−	1.30656i
$682$		0			0
$683$	0.923880	−	1.60021i	0.923880	−	1.60021i	0.130526	−	0.991445i	$-0.458333\pi$
$683$	0.923880	−	1.60021i	0.923880	−	1.60021i	0.793353	−	0.608761i	$-0.208333\pi$
$684$		0			0
$685$	0.241181	−	1.83195i	0.241181	−	1.83195i
$686$		0			0
$687$		0			0
$688$	−2.41421	+	2.41421i	−2.41421	+	2.41421i
$689$		0			0
$690$		0			0
$691$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$691$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$692$		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
$704$	0.739288	+	0.198092i	0.739288	+	0.198092i
$705$	−0.0999004	−	0.758819i	−0.0999004	−	0.758819i
$706$	2.95680	+	1.70711i	2.95680	+	1.70711i
$707$		0			0
$708$	−3.86324	−	2.23044i	−3.86324	−	2.23044i
$709$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$709$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$710$	−1.30656	+	3.15432i	−1.30656	+	3.15432i
$711$	0.707107	−	1.22474i	0.707107	−	1.22474i
$712$	0.517638	−	1.93185i	0.517638	−	1.93185i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.923880	+	1.60021i	0.923880	+	1.60021i
$718$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	−2.23044	+	0.923880i	−2.23044	+	0.923880i
$721$		0			0
$722$	−1.60021	−	0.923880i	−1.60021	−	0.923880i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	0.739288	+	0.198092i	0.739288	+	0.198092i
$727$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$727$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$728$		0			0
$729$		−	1.00000i		−	1.00000i
$730$		0			0
$731$		0			0
$732$	3.29788	−	0.883663i	3.29788	−	0.883663i
$733$		0			0			−	1.00000i	$-0.5\pi$
$733$		0			0				1.00000i	$0.5\pi$
$734$	0.676327	+	2.52409i	0.676327	+	2.52409i
$735$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$736$		0			0
$737$		0			0
$738$	−3.29788	−	0.883663i	−3.29788	−	0.883663i
$739$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$739$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.662827	−	0.382683i	0.662827	−	0.382683i	−0.130526	−	0.991445i	$-0.541667\pi$
$743$	0.662827	−	0.382683i	0.662827	−	0.382683i	0.793353	+	0.608761i	$0.208333\pi$
$744$		0			0
$745$	1.46593	−	1.12484i	1.46593	−	1.12484i
$746$	2.61313	+	2.61313i	2.61313	+	2.61313i
$747$	−0.382683	+	0.662827i	−0.382683	+	0.662827i
$748$		0			0
$749$		0			0
$750$	1.83195	+	0.241181i	1.83195	+	0.241181i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	1.60021	−	0.923880i	1.60021	−	0.923880i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.93185	−	0.517638i	−1.93185	−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$757$	−1.93185	−	0.517638i	−1.93185	−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	−0.991445	−	0.130526i	$-0.958333\pi$
$761$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	0.793353	−	0.608761i	$-0.208333\pi$
$762$		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		−0.965926	−	0.258819i	$-0.916667\pi$
$769$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.662827	−	0.382683i	−0.662827	−	0.382683i	0.130526	−	0.991445i	$-0.458333\pi$
$773$	−0.662827	−	0.382683i	−0.662827	−	0.382683i	−0.793353	+	0.608761i	$0.791667\pi$
$774$	−2.52409	+	0.676327i	−2.52409	+	0.676327i
$775$		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
$784$	1.20711	−	2.09077i	1.20711	−	2.09077i
$785$	−1.30656	−	0.541196i	−1.30656	−	0.541196i
$786$		0			0
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	−1.84776			−1.84776
$789$		0			0
$790$	−2.07313	−	1.59077i	−2.07313	−	1.59077i
$791$		0			0
$792$	1.41421	+	1.41421i	1.41421	+	1.41421i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	1.70711	+	2.95680i	1.70711	+	2.95680i
$797$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$797$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$798$		0			0
$799$		0			0
$800$	0.478235	+	1.78480i	0.478235	+	1.78480i
$801$	0.541196	−	0.541196i	0.541196	−	0.541196i
$802$	0.883663	+	3.29788i	0.883663	+	3.29788i
$803$		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	$0.833333\pi$
$810$	−1.83195	−	0.241181i	−1.83195	−	0.241181i
$811$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$811$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	−1.70711	+	4.12132i	−1.70711	+	4.12132i
$821$	−0.198092	+	0.739288i	−0.198092	+	0.739288i	0.793353	+	0.608761i	$0.208333\pi$
$821$	−0.198092	+	0.739288i	−0.198092	+	0.739288i	−0.991445	+	0.130526i	$0.958333\pi$
$822$	3.29788	+	0.883663i	3.29788	+	0.883663i
$823$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$823$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$824$	2.61313	−	2.61313i	2.61313	−	2.61313i
$825$	−0.198092	−	0.739288i	−0.198092	−	0.739288i
$826$		0			0
$827$		−	0.765367i		−	0.765367i	−0.923880	−	0.382683i	$-0.875000\pi$
$827$		−	0.765367i		−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$828$		0			0
$829$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$829$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$830$	1.12197	+	0.860919i	1.12197	+	0.860919i
$831$		−	1.41421i		−	1.41421i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.46593	+	1.12484i	1.46593	+	1.12484i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	0.739288	−	0.198092i	0.739288	−	0.198092i	0.130526	−	0.991445i	$-0.458333\pi$
$839$	0.739288	−	0.198092i	0.739288	−	0.198092i	0.608761	+	0.793353i	$0.291667\pi$
$840$		0			0
$841$	0.500000	−	0.866025i	0.500000	−	0.866025i
$842$		0			0
$843$	−0.382683	−	0.662827i	−0.382683	−	0.662827i
$844$	3.41421			3.41421
$845$		0			0
$846$	1.41421			1.41421
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−3.86324	−	2.23044i	−3.86324	−	2.23044i
$853$		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	$-0.750000\pi$
$857$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$858$		0			0
$859$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$859$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$860$	0.445644	+	3.38500i	0.445644	+	3.38500i
$861$		0			0
$862$	1.36603	−	0.366025i	1.36603	−	0.366025i
$863$		−	1.84776i		−	1.84776i	−0.382683	−	0.923880i	$-0.625000\pi$
$863$		−	1.84776i		−	1.84776i	0.382683	−	0.923880i	$-0.375000\pi$
$864$	−0.478235	−	1.78480i	−0.478235	−	1.78480i
$865$		0			0
$866$	−2.61313	+	2.61313i	−2.61313	+	2.61313i
$867$	0.258819	+	0.965926i	0.258819	+	0.965926i
$868$		0			0
$869$	−0.280144	+	1.04551i	−0.280144	+	1.04551i
$870$		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
$879$	−1.30656	−	1.30656i	−1.30656	−	1.30656i
$880$	1.46593	−	1.12484i	1.46593	−	1.12484i
$881$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$881$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$882$	1.60021	−	0.923880i	1.60021	−	0.923880i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$	−1.70711	+	0.707107i	−1.70711	+	0.707107i
$886$		0			0
$887$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$887$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$888$		0			0
$889$		0			0
$890$	−0.860919	−	1.12197i	−0.860919	−	1.12197i
$891$	0.198092	+	0.739288i	0.198092	+	0.739288i
$892$		0			0
$893$		0			0
$894$	1.70711	+	2.95680i	1.70711	+	2.95680i
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−2.41421	−	2.41421i	−2.41421	−	2.41421i
$899$		0			0
$900$	−0.624844	+	2.33195i	−0.624844	+	2.33195i
$901$		0			0
$902$	2.61313			2.61313
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$907$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$908$	−2.23044	−	3.86324i	−2.23044	−	3.86324i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	0.151613	−	0.565826i	0.151613	−	0.565826i
$914$		0			0
$915$	0.541196	−	1.30656i	0.541196	−	1.30656i
$916$		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
$927$	1.36603	−	0.366025i	1.36603	−	0.366025i
$928$		0			0
$929$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	−0.991445	−	0.130526i	$-0.958333\pi$
$929$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	0.793353	−	0.608761i	$-0.208333\pi$
$930$		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	$-0.750000\pi$
$937$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$938$		0			0
$939$		0			0
$940$	0.241181	−	1.83195i	0.241181	−	1.83195i
$941$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.923880	+	0.382683i	$0.125000\pi$
$941$	1.30656	+	1.30656i	1.30656	+	1.30656i	0.382683	+	0.923880i	$0.375000\pi$
$942$	1.30656	−	2.26303i	1.30656	−	2.26303i
$943$		0			0
$944$	−3.15432	−	3.15432i	−3.15432	−	3.15432i
$945$		0			0
$946$	1.73205	−	1.00000i	1.73205	−	1.00000i
$947$	−0.662827	+	0.382683i	−0.662827	+	0.382683i	−0.793353	−	0.608761i	$-0.791667\pi$
$947$	−0.662827	+	0.382683i	−0.662827	+	0.382683i	0.130526	+	0.991445i	$0.458333\pi$
$948$	2.41421	−	2.41421i	2.41421	−	2.41421i
$949$		0			0
$950$		0			0
$951$	−0.198092	+	0.739288i	−0.198092	+	0.739288i
$952$		0			0
$953$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$953$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$954$		0			0
$955$		0			0
$956$	1.15456	+	4.30888i	1.15456	+	4.30888i
$957$		0			0
$958$	1.36603	−	0.366025i	1.36603	−	0.366025i
$959$		0			0
$960$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$961$			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			$\pi$
$968$	0.937379	+	0.541196i	0.937379	+	0.541196i
$969$		0			0
$970$		0			0
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$	0.624844	−	2.33195i	0.624844	−	2.33195i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	3.41421			3.41421
$977$	−0.382683	−	0.662827i	−0.382683	−	0.662827i	0.608761	−	0.793353i	$-0.291667\pi$
$977$	−0.382683	−	0.662827i	−0.382683	−	0.662827i	−0.991445	+	0.130526i	$0.958333\pi$
$978$		0			0
$979$	−0.292893	+	0.507306i	−0.292893	+	0.507306i
$980$	−0.923880	−	2.23044i	−0.923880	−	2.23044i
$981$		0			0
$982$		0			0
$983$	1.84776			1.84776			0.923880	−	0.382683i	$-0.125000\pi$
$983$	1.84776			1.84776			0.923880	+	0.382683i	$0.125000\pi$
$984$	−4.18154	−	2.41421i	−4.18154	−	2.41421i
$985$	−0.465926	+	0.607206i	−0.465926	+	0.607206i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	1.40211	−	0.184592i	1.40211	−	0.184592i
$991$	−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
$995$	1.40211	+	0.184592i	1.40211	+	0.184592i
$996$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$997$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$997$	0.366025	+	1.36603i	0.366025	+	1.36603i	−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.2108.4		16
3.2	odd	2	inner	2535.1.bc.a.2108.1		16
5.2	odd	4		2535.1.bn.a.587.1		16
13.2	odd	12		2535.1.j.a.1958.4	yes	8
13.3	even	3		2535.1.u.a.1253.1	yes	8
13.4	even	6	inner	2535.1.bc.a.188.1		16
13.5	odd	4		2535.1.bn.a.1103.4		16
13.6	odd	12		2535.1.bn.a.488.1		16
13.7	odd	12		2535.1.bn.a.488.4		16
13.8	odd	4		2535.1.bn.a.1103.1		16
13.9	even	3	inner	2535.1.bc.a.188.4		16
13.10	even	6		2535.1.u.a.1253.4	yes	8
13.11	odd	12		2535.1.j.a.1958.1	✓	8
13.12	even	2	inner	2535.1.bc.a.2108.1		16
15.2	even	4		2535.1.bn.a.587.4		16
39.2	even	12		2535.1.j.a.1958.1	✓	8
39.5	even	4		2535.1.bn.a.1103.1		16
39.8	even	4		2535.1.bn.a.1103.4		16
39.11	even	12		2535.1.j.a.1958.4	yes	8
39.17	odd	6	inner	2535.1.bc.a.188.4		16
39.20	even	12		2535.1.bn.a.488.1		16
39.23	odd	6		2535.1.u.a.1253.1	yes	8
39.29	odd	6		2535.1.u.a.1253.4	yes	8
39.32	even	12		2535.1.bn.a.488.4		16
39.35	odd	6	inner	2535.1.bc.a.188.1		16
39.38	odd	2	CM	2535.1.bc.a.2108.4		16
65.2	even	12		2535.1.u.a.437.1	yes	8
65.7	even	12	inner	2535.1.bc.a.1502.1		16
65.12	odd	4		2535.1.bn.a.587.4		16
65.17	odd	12		2535.1.bn.a.1202.1		16
65.22	odd	12		2535.1.bn.a.1202.4		16
65.32	even	12	inner	2535.1.bc.a.1502.4		16
65.37	even	12		2535.1.u.a.437.4	yes	8
65.42	odd	12		2535.1.j.a.2267.1	yes	8
65.47	even	4	inner	2535.1.bc.a.2117.1		16
65.57	even	4	inner	2535.1.bc.a.2117.4		16
65.62	odd	12		2535.1.j.a.2267.4	yes	8
195.2	odd	12		2535.1.u.a.437.4	yes	8
195.17	even	12		2535.1.bn.a.1202.4		16
195.32	odd	12	inner	2535.1.bc.a.1502.1		16
195.47	odd	4	inner	2535.1.bc.a.2117.4		16
195.62	even	12		2535.1.j.a.2267.1	yes	8
195.77	even	4		2535.1.bn.a.587.1		16
195.107	even	12		2535.1.j.a.2267.4	yes	8
195.122	odd	4	inner	2535.1.bc.a.2117.1		16
195.137	odd	12	inner	2535.1.bc.a.1502.4		16
195.152	even	12		2535.1.bn.a.1202.1		16
195.167	odd	12		2535.1.u.a.437.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2535.1.j.a.1958.1	✓	8	13.11	odd	12
2535.1.j.a.1958.1	✓	8	39.2	even	12
2535.1.j.a.1958.4	yes	8	13.2	odd	12
2535.1.j.a.1958.4	yes	8	39.11	even	12
2535.1.j.a.2267.1	yes	8	65.42	odd	12
2535.1.j.a.2267.1	yes	8	195.62	even	12
2535.1.j.a.2267.4	yes	8	65.62	odd	12
2535.1.j.a.2267.4	yes	8	195.107	even	12
2535.1.u.a.437.1	yes	8	65.2	even	12
2535.1.u.a.437.1	yes	8	195.167	odd	12
2535.1.u.a.437.4	yes	8	65.37	even	12
2535.1.u.a.437.4	yes	8	195.2	odd	12
2535.1.u.a.1253.1	yes	8	13.3	even	3
2535.1.u.a.1253.1	yes	8	39.23	odd	6
2535.1.u.a.1253.4	yes	8	13.10	even	6
2535.1.u.a.1253.4	yes	8	39.29	odd	6
2535.1.bc.a.188.1		16	13.4	even	6	inner
2535.1.bc.a.188.1		16	39.35	odd	6	inner
2535.1.bc.a.188.4		16	13.9	even	3	inner
2535.1.bc.a.188.4		16	39.17	odd	6	inner
2535.1.bc.a.1502.1		16	65.7	even	12	inner
2535.1.bc.a.1502.1		16	195.32	odd	12	inner
2535.1.bc.a.1502.4		16	65.32	even	12	inner
2535.1.bc.a.1502.4		16	195.137	odd	12	inner
2535.1.bc.a.2108.1		16	3.2	odd	2	inner
2535.1.bc.a.2108.1		16	13.12	even	2	inner
2535.1.bc.a.2108.4		16	1.1	even	1	trivial
2535.1.bc.a.2108.4		16	39.38	odd	2	CM
2535.1.bc.a.2117.1		16	65.47	even	4	inner
2535.1.bc.a.2117.1		16	195.122	odd	4	inner
2535.1.bc.a.2117.4		16	65.57	even	4	inner
2535.1.bc.a.2117.4		16	195.47	odd	4	inner
2535.1.bn.a.488.1		16	13.6	odd	12
2535.1.bn.a.488.1		16	39.20	even	12
2535.1.bn.a.488.4		16	13.7	odd	12
2535.1.bn.a.488.4		16	39.32	even	12
2535.1.bn.a.587.1		16	5.2	odd	4
2535.1.bn.a.587.1		16	195.77	even	4
2535.1.bn.a.587.4		16	15.2	even	4
2535.1.bn.a.587.4		16	65.12	odd	4
2535.1.bn.a.1103.1		16	13.8	odd	4
2535.1.bn.a.1103.1		16	39.5	even	4
2535.1.bn.a.1103.4		16	13.5	odd	4
2535.1.bn.a.1103.4		16	39.8	even	4
2535.1.bn.a.1202.1		16	65.17	odd	12
2535.1.bn.a.1202.1		16	195.152	even	12
2535.1.bn.a.1202.4		16	65.22	odd	12
2535.1.bn.a.1202.4		16	195.17	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)

\(f(q)\)	\(=\)	\(q+(0.923880 + 1.60021i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.20711 + 2.09077i) q^{4} +(0.382683 + 0.923880i) q^{5} +(-1.78480 + 0.478235i) q^{6} -2.61313 q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.923880 + 1.60021i) q^{2} +(-0.258819 + 0.965926i) q^{3} +(-1.20711 + 2.09077i) q^{4} +(0.382683 + 0.923880i) q^{5} +(-1.78480 + 0.478235i) q^{6} -2.61313 q^{8} +(-0.866025 - 0.500000i) q^{9} +(-1.12484 + 1.46593i) q^{10} +(0.739288 + 0.198092i) q^{11} +(-1.70711 - 1.70711i) q^{12} +(-0.991445 + 0.130526i) q^{15} +(-1.20711 - 2.09077i) q^{16} -1.84776i q^{18} +(-2.39356 - 0.315118i) q^{20} +(0.366025 + 1.36603i) q^{22} +(0.676327 - 2.52409i) q^{24} +(-0.707107 + 0.707107i) q^{25} +(0.707107 - 0.707107i) q^{27} +(-1.12484 - 1.46593i) q^{30} +(0.923880 - 1.60021i) q^{32} +(-0.382683 + 0.662827i) q^{33} +(2.09077 - 1.20711i) q^{36} +(-1.00000 - 2.41421i) q^{40} +(0.478235 - 1.78480i) q^{41} +(-0.366025 - 1.36603i) q^{43} +(-1.30656 + 1.30656i) q^{44} +(0.130526 - 0.991445i) q^{45} +0.765367i q^{47} +(2.33195 - 0.624844i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.78480 - 0.478235i) q^{50} +(1.78480 + 0.478235i) q^{54} +(0.0999004 + 0.758819i) q^{55} +(1.78480 - 0.478235i) q^{59} +(0.923880 - 2.23044i) q^{60} +(-0.707107 + 1.22474i) q^{61} +1.00000 q^{64} -1.41421 q^{66} +(1.78480 - 0.478235i) q^{71} +(2.26303 + 1.30656i) q^{72} +(-0.500000 - 0.866025i) q^{75} +1.41421i q^{79} +(1.46968 - 1.91532i) q^{80} +(0.500000 + 0.866025i) q^{81} +(3.29788 - 0.883663i) q^{82} -0.765367i q^{83} +(1.84776 - 1.84776i) q^{86} +(-1.93185 - 0.517638i) q^{88} +(-0.198092 + 0.739288i) q^{89} +(1.70711 - 0.707107i) q^{90} +(-1.22474 + 0.707107i) q^{94} +(1.30656 + 1.30656i) q^{96} +(-0.923880 + 1.60021i) q^{98} +(-0.541196 - 0.541196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4}+O(q^{10}) \) 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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