LMFDB - Embedded newform 2520.1.hf.b.1973.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,1,Mod(293,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 9, 6]))

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

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

chi := DirichletCharacter("2520.293");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2520.hf (of order $12$, degree $4$, 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:	$1.25764383184$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{24}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{24} - \cdots)$

Embedding invariants

Embedding label			1973.1
Root			$0.793353 + 0.608761i$ of defining polynomial
Character	$\chi$	$=$	2520.1973
Dual form			2520.1.hf.b.797.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.793353 + 0.608761i) q^{5} +(0.991445 + 0.130526i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.793353 + 0.608761i) q^{5} +(0.991445 + 0.130526i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.707107 + 0.707107i) q^{9} +(0.608761 - 0.793353i) q^{10} +(-0.991445 + 0.130526i) q^{12} +(-0.198092 + 0.739288i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.965926 - 0.258819i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.866025 - 0.500000i) q^{18} -0.261052i q^{19} +(-0.382683 + 0.923880i) q^{20} +(-0.130526 + 0.991445i) q^{21} +(-0.500000 - 0.133975i) q^{23} +(0.923880 - 0.382683i) q^{24} +(0.258819 - 0.965926i) q^{25} -0.765367i q^{26} +(-0.382683 - 0.923880i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-0.866025 + 0.500000i) q^{30} +(-0.258819 + 0.965926i) q^{32} +(0.793353 + 0.608761i) q^{35} +(0.965926 + 0.258819i) q^{36} +(0.0675653 + 0.252157i) q^{38} +(0.465926 - 0.607206i) q^{39} +(0.130526 - 0.991445i) q^{40} +(-0.130526 - 0.991445i) q^{42} +(-0.991445 - 0.130526i) q^{45} +0.517638 q^{46} +(-0.793353 + 0.608761i) q^{48} +(-0.866025 + 0.500000i) q^{49} +1.00000i q^{50} +(0.198092 + 0.739288i) q^{52} +(0.608761 + 0.793353i) q^{54} +(0.866025 + 0.500000i) q^{56} +(-0.0999004 + 0.241181i) q^{57} +(-0.923880 - 1.60021i) q^{59} +(0.707107 - 0.707107i) q^{60} +(-0.991445 + 1.71723i) q^{61} +(0.500000 - 0.866025i) q^{63} -1.00000i q^{64} +(-0.292893 - 0.707107i) q^{65} +(0.410670 + 0.315118i) q^{69} +(-0.923880 - 0.382683i) q^{70} +1.93185i q^{71} -1.00000 q^{72} +(-0.608761 + 0.793353i) q^{75} +(-0.130526 - 0.226078i) q^{76} +(-0.292893 + 0.707107i) q^{78} +(-1.67303 - 0.965926i) q^{79} +(0.130526 + 0.991445i) q^{80} +1.00000i q^{81} +(0.478235 + 1.78480i) q^{83} +(0.382683 + 0.923880i) q^{84} +(0.991445 - 0.130526i) q^{90} +0.765367 q^{91} +(-0.500000 + 0.133975i) q^{92} +(0.158919 + 0.207107i) q^{95} +(0.608761 - 0.793353i) q^{96} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 8 q^{14} + 8 q^{16} - 8 q^{23} - 8 q^{39} + 8 q^{63} - 16 q^{65} - 16 q^{72} - 16 q^{78} - 8 q^{92}+O(q^{100}) $ 16 * q + 8 * q^14 + 8 * q^16 - 8 * q^23 - 8 * q^39 + 8 * q^63 - 16 * q^65 - 16 * q^72 - 16 * q^78 - 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$2$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$3$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$3$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$4$	0.866025	−	0.500000i	0.866025	−	0.500000i
$5$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$5$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$6$	0.991445	+	0.130526i	0.991445	+	0.130526i
$7$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$7$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$8$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$9$	0.707107	+	0.707107i	0.707107	+	0.707107i
$10$	0.608761	−	0.793353i	0.608761	−	0.793353i
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$13$	−0.198092	+	0.739288i	−0.198092	+	0.739288i	0.793353	+	0.608761i	$0.208333\pi$
$13$	−0.198092	+	0.739288i	−0.198092	+	0.739288i	−0.991445	+	0.130526i	$0.958333\pi$
$14$	0.500000	+	0.866025i	0.500000	+	0.866025i
$15$	0.965926	−	0.258819i	0.965926	−	0.258819i
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$19$		−	0.261052i		−	0.261052i	−0.991445	−	0.130526i	$-0.958333\pi$
$19$		−	0.261052i		−	0.261052i	0.991445	−	0.130526i	$-0.0416667\pi$
$20$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$21$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$22$		0			0
$23$	−0.500000	−	0.133975i	−0.500000	−	0.133975i		−	1.00000i	$-0.5\pi$
$23$	−0.500000	−	0.133975i	−0.500000	−	0.133975i	−0.500000	+	0.866025i	$0.666667\pi$
$24$	0.923880	−	0.382683i	0.923880	−	0.382683i
$25$	0.258819	−	0.965926i	0.258819	−	0.965926i
$26$		−	0.765367i		−	0.765367i
$27$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$28$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$29$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$33$		0			0
$34$		0			0
$35$	0.793353	+	0.608761i	0.793353	+	0.608761i
$36$	0.965926	+	0.258819i	0.965926	+	0.258819i
$37$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$37$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$38$	0.0675653	+	0.252157i	0.0675653	+	0.252157i
$39$	0.465926	−	0.607206i	0.465926	−	0.607206i
$40$	0.130526	−	0.991445i	0.130526	−	0.991445i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$43$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$43$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$44$		0			0
$45$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$46$	0.517638			0.517638
$47$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$47$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$48$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$49$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$50$			1.00000i			1.00000i
$51$		0			0
$52$	0.198092	+	0.739288i	0.198092	+	0.739288i
$53$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$53$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$54$	0.608761	+	0.793353i	0.608761	+	0.793353i
$55$		0			0
$56$	0.866025	+	0.500000i	0.866025	+	0.500000i
$57$	−0.0999004	+	0.241181i	−0.0999004	+	0.241181i
$58$		0			0
$59$	−0.923880	−	1.60021i	−0.923880	−	1.60021i	−0.793353	−	0.608761i	$-0.791667\pi$
$59$	−0.923880	−	1.60021i	−0.923880	−	1.60021i	−0.130526	−	0.991445i	$-0.541667\pi$
$60$	0.707107	−	0.707107i	0.707107	−	0.707107i
$61$	−0.991445	+	1.71723i	−0.991445	+	1.71723i	−0.382683	+	0.923880i	$0.625000\pi$
$61$	−0.991445	+	1.71723i	−0.991445	+	1.71723i	−0.608761	+	0.793353i	$0.708333\pi$
$62$		0			0
$63$	0.500000	−	0.866025i	0.500000	−	0.866025i
$64$		−	1.00000i		−	1.00000i
$65$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$66$		0			0
$67$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$67$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$68$		0			0
$69$	0.410670	+	0.315118i	0.410670	+	0.315118i
$70$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$71$			1.93185i			1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$71$			1.93185i			1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$72$	−1.00000			−1.00000
$73$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$73$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$74$		0			0
$75$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$76$	−0.130526	−	0.226078i	−0.130526	−	0.226078i
$77$		0			0
$78$	−0.292893	+	0.707107i	−0.292893	+	0.707107i
$79$	−1.67303	−	0.965926i	−1.67303	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$79$	−1.67303	−	0.965926i	−1.67303	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$80$	0.130526	+	0.991445i	0.130526	+	0.991445i
$81$			1.00000i			1.00000i
$82$		0			0
$83$	0.478235	+	1.78480i	0.478235	+	1.78480i	0.608761	+	0.793353i	$0.291667\pi$
$83$	0.478235	+	1.78480i	0.478235	+	1.78480i	−0.130526	+	0.991445i	$0.541667\pi$
$84$	0.382683	+	0.923880i	0.382683	+	0.923880i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	0.991445	−	0.130526i	0.991445	−	0.130526i
$91$	0.765367			0.765367
$92$	−0.500000	+	0.133975i	−0.500000	+	0.133975i
$93$		0			0
$94$		0			0
$95$	0.158919	+	0.207107i	0.158919	+	0.207107i
$96$	0.608761	−	0.793353i	0.608761	−	0.793353i
$97$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$97$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$98$	0.707107	−	0.707107i	0.707107	−	0.707107i
$99$		0			0
$100$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$101$	−1.37413	−	0.793353i	−1.37413	−	0.793353i	−0.382683	−	0.923880i	$-0.625000\pi$
$101$	−1.37413	−	0.793353i	−1.37413	−	0.793353i	−0.991445	+	0.130526i	$0.958333\pi$
$102$		0			0
$103$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$103$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$104$	−0.382683	−	0.662827i	−0.382683	−	0.662827i
$105$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$106$		0			0
$107$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$107$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$108$	−0.793353	−	0.608761i	−0.793353	−	0.608761i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$		0			0
$112$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$113$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.707107	−	0.707107i	$-0.750000\pi$
$113$	−1.67303	−	0.448288i	−1.67303	−	0.448288i	−0.965926	+	0.258819i	$0.916667\pi$
$114$	0.0340742	−	0.258819i	0.0340742	−	0.258819i
$115$	0.478235	−	0.198092i	0.478235	−	0.198092i
$116$		0			0
$117$	−0.662827	+	0.382683i	−0.662827	+	0.382683i
$118$	1.30656	+	1.30656i	1.30656	+	1.30656i
$119$		0			0
$120$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$121$	0.500000	+	0.866025i	0.500000	+	0.866025i
$122$	0.513210	−	1.91532i	0.513210	−	1.91532i
$123$		0			0
$124$		0			0
$125$	0.382683	+	0.923880i	0.382683	+	0.923880i
$126$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$127$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$127$	−0.366025	+	0.366025i	−0.366025	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$128$	0.258819	+	0.965926i	0.258819	+	0.965926i
$129$		0			0
$130$	0.465926	+	0.607206i	0.465926	+	0.607206i
$131$	1.05441	−	0.608761i	1.05441	−	0.608761i	0.130526	−	0.991445i	$-0.458333\pi$
$131$	1.05441	−	0.608761i	1.05441	−	0.608761i	0.923880	+	0.382683i	$0.125000\pi$
$132$		0			0
$133$	−0.252157	+	0.0675653i	−0.252157	+	0.0675653i
$134$		0			0
$135$	0.866025	+	0.500000i	0.866025	+	0.500000i
$136$		0			0
$137$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$137$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$138$	−0.478235	−	0.198092i	−0.478235	−	0.198092i
$139$	−1.05441	+	0.608761i	−1.05441	+	0.608761i	−0.923880	−	0.382683i	$-0.875000\pi$
$139$	−1.05441	+	0.608761i	−1.05441	+	0.608761i	−0.130526	+	0.991445i	$0.541667\pi$
$140$	0.991445	+	0.130526i	0.991445	+	0.130526i
$141$		0			0
$142$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$143$		0			0
$144$	0.965926	−	0.258819i	0.965926	−	0.258819i
$145$		0			0
$146$		0			0
$147$	0.991445	−	0.130526i	0.991445	−	0.130526i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	0.382683	−	0.923880i	0.382683	−	0.923880i
$151$	−0.866025	+	1.50000i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$151$	−0.866025	+	1.50000i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$152$	0.184592	+	0.184592i	0.184592	+	0.184592i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.0999004	−	0.758819i	0.0999004	−	0.758819i
$157$	−1.53264	−	0.410670i	−1.53264	−	0.410670i	−0.608761	−	0.793353i	$-0.708333\pi$
$157$	−1.53264	−	0.410670i	−1.53264	−	0.410670i	−0.923880	+	0.382683i	$0.875000\pi$
$158$	1.86603	+	0.500000i	1.86603	+	0.500000i
$159$		0			0
$160$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$161$			0.517638i			0.517638i
$162$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$163$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$163$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$164$		0			0
$165$		0			0
$166$	−0.923880	−	1.60021i	−0.923880	−	1.60021i
$167$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$167$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$168$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$169$	0.358719	+	0.207107i	0.358719	+	0.207107i
$170$		0			0
$171$	0.184592	−	0.184592i	0.184592	−	0.184592i
$172$		0			0
$173$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	−0.991445	−	0.130526i	$-0.958333\pi$
$173$	−0.198092	−	0.739288i	−0.198092	−	0.739288i	0.793353	−	0.608761i	$-0.208333\pi$
$174$		0			0
$175$	−1.00000			−1.00000
$176$		0			0
$177$	0.241181	+	1.83195i	0.241181	+	1.83195i
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$181$	−1.58671			−1.58671			−0.793353	−	0.608761i	$-0.791667\pi$
$181$	−1.58671			−1.58671			−0.793353	+	0.608761i	$0.791667\pi$
$182$	−0.739288	+	0.198092i	−0.739288	+	0.198092i
$183$	1.57313	−	1.20711i	1.57313	−	1.20711i
$184$	0.448288	−	0.258819i	0.448288	−	0.258819i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.793353	+	0.608761i	−0.793353	+	0.608761i
$190$	−0.207107	−	0.158919i	−0.207107	−	0.158919i
$191$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$191$	−0.448288	−	0.258819i	−0.448288	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$192$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$193$	−0.448288	+	1.67303i	−0.448288	+	1.67303i	0.258819	+	0.965926i	$0.416667\pi$
$193$	−0.448288	+	1.67303i	−0.448288	+	1.67303i	−0.707107	+	0.707107i	$0.750000\pi$
$194$		0			0
$195$			0.765367i			0.765367i
$196$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$197$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$197$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	0.500000	+	0.866025i	0.500000	+	0.866025i
$201$		0			0
$202$	1.53264	+	0.410670i	1.53264	+	0.410670i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.258819	−	0.448288i	−0.258819	−	0.448288i
$208$	0.541196	+	0.541196i	0.541196	+	0.541196i
$209$		0			0
$210$	0.707107	+	0.707107i	0.707107	+	0.707107i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	0.739288	−	1.78480i	0.739288	−	1.78480i
$214$		0			0
$215$		0			0
$216$	0.923880	+	0.382683i	0.923880	+	0.382683i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$223$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$224$	1.00000			1.00000
$225$	0.866025	−	0.500000i	0.866025	−	0.500000i
$226$	1.73205			1.73205
$227$	−1.53264	+	0.410670i	−1.53264	+	0.410670i	−0.923880	−	0.382683i	$-0.875000\pi$
$227$	−1.53264	+	0.410670i	−1.53264	+	0.410670i	−0.608761	+	0.793353i	$0.708333\pi$
$228$	0.0340742	+	0.258819i	0.0340742	+	0.258819i
$229$	1.05441	−	0.608761i	1.05441	−	0.608761i	0.130526	−	0.991445i	$-0.458333\pi$
$229$	1.05441	−	0.608761i	1.05441	−	0.608761i	0.923880	+	0.382683i	$0.125000\pi$
$230$	−0.410670	+	0.315118i	−0.410670	+	0.315118i
$231$		0			0
$232$		0			0
$233$	1.36603	−	1.36603i	1.36603	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$233$	1.36603	−	1.36603i	1.36603	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$234$	0.541196	−	0.541196i	0.541196	−	0.541196i
$235$		0			0
$236$	−1.60021	−	0.923880i	−1.60021	−	0.923880i
$237$	1.17604	+	1.53264i	1.17604	+	1.53264i
$238$		0			0
$239$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$239$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$240$	0.258819	−	0.965926i	0.258819	−	0.965926i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$243$	0.382683	−	0.923880i	0.382683	−	0.923880i
$244$			1.98289i			1.98289i
$245$	0.382683	−	0.923880i	0.382683	−	0.923880i
$246$		0			0
$247$	0.192993	+	0.0517123i	0.192993	+	0.0517123i
$248$		0			0
$249$	0.241181	−	1.83195i	0.241181	−	1.83195i
$250$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$251$		−	0.261052i		−	0.261052i	−0.991445	−	0.130526i	$-0.958333\pi$
$251$		−	0.261052i		−	0.261052i	0.991445	−	0.130526i	$-0.0416667\pi$
$252$		−	1.00000i		−	1.00000i
$253$		0			0
$254$	0.258819	−	0.448288i	0.258819	−	0.448288i
$255$		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	$0.583333\pi$
$258$		0			0
$259$		0			0
$260$	−0.607206	−	0.465926i	−0.607206	−	0.465926i
$261$		0			0
$262$	−0.860919	+	0.860919i	−0.860919	+	0.860919i
$263$	0.448288	+	1.67303i	0.448288	+	1.67303i	0.707107	+	0.707107i	$0.250000\pi$
$263$	0.448288	+	1.67303i	0.448288	+	1.67303i	−0.258819	+	0.965926i	$0.583333\pi$
$264$		0			0
$265$		0			0
$266$	0.226078	−	0.130526i	0.226078	−	0.130526i
$267$		0			0
$268$		0			0
$269$	−1.21752			−1.21752			−0.608761	−	0.793353i	$-0.708333\pi$
$269$	−1.21752			−1.21752			−0.608761	+	0.793353i	$0.708333\pi$
$270$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$	−0.707107	−	0.292893i	−0.707107	−	0.292893i
$274$	1.22474	−	0.707107i	1.22474	−	0.707107i
$275$		0			0
$276$	0.513210	+	0.0675653i	0.513210	+	0.0675653i
$277$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$277$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$278$	0.860919	−	0.860919i	0.860919	−	0.860919i
$279$		0			0
$280$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$281$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$281$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$282$		0			0
$283$	0.315118	−	1.17604i	0.315118	−	1.17604i	−0.608761	−	0.793353i	$-0.708333\pi$
$283$	0.315118	−	1.17604i	0.315118	−	1.17604i	0.923880	−	0.382683i	$-0.125000\pi$
$284$	0.965926	+	1.67303i	0.965926	+	1.67303i
$285$	−0.0675653	−	0.252157i	−0.0675653	−	0.252157i
$286$		0			0
$287$		0			0
$288$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$289$			1.00000i			1.00000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.91532	+	0.513210i	1.91532	+	0.513210i	0.991445	+	0.130526i	$0.0416667\pi$
$293$	1.91532	+	0.513210i	1.91532	+	0.513210i	0.923880	+	0.382683i	$0.125000\pi$
$294$	−0.923880	+	0.382683i	−0.923880	+	0.382683i
$295$	1.70711	+	0.707107i	1.70711	+	0.707107i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.198092	−	0.343105i	0.198092	−	0.343105i
$300$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$301$		0			0
$302$	0.448288	−	1.67303i	0.448288	−	1.67303i
$303$	0.965926	+	1.25882i	0.965926	+	1.25882i
$304$	−0.226078	−	0.130526i	−0.226078	−	0.130526i
$305$	−0.258819	−	1.96593i	−0.258819	−	1.96593i
$306$		0			0
$307$	1.40211	−	1.40211i	1.40211	−	1.40211i	0.608761	−	0.793353i	$-0.291667\pi$
$307$	1.40211	−	1.40211i	1.40211	−	1.40211i	0.793353	−	0.608761i	$-0.208333\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$	0.0999004	+	0.758819i	0.0999004	+	0.758819i
$313$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$313$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$314$	1.58671			1.58671
$315$	0.130526	+	0.991445i	0.130526	+	0.991445i
$316$	−1.93185			−1.93185
$317$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$317$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$318$		0			0
$319$		0			0
$320$	0.608761	+	0.793353i	0.608761	+	0.793353i
$321$		0			0
$322$	−0.133975	−	0.500000i	−0.133975	−	0.500000i
$323$		0			0
$324$	0.500000	+	0.866025i	0.500000	+	0.866025i
$325$	0.662827	+	0.382683i	0.662827	+	0.382683i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	1.30656	+	1.30656i	1.30656	+	1.30656i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.793353	+	0.608761i	0.793353	+	0.608761i
$337$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$337$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$338$	−0.400100	−	0.107206i	−0.400100	−	0.107206i
$339$	1.37413	+	1.05441i	1.37413	+	1.05441i
$340$		0			0
$341$		0			0
$342$	−0.130526	+	0.226078i	−0.130526	+	0.226078i
$343$	0.707107	+	0.707107i	0.707107	+	0.707107i
$344$		0			0
$345$	−0.517638			−0.517638
$346$	0.382683	+	0.662827i	0.382683	+	0.662827i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	1.60021	+	0.923880i	1.60021	+	0.923880i	0.991445	+	0.130526i	$0.0416667\pi$
$349$	1.60021	+	0.923880i	1.60021	+	0.923880i	0.608761	+	0.793353i	$0.291667\pi$
$350$	0.965926	−	0.258819i	0.965926	−	0.258819i
$351$	0.758819	−	0.0999004i	0.758819	−	0.0999004i
$352$		0			0
$353$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$353$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$354$	−0.707107	−	1.70711i	−0.707107	−	1.70711i
$355$	−1.17604	−	1.53264i	−1.17604	−	1.53264i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.73205			−1.73205			−0.866025	−	0.500000i	$-0.833333\pi$
$359$	−1.73205			−1.73205			−0.866025	+	0.500000i	$0.833333\pi$
$360$	0.793353	−	0.608761i	0.793353	−	0.608761i
$361$	0.931852			0.931852
$362$	1.53264	−	0.410670i	1.53264	−	0.410670i
$363$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$364$	0.662827	−	0.382683i	0.662827	−	0.382683i
$365$		0			0
$366$	−1.20711	+	1.57313i	−1.20711	+	1.57313i
$367$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$367$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$368$	−0.366025	+	0.366025i	−0.366025	+	0.366025i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$373$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$374$		0			0
$375$		−	1.00000i		−	1.00000i
$376$		0			0
$377$		0			0
$378$	0.608761	−	0.793353i	0.608761	−	0.793353i
$379$		0			0			−	1.00000i	$-0.5\pi$
$379$		0			0				1.00000i	$0.5\pi$
$380$	0.241181	+	0.0999004i	0.241181	+	0.0999004i
$381$	0.478235	−	0.198092i	0.478235	−	0.198092i
$382$	0.500000	+	0.133975i	0.500000	+	0.133975i
$383$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$383$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$384$	0.130526	−	0.991445i	0.130526	−	0.991445i
$385$		0			0
$386$		−	1.73205i		−	1.73205i
$387$		0			0
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$	−0.198092	−	0.739288i	−0.198092	−	0.739288i
$391$		0			0
$392$	0.258819	−	0.965926i	0.258819	−	0.965926i
$393$	−1.20711	+	0.158919i	−1.20711	+	0.158919i
$394$		0			0
$395$	1.91532	−	0.252157i	1.91532	−	0.252157i
$396$		0			0
$397$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.382683	−	0.923880i	$-0.375000\pi$
$397$	1.30656	−	1.30656i	1.30656	−	1.30656i	0.923880	−	0.382683i	$-0.125000\pi$
$398$		0			0
$399$	0.258819	+	0.0340742i	0.258819	+	0.0340742i
$400$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$401$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$401$	1.67303	−	0.965926i	1.67303	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$402$		0			0
$403$		0			0
$404$	−1.58671			−1.58671
$405$	−0.608761	−	0.793353i	−0.608761	−	0.793353i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$409$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$410$		0			0
$411$	1.40211	+	0.184592i	1.40211	+	0.184592i
$412$		0			0
$413$	−1.30656	+	1.30656i	−1.30656	+	1.30656i
$414$	0.366025	+	0.366025i	0.366025	+	0.366025i
$415$	−1.46593	−	1.12484i	−1.46593	−	1.12484i
$416$	−0.662827	−	0.382683i	−0.662827	−	0.382683i
$417$	1.20711	−	0.158919i	1.20711	−	0.158919i
$418$		0			0
$419$	−0.991445	−	1.71723i	−0.991445	−	1.71723i	−0.608761	−	0.793353i	$-0.708333\pi$
$419$	−0.991445	−	1.71723i	−0.991445	−	1.71723i	−0.382683	−	0.923880i	$-0.625000\pi$
$420$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$421$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$421$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.252157	+	1.91532i	−0.252157	+	1.91532i
$427$	1.91532	+	0.513210i	1.91532	+	0.513210i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	−0.991445	−	0.130526i	−0.991445	−	0.130526i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.0349744	+	0.130526i	−0.0349744	+	0.130526i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$442$		0			0
$443$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$443$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$449$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$450$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$451$		0			0
$452$	−1.67303	+	0.448288i	−1.67303	+	0.448288i
$453$	1.37413	−	1.05441i	1.37413	−	1.05441i
$454$	1.37413	−	0.793353i	1.37413	−	0.793353i
$455$	−0.607206	+	0.465926i	−0.607206	+	0.465926i
$456$	−0.0999004	−	0.241181i	−0.0999004	−	0.241181i
$457$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$457$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$458$	−0.860919	+	0.860919i	−0.860919	+	0.860919i
$459$		0			0
$460$	0.315118	−	0.410670i	0.315118	−	0.410670i
$461$	1.05441	+	0.608761i	1.05441	+	0.608761i	0.923880	−	0.382683i	$-0.125000\pi$
$461$	1.05441	+	0.608761i	1.05441	+	0.608761i	0.130526	+	0.991445i	$0.458333\pi$
$462$		0			0
$463$	0.448288	−	1.67303i	0.448288	−	1.67303i	−0.258819	−	0.965926i	$-0.583333\pi$
$463$	0.448288	−	1.67303i	0.448288	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$464$		0			0
$465$		0			0
$466$	−0.965926	+	1.67303i	−0.965926	+	1.67303i
$467$	0.541196	+	0.541196i	0.541196	+	0.541196i	0.923880	−	0.382683i	$-0.125000\pi$
$467$	0.541196	+	0.541196i	0.541196	+	0.541196i	−0.382683	+	0.923880i	$0.625000\pi$
$468$	−0.382683	+	0.662827i	−0.382683	+	0.662827i
$469$		0			0
$470$		0			0
$471$	1.25882	+	0.965926i	1.25882	+	0.965926i
$472$	1.78480	+	0.478235i	1.78480	+	0.478235i
$473$		0			0
$474$	−1.53264	−	1.17604i	−1.53264	−	1.17604i
$475$	−0.252157	−	0.0675653i	−0.252157	−	0.0675653i
$476$		0			0
$477$		0			0
$478$	0.707107	+	0.707107i	0.707107	+	0.707107i
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$			1.00000i			1.00000i
$481$		0			0
$482$		0			0
$483$	0.198092	−	0.478235i	0.198092	−	0.478235i
$484$	0.866025	+	0.500000i	0.866025	+	0.500000i
$485$		0			0
$486$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$487$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$487$	−1.36603	+	1.36603i	−1.36603	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$488$	−0.513210	−	1.91532i	−0.513210	−	1.91532i
$489$		0			0
$490$	−0.130526	+	0.991445i	−0.130526	+	0.991445i
$491$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$491$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		0			0
$494$	−0.199801			−0.199801
$495$		0			0
$496$		0			0
$497$	1.86603	−	0.500000i	1.86603	−	0.500000i
$498$	0.241181	+	1.83195i	0.241181	+	1.83195i
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	0.793353	+	0.608761i	0.793353	+	0.608761i
$501$		0			0
$502$	0.0675653	+	0.252157i	0.0675653	+	0.252157i
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$	0.258819	+	0.965926i	0.258819	+	0.965926i
$505$	1.57313	−	0.207107i	1.57313	−	0.207107i
$506$		0			0
$507$	−0.252157	−	0.328618i	−0.252157	−	0.328618i
$508$	−0.133975	+	0.500000i	−0.133975	+	0.500000i
$509$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.793353	+	0.608761i	$0.208333\pi$
$509$	0.923880	+	1.60021i	0.923880	+	1.60021i	0.130526	+	0.991445i	$0.458333\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	+	0.707107i	0.707107	+	0.707107i
$513$	−0.241181	+	0.0999004i	−0.241181	+	0.0999004i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.0999004	+	0.758819i	−0.0999004	+	0.758819i
$520$	0.707107	+	0.292893i	0.707107	+	0.292893i
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	−0.184592	−	0.184592i	−0.184592	−	0.184592i	0.608761	−	0.793353i	$-0.291667\pi$
$523$	−0.184592	−	0.184592i	−0.184592	−	0.184592i	−0.793353	+	0.608761i	$0.791667\pi$
$524$	0.608761	−	1.05441i	0.608761	−	1.05441i
$525$	0.923880	+	0.382683i	0.923880	+	0.382683i
$526$	−0.866025	−	1.50000i	−0.866025	−	1.50000i
$527$		0			0
$528$		0			0
$529$	−0.633975	−	0.366025i	−0.633975	−	0.366025i
$530$		0			0
$531$	0.478235	−	1.78480i	0.478235	−	1.78480i
$532$	−0.184592	+	0.184592i	−0.184592	+	0.184592i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	1.17604	−	0.315118i	1.17604	−	0.315118i
$539$		0			0
$540$	1.00000			1.00000
$541$		0			0		1.00000			$0$
$541$		0			0		−1.00000			$\pi$
$542$		0			0
$543$	1.46593	+	0.607206i	1.46593	+	0.607206i
$544$		0			0
$545$		0			0
$546$	0.758819	+	0.0999004i	0.758819	+	0.0999004i
$547$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$547$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$548$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$549$	−1.91532	+	0.513210i	−1.91532	+	0.513210i
$550$		0			0
$551$		0			0
$552$	−0.513210	+	0.0675653i	−0.513210	+	0.0675653i
$553$	−0.500000	+	1.86603i	−0.500000	+	1.86603i
$554$		0			0
$555$		0			0
$556$	−0.608761	+	1.05441i	−0.608761	+	1.05441i
$557$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$557$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$558$		0			0
$559$		0			0
$560$	0.923880	−	0.382683i	0.923880	−	0.382683i
$561$		0			0
$562$	0.965926	+	0.258819i	0.965926	+	0.258819i
$563$	1.17604	+	0.315118i	1.17604	+	0.315118i	0.793353	−	0.608761i	$-0.208333\pi$
$563$	1.17604	+	0.315118i	1.17604	+	0.315118i	0.382683	+	0.923880i	$0.375000\pi$
$564$		0			0
$565$	1.60021	−	0.662827i	1.60021	−	0.662827i
$566$			1.21752i			1.21752i
$567$	0.965926	−	0.258819i	0.965926	−	0.258819i
$568$	−1.36603	−	1.36603i	−1.36603	−	1.36603i
$569$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$569$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$570$	0.130526	+	0.226078i	0.130526	+	0.226078i
$571$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$571$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$572$		0			0
$573$	0.315118	+	0.410670i	0.315118	+	0.410670i
$574$		0			0
$575$	−0.258819	+	0.448288i	−0.258819	+	0.448288i
$576$	0.707107	−	0.707107i	0.707107	−	0.707107i
$577$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$577$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$578$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$579$	1.05441	−	1.37413i	1.05441	−	1.37413i
$580$		0			0
$581$	1.60021	−	0.923880i	1.60021	−	0.923880i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.292893	−	0.707107i	0.292893	−	0.707107i
$586$	−1.98289			−1.98289
$587$	−1.91532	+	0.513210i	−1.91532	+	0.513210i	−0.923880	+	0.382683i	$0.875000\pi$
$587$	−1.91532	+	0.513210i	−1.91532	+	0.513210i	−0.991445	+	0.130526i	$0.958333\pi$
$588$	0.793353	−	0.608761i	0.793353	−	0.608761i
$589$		0			0
$590$	−1.83195	−	0.241181i	−1.83195	−	0.241181i
$591$		0			0
$592$		0			0
$593$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$593$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−0.102540	+	0.382683i	−0.102540	+	0.382683i
$599$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$599$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$600$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$		0			0
$604$			1.73205i			1.73205i
$605$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$606$	−1.25882	−	0.965926i	−1.25882	−	0.965926i
$607$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$607$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$608$	0.252157	+	0.0675653i	0.252157	+	0.0675653i
$609$		0			0
$610$	0.758819	+	1.83195i	0.758819	+	1.83195i
$611$		0			0
$612$		0			0
$613$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$613$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$614$	−0.991445	+	1.71723i	−0.991445	+	1.71723i
$615$		0			0
$616$		0			0
$617$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$617$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$618$		0			0
$619$	1.71723	+	0.991445i	1.71723	+	0.991445i	0.923880	+	0.382683i	$0.125000\pi$
$619$	1.71723	+	0.991445i	1.71723	+	0.991445i	0.793353	+	0.608761i	$0.208333\pi$
$620$		0			0
$621$	0.0675653	+	0.513210i	0.0675653	+	0.513210i
$622$		0			0
$623$		0			0
$624$	−0.292893	−	0.707107i	−0.292893	−	0.707107i
$625$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$626$		0			0
$627$		0			0
$628$	−1.53264	+	0.410670i	−1.53264	+	0.410670i
$629$		0			0
$630$	−0.382683	−	0.923880i	−0.382683	−	0.923880i
$631$	−0.517638			−0.517638			−0.258819	−	0.965926i	$-0.583333\pi$
$631$	−0.517638			−0.517638			−0.258819	+	0.965926i	$0.583333\pi$
$632$	1.86603	−	0.500000i	1.86603	−	0.500000i
$633$		0			0
$634$		0			0
$635$	0.0675653	−	0.513210i	0.0675653	−	0.513210i
$636$		0			0
$637$	−0.198092	−	0.739288i	−0.198092	−	0.739288i
$638$		0			0
$639$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$640$	−0.793353	−	0.608761i	−0.793353	−	0.608761i
$641$	−1.67303	−	0.965926i	−1.67303	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$641$	−1.67303	−	0.965926i	−1.67303	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$642$		0			0
$643$	−0.478235	+	1.78480i	−0.478235	+	1.78480i	0.130526	+	0.991445i	$0.458333\pi$
$643$	−0.478235	+	1.78480i	−0.478235	+	1.78480i	−0.608761	+	0.793353i	$0.708333\pi$
$644$	0.258819	+	0.448288i	0.258819	+	0.448288i
$645$		0			0
$646$		0			0
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$649$		0			0
$650$	−0.739288	−	0.198092i	−0.739288	−	0.198092i
$651$		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
$655$	−0.465926	+	1.12484i	−0.465926	+	1.12484i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$659$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$	−0.793353	−	1.37413i	−0.793353	−	1.37413i	−0.923880	−	0.382683i	$-0.875000\pi$
$661$	−0.793353	−	1.37413i	−0.793353	−	1.37413i	0.130526	−	0.991445i	$-0.458333\pi$
$662$		0			0
$663$		0			0
$664$	−1.60021	−	0.923880i	−1.60021	−	0.923880i
$665$	0.158919	−	0.207107i	0.158919	−	0.207107i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.923880	−	0.382683i	−0.923880	−	0.382683i
$673$	0.500000	−	0.133975i	0.500000	−	0.133975i		−	1.00000i	$-0.5\pi$
$673$	0.500000	−	0.133975i	0.500000	−	0.133975i	0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−0.991445	+	0.130526i	−0.991445	+	0.130526i
$676$	0.414214			0.414214
$677$	0.739288	−	0.198092i	0.739288	−	0.198092i	0.130526	−	0.991445i	$-0.458333\pi$
$677$	0.739288	−	0.198092i	0.739288	−	0.198092i	0.608761	+	0.793353i	$0.291667\pi$
$678$	−1.60021	−	0.662827i	−1.60021	−	0.662827i
$679$		0			0
$680$		0			0
$681$	1.57313	+	0.207107i	1.57313	+	0.207107i
$682$		0			0
$683$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$683$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$684$	0.0675653	−	0.252157i	0.0675653	−	0.252157i
$685$	0.860919	−	1.12197i	0.860919	−	1.12197i
$686$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$687$	−1.20711	+	0.158919i	−1.20711	+	0.158919i
$688$		0			0
$689$		0			0
$690$	0.500000	−	0.133975i	0.500000	−	0.133975i
$691$	−0.793353	+	1.37413i	−0.793353	+	1.37413i	0.130526	+	0.991445i	$0.458333\pi$
$691$	−0.793353	+	1.37413i	−0.793353	+	1.37413i	−0.923880	+	0.382683i	$0.875000\pi$
$692$	−0.541196	−	0.541196i	−0.541196	−	0.541196i
$693$		0			0
$694$		0			0
$695$	0.465926	−	1.12484i	0.465926	−	1.12484i
$696$		0			0
$697$		0			0
$698$	−1.78480	−	0.478235i	−1.78480	−	0.478235i
$699$	−1.78480	+	0.739288i	−1.78480	+	0.739288i
$700$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−0.707107	+	0.292893i	−0.707107	+	0.292893i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.410670	+	1.53264i	−0.410670	+	1.53264i
$708$	1.12484	+	1.46593i	1.12484	+	1.46593i
$709$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$709$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$710$	1.53264	+	1.17604i	1.53264	+	1.17604i
$711$	−0.500000	−	1.86603i	−0.500000	−	1.86603i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	0.130526	+	0.991445i	0.130526	+	0.991445i
$718$	1.67303	−	0.448288i	1.67303	−	0.448288i
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$	−0.608761	+	0.793353i	−0.608761	+	0.793353i
$721$		0			0
$722$	−0.900100	+	0.241181i	−0.900100	+	0.241181i
$723$		0			0
$724$	−1.37413	+	0.793353i	−1.37413	+	0.793353i
$725$		0			0
$726$	0.382683	+	0.923880i	0.382683	+	0.923880i
$727$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$727$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$728$	−0.541196	+	0.541196i	−0.541196	+	0.541196i
$729$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$730$		0			0
$731$		0			0
$732$	0.758819	−	1.83195i	0.758819	−	1.83195i
$733$	−0.410670	+	1.53264i	−0.410670	+	1.53264i	0.382683	+	0.923880i	$0.375000\pi$
$733$	−0.410670	+	1.53264i	−0.410670	+	1.53264i	−0.793353	+	0.608761i	$0.791667\pi$
$734$		0			0
$735$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$736$	0.258819	−	0.448288i	0.258819	−	0.448288i
$737$		0			0
$738$		0			0
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$		0			0
$741$	−0.158513	−	0.121631i	−0.158513	−	0.121631i
$742$		0			0
$743$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.923880	+	1.60021i	−0.923880	+	1.60021i
$748$		0			0
$749$		0			0
$750$	0.258819	+	0.965926i	0.258819	+	0.965926i
$751$	−0.866025	−	1.50000i	−0.866025	−	1.50000i	−0.866025	−	0.500000i	$-0.833333\pi$
$751$	−0.866025	−	1.50000i	−0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$752$		0			0
$753$	−0.0999004	+	0.241181i	−0.0999004	+	0.241181i
$754$		0			0
$755$	−0.226078	−	1.71723i	−0.226078	−	1.71723i
$756$	−0.382683	+	0.923880i	−0.382683	+	0.923880i
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$		0			0
$759$		0			0
$760$	−0.258819	−	0.0340742i	−0.258819	−	0.0340742i
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$	−0.410670	+	0.315118i	−0.410670	+	0.315118i
$763$		0			0
$764$	−0.517638			−0.517638
$765$		0			0
$766$		0			0
$767$	1.36603	−	0.366025i	1.36603	−	0.366025i
$768$	0.130526	+	0.991445i	0.130526	+	0.991445i
$769$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$769$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$770$		0			0
$771$		0			0
$772$	0.448288	+	1.67303i	0.448288	+	1.67303i
$773$	−0.184592	+	0.184592i	−0.184592	+	0.184592i	−0.793353	−	0.608761i	$-0.791667\pi$
$773$	−0.184592	+	0.184592i	−0.184592	+	0.184592i	0.608761	+	0.793353i	$0.291667\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	0.382683	+	0.662827i	0.382683	+	0.662827i
$781$		0			0
$782$		0			0
$783$		0			0
$784$			1.00000i			1.00000i
$785$	1.46593	−	0.607206i	1.46593	−	0.607206i
$786$	1.12484	−	0.465926i	1.12484	−	0.465926i
$787$	−1.78480	−	0.478235i	−1.78480	−	0.478235i	−0.793353	−	0.608761i	$-0.791667\pi$
$787$	−1.78480	−	0.478235i	−1.78480	−	0.478235i	−0.991445	+	0.130526i	$0.958333\pi$
$788$		0			0
$789$	0.226078	−	1.71723i	0.226078	−	1.71723i
$790$	−1.78480	+	0.739288i	−1.78480	+	0.739288i
$791$			1.73205i			1.73205i
$792$		0			0
$793$	−1.07313	−	1.07313i	−1.07313	−	1.07313i
$794$	−0.923880	+	1.60021i	−0.923880	+	1.60021i
$795$		0			0
$796$		0			0
$797$	0.0675653	−	0.252157i	0.0675653	−	0.252157i	−0.923880	−	0.382683i	$-0.875000\pi$
$797$	0.0675653	−	0.252157i	0.0675653	−	0.252157i	0.991445	+	0.130526i	$0.0416667\pi$
$798$	−0.258819	+	0.0340742i	−0.258819	+	0.0340742i
$799$		0			0
$800$	0.866025	+	0.500000i	0.866025	+	0.500000i
$801$		0			0
$802$	−1.36603	+	1.36603i	−1.36603	+	1.36603i
$803$		0			0
$804$		0			0
$805$	−0.315118	−	0.410670i	−0.315118	−	0.410670i
$806$		0			0
$807$	1.12484	+	0.465926i	1.12484	+	0.465926i
$808$	1.53264	−	0.410670i	1.53264	−	0.410670i
$809$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$809$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$810$	0.793353	+	0.608761i	0.793353	+	0.608761i
$811$	−1.84776			−1.84776			−0.923880	−	0.382683i	$-0.875000\pi$
$811$	−1.84776			−1.84776			−0.923880	+	0.382683i	$0.875000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.541196	+	0.541196i	0.541196	+	0.541196i
$820$		0			0
$821$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$821$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$822$	−1.40211	+	0.184592i	−1.40211	+	0.184592i
$823$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$823$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$824$		0			0
$825$		0			0
$826$	0.923880	−	1.60021i	0.923880	−	1.60021i
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	−0.448288	−	0.258819i	−0.448288	−	0.258819i
$829$		−	0.765367i		−	0.765367i	−0.923880	−	0.382683i	$-0.875000\pi$
$829$		−	0.765367i		−	0.765367i	0.923880	−	0.382683i	$-0.125000\pi$
$830$	1.70711	+	0.707107i	1.70711	+	0.707107i
$831$		0			0
$832$	0.739288	+	0.198092i	0.739288	+	0.198092i
$833$		0			0
$834$	−1.12484	+	0.465926i	−1.12484	+	0.465926i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	1.40211	+	1.40211i	1.40211	+	1.40211i
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$	0.965926	+	0.258819i	0.965926	+	0.258819i
$841$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$842$		0			0
$843$	0.608761	+	0.793353i	0.608761	+	0.793353i
$844$		0			0
$845$	−0.410670	+	0.0540657i	−0.410670	+	0.0540657i
$846$		0			0
$847$	0.707107	−	0.707107i	0.707107	−	0.707107i
$848$		0			0
$849$	−0.741181	+	0.965926i	−0.741181	+	0.965926i
$850$		0			0
$851$		0			0
$852$	−0.252157	−	1.91532i	−0.252157	−	1.91532i
$853$	0.252157	−	0.0675653i	0.252157	−	0.0675653i	−0.130526	−	0.991445i	$-0.541667\pi$
$853$	0.252157	−	0.0675653i	0.252157	−	0.0675653i	0.382683	+	0.923880i	$0.375000\pi$
$854$	−1.98289			−1.98289
$855$	−0.0340742	+	0.258819i	−0.0340742	+	0.258819i
$856$		0			0
$857$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$857$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$858$		0			0
$859$	−1.60021	+	0.923880i	−1.60021	+	0.923880i	−0.608761	+	0.793353i	$0.708333\pi$
$859$	−1.60021	+	0.923880i	−1.60021	+	0.923880i	−0.991445	+	0.130526i	$0.958333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$863$	1.22474	−	1.22474i	1.22474	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$864$	0.991445	−	0.130526i	0.991445	−	0.130526i
$865$	0.607206	+	0.465926i	0.607206	+	0.465926i
$866$		0			0
$867$	0.382683	−	0.923880i	0.382683	−	0.923880i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		−	0.135131i		−	0.135131i
$875$	0.793353	−	0.608761i	0.793353	−	0.608761i
$876$		0			0
$877$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$877$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$878$		0			0
$879$	−1.57313	−	1.20711i	−1.57313	−	1.20711i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	1.00000			1.00000
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$	−1.30656	−	1.30656i	−1.30656	−	1.30656i
$886$		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
$889$	0.448288	+	0.258819i	0.448288	+	0.258819i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.866025	−	0.500000i	0.866025	−	0.500000i
$897$	−0.314313	+	0.241181i	−0.314313	+	0.241181i
$898$	0.965926	−	0.258819i	0.965926	−	0.258819i
$899$		0			0
$900$	0.500000	−	0.866025i	0.500000	−	0.866025i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	1.50000	−	0.866025i	1.50000	−	0.866025i
$905$	1.25882	−	0.965926i	1.25882	−	0.965926i
$906$	−1.05441	+	1.37413i	−1.05441	+	1.37413i
$907$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$907$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$908$	−1.12197	+	1.12197i	−1.12197	+	1.12197i
$909$	−0.410670	−	1.53264i	−0.410670	−	1.53264i
$910$	0.465926	−	0.607206i	0.465926	−	0.607206i
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$911$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$912$	0.158919	+	0.207107i	0.158919	+	0.207107i
$913$		0			0
$914$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$915$	−0.513210	+	1.91532i	−0.513210	+	1.91532i
$916$	0.608761	−	1.05441i	0.608761	−	1.05441i
$917$	−0.860919	−	0.860919i	−0.860919	−	0.860919i
$918$		0			0
$919$			0.517638i			0.517638i	0.965926	+	0.258819i	$0.0833333\pi$
$919$			0.517638i			0.517638i	−0.965926	+	0.258819i	$0.916667\pi$
$920$	−0.198092	+	0.478235i	−0.198092	+	0.478235i
$921$	−1.83195	+	0.758819i	−1.83195	+	0.758819i
$922$	−1.17604	−	0.315118i	−1.17604	−	0.315118i
$923$	−1.42819	−	0.382683i	−1.42819	−	0.382683i
$924$		0			0
$925$		0			0
$926$			1.73205i			1.73205i
$927$		0			0
$928$		0			0
$929$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$929$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$	0.130526	+	0.226078i	0.130526	+	0.226078i
$932$	0.500000	−	1.86603i	0.500000	−	1.86603i
$933$		0			0
$934$	−0.662827	−	0.382683i	−0.662827	−	0.382683i
$935$		0			0
$936$	0.198092	−	0.739288i	0.198092	−	0.739288i
$937$		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			0
$941$	1.71723	−	0.991445i	1.71723	−	0.991445i	0.793353	−	0.608761i	$-0.208333\pi$
$941$	1.71723	−	0.991445i	1.71723	−	0.991445i	0.923880	−	0.382683i	$-0.125000\pi$
$942$	−1.46593	−	0.607206i	−1.46593	−	0.607206i
$943$		0			0
$944$	−1.84776			−1.84776
$945$	0.258819	−	0.965926i	0.258819	−	0.965926i
$946$		0			0
$947$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$947$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$948$	1.78480	+	0.739288i	1.78480	+	0.739288i
$949$		0			0
$950$	0.261052			0.261052
$951$		0			0
$952$		0			0
$953$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$953$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$954$		0			0
$955$	0.513210	−	0.0675653i	0.513210	−	0.0675653i
$956$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$957$		0			0
$958$		0			0
$959$	0.707107	+	1.22474i	0.707107	+	1.22474i
$960$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.662827	−	1.60021i	−0.662827	−	1.60021i
$966$	−0.0675653	+	0.513210i	−0.0675653	+	0.513210i
$967$	0.500000	+	0.133975i	0.500000	+	0.133975i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	0.500000	+	0.133975i	0.500000	+	0.133975i			1.00000i	$0.5\pi$
$968$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$969$		0			0
$970$		0			0
$971$			0.261052i			0.261052i	0.991445	+	0.130526i	$0.0416667\pi$
$971$			0.261052i			0.261052i	−0.991445	+	0.130526i	$0.958333\pi$
$972$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$973$	0.860919	+	0.860919i	0.860919	+	0.860919i
$974$	0.965926	−	1.67303i	0.965926	−	1.67303i
$975$	−0.465926	−	0.607206i	−0.465926	−	0.607206i
$976$	0.991445	+	1.71723i	0.991445	+	1.71723i
$977$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$977$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$978$		0			0
$979$		0			0
$980$	−0.130526	−	0.991445i	−0.130526	−	0.991445i
$981$		0			0
$982$		0			0
$983$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$983$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.192993	−	0.0517123i	0.192993	−	0.0517123i
$989$		0			0
$990$		0			0
$991$	−1.41421			−1.41421			−0.707107	−	0.707107i	$-0.750000\pi$
$991$	−1.41421			−1.41421			−0.707107	+	0.707107i	$0.750000\pi$
$992$		0			0
$993$		0			0
$994$	−1.67303	+	0.965926i	−1.67303	+	0.965926i
$995$		0			0
$996$	−0.707107	−	1.70711i	−0.707107	−	1.70711i
$997$	−0.513210	−	1.91532i	−0.513210	−	1.91532i	−0.382683	−	0.923880i	$-0.625000\pi$
$997$	−0.513210	−	1.91532i	−0.513210	−	1.91532i	−0.130526	−	0.991445i	$-0.541667\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.1.hf.b.1973.1	yes	16
5.2	odd	4		2520.1.hf.a.2477.1	yes	16
7.6	odd	2	inner	2520.1.hf.b.1973.2	yes	16
8.5	even	2	inner	2520.1.hf.b.1973.2	yes	16
9.5	odd	6		2520.1.hf.a.293.1	✓	16
35.27	even	4		2520.1.hf.a.2477.2	yes	16
40.37	odd	4		2520.1.hf.a.2477.2	yes	16
45.32	even	12	inner	2520.1.hf.b.797.1	yes	16
56.13	odd	2	CM	2520.1.hf.b.1973.1	yes	16
63.41	even	6		2520.1.hf.a.293.2	yes	16
72.5	odd	6		2520.1.hf.a.293.2	yes	16
280.237	even	4		2520.1.hf.a.2477.1	yes	16
315.167	odd	12	inner	2520.1.hf.b.797.2	yes	16
360.77	even	12	inner	2520.1.hf.b.797.2	yes	16
504.293	even	6		2520.1.hf.a.293.1	✓	16
2520.797	odd	12	inner	2520.1.hf.b.797.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2520.1.hf.a.293.1	✓	16	9.5	odd	6
2520.1.hf.a.293.1	✓	16	504.293	even	6
2520.1.hf.a.293.2	yes	16	63.41	even	6
2520.1.hf.a.293.2	yes	16	72.5	odd	6
2520.1.hf.a.2477.1	yes	16	5.2	odd	4
2520.1.hf.a.2477.1	yes	16	280.237	even	4
2520.1.hf.a.2477.2	yes	16	35.27	even	4
2520.1.hf.a.2477.2	yes	16	40.37	odd	4
2520.1.hf.b.797.1	yes	16	45.32	even	12	inner
2520.1.hf.b.797.1	yes	16	2520.797	odd	12	inner
2520.1.hf.b.797.2	yes	16	315.167	odd	12	inner
2520.1.hf.b.797.2	yes	16	360.77	even	12	inner
2520.1.hf.b.1973.1	yes	16	1.1	even	1	trivial
2520.1.hf.b.1973.1	yes	16	56.13	odd	2	CM
2520.1.hf.b.1973.2	yes	16	7.6	odd	2	inner
2520.1.hf.b.1973.2	yes	16	8.5	even	2	inner

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:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2520.hf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.793353 + 0.608761i) q^{5} +(0.991445 + 0.130526i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.707107 + 0.707107i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.923880 - 0.382683i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.793353 + 0.608761i) q^{5} +(0.991445 + 0.130526i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.707107 + 0.707107i) q^{9} +(0.608761 - 0.793353i) q^{10} +(-0.991445 + 0.130526i) q^{12} +(-0.198092 + 0.739288i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.965926 - 0.258819i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.866025 - 0.500000i) q^{18} -0.261052i q^{19} +(-0.382683 + 0.923880i) q^{20} +(-0.130526 + 0.991445i) q^{21} +(-0.500000 - 0.133975i) q^{23} +(0.923880 - 0.382683i) q^{24} +(0.258819 - 0.965926i) q^{25} -0.765367i q^{26} +(-0.382683 - 0.923880i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-0.866025 + 0.500000i) q^{30} +(-0.258819 + 0.965926i) q^{32} +(0.793353 + 0.608761i) q^{35} +(0.965926 + 0.258819i) q^{36} +(0.0675653 + 0.252157i) q^{38} +(0.465926 - 0.607206i) q^{39} +(0.130526 - 0.991445i) q^{40} +(-0.130526 - 0.991445i) q^{42} +(-0.991445 - 0.130526i) q^{45} +0.517638 q^{46} +(-0.793353 + 0.608761i) q^{48} +(-0.866025 + 0.500000i) q^{49} +1.00000i q^{50} +(0.198092 + 0.739288i) q^{52} +(0.608761 + 0.793353i) q^{54} +(0.866025 + 0.500000i) q^{56} +(-0.0999004 + 0.241181i) q^{57} +(-0.923880 - 1.60021i) q^{59} +(0.707107 - 0.707107i) q^{60} +(-0.991445 + 1.71723i) q^{61} +(0.500000 - 0.866025i) q^{63} -1.00000i q^{64} +(-0.292893 - 0.707107i) q^{65} +(0.410670 + 0.315118i) q^{69} +(-0.923880 - 0.382683i) q^{70} +1.93185i q^{71} -1.00000 q^{72} +(-0.608761 + 0.793353i) q^{75} +(-0.130526 - 0.226078i) q^{76} +(-0.292893 + 0.707107i) q^{78} +(-1.67303 - 0.965926i) q^{79} +(0.130526 + 0.991445i) q^{80} +1.00000i q^{81} +(0.478235 + 1.78480i) q^{83} +(0.382683 + 0.923880i) q^{84} +(0.991445 - 0.130526i) q^{90} +0.765367 q^{91} +(-0.500000 + 0.133975i) q^{92} +(0.158919 + 0.207107i) q^{95} +(0.608761 - 0.793353i) q^{96} +(0.707107 - 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 8 q^{14} + 8 q^{16} - 8 q^{23} - 8 q^{39} + 8 q^{63} - 16 q^{65} - 16 q^{72} - 16 q^{78} - 8 q^{92}+O(q^{100}) \) 16 * q + 8 * q^14 + 8 * q^16 - 8 * q^23 - 8 * q^39 + 8 * q^63 - 16 * q^65 - 16 * q^72 - 16 * q^78 - 8 * q^92

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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