LMFDB - Embedded newform 1260.1.eb.a.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,1,Mod(223,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 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("1260.223");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1260.eb (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:	$0.628821915918$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.1134000.1

Embedding invariants

Embedding label			223.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1260.223
Dual form			1260.1.eb.a.1147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.258819 + 0.965926i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.258819 + 0.965926i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +(-0.707107 + 0.707107i) q^{10} +(0.866025 + 0.500000i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-0.965926 - 0.258819i) q^{13} +(-0.965926 - 0.258819i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.707107 - 0.707107i) q^{17} +(-0.866025 - 0.500000i) q^{18} +1.41421i q^{19} +(-0.258819 - 0.965926i) q^{20} +(0.500000 - 0.866025i) q^{21} +(-0.866025 + 0.500000i) q^{22} +(-0.707107 - 0.707107i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.707107 - 0.707107i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.707107 - 0.707107i) q^{28} +1.00000 q^{30} +(-0.500000 - 0.866025i) q^{32} +(-0.258819 - 0.965926i) q^{33} +(0.965926 - 0.258819i) q^{34} +1.00000i q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.22474 - 0.707107i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.965926 + 0.258819i) q^{40} +(0.500000 + 0.866025i) q^{42} +(0.366025 + 1.36603i) q^{43} -1.00000i q^{44} +(-0.258819 + 0.965926i) q^{45} +(-0.258819 - 0.965926i) q^{47} +(0.965926 - 0.258819i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.866025 + 0.500000i) q^{50} +1.00000i q^{51} +(0.258819 + 0.965926i) q^{52} +(1.00000 + 1.00000i) q^{53} +(0.258819 + 0.965926i) q^{54} +(0.707107 + 0.707107i) q^{55} +(0.258819 + 0.965926i) q^{56} +(1.00000 - 1.00000i) q^{57} +(-0.500000 + 0.866025i) q^{60} +(1.22474 + 0.707107i) q^{61} +(-0.965926 + 0.258819i) q^{63} +1.00000 q^{64} +(-0.866025 - 0.500000i) q^{65} +(0.965926 + 0.258819i) q^{66} +(-0.258819 + 0.965926i) q^{68} +(-0.866025 - 0.500000i) q^{70} -1.00000i q^{71} +1.00000i q^{72} +(-0.707107 + 0.707107i) q^{73} +(-0.258819 - 0.965926i) q^{75} +(1.22474 - 0.707107i) q^{76} +(-0.258819 + 0.965926i) q^{77} -1.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.707107 + 0.707107i) q^{80} -1.00000 q^{81} +(0.965926 - 0.258819i) q^{83} -1.00000 q^{84} +(-0.500000 - 0.866025i) q^{85} +(-1.36603 - 0.366025i) q^{86} +(0.866025 + 0.500000i) q^{88} +(-0.707107 - 0.707107i) q^{90} -1.00000i q^{91} +(0.965926 + 0.258819i) q^{94} +(-0.366025 + 1.36603i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-0.965926 + 0.258819i) q^{97} -1.00000i q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{15} - 4 q^{16} + 4 q^{21} + 8 q^{30} - 4 q^{32} + 4 q^{39} + 4 q^{42} - 4 q^{43} + 8 q^{53} + 8 q^{57} - 4 q^{60} + 8 q^{64} - 8 q^{78} + 4 q^{79} - 8 q^{81} - 8 q^{84} - 4 q^{85} - 4 q^{86} + 4 q^{95} - 4 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^15 - 4 * q^16 + 4 * q^21 + 8 * q^30 - 4 * q^32 + 4 * q^39 + 4 * q^42 - 4 * q^43 + 8 * q^53 + 8 * q^57 - 4 * q^60 + 8 * q^64 - 8 * q^78 + 4 * q^79 - 8 * q^81 - 8 * q^84 - 4 * q^85 - 4 * q^86 + 4 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.1.eb.a.223.1	✓	8
3.2	odd	2		3780.1.ee.b.3583.1		8
4.3	odd	2		1260.1.eb.b.223.2	yes	8
5.2	odd	4		1260.1.eb.b.727.1	yes	8
7.6	odd	2	inner	1260.1.eb.a.223.2	yes	8
9.4	even	3	inner	1260.1.eb.a.643.1	yes	8
9.5	odd	6		3780.1.ee.b.1063.2		8
12.11	even	2		3780.1.ee.a.3583.1		8
15.2	even	4		3780.1.ee.a.2827.1		8
20.7	even	4	inner	1260.1.eb.a.727.2	yes	8
21.20	even	2		3780.1.ee.b.3583.2		8
28.27	even	2		1260.1.eb.b.223.1	yes	8
35.27	even	4		1260.1.eb.b.727.2	yes	8
36.23	even	6		3780.1.ee.a.1063.2		8
36.31	odd	6		1260.1.eb.b.643.2	yes	8
45.22	odd	12		1260.1.eb.b.1147.1	yes	8
45.32	even	12		3780.1.ee.a.307.2		8
60.47	odd	4		3780.1.ee.b.2827.1		8
63.13	odd	6	inner	1260.1.eb.a.643.2	yes	8
63.41	even	6		3780.1.ee.b.1063.1		8
84.83	odd	2		3780.1.ee.a.3583.2		8
105.62	odd	4		3780.1.ee.a.2827.2		8
140.27	odd	4	inner	1260.1.eb.a.727.1	yes	8
180.67	even	12	inner	1260.1.eb.a.1147.2	yes	8
180.167	odd	12		3780.1.ee.b.307.2		8
252.139	even	6		1260.1.eb.b.643.1	yes	8
252.167	odd	6		3780.1.ee.a.1063.1		8
315.167	odd	12		3780.1.ee.a.307.1		8
315.202	even	12		1260.1.eb.b.1147.2	yes	8
420.167	even	4		3780.1.ee.b.2827.2		8
1260.167	even	12		3780.1.ee.b.307.1		8
1260.1147	odd	12	inner	1260.1.eb.a.1147.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.1.eb.a.223.1	✓	8	1.1	even	1	trivial
1260.1.eb.a.223.2	yes	8	7.6	odd	2	inner
1260.1.eb.a.643.1	yes	8	9.4	even	3	inner
1260.1.eb.a.643.2	yes	8	63.13	odd	6	inner
1260.1.eb.a.727.1	yes	8	140.27	odd	4	inner
1260.1.eb.a.727.2	yes	8	20.7	even	4	inner
1260.1.eb.a.1147.1	yes	8	1260.1147	odd	12	inner
1260.1.eb.a.1147.2	yes	8	180.67	even	12	inner
1260.1.eb.b.223.1	yes	8	28.27	even	2
1260.1.eb.b.223.2	yes	8	4.3	odd	2
1260.1.eb.b.643.1	yes	8	252.139	even	6
1260.1.eb.b.643.2	yes	8	36.31	odd	6
1260.1.eb.b.727.1	yes	8	5.2	odd	4
1260.1.eb.b.727.2	yes	8	35.27	even	4
1260.1.eb.b.1147.1	yes	8	45.22	odd	12
1260.1.eb.b.1147.2	yes	8	315.202	even	12
3780.1.ee.a.307.1		8	315.167	odd	12
3780.1.ee.a.307.2		8	45.32	even	12
3780.1.ee.a.1063.1		8	252.167	odd	6
3780.1.ee.a.1063.2		8	36.23	even	6
3780.1.ee.a.2827.1		8	15.2	even	4
3780.1.ee.a.2827.2		8	105.62	odd	4
3780.1.ee.a.3583.1		8	12.11	even	2
3780.1.ee.a.3583.2		8	84.83	odd	2
3780.1.ee.b.307.1		8	1260.167	even	12
3780.1.ee.b.307.2		8	180.167	odd	12
3780.1.ee.b.1063.1		8	63.41	even	6
3780.1.ee.b.1063.2		8	9.5	odd	6
3780.1.ee.b.2827.1		8	60.47	odd	4
3780.1.ee.b.2827.2		8	420.167	even	4
3780.1.ee.b.3583.1		8	3.2	odd	2
3780.1.ee.b.3583.2		8	21.20	even	2

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1260.eb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.258819 + 0.965926i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.965926 - 0.258819i) q^{6} +(0.258819 + 0.965926i) q^{7} +1.00000 q^{8} +1.00000i q^{9} +(-0.707107 + 0.707107i) q^{10} +(0.866025 + 0.500000i) q^{11} +(-0.258819 + 0.965926i) q^{12} +(-0.965926 - 0.258819i) q^{13} +(-0.965926 - 0.258819i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.707107 - 0.707107i) q^{17} +(-0.866025 - 0.500000i) q^{18} +1.41421i q^{19} +(-0.258819 - 0.965926i) q^{20} +(0.500000 - 0.866025i) q^{21} +(-0.866025 + 0.500000i) q^{22} +(-0.707107 - 0.707107i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.707107 - 0.707107i) q^{26} +(0.707107 - 0.707107i) q^{27} +(0.707107 - 0.707107i) q^{28} +1.00000 q^{30} +(-0.500000 - 0.866025i) q^{32} +(-0.258819 - 0.965926i) q^{33} +(0.965926 - 0.258819i) q^{34} +1.00000i q^{35} +(0.866025 - 0.500000i) q^{36} +(-1.22474 - 0.707107i) q^{38} +(0.500000 + 0.866025i) q^{39} +(0.965926 + 0.258819i) q^{40} +(0.500000 + 0.866025i) q^{42} +(0.366025 + 1.36603i) q^{43} -1.00000i q^{44} +(-0.258819 + 0.965926i) q^{45} +(-0.258819 - 0.965926i) q^{47} +(0.965926 - 0.258819i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-0.866025 + 0.500000i) q^{50} +1.00000i q^{51} +(0.258819 + 0.965926i) q^{52} +(1.00000 + 1.00000i) q^{53} +(0.258819 + 0.965926i) q^{54} +(0.707107 + 0.707107i) q^{55} +(0.258819 + 0.965926i) q^{56} +(1.00000 - 1.00000i) q^{57} +(-0.500000 + 0.866025i) q^{60} +(1.22474 + 0.707107i) q^{61} +(-0.965926 + 0.258819i) q^{63} +1.00000 q^{64} +(-0.866025 - 0.500000i) q^{65} +(0.965926 + 0.258819i) q^{66} +(-0.258819 + 0.965926i) q^{68} +(-0.866025 - 0.500000i) q^{70} -1.00000i q^{71} +1.00000i q^{72} +(-0.707107 + 0.707107i) q^{73} +(-0.258819 - 0.965926i) q^{75} +(1.22474 - 0.707107i) q^{76} +(-0.258819 + 0.965926i) q^{77} -1.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.707107 + 0.707107i) q^{80} -1.00000 q^{81} +(0.965926 - 0.258819i) q^{83} -1.00000 q^{84} +(-0.500000 - 0.866025i) q^{85} +(-1.36603 - 0.366025i) q^{86} +(0.866025 + 0.500000i) q^{88} +(-0.707107 - 0.707107i) q^{90} -1.00000i q^{91} +(0.965926 + 0.258819i) q^{94} +(-0.366025 + 1.36603i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-0.965926 + 0.258819i) q^{97} -1.00000i q^{98} +(-0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{15} - 4 q^{16} + 4 q^{21} + 8 q^{30} - 4 q^{32} + 4 q^{39} + 4 q^{42} - 4 q^{43} + 8 q^{53} + 8 q^{57} - 4 q^{60} + 8 q^{64} - 8 q^{78} + 4 q^{79} - 8 q^{81} - 8 q^{84} - 4 q^{85} - 4 q^{86} + 4 q^{95} - 4 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 4 * q^15 - 4 * q^16 + 4 * q^21 + 8 * q^30 - 4 * q^32 + 4 * q^39 + 4 * q^42 - 4 * q^43 + 8 * q^53 + 8 * q^57 - 4 * q^60 + 8 * q^64 - 8 * q^78 + 4 * q^79 - 8 * q^81 - 8 * q^84 - 4 * q^85 - 4 * q^86 + 4 * q^95 - 4 * q^99

Introduction

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