LMFDB - Embedded newform 1148.1.bj.a.319.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,1,Mod(319,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 3]))

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

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

chi := DirichletCharacter("1148.319");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1148.bj (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:	$0.572926634503$
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 4.2.13508516.2

Embedding invariants

Embedding label			319.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1148.319
Dual form			1148.1.bj.a.583.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(0.965926 - 0.258819i) q^{11} +(0.258819 - 0.965926i) q^{12} +(-1.00000 + 1.00000i) q^{13} +(-0.258819 - 0.965926i) q^{14} +(-0.707107 + 0.707107i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.965926 + 0.258819i) q^{19} +1.00000i q^{20} -1.00000i q^{21} +(0.707107 - 0.707107i) q^{22} +(-0.258819 - 0.965926i) q^{24} +(-0.366025 + 1.36603i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-0.258819 + 0.965926i) q^{30} +(-1.22474 - 0.707107i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +(0.258819 + 0.965926i) q^{35} +(0.965926 - 0.258819i) q^{38} +(-0.707107 + 1.22474i) q^{39} +(0.500000 + 0.866025i) q^{40} +1.00000i q^{41} +(-0.500000 - 0.866025i) q^{42} +(0.258819 - 0.965926i) q^{44} +(-0.707107 - 0.707107i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.366025 + 1.36603i) q^{52} +(0.366025 + 1.36603i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-0.707107 + 0.707107i) q^{55} +(-0.965926 - 0.258819i) q^{56} +1.00000 q^{57} +(1.22474 + 0.707107i) q^{59} +(0.258819 + 0.965926i) q^{60} +(0.866025 - 0.500000i) q^{61} -1.41421 q^{62} -1.00000 q^{64} +(0.366025 - 1.36603i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-0.517638 - 1.93185i) q^{67} +(0.707107 + 0.707107i) q^{70} +(0.707107 + 0.707107i) q^{71} +(0.707107 - 0.707107i) q^{76} -1.00000i q^{77} +1.41421i q^{78} +(-0.258819 + 0.965926i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +1.41421i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-0.258819 - 0.965926i) q^{88} +(-1.36603 - 0.366025i) q^{89} +(0.707107 + 1.22474i) q^{91} +(-1.36603 - 0.366025i) q^{93} +(-0.965926 + 0.258819i) q^{95} +(-0.965926 - 0.258819i) q^{96} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4}+O(q^{10}) $ 8 * q + 4 * q^4	$ 8 q + 4 q^{4} - 4 q^{10} - 8 q^{13} - 4 q^{16} + 4 q^{26} + 4 q^{40} - 4 q^{42} - 4 q^{52} - 4 q^{53} + 8 q^{57} - 8 q^{64} - 4 q^{65} + 4 q^{66} - 4 q^{81} + 4 q^{82} - 4 q^{89} - 4 q^{93} - 8 q^{98}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^10 - 8 * q^13 - 4 * q^16 + 4 * q^26 + 4 * q^40 - 4 * q^42 - 4 * q^52 - 4 * q^53 + 8 * q^57 - 8 * q^64 - 4 * q^65 + 4 * q^66 - 4 * q^81 + 4 * q^82 - 4 * q^89 - 4 * q^93 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.866025	−	0.500000i	0.866025	−	0.500000i
$2$	0.866025	−	0.500000i	0.866025	−	0.500000i
$3$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$4$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$5$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$6$	0.707107	−	0.707107i	0.707107	−	0.707107i
$7$	0.258819	−	0.965926i	0.258819	−	0.965926i
$7$	0.258819	−	0.965926i	0.258819	−	0.965926i
$8$		−	1.00000i		−	1.00000i
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$11$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$11$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$12$	0.258819	−	0.965926i	0.258819	−	0.965926i
$13$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$13$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$14$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$15$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$17$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$18$		0			0
$19$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$19$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$20$			1.00000i			1.00000i
$21$		−	1.00000i		−	1.00000i
$22$	0.707107	−	0.707107i	0.707107	−	0.707107i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$25$		0			0
$26$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$27$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$28$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$29$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$29$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$30$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$31$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$31$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$32$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$33$	0.866025	−	0.500000i	0.866025	−	0.500000i
$34$		0			0
$35$	0.258819	+	0.965926i	0.258819	+	0.965926i
$36$		0			0
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	0.965926	−	0.258819i	0.965926	−	0.258819i
$39$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$40$	0.500000	+	0.866025i	0.500000	+	0.866025i
$41$			1.00000i			1.00000i
$41$			1.00000i			1.00000i
$42$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$	0.258819	−	0.965926i	0.258819	−	0.965926i
$45$		0			0
$46$		0			0
$47$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$47$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$48$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$49$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$50$		0			0
$51$		0			0
$52$	0.366025	+	1.36603i	0.366025	+	1.36603i
$53$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$53$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$54$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$55$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$56$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$57$	1.00000			1.00000
$58$		0			0
$59$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$59$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$60$	0.258819	+	0.965926i	0.258819	+	0.965926i
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$62$	−1.41421			−1.41421
$63$		0			0
$64$	−1.00000			−1.00000
$65$	0.366025	−	1.36603i	0.366025	−	1.36603i
$66$	0.500000	−	0.866025i	0.500000	−	0.866025i
$67$	−0.517638	−	1.93185i	−0.517638	−	1.93185i	−0.258819	−	0.965926i	$-0.583333\pi$
$67$	−0.517638	−	1.93185i	−0.517638	−	1.93185i	−0.258819	−	0.965926i	$-0.583333\pi$
$68$		0			0
$69$		0			0
$70$	0.707107	+	0.707107i	0.707107	+	0.707107i
$71$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$71$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$72$		0			0
$73$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$73$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$74$		0			0
$75$		0			0
$76$	0.707107	−	0.707107i	0.707107	−	0.707107i
$77$		−	1.00000i		−	1.00000i
$78$			1.41421i			1.41421i
$79$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$79$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$80$	0.866025	+	0.500000i	0.866025	+	0.500000i
$81$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$82$	0.500000	+	0.866025i	0.500000	+	0.866025i
$83$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$83$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$84$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$89$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$89$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	0.707107	+	1.22474i	0.707107	+	1.22474i
$92$		0			0
$93$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$94$		0			0
$95$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$96$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$97$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$97$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$98$	−1.00000			−1.00000
$99$		0			0
$100$		0			0
$101$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$101$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$102$		0			0
$103$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$103$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$104$	1.00000	+	1.00000i	1.00000	+	1.00000i
$105$	0.500000	+	0.866025i	0.500000	+	0.866025i
$106$	1.00000	+	1.00000i	1.00000	+	1.00000i
$107$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$107$	−1.22474	+	0.707107i	−1.22474	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$108$	0.258819	+	0.965926i	0.258819	+	0.965926i
$109$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$109$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$110$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$111$		0			0
$112$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$113$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$113$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$114$	0.866025	−	0.500000i	0.866025	−	0.500000i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.41421			1.41421
$119$		0			0
$120$	0.707107	+	0.707107i	0.707107	+	0.707107i
$121$		0			0
$122$	0.500000	−	0.866025i	0.500000	−	0.866025i
$123$	0.258819	+	0.965926i	0.258819	+	0.965926i
$124$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$125$		−	1.00000i		−	1.00000i
$126$		0			0
$127$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$127$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$128$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$129$		0			0
$130$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		−	1.00000i		−	1.00000i
$133$	0.500000	−	0.866025i	0.500000	−	0.866025i
$134$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$135$	0.258819	−	0.965926i	0.258819	−	0.965926i
$136$		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			0
$139$		−	1.41421i		−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$139$		−	1.41421i		−	1.41421i	0.707107	−	0.707107i	$-0.250000\pi$
$140$	0.965926	+	0.258819i	0.965926	+	0.258819i
$141$		0			0
$142$	0.965926	+	0.258819i	0.965926	+	0.258819i
$143$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$148$		0			0
$149$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$149$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$150$		0			0
$151$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$151$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$152$	0.258819	−	0.965926i	0.258819	−	0.965926i
$153$		0			0
$154$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$155$	1.41421			1.41421
$156$	0.707107	+	1.22474i	0.707107	+	1.22474i
$157$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$157$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$158$	0.258819	+	0.965926i	0.258819	+	0.965926i
$159$	0.707107	+	1.22474i	0.707107	+	1.22474i
$160$	1.00000			1.00000
$161$		0			0
$162$			1.00000i			1.00000i
$163$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$163$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$164$	0.866025	+	0.500000i	0.866025	+	0.500000i
$165$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$166$	0.707107	+	1.22474i	0.707107	+	1.22474i
$167$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$167$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$168$	−1.00000			−1.00000
$169$		−	1.00000i		−	1.00000i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$173$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$174$		0			0
$175$		0			0
$176$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$177$	1.36603	+	0.366025i	1.36603	+	0.366025i
$178$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$179$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$179$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$180$		0			0
$181$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$181$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$182$	1.22474	+	0.707107i	1.22474	+	0.707107i
$183$	0.707107	−	0.707107i	0.707107	−	0.707107i
$184$		0			0
$185$		0			0
$186$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$187$		0			0
$188$		0			0
$189$	0.500000	+	0.866025i	0.500000	+	0.866025i
$190$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$191$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$191$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$192$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$193$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$193$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$194$		0			0
$195$		−	1.41421i		−	1.41421i
$196$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$197$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$197$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$198$		0			0
$199$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$199$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$200$		0			0
$201$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$206$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$207$		0			0
$208$	1.36603	+	0.366025i	1.36603	+	0.366025i
$209$	1.00000			1.00000
$210$	0.866025	+	0.500000i	0.866025	+	0.500000i
$211$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$211$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$212$	1.36603	+	0.366025i	1.36603	+	0.366025i
$213$	0.866025	+	0.500000i	0.866025	+	0.500000i
$214$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$215$		0			0
$216$	0.707107	+	0.707107i	0.707107	+	0.707107i
$217$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$218$		0			0
$219$		0			0
$220$	0.258819	+	0.965926i	0.258819	+	0.965926i
$221$		0			0
$222$		0			0
$223$		0			0		1.00000			$0$
$223$		0			0		−1.00000			$\pi$
$224$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$225$		0			0
$226$	0.866025	−	0.500000i	0.866025	−	0.500000i
$227$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$227$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$228$	0.500000	−	0.866025i	0.500000	−	0.866025i
$229$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$229$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$230$		0			0
$231$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$232$		0			0
$233$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$233$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$234$		0			0
$235$		0			0
$236$	1.22474	−	0.707107i	1.22474	−	0.707107i
$237$			1.00000i			1.00000i
$238$		0			0
$239$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$239$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$240$	0.965926	+	0.258819i	0.965926	+	0.258819i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$		0			0
$243$		0			0
$244$		−	1.00000i		−	1.00000i
$245$	1.00000			1.00000
$246$	0.707107	+	0.707107i	0.707107	+	0.707107i
$247$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$248$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$249$	0.366025	+	1.36603i	0.366025	+	1.36603i
$250$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$251$	1.41421			1.41421			0.707107	−	0.707107i	$-0.250000\pi$
$251$	1.41421			1.41421			0.707107	+	0.707107i	$0.250000\pi$
$252$		0			0
$253$		0			0
$254$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$255$		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
$260$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$261$		0			0
$262$		0			0
$263$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$263$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$264$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$265$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$266$		−	1.00000i		−	1.00000i
$267$	−1.41421			−1.41421
$268$	−1.93185	−	0.517638i	−1.93185	−	0.517638i
$269$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$270$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$		0			0
$273$	1.00000	+	1.00000i	1.00000	+	1.00000i
$274$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$275$		0			0
$276$		0			0
$277$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$277$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$278$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$279$		0			0
$280$	0.965926	−	0.258819i	0.965926	−	0.258819i
$281$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$281$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$282$		0			0
$283$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$283$	−1.22474	−	0.707107i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$284$	0.965926	−	0.258819i	0.965926	−	0.258819i
$285$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$286$			1.41421i			1.41421i
$287$	0.965926	+	0.258819i	0.965926	+	0.258819i
$288$		0			0
$289$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$293$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$294$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$295$	−1.41421			−1.41421
$296$		0			0
$297$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$298$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$305$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$309$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$310$	1.22474	−	0.707107i	1.22474	−	0.707107i
$311$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$311$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$312$	1.22474	+	0.707107i	1.22474	+	0.707107i
$313$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$313$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$314$		0			0
$315$		0			0
$316$	0.707107	+	0.707107i	0.707107	+	0.707107i
$317$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$317$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$318$	1.22474	+	0.707107i	1.22474	+	0.707107i
$319$		0			0
$320$	0.866025	−	0.500000i	0.866025	−	0.500000i
$321$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$322$		0			0
$323$		0			0
$324$	0.500000	+	0.866025i	0.500000	+	0.866025i
$325$		0			0
$326$	0.707107	−	1.22474i	0.707107	−	1.22474i
$327$		0			0
$328$	1.00000			1.00000
$329$		0			0
$330$			1.00000i			1.00000i
$331$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$331$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$332$	1.22474	+	0.707107i	1.22474	+	0.707107i
$333$		0			0
$334$		0			0
$335$	1.41421	+	1.41421i	1.41421	+	1.41421i
$336$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$337$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$337$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$338$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$339$	0.965926	−	0.258819i	0.965926	−	0.258819i
$340$		0			0
$341$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$344$		0			0
$345$		0			0
$346$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$347$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$347$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$348$		0			0
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		−	1.41421i		−	1.41421i
$352$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$354$	1.36603	−	0.366025i	1.36603	−	0.366025i
$355$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$356$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$357$		0			0
$358$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$359$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$359$	1.22474	−	0.707107i	1.22474	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$360$		0			0
$361$		0			0
$362$	1.36603	+	0.366025i	1.36603	+	0.366025i
$363$		0			0
$364$	1.41421			1.41421
$365$		0			0
$366$	0.258819	−	0.965926i	0.258819	−	0.965926i
$367$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$367$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.41421			1.41421
$372$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$373$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$373$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$376$		0			0
$377$		0			0
$378$	0.866025	+	0.500000i	0.866025	+	0.500000i
$379$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$379$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$380$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$381$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$382$		0			0
$383$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$383$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$384$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$385$	0.500000	+	0.866025i	0.500000	+	0.866025i
$386$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$387$		0			0
$388$		0			0
$389$	−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	$0.833333\pi$
$390$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$391$		0			0
$392$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$393$		0			0
$394$	0.500000	+	0.866025i	0.500000	+	0.866025i
$395$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$396$		0			0
$397$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$397$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$398$		0			0
$399$	0.258819	−	0.965926i	0.258819	−	0.965926i
$400$		0			0
$401$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$401$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$402$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$403$	1.93185	−	0.517638i	1.93185	−	0.517638i
$404$		0			0
$405$		−	1.00000i		−	1.00000i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$409$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$410$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$411$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$412$	−1.41421			−1.41421
$413$	1.00000	−	1.00000i	1.00000	−	1.00000i
$414$		0			0
$415$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$416$	1.36603	−	0.366025i	1.36603	−	0.366025i
$417$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$418$	0.866025	−	0.500000i	0.866025	−	0.500000i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	1.00000			1.00000
$421$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$421$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$422$	0.258819	−	0.965926i	0.258819	−	0.965926i
$423$		0			0
$424$	1.36603	−	0.366025i	1.36603	−	0.366025i
$425$		0			0
$426$	1.00000			1.00000
$427$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$428$			1.41421i			1.41421i
$429$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	0.965926	+	0.258819i	0.965926	+	0.258819i
$433$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$433$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$434$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$439$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$440$	0.707107	+	0.707107i	0.707107	+	0.707107i
$441$		0			0
$442$		0			0
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$	1.36603	−	0.366025i	1.36603	−	0.366025i
$446$		0			0
$447$		−	1.41421i		−	1.41421i
$448$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$449$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$449$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$450$		0			0
$451$	0.258819	+	0.965926i	0.258819	+	0.965926i
$452$	0.500000	−	0.866025i	0.500000	−	0.866025i
$453$		0			0
$454$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$455$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$456$		−	1.00000i		−	1.00000i
$457$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$457$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$461$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$462$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$463$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$463$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$464$		0			0
$465$	1.36603	−	0.366025i	1.36603	−	0.366025i
$466$	1.36603	−	0.366025i	1.36603	−	0.366025i
$467$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$467$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$468$		0			0
$469$	−2.00000			−2.00000
$470$		0			0
$471$		0			0
$472$	0.707107	−	1.22474i	0.707107	−	1.22474i
$473$		0			0
$474$	0.500000	+	0.866025i	0.500000	+	0.866025i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$479$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$479$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$480$	0.965926	−	0.258819i	0.965926	−	0.258819i
$481$		0			0
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$487$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$488$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$489$	1.00000	−	1.00000i	1.00000	−	1.00000i
$490$	0.866025	−	0.500000i	0.866025	−	0.500000i
$491$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$491$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$492$	0.965926	+	0.258819i	0.965926	+	0.258819i
$493$		0			0
$494$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$495$		0			0
$496$			1.41421i			1.41421i
$497$	0.866025	−	0.500000i	0.866025	−	0.500000i
$498$	1.00000	+	1.00000i	1.00000	+	1.00000i
$499$	0.517638	−	1.93185i	0.517638	−	1.93185i	0.258819	−	0.965926i	$-0.416667\pi$
$499$	0.517638	−	1.93185i	0.517638	−	1.93185i	0.258819	−	0.965926i	$-0.416667\pi$
$500$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$501$		0			0
$502$	1.22474	−	0.707107i	1.22474	−	0.707107i
$503$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$503$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$508$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$509$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$509$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			1.00000i
$513$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$514$		0			0
$515$	1.22474	+	0.707107i	1.22474	+	0.707107i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$520$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$521$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$521$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$522$		0			0
$523$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$523$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$531$		0			0
$532$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$533$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$534$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$535$	0.707107	−	1.22474i	0.707107	−	1.22474i
$536$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$537$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$538$		−	1.00000i		−	1.00000i
$539$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$540$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$541$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$541$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$542$		0			0
$543$	1.22474	+	0.707107i	1.22474	+	0.707107i
$544$		0			0
$545$		0			0
$546$	1.36603	+	0.366025i	1.36603	+	0.366025i
$547$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$547$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$548$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.866025	+	0.500000i	0.866025	+	0.500000i
$554$			1.00000i			1.00000i
$555$		0			0
$556$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$557$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$557$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$558$		0			0
$559$		0			0
$560$	0.707107	−	0.707107i	0.707107	−	0.707107i
$561$		0			0
$562$		0			0
$563$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$563$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$564$		0			0
$565$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$566$	−1.41421			−1.41421
$567$	0.707107	+	0.707107i	0.707107	+	0.707107i
$568$	0.707107	−	0.707107i	0.707107	−	0.707107i
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$571$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$571$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$572$	0.707107	+	1.22474i	0.707107	+	1.22474i
$573$		0			0
$574$	0.965926	−	0.258819i	0.965926	−	0.258819i
$575$		0			0
$576$		0			0
$577$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$577$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$578$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$579$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$580$		0			0
$581$	1.36603	+	0.366025i	1.36603	+	0.366025i
$582$		0			0
$583$	0.707107	+	1.22474i	0.707107	+	1.22474i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$587$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$588$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$589$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$590$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$591$	0.258819	+	0.965926i	0.258819	+	0.965926i
$592$		0			0
$593$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$593$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$594$			1.00000i			1.00000i
$595$		0			0
$596$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$597$		0			0
$598$		0			0
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$		0			0
$601$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$601$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$607$	−0.707107	−	1.22474i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$608$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$609$		0			0
$610$			1.00000i			1.00000i
$611$		0			0
$612$		0			0
$613$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$613$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$614$		0			0
$615$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$616$	−1.00000			−1.00000
$617$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$617$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$618$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$619$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$619$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$620$	0.707107	−	1.22474i	0.707107	−	1.22474i
$621$		0			0
$622$		0			0
$623$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$624$	1.41421			1.41421
$625$	0.500000	+	0.866025i	0.500000	+	0.866025i
$626$		0			0
$627$	0.965926	−	0.258819i	0.965926	−	0.258819i
$628$		0			0
$629$		0			0
$630$		0			0
$631$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$631$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$632$	0.965926	+	0.258819i	0.965926	+	0.258819i
$633$	0.500000	−	0.866025i	0.500000	−	0.866025i
$634$		0			0
$635$	0.707107	+	1.22474i	0.707107	+	1.22474i
$636$	1.41421			1.41421
$637$	1.36603	−	0.366025i	1.36603	−	0.366025i
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.500000	−	0.866025i
$641$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$641$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$643$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$643$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.707107	−	1.22474i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$647$	0.707107	−	1.22474i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$648$	0.866025	+	0.500000i	0.866025	+	0.500000i
$649$	1.36603	+	0.366025i	1.36603	+	0.366025i
$650$		0			0
$651$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$652$		−	1.41421i		−	1.41421i
$653$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$653$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$654$		0			0
$655$		0			0
$656$	0.866025	−	0.500000i	0.866025	−	0.500000i
$657$		0			0
$658$		0			0
$659$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$659$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$660$	0.500000	+	0.866025i	0.500000	+	0.866025i
$661$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$661$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$662$		0			0
$663$		0			0
$664$	1.41421			1.41421
$665$			1.00000i			1.00000i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$	1.93185	+	0.517638i	1.93185	+	0.517638i
$671$	0.707107	−	0.707107i	0.707107	−	0.707107i
$672$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$673$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$673$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$674$	0.500000	+	0.866025i	0.500000	+	0.866025i
$675$		0			0
$676$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$677$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$677$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$678$	0.707107	−	0.707107i	0.707107	−	0.707107i
$679$		0			0
$680$		0			0
$681$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$682$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$683$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$683$	0.517638	+	1.93185i	0.517638	+	1.93185i	0.258819	+	0.965926i	$0.416667\pi$
$684$		0			0
$685$	1.00000	−	1.00000i	1.00000	−	1.00000i
$686$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$687$		0			0
$688$		0			0
$689$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$690$		0			0
$691$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$691$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$692$			1.00000i			1.00000i
$693$		0			0
$694$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$695$	0.707107	+	1.22474i	0.707107	+	1.22474i
$696$		0			0
$697$		0			0
$698$		0			0
$699$	1.41421			1.41421
$700$		0			0
$701$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$701$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$702$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$703$		0			0
$704$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$705$		0			0
$706$		−	1.00000i		−	1.00000i
$707$		0			0
$708$	1.00000	−	1.00000i	1.00000	−	1.00000i
$709$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$709$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$710$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$711$		0			0
$712$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$713$		0			0
$714$		0			0
$715$		−	1.41421i		−	1.41421i
$716$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$717$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$718$	0.707107	−	1.22474i	0.707107	−	1.22474i
$719$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$719$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$720$		0			0
$721$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$722$		0			0
$723$		0			0
$724$	1.36603	−	0.366025i	1.36603	−	0.366025i
$725$		0			0
$726$		0			0
$727$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$727$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$728$	1.22474	−	0.707107i	1.22474	−	0.707107i
$729$		−	1.00000i		−	1.00000i
$730$		0			0
$731$		0			0
$732$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$			1.41421i			1.41421i
$735$	0.965926	−	0.258819i	0.965926	−	0.258819i
$736$		0			0
$737$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$738$		0			0
$739$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$739$	1.22474	+	0.707107i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$740$		0			0
$741$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$742$	1.22474	−	0.707107i	1.22474	−	0.707107i
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$745$	0.366025	+	1.36603i	0.366025	+	1.36603i
$746$	0.866025	+	0.500000i	0.866025	+	0.500000i
$747$		0			0
$748$		0			0
$749$	0.366025	+	1.36603i	0.366025	+	1.36603i
$750$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$751$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$751$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$752$		0			0
$753$	1.36603	−	0.366025i	1.36603	−	0.366025i
$754$		0			0
$755$		0			0
$756$	1.00000			1.00000
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$	0.707107	+	1.22474i	0.707107	+	1.22474i
$759$		0			0
$760$	0.258819	+	0.965926i	0.258819	+	0.965926i
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.965926	−	0.258819i	0.965926	−	0.258819i
$767$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$768$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$769$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$769$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$770$	0.866025	+	0.500000i	0.866025	+	0.500000i
$771$		0			0
$772$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$773$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.866025	−	0.500000i	$-0.833333\pi$
$773$	−1.36603	+	0.366025i	−1.36603	+	0.366025i	−0.500000	+	0.866025i	$0.666667\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.00000			−1.00000
$779$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$780$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$781$	0.866025	+	0.500000i	0.866025	+	0.500000i
$782$		0			0
$783$		0			0
$784$			1.00000i			1.00000i
$785$		0			0
$786$		0			0
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	0.866025	+	0.500000i	0.866025	+	0.500000i
$789$		0			0
$790$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$791$	0.258819	−	0.965926i	0.258819	−	0.965926i
$792$		0			0
$793$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$794$	1.36603	−	0.366025i	1.36603	−	0.366025i
$795$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	0.500000	−	0.866025i	0.500000	−	0.866025i
$803$		0			0
$804$	−2.00000			−2.00000
$805$		0			0
$806$	1.41421	−	1.41421i	1.41421	−	1.41421i
$807$	0.258819	−	0.965926i	0.258819	−	0.965926i
$808$		0			0
$809$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$809$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$810$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$811$	−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
$815$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$816$		0			0
$817$		0			0
$818$		−	1.00000i		−	1.00000i
$819$		0			0
$820$	−1.00000			−1.00000
$821$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$821$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$822$	−0.707107	+	1.22474i	−0.707107	+	1.22474i
$823$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$823$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$824$	−1.22474	+	0.707107i	−1.22474	+	0.707107i
$825$		0			0
$826$	0.366025	−	1.36603i	0.366025	−	1.36603i
$827$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$827$	1.41421	+	1.41421i	1.41421	+	1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$828$		0			0
$829$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$829$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$830$	−1.22474	−	0.707107i	−1.22474	−	0.707107i
$831$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$832$	1.00000	−	1.00000i	1.00000	−	1.00000i
$833$		0			0
$834$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$835$		0			0
$836$	0.500000	−	0.866025i	0.500000	−	0.866025i
$837$	1.36603	−	0.366025i	1.36603	−	0.366025i
$838$		0			0
$839$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$839$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$840$	0.866025	−	0.500000i	0.866025	−	0.500000i
$841$			1.00000i			1.00000i
$842$	0.366025	−	1.36603i	0.366025	−	1.36603i
$843$		0			0
$844$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$845$	0.500000	+	0.866025i	0.500000	+	0.866025i
$846$		0			0
$847$		0			0
$848$	1.00000	−	1.00000i	1.00000	−	1.00000i
$849$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$850$		0			0
$851$		0			0
$852$	0.866025	−	0.500000i	0.866025	−	0.500000i
$853$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$853$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$854$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$855$		0			0
$856$	0.707107	+	1.22474i	0.707107	+	1.22474i
$857$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$857$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$858$	0.366025	+	1.36603i	0.366025	+	1.36603i
$859$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$859$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$860$		0			0
$861$	1.00000			1.00000
$862$		0			0
$863$	0.707107	+	1.22474i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$863$	0.707107	+	1.22474i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$864$	0.965926	−	0.258819i	0.965926	−	0.258819i
$865$	0.500000	−	0.866025i	0.500000	−	0.866025i
$866$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$867$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$868$	0.366025	+	1.36603i	0.366025	+	1.36603i
$869$			1.00000i			1.00000i
$870$		0			0
$871$	2.44949	+	1.41421i	2.44949	+	1.41421i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$876$		0			0
$877$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$877$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$878$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$879$		0			0
$880$	0.965926	+	0.258819i	0.965926	+	0.258819i
$881$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$881$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$882$		0			0
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$886$		0			0
$887$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$887$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$888$		0			0
$889$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$890$	1.00000	−	1.00000i	1.00000	−	1.00000i
$891$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$892$		0			0
$893$		0			0
$894$	−0.707107	−	1.22474i	−0.707107	−	1.22474i
$895$	0.707107	+	0.707107i	0.707107	+	0.707107i
$896$	0.258819	+	0.965926i	0.258819	+	0.965926i
$897$		0			0
$898$	0.500000	+	0.866025i	0.500000	+	0.866025i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	0.707107	+	0.707107i	0.707107	+	0.707107i
$903$		0			0
$904$		−	1.00000i		−	1.00000i
$905$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$906$		0			0
$907$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$907$	−0.707107	+	1.22474i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$908$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$909$		0			0
$910$	−1.41421			−1.41421
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$913$	0.366025	+	1.36603i	0.366025	+	1.36603i
$914$		0			0
$915$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$919$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$920$		0			0
$921$		0			0
$922$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$923$	−1.41421			−1.41421
$924$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$925$		0			0
$926$	0.965926	+	0.258819i	0.965926	+	0.258819i
$927$		0			0
$928$		0			0
$929$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$929$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$930$	1.00000	−	1.00000i	1.00000	−	1.00000i
$931$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$932$	1.00000	−	1.00000i	1.00000	−	1.00000i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$937$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$938$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$939$		0			0
$940$		0			0
$941$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$941$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$942$		0			0
$943$		0			0
$944$		−	1.41421i		−	1.41421i
$945$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$946$		0			0
$947$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$947$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$948$	0.866025	+	0.500000i	0.866025	+	0.500000i
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$957$		0			0
$958$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$959$			1.41421i			1.41421i
$960$	0.707107	−	0.707107i	0.707107	−	0.707107i
$961$	0.500000	+	0.866025i	0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.00000	+	1.00000i	1.00000	+	1.00000i
$966$		0			0
$967$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$967$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$971$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$972$		0			0
$973$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$974$			1.41421i			1.41421i
$975$		0			0
$976$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$977$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$977$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$978$	0.366025	−	1.36603i	0.366025	−	1.36603i
$979$	−1.41421			−1.41421
$980$	0.500000	−	0.866025i	0.500000	−	0.866025i
$981$		0			0
$982$	0.707107	+	1.22474i	0.707107	+	1.22474i
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$	0.965926	−	0.258819i	0.965926	−	0.258819i
$985$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$986$		0			0
$987$		0			0
$988$			1.41421i			1.41421i
$989$		0			0
$990$		0			0
$991$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$991$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$992$	0.707107	+	1.22474i	0.707107	+	1.22474i
$993$		0			0
$994$	0.500000	−	0.866025i	0.500000	−	0.866025i
$995$		0			0
$996$	1.36603	+	0.366025i	1.36603	+	0.366025i
$997$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$997$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$998$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.1.bj.a.319.2	yes	8
4.3	odd	2	inner	1148.1.bj.a.319.1	✓	8
7.2	even	3	inner	1148.1.bj.a.975.1	yes	8
28.23	odd	6	inner	1148.1.bj.a.975.2	yes	8
41.9	even	4	inner	1148.1.bj.a.1075.2	yes	8
164.91	odd	4	inner	1148.1.bj.a.1075.1	yes	8
287.9	even	12	inner	1148.1.bj.a.583.1	yes	8
1148.583	odd	12	inner	1148.1.bj.a.583.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.1.bj.a.319.1	✓	8	4.3	odd	2	inner
1148.1.bj.a.319.2	yes	8	1.1	even	1	trivial
1148.1.bj.a.583.1	yes	8	287.9	even	12	inner
1148.1.bj.a.583.2	yes	8	1148.583	odd	12	inner
1148.1.bj.a.975.1	yes	8	7.2	even	3	inner
1148.1.bj.a.975.2	yes	8	28.23	odd	6	inner
1148.1.bj.a.1075.1	yes	8	164.91	odd	4	inner
1148.1.bj.a.1075.2	yes	8	41.9	even	4	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1148.bj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.965926 - 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(0.707107 - 0.707107i) q^{6} +(0.258819 - 0.965926i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(0.965926 - 0.258819i) q^{11} +(0.258819 - 0.965926i) q^{12} +(-1.00000 + 1.00000i) q^{13} +(-0.258819 - 0.965926i) q^{14} +(-0.707107 + 0.707107i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.965926 + 0.258819i) q^{19} +1.00000i q^{20} -1.00000i q^{21} +(0.707107 - 0.707107i) q^{22} +(-0.258819 - 0.965926i) q^{24} +(-0.366025 + 1.36603i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-0.258819 + 0.965926i) q^{30} +(-1.22474 - 0.707107i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +(0.258819 + 0.965926i) q^{35} +(0.965926 - 0.258819i) q^{38} +(-0.707107 + 1.22474i) q^{39} +(0.500000 + 0.866025i) q^{40} +1.00000i q^{41} +(-0.500000 - 0.866025i) q^{42} +(0.258819 - 0.965926i) q^{44} +(-0.707107 - 0.707107i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(0.366025 + 1.36603i) q^{52} +(0.366025 + 1.36603i) q^{53} +(-0.258819 + 0.965926i) q^{54} +(-0.707107 + 0.707107i) q^{55} +(-0.965926 - 0.258819i) q^{56} +1.00000 q^{57} +(1.22474 + 0.707107i) q^{59} +(0.258819 + 0.965926i) q^{60} +(0.866025 - 0.500000i) q^{61} -1.41421 q^{62} -1.00000 q^{64} +(0.366025 - 1.36603i) q^{65} +(0.500000 - 0.866025i) q^{66} +(-0.517638 - 1.93185i) q^{67} +(0.707107 + 0.707107i) q^{70} +(0.707107 + 0.707107i) q^{71} +(0.707107 - 0.707107i) q^{76} -1.00000i q^{77} +1.41421i q^{78} +(-0.258819 + 0.965926i) q^{79} +(0.866025 + 0.500000i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.500000 + 0.866025i) q^{82} +1.41421i q^{83} +(-0.866025 - 0.500000i) q^{84} +(-0.258819 - 0.965926i) q^{88} +(-1.36603 - 0.366025i) q^{89} +(0.707107 + 1.22474i) q^{91} +(-1.36603 - 0.366025i) q^{93} +(-0.965926 + 0.258819i) q^{95} +(-0.965926 - 0.258819i) q^{96} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4}+O(q^{10}) \) 8 * q + 4 * q^4	\( 8 q + 4 q^{4} - 4 q^{10} - 8 q^{13} - 4 q^{16} + 4 q^{26} + 4 q^{40} - 4 q^{42} - 4 q^{52} - 4 q^{53} + 8 q^{57} - 8 q^{64} - 4 q^{65} + 4 q^{66} - 4 q^{81} + 4 q^{82} - 4 q^{89} - 4 q^{93} - 8 q^{98}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^10 - 8 * q^13 - 4 * q^16 + 4 * q^26 + 4 * q^40 - 4 * q^42 - 4 * q^52 - 4 * q^53 + 8 * q^57 - 8 * q^64 - 4 * q^65 + 4 * q^66 - 4 * q^81 + 4 * q^82 - 4 * q^89 - 4 * q^93 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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