LMFDB - Embedded newform 1456.1.bc.b.181.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1456,1,Mod(181,1456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1456, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 2]))

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

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

chi := DirichletCharacter("1456.181");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1456 = 2^{4} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1456.bc (of order $4$, degree $2$, 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:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.2.186368.2

Embedding invariants

Embedding label			181.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1456.181
Dual form			1456.1.bc.b.909.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 1.00000i) q^{5} +1.00000i q^{6} -1.00000i q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 1.00000i) q^{5} +1.00000i q^{6} -1.00000i q^{7} +(0.707107 - 0.707107i) q^{8} -1.41421i q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 - 0.707107i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.707107 + 0.707107i) q^{14} -1.41421i q^{15} -1.00000 q^{16} +1.41421i q^{17} +(-1.00000 + 1.00000i) q^{20} +(-0.707107 + 0.707107i) q^{21} -1.00000 q^{22} +1.00000i q^{23} -1.00000 q^{24} +1.00000i q^{25} -1.00000i q^{26} +(-0.707107 + 0.707107i) q^{27} +1.00000 q^{28} +(1.00000 - 1.00000i) q^{29} +(-1.00000 + 1.00000i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} -1.00000 q^{33} +(1.00000 - 1.00000i) q^{34} +(1.00000 - 1.00000i) q^{35} +(0.707107 - 0.707107i) q^{37} -1.00000i q^{39} +1.41421 q^{40} -1.00000i q^{41} +1.00000 q^{42} +(1.00000 + 1.00000i) q^{43} +(0.707107 + 0.707107i) q^{44} +(0.707107 - 0.707107i) q^{46} +1.00000 q^{47} +(0.707107 + 0.707107i) q^{48} -1.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(1.00000 - 1.00000i) q^{51} +(-0.707107 + 0.707107i) q^{52} +(-1.00000 - 1.00000i) q^{53} +1.00000 q^{54} +1.41421 q^{55} +(-0.707107 - 0.707107i) q^{56} -1.41421 q^{58} +1.41421 q^{60} +(-0.707107 - 0.707107i) q^{61} +(0.707107 + 0.707107i) q^{62} -1.00000i q^{64} +1.41421i q^{65} +(0.707107 + 0.707107i) q^{66} +(-0.707107 - 0.707107i) q^{67} -1.41421 q^{68} +(0.707107 - 0.707107i) q^{69} -1.41421 q^{70} +1.41421 q^{71} +1.00000i q^{73} -1.00000 q^{74} +(0.707107 - 0.707107i) q^{75} +(-0.707107 - 0.707107i) q^{77} +(-0.707107 + 0.707107i) q^{78} -1.00000 q^{79} +(-1.00000 - 1.00000i) q^{80} +1.00000 q^{81} +(-0.707107 + 0.707107i) q^{82} +(-0.707107 - 0.707107i) q^{84} +(-1.41421 + 1.41421i) q^{85} -1.41421i q^{86} -1.41421 q^{87} -1.00000i q^{88} +(0.707107 - 0.707107i) q^{91} -1.00000 q^{92} +(0.707107 + 0.707107i) q^{93} +(-0.707107 - 0.707107i) q^{94} -1.00000i q^{96} -1.00000 q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{5}+O(q^{10}) $ 4 * q + 4 * q^5	$ 4 q + 4 q^{5} - 4 q^{16} - 4 q^{20} - 4 q^{22} - 4 q^{24} + 4 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 4 q^{33} + 4 q^{34} + 4 q^{35} + 4 q^{42} + 4 q^{43} + 4 q^{47} - 4 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{54} - 4 q^{74} - 4 q^{79} - 4 q^{80} + 4 q^{81} - 4 q^{92} - 4 q^{97}+O(q^{100}) $ 4 * q + 4 * q^5 - 4 * q^16 - 4 * q^20 - 4 * q^22 - 4 * q^24 + 4 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 4 * q^33 + 4 * q^34 + 4 * q^35 + 4 * q^42 + 4 * q^43 + 4 * q^47 - 4 * q^49 + 4 * q^51 - 4 * q^53 + 4 * q^54 - 4 * q^74 - 4 * q^79 - 4 * q^80 + 4 * q^81 - 4 * q^92 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times$.

$n$	$561$	$911$	$1093$	$1249$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

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

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1456.1.bc.b.181.1	yes	4
7.6	odd	2		1456.1.bc.a.181.1	✓	4
13.12	even	2		1456.1.bc.a.181.2	yes	4
16.13	even	4	inner	1456.1.bc.b.909.2	yes	4
91.90	odd	2	inner	1456.1.bc.b.181.2	yes	4
112.13	odd	4		1456.1.bc.a.909.2	yes	4
208.77	even	4		1456.1.bc.a.909.1	yes	4
1456.909	odd	4	inner	1456.1.bc.b.909.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1456.1.bc.a.181.1	✓	4	7.6	odd	2
1456.1.bc.a.181.2	yes	4	13.12	even	2
1456.1.bc.a.909.1	yes	4	208.77	even	4
1456.1.bc.a.909.2	yes	4	112.13	odd	4
1456.1.bc.b.181.1	yes	4	1.1	even	1	trivial
1456.1.bc.b.181.2	yes	4	91.90	odd	2	inner
1456.1.bc.b.909.1	yes	4	1456.909	odd	4	inner
1456.1.bc.b.909.2	yes	4	16.13	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:	\( N \)	\(=\)	\( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1456.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 1.00000i) q^{5} +1.00000i q^{6} -1.00000i q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(1.00000 + 1.00000i) q^{5} +1.00000i q^{6} -1.00000i q^{7} +(0.707107 - 0.707107i) q^{8} -1.41421i q^{10} +(0.707107 - 0.707107i) q^{11} +(0.707107 - 0.707107i) q^{12} +(0.707107 + 0.707107i) q^{13} +(-0.707107 + 0.707107i) q^{14} -1.41421i q^{15} -1.00000 q^{16} +1.41421i q^{17} +(-1.00000 + 1.00000i) q^{20} +(-0.707107 + 0.707107i) q^{21} -1.00000 q^{22} +1.00000i q^{23} -1.00000 q^{24} +1.00000i q^{25} -1.00000i q^{26} +(-0.707107 + 0.707107i) q^{27} +1.00000 q^{28} +(1.00000 - 1.00000i) q^{29} +(-1.00000 + 1.00000i) q^{30} -1.00000 q^{31} +(0.707107 + 0.707107i) q^{32} -1.00000 q^{33} +(1.00000 - 1.00000i) q^{34} +(1.00000 - 1.00000i) q^{35} +(0.707107 - 0.707107i) q^{37} -1.00000i q^{39} +1.41421 q^{40} -1.00000i q^{41} +1.00000 q^{42} +(1.00000 + 1.00000i) q^{43} +(0.707107 + 0.707107i) q^{44} +(0.707107 - 0.707107i) q^{46} +1.00000 q^{47} +(0.707107 + 0.707107i) q^{48} -1.00000 q^{49} +(0.707107 - 0.707107i) q^{50} +(1.00000 - 1.00000i) q^{51} +(-0.707107 + 0.707107i) q^{52} +(-1.00000 - 1.00000i) q^{53} +1.00000 q^{54} +1.41421 q^{55} +(-0.707107 - 0.707107i) q^{56} -1.41421 q^{58} +1.41421 q^{60} +(-0.707107 - 0.707107i) q^{61} +(0.707107 + 0.707107i) q^{62} -1.00000i q^{64} +1.41421i q^{65} +(0.707107 + 0.707107i) q^{66} +(-0.707107 - 0.707107i) q^{67} -1.41421 q^{68} +(0.707107 - 0.707107i) q^{69} -1.41421 q^{70} +1.41421 q^{71} +1.00000i q^{73} -1.00000 q^{74} +(0.707107 - 0.707107i) q^{75} +(-0.707107 - 0.707107i) q^{77} +(-0.707107 + 0.707107i) q^{78} -1.00000 q^{79} +(-1.00000 - 1.00000i) q^{80} +1.00000 q^{81} +(-0.707107 + 0.707107i) q^{82} +(-0.707107 - 0.707107i) q^{84} +(-1.41421 + 1.41421i) q^{85} -1.41421i q^{86} -1.41421 q^{87} -1.00000i q^{88} +(0.707107 - 0.707107i) q^{91} -1.00000 q^{92} +(0.707107 + 0.707107i) q^{93} +(-0.707107 - 0.707107i) q^{94} -1.00000i q^{96} -1.00000 q^{97} +(0.707107 + 0.707107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{5}+O(q^{10}) \) 4 * q + 4 * q^5	\( 4 q + 4 q^{5} - 4 q^{16} - 4 q^{20} - 4 q^{22} - 4 q^{24} + 4 q^{28} + 4 q^{29} - 4 q^{30} - 4 q^{31} - 4 q^{33} + 4 q^{34} + 4 q^{35} + 4 q^{42} + 4 q^{43} + 4 q^{47} - 4 q^{49} + 4 q^{51} - 4 q^{53} + 4 q^{54} - 4 q^{74} - 4 q^{79} - 4 q^{80} + 4 q^{81} - 4 q^{92} - 4 q^{97}+O(q^{100}) \) 4 * q + 4 * q^5 - 4 * q^16 - 4 * q^20 - 4 * q^22 - 4 * q^24 + 4 * q^28 + 4 * q^29 - 4 * q^30 - 4 * q^31 - 4 * q^33 + 4 * q^34 + 4 * q^35 + 4 * q^42 + 4 * q^43 + 4 * q^47 - 4 * q^49 + 4 * q^51 - 4 * q^53 + 4 * q^54 - 4 * q^74 - 4 * q^79 - 4 * q^80 + 4 * q^81 - 4 * q^92 - 4 * q^97

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