LMFDB - Embedded newform 1575.1.cb.a.1507.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1575,1,Mod(718,1575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1575, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([8, 9, 8]))

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

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

chi := DirichletCharacter("1575.718");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1575.cb (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:	$0.786027394897$
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:	$A_{4}$
Projective field:	Galois closure of 4.0.99225.1

Embedding invariants

Embedding label			1507.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1575.1507
Dual form			1575.1.cb.a.718.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.258819 + 0.965926i) q^{13} +(0.866025 + 0.500000i) q^{14} +1.00000 q^{16} +(0.258819 - 0.965926i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.866025 - 0.500000i) q^{19} +(-0.500000 - 0.866025i) q^{21} +(-0.866025 - 0.500000i) q^{24} +(-0.500000 + 0.866025i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.866025 + 0.500000i) q^{29} -1.00000 q^{31} +(0.866025 - 0.500000i) q^{34} +(0.965926 - 0.258819i) q^{37} +(-0.258819 - 0.965926i) q^{38} +(0.866025 - 0.500000i) q^{39} +(-0.500000 + 0.866025i) q^{41} +(0.258819 - 0.965926i) q^{42} +(0.965926 + 0.258819i) q^{43} +(-0.707107 - 0.707107i) q^{47} +(-0.258819 - 0.965926i) q^{48} +(0.866025 - 0.500000i) q^{49} -1.00000 q^{51} +(0.965926 + 0.258819i) q^{53} +1.00000i q^{54} +(0.500000 - 0.866025i) q^{56} +(-0.258819 + 0.965926i) q^{57} +(-0.965926 - 0.258819i) q^{58} -1.00000i q^{59} +1.00000 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-0.707107 + 0.707107i) q^{63} -1.00000i q^{64} +(0.707107 + 0.707107i) q^{67} -2.00000 q^{71} +(-0.258819 + 0.965926i) q^{72} +(-0.965926 - 0.258819i) q^{73} +(0.866025 + 0.500000i) q^{74} +(0.965926 + 0.258819i) q^{78} +1.00000i q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.965926 + 0.258819i) q^{82} +(-0.965926 - 0.258819i) q^{83} +(0.500000 + 0.866025i) q^{86} +(0.707107 + 0.707107i) q^{87} +(0.866025 + 0.500000i) q^{89} +(0.500000 + 0.866025i) q^{91} +(0.258819 + 0.965926i) q^{93} -1.00000i q^{94} +(-0.258819 + 0.965926i) q^{97} +(0.965926 + 0.258819i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{6}+O(q^{10}) $ 8 * q + 4 * q^6	$ 8 q + 4 q^{6} + 8 q^{16} - 4 q^{21} - 4 q^{26} - 8 q^{31} - 4 q^{41} - 8 q^{51} + 4 q^{56} + 8 q^{61} - 16 q^{71} + 4 q^{81} + 4 q^{86} + 4 q^{91}+O(q^{100}) $ 8 * q + 4 * q^6 + 8 * q^16 - 4 * q^21 - 4 * q^26 - 8 * q^31 - 4 * q^41 - 8 * q^51 + 4 * q^56 + 8 * q^61 - 16 * q^71 + 4 * q^81 + 4 * q^86 + 4 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$2$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$3$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$3$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$4$		0			0
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.500000	−	0.866025i
$7$	0.965926	−	0.258819i	0.965926	−	0.258819i
$7$	0.965926	−	0.258819i	0.965926	−	0.258819i
$8$	0.707107	−	0.707107i	0.707107	−	0.707107i
$9$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$10$		0			0
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$		0			0
$13$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$13$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$14$	0.866025	+	0.500000i	0.866025	+	0.500000i
$15$		0			0
$16$	1.00000			1.00000
$17$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$17$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$18$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$19$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$19$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$20$		0			0
$21$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$22$		0			0
$23$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$23$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$24$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$25$		0			0
$26$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$27$	0.707107	+	0.707107i	0.707107	+	0.707107i
$28$		0			0
$29$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$29$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$30$		0			0
$31$	−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			0
$33$		0			0
$34$	0.866025	−	0.500000i	0.866025	−	0.500000i
$35$		0			0
$36$		0			0
$37$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$37$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$38$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$39$	0.866025	−	0.500000i	0.866025	−	0.500000i
$40$		0			0
$41$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$41$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$42$	0.258819	−	0.965926i	0.258819	−	0.965926i
$43$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$43$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$47$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$48$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$49$	0.866025	−	0.500000i	0.866025	−	0.500000i
$50$		0			0
$51$	−1.00000			−1.00000
$52$		0			0
$53$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$53$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$54$			1.00000i			1.00000i
$55$		0			0
$56$	0.500000	−	0.866025i	0.500000	−	0.866025i
$57$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$58$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$59$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$59$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$60$		0			0
$61$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$61$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$62$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$63$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$64$		−	1.00000i		−	1.00000i
$65$		0			0
$66$		0			0
$67$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$67$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.00000			−2.00000			−1.00000			$\pi$
$71$	−2.00000			−2.00000			−1.00000			$\pi$
$72$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$73$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$73$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$74$	0.866025	+	0.500000i	0.866025	+	0.500000i
$75$		0			0
$76$		0			0
$77$		0			0
$78$	0.965926	+	0.258819i	0.965926	+	0.258819i
$79$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$79$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$83$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$83$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$84$		0			0
$85$		0			0
$86$	0.500000	+	0.866025i	0.500000	+	0.866025i
$87$	0.707107	+	0.707107i	0.707107	+	0.707107i
$88$		0			0
$89$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$89$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$90$		0			0
$91$	0.500000	+	0.866025i	0.500000	+	0.866025i
$92$		0			0
$93$	0.258819	+	0.965926i	0.258819	+	0.965926i
$94$		−	1.00000i		−	1.00000i
$95$		0			0
$96$		0			0
$97$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$97$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$98$	0.965926	+	0.258819i	0.965926	+	0.258819i
$99$		0			0
$100$		0			0
$101$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$101$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$102$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$103$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$103$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$104$	0.866025	+	0.500000i	0.866025	+	0.500000i
$105$		0			0
$106$	0.500000	+	0.866025i	0.500000	+	0.866025i
$107$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$107$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$108$		0			0
$109$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$109$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$110$		0			0
$111$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$112$	0.965926	−	0.258819i	0.965926	−	0.258819i
$113$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$113$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$114$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$115$		0			0
$116$		0			0
$117$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$118$	0.707107	−	0.707107i	0.707107	−	0.707107i
$119$		−	1.00000i		−	1.00000i
$120$		0			0
$121$	0.500000	+	0.866025i	0.500000	+	0.866025i
$122$	0.707107	+	0.707107i	0.707107	+	0.707107i
$123$	0.965926	+	0.258819i	0.965926	+	0.258819i
$124$		0			0
$125$		0			0
$126$	−1.00000			−1.00000
$127$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$127$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$128$	0.707107	−	0.707107i	0.707107	−	0.707107i
$129$		−	1.00000i		−	1.00000i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$134$			1.00000i			1.00000i
$135$		0			0
$136$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$137$	−1.93185	+	0.517638i	−1.93185	+	0.517638i	−0.965926	+	0.258819i	$0.916667\pi$
$137$	−1.93185	+	0.517638i	−1.93185	+	0.517638i	−0.965926	+	0.258819i	$0.916667\pi$
$138$		0			0
$139$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$139$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$140$		0			0
$141$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$142$	−1.41421	−	1.41421i	−1.41421	−	1.41421i
$143$		0			0
$144$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$145$		0			0
$146$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$147$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$148$		0			0
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$		0			0
$151$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$151$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$152$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$153$	0.258819	+	0.965926i	0.258819	+	0.965926i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−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
$159$		−	1.00000i		−	1.00000i
$160$		0			0
$161$		0			0
$162$	0.965926	−	0.258819i	0.965926	−	0.258819i
$163$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$163$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$164$		0			0
$165$		0			0
$166$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$167$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$167$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$168$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$169$		0			0
$170$		0			0
$171$	1.00000			1.00000
$172$		0			0
$173$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$173$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$174$			1.00000i			1.00000i
$175$		0			0
$176$		0			0
$177$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$178$	0.258819	+	0.965926i	0.258819	+	0.965926i
$179$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$179$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$183$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$184$		0			0
$185$		0			0
$186$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$187$		0			0
$188$		0			0
$189$	0.866025	+	0.500000i	0.866025	+	0.500000i
$190$		0			0
$191$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$191$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$192$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$193$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$193$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$194$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$195$		0			0
$196$		0			0
$197$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$197$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$198$		0			0
$199$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$199$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$200$		0			0
$201$	0.500000	−	0.866025i	0.500000	−	0.866025i
$202$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$203$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	0.258819	+	0.965926i	0.258819	+	0.965926i
$209$		0			0
$210$		0			0
$211$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$211$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$212$		0			0
$213$	0.517638	+	1.93185i	0.517638	+	1.93185i
$214$	0.866025	+	0.500000i	0.866025	+	0.500000i
$215$		0			0
$216$	1.00000			1.00000
$217$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$218$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$219$			1.00000i			1.00000i
$220$		0			0
$221$	1.00000			1.00000
$222$	0.258819	−	0.965926i	0.258819	−	0.965926i
$223$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$223$	−0.965926	−	0.258819i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$224$		0			0
$225$		0			0
$226$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$227$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$227$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$		0			0
$232$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$233$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$233$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$234$		−	1.00000i		−	1.00000i
$235$		0			0
$236$		0			0
$237$	0.965926	−	0.258819i	0.965926	−	0.258819i
$238$	0.707107	−	0.707107i	0.707107	−	0.707107i
$239$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$239$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$243$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$244$		0			0
$245$		0			0
$246$	0.500000	+	0.866025i	0.500000	+	0.866025i
$247$	0.258819	−	0.965926i	0.258819	−	0.965926i
$248$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$249$			1.00000i			1.00000i
$250$		0			0
$251$	2.00000			2.00000			1.00000			$0$
$251$	2.00000			2.00000			1.00000			$0$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$257$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$258$	0.707107	−	0.707107i	0.707107	−	0.707107i
$259$	0.866025	−	0.500000i	0.866025	−	0.500000i
$260$		0			0
$261$	0.500000	−	0.866025i	0.500000	−	0.866025i
$262$		0			0
$263$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$263$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$264$		0			0
$265$		0			0
$266$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$267$	0.258819	−	0.965926i	0.258819	−	0.965926i
$268$		0			0
$269$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$269$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$271$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$272$	0.258819	−	0.965926i	0.258819	−	0.965926i
$273$	0.707107	−	0.707107i	0.707107	−	0.707107i
$274$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$275$		0			0
$276$		0			0
$277$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$277$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$278$	0.258819	+	0.965926i	0.258819	+	0.965926i
$279$	0.866025	−	0.500000i	0.866025	−	0.500000i
$280$		0			0
$281$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$281$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$282$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$283$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$283$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$288$		0			0
$289$		0			0
$290$		0			0
$291$	1.00000			1.00000
$292$		0			0
$293$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$293$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$294$		−	1.00000i		−	1.00000i
$295$		0			0
$296$	0.500000	−	0.866025i	0.500000	−	0.866025i
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.00000			1.00000
$302$		0			0
$303$	1.93185	+	0.517638i	1.93185	+	0.517638i
$304$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$305$		0			0
$306$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$311$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$312$	0.258819	−	0.965926i	0.258819	−	0.965926i
$313$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$313$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$314$		−	1.00000i		−	1.00000i
$315$		0			0
$316$		0			0
$317$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$317$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$318$	0.707107	−	0.707107i	0.707107	−	0.707107i
$319$		0			0
$320$		0			0
$321$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$322$		0			0
$323$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$324$		0			0
$325$		0			0
$326$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$327$	0.707107	+	0.707107i	0.707107	+	0.707107i
$328$	0.258819	+	0.965926i	0.258819	+	0.965926i
$329$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$330$		0			0
$331$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$331$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$334$	0.866025	+	0.500000i	0.866025	+	0.500000i
$335$		0			0
$336$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$337$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$337$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$338$		0			0
$339$	0.866025	−	0.500000i	0.866025	−	0.500000i
$340$		0			0
$341$		0			0
$342$	0.707107	+	0.707107i	0.707107	+	0.707107i
$343$	0.707107	−	0.707107i	0.707107	−	0.707107i
$344$	0.866025	−	0.500000i	0.866025	−	0.500000i
$345$		0			0
$346$	−1.00000			−1.00000
$347$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$347$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$349$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$350$		0			0
$351$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$352$		0			0
$353$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$353$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$354$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$355$		0			0
$356$		0			0
$357$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$358$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$359$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$359$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	0.707107	−	0.707107i	0.707107	−	0.707107i
$364$		0			0
$365$		0			0
$366$	0.500000	−	0.866025i	0.500000	−	0.866025i
$367$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$367$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$368$		0			0
$369$		−	1.00000i		−	1.00000i
$370$		0			0
$371$	1.00000			1.00000
$372$		0			0
$373$	−1.93185	−	0.517638i	−1.93185	−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$373$	−1.93185	−	0.517638i	−1.93185	−	0.517638i	−0.965926	−	0.258819i	$-0.916667\pi$
$374$		0			0
$375$		0			0
$376$	−1.00000			−1.00000
$377$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$378$	0.258819	+	0.965926i	0.258819	+	0.965926i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$	0.707107	+	0.707107i	0.707107	+	0.707107i
$383$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$383$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$384$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$385$		0			0
$386$	1.00000			1.00000
$387$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	0.258819	−	0.965926i	0.258819	−	0.965926i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$397$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$398$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$399$			1.00000i			1.00000i
$400$		0			0
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$	0.965926	−	0.258819i	0.965926	−	0.258819i
$403$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$404$		0			0
$405$		0			0
$406$	−1.00000			−1.00000
$407$		0			0
$408$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$409$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$409$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$410$		0			0
$411$	1.00000	+	1.73205i	1.00000	+	1.73205i
$412$		0			0
$413$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.258819	−	0.965926i	0.258819	−	0.965926i
$418$		0			0
$419$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$419$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$420$		0			0
$421$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$421$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$422$	0.965926	−	0.258819i	0.965926	−	0.258819i
$423$	0.965926	+	0.258819i	0.965926	+	0.258819i
$424$	0.866025	−	0.500000i	0.866025	−	0.500000i
$425$		0			0
$426$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$427$	0.965926	−	0.258819i	0.965926	−	0.258819i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$431$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$432$	0.707107	+	0.707107i	0.707107	+	0.707107i
$433$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$433$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$434$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$439$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$439$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$440$		0			0
$441$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$442$	0.707107	+	0.707107i	0.707107	+	0.707107i
$443$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$443$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$444$		0			0
$445$		0			0
$446$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$447$		0			0
$448$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	0.500000	+	0.866025i	0.500000	+	0.866025i
$457$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$457$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$458$		0			0
$459$	0.866025	−	0.500000i	0.866025	−	0.500000i
$460$		0			0
$461$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$461$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$462$		0			0
$463$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$463$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$464$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$465$		0			0
$466$	0.500000	−	0.866025i	0.500000	−	0.866025i
$467$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$467$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$468$		0			0
$469$	0.866025	+	0.500000i	0.866025	+	0.500000i
$470$		0			0
$471$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$472$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$473$		0			0
$474$	0.866025	+	0.500000i	0.866025	+	0.500000i
$475$		0			0
$476$		0			0
$477$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$478$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$		0			0
$481$	0.500000	+	0.866025i	0.500000	+	0.866025i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$487$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$487$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$488$	0.707107	−	0.707107i	0.707107	−	0.707107i
$489$	0.866025	−	0.500000i	0.866025	−	0.500000i
$490$		0			0
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$491$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$492$		0			0
$493$	0.258819	+	0.965926i	0.258819	+	0.965926i
$494$	0.866025	−	0.500000i	0.866025	−	0.500000i
$495$		0			0
$496$	−1.00000			−1.00000
$497$	−1.93185	+	0.517638i	−1.93185	+	0.517638i
$498$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$		0			0
$501$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$502$	1.41421	+	1.41421i	1.41421	+	1.41421i
$503$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$503$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$504$			1.00000i			1.00000i
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$	−1.00000			−1.00000
$512$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$513$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	0.965926	+	0.258819i	0.965926	+	0.258819i
$519$	0.866025	+	0.500000i	0.866025	+	0.500000i
$520$		0			0
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$521$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$522$	0.965926	−	0.258819i	0.965926	−	0.258819i
$523$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$523$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$528$		0			0
$529$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$530$		0			0
$531$	0.500000	+	0.866025i	0.500000	+	0.866025i
$532$		0			0
$533$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$534$	0.866025	−	0.500000i	0.866025	−	0.500000i
$535$		0			0
$536$	1.00000			1.00000
$537$	0.707107	+	0.707107i	0.707107	+	0.707107i
$538$	0.965926	+	0.258819i	0.965926	+	0.258819i
$539$		0			0
$540$		0			0
$541$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$541$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$542$	0.965926	−	0.258819i	0.965926	−	0.258819i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	1.00000			1.00000
$547$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$547$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$548$		0			0
$549$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$550$		0			0
$551$	1.00000			1.00000
$552$		0			0
$553$	0.258819	+	0.965926i	0.258819	+	0.965926i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$557$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$558$	0.965926	+	0.258819i	0.965926	+	0.258819i
$559$			1.00000i			1.00000i
$560$		0			0
$561$		0			0
$562$	0.258819	−	0.965926i	0.258819	−	0.965926i
$563$	0.707107	−	0.707107i	0.707107	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$563$	0.707107	−	0.707107i	0.707107	−	0.707107i	0.965926	+	0.258819i	$0.0833333\pi$
$564$		0			0
$565$		0			0
$566$	1.00000			1.00000
$567$	0.258819	−	0.965926i	0.258819	−	0.965926i
$568$	−1.41421	+	1.41421i	−1.41421	+	1.41421i
$569$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$569$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$570$		0			0
$571$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$574$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$575$		0			0
$576$	0.500000	+	0.866025i	0.500000	+	0.866025i
$577$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$577$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$578$		0			0
$579$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$580$		0			0
$581$	−1.00000			−1.00000
$582$	0.707107	+	0.707107i	0.707107	+	0.707107i
$583$		0			0
$584$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$585$		0			0
$586$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$587$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$587$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$588$		0			0
$589$	0.866025	+	0.500000i	0.866025	+	0.500000i
$590$		0			0
$591$		0			0
$592$	0.965926	−	0.258819i	0.965926	−	0.258819i
$593$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$593$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.707107	+	0.707107i	0.707107	+	0.707107i
$598$		0			0
$599$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$599$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$600$		0			0
$601$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$601$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$602$	0.707107	+	0.707107i	0.707107	+	0.707107i
$603$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$604$		0			0
$605$		0			0
$606$	1.00000	+	1.73205i	1.00000	+	1.73205i
$607$	−0.517638	+	1.93185i	−0.517638	+	1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$607$	−0.517638	+	1.93185i	−0.517638	+	1.93185i	−0.258819	+	0.965926i	$0.583333\pi$
$608$		0			0
$609$	0.866025	+	0.500000i	0.866025	+	0.500000i
$610$		0			0
$611$	0.500000	−	0.866025i	0.500000	−	0.866025i
$612$		0			0
$613$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$613$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$617$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$		0			0
$621$		0			0
$622$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$623$	0.965926	+	0.258819i	0.965926	+	0.258819i
$624$	0.866025	−	0.500000i	0.866025	−	0.500000i
$625$		0			0
$626$	1.00000			1.00000
$627$		0			0
$628$		0			0
$629$		−	1.00000i		−	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
$633$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$634$			1.00000i			1.00000i
$635$		0			0
$636$		0			0
$637$	0.707107	+	0.707107i	0.707107	+	0.707107i
$638$		0			0
$639$	1.73205	−	1.00000i	1.73205	−	1.00000i
$640$		0			0
$641$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$641$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	0.258819	−	0.965926i	0.258819	−	0.965926i
$643$	0.258819	+	0.965926i	0.258819	+	0.965926i	0.965926	+	0.258819i	$0.0833333\pi$
$643$	0.258819	+	0.965926i	0.258819	+	0.965926i	−0.707107	+	0.707107i	$0.750000\pi$
$644$		0			0
$645$		0			0
$646$	−1.00000			−1.00000
$647$	0.258819	−	0.965926i	0.258819	−	0.965926i	−0.707107	−	0.707107i	$-0.750000\pi$
$647$	0.258819	−	0.965926i	0.258819	−	0.965926i	0.965926	−	0.258819i	$-0.0833333\pi$
$648$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$649$		0			0
$650$		0			0
$651$	0.500000	+	0.866025i	0.500000	+	0.866025i
$652$		0			0
$653$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$653$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$654$			1.00000i			1.00000i
$655$		0			0
$656$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$657$	0.965926	−	0.258819i	0.965926	−	0.258819i
$658$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$659$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$659$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$660$		0			0
$661$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$661$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$662$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$663$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$664$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$665$		0			0
$666$	−1.00000			−1.00000
$667$		0			0
$668$		0			0
$669$			1.00000i			1.00000i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$673$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$674$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$675$		0			0
$676$		0			0
$677$	0.707107	+	0.707107i	0.707107	+	0.707107i	0.965926	−	0.258819i	$-0.0833333\pi$
$677$	0.707107	+	0.707107i	0.707107	+	0.707107i	−0.258819	+	0.965926i	$0.583333\pi$
$678$	0.965926	+	0.258819i	0.965926	+	0.258819i
$679$			1.00000i			1.00000i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$683$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$684$		0			0
$685$		0			0
$686$	1.00000			1.00000
$687$		0			0
$688$	0.965926	+	0.258819i	0.965926	+	0.258819i
$689$			1.00000i			1.00000i
$690$		0			0
$691$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$691$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$		0			0
$694$			1.00000i			1.00000i
$695$		0			0
$696$	1.00000			1.00000
$697$	0.707107	+	0.707107i	0.707107	+	0.707107i
$698$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$699$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$703$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$708$		0			0
$709$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$709$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$710$		0			0
$711$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$712$	0.965926	−	0.258819i	0.965926	−	0.258819i
$713$		0			0
$714$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$715$		0			0
$716$		0			0
$717$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$718$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$719$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$719$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$		0			0
$726$	1.00000			1.00000
$727$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	0.707107	+	0.707107i	$0.250000\pi$
$727$	−0.258819	+	0.965926i	−0.258819	+	0.965926i	−0.965926	+	0.258819i	$0.916667\pi$
$728$	0.965926	+	0.258819i	0.965926	+	0.258819i
$729$			1.00000i			1.00000i
$730$		0			0
$731$	0.500000	−	0.866025i	0.500000	−	0.866025i
$732$		0			0
$733$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$733$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	0.707107	−	0.707107i	0.707107	−	0.707107i
$739$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$739$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$740$		0			0
$741$	−1.00000			−1.00000
$742$	0.707107	+	0.707107i	0.707107	+	0.707107i
$743$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$743$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$744$	0.866025	+	0.500000i	0.866025	+	0.500000i
$745$		0			0
$746$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$747$	0.965926	−	0.258819i	0.965926	−	0.258819i
$748$		0			0
$749$	0.866025	−	0.500000i	0.866025	−	0.500000i
$750$		0			0
$751$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$751$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$752$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$753$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$754$		−	1.00000i		−	1.00000i
$755$		0			0
$756$		0			0
$757$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$757$	−1.41421	−	1.41421i	−1.41421	−	1.41421i	−0.707107	−	0.707107i	$-0.750000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$762$		0			0
$763$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.965926	−	0.258819i	0.965926	−	0.258819i
$768$		0			0
$769$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$769$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$773$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$774$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$775$		0			0
$776$	0.500000	+	0.866025i	0.500000	+	0.866025i
$777$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$778$		0			0
$779$	0.866025	−	0.500000i	0.866025	−	0.500000i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$784$	0.866025	−	0.500000i	0.866025	−	0.500000i
$785$		0			0
$786$		0			0
$787$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$787$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.500000	+	0.866025i	0.500000	+	0.866025i
$792$		0			0
$793$	0.258819	+	0.965926i	0.258819	+	0.965926i
$794$	0.866025	+	0.500000i	0.866025	+	0.500000i
$795$		0			0
$796$		0			0
$797$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.707107	−	0.707107i	$-0.750000\pi$
$797$	−0.965926	+	0.258819i	−0.965926	+	0.258819i	−0.258819	+	0.965926i	$0.583333\pi$
$798$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$799$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$800$		0			0
$801$	−1.00000			−1.00000
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.500000	−	0.866025i	0.500000	−	0.866025i
$807$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$808$	0.517638	+	1.93185i	0.517638	+	1.93185i
$809$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$809$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$810$		0			0
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$814$		0			0
$815$		0			0
$816$	−1.00000			−1.00000
$817$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$818$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$819$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$820$		0			0
$821$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$821$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$822$	−0.517638	+	1.93185i	−0.517638	+	1.93185i
$823$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	−0.965926	−	0.258819i	$-0.916667\pi$
$823$	−0.707107	+	0.707107i	−0.707107	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$824$		0			0
$825$		0			0
$826$	0.500000	−	0.866025i	0.500000	−	0.866025i
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$		0			0
$829$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$829$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$830$		0			0
$831$		0			0
$832$	0.965926	−	0.258819i	0.965926	−	0.258819i
$833$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$834$	0.866025	−	0.500000i	0.866025	−	0.500000i
$835$		0			0
$836$		0			0
$837$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$838$	0.258819	+	0.965926i	0.258819	+	0.965926i
$839$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$839$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$840$		0			0
$841$		0			0
$842$	0.258819	−	0.965926i	0.258819	−	0.965926i
$843$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$844$		0			0
$845$		0			0
$846$	0.500000	+	0.866025i	0.500000	+	0.866025i
$847$	0.707107	+	0.707107i	0.707107	+	0.707107i
$848$	0.965926	+	0.258819i	0.965926	+	0.258819i
$849$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.707107	−	0.707107i	$-0.250000\pi$
$853$	0.965926	+	0.258819i	0.965926	+	0.258819i	0.258819	+	0.965926i	$0.416667\pi$
$854$	0.866025	+	0.500000i	0.866025	+	0.500000i
$855$		0			0
$856$	0.500000	−	0.866025i	0.500000	−	0.866025i
$857$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$857$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$858$		0			0
$859$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$859$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$860$		0			0
$861$	1.00000			1.00000
$862$	0.258819	−	0.965926i	0.258819	−	0.965926i
$863$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	−0.965926	−	0.258819i	$-0.916667\pi$
$863$	−0.258819	−	0.965926i	−0.258819	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$872$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$873$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$877$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$878$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$879$	0.866025	−	0.500000i	0.866025	−	0.500000i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$883$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$883$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$884$		0			0
$885$		0			0
$886$	1.00000			1.00000
$887$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$887$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$888$	−0.965926	−	0.258819i	−0.965926	−	0.258819i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.258819	+	0.965926i	0.258819	+	0.965926i
$894$		0			0
$895$		0			0
$896$	0.500000	−	0.866025i	0.500000	−	0.866025i
$897$		0			0
$898$		0			0
$899$	0.866025	−	0.500000i	0.866025	−	0.500000i
$900$		0			0
$901$	0.500000	−	0.866025i	0.500000	−	0.866025i
$902$		0			0
$903$	−0.258819	−	0.965926i	−0.258819	−	0.965926i
$904$	0.866025	+	0.500000i	0.866025	+	0.500000i
$905$		0			0
$906$		0			0
$907$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$907$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$908$		0			0
$909$		−	2.00000i		−	2.00000i
$910$		0			0
$911$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$911$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$912$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$913$		0			0
$914$		−	1.00000i		−	1.00000i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.965926	+	0.258819i	0.965926	+	0.258819i
$919$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$919$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$920$		0			0
$921$		0			0
$922$	0.258819	−	0.965926i	0.258819	−	0.965926i
$923$	−0.517638	−	1.93185i	−0.517638	−	1.93185i
$924$		0			0
$925$		0			0
$926$	0.500000	−	0.866025i	0.500000	−	0.866025i
$927$		0			0
$928$		0			0
$929$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$929$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$930$		0			0
$931$	−1.00000			−1.00000
$932$		0			0
$933$	0.258819	+	0.965926i	0.258819	+	0.965926i
$934$	0.866025	+	0.500000i	0.866025	+	0.500000i
$935$		0			0
$936$	−1.00000			−1.00000
$937$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$937$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$938$	0.258819	+	0.965926i	0.258819	+	0.965926i
$939$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$940$		0			0
$941$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$941$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$942$	−0.965926	+	0.258819i	−0.965926	+	0.258819i
$943$		0			0
$944$		−	1.00000i		−	1.00000i
$945$		0			0
$946$		0			0
$947$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$947$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$948$		0			0
$949$		−	1.00000i		−	1.00000i
$950$		0			0
$951$	0.500000	−	0.866025i	0.500000	−	0.866025i
$952$	−0.707107	−	0.707107i	−0.707107	−	0.707107i
$953$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$953$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$954$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$960$		0			0
$961$		0			0
$962$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$963$	−0.707107	+	0.707107i	−0.707107	+	0.707107i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.258819	−	0.965926i	$-0.416667\pi$
$967$	0.965926	−	0.258819i	0.965926	−	0.258819i	0.707107	+	0.707107i	$0.250000\pi$
$968$	0.965926	+	0.258819i	0.965926	+	0.258819i
$969$	0.866025	+	0.500000i	0.866025	+	0.500000i
$970$		0			0
$971$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$971$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$972$		0			0
$973$	0.965926	+	0.258819i	0.965926	+	0.258819i
$974$	0.866025	−	0.500000i	0.866025	−	0.500000i
$975$		0			0
$976$	1.00000			1.00000
$977$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	0.258819	−	0.965926i	$-0.416667\pi$
$977$	−0.707107	−	0.707107i	−0.707107	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$978$	0.965926	+	0.258819i	0.965926	+	0.258819i
$979$		0			0
$980$		0			0
$981$	0.500000	−	0.866025i	0.500000	−	0.866025i
$982$	0.965926	−	0.258819i	0.965926	−	0.258819i
$983$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$983$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$984$	0.866025	−	0.500000i	0.866025	−	0.500000i
$985$		0			0
$986$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$987$	−0.258819	+	0.965926i	−0.258819	+	0.965926i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$991$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$992$		0			0
$993$	0.258819	+	0.965926i	0.258819	+	0.965926i
$994$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$995$		0			0
$996$		0			0
$997$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$997$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$998$		0			0
$999$	0.866025	+	0.500000i	0.866025	+	0.500000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.1.cb.a.1507.2	yes	8
5.2	odd	4	inner	1575.1.cb.a.1318.1	yes	8
5.3	odd	4	inner	1575.1.cb.a.1318.2	yes	8
5.4	even	2	inner	1575.1.cb.a.1507.1	yes	8
7.4	even	3		1575.1.cp.a.382.1	yes	8
9.7	even	3		1575.1.cp.a.457.2	yes	8
35.4	even	6		1575.1.cp.a.382.2	yes	8
35.18	odd	12		1575.1.cp.a.193.2	yes	8
35.32	odd	12		1575.1.cp.a.193.1	yes	8
45.7	odd	12		1575.1.cp.a.268.2	yes	8
45.34	even	6		1575.1.cp.a.457.1	yes	8
45.43	odd	12		1575.1.cp.a.268.1	yes	8
63.25	even	3	inner	1575.1.cb.a.907.2	yes	8
315.88	odd	12	inner	1575.1.cb.a.718.2	yes	8
315.214	even	6	inner	1575.1.cb.a.907.1	yes	8
315.277	odd	12	inner	1575.1.cb.a.718.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1575.1.cb.a.718.1	✓	8	315.277	odd	12	inner
1575.1.cb.a.718.2	yes	8	315.88	odd	12	inner
1575.1.cb.a.907.1	yes	8	315.214	even	6	inner
1575.1.cb.a.907.2	yes	8	63.25	even	3	inner
1575.1.cb.a.1318.1	yes	8	5.2	odd	4	inner
1575.1.cb.a.1318.2	yes	8	5.3	odd	4	inner
1575.1.cb.a.1507.1	yes	8	5.4	even	2	inner
1575.1.cb.a.1507.2	yes	8	1.1	even	1	trivial
1575.1.cp.a.193.1	yes	8	35.32	odd	12
1575.1.cp.a.193.2	yes	8	35.18	odd	12
1575.1.cp.a.268.1	yes	8	45.43	odd	12
1575.1.cp.a.268.2	yes	8	45.7	odd	12
1575.1.cp.a.382.1	yes	8	7.4	even	3
1575.1.cp.a.382.2	yes	8	35.4	even	6
1575.1.cp.a.457.1	yes	8	45.34	even	6
1575.1.cp.a.457.2	yes	8	9.7	even	3

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:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1575.cb (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{6} +(0.965926 - 0.258819i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.258819 + 0.965926i) q^{13} +(0.866025 + 0.500000i) q^{14} +1.00000 q^{16} +(0.258819 - 0.965926i) q^{17} +(-0.965926 - 0.258819i) q^{18} +(-0.866025 - 0.500000i) q^{19} +(-0.500000 - 0.866025i) q^{21} +(-0.866025 - 0.500000i) q^{24} +(-0.500000 + 0.866025i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.866025 + 0.500000i) q^{29} -1.00000 q^{31} +(0.866025 - 0.500000i) q^{34} +(0.965926 - 0.258819i) q^{37} +(-0.258819 - 0.965926i) q^{38} +(0.866025 - 0.500000i) q^{39} +(-0.500000 + 0.866025i) q^{41} +(0.258819 - 0.965926i) q^{42} +(0.965926 + 0.258819i) q^{43} +(-0.707107 - 0.707107i) q^{47} +(-0.258819 - 0.965926i) q^{48} +(0.866025 - 0.500000i) q^{49} -1.00000 q^{51} +(0.965926 + 0.258819i) q^{53} +1.00000i q^{54} +(0.500000 - 0.866025i) q^{56} +(-0.258819 + 0.965926i) q^{57} +(-0.965926 - 0.258819i) q^{58} -1.00000i q^{59} +1.00000 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-0.707107 + 0.707107i) q^{63} -1.00000i q^{64} +(0.707107 + 0.707107i) q^{67} -2.00000 q^{71} +(-0.258819 + 0.965926i) q^{72} +(-0.965926 - 0.258819i) q^{73} +(0.866025 + 0.500000i) q^{74} +(0.965926 + 0.258819i) q^{78} +1.00000i q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.965926 + 0.258819i) q^{82} +(-0.965926 - 0.258819i) q^{83} +(0.500000 + 0.866025i) q^{86} +(0.707107 + 0.707107i) q^{87} +(0.866025 + 0.500000i) q^{89} +(0.500000 + 0.866025i) q^{91} +(0.258819 + 0.965926i) q^{93} -1.00000i q^{94} +(-0.258819 + 0.965926i) q^{97} +(0.965926 + 0.258819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{6}+O(q^{10}) \) 8 * q + 4 * q^6	\( 8 q + 4 q^{6} + 8 q^{16} - 4 q^{21} - 4 q^{26} - 8 q^{31} - 4 q^{41} - 8 q^{51} + 4 q^{56} + 8 q^{61} - 16 q^{71} + 4 q^{81} + 4 q^{86} + 4 q^{91}+O(q^{100}) \) 8 * q + 4 * q^6 + 8 * q^16 - 4 * q^21 - 4 * q^26 - 8 * q^31 - 4 * q^41 - 8 * q^51 + 4 * q^56 + 8 * q^61 - 16 * q^71 + 4 * q^81 + 4 * q^86 + 4 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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