LMFDB - Embedded newform 2015.1.bq.c.464.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2015,1,Mod(464,2015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2015, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("2015.464");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2015 = 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2015.bq (of order $6$, 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:	$1.00561600046$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.4060225.2

Embedding invariants

Embedding label			464.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	2015.464
Dual form			2015.1.bq.c.1394.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.866025 - 0.500000i) q^{11} -1.00000 q^{13} -1.00000 q^{14} +(-0.866025 - 0.500000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{19} -1.00000i q^{21} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-0.866025 - 0.500000i) q^{26} -1.00000 q^{27} +(-0.866025 - 0.500000i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.00000 q^{31} +(0.866025 - 0.500000i) q^{33} +1.00000i q^{34} +(-0.500000 - 0.866025i) q^{35} +(0.500000 - 0.866025i) q^{37} +1.00000i q^{38} +(0.500000 - 0.866025i) q^{39} +1.00000 q^{40} +(0.500000 - 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-0.866025 + 0.500000i) q^{46} +(0.500000 + 0.866025i) q^{48} +(-0.866025 - 0.500000i) q^{50} -1.00000 q^{51} +(-0.866025 - 0.500000i) q^{54} +(0.500000 - 0.866025i) q^{55} +(0.500000 + 0.866025i) q^{56} -1.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(0.500000 + 0.866025i) q^{59} +(0.866025 - 0.500000i) q^{61} +(-0.866025 - 0.500000i) q^{62} -1.00000 q^{64} -1.00000i q^{65} +1.00000 q^{66} +(-0.866025 - 0.500000i) q^{67} +(-0.500000 - 0.866025i) q^{69} -1.00000i q^{70} +(0.500000 + 0.866025i) q^{71} +(0.866025 - 0.500000i) q^{74} +(0.500000 - 0.866025i) q^{75} +1.00000 q^{77} +(0.866025 - 0.500000i) q^{78} +2.00000i q^{79} +(0.866025 + 0.500000i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{82} +2.00000 q^{83} +(-0.866025 + 0.500000i) q^{85} +1.00000i q^{86} +(0.866025 - 0.500000i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(0.866025 + 0.500000i) q^{89} +(0.866025 - 0.500000i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-0.866025 + 0.500000i) q^{95} +(0.866025 - 0.500000i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3}+O(q^{10}) $ 4 * q - 2 * q^3	$ 4 q - 2 q^{3} - 2 q^{10} - 4 q^{13} - 4 q^{14} + 2 q^{16} + 2 q^{17} + 2 q^{19} - 2 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{27} - 2 q^{30} - 4 q^{31} - 2 q^{35} + 2 q^{37} + 2 q^{39} + 4 q^{40} + 2 q^{41} + 2 q^{42} + 2 q^{43} + 2 q^{48} - 4 q^{51} + 2 q^{55} + 2 q^{56} - 4 q^{57} - 2 q^{58} + 2 q^{59} - 4 q^{64} + 4 q^{66} - 2 q^{69} + 2 q^{71} + 2 q^{75} + 4 q^{77} + 2 q^{81} + 8 q^{83} - 2 q^{88} + 2 q^{93}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^10 - 4 * q^13 - 4 * q^14 + 2 * q^16 + 2 * q^17 + 2 * q^19 - 2 * q^22 - 2 * q^23 - 4 * q^25 - 4 * q^27 - 2 * q^30 - 4 * q^31 - 2 * q^35 + 2 * q^37 + 2 * q^39 + 4 * q^40 + 2 * q^41 + 2 * q^42 + 2 * q^43 + 2 * q^48 - 4 * q^51 + 2 * q^55 + 2 * q^56 - 4 * q^57 - 2 * q^58 + 2 * q^59 - 4 * q^64 + 4 * q^66 - 2 * q^69 + 2 * q^71 + 2 * q^75 + 4 * q^77 + 2 * q^81 + 8 * q^83 - 2 * q^88 + 2 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2015\mathbb{Z}\right)^\times$.

$n$	$716$	$807$	$1861$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$4$		0			0
$5$			1.00000i			1.00000i
$5$			1.00000i			1.00000i
$6$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$		−	1.00000i		−	1.00000i
$9$		0			0
$10$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$11$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$11$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	−1.00000			−1.00000
$13$	−1.00000			−1.00000
$14$	−1.00000			−1.00000
$15$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$17$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$19$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$20$		0			0
$21$		−	1.00000i		−	1.00000i
$22$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$23$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$23$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$24$	0.866025	+	0.500000i	0.866025	+	0.500000i
$25$	−1.00000			−1.00000
$26$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$27$	−1.00000			−1.00000
$28$		0			0
$29$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$29$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$30$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$31$	−1.00000			−1.00000
$31$	−1.00000			−1.00000
$32$		0			0
$33$	0.866025	−	0.500000i	0.866025	−	0.500000i
$34$			1.00000i			1.00000i
$35$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$36$		0			0
$37$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$37$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$38$			1.00000i			1.00000i
$39$	0.500000	−	0.866025i	0.500000	−	0.866025i
$40$	1.00000			1.00000
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$41$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$42$	0.500000	−	0.866025i	0.500000	−	0.866025i
$43$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$43$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$44$		0			0
$45$		0			0
$46$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	0.500000	+	0.866025i	0.500000	+	0.866025i
$49$		0			0
$50$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$51$	−1.00000			−1.00000
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$55$	0.500000	−	0.866025i	0.500000	−	0.866025i
$56$	0.500000	+	0.866025i	0.500000	+	0.866025i
$57$	−1.00000			−1.00000
$58$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$59$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$59$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$61$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$62$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$63$		0			0
$64$	−1.00000			−1.00000
$65$		−	1.00000i		−	1.00000i
$66$	1.00000			1.00000
$67$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$67$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$68$		0			0
$69$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$70$		−	1.00000i		−	1.00000i
$71$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$71$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	0.866025	−	0.500000i	0.866025	−	0.500000i
$75$	0.500000	−	0.866025i	0.500000	−	0.866025i
$76$		0			0
$77$	1.00000			1.00000
$78$	0.866025	−	0.500000i	0.866025	−	0.500000i
$79$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$79$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$80$	0.866025	+	0.500000i	0.866025	+	0.500000i
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$	0.866025	−	0.500000i	0.866025	−	0.500000i
$83$	2.00000			2.00000			1.00000			$0$
$83$	2.00000			2.00000			1.00000			$0$
$84$		0			0
$85$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$86$			1.00000i			1.00000i
$87$	0.866025	−	0.500000i	0.866025	−	0.500000i
$88$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$89$	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
$91$	0.866025	−	0.500000i	0.866025	−	0.500000i
$92$		0			0
$93$	0.500000	−	0.866025i	0.500000	−	0.866025i
$94$		0			0
$95$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$96$		0			0
$97$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$97$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$101$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$102$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$103$		0			0		1.00000			$0$
$103$		0			0		−1.00000			$\pi$
$104$			1.00000i			1.00000i
$105$	1.00000			1.00000
$106$		0			0
$107$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$107$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	0.866025	−	0.500000i	0.866025	−	0.500000i
$111$	0.500000	+	0.866025i	0.500000	+	0.866025i
$112$			1.00000i			1.00000i
$113$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$113$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$114$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$115$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$116$		0			0
$117$		0			0
$118$			1.00000i			1.00000i
$119$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$120$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$121$		0			0
$122$	1.00000			1.00000
$123$	0.500000	+	0.866025i	0.500000	+	0.866025i
$124$		0			0
$125$		−	1.00000i		−	1.00000i
$126$		0			0
$127$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$127$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$128$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$129$	−1.00000			−1.00000
$130$	0.500000	−	0.866025i	0.500000	−	0.866025i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$134$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$135$		−	1.00000i		−	1.00000i
$136$	0.866025	−	0.500000i	0.866025	−	0.500000i
$137$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$137$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$138$		−	1.00000i		−	1.00000i
$139$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$139$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$140$		0			0
$141$		0			0
$142$			1.00000i			1.00000i
$143$	0.866025	+	0.500000i	0.866025	+	0.500000i
$144$		0			0
$145$	0.500000	−	0.866025i	0.500000	−	0.866025i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$149$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$150$	0.866025	−	0.500000i	0.866025	−	0.500000i
$151$		0			0		1.00000			$0$
$151$		0			0		−1.00000			$\pi$
$152$	0.866025	−	0.500000i	0.866025	−	0.500000i
$153$		0			0
$154$	0.866025	+	0.500000i	0.866025	+	0.500000i
$155$		−	1.00000i		−	1.00000i
$156$		0			0
$157$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$157$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$158$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$159$		0			0
$160$		0			0
$161$		−	1.00000i		−	1.00000i
$162$	0.866025	−	0.500000i	0.866025	−	0.500000i
$163$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$163$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$164$		0			0
$165$	0.500000	+	0.866025i	0.500000	+	0.866025i
$166$	1.73205	+	1.00000i	1.73205	+	1.00000i
$167$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$167$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$168$	−1.00000			−1.00000
$169$	1.00000			1.00000
$170$	−1.00000			−1.00000
$171$		0			0
$172$		0			0
$173$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$173$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$174$	1.00000			1.00000
$175$	0.866025	−	0.500000i	0.866025	−	0.500000i
$176$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$177$	−1.00000			−1.00000
$178$	0.500000	+	0.866025i	0.500000	+	0.866025i
$179$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$179$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$180$		0			0
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	1.00000			1.00000
$183$			1.00000i			1.00000i
$184$	0.866025	+	0.500000i	0.866025	+	0.500000i
$185$	0.866025	+	0.500000i	0.866025	+	0.500000i
$186$	0.866025	−	0.500000i	0.866025	−	0.500000i
$187$		−	1.00000i		−	1.00000i
$188$		0			0
$189$	0.866025	−	0.500000i	0.866025	−	0.500000i
$190$	−1.00000			−1.00000
$191$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$191$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$192$	0.500000	−	0.866025i	0.500000	−	0.866025i
$193$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$193$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$194$	1.00000			1.00000
$195$	0.866025	+	0.500000i	0.866025	+	0.500000i
$196$		0			0
$197$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$197$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$198$		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	$0.5\pi$
$200$			1.00000i			1.00000i
$201$	0.866025	−	0.500000i	0.866025	−	0.500000i
$202$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$203$	1.00000			1.00000
$204$		0			0
$205$	0.866025	+	0.500000i	0.866025	+	0.500000i
$206$		0			0
$207$		0			0
$208$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$209$		−	1.00000i		−	1.00000i
$210$	0.866025	+	0.500000i	0.866025	+	0.500000i
$211$	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
$213$	−1.00000			−1.00000
$214$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$215$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$216$			1.00000i			1.00000i
$217$	0.866025	−	0.500000i	0.866025	−	0.500000i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$222$			1.00000i			1.00000i
$223$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$223$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$224$		0			0
$225$		0			0
$226$	−1.00000			−1.00000
$227$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$227$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$		0			0		1.00000			$0$
$229$		0			0		−1.00000			$\pi$
$230$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$231$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$232$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$233$		0			0		1.00000			$0$
$233$		0			0		−1.00000			$\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$238$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$241$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$241$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$		0			0
$246$			1.00000i			1.00000i
$247$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$248$			1.00000i			1.00000i
$249$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$250$	0.500000	−	0.866025i	0.500000	−	0.866025i
$251$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$251$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$	0.866025	−	0.500000i	0.866025	−	0.500000i
$254$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$255$		−	1.00000i		−	1.00000i
$256$		0			0
$257$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$257$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$258$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$259$			1.00000i			1.00000i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$263$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$264$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$265$		0			0
$266$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$267$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$268$		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	$0.166667\pi$
$270$	0.500000	−	0.866025i	0.500000	−	0.866025i
$271$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$271$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$272$	1.00000			1.00000
$273$			1.00000i			1.00000i
$274$			1.00000i			1.00000i
$275$	0.866025	+	0.500000i	0.866025	+	0.500000i
$276$		0			0
$277$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$277$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$278$	−1.00000			−1.00000
$279$		0			0
$280$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$281$		0			0			−	1.00000i	$-0.5\pi$
$281$		0			0				1.00000i	$0.5\pi$
$282$		0			0
$283$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$283$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$		−	1.00000i		−	1.00000i
$286$	0.500000	+	0.866025i	0.500000	+	0.866025i
$287$			1.00000i			1.00000i
$288$		0			0
$289$		0			0
$290$	0.866025	−	0.500000i	0.866025	−	0.500000i
$291$			1.00000i			1.00000i
$292$		0			0
$293$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$293$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$294$		0			0
$295$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$296$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$297$	0.866025	+	0.500000i	0.866025	+	0.500000i
$298$			1.00000i			1.00000i
$299$	0.500000	−	0.866025i	0.500000	−	0.866025i
$300$		0			0
$301$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$302$		0			0
$303$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$304$	1.00000			1.00000
$305$	0.500000	+	0.866025i	0.500000	+	0.866025i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	0.500000	−	0.866025i	0.500000	−	0.866025i
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$315$		0			0
$316$		0			0
$317$		0			0		1.00000			$0$
$317$		0			0		−1.00000			$\pi$
$318$		0			0
$319$	0.500000	+	0.866025i	0.500000	+	0.866025i
$320$		−	1.00000i		−	1.00000i
$321$	0.866025	−	0.500000i	0.866025	−	0.500000i
$322$	0.500000	−	0.866025i	0.500000	−	0.866025i
$323$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$324$		0			0
$325$	1.00000			1.00000
$326$	−1.00000			−1.00000
$327$		0			0
$328$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$329$		0			0
$330$			1.00000i			1.00000i
$331$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$331$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$332$		0			0
$333$		0			0
$334$	0.866025	−	0.500000i	0.866025	−	0.500000i
$335$	0.500000	−	0.866025i	0.500000	−	0.866025i
$336$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$337$	−2.00000			−2.00000			−1.00000			$\pi$
$337$	−2.00000			−2.00000			−1.00000			$\pi$
$338$	0.866025	+	0.500000i	0.866025	+	0.500000i
$339$		−	1.00000i		−	1.00000i
$340$		0			0
$341$	0.866025	+	0.500000i	0.866025	+	0.500000i
$342$		0			0
$343$		−	1.00000i		−	1.00000i
$344$	0.866025	−	0.500000i	0.866025	−	0.500000i
$345$	0.866025	−	0.500000i	0.866025	−	0.500000i
$346$	−1.00000			−1.00000
$347$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$347$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$348$		0			0
$349$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$349$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$350$	1.00000			1.00000
$351$	1.00000			1.00000
$352$		0			0
$353$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$353$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$354$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$355$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$356$		0			0
$357$	0.866025	−	0.500000i	0.866025	−	0.500000i
$358$	0.500000	+	0.866025i	0.500000	+	0.866025i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$367$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$367$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$368$	0.500000	+	0.866025i	0.500000	+	0.866025i
$369$		0			0
$370$	0.500000	+	0.866025i	0.500000	+	0.866025i
$371$		0			0
$372$		0			0
$373$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$373$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$374$	0.500000	−	0.866025i	0.500000	−	0.866025i
$375$	0.866025	+	0.500000i	0.866025	+	0.500000i
$376$		0			0
$377$	0.866025	+	0.500000i	0.866025	+	0.500000i
$378$	1.00000			1.00000
$379$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$379$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$380$		0			0
$381$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$382$		−	1.00000i		−	1.00000i
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$384$	0.866025	−	0.500000i	0.866025	−	0.500000i
$385$			1.00000i			1.00000i
$386$	0.500000	+	0.866025i	0.500000	+	0.866025i
$387$		0			0
$388$		0			0
$389$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$389$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$390$	0.500000	+	0.866025i	0.500000	+	0.866025i
$391$	−1.00000			−1.00000
$392$		0			0
$393$		0			0
$394$	0.866025	−	0.500000i	0.866025	−	0.500000i
$395$	−2.00000			−2.00000
$396$		0			0
$397$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$397$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$398$	−1.00000			−1.00000
$399$	0.866025	−	0.500000i	0.866025	−	0.500000i
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$401$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$402$	1.00000			1.00000
$403$	1.00000			1.00000
$404$		0			0
$405$	0.866025	+	0.500000i	0.866025	+	0.500000i
$406$	0.866025	+	0.500000i	0.866025	+	0.500000i
$407$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$408$			1.00000i			1.00000i
$409$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$409$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$410$	0.500000	+	0.866025i	0.500000	+	0.866025i
$411$	−1.00000			−1.00000
$412$		0			0
$413$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$414$		0			0
$415$			2.00000i			2.00000i
$416$		0			0
$417$		−	1.00000i		−	1.00000i
$418$	0.500000	−	0.866025i	0.500000	−	0.866025i
$419$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$419$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$	0.866025	−	0.500000i	0.866025	−	0.500000i
$423$		0			0
$424$		0			0
$425$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$426$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$427$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$428$		0			0
$429$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$430$	−1.00000			−1.00000
$431$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$431$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$432$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$433$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$433$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$434$	1.00000			1.00000
$435$	0.500000	+	0.866025i	0.500000	+	0.866025i
$436$		0			0
$437$	−1.00000			−1.00000
$438$		0			0
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$440$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$441$		0			0
$442$		−	1.00000i		−	1.00000i
$443$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$443$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$444$		0			0
$445$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$446$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$447$	−1.00000			−1.00000
$448$	0.866025	−	0.500000i	0.866025	−	0.500000i
$449$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$449$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$450$		0			0
$451$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$452$		0			0
$453$		0			0
$454$	1.00000			1.00000
$455$	0.500000	+	0.866025i	0.500000	+	0.866025i
$456$			1.00000i			1.00000i
$457$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$457$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$458$		0			0
$459$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$460$		0			0
$461$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$461$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$462$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$465$	0.866025	+	0.500000i	0.866025	+	0.500000i
$466$		0			0
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$		0			0
$469$	1.00000			1.00000
$470$		0			0
$471$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$472$	0.866025	−	0.500000i	0.866025	−	0.500000i
$473$		−	1.00000i		−	1.00000i
$474$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$475$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$479$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$480$		0			0
$481$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$482$	1.00000			1.00000
$483$	0.866025	+	0.500000i	0.866025	+	0.500000i
$484$		0			0
$485$	0.500000	+	0.866025i	0.500000	+	0.866025i
$486$		0			0
$487$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$487$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$488$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$489$		−	1.00000i		−	1.00000i
$490$		0			0
$491$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$491$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$		−	1.00000i		−	1.00000i
$494$		−	1.00000i		−	1.00000i
$495$		0			0
$496$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$497$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$498$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$499$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$499$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$500$		0			0
$501$	0.500000	+	0.866025i	0.500000	+	0.866025i
$502$	1.00000			1.00000
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$504$		0			0
$505$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$506$	1.00000			1.00000
$507$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$508$		0			0
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$510$	0.500000	−	0.866025i	0.500000	−	0.866025i
$511$		0			0
$512$			1.00000i			1.00000i
$513$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$514$	0.500000	+	0.866025i	0.500000	+	0.866025i
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$519$		−	1.00000i		−	1.00000i
$520$	−1.00000			−1.00000
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$523$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$524$		0			0
$525$			1.00000i			1.00000i
$526$	0.866025	−	0.500000i	0.866025	−	0.500000i
$527$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$528$		−	1.00000i		−	1.00000i
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$534$	−1.00000			−1.00000
$535$	0.500000	−	0.866025i	0.500000	−	0.866025i
$536$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$537$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$538$	1.00000			1.00000
$539$		0			0
$540$		0			0
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$	0.500000	+	0.866025i	0.500000	+	0.866025i
$543$		0			0
$544$		0			0
$545$		0			0
$546$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$547$		0			0		1.00000			$0$
$547$		0			0		−1.00000			$\pi$
$548$		0			0
$549$		0			0
$550$	0.500000	+	0.866025i	0.500000	+	0.866025i
$551$		−	1.00000i		−	1.00000i
$552$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$553$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$554$		−	1.00000i		−	1.00000i
$555$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$556$		0			0
$557$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$557$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$558$		0			0
$559$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$560$	−1.00000			−1.00000
$561$	0.866025	+	0.500000i	0.866025	+	0.500000i
$562$		0			0
$563$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$563$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$566$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$567$			1.00000i			1.00000i
$568$	0.866025	−	0.500000i	0.866025	−	0.500000i
$569$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$569$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$570$	0.500000	−	0.866025i	0.500000	−	0.866025i
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$		0			0
$573$	1.00000			1.00000
$574$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$575$	0.500000	−	0.866025i	0.500000	−	0.866025i
$576$		0			0
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$		0			0
$579$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$580$		0			0
$581$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$582$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$583$		0			0
$584$		0			0
$585$		0			0
$586$	1.00000			1.00000
$587$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$587$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$588$		0			0
$589$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$590$	−1.00000			−1.00000
$591$	0.500000	+	0.866025i	0.500000	+	0.866025i
$592$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$	0.500000	+	0.866025i	0.500000	+	0.866025i
$595$	0.500000	−	0.866025i	0.500000	−	0.866025i
$596$		0			0
$597$		−	1.00000i		−	1.00000i
$598$	0.866025	−	0.500000i	0.866025	−	0.500000i
$599$	−2.00000			−2.00000			−1.00000			$\pi$
$599$	−2.00000			−2.00000			−1.00000			$\pi$
$600$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$601$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$601$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$602$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$603$		0			0
$604$		0			0
$605$		0			0
$606$		−	1.00000i		−	1.00000i
$607$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$607$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$608$		0			0
$609$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$610$			1.00000i			1.00000i
$611$		0			0
$612$		0			0
$613$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$613$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$614$		0			0
$615$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$616$		−	1.00000i		−	1.00000i
$617$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$617$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$618$		0			0
$619$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$619$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$620$		0			0
$621$	0.500000	−	0.866025i	0.500000	−	0.866025i
$622$		0			0
$623$	−1.00000			−1.00000
$624$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$625$	1.00000			1.00000
$626$		0			0
$627$	0.866025	+	0.500000i	0.866025	+	0.500000i
$628$		0			0
$629$	1.00000			1.00000
$630$		0			0
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$631$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$632$	2.00000			2.00000
$633$	0.500000	+	0.866025i	0.500000	+	0.866025i
$634$		0			0
$635$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$636$		0			0
$637$		0			0
$638$			1.00000i			1.00000i
$639$		0			0
$640$	0.500000	−	0.866025i	0.500000	−	0.866025i
$641$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$641$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$642$	1.00000			1.00000
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$644$		0			0
$645$		−	1.00000i		−	1.00000i
$646$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$647$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$647$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$648$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$649$		−	1.00000i		−	1.00000i
$650$	0.866025	+	0.500000i	0.866025	+	0.500000i
$651$			1.00000i			1.00000i
$652$		0			0
$653$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$653$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$654$		0			0
$655$		0			0
$656$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$657$		0			0
$658$		0			0
$659$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$659$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$660$		0			0
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$661$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$662$	−1.00000			−1.00000
$663$	1.00000			1.00000
$664$		−	2.00000i		−	2.00000i
$665$	0.500000	−	0.866025i	0.500000	−	0.866025i
$666$		0			0
$667$	0.866025	−	0.500000i	0.866025	−	0.500000i
$668$		0			0
$669$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$670$	0.866025	−	0.500000i	0.866025	−	0.500000i
$671$	−1.00000			−1.00000
$672$		0			0
$673$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$673$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$674$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$675$	1.00000			1.00000
$676$		0			0
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$	0.500000	−	0.866025i	0.500000	−	0.866025i
$679$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$680$	0.500000	+	0.866025i	0.500000	+	0.866025i
$681$			1.00000i			1.00000i
$682$	0.500000	+	0.866025i	0.500000	+	0.866025i
$683$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$683$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$684$		0			0
$685$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$686$	0.500000	−	0.866025i	0.500000	−	0.866025i
$687$		0			0
$688$	1.00000			1.00000
$689$		0			0
$690$	1.00000			1.00000
$691$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$691$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$		−	1.00000i		−	1.00000i
$695$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$696$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$697$	1.00000			1.00000
$698$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$699$		0			0
$700$		0			0
$701$	−2.00000			−2.00000			−1.00000			$\pi$
$701$	−2.00000			−2.00000			−1.00000			$\pi$
$702$	0.866025	+	0.500000i	0.866025	+	0.500000i
$703$	1.00000			1.00000
$704$	0.866025	+	0.500000i	0.866025	+	0.500000i
$705$		0			0
$706$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$707$		−	1.00000i		−	1.00000i
$708$		0			0
$709$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$709$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$710$	−1.00000			−1.00000
$711$		0			0
$712$	0.500000	−	0.866025i	0.500000	−	0.866025i
$713$	0.500000	−	0.866025i	0.500000	−	0.866025i
$714$	1.00000			1.00000
$715$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$719$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$			1.00000i			1.00000i
$724$		0			0
$725$	0.866025	+	0.500000i	0.866025	+	0.500000i
$726$		0			0
$727$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$727$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$728$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$729$	1.00000			1.00000
$730$		0			0
$731$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$732$		0			0
$733$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$733$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$734$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$735$		0			0
$736$		0			0
$737$	0.500000	+	0.866025i	0.500000	+	0.866025i
$738$		0			0
$739$	−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	$0.833333\pi$
$740$		0			0
$741$	1.00000			1.00000
$742$		0			0
$743$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$743$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$744$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$745$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$746$	1.00000			1.00000
$747$		0			0
$748$		0			0
$749$	1.00000			1.00000
$750$	0.500000	+	0.866025i	0.500000	+	0.866025i
$751$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$751$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$752$		0			0
$753$			1.00000i			1.00000i
$754$	0.500000	+	0.866025i	0.500000	+	0.866025i
$755$		0			0
$756$		0			0
$757$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$757$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$758$	0.866025	−	0.500000i	0.866025	−	0.500000i
$759$			1.00000i			1.00000i
$760$	0.500000	+	0.866025i	0.500000	+	0.866025i
$761$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$761$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$762$		−	1.00000i		−	1.00000i
$763$		0			0
$764$		0			0
$765$		0			0
$766$		−	1.00000i		−	1.00000i
$767$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$768$		0			0
$769$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$769$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$770$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$771$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$772$		0			0
$773$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$773$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$774$		0			0
$775$	1.00000			1.00000
$776$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$777$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$778$	1.00000	−	1.73205i	1.00000	−	1.73205i
$779$	1.00000			1.00000
$780$		0			0
$781$		−	1.00000i		−	1.00000i
$782$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$783$	0.866025	+	0.500000i	0.866025	+	0.500000i
$784$		0			0
$785$	−2.00000			−2.00000
$786$		0			0
$787$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$787$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$	0.500000	+	0.866025i	0.500000	+	0.866025i
$790$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$791$	0.500000	−	0.866025i	0.500000	−	0.866025i
$792$		0			0
$793$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$794$	−1.00000			−1.00000
$795$		0			0
$796$		0			0
$797$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$797$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$798$	1.00000			1.00000
$799$		0			0
$800$		0			0
$801$		0			0
$802$	0.500000	+	0.866025i	0.500000	+	0.866025i
$803$		0			0
$804$		0			0
$805$	1.00000			1.00000
$806$	0.866025	+	0.500000i	0.866025	+	0.500000i
$807$			1.00000i			1.00000i
$808$	0.866025	+	0.500000i	0.866025	+	0.500000i
$809$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$809$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$810$	0.500000	+	0.866025i	0.500000	+	0.866025i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$814$	−1.00000			−1.00000
$815$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$816$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$817$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$818$	−1.00000			−1.00000
$819$		0			0
$820$		0			0
$821$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$821$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$822$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$823$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$823$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$824$		0			0
$825$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$826$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		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	$0.833333\pi$
$830$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$831$	1.00000			1.00000
$832$	1.00000			1.00000
$833$		0			0
$834$	0.500000	−	0.866025i	0.500000	−	0.866025i
$835$	0.866025	+	0.500000i	0.866025	+	0.500000i
$836$		0			0
$837$	1.00000			1.00000
$838$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$839$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$839$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$840$		−	1.00000i		−	1.00000i
$841$		0			0
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.00000i			1.00000i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.866025	−	0.500000i	0.866025	−	0.500000i
$850$		−	1.00000i		−	1.00000i
$851$	0.500000	+	0.866025i	0.500000	+	0.866025i
$852$		0			0
$853$		0			0		1.00000			$0$
$853$		0			0		−1.00000			$\pi$
$854$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$855$		0			0
$856$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$	−1.00000			−1.00000
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$		0			0
$861$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$862$	0.866025	−	0.500000i	0.866025	−	0.500000i
$863$	2.00000			2.00000			1.00000			$0$
$863$	2.00000			2.00000			1.00000			$0$
$864$		0			0
$865$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$866$			1.00000i			1.00000i
$867$		0			0
$868$		0			0
$869$	1.00000	−	1.73205i	1.00000	−	1.73205i
$870$			1.00000i			1.00000i
$871$	0.866025	+	0.500000i	0.866025	+	0.500000i
$872$		0			0
$873$		0			0
$874$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$875$	0.500000	+	0.866025i	0.500000	+	0.866025i
$876$		0			0
$877$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$877$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$878$	0.866025	−	0.500000i	0.866025	−	0.500000i
$879$			1.00000i			1.00000i
$880$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$881$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$881$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$		0			0
$885$		−	1.00000i		−	1.00000i
$886$	1.00000	−	1.73205i	1.00000	−	1.73205i
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$	0.866025	−	0.500000i	0.866025	−	0.500000i
$889$		−	1.00000i		−	1.00000i
$890$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$891$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$892$		0			0
$893$		0			0
$894$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$895$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$896$	1.00000			1.00000
$897$	0.500000	+	0.866025i	0.500000	+	0.866025i
$898$	1.00000			1.00000
$899$	0.866025	+	0.500000i	0.866025	+	0.500000i
$900$		0			0
$901$		0			0
$902$	−1.00000			−1.00000
$903$	0.866025	−	0.500000i	0.866025	−	0.500000i
$904$	0.500000	+	0.866025i	0.500000	+	0.866025i
$905$		0			0
$906$		0			0
$907$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$907$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$908$		0			0
$909$		0			0
$910$			1.00000i			1.00000i
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$913$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$914$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$915$	−1.00000			−1.00000
$916$		0			0
$917$		0			0
$918$		−	1.00000i		−	1.00000i
$919$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$919$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$920$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$921$		0			0
$922$	−1.00000			−1.00000
$923$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$924$		0			0
$925$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$929$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$930$	0.500000	+	0.866025i	0.500000	+	0.866025i
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.00000			1.00000
$936$		0			0
$937$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$937$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$938$	0.866025	+	0.500000i	0.866025	+	0.500000i
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$943$	0.500000	+	0.866025i	0.500000	+	0.866025i
$944$	1.00000			1.00000
$945$	0.500000	+	0.866025i	0.500000	+	0.866025i
$946$	0.500000	−	0.866025i	0.500000	−	0.866025i
$947$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$947$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$948$		0			0
$949$		0			0
$950$		−	1.00000i		−	1.00000i
$951$		0			0
$952$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$953$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$953$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$954$		0			0
$955$	0.866025	−	0.500000i	0.866025	−	0.500000i
$956$		0			0
$957$	−1.00000			−1.00000
$958$	0.866025	−	0.500000i	0.866025	−	0.500000i
$959$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$960$	0.866025	+	0.500000i	0.866025	+	0.500000i
$961$	1.00000			1.00000
$962$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$963$		0			0
$964$		0			0
$965$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$966$	0.500000	+	0.866025i	0.500000	+	0.866025i
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$		0			0
$969$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$970$			1.00000i			1.00000i
$971$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$971$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$	0.500000	−	0.866025i	0.500000	−	0.866025i
$974$			1.00000i			1.00000i
$975$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$976$		−	1.00000i		−	1.00000i
$977$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$977$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$978$	0.500000	−	0.866025i	0.500000	−	0.866025i
$979$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$980$		0			0
$981$		0			0
$982$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$983$		0			0			−	1.00000i	$-0.5\pi$
$983$		0			0				1.00000i	$0.5\pi$
$984$	0.866025	−	0.500000i	0.866025	−	0.500000i
$985$	0.866025	+	0.500000i	0.866025	+	0.500000i
$986$	0.500000	−	0.866025i	0.500000	−	0.866025i
$987$		0			0
$988$		0			0
$989$	−1.00000			−1.00000
$990$		0			0
$991$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$991$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$992$		0			0
$993$		−	1.00000i		−	1.00000i
$994$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$995$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$996$		0			0
$997$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$997$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$998$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$999$	−0.500000	+	0.866025i	−0.500000	+	0.866025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2015.1.bq.c.464.2	yes	4
5.4	even	2		2015.1.bq.e.464.1	yes	4
13.3	even	3	inner	2015.1.bq.c.1394.1	yes	4
31.30	odd	2		2015.1.bq.e.464.2	yes	4
65.29	even	6		2015.1.bq.e.1394.2	yes	4
155.154	odd	2	inner	2015.1.bq.c.464.1	✓	4
403.185	odd	6		2015.1.bq.e.1394.1	yes	4
2015.1394	odd	6	inner	2015.1.bq.c.1394.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2015.1.bq.c.464.1	✓	4	155.154	odd	2	inner
2015.1.bq.c.464.2	yes	4	1.1	even	1	trivial
2015.1.bq.c.1394.1	yes	4	13.3	even	3	inner
2015.1.bq.c.1394.2	yes	4	2015.1394	odd	6	inner
2015.1.bq.e.464.1	yes	4	5.4	even	2
2015.1.bq.e.464.2	yes	4	31.30	odd	2
2015.1.bq.e.1394.1	yes	4	403.185	odd	6
2015.1.bq.e.1394.2	yes	4	65.29	even	6

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:	\( N \)	\(=\)	\( 2015 = 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2015.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000i q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.866025 + 0.500000i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{10} +(-0.866025 - 0.500000i) q^{11} -1.00000 q^{13} -1.00000 q^{14} +(-0.866025 - 0.500000i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.500000 + 0.866025i) q^{17} +(0.500000 + 0.866025i) q^{19} -1.00000i q^{21} +(-0.500000 - 0.866025i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.866025 + 0.500000i) q^{24} -1.00000 q^{25} +(-0.866025 - 0.500000i) q^{26} -1.00000 q^{27} +(-0.866025 - 0.500000i) q^{29} +(-0.500000 - 0.866025i) q^{30} -1.00000 q^{31} +(0.866025 - 0.500000i) q^{33} +1.00000i q^{34} +(-0.500000 - 0.866025i) q^{35} +(0.500000 - 0.866025i) q^{37} +1.00000i q^{38} +(0.500000 - 0.866025i) q^{39} +1.00000 q^{40} +(0.500000 - 0.866025i) q^{41} +(0.500000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-0.866025 + 0.500000i) q^{46} +(0.500000 + 0.866025i) q^{48} +(-0.866025 - 0.500000i) q^{50} -1.00000 q^{51} +(-0.866025 - 0.500000i) q^{54} +(0.500000 - 0.866025i) q^{55} +(0.500000 + 0.866025i) q^{56} -1.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(0.500000 + 0.866025i) q^{59} +(0.866025 - 0.500000i) q^{61} +(-0.866025 - 0.500000i) q^{62} -1.00000 q^{64} -1.00000i q^{65} +1.00000 q^{66} +(-0.866025 - 0.500000i) q^{67} +(-0.500000 - 0.866025i) q^{69} -1.00000i q^{70} +(0.500000 + 0.866025i) q^{71} +(0.866025 - 0.500000i) q^{74} +(0.500000 - 0.866025i) q^{75} +1.00000 q^{77} +(0.866025 - 0.500000i) q^{78} +2.00000i q^{79} +(0.866025 + 0.500000i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{82} +2.00000 q^{83} +(-0.866025 + 0.500000i) q^{85} +1.00000i q^{86} +(0.866025 - 0.500000i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(0.866025 + 0.500000i) q^{89} +(0.866025 - 0.500000i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-0.866025 + 0.500000i) q^{95} +(0.866025 - 0.500000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3}+O(q^{10}) \) 4 * q - 2 * q^3	\( 4 q - 2 q^{3} - 2 q^{10} - 4 q^{13} - 4 q^{14} + 2 q^{16} + 2 q^{17} + 2 q^{19} - 2 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{27} - 2 q^{30} - 4 q^{31} - 2 q^{35} + 2 q^{37} + 2 q^{39} + 4 q^{40} + 2 q^{41} + 2 q^{42} + 2 q^{43} + 2 q^{48} - 4 q^{51} + 2 q^{55} + 2 q^{56} - 4 q^{57} - 2 q^{58} + 2 q^{59} - 4 q^{64} + 4 q^{66} - 2 q^{69} + 2 q^{71} + 2 q^{75} + 4 q^{77} + 2 q^{81} + 8 q^{83} - 2 q^{88} + 2 q^{93}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^10 - 4 * q^13 - 4 * q^14 + 2 * q^16 + 2 * q^17 + 2 * q^19 - 2 * q^22 - 2 * q^23 - 4 * q^25 - 4 * q^27 - 2 * q^30 - 4 * q^31 - 2 * q^35 + 2 * q^37 + 2 * q^39 + 4 * q^40 + 2 * q^41 + 2 * q^42 + 2 * q^43 + 2 * q^48 - 4 * q^51 + 2 * q^55 + 2 * q^56 - 4 * q^57 - 2 * q^58 + 2 * q^59 - 4 * q^64 + 4 * q^66 - 2 * q^69 + 2 * q^71 + 2 * q^75 + 4 * q^77 + 2 * q^81 + 8 * q^83 - 2 * q^88 + 2 * q^93

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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