LMFDB - Embedded newform 3724.1.bk.a.1451.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3724,1,Mod(1451,3724)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3724, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 2]))

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

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

chi := DirichletCharacter("3724.1451");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3724 = 2^{2} \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3724.bk (of order $6$, degree $2$, not 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:	$1.85851810705$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 532)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.283024.1

Embedding invariants

Embedding label			1451.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3724.1451
Dual form			3724.1.bk.a.3203.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +O(q^{10})$	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.500000 + 0.866025i) q^{13} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{17} +1.00000i q^{19} +(-0.500000 - 0.866025i) q^{22} +(0.866025 - 0.500000i) q^{23} +(0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-0.866025 - 0.500000i) q^{26} -1.00000i q^{27} +(-0.500000 + 0.866025i) q^{29} +(-0.866025 + 0.500000i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-0.866025 - 0.500000i) q^{34} +(-0.500000 + 0.866025i) q^{37} -1.00000 q^{38} +(-0.866025 + 0.500000i) q^{39} +(0.500000 + 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{43} +(0.866025 - 0.500000i) q^{44} +(0.500000 + 0.866025i) q^{46} +(0.866025 - 0.500000i) q^{47} +(0.866025 + 0.500000i) q^{48} -1.00000i q^{50} +(-0.866025 + 0.500000i) q^{51} +(0.500000 - 0.866025i) q^{52} +1.00000 q^{54} +(-0.500000 + 0.866025i) q^{57} +(-0.866025 - 0.500000i) q^{58} +(-0.866025 - 0.500000i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-0.500000 - 0.866025i) q^{62} -1.00000 q^{64} -1.00000i q^{66} +(0.500000 - 0.866025i) q^{68} +1.00000 q^{69} +(-0.866025 + 0.500000i) q^{71} +(-0.500000 + 0.866025i) q^{73} +(-0.866025 - 0.500000i) q^{74} +(-0.866025 - 0.500000i) q^{75} -1.00000i q^{76} +(-0.500000 - 0.866025i) q^{78} +(0.500000 - 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{82} +(0.500000 + 0.866025i) q^{86} +(-0.866025 + 0.500000i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} +(-0.866025 + 0.500000i) q^{92} -1.00000 q^{93} +(0.500000 + 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} - 2 q^{6}+O(q^{10}) $ 4 * q - 4 * q^4 - 2 * q^6	$ 4 q - 4 q^{4} - 2 q^{6} - 2 q^{13} + 4 q^{16} - 2 q^{17} - 2 q^{22} + 2 q^{24} - 4 q^{25} - 2 q^{29} - 4 q^{33} - 2 q^{37} - 4 q^{38} + 2 q^{41} + 2 q^{46} + 2 q^{52} + 4 q^{54} - 2 q^{57} + 2 q^{61} - 2 q^{62} - 4 q^{64} + 2 q^{68} + 4 q^{69} - 2 q^{73} - 2 q^{78} + 2 q^{81} + 2 q^{86} + 2 q^{88} - 2 q^{89} - 4 q^{93} + 2 q^{94} - 2 q^{96} - 2 q^{97}+O(q^{100}) $ 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^13 + 4 * q^16 - 2 * q^17 - 2 * q^22 + 2 * q^24 - 4 * q^25 - 2 * q^29 - 4 * q^33 - 2 * q^37 - 4 * q^38 + 2 * q^41 + 2 * q^46 + 2 * q^52 + 4 * q^54 - 2 * q^57 + 2 * q^61 - 2 * q^62 - 4 * q^64 + 2 * q^68 + 4 * q^69 - 2 * q^73 - 2 * q^78 + 2 * q^81 + 2 * q^86 + 2 * q^88 - 2 * q^89 - 4 * q^93 + 2 * q^94 - 2 * q^96 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3724\mathbb{Z}\right)^\times$.

$n$	$1863$	$3041$	$3137$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			1.00000i			1.00000i
$2$			1.00000i			1.00000i
$3$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$3$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$4$	−1.00000			−1.00000
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	1.00000i
$9$		0			0
$10$		0			0
$11$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$11$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$12$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$13$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$13$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			1.00000
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$17$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$18$		0			0
$19$			1.00000i			1.00000i
$19$			1.00000i			1.00000i
$20$		0			0
$21$		0			0
$22$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$23$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$23$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$24$	0.500000	−	0.866025i	0.500000	−	0.866025i
$25$	−1.00000			−1.00000
$26$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$27$		−	1.00000i		−	1.00000i
$28$		0			0
$29$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$29$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$30$		0			0
$31$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$31$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$32$			1.00000i			1.00000i
$33$	−1.00000			−1.00000
$34$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$35$		0			0
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$38$	−1.00000			−1.00000
$39$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$40$		0			0
$41$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$41$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$42$		0			0
$43$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$43$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$44$	0.866025	−	0.500000i	0.866025	−	0.500000i
$45$		0			0
$46$	0.500000	+	0.866025i	0.500000	+	0.866025i
$47$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$47$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$48$	0.866025	+	0.500000i	0.866025	+	0.500000i
$49$		0			0
$50$		−	1.00000i		−	1.00000i
$51$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$52$	0.500000	−	0.866025i	0.500000	−	0.866025i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	1.00000			1.00000
$55$		0			0
$56$		0			0
$57$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$58$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$59$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$59$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$61$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$62$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$63$		0			0
$64$	−1.00000			−1.00000
$65$		0			0
$66$		−	1.00000i		−	1.00000i
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$	0.500000	−	0.866025i	0.500000	−	0.866025i
$69$	1.00000			1.00000
$70$		0			0
$71$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$71$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$72$		0			0
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$73$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$74$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$75$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$76$		−	1.00000i		−	1.00000i
$77$		0			0
$78$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.500000	−	0.866025i
$82$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$		0			0
$86$	0.500000	+	0.866025i	0.500000	+	0.866025i
$87$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$88$	0.500000	+	0.866025i	0.500000	+	0.866025i
$89$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$89$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$90$		0			0
$91$		0			0
$92$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$93$	−1.00000			−1.00000
$94$	0.500000	+	0.866025i	0.500000	+	0.866025i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$97$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$97$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$98$		0			0
$99$		0			0
$100$	1.00000			1.00000
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$103$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$104$	0.866025	+	0.500000i	0.866025	+	0.500000i
$105$		0			0
$106$		0			0
$107$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$107$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$108$			1.00000i			1.00000i
$109$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$109$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$110$		0			0
$111$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$112$		0			0
$113$	2.00000			2.00000			1.00000			$0$
$113$	2.00000			2.00000			1.00000			$0$
$114$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$115$		0			0
$116$	0.500000	−	0.866025i	0.500000	−	0.866025i
$117$		0			0
$118$	0.500000	−	0.866025i	0.500000	−	0.866025i
$119$		0			0
$120$		0			0
$121$		0			0
$122$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$123$			1.00000i			1.00000i
$124$	0.866025	−	0.500000i	0.866025	−	0.500000i
$125$		0			0
$126$		0			0
$127$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$127$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$128$		−	1.00000i		−	1.00000i
$129$	1.00000			1.00000
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	1.00000			1.00000
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.866025	+	0.500000i	0.866025	+	0.500000i
$137$	2.00000			2.00000			1.00000			$0$
$137$	2.00000			2.00000			1.00000			$0$
$138$			1.00000i			1.00000i
$139$	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
$141$	1.00000			1.00000
$142$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$143$		−	1.00000i		−	1.00000i
$144$		0			0
$145$		0			0
$146$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$147$		0			0
$148$	0.500000	−	0.866025i	0.500000	−	0.866025i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	0.500000	−	0.866025i	0.500000	−	0.866025i
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$151$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$152$	1.00000			1.00000
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.866025	−	0.500000i	0.866025	−	0.500000i
$157$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$157$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.866025	+	0.500000i	0.866025	+	0.500000i
$163$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$163$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$164$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$165$		0			0
$166$		0			0
$167$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$167$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$		0			0
$170$		0			0
$171$		0			0
$172$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$173$		0			0			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$175$		0			0
$176$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$177$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$178$	0.866025	−	0.500000i	0.866025	−	0.500000i
$179$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$179$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$181$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$182$		0			0
$183$			1.00000i			1.00000i
$184$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$185$		0			0
$186$		−	1.00000i		−	1.00000i
$187$		−	1.00000i		−	1.00000i
$188$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$189$		0			0
$190$		0			0
$191$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$191$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$192$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$193$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$193$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$194$	0.866025	−	0.500000i	0.866025	−	0.500000i
$195$		0			0
$196$		0			0
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$			1.00000i			1.00000i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.866025	−	0.500000i	0.866025	−	0.500000i
$205$		0			0
$206$	0.500000	−	0.866025i	0.500000	−	0.866025i
$207$		0			0
$208$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$209$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$210$		0			0
$211$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$211$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$212$		0			0
$213$	−1.00000			−1.00000
$214$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$215$		0			0
$216$	−1.00000			−1.00000
$217$		0			0
$218$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$219$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$220$		0			0
$221$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$222$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$223$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$223$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$224$		0			0
$225$		0			0
$226$			2.00000i			2.00000i
$227$	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	$0.166667\pi$
$228$	0.500000	−	0.866025i	0.500000	−	0.866025i
$229$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$229$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$230$		0			0
$231$		0			0
$232$	0.866025	+	0.500000i	0.866025	+	0.500000i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		0			0
$236$	0.866025	+	0.500000i	0.866025	+	0.500000i
$237$		0			0
$238$		0			0
$239$		0			0		1.00000			$0$
$239$		0			0		−1.00000			$\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$		0			0
$244$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$245$		0			0
$246$	−1.00000			−1.00000
$247$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$248$	0.500000	+	0.866025i	0.500000	+	0.866025i
$249$		0			0
$250$		0			0
$251$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$251$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$252$		0			0
$253$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$254$	0.500000	−	0.866025i	0.500000	−	0.866025i
$255$		0			0
$256$	1.00000			1.00000
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$257$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$258$			1.00000i			1.00000i
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$263$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$264$			1.00000i			1.00000i
$265$		0			0
$266$		0			0
$267$		−	1.00000i		−	1.00000i
$268$		0			0
$269$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$269$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$270$		0			0
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$273$		0			0
$274$			2.00000i			2.00000i
$275$	0.866025	−	0.500000i	0.866025	−	0.500000i
$276$	−1.00000			−1.00000
$277$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$277$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$278$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$279$		0			0
$280$		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			$\pi$
$282$			1.00000i			1.00000i
$283$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$283$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$284$	0.866025	−	0.500000i	0.866025	−	0.500000i
$285$		0			0
$286$	1.00000			1.00000
$287$		0			0
$288$		0			0
$289$		0			0
$290$		0			0
$291$		−	1.00000i		−	1.00000i
$292$	0.500000	−	0.866025i	0.500000	−	0.866025i
$293$	2.00000			2.00000			1.00000			$0$
$293$	2.00000			2.00000			1.00000			$0$
$294$		0			0
$295$		0			0
$296$	0.866025	+	0.500000i	0.866025	+	0.500000i
$297$	0.500000	+	0.866025i	0.500000	+	0.866025i
$298$		0			0
$299$			1.00000i			1.00000i
$300$	0.866025	+	0.500000i	0.866025	+	0.500000i
$301$		0			0
$302$	0.500000	+	0.866025i	0.500000	+	0.866025i
$303$		0			0
$304$			1.00000i			1.00000i
$305$		0			0
$306$		0			0
$307$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$307$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$308$		0			0
$309$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$310$		0			0
$311$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$311$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$312$	0.500000	+	0.866025i	0.500000	+	0.866025i
$313$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$313$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$314$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$315$		0			0
$316$		0			0
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$317$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$318$		0			0
$319$		−	1.00000i		−	1.00000i
$320$		0			0
$321$	0.500000	+	0.866025i	0.500000	+	0.866025i
$322$		0			0
$323$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$324$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$325$	0.500000	−	0.866025i	0.500000	−	0.866025i
$326$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$327$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$328$	0.866025	−	0.500000i	0.866025	−	0.500000i
$329$		0			0
$330$		0			0
$331$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$331$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$332$		0			0
$333$		0			0
$334$	0.500000	−	0.866025i	0.500000	−	0.866025i
$335$		0			0
$336$		0			0
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$337$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$338$		0			0
$339$	1.73205	+	1.00000i	1.73205	+	1.00000i
$340$		0			0
$341$	0.500000	−	0.866025i	0.500000	−	0.866025i
$342$		0			0
$343$		0			0
$344$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$345$		0			0
$346$		0			0
$347$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$347$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$348$	0.866025	−	0.500000i	0.866025	−	0.500000i
$349$	−2.00000			−2.00000			−1.00000			$\pi$
$349$	−2.00000			−2.00000			−1.00000			$\pi$
$350$		0			0
$351$	0.866025	+	0.500000i	0.866025	+	0.500000i
$352$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$353$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$353$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$354$	0.866025	−	0.500000i	0.866025	−	0.500000i
$355$		0			0
$356$	0.500000	+	0.866025i	0.500000	+	0.866025i
$357$		0			0
$358$	0.500000	+	0.866025i	0.500000	+	0.866025i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	−1.00000			−1.00000
$362$	0.866025	+	0.500000i	0.866025	+	0.500000i
$363$		0			0
$364$		0			0
$365$		0			0
$366$	−1.00000			−1.00000
$367$		0			0		1.00000			$0$
$367$		0			0		−1.00000			$\pi$
$368$	0.866025	−	0.500000i	0.866025	−	0.500000i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	1.00000			1.00000
$373$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$373$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$374$	1.00000			1.00000
$375$		0			0
$376$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$377$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$378$		0			0
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$382$	0.500000	−	0.866025i	0.500000	−	0.866025i
$383$		0			0		1.00000			$0$
$383$		0			0		−1.00000			$\pi$
$384$	0.500000	−	0.866025i	0.500000	−	0.866025i
$385$		0			0
$386$	0.866025	+	0.500000i	0.866025	+	0.500000i
$387$		0			0
$388$	0.500000	+	0.866025i	0.500000	+	0.866025i
$389$		0			0			−	1.00000i	$-0.5\pi$
$389$		0			0				1.00000i	$0.5\pi$
$390$		0			0
$391$			1.00000i			1.00000i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.00000			−2.00000			−1.00000			$\pi$
$397$	−2.00000			−2.00000			−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	−1.00000			−1.00000
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		−	1.00000i		−	1.00000i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.00000i		−	1.00000i
$408$	0.500000	+	0.866025i	0.500000	+	0.866025i
$409$		0			0			−	1.00000i	$-0.5\pi$
$409$		0			0				1.00000i	$0.5\pi$
$410$		0			0
$411$	1.73205	+	1.00000i	1.73205	+	1.00000i
$412$	0.866025	+	0.500000i	0.866025	+	0.500000i
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$417$	0.500000	+	0.866025i	0.500000	+	0.866025i
$418$	0.866025	−	0.500000i	0.866025	−	0.500000i
$419$		0			0		1.00000			$0$
$419$		0			0		−1.00000			$\pi$
$420$		0			0
$421$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$421$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$422$	0.500000	+	0.866025i	0.500000	+	0.866025i
$423$		0			0
$424$		0			0
$425$	0.500000	−	0.866025i	0.500000	−	0.866025i
$426$		−	1.00000i		−	1.00000i
$427$		0			0
$428$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$429$	0.500000	−	0.866025i	0.500000	−	0.866025i
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$		−	1.00000i		−	1.00000i
$433$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$433$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$434$		0			0
$435$		0			0
$436$	0.500000	−	0.866025i	0.500000	−	0.866025i
$437$	0.500000	+	0.866025i	0.500000	+	0.866025i
$438$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$		0			0
$442$	0.866025	−	0.500000i	0.866025	−	0.500000i
$443$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$443$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$444$	0.866025	−	0.500000i	0.866025	−	0.500000i
$445$		0			0
$446$	0.500000	+	0.866025i	0.500000	+	0.866025i
$447$		0			0
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$452$	−2.00000			−2.00000
$453$	1.00000			1.00000
$454$	0.500000	+	0.866025i	0.500000	+	0.866025i
$455$		0			0
$456$	0.866025	+	0.500000i	0.866025	+	0.500000i
$457$	−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			$\pi$
$458$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$459$	0.866025	+	0.500000i	0.866025	+	0.500000i
$460$		0			0
$461$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$461$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$463$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$464$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$465$		0			0
$466$		0			0
$467$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$467$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$472$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$473$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$474$		0			0
$475$		−	1.00000i		−	1.00000i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$479$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$480$		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			0
$487$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$487$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$488$	0.866025	−	0.500000i	0.866025	−	0.500000i
$489$	0.500000	+	0.866025i	0.500000	+	0.866025i
$490$		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	$0.166667\pi$
$492$		−	1.00000i		−	1.00000i
$493$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$494$	0.500000	−	0.866025i	0.500000	−	0.866025i
$495$		0			0
$496$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$497$		0			0
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$		0			0
$501$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$502$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$503$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$503$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$504$		0			0
$505$		0			0
$506$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$507$		0			0
$508$	0.866025	+	0.500000i	0.866025	+	0.500000i
$509$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$509$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			1.00000i
$513$	1.00000			1.00000
$514$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$515$		0			0
$516$	−1.00000			−1.00000
$517$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$521$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$522$		0			0
$523$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$523$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$524$		0			0
$525$		0			0
$526$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$527$		−	1.00000i		−	1.00000i
$528$	−1.00000			−1.00000
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.00000			−1.00000
$534$	1.00000			1.00000
$535$		0			0
$536$		0			0
$537$	1.00000			1.00000
$538$	0.866025	+	0.500000i	0.866025	+	0.500000i
$539$		0			0
$540$		0			0
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$541$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$542$		0			0
$543$	0.866025	−	0.500000i	0.866025	−	0.500000i
$544$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$545$		0			0
$546$		0			0
$547$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$547$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$548$	−2.00000			−2.00000
$549$		0			0
$550$	0.500000	+	0.866025i	0.500000	+	0.866025i
$551$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$552$		−	1.00000i		−	1.00000i
$553$		0			0
$554$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$555$		0			0
$556$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$557$	−2.00000			−2.00000			−1.00000			$\pi$
$557$	−2.00000			−2.00000			−1.00000			$\pi$
$558$		0			0
$559$			1.00000i			1.00000i
$560$		0			0
$561$	0.500000	−	0.866025i	0.500000	−	0.866025i
$562$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$563$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$563$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$564$	−1.00000			−1.00000
$565$		0			0
$566$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$567$		0			0
$568$	0.500000	+	0.866025i	0.500000	+	0.866025i
$569$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$569$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$570$		0			0
$571$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$571$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$572$			1.00000i			1.00000i
$573$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$574$		0			0
$575$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$576$		0			0
$577$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$577$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$578$		0			0
$579$	0.866025	−	0.500000i	0.866025	−	0.500000i
$580$		0			0
$581$		0			0
$582$	1.00000			1.00000
$583$		0			0
$584$	0.866025	+	0.500000i	0.866025	+	0.500000i
$585$		0			0
$586$			2.00000i			2.00000i
$587$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$587$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$588$		0			0
$589$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$590$		0			0
$591$		0			0
$592$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$593$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$593$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$594$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$595$		0			0
$596$		0			0
$597$		0			0
$598$	−1.00000			−1.00000
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$601$		0			0			−	1.00000i	$-0.5\pi$
$601$		0			0				1.00000i	$0.5\pi$
$602$		0			0
$603$		0			0
$604$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$605$		0			0
$606$		0			0
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$607$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$608$	−1.00000			−1.00000
$609$		0			0
$610$		0			0
$611$			1.00000i			1.00000i
$612$		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			$0$
$614$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$615$		0			0
$616$		0			0
$617$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$617$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$618$	0.866025	−	0.500000i	0.866025	−	0.500000i
$619$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$619$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$622$	0.500000	+	0.866025i	0.500000	+	0.866025i
$623$		0			0
$624$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$625$	1.00000			1.00000
$626$	0.866025	−	0.500000i	0.866025	−	0.500000i
$627$		−	1.00000i		−	1.00000i
$628$	0.500000	−	0.866025i	0.500000	−	0.866025i
$629$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$630$		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	$0.833333\pi$
$632$		0			0
$633$	1.00000			1.00000
$634$	0.866025	−	0.500000i	0.866025	−	0.500000i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	1.00000			1.00000
$639$		0			0
$640$		0			0
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$641$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$642$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$643$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$643$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$644$		0			0
$645$		0			0
$646$	0.500000	−	0.866025i	0.500000	−	0.866025i
$647$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$647$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$648$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$649$	1.00000			1.00000
$650$	0.866025	+	0.500000i	0.866025	+	0.500000i
$651$		0			0
$652$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$653$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$654$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$655$		0			0
$656$	0.500000	+	0.866025i	0.500000	+	0.866025i
$657$		0			0
$658$		0			0
$659$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$659$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	0.500000	−	0.866025i	0.500000	−	0.866025i
$663$		−	1.00000i		−	1.00000i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			1.00000i			1.00000i
$668$	0.866025	+	0.500000i	0.866025	+	0.500000i
$669$	1.00000			1.00000
$670$		0			0
$671$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$672$		0			0
$673$		0			0			−	1.00000i	$-0.5\pi$
$673$		0			0				1.00000i	$0.5\pi$
$674$	0.866025	−	0.500000i	0.866025	−	0.500000i
$675$			1.00000i			1.00000i
$676$		0			0
$677$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$677$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$678$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$679$		0			0
$680$		0			0
$681$	1.00000			1.00000
$682$	0.866025	+	0.500000i	0.866025	+	0.500000i
$683$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$683$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$688$	0.866025	−	0.500000i	0.866025	−	0.500000i
$689$		0			0
$690$		0			0
$691$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$691$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$692$		0			0
$693$		0			0
$694$	0.500000	−	0.866025i	0.500000	−	0.866025i
$695$		0			0
$696$	0.500000	+	0.866025i	0.500000	+	0.866025i
$697$	−1.00000			−1.00000
$698$		−	2.00000i		−	2.00000i
$699$		0			0
$700$		0			0
$701$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$701$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$702$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$703$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$704$	0.866025	−	0.500000i	0.866025	−	0.500000i
$705$		0			0
$706$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$707$		0			0
$708$	0.500000	+	0.866025i	0.500000	+	0.866025i
$709$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$709$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$710$		0			0
$711$		0			0
$712$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$713$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$714$		0			0
$715$		0			0
$716$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$717$		0			0
$718$		0			0
$719$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$719$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$720$		0			0
$721$		0			0
$722$		−	1.00000i		−	1.00000i
$723$		0			0
$724$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$725$	0.500000	−	0.866025i	0.500000	−	0.866025i
$726$		0			0
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$727$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$728$		0			0
$729$	−1.00000			−1.00000
$730$		0			0
$731$			1.00000i			1.00000i
$732$		−	1.00000i		−	1.00000i
$733$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$733$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$734$		0			0
$735$		0			0
$736$	0.500000	+	0.866025i	0.500000	+	0.866025i
$737$		0			0
$738$		0			0
$739$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$739$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$740$		0			0
$741$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$742$		0			0
$743$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$743$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$744$			1.00000i			1.00000i
$745$		0			0
$746$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$747$		0			0
$748$			1.00000i			1.00000i
$749$		0			0
$750$		0			0
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$751$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$752$	0.866025	−	0.500000i	0.866025	−	0.500000i
$753$	0.500000	+	0.866025i	0.500000	+	0.866025i
$754$	0.866025	−	0.500000i	0.866025	−	0.500000i
$755$		0			0
$756$		0			0
$757$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$757$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$758$		0			0
$759$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$760$		0			0
$761$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$762$	0.866025	−	0.500000i	0.866025	−	0.500000i
$763$		0			0
$764$	0.866025	+	0.500000i	0.866025	+	0.500000i
$765$		0			0
$766$		0			0
$767$	0.866025	−	0.500000i	0.866025	−	0.500000i
$768$	0.866025	+	0.500000i	0.866025	+	0.500000i
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$769$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$770$		0			0
$771$			1.00000i			1.00000i
$772$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$		0			0
$775$	0.866025	−	0.500000i	0.866025	−	0.500000i
$776$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$777$		0			0
$778$		0			0
$779$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$780$		0			0
$781$	0.500000	−	0.866025i	0.500000	−	0.866025i
$782$	−1.00000			−1.00000
$783$	0.866025	+	0.500000i	0.866025	+	0.500000i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$787$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$788$		0			0
$789$	0.500000	+	0.866025i	0.500000	+	0.866025i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.00000			−1.00000
$794$		−	2.00000i		−	2.00000i
$795$		0			0
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$			1.00000i			1.00000i
$800$		−	1.00000i		−	1.00000i
$801$		0			0
$802$		0			0
$803$		−	1.00000i		−	1.00000i
$804$		0			0
$805$		0			0
$806$	1.00000			1.00000
$807$	0.866025	−	0.500000i	0.866025	−	0.500000i
$808$		0			0
$809$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$809$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$811$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$812$		0			0
$813$		0			0
$814$	1.00000			1.00000
$815$		0			0
$816$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$817$	0.500000	+	0.866025i	0.500000	+	0.866025i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$821$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$822$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$823$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$823$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$824$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$825$	1.00000			1.00000
$826$		0			0
$827$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$827$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$829$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$830$		0			0
$831$			1.00000i			1.00000i
$832$	0.500000	−	0.866025i	0.500000	−	0.866025i
$833$		0			0
$834$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$835$		0			0
$836$	0.500000	+	0.866025i	0.500000	+	0.866025i
$837$	0.500000	+	0.866025i	0.500000	+	0.866025i
$838$		0			0
$839$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$839$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$		0			0
$842$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$843$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$844$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.500000	+	0.866025i	0.500000	+	0.866025i
$850$	0.866025	+	0.500000i	0.866025	+	0.500000i
$851$			1.00000i			1.00000i
$852$	1.00000			1.00000
$853$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$853$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$	0.500000	−	0.866025i	0.500000	−	0.866025i
$857$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$857$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$858$	0.866025	+	0.500000i	0.866025	+	0.500000i
$859$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$859$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$863$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$864$	1.00000			1.00000
$865$		0			0
$866$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.866025	+	0.500000i	0.866025	+	0.500000i
$873$		0			0
$874$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$875$		0			0
$876$	0.866025	−	0.500000i	0.866025	−	0.500000i
$877$		0			0			−	1.00000i	$-0.5\pi$
$877$		0			0				1.00000i	$0.5\pi$
$878$		0			0
$879$	1.73205	+	1.00000i	1.73205	+	1.00000i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$883$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$884$	0.500000	+	0.866025i	0.500000	+	0.866025i
$885$		0			0
$886$	0.500000	+	0.866025i	0.500000	+	0.866025i
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$887$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$	0.500000	+	0.866025i	0.500000	+	0.866025i
$889$		0			0
$890$		0			0
$891$			1.00000i			1.00000i
$892$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$893$	0.500000	+	0.866025i	0.500000	+	0.866025i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$898$		0			0
$899$		−	1.00000i		−	1.00000i
$900$		0			0
$901$		0			0
$902$	0.500000	−	0.866025i	0.500000	−	0.866025i
$903$		0			0
$904$		−	2.00000i		−	2.00000i
$905$		0			0
$906$			1.00000i			1.00000i
$907$	−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	$0.833333\pi$
$908$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$913$		0			0
$914$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$915$		0			0
$916$	0.500000	−	0.866025i	0.500000	−	0.866025i
$917$		0			0
$918$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$919$	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
$921$	−1.00000			−1.00000
$922$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$923$		−	1.00000i		−	1.00000i
$924$		0			0
$925$	0.500000	−	0.866025i	0.500000	−	0.866025i
$926$	−2.00000			−2.00000
$927$		0			0
$928$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$929$	2.00000			2.00000			1.00000			$0$
$929$	2.00000			2.00000			1.00000			$0$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.00000			1.00000
$934$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$935$		0			0
$936$		0			0
$937$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$937$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$938$		0			0
$939$		−	1.00000i		−	1.00000i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$943$	0.866025	+	0.500000i	0.866025	+	0.500000i
$944$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$945$		0			0
$946$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$950$	1.00000			1.00000
$951$		−	1.00000i		−	1.00000i
$952$		0			0
$953$	−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			0
$956$		0			0
$957$	0.500000	−	0.866025i	0.500000	−	0.866025i
$958$	2.00000			2.00000
$959$		0			0
$960$		0			0
$961$		0			0
$962$	0.866025	−	0.500000i	0.866025	−	0.500000i
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$967$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$968$		0			0
$969$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$		0			0
$973$		0			0
$974$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$975$	0.866025	−	0.500000i	0.866025	−	0.500000i
$976$	0.500000	+	0.866025i	0.500000	+	0.866025i
$977$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$977$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$978$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$979$	0.866025	+	0.500000i	0.866025	+	0.500000i
$980$		0			0
$981$		0			0
$982$	0.500000	+	0.866025i	0.500000	+	0.866025i
$983$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$983$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$984$	1.00000			1.00000
$985$		0			0
$986$	0.866025	−	0.500000i	0.866025	−	0.500000i
$987$		0			0
$988$	0.866025	+	0.500000i	0.866025	+	0.500000i
$989$	0.500000	−	0.866025i	0.500000	−	0.866025i
$990$		0			0
$991$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$991$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$992$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$993$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$994$		0			0
$995$		0			0
$996$		0			0
$997$		0			0			−	1.00000i	$-0.5\pi$
$997$		0			0				1.00000i	$0.5\pi$
$998$		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	3724.1.bk.a.1451.2		4
4.3	odd	2	inner	3724.1.bk.a.1451.1		4
7.2	even	3		3724.1.bb.a.2059.2		4
7.3	odd	6		532.1.n.a.235.1	yes	4
7.4	even	3		3724.1.n.a.1831.1		4
7.5	odd	6		3724.1.bb.b.2059.2		4
7.6	odd	2		532.1.bk.a.387.2	yes	4
19.11	even	3		3724.1.n.a.2823.2		4
28.3	even	6		532.1.n.a.235.2	yes	4
28.11	odd	6		3724.1.n.a.1831.2		4
28.19	even	6		3724.1.bb.b.2059.1		4
28.23	odd	6		3724.1.bb.a.2059.1		4
28.27	even	2		532.1.bk.a.387.1	yes	4
76.11	odd	6		3724.1.n.a.2823.1		4
133.11	even	3	inner	3724.1.bk.a.3203.2		4
133.30	even	3		3724.1.bb.a.3431.1		4
133.68	odd	6		3724.1.bb.b.3431.1		4
133.87	odd	6		532.1.bk.a.11.2	yes	4
133.125	odd	6		532.1.n.a.163.2	yes	4
532.11	odd	6	inner	3724.1.bk.a.3203.1		4
532.87	even	6		532.1.bk.a.11.1	yes	4
532.163	odd	6		3724.1.bb.a.3431.2		4
532.391	even	6		532.1.n.a.163.1	✓	4
532.467	even	6		3724.1.bb.b.3431.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
532.1.n.a.163.1	✓	4	532.391	even	6
532.1.n.a.163.2	yes	4	133.125	odd	6
532.1.n.a.235.1	yes	4	7.3	odd	6
532.1.n.a.235.2	yes	4	28.3	even	6
532.1.bk.a.11.1	yes	4	532.87	even	6
532.1.bk.a.11.2	yes	4	133.87	odd	6
532.1.bk.a.387.1	yes	4	28.27	even	2
532.1.bk.a.387.2	yes	4	7.6	odd	2
3724.1.n.a.1831.1		4	7.4	even	3
3724.1.n.a.1831.2		4	28.11	odd	6
3724.1.n.a.2823.1		4	76.11	odd	6
3724.1.n.a.2823.2		4	19.11	even	3
3724.1.bb.a.2059.1		4	28.23	odd	6
3724.1.bb.a.2059.2		4	7.2	even	3
3724.1.bb.a.3431.1		4	133.30	even	3
3724.1.bb.a.3431.2		4	532.163	odd	6
3724.1.bb.b.2059.1		4	28.19	even	6
3724.1.bb.b.2059.2		4	7.5	odd	6
3724.1.bb.b.3431.1		4	133.68	odd	6
3724.1.bb.b.3431.2		4	532.467	even	6
3724.1.bk.a.1451.1		4	4.3	odd	2	inner
3724.1.bk.a.1451.2		4	1.1	even	1	trivial
3724.1.bk.a.3203.1		4	532.11	odd	6	inner
3724.1.bk.a.3203.2		4	133.11	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3724 = 2^{2} \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3724.bk (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.866025 + 0.500000i) q^{3} -1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{11} +(-0.866025 - 0.500000i) q^{12} +(-0.500000 + 0.866025i) q^{13} +1.00000 q^{16} +(-0.500000 + 0.866025i) q^{17} +1.00000i q^{19} +(-0.500000 - 0.866025i) q^{22} +(0.866025 - 0.500000i) q^{23} +(0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-0.866025 - 0.500000i) q^{26} -1.00000i q^{27} +(-0.500000 + 0.866025i) q^{29} +(-0.866025 + 0.500000i) q^{31} +1.00000i q^{32} -1.00000 q^{33} +(-0.866025 - 0.500000i) q^{34} +(-0.500000 + 0.866025i) q^{37} -1.00000 q^{38} +(-0.866025 + 0.500000i) q^{39} +(0.500000 + 0.866025i) q^{41} +(0.866025 - 0.500000i) q^{43} +(0.866025 - 0.500000i) q^{44} +(0.500000 + 0.866025i) q^{46} +(0.866025 - 0.500000i) q^{47} +(0.866025 + 0.500000i) q^{48} -1.00000i q^{50} +(-0.866025 + 0.500000i) q^{51} +(0.500000 - 0.866025i) q^{52} +1.00000 q^{54} +(-0.500000 + 0.866025i) q^{57} +(-0.866025 - 0.500000i) q^{58} +(-0.866025 - 0.500000i) q^{59} +(0.500000 + 0.866025i) q^{61} +(-0.500000 - 0.866025i) q^{62} -1.00000 q^{64} -1.00000i q^{66} +(0.500000 - 0.866025i) q^{68} +1.00000 q^{69} +(-0.866025 + 0.500000i) q^{71} +(-0.500000 + 0.866025i) q^{73} +(-0.866025 - 0.500000i) q^{74} +(-0.866025 - 0.500000i) q^{75} -1.00000i q^{76} +(-0.500000 - 0.866025i) q^{78} +(0.500000 - 0.866025i) q^{81} +(-0.866025 + 0.500000i) q^{82} +(0.500000 + 0.866025i) q^{86} +(-0.866025 + 0.500000i) q^{87} +(0.500000 + 0.866025i) q^{88} +(-0.500000 - 0.866025i) q^{89} +(-0.866025 + 0.500000i) q^{92} -1.00000 q^{93} +(0.500000 + 0.866025i) q^{94} +(-0.500000 + 0.866025i) q^{96} +(-0.500000 - 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} - 2 q^{6}+O(q^{10}) \) 4 * q - 4 * q^4 - 2 * q^6	\( 4 q - 4 q^{4} - 2 q^{6} - 2 q^{13} + 4 q^{16} - 2 q^{17} - 2 q^{22} + 2 q^{24} - 4 q^{25} - 2 q^{29} - 4 q^{33} - 2 q^{37} - 4 q^{38} + 2 q^{41} + 2 q^{46} + 2 q^{52} + 4 q^{54} - 2 q^{57} + 2 q^{61} - 2 q^{62} - 4 q^{64} + 2 q^{68} + 4 q^{69} - 2 q^{73} - 2 q^{78} + 2 q^{81} + 2 q^{86} + 2 q^{88} - 2 q^{89} - 4 q^{93} + 2 q^{94} - 2 q^{96} - 2 q^{97}+O(q^{100}) \) 4 * q - 4 * q^4 - 2 * q^6 - 2 * q^13 + 4 * q^16 - 2 * q^17 - 2 * q^22 + 2 * q^24 - 4 * q^25 - 2 * q^29 - 4 * q^33 - 2 * q^37 - 4 * q^38 + 2 * q^41 + 2 * q^46 + 2 * q^52 + 4 * q^54 - 2 * q^57 + 2 * q^61 - 2 * q^62 - 4 * q^64 + 2 * q^68 + 4 * q^69 - 2 * q^73 - 2 * q^78 + 2 * q^81 + 2 * q^86 + 2 * q^88 - 2 * q^89 - 4 * q^93 + 2 * q^94 - 2 * q^96 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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