LMFDB - Embedded newform 3549.1.w.e.506.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3549,1,Mod(506,3549)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3549.506"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3549, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 3])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3549.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,2,0,0,2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.77118172983$
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 273)
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.74529.1

Embedding invariants

Embedding label			506.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3549.506
Dual form			3549.1.w.e.2027.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{5} -1.00000i q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.866025 + 0.500000i) q^{14} -1.00000i q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{17} +(-0.500000 - 0.866025i) q^{18} -1.00000 q^{21} +(0.866025 + 0.500000i) q^{23} +(0.866025 - 0.500000i) q^{24} -1.00000i q^{27} +1.00000i q^{29} +(-0.866025 - 0.500000i) q^{30} +(0.866025 - 0.500000i) q^{31} +1.00000i q^{34} +(-0.866025 + 0.500000i) q^{35} +(-0.866025 - 0.500000i) q^{37} +(0.500000 - 0.866025i) q^{40} -1.00000 q^{41} +(-0.500000 + 0.866025i) q^{42} -1.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(0.866025 - 0.500000i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000i q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{51} +(-0.866025 + 0.500000i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.866025 - 0.500000i) q^{56} +(0.866025 + 0.500000i) q^{58} +(-0.500000 - 0.866025i) q^{59} -1.00000i q^{62} +(-0.866025 + 0.500000i) q^{63} +1.00000 q^{64} +1.00000 q^{69} +1.00000i q^{70} +1.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(0.866025 - 0.500000i) q^{73} +(-0.866025 + 0.500000i) q^{74} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +1.00000i q^{85} +(-0.500000 + 0.866025i) q^{86} +(0.500000 + 0.866025i) q^{87} +(-0.500000 + 0.866025i) q^{89} -1.00000 q^{90} +(0.500000 - 0.866025i) q^{93} +(0.500000 + 0.866025i) q^{94} +1.00000i q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{5} + 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{16} - 2 q^{18} - 4 q^{21} + 2 q^{40} - 4 q^{41} - 2 q^{42} - 4 q^{43} - 2 q^{45} - 2 q^{47} + 2 q^{49} - 2 q^{51} - 2 q^{59} + 4 q^{64} + 4 q^{69}+ \cdots + 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^5 + 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^16 - 2 * q^18 - 4 * q^21 + 2 * q^40 - 4 * q^41 - 2 * q^42 - 4 * q^43 - 2 * q^45 - 2 * q^47 + 2 * q^49 - 2 * q^51 - 2 * q^59 + 4 * q^64 + 4 * q^69 + 4 * q^71 + 2 * q^72 - 2 * q^79 - 2 * q^80 - 2 * q^81 - 2 * q^82 - 2 * q^86 + 2 * q^87 - 2 * q^89 - 4 * q^90 + 2 * q^93 + 2 * q^94 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3549\mathbb{Z}\right)^\times$.

$n$	$1184$	$1522$	$3382$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$3$	0.866025	−	0.500000i	0.866025	−	0.500000i
$3$	0.866025	−	0.500000i	0.866025	−	0.500000i
$4$		0			0
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$6$		−	1.00000i		−	1.00000i
$7$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$7$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$8$	1.00000			1.00000
$9$	0.500000	−	0.866025i	0.500000	−	0.866025i
$10$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$		0			0
$13$		0			0
$14$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$15$		−	1.00000i		−	1.00000i
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$17$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$18$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$		0			0
$21$	−1.00000			−1.00000
$22$		0			0
$23$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$23$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$24$	0.866025	−	0.500000i	0.866025	−	0.500000i
$25$		0			0
$26$		0			0
$27$		−	1.00000i		−	1.00000i
$28$		0			0
$29$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$29$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$30$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$31$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$31$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$32$		0			0
$33$		0			0
$34$			1.00000i			1.00000i
$35$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$36$		0			0
$37$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$37$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$38$		0			0
$39$		0			0
$40$	0.500000	−	0.866025i	0.500000	−	0.866025i
$41$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$41$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$42$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$43$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$43$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$46$	0.866025	−	0.500000i	0.866025	−	0.500000i
$47$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$47$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$48$		−	1.00000i		−	1.00000i
$49$	0.500000	+	0.866025i	0.500000	+	0.866025i
$50$		0			0
$51$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$52$		0			0
$53$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$53$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$54$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$55$		0			0
$56$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$57$		0			0
$58$	0.866025	+	0.500000i	0.866025	+	0.500000i
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$59$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$60$		0			0
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$		−	1.00000i		−	1.00000i
$63$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$64$	1.00000			1.00000
$65$		0			0
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$		0			0
$69$	1.00000			1.00000
$70$			1.00000i			1.00000i
$71$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$71$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$72$	0.500000	−	0.866025i	0.500000	−	0.866025i
$73$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$73$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$74$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$79$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$80$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$			1.00000i			1.00000i
$86$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$87$	0.500000	+	0.866025i	0.500000	+	0.866025i
$88$		0			0
$89$	−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			$\pi$
$90$	−1.00000			−1.00000
$91$		0			0
$92$		0			0
$93$	0.500000	−	0.866025i	0.500000	−	0.866025i
$94$	0.500000	+	0.866025i	0.500000	+	0.866025i
$95$		0			0
$96$		0			0
$97$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$97$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$98$	1.00000			1.00000
$99$		0			0
$100$		0			0
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$	0.500000	+	0.866025i	0.500000	+	0.866025i
$103$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$103$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$104$		0			0
$105$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$106$			1.00000i			1.00000i
$107$	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	$0.5\pi$
$108$		0			0
$109$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$109$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$110$		0			0
$111$	−1.00000			−1.00000
$112$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$113$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$113$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$114$		0			0
$115$	0.866025	−	0.500000i	0.866025	−	0.500000i
$116$		0			0
$117$		0			0
$118$	−1.00000			−1.00000
$119$	1.00000			1.00000
$120$		−	1.00000i		−	1.00000i
$121$	0.500000	−	0.866025i	0.500000	−	0.866025i
$122$		0			0
$123$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$124$		0			0
$125$	1.00000			1.00000
$126$			1.00000i			1.00000i
$127$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$127$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$128$	0.500000	−	0.866025i	0.500000	−	0.866025i
$129$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$130$		0			0
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$131$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$136$	−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	$0.666667\pi$
$138$	0.500000	−	0.866025i	0.500000	−	0.866025i
$139$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$139$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$140$		0			0
$141$			1.00000i			1.00000i
$142$	0.500000	−	0.866025i	0.500000	−	0.866025i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$145$	0.866025	+	0.500000i	0.866025	+	0.500000i
$146$		−	1.00000i		−	1.00000i
$147$	0.866025	+	0.500000i	0.866025	+	0.500000i
$148$		0			0
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	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	$0.166667\pi$
$152$		0			0
$153$			1.00000i			1.00000i
$154$		0			0
$155$		−	1.00000i		−	1.00000i
$156$		0			0
$157$	−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			$\pi$
$158$	0.500000	+	0.866025i	0.500000	+	0.866025i
$159$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$160$		0			0
$161$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$162$	−1.00000			−1.00000
$163$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$163$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$167$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$168$	−1.00000			−1.00000
$169$		0			0
$170$	0.866025	+	0.500000i	0.866025	+	0.500000i
$171$		0			0
$172$		0			0
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	1.00000			1.00000
$175$		0			0
$176$		0			0
$177$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$178$	0.500000	+	0.866025i	0.500000	+	0.866025i
$179$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$179$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$		0			0
$184$	0.866025	+	0.500000i	0.866025	+	0.500000i
$185$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$186$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$187$		0			0
$188$		0			0
$189$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$190$		0			0
$191$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$191$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$192$	0.866025	−	0.500000i	0.866025	−	0.500000i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$	0.866025	+	0.500000i	0.866025	+	0.500000i
$195$		0			0
$196$		0			0
$197$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$197$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$198$		0			0
$199$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$199$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.500000	−	0.866025i	0.500000	−	0.866025i
$204$		0			0
$205$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$206$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$207$	0.866025	−	0.500000i	0.866025	−	0.500000i
$208$		0			0
$209$		0			0
$210$	0.500000	+	0.866025i	0.500000	+	0.866025i
$211$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$211$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$212$		0			0
$213$	0.866025	−	0.500000i	0.866025	−	0.500000i
$214$	0.866025	−	0.500000i	0.866025	−	0.500000i
$215$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$216$		−	1.00000i		−	1.00000i
$217$	−1.00000			−1.00000
$218$			1.00000i			1.00000i
$219$	0.500000	−	0.866025i	0.500000	−	0.866025i
$220$		0			0
$221$		0			0
$222$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$223$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$223$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$224$		0			0
$225$		0			0
$226$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$227$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$227$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$229$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$230$		−	1.00000i		−	1.00000i
$231$		0			0
$232$			1.00000i			1.00000i
$233$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$233$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$234$		0			0
$235$	0.500000	+	0.866025i	0.500000	+	0.866025i
$236$		0			0
$237$			1.00000i			1.00000i
$238$	0.500000	−	0.866025i	0.500000	−	0.866025i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−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	$0.166667\pi$
$242$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$243$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$244$		0			0
$245$	1.00000			1.00000
$246$			1.00000i			1.00000i
$247$		0			0
$248$	0.866025	−	0.500000i	0.866025	−	0.500000i
$249$		0			0
$250$	0.500000	−	0.866025i	0.500000	−	0.866025i
$251$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$251$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$		0			0
$254$	0.500000	−	0.866025i	0.500000	−	0.866025i
$255$	0.500000	+	0.866025i	0.500000	+	0.866025i
$256$		0			0
$257$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$257$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$258$			1.00000i			1.00000i
$259$	0.500000	+	0.866025i	0.500000	+	0.866025i
$260$		0			0
$261$	0.866025	+	0.500000i	0.866025	+	0.500000i
$262$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$263$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$263$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$			1.00000i			1.00000i
$266$		0			0
$267$			1.00000i			1.00000i
$268$		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	$0.166667\pi$
$270$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$271$	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	$0.5\pi$
$272$			1.00000i			1.00000i
$273$		0			0
$274$	1.00000			1.00000
$275$		0			0
$276$		0			0
$277$	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
$279$		−	1.00000i		−	1.00000i
$280$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$281$	−2.00000			−2.00000			−1.00000			$\pi$
$281$	−2.00000			−2.00000			−1.00000			$\pi$
$282$	0.866025	+	0.500000i	0.866025	+	0.500000i
$283$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$283$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.866025	+	0.500000i	0.866025	+	0.500000i
$288$		0			0
$289$		0			0
$290$	0.866025	−	0.500000i	0.866025	−	0.500000i
$291$	0.500000	+	0.866025i	0.500000	+	0.866025i
$292$		0			0
$293$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$293$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$294$	0.866025	−	0.500000i	0.866025	−	0.500000i
$295$	−1.00000			−1.00000
$296$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	0.866025	+	0.500000i	0.866025	+	0.500000i
$302$		−	1.00000i		−	1.00000i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	0.866025	+	0.500000i	0.866025	+	0.500000i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		−	1.00000i		−	1.00000i
$310$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$311$	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			0
$313$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$313$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$314$	−1.00000			−1.00000
$315$			1.00000i			1.00000i
$316$		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			$\pi$
$318$	0.500000	+	0.866025i	0.500000	+	0.866025i
$319$		0			0
$320$	0.500000	−	0.866025i	0.500000	−	0.866025i
$321$	1.00000			1.00000
$322$	−1.00000			−1.00000
$323$		0			0
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$328$	−1.00000			−1.00000
$329$	0.866025	−	0.500000i	0.866025	−	0.500000i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$334$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$335$		0			0
$336$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$		0			0
$339$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$340$		0			0
$341$		0			0
$342$		0			0
$343$		−	1.00000i		−	1.00000i
$344$	−1.00000			−1.00000
$345$	0.500000	−	0.866025i	0.500000	−	0.866025i
$346$		0			0
$347$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$347$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$348$		0			0
$349$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$349$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$355$	0.500000	−	0.866025i	0.500000	−	0.866025i
$356$		0			0
$357$	0.866025	−	0.500000i	0.866025	−	0.500000i
$358$		0			0
$359$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$359$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$360$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$		−	1.00000i		−	1.00000i
$364$		0			0
$365$		−	1.00000i		−	1.00000i
$366$		0			0
$367$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$367$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$368$	0.866025	−	0.500000i	0.866025	−	0.500000i
$369$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$370$			1.00000i			1.00000i
$371$	1.00000			1.00000
$372$		0			0
$373$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$373$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$374$		0			0
$375$	0.866025	−	0.500000i	0.866025	−	0.500000i
$376$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$377$		0			0
$378$	0.500000	+	0.866025i	0.500000	+	0.866025i
$379$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$379$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$380$		0			0
$381$	0.866025	−	0.500000i	0.866025	−	0.500000i
$382$	1.73205	−	1.00000i	1.73205	−	1.00000i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		−	1.00000i		−	1.00000i
$385$		0			0
$386$		0			0
$387$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$388$		0			0
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$389$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$390$		0			0
$391$	−1.00000			−1.00000
$392$	0.500000	+	0.866025i	0.500000	+	0.866025i
$393$	−1.00000			−1.00000
$394$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$395$	0.500000	+	0.866025i	0.500000	+	0.866025i
$396$		0			0
$397$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$397$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$398$	1.00000			1.00000
$399$		0			0
$400$		0			0
$401$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$401$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−1.00000			−1.00000
$406$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$407$		0			0
$408$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$409$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$409$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$410$	0.500000	+	0.866025i	0.500000	+	0.866025i
$411$	0.866025	+	0.500000i	0.866025	+	0.500000i
$412$		0			0
$413$			1.00000i			1.00000i
$414$		−	1.00000i		−	1.00000i
$415$		0			0
$416$		0			0
$417$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$418$		0			0
$419$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$419$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$420$		0			0
$421$		0			0		1.00000			$0$
$421$		0			0		−1.00000			$\pi$
$422$	0.500000	−	0.866025i	0.500000	−	0.866025i
$423$	0.500000	+	0.866025i	0.500000	+	0.866025i
$424$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$425$		0			0
$426$		−	1.00000i		−	1.00000i
$427$		0			0
$428$		0			0
$429$		0			0
$430$	0.500000	+	0.866025i	0.500000	+	0.866025i
$431$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$431$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$432$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$433$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$433$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$434$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$435$	1.00000			1.00000
$436$		0			0
$437$		0			0
$438$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$439$	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			0
$441$	1.00000			1.00000
$442$		0			0
$443$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$443$	0.866025	+	0.500000i	0.866025	+	0.500000i			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
$447$		0			0
$448$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$449$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	0.500000	−	0.866025i	0.500000	−	0.866025i
$454$	1.00000			1.00000
$455$		0			0
$456$		0			0
$457$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$457$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$458$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$459$	0.500000	+	0.866025i	0.500000	+	0.866025i
$460$		0			0
$461$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$461$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	0.866025	+	0.500000i	0.866025	+	0.500000i
$465$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$466$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$467$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$467$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$		0			0
$470$	1.00000			1.00000
$471$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$472$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$473$		0			0
$474$	0.866025	+	0.500000i	0.866025	+	0.500000i
$475$		0			0
$476$		0			0
$477$			1.00000i			1.00000i
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$		0			0
$481$		0			0
$482$		−	1.00000i		−	1.00000i
$483$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$484$		0			0
$485$	0.866025	+	0.500000i	0.866025	+	0.500000i
$486$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$487$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$487$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$488$		0			0
$489$		0			0
$490$	0.500000	−	0.866025i	0.500000	−	0.866025i
$491$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$491$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$492$		0			0
$493$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$494$		0			0
$495$		0			0
$496$		−	1.00000i		−	1.00000i
$497$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$498$		0			0
$499$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$499$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$500$		0			0
$501$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$502$	0.866025	+	0.500000i	0.866025	+	0.500000i
$503$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$503$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$504$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$505$		0			0
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$509$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$510$	1.00000			1.00000
$511$	−1.00000			−1.00000
$512$	1.00000			1.00000
$513$		0			0
$514$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$515$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$516$		0			0
$517$		0			0
$518$	1.00000			1.00000
$519$		0			0
$520$		0			0
$521$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$521$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$522$	0.866025	−	0.500000i	0.866025	−	0.500000i
$523$	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
$525$		0			0
$526$		0			0
$527$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$528$		0			0
$529$		0			0
$530$	0.866025	+	0.500000i	0.866025	+	0.500000i
$531$	−1.00000			−1.00000
$532$		0			0
$533$		0			0
$534$	0.866025	+	0.500000i	0.866025	+	0.500000i
$535$	0.866025	−	0.500000i	0.866025	−	0.500000i
$536$		0			0
$537$		0			0
$538$		−	1.00000i		−	1.00000i
$539$		0			0
$540$		0			0
$541$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$541$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$542$	0.866025	−	0.500000i	0.866025	−	0.500000i
$543$		0			0
$544$		0			0
$545$			1.00000i			1.00000i
$546$		0			0
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$	1.00000			1.00000
$553$	0.866025	−	0.500000i	0.866025	−	0.500000i
$554$	1.00000			1.00000
$555$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$556$		0			0
$557$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$557$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$558$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$559$		0			0
$560$			1.00000i			1.00000i
$561$		0			0
$562$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$563$	−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	$0.5\pi$
$564$		0			0
$565$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$566$		0			0
$567$			1.00000i			1.00000i
$568$	1.00000			1.00000
$569$	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			0
$571$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$571$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$572$		0			0
$573$	2.00000			2.00000
$574$	0.866025	−	0.500000i	0.866025	−	0.500000i
$575$		0			0
$576$	0.500000	−	0.866025i	0.500000	−	0.866025i
$577$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$577$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$578$		0			0
$579$		0			0
$580$		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
$586$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$587$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$587$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$588$		0			0
$589$		0			0
$590$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$591$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$592$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$593$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$593$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$594$		0			0
$595$	0.500000	−	0.866025i	0.500000	−	0.866025i
$596$		0			0
$597$	0.866025	+	0.500000i	0.866025	+	0.500000i
$598$		0			0
$599$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$599$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$601$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$602$	0.866025	−	0.500000i	0.866025	−	0.500000i
$603$		0			0
$604$		0			0
$605$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$606$		0			0
$607$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$607$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$608$		0			0
$609$		−	1.00000i		−	1.00000i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$613$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$614$		0			0
$615$			1.00000i			1.00000i
$616$		0			0
$617$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$617$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$618$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$619$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$619$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$620$		0			0
$621$	0.500000	−	0.866025i	0.500000	−	0.866025i
$622$		−	1.00000i		−	1.00000i
$623$	0.866025	−	0.500000i	0.866025	−	0.500000i
$624$		0			0
$625$	0.500000	−	0.866025i	0.500000	−	0.866025i
$626$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$627$		0			0
$628$		0			0
$629$	1.00000			1.00000
$630$	0.866025	+	0.500000i	0.866025	+	0.500000i
$631$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$631$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$632$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$633$	0.866025	−	0.500000i	0.866025	−	0.500000i
$634$	0.500000	+	0.866025i	0.500000	+	0.866025i
$635$	0.500000	−	0.866025i	0.500000	−	0.866025i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.500000	−	0.866025i	0.500000	−	0.866025i
$640$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$641$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$641$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$642$	0.500000	−	0.866025i	0.500000	−	0.866025i
$643$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$643$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$644$		0			0
$645$			1.00000i			1.00000i
$646$		0			0
$647$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$647$	−1.73205	+	1.00000i	−1.73205	+	1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$648$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$649$		0			0
$650$		0			0
$651$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$652$		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	$0.5\pi$
$654$	0.500000	+	0.866025i	0.500000	+	0.866025i
$655$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$656$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$657$		−	1.00000i		−	1.00000i
$658$		−	1.00000i		−	1.00000i
$659$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$659$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$661$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$			1.00000i			1.00000i
$667$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$668$		0			0
$669$	0.500000	+	0.866025i	0.500000	+	0.866025i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$673$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$677$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$678$	−1.00000			−1.00000
$679$	0.500000	−	0.866025i	0.500000	−	0.866025i
$680$			1.00000i			1.00000i
$681$	0.866025	+	0.500000i	0.866025	+	0.500000i
$682$		0			0
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$683$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$684$		0			0
$685$	1.00000			1.00000
$686$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$687$	−1.00000			−1.00000
$688$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$689$		0			0
$690$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$691$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$691$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$692$		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
$697$	0.866025	−	0.500000i	0.866025	−	0.500000i
$698$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$699$	−1.00000			−1.00000
$700$		0			0
$701$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$701$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.866025	+	0.500000i	0.866025	+	0.500000i
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$711$	0.500000	+	0.866025i	0.500000	+	0.866025i
$712$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$713$	1.00000			1.00000
$714$		−	1.00000i		−	1.00000i
$715$		0			0
$716$		0			0
$717$		0			0
$718$	0.500000	+	0.866025i	0.500000	+	0.866025i
$719$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$719$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$720$	−1.00000			−1.00000
$721$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$722$	−1.00000			−1.00000
$723$	0.500000	−	0.866025i	0.500000	−	0.866025i
$724$		0			0
$725$		0			0
$726$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−1.00000			−1.00000
$730$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$731$	0.866025	−	0.500000i	0.866025	−	0.500000i
$732$		0			0
$733$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$733$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$734$		0			0
$735$	0.866025	−	0.500000i	0.866025	−	0.500000i
$736$		0			0
$737$		0			0
$738$	0.500000	+	0.866025i	0.500000	+	0.866025i
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$		0			0
$741$		0			0
$742$	0.500000	−	0.866025i	0.500000	−	0.866025i
$743$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$743$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$744$	0.500000	−	0.866025i	0.500000	−	0.866025i
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$750$		−	1.00000i		−	1.00000i
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$751$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$752$	0.500000	+	0.866025i	0.500000	+	0.866025i
$753$	0.500000	+	0.866025i	0.500000	+	0.866025i
$754$		0			0
$755$		−	1.00000i		−	1.00000i
$756$		0			0
$757$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$757$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$758$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$759$		0			0
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$		−	1.00000i		−	1.00000i
$763$	1.00000			1.00000
$764$		0			0
$765$	0.866025	+	0.500000i	0.866025	+	0.500000i
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$769$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$770$		0			0
$771$	−1.00000			−1.00000
$772$		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			$\pi$
$774$	0.500000	+	0.866025i	0.500000	+	0.866025i
$775$		0			0
$776$			1.00000i			1.00000i
$777$	0.866025	+	0.500000i	0.866025	+	0.500000i
$778$			1.00000i			1.00000i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$783$	1.00000			1.00000
$784$	1.00000			1.00000
$785$	−1.00000			−1.00000
$786$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$787$	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			0
$790$	1.00000			1.00000
$791$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	0.500000	+	0.866025i	0.500000	+	0.866025i
$796$		0			0
$797$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$797$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$798$		0			0
$799$		−	1.00000i		−	1.00000i
$800$		0			0
$801$	0.500000	+	0.866025i	0.500000	+	0.866025i
$802$	0.500000	+	0.866025i	0.500000	+	0.866025i
$803$		0			0
$804$		0			0
$805$	−1.00000			−1.00000
$806$		0			0
$807$	0.500000	−	0.866025i	0.500000	−	0.866025i
$808$		0			0
$809$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$809$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$810$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	1.00000			1.00000
$814$		0			0
$815$		0			0
$816$	0.500000	+	0.866025i	0.500000	+	0.866025i
$817$		0			0
$818$		−	1.00000i		−	1.00000i
$819$		0			0
$820$		0			0
$821$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$821$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$822$	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			$\pi$
$824$	0.500000	−	0.866025i	0.500000	−	0.866025i
$825$		0			0
$826$	0.866025	+	0.500000i	0.866025	+	0.500000i
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$829$	1.00000	+	1.73205i	1.00000	+	1.73205i	0.500000	+	0.866025i	$0.333333\pi$
$830$		0			0
$831$	0.866025	+	0.500000i	0.866025	+	0.500000i
$832$		0			0
$833$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$834$			1.00000i			1.00000i
$835$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$836$		0			0
$837$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$838$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$839$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$839$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$840$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$841$		0			0
$842$		0			0
$843$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$844$		0			0
$845$		0			0
$846$	1.00000			1.00000
$847$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$848$			1.00000i			1.00000i
$849$		0			0
$850$		0			0
$851$	−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			0
$855$		0			0
$856$	0.866025	+	0.500000i	0.866025	+	0.500000i
$857$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$857$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$858$		0			0
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$860$		0			0
$861$	1.00000			1.00000
$862$	2.00000			2.00000
$863$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$863$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$864$		0			0
$865$		0			0
$866$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$867$		0			0
$868$		0			0
$869$		0			0
$870$	0.500000	−	0.866025i	0.500000	−	0.866025i
$871$		0			0
$872$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$873$	0.866025	+	0.500000i	0.866025	+	0.500000i
$874$		0			0
$875$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$879$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$880$		0			0
$881$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$881$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$882$	0.500000	−	0.866025i	0.500000	−	0.866025i
$883$	−2.00000			−2.00000			−1.00000			$\pi$
$883$	−2.00000			−2.00000			−1.00000			$\pi$
$884$		0			0
$885$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$886$	0.866025	−	0.500000i	0.866025	−	0.500000i
$887$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$887$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$888$	−1.00000			−1.00000
$889$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$890$	1.00000			1.00000
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$897$		0			0
$898$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$899$	0.500000	+	0.866025i	0.500000	+	0.866025i
$900$		0			0
$901$	0.500000	−	0.866025i	0.500000	−	0.866025i
$902$		0			0
$903$	1.00000			1.00000
$904$		−	1.00000i		−	1.00000i
$905$		0			0
$906$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$		0			0
$914$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$915$		0			0
$916$		0			0
$917$	0.500000	+	0.866025i	0.500000	+	0.866025i
$918$	1.00000			1.00000
$919$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$919$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$920$	0.866025	−	0.500000i	0.866025	−	0.500000i
$921$		0			0
$922$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$928$		0			0
$929$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$929$	1.00000	−	1.73205i	1.00000	−	1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$930$	−1.00000			−1.00000
$931$		0			0
$932$		0			0
$933$	0.500000	−	0.866025i	0.500000	−	0.866025i
$934$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$		−	1.00000i		−	1.00000i
$940$		0			0
$941$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$941$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$942$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$943$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$944$	−1.00000			−1.00000
$945$	0.500000	+	0.866025i	0.500000	+	0.866025i
$946$		0			0
$947$	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
$950$		0			0
$951$			1.00000i			1.00000i
$952$	1.00000			1.00000
$953$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$953$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$954$	0.866025	+	0.500000i	0.866025	+	0.500000i
$955$	1.73205	−	1.00000i	1.73205	−	1.00000i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		−	1.00000i		−	1.00000i
$960$		−	1.00000i		−	1.00000i
$961$		0			0
$962$		0			0
$963$	0.866025	−	0.500000i	0.866025	−	0.500000i
$964$		0			0
$965$		0			0
$966$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	0.500000	−	0.866025i	0.500000	−	0.866025i
$969$		0			0
$970$	0.866025	−	0.500000i	0.866025	−	0.500000i
$971$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$971$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$	0.866025	+	0.500000i	0.866025	+	0.500000i
$974$		−	1.00000i		−	1.00000i
$975$		0			0
$976$		0			0
$977$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$977$	−1.00000	−	1.73205i	−1.00000	−	1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$			1.00000i			1.00000i
$982$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$983$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$983$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$984$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$985$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$986$	−1.00000			−1.00000
$987$	0.500000	−	0.866025i	0.500000	−	0.866025i
$988$		0			0
$989$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$990$		0			0
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$		0			0
$993$		0			0
$994$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$995$	1.00000			1.00000
$996$		0			0
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$997$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$998$	0.866025	−	0.500000i	0.866025	−	0.500000i
$999$	−0.500000	+	0.866025i	−0.500000	+	0.866025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.1.w.e.506.2		4
3.2	odd	2		3549.1.w.c.506.1		4
7.4	even	3	inner	3549.1.w.e.2027.1		4
13.2	odd	12		3549.1.bm.c.191.2		4
13.3	even	3		3549.1.x.d.485.2		4
13.4	even	6		3549.1.bp.d.23.1		4
13.5	odd	4		3549.1.bk.c.170.1		4
13.6	odd	12		3549.1.s.b.653.2		4
13.7	odd	12		273.1.s.b.107.1	yes	4
13.8	odd	4		3549.1.bk.d.170.2		4
13.9	even	3		3549.1.bp.b.23.1		4
13.10	even	6		3549.1.x.b.485.2		4
13.11	odd	12		273.1.bm.b.191.1	yes	4
13.12	even	2		3549.1.w.c.506.2		4
21.11	odd	6		3549.1.w.c.2027.2		4
39.2	even	12		3549.1.bm.c.191.1		4
39.5	even	4		3549.1.bk.c.170.2		4
39.8	even	4		3549.1.bk.d.170.1		4
39.11	even	12		273.1.bm.b.191.2	yes	4
39.17	odd	6		3549.1.bp.b.23.2		4
39.20	even	12		273.1.s.b.107.2	yes	4
39.23	odd	6		3549.1.x.d.485.1		4
39.29	odd	6		3549.1.x.b.485.1		4
39.32	even	12		3549.1.s.b.653.1		4
39.35	odd	6		3549.1.bp.d.23.2		4
39.38	odd	2	inner	3549.1.w.e.506.1		4
91.4	even	6		3549.1.x.b.1544.2		4
91.11	odd	12		273.1.s.b.74.1	✓	4
91.18	odd	12		3549.1.bk.c.1691.2		4
91.20	even	12		1911.1.s.b.1745.1		4
91.24	even	12		1911.1.s.b.1439.1		4
91.25	even	6		3549.1.w.c.2027.1		4
91.32	odd	12		3549.1.bm.c.2174.1		4
91.33	even	12		1911.1.be.d.1667.1		4
91.37	odd	12		1911.1.be.c.932.2		4
91.46	odd	12		273.1.bm.b.263.2	yes	4
91.59	even	12		1911.1.bm.b.263.2		4
91.60	odd	12		3549.1.bk.d.1691.1		4
91.67	odd	12		3549.1.s.b.1712.2		4
91.72	odd	12		1911.1.be.c.1667.1		4
91.74	even	3		3549.1.x.d.1544.2		4
91.76	even	12		1911.1.bm.b.1010.1		4
91.81	even	3		3549.1.bp.b.2006.2		4
91.88	even	6		3549.1.bp.d.2006.2		4
91.89	even	12		1911.1.be.d.932.2		4
273.11	even	12		273.1.s.b.74.2	yes	4
273.20	odd	12		1911.1.s.b.1745.2		4
273.32	even	12		3549.1.bm.c.2174.2		4
273.59	odd	12		1911.1.bm.b.263.1		4
273.74	odd	6		3549.1.x.b.1544.1		4
273.89	odd	12		1911.1.be.d.932.1		4
273.95	odd	6		3549.1.x.d.1544.1		4
273.116	odd	6	inner	3549.1.w.e.2027.2		4
273.128	even	12		1911.1.be.c.932.1		4
273.137	even	12		273.1.bm.b.263.1	yes	4
273.158	even	12		3549.1.s.b.1712.1		4
273.167	odd	12		1911.1.bm.b.1010.2		4
273.179	odd	6		3549.1.bp.b.2006.1		4
273.200	even	12		3549.1.bk.c.1691.1		4
273.206	odd	12		1911.1.s.b.1439.2		4
273.215	odd	12		1911.1.be.d.1667.2		4
273.242	even	12		3549.1.bk.d.1691.2		4
273.254	even	12		1911.1.be.c.1667.2		4
273.263	odd	6		3549.1.bp.d.2006.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.1.s.b.74.1	✓	4	91.11	odd	12
273.1.s.b.74.2	yes	4	273.11	even	12
273.1.s.b.107.1	yes	4	13.7	odd	12
273.1.s.b.107.2	yes	4	39.20	even	12
273.1.bm.b.191.1	yes	4	13.11	odd	12
273.1.bm.b.191.2	yes	4	39.11	even	12
273.1.bm.b.263.1	yes	4	273.137	even	12
273.1.bm.b.263.2	yes	4	91.46	odd	12
1911.1.s.b.1439.1		4	91.24	even	12
1911.1.s.b.1439.2		4	273.206	odd	12
1911.1.s.b.1745.1		4	91.20	even	12
1911.1.s.b.1745.2		4	273.20	odd	12
1911.1.be.c.932.1		4	273.128	even	12
1911.1.be.c.932.2		4	91.37	odd	12
1911.1.be.c.1667.1		4	91.72	odd	12
1911.1.be.c.1667.2		4	273.254	even	12
1911.1.be.d.932.1		4	273.89	odd	12
1911.1.be.d.932.2		4	91.89	even	12
1911.1.be.d.1667.1		4	91.33	even	12
1911.1.be.d.1667.2		4	273.215	odd	12
1911.1.bm.b.263.1		4	273.59	odd	12
1911.1.bm.b.263.2		4	91.59	even	12
1911.1.bm.b.1010.1		4	91.76	even	12
1911.1.bm.b.1010.2		4	273.167	odd	12
3549.1.s.b.653.1		4	39.32	even	12
3549.1.s.b.653.2		4	13.6	odd	12
3549.1.s.b.1712.1		4	273.158	even	12
3549.1.s.b.1712.2		4	91.67	odd	12
3549.1.w.c.506.1		4	3.2	odd	2
3549.1.w.c.506.2		4	13.12	even	2
3549.1.w.c.2027.1		4	91.25	even	6
3549.1.w.c.2027.2		4	21.11	odd	6
3549.1.w.e.506.1		4	39.38	odd	2	inner
3549.1.w.e.506.2		4	1.1	even	1	trivial
3549.1.w.e.2027.1		4	7.4	even	3	inner
3549.1.w.e.2027.2		4	273.116	odd	6	inner
3549.1.x.b.485.1		4	39.29	odd	6
3549.1.x.b.485.2		4	13.10	even	6
3549.1.x.b.1544.1		4	273.74	odd	6
3549.1.x.b.1544.2		4	91.4	even	6
3549.1.x.d.485.1		4	39.23	odd	6
3549.1.x.d.485.2		4	13.3	even	3
3549.1.x.d.1544.1		4	273.95	odd	6
3549.1.x.d.1544.2		4	91.74	even	3
3549.1.bk.c.170.1		4	13.5	odd	4
3549.1.bk.c.170.2		4	39.5	even	4
3549.1.bk.c.1691.1		4	273.200	even	12
3549.1.bk.c.1691.2		4	91.18	odd	12
3549.1.bk.d.170.1		4	39.8	even	4
3549.1.bk.d.170.2		4	13.8	odd	4
3549.1.bk.d.1691.1		4	91.60	odd	12
3549.1.bk.d.1691.2		4	273.242	even	12
3549.1.bm.c.191.1		4	39.2	even	12
3549.1.bm.c.191.2		4	13.2	odd	12
3549.1.bm.c.2174.1		4	91.32	odd	12
3549.1.bm.c.2174.2		4	273.32	even	12
3549.1.bp.b.23.1		4	13.9	even	3
3549.1.bp.b.23.2		4	39.17	odd	6
3549.1.bp.b.2006.1		4	273.179	odd	6
3549.1.bp.b.2006.2		4	91.81	even	3
3549.1.bp.d.23.1		4	13.4	even	6
3549.1.bp.d.23.2		4	39.35	odd	6
3549.1.bp.d.2006.1		4	273.263	odd	6
3549.1.bp.d.2006.2		4	91.88	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3549.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{5} -1.00000i q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-0.866025 + 0.500000i) q^{14} -1.00000i q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.866025 + 0.500000i) q^{17} +(-0.500000 - 0.866025i) q^{18} -1.00000 q^{21} +(0.866025 + 0.500000i) q^{23} +(0.866025 - 0.500000i) q^{24} -1.00000i q^{27} +1.00000i q^{29} +(-0.866025 - 0.500000i) q^{30} +(0.866025 - 0.500000i) q^{31} +1.00000i q^{34} +(-0.866025 + 0.500000i) q^{35} +(-0.866025 - 0.500000i) q^{37} +(0.500000 - 0.866025i) q^{40} -1.00000 q^{41} +(-0.500000 + 0.866025i) q^{42} -1.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(0.866025 - 0.500000i) q^{46} +(-0.500000 + 0.866025i) q^{47} -1.00000i q^{48} +(0.500000 + 0.866025i) q^{49} +(-0.500000 + 0.866025i) q^{51} +(-0.866025 + 0.500000i) q^{53} +(-0.866025 - 0.500000i) q^{54} +(-0.866025 - 0.500000i) q^{56} +(0.866025 + 0.500000i) q^{58} +(-0.500000 - 0.866025i) q^{59} -1.00000i q^{62} +(-0.866025 + 0.500000i) q^{63} +1.00000 q^{64} +1.00000 q^{69} +1.00000i q^{70} +1.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(0.866025 - 0.500000i) q^{73} +(-0.866025 + 0.500000i) q^{74} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.500000 + 0.866025i) q^{82} +1.00000i q^{85} +(-0.500000 + 0.866025i) q^{86} +(0.500000 + 0.866025i) q^{87} +(-0.500000 + 0.866025i) q^{89} -1.00000 q^{90} +(0.500000 - 0.866025i) q^{93} +(0.500000 + 0.866025i) q^{94} +1.00000i q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{5} + 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{16} - 2 q^{18} - 4 q^{21} + 2 q^{40} - 4 q^{41} - 2 q^{42} - 4 q^{43} - 2 q^{45} - 2 q^{47} + 2 q^{49} - 2 q^{51} - 2 q^{59} + 4 q^{64} + 4 q^{69}+ \cdots + 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^5 + 4 * q^8 + 2 * q^9 - 2 * q^10 + 2 * q^16 - 2 * q^18 - 4 * q^21 + 2 * q^40 - 4 * q^41 - 2 * q^42 - 4 * q^43 - 2 * q^45 - 2 * q^47 + 2 * q^49 - 2 * q^51 - 2 * q^59 + 4 * q^64 + 4 * q^69 + 4 * q^71 + 2 * q^72 - 2 * q^79 - 2 * q^80 - 2 * q^81 - 2 * q^82 - 2 * q^86 + 2 * q^87 - 2 * q^89 - 4 * q^90 + 2 * q^93 + 2 * q^94 + 4 * q^98

Introduction

L-functions

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