LMFDB - Embedded newform 3960.1.cm.d.1429.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3960,1,Mod(1429,3960)] 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("3960.1429"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3960, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4, 3, 3])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3960.cm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,3,0,-3,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$1.97629745003$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{18})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{9}$
Projective field:	Galois closure of 9.1.19918918863360000.2

Embedding invariants

Embedding label			1429.2
Root			$-0.766044 + 0.642788i$ of defining polynomial
Character	$\chi$	$=$	3960.1429
Dual form			3960.1.cm.d.2749.2

$q$-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} +(-0.173648 + 0.984808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.766044 + 0.642788i) q^{6} +(0.173648 - 0.300767i) q^{7} -1.00000 q^{8} +(-0.939693 - 0.342020i) q^{9} +1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.939693 - 0.342020i) q^{12} +(-0.173648 - 0.300767i) q^{14} +(-0.939693 + 0.342020i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.53209 q^{17} +(-0.766044 + 0.642788i) q^{18} -1.87939 q^{19} +(0.500000 - 0.866025i) q^{20} +(0.266044 + 0.223238i) q^{21} +(0.500000 + 0.866025i) q^{22} +(0.173648 - 0.984808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{27} -0.347296 q^{28} +(-0.766044 + 1.32683i) q^{29} +(-0.173648 + 0.984808i) q^{30} +(-0.173648 - 0.300767i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.766044 - 0.642788i) q^{33} +(-0.766044 + 1.32683i) q^{34} +0.347296 q^{35} +(0.173648 + 0.984808i) q^{36} +1.87939 q^{37} +(-0.939693 + 1.62760i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(0.326352 - 0.118782i) q^{42} +1.00000 q^{44} +(-0.173648 - 0.984808i) q^{45} +(-0.766044 - 0.642788i) q^{48} +(0.439693 + 0.761570i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.266044 - 1.50881i) q^{51} -1.53209 q^{53} +(-0.500000 - 0.866025i) q^{54} -1.00000 q^{55} +(-0.173648 + 0.300767i) q^{56} +(0.326352 - 1.85083i) q^{57} +(0.766044 + 1.32683i) q^{58} +(0.766044 + 0.642788i) q^{60} +(-0.173648 + 0.300767i) q^{61} -0.347296 q^{62} +(-0.266044 + 0.223238i) q^{63} +1.00000 q^{64} +(-0.939693 + 0.342020i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(0.766044 + 1.32683i) q^{68} +(0.173648 - 0.300767i) q^{70} -1.87939 q^{71} +(0.939693 + 0.342020i) q^{72} +1.00000 q^{73} +(0.939693 - 1.62760i) q^{74} +(-0.766044 - 0.642788i) q^{75} +(0.939693 + 1.62760i) q^{76} +(0.173648 + 0.300767i) q^{77} -1.00000 q^{80} +(0.766044 + 0.642788i) q^{81} +(0.0603074 - 0.342020i) q^{84} +(-0.766044 - 1.32683i) q^{85} +(-1.17365 - 0.984808i) q^{87} +(0.500000 - 0.866025i) q^{88} +1.53209 q^{89} +(-0.939693 - 0.342020i) q^{90} +(0.326352 - 0.118782i) q^{93} +(-0.939693 - 1.62760i) q^{95} +(-0.939693 + 0.342020i) q^{96} +0.879385 q^{98} +(0.766044 - 0.642788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{8} + 6 q^{10} - 3 q^{11} - 3 q^{16} + 3 q^{20} - 3 q^{21} + 3 q^{22} - 3 q^{25} + 3 q^{27} + 3 q^{32} - 3 q^{40} + 3 q^{42} + 6 q^{44} - 3 q^{49} + 3 q^{50} - 3 q^{51}+ \cdots - 6 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^8 + 6 * q^10 - 3 * q^11 - 3 * q^16 + 3 * q^20 - 3 * q^21 + 3 * q^22 - 3 * q^25 + 3 * q^27 + 3 * q^32 - 3 * q^40 + 3 * q^42 + 6 * q^44 - 3 * q^49 + 3 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^55 + 3 * q^57 + 3 * q^63 + 6 * q^64 - 3 * q^67 + 6 * q^73 - 6 * q^80 + 6 * q^84 - 6 * q^87 + 3 * q^88 + 3 * q^93 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3960\mathbb{Z}\right)^\times$.

$n$	$991$	$1981$	$2377$	$2521$	$3521$
$\chi(n)$	$1$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.500000	−	0.866025i
$2$	0.500000	−	0.866025i	0.500000	−	0.866025i
$3$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$3$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	0.500000	+	0.866025i	0.500000	+	0.866025i
$5$	0.500000	+	0.866025i	0.500000	+	0.866025i
$6$	0.766044	+	0.642788i	0.766044	+	0.642788i
$7$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$7$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$8$	−1.00000			−1.00000
$9$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$10$	1.00000			1.00000
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$11$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$12$	0.939693	−	0.342020i	0.939693	−	0.342020i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$15$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$17$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$18$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$19$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$19$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$20$	0.500000	−	0.866025i	0.500000	−	0.866025i
$21$	0.266044	+	0.223238i	0.266044	+	0.223238i
$22$	0.500000	+	0.866025i	0.500000	+	0.866025i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$	0.173648	−	0.984808i	0.173648	−	0.984808i
$25$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$26$		0			0
$27$	0.500000	−	0.866025i	0.500000	−	0.866025i
$28$	−0.347296			−0.347296
$29$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$29$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$30$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$31$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$31$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$32$	0.500000	+	0.866025i	0.500000	+	0.866025i
$33$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$34$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$35$	0.347296			0.347296
$36$	0.173648	+	0.984808i	0.173648	+	0.984808i
$37$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$37$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$38$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	0.326352	−	0.118782i	0.326352	−	0.118782i
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	1.00000			1.00000
$45$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$49$	0.439693	+	0.761570i	0.439693	+	0.761570i
$50$	0.500000	+	0.866025i	0.500000	+	0.866025i
$51$	0.266044	−	1.50881i	0.266044	−	1.50881i
$52$		0			0
$53$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$53$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$54$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$55$	−1.00000			−1.00000
$56$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$57$	0.326352	−	1.85083i	0.326352	−	1.85083i
$58$	0.766044	+	1.32683i	0.766044	+	1.32683i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$	0.766044	+	0.642788i	0.766044	+	0.642788i
$61$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$61$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$62$	−0.347296			−0.347296
$63$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$64$	1.00000			1.00000
$65$		0			0
$66$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$67$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$67$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$68$	0.766044	+	1.32683i	0.766044	+	1.32683i
$69$		0			0
$70$	0.173648	−	0.300767i	0.173648	−	0.300767i
$71$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$71$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$72$	0.939693	+	0.342020i	0.939693	+	0.342020i
$73$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$73$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$74$	0.939693	−	1.62760i	0.939693	−	1.62760i
$75$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$76$	0.939693	+	1.62760i	0.939693	+	1.62760i
$77$	0.173648	+	0.300767i	0.173648	+	0.300767i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	−1.00000			−1.00000
$81$	0.766044	+	0.642788i	0.766044	+	0.642788i
$82$		0			0
$83$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$83$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$84$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$85$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$86$		0			0
$87$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$88$	0.500000	−	0.866025i	0.500000	−	0.866025i
$89$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$89$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$90$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$91$		0			0
$92$		0			0
$93$	0.326352	−	0.118782i	0.326352	−	0.118782i
$94$		0			0
$95$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$96$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	0.879385			0.879385
$99$	0.766044	−	0.642788i	0.766044	−	0.642788i
$100$	1.00000			1.00000
$101$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$101$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$102$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$		0			0
$105$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$106$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	−1.00000			−1.00000
$109$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$109$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$110$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$111$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$112$	0.173648	+	0.300767i	0.173648	+	0.300767i
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$115$		0			0
$116$	1.53209			1.53209
$117$		0			0
$118$		0			0
$119$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$120$	0.939693	−	0.342020i	0.939693	−	0.342020i
$121$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$122$	0.173648	+	0.300767i	0.173648	+	0.300767i
$123$		0			0
$124$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$125$	−1.00000			−1.00000
$126$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$127$	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			0
$130$		0			0
$131$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$131$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$132$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$133$	−0.326352	+	0.565258i	−0.326352	+	0.565258i
$134$	−1.00000			−1.00000
$135$	1.00000			1.00000
$136$	1.53209			1.53209
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$139$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$140$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$141$		0			0
$142$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$143$		0			0
$144$	0.766044	−	0.642788i	0.766044	−	0.642788i
$145$	−1.53209			−1.53209
$146$	0.500000	−	0.866025i	0.500000	−	0.866025i
$147$	−0.826352	+	0.300767i	−0.826352	+	0.300767i
$148$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$149$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$149$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$150$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$	1.87939			1.87939
$153$	1.43969	+	0.524005i	1.43969	+	0.524005i
$154$	0.347296			0.347296
$155$	0.173648	−	0.300767i	0.173648	−	0.300767i
$156$		0			0
$157$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$157$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$158$		0			0
$159$	0.266044	−	1.50881i	0.266044	−	1.50881i
$160$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$161$		0			0
$162$	0.939693	−	0.342020i	0.939693	−	0.342020i
$163$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$163$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$164$		0			0
$165$	0.173648	−	0.984808i	0.173648	−	0.984808i
$166$		0			0
$167$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$167$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$168$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$169$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$170$	−1.53209			−1.53209
$171$	1.76604	+	0.642788i	1.76604	+	0.642788i
$172$		0			0
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$175$	0.173648	+	0.300767i	0.173648	+	0.300767i
$176$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$177$		0			0
$178$	0.766044	−	1.32683i	0.766044	−	1.32683i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$184$		0			0
$185$	0.939693	+	1.62760i	0.939693	+	1.62760i
$186$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$187$	0.766044	−	1.32683i	0.766044	−	1.32683i
$188$		0			0
$189$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$190$	−1.87939			−1.87939
$191$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$191$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$193$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$193$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$194$		0			0
$195$		0			0
$196$	0.439693	−	0.761570i	0.439693	−	0.761570i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$199$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$199$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$200$	0.500000	−	0.866025i	0.500000	−	0.866025i
$201$	0.939693	−	0.342020i	0.939693	−	0.342020i
$202$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$203$	0.266044	+	0.460802i	0.266044	+	0.460802i
$204$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.939693	−	1.62760i	0.939693	−	1.62760i
$210$	0.266044	+	0.223238i	0.266044	+	0.223238i
$211$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$211$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$212$	0.766044	+	1.32683i	0.766044	+	1.32683i
$213$	0.326352	−	1.85083i	0.326352	−	1.85083i
$214$		0			0
$215$		0			0
$216$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$217$	−0.120615			−0.120615
$218$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$219$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$220$	0.500000	+	0.866025i	0.500000	+	0.866025i
$221$		0			0
$222$	1.43969	+	1.20805i	1.43969	+	1.20805i
$223$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$223$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$224$	0.347296			0.347296
$225$	0.766044	−	0.642788i	0.766044	−	0.642788i
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$		0			0
$231$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$232$	0.766044	−	1.32683i	0.766044	−	1.32683i
$233$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$233$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	0.266044	+	0.460802i	0.266044	+	0.460802i
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	0.173648	−	0.984808i	0.173648	−	0.984808i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	−1.00000			−1.00000
$243$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$244$	0.347296			0.347296
$245$	−0.439693	+	0.761570i	−0.439693	+	0.761570i
$246$		0			0
$247$		0			0
$248$	0.173648	+	0.300767i	0.173648	+	0.300767i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$	0.326352	+	0.118782i	0.326352	+	0.118782i
$253$		0			0
$254$	0.500000	−	0.866025i	0.500000	−	0.866025i
$255$	1.43969	−	0.524005i	1.43969	−	0.524005i
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$	0.326352	−	0.565258i	0.326352	−	0.565258i
$260$		0			0
$261$	1.17365	−	0.984808i	1.17365	−	0.984808i
$262$	1.87939			1.87939
$263$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$263$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$264$	0.766044	+	0.642788i	0.766044	+	0.642788i
$265$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$266$	0.326352	+	0.565258i	0.326352	+	0.565258i
$267$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$268$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	0.500000	−	0.866025i	0.500000	−	0.866025i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$	0.766044	−	1.32683i	0.766044	−	1.32683i
$273$		0			0
$274$		0			0
$275$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$	1.00000			1.00000
$279$	0.0603074	+	0.342020i	0.0603074	+	0.342020i
$280$	−0.347296			−0.347296
$281$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$281$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$283$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$284$	0.939693	+	1.62760i	0.939693	+	1.62760i
$285$	1.76604	−	0.642788i	1.76604	−	0.642788i
$286$		0			0
$287$		0			0
$288$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$289$	1.34730			1.34730
$290$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$291$		0			0
$292$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−0.152704	+	0.866025i	−0.152704	+	0.866025i
$295$		0			0
$296$	−1.87939			−1.87939
$297$	0.500000	+	0.866025i	0.500000	+	0.866025i
$298$	1.87939			1.87939
$299$		0			0
$300$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$301$		0			0
$302$		0			0
$303$	0.766044	+	0.642788i	0.766044	+	0.642788i
$304$	0.939693	−	1.62760i	0.939693	−	1.62760i
$305$	−0.347296			−0.347296
$306$	1.17365	−	0.984808i	1.17365	−	0.984808i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	0.173648	−	0.300767i	0.173648	−	0.300767i
$309$		0			0
$310$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$311$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$311$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	1.53209			1.53209
$315$	−0.326352	−	0.118782i	−0.326352	−	0.118782i
$316$		0			0
$317$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$317$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$318$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$319$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$320$	0.500000	+	0.866025i	0.500000	+	0.866025i
$321$		0			0
$322$		0			0
$323$	2.87939			2.87939
$324$	0.173648	−	0.984808i	0.173648	−	0.984808i
$325$		0			0
$326$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$327$	0.173648	−	0.984808i	0.173648	−	0.984808i
$328$		0			0
$329$		0			0
$330$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	−1.76604	−	0.642788i	−1.76604	−	0.642788i
$334$	0.347296			0.347296
$335$	0.500000	−	0.866025i	0.500000	−	0.866025i
$336$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$337$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$337$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$338$	0.500000	+	0.866025i	0.500000	+	0.866025i
$339$		0			0
$340$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$341$	0.347296			0.347296
$342$	1.43969	−	1.20805i	1.43969	−	1.20805i
$343$	0.652704			0.652704
$344$		0			0
$345$		0			0
$346$		0			0
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$349$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$350$	0.347296			0.347296
$351$		0			0
$352$	−1.00000			−1.00000
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$356$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$357$	−0.407604	−	0.342020i	−0.407604	−	0.342020i
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	0.173648	+	0.984808i	0.173648	+	0.984808i
$361$	2.53209			2.53209
$362$		0			0
$363$	0.939693	−	0.342020i	0.939693	−	0.342020i
$364$		0			0
$365$	0.500000	+	0.866025i	0.500000	+	0.866025i
$366$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$		0			0
$369$		0			0
$370$	1.87939			1.87939
$371$	−0.266044	+	0.460802i	−0.266044	+	0.460802i
$372$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$375$	0.173648	−	0.984808i	0.173648	−	0.984808i
$376$		0			0
$377$		0			0
$378$	−0.347296			−0.347296
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$381$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$382$	1.00000	+	1.73205i	1.00000	+	1.73205i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$	0.766044	+	0.642788i	0.766044	+	0.642788i
$385$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$386$	−1.87939			−1.87939
$387$		0			0
$388$		0			0
$389$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$389$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	−0.439693	−	0.761570i	−0.439693	−	0.761570i
$393$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$394$		0			0
$395$		0			0
$396$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$397$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$397$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$398$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$399$	−0.500000	−	0.419550i	−0.500000	−	0.419550i
$400$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$401$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$401$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$402$	0.173648	−	0.984808i	0.173648	−	0.984808i
$403$		0			0
$404$	−1.00000			−1.00000
$405$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$406$	0.532089			0.532089
$407$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$408$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$418$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$419$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$419$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$420$	0.326352	−	0.118782i	0.326352	−	0.118782i
$421$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$421$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$422$	−1.53209			−1.53209
$423$		0			0
$424$	1.53209			1.53209
$425$	0.766044	−	1.32683i	0.766044	−	1.32683i
$426$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$427$	0.0603074	+	0.104455i	0.0603074	+	0.104455i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		1.00000			$0$
$431$		0			0		−1.00000			$\pi$
$432$	0.500000	+	0.866025i	0.500000	+	0.866025i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$	−0.0603074	+	0.104455i	−0.0603074	+	0.104455i
$435$	0.266044	−	1.50881i	0.266044	−	1.50881i
$436$	0.500000	+	0.866025i	0.500000	+	0.866025i
$437$		0			0
$438$	0.766044	+	0.642788i	0.766044	+	0.642788i
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$	1.00000			1.00000
$441$	−0.152704	−	0.866025i	−0.152704	−	0.866025i
$442$		0			0
$443$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$443$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$444$	1.76604	−	0.642788i	1.76604	−	0.642788i
$445$	0.766044	+	1.32683i	0.766044	+	1.32683i
$446$		0			0
$447$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$448$	0.173648	−	0.300767i	0.173648	−	0.300767i
$449$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$449$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$450$	−0.173648	−	0.984808i	−0.173648	−	0.984808i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$457$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$457$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$458$		0			0
$459$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$460$		0			0
$461$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$461$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$462$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$463$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$463$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$464$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$465$	0.266044	+	0.223238i	0.266044	+	0.223238i
$466$	0.939693	−	1.62760i	0.939693	−	1.62760i
$467$	1.87939			1.87939			0.939693	−	0.342020i	$-0.111111\pi$
$467$	1.87939			1.87939			0.939693	+	0.342020i	$0.111111\pi$
$468$		0			0
$469$	−0.347296			−0.347296
$470$		0			0
$471$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.939693	−	1.62760i	0.939693	−	1.62760i
$476$	0.532089			0.532089
$477$	1.43969	+	0.524005i	1.43969	+	0.524005i
$478$		0			0
$479$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$479$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$480$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$485$		0			0
$486$	0.173648	+	0.984808i	0.173648	+	0.984808i
$487$		0			0		1.00000			$0$
$487$		0			0		−1.00000			$\pi$
$488$	0.173648	−	0.300767i	0.173648	−	0.300767i
$489$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$490$	0.439693	+	0.761570i	0.439693	+	0.761570i
$491$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	−0.939693	−	0.342020i	$-0.888889\pi$
$491$	−0.766044	−	1.32683i	−0.766044	−	1.32683i	0.173648	−	0.984808i	$-0.444444\pi$
$492$		0			0
$493$	1.17365	−	2.03282i	1.17365	−	2.03282i
$494$		0			0
$495$	0.939693	+	0.342020i	0.939693	+	0.342020i
$496$	0.347296			0.347296
$497$	−0.326352	+	0.565258i	−0.326352	+	0.565258i
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	0.500000	+	0.866025i	0.500000	+	0.866025i
$501$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$502$		0			0
$503$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$503$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$504$	0.266044	−	0.223238i	0.266044	−	0.223238i
$505$	1.00000			1.00000
$506$		0			0
$507$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$508$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$	0.266044	−	1.50881i	0.266044	−	1.50881i
$511$	0.173648	−	0.300767i	0.173648	−	0.300767i
$512$	−1.00000			−1.00000
$513$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.326352	−	0.565258i	−0.326352	−	0.565258i
$519$		0			0
$520$		0			0
$521$	2.00000			2.00000			1.00000			$0$
$521$	2.00000			2.00000			1.00000			$0$
$522$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$	0.939693	−	1.62760i	0.939693	−	1.62760i
$525$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$526$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$527$	0.266044	+	0.460802i	0.266044	+	0.460802i
$528$	0.939693	−	0.342020i	0.939693	−	0.342020i
$529$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$530$	−1.53209			−1.53209
$531$		0			0
$532$	0.652704			0.652704
$533$		0			0
$534$	1.17365	+	0.984808i	1.17365	+	0.984808i
$535$		0			0
$536$	0.500000	+	0.866025i	0.500000	+	0.866025i
$537$		0			0
$538$		0			0
$539$	−0.879385			−0.879385
$540$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$541$	−1.87939			−1.87939			−0.939693	−	0.342020i	$-0.888889\pi$
$541$	−1.87939			−1.87939			−0.939693	+	0.342020i	$0.888889\pi$
$542$		0			0
$543$		0			0
$544$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$545$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$546$		0			0
$547$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$547$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$	0.266044	−	0.223238i	0.266044	−	0.223238i
$550$	−1.00000			−1.00000
$551$	1.43969	−	2.49362i	1.43969	−	2.49362i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$556$	0.500000	−	0.866025i	0.500000	−	0.866025i
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$	0.326352	+	0.118782i	0.326352	+	0.118782i
$559$		0			0
$560$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$561$	1.17365	+	0.984808i	1.17365	+	0.984808i
$562$		0			0
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.326352	−	0.118782i	0.326352	−	0.118782i
$568$	1.87939			1.87939
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$	0.326352	−	1.85083i	0.326352	−	1.85083i
$571$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$571$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$572$		0			0
$573$	−1.53209	−	1.28558i	−1.53209	−	1.28558i
$574$		0			0
$575$		0			0
$576$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.673648	−	1.16679i	0.673648	−	1.16679i
$579$	1.76604	−	0.642788i	1.76604	−	0.642788i
$580$	0.766044	+	1.32683i	0.766044	+	1.32683i
$581$		0			0
$582$		0			0
$583$	0.766044	−	1.32683i	0.766044	−	1.32683i
$584$	−1.00000			−1.00000
$585$		0			0
$586$		0			0
$587$	0.766044	−	1.32683i	0.766044	−	1.32683i	−0.173648	−	0.984808i	$-0.555556\pi$
$587$	0.766044	−	1.32683i	0.766044	−	1.32683i	0.939693	−	0.342020i	$-0.111111\pi$
$588$	0.673648	+	0.565258i	0.673648	+	0.565258i
$589$	0.326352	+	0.565258i	0.326352	+	0.565258i
$590$		0			0
$591$		0			0
$592$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$593$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$593$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$594$	1.00000			1.00000
$595$	−0.532089			−0.532089
$596$	0.939693	−	1.62760i	0.939693	−	1.62760i
$597$	0.326352	−	1.85083i	0.326352	−	1.85083i
$598$		0			0
$599$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$599$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$600$	0.766044	+	0.642788i	0.766044	+	0.642788i
$601$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$601$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$602$		0			0
$603$	0.173648	+	0.984808i	0.173648	+	0.984808i
$604$		0			0
$605$	0.500000	−	0.866025i	0.500000	−	0.866025i
$606$	0.939693	−	0.342020i	0.939693	−	0.342020i
$607$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.766044	−	0.642788i	$-0.777778\pi$
$607$	−0.939693	−	1.62760i	−0.939693	−	1.62760i	−0.173648	−	0.984808i	$-0.555556\pi$
$608$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$609$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$610$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$611$		0			0
$612$	−0.266044	−	1.50881i	−0.266044	−	1.50881i
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$617$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$617$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$	−0.347296			−0.347296
$621$		0			0
$622$	−1.53209			−1.53209
$623$	0.266044	−	0.460802i	0.266044	−	0.460802i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$626$		0			0
$627$	1.43969	+	1.20805i	1.43969	+	1.20805i
$628$	0.766044	−	1.32683i	0.766044	−	1.32683i
$629$	−2.87939			−2.87939
$630$	−0.266044	+	0.223238i	−0.266044	+	0.223238i
$631$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$631$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$632$		0			0
$633$	1.43969	−	0.524005i	1.43969	−	0.524005i
$634$	0.939693	+	1.62760i	0.939693	+	1.62760i
$635$	0.500000	+	0.866025i	0.500000	+	0.866025i
$636$	−1.43969	+	0.524005i	−1.43969	+	0.524005i
$637$		0			0
$638$	−1.53209			−1.53209
$639$	1.76604	+	0.642788i	1.76604	+	0.642788i
$640$	1.00000			1.00000
$641$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$641$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$642$		0			0
$643$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$643$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$644$		0			0
$645$		0			0
$646$	1.43969	−	2.49362i	1.43969	−	2.49362i
$647$		0			0		1.00000			$0$
$647$		0			0		−1.00000			$\pi$
$648$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$649$		0			0
$650$		0			0
$651$	0.0209445	−	0.118782i	0.0209445	−	0.118782i
$652$	0.173648	+	0.300767i	0.173648	+	0.300767i
$653$	0.173648	+	0.300767i	0.173648	+	0.300767i	0.939693	−	0.342020i	$-0.111111\pi$
$653$	0.173648	+	0.300767i	0.173648	+	0.300767i	−0.766044	+	0.642788i	$0.777778\pi$
$654$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$655$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$656$		0			0
$657$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$658$		0			0
$659$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	0.173648	+	0.984808i	$0.444444\pi$
$659$	−0.766044	+	1.32683i	−0.766044	+	1.32683i	−0.939693	+	0.342020i	$0.888889\pi$
$660$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$661$		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
$665$	−0.652704			−0.652704
$666$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$667$		0			0
$668$	0.173648	−	0.300767i	0.173648	−	0.300767i
$669$		0			0
$670$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$671$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$672$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$673$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$673$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$674$	1.53209			1.53209
$675$	0.500000	+	0.866025i	0.500000	+	0.866025i
$676$	1.00000			1.00000
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$		0			0
$679$		0			0
$680$	0.766044	+	1.32683i	0.766044	+	1.32683i
$681$		0			0
$682$	0.173648	−	0.300767i	0.173648	−	0.300767i
$683$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$683$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$684$	−0.326352	−	1.85083i	−0.326352	−	1.85083i
$685$		0			0
$686$	0.326352	−	0.565258i	0.326352	−	0.565258i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−0.0603074	−	0.342020i	−0.0603074	−	0.342020i
$694$		0			0
$695$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$696$	1.17365	+	0.984808i	1.17365	+	0.984808i
$697$		0			0
$698$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$699$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$700$	0.173648	−	0.300767i	0.173648	−	0.300767i
$701$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$701$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$702$		0			0
$703$	−3.53209			−3.53209
$704$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$705$		0			0
$706$		0			0
$707$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$708$		0			0
$709$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$709$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$710$	−1.87939			−1.87939
$711$		0			0
$712$	−1.53209			−1.53209
$713$		0			0
$714$	−0.500000	+	0.181985i	−0.500000	+	0.181985i
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.347296			0.347296			0.173648	−	0.984808i	$-0.444444\pi$
$719$	0.347296			0.347296			0.173648	+	0.984808i	$0.444444\pi$
$720$	0.939693	+	0.342020i	0.939693	+	0.342020i
$721$		0			0
$722$	1.26604	−	2.19285i	1.26604	−	2.19285i
$723$		0			0
$724$		0			0
$725$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$726$	0.173648	−	0.984808i	0.173648	−	0.984808i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		0			0
$729$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$730$	1.00000			1.00000
$731$		0			0
$732$	−0.0603074	+	0.342020i	−0.0603074	+	0.342020i
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$	−0.673648	−	0.565258i	−0.673648	−	0.565258i
$736$		0			0
$737$	1.00000			1.00000
$738$		0			0
$739$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$739$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$740$	0.939693	−	1.62760i	0.939693	−	1.62760i
$741$		0			0
$742$	0.266044	+	0.460802i	0.266044	+	0.460802i
$743$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$743$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$744$	−0.326352	+	0.118782i	−0.326352	+	0.118782i
$745$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$746$		0			0
$747$		0			0
$748$	−1.53209			−1.53209
$749$		0			0
$750$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$751$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.766044	+	0.642788i	$0.222222\pi$
$751$	0.939693	+	1.62760i	0.939693	+	1.62760i	0.173648	+	0.984808i	$0.444444\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$757$	−2.00000			−2.00000			−1.00000			$\pi$
$757$	−2.00000			−2.00000			−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	0.939693	+	1.62760i	0.939693	+	1.62760i
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$	0.766044	+	0.642788i	0.766044	+	0.642788i
$763$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$764$	2.00000			2.00000
$765$	0.266044	+	1.50881i	0.266044	+	1.50881i
$766$		0			0
$767$		0			0
$768$	0.939693	−	0.342020i	0.939693	−	0.342020i
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$	0.173648	+	0.300767i	0.173648	+	0.300767i
$771$		0			0
$772$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$773$	−1.53209			−1.53209			−0.766044	−	0.642788i	$-0.777778\pi$
$773$	−1.53209			−1.53209			−0.766044	+	0.642788i	$0.777778\pi$
$774$		0			0
$775$	0.347296			0.347296
$776$		0			0
$777$	0.500000	+	0.419550i	0.500000	+	0.419550i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	0.939693	−	1.62760i	0.939693	−	1.62760i
$782$		0			0
$783$	0.766044	+	1.32683i	0.766044	+	1.32683i
$784$	−0.879385			−0.879385
$785$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$786$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$		0			0
$789$	0.266044	+	0.223238i	0.266044	+	0.223238i
$790$		0			0
$791$		0			0
$792$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$793$		0			0
$794$	0.500000	−	0.866025i	0.500000	−	0.866025i
$795$	1.43969	−	0.524005i	1.43969	−	0.524005i
$796$	0.939693	+	1.62760i	0.939693	+	1.62760i
$797$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$797$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$798$	−0.613341	+	0.223238i	−0.613341	+	0.223238i
$799$		0			0
$800$	−1.00000			−1.00000
$801$	−1.43969	−	0.524005i	−1.43969	−	0.524005i
$802$	−1.53209			−1.53209
$803$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$804$	−0.766044	−	0.642788i	−0.766044	−	0.642788i
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	0.766044	+	0.642788i	0.766044	+	0.642788i
$811$	1.53209			1.53209			0.766044	−	0.642788i	$-0.222222\pi$
$811$	1.53209			1.53209			0.766044	+	0.642788i	$0.222222\pi$
$812$	0.266044	−	0.460802i	0.266044	−	0.460802i
$813$		0			0
$814$	0.939693	+	1.62760i	0.939693	+	1.62760i
$815$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$816$	1.17365	+	0.984808i	1.17365	+	0.984808i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$821$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$822$		0			0
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$	0.939693	−	0.342020i	0.939693	−	0.342020i
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$834$	−0.173648	+	0.984808i	−0.173648	+	0.984808i
$835$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$836$	−1.87939			−1.87939
$837$	−0.347296			−0.347296
$838$		0			0
$839$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$839$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$840$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$841$	−0.673648	−	1.16679i	−0.673648	−	1.16679i
$842$		0			0
$843$		0			0
$844$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$845$	−1.00000			−1.00000
$846$		0			0
$847$	−0.347296			−0.347296
$848$	0.766044	−	1.32683i	0.766044	−	1.32683i
$849$		0			0
$850$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$851$		0			0
$852$	−1.76604	+	0.642788i	−1.76604	+	0.642788i
$853$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$853$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$854$	0.120615			0.120615
$855$	0.326352	+	1.85083i	0.326352	+	1.85083i
$856$		0			0
$857$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$857$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$858$		0			0
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	1.00000			1.00000
$865$		0			0
$866$		0			0
$867$	−0.233956	+	1.32683i	−0.233956	+	1.32683i
$868$	0.0603074	+	0.104455i	0.0603074	+	0.104455i
$869$		0			0
$870$	−1.17365	−	0.984808i	−1.17365	−	0.984808i
$871$		0			0
$872$	1.00000			1.00000
$873$		0			0
$874$		0			0
$875$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$876$	0.939693	−	0.342020i	0.939693	−	0.342020i
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$		0			0
$879$		0			0
$880$	0.500000	−	0.866025i	0.500000	−	0.866025i
$881$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$882$	−0.826352	−	0.300767i	−0.826352	−	0.300767i
$883$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$883$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$884$		0			0
$885$		0			0
$886$	0.500000	+	0.866025i	0.500000	+	0.866025i
$887$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$887$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$888$	0.326352	−	1.85083i	0.326352	−	1.85083i
$889$	0.173648	−	0.300767i	0.173648	−	0.300767i
$890$	1.53209			1.53209
$891$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$892$		0			0
$893$		0			0
$894$	−0.326352	+	1.85083i	−0.326352	+	1.85083i
$895$		0			0
$896$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$897$		0			0
$898$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$899$	0.532089			0.532089
$900$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$901$	2.34730			2.34730
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.173648	+	0.984808i	$0.555556\pi$
$907$	−0.939693	+	1.62760i	−0.939693	+	1.62760i	−0.766044	+	0.642788i	$0.777778\pi$
$908$		0			0
$909$	−0.766044	+	0.642788i	−0.766044	+	0.642788i
$910$		0			0
$911$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$911$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$912$	1.43969	+	1.20805i	1.43969	+	1.20805i
$913$		0			0
$914$	−0.766044	−	1.32683i	−0.766044	−	1.32683i
$915$	0.0603074	−	0.342020i	0.0603074	−	0.342020i
$916$		0			0
$917$	0.652704			0.652704
$918$	0.766044	+	1.32683i	0.766044	+	1.32683i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	0.173648	+	0.300767i	0.173648	+	0.300767i
$923$		0			0
$924$	0.266044	+	0.223238i	0.266044	+	0.223238i
$925$	−0.939693	+	1.62760i	−0.939693	+	1.62760i
$926$		0			0
$927$		0			0
$928$	−1.53209			−1.53209
$929$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	−0.939693	−	0.342020i	$-0.888889\pi$
$929$	−0.173648	+	0.300767i	−0.173648	+	0.300767i	0.766044	+	0.642788i	$0.222222\pi$
$930$	0.326352	−	0.118782i	0.326352	−	0.118782i
$931$	−0.826352	−	1.43128i	−0.826352	−	1.43128i
$932$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$933$	1.43969	−	0.524005i	1.43969	−	0.524005i
$934$	0.939693	−	1.62760i	0.939693	−	1.62760i
$935$	1.53209			1.53209
$936$		0			0
$937$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$937$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$938$	−0.173648	+	0.300767i	−0.173648	+	0.300767i
$939$		0			0
$940$		0			0
$941$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	0.766044	−	0.642788i	$-0.222222\pi$
$941$	−0.173648	−	0.300767i	−0.173648	−	0.300767i	−0.939693	+	0.342020i	$0.888889\pi$
$942$	−0.266044	+	1.50881i	−0.266044	+	1.50881i
$943$		0			0
$944$		0			0
$945$	0.173648	−	0.300767i	0.173648	−	0.300767i
$946$		0			0
$947$	0.173648	−	0.300767i	0.173648	−	0.300767i	−0.766044	−	0.642788i	$-0.777778\pi$
$947$	0.173648	−	0.300767i	0.173648	−	0.300767i	0.939693	+	0.342020i	$0.111111\pi$
$948$		0			0
$949$		0			0
$950$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$951$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$952$	0.266044	−	0.460802i	0.266044	−	0.460802i
$953$	−0.347296			−0.347296			−0.173648	−	0.984808i	$-0.555556\pi$
$953$	−0.347296			−0.347296			−0.173648	+	0.984808i	$0.555556\pi$
$954$	1.17365	−	0.984808i	1.17365	−	0.984808i
$955$	−2.00000			−2.00000
$956$		0			0
$957$	1.43969	−	0.524005i	1.43969	−	0.524005i
$958$		0			0
$959$		0			0
$960$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$961$	0.439693	−	0.761570i	0.439693	−	0.761570i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.939693	−	1.62760i	0.939693	−	1.62760i
$966$		0			0
$967$	0.766044	+	1.32683i	0.766044	+	1.32683i	0.939693	+	0.342020i	$0.111111\pi$
$967$	0.766044	+	1.32683i	0.766044	+	1.32683i	−0.173648	+	0.984808i	$0.555556\pi$
$968$	0.500000	+	0.866025i	0.500000	+	0.866025i
$969$	−0.500000	+	2.83564i	−0.500000	+	2.83564i
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	0.939693	+	0.342020i	0.939693	+	0.342020i
$973$	0.347296			0.347296
$974$		0			0
$975$		0			0
$976$	−0.173648	−	0.300767i	−0.173648	−	0.300767i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$	−0.266044	−	0.223238i	−0.266044	−	0.223238i
$979$	−0.766044	+	1.32683i	−0.766044	+	1.32683i
$980$	0.879385			0.879385
$981$	0.939693	+	0.342020i	0.939693	+	0.342020i
$982$	−1.53209			−1.53209
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$		0			0
$985$		0			0
$986$	−1.17365	−	2.03282i	−1.17365	−	2.03282i
$987$		0			0
$988$		0			0
$989$		0			0
$990$	0.766044	−	0.642788i	0.766044	−	0.642788i
$991$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$991$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$992$	0.173648	−	0.300767i	0.173648	−	0.300767i
$993$		0			0
$994$	0.326352	+	0.565258i	0.326352	+	0.565258i
$995$	−0.939693	−	1.62760i	−0.939693	−	1.62760i
$996$		0			0
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$		0			0
$999$	0.939693	−	1.62760i	0.939693	−	1.62760i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3960.1.cm.d.1429.2	yes	6
5.4	even	2		3960.1.cm.a.1429.2	✓	6
8.5	even	2		3960.1.cm.c.1429.2	yes	6
9.4	even	3	inner	3960.1.cm.d.2749.2	yes	6
11.10	odd	2		3960.1.cm.b.1429.2	yes	6
40.29	even	2		3960.1.cm.b.1429.2	yes	6
45.4	even	6		3960.1.cm.a.2749.2	yes	6
55.54	odd	2		3960.1.cm.c.1429.2	yes	6
72.13	even	6		3960.1.cm.c.2749.2	yes	6
88.21	odd	2		3960.1.cm.a.1429.2	✓	6
99.76	odd	6		3960.1.cm.b.2749.2	yes	6
360.229	even	6		3960.1.cm.b.2749.2	yes	6
440.109	odd	2	CM	3960.1.cm.d.1429.2	yes	6
495.274	odd	6		3960.1.cm.c.2749.2	yes	6
792.373	odd	6		3960.1.cm.a.2749.2	yes	6
3960.2749	odd	6	inner	3960.1.cm.d.2749.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3960.1.cm.a.1429.2	✓	6	5.4	even	2
3960.1.cm.a.1429.2	✓	6	88.21	odd	2
3960.1.cm.a.2749.2	yes	6	45.4	even	6
3960.1.cm.a.2749.2	yes	6	792.373	odd	6
3960.1.cm.b.1429.2	yes	6	11.10	odd	2
3960.1.cm.b.1429.2	yes	6	40.29	even	2
3960.1.cm.b.2749.2	yes	6	99.76	odd	6
3960.1.cm.b.2749.2	yes	6	360.229	even	6
3960.1.cm.c.1429.2	yes	6	8.5	even	2
3960.1.cm.c.1429.2	yes	6	55.54	odd	2
3960.1.cm.c.2749.2	yes	6	72.13	even	6
3960.1.cm.c.2749.2	yes	6	495.274	odd	6
3960.1.cm.d.1429.2	yes	6	1.1	even	1	trivial
3960.1.cm.d.1429.2	yes	6	440.109	odd	2	CM
3960.1.cm.d.2749.2	yes	6	9.4	even	3	inner
3960.1.cm.d.2749.2	yes	6	3960.2749	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3960.cm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.766044 + 0.642788i) q^{6} +(0.173648 - 0.300767i) q^{7} -1.00000 q^{8} +(-0.939693 - 0.342020i) q^{9} +1.00000 q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.939693 - 0.342020i) q^{12} +(-0.173648 - 0.300767i) q^{14} +(-0.939693 + 0.342020i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.53209 q^{17} +(-0.766044 + 0.642788i) q^{18} -1.87939 q^{19} +(0.500000 - 0.866025i) q^{20} +(0.266044 + 0.223238i) q^{21} +(0.500000 + 0.866025i) q^{22} +(0.173648 - 0.984808i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.500000 - 0.866025i) q^{27} -0.347296 q^{28} +(-0.766044 + 1.32683i) q^{29} +(-0.173648 + 0.984808i) q^{30} +(-0.173648 - 0.300767i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.766044 - 0.642788i) q^{33} +(-0.766044 + 1.32683i) q^{34} +0.347296 q^{35} +(0.173648 + 0.984808i) q^{36} +1.87939 q^{37} +(-0.939693 + 1.62760i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(0.326352 - 0.118782i) q^{42} +1.00000 q^{44} +(-0.173648 - 0.984808i) q^{45} +(-0.766044 - 0.642788i) q^{48} +(0.439693 + 0.761570i) q^{49} +(0.500000 + 0.866025i) q^{50} +(0.266044 - 1.50881i) q^{51} -1.53209 q^{53} +(-0.500000 - 0.866025i) q^{54} -1.00000 q^{55} +(-0.173648 + 0.300767i) q^{56} +(0.326352 - 1.85083i) q^{57} +(0.766044 + 1.32683i) q^{58} +(0.766044 + 0.642788i) q^{60} +(-0.173648 + 0.300767i) q^{61} -0.347296 q^{62} +(-0.266044 + 0.223238i) q^{63} +1.00000 q^{64} +(-0.939693 + 0.342020i) q^{66} +(-0.500000 - 0.866025i) q^{67} +(0.766044 + 1.32683i) q^{68} +(0.173648 - 0.300767i) q^{70} -1.87939 q^{71} +(0.939693 + 0.342020i) q^{72} +1.00000 q^{73} +(0.939693 - 1.62760i) q^{74} +(-0.766044 - 0.642788i) q^{75} +(0.939693 + 1.62760i) q^{76} +(0.173648 + 0.300767i) q^{77} -1.00000 q^{80} +(0.766044 + 0.642788i) q^{81} +(0.0603074 - 0.342020i) q^{84} +(-0.766044 - 1.32683i) q^{85} +(-1.17365 - 0.984808i) q^{87} +(0.500000 - 0.866025i) q^{88} +1.53209 q^{89} +(-0.939693 - 0.342020i) q^{90} +(0.326352 - 0.118782i) q^{93} +(-0.939693 - 1.62760i) q^{95} +(-0.939693 + 0.342020i) q^{96} +0.879385 q^{98} +(0.766044 - 0.642788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{8} + 6 q^{10} - 3 q^{11} - 3 q^{16} + 3 q^{20} - 3 q^{21} + 3 q^{22} - 3 q^{25} + 3 q^{27} + 3 q^{32} - 3 q^{40} + 3 q^{42} + 6 q^{44} - 3 q^{49} + 3 q^{50} - 3 q^{51}+ \cdots - 6 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^8 + 6 * q^10 - 3 * q^11 - 3 * q^16 + 3 * q^20 - 3 * q^21 + 3 * q^22 - 3 * q^25 + 3 * q^27 + 3 * q^32 - 3 * q^40 + 3 * q^42 + 6 * q^44 - 3 * q^49 + 3 * q^50 - 3 * q^51 - 3 * q^54 - 6 * q^55 + 3 * q^57 + 3 * q^63 + 6 * q^64 - 3 * q^67 + 6 * q^73 - 6 * q^80 + 6 * q^84 - 6 * q^87 + 3 * q^88 + 3 * q^93 - 6 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more