LMFDB - Embedded newform 765.1.bs.b.13.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,1,Mod(13,765)] 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("765.13"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 9, 3])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	765.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.381784734664$
Analytic rank:	$0$
Dimension:	$4$
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:	yes
Projective image:	$S_{4}$
Projective field:	Galois closure of 4.0.49744125.1

Embedding invariants

Embedding label			13.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	765.13
Dual form			765.1.bs.b.412.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 + 1.36603i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.366025 + 1.36603i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.00000i) q^{10} +(1.36603 + 0.366025i) q^{11} -1.00000 q^{12} +(-0.366025 - 1.36603i) q^{14} -1.00000i q^{15} +(-0.500000 - 0.866025i) q^{16} +1.00000 q^{17} +(1.00000 + 1.00000i) q^{18} -1.00000 q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000i q^{27} +1.00000 q^{28} +(1.36603 + 0.366025i) q^{29} +(1.36603 + 0.366025i) q^{30} +(1.36603 - 0.366025i) q^{32} +(1.36603 - 0.366025i) q^{33} +(-0.366025 + 1.36603i) q^{34} +1.00000i q^{35} +(-0.866025 + 0.500000i) q^{36} -1.00000 q^{37} +(0.366025 - 1.36603i) q^{38} +(-1.00000 - 1.00000i) q^{42} +(-1.00000 - 1.00000i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-1.00000 - 1.00000i) q^{46} +(-1.36603 - 0.366025i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.36603 - 0.366025i) q^{50} +(0.866025 - 0.500000i) q^{51} +(1.36603 + 0.366025i) q^{54} +(1.00000 - 1.00000i) q^{55} +(-0.866025 + 0.500000i) q^{57} +(-1.00000 + 1.73205i) q^{58} +(-0.500000 + 0.866025i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-1.36603 - 0.366025i) q^{61} +1.00000i q^{63} +1.00000i q^{64} +2.00000i q^{66} +(-0.866025 - 0.500000i) q^{68} +1.00000i q^{69} +(-1.36603 - 0.366025i) q^{70} +(-1.00000 - 1.00000i) q^{71} +1.00000i q^{73} +(0.366025 - 1.36603i) q^{74} +(-0.866025 - 0.500000i) q^{75} +(0.866025 + 0.500000i) q^{76} +(-1.36603 + 0.366025i) q^{77} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.36603 - 0.366025i) q^{83} +(0.866025 - 0.500000i) q^{84} +(0.500000 - 0.866025i) q^{85} +(1.36603 - 0.366025i) q^{87} -1.00000i q^{89} +(1.36603 - 0.366025i) q^{90} +(0.866025 - 0.500000i) q^{92} +(1.00000 - 1.73205i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(1.00000 - 1.00000i) q^{96} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{5} - 2 q^{6} + 2 q^{9} + 4 q^{10} + 2 q^{11} - 4 q^{12} + 2 q^{14} - 2 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{21} - 4 q^{22} - 2 q^{23} - 2 q^{25} + 4 q^{28} + 2 q^{29} + 2 q^{30}+ \cdots + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^5 - 2 * q^6 + 2 * q^9 + 4 * q^10 + 2 * q^11 - 4 * q^12 + 2 * q^14 - 2 * q^16 + 4 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^21 - 4 * q^22 - 2 * q^23 - 2 * q^25 + 4 * q^28 + 2 * q^29 + 2 * q^30 + 2 * q^32 + 2 * q^33 + 2 * q^34 - 4 * q^37 - 2 * q^38 - 4 * q^42 - 4 * q^44 - 2 * q^45 - 4 * q^46 - 2 * q^47 + 2 * q^50 + 2 * q^54 + 4 * q^55 - 4 * q^58 - 2 * q^59 - 2 * q^60 - 2 * q^61 - 2 * q^70 - 4 * q^71 - 2 * q^74 - 2 * q^77 - 4 * q^80 - 2 * q^81 - 2 * q^83 + 2 * q^85 + 2 * q^87 + 2 * q^90 + 4 * q^94 - 2 * q^95 + 4 * q^96 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$2$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.866025	−	0.500000i	0.866025	−	0.500000i
$3$	0.866025	−	0.500000i	0.866025	−	0.500000i
$4$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$6$	0.366025	+	1.36603i	0.366025	+	1.36603i
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$7$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$		0			0
$9$	0.500000	−	0.866025i	0.500000	−	0.866025i
$10$	1.00000	+	1.00000i	1.00000	+	1.00000i
$11$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$11$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$12$	−1.00000			−1.00000
$13$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$13$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$14$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$15$		−	1.00000i		−	1.00000i
$16$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$17$	1.00000			1.00000
$17$	1.00000			1.00000
$18$	1.00000	+	1.00000i	1.00000	+	1.00000i
$19$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$19$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$20$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$21$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$22$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$23$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$23$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$26$		0			0
$27$		−	1.00000i		−	1.00000i
$28$	1.00000			1.00000
$29$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$29$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$30$	1.36603	+	0.366025i	1.36603	+	0.366025i
$31$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$31$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$32$	1.36603	−	0.366025i	1.36603	−	0.366025i
$33$	1.36603	−	0.366025i	1.36603	−	0.366025i
$34$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$35$			1.00000i			1.00000i
$36$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$37$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$37$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$38$	0.366025	−	1.36603i	0.366025	−	1.36603i
$39$		0			0
$40$		0			0
$41$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$41$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$42$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$43$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$43$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$44$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$45$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$46$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$47$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$47$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$48$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$49$		0			0
$50$	1.36603	−	0.366025i	1.36603	−	0.366025i
$51$	0.866025	−	0.500000i	0.866025	−	0.500000i
$52$		0			0
$53$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$53$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$54$	1.36603	+	0.366025i	1.36603	+	0.366025i
$55$	1.00000	−	1.00000i	1.00000	−	1.00000i
$56$		0			0
$57$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$58$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$59$	−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			$\pi$
$60$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$61$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$61$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$62$		0			0
$63$			1.00000i			1.00000i
$64$			1.00000i			1.00000i
$65$		0			0
$66$			2.00000i			2.00000i
$67$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$67$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$68$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$69$			1.00000i			1.00000i
$70$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$71$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$71$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$72$		0			0
$73$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$73$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$74$	0.366025	−	1.36603i	0.366025	−	1.36603i
$75$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$76$	0.866025	+	0.500000i	0.866025	+	0.500000i
$77$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$78$		0			0
$79$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$79$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$80$	−1.00000			−1.00000
$81$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$82$		0			0
$83$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$84$	0.866025	−	0.500000i	0.866025	−	0.500000i
$85$	0.500000	−	0.866025i	0.500000	−	0.866025i
$86$		0			0
$87$	1.36603	−	0.366025i	1.36603	−	0.366025i
$88$		0			0
$89$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$89$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$90$	1.36603	−	0.366025i	1.36603	−	0.366025i
$91$		0			0
$92$	0.866025	−	0.500000i	0.866025	−	0.500000i
$93$		0			0
$94$	1.00000	−	1.73205i	1.00000	−	1.73205i
$95$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$96$	1.00000	−	1.00000i	1.00000	−	1.00000i
$97$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$97$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$98$		0			0
$99$	1.00000	−	1.00000i	1.00000	−	1.00000i
$100$			1.00000i			1.00000i
$101$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$101$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$102$	0.366025	+	1.36603i	0.366025	+	1.36603i
$103$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$103$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$104$		0			0
$105$	0.500000	+	0.866025i	0.500000	+	0.866025i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$109$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$109$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$110$	1.00000	+	1.73205i	1.00000	+	1.73205i
$111$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$112$	0.866025	+	0.500000i	0.866025	+	0.500000i
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$113$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$114$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$115$	0.500000	+	0.866025i	0.500000	+	0.866025i
$116$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$117$		0			0
$118$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$119$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$120$		0			0
$121$	0.866025	+	0.500000i	0.866025	+	0.500000i
$122$	1.00000	−	1.73205i	1.00000	−	1.73205i
$123$		0			0
$124$		0			0
$125$	−1.00000			−1.00000
$126$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$127$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$127$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$131$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$132$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$133$	0.866025	−	0.500000i	0.866025	−	0.500000i
$134$		0			0
$135$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$136$		0			0
$137$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$137$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$138$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$139$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$139$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$140$	0.500000	−	0.866025i	0.500000	−	0.866025i
$141$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$142$	1.73205	−	1.00000i	1.73205	−	1.00000i
$143$		0			0
$144$	−1.00000			−1.00000
$145$	1.00000	−	1.00000i	1.00000	−	1.00000i
$146$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$147$		0			0
$148$	0.866025	+	0.500000i	0.866025	+	0.500000i
$149$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$149$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$150$	1.00000	−	1.00000i	1.00000	−	1.00000i
$151$	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
$153$	0.500000	−	0.866025i	0.500000	−	0.866025i
$154$		−	2.00000i		−	2.00000i
$155$		0			0
$156$		0			0
$157$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$157$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$158$		0			0
$159$		0			0
$160$	0.366025	−	1.36603i	0.366025	−	1.36603i
$161$		−	1.00000i		−	1.00000i
$162$	1.36603	−	0.366025i	1.36603	−	0.366025i
$163$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$163$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$164$		0			0
$165$	0.366025	−	1.36603i	0.366025	−	1.36603i
$166$	1.00000	−	1.73205i	1.00000	−	1.73205i
$167$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$167$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$168$		0			0
$169$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$170$	1.00000	+	1.00000i	1.00000	+	1.00000i
$171$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$172$		0			0
$173$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$173$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$174$			2.00000i			2.00000i
$175$	0.866025	+	0.500000i	0.866025	+	0.500000i
$176$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$177$			1.00000i			1.00000i
$178$	1.36603	+	0.366025i	1.36603	+	0.366025i
$179$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$179$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$180$			1.00000i			1.00000i
$181$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$181$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$182$		0			0
$183$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$184$		0			0
$185$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$186$		0			0
$187$	1.36603	+	0.366025i	1.36603	+	0.366025i
$188$	1.00000	+	1.00000i	1.00000	+	1.00000i
$189$	0.500000	+	0.866025i	0.500000	+	0.866025i
$190$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$191$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$192$	0.500000	+	0.866025i	0.500000	+	0.866025i
$193$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$193$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$197$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$198$	1.00000	+	1.73205i	1.00000	+	1.73205i
$199$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$199$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$200$		0			0
$201$		0			0
$202$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$203$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$204$	−1.00000			−1.00000
$205$		0			0
$206$		0			0
$207$	0.500000	+	0.866025i	0.500000	+	0.866025i
$208$		0			0
$209$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$210$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$211$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	−0.866025	−	0.500000i	$-0.833333\pi$
$211$	−0.366025	−	1.36603i	−0.366025	−	1.36603i	0.500000	−	0.866025i	$-0.333333\pi$
$212$		0			0
$213$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	1.73205	−	1.00000i	1.73205	−	1.00000i
$219$	0.500000	+	0.866025i	0.500000	+	0.866025i
$220$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$221$		0			0
$222$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$223$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$223$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$224$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$225$	−1.00000			−1.00000
$226$	1.00000	+	1.00000i	1.00000	+	1.00000i
$227$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$227$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$228$	1.00000			1.00000
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$229$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$230$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$231$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$232$		0			0
$233$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$233$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$234$		0			0
$235$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$236$	0.866025	−	0.500000i	0.866025	−	0.500000i
$237$		0			0
$238$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$239$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$239$	1.73205	+	1.00000i	1.73205	+	1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$240$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$241$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	0.500000	+	0.866025i	$0.333333\pi$
$241$	−0.366025	+	1.36603i	−0.366025	+	1.36603i	−0.866025	+	0.500000i	$0.833333\pi$
$242$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$243$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$244$	1.00000	+	1.00000i	1.00000	+	1.00000i
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$250$	0.366025	−	1.36603i	0.366025	−	1.36603i
$251$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$251$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$252$	0.500000	−	0.866025i	0.500000	−	0.866025i
$253$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$254$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$255$		−	1.00000i		−	1.00000i
$256$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$257$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$257$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$258$		0			0
$259$	0.866025	−	0.500000i	0.866025	−	0.500000i
$260$		0			0
$261$	1.00000	−	1.00000i	1.00000	−	1.00000i
$262$		0			0
$263$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$263$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$264$		0			0
$265$		0			0
$266$	0.366025	+	1.36603i	0.366025	+	1.36603i
$267$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$268$		0			0
$269$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$269$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$270$	1.00000	−	1.00000i	1.00000	−	1.00000i
$271$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$271$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$272$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$273$		0			0
$274$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$275$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$276$	0.500000	−	0.866025i	0.500000	−	0.866025i
$277$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$277$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$281$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$282$		−	2.00000i		−	2.00000i
$283$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$283$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$284$	0.366025	+	1.36603i	0.366025	+	1.36603i
$285$			1.00000i			1.00000i
$286$		0			0
$287$		0			0
$288$	0.366025	−	1.36603i	0.366025	−	1.36603i
$289$	1.00000			1.00000
$290$	1.00000	+	1.73205i	1.00000	+	1.73205i
$291$		0			0
$292$	0.500000	−	0.866025i	0.500000	−	0.866025i
$293$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$293$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$294$		0			0
$295$	0.500000	+	0.866025i	0.500000	+	0.866025i
$296$		0			0
$297$	0.366025	−	1.36603i	0.366025	−	1.36603i
$298$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$299$		0			0
$300$	0.500000	+	0.866025i	0.500000	+	0.866025i
$301$		0			0
$302$	0.366025	+	1.36603i	0.366025	+	1.36603i
$303$	0.866025	+	0.500000i	0.866025	+	0.500000i
$304$	0.500000	+	0.866025i	0.500000	+	0.866025i
$305$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$306$	1.00000	+	1.00000i	1.00000	+	1.00000i
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$	1.36603	+	0.366025i	1.36603	+	0.366025i
$309$		0			0
$310$		0			0
$311$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$311$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$313$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$314$		0			0
$315$	0.866025	+	0.500000i	0.866025	+	0.500000i
$316$		0			0
$317$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$317$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$318$		0			0
$319$	1.73205	+	1.00000i	1.73205	+	1.00000i
$320$	0.866025	+	0.500000i	0.866025	+	0.500000i
$321$		0			0
$322$	1.36603	+	0.366025i	1.36603	+	0.366025i
$323$	−1.00000			−1.00000
$324$			1.00000i			1.00000i
$325$		0			0
$326$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$327$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$328$		0			0
$329$	1.36603	−	0.366025i	1.36603	−	0.366025i
$330$	1.73205	+	1.00000i	1.73205	+	1.00000i
$331$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$331$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$332$	1.00000	+	1.00000i	1.00000	+	1.00000i
$333$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$334$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$335$		0			0
$336$	1.00000			1.00000
$337$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$337$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$338$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$339$		−	1.00000i		−	1.00000i
$340$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$341$		0			0
$342$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$343$		−	1.00000i		−	1.00000i
$344$		0			0
$345$	0.866025	+	0.500000i	0.866025	+	0.500000i
$346$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$347$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$347$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$348$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$349$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$349$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$350$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$351$		0			0
$352$	2.00000			2.00000
$353$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$353$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$354$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$355$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$356$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$357$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$358$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$359$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$359$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$360$		0			0
$361$		0			0
$362$		0			0
$363$	1.00000			1.00000
$364$		0			0
$365$	0.866025	+	0.500000i	0.866025	+	0.500000i
$366$		−	2.00000i		−	2.00000i
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$367$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$368$	1.00000			1.00000
$369$		0			0
$370$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$371$		0			0
$372$		0			0
$373$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$373$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$374$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$375$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$376$		0			0
$377$		0			0
$378$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$379$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$379$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$380$	0.866025	−	0.500000i	0.866025	−	0.500000i
$381$	1.36603	+	0.366025i	1.36603	+	0.366025i
$382$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$383$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$383$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$384$		0			0
$385$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$		0			0
$391$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$392$		0			0
$393$		0			0
$394$	1.36603	+	0.366025i	1.36603	+	0.366025i
$395$		0			0
$396$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$	0.500000	−	0.866025i	0.500000	−	0.866025i
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$401$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$402$		0			0
$403$		0			0
$404$		−	1.00000i		−	1.00000i
$405$	−1.00000			−1.00000
$406$		−	2.00000i		−	2.00000i
$407$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$408$		0			0
$409$	−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	$0.833333\pi$
$410$		0			0
$411$	1.36603	−	0.366025i	1.36603	−	0.366025i
$412$		0			0
$413$		−	1.00000i		−	1.00000i
$414$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$415$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$416$		0			0
$417$		0			0
$418$	1.00000	−	1.73205i	1.00000	−	1.73205i
$419$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$419$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$420$		−	1.00000i		−	1.00000i
$421$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$421$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$422$	2.00000			2.00000
$423$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$424$		0			0
$425$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$426$	1.00000	−	1.73205i	1.00000	−	1.73205i
$427$	1.36603	−	0.366025i	1.36603	−	0.366025i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$431$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$432$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$433$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$433$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$434$		0			0
$435$	0.366025	−	1.36603i	0.366025	−	1.36603i
$436$	0.366025	+	1.36603i	0.366025	+	1.36603i
$437$	0.500000	−	0.866025i	0.500000	−	0.866025i
$438$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$439$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$439$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$443$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$444$	1.00000			1.00000
$445$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$446$		0			0
$447$	1.00000			1.00000
$448$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$449$	1.00000	+	1.00000i	1.00000	+	1.00000i	1.00000			$0$
$449$	1.00000	+	1.00000i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$450$	0.366025	−	1.36603i	0.366025	−	1.36603i
$451$		0			0
$452$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$453$	0.500000	−	0.866025i	0.500000	−	0.866025i
$454$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$455$		0			0
$456$		0			0
$457$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$457$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$458$	1.00000	+	1.00000i	1.00000	+	1.00000i
$459$		−	1.00000i		−	1.00000i
$460$		−	1.00000i		−	1.00000i
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$463$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$463$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$464$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$465$		0			0
$466$	1.36603	+	0.366025i	1.36603	+	0.366025i
$467$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$467$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$468$		0			0
$469$		0			0
$470$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	0.500000	+	0.866025i	0.500000	+	0.866025i
$476$	1.00000			1.00000
$477$		0			0
$478$	−2.00000	+	2.00000i	−2.00000	+	2.00000i
$479$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$479$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$480$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$481$		0			0
$482$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$483$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$484$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$485$		0			0
$486$	1.00000	−	1.00000i	1.00000	−	1.00000i
$487$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$487$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$488$		0			0
$489$	0.866025	−	0.500000i	0.866025	−	0.500000i
$490$		0			0
$491$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$491$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$492$		0			0
$493$	1.36603	+	0.366025i	1.36603	+	0.366025i
$494$		0			0
$495$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$496$		0			0
$497$	1.36603	+	0.366025i	1.36603	+	0.366025i
$498$		−	2.00000i		−	2.00000i
$499$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$499$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$500$	0.866025	+	0.500000i	0.866025	+	0.500000i
$501$			1.00000i			1.00000i
$502$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$503$	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			0
$505$	1.00000			1.00000
$506$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$507$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$508$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$509$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$510$	1.36603	+	0.366025i	1.36603	+	0.366025i
$511$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$512$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$513$			1.00000i			1.00000i
$514$			2.00000i			2.00000i
$515$		0			0
$516$		0			0
$517$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$518$	0.366025	+	1.36603i	0.366025	+	1.36603i
$519$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$520$		0			0
$521$	−1.00000	+	1.00000i	−1.00000	+	1.00000i			1.00000i	$0.5\pi$
$521$	−1.00000	+	1.00000i	−1.00000	+	1.00000i	−1.00000			$\pi$
$522$	1.00000	+	1.73205i	1.00000	+	1.73205i
$523$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$523$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$524$		0			0
$525$	1.00000			1.00000
$526$		0			0
$527$		0			0
$528$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$529$		0			0
$530$		0			0
$531$	0.500000	+	0.866025i	0.500000	+	0.866025i
$532$	−1.00000			−1.00000
$533$		0			0
$534$	1.36603	−	0.366025i	1.36603	−	0.366025i
$535$		0			0
$536$		0			0
$537$	0.866025	−	0.500000i	0.866025	−	0.500000i
$538$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$539$		0			0
$540$	0.500000	+	0.866025i	0.500000	+	0.866025i
$541$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$541$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$542$	0.366025	−	1.36603i	0.366025	−	1.36603i
$543$		0			0
$544$	1.36603	−	0.366025i	1.36603	−	0.366025i
$545$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$546$		0			0
$547$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$547$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$548$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$549$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$550$	2.00000			2.00000
$551$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$552$		0			0
$553$		0			0
$554$	1.36603	−	0.366025i	1.36603	−	0.366025i
$555$			1.00000i			1.00000i
$556$		0			0
$557$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$557$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$558$		0			0
$559$		0			0
$560$	0.866025	−	0.500000i	0.866025	−	0.500000i
$561$	1.36603	−	0.366025i	1.36603	−	0.366025i
$562$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$563$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$563$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$564$	1.36603	+	0.366025i	1.36603	+	0.366025i
$565$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$566$		0			0
$567$	0.866025	+	0.500000i	0.866025	+	0.500000i
$568$		0			0
$569$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$569$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$570$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$571$	0.366025	+	1.36603i	0.366025	+	1.36603i	0.866025	+	0.500000i	$0.166667\pi$
$571$	0.366025	+	1.36603i	0.366025	+	1.36603i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$	0.866025	+	0.500000i	0.866025	+	0.500000i
$574$		0			0
$575$	1.00000			1.00000
$576$	0.866025	+	0.500000i	0.866025	+	0.500000i
$577$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$577$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$578$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$579$		0			0
$580$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$581$	1.36603	−	0.366025i	1.36603	−	0.366025i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$587$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$588$		0			0
$589$		0			0
$590$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$591$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$592$	0.500000	+	0.866025i	0.500000	+	0.866025i
$593$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$593$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$594$	1.73205	+	1.00000i	1.73205	+	1.00000i
$595$			1.00000i			1.00000i
$596$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$597$		0			0
$598$		0			0
$599$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$599$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$600$		0			0
$601$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$601$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$602$		0			0
$603$		0			0
$604$	−1.00000			−1.00000
$605$	0.866025	−	0.500000i	0.866025	−	0.500000i
$606$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$607$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$607$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$608$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$609$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$610$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$611$		0			0
$612$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$613$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$613$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$617$	−1.00000	+	1.73205i	−1.00000	+	1.73205i	−0.500000	+	0.866025i	$0.666667\pi$
$618$		0			0
$619$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$619$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$620$		0			0
$621$	0.866025	+	0.500000i	0.866025	+	0.500000i
$622$			2.00000i			2.00000i
$623$	0.500000	+	0.866025i	0.500000	+	0.866025i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$626$		0			0
$627$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$628$		0			0
$629$	−1.00000			−1.00000
$630$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$634$		0			0
$635$	1.36603	−	0.366025i	1.36603	−	0.366025i
$636$		0			0
$637$		0			0
$638$	−2.00000	+	2.00000i	−2.00000	+	2.00000i
$639$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$640$		0			0
$641$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$641$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$642$		0			0
$643$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$643$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$644$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$645$		0			0
$646$	0.366025	−	1.36603i	0.366025	−	1.36603i
$647$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$647$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$648$		0			0
$649$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$650$		0			0
$651$		0			0
$652$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$653$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$653$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$654$	1.00000	−	1.73205i	1.00000	−	1.73205i
$655$		0			0
$656$		0			0
$657$	0.866025	+	0.500000i	0.866025	+	0.500000i
$658$			2.00000i			2.00000i
$659$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$659$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$660$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$661$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$661$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$662$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$663$		0			0
$664$		0			0
$665$		−	1.00000i		−	1.00000i
$666$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$667$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$668$	0.866025	−	0.500000i	0.866025	−	0.500000i
$669$		0			0
$670$		0			0
$671$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$672$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$673$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$674$		0			0
$675$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$676$	1.00000			1.00000
$677$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$677$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$678$	1.36603	+	0.366025i	1.36603	+	0.366025i
$679$		0			0
$680$		0			0
$681$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$682$		0			0
$683$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$683$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$684$	0.866025	−	0.500000i	0.866025	−	0.500000i
$685$	1.00000	−	1.00000i	1.00000	−	1.00000i
$686$	1.36603	+	0.366025i	1.36603	+	0.366025i
$687$		−	1.00000i		−	1.00000i
$688$		0			0
$689$		0			0
$690$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$691$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.866025	−	0.500000i	$-0.166667\pi$
$691$	1.36603	+	0.366025i	1.36603	+	0.366025i	0.500000	+	0.866025i	$0.333333\pi$
$692$	1.00000			1.00000
$693$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$694$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$700$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$701$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$701$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$702$		0			0
$703$	1.00000			1.00000
$704$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$705$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$706$	1.73205	+	1.00000i	1.73205	+	1.00000i
$707$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$708$	0.500000	−	0.866025i	0.500000	−	0.866025i
$709$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$709$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$710$		−	2.00000i		−	2.00000i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$715$		0			0
$716$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$717$	2.00000			2.00000
$718$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$719$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$719$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$720$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$721$		0			0
$722$		0			0
$723$	0.366025	+	1.36603i	0.366025	+	1.36603i
$724$		0			0
$725$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$726$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$727$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$727$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$728$		0			0
$729$	−1.00000			−1.00000
$730$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$731$		0			0
$732$	1.36603	+	0.366025i	1.36603	+	0.366025i
$733$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$733$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$734$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$735$		0			0
$736$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$737$		0			0
$738$		0			0
$739$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$739$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$740$	0.866025	−	0.500000i	0.866025	−	0.500000i
$741$		0			0
$742$		0			0
$743$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$743$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$744$		0			0
$745$	0.866025	−	0.500000i	0.866025	−	0.500000i
$746$			2.00000i			2.00000i
$747$	−1.00000	+	1.00000i	−1.00000	+	1.00000i
$748$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$749$		0			0
$750$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$751$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$751$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$752$	0.366025	+	1.36603i	0.366025	+	1.36603i
$753$	0.866025	−	0.500000i	0.866025	−	0.500000i
$754$		0			0
$755$		−	1.00000i		−	1.00000i
$756$		−	1.00000i		−	1.00000i
$757$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$757$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$758$		0			0
$759$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$760$		0			0
$761$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$761$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$762$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$763$	1.36603	+	0.366025i	1.36603	+	0.366025i
$764$		−	1.00000i		−	1.00000i
$765$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$766$		0			0
$767$		0			0
$768$			1.00000i			1.00000i
$769$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$769$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$770$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$771$	1.00000	−	1.00000i	1.00000	−	1.00000i
$772$		0			0
$773$	1.00000	−	1.00000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$773$	1.00000	−	1.00000i	1.00000	−	1.00000i	1.00000			$0$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	0.500000	−	0.866025i	0.500000	−	0.866025i
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$782$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$783$	0.366025	−	1.36603i	0.366025	−	1.36603i
$784$		0			0
$785$		0			0
$786$		0			0
$787$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$787$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$788$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$789$		0			0
$790$		0			0
$791$			1.00000i			1.00000i
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$797$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$798$	1.00000	+	1.00000i	1.00000	+	1.00000i
$799$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$800$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$801$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$802$		0			0
$803$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$804$		0			0
$805$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$806$		0			0
$807$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$808$		0			0
$809$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$809$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$810$	0.366025	−	1.36603i	0.366025	−	1.36603i
$811$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$811$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$812$	1.36603	+	0.366025i	1.36603	+	0.366025i
$813$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$814$	1.00000	−	1.73205i	1.00000	−	1.73205i
$815$	0.500000	−	0.866025i	0.500000	−	0.866025i
$816$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$817$		0			0
$818$	1.00000	−	1.00000i	1.00000	−	1.00000i
$819$		0			0
$820$		0			0
$821$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$821$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$822$			2.00000i			2.00000i
$823$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$823$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$824$		0			0
$825$	−1.00000	−	1.00000i	−1.00000	−	1.00000i
$826$	1.36603	+	0.366025i	1.36603	+	0.366025i
$827$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$827$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$828$		−	1.00000i		−	1.00000i
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$831$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.500000	+	0.866025i	0.500000	+	0.866025i
$836$	1.00000	+	1.00000i	1.00000	+	1.00000i
$837$		0			0
$838$		0			0
$839$	0.366025	−	1.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$839$	0.366025	−	1.36603i	0.366025	−	1.36603i	0.866025	−	0.500000i	$-0.166667\pi$
$840$		0			0
$841$	0.866025	+	0.500000i	0.866025	+	0.500000i
$842$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$843$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$844$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$845$			1.00000i			1.00000i
$846$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$847$	−1.00000			−1.00000
$848$		0			0
$849$		0			0
$850$	1.36603	−	0.366025i	1.36603	−	0.366025i
$851$	0.500000	−	0.866025i	0.500000	−	0.866025i
$852$	1.00000	+	1.00000i	1.00000	+	1.00000i
$853$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$853$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$854$			2.00000i			2.00000i
$855$	0.500000	+	0.866025i	0.500000	+	0.866025i
$856$		0			0
$857$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$857$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$		0			0
$861$		0			0
$862$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$863$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$863$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$864$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$865$			1.00000i			1.00000i
$866$	1.00000	+	1.73205i	1.00000	+	1.73205i
$867$	0.866025	−	0.500000i	0.866025	−	0.500000i
$868$		0			0
$869$		0			0
$870$	1.73205	+	1.00000i	1.73205	+	1.00000i
$871$		0			0
$872$		0			0
$873$		0			0
$874$	1.00000	+	1.00000i	1.00000	+	1.00000i
$875$	0.866025	−	0.500000i	0.866025	−	0.500000i
$876$		−	1.00000i		−	1.00000i
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$		0			0
$880$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$881$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$881$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$882$		0			0
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$		0			0
$885$	0.866025	+	0.500000i	0.866025	+	0.500000i
$886$		0			0
$887$	−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			0
$889$	−1.36603	−	0.366025i	−1.36603	−	0.366025i
$890$	1.00000	−	1.00000i	1.00000	−	1.00000i
$891$	−0.366025	−	1.36603i	−0.366025	−	1.36603i
$892$		0			0
$893$	1.36603	+	0.366025i	1.36603	+	0.366025i
$894$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$895$	0.500000	−	0.866025i	0.500000	−	0.866025i
$896$		0			0
$897$		0			0
$898$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$899$		0			0
$900$	0.866025	+	0.500000i	0.866025	+	0.500000i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	1.00000	+	1.00000i	1.00000	+	1.00000i
$907$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$907$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$908$	1.00000			1.00000
$909$	1.00000			1.00000
$910$		0			0
$911$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.500000	−	0.866025i	$-0.666667\pi$
$911$	−1.36603	−	0.366025i	−1.36603	−	0.366025i	−0.866025	+	0.500000i	$0.833333\pi$
$912$	0.866025	+	0.500000i	0.866025	+	0.500000i
$913$	−1.73205	−	1.00000i	−1.73205	−	1.00000i
$914$		0			0
$915$	−0.366025	+	1.36603i	−0.366025	+	1.36603i
$916$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$917$		0			0
$918$	1.36603	+	0.366025i	1.36603	+	0.366025i
$919$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$919$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$	1.36603	−	0.366025i	1.36603	−	0.366025i
$925$	0.500000	+	0.866025i	0.500000	+	0.866025i
$926$		0			0
$927$		0			0
$928$	2.00000			2.00000
$929$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$929$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$930$		0			0
$931$		0			0
$932$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$933$	1.00000	−	1.00000i	1.00000	−	1.00000i
$934$		0			0
$935$	1.00000	−	1.00000i	1.00000	−	1.00000i
$936$		0			0
$937$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$937$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$938$		0			0
$939$		0			0
$940$	1.36603	−	0.366025i	1.36603	−	0.366025i
$941$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$941$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$942$		0			0
$943$		0			0
$944$	1.00000			1.00000
$945$	1.00000			1.00000
$946$		0			0
$947$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$947$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$948$		0			0
$949$		0			0
$950$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$951$		0			0
$952$		0			0
$953$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$953$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$954$		0			0
$955$	1.00000			1.00000
$956$	−1.00000	−	1.73205i	−1.00000	−	1.73205i
$957$	2.00000			2.00000
$958$		0			0
$959$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$960$	1.00000			1.00000
$961$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$962$		0			0
$963$		0			0
$964$	1.00000	−	1.00000i	1.00000	−	1.00000i
$965$		0			0
$966$	1.36603	−	0.366025i	1.36603	−	0.366025i
$967$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$967$	1.36603	−	0.366025i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$968$		0			0
$969$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$970$		0			0
$971$		0			0		1.00000			$0$
$971$		0			0		−1.00000			$\pi$
$972$	0.500000	+	0.866025i	0.500000	+	0.866025i
$973$		0			0
$974$	1.36603	+	0.366025i	1.36603	+	0.366025i
$975$		0			0
$976$	0.366025	+	1.36603i	0.366025	+	1.36603i
$977$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$977$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$978$	0.366025	+	1.36603i	0.366025	+	1.36603i
$979$	0.366025	−	1.36603i	0.366025	−	1.36603i
$980$		0			0
$981$	−1.36603	+	0.366025i	−1.36603	+	0.366025i
$982$	1.00000	−	1.00000i	1.00000	−	1.00000i
$983$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$983$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$984$		0			0
$985$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$986$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$987$	1.00000	−	1.00000i	1.00000	−	1.00000i
$988$		0			0
$989$		0			0
$990$	2.00000			2.00000
$991$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$991$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$992$		0			0
$993$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$994$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$995$		0			0
$996$	1.36603	+	0.366025i	1.36603	+	0.366025i
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$			1.00000i			1.00000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.1.bs.b.13.1	yes	4
3.2	odd	2		2295.1.bt.a.523.1		4
5.2	odd	4		765.1.bn.a.472.1	yes	4
5.3	odd	4		3825.1.bv.b.3532.1		4
5.4	even	2		3825.1.ca.a.1543.1		4
9.2	odd	6		2295.1.bt.a.1288.1		4
9.7	even	3	inner	765.1.bs.b.268.1	yes	4
15.2	even	4		2295.1.bo.b.982.1		4
17.4	even	4		765.1.bn.a.463.1	✓	4
45.2	even	12		2295.1.bo.b.1747.1		4
45.7	odd	12		765.1.bn.a.727.1	yes	4
45.34	even	6		3825.1.ca.a.268.1		4
45.43	odd	12		3825.1.bv.b.2257.1		4
51.38	odd	4		2295.1.bo.b.1738.1		4
85.4	even	4		3825.1.bv.b.1993.1		4
85.38	odd	4		3825.1.ca.a.157.1		4
85.72	odd	4	inner	765.1.bs.b.157.1	yes	4
153.38	odd	12		2295.1.bo.b.208.1		4
153.106	even	12		765.1.bn.a.718.1	yes	4
255.242	even	4		2295.1.bt.a.2197.1		4
765.259	even	12		3825.1.bv.b.718.1		4
765.412	odd	12	inner	765.1.bs.b.412.1	yes	4
765.497	even	12		2295.1.bt.a.667.1		4
765.718	odd	12		3825.1.ca.a.2707.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
765.1.bn.a.463.1	✓	4	17.4	even	4
765.1.bn.a.472.1	yes	4	5.2	odd	4
765.1.bn.a.718.1	yes	4	153.106	even	12
765.1.bn.a.727.1	yes	4	45.7	odd	12
765.1.bs.b.13.1	yes	4	1.1	even	1	trivial
765.1.bs.b.157.1	yes	4	85.72	odd	4	inner
765.1.bs.b.268.1	yes	4	9.7	even	3	inner
765.1.bs.b.412.1	yes	4	765.412	odd	12	inner
2295.1.bo.b.208.1		4	153.38	odd	12
2295.1.bo.b.982.1		4	15.2	even	4
2295.1.bo.b.1738.1		4	51.38	odd	4
2295.1.bo.b.1747.1		4	45.2	even	12
2295.1.bt.a.523.1		4	3.2	odd	2
2295.1.bt.a.667.1		4	765.497	even	12
2295.1.bt.a.1288.1		4	9.2	odd	6
2295.1.bt.a.2197.1		4	255.242	even	4
3825.1.bv.b.718.1		4	765.259	even	12
3825.1.bv.b.1993.1		4	85.4	even	4
3825.1.bv.b.2257.1		4	45.43	odd	12
3825.1.bv.b.3532.1		4	5.3	odd	4
3825.1.ca.a.157.1		4	85.38	odd	4
3825.1.ca.a.268.1		4	45.34	even	6
3825.1.ca.a.1543.1		4	5.4	even	2
3825.1.ca.a.2707.1		4	765.718	odd	12

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:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	765.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 + 1.36603i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.366025 + 1.36603i) q^{6} +(-0.866025 + 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(1.00000 + 1.00000i) q^{10} +(1.36603 + 0.366025i) q^{11} -1.00000 q^{12} +(-0.366025 - 1.36603i) q^{14} -1.00000i q^{15} +(-0.500000 - 0.866025i) q^{16} +1.00000 q^{17} +(1.00000 + 1.00000i) q^{18} -1.00000 q^{19} +(-0.866025 + 0.500000i) q^{20} +(-0.500000 + 0.866025i) q^{21} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000i q^{27} +1.00000 q^{28} +(1.36603 + 0.366025i) q^{29} +(1.36603 + 0.366025i) q^{30} +(1.36603 - 0.366025i) q^{32} +(1.36603 - 0.366025i) q^{33} +(-0.366025 + 1.36603i) q^{34} +1.00000i q^{35} +(-0.866025 + 0.500000i) q^{36} -1.00000 q^{37} +(0.366025 - 1.36603i) q^{38} +(-1.00000 - 1.00000i) q^{42} +(-1.00000 - 1.00000i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-1.00000 - 1.00000i) q^{46} +(-1.36603 - 0.366025i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.36603 - 0.366025i) q^{50} +(0.866025 - 0.500000i) q^{51} +(1.36603 + 0.366025i) q^{54} +(1.00000 - 1.00000i) q^{55} +(-0.866025 + 0.500000i) q^{57} +(-1.00000 + 1.73205i) q^{58} +(-0.500000 + 0.866025i) q^{59} +(-0.500000 + 0.866025i) q^{60} +(-1.36603 - 0.366025i) q^{61} +1.00000i q^{63} +1.00000i q^{64} +2.00000i q^{66} +(-0.866025 - 0.500000i) q^{68} +1.00000i q^{69} +(-1.36603 - 0.366025i) q^{70} +(-1.00000 - 1.00000i) q^{71} +1.00000i q^{73} +(0.366025 - 1.36603i) q^{74} +(-0.866025 - 0.500000i) q^{75} +(0.866025 + 0.500000i) q^{76} +(-1.36603 + 0.366025i) q^{77} -1.00000 q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.36603 - 0.366025i) q^{83} +(0.866025 - 0.500000i) q^{84} +(0.500000 - 0.866025i) q^{85} +(1.36603 - 0.366025i) q^{87} -1.00000i q^{89} +(1.36603 - 0.366025i) q^{90} +(0.866025 - 0.500000i) q^{92} +(1.00000 - 1.73205i) q^{94} +(-0.500000 + 0.866025i) q^{95} +(1.00000 - 1.00000i) q^{96} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{5} - 2 q^{6} + 2 q^{9} + 4 q^{10} + 2 q^{11} - 4 q^{12} + 2 q^{14} - 2 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} - 2 q^{21} - 4 q^{22} - 2 q^{23} - 2 q^{25} + 4 q^{28} + 2 q^{29} + 2 q^{30}+ \cdots + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^5 - 2 * q^6 + 2 * q^9 + 4 * q^10 + 2 * q^11 - 4 * q^12 + 2 * q^14 - 2 * q^16 + 4 * q^17 + 4 * q^18 - 4 * q^19 - 2 * q^21 - 4 * q^22 - 2 * q^23 - 2 * q^25 + 4 * q^28 + 2 * q^29 + 2 * q^30 + 2 * q^32 + 2 * q^33 + 2 * q^34 - 4 * q^37 - 2 * q^38 - 4 * q^42 - 4 * q^44 - 2 * q^45 - 4 * q^46 - 2 * q^47 + 2 * q^50 + 2 * q^54 + 4 * q^55 - 4 * q^58 - 2 * q^59 - 2 * q^60 - 2 * q^61 - 2 * q^70 - 4 * q^71 - 2 * q^74 - 2 * q^77 - 4 * q^80 - 2 * q^81 - 2 * q^83 + 2 * q^85 + 2 * q^87 + 2 * q^90 + 4 * q^94 - 2 * q^95 + 4 * q^96 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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