LMFDB - Embedded newform 201.1.g.a.29.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [201,1,Mod(29,201)] 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("201.29"); S:= CuspForms(chi, 1); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(201, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 4])) B = ModularForms(chi, 1).cuspidal_submodule().basis() N = [B[i] for i in range(len(B))]

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	201.g (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.100312067539$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{4}$
Projective field:	Galois closure of 4.0.40401.1
Artin image:	$\SL(2,3):C_2$
Artin field:	Galois closure of $\mathbb{Q}[x]/(x^{16} - \cdots)$

Embedding invariants

Embedding label			29.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	201.29
Dual form			201.1.g.a.104.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-0.866025 + 0.500000i) q^{11} +(-0.500000 + 0.866025i) q^{13} -1.00000i q^{14} +(0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.866025 - 0.500000i) q^{21} -1.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +1.00000 q^{24} +1.00000 q^{25} +(-0.866025 + 0.500000i) q^{26} -1.00000i q^{27} +(-0.866025 + 0.500000i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(0.500000 + 0.866025i) q^{34} +(-0.500000 + 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{38} +(-0.866025 - 0.500000i) q^{39} +(0.866025 - 0.500000i) q^{41} +1.00000 q^{42} +(-0.500000 - 0.866025i) q^{46} +(-0.866025 + 0.500000i) q^{47} +(0.866025 + 0.500000i) q^{48} +(0.866025 + 0.500000i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(0.500000 - 0.866025i) q^{54} +(-0.866025 + 0.500000i) q^{56} +(0.866025 + 0.500000i) q^{57} -1.00000 q^{58} +(-0.500000 + 0.866025i) q^{61} +1.00000i q^{62} +(0.500000 + 0.866025i) q^{63} -1.00000 q^{64} -1.00000i q^{66} -1.00000 q^{67} +(0.500000 - 0.866025i) q^{69} +(0.866025 - 0.500000i) q^{71} +1.00000i q^{72} +(0.500000 - 0.866025i) q^{73} +(-0.866025 + 0.500000i) q^{74} +1.00000i q^{75} +(0.866025 + 0.500000i) q^{77} +(-0.500000 - 0.866025i) q^{78} +(-0.500000 - 0.866025i) q^{79} +1.00000 q^{81} +1.00000 q^{82} +(0.866025 + 0.500000i) q^{83} +(-0.500000 - 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{88} -2.00000i q^{89} +1.00000 q^{91} +(-0.866025 + 0.500000i) q^{93} -1.00000 q^{94} +(-0.500000 + 0.866025i) q^{97} +(0.866025 - 0.500000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{6} - 2 q^{7} - 4 q^{9} - 2 q^{13} + 2 q^{16} + 2 q^{19} - 4 q^{22} + 4 q^{24} + 4 q^{25} + 2 q^{31} - 2 q^{33} + 2 q^{34} - 2 q^{37} + 4 q^{42} - 2 q^{46} - 2 q^{51} + 2 q^{54} - 4 q^{58} - 2 q^{61}+ \cdots - 2 q^{97}+O(q^{100}) $ 4 * q - 2 * q^6 - 2 * q^7 - 4 * q^9 - 2 * q^13 + 2 * q^16 + 2 * q^19 - 4 * q^22 + 4 * q^24 + 4 * q^25 + 2 * q^31 - 2 * q^33 + 2 * q^34 - 2 * q^37 + 4 * q^42 - 2 * q^46 - 2 * q^51 + 2 * q^54 - 4 * q^58 - 2 * q^61 + 2 * q^63 - 4 * q^64 - 4 * q^67 + 2 * q^69 + 2 * q^73 - 2 * q^78 - 2 * q^79 + 4 * q^81 + 4 * q^82 - 2 * q^87 + 2 * q^88 + 4 * q^91 - 4 * q^94 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$2$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$3$			1.00000i			1.00000i
$3$			1.00000i			1.00000i
$4$		0			0
$5$		0			0		1.00000			$0$
$5$		0			0		−1.00000			$\pi$
$6$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$7$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$7$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$8$		−	1.00000i		−	1.00000i
$9$	−1.00000			−1.00000
$10$		0			0
$11$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$11$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$13$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$14$		−	1.00000i		−	1.00000i
$15$		0			0
$16$	0.500000	−	0.866025i	0.500000	−	0.866025i
$17$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$17$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$18$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$19$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$20$		0			0
$21$	0.866025	−	0.500000i	0.866025	−	0.500000i
$22$	−1.00000			−1.00000
$23$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$23$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$24$	1.00000			1.00000
$25$	1.00000			1.00000
$26$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$27$		−	1.00000i		−	1.00000i
$28$		0			0
$29$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$29$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$31$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$32$		0			0
$33$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$34$	0.500000	+	0.866025i	0.500000	+	0.866025i
$35$		0			0
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$37$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$38$	0.866025	−	0.500000i	0.866025	−	0.500000i
$39$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$40$		0			0
$41$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$41$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$42$	1.00000			1.00000
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$47$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$47$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$48$	0.866025	+	0.500000i	0.866025	+	0.500000i
$49$		0			0
$50$	0.866025	+	0.500000i	0.866025	+	0.500000i
$51$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$52$		0			0
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	0.500000	−	0.866025i	0.500000	−	0.866025i
$55$		0			0
$56$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$57$	0.866025	+	0.500000i	0.866025	+	0.500000i
$58$	−1.00000			−1.00000
$59$		0			0		1.00000			$0$
$59$		0			0		−1.00000			$\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$61$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$62$			1.00000i			1.00000i
$63$	0.500000	+	0.866025i	0.500000	+	0.866025i
$64$	−1.00000			−1.00000
$65$		0			0
$66$		−	1.00000i		−	1.00000i
$67$	−1.00000			−1.00000
$67$	−1.00000			−1.00000
$68$		0			0
$69$	0.500000	−	0.866025i	0.500000	−	0.866025i
$70$		0			0
$71$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$71$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$72$			1.00000i			1.00000i
$73$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$73$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$74$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$75$			1.00000i			1.00000i
$76$		0			0
$77$	0.866025	+	0.500000i	0.866025	+	0.500000i
$78$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$79$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$79$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$80$		0			0
$81$	1.00000			1.00000
$82$	1.00000			1.00000
$83$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$83$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$88$	0.500000	+	0.866025i	0.500000	+	0.866025i
$89$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$89$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$90$		0			0
$91$	1.00000			1.00000
$92$		0			0
$93$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$94$	−1.00000			−1.00000
$95$		0			0
$96$		0			0
$97$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$97$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$98$		0			0
$99$	0.866025	−	0.500000i	0.866025	−	0.500000i
$100$		0			0
$101$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$101$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$102$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$103$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$103$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$104$	0.866025	+	0.500000i	0.866025	+	0.500000i
$105$		0			0
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$112$	−1.00000			−1.00000
$113$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$113$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$114$	0.500000	+	0.866025i	0.500000	+	0.866025i
$115$		0			0
$116$		0			0
$117$	0.500000	−	0.866025i	0.500000	−	0.866025i
$118$		0			0
$119$		−	1.00000i		−	1.00000i
$120$		0			0
$121$		0			0
$122$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$123$	0.500000	+	0.866025i	0.500000	+	0.866025i
$124$		0			0
$125$		0			0
$126$			1.00000i			1.00000i
$127$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$127$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$128$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$129$		0			0
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		0			0
$133$	−1.00000			−1.00000
$134$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$135$		0			0
$136$	0.500000	−	0.866025i	0.500000	−	0.866025i
$137$		0			0		1.00000			$0$
$137$		0			0		−1.00000			$\pi$
$138$	0.866025	−	0.500000i	0.866025	−	0.500000i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$142$	1.00000			1.00000
$143$		−	1.00000i		−	1.00000i
$144$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$145$		0			0
$146$	0.866025	−	0.500000i	0.866025	−	0.500000i
$147$		0			0
$148$		0			0
$149$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$149$		−	2.00000i		−	2.00000i		−	1.00000i	$-0.5\pi$
$150$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$151$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$151$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$152$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$153$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$154$	0.500000	+	0.866025i	0.500000	+	0.866025i
$155$		0			0
$156$		0			0
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$157$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$158$		−	1.00000i		−	1.00000i
$159$		0			0
$160$		0			0
$161$			1.00000i			1.00000i
$162$	0.866025	+	0.500000i	0.866025	+	0.500000i
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$163$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$	0.500000	+	0.866025i	0.500000	+	0.866025i
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$167$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$168$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$169$		0			0
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$172$		0			0
$173$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$173$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$174$		−	1.00000i		−	1.00000i
$175$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$176$			1.00000i			1.00000i
$177$		0			0
$178$	1.00000	−	1.73205i	1.00000	−	1.73205i
$179$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$179$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$180$		0			0
$181$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$181$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$182$	0.866025	+	0.500000i	0.866025	+	0.500000i
$183$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$184$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$185$		0			0
$186$	−1.00000			−1.00000
$187$	−1.00000			−1.00000
$188$		0			0
$189$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$190$		0			0
$191$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$191$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$192$		−	1.00000i		−	1.00000i
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$195$		0			0
$196$		0			0
$197$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$197$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$198$	1.00000			1.00000
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$199$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$200$		−	1.00000i		−	1.00000i
$201$		−	1.00000i		−	1.00000i
$202$	1.00000			1.00000
$203$	0.866025	+	0.500000i	0.866025	+	0.500000i
$204$		0			0
$205$		0			0
$206$			1.00000i			1.00000i
$207$	0.866025	+	0.500000i	0.866025	+	0.500000i
$208$	0.500000	+	0.866025i	0.500000	+	0.866025i
$209$			1.00000i			1.00000i
$210$		0			0
$211$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$211$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$212$		0			0
$213$	0.500000	+	0.866025i	0.500000	+	0.866025i
$214$		0			0
$215$		0			0
$216$	−1.00000			−1.00000
$217$	0.500000	−	0.866025i	0.500000	−	0.866025i
$218$		0			0
$219$	0.866025	+	0.500000i	0.866025	+	0.500000i
$220$		0			0
$221$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$222$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$		0			0
$225$	−1.00000			−1.00000
$226$	−1.00000			−1.00000
$227$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$227$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$229$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$230$		0			0
$231$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$232$	0.500000	+	0.866025i	0.500000	+	0.866025i
$233$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$233$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$234$	0.866025	−	0.500000i	0.866025	−	0.500000i
$235$		0			0
$236$		0			0
$237$	0.866025	−	0.500000i	0.866025	−	0.500000i
$238$	0.500000	−	0.866025i	0.500000	−	0.866025i
$239$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$239$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$240$		0			0
$241$		0			0			−	1.00000i	$-0.5\pi$
$241$		0			0				1.00000i	$0.5\pi$
$242$		0			0
$243$			1.00000i			1.00000i
$244$		0			0
$245$		0			0
$246$			1.00000i			1.00000i
$247$	0.500000	+	0.866025i	0.500000	+	0.866025i
$248$	0.866025	−	0.500000i	0.866025	−	0.500000i
$249$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$250$		0			0
$251$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$251$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$252$		0			0
$253$	1.00000			1.00000
$254$			1.00000i			1.00000i
$255$		0			0
$256$		0			0
$257$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$257$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$258$		0			0
$259$	1.00000			1.00000
$260$		0			0
$261$	0.866025	−	0.500000i	0.866025	−	0.500000i
$262$		0			0
$263$		0			0		1.00000			$0$
$263$		0			0		−1.00000			$\pi$
$264$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$265$		0			0
$266$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$267$	2.00000			2.00000
$268$		0			0
$269$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$269$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	0.866025	−	0.500000i	0.866025	−	0.500000i
$273$			1.00000i			1.00000i
$274$		0			0
$275$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$276$		0			0
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$		0			0
$279$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$280$		0			0
$281$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$281$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$282$		−	1.00000i		−	1.00000i
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$		0			0
$285$		0			0
$286$	0.500000	−	0.866025i	0.500000	−	0.866025i
$287$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$288$		0			0
$289$		0			0
$290$		0			0
$291$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$		0			0
$295$		0			0
$296$	0.866025	+	0.500000i	0.866025	+	0.500000i
$297$	0.500000	+	0.866025i	0.500000	+	0.866025i
$298$	1.00000	−	1.73205i	1.00000	−	1.73205i
$299$	0.866025	−	0.500000i	0.866025	−	0.500000i
$300$		0			0
$301$		0			0
$302$	0.866025	−	0.500000i	0.866025	−	0.500000i
$303$	0.500000	+	0.866025i	0.500000	+	0.866025i
$304$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$305$		0			0
$306$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$307$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$307$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$308$		0			0
$309$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$313$		0			0			−	1.00000i	$-0.5\pi$
$313$		0			0				1.00000i	$0.5\pi$
$314$	0.866025	−	0.500000i	0.866025	−	0.500000i
$315$		0			0
$316$		0			0
$317$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$317$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$318$		0			0
$319$	0.500000	−	0.866025i	0.500000	−	0.866025i
$320$		0			0
$321$		0			0
$322$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$323$	0.866025	−	0.500000i	0.866025	−	0.500000i
$324$		0			0
$325$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$326$		−	1.00000i		−	1.00000i
$327$		0			0
$328$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$329$	0.866025	+	0.500000i	0.866025	+	0.500000i
$330$		0			0
$331$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$331$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$332$		0			0
$333$	0.500000	−	0.866025i	0.500000	−	0.866025i
$334$	−1.00000			−1.00000
$335$		0			0
$336$		−	1.00000i		−	1.00000i
$337$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$337$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$338$		0			0
$339$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$340$		0			0
$341$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$342$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$343$	−1.00000			−1.00000
$344$		0			0
$345$		0			0
$346$	0.500000	+	0.866025i	0.500000	+	0.866025i
$347$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$347$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$348$		0			0
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		−	1.00000i		−	1.00000i
$351$	0.866025	+	0.500000i	0.866025	+	0.500000i
$352$		0			0
$353$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$353$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.00000			1.00000
$358$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$		0			0
$362$		−	1.00000i		−	1.00000i
$363$		0			0
$364$		0			0
$365$		0			0
$366$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$367$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$367$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$368$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$369$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$373$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$374$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$375$		0			0
$376$	0.500000	+	0.866025i	0.500000	+	0.866025i
$377$		−	1.00000i		−	1.00000i
$378$	−1.00000			−1.00000
$379$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$379$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$380$		0			0
$381$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$382$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$383$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$383$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$384$	0.500000	−	0.866025i	0.500000	−	0.866025i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$389$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−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
$394$	1.00000			1.00000
$395$		0			0
$396$		0			0
$397$		0			0			−	1.00000i	$-0.5\pi$
$397$		0			0				1.00000i	$0.5\pi$
$398$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$399$		−	1.00000i		−	1.00000i
$400$	0.500000	−	0.866025i	0.500000	−	0.866025i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$	0.500000	−	0.866025i	0.500000	−	0.866025i
$403$	−1.00000			−1.00000
$404$		0			0
$405$		0			0
$406$	0.500000	+	0.866025i	0.500000	+	0.866025i
$407$		−	1.00000i		−	1.00000i
$408$	0.866025	+	0.500000i	0.866025	+	0.500000i
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$409$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	0.500000	+	0.866025i	0.500000	+	0.866025i
$415$		0			0
$416$		0			0
$417$		0			0
$418$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$419$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$419$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$420$		0			0
$421$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$421$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$422$	0.866025	−	0.500000i	0.866025	−	0.500000i
$423$	0.866025	−	0.500000i	0.866025	−	0.500000i
$424$		0			0
$425$	0.866025	+	0.500000i	0.866025	+	0.500000i
$426$			1.00000i			1.00000i
$427$	1.00000			1.00000
$428$		0			0
$429$	1.00000			1.00000
$430$		0			0
$431$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$431$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$432$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$433$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$433$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$434$	0.866025	−	0.500000i	0.866025	−	0.500000i
$435$		0			0
$436$		0			0
$437$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$438$	0.500000	+	0.866025i	0.500000	+	0.866025i
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$439$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$440$		0			0
$441$		0			0
$442$	−1.00000			−1.00000
$443$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$443$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.00000			2.00000
$448$	0.500000	+	0.866025i	0.500000	+	0.866025i
$449$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$449$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$450$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$451$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$452$		0			0
$453$	0.866025	+	0.500000i	0.866025	+	0.500000i
$454$	1.00000			1.00000
$455$		0			0
$456$	0.500000	−	0.866025i	0.500000	−	0.866025i
$457$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$457$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$458$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$459$	0.500000	−	0.866025i	0.500000	−	0.866025i
$460$		0			0
$461$		0			0		1.00000			$0$
$461$		0			0		−1.00000			$\pi$
$462$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$463$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$463$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$464$			1.00000i			1.00000i
$465$		0			0
$466$	−1.00000			−1.00000
$467$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$467$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$468$		0			0
$469$	0.500000	+	0.866025i	0.500000	+	0.866025i
$470$		0			0
$471$	0.866025	+	0.500000i	0.866025	+	0.500000i
$472$		0			0
$473$		0			0
$474$	1.00000			1.00000
$475$	0.500000	−	0.866025i	0.500000	−	0.866025i
$476$		0			0
$477$		0			0
$478$	1.00000			1.00000
$479$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$479$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$480$		0			0
$481$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$482$		0			0
$483$	−1.00000			−1.00000
$484$		0			0
$485$		0			0
$486$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$487$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$487$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$488$	0.866025	+	0.500000i	0.866025	+	0.500000i
$489$	0.866025	−	0.500000i	0.866025	−	0.500000i
$490$		0			0
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$	−1.00000			−1.00000
$494$			1.00000i			1.00000i
$495$		0			0
$496$	1.00000			1.00000
$497$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$498$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$500$		0			0
$501$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$502$	0.500000	+	0.866025i	0.500000	+	0.866025i
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$503$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$504$	0.866025	−	0.500000i	0.866025	−	0.500000i
$505$		0			0
$506$	0.866025	+	0.500000i	0.866025	+	0.500000i
$507$		0			0
$508$		0			0
$509$		0			0		1.00000			$0$
$509$		0			0		−1.00000			$\pi$
$510$		0			0
$511$	−1.00000			−1.00000
$512$			1.00000i			1.00000i
$513$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$514$	−1.00000			−1.00000
$515$		0			0
$516$		0			0
$517$	0.500000	−	0.866025i	0.500000	−	0.866025i
$518$	0.866025	+	0.500000i	0.866025	+	0.500000i
$519$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$520$		0			0
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	1.00000			1.00000
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$523$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$524$		0			0
$525$	0.866025	−	0.500000i	0.866025	−	0.500000i
$526$		0			0
$527$			1.00000i			1.00000i
$528$	−1.00000			−1.00000
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$			1.00000i			1.00000i
$534$	1.73205	+	1.00000i	1.73205	+	1.00000i
$535$		0			0
$536$			1.00000i			1.00000i
$537$	−2.00000			−2.00000
$538$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$539$		0			0
$540$		0			0
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$		0			0
$543$	0.866025	−	0.500000i	0.866025	−	0.500000i
$544$		0			0
$545$		0			0
$546$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$547$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$547$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$548$		0			0
$549$	0.500000	−	0.866025i	0.500000	−	0.866025i
$550$	−1.00000			−1.00000
$551$			1.00000i			1.00000i
$552$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$553$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$557$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$558$		−	1.00000i		−	1.00000i
$559$		0			0
$560$		0			0
$561$		−	1.00000i		−	1.00000i
$562$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$563$		0			0		1.00000			$0$
$563$		0			0		−1.00000			$\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$568$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$569$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$569$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$570$		0			0
$571$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$571$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$572$		0			0
$573$	0.500000	−	0.866025i	0.500000	−	0.866025i
$574$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$575$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$576$	1.00000			1.00000
$577$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$577$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		−	1.00000i		−	1.00000i
$582$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$583$		0			0
$584$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$585$		0			0
$586$		0			0
$587$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$587$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$588$		0			0
$589$	1.00000			1.00000
$590$		0			0
$591$	0.500000	+	0.866025i	0.500000	+	0.866025i
$592$	0.500000	+	0.866025i	0.500000	+	0.866025i
$593$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$593$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$594$			1.00000i			1.00000i
$595$		0			0
$596$		0			0
$597$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$598$	1.00000			1.00000
$599$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$599$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$600$	1.00000			1.00000
$601$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$601$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$602$		0			0
$603$	1.00000			1.00000
$604$		0			0
$605$		0			0
$606$			1.00000i			1.00000i
$607$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$607$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$610$		0			0
$611$		−	1.00000i		−	1.00000i
$612$		0			0
$613$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$613$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$614$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$615$		0			0
$616$	0.500000	−	0.866025i	0.500000	−	0.866025i
$617$		0			0		1.00000			$0$
$617$		0			0		−1.00000			$\pi$
$618$	−1.00000			−1.00000
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$619$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$620$		0			0
$621$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$622$		0			0
$623$	−1.73205	+	1.00000i	−1.73205	+	1.00000i
$624$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$625$	1.00000			1.00000
$626$		0			0
$627$	−1.00000			−1.00000
$628$		0			0
$629$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$630$		0			0
$631$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$631$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$632$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$633$	0.866025	+	0.500000i	0.866025	+	0.500000i
$634$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.866025	−	0.500000i	0.866025	−	0.500000i
$639$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$640$		0			0
$641$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$641$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$		0			0			−	1.00000i	$-0.5\pi$
$643$		0			0				1.00000i	$0.5\pi$
$644$		0			0
$645$		0			0
$646$	1.00000			1.00000
$647$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$647$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$648$		−	1.00000i		−	1.00000i
$649$		0			0
$650$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$651$	0.866025	+	0.500000i	0.866025	+	0.500000i
$652$		0			0
$653$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$653$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$654$		0			0
$655$		0			0
$656$		−	1.00000i		−	1.00000i
$657$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$658$	0.500000	+	0.866025i	0.500000	+	0.866025i
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$659$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$660$		0			0
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$		−	1.00000i		−	1.00000i
$663$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$664$	0.500000	−	0.866025i	0.500000	−	0.866025i
$665$		0			0
$666$	0.866025	−	0.500000i	0.866025	−	0.500000i
$667$	1.00000			1.00000
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	1.00000i		−	1.00000i
$672$		0			0
$673$	2.00000			2.00000			1.00000			$0$
$673$	2.00000			2.00000			1.00000			$0$
$674$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$675$		−	1.00000i		−	1.00000i
$676$		0			0
$677$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$677$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$678$		−	1.00000i		−	1.00000i
$679$	1.00000			1.00000
$680$		0			0
$681$	0.500000	+	0.866025i	0.500000	+	0.866025i
$682$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$683$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$683$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$684$		0			0
$685$		0			0
$686$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$687$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$691$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$694$	−1.00000			−1.00000
$695$		0			0
$696$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$697$	1.00000			1.00000
$698$		0			0
$699$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$700$		0			0
$701$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$701$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$702$	0.500000	+	0.866025i	0.500000	+	0.866025i
$703$	0.500000	+	0.866025i	0.500000	+	0.866025i
$704$	0.866025	−	0.500000i	0.866025	−	0.500000i
$705$		0			0
$706$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$707$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$708$		0			0
$709$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$709$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$710$		0			0
$711$	0.500000	+	0.866025i	0.500000	+	0.866025i
$712$	−2.00000			−2.00000
$713$		−	1.00000i		−	1.00000i
$714$	0.866025	+	0.500000i	0.866025	+	0.500000i
$715$		0			0
$716$		0			0
$717$	0.500000	+	0.866025i	0.500000	+	0.866025i
$718$		0			0
$719$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$719$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$720$		0			0
$721$	0.500000	−	0.866025i	0.500000	−	0.866025i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$726$		0			0
$727$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$727$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$728$		−	1.00000i		−	1.00000i
$729$	−1.00000			−1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$733$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$734$		−	1.00000i		−	1.00000i
$735$		0			0
$736$		0			0
$737$	0.866025	−	0.500000i	0.866025	−	0.500000i
$738$	−1.00000			−1.00000
$739$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$739$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$740$		0			0
$741$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$742$		0			0
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$743$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$744$	0.500000	+	0.866025i	0.500000	+	0.866025i
$745$		0			0
$746$			1.00000i			1.00000i
$747$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$			1.00000i			1.00000i
$753$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$754$	0.500000	−	0.866025i	0.500000	−	0.866025i
$755$		0			0
$756$		0			0
$757$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$757$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$758$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$759$			1.00000i			1.00000i
$760$		0			0
$761$		0			0		1.00000			$0$
$761$		0			0		−1.00000			$\pi$
$762$	−1.00000			−1.00000
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.500000	+	0.866025i	0.500000	+	0.866025i
$767$		0			0
$768$		0			0
$769$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$769$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$770$		0			0
$771$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$772$		0			0
$773$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$773$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$774$		0			0
$775$	0.500000	+	0.866025i	0.500000	+	0.866025i
$776$	0.866025	+	0.500000i	0.866025	+	0.500000i
$777$			1.00000i			1.00000i
$778$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$779$		−	1.00000i		−	1.00000i
$780$		0			0
$781$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$782$		−	1.00000i		−	1.00000i
$783$	0.500000	+	0.866025i	0.500000	+	0.866025i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$787$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	0.866025	+	0.500000i	0.866025	+	0.500000i
$792$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$793$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$797$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$798$	0.500000	−	0.866025i	0.500000	−	0.866025i
$799$	−1.00000			−1.00000
$800$		0			0
$801$			2.00000i			2.00000i
$802$		0			0
$803$			1.00000i			1.00000i
$804$		0			0
$805$		0			0
$806$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$807$	−2.00000			−2.00000
$808$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$		0			0
$811$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$811$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$812$		0			0
$813$		0			0
$814$	0.500000	−	0.866025i	0.500000	−	0.866025i
$815$		0			0
$816$	0.500000	+	0.866025i	0.500000	+	0.866025i
$817$		0			0
$818$			1.00000i			1.00000i
$819$	−1.00000			−1.00000
$820$		0			0
$821$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$821$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$822$		0			0
$823$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$823$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$824$	0.866025	−	0.500000i	0.866025	−	0.500000i
$825$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$826$		0			0
$827$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$827$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$	−2.00000			−2.00000			−1.00000			$\pi$
$829$	−2.00000			−2.00000			−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$	0.500000	−	0.866025i	0.500000	−	0.866025i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.866025	−	0.500000i	0.866025	−	0.500000i
$838$	0.500000	+	0.866025i	0.500000	+	0.866025i
$839$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$839$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$840$		0			0
$841$		0			0
$842$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$843$	0.500000	−	0.866025i	0.500000	−	0.866025i
$844$		0			0
$845$		0			0
$846$	1.00000			1.00000
$847$		0			0
$848$		0			0
$849$		0			0
$850$	0.500000	+	0.866025i	0.500000	+	0.866025i
$851$	0.866025	−	0.500000i	0.866025	−	0.500000i
$852$		0			0
$853$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$853$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$854$	0.866025	+	0.500000i	0.866025	+	0.500000i
$855$		0			0
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$	0.866025	+	0.500000i	0.866025	+	0.500000i
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$859$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$	0.500000	−	0.866025i	0.500000	−	0.866025i
$862$	1.00000			1.00000
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$		0			0
$865$		0			0
$866$		−	1.00000i		−	1.00000i
$867$		0			0
$868$		0			0
$869$	0.866025	+	0.500000i	0.866025	+	0.500000i
$870$		0			0
$871$	0.500000	−	0.866025i	0.500000	−	0.866025i
$872$		0			0
$873$	0.500000	−	0.866025i	0.500000	−	0.866025i
$874$	−1.00000			−1.00000
$875$		0			0
$876$		0			0
$877$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$877$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$878$	0.866025	−	0.500000i	0.866025	−	0.500000i
$879$		0			0
$880$		0			0
$881$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$881$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$882$		0			0
$883$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$883$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$884$		0			0
$885$		0			0
$886$	1.00000			1.00000
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$887$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$888$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$889$	0.500000	−	0.866025i	0.500000	−	0.866025i
$890$		0			0
$891$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$892$		0			0
$893$			1.00000i			1.00000i
$894$	1.73205	+	1.00000i	1.73205	+	1.00000i
$895$		0			0
$896$			1.00000i			1.00000i
$897$	0.500000	+	0.866025i	0.500000	+	0.866025i
$898$	−1.00000			−1.00000
$899$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$900$		0			0
$901$		0			0
$902$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$903$		0			0
$904$	0.500000	+	0.866025i	0.500000	+	0.866025i
$905$		0			0
$906$	0.500000	+	0.866025i	0.500000	+	0.866025i
$907$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$907$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$908$		0			0
$909$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$	0.866025	−	0.500000i	0.866025	−	0.500000i
$913$	−1.00000			−1.00000
$914$		−	1.00000i		−	1.00000i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.866025	−	0.500000i	0.866025	−	0.500000i
$919$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$919$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$920$		0			0
$921$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$922$		0			0
$923$			1.00000i			1.00000i
$924$		0			0
$925$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$926$	0.866025	−	0.500000i	0.866025	−	0.500000i
$927$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$928$		0			0
$929$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$929$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$935$		0			0
$936$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$			1.00000i			1.00000i
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$	0.500000	+	0.866025i	0.500000	+	0.866025i
$943$	−1.00000			−1.00000
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$		0			0
$949$	0.500000	+	0.866025i	0.500000	+	0.866025i
$950$	0.866025	−	0.500000i	0.866025	−	0.500000i
$951$	0.500000	−	0.866025i	0.500000	−	0.866025i
$952$	−1.00000			−1.00000
$953$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$953$			2.00000i			2.00000i			1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.866025	+	0.500000i	0.866025	+	0.500000i
$958$	0.500000	+	0.866025i	0.500000	+	0.866025i
$959$		0			0
$960$		0			0
$961$		0			0
$962$		−	1.00000i		−	1.00000i
$963$		0			0
$964$		0			0
$965$		0			0
$966$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$967$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$967$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$968$		0			0
$969$	0.500000	+	0.866025i	0.500000	+	0.866025i
$970$		0			0
$971$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$971$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$972$		0			0
$973$		0			0
$974$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$975$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$976$	0.500000	+	0.866025i	0.500000	+	0.866025i
$977$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$977$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$978$	1.00000			1.00000
$979$	1.00000	+	1.73205i	1.00000	+	1.73205i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		0			0		1.00000			$0$
$983$		0			0		−1.00000			$\pi$
$984$	0.866025	−	0.500000i	0.866025	−	0.500000i
$985$		0			0
$986$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$987$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0			−	1.00000i	$-0.5\pi$
$991$		0			0				1.00000i	$0.5\pi$
$992$		0			0
$993$	0.866025	−	0.500000i	0.866025	−	0.500000i
$994$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$995$		0			0
$996$		0			0
$997$		0			0			−	1.00000i	$-0.5\pi$
$997$		0			0				1.00000i	$0.5\pi$
$998$	0.866025	−	0.500000i	0.866025	−	0.500000i
$999$	0.866025	+	0.500000i	0.866025	+	0.500000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.1.g.a.29.2	yes	4
3.2	odd	2	inner	201.1.g.a.29.1	✓	4
4.3	odd	2		3216.1.bb.b.833.1		4
12.11	even	2		3216.1.bb.b.833.2		4
67.37	even	3	inner	201.1.g.a.104.1	yes	4
201.104	odd	6	inner	201.1.g.a.104.2	yes	4
268.171	odd	6		3216.1.bb.b.305.1		4
804.707	even	6		3216.1.bb.b.305.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.1.g.a.29.1	✓	4	3.2	odd	2	inner
201.1.g.a.29.2	yes	4	1.1	even	1	trivial
201.1.g.a.104.1	yes	4	67.37	even	3	inner
201.1.g.a.104.2	yes	4	201.104	odd	6	inner
3216.1.bb.b.305.1		4	268.171	odd	6
3216.1.bb.b.305.2		4	804.707	even	6
3216.1.bb.b.833.1		4	4.3	odd	2
3216.1.bb.b.833.2		4	12.11	even	2

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	201.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-0.866025 + 0.500000i) q^{11} +(-0.500000 + 0.866025i) q^{13} -1.00000i q^{14} +(0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.866025 - 0.500000i) q^{21} -1.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +1.00000 q^{24} +1.00000 q^{25} +(-0.866025 + 0.500000i) q^{26} -1.00000i q^{27} +(-0.866025 + 0.500000i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(0.500000 + 0.866025i) q^{34} +(-0.500000 + 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{38} +(-0.866025 - 0.500000i) q^{39} +(0.866025 - 0.500000i) q^{41} +1.00000 q^{42} +(-0.500000 - 0.866025i) q^{46} +(-0.866025 + 0.500000i) q^{47} +(0.866025 + 0.500000i) q^{48} +(0.866025 + 0.500000i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(0.500000 - 0.866025i) q^{54} +(-0.866025 + 0.500000i) q^{56} +(0.866025 + 0.500000i) q^{57} -1.00000 q^{58} +(-0.500000 + 0.866025i) q^{61} +1.00000i q^{62} +(0.500000 + 0.866025i) q^{63} -1.00000 q^{64} -1.00000i q^{66} -1.00000 q^{67} +(0.500000 - 0.866025i) q^{69} +(0.866025 - 0.500000i) q^{71} +1.00000i q^{72} +(0.500000 - 0.866025i) q^{73} +(-0.866025 + 0.500000i) q^{74} +1.00000i q^{75} +(0.866025 + 0.500000i) q^{77} +(-0.500000 - 0.866025i) q^{78} +(-0.500000 - 0.866025i) q^{79} +1.00000 q^{81} +1.00000 q^{82} +(0.866025 + 0.500000i) q^{83} +(-0.500000 - 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{88} -2.00000i q^{89} +1.00000 q^{91} +(-0.866025 + 0.500000i) q^{93} -1.00000 q^{94} +(-0.500000 + 0.866025i) q^{97} +(0.866025 - 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{6} - 2 q^{7} - 4 q^{9} - 2 q^{13} + 2 q^{16} + 2 q^{19} - 4 q^{22} + 4 q^{24} + 4 q^{25} + 2 q^{31} - 2 q^{33} + 2 q^{34} - 2 q^{37} + 4 q^{42} - 2 q^{46} - 2 q^{51} + 2 q^{54} - 4 q^{58} - 2 q^{61}+ \cdots - 2 q^{97}+O(q^{100}) \) 4 * q - 2 * q^6 - 2 * q^7 - 4 * q^9 - 2 * q^13 + 2 * q^16 + 2 * q^19 - 4 * q^22 + 4 * q^24 + 4 * q^25 + 2 * q^31 - 2 * q^33 + 2 * q^34 - 2 * q^37 + 4 * q^42 - 2 * q^46 - 2 * q^51 + 2 * q^54 - 4 * q^58 - 2 * q^61 + 2 * q^63 - 4 * q^64 - 4 * q^67 + 2 * q^69 + 2 * q^73 - 2 * q^78 - 2 * q^79 + 4 * q^81 + 4 * q^82 - 2 * q^87 + 2 * q^88 + 4 * q^91 - 4 * q^94 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more