LMFDB - Embedded newform 1320.1.cp.d.269.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1320,1,Mod(269,1320)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1320, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 5, 5, 4]))

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

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

chi := DirichletCharacter("1320.269");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1320.cp (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.658765816676$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{5}$
Projective field:	Galois closure of 5.1.210830400.1

Embedding invariants

Embedding label			269.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	1320.269
Dual form			1320.1.cp.d.1109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{10} +(0.309017 + 0.951057i) q^{11} -1.00000 q^{12} +(0.500000 + 1.53884i) q^{13} +(0.809017 - 0.587785i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.190983 + 0.587785i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.309017 + 0.951057i) q^{20} +(0.809017 - 0.587785i) q^{22} -0.618034 q^{23} +(0.309017 + 0.951057i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(1.30902 - 0.951057i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.30902 - 0.951057i) q^{29} +(-0.809017 - 0.587785i) q^{30} +(-0.500000 - 1.53884i) q^{31} -1.00000 q^{32} +(-0.309017 + 0.951057i) q^{33} +0.618034 q^{34} +(-0.809017 - 0.587785i) q^{36} +(0.500000 - 0.363271i) q^{37} +(-0.500000 + 1.53884i) q^{39} +(0.809017 - 0.587785i) q^{40} -0.618034 q^{43} +(-0.809017 - 0.587785i) q^{44} +1.00000 q^{45} +(0.190983 + 0.587785i) q^{46} +(-1.30902 - 0.951057i) q^{47} +(0.809017 - 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{51} +(-1.30902 - 0.951057i) q^{52} +1.00000 q^{54} +1.00000 q^{55} +(-1.30902 - 0.951057i) q^{58} +(-0.500000 + 0.363271i) q^{59} +(-0.309017 + 0.951057i) q^{60} +(-1.30902 + 0.951057i) q^{62} +(0.309017 + 0.951057i) q^{64} +1.61803 q^{65} +1.00000 q^{66} +1.61803 q^{67} +(-0.190983 - 0.587785i) q^{68} +(-0.500000 - 0.363271i) q^{69} +(-0.309017 + 0.951057i) q^{72} +(-0.500000 - 0.363271i) q^{74} +(-0.309017 - 0.951057i) q^{75} +1.61803 q^{78} +(0.190983 + 0.587785i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.500000 + 0.363271i) q^{85} +(0.190983 + 0.587785i) q^{86} +1.61803 q^{87} +(-0.309017 + 0.951057i) q^{88} +(-0.309017 - 0.951057i) q^{90} +(0.500000 - 0.363271i) q^{92} +(0.500000 - 1.53884i) q^{93} +(-0.500000 + 1.53884i) q^{94} +(-0.809017 - 0.587785i) q^{96} -1.00000 q^{98} +(-0.809017 + 0.587785i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + q^{8} - q^{9} - 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + q^{15} - q^{16} - 3 q^{17} + q^{18} - q^{20} + q^{22} + 2 q^{23} - q^{24} - q^{25}+ \cdots - q^{99}+O(q^{100}) $ 4 * q + q^2 + q^3 - q^4 - q^5 - q^6 + q^8 - q^9 - 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + q^15 - q^16 - 3 * q^17 + q^18 - q^20 + q^22 + 2 * q^23 - q^24 - q^25 + 3 * q^26 + q^27 + 3 * q^29 - q^30 - 2 * q^31 - 4 * q^32 + q^33 - 2 * q^34 - q^36 + 2 * q^37 - 2 * q^39 + q^40 + 2 * q^43 - q^44 + 4 * q^45 + 3 * q^46 - 3 * q^47 + q^48 - q^49 + q^50 - 2 * q^51 - 3 * q^52 + 4 * q^54 + 4 * q^55 - 3 * q^58 - 2 * q^59 + q^60 - 3 * q^62 - q^64 + 2 * q^65 + 4 * q^66 + 2 * q^67 - 3 * q^68 - 2 * q^69 + q^72 - 2 * q^74 + q^75 + 2 * q^78 + 3 * q^79 - q^80 - q^81 + 2 * q^85 + 3 * q^86 + 2 * q^87 + q^88 + q^90 + 2 * q^92 + 2 * q^93 - 2 * q^94 - q^96 - 4 * q^98 - q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1320\mathbb{Z}\right)^\times$.

$n$	$661$	$881$	$991$	$1057$	$1201$
$\chi(n)$	$-1$	$-1$	$1$	$-1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$2$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$3$	0.809017	+	0.587785i	0.809017	+	0.587785i
$3$	0.809017	+	0.587785i	0.809017	+	0.587785i
$4$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$5$	0.309017	−	0.951057i	0.309017	−	0.951057i
$5$	0.309017	−	0.951057i	0.309017	−	0.951057i
$6$	0.309017	−	0.951057i	0.309017	−	0.951057i
$7$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$7$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$8$	0.809017	+	0.587785i	0.809017	+	0.587785i
$9$	0.309017	+	0.951057i	0.309017	+	0.951057i
$10$	−1.00000			−1.00000
$11$	0.309017	+	0.951057i	0.309017	+	0.951057i
$11$	0.309017	+	0.951057i	0.309017	+	0.951057i
$12$	−1.00000			−1.00000
$13$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$13$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$14$		0			0
$15$	0.809017	−	0.587785i	0.809017	−	0.587785i
$16$	0.309017	−	0.951057i	0.309017	−	0.951057i
$17$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$17$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$18$	0.809017	−	0.587785i	0.809017	−	0.587785i
$19$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$19$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$20$	0.309017	+	0.951057i	0.309017	+	0.951057i
$21$		0			0
$22$	0.809017	−	0.587785i	0.809017	−	0.587785i
$23$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$23$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$24$	0.309017	+	0.951057i	0.309017	+	0.951057i
$25$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$26$	1.30902	−	0.951057i	1.30902	−	0.951057i
$27$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$28$		0			0
$29$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$29$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$30$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$31$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$31$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$32$	−1.00000			−1.00000
$33$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$34$	0.618034			0.618034
$35$		0			0
$36$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$37$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$37$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$38$		0			0
$39$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$40$	0.809017	−	0.587785i	0.809017	−	0.587785i
$41$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$41$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$42$		0			0
$43$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$43$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$44$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$45$	1.00000			1.00000
$46$	0.190983	+	0.587785i	0.190983	+	0.587785i
$47$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$47$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$48$	0.809017	−	0.587785i	0.809017	−	0.587785i
$49$	0.309017	−	0.951057i	0.309017	−	0.951057i
$50$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$51$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$52$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$53$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$53$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$54$	1.00000			1.00000
$55$	1.00000			1.00000
$56$		0			0
$57$		0			0
$58$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$59$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$60$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$61$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$61$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$62$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$63$		0			0
$64$	0.309017	+	0.951057i	0.309017	+	0.951057i
$65$	1.61803			1.61803
$66$	1.00000			1.00000
$67$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$67$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$68$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$69$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$70$		0			0
$71$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$71$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$72$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$73$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$73$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$74$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$75$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$76$		0			0
$77$		0			0
$78$	1.61803			1.61803
$79$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$79$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$80$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$81$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$82$		0			0
$83$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$83$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$84$		0			0
$85$	0.500000	+	0.363271i	0.500000	+	0.363271i
$86$	0.190983	+	0.587785i	0.190983	+	0.587785i
$87$	1.61803			1.61803
$88$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$91$		0			0
$92$	0.500000	−	0.363271i	0.500000	−	0.363271i
$93$	0.500000	−	1.53884i	0.500000	−	1.53884i
$94$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$95$		0			0
$96$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$97$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$97$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$98$	−1.00000			−1.00000
$99$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$100$	1.00000			1.00000
$101$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$101$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$102$	0.500000	+	0.363271i	0.500000	+	0.363271i
$103$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$103$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$104$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$105$		0			0
$106$		0			0
$107$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$107$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$108$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$109$		0			0		1.00000			$0$
$109$		0			0		−1.00000			$\pi$
$110$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$111$	0.618034			0.618034
$112$		0			0
$113$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$113$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$114$		0			0
$115$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$116$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$117$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$118$	0.500000	+	0.363271i	0.500000	+	0.363271i
$119$		0			0
$120$	1.00000			1.00000
$121$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$122$		0			0
$123$		0			0
$124$	1.30902	+	0.951057i	1.30902	+	0.951057i
$125$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$126$		0			0
$127$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$127$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$128$	0.809017	−	0.587785i	0.809017	−	0.587785i
$129$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$130$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$131$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$131$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$132$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$133$		0			0
$134$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$135$	0.809017	+	0.587785i	0.809017	+	0.587785i
$136$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$137$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$137$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$138$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$139$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$139$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$140$		0			0
$141$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$142$		0			0
$143$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$144$	1.00000			1.00000
$145$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$146$		0			0
$147$	0.809017	−	0.587785i	0.809017	−	0.587785i
$148$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$149$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$149$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$150$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$151$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$151$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$152$		0			0
$153$	−0.618034			−0.618034
$154$		0			0
$155$	−1.61803			−1.61803
$156$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$157$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$157$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$158$	0.500000	−	0.363271i	0.500000	−	0.363271i
$159$		0			0
$160$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$161$		0			0
$162$	0.809017	+	0.587785i	0.809017	+	0.587785i
$163$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$163$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$164$		0			0
$165$	0.809017	+	0.587785i	0.809017	+	0.587785i
$166$		0			0
$167$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$167$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$168$		0			0
$169$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$170$	0.190983	−	0.587785i	0.190983	−	0.587785i
$171$		0			0
$172$	0.500000	−	0.363271i	0.500000	−	0.363271i
$173$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$173$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$174$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$175$		0			0
$176$	1.00000			1.00000
$177$	−0.618034			−0.618034
$178$		0			0
$179$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$179$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$180$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$181$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$181$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$182$		0			0
$183$		0			0
$184$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$185$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$186$	−1.61803			−1.61803
$187$	−0.618034			−0.618034
$188$	1.61803			1.61803
$189$		0			0
$190$		0			0
$191$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$191$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$192$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$193$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$193$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$194$		0			0
$195$	1.30902	+	0.951057i	1.30902	+	0.951057i
$196$	0.309017	+	0.951057i	0.309017	+	0.951057i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.809017	+	0.587785i	0.809017	+	0.587785i
$199$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$199$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$200$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$201$	1.30902	+	0.951057i	1.30902	+	0.951057i
$202$	0.500000	−	0.363271i	0.500000	−	0.363271i
$203$		0			0
$204$	0.190983	−	0.587785i	0.190983	−	0.587785i
$205$		0			0
$206$		0			0
$207$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$208$	1.61803			1.61803
$209$		0			0
$210$		0			0
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$216$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$217$		0			0
$218$		0			0
$219$		0			0
$220$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$221$	−1.00000			−1.00000
$222$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$223$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$223$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$224$		0			0
$225$	0.309017	−	0.951057i	0.309017	−	0.951057i
$226$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$227$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$227$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$228$		0			0
$229$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$229$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$230$	0.618034			0.618034
$231$		0			0
$232$	1.61803			1.61803
$233$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$233$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$234$	1.30902	+	0.951057i	1.30902	+	0.951057i
$235$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$236$	0.190983	−	0.587785i	0.190983	−	0.587785i
$237$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$238$		0			0
$239$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$239$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$240$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$241$	2.00000			2.00000			1.00000			$0$
$241$	2.00000			2.00000			1.00000			$0$
$242$	0.809017	+	0.587785i	0.809017	+	0.587785i
$243$	−1.00000			−1.00000
$244$		0			0
$245$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$246$		0			0
$247$		0			0
$248$	0.500000	−	1.53884i	0.500000	−	1.53884i
$249$		0			0
$250$	0.809017	+	0.587785i	0.809017	+	0.587785i
$251$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$251$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$254$		0			0
$255$	0.190983	+	0.587785i	0.190983	+	0.587785i
$256$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$257$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$257$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$258$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$259$		0			0
$260$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$261$	1.30902	+	0.951057i	1.30902	+	0.951057i
$262$	0.500000	+	1.53884i	0.500000	+	1.53884i
$263$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$263$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$264$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$269$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$269$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$270$	0.309017	−	0.951057i	0.309017	−	0.951057i
$271$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$271$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$272$	0.500000	+	0.363271i	0.500000	+	0.363271i
$273$		0			0
$274$	−1.61803			−1.61803
$275$	0.309017	−	0.951057i	0.309017	−	0.951057i
$276$	0.618034			0.618034
$277$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$277$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$278$		0			0
$279$	1.30902	−	0.951057i	1.30902	−	0.951057i
$280$		0			0
$281$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$281$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$282$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$283$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$283$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$284$		0			0
$285$		0			0
$286$	1.30902	+	0.951057i	1.30902	+	0.951057i
$287$		0			0
$288$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$289$	0.500000	+	0.363271i	0.500000	+	0.363271i
$290$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$291$		0			0
$292$		0			0
$293$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$293$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$294$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$295$	0.190983	+	0.587785i	0.190983	+	0.587785i
$296$	0.618034			0.618034
$297$	−1.00000			−1.00000
$298$	−0.618034			−0.618034
$299$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$300$	0.809017	+	0.587785i	0.809017	+	0.587785i
$301$		0			0
$302$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$303$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$304$		0			0
$305$		0			0
$306$	0.190983	+	0.587785i	0.190983	+	0.587785i
$307$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$307$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$308$		0			0
$309$		0			0
$310$	0.500000	+	1.53884i	0.500000	+	1.53884i
$311$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$311$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$312$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$313$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$313$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$314$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$315$		0			0
$316$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$317$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$317$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$318$		0			0
$319$	1.30902	+	0.951057i	1.30902	+	0.951057i
$320$	1.00000			1.00000
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.309017	−	0.951057i	0.309017	−	0.951057i
$325$	0.500000	−	1.53884i	0.500000	−	1.53884i
$326$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$327$		0			0
$328$		0			0
$329$		0			0
$330$	0.309017	−	0.951057i	0.309017	−	0.951057i
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$		0			0
$333$	0.500000	+	0.363271i	0.500000	+	0.363271i
$334$	1.30902	−	0.951057i	1.30902	−	0.951057i
$335$	0.500000	−	1.53884i	0.500000	−	1.53884i
$336$		0			0
$337$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$337$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$338$	1.30902	+	0.951057i	1.30902	+	0.951057i
$339$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$340$	−0.618034			−0.618034
$341$	1.30902	−	0.951057i	1.30902	−	0.951057i
$342$		0			0
$343$		0			0
$344$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$345$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$346$		0			0
$347$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$347$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$348$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$349$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$349$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$350$		0			0
$351$	−1.61803			−1.61803
$352$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$353$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$353$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$354$	0.190983	+	0.587785i	0.190983	+	0.587785i
$355$		0			0
$356$		0			0
$357$		0			0
$358$	0.500000	−	1.53884i	0.500000	−	1.53884i
$359$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$359$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$360$	0.809017	+	0.587785i	0.809017	+	0.587785i
$361$	0.309017	+	0.951057i	0.309017	+	0.951057i
$362$		0			0
$363$	−1.00000			−1.00000
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$367$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$368$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$369$		0			0
$370$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$371$		0			0
$372$	0.500000	+	1.53884i	0.500000	+	1.53884i
$373$	−2.00000			−2.00000			−1.00000			$\pi$
$373$	−2.00000			−2.00000			−1.00000			$\pi$
$374$	0.190983	+	0.587785i	0.190983	+	0.587785i
$375$	−1.00000			−1.00000
$376$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$377$	2.11803	+	1.53884i	2.11803	+	1.53884i
$378$		0			0
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$383$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$384$	1.00000			1.00000
$385$		0			0
$386$		0			0
$387$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$388$		0			0
$389$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$389$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$390$	0.500000	−	1.53884i	0.500000	−	1.53884i
$391$	0.118034	−	0.363271i	0.118034	−	0.363271i
$392$	0.809017	−	0.587785i	0.809017	−	0.587785i
$393$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$394$		0			0
$395$	0.618034			0.618034
$396$	0.309017	−	0.951057i	0.309017	−	0.951057i
$397$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$397$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$398$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$399$		0			0
$400$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$401$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$401$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$402$	0.500000	−	1.53884i	0.500000	−	1.53884i
$403$	2.11803	−	1.53884i	2.11803	−	1.53884i
$404$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$405$	0.309017	+	0.951057i	0.309017	+	0.951057i
$406$		0			0
$407$	0.500000	+	0.363271i	0.500000	+	0.363271i
$408$	−0.618034			−0.618034
$409$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$409$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$410$		0			0
$411$	1.30902	−	0.951057i	1.30902	−	0.951057i
$412$		0			0
$413$		0			0
$414$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$415$		0			0
$416$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$417$		0			0
$418$		0			0
$419$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$419$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$420$		0			0
$421$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$421$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$422$		0			0
$423$	0.500000	−	1.53884i	0.500000	−	1.53884i
$424$		0			0
$425$	0.500000	−	0.363271i	0.500000	−	0.363271i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.61803			−1.61803
$430$	0.618034			0.618034
$431$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$431$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$432$	0.809017	+	0.587785i	0.809017	+	0.587785i
$433$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$433$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$434$		0			0
$435$	0.500000	−	1.53884i	0.500000	−	1.53884i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$439$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$440$	0.809017	+	0.587785i	0.809017	+	0.587785i
$441$	1.00000			1.00000
$442$	0.309017	+	0.951057i	0.309017	+	0.951057i
$443$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$443$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$444$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$445$		0			0
$446$		0			0
$447$	0.500000	−	0.363271i	0.500000	−	0.363271i
$448$		0			0
$449$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$449$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$450$	−1.00000			−1.00000
$451$		0			0
$452$	1.61803			1.61803
$453$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$457$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$458$		0			0
$459$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$460$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$461$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$461$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$462$		0			0
$463$		0			0		1.00000			$0$
$463$		0			0		−1.00000			$\pi$
$464$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$465$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$466$	1.30902	−	0.951057i	1.30902	−	0.951057i
$467$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$467$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$468$	0.500000	−	1.53884i	0.500000	−	1.53884i
$469$		0			0
$470$	1.30902	+	0.951057i	1.30902	+	0.951057i
$471$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$472$	−0.618034			−0.618034
$473$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$474$	0.618034			0.618034
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$479$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$480$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$481$	0.809017	+	0.587785i	0.809017	+	0.587785i
$482$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$483$		0			0
$484$	0.309017	−	0.951057i	0.309017	−	0.951057i
$485$		0			0
$486$	0.309017	+	0.951057i	0.309017	+	0.951057i
$487$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$487$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$488$		0			0
$489$	0.190983	−	0.587785i	0.190983	−	0.587785i
$490$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$491$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$491$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$492$		0			0
$493$	0.309017	+	0.951057i	0.309017	+	0.951057i
$494$		0			0
$495$	0.309017	+	0.951057i	0.309017	+	0.951057i
$496$	−1.61803			−1.61803
$497$		0			0
$498$		0			0
$499$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$499$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$500$	0.309017	−	0.951057i	0.309017	−	0.951057i
$501$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$502$	0.500000	−	0.363271i	0.500000	−	0.363271i
$503$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$503$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$504$		0			0
$505$	0.618034			0.618034
$506$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$507$	−1.61803			−1.61803
$508$		0			0
$509$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$509$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$510$	0.500000	−	0.363271i	0.500000	−	0.363271i
$511$		0			0
$512$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$513$		0			0
$514$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$515$		0			0
$516$	0.618034			0.618034
$517$	0.500000	−	1.53884i	0.500000	−	1.53884i
$518$		0			0
$519$		0			0
$520$	1.30902	+	0.951057i	1.30902	+	0.951057i
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$	0.500000	−	1.53884i	0.500000	−	1.53884i
$523$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$523$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$524$	1.30902	−	0.951057i	1.30902	−	0.951057i
$525$		0			0
$526$	0.190983	+	0.587785i	0.190983	+	0.587785i
$527$	1.00000			1.00000
$528$	0.809017	+	0.587785i	0.809017	+	0.587785i
$529$	−0.618034			−0.618034
$530$		0			0
$531$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	1.30902	+	0.951057i	1.30902	+	0.951057i
$537$	0.500000	+	1.53884i	0.500000	+	1.53884i
$538$	1.61803			1.61803
$539$	1.00000			1.00000
$540$	−1.00000			−1.00000
$541$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$541$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$542$	0.500000	+	0.363271i	0.500000	+	0.363271i
$543$		0			0
$544$	0.190983	−	0.587785i	0.190983	−	0.587785i
$545$		0			0
$546$		0			0
$547$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$547$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$548$	0.500000	+	1.53884i	0.500000	+	1.53884i
$549$		0			0
$550$	−1.00000			−1.00000
$551$		0			0
$552$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$553$		0			0
$554$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$555$	0.190983	−	0.587785i	0.190983	−	0.587785i
$556$		0			0
$557$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$557$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$558$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$559$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$560$		0			0
$561$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$562$		0			0
$563$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$563$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$564$	1.30902	+	0.951057i	1.30902	+	0.951057i
$565$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$566$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$567$		0			0
$568$		0			0
$569$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$569$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$570$		0			0
$571$		0			0		1.00000			$0$
$571$		0			0		−1.00000			$\pi$
$572$	0.500000	−	1.53884i	0.500000	−	1.53884i
$573$		0			0
$574$		0			0
$575$	0.500000	+	0.363271i	0.500000	+	0.363271i
$576$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$577$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$577$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$578$	0.190983	−	0.587785i	0.190983	−	0.587785i
$579$		0			0
$580$	1.30902	+	0.951057i	1.30902	+	0.951057i
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.500000	+	1.53884i	0.500000	+	1.53884i
$586$		0			0
$587$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$587$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$588$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$589$		0			0
$590$	0.500000	−	0.363271i	0.500000	−	0.363271i
$591$		0			0
$592$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$593$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$593$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$594$	0.309017	+	0.951057i	0.309017	+	0.951057i
$595$		0			0
$596$	0.190983	+	0.587785i	0.190983	+	0.587785i
$597$	0.500000	+	0.363271i	0.500000	+	0.363271i
$598$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$599$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$599$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$600$	0.309017	−	0.951057i	0.309017	−	0.951057i
$601$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$601$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$602$		0			0
$603$	0.500000	+	1.53884i	0.500000	+	1.53884i
$604$	2.00000			2.00000
$605$	0.309017	+	0.951057i	0.309017	+	0.951057i
$606$	0.618034			0.618034
$607$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$607$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.809017	−	2.48990i	0.809017	−	2.48990i
$612$	0.500000	−	0.363271i	0.500000	−	0.363271i
$613$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$613$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$614$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$615$		0			0
$616$		0			0
$617$	−2.00000			−2.00000			−1.00000			$\pi$
$617$	−2.00000			−2.00000			−1.00000			$\pi$
$618$		0			0
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$	1.30902	−	0.951057i	1.30902	−	0.951057i
$621$	0.190983	−	0.587785i	0.190983	−	0.587785i
$622$		0			0
$623$		0			0
$624$	1.30902	+	0.951057i	1.30902	+	0.951057i
$625$	0.309017	+	0.951057i	0.309017	+	0.951057i
$626$		0			0
$627$		0			0
$628$	1.61803			1.61803
$629$	0.118034	+	0.363271i	0.118034	+	0.363271i
$630$		0			0
$631$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$631$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$632$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.61803			1.61803
$638$	0.500000	−	1.53884i	0.500000	−	1.53884i
$639$		0			0
$640$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$641$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$641$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$642$		0			0
$643$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$643$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$644$		0			0
$645$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$646$		0			0
$647$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$647$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$648$	−1.00000			−1.00000
$649$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$650$	−1.61803			−1.61803
$651$		0			0
$652$	0.500000	+	0.363271i	0.500000	+	0.363271i
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$		0			0
$655$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.00000			2.00000			1.00000			$0$
$659$	2.00000			2.00000			1.00000			$0$
$660$	−1.00000			−1.00000
$661$		0			0		1.00000			$0$
$661$		0			0		−1.00000			$\pi$
$662$		0			0
$663$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$664$		0			0
$665$		0			0
$666$	0.190983	−	0.587785i	0.190983	−	0.587785i
$667$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$668$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$669$		0			0
$670$	−1.61803			−1.61803
$671$		0			0
$672$		0			0
$673$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$673$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$674$		0			0
$675$	0.809017	−	0.587785i	0.809017	−	0.587785i
$676$	0.500000	−	1.53884i	0.500000	−	1.53884i
$677$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$677$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$678$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$679$		0			0
$680$	0.190983	+	0.587785i	0.190983	+	0.587785i
$681$		0			0
$682$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$686$		0			0
$687$		0			0
$688$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$689$		0			0
$690$	0.500000	+	0.363271i	0.500000	+	0.363271i
$691$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$691$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	1.30902	+	0.951057i	1.30902	+	0.951057i
$697$		0			0
$698$		0			0
$699$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$700$		0			0
$701$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$701$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$702$	0.500000	+	1.53884i	0.500000	+	1.53884i
$703$		0			0
$704$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$705$	−1.61803			−1.61803
$706$	0.190983	+	0.587785i	0.190983	+	0.587785i
$707$		0			0
$708$	0.500000	−	0.363271i	0.500000	−	0.363271i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$		0			0
$711$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$712$		0			0
$713$	0.309017	+	0.951057i	0.309017	+	0.951057i
$714$		0			0
$715$	0.500000	+	1.53884i	0.500000	+	1.53884i
$716$	−1.61803			−1.61803
$717$		0			0
$718$		0			0
$719$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$719$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$720$	0.309017	−	0.951057i	0.309017	−	0.951057i
$721$		0			0
$722$	0.809017	−	0.587785i	0.809017	−	0.587785i
$723$	1.61803	+	1.17557i	1.61803	+	1.17557i
$724$		0			0
$725$	−1.61803			−1.61803
$726$	0.309017	+	0.951057i	0.309017	+	0.951057i
$727$		0			0		1.00000			$0$
$727$		0			0		−1.00000			$\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$730$		0			0
$731$	0.118034	−	0.363271i	0.118034	−	0.363271i
$732$		0			0
$733$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$733$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$734$		0			0
$735$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$736$	0.618034			0.618034
$737$	0.500000	+	1.53884i	0.500000	+	1.53884i
$738$		0			0
$739$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$739$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$740$	0.500000	+	0.363271i	0.500000	+	0.363271i
$741$		0			0
$742$		0			0
$743$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$743$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$744$	1.30902	−	0.951057i	1.30902	−	0.951057i
$745$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$746$	0.618034	+	1.90211i	0.618034	+	1.90211i
$747$		0			0
$748$	0.500000	−	0.363271i	0.500000	−	0.363271i
$749$		0			0
$750$	0.309017	+	0.951057i	0.309017	+	0.951057i
$751$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$751$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$752$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$753$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$754$	0.809017	−	2.48990i	0.809017	−	2.48990i
$755$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$756$		0			0
$757$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$757$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$758$		0			0
$759$	0.190983	−	0.587785i	0.190983	−	0.587785i
$760$		0			0
$761$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$761$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$766$	1.30902	−	0.951057i	1.30902	−	0.951057i
$767$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$768$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$769$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$769$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$770$		0			0
$771$	2.00000			2.00000
$772$		0			0
$773$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$773$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$774$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$775$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$776$		0			0
$777$		0			0
$778$	0.500000	+	0.363271i	0.500000	+	0.363271i
$779$		0			0
$780$	−1.61803			−1.61803
$781$		0			0
$782$	−0.381966			−0.381966
$783$	0.500000	+	1.53884i	0.500000	+	1.53884i
$784$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$785$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$786$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$787$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$787$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$788$		0			0
$789$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$790$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$791$		0			0
$792$	−1.00000			−1.00000
$793$		0			0
$794$	0.190983	+	0.587785i	0.190983	+	0.587785i
$795$		0			0
$796$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$	0.809017	−	0.587785i	0.809017	−	0.587785i
$800$	0.809017	+	0.587785i	0.809017	+	0.587785i
$801$		0			0
$802$		0			0
$803$		0			0
$804$	−1.61803			−1.61803
$805$		0			0
$806$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$807$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$808$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$809$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$809$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$810$	0.809017	−	0.587785i	0.809017	−	0.587785i
$811$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$811$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$812$		0			0
$813$	−0.618034			−0.618034
$814$	0.190983	−	0.587785i	0.190983	−	0.587785i
$815$	−0.618034			−0.618034
$816$	0.190983	+	0.587785i	0.190983	+	0.587785i
$817$		0			0
$818$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$819$		0			0
$820$		0			0
$821$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$821$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$822$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$823$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$823$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$824$		0			0
$825$	0.809017	−	0.587785i	0.809017	−	0.587785i
$826$		0			0
$827$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$827$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$828$	0.500000	+	0.363271i	0.500000	+	0.363271i
$829$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$829$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$830$		0			0
$831$	0.190983	−	0.587785i	0.190983	−	0.587785i
$832$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$833$	0.500000	+	0.363271i	0.500000	+	0.363271i
$834$		0			0
$835$	1.61803			1.61803
$836$		0			0
$837$	1.61803			1.61803
$838$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$839$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$839$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$840$		0			0
$841$	0.500000	−	1.53884i	0.500000	−	1.53884i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.500000	+	1.53884i	0.500000	+	1.53884i
$846$	−1.61803			−1.61803
$847$		0			0
$848$		0			0
$849$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$850$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$851$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$852$		0			0
$853$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$853$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$857$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$858$	0.500000	+	1.53884i	0.500000	+	1.53884i
$859$		0			0		1.00000			$0$
$859$		0			0		−1.00000			$\pi$
$860$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$861$		0			0
$862$		0			0
$863$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$863$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$864$	0.309017	−	0.951057i	0.309017	−	0.951057i
$865$		0			0
$866$		0			0
$867$	0.190983	+	0.587785i	0.190983	+	0.587785i
$868$		0			0
$869$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$870$	−1.61803			−1.61803
$871$	0.809017	+	2.48990i	0.809017	+	2.48990i
$872$		0			0
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$877$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$878$	0.500000	+	1.53884i	0.500000	+	1.53884i
$879$		0			0
$880$	0.309017	−	0.951057i	0.309017	−	0.951057i
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$883$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$883$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$884$	0.809017	−	0.587785i	0.809017	−	0.587785i
$885$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$886$		0			0
$887$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$887$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$888$	0.500000	+	0.363271i	0.500000	+	0.363271i
$889$		0			0
$890$		0			0
$891$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$892$		0			0
$893$		0			0
$894$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$895$	1.30902	−	0.951057i	1.30902	−	0.951057i
$896$		0			0
$897$	0.309017	−	0.951057i	0.309017	−	0.951057i
$898$		0			0
$899$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$900$	0.309017	+	0.951057i	0.309017	+	0.951057i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$905$		0			0
$906$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$907$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$907$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$908$		0			0
$909$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$919$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$919$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$920$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$921$	1.30902	+	0.951057i	1.30902	+	0.951057i
$922$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$923$		0			0
$924$		0			0
$925$	−0.618034			−0.618034
$926$		0			0
$927$		0			0
$928$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$929$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$929$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$930$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$931$		0			0
$932$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$933$		0			0
$934$		0			0
$935$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$936$	−1.61803			−1.61803
$937$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$937$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$938$		0			0
$939$		0			0
$940$	0.500000	−	1.53884i	0.500000	−	1.53884i
$941$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$941$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$942$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$943$		0			0
$944$	0.190983	+	0.587785i	0.190983	+	0.587785i
$945$		0			0
$946$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$947$		0			0		1.00000			$0$
$947$		0			0		−1.00000			$\pi$
$948$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$953$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.500000	+	1.53884i	0.500000	+	1.53884i
$958$		0			0
$959$		0			0
$960$	0.809017	+	0.587785i	0.809017	+	0.587785i
$961$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$962$	0.309017	−	0.951057i	0.309017	−	0.951057i
$963$		0			0
$964$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$965$		0			0
$966$		0			0
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$		0			0
$971$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$971$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$972$	0.809017	−	0.587785i	0.809017	−	0.587785i
$973$		0			0
$974$		0			0
$975$	1.30902	−	0.951057i	1.30902	−	0.951057i
$976$		0			0
$977$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$977$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$978$	−0.618034			−0.618034
$979$		0			0
$980$	1.00000			1.00000
$981$		0			0
$982$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$983$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$983$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$984$		0			0
$985$		0			0
$986$	0.809017	−	0.587785i	0.809017	−	0.587785i
$987$		0			0
$988$		0			0
$989$	0.381966			0.381966
$990$	0.809017	−	0.587785i	0.809017	−	0.587785i
$991$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$991$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$992$	0.500000	+	1.53884i	0.500000	+	1.53884i
$993$		0			0
$994$		0			0
$995$	0.190983	−	0.587785i	0.190983	−	0.587785i
$996$		0			0
$997$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$997$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$998$		0			0
$999$	0.190983	+	0.587785i	0.190983	+	0.587785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1320.1.cp.d.269.1	yes	4
3.2	odd	2		1320.1.cp.b.269.1	yes	4
5.4	even	2		1320.1.cp.a.269.1	✓	4
8.5	even	2		1320.1.cp.c.269.1	yes	4
11.9	even	5	inner	1320.1.cp.d.1109.1	yes	4
15.14	odd	2		1320.1.cp.c.269.1	yes	4
24.5	odd	2		1320.1.cp.a.269.1	✓	4
33.20	odd	10		1320.1.cp.b.1109.1	yes	4
40.29	even	2		1320.1.cp.b.269.1	yes	4
55.9	even	10		1320.1.cp.a.1109.1	yes	4
88.53	even	10		1320.1.cp.c.1109.1	yes	4
120.29	odd	2	CM	1320.1.cp.d.269.1	yes	4
165.119	odd	10		1320.1.cp.c.1109.1	yes	4
264.53	odd	10		1320.1.cp.a.1109.1	yes	4
440.229	even	10		1320.1.cp.b.1109.1	yes	4
1320.1109	odd	10	inner	1320.1.cp.d.1109.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1320.1.cp.a.269.1	✓	4	5.4	even	2
1320.1.cp.a.269.1	✓	4	24.5	odd	2
1320.1.cp.a.1109.1	yes	4	55.9	even	10
1320.1.cp.a.1109.1	yes	4	264.53	odd	10
1320.1.cp.b.269.1	yes	4	3.2	odd	2
1320.1.cp.b.269.1	yes	4	40.29	even	2
1320.1.cp.b.1109.1	yes	4	33.20	odd	10
1320.1.cp.b.1109.1	yes	4	440.229	even	10
1320.1.cp.c.269.1	yes	4	8.5	even	2
1320.1.cp.c.269.1	yes	4	15.14	odd	2
1320.1.cp.c.1109.1	yes	4	88.53	even	10
1320.1.cp.c.1109.1	yes	4	165.119	odd	10
1320.1.cp.d.269.1	yes	4	1.1	even	1	trivial
1320.1.cp.d.269.1	yes	4	120.29	odd	2	CM
1320.1.cp.d.1109.1	yes	4	11.9	even	5	inner
1320.1.cp.d.1109.1	yes	4	1320.1109	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1320.cp (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.309017 - 0.951057i) q^{5} +(0.309017 - 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{9} -1.00000 q^{10} +(0.309017 + 0.951057i) q^{11} -1.00000 q^{12} +(0.500000 + 1.53884i) q^{13} +(0.809017 - 0.587785i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.190983 + 0.587785i) q^{17} +(0.809017 - 0.587785i) q^{18} +(0.309017 + 0.951057i) q^{20} +(0.809017 - 0.587785i) q^{22} -0.618034 q^{23} +(0.309017 + 0.951057i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(1.30902 - 0.951057i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(1.30902 - 0.951057i) q^{29} +(-0.809017 - 0.587785i) q^{30} +(-0.500000 - 1.53884i) q^{31} -1.00000 q^{32} +(-0.309017 + 0.951057i) q^{33} +0.618034 q^{34} +(-0.809017 - 0.587785i) q^{36} +(0.500000 - 0.363271i) q^{37} +(-0.500000 + 1.53884i) q^{39} +(0.809017 - 0.587785i) q^{40} -0.618034 q^{43} +(-0.809017 - 0.587785i) q^{44} +1.00000 q^{45} +(0.190983 + 0.587785i) q^{46} +(-1.30902 - 0.951057i) q^{47} +(0.809017 - 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-0.500000 + 0.363271i) q^{51} +(-1.30902 - 0.951057i) q^{52} +1.00000 q^{54} +1.00000 q^{55} +(-1.30902 - 0.951057i) q^{58} +(-0.500000 + 0.363271i) q^{59} +(-0.309017 + 0.951057i) q^{60} +(-1.30902 + 0.951057i) q^{62} +(0.309017 + 0.951057i) q^{64} +1.61803 q^{65} +1.00000 q^{66} +1.61803 q^{67} +(-0.190983 - 0.587785i) q^{68} +(-0.500000 - 0.363271i) q^{69} +(-0.309017 + 0.951057i) q^{72} +(-0.500000 - 0.363271i) q^{74} +(-0.309017 - 0.951057i) q^{75} +1.61803 q^{78} +(0.190983 + 0.587785i) q^{79} +(-0.809017 - 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(0.500000 + 0.363271i) q^{85} +(0.190983 + 0.587785i) q^{86} +1.61803 q^{87} +(-0.309017 + 0.951057i) q^{88} +(-0.309017 - 0.951057i) q^{90} +(0.500000 - 0.363271i) q^{92} +(0.500000 - 1.53884i) q^{93} +(-0.500000 + 1.53884i) q^{94} +(-0.809017 - 0.587785i) q^{96} -1.00000 q^{98} +(-0.809017 + 0.587785i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + q^{8} - q^{9} - 4 q^{10} - q^{11} - 4 q^{12} + 2 q^{13} + q^{15} - q^{16} - 3 q^{17} + q^{18} - q^{20} + q^{22} + 2 q^{23} - q^{24} - q^{25}+ \cdots - q^{99}+O(q^{100}) \) 4 * q + q^2 + q^3 - q^4 - q^5 - q^6 + q^8 - q^9 - 4 * q^10 - q^11 - 4 * q^12 + 2 * q^13 + q^15 - q^16 - 3 * q^17 + q^18 - q^20 + q^22 + 2 * q^23 - q^24 - q^25 + 3 * q^26 + q^27 + 3 * q^29 - q^30 - 2 * q^31 - 4 * q^32 + q^33 - 2 * q^34 - q^36 + 2 * q^37 - 2 * q^39 + q^40 + 2 * q^43 - q^44 + 4 * q^45 + 3 * q^46 - 3 * q^47 + q^48 - q^49 + q^50 - 2 * q^51 - 3 * q^52 + 4 * q^54 + 4 * q^55 - 3 * q^58 - 2 * q^59 + q^60 - 3 * q^62 - q^64 + 2 * q^65 + 4 * q^66 + 2 * q^67 - 3 * q^68 - 2 * q^69 + q^72 - 2 * q^74 + q^75 + 2 * q^78 + 3 * q^79 - q^80 - q^81 + 2 * q^85 + 3 * q^86 + 2 * q^87 + q^88 + q^90 + 2 * q^92 + 2 * q^93 - 2 * q^94 - q^96 - 4 * q^98 - q^99

Introduction

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