LMFDB - Embedded newform 2664.1.bw.d.1627.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2664,1,Mod(1627,2664)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2664, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 3]))

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

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

chi := DirichletCharacter("2664.1627");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2664 = 2^{3} \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2664.bw (of order $6$, degree $2$, 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:	$1.32950919365$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{15}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{15} - \cdots)$

Embedding invariants

Embedding label			1627.4
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	2664.1627
Dual form			2664.1.bw.d.2515.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.809017 - 1.40126i) q^{5} +(0.978148 + 0.207912i) q^{6} -1.00000 q^{8} +(-0.809017 + 0.587785i) q^{9} -1.61803 q^{10} +(0.104528 - 0.181049i) q^{11} +(0.669131 - 0.743145i) q^{12} +(-0.978148 - 1.69420i) q^{13} +(1.08268 - 1.20243i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.104528 + 0.994522i) q^{18} +(-0.809017 + 1.40126i) q^{20} +(-0.104528 - 0.181049i) q^{22} +(0.669131 + 1.15897i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(-0.809017 + 1.40126i) q^{25} -1.95630 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.978148 + 1.69420i) q^{29} +(-0.500000 - 1.53884i) q^{30} +(-0.809017 - 1.40126i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.204489 + 0.0434654i) q^{33} +(0.913545 + 0.406737i) q^{36} -1.00000 q^{37} +(1.30902 - 1.45381i) q^{39} +(0.809017 + 1.40126i) q^{40} +(-0.309017 - 0.535233i) q^{41} -0.209057 q^{44} +(1.47815 + 0.658114i) q^{45} +1.33826 q^{46} +(-0.978148 - 0.207912i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.809017 + 1.40126i) q^{50} +(-0.978148 + 1.69420i) q^{52} +(-0.913545 + 0.406737i) q^{54} -0.338261 q^{55} +(0.978148 + 1.69420i) q^{58} +(-1.58268 - 0.336408i) q^{60} +(0.913545 - 1.58231i) q^{61} -1.61803 q^{62} +1.00000 q^{64} +(-1.58268 + 2.74128i) q^{65} +(0.139886 - 0.155360i) q^{66} +(-0.913545 - 1.58231i) q^{67} +(-0.895472 + 0.994522i) q^{69} +(0.809017 - 0.587785i) q^{72} -0.209057 q^{73} +(-0.500000 + 0.866025i) q^{74} +(-1.58268 - 0.336408i) q^{75} +(-0.604528 - 1.86055i) q^{78} +(0.309017 - 0.535233i) q^{79} +1.61803 q^{80} +(0.309017 - 0.951057i) q^{81} -0.618034 q^{82} +(0.500000 - 0.866025i) q^{83} +(-1.91355 - 0.406737i) q^{87} +(-0.104528 + 0.181049i) q^{88} +(1.30902 - 0.951057i) q^{90} +(0.669131 - 1.15897i) q^{92} +(1.08268 - 1.20243i) q^{93} +(-0.669131 + 0.743145i) q^{96} -1.00000 q^{98} +(0.0218524 + 0.207912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{5} - q^{6} - 8 q^{8} - 2 q^{9} - 4 q^{10} - q^{11} + q^{12} + q^{13} - 2 q^{15} - 4 q^{16} - q^{18} - 2 q^{20} + q^{22} + q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26}+ \cdots + 9 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^5 - q^6 - 8 * q^8 - 2 * q^9 - 4 * q^10 - q^11 + q^12 + q^13 - 2 * q^15 - 4 * q^16 - q^18 - 2 * q^20 + q^22 + q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 2 * q^27 + q^29 - 4 * q^30 - 2 * q^31 + 4 * q^32 - q^33 + q^36 - 8 * q^37 + 6 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^44 + 3 * q^45 + 2 * q^46 + q^48 - 4 * q^49 + 2 * q^50 + q^52 - q^54 + 6 * q^55 - q^58 - 2 * q^60 + q^61 - 4 * q^62 + 8 * q^64 - 2 * q^65 + q^66 - q^67 - 9 * q^69 + 2 * q^72 + 2 * q^73 - 4 * q^74 - 2 * q^75 - 3 * q^78 - 2 * q^79 + 4 * q^80 - 2 * q^81 + 4 * q^82 + 4 * q^83 - 9 * q^87 + q^88 + 6 * q^90 + q^92 - 2 * q^93 - q^96 - 8 * q^98 + 9 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2664\mathbb{Z}\right)^\times$.

$n$	$1297$	$1333$	$1999$	$2369$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.500000	−	0.866025i
$2$	0.500000	−	0.866025i	0.500000	−	0.866025i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$3$	0.309017	+	0.951057i	0.309017	+	0.951057i
$4$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$5$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$5$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$6$	0.978148	+	0.207912i	0.978148	+	0.207912i
$7$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$7$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$8$	−1.00000			−1.00000
$9$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$10$	−1.61803			−1.61803
$11$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$11$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$12$	0.669131	−	0.743145i	0.669131	−	0.743145i
$13$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.669131	−	0.743145i	$-0.733333\pi$
$13$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.309017	−	0.951057i	$-0.600000\pi$
$14$		0			0
$15$	1.08268	−	1.20243i	1.08268	−	1.20243i
$16$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$17$		0			0		1.00000			$0$
$17$		0			0		−1.00000			$\pi$
$18$	0.104528	+	0.994522i	0.104528	+	0.994522i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$21$		0			0
$22$	−0.104528	−	0.181049i	−0.104528	−	0.181049i
$23$	0.669131	+	1.15897i	0.669131	+	1.15897i	0.978148	+	0.207912i	$0.0666667\pi$
$23$	0.669131	+	1.15897i	0.669131	+	1.15897i	−0.309017	+	0.951057i	$0.600000\pi$
$24$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$25$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$26$	−1.95630			−1.95630
$27$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$28$		0			0
$29$	−0.978148	+	1.69420i	−0.978148	+	1.69420i	−0.309017	+	0.951057i	$0.600000\pi$
$29$	−0.978148	+	1.69420i	−0.978148	+	1.69420i	−0.669131	+	0.743145i	$0.733333\pi$
$30$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$31$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$31$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$32$	0.500000	+	0.866025i	0.500000	+	0.866025i
$33$	0.204489	+	0.0434654i	0.204489	+	0.0434654i
$34$		0			0
$35$		0			0
$36$	0.913545	+	0.406737i	0.913545	+	0.406737i
$37$	−1.00000			−1.00000
$37$	−1.00000			−1.00000
$38$		0			0
$39$	1.30902	−	1.45381i	1.30902	−	1.45381i
$40$	0.809017	+	1.40126i	0.809017	+	1.40126i
$41$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$41$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$42$		0			0
$43$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$43$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$44$	−0.209057			−0.209057
$45$	1.47815	+	0.658114i	1.47815	+	0.658114i
$46$	1.33826			1.33826
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$49$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$50$	0.809017	+	1.40126i	0.809017	+	1.40126i
$51$		0			0
$52$	−0.978148	+	1.69420i	−0.978148	+	1.69420i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$55$	−0.338261			−0.338261
$56$		0			0
$57$		0			0
$58$	0.978148	+	1.69420i	0.978148	+	1.69420i
$59$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$59$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$60$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$61$	0.913545	−	1.58231i	0.913545	−	1.58231i	0.104528	−	0.994522i	$-0.466667\pi$
$61$	0.913545	−	1.58231i	0.913545	−	1.58231i	0.809017	−	0.587785i	$-0.200000\pi$
$62$	−1.61803			−1.61803
$63$		0			0
$64$	1.00000			1.00000
$65$	−1.58268	+	2.74128i	−1.58268	+	2.74128i
$66$	0.139886	−	0.155360i	0.139886	−	0.155360i
$67$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.809017	−	0.587785i	$-0.800000\pi$
$67$	−0.913545	−	1.58231i	−0.913545	−	1.58231i	−0.104528	−	0.994522i	$-0.533333\pi$
$68$		0			0
$69$	−0.895472	+	0.994522i	−0.895472	+	0.994522i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	0.809017	−	0.587785i	0.809017	−	0.587785i
$73$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$73$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$74$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$75$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$76$		0			0
$77$		0			0
$78$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$79$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$79$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$80$	1.61803			1.61803
$81$	0.309017	−	0.951057i	0.309017	−	0.951057i
$82$	−0.618034			−0.618034
$83$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.91355	−	0.406737i	−1.91355	−	0.406737i
$88$	−0.104528	+	0.181049i	−0.104528	+	0.181049i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	1.30902	−	0.951057i	1.30902	−	0.951057i
$91$		0			0
$92$	0.669131	−	1.15897i	0.669131	−	1.15897i
$93$	1.08268	−	1.20243i	1.08268	−	1.20243i
$94$		0			0
$95$		0			0
$96$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	−1.00000			−1.00000
$99$	0.0218524	+	0.207912i	0.0218524	+	0.207912i
$100$	1.61803			1.61803
$101$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$101$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$102$		0			0
$103$	0.913545	+	1.58231i	0.913545	+	1.58231i	0.809017	+	0.587785i	$0.200000\pi$
$103$	0.913545	+	1.58231i	0.913545	+	1.58231i	0.104528	+	0.994522i	$0.466667\pi$
$104$	0.978148	+	1.69420i	0.978148	+	1.69420i
$105$		0			0
$106$		0			0
$107$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$107$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$108$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$109$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$109$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$110$	−0.169131	+	0.292943i	−0.169131	+	0.292943i
$111$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$112$		0			0
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$		0			0
$115$	1.08268	−	1.87525i	1.08268	−	1.87525i
$116$	1.95630			1.95630
$117$	1.78716	+	0.795697i	1.78716	+	0.795697i
$118$		0			0
$119$		0			0
$120$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$121$	0.478148	+	0.828176i	0.478148	+	0.828176i
$122$	−0.913545	−	1.58231i	−0.913545	−	1.58231i
$123$	0.413545	−	0.459289i	0.413545	−	0.459289i
$124$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$125$	1.00000			1.00000
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	0.500000	−	0.866025i	0.500000	−	0.866025i
$129$		0			0
$130$	1.58268	+	2.74128i	1.58268	+	2.74128i
$131$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$131$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$132$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$133$		0			0
$134$	−1.82709			−1.82709
$135$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$136$		0			0
$137$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$137$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$138$	0.413545	+	1.27276i	0.413545	+	1.27276i
$139$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$139$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.408977			−0.408977
$144$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$145$	3.16535			3.16535
$146$	−0.104528	+	0.181049i	−0.104528	+	0.181049i
$147$	0.669131	−	0.743145i	0.669131	−	0.743145i
$148$	0.500000	+	0.866025i	0.500000	+	0.866025i
$149$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$149$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$150$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$151$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$151$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.30902	+	2.26728i	−1.30902	+	2.26728i
$156$	−1.91355	−	0.406737i	−1.91355	−	0.406737i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$159$		0			0
$160$	0.809017	−	1.40126i	0.809017	−	1.40126i
$161$		0			0
$162$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$165$	−0.104528	−	0.321706i	−0.104528	−	0.321706i
$166$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$167$	0.913545	+	1.58231i	0.913545	+	1.58231i	0.809017	+	0.587785i	$0.200000\pi$
$167$	0.913545	+	1.58231i	0.913545	+	1.58231i	0.104528	+	0.994522i	$0.466667\pi$
$168$		0			0
$169$	−1.41355	+	2.44833i	−1.41355	+	2.44833i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$173$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$174$	−1.30902	+	1.45381i	−1.30902	+	1.45381i
$175$		0			0
$176$	0.104528	+	0.181049i	0.104528	+	0.181049i
$177$		0			0
$178$		0			0
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$		0			0
$183$	1.78716	+	0.379874i	1.78716	+	0.379874i
$184$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$185$	0.809017	+	1.40126i	0.809017	+	1.40126i
$186$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.913545	−	1.58231i	0.913545	−	1.58231i	0.104528	−	0.994522i	$-0.466667\pi$
$191$	0.913545	−	1.58231i	0.913545	−	1.58231i	0.809017	−	0.587785i	$-0.200000\pi$
$192$	0.309017	+	0.951057i	0.309017	+	0.951057i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$	−3.09618	−	0.658114i	−3.09618	−	0.658114i
$196$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	0.190983	+	0.0850311i	0.190983	+	0.0850311i
$199$	−2.00000			−2.00000			−1.00000			$\pi$
$199$	−2.00000			−2.00000			−1.00000			$\pi$
$200$	0.809017	−	1.40126i	0.809017	−	1.40126i
$201$	1.22256	−	1.35779i	1.22256	−	1.35779i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$206$	1.82709			1.82709
$207$	−1.22256	−	0.544320i	−1.22256	−	0.544320i
$208$	1.95630			1.95630
$209$		0			0
$210$		0			0
$211$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$211$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$212$		0			0
$213$		0			0
$214$	0.669131	−	1.15897i	0.669131	−	1.15897i
$215$		0			0
$216$	0.809017	+	0.587785i	0.809017	+	0.587785i
$217$		0			0
$218$	0.500000	−	0.866025i	0.500000	−	0.866025i
$219$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$220$	0.169131	+	0.292943i	0.169131	+	0.292943i
$221$		0			0
$222$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$223$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$223$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$224$		0			0
$225$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$229$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$230$	−1.08268	−	1.87525i	−1.08268	−	1.87525i
$231$		0			0
$232$	0.978148	−	1.69420i	0.978148	−	1.69420i
$233$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$233$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$234$	1.58268	−	1.14988i	1.58268	−	1.14988i
$235$		0			0
$236$		0			0
$237$	0.604528	+	0.128496i	0.604528	+	0.128496i
$238$		0			0
$239$	−0.104528	−	0.181049i	−0.104528	−	0.181049i	0.809017	−	0.587785i	$-0.200000\pi$
$239$	−0.104528	−	0.181049i	−0.104528	−	0.181049i	−0.913545	+	0.406737i	$0.866667\pi$
$240$	0.500000	+	1.53884i	0.500000	+	1.53884i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$	0.956295			0.956295
$243$	1.00000			1.00000
$244$	−1.82709			−1.82709
$245$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$246$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$247$		0			0
$248$	0.809017	+	1.40126i	0.809017	+	1.40126i
$249$	0.978148	+	0.207912i	0.978148	+	0.207912i
$250$	0.500000	−	0.866025i	0.500000	−	0.866025i
$251$		0			0		1.00000			$0$
$251$		0			0		−1.00000			$\pi$
$252$		0			0
$253$	0.279773			0.279773
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$257$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$257$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$258$		0			0
$259$		0			0
$260$	3.16535			3.16535
$261$	−0.204489	−	1.94558i	−0.204489	−	1.94558i
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−0.913545	+	1.58231i	−0.913545	+	1.58231i
$269$		0			0		1.00000			$0$
$269$		0			0		−1.00000			$\pi$
$270$	1.30902	+	0.951057i	1.30902	+	0.951057i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$275$	0.169131	+	0.292943i	0.169131	+	0.292943i
$276$	1.30902	+	0.278240i	1.30902	+	0.278240i
$277$	−0.104528	+	0.181049i	−0.104528	+	0.181049i	−0.913545	−	0.406737i	$-0.866667\pi$
$277$	−0.104528	+	0.181049i	−0.104528	+	0.181049i	0.809017	+	0.587785i	$0.200000\pi$
$278$	−1.33826			−1.33826
$279$	1.47815	+	0.658114i	1.47815	+	0.658114i
$280$		0			0
$281$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$281$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$282$		0			0
$283$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$283$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$284$		0			0
$285$		0			0
$286$	−0.204489	+	0.354185i	−0.204489	+	0.354185i
$287$		0			0
$288$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$289$	1.00000			1.00000
$290$	1.58268	−	2.74128i	1.58268	−	2.74128i
$291$		0			0
$292$	0.104528	+	0.181049i	0.104528	+	0.181049i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$295$		0			0
$296$	1.00000			1.00000
$297$	−0.190983	+	0.0850311i	−0.190983	+	0.0850311i
$298$		0			0
$299$	1.30902	−	2.26728i	1.30902	−	2.26728i
$300$	0.500000	+	1.53884i	0.500000	+	1.53884i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.95630			−2.95630
$306$		0			0
$307$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$307$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$308$		0			0
$309$	−1.22256	+	1.35779i	−1.22256	+	1.35779i
$310$	1.30902	+	2.26728i	1.30902	+	2.26728i
$311$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.669131	−	0.743145i	$-0.733333\pi$
$311$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.309017	−	0.951057i	$-0.600000\pi$
$312$	−1.30902	+	1.45381i	−1.30902	+	1.45381i
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$		0			0
$316$	−0.618034			−0.618034
$317$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$317$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$318$		0			0
$319$	0.204489	+	0.354185i	0.204489	+	0.354185i
$320$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$321$	0.413545	+	1.27276i	0.413545	+	1.27276i
$322$		0			0
$323$		0			0
$324$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$325$	3.16535			3.16535
$326$		0			0
$327$	0.309017	+	0.951057i	0.309017	+	0.951057i
$328$	0.309017	+	0.535233i	0.309017	+	0.535233i
$329$		0			0
$330$	−0.330869	−	0.0703285i	−0.330869	−	0.0703285i
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	−1.00000			−1.00000
$333$	0.809017	−	0.587785i	0.809017	−	0.587785i
$334$	1.82709			1.82709
$335$	−1.47815	+	2.56023i	−1.47815	+	2.56023i
$336$		0			0
$337$	0.104528	+	0.181049i	0.104528	+	0.181049i	0.913545	−	0.406737i	$-0.133333\pi$
$337$	0.104528	+	0.181049i	0.104528	+	0.181049i	−0.809017	+	0.587785i	$0.800000\pi$
$338$	1.41355	+	2.44833i	1.41355	+	2.44833i
$339$		0			0
$340$		0			0
$341$	−0.338261			−0.338261
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.11803	+	0.450202i	2.11803	+	0.450202i
$346$		0			0
$347$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$347$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$348$	0.604528	+	1.86055i	0.604528	+	1.86055i
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$		0			0
$351$	−0.204489	+	1.94558i	−0.204489	+	1.94558i
$352$	0.209057			0.209057
$353$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$353$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$361$	1.00000			1.00000
$362$		0			0
$363$	−0.639886	+	0.710666i	−0.639886	+	0.710666i
$364$		0			0
$365$	0.169131	+	0.292943i	0.169131	+	0.292943i
$366$	1.22256	−	1.35779i	1.22256	−	1.35779i
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$	−1.33826			−1.33826
$369$	0.564602	+	0.251377i	0.564602	+	0.251377i
$370$	1.61803			1.61803
$371$		0			0
$372$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	0.309017	+	0.951057i	0.309017	+	0.951057i
$376$		0			0
$377$	3.82709			3.82709
$378$		0			0
$379$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$379$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$380$		0			0
$381$		0			0
$382$	−0.913545	−	1.58231i	−0.913545	−	1.58231i
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$383$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$384$	0.978148	+	0.207912i	0.978148	+	0.207912i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$389$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$390$	−2.11803	+	2.35232i	−2.11803	+	2.35232i
$391$		0			0
$392$	0.500000	+	0.866025i	0.500000	+	0.866025i
$393$		0			0
$394$		0			0
$395$	−1.00000			−1.00000
$396$	0.169131	−	0.122881i	0.169131	−	0.122881i
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$	−1.00000	+	1.73205i	−1.00000	+	1.73205i
$399$		0			0
$400$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$401$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$401$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$402$	−0.564602	−	1.73767i	−0.564602	−	1.73767i
$403$	−1.58268	+	2.74128i	−1.58268	+	2.74128i
$404$		0			0
$405$	−1.58268	+	0.336408i	−1.58268	+	0.336408i
$406$		0			0
$407$	−0.104528	+	0.181049i	−0.104528	+	0.181049i
$408$		0			0
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$	0.500000	+	0.866025i	0.500000	+	0.866025i
$411$	1.58268	+	0.336408i	1.58268	+	0.336408i
$412$	0.913545	−	1.58231i	0.913545	−	1.58231i
$413$		0			0
$414$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$415$	−1.61803			−1.61803
$416$	0.978148	−	1.69420i	0.978148	−	1.69420i
$417$	0.895472	−	0.994522i	0.895472	−	0.994522i
$418$		0			0
$419$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.669131	+	0.743145i	$0.266667\pi$
$419$	0.978148	+	1.69420i	0.978148	+	1.69420i	0.309017	+	0.951057i	$0.400000\pi$
$420$		0			0
$421$	0.669131	−	1.15897i	0.669131	−	1.15897i	−0.309017	−	0.951057i	$-0.600000\pi$
$421$	0.669131	−	1.15897i	0.669131	−	1.15897i	0.978148	−	0.207912i	$-0.0666667\pi$
$422$	0.209057			0.209057
$423$		0			0
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$429$	−0.126381	−	0.388960i	−0.126381	−	0.388960i
$430$		0			0
$431$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$431$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$432$	0.913545	−	0.406737i	0.913545	−	0.406737i
$433$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$433$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$434$		0			0
$435$	0.978148	+	3.01043i	0.978148	+	3.01043i
$436$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$437$		0			0
$438$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i
$439$	0.669131	−	1.15897i	0.669131	−	1.15897i	−0.309017	−	0.951057i	$-0.600000\pi$
$439$	0.669131	−	1.15897i	0.669131	−	1.15897i	0.978148	−	0.207912i	$-0.0666667\pi$
$440$	0.338261			0.338261
$441$	0.913545	+	0.406737i	0.913545	+	0.406737i
$442$		0			0
$443$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.104528	+	0.994522i	$0.533333\pi$
$443$	−0.913545	+	1.58231i	−0.913545	+	1.58231i	−0.809017	+	0.587785i	$0.800000\pi$
$444$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$451$	−0.129204			−0.129204
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$		0			0
$459$		0			0
$460$	−2.16535			−2.16535
$461$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$461$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$462$		0			0
$463$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.669131	−	0.743145i	$-0.733333\pi$
$463$	−0.978148	−	1.69420i	−0.978148	−	1.69420i	−0.309017	−	0.951057i	$-0.600000\pi$
$464$	−0.978148	−	1.69420i	−0.978148	−	1.69420i
$465$	−2.56082	−	0.544320i	−2.56082	−	0.544320i
$466$	−0.978148	+	1.69420i	−0.978148	+	1.69420i
$467$		0			0		1.00000			$0$
$467$		0			0		−1.00000			$\pi$
$468$	−0.204489	−	1.94558i	−0.204489	−	1.94558i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.413545	−	0.459289i	0.413545	−	0.459289i
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−0.209057			−0.209057
$479$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$479$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$480$	1.58268	+	0.336408i	1.58268	+	0.336408i
$481$	0.978148	+	1.69420i	0.978148	+	1.69420i
$482$		0			0
$483$		0			0
$484$	0.478148	−	0.828176i	0.478148	−	0.828176i
$485$		0			0
$486$	0.500000	−	0.866025i	0.500000	−	0.866025i
$487$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$487$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$488$	−0.913545	+	1.58231i	−0.913545	+	1.58231i
$489$		0			0
$490$	0.809017	+	1.40126i	0.809017	+	1.40126i
$491$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$491$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$492$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$493$		0			0
$494$		0			0
$495$	0.273659	−	0.198825i	0.273659	−	0.198825i
$496$	1.61803			1.61803
$497$		0			0
$498$	0.669131	−	0.743145i	0.669131	−	0.743145i
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$501$	−1.22256	+	1.35779i	−1.22256	+	1.35779i
$502$		0			0
$503$	−1.82709			−1.82709			−0.913545	−	0.406737i	$-0.866667\pi$
$503$	−1.82709			−1.82709			−0.913545	+	0.406737i	$0.866667\pi$
$504$		0			0
$505$		0			0
$506$	0.139886	−	0.242290i	0.139886	−	0.242290i
$507$	−2.76531	−	0.587785i	−2.76531	−	0.587785i
$508$		0			0
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−1.00000
$513$		0			0
$514$		0			0
$515$	1.47815	−	2.56023i	1.47815	−	2.56023i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	1.58268	−	2.74128i	1.58268	−	2.74128i
$521$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$521$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$522$	−1.78716	−	0.795697i	−1.78716	−	0.795697i
$523$		0			0		1.00000			$0$
$523$		0			0		−1.00000			$\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$529$	−0.395472	+	0.684977i	−0.395472	+	0.684977i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.604528	+	1.04707i	−0.604528	+	1.04707i
$534$		0			0
$535$	−1.08268	−	1.87525i	−1.08268	−	1.87525i
$536$	0.913545	+	1.58231i	0.913545	+	1.58231i
$537$		0			0
$538$		0			0
$539$	−0.209057			−0.209057
$540$	1.47815	−	0.658114i	1.47815	−	0.658114i
$541$	−1.82709			−1.82709			−0.913545	−	0.406737i	$-0.866667\pi$
$541$	−1.82709			−1.82709			−0.913545	+	0.406737i	$0.866667\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$546$		0			0
$547$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$547$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$548$	−1.61803			−1.61803
$549$	0.190983	+	1.81708i	0.190983	+	1.81708i
$550$	0.338261			0.338261
$551$		0			0
$552$	0.895472	−	0.994522i	0.895472	−	0.994522i
$553$		0			0
$554$	0.104528	+	0.181049i	0.104528	+	0.181049i
$555$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$556$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$557$	−1.82709			−1.82709			−0.913545	−	0.406737i	$-0.866667\pi$
$557$	−1.82709			−1.82709			−0.913545	+	0.406737i	$0.866667\pi$
$558$	1.30902	−	0.951057i	1.30902	−	0.951057i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$571$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$572$	0.204489	+	0.354185i	0.204489	+	0.354185i
$573$	1.78716	+	0.379874i	1.78716	+	0.379874i
$574$		0			0
$575$	−2.16535			−2.16535
$576$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	0.500000	−	0.866025i	0.500000	−	0.866025i
$579$		0			0
$580$	−1.58268	−	2.74128i	−1.58268	−	2.74128i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	0.209057			0.209057
$585$	−0.330869	−	3.14801i	−0.330869	−	3.14801i
$586$		0			0
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	0.500000	−	0.866025i	0.500000	−	0.866025i
$593$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$593$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$594$	−0.0218524	+	0.207912i	−0.0218524	+	0.207912i
$595$		0			0
$596$		0			0
$597$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$598$	−1.30902	−	2.26728i	−1.30902	−	2.26728i
$599$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$599$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$600$	1.58268	+	0.336408i	1.58268	+	0.336408i
$601$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$601$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$602$		0			0
$603$	1.66913	+	0.743145i	1.66913	+	0.743145i
$604$		0			0
$605$	0.773659	−	1.34002i	0.773659	−	1.34002i
$606$		0			0
$607$	0.669131	+	1.15897i	0.669131	+	1.15897i	0.978148	+	0.207912i	$0.0666667\pi$
$607$	0.669131	+	1.15897i	0.669131	+	1.15897i	−0.309017	+	0.951057i	$0.600000\pi$
$608$		0			0
$609$		0			0
$610$	−1.47815	+	2.56023i	−1.47815	+	2.56023i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	0.309017	−	0.535233i	0.309017	−	0.535233i
$615$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$616$		0			0
$617$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	−0.978148	−	0.207912i	$-0.933333\pi$
$617$	−0.669131	−	1.15897i	−0.669131	−	1.15897i	0.309017	−	0.951057i	$-0.400000\pi$
$618$	0.564602	+	1.73767i	0.564602	+	1.73767i
$619$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$619$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$620$	2.61803			2.61803
$621$	0.139886	−	1.33093i	0.139886	−	1.33093i
$622$	−1.95630			−1.95630
$623$		0			0
$624$	0.604528	+	1.86055i	0.604528	+	1.86055i
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	1.95630			1.95630			0.978148	−	0.207912i	$-0.0666667\pi$
$631$	1.95630			1.95630			0.978148	+	0.207912i	$0.0666667\pi$
$632$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$633$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.978148	+	1.69420i	−0.978148	+	1.69420i
$638$	0.408977			0.408977
$639$		0			0
$640$	−1.61803			−1.61803
$641$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	0.309017	+	0.951057i	$0.400000\pi$
$641$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	−0.978148	+	0.207912i	$0.933333\pi$
$642$	1.30902	+	0.278240i	1.30902	+	0.278240i
$643$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$643$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.95630			1.95630			0.978148	−	0.207912i	$-0.0666667\pi$
$647$	1.95630			1.95630			0.978148	+	0.207912i	$0.0666667\pi$
$648$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$649$		0			0
$650$	1.58268	−	2.74128i	1.58268	−	2.74128i
$651$		0			0
$652$		0			0
$653$	0.669131	+	1.15897i	0.669131	+	1.15897i	0.978148	+	0.207912i	$0.0666667\pi$
$653$	0.669131	+	1.15897i	0.669131	+	1.15897i	−0.309017	+	0.951057i	$0.600000\pi$
$654$	0.978148	+	0.207912i	0.978148	+	0.207912i
$655$		0			0
$656$	0.618034			0.618034
$657$	0.169131	−	0.122881i	0.169131	−	0.122881i
$658$		0			0
$659$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	−0.978148	−	0.207912i	$-0.933333\pi$
$659$	−0.309017	+	0.535233i	−0.309017	+	0.535233i	0.669131	+	0.743145i	$0.266667\pi$
$660$	−0.226341	+	0.251377i	−0.226341	+	0.251377i
$661$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$661$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$662$		0			0
$663$		0			0
$664$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$665$		0			0
$666$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$667$	−2.61803			−2.61803
$668$	0.913545	−	1.58231i	0.913545	−	1.58231i
$669$		0			0
$670$	1.47815	+	2.56023i	1.47815	+	2.56023i
$671$	−0.190983	−	0.330792i	−0.190983	−	0.330792i
$672$		0			0
$673$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	0.309017	+	0.951057i	$0.400000\pi$
$673$	−0.669131	+	1.15897i	−0.669131	+	1.15897i	−0.978148	+	0.207912i	$0.933333\pi$
$674$	0.209057			0.209057
$675$	1.47815	−	0.658114i	1.47815	−	0.658114i
$676$	2.82709			2.82709
$677$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$677$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−0.169131	+	0.292943i	−0.169131	+	0.292943i
$683$		0			0		1.00000			$0$
$683$		0			0		−1.00000			$\pi$
$684$		0			0
$685$	−2.61803			−2.61803
$686$		0			0
$687$		0			0
$688$		0			0
$689$		0			0
$690$	1.44890	−	1.60917i	1.44890	−	1.60917i
$691$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$691$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.08268	+	1.87525i	−1.08268	+	1.87525i
$696$	1.91355	+	0.406737i	1.91355	+	0.406737i
$697$		0			0
$698$		0			0
$699$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$700$		0			0
$701$	0.209057			0.209057			0.104528	−	0.994522i	$-0.466667\pi$
$701$	0.209057			0.209057			0.104528	+	0.994522i	$0.466667\pi$
$702$	1.58268	+	1.14988i	1.58268	+	1.14988i
$703$		0			0
$704$	0.104528	−	0.181049i	0.104528	−	0.181049i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.104528	+	0.181049i	−0.104528	+	0.181049i	−0.913545	−	0.406737i	$-0.866667\pi$
$709$	−0.104528	+	0.181049i	−0.104528	+	0.181049i	0.809017	+	0.587785i	$0.200000\pi$
$710$		0			0
$711$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$712$		0			0
$713$	1.08268	−	1.87525i	1.08268	−	1.87525i
$714$		0			0
$715$	0.330869	+	0.573083i	0.330869	+	0.573083i
$716$		0			0
$717$	0.139886	−	0.155360i	0.139886	−	0.155360i
$718$		0			0
$719$		0			0		1.00000			$0$
$719$		0			0		−1.00000			$\pi$
$720$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$721$		0			0
$722$	0.500000	−	0.866025i	0.500000	−	0.866025i
$723$		0			0
$724$		0			0
$725$	−1.58268	−	2.74128i	−1.58268	−	2.74128i
$726$	0.295511	+	0.909491i	0.295511	+	0.909491i
$727$	−0.104528	+	0.181049i	−0.104528	+	0.181049i	−0.913545	−	0.406737i	$-0.866667\pi$
$727$	−0.104528	+	0.181049i	−0.104528	+	0.181049i	0.809017	+	0.587785i	$0.200000\pi$
$728$		0			0
$729$	0.309017	+	0.951057i	0.309017	+	0.951057i
$730$	0.338261			0.338261
$731$		0			0
$732$	−0.564602	−	1.73767i	−0.564602	−	1.73767i
$733$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$733$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$734$		0			0
$735$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$736$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$737$	−0.381966			−0.381966
$738$	0.500000	−	0.363271i	0.500000	−	0.363271i
$739$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$739$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$740$	0.809017	−	1.40126i	0.809017	−	1.40126i
$741$		0			0
$742$		0			0
$743$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$743$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$744$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$745$		0			0
$746$		0			0
$747$	0.104528	+	0.994522i	0.104528	+	0.994522i
$748$		0			0
$749$		0			0
$750$	0.978148	+	0.207912i	0.978148	+	0.207912i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$		0			0
$753$		0			0
$754$	1.91355	−	3.31436i	1.91355	−	3.31436i
$755$		0			0
$756$		0			0
$757$	−1.82709			−1.82709			−0.913545	−	0.406737i	$-0.866667\pi$
$757$	−1.82709			−1.82709			−0.913545	+	0.406737i	$0.866667\pi$
$758$	0.309017	−	0.535233i	0.309017	−	0.535233i
$759$	0.0864545	+	0.266080i	0.0864545	+	0.266080i
$760$		0			0
$761$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	0.669131	−	0.743145i	$-0.266667\pi$
$761$	−0.309017	−	0.535233i	−0.309017	−	0.535233i	−0.978148	+	0.207912i	$0.933333\pi$
$762$		0			0
$763$		0			0
$764$	−1.82709			−1.82709
$765$		0			0
$766$	−1.00000			−1.00000
$767$		0			0
$768$	0.669131	−	0.743145i	0.669131	−	0.743145i
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$	2.61803			2.61803
$776$		0			0
$777$		0			0
$778$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$779$		0			0
$780$	0.978148	+	3.01043i	0.978148	+	3.01043i
$781$		0			0
$782$		0			0
$783$	1.78716	−	0.795697i	1.78716	−	0.795697i
$784$	1.00000			1.00000
$785$		0			0
$786$		0			0
$787$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$787$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$		0			0
$790$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$791$		0			0
$792$	−0.0218524	−	0.207912i	−0.0218524	−	0.207912i
$793$	−3.57433			−3.57433
$794$		0			0
$795$		0			0
$796$	1.00000	+	1.73205i	1.00000	+	1.73205i
$797$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$797$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$798$		0			0
$799$		0			0
$800$	−1.61803			−1.61803
$801$		0			0
$802$		0			0
$803$	−0.0218524	+	0.0378495i	−0.0218524	+	0.0378495i
$804$	−1.78716	−	0.379874i	−1.78716	−	0.379874i
$805$		0			0
$806$	1.58268	+	2.74128i	1.58268	+	2.74128i
$807$		0			0
$808$		0			0
$809$		0			0		1.00000			$0$
$809$		0			0		−1.00000			$\pi$
$810$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$811$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$811$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$	0.104528	+	0.181049i	0.104528	+	0.181049i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$	1.00000			1.00000
$821$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$821$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$822$	1.08268	−	1.20243i	1.08268	−	1.20243i
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$	−0.913545	−	1.58231i	−0.913545	−	1.58231i
$825$	−0.226341	+	0.251377i	−0.226341	+	0.251377i
$826$		0			0
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$	0.139886	+	1.33093i	0.139886	+	1.33093i
$829$	−1.33826			−1.33826			−0.669131	−	0.743145i	$-0.733333\pi$
$829$	−1.33826			−1.33826			−0.669131	+	0.743145i	$0.733333\pi$
$830$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$831$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i
$832$	−0.978148	−	1.69420i	−0.978148	−	1.69420i
$833$		0			0
$834$	−0.413545	−	1.27276i	−0.413545	−	1.27276i
$835$	1.47815	−	2.56023i	1.47815	−	2.56023i
$836$		0			0
$837$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$838$	1.95630			1.95630
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$		0			0
$841$	−1.41355	−	2.44833i	−1.41355	−	2.44833i
$842$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$843$		0			0
$844$	0.104528	−	0.181049i	0.104528	−	0.181049i
$845$	4.57433			4.57433
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$852$		0			0
$853$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$853$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$854$		0			0
$855$		0			0
$856$	−1.33826			−1.33826
$857$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$857$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$858$	−0.400040	−	0.0850311i	−0.400040	−	0.0850311i
$859$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$859$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$860$		0			0
$861$		0			0
$862$	0.500000	−	0.866025i	0.500000	−	0.866025i
$863$		0			0		1.00000			$0$
$863$		0			0		−1.00000			$\pi$
$864$	0.104528	−	0.994522i	0.104528	−	0.994522i
$865$		0			0
$866$	0.669131	−	1.15897i	0.669131	−	1.15897i
$867$	0.309017	+	0.951057i	0.309017	+	0.951057i
$868$		0			0
$869$	−0.0646021	−	0.111894i	−0.0646021	−	0.111894i
$870$	3.09618	+	0.658114i	3.09618	+	0.658114i
$871$	−1.78716	+	3.09546i	−1.78716	+	3.09546i
$872$	−1.00000			−1.00000
$873$		0			0
$874$		0			0
$875$		0			0
$876$	−0.139886	+	0.155360i	−0.139886	+	0.155360i
$877$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$877$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$878$	−0.669131	−	1.15897i	−0.669131	−	1.15897i
$879$		0			0
$880$	0.169131	−	0.292943i	0.169131	−	0.292943i
$881$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$881$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$882$	0.809017	−	0.587785i	0.809017	−	0.587785i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$		0			0
$886$	0.913545	+	1.58231i	0.913545	+	1.58231i
$887$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$887$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$888$	0.309017	+	0.951057i	0.309017	+	0.951057i
$889$		0			0
$890$		0			0
$891$	−0.139886	−	0.155360i	−0.139886	−	0.155360i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.56082	+	0.544320i	2.56082	+	0.544320i
$898$		0			0
$899$	3.16535			3.16535
$900$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$901$		0			0
$902$	−0.0646021	+	0.111894i	−0.0646021	+	0.111894i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$907$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$911$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$912$		0			0
$913$	−0.104528	−	0.181049i	−0.104528	−	0.181049i
$914$		0			0
$915$	−0.913545	−	2.81160i	−0.913545	−	2.81160i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$919$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$920$	−1.08268	+	1.87525i	−1.08268	+	1.87525i
$921$	0.190983	+	0.587785i	0.190983	+	0.587785i
$922$	0.500000	+	0.866025i	0.500000	+	0.866025i
$923$		0			0
$924$		0			0
$925$	0.809017	−	1.40126i	0.809017	−	1.40126i
$926$	−1.95630			−1.95630
$927$	−1.66913	−	0.743145i	−1.66913	−	0.743145i
$928$	−1.95630			−1.95630
$929$	0.104528	−	0.181049i	0.104528	−	0.181049i	−0.809017	−	0.587785i	$-0.800000\pi$
$929$	0.104528	−	0.181049i	0.104528	−	0.181049i	0.913545	+	0.406737i	$0.133333\pi$
$930$	−1.75181	+	1.94558i	−1.75181	+	1.94558i
$931$		0			0
$932$	0.978148	+	1.69420i	0.978148	+	1.69420i
$933$	1.30902	−	1.45381i	1.30902	−	1.45381i
$934$		0			0
$935$		0			0
$936$	−1.78716	−	0.795697i	−1.78716	−	0.795697i
$937$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$937$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$941$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$942$		0			0
$943$	0.413545	−	0.716282i	0.413545	−	0.716282i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$947$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$948$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$949$	0.204489	+	0.354185i	0.204489	+	0.354185i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$953$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$954$		0			0
$955$	−2.95630			−2.95630
$956$	−0.104528	+	0.181049i	−0.104528	+	0.181049i
$957$	−0.273659	+	0.303929i	−0.273659	+	0.303929i
$958$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$959$		0			0
$960$	1.08268	−	1.20243i	1.08268	−	1.20243i
$961$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$962$	1.95630			1.95630
$963$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.913545	+	1.58231i	0.913545	+	1.58231i	0.809017	+	0.587785i	$0.200000\pi$
$967$	0.913545	+	1.58231i	0.913545	+	1.58231i	0.104528	+	0.994522i	$0.466667\pi$
$968$	−0.478148	−	0.828176i	−0.478148	−	0.828176i
$969$		0			0
$970$		0			0
$971$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$971$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$972$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$973$		0			0
$974$	0.500000	−	0.866025i	0.500000	−	0.866025i
$975$	0.978148	+	3.01043i	0.978148	+	3.01043i
$976$	0.913545	+	1.58231i	0.913545	+	1.58231i
$977$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$977$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$978$		0			0
$979$		0			0
$980$	1.61803			1.61803
$981$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$982$	−1.33826			−1.33826
$983$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$983$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$984$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	−0.0353579	−	0.336408i	−0.0353579	−	0.336408i
$991$	1.95630			1.95630			0.978148	−	0.207912i	$-0.0666667\pi$
$991$	1.95630			1.95630			0.978148	+	0.207912i	$0.0666667\pi$
$992$	0.809017	−	1.40126i	0.809017	−	1.40126i
$993$		0			0
$994$		0			0
$995$	1.61803	+	2.80252i	1.61803	+	2.80252i
$996$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$997$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$997$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$998$		0			0
$999$	0.809017	+	0.587785i	0.809017	+	0.587785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2664.1.bw.d.1627.4	yes	8
8.3	odd	2		2664.1.bw.c.1627.4	✓	8
9.4	even	3	inner	2664.1.bw.d.2515.3	yes	8
37.36	even	2		2664.1.bw.c.1627.4	✓	8
72.67	odd	6		2664.1.bw.c.2515.3	yes	8
296.147	odd	2	CM	2664.1.bw.d.1627.4	yes	8
333.184	even	6		2664.1.bw.c.2515.3	yes	8
2664.2515	odd	6	inner	2664.1.bw.d.2515.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2664.1.bw.c.1627.4	✓	8	8.3	odd	2
2664.1.bw.c.1627.4	✓	8	37.36	even	2
2664.1.bw.c.2515.3	yes	8	72.67	odd	6
2664.1.bw.c.2515.3	yes	8	333.184	even	6
2664.1.bw.d.1627.4	yes	8	1.1	even	1	trivial
2664.1.bw.d.1627.4	yes	8	296.147	odd	2	CM
2664.1.bw.d.2515.3	yes	8	9.4	even	3	inner
2664.1.bw.d.2515.3	yes	8	2664.2515	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2664 = 2^{3} \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2664.bw (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.809017 - 1.40126i) q^{5} +(0.978148 + 0.207912i) q^{6} -1.00000 q^{8} +(-0.809017 + 0.587785i) q^{9} -1.61803 q^{10} +(0.104528 - 0.181049i) q^{11} +(0.669131 - 0.743145i) q^{12} +(-0.978148 - 1.69420i) q^{13} +(1.08268 - 1.20243i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.104528 + 0.994522i) q^{18} +(-0.809017 + 1.40126i) q^{20} +(-0.104528 - 0.181049i) q^{22} +(0.669131 + 1.15897i) q^{23} +(-0.309017 - 0.951057i) q^{24} +(-0.809017 + 1.40126i) q^{25} -1.95630 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.978148 + 1.69420i) q^{29} +(-0.500000 - 1.53884i) q^{30} +(-0.809017 - 1.40126i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.204489 + 0.0434654i) q^{33} +(0.913545 + 0.406737i) q^{36} -1.00000 q^{37} +(1.30902 - 1.45381i) q^{39} +(0.809017 + 1.40126i) q^{40} +(-0.309017 - 0.535233i) q^{41} -0.209057 q^{44} +(1.47815 + 0.658114i) q^{45} +1.33826 q^{46} +(-0.978148 - 0.207912i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.809017 + 1.40126i) q^{50} +(-0.978148 + 1.69420i) q^{52} +(-0.913545 + 0.406737i) q^{54} -0.338261 q^{55} +(0.978148 + 1.69420i) q^{58} +(-1.58268 - 0.336408i) q^{60} +(0.913545 - 1.58231i) q^{61} -1.61803 q^{62} +1.00000 q^{64} +(-1.58268 + 2.74128i) q^{65} +(0.139886 - 0.155360i) q^{66} +(-0.913545 - 1.58231i) q^{67} +(-0.895472 + 0.994522i) q^{69} +(0.809017 - 0.587785i) q^{72} -0.209057 q^{73} +(-0.500000 + 0.866025i) q^{74} +(-1.58268 - 0.336408i) q^{75} +(-0.604528 - 1.86055i) q^{78} +(0.309017 - 0.535233i) q^{79} +1.61803 q^{80} +(0.309017 - 0.951057i) q^{81} -0.618034 q^{82} +(0.500000 - 0.866025i) q^{83} +(-1.91355 - 0.406737i) q^{87} +(-0.104528 + 0.181049i) q^{88} +(1.30902 - 0.951057i) q^{90} +(0.669131 - 1.15897i) q^{92} +(1.08268 - 1.20243i) q^{93} +(-0.669131 + 0.743145i) q^{96} -1.00000 q^{98} +(0.0218524 + 0.207912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 2 q^{5} - q^{6} - 8 q^{8} - 2 q^{9} - 4 q^{10} - q^{11} + q^{12} + q^{13} - 2 q^{15} - 4 q^{16} - q^{18} - 2 q^{20} + q^{22} + q^{23} + 2 q^{24} - 2 q^{25} + 2 q^{26}+ \cdots + 9 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 2 * q^5 - q^6 - 8 * q^8 - 2 * q^9 - 4 * q^10 - q^11 + q^12 + q^13 - 2 * q^15 - 4 * q^16 - q^18 - 2 * q^20 + q^22 + q^23 + 2 * q^24 - 2 * q^25 + 2 * q^26 - 2 * q^27 + q^29 - 4 * q^30 - 2 * q^31 + 4 * q^32 - q^33 + q^36 - 8 * q^37 + 6 * q^39 + 2 * q^40 + 2 * q^41 + 2 * q^44 + 3 * q^45 + 2 * q^46 + q^48 - 4 * q^49 + 2 * q^50 + q^52 - q^54 + 6 * q^55 - q^58 - 2 * q^60 + q^61 - 4 * q^62 + 8 * q^64 - 2 * q^65 + q^66 - q^67 - 9 * q^69 + 2 * q^72 + 2 * q^73 - 4 * q^74 - 2 * q^75 - 3 * q^78 - 2 * q^79 + 4 * q^80 - 2 * q^81 + 4 * q^82 + 4 * q^83 - 9 * q^87 + q^88 + 6 * q^90 + q^92 - 2 * q^93 - q^96 - 8 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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