LMFDB - Embedded newform 1400.1.bs.a.461.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,1,Mod(181,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("1400.181");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1400.bs (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:	$0.698691017686$
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 5.1.1225000000.2

Embedding invariants

Embedding label			461.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	1400.461
Dual form			1400.1.bs.a.741.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.190983 - 0.587785i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.500000 + 0.363271i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.190983 - 0.587785i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.500000 + 0.363271i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(0.500000 + 0.363271i) q^{12} +(0.500000 + 0.363271i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.190983 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} -0.618034 q^{18} +(-0.618034 - 1.90211i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-0.190983 + 0.587785i) q^{21} +(-0.500000 + 0.363271i) q^{23} -0.618034 q^{24} +(0.309017 - 0.951057i) q^{25} -0.618034 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-0.500000 - 0.363271i) q^{30} +1.00000 q^{32} +(0.809017 - 0.587785i) q^{35} +(0.500000 - 0.363271i) q^{36} +(1.61803 + 1.17557i) q^{38} +(-0.309017 + 0.224514i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-0.190983 - 0.587785i) q^{42} +0.618034 q^{45} +(0.190983 - 0.587785i) q^{46} +(0.500000 - 0.363271i) q^{48} +1.00000 q^{49} +(0.309017 + 0.951057i) q^{50} +(0.500000 - 0.363271i) q^{52} +(0.309017 - 0.951057i) q^{54} +(0.309017 + 0.951057i) q^{56} +1.23607 q^{57} +(-1.30902 - 0.951057i) q^{59} +0.618034 q^{60} +(-1.30902 + 0.951057i) q^{61} +(0.500000 + 0.363271i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.618034 q^{65} +(-0.118034 - 0.363271i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(-0.500000 + 1.53884i) q^{71} +(-0.190983 + 0.587785i) q^{72} +(0.500000 + 0.363271i) q^{75} -2.00000 q^{76} +(0.118034 - 0.363271i) q^{78} +(0.190983 - 0.587785i) q^{79} -1.00000 q^{80} +(0.500000 + 1.53884i) q^{83} +(0.500000 + 0.363271i) q^{84} +(-0.500000 + 0.363271i) q^{90} +(0.500000 + 0.363271i) q^{91} +(0.190983 + 0.587785i) q^{92} +(-1.61803 - 1.17557i) q^{95} +(-0.190983 + 0.587785i) q^{96} +(-0.809017 + 0.587785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + 4 * q^7 - q^8 + 2 * q^9	$ 4 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - q^{8} + 2 q^{9} + q^{10} + 2 q^{12} + 2 q^{13} - q^{14} + 3 q^{15} - q^{16} + 2 q^{18} + 2 q^{19} + q^{20} - 3 q^{21} - 2 q^{23} + 2 q^{24} - q^{25} + 2 q^{26} - q^{27} - q^{28} - 2 q^{30} + 4 q^{32} + q^{35} + 2 q^{36} + 2 q^{38} + q^{39} + q^{40} - 3 q^{42} - 2 q^{45} + 3 q^{46} + 2 q^{48} + 4 q^{49} - q^{50} + 2 q^{52} - q^{54} - q^{56} - 4 q^{57} - 3 q^{59} - 2 q^{60} - 3 q^{61} + 2 q^{63} - q^{64} - 2 q^{65} + 4 q^{69} + q^{70} - 2 q^{71} - 3 q^{72} + 2 q^{75} - 8 q^{76} - 4 q^{78} + 3 q^{79} - 4 q^{80} + 2 q^{83} + 2 q^{84} - 2 q^{90} + 2 q^{91} + 3 q^{92} - 2 q^{95} - 3 q^{96} - q^{98}+O(q^{100}) $ 4 * q - q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + 4 * q^7 - q^8 + 2 * q^9 + q^10 + 2 * q^12 + 2 * q^13 - q^14 + 3 * q^15 - q^16 + 2 * q^18 + 2 * q^19 + q^20 - 3 * q^21 - 2 * q^23 + 2 * q^24 - q^25 + 2 * q^26 - q^27 - q^28 - 2 * q^30 + 4 * q^32 + q^35 + 2 * q^36 + 2 * q^38 + q^39 + q^40 - 3 * q^42 - 2 * q^45 + 3 * q^46 + 2 * q^48 + 4 * q^49 - q^50 + 2 * q^52 - q^54 - q^56 - 4 * q^57 - 3 * q^59 - 2 * q^60 - 3 * q^61 + 2 * q^63 - q^64 - 2 * q^65 + 4 * q^69 + q^70 - 2 * q^71 - 3 * q^72 + 2 * q^75 - 8 * q^76 - 4 * q^78 + 3 * q^79 - 4 * q^80 + 2 * q^83 + 2 * q^84 - 2 * q^90 + 2 * q^91 + 3 * q^92 - 2 * q^95 - 3 * q^96 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$2$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$3$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$3$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$4$	0.309017	−	0.951057i	0.309017	−	0.951057i
$5$	0.809017	−	0.587785i	0.809017	−	0.587785i
$5$	0.809017	−	0.587785i	0.809017	−	0.587785i
$6$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$7$	1.00000			1.00000
$7$	1.00000			1.00000
$8$	0.309017	+	0.951057i	0.309017	+	0.951057i
$9$	0.500000	+	0.363271i	0.500000	+	0.363271i
$10$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$11$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$11$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$12$	0.500000	+	0.363271i	0.500000	+	0.363271i
$13$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$13$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$14$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$15$	0.190983	+	0.587785i	0.190983	+	0.587785i
$16$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$17$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$17$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$18$	−0.618034			−0.618034
$19$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$19$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$20$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$21$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$22$		0			0
$23$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$23$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$24$	−0.618034			−0.618034
$25$	0.309017	−	0.951057i	0.309017	−	0.951057i
$26$	−0.618034			−0.618034
$27$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$28$	0.309017	−	0.951057i	0.309017	−	0.951057i
$29$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$29$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$30$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$31$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$31$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$32$	1.00000			1.00000
$33$		0			0
$34$		0			0
$35$	0.809017	−	0.587785i	0.809017	−	0.587785i
$36$	0.500000	−	0.363271i	0.500000	−	0.363271i
$37$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$37$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$38$	1.61803	+	1.17557i	1.61803	+	1.17557i
$39$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$40$	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	$0.200000\pi$
$42$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$		0			0
$45$	0.618034			0.618034
$46$	0.190983	−	0.587785i	0.190983	−	0.587785i
$47$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$47$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$48$	0.500000	−	0.363271i	0.500000	−	0.363271i
$49$	1.00000			1.00000
$50$	0.309017	+	0.951057i	0.309017	+	0.951057i
$51$		0			0
$52$	0.500000	−	0.363271i	0.500000	−	0.363271i
$53$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$53$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$54$	0.309017	−	0.951057i	0.309017	−	0.951057i
$55$		0			0
$56$	0.309017	+	0.951057i	0.309017	+	0.951057i
$57$	1.23607			1.23607
$58$		0			0
$59$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$59$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$60$	0.618034			0.618034
$61$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$61$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$62$		0			0
$63$	0.500000	+	0.363271i	0.500000	+	0.363271i
$64$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$65$	0.618034			0.618034
$66$		0			0
$67$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$67$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$68$		0			0
$69$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$70$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$71$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$71$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$72$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$73$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$73$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$74$		0			0
$75$	0.500000	+	0.363271i	0.500000	+	0.363271i
$76$	−2.00000			−2.00000
$77$		0			0
$78$	0.118034	−	0.363271i	0.118034	−	0.363271i
$79$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$79$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$80$	−1.00000			−1.00000
$81$		0			0
$82$		0			0
$83$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$83$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$84$	0.500000	+	0.363271i	0.500000	+	0.363271i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$89$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$90$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$91$	0.500000	+	0.363271i	0.500000	+	0.363271i
$92$	0.190983	+	0.587785i	0.190983	+	0.587785i
$93$		0			0
$94$		0			0
$95$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$96$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$97$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$97$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$98$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$99$		0			0
$100$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$101$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$101$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$102$		0			0
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$105$	0.190983	+	0.587785i	0.190983	+	0.587785i
$106$		0			0
$107$		0			0		1.00000			$0$
$107$		0			0		−1.00000			$\pi$
$108$	0.309017	+	0.951057i	0.309017	+	0.951057i
$109$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$109$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$110$		0			0
$111$		0			0
$112$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$113$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$113$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$114$	−1.00000	+	0.726543i	−1.00000	+	0.726543i
$115$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$116$		0			0
$117$	0.118034	+	0.363271i	0.118034	+	0.363271i
$118$	1.61803			1.61803
$119$		0			0
$120$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$121$	0.309017	−	0.951057i	0.309017	−	0.951057i
$122$	0.500000	−	1.53884i	0.500000	−	1.53884i
$123$		0			0
$124$		0			0
$125$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$126$	−0.618034			−0.618034
$127$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$127$	−1.61803	+	1.17557i	−1.61803	+	1.17557i	−0.809017	+	0.587785i	$0.800000\pi$
$128$	0.309017	−	0.951057i	0.309017	−	0.951057i
$129$		0			0
$130$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$131$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$131$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$132$		0			0
$133$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$134$		0			0
$135$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$136$		0			0
$137$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$137$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$138$	0.309017	+	0.224514i	0.309017	+	0.224514i
$139$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$139$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$140$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$141$		0			0
$142$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$143$		0			0
$144$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$145$		0			0
$146$		0			0
$147$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−0.618034			−0.618034
$151$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$151$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$152$	1.61803	−	1.17557i	1.61803	−	1.17557i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.118034	+	0.363271i	0.118034	+	0.363271i
$157$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$157$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$158$	0.190983	+	0.587785i	0.190983	+	0.587785i
$159$		0			0
$160$	0.809017	−	0.587785i	0.809017	−	0.587785i
$161$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$162$		0			0
$163$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$163$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$164$		0			0
$165$		0			0
$166$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$167$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$167$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$168$	−0.618034			−0.618034
$169$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$170$		0			0
$171$	0.381966	−	1.17557i	0.381966	−	1.17557i
$172$		0			0
$173$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$173$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$174$		0			0
$175$	0.309017	−	0.951057i	0.309017	−	0.951057i
$176$		0			0
$177$	0.809017	−	0.587785i	0.809017	−	0.587785i
$178$		0			0
$179$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$179$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$180$	0.190983	−	0.587785i	0.190983	−	0.587785i
$181$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$181$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$182$	−0.618034			−0.618034
$183$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$184$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$190$	2.00000			2.00000
$191$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$191$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$192$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$193$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$193$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$194$		0			0
$195$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$196$	0.309017	−	0.951057i	0.309017	−	0.951057i
$197$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$197$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	1.00000			1.00000
$201$		0			0
$202$	0.500000	−	0.363271i	0.500000	−	0.363271i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.381966			−0.381966
$208$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$209$		0			0
$210$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$211$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$211$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$212$		0			0
$213$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$214$		0			0
$215$		0			0
$216$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$223$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$224$	1.00000			1.00000
$225$	0.500000	−	0.363271i	0.500000	−	0.363271i
$226$	−1.61803			−1.61803
$227$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$227$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$228$	0.381966	−	1.17557i	0.381966	−	1.17557i
$229$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$229$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$230$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$231$		0			0
$232$		0			0
$233$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$233$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$234$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$235$		0			0
$236$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$237$	0.309017	+	0.224514i	0.309017	+	0.224514i
$238$		0			0
$239$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$239$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$240$	0.190983	−	0.587785i	0.190983	−	0.587785i
$241$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$241$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$242$	0.309017	+	0.951057i	0.309017	+	0.951057i
$243$	−1.00000			−1.00000
$244$	0.500000	+	1.53884i	0.500000	+	1.53884i
$245$	0.809017	−	0.587785i	0.809017	−	0.587785i
$246$		0			0
$247$	0.381966	−	1.17557i	0.381966	−	1.17557i
$248$		0			0
$249$	−1.00000			−1.00000
$250$	0.809017	+	0.587785i	0.809017	+	0.587785i
$251$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$251$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$252$	0.500000	−	0.363271i	0.500000	−	0.363271i
$253$		0			0
$254$	0.618034	−	1.90211i	0.618034	−	1.90211i
$255$		0			0
$256$	0.309017	+	0.951057i	0.309017	+	0.951057i
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$		0			0
$259$		0			0
$260$	0.190983	−	0.587785i	0.190983	−	0.587785i
$261$		0			0
$262$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$263$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$263$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$264$		0			0
$265$		0			0
$266$	1.61803	+	1.17557i	1.61803	+	1.17557i
$267$		0			0
$268$		0			0
$269$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$269$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$270$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$271$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$271$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$272$		0			0
$273$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$274$	2.00000			2.00000
$275$		0			0
$276$	−0.381966			−0.381966
$277$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$277$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$278$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$279$		0			0
$280$	0.809017	+	0.587785i	0.809017	+	0.587785i
$281$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$281$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$282$		0			0
$283$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$283$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$284$	1.30902	+	0.951057i	1.30902	+	0.951057i
$285$	1.00000	−	0.726543i	1.00000	−	0.726543i
$286$		0			0
$287$		0			0
$288$	0.500000	+	0.363271i	0.500000	+	0.363271i
$289$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.00000			−2.00000			−1.00000			$\pi$
$293$	−2.00000			−2.00000			−1.00000			$\pi$
$294$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$295$	−1.61803			−1.61803
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.381966			−0.381966
$300$	0.500000	−	0.363271i	0.500000	−	0.363271i
$301$		0			0
$302$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$303$	0.118034	−	0.363271i	0.118034	−	0.363271i
$304$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$305$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$306$		0			0
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$307$	−2.00000			−2.00000			−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$313$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$313$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$314$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$315$	0.618034			0.618034
$316$	−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
$319$		0			0
$320$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$321$		0			0
$322$	0.190983	−	0.587785i	0.190983	−	0.587785i
$323$		0			0
$324$		0			0
$325$	0.500000	−	0.363271i	0.500000	−	0.363271i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$331$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$332$	1.61803			1.61803
$333$		0			0
$334$		0			0
$335$		0			0
$336$	0.500000	−	0.363271i	0.500000	−	0.363271i
$337$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$337$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$338$	0.500000	+	0.363271i	0.500000	+	0.363271i
$339$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$340$		0			0
$341$		0			0
$342$	0.381966	+	1.17557i	0.381966	+	1.17557i
$343$	1.00000			1.00000
$344$		0			0
$345$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$346$	0.500000	−	1.53884i	0.500000	−	1.53884i
$347$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$347$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$348$		0			0
$349$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$349$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$350$	0.309017	+	0.951057i	0.309017	+	0.951057i
$351$	−0.618034			−0.618034
$352$		0			0
$353$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$353$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$354$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$355$	0.500000	+	1.53884i	0.500000	+	1.53884i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$359$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$360$	0.190983	+	0.587785i	0.190983	+	0.587785i
$361$	−2.42705	+	1.76336i	−2.42705	+	1.76336i
$362$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$363$	0.500000	+	0.363271i	0.500000	+	0.363271i
$364$	0.500000	−	0.363271i	0.500000	−	0.363271i
$365$		0			0
$366$	0.809017	+	0.587785i	0.809017	+	0.587785i
$367$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$367$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$368$	0.618034			0.618034
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$373$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$374$		0			0
$375$	0.618034			0.618034
$376$		0			0
$377$		0			0
$378$	0.309017	−	0.951057i	0.309017	−	0.951057i
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$381$	−0.381966	−	1.17557i	−0.381966	−	1.17557i
$382$	0.618034			0.618034
$383$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$383$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$384$	0.500000	+	0.363271i	0.500000	+	0.363271i
$385$		0			0
$386$	1.30902	−	0.951057i	1.30902	−	0.951057i
$387$		0			0
$388$		0			0
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$391$		0			0
$392$	0.309017	+	0.951057i	0.309017	+	0.951057i
$393$	−1.00000			−1.00000
$394$		0			0
$395$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$396$		0			0
$397$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$397$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$398$		0			0
$399$	1.23607			1.23607
$400$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$401$	2.00000			2.00000			1.00000			$0$
$401$	2.00000			2.00000			1.00000			$0$
$402$		0			0
$403$		0			0
$404$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$405$		0			0
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$409$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$410$		0			0
$411$	1.00000	−	0.726543i	1.00000	−	0.726543i
$412$		0			0
$413$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$414$	0.309017	−	0.224514i	0.309017	−	0.224514i
$415$	1.30902	+	0.951057i	1.30902	+	0.951057i
$416$	0.500000	+	0.363271i	0.500000	+	0.363271i
$417$	0.381966	+	1.17557i	0.381966	+	1.17557i
$418$		0			0
$419$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$419$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$420$	0.618034			0.618034
$421$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$421$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	1.00000			1.00000
$427$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$431$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$432$	1.00000			1.00000
$433$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$433$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.00000	+	0.726543i	1.00000	+	0.726543i
$438$		0			0
$439$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$439$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$440$		0			0
$441$	0.500000	+	0.363271i	0.500000	+	0.363271i
$442$		0			0
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$449$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$449$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$450$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$451$		0			0
$452$	1.30902	−	0.951057i	1.30902	−	0.951057i
$453$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$454$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$455$	0.618034			0.618034
$456$	0.381966	+	1.17557i	0.381966	+	1.17557i
$457$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$458$	0.500000	+	1.53884i	0.500000	+	1.53884i
$459$		0			0
$460$	0.500000	+	0.363271i	0.500000	+	0.363271i
$461$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$461$	1.61803	−	1.17557i	1.61803	−	1.17557i	0.809017	−	0.587785i	$-0.200000\pi$
$462$		0			0
$463$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$463$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$464$		0			0
$465$		0			0
$466$	1.30902	+	0.951057i	1.30902	+	0.951057i
$467$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$467$	−0.618034	−	1.90211i	−0.618034	−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$468$	0.381966			0.381966
$469$		0			0
$470$		0			0
$471$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$472$	0.500000	−	1.53884i	0.500000	−	1.53884i
$473$		0			0
$474$	−0.381966			−0.381966
$475$	−2.00000			−2.00000
$476$		0			0
$477$		0			0
$478$	0.190983	−	0.587785i	0.190983	−	0.587785i
$479$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$479$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$480$	0.190983	+	0.587785i	0.190983	+	0.587785i
$481$		0			0
$482$		0			0
$483$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$484$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$485$		0			0
$486$	0.809017	−	0.587785i	0.809017	−	0.587785i
$487$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$487$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$488$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$489$		0			0
$490$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$491$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$491$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$492$		0			0
$493$		0			0
$494$	0.381966	+	1.17557i	0.381966	+	1.17557i
$495$		0			0
$496$		0			0
$497$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$498$	0.809017	−	0.587785i	0.809017	−	0.587785i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	−1.00000			−1.00000
$501$		0			0
$502$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$503$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$503$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$504$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$505$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$506$		0			0
$507$	0.381966			0.381966
$508$	0.618034	+	1.90211i	0.618034	+	1.90211i
$509$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$509$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$510$		0			0
$511$		0			0
$512$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$513$	1.61803	+	1.17557i	1.61803	+	1.17557i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$520$	0.190983	+	0.587785i	0.190983	+	0.587785i
$521$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$521$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$522$		0			0
$523$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$523$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$524$	1.61803			1.61803
$525$	0.500000	+	0.363271i	0.500000	+	0.363271i
$526$	0.618034			0.618034
$527$		0			0
$528$		0			0
$529$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$530$		0			0
$531$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$532$	−2.00000			−2.00000
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$539$		0			0
$540$	0.809017	+	0.587785i	0.809017	+	0.587785i
$541$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$541$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$542$		0			0
$543$	−1.00000			−1.00000
$544$		0			0
$545$		0			0
$546$	0.118034	−	0.363271i	0.118034	−	0.363271i
$547$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$547$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$548$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$549$	−1.00000			−1.00000
$550$		0			0
$551$		0			0
$552$	0.309017	−	0.224514i	0.309017	−	0.224514i
$553$	0.190983	−	0.587785i	0.190983	−	0.587785i
$554$		0			0
$555$		0			0
$556$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$		0			0
$560$	−1.00000			−1.00000
$561$		0			0
$562$	1.30902	+	0.951057i	1.30902	+	0.951057i
$563$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$563$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$564$		0			0
$565$	1.61803			1.61803
$566$	0.500000	+	0.363271i	0.500000	+	0.363271i
$567$		0			0
$568$	−1.61803			−1.61803
$569$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$569$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$570$	−0.381966	+	1.17557i	−0.381966	+	1.17557i
$571$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$571$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$572$		0			0
$573$	0.309017	−	0.224514i	0.309017	−	0.224514i
$574$		0			0
$575$	0.190983	+	0.587785i	0.190983	+	0.587785i
$576$	−0.618034			−0.618034
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	0.309017	−	0.951057i	0.309017	−	0.951057i
$579$	0.309017	−	0.951057i	0.309017	−	0.951057i
$580$		0			0
$581$	0.500000	+	1.53884i	0.500000	+	1.53884i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	0.309017	+	0.224514i	0.309017	+	0.224514i
$586$	1.61803	−	1.17557i	1.61803	−	1.17557i
$587$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$587$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$588$	0.500000	+	0.363271i	0.500000	+	0.363271i
$589$		0			0
$590$	1.30902	−	0.951057i	1.30902	−	0.951057i
$591$		0			0
$592$		0			0
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.309017	−	0.224514i	0.309017	−	0.224514i
$599$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$599$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$600$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	0.190983	−	0.587785i	0.190983	−	0.587785i
$605$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$606$	0.118034	+	0.363271i	0.118034	+	0.363271i
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$609$		0			0
$610$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$611$		0			0
$612$		0			0
$613$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$613$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$614$	1.61803	−	1.17557i	1.61803	−	1.17557i
$615$		0			0
$616$		0			0
$617$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$617$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$618$		0			0
$619$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$619$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$620$		0			0
$621$	0.190983	−	0.587785i	0.190983	−	0.587785i
$622$		0			0
$623$		0			0
$624$	0.381966			0.381966
$625$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$626$		0			0
$627$		0			0
$628$	0.500000	−	1.53884i	0.500000	−	1.53884i
$629$		0			0
$630$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$631$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$631$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$632$	0.618034			0.618034
$633$		0			0
$634$		0			0
$635$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$636$		0			0
$637$	0.500000	+	0.363271i	0.500000	+	0.363271i
$638$		0			0
$639$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$640$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$641$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$641$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$642$		0			0
$643$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$643$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$644$	0.190983	+	0.587785i	0.190983	+	0.587785i
$645$		0			0
$646$		0			0
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$		0			0
$649$		0			0
$650$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$651$		0			0
$652$		0			0
$653$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$653$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$654$		0			0
$655$	1.30902	+	0.951057i	1.30902	+	0.951057i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$659$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$660$		0			0
$661$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$661$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$662$		0			0
$663$		0			0
$664$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$665$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$673$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$673$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$674$	0.618034			0.618034
$675$	0.309017	+	0.951057i	0.309017	+	0.951057i
$676$	−0.618034			−0.618034
$677$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$677$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$678$	0.309017	−	0.951057i	0.309017	−	0.951057i
$679$		0			0
$680$		0			0
$681$	0.118034	+	0.363271i	0.118034	+	0.363271i
$682$		0			0
$683$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$683$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$684$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$685$	−2.00000			−2.00000
$686$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$687$	0.809017	+	0.587785i	0.809017	+	0.587785i
$688$		0			0
$689$		0			0
$690$	0.381966			0.381966
$691$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$691$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$692$	0.500000	+	1.53884i	0.500000	+	1.53884i
$693$		0			0
$694$		0			0
$695$	0.618034	−	1.90211i	0.618034	−	1.90211i
$696$		0			0
$697$		0			0
$698$	0.500000	−	0.363271i	0.500000	−	0.363271i
$699$	1.00000			1.00000
$700$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	0.500000	−	0.363271i	0.500000	−	0.363271i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.618034			−0.618034
$708$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$709$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$709$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$710$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$711$	0.309017	−	0.224514i	0.309017	−	0.224514i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$718$	0.618034			0.618034
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$721$		0			0
$722$	0.927051	−	2.85317i	0.927051	−	2.85317i
$723$		0			0
$724$	1.61803			1.61803
$725$		0			0
$726$	−0.618034			−0.618034
$727$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$727$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$728$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$729$	0.190983	−	0.587785i	0.190983	−	0.587785i
$730$		0			0
$731$		0			0
$732$	−1.00000			−1.00000
$733$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$733$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$734$		0			0
$735$	0.190983	+	0.587785i	0.190983	+	0.587785i
$736$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$737$		0			0
$738$		0			0
$739$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$739$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$	0.618034	+	0.449028i	0.618034	+	0.449028i
$742$		0			0
$743$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$743$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$748$		0			0
$749$		0			0
$750$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$751$	2.00000			2.00000			1.00000			$0$
$751$	2.00000			2.00000			1.00000			$0$
$752$		0			0
$753$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$754$		0			0
$755$	0.500000	−	0.363271i	0.500000	−	0.363271i
$756$	0.309017	+	0.951057i	0.309017	+	0.951057i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$	0.618034	−	1.90211i	0.618034	−	1.90211i
$761$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$761$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$762$	1.00000	+	0.726543i	1.00000	+	0.726543i
$763$		0			0
$764$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$765$		0			0
$766$		0			0
$767$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$768$	−0.618034			−0.618034
$769$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$769$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$770$		0			0
$771$		0			0
$772$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$773$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$773$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	0.309017	+	0.224514i	0.309017	+	0.224514i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$785$	1.30902	−	0.951057i	1.30902	−	0.951057i
$786$	0.809017	−	0.587785i	0.809017	−	0.587785i
$787$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$787$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$788$		0			0
$789$	0.309017	−	0.224514i	0.309017	−	0.224514i
$790$	0.500000	+	0.363271i	0.500000	+	0.363271i
$791$	1.30902	+	0.951057i	1.30902	+	0.951057i
$792$		0			0
$793$	−1.00000			−1.00000
$794$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$795$		0			0
$796$		0			0
$797$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$797$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$798$	−1.00000	+	0.726543i	−1.00000	+	0.726543i
$799$		0			0
$800$	0.309017	−	0.951057i	0.309017	−	0.951057i
$801$		0			0
$802$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$803$		0			0
$804$		0			0
$805$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$806$		0			0
$807$	−1.00000			−1.00000
$808$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$809$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$809$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$810$		0			0
$811$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$811$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.118034	+	0.363271i	0.118034	+	0.363271i
$820$		0			0
$821$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$821$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$822$	−0.381966	+	1.17557i	−0.381966	+	1.17557i
$823$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$823$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$824$		0			0
$825$		0			0
$826$	1.61803			1.61803
$827$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$827$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$828$	−0.118034	+	0.363271i	−0.118034	+	0.363271i
$829$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$829$	−0.618034	+	1.90211i	−0.618034	+	1.90211i	−0.309017	+	0.951057i	$0.600000\pi$
$830$	−1.61803			−1.61803
$831$		0			0
$832$	−0.618034			−0.618034
$833$		0			0
$834$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	0.500000	+	0.363271i	0.500000	+	0.363271i
$839$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$839$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$840$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$841$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$842$		0			0
$843$	1.00000			1.00000
$844$		0			0
$845$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$846$		0			0
$847$	0.309017	−	0.951057i	0.309017	−	0.951057i
$848$		0			0
$849$	0.381966			0.381966
$850$		0			0
$851$		0			0
$852$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$853$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$853$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$854$	0.500000	−	1.53884i	0.500000	−	1.53884i
$855$	−0.381966	−	1.17557i	−0.381966	−	1.17557i
$856$		0			0
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$859$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$860$		0			0
$861$		0			0
$862$	1.30902	+	0.951057i	1.30902	+	0.951057i
$863$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$863$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$864$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$865$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$866$		0			0
$867$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	−1.23607			−1.23607
$875$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$876$		0			0
$877$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$877$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$878$		0			0
$879$	0.381966	−	1.17557i	0.381966	−	1.17557i
$880$		0			0
$881$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$881$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$882$	−0.618034			−0.618034
$883$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$883$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$884$		0			0
$885$	0.309017	−	0.951057i	0.309017	−	0.951057i
$886$		0			0
$887$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$887$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$888$		0			0
$889$	−1.61803	+	1.17557i	−1.61803	+	1.17557i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.309017	−	0.951057i	0.309017	−	0.951057i
$897$	0.0729490	−	0.224514i	0.0729490	−	0.224514i
$898$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$899$		0			0
$900$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$905$	1.30902	+	0.951057i	1.30902	+	0.951057i
$906$	−0.118034	−	0.363271i	−0.118034	−	0.363271i
$907$		0			0		1.00000			$0$
$907$		0			0		−1.00000			$\pi$
$908$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$909$	−0.309017	−	0.224514i	−0.309017	−	0.224514i
$910$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$911$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$911$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$912$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$913$		0			0
$914$	1.30902	−	0.951057i	1.30902	−	0.951057i
$915$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$916$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$917$	0.500000	+	1.53884i	0.500000	+	1.53884i
$918$		0			0
$919$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$919$	0.618034	+	1.90211i	0.618034	+	1.90211i	0.309017	+	0.951057i	$0.400000\pi$
$920$	−0.618034			−0.618034
$921$	0.381966	−	1.17557i	0.381966	−	1.17557i
$922$	−0.618034	+	1.90211i	−0.618034	+	1.90211i
$923$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$924$		0			0
$925$		0			0
$926$	−1.61803			−1.61803
$927$		0			0
$928$		0			0
$929$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$929$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$930$		0			0
$931$	−0.618034	−	1.90211i	−0.618034	−	1.90211i
$932$	−1.61803			−1.61803
$933$		0			0
$934$	1.61803	+	1.17557i	1.61803	+	1.17557i
$935$		0			0
$936$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$937$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$937$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$941$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$942$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$943$		0			0
$944$	0.500000	+	1.53884i	0.500000	+	1.53884i
$945$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$946$		0			0
$947$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$947$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$948$	0.309017	−	0.224514i	0.309017	−	0.224514i
$949$		0			0
$950$	1.61803	−	1.17557i	1.61803	−	1.17557i
$951$		0			0
$952$		0			0
$953$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$953$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$954$		0			0
$955$	−0.618034			−0.618034
$956$	0.190983	+	0.587785i	0.190983	+	0.587785i
$957$		0			0
$958$		0			0
$959$	−1.61803	−	1.17557i	−1.61803	−	1.17557i
$960$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$961$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$966$	0.309017	+	0.224514i	0.309017	+	0.224514i
$967$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$967$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$968$	1.00000			1.00000
$969$		0			0
$970$		0			0
$971$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$971$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$972$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$973$	1.61803	−	1.17557i	1.61803	−	1.17557i
$974$	−1.61803			−1.61803
$975$	0.118034	+	0.363271i	0.118034	+	0.363271i
$976$	1.61803			1.61803
$977$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$977$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$978$		0			0
$979$		0			0
$980$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$981$		0			0
$982$		0			0
$983$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$983$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−1.00000	−	0.726543i	−1.00000	−	0.726543i
$989$		0			0
$990$		0			0
$991$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$991$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$992$		0			0
$993$		0			0
$994$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$995$		0			0
$996$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$997$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$997$	−0.190983	+	0.587785i	−0.190983	+	0.587785i	−1.00000			$\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.1.bs.a.461.1	✓	4
7.6	odd	2		1400.1.bs.b.461.1	yes	4
8.5	even	2		1400.1.bs.b.461.1	yes	4
25.16	even	5	inner	1400.1.bs.a.741.1	yes	4
56.13	odd	2	CM	1400.1.bs.a.461.1	✓	4
175.41	odd	10		1400.1.bs.b.741.1	yes	4
200.141	even	10		1400.1.bs.b.741.1	yes	4
1400.741	odd	10	inner	1400.1.bs.a.741.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.1.bs.a.461.1	✓	4	1.1	even	1	trivial
1400.1.bs.a.461.1	✓	4	56.13	odd	2	CM
1400.1.bs.a.741.1	yes	4	25.16	even	5	inner
1400.1.bs.a.741.1	yes	4	1400.741	odd	10	inner
1400.1.bs.b.461.1	yes	4	7.6	odd	2
1400.1.bs.b.461.1	yes	4	8.5	even	2
1400.1.bs.b.741.1	yes	4	175.41	odd	10
1400.1.bs.b.741.1	yes	4	200.141	even	10

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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1400.bs (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.190983 - 0.587785i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.500000 + 0.363271i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.190983 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.190983 - 0.587785i) q^{6} +1.00000 q^{7} +(0.309017 + 0.951057i) q^{8} +(0.500000 + 0.363271i) q^{9} +(-0.309017 + 0.951057i) q^{10} +(0.500000 + 0.363271i) q^{12} +(0.500000 + 0.363271i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(0.190983 + 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} -0.618034 q^{18} +(-0.618034 - 1.90211i) q^{19} +(-0.309017 - 0.951057i) q^{20} +(-0.190983 + 0.587785i) q^{21} +(-0.500000 + 0.363271i) q^{23} -0.618034 q^{24} +(0.309017 - 0.951057i) q^{25} -0.618034 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-0.500000 - 0.363271i) q^{30} +1.00000 q^{32} +(0.809017 - 0.587785i) q^{35} +(0.500000 - 0.363271i) q^{36} +(1.61803 + 1.17557i) q^{38} +(-0.309017 + 0.224514i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-0.190983 - 0.587785i) q^{42} +0.618034 q^{45} +(0.190983 - 0.587785i) q^{46} +(0.500000 - 0.363271i) q^{48} +1.00000 q^{49} +(0.309017 + 0.951057i) q^{50} +(0.500000 - 0.363271i) q^{52} +(0.309017 - 0.951057i) q^{54} +(0.309017 + 0.951057i) q^{56} +1.23607 q^{57} +(-1.30902 - 0.951057i) q^{59} +0.618034 q^{60} +(-1.30902 + 0.951057i) q^{61} +(0.500000 + 0.363271i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.618034 q^{65} +(-0.118034 - 0.363271i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(-0.500000 + 1.53884i) q^{71} +(-0.190983 + 0.587785i) q^{72} +(0.500000 + 0.363271i) q^{75} -2.00000 q^{76} +(0.118034 - 0.363271i) q^{78} +(0.190983 - 0.587785i) q^{79} -1.00000 q^{80} +(0.500000 + 1.53884i) q^{83} +(0.500000 + 0.363271i) q^{84} +(-0.500000 + 0.363271i) q^{90} +(0.500000 + 0.363271i) q^{91} +(0.190983 + 0.587785i) q^{92} +(-1.61803 - 1.17557i) q^{95} +(-0.190983 + 0.587785i) q^{96} +(-0.809017 + 0.587785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + 4 * q^7 - q^8 + 2 * q^9	\( 4 q - q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} + 4 q^{7} - q^{8} + 2 q^{9} + q^{10} + 2 q^{12} + 2 q^{13} - q^{14} + 3 q^{15} - q^{16} + 2 q^{18} + 2 q^{19} + q^{20} - 3 q^{21} - 2 q^{23} + 2 q^{24} - q^{25} + 2 q^{26} - q^{27} - q^{28} - 2 q^{30} + 4 q^{32} + q^{35} + 2 q^{36} + 2 q^{38} + q^{39} + q^{40} - 3 q^{42} - 2 q^{45} + 3 q^{46} + 2 q^{48} + 4 q^{49} - q^{50} + 2 q^{52} - q^{54} - q^{56} - 4 q^{57} - 3 q^{59} - 2 q^{60} - 3 q^{61} + 2 q^{63} - q^{64} - 2 q^{65} + 4 q^{69} + q^{70} - 2 q^{71} - 3 q^{72} + 2 q^{75} - 8 q^{76} - 4 q^{78} + 3 q^{79} - 4 q^{80} + 2 q^{83} + 2 q^{84} - 2 q^{90} + 2 q^{91} + 3 q^{92} - 2 q^{95} - 3 q^{96} - q^{98}+O(q^{100}) \) 4 * q - q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 + 4 * q^7 - q^8 + 2 * q^9 + q^10 + 2 * q^12 + 2 * q^13 - q^14 + 3 * q^15 - q^16 + 2 * q^18 + 2 * q^19 + q^20 - 3 * q^21 - 2 * q^23 + 2 * q^24 - q^25 + 2 * q^26 - q^27 - q^28 - 2 * q^30 + 4 * q^32 + q^35 + 2 * q^36 + 2 * q^38 + q^39 + q^40 - 3 * q^42 - 2 * q^45 + 3 * q^46 + 2 * q^48 + 4 * q^49 - q^50 + 2 * q^52 - q^54 - q^56 - 4 * q^57 - 3 * q^59 - 2 * q^60 - 3 * q^61 + 2 * q^63 - q^64 - 2 * q^65 + 4 * q^69 + q^70 - 2 * q^71 - 3 * q^72 + 2 * q^75 - 8 * q^76 - 4 * q^78 + 3 * q^79 - 4 * q^80 + 2 * q^83 + 2 * q^84 - 2 * q^90 + 2 * q^91 + 3 * q^92 - 2 * q^95 - 3 * q^96 - q^98

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