LMFDB - Embedded newform 2600.1.ck.d.1611.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2600,1,Mod(571,2600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2600, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 6, 5]))

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

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

chi := DirichletCharacter("2600.571");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2600 = 2^{3} \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2600.ck (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:	$1.29756903285$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
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:	$\Z[a_1, \ldots, a_{5}]$
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			1611.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	2600.1611
Dual form			2600.1.ck.d.1091.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.309017 + 0.951057i) q^{6} +0.209057 q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.309017 + 0.951057i) q^{6} +0.209057 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{10} +(0.809017 + 0.587785i) q^{12} +(0.809017 + 0.587785i) q^{13} +(0.169131 - 0.122881i) q^{14} +(0.669131 + 0.743145i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.604528 - 1.86055i) q^{17} +(-0.669131 - 0.743145i) q^{20} +(-0.0646021 + 0.198825i) q^{21} +1.00000 q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.0646021 - 0.198825i) q^{28} +(0.978148 + 0.207912i) q^{30} +(0.500000 + 1.53884i) q^{31} -1.00000 q^{32} +(-1.58268 - 1.14988i) q^{34} +(0.104528 - 0.181049i) q^{35} +(1.08268 + 0.786610i) q^{37} +(-0.809017 + 0.587785i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(0.0646021 + 0.198825i) q^{42} -0.209057 q^{43} +(0.604528 - 1.86055i) q^{47} +(0.809017 - 0.587785i) q^{48} -0.956295 q^{49} +(-0.913545 - 0.406737i) q^{50} +1.95630 q^{51} +(0.809017 - 0.587785i) q^{52} +(-0.309017 + 0.951057i) q^{54} +(-0.0646021 - 0.198825i) q^{56} +(0.913545 - 0.406737i) q^{60} +(1.30902 + 0.951057i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(0.913545 - 0.406737i) q^{65} -1.95630 q^{68} +(-0.0218524 - 0.207912i) q^{70} +(-0.413545 + 1.27276i) q^{71} +1.33826 q^{74} +(0.978148 - 0.207912i) q^{75} +(-0.309017 + 0.951057i) q^{78} +(-0.913545 + 0.406737i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(0.169131 + 0.122881i) q^{84} +(-1.91355 - 0.406737i) q^{85} +(-0.169131 + 0.122881i) q^{86} +(0.169131 + 0.122881i) q^{91} -1.61803 q^{93} +(-0.604528 - 1.86055i) q^{94} +(0.309017 - 0.951057i) q^{96} +(-0.773659 + 0.562096i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + q^{10} + 2 q^{12} + 2 q^{13} - 3 q^{14} + q^{15} - 2 q^{16} - 3 q^{17} - q^{20} + 2 q^{21} + 8 q^{24} - 4 q^{25} + 8 q^{26} - 2 q^{27} - 2 q^{28} - q^{30} + 4 q^{31} - 8 q^{32} - 2 q^{34} - q^{35} - 2 q^{37} - 2 q^{39} + q^{40} - 2 q^{42} + 2 q^{43} + 3 q^{47} + 2 q^{48} + 10 q^{49} - q^{50} - 2 q^{51} + 2 q^{52} + 2 q^{54} + 2 q^{56} + q^{60} + 6 q^{62} - 2 q^{64} + q^{65} + 2 q^{68} - 9 q^{70} + 3 q^{71} + 2 q^{74} - q^{75} + 2 q^{78} - q^{80} + 2 q^{81} - 3 q^{84} - 9 q^{85} + 3 q^{86} - 3 q^{91} - 4 q^{93} - 3 q^{94} - 2 q^{96}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + q^10 + 2 * q^12 + 2 * q^13 - 3 * q^14 + q^15 - 2 * q^16 - 3 * q^17 - q^20 + 2 * q^21 + 8 * q^24 - 4 * q^25 + 8 * q^26 - 2 * q^27 - 2 * q^28 - q^30 + 4 * q^31 - 8 * q^32 - 2 * q^34 - q^35 - 2 * q^37 - 2 * q^39 + q^40 - 2 * q^42 + 2 * q^43 + 3 * q^47 + 2 * q^48 + 10 * q^49 - q^50 - 2 * q^51 + 2 * q^52 + 2 * q^54 + 2 * q^56 + q^60 + 6 * q^62 - 2 * q^64 + q^65 + 2 * q^68 - 9 * q^70 + 3 * q^71 + 2 * q^74 - q^75 + 2 * q^78 - q^80 + 2 * q^81 - 3 * q^84 - 9 * q^85 + 3 * q^86 - 3 * q^91 - 4 * q^93 - 3 * q^94 - 2 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2600\mathbb{Z}\right)^\times$.

$n$	$1301$	$1601$	$1951$	$1977$
$\chi(n)$	$-1$	$-1$	$-1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$3$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$4$	0.309017	−	0.951057i	0.309017	−	0.951057i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$5$	0.500000	−	0.866025i	0.500000	−	0.866025i
$6$	0.309017	+	0.951057i	0.309017	+	0.951057i
$7$	0.209057			0.209057			0.104528	−	0.994522i	$-0.466667\pi$
$7$	0.209057			0.209057			0.104528	+	0.994522i	$0.466667\pi$
$8$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$9$		0			0
$10$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$11$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$11$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$12$	0.809017	+	0.587785i	0.809017	+	0.587785i
$13$	0.809017	+	0.587785i	0.809017	+	0.587785i
$13$	0.809017	+	0.587785i	0.809017	+	0.587785i
$14$	0.169131	−	0.122881i	0.169131	−	0.122881i
$15$	0.669131	+	0.743145i	0.669131	+	0.743145i
$16$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$17$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.500000	−	0.866025i	$-0.666667\pi$
$17$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.104528	−	0.994522i	$-0.533333\pi$
$18$		0			0
$19$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$19$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$20$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$21$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$22$		0			0
$23$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$23$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$24$	1.00000			1.00000
$25$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$26$	1.00000			1.00000
$27$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$28$	0.0646021	−	0.198825i	0.0646021	−	0.198825i
$29$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$29$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$30$	0.978148	+	0.207912i	0.978148	+	0.207912i
$31$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$31$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$32$	−1.00000			−1.00000
$33$		0			0
$34$	−1.58268	−	1.14988i	−1.58268	−	1.14988i
$35$	0.104528	−	0.181049i	0.104528	−	0.181049i
$36$		0			0
$37$	1.08268	+	0.786610i	1.08268	+	0.786610i	0.978148	−	0.207912i	$-0.0666667\pi$
$37$	1.08268	+	0.786610i	1.08268	+	0.786610i	0.104528	+	0.994522i	$0.466667\pi$
$38$		0			0
$39$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$40$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$41$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$41$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$42$	0.0646021	+	0.198825i	0.0646021	+	0.198825i
$43$	−0.209057			−0.209057			−0.104528	−	0.994522i	$-0.533333\pi$
$43$	−0.209057			−0.209057			−0.104528	+	0.994522i	$0.533333\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.604528	−	1.86055i	0.604528	−	1.86055i	0.104528	−	0.994522i	$-0.466667\pi$
$47$	0.604528	−	1.86055i	0.604528	−	1.86055i	0.500000	−	0.866025i	$-0.333333\pi$
$48$	0.809017	−	0.587785i	0.809017	−	0.587785i
$49$	−0.956295			−0.956295
$50$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$51$	1.95630			1.95630
$52$	0.809017	−	0.587785i	0.809017	−	0.587785i
$53$		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
$56$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$57$		0			0
$58$		0			0
$59$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$59$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$60$	0.913545	−	0.406737i	0.913545	−	0.406737i
$61$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$61$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$62$	1.30902	+	0.951057i	1.30902	+	0.951057i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$65$	0.913545	−	0.406737i	0.913545	−	0.406737i
$66$		0			0
$67$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$67$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$68$	−1.95630			−1.95630
$69$		0			0
$70$	−0.0218524	−	0.207912i	−0.0218524	−	0.207912i
$71$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	0.500000	+	0.866025i	$0.333333\pi$
$71$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	−0.913545	+	0.406737i	$0.866667\pi$
$72$		0			0
$73$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$73$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$74$	1.33826			1.33826
$75$	0.978148	−	0.207912i	0.978148	−	0.207912i
$76$		0			0
$77$		0			0
$78$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$79$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$79$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$80$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$81$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$82$		0			0
$83$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$83$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$84$	0.169131	+	0.122881i	0.169131	+	0.122881i
$85$	−1.91355	−	0.406737i	−1.91355	−	0.406737i
$86$	−0.169131	+	0.122881i	−0.169131	+	0.122881i
$87$		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			0
$91$	0.169131	+	0.122881i	0.169131	+	0.122881i
$92$		0			0
$93$	−1.61803			−1.61803
$94$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$95$		0			0
$96$	0.309017	−	0.951057i	0.309017	−	0.951057i
$97$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$97$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$98$	−0.773659	+	0.562096i	−0.773659	+	0.562096i
$99$		0			0
$100$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	1.58268	−	1.14988i	1.58268	−	1.14988i
$103$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$103$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$104$	0.309017	−	0.951057i	0.309017	−	0.951057i
$105$	0.139886	+	0.155360i	0.139886	+	0.155360i
$106$		0			0
$107$	0.618034			0.618034			0.309017	−	0.951057i	$-0.400000\pi$
$107$	0.618034			0.618034			0.309017	+	0.951057i	$0.400000\pi$
$108$	0.309017	+	0.951057i	0.309017	+	0.951057i
$109$	1.47815	+	1.07394i	1.47815	+	1.07394i	0.978148	+	0.207912i	$0.0666667\pi$
$109$	1.47815	+	1.07394i	1.47815	+	1.07394i	0.500000	+	0.866025i	$0.333333\pi$
$110$		0			0
$111$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$112$	−0.169131	−	0.122881i	−0.169131	−	0.122881i
$113$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$113$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.126381	−	0.388960i	−0.126381	−	0.388960i
$120$	0.500000	−	0.866025i	0.500000	−	0.866025i
$121$	0.309017	−	0.951057i	0.309017	−	0.951057i
$122$		0			0
$123$		0			0
$124$	1.61803			1.61803
$125$	−1.00000			−1.00000
$126$		0			0
$127$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$127$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$128$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$129$	0.0646021	−	0.198825i	0.0646021	−	0.198825i
$130$	0.500000	−	0.866025i	0.500000	−	0.866025i
$131$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$131$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	0.104528	+	0.994522i	0.104528	+	0.994522i
$136$	−1.58268	+	1.14988i	−1.58268	+	1.14988i
$137$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$137$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$138$		0			0
$139$	−1.47815	+	1.07394i	−1.47815	+	1.07394i	−0.500000	+	0.866025i	$0.666667\pi$
$139$	−1.47815	+	1.07394i	−1.47815	+	1.07394i	−0.978148	+	0.207912i	$0.933333\pi$
$140$	−0.139886	−	0.155360i	−0.139886	−	0.155360i
$141$	1.58268	+	1.14988i	1.58268	+	1.14988i
$142$	0.413545	+	1.27276i	0.413545	+	1.27276i
$143$		0			0
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.295511	−	0.909491i	0.295511	−	0.909491i
$148$	1.08268	−	0.786610i	1.08268	−	0.786610i
$149$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$149$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$150$	0.669131	−	0.743145i	0.669131	−	0.743145i
$151$	−1.33826			−1.33826			−0.669131	−	0.743145i	$-0.733333\pi$
$151$	−1.33826			−1.33826			−0.669131	+	0.743145i	$0.733333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.58268	+	0.336408i	1.58268	+	0.336408i
$156$	0.309017	+	0.951057i	0.309017	+	0.951057i
$157$		0			0		1.00000			$0$
$157$		0			0		−1.00000			$\pi$
$158$		0			0
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$161$		0			0
$162$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$163$		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
$166$		0			0
$167$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$167$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$168$	0.209057			0.209057
$169$	0.309017	+	0.951057i	0.309017	+	0.951057i
$170$	−1.78716	+	0.795697i	−1.78716	+	0.795697i
$171$		0			0
$172$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$173$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$173$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$	−0.104528	−	0.181049i	−0.104528	−	0.181049i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.104528	+	0.994522i	$0.533333\pi$
$179$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.500000	+	0.866025i	$0.666667\pi$
$180$		0			0
$181$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$181$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$182$	0.209057			0.209057
$183$		0			0
$184$		0			0
$185$	1.22256	−	0.544320i	1.22256	−	0.544320i
$186$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$187$		0			0
$188$	−1.58268	−	1.14988i	−1.58268	−	1.14988i
$189$	−0.169131	+	0.122881i	−0.169131	+	0.122881i
$190$		0			0
$191$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$191$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$192$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$193$		0			0		1.00000			$0$
$193$		0			0		−1.00000			$\pi$
$194$		0			0
$195$	0.104528	+	0.994522i	0.104528	+	0.994522i
$196$	−0.295511	+	0.909491i	−0.295511	+	0.909491i
$197$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	0.500000	+	0.866025i	$0.333333\pi$
$197$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	−0.913545	+	0.406737i	$0.866667\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.604528	−	1.86055i	0.604528	−	1.86055i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$209$		0			0
$210$	0.204489	+	0.0434654i	0.204489	+	0.0434654i
$211$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$211$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$212$		0			0
$213$	−1.08268	−	0.786610i	−1.08268	−	0.786610i
$214$	0.500000	−	0.363271i	0.500000	−	0.363271i
$215$	−0.104528	+	0.181049i	−0.104528	+	0.181049i
$216$	0.809017	+	0.587785i	0.809017	+	0.587785i
$217$	0.104528	+	0.321706i	0.104528	+	0.321706i
$218$	1.82709			1.82709
$219$		0			0
$220$		0			0
$221$	0.604528	−	1.86055i	0.604528	−	1.86055i
$222$	−0.413545	+	1.27276i	−0.413545	+	1.27276i
$223$	−0.169131	+	0.122881i	−0.169131	+	0.122881i	−0.669131	−	0.743145i	$-0.733333\pi$
$223$	−0.169131	+	0.122881i	−0.169131	+	0.122881i	0.500000	+	0.866025i	$0.333333\pi$
$224$	−0.209057			−0.209057
$225$		0			0
$226$	−0.618034			−0.618034
$227$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$227$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$228$		0			0
$229$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	0.500000	+	0.866025i	$0.333333\pi$
$229$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	−0.913545	+	0.406737i	$0.866667\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	0.913545	−	0.406737i	$-0.133333\pi$
$233$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	−0.978148	+	0.207912i	$0.933333\pi$
$234$		0			0
$235$	−1.30902	−	1.45381i	−1.30902	−	1.45381i
$236$		0			0
$237$		0			0
$238$	−0.330869	−	0.240391i	−0.330869	−	0.240391i
$239$	1.47815	−	1.07394i	1.47815	−	1.07394i	0.500000	−	0.866025i	$-0.333333\pi$
$239$	1.47815	−	1.07394i	1.47815	−	1.07394i	0.978148	−	0.207912i	$-0.0666667\pi$
$240$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$241$		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
$243$		0			0
$244$		0			0
$245$	−0.478148	+	0.828176i	−0.478148	+	0.828176i
$246$		0			0
$247$		0			0
$248$	1.30902	−	0.951057i	1.30902	−	0.951057i
$249$		0			0
$250$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$251$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$251$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	0.978148	−	1.69420i	0.978148	−	1.69420i
$256$	0.309017	+	0.951057i	0.309017	+	0.951057i
$257$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$257$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$258$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$259$	0.226341	+	0.164446i	0.226341	+	0.164446i
$260$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$261$		0			0
$262$	1.47815	+	1.07394i	1.47815	+	1.07394i
$263$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$263$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$269$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$270$	0.669131	+	0.743145i	0.669131	+	0.743145i
$271$	0.0646021	−	0.198825i	0.0646021	−	0.198825i	−0.913545	−	0.406737i	$-0.866667\pi$
$271$	0.0646021	−	0.198825i	0.0646021	−	0.198825i	0.978148	+	0.207912i	$0.0666667\pi$
$272$	−0.604528	+	1.86055i	−0.604528	+	1.86055i
$273$	−0.169131	+	0.122881i	−0.169131	+	0.122881i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$277$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$278$	−0.564602	+	1.73767i	−0.564602	+	1.73767i
$279$		0			0
$280$	−0.204489	−	0.0434654i	−0.204489	−	0.0434654i
$281$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$281$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$282$	1.95630			1.95630
$283$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$283$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$284$	1.08268	+	0.786610i	1.08268	+	0.786610i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−2.28716	+	1.66172i	−2.28716	+	1.66172i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.82709			−1.82709			−0.913545	−	0.406737i	$-0.866667\pi$
$293$	−1.82709			−1.82709			−0.913545	+	0.406737i	$0.866667\pi$
$294$	−0.295511	−	0.909491i	−0.295511	−	0.909491i
$295$		0			0
$296$	0.413545	−	1.27276i	0.413545	−	1.27276i
$297$		0			0
$298$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$299$		0			0
$300$	0.104528	−	0.994522i	0.104528	−	0.994522i
$301$	−0.0437048			−0.0437048
$302$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	1.47815	−	0.658114i	1.47815	−	0.658114i
$311$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$311$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$312$	0.809017	+	0.587785i	0.809017	+	0.587785i
$313$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$313$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$317$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$318$		0			0
$319$		0			0
$320$	0.104528	+	0.994522i	0.104528	+	0.994522i
$321$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$322$		0			0
$323$		0			0
$324$	−1.00000			−1.00000
$325$	0.104528	−	0.994522i	0.104528	−	0.994522i
$326$		0			0
$327$	−1.47815	+	1.07394i	−1.47815	+	1.07394i
$328$		0			0
$329$	0.126381	−	0.388960i	0.126381	−	0.388960i
$330$		0			0
$331$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$331$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$332$		0			0
$333$		0			0
$334$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$335$		0			0
$336$	0.169131	−	0.122881i	0.169131	−	0.122881i
$337$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.913545	+	0.406737i	$0.133333\pi$
$337$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$338$	0.809017	+	0.587785i	0.809017	+	0.587785i
$339$	0.500000	−	0.363271i	0.500000	−	0.363271i
$340$	−0.978148	+	1.69420i	−0.978148	+	1.69420i
$341$		0			0
$342$		0			0
$343$	−0.408977			−0.408977
$344$	0.0646021	+	0.198825i	0.0646021	+	0.198825i
$345$		0			0
$346$		0			0
$347$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	0.669131	+	0.743145i	$0.266667\pi$
$347$	−0.309017	+	0.951057i	−0.309017	+	0.951057i	−0.978148	+	0.207912i	$0.933333\pi$
$348$		0			0
$349$	0.209057			0.209057			0.104528	−	0.994522i	$-0.466667\pi$
$349$	0.209057			0.209057			0.104528	+	0.994522i	$0.466667\pi$
$350$	−0.190983	−	0.0850311i	−0.190983	−	0.0850311i
$351$	−1.00000			−1.00000
$352$		0			0
$353$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$353$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$354$		0			0
$355$	0.895472	+	0.994522i	0.895472	+	0.994522i
$356$		0			0
$357$	0.408977			0.408977
$358$	0.604528	+	1.86055i	0.604528	+	1.86055i
$359$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$359$	1.61803	+	1.17557i	1.61803	+	1.17557i	0.809017	+	0.587785i	$0.200000\pi$
$360$		0			0
$361$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$362$		0			0
$363$	0.809017	+	0.587785i	0.809017	+	0.587785i
$364$	0.169131	−	0.122881i	0.169131	−	0.122881i
$365$		0			0
$366$		0			0
$367$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$367$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$368$		0			0
$369$		0			0
$370$	0.669131	−	1.15897i	0.669131	−	1.15897i
$371$		0			0
$372$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$373$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$373$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$374$		0			0
$375$	0.309017	−	0.951057i	0.309017	−	0.951057i
$376$	−1.95630			−1.95630
$377$		0			0
$378$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$379$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$379$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$383$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$384$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$389$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$390$	0.669131	+	0.743145i	0.669131	+	0.743145i
$391$		0			0
$392$	0.295511	+	0.909491i	0.295511	+	0.909491i
$393$	−1.82709			−1.82709
$394$	0.413545	+	1.27276i	0.413545	+	1.27276i
$395$		0			0
$396$		0			0
$397$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$397$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$398$		0			0
$399$		0			0
$400$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$404$		0			0
$405$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$406$		0			0
$407$		0			0
$408$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$409$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$409$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$417$	−0.564602	−	1.73767i	−0.564602	−	1.73767i
$418$		0			0
$419$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$419$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$420$	0.190983	−	0.0850311i	0.190983	−	0.0850311i
$421$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$421$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$422$	0.309017	−	0.951057i	0.309017	−	0.951057i
$423$		0			0
$424$		0			0
$425$	−1.30902	+	1.45381i	−1.30902	+	1.45381i
$426$	−1.33826			−1.33826
$427$		0			0
$428$	0.190983	−	0.587785i	0.190983	−	0.587785i
$429$		0			0
$430$	0.0218524	+	0.207912i	0.0218524	+	0.207912i
$431$	−0.413545	−	1.27276i	−0.413545	−	1.27276i	−0.913545	−	0.406737i	$-0.866667\pi$
$431$	−0.413545	−	1.27276i	−0.413545	−	1.27276i	0.500000	−	0.866025i	$-0.333333\pi$
$432$	1.00000			1.00000
$433$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$433$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$434$	0.273659	+	0.198825i	0.273659	+	0.198825i
$435$		0			0
$436$	1.47815	−	1.07394i	1.47815	−	1.07394i
$437$		0			0
$438$		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			0
$442$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$443$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$443$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$444$	0.413545	+	1.27276i	0.413545	+	1.27276i
$445$		0			0
$446$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$447$	0.190983	−	0.587785i	0.190983	−	0.587785i
$448$	−0.169131	+	0.122881i	−0.169131	+	0.122881i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$		0			0
$452$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$453$	0.413545	−	1.27276i	0.413545	−	1.27276i
$454$		0			0
$455$	0.190983	−	0.0850311i	0.190983	−	0.0850311i
$456$		0			0
$457$		0			0		1.00000			$0$
$457$		0			0		−1.00000			$\pi$
$458$	0.413545	+	1.27276i	0.413545	+	1.27276i
$459$	1.58268	+	1.14988i	1.58268	+	1.14988i
$460$		0			0
$461$	1.08268	−	0.786610i	1.08268	−	0.786610i	0.104528	−	0.994522i	$-0.466667\pi$
$461$	1.08268	−	0.786610i	1.08268	−	0.786610i	0.978148	+	0.207912i	$0.0666667\pi$
$462$		0			0
$463$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$463$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$464$		0			0
$465$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$466$	−0.169131	−	0.122881i	−0.169131	−	0.122881i
$467$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$467$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$468$		0			0
$469$		0			0
$470$	−1.91355	−	0.406737i	−1.91355	−	0.406737i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$	−0.408977			−0.408977
$477$		0			0
$478$	0.564602	−	1.73767i	0.564602	−	1.73767i
$479$	0.604528	−	1.86055i	0.604528	−	1.86055i	0.104528	−	0.994522i	$-0.466667\pi$
$479$	0.604528	−	1.86055i	0.604528	−	1.86055i	0.500000	−	0.866025i	$-0.333333\pi$
$480$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$481$	0.413545	+	1.27276i	0.413545	+	1.27276i
$482$		0			0
$483$		0			0
$484$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$485$		0			0
$486$		0			0
$487$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$487$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$488$		0			0
$489$		0			0
$490$	0.0999601	+	0.951057i	0.0999601	+	0.951057i
$491$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$491$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.500000	−	1.53884i	0.500000	−	1.53884i
$497$	−0.0864545	+	0.266080i	−0.0864545	+	0.266080i
$498$		0			0
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$501$	0.618034			0.618034
$502$	−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			0
$505$		0			0
$506$		0			0
$507$	−1.00000			−1.00000
$508$		0			0
$509$	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	$0.200000\pi$
$510$	−0.204489	−	1.94558i	−0.204489	−	1.94558i
$511$		0			0
$512$	0.809017	+	0.587785i	0.809017	+	0.587785i
$513$		0			0
$514$	−1.58268	+	1.14988i	−1.58268	+	1.14988i
$515$		0			0
$516$	−0.169131	−	0.122881i	−0.169131	−	0.122881i
$517$		0			0
$518$	0.279773			0.279773
$519$		0			0
$520$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$521$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$521$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$522$		0			0
$523$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$523$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$524$	1.82709			1.82709
$525$	0.204489	−	0.0434654i	0.204489	−	0.0434654i
$526$		0			0
$527$	2.56082	−	1.86055i	2.56082	−	1.86055i
$528$		0			0
$529$	0.309017	−	0.951057i	0.309017	−	0.951057i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	0.309017	−	0.535233i	0.309017	−	0.535233i
$536$		0			0
$537$	−1.58268	−	1.14988i	−1.58268	−	1.14988i
$538$		0			0
$539$		0			0
$540$	0.978148	+	0.207912i	0.978148	+	0.207912i
$541$	−0.169131	−	0.122881i	−0.169131	−	0.122881i	0.500000	−	0.866025i	$-0.333333\pi$
$541$	−0.169131	−	0.122881i	−0.169131	−	0.122881i	−0.669131	+	0.743145i	$0.733333\pi$
$542$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$543$		0			0
$544$	0.604528	+	1.86055i	0.604528	+	1.86055i
$545$	1.66913	−	0.743145i	1.66913	−	0.743145i
$546$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$547$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$547$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.139886	+	1.33093i	0.139886	+	1.33093i
$556$	0.564602	+	1.73767i	0.564602	+	1.73767i
$557$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$557$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$	−0.169131	−	0.122881i	−0.169131	−	0.122881i
$560$	−0.190983	+	0.0850311i	−0.190983	+	0.0850311i
$561$		0			0
$562$		0			0
$563$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.978148	−	0.207912i	$-0.933333\pi$
$563$	−1.47815	−	1.07394i	−1.47815	−	1.07394i	−0.500000	−	0.866025i	$-0.666667\pi$
$564$	1.58268	−	1.14988i	1.58268	−	1.14988i
$565$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$566$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$567$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$568$	1.33826			1.33826
$569$	0.413545	+	1.27276i	0.413545	+	1.27276i	0.913545	+	0.406737i	$0.133333\pi$
$569$	0.413545	+	1.27276i	0.413545	+	1.27276i	−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$571$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$		0			0
$577$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$577$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$578$	−0.873619	+	2.68872i	−0.873619	+	2.68872i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−1.47815	+	1.07394i	−1.47815	+	1.07394i
$587$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$587$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$588$	−0.773659	−	0.562096i	−0.773659	−	0.562096i
$589$		0			0
$590$		0			0
$591$	−1.08268	−	0.786610i	−1.08268	−	0.786610i
$592$	−0.413545	−	1.27276i	−0.413545	−	1.27276i
$593$		0			0		1.00000			$0$
$593$		0			0		−1.00000			$\pi$
$594$		0			0
$595$	−0.400040	−	0.0850311i	−0.400040	−	0.0850311i
$596$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$597$		0			0
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$601$	1.33826			1.33826			0.669131	−	0.743145i	$-0.266667\pi$
$601$	1.33826			1.33826			0.669131	+	0.743145i	$0.266667\pi$
$602$	−0.0353579	+	0.0256890i	−0.0353579	+	0.0256890i
$603$		0			0
$604$	−0.413545	+	1.27276i	−0.413545	+	1.27276i
$605$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$606$		0			0
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.58268	−	1.14988i	1.58268	−	1.14988i
$612$		0			0
$613$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$613$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$617$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$618$		0			0
$619$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$619$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$620$	0.809017	−	1.40126i	0.809017	−	1.40126i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	1.00000			1.00000
$625$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$626$	−1.82709			−1.82709
$627$		0			0
$628$		0			0
$629$	0.809017	−	2.48990i	0.809017	−	2.48990i
$630$		0			0
$631$	0.604528	+	1.86055i	0.604528	+	1.86055i	0.500000	+	0.866025i	$0.333333\pi$
$631$	0.604528	+	1.86055i	0.604528	+	1.86055i	0.104528	+	0.994522i	$0.466667\pi$
$632$		0			0
$633$	0.309017	+	0.951057i	0.309017	+	0.951057i
$634$	1.30902	+	0.951057i	1.30902	+	0.951057i
$635$		0			0
$636$		0			0
$637$	−0.773659	−	0.562096i	−0.773659	−	0.562096i
$638$		0			0
$639$		0			0
$640$	0.669131	+	0.743145i	0.669131	+	0.743145i
$641$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$641$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$642$	0.190983	+	0.587785i	0.190983	+	0.587785i
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$	−0.139886	−	0.155360i	−0.139886	−	0.155360i
$646$		0			0
$647$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$647$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$648$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$649$		0			0
$650$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$651$	−0.338261			−0.338261
$652$		0			0
$653$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$653$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$654$	−0.564602	+	1.73767i	−0.564602	+	1.73767i
$655$	1.78716	+	0.379874i	1.78716	+	0.379874i
$656$		0			0
$657$		0			0
$658$	−0.126381	−	0.388960i	−0.126381	−	0.388960i
$659$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$659$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$660$		0			0
$661$	0.500000	−	0.363271i	0.500000	−	0.363271i	−0.309017	−	0.951057i	$-0.600000\pi$
$661$	0.500000	−	0.363271i	0.500000	−	0.363271i	0.809017	+	0.587785i	$0.200000\pi$
$662$		0			0
$663$	1.58268	+	1.14988i	1.58268	+	1.14988i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.618034			−0.618034
$669$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i
$670$		0			0
$671$		0			0
$672$	0.0646021	−	0.198825i	0.0646021	−	0.198825i
$673$	0.169131	−	0.122881i	0.169131	−	0.122881i	−0.500000	−	0.866025i	$-0.666667\pi$
$673$	0.169131	−	0.122881i	0.169131	−	0.122881i	0.669131	+	0.743145i	$0.266667\pi$
$674$	1.95630			1.95630
$675$	0.913545	+	0.406737i	0.913545	+	0.406737i
$676$	1.00000			1.00000
$677$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$677$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$678$	0.190983	−	0.587785i	0.190983	−	0.587785i
$679$		0			0
$680$	0.204489	+	1.94558i	0.204489	+	1.94558i
$681$		0			0
$682$		0			0
$683$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$683$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$684$		0			0
$685$		0			0
$686$	−0.330869	+	0.240391i	−0.330869	+	0.240391i
$687$	−1.08268	−	0.786610i	−1.08268	−	0.786610i
$688$	0.169131	+	0.122881i	0.169131	+	0.122881i
$689$		0			0
$690$		0			0
$691$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$691$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$692$		0			0
$693$		0			0
$694$	0.309017	+	0.951057i	0.309017	+	0.951057i
$695$	0.190983	+	1.81708i	0.190983	+	1.81708i
$696$		0			0
$697$		0			0
$698$	0.169131	−	0.122881i	0.169131	−	0.122881i
$699$	0.209057			0.209057
$700$	−0.204489	+	0.0434654i	−0.204489	+	0.0434654i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$703$		0			0
$704$		0			0
$705$	1.78716	−	0.795697i	1.78716	−	0.795697i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$709$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$710$	1.30902	+	0.278240i	1.30902	+	0.278240i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	0.330869	−	0.240391i	0.330869	−	0.240391i
$715$		0			0
$716$	1.58268	+	1.14988i	1.58268	+	1.14988i
$717$	0.564602	+	1.73767i	0.564602	+	1.73767i
$718$	2.00000			2.00000
$719$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$719$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$720$		0			0
$721$		0			0
$722$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	1.00000			1.00000
$727$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$727$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$728$	0.0646021	−	0.198825i	0.0646021	−	0.198825i
$729$	0.309017	−	0.951057i	0.309017	−	0.951057i
$730$		0			0
$731$	0.126381	+	0.388960i	0.126381	+	0.388960i
$732$		0			0
$733$	−0.564602	−	1.73767i	−0.564602	−	1.73767i	−0.669131	−	0.743145i	$-0.733333\pi$
$733$	−0.564602	−	1.73767i	−0.564602	−	1.73767i	0.104528	−	0.994522i	$-0.466667\pi$
$734$		0			0
$735$	−0.639886	−	0.710666i	−0.639886	−	0.710666i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$739$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$740$	−0.139886	−	1.33093i	−0.139886	−	1.33093i
$741$		0			0
$742$		0			0
$743$	−1.33826			−1.33826			−0.669131	−	0.743145i	$-0.733333\pi$
$743$	−1.33826			−1.33826			−0.669131	+	0.743145i	$0.733333\pi$
$744$	0.500000	+	1.53884i	0.500000	+	1.53884i
$745$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.129204			0.129204
$750$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$	−1.58268	+	1.14988i	−1.58268	+	1.14988i
$753$	0.500000	−	1.53884i	0.500000	−	1.53884i
$754$		0			0
$755$	−0.669131	+	1.15897i	−0.669131	+	1.15897i
$756$	0.0646021	+	0.198825i	0.0646021	+	0.198825i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$761$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$762$		0			0
$763$	0.309017	+	0.224514i	0.309017	+	0.224514i
$764$		0			0
$765$		0			0
$766$	0.809017	+	0.587785i	0.809017	+	0.587785i
$767$		0			0
$768$	−1.00000			−1.00000
$769$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$769$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$770$		0			0
$771$	0.604528	−	1.86055i	0.604528	−	1.86055i
$772$		0			0
$773$	1.47815	−	1.07394i	1.47815	−	1.07394i	0.500000	−	0.866025i	$-0.333333\pi$
$773$	1.47815	−	1.07394i	1.47815	−	1.07394i	0.978148	−	0.207912i	$-0.0666667\pi$
$774$		0			0
$775$	1.08268	−	1.20243i	1.08268	−	1.20243i
$776$		0			0
$777$	−0.226341	+	0.164446i	−0.226341	+	0.164446i
$778$		0			0
$779$		0			0
$780$	0.978148	+	0.207912i	0.978148	+	0.207912i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.773659	+	0.562096i	0.773659	+	0.562096i
$785$		0			0
$786$	−1.47815	+	1.07394i	−1.47815	+	1.07394i
$787$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$787$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$788$	1.08268	+	0.786610i	1.08268	+	0.786610i
$789$		0			0
$790$		0			0
$791$	−0.104528	−	0.0759444i	−0.104528	−	0.0759444i
$792$		0			0
$793$		0			0
$794$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$795$		0			0
$796$		0			0
$797$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$797$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$798$		0			0
$799$	−3.82709			−3.82709
$800$	0.500000	+	0.866025i	0.500000	+	0.866025i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	0.500000	+	1.53884i	0.500000	+	1.53884i
$807$		0			0
$808$		0			0
$809$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$809$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$810$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$811$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$811$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$	0.169131	+	0.122881i	0.169131	+	0.122881i
$814$		0			0
$815$		0			0
$816$	−1.58268	−	1.14988i	−1.58268	−	1.14988i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.604528	−	1.86055i	0.604528	−	1.86055i	0.104528	−	0.994522i	$-0.466667\pi$
$821$	0.604528	−	1.86055i	0.604528	−	1.86055i	0.500000	−	0.866025i	$-0.333333\pi$
$822$		0			0
$823$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$823$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$827$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$829$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$830$		0			0
$831$		0			0
$832$	−1.00000			−1.00000
$833$	0.578108	+	1.77923i	0.578108	+	1.77923i
$834$	−1.47815	−	1.07394i	−1.47815	−	1.07394i
$835$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$836$		0			0
$837$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$838$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$839$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$839$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$840$	0.104528	−	0.181049i	0.104528	−	0.181049i
$841$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$842$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$843$		0			0
$844$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$845$	0.978148	+	0.207912i	0.978148	+	0.207912i
$846$		0			0
$847$	0.0646021	−	0.198825i	0.0646021	−	0.198825i
$848$		0			0
$849$	1.61803			1.61803
$850$	−0.204489	+	1.94558i	−0.204489	+	1.94558i
$851$		0			0
$852$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$853$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	0.500000	+	0.866025i	$0.333333\pi$
$853$	−0.413545	+	1.27276i	−0.413545	+	1.27276i	−0.913545	+	0.406737i	$0.866667\pi$
$854$		0			0
$855$		0			0
$856$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$857$	2.00000			2.00000			1.00000			$0$
$857$	2.00000			2.00000			1.00000			$0$
$858$		0			0
$859$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$859$	−1.61803	−	1.17557i	−1.61803	−	1.17557i	−0.809017	−	0.587785i	$-0.800000\pi$
$860$	0.139886	+	0.155360i	0.139886	+	0.155360i
$861$		0			0
$862$	−1.08268	−	0.786610i	−1.08268	−	0.786610i
$863$	−0.169131	−	0.122881i	−0.169131	−	0.122881i	0.500000	−	0.866025i	$-0.333333\pi$
$863$	−0.169131	−	0.122881i	−0.169131	−	0.122881i	−0.669131	+	0.743145i	$0.733333\pi$
$864$	0.809017	−	0.587785i	0.809017	−	0.587785i
$865$		0			0
$866$	1.47815	+	1.07394i	1.47815	+	1.07394i
$867$	−0.873619	−	2.68872i	−0.873619	−	2.68872i
$868$	0.338261			0.338261
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.564602	−	1.73767i	0.564602	−	1.73767i
$873$		0			0
$874$		0			0
$875$	−0.209057			−0.209057
$876$		0			0
$877$	−1.58268	+	1.14988i	−1.58268	+	1.14988i	−0.669131	+	0.743145i	$0.733333\pi$
$877$	−1.58268	+	1.14988i	−1.58268	+	1.14988i	−0.913545	+	0.406737i	$0.866667\pi$
$878$		0			0
$879$	0.564602	−	1.73767i	0.564602	−	1.73767i
$880$		0			0
$881$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.500000	−	0.866025i	$-0.666667\pi$
$881$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.104528	−	0.994522i	$-0.533333\pi$
$882$		0			0
$883$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.500000	−	0.866025i	$-0.666667\pi$
$883$	−0.604528	−	1.86055i	−0.604528	−	1.86055i	−0.104528	−	0.994522i	$-0.533333\pi$
$884$	−1.58268	−	1.14988i	−1.58268	−	1.14988i
$885$		0			0
$886$	1.08268	−	0.786610i	1.08268	−	0.786610i
$887$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$887$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$888$	1.08268	+	0.786610i	1.08268	+	0.786610i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	0.0646021	+	0.198825i	0.0646021	+	0.198825i
$893$		0			0
$894$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$895$	1.30902	+	1.45381i	1.30902	+	1.45381i
$896$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	0.0135055	−	0.0415657i	0.0135055	−	0.0415657i
$904$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$905$		0			0
$906$	−0.413545	−	1.27276i	−0.413545	−	1.27276i
$907$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$907$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$908$		0			0
$909$		0			0
$910$	0.104528	−	0.181049i	0.104528	−	0.181049i
$911$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$911$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.08268	+	0.786610i	1.08268	+	0.786610i
$917$	0.118034	+	0.363271i	0.118034	+	0.363271i
$918$	1.95630			1.95630
$919$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$919$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$920$		0			0
$921$		0			0
$922$	0.413545	−	1.27276i	0.413545	−	1.27276i
$923$	−1.08268	+	0.786610i	−1.08268	+	0.786610i
$924$		0			0
$925$	0.139886	−	1.33093i	0.139886	−	1.33093i
$926$	0.618034			0.618034
$927$		0			0
$928$		0			0
$929$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$929$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$930$	0.169131	+	1.60917i	0.169131	+	1.60917i
$931$		0			0
$932$	−0.209057			−0.209057
$933$		0			0
$934$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$935$		0			0
$936$		0			0
$937$	1.30902	+	0.951057i	1.30902	+	0.951057i	1.00000			$0$
$937$	1.30902	+	0.951057i	1.30902	+	0.951057i	0.309017	+	0.951057i	$0.400000\pi$
$938$		0			0
$939$	1.47815	−	1.07394i	1.47815	−	1.07394i
$940$	−1.78716	+	0.795697i	−1.78716	+	0.795697i
$941$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$941$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	0.0218524	+	0.207912i	0.0218524	+	0.207912i
$946$		0			0
$947$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$947$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−1.61803			−1.61803
$952$	−0.330869	+	0.240391i	−0.330869	+	0.240391i
$953$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$953$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$954$		0			0
$955$		0			0
$956$	−0.564602	−	1.73767i	−0.564602	−	1.73767i
$957$		0			0
$958$	−0.604528	−	1.86055i	−0.604528	−	1.86055i
$959$		0			0
$960$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$961$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$962$	1.08268	+	0.786610i	1.08268	+	0.786610i
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$967$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$968$	−1.00000			−1.00000
$969$		0			0
$970$		0			0
$971$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.104528	+	0.994522i	$0.533333\pi$
$971$	−0.604528	+	1.86055i	−0.604528	+	1.86055i	−0.500000	+	0.866025i	$0.666667\pi$
$972$		0			0
$973$	−0.309017	+	0.224514i	−0.309017	+	0.224514i
$974$	−1.61803			−1.61803
$975$	0.913545	+	0.406737i	0.913545	+	0.406737i
$976$		0			0
$977$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$977$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$978$		0			0
$979$		0			0
$980$	0.639886	+	0.710666i	0.639886	+	0.710666i
$981$		0			0
$982$	−1.82709			−1.82709
$983$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$983$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$984$		0			0
$985$	0.895472	+	0.994522i	0.895472	+	0.994522i
$986$		0			0
$987$	0.330869	+	0.240391i	0.330869	+	0.240391i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$991$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$992$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$993$		0			0
$994$	0.0864545	+	0.266080i	0.0864545	+	0.266080i
$995$		0			0
$996$		0			0
$997$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$997$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$998$		0			0
$999$	−1.33826			−1.33826

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2600.1.ck.d.1611.1	yes	8
8.3	odd	2		2600.1.ck.c.1611.2	yes	8
13.12	even	2		2600.1.ck.c.1611.2	yes	8
25.16	even	5	inner	2600.1.ck.d.1091.2	yes	8
104.51	odd	2	CM	2600.1.ck.d.1611.1	yes	8
200.91	odd	10		2600.1.ck.c.1091.1	✓	8
325.116	even	10		2600.1.ck.c.1091.1	✓	8
2600.1091	odd	10	inner	2600.1.ck.d.1091.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2600.1.ck.c.1091.1	✓	8	200.91	odd	10
2600.1.ck.c.1091.1	✓	8	325.116	even	10
2600.1.ck.c.1611.2	yes	8	8.3	odd	2
2600.1.ck.c.1611.2	yes	8	13.12	even	2
2600.1.ck.d.1091.2	yes	8	25.16	even	5	inner
2600.1.ck.d.1091.2	yes	8	2600.1091	odd	10	inner
2600.1.ck.d.1611.1	yes	8	1.1	even	1	trivial
2600.1.ck.d.1611.1	yes	8	104.51	odd	2	CM

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:	\( N \)	\(=\)	\( 2600 = 2^{3} \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2600.ck (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.309017 + 0.951057i) q^{6} +0.209057 q^{7} +(-0.309017 - 0.951057i) q^{8} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.309017 - 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.309017 + 0.951057i) q^{6} +0.209057 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{10} +(0.809017 + 0.587785i) q^{12} +(0.809017 + 0.587785i) q^{13} +(0.169131 - 0.122881i) q^{14} +(0.669131 + 0.743145i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.604528 - 1.86055i) q^{17} +(-0.669131 - 0.743145i) q^{20} +(-0.0646021 + 0.198825i) q^{21} +1.00000 q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +(-0.809017 + 0.587785i) q^{27} +(0.0646021 - 0.198825i) q^{28} +(0.978148 + 0.207912i) q^{30} +(0.500000 + 1.53884i) q^{31} -1.00000 q^{32} +(-1.58268 - 1.14988i) q^{34} +(0.104528 - 0.181049i) q^{35} +(1.08268 + 0.786610i) q^{37} +(-0.809017 + 0.587785i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(0.0646021 + 0.198825i) q^{42} -0.209057 q^{43} +(0.604528 - 1.86055i) q^{47} +(0.809017 - 0.587785i) q^{48} -0.956295 q^{49} +(-0.913545 - 0.406737i) q^{50} +1.95630 q^{51} +(0.809017 - 0.587785i) q^{52} +(-0.309017 + 0.951057i) q^{54} +(-0.0646021 - 0.198825i) q^{56} +(0.913545 - 0.406737i) q^{60} +(1.30902 + 0.951057i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(0.913545 - 0.406737i) q^{65} -1.95630 q^{68} +(-0.0218524 - 0.207912i) q^{70} +(-0.413545 + 1.27276i) q^{71} +1.33826 q^{74} +(0.978148 - 0.207912i) q^{75} +(-0.309017 + 0.951057i) q^{78} +(-0.913545 + 0.406737i) q^{80} +(-0.309017 - 0.951057i) q^{81} +(0.169131 + 0.122881i) q^{84} +(-1.91355 - 0.406737i) q^{85} +(-0.169131 + 0.122881i) q^{86} +(0.169131 + 0.122881i) q^{91} -1.61803 q^{93} +(-0.604528 - 1.86055i) q^{94} +(0.309017 - 0.951057i) q^{96} +(-0.773659 + 0.562096i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + q^{10} + 2 q^{12} + 2 q^{13} - 3 q^{14} + q^{15} - 2 q^{16} - 3 q^{17} - q^{20} + 2 q^{21} + 8 q^{24} - 4 q^{25} + 8 q^{26} - 2 q^{27} - 2 q^{28} - q^{30} + 4 q^{31} - 8 q^{32} - 2 q^{34} - q^{35} - 2 q^{37} - 2 q^{39} + q^{40} - 2 q^{42} + 2 q^{43} + 3 q^{47} + 2 q^{48} + 10 q^{49} - q^{50} - 2 q^{51} + 2 q^{52} + 2 q^{54} + 2 q^{56} + q^{60} + 6 q^{62} - 2 q^{64} + q^{65} + 2 q^{68} - 9 q^{70} + 3 q^{71} + 2 q^{74} - q^{75} + 2 q^{78} - q^{80} + 2 q^{81} - 3 q^{84} - 9 q^{85} + 3 q^{86} - 3 q^{91} - 4 q^{93} - 3 q^{94} - 2 q^{96}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + q^10 + 2 * q^12 + 2 * q^13 - 3 * q^14 + q^15 - 2 * q^16 - 3 * q^17 - q^20 + 2 * q^21 + 8 * q^24 - 4 * q^25 + 8 * q^26 - 2 * q^27 - 2 * q^28 - q^30 + 4 * q^31 - 8 * q^32 - 2 * q^34 - q^35 - 2 * q^37 - 2 * q^39 + q^40 - 2 * q^42 + 2 * q^43 + 3 * q^47 + 2 * q^48 + 10 * q^49 - q^50 - 2 * q^51 + 2 * q^52 + 2 * q^54 + 2 * q^56 + q^60 + 6 * q^62 - 2 * q^64 + q^65 + 2 * q^68 - 9 * q^70 + 3 * q^71 + 2 * q^74 - q^75 + 2 * q^78 - q^80 + 2 * q^81 - 3 * q^84 - 9 * q^85 + 3 * q^86 - 3 * q^91 - 4 * q^93 - 3 * q^94 - 2 * q^96

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