LMFDB - Embedded newform 3225.1.cc.a.2831.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3225,1,Mod(221,3225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 18, 20]))

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

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

chi := DirichletCharacter("3225.221");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3225 = 3 \cdot 5^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3225.cc (of order $30$, degree $8$, 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:	$1.60948466574$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{30})$
Coefficient field:	$\Q(\zeta_{60})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 $ x^16 + x^14 - x^10 - x^8 - x^6 + x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{5}$
Projective field:	Galois closure of 5.1.6500390625.1

Embedding invariants

Embedding label			2831.1
Root			$-0.994522 + 0.104528i$ of defining polynomial
Character	$\chi$	$=$	3225.2831
Dual form			3225.1.cc.a.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.994522 + 0.104528i) q^{5} +(-0.994522 - 0.104528i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.994522 + 0.104528i) q^{5} +(-0.994522 - 0.104528i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(0.951057 - 0.309017i) q^{11} +(1.08268 + 1.20243i) q^{13} +(-0.207912 + 0.978148i) q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.866025 - 0.500000i) q^{18} +(0.809017 - 0.587785i) q^{21} +(-0.809017 + 0.587785i) q^{22} +(-1.20243 - 1.08268i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.978148 + 0.207912i) q^{25} +(-1.40126 - 0.809017i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.614648 + 0.0646021i) q^{29} +(-0.978148 - 0.207912i) q^{30} +(0.104528 - 0.994522i) q^{31} +(0.994522 + 0.104528i) q^{33} +(0.587785 - 0.809017i) q^{35} +(-1.58268 + 0.336408i) q^{37} +(0.500000 + 1.53884i) q^{39} +(0.669131 - 0.743145i) q^{40} +(-0.951057 - 0.309017i) q^{41} +(-0.587785 + 0.809017i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.587785 + 0.809017i) q^{45} +(1.47815 + 0.658114i) q^{46} +(-0.669131 + 0.743145i) q^{48} +(-0.994522 + 0.104528i) q^{50} +(-0.587785 - 0.809017i) q^{54} +(0.978148 - 0.207912i) q^{55} +(-0.406737 - 0.913545i) q^{56} +(0.564602 - 0.251377i) q^{58} +(-0.951057 - 0.309017i) q^{59} +(0.207912 + 0.978148i) q^{62} +(0.978148 - 0.207912i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.951057 + 1.30902i) q^{65} +(-0.978148 + 0.207912i) q^{66} +(0.104528 - 0.994522i) q^{67} +(-0.658114 - 1.47815i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(0.614648 - 0.0646021i) q^{71} +(0.994522 - 0.104528i) q^{72} +(-0.604528 - 0.128496i) q^{73} +(1.40126 - 0.809017i) q^{74} +(0.809017 + 0.587785i) q^{75} +(0.207912 - 0.978148i) q^{77} +(-0.951057 - 1.30902i) q^{78} +(-0.406737 + 0.913545i) q^{80} +(-0.104528 + 0.994522i) q^{81} +1.00000 q^{82} +(0.743145 + 0.669131i) q^{86} +(-0.587785 - 0.190983i) q^{87} +(0.309017 - 0.951057i) q^{88} +(0.743145 + 0.669131i) q^{89} +(-0.809017 - 0.587785i) q^{90} +(1.58268 - 0.336408i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-0.500000 + 0.363271i) q^{97} +(0.866025 + 0.500000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} + 8 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 + 8 * q^7 + 2 * q^9	$ 16 q + 2 q^{3} + 8 q^{7} + 2 q^{9} + 2 q^{10} - 4 q^{13} + 4 q^{16} + 4 q^{21} - 4 q^{22} - 2 q^{25} - 4 q^{27} + 2 q^{30} - 2 q^{31} - 4 q^{37} + 8 q^{39} + 2 q^{40} - 8 q^{43} + 6 q^{46} - 2 q^{48} - 2 q^{55} + 4 q^{58} - 2 q^{63} + 4 q^{64} + 2 q^{66} - 2 q^{67} + 4 q^{70} - 6 q^{73} + 4 q^{75} + 2 q^{81} + 16 q^{82} - 4 q^{88} - 4 q^{90} + 4 q^{91} + 8 q^{93} - 8 q^{97}+O(q^{100}) $ 16 * q + 2 * q^3 + 8 * q^7 + 2 * q^9 + 2 * q^10 - 4 * q^13 + 4 * q^16 + 4 * q^21 - 4 * q^22 - 2 * q^25 - 4 * q^27 + 2 * q^30 - 2 * q^31 - 4 * q^37 + 8 * q^39 + 2 * q^40 - 8 * q^43 + 6 * q^46 - 2 * q^48 - 2 * q^55 + 4 * q^58 - 2 * q^63 + 4 * q^64 + 2 * q^66 - 2 * q^67 + 4 * q^70 - 6 * q^73 + 4 * q^75 + 2 * q^81 + 16 * q^82 - 4 * q^88 - 4 * q^90 + 4 * q^91 + 8 * q^93 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3225\mathbb{Z}\right)^\times$.

$n$	$1076$	$2452$	$2626$
$\chi(n)$	$-1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.743145	−	0.669131i	$-0.766667\pi$
$2$	−0.951057	+	0.309017i	−0.951057	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$3$	0.913545	+	0.406737i	0.913545	+	0.406737i
$3$	0.913545	+	0.406737i	0.913545	+	0.406737i
$4$		0			0
$5$	0.994522	+	0.104528i	0.994522	+	0.104528i
$5$	0.994522	+	0.104528i	0.994522	+	0.104528i
$6$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$7$	0.500000	−	0.866025i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$7$	0.500000	−	0.866025i	0.500000	−	0.866025i	1.00000			$0$
$8$	0.587785	−	0.809017i	0.587785	−	0.809017i
$9$	0.669131	+	0.743145i	0.669131	+	0.743145i
$10$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$11$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$11$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$12$		0			0
$13$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.978148	+	0.207912i	$0.0666667\pi$
$13$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.104528	+	0.994522i	$0.466667\pi$
$14$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$15$	0.866025	+	0.500000i	0.866025	+	0.500000i
$16$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$17$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$17$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$18$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$19$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$19$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$20$		0			0
$21$	0.809017	−	0.587785i	0.809017	−	0.587785i
$22$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$23$	−1.20243	−	1.08268i	−1.20243	−	1.08268i	−0.994522	−	0.104528i	$-0.966667\pi$
$23$	−1.20243	−	1.08268i	−1.20243	−	1.08268i	−0.207912	−	0.978148i	$-0.566667\pi$
$24$	0.866025	−	0.500000i	0.866025	−	0.500000i
$25$	0.978148	+	0.207912i	0.978148	+	0.207912i
$26$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$27$	0.309017	+	0.951057i	0.309017	+	0.951057i
$28$		0			0
$29$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i	−0.406737	−	0.913545i	$-0.633333\pi$
$29$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i	−0.207912	+	0.978148i	$0.566667\pi$
$30$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$31$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$31$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$32$		0			0
$33$	0.994522	+	0.104528i	0.994522	+	0.104528i
$34$		0			0
$35$	0.587785	−	0.809017i	0.587785	−	0.809017i
$36$		0			0
$37$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.913545	−	0.406737i	$-0.866667\pi$
$37$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.669131	+	0.743145i	$0.733333\pi$
$38$		0			0
$39$	0.500000	+	1.53884i	0.500000	+	1.53884i
$40$	0.669131	−	0.743145i	0.669131	−	0.743145i
$41$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$41$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$42$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$43$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$44$		0			0
$45$	0.587785	+	0.809017i	0.587785	+	0.809017i
$46$	1.47815	+	0.658114i	1.47815	+	0.658114i
$47$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$47$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$48$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$49$		0			0
$50$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$51$		0			0
$52$		0			0
$53$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$53$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$54$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$55$	0.978148	−	0.207912i	0.978148	−	0.207912i
$56$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$57$		0			0
$58$	0.564602	−	0.251377i	0.564602	−	0.251377i
$59$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$59$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$60$		0			0
$61$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$61$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$62$	0.207912	+	0.978148i	0.207912	+	0.978148i
$63$	0.978148	−	0.207912i	0.978148	−	0.207912i
$64$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$65$	0.951057	+	1.30902i	0.951057	+	1.30902i
$66$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$67$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$67$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$68$		0			0
$69$	−0.658114	−	1.47815i	−0.658114	−	1.47815i
$70$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$71$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.207912	−	0.978148i	$-0.433333\pi$
$71$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$72$	0.994522	−	0.104528i	0.994522	−	0.104528i
$73$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.104528	−	0.994522i	$-0.533333\pi$
$73$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.500000	+	0.866025i	$0.666667\pi$
$74$	1.40126	−	0.809017i	1.40126	−	0.809017i
$75$	0.809017	+	0.587785i	0.809017	+	0.587785i
$76$		0			0
$77$	0.207912	−	0.978148i	0.207912	−	0.978148i
$78$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$79$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$79$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$80$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$81$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$82$	1.00000			1.00000
$83$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$83$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$84$		0			0
$85$		0			0
$86$	0.743145	+	0.669131i	0.743145	+	0.669131i
$87$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$88$	0.309017	−	0.951057i	0.309017	−	0.951057i
$89$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$89$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$90$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$91$	1.58268	−	0.336408i	1.58268	−	0.336408i
$92$		0			0
$93$	0.500000	−	0.866025i	0.500000	−	0.866025i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$97$	−0.500000	+	0.363271i	−0.500000	+	0.363271i	0.309017	+	0.951057i	$0.400000\pi$
$98$		0			0
$99$	0.866025	+	0.500000i	0.866025	+	0.500000i
$100$		0			0
$101$	0.535233	+	0.309017i	0.535233	+	0.309017i	0.743145	−	0.669131i	$-0.233333\pi$
$101$	0.535233	+	0.309017i	0.535233	+	0.309017i	−0.207912	+	0.978148i	$0.566667\pi$
$102$		0			0
$103$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	−0.913545	−	0.406737i	$-0.866667\pi$
$103$	−0.104528	−	0.994522i	−0.104528	−	0.994522i	0.809017	−	0.587785i	$-0.200000\pi$
$104$	1.60917	−	0.169131i	1.60917	−	0.169131i
$105$	0.866025	−	0.500000i	0.866025	−	0.500000i
$106$		0			0
$107$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$107$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$108$		0			0
$109$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.913545	−	0.406737i	$-0.866667\pi$
$109$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.669131	+	0.743145i	$0.733333\pi$
$110$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$111$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$112$	0.669131	+	0.743145i	0.669131	+	0.743145i
$113$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$113$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$114$		0			0
$115$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$116$		0			0
$117$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$118$	1.00000			1.00000
$119$		0			0
$120$	0.913545	−	0.406737i	0.913545	−	0.406737i
$121$		0			0
$122$		0			0
$123$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$124$		0			0
$125$	0.951057	+	0.309017i	0.951057	+	0.309017i
$126$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$	0.587785	+	0.809017i	0.587785	+	0.809017i
$129$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$130$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$131$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$131$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$132$		0			0
$133$		0			0
$134$	0.207912	+	0.978148i	0.207912	+	0.978148i
$135$	0.207912	+	0.978148i	0.207912	+	0.978148i
$136$		0			0
$137$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$137$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$138$	1.08268	+	1.20243i	1.08268	+	1.20243i
$139$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.104528	+	0.994522i	$0.533333\pi$
$139$	−1.08268	+	1.20243i	−1.08268	+	1.20243i	−0.978148	+	0.207912i	$0.933333\pi$
$140$		0			0
$141$		0			0
$142$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$143$	1.40126	+	0.809017i	1.40126	+	0.809017i
$144$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$145$	−0.618034			−0.618034
$146$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$147$		0			0
$148$		0			0
$149$	−1.40126	+	0.809017i	−1.40126	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$149$	−1.40126	+	0.809017i	−1.40126	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$150$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$		0			0
$153$		0			0
$154$	0.104528	+	0.994522i	0.104528	+	0.994522i
$155$	0.207912	−	0.978148i	0.207912	−	0.978148i
$156$		0			0
$157$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$157$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$162$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$163$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$163$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$164$		0			0
$165$	0.978148	+	0.207912i	0.978148	+	0.207912i
$166$		0			0
$167$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$167$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$168$		−	1.00000i		−	1.00000i
$169$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$173$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$174$	0.618034			0.618034
$175$	0.669131	−	0.743145i	0.669131	−	0.743145i
$176$			1.00000i			1.00000i
$177$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$178$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$179$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$179$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$180$		0			0
$181$		0			0		−0.406737	−	0.913545i	$-0.633333\pi$
$181$		0			0		0.406737	+	0.913545i	$0.366667\pi$
$182$	−1.40126	+	0.809017i	−1.40126	+	0.809017i
$183$		0			0
$184$	−1.58268	+	0.336408i	−1.58268	+	0.336408i
$185$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$186$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$187$		0			0
$188$		0			0
$189$	0.978148	+	0.207912i	0.978148	+	0.207912i
$190$		0			0
$191$	0.336408	+	1.58268i	0.336408	+	1.58268i	0.743145	+	0.669131i	$0.233333\pi$
$191$	0.336408	+	1.58268i	0.336408	+	1.58268i	−0.406737	+	0.913545i	$0.633333\pi$
$192$	0.104528	−	0.994522i	0.104528	−	0.994522i
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$	0.363271	−	0.500000i	0.363271	−	0.500000i
$195$	0.336408	+	1.58268i	0.336408	+	1.58268i
$196$		0			0
$197$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$197$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$198$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$199$	1.00000			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$199$	1.00000			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$200$	0.743145	−	0.669131i	0.743145	−	0.669131i
$201$	0.500000	−	0.866025i	0.500000	−	0.866025i
$202$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$203$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$204$		0			0
$205$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$206$	0.406737	+	0.913545i	0.406737	+	0.913545i
$207$		−	1.61803i		−	1.61803i
$208$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$209$		0			0
$210$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$211$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$211$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$212$		0			0
$213$	0.587785	+	0.190983i	0.587785	+	0.190983i
$214$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$215$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$216$	0.951057	+	0.309017i	0.951057	+	0.309017i
$217$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$218$	1.40126	−	0.809017i	1.40126	−	0.809017i
$219$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$220$		0			0
$221$		0			0
$222$	1.60917	−	0.169131i	1.60917	−	0.169131i
$223$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$223$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$224$		0			0
$225$	0.500000	+	0.866025i	0.500000	+	0.866025i
$226$		0			0
$227$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$227$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$228$		0			0
$229$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$229$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$230$	1.40126	+	0.809017i	1.40126	+	0.809017i
$231$	0.587785	−	0.809017i	0.587785	−	0.809017i
$232$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$233$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$233$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$234$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.994522	+	0.104528i	$0.0333333\pi$
$239$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.207912	+	0.978148i	$0.433333\pi$
$240$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$241$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.978148	+	0.207912i	$0.0666667\pi$
$241$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.104528	+	0.994522i	$0.466667\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$244$		0			0
$245$		0			0
$246$	0.913545	+	0.406737i	0.913545	+	0.406737i
$247$		0			0
$248$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$249$		0			0
$250$	−1.00000			−1.00000
$251$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$251$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$252$		0			0
$253$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		0			0		1.00000			$0$
$257$		0			0		−1.00000			$\pi$
$258$	0.406737	+	0.913545i	0.406737	+	0.913545i
$259$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$260$		0			0
$261$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$262$	0.309017	−	0.951057i	0.309017	−	0.951057i
$263$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	−0.951057	−	0.309017i	$-0.900000\pi$
$263$	−0.207912	−	0.978148i	−0.207912	−	0.978148i	0.743145	−	0.669131i	$-0.233333\pi$
$264$	0.669131	−	0.743145i	0.669131	−	0.743145i
$265$		0			0
$266$		0			0
$267$	0.406737	+	0.913545i	0.406737	+	0.913545i
$268$		0			0
$269$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$269$	−0.587785	+	0.809017i	−0.587785	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$270$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$271$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$271$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	0.913545	−	0.406737i	$-0.133333\pi$
$272$		0			0
$273$	1.58268	+	0.336408i	1.58268	+	0.336408i
$274$	1.61803			1.61803
$275$	0.994522	−	0.104528i	0.994522	−	0.104528i
$276$		0			0
$277$	1.08268	−	1.20243i	1.08268	−	1.20243i	0.104528	−	0.994522i	$-0.466667\pi$
$277$	1.08268	−	1.20243i	1.08268	−	1.20243i	0.978148	−	0.207912i	$-0.0666667\pi$
$278$	0.658114	−	1.47815i	0.658114	−	1.47815i
$279$	0.809017	−	0.587785i	0.809017	−	0.587785i
$280$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$281$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.406737	−	0.913545i	$-0.366667\pi$
$281$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.207912	+	0.978148i	$0.433333\pi$
$282$		0			0
$283$	−0.564602	+	0.251377i	−0.564602	+	0.251377i	−0.669131	−	0.743145i	$-0.733333\pi$
$283$	−0.564602	+	0.251377i	−0.564602	+	0.251377i	0.104528	+	0.994522i	$0.466667\pi$
$284$		0			0
$285$		0			0
$286$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$287$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$288$		0			0
$289$	0.669131	−	0.743145i	0.669131	−	0.743145i
$290$	0.587785	−	0.190983i	0.587785	−	0.190983i
$291$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$292$		0			0
$293$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$293$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$294$		0			0
$295$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$296$	−0.658114	+	1.47815i	−0.658114	+	1.47815i
$297$	0.587785	+	0.809017i	0.587785	+	0.809017i
$298$	1.08268	−	1.20243i	1.08268	−	1.20243i
$299$		−	2.61803i		−	2.61803i
$300$		0			0
$301$	−1.00000			−1.00000
$302$		0			0
$303$	0.363271	+	0.500000i	0.363271	+	0.500000i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	0.309017	+	0.535233i	0.309017	+	0.535233i	0.978148	−	0.207912i	$-0.0666667\pi$
$307$	0.309017	+	0.535233i	0.309017	+	0.535233i	−0.669131	+	0.743145i	$0.733333\pi$
$308$		0			0
$309$	0.309017	−	0.951057i	0.309017	−	0.951057i
$310$	0.104528	+	0.994522i	0.104528	+	0.994522i
$311$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.994522	+	0.104528i	$0.0333333\pi$
$311$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.207912	+	0.978148i	$0.433333\pi$
$312$	1.53884	+	0.500000i	1.53884	+	0.500000i
$313$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$313$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$314$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$315$	0.994522	−	0.104528i	0.994522	−	0.104528i
$316$		0			0
$317$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$317$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$318$		0			0
$319$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$320$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$321$	−0.658114	+	1.47815i	−0.658114	+	1.47815i
$322$	1.30902	−	0.951057i	1.30902	−	0.951057i
$323$		0			0
$324$		0			0
$325$	0.809017	+	1.40126i	0.809017	+	1.40126i
$326$		0			0
$327$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$328$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$329$		0			0
$330$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$331$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.104528	−	0.994522i	$-0.466667\pi$
$331$	0.913545	−	0.406737i	0.913545	−	0.406737i	0.809017	+	0.587785i	$0.200000\pi$
$332$		0			0
$333$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$334$	0.978148	−	0.207912i	0.978148	−	0.207912i
$335$	0.207912	−	0.978148i	0.207912	−	0.978148i
$336$	0.309017	+	0.951057i	0.309017	+	0.951057i
$337$	0.669131	+	0.743145i	0.669131	+	0.743145i	0.978148	−	0.207912i	$-0.0666667\pi$
$337$	0.669131	+	0.743145i	0.669131	+	0.743145i	−0.309017	+	0.951057i	$0.600000\pi$
$338$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$339$		0			0
$340$		0			0
$341$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$342$		0			0
$343$	1.00000			1.00000
$344$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$345$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$346$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$347$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$347$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$348$		0			0
$349$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$349$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$350$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$351$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$352$		0			0
$353$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$353$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$354$	0.913545	+	0.406737i	0.913545	+	0.406737i
$355$	0.618034			0.618034
$356$		0			0
$357$		0			0
$358$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$359$	−1.20243	+	1.08268i	−1.20243	+	1.08268i	−0.207912	+	0.978148i	$0.566667\pi$
$359$	−1.20243	+	1.08268i	−1.20243	+	1.08268i	−0.994522	+	0.104528i	$0.966667\pi$
$360$	1.00000			1.00000
$361$	0.978148	+	0.207912i	0.978148	+	0.207912i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$366$		0			0
$367$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	0.913545	+	0.406737i	$0.133333\pi$
$367$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	−0.978148	+	0.207912i	$0.933333\pi$
$368$	1.40126	−	0.809017i	1.40126	−	0.809017i
$369$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$370$	1.47815	−	0.658114i	1.47815	−	0.658114i
$371$		0			0
$372$		0			0
$373$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.104528	−	0.994522i	$-0.533333\pi$
$373$	−0.604528	−	0.128496i	−0.604528	−	0.128496i	−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	0.743145	+	0.669131i	0.743145	+	0.669131i
$376$		0			0
$377$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$378$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$379$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$379$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$380$		0			0
$381$		0			0
$382$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$383$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$383$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$384$	0.207912	+	0.978148i	0.207912	+	0.978148i
$385$	0.309017	−	0.951057i	0.309017	−	0.951057i
$386$		0			0
$387$	0.309017	−	0.951057i	0.309017	−	0.951057i
$388$		0			0
$389$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$389$	0.951057	−	0.309017i	0.951057	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$390$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$391$		0			0
$392$		0			0
$393$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.500000	−	0.866025i	$-0.666667\pi$
$397$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.978148	+	0.207912i	$0.933333\pi$
$398$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$401$	1.40126	+	0.809017i	1.40126	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$401$	1.40126	+	0.809017i	1.40126	+	0.809017i	0.406737	+	0.913545i	$0.366667\pi$
$402$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$403$	1.30902	−	0.951057i	1.30902	−	0.951057i
$404$		0			0
$405$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$406$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$407$	−1.40126	+	0.809017i	−1.40126	+	0.809017i
$408$		0			0
$409$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$409$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$410$	0.994522	+	0.104528i	0.994522	+	0.104528i
$411$	−1.20243	−	1.08268i	−1.20243	−	1.08268i
$412$		0			0
$413$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$414$	0.500000	+	1.53884i	0.500000	+	1.53884i
$415$		0			0
$416$		0			0
$417$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$418$		0			0
$419$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$419$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$420$		0			0
$421$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$421$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	0.913545	−	0.406737i	$-0.133333\pi$
$422$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$423$		0			0
$424$		0			0
$425$		0			0
$426$	−0.618034			−0.618034
$427$		0			0
$428$		0			0
$429$	0.951057	+	1.30902i	0.951057	+	1.30902i
$430$	0.669131	+	0.743145i	0.669131	+	0.743145i
$431$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$431$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$432$	−1.00000			−1.00000
$433$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	0.913545	+	0.406737i	$0.133333\pi$
$433$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	−0.978148	+	0.207912i	$0.933333\pi$
$434$	0.951057	+	0.309017i	0.951057	+	0.309017i
$435$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$436$		0			0
$437$		0			0
$438$	0.587785	+	0.190983i	0.587785	+	0.190983i
$439$	0.604528	+	0.128496i	0.604528	+	0.128496i	0.500000	−	0.866025i	$-0.333333\pi$
$439$	0.604528	+	0.128496i	0.604528	+	0.128496i	0.104528	+	0.994522i	$0.466667\pi$
$440$	0.406737	−	0.913545i	0.406737	−	0.913545i
$441$		0			0
$442$		0			0
$443$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$443$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$444$		0			0
$445$	0.669131	+	0.743145i	0.669131	+	0.743145i
$446$	0.587785	+	0.809017i	0.587785	+	0.809017i
$447$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$448$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$449$	0.535233	−	0.309017i	0.535233	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$449$	0.535233	−	0.309017i	0.535233	−	0.309017i	0.743145	+	0.669131i	$0.233333\pi$
$450$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$451$	−1.00000			−1.00000
$452$		0			0
$453$		0			0
$454$	0.913545	+	0.406737i	0.913545	+	0.406737i
$455$	1.60917	−	0.169131i	1.60917	−	0.169131i
$456$		0			0
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$461$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$462$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$463$	0.604528	−	0.128496i	0.604528	−	0.128496i	0.104528	−	0.994522i	$-0.466667\pi$
$463$	0.604528	−	0.128496i	0.604528	−	0.128496i	0.500000	+	0.866025i	$0.333333\pi$
$464$	0.128496	−	0.604528i	0.128496	−	0.604528i
$465$	0.587785	−	0.809017i	0.587785	−	0.809017i
$466$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$467$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.587785	−	0.809017i	$-0.300000\pi$
$467$	0.994522	+	0.104528i	0.994522	+	0.104528i	0.406737	+	0.913545i	$0.366667\pi$
$468$		0			0
$469$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$470$		0			0
$471$	0.500000	−	0.363271i	0.500000	−	0.363271i
$472$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$473$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$479$	0.658114	−	1.47815i	0.658114	−	1.47815i	−0.207912	−	0.978148i	$-0.566667\pi$
$479$	0.658114	−	1.47815i	0.658114	−	1.47815i	0.866025	−	0.500000i	$-0.166667\pi$
$480$		0			0
$481$	−2.11803	−	1.53884i	−2.11803	−	1.53884i
$482$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$483$	−1.60917	−	0.169131i	−1.60917	−	0.169131i
$484$		0			0
$485$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$486$	0.207912	−	0.978148i	0.207912	−	0.978148i
$487$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$487$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.459289	−	0.413545i	0.459289	−	0.413545i	−0.406737	−	0.913545i	$-0.633333\pi$
$491$	0.459289	−	0.413545i	0.459289	−	0.413545i	0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	0.809017	+	0.587785i	0.809017	+	0.587785i
$496$	0.913545	+	0.406737i	0.913545	+	0.406737i
$497$	0.251377	−	0.564602i	0.251377	−	0.564602i
$498$		0			0
$499$	0.809017	−	1.40126i	0.809017	−	1.40126i	−0.104528	−	0.994522i	$-0.533333\pi$
$499$	0.809017	−	1.40126i	0.809017	−	1.40126i	0.913545	−	0.406737i	$-0.133333\pi$
$500$		0			0
$501$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$502$	0.978148	+	0.207912i	0.978148	+	0.207912i
$503$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$503$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$504$	0.406737	−	0.913545i	0.406737	−	0.913545i
$505$	0.500000	+	0.363271i	0.500000	+	0.363271i
$506$	1.60917	+	0.169131i	1.60917	+	0.169131i
$507$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$508$		0			0
$509$	−1.48629	+	1.33826i	−1.48629	+	1.33826i	−0.743145	+	0.669131i	$0.766667\pi$
$509$	−1.48629	+	1.33826i	−1.48629	+	1.33826i	−0.743145	+	0.669131i	$0.766667\pi$
$510$		0			0
$511$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$512$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$513$		0			0
$514$		0			0
$515$		−	1.00000i		−	1.00000i
$516$		0			0
$517$		0			0
$518$		−	1.61803i		−	1.61803i
$519$	0.994522	+	0.104528i	0.994522	+	0.104528i
$520$	1.61803			1.61803
$521$	0.251377	−	0.564602i	0.251377	−	0.564602i	−0.743145	−	0.669131i	$-0.766667\pi$
$521$	0.251377	−	0.564602i	0.251377	−	0.564602i	0.994522	+	0.104528i	$0.0333333\pi$
$522$	0.564602	+	0.251377i	0.564602	+	0.251377i
$523$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$523$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$524$		0			0
$525$	0.913545	−	0.406737i	0.913545	−	0.406737i
$526$	0.500000	+	0.866025i	0.500000	+	0.866025i
$527$		0			0
$528$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$529$	0.169131	+	1.60917i	0.169131	+	1.60917i
$530$		0			0
$531$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$532$		0			0
$533$	−0.658114	−	1.47815i	−0.658114	−	1.47815i
$534$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$535$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$536$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$537$	0.951057	+	0.309017i	0.951057	+	0.309017i
$538$	0.309017	−	0.951057i	0.309017	−	0.951057i
$539$		0			0
$540$		0			0
$541$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$541$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$542$	0.251377	+	0.564602i	0.251377	+	0.564602i
$543$		0			0
$544$		0			0
$545$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$546$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$547$	0.564602	+	0.251377i	0.564602	+	0.251377i	0.669131	−	0.743145i	$-0.266667\pi$
$547$	0.564602	+	0.251377i	0.564602	+	0.251377i	−0.104528	+	0.994522i	$0.533333\pi$
$548$		0			0
$549$		0			0
$550$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$551$		0			0
$552$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$553$		0			0
$554$	−0.658114	+	1.47815i	−0.658114	+	1.47815i
$555$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$556$		0			0
$557$		−	1.00000i		−	1.00000i	−0.866025	−	0.500000i	$-0.833333\pi$
$557$		−	1.00000i		−	1.00000i	0.866025	−	0.500000i	$-0.166667\pi$
$558$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$559$	0.500000	−	1.53884i	0.500000	−	1.53884i
$560$	0.587785	+	0.809017i	0.587785	+	0.809017i
$561$		0			0
$562$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$563$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$563$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$564$		0			0
$565$		0			0
$566$	0.459289	−	0.413545i	0.459289	−	0.413545i
$567$	0.809017	+	0.587785i	0.809017	+	0.587785i
$568$	0.309017	−	0.535233i	0.309017	−	0.535233i
$569$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$569$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$570$		0			0
$571$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.809017	−	0.587785i	$-0.200000\pi$
$571$	0.913545	+	0.406737i	0.913545	+	0.406737i	0.104528	+	0.994522i	$0.466667\pi$
$572$		0			0
$573$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$574$	0.500000	−	0.866025i	0.500000	−	0.866025i
$575$	−0.951057	−	1.30902i	−0.951057	−	1.30902i
$576$	0.500000	−	0.866025i	0.500000	−	0.866025i
$577$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$577$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$578$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$579$		0			0
$580$		0			0
$581$		0			0
$582$	0.535233	−	0.309017i	0.535233	−	0.309017i
$583$		0			0
$584$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$585$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$586$	0.190983	+	0.587785i	0.190983	+	0.587785i
$587$	0.459289	−	0.413545i	0.459289	−	0.413545i	−0.406737	−	0.913545i	$-0.633333\pi$
$587$	0.459289	−	0.413545i	0.459289	−	0.413545i	0.866025	+	0.500000i	$0.166667\pi$
$588$		0			0
$589$		0			0
$590$	0.994522	+	0.104528i	0.994522	+	0.104528i
$591$		0			0
$592$	0.169131	−	1.60917i	0.169131	−	1.60917i
$593$	−0.535233	−	0.309017i	−0.535233	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$593$	−0.535233	−	0.309017i	−0.535233	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$594$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$595$		0			0
$596$		0			0
$597$	0.913545	+	0.406737i	0.913545	+	0.406737i
$598$	0.809017	+	2.48990i	0.809017	+	2.48990i
$599$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$599$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$600$	0.951057	−	0.309017i	0.951057	−	0.309017i
$601$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$601$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$602$	0.951057	−	0.309017i	0.951057	−	0.309017i
$603$	0.809017	−	0.587785i	0.809017	−	0.587785i
$604$		0			0
$605$		0			0
$606$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$607$	0.809017	+	1.40126i	0.809017	+	1.40126i	0.913545	+	0.406737i	$0.133333\pi$
$607$	0.809017	+	1.40126i	0.809017	+	1.40126i	−0.104528	+	0.994522i	$0.533333\pi$
$608$		0			0
$609$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$613$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$614$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$615$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$616$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$617$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	−0.994522	−	0.104528i	$-0.966667\pi$
$617$	−0.406737	−	0.913545i	−0.406737	−	0.913545i	0.587785	−	0.809017i	$-0.300000\pi$
$618$			1.00000i			1.00000i
$619$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$619$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$620$		0			0
$621$	0.658114	−	1.47815i	0.658114	−	1.47815i
$622$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$623$	0.951057	−	0.309017i	0.951057	−	0.309017i
$624$	−1.61803			−1.61803
$625$	0.913545	+	0.406737i	0.913545	+	0.406737i
$626$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$631$	0.564602	−	0.251377i	0.564602	−	0.251377i	−0.104528	−	0.994522i	$-0.533333\pi$
$631$	0.564602	−	0.251377i	0.564602	−	0.251377i	0.669131	+	0.743145i	$0.266667\pi$
$632$		0			0
$633$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$634$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	0.459289	−	0.413545i	0.459289	−	0.413545i
$639$	0.459289	+	0.413545i	0.459289	+	0.413545i
$640$	0.500000	+	0.866025i	0.500000	+	0.866025i
$641$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$641$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$642$	0.169131	−	1.60917i	0.169131	−	1.60917i
$643$	−1.00000			−1.00000			−0.500000	−	0.866025i	$-0.666667\pi$
$643$	−1.00000			−1.00000			−0.500000	+	0.866025i	$0.666667\pi$
$644$		0			0
$645$		−	1.00000i		−	1.00000i
$646$		0			0
$647$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$647$	−0.363271	−	0.500000i	−0.363271	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$648$	0.743145	+	0.669131i	0.743145	+	0.669131i
$649$	−1.00000			−1.00000
$650$	−1.20243	−	1.08268i	−1.20243	−	1.08268i
$651$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$652$		0			0
$653$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$653$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$654$	1.60917	−	0.169131i	1.60917	−	0.169131i
$655$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$656$	0.587785	−	0.809017i	0.587785	−	0.809017i
$657$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$658$		0			0
$659$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$659$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$660$		0			0
$661$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$661$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$662$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.53884	+	0.500000i	1.53884	+	0.500000i
$667$	0.809017	+	0.587785i	0.809017	+	0.587785i
$668$		0			0
$669$	0.104528	−	0.994522i	0.104528	−	0.994522i
$670$	0.104528	+	0.994522i	0.104528	+	0.994522i
$671$		0			0
$672$		0			0
$673$		0			0		0.207912	−	0.978148i	$-0.433333\pi$
$673$		0			0		−0.207912	+	0.978148i	$0.566667\pi$
$674$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$675$	0.104528	+	0.994522i	0.104528	+	0.994522i
$676$		0			0
$677$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$677$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$678$		0			0
$679$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$680$		0			0
$681$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$682$	0.500000	+	0.866025i	0.500000	+	0.866025i
$683$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.406737	−	0.913545i	$-0.366667\pi$
$683$	0.614648	+	0.0646021i	0.614648	+	0.0646021i	0.207912	+	0.978148i	$0.433333\pi$
$684$		0			0
$685$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$686$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$687$		0			0
$688$	0.978148	−	0.207912i	0.978148	−	0.207912i
$689$		0			0
$690$	0.951057	+	1.30902i	0.951057	+	1.30902i
$691$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$691$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$692$		0			0
$693$	0.866025	−	0.500000i	0.866025	−	0.500000i
$694$		0			0
$695$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$696$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$697$		0			0
$698$	1.20243	+	1.08268i	1.20243	+	1.08268i
$699$			1.00000i			1.00000i
$700$		0			0
$701$	−0.866025	−	0.500000i	−0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$701$	−0.866025	−	0.500000i	−0.866025	−	0.500000i	−0.866025	+	0.500000i	$0.833333\pi$
$702$	0.336408	−	1.58268i	0.336408	−	1.58268i
$703$		0			0
$704$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$705$		0			0
$706$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$707$	0.535233	−	0.309017i	0.535233	−	0.309017i
$708$		0			0
$709$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$709$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$710$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$711$		0			0
$712$	0.978148	−	0.207912i	0.978148	−	0.207912i
$713$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$714$		0			0
$715$	1.30902	+	0.951057i	1.30902	+	0.951057i
$716$		0			0
$717$	0.658114	+	1.47815i	0.658114	+	1.47815i
$718$	0.809017	−	1.40126i	0.809017	−	1.40126i
$719$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.207912	−	0.978148i	$-0.566667\pi$
$719$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.406737	+	0.913545i	$0.633333\pi$
$720$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$721$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$722$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$723$	0.500000	+	1.53884i	0.500000	+	1.53884i
$724$		0			0
$725$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$726$		0			0
$727$	0.190983	+	0.587785i	0.190983	+	0.587785i	1.00000			$0$
$727$	0.190983	+	0.587785i	0.190983	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$728$	0.658114	−	1.47815i	0.658114	−	1.47815i
$729$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$730$	0.618034			0.618034
$731$		0			0
$732$		0			0
$733$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$733$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$734$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$735$		0			0
$736$		0			0
$737$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$738$	0.669131	+	0.743145i	0.669131	+	0.743145i
$739$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$739$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.40126	+	0.809017i	−1.40126	+	0.809017i	−0.994522	−	0.104528i	$-0.966667\pi$
$743$	−1.40126	+	0.809017i	−1.40126	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$744$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$745$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$746$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$747$		0			0
$748$		0			0
$749$	1.40126	+	0.809017i	1.40126	+	0.809017i
$750$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$751$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$751$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$752$		0			0
$753$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$754$	0.913545	+	0.406737i	0.913545	+	0.406737i
$755$		0			0
$756$		0			0
$757$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$757$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$758$	0.587785	−	0.809017i	0.587785	−	0.809017i
$759$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$760$		0			0
$761$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$761$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$762$		0			0
$763$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$764$		0			0
$765$		0			0
$766$	0.500000	−	1.53884i	0.500000	−	1.53884i
$767$	−0.658114	−	1.47815i	−0.658114	−	1.47815i
$768$		0			0
$769$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	0.500000	+	0.866025i	$0.333333\pi$
$769$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	−0.669131	+	0.743145i	$0.733333\pi$
$770$			1.00000i			1.00000i
$771$		0			0
$772$		0			0
$773$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.951057	−	0.309017i	$-0.900000\pi$
$773$	−1.53884	+	0.500000i	−1.53884	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$774$			1.00000i			1.00000i
$775$	0.309017	−	0.951057i	0.309017	−	0.951057i
$776$			0.618034i			0.618034i
$777$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$778$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$779$		0			0
$780$		0			0
$781$	0.564602	−	0.251377i	0.564602	−	0.251377i
$782$		0			0
$783$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$784$		0			0
$785$	0.363271	−	0.500000i	0.363271	−	0.500000i
$786$	0.669131	−	0.743145i	0.669131	−	0.743145i
$787$	−1.08268	−	1.20243i	−1.08268	−	1.20243i	−0.978148	−	0.207912i	$-0.933333\pi$
$787$	−1.08268	−	1.20243i	−1.08268	−	1.20243i	−0.104528	−	0.994522i	$-0.533333\pi$
$788$		0			0
$789$	0.207912	−	0.978148i	0.207912	−	0.978148i
$790$		0			0
$791$		0			0
$792$	0.913545	−	0.406737i	0.913545	−	0.406737i
$793$		0			0
$794$	1.60917	+	0.169131i	1.60917	+	0.169131i
$795$		0			0
$796$		0			0
$797$	0.406737	−	0.913545i	0.406737	−	0.913545i	−0.587785	−	0.809017i	$-0.700000\pi$
$797$	0.406737	−	0.913545i	0.406737	−	0.913545i	0.994522	−	0.104528i	$-0.0333333\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$			1.00000i			1.00000i
$802$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$803$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$804$		0			0
$805$	−1.58268	+	0.336408i	−1.58268	+	0.336408i
$806$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$807$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$808$	0.564602	−	0.251377i	0.564602	−	0.251377i
$809$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$809$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$810$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$811$	−0.413545	+	0.459289i	−0.413545	+	0.459289i	−0.913545	−	0.406737i	$-0.866667\pi$
$811$	−0.413545	+	0.459289i	−0.413545	+	0.459289i	0.500000	+	0.866025i	$0.333333\pi$
$812$		0			0
$813$	0.190983	−	0.587785i	0.190983	−	0.587785i
$814$	1.08268	−	1.20243i	1.08268	−	1.20243i
$815$		0			0
$816$		0			0
$817$		0			0
$818$			1.00000i			1.00000i
$819$	1.30902	+	0.951057i	1.30902	+	0.951057i
$820$		0			0
$821$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$821$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$822$	1.47815	+	0.658114i	1.47815	+	0.658114i
$823$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	−0.978148	−	0.207912i	$-0.933333\pi$
$823$	−0.669131	+	0.743145i	−0.669131	+	0.743145i	0.309017	+	0.951057i	$0.400000\pi$
$824$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$825$	0.951057	+	0.309017i	0.951057	+	0.309017i
$826$	0.500000	−	0.866025i	0.500000	−	0.866025i
$827$	−0.459289	−	0.413545i	−0.459289	−	0.413545i	0.406737	−	0.913545i	$-0.366667\pi$
$827$	−0.459289	−	0.413545i	−0.459289	−	0.413545i	−0.866025	+	0.500000i	$0.833333\pi$
$828$		0			0
$829$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.500000	−	0.866025i	$-0.666667\pi$
$829$	−1.47815	−	0.658114i	−1.47815	−	0.658114i	−0.978148	+	0.207912i	$0.933333\pi$
$830$		0			0
$831$	1.47815	−	0.658114i	1.47815	−	0.658114i
$832$	0.809017	−	1.40126i	0.809017	−	1.40126i
$833$		0			0
$834$	1.20243	−	1.08268i	1.20243	−	1.08268i
$835$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$836$		0			0
$837$	0.978148	−	0.207912i	0.978148	−	0.207912i
$838$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$	0.104528	−	0.994522i	0.104528	−	0.994522i
$841$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$842$	0.251377	+	0.564602i	0.251377	+	0.564602i
$843$	0.535233	+	0.309017i	0.535233	+	0.309017i
$844$		0			0
$845$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.618034			−0.618034
$850$		0			0
$851$	2.26728	+	1.30902i	2.26728	+	1.30902i
$852$		0			0
$853$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$853$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$854$		0			0
$855$		0			0
$856$	1.30902	+	0.951057i	1.30902	+	0.951057i
$857$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$857$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$858$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$859$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$859$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$860$		0			0
$861$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$862$	0.500000	−	1.53884i	0.500000	−	1.53884i
$863$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$863$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$864$		0			0
$865$	0.978148	−	0.207912i	0.978148	−	0.207912i
$866$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$867$	0.913545	−	0.406737i	0.913545	−	0.406737i
$868$		0			0
$869$		0			0
$870$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$871$	1.30902	−	0.951057i	1.30902	−	0.951057i
$872$	−0.658114	+	1.47815i	−0.658114	+	1.47815i
$873$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$874$		0			0
$875$	0.743145	−	0.669131i	0.743145	−	0.669131i
$876$		0			0
$877$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.913545	−	0.406737i	$-0.133333\pi$
$877$	1.58268	+	0.336408i	1.58268	+	0.336408i	0.669131	+	0.743145i	$0.266667\pi$
$878$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$879$	0.251377	−	0.564602i	0.251377	−	0.564602i
$880$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$881$	−0.951057	+	1.30902i	−0.951057	+	1.30902i			1.00000i	$0.5\pi$
$881$	−0.951057	+	1.30902i	−0.951057	+	1.30902i	−0.951057	+	0.309017i	$0.900000\pi$
$882$		0			0
$883$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	0.913545	+	0.406737i	$0.133333\pi$
$883$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i	−0.978148	+	0.207912i	$0.933333\pi$
$884$		0			0
$885$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$886$	0.978148	+	0.207912i	0.978148	+	0.207912i
$887$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$887$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$888$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$889$		0			0
$890$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$891$	0.207912	+	0.978148i	0.207912	+	0.978148i
$892$		0			0
$893$		0			0
$894$	1.47815	−	0.658114i	1.47815	−	0.658114i
$895$	1.00000			1.00000
$896$	0.994522	−	0.104528i	0.994522	−	0.104528i
$897$	1.06485	−	2.39169i	1.06485	−	2.39169i
$898$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$899$			0.618034i			0.618034i
$900$		0			0
$901$		0			0
$902$	0.951057	−	0.309017i	0.951057	−	0.309017i
$903$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0			−	1.00000i	$-0.5\pi$
$907$		0			0				1.00000i	$0.5\pi$
$908$		0			0
$909$	0.128496	+	0.604528i	0.128496	+	0.604528i
$910$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$911$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.587785	−	0.809017i	$-0.300000\pi$
$911$	1.53884	−	0.500000i	1.53884	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.406737	+	0.913545i	0.406737	+	0.913545i
$918$		0			0
$919$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$919$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$920$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$921$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$922$		0			0
$923$	0.743145	+	0.669131i	0.743145	+	0.669131i
$924$		0			0
$925$	−1.61803			−1.61803
$926$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$927$	0.669131	−	0.743145i	0.669131	−	0.743145i
$928$		0			0
$929$	1.60917	−	0.169131i	1.60917	−	0.169131i	0.743145	−	0.669131i	$-0.233333\pi$
$929$	1.60917	−	0.169131i	1.60917	−	0.169131i	0.866025	+	0.500000i	$0.166667\pi$
$930$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$931$		0			0
$932$		0			0
$933$	0.658114	+	1.47815i	0.658114	+	1.47815i
$934$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$935$		0			0
$936$	1.20243	+	1.08268i	1.20243	+	1.08268i
$937$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	0.500000	−	0.866025i	$-0.333333\pi$
$937$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	−0.913545	+	0.406737i	$0.866667\pi$
$938$	0.951057	+	0.309017i	0.951057	+	0.309017i
$939$	0.978148	+	0.207912i	0.978148	+	0.207912i
$940$		0			0
$941$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$941$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$942$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$943$	0.809017	+	1.40126i	0.809017	+	1.40126i
$944$	0.587785	−	0.809017i	0.587785	−	0.809017i
$945$	0.951057	+	0.309017i	0.951057	+	0.309017i
$946$	0.913545	+	0.406737i	0.913545	+	0.406737i
$947$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$947$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$948$		0			0
$949$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$950$		0			0
$951$	0.535233	−	0.309017i	0.535233	−	0.309017i
$952$		0			0
$953$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i	−0.406737	−	0.913545i	$-0.633333\pi$
$953$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i	−0.207912	+	0.978148i	$0.566667\pi$
$954$		0			0
$955$	0.169131	+	1.60917i	0.169131	+	1.60917i
$956$		0			0
$957$	−0.618034			−0.618034
$958$	−0.169131	+	1.60917i	−0.169131	+	1.60917i
$959$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$960$	0.207912	−	0.978148i	0.207912	−	0.978148i
$961$		0			0
$962$	2.48990	+	0.809017i	2.48990	+	0.809017i
$963$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$964$		0			0
$965$		0			0
$966$	1.58268	−	0.336408i	1.58268	−	0.336408i
$967$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$967$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$968$		0			0
$969$		0			0
$970$	0.413545	−	0.459289i	0.413545	−	0.459289i
$971$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$971$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$972$		0			0
$973$	0.500000	+	1.53884i	0.500000	+	1.53884i
$974$		0			0
$975$	0.169131	+	1.60917i	0.169131	+	1.60917i
$976$		0			0
$977$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$977$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$978$		0			0
$979$	0.913545	+	0.406737i	0.913545	+	0.406737i
$980$		0			0
$981$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$982$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$983$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$983$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$984$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$990$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$991$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$991$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$992$		0			0
$993$	1.00000			1.00000
$994$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$995$	0.994522	+	0.104528i	0.994522	+	0.104528i
$996$		0			0
$997$	1.30902	−	0.951057i	1.30902	−	0.951057i	0.309017	−	0.951057i	$-0.400000\pi$
$997$	1.30902	−	0.951057i	1.30902	−	0.951057i	1.00000			$0$
$998$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$999$	−0.809017	−	1.40126i	−0.809017	−	1.40126i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3225.1.cc.a.2831.1	yes	16
3.2	odd	2	inner	3225.1.cc.a.2831.2	yes	16
25.21	even	5	inner	3225.1.cc.a.896.2	yes	16
43.6	even	3	inner	3225.1.cc.a.2156.1	yes	16
75.71	odd	10	inner	3225.1.cc.a.896.1	yes	16
129.92	odd	6	inner	3225.1.cc.a.2156.2	yes	16
1075.221	even	15	inner	3225.1.cc.a.221.2	yes	16
3225.221	odd	30	inner	3225.1.cc.a.221.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3225.1.cc.a.221.1	✓	16	3225.221	odd	30	inner
3225.1.cc.a.221.2	yes	16	1075.221	even	15	inner
3225.1.cc.a.896.1	yes	16	75.71	odd	10	inner
3225.1.cc.a.896.2	yes	16	25.21	even	5	inner
3225.1.cc.a.2156.1	yes	16	43.6	even	3	inner
3225.1.cc.a.2156.2	yes	16	129.92	odd	6	inner
3225.1.cc.a.2831.1	yes	16	1.1	even	1	trivial
3225.1.cc.a.2831.2	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3225 = 3 \cdot 5^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3225.cc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.994522 + 0.104528i) q^{5} +(-0.994522 - 0.104528i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.913545 + 0.406737i) q^{3} +(0.994522 + 0.104528i) q^{5} +(-0.994522 - 0.104528i) q^{6} +(0.500000 - 0.866025i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.978148 + 0.207912i) q^{10} +(0.951057 - 0.309017i) q^{11} +(1.08268 + 1.20243i) q^{13} +(-0.207912 + 0.978148i) q^{14} +(0.866025 + 0.500000i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-0.866025 - 0.500000i) q^{18} +(0.809017 - 0.587785i) q^{21} +(-0.809017 + 0.587785i) q^{22} +(-1.20243 - 1.08268i) q^{23} +(0.866025 - 0.500000i) q^{24} +(0.978148 + 0.207912i) q^{25} +(-1.40126 - 0.809017i) q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.614648 + 0.0646021i) q^{29} +(-0.978148 - 0.207912i) q^{30} +(0.104528 - 0.994522i) q^{31} +(0.994522 + 0.104528i) q^{33} +(0.587785 - 0.809017i) q^{35} +(-1.58268 + 0.336408i) q^{37} +(0.500000 + 1.53884i) q^{39} +(0.669131 - 0.743145i) q^{40} +(-0.951057 - 0.309017i) q^{41} +(-0.587785 + 0.809017i) q^{42} +(-0.500000 - 0.866025i) q^{43} +(0.587785 + 0.809017i) q^{45} +(1.47815 + 0.658114i) q^{46} +(-0.669131 + 0.743145i) q^{48} +(-0.994522 + 0.104528i) q^{50} +(-0.587785 - 0.809017i) q^{54} +(0.978148 - 0.207912i) q^{55} +(-0.406737 - 0.913545i) q^{56} +(0.564602 - 0.251377i) q^{58} +(-0.951057 - 0.309017i) q^{59} +(0.207912 + 0.978148i) q^{62} +(0.978148 - 0.207912i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(0.951057 + 1.30902i) q^{65} +(-0.978148 + 0.207912i) q^{66} +(0.104528 - 0.994522i) q^{67} +(-0.658114 - 1.47815i) q^{69} +(-0.309017 + 0.951057i) q^{70} +(0.614648 - 0.0646021i) q^{71} +(0.994522 - 0.104528i) q^{72} +(-0.604528 - 0.128496i) q^{73} +(1.40126 - 0.809017i) q^{74} +(0.809017 + 0.587785i) q^{75} +(0.207912 - 0.978148i) q^{77} +(-0.951057 - 1.30902i) q^{78} +(-0.406737 + 0.913545i) q^{80} +(-0.104528 + 0.994522i) q^{81} +1.00000 q^{82} +(0.743145 + 0.669131i) q^{86} +(-0.587785 - 0.190983i) q^{87} +(0.309017 - 0.951057i) q^{88} +(0.743145 + 0.669131i) q^{89} +(-0.809017 - 0.587785i) q^{90} +(1.58268 - 0.336408i) q^{91} +(0.500000 - 0.866025i) q^{93} +(-0.500000 + 0.363271i) q^{97} +(0.866025 + 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} + 8 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 + 8 * q^7 + 2 * q^9	\( 16 q + 2 q^{3} + 8 q^{7} + 2 q^{9} + 2 q^{10} - 4 q^{13} + 4 q^{16} + 4 q^{21} - 4 q^{22} - 2 q^{25} - 4 q^{27} + 2 q^{30} - 2 q^{31} - 4 q^{37} + 8 q^{39} + 2 q^{40} - 8 q^{43} + 6 q^{46} - 2 q^{48} - 2 q^{55} + 4 q^{58} - 2 q^{63} + 4 q^{64} + 2 q^{66} - 2 q^{67} + 4 q^{70} - 6 q^{73} + 4 q^{75} + 2 q^{81} + 16 q^{82} - 4 q^{88} - 4 q^{90} + 4 q^{91} + 8 q^{93} - 8 q^{97}+O(q^{100}) \) 16 * q + 2 * q^3 + 8 * q^7 + 2 * q^9 + 2 * q^10 - 4 * q^13 + 4 * q^16 + 4 * q^21 - 4 * q^22 - 2 * q^25 - 4 * q^27 + 2 * q^30 - 2 * q^31 - 4 * q^37 + 8 * q^39 + 2 * q^40 - 8 * q^43 + 6 * q^46 - 2 * q^48 - 2 * q^55 + 4 * q^58 - 2 * q^63 + 4 * q^64 + 2 * q^66 - 2 * q^67 + 4 * q^70 - 6 * q^73 + 4 * q^75 + 2 * q^81 + 16 * q^82 - 4 * q^88 - 4 * q^90 + 4 * q^91 + 8 * q^93 - 8 * q^97

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