LMFDB - Embedded newform 1800.1.dg.a.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,1,Mod(211,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 15, 10, 24]))

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

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

chi := DirichletCharacter("1800.211");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1800.dg (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:	$0.898317022739$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$A_{5}$
Projective field:	Galois closure of 5.1.2025000000.9

Embedding invariants

Embedding label			331.1
Root			$0.207912 + 0.978148i$ of defining polynomial
Character	$\chi$	$=$	1800.331
Dual form			1800.1.dg.a.571.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.406737 - 0.913545i) q^{5} +(0.406737 + 0.913545i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.406737 - 0.913545i) q^{5} +(0.406737 + 0.913545i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.604528 + 0.128496i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(0.336408 + 1.58268i) q^{13} +(-0.669131 + 0.743145i) q^{14} +(-0.207912 - 0.978148i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-0.743145 + 0.669131i) q^{20} +(0.994522 - 0.104528i) q^{21} +(-0.251377 + 0.564602i) q^{22} +(0.743145 + 0.669131i) q^{23} -1.00000i q^{24} +(-0.669131 - 0.743145i) q^{25} -1.61803 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-0.614648 + 0.0646021i) q^{29} +1.00000 q^{30} +(-0.994522 - 0.104528i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.564602 - 0.251377i) q^{33} +(0.743145 - 0.669131i) q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.669131 + 0.743145i) q^{36} +(0.743145 - 0.669131i) q^{38} +(1.20243 + 1.08268i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.58268 - 0.336408i) q^{41} +(-0.104528 + 0.994522i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-0.500000 - 0.363271i) q^{44} +(-0.743145 - 0.669131i) q^{45} +(-0.809017 + 0.587785i) q^{46} +(0.614648 - 0.0646021i) q^{47} +(0.978148 + 0.207912i) q^{48} +(0.866025 - 0.500000i) q^{50} -1.00000 q^{51} +(0.336408 - 1.58268i) q^{52} +(-0.951057 - 1.30902i) q^{53} +(0.994522 - 0.104528i) q^{54} +(0.363271 - 0.500000i) q^{55} +(0.913545 - 0.406737i) q^{56} -1.00000 q^{57} +(0.0646021 - 0.614648i) q^{58} +(-0.207912 + 0.978148i) q^{60} +(-0.207912 + 0.978148i) q^{61} +(0.309017 - 0.951057i) q^{62} +(0.743145 - 0.669131i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.58268 + 0.336408i) q^{65} +(0.128496 + 0.604528i) q^{66} +(-0.169131 + 1.60917i) q^{67} +(0.500000 + 0.866025i) q^{68} +(0.994522 + 0.104528i) q^{69} +(0.406737 + 0.913545i) q^{70} +(-0.587785 - 0.809017i) q^{72} +(-0.978148 - 0.207912i) q^{75} +(0.500000 + 0.866025i) q^{76} +(0.459289 + 0.413545i) q^{77} +(-1.30902 + 0.951057i) q^{78} +(0.614648 - 0.0646021i) q^{79} +(0.951057 - 0.309017i) q^{80} +(-0.809017 - 0.587785i) q^{81} +1.61803i q^{82} +(0.564602 - 0.251377i) q^{83} +(-0.951057 - 0.309017i) q^{84} +(-0.866025 + 0.500000i) q^{85} +(-0.743145 - 0.669131i) q^{86} +(-0.459289 + 0.413545i) q^{87} +(0.459289 - 0.413545i) q^{88} +(0.309017 + 0.951057i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-0.500000 + 1.53884i) q^{91} +(-0.406737 - 0.913545i) q^{92} +(-0.866025 + 0.500000i) q^{93} +(-0.0646021 + 0.614648i) q^{94} +(-0.866025 + 0.500000i) q^{95} +(-0.406737 + 0.913545i) q^{96} +(0.309017 - 0.535233i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 2 q^{4} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^3 - 2 * q^4 - 4 * q^9	$ 16 q + 4 q^{3} - 2 q^{4} - 4 q^{9} + 4 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{25} - 8 q^{26} + 4 q^{27} + 16 q^{30} + 4 q^{33} + 4 q^{35} - 2 q^{36} - 8 q^{40} + 4 q^{41} + 2 q^{42} - 8 q^{43} - 8 q^{44} - 4 q^{46} - 2 q^{48} - 16 q^{51} + 2 q^{56} - 16 q^{57} - 4 q^{58} - 4 q^{62} + 4 q^{64} + 4 q^{65} + 6 q^{67} + 8 q^{68} + 2 q^{75} + 8 q^{76} - 12 q^{78} - 4 q^{81} + 4 q^{83} - 4 q^{89} + 4 q^{90} - 8 q^{91} + 4 q^{94} - 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 2 * q^4 - 4 * q^9 + 4 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^25 - 8 * q^26 + 4 * q^27 + 16 * q^30 + 4 * q^33 + 4 * q^35 - 2 * q^36 - 8 * q^40 + 4 * q^41 + 2 * q^42 - 8 * q^43 - 8 * q^44 - 4 * q^46 - 2 * q^48 - 16 * q^51 + 2 * q^56 - 16 * q^57 - 4 * q^58 - 4 * q^62 + 4 * q^64 + 4 * q^65 + 6 * q^67 + 8 * q^68 + 2 * q^75 + 8 * q^76 - 12 * q^78 - 4 * q^81 + 4 * q^83 - 4 * q^89 + 4 * q^90 - 8 * q^91 + 4 * q^94 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$2$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$3$	0.809017	−	0.587785i	0.809017	−	0.587785i
$3$	0.809017	−	0.587785i	0.809017	−	0.587785i
$4$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$5$	0.406737	−	0.913545i	0.406737	−	0.913545i
$5$	0.406737	−	0.913545i	0.406737	−	0.913545i
$6$	0.406737	+	0.913545i	0.406737	+	0.913545i
$7$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$7$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$8$	0.587785	−	0.809017i	0.587785	−	0.809017i
$9$	0.309017	−	0.951057i	0.309017	−	0.951057i
$10$	0.809017	+	0.587785i	0.809017	+	0.587785i
$11$	0.604528	+	0.128496i	0.604528	+	0.128496i	0.500000	−	0.866025i	$-0.333333\pi$
$11$	0.604528	+	0.128496i	0.604528	+	0.128496i	0.104528	+	0.994522i	$0.466667\pi$
$12$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$13$	0.336408	+	1.58268i	0.336408	+	1.58268i	0.743145	+	0.669131i	$0.233333\pi$
$13$	0.336408	+	1.58268i	0.336408	+	1.58268i	−0.406737	+	0.913545i	$0.633333\pi$
$14$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$15$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$16$	0.669131	+	0.743145i	0.669131	+	0.743145i
$17$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$17$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$18$	0.866025	+	0.500000i	0.866025	+	0.500000i
$19$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	0.104528	−	0.994522i	$-0.466667\pi$
$19$	−0.809017	−	0.587785i	−0.809017	−	0.587785i	−0.913545	+	0.406737i	$0.866667\pi$
$20$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$21$	0.994522	−	0.104528i	0.994522	−	0.104528i
$22$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$23$	0.743145	+	0.669131i	0.743145	+	0.669131i	0.951057	−	0.309017i	$-0.100000\pi$
$23$	0.743145	+	0.669131i	0.743145	+	0.669131i	−0.207912	+	0.978148i	$0.566667\pi$
$24$		−	1.00000i		−	1.00000i
$25$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$26$	−1.61803			−1.61803
$27$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$28$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$29$	−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	$0.566667\pi$
$30$	1.00000			1.00000
$31$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$31$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$32$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$33$	0.564602	−	0.251377i	0.564602	−	0.251377i
$34$	0.743145	−	0.669131i	0.743145	−	0.669131i
$35$	0.809017	−	0.587785i	0.809017	−	0.587785i
$36$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$37$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$37$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$38$	0.743145	−	0.669131i	0.743145	−	0.669131i
$39$	1.20243	+	1.08268i	1.20243	+	1.08268i
$40$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$41$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.669131	−	0.743145i	$-0.266667\pi$
$41$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.913545	+	0.406737i	$0.133333\pi$
$42$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$43$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$43$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$44$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$45$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$46$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$47$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.207912	−	0.978148i	$-0.433333\pi$
$47$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$48$	0.978148	+	0.207912i	0.978148	+	0.207912i
$49$		0			0
$50$	0.866025	−	0.500000i	0.866025	−	0.500000i
$51$	−1.00000			−1.00000
$52$	0.336408	−	1.58268i	0.336408	−	1.58268i
$53$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$53$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$54$	0.994522	−	0.104528i	0.994522	−	0.104528i
$55$	0.363271	−	0.500000i	0.363271	−	0.500000i
$56$	0.913545	−	0.406737i	0.913545	−	0.406737i
$57$	−1.00000			−1.00000
$58$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$59$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$59$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$60$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$61$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	0.743145	+	0.669131i	$0.233333\pi$
$61$	−0.207912	+	0.978148i	−0.207912	+	0.978148i	−0.951057	+	0.309017i	$0.900000\pi$
$62$	0.309017	−	0.951057i	0.309017	−	0.951057i
$63$	0.743145	−	0.669131i	0.743145	−	0.669131i
$64$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$65$	1.58268	+	0.336408i	1.58268	+	0.336408i
$66$	0.128496	+	0.604528i	0.128496	+	0.604528i
$67$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	0.500000	+	0.866025i	$0.333333\pi$
$67$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	−0.669131	+	0.743145i	$0.733333\pi$
$68$	0.500000	+	0.866025i	0.500000	+	0.866025i
$69$	0.994522	+	0.104528i	0.994522	+	0.104528i
$70$	0.406737	+	0.913545i	0.406737	+	0.913545i
$71$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$71$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$72$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$		0			0
$75$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$76$	0.500000	+	0.866025i	0.500000	+	0.866025i
$77$	0.459289	+	0.413545i	0.459289	+	0.413545i
$78$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$79$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.207912	−	0.978148i	$-0.433333\pi$
$79$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$80$	0.951057	−	0.309017i	0.951057	−	0.309017i
$81$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$82$			1.61803i			1.61803i
$83$	0.564602	−	0.251377i	0.564602	−	0.251377i	−0.104528	−	0.994522i	$-0.533333\pi$
$83$	0.564602	−	0.251377i	0.564602	−	0.251377i	0.669131	+	0.743145i	$0.266667\pi$
$84$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$85$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$86$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$87$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$88$	0.459289	−	0.413545i	0.459289	−	0.413545i
$89$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$89$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$90$	0.809017	−	0.587785i	0.809017	−	0.587785i
$91$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$92$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$93$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$94$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$95$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$96$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$97$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$97$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$98$		0			0
$99$	0.309017	−	0.535233i	0.309017	−	0.535233i
$100$	0.309017	+	0.951057i	0.309017	+	0.951057i
$101$	−1.40126	−	0.809017i	−1.40126	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$101$	−1.40126	−	0.809017i	−1.40126	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$102$	0.207912	−	0.978148i	0.207912	−	0.978148i
$103$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$103$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$104$	1.47815	+	0.658114i	1.47815	+	0.658114i
$105$	0.309017	−	0.951057i	0.309017	−	0.951057i
$106$	1.47815	−	0.658114i	1.47815	−	0.658114i
$107$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$107$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$108$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$109$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$109$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$110$	0.413545	+	0.459289i	0.413545	+	0.459289i
$111$		0			0
$112$	0.207912	+	0.978148i	0.207912	+	0.978148i
$113$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.669131	−	0.743145i	$-0.733333\pi$
$113$	−0.978148	+	0.207912i	−0.978148	+	0.207912i	−0.309017	+	0.951057i	$0.600000\pi$
$114$	0.207912	−	0.978148i	0.207912	−	0.978148i
$115$	0.913545	−	0.406737i	0.913545	−	0.406737i
$116$	0.587785	+	0.190983i	0.587785	+	0.190983i
$117$	1.60917	+	0.169131i	1.60917	+	0.169131i
$118$		0			0
$119$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$120$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$121$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$122$	−0.913545	−	0.406737i	−0.913545	−	0.406737i
$123$	1.08268	−	1.20243i	1.08268	−	1.20243i
$124$	0.866025	+	0.500000i	0.866025	+	0.500000i
$125$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$126$	0.500000	+	0.866025i	0.500000	+	0.866025i
$127$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$127$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$128$	0.994522	−	0.104528i	0.994522	−	0.104528i
$129$	0.104528	+	0.994522i	0.104528	+	0.994522i
$130$	−0.658114	+	1.47815i	−0.658114	+	1.47815i
$131$	0.0646021	−	0.614648i	0.0646021	−	0.614648i	−0.913545	−	0.406737i	$-0.866667\pi$
$131$	0.0646021	−	0.614648i	0.0646021	−	0.614648i	0.978148	−	0.207912i	$-0.0666667\pi$
$132$	−0.618034			−0.618034
$133$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$134$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$135$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$136$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$137$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	0.500000	−	0.866025i	$-0.333333\pi$
$137$	−0.413545	−	0.459289i	−0.413545	−	0.459289i	−0.913545	+	0.406737i	$0.866667\pi$
$138$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$139$		0			0		−0.743145	−	0.669131i	$-0.766667\pi$
$139$		0			0		0.743145	+	0.669131i	$0.233333\pi$
$140$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$141$	0.459289	−	0.413545i	0.459289	−	0.413545i
$142$		0			0
$143$			1.00000i			1.00000i
$144$	0.913545	−	0.406737i	0.913545	−	0.406737i
$145$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$146$		0			0
$147$		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	$0.633333\pi$
$150$	0.406737	−	0.913545i	0.406737	−	0.913545i
$151$	0.866025	+	0.500000i	0.866025	+	0.500000i	0.866025	−	0.500000i	$-0.166667\pi$
$151$	0.866025	+	0.500000i	0.866025	+	0.500000i			1.00000i	$0.5\pi$
$152$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$153$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$154$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$155$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$156$	−0.658114	−	1.47815i	−0.658114	−	1.47815i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$159$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$160$	0.104528	+	0.994522i	0.104528	+	0.994522i
$161$	0.309017	+	0.951057i	0.309017	+	0.951057i
$162$	0.743145	−	0.669131i	0.743145	−	0.669131i
$163$	0.309017	−	0.951057i	0.309017	−	0.951057i	−0.669131	−	0.743145i	$-0.733333\pi$
$163$	0.309017	−	0.951057i	0.309017	−	0.951057i	0.978148	−	0.207912i	$-0.0666667\pi$
$164$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$165$		−	0.618034i		−	0.618034i
$166$	0.128496	+	0.604528i	0.128496	+	0.604528i
$167$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$167$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$168$	0.500000	−	0.866025i	0.500000	−	0.866025i
$169$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$170$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$171$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$172$	0.809017	−	0.587785i	0.809017	−	0.587785i
$173$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$173$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$174$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$175$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$176$	0.309017	+	0.535233i	0.309017	+	0.535233i
$177$		0			0
$178$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$179$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	−0.913545	−	0.406737i	$-0.866667\pi$
$179$	−0.809017	+	0.587785i	−0.809017	+	0.587785i	0.104528	+	0.994522i	$0.466667\pi$
$180$	0.406737	+	0.913545i	0.406737	+	0.913545i
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$183$	0.406737	+	0.913545i	0.406737	+	0.913545i
$184$	0.978148	−	0.207912i	0.978148	−	0.207912i
$185$		0			0
$186$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$187$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$188$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$189$	0.207912	−	0.978148i	0.207912	−	0.978148i
$190$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$191$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$191$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$192$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$193$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$193$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$	1.47815	−	0.658114i	1.47815	−	0.658114i
$196$		0			0
$197$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$197$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$198$	0.459289	+	0.413545i	0.459289	+	0.413545i
$199$			1.61803i			1.61803i	0.587785	+	0.809017i	$0.300000\pi$
$199$			1.61803i			1.61803i	−0.587785	+	0.809017i	$0.700000\pi$
$200$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$201$	0.809017	+	1.40126i	0.809017	+	1.40126i
$202$	1.08268	−	1.20243i	1.08268	−	1.20243i
$203$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$204$	0.913545	+	0.406737i	0.913545	+	0.406737i
$205$	0.336408	−	1.58268i	0.336408	−	1.58268i
$206$		0			0
$207$	0.866025	−	0.500000i	0.866025	−	0.500000i
$208$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$209$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$210$	0.866025	+	0.500000i	0.866025	+	0.500000i
$211$	−0.413545	+	0.459289i	−0.413545	+	0.459289i	−0.913545	−	0.406737i	$-0.866667\pi$
$211$	−0.413545	+	0.459289i	−0.413545	+	0.459289i	0.500000	+	0.866025i	$0.333333\pi$
$212$	0.336408	+	1.58268i	0.336408	+	1.58268i
$213$		0			0
$214$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$215$	0.587785	+	0.809017i	0.587785	+	0.809017i
$216$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$217$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$218$	0.809017	−	1.40126i	0.809017	−	1.40126i
$219$		0			0
$220$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$221$	0.658114	−	1.47815i	0.658114	−	1.47815i
$222$		0			0
$223$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$223$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$224$	−1.00000			−1.00000
$225$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$226$		−	1.00000i		−	1.00000i
$227$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.669131	−	0.743145i	$-0.266667\pi$
$227$	0.978148	+	0.207912i	0.978148	+	0.207912i	0.309017	+	0.951057i	$0.400000\pi$
$228$	0.913545	+	0.406737i	0.913545	+	0.406737i
$229$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	0.207912	+	0.978148i	$0.433333\pi$
$229$	−0.658114	+	1.47815i	−0.658114	+	1.47815i	−0.866025	+	0.500000i	$0.833333\pi$
$230$	0.207912	+	0.978148i	0.207912	+	0.978148i
$231$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$232$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$233$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$233$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$234$	−0.500000	+	1.53884i	−0.500000	+	1.53884i
$235$	0.190983	−	0.587785i	0.190983	−	0.587785i
$236$		0			0
$237$	0.459289	−	0.413545i	0.459289	−	0.413545i
$238$	0.978148	−	0.207912i	0.978148	−	0.207912i
$239$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$239$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$240$	0.587785	−	0.809017i	0.587785	−	0.809017i
$241$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$241$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$242$	0.363271	−	0.500000i	0.363271	−	0.500000i
$243$	−1.00000			−1.00000
$244$	0.587785	−	0.809017i	0.587785	−	0.809017i
$245$		0			0
$246$	0.951057	+	1.30902i	0.951057	+	1.30902i
$247$	0.658114	−	1.47815i	0.658114	−	1.47815i
$248$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$249$	0.309017	−	0.535233i	0.309017	−	0.535233i
$250$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$251$	−0.618034			−0.618034			−0.309017	−	0.951057i	$-0.600000\pi$
$251$	−0.618034			−0.618034			−0.309017	+	0.951057i	$0.600000\pi$
$252$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$253$	0.363271	+	0.500000i	0.363271	+	0.500000i
$254$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$255$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$256$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$257$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$257$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$258$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$259$		0			0
$260$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$261$	−0.128496	+	0.604528i	−0.128496	+	0.604528i
$262$	0.587785	+	0.190983i	0.587785	+	0.190983i
$263$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	−0.951057	−	0.309017i	$-0.900000\pi$
$263$	−0.743145	+	0.669131i	−0.743145	+	0.669131i	0.207912	+	0.978148i	$0.433333\pi$
$264$	0.128496	−	0.604528i	0.128496	−	0.604528i
$265$	−1.58268	+	0.336408i	−1.58268	+	0.336408i
$266$	0.978148	−	0.207912i	0.978148	−	0.207912i
$267$	0.809017	+	0.587785i	0.809017	+	0.587785i
$268$	0.809017	−	1.40126i	0.809017	−	1.40126i
$269$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$269$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$270$	0.309017	−	0.951057i	0.309017	−	0.951057i
$271$	0.587785	+	0.809017i	0.587785	+	0.809017i	0.994522	−	0.104528i	$-0.0333333\pi$
$271$	0.587785	+	0.809017i	0.587785	+	0.809017i	−0.406737	+	0.913545i	$0.633333\pi$
$272$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$273$	0.500000	+	1.53884i	0.500000	+	1.53884i
$274$	0.535233	−	0.309017i	0.535233	−	0.309017i
$275$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$276$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$277$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$277$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$278$		0			0
$279$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$280$		−	1.00000i		−	1.00000i
$281$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$281$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$282$	0.309017	+	0.535233i	0.309017	+	0.535233i
$283$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$283$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$284$		0			0
$285$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$286$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$287$	1.53884	+	0.500000i	1.53884	+	0.500000i
$288$	0.207912	+	0.978148i	0.207912	+	0.978148i
$289$		0			0
$290$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$291$		0			0
$292$		0			0
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$298$	−0.500000	−	1.53884i	−0.500000	−	1.53884i
$299$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$300$	0.809017	+	0.587785i	0.809017	+	0.587785i
$301$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$302$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$303$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$304$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$305$	0.809017	+	0.587785i	0.809017	+	0.587785i
$306$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$307$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$307$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$308$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$309$		0			0
$310$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$311$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	0.207912	−	0.978148i	$-0.433333\pi$
$311$	−0.743145	−	0.669131i	−0.743145	−	0.669131i	−0.951057	+	0.309017i	$0.900000\pi$
$312$	1.58268	−	0.336408i	1.58268	−	0.336408i
$313$	0.669131	+	0.743145i	0.669131	+	0.743145i	0.978148	−	0.207912i	$-0.0666667\pi$
$313$	0.669131	+	0.743145i	0.669131	+	0.743145i	−0.309017	+	0.951057i	$0.600000\pi$
$314$		0			0
$315$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$316$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$317$	0.406737	+	0.913545i	0.406737	+	0.913545i	0.994522	+	0.104528i	$0.0333333\pi$
$317$	0.406737	+	0.913545i	0.406737	+	0.913545i	−0.587785	+	0.809017i	$0.700000\pi$
$318$	0.809017	−	1.40126i	0.809017	−	1.40126i
$319$	−0.379874	−	0.0399263i	−0.379874	−	0.0399263i
$320$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$321$	1.30902	−	0.951057i	1.30902	−	0.951057i
$322$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$323$	0.309017	+	0.951057i	0.309017	+	0.951057i
$324$	0.500000	+	0.866025i	0.500000	+	0.866025i
$325$	0.951057	−	1.30902i	0.951057	−	1.30902i
$326$	0.866025	+	0.500000i	0.866025	+	0.500000i
$327$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$328$	0.658114	−	1.47815i	0.658114	−	1.47815i
$329$	0.564602	+	0.251377i	0.564602	+	0.251377i
$330$	0.604528	+	0.128496i	0.604528	+	0.128496i
$331$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.978148	−	0.207912i	$-0.933333\pi$
$331$	−1.47815	+	0.658114i	−1.47815	+	0.658114i	−0.500000	+	0.866025i	$0.666667\pi$
$332$	−0.618034			−0.618034
$333$		0			0
$334$		0			0
$335$	1.40126	+	0.809017i	1.40126	+	0.809017i
$336$	0.743145	+	0.669131i	0.743145	+	0.669131i
$337$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.669131	−	0.743145i	$-0.266667\pi$
$337$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.913545	+	0.406737i	$0.133333\pi$
$338$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$339$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$340$	0.994522	−	0.104528i	0.994522	−	0.104528i
$341$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$342$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$343$		−	1.00000i		−	1.00000i
$344$	0.406737	+	0.913545i	0.406737	+	0.913545i
$345$	0.500000	−	0.866025i	0.500000	−	0.866025i
$346$		0			0
$347$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.104528	−	0.994522i	$-0.533333\pi$
$347$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.809017	+	0.587785i	$0.800000\pi$
$348$	0.587785	−	0.190983i	0.587785	−	0.190983i
$349$	−0.535233	−	0.309017i	−0.535233	−	0.309017i	0.207912	−	0.978148i	$-0.433333\pi$
$349$	−0.535233	−	0.309017i	−0.535233	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$350$	1.00000			1.00000
$351$	1.40126	−	0.809017i	1.40126	−	0.809017i
$352$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$353$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	−0.978148	−	0.207912i	$-0.933333\pi$
$353$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i	0.913545	−	0.406737i	$-0.133333\pi$
$354$		0			0
$355$		0			0
$356$	0.104528	−	0.994522i	0.104528	−	0.994522i
$357$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$358$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$359$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$359$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$360$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$361$		0			0
$362$		0			0
$363$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$364$	1.08268	−	1.20243i	1.08268	−	1.20243i
$365$		0			0
$366$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$367$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$367$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$368$			1.00000i			1.00000i
$369$	0.169131	−	1.60917i	0.169131	−	1.60917i
$370$		0			0
$371$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$372$	0.994522	−	0.104528i	0.994522	−	0.104528i
$373$	0.459289	+	0.413545i	0.459289	+	0.413545i	0.866025	−	0.500000i	$-0.166667\pi$
$373$	0.459289	+	0.413545i	0.459289	+	0.413545i	−0.406737	+	0.913545i	$0.633333\pi$
$374$	0.535233	−	0.309017i	0.535233	−	0.309017i
$375$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$376$	0.309017	−	0.535233i	0.309017	−	0.535233i
$377$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$378$	0.913545	+	0.406737i	0.913545	+	0.406737i
$379$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$379$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$380$	0.994522	−	0.104528i	0.994522	−	0.104528i
$381$	0.363271	−	0.500000i	0.363271	−	0.500000i
$382$		0			0
$383$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.207912	−	0.978148i	$-0.566667\pi$
$383$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i	−0.406737	+	0.913545i	$0.633333\pi$
$384$	0.743145	−	0.669131i	0.743145	−	0.669131i
$385$	0.564602	−	0.251377i	0.564602	−	0.251377i
$386$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$387$	0.669131	+	0.743145i	0.669131	+	0.743145i
$388$		0			0
$389$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$389$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$390$	0.336408	+	1.58268i	0.336408	+	1.58268i
$391$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$392$		0			0
$393$	−0.309017	−	0.535233i	−0.309017	−	0.535233i
$394$		0			0
$395$	0.190983	−	0.587785i	0.190983	−	0.587785i
$396$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$397$	−0.951057	−	1.30902i	−0.951057	−	1.30902i	−0.951057	−	0.309017i	$-0.900000\pi$
$397$	−0.951057	−	1.30902i	−0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$398$	−1.58268	−	0.336408i	−1.58268	−	0.336408i
$399$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$400$	0.104528	−	0.994522i	0.104528	−	0.994522i
$401$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$401$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$402$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$403$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$404$	0.951057	+	1.30902i	0.951057	+	1.30902i
$405$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$406$	0.363271	−	0.500000i	0.363271	−	0.500000i
$407$		0			0
$408$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$409$	0.604528	−	0.128496i	0.604528	−	0.128496i	0.104528	−	0.994522i	$-0.466667\pi$
$409$	0.604528	−	0.128496i	0.604528	−	0.128496i	0.500000	+	0.866025i	$0.333333\pi$
$410$	1.47815	+	0.658114i	1.47815	+	0.658114i
$411$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$412$		0			0
$413$		0			0
$414$	0.309017	+	0.951057i	0.309017	+	0.951057i
$415$		−	0.618034i		−	0.618034i
$416$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$417$		0			0
$418$	0.535233	−	0.309017i	0.535233	−	0.309017i
$419$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	0.500000	+	0.866025i	$0.333333\pi$
$419$	−0.169131	+	1.60917i	−0.169131	+	1.60917i	−0.669131	+	0.743145i	$0.733333\pi$
$420$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$421$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$421$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$422$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$423$	0.128496	−	0.604528i	0.128496	−	0.604528i
$424$	−1.61803			−1.61803
$425$	0.104528	+	0.994522i	0.104528	+	0.994522i
$426$		0			0
$427$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$428$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$429$	0.587785	+	0.809017i	0.587785	+	0.809017i
$430$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$431$	0.363271	−	0.500000i	0.363271	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$431$	0.363271	−	0.500000i	0.363271	−	0.500000i	0.951057	+	0.309017i	$0.100000\pi$
$432$	0.500000	−	0.866025i	0.500000	−	0.866025i
$433$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$433$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$434$	0.743145	−	0.669131i	0.743145	−	0.669131i
$435$	0.190983	+	0.587785i	0.190983	+	0.587785i
$436$	1.20243	+	1.08268i	1.20243	+	1.08268i
$437$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$438$		0			0
$439$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$439$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$440$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$441$		0			0
$442$	1.30902	+	0.951057i	1.30902	+	0.951057i
$443$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	0.104528	+	0.994522i	$0.466667\pi$
$443$	−0.809017	+	1.40126i	−0.809017	+	1.40126i	−0.913545	+	0.406737i	$0.866667\pi$
$444$		0			0
$445$	0.994522	+	0.104528i	0.994522	+	0.104528i
$446$		0			0
$447$	−0.658114	+	1.47815i	−0.658114	+	1.47815i
$448$	0.207912	−	0.978148i	0.207912	−	0.978148i
$449$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$449$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$450$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$451$	1.00000			1.00000
$452$	0.978148	+	0.207912i	0.978148	+	0.207912i
$453$	0.994522	−	0.104528i	0.994522	−	0.104528i
$454$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$455$	1.20243	+	1.08268i	1.20243	+	1.08268i
$456$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$457$	0.309017	−	0.535233i	0.309017	−	0.535233i	−0.669131	−	0.743145i	$-0.733333\pi$
$457$	0.309017	−	0.535233i	0.309017	−	0.535233i	0.978148	+	0.207912i	$0.0666667\pi$
$458$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$459$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$460$	−1.00000			−1.00000
$461$	0.128496	−	0.604528i	0.128496	−	0.604528i	−0.866025	−	0.500000i	$-0.833333\pi$
$461$	0.128496	−	0.604528i	0.128496	−	0.604528i	0.994522	−	0.104528i	$-0.0333333\pi$
$462$	−0.190983	+	0.587785i	−0.190983	+	0.587785i
$463$	0.207912	+	0.978148i	0.207912	+	0.978148i	0.951057	+	0.309017i	$0.100000\pi$
$463$	0.207912	+	0.978148i	0.207912	+	0.978148i	−0.743145	+	0.669131i	$0.766667\pi$
$464$	−0.459289	−	0.413545i	−0.459289	−	0.413545i
$465$	0.104528	+	0.994522i	0.104528	+	0.994522i
$466$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$467$	0.809017	+	0.587785i	0.809017	+	0.587785i	0.913545	−	0.406737i	$-0.133333\pi$
$467$	0.809017	+	0.587785i	0.809017	+	0.587785i	−0.104528	+	0.994522i	$0.533333\pi$
$468$	−1.40126	−	0.809017i	−1.40126	−	0.809017i
$469$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$470$	0.535233	+	0.309017i	0.535233	+	0.309017i
$471$		0			0
$472$		0			0
$473$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$474$	0.309017	+	0.535233i	0.309017	+	0.535233i
$475$	0.104528	+	0.994522i	0.104528	+	0.994522i
$476$			1.00000i			1.00000i
$477$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$478$		0			0
$479$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$479$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$480$	0.669131	+	0.743145i	0.669131	+	0.743145i
$481$		0			0
$482$		0			0
$483$	0.809017	+	0.587785i	0.809017	+	0.587785i
$484$	0.413545	+	0.459289i	0.413545	+	0.459289i
$485$		0			0
$486$	0.207912	−	0.978148i	0.207912	−	0.978148i
$487$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$487$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$488$	0.669131	+	0.743145i	0.669131	+	0.743145i
$489$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$490$		0			0
$491$		0			0		−0.207912	−	0.978148i	$-0.566667\pi$
$491$		0			0		0.207912	+	0.978148i	$0.433333\pi$
$492$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$493$	0.535233	+	0.309017i	0.535233	+	0.309017i
$494$	1.30902	+	0.951057i	1.30902	+	0.951057i
$495$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$496$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$497$		0			0
$498$	0.459289	+	0.413545i	0.459289	+	0.413545i
$499$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	−0.913545	−	0.406737i	$-0.866667\pi$
$499$	−0.809017	−	1.40126i	−0.809017	−	1.40126i	0.104528	−	0.994522i	$-0.466667\pi$
$500$	0.994522	+	0.104528i	0.994522	+	0.104528i
$501$		0			0
$502$	0.128496	−	0.604528i	0.128496	−	0.604528i
$503$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$503$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$504$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$505$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$506$	−0.564602	+	0.251377i	−0.564602	+	0.251377i
$507$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$508$	−0.614648	−	0.0646021i	−0.614648	−	0.0646021i
$509$	−0.128496	−	0.604528i	−0.128496	−	0.604528i	−0.994522	−	0.104528i	$-0.966667\pi$
$509$	−0.128496	−	0.604528i	−0.128496	−	0.604528i	0.866025	−	0.500000i	$-0.166667\pi$
$510$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$511$		0			0
$512$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$513$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$514$	1.53884	−	0.500000i	1.53884	−	0.500000i
$515$		0			0
$516$	0.309017	−	0.951057i	0.309017	−	0.951057i
$517$	0.379874	+	0.0399263i	0.379874	+	0.0399263i
$518$		0			0
$519$		0			0
$520$	1.20243	−	1.08268i	1.20243	−	1.08268i
$521$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$521$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$522$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$525$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$526$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$527$	0.743145	+	0.669131i	0.743145	+	0.669131i
$528$	0.564602	+	0.251377i	0.564602	+	0.251377i
$529$		0			0
$530$		−	1.61803i		−	1.61803i
$531$		0			0
$532$			1.00000i			1.00000i
$533$	1.06485	+	2.39169i	1.06485	+	2.39169i
$534$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$535$	0.658114	−	1.47815i	0.658114	−	1.47815i
$536$	1.20243	+	1.08268i	1.20243	+	1.08268i
$537$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$538$	1.08268	+	1.20243i	1.08268	+	1.20243i
$539$		0			0
$540$	0.866025	+	0.500000i	0.866025	+	0.500000i
$541$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$541$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$542$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$543$		0			0
$544$	0.994522	+	0.104528i	0.994522	+	0.104528i
$545$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$546$	−1.60917	+	0.169131i	−1.60917	+	0.169131i
$547$		0			0		0.994522	−	0.104528i	$-0.0333333\pi$
$547$		0			0		−0.994522	+	0.104528i	$0.966667\pi$
$548$	0.190983	+	0.587785i	0.190983	+	0.587785i
$549$	0.866025	+	0.500000i	0.866025	+	0.500000i
$550$	0.587785	−	0.190983i	0.587785	−	0.190983i
$551$	0.535233	+	0.309017i	0.535233	+	0.309017i
$552$	0.669131	−	0.743145i	0.669131	−	0.743145i
$553$	0.564602	+	0.251377i	0.564602	+	0.251377i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1.00000i			1.00000i	0.866025	+	0.500000i	$0.166667\pi$
$557$			1.00000i			1.00000i	−0.866025	+	0.500000i	$0.833333\pi$
$558$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$559$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$560$	0.978148	+	0.207912i	0.978148	+	0.207912i
$561$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$562$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$563$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.669131	−	0.743145i	$-0.266667\pi$
$563$	1.58268	−	0.336408i	1.58268	−	0.336408i	0.913545	+	0.406737i	$0.133333\pi$
$564$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$565$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$566$	0.951057	+	0.309017i	0.951057	+	0.309017i
$567$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$568$		0			0
$569$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$569$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$570$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$571$	0.564602	+	0.251377i	0.564602	+	0.251377i	0.669131	−	0.743145i	$-0.266667\pi$
$571$	0.564602	+	0.251377i	0.564602	+	0.251377i	−0.104528	+	0.994522i	$0.533333\pi$
$572$	0.406737	−	0.913545i	0.406737	−	0.913545i
$573$		0			0
$574$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$575$		−	1.00000i		−	1.00000i
$576$	−1.00000			−1.00000
$577$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$577$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$578$		0			0
$579$	0.913545	+	0.406737i	0.913545	+	0.406737i
$580$	0.413545	−	0.459289i	0.413545	−	0.459289i
$581$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$582$		0			0
$583$	−0.406737	−	0.913545i	−0.406737	−	0.913545i
$584$		0			0
$585$	0.809017	−	1.40126i	0.809017	−	1.40126i
$586$		0			0
$587$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$587$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$588$		0			0
$589$	0.743145	+	0.669131i	0.743145	+	0.669131i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$595$	−1.00000			−1.00000
$596$	1.60917	−	0.169131i	1.60917	−	0.169131i
$597$	0.951057	+	1.30902i	0.951057	+	1.30902i
$598$	−1.20243	−	1.08268i	−1.20243	−	1.08268i
$599$	−0.866025	+	0.500000i	−0.866025	+	0.500000i	−0.866025	−	0.500000i	$-0.833333\pi$
$599$	−0.866025	+	0.500000i	−0.866025	+	0.500000i			1.00000i	$0.5\pi$
$600$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$601$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$601$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$602$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$603$	1.47815	+	0.658114i	1.47815	+	0.658114i
$604$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$605$	−0.459289	+	0.413545i	−0.459289	+	0.413545i
$606$	0.169131	−	1.60917i	0.169131	−	1.60917i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$	0.994522	+	0.104528i	0.994522	+	0.104528i
$609$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$610$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$611$	0.309017	+	0.951057i	0.309017	+	0.951057i
$612$	0.978148	−	0.207912i	0.978148	−	0.207912i
$613$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$613$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$614$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$615$	−0.658114	−	1.47815i	−0.658114	−	1.47815i
$616$	0.604528	−	0.128496i	0.604528	−	0.128496i
$617$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	0.809017	+	0.587785i	$0.200000\pi$
$617$	−0.104528	+	0.994522i	−0.104528	+	0.994522i	−0.913545	+	0.406737i	$0.866667\pi$
$618$		0			0
$619$	1.47815	−	0.658114i	1.47815	−	0.658114i	0.500000	−	0.866025i	$-0.333333\pi$
$619$	1.47815	−	0.658114i	1.47815	−	0.658114i	0.978148	+	0.207912i	$0.0666667\pi$
$620$	0.809017	−	0.587785i	0.809017	−	0.587785i
$621$	0.406737	−	0.913545i	0.406737	−	0.913545i
$622$	0.809017	−	0.587785i	0.809017	−	0.587785i
$623$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$624$			1.61803i			1.61803i
$625$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$626$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$627$	−0.604528	−	0.128496i	−0.604528	−	0.128496i
$628$		0			0
$629$		0			0
$630$	0.994522	−	0.104528i	0.994522	−	0.104528i
$631$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$631$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$632$	0.309017	−	0.535233i	0.309017	−	0.535233i
$633$	−0.0646021	+	0.614648i	−0.0646021	+	0.614648i
$634$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$635$	0.0646021	−	0.614648i	0.0646021	−	0.614648i
$636$	1.20243	+	1.08268i	1.20243	+	1.08268i
$637$		0			0
$638$	0.118034	−	0.363271i	0.118034	−	0.363271i
$639$		0			0
$640$	0.309017	−	0.951057i	0.309017	−	0.951057i
$641$	0.413545	+	0.459289i	0.413545	+	0.459289i	0.913545	−	0.406737i	$-0.133333\pi$
$641$	0.413545	+	0.459289i	0.413545	+	0.459289i	−0.500000	+	0.866025i	$0.666667\pi$
$642$	0.658114	+	1.47815i	0.658114	+	1.47815i
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$643$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$644$	0.104528	−	0.994522i	0.104528	−	0.994522i
$645$	0.951057	+	0.309017i	0.951057	+	0.309017i
$646$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$647$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$647$	−0.587785	−	0.809017i	−0.587785	−	0.809017i	−0.994522	+	0.104528i	$0.966667\pi$
$648$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$649$		0			0
$650$	1.08268	+	1.20243i	1.08268	+	1.20243i
$651$	−1.00000			−1.00000
$652$	−0.669131	+	0.743145i	−0.669131	+	0.743145i
$653$	−0.251377	+	0.564602i	−0.251377	+	0.564602i	−0.994522	−	0.104528i	$-0.966667\pi$
$653$	−0.251377	+	0.564602i	−0.251377	+	0.564602i	0.743145	+	0.669131i	$0.233333\pi$
$654$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$655$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$656$	1.30902	+	0.951057i	1.30902	+	0.951057i
$657$		0			0
$658$	−0.363271	+	0.500000i	−0.363271	+	0.500000i
$659$		0			0		0.743145	−	0.669131i	$-0.233333\pi$
$659$		0			0		−0.743145	+	0.669131i	$0.766667\pi$
$660$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$661$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$661$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$662$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$663$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$664$	0.128496	−	0.604528i	0.128496	−	0.604528i
$665$	−1.00000			−1.00000
$666$		0			0
$667$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$668$		0			0
$669$		0			0
$670$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$671$	−0.251377	+	0.564602i	−0.251377	+	0.564602i
$672$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$673$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.309017	−	0.951057i	$-0.600000\pi$
$673$	−0.978148	−	0.207912i	−0.978148	−	0.207912i	−0.669131	+	0.743145i	$0.733333\pi$
$674$			1.61803i			1.61803i
$675$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$676$	1.61803			1.61803
$677$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$677$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$678$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$679$		0			0
$680$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$681$	0.913545	−	0.406737i	0.913545	−	0.406737i
$682$	0.309017	−	0.535233i	0.309017	−	0.535233i
$683$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−0.309017	−	0.951057i	$-0.600000\pi$
$683$	−1.30902	−	0.951057i	−1.30902	−	0.951057i	−1.00000			$\pi$
$684$	0.978148	−	0.207912i	0.978148	−	0.207912i
$685$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$686$	0.978148	+	0.207912i	0.978148	+	0.207912i
$687$	0.336408	+	1.58268i	0.336408	+	1.58268i
$688$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$689$	1.75181	−	1.94558i	1.75181	−	1.94558i
$690$	0.743145	+	0.669131i	0.743145	+	0.669131i
$691$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.978148	+	0.207912i	$0.0666667\pi$
$691$	1.08268	+	1.20243i	1.08268	+	1.20243i	0.104528	+	0.994522i	$0.466667\pi$
$692$		0			0
$693$	0.535233	−	0.309017i	0.535233	−	0.309017i
$694$	0.587785	−	0.809017i	0.587785	−	0.809017i
$695$		0			0
$696$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$697$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$698$	0.413545	−	0.459289i	0.413545	−	0.459289i
$699$	1.00000			1.00000
$700$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	0.500000	+	1.53884i	0.500000	+	1.53884i
$703$		0			0
$704$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$705$	−0.190983	−	0.587785i	−0.190983	−	0.587785i
$706$	0.614648	+	0.0646021i	0.614648	+	0.0646021i
$707$	−0.809017	−	1.40126i	−0.809017	−	1.40126i
$708$		0			0
$709$	0.743145	−	0.669131i	0.743145	−	0.669131i	−0.207912	−	0.978148i	$-0.566667\pi$
$709$	0.743145	−	0.669131i	0.743145	−	0.669131i	0.951057	+	0.309017i	$0.100000\pi$
$710$		0			0
$711$	0.128496	−	0.604528i	0.128496	−	0.604528i
$712$	0.951057	+	0.309017i	0.951057	+	0.309017i
$713$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$714$	0.669131	−	0.743145i	0.669131	−	0.743145i
$715$	0.913545	+	0.406737i	0.913545	+	0.406737i
$716$	0.978148	−	0.207912i	0.978148	−	0.207912i
$717$		0			0
$718$	−0.309017	+	0.535233i	−0.309017	+	0.535233i
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$		−	1.00000i		−	1.00000i
$721$		0			0
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.459289	+	0.413545i	0.459289	+	0.413545i
$726$		−	0.618034i		−	0.618034i
$727$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$727$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$728$	0.951057	+	1.30902i	0.951057	+	1.30902i
$729$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$730$		0			0
$731$	0.913545	−	0.406737i	0.913545	−	0.406737i
$732$		−	1.00000i		−	1.00000i
$733$	1.60917	+	0.169131i	1.60917	+	0.169131i	0.866025	−	0.500000i	$-0.166667\pi$
$733$	1.60917	+	0.169131i	1.60917	+	0.169131i	0.743145	+	0.669131i	$0.233333\pi$
$734$		0			0
$735$		0			0
$736$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$737$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$738$	1.53884	+	0.500000i	1.53884	+	0.500000i
$739$	0.500000	+	1.53884i	0.500000	+	1.53884i	0.809017	+	0.587785i	$0.200000\pi$
$739$	0.500000	+	1.53884i	0.500000	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$740$		0			0
$741$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$742$	1.60917	+	0.169131i	1.60917	+	0.169131i
$743$	0.866025	−	0.500000i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$743$	0.866025	−	0.500000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$744$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$745$	0.169131	+	1.60917i	0.169131	+	1.60917i
$746$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$747$	−0.0646021	−	0.614648i	−0.0646021	−	0.614648i
$748$	0.190983	+	0.587785i	0.190983	+	0.587785i
$749$	1.40126	+	0.809017i	1.40126	+	0.809017i
$750$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$751$	1.40126	−	0.809017i	1.40126	−	0.809017i	0.406737	−	0.913545i	$-0.366667\pi$
$751$	1.40126	−	0.809017i	1.40126	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$752$	0.459289	+	0.413545i	0.459289	+	0.413545i
$753$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$754$	0.994522	−	0.104528i	0.994522	−	0.104528i
$755$	0.809017	−	0.587785i	0.809017	−	0.587785i
$756$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$757$			0.618034i			0.618034i	0.951057	+	0.309017i	$0.100000\pi$
$757$			0.618034i			0.618034i	−0.951057	+	0.309017i	$0.900000\pi$
$758$		0			0
$759$	0.587785	+	0.190983i	0.587785	+	0.190983i
$760$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$761$	0.413545	−	0.459289i	0.413545	−	0.459289i	−0.500000	−	0.866025i	$-0.666667\pi$
$761$	0.413545	−	0.459289i	0.413545	−	0.459289i	0.913545	+	0.406737i	$0.133333\pi$
$762$	0.413545	+	0.459289i	0.413545	+	0.459289i
$763$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$764$		0			0
$765$	0.207912	+	0.978148i	0.207912	+	0.978148i
$766$	0.190983	−	0.587785i	0.190983	−	0.587785i
$767$		0			0
$768$	0.500000	+	0.866025i	0.500000	+	0.866025i
$769$		0			0		−0.994522	−	0.104528i	$-0.966667\pi$
$769$		0			0		0.994522	+	0.104528i	$0.0333333\pi$
$770$	0.128496	+	0.604528i	0.128496	+	0.604528i
$771$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$772$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$775$	0.587785	+	0.809017i	0.587785	+	0.809017i
$776$		0			0
$777$		0			0
$778$	0.913545	+	0.406737i	0.913545	+	0.406737i
$779$	−1.47815	−	0.658114i	−1.47815	−	0.658114i
$780$	−1.61803			−1.61803
$781$		0			0
$782$	1.00000			1.00000
$783$	0.251377	+	0.564602i	0.251377	+	0.564602i
$784$		0			0
$785$		0			0
$786$	0.587785	−	0.190983i	0.587785	−	0.190983i
$787$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$787$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$788$		0			0
$789$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$790$	0.535233	+	0.309017i	0.535233	+	0.309017i
$791$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$792$	−0.251377	−	0.564602i	−0.251377	−	0.564602i
$793$	−1.61803			−1.61803
$794$	1.47815	−	0.658114i	1.47815	−	0.658114i
$795$	−1.08268	+	1.20243i	−1.08268	+	1.20243i
$796$	0.658114	−	1.47815i	0.658114	−	1.47815i
$797$	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	$-0.0333333\pi$
$798$	0.669131	−	0.743145i	0.669131	−	0.743145i
$799$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$800$	0.951057	+	0.309017i	0.951057	+	0.309017i
$801$	1.00000			1.00000
$802$	0.951057	−	0.309017i	0.951057	−	0.309017i
$803$		0			0
$804$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$805$	0.994522	+	0.104528i	0.994522	+	0.104528i
$806$	1.60917	+	0.169131i	1.60917	+	0.169131i
$807$		−	1.61803i		−	1.61803i
$808$	−1.47815	+	0.658114i	−1.47815	+	0.658114i
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$811$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	−0.978148	−	0.207912i	$-0.933333\pi$
$811$	−0.309017	−	0.951057i	−0.309017	−	0.951057i	0.669131	−	0.743145i	$-0.266667\pi$
$812$	0.413545	+	0.459289i	0.413545	+	0.459289i
$813$	0.951057	+	0.309017i	0.951057	+	0.309017i
$814$		0			0
$815$	−0.743145	−	0.669131i	−0.743145	−	0.669131i
$816$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$817$	0.913545	−	0.406737i	0.913545	−	0.406737i
$818$			0.618034i			0.618034i
$819$	1.30902	+	0.951057i	1.30902	+	0.951057i
$820$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$821$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.207912	−	0.978148i	$-0.433333\pi$
$821$	0.614648	−	0.0646021i	0.614648	−	0.0646021i	0.406737	+	0.913545i	$0.366667\pi$
$822$	0.251377	−	0.564602i	0.251377	−	0.564602i
$823$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.994522	+	0.104528i	$0.0333333\pi$
$823$	1.20243	+	1.08268i	1.20243	+	1.08268i	0.207912	+	0.978148i	$0.433333\pi$
$824$		0			0
$825$	−0.564602	−	0.251377i	−0.564602	−	0.251377i
$826$		0			0
$827$	0.309017	+	0.951057i	0.309017	+	0.951057i	0.978148	+	0.207912i	$0.0666667\pi$
$827$	0.309017	+	0.951057i	0.309017	+	0.951057i	−0.669131	+	0.743145i	$0.733333\pi$
$828$	−0.994522	+	0.104528i	−0.994522	+	0.104528i
$829$	0.363271	+	0.500000i	0.363271	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$829$	0.363271	+	0.500000i	0.363271	+	0.500000i	−0.587785	+	0.809017i	$0.700000\pi$
$830$	0.604528	+	0.128496i	0.604528	+	0.128496i
$831$		0			0
$832$	1.40126	−	0.809017i	1.40126	−	0.809017i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	0.190983	+	0.587785i	0.190983	+	0.587785i
$837$	0.207912	+	0.978148i	0.207912	+	0.978148i
$838$	−1.53884	−	0.500000i	−1.53884	−	0.500000i
$839$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$839$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$840$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$841$	−0.604528	+	0.128496i	−0.604528	+	0.128496i
$842$		0			0
$843$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$844$	0.564602	−	0.251377i	0.564602	−	0.251377i
$845$			1.61803i			1.61803i
$846$	0.564602	+	0.251377i	0.564602	+	0.251377i
$847$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$848$	0.336408	−	1.58268i	0.336408	−	1.58268i
$849$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$850$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$851$		0			0
$852$		0			0
$853$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.406737	−	0.913545i	$-0.366667\pi$
$853$	0.994522	−	0.104528i	0.994522	−	0.104528i	0.587785	+	0.809017i	$0.300000\pi$
$854$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$855$	0.207912	+	0.978148i	0.207912	+	0.978148i
$856$	0.951057	−	1.30902i	0.951057	−	1.30902i
$857$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$857$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$858$	−0.913545	+	0.406737i	−0.913545	+	0.406737i
$859$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.913545	−	0.406737i	$-0.866667\pi$
$859$	−1.58268	+	0.336408i	−1.58268	+	0.336408i	−0.669131	+	0.743145i	$0.733333\pi$
$860$	−0.207912	−	0.978148i	−0.207912	−	0.978148i
$861$	1.53884	−	0.500000i	1.53884	−	0.500000i
$862$	0.413545	+	0.459289i	0.413545	+	0.459289i
$863$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.207912	−	0.978148i	$-0.566667\pi$
$863$	−0.951057	−	0.309017i	−0.951057	−	0.309017i	−0.743145	+	0.669131i	$0.766667\pi$
$864$	0.743145	+	0.669131i	0.743145	+	0.669131i
$865$		0			0
$866$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$867$		0			0
$868$	0.500000	+	0.866025i	0.500000	+	0.866025i
$869$	0.379874	+	0.0399263i	0.379874	+	0.0399263i
$870$	−0.614648	+	0.0646021i	−0.614648	+	0.0646021i
$871$	−2.60369	+	0.273659i	−2.60369	+	0.273659i
$872$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$873$		0			0
$874$	1.00000			1.00000
$875$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$876$		0			0
$877$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$877$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$878$		0			0
$879$		0			0
$880$	0.614648	−	0.0646021i	0.614648	−	0.0646021i
$881$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$881$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$882$		0			0
$883$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$883$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$884$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$885$		0			0
$886$	−1.20243	−	1.08268i	−1.20243	−	1.08268i
$887$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$887$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$888$		0			0
$889$	0.604528	+	0.128496i	0.604528	+	0.128496i
$890$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$891$	−0.413545	−	0.459289i	−0.413545	−	0.459289i
$892$		0			0
$893$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$894$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$895$	0.207912	+	0.978148i	0.207912	+	0.978148i
$896$	0.913545	+	0.406737i	0.913545	+	0.406737i
$897$	0.169131	+	1.60917i	0.169131	+	1.60917i
$898$	−0.336408	+	1.58268i	−0.336408	+	1.58268i
$899$	0.618034			0.618034
$900$	1.00000			1.00000
$901$			1.61803i			1.61803i
$902$	−0.207912	+	0.978148i	−0.207912	+	0.978148i
$903$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$904$	−0.406737	+	0.913545i	−0.406737	+	0.913545i
$905$		0			0
$906$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	0.500000	+	0.866025i	$0.333333\pi$
$907$	−0.500000	+	0.866025i	−0.500000	+	0.866025i	−1.00000			$\pi$
$908$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$909$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$910$	−1.30902	+	0.951057i	−1.30902	+	0.951057i
$911$	0.207912	−	0.978148i	0.207912	−	0.978148i	−0.743145	−	0.669131i	$-0.766667\pi$
$911$	0.207912	−	0.978148i	0.207912	−	0.978148i	0.951057	−	0.309017i	$-0.100000\pi$
$912$	−0.669131	−	0.743145i	−0.669131	−	0.743145i
$913$	0.373619	−	0.0794152i	0.373619	−	0.0794152i
$914$	0.459289	+	0.413545i	0.459289	+	0.413545i
$915$	1.00000			1.00000
$916$	1.20243	−	1.08268i	1.20243	−	1.08268i
$917$	0.363271	−	0.500000i	0.363271	−	0.500000i
$918$	−0.866025	−	0.500000i	−0.866025	−	0.500000i
$919$	0.587785	−	0.809017i	0.587785	−	0.809017i	−0.406737	−	0.913545i	$-0.633333\pi$
$919$	0.587785	−	0.809017i	0.587785	−	0.809017i	0.994522	+	0.104528i	$0.0333333\pi$
$920$	0.207912	−	0.978148i	0.207912	−	0.978148i
$921$	1.30902	−	0.951057i	1.30902	−	0.951057i
$922$	0.564602	+	0.251377i	0.564602	+	0.251377i
$923$		0			0
$924$	−0.535233	−	0.309017i	−0.535233	−	0.309017i
$925$		0			0
$926$	−1.00000			−1.00000
$927$		0			0
$928$	0.500000	−	0.363271i	0.500000	−	0.363271i
$929$	−0.169131	−	1.60917i	−0.169131	−	1.60917i	−0.669131	−	0.743145i	$-0.733333\pi$
$929$	−0.169131	−	1.60917i	−0.169131	−	1.60917i	0.500000	−	0.866025i	$-0.333333\pi$
$930$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$931$		0			0
$932$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$933$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$934$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$935$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$936$	1.08268	−	1.20243i	1.08268	−	1.20243i
$937$	0.190983	−	0.587785i	0.190983	−	0.587785i	−0.809017	−	0.587785i	$-0.800000\pi$
$937$	0.190983	−	0.587785i	0.190983	−	0.587785i	1.00000			$0$
$938$	−1.08268	−	1.20243i	−1.08268	−	1.20243i
$939$	0.978148	+	0.207912i	0.978148	+	0.207912i
$940$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$941$	0.128496	+	0.604528i	0.128496	+	0.604528i	0.994522	+	0.104528i	$0.0333333\pi$
$941$	0.128496	+	0.604528i	0.128496	+	0.604528i	−0.866025	+	0.500000i	$0.833333\pi$
$942$		0			0
$943$	1.40126	+	0.809017i	1.40126	+	0.809017i
$944$		0			0
$945$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$946$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$947$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$947$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$948$	−0.587785	+	0.190983i	−0.587785	+	0.190983i
$949$		0			0
$950$	−0.994522	−	0.104528i	−0.994522	−	0.104528i
$951$	0.866025	+	0.500000i	0.866025	+	0.500000i
$952$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$953$	0.809017	−	0.587785i	0.809017	−	0.587785i	−0.104528	−	0.994522i	$-0.533333\pi$
$953$	0.809017	−	0.587785i	0.809017	−	0.587785i	0.913545	+	0.406737i	$0.133333\pi$
$954$	−0.169131	−	1.60917i	−0.169131	−	1.60917i
$955$		0			0
$956$		0			0
$957$	−0.330792	+	0.190983i	−0.330792	+	0.190983i
$958$		0			0
$959$	−0.128496	−	0.604528i	−0.128496	−	0.604528i
$960$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$961$		0			0
$962$		0			0
$963$	0.500000	−	1.53884i	0.500000	−	1.53884i
$964$		0			0
$965$	0.994522	−	0.104528i	0.994522	−	0.104528i
$966$	−0.743145	+	0.669131i	−0.743145	+	0.669131i
$967$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.406737	−	0.913545i	$-0.633333\pi$
$967$	−0.994522	−	0.104528i	−0.994522	−	0.104528i	−0.587785	+	0.809017i	$0.700000\pi$
$968$	−0.535233	+	0.309017i	−0.535233	+	0.309017i
$969$	0.809017	+	0.587785i	0.809017	+	0.587785i
$970$		0			0
$971$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$971$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$972$	0.913545	+	0.406737i	0.913545	+	0.406737i
$973$		0			0
$974$	0.500000	−	0.866025i	0.500000	−	0.866025i
$975$		−	1.61803i		−	1.61803i
$976$	−0.866025	+	0.500000i	−0.866025	+	0.500000i
$977$	0.413545	−	0.459289i	0.413545	−	0.459289i	−0.500000	−	0.866025i	$-0.666667\pi$
$977$	0.413545	−	0.459289i	0.413545	−	0.459289i	0.913545	+	0.406737i	$0.133333\pi$
$978$	0.994522	−	0.104528i	0.994522	−	0.104528i
$979$	0.0646021	+	0.614648i	0.0646021	+	0.614648i
$980$		0			0
$981$	−0.951057	+	1.30902i	−0.951057	+	1.30902i
$982$		0			0
$983$	−0.658114	−	1.47815i	−0.658114	−	1.47815i	−0.866025	−	0.500000i	$-0.833333\pi$
$983$	−0.658114	−	1.47815i	−0.658114	−	1.47815i	0.207912	−	0.978148i	$-0.433333\pi$
$984$	−0.336408	−	1.58268i	−0.336408	−	1.58268i
$985$		0			0
$986$	−0.413545	+	0.459289i	−0.413545	+	0.459289i
$987$	0.604528	−	0.128496i	0.604528	−	0.128496i
$988$	−1.20243	+	1.08268i	−1.20243	+	1.08268i
$989$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$990$	0.564602	−	0.251377i	0.564602	−	0.251377i
$991$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.951057	−	0.309017i	$-0.100000\pi$
$991$	1.53884	+	0.500000i	1.53884	+	0.500000i	0.587785	+	0.809017i	$0.300000\pi$
$992$	0.913545	−	0.406737i	0.913545	−	0.406737i
$993$	−0.809017	+	1.40126i	−0.809017	+	1.40126i
$994$		0			0
$995$	1.47815	+	0.658114i	1.47815	+	0.658114i
$996$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$997$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$997$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$998$	1.53884	−	0.500000i	1.53884	−	0.500000i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.1.dg.a.331.1	✓	16
8.3	odd	2	inner	1800.1.dg.a.331.2	yes	16
9.4	even	3	inner	1800.1.dg.a.931.1	yes	16
25.21	even	5	inner	1800.1.dg.a.1771.2	yes	16
72.67	odd	6	inner	1800.1.dg.a.931.2	yes	16
200.171	odd	10	inner	1800.1.dg.a.1771.1	yes	16
225.121	even	15	inner	1800.1.dg.a.571.2	yes	16
1800.571	odd	30	inner	1800.1.dg.a.571.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1800.1.dg.a.331.1	✓	16	1.1	even	1	trivial
1800.1.dg.a.331.2	yes	16	8.3	odd	2	inner
1800.1.dg.a.571.1	yes	16	1800.571	odd	30	inner
1800.1.dg.a.571.2	yes	16	225.121	even	15	inner
1800.1.dg.a.931.1	yes	16	9.4	even	3	inner
1800.1.dg.a.931.2	yes	16	72.67	odd	6	inner
1800.1.dg.a.1771.1	yes	16	200.171	odd	10	inner
1800.1.dg.a.1771.2	yes	16	25.21	even	5	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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1800.dg (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.406737 - 0.913545i) q^{5} +(0.406737 + 0.913545i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(0.406737 - 0.913545i) q^{5} +(0.406737 + 0.913545i) q^{6} +(0.866025 + 0.500000i) q^{7} +(0.587785 - 0.809017i) q^{8} +(0.309017 - 0.951057i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.604528 + 0.128496i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(0.336408 + 1.58268i) q^{13} +(-0.669131 + 0.743145i) q^{14} +(-0.207912 - 0.978148i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.809017 - 0.587785i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.809017 - 0.587785i) q^{19} +(-0.743145 + 0.669131i) q^{20} +(0.994522 - 0.104528i) q^{21} +(-0.251377 + 0.564602i) q^{22} +(0.743145 + 0.669131i) q^{23} -1.00000i q^{24} +(-0.669131 - 0.743145i) q^{25} -1.61803 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(-0.614648 + 0.0646021i) q^{29} +1.00000 q^{30} +(-0.994522 - 0.104528i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.564602 - 0.251377i) q^{33} +(0.743145 - 0.669131i) q^{34} +(0.809017 - 0.587785i) q^{35} +(-0.669131 + 0.743145i) q^{36} +(0.743145 - 0.669131i) q^{38} +(1.20243 + 1.08268i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.58268 - 0.336408i) q^{41} +(-0.104528 + 0.994522i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-0.500000 - 0.363271i) q^{44} +(-0.743145 - 0.669131i) q^{45} +(-0.809017 + 0.587785i) q^{46} +(0.614648 - 0.0646021i) q^{47} +(0.978148 + 0.207912i) q^{48} +(0.866025 - 0.500000i) q^{50} -1.00000 q^{51} +(0.336408 - 1.58268i) q^{52} +(-0.951057 - 1.30902i) q^{53} +(0.994522 - 0.104528i) q^{54} +(0.363271 - 0.500000i) q^{55} +(0.913545 - 0.406737i) q^{56} -1.00000 q^{57} +(0.0646021 - 0.614648i) q^{58} +(-0.207912 + 0.978148i) q^{60} +(-0.207912 + 0.978148i) q^{61} +(0.309017 - 0.951057i) q^{62} +(0.743145 - 0.669131i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(1.58268 + 0.336408i) q^{65} +(0.128496 + 0.604528i) q^{66} +(-0.169131 + 1.60917i) q^{67} +(0.500000 + 0.866025i) q^{68} +(0.994522 + 0.104528i) q^{69} +(0.406737 + 0.913545i) q^{70} +(-0.587785 - 0.809017i) q^{72} +(-0.978148 - 0.207912i) q^{75} +(0.500000 + 0.866025i) q^{76} +(0.459289 + 0.413545i) q^{77} +(-1.30902 + 0.951057i) q^{78} +(0.614648 - 0.0646021i) q^{79} +(0.951057 - 0.309017i) q^{80} +(-0.809017 - 0.587785i) q^{81} +1.61803i q^{82} +(0.564602 - 0.251377i) q^{83} +(-0.951057 - 0.309017i) q^{84} +(-0.866025 + 0.500000i) q^{85} +(-0.743145 - 0.669131i) q^{86} +(-0.459289 + 0.413545i) q^{87} +(0.459289 - 0.413545i) q^{88} +(0.309017 + 0.951057i) q^{89} +(0.809017 - 0.587785i) q^{90} +(-0.500000 + 1.53884i) q^{91} +(-0.406737 - 0.913545i) q^{92} +(-0.866025 + 0.500000i) q^{93} +(-0.0646021 + 0.614648i) q^{94} +(-0.866025 + 0.500000i) q^{95} +(-0.406737 + 0.913545i) q^{96} +(0.309017 - 0.535233i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 2 q^{4} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^3 - 2 * q^4 - 4 * q^9	\( 16 q + 4 q^{3} - 2 q^{4} - 4 q^{9} + 4 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{14} + 2 q^{16} - 4 q^{17} - 4 q^{19} - 2 q^{25} - 8 q^{26} + 4 q^{27} + 16 q^{30} + 4 q^{33} + 4 q^{35} - 2 q^{36} - 8 q^{40} + 4 q^{41} + 2 q^{42} - 8 q^{43} - 8 q^{44} - 4 q^{46} - 2 q^{48} - 16 q^{51} + 2 q^{56} - 16 q^{57} - 4 q^{58} - 4 q^{62} + 4 q^{64} + 4 q^{65} + 6 q^{67} + 8 q^{68} + 2 q^{75} + 8 q^{76} - 12 q^{78} - 4 q^{81} + 4 q^{83} - 4 q^{89} + 4 q^{90} - 8 q^{91} + 4 q^{94} - 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 2 * q^4 - 4 * q^9 + 4 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^14 + 2 * q^16 - 4 * q^17 - 4 * q^19 - 2 * q^25 - 8 * q^26 + 4 * q^27 + 16 * q^30 + 4 * q^33 + 4 * q^35 - 2 * q^36 - 8 * q^40 + 4 * q^41 + 2 * q^42 - 8 * q^43 - 8 * q^44 - 4 * q^46 - 2 * q^48 - 16 * q^51 + 2 * q^56 - 16 * q^57 - 4 * q^58 - 4 * q^62 + 4 * q^64 + 4 * q^65 + 6 * q^67 + 8 * q^68 + 2 * q^75 + 8 * q^76 - 12 * q^78 - 4 * q^81 + 4 * q^83 - 4 * q^89 + 4 * q^90 - 8 * q^91 + 4 * q^94 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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